Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(19,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.l (of order \(4\), 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: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 19.6 | ||
Root | \(-1.25564 + 1.55672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.19 |
Dual form | 48.3.l.a.43.6 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25564 | + | 1.55672i | 0.627818 | + | 0.778360i | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | −0.846753 | + | 3.90935i | −0.211688 | + | 0.977337i | ||||
\(5\) | 0.909023 | − | 0.909023i | 0.181805 | − | 0.181805i | −0.610337 | − | 0.792142i | \(-0.708966\pi\) |
0.792142 | + | 0.610337i | \(0.208966\pi\) | |||||||
\(6\) | 3.44442 | + | 0.368750i | 0.574070 | + | 0.0614583i | ||||
\(7\) | −0.654713 | −0.0935305 | −0.0467652 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467652 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(8\) | −7.14897 | + | 3.59057i | −0.893622 | + | 0.448821i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 2.55650 | + | 0.273691i | 0.255650 | + | 0.0273691i | ||||
\(11\) | −13.3760 | − | 13.3760i | −1.21600 | − | 1.21600i | −0.969021 | − | 0.246980i | \(-0.920562\pi\) |
−0.246980 | − | 0.969021i | \(-0.579438\pi\) | |||||||
\(12\) | 3.75090 | + | 5.82501i | 0.312575 | + | 0.485418i | ||||
\(13\) | 8.32795 | + | 8.32795i | 0.640612 | + | 0.640612i | 0.950706 | − | 0.310094i | \(-0.100361\pi\) |
−0.310094 | + | 0.950706i | \(0.600361\pi\) | |||||||
\(14\) | −0.822082 | − | 1.01921i | −0.0587202 | − | 0.0728004i | ||||
\(15\) | − | 2.22664i | − | 0.148443i | ||||||
\(16\) | −14.5660 | − | 6.62050i | −0.910376 | − | 0.413781i | ||||
\(17\) | −3.93529 | −0.231488 | −0.115744 | − | 0.993279i | \(-0.536925\pi\) | ||||
−0.115744 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(18\) | 4.67016 | − | 3.76691i | 0.259453 | − | 0.209273i | ||||
\(19\) | 16.8974 | − | 16.8974i | 0.889336 | − | 0.889336i | −0.105123 | − | 0.994459i | \(-0.533524\pi\) |
0.994459 | + | 0.105123i | \(0.0335236\pi\) | |||||||
\(20\) | 2.78397 | + | 4.32340i | 0.139198 | + | 0.216170i | ||||
\(21\) | −0.801857 | + | 0.801857i | −0.0381837 | + | 0.0381837i | ||||
\(22\) | 4.02729 | − | 37.6181i | 0.183059 | − | 1.70991i | ||||
\(23\) | −23.1787 | −1.00777 | −0.503884 | − | 0.863771i | \(-0.668096\pi\) | ||||
−0.503884 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(24\) | −4.35814 | + | 13.1532i | −0.181589 | + | 0.548050i | ||||
\(25\) | 23.3474i | 0.933894i | ||||||||
\(26\) | −2.50740 | + | 23.4212i | −0.0964386 | + | 0.900814i | ||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0.554380 | − | 2.55950i | 0.0197993 | − | 0.0914108i | ||||
\(29\) | 35.6105 | + | 35.6105i | 1.22795 | + | 1.22795i | 0.964739 | + | 0.263209i | \(0.0847809\pi\) |
0.263209 | + | 0.964739i | \(0.415219\pi\) | |||||||
\(30\) | 3.46626 | − | 2.79585i | 0.115542 | − | 0.0931951i | ||||
\(31\) | 45.5687i | 1.46996i | 0.678089 | + | 0.734980i | \(0.262808\pi\) | ||||
−0.678089 | + | 0.734980i | \(0.737192\pi\) | |||||||
\(32\) | −7.98336 | − | 30.9882i | −0.249480 | − | 0.968380i | ||||
\(33\) | −32.7644 | −0.992860 | ||||||||
\(34\) | −4.94130 | − | 6.12615i | −0.145332 | − | 0.180181i | ||||
\(35\) | −0.595149 | + | 0.595149i | −0.0170043 | + | 0.0170043i | ||||
\(36\) | 11.7280 | + | 2.54026i | 0.325779 | + | 0.0705627i | ||||
\(37\) | 10.1527 | − | 10.1527i | 0.274398 | − | 0.274398i | −0.556470 | − | 0.830868i | \(-0.687844\pi\) |
0.830868 | + | 0.556470i | \(0.187844\pi\) | |||||||
\(38\) | 47.5215 | + | 5.08752i | 1.25057 | + | 0.133882i | ||||
\(39\) | 20.3992 | 0.523057 | ||||||||
\(40\) | −3.23467 | + | 9.76249i | −0.0808669 | + | 0.244062i | ||||
\(41\) | − | 28.4661i | − | 0.694295i | −0.937811 | − | 0.347148i | \(-0.887150\pi\) | ||
0.937811 | − | 0.347148i | \(-0.112850\pi\) | |||||||
\(42\) | −2.25511 | − | 0.241425i | −0.0536930 | − | 0.00574823i | ||||
\(43\) | 22.7354 | + | 22.7354i | 0.528730 | + | 0.528730i | 0.920194 | − | 0.391464i | \(-0.128031\pi\) |
−0.391464 | + | 0.920194i | \(0.628031\pi\) | |||||||
\(44\) | 63.6176 | − | 40.9653i | 1.44586 | − | 0.931030i | ||||
\(45\) | −2.72707 | − | 2.72707i | −0.0606015 | − | 0.0606015i | ||||
\(46\) | −29.1040 | − | 36.0827i | −0.632696 | − | 0.784407i | ||||
\(47\) | 10.7746i | 0.229247i | 0.993409 | + | 0.114623i | \(0.0365661\pi\) | ||||
−0.993409 | + | 0.114623i | \(0.963434\pi\) | |||||||
\(48\) | −25.9481 | + | 9.73123i | −0.540585 | + | 0.202734i | ||||
\(49\) | −48.5714 | −0.991252 | ||||||||
\(50\) | −36.3453 | + | 29.3158i | −0.726906 | + | 0.586316i | ||||
\(51\) | −4.81973 | + | 4.81973i | −0.0945045 | + | 0.0945045i | ||||
\(52\) | −39.6086 | + | 25.5051i | −0.761703 | + | 0.490484i | ||||
\(53\) | 41.5142 | − | 41.5142i | 0.783287 | − | 0.783287i | −0.197097 | − | 0.980384i | \(-0.563151\pi\) |
0.980384 | + | 0.197097i | \(0.0631514\pi\) | |||||||
\(54\) | 1.10625 | − | 10.3333i | 0.0204861 | − | 0.191357i | ||||
\(55\) | −24.3182 | −0.442149 | ||||||||
\(56\) | 4.68053 | − | 2.35079i | 0.0835809 | − | 0.0419784i | ||||
\(57\) | − | 41.3900i | − | 0.726140i | ||||||
\(58\) | −10.7217 | + | 100.149i | −0.184857 | + | 1.72671i | ||||
\(59\) | −21.0646 | − | 21.0646i | −0.357027 | − | 0.357027i | 0.505689 | − | 0.862716i | \(-0.331238\pi\) |
−0.862716 | + | 0.505689i | \(0.831238\pi\) | |||||||
\(60\) | 8.70472 | + | 1.88541i | 0.145079 | + | 0.0314236i | ||||
\(61\) | −68.7531 | − | 68.7531i | −1.12710 | − | 1.12710i | −0.990647 | − | 0.136453i | \(-0.956430\pi\) |
−0.136453 | − | 0.990647i | \(-0.543570\pi\) | |||||||
\(62\) | −70.9377 | + | 57.2178i | −1.14416 | + | 0.922867i | ||||
\(63\) | 1.96414i | 0.0311768i | ||||||||
\(64\) | 38.2157 | − | 51.3377i | 0.597120 | − | 0.802152i | ||||
\(65\) | 15.1406 | 0.232932 | ||||||||
\(66\) | −41.1402 | − | 51.0050i | −0.623336 | − | 0.772803i | ||||
\(67\) | 67.8242 | − | 67.8242i | 1.01230 | − | 1.01230i | 0.0123779 | − | 0.999923i | \(-0.496060\pi\) |
0.999923 | − | 0.0123779i | \(-0.00394012\pi\) | |||||||
\(68\) | 3.33222 | − | 15.3844i | 0.0490033 | − | 0.226242i | ||||
\(69\) | −28.3880 | + | 28.3880i | −0.411420 | + | 0.411420i | ||||
\(70\) | −1.67377 | − | 0.179189i | −0.0239110 | − | 0.00255985i | ||||
\(71\) | 33.3094 | 0.469147 | 0.234573 | − | 0.972098i | \(-0.424631\pi\) | ||||
0.234573 | + | 0.972098i | \(0.424631\pi\) | |||||||
\(72\) | 10.7717 | + | 21.4469i | 0.149607 | + | 0.297874i | ||||
\(73\) | − | 18.6331i | − | 0.255248i | −0.991823 | − | 0.127624i | \(-0.959265\pi\) | ||
0.991823 | − | 0.127624i | \(-0.0407351\pi\) | |||||||
\(74\) | 28.5531 | + | 3.05682i | 0.385853 | + | 0.0413083i | ||||
\(75\) | 28.5946 | + | 28.5946i | 0.381261 | + | 0.381261i | ||||
\(76\) | 51.7499 | + | 80.3657i | 0.680920 | + | 1.05744i | ||||
\(77\) | 8.75745 | + | 8.75745i | 0.113733 | + | 0.113733i | ||||
\(78\) | 25.6140 | + | 31.7559i | 0.328385 | + | 0.407127i | ||||
\(79\) | 6.29222i | 0.0796483i | 0.999207 | + | 0.0398242i | \(0.0126798\pi\) | ||||
−0.999207 | + | 0.0398242i | \(0.987320\pi\) | |||||||
\(80\) | −19.2590 | + | 7.22265i | −0.240738 | + | 0.0902832i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 44.3137 | − | 35.7431i | 0.540411 | − | 0.435891i | ||||
\(83\) | −72.0774 | + | 72.0774i | −0.868402 | + | 0.868402i | −0.992296 | − | 0.123894i | \(-0.960462\pi\) |
0.123894 | + | 0.992296i | \(0.460462\pi\) | |||||||
\(84\) | −2.45576 | − | 3.81371i | −0.0292353 | − | 0.0454013i | ||||
\(85\) | −3.57727 | + | 3.57727i | −0.0420855 | + | 0.0420855i | ||||
\(86\) | −6.84524 | + | 63.9400i | −0.0795958 | + | 0.743489i | ||||
\(87\) | 87.2275 | 1.00262 | ||||||||
\(88\) | 143.652 | + | 47.5973i | 1.63241 | + | 0.540878i | ||||
\(89\) | 10.6131i | 0.119248i | 0.998221 | + | 0.0596240i | \(0.0189902\pi\) | ||||
−0.998221 | + | 0.0596240i | \(0.981010\pi\) | |||||||
\(90\) | 0.821074 | − | 7.66949i | 0.00912304 | − | 0.0852165i | ||||
\(91\) | −5.45242 | − | 5.45242i | −0.0599167 | − | 0.0599167i | ||||
\(92\) | 19.6266 | − | 90.6135i | 0.213333 | − | 0.984930i | ||||
\(93\) | 55.8101 | + | 55.8101i | 0.600108 | + | 0.600108i | ||||
\(94\) | −16.7730 | + | 13.5290i | −0.178436 | + | 0.143925i | ||||
\(95\) | − | 30.7202i | − | 0.323371i | ||||||
\(96\) | −47.7302 | − | 28.1750i | −0.497189 | − | 0.293490i | ||||
\(97\) | 143.631 | 1.48073 | 0.740366 | − | 0.672204i | \(-0.234652\pi\) | ||||
0.740366 | + | 0.672204i | \(0.234652\pi\) | |||||||
\(98\) | −60.9880 | − | 75.6120i | −0.622326 | − | 0.771551i | ||||
\(99\) | −40.1280 | + | 40.1280i | −0.405334 | + | 0.405334i | ||||
\(100\) | −91.2730 | − | 19.7694i | −0.912730 | − | 0.197694i | ||||
\(101\) | −90.3100 | + | 90.3100i | −0.894159 | + | 0.894159i | −0.994912 | − | 0.100753i | \(-0.967875\pi\) |
0.100753 | + | 0.994912i | \(0.467875\pi\) | |||||||
\(102\) | −13.5548 | − | 1.45114i | −0.132890 | − | 0.0142269i | ||||
\(103\) | −95.1656 | −0.923938 | −0.461969 | − | 0.886896i | \(-0.652857\pi\) | ||||
−0.461969 | + | 0.886896i | \(0.652857\pi\) | |||||||
\(104\) | −89.4384 | − | 29.6343i | −0.859984 | − | 0.284945i | ||||
\(105\) | 1.45781i | 0.0138839i | ||||||||
\(106\) | 116.753 | + | 12.4992i | 1.10144 | + | 0.117917i | ||||
\(107\) | 27.2524 | + | 27.2524i | 0.254695 | + | 0.254695i | 0.822892 | − | 0.568197i | \(-0.192359\pi\) |
−0.568197 | + | 0.822892i | \(0.692359\pi\) | |||||||
\(108\) | 17.4750 | − | 11.2527i | 0.161806 | − | 0.104192i | ||||
\(109\) | −132.413 | − | 132.413i | −1.21480 | − | 1.21480i | −0.969430 | − | 0.245366i | \(-0.921092\pi\) |
−0.245366 | − | 0.969430i | \(-0.578908\pi\) | |||||||
\(110\) | −30.5348 | − | 37.8566i | −0.277589 | − | 0.344151i | ||||
\(111\) | − | 24.8690i | − | 0.224045i | ||||||
\(112\) | 9.53657 | + | 4.33453i | 0.0851479 | + | 0.0387012i | ||||
\(113\) | 37.9551 | 0.335886 | 0.167943 | − | 0.985797i | \(-0.446288\pi\) | ||||
0.167943 | + | 0.985797i | \(0.446288\pi\) | |||||||
\(114\) | 64.4326 | − | 51.9708i | 0.565198 | − | 0.455884i | ||||
\(115\) | −21.0699 | + | 21.0699i | −0.183217 | + | 0.183217i | ||||
\(116\) | −169.367 | + | 109.061i | −1.46006 | + | 0.940177i | ||||
\(117\) | 24.9838 | − | 24.9838i | 0.213537 | − | 0.213537i | ||||
\(118\) | 6.34219 | − | 59.2411i | 0.0537474 | − | 0.502044i | ||||
\(119\) | 2.57649 | 0.0216512 | ||||||||
\(120\) | 7.99490 | + | 15.9182i | 0.0666242 | + | 0.132652i | ||||
\(121\) | 236.835i | 1.95731i | ||||||||
\(122\) | 20.7004 | − | 193.358i | 0.169675 | − | 1.58490i | ||||
\(123\) | −34.8637 | − | 34.8637i | −0.283445 | − | 0.283445i | ||||
\(124\) | −178.144 | − | 38.5854i | −1.43665 | − | 0.311173i | ||||
\(125\) | 43.9488 | + | 43.9488i | 0.351591 | + | 0.351591i | ||||
\(126\) | −3.05762 | + | 2.46625i | −0.0242668 | + | 0.0195734i | ||||
\(127\) | − | 96.5399i | − | 0.760157i | −0.924954 | − | 0.380078i | \(-0.875897\pi\) | ||
0.924954 | − | 0.380078i | \(-0.124103\pi\) | |||||||
\(128\) | 127.903 | − | 4.97043i | 0.999246 | − | 0.0388315i | ||||
\(129\) | 55.6901 | 0.431706 | ||||||||
\(130\) | 19.0111 | + | 23.5697i | 0.146239 | + | 0.181305i | ||||
\(131\) | −54.5082 | + | 54.5082i | −0.416093 | + | 0.416093i | −0.883855 | − | 0.467762i | \(-0.845061\pi\) |
0.467762 | + | 0.883855i | \(0.345061\pi\) | |||||||
\(132\) | 27.7433 | − | 128.087i | 0.210177 | − | 0.970359i | ||||
\(133\) | −11.0629 | + | 11.0629i | −0.0831801 | + | 0.0831801i | ||||
\(134\) | 190.746 | + | 20.4207i | 1.42348 | + | 0.152393i | ||||
\(135\) | −6.67992 | −0.0494809 | ||||||||
\(136\) | 28.1333 | − | 14.1299i | 0.206863 | − | 0.103897i | ||||
\(137\) | − | 25.9333i | − | 0.189294i | −0.995511 | − | 0.0946471i | \(-0.969828\pi\) | ||
0.995511 | − | 0.0946471i | \(-0.0301723\pi\) | |||||||
\(138\) | −79.8371 | − | 8.54713i | −0.578530 | − | 0.0619358i | ||||
\(139\) | 3.64066 | + | 3.64066i | 0.0261918 | + | 0.0261918i | 0.720081 | − | 0.693890i | \(-0.244104\pi\) |
−0.693890 | + | 0.720081i | \(0.744104\pi\) | |||||||
\(140\) | −1.82270 | − | 2.83059i | −0.0130193 | − | 0.0202185i | ||||
\(141\) | 13.1961 | + | 13.1961i | 0.0935896 | + | 0.0935896i | ||||
\(142\) | 41.8245 | + | 51.8534i | 0.294539 | + | 0.365165i | ||||
\(143\) | − | 222.789i | − | 1.55797i | ||||||
\(144\) | −19.8615 | + | 43.6981i | −0.137927 | + | 0.303459i | ||||
\(145\) | 64.7415 | 0.446493 | ||||||||
\(146\) | 29.0066 | − | 23.3964i | 0.198675 | − | 0.160250i | ||||
\(147\) | −59.4875 | + | 59.4875i | −0.404677 | + | 0.404677i | ||||
\(148\) | 31.0937 | + | 48.2874i | 0.210093 | + | 0.326266i | ||||
\(149\) | −18.9718 | + | 18.9718i | −0.127328 | + | 0.127328i | −0.767899 | − | 0.640571i | \(-0.778698\pi\) |
0.640571 | + | 0.767899i | \(0.278698\pi\) | |||||||
\(150\) | −8.60933 | + | 80.4181i | −0.0573956 | + | 0.536121i | ||||
\(151\) | −103.209 | −0.683503 | −0.341751 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341751 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(152\) | −60.1278 | + | 181.470i | −0.395578 | + | 1.19388i | ||||
\(153\) | 11.8059i | 0.0771626i | ||||||||
\(154\) | −2.63672 | + | 24.6291i | −0.0171216 | + | 0.159929i | ||||
\(155\) | 41.4230 | + | 41.4230i | 0.267245 | + | 0.267245i | ||||
\(156\) | −17.2731 | + | 79.7477i | −0.110725 | + | 0.511203i | ||||
\(157\) | 88.2067 | + | 88.2067i | 0.561826 | + | 0.561826i | 0.929826 | − | 0.368000i | \(-0.119957\pi\) |
−0.368000 | + | 0.929826i | \(0.619957\pi\) | |||||||
\(158\) | −9.79522 | + | 7.90074i | −0.0619951 | + | 0.0500047i | ||||
\(159\) | − | 101.689i | − | 0.639551i | ||||||
\(160\) | −35.4260 | − | 20.9119i | −0.221412 | − | 0.130699i | ||||
\(161\) | 15.1754 | 0.0942571 | ||||||||
\(162\) | −11.3007 | − | 14.0105i | −0.0697576 | − | 0.0864844i | ||||
\(163\) | 18.8038 | − | 18.8038i | 0.115361 | − | 0.115361i | −0.647070 | − | 0.762431i | \(-0.724006\pi\) |
0.762431 | + | 0.647070i | \(0.224006\pi\) | |||||||
\(164\) | 111.284 | + | 24.1037i | 0.678561 | + | 0.146974i | ||||
\(165\) | −29.7836 | + | 29.7836i | −0.180507 | + | 0.180507i | ||||
\(166\) | −202.707 | − | 21.7013i | −1.22113 | − | 0.130731i | ||||
\(167\) | 267.105 | 1.59943 | 0.799715 | − | 0.600380i | \(-0.204984\pi\) | ||||
0.799715 | + | 0.600380i | \(0.204984\pi\) | |||||||
\(168\) | 2.85333 | − | 8.61157i | 0.0169841 | − | 0.0512594i | ||||
\(169\) | − | 30.2905i | − | 0.179234i | ||||||
\(170\) | −10.0606 | − | 1.07706i | −0.0591798 | − | 0.00633562i | ||||
\(171\) | −50.6922 | − | 50.6922i | −0.296445 | − | 0.296445i | ||||
\(172\) | −108.132 | + | 69.6293i | −0.628673 | + | 0.404822i | ||||
\(173\) | −153.520 | − | 153.520i | −0.887396 | − | 0.887396i | 0.106876 | − | 0.994272i | \(-0.465915\pi\) |
−0.994272 | + | 0.106876i | \(0.965915\pi\) | |||||||
\(174\) | 109.526 | + | 135.789i | 0.629460 | + | 0.780396i | ||||
\(175\) | − | 15.2858i | − | 0.0873476i | ||||||
\(176\) | 106.279 | + | 283.391i | 0.603859 | + | 1.61018i | ||||
\(177\) | −51.5975 | −0.291511 | ||||||||
\(178\) | −16.5216 | + | 13.3262i | −0.0928179 | + | 0.0748661i | ||||
\(179\) | 123.581 | − | 123.581i | 0.690399 | − | 0.690399i | −0.271921 | − | 0.962320i | \(-0.587659\pi\) |
0.962320 | + | 0.271921i | \(0.0876589\pi\) | |||||||
\(180\) | 12.9702 | − | 8.35191i | 0.0720567 | − | 0.0463995i | ||||
\(181\) | 122.965 | − | 122.965i | 0.679364 | − | 0.679364i | −0.280493 | − | 0.959856i | \(-0.590498\pi\) |
0.959856 | + | 0.280493i | \(0.0904978\pi\) | |||||||
\(182\) | 1.64163 | − | 15.3341i | 0.00901995 | − | 0.0842536i | ||||
\(183\) | −168.410 | −0.920273 | ||||||||
\(184\) | 165.704 | − | 83.2246i | 0.900564 | − | 0.452307i | ||||
\(185\) | − | 18.4581i | − | 0.0997737i | ||||||
\(186\) | −16.8035 | + | 156.958i | −0.0903412 | + | 0.843859i | ||||
\(187\) | 52.6385 | + | 52.6385i | 0.281489 | + | 0.281489i | ||||
\(188\) | −42.1217 | − | 9.12342i | −0.224051 | − | 0.0485288i | ||||
\(189\) | 2.40557 | + | 2.40557i | 0.0127279 | + | 0.0127279i | ||||
\(190\) | 47.8228 | − | 38.5734i | 0.251699 | − | 0.203018i | ||||
\(191\) | 193.992i | 1.01566i | 0.861456 | + | 0.507832i | \(0.169553\pi\) | ||||
−0.861456 | + | 0.507832i | \(0.830447\pi\) | |||||||
\(192\) | −16.0712 | − | 109.680i | −0.0837040 | − | 0.571250i | ||||
\(193\) | 141.555 | 0.733444 | 0.366722 | − | 0.930331i | \(-0.380480\pi\) | ||||
0.366722 | + | 0.930331i | \(0.380480\pi\) | |||||||
\(194\) | 180.348 | + | 223.593i | 0.929631 | + | 1.15254i | ||||
\(195\) | 18.5434 | − | 18.5434i | 0.0950942 | − | 0.0950942i | ||||
\(196\) | 41.1279 | − | 189.882i | 0.209836 | − | 0.968788i | ||||
\(197\) | 28.9507 | − | 28.9507i | 0.146958 | − | 0.146958i | −0.629800 | − | 0.776758i | \(-0.716863\pi\) |
0.776758 | + | 0.629800i | \(0.216863\pi\) | |||||||
\(198\) | −112.854 | − | 12.0819i | −0.569971 | − | 0.0610195i | ||||
\(199\) | −27.6253 | −0.138821 | −0.0694104 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694104 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(200\) | −83.8302 | − | 166.910i | −0.419151 | − | 0.834548i | ||||
\(201\) | − | 166.135i | − | 0.826541i | ||||||
\(202\) | −253.984 | − | 27.1908i | −1.25735 | − | 0.134608i | ||||
\(203\) | −23.3147 | − | 23.3147i | −0.114851 | − | 0.114851i | ||||
\(204\) | −14.7609 | − | 22.9231i | −0.0723573 | − | 0.112368i | ||||
\(205\) | −25.8763 | − | 25.8763i | −0.126226 | − | 0.126226i | ||||
\(206\) | −119.493 | − | 148.146i | −0.580065 | − | 0.719156i | ||||
\(207\) | 69.5360i | 0.335923i | ||||||||
\(208\) | −66.1699 | − | 176.440i | −0.318124 | − | 0.848271i | ||||
\(209\) | −452.039 | −2.16287 | ||||||||
\(210\) | −2.26940 | + | 1.83048i | −0.0108067 | + | 0.00871658i | ||||
\(211\) | 7.35041 | − | 7.35041i | 0.0348361 | − | 0.0348361i | −0.689474 | − | 0.724310i | \(-0.742158\pi\) |
0.724310 | + | 0.689474i | \(0.242158\pi\) | |||||||
\(212\) | 127.141 | + | 197.446i | 0.599723 | + | 0.931348i | ||||
\(213\) | 40.7955 | − | 40.7955i | 0.191528 | − | 0.191528i | ||||
\(214\) | −8.20523 | + | 76.6435i | −0.0383422 | + | 0.358147i | ||||
\(215\) | 41.3340 | 0.192251 | ||||||||
\(216\) | 39.4596 | + | 13.0744i | 0.182683 | + | 0.0605298i | ||||
\(217\) | − | 29.8345i | − | 0.137486i | ||||||
\(218\) | 39.8673 | − | 372.392i | 0.182877 | − | 1.70822i | ||||
\(219\) | −22.8208 | − | 22.8208i | −0.104205 | − | 0.104205i | ||||
\(220\) | 20.5915 | − | 95.0683i | 0.0935977 | − | 0.432129i | ||||
\(221\) | −32.7729 | − | 32.7729i | −0.148294 | − | 0.148294i | ||||
\(222\) | 38.7141 | − | 31.2265i | 0.174388 | − | 0.140660i | ||||
\(223\) | 386.106i | 1.73142i | 0.500549 | + | 0.865708i | \(0.333131\pi\) | ||||
−0.500549 | + | 0.865708i | \(0.666869\pi\) | |||||||
\(224\) | 5.22681 | + | 20.2884i | 0.0233340 | + | 0.0905730i | ||||
\(225\) | 70.0421 | 0.311298 | ||||||||
\(226\) | 47.6579 | + | 59.0855i | 0.210875 | + | 0.261440i | ||||
\(227\) | −49.7286 | + | 49.7286i | −0.219069 | + | 0.219069i | −0.808106 | − | 0.589037i | \(-0.799507\pi\) |
0.589037 | + | 0.808106i | \(0.299507\pi\) | |||||||
\(228\) | 161.808 | + | 35.0471i | 0.709684 | + | 0.153715i | ||||
\(229\) | −191.870 | + | 191.870i | −0.837861 | + | 0.837861i | −0.988577 | − | 0.150716i | \(-0.951842\pi\) |
0.150716 | + | 0.988577i | \(0.451842\pi\) | |||||||
\(230\) | −59.2562 | − | 6.34380i | −0.257636 | − | 0.0275817i | ||||
\(231\) | 21.4513 | 0.0928627 | ||||||||
\(232\) | −382.440 | − | 126.717i | −1.64845 | − | 0.546193i | ||||
\(233\) | − | 298.610i | − | 1.28159i | −0.767712 | − | 0.640795i | \(-0.778605\pi\) | ||
0.767712 | − | 0.640795i | \(-0.221395\pi\) | |||||||
\(234\) | 70.2635 | + | 7.52221i | 0.300271 | + | 0.0321462i | ||||
\(235\) | 9.79435 | + | 9.79435i | 0.0416781 | + | 0.0416781i | ||||
\(236\) | 100.185 | − | 64.5123i | 0.424514 | − | 0.273357i | ||||
\(237\) | 7.70636 | + | 7.70636i | 0.0325163 | + | 0.0325163i | ||||
\(238\) | 3.23514 | + | 4.01087i | 0.0135930 | + | 0.0168524i | ||||
\(239\) | 247.352i | 1.03495i | 0.855700 | + | 0.517473i | \(0.173127\pi\) | ||||
−0.855700 | + | 0.517473i | \(0.826873\pi\) | |||||||
\(240\) | −14.7415 | + | 32.4333i | −0.0614229 | + | 0.135139i | ||||
\(241\) | −220.337 | −0.914260 | −0.457130 | − | 0.889400i | \(-0.651123\pi\) | ||||
−0.457130 | + | 0.889400i | \(0.651123\pi\) | |||||||
\(242\) | −368.686 | + | 297.379i | −1.52350 | + | 1.22884i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 326.997 | − | 210.563i | 1.34015 | − | 0.862963i | ||||
\(245\) | −44.1525 | + | 44.1525i | −0.180214 | + | 0.180214i | ||||
\(246\) | 10.4969 | − | 98.0492i | 0.0426702 | − | 0.398574i | ||||
\(247\) | 281.441 | 1.13944 | ||||||||
\(248\) | −163.618 | − | 325.770i | −0.659748 | − | 1.31359i | ||||
\(249\) | 176.553i | 0.709047i | ||||||||
\(250\) | −13.2322 | + | 123.600i | −0.0529290 | + | 0.494399i | ||||
\(251\) | 162.716 | + | 162.716i | 0.648272 | + | 0.648272i | 0.952575 | − | 0.304303i | \(-0.0984235\pi\) |
−0.304303 | + | 0.952575i | \(0.598424\pi\) | |||||||
\(252\) | −7.67851 | − | 1.66314i | −0.0304703 | − | 0.00659977i | ||||
\(253\) | 310.038 | + | 310.038i | 1.22545 | + | 1.22545i | ||||
\(254\) | 150.286 | − | 121.219i | 0.591675 | − | 0.477240i | ||||
\(255\) | 8.76249i | 0.0343627i | ||||||||
\(256\) | 168.338 | + | 192.869i | 0.657570 | + | 0.753394i | ||||
\(257\) | 101.165 | 0.393637 | 0.196819 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196819 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(258\) | 69.9265 | + | 86.6939i | 0.271033 | + | 0.336023i | ||||
\(259\) | −6.64713 | + | 6.64713i | −0.0256646 | + | 0.0256646i | ||||
\(260\) | −12.8203 | + | 59.1899i | −0.0493090 | + | 0.227653i | ||||
\(261\) | 106.831 | − | 106.831i | 0.409316 | − | 0.409316i | ||||
\(262\) | −153.296 | − | 16.4115i | −0.585101 | − | 0.0626393i | ||||
\(263\) | −323.635 | −1.23055 | −0.615276 | − | 0.788312i | \(-0.710955\pi\) | ||||
−0.615276 | + | 0.788312i | \(0.710955\pi\) | |||||||
\(264\) | 234.232 | − | 117.643i | 0.887242 | − | 0.445616i | ||||
\(265\) | − | 75.4747i | − | 0.284810i | ||||||
\(266\) | −31.1130 | − | 3.33087i | −0.116966 | − | 0.0125220i | ||||
\(267\) | 12.9983 | + | 12.9983i | 0.0486828 | + | 0.0486828i | ||||
\(268\) | 207.718 | + | 322.579i | 0.775068 | + | 1.20365i | ||||
\(269\) | 1.51275 | + | 1.51275i | 0.00562361 | + | 0.00562361i | 0.709913 | − | 0.704289i | \(-0.248734\pi\) |
−0.704289 | + | 0.709913i | \(0.748734\pi\) | |||||||
\(270\) | −8.38756 | − | 10.3988i | −0.0310650 | − | 0.0385140i | ||||
\(271\) | 166.098i | 0.612909i | 0.951885 | + | 0.306454i | \(0.0991427\pi\) | ||||
−0.951885 | + | 0.306454i | \(0.900857\pi\) | |||||||
\(272\) | 57.3216 | + | 26.0536i | 0.210741 | + | 0.0957854i | ||||
\(273\) | −13.3556 | −0.0489218 | ||||||||
\(274\) | 40.3709 | − | 32.5628i | 0.147339 | − | 0.118842i | ||||
\(275\) | 312.294 | − | 312.294i | 1.13562 | − | 1.13562i | ||||
\(276\) | −86.9409 | − | 135.016i | −0.315003 | − | 0.489189i | ||||
\(277\) | 317.830 | − | 317.830i | 1.14740 | − | 1.14740i | 0.160338 | − | 0.987062i | \(-0.448741\pi\) |
0.987062 | − | 0.160338i | \(-0.0512586\pi\) | |||||||
\(278\) | −1.09614 | + | 10.2388i | −0.00394296 | + | 0.0368304i | ||||
\(279\) | 136.706 | 0.489986 | ||||||||
\(280\) | 2.11778 | − | 6.39163i | 0.00756352 | − | 0.0228272i | ||||
\(281\) | 402.790i | 1.43342i | 0.697374 | + | 0.716708i | \(0.254352\pi\) | ||||
−0.697374 | + | 0.716708i | \(0.745648\pi\) | |||||||
\(282\) | −3.97313 | + | 37.1122i | −0.0140891 | + | 0.131604i | ||||
\(283\) | −192.406 | − | 192.406i | −0.679881 | − | 0.679881i | 0.280092 | − | 0.959973i | \(-0.409635\pi\) |
−0.959973 | + | 0.280092i | \(0.909635\pi\) | |||||||
\(284\) | −28.2048 | + | 130.218i | −0.0993128 | + | 0.458515i | ||||
\(285\) | −37.6244 | − | 37.6244i | −0.132016 | − | 0.132016i | ||||
\(286\) | 346.821 | − | 279.743i | 1.21266 | − | 0.978121i | ||||
\(287\) | 18.6371i | 0.0649378i | ||||||||
\(288\) | −92.9645 | + | 23.9501i | −0.322793 | + | 0.0831600i | ||||
\(289\) | −273.513 | −0.946413 | ||||||||
\(290\) | 81.2918 | + | 100.784i | 0.280317 | + | 0.347532i | ||||
\(291\) | 175.911 | − | 175.911i | 0.604506 | − | 0.604506i | ||||
\(292\) | 72.8434 | + | 15.7777i | 0.249464 | + | 0.0540331i | ||||
\(293\) | −75.3645 | + | 75.3645i | −0.257217 | + | 0.257217i | −0.823921 | − | 0.566704i | \(-0.808218\pi\) |
0.566704 | + | 0.823921i | \(0.308218\pi\) | |||||||
\(294\) | −167.300 | − | 17.9107i | −0.569048 | − | 0.0609207i | ||||
\(295\) | −38.2964 | −0.129818 | ||||||||
\(296\) | −36.1276 | + | 109.036i | −0.122053 | + | 0.368364i | ||||
\(297\) | 98.2932i | 0.330953i | ||||||||
\(298\) | −53.3556 | − | 5.71210i | −0.179046 | − | 0.0191681i | ||||
\(299\) | −193.031 | − | 193.031i | −0.645588 | − | 0.645588i | ||||
\(300\) | −135.999 | + | 87.5736i | −0.453329 | + | 0.291912i | ||||
\(301\) | −14.8852 | − | 14.8852i | −0.0494524 | − | 0.0494524i | ||||
\(302\) | −129.593 | − | 160.667i | −0.429116 | − | 0.532011i | ||||
\(303\) | 221.214i | 0.730078i | ||||||||
\(304\) | −357.997 | + | 134.258i | −1.17762 | + | 0.441640i | ||||
\(305\) | −124.996 | −0.409824 | ||||||||
\(306\) | −18.3785 | + | 14.8239i | −0.0600603 | + | 0.0484441i | ||||
\(307\) | −111.544 | + | 111.544i | −0.363337 | + | 0.363337i | −0.865040 | − | 0.501703i | \(-0.832707\pi\) |
0.501703 | + | 0.865040i | \(0.332707\pi\) | |||||||
\(308\) | −41.6513 | + | 26.8205i | −0.135232 | + | 0.0870797i | ||||
\(309\) | −116.554 | + | 116.554i | −0.377196 | + | 0.377196i | ||||
\(310\) | −12.4718 | + | 116.496i | −0.0402315 | + | 0.375794i | ||||
\(311\) | −224.484 | −0.721813 | −0.360906 | − | 0.932602i | \(-0.617533\pi\) | ||||
−0.360906 | + | 0.932602i | \(0.617533\pi\) | |||||||
\(312\) | −145.834 | + | 73.2448i | −0.467415 | + | 0.234759i | ||||
\(313\) | − | 488.339i | − | 1.56019i | −0.625661 | − | 0.780095i | \(-0.715171\pi\) | ||
0.625661 | − | 0.780095i | \(-0.284829\pi\) | |||||||
\(314\) | −26.5575 | + | 248.069i | −0.0845781 | + | 0.790027i | ||||
\(315\) | 1.78545 | + | 1.78545i | 0.00566809 | + | 0.00566809i | ||||
\(316\) | −24.5985 | − | 5.32795i | −0.0778433 | − | 0.0168606i | ||||
\(317\) | 257.361 | + | 257.361i | 0.811863 | + | 0.811863i | 0.984913 | − | 0.173050i | \(-0.0553621\pi\) |
−0.173050 | + | 0.984913i | \(0.555362\pi\) | |||||||
\(318\) | 158.301 | − | 127.684i | 0.497801 | − | 0.401522i | ||||
\(319\) | − | 952.652i | − | 2.98637i | ||||||
\(320\) | −11.9282 | − | 81.4061i | −0.0372757 | − | 0.254394i | ||||
\(321\) | 66.7545 | 0.207958 | ||||||||
\(322\) | 19.0548 | + | 23.6238i | 0.0591763 | + | 0.0733659i | ||||
\(323\) | −66.4962 | + | 66.4962i | −0.205871 | + | 0.205871i | ||||
\(324\) | 7.62077 | − | 35.1841i | 0.0235209 | − | 0.108593i | ||||
\(325\) | −194.436 | + | 194.436i | −0.598263 | + | 0.598263i | ||||
\(326\) | 52.8829 | + | 5.66150i | 0.162218 | + | 0.0173666i | ||||
\(327\) | −324.344 | −0.991877 | ||||||||
\(328\) | 102.209 | + | 203.503i | 0.311614 | + | 0.620437i | ||||
\(329\) | − | 7.05427i | − | 0.0214416i | ||||||
\(330\) | −83.7620 | − | 8.96733i | −0.253824 | − | 0.0271737i | ||||
\(331\) | −123.553 | − | 123.553i | −0.373271 | − | 0.373271i | 0.495396 | − | 0.868667i | \(-0.335023\pi\) |
−0.868667 | + | 0.495396i | \(0.835023\pi\) | |||||||
\(332\) | −220.744 | − | 342.807i | −0.664891 | − | 1.03255i | ||||
\(333\) | −30.4582 | − | 30.4582i | −0.0914661 | − | 0.0914661i | ||||
\(334\) | 335.387 | + | 415.807i | 1.00415 | + | 1.24493i | ||||
\(335\) | − | 123.307i | − | 0.368082i | ||||||
\(336\) | 16.9886 | − | 6.37117i | 0.0505612 | − | 0.0189618i | ||||
\(337\) | −246.234 | −0.730665 | −0.365333 | − | 0.930877i | \(-0.619045\pi\) | ||||
−0.365333 | + | 0.930877i | \(0.619045\pi\) | |||||||
\(338\) | 47.1538 | − | 38.0339i | 0.139508 | − | 0.112526i | ||||
\(339\) | 46.4853 | − | 46.4853i | 0.137125 | − | 0.137125i | ||||
\(340\) | −10.9557 | − | 17.0139i | −0.0322228 | − | 0.0500408i | ||||
\(341\) | 609.528 | − | 609.528i | 1.78747 | − | 1.78747i | ||||
\(342\) | 15.2626 | − | 142.564i | 0.0446273 | − | 0.416855i | ||||
\(343\) | 63.8813 | 0.186243 | ||||||||
\(344\) | −244.168 | − | 80.9018i | −0.709790 | − | 0.235180i | ||||
\(345\) | 51.6106i | 0.149596i | ||||||||
\(346\) | 46.2221 | − | 431.752i | 0.133590 | − | 1.24784i | ||||
\(347\) | −123.212 | − | 123.212i | −0.355076 | − | 0.355076i | 0.506918 | − | 0.861994i | \(-0.330785\pi\) |
−0.861994 | + | 0.506918i | \(0.830785\pi\) | |||||||
\(348\) | −73.8601 | + | 341.003i | −0.212242 | + | 0.979893i | ||||
\(349\) | 115.371 | + | 115.371i | 0.330575 | + | 0.330575i | 0.852805 | − | 0.522230i | \(-0.174900\pi\) |
−0.522230 | + | 0.852805i | \(0.674900\pi\) | |||||||
\(350\) | 23.7957 | − | 19.1934i | 0.0679878 | − | 0.0548384i | ||||
\(351\) | − | 61.1977i | − | 0.174352i | ||||||
\(352\) | −307.712 | + | 521.283i | −0.874183 | + | 1.48092i | ||||
\(353\) | 650.544 | 1.84290 | 0.921451 | − | 0.388495i | \(-0.127005\pi\) | ||||
0.921451 | + | 0.388495i | \(0.127005\pi\) | |||||||
\(354\) | −64.7877 | − | 80.3228i | −0.183016 | − | 0.226901i | ||||
\(355\) | 30.2790 | − | 30.2790i | 0.0852930 | − | 0.0852930i | ||||
\(356\) | −41.4902 | − | 8.98665i | −0.116546 | − | 0.0252434i | ||||
\(357\) | 3.15554 | − | 3.15554i | 0.00883906 | − | 0.00883906i | ||||
\(358\) | 347.555 | + | 37.2083i | 0.970824 | + | 0.103934i | ||||
\(359\) | 94.4878 | 0.263197 | 0.131599 | − | 0.991303i | \(-0.457989\pi\) | ||||
0.131599 | + | 0.991303i | \(0.457989\pi\) | |||||||
\(360\) | 29.2875 | + | 9.70402i | 0.0813540 | + | 0.0269556i | ||||
\(361\) | − | 210.044i | − | 0.581838i | ||||||
\(362\) | 345.821 | + | 37.0226i | 0.955306 | + | 0.102272i | ||||
\(363\) | 290.063 | + | 290.063i | 0.799070 | + | 0.799070i | ||||
\(364\) | 25.9323 | − | 16.6986i | 0.0712425 | − | 0.0458752i | ||||
\(365\) | −16.9379 | − | 16.9379i | −0.0464053 | − | 0.0464053i | ||||
\(366\) | −211.462 | − | 262.167i | −0.577764 | − | 0.716304i | ||||
\(367\) | 131.379i | 0.357982i | 0.983851 | + | 0.178991i | \(0.0572832\pi\) | ||||
−0.983851 | + | 0.178991i | \(0.942717\pi\) | |||||||
\(368\) | 337.621 | + | 153.455i | 0.917449 | + | 0.416996i | ||||
\(369\) | −85.3983 | −0.231432 | ||||||||
\(370\) | 28.7341 | − | 23.1767i | 0.0776598 | − | 0.0626398i | ||||
\(371\) | −27.1799 | + | 27.1799i | −0.0732612 | + | 0.0732612i | ||||
\(372\) | −265.438 | + | 170.924i | −0.713544 | + | 0.459472i | ||||
\(373\) | −275.796 | + | 275.796i | −0.739400 | + | 0.739400i | −0.972462 | − | 0.233062i | \(-0.925126\pi\) |
0.233062 | + | 0.972462i | \(0.425126\pi\) | |||||||
\(374\) | −15.8486 | + | 148.038i | −0.0423758 | + | 0.395824i | ||||
\(375\) | 107.652 | 0.287073 | ||||||||
\(376\) | −38.6869 | − | 77.0273i | −0.102891 | − | 0.204860i | ||||
\(377\) | 593.125i | 1.57328i | ||||||||
\(378\) | −0.724276 | + | 6.76532i | −0.00191608 | + | 0.0178977i | ||||
\(379\) | −13.0427 | − | 13.0427i | −0.0344135 | − | 0.0344135i | 0.689691 | − | 0.724104i | \(-0.257747\pi\) |
−0.724104 | + | 0.689691i | \(0.757747\pi\) | |||||||
\(380\) | 120.096 | + | 26.0124i | 0.316042 | + | 0.0684538i | ||||
\(381\) | −118.237 | − | 118.237i | −0.310333 | − | 0.310333i | ||||
\(382\) | −301.991 | + | 243.583i | −0.790553 | + | 0.637653i | ||||
\(383\) | 121.974i | 0.318470i | 0.987241 | + | 0.159235i | \(0.0509027\pi\) | ||||
−0.987241 | + | 0.159235i | \(0.949097\pi\) | |||||||
\(384\) | 150.562 | − | 162.737i | 0.392087 | − | 0.423793i | ||||
\(385\) | 15.9214 | 0.0413544 | ||||||||
\(386\) | 177.741 | + | 220.361i | 0.460470 | + | 0.570883i | ||||
\(387\) | 68.2062 | − | 68.2062i | 0.176243 | − | 0.176243i | ||||
\(388\) | −121.620 | + | 561.504i | −0.313454 | + | 1.44717i | ||||
\(389\) | −233.267 | + | 233.267i | −0.599659 | + | 0.599659i | −0.940222 | − | 0.340563i | \(-0.889382\pi\) |
0.340563 | + | 0.940222i | \(0.389382\pi\) | |||||||
\(390\) | 52.1505 | + | 5.58309i | 0.133719 | + | 0.0143156i | ||||
\(391\) | 91.2149 | 0.233286 | ||||||||
\(392\) | 347.235 | − | 174.399i | 0.885804 | − | 0.444894i | ||||
\(393\) | 133.517i | 0.339738i | ||||||||
\(394\) | 81.4198 | + | 8.71657i | 0.206649 | + | 0.0221233i | ||||
\(395\) | 5.71977 | + | 5.71977i | 0.0144804 | + | 0.0144804i | ||||
\(396\) | −122.896 | − | 190.853i | −0.310343 | − | 0.481952i | ||||
\(397\) | −83.7693 | − | 83.7693i | −0.211006 | − | 0.211006i | 0.593689 | − | 0.804695i | \(-0.297671\pi\) |
−0.804695 | + | 0.593689i | \(0.797671\pi\) | |||||||
\(398\) | −34.6874 | − | 43.0049i | −0.0871542 | − | 0.108053i | ||||
\(399\) | 27.0986i | 0.0679162i | ||||||||
\(400\) | 154.571 | − | 340.078i | 0.386428 | − | 0.850195i | ||||
\(401\) | 589.134 | 1.46916 | 0.734581 | − | 0.678521i | \(-0.237379\pi\) | ||||
0.734581 | + | 0.678521i | \(0.237379\pi\) | |||||||
\(402\) | 258.625 | − | 208.605i | 0.643346 | − | 0.518917i | ||||
\(403\) | −379.494 | + | 379.494i | −0.941673 | + | 0.941673i | ||||
\(404\) | −276.583 | − | 429.524i | −0.684612 | − | 1.06318i | ||||
\(405\) | −8.18120 | + | 8.18120i | −0.0202005 | + | 0.0202005i | ||||
\(406\) | 7.01965 | − | 65.5691i | 0.0172898 | − | 0.161500i | ||||
\(407\) | −271.606 | −0.667337 | ||||||||
\(408\) | 17.1506 | − | 51.7617i | 0.0420357 | − | 0.126867i | ||||
\(409\) | 449.285i | 1.09850i | 0.835659 | + | 0.549248i | \(0.185086\pi\) | ||||
−0.835659 | + | 0.549248i | \(0.814914\pi\) | |||||||
\(410\) | 7.79092 | − | 72.7735i | 0.0190023 | − | 0.177496i | ||||
\(411\) | −31.7617 | − | 31.7617i | −0.0772790 | − | 0.0772790i | ||||
\(412\) | 80.5818 | − | 372.036i | 0.195587 | − | 0.902999i | ||||
\(413\) | 13.7913 | + | 13.7913i | 0.0333929 | + | 0.0333929i | ||||
\(414\) | −108.248 | + | 87.3120i | −0.261469 | + | 0.210899i | ||||
\(415\) | 131.040i | 0.315759i | ||||||||
\(416\) | 191.583 | − | 324.553i | 0.460536 | − | 0.780175i | ||||
\(417\) | 8.91777 | 0.0213855 | ||||||||
\(418\) | −567.597 | − | 703.698i | −1.35789 | − | 1.68349i | ||||
\(419\) | −218.639 | + | 218.639i | −0.521811 | + | 0.521811i | −0.918118 | − | 0.396307i | \(-0.870292\pi\) |
0.396307 | + | 0.918118i | \(0.370292\pi\) | |||||||
\(420\) | −5.69910 | − | 1.23441i | −0.0135693 | − | 0.00293906i | ||||
\(421\) | −61.2101 | + | 61.2101i | −0.145392 | + | 0.145392i | −0.776056 | − | 0.630664i | \(-0.782783\pi\) |
0.630664 | + | 0.776056i | \(0.282783\pi\) | |||||||
\(422\) | 20.6720 | + | 2.21308i | 0.0489857 | + | 0.00524427i | ||||
\(423\) | 32.3238 | 0.0764156 | ||||||||
\(424\) | −147.725 | + | 445.844i | −0.348407 | + | 1.05152i | ||||
\(425\) | − | 91.8787i | − | 0.216185i | ||||||
\(426\) | 114.732 | + | 12.2828i | 0.269323 | + | 0.0288330i | ||||
\(427\) | 45.0136 | + | 45.0136i | 0.105418 | + | 0.105418i | ||||
\(428\) | −129.615 | + | 83.4631i | −0.302839 | + | 0.195007i | ||||
\(429\) | −272.860 | − | 272.860i | −0.636038 | − | 0.636038i | ||||
\(430\) | 51.9004 | + | 64.3454i | 0.120699 | + | 0.149640i | ||||
\(431\) | − | 501.119i | − | 1.16269i | −0.813657 | − | 0.581345i | \(-0.802527\pi\) | ||
0.813657 | − | 0.581345i | \(-0.197473\pi\) | |||||||
\(432\) | 29.1937 | + | 77.8443i | 0.0675780 | + | 0.180195i | ||||
\(433\) | 75.5505 | 0.174482 | 0.0872408 | − | 0.996187i | \(-0.472195\pi\) | ||||
0.0872408 | + | 0.996187i | \(0.472195\pi\) | |||||||
\(434\) | 46.4439 | − | 37.4612i | 0.107014 | − | 0.0863162i | ||||
\(435\) | 79.2918 | − | 79.2918i | 0.182280 | − | 0.182280i | ||||
\(436\) | 629.769 | − | 405.527i | 1.44442 | − | 0.930108i | ||||
\(437\) | −391.659 | + | 391.659i | −0.896245 | + | 0.896245i | ||||
\(438\) | 6.87096 | − | 64.1803i | 0.0156871 | − | 0.146530i | ||||
\(439\) | 717.251 | 1.63383 | 0.816915 | − | 0.576758i | \(-0.195682\pi\) | ||||
0.816915 | + | 0.576758i | \(0.195682\pi\) | |||||||
\(440\) | 173.850 | − | 87.3160i | 0.395114 | − | 0.198446i | ||||
\(441\) | 145.714i | 0.330417i | ||||||||
\(442\) | 9.86737 | − | 92.1692i | 0.0223244 | − | 0.208528i | ||||
\(443\) | 299.093 | + | 299.093i | 0.675153 | + | 0.675153i | 0.958899 | − | 0.283746i | \(-0.0915773\pi\) |
−0.283746 | + | 0.958899i | \(0.591577\pi\) | |||||||
\(444\) | 97.2217 | + | 21.0579i | 0.218968 | + | 0.0474277i | ||||
\(445\) | 9.64753 | + | 9.64753i | 0.0216798 | + | 0.0216798i | ||||
\(446\) | −601.059 | + | 484.809i | −1.34767 | + | 1.08702i | ||||
\(447\) | 46.4714i | 0.103963i | ||||||||
\(448\) | −25.0203 | + | 33.6115i | −0.0558489 | + | 0.0750257i | ||||
\(449\) | −44.5560 | −0.0992339 | −0.0496170 | − | 0.998768i | \(-0.515800\pi\) | ||||
−0.0496170 | + | 0.998768i | \(0.515800\pi\) | |||||||
\(450\) | 87.9474 | + | 109.036i | 0.195439 | + | 0.242302i | ||||
\(451\) | −380.763 | + | 380.763i | −0.844263 | + | 0.844263i | ||||
\(452\) | −32.1386 | + | 148.380i | −0.0711031 | + | 0.328274i | ||||
\(453\) | −126.405 | + | 126.405i | −0.279039 | + | 0.279039i | ||||
\(454\) | −139.855 | − | 14.9725i | −0.308050 | − | 0.0329790i | ||||
\(455\) | −9.91275 | −0.0217863 | ||||||||
\(456\) | 148.613 | + | 295.896i | 0.325907 | + | 0.648895i | ||||
\(457\) | − | 641.227i | − | 1.40312i | −0.712609 | − | 0.701562i | \(-0.752486\pi\) | ||
0.712609 | − | 0.701562i | \(-0.247514\pi\) | |||||||
\(458\) | −539.607 | − | 57.7689i | −1.17818 | − | 0.126133i | ||||
\(459\) | 14.4592 | + | 14.4592i | 0.0315015 | + | 0.0315015i | ||||
\(460\) | −64.5287 | − | 100.211i | −0.140280 | − | 0.217850i | ||||
\(461\) | −393.690 | − | 393.690i | −0.853991 | − | 0.853991i | 0.136631 | − | 0.990622i | \(-0.456373\pi\) |
−0.990622 | + | 0.136631i | \(0.956373\pi\) | |||||||
\(462\) | 26.9350 | + | 33.3936i | 0.0583009 | + | 0.0722806i | ||||
\(463\) | − | 395.861i | − | 0.854991i | −0.904018 | − | 0.427495i | \(-0.859396\pi\) | ||
0.904018 | − | 0.427495i | \(-0.140604\pi\) | |||||||
\(464\) | −282.944 | − | 754.462i | −0.609792 | − | 1.62600i | ||||
\(465\) | 101.465 | 0.218205 | ||||||||
\(466\) | 464.853 | − | 374.946i | 0.997538 | − | 0.804606i | ||||
\(467\) | −83.1457 | + | 83.1457i | −0.178042 | + | 0.178042i | −0.790502 | − | 0.612460i | \(-0.790180\pi\) |
0.612460 | + | 0.790502i | \(0.290180\pi\) | |||||||
\(468\) | 76.5154 | + | 118.826i | 0.163495 | + | 0.253901i | ||||
\(469\) | −44.4054 | + | 44.4054i | −0.0946810 | + | 0.0946810i | ||||
\(470\) | −2.94891 | + | 27.5452i | −0.00627428 | + | 0.0586068i | ||||
\(471\) | 216.061 | 0.458729 | ||||||||
\(472\) | 226.224 | + | 74.9564i | 0.479288 | + | 0.158806i | ||||
\(473\) | − | 608.217i | − | 1.28587i | ||||||
\(474\) | −2.32025 | + | 21.6730i | −0.00489505 | + | 0.0457237i | ||||
\(475\) | 394.509 | + | 394.509i | 0.830546 | + | 0.830546i | ||||
\(476\) | −2.18165 | + | 10.0724i | −0.00458330 | + | 0.0211605i | ||||
\(477\) | −124.543 | − | 124.543i | −0.261096 | − | 0.261096i | ||||
\(478\) | −385.058 | + | 310.584i | −0.805560 | + | 0.649758i | ||||
\(479\) | 430.043i | 0.897793i | 0.893584 | + | 0.448896i | \(0.148183\pi\) | ||||
−0.893584 | + | 0.448896i | \(0.851817\pi\) | |||||||
\(480\) | −68.9995 | + | 17.7761i | −0.143749 | + | 0.0370335i | ||||
\(481\) | 169.103 | 0.351565 | ||||||||
\(482\) | −276.663 | − | 343.003i | −0.573989 | − | 0.711624i | ||||
\(483\) | 18.5860 | − | 18.5860i | 0.0384803 | − | 0.0384803i | ||||
\(484\) | −925.871 | − | 200.541i | −1.91296 | − | 0.414340i | ||||
\(485\) | 130.564 | − | 130.564i | 0.269204 | − | 0.269204i | ||||
\(486\) | −30.9998 | − | 3.31875i | −0.0637855 | − | 0.00682870i | ||||
\(487\) | 573.790 | 1.17821 | 0.589107 | − | 0.808055i | \(-0.299480\pi\) | ||||
0.589107 | + | 0.808055i | \(0.299480\pi\) | |||||||
\(488\) | 738.376 | + | 244.652i | 1.51307 | + | 0.501335i | ||||
\(489\) | − | 46.0597i | − | 0.0941916i | ||||||
\(490\) | −124.172 | − | 13.2936i | −0.253413 | − | 0.0271297i | ||||
\(491\) | −489.133 | − | 489.133i | −0.996197 | − | 0.996197i | 0.00379588 | − | 0.999993i | \(-0.498792\pi\) |
−0.999993 | + | 0.00379588i | \(0.998792\pi\) | |||||||
\(492\) | 165.815 | − | 106.773i | 0.337023 | − | 0.217019i | ||||
\(493\) | −140.138 | − | 140.138i | −0.284255 | − | 0.284255i | ||||
\(494\) | 353.388 | + | 438.125i | 0.715360 | + | 0.886893i | ||||
\(495\) | 72.9546i | 0.147383i | ||||||||
\(496\) | 301.688 | − | 663.755i | 0.608242 | − | 1.33822i | ||||
\(497\) | −21.8081 | −0.0438795 | ||||||||
\(498\) | −274.843 | + | 221.686i | −0.551894 | + | 0.445153i | ||||
\(499\) | 260.469 | − | 260.469i | 0.521982 | − | 0.521982i | −0.396188 | − | 0.918170i | \(-0.629667\pi\) |
0.918170 | + | 0.396188i | \(0.129667\pi\) | |||||||
\(500\) | −209.025 | + | 134.598i | −0.418050 | + | 0.269195i | ||||
\(501\) | 327.135 | − | 327.135i | 0.652965 | − | 0.652965i | ||||
\(502\) | −48.9911 | + | 457.616i | −0.0975919 | + | 0.911586i | ||||
\(503\) | −975.416 | −1.93920 | −0.969598 | − | 0.244701i | \(-0.921310\pi\) | ||||
−0.969598 | + | 0.244701i | \(0.921310\pi\) | |||||||
\(504\) | −7.05237 | − | 14.0416i | −0.0139928 | − | 0.0278603i | ||||
\(505\) | 164.188i | 0.325124i | ||||||||
\(506\) | −93.3472 | + | 871.938i | −0.184481 | + | 1.72320i | ||||
\(507\) | −37.0981 | − | 37.0981i | −0.0731719 | − | 0.0731719i | ||||
\(508\) | 377.408 | + | 81.7454i | 0.742929 | + | 0.160916i | ||||
\(509\) | −420.191 | − | 420.191i | −0.825523 | − | 0.825523i | 0.161371 | − | 0.986894i | \(-0.448408\pi\) |
−0.986894 | + | 0.161371i | \(0.948408\pi\) | |||||||
\(510\) | −13.6407 | + | 11.0025i | −0.0267466 | + | 0.0215735i | ||||
\(511\) | 12.1994i | 0.0238735i | ||||||||
\(512\) | −88.8714 | + | 504.228i | −0.173577 | + | 0.984820i | ||||
\(513\) | −124.170 | −0.242047 | ||||||||
\(514\) | 127.026 | + | 157.485i | 0.247133 | + | 0.306391i | ||||
\(515\) | −86.5077 | + | 86.5077i | −0.167976 | + | 0.167976i | ||||
\(516\) | −47.1557 | + | 217.712i | −0.0913871 | + | 0.421923i | ||||
\(517\) | 144.121 | − | 144.121i | 0.278764 | − | 0.278764i | ||||
\(518\) | −18.6941 | − | 2.00134i | −0.0360890 | − | 0.00386359i | ||||
\(519\) | −376.044 | −0.724556 | ||||||||
\(520\) | −108.240 | + | 54.3633i | −0.208153 | + | 0.104545i | ||||
\(521\) | 396.333i | 0.760716i | 0.924839 | + | 0.380358i | \(0.124199\pi\) | ||||
−0.924839 | + | 0.380358i | \(0.875801\pi\) | |||||||
\(522\) | 300.448 | + | 32.1651i | 0.575571 | + | 0.0616190i | ||||
\(523\) | 564.600 | + | 564.600i | 1.07954 | + | 1.07954i | 0.996550 | + | 0.0829913i | \(0.0264474\pi\) |
0.0829913 | + | 0.996550i | \(0.473553\pi\) | |||||||
\(524\) | −166.937 | − | 259.246i | −0.318581 | − | 0.494745i | ||||
\(525\) | −18.7212 | − | 18.7212i | −0.0356595 | − | 0.0356595i | ||||
\(526\) | −406.368 | − | 503.809i | −0.772563 | − | 0.957812i | ||||
\(527\) | − | 179.326i | − | 0.340278i | ||||||
\(528\) | 477.247 | + | 216.917i | 0.903876 | + | 0.410827i | ||||
\(529\) | 8.25115 | 0.0155976 | ||||||||
\(530\) | 117.493 | − | 94.7688i | 0.221685 | − | 0.178809i | ||||
\(531\) | −63.1938 | + | 63.1938i | −0.119009 | + | 0.119009i | ||||
\(532\) | −33.8813 | − | 52.6165i | −0.0636867 | − | 0.0989032i | ||||
\(533\) | 237.064 | − | 237.064i | 0.444773 | − | 0.444773i | ||||
\(534\) | −3.91357 | + | 36.5559i | −0.00732878 | + | 0.0684567i | ||||
\(535\) | 49.5461 | 0.0926095 | ||||||||
\(536\) | −241.346 | + | 728.401i | −0.450273 | + | 1.35896i | ||||
\(537\) | − | 302.711i | − | 0.563708i | ||||||
\(538\) | −0.455463 | + | 4.25439i | −0.000846586 | + | 0.00790779i | ||||
\(539\) | 649.691 | + | 649.691i | 1.20536 | + | 1.20536i | ||||
\(540\) | 5.65624 | − | 26.1142i | 0.0104745 | − | 0.0483596i | ||||
\(541\) | −29.5601 | − | 29.5601i | −0.0546398 | − | 0.0546398i | 0.679259 | − | 0.733899i | \(-0.262301\pi\) |
−0.733899 | + | 0.679259i | \(0.762301\pi\) | |||||||
\(542\) | −258.568 | + | 208.559i | −0.477064 | + | 0.384795i | ||||
\(543\) | − | 301.201i | − | 0.554698i | ||||||
\(544\) | 31.4169 | + | 121.948i | 0.0577516 | + | 0.224168i | ||||
\(545\) | −240.733 | −0.441711 | ||||||||
\(546\) | −16.7698 | − | 20.7910i | −0.0307140 | − | 0.0380788i | ||||
\(547\) | −138.608 | + | 138.608i | −0.253397 | + | 0.253397i | −0.822362 | − | 0.568965i | \(-0.807344\pi\) |
0.568965 | + | 0.822362i | \(0.307344\pi\) | |||||||
\(548\) | 101.382 | + | 21.9591i | 0.185004 | + | 0.0400713i | ||||
\(549\) | −206.259 | + | 206.259i | −0.375700 | + | 0.375700i | ||||
\(550\) | 878.283 | + | 94.0265i | 1.59688 | + | 0.170957i | ||||
\(551\) | 1203.45 | 2.18412 | ||||||||
\(552\) | 101.016 | − | 304.874i | 0.183000 | − | 0.552307i | ||||
\(553\) | − | 4.11960i | − | 0.00744955i | ||||||
\(554\) | 893.851 | + | 95.6932i | 1.61345 | + | 0.172731i | ||||
\(555\) | −22.6065 | − | 22.6065i | −0.0407324 | − | 0.0407324i | ||||
\(556\) | −17.3154 | + | 11.1499i | −0.0311428 | + | 0.0200538i | ||||
\(557\) | 60.4400 | + | 60.4400i | 0.108510 | + | 0.108510i | 0.759277 | − | 0.650767i | \(-0.225553\pi\) |
−0.650767 | + | 0.759277i | \(0.725553\pi\) | |||||||
\(558\) | 171.653 | + | 212.813i | 0.307622 | + | 0.381386i | ||||
\(559\) | 378.678i | 0.677421i | ||||||||
\(560\) | 12.6091 | − | 4.72877i | 0.0225163 | − | 0.00844423i | ||||
\(561\) | 128.938 | 0.229835 | ||||||||
\(562\) | −627.031 | + | 505.758i | −1.11571 | + | 0.899924i | ||||
\(563\) | 267.325 | − | 267.325i | 0.474822 | − | 0.474822i | −0.428649 | − | 0.903471i | \(-0.641010\pi\) |
0.903471 | + | 0.428649i | \(0.141010\pi\) | |||||||
\(564\) | −62.7621 | + | 40.4144i | −0.111280 | + | 0.0716568i | ||||
\(565\) | 34.5021 | − | 34.5021i | 0.0610656 | − | 0.0610656i | ||||
\(566\) | 57.9303 | − | 541.115i | 0.102350 | − | 0.956034i | ||||
\(567\) | 5.89242 | 0.0103923 | ||||||||
\(568\) | −238.128 | + | 119.600i | −0.419240 | + | 0.210563i | ||||
\(569\) | − | 315.715i | − | 0.554859i | −0.960746 | − | 0.277429i | \(-0.910518\pi\) | ||
0.960746 | − | 0.277429i | \(-0.0894825\pi\) | |||||||
\(570\) | 11.3281 | − | 105.813i | 0.0198738 | − | 0.185637i | ||||
\(571\) | −670.572 | − | 670.572i | −1.17438 | − | 1.17438i | −0.981154 | − | 0.193228i | \(-0.938104\pi\) |
−0.193228 | − | 0.981154i | \(-0.561896\pi\) | |||||||
\(572\) | 870.962 | + | 188.648i | 1.52266 | + | 0.329803i | ||||
\(573\) | 237.591 | + | 237.591i | 0.414643 | + | 0.414643i | ||||
\(574\) | −29.0128 | + | 23.4015i | −0.0505449 | + | 0.0407691i | ||||
\(575\) | − | 541.161i | − | 0.941149i | ||||||
\(576\) | −154.013 | − | 114.647i | −0.267384 | − | 0.199040i | ||||
\(577\) | 413.628 | 0.716859 | 0.358430 | − | 0.933557i | \(-0.383312\pi\) | ||||
0.358430 | + | 0.933557i | \(0.383312\pi\) | |||||||
\(578\) | −343.434 | − | 425.784i | −0.594176 | − | 0.736650i | ||||
\(579\) | 173.368 | − | 173.368i | 0.299427 | − | 0.299427i | ||||
\(580\) | −54.8200 | + | 253.097i | −0.0945173 | + | 0.436374i | ||||
\(581\) | 47.1900 | − | 47.1900i | 0.0812220 | − | 0.0812220i | ||||
\(582\) | 494.726 | + | 52.9639i | 0.850044 | + | 0.0910033i | ||||
\(583\) | −1110.59 | −1.90495 | ||||||||
\(584\) | 66.9035 | + | 133.208i | 0.114561 | + | 0.228095i | ||||
\(585\) | − | 45.4218i | − | 0.0776441i | ||||||
\(586\) | −211.952 | − | 22.6910i | −0.361693 | − | 0.0387218i | ||||
\(587\) | −420.085 | − | 420.085i | −0.715647 | − | 0.715647i | 0.252064 | − | 0.967711i | \(-0.418891\pi\) |
−0.967711 | + | 0.252064i | \(0.918891\pi\) | |||||||
\(588\) | −182.186 | − | 282.929i | −0.309841 | − | 0.481171i | ||||
\(589\) | 769.993 | + | 769.993i | 1.30729 | + | 1.30729i | ||||
\(590\) | −48.0863 | − | 59.6167i | −0.0815023 | − | 0.101045i | ||||
\(591\) | − | 70.9145i | − | 0.119991i | ||||||
\(592\) | −215.101 | + | 80.6687i | −0.363347 | + | 0.136265i | ||||
\(593\) | −740.798 | −1.24924 | −0.624619 | − | 0.780930i | \(-0.714746\pi\) | ||||
−0.624619 | + | 0.780930i | \(0.714746\pi\) | |||||||
\(594\) | −153.015 | + | 123.421i | −0.257601 | + | 0.207779i | ||||
\(595\) | 2.34209 | − | 2.34209i | 0.00393628 | − | 0.00393628i | ||||
\(596\) | −58.1031 | − | 90.2320i | −0.0974885 | − | 0.151396i | ||||
\(597\) | −33.8340 | + | 33.8340i | −0.0566733 | + | 0.0566733i | ||||
\(598\) | 58.1183 | − | 542.872i | 0.0971878 | − | 0.907812i | ||||
\(599\) | 435.161 | 0.726479 | 0.363240 | − | 0.931696i | \(-0.381671\pi\) | ||||
0.363240 | + | 0.931696i | \(0.381671\pi\) | |||||||
\(600\) | −307.092 | − | 101.751i | −0.511821 | − | 0.169585i | ||||
\(601\) | 380.001i | 0.632280i | 0.948712 | + | 0.316140i | \(0.102387\pi\) | ||||
−0.948712 | + | 0.316140i | \(0.897613\pi\) | |||||||
\(602\) | 4.48167 | − | 41.8624i | 0.00744463 | − | 0.0695388i | ||||
\(603\) | −203.473 | − | 203.473i | −0.337434 | − | 0.337434i | ||||
\(604\) | 87.3924 | − | 403.480i | 0.144689 | − | 0.668013i | ||||
\(605\) | 215.288 | + | 215.288i | 0.355849 | + | 0.355849i | ||||
\(606\) | −344.367 | + | 277.764i | −0.568263 | + | 0.458356i | ||||
\(607\) | 181.813i | 0.299527i | 0.988722 | + | 0.149763i | \(0.0478512\pi\) | ||||
−0.988722 | + | 0.149763i | \(0.952149\pi\) | |||||||
\(608\) | −658.517 | − | 388.721i | −1.08309 | − | 0.639344i | ||||
\(609\) | −57.1090 | −0.0937751 | ||||||||
\(610\) | −156.950 | − | 194.584i | −0.257295 | − | 0.318990i | ||||
\(611\) | −89.7303 | + | 89.7303i | −0.146858 | + | 0.146858i | ||||
\(612\) | −46.1533 | − | 9.99666i | −0.0754139 | − | 0.0163344i | ||||
\(613\) | 55.1479 | − | 55.1479i | 0.0899640 | − | 0.0899640i | −0.660693 | − | 0.750657i | \(-0.729737\pi\) |
0.750657 | + | 0.660693i | \(0.229737\pi\) | |||||||
\(614\) | −313.703 | − | 33.5841i | −0.510917 | − | 0.0546973i | ||||
\(615\) | −63.3838 | −0.103063 | ||||||||
\(616\) | −94.0510 | − | 31.1626i | −0.152680 | − | 0.0505886i | ||||
\(617\) | 579.674i | 0.939504i | 0.882798 | + | 0.469752i | \(0.155657\pi\) | ||||
−0.882798 | + | 0.469752i | \(0.844343\pi\) | |||||||
\(618\) | −327.790 | − | 35.0923i | −0.530405 | − | 0.0567837i | ||||
\(619\) | 91.1070 | + | 91.1070i | 0.147184 | + | 0.147184i | 0.776859 | − | 0.629675i | \(-0.216812\pi\) |
−0.629675 | + | 0.776859i | \(0.716812\pi\) | |||||||
\(620\) | −197.012 | + | 126.862i | −0.317761 | + | 0.204616i | ||||
\(621\) | 85.1639 | + | 85.1639i | 0.137140 | + | 0.137140i | ||||
\(622\) | −281.870 | − | 349.458i | −0.453167 | − | 0.561830i | ||||
\(623\) | − | 6.94852i | − | 0.0111533i | ||||||
\(624\) | −297.136 | − | 135.053i | −0.476179 | − | 0.216431i | ||||
\(625\) | −503.783 | −0.806053 | ||||||||
\(626\) | 760.208 | − | 613.177i | 1.21439 | − | 0.979516i | ||||
\(627\) | −553.633 | + | 553.633i | −0.882987 | + | 0.882987i | ||||
\(628\) | −419.520 | + | 270.141i | −0.668025 | + | 0.430162i | ||||
\(629\) | −39.9540 | + | 39.9540i | −0.0635199 | + | 0.0635199i | ||||
\(630\) | −0.537568 | + | 5.02132i | −0.000853283 | + | 0.00797034i | ||||
\(631\) | −693.474 | −1.09901 | −0.549504 | − | 0.835491i | \(-0.685183\pi\) | ||||
−0.549504 | + | 0.835491i | \(0.685183\pi\) | |||||||
\(632\) | −22.5926 | − | 44.9829i | −0.0357478 | − | 0.0711755i | ||||
\(633\) | − | 18.0048i | − | 0.0284435i | ||||||
\(634\) | −77.4869 | + | 723.790i | −0.122219 | + | 1.14162i | ||||
\(635\) | −87.7570 | − | 87.7570i | −0.138200 | − | 0.138200i | ||||
\(636\) | 397.536 | + | 86.1051i | 0.625057 | + | 0.135385i | ||||
\(637\) | −404.500 | − | 404.500i | −0.635007 | − | 0.635007i | ||||
\(638\) | 1483.01 | − | 1196.19i | 2.32447 | − | 1.87490i | ||||
\(639\) | − | 99.9283i | − | 0.156382i | ||||||
\(640\) | 111.749 | − | 120.785i | 0.174608 | − | 0.188727i | ||||
\(641\) | −218.329 | −0.340607 | −0.170304 | − | 0.985392i | \(-0.554475\pi\) | ||||
−0.170304 | + | 0.985392i | \(0.554475\pi\) | |||||||
\(642\) | 83.8194 | + | 103.918i | 0.130560 | + | 0.161866i | ||||
\(643\) | 887.430 | − | 887.430i | 1.38014 | − | 1.38014i | 0.535787 | − | 0.844353i | \(-0.320015\pi\) |
0.844353 | − | 0.535787i | \(-0.179985\pi\) | |||||||
\(644\) | −12.8498 | + | 59.3259i | −0.0199531 | + | 0.0921210i | ||||
\(645\) | 50.6236 | − | 50.6236i | 0.0784861 | − | 0.0784861i | ||||
\(646\) | −187.011 | − | 20.0209i | −0.289491 | − | 0.0309921i | ||||
\(647\) | −223.177 | −0.344941 | −0.172470 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172470 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(648\) | 64.3408 | − | 32.3151i | 0.0992913 | − | 0.0498690i | ||||
\(649\) | 563.520i | 0.868290i | ||||||||
\(650\) | −546.822 | − | 58.5413i | −0.841265 | − | 0.0900635i | ||||
\(651\) | −36.5396 | − | 36.5396i | −0.0561284 | − | 0.0561284i | ||||
\(652\) | 57.5884 | + | 89.4327i | 0.0883258 | + | 0.137167i | ||||
\(653\) | 539.691 | + | 539.691i | 0.826479 | + | 0.826479i | 0.987028 | − | 0.160549i | \(-0.0513264\pi\) |
−0.160549 | + | 0.987028i | \(0.551326\pi\) | |||||||
\(654\) | −407.258 | − | 504.913i | −0.622719 | − | 0.772037i | ||||
\(655\) | 99.0983i | 0.151295i | ||||||||
\(656\) | −188.460 | + | 414.638i | −0.287286 | + | 0.632070i | ||||
\(657\) | −55.8994 | −0.0850828 | ||||||||
\(658\) | 10.9815 | − | 8.85760i | 0.0166892 | − | 0.0134614i | ||||
\(659\) | 625.166 | − | 625.166i | 0.948659 | − | 0.948659i | −0.0500862 | − | 0.998745i | \(-0.515950\pi\) |
0.998745 | + | 0.0500862i | \(0.0159496\pi\) | |||||||
\(660\) | −91.2151 | − | 141.654i | −0.138205 | − | 0.214627i | ||||
\(661\) | −326.893 | + | 326.893i | −0.494544 | + | 0.494544i | −0.909734 | − | 0.415191i | \(-0.863715\pi\) |
0.415191 | + | 0.909734i | \(0.363715\pi\) | |||||||
\(662\) | 37.1996 | − | 347.474i | 0.0561928 | − | 0.524886i | ||||
\(663\) | −80.2770 | −0.121081 | ||||||||
\(664\) | 256.481 | − | 774.078i | 0.386266 | − | 1.16578i | ||||
\(665\) | 20.1129i | 0.0302450i | ||||||||
\(666\) | 9.17045 | − | 85.6593i | 0.0137694 | − | 0.128618i | ||||
\(667\) | −825.404 | − | 825.404i | −1.23749 | − | 1.23749i | ||||
\(668\) | −226.172 | + | 1044.21i | −0.338581 | + | 1.56318i | ||||
\(669\) | 472.881 | + | 472.881i | 0.706848 | + | 0.706848i | ||||
\(670\) | 191.955 | − | 154.829i | 0.286500 | − | 0.231089i | ||||
\(671\) | 1839.28i | 2.74111i | ||||||||
\(672\) | 31.2496 | + | 18.4466i | 0.0465023 | + | 0.0274502i | ||||
\(673\) | 422.147 | 0.627262 | 0.313631 | − | 0.949545i | \(-0.398455\pi\) | ||||
0.313631 | + | 0.949545i | \(0.398455\pi\) | |||||||
\(674\) | −309.181 | − | 383.318i | −0.458725 | − | 0.568720i | ||||
\(675\) | 85.7837 | − | 85.7837i | 0.127087 | − | 0.127087i | ||||
\(676\) | 118.416 | + | 25.6486i | 0.175172 | + | 0.0379417i | ||||
\(677\) | −126.017 | + | 126.017i | −0.186140 | + | 0.186140i | −0.794025 | − | 0.607885i | \(-0.792018\pi\) |
0.607885 | + | 0.794025i | \(0.292018\pi\) | |||||||
\(678\) | 130.733 | + | 13.9959i | 0.192822 | + | 0.0206430i | ||||
\(679\) | −94.0372 | −0.138494 | ||||||||
\(680\) | 12.7294 | − | 38.4183i | 0.0187197 | − | 0.0564974i | ||||
\(681\) | 121.810i | 0.178869i | ||||||||
\(682\) | 1714.21 | + | 183.518i | 2.51350 | + | 0.269089i | ||||
\(683\) | 621.906 | + | 621.906i | 0.910551 | + | 0.910551i | 0.996315 | − | 0.0857647i | \(-0.0273333\pi\) |
−0.0857647 | + | 0.996315i | \(0.527333\pi\) | |||||||
\(684\) | 241.097 | − | 155.250i | 0.352481 | − | 0.226973i | ||||
\(685\) | −23.5740 | − | 23.5740i | −0.0344145 | − | 0.0344145i | ||||
\(686\) | 80.2117 | + | 99.4452i | 0.116927 | + | 0.144964i | ||||
\(687\) | 469.984i | 0.684111i | ||||||||
\(688\) | −180.644 | − | 481.684i | −0.262564 | − | 0.700122i | ||||
\(689\) | 691.456 | 1.00357 | ||||||||
\(690\) | −80.3433 | + | 64.8042i | −0.116440 | + | 0.0939191i | ||||
\(691\) | −403.376 | + | 403.376i | −0.583758 | + | 0.583758i | −0.935934 | − | 0.352176i | \(-0.885442\pi\) |
0.352176 | + | 0.935934i | \(0.385442\pi\) | |||||||
\(692\) | 730.154 | − | 470.168i | 1.05514 | − | 0.679434i | ||||
\(693\) | 26.2724 | − | 26.2724i | 0.0379110 | − | 0.0379110i | ||||
\(694\) | 37.0969 | − | 346.515i | 0.0534537 | − | 0.499301i | ||||
\(695\) | 6.61889 | 0.00952359 | ||||||||
\(696\) | −623.587 | + | 313.196i | −0.895959 | + | 0.449995i | ||||
\(697\) | 112.022i | 0.160721i | ||||||||
\(698\) | −34.7361 | + | 324.463i | −0.0497652 | + | 0.464847i | ||||
\(699\) | −365.722 | − | 365.722i | −0.523207 | − | 0.523207i | ||||
\(700\) | 59.7576 | + | 12.9433i | 0.0853680 | + | 0.0184904i | ||||
\(701\) | 466.593 | + | 466.593i | 0.665611 | + | 0.665611i | 0.956697 | − | 0.291086i | \(-0.0940166\pi\) |
−0.291086 | + | 0.956697i | \(0.594017\pi\) | |||||||
\(702\) | 95.2676 | − | 76.8421i | 0.135709 | − | 0.109462i | ||||
\(703\) | − | 343.109i | − | 0.488065i | ||||||
\(704\) | −1197.87 | + | 175.521i | −1.70152 | + | 0.249319i | ||||
\(705\) | 23.9912 | 0.0340300 | ||||||||
\(706\) | 816.847 | + | 1012.72i | 1.15701 | + | 1.43444i | ||||
\(707\) | 59.1272 | − | 59.1272i | 0.0836311 | − | 0.0836311i | ||||
\(708\) | 43.6903 | − | 201.713i | 0.0617095 | − | 0.284905i | ||||
\(709\) | 822.764 | − | 822.764i | 1.16046 | − | 1.16046i | 0.176081 | − | 0.984376i | \(-0.443658\pi\) |
0.984376 | − | 0.176081i | \(-0.0563422\pi\) | |||||||
\(710\) | 85.1554 | + | 9.11650i | 0.119937 | + | 0.0128401i | ||||
\(711\) | 18.8767 | 0.0265494 | ||||||||
\(712\) | −38.1069 | − | 75.8726i | −0.0535210 | − | 0.106563i | ||||
\(713\) | − | 1056.22i | − | 1.48138i | ||||||
\(714\) | 8.87451 | + | 0.950080i | 0.0124293 | + | 0.00133064i | ||||
\(715\) | −202.521 | − | 202.521i | −0.283246 | − | 0.283246i | ||||
\(716\) | 378.480 | + | 587.766i | 0.528603 | + | 0.820902i | ||||
\(717\) | 302.943 | + | 302.943i | 0.422515 | + | 0.422515i | ||||
\(718\) | 118.642 | + | 147.091i | 0.165240 | + | 0.204862i | ||||
\(719\) | − | 710.142i | − | 0.987681i | −0.869553 | − | 0.493840i | \(-0.835593\pi\) | ||
0.869553 | − | 0.493840i | \(-0.164407\pi\) | |||||||
\(720\) | 21.6680 | + | 57.7771i | 0.0300944 | + | 0.0802460i | ||||
\(721\) | 62.3062 | 0.0864164 | ||||||||
\(722\) | 326.979 | − | 263.738i | 0.452879 | − | 0.365289i | ||||
\(723\) | −269.856 | + | 269.856i | −0.373245 | + | 0.373245i | ||||
\(724\) | 376.592 | + | 584.833i | 0.520154 | + | 0.807781i | ||||
\(725\) | −831.411 | + | 831.411i | −1.14677 | + | 1.14677i | ||||
\(726\) | −87.3329 | + | 815.759i | −0.120293 | + | 1.12364i | ||||
\(727\) | −214.095 | −0.294490 | −0.147245 | − | 0.989100i | \(-0.547041\pi\) | ||||
−0.147245 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(728\) | 58.5565 | + | 19.4019i | 0.0804347 | + | 0.0266510i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 5.09972 | − | 47.6355i | 0.00698592 | − | 0.0652541i | ||||
\(731\) | −89.4704 | − | 89.4704i | −0.122395 | − | 0.122395i | ||||
\(732\) | 142.602 | − | 658.373i | 0.194811 | − | 0.899417i | ||||
\(733\) | −96.1768 | − | 96.1768i | −0.131210 | − | 0.131210i | 0.638452 | − | 0.769662i | \(-0.279575\pi\) |
−0.769662 | + | 0.638452i | \(0.779575\pi\) | |||||||
\(734\) | −204.521 | + | 164.965i | −0.278638 | + | 0.224747i | ||||
\(735\) | 108.151i | 0.147144i | ||||||||
\(736\) | 185.044 | + | 718.265i | 0.251418 | + | 0.975903i | ||||
\(737\) | −1814.43 | −2.46192 | ||||||||
\(738\) | −107.229 | − | 132.941i | −0.145297 | − | 0.180137i | ||||
\(739\) | 885.341 | − | 885.341i | 1.19803 | − | 1.19803i | 0.223268 | − | 0.974757i | \(-0.428327\pi\) |
0.974757 | − | 0.223268i | \(-0.0716726\pi\) | |||||||
\(740\) | 72.1593 | + | 15.6295i | 0.0975125 | + | 0.0211209i | ||||
\(741\) | 344.694 | − | 344.694i | 0.465174 | − | 0.465174i | ||||
\(742\) | −76.4396 | − | 8.18341i | −0.103018 | − | 0.0110289i | ||||
\(743\) | 906.258 | 1.21973 | 0.609864 | − | 0.792506i | \(-0.291224\pi\) | ||||
0.609864 | + | 0.792506i | \(0.291224\pi\) | |||||||
\(744\) | −599.374 | − | 198.595i | −0.805611 | − | 0.266929i | ||||
\(745\) | 34.4917i | 0.0462976i | ||||||||
\(746\) | −775.637 | − | 83.0376i | −1.03973 | − | 0.111310i | ||||
\(747\) | 216.232 | + | 216.232i | 0.289467 | + | 0.289467i | ||||
\(748\) | −250.354 | + | 161.211i | −0.334698 | + | 0.215522i | ||||
\(749\) | −17.8425 | − | 17.8425i | −0.0238218 | − | 0.0238218i | ||||
\(750\) | 135.172 | + | 167.584i | 0.180229 | + | 0.223446i | ||||
\(751\) | 1147.02i | 1.52732i | 0.645618 | + | 0.763661i | \(0.276600\pi\) | ||||
−0.645618 | + | 0.763661i | \(0.723400\pi\) | |||||||
\(752\) | 71.3333 | − | 156.943i | 0.0948581 | − | 0.208701i | ||||
\(753\) | 398.572 | 0.529312 | ||||||||
\(754\) | −923.329 | + | 744.749i | −1.22457 | + | 0.987731i | ||||
\(755\) | −93.8192 | + | 93.8192i | −0.124264 | + | 0.124264i | ||||
\(756\) | −11.4411 | + | 7.36729i | −0.0151338 | + | 0.00974509i | ||||
\(757\) | 525.591 | − | 525.591i | 0.694308 | − | 0.694308i | −0.268869 | − | 0.963177i | \(-0.586650\pi\) |
0.963177 | + | 0.268869i | \(0.0866497\pi\) | |||||||
\(758\) | 3.92694 | − | 36.6808i | 0.00518066 | − | 0.0483915i | ||||
\(759\) | 759.435 | 1.00057 | ||||||||
\(760\) | 110.303 | + | 219.618i | 0.145135 | + | 0.288971i | ||||
\(761\) | − | 788.107i | − | 1.03562i | −0.855495 | − | 0.517810i | \(-0.826747\pi\) | ||
0.855495 | − | 0.517810i | \(-0.173253\pi\) | |||||||
\(762\) | 35.5991 | − | 332.524i | 0.0467179 | − | 0.436383i | ||||
\(763\) | 86.6925 | + | 86.6925i | 0.113621 | + | 0.113621i | ||||
\(764\) | −758.382 | − | 164.263i | −0.992647 | − | 0.215004i | ||||
\(765\) | 10.7318 | + | 10.7318i | 0.0140285 | + | 0.0140285i | ||||
\(766\) | −189.879 | + | 153.155i | −0.247884 | + | 0.199941i | ||||
\(767\) | − | 350.850i | − | 0.457431i | ||||||
\(768\) | 442.386 | + | 30.0441i | 0.576023 | + | 0.0391199i | ||||
\(769\) | −768.187 | −0.998943 | −0.499471 | − | 0.866330i | \(-0.666472\pi\) | ||||
−0.499471 | + | 0.866330i | \(0.666472\pi\) | |||||||
\(770\) | 19.9915 | + | 24.7852i | 0.0259630 | + | 0.0321886i | ||||
\(771\) | 123.901 | − | 123.901i | 0.160702 | − | 0.160702i | ||||
\(772\) | −119.862 | + | 553.387i | −0.155261 | + | 0.716822i | ||||
\(773\) | 275.915 | − | 275.915i | 0.356941 | − | 0.356941i | −0.505743 | − | 0.862684i | \(-0.668782\pi\) |
0.862684 | + | 0.505743i | \(0.168782\pi\) | |||||||
\(774\) | 191.820 | + | 20.5357i | 0.247830 | + | 0.0265319i | ||||
\(775\) | −1063.91 | −1.37279 | ||||||||
\(776\) | −1026.81 | + | 515.717i | −1.32321 | + | 0.664583i | ||||
\(777\) | 16.2821i | 0.0209551i | ||||||||
\(778\) | −656.031 | − | 70.2328i | −0.843227 | − | 0.0902735i | ||||
\(779\) | −481.003 | − | 481.003i | −0.617462 | − | 0.617462i | ||||
\(780\) | 56.7908 | + | 88.1941i | 0.0728088 | + | 0.113069i | ||||
\(781\) | −445.547 | − | 445.547i | −0.570483 | − | 0.570483i | ||||
\(782\) | 114.533 | + | 141.996i | 0.146461 | + | 0.181581i | ||||
\(783\) | − | 261.683i | − | 0.334205i | ||||||
\(784\) | 707.491 | + | 321.567i | 0.902412 | + | 0.410162i | ||||
\(785\) | 160.364 | 0.204285 | ||||||||
\(786\) | −207.849 | + | 167.649i | −0.264439 | + | 0.213294i | ||||
\(787\) | 240.824 | − | 240.824i | 0.306002 | − | 0.306002i | −0.537354 | − | 0.843356i | \(-0.680576\pi\) |
0.843356 | + | 0.537354i | \(0.180576\pi\) | |||||||
\(788\) | 88.6644 | + | 137.693i | 0.112518 | + | 0.174737i | ||||
\(789\) | −396.371 | + | 396.371i | −0.502371 | + | 0.502371i | ||||
\(790\) | −1.72213 | + | 16.0860i | −0.00217991 | + | 0.0203621i | ||||
\(791\) | −24.8497 | −0.0314156 | ||||||||
\(792\) | 142.792 | − | 430.956i | 0.180293 | − | 0.544137i | ||||
\(793\) | − | 1145.14i | − | 1.44407i | ||||||
\(794\) | 25.2215 | − | 235.589i | 0.0317651 | − | 0.296712i | ||||
\(795\) | −92.4373 | − | 92.4373i | −0.116273 | − | 0.116273i | ||||
\(796\) | 23.3918 | − | 107.997i | 0.0293867 | − | 0.135675i | ||||
\(797\) | −681.033 | − | 681.033i | −0.854496 | − | 0.854496i | 0.136187 | − | 0.990683i | \(-0.456515\pi\) |
−0.990683 | + | 0.136187i | \(0.956515\pi\) | |||||||
\(798\) | −42.1849 | + | 34.0260i | −0.0528633 | + | 0.0426391i | ||||
\(799\) | − | 42.4012i | − | 0.0530678i | ||||||
\(800\) | 723.492 | − | 186.390i | 0.904364 | − | 0.232988i | ||||
\(801\) | 31.8392 | 0.0397493 | ||||||||
\(802\) | 739.739 | + | 917.117i | 0.922367 | + | 1.14354i | ||||
\(803\) | −249.237 | + | 249.237i | −0.310382 | + | 0.310382i | ||||
\(804\) | 649.478 | + | 140.675i | 0.807809 | + | 0.174969i | ||||
\(805\) | 13.7948 | − | 13.7948i | 0.0171364 | − | 0.0171364i | ||||
\(806\) | −1067.27 | − | 114.259i | −1.32416 | − | 0.141761i | ||||
\(807\) | 3.70547 | 0.00459166 | ||||||||
\(808\) | 321.360 | − | 969.888i | 0.397723 | − | 1.20036i | ||||
\(809\) | 445.322i | 0.550459i | 0.961379 | + | 0.275230i | \(0.0887539\pi\) | ||||
−0.961379 | + | 0.275230i | \(0.911246\pi\) | |||||||
\(810\) | −23.0085 | − | 2.46322i | −0.0284055 | − | 0.00304101i | ||||
\(811\) | 223.787 | + | 223.787i | 0.275939 | + | 0.275939i | 0.831485 | − | 0.555546i | \(-0.187491\pi\) |
−0.555546 | + | 0.831485i | \(0.687491\pi\) | |||||||
\(812\) | 110.887 | − | 71.4034i | 0.136560 | − | 0.0879352i | ||||
\(813\) | 203.428 | + | 203.428i | 0.250219 | + | 0.250219i | ||||
\(814\) | −341.039 | − | 422.815i | −0.418966 | − | 0.519428i | ||||
\(815\) | − | 34.1861i | − | 0.0419462i | ||||||
\(816\) | 102.113 | − | 38.2953i | 0.125139 | − | 0.0469305i | ||||
\(817\) | 768.337 | 0.940437 | ||||||||
\(818\) | −699.411 | + | 564.139i | −0.855026 | + | 0.689656i | ||||
\(819\) | −16.3573 | + | 16.3573i | −0.0199722 | + | 0.0199722i | ||||
\(820\) | 123.070 | − | 79.2488i | 0.150086 | − | 0.0966448i | ||||
\(821\) | 382.528 | − | 382.528i | 0.465929 | − | 0.465929i | −0.434664 | − | 0.900593i | \(-0.643133\pi\) |
0.900593 | + | 0.434664i | \(0.143133\pi\) | |||||||
\(822\) | 9.56290 | − | 89.3251i | 0.0116337 | − | 0.108668i | ||||
\(823\) | −730.046 | −0.887055 | −0.443527 | − | 0.896261i | \(-0.646273\pi\) | ||||
−0.443527 | + | 0.896261i | \(0.646273\pi\) | |||||||
\(824\) | 680.337 | − | 341.698i | 0.825651 | − | 0.414683i | ||||
\(825\) | − | 764.962i | − | 0.927227i | ||||||
\(826\) | −4.15232 | + | 38.7860i | −0.00502702 | + | 0.0469564i | ||||
\(827\) | 252.094 | + | 252.094i | 0.304829 | + | 0.304829i | 0.842900 | − | 0.538071i | \(-0.180847\pi\) |
−0.538071 | + | 0.842900i | \(0.680847\pi\) | |||||||
\(828\) | −271.841 | − | 58.8798i | −0.328310 | − | 0.0711109i | ||||
\(829\) | −870.285 | − | 870.285i | −1.04980 | − | 1.04980i | −0.998693 | − | 0.0511072i | \(-0.983725\pi\) |
−0.0511072 | − | 0.998693i | \(-0.516275\pi\) | |||||||
\(830\) | −203.992 | + | 164.539i | −0.245774 | + | 0.198239i | ||||
\(831\) | − | 778.521i | − | 0.936849i | ||||||
\(832\) | 745.796 | − | 109.280i | 0.896390 | − | 0.131346i | ||||
\(833\) | 191.143 | 0.229463 | ||||||||
\(834\) | 11.1975 | + | 13.8825i | 0.0134262 | + | 0.0166456i | ||||
\(835\) | 242.804 | − | 242.804i | 0.290784 | − | 0.290784i | ||||
\(836\) | 382.765 | − | 1767.18i | 0.457853 | − | 2.11385i | ||||
\(837\) | 167.430 | − | 167.430i | 0.200036 | − | 0.200036i | ||||
\(838\) | −614.890 | − | 65.8284i | −0.733759 | − | 0.0785542i | ||||
\(839\) | 550.145 | 0.655715 | 0.327858 | − | 0.944727i | \(-0.393673\pi\) | ||||
0.327858 | + | 0.944727i | \(0.393673\pi\) | |||||||
\(840\) | −5.23437 | − | 10.4219i | −0.00623139 | − | 0.0124070i | ||||
\(841\) | 1695.21i | 2.01571i | ||||||||
\(842\) | −172.145 | − | 18.4293i | −0.204447 | − | 0.0218876i | ||||
\(843\) | 493.315 | + | 493.315i | 0.585189 | + | 0.585189i | ||||
\(844\) | 22.5113 | + | 34.9593i | 0.0266722 | + | 0.0414210i | ||||
\(845\) | −27.5348 | − | 27.5348i | −0.0325855 | − | 0.0325855i | ||||
\(846\) | 40.5869 | + | 50.3191i | 0.0479751 | + | 0.0594788i | ||||
\(847\) | − | 155.059i | − | 0.183069i | ||||||
\(848\) | −879.542 | + | 329.852i | −1.03720 | + | 0.388976i | ||||
\(849\) | −471.298 | −0.555121 | ||||||||
\(850\) | 143.029 | − | 115.366i | 0.168270 | − | 0.135725i | ||||
\(851\) | −235.327 | + | 235.327i | −0.276530 | + | 0.276530i | ||||
\(852\) | 124.940 | + | 194.028i | 0.146644 | + | 0.227732i | ||||
\(853\) | −676.266 | + | 676.266i | −0.792809 | + | 0.792809i | −0.981950 | − | 0.189141i | \(-0.939430\pi\) |
0.189141 | + | 0.981950i | \(0.439430\pi\) | |||||||
\(854\) | −13.5528 | + | 126.594i | −0.0158698 | + | 0.148237i | ||||
\(855\) | −92.1607 | −0.107790 | ||||||||
\(856\) | −292.678 | − | 96.9752i | −0.341914 | − | 0.113289i | ||||
\(857\) | 291.272i | 0.339874i | 0.985455 | + | 0.169937i | \(0.0543563\pi\) | ||||
−0.985455 | + | 0.169937i | \(0.945644\pi\) | |||||||
\(858\) | 82.1536 | − | 767.380i | 0.0957501 | − | 0.894382i | ||||
\(859\) | 988.357 | + | 988.357i | 1.15059 | + | 1.15059i | 0.986434 | + | 0.164156i | \(0.0524899\pi\) |
0.164156 | + | 0.986434i | \(0.447510\pi\) | |||||||
\(860\) | −34.9996 | + | 161.589i | −0.0406973 | + | 0.187894i | ||||
\(861\) | 22.8257 | + | 22.8257i | 0.0265107 | + | 0.0265107i | ||||
\(862\) | 780.102 | − | 629.224i | 0.904991 | − | 0.729958i | ||||
\(863\) | 922.512i | 1.06896i | 0.845181 | + | 0.534480i | \(0.179492\pi\) | ||||
−0.845181 | + | 0.534480i | \(0.820508\pi\) | |||||||
\(864\) | −84.5250 | + | 143.191i | −0.0978299 | + | 0.165730i | ||||
\(865\) | −279.105 | −0.322665 | ||||||||
\(866\) | 94.8640 | + | 117.611i | 0.109543 | + | 0.135809i | ||||
\(867\) | −334.984 | + | 334.984i | −0.386372 | + | 0.386372i | ||||
\(868\) | 116.633 | + | 25.2624i | 0.134370 | + | 0.0291042i | ||||
\(869\) | 84.1648 | − | 84.1648i | 0.0968524 | − | 0.0968524i | ||||
\(870\) | 222.997 | + | 23.8734i | 0.256318 | + | 0.0274407i | ||||
\(871\) | 1129.67 | 1.29698 | ||||||||
\(872\) | 1422.05 | + | 471.179i | 1.63079 | + | 0.540343i | ||||
\(873\) | − | 430.893i | − | 0.493577i | ||||||
\(874\) | −1101.49 | − | 117.922i | −1.26028 | − | 0.134922i | ||||
\(875\) | −28.7739 | − | 28.7739i | −0.0328845 | − | 0.0328845i | ||||
\(876\) | 108.538 | − | 69.8910i | 0.123902 | − | 0.0797842i | ||||
\(877\) | −406.278 | − | 406.278i | −0.463259 | − | 0.463259i | 0.436463 | − | 0.899722i | \(-0.356231\pi\) |
−0.899722 | + | 0.436463i | \(0.856231\pi\) | |||||||
\(878\) | 900.607 | + | 1116.56i | 1.02575 | + | 1.27171i | ||||
\(879\) | 184.605i | 0.210017i | ||||||||
\(880\) | 354.219 | + | 160.999i | 0.402522 | + | 0.182953i | ||||
\(881\) | −1009.42 | −1.14577 | −0.572884 | − | 0.819637i | \(-0.694175\pi\) | ||||
−0.572884 | + | 0.819637i | \(0.694175\pi\) | |||||||
\(882\) | −226.836 | + | 182.964i | −0.257184 | + | 0.207442i | ||||
\(883\) | 56.3792 | − | 56.3792i | 0.0638496 | − | 0.0638496i | −0.674461 | − | 0.738311i | \(-0.735624\pi\) |
0.738311 | + | 0.674461i | \(0.235624\pi\) | |||||||
\(884\) | 155.871 | − | 100.370i | 0.176325 | − | 0.113541i | ||||
\(885\) | −46.9033 | + | 46.9033i | −0.0529981 | + | 0.0529981i | ||||
\(886\) | −90.0518 | + | 841.156i | −0.101639 | + | 0.949386i | ||||
\(887\) | 21.0431 | 0.0237239 | 0.0118620 | − | 0.999930i | \(-0.496224\pi\) | ||||
0.0118620 | + | 0.999930i | \(0.496224\pi\) | |||||||
\(888\) | 89.2938 | + | 177.788i | 0.100556 | + | 0.200212i | ||||
\(889\) | 63.2060i | 0.0710978i | ||||||||
\(890\) | −2.90471 | + | 27.1323i | −0.00326371 | + | 0.0304857i | ||||
\(891\) | 120.384 | + | 120.384i | 0.135111 | + | 0.135111i | ||||
\(892\) | −1509.42 | − | 326.936i | −1.69218 | − | 0.366520i | ||||
\(893\) | 182.063 | + | 182.063i | 0.203877 | + | 0.203877i | ||||
\(894\) | −72.3429 | + | 58.3511i | −0.0809204 | + | 0.0652697i | ||||
\(895\) | − | 224.677i | − | 0.251035i | ||||||
\(896\) | −83.7401 | + | 3.25421i | −0.0934599 | + | 0.00363193i | ||||
\(897\) | −472.827 | −0.527121 | ||||||||
\(898\) | −55.9462 | − | 69.3613i | −0.0623009 | − | 0.0772397i | ||||
\(899\) | −1622.72 | + | 1622.72i | −1.80503 | + | 1.80503i | ||||
\(900\) | −59.3083 | + | 273.819i | −0.0658981 | + | 0.304243i | ||||
\(901\) | −163.371 | + | 163.371i | −0.181321 | + | 0.181321i | ||||
\(902\) | −1070.84 | − | 114.641i | −1.18718 | − | 0.127097i | ||||
\(903\) | −36.4610 | −0.0403777 | ||||||||
\(904\) | −271.340 | + | 136.280i | −0.300155 | + | 0.150753i | ||||
\(905\) | − | 223.556i | − | 0.247023i | ||||||
\(906\) | −355.495 | − | 38.0583i | −0.392378 | − | 0.0420069i | ||||
\(907\) | 496.202 | + | 496.202i | 0.547080 | + | 0.547080i | 0.925595 | − | 0.378515i | \(-0.123565\pi\) |
−0.378515 | + | 0.925595i | \(0.623565\pi\) | |||||||
\(908\) | −152.299 | − | 236.515i | −0.167730 | − | 0.260479i | ||||
\(909\) | 270.930 | + | 270.930i | 0.298053 | + | 0.298053i | ||||
\(910\) | −12.4468 | − | 15.4314i | −0.0136778 | − | 0.0169575i | ||||
\(911\) | − | 1532.15i | − | 1.68183i | −0.541163 | − | 0.840917i | \(-0.682016\pi\) | ||
0.541163 | − | 0.840917i | \(-0.317984\pi\) | |||||||
\(912\) | −274.023 | + | 602.887i | −0.300463 | + | 0.661061i | ||||
\(913\) | 1928.21 | 2.11195 | ||||||||
\(914\) | 998.211 | − | 805.149i | 1.09213 | − | 0.880907i | ||||
\(915\) | −153.088 | + | 153.088i | −0.167310 | + | 0.167310i | ||||
\(916\) | −587.621 | − | 912.554i | −0.641508 | − | 0.996238i | ||||
\(917\) | 35.6872 | − | 35.6872i | 0.0389174 | − | 0.0389174i | ||||
\(918\) | −4.35342 | + | 40.6644i | −0.00474229 | + | 0.0442967i | ||||
\(919\) | 727.639 | 0.791773 | 0.395886 | − | 0.918299i | \(-0.370437\pi\) | ||||
0.395886 | + | 0.918299i | \(0.370437\pi\) | |||||||
\(920\) | 74.9755 | − | 226.282i | 0.0814951 | − | 0.245958i | ||||
\(921\) | 273.227i | 0.296663i | ||||||||
\(922\) | 118.533 | − | 1107.20i | 0.128561 | − | 1.20086i | ||||
\(923\) | 277.399 | + | 277.399i | 0.300541 | + | 0.300541i | ||||
\(924\) | −18.1639 | + | 83.8606i | −0.0196579 | + | 0.0907582i | ||||
\(925\) | 237.040 | + | 237.040i | 0.256259 | + | 0.256259i | ||||
\(926\) | 616.244 | − | 497.057i | 0.665490 | − | 0.536779i | ||||
\(927\) | 285.497i | 0.307979i | ||||||||
\(928\) | 819.212 | − | 1387.79i | 0.882772 | − | 1.49547i | ||||
\(929\) | 1544.59 | 1.66264 | 0.831318 | − | 0.555797i | \(-0.187587\pi\) | ||||
0.831318 | + | 0.555797i | \(0.187587\pi\) | |||||||
\(930\) | 127.403 | + | 157.953i | 0.136993 | + | 0.169842i | ||||
\(931\) | −820.729 | + | 820.729i | −0.881556 | + | 0.881556i | ||||
\(932\) | 1167.37 | + | 252.849i | 1.25255 | + | 0.271297i | ||||
\(933\) | −274.935 | + | 274.935i | −0.294679 | + | 0.294679i | ||||
\(934\) | −233.835 | − | 25.0338i | −0.250359 | − | 0.0268027i | ||||
\(935\) | 95.6992 | 0.102352 | ||||||||
\(936\) | −88.9028 | + | 268.315i | −0.0949816 | + | 0.286661i | ||||
\(937\) | 716.111i | 0.764259i | 0.924109 | + | 0.382130i | \(0.124809\pi\) | ||||
−0.924109 | + | 0.382130i | \(0.875191\pi\) | |||||||
\(938\) | −124.884 | − | 13.3697i | −0.133138 | − | 0.0142534i | ||||
\(939\) | −598.091 | − | 598.091i | −0.636945 | − | 0.636945i | ||||
\(940\) | −46.5829 | + | 29.9961i | −0.0495563 | + | 0.0319108i | ||||
\(941\) | 537.759 | + | 537.759i | 0.571476 | + | 0.571476i | 0.932541 | − | 0.361065i | \(-0.117587\pi\) |
−0.361065 | + | 0.932541i | \(0.617587\pi\) | |||||||
\(942\) | 271.295 | + | 336.347i | 0.287998 | + | 0.357056i | ||||
\(943\) | 659.807i | 0.699689i | ||||||||
\(944\) | 167.369 | + | 446.285i | 0.177298 | + | 0.472760i | ||||
\(945\) | 4.37344 | 0.00462797 | ||||||||
\(946\) | 946.824 | − | 763.700i | 1.00087 | − | 0.807294i | ||||
\(947\) | 734.420 | − | 734.420i | 0.775523 | − | 0.775523i | −0.203543 | − | 0.979066i | \(-0.565246\pi\) |
0.979066 | + | 0.203543i | \(0.0652457\pi\) | |||||||
\(948\) | −36.6522 | + | 23.6015i | −0.0386627 | + | 0.0248961i | ||||
\(949\) | 155.176 | − | 155.176i | 0.163515 | − | 0.163515i | ||||
\(950\) | −118.780 | + | 1109.50i | −0.125032 | + | 1.16790i | ||||
\(951\) | 630.402 | 0.662884 | ||||||||
\(952\) | −18.4193 | + | 9.25106i | −0.0193480 | + | 0.00971750i | ||||
\(953\) | 138.512i | 0.145343i | 0.997356 | + | 0.0726714i | \(0.0231524\pi\) | ||||
−0.997356 | + | 0.0726714i | \(0.976848\pi\) | |||||||
\(954\) | 37.4977 | − | 350.258i | 0.0393057 | − | 0.367147i | ||||
\(955\) | 176.343 | + | 176.343i | 0.184652 | + | 0.184652i | ||||
\(956\) | −966.986 | − | 209.446i | −1.01149 | − | 0.219086i | ||||
\(957\) | −1166.76 | − | 1166.76i | −1.21918 | − | 1.21918i | ||||
\(958\) | −669.456 | + | 539.977i | −0.698806 | + | 0.563651i | ||||
\(959\) | 16.9789i | 0.0177048i | ||||||||
\(960\) | −114.311 | − | 85.0926i | −0.119074 | − | 0.0886381i | ||||
\(961\) | −1115.51 | −1.16078 | ||||||||
\(962\) | 212.332 | + | 263.246i | 0.220719 | + | 0.273644i | ||||
\(963\) | 81.7572 | − | 81.7572i | 0.0848984 | − | 0.0848984i | ||||
\(964\) | 186.571 | − | 861.373i | 0.193538 | − | 0.893541i | ||||
\(965\) | 128.676 | − | 128.676i | 0.133343 | − | 0.133343i | ||||
\(966\) | 52.2704 | + | 5.59592i | 0.0541102 | + | 0.00579288i | ||||
\(967\) | −701.820 | −0.725770 | −0.362885 | − | 0.931834i | \(-0.618208\pi\) | ||||
−0.362885 | + | 0.931834i | \(0.618208\pi\) | |||||||
\(968\) | −850.372 | − | 1693.13i | −0.878483 | − | 1.74910i | ||||
\(969\) | 162.882i | 0.168093i | ||||||||
\(970\) | 367.192 | + | 39.3106i | 0.378549 | + | 0.0405264i | ||||
\(971\) | −62.5684 | − | 62.5684i | −0.0644371 | − | 0.0644371i | 0.674154 | − | 0.738591i | \(-0.264508\pi\) |
−0.738591 | + | 0.674154i | \(0.764508\pi\) | |||||||
\(972\) | −33.7581 | − | 52.4251i | −0.0347305 | − | 0.0539353i | ||||
\(973\) | −2.38359 | − | 2.38359i | −0.00244973 | − | 0.00244973i | ||||
\(974\) | 720.472 | + | 893.230i | 0.739704 | + | 0.917074i | ||||
\(975\) | 476.268i | 0.488480i | ||||||||
\(976\) | 546.279 | + | 1456.64i | 0.559712 | + | 1.49246i | ||||
\(977\) | 1740.21 | 1.78117 | 0.890587 | − | 0.454814i | \(-0.150294\pi\) | ||||
0.890587 | + | 0.454814i | \(0.150294\pi\) | |||||||
\(978\) | 71.7020 | − | 57.8342i | 0.0733149 | − | 0.0591352i | ||||
\(979\) | 141.961 | − | 141.961i | 0.145006 | − | 0.145006i | ||||
\(980\) | −135.221 | − | 209.994i | −0.137981 | − | 0.214279i | ||||
\(981\) | −397.239 | + | 397.239i | −0.404932 | + | 0.404932i | ||||
\(982\) | 147.270 | − | 1375.62i | 0.149969 | − | 1.40083i | ||||
\(983\) | −1451.81 | −1.47692 | −0.738460 | − | 0.674298i | \(-0.764446\pi\) | ||||
−0.738460 | + | 0.674298i | \(0.764446\pi\) | |||||||
\(984\) | 374.420 | + | 124.059i | 0.380508 | + | 0.126077i | ||||
\(985\) | − | 52.6337i | − | 0.0534353i | ||||||
\(986\) | 42.1931 | − | 394.117i | 0.0427922 | − | 0.399713i | ||||
\(987\) | −8.63968 | − | 8.63968i | −0.00875348 | − | 0.00875348i | ||||
\(988\) | −238.311 | + | 1100.25i | −0.241206 | + | 1.11362i | ||||
\(989\) | −526.976 | − | 526.976i | −0.532837 | − | 0.532837i | ||||
\(990\) | −113.570 | + | 91.6044i | −0.114717 | + | 0.0925297i | ||||
\(991\) | − | 22.1684i | − | 0.0223698i | −0.999937 | − | 0.0111849i | \(-0.996440\pi\) | ||
0.999937 | − | 0.0111849i | \(-0.00356033\pi\) | |||||||
\(992\) | 1412.09 | − | 363.792i | 1.42348 | − | 0.366725i | ||||
\(993\) | −302.641 | −0.304775 | ||||||||
\(994\) | −27.3831 | − | 33.9491i | −0.0275484 | − | 0.0341541i | ||||
\(995\) | −25.1121 | + | 25.1121i | −0.0252382 | + | 0.0252382i | ||||
\(996\) | −690.206 | − | 149.497i | −0.692978 | − | 0.150097i | ||||
\(997\) | 13.5020 | − | 13.5020i | 0.0135426 | − | 0.0135426i | −0.700303 | − | 0.713846i | \(-0.746952\pi\) |
0.713846 | + | 0.700303i | \(0.246952\pi\) | |||||||
\(998\) | 732.532 | + | 78.4228i | 0.734000 | + | 0.0785799i | ||||
\(999\) | −74.6071 | −0.0746817 |
(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 | 48.3.l.a.19.6 | ✓ | 16 | |
3.2 | odd | 2 | 144.3.m.c.19.3 | 16 | |||
4.3 | odd | 2 | 192.3.l.a.175.2 | 16 | |||
8.3 | odd | 2 | 384.3.l.b.223.7 | 16 | |||
8.5 | even | 2 | 384.3.l.a.223.3 | 16 | |||
12.11 | even | 2 | 576.3.m.c.559.5 | 16 | |||
16.3 | odd | 4 | 384.3.l.a.31.3 | 16 | |||
16.5 | even | 4 | 192.3.l.a.79.2 | 16 | |||
16.11 | odd | 4 | inner | 48.3.l.a.43.6 | yes | 16 | |
16.13 | even | 4 | 384.3.l.b.31.7 | 16 | |||
24.5 | odd | 2 | 1152.3.m.f.991.4 | 16 | |||
24.11 | even | 2 | 1152.3.m.c.991.4 | 16 | |||
48.5 | odd | 4 | 576.3.m.c.271.5 | 16 | |||
48.11 | even | 4 | 144.3.m.c.91.3 | 16 | |||
48.29 | odd | 4 | 1152.3.m.c.415.4 | 16 | |||
48.35 | even | 4 | 1152.3.m.f.415.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
48.3.l.a.43.6 | yes | 16 | 16.11 | odd | 4 | inner | |
144.3.m.c.19.3 | 16 | 3.2 | odd | 2 | |||
144.3.m.c.91.3 | 16 | 48.11 | even | 4 | |||
192.3.l.a.79.2 | 16 | 16.5 | even | 4 | |||
192.3.l.a.175.2 | 16 | 4.3 | odd | 2 | |||
384.3.l.a.31.3 | 16 | 16.3 | odd | 4 | |||
384.3.l.a.223.3 | 16 | 8.5 | even | 2 | |||
384.3.l.b.31.7 | 16 | 16.13 | even | 4 | |||
384.3.l.b.223.7 | 16 | 8.3 | odd | 2 | |||
576.3.m.c.271.5 | 16 | 48.5 | odd | 4 | |||
576.3.m.c.559.5 | 16 | 12.11 | even | 2 | |||
1152.3.m.c.415.4 | 16 | 48.29 | odd | 4 | |||
1152.3.m.c.991.4 | 16 | 24.11 | even | 2 | |||
1152.3.m.f.415.4 | 16 | 48.35 | even | 4 | |||
1152.3.m.f.991.4 | 16 | 24.5 | odd | 2 |