Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,3,Mod(97,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.l (of order \(6\), 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: | \(12.0163796583\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Character | \(\chi\) | \(=\) | 441.97 |
Dual form | 441.3.l.a.391.5 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.840995 | + | 1.45665i | −0.420498 | + | 0.728323i | −0.995988 | − | 0.0894852i | \(-0.971478\pi\) |
0.575490 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(3\) | 2.99659 | − | 0.143035i | 0.998863 | − | 0.0476785i | ||||
\(4\) | 0.585454 | + | 1.01404i | 0.146363 | + | 0.253509i | ||||
\(5\) | 2.03050 | − | 1.17231i | 0.406100 | − | 0.234462i | −0.283012 | − | 0.959116i | \(-0.591334\pi\) |
0.689113 | + | 0.724654i | \(0.258000\pi\) | |||||||
\(6\) | −2.31176 | + | 4.48526i | −0.385294 | + | 0.747544i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.69742 | −1.08718 | ||||||||
\(9\) | 8.95908 | − | 0.857237i | 0.995454 | − | 0.0952486i | ||||
\(10\) | 3.94363i | 0.394363i | ||||||||
\(11\) | 3.10369 | − | 5.37574i | 0.282153 | − | 0.488704i | −0.689762 | − | 0.724037i | \(-0.742285\pi\) |
0.971915 | + | 0.235333i | \(0.0756180\pi\) | |||||||
\(12\) | 1.89941 | + | 2.95491i | 0.158284 | + | 0.246242i | ||||
\(13\) | 21.3461 | − | 12.3242i | 1.64201 | − | 0.948013i | 0.661889 | − | 0.749602i | \(-0.269755\pi\) |
0.980119 | − | 0.198411i | \(-0.0635782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.91690 | − | 3.80337i | 0.394460 | − | 0.253558i | ||||
\(16\) | 4.97267 | − | 8.61292i | 0.310792 | − | 0.538308i | ||||
\(17\) | 22.5368i | 1.32569i | 0.748754 | + | 0.662847i | \(0.230652\pi\) | ||||
−0.748754 | + | 0.662847i | \(0.769348\pi\) | |||||||
\(18\) | −6.28585 | + | 13.7711i | −0.349214 | + | 0.765064i | ||||
\(19\) | 10.7958i | 0.568198i | 0.958795 | + | 0.284099i | \(0.0916945\pi\) | ||||
−0.958795 | + | 0.284099i | \(0.908306\pi\) | |||||||
\(20\) | 2.37753 | + | 1.37267i | 0.118877 | + | 0.0686334i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.22037 | + | 9.04195i | 0.237290 | + | 0.410998i | ||||
\(23\) | 4.27197 | + | 7.39927i | 0.185738 | + | 0.321707i | 0.943825 | − | 0.330446i | \(-0.107199\pi\) |
−0.758087 | + | 0.652153i | \(0.773866\pi\) | |||||||
\(24\) | −26.0626 | + | 1.24404i | −1.08594 | + | 0.0518350i | ||||
\(25\) | −9.75137 | + | 16.8899i | −0.390055 | + | 0.675595i | ||||
\(26\) | 41.4583i | 1.59455i | ||||||||
\(27\) | 26.7241 | − | 3.85025i | 0.989780 | − | 0.142602i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.1494 | − | 27.9715i | 0.556874 | − | 0.964535i | −0.440881 | − | 0.897566i | \(-0.645334\pi\) |
0.997755 | − | 0.0669689i | \(-0.0213328\pi\) | |||||||
\(30\) | 0.564079 | + | 11.8174i | 0.0188026 | + | 0.393915i | ||||
\(31\) | −1.44290 | + | 0.833060i | −0.0465452 | + | 0.0268729i | −0.523092 | − | 0.852276i | \(-0.675222\pi\) |
0.476547 | + | 0.879149i | \(0.341888\pi\) | |||||||
\(32\) | −9.03085 | − | 15.6419i | −0.282214 | − | 0.488809i | ||||
\(33\) | 8.53154 | − | 16.5528i | 0.258532 | − | 0.501601i | ||||
\(34\) | −32.8282 | − | 18.9534i | −0.965535 | − | 0.557452i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.11440 | + | 8.58296i | 0.169844 | + | 0.238415i | ||||
\(37\) | 39.5686 | 1.06942 | 0.534711 | − | 0.845035i | \(-0.320421\pi\) | ||||
0.534711 | + | 0.845035i | \(0.320421\pi\) | |||||||
\(38\) | −15.7256 | − | 9.07919i | −0.413832 | − | 0.238926i | ||||
\(39\) | 62.2027 | − | 39.9837i | 1.59494 | − | 1.02522i | ||||
\(40\) | −17.6601 | + | 10.1961i | −0.441503 | + | 0.254902i | ||||
\(41\) | −27.9638 | + | 16.1449i | −0.682044 | + | 0.393778i | −0.800625 | − | 0.599166i | \(-0.795499\pi\) |
0.118581 | + | 0.992944i | \(0.462165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.15380 | + | 3.73049i | −0.0500884 | + | 0.0867556i | −0.889983 | − | 0.455995i | \(-0.849284\pi\) |
0.839894 | + | 0.542750i | \(0.182617\pi\) | |||||||
\(44\) | 7.26826 | 0.165188 | ||||||||
\(45\) | 17.1865 | − | 12.2435i | 0.381922 | − | 0.272077i | ||||
\(46\) | −14.3708 | −0.312409 | ||||||||
\(47\) | −42.0916 | − | 24.3016i | −0.895565 | − | 0.517055i | −0.0198064 | − | 0.999804i | \(-0.506305\pi\) |
−0.875759 | + | 0.482749i | \(0.839638\pi\) | |||||||
\(48\) | 13.6691 | − | 26.5206i | 0.284773 | − | 0.552514i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −16.4017 | − | 28.4086i | −0.328034 | − | 0.568172i | ||||
\(51\) | 3.22356 | + | 67.5336i | 0.0632071 | + | 1.32419i | ||||
\(52\) | 24.9943 | + | 14.4305i | 0.480660 | + | 0.277509i | ||||
\(53\) | 2.09872 | 0.0395984 | 0.0197992 | − | 0.999804i | \(-0.493697\pi\) | ||||
0.0197992 | + | 0.999804i | \(0.493697\pi\) | |||||||
\(54\) | −16.8664 | + | 42.1656i | −0.312340 | + | 0.780844i | ||||
\(55\) | − | 14.5539i | − | 0.264617i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.54418 | + | 32.3505i | 0.0270908 | + | 0.567552i | ||||
\(58\) | 27.1631 | + | 47.0478i | 0.468329 | + | 0.811169i | ||||
\(59\) | −91.7236 | + | 52.9566i | −1.55464 | + | 0.897570i | −0.556883 | + | 0.830591i | \(0.688003\pi\) |
−0.997754 | + | 0.0669793i | \(0.978664\pi\) | |||||||
\(60\) | 7.32082 | + | 3.77325i | 0.122014 | + | 0.0628875i | ||||
\(61\) | 20.0381 | + | 11.5690i | 0.328493 | + | 0.189656i | 0.655172 | − | 0.755480i | \(-0.272596\pi\) |
−0.326679 | + | 0.945135i | \(0.605930\pi\) | |||||||
\(62\) | − | 2.80240i | − | 0.0452000i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 70.1610 | 1.09627 | ||||||||
\(65\) | 28.8955 | − | 50.0485i | 0.444547 | − | 0.769977i | ||||
\(66\) | 16.9366 | + | 26.3483i | 0.256615 | + | 0.399216i | ||||
\(67\) | 1.29860 | + | 2.24925i | 0.0193822 | + | 0.0335709i | 0.875554 | − | 0.483121i | \(-0.160497\pi\) |
−0.856172 | + | 0.516692i | \(0.827163\pi\) | |||||||
\(68\) | −22.8531 | + | 13.1943i | −0.336075 | + | 0.194033i | ||||
\(69\) | 13.8597 | + | 21.5615i | 0.200865 | + | 0.312486i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −66.6892 | −0.939285 | −0.469642 | − | 0.882857i | \(-0.655617\pi\) | ||||
−0.469642 | + | 0.882857i | \(0.655617\pi\) | |||||||
\(72\) | −77.9209 | + | 7.45575i | −1.08223 | + | 0.103552i | ||||
\(73\) | 21.3604i | 0.292608i | 0.989240 | + | 0.146304i | \(0.0467378\pi\) | ||||
−0.989240 | + | 0.146304i | \(0.953262\pi\) | |||||||
\(74\) | −33.2770 | + | 57.6375i | −0.449689 | + | 0.778885i | ||||
\(75\) | −26.8050 | + | 52.0068i | −0.357400 | + | 0.693424i | ||||
\(76\) | −10.9473 | + | 6.32042i | −0.144043 | + | 0.0831634i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.93001 | + | 124.233i | 0.0760257 | + | 1.59274i | ||||
\(79\) | 51.5954 | − | 89.3659i | 0.653107 | − | 1.13121i | −0.329258 | − | 0.944240i | \(-0.606799\pi\) |
0.982365 | − | 0.186974i | \(-0.0598680\pi\) | |||||||
\(80\) | − | 23.3181i | − | 0.291476i | ||||||
\(81\) | 79.5303 | − | 15.3601i | 0.981855 | − | 0.189631i | ||||
\(82\) | − | 54.3111i | − | 0.662331i | ||||||
\(83\) | −10.0537 | − | 5.80449i | −0.121129 | − | 0.0699337i | 0.438211 | − | 0.898872i | \(-0.355612\pi\) |
−0.559340 | + | 0.828938i | \(0.688945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.4202 | + | 45.7611i | 0.310825 | + | 0.538365i | ||||
\(86\) | −3.62267 | − | 6.27465i | −0.0421241 | − | 0.0729611i | ||||
\(87\) | 44.3920 | − | 86.1290i | 0.510253 | − | 0.989989i | ||||
\(88\) | −26.9940 | + | 46.7551i | −0.306751 | + | 0.531308i | ||||
\(89\) | 13.8710i | 0.155854i | 0.996959 | + | 0.0779270i | \(0.0248301\pi\) | ||||
−0.996959 | + | 0.0779270i | \(0.975170\pi\) | |||||||
\(90\) | 3.38063 | + | 35.3313i | 0.0375625 | + | 0.392570i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.00208 | + | 8.66386i | −0.0543704 | + | 0.0941723i | ||||
\(93\) | −4.20463 | + | 2.70272i | −0.0452110 | + | 0.0290615i | ||||
\(94\) | 70.7976 | − | 40.8750i | 0.753166 | − | 0.434841i | ||||
\(95\) | 12.6560 | + | 21.9208i | 0.133221 | + | 0.230746i | ||||
\(96\) | −29.2991 | − | 45.5806i | −0.305199 | − | 0.474797i | ||||
\(97\) | −13.0649 | − | 7.54303i | −0.134690 | − | 0.0777632i | 0.431141 | − | 0.902285i | \(-0.358111\pi\) |
−0.565831 | + | 0.824521i | \(0.691444\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.1979 | − | 50.8223i | 0.234322 | − | 0.513356i | ||||
\(100\) | −22.8359 | −0.228359 | ||||||||
\(101\) | 86.1345 | + | 49.7297i | 0.852816 | + | 0.492374i | 0.861600 | − | 0.507588i | \(-0.169463\pi\) |
−0.00878376 | + | 0.999961i | \(0.502796\pi\) | |||||||
\(102\) | −101.084 | − | 52.0998i | −0.991015 | − | 0.510782i | ||||
\(103\) | 18.1666 | − | 10.4885i | 0.176374 | − | 0.101830i | −0.409214 | − | 0.912439i | \(-0.634197\pi\) |
0.585588 | + | 0.810609i | \(0.300864\pi\) | |||||||
\(104\) | −185.656 | + | 107.189i | −1.78515 | + | 1.03066i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.76501 | + | 3.05709i | −0.0166510 | + | 0.0288404i | ||||
\(107\) | −125.432 | −1.17226 | −0.586130 | − | 0.810217i | \(-0.699349\pi\) | ||||
−0.586130 | + | 0.810217i | \(0.699349\pi\) | |||||||
\(108\) | 19.5500 | + | 24.8450i | 0.181018 | + | 0.230046i | ||||
\(109\) | −103.333 | −0.948011 | −0.474005 | − | 0.880522i | \(-0.657192\pi\) | ||||
−0.474005 | + | 0.880522i | \(0.657192\pi\) | |||||||
\(110\) | 21.1999 | + | 12.2398i | 0.192727 | + | 0.111271i | ||||
\(111\) | 118.571 | − | 5.65971i | 1.06821 | − | 0.0509884i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −95.5545 | − | 165.505i | −0.845615 | − | 1.46465i | −0.885086 | − | 0.465427i | \(-0.845901\pi\) |
0.0394714 | − | 0.999221i | \(-0.487433\pi\) | |||||||
\(114\) | −48.4218 | − | 24.9573i | −0.424753 | − | 0.218923i | ||||
\(115\) | 17.3485 | + | 10.0162i | 0.150856 | + | 0.0870970i | ||||
\(116\) | 37.8188 | 0.326024 | ||||||||
\(117\) | 180.677 | − | 128.712i | 1.54425 | − | 1.10010i | ||||
\(118\) | − | 178.145i | − | 1.50970i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −51.4617 | + | 33.0795i | −0.428848 | + | 0.275662i | ||||
\(121\) | 41.2343 | + | 71.4199i | 0.340779 | + | 0.590247i | ||||
\(122\) | −33.7039 | + | 19.4589i | −0.276261 | + | 0.159499i | ||||
\(123\) | −81.4867 | + | 52.3794i | −0.662493 | + | 0.425849i | ||||
\(124\) | −1.68950 | − | 0.975436i | −0.0136250 | − | 0.00786642i | ||||
\(125\) | 104.342i | 0.834737i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 45.5817 | 0.358911 | 0.179456 | − | 0.983766i | \(-0.442566\pi\) | ||||
0.179456 | + | 0.983766i | \(0.442566\pi\) | |||||||
\(128\) | −22.8817 | + | 39.6322i | −0.178763 | + | 0.309627i | ||||
\(129\) | −5.92046 | + | 11.4868i | −0.0458950 | + | 0.0890451i | ||||
\(130\) | 48.6020 | + | 84.1812i | 0.373862 | + | 0.647547i | ||||
\(131\) | 83.9828 | − | 48.4875i | 0.641090 | − | 0.370134i | −0.143944 | − | 0.989586i | \(-0.545979\pi\) |
0.785034 | + | 0.619452i | \(0.212645\pi\) | |||||||
\(132\) | 21.7800 | − | 1.03962i | 0.165000 | − | 0.00787590i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.36848 | −0.0326006 | ||||||||
\(135\) | 49.7496 | − | 39.1469i | 0.368515 | − | 0.289977i | ||||
\(136\) | − | 196.012i | − | 1.44127i | ||||||
\(137\) | 93.1817 | − | 161.395i | 0.680158 | − | 1.17807i | −0.294774 | − | 0.955567i | \(-0.595244\pi\) |
0.974932 | − | 0.222502i | \(-0.0714224\pi\) | |||||||
\(138\) | −43.0634 | + | 2.05554i | −0.312054 | + | 0.0148952i | ||||
\(139\) | 144.973 | − | 83.7005i | 1.04297 | − | 0.602162i | 0.122300 | − | 0.992493i | \(-0.460973\pi\) |
0.920674 | + | 0.390331i | \(0.127640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −129.607 | − | 66.8012i | −0.919199 | − | 0.473768i | ||||
\(142\) | 56.0853 | − | 97.1426i | 0.394967 | − | 0.684103i | ||||
\(143\) | − | 153.001i | − | 1.06994i | ||||||
\(144\) | 37.1673 | − | 81.4266i | 0.258106 | − | 0.565463i | ||||
\(145\) | − | 75.7283i | − | 0.522264i | ||||||
\(146\) | −31.1146 | − | 17.9640i | −0.213114 | − | 0.123041i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.1656 | + | 40.1240i | 0.156524 | + | 0.271108i | ||||
\(149\) | −126.319 | − | 218.791i | −0.847779 | − | 1.46840i | −0.883186 | − | 0.469023i | \(-0.844606\pi\) |
0.0354077 | − | 0.999373i | \(-0.488727\pi\) | |||||||
\(150\) | −53.2126 | − | 82.7829i | −0.354751 | − | 0.551886i | ||||
\(151\) | 42.5237 | − | 73.6531i | 0.281614 | − | 0.487769i | −0.690169 | − | 0.723648i | \(-0.742464\pi\) |
0.971782 | + | 0.235879i | \(0.0757970\pi\) | |||||||
\(152\) | − | 93.8953i | − | 0.617732i | ||||||
\(153\) | 19.3194 | + | 201.909i | 0.126271 | + | 1.31967i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.95321 | + | 3.38306i | −0.0126014 | + | 0.0218262i | ||||
\(156\) | 76.9617 | + | 39.6671i | 0.493344 | + | 0.254276i | ||||
\(157\) | −215.937 | + | 124.671i | −1.37539 | + | 0.794083i | −0.991601 | − | 0.129336i | \(-0.958715\pi\) |
−0.383792 | + | 0.923420i | \(0.625382\pi\) | |||||||
\(158\) | 86.7830 | + | 150.313i | 0.549260 | + | 0.951346i | ||||
\(159\) | 6.28899 | − | 0.300191i | 0.0395534 | − | 0.00188799i | ||||
\(160\) | −36.6743 | − | 21.1739i | −0.229214 | − | 0.132337i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −44.5103 | + | 128.765i | −0.274755 | + | 0.794848i | ||||
\(163\) | −176.577 | −1.08329 | −0.541646 | − | 0.840607i | \(-0.682199\pi\) | ||||
−0.541646 | + | 0.840607i | \(0.682199\pi\) | |||||||
\(164\) | −32.7430 | − | 18.9042i | −0.199652 | − | 0.115269i | ||||
\(165\) | −2.08173 | − | 43.6122i | −0.0126165 | − | 0.264316i | ||||
\(166\) | 16.9102 | − | 9.76310i | 0.101869 | − | 0.0588139i | ||||
\(167\) | 48.6253 | − | 28.0738i | 0.291169 | − | 0.168107i | −0.347300 | − | 0.937754i | \(-0.612901\pi\) |
0.638469 | + | 0.769647i | \(0.279568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 219.271 | − | 379.788i | 1.29746 | − | 2.24726i | ||||
\(170\) | −88.8769 | −0.522805 | ||||||||
\(171\) | 9.25453 | + | 96.7201i | 0.0541201 | + | 0.565615i | ||||
\(172\) | −5.04380 | −0.0293244 | ||||||||
\(173\) | −5.15846 | − | 2.97824i | −0.0298177 | − | 0.0172152i | 0.485017 | − | 0.874505i | \(-0.338813\pi\) |
−0.514835 | + | 0.857289i | \(0.672147\pi\) | |||||||
\(174\) | 88.1260 | + | 137.098i | 0.506471 | + | 0.787917i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −30.8672 | − | 53.4636i | −0.175382 | − | 0.303770i | ||||
\(177\) | −267.283 | + | 171.809i | −1.51007 | + | 0.970672i | ||||
\(178\) | −20.2052 | − | 11.6654i | −0.113512 | − | 0.0655362i | ||||
\(179\) | −256.849 | −1.43491 | −0.717454 | − | 0.696606i | \(-0.754693\pi\) | ||||
−0.717454 | + | 0.696606i | \(0.754693\pi\) | |||||||
\(180\) | 22.4772 | + | 10.2597i | 0.124873 | + | 0.0569985i | ||||
\(181\) | 102.528i | 0.566453i | 0.959053 | + | 0.283226i | \(0.0914048\pi\) | ||||
−0.959053 | + | 0.283226i | \(0.908595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 61.7006 | + | 31.8013i | 0.337162 | + | 0.173778i | ||||
\(184\) | −37.1551 | − | 64.3545i | −0.201930 | − | 0.349753i | ||||
\(185\) | 80.3441 | − | 46.3867i | 0.434293 | − | 0.250739i | ||||
\(186\) | −0.400842 | − | 8.39763i | −0.00215507 | − | 0.0451486i | ||||
\(187\) | 121.152 | + | 69.9472i | 0.647872 | + | 0.374049i | ||||
\(188\) | − | 56.9098i | − | 0.302712i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −42.5745 | −0.224076 | ||||||||
\(191\) | 60.5381 | − | 104.855i | 0.316953 | − | 0.548979i | −0.662898 | − | 0.748710i | \(-0.730674\pi\) |
0.979851 | + | 0.199731i | \(0.0640068\pi\) | |||||||
\(192\) | 210.244 | − | 10.0355i | 1.09502 | − | 0.0522683i | ||||
\(193\) | −135.025 | − | 233.870i | −0.699610 | − | 1.21176i | −0.968602 | − | 0.248617i | \(-0.920024\pi\) |
0.268992 | − | 0.963142i | \(-0.413309\pi\) | |||||||
\(194\) | 21.9750 | − | 12.6873i | 0.113273 | − | 0.0653985i | ||||
\(195\) | 79.4293 | − | 154.108i | 0.407330 | − | 0.790297i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6897 | −0.0593383 | −0.0296692 | − | 0.999560i | \(-0.509445\pi\) | ||||
−0.0296692 | + | 0.999560i | \(0.509445\pi\) | |||||||
\(198\) | 54.5208 | + | 76.5324i | 0.275358 | + | 0.386527i | ||||
\(199\) | − | 264.578i | − | 1.32954i | −0.747050 | − | 0.664768i | \(-0.768530\pi\) | ||
0.747050 | − | 0.664768i | \(-0.231470\pi\) | |||||||
\(200\) | 84.8118 | − | 146.898i | 0.424059 | − | 0.734491i | ||||
\(201\) | 4.21310 | + | 6.55433i | 0.0209607 | + | 0.0326086i | ||||
\(202\) | −144.877 | + | 83.6450i | −0.717215 | + | 0.414084i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −66.5942 | + | 42.8066i | −0.326442 | + | 0.209836i | ||||
\(205\) | −37.8537 | + | 65.5645i | −0.184652 | + | 0.319827i | ||||
\(206\) | 35.2830i | 0.171277i | ||||||||
\(207\) | 44.6158 | + | 62.6285i | 0.215535 | + | 0.302553i | ||||
\(208\) | − | 245.136i | − | 1.17854i | ||||||
\(209\) | 58.0352 | + | 33.5067i | 0.277681 | + | 0.160319i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −60.7117 | − | 105.156i | −0.287733 | − | 0.498369i | 0.685535 | − | 0.728040i | \(-0.259568\pi\) |
−0.973268 | + | 0.229671i | \(0.926235\pi\) | |||||||
\(212\) | 1.22870 | + | 2.12817i | 0.00579576 | + | 0.0100385i | ||||
\(213\) | −199.840 | + | 9.53892i | −0.938216 | + | 0.0447837i | ||||
\(214\) | 105.488 | − | 182.710i | 0.492933 | − | 0.853785i | ||||
\(215\) | 10.0997i | 0.0469753i | ||||||||
\(216\) | −232.430 | + | 33.4873i | −1.07607 | + | 0.155034i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 86.9027 | − | 150.520i | 0.398636 | − | 0.690459i | ||||
\(219\) | 3.05530 | + | 64.0084i | 0.0139511 | + | 0.292276i | ||||
\(220\) | 14.7582 | − | 8.52066i | 0.0670828 | − | 0.0387303i | ||||
\(221\) | 277.748 | + | 481.073i | 1.25678 | + | 2.17680i | ||||
\(222\) | −91.4733 | + | 177.476i | −0.412042 | + | 0.799439i | ||||
\(223\) | −262.513 | − | 151.562i | −1.17719 | − | 0.679651i | −0.221828 | − | 0.975086i | \(-0.571202\pi\) |
−0.955363 | + | 0.295435i | \(0.904536\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −72.8847 | + | 159.677i | −0.323932 | + | 0.709676i | ||||
\(226\) | 321.443 | 1.42232 | ||||||||
\(227\) | 154.342 | + | 89.1093i | 0.679920 | + | 0.392552i | 0.799825 | − | 0.600233i | \(-0.204926\pi\) |
−0.119905 | + | 0.992785i | \(0.538259\pi\) | |||||||
\(228\) | −31.9005 | + | 20.5055i | −0.139914 | + | 0.0899366i | ||||
\(229\) | −245.158 | + | 141.542i | −1.07056 | + | 0.618088i | −0.928334 | − | 0.371746i | \(-0.878759\pi\) |
−0.142225 | + | 0.989834i | \(0.545426\pi\) | |||||||
\(230\) | −29.1800 | + | 16.8471i | −0.126870 | + | 0.0732481i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −140.458 | + | 243.280i | −0.605421 | + | 1.04862i | ||||
\(233\) | 239.439 | 1.02763 | 0.513817 | − | 0.857900i | \(-0.328231\pi\) | ||||
0.513817 | + | 0.857900i | \(0.328231\pi\) | |||||||
\(234\) | 35.5396 | + | 371.428i | 0.151879 | + | 1.58730i | ||||
\(235\) | −113.956 | −0.484919 | ||||||||
\(236\) | −107.400 | − | 62.0073i | −0.455084 | − | 0.262743i | ||||
\(237\) | 141.828 | − | 275.173i | 0.598429 | − | 1.16107i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 219.092 | + | 379.478i | 0.916702 | + | 1.58777i | 0.804391 | + | 0.594101i | \(0.202492\pi\) |
0.112311 | + | 0.993673i | \(0.464175\pi\) | |||||||
\(240\) | −3.33531 | − | 69.8747i | −0.0138971 | − | 0.291144i | ||||
\(241\) | 4.96577 | + | 2.86699i | 0.0206048 | + | 0.0118962i | 0.510267 | − | 0.860016i | \(-0.329547\pi\) |
−0.489662 | + | 0.871912i | \(0.662880\pi\) | |||||||
\(242\) | −138.711 | −0.573187 | ||||||||
\(243\) | 236.122 | − | 57.4036i | 0.971697 | − | 0.236229i | ||||
\(244\) | 27.0924i | 0.111035i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.76842 | − | 162.748i | −0.0315789 | − | 0.661578i | ||||
\(247\) | 133.049 | + | 230.447i | 0.538659 | + | 0.932986i | ||||
\(248\) | 12.5495 | − | 7.24547i | 0.0506029 | − | 0.0292156i | ||||
\(249\) | −30.9570 | − | 15.9556i | −0.124325 | − | 0.0640789i | ||||
\(250\) | −151.990 | − | 87.7512i | −0.607958 | − | 0.351005i | ||||
\(251\) | 3.69228i | 0.0147103i | 0.999973 | + | 0.00735514i | \(0.00234124\pi\) | ||||
−0.999973 | + | 0.00735514i | \(0.997659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 53.0354 | 0.209626 | ||||||||
\(254\) | −38.3340 | + | 66.3965i | −0.150921 | + | 0.261403i | ||||
\(255\) | 85.7158 | + | 133.348i | 0.336140 | + | 0.522933i | ||||
\(256\) | 101.835 | + | 176.384i | 0.397794 | + | 0.688999i | ||||
\(257\) | −178.998 | + | 103.344i | −0.696489 | + | 0.402118i | −0.806038 | − | 0.591863i | \(-0.798392\pi\) |
0.109550 | + | 0.993981i | \(0.465059\pi\) | |||||||
\(258\) | −11.7532 | − | 18.2844i | −0.0455549 | − | 0.0708697i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 67.6680 | 0.260262 | ||||||||
\(261\) | 120.705 | − | 264.443i | 0.462472 | − | 1.01319i | ||||
\(262\) | 163.111i | 0.622561i | ||||||||
\(263\) | −63.1809 | + | 109.433i | −0.240232 | + | 0.416094i | −0.960780 | − | 0.277311i | \(-0.910557\pi\) |
0.720548 | + | 0.693405i | \(0.243890\pi\) | |||||||
\(264\) | −74.2024 | + | 143.967i | −0.281070 | + | 0.545329i | ||||
\(265\) | 4.26145 | − | 2.46035i | 0.0160809 | − | 0.00928433i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.98405 | + | 41.5657i | 0.00743088 | + | 0.155677i | ||||
\(268\) | −1.52055 | + | 2.63366i | −0.00567368 | + | 0.00982710i | ||||
\(269\) | − | 246.229i | − | 0.915351i | −0.889119 | − | 0.457676i | \(-0.848682\pi\) | ||
0.889119 | − | 0.457676i | \(-0.151318\pi\) | |||||||
\(270\) | 15.1840 | + | 105.390i | 0.0562370 | + | 0.390333i | ||||
\(271\) | 238.276i | 0.879247i | 0.898182 | + | 0.439623i | \(0.144888\pi\) | ||||
−0.898182 | + | 0.439623i | \(0.855112\pi\) | |||||||
\(272\) | 194.108 | + | 112.068i | 0.713632 | + | 0.412015i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 156.731 | + | 271.466i | 0.572010 | + | 0.990751i | ||||
\(275\) | 60.5304 | + | 104.842i | 0.220110 | + | 0.381243i | ||||
\(276\) | −13.7499 | + | 26.6775i | −0.0498186 | + | 0.0966575i | ||||
\(277\) | −84.9697 | + | 147.172i | −0.306750 | + | 0.531306i | −0.977649 | − | 0.210242i | \(-0.932575\pi\) |
0.670900 | + | 0.741548i | \(0.265908\pi\) | |||||||
\(278\) | 281.567i | 1.01283i | ||||||||
\(279\) | −12.2129 | + | 8.70036i | −0.0437740 | + | 0.0311841i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −113.910 | + | 197.298i | −0.405374 | + | 0.702128i | −0.994365 | − | 0.106011i | \(-0.966192\pi\) |
0.588991 | + | 0.808140i | \(0.299525\pi\) | |||||||
\(282\) | 206.305 | − | 132.612i | 0.731577 | − | 0.470256i | ||||
\(283\) | −112.569 | + | 64.9915i | −0.397769 | + | 0.229652i | −0.685521 | − | 0.728053i | \(-0.740425\pi\) |
0.287752 | + | 0.957705i | \(0.407092\pi\) | |||||||
\(284\) | −39.0434 | − | 67.6252i | −0.137477 | − | 0.238117i | ||||
\(285\) | 41.0603 | + | 63.8774i | 0.144071 | + | 0.224131i | ||||
\(286\) | 222.869 | + | 128.673i | 0.779262 | + | 0.449907i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −94.3169 | − | 132.395i | −0.327489 | − | 0.459706i | ||||
\(289\) | −218.908 | −0.757467 | ||||||||
\(290\) | 110.309 | + | 63.6871i | 0.380377 | + | 0.219611i | ||||
\(291\) | −40.2291 | − | 20.7346i | −0.138244 | − | 0.0712529i | ||||
\(292\) | −21.6602 | + | 12.5055i | −0.0741788 | + | 0.0428272i | ||||
\(293\) | −129.475 | + | 74.7526i | −0.441895 | + | 0.255128i | −0.704401 | − | 0.709802i | \(-0.748784\pi\) |
0.262506 | + | 0.964930i | \(0.415451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −124.163 | + | 215.057i | −0.420893 | + | 0.729007i | ||||
\(296\) | −344.145 | −1.16265 | ||||||||
\(297\) | 62.2451 | − | 155.612i | 0.209580 | − | 0.523945i | ||||
\(298\) | 424.935 | 1.42596 | ||||||||
\(299\) | 182.380 | + | 105.297i | 0.609966 | + | 0.352164i | ||||
\(300\) | −68.4298 | + | 3.26635i | −0.228099 | + | 0.0108878i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 71.5244 | + | 123.884i | 0.236836 | + | 0.410211i | ||||
\(303\) | 265.223 | + | 136.699i | 0.875322 | + | 0.451153i | ||||
\(304\) | 92.9831 | + | 53.6838i | 0.305865 | + | 0.176591i | ||||
\(305\) | 54.2498 | 0.177868 | ||||||||
\(306\) | −310.358 | − | 141.663i | −1.01424 | − | 0.462951i | ||||
\(307\) | − | 10.5618i | − | 0.0344031i | −0.999852 | − | 0.0172016i | \(-0.994524\pi\) | ||
0.999852 | − | 0.0172016i | \(-0.00547570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.9375 | − | 34.0281i | 0.171319 | − | 0.110123i | ||||
\(310\) | −3.28528 | − | 5.69028i | −0.0105977 | − | 0.0183557i | ||||
\(311\) | −391.106 | + | 225.805i | −1.25757 | + | 0.726061i | −0.972602 | − | 0.232475i | \(-0.925318\pi\) |
−0.284972 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(312\) | −541.003 | + | 347.755i | −1.73398 | + | 1.11460i | ||||
\(313\) | 146.790 | + | 84.7492i | 0.468977 | + | 0.270764i | 0.715812 | − | 0.698293i | \(-0.246057\pi\) |
−0.246834 | + | 0.969058i | \(0.579390\pi\) | |||||||
\(314\) | − | 419.391i | − | 1.33564i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 120.827 | 0.382364 | ||||||||
\(317\) | 83.0363 | − | 143.823i | 0.261944 | − | 0.453701i | −0.704814 | − | 0.709392i | \(-0.748970\pi\) |
0.966759 | + | 0.255691i | \(0.0823030\pi\) | |||||||
\(318\) | −4.85174 | + | 9.41329i | −0.0152570 | + | 0.0296015i | ||||
\(319\) | −100.245 | − | 173.629i | −0.314248 | − | 0.544293i | ||||
\(320\) | 142.462 | − | 82.2505i | 0.445194 | − | 0.257033i | ||||
\(321\) | −375.868 | + | 17.9412i | −1.17093 | + | 0.0558916i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −243.302 | −0.753257 | ||||||||
\(324\) | 62.1370 | + | 71.6539i | 0.191781 | + | 0.221154i | ||||
\(325\) | 480.711i | 1.47911i | ||||||||
\(326\) | 148.500 | − | 257.210i | 0.455522 | − | 0.788987i | ||||
\(327\) | −309.647 | + | 14.7803i | −0.946933 | + | 0.0451997i | ||||
\(328\) | 243.213 | − | 140.419i | 0.741502 | − | 0.428107i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 65.2782 | + | 33.6453i | 0.197813 | + | 0.101955i | ||||
\(331\) | −43.0182 | + | 74.5096i | −0.129964 | + | 0.225105i | −0.923662 | − | 0.383207i | \(-0.874820\pi\) |
0.793698 | + | 0.608312i | \(0.208153\pi\) | |||||||
\(332\) | − | 13.5931i | − | 0.0409429i | ||||||
\(333\) | 354.498 | − | 33.9197i | 1.06456 | − | 0.101861i | ||||
\(334\) | 94.4398i | 0.282754i | ||||||||
\(335\) | 5.27364 | + | 3.04474i | 0.0157422 | + | 0.00908876i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −274.510 | − | 475.466i | −0.814570 | − | 1.41088i | −0.909636 | − | 0.415406i | \(-0.863639\pi\) |
0.0950656 | − | 0.995471i | \(-0.469694\pi\) | |||||||
\(338\) | 368.811 | + | 638.799i | 1.09116 | + | 1.88994i | ||||
\(339\) | −310.011 | − | 482.283i | −0.914485 | − | 1.42266i | ||||
\(340\) | −30.9356 | + | 53.5820i | −0.0909869 | + | 0.157594i | ||||
\(341\) | 10.3422i | 0.0303291i | ||||||||
\(342\) | −148.670 | − | 67.8606i | −0.434708 | − | 0.198423i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.7325 | − | 32.4456i | 0.0544549 | − | 0.0943187i | ||||
\(345\) | 53.4189 | + | 27.5328i | 0.154837 | + | 0.0798053i | ||||
\(346\) | 8.67647 | − | 5.00936i | 0.0250765 | − | 0.0144779i | ||||
\(347\) | −207.465 | − | 359.340i | −0.597882 | − | 1.03556i | −0.993133 | − | 0.116990i | \(-0.962676\pi\) |
0.395251 | − | 0.918573i | \(-0.370658\pi\) | |||||||
\(348\) | 113.327 | − | 5.40943i | 0.325653 | − | 0.0155443i | ||||
\(349\) | 307.486 | + | 177.527i | 0.881050 | + | 0.508674i | 0.871004 | − | 0.491275i | \(-0.163469\pi\) |
0.0100455 | + | 0.999950i | \(0.496802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 523.003 | − | 411.540i | 1.49004 | − | 1.17248i | ||||
\(352\) | −112.116 | −0.318510 | ||||||||
\(353\) | 411.949 | + | 237.839i | 1.16699 | + | 0.673764i | 0.952970 | − | 0.303064i | \(-0.0980096\pi\) |
0.214024 | + | 0.976828i | \(0.431343\pi\) | |||||||
\(354\) | −25.4811 | − | 533.828i | −0.0719805 | − | 1.50799i | ||||
\(355\) | −135.413 | + | 78.1805i | −0.381444 | + | 0.220227i | ||||
\(356\) | −14.0657 | + | 8.12083i | −0.0395104 | + | 0.0228113i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 216.008 | − | 374.138i | 0.603375 | − | 1.04508i | ||||
\(359\) | 219.114 | 0.610346 | 0.305173 | − | 0.952297i | \(-0.401286\pi\) | ||||
0.305173 | + | 0.952297i | \(0.401286\pi\) | |||||||
\(360\) | −149.478 | + | 106.486i | −0.415217 | + | 0.295796i | ||||
\(361\) | 244.451 | 0.677151 | ||||||||
\(362\) | −149.347 | − | 86.2256i | −0.412561 | − | 0.238192i | ||||
\(363\) | 133.778 | + | 208.118i | 0.368534 | + | 0.573328i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.0410 | + | 43.3724i | 0.0686056 | + | 0.118828i | ||||
\(366\) | −98.2132 | + | 63.1312i | −0.268342 | + | 0.172490i | ||||
\(367\) | −181.195 | − | 104.613i | −0.493720 | − | 0.285049i | 0.232396 | − | 0.972621i | \(-0.425343\pi\) |
−0.726116 | + | 0.687572i | \(0.758677\pi\) | |||||||
\(368\) | 84.9724 | 0.230903 | ||||||||
\(369\) | −236.690 | + | 168.615i | −0.641436 | + | 0.456951i | ||||
\(370\) | 156.044i | 0.421741i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.20227 | − | 2.68132i | −0.0139846 | − | 0.00720785i | ||||
\(373\) | −127.379 | − | 220.626i | −0.341498 | − | 0.591492i | 0.643213 | − | 0.765687i | \(-0.277601\pi\) |
−0.984711 | + | 0.174196i | \(0.944268\pi\) | |||||||
\(374\) | −203.777 | + | 117.650i | −0.544857 | + | 0.314574i | ||||
\(375\) | 14.9246 | + | 312.670i | 0.0397990 | + | 0.833788i | ||||
\(376\) | 366.088 | + | 211.361i | 0.973638 | + | 0.562130i | ||||
\(377\) | − | 796.110i | − | 2.11170i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −437.733 | −1.15497 | −0.577484 | − | 0.816402i | \(-0.695965\pi\) | ||||
−0.577484 | + | 0.816402i | \(0.695965\pi\) | |||||||
\(380\) | −14.8190 | + | 25.6673i | −0.0389974 | + | 0.0675454i | ||||
\(381\) | 136.590 | − | 6.51980i | 0.358503 | − | 0.0171123i | ||||
\(382\) | 101.824 | + | 176.365i | 0.266556 | + | 0.461689i | ||||
\(383\) | 239.024 | − | 138.001i | 0.624084 | − | 0.360315i | −0.154373 | − | 0.988013i | \(-0.549336\pi\) |
0.778457 | + | 0.627697i | \(0.216002\pi\) | |||||||
\(384\) | −62.8981 | + | 122.034i | −0.163797 | + | 0.317798i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 454.220 | 1.17674 | ||||||||
\(387\) | −16.0982 | + | 35.2681i | −0.0415973 | + | 0.0911320i | ||||
\(388\) | − | 17.6644i | − | 0.0455267i | ||||||
\(389\) | 31.9090 | − | 55.2681i | 0.0820284 | − | 0.142077i | −0.822093 | − | 0.569354i | \(-0.807194\pi\) |
0.904121 | + | 0.427276i | \(0.140527\pi\) | |||||||
\(390\) | 157.681 | + | 245.304i | 0.404311 | + | 0.628986i | ||||
\(391\) | −166.756 | + | 96.2766i | −0.426486 | + | 0.246232i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 244.727 | − | 157.310i | 0.622714 | − | 0.400279i | ||||
\(394\) | 9.83094 | − | 17.0277i | 0.0249516 | − | 0.0432175i | ||||
\(395\) | − | 241.944i | − | 0.612515i | ||||||
\(396\) | 65.1169 | − | 6.23062i | 0.164437 | − | 0.0157339i | ||||
\(397\) | − | 128.830i | − | 0.324509i | −0.986749 | − | 0.162254i | \(-0.948123\pi\) | ||
0.986749 | − | 0.162254i | \(-0.0518765\pi\) | |||||||
\(398\) | 385.396 | + | 222.509i | 0.968332 | + | 0.559067i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 96.9808 | + | 167.976i | 0.242452 | + | 0.419939i | ||||
\(401\) | 179.729 | + | 311.299i | 0.448201 | + | 0.776307i | 0.998269 | − | 0.0588127i | \(-0.0187315\pi\) |
−0.550068 | + | 0.835120i | \(0.685398\pi\) | |||||||
\(402\) | −13.0905 | + | 0.624848i | −0.0325635 | + | 0.00155435i | ||||
\(403\) | −20.5336 | + | 35.5652i | −0.0509517 | + | 0.0882510i | ||||
\(404\) | 116.458i | 0.288262i | ||||||||
\(405\) | 143.480 | − | 124.423i | 0.354271 | − | 0.307217i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 122.808 | − | 212.711i | 0.301741 | − | 0.522630i | ||||
\(408\) | −28.0367 | − | 587.368i | −0.0687174 | − | 1.43963i | ||||
\(409\) | 24.8046 | − | 14.3210i | 0.0606470 | − | 0.0350146i | −0.469370 | − | 0.883002i | \(-0.655519\pi\) |
0.530017 | + | 0.847987i | \(0.322186\pi\) | |||||||
\(410\) | −63.6696 | − | 110.279i | −0.155292 | − | 0.268973i | ||||
\(411\) | 256.142 | − | 496.964i | 0.623216 | − | 1.20916i | ||||
\(412\) | 21.2714 | + | 12.2810i | 0.0516295 | + | 0.0298083i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −128.749 | + | 12.3192i | −0.310989 | + | 0.0297565i | ||||
\(415\) | −27.2187 | −0.0655872 | ||||||||
\(416\) | −385.547 | − | 222.595i | −0.926795 | − | 0.535085i | ||||
\(417\) | 422.454 | − | 271.552i | 1.01308 | − | 0.651204i | ||||
\(418\) | −97.6147 | + | 56.3579i | −0.233528 | + | 0.134827i | ||||
\(419\) | 174.539 | − | 100.770i | 0.416560 | − | 0.240501i | −0.277044 | − | 0.960857i | \(-0.589355\pi\) |
0.693604 | + | 0.720356i | \(0.256022\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −324.035 | + | 561.245i | −0.769680 | + | 1.33312i | 0.168057 | + | 0.985777i | \(0.446251\pi\) |
−0.937737 | + | 0.347347i | \(0.887083\pi\) | |||||||
\(422\) | 204.233 | 0.483965 | ||||||||
\(423\) | −397.934 | − | 181.637i | −0.940742 | − | 0.429403i | ||||
\(424\) | −18.2534 | −0.0430505 | ||||||||
\(425\) | −380.644 | − | 219.765i | −0.895633 | − | 0.517094i | ||||
\(426\) | 154.170 | − | 299.119i | 0.361901 | − | 0.702156i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −73.4346 | − | 127.192i | −0.171576 | − | 0.297178i | ||||
\(429\) | −21.8846 | − | 458.482i | −0.0510131 | − | 1.06872i | ||||
\(430\) | −14.7117 | − | 8.49380i | −0.0342132 | − | 0.0197530i | ||||
\(431\) | −477.826 | −1.10864 | −0.554322 | − | 0.832302i | \(-0.687023\pi\) | ||||
−0.554322 | + | 0.832302i | \(0.687023\pi\) | |||||||
\(432\) | 99.7281 | − | 249.318i | 0.230852 | − | 0.577126i | ||||
\(433\) | 760.468i | 1.75628i | 0.478406 | + | 0.878139i | \(0.341215\pi\) | ||||
−0.478406 | + | 0.878139i | \(0.658785\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.8318 | − | 226.926i | −0.0249008 | − | 0.521670i | ||||
\(436\) | −60.4968 | − | 104.784i | −0.138754 | − | 0.240329i | ||||
\(437\) | −79.8807 | + | 46.1192i | −0.182793 | + | 0.105536i | ||||
\(438\) | −95.8070 | − | 49.3802i | −0.218738 | − | 0.112740i | ||||
\(439\) | −299.570 | − | 172.957i | −0.682391 | − | 0.393979i | 0.118364 | − | 0.992970i | \(-0.462235\pi\) |
−0.800755 | + | 0.598992i | \(0.795568\pi\) | |||||||
\(440\) | 126.582i | 0.287686i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −934.338 | −2.11389 | ||||||||
\(443\) | 26.1810 | − | 45.3468i | 0.0590993 | − | 0.102363i | −0.834962 | − | 0.550308i | \(-0.814510\pi\) |
0.894061 | + | 0.447945i | \(0.147844\pi\) | |||||||
\(444\) | 75.1569 | + | 116.922i | 0.169272 | + | 0.263337i | ||||
\(445\) | 16.2611 | + | 28.1651i | 0.0365419 | + | 0.0632924i | ||||
\(446\) | 441.545 | − | 254.926i | 0.990012 | − | 0.571584i | ||||
\(447\) | −409.821 | − | 637.558i | −0.916825 | − | 1.42630i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.7022 | 0.0661518 | 0.0330759 | − | 0.999453i | \(-0.489470\pi\) | ||||
0.0330759 | + | 0.999453i | \(0.489470\pi\) | |||||||
\(450\) | −171.297 | − | 240.455i | −0.380661 | − | 0.534344i | ||||
\(451\) | 200.435i | 0.444423i | ||||||||
\(452\) | 111.885 | − | 193.791i | 0.247534 | − | 0.428742i | ||||
\(453\) | 116.891 | − | 226.790i | 0.258037 | − | 0.500641i | ||||
\(454\) | −259.602 | + | 149.881i | −0.571810 | + | 0.330134i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.4304 | − | 281.365i | −0.0294525 | − | 0.617030i | ||||
\(457\) | −59.4080 | + | 102.898i | −0.129996 | + | 0.225159i | −0.923675 | − | 0.383178i | \(-0.874830\pi\) |
0.793679 | + | 0.608337i | \(0.208163\pi\) | |||||||
\(458\) | − | 476.145i | − | 1.03962i | ||||||
\(459\) | 86.7724 | + | 602.275i | 0.189047 | + | 1.31215i | ||||
\(460\) | 23.4560i | 0.0509912i | ||||||||
\(461\) | 657.900 | + | 379.839i | 1.42711 | + | 0.823945i | 0.996892 | − | 0.0787777i | \(-0.0251017\pi\) |
0.430223 | + | 0.902723i | \(0.358435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 59.1866 | + | 102.514i | 0.127833 | + | 0.221413i | 0.922837 | − | 0.385191i | \(-0.125865\pi\) |
−0.795004 | + | 0.606604i | \(0.792531\pi\) | |||||||
\(464\) | −160.611 | − | 278.186i | −0.346144 | − | 0.599539i | ||||
\(465\) | −5.36907 | + | 10.4170i | −0.0115464 | + | 0.0224022i | ||||
\(466\) | −201.367 | + | 348.778i | −0.432118 | + | 0.748450i | ||||
\(467\) | 100.271i | 0.214713i | 0.994221 | + | 0.107356i | \(0.0342386\pi\) | ||||
−0.994221 | + | 0.107356i | \(0.965761\pi\) | |||||||
\(468\) | 236.296 | + | 107.858i | 0.504907 | + | 0.230465i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 95.8365 | − | 165.994i | 0.203907 | − | 0.353178i | ||||
\(471\) | −629.241 | + | 404.475i | −1.33597 | + | 0.858757i | ||||
\(472\) | 797.759 | − | 460.586i | 1.69017 | − | 0.975818i | ||||
\(473\) | 13.3694 | + | 23.1565i | 0.0282652 | + | 0.0489567i | ||||
\(474\) | 281.553 | + | 438.012i | 0.593994 | + | 0.924076i | ||||
\(475\) | −182.339 | − | 105.274i | −0.383872 | − | 0.221628i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.8026 | − | 1.79910i | 0.0394184 | − | 0.00377169i | ||||
\(478\) | −737.020 | −1.54188 | ||||||||
\(479\) | 561.950 | + | 324.442i | 1.17317 | + | 0.677331i | 0.954425 | − | 0.298450i | \(-0.0964697\pi\) |
0.218747 | + | 0.975782i | \(0.429803\pi\) | |||||||
\(480\) | −112.926 | − | 58.2038i | −0.235263 | − | 0.121258i | ||||
\(481\) | 844.635 | − | 487.650i | 1.75600 | − | 1.01383i | ||||
\(482\) | −8.35237 | + | 4.82224i | −0.0173286 | + | 0.0100047i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −48.2815 | + | 83.6260i | −0.0997552 | + | 0.172781i | ||||
\(485\) | −35.3711 | −0.0729301 | ||||||||
\(486\) | −114.961 | + | 392.223i | −0.236546 | + | 0.807044i | ||||
\(487\) | −630.412 | −1.29448 | −0.647240 | − | 0.762286i | \(-0.724077\pi\) | ||||
−0.647240 | + | 0.762286i | \(0.724077\pi\) | |||||||
\(488\) | −174.279 | − | 100.620i | −0.357130 | − | 0.206189i | ||||
\(489\) | −529.127 | + | 25.2567i | −1.08206 | + | 0.0516497i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 392.755 | + | 680.271i | 0.799908 | + | 1.38548i | 0.919676 | + | 0.392679i | \(0.128452\pi\) |
−0.119768 | + | 0.992802i | \(0.538215\pi\) | |||||||
\(492\) | −100.821 | − | 51.9646i | −0.204921 | − | 0.105619i | ||||
\(493\) | 630.389 | + | 363.955i | 1.27868 | + | 0.738245i | ||||
\(494\) | −447.574 | −0.906020 | ||||||||
\(495\) | −12.4762 | − | 130.390i | −0.0252044 | − | 0.263414i | ||||
\(496\) | 16.5701i | 0.0334075i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 49.2764 | − | 31.6748i | 0.0989486 | − | 0.0636039i | ||||
\(499\) | −116.379 | − | 201.574i | −0.233224 | − | 0.403956i | 0.725531 | − | 0.688190i | \(-0.241594\pi\) |
−0.958755 | + | 0.284233i | \(0.908261\pi\) | |||||||
\(500\) | −105.807 | + | 61.0875i | −0.211613 | + | 0.122175i | ||||
\(501\) | 141.694 | − | 91.0808i | 0.282823 | − | 0.181798i | ||||
\(502\) | −5.37835 | − | 3.10519i | −0.0107138 | − | 0.00618564i | ||||
\(503\) | − | 47.6335i | − | 0.0946989i | −0.998878 | − | 0.0473494i | \(-0.984923\pi\) | ||
0.998878 | − | 0.0473494i | \(-0.0150774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 233.195 | 0.461772 | ||||||||
\(506\) | −44.6025 | + | 77.2538i | −0.0881472 | + | 0.152675i | ||||
\(507\) | 602.740 | − | 1169.43i | 1.18884 | − | 2.30657i | ||||
\(508\) | 26.6860 | + | 46.2215i | 0.0525315 | + | 0.0909872i | ||||
\(509\) | −370.733 | + | 214.043i | −0.728356 | + | 0.420517i | −0.817821 | − | 0.575473i | \(-0.804818\pi\) |
0.0894642 | + | 0.995990i | \(0.471485\pi\) | |||||||
\(510\) | −266.328 | + | 12.7126i | −0.522211 | + | 0.0249266i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −525.625 | −1.02661 | ||||||||
\(513\) | 41.5664 | + | 288.507i | 0.0810262 | + | 0.562391i | ||||
\(514\) | − | 347.648i | − | 0.676358i | ||||||
\(515\) | 24.5915 | − | 42.5937i | 0.0477505 | − | 0.0827062i | ||||
\(516\) | −15.1142 | + | 0.721443i | −0.0292911 | + | 0.00139814i | ||||
\(517\) | −261.278 | + | 150.849i | −0.505373 | + | 0.291777i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.8838 | − | 8.18670i | −0.0306045 | − | 0.0157740i | ||||
\(520\) | −251.317 | + | 435.293i | −0.483301 | + | 0.837102i | ||||
\(521\) | 537.389i | 1.03146i | 0.856752 | + | 0.515728i | \(0.172479\pi\) | ||||
−0.856752 | + | 0.515728i | \(0.827521\pi\) | |||||||
\(522\) | 283.687 | + | 398.220i | 0.543462 | + | 0.762873i | ||||
\(523\) | 548.211i | 1.04820i | 0.851655 | + | 0.524102i | \(0.175599\pi\) | ||||
−0.851655 | + | 0.524102i | \(0.824401\pi\) | |||||||
\(524\) | 98.3361 | + | 56.7744i | 0.187664 | + | 0.108348i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −106.270 | − | 184.065i | −0.202034 | − | 0.349933i | ||||
\(527\) | −18.7745 | − | 32.5184i | −0.0356253 | − | 0.0617048i | ||||
\(528\) | −100.144 | − | 155.793i | −0.189666 | − | 0.295063i | ||||
\(529\) | 228.001 | − | 394.909i | 0.431003 | − | 0.746519i | ||||
\(530\) | 8.27656i | 0.0156162i | ||||||||
\(531\) | −776.363 | + | 553.072i | −1.46208 | + | 1.04157i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −397.945 | + | 689.261i | −0.746614 | + | 1.29317i | ||||
\(534\) | −62.2151 | − | 32.0665i | −0.116508 | − | 0.0600496i | ||||
\(535\) | −254.690 | + | 147.045i | −0.476056 | + | 0.274851i | ||||
\(536\) | −11.2945 | − | 19.5627i | −0.0210718 | − | 0.0364975i | ||||
\(537\) | −769.669 | + | 36.7385i | −1.43328 | + | 0.0684143i | ||||
\(538\) | 358.669 | + | 207.078i | 0.666672 | + | 0.384903i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 68.8224 | + | 27.5292i | 0.127449 | + | 0.0509799i | ||||
\(541\) | 484.286 | 0.895168 | 0.447584 | − | 0.894242i | \(-0.352284\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352284\pi\) | |||||||
\(542\) | −347.084 | − | 200.389i | −0.640376 | − | 0.369721i | ||||
\(543\) | 14.6651 | + | 307.234i | 0.0270076 | + | 0.565809i | ||||
\(544\) | 352.518 | − | 203.527i | 0.648011 | − | 0.374130i | ||||
\(545\) | −209.818 | + | 121.139i | −0.384988 | + | 0.222273i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −274.632 | + | 475.676i | −0.502069 | + | 0.869610i | 0.497928 | + | 0.867219i | \(0.334094\pi\) |
−0.999997 | + | 0.00239116i | \(0.999239\pi\) | |||||||
\(548\) | 218.214 | 0.398201 | ||||||||
\(549\) | 189.440 | + | 86.4701i | 0.345064 | + | 0.157505i | ||||
\(550\) | −203.623 | −0.370224 | ||||||||
\(551\) | 301.974 | + | 174.345i | 0.548047 | + | 0.316415i | ||||
\(552\) | −120.543 | − | 187.529i | −0.218376 | − | 0.339727i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −142.918 | − | 247.542i | −0.257975 | − | 0.446826i | ||||
\(555\) | 234.123 | − | 150.494i | 0.421844 | − | 0.271160i | ||||
\(556\) | 169.751 | + | 98.0055i | 0.305307 | + | 0.176269i | ||||
\(557\) | −460.020 | −0.825888 | −0.412944 | − | 0.910756i | \(-0.635500\pi\) | ||||
−0.412944 | + | 0.910756i | \(0.635500\pi\) | |||||||
\(558\) | −2.40232 | − | 25.1069i | −0.00430523 | − | 0.0449945i | ||||
\(559\) | 106.175i | 0.189938i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 373.048 | + | 192.274i | 0.664969 | + | 0.342734i | ||||
\(562\) | −191.596 | − | 331.853i | −0.340918 | − | 0.590487i | ||||
\(563\) | 550.709 | − | 317.952i | 0.978169 | − | 0.564746i | 0.0764520 | − | 0.997073i | \(-0.475641\pi\) |
0.901717 | + | 0.432327i | \(0.142307\pi\) | |||||||
\(564\) | −8.14012 | − | 170.535i | −0.0144328 | − | 0.302367i | ||||
\(565\) | −388.047 | − | 224.039i | −0.686809 | − | 0.396529i | ||||
\(566\) | − | 218.630i | − | 0.386272i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 580.024 | 1.02117 | ||||||||
\(569\) | −10.5129 | + | 18.2089i | −0.0184761 | + | 0.0320016i | −0.875116 | − | 0.483914i | \(-0.839215\pi\) |
0.856640 | + | 0.515915i | \(0.172548\pi\) | |||||||
\(570\) | −127.578 | + | 6.08967i | −0.223822 | + | 0.0106836i | ||||
\(571\) | 224.928 | + | 389.586i | 0.393919 | + | 0.682287i | 0.992963 | − | 0.118429i | \(-0.0377858\pi\) |
−0.599044 | + | 0.800716i | \(0.704453\pi\) | |||||||
\(572\) | 155.149 | − | 89.5753i | 0.271239 | − | 0.156600i | ||||
\(573\) | 166.410 | − | 322.866i | 0.290418 | − | 0.563467i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −166.630 | −0.289792 | ||||||||
\(576\) | 628.578 | − | 60.1446i | 1.09128 | − | 0.104418i | ||||
\(577\) | − | 78.5449i | − | 0.136126i | −0.997681 | − | 0.0680631i | \(-0.978318\pi\) | ||
0.997681 | − | 0.0680631i | \(-0.0216819\pi\) | |||||||
\(578\) | 184.101 | − | 318.872i | 0.318513 | − | 0.551681i | ||||
\(579\) | −438.065 | − | 681.497i | −0.756589 | − | 1.17702i | ||||
\(580\) | 76.7912 | − | 44.3354i | 0.132399 | − | 0.0764403i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 64.0354 | − | 41.1618i | 0.110027 | − | 0.0707248i | ||||
\(583\) | 6.51375 | − | 11.2822i | 0.0111728 | − | 0.0193519i | ||||
\(584\) | − | 185.780i | − | 0.318117i | ||||||
\(585\) | 215.974 | − | 473.159i | 0.369186 | − | 0.808819i | ||||
\(586\) | − | 251.466i | − | 0.429124i | ||||||
\(587\) | −637.878 | − | 368.279i | −1.08667 | − | 0.627392i | −0.153985 | − | 0.988073i | \(-0.549211\pi\) |
−0.932689 | + | 0.360681i | \(0.882544\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.99352 | − | 15.5772i | −0.0152691 | − | 0.0264469i | ||||
\(590\) | −208.842 | − | 361.724i | −0.353969 | − | 0.613092i | ||||
\(591\) | −35.0291 | + | 1.67204i | −0.0592709 | + | 0.00282916i | ||||
\(592\) | 196.762 | − | 340.801i | 0.332368 | − | 0.575678i | ||||
\(593\) | − | 884.110i | − | 1.49091i | −0.666556 | − | 0.745455i | \(-0.732232\pi\) | ||
0.666556 | − | 0.745455i | \(-0.267768\pi\) | |||||||
\(594\) | 174.323 | + | 221.538i | 0.293473 | + | 0.372959i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 147.908 | − | 256.184i | 0.248168 | − | 0.429839i | ||||
\(597\) | −37.8440 | − | 792.830i | −0.0633903 | − | 1.32802i | ||||
\(598\) | −306.761 | + | 177.109i | −0.512978 | + | 0.296168i | ||||
\(599\) | 365.642 | + | 633.311i | 0.610421 | + | 1.05728i | 0.991169 | + | 0.132602i | \(0.0423332\pi\) |
−0.380748 | + | 0.924679i | \(0.624333\pi\) | |||||||
\(600\) | 233.134 | − | 452.325i | 0.388557 | − | 0.753875i | ||||
\(601\) | 378.525 | + | 218.541i | 0.629825 | + | 0.363630i | 0.780684 | − | 0.624926i | \(-0.214871\pi\) |
−0.150859 | + | 0.988555i | \(0.548204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5624 | + | 19.0380i | 0.0224916 | + | 0.0315721i | ||||
\(604\) | 99.5825 | 0.164872 | ||||||||
\(605\) | 167.453 | + | 96.6788i | 0.276781 | + | 0.159800i | ||||
\(606\) | −422.174 | + | 271.372i | −0.696656 | + | 0.447809i | ||||
\(607\) | −342.651 | + | 197.830i | −0.564500 | + | 0.325914i | −0.754950 | − | 0.655783i | \(-0.772339\pi\) |
0.190450 | + | 0.981697i | \(0.439005\pi\) | |||||||
\(608\) | 168.866 | − | 97.4949i | 0.277740 | − | 0.160353i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45.6238 | + | 79.0228i | −0.0747932 | + | 0.129546i | ||||
\(611\) | −1197.99 | −1.96070 | ||||||||
\(612\) | −193.432 | + | 137.799i | −0.316066 | + | 0.225162i | ||||
\(613\) | 322.644 | 0.526336 | 0.263168 | − | 0.964750i | \(-0.415233\pi\) | ||||
0.263168 | + | 0.964750i | \(0.415233\pi\) | |||||||
\(614\) | 15.3848 | + | 8.88240i | 0.0250566 | + | 0.0144664i | ||||
\(615\) | −104.054 | + | 201.884i | −0.169193 | + | 0.328267i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 71.0592 | + | 123.078i | 0.115169 | + | 0.199478i | 0.917847 | − | 0.396934i | \(-0.129926\pi\) |
−0.802678 | + | 0.596412i | \(0.796592\pi\) | |||||||
\(618\) | 5.04672 | + | 105.729i | 0.00816622 | + | 0.171082i | ||||
\(619\) | −751.468 | − | 433.860i | −1.21400 | − | 0.700905i | −0.250374 | − | 0.968149i | \(-0.580554\pi\) |
−0.963629 | + | 0.267244i | \(0.913887\pi\) | |||||||
\(620\) | −4.57406 | −0.00737751 | ||||||||
\(621\) | 142.653 | + | 181.290i | 0.229716 | + | 0.291933i | ||||
\(622\) | − | 759.604i | − | 1.22123i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −35.0632 | − | 734.573i | −0.0561910 | − | 1.17720i | ||||
\(625\) | −121.463 | − | 210.380i | −0.194341 | − | 0.336608i | ||||
\(626\) | −246.899 | + | 142.547i | −0.394408 | + | 0.227711i | ||||
\(627\) | 178.700 | + | 92.1046i | 0.285008 | + | 0.146897i | ||||
\(628\) | −252.842 | − | 145.978i | −0.402614 | − | 0.232450i | ||||
\(629\) | 891.750i | 1.41773i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −467.813 | −0.741383 | −0.370691 | − | 0.928756i | \(-0.620879\pi\) | ||||
−0.370691 | + | 0.928756i | \(0.620879\pi\) | |||||||
\(632\) | −448.747 | + | 777.253i | −0.710043 | + | 1.22983i | ||||
\(633\) | −196.969 | − | 306.425i | −0.311167 | − | 0.484083i | ||||
\(634\) | 139.666 | + | 241.909i | 0.220294 | + | 0.381560i | ||||
\(635\) | 92.5538 | − | 53.4360i | 0.145754 | − | 0.0841511i | ||||
\(636\) | 3.98631 | + | 6.20151i | 0.00626779 | + | 0.00975080i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 337.222 | 0.528562 | ||||||||
\(639\) | −597.474 | + | 57.1684i | −0.935014 | + | 0.0894655i | ||||
\(640\) | 107.298i | 0.167653i | ||||||||
\(641\) | 335.299 | − | 580.755i | 0.523087 | − | 0.906014i | −0.476552 | − | 0.879146i | \(-0.658113\pi\) |
0.999639 | − | 0.0268674i | \(-0.00855318\pi\) | |||||||
\(642\) | 289.969 | − | 562.595i | 0.451665 | − | 0.876316i | ||||
\(643\) | 115.738 | − | 66.8215i | 0.179997 | − | 0.103921i | −0.407294 | − | 0.913297i | \(-0.633528\pi\) |
0.587291 | + | 0.809376i | \(0.300194\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44461 | + | 30.2646i | 0.00223971 | + | 0.0469219i | ||||
\(646\) | 204.616 | − | 354.405i | 0.316743 | − | 0.548615i | ||||
\(647\) | − | 320.900i | − | 0.495981i | −0.968762 | − | 0.247991i | \(-0.920230\pi\) | ||
0.968762 | − | 0.247991i | \(-0.0797702\pi\) | |||||||
\(648\) | −691.708 | + | 133.593i | −1.06745 | + | 0.206163i | ||||
\(649\) | 657.443i | 1.01301i | ||||||||
\(650\) | −700.225 | − | 404.275i | −1.07727 | − | 0.621962i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −103.377 | − | 179.055i | −0.158554 | − | 0.274624i | ||||
\(653\) | 407.688 | + | 706.137i | 0.624331 | + | 1.08137i | 0.988670 | + | 0.150107i | \(0.0479617\pi\) |
−0.364339 | + | 0.931266i | \(0.618705\pi\) | |||||||
\(654\) | 238.882 | − | 463.476i | 0.365263 | − | 0.708680i | ||||
\(655\) | 113.685 | − | 196.908i | 0.173565 | − | 0.300623i | ||||
\(656\) | 321.133i | 0.489532i | ||||||||
\(657\) | 18.3109 | + | 191.370i | 0.0278705 | + | 0.291278i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 193.167 | − | 334.575i | 0.293121 | − | 0.507701i | −0.681425 | − | 0.731888i | \(-0.738639\pi\) |
0.974546 | + | 0.224187i | \(0.0719727\pi\) | |||||||
\(660\) | 43.0055 | − | 27.6438i | 0.0651599 | − | 0.0418846i | ||||
\(661\) | 103.735 | − | 59.8912i | 0.156936 | − | 0.0906069i | −0.419475 | − | 0.907767i | \(-0.637786\pi\) |
0.576411 | + | 0.817160i | \(0.304453\pi\) | |||||||
\(662\) | −72.3561 | − | 125.324i | −0.109299 | − | 0.189312i | ||||
\(663\) | 901.106 | + | 1401.85i | 1.35913 | + | 2.11440i | ||||
\(664\) | 87.4410 | + | 50.4841i | 0.131688 | + | 0.0760303i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −248.722 | + | 544.905i | −0.373457 | + | 0.818176i | ||||
\(667\) | 275.958 | 0.413730 | ||||||||
\(668\) | 56.9357 | + | 32.8719i | 0.0852331 | + | 0.0492094i | ||||
\(669\) | −808.324 | − | 416.621i | −1.20826 | − | 0.622752i | ||||
\(670\) | −8.87021 | + | 5.12122i | −0.0132391 | + | 0.00764361i | ||||
\(671\) | 124.384 | − | 71.8130i | 0.185371 | − | 0.107024i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 242.303 | − | 419.682i | 0.360035 | − | 0.623599i | −0.627931 | − | 0.778269i | \(-0.716098\pi\) |
0.987966 | + | 0.154670i | \(0.0494315\pi\) | |||||||
\(674\) | 923.447 | 1.37010 | ||||||||
\(675\) | −195.566 | + | 488.911i | −0.289727 | + | 0.724313i | ||||
\(676\) | 513.491 | 0.759602 | ||||||||
\(677\) | 406.464 | + | 234.672i | 0.600390 | + | 0.346635i | 0.769195 | − | 0.639014i | \(-0.220657\pi\) |
−0.168805 | + | 0.985649i | \(0.553991\pi\) | |||||||
\(678\) | 963.234 | − | 45.9778i | 1.42070 | − | 0.0678139i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −229.787 | − | 398.003i | −0.337922 | − | 0.585299i | ||||
\(681\) | 475.245 | + | 244.948i | 0.697863 | + | 0.359688i | ||||
\(682\) | −15.0650 | − | 8.69776i | −0.0220894 | − | 0.0127533i | ||||
\(683\) | 197.068 | 0.288533 | 0.144267 | − | 0.989539i | \(-0.453918\pi\) | ||||
0.144267 | + | 0.989539i | \(0.453918\pi\) | |||||||
\(684\) | −92.6596 | + | 66.0096i | −0.135467 | + | 0.0965052i | ||||
\(685\) | − | 436.952i | − | 0.637886i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −714.392 | + | 459.210i | −1.03987 | + | 0.668428i | ||||
\(688\) | 21.4203 | + | 37.1010i | 0.0311341 | + | 0.0539259i | ||||
\(689\) | 44.7994 | − | 25.8649i | 0.0650209 | − | 0.0375398i | ||||
\(690\) | −85.0307 | + | 54.6575i | −0.123233 | + | 0.0792138i | ||||
\(691\) | −983.708 | − | 567.944i | −1.42360 | − | 0.821916i | −0.426996 | − | 0.904254i | \(-0.640428\pi\) |
−0.996605 | + | 0.0823375i | \(0.973761\pi\) | |||||||
\(692\) | − | 6.97448i | − | 0.0100787i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 697.909 | 1.00563 | ||||||||
\(695\) | 196.246 | − | 339.908i | 0.282368 | − | 0.489076i | ||||
\(696\) | −386.096 | + | 749.100i | −0.554736 | + | 1.07629i | ||||
\(697\) | −363.855 | − | 630.215i | −0.522030 | − | 0.904182i | ||||
\(698\) | −517.189 | + | 298.599i | −0.740959 | + | 0.427793i | ||||
\(699\) | 717.500 | − | 34.2483i | 1.02647 | − | 0.0489961i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1125.84 | 1.60605 | 0.803023 | − | 0.595947i | \(-0.203223\pi\) | ||||
0.803023 | + | 0.595947i | \(0.203223\pi\) | |||||||
\(702\) | 159.625 | + | 1107.93i | 0.227386 | + | 1.57825i | ||||
\(703\) | 427.173i | 0.607643i | ||||||||
\(704\) | 217.758 | − | 377.167i | 0.309315 | − | 0.535749i | ||||
\(705\) | −341.479 | + | 16.2998i | −0.484368 | + | 0.0231202i | ||||
\(706\) | −692.894 | + | 400.043i | −0.981437 | + | 0.566633i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −330.702 | − | 170.448i | −0.467094 | − | 0.240746i | ||||
\(709\) | −322.562 | + | 558.693i | −0.454953 | + | 0.788002i | −0.998686 | − | 0.0512568i | \(-0.983677\pi\) |
0.543732 | + | 0.839259i | \(0.317011\pi\) | |||||||
\(710\) | − | 262.998i | − | 0.370419i | ||||||
\(711\) | 385.640 | − | 844.866i | 0.542391 | − | 1.18828i | ||||
\(712\) | − | 120.642i | − | 0.169441i | ||||||
\(713\) | −12.3281 | − | 7.11761i | −0.0172904 | − | 0.00998262i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −179.365 | − | 310.670i | −0.250861 | − | 0.434503i | ||||
\(716\) | −150.373 | − | 260.454i | −0.210018 | − | 0.363762i | ||||
\(717\) | 710.806 | + | 1105.80i | 0.991362 | + | 1.54226i | ||||
\(718\) | −184.274 | + | 319.172i | −0.256649 | + | 0.444529i | ||||
\(719\) | 989.484i | 1.37620i | 0.725618 | + | 0.688098i | \(0.241554\pi\) | ||||
−0.725618 | + | 0.688098i | \(0.758446\pi\) | |||||||
\(720\) | −19.9891 | − | 208.909i | −0.0277627 | − | 0.290151i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −205.583 | + | 356.079i | −0.284740 | + | 0.493185i | ||||
\(723\) | 15.2904 | + | 7.88090i | 0.0211486 | + | 0.0109003i | ||||
\(724\) | −103.967 | + | 60.0254i | −0.143601 | + | 0.0829080i | ||||
\(725\) | 314.957 | + | 545.521i | 0.434423 | + | 0.752443i | ||||
\(726\) | −415.661 | + | 19.8406i | −0.572535 | + | 0.0273287i | ||||
\(727\) | −691.647 | − | 399.323i | −0.951371 | − | 0.549274i | −0.0578647 | − | 0.998324i | \(-0.518429\pi\) |
−0.893507 | + | 0.449050i | \(0.851763\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 699.351 | − | 205.789i | 0.959329 | − | 0.282289i | ||||
\(730\) | −84.2376 | −0.115394 | ||||||||
\(731\) | −84.0734 | − | 48.5398i | −0.115011 | − | 0.0664019i | ||||
\(732\) | 3.87518 | + | 81.1848i | 0.00529396 | + | 0.110908i | ||||
\(733\) | −4.86788 | + | 2.81047i | −0.00664104 | + | 0.00383421i | −0.503317 | − | 0.864102i | \(-0.667887\pi\) |
0.496676 | + | 0.867936i | \(0.334554\pi\) | |||||||
\(734\) | 304.769 | − | 175.958i | 0.415216 | − | 0.239725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 77.1590 | − | 133.643i | 0.104836 | − | 0.181581i | ||||
\(737\) | 16.1218 | 0.0218749 | ||||||||
\(738\) | −46.5575 | − | 486.578i | −0.0630861 | − | 0.659320i | ||||
\(739\) | 390.819 | 0.528849 | 0.264424 | − | 0.964406i | \(-0.414818\pi\) | ||||
0.264424 | + | 0.964406i | \(0.414818\pi\) | |||||||
\(740\) | 94.0755 | + | 54.3145i | 0.127129 | + | 0.0733980i | ||||
\(741\) | 431.655 | + | 671.525i | 0.582530 | + | 0.906242i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −186.515 | − | 323.053i | −0.251029 | − | 0.434795i | 0.712780 | − | 0.701387i | \(-0.247436\pi\) |
−0.963809 | + | 0.266592i | \(0.914102\pi\) | |||||||
\(744\) | 36.5694 | − | 23.5067i | 0.0491524 | − | 0.0315951i | ||||
\(745\) | −512.982 | − | 296.170i | −0.688567 | − | 0.397544i | ||||
\(746\) | 428.499 | 0.574396 | ||||||||
\(747\) | −95.0476 | − | 43.3846i | −0.127239 | − | 0.0580784i | ||||
\(748\) | 163.803i | 0.218988i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −468.002 | − | 241.214i | −0.624002 | − | 0.321619i | ||||
\(751\) | 246.052 | + | 426.175i | 0.327633 | + | 0.567477i | 0.982042 | − | 0.188664i | \(-0.0604157\pi\) |
−0.654409 | + | 0.756141i | \(0.727082\pi\) | |||||||
\(752\) | −418.615 | + | 241.688i | −0.556669 | + | 0.321393i | ||||
\(753\) | 0.528127 | + | 11.0642i | 0.000701364 | + | 0.0146936i | ||||
\(754\) | 1159.65 | + | 669.525i | 1.53800 | + | 0.887964i | ||||
\(755\) | − | 199.404i | − | 0.264111i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 591.819 | 0.781795 | 0.390898 | − | 0.920434i | \(-0.372165\pi\) | ||||
0.390898 | + | 0.920434i | \(0.372165\pi\) | |||||||
\(758\) | 368.131 | − | 637.622i | 0.485661 | − | 0.841190i | ||||
\(759\) | 158.925 | − | 7.58594i | 0.209388 | − | 0.00999465i | ||||
\(760\) | −110.074 | − | 190.655i | −0.144835 | − | 0.250861i | ||||
\(761\) | 250.799 | − | 144.799i | 0.329564 | − | 0.190274i | −0.326083 | − | 0.945341i | \(-0.605729\pi\) |
0.655648 | + | 0.755067i | \(0.272396\pi\) | |||||||
\(762\) | −105.374 | + | 204.446i | −0.138286 | + | 0.268302i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 141.769 | 0.185561 | ||||||||
\(765\) | 275.928 | + | 387.329i | 0.360691 | + | 0.506312i | ||||
\(766\) | 464.232i | 0.606047i | ||||||||
\(767\) | −1305.29 | + | 2260.84i | −1.70182 | + | 2.94763i | ||||
\(768\) | 330.387 | + | 513.983i | 0.430192 | + | 0.669249i | ||||
\(769\) | 388.241 | − | 224.151i | 0.504865 | − | 0.291484i | −0.225855 | − | 0.974161i | \(-0.572518\pi\) |
0.730720 | + | 0.682677i | \(0.239184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −521.600 | + | 335.283i | −0.676524 | + | 0.434868i | ||||
\(772\) | 158.101 | − | 273.840i | 0.204795 | − | 0.354715i | ||||
\(773\) | 329.273i | 0.425967i | 0.977056 | + | 0.212984i | \(0.0683181\pi\) | ||||
−0.977056 | + | 0.212984i | \(0.931682\pi\) | |||||||
\(774\) | −37.8347 | − | 53.1096i | −0.0488820 | − | 0.0686171i | ||||
\(775\) | − | 32.4939i | − | 0.0419276i | ||||||
\(776\) | 113.631 | + | 65.6049i | 0.146432 | + | 0.0845423i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 53.6707 | + | 92.9604i | 0.0689855 | + | 0.119486i | ||||
\(779\) | −174.297 | − | 301.890i | −0.223744 | − | 0.387536i | ||||
\(780\) | 202.773 | − | 9.67892i | 0.259966 | − | 0.0124089i | ||||
\(781\) | −206.982 | + | 358.504i | −0.265022 | + | 0.459032i | ||||
\(782\) | − | 323.873i | − | 0.414159i | ||||||
\(783\) | 323.879 | − | 809.691i | 0.413639 | − | 1.03409i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −292.307 | + | 506.290i | −0.372365 | + | 0.644955i | ||||
\(786\) | 23.3307 | + | 488.777i | 0.0296828 | + | 0.621853i | ||||
\(787\) | −157.300 | + | 90.8171i | −0.199873 | + | 0.115397i | −0.596596 | − | 0.802542i | \(-0.703481\pi\) |
0.396723 | + | 0.917938i | \(0.370147\pi\) | |||||||
\(788\) | −6.84375 | − | 11.8537i | −0.00868496 | − | 0.0150428i | ||||
\(789\) | −173.675 | + | 336.962i | −0.220120 | + | 0.427074i | ||||
\(790\) | 352.426 | + | 203.473i | 0.446109 | + | 0.257561i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −201.762 | + | 442.023i | −0.254750 | + | 0.558109i | ||||
\(793\) | 570.313 | 0.719184 | ||||||||
\(794\) | 187.660 | + | 108.345i | 0.236347 | + | 0.136455i | ||||
\(795\) | 12.4179 | − | 7.98219i | 0.0156200 | − | 0.0100405i | ||||
\(796\) | 268.291 | − | 154.898i | 0.337049 | − | 0.194595i | ||||
\(797\) | 24.1857 | − | 13.9636i | 0.0303460 | − | 0.0175202i | −0.484750 | − | 0.874653i | \(-0.661090\pi\) |
0.515096 | + | 0.857132i | \(0.327756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 547.680 | − | 948.610i | 0.685457 | − | 1.18725i | ||||
\(800\) | 352.253 | 0.440316 | ||||||||
\(801\) | 11.8907 | + | 124.271i | 0.0148449 | + | 0.155145i | ||||
\(802\) | −604.604 | −0.753870 | ||||||||
\(803\) | 114.828 | + | 66.2960i | 0.142999 | + | 0.0825604i | ||||
\(804\) | −4.17974 | + | 8.10949i | −0.00519868 | + | 0.0100864i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −34.5372 | − | 59.8203i | −0.0428502 | − | 0.0742187i | ||||
\(807\) | −35.2196 | − | 737.848i | −0.0436426 | − | 0.914310i | ||||
\(808\) | −749.147 | − | 432.520i | −0.927163 | − | 0.535298i | ||||
\(809\) | 493.946 | 0.610563 | 0.305282 | − | 0.952262i | \(-0.401249\pi\) | ||||
0.305282 | + | 0.952262i | \(0.401249\pi\) | |||||||
\(810\) | 60.5746 | + | 313.638i | 0.0747835 | + | 0.387208i | ||||
\(811\) | − | 386.208i | − | 0.476212i | −0.971239 | − | 0.238106i | \(-0.923473\pi\) | ||
0.971239 | − | 0.238106i | \(-0.0765266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.0819 | + | 714.015i | 0.0419212 | + | 0.878247i | ||||
\(814\) | 206.563 | + | 357.777i | 0.253763 | + | 0.439530i | ||||
\(815\) | −358.539 | + | 207.003i | −0.439925 | + | 0.253991i | ||||
\(816\) | 597.691 | + | 308.058i | 0.732464 | + | 0.377522i | ||||
\(817\) | −40.2735 | − | 23.2519i | −0.0492944 | − | 0.0284601i | ||||
\(818\) | 48.1754i | 0.0588942i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −88.6463 | −0.108105 | ||||||||
\(821\) | 611.025 | − | 1058.33i | 0.744244 | − | 1.28907i | −0.206303 | − | 0.978488i | \(-0.566143\pi\) |
0.950547 | − | 0.310581i | \(-0.100524\pi\) | |||||||
\(822\) | 508.487 | + | 791.053i | 0.618597 | + | 0.962351i | ||||
\(823\) | −582.687 | − | 1009.24i | −0.708004 | − | 1.22630i | −0.965597 | − | 0.260045i | \(-0.916263\pi\) |
0.257593 | − | 0.966254i | \(-0.417071\pi\) | |||||||
\(824\) | −158.002 | + | 91.2226i | −0.191750 | + | 0.110707i | ||||
\(825\) | 196.381 | + | 305.509i | 0.238037 | + | 0.370314i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1250.89 | −1.51257 | −0.756283 | − | 0.654244i | \(-0.772987\pi\) | ||||
−0.756283 | + | 0.654244i | \(0.772987\pi\) | |||||||
\(828\) | −37.3871 | + | 81.9082i | −0.0451535 | + | 0.0989229i | ||||
\(829\) | − | 121.096i | − | 0.146075i | −0.997329 | − | 0.0730374i | \(-0.976731\pi\) | ||
0.997329 | − | 0.0730374i | \(-0.0232692\pi\) | |||||||
\(830\) | 22.8908 | − | 39.6480i | 0.0275793 | − | 0.0477687i | ||||
\(831\) | −233.568 | + | 453.167i | −0.281069 | + | 0.545327i | ||||
\(832\) | 1497.66 | − | 864.676i | 1.80008 | − | 1.03927i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 40.2741 | + | 843.740i | 0.0482902 | + | 1.01168i | ||||
\(835\) | 65.8225 | − | 114.008i | 0.0788294 | − | 0.136536i | ||||
\(836\) | 78.4664i | 0.0938593i | ||||||||
\(837\) | −35.3527 | + | 27.8183i | −0.0422374 | + | 0.0332357i | ||||
\(838\) | 338.988i | 0.404521i | ||||||||
\(839\) | 530.632 | + | 306.360i | 0.632457 | + | 0.365149i | 0.781703 | − | 0.623651i | \(-0.214351\pi\) |
−0.149246 | + | 0.988800i | \(0.547685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −101.103 | − | 175.116i | −0.120218 | − | 0.208224i | ||||
\(842\) | −545.024 | − | 944.009i | −0.647297 | − | 1.12115i | ||||
\(843\) | −313.121 | + | 607.514i | −0.371437 | + | 0.720657i | ||||
\(844\) | 71.0878 | − | 123.128i | 0.0842272 | − | 0.145886i | ||||
\(845\) | − | 1028.21i | − | 1.21682i | ||||||
\(846\) | 599.242 | − | 426.893i | 0.708324 | − | 0.504602i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.4362 | − | 18.0761i | 0.0123069 | − | 0.0213161i | ||||
\(849\) | −328.025 | + | 210.854i | −0.386367 | + | 0.248356i | ||||
\(850\) | 640.240 | − | 369.642i | 0.753223 | − | 0.434874i | ||||
\(851\) | 169.036 | + | 292.779i | 0.198632 | + | 0.344041i | ||||
\(852\) | −126.670 | − | 197.060i | −0.148674 | − | 0.231291i | ||||
\(853\) | −1000.90 | − | 577.868i | −1.17338 | − | 0.677453i | −0.218909 | − | 0.975745i | \(-0.570250\pi\) |
−0.954475 | + | 0.298292i | \(0.903583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 132.177 | + | 185.541i | 0.154593 | + | 0.217007i | ||||
\(856\) | 1090.93 | 1.27445 | ||||||||
\(857\) | 352.355 | + | 203.432i | 0.411149 | + | 0.237377i | 0.691283 | − | 0.722584i | \(-0.257046\pi\) |
−0.280134 | + | 0.959961i | \(0.590379\pi\) | |||||||
\(858\) | 686.252 | + | 353.703i | 0.799827 | + | 0.412242i | ||||
\(859\) | 325.728 | − | 188.059i | 0.379194 | − | 0.218928i | −0.298273 | − | 0.954480i | \(-0.596411\pi\) |
0.677468 | + | 0.735553i | \(0.263077\pi\) | |||||||
\(860\) | −10.2415 | + | 5.91290i | −0.0119087 | + | 0.00687547i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 401.849 | − | 696.024i | 0.466183 | − | 0.807452i | ||||
\(863\) | −631.055 | −0.731234 | −0.365617 | − | 0.930765i | \(-0.619142\pi\) | ||||
−0.365617 | + | 0.930765i | \(0.619142\pi\) | |||||||
\(864\) | −301.566 | − | 383.244i | −0.349035 | − | 0.443569i | ||||
\(865\) | −13.9657 | −0.0161453 | ||||||||
\(866\) | −1107.73 | − | 639.550i | −1.27914 | − | 0.738511i | ||||
\(867\) | −655.977 | + | 31.3116i | −0.756606 | + | 0.0361149i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −320.272 | − | 554.727i | −0.368552 | − | 0.638351i | ||||
\(870\) | 339.661 | + | 175.066i | 0.390415 | + | 0.201225i | ||||
\(871\) | 55.4403 | + | 32.0085i | 0.0636513 | + | 0.0367491i | ||||
\(872\) | 898.732 | 1.03066 | ||||||||
\(873\) | −123.516 | − | 56.3789i | −0.141484 | − | 0.0645806i | ||||
\(874\) | − | 155.144i | − | 0.177510i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −63.1180 | + | 40.5721i | −0.0720525 | + | 0.0463152i | ||||
\(877\) | 609.906 | + | 1056.39i | 0.695445 | + | 1.20455i | 0.970030 | + | 0.242984i | \(0.0781262\pi\) |
−0.274585 | + | 0.961563i | \(0.588540\pi\) | |||||||
\(878\) | 503.873 | − | 290.911i | 0.573888 | − | 0.331334i | ||||
\(879\) | −377.292 | + | 242.522i | −0.429229 | + | 0.275907i | ||||
\(880\) | −125.352 | − | 72.3720i | −0.142445 | − | 0.0822409i | ||||
\(881\) | 543.964i | 0.617439i | 0.951153 | + | 0.308719i | \(0.0999004\pi\) | ||||
−0.951153 | + | 0.308719i | \(0.900100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1196.59 | 1.35514 | 0.677570 | − | 0.735458i | \(-0.263033\pi\) | ||||
0.677570 | + | 0.735458i | \(0.263033\pi\) | |||||||
\(884\) | −325.217 | + | 563.292i | −0.367892 | + | 0.637208i | ||||
\(885\) | −341.306 | + | 662.198i | −0.385656 | + | 0.748246i | ||||
\(886\) | 44.0362 | + | 76.2729i | 0.0497022 | + | 0.0860868i | ||||
\(887\) | −916.233 | + | 528.987i | −1.03296 | + | 0.596378i | −0.917830 | − | 0.396973i | \(-0.870061\pi\) |
−0.115126 | + | 0.993351i | \(0.536727\pi\) | |||||||
\(888\) | −1031.26 | + | 49.2249i | −1.16133 | + | 0.0554334i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −54.7021 | −0.0614631 | ||||||||
\(891\) | 164.265 | − | 475.207i | 0.184360 | − | 0.533341i | ||||
\(892\) | − | 354.931i | − | 0.397904i | ||||||
\(893\) | 262.354 | − | 454.411i | 0.293790 | − | 0.508858i | ||||
\(894\) | 1273.35 | − | 60.7808i | 1.42433 | − | 0.0679874i | ||||
\(895\) | −521.532 | + | 301.106i | −0.582717 | + | 0.336432i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 561.578 | + | 289.445i | 0.626062 | + | 0.322681i | ||||
\(898\) | −24.9794 | + | 43.2656i | −0.0278167 | + | 0.0481799i | ||||
\(899\) | 53.8135i | 0.0598593i | ||||||||
\(900\) | −204.589 | + | 19.5758i | −0.227321 | + | 0.0217509i | ||||
\(901\) | 47.2984i | 0.0524954i | ||||||||
\(902\) | −291.963 | − | 168.565i | −0.323684 | − | 0.186879i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 831.077 | + | 1439.47i | 0.919333 | + | 1.59233i | ||||
\(905\) | 120.195 | + | 208.183i | 0.132812 | + | 0.230037i | ||||
\(906\) | 232.049 | + | 360.998i | 0.256125 | + | 0.398453i | ||||
\(907\) | −46.8954 | + | 81.2252i | −0.0517038 | + | 0.0895537i | −0.890719 | − | 0.454554i | \(-0.849799\pi\) |
0.839015 | + | 0.544108i | \(0.183132\pi\) | |||||||
\(908\) | 208.678i | 0.229821i | ||||||||
\(909\) | 814.316 | + | 371.695i | 0.895837 | + | 0.408906i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 357.105 | − | 618.525i | 0.391993 | − | 0.678951i | −0.600720 | − | 0.799460i | \(-0.705119\pi\) |
0.992712 | + | 0.120509i | \(0.0384525\pi\) | |||||||
\(912\) | 286.311 | + | 147.568i | 0.313937 | + | 0.161807i | ||||
\(913\) | −62.4069 | + | 36.0306i | −0.0683537 | + | 0.0394640i | ||||
\(914\) | −99.9237 | − | 173.073i | −0.109326 | − | 0.189358i | ||||
\(915\) | 162.564 | − | 7.75965i | 0.177666 | − | 0.00848049i | ||||
\(916\) | −287.057 | − | 165.733i | −0.313382 | − | 0.180931i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −950.277 | − | 380.114i | −1.03516 | − | 0.414067i | ||||
\(919\) | 1672.93 | 1.82038 | 0.910191 | − | 0.414189i | \(-0.135935\pi\) | ||||
0.910191 | + | 0.414189i | \(0.135935\pi\) | |||||||
\(920\) | −150.887 | − | 87.1147i | −0.164008 | − | 0.0946898i | ||||
\(921\) | −1.51071 | − | 31.6493i | −0.00164029 | − | 0.0343640i | ||||
\(922\) | −1106.58 | + | 638.885i | −1.20020 | + | 0.692934i | ||||
\(923\) | −1423.55 | + | 821.889i | −1.54231 | + | 0.890454i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −385.848 | + | 668.309i | −0.417133 | + | 0.722496i | ||||
\(926\) | −199.103 | −0.215014 | ||||||||
\(927\) | 153.765 | − | 109.540i | 0.165873 | − | 0.118166i | ||||
\(928\) | −583.369 | −0.628631 | ||||||||
\(929\) | 600.433 | + | 346.660i | 0.646322 | + | 0.373154i | 0.787046 | − | 0.616895i | \(-0.211610\pi\) |
−0.140724 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(930\) | −10.6585 | − | 16.5815i | −0.0114608 | − | 0.0178296i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 140.180 | + | 242.800i | 0.150408 | + | 0.260515i | ||||
\(933\) | −1139.68 | + | 732.586i | −1.22153 | + | 0.785194i | ||||
\(934\) | −146.059 | − | 84.3273i | −0.156380 | − | 0.0902862i | ||||
\(935\) | 327.999 | 0.350801 | ||||||||
\(936\) | −1571.42 | + | 1119.46i | −1.67887 | + | 1.19601i | ||||
\(937\) | − | 909.088i | − | 0.970211i | −0.874456 | − | 0.485105i | \(-0.838781\pi\) | ||
0.874456 | − | 0.485105i | \(-0.161219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 451.991 | + | 232.962i | 0.481354 | + | 0.248096i | ||||
\(940\) | −66.7160 | − | 115.555i | −0.0709744 | − | 0.122931i | ||||
\(941\) | 1095.81 | − | 632.664i | 1.16451 | − | 0.672332i | 0.212132 | − | 0.977241i | \(-0.431959\pi\) |
0.952381 | + | 0.304909i | \(0.0986261\pi\) | |||||||
\(942\) | −59.9878 | − | 1256.74i | −0.0636814 | − | 1.33412i | ||||
\(943\) | −238.921 | − | 137.941i | −0.253362 | − | 0.146279i | ||||
\(944\) | 1053.34i | 1.11583i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.9745 | −0.0475418 | ||||||||
\(947\) | −489.835 | + | 848.420i | −0.517249 | + | 0.895902i | 0.482550 | + | 0.875869i | \(0.339711\pi\) |
−0.999799 | + | 0.0200339i | \(0.993623\pi\) | |||||||
\(948\) | 362.069 | − | 17.2825i | 0.381929 | − | 0.0182305i | ||||
\(949\) | 263.249 | + | 455.961i | 0.277397 | + | 0.480465i | ||||
\(950\) | 306.693 | − | 177.069i | 0.322834 | − | 0.186389i | ||||
\(951\) | 228.254 | − | 442.856i | 0.240015 | − | 0.465674i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −307.846 | −0.323029 | −0.161514 | − | 0.986870i | \(-0.551638\pi\) | ||||
−0.161514 | + | 0.986870i | \(0.551638\pi\) | |||||||
\(954\) | −13.1922 | + | 28.9017i | −0.0138283 | + | 0.0302953i | ||||
\(955\) | − | 283.878i | − | 0.297254i | ||||||
\(956\) | −256.536 | + | 444.334i | −0.268343 | + | 0.464784i | ||||
\(957\) | −325.228 | − | 505.957i | −0.339841 | − | 0.528691i | ||||
\(958\) | −945.194 | + | 545.708i | −0.986632 | + | 0.569633i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 415.135 | − | 266.848i | 0.432433 | − | 0.277967i | ||||
\(961\) | −479.112 | + | 829.846i | −0.498556 | + | 0.863524i | ||||
\(962\) | 1640.45i | 1.70525i | ||||||||
\(963\) | −1123.75 | + | 107.525i | −1.16693 | + | 0.111656i | ||||
\(964\) | 6.71395i | 0.00696468i | ||||||||
\(965\) | −548.336 | − | 316.582i | −0.568224 | − | 0.328064i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.5677 | + | 49.4807i | 0.0295426 | + | 0.0511693i | 0.880419 | − | 0.474197i | \(-0.157262\pi\) |
−0.850876 | + | 0.525366i | \(0.823928\pi\) | |||||||
\(968\) | −358.632 | − | 621.168i | −0.370487 | − | 0.641703i | ||||
\(969\) | −729.076 | + | 34.8008i | −0.752401 | + | 0.0359142i | ||||
\(970\) | 29.7469 | − | 51.5232i | 0.0306669 | − | 0.0531167i | ||||
\(971\) | 1757.15i | 1.80963i | 0.425808 | + | 0.904813i | \(0.359990\pi\) | ||||
−0.425808 | + | 0.904813i | \(0.640010\pi\) | |||||||
\(972\) | 196.448 | + | 205.829i | 0.202107 | + | 0.211759i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 530.173 | − | 918.287i | 0.544326 | − | 0.942800i | ||||
\(975\) | 68.7587 | + | 1440.49i | 0.0705217 | + | 1.47743i | ||||
\(976\) | 199.286 | − | 115.058i | 0.204186 | − | 0.117887i | ||||
\(977\) | −262.748 | − | 455.093i | −0.268934 | − | 0.465807i | 0.699653 | − | 0.714483i | \(-0.253338\pi\) |
−0.968587 | + | 0.248676i | \(0.920005\pi\) | |||||||
\(978\) | 408.204 | − | 791.992i | 0.417386 | − | 0.809808i | ||||
\(979\) | 74.5669 | + | 43.0512i | 0.0761664 | + | 0.0439747i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −925.771 | + | 88.5810i | −0.943701 | + | 0.0902967i | ||||
\(982\) | −1321.22 | −1.34544 | ||||||||
\(983\) | −1303.53 | − | 752.592i | −1.32607 | − | 0.765607i | −0.341381 | − | 0.939925i | \(-0.610895\pi\) |
−0.984689 | + | 0.174318i | \(0.944228\pi\) | |||||||
\(984\) | 708.724 | − | 455.566i | 0.720247 | − | 0.462973i | ||||
\(985\) | −23.7359 | + | 13.7039i | −0.0240973 | + | 0.0139126i | ||||
\(986\) | −1060.31 | + | 612.169i | −1.07536 | + | 0.620861i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −155.788 | + | 269.833i | −0.157680 | + | 0.273110i | ||||
\(989\) | −36.8039 | −0.0372132 | ||||||||
\(990\) | 200.424 | + | 91.4839i | 0.202449 | + | 0.0924080i | ||||
\(991\) | 183.562 | 0.185229 | 0.0926143 | − | 0.995702i | \(-0.470478\pi\) | ||||
0.0926143 | + | 0.995702i | \(0.470478\pi\) | |||||||
\(992\) | 26.0613 | + | 15.0465i | 0.0262714 | + | 0.0151678i | ||||
\(993\) | −118.250 | + | 229.428i | −0.119084 | + | 0.231045i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −310.167 | − | 537.226i | −0.311726 | − | 0.539925i | ||||
\(996\) | −1.94429 | − | 40.7328i | −0.00195210 | − | 0.0408964i | ||||
\(997\) | 518.220 | + | 299.195i | 0.519780 | + | 0.300095i | 0.736845 | − | 0.676062i | \(-0.236315\pi\) |
−0.217065 | + | 0.976157i | \(0.569648\pi\) | |||||||
\(998\) | 391.497 | 0.392281 | ||||||||
\(999\) | 1057.43 | − | 152.349i | 1.05849 | − | 0.152502i |
(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 | 441.3.l.a.97.5 | 28 | ||
7.2 | even | 3 | 441.3.t.a.178.10 | 28 | |||
7.3 | odd | 6 | 441.3.k.b.313.5 | 28 | |||
7.4 | even | 3 | 63.3.k.a.61.5 | yes | 28 | ||
7.5 | odd | 6 | 63.3.t.a.52.10 | yes | 28 | ||
7.6 | odd | 2 | 441.3.l.b.97.5 | 28 | |||
9.4 | even | 3 | 441.3.l.b.391.5 | 28 | |||
21.5 | even | 6 | 189.3.t.a.73.5 | 28 | |||
21.11 | odd | 6 | 189.3.k.a.19.10 | 28 | |||
63.4 | even | 3 | 63.3.t.a.40.10 | yes | 28 | ||
63.5 | even | 6 | 189.3.k.a.10.10 | 28 | |||
63.13 | odd | 6 | inner | 441.3.l.a.391.5 | 28 | ||
63.31 | odd | 6 | 441.3.t.a.166.10 | 28 | |||
63.32 | odd | 6 | 189.3.t.a.145.5 | 28 | |||
63.40 | odd | 6 | 63.3.k.a.31.5 | ✓ | 28 | ||
63.58 | even | 3 | 441.3.k.b.31.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.k.a.31.5 | ✓ | 28 | 63.40 | odd | 6 | ||
63.3.k.a.61.5 | yes | 28 | 7.4 | even | 3 | ||
63.3.t.a.40.10 | yes | 28 | 63.4 | even | 3 | ||
63.3.t.a.52.10 | yes | 28 | 7.5 | odd | 6 | ||
189.3.k.a.10.10 | 28 | 63.5 | even | 6 | |||
189.3.k.a.19.10 | 28 | 21.11 | odd | 6 | |||
189.3.t.a.73.5 | 28 | 21.5 | even | 6 | |||
189.3.t.a.145.5 | 28 | 63.32 | odd | 6 | |||
441.3.k.b.31.5 | 28 | 63.58 | even | 3 | |||
441.3.k.b.313.5 | 28 | 7.3 | odd | 6 | |||
441.3.l.a.97.5 | 28 | 1.1 | even | 1 | trivial | ||
441.3.l.a.391.5 | 28 | 63.13 | odd | 6 | inner | ||
441.3.l.b.97.5 | 28 | 7.6 | odd | 2 | |||
441.3.l.b.391.5 | 28 | 9.4 | even | 3 | |||
441.3.t.a.166.10 | 28 | 63.31 | odd | 6 | |||
441.3.t.a.178.10 | 28 | 7.2 | even | 3 |