Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 275.5 | ||
Root | \(-1.78423 + 0.903622i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.275 |
Dual form | 392.3.k.n.67.5 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.109554 | − | 1.99700i | −0.0547769 | − | 0.998499i | ||||
\(3\) | 2.28374 | + | 3.95555i | 0.761245 | + | 1.31852i | 0.942209 | + | 0.335026i | \(0.108745\pi\) |
−0.180964 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(4\) | −3.97600 | + | 0.437557i | −0.993999 | + | 0.109389i | ||||
\(5\) | −4.96451 | − | 2.86626i | −0.992902 | − | 0.573252i | −0.0867614 | − | 0.996229i | \(-0.527652\pi\) |
−0.906140 | + | 0.422977i | \(0.860985\pi\) | |||||||
\(6\) | 7.64902 | − | 4.99396i | 1.27484 | − | 0.832327i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.30939 | + | 7.89212i | 0.163673 | + | 0.986515i | ||||
\(9\) | −5.93090 | + | 10.2726i | −0.658989 | + | 1.14140i | ||||
\(10\) | −5.18003 | + | 10.2281i | −0.518003 | + | 1.02281i | ||||
\(11\) | 0.700323 | + | 1.21300i | 0.0636658 | + | 0.110272i | 0.896101 | − | 0.443849i | \(-0.146388\pi\) |
−0.832436 | + | 0.554122i | \(0.813054\pi\) | |||||||
\(12\) | −10.8109 | − | 14.7280i | −0.900909 | − | 1.22733i | ||||
\(13\) | − | 19.0821i | − | 1.46785i | −0.679228 | − | 0.733927i | \(-0.737685\pi\) | ||
0.679228 | − | 0.733927i | \(-0.262315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 26.1831i | − | 1.74554i | ||||||
\(16\) | 15.6171 | − | 3.47945i | 0.976068 | − | 0.217466i | ||||
\(17\) | −16.1349 | − | 27.9465i | −0.949114 | − | 1.64391i | −0.747296 | − | 0.664491i | \(-0.768648\pi\) |
−0.201818 | − | 0.979423i | \(-0.564685\pi\) | |||||||
\(18\) | 21.1641 | + | 10.7186i | 1.17579 | + | 0.595477i | ||||
\(19\) | 6.28374 | − | 10.8837i | 0.330723 | − | 0.572829i | −0.651931 | − | 0.758278i | \(-0.726041\pi\) |
0.982654 | + | 0.185449i | \(0.0593741\pi\) | |||||||
\(20\) | 20.9930 | + | 9.22398i | 1.04965 | + | 0.461199i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.34563 | − | 1.53143i | 0.106619 | − | 0.0696105i | ||||
\(23\) | 13.7605 | + | 7.94464i | 0.598284 | + | 0.345419i | 0.768366 | − | 0.640011i | \(-0.221070\pi\) |
−0.170082 | + | 0.985430i | \(0.554403\pi\) | |||||||
\(24\) | −28.2273 | + | 23.2028i | −1.17614 | + | 0.966785i | ||||
\(25\) | 3.93090 | + | 6.80852i | 0.157236 | + | 0.272341i | ||||
\(26\) | −38.1069 | + | 2.09052i | −1.46565 | + | 0.0804045i | ||||
\(27\) | −13.0712 | −0.484118 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.29194i | 0.113515i | 0.998388 | + | 0.0567576i | \(0.0180762\pi\) | ||||
−0.998388 | + | 0.0567576i | \(0.981924\pi\) | |||||||
\(30\) | −52.2876 | + | 2.86846i | −1.74292 | + | 0.0956153i | ||||
\(31\) | 19.6332 | − | 11.3352i | 0.633329 | − | 0.365653i | −0.148711 | − | 0.988881i | \(-0.547512\pi\) |
0.782040 | + | 0.623228i | \(0.214179\pi\) | |||||||
\(32\) | −8.65936 | − | 30.8061i | −0.270605 | − | 0.962690i | ||||
\(33\) | −3.19871 | + | 5.54032i | −0.0969305 | + | 0.167889i | ||||
\(34\) | −54.0415 | + | 35.2831i | −1.58946 | + | 1.03774i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.0864 | − | 43.4390i | 0.530177 | − | 1.20664i | ||||
\(37\) | −46.8985 | − | 27.0769i | −1.26753 | − | 0.731807i | −0.293008 | − | 0.956110i | \(-0.594656\pi\) |
−0.974519 | + | 0.224303i | \(0.927990\pi\) | |||||||
\(38\) | −22.4232 | − | 11.3562i | −0.590085 | − | 0.298849i | ||||
\(39\) | 75.4801 | − | 43.5785i | 1.93539 | − | 1.11740i | ||||
\(40\) | 16.1204 | − | 42.9335i | 0.403010 | − | 1.07334i | ||||
\(41\) | 7.59607 | 0.185270 | 0.0926350 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926350 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.8478 | −0.484833 | −0.242417 | − | 0.970172i | \(-0.577940\pi\) | ||||
−0.242417 | + | 0.970172i | \(0.577940\pi\) | |||||||
\(44\) | −3.31524 | − | 4.51643i | −0.0753463 | − | 0.102646i | ||||
\(45\) | 58.8880 | − | 33.9990i | 1.30862 | − | 0.755533i | ||||
\(46\) | 14.3579 | − | 28.3501i | 0.312129 | − | 0.616306i | ||||
\(47\) | −18.7394 | − | 10.8192i | −0.398711 | − | 0.230196i | 0.287217 | − | 0.957866i | \(-0.407270\pi\) |
−0.685928 | + | 0.727670i | \(0.740603\pi\) | |||||||
\(48\) | 49.4284 | + | 53.8280i | 1.02976 | + | 1.12142i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.1659 | − | 8.59589i | 0.263319 | − | 0.171918i | ||||
\(51\) | 73.6959 | − | 127.645i | 1.44502 | − | 2.50284i | ||||
\(52\) | 8.34951 | + | 75.8703i | 0.160567 | + | 1.45905i | ||||
\(53\) | −0.308883 | + | 0.178334i | −0.00582798 | + | 0.00336479i | −0.502911 | − | 0.864338i | \(-0.667738\pi\) |
0.497083 | + | 0.867703i | \(0.334404\pi\) | |||||||
\(54\) | 1.43200 | + | 26.1031i | 0.0265185 | + | 0.483391i | ||||
\(55\) | − | 8.02924i | − | 0.145986i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.4016 | 1.00705 | ||||||||
\(58\) | 6.57400 | − | 0.360645i | 0.113345 | − | 0.00621801i | ||||
\(59\) | 13.4292 | + | 23.2600i | 0.227613 | + | 0.394237i | 0.957100 | − | 0.289757i | \(-0.0935746\pi\) |
−0.729487 | + | 0.683994i | \(0.760241\pi\) | |||||||
\(60\) | 11.4566 | + | 104.104i | 0.190944 | + | 1.73507i | ||||
\(61\) | −74.6763 | − | 43.1144i | −1.22420 | − | 0.706793i | −0.258390 | − | 0.966041i | \(-0.583192\pi\) |
−0.965811 | + | 0.259248i | \(0.916525\pi\) | |||||||
\(62\) | −24.7873 | − | 37.9656i | −0.399796 | − | 0.612349i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −60.5710 | + | 20.6676i | −0.946422 | + | 0.322932i | ||||
\(65\) | −54.6943 | + | 94.7333i | −0.841450 | + | 1.45743i | ||||
\(66\) | 11.4144 | + | 5.78085i | 0.172946 | + | 0.0875886i | ||||
\(67\) | −57.2613 | − | 99.1794i | −0.854646 | − | 1.48029i | −0.876973 | − | 0.480539i | \(-0.840441\pi\) |
0.0223272 | − | 0.999751i | \(-0.492892\pi\) | |||||||
\(68\) | 76.3807 | + | 104.055i | 1.12325 | + | 1.53023i | ||||
\(69\) | 72.5739i | 1.05180i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 104.792i | 1.47594i | 0.674834 | + | 0.737969i | \(0.264215\pi\) | ||||
−0.674834 | + | 0.737969i | \(0.735785\pi\) | |||||||
\(72\) | −88.8385 | − | 33.3565i | −1.23387 | − | 0.463285i | ||||
\(73\) | −12.1987 | − | 21.1288i | −0.167106 | − | 0.289435i | 0.770295 | − | 0.637687i | \(-0.220109\pi\) |
−0.937401 | + | 0.348252i | \(0.886775\pi\) | |||||||
\(74\) | −48.9345 | + | 96.6226i | −0.661277 | + | 1.30571i | ||||
\(75\) | −17.9543 | + | 31.0977i | −0.239390 | + | 0.414636i | ||||
\(76\) | −20.2218 | + | 46.0232i | −0.266077 | + | 0.605569i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −95.2952 | − | 145.959i | −1.22173 | − | 1.87127i | ||||
\(79\) | 101.436 | + | 58.5639i | 1.28400 | + | 0.741315i | 0.977576 | − | 0.210581i | \(-0.0675356\pi\) |
0.306420 | + | 0.951897i | \(0.400869\pi\) | |||||||
\(80\) | −87.5042 | − | 27.4889i | −1.09380 | − | 0.343611i | ||||
\(81\) | 23.5270 | + | 40.7499i | 0.290456 | + | 0.503085i | ||||
\(82\) | −0.832178 | − | 15.1693i | −0.0101485 | − | 0.184992i | ||||
\(83\) | −79.2706 | −0.955067 | −0.477534 | − | 0.878614i | \(-0.658469\pi\) | ||||
−0.477534 | + | 0.878614i | \(0.658469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 184.988i | 2.17633i | ||||||||
\(86\) | 2.28396 | + | 41.6331i | 0.0265577 | + | 0.484106i | ||||
\(87\) | −13.0214 | + | 7.51793i | −0.149672 | + | 0.0864130i | ||||
\(88\) | −8.65611 | + | 7.11531i | −0.0983649 | + | 0.0808558i | ||||
\(89\) | 1.33039 | − | 2.30431i | 0.0149482 | − | 0.0258911i | −0.858455 | − | 0.512890i | \(-0.828575\pi\) |
0.873403 | + | 0.486999i | \(0.161908\pi\) | |||||||
\(90\) | −74.3473 | − | 113.874i | −0.826081 | − | 1.26527i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −58.1880 | − | 25.5669i | −0.632479 | − | 0.277901i | ||||
\(93\) | 89.6741 | + | 51.7734i | 0.964238 | + | 0.556703i | ||||
\(94\) | −19.5530 | + | 38.6079i | −0.208010 | + | 0.410722i | ||||
\(95\) | −62.3913 | + | 36.0216i | −0.656751 | + | 0.379175i | ||||
\(96\) | 102.079 | − | 104.605i | 1.06333 | − | 1.08964i | ||||
\(97\) | 52.0930 | 0.537042 | 0.268521 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268521 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.6142 | −0.167820 | ||||||||
\(100\) | −18.6084 | − | 25.3506i | −0.186084 | − | 0.253506i | ||||
\(101\) | 79.2189 | − | 45.7371i | 0.784346 | − | 0.452842i | −0.0536223 | − | 0.998561i | \(-0.517077\pi\) |
0.837968 | + | 0.545719i | \(0.183743\pi\) | |||||||
\(102\) | −262.980 | − | 133.187i | −2.57824 | − | 1.30575i | ||||
\(103\) | −34.4584 | − | 19.8946i | −0.334548 | − | 0.193151i | 0.323311 | − | 0.946293i | \(-0.395204\pi\) |
−0.657858 | + | 0.753142i | \(0.728537\pi\) | |||||||
\(104\) | 150.598 | − | 24.9858i | 1.44806 | − | 0.240248i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.389971 | + | 0.597301i | 0.00367897 | + | 0.00563492i | ||||
\(107\) | −41.3316 | + | 71.5884i | −0.386276 | + | 0.669050i | −0.991945 | − | 0.126667i | \(-0.959572\pi\) |
0.605669 | + | 0.795717i | \(0.292906\pi\) | |||||||
\(108\) | 51.9710 | − | 5.71939i | 0.481213 | − | 0.0529573i | ||||
\(109\) | 25.5234 | − | 14.7359i | 0.234160 | − | 0.135192i | −0.378330 | − | 0.925671i | \(-0.623501\pi\) |
0.612490 | + | 0.790479i | \(0.290168\pi\) | |||||||
\(110\) | −16.0344 | + | 0.879633i | −0.145767 | + | 0.00799666i | ||||
\(111\) | − | 247.346i | − | 2.22834i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 159.133 | 1.40826 | 0.704130 | − | 0.710071i | \(-0.251337\pi\) | ||||
0.704130 | + | 0.710071i | \(0.251337\pi\) | |||||||
\(114\) | −6.28856 | − | 114.631i | −0.0551628 | − | 1.00553i | ||||
\(115\) | −45.5428 | − | 78.8825i | −0.396025 | − | 0.685935i | ||||
\(116\) | −1.44041 | − | 13.0887i | −0.0124174 | − | 0.112834i | ||||
\(117\) | 196.023 | + | 113.174i | 1.67541 | + | 0.967299i | ||||
\(118\) | 44.9789 | − | 29.3662i | 0.381177 | − | 0.248866i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 206.640 | − | 34.2838i | 1.72200 | − | 0.285698i | ||||
\(121\) | 59.5191 | − | 103.090i | 0.491893 | − | 0.851984i | ||||
\(122\) | −77.9182 | + | 153.852i | −0.638674 | + | 1.26108i | ||||
\(123\) | 17.3474 | + | 30.0466i | 0.141036 | + | 0.244281i | ||||
\(124\) | −73.1017 | + | 53.6595i | −0.589530 | + | 0.432738i | ||||
\(125\) | 98.2451i | 0.785961i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.0834i | − | 0.126641i | −0.997993 | − | 0.0633205i | \(-0.979831\pi\) | ||
0.997993 | − | 0.0633205i | \(-0.0201690\pi\) | |||||||
\(128\) | 47.9090 | + | 118.696i | 0.374289 | + | 0.927312i | ||||
\(129\) | −47.6110 | − | 82.4646i | −0.369077 | − | 0.639260i | ||||
\(130\) | 195.174 | + | 98.8459i | 1.50134 | + | 0.760353i | ||||
\(131\) | −59.0678 | + | 102.308i | −0.450899 | + | 0.780981i | −0.998442 | − | 0.0557972i | \(-0.982230\pi\) |
0.547543 | + | 0.836778i | \(0.315563\pi\) | |||||||
\(132\) | 10.2938 | − | 23.4279i | 0.0779836 | − | 0.177484i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −191.788 | + | 125.216i | −1.43125 | + | 0.934448i | ||||
\(135\) | 64.8920 | + | 37.4654i | 0.480681 | + | 0.277522i | ||||
\(136\) | 199.431 | − | 163.932i | 1.46640 | − | 1.20538i | ||||
\(137\) | 9.58539 | + | 16.6024i | 0.0699664 | + | 0.121185i | 0.898886 | − | 0.438182i | \(-0.144377\pi\) |
−0.828920 | + | 0.559367i | \(0.811044\pi\) | |||||||
\(138\) | 144.930 | − | 7.95074i | 1.05022 | − | 0.0576141i | ||||
\(139\) | −104.954 | −0.755062 | −0.377531 | − | 0.925997i | \(-0.623227\pi\) | ||||
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 98.8329i | − | 0.700942i | ||||||
\(142\) | 209.269 | − | 11.4803i | 1.47372 | − | 0.0808473i | ||||
\(143\) | 23.1465 | − | 13.3636i | 0.161864 | − | 0.0934520i | ||||
\(144\) | −56.8803 | + | 181.065i | −0.395002 | + | 1.25739i | ||||
\(145\) | 9.43556 | − | 16.3429i | 0.0650729 | − | 0.112709i | ||||
\(146\) | −40.8577 | + | 26.6755i | −0.279847 | + | 0.182709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 198.316 | + | 87.1367i | 1.33997 | + | 0.588762i | ||||
\(149\) | −71.3523 | − | 41.1953i | −0.478875 | − | 0.276478i | 0.241073 | − | 0.970507i | \(-0.422501\pi\) |
−0.719947 | + | 0.694029i | \(0.755834\pi\) | |||||||
\(150\) | 64.0690 | + | 32.4478i | 0.427127 | + | 0.216318i | ||||
\(151\) | 50.0038 | − | 28.8697i | 0.331151 | − | 0.191190i | −0.325201 | − | 0.945645i | \(-0.605432\pi\) |
0.656352 | + | 0.754455i | \(0.272099\pi\) | |||||||
\(152\) | 94.1237 | + | 35.3410i | 0.619235 | + | 0.232506i | ||||
\(153\) | 382.779 | 2.50182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −129.959 | −0.838445 | ||||||||
\(156\) | −281.041 | + | 206.295i | −1.80154 | + | 1.32240i | ||||
\(157\) | 3.23006 | − | 1.86488i | 0.0205736 | − | 0.0118782i | −0.489678 | − | 0.871903i | \(-0.662886\pi\) |
0.510252 | + | 0.860025i | \(0.329552\pi\) | |||||||
\(158\) | 105.839 | − | 208.983i | 0.669869 | − | 1.32268i | ||||
\(159\) | −1.41081 | − | 0.814534i | −0.00887305 | − | 0.00512286i | ||||
\(160\) | −45.3088 | + | 177.757i | −0.283180 | + | 1.11098i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 78.8000 | − | 51.4476i | 0.486420 | − | 0.317578i | ||||
\(163\) | −38.8534 | + | 67.2961i | −0.238365 | + | 0.412860i | −0.960245 | − | 0.279158i | \(-0.909945\pi\) |
0.721881 | + | 0.692018i | \(0.243278\pi\) | |||||||
\(164\) | −30.2019 | + | 3.32371i | −0.184158 | + | 0.0202665i | ||||
\(165\) | 31.7600 | − | 18.3367i | 0.192485 | − | 0.111131i | ||||
\(166\) | 8.68439 | + | 158.303i | 0.0523156 | + | 0.953633i | ||||
\(167\) | 62.0837i | 0.371759i | 0.982573 | + | 0.185879i | \(0.0595133\pi\) | ||||
−0.982573 | + | 0.185879i | \(0.940487\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −195.127 | −1.15459 | ||||||||
\(170\) | 369.420 | − | 20.2661i | 2.17306 | − | 0.119212i | ||||
\(171\) | 74.5364 | + | 129.101i | 0.435885 | + | 0.754976i | ||||
\(172\) | 82.8909 | − | 9.12212i | 0.481924 | − | 0.0530356i | ||||
\(173\) | 169.407 | + | 97.8069i | 0.979228 | + | 0.565358i | 0.902037 | − | 0.431659i | \(-0.142071\pi\) |
0.0771913 | + | 0.997016i | \(0.475405\pi\) | |||||||
\(174\) | 16.4398 | + | 25.1801i | 0.0944818 | + | 0.144713i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.1576 | + | 16.5067i | 0.0861225 | + | 0.0937882i | ||||
\(177\) | −61.3373 | + | 106.239i | −0.346538 | + | 0.600222i | ||||
\(178\) | −4.74744 | − | 2.40434i | −0.0266710 | − | 0.0135075i | ||||
\(179\) | −36.1049 | − | 62.5356i | −0.201704 | − | 0.349361i | 0.747374 | − | 0.664404i | \(-0.231314\pi\) |
−0.949077 | + | 0.315043i | \(0.897981\pi\) | |||||||
\(180\) | −219.262 | + | 160.947i | −1.21812 | + | 0.894149i | ||||
\(181\) | − | 140.980i | − | 0.778895i | −0.921049 | − | 0.389448i | \(-0.872666\pi\) | ||
0.921049 | − | 0.389448i | \(-0.127334\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 393.847i | − | 2.15217i | ||||||
\(184\) | −44.6822 | + | 119.002i | −0.242838 | + | 0.646752i | ||||
\(185\) | 155.219 | + | 268.847i | 0.839020 | + | 1.45323i | ||||
\(186\) | 93.5672 | − | 184.751i | 0.503049 | − | 0.993285i | ||||
\(187\) | 22.5994 | − | 39.1432i | 0.120852 | − | 0.209322i | ||||
\(188\) | 79.2419 | + | 34.8176i | 0.421499 | + | 0.185200i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 78.7703 | + | 120.649i | 0.414581 | + | 0.634995i | ||||
\(191\) | −246.361 | − | 142.236i | −1.28985 | − | 0.744693i | −0.311219 | − | 0.950338i | \(-0.600737\pi\) |
−0.978627 | + | 0.205645i | \(0.934071\pi\) | |||||||
\(192\) | −220.080 | − | 192.392i | −1.14625 | − | 1.00204i | ||||
\(193\) | 61.9251 | + | 107.257i | 0.320855 | + | 0.555738i | 0.980665 | − | 0.195695i | \(-0.0626964\pi\) |
−0.659810 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(194\) | −5.70699 | − | 104.030i | −0.0294175 | − | 0.536235i | ||||
\(195\) | −499.629 | −2.56220 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 108.098i | − | 0.548721i | −0.961627 | − | 0.274361i | \(-0.911534\pi\) | ||
0.961627 | − | 0.274361i | \(-0.0884662\pi\) | |||||||
\(198\) | 1.82015 | + | 33.1785i | 0.00919266 | + | 0.167568i | ||||
\(199\) | 287.394 | − | 165.927i | 1.44419 | − | 0.833804i | 0.446065 | − | 0.895000i | \(-0.352825\pi\) |
0.998126 | + | 0.0611961i | \(0.0194915\pi\) | |||||||
\(200\) | −48.5865 | + | 39.9381i | −0.242933 | + | 0.199690i | ||||
\(201\) | 261.539 | − | 452.999i | 1.30119 | − | 2.25373i | ||||
\(202\) | −100.016 | − | 153.189i | −0.495127 | − | 0.758363i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −237.163 | + | 539.762i | −1.16256 | + | 2.64589i | ||||
\(205\) | −37.7107 | − | 21.7723i | −0.183955 | − | 0.106206i | ||||
\(206\) | −35.9543 | + | 70.9928i | −0.174536 | + | 0.344625i | ||||
\(207\) | −163.225 | + | 94.2378i | −0.788525 | + | 0.455255i | ||||
\(208\) | −66.3952 | − | 298.007i | −0.319208 | − | 1.43273i | ||||
\(209\) | 17.6026 | 0.0842229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.3950 | 0.125095 | 0.0625475 | − | 0.998042i | \(-0.480078\pi\) | ||||
0.0625475 | + | 0.998042i | \(0.480078\pi\) | |||||||
\(212\) | 1.15009 | − | 0.844208i | 0.00542494 | − | 0.00398211i | ||||
\(213\) | −414.508 | + | 239.316i | −1.94605 | + | 1.12355i | ||||
\(214\) | 147.490 | + | 74.6962i | 0.689205 | + | 0.349048i | ||||
\(215\) | 103.499 | + | 59.7553i | 0.481392 | + | 0.277932i | ||||
\(216\) | −17.1152 | − | 103.159i | −0.0792371 | − | 0.477589i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −32.2238 | − | 49.3558i | −0.147816 | − | 0.226403i | ||||
\(219\) | 55.7172 | − | 96.5051i | 0.254417 | − | 0.440663i | ||||
\(220\) | 3.51325 | + | 31.9242i | 0.0159693 | + | 0.145110i | ||||
\(221\) | −533.279 | + | 307.889i | −2.41303 | + | 1.39316i | ||||
\(222\) | −493.949 | + | 27.0976i | −2.22499 | + | 0.122061i | ||||
\(223\) | − | 161.183i | − | 0.722796i | −0.932412 | − | 0.361398i | \(-0.882300\pi\) | ||
0.932412 | − | 0.361398i | \(-0.117700\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −93.2551 | −0.414467 | ||||||||
\(226\) | −17.4337 | − | 317.789i | −0.0771401 | − | 1.40615i | ||||
\(227\) | −85.6395 | − | 148.332i | −0.377266 | − | 0.653445i | 0.613397 | − | 0.789775i | \(-0.289803\pi\) |
−0.990663 | + | 0.136330i | \(0.956469\pi\) | |||||||
\(228\) | −228.228 | + | 25.1165i | −1.00100 | + | 0.110160i | ||||
\(229\) | −198.537 | − | 114.626i | −0.866975 | − | 0.500548i | −0.000632973 | − | 1.00000i | \(-0.500201\pi\) |
−0.866342 | + | 0.499452i | \(0.833535\pi\) | |||||||
\(230\) | −152.539 | + | 99.5908i | −0.663212 | + | 0.433003i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.9804 | + | 4.31042i | −0.111984 | + | 0.0185794i | ||||
\(233\) | 135.077 | − | 233.961i | 0.579730 | − | 1.00412i | −0.415780 | − | 0.909465i | \(-0.636491\pi\) |
0.995510 | − | 0.0946571i | \(-0.0301755\pi\) | |||||||
\(234\) | 204.533 | − | 403.856i | 0.874073 | − | 1.72588i | ||||
\(235\) | 62.0214 | + | 107.424i | 0.263921 | + | 0.457124i | ||||
\(236\) | −63.5718 | − | 86.6056i | −0.269372 | − | 0.366973i | ||||
\(237\) | 534.978i | 2.25729i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 157.155i | 0.657551i | 0.944408 | + | 0.328776i | \(0.106636\pi\) | ||||
−0.944408 | + | 0.328776i | \(0.893364\pi\) | |||||||
\(240\) | −91.1029 | − | 408.904i | −0.379595 | − | 1.70377i | ||||
\(241\) | −48.8562 | − | 84.6214i | −0.202723 | − | 0.351126i | 0.746682 | − | 0.665181i | \(-0.231646\pi\) |
−0.949405 | + | 0.314055i | \(0.898312\pi\) | |||||||
\(242\) | −212.391 | − | 107.566i | −0.877649 | − | 0.444486i | ||||
\(243\) | −166.279 | + | 288.004i | −0.684276 | + | 1.18520i | ||||
\(244\) | 315.778 | + | 138.747i | 1.29417 | + | 0.568637i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 58.1025 | − | 37.9345i | 0.236189 | − | 0.154205i | ||||
\(247\) | −207.685 | − | 119.907i | −0.840829 | − | 0.485453i | ||||
\(248\) | 115.166 | + | 140.105i | 0.464381 | + | 0.564941i | ||||
\(249\) | −181.033 | − | 313.558i | −0.727040 | − | 1.25927i | ||||
\(250\) | 196.195 | − | 10.7631i | 0.784781 | − | 0.0430525i | ||||
\(251\) | 313.145 | 1.24759 | 0.623796 | − | 0.781587i | \(-0.285590\pi\) | ||||
0.623796 | + | 0.781587i | \(0.285590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.2553i | 0.0879655i | ||||||||
\(254\) | −32.1185 | + | 1.76200i | −0.126451 | + | 0.00693700i | ||||
\(255\) | −731.728 | + | 422.463i | −2.86952 | + | 1.65672i | ||||
\(256\) | 231.787 | − | 108.678i | 0.905417 | − | 0.424523i | ||||
\(257\) | −174.428 | + | 302.118i | −0.678707 | + | 1.17555i | 0.296664 | + | 0.954982i | \(0.404126\pi\) |
−0.975371 | + | 0.220573i | \(0.929207\pi\) | |||||||
\(258\) | −159.466 | + | 104.113i | −0.618084 | + | 0.403540i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 176.013 | − | 400.591i | 0.676973 | − | 1.54073i | ||||
\(261\) | −33.8169 | − | 19.5242i | −0.129567 | − | 0.0748053i | ||||
\(262\) | 210.781 | + | 106.750i | 0.804507 | + | 0.407443i | ||||
\(263\) | 332.869 | − | 192.182i | 1.26566 | − | 0.730729i | 0.291496 | − | 0.956572i | \(-0.405847\pi\) |
0.974164 | + | 0.225843i | \(0.0725135\pi\) | |||||||
\(264\) | −47.9132 | − | 17.9901i | −0.181489 | − | 0.0681445i | ||||
\(265\) | 2.04460 | 0.00771548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1530 | 0.0455170 | ||||||||
\(268\) | 271.067 | + | 369.282i | 1.01145 | + | 1.37792i | ||||
\(269\) | −32.7022 | + | 18.8806i | −0.121570 | + | 0.0701882i | −0.559552 | − | 0.828795i | \(-0.689027\pi\) |
0.437982 | + | 0.898984i | \(0.355693\pi\) | |||||||
\(270\) | 67.7092 | − | 133.694i | 0.250775 | − | 0.495161i | ||||
\(271\) | −267.368 | − | 154.365i | −0.986597 | − | 0.569612i | −0.0823420 | − | 0.996604i | \(-0.526240\pi\) |
−0.904255 | + | 0.426992i | \(0.859573\pi\) | |||||||
\(272\) | −349.219 | − | 380.303i | −1.28389 | − | 1.39817i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.1048 | − | 20.9609i | 0.117171 | − | 0.0764995i | ||||
\(275\) | −5.50580 | + | 9.53633i | −0.0200211 | + | 0.0346775i | ||||
\(276\) | −31.7552 | − | 288.553i | −0.115055 | − | 1.04548i | ||||
\(277\) | 211.492 | − | 122.105i | 0.763508 | − | 0.440812i | −0.0670458 | − | 0.997750i | \(-0.521357\pi\) |
0.830554 | + | 0.556938i | \(0.188024\pi\) | |||||||
\(278\) | 11.4981 | + | 209.592i | 0.0413600 | + | 0.753929i | ||||
\(279\) | 268.913i | 0.963845i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 266.569 | 0.948646 | 0.474323 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474323 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(282\) | −197.369 | + | 10.8275i | −0.699890 | + | 0.0383954i | ||||
\(283\) | 82.8026 | + | 143.418i | 0.292589 | + | 0.506778i | 0.974421 | − | 0.224730i | \(-0.0721501\pi\) |
−0.681833 | + | 0.731508i | \(0.738817\pi\) | |||||||
\(284\) | −45.8523 | − | 416.651i | −0.161452 | − | 1.46708i | ||||
\(285\) | −284.971 | − | 164.528i | −0.999897 | − | 0.577291i | ||||
\(286\) | −29.2229 | − | 44.7595i | −0.102178 | − | 0.156502i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 367.817 | + | 93.7535i | 1.27714 | + | 0.325533i | ||||
\(289\) | −376.173 | + | 651.550i | −1.30164 | + | 2.25450i | ||||
\(290\) | −33.6704 | − | 17.0524i | −0.116105 | − | 0.0588013i | ||||
\(291\) | 118.967 | + | 206.056i | 0.408820 | + | 0.708098i | ||||
\(292\) | 57.7471 | + | 78.6703i | 0.197764 | + | 0.269419i | ||||
\(293\) | − | 34.3652i | − | 0.117288i | −0.998279 | − | 0.0586438i | \(-0.981322\pi\) | ||
0.998279 | − | 0.0586438i | \(-0.0186776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 153.966i | − | 0.521918i | ||||||
\(296\) | 152.286 | − | 405.583i | 0.514478 | − | 1.37021i | ||||
\(297\) | −9.15405 | − | 15.8553i | −0.0308217 | − | 0.0533848i | ||||
\(298\) | −74.4500 | + | 147.004i | −0.249832 | + | 0.493300i | ||||
\(299\) | 151.600 | − | 262.580i | 0.507025 | − | 0.878193i | ||||
\(300\) | 57.7791 | − | 131.500i | 0.192597 | − | 0.438335i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −63.1309 | − | 96.6947i | −0.209043 | − | 0.320181i | ||||
\(303\) | 361.830 | + | 208.903i | 1.19416 | + | 0.689448i | ||||
\(304\) | 60.2642 | − | 191.836i | 0.198237 | − | 0.631041i | ||||
\(305\) | 247.154 | + | 428.083i | 0.810341 | + | 1.40355i | ||||
\(306\) | −41.9349 | − | 764.408i | −0.137042 | − | 2.49807i | ||||
\(307\) | 222.934 | 0.726170 | 0.363085 | − | 0.931756i | \(-0.381724\pi\) | ||||
0.363085 | + | 0.931756i | \(0.381724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 181.736i | − | 0.588141i | ||||||
\(310\) | 14.2375 | + | 259.528i | 0.0459274 | + | 0.837186i | ||||
\(311\) | −363.673 | + | 209.967i | −1.16937 | + | 0.675135i | −0.953531 | − | 0.301294i | \(-0.902581\pi\) |
−0.215837 | + | 0.976429i | \(0.569248\pi\) | |||||||
\(312\) | 442.759 | + | 538.637i | 1.41910 | + | 1.72640i | ||||
\(313\) | −146.934 | + | 254.498i | −0.469439 | + | 0.813092i | −0.999390 | − | 0.0349363i | \(-0.988877\pi\) |
0.529950 | + | 0.848029i | \(0.322211\pi\) | |||||||
\(314\) | −4.07802 | − | 6.24612i | −0.0129873 | − | 0.0198921i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −428.933 | − | 188.466i | −1.35738 | − | 0.596411i | ||||
\(317\) | −366.728 | − | 211.730i | −1.15687 | − | 0.667919i | −0.206318 | − | 0.978485i | \(-0.566148\pi\) |
−0.950552 | + | 0.310566i | \(0.899481\pi\) | |||||||
\(318\) | −1.47206 | + | 2.90663i | −0.00462913 | + | 0.00914034i | ||||
\(319\) | −3.99311 | + | 2.30542i | −0.0125176 | + | 0.00722703i | ||||
\(320\) | 359.944 | + | 71.0076i | 1.12483 | + | 0.221899i | ||||
\(321\) | −377.561 | −1.17620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −405.551 | −1.25558 | ||||||||
\(324\) | −111.374 | − | 151.727i | −0.343745 | − | 0.468293i | ||||
\(325\) | 129.921 | − | 75.0098i | 0.399756 | − | 0.230799i | ||||
\(326\) | 138.647 | + | 70.2177i | 0.425297 | + | 0.215392i | ||||
\(327\) | 116.577 | + | 67.3060i | 0.356506 | + | 0.205829i | ||||
\(328\) | 9.94618 | + | 59.9491i | 0.0303237 | + | 0.182772i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −40.0977 | − | 61.4158i | −0.121508 | − | 0.186109i | ||||
\(331\) | 63.3332 | − | 109.696i | 0.191339 | − | 0.331409i | −0.754355 | − | 0.656467i | \(-0.772050\pi\) |
0.945694 | + | 0.325057i | \(0.105384\pi\) | |||||||
\(332\) | 315.179 | − | 34.6854i | 0.949336 | − | 0.104474i | ||||
\(333\) | 556.301 | − | 321.180i | 1.67057 | − | 0.964505i | ||||
\(334\) | 123.981 | − | 6.80150i | 0.371200 | − | 0.0203638i | ||||
\(335\) | 656.503i | 1.95971i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 302.404 | 0.897341 | 0.448671 | − | 0.893697i | \(-0.351898\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351898\pi\) | |||||||
\(338\) | 21.3768 | + | 389.667i | 0.0632451 | + | 1.15286i | ||||
\(339\) | 363.419 | + | 629.460i | 1.07203 | + | 1.85681i | ||||
\(340\) | −80.9427 | − | 735.511i | −0.238067 | − | 2.16327i | ||||
\(341\) | 27.4992 | + | 15.8767i | 0.0806428 | + | 0.0465591i | ||||
\(342\) | 249.648 | − | 162.992i | 0.729966 | − | 0.476586i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −27.2979 | − | 164.534i | −0.0793542 | − | 0.478295i | ||||
\(345\) | 208.016 | − | 360.294i | 0.602944 | − | 1.04433i | ||||
\(346\) | 176.761 | − | 349.019i | 0.510870 | − | 1.00873i | ||||
\(347\) | −160.266 | − | 277.589i | −0.461862 | − | 0.799969i | 0.537192 | − | 0.843460i | \(-0.319485\pi\) |
−0.999054 | + | 0.0434916i | \(0.986152\pi\) | |||||||
\(348\) | 48.4836 | − | 35.5889i | 0.139321 | − | 0.102267i | ||||
\(349\) | − | 380.678i | − | 1.09077i | −0.838186 | − | 0.545385i | \(-0.816384\pi\) | ||
0.838186 | − | 0.545385i | \(-0.183616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 249.426i | 0.710614i | ||||||||
\(352\) | 31.3033 | − | 32.0780i | 0.0889298 | − | 0.0911307i | ||||
\(353\) | −182.185 | − | 315.553i | −0.516104 | − | 0.893918i | −0.999825 | − | 0.0186962i | \(-0.994048\pi\) |
0.483721 | − | 0.875222i | \(-0.339285\pi\) | |||||||
\(354\) | 218.879 | + | 110.852i | 0.618303 | + | 0.313140i | ||||
\(355\) | 300.360 | − | 520.239i | 0.846085 | − | 1.46546i | ||||
\(356\) | −4.28137 | + | 9.74403i | −0.0120263 | + | 0.0273709i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −120.928 | + | 78.9525i | −0.337788 | + | 0.220538i | ||||
\(359\) | −96.9908 | − | 55.9977i | −0.270169 | − | 0.155982i | 0.358795 | − | 0.933416i | \(-0.383188\pi\) |
−0.628965 | + | 0.777434i | \(0.716521\pi\) | |||||||
\(360\) | 345.431 | + | 420.233i | 0.959531 | + | 1.16731i | ||||
\(361\) | 101.529 | + | 175.854i | 0.281245 | + | 0.487130i | ||||
\(362\) | −281.537 | + | 15.4449i | −0.777726 | + | 0.0426655i | ||||
\(363\) | 543.704 | 1.49781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 139.859i | 0.383174i | ||||||||
\(366\) | −786.512 | + | 43.1475i | −2.14894 | + | 0.117889i | ||||
\(367\) | 380.222 | − | 219.521i | 1.03603 | − | 0.598150i | 0.117321 | − | 0.993094i | \(-0.462569\pi\) |
0.918705 | + | 0.394944i | \(0.129236\pi\) | |||||||
\(368\) | 242.542 | + | 76.1931i | 0.659082 | + | 0.207047i | ||||
\(369\) | −45.0515 | + | 78.0315i | −0.122091 | + | 0.211468i | ||||
\(370\) | 519.881 | − | 339.424i | 1.40508 | − | 0.917363i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −379.198 | − | 166.613i | −1.01935 | − | 0.447885i | ||||
\(373\) | 220.833 | + | 127.498i | 0.592047 | + | 0.341818i | 0.765906 | − | 0.642952i | \(-0.222291\pi\) |
−0.173860 | + | 0.984770i | \(0.555624\pi\) | |||||||
\(374\) | −80.6448 | − | 40.8426i | −0.215628 | − | 0.109205i | ||||
\(375\) | −388.613 | + | 224.366i | −1.03630 | + | 0.598309i | ||||
\(376\) | 60.8493 | − | 162.060i | 0.161833 | − | 0.431011i | ||||
\(377\) | 62.8172 | 0.166624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 603.048 | 1.59116 | 0.795578 | − | 0.605852i | \(-0.207167\pi\) | ||||
0.795578 | + | 0.605852i | \(0.207167\pi\) | |||||||
\(380\) | 232.306 | − | 170.522i | 0.611332 | − | 0.448741i | ||||
\(381\) | 63.6187 | − | 36.7303i | 0.166978 | − | 0.0964049i | ||||
\(382\) | −257.056 | + | 507.564i | −0.672921 | + | 1.32870i | ||||
\(383\) | −63.5537 | − | 36.6927i | −0.165937 | − | 0.0958035i | 0.414732 | − | 0.909944i | \(-0.363875\pi\) |
−0.580668 | + | 0.814140i | \(0.697209\pi\) | |||||||
\(384\) | −360.096 | + | 460.577i | −0.937749 | + | 1.19942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 207.408 | − | 135.415i | 0.537328 | − | 0.350815i | ||||
\(387\) | 123.646 | − | 214.162i | 0.319500 | − | 0.553390i | ||||
\(388\) | −207.122 | + | 22.7937i | −0.533819 | + | 0.0587466i | ||||
\(389\) | −295.141 | + | 170.400i | −0.758718 | + | 0.438046i | −0.828835 | − | 0.559493i | \(-0.810996\pi\) |
0.0701174 | + | 0.997539i | \(0.477663\pi\) | |||||||
\(390\) | 54.7362 | + | 997.758i | 0.140349 | + | 2.55835i | ||||
\(391\) | − | 512.745i | − | 1.31137i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −539.581 | −1.37298 | ||||||||
\(394\) | −215.872 | + | 11.8426i | −0.547898 | + | 0.0300572i | ||||
\(395\) | −335.719 | − | 581.482i | −0.849921 | − | 1.47211i | ||||
\(396\) | 66.0579 | − | 7.26966i | 0.166813 | − | 0.0183577i | ||||
\(397\) | 96.5963 | + | 55.7699i | 0.243316 | + | 0.140478i | 0.616700 | − | 0.787199i | \(-0.288469\pi\) |
−0.373384 | + | 0.927677i | \(0.621803\pi\) | |||||||
\(398\) | −362.841 | − | 555.747i | −0.911661 | − | 1.39635i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 85.0791 | + | 92.6518i | 0.212698 | + | 0.231630i | ||||
\(401\) | −170.268 | + | 294.912i | −0.424607 | + | 0.735441i | −0.996384 | − | 0.0849681i | \(-0.972921\pi\) |
0.571776 | + | 0.820410i | \(0.306254\pi\) | |||||||
\(402\) | −933.291 | − | 472.665i | −2.32162 | − | 1.17578i | ||||
\(403\) | −216.300 | − | 374.643i | −0.536725 | − | 0.929635i | ||||
\(404\) | −294.962 | + | 216.513i | −0.730103 | + | 0.535924i | ||||
\(405\) | − | 269.738i | − | 0.666019i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 75.8502i | − | 0.186364i | ||||||
\(408\) | 1103.89 | + | 414.480i | 2.70560 | + | 1.01588i | ||||
\(409\) | 333.480 | + | 577.604i | 0.815354 | + | 1.41223i | 0.909074 | + | 0.416635i | \(0.136791\pi\) |
−0.0937202 | + | 0.995599i | \(0.529876\pi\) | |||||||
\(410\) | −39.3479 | + | 77.6935i | −0.0959705 | + | 0.189496i | ||||
\(411\) | −43.7810 | + | 75.8309i | −0.106523 | + | 0.184503i | ||||
\(412\) | 145.711 | + | 64.0232i | 0.353669 | + | 0.155396i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 206.074 | + | 315.635i | 0.497764 | + | 0.762403i | ||||
\(415\) | 393.539 | + | 227.210i | 0.948288 | + | 0.547494i | ||||
\(416\) | −587.845 | + | 165.239i | −1.41309 | + | 0.397209i | ||||
\(417\) | −239.686 | − | 415.149i | −0.574788 | − | 0.995561i | ||||
\(418\) | −1.92843 | − | 35.1523i | −0.00461347 | − | 0.0840965i | ||||
\(419\) | 200.191 | 0.477783 | 0.238891 | − | 0.971046i | \(-0.423216\pi\) | ||||
0.238891 | + | 0.971046i | \(0.423216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9136i | 0.0377996i | 0.999821 | + | 0.0188998i | \(0.00601636\pi\) | ||||
−0.999821 | + | 0.0188998i | \(0.993984\pi\) | |||||||
\(422\) | −2.89167 | − | 52.7108i | −0.00685231 | − | 0.124907i | ||||
\(423\) | 222.283 | − | 128.335i | 0.525492 | − | 0.303393i | ||||
\(424\) | −1.81188 | − | 2.20423i | −0.00427330 | − | 0.00519866i | ||||
\(425\) | 126.850 | − | 219.710i | 0.298470 | − | 0.516965i | ||||
\(426\) | 523.325 | + | 801.554i | 1.22846 | + | 1.88158i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 133.010 | − | 302.720i | 0.310771 | − | 0.707290i | ||||
\(429\) | 105.721 | + | 61.0380i | 0.246436 | + | 0.142280i | ||||
\(430\) | 107.993 | − | 213.234i | 0.251145 | − | 0.495893i | ||||
\(431\) | −543.875 | + | 314.006i | −1.26189 | + | 0.728553i | −0.973440 | − | 0.228941i | \(-0.926474\pi\) |
−0.288451 | + | 0.957495i | \(0.593140\pi\) | |||||||
\(432\) | −204.134 | + | 45.4805i | −0.472532 | + | 0.105279i | ||||
\(433\) | −789.232 | −1.82271 | −0.911353 | − | 0.411625i | \(-0.864961\pi\) | ||||
−0.911353 | + | 0.411625i | \(0.864961\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 86.1933 | 0.198146 | ||||||||
\(436\) | −95.0331 | + | 69.7580i | −0.217966 | + | 0.159995i | ||||
\(437\) | 172.935 | − | 99.8441i | 0.395732 | − | 0.228476i | ||||
\(438\) | −198.824 | − | 100.695i | −0.453937 | − | 0.229897i | ||||
\(439\) | 576.400 | + | 332.785i | 1.31298 | + | 0.758052i | 0.982589 | − | 0.185791i | \(-0.0594846\pi\) |
0.330395 | + | 0.943843i | \(0.392818\pi\) | |||||||
\(440\) | 63.3677 | − | 10.5134i | 0.144017 | − | 0.0238940i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 673.275 | + | 1031.23i | 1.52325 | + | 2.33309i | ||||
\(443\) | −253.576 | + | 439.206i | −0.572406 | + | 0.991436i | 0.423912 | + | 0.905703i | \(0.360656\pi\) |
−0.996318 | + | 0.0857327i | \(0.972677\pi\) | |||||||
\(444\) | 108.228 | + | 983.445i | 0.243756 | + | 2.21497i | ||||
\(445\) | −13.2095 | + | 7.62650i | −0.0296842 | + | 0.0171382i | ||||
\(446\) | −321.883 | + | 17.6583i | −0.721711 | + | 0.0395925i | ||||
\(447\) | − | 376.317i | − | 0.841872i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −279.029 | −0.621446 | −0.310723 | − | 0.950501i | \(-0.600571\pi\) | ||||
−0.310723 | + | 0.950501i | \(0.600571\pi\) | |||||||
\(450\) | 10.2164 | + | 186.230i | 0.0227032 | + | 0.413845i | ||||
\(451\) | 5.31970 | + | 9.21400i | 0.0117954 | + | 0.0204301i | ||||
\(452\) | −632.714 | + | 69.6300i | −1.39981 | + | 0.154049i | ||||
\(453\) | 228.391 | + | 131.862i | 0.504175 | + | 0.291085i | ||||
\(454\) | −286.836 | + | 187.272i | −0.631798 | + | 0.412494i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 75.1608 | + | 453.020i | 0.164826 | + | 0.993465i | ||||
\(457\) | 360.441 | − | 624.302i | 0.788710 | − | 1.36609i | −0.138047 | − | 0.990426i | \(-0.544082\pi\) |
0.926757 | − | 0.375661i | \(-0.122584\pi\) | |||||||
\(458\) | −207.156 | + | 409.036i | −0.452306 | + | 0.893091i | ||||
\(459\) | 210.903 | + | 365.294i | 0.459483 | + | 0.795848i | ||||
\(460\) | 215.594 | + | 293.709i | 0.468682 | + | 0.638498i | ||||
\(461\) | − | 483.262i | − | 1.04829i | −0.851629 | − | 0.524145i | \(-0.824385\pi\) | ||
0.851629 | − | 0.524145i | \(-0.175615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.6326i | − | 0.0855995i | −0.999084 | − | 0.0427997i | \(-0.986372\pi\) | ||
0.999084 | − | 0.0427997i | \(-0.0136277\pi\) | |||||||
\(464\) | 11.4542 | + | 51.4106i | 0.0246857 | + | 0.110799i | ||||
\(465\) | −296.792 | − | 514.059i | −0.638262 | − | 1.10550i | ||||
\(466\) | −482.017 | − | 244.118i | −1.03437 | − | 0.523857i | ||||
\(467\) | 8.89340 | − | 15.4038i | 0.0190437 | − | 0.0329846i | −0.856347 | − | 0.516402i | \(-0.827271\pi\) |
0.875390 | + | 0.483417i | \(0.160605\pi\) | |||||||
\(468\) | −828.907 | − | 364.208i | −1.77117 | − | 0.778222i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 207.731 | − | 135.625i | 0.441981 | − | 0.288564i | ||||
\(471\) | 14.7532 | + | 8.51777i | 0.0313232 | + | 0.0180844i | ||||
\(472\) | −165.987 | + | 136.441i | −0.351666 | + | 0.289069i | ||||
\(473\) | −14.6002 | − | 25.2883i | −0.0308673 | − | 0.0534637i | ||||
\(474\) | 1068.35 | − | 58.6089i | 2.25390 | − | 0.123647i | ||||
\(475\) | 98.8029 | 0.208006 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.23072i | − | 0.00886943i | ||||||
\(478\) | 313.837 | − | 17.2169i | 0.656564 | − | 0.0360186i | ||||
\(479\) | 579.039 | − | 334.308i | 1.20885 | − | 0.697930i | 0.246341 | − | 0.969183i | \(-0.420772\pi\) |
0.962508 | + | 0.271254i | \(0.0874382\pi\) | |||||||
\(480\) | −806.600 | + | 226.729i | −1.68042 | + | 0.472353i | ||||
\(481\) | −516.683 | + | 894.922i | −1.07419 | + | 1.86054i | ||||
\(482\) | −163.636 | + | 106.836i | −0.339494 | + | 0.221652i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −191.540 | + | 435.929i | −0.395744 | + | 0.900679i | ||||
\(485\) | −258.616 | − | 149.312i | −0.533230 | − | 0.307860i | ||||
\(486\) | 593.359 | + | 300.507i | 1.22090 | + | 0.618327i | ||||
\(487\) | 362.418 | − | 209.242i | 0.744185 | − | 0.429656i | −0.0794038 | − | 0.996843i | \(-0.525302\pi\) |
0.823589 | + | 0.567187i | \(0.191968\pi\) | |||||||
\(488\) | 242.484 | − | 645.807i | 0.496893 | − | 1.32338i | ||||
\(489\) | −354.924 | −0.725816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 381.031 | 0.776030 | 0.388015 | − | 0.921653i | \(-0.373161\pi\) | ||||
0.388015 | + | 0.921653i | \(0.373161\pi\) | |||||||
\(492\) | −82.1204 | − | 111.875i | −0.166911 | − | 0.227388i | ||||
\(493\) | 91.9984 | − | 53.1153i | 0.186609 | − | 0.107739i | ||||
\(494\) | −216.701 | + | 427.882i | −0.438666 | + | 0.866158i | ||||
\(495\) | 82.4813 | + | 47.6206i | 0.166629 | + | 0.0962032i | ||||
\(496\) | 267.173 | − | 245.336i | 0.538656 | − | 0.494629i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −606.342 | + | 395.874i | −1.21756 | + | 0.794928i | ||||
\(499\) | 219.196 | − | 379.659i | 0.439271 | − | 0.760839i | −0.558363 | − | 0.829597i | \(-0.688570\pi\) |
0.997633 | + | 0.0687578i | \(0.0219036\pi\) | |||||||
\(500\) | −42.9878 | − | 390.622i | −0.0859757 | − | 0.781244i | ||||
\(501\) | −245.575 | + | 141.783i | −0.490169 | + | 0.282999i | ||||
\(502\) | −34.3063 | − | 625.351i | −0.0683392 | − | 1.24572i | ||||
\(503\) | 754.754i | 1.50050i | 0.661151 | + | 0.750252i | \(0.270068\pi\) | ||||
−0.661151 | + | 0.750252i | \(0.729932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −524.378 | −1.03837 | ||||||||
\(506\) | 44.4437 | − | 2.43815i | 0.0878334 | − | 0.00481848i | ||||
\(507\) | −445.617 | − | 771.832i | −0.878930 | − | 1.52235i | ||||
\(508\) | 7.03741 | + | 63.9476i | 0.0138532 | + | 0.125881i | ||||
\(509\) | 427.842 | + | 247.015i | 0.840554 | + | 0.485294i | 0.857452 | − | 0.514563i | \(-0.172046\pi\) |
−0.0168985 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(510\) | 923.822 | + | 1414.98i | 1.81141 | + | 2.77446i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −242.422 | − | 450.972i | −0.473481 | − | 0.880804i | ||||
\(513\) | −82.1358 | + | 142.263i | −0.160109 | + | 0.277317i | ||||
\(514\) | 622.437 | + | 315.233i | 1.21097 | + | 0.613295i | ||||
\(515\) | 114.046 | + | 197.533i | 0.221449 | + | 0.383560i | ||||
\(516\) | 225.384 | + | 307.046i | 0.436791 | + | 0.595051i | ||||
\(517\) | − | 30.3078i | − | 0.0586224i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 893.460i | 1.72150i | ||||||||
\(520\) | −819.262 | − | 307.611i | −1.57550 | − | 0.591560i | ||||
\(521\) | −16.4374 | − | 28.4704i | −0.0315496 | − | 0.0546456i | 0.849819 | − | 0.527074i | \(-0.176711\pi\) |
−0.881369 | + | 0.472428i | \(0.843378\pi\) | |||||||
\(522\) | −35.2850 | + | 69.6711i | −0.0675957 | + | 0.133470i | ||||
\(523\) | −14.1377 | + | 24.4873i | −0.0270320 | + | 0.0468208i | −0.879225 | − | 0.476407i | \(-0.841939\pi\) |
0.852193 | + | 0.523228i | \(0.175272\pi\) | |||||||
\(524\) | 190.088 | − | 432.624i | 0.362763 | − | 0.825617i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −420.254 | − | 643.684i | −0.798961 | − | 1.22373i | ||||
\(527\) | −633.561 | − | 365.787i | −1.20220 | − | 0.694093i | ||||
\(528\) | −30.6772 | + | 97.6534i | −0.0581008 | + | 0.184950i | ||||
\(529\) | −138.265 | − | 239.482i | −0.261371 | − | 0.452708i | ||||
\(530\) | −0.223994 | − | 4.08307i | −0.000422630 | − | 0.00770390i | ||||
\(531\) | −318.588 | −0.599977 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 144.949i | − | 0.271949i | ||||||
\(534\) | −1.33141 | − | 24.2696i | −0.00249328 | − | 0.0454487i | ||||
\(535\) | 410.382 | − | 236.934i | 0.767069 | − | 0.442867i | ||||
\(536\) | 707.759 | − | 581.777i | 1.32045 | − | 1.08540i | ||||
\(537\) | 164.908 | − | 285.629i | 0.307092 | − | 0.531898i | ||||
\(538\) | 41.2872 | + | 63.2378i | 0.0767420 | + | 0.117542i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −274.404 | − | 120.568i | −0.508155 | − | 0.223275i | ||||
\(541\) | 928.028 | + | 535.797i | 1.71539 | + | 0.990383i | 0.926873 | + | 0.375375i | \(0.122486\pi\) |
0.788521 | + | 0.615008i | \(0.210847\pi\) | |||||||
\(542\) | −278.975 | + | 550.844i | −0.514714 | + | 1.01632i | ||||
\(543\) | 557.653 | − | 321.961i | 1.02699 | − | 0.592930i | ||||
\(544\) | −721.205 | + | 739.054i | −1.32575 | + | 1.35855i | ||||
\(545\) | −168.948 | −0.309997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −986.888 | −1.80418 | −0.902091 | − | 0.431545i | \(-0.857968\pi\) | ||||
−0.902091 | + | 0.431545i | \(0.857968\pi\) | |||||||
\(548\) | −45.3760 | − | 61.8169i | −0.0828029 | − | 0.112805i | ||||
\(549\) | 885.795 | − | 511.414i | 1.61347 | − | 0.931537i | ||||
\(550\) | 19.6472 | + | 9.95033i | 0.0357222 | + | 0.0180915i | ||||
\(551\) | 35.8287 | + | 20.6857i | 0.0650248 | + | 0.0375421i | ||||
\(552\) | −572.761 | + | 95.0272i | −1.03761 | + | 0.172151i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −267.013 | − | 408.971i | −0.481972 | − | 0.738215i | ||||
\(555\) | −708.957 | + | 1227.95i | −1.27740 | + | 2.21252i | ||||
\(556\) | 417.295 | − | 45.9232i | 0.750531 | − | 0.0825957i | ||||
\(557\) | 418.767 | − | 241.775i | 0.751826 | − | 0.434067i | −0.0745276 | − | 0.997219i | \(-0.523745\pi\) |
0.826353 | + | 0.563152i | \(0.190412\pi\) | |||||||
\(558\) | 537.018 | − | 29.4604i | 0.962397 | − | 0.0527964i | ||||
\(559\) | 397.821i | 0.711665i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 206.444 | 0.367993 | ||||||||
\(562\) | −29.2037 | − | 532.338i | −0.0519639 | − | 0.947221i | ||||
\(563\) | 260.447 | + | 451.107i | 0.462605 | + | 0.801256i | 0.999090 | − | 0.0426543i | \(-0.0135814\pi\) |
−0.536485 | + | 0.843910i | \(0.680248\pi\) | |||||||
\(564\) | 43.2450 | + | 392.959i | 0.0766756 | + | 0.696736i | ||||
\(565\) | −790.020 | − | 456.118i | −1.39826 | − | 0.807289i | ||||
\(566\) | 277.334 | − | 181.068i | 0.489990 | − | 0.319909i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −827.028 | + | 137.213i | −1.45603 | + | 0.241572i | ||||
\(569\) | 366.480 | − | 634.761i | 0.644077 | − | 1.11557i | −0.340437 | − | 0.940267i | \(-0.610575\pi\) |
0.984514 | − | 0.175306i | \(-0.0560916\pi\) | |||||||
\(570\) | −297.342 | + | 587.110i | −0.521653 | + | 1.03002i | ||||
\(571\) | 499.792 | + | 865.665i | 0.875292 | + | 1.51605i | 0.856451 | + | 0.516228i | \(0.172664\pi\) |
0.0188408 | + | 0.999822i | \(0.494002\pi\) | |||||||
\(572\) | −86.1830 | + | 63.2617i | −0.150670 | + | 0.110597i | ||||
\(573\) | − | 1299.32i | − | 2.26758i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 124.918i | 0.217249i | ||||||||
\(576\) | 146.930 | − | 744.801i | 0.255086 | − | 1.29306i | ||||
\(577\) | 232.929 | + | 403.445i | 0.403690 | + | 0.699212i | 0.994168 | − | 0.107842i | \(-0.0343940\pi\) |
−0.590478 | + | 0.807054i | \(0.701061\pi\) | |||||||
\(578\) | 1342.36 | + | 679.836i | 2.32241 | + | 1.17619i | ||||
\(579\) | −282.841 | + | 489.895i | −0.488499 | + | 0.846105i | ||||
\(580\) | −30.3648 | + | 69.1078i | −0.0523531 | + | 0.119151i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 398.461 | − | 260.150i | 0.684641 | − | 0.446994i | ||||
\(583\) | −0.432636 | − | 0.249782i | −0.000742086 | − | 0.000428443i | ||||
\(584\) | 150.778 | − | 123.939i | 0.258181 | − | 0.212225i | ||||
\(585\) | −648.772 | − | 1123.71i | −1.10901 | − | 1.92087i | ||||
\(586\) | −68.6273 | + | 3.76484i | −0.117111 | + | 0.00642465i | ||||
\(587\) | 574.851 | 0.979303 | 0.489651 | − | 0.871918i | \(-0.337124\pi\) | ||||
0.489651 | + | 0.871918i | \(0.337124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 284.911i | − | 0.483719i | ||||||
\(590\) | −307.469 | + | 16.8675i | −0.521135 | + | 0.0285891i | ||||
\(591\) | 427.587 | − | 246.868i | 0.723498 | − | 0.417712i | ||||
\(592\) | −826.631 | − | 259.681i | −1.39634 | − | 0.438650i | ||||
\(593\) | 471.528 | − | 816.710i | 0.795156 | − | 1.37725i | −0.127584 | − | 0.991828i | \(-0.540722\pi\) |
0.922740 | − | 0.385423i | \(-0.125945\pi\) | |||||||
\(594\) | −30.6601 | + | 20.0176i | −0.0516163 | + | 0.0336997i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 301.722 | + | 132.572i | 0.506245 | + | 0.222436i | ||||
\(597\) | 1312.66 | + | 757.867i | 2.19877 | + | 1.26946i | ||||
\(598\) | −540.979 | − | 273.979i | −0.904648 | − | 0.458159i | ||||
\(599\) | −8.02545 | + | 4.63349i | −0.0133981 | + | 0.00773538i | −0.506684 | − | 0.862132i | \(-0.669129\pi\) |
0.493286 | + | 0.869867i | \(0.335796\pi\) | |||||||
\(600\) | −268.936 | − | 100.978i | −0.448226 | − | 0.168297i | ||||
\(601\) | −57.7003 | −0.0960072 | −0.0480036 | − | 0.998847i | \(-0.515286\pi\) | ||||
−0.0480036 | + | 0.998847i | \(0.515286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1358.44 | 2.25281 | ||||||||
\(604\) | −186.183 | + | 136.665i | −0.308250 | + | 0.226267i | ||||
\(605\) | −590.966 | + | 341.194i | −0.976804 | + | 0.563958i | ||||
\(606\) | 377.538 | − | 745.460i | 0.623001 | − | 1.23013i | ||||
\(607\) | 887.396 | + | 512.339i | 1.46194 | + | 0.844050i | 0.999101 | − | 0.0423930i | \(-0.0134982\pi\) |
0.462837 | + | 0.886443i | \(0.346831\pi\) | |||||||
\(608\) | −389.699 | − | 99.3310i | −0.640952 | − | 0.163373i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 827.805 | − | 540.464i | 1.35706 | − | 0.886007i | ||||
\(611\) | −206.453 | + | 357.588i | −0.337894 | + | 0.585250i | ||||
\(612\) | −1521.93 | + | 167.488i | −2.48681 | + | 0.273673i | ||||
\(613\) | 350.583 | − | 202.409i | 0.571914 | − | 0.330195i | −0.186000 | − | 0.982550i | \(-0.559552\pi\) |
0.757913 | + | 0.652355i | \(0.226219\pi\) | |||||||
\(614\) | −24.4233 | − | 445.199i | −0.0397773 | − | 0.725079i | ||||
\(615\) | − | 198.889i | − | 0.323396i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 894.209 | 1.44928 | 0.724642 | − | 0.689125i | \(-0.242005\pi\) | ||||
0.724642 | + | 0.689125i | \(0.242005\pi\) | |||||||
\(618\) | −362.926 | + | 19.9098i | −0.587258 | + | 0.0322166i | ||||
\(619\) | −389.694 | − | 674.970i | −0.629554 | − | 1.09042i | −0.987641 | − | 0.156731i | \(-0.949904\pi\) |
0.358087 | − | 0.933688i | \(-0.383429\pi\) | |||||||
\(620\) | 516.716 | − | 56.8645i | 0.833414 | − | 0.0917169i | ||||
\(621\) | −179.866 | − | 103.846i | −0.289640 | − | 0.167224i | ||||
\(622\) | 459.145 | + | 703.252i | 0.738176 | + | 1.13063i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1027.15 | − | 943.198i | 1.64607 | − | 1.51154i | ||||
\(625\) | 379.869 | − | 657.952i | 0.607790 | − | 1.05272i | ||||
\(626\) | 524.329 | + | 265.546i | 0.837586 | + | 0.424196i | ||||
\(627\) | 40.1997 | + | 69.6278i | 0.0641143 | + | 0.111049i | ||||
\(628\) | −12.0267 | + | 8.82808i | −0.0191508 | + | 0.0140574i | ||||
\(629\) | 1747.53i | 2.77827i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 780.191i | 1.23644i | 0.786007 | + | 0.618218i | \(0.212145\pi\) | ||||
−0.786007 | + | 0.618218i | \(0.787855\pi\) | |||||||
\(632\) | −329.375 | + | 877.225i | −0.521163 | + | 1.38801i | ||||
\(633\) | 60.2793 | + | 104.407i | 0.0952279 | + | 0.164940i | ||||
\(634\) | −382.648 | + | 755.550i | −0.603546 | + | 1.19172i | ||||
\(635\) | −46.0992 | + | 79.8462i | −0.0725972 | + | 0.125742i | ||||
\(636\) | 5.96580 | + | 2.62127i | 0.00938018 | + | 0.00412150i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.04139 | + | 7.72166i | 0.00790186 | + | 0.0121029i | ||||
\(639\) | −1076.48 | − | 621.509i | −1.68464 | − | 0.972627i | ||||
\(640\) | 102.369 | − | 726.587i | 0.159951 | − | 1.13529i | ||||
\(641\) | 11.6570 | + | 20.1905i | 0.0181856 | + | 0.0314984i | 0.874975 | − | 0.484168i | \(-0.160878\pi\) |
−0.856789 | + | 0.515667i | \(0.827544\pi\) | |||||||
\(642\) | 41.3633 | + | 753.989i | 0.0644288 | + | 1.17444i | ||||
\(643\) | −530.706 | −0.825360 | −0.412680 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 545.862i | 0.846297i | ||||||||
\(646\) | 44.4296 | + | 809.884i | 0.0687765 | + | 1.25369i | ||||
\(647\) | −184.840 | + | 106.717i | −0.285687 | + | 0.164942i | −0.635995 | − | 0.771693i | \(-0.719410\pi\) |
0.350308 | + | 0.936635i | \(0.386077\pi\) | |||||||
\(648\) | −290.797 | + | 239.035i | −0.448761 | + | 0.368881i | ||||
\(649\) | −18.8095 | + | 32.5790i | −0.0289823 | + | 0.0501988i | ||||
\(650\) | −164.028 | − | 251.234i | −0.252350 | − | 0.386514i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 125.035 | − | 284.570i | 0.191772 | − | 0.436457i | ||||
\(653\) | 238.048 | + | 137.437i | 0.364545 | + | 0.210470i | 0.671073 | − | 0.741392i | \(-0.265834\pi\) |
−0.306528 | + | 0.951862i | \(0.599167\pi\) | |||||||
\(654\) | 121.638 | − | 240.178i | 0.185991 | − | 0.367245i | ||||
\(655\) | 586.485 | − | 338.607i | 0.895397 | − | 0.516958i | ||||
\(656\) | 118.628 | − | 26.4301i | 0.180836 | − | 0.0402899i | ||||
\(657\) | 289.397 | 0.440483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1234.48 | 1.87327 | 0.936633 | − | 0.350313i | \(-0.113925\pi\) | ||||
0.936633 | + | 0.350313i | \(0.113925\pi\) | |||||||
\(660\) | −118.254 | + | 86.8033i | −0.179173 | + | 0.131520i | ||||
\(661\) | −504.662 | + | 291.367i | −0.763482 | + | 0.440797i | −0.830545 | − | 0.556952i | \(-0.811971\pi\) |
0.0670625 | + | 0.997749i | \(0.478637\pi\) | |||||||
\(662\) | −226.002 | − | 114.459i | −0.341392 | − | 0.172898i | ||||
\(663\) | −2435.74 | − | 1406.27i | −3.67381 | − | 2.12107i | ||||
\(664\) | −103.796 | − | 625.613i | −0.156319 | − | 0.942188i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −702.341 | − | 1075.74i | −1.05457 | − | 1.61523i | ||||
\(667\) | −26.1533 | + | 45.2989i | −0.0392104 | + | 0.0679143i | ||||
\(668\) | −27.1652 | − | 246.844i | −0.0406664 | − | 0.369528i | ||||
\(669\) | 637.569 | − | 368.101i | 0.953018 | − | 0.550225i | ||||
\(670\) | 1311.03 | − | 71.9224i | 1.95677 | − | 0.107347i | ||||
\(671\) | − | 120.776i | − | 0.179994i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −399.145 | −0.593083 | −0.296542 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296542 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(674\) | −33.1295 | − | 603.900i | −0.0491536 | − | 0.895994i | ||||
\(675\) | −51.3815 | − | 88.9953i | −0.0761207 | − | 0.131845i | ||||
\(676\) | 775.822 | − | 85.3790i | 1.14767 | − | 0.126300i | ||||
\(677\) | −653.388 | − | 377.234i | −0.965123 | − | 0.557214i | −0.0673768 | − | 0.997728i | \(-0.521463\pi\) |
−0.897746 | + | 0.440514i | \(0.854796\pi\) | |||||||
\(678\) | 1217.22 | − | 794.706i | 1.79530 | − | 1.17213i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1459.95 | + | 242.220i | −2.14698 | + | 0.356206i | ||||
\(681\) | 391.156 | − | 677.502i | 0.574384 | − | 0.994863i | ||||
\(682\) | 28.6930 | − | 56.6552i | 0.0420719 | − | 0.0830721i | ||||
\(683\) | −144.132 | − | 249.644i | −0.211028 | − | 0.365511i | 0.741009 | − | 0.671495i | \(-0.234348\pi\) |
−0.952036 | + | 0.305985i | \(0.901014\pi\) | |||||||
\(684\) | −352.845 | − | 480.690i | −0.515856 | − | 0.702764i | ||||
\(685\) | − | 109.897i | − | 0.160433i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1047.10i | − | 1.52416i | ||||||
\(688\) | −325.583 | + | 72.5390i | −0.473230 | + | 0.105435i | ||||
\(689\) | 3.40298 | + | 5.89414i | 0.00493901 | + | 0.00855462i | ||||
\(690\) | −742.294 | − | 375.935i | −1.07579 | − | 0.544833i | ||||
\(691\) | −78.3458 | + | 135.699i | −0.113380 | + | 0.196380i | −0.917131 | − | 0.398586i | \(-0.869501\pi\) |
0.803751 | + | 0.594966i | \(0.202835\pi\) | |||||||
\(692\) | −716.356 | − | 314.755i | −1.03520 | − | 0.454848i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −536.787 | + | 350.462i | −0.773468 | + | 0.504988i | ||||
\(695\) | 521.043 | + | 300.824i | 0.749703 | + | 0.432841i | ||||
\(696\) | −76.3824 | − | 92.9228i | −0.109745 | − | 0.133510i | ||||
\(697\) | −122.562 | − | 212.284i | −0.175842 | − | 0.304568i | ||||
\(698\) | −760.214 | + | 41.7048i | −1.08913 | + | 0.0597489i | ||||
\(699\) | 1233.92 | 1.76527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1126.50i | 1.60700i | 0.595307 | + | 0.803498i | \(0.297030\pi\) | ||||
−0.595307 | + | 0.803498i | \(0.702970\pi\) | |||||||
\(702\) | 498.102 | − | 27.3255i | 0.709547 | − | 0.0389252i | ||||
\(703\) | −589.396 | + | 340.288i | −0.838401 | + | 0.484051i | ||||
\(704\) | −67.4891 | − | 58.9983i | −0.0958651 | − | 0.0838045i | ||||
\(705\) | −283.281 | + | 490.657i | −0.401817 | + | 0.695967i | ||||
\(706\) | −610.200 | + | 398.392i | −0.864306 | + | 0.564295i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 197.391 | − | 449.246i | 0.278801 | − | 0.634528i | ||||
\(709\) | −949.313 | − | 548.086i | −1.33895 | − | 0.773041i | −0.352296 | − | 0.935889i | \(-0.614599\pi\) |
−0.986651 | + | 0.162847i | \(0.947932\pi\) | |||||||
\(710\) | −1071.82 | − | 542.824i | −1.50961 | − | 0.764541i | ||||
\(711\) | −1203.21 | + | 694.673i | −1.69228 | + | 0.977037i | ||||
\(712\) | 19.9278 | + | 7.48238i | 0.0279885 | + | 0.0105090i | ||||
\(713\) | 360.218 | 0.505214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −153.215 | −0.214286 | ||||||||
\(716\) | 170.916 | + | 232.843i | 0.238709 | + | 0.325200i | ||||
\(717\) | −621.633 | + | 358.900i | −0.866991 | + | 0.500558i | ||||
\(718\) | −101.201 | + | 199.825i | −0.140949 | + | 0.278308i | ||||
\(719\) | −524.259 | − | 302.681i | −0.729150 | − | 0.420975i | 0.0889614 | − | 0.996035i | \(-0.471645\pi\) |
−0.818111 | + | 0.575060i | \(0.804979\pi\) | |||||||
\(720\) | 801.361 | − | 735.863i | 1.11300 | − | 1.02203i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 340.057 | − | 222.019i | 0.470993 | − | 0.307506i | ||||
\(723\) | 223.149 | − | 386.506i | 0.308643 | − | 0.534586i | ||||
\(724\) | 61.6868 | + | 560.536i | 0.0852028 | + | 0.774221i | ||||
\(725\) | −22.4132 | + | 12.9403i | −0.0309148 | + | 0.0178487i | ||||
\(726\) | −59.5648 | − | 1085.77i | −0.0820451 | − | 1.49556i | ||||
\(727\) | − | 443.659i | − | 0.610260i | −0.952311 | − | 0.305130i | \(-0.901300\pi\) | ||
0.952311 | − | 0.305130i | \(-0.0986999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1095.46 | −1.50269 | ||||||||
\(730\) | 279.297 | − | 15.3220i | 0.382599 | − | 0.0209891i | ||||
\(731\) | 336.379 | + | 582.625i | 0.460162 | + | 0.797025i | ||||
\(732\) | 172.331 | + | 1565.94i | 0.235424 | + | 2.13926i | ||||
\(733\) | −649.541 | − | 375.013i | −0.886141 | − | 0.511614i | −0.0134626 | − | 0.999909i | \(-0.504285\pi\) |
−0.872678 | + | 0.488296i | \(0.837619\pi\) | |||||||
\(734\) | −480.038 | − | 735.252i | −0.654002 | − | 1.00171i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 125.586 | − | 492.704i | 0.170633 | − | 0.669434i | ||||
\(737\) | 80.2028 | − | 138.915i | 0.108823 | − | 0.188488i | ||||
\(738\) | 160.764 | + | 81.4191i | 0.217838 | + | 0.110324i | ||||
\(739\) | −309.646 | − | 536.323i | −0.419007 | − | 0.725742i | 0.576833 | − | 0.816862i | \(-0.304288\pi\) |
−0.995840 | + | 0.0911205i | \(0.970955\pi\) | |||||||
\(740\) | −734.785 | − | 1001.02i | −0.992952 | − | 1.35272i | ||||
\(741\) | − | 1095.34i | − | 1.47819i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.5255i | 0.0410842i | 0.999789 | + | 0.0205421i | \(0.00653921\pi\) | ||||
−0.999789 | + | 0.0205421i | \(0.993461\pi\) | |||||||
\(744\) | −291.184 | + | 775.510i | −0.391376 | + | 1.04235i | ||||
\(745\) | 236.153 | + | 409.029i | 0.316984 | + | 0.549032i | ||||
\(746\) | 230.420 | − | 454.972i | 0.308875 | − | 0.609882i | ||||
\(747\) | 470.146 | − | 814.316i | 0.629378 | − | 1.09012i | ||||
\(748\) | −72.7275 | + | 165.522i | −0.0972293 | + | 0.221286i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 490.632 | + | 751.479i | 0.654176 | + | 1.00197i | ||||
\(751\) | 838.498 | + | 484.107i | 1.11651 | + | 0.644616i | 0.940507 | − | 0.339773i | \(-0.110350\pi\) |
0.176001 | + | 0.984390i | \(0.443684\pi\) | |||||||
\(752\) | −330.300 | − | 103.762i | −0.439229 | − | 0.137981i | ||||
\(753\) | 715.142 | + | 1238.66i | 0.949723 | + | 1.64497i | ||||
\(754\) | −6.88186 | − | 125.446i | −0.00912713 | − | 0.166374i | ||||
\(755\) | −330.993 | −0.438401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1171.15i | − | 1.54710i | −0.633736 | − | 0.773550i | \(-0.718479\pi\) | ||
0.633736 | − | 0.773550i | \(-0.281521\pi\) | |||||||
\(758\) | −66.0662 | − | 1204.28i | −0.0871585 | − | 1.58877i | ||||
\(759\) | −88.0318 | + | 50.8252i | −0.115984 | + | 0.0669633i | ||||
\(760\) | −365.981 | − | 445.233i | −0.481554 | − | 0.585833i | ||||
\(761\) | 117.998 | − | 204.379i | 0.155057 | − | 0.268566i | −0.778023 | − | 0.628236i | \(-0.783777\pi\) |
0.933080 | + | 0.359670i | \(0.117111\pi\) | |||||||
\(762\) | −80.3199 | − | 123.022i | −0.105407 | − | 0.161447i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1041.77 | + | 457.734i | 1.36357 | + | 0.599129i | ||||
\(765\) | −1900.31 | − | 1097.14i | −2.48406 | − | 1.43418i | ||||
\(766\) | −66.3128 | + | 130.936i | −0.0865702 | + | 0.170935i | ||||
\(767\) | 443.849 | − | 256.257i | 0.578682 | − | 0.334102i | ||||
\(768\) | 959.220 | + | 668.652i | 1.24898 | + | 0.870641i | ||||
\(769\) | 124.257 | 0.161582 | 0.0807912 | − | 0.996731i | \(-0.474255\pi\) | ||||
0.0807912 | + | 0.996731i | \(0.474255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1593.39 | −2.06665 | ||||||||
\(772\) | −293.145 | − | 399.359i | −0.379721 | − | 0.517304i | ||||
\(773\) | −154.345 | + | 89.1114i | −0.199671 | + | 0.115280i | −0.596502 | − | 0.802612i | \(-0.703443\pi\) |
0.396831 | + | 0.917892i | \(0.370110\pi\) | |||||||
\(774\) | −441.227 | − | 223.459i | −0.570060 | − | 0.288707i | ||||
\(775\) | 154.352 | + | 89.1154i | 0.199164 | + | 0.114988i | ||||
\(776\) | 68.2099 | + | 411.124i | 0.0878993 | + | 0.529799i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 372.622 | + | 570.728i | 0.478948 | + | 0.733584i | ||||
\(779\) | 47.7317 | − | 82.6737i | 0.0612730 | − | 0.106128i | ||||
\(780\) | 1986.52 | − | 218.616i | 2.54682 | − | 0.280277i | ||||
\(781\) | −127.112 | + | 73.3880i | −0.162755 | + | 0.0939667i | ||||
\(782\) | −1023.95 | + | 56.1732i | −1.30940 | + | 0.0718327i | ||||
\(783\) | − | 43.0296i | − | 0.0549548i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3809 | −0.0272368 | ||||||||
\(786\) | 59.1131 | + | 1077.54i | 0.0752076 | + | 1.37092i | ||||
\(787\) | −553.948 | − | 959.466i | −0.703873 | − | 1.21914i | −0.967097 | − | 0.254409i | \(-0.918119\pi\) |
0.263224 | − | 0.964735i | \(-0.415214\pi\) | |||||||
\(788\) | 47.2991 | + | 429.798i | 0.0600242 | + | 0.545429i | ||||
\(789\) | 1520.37 | + | 877.785i | 1.92696 | + | 1.11253i | ||||
\(790\) | −1124.44 | + | 734.133i | −1.42334 | + | 0.929283i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −21.7544 | − | 131.121i | −0.0274676 | − | 0.165557i | ||||
\(793\) | −822.713 | + | 1424.98i | −1.03747 | + | 1.79695i | ||||
\(794\) | 100.790 | − | 199.012i | 0.126939 | − | 0.250645i | ||||
\(795\) | 4.66933 | + | 8.08752i | 0.00587338 | + | 0.0101730i | ||||
\(796\) | −1070.08 | + | 785.477i | −1.34432 | + | 0.986780i | ||||
\(797\) | 1094.69i | 1.37351i | 0.726889 | + | 0.686755i | \(0.240966\pi\) | ||||
−0.726889 | + | 0.686755i | \(0.759034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 698.269i | 0.873929i | ||||||||
\(800\) | 175.705 | − | 180.053i | 0.219631 | − | 0.225066i | ||||
\(801\) | 15.7808 | + | 27.3332i | 0.0197014 | + | 0.0341238i | ||||
\(802\) | 607.592 | + | 307.715i | 0.757596 | + | 0.383685i | ||||
\(803\) | 17.0861 | − | 29.5940i | 0.0212778 | − | 0.0368542i | ||||
\(804\) | −841.666 | + | 1915.56i | −1.04685 | + | 2.38254i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −724.464 | + | 472.994i | −0.898839 | + | 0.586842i | ||||
\(807\) | −149.366 | − | 86.2367i | −0.185089 | − | 0.106861i | ||||
\(808\) | 464.691 | + | 565.318i | 0.575112 | + | 0.699651i | ||||
\(809\) | 693.377 | + | 1200.96i | 0.857079 | + | 1.48450i | 0.874703 | + | 0.484659i | \(0.161056\pi\) |
−0.0176240 | + | 0.999845i | \(0.505610\pi\) | |||||||
\(810\) | −538.665 | + | 29.5508i | −0.665019 | + | 0.0364824i | ||||
\(811\) | 312.204 | 0.384962 | 0.192481 | − | 0.981301i | \(-0.438347\pi\) | ||||
0.192481 | + | 0.981301i | \(0.438347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1410.11i | − | 1.73446i | ||||||
\(814\) | −151.473 | + | 8.30968i | −0.186084 | + | 0.0102085i | ||||
\(815\) | 385.776 | − | 222.728i | 0.473345 | − | 0.273286i | ||||
\(816\) | 706.781 | − | 2249.86i | 0.866153 | − | 2.75719i | ||||
\(817\) | −131.002 | + | 226.903i | −0.160346 | + | 0.277727i | ||||
\(818\) | 1116.94 | − | 729.237i | 1.36545 | − | 0.891487i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 159.464 | + | 70.0660i | 0.194469 | + | 0.0854464i | ||||
\(821\) | 946.469 | + | 546.444i | 1.15282 | + | 0.665583i | 0.949574 | − | 0.313544i | \(-0.101516\pi\) |
0.203250 | + | 0.979127i | \(0.434850\pi\) | |||||||
\(822\) | 156.231 | + | 79.1230i | 0.190061 | + | 0.0962567i | ||||
\(823\) | −785.625 | + | 453.581i | −0.954587 | + | 0.551131i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(824\) | 111.891 | − | 297.999i | 0.135790 | − | 0.361650i | ||||
\(825\) | −50.2952 | −0.0609638 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −607.144 | −0.734152 | −0.367076 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367076 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(828\) | 607.746 | − | 446.109i | 0.733993 | − | 0.538779i | ||||
\(829\) | 370.632 | − | 213.984i | 0.447083 | − | 0.258124i | −0.259514 | − | 0.965739i | \(-0.583562\pi\) |
0.706598 | + | 0.707616i | \(0.250229\pi\) | |||||||
\(830\) | 410.624 | − | 810.789i | 0.494728 | − | 0.976854i | ||||
\(831\) | 965.982 | + | 557.710i | 1.16243 | + | 0.671131i | ||||
\(832\) | 394.382 | + | 1155.82i | 0.474017 | + | 1.38921i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −802.793 | + | 524.134i | −0.962581 | + | 0.628458i | ||||
\(835\) | 177.948 | − | 308.215i | 0.213111 | − | 0.369120i | ||||
\(836\) | −69.9878 | + | 7.70214i | −0.0837175 | + | 0.00921308i | ||||
\(837\) | −256.629 | + | 148.165i | −0.306606 | + | 0.177019i | ||||
\(838\) | −21.9317 | − | 399.781i | −0.0261715 | − | 0.477066i | ||||
\(839\) | 1133.09i | 1.35053i | 0.737575 | + | 0.675265i | \(0.235971\pi\) | ||||
−0.737575 | + | 0.675265i | \(0.764029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 830.163 | 0.987114 | ||||||||
\(842\) | 31.7795 | − | 1.74340i | 0.0377429 | − | 0.00207055i | ||||
\(843\) | 608.774 | + | 1054.43i | 0.722152 | + | 1.25080i | ||||
\(844\) | −104.947 | + | 11.5493i | −0.124344 | + | 0.0136840i | ||||
\(845\) | 968.707 | + | 559.283i | 1.14640 | + | 0.661874i | ||||
\(846\) | −280.637 | − | 429.839i | −0.331722 | − | 0.508084i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.20335 | + | 3.85980i | −0.00495678 | + | 0.00455165i | ||||
\(849\) | −378.198 | + | 655.059i | −0.445463 | + | 0.771565i | ||||
\(850\) | −452.657 | − | 229.248i | −0.532538 | − | 0.269704i | ||||
\(851\) | −430.232 | − | 745.184i | −0.505561 | − | 0.875657i | ||||
\(852\) | 1543.37 | − | 1132.89i | 1.81146 | − | 1.32969i | ||||
\(853\) | 169.502i | 0.198712i | 0.995052 | + | 0.0993562i | \(0.0316783\pi\) | ||||
−0.995052 | + | 0.0993562i | \(0.968322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 854.563i | − | 0.999489i | ||||||
\(856\) | −619.103 | − | 232.457i | −0.723251 | − | 0.271562i | ||||
\(857\) | −117.039 | − | 202.718i | −0.136569 | − | 0.236544i | 0.789627 | − | 0.613587i | \(-0.210274\pi\) |
−0.926196 | + | 0.377043i | \(0.876941\pi\) | |||||||
\(858\) | 110.311 | − | 217.811i | 0.128567 | − | 0.253860i | ||||
\(859\) | 447.171 | − | 774.523i | 0.520571 | − | 0.901656i | −0.479143 | − | 0.877737i | \(-0.659052\pi\) |
0.999714 | − | 0.0239189i | \(-0.00761436\pi\) | |||||||
\(860\) | −437.659 | − | 192.300i | −0.508906 | − | 0.223605i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 686.654 | + | 1051.72i | 0.796582 | + | 1.22009i | ||||
\(863\) | −674.270 | − | 389.290i | −0.781309 | − | 0.451089i | 0.0555850 | − | 0.998454i | \(-0.482298\pi\) |
−0.836894 | + | 0.547365i | \(0.815631\pi\) | |||||||
\(864\) | 113.188 | + | 402.672i | 0.131005 | + | 0.466056i | ||||
\(865\) | −560.680 | − | 971.126i | −0.648185 | − | 1.12269i | ||||
\(866\) | 86.4633 | + | 1576.09i | 0.0998422 | + | 1.81997i | ||||
\(867\) | −3436.32 | −3.96346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 164.055i | 0.188786i | ||||||||
\(870\) | −9.44281 | − | 172.128i | −0.0108538 | − | 0.197848i | ||||
\(871\) | −1892.55 | + | 1092.67i | −2.17285 | + | 1.25450i | ||||
\(872\) | 149.718 | + | 182.139i | 0.171695 | + | 0.208875i | ||||
\(873\) | −308.959 | + | 535.132i | −0.353904 | + | 0.612980i | ||||
\(874\) | −218.334 | − | 334.412i | −0.249810 | − | 0.382623i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −179.305 | + | 408.083i | −0.204686 | + | 0.465849i | ||||
\(877\) | −14.9632 | − | 8.63901i | −0.0170618 | − | 0.00985064i | 0.491445 | − | 0.870909i | \(-0.336469\pi\) |
−0.508507 | + | 0.861058i | \(0.669802\pi\) | |||||||
\(878\) | 601.424 | − | 1187.53i | 0.684993 | − | 1.35254i | ||||
\(879\) | 135.933 | − | 78.4811i | 0.154645 | − | 0.0892846i | ||||
\(880\) | −27.9373 | − | 125.393i | −0.0317470 | − | 0.142492i | ||||
\(881\) | −770.918 | −0.875049 | −0.437524 | − | 0.899207i | \(-0.644145\pi\) | ||||
−0.437524 | + | 0.899207i | \(0.644145\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 776.362 | 0.879232 | 0.439616 | − | 0.898186i | \(-0.355114\pi\) | ||||
0.439616 | + | 0.898186i | \(0.355114\pi\) | |||||||
\(884\) | 1985.60 | − | 1457.50i | 2.24615 | − | 1.64876i | ||||
\(885\) | 609.019 | − | 351.617i | 0.688157 | − | 0.397308i | ||||
\(886\) | 904.874 | + | 458.273i | 1.02130 | + | 0.517239i | ||||
\(887\) | 1412.32 | + | 815.402i | 1.59224 | + | 0.919280i | 0.992922 | + | 0.118770i | \(0.0378950\pi\) |
0.599319 | + | 0.800511i | \(0.295438\pi\) | |||||||
\(888\) | 1952.08 | − | 323.871i | 2.19829 | − | 0.364719i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.6772 | + | 25.5438i | 0.0187385 | + | 0.0287009i | ||||
\(891\) | −32.9530 | + | 57.0762i | −0.0369842 | + | 0.0640586i | ||||
\(892\) | 70.5270 | + | 640.865i | 0.0790661 | + | 0.718458i | ||||
\(893\) | −235.507 | + | 135.970i | −0.263726 | + | 0.152262i | ||||
\(894\) | −751.503 | + | 41.2269i | −0.840608 | + | 0.0461151i | ||||
\(895\) | 413.945i | 0.462508i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1384.86 | 1.54388 | ||||||||
\(898\) | 30.5687 | + | 557.221i | 0.0340409 | + | 0.620513i | ||||
\(899\) | 37.3150 | + | 64.6314i | 0.0415072 | + | 0.0718925i | ||||
\(900\) | 370.782 | − | 40.8044i | 0.411980 | − | 0.0453382i | ||||
\(901\) | 9.96762 | + | 5.75481i | 0.0110628 | + | 0.00638713i | ||||
\(902\) | 17.8175 | − | 11.6329i | 0.0197534 | − | 0.0128967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 208.367 | + | 1255.90i | 0.230495 | + | 1.38927i | ||||
\(905\) | −404.086 | + | 699.897i | −0.446503 | + | 0.773367i | ||||
\(906\) | 238.306 | − | 470.542i | 0.263031 | − | 0.519362i | ||||
\(907\) | 476.931 | + | 826.069i | 0.525834 | + | 0.910771i | 0.999547 | + | 0.0300919i | \(0.00958001\pi\) |
−0.473713 | + | 0.880679i | \(0.657087\pi\) | |||||||
\(908\) | 405.406 | + | 552.295i | 0.446482 | + | 0.608254i | ||||
\(909\) | 1085.05i | 1.19367i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1681.15i | − | 1.84539i | −0.385534 | − | 0.922694i | \(-0.625983\pi\) | ||
0.385534 | − | 0.922694i | \(-0.374017\pi\) | |||||||
\(912\) | 896.445 | − | 199.726i | 0.982944 | − | 0.218998i | ||||
\(913\) | −55.5150 | − | 96.1548i | −0.0608051 | − | 0.105317i | ||||
\(914\) | −1286.22 | − | 651.404i | −1.40724 | − | 0.712696i | ||||
\(915\) | −1128.87 | + | 1955.26i | −1.23374 | + | 2.13689i | ||||
\(916\) | 839.538 | + | 368.879i | 0.916527 | + | 0.402707i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 706.386 | − | 461.192i | 0.769484 | − | 0.502387i | ||||
\(919\) | 437.335 | + | 252.495i | 0.475881 | + | 0.274750i | 0.718698 | − | 0.695322i | \(-0.244738\pi\) |
−0.242817 | + | 0.970072i | \(0.578071\pi\) | |||||||
\(920\) | 562.917 | − | 462.717i | 0.611866 | − | 0.502953i | ||||
\(921\) | 509.122 | + | 881.826i | 0.552793 | + | 0.957466i | ||||
\(922\) | −965.073 | + | 52.9432i | −1.04672 | + | 0.0574221i | ||||
\(923\) | 1999.64 | 2.16646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 425.746i | − | 0.460266i | ||||||
\(926\) | −79.1461 | + | 4.34190i | −0.0854710 | + | 0.00468887i | ||||
\(927\) | 408.739 | − | 235.985i | 0.440926 | − | 0.254569i | ||||
\(928\) | 101.412 | − | 28.5061i | 0.109280 | − | 0.0307178i | ||||
\(929\) | 491.925 | − | 852.040i | 0.529521 | − | 0.917158i | −0.469886 | − | 0.882727i | \(-0.655705\pi\) |
0.999407 | − | 0.0344306i | \(-0.0109618\pi\) | |||||||
\(930\) | −994.059 | + | 649.010i | −1.06888 | + | 0.697860i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −434.695 | + | 989.330i | −0.466411 | + | 1.06151i | ||||
\(933\) | −1661.07 | − | 959.018i | −1.78035 | − | 1.02789i | ||||
\(934\) | −31.7357 | − | 16.0725i | −0.0339782 | − | 0.0172083i | ||||
\(935\) | −224.389 | + | 129.551i | −0.239989 | + | 0.138558i | ||||
\(936\) | −636.513 | + | 1695.23i | −0.680035 | + | 1.81114i | ||||
\(937\) | 389.648 | 0.415846 | 0.207923 | − | 0.978145i | \(-0.433330\pi\) | ||||
0.207923 | + | 0.978145i | \(0.433330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1342.24 | −1.42943 | ||||||||
\(940\) | −293.601 | − | 399.980i | −0.312341 | − | 0.425511i | ||||
\(941\) | 758.175 | − | 437.732i | 0.805712 | − | 0.465178i | −0.0397529 | − | 0.999210i | \(-0.512657\pi\) |
0.845464 | + | 0.534032i | \(0.179324\pi\) | |||||||
\(942\) | 15.3937 | − | 30.3953i | 0.0163415 | − | 0.0322667i | ||||
\(943\) | 104.526 | + | 60.3481i | 0.110844 | + | 0.0639958i | ||||
\(944\) | 290.656 | + | 316.527i | 0.307899 | + | 0.335304i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −48.9012 | + | 31.9270i | −0.0516926 | + | 0.0337495i | ||||
\(947\) | 625.646 | − | 1083.65i | 0.660661 | − | 1.14430i | −0.319781 | − | 0.947491i | \(-0.603609\pi\) |
0.980442 | − | 0.196807i | \(-0.0630572\pi\) | |||||||
\(948\) | −234.083 | − | 2127.07i | −0.246923 | − | 2.24375i | ||||
\(949\) | −403.181 | + | 232.777i | −0.424849 | + | 0.245287i | ||||
\(950\) | −10.8242 | − | 197.309i | −0.0113939 | − | 0.207694i | ||||
\(951\) | − | 1934.14i | − | 2.03380i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −882.129 | −0.925633 | −0.462817 | − | 0.886454i | \(-0.653161\pi\) | ||||
−0.462817 | + | 0.886454i | \(0.653161\pi\) | |||||||
\(954\) | −8.44873 | + | 0.463491i | −0.00885611 | + | 0.000485839i | ||||
\(955\) | 815.373 | + | 1412.27i | 0.853793 | + | 1.47881i | ||||
\(956\) | −68.7642 | − | 624.846i | −0.0719290 | − | 0.653605i | ||||
\(957\) | −18.2384 | − | 10.5300i | −0.0190579 | − | 0.0110031i | ||||
\(958\) | −731.049 | − | 1119.71i | −0.763099 | − | 1.16880i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 541.144 | + | 1585.94i | 0.563691 | + | 1.65202i | ||||
\(961\) | −223.525 | + | 387.156i | −0.232596 | + | 0.402868i | ||||
\(962\) | 1843.76 | + | 933.773i | 1.91659 | + | 0.970658i | ||||
\(963\) | −490.267 | − | 849.167i | −0.509103 | − | 0.881793i | ||||
\(964\) | 231.279 | + | 315.077i | 0.239916 | + | 0.326843i | ||||
\(965\) | − | 709.973i | − | 0.735724i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1410.24i | − | 1.45836i | −0.684320 | − | 0.729182i | \(-0.739901\pi\) | ||
0.684320 | − | 0.729182i | \(-0.260099\pi\) | |||||||
\(968\) | 891.533 | + | 334.747i | 0.921005 | + | 0.345813i | ||||
\(969\) | −926.171 | − | 1604.18i | −0.955801 | − | 1.65550i | ||||
\(970\) | −269.844 | + | 532.814i | −0.278189 | + | 0.549293i | ||||
\(971\) | 339.275 | − | 587.641i | 0.349408 | − | 0.605192i | −0.636737 | − | 0.771081i | \(-0.719716\pi\) |
0.986144 | + | 0.165889i | \(0.0530495\pi\) | |||||||
\(972\) | 535.107 | − | 1217.86i | 0.550521 | − | 1.25294i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −457.560 | − | 700.825i | −0.469775 | − | 0.719533i | ||||
\(975\) | 593.410 | + | 342.605i | 0.608625 | + | 0.351390i | ||||
\(976\) | −1316.24 | − | 413.488i | −1.34861 | − | 0.423656i | ||||
\(977\) | −55.9074 | − | 96.8344i | −0.0572235 | − | 0.0991141i | 0.835995 | − | 0.548738i | \(-0.184891\pi\) |
−0.893218 | + | 0.449624i | \(0.851558\pi\) | |||||||
\(978\) | 38.8833 | + | 708.782i | 0.0397579 | + | 0.724726i | ||||
\(979\) | 3.72682 | 0.00380676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 349.590i | 0.356360i | ||||||||
\(982\) | −41.7434 | − | 760.917i | −0.0425085 | − | 0.774865i | ||||
\(983\) | −175.133 | + | 101.113i | −0.178162 | + | 0.102862i | −0.586429 | − | 0.810001i | \(-0.699467\pi\) |
0.408267 | + | 0.912863i | \(0.366133\pi\) | |||||||
\(984\) | −214.417 | + | 176.250i | −0.217903 | + | 0.179116i | ||||
\(985\) | −309.837 | + | 536.654i | −0.314556 | + | 0.544826i | ||||
\(986\) | −116.150 | − | 177.902i | −0.117799 | − | 0.180428i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 878.220 | + | 385.875i | 0.888887 | + | 0.390562i | ||||
\(989\) | −286.877 | − | 165.629i | −0.290068 | − | 0.167471i | ||||
\(990\) | 86.0620 | − | 169.932i | 0.0869314 | − | 0.171648i | ||||
\(991\) | −163.735 | + | 94.5322i | −0.165222 | + | 0.0953907i | −0.580331 | − | 0.814381i | \(-0.697077\pi\) |
0.415109 | + | 0.909772i | \(0.363743\pi\) | |||||||
\(992\) | −519.206 | − | 506.667i | −0.523393 | − | 0.510753i | ||||
\(993\) | 578.546 | 0.582624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1902.36 | −1.91192 | ||||||||
\(996\) | 856.986 | + | 1167.49i | 0.860428 | + | 1.17218i | ||||
\(997\) | −1414.14 | + | 816.457i | −1.41840 | + | 0.818914i | −0.996158 | − | 0.0875699i | \(-0.972090\pi\) |
−0.422241 | + | 0.906483i | \(0.638757\pi\) | |||||||
\(998\) | −782.191 | − | 396.141i | −0.783759 | − | 0.396935i | ||||
\(999\) | 613.019 | + | 353.927i | 0.613632 | + | 0.354281i |
(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 | 392.3.k.n.275.5 | 16 | ||
7.2 | even | 3 | 392.3.g.m.99.2 | 8 | |||
7.3 | odd | 6 | 392.3.k.o.67.7 | 16 | |||
7.4 | even | 3 | inner | 392.3.k.n.67.7 | 16 | ||
7.5 | odd | 6 | 56.3.g.b.43.2 | yes | 8 | ||
7.6 | odd | 2 | 392.3.k.o.275.5 | 16 | |||
8.3 | odd | 2 | inner | 392.3.k.n.275.7 | 16 | ||
21.5 | even | 6 | 504.3.g.b.379.7 | 8 | |||
28.19 | even | 6 | 224.3.g.b.15.1 | 8 | |||
28.23 | odd | 6 | 1568.3.g.m.687.8 | 8 | |||
56.3 | even | 6 | 392.3.k.o.67.5 | 16 | |||
56.5 | odd | 6 | 224.3.g.b.15.2 | 8 | |||
56.11 | odd | 6 | inner | 392.3.k.n.67.5 | 16 | ||
56.19 | even | 6 | 56.3.g.b.43.1 | ✓ | 8 | ||
56.27 | even | 2 | 392.3.k.o.275.7 | 16 | |||
56.37 | even | 6 | 1568.3.g.m.687.7 | 8 | |||
56.51 | odd | 6 | 392.3.g.m.99.1 | 8 | |||
84.47 | odd | 6 | 2016.3.g.b.1135.7 | 8 | |||
112.5 | odd | 12 | 1792.3.d.j.1023.4 | 16 | |||
112.19 | even | 12 | 1792.3.d.j.1023.3 | 16 | |||
112.61 | odd | 12 | 1792.3.d.j.1023.13 | 16 | |||
112.75 | even | 12 | 1792.3.d.j.1023.14 | 16 | |||
168.5 | even | 6 | 2016.3.g.b.1135.2 | 8 | |||
168.131 | odd | 6 | 504.3.g.b.379.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.1 | ✓ | 8 | 56.19 | even | 6 | ||
56.3.g.b.43.2 | yes | 8 | 7.5 | odd | 6 | ||
224.3.g.b.15.1 | 8 | 28.19 | even | 6 | |||
224.3.g.b.15.2 | 8 | 56.5 | odd | 6 | |||
392.3.g.m.99.1 | 8 | 56.51 | odd | 6 | |||
392.3.g.m.99.2 | 8 | 7.2 | even | 3 | |||
392.3.k.n.67.5 | 16 | 56.11 | odd | 6 | inner | ||
392.3.k.n.67.7 | 16 | 7.4 | even | 3 | inner | ||
392.3.k.n.275.5 | 16 | 1.1 | even | 1 | trivial | ||
392.3.k.n.275.7 | 16 | 8.3 | odd | 2 | inner | ||
392.3.k.o.67.5 | 16 | 56.3 | even | 6 | |||
392.3.k.o.67.7 | 16 | 7.3 | odd | 6 | |||
392.3.k.o.275.5 | 16 | 7.6 | odd | 2 | |||
392.3.k.o.275.7 | 16 | 56.27 | even | 2 | |||
504.3.g.b.379.7 | 8 | 21.5 | even | 6 | |||
504.3.g.b.379.8 | 8 | 168.131 | odd | 6 | |||
1568.3.g.m.687.7 | 8 | 56.37 | even | 6 | |||
1568.3.g.m.687.8 | 8 | 28.23 | odd | 6 | |||
1792.3.d.j.1023.3 | 16 | 112.19 | even | 12 | |||
1792.3.d.j.1023.4 | 16 | 112.5 | odd | 12 | |||
1792.3.d.j.1023.13 | 16 | 112.61 | odd | 12 | |||
1792.3.d.j.1023.14 | 16 | 112.75 | even | 12 | |||
2016.3.g.b.1135.2 | 8 | 168.5 | even | 6 | |||
2016.3.g.b.1135.7 | 8 | 84.47 | odd | 6 |