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: | \( x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} - 448 x^{7} - 320 x^{6} + 2816 x^{5} - 5632 x^{4} + 6144 x^{3} + 12288 x^{2} + \cdots + 65536 \) |
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 | 275.7 | ||
Root | \(0.109554 + 1.99700i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.275 |
Dual form | 392.3.k.n.67.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.78423 | − | 0.903622i | 0.892114 | − | 0.451811i | ||||
\(3\) | 2.28374 | + | 3.95555i | 0.761245 | + | 1.31852i | 0.942209 | + | 0.335026i | \(0.108745\pi\) |
−0.180964 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(4\) | 2.36693 | − | 3.22453i | 0.591733 | − | 0.806134i | ||||
\(5\) | 4.96451 | + | 2.86626i | 0.992902 | + | 0.573252i | 0.906140 | − | 0.422977i | \(-0.139015\pi\) |
0.0867614 | + | 0.996229i | \(0.472348\pi\) | |||||||
\(6\) | 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 | ||||
\(10\) | 11.4478 | + | 0.628019i | 1.14478 | + | 0.0628019i | ||||
\(11\) | 0.700323 | + | 1.21300i | 0.0636658 | + | 0.110272i | 0.896101 | − | 0.443849i | \(-0.146388\pi\) |
−0.832436 | + | 0.554122i | \(0.813054\pi\) | |||||||
\(12\) | 18.1602 | + | 1.99853i | 1.51335 | + | 0.166544i | ||||
\(13\) | 19.0821i | 1.46785i | 0.679228 | + | 0.733927i | \(0.262315\pi\) | ||||
−0.679228 | + | 0.733927i | \(0.737685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.1831i | 1.74554i | ||||||||
\(16\) | −4.79525 | − | 15.2645i | −0.299703 | − | 0.954032i | ||||
\(17\) | −16.1349 | − | 27.9465i | −0.949114 | − | 1.64391i | −0.747296 | − | 0.664491i | \(-0.768648\pi\) |
−0.201818 | − | 0.979423i | \(-0.564685\pi\) | |||||||
\(18\) | −1.29950 | + | 23.6880i | −0.0721947 | + | 1.31600i | ||||
\(19\) | 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 | 0.170082 | − | 0.985430i | \(-0.445597\pi\) |
−0.768366 | + | 0.640011i | \(0.778930\pi\) | |||||||
\(24\) | 34.2079 | − | 12.8442i | 1.42533 | − | 0.535174i | ||||
\(25\) | 3.93090 | + | 6.80852i | 0.157236 | + | 0.272341i | ||||
\(26\) | 17.2430 | + | 34.0468i | 0.663193 | + | 1.30949i | ||||
\(27\) | −13.0712 | −0.484118 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.29194i | − | 0.113515i | −0.998388 | − | 0.0567576i | \(-0.981924\pi\) | ||
0.998388 | − | 0.0567576i | \(-0.0180762\pi\) | |||||||
\(30\) | 23.6597 | + | 46.7166i | 0.788655 | + | 1.55722i | ||||
\(31\) | −19.6332 | + | 11.3352i | −0.633329 | + | 0.365653i | −0.782040 | − | 0.623228i | \(-0.785821\pi\) |
0.148711 | + | 0.988881i | \(0.452488\pi\) | |||||||
\(32\) | −22.3492 | − | 22.9023i | −0.698412 | − | 0.715696i | ||||
\(33\) | −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 | 0.974519 | − | 0.224303i | \(-0.0720105\pi\) |
0.293008 | + | 0.956110i | \(0.405344\pi\) | |||||||
\(38\) | 1.37681 | − | 25.0972i | 0.0362319 | − | 0.660453i | ||||
\(39\) | −75.4801 | + | 43.5785i | −1.93539 | + | 1.11740i | ||||
\(40\) | 29.1213 | − | 35.4274i | 0.728033 | − | 0.885686i | ||||
\(41\) | 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 | \(0.577940\pi\) | |||||||
\(44\) | 5.56897 | + | 0.612863i | 0.126567 | + | 0.0139287i | ||||
\(45\) | −58.8880 | + | 33.9990i | −1.30862 | + | 0.755533i | ||||
\(46\) | −31.7309 | − | 1.74073i | −0.689801 | − | 0.0378420i | ||||
\(47\) | 18.7394 | + | 10.8192i | 0.398711 | + | 0.230196i | 0.685928 | − | 0.727670i | \(-0.259397\pi\) |
−0.287217 | + | 0.957866i | \(0.592730\pi\) | |||||||
\(48\) | 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 | ||||
\(52\) | 61.5309 | + | 45.1661i | 1.18329 | + | 0.868578i | ||||
\(53\) | 0.308883 | − | 0.178334i | 0.00582798 | − | 0.00336479i | −0.497083 | − | 0.867703i | \(-0.665596\pi\) |
0.502911 | + | 0.864338i | \(0.332262\pi\) | |||||||
\(54\) | −23.3220 | + | 11.8114i | −0.431888 | + | 0.218730i | ||||
\(55\) | 8.02924i | 0.145986i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.4016 | 1.00705 | ||||||||
\(58\) | −2.97467 | − | 5.87357i | −0.0512875 | − | 0.101269i | ||||
\(59\) | 13.4292 | + | 23.2600i | 0.227613 | + | 0.394237i | 0.957100 | − | 0.289757i | \(-0.0935746\pi\) |
−0.729487 | + | 0.683994i | \(0.760241\pi\) | |||||||
\(60\) | 84.4284 | + | 61.9737i | 1.40714 | + | 1.03290i | ||||
\(61\) | 74.6763 | + | 43.1144i | 1.22420 | + | 0.706793i | 0.965811 | − | 0.259248i | \(-0.0834746\pi\) |
0.258390 | + | 0.966041i | \(0.416808\pi\) | |||||||
\(62\) | −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 | ||||
\(66\) | −0.700861 | + | 12.7756i | −0.0106191 | + | 0.193570i | ||||
\(67\) | −57.2613 | − | 99.1794i | −0.854646 | − | 1.48029i | −0.876973 | − | 0.480539i | \(-0.840441\pi\) |
0.0223272 | − | 0.999751i | \(-0.492892\pi\) | |||||||
\(68\) | −128.305 | − | 14.1199i | −1.88684 | − | 0.207646i | ||||
\(69\) | − | 72.5739i | − | 1.05180i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 104.792i | − | 1.47594i | −0.674834 | − | 0.737969i | \(-0.735785\pi\) | ||
0.674834 | − | 0.737969i | \(-0.264215\pi\) | |||||||
\(72\) | 73.3069 | + | 60.2582i | 1.01815 | + | 0.836919i | ||||
\(73\) | −12.1987 | − | 21.1288i | −0.167106 | − | 0.289435i | 0.770295 | − | 0.637687i | \(-0.220109\pi\) |
−0.937401 | + | 0.348252i | \(0.886775\pi\) | |||||||
\(74\) | 108.145 | + | 5.93274i | 1.46142 | + | 0.0801722i | ||||
\(75\) | −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 | −0.306420 | − | 0.951897i | \(-0.599131\pi\) |
−0.977576 | + | 0.210581i | \(0.932464\pi\) | |||||||
\(80\) | 19.9460 | − | 89.5253i | 0.249325 | − | 1.11907i | ||||
\(81\) | 23.5270 | + | 40.7499i | 0.290456 | + | 0.503085i | ||||
\(82\) | 13.5531 | − | 6.86398i | 0.165282 | − | 0.0837070i | ||||
\(83\) | −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 | ||||||
\(86\) | −37.1973 | + | 18.8386i | −0.432526 | + | 0.219053i | ||||
\(87\) | 13.0214 | − | 7.51793i | 0.149672 | − | 0.0864130i | ||||
\(88\) | 10.4901 | − | 3.93875i | 0.119206 | − | 0.0447586i | ||||
\(89\) | 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 | ||||
\(94\) | 43.2119 | + | 2.37057i | 0.459701 | + | 0.0252188i | ||||
\(95\) | 62.3913 | − | 36.0216i | 0.656751 | − | 0.379175i | ||||
\(96\) | 39.5514 | − | 140.706i | 0.411994 | − | 1.46569i | ||||
\(97\) | 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 | ||||||||
\(100\) | 31.2585 | + | 3.43999i | 0.312585 | + | 0.0343999i | ||||
\(101\) | −79.2189 | + | 45.7371i | −0.784346 | + | 0.452842i | −0.837968 | − | 0.545719i | \(-0.816257\pi\) |
0.0536223 | + | 0.998561i | \(0.482923\pi\) | |||||||
\(102\) | 16.1473 | − | 294.341i | 0.158307 | − | 2.88570i | ||||
\(103\) | 34.4584 | + | 19.8946i | 0.334548 | + | 0.193151i | 0.657858 | − | 0.753142i | \(-0.271463\pi\) |
−0.323311 | + | 0.946293i | \(0.604796\pi\) | |||||||
\(104\) | 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 | \(0.292906\pi\) | |||||||
\(108\) | −30.9386 | + | 42.1485i | −0.286469 | + | 0.390264i | ||||
\(109\) | −25.5234 | + | 14.7359i | −0.234160 | + | 0.135192i | −0.612490 | − | 0.790479i | \(-0.709832\pi\) |
0.378330 | + | 0.925671i | \(0.376499\pi\) | |||||||
\(110\) | 7.25540 | + | 14.3260i | 0.0659582 | + | 0.130236i | ||||
\(111\) | 247.346i | 2.22834i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 159.133 | 1.40826 | 0.704130 | − | 0.710071i | \(-0.251337\pi\) | ||||
0.704130 | + | 0.710071i | \(0.251337\pi\) | |||||||
\(114\) | 102.417 | − | 51.8693i | 0.898399 | − | 0.454994i | ||||
\(115\) | −45.5428 | − | 78.8825i | −0.396025 | − | 0.685935i | ||||
\(116\) | −10.6150 | − | 7.79181i | −0.0915085 | − | 0.0671708i | ||||
\(117\) | −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 | ||||
\(122\) | 172.199 | + | 9.44668i | 1.41146 | + | 0.0774318i | ||||
\(123\) | 17.3474 | + | 30.0466i | 0.141036 | + | 0.244281i | ||||
\(124\) | −9.91963 | + | 90.1377i | −0.0799970 | + | 0.726917i | ||||
\(125\) | − | 98.2451i | − | 0.785961i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0834i | 0.126641i | 0.997993 | + | 0.0633205i | \(0.0201690\pi\) | ||||
−0.997993 | + | 0.0633205i | \(0.979831\pi\) | |||||||
\(128\) | −126.748 | + | 17.8575i | −0.990220 | + | 0.139512i | ||||
\(129\) | −47.6110 | − | 82.4646i | −0.369077 | − | 0.639260i | ||||
\(130\) | −11.9839 | + | 218.449i | −0.0921840 | + | 1.68037i | ||||
\(131\) | −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 | ||||
\(136\) | −241.684 | + | 90.7461i | −1.77709 | + | 0.667250i | ||||
\(137\) | 9.58539 | + | 16.6024i | 0.0699664 | + | 0.121185i | 0.898886 | − | 0.438182i | \(-0.144377\pi\) |
−0.828920 | + | 0.559367i | \(0.811044\pi\) | |||||||
\(138\) | −65.5794 | − | 129.488i | −0.475213 | − | 0.938321i | ||||
\(139\) | −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 | ||||||||
\(142\) | −94.6920 | − | 186.972i | −0.666845 | − | 1.31670i | ||||
\(143\) | −23.1465 | + | 13.3636i | −0.161864 | + | 0.0934520i | ||||
\(144\) | 185.247 | + | 41.2725i | 1.28644 | + | 0.286615i | ||||
\(145\) | 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 | 0.719947 | − | 0.694029i | \(-0.244166\pi\) |
−0.241073 | + | 0.970507i | \(0.577499\pi\) | |||||||
\(150\) | −3.93392 | + | 71.7093i | −0.0262261 | + | 0.478062i | ||||
\(151\) | −50.0038 | + | 28.8697i | −0.331151 | + | 0.191190i | −0.656352 | − | 0.754455i | \(-0.727901\pi\) |
0.325201 | + | 0.945645i | \(0.394568\pi\) | |||||||
\(152\) | −77.6680 | − | 63.8430i | −0.510974 | − | 0.420020i | ||||
\(153\) | 382.779 | 2.50182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −129.959 | −0.838445 | ||||||||
\(156\) | −38.1361 | + | 346.536i | −0.244462 | + | 2.22138i | ||||
\(157\) | −3.23006 | + | 1.86488i | −0.0205736 | + | 0.0118782i | −0.510252 | − | 0.860025i | \(-0.670448\pi\) |
0.489678 | + | 0.871903i | \(0.337114\pi\) | |||||||
\(158\) | −233.904 | − | 12.8318i | −1.48040 | − | 0.0812139i | ||||
\(159\) | 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 | \(0.243278\pi\) | |||||||
\(164\) | 17.9794 | − | 24.4938i | 0.109630 | − | 0.149352i | ||||
\(165\) | −31.7600 | + | 18.3367i | −0.192485 | + | 0.111131i | ||||
\(166\) | −141.437 | + | 71.6306i | −0.852028 | + | 0.431510i | ||||
\(167\) | − | 62.0837i | − | 0.371759i | −0.982573 | − | 0.185879i | \(-0.940487\pi\) | ||
0.982573 | − | 0.185879i | \(-0.0595133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −195.127 | −1.15459 | ||||||||
\(170\) | −167.159 | − | 330.060i | −0.983289 | − | 1.94153i | ||||
\(171\) | 74.5364 | + | 129.101i | 0.435885 | + | 0.754976i | ||||
\(172\) | −49.3454 | + | 67.2246i | −0.286892 | + | 0.390841i | ||||
\(173\) | −169.407 | − | 97.8069i | −0.979228 | − | 0.565358i | −0.0771913 | − | 0.997016i | \(-0.524595\pi\) |
−0.902037 | + | 0.431659i | \(0.857929\pi\) | |||||||
\(174\) | 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 | ||||
\(178\) | 0.291499 | − | 5.31358i | 0.00163763 | − | 0.0298515i | ||||
\(179\) | −36.1049 | − | 62.5356i | −0.201704 | − | 0.349361i | 0.747374 | − | 0.664404i | \(-0.231314\pi\) |
−0.949077 | + | 0.315043i | \(0.897981\pi\) | |||||||
\(180\) | −29.7530 | + | 270.360i | −0.165295 | + | 1.50200i | ||||
\(181\) | 140.980i | 0.778895i | 0.921049 | + | 0.389448i | \(0.127334\pi\) | ||||
−0.921049 | + | 0.389448i | \(0.872666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 393.847i | 2.15217i | ||||||||
\(184\) | −80.7179 | + | 98.1971i | −0.438684 | + | 0.533680i | ||||
\(185\) | 155.219 | + | 268.847i | 0.839020 | + | 1.45323i | ||||
\(186\) | −206.783 | − | 11.3439i | −1.11173 | − | 0.0609889i | ||||
\(187\) | 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 | 0.978627 | − | 0.205645i | \(-0.0659293\pi\) |
0.311219 | + | 0.950338i | \(0.399263\pi\) | |||||||
\(192\) | −56.5764 | − | 286.791i | −0.294669 | − | 1.49370i | ||||
\(193\) | 61.9251 | + | 107.257i | 0.320855 | + | 0.555738i | 0.980665 | − | 0.195695i | \(-0.0626964\pi\) |
−0.659810 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(194\) | 92.9458 | − | 47.0724i | 0.479102 | − | 0.242641i | ||||
\(195\) | −499.629 | −2.56220 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 108.098i | 0.548721i | 0.961627 | + | 0.274361i | \(0.0884662\pi\) | ||||
−0.961627 | + | 0.274361i | \(0.911534\pi\) | |||||||
\(198\) | −29.6435 | + | 15.0129i | −0.149715 | + | 0.0758230i | ||||
\(199\) | −287.394 | + | 165.927i | −1.44419 | + | 0.833804i | −0.998126 | − | 0.0611961i | \(-0.980508\pi\) |
−0.446065 | + | 0.895000i | \(0.647175\pi\) | |||||||
\(200\) | 58.8807 | − | 22.1081i | 0.294403 | − | 0.110541i | ||||
\(201\) | 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 | ||||
\(206\) | 79.4588 | + | 4.35905i | 0.385722 | + | 0.0211604i | ||||
\(207\) | 163.225 | − | 94.2378i | 0.788525 | − | 0.455255i | ||||
\(208\) | 291.279 | − | 91.5035i | 1.40038 | − | 0.439920i | ||||
\(209\) | 17.6026 | 0.0842229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.3950 | 0.125095 | 0.0625475 | − | 0.998042i | \(-0.480078\pi\) | ||||
0.0625475 | + | 0.998042i | \(0.480078\pi\) | |||||||
\(212\) | 0.156062 | − | 1.41811i | 0.000736143 | − | 0.00668919i | ||||
\(213\) | 414.508 | − | 239.316i | 1.94605 | − | 1.12355i | ||||
\(214\) | −9.05606 | + | 165.078i | −0.0423180 | + | 0.771393i | ||||
\(215\) | −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 | ||||
\(220\) | 25.8906 | + | 19.0047i | 0.117684 | + | 0.0863849i | ||||
\(221\) | 533.279 | − | 307.889i | 2.41303 | − | 1.39316i | ||||
\(222\) | 223.507 | + | 441.321i | 1.00679 | + | 1.98793i | ||||
\(223\) | 161.183i | 0.722796i | 0.932412 | + | 0.361398i | \(0.117700\pi\) | ||||
−0.932412 | + | 0.361398i | \(0.882300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −93.2551 | −0.414467 | ||||||||
\(226\) | 283.930 | − | 143.797i | 1.25633 | − | 0.636268i | ||||
\(227\) | −85.6395 | − | 148.332i | −0.377266 | − | 0.653445i | 0.613397 | − | 0.789775i | \(-0.289803\pi\) |
−0.990663 | + | 0.136330i | \(0.956469\pi\) | |||||||
\(228\) | 135.866 | − | 185.093i | 0.595902 | − | 0.811813i | ||||
\(229\) | 198.537 | + | 114.626i | 0.866975 | + | 0.500548i | 0.866342 | − | 0.499452i | \(-0.166465\pi\) |
0.000632973 | 1.00000i | \(0.499799\pi\) | ||||||||
\(230\) | −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 | \(-0.0301755\pi\) | |||||||
\(234\) | −452.016 | − | 24.7973i | −1.93169 | − | 0.105971i | ||||
\(235\) | 62.0214 | + | 107.424i | 0.263921 | + | 0.457124i | ||||
\(236\) | 106.789 | + | 11.7520i | 0.452494 | + | 0.0497968i | ||||
\(237\) | − | 534.978i | − | 2.25729i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 157.155i | − | 0.657551i | −0.944408 | − | 0.328776i | \(-0.893364\pi\) | ||
0.944408 | − | 0.328776i | \(-0.106636\pi\) | |||||||
\(240\) | 399.673 | − | 125.555i | 1.66530 | − | 0.523144i | ||||
\(241\) | −48.8562 | − | 84.6214i | −0.202723 | − | 0.351126i | 0.746682 | − | 0.665181i | \(-0.231646\pi\) |
−0.949405 | + | 0.314055i | \(0.898312\pi\) | |||||||
\(242\) | 13.0411 | − | 237.719i | 0.0538888 | − | 0.982310i | ||||
\(243\) | −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 | ||||
\(248\) | 63.7516 | + | 169.790i | 0.257063 | + | 0.684636i | ||||
\(249\) | −181.033 | − | 313.558i | −0.727040 | − | 1.25927i | ||||
\(250\) | −88.7765 | − | 175.292i | −0.355106 | − | 0.701166i | ||||
\(251\) | 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 | ||||||
\(254\) | 14.5333 | + | 28.6965i | 0.0572178 | + | 0.112978i | ||||
\(255\) | 731.728 | − | 422.463i | 2.86952 | − | 1.65672i | ||||
\(256\) | −210.011 | + | 146.394i | −0.820356 | + | 0.571853i | ||||
\(257\) | −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 | ||||
\(262\) | −12.9422 | + | 235.917i | −0.0493977 | + | 0.900445i | ||||
\(263\) | −332.869 | + | 192.182i | −1.26566 | + | 0.730729i | −0.974164 | − | 0.225843i | \(-0.927486\pi\) |
−0.291496 | + | 0.956572i | \(0.594153\pi\) | |||||||
\(264\) | 39.5365 | + | 32.4990i | 0.149760 | + | 0.123102i | ||||
\(265\) | 2.04460 | 0.00771548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1530 | 0.0455170 | ||||||||
\(268\) | −455.341 | − | 50.1102i | −1.69903 | − | 0.186978i | ||||
\(269\) | 32.7022 | − | 18.8806i | 0.121570 | − | 0.0701882i | −0.437982 | − | 0.898984i | \(-0.644307\pi\) |
0.559552 | + | 0.828795i | \(0.310973\pi\) | |||||||
\(270\) | −149.637 | − | 8.20895i | −0.554210 | − | 0.0304035i | ||||
\(271\) | 267.368 | + | 154.365i | 0.986597 | + | 0.569612i | 0.904255 | − | 0.426992i | \(-0.140427\pi\) |
0.0823420 | + | 0.996604i | \(0.473760\pi\) | |||||||
\(272\) | −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 | ||||
\(276\) | −234.017 | − | 171.778i | −0.847888 | − | 0.622382i | ||||
\(277\) | −211.492 | + | 122.105i | −0.763508 | + | 0.440812i | −0.830554 | − | 0.556938i | \(-0.811976\pi\) |
0.0670458 | + | 0.997750i | \(0.478643\pi\) | |||||||
\(278\) | −187.261 | + | 94.8385i | −0.673601 | + | 0.341146i | ||||
\(279\) | − | 268.913i | − | 0.963845i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 266.569 | 0.948646 | 0.474323 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474323 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(282\) | 89.3076 | + | 176.340i | 0.316694 | + | 0.625320i | ||||
\(283\) | 82.8026 | + | 143.418i | 0.292589 | + | 0.506778i | 0.974421 | − | 0.224730i | \(-0.0721501\pi\) |
−0.681833 | + | 0.731508i | \(0.738817\pi\) | |||||||
\(284\) | −337.904 | − | 248.035i | −1.18980 | − | 0.873362i | ||||
\(285\) | 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 | ||||
\(290\) | 2.06740 | − | 37.6856i | 0.00712898 | − | 0.129950i | ||||
\(291\) | 118.967 | + | 206.056i | 0.408820 | + | 0.708098i | ||||
\(292\) | −97.0040 | − | 10.6753i | −0.332206 | − | 0.0365591i | ||||
\(293\) | 34.3652i | 0.117288i | 0.998279 | + | 0.0586438i | \(0.0186776\pi\) | ||||
−0.998279 | + | 0.0586438i | \(0.981322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 153.966i | 0.521918i | ||||||||
\(296\) | 275.102 | − | 334.674i | 0.929399 | − | 1.13066i | ||||
\(297\) | −9.15405 | − | 15.8553i | −0.0308217 | − | 0.0533848i | ||||
\(298\) | 164.534 | + | 9.02620i | 0.552127 | + | 0.0302893i | ||||
\(299\) | 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 | ||||
\(304\) | −196.267 | − | 43.7279i | −0.645616 | − | 0.143842i | ||||
\(305\) | 247.154 | + | 428.083i | 0.810341 | + | 1.40355i | ||||
\(306\) | 682.964 | − | 345.888i | 2.23191 | − | 1.13035i | ||||
\(307\) | 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 | ||||||||
\(310\) | −231.876 | + | 117.434i | −0.747988 | + | 0.378819i | ||||
\(311\) | 363.673 | − | 209.967i | 1.16937 | − | 0.675135i | 0.215837 | − | 0.976429i | \(-0.430752\pi\) |
0.953531 | + | 0.301294i | \(0.0974187\pi\) | |||||||
\(312\) | 245.094 | + | 652.759i | 0.785557 | + | 2.09218i | ||||
\(313\) | −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 | 0.950552 | − | 0.310566i | \(-0.100519\pi\) |
0.206318 | + | 0.978485i | \(0.433852\pi\) | |||||||
\(318\) | 3.25324 | + | 0.178471i | 0.0102303 | + | 0.000561228i | ||||
\(319\) | 3.99311 | − | 2.30542i | 0.0125176 | − | 0.00722703i | ||||
\(320\) | −241.466 | − | 276.217i | −0.754583 | − | 0.863178i | ||||
\(321\) | −377.561 | −1.17620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −405.551 | −1.25558 | ||||||||
\(324\) | 187.086 | + | 20.5888i | 0.577427 | + | 0.0635456i | ||||
\(325\) | −129.921 | + | 75.0098i | −0.399756 | + | 0.230799i | ||||
\(326\) | −8.51308 | + | 155.180i | −0.0261137 | + | 0.476014i | ||||
\(327\) | −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 | \(0.105384\pi\) | |||||||
\(332\) | −187.628 | + | 255.611i | −0.565145 | + | 0.769912i | ||||
\(333\) | −556.301 | + | 321.180i | −1.67057 | + | 0.964505i | ||||
\(334\) | −56.1002 | − | 110.771i | −0.167965 | − | 0.331651i | ||||
\(335\) | − | 656.503i | − | 1.95971i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 302.404 | 0.897341 | 0.448671 | − | 0.893697i | \(-0.351898\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351898\pi\) | |||||||
\(338\) | −348.150 | + | 176.321i | −1.03003 | + | 0.521659i | ||||
\(339\) | 363.419 | + | 629.460i | 1.07203 | + | 1.85681i | ||||
\(340\) | −596.500 | − | 437.854i | −1.75441 | − | 1.28781i | ||||
\(341\) | −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 | ||||
\(346\) | −390.640 | − | 21.4302i | −1.12902 | − | 0.0619371i | ||||
\(347\) | −160.266 | − | 277.589i | −0.461862 | − | 0.799969i | 0.537192 | − | 0.843460i | \(-0.319485\pi\) |
−0.999054 | + | 0.0434916i | \(0.986152\pi\) | |||||||
\(348\) | 6.57904 | − | 59.7825i | 0.0189053 | − | 0.171789i | ||||
\(349\) | 380.678i | 1.09077i | 0.838186 | + | 0.545385i | \(0.183616\pi\) | ||||
−0.838186 | + | 0.545385i | \(0.816384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 249.426i | − | 0.710614i | ||||||
\(352\) | 12.1287 | − | 43.1485i | 0.0344566 | − | 0.122581i | ||||
\(353\) | −182.185 | − | 315.553i | −0.516104 | − | 0.893918i | −0.999825 | − | 0.0186962i | \(-0.994048\pi\) |
0.483721 | − | 0.875222i | \(-0.339285\pi\) | |||||||
\(354\) | −13.4395 | + | 244.981i | −0.0379646 | + | 0.692036i | ||||
\(355\) | 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 | 0.628965 | − | 0.777434i | \(-0.283479\pi\) |
−0.358795 | + | 0.933416i | \(0.616812\pi\) | |||||||
\(360\) | 191.217 | + | 509.269i | 0.531158 | + | 1.41464i | ||||
\(361\) | 101.529 | + | 175.854i | 0.281245 | + | 0.487130i | ||||
\(362\) | 127.393 | + | 251.540i | 0.351914 | + | 0.694863i | ||||
\(363\) | 543.704 | 1.49781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 139.859i | − | 0.383174i | ||||||
\(366\) | 355.889 | + | 702.713i | 0.972375 | + | 1.91998i | ||||
\(367\) | −380.222 | + | 219.521i | −1.03603 | + | 0.598150i | −0.918705 | − | 0.394944i | \(-0.870764\pi\) |
−0.117321 | + | 0.993094i | \(0.537431\pi\) | |||||||
\(368\) | −55.2860 | + | 248.144i | −0.150234 | + | 0.674305i | ||||
\(369\) | −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 | 0.173860 | − | 0.984770i | \(-0.444376\pi\) |
−0.765906 | + | 0.642952i | \(0.777709\pi\) | |||||||
\(374\) | 4.95169 | − | 90.2617i | 0.0132398 | − | 0.241341i | ||||
\(375\) | 388.613 | − | 224.366i | 1.03630 | − | 0.598309i | ||||
\(376\) | 109.924 | − | 133.727i | 0.292350 | − | 0.355657i | ||||
\(377\) | 62.8172 | 0.166624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 603.048 | 1.59116 | 0.795578 | − | 0.605852i | \(-0.207167\pi\) | ||||
0.795578 | + | 0.605852i | \(0.207167\pi\) | |||||||
\(380\) | 31.5231 | − | 286.444i | 0.0829554 | − | 0.753800i | ||||
\(381\) | −63.6187 | + | 36.7303i | −0.166978 | + | 0.0964049i | ||||
\(382\) | 568.091 | + | 31.1651i | 1.48715 | + | 0.0815839i | ||||
\(383\) | 63.5537 | + | 36.6927i | 0.165937 | + | 0.0958035i | 0.580668 | − | 0.814140i | \(-0.302791\pi\) |
−0.414732 | + | 0.909944i | \(0.636125\pi\) | |||||||
\(384\) | −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 | ||||
\(388\) | 123.301 | − | 167.976i | 0.317785 | − | 0.432927i | ||||
\(389\) | 295.141 | − | 170.400i | 0.758718 | − | 0.438046i | −0.0701174 | − | 0.997539i | \(-0.522337\pi\) |
0.828835 | + | 0.559493i | \(0.189004\pi\) | |||||||
\(390\) | −891.452 | + | 451.476i | −2.28577 | + | 1.15763i | ||||
\(391\) | 512.745i | 1.31137i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −539.581 | −1.37298 | ||||||||
\(394\) | 97.6799 | + | 192.872i | 0.247918 | + | 0.489522i | ||||
\(395\) | −335.719 | − | 581.482i | −0.849921 | − | 1.47211i | ||||
\(396\) | −39.3247 | + | 53.5730i | −0.0993047 | + | 0.135285i | ||||
\(397\) | −96.5963 | − | 55.7699i | −0.243316 | − | 0.140478i | 0.373384 | − | 0.927677i | \(-0.378197\pi\) |
−0.616700 | + | 0.787199i | \(0.711531\pi\) | |||||||
\(398\) | −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 | \(0.306254\pi\) | |||||||
\(402\) | 57.3052 | − | 1044.59i | 0.142550 | − | 2.59847i | ||||
\(403\) | −216.300 | − | 374.643i | −0.536725 | − | 0.929635i | ||||
\(404\) | −40.0252 | + | 363.701i | −0.0990722 | + | 0.900250i | ||||
\(405\) | 269.738i | 0.666019i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 75.8502i | 0.186364i | ||||||||
\(408\) | −910.893 | − | 748.753i | −2.23258 | − | 1.83518i | ||||
\(409\) | 333.480 | + | 577.604i | 0.815354 | + | 1.41223i | 0.909074 | + | 0.416635i | \(0.136791\pi\) |
−0.0937202 | + | 0.995599i | \(0.529876\pi\) | |||||||
\(410\) | 86.9585 | + | 4.77048i | 0.212094 | + | 0.0116353i | ||||
\(411\) | −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 | ||||
\(416\) | 437.024 | − | 426.469i | 1.05054 | − | 1.02517i | ||||
\(417\) | −239.686 | − | 415.149i | −0.574788 | − | 0.995561i | ||||
\(418\) | 31.4070 | − | 15.9061i | 0.0751364 | − | 0.0380528i | ||||
\(419\) | 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 | \(-0.993984\pi\) | ||
0.999821 | − | 0.0188998i | \(-0.00601636\pi\) | |||||||
\(422\) | 47.0947 | − | 23.8511i | 0.111599 | − | 0.0565193i | ||||
\(423\) | −222.283 | + | 128.335i | −0.525492 | + | 0.303393i | ||||
\(424\) | −1.00298 | − | 2.67125i | −0.00236553 | − | 0.00630011i | ||||
\(425\) | 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 | ||||
\(430\) | −238.662 | − | 13.0928i | −0.555029 | − | 0.0304485i | ||||
\(431\) | 543.875 | − | 314.006i | 1.26189 | − | 0.728553i | 0.288451 | − | 0.957495i | \(-0.406860\pi\) |
0.973440 | + | 0.228941i | \(0.0735264\pi\) | |||||||
\(432\) | 62.6796 | + | 199.525i | 0.145092 | + | 0.461864i | ||||
\(433\) | −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 | ||||||||
\(436\) | −12.8956 | + | 117.180i | −0.0295771 | + | 0.268762i | ||||
\(437\) | −172.935 | + | 99.8441i | −0.395732 | + | 0.228476i | ||||
\(438\) | 12.2081 | − | 222.534i | 0.0278723 | − | 0.508069i | ||||
\(439\) | −576.400 | − | 332.785i | −1.31298 | − | 0.758052i | −0.330395 | − | 0.943843i | \(-0.607182\pi\) |
−0.982589 | + | 0.185791i | \(0.940515\pi\) | |||||||
\(440\) | 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 | \(0.972677\pi\) | |||||||
\(444\) | 797.575 | + | 585.451i | 1.79634 | + | 1.31858i | ||||
\(445\) | 13.2095 | − | 7.62650i | 0.0296842 | − | 0.0171382i | ||||
\(446\) | 145.649 | + | 287.588i | 0.326567 | + | 0.644816i | ||||
\(447\) | 376.317i | 0.841872i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −279.029 | −0.621446 | −0.310723 | − | 0.950501i | \(-0.600571\pi\) | ||||
−0.310723 | + | 0.950501i | \(0.600571\pi\) | |||||||
\(450\) | −166.388 | + | 84.2673i | −0.369752 | + | 0.187261i | ||||
\(451\) | 5.31970 | + | 9.21400i | 0.0117954 | + | 0.0204301i | ||||
\(452\) | 376.658 | − | 513.131i | 0.833315 | − | 1.13525i | ||||
\(453\) | −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 | \(-0.122584\pi\) | |||||||
\(458\) | 457.814 | + | 25.1153i | 0.999593 | + | 0.0548369i | ||||
\(459\) | 210.903 | + | 365.294i | 0.459483 | + | 0.795848i | ||||
\(460\) | −362.156 | − | 39.8552i | −0.787296 | − | 0.0866417i | ||||
\(461\) | 483.262i | 1.04829i | 0.851629 | + | 0.524145i | \(0.175615\pi\) | ||||
−0.851629 | + | 0.524145i | \(0.824385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6326i | 0.0855995i | 0.999084 | + | 0.0427997i | \(0.0136277\pi\) | ||||
−0.999084 | + | 0.0427997i | \(0.986372\pi\) | |||||||
\(464\) | −50.2499 | + | 15.7857i | −0.108297 | + | 0.0340209i | ||||
\(465\) | −296.792 | − | 514.059i | −0.638262 | − | 1.10550i | ||||
\(466\) | 29.5964 | − | 539.498i | 0.0635116 | − | 1.15772i | ||||
\(467\) | 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 | ||||
\(472\) | 201.154 | − | 75.5282i | 0.426175 | − | 0.160017i | ||||
\(473\) | −14.6002 | − | 25.2883i | −0.0308673 | − | 0.0534637i | ||||
\(474\) | −483.418 | − | 954.522i | −1.01987 | − | 2.01376i | ||||
\(475\) | 98.8029 | 0.208006 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.23072i | 0.00886943i | ||||||||
\(478\) | −142.008 | − | 280.400i | −0.297089 | − | 0.586610i | ||||
\(479\) | −579.039 | + | 334.308i | −1.20885 | + | 0.697930i | −0.962508 | − | 0.271254i | \(-0.912562\pi\) |
−0.246341 | + | 0.969183i | \(0.579228\pi\) | |||||||
\(480\) | 599.653 | − | 585.171i | 1.24928 | − | 1.21911i | ||||
\(481\) | −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 | ||||
\(486\) | −36.4330 | + | 664.118i | −0.0749650 | + | 1.36650i | ||||
\(487\) | −362.418 | + | 209.242i | −0.744185 | + | 0.429656i | −0.823589 | − | 0.567187i | \(-0.808032\pi\) |
0.0794038 | + | 0.996843i | \(0.474698\pi\) | |||||||
\(488\) | 438.044 | − | 532.901i | 0.897631 | − | 1.09201i | ||||
\(489\) | −354.924 | −0.725816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 381.031 | 0.776030 | 0.388015 | − | 0.921653i | \(-0.373161\pi\) | ||||
0.388015 | + | 0.921653i | \(0.373161\pi\) | |||||||
\(492\) | 137.946 | + | 15.1810i | 0.280379 | + | 0.0308556i | ||||
\(493\) | −91.9984 | + | 53.1153i | −0.186609 | + | 0.107739i | ||||
\(494\) | 478.907 | + | 26.2725i | 0.969448 | + | 0.0531832i | ||||
\(495\) | −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 | \(0.0219036\pi\) | |||||||
\(500\) | −316.795 | − | 232.540i | −0.633590 | − | 0.465079i | ||||
\(501\) | 245.575 | − | 141.783i | 0.490169 | − | 0.282999i | ||||
\(502\) | 558.723 | − | 282.965i | 1.11299 | − | 0.563676i | ||||
\(503\) | − | 754.754i | − | 1.50050i | −0.661151 | − | 0.750252i | \(-0.729932\pi\) | ||
0.661151 | − | 0.750252i | \(-0.270068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −524.378 | −1.03837 | ||||||||
\(506\) | −20.1104 | − | 39.7085i | −0.0397438 | − | 0.0784752i | ||||
\(507\) | −445.617 | − | 771.832i | −0.878930 | − | 1.52235i | ||||
\(508\) | 51.8615 | + | 38.0684i | 0.102090 | + | 0.0749377i | ||||
\(509\) | −427.842 | − | 247.015i | −0.840554 | − | 0.485294i | 0.0168985 | − | 0.999857i | \(-0.494621\pi\) |
−0.857452 | + | 0.514563i | \(0.827954\pi\) | |||||||
\(510\) | 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 | ||||
\(514\) | −38.2184 | + | 696.663i | −0.0743549 | + | 1.35538i | ||||
\(515\) | 114.046 | + | 197.533i | 0.221449 | + | 0.383560i | ||||
\(516\) | −378.602 | − | 41.6650i | −0.733725 | − | 0.0807462i | ||||
\(517\) | 30.3078i | 0.0586224i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 893.460i | − | 1.72150i | ||||||
\(520\) | 676.030 | + | 555.696i | 1.30006 | + | 1.06865i | ||||
\(521\) | −16.4374 | − | 28.4704i | −0.0315496 | − | 0.0546456i | 0.849819 | − | 0.527074i | \(-0.176711\pi\) |
−0.881369 | + | 0.472428i | \(0.843378\pi\) | |||||||
\(522\) | 77.9795 | + | 4.27789i | 0.149386 | + | 0.00819520i | ||||
\(523\) | −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 | ||||
\(528\) | 99.9090 | + | 22.2595i | 0.189222 | + | 0.0421581i | ||||
\(529\) | −138.265 | − | 239.482i | −0.261371 | − | 0.452708i | ||||
\(530\) | 3.64804 | − | 1.84755i | 0.00688309 | − | 0.00348594i | ||||
\(531\) | −318.588 | −0.599977 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 144.949i | 0.271949i | ||||||||
\(534\) | 21.6838 | − | 10.9818i | 0.0406064 | − | 0.0205651i | ||||
\(535\) | −410.382 | + | 236.934i | −0.767069 | + | 0.442867i | ||||
\(536\) | −857.713 | + | 322.049i | −1.60021 | + | 0.600837i | ||||
\(537\) | 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 | \(-0.877514\pi\) |
−0.788521 | − | 0.615008i | \(-0.789153\pi\) | |||||||
\(542\) | 616.533 | + | 33.8225i | 1.13751 | + | 0.0624032i | ||||
\(543\) | −557.653 | + | 321.961i | −1.02699 | + | 0.592930i | ||||
\(544\) | −279.437 | + | 994.109i | −0.513670 | + | 1.82741i | ||||
\(545\) | −168.948 | −0.309997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −986.888 | −1.80418 | −0.902091 | − | 0.431545i | \(-0.857968\pi\) | ||||
−0.902091 | + | 0.431545i | \(0.857968\pi\) | |||||||
\(548\) | 76.2230 | + | 8.38831i | 0.139093 | + | 0.0153071i | ||||
\(549\) | −885.795 | + | 511.414i | −1.61347 | + | 0.931537i | ||||
\(550\) | −1.20636 | + | 21.9901i | −0.00219339 | + | 0.0399821i | ||||
\(551\) | −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 | ||||
\(556\) | −248.418 | + | 338.427i | −0.446796 | + | 0.608681i | ||||
\(557\) | −418.767 | + | 241.775i | −0.751826 | + | 0.434067i | −0.826353 | − | 0.563152i | \(-0.809588\pi\) |
0.0745276 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(558\) | −242.995 | − | 479.801i | −0.435476 | − | 0.859859i | ||||
\(559\) | − | 397.821i | − | 0.711665i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 206.444 | 0.367993 | ||||||||
\(562\) | 475.620 | − | 240.878i | 0.846300 | − | 0.428609i | ||||
\(563\) | 260.447 | + | 451.107i | 0.462605 | + | 0.801256i | 0.999090 | − | 0.0426543i | \(-0.0135814\pi\) |
−0.536485 | + | 0.843910i | \(0.680248\pi\) | |||||||
\(564\) | 318.690 | + | 233.931i | 0.565053 | + | 0.414771i | ||||
\(565\) | 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 | \(-0.0560916\pi\) | |||||||
\(570\) | 657.123 | + | 36.0493i | 1.15285 | + | 0.0632444i | ||||
\(571\) | 499.792 | + | 865.665i | 0.875292 | + | 1.51605i | 0.856451 | + | 0.516228i | \(0.172664\pi\) |
0.0188408 | + | 0.999822i | \(0.494002\pi\) | |||||||
\(572\) | −11.6947 | + | 106.268i | −0.0204453 | + | 0.185782i | ||||
\(573\) | 1299.32i | 2.26758i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 124.918i | − | 0.217249i | ||||||
\(576\) | 571.551 | − | 499.645i | 0.992277 | − | 0.867440i | ||||
\(577\) | 232.929 | + | 403.445i | 0.403690 | + | 0.699212i | 0.994168 | − | 0.107842i | \(-0.0343940\pi\) |
−0.590478 | + | 0.807054i | \(0.701061\pi\) | |||||||
\(578\) | −82.4223 | + | 1502.43i | −0.142599 | + | 2.59936i | ||||
\(579\) | −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 | ||||
\(584\) | −182.724 | + | 68.6079i | −0.312883 | + | 0.117479i | ||||
\(585\) | −648.772 | − | 1123.71i | −1.10901 | − | 1.92087i | ||||
\(586\) | 31.0532 | + | 61.3154i | 0.0529918 | + | 0.104634i | ||||
\(587\) | 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 | ||||||||
\(590\) | 139.127 | + | 274.710i | 0.235808 | + | 0.465610i | ||||
\(591\) | −427.587 | + | 246.868i | −0.723498 | + | 0.417712i | ||||
\(592\) | 188.425 | − | 845.724i | 0.318286 | − | 1.42859i | ||||
\(593\) | 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 | ||||
\(598\) | 33.2168 | − | 605.491i | 0.0555465 | − | 1.01253i | ||||
\(599\) | 8.02545 | − | 4.63349i | 0.0133981 | − | 0.00773538i | −0.493286 | − | 0.869867i | \(-0.664204\pi\) |
0.506684 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(600\) | 221.918 | + | 182.416i | 0.369863 | + | 0.304027i | ||||
\(601\) | −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 | ||||||||
\(604\) | −25.2643 | + | 229.572i | −0.0418283 | + | 0.380086i | ||||
\(605\) | 590.966 | − | 341.194i | 0.976804 | − | 0.563958i | ||||
\(606\) | −834.357 | − | 45.7722i | −1.37683 | − | 0.0755316i | ||||
\(607\) | −887.396 | − | 512.339i | −1.46194 | − | 0.844050i | −0.462837 | − | 0.886443i | \(-0.653169\pi\) |
−0.999101 | + | 0.0423930i | \(0.986502\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 906.012 | − | 1234.28i | 1.48041 | − | 2.01680i | ||||
\(613\) | −350.583 | + | 202.409i | −0.571914 | + | 0.330195i | −0.757913 | − | 0.652355i | \(-0.773781\pi\) |
0.186000 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(614\) | 397.765 | − | 201.448i | 0.647826 | − | 0.328091i | ||||
\(615\) | 198.889i | 0.323396i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 894.209 | 1.44928 | 0.724642 | − | 0.689125i | \(-0.242005\pi\) | ||||
0.724642 | + | 0.689125i | \(0.242005\pi\) | |||||||
\(618\) | 164.220 | + | 324.258i | 0.265729 | + | 0.524689i | ||||
\(619\) | −389.694 | − | 674.970i | −0.629554 | − | 1.09042i | −0.987641 | − | 0.156731i | \(-0.949904\pi\) |
0.358087 | − | 0.933688i | \(-0.383429\pi\) | |||||||
\(620\) | −307.604 | + | 419.057i | −0.496136 | + | 0.675899i | ||||
\(621\) | 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 | ||||
\(626\) | −32.1944 | + | 586.855i | −0.0514288 | + | 0.937469i | ||||
\(627\) | 40.1997 | + | 69.6278i | 0.0641143 | + | 0.111049i | ||||
\(628\) | −1.63198 | + | 14.8295i | −0.00259869 | + | 0.0236138i | ||||
\(629\) | − | 1747.53i | − | 2.77827i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 780.191i | − | 1.23644i | −0.786007 | − | 0.618218i | \(-0.787855\pi\) | ||
0.786007 | − | 0.618218i | \(-0.212145\pi\) | |||||||
\(632\) | −595.012 | + | 723.859i | −0.941474 | + | 1.14535i | ||||
\(633\) | 60.2793 | + | 104.407i | 0.0952279 | + | 0.164940i | ||||
\(634\) | 845.650 | + | 46.3917i | 1.33383 | + | 0.0731730i | ||||
\(635\) | −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 | ||||
\(640\) | −680.427 | − | 274.639i | −1.06317 | − | 0.429124i | ||||
\(641\) | 11.6570 | + | 20.1905i | 0.0181856 | + | 0.0314984i | 0.874975 | − | 0.484168i | \(-0.160878\pi\) |
−0.856789 | + | 0.515667i | \(0.827544\pi\) | |||||||
\(642\) | −673.655 | + | 341.173i | −1.04931 | + | 0.531422i | ||||
\(643\) | −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 | ||||||
\(646\) | −723.595 | + | 366.465i | −1.12012 | + | 0.567283i | ||||
\(647\) | 184.840 | − | 106.717i | 0.285687 | − | 0.164942i | −0.350308 | − | 0.936635i | \(-0.613923\pi\) |
0.635995 | + | 0.771693i | \(0.280590\pi\) | |||||||
\(648\) | 352.409 | − | 132.320i | 0.543841 | − | 0.204198i | ||||
\(649\) | −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 | 0.306528 | − | 0.951862i | \(-0.400833\pi\) |
−0.671073 | + | 0.741392i | \(0.734166\pi\) | |||||||
\(654\) | −268.820 | − | 14.7473i | −0.411039 | − | 0.0225493i | ||||
\(655\) | −586.485 | + | 338.607i | −0.895397 | + | 0.516958i | ||||
\(656\) | −36.4251 | − | 115.950i | −0.0555260 | − | 0.176754i | ||||
\(657\) | 289.397 | 0.440483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1234.48 | 1.87327 | 0.936633 | − | 0.350313i | \(-0.113925\pi\) | ||||
0.936633 | + | 0.350313i | \(0.113925\pi\) | |||||||
\(660\) | −16.0467 | + | 145.813i | −0.0243131 | + | 0.220929i | ||||
\(661\) | 504.662 | − | 291.367i | 0.763482 | − | 0.440797i | −0.0670625 | − | 0.997749i | \(-0.521363\pi\) |
0.830545 | + | 0.556952i | \(0.188029\pi\) | |||||||
\(662\) | 13.8768 | − | 252.953i | 0.0209619 | − | 0.382104i | ||||
\(663\) | 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 | ||||
\(668\) | −200.191 | − | 146.948i | −0.299687 | − | 0.219982i | ||||
\(669\) | −637.569 | + | 368.101i | −0.953018 | + | 0.550225i | ||||
\(670\) | −593.231 | − | 1171.35i | −0.885419 | − | 1.74828i | ||||
\(671\) | 120.776i | 0.179994i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −399.145 | −0.593083 | −0.296542 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296542 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(674\) | 539.558 | − | 273.259i | 0.800530 | − | 0.405429i | ||||
\(675\) | −51.3815 | − | 88.9953i | −0.0761207 | − | 0.131845i | ||||
\(676\) | −461.851 | + | 629.192i | −0.683212 | + | 0.930758i | ||||
\(677\) | 653.388 | + | 377.234i | 0.965123 | + | 0.557214i | 0.897746 | − | 0.440514i | \(-0.145204\pi\) |
0.0673768 | + | 0.997728i | \(0.478537\pi\) | |||||||
\(678\) | 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 | ||||
\(682\) | −63.4113 | − | 3.47870i | −0.0929785 | − | 0.00510073i | ||||
\(683\) | −144.132 | − | 249.644i | −0.211028 | − | 0.365511i | 0.741009 | − | 0.671495i | \(-0.234348\pi\) |
−0.952036 | + | 0.305985i | \(0.901014\pi\) | |||||||
\(684\) | 592.713 | + | 65.2279i | 0.866539 | + | 0.0953624i | ||||
\(685\) | 109.897i | 0.160433i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1047.10i | 1.52416i | ||||||||
\(688\) | 99.9706 | + | 318.232i | 0.145306 | + | 0.462547i | ||||
\(689\) | 3.40298 | + | 5.89414i | 0.00493901 | + | 0.00855462i | ||||
\(690\) | 45.5778 | − | 830.813i | 0.0660548 | − | 1.20408i | ||||
\(691\) | −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 | ||||
\(696\) | −42.2823 | − | 112.611i | −0.0607504 | − | 0.161797i | ||||
\(697\) | −122.562 | − | 212.284i | −0.175842 | − | 0.304568i | ||||
\(698\) | 343.990 | + | 679.217i | 0.492822 | + | 0.973090i | ||||
\(699\) | 1233.92 | 1.76527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1126.50i | − | 1.60700i | −0.595307 | − | 0.803498i | \(-0.702970\pi\) | ||
0.595307 | − | 0.803498i | \(-0.297030\pi\) | |||||||
\(702\) | −225.386 | − | 445.032i | −0.321063 | − | 0.633949i | ||||
\(703\) | 589.396 | − | 340.288i | 0.838401 | − | 0.484051i | ||||
\(704\) | −17.3495 | − | 87.9464i | −0.0246442 | − | 0.124924i | ||||
\(705\) | −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 | 0.986651 | − | 0.162847i | \(-0.0520678\pi\) |
0.352296 | + | 0.935889i | \(0.385401\pi\) | |||||||
\(710\) | 65.8112 | − | 1199.64i | 0.0926918 | − | 1.68963i | ||||
\(711\) | 1203.21 | − | 694.673i | 1.69228 | − | 0.977037i | ||||
\(712\) | −16.4439 | − | 13.5168i | −0.0230953 | − | 0.0189843i | ||||
\(713\) | 360.218 | 0.505214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −153.215 | −0.214286 | ||||||||
\(716\) | −287.106 | − | 31.5959i | −0.400986 | − | 0.0441284i | ||||
\(717\) | 621.633 | − | 358.900i | 0.866991 | − | 0.500558i | ||||
\(718\) | 223.654 | + | 12.2695i | 0.311496 | + | 0.0170885i | ||||
\(719\) | 524.259 | + | 302.681i | 0.729150 | + | 0.420975i | 0.818111 | − | 0.575060i | \(-0.195021\pi\) |
−0.0889614 | + | 0.996035i | \(0.528355\pi\) | |||||||
\(720\) | 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 | ||||
\(724\) | 454.595 | + | 333.690i | 0.627894 | + | 0.460898i | ||||
\(725\) | 22.4132 | − | 12.9403i | 0.0309148 | − | 0.0178487i | ||||
\(726\) | 970.091 | − | 491.303i | 1.33621 | − | 0.676725i | ||||
\(727\) | 443.659i | 0.610260i | 0.952311 | + | 0.305130i | \(0.0986999\pi\) | ||||
−0.952311 | + | 0.305130i | \(0.901300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1095.46 | −1.50269 | ||||||||
\(730\) | −126.379 | − | 249.540i | −0.173123 | − | 0.341835i | ||||
\(731\) | 336.379 | + | 582.625i | 0.460162 | + | 0.797025i | ||||
\(732\) | 1269.97 | + | 932.210i | 1.73494 | + | 1.27351i | ||||
\(733\) | 649.541 | + | 375.013i | 0.886141 | + | 0.511614i | 0.872678 | − | 0.488296i | \(-0.162381\pi\) |
0.0134626 | + | 0.999909i | \(0.495715\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | −9.87113 | + | 179.935i | −0.0133755 | + | 0.243815i | ||||
\(739\) | −309.646 | − | 536.323i | −0.419007 | − | 0.725742i | 0.576833 | − | 0.816862i | \(-0.304288\pi\) |
−0.995840 | + | 0.0911205i | \(0.970955\pi\) | |||||||
\(740\) | 1234.30 | + | 135.834i | 1.66797 | + | 0.183560i | ||||
\(741\) | 1095.34i | 1.47819i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.5255i | − | 0.0410842i | −0.999789 | − | 0.0205421i | \(-0.993461\pi\) | ||
0.999789 | − | 0.0205421i | \(-0.00653921\pi\) | |||||||
\(744\) | −526.020 | + | 639.927i | −0.707016 | + | 0.860117i | ||||
\(745\) | 236.153 | + | 409.029i | 0.316984 | + | 0.549032i | ||||
\(746\) | −509.227 | − | 27.9358i | −0.682610 | − | 0.0374475i | ||||
\(747\) | 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 | −0.176001 | − | 0.984390i | \(-0.556316\pi\) |
−0.940507 | + | 0.339773i | \(0.889650\pi\) | |||||||
\(752\) | 75.2898 | − | 337.929i | 0.100119 | − | 0.449374i | ||||
\(753\) | 715.142 | + | 1238.66i | 0.949723 | + | 1.64497i | ||||
\(754\) | 112.080 | − | 56.7630i | 0.148647 | − | 0.0752825i | ||||
\(755\) | −330.993 | −0.438401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1171.15i | 1.54710i | 0.633736 | + | 0.773550i | \(0.281521\pi\) | ||||
−0.633736 | + | 0.773550i | \(0.718479\pi\) | |||||||
\(758\) | 1075.97 | − | 544.927i | 1.41949 | − | 0.718902i | ||||
\(759\) | 88.0318 | − | 50.8252i | 0.115984 | − | 0.0669633i | ||||
\(760\) | −202.593 | − | 539.566i | −0.266569 | − | 0.709955i | ||||
\(761\) | 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 | ||||
\(766\) | 146.551 | + | 8.03966i | 0.191319 | + | 0.0104956i | ||||
\(767\) | −443.849 | + | 256.257i | −0.578682 | + | 0.334102i | ||||
\(768\) | −1058.68 | − | 496.383i | −1.37849 | − | 0.646332i | ||||
\(769\) | 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 | ||||||||
\(772\) | 492.428 | + | 54.1915i | 0.637859 | + | 0.0701962i | ||||
\(773\) | 154.345 | − | 89.1114i | 0.199671 | − | 0.115280i | −0.396831 | − | 0.917892i | \(-0.629890\pi\) |
0.596502 | + | 0.802612i | \(0.296557\pi\) | |||||||
\(774\) | 27.0919 | − | 493.843i | 0.0350024 | − | 0.638040i | ||||
\(775\) | −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 | ||||
\(780\) | −1182.59 | + | 1611.07i | −1.51614 | + | 2.06548i | ||||
\(781\) | 127.112 | − | 73.3880i | 0.162755 | − | 0.0939667i | ||||
\(782\) | 463.328 | + | 914.854i | 0.592491 | + | 1.16989i | ||||
\(783\) | 43.0296i | 0.0549548i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3809 | −0.0272368 | ||||||||
\(786\) | −962.735 | + | 487.578i | −1.22485 | + | 0.620328i | ||||
\(787\) | −553.948 | − | 959.466i | −0.703873 | − | 1.21914i | −0.967097 | − | 0.254409i | \(-0.918119\pi\) |
0.263224 | − | 0.964735i | \(-0.415214\pi\) | |||||||
\(788\) | 348.566 | + | 255.861i | 0.442343 | + | 0.324697i | ||||
\(789\) | −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 | ||||
\(794\) | −222.745 | − | 12.2196i | −0.280535 | − | 0.0153899i | ||||
\(795\) | 4.66933 | + | 8.08752i | 0.00587338 | + | 0.0101730i | ||||
\(796\) | −145.205 | + | 1319.45i | −0.182418 | + | 1.65760i | ||||
\(797\) | − | 1094.69i | − | 1.37351i | −0.726889 | − | 0.686755i | \(-0.759034\pi\) | ||
0.726889 | − | 0.686755i | \(-0.240966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 698.269i | − | 0.873929i | ||||||
\(800\) | 68.0782 | − | 242.191i | 0.0850977 | − | 0.302739i | ||||
\(801\) | 15.7808 | + | 27.3332i | 0.0197014 | + | 0.0341238i | ||||
\(802\) | −37.3069 | + | 680.048i | −0.0465173 | + | 0.847940i | ||||
\(803\) | 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 | ||||
\(808\) | 257.234 | + | 685.093i | 0.318359 | + | 0.847887i | ||||
\(809\) | 693.377 | + | 1200.96i | 0.857079 | + | 1.48450i | 0.874703 | + | 0.484659i | \(0.161056\pi\) |
−0.0176240 | + | 0.999845i | \(0.505610\pi\) | |||||||
\(810\) | 243.741 | + | 481.273i | 0.300915 | + | 0.594165i | ||||
\(811\) | 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 | ||||||||
\(814\) | 68.5400 | + | 135.334i | 0.0842014 | + | 0.166258i | ||||
\(815\) | −385.776 | + | 222.728i | −0.473345 | + | 0.273286i | ||||
\(816\) | −2301.83 | − | 512.842i | −2.82087 | − | 0.628483i | ||||
\(817\) | −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 | −0.203250 | − | 0.979127i | \(-0.565150\pi\) |
−0.949574 | + | 0.313544i | \(0.898484\pi\) | |||||||
\(822\) | −9.59275 | + | 174.861i | −0.0116700 | + | 0.212726i | ||||
\(823\) | 785.625 | − | 453.581i | 0.954587 | − | 0.551131i | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(824\) | 202.130 | − | 245.900i | 0.245303 | − | 0.298422i | ||||
\(825\) | −50.2952 | −0.0609638 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −607.144 | −0.734152 | −0.367076 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367076 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(828\) | 82.4688 | − | 749.378i | 0.0996000 | − | 0.905046i | ||||
\(829\) | −370.632 | + | 213.984i | −0.447083 | + | 0.258124i | −0.706598 | − | 0.707616i | \(-0.749771\pi\) |
0.259514 | + | 0.965739i | \(0.416438\pi\) | |||||||
\(830\) | −907.476 | − | 49.7834i | −1.09334 | − | 0.0599800i | ||||
\(831\) | −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 | ||||
\(836\) | 41.6642 | − | 56.7602i | 0.0498375 | − | 0.0678949i | ||||
\(837\) | 256.629 | − | 148.165i | 0.306606 | − | 0.177019i | ||||
\(838\) | 357.186 | − | 180.897i | 0.426237 | − | 0.215868i | ||||
\(839\) | − | 1133.09i | − | 1.35053i | −0.737575 | − | 0.675265i | \(-0.764029\pi\) | ||
0.737575 | − | 0.675265i | \(-0.235971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 830.163 | 0.987114 | ||||||||
\(842\) | −14.3799 | − | 28.3936i | −0.0170783 | − | 0.0337216i | ||||
\(843\) | 608.774 | + | 1054.43i | 0.722152 | + | 1.25080i | ||||
\(844\) | 62.4753 | − | 85.1117i | 0.0740228 | − | 0.100843i | ||||
\(845\) | −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 | ||||
\(850\) | 27.7937 | − | 506.637i | 0.0326985 | − | 0.596043i | ||||
\(851\) | −430.232 | − | 745.184i | −0.505561 | − | 0.875657i | ||||
\(852\) | 209.429 | − | 1903.04i | 0.245809 | − | 2.23362i | ||||
\(853\) | − | 169.502i | − | 0.198712i | −0.995052 | − | 0.0993562i | \(-0.968322\pi\) | ||
0.995052 | − | 0.0993562i | \(-0.0316783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 854.563i | 0.999489i | ||||||||
\(856\) | 510.865 | + | 419.930i | 0.596805 | + | 0.490573i | ||||
\(857\) | −117.039 | − | 202.718i | −0.136569 | − | 0.236544i | 0.789627 | − | 0.613587i | \(-0.210274\pi\) |
−0.926196 | + | 0.377043i | \(0.876941\pi\) | |||||||
\(858\) | −243.786 | − | 13.3739i | −0.284132 | − | 0.0155873i | ||||
\(859\) | 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 | 0.836894 | − | 0.547365i | \(-0.184369\pi\) |
−0.0555850 | + | 0.998454i | \(0.517702\pi\) | |||||||
\(864\) | 292.130 | + | 299.360i | 0.338114 | + | 0.346481i | ||||
\(865\) | −560.680 | − | 971.126i | −0.648185 | − | 1.12269i | ||||
\(866\) | −1408.17 | + | 713.168i | −1.62606 | + | 0.823519i | ||||
\(867\) | −3436.32 | −3.96346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 164.055i | − | 0.188786i | ||||||
\(870\) | 153.789 | − | 77.8862i | 0.176768 | − | 0.0895244i | ||||
\(871\) | 1892.55 | − | 1092.67i | 2.17285 | − | 1.25450i | ||||
\(872\) | 82.8778 | + | 220.729i | 0.0950434 | + | 0.253129i | ||||
\(873\) | −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 | 0.508507 | − | 0.861058i | \(-0.330198\pi\) |
−0.491445 | + | 0.870909i | \(0.663531\pi\) | |||||||
\(878\) | −1329.14 | − | 72.9157i | −1.51383 | − | 0.0830475i | ||||
\(879\) | −135.933 | + | 78.4811i | −0.154645 | + | 0.0892846i | ||||
\(880\) | 122.562 | − | 38.5022i | 0.139275 | − | 0.0437525i | ||||
\(881\) | −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 | \(0.355114\pi\) | |||||||
\(884\) | 269.438 | − | 2448.33i | 0.304794 | − | 2.76960i | ||||
\(885\) | −609.019 | + | 351.617i | −0.688157 | + | 0.397308i | ||||
\(886\) | −55.5604 | + | 1012.78i | −0.0627092 | + | 1.14309i | ||||
\(887\) | −1412.32 | − | 815.402i | −1.59224 | − | 0.919280i | −0.992922 | − | 0.118770i | \(-0.962105\pi\) |
−0.599319 | − | 0.800511i | \(-0.704562\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 519.742 | + | 381.511i | 0.582670 | + | 0.427702i | ||||
\(893\) | 235.507 | − | 135.970i | 0.263726 | − | 0.152262i | ||||
\(894\) | 340.048 | + | 671.434i | 0.380367 | + | 0.751045i | ||||
\(895\) | − | 413.945i | − | 0.462508i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1384.86 | 1.54388 | ||||||||
\(898\) | −497.852 | + | 252.137i | −0.554400 | + | 0.280776i | ||||
\(899\) | 37.3150 | + | 64.6314i | 0.0415072 | + | 0.0718925i | ||||
\(900\) | −220.729 | + | 300.704i | −0.245254 | + | 0.334116i | ||||
\(901\) | −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 | ||||
\(906\) | −526.655 | − | 28.8919i | −0.581297 | − | 0.0318895i | ||||
\(907\) | 476.931 | + | 826.069i | 0.525834 | + | 0.910771i | 0.999547 | + | 0.0300919i | \(0.00958001\pi\) |
−0.473713 | + | 0.880679i | \(0.657087\pi\) | |||||||
\(908\) | −681.004 | − | 74.9443i | −0.750005 | − | 0.0825378i | ||||
\(909\) | − | 1085.05i | − | 1.19367i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1681.15i | 1.84539i | 0.385534 | + | 0.922694i | \(0.374017\pi\) | ||||
−0.385534 | + | 0.922694i | \(0.625983\pi\) | |||||||
\(912\) | −275.255 | − | 876.207i | −0.301815 | − | 0.960754i | ||||
\(913\) | −55.5150 | − | 96.1548i | −0.0608051 | − | 0.105317i | ||||
\(914\) | 78.9753 | − | 1439.60i | 0.0864062 | − | 1.57505i | ||||
\(915\) | −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 | 0.242817 | − | 0.970072i | \(-0.421929\pi\) |
−0.718698 | + | 0.695322i | \(0.755262\pi\) | |||||||
\(920\) | −682.183 | + | 256.142i | −0.741503 | + | 0.278415i | ||||
\(921\) | 509.122 | + | 881.826i | 0.552793 | + | 0.957466i | ||||
\(922\) | 436.686 | + | 862.249i | 0.473630 | + | 0.935195i | ||||
\(923\) | 1999.64 | 2.16646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 425.746i | 0.460266i | ||||||||
\(926\) | 35.8129 | + | 70.7135i | 0.0386748 | + | 0.0763645i | ||||
\(927\) | −408.739 | + | 235.985i | −0.440926 | + | 0.254569i | ||||
\(928\) | −75.3930 | + | 73.5722i | −0.0812424 | + | 0.0792804i | ||||
\(929\) | 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 | ||||
\(934\) | 1.94861 | − | 35.5202i | 0.00208631 | − | 0.0380302i | ||||
\(935\) | 224.389 | − | 129.551i | 0.239989 | − | 0.138558i | ||||
\(936\) | −1149.85 | + | 1398.85i | −1.22847 | + | 1.49450i | ||||
\(937\) | 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 | ||||||||
\(940\) | 493.193 | + | 54.2758i | 0.524674 | + | 0.0577402i | ||||
\(941\) | −758.175 | + | 437.732i | −0.805712 | + | 0.465178i | −0.845464 | − | 0.534032i | \(-0.820676\pi\) |
0.0397529 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(942\) | −34.0199 | − | 1.86631i | −0.0361146 | − | 0.00198122i | ||||
\(943\) | −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 | \(-0.0630572\pi\) | |||||||
\(948\) | −1725.06 | − | 1266.26i | −1.81968 | − | 1.33571i | ||||
\(949\) | 403.181 | − | 232.777i | 0.424849 | − | 0.245287i | ||||
\(950\) | 176.287 | − | 89.2805i | 0.185565 | − | 0.0939795i | ||||
\(951\) | 1934.14i | 2.03380i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −882.129 | −0.925633 | −0.462817 | − | 0.886454i | \(-0.653161\pi\) | ||||
−0.462817 | + | 0.886454i | \(0.653161\pi\) | |||||||
\(954\) | 3.82297 | + | 7.54856i | 0.00400731 | + | 0.00791254i | ||||
\(955\) | 815.373 | + | 1412.27i | 0.853793 | + | 1.47881i | ||||
\(956\) | −506.751 | − | 371.975i | −0.530074 | − | 0.389095i | ||||
\(957\) | 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 | ||||
\(962\) | −113.209 | + | 2063.63i | −0.117681 | + | 2.14515i | ||||
\(963\) | −490.267 | − | 849.167i | −0.509103 | − | 0.881793i | ||||
\(964\) | −388.504 | − | 42.7547i | −0.403012 | − | 0.0443514i | ||||
\(965\) | 709.973i | 0.735724i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1410.24i | 1.45836i | 0.684320 | + | 0.729182i | \(0.260099\pi\) | ||||
−0.684320 | + | 0.729182i | \(0.739901\pi\) | |||||||
\(968\) | −735.666 | − | 604.716i | −0.759985 | − | 0.624707i | ||||
\(969\) | −926.171 | − | 1604.18i | −0.955801 | − | 1.65550i | ||||
\(970\) | 596.352 | + | 32.7154i | 0.614796 | + | 0.0337272i | ||||
\(971\) | 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 | ||||
\(976\) | 300.029 | − | 1346.64i | 0.307406 | − | 1.37976i | ||||
\(977\) | −55.9074 | − | 96.8344i | −0.0572235 | − | 0.0991141i | 0.835995 | − | 0.548738i | \(-0.184891\pi\) |
−0.893218 | + | 0.449624i | \(0.851558\pi\) | |||||||
\(978\) | −633.265 | + | 320.717i | −0.647510 | + | 0.327932i | ||||
\(979\) | 3.72682 | 0.00380676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 349.590i | − | 0.356360i | ||||||
\(982\) | 679.845 | − | 344.308i | 0.692307 | − | 0.350619i | ||||
\(983\) | 175.133 | − | 101.113i | 0.178162 | − | 0.102862i | −0.408267 | − | 0.912863i | \(-0.633867\pi\) |
0.586429 | + | 0.810001i | \(0.300533\pi\) | |||||||
\(984\) | 259.846 | − | 97.5652i | 0.264071 | − | 0.0991517i | ||||
\(985\) | −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 | ||||
\(990\) | −190.196 | − | 10.4340i | −0.192118 | − | 0.0105394i | ||||
\(991\) | 163.735 | − | 94.5322i | 0.165222 | − | 0.0953907i | −0.415109 | − | 0.909772i | \(-0.636257\pi\) |
0.580331 | + | 0.814381i | \(0.302923\pi\) | |||||||
\(992\) | 698.389 | + | 196.312i | 0.704021 | + | 0.197895i | ||||
\(993\) | 578.546 | 0.582624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1902.36 | −1.91192 | ||||||||
\(996\) | −1439.57 | − | 158.425i | −1.44535 | − | 0.159061i | ||||
\(997\) | 1414.14 | − | 816.457i | 1.41840 | − | 0.818914i | 0.422241 | − | 0.906483i | \(-0.361243\pi\) |
0.996158 | + | 0.0875699i | \(0.0279101\pi\) | |||||||
\(998\) | 48.0275 | − | 875.468i | 0.0481238 | − | 0.877222i | ||||
\(999\) | −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.275.7 | 16 | ||
7.2 | even | 3 | 392.3.g.m.99.1 | 8 | |||
7.3 | odd | 6 | 392.3.k.o.67.5 | 16 | |||
7.4 | even | 3 | inner | 392.3.k.n.67.5 | 16 | ||
7.5 | odd | 6 | 56.3.g.b.43.1 | ✓ | 8 | ||
7.6 | odd | 2 | 392.3.k.o.275.7 | 16 | |||
8.3 | odd | 2 | inner | 392.3.k.n.275.5 | 16 | ||
21.5 | even | 6 | 504.3.g.b.379.8 | 8 | |||
28.19 | even | 6 | 224.3.g.b.15.2 | 8 | |||
28.23 | odd | 6 | 1568.3.g.m.687.7 | 8 | |||
56.3 | even | 6 | 392.3.k.o.67.7 | 16 | |||
56.5 | odd | 6 | 224.3.g.b.15.1 | 8 | |||
56.11 | odd | 6 | inner | 392.3.k.n.67.7 | 16 | ||
56.19 | even | 6 | 56.3.g.b.43.2 | yes | 8 | ||
56.27 | even | 2 | 392.3.k.o.275.5 | 16 | |||
56.37 | even | 6 | 1568.3.g.m.687.8 | 8 | |||
56.51 | odd | 6 | 392.3.g.m.99.2 | 8 | |||
84.47 | odd | 6 | 2016.3.g.b.1135.2 | 8 | |||
112.5 | odd | 12 | 1792.3.d.j.1023.3 | 16 | |||
112.19 | even | 12 | 1792.3.d.j.1023.4 | 16 | |||
112.61 | odd | 12 | 1792.3.d.j.1023.14 | 16 | |||
112.75 | even | 12 | 1792.3.d.j.1023.13 | 16 | |||
168.5 | even | 6 | 2016.3.g.b.1135.7 | 8 | |||
168.131 | odd | 6 | 504.3.g.b.379.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.1 | ✓ | 8 | 7.5 | odd | 6 | ||
56.3.g.b.43.2 | yes | 8 | 56.19 | even | 6 | ||
224.3.g.b.15.1 | 8 | 56.5 | odd | 6 | |||
224.3.g.b.15.2 | 8 | 28.19 | even | 6 | |||
392.3.g.m.99.1 | 8 | 7.2 | even | 3 | |||
392.3.g.m.99.2 | 8 | 56.51 | odd | 6 | |||
392.3.k.n.67.5 | 16 | 7.4 | even | 3 | inner | ||
392.3.k.n.67.7 | 16 | 56.11 | odd | 6 | inner | ||
392.3.k.n.275.5 | 16 | 8.3 | odd | 2 | inner | ||
392.3.k.n.275.7 | 16 | 1.1 | even | 1 | trivial | ||
392.3.k.o.67.5 | 16 | 7.3 | odd | 6 | |||
392.3.k.o.67.7 | 16 | 56.3 | even | 6 | |||
392.3.k.o.275.5 | 16 | 56.27 | even | 2 | |||
392.3.k.o.275.7 | 16 | 7.6 | odd | 2 | |||
504.3.g.b.379.7 | 8 | 168.131 | odd | 6 | |||
504.3.g.b.379.8 | 8 | 21.5 | even | 6 | |||
1568.3.g.m.687.7 | 8 | 28.23 | odd | 6 | |||
1568.3.g.m.687.8 | 8 | 56.37 | even | 6 | |||
1792.3.d.j.1023.3 | 16 | 112.5 | odd | 12 | |||
1792.3.d.j.1023.4 | 16 | 112.19 | even | 12 | |||
1792.3.d.j.1023.13 | 16 | 112.75 | even | 12 | |||
1792.3.d.j.1023.14 | 16 | 112.61 | odd | 12 | |||
2016.3.g.b.1135.2 | 8 | 84.47 | odd | 6 | |||
2016.3.g.b.1135.7 | 8 | 168.5 | even | 6 |