Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(107,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 179.21 | ||
Character | \(\chi\) | \(=\) | 504.179 |
Dual form | 504.2.bm.c.107.21 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23551 | + | 0.688125i | 0.873637 | + | 0.486578i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.05297 | + | 1.70037i | 0.526484 | + | 0.850185i | ||||
\(5\) | −0.317795 | − | 0.550436i | −0.142122 | − | 0.246163i | 0.786173 | − | 0.618006i | \(-0.212059\pi\) |
−0.928296 | + | 0.371843i | \(0.878726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.11900 | + | 1.58425i | −0.800906 | + | 0.598790i | ||||
\(8\) | 0.130884 | + | 2.82540i | 0.0462746 | + | 0.998929i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0138692 | − | 0.898752i | −0.00438582 | − | 0.284210i | ||||
\(11\) | 3.16457 | + | 1.82707i | 0.954155 | + | 0.550881i | 0.894369 | − | 0.447330i | \(-0.147625\pi\) |
0.0597855 | + | 0.998211i | \(0.480958\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.15869i | 1.15341i | 0.816951 | + | 0.576707i | \(0.195662\pi\) | ||||
−0.816951 | + | 0.576707i | \(0.804338\pi\) | |||||||
\(14\) | −3.70820 | + | 0.499220i | −0.991059 | + | 0.133422i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.78252 | + | 3.58087i | −0.445629 | + | 0.895218i | ||||
\(17\) | 3.01908 | + | 1.74306i | 0.732233 | + | 0.422755i | 0.819239 | − | 0.573453i | \(-0.194396\pi\) |
−0.0870053 | + | 0.996208i | \(0.527730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.99238 | − | 3.45090i | −0.457083 | − | 0.791691i | 0.541722 | − | 0.840558i | \(-0.317772\pi\) |
−0.998805 | + | 0.0488665i | \(0.984439\pi\) | |||||||
\(20\) | 0.601318 | − | 1.11996i | 0.134459 | − | 0.250431i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.65261 | + | 4.43498i | 0.565538 | + | 0.945541i | ||||
\(23\) | 1.47015 | + | 2.54638i | 0.306548 | + | 0.530957i | 0.977605 | − | 0.210449i | \(-0.0674925\pi\) |
−0.671056 | + | 0.741406i | \(0.734159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.29801 | − | 3.98028i | 0.459603 | − | 0.796055i | ||||
\(26\) | −2.86170 | + | 5.13810i | −0.561226 | + | 1.00767i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.92505 | − | 1.93492i | −0.930746 | − | 0.365665i | ||||
\(29\) | 6.35746 | 1.18055 | 0.590275 | − | 0.807202i | \(-0.299019\pi\) | ||||
0.590275 | + | 0.807202i | \(0.299019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.20467 | − | 3.00492i | −0.934787 | − | 0.539699i | −0.0464645 | − | 0.998920i | \(-0.514795\pi\) |
−0.888322 | + | 0.459221i | \(0.848129\pi\) | |||||||
\(32\) | −4.66640 | + | 3.19760i | −0.824911 | + | 0.565262i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.53065 | + | 4.23107i | 0.434003 | + | 0.725623i | ||||
\(35\) | 1.54543 | + | 0.662908i | 0.261226 | + | 0.112052i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.59870 | + | 0.923007i | −0.262824 | + | 0.151741i | −0.625622 | − | 0.780126i | \(-0.715155\pi\) |
0.362798 | + | 0.931868i | \(0.381821\pi\) | |||||||
\(38\) | −0.0869514 | − | 5.63463i | −0.0141054 | − | 0.914057i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.51361 | − | 0.969939i | 0.239322 | − | 0.153361i | ||||
\(41\) | − | 10.4931i | − | 1.63874i | −0.573262 | − | 0.819372i | \(-0.694322\pi\) | ||
0.573262 | − | 0.819372i | \(-0.305678\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.83895 | −0.432935 | −0.216468 | − | 0.976290i | \(-0.569454\pi\) | ||||
−0.216468 | + | 0.976290i | \(0.569454\pi\) | |||||||
\(44\) | 0.225503 | + | 7.30479i | 0.0339959 | + | 1.10124i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0641605 | + | 4.15773i | 0.00945995 | + | 0.613024i | ||||
\(47\) | −4.61494 | − | 7.99332i | −0.673159 | − | 1.16595i | −0.977003 | − | 0.213224i | \(-0.931604\pi\) |
0.303845 | − | 0.952722i | \(-0.401730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.98031 | − | 6.71404i | 0.282901 | − | 0.959149i | ||||
\(50\) | 5.57814 | − | 3.33635i | 0.788869 | − | 0.471831i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.07132 | + | 4.37897i | −0.980615 | + | 0.607254i | ||||
\(53\) | 2.99666 | − | 5.19038i | 0.411624 | − | 0.712953i | −0.583444 | − | 0.812153i | \(-0.698295\pi\) |
0.995067 | + | 0.0992005i | \(0.0316285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.32253i | − | 0.313170i | ||||||
\(56\) | −4.75348 | − | 5.77966i | −0.635210 | − | 0.772339i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.85470 | + | 4.37473i | 1.03137 | + | 0.574430i | ||||
\(59\) | 9.10070 | + | 5.25429i | 1.18481 | + | 0.684050i | 0.957122 | − | 0.289684i | \(-0.0935502\pi\) |
0.227688 | + | 0.973734i | \(0.426883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72447 | + | 0.995622i | −0.220795 | + | 0.127476i | −0.606319 | − | 0.795222i | \(-0.707354\pi\) |
0.385523 | + | 0.922698i | \(0.374021\pi\) | |||||||
\(62\) | −4.36266 | − | 7.29407i | −0.554059 | − | 0.926348i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.96574 | + | 0.739601i | −0.995717 | + | 0.0924501i | ||||
\(65\) | 2.28909 | − | 1.32161i | 0.283927 | − | 0.163925i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.01122 | + | 13.8758i | −0.978726 | + | 1.69520i | −0.311678 | + | 0.950188i | \(0.600891\pi\) |
−0.667048 | + | 0.745015i | \(0.732442\pi\) | |||||||
\(68\) | 0.215135 | + | 6.96894i | 0.0260890 | + | 0.845108i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.45324 | + | 1.88248i | 0.173695 | + | 0.225000i | ||||
\(71\) | 0.737952 | 0.0875788 | 0.0437894 | − | 0.999041i | \(-0.486057\pi\) | ||||
0.0437894 | + | 0.999041i | \(0.486057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.13696 | − | 3.70132i | 0.250112 | − | 0.433207i | −0.713444 | − | 0.700712i | \(-0.752866\pi\) |
0.963557 | + | 0.267505i | \(0.0861991\pi\) | |||||||
\(74\) | −2.61035 | + | 0.0402819i | −0.303447 | + | 0.00468267i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.76990 | − | 7.02147i | 0.432437 | − | 0.805418i | ||||
\(77\) | −9.60025 | + | 1.14192i | −1.09405 | + | 0.130134i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.74900 | − | 4.47389i | 0.871830 | − | 0.503351i | 0.00387425 | − | 0.999992i | \(-0.498767\pi\) |
0.867956 | + | 0.496641i | \(0.165433\pi\) | |||||||
\(80\) | 2.53752 | − | 0.156819i | 0.283703 | − | 0.0175328i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.22055 | − | 12.9643i | 0.797377 | − | 1.43167i | ||||
\(83\) | 3.67740i | 0.403647i | 0.979422 | + | 0.201823i | \(0.0646867\pi\) | ||||
−0.979422 | + | 0.201823i | \(0.935313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.21574i | − | 0.240331i | ||||||
\(86\) | −3.50755 | − | 1.95355i | −0.378229 | − | 0.210657i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.74800 | + | 9.18031i | −0.506138 | + | 0.978624i | ||||
\(89\) | −4.63483 | + | 2.67592i | −0.491291 | + | 0.283647i | −0.725110 | − | 0.688633i | \(-0.758211\pi\) |
0.233819 | + | 0.972280i | \(0.424878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.58841 | − | 8.81226i | −0.690653 | − | 0.923776i | ||||
\(92\) | −2.78177 | + | 5.18107i | −0.290019 | + | 0.540163i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.201405 | − | 13.0515i | −0.0207734 | − | 1.34616i | ||||
\(95\) | −1.26633 | + | 2.19335i | −0.129923 | + | 0.225033i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.6696 | 1.79407 | 0.897036 | − | 0.441958i | \(-0.145716\pi\) | ||||
0.897036 | + | 0.441958i | \(0.145716\pi\) | |||||||
\(98\) | 7.06679 | − | 6.93257i | 0.713854 | − | 0.700295i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.18768 | − | 0.283629i | 0.918768 | − | 0.0283629i | ||||
\(101\) | 6.12560 | − | 10.6099i | 0.609520 | − | 1.05572i | −0.381799 | − | 0.924245i | \(-0.624695\pi\) |
0.991320 | − | 0.131475i | \(-0.0419712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.71030 | + | 1.56479i | −0.267054 | + | 0.154184i | −0.627548 | − | 0.778578i | \(-0.715941\pi\) |
0.360494 | + | 0.932761i | \(0.382608\pi\) | |||||||
\(104\) | −11.7500 | + | 0.544308i | −1.15218 | + | 0.0533738i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.27404 | − | 4.35068i | 0.706517 | − | 0.422575i | ||||
\(107\) | 5.64238 | − | 3.25763i | 0.545470 | − | 0.314927i | −0.201823 | − | 0.979422i | \(-0.564687\pi\) |
0.747293 | + | 0.664495i | \(0.231353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.23586 | + | 0.713527i | 0.118374 | + | 0.0683435i | 0.558018 | − | 0.829829i | \(-0.311562\pi\) |
−0.439644 | + | 0.898172i | \(0.644895\pi\) | |||||||
\(110\) | 1.59819 | − | 2.86950i | 0.152381 | − | 0.273597i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.89584 | − | 10.4118i | −0.179140 | − | 0.983824i | ||||
\(113\) | − | 3.27992i | − | 0.308549i | −0.988028 | − | 0.154275i | \(-0.950696\pi\) | ||
0.988028 | − | 0.154275i | \(-0.0493040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.934414 | − | 1.61845i | 0.0871346 | − | 0.150922i | ||||
\(116\) | 6.69420 | + | 10.8100i | 0.621541 | + | 1.00369i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.62839 | + | 12.7541i | 0.702250 | + | 1.17411i | ||||
\(119\) | −9.15886 | + | 1.08942i | −0.839592 | + | 0.0998669i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.17635 | + | 2.03749i | 0.106941 | + | 0.185226i | ||||
\(122\) | −2.81571 | + | 0.0434509i | −0.254922 | + | 0.00393386i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.370878 | − | 12.0140i | −0.0333058 | − | 1.07888i | ||||
\(125\) | −6.09913 | −0.545523 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.0629i | − | 1.69156i | −0.533535 | − | 0.845778i | \(-0.679137\pi\) | ||
0.533535 | − | 0.845778i | \(-0.320863\pi\) | |||||||
\(128\) | −10.3507 | − | 4.56764i | −0.914880 | − | 0.403726i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.73763 | − | 0.0576777i | 0.327812 | − | 0.00505867i | ||||
\(131\) | −11.2577 | + | 6.49965i | −0.983591 | + | 0.567877i | −0.903352 | − | 0.428899i | \(-0.858902\pi\) |
−0.0802388 | + | 0.996776i | \(0.525568\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.68893 | + | 4.15603i | 0.840137 | + | 0.360373i | ||||
\(134\) | −19.4462 | + | 11.6310i | −1.67990 | + | 1.00477i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.52970 | + | 8.75823i | −0.388418 | + | 0.751012i | ||||
\(137\) | −1.17651 | − | 0.679257i | −0.100516 | − | 0.0580329i | 0.448899 | − | 0.893582i | \(-0.351816\pi\) |
−0.549415 | + | 0.835549i | \(0.685149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.06037 | −0.259577 | −0.129788 | − | 0.991542i | \(-0.541430\pi\) | ||||
−0.129788 | + | 0.991542i | \(0.541430\pi\) | |||||||
\(140\) | 0.500104 | + | 3.32583i | 0.0422665 | + | 0.281084i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.911747 | + | 0.507803i | 0.0765121 | + | 0.0426139i | ||||
\(143\) | −7.59821 | + | 13.1605i | −0.635394 | + | 1.10053i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.02037 | − | 3.49938i | −0.167782 | − | 0.290607i | ||||
\(146\) | 5.18721 | − | 3.10253i | 0.429297 | − | 0.256767i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.25283 | − | 1.74648i | −0.267381 | − | 0.143560i | ||||
\(149\) | 8.15986 | + | 14.1333i | 0.668481 | + | 1.15784i | 0.978329 | + | 0.207057i | \(0.0663887\pi\) |
−0.309847 | + | 0.950786i | \(0.600278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.81057 | − | 4.50943i | −0.635615 | − | 0.366972i | 0.147309 | − | 0.989091i | \(-0.452939\pi\) |
−0.782923 | + | 0.622118i | \(0.786272\pi\) | |||||||
\(152\) | 9.48939 | − | 6.08093i | 0.769692 | − | 0.493229i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.6470 | − | 5.19532i | −1.01912 | − | 0.418651i | ||||
\(155\) | 3.81979i | 0.306813i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0104 | + | 11.5530i | 1.59700 | + | 0.922031i | 0.992060 | + | 0.125763i | \(0.0401378\pi\) |
0.604944 | + | 0.796268i | \(0.293196\pi\) | |||||||
\(158\) | 12.6526 | − | 0.195249i | 1.00658 | − | 0.0155332i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.24304 | + | 1.55238i | 0.256384 | + | 0.122726i | ||||
\(161\) | −7.14936 | − | 3.06669i | −0.563449 | − | 0.241689i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.10214 | + | 10.5692i | 0.477956 | + | 0.827845i | 0.999681 | − | 0.0252693i | \(-0.00804434\pi\) |
−0.521724 | + | 0.853114i | \(0.674711\pi\) | |||||||
\(164\) | 17.8421 | − | 11.0489i | 1.39324 | − | 0.862773i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.53051 | + | 4.54346i | −0.196406 | + | 0.352641i | ||||
\(167\) | 3.33534 | 0.258096 | 0.129048 | − | 0.991638i | \(-0.458808\pi\) | ||||
0.129048 | + | 0.991638i | \(0.458808\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.29472 | −0.330363 | ||||||||
\(170\) | 1.52471 | − | 2.73757i | 0.116940 | − | 0.209962i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.98932 | − | 4.82726i | −0.227934 | − | 0.368075i | ||||
\(173\) | −4.79217 | − | 8.30028i | −0.364342 | − | 0.631058i | 0.624329 | − | 0.781162i | \(-0.285373\pi\) |
−0.988670 | + | 0.150104i | \(0.952039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.43626 | + | 12.0748i | 0.108571 | + | 0.912771i | ||||
\(176\) | −12.1834 | + | 8.07514i | −0.918358 | + | 0.608687i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.56774 | + | 0.116782i | −0.567226 | + | 0.00875321i | ||||
\(179\) | −0.0283182 | − | 0.0163495i | −0.00211660 | − | 0.00122202i | 0.498941 | − | 0.866636i | \(-0.333722\pi\) |
−0.501058 | + | 0.865414i | \(0.667056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.3654i | − | 1.43942i | −0.694277 | − | 0.719708i | \(-0.744276\pi\) | ||
0.694277 | − | 0.719708i | \(-0.255724\pi\) | |||||||
\(182\) | −2.07610 | − | 15.4213i | −0.153891 | − | 1.14310i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.00212 | + | 4.48705i | −0.516203 | + | 0.330790i | ||||
\(185\) | 1.01611 | + | 0.586653i | 0.0747061 | + | 0.0431316i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.36939 | + | 11.0321i | 0.465776 | + | 0.806747i | ||||
\(188\) | 8.73221 | − | 16.2638i | 0.636862 | − | 1.18616i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.07387 | + | 1.83851i | −0.223002 | + | 0.133380i | ||||
\(191\) | −1.50826 | − | 2.61239i | −0.109134 | − | 0.189026i | 0.806286 | − | 0.591526i | \(-0.201474\pi\) |
−0.915420 | + | 0.402501i | \(0.868141\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9565 | + | 18.9772i | −0.788666 | + | 1.36601i | 0.138119 | + | 0.990416i | \(0.455894\pi\) |
−0.926785 | + | 0.375593i | \(0.877439\pi\) | |||||||
\(194\) | 21.8309 | + | 12.1589i | 1.56737 | + | 0.872955i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.5016 | − | 3.70242i | 0.964397 | − | 0.264458i | ||||
\(197\) | 15.2950 | 1.08972 | 0.544860 | − | 0.838527i | \(-0.316583\pi\) | ||||
0.544860 | + | 0.838527i | \(0.316583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.77706 | + | 1.60334i | 0.196861 | + | 0.113658i | 0.595190 | − | 0.803585i | \(-0.297077\pi\) |
−0.398330 | + | 0.917242i | \(0.630410\pi\) | |||||||
\(200\) | 11.5466 | + | 5.97184i | 0.816470 | + | 0.422273i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.8691 | − | 8.89340i | 1.04619 | − | 0.625737i | ||||
\(203\) | −13.4715 | + | 10.0718i | −0.945510 | + | 0.706902i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.77577 | + | 3.33464i | −0.403398 | + | 0.232902i | ||||
\(206\) | −4.42538 | + | 0.0682907i | −0.308330 | + | 0.00475804i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.8917 | − | 7.41294i | −1.03256 | − | 0.513995i | ||||
\(209\) | − | 14.5608i | − | 1.00719i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7059 | −1.15008 | −0.575040 | − | 0.818125i | \(-0.695014\pi\) | ||||
−0.575040 | + | 0.818125i | \(0.695014\pi\) | |||||||
\(212\) | 11.9810 | − | 0.369859i | 0.822855 | − | 0.0254020i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.21287 | − | 0.142169i | 0.629779 | − | 0.00971851i | ||||
\(215\) | 0.902202 | + | 1.56266i | 0.0615297 | + | 0.106573i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.7892 | − | 1.87808i | 1.07184 | − | 0.127492i | ||||
\(218\) | 1.03593 | + | 1.73200i | 0.0701618 | + | 0.117306i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.94916 | − | 2.44555i | 0.266252 | − | 0.164879i | ||||
\(221\) | −7.24887 | + | 12.5554i | −0.487611 | + | 0.844568i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.1547i | 1.28270i | 0.767250 | + | 0.641348i | \(0.221625\pi\) | ||||
−0.767250 | + | 0.641348i | \(0.778375\pi\) | |||||||
\(224\) | 4.82230 | − | 14.1685i | 0.322203 | − | 0.946670i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.25700 | − | 4.05237i | 0.150133 | − | 0.269560i | ||||
\(227\) | −14.4962 | − | 8.36938i | −0.962147 | − | 0.555496i | −0.0653135 | − | 0.997865i | \(-0.520805\pi\) |
−0.896833 | + | 0.442369i | \(0.854138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5029 | + | 10.1053i | −1.15662 | + | 0.667777i | −0.950492 | − | 0.310747i | \(-0.899421\pi\) |
−0.206131 | + | 0.978524i | \(0.566087\pi\) | |||||||
\(230\) | 2.26818 | − | 1.35662i | 0.149559 | − | 0.0894529i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.832093 | + | 17.9624i | 0.0546296 | + | 1.17929i | ||||
\(233\) | −17.3998 | + | 10.0458i | −1.13990 | + | 0.658122i | −0.946406 | − | 0.322979i | \(-0.895316\pi\) |
−0.193495 | + | 0.981101i | \(0.561982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.93321 | + | 5.08047i | −0.191341 | + | 0.331413i | ||||
\(236\) | 0.648503 | + | 21.0072i | 0.0422140 | + | 1.36745i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.0655 | − | 4.95646i | −0.782091 | − | 0.321279i | ||||
\(239\) | 13.2312 | 0.855855 | 0.427928 | − | 0.903813i | \(-0.359244\pi\) | ||||
0.427928 | + | 0.903813i | \(0.359244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.90444 | + | 10.2268i | −0.380338 | + | 0.658765i | −0.991111 | − | 0.133041i | \(-0.957526\pi\) |
0.610772 | + | 0.791806i | \(0.290859\pi\) | |||||||
\(242\) | 0.0513381 | + | 3.32681i | 0.00330014 | + | 0.213856i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.50873 | − | 1.88388i | −0.224624 | − | 0.120603i | ||||
\(245\) | −4.32498 | + | 1.04365i | −0.276313 | + | 0.0666766i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3512 | − | 8.28569i | 0.913147 | − | 0.527206i | ||||
\(248\) | 7.80888 | − | 15.0986i | 0.495864 | − | 0.958760i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.53553 | − | 4.19696i | −0.476589 | − | 0.265439i | ||||
\(251\) | − | 18.9939i | − | 1.19888i | −0.800419 | − | 0.599441i | \(-0.795390\pi\) | ||
0.800419 | − | 0.599441i | \(-0.204610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7443i | 0.675487i | ||||||||
\(254\) | 13.1176 | − | 23.5524i | 0.823074 | − | 1.47781i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.64526 | − | 12.7659i | −0.602829 | − | 0.797871i | ||||
\(257\) | −22.5458 | + | 13.0168i | −1.40637 | + | 0.811966i | −0.995036 | − | 0.0995204i | \(-0.968269\pi\) |
−0.411331 | + | 0.911486i | \(0.634936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.92536 | − | 4.48858i | 0.119636 | − | 0.278907i | ||||
\(260\) | 4.65757 | + | 2.50070i | 0.288850 | + | 0.155087i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.3816 | + | 0.283658i | −1.13562 | + | 0.0175244i | ||||
\(263\) | 13.3095 | − | 23.0527i | 0.820698 | − | 1.42149i | −0.0844650 | − | 0.996426i | \(-0.526918\pi\) |
0.905163 | − | 0.425064i | \(-0.139749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.80929 | −0.234003 | ||||||||
\(266\) | 9.11090 | + | 11.8020i | 0.558625 | + | 0.723628i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −32.0296 | + | 0.988772i | −1.95652 | + | 0.0603989i | ||||
\(269\) | −12.6453 | + | 21.9022i | −0.770995 | + | 1.33540i | 0.166022 | + | 0.986122i | \(0.446908\pi\) |
−0.937018 | + | 0.349281i | \(0.886426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4561 | + | 8.34622i | −0.878145 | + | 0.506997i | −0.870046 | − | 0.492970i | \(-0.835911\pi\) |
−0.00809834 | + | 0.999967i | \(0.502578\pi\) | |||||||
\(272\) | −11.6232 | + | 7.70387i | −0.704762 | + | 0.467116i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.986173 | − | 1.64881i | −0.0595769 | − | 0.0996085i | ||||
\(275\) | 14.5445 | − | 8.39725i | 0.877064 | − | 0.506373i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.0279 | − | 13.2952i | −1.38361 | − | 0.798830i | −0.391029 | − | 0.920379i | \(-0.627881\pi\) |
−0.992585 | + | 0.121549i | \(0.961214\pi\) | |||||||
\(278\) | −3.78111 | − | 2.10591i | −0.226776 | − | 0.126304i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.67070 | + | 4.45323i | −0.0998437 | + | 0.266131i | ||||
\(281\) | − | 8.11615i | − | 0.484169i | −0.970255 | − | 0.242085i | \(-0.922169\pi\) | ||
0.970255 | − | 0.242085i | \(-0.0778311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.12929 | − | 7.15214i | 0.245461 | − | 0.425150i | −0.716800 | − | 0.697278i | \(-0.754394\pi\) |
0.962261 | + | 0.272128i | \(0.0877274\pi\) | |||||||
\(284\) | 0.777040 | + | 1.25479i | 0.0461088 | + | 0.0744582i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.4437 | + | 11.0314i | −1.09060 | + | 0.652299i | ||||
\(287\) | 16.6237 | + | 22.2348i | 0.981264 | + | 1.31248i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.42346 | − | 4.19755i | −0.142556 | − | 0.246915i | ||||
\(290\) | −0.0881728 | − | 5.71378i | −0.00517769 | − | 0.335525i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.54377 | − | 0.263751i | 0.499987 | − | 0.0154349i | ||||
\(293\) | 20.9952 | 1.22655 | 0.613277 | − | 0.789868i | \(-0.289851\pi\) | ||||
0.613277 | + | 0.789868i | \(0.289851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.67914i | − | 0.388875i | ||||||
\(296\) | −2.81711 | − | 4.39614i | −0.163741 | − | 0.255521i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.356112 | + | 23.0768i | 0.0206290 | + | 1.33680i | ||||
\(299\) | −10.5896 | + | 6.11392i | −0.612414 | + | 0.353577i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.01572 | − | 4.49760i | 0.346741 | − | 0.259237i | ||||
\(302\) | −6.54698 | − | 10.9461i | −0.376736 | − | 0.629877i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.9087 | − | 0.983157i | 0.912425 | − | 0.0563879i | ||||
\(305\) | 1.09605 | + | 0.632806i | 0.0627598 | + | 0.0362344i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1231 | 1.03434 | 0.517170 | − | 0.855882i | \(-0.326985\pi\) | ||||
0.517170 | + | 0.855882i | \(0.326985\pi\) | |||||||
\(308\) | −12.0504 | − | 15.1216i | −0.686638 | − | 0.861632i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.62849 | + | 4.71938i | −0.149288 | + | 0.268043i | ||||
\(311\) | −15.4208 | + | 26.7096i | −0.874433 | + | 1.51456i | −0.0170667 | + | 0.999854i | \(0.505433\pi\) |
−0.857366 | + | 0.514707i | \(0.827901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.521916 | + | 0.903984i | 0.0295004 | + | 0.0510962i | 0.880399 | − | 0.474234i | \(-0.157275\pi\) |
−0.850898 | + | 0.525330i | \(0.823942\pi\) | |||||||
\(314\) | 16.7731 | + | 28.0435i | 0.946562 | + | 1.58259i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.7667 | + | 8.46531i | 0.886946 | + | 0.476211i | ||||
\(317\) | 5.12901 | + | 8.88370i | 0.288074 | + | 0.498958i | 0.973350 | − | 0.229325i | \(-0.0736518\pi\) |
−0.685276 | + | 0.728283i | \(0.740319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1186 | + | 11.6155i | 1.12643 | + | 0.650344i | ||||
\(320\) | 2.93857 | + | 4.14959i | 0.164271 | + | 0.231969i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.72284 | − | 8.70858i | −0.374649 | − | 0.485310i | ||||
\(323\) | − | 13.8914i | − | 0.772937i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.5527 | + | 9.55673i | 0.918181 | + | 0.530112i | ||||
\(326\) | 0.266310 | + | 17.2574i | 0.0147495 | + | 0.955799i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29.6471 | − | 1.37338i | 1.63699 | − | 0.0758323i | ||||
\(329\) | 22.4425 | + | 9.62660i | 1.23729 | + | 0.530732i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.31756 | + | 4.01414i | 0.127385 | + | 0.220637i | 0.922663 | − | 0.385608i | \(-0.126008\pi\) |
−0.795278 | + | 0.606245i | \(0.792675\pi\) | |||||||
\(332\) | −6.25293 | + | 3.87218i | −0.343174 | + | 0.212513i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.12085 | + | 2.29513i | 0.225483 | + | 0.125584i | ||||
\(335\) | 10.1837 | 0.556394 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0263 | −1.79906 | −0.899528 | − | 0.436863i | \(-0.856089\pi\) | ||||
−0.899528 | + | 0.436863i | \(0.856089\pi\) | |||||||
\(338\) | −5.30616 | − | 2.95530i | −0.288617 | − | 0.160747i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.76759 | − | 2.33311i | 0.204326 | − | 0.126531i | ||||
\(341\) | −10.9804 | − | 19.0186i | −0.594621 | − | 1.02991i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.44045 | + | 17.3643i | 0.347752 | + | 0.937587i | ||||
\(344\) | −0.371574 | − | 8.02115i | −0.0200339 | − | 0.432472i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.209140 | − | 13.5527i | −0.0112434 | − | 0.728597i | ||||
\(347\) | −3.47551 | − | 2.00659i | −0.186575 | − | 0.107719i | 0.403803 | − | 0.914846i | \(-0.367688\pi\) |
−0.590378 | + | 0.807127i | \(0.701021\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.4671i | − | 0.560291i | −0.959958 | − | 0.280145i | \(-0.909617\pi\) | ||
0.959958 | − | 0.280145i | \(-0.0903826\pi\) | |||||||
\(350\) | −6.53447 | + | 15.9069i | −0.349282 | + | 0.850259i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.6094 | + | 1.59322i | −1.09849 | + | 0.0849188i | ||||
\(353\) | 15.3486 | + | 8.86154i | 0.816925 | + | 0.471652i | 0.849355 | − | 0.527822i | \(-0.176991\pi\) |
−0.0324298 | + | 0.999474i | \(0.510325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.234517 | − | 0.406196i | −0.0124469 | − | 0.0215586i | ||||
\(356\) | −9.43037 | − | 5.06326i | −0.499809 | − | 0.268352i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0237369 | − | 0.0396865i | −0.00125453 | − | 0.00209750i | ||||
\(359\) | −6.52933 | − | 11.3091i | −0.344605 | − | 0.596873i | 0.640677 | − | 0.767811i | \(-0.278654\pi\) |
−0.985282 | + | 0.170937i | \(0.945320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.56085 | − | 2.70348i | 0.0821503 | − | 0.142288i | ||||
\(362\) | 13.3258 | − | 23.9261i | 0.700388 | − | 1.25753i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.04673 | − | 20.4818i | 0.421763 | − | 1.07354i | ||||
\(365\) | −2.71646 | −0.142186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.3899 | − | 11.1948i | −1.01215 | − | 0.584363i | −0.100327 | − | 0.994955i | \(-0.531989\pi\) |
−0.911819 | + | 0.410592i | \(0.865322\pi\) | |||||||
\(368\) | −11.7388 | + | 0.725461i | −0.611929 | + | 0.0378173i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.851727 | + | 1.42403i | 0.0442792 | + | 0.0740317i | ||||
\(371\) | 1.87292 | + | 15.7459i | 0.0972373 | + | 0.817484i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.83798 | + | 2.21586i | −0.198723 | + | 0.114733i | −0.596060 | − | 0.802940i | \(-0.703268\pi\) |
0.397337 | + | 0.917673i | \(0.369935\pi\) | |||||||
\(374\) | 0.277973 | + | 18.0132i | 0.0143736 | + | 0.931441i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.9803 | − | 14.0853i | 1.13355 | − | 0.726391i | ||||
\(377\) | 26.4387i | 1.36166i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8901 | 1.48399 | 0.741993 | − | 0.670407i | \(-0.233881\pi\) | ||||
0.741993 | + | 0.670407i | \(0.233881\pi\) | |||||||
\(380\) | −5.06292 | + | 0.156295i | −0.259723 | + | 0.00801779i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.0658237 | − | 4.26551i | −0.00336783 | − | 0.218242i | ||||
\(383\) | −16.3811 | − | 28.3729i | −0.837037 | − | 1.44979i | −0.892361 | − | 0.451322i | \(-0.850953\pi\) |
0.0553247 | − | 0.998468i | \(-0.482381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.67946 | + | 4.92143i | 0.187523 | + | 0.250819i | ||||
\(386\) | −26.5955 | + | 15.9071i | −1.35368 | + | 0.809649i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.6055 | + | 30.0448i | 0.944550 | + | 1.52529i | ||||
\(389\) | 6.24881 | − | 10.8233i | 0.316827 | − | 0.548761i | −0.662997 | − | 0.748622i | \(-0.730716\pi\) |
0.979824 | + | 0.199861i | \(0.0640490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2503i | 0.518380i | ||||||||
\(392\) | 19.2290 | + | 4.71639i | 0.971213 | + | 0.238214i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8971 | + | 10.5248i | 0.952020 | + | 0.530234i | ||||
\(395\) | −4.92518 | − | 2.84355i | −0.247813 | − | 0.143075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.09678 | + | 3.51998i | −0.305989 | + | 0.176663i | −0.645130 | − | 0.764073i | \(-0.723197\pi\) |
0.339141 | + | 0.940735i | \(0.389863\pi\) | |||||||
\(398\) | 2.32779 | + | 3.89191i | 0.116682 | + | 0.195084i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.1566 | + | 15.3238i | 0.507830 | + | 0.766190i | ||||
\(401\) | 25.7480 | − | 14.8656i | 1.28579 | − | 0.742353i | 0.307893 | − | 0.951421i | \(-0.400376\pi\) |
0.977901 | + | 0.209068i | \(0.0670429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4965 | − | 21.6446i | 0.622497 | − | 1.07820i | ||||
\(404\) | 24.4907 | − | 0.756043i | 1.21846 | − | 0.0376146i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.5748 | + | 3.17377i | −1.17000 | + | 0.157512i | ||||
\(407\) | −6.74558 | −0.334366 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.6222 | + | 28.7905i | −0.821914 | + | 1.42360i | 0.0823411 | + | 0.996604i | \(0.473760\pi\) |
−0.904255 | + | 0.426993i | \(0.859573\pi\) | |||||||
\(410\) | −9.43068 | + | 0.145531i | −0.465748 | + | 0.00718724i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.51459 | − | 2.96084i | −0.271684 | − | 0.145870i | ||||
\(413\) | −27.6085 | + | 3.28394i | −1.35852 | + | 0.161592i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.02417 | − | 1.16866i | 0.0993627 | − | 0.0573671i | ||||
\(416\) | −13.2979 | − | 19.4061i | −0.651981 | − | 0.951464i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.0197 | − | 17.9901i | 0.490078 | − | 0.879922i | ||||
\(419\) | 8.95024i | 0.437248i | 0.975809 | + | 0.218624i | \(0.0701568\pi\) | ||||
−0.975809 | + | 0.218624i | \(0.929843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.3473i | − | 1.28409i | −0.766667 | − | 0.642044i | \(-0.778086\pi\) | ||
0.766667 | − | 0.642044i | \(-0.221914\pi\) | |||||||
\(422\) | −20.6403 | − | 11.4957i | −1.00475 | − | 0.559604i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.0571 | + | 7.78743i | 0.731237 | + | 0.378191i | ||||
\(425\) | 13.8758 | − | 8.01117i | 0.673073 | − | 0.388599i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.07683 | − | 4.84171i | 0.100505 | − | 0.234307i | ||||
\(428\) | 11.4804 | + | 6.16396i | 0.554927 | + | 0.297946i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0393739 | + | 2.55151i | 0.00189878 | + | 0.123045i | ||||
\(431\) | 7.97354 | − | 13.8106i | 0.384072 | − | 0.665232i | −0.607568 | − | 0.794268i | \(-0.707855\pi\) |
0.991640 | + | 0.129036i | \(0.0411882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5058 | 0.600991 | 0.300496 | − | 0.953783i | \(-0.402848\pi\) | ||||
0.300496 | + | 0.953783i | \(0.402848\pi\) | |||||||
\(434\) | 20.8001 | + | 8.54458i | 0.998437 | + | 0.410153i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0880660 | + | 2.85275i | 0.00421760 | + | 0.136622i | ||||
\(437\) | 5.85821 | − | 10.1467i | 0.280236 | − | 0.485383i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0552 | − | 8.11479i | 0.670820 | − | 0.387298i | −0.125568 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(440\) | 6.56206 | − | 0.303983i | 0.312834 | − | 0.0144918i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.5957 | + | 10.5242i | −0.836944 | + | 0.500585i | ||||
\(443\) | −5.80303 | + | 3.35038i | −0.275710 | + | 0.159181i | −0.631480 | − | 0.775392i | \(-0.717552\pi\) |
0.355769 | + | 0.934574i | \(0.384219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.94584 | + | 1.70078i | 0.139646 | + | 0.0806249i | ||||
\(446\) | −13.1809 | + | 23.6659i | −0.624132 | + | 1.12061i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.7077 | − | 14.1869i | 0.742118 | − | 0.670269i | ||||
\(449\) | 26.1155i | 1.23246i | 0.787565 | + | 0.616232i | \(0.211342\pi\) | ||||
−0.787565 | + | 0.616232i | \(0.788658\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1716 | − | 33.2061i | 0.902754 | − | 1.56362i | ||||
\(452\) | 5.57708 | − | 3.45365i | 0.262324 | − | 0.162446i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.1510 | − | 20.3157i | −0.570275 | − | 0.953461i | ||||
\(455\) | −2.75683 | + | 6.42699i | −0.129242 | + | 0.301302i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.0328 | − | 27.7697i | −0.749984 | − | 1.29901i | −0.947830 | − | 0.318777i | \(-0.896728\pi\) |
0.197846 | − | 0.980233i | \(-0.436606\pi\) | |||||||
\(458\) | −28.5787 | + | 0.441015i | −1.33539 | + | 0.0206073i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.73588 | − | 0.115329i | 0.174186 | − | 0.00537723i | ||||
\(461\) | −39.2781 | −1.82936 | −0.914682 | − | 0.404175i | \(-0.867559\pi\) | ||||
−0.914682 | + | 0.404175i | \(0.867559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.26863i | 0.105432i | 0.998610 | + | 0.0527161i | \(0.0167878\pi\) | ||||
−0.998610 | + | 0.0527161i | \(0.983212\pi\) | |||||||
\(464\) | −11.3323 | + | 22.7652i | −0.526088 | + | 1.05685i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.4104 | + | 0.438419i | −1.31609 | + | 0.0203094i | ||||
\(467\) | 20.8867 | − | 12.0590i | 0.966522 | − | 0.558022i | 0.0683480 | − | 0.997662i | \(-0.478227\pi\) |
0.898174 | + | 0.439640i | \(0.144894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00703 | − | 42.0946i | −0.231203 | − | 1.94375i | ||||
\(470\) | −7.12000 | + | 4.25855i | −0.328421 | + | 0.196432i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.6543 | + | 26.4008i | −0.628491 | + | 1.21519i | ||||
\(473\) | −8.98406 | − | 5.18695i | −0.413087 | − | 0.238496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.3141 | −0.840306 | ||||||||
\(476\) | −11.4964 | − | 14.4263i | −0.526937 | − | 0.661230i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.3473 | + | 9.10472i | 0.747707 | + | 0.416440i | ||||
\(479\) | −6.19574 | + | 10.7313i | −0.283091 | + | 0.490328i | −0.972144 | − | 0.234383i | \(-0.924693\pi\) |
0.689054 | + | 0.724710i | \(0.258026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.83850 | − | 6.64848i | −0.175021 | − | 0.303145i | ||||
\(482\) | −14.3323 | + | 8.57230i | −0.652818 | + | 0.390458i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.22583 | + | 4.14564i | −0.101174 | + | 0.188438i | ||||
\(485\) | −5.61529 | − | 9.72596i | −0.254977 | − | 0.441633i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1179 | − | 5.84159i | −0.458487 | − | 0.264708i | 0.252921 | − | 0.967487i | \(-0.418609\pi\) |
−0.711408 | + | 0.702779i | \(0.751942\pi\) | |||||||
\(488\) | −3.03873 | − | 4.74199i | −0.137557 | − | 0.214660i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.06172 | − | 1.68669i | −0.273841 | − | 0.0761967i | ||||
\(491\) | − | 42.8926i | − | 1.93572i | −0.251498 | − | 0.967858i | \(-0.580923\pi\) | ||
0.251498 | − | 0.967858i | \(-0.419077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.1937 | + | 11.0815i | 0.864439 | + | 0.499084i | ||||
\(494\) | 23.4327 | − | 0.361604i | 1.05429 | − | 0.0162693i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0376 | − | 13.2809i | 0.899717 | − | 0.596332i | ||||
\(497\) | −1.56372 | + | 1.16910i | −0.0701424 | + | 0.0524413i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.49173 | − | 7.77991i | −0.201078 | − | 0.348277i | 0.747798 | − | 0.663926i | \(-0.231111\pi\) |
−0.948876 | + | 0.315649i | \(0.897778\pi\) | |||||||
\(500\) | −6.42219 | − | 10.3708i | −0.287209 | − | 0.463795i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.0702 | − | 23.4671i | 0.583349 | − | 1.04739i | ||||
\(503\) | 43.5055 | 1.93981 | 0.969907 | − | 0.243476i | \(-0.0782878\pi\) | ||||
0.969907 | + | 0.243476i | \(0.0782878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.78673 | −0.346505 | ||||||||
\(506\) | −7.39341 | + | 13.2747i | −0.328677 | + | 0.590131i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.4139 | − | 20.0726i | 1.43814 | − | 0.890577i | ||||
\(509\) | −5.45911 | − | 9.45546i | −0.241971 | − | 0.419106i | 0.719305 | − | 0.694695i | \(-0.244460\pi\) |
−0.961276 | + | 0.275589i | \(0.911127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.33561 | + | 11.2286i | 0.0590837 | + | 0.496723i | ||||
\(512\) | −3.13226 | − | 22.4096i | −0.138428 | − | 0.990373i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.8127 | + | 0.568079i | −1.62374 | + | 0.0250569i | ||||
\(515\) | 1.72264 | + | 0.994565i | 0.0759085 | + | 0.0438258i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 33.7272i | − | 1.48332i | ||||||
\(518\) | 5.46750 | − | 4.22080i | 0.240228 | − | 0.185451i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.03368 | + | 6.29462i | 0.176889 | + | 0.276038i | ||||
\(521\) | 19.4185 | + | 11.2113i | 0.850739 | + | 0.491174i | 0.860900 | − | 0.508774i | \(-0.169901\pi\) |
−0.0101612 | + | 0.999948i | \(0.503234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.483187 | − | 0.836904i | −0.0211283 | − | 0.0365953i | 0.855268 | − | 0.518186i | \(-0.173393\pi\) |
−0.876396 | + | 0.481591i | \(0.840059\pi\) | |||||||
\(524\) | −22.9058 | − | 12.2984i | −1.00065 | − | 0.537257i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.3071 | − | 19.3232i | 1.40866 | − | 0.842534i | ||||
\(527\) | −10.4755 | − | 18.1442i | −0.456321 | − | 0.790372i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.17729 | − | 12.4314i | 0.312056 | − | 0.540497i | ||||
\(530\) | −4.70642 | − | 2.62127i | −0.204434 | − | 0.113861i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.13535 | + | 20.8509i | 0.135935 | + | 0.904003i | ||||
\(533\) | 43.6375 | 1.89015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.58624 | − | 2.07051i | −0.155046 | − | 0.0895161i | ||||
\(536\) | −40.2533 | − | 20.8187i | −1.73868 | − | 0.899232i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.6948 | + | 18.3589i | −1.32335 | + | 0.791509i | ||||
\(539\) | 18.5338 | − | 17.6289i | 0.798309 | − | 0.759332i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.5318 | + | 18.7823i | −1.39865 | + | 0.807512i | −0.994251 | − | 0.107070i | \(-0.965853\pi\) |
−0.404400 | + | 0.914582i | \(0.632520\pi\) | |||||||
\(542\) | −23.6039 | + | 0.364246i | −1.01387 | + | 0.0156457i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.6619 | + | 1.51997i | −0.842995 | + | 0.0651681i | ||||
\(545\) | − | 0.907020i | − | 0.0388525i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8253 | 0.591126 | 0.295563 | − | 0.955323i | \(-0.404493\pi\) | ||||
0.295563 | + | 0.955323i | \(0.404493\pi\) | |||||||
\(548\) | −0.0838363 | − | 2.71574i | −0.00358131 | − | 0.116010i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23.7482 | − | 0.366473i | 1.01263 | − | 0.0156264i | ||||
\(551\) | −12.6665 | − | 21.9390i | −0.539610 | − | 0.934632i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.33236 | + | 21.7565i | −0.396852 | + | 0.925180i | ||||
\(554\) | −19.3025 | − | 32.2724i | −0.820084 | − | 1.37112i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.22247 | − | 5.20376i | −0.136663 | − | 0.220688i | ||||
\(557\) | −2.15732 | + | 3.73659i | −0.0914087 | + | 0.158325i | −0.908104 | − | 0.418744i | \(-0.862470\pi\) |
0.816695 | + | 0.577069i | \(0.195804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 11.8063i | − | 0.499354i | ||||||
\(560\) | −5.12855 | + | 4.35236i | −0.216721 | + | 0.183921i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.58493 | − | 10.0276i | 0.235586 | − | 0.422988i | ||||
\(563\) | −5.35371 | − | 3.09097i | −0.225632 | − | 0.130269i | 0.382923 | − | 0.923780i | \(-0.374917\pi\) |
−0.608555 | + | 0.793511i | \(0.708251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.80539 | + | 1.04234i | −0.0759532 | + | 0.0438516i | ||||
\(566\) | 10.0233 | − | 5.99507i | 0.421312 | − | 0.251991i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.0965865 | + | 2.08501i | 0.00405268 | + | 0.0874850i | ||||
\(569\) | 5.65848 | − | 3.26692i | 0.237216 | − | 0.136957i | −0.376681 | − | 0.926343i | \(-0.622935\pi\) |
0.613896 | + | 0.789387i | \(0.289601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00146 | + | 10.3948i | −0.251153 | + | 0.435011i | −0.963844 | − | 0.266468i | \(-0.914143\pi\) |
0.712690 | + | 0.701479i | \(0.247477\pi\) | |||||||
\(572\) | −30.3784 | + | 0.937798i | −1.27018 | + | 0.0392113i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.23835 | + | 38.9105i | 0.218645 | + | 1.62409i | ||||
\(575\) | 13.5137 | 0.563562 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.42990 | − | 2.47666i | 0.0595276 | − | 0.103105i | −0.834726 | − | 0.550666i | \(-0.814374\pi\) |
0.894253 | + | 0.447561i | \(0.147707\pi\) | |||||||
\(578\) | −0.105764 | − | 6.85375i | −0.00439922 | − | 0.285079i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.82286 | − | 7.12010i | 0.158735 | − | 0.295646i | ||||
\(581\) | −5.82591 | − | 7.79240i | −0.241700 | − | 0.323283i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.9663 | − | 10.9502i | 0.785505 | − | 0.453512i | ||||
\(584\) | 10.7374 | + | 5.55332i | 0.444317 | + | 0.229798i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.9398 | + | 14.4473i | 1.07156 | + | 0.596814i | ||||
\(587\) | 30.3998i | 1.25473i | 0.778723 | + | 0.627367i | \(0.215868\pi\) | ||||
−0.778723 | + | 0.627367i | \(0.784132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.9477i | 0.986750i | ||||||||
\(590\) | 4.59608 | − | 8.25214i | 0.189218 | − | 0.339735i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.455466 | − | 7.37000i | −0.0187195 | − | 0.302905i | ||||
\(593\) | 1.46791 | − | 0.847496i | 0.0602797 | − | 0.0348025i | −0.469557 | − | 0.882902i | \(-0.655586\pi\) |
0.529837 | + | 0.848100i | \(0.322253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.51029 | + | 4.69516i | 0.143908 | + | 0.192483i | ||||
\(596\) | −15.4398 | + | 28.7567i | −0.632437 | + | 1.17792i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.2907 | + | 0.266824i | −0.707070 | + | 0.0109112i | ||||
\(599\) | 2.00010 | − | 3.46428i | 0.0817219 | − | 0.141547i | −0.822268 | − | 0.569101i | \(-0.807291\pi\) |
0.903990 | + | 0.427554i | \(0.140625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.9144 | −1.38340 | −0.691699 | − | 0.722186i | \(-0.743138\pi\) | ||||
−0.691699 | + | 0.722186i | \(0.743138\pi\) | |||||||
\(602\) | 10.5274 | − | 1.41726i | 0.429065 | − | 0.0577631i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.556570 | − | 18.0291i | −0.0226465 | − | 0.733595i | ||||
\(605\) | 0.747673 | − | 1.29501i | 0.0303972 | − | 0.0526495i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.15442 | + | 1.24386i | −0.0874452 | + | 0.0504865i | −0.543085 | − | 0.839678i | \(-0.682744\pi\) |
0.455640 | + | 0.890164i | \(0.349411\pi\) | |||||||
\(608\) | 20.3319 | + | 9.73246i | 0.824566 | + | 0.394703i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.918734 | + | 1.53606i | 0.0371984 | + | 0.0621932i | ||||
\(611\) | 33.2417 | − | 19.1921i | 1.34482 | − | 0.776431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.9572 | − | 15.5638i | −1.08879 | − | 0.628614i | −0.155537 | − | 0.987830i | \(-0.549711\pi\) |
−0.933255 | + | 0.359216i | \(0.883044\pi\) | |||||||
\(614\) | 22.3913 | + | 12.4710i | 0.903639 | + | 0.503287i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.48290 | − | 26.9751i | −0.180621 | − | 1.08686i | ||||
\(617\) | − | 8.23255i | − | 0.331430i | −0.986174 | − | 0.165715i | \(-0.947007\pi\) | ||
0.986174 | − | 0.165715i | \(-0.0529932\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.6796 | − | 32.3540i | 0.750796 | − | 1.30042i | −0.196641 | − | 0.980475i | \(-0.563003\pi\) |
0.947437 | − | 0.319941i | \(-0.103663\pi\) | |||||||
\(620\) | −6.49505 | + | 4.02211i | −0.260848 | + | 0.161532i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37.4321 | + | 22.3885i | −1.50089 | + | 0.897698i | ||||
\(623\) | 5.58187 | − | 13.0130i | 0.223633 | − | 0.521354i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.55180 | − | 16.5442i | −0.382072 | − | 0.661768i | ||||
\(626\) | 0.0227774 | + | 1.47602i | 0.000910370 | + | 0.0589938i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.42591 | + | 46.1900i | 0.0569001 | + | 1.84318i | ||||
\(629\) | −6.43544 | −0.256598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.68550i | − | 0.0670986i | −0.999437 | − | 0.0335493i | \(-0.989319\pi\) | ||
0.999437 | − | 0.0335493i | \(-0.0106811\pi\) | |||||||
\(632\) | 13.6547 | + | 21.3084i | 0.543156 | + | 0.847604i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.223840 | + | 14.5053i | 0.00888983 | + | 0.576079i | ||||
\(635\) | −10.4929 | + | 6.05808i | −0.416398 | + | 0.240407i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.9216 | + | 8.23549i | 1.10630 | + | 0.326302i | ||||
\(638\) | 16.8639 | + | 28.1952i | 0.667647 | + | 1.11626i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.775196 | + | 7.14896i | 0.0306423 | + | 0.282588i | ||||
\(641\) | 9.16827 | + | 5.29330i | 0.362125 | + | 0.209073i | 0.670012 | − | 0.742350i | \(-0.266289\pi\) |
−0.307888 | + | 0.951423i | \(0.599622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.0154 | −1.06538 | −0.532692 | − | 0.846309i | \(-0.678820\pi\) | ||||
−0.532692 | + | 0.846309i | \(0.678820\pi\) | |||||||
\(644\) | −2.31354 | − | 15.3857i | −0.0911663 | − | 0.606281i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.55900 | − | 17.1629i | 0.376094 | − | 0.675266i | ||||
\(647\) | −1.31353 | + | 2.27510i | −0.0516402 | + | 0.0894434i | −0.890690 | − | 0.454611i | \(-0.849778\pi\) |
0.839050 | + | 0.544055i | \(0.183112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.1999 | + | 33.2552i | 0.753661 | + | 1.30538i | ||||
\(650\) | 13.8748 | + | 23.1978i | 0.544216 | + | 0.909892i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.5462 | + | 21.5049i | −0.452185 | + | 0.842198i | ||||
\(653\) | 16.6027 | + | 28.7567i | 0.649712 | + | 1.12533i | 0.983191 | + | 0.182577i | \(0.0584440\pi\) |
−0.333479 | + | 0.942757i | \(0.608223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.15528 | + | 4.13110i | 0.279580 | + | 0.161416i | ||||
\(656\) | 37.5744 | + | 18.7041i | 1.46703 | + | 0.730273i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.1036 | + | 27.3370i | 0.822703 | + | 1.06571i | ||||
\(659\) | − | 0.108371i | − | 0.00422154i | −0.999998 | − | 0.00211077i | \(-0.999328\pi\) | ||
0.999998 | − | 0.00211077i | \(-0.000671879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.37028 | + | 1.36848i | 0.0921932 | + | 0.0532278i | 0.545388 | − | 0.838184i | \(-0.316382\pi\) |
−0.453195 | + | 0.891412i | \(0.649716\pi\) | |||||||
\(662\) | 0.101143 | + | 6.55428i | 0.00393104 | + | 0.254739i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.3901 | + | 0.481314i | −0.403214 | + | 0.0186786i | ||||
\(665\) | −0.791462 | − | 6.65390i | −0.0306916 | − | 0.258027i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.34645 | + | 16.1885i | 0.361896 | + | 0.626822i | ||||
\(668\) | 3.51201 | + | 5.67131i | 0.135884 | + | 0.219430i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.5820 | + | 7.00765i | 0.486086 | + | 0.270729i | ||||
\(671\) | −7.27627 | −0.280897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7488 | 0.607071 | 0.303536 | − | 0.952820i | \(-0.401833\pi\) | ||||
0.303536 | + | 0.952820i | \(0.401833\pi\) | |||||||
\(674\) | −40.8043 | − | 22.7262i | −1.57172 | − | 0.875381i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.52220 | − | 7.30261i | −0.173931 | − | 0.280870i | ||||
\(677\) | 19.1246 | + | 33.1248i | 0.735019 | + | 1.27309i | 0.954715 | + | 0.297522i | \(0.0961601\pi\) |
−0.219696 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.4418 | + | 27.9930i | −1.43688 | + | 1.07427i | ||||
\(680\) | 6.26036 | − | 0.290006i | 0.240074 | − | 0.0111212i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.479206 | − | 31.0535i | −0.0183497 | − | 1.18910i | ||||
\(683\) | −3.06255 | − | 1.76816i | −0.117185 | − | 0.0676569i | 0.440262 | − | 0.897869i | \(-0.354886\pi\) |
−0.557447 | + | 0.830213i | \(0.688219\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.863457i | 0.0329910i | ||||||||
\(686\) | −3.99160 | + | 25.8857i | −0.152400 | + | 0.988319i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.06047 | − | 10.1659i | 0.192929 | − | 0.387571i | ||||
\(689\) | 21.5852 | + | 12.4622i | 0.822330 | + | 0.474772i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.99597 | + | 13.8494i | 0.304181 | + | 0.526857i | 0.977079 | − | 0.212879i | \(-0.0682839\pi\) |
−0.672898 | + | 0.739736i | \(0.734951\pi\) | |||||||
\(692\) | 9.06754 | − | 16.8884i | 0.344696 | − | 0.642000i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.91324 | − | 4.87074i | −0.110585 | − | 0.184891i | ||||
\(695\) | 0.972568 | + | 1.68454i | 0.0368916 | + | 0.0638981i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.2901 | − | 31.6794i | 0.692788 | − | 1.19994i | ||||
\(698\) | 7.20267 | − | 12.9322i | 0.272625 | − | 0.489491i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −19.0193 | + | 15.1566i | −0.718863 | + | 0.572865i | ||||
\(701\) | −42.7818 | −1.61585 | −0.807924 | − | 0.589287i | \(-0.799409\pi\) | ||||
−0.807924 | + | 0.589287i | \(0.799409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.37041 | + | 3.67796i | 0.240265 | + | 0.138717i | ||||
\(704\) | −26.5595 | − | 12.2134i | −1.00100 | − | 0.460310i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.8655 | + | 21.5103i | 0.484201 | + | 0.809550i | ||||
\(707\) | 3.82852 | + | 32.1867i | 0.143986 | + | 1.21051i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0615 | + | 9.85048i | −0.640759 | + | 0.369943i | −0.784907 | − | 0.619614i | \(-0.787289\pi\) |
0.144148 | + | 0.989556i | \(0.453956\pi\) | |||||||
\(710\) | −0.0102348 | − | 0.663236i | −0.000384105 | − | 0.0248908i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.16716 | − | 12.7450i | −0.306077 | − | 0.477639i | ||||
\(713\) | − | 17.6708i | − | 0.661776i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.65868 | 0.361214 | ||||||||
\(716\) | −0.00201792 | − | 0.0653670i | −7.54131e−5 | − | 0.00244288i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.284953 | − | 18.4655i | −0.0106344 | − | 0.689128i | ||||
\(719\) | 5.14423 | + | 8.91007i | 0.191847 | + | 0.332290i | 0.945863 | − | 0.324568i | \(-0.105219\pi\) |
−0.754015 | + | 0.656857i | \(0.771885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.26410 | − | 7.60958i | 0.121561 | − | 0.283396i | ||||
\(722\) | 3.78878 | − | 2.26611i | 0.141004 | − | 0.0843360i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32.9283 | − | 20.3911i | 1.22377 | − | 0.757829i | ||||
\(725\) | 14.6095 | − | 25.3045i | 0.542584 | − | 0.939784i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.0773i | 1.48638i | 0.669078 | + | 0.743192i | \(0.266689\pi\) | ||||
−0.669078 | + | 0.743192i | \(0.733311\pi\) | |||||||
\(728\) | 24.0358 | − | 19.7682i | 0.890827 | − | 0.732660i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.35621 | − | 1.86926i | −0.124219 | − | 0.0691845i | ||||
\(731\) | −8.57100 | − | 4.94847i | −0.317010 | − | 0.183026i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.9716 | + | 10.3759i | −0.663795 | + | 0.383242i | −0.793721 | − | 0.608281i | \(-0.791859\pi\) |
0.129926 | + | 0.991524i | \(0.458526\pi\) | |||||||
\(734\) | −16.2530 | − | 27.1740i | −0.599910 | − | 1.00301i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.0027 | − | 7.18148i | −0.553005 | − | 0.264713i | ||||
\(737\) | −50.7041 | + | 29.2741i | −1.86771 | + | 1.07832i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.47770 | − | 14.6838i | 0.311857 | − | 0.540152i | −0.666907 | − | 0.745141i | \(-0.732382\pi\) |
0.978764 | + | 0.204988i | \(0.0657157\pi\) | |||||||
\(740\) | 0.0724068 | + | 2.34550i | 0.00266173 | + | 0.0862221i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.52111 | + | 20.7430i | −0.312820 | + | 0.761498i | ||||
\(743\) | −5.45125 | −0.199987 | −0.0999935 | − | 0.994988i | \(-0.531882\pi\) | ||||
−0.0999935 | + | 0.994988i | \(0.531882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.18631 | − | 8.98296i | 0.190012 | − | 0.329110i | ||||
\(746\) | −6.26665 | + | 0.0967045i | −0.229438 | + | 0.00354060i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.0519 | + | 22.4468i | −0.440661 | + | 0.820735i | ||||
\(749\) | −6.79530 | + | 15.8419i | −0.248295 | + | 0.578849i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5551 | − | 7.82606i | 0.494634 | − | 0.285577i | −0.231861 | − | 0.972749i | \(-0.574481\pi\) |
0.726495 | + | 0.687172i | \(0.241148\pi\) | |||||||
\(752\) | 36.8493 | − | 2.27729i | 1.34375 | − | 0.0830441i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.1931 | + | 32.6653i | −0.662555 | + | 1.18960i | ||||
\(755\) | 5.73229i | 0.208619i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.16577i | 0.333136i | 0.986030 | + | 0.166568i | \(0.0532685\pi\) | ||||
−0.986030 | + | 0.166568i | \(0.946732\pi\) | |||||||
\(758\) | 35.6940 | + | 19.8800i | 1.29647 | + | 0.722075i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.36284 | − | 3.29082i | −0.230805 | − | 0.119371i | ||||
\(761\) | −1.73152 | + | 0.999696i | −0.0627677 | + | 0.0362389i | −0.531055 | − | 0.847337i | \(-0.678204\pi\) |
0.468288 | + | 0.883576i | \(0.344871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.74920 | + | 0.445956i | −0.135730 | + | 0.0161447i | ||||
\(764\) | 2.85388 | − | 5.31537i | 0.103250 | − | 0.192303i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.714905 | − | 46.3273i | −0.0258306 | − | 1.67387i | ||||
\(767\) | −21.8510 | + | 37.8470i | −0.788993 | + | 1.36658i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.48446 | 0.0895920 | 0.0447960 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447960 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(770\) | 1.15945 | + | 8.61241i | 0.0417837 | + | 0.310370i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −43.8051 | + | 1.35229i | −1.57658 | + | 0.0486700i | ||||
\(773\) | 26.3968 | − | 45.7206i | 0.949427 | − | 1.64446i | 0.202792 | − | 0.979222i | \(-0.434998\pi\) |
0.746635 | − | 0.665234i | \(-0.231668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.9208 | + | 13.8107i | −0.859261 | + | 0.496095i | ||||
\(776\) | 2.31267 | + | 49.9235i | 0.0830200 | + | 1.79215i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.1682 | − | 9.07228i | 0.543807 | − | 0.325257i | ||||
\(779\) | −36.2106 | + | 20.9062i | −1.29738 | + | 0.749042i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.33530 | + | 1.34829i | 0.0835637 | + | 0.0482455i | ||||
\(782\) | −7.05348 | + | 12.6643i | −0.252232 | + | 0.452876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.5122 | + | 19.0591i | 0.732578 | + | 0.680683i | ||||
\(785\) | − | 14.6859i | − | 0.524164i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0243 | + | 34.6831i | −0.713789 | + | 1.23632i | 0.249635 | + | 0.968340i | \(0.419689\pi\) |
−0.963425 | + | 0.267979i | \(0.913644\pi\) | |||||||
\(788\) | 16.1051 | + | 26.0071i | 0.573720 | + | 0.926464i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.12838 | − | 6.90237i | −0.146881 | − | 0.245575i | ||||
\(791\) | 5.19621 | + | 6.95015i | 0.184756 | + | 0.247119i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.14048 | − | 7.17153i | −0.147033 | − | 0.254668i | ||||
\(794\) | −9.95481 | + | 0.153619i | −0.353283 | + | 0.00545173i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.197890 | + | 6.41030i | 0.00701401 | + | 0.227207i | ||||
\(797\) | −23.9157 | −0.847139 | −0.423570 | − | 0.905864i | \(-0.639223\pi\) | ||||
−0.423570 | + | 0.905864i | \(0.639223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 32.1766i | − | 1.13833i | ||||||
\(800\) | 2.00389 | + | 25.9217i | 0.0708481 | + | 0.916471i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 42.0413 | − | 0.648765i | 1.48453 | − | 0.0229087i | ||||
\(803\) | 13.5251 | − | 7.80874i | 0.477292 | − | 0.275564i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.584011 | + | 4.90984i | 0.0205837 | + | 0.173049i | ||||
\(806\) | 30.3338 | − | 18.1430i | 1.06846 | − | 0.639059i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.7788 | + | 15.9186i | 1.08279 | + | 0.560014i | ||||
\(809\) | −23.2044 | − | 13.3971i | −0.815824 | − | 0.471016i | 0.0331504 | − | 0.999450i | \(-0.489446\pi\) |
−0.848974 | + | 0.528434i | \(0.822779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.7619 | −1.53669 | −0.768345 | − | 0.640036i | \(-0.778919\pi\) | ||||
−0.768345 | + | 0.640036i | \(0.778919\pi\) | |||||||
\(812\) | −31.3108 | − | 12.3012i | −1.09879 | − | 0.431686i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.33423 | − | 4.64180i | −0.292115 | − | 0.162695i | ||||
\(815\) | 3.87845 | − | 6.71768i | 0.135856 | − | 0.235310i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.65626 | + | 9.79693i | 0.197887 | + | 0.342751i | ||||
\(818\) | −40.3483 | + | 24.1328i | −1.41075 | + | 0.843782i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.7518 | − | 6.30968i | −0.410392 | − | 0.220344i | ||||
\(821\) | 18.9005 | + | 32.7366i | 0.659632 | + | 1.14252i | 0.980711 | + | 0.195463i | \(0.0626210\pi\) |
−0.321080 | + | 0.947052i | \(0.604046\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.9129 | + | 11.4967i | 0.694121 | + | 0.400751i | 0.805154 | − | 0.593066i | \(-0.202083\pi\) |
−0.111033 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(824\) | −4.77590 | − | 7.45287i | −0.166376 | − | 0.259633i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.3703 | − | 14.9407i | −1.26548 | − | 0.519855i | ||||
\(827\) | 31.3424i | 1.08988i | 0.838474 | + | 0.544941i | \(0.183448\pi\) | ||||
−0.838474 | + | 0.544941i | \(0.816552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.5914 | + | 20.5487i | 1.23614 | + | 0.713686i | 0.968303 | − | 0.249779i | \(-0.0803579\pi\) |
0.267837 | + | 0.963464i | \(0.413691\pi\) | |||||||
\(830\) | 3.30507 | − | 0.0510025i | 0.114721 | − | 0.00177032i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.07577 | − | 33.1271i | −0.106633 | − | 1.14847i | ||||
\(833\) | 17.6817 | − | 16.8184i | 0.612635 | − | 0.582723i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.05995 | − | 1.83589i | −0.0366812 | − | 0.0635337i | ||||
\(836\) | 24.7588 | − | 15.3321i | 0.856301 | − | 0.530271i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.15889 | + | 11.0581i | −0.212755 | + | 0.381996i | ||||
\(839\) | 5.17046 | 0.178504 | 0.0892520 | − | 0.996009i | \(-0.471552\pi\) | ||||
0.0892520 | + | 0.996009i | \(0.471552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4173 | 0.393701 | ||||||||
\(842\) | 18.1302 | − | 32.5523i | 0.624809 | − | 1.12183i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.5908 | − | 28.4062i | −0.605499 | − | 0.977781i | ||||
\(845\) | 1.36484 | + | 2.36397i | 0.0469518 | + | 0.0813230i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.72057 | − | 2.45381i | −0.196561 | − | 0.0843141i | ||||
\(848\) | 13.2445 | + | 19.9826i | 0.454816 | + | 0.686205i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.6563 | − | 0.349623i | 0.777105 | − | 0.0119920i | ||||
\(851\) | −4.70066 | − | 2.71393i | −0.161136 | − | 0.0930322i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.8844i | 0.817786i | 0.912582 | + | 0.408893i | \(0.134085\pi\) | ||||
−0.912582 | + | 0.408893i | \(0.865915\pi\) | |||||||
\(854\) | 5.89764 | − | 4.55286i | 0.201813 | − | 0.155796i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.94260 | + | 15.5156i | 0.339831 | + | 0.530312i | ||||
\(857\) | −16.7053 | − | 9.64484i | −0.570644 | − | 0.329461i | 0.186763 | − | 0.982405i | \(-0.440200\pi\) |
−0.757406 | + | 0.652944i | \(0.773534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.54550 | + | 7.87303i | 0.155090 | + | 0.268624i | 0.933092 | − | 0.359638i | \(-0.117100\pi\) |
−0.778002 | + | 0.628262i | \(0.783766\pi\) | |||||||
\(860\) | −1.70711 | + | 3.17951i | −0.0582120 | + | 0.108420i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.3548 | − | 11.5763i | 0.659226 | − | 0.394290i | ||||
\(863\) | 11.0104 | + | 19.0706i | 0.374799 | + | 0.649170i | 0.990297 | − | 0.138968i | \(-0.0443785\pi\) |
−0.615498 | + | 0.788138i | \(0.711045\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.04585 | + | 5.27556i | −0.103562 | + | 0.179375i | ||||
\(866\) | 15.4511 | + | 8.60557i | 0.525048 | + | 0.292429i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.8190 | + | 24.8700i | 0.672700 | + | 0.844142i | ||||
\(869\) | 32.6964 | 1.10915 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.7053 | − | 33.3162i | −1.95527 | − | 1.12888i | ||||
\(872\) | −1.85424 | + | 3.58520i | −0.0627925 | + | 0.121410i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.2201 | − | 8.50518i | 0.481002 | − | 0.287692i | ||||
\(875\) | 12.9240 | − | 9.66254i | 0.436912 | − | 0.326654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0512 | − | 13.3086i | 0.778385 | − | 0.449401i | −0.0574726 | − | 0.998347i | \(-0.518304\pi\) |
0.835858 | + | 0.548946i | \(0.184971\pi\) | |||||||
\(878\) | 22.9494 | − | 0.354146i | 0.774504 | − | 0.0119518i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.31667 | + | 4.13995i | 0.280355 | + | 0.139558i | ||||
\(881\) | 5.95975i | 0.200789i | 0.994948 | + | 0.100395i | \(0.0320105\pi\) | ||||
−0.994948 | + | 0.100395i | \(0.967990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.91564 | −0.300035 | −0.150018 | − | 0.988683i | \(-0.547933\pi\) | ||||
−0.150018 | + | 0.988683i | \(0.547933\pi\) | |||||||
\(884\) | −28.9817 | + | 0.894681i | −0.974759 | + | 0.0300914i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.47518 | + | 0.146217i | −0.318325 | + | 0.00491227i | ||||
\(887\) | 26.1142 | + | 45.2311i | 0.876829 | + | 1.51871i | 0.854802 | + | 0.518955i | \(0.173679\pi\) |
0.0220275 | + | 0.999757i | \(0.492988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.2003 | + | 40.3942i | 1.01289 | + | 1.35478i | ||||
\(890\) | 2.46927 | + | 4.12844i | 0.0827700 | + | 0.138386i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.5702 | + | 20.1693i | −1.09053 | + | 0.675319i | ||||
\(893\) | −18.3894 | + | 31.8514i | −0.615379 | + | 1.06587i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0207832i | 0.000694704i | ||||||||
\(896\) | 29.1694 | − | 6.71924i | 0.974480 | − | 0.224474i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.9707 | + | 32.2659i | −0.599690 | + | 1.07673i | ||||
\(899\) | −33.0885 | − | 19.1037i | −1.10356 | − | 0.637143i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0943 | − | 10.4468i | 0.602809 | − | 0.348032i | ||||
\(902\) | 46.5366 | − | 27.8341i | 1.54950 | − | 0.926773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.26708 | − | 0.429291i | 0.308219 | − | 0.0142780i | ||||
\(905\) | −10.6594 | + | 6.15421i | −0.354330 | + | 0.204573i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.71744 | + | 15.0990i | −0.289458 | + | 0.501355i | −0.973680 | − | 0.227918i | \(-0.926808\pi\) |
0.684223 | + | 0.729273i | \(0.260142\pi\) | |||||||
\(908\) | −1.03298 | − | 33.4616i | −0.0342806 | − | 1.11046i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.82866 | + | 6.04356i | −0.259517 | + | 0.200342i | ||||
\(911\) | −39.1655 | −1.29761 | −0.648805 | − | 0.760954i | \(-0.724731\pi\) | ||||
−0.648805 | + | 0.760954i | \(0.724731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.71885 | + | 11.6374i | −0.222361 | + | 0.385141i | ||||
\(914\) | −0.699705 | − | 45.3423i | −0.0231442 | − | 1.49979i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.6127 | − | 19.1208i | −1.17668 | − | 0.631770i | ||||
\(917\) | 13.5580 | − | 31.6078i | 0.447725 | − | 1.04378i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0892 | − | 20.2588i | 1.15749 | − | 0.668276i | 0.206787 | − | 0.978386i | \(-0.433699\pi\) |
0.950701 | + | 0.310110i | \(0.100366\pi\) | |||||||
\(920\) | 4.69507 | + | 2.42826i | 0.154792 | + | 0.0800574i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.5285 | − | 27.0282i | −1.59820 | − | 0.890128i | ||||
\(923\) | 3.06892i | 0.101015i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.48433i | 0.278963i | ||||||||
\(926\) | −1.56110 | + | 2.80292i | −0.0513010 | + | 0.0921095i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.6665 | + | 20.3286i | −0.973850 | + | 0.667321i | ||||
\(929\) | 14.0117 | − | 8.08966i | 0.459709 | − | 0.265413i | −0.252213 | − | 0.967672i | \(-0.581158\pi\) |
0.711922 | + | 0.702259i | \(0.247825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.1150 | + | 6.54307i | −0.888659 | + | 0.214441i | ||||
\(932\) | −35.4030 | − | 19.0083i | −1.15966 | − | 0.622636i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.1038 | − | 0.526277i | 1.11591 | − | 0.0172203i | ||||
\(935\) | 4.04831 | − | 7.01188i | 0.132394 | − | 0.229313i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.65486 | 0.250073 | 0.125037 | − | 0.992152i | \(-0.460095\pi\) | ||||
0.125037 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(938\) | 22.7801 | − | 55.4538i | 0.743798 | − | 1.81063i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11.7272 | + | 0.362027i | −0.382501 | + | 0.0118080i | ||||
\(941\) | 11.8841 | − | 20.5839i | 0.387411 | − | 0.671016i | −0.604689 | − | 0.796462i | \(-0.706703\pi\) |
0.992101 | + | 0.125445i | \(0.0400360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.7194 | − | 15.4265i | 0.870104 | − | 0.502355i | ||||
\(944\) | −35.0371 | + | 23.2226i | −1.14036 | + | 0.755830i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.53062 | − | 12.5907i | −0.244842 | − | 0.409358i | ||||
\(947\) | −35.2481 | + | 20.3505i | −1.14541 | + | 0.661302i | −0.947764 | − | 0.318972i | \(-0.896662\pi\) |
−0.197644 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3927 | + | 8.88696i | 0.499667 | + | 0.288483i | ||||
\(950\) | −22.6272 | − | 12.6024i | −0.734123 | − | 0.408874i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.27679 | − | 25.7348i | −0.138612 | − | 0.834071i | ||||
\(953\) | 19.5679i | 0.633867i | 0.948448 | + | 0.316934i | \(0.102653\pi\) | ||||
−0.948448 | + | 0.316934i | \(0.897347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.958636 | + | 1.66041i | −0.0310207 | + | 0.0537295i | ||||
\(956\) | 13.9320 | + | 22.4979i | 0.450594 | + | 0.727635i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.0394 | + | 8.99523i | −0.485901 | + | 0.290623i | ||||
\(959\) | 3.56913 | − | 0.424537i | 0.115253 | − | 0.0137090i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.55908 | + | 4.43245i | 0.0825509 | + | 0.142982i | ||||
\(962\) | −0.167520 | − | 10.8556i | −0.00540106 | − | 0.350000i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.6065 | + | 0.728746i | −0.760314 | + | 0.0234713i | ||||
\(965\) | 13.9277 | 0.448347 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.6339i | − | 0.792174i | −0.918213 | − | 0.396087i | \(-0.870368\pi\) | ||
0.918213 | − | 0.396087i | \(-0.129632\pi\) | |||||||
\(968\) | −5.60276 | + | 3.59032i | −0.180079 | + | 0.115397i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.245062 | − | 15.8805i | −0.00786848 | − | 0.509893i | ||||
\(971\) | 41.0803 | − | 23.7177i | 1.31833 | − | 0.761137i | 0.334869 | − | 0.942265i | \(-0.391308\pi\) |
0.983460 | + | 0.181128i | \(0.0579747\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.48491 | − | 4.84838i | 0.207897 | − | 0.155432i | ||||
\(974\) | −8.48106 | − | 14.1797i | −0.271751 | − | 0.454348i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.491299 | − | 7.94981i | −0.0157261 | − | 0.254467i | ||||
\(977\) | −48.9364 | − | 28.2534i | −1.56561 | − | 0.903908i | −0.996671 | − | 0.0815309i | \(-0.974019\pi\) |
−0.568943 | − | 0.822377i | \(-0.692648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.5563 | −0.625023 | ||||||||
\(980\) | −6.32867 | − | 6.25514i | −0.202162 | − | 0.199813i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29.5155 | − | 52.9942i | 0.941876 | − | 1.69111i | ||||
\(983\) | −18.0801 | + | 31.3156i | −0.576665 | + | 0.998814i | 0.419193 | + | 0.907897i | \(0.362313\pi\) |
−0.995859 | + | 0.0909167i | \(0.971020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.86065 | − | 8.41890i | −0.154873 | − | 0.268248i | ||||
\(986\) | 16.0885 | + | 26.8989i | 0.512363 | + | 0.856635i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.2001 | + | 15.6778i | 0.928980 | + | 0.498779i | ||||
\(989\) | −4.17369 | − | 7.22905i | −0.132716 | − | 0.229870i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.72687 | + | 5.03846i | 0.277218 | + | 0.160052i | 0.632163 | − | 0.774835i | \(-0.282167\pi\) |
−0.354945 | + | 0.934887i | \(0.615500\pi\) | |||||||
\(992\) | 33.8956 | − | 2.62032i | 1.07619 | − | 0.0831951i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.73648 | + | 0.368400i | −0.0867958 | + | 0.0116849i | ||||
\(995\) | − | 2.03813i | − | 0.0646130i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.5584 | − | 8.40532i | −0.461070 | − | 0.266199i | 0.251424 | − | 0.967877i | \(-0.419101\pi\) |
−0.712494 | + | 0.701678i | \(0.752435\pi\) | |||||||
\(998\) | −0.196028 | − | 12.7030i | −0.00620516 | − | 0.402107i | ||||
\(999\) | 0 | 0 |
(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 | 504.2.bm.c.179.21 | yes | 48 | |
3.2 | odd | 2 | inner | 504.2.bm.c.179.4 | yes | 48 | |
4.3 | odd | 2 | 2016.2.bu.c.431.9 | 48 | |||
7.2 | even | 3 | inner | 504.2.bm.c.107.12 | yes | 48 | |
8.3 | odd | 2 | inner | 504.2.bm.c.179.13 | yes | 48 | |
8.5 | even | 2 | 2016.2.bu.c.431.15 | 48 | |||
12.11 | even | 2 | 2016.2.bu.c.431.16 | 48 | |||
21.2 | odd | 6 | inner | 504.2.bm.c.107.13 | yes | 48 | |
24.5 | odd | 2 | 2016.2.bu.c.431.10 | 48 | |||
24.11 | even | 2 | inner | 504.2.bm.c.179.12 | yes | 48 | |
28.23 | odd | 6 | 2016.2.bu.c.1871.10 | 48 | |||
56.37 | even | 6 | 2016.2.bu.c.1871.16 | 48 | |||
56.51 | odd | 6 | inner | 504.2.bm.c.107.4 | ✓ | 48 | |
84.23 | even | 6 | 2016.2.bu.c.1871.15 | 48 | |||
168.107 | even | 6 | inner | 504.2.bm.c.107.21 | yes | 48 | |
168.149 | odd | 6 | 2016.2.bu.c.1871.9 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bm.c.107.4 | ✓ | 48 | 56.51 | odd | 6 | inner | |
504.2.bm.c.107.12 | yes | 48 | 7.2 | even | 3 | inner | |
504.2.bm.c.107.13 | yes | 48 | 21.2 | odd | 6 | inner | |
504.2.bm.c.107.21 | yes | 48 | 168.107 | even | 6 | inner | |
504.2.bm.c.179.4 | yes | 48 | 3.2 | odd | 2 | inner | |
504.2.bm.c.179.12 | yes | 48 | 24.11 | even | 2 | inner | |
504.2.bm.c.179.13 | yes | 48 | 8.3 | odd | 2 | inner | |
504.2.bm.c.179.21 | yes | 48 | 1.1 | even | 1 | trivial | |
2016.2.bu.c.431.9 | 48 | 4.3 | odd | 2 | |||
2016.2.bu.c.431.10 | 48 | 24.5 | odd | 2 | |||
2016.2.bu.c.431.15 | 48 | 8.5 | even | 2 | |||
2016.2.bu.c.431.16 | 48 | 12.11 | even | 2 | |||
2016.2.bu.c.1871.9 | 48 | 168.149 | odd | 6 | |||
2016.2.bu.c.1871.10 | 48 | 28.23 | odd | 6 | |||
2016.2.bu.c.1871.15 | 48 | 84.23 | even | 6 | |||
2016.2.bu.c.1871.16 | 48 | 56.37 | even | 6 |