Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 459.3 | ||
Root | \(-1.08105 - 0.911778i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.459 |
Dual form | 637.2.k.g.569.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.823556i | − | 0.582342i | −0.956671 | − | 0.291171i | \(-0.905955\pi\) | ||
0.956671 | − | 0.291171i | \(-0.0940449\pi\) | |||||||
\(3\) | 1.33015 | + | 2.30388i | 0.767960 | + | 1.33015i | 0.938667 | + | 0.344824i | \(0.112061\pi\) |
−0.170707 | + | 0.985322i | \(0.554605\pi\) | |||||||
\(4\) | 1.32176 | 0.660878 | ||||||||
\(5\) | −2.73845 | + | 1.58105i | −1.22467 | + | 0.707065i | −0.965911 | − | 0.258876i | \(-0.916648\pi\) |
−0.258762 | + | 0.965941i | \(0.583315\pi\) | |||||||
\(6\) | 1.89737 | − | 1.09545i | 0.774600 | − | 0.447215i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.73565i | − | 0.967199i | ||||||
\(9\) | −2.03858 | + | 3.53092i | −0.679526 | + | 1.17697i | ||||
\(10\) | 1.30208 | + | 2.25527i | 0.411754 | + | 0.713179i | ||||
\(11\) | −5.14653 | + | 2.97135i | −1.55174 | + | 0.895895i | −0.553735 | + | 0.832693i | \(0.686798\pi\) |
−0.998001 | + | 0.0632025i | \(0.979869\pi\) | |||||||
\(12\) | 1.75813 | + | 3.04517i | 0.507528 | + | 0.879064i | ||||
\(13\) | 0.0766193 | + | 3.60474i | 0.0212504 | + | 0.999774i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.28508 | − | 4.20604i | −1.88100 | − | 1.08600i | ||||
\(16\) | 0.390549 | 0.0976372 | ||||||||
\(17\) | −2.69964 | −0.654760 | −0.327380 | − | 0.944893i | \(-0.606166\pi\) | ||||
−0.327380 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(18\) | 2.90791 | + | 1.67888i | 0.685401 | + | 0.395716i | ||||
\(19\) | 1.69485 | + | 0.978524i | 0.388826 | + | 0.224489i | 0.681651 | − | 0.731677i | \(-0.261262\pi\) |
−0.292825 | + | 0.956166i | \(0.594595\pi\) | |||||||
\(20\) | −3.61956 | + | 2.08976i | −0.809359 | + | 0.467284i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.44707 | + | 4.23845i | 0.521717 | + | 0.903641i | ||||
\(23\) | 2.72941 | 0.569122 | 0.284561 | − | 0.958658i | \(-0.408152\pi\) | ||||
0.284561 | + | 0.958658i | \(0.408152\pi\) | |||||||
\(24\) | 6.30261 | − | 3.63882i | 1.28652 | − | 0.742770i | ||||
\(25\) | 2.49941 | − | 4.32911i | 0.499883 | − | 0.865822i | ||||
\(26\) | 2.96870 | − | 0.0631003i | 0.582211 | − | 0.0123750i | ||||
\(27\) | −2.86554 | −0.551474 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.99923 | − | 5.19481i | 0.556942 | − | 0.964652i | −0.440807 | − | 0.897602i | \(-0.645308\pi\) |
0.997750 | − | 0.0670505i | \(-0.0213589\pi\) | |||||||
\(30\) | −3.46391 | + | 5.99967i | −0.632421 | + | 1.09539i | ||||
\(31\) | 0.997270 | + | 0.575774i | 0.179115 | + | 0.103412i | 0.586877 | − | 0.809676i | \(-0.300357\pi\) |
−0.407762 | + | 0.913088i | \(0.633691\pi\) | |||||||
\(32\) | − | 5.79294i | − | 1.02406i | ||||||
\(33\) | −13.6913 | − | 7.90465i | −2.38334 | − | 1.37602i | ||||
\(34\) | 2.22331i | 0.381294i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.69450 | + | 4.66701i | −0.449083 | + | 0.777835i | ||||
\(37\) | 6.50454i | 1.06934i | 0.845061 | + | 0.534670i | \(0.179564\pi\) | ||||
−0.845061 | + | 0.534670i | \(0.820436\pi\) | |||||||
\(38\) | 0.805869 | − | 1.39581i | 0.130729 | − | 0.226430i | ||||
\(39\) | −8.20297 | + | 4.97135i | −1.31353 | + | 0.796053i | ||||
\(40\) | 4.32519 | + | 7.49145i | 0.683873 | + | 1.18450i | ||||
\(41\) | 3.23351 | + | 1.86687i | 0.504990 | + | 0.291556i | 0.730772 | − | 0.682622i | \(-0.239160\pi\) |
−0.225782 | + | 0.974178i | \(0.572494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.49562 | + | 6.05460i | 0.533078 | + | 0.923318i | 0.999254 | + | 0.0386258i | \(0.0122980\pi\) |
−0.466176 | + | 0.884692i | \(0.654369\pi\) | |||||||
\(44\) | −6.80245 | + | 3.92740i | −1.02551 | + | 0.592077i | ||||
\(45\) | − | 12.8923i | − | 1.92188i | ||||||
\(46\) | − | 2.24783i | − | 0.331424i | ||||||
\(47\) | 0.394969 | − | 0.228035i | 0.0576121 | − | 0.0332624i | −0.470917 | − | 0.882177i | \(-0.656077\pi\) |
0.528529 | + | 0.848915i | \(0.322744\pi\) | |||||||
\(48\) | 0.519487 | + | 0.899778i | 0.0749815 | + | 0.129872i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.56527 | − | 2.05841i | −0.504205 | − | 0.291103i | ||||
\(51\) | −3.59092 | − | 6.21965i | −0.502829 | − | 0.870926i | ||||
\(52\) | 0.101272 | + | 4.76458i | 0.0140439 | + | 0.660729i | ||||
\(53\) | −0.199643 | + | 0.345792i | −0.0274231 | + | 0.0474982i | −0.879411 | − | 0.476063i | \(-0.842063\pi\) |
0.851988 | + | 0.523561i | \(0.175397\pi\) | |||||||
\(54\) | 2.35994i | 0.321146i | ||||||||
\(55\) | 9.39568 | − | 16.2738i | 1.26691 | − | 2.19436i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.20632i | 0.689594i | ||||||||
\(58\) | −4.27822 | − | 2.47003i | −0.561758 | − | 0.324331i | ||||
\(59\) | − | 4.80586i | − | 0.625670i | −0.949807 | − | 0.312835i | \(-0.898721\pi\) | ||
0.949807 | − | 0.312835i | \(-0.101279\pi\) | |||||||
\(60\) | −9.62910 | − | 5.55936i | −1.24311 | − | 0.717711i | ||||
\(61\) | −0.578514 | + | 1.00201i | −0.0740711 | + | 0.128295i | −0.900682 | − | 0.434479i | \(-0.856933\pi\) |
0.826611 | + | 0.562774i | \(0.190266\pi\) | |||||||
\(62\) | 0.474182 | − | 0.821308i | 0.0602212 | − | 0.104306i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.98971 | −0.498714 | ||||||||
\(65\) | −5.90907 | − | 9.75026i | −0.732930 | − | 1.20937i | ||||
\(66\) | −6.50993 | + | 11.2755i | −0.801316 | + | 1.38792i | ||||
\(67\) | 5.43793 | − | 3.13959i | 0.664349 | − | 0.383562i | −0.129583 | − | 0.991569i | \(-0.541364\pi\) |
0.793932 | + | 0.608007i | \(0.208031\pi\) | |||||||
\(68\) | −3.56827 | −0.432716 | ||||||||
\(69\) | 3.63052 | + | 6.28825i | 0.437063 | + | 0.757016i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.90335 | − | 2.25360i | 0.463242 | − | 0.267453i | −0.250165 | − | 0.968203i | \(-0.580485\pi\) |
0.713406 | + | 0.700751i | \(0.247151\pi\) | |||||||
\(72\) | 9.65936 | + | 5.57684i | 1.13837 | + | 0.657236i | ||||
\(73\) | −7.19299 | − | 4.15288i | −0.841876 | − | 0.486057i | 0.0160254 | − | 0.999872i | \(-0.494899\pi\) |
−0.857901 | + | 0.513814i | \(0.828232\pi\) | |||||||
\(74\) | 5.35685 | 0.622721 | ||||||||
\(75\) | 13.2983 | 1.53556 | ||||||||
\(76\) | 2.24018 | + | 1.29337i | 0.256966 | + | 0.148360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.09418 | + | 6.75560i | 0.463575 | + | 0.764921i | ||||
\(79\) | 3.95705 | + | 6.85381i | 0.445203 | + | 0.771114i | 0.998066 | − | 0.0621581i | \(-0.0197983\pi\) |
−0.552864 | + | 0.833272i | \(0.686465\pi\) | |||||||
\(80\) | −1.06950 | + | 0.617476i | −0.119574 | + | 0.0690359i | ||||
\(81\) | 2.30414 | + | 3.99089i | 0.256016 | + | 0.443432i | ||||
\(82\) | 1.53747 | − | 2.66298i | 0.169785 | − | 0.294077i | ||||
\(83\) | 6.19795i | 0.680313i | 0.940369 | + | 0.340156i | \(0.110480\pi\) | ||||
−0.940369 | + | 0.340156i | \(0.889520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.39284 | − | 4.26826i | 0.801866 | − | 0.462958i | ||||
\(86\) | 4.98630 | − | 2.87884i | 0.537687 | − | 0.310434i | ||||
\(87\) | 15.9576 | 1.71084 | ||||||||
\(88\) | 8.12857 | + | 14.0791i | 0.866509 | + | 1.50084i | ||||
\(89\) | 3.56136i | 0.377504i | 0.982025 | + | 0.188752i | \(0.0604442\pi\) | ||||
−0.982025 | + | 0.188752i | \(0.939556\pi\) | |||||||
\(90\) | −10.6176 | −1.11919 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.60762 | 0.376120 | ||||||||
\(93\) | 3.06345i | 0.317665i | ||||||||
\(94\) | −0.187800 | − | 0.325279i | −0.0193701 | − | 0.0335500i | ||||
\(95\) | −6.18837 | −0.634913 | ||||||||
\(96\) | 13.3462 | − | 7.70546i | 1.36215 | − | 0.786435i | ||||
\(97\) | 2.96831 | − | 1.71375i | 0.301386 | − | 0.174005i | −0.341679 | − | 0.939817i | \(-0.610996\pi\) |
0.643065 | + | 0.765811i | \(0.277662\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 24.2293i | − | 2.43513i | ||||||
\(100\) | 3.30361 | − | 5.72203i | 0.330361 | − | 0.572203i | ||||
\(101\) | 6.66474 | + | 11.5437i | 0.663167 | + | 1.14864i | 0.979779 | + | 0.200084i | \(0.0641214\pi\) |
−0.316612 | + | 0.948555i | \(0.602545\pi\) | |||||||
\(102\) | −5.12223 | + | 2.95732i | −0.507177 | + | 0.292819i | ||||
\(103\) | −5.82248 | − | 10.0848i | −0.573706 | − | 0.993688i | −0.996181 | − | 0.0873131i | \(-0.972172\pi\) |
0.422475 | − | 0.906375i | \(-0.361161\pi\) | |||||||
\(104\) | 9.86130 | − | 0.209604i | 0.966981 | − | 0.0205533i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.284779 | + | 0.164417i | 0.0276602 | + | 0.0159696i | ||||
\(107\) | 3.92966 | 0.379894 | 0.189947 | − | 0.981794i | \(-0.439168\pi\) | ||||
0.189947 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(108\) | −3.78755 | −0.364457 | ||||||||
\(109\) | 9.74566 | + | 5.62666i | 0.933465 | + | 0.538936i | 0.887906 | − | 0.460025i | \(-0.152160\pi\) |
0.0455595 | + | 0.998962i | \(0.485493\pi\) | |||||||
\(110\) | −13.4024 | − | 7.73787i | −1.27787 | − | 0.737777i | ||||
\(111\) | −14.9857 | + | 8.65199i | −1.42238 | + | 0.821210i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.88709 | + | 5.00059i | 0.271595 | + | 0.470416i | 0.969270 | − | 0.245998i | \(-0.0791157\pi\) |
−0.697676 | + | 0.716414i | \(0.745782\pi\) | |||||||
\(114\) | 4.28770 | 0.401579 | ||||||||
\(115\) | −7.47437 | + | 4.31533i | −0.696989 | + | 0.402407i | ||||
\(116\) | 3.96424 | − | 6.86627i | 0.368071 | − | 0.637517i | ||||
\(117\) | −12.8842 | − | 7.07800i | −1.19115 | − | 0.654361i | ||||
\(118\) | −3.95790 | −0.364354 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.5063 | + | 19.9294i | −1.05037 | + | 1.81930i | ||||
\(121\) | 12.1578 | − | 21.0580i | 1.10526 | − | 1.91436i | ||||
\(122\) | 0.825215 | + | 0.476438i | 0.0747115 | + | 0.0431347i | ||||
\(123\) | 9.93284i | 0.895614i | ||||||||
\(124\) | 1.31815 | + | 0.761033i | 0.118373 | + | 0.0683428i | ||||
\(125\) | − | 0.00370455i | − | 0.000331345i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.06558 | − | 5.30975i | 0.272027 | − | 0.471164i | −0.697354 | − | 0.716727i | \(-0.745639\pi\) |
0.969381 | + | 0.245563i | \(0.0789728\pi\) | |||||||
\(128\) | − | 8.30013i | − | 0.733635i | ||||||
\(129\) | −9.29938 | + | 16.1070i | −0.818765 | + | 1.41814i | ||||
\(130\) | −8.02989 | + | 4.86645i | −0.704268 | + | 0.426816i | ||||
\(131\) | 5.11084 | + | 8.85224i | 0.446537 | + | 0.773424i | 0.998158 | − | 0.0606707i | \(-0.0193240\pi\) |
−0.551621 | + | 0.834095i | \(0.685991\pi\) | |||||||
\(132\) | −18.0965 | − | 10.4480i | −1.57510 | − | 0.909383i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.58563 | − | 4.47844i | −0.223364 | − | 0.386878i | ||||
\(135\) | 7.84715 | − | 4.53056i | 0.675375 | − | 0.389928i | ||||
\(136\) | 7.38528i | 0.633283i | ||||||||
\(137\) | − | 19.9475i | − | 1.70423i | −0.523353 | − | 0.852116i | \(-0.675319\pi\) | ||
0.523353 | − | 0.852116i | \(-0.324681\pi\) | |||||||
\(138\) | 5.17872 | − | 2.98994i | 0.440842 | − | 0.254520i | ||||
\(139\) | −10.1637 | − | 17.6041i | −0.862077 | − | 1.49316i | −0.869921 | − | 0.493192i | \(-0.835830\pi\) |
0.00784365 | − | 0.999969i | \(-0.497503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.05073 | + | 0.606641i | 0.0884877 | + | 0.0510884i | ||||
\(142\) | −1.85596 | − | 3.21462i | −0.155749 | − | 0.269765i | ||||
\(143\) | −11.1053 | − | 18.3242i | −0.928668 | − | 1.53235i | ||||
\(144\) | −0.796164 | + | 1.37900i | −0.0663470 | + | 0.114916i | ||||
\(145\) | 18.9677i | 1.57518i | ||||||||
\(146\) | −3.42013 | + | 5.92383i | −0.283052 | + | 0.490260i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.59741i | 0.706703i | ||||||||
\(149\) | 9.28046 | + | 5.35808i | 0.760285 | + | 0.438951i | 0.829398 | − | 0.558658i | \(-0.188684\pi\) |
−0.0691132 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(150\) | − | 10.9519i | − | 0.894221i | ||||||
\(151\) | −7.57267 | − | 4.37208i | −0.616255 | − | 0.355795i | 0.159155 | − | 0.987254i | \(-0.449123\pi\) |
−0.775409 | + | 0.631459i | \(0.782456\pi\) | |||||||
\(152\) | 2.67690 | − | 4.63653i | 0.217125 | − | 0.376072i | ||||
\(153\) | 5.50343 | − | 9.53222i | 0.444926 | − | 0.770634i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.64130 | −0.292476 | ||||||||
\(156\) | −10.8423 | + | 6.57091i | −0.868080 | + | 0.526094i | ||||
\(157\) | 3.25367 | − | 5.63552i | 0.259671 | − | 0.449763i | −0.706483 | − | 0.707730i | \(-0.749719\pi\) |
0.966154 | + | 0.257967i | \(0.0830525\pi\) | |||||||
\(158\) | 5.64449 | − | 3.25885i | 0.449052 | − | 0.259260i | ||||
\(159\) | −1.06222 | −0.0842393 | ||||||||
\(160\) | 9.15891 | + | 15.8637i | 0.724075 | + | 1.25414i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.28672 | − | 1.89759i | 0.258229 | − | 0.149089i | ||||
\(163\) | −2.26264 | − | 1.30634i | −0.177224 | − | 0.102320i | 0.408764 | − | 0.912640i | \(-0.365960\pi\) |
−0.585988 | + | 0.810320i | \(0.699293\pi\) | |||||||
\(164\) | 4.27392 | + | 2.46755i | 0.333737 | + | 0.192683i | ||||
\(165\) | 49.9905 | 3.89175 | ||||||||
\(166\) | 5.10436 | 0.396175 | ||||||||
\(167\) | 3.36558 | + | 1.94312i | 0.260436 | + | 0.150363i | 0.624534 | − | 0.780998i | \(-0.285289\pi\) |
−0.364097 | + | 0.931361i | \(0.618622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9883 | + | 0.552385i | −0.999097 | + | 0.0424911i | ||||
\(170\) | −3.51515 | − | 6.08842i | −0.269600 | − | 0.466961i | ||||
\(171\) | −6.91018 | + | 3.98959i | −0.528434 | + | 0.305092i | ||||
\(172\) | 4.62036 | + | 8.00270i | 0.352299 | + | 0.610200i | ||||
\(173\) | −6.98838 | + | 12.1042i | −0.531317 | + | 0.920267i | 0.468015 | + | 0.883720i | \(0.344969\pi\) |
−0.999332 | + | 0.0365470i | \(0.988364\pi\) | |||||||
\(174\) | − | 13.1420i | − | 0.996293i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00997 | + | 1.16046i | −0.151507 | + | 0.0874727i | ||||
\(177\) | 11.0721 | − | 6.39250i | 0.832232 | − | 0.480490i | ||||
\(178\) | 2.93298 | 0.219836 | ||||||||
\(179\) | −12.6422 | − | 21.8968i | −0.944919 | − | 1.63665i | −0.755914 | − | 0.654671i | \(-0.772807\pi\) |
−0.189005 | − | 0.981976i | \(-0.560526\pi\) | |||||||
\(180\) | − | 17.0405i | − | 1.27013i | ||||||
\(181\) | 0.864474 | 0.0642559 | 0.0321279 | − | 0.999484i | \(-0.489772\pi\) | ||||
0.0321279 | + | 0.999484i | \(0.489772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.07803 | −0.227535 | ||||||||
\(184\) | − | 7.46673i | − | 0.550454i | ||||||
\(185\) | −10.2840 | − | 17.8124i | −0.756093 | − | 1.30959i | ||||
\(186\) | 2.52293 | 0.184990 | ||||||||
\(187\) | 13.8938 | − | 8.02158i | 1.01601 | − | 0.586596i | ||||
\(188\) | 0.522052 | − | 0.301407i | 0.0380746 | − | 0.0219824i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.09647i | 0.369737i | ||||||||
\(191\) | −7.33382 | + | 12.7026i | −0.530657 | + | 0.919125i | 0.468703 | + | 0.883356i | \(0.344721\pi\) |
−0.999360 | + | 0.0357690i | \(0.988612\pi\) | |||||||
\(192\) | −5.30690 | − | 9.19182i | −0.382993 | − | 0.663363i | ||||
\(193\) | −14.2859 | + | 8.24794i | −1.02832 | + | 0.593700i | −0.916503 | − | 0.400029i | \(-0.869000\pi\) |
−0.111816 | + | 0.993729i | \(0.535667\pi\) | |||||||
\(194\) | −1.41137 | − | 2.44457i | −0.101331 | − | 0.175510i | ||||
\(195\) | 14.6035 | − | 26.5831i | 1.04578 | − | 1.90365i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.53510 | + | 5.50509i | 0.679348 | + | 0.392222i | 0.799609 | − | 0.600521i | \(-0.205040\pi\) |
−0.120262 | + | 0.992742i | \(0.538373\pi\) | |||||||
\(198\) | −19.9542 | −1.41808 | ||||||||
\(199\) | −21.2117 | −1.50366 | −0.751829 | − | 0.659358i | \(-0.770828\pi\) | ||||
−0.751829 | + | 0.659358i | \(0.770828\pi\) | |||||||
\(200\) | −11.8429 | − | 6.83753i | −0.837423 | − | 0.483486i | ||||
\(201\) | 14.4665 | + | 8.35223i | 1.02039 | + | 0.589121i | ||||
\(202\) | 9.50686 | − | 5.48879i | 0.668901 | − | 0.386190i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.74632 | − | 8.22086i | −0.332309 | − | 0.575576i | ||||
\(205\) | −11.8064 | −0.824597 | ||||||||
\(206\) | −8.30542 | + | 4.79514i | −0.578666 | + | 0.334093i | ||||
\(207\) | −5.56412 | + | 9.63734i | −0.386733 | + | 0.669842i | ||||
\(208\) | 0.0299236 | + | 1.40783i | 0.00207483 | + | 0.0976152i | ||||
\(209\) | −11.6301 | −0.804474 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.96788 | − | 15.5328i | 0.617375 | − | 1.06932i | −0.372588 | − | 0.927997i | \(-0.621530\pi\) |
0.989963 | − | 0.141327i | \(-0.0451370\pi\) | |||||||
\(212\) | −0.263879 | + | 0.457052i | −0.0181233 | + | 0.0313905i | ||||
\(213\) | 10.3840 | + | 5.99523i | 0.711503 | + | 0.410786i | ||||
\(214\) | − | 3.23629i | − | 0.221228i | ||||||
\(215\) | −19.1452 | − | 11.0535i | −1.30569 | − | 0.753842i | ||||
\(216\) | 7.83913i | 0.533385i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.63387 | − | 8.02610i | 0.313845 | − | 0.543596i | ||||
\(219\) | − | 22.0957i | − | 1.49309i | ||||||
\(220\) | 12.4188 | − | 21.5100i | 0.837275 | − | 1.45020i | ||||
\(221\) | −0.206845 | − | 9.73150i | −0.0139139 | − | 0.654612i | ||||
\(222\) | 7.12540 | + | 12.3415i | 0.478225 | + | 0.828311i | ||||
\(223\) | 13.8834 | + | 8.01558i | 0.929700 | + | 0.536763i | 0.886717 | − | 0.462313i | \(-0.152980\pi\) |
0.0429835 | + | 0.999076i | \(0.486314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.1905 | + | 17.6505i | 0.679366 | + | 1.17670i | ||||
\(226\) | 4.11826 | − | 2.37768i | 0.273943 | − | 0.158161i | ||||
\(227\) | 16.3750i | 1.08685i | 0.839458 | + | 0.543424i | \(0.182873\pi\) | ||||
−0.839458 | + | 0.543424i | \(0.817127\pi\) | |||||||
\(228\) | 6.88148i | 0.455737i | ||||||||
\(229\) | 23.3917 | − | 13.5052i | 1.54577 | − | 0.892449i | 0.547310 | − | 0.836930i | \(-0.315652\pi\) |
0.998458 | − | 0.0555193i | \(-0.0176814\pi\) | |||||||
\(230\) | 3.55392 | + | 6.15556i | 0.234338 | + | 0.405886i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.2112 | − | 8.20484i | −0.933011 | − | 0.538674i | ||||
\(233\) | 5.78406 | + | 10.0183i | 0.378926 | + | 0.656320i | 0.990906 | − | 0.134554i | \(-0.0429601\pi\) |
−0.611980 | + | 0.790873i | \(0.709627\pi\) | |||||||
\(234\) | −5.82913 | + | 10.6109i | −0.381062 | + | 0.693655i | ||||
\(235\) | −0.721069 | + | 1.24893i | −0.0470374 | + | 0.0814711i | ||||
\(236\) | − | 6.35217i | − | 0.413491i | ||||||
\(237\) | −10.5269 | + | 18.2331i | −0.683796 | + | 1.18437i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6731i | 0.949122i | 0.880223 | + | 0.474561i | \(0.157393\pi\) | ||||
−0.880223 | + | 0.474561i | \(0.842607\pi\) | |||||||
\(240\) | −2.84518 | − | 1.64267i | −0.183656 | − | 0.106034i | ||||
\(241\) | − | 14.3467i | − | 0.924151i | −0.886841 | − | 0.462076i | \(-0.847105\pi\) | ||
0.886841 | − | 0.462076i | \(-0.152895\pi\) | |||||||
\(242\) | −17.3424 | − | 10.0126i | −1.11481 | − | 0.643637i | ||||
\(243\) | −10.4280 | + | 18.0618i | −0.668956 | + | 1.15867i | ||||
\(244\) | −0.764654 | + | 1.32442i | −0.0489519 | + | 0.0847872i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.18025 | 0.521554 | ||||||||
\(247\) | −3.39746 | + | 6.18447i | −0.216175 | + | 0.393509i | ||||
\(248\) | 1.57512 | − | 2.72818i | 0.100020 | − | 0.173240i | ||||
\(249\) | −14.2793 | + | 8.24417i | −0.904916 | + | 0.522453i | ||||
\(250\) | −0.00305091 | −0.000192956 | ||||||||
\(251\) | −4.30726 | − | 7.46040i | −0.271872 | − | 0.470896i | 0.697469 | − | 0.716615i | \(-0.254309\pi\) |
−0.969341 | + | 0.245719i | \(0.920976\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0470 | + | 8.11004i | −0.883128 | + | 0.509874i | ||||
\(254\) | −4.37287 | − | 2.52468i | −0.274378 | − | 0.158412i | ||||
\(255\) | 19.6671 | + | 11.3548i | 1.23160 | + | 0.711066i | ||||
\(256\) | −14.8151 | −0.925941 | ||||||||
\(257\) | 10.3639 | 0.646485 | 0.323243 | − | 0.946316i | \(-0.395227\pi\) | ||||
0.323243 | + | 0.946316i | \(0.395227\pi\) | |||||||
\(258\) | 13.2650 | + | 7.65856i | 0.825844 | + | 0.476801i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.81035 | − | 12.8875i | −0.484377 | − | 0.799247i | ||||
\(261\) | 12.2283 | + | 21.1800i | 0.756913 | + | 1.31101i | ||||
\(262\) | 7.29032 | − | 4.20907i | 0.450397 | − | 0.260037i | ||||
\(263\) | 11.0413 | + | 19.1241i | 0.680835 | + | 1.17924i | 0.974726 | + | 0.223403i | \(0.0717165\pi\) |
−0.293891 | + | 0.955839i | \(0.594950\pi\) | |||||||
\(264\) | −21.6244 | + | 37.4545i | −1.33089 | + | 2.30517i | ||||
\(265\) | − | 1.26258i | − | 0.0775596i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.20495 | + | 4.73713i | −0.502135 | + | 0.289908i | ||||
\(268\) | 7.18761 | − | 4.14977i | 0.439053 | − | 0.253488i | ||||
\(269\) | −12.9399 | −0.788960 | −0.394480 | − | 0.918905i | \(-0.629075\pi\) | ||||
−0.394480 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(270\) | −3.73117 | − | 6.46257i | −0.227072 | − | 0.393299i | ||||
\(271\) | − | 17.6749i | − | 1.07367i | −0.843686 | − | 0.536837i | \(-0.819619\pi\) | ||
0.843686 | − | 0.536837i | \(-0.180381\pi\) | |||||||
\(272\) | −1.05434 | −0.0639289 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4279 | −0.992446 | ||||||||
\(275\) | 29.7065i | 1.79137i | ||||||||
\(276\) | 4.79866 | + | 8.31152i | 0.288845 | + | 0.500295i | ||||
\(277\) | 18.0150 | 1.08242 | 0.541209 | − | 0.840888i | \(-0.317967\pi\) | ||||
0.541209 | + | 0.840888i | \(0.317967\pi\) | |||||||
\(278\) | −14.4980 | + | 8.37041i | −0.869530 | + | 0.502024i | ||||
\(279\) | −4.06602 | + | 2.34752i | −0.243426 | + | 0.140542i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.44178i | − | 0.145665i | −0.997344 | − | 0.0728323i | \(-0.976796\pi\) | ||
0.997344 | − | 0.0728323i | \(-0.0232038\pi\) | |||||||
\(282\) | 0.499603 | − | 0.865337i | 0.0297509 | − | 0.0515301i | ||||
\(283\) | 14.3620 | + | 24.8757i | 0.853732 | + | 1.47871i | 0.877817 | + | 0.478996i | \(0.158999\pi\) |
−0.0240853 | + | 0.999710i | \(0.507667\pi\) | |||||||
\(284\) | 5.15927 | − | 2.97871i | 0.306146 | − | 0.176754i | ||||
\(285\) | −8.23143 | − | 14.2573i | −0.487588 | − | 0.844527i | ||||
\(286\) | −15.0910 | + | 9.14580i | −0.892350 | + | 0.540802i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 20.4544 | + | 11.8094i | 1.20529 | + | 0.695873i | ||||
\(289\) | −9.71193 | −0.571290 | ||||||||
\(290\) | 15.6209 | 0.917292 | ||||||||
\(291\) | 7.89657 | + | 4.55909i | 0.462905 | + | 0.267258i | ||||
\(292\) | −9.50738 | − | 5.48909i | −0.556377 | − | 0.321225i | ||||
\(293\) | −25.4013 | + | 14.6654i | −1.48396 | + | 0.856763i | −0.999834 | − | 0.0182359i | \(-0.994195\pi\) |
−0.484124 | + | 0.874999i | \(0.660862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.59829 | + | 13.1606i | 0.442390 | + | 0.766241i | ||||
\(296\) | 17.7942 | 1.03426 | ||||||||
\(297\) | 14.7476 | − | 8.51453i | 0.855742 | − | 0.494063i | ||||
\(298\) | 4.41267 | − | 7.64298i | 0.255619 | − | 0.442746i | ||||
\(299\) | 0.209126 | + | 9.83882i | 0.0120941 | + | 0.568994i | ||||
\(300\) | 17.5772 | 1.01482 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.60065 | + | 6.23651i | −0.207194 | + | 0.358871i | ||||
\(303\) | −17.7302 | + | 30.7096i | −1.01857 | + | 1.76422i | ||||
\(304\) | 0.661923 | + | 0.382161i | 0.0379639 | + | 0.0219185i | ||||
\(305\) | − | 3.65863i | − | 0.209492i | ||||||
\(306\) | −7.85032 | − | 4.53238i | −0.448773 | − | 0.259099i | ||||
\(307\) | − | 7.06910i | − | 0.403455i | −0.979442 | − | 0.201728i | \(-0.935344\pi\) | ||
0.979442 | − | 0.201728i | \(-0.0646555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.4895 | − | 26.8286i | 0.881166 | − | 1.52623i | ||||
\(310\) | 2.99882i | 0.170321i | ||||||||
\(311\) | 11.1343 | − | 19.2852i | 0.631368 | − | 1.09356i | −0.355904 | − | 0.934522i | \(-0.615827\pi\) |
0.987272 | − | 0.159039i | \(-0.0508396\pi\) | |||||||
\(312\) | 13.5999 | + | 22.4405i | 0.769941 | + | 1.27044i | ||||
\(313\) | −14.0420 | − | 24.3214i | −0.793700 | − | 1.37473i | −0.923661 | − | 0.383210i | \(-0.874819\pi\) |
0.129961 | − | 0.991519i | \(-0.458515\pi\) | |||||||
\(314\) | −4.64117 | − | 2.67958i | −0.261916 | − | 0.151217i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.23025 | + | 9.05906i | 0.294225 | + | 0.509612i | ||||
\(317\) | 16.9009 | − | 9.75774i | 0.949249 | − | 0.548049i | 0.0564015 | − | 0.998408i | \(-0.482037\pi\) |
0.892848 | + | 0.450359i | \(0.148704\pi\) | |||||||
\(318\) | 0.874796i | 0.0490561i | ||||||||
\(319\) | 35.6470i | 1.99585i | ||||||||
\(320\) | 10.9256 | − | 6.30792i | 0.610762 | − | 0.352624i | ||||
\(321\) | 5.22702 | + | 9.05346i | 0.291744 | + | 0.505315i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.57550 | − | 2.64167i | −0.254588 | − | 0.146986i | ||||
\(324\) | 3.04551 | + | 5.27498i | 0.169195 | + | 0.293054i | ||||
\(325\) | 15.7968 | + | 8.67804i | 0.876250 | + | 0.481371i | ||||
\(326\) | −1.07584 | + | 1.86341i | −0.0595853 | + | 0.103205i | ||||
\(327\) | 29.9371i | 1.65553i | ||||||||
\(328\) | 5.10711 | − | 8.84577i | 0.281993 | − | 0.488426i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 41.1700i | − | 2.26633i | ||||||
\(331\) | −13.5367 | − | 7.81539i | −0.744042 | − | 0.429573i | 0.0794953 | − | 0.996835i | \(-0.474669\pi\) |
−0.823537 | + | 0.567263i | \(0.808002\pi\) | |||||||
\(332\) | 8.19217i | 0.449604i | ||||||||
\(333\) | −22.9670 | − | 13.2600i | −1.25858 | − | 0.726644i | ||||
\(334\) | 1.60027 | − | 2.77174i | 0.0875627 | − | 0.151663i | ||||
\(335\) | −9.92767 | + | 17.1952i | −0.542407 | + | 0.939476i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7501 | 1.18480 | 0.592401 | − | 0.805643i | \(-0.298180\pi\) | ||||
0.592401 | + | 0.805643i | \(0.298180\pi\) | |||||||
\(338\) | 0.454920 | + | 10.6966i | 0.0247444 | + | 0.581816i | ||||
\(339\) | −7.68050 | + | 13.3030i | −0.417148 | + | 0.722521i | ||||
\(340\) | 9.77153 | − | 5.64160i | 0.529936 | − | 0.305959i | ||||
\(341\) | −6.84330 | −0.370586 | ||||||||
\(342\) | 3.28565 | + | 5.69092i | 0.177668 | + | 0.307730i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 16.5633 | − | 9.56281i | 0.893032 | − | 0.515592i | ||||
\(345\) | −19.8840 | − | 11.4800i | −1.07052 | − | 0.618065i | ||||
\(346\) | 9.96851 | + | 5.75532i | 0.535910 | + | 0.309408i | ||||
\(347\) | −15.9590 | −0.856726 | −0.428363 | − | 0.903607i | \(-0.640909\pi\) | ||||
−0.428363 | + | 0.903607i | \(0.640909\pi\) | |||||||
\(348\) | 21.0921 | 1.13065 | ||||||||
\(349\) | −5.90375 | − | 3.40853i | −0.316021 | − | 0.182455i | 0.333597 | − | 0.942716i | \(-0.391738\pi\) |
−0.649617 | + | 0.760261i | \(0.725071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.219556 | − | 10.3295i | −0.0117190 | − | 0.551349i | ||||
\(352\) | 17.2128 | + | 29.8135i | 0.917448 | + | 1.58907i | ||||
\(353\) | 12.1272 | − | 7.00163i | 0.645465 | − | 0.372659i | −0.141252 | − | 0.989974i | \(-0.545113\pi\) |
0.786716 | + | 0.617314i | \(0.211779\pi\) | |||||||
\(354\) | −5.26458 | − | 9.11852i | −0.279809 | − | 0.484644i | ||||
\(355\) | −7.12608 | + | 12.3427i | −0.378213 | + | 0.655085i | ||||
\(356\) | 4.70725i | 0.249484i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.0333 | + | 10.4115i | −0.953088 | + | 0.550266i | ||||
\(359\) | −4.68947 | + | 2.70747i | −0.247501 | + | 0.142895i | −0.618619 | − | 0.785691i | \(-0.712308\pi\) |
0.371119 | + | 0.928586i | \(0.378974\pi\) | |||||||
\(360\) | −35.2689 | −1.85884 | ||||||||
\(361\) | −7.58498 | − | 13.1376i | −0.399210 | − | 0.691451i | ||||
\(362\) | − | 0.711943i | − | 0.0374189i | ||||||
\(363\) | 64.6867 | 3.39517 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.2636 | 1.37470 | ||||||||
\(366\) | 2.53493i | 0.132503i | ||||||||
\(367\) | 15.0159 | + | 26.0083i | 0.783822 | + | 1.35762i | 0.929700 | + | 0.368317i | \(0.120066\pi\) |
−0.145878 | + | 0.989303i | \(0.546601\pi\) | |||||||
\(368\) | 1.06597 | 0.0555675 | ||||||||
\(369\) | −13.1835 | + | 7.61152i | −0.686307 | + | 0.396240i | ||||
\(370\) | −14.6695 | + | 8.46943i | −0.762630 | + | 0.440305i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.04914i | 0.209938i | ||||||||
\(373\) | −10.7049 | + | 18.5414i | −0.554278 | + | 0.960037i | 0.443682 | + | 0.896184i | \(0.353672\pi\) |
−0.997959 | + | 0.0638526i | \(0.979661\pi\) | |||||||
\(374\) | −6.60622 | − | 11.4423i | −0.341599 | − | 0.591668i | ||||
\(375\) | 0.00853484 | − | 0.00492759i | 0.000440737 | − | 0.000254460i | ||||
\(376\) | −0.623826 | − | 1.08050i | −0.0321713 | − | 0.0557224i | ||||
\(377\) | 18.9557 | + | 10.4134i | 0.976270 | + | 0.536317i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.20693 | − | 4.73827i | −0.421562 | − | 0.243389i | 0.274184 | − | 0.961677i | \(-0.411592\pi\) |
−0.695745 | + | 0.718289i | \(0.744926\pi\) | |||||||
\(380\) | −8.17951 | −0.419600 | ||||||||
\(381\) | 16.3107 | 0.835622 | ||||||||
\(382\) | 10.4613 | + | 6.03982i | 0.535245 | + | 0.309024i | ||||
\(383\) | −4.70304 | − | 2.71530i | −0.240314 | − | 0.138746i | 0.375007 | − | 0.927022i | \(-0.377640\pi\) |
−0.615321 | + | 0.788277i | \(0.710974\pi\) | |||||||
\(384\) | 19.1225 | − | 11.0404i | 0.975842 | − | 0.563402i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.79264 | + | 11.7652i | 0.345736 | + | 0.598833i | ||||
\(387\) | −28.5044 | −1.44896 | ||||||||
\(388\) | 3.92338 | − | 2.26516i | 0.199179 | − | 0.114996i | ||||
\(389\) | −5.32109 | + | 9.21640i | −0.269790 | + | 0.467290i | −0.968807 | − | 0.247815i | \(-0.920288\pi\) |
0.699018 | + | 0.715105i | \(0.253621\pi\) | |||||||
\(390\) | −21.8926 | − | 12.0268i | −1.10858 | − | 0.609001i | ||||
\(391\) | −7.36845 | −0.372638 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.5963 | + | 23.5495i | −0.685845 | + | 1.18792i | ||||
\(394\) | 4.53375 | − | 7.85269i | 0.228407 | − | 0.395613i | ||||
\(395\) | −21.6724 | − | 12.5126i | −1.09046 | − | 0.629575i | ||||
\(396\) | − | 32.0252i | − | 1.60933i | ||||||
\(397\) | 32.2035 | + | 18.5927i | 1.61625 | + | 0.933140i | 0.987879 | + | 0.155223i | \(0.0496097\pi\) |
0.628367 | + | 0.777917i | \(0.283724\pi\) | |||||||
\(398\) | 17.4690i | 0.875644i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.976143 | − | 1.69073i | 0.0488072 | − | 0.0845365i | ||||
\(401\) | 0.896610i | 0.0447746i | 0.999749 | + | 0.0223873i | \(0.00712669\pi\) | ||||
−0.999749 | + | 0.0223873i | \(0.992873\pi\) | |||||||
\(402\) | 6.87853 | − | 11.9140i | 0.343070 | − | 0.594214i | ||||
\(403\) | −1.99910 | + | 3.63901i | −0.0995825 | + | 0.181272i | ||||
\(404\) | 8.80916 | + | 15.2579i | 0.438272 | + | 0.759110i | ||||
\(405\) | −12.6196 | − | 7.28590i | −0.627071 | − | 0.362039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.3273 | − | 33.4758i | −0.958016 | − | 1.65933i | ||||
\(408\) | −17.0148 | + | 9.82350i | −0.842359 | + | 0.486336i | ||||
\(409\) | − | 24.5773i | − | 1.21527i | −0.794217 | − | 0.607635i | \(-0.792119\pi\) | ||
0.794217 | − | 0.607635i | \(-0.207881\pi\) | |||||||
\(410\) | 9.72326i | 0.480198i | ||||||||
\(411\) | 45.9567 | − | 26.5331i | 2.26688 | − | 1.30878i | ||||
\(412\) | −7.69589 | − | 13.3297i | −0.379149 | − | 0.656706i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.93689 | + | 4.58237i | 0.390077 | + | 0.225211i | ||||
\(415\) | −9.79924 | − | 16.9728i | −0.481026 | − | 0.833161i | ||||
\(416\) | 20.8820 | − | 0.443851i | 1.02383 | − | 0.0217616i | ||||
\(417\) | 27.0385 | − | 46.8321i | 1.32408 | − | 2.29338i | ||||
\(418\) | 9.57807i | 0.468479i | ||||||||
\(419\) | −3.82279 | + | 6.62126i | −0.186755 | + | 0.323470i | −0.944167 | − | 0.329468i | \(-0.893131\pi\) |
0.757411 | + | 0.652938i | \(0.226464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.0780i | − | 1.22223i | −0.791544 | − | 0.611113i | \(-0.790722\pi\) | ||
0.791544 | − | 0.611113i | \(-0.209278\pi\) | |||||||
\(422\) | −12.7922 | − | 7.38555i | −0.622712 | − | 0.359523i | ||||
\(423\) | 1.85947i | 0.0904106i | ||||||||
\(424\) | 0.945966 | + | 0.546154i | 0.0459402 | + | 0.0265236i | ||||
\(425\) | −6.74753 | + | 11.6871i | −0.327303 | + | 0.566906i | ||||
\(426\) | 4.93741 | − | 8.55184i | 0.239218 | − | 0.414338i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.19405 | 0.251064 | ||||||||
\(429\) | 27.4452 | − | 49.9591i | 1.32507 | − | 2.41205i | ||||
\(430\) | −9.10317 | + | 15.7671i | −0.438994 | + | 0.760359i | ||||
\(431\) | −6.71520 | + | 3.87702i | −0.323460 | + | 0.186750i | −0.652934 | − | 0.757415i | \(-0.726462\pi\) |
0.329474 | + | 0.944165i | \(0.393129\pi\) | |||||||
\(432\) | −1.11913 | −0.0538444 | ||||||||
\(433\) | −17.9880 | − | 31.1561i | −0.864448 | − | 1.49727i | −0.867594 | − | 0.497273i | \(-0.834335\pi\) |
0.00314644 | − | 0.999995i | \(-0.498998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −43.6992 | + | 25.2298i | −2.09522 | + | 1.20967i | ||||
\(436\) | 12.8814 | + | 7.43707i | 0.616907 | + | 0.356171i | ||||
\(437\) | 4.62596 | + | 2.67080i | 0.221290 | + | 0.127762i | ||||
\(438\) | −18.1971 | −0.869489 | ||||||||
\(439\) | −28.2350 | −1.34758 | −0.673792 | − | 0.738921i | \(-0.735336\pi\) | ||||
−0.673792 | + | 0.738921i | \(0.735336\pi\) | |||||||
\(440\) | −44.5194 | − | 25.7033i | −2.12238 | − | 1.22536i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.01444 | + | 0.170348i | −0.381208 | + | 0.00810264i | ||||
\(443\) | −14.3959 | − | 24.9344i | −0.683970 | − | 1.18467i | −0.973759 | − | 0.227580i | \(-0.926919\pi\) |
0.289790 | − | 0.957090i | \(-0.406415\pi\) | |||||||
\(444\) | −19.8074 | + | 11.4358i | −0.940018 | + | 0.542720i | ||||
\(445\) | −5.63068 | − | 9.75262i | −0.266920 | − | 0.462319i | ||||
\(446\) | 6.60128 | − | 11.4337i | 0.312579 | − | 0.541404i | ||||
\(447\) | 28.5081i | 1.34839i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2795 | + | 14.5951i | −1.19301 | + | 0.688785i | −0.958988 | − | 0.283446i | \(-0.908522\pi\) |
−0.234023 | + | 0.972231i | \(0.575189\pi\) | |||||||
\(450\) | 14.5361 | − | 8.39244i | 0.685240 | − | 0.395624i | ||||
\(451\) | −22.1885 | −1.04482 | ||||||||
\(452\) | 3.81603 | + | 6.60955i | 0.179491 | + | 0.310887i | ||||
\(453\) | − | 23.2620i | − | 1.09295i | ||||||
\(454\) | 13.4858 | 0.632918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.2427 | 0.666974 | ||||||||
\(457\) | 31.6848i | 1.48215i | 0.671420 | + | 0.741077i | \(0.265684\pi\) | ||||
−0.671420 | + | 0.741077i | \(0.734316\pi\) | |||||||
\(458\) | −11.1223 | − | 19.2644i | −0.519711 | − | 0.900165i | ||||
\(459\) | 7.73594 | 0.361083 | ||||||||
\(460\) | −9.87929 | + | 5.70381i | −0.460624 | + | 0.265942i | ||||
\(461\) | 19.1407 | − | 11.0509i | 0.891471 | − | 0.514691i | 0.0170480 | − | 0.999855i | \(-0.494573\pi\) |
0.874424 | + | 0.485163i | \(0.161240\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.8811i | 1.80696i | 0.428632 | + | 0.903479i | \(0.358996\pi\) | ||||
−0.428632 | + | 0.903479i | \(0.641004\pi\) | |||||||
\(464\) | 1.17134 | − | 2.02883i | 0.0543783 | − | 0.0941860i | ||||
\(465\) | −4.84346 | − | 8.38913i | −0.224610 | − | 0.389036i | ||||
\(466\) | 8.25062 | − | 4.76350i | 0.382202 | − | 0.220665i | ||||
\(467\) | −6.64116 | − | 11.5028i | −0.307316 | − | 0.532287i | 0.670458 | − | 0.741947i | \(-0.266098\pi\) |
−0.977774 | + | 0.209660i | \(0.932764\pi\) | |||||||
\(468\) | −17.0298 | − | 9.35538i | −0.787203 | − | 0.432453i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.02856 | + | 0.593841i | 0.0474440 | + | 0.0273918i | ||||
\(471\) | 17.3114 | 0.797668 | ||||||||
\(472\) | −13.1472 | −0.605147 | ||||||||
\(473\) | −35.9807 | − | 20.7734i | −1.65439 | − | 0.955164i | ||||
\(474\) | 15.0160 | + | 8.66949i | 0.689708 | + | 0.398203i | ||||
\(475\) | 8.47228 | − | 4.89147i | 0.388735 | − | 0.224436i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.813975 | − | 1.40985i | −0.0372694 | − | 0.0645524i | ||||
\(478\) | 12.0841 | 0.552714 | ||||||||
\(479\) | 5.74618 | − | 3.31756i | 0.262550 | − | 0.151583i | −0.362947 | − | 0.931810i | \(-0.618230\pi\) |
0.625497 | + | 0.780226i | \(0.284896\pi\) | |||||||
\(480\) | −24.3654 | + | 42.2021i | −1.11212 | + | 1.92625i | ||||
\(481\) | −23.4472 | + | 0.498373i | −1.06910 | + | 0.0227239i | ||||
\(482\) | −11.8153 | −0.538172 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.0697 | − | 27.8335i | 0.730439 | − | 1.26516i | ||||
\(485\) | −5.41905 | + | 9.38607i | −0.246066 | + | 0.426200i | ||||
\(486\) | 14.8749 | + | 8.58804i | 0.674740 | + | 0.389561i | ||||
\(487\) | 33.4701i | 1.51668i | 0.651861 | + | 0.758338i | \(0.273988\pi\) | ||||
−0.651861 | + | 0.758338i | \(0.726012\pi\) | |||||||
\(488\) | 2.74116 | + | 1.58261i | 0.124087 | + | 0.0716415i | ||||
\(489\) | − | 6.95047i | − | 0.314311i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6643 | + | 32.3276i | −0.842310 | + | 1.45892i | 0.0456264 | + | 0.998959i | \(0.485472\pi\) |
−0.887937 | + | 0.459966i | \(0.847862\pi\) | |||||||
\(492\) | 13.1288i | 0.591891i | ||||||||
\(493\) | −8.09684 | + | 14.0241i | −0.364663 | + | 0.631615i | ||||
\(494\) | 5.09326 | + | 2.79800i | 0.229157 | + | 0.125888i | ||||
\(495\) | 38.3076 | + | 66.3507i | 1.72180 | + | 2.98224i | ||||
\(496\) | 0.389483 | + | 0.224868i | 0.0174883 | + | 0.0100969i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.78954 | + | 11.7598i | 0.304246 | + | 0.526970i | ||||
\(499\) | 29.5598 | − | 17.0663i | 1.32328 | − | 0.763994i | 0.339027 | − | 0.940777i | \(-0.389902\pi\) |
0.984250 | + | 0.176783i | \(0.0565690\pi\) | |||||||
\(500\) | − | 0.00489651i | − | 0.000218979i | ||||||
\(501\) | 10.3385i | 0.461891i | ||||||||
\(502\) | −6.14405 | + | 3.54727i | −0.274223 | + | 0.158322i | ||||
\(503\) | 7.65447 | + | 13.2579i | 0.341296 | + | 0.591142i | 0.984674 | − | 0.174407i | \(-0.0558008\pi\) |
−0.643378 | + | 0.765549i | \(0.722467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.5022 | − | 21.0745i | −1.62433 | − | 0.937805i | ||||
\(506\) | 6.67907 | + | 11.5685i | 0.296921 | + | 0.514282i | ||||
\(507\) | −18.5489 | − | 29.1886i | −0.823786 | − | 1.29631i | ||||
\(508\) | 4.05195 | − | 7.01819i | 0.179776 | − | 0.311382i | ||||
\(509\) | − | 18.4970i | − | 0.819866i | −0.912116 | − | 0.409933i | \(-0.865552\pi\) | ||
0.912116 | − | 0.409933i | \(-0.134448\pi\) | |||||||
\(510\) | 9.35133 | − | 16.1970i | 0.414084 | − | 0.717214i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 4.39924i | − | 0.194421i | ||||||
\(513\) | −4.85668 | − | 2.80400i | −0.214427 | − | 0.123800i | ||||
\(514\) | − | 8.53529i | − | 0.376476i | ||||||
\(515\) | 31.8892 | + | 18.4112i | 1.40520 | + | 0.811295i | ||||
\(516\) | −12.2915 | + | 21.2895i | −0.541104 | + | 0.937219i | ||||
\(517\) | −1.35515 | + | 2.34718i | −0.0595992 | + | 0.103229i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.1823 | −1.63212 | ||||||||
\(520\) | −26.6733 | + | 16.1652i | −1.16970 | + | 0.708890i | ||||
\(521\) | 11.7932 | − | 20.4265i | 0.516671 | − | 0.894901i | −0.483141 | − | 0.875542i | \(-0.660504\pi\) |
0.999813 | − | 0.0193585i | \(-0.00616239\pi\) | |||||||
\(522\) | 17.4430 | − | 10.0707i | 0.763457 | − | 0.440782i | ||||
\(523\) | −12.3059 | −0.538099 | −0.269049 | − | 0.963126i | \(-0.586709\pi\) | ||||
−0.269049 | + | 0.963126i | \(0.586709\pi\) | |||||||
\(524\) | 6.75529 | + | 11.7005i | 0.295106 | + | 0.511139i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.7498 | − | 9.09312i | 0.686722 | − | 0.396479i | ||||
\(527\) | −2.69227 | − | 1.55438i | −0.117277 | − | 0.0677101i | ||||
\(528\) | −5.34711 | − | 3.08715i | −0.232703 | − | 0.134351i | ||||
\(529\) | −15.5503 | −0.676100 | ||||||||
\(530\) | −1.03980 | −0.0451662 | ||||||||
\(531\) | 16.9691 | + | 9.79712i | 0.736397 | + | 0.425159i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.48183 | + | 11.7990i | −0.280759 | + | 0.511072i | ||||
\(534\) | 3.90129 | + | 6.75724i | 0.168825 | + | 0.292414i | ||||
\(535\) | −10.7612 | + | 6.21297i | −0.465246 | + | 0.268610i | ||||
\(536\) | −8.58883 | − | 14.8763i | −0.370981 | − | 0.642558i | ||||
\(537\) | 33.6318 | − | 58.2520i | 1.45132 | − | 2.51376i | ||||
\(538\) | 10.6567i | 0.459444i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.3720 | − | 5.98829i | 0.446341 | − | 0.257695i | ||||
\(541\) | −16.8365 | + | 9.72054i | −0.723857 | + | 0.417919i | −0.816170 | − | 0.577811i | \(-0.803907\pi\) |
0.0923139 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(542\) | −14.5563 | −0.625245 | ||||||||
\(543\) | 1.14988 | + | 1.99165i | 0.0493460 | + | 0.0854697i | ||||
\(544\) | 15.6389i | 0.670511i | ||||||||
\(545\) | −35.5841 | −1.52425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.2163 | 1.71953 | 0.859763 | − | 0.510693i | \(-0.170611\pi\) | ||||
0.859763 | + | 0.510693i | \(0.170611\pi\) | |||||||
\(548\) | − | 26.3658i | − | 1.12629i | ||||||
\(549\) | −2.35869 | − | 4.08537i | −0.100666 | − | 0.174359i | ||||
\(550\) | 24.4650 | 1.04319 | ||||||||
\(551\) | 10.1665 | − | 5.86963i | 0.433107 | − | 0.250055i | ||||
\(552\) | 17.2024 | − | 9.93184i | 0.732185 | − | 0.422727i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 14.8364i | − | 0.630337i | ||||||
\(555\) | 27.3584 | − | 47.3861i | 1.16130 | − | 2.01143i | ||||
\(556\) | −13.4340 | − | 23.2683i | −0.569727 | − | 0.986797i | ||||
\(557\) | −6.89702 | + | 3.98199i | −0.292236 | + | 0.168722i | −0.638950 | − | 0.769248i | \(-0.720631\pi\) |
0.346714 | + | 0.937971i | \(0.387297\pi\) | |||||||
\(558\) | 1.93331 | + | 3.34860i | 0.0818437 | + | 0.141757i | ||||
\(559\) | −21.5574 | + | 13.0647i | −0.911781 | + | 0.552578i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.9615 | + | 21.3397i | 1.56052 | + | 0.900965i | ||||
\(562\) | −2.01095 | −0.0848266 | ||||||||
\(563\) | −1.42396 | −0.0600128 | −0.0300064 | − | 0.999550i | \(-0.509553\pi\) | ||||
−0.0300064 | + | 0.999550i | \(0.509553\pi\) | |||||||
\(564\) | 1.38881 | + | 0.801831i | 0.0584795 | + | 0.0337632i | ||||
\(565\) | −15.8123 | − | 9.12924i | −0.665229 | − | 0.384070i | ||||
\(566\) | 20.4865 | − | 11.8279i | 0.861113 | − | 0.497164i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.16506 | − | 10.6782i | −0.258680 | − | 0.448047i | ||||
\(569\) | 18.5189 | 0.776353 | 0.388177 | − | 0.921585i | \(-0.373105\pi\) | ||||
0.388177 | + | 0.921585i | \(0.373105\pi\) | |||||||
\(570\) | −11.7417 | + | 6.77904i | −0.491804 | + | 0.283943i | ||||
\(571\) | 2.17883 | − | 3.77384i | 0.0911812 | − | 0.157930i | −0.816827 | − | 0.576882i | \(-0.804269\pi\) |
0.908008 | + | 0.418952i | \(0.137602\pi\) | |||||||
\(572\) | −14.6784 | − | 24.2201i | −0.613736 | − | 1.01269i | ||||
\(573\) | −39.0202 | −1.63009 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.82194 | − | 11.8159i | 0.284494 | − | 0.492759i | ||||
\(576\) | 8.13334 | − | 14.0874i | 0.338889 | − | 0.586973i | ||||
\(577\) | −8.28280 | − | 4.78208i | −0.344818 | − | 0.199081i | 0.317583 | − | 0.948231i | \(-0.397129\pi\) |
−0.662400 | + | 0.749150i | \(0.730462\pi\) | |||||||
\(578\) | 7.99832i | 0.332686i | ||||||||
\(579\) | −38.0046 | − | 21.9419i | −1.57942 | − | 0.911876i | ||||
\(580\) | 25.0706i | 1.04100i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.75466 | − | 6.50327i | 0.155636 | − | 0.269569i | ||||
\(583\) | − | 2.37284i | − | 0.0982728i | ||||||
\(584\) | −11.3608 | + | 19.6775i | −0.470114 | + | 0.814262i | ||||
\(585\) | 46.4735 | − | 0.987801i | 1.92144 | − | 0.0408406i | ||||
\(586\) | 12.0778 | + | 20.9194i | 0.498929 | + | 0.864171i | ||||
\(587\) | 2.04428 | + | 1.18027i | 0.0843765 | + | 0.0487148i | 0.541595 | − | 0.840640i | \(-0.317821\pi\) |
−0.457218 | + | 0.889355i | \(0.651154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.12682 | + | 1.95171i | 0.0464297 | + | 0.0804186i | ||||
\(590\) | 10.8385 | − | 6.25762i | 0.446214 | − | 0.257622i | ||||
\(591\) | 29.2903i | 1.20484i | ||||||||
\(592\) | 2.54034i | 0.104407i | ||||||||
\(593\) | 35.0127 | − | 20.2146i | 1.43780 | − | 0.830114i | 0.440103 | − | 0.897947i | \(-0.354942\pi\) |
0.997697 | + | 0.0678337i | \(0.0216087\pi\) | |||||||
\(594\) | −7.01219 | − | 12.1455i | −0.287714 | − | 0.498335i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.2665 | + | 7.08207i | 0.502455 | + | 0.290093i | ||||
\(597\) | −28.2147 | − | 48.8693i | −1.15475 | − | 2.00009i | ||||
\(598\) | 8.10282 | − | 0.172227i | 0.331349 | − | 0.00704288i | ||||
\(599\) | 19.2936 | − | 33.4176i | 0.788316 | − | 1.36540i | −0.138681 | − | 0.990337i | \(-0.544286\pi\) |
0.926998 | − | 0.375067i | \(-0.122380\pi\) | |||||||
\(600\) | − | 36.3796i | − | 1.48519i | ||||||
\(601\) | 4.08115 | − | 7.06877i | 0.166474 | − | 0.288341i | −0.770704 | − | 0.637193i | \(-0.780095\pi\) |
0.937178 | + | 0.348852i | \(0.113429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.6012i | 1.04256i | ||||||||
\(604\) | −10.0092 | − | 5.77882i | −0.407269 | − | 0.235137i | ||||
\(605\) | 76.8883i | 3.12595i | ||||||||
\(606\) | 25.2910 | + | 14.6018i | 1.02738 | + | 0.593157i | ||||
\(607\) | 3.79263 | − | 6.56902i | 0.153938 | − | 0.266628i | −0.778734 | − | 0.627354i | \(-0.784138\pi\) |
0.932672 | + | 0.360726i | \(0.117471\pi\) | |||||||
\(608\) | 5.66853 | − | 9.81819i | 0.229889 | − | 0.398180i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.01308 | −0.121996 | ||||||||
\(611\) | 0.852270 | + | 1.40629i | 0.0344792 | + | 0.0568923i | ||||
\(612\) | 7.27419 | − | 12.5993i | 0.294042 | − | 0.509295i | ||||
\(613\) | 13.4908 | − | 7.78892i | 0.544889 | − | 0.314592i | −0.202169 | − | 0.979351i | \(-0.564799\pi\) |
0.747058 | + | 0.664759i | \(0.231466\pi\) | |||||||
\(614\) | −5.82180 | −0.234949 | ||||||||
\(615\) | −15.7043 | − | 27.2006i | −0.633258 | − | 1.09683i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.6709 | − | 11.9343i | 0.832177 | − | 0.480458i | −0.0224202 | − | 0.999749i | \(-0.507137\pi\) |
0.854598 | + | 0.519291i | \(0.173804\pi\) | |||||||
\(618\) | −22.0948 | − | 12.7565i | −0.888785 | − | 0.513140i | ||||
\(619\) | 16.8843 | + | 9.74814i | 0.678636 | + | 0.391811i | 0.799341 | − | 0.600878i | \(-0.205182\pi\) |
−0.120705 | + | 0.992688i | \(0.538515\pi\) | |||||||
\(620\) | −4.81291 | −0.193291 | ||||||||
\(621\) | −7.82126 | −0.313856 | ||||||||
\(622\) | −15.8824 | − | 9.16972i | −0.636827 | − | 0.367672i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.20366 | + | 1.94155i | −0.128249 | + | 0.0777244i | ||||
\(625\) | 12.5029 | + | 21.6557i | 0.500117 | + | 0.866228i | ||||
\(626\) | −20.0301 | + | 11.5644i | −0.800562 | + | 0.462205i | ||||
\(627\) | −15.4698 | − | 26.7945i | −0.617804 | − | 1.07007i | ||||
\(628\) | 4.30055 | − | 7.44878i | 0.171611 | − | 0.297239i | ||||
\(629\) | − | 17.5599i | − | 0.700161i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.2239 | + | 12.8309i | −0.884718 | + | 0.510792i | −0.872211 | − | 0.489130i | \(-0.837314\pi\) |
−0.0125066 | + | 0.999922i | \(0.503981\pi\) | |||||||
\(632\) | 18.7496 | − | 10.8251i | 0.745820 | − | 0.430600i | ||||
\(633\) | 47.7144 | 1.89648 | ||||||||
\(634\) | −8.03604 | − | 13.9188i | −0.319152 | − | 0.552788i | ||||
\(635\) | 19.3873i | 0.769362i | ||||||||
\(636\) | −1.40399 | −0.0556719 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.3573 | 1.16227 | ||||||||
\(639\) | 18.3765i | 0.726964i | ||||||||
\(640\) | 13.1229 | + | 22.7295i | 0.518728 | + | 0.898463i | ||||
\(641\) | 1.10604 | 0.0436860 | 0.0218430 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218430 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(642\) | 7.45603 | − | 4.30474i | 0.294266 | − | 0.169895i | ||||
\(643\) | −10.9437 | + | 6.31833i | −0.431576 | + | 0.249171i | −0.700018 | − | 0.714125i | \(-0.746825\pi\) |
0.268442 | + | 0.963296i | \(0.413491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 58.8110i | − | 2.31568i | ||||||
\(646\) | −2.17556 | + | 3.76818i | −0.0855962 | + | 0.148257i | ||||
\(647\) | −12.8574 | − | 22.2697i | −0.505477 | − | 0.875512i | −0.999980 | − | 0.00633579i | \(-0.997983\pi\) |
0.494503 | − | 0.869176i | \(-0.335350\pi\) | |||||||
\(648\) | 10.9177 | − | 6.30332i | 0.428887 | − | 0.247618i | ||||
\(649\) | 14.2799 | + | 24.7335i | 0.560535 | + | 0.970875i | ||||
\(650\) | 7.14685 | − | 13.0096i | 0.280323 | − | 0.510277i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.99066 | − | 1.72666i | −0.117123 | − | 0.0676211i | ||||
\(653\) | 25.2607 | 0.988527 | 0.494263 | − | 0.869312i | \(-0.335438\pi\) | ||||
0.494263 | + | 0.869312i | \(0.335438\pi\) | |||||||
\(654\) | 24.6549 | 0.964083 | ||||||||
\(655\) | −27.9916 | − | 16.1610i | −1.09372 | − | 0.631461i | ||||
\(656\) | 1.26285 | + | 0.729104i | 0.0493058 | + | 0.0284667i | ||||
\(657\) | 29.3269 | − | 16.9319i | 1.14415 | − | 0.660577i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.4882 | − | 19.8982i | −0.447517 | − | 0.775123i | 0.550707 | − | 0.834699i | \(-0.314358\pi\) |
−0.998224 | + | 0.0595764i | \(0.981025\pi\) | |||||||
\(660\) | 66.0752 | 2.57197 | ||||||||
\(661\) | 26.3554 | − | 15.2163i | 1.02511 | − | 0.591845i | 0.109528 | − | 0.993984i | \(-0.465066\pi\) |
0.915579 | + | 0.402138i | \(0.131733\pi\) | |||||||
\(662\) | −6.43641 | + | 11.1482i | −0.250158 | + | 0.433287i | ||||
\(663\) | 22.1451 | − | 13.4209i | 0.860044 | − | 0.521223i | ||||
\(664\) | 16.9554 | 0.657998 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.9204 | + | 18.9146i | −0.423155 | + | 0.732926i | ||||
\(667\) | 8.18613 | − | 14.1788i | 0.316968 | − | 0.549005i | ||||
\(668\) | 4.44847 | + | 2.56833i | 0.172117 | + | 0.0993715i | ||||
\(669\) | 42.6475i | 1.64885i | ||||||||
\(670\) | 14.1612 | + | 8.17600i | 0.547096 | + | 0.315866i | ||||
\(671\) | − | 6.87586i | − | 0.265440i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.41933 | − | 9.38656i | 0.208900 | − | 0.361825i | −0.742468 | − | 0.669881i | \(-0.766345\pi\) |
0.951368 | + | 0.308056i | \(0.0996784\pi\) | |||||||
\(674\) | − | 17.9124i | − | 0.689960i | ||||||
\(675\) | −7.16218 | + | 12.4053i | −0.275672 | + | 0.477479i | ||||
\(676\) | −17.1673 | + | 0.730117i | −0.660281 | + | 0.0280814i | ||||
\(677\) | −9.06044 | − | 15.6931i | −0.348221 | − | 0.603137i | 0.637712 | − | 0.770275i | \(-0.279881\pi\) |
−0.985934 | + | 0.167138i | \(0.946547\pi\) | |||||||
\(678\) | 10.9558 | + | 6.32532i | 0.420754 | + | 0.242923i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.6765 | − | 20.2242i | −0.447772 | − | 0.775564i | ||||
\(681\) | −37.7261 | + | 21.7812i | −1.44567 | + | 0.834656i | ||||
\(682\) | 5.63584i | 0.215808i | ||||||||
\(683\) | 37.8352i | 1.44772i | 0.689946 | + | 0.723861i | \(0.257634\pi\) | ||||
−0.689946 | + | 0.723861i | \(0.742366\pi\) | |||||||
\(684\) | −9.13357 | + | 5.27327i | −0.349231 | + | 0.201628i | ||||
\(685\) | 31.5380 | + | 54.6254i | 1.20500 | + | 2.08713i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 62.2288 | + | 35.9278i | 2.37418 | + | 1.37073i | ||||
\(688\) | 1.36521 | + | 2.36462i | 0.0520482 | + | 0.0901502i | ||||
\(689\) | −1.26179 | − | 0.693166i | −0.0480702 | − | 0.0264075i | ||||
\(690\) | −9.45446 | + | 16.3756i | −0.359925 | + | 0.623408i | ||||
\(691\) | 30.0261i | 1.14225i | 0.820864 | + | 0.571124i | \(0.193492\pi\) | ||||
−0.820864 | + | 0.571124i | \(0.806508\pi\) | |||||||
\(692\) | −9.23693 | + | 15.9988i | −0.351135 | + | 0.608184i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.1432i | 0.498907i | ||||||||
\(695\) | 55.6658 | + | 32.1387i | 2.11152 | + | 1.21909i | ||||
\(696\) | − | 43.6545i | − | 1.65472i | ||||||
\(697\) | −8.72934 | − | 5.03988i | −0.330647 | − | 0.190899i | ||||
\(698\) | −2.80712 | + | 4.86207i | −0.106251 | + | 0.184032i | ||||
\(699\) | −15.3873 | + | 26.6516i | −0.582001 | + | 1.00805i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.116177 | 0.00438796 | 0.00219398 | − | 0.999998i | \(-0.499302\pi\) | ||||
0.00219398 | + | 0.999998i | \(0.499302\pi\) | |||||||
\(702\) | −8.50695 | + | 0.180816i | −0.321074 | + | 0.00682448i | ||||
\(703\) | −6.36485 | + | 11.0242i | −0.240055 | + | 0.415787i | ||||
\(704\) | 20.5332 | − | 11.8548i | 0.773873 | − | 0.446796i | ||||
\(705\) | −3.83651 | −0.144491 | ||||||||
\(706\) | −5.76624 | − | 9.98741i | −0.217015 | − | 0.375881i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14.6347 | − | 8.44932i | 0.550004 | − | 0.317545i | ||||
\(709\) | −5.82829 | − | 3.36497i | −0.218886 | − | 0.126374i | 0.386548 | − | 0.922269i | \(-0.373667\pi\) |
−0.605434 | + | 0.795895i | \(0.707001\pi\) | |||||||
\(710\) | 10.1649 | + | 5.86873i | 0.381483 | + | 0.220249i | ||||
\(711\) | −32.2670 | −1.21011 | ||||||||
\(712\) | 9.74265 | 0.365121 | ||||||||
\(713\) | 2.72196 | + | 1.57153i | 0.101938 | + | 0.0588541i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 59.3826 | + | 32.6221i | 2.22078 | + | 1.22000i | ||||
\(716\) | −16.7098 | − | 28.9423i | −0.624476 | − | 1.08162i | ||||
\(717\) | −33.8050 | + | 19.5173i | −1.26247 | + | 0.728888i | ||||
\(718\) | 2.22975 | + | 3.86204i | 0.0832136 | + | 0.144130i | ||||
\(719\) | −23.4039 | + | 40.5367i | −0.872818 | + | 1.51177i | −0.0137492 | + | 0.999905i | \(0.504377\pi\) |
−0.859069 | + | 0.511860i | \(0.828957\pi\) | |||||||
\(720\) | − | 5.03509i | − | 0.187647i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.8195 | + | 6.24666i | −0.402661 | + | 0.232476i | ||||
\(723\) | 33.0530 | − | 19.0832i | 1.22926 | − | 0.709711i | ||||
\(724\) | 1.14262 | 0.0424653 | ||||||||
\(725\) | −14.9926 | − | 25.9680i | −0.556812 | − | 0.964426i | ||||
\(726\) | − | 53.2731i | − | 1.97715i | ||||||
\(727\) | −13.3362 | −0.494611 | −0.247305 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247305 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.6582 | −1.54290 | ||||||||
\(730\) | − | 21.6295i | − | 0.800544i | ||||||
\(731\) | −9.43694 | − | 16.3453i | −0.349038 | − | 0.604551i | ||||
\(732\) | −4.06840 | −0.150373 | ||||||||
\(733\) | 25.5142 | − | 14.7306i | 0.942387 | − | 0.544087i | 0.0516792 | − | 0.998664i | \(-0.483543\pi\) |
0.890708 | + | 0.454576i | \(0.150209\pi\) | |||||||
\(734\) | 21.4193 | − | 12.3664i | 0.790599 | − | 0.456453i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 15.8113i | − | 0.582814i | ||||||
\(737\) | −18.6576 | + | 32.3160i | −0.687263 | + | 1.19037i | ||||
\(738\) | 6.26851 | + | 10.8574i | 0.230747 | + | 0.399666i | ||||
\(739\) | 10.4184 | − | 6.01509i | 0.383249 | − | 0.221269i | −0.295982 | − | 0.955193i | \(-0.595647\pi\) |
0.679231 | + | 0.733925i | \(0.262314\pi\) | |||||||
\(740\) | −13.5929 | − | 23.5436i | −0.499685 | − | 0.865480i | ||||
\(741\) | −18.7674 | + | 0.398904i | −0.689438 | + | 0.0146541i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.9509 | − | 10.9413i | −0.695242 | − | 0.401398i | 0.110331 | − | 0.993895i | \(-0.464809\pi\) |
−0.805573 | + | 0.592497i | \(0.798142\pi\) | |||||||
\(744\) | 8.38055 | 0.307246 | ||||||||
\(745\) | −33.8855 | −1.24147 | ||||||||
\(746\) | 15.2699 | + | 8.81607i | 0.559070 | + | 0.322779i | ||||
\(747\) | −21.8844 | − | 12.6350i | −0.800710 | − | 0.462290i | ||||
\(748\) | 18.3642 | − | 10.6026i | 0.671461 | − | 0.387668i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.00405815 | − | 0.00702892i | −0.000148183 | − | 0.000256660i | ||||
\(751\) | −34.7492 | −1.26802 | −0.634008 | − | 0.773327i | \(-0.718591\pi\) | ||||
−0.634008 | + | 0.773327i | \(0.718591\pi\) | |||||||
\(752\) | 0.154255 | − | 0.0890590i | 0.00562509 | − | 0.00324765i | ||||
\(753\) | 11.4586 | − | 19.8468i | 0.417574 | − | 0.723259i | ||||
\(754\) | 8.57602 | − | 15.6111i | 0.312320 | − | 0.568523i | ||||
\(755\) | 27.6498 | 1.00628 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.9632 | + | 38.0413i | −0.798265 | + | 1.38264i | 0.122481 | + | 0.992471i | \(0.460915\pi\) |
−0.920745 | + | 0.390164i | \(0.872418\pi\) | |||||||
\(758\) | −3.90223 | + | 6.75887i | −0.141736 | + | 0.245493i | ||||
\(759\) | −37.3691 | − | 21.5751i | −1.35641 | − | 0.783126i | ||||
\(760\) | 16.9292i | 0.614087i | ||||||||
\(761\) | 0.122449 | + | 0.0706957i | 0.00443876 | + | 0.00256272i | 0.502218 | − | 0.864741i | \(-0.332518\pi\) |
−0.497779 | + | 0.867304i | \(0.665851\pi\) | |||||||
\(762\) | − | 13.4328i | − | 0.486618i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.69352 | + | 16.7897i | −0.350699 | + | 0.607429i | ||||
\(765\) | 34.8047i | 1.25837i | ||||||||
\(766\) | −2.23620 | + | 3.87322i | −0.0807973 | + | 0.139945i | ||||
\(767\) | 17.3239 | − | 0.368222i | 0.625529 | − | 0.0132957i | ||||
\(768\) | −19.7062 | − | 34.1321i | −0.711086 | − | 1.23164i | ||||
\(769\) | −11.8200 | − | 6.82429i | −0.426241 | − | 0.246090i | 0.271503 | − | 0.962438i | \(-0.412479\pi\) |
−0.697744 | + | 0.716347i | \(0.745813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.7856 | + | 23.8773i | 0.496475 | + | 0.859920i | ||||
\(772\) | −18.8824 | + | 10.9018i | −0.679593 | + | 0.392363i | ||||
\(773\) | − | 17.5894i | − | 0.632646i | −0.948652 | − | 0.316323i | \(-0.897552\pi\) | ||
0.948652 | − | 0.316323i | \(-0.102448\pi\) | |||||||
\(774\) | 23.4750i | 0.843790i | ||||||||
\(775\) | 4.98518 | − | 2.87820i | 0.179073 | − | 0.103388i | ||||
\(776\) | −4.68824 | − | 8.12026i | −0.168298 | − | 0.291500i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.59022 | + | 4.38221i | 0.272123 | + | 0.157110i | ||||
\(779\) | 3.65356 | + | 6.32814i | 0.130902 | + | 0.226729i | ||||
\(780\) | 19.3023 | − | 35.1363i | 0.691132 | − | 1.25808i | ||||
\(781\) | −13.3924 | + | 23.1964i | −0.479219 | + | 0.830032i | ||||
\(782\) | 6.06833i | 0.217003i | ||||||||
\(783\) | −8.59441 | + | 14.8860i | −0.307139 | + | 0.531981i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.5768i | 0.734418i | ||||||||
\(786\) | 19.3944 | + | 11.1973i | 0.691774 | + | 0.399396i | ||||
\(787\) | − | 2.96845i | − | 0.105814i | −0.998599 | − | 0.0529069i | \(-0.983151\pi\) | ||
0.998599 | − | 0.0529069i | \(-0.0168487\pi\) | |||||||
\(788\) | 12.6031 | + | 7.27639i | 0.448966 | + | 0.259210i | ||||
\(789\) | −29.3731 | + | 50.8756i | −1.04571 | + | 1.81122i | ||||
\(790\) | −10.3048 | + | 17.8484i | −0.366628 | + | 0.635018i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −66.2829 | −2.35526 | ||||||||
\(793\) | −3.65633 | − | 2.00862i | −0.129840 | − | 0.0713280i | ||||
\(794\) | 15.3121 | − | 26.5214i | 0.543407 | − | 0.941208i | ||||
\(795\) | 2.90883 | − | 1.67941i | 0.103166 | − | 0.0595627i | ||||
\(796\) | −28.0367 | −0.993735 | ||||||||
\(797\) | −4.72611 | − | 8.18586i | −0.167407 | − | 0.289958i | 0.770100 | − | 0.637923i | \(-0.220206\pi\) |
−0.937508 | + | 0.347965i | \(0.886873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.06628 | + | 0.615614i | −0.0377221 | + | 0.0217789i | ||||
\(800\) | −25.0783 | − | 14.4790i | −0.886652 | − | 0.511909i | ||||
\(801\) | −12.5749 | − | 7.26011i | −0.444312 | − | 0.256523i | ||||
\(802\) | 0.738409 | 0.0260741 | ||||||||
\(803\) | 49.3586 | 1.74183 | ||||||||
\(804\) | 19.1212 | + | 11.0396i | 0.674351 | + | 0.389337i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.99693 | + | 1.64637i | 0.105562 | + | 0.0579911i | ||||
\(807\) | −17.2120 | − | 29.8120i | −0.605890 | − | 1.04943i | ||||
\(808\) | 31.5795 | − | 18.2324i | 1.11096 | − | 0.641414i | ||||
\(809\) | 0.581273 | + | 1.00679i | 0.0204365 | + | 0.0353970i | 0.876063 | − | 0.482197i | \(-0.160161\pi\) |
−0.855626 | + | 0.517594i | \(0.826828\pi\) | |||||||
\(810\) | −6.00035 | + | 10.3929i | −0.210831 | + | 0.365170i | ||||
\(811\) | 19.5561i | 0.686706i | 0.939206 | + | 0.343353i | \(0.111563\pi\) | ||||
−0.939206 | + | 0.343353i | \(0.888437\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.7209 | − | 23.5102i | 1.42814 | − | 0.824538i | ||||
\(814\) | −27.5692 | + | 15.9171i | −0.966299 | + | 0.557893i | ||||
\(815\) | 8.26151 | 0.289388 | ||||||||
\(816\) | −1.40243 | − | 2.42908i | −0.0490949 | − | 0.0850348i | ||||
\(817\) | 13.6822i | 0.478680i | ||||||||
\(818\) | −20.2408 | −0.707702 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6052 | −0.544958 | ||||||||
\(821\) | − | 12.6189i | − | 0.440403i | −0.975454 | − | 0.220201i | \(-0.929329\pi\) | ||
0.975454 | − | 0.220201i | \(-0.0706714\pi\) | |||||||
\(822\) | −21.8515 | − | 37.8479i | −0.762159 | − | 1.32010i | ||||
\(823\) | 6.56808 | 0.228949 | 0.114474 | − | 0.993426i | \(-0.463482\pi\) | ||||
0.114474 | + | 0.993426i | \(0.463482\pi\) | |||||||
\(824\) | −27.5886 | + | 15.9283i | −0.961094 | + | 0.554888i | ||||
\(825\) | −68.4403 | + | 39.5140i | −2.38278 | + | 1.37570i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.3050i | 0.601754i | 0.953663 | + | 0.300877i | \(0.0972794\pi\) | ||||
−0.953663 | + | 0.300877i | \(0.902721\pi\) | |||||||
\(828\) | −7.35441 | + | 12.7382i | −0.255583 | + | 0.442683i | ||||
\(829\) | 1.87837 | + | 3.25343i | 0.0652385 | + | 0.112996i | 0.896800 | − | 0.442437i | \(-0.145886\pi\) |
−0.831561 | + | 0.555433i | \(0.812553\pi\) | |||||||
\(830\) | −13.9780 | + | 8.07022i | −0.485185 | + | 0.280122i | ||||
\(831\) | 23.9626 | + | 41.5044i | 0.831253 | + | 1.43977i | ||||
\(832\) | −0.305689 | − | 14.3819i | −0.0105979 | − | 0.498602i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −38.5688 | − | 22.2677i | −1.33553 | − | 0.771068i | ||||
\(835\) | −12.2886 | −0.425266 | ||||||||
\(836\) | −15.3722 | −0.531659 | ||||||||
\(837\) | −2.85772 | − | 1.64991i | −0.0987773 | − | 0.0570291i | ||||
\(838\) | 5.45298 | + | 3.14828i | 0.188370 | + | 0.108756i | ||||
\(839\) | 40.1340 | − | 23.1714i | 1.38558 | − | 0.799965i | 0.392766 | − | 0.919638i | \(-0.371518\pi\) |
0.992813 | + | 0.119674i | \(0.0381849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.49071 | − | 6.04609i | −0.120369 | − | 0.208486i | ||||
\(842\) | −20.6531 | −0.711753 | ||||||||
\(843\) | 5.62558 | − | 3.24793i | 0.193755 | − | 0.111865i | ||||
\(844\) | 11.8534 | − | 20.5306i | 0.408009 | − | 0.706693i | ||||
\(845\) | 34.6944 | − | 22.0477i | 1.19352 | − | 0.758465i | ||||
\(846\) | 1.53138 | 0.0526499 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.0779704 | + | 0.135049i | −0.00267751 | + | 0.00463759i | ||||
\(849\) | −38.2071 | + | 66.1766i | −1.31126 | + | 2.27118i | ||||
\(850\) | 9.62495 | + | 5.55697i | 0.330133 | + | 0.190602i | ||||
\(851\) | 17.7536i | 0.608585i | ||||||||
\(852\) | 13.7252 | + | 7.92423i | 0.470216 | + | 0.271479i | ||||
\(853\) | − | 15.3103i | − | 0.524215i | −0.965039 | − | 0.262107i | \(-0.915583\pi\) | ||
0.965039 | − | 0.262107i | \(-0.0844174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.6155 | − | 21.8506i | 0.431440 | − | 0.747275i | ||||
\(856\) | − | 10.7502i | − | 0.367433i | ||||||
\(857\) | −1.29624 | + | 2.24515i | −0.0442787 | + | 0.0766929i | −0.887315 | − | 0.461163i | \(-0.847432\pi\) |
0.843037 | + | 0.537856i | \(0.180766\pi\) | |||||||
\(858\) | −41.1441 | − | 22.6026i | −1.40464 | − | 0.771642i | ||||
\(859\) | −6.88689 | − | 11.9284i | −0.234978 | − | 0.406993i | 0.724289 | − | 0.689497i | \(-0.242168\pi\) |
−0.959266 | + | 0.282504i | \(0.908835\pi\) | |||||||
\(860\) | −25.3053 | − | 14.6100i | −0.862903 | − | 0.498197i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.19294 | + | 5.53034i | 0.108752 | + | 0.188364i | ||||
\(863\) | −25.7723 | + | 14.8796i | −0.877298 | + | 0.506508i | −0.869767 | − | 0.493463i | \(-0.835731\pi\) |
−0.00753143 | + | 0.999972i | \(0.502397\pi\) | |||||||
\(864\) | 16.5999i | 0.564741i | ||||||||
\(865\) | − | 44.1958i | − | 1.50270i | ||||||
\(866\) | −25.6588 | + | 14.8141i | −0.871922 | + | 0.503404i | ||||
\(867\) | −12.9183 | − | 22.3751i | −0.438728 | − | 0.759899i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.7301 | − | 23.5155i | −1.38167 | − | 0.797710i | ||||
\(870\) | 20.7781 | + | 35.9888i | 0.704444 | + | 1.22013i | ||||
\(871\) | 11.7340 | + | 19.3618i | 0.397593 | + | 0.656048i | ||||
\(872\) | 15.3926 | − | 26.6607i | 0.521259 | − | 0.902847i | ||||
\(873\) | 13.9745i | 0.472965i | ||||||||
\(874\) | 2.19955 | − | 3.80974i | 0.0744009 | − | 0.128866i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 29.2051i | − | 0.986750i | ||||||
\(877\) | 1.24995 | + | 0.721660i | 0.0422079 | + | 0.0243687i | 0.520955 | − | 0.853584i | \(-0.325576\pi\) |
−0.478748 | + | 0.877953i | \(0.658909\pi\) | |||||||
\(878\) | 23.2531i | 0.784755i | ||||||||
\(879\) | −67.5748 | − | 39.0143i | −2.27924 | − | 1.31592i | ||||
\(880\) | 3.66947 | − | 6.35571i | 0.123698 | − | 0.214251i | ||||
\(881\) | 17.9402 | − | 31.0733i | 0.604420 | − | 1.04689i | −0.387723 | − | 0.921776i | \(-0.626738\pi\) |
0.992143 | − | 0.125110i | \(-0.0399284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5626 | 0.355458 | 0.177729 | − | 0.984079i | \(-0.443125\pi\) | ||||
0.177729 | + | 0.984079i | \(0.443125\pi\) | |||||||
\(884\) | −0.273398 | − | 12.8627i | −0.00919537 | − | 0.432618i | ||||
\(885\) | −20.2137 | + | 35.0111i | −0.679475 | + | 1.17689i | ||||
\(886\) | −20.5349 | + | 11.8558i | −0.689883 | + | 0.398304i | ||||
\(887\) | −12.2280 | −0.410577 | −0.205288 | − | 0.978702i | \(-0.565813\pi\) | ||||
−0.205288 | + | 0.978702i | \(0.565813\pi\) | |||||||
\(888\) | 23.6688 | + | 40.9956i | 0.794274 | + | 1.37572i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.03183 | + | 4.63718i | −0.269228 | + | 0.155439i | ||||
\(891\) | −23.7166 | − | 13.6928i | −0.794537 | − | 0.458726i | ||||
\(892\) | 18.3504 | + | 10.5946i | 0.614418 | + | 0.354735i | ||||
\(893\) | 0.892553 | 0.0298681 | ||||||||
\(894\) | 23.4780 | 0.785222 | ||||||||
\(895\) | 69.2399 | + | 39.9757i | 2.31443 | + | 1.33624i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.3893 | + | 13.5689i | −0.747557 | + | 0.453051i | ||||
\(898\) | 12.0199 | + | 20.8190i | 0.401109 | + | 0.694741i | ||||
\(899\) | 5.98208 | − | 3.45375i | 0.199513 | − | 0.115189i | ||||
\(900\) | 13.4693 | + | 23.3296i | 0.448978 | + | 0.777653i | ||||
\(901\) | 0.538965 | − | 0.933515i | 0.0179555 | − | 0.0310999i | ||||
\(902\) | 18.2735i | 0.608440i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6799 | − | 7.89807i | 0.454985 | − | 0.262686i | ||||
\(905\) | −2.36732 | + | 1.36677i | −0.0786924 | + | 0.0454331i | ||||
\(906\) | −19.1576 | −0.636468 | ||||||||
\(907\) | 2.26278 | + | 3.91924i | 0.0751343 | + | 0.130136i | 0.901145 | − | 0.433519i | \(-0.142728\pi\) |
−0.826010 | + | 0.563655i | \(0.809395\pi\) | |||||||
\(908\) | 21.6438i | 0.718274i | ||||||||
\(909\) | −54.3464 | −1.80256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.2723 | −1.89751 | −0.948757 | − | 0.316006i | \(-0.897658\pi\) | ||||
−0.948757 | + | 0.316006i | \(0.897658\pi\) | |||||||
\(912\) | 2.03332i | 0.0673300i | ||||||||
\(913\) | −18.4163 | − | 31.8979i | −0.609489 | − | 1.05567i | ||||
\(914\) | 26.0942 | 0.863120 | ||||||||
\(915\) | 8.42904 | − | 4.86651i | 0.278655 | − | 0.160882i | ||||
\(916\) | 30.9181 | − | 17.8506i | 1.02156 | − | 0.589800i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 6.37098i | − | 0.210274i | ||||||
\(919\) | 20.3775 | − | 35.2949i | 0.672193 | − | 1.16427i | −0.305088 | − | 0.952324i | \(-0.598686\pi\) |
0.977281 | − | 0.211948i | \(-0.0679809\pi\) | |||||||
\(920\) | 11.8052 | + | 20.4473i | 0.389207 | + | 0.674127i | ||||
\(921\) | 16.2864 | − | 9.40294i | 0.536654 | − | 0.309837i | ||||
\(922\) | −9.10103 | − | 15.7634i | −0.299726 | − | 0.519141i | ||||
\(923\) | 8.42270 | + | 13.8979i | 0.277236 | + | 0.457454i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.1589 | + | 16.2575i | 0.925858 | + | 0.534545i | ||||
\(926\) | 32.0208 | 1.05227 | ||||||||
\(927\) | 47.4783 | 1.55939 | ||||||||
\(928\) | −30.0932 | − | 17.3743i | −0.987859 | − | 0.570341i | ||||
\(929\) | 45.2751 | + | 26.1396i | 1.48543 | + | 0.857611i | 0.999862 | − | 0.0165897i | \(-0.00528089\pi\) |
0.485564 | + | 0.874201i | \(0.338614\pi\) | |||||||
\(930\) | −6.90891 | + | 3.98886i | −0.226552 | + | 0.130800i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.64511 | + | 13.2417i | 0.250424 | + | 0.433747i | ||||
\(933\) | 59.2410 | 1.93946 | ||||||||
\(934\) | −9.47322 | + | 5.46937i | −0.309973 | + | 0.178963i | ||||
\(935\) | −25.3650 | + | 43.9334i | −0.829523 | + | 1.43678i | ||||
\(936\) | −19.3629 | + | 35.2468i | −0.632897 | + | 1.15208i | ||||
\(937\) | 6.38634 | 0.208633 | 0.104316 | − | 0.994544i | \(-0.466735\pi\) | ||||
0.104316 | + | 0.994544i | \(0.466735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.3558 | − | 64.7021i | 1.21906 | − | 2.11147i | ||||
\(940\) | −0.953077 | + | 1.65078i | −0.0310859 | + | 0.0538424i | ||||
\(941\) | 21.9720 | + | 12.6855i | 0.716266 | + | 0.413536i | 0.813377 | − | 0.581737i | \(-0.197627\pi\) |
−0.0971107 | + | 0.995274i | \(0.530960\pi\) | |||||||
\(942\) | − | 14.2569i | − | 0.464516i | ||||||
\(943\) | 8.82560 | + | 5.09546i | 0.287401 | + | 0.165931i | ||||
\(944\) | − | 1.87692i | − | 0.0610887i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.1081 | + | 29.6321i | −0.556232 | + | 0.963422i | ||||
\(947\) | − | 27.2061i | − | 0.884080i | −0.896995 | − | 0.442040i | \(-0.854255\pi\) | ||
0.896995 | − | 0.442040i | \(-0.145745\pi\) | |||||||
\(948\) | −13.9140 | + | 24.0997i | −0.451905 | + | 0.782723i | ||||
\(949\) | 14.4189 | − | 26.2470i | 0.468057 | − | 0.852015i | ||||
\(950\) | −4.02840 | − | 6.97740i | −0.130699 | − | 0.226377i | ||||
\(951\) | 44.9613 | + | 25.9584i | 1.45797 | + | 0.841760i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.2939 | + | 23.0258i | 0.430633 | + | 0.745878i | 0.996928 | − | 0.0783248i | \(-0.0249571\pi\) |
−0.566295 | + | 0.824203i | \(0.691624\pi\) | |||||||
\(954\) | −1.16109 | + | 0.670354i | −0.0375916 | + | 0.0217035i | ||||
\(955\) | − | 46.3805i | − | 1.50084i | ||||||
\(956\) | 19.3942i | 0.627254i | ||||||||
\(957\) | −82.1264 | + | 47.4157i | −2.65477 | + | 1.53273i | ||||
\(958\) | −2.73220 | − | 4.73230i | −0.0882732 | − | 0.152894i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 29.0654 | + | 16.7809i | 0.938082 | + | 0.541602i | ||||
\(961\) | −14.8370 | − | 25.6984i | −0.478612 | − | 0.828980i | ||||
\(962\) | 0.410438 | + | 19.3100i | 0.0132331 | + | 0.622581i | ||||
\(963\) | −8.01091 | + | 13.8753i | −0.258148 | + | 0.447125i | ||||
\(964\) | − | 18.9628i | − | 0.610751i | ||||||
\(965\) | 26.0808 | − | 45.1732i | 0.839569 | − | 1.45418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.2467i | − | 1.13346i | −0.823904 | − | 0.566729i | \(-0.808209\pi\) | ||
0.823904 | − | 0.566729i | \(-0.191791\pi\) | |||||||
\(968\) | −57.6073 | − | 33.2596i | −1.85157 | − | 1.06900i | ||||
\(969\) | − | 14.0552i | − | 0.451518i | ||||||
\(970\) | 7.72995 | + | 4.46289i | 0.248194 | + | 0.143295i | ||||
\(971\) | 18.4891 | − | 32.0241i | 0.593344 | − | 1.02770i | −0.400434 | − | 0.916326i | \(-0.631141\pi\) |
0.993778 | − | 0.111377i | \(-0.0355261\pi\) | |||||||
\(972\) | −13.7833 | + | 23.8733i | −0.442098 | + | 0.765737i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 27.5645 | 0.883224 | ||||||||
\(975\) | 1.01891 | + | 47.9370i | 0.0326312 | + | 1.53521i | ||||
\(976\) | −0.225938 | + | 0.391336i | −0.00723209 | + | 0.0125264i | ||||
\(977\) | 21.4363 | − | 12.3762i | 0.685807 | − | 0.395951i | −0.116232 | − | 0.993222i | \(-0.537082\pi\) |
0.802039 | + | 0.597271i | \(0.203748\pi\) | |||||||
\(978\) | −5.72410 | −0.183036 | ||||||||
\(979\) | −10.5820 | − | 18.3286i | −0.338204 | − | 0.585786i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.7346 | + | 22.9408i | −1.26863 | + | 0.732442i | ||||
\(982\) | 26.6236 | + | 15.3711i | 0.849593 | + | 0.490513i | ||||
\(983\) | −3.94679 | − | 2.27868i | −0.125883 | − | 0.0726786i | 0.435736 | − | 0.900074i | \(-0.356488\pi\) |
−0.561619 | + | 0.827396i | \(0.689821\pi\) | |||||||
\(984\) | 27.1728 | 0.866237 | ||||||||
\(985\) | −34.8152 | −1.10930 | ||||||||
\(986\) | 11.5497 | + | 6.66820i | 0.367816 | + | 0.212359i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.49062 | + | 8.17436i | −0.142866 | + | 0.260061i | ||||
\(989\) | 9.54101 | + | 16.5255i | 0.303386 | + | 0.525481i | ||||
\(990\) | 54.6436 | − | 31.5485i | 1.73669 | − | 1.00268i | ||||
\(991\) | 13.5982 | + | 23.5527i | 0.431960 | + | 0.748176i | 0.997042 | − | 0.0768584i | \(-0.0244890\pi\) |
−0.565082 | + | 0.825034i | \(0.691156\pi\) | |||||||
\(992\) | 3.33543 | − | 5.77713i | 0.105900 | − | 0.183424i | ||||
\(993\) | − | 41.5824i | − | 1.31958i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 58.0873 | − | 33.5367i | 1.84149 | − | 1.06319i | ||||
\(996\) | −18.8738 | + | 10.8968i | −0.598039 | + | 0.345278i | ||||
\(997\) | 30.2274 | 0.957312 | 0.478656 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478656 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(998\) | −14.0551 | − | 24.3441i | −0.444906 | − | 0.770600i | ||||
\(999\) | − | 18.6390i | − | 0.589713i |
(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 | 637.2.k.g.459.3 | 12 | ||
7.2 | even | 3 | 637.2.u.i.30.3 | 12 | |||
7.3 | odd | 6 | 91.2.q.a.43.4 | yes | 12 | ||
7.4 | even | 3 | 637.2.q.h.589.4 | 12 | |||
7.5 | odd | 6 | 637.2.u.h.30.3 | 12 | |||
7.6 | odd | 2 | 637.2.k.h.459.3 | 12 | |||
13.10 | even | 6 | 637.2.u.i.361.3 | 12 | |||
21.17 | even | 6 | 819.2.ct.a.316.3 | 12 | |||
28.3 | even | 6 | 1456.2.cc.c.225.6 | 12 | |||
91.10 | odd | 6 | 91.2.q.a.36.4 | ✓ | 12 | ||
91.17 | odd | 6 | 1183.2.c.i.337.8 | 12 | |||
91.23 | even | 6 | inner | 637.2.k.g.569.4 | 12 | ||
91.32 | odd | 12 | 8281.2.a.ch.1.2 | 6 | |||
91.45 | even | 12 | 1183.2.a.p.1.2 | 6 | |||
91.46 | odd | 12 | 8281.2.a.by.1.5 | 6 | |||
91.59 | even | 12 | 1183.2.a.m.1.5 | 6 | |||
91.62 | odd | 6 | 637.2.u.h.361.3 | 12 | |||
91.75 | odd | 6 | 637.2.k.h.569.4 | 12 | |||
91.87 | odd | 6 | 1183.2.c.i.337.5 | 12 | |||
91.88 | even | 6 | 637.2.q.h.491.4 | 12 | |||
273.101 | even | 6 | 819.2.ct.a.127.3 | 12 | |||
364.283 | even | 6 | 1456.2.cc.c.673.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.4 | ✓ | 12 | 91.10 | odd | 6 | ||
91.2.q.a.43.4 | yes | 12 | 7.3 | odd | 6 | ||
637.2.k.g.459.3 | 12 | 1.1 | even | 1 | trivial | ||
637.2.k.g.569.4 | 12 | 91.23 | even | 6 | inner | ||
637.2.k.h.459.3 | 12 | 7.6 | odd | 2 | |||
637.2.k.h.569.4 | 12 | 91.75 | odd | 6 | |||
637.2.q.h.491.4 | 12 | 91.88 | even | 6 | |||
637.2.q.h.589.4 | 12 | 7.4 | even | 3 | |||
637.2.u.h.30.3 | 12 | 7.5 | odd | 6 | |||
637.2.u.h.361.3 | 12 | 91.62 | odd | 6 | |||
637.2.u.i.30.3 | 12 | 7.2 | even | 3 | |||
637.2.u.i.361.3 | 12 | 13.10 | even | 6 | |||
819.2.ct.a.127.3 | 12 | 273.101 | even | 6 | |||
819.2.ct.a.316.3 | 12 | 21.17 | even | 6 | |||
1183.2.a.m.1.5 | 6 | 91.59 | even | 12 | |||
1183.2.a.p.1.2 | 6 | 91.45 | even | 12 | |||
1183.2.c.i.337.5 | 12 | 91.87 | odd | 6 | |||
1183.2.c.i.337.8 | 12 | 91.17 | odd | 6 | |||
1456.2.cc.c.225.6 | 12 | 28.3 | even | 6 | |||
1456.2.cc.c.673.6 | 12 | 364.283 | even | 6 | |||
8281.2.a.by.1.5 | 6 | 91.46 | odd | 12 | |||
8281.2.a.ch.1.2 | 6 | 91.32 | odd | 12 |