Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.1 | ||
Character | \(\chi\) | \(=\) | 1386.89 |
Dual form | 1386.2.r.d.1277.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.36138 | − | 2.35797i | 0.608826 | − | 1.05452i | −0.382608 | − | 0.923911i | \(-0.624974\pi\) |
0.991434 | − | 0.130607i | \(-0.0416926\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13605 | + | 1.56119i | −0.807350 | + | 0.590073i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.35797 | + | 1.36138i | −0.745657 | + | 0.430505i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.193887i | 0.0537746i | 0.999638 | + | 0.0268873i | \(0.00855953\pi\) | ||||
−0.999638 | + | 0.0268873i | \(0.991440\pi\) | |||||||
\(14\) | 2.63046 | − | 0.284003i | 0.703021 | − | 0.0759029i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.07388 | + | 5.32411i | 0.745524 | + | 1.29129i | 0.949949 | + | 0.312404i | \(0.101134\pi\) |
−0.204425 | + | 0.978882i | \(0.565532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.269276 | + | 0.155466i | 0.0617760 | + | 0.0356664i | 0.530570 | − | 0.847641i | \(-0.321978\pi\) |
−0.468794 | + | 0.883308i | \(0.655311\pi\) | |||||||
\(20\) | 2.72275 | 0.608826 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 4.50799 | + | 2.60269i | 0.939981 | + | 0.542698i | 0.889954 | − | 0.456050i | \(-0.150736\pi\) |
0.0500264 | + | 0.998748i | \(0.484069\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.20669 | − | 2.09005i | −0.241339 | − | 0.418011i | ||||
\(26\) | 0.0969436 | − | 0.167911i | 0.0190122 | − | 0.0329301i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.42005 | − | 1.06928i | −0.457347 | − | 0.202075i | ||||
\(29\) | − | 4.17192i | − | 0.774705i | −0.921932 | − | 0.387353i | \(-0.873390\pi\) | ||
0.921932 | − | 0.387353i | \(-0.126610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.38127 | − | 0.797476i | 0.248083 | − | 0.143231i | −0.370803 | − | 0.928712i | \(-0.620918\pi\) |
0.618886 | + | 0.785481i | \(0.287584\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.14775i | − | 1.05433i | ||||||
\(35\) | 0.773269 | + | 7.16211i | 0.130706 | + | 1.21062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.21011 | − | 3.82803i | 0.363340 | − | 0.629324i | −0.625168 | − | 0.780490i | \(-0.714970\pi\) |
0.988508 | + | 0.151167i | \(0.0483030\pi\) | |||||||
\(38\) | −0.155466 | − | 0.269276i | −0.0252200 | − | 0.0436823i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.35797 | − | 1.36138i | −0.372828 | − | 0.215253i | ||||
\(41\) | 4.29859 | 0.671326 | 0.335663 | − | 0.941982i | \(-0.391040\pi\) | ||||
0.335663 | + | 0.941982i | \(0.391040\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.10271 | 0.625657 | 0.312829 | − | 0.949810i | \(-0.398723\pi\) | ||||
0.312829 | + | 0.949810i | \(0.398723\pi\) | |||||||
\(44\) | 0.866025 | + | 0.500000i | 0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.60269 | − | 4.50799i | −0.383746 | − | 0.664667i | ||||
\(47\) | 3.63535 | − | 6.29661i | 0.530270 | − | 0.918454i | −0.469107 | − | 0.883142i | \(-0.655424\pi\) |
0.999376 | − | 0.0353126i | \(-0.0112427\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.12540 | − | 6.66953i | 0.303628 | − | 0.952791i | ||||
\(50\) | 2.41339i | 0.341304i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.167911 | + | 0.0969436i | −0.0232851 | + | 0.0134437i | ||||
\(53\) | −1.04499 | + | 0.603325i | −0.143540 | + | 0.0828730i | −0.570050 | − | 0.821610i | \(-0.693076\pi\) |
0.426510 | + | 0.904483i | \(0.359743\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.72275i | − | 0.367136i | ||||||
\(56\) | 1.56119 | + | 2.13605i | 0.208622 | + | 0.285441i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.08596 | + | 3.61299i | −0.273900 | + | 0.474408i | ||||
\(59\) | 5.43057 | + | 9.40603i | 0.707001 | + | 1.22456i | 0.965965 | + | 0.258674i | \(0.0832855\pi\) |
−0.258964 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.20619 | − | 4.73784i | −1.05069 | − | 0.606619i | −0.127851 | − | 0.991793i | \(-0.540808\pi\) |
−0.922844 | + | 0.385175i | \(0.874141\pi\) | |||||||
\(62\) | −1.59495 | −0.202559 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.457181 | + | 0.263953i | 0.0567063 | + | 0.0327394i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.69458 | + | 4.66714i | 0.329195 | + | 0.570182i | 0.982352 | − | 0.187040i | \(-0.0598894\pi\) |
−0.653158 | + | 0.757222i | \(0.726556\pi\) | |||||||
\(68\) | −3.07388 | + | 5.32411i | −0.372762 | + | 0.645643i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.91138 | − | 6.58920i | 0.347977 | − | 0.787560i | ||||
\(71\) | − | 9.63462i | − | 1.14342i | −0.820456 | − | 0.571710i | \(-0.806280\pi\) | ||
0.820456 | − | 0.571710i | \(-0.193720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.50213 | + | 1.44461i | −0.292853 | + | 0.169079i | −0.639228 | − | 0.769018i | \(-0.720746\pi\) |
0.346375 | + | 0.938096i | \(0.387412\pi\) | |||||||
\(74\) | −3.82803 | + | 2.21011i | −0.444999 | + | 0.256920i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.310933i | 0.0356664i | ||||||||
\(77\) | −1.06928 | + | 2.42005i | −0.121856 | + | 0.275790i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.60345 | + | 13.1696i | −0.855455 | + | 1.48169i | 0.0207679 | + | 0.999784i | \(0.493389\pi\) |
−0.876223 | + | 0.481907i | \(0.839944\pi\) | |||||||
\(80\) | 1.36138 | + | 2.35797i | 0.152207 | + | 0.263629i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.72268 | − | 2.14929i | −0.411102 | − | 0.237350i | ||||
\(83\) | 10.0883 | 1.10734 | 0.553668 | − | 0.832737i | \(-0.313228\pi\) | ||||
0.553668 | + | 0.832737i | \(0.313228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.7388 | 1.81558 | ||||||||
\(86\) | −3.55305 | − | 2.05135i | −0.383135 | − | 0.221203i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 5.67955 | − | 9.83727i | 0.602031 | − | 1.04275i | −0.390482 | − | 0.920610i | \(-0.627692\pi\) |
0.992513 | − | 0.122138i | \(-0.0389750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.302694 | − | 0.414152i | −0.0317309 | − | 0.0434149i | ||||
\(92\) | 5.20538i | 0.542698i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.29661 | + | 3.63535i | −0.649445 | + | 0.374957i | ||||
\(95\) | 0.733171 | − | 0.423296i | 0.0752217 | − | 0.0434293i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.77249i | − | 0.687642i | −0.939035 | − | 0.343821i | \(-0.888279\pi\) | ||
0.939035 | − | 0.343821i | \(-0.111721\pi\) | |||||||
\(98\) | −5.17542 | + | 4.71329i | −0.522796 | + | 0.476114i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.20669 | − | 2.09005i | 0.120669 | − | 0.209005i | ||||
\(101\) | −6.35755 | − | 11.0116i | −0.632600 | − | 1.09570i | −0.987018 | − | 0.160608i | \(-0.948654\pi\) |
0.354418 | − | 0.935087i | \(-0.384679\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.88096 | + | 1.08597i | 0.185336 | + | 0.107004i | 0.589797 | − | 0.807551i | \(-0.299208\pi\) |
−0.404461 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(104\) | 0.193887 | 0.0190122 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.20665 | 0.117200 | ||||||||
\(107\) | 4.39707 | + | 2.53865i | 0.425081 | + | 0.245421i | 0.697249 | − | 0.716829i | \(-0.254407\pi\) |
−0.272168 | + | 0.962250i | \(0.587741\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.813357 | + | 1.40878i | 0.0779054 | + | 0.134936i | 0.902346 | − | 0.431012i | \(-0.141843\pi\) |
−0.824441 | + | 0.565948i | \(0.808510\pi\) | |||||||
\(110\) | −1.36138 | + | 2.35797i | −0.129802 | + | 0.224824i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.284003 | − | 2.63046i | −0.0268357 | − | 0.248556i | ||||
\(113\) | − | 9.08122i | − | 0.854290i | −0.904183 | − | 0.427145i | \(-0.859519\pi\) | ||
0.904183 | − | 0.427145i | \(-0.140481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2741 | − | 7.08648i | 1.14457 | − | 0.660818i | ||||
\(116\) | 3.61299 | − | 2.08596i | 0.335457 | − | 0.193676i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.8611i | − | 0.999850i | ||||||
\(119\) | −14.8779 | − | 6.57366i | −1.36385 | − | 0.602606i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 4.73784 | + | 8.20619i | 0.428944 | + | 0.742953i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.38127 | + | 0.797476i | 0.124042 | + | 0.0716155i | ||||
\(125\) | 7.04271 | 0.629919 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00619 | 0.266756 | 0.133378 | − | 0.991065i | \(-0.457418\pi\) | ||||
0.133378 | + | 0.991065i | \(0.457418\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.263953 | − | 0.457181i | −0.0231502 | − | 0.0400974i | ||||
\(131\) | 3.10422 | − | 5.37666i | 0.271217 | − | 0.469761i | −0.697957 | − | 0.716140i | \(-0.745907\pi\) |
0.969174 | + | 0.246378i | \(0.0792406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.817897 | + | 0.0883057i | −0.0709207 | + | 0.00765708i | ||||
\(134\) | − | 5.38915i | − | 0.465552i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.32411 | − | 3.07388i | 0.456539 | − | 0.263583i | ||||
\(137\) | 8.22265 | − | 4.74735i | 0.702508 | − | 0.405593i | −0.105773 | − | 0.994390i | \(-0.533732\pi\) |
0.808281 | + | 0.588797i | \(0.200398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2020i | 1.11978i | 0.828568 | + | 0.559888i | \(0.189156\pi\) | ||||
−0.828568 | + | 0.559888i | \(0.810844\pi\) | |||||||
\(140\) | −5.81593 | + | 4.25072i | −0.491536 | + | 0.359252i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.81731 | + | 8.34383i | −0.404260 | + | 0.700198i | ||||
\(143\) | 0.0969436 | + | 0.167911i | 0.00810683 | + | 0.0140414i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.83727 | − | 5.67955i | −0.816941 | − | 0.471661i | ||||
\(146\) | 2.88921 | 0.239113 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.42022 | 0.363340 | ||||||||
\(149\) | 11.9136 | + | 6.87830i | 0.975997 | + | 0.563492i | 0.901059 | − | 0.433696i | \(-0.142791\pi\) |
0.0749376 | + | 0.997188i | \(0.476124\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4182 | + | 18.0449i | 0.847823 | + | 1.46847i | 0.883146 | + | 0.469097i | \(0.155421\pi\) |
−0.0353230 | + | 0.999376i | \(0.511246\pi\) | |||||||
\(152\) | 0.155466 | − | 0.269276i | 0.0126100 | − | 0.0218411i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.13605 | − | 1.56119i | 0.172128 | − | 0.125804i | ||||
\(155\) | − | 4.34266i | − | 0.348811i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5367 | − | 7.81541i | 1.08034 | − | 0.623737i | 0.149355 | − | 0.988784i | \(-0.452280\pi\) |
0.930989 | + | 0.365046i | \(0.118947\pi\) | |||||||
\(158\) | 13.1696 | − | 7.60345i | 1.04771 | − | 0.604898i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.72275i | − | 0.215253i | ||||||
\(161\) | −13.6926 | + | 1.47834i | −1.07912 | + | 0.116510i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.53891 | + | 4.39752i | −0.198863 | + | 0.344441i | −0.948160 | − | 0.317793i | \(-0.897058\pi\) |
0.749297 | + | 0.662234i | \(0.230392\pi\) | |||||||
\(164\) | 2.14929 | + | 3.72268i | 0.167832 | + | 0.290693i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.73673 | − | 5.04416i | −0.678102 | − | 0.391502i | ||||
\(167\) | 3.13718 | 0.242762 | 0.121381 | − | 0.992606i | \(-0.461268\pi\) | ||||
0.121381 | + | 0.992606i | \(0.461268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9624 | 0.997108 | ||||||||
\(170\) | −14.4962 | − | 8.36940i | −1.11181 | − | 0.641904i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.05135 | + | 3.55305i | 0.156414 | + | 0.270918i | ||||
\(173\) | 8.61420 | − | 14.9202i | 0.654925 | − | 1.13436i | −0.326987 | − | 0.945029i | \(-0.606033\pi\) |
0.981913 | − | 0.189335i | \(-0.0606332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.84051 | + | 2.58058i | 0.441501 | + | 0.195074i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.83727 | + | 5.67955i | −0.737334 | + | 0.425700i | ||||
\(179\) | −10.0700 | + | 5.81389i | −0.752664 | + | 0.434551i | −0.826656 | − | 0.562708i | \(-0.809759\pi\) |
0.0739917 | + | 0.997259i | \(0.476426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.3940i | − | 0.772577i | −0.922378 | − | 0.386288i | \(-0.873757\pi\) | ||
0.922378 | − | 0.386288i | \(-0.126243\pi\) | |||||||
\(182\) | 0.0550645 | + | 0.510013i | 0.00408165 | + | 0.0378047i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.60269 | − | 4.50799i | 0.191873 | − | 0.332333i | ||||
\(185\) | −6.01759 | − | 10.4228i | −0.442422 | − | 0.766297i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.32411 | + | 3.07388i | 0.389337 | + | 0.224784i | ||||
\(188\) | 7.27069 | 0.530270 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.846593 | −0.0614183 | ||||||||
\(191\) | −15.4420 | − | 8.91542i | −1.11734 | − | 0.645097i | −0.176620 | − | 0.984279i | \(-0.556516\pi\) |
−0.940721 | + | 0.339182i | \(0.889850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.66535 | − | 13.2768i | −0.551764 | − | 0.955683i | −0.998147 | − | 0.0608416i | \(-0.980622\pi\) |
0.446383 | − | 0.894842i | \(-0.352712\pi\) | |||||||
\(194\) | −3.38624 | + | 5.86514i | −0.243118 | + | 0.421093i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.83868 | − | 1.49412i | 0.488477 | − | 0.106723i | ||||
\(197\) | 23.5506i | 1.67791i | 0.544199 | + | 0.838956i | \(0.316834\pi\) | ||||
−0.544199 | + | 0.838956i | \(0.683166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4609 | + | 6.61697i | −0.812443 | + | 0.469064i | −0.847804 | − | 0.530310i | \(-0.822075\pi\) |
0.0353603 | + | 0.999375i | \(0.488742\pi\) | |||||||
\(200\) | −2.09005 | + | 1.20669i | −0.147789 | + | 0.0853260i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.7151i | 0.894632i | ||||||||
\(203\) | 6.51314 | + | 8.91141i | 0.457133 | + | 0.625458i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.85199 | − | 10.1360i | 0.408721 | − | 0.707926i | ||||
\(206\) | −1.08597 | − | 1.88096i | −0.0756632 | − | 0.131052i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.167911 | − | 0.0969436i | −0.0116425 | − | 0.00672183i | ||||
\(209\) | 0.310933 | 0.0215077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.937344 | 0.0645294 | 0.0322647 | − | 0.999479i | \(-0.489728\pi\) | ||||
0.0322647 | + | 0.999479i | \(0.489728\pi\) | |||||||
\(212\) | −1.04499 | − | 0.603325i | −0.0717702 | − | 0.0414365i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.53865 | − | 4.39707i | −0.173539 | − | 0.300578i | ||||
\(215\) | 5.58533 | − | 9.67408i | 0.380916 | − | 0.659767i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.70545 | + | 3.85986i | −0.115773 | + | 0.262025i | ||||
\(218\) | − | 1.62671i | − | 0.110175i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.35797 | − | 1.36138i | 0.158975 | − | 0.0917840i | ||||
\(221\) | −1.03228 | + | 0.595985i | −0.0694384 | + | 0.0400903i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8750i | 0.728242i | 0.931352 | + | 0.364121i | \(0.118631\pi\) | ||||
−0.931352 | + | 0.364121i | \(0.881369\pi\) | |||||||
\(224\) | −1.06928 | + | 2.42005i | −0.0714442 | + | 0.161696i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.54061 | + | 7.86457i | −0.302037 | + | 0.523143i | ||||
\(227\) | 3.87060 | + | 6.70408i | 0.256901 | + | 0.444965i | 0.965410 | − | 0.260736i | \(-0.0839653\pi\) |
−0.708509 | + | 0.705701i | \(0.750632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.44434 | + | 2.56594i | 0.293691 | + | 0.169562i | 0.639605 | − | 0.768704i | \(-0.279098\pi\) |
−0.345914 | + | 0.938266i | \(0.612431\pi\) | |||||||
\(230\) | −14.1730 | −0.934537 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.17192 | −0.273900 | ||||||||
\(233\) | −16.5376 | − | 9.54801i | −1.08342 | − | 0.625511i | −0.151600 | − | 0.988442i | \(-0.548443\pi\) |
−0.931816 | + | 0.362931i | \(0.881776\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.89815 | − | 17.1441i | −0.645684 | − | 1.11836i | ||||
\(236\) | −5.43057 | + | 9.40603i | −0.353500 | + | 0.612280i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.59778 | + | 13.1319i | 0.622132 | + | 0.851214i | ||||
\(239\) | − | 12.4259i | − | 0.803762i | −0.915692 | − | 0.401881i | \(-0.868357\pi\) | ||
0.915692 | − | 0.401881i | \(-0.131643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5847 | + | 11.3072i | −1.26156 | + | 0.728363i | −0.973377 | − | 0.229212i | \(-0.926385\pi\) |
−0.288185 | + | 0.957575i | \(0.593052\pi\) | |||||||
\(242\) | −0.866025 | + | 0.500000i | −0.0556702 | + | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.47569i | − | 0.606619i | ||||||
\(245\) | −12.8331 | − | 14.0914i | −0.819878 | − | 0.900265i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0301429 | + | 0.0522091i | −0.00191795 | + | 0.00332198i | ||||
\(248\) | −0.797476 | − | 1.38127i | −0.0506398 | − | 0.0877107i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.09917 | − | 3.52136i | −0.385745 | − | 0.222710i | ||||
\(251\) | −6.22476 | −0.392903 | −0.196452 | − | 0.980514i | \(-0.562942\pi\) | ||||
−0.196452 | + | 0.980514i | \(0.562942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.20538 | 0.327259 | ||||||||
\(254\) | −2.60344 | − | 1.50310i | −0.163354 | − | 0.0943126i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.6647 | + | 21.9359i | −0.790003 | + | 1.36832i | 0.135962 | + | 0.990714i | \(0.456588\pi\) |
−0.925964 | + | 0.377611i | \(0.876746\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.25536 | + | 11.6272i | 0.0780040 | + | 0.722482i | ||||
\(260\) | 0.527907i | 0.0327394i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.37666 | + | 3.10422i | −0.332171 | + | 0.191779i | ||||
\(263\) | −20.6740 | + | 11.9361i | −1.27481 | + | 0.736014i | −0.975890 | − | 0.218263i | \(-0.929961\pi\) |
−0.298924 | + | 0.954277i | \(0.596628\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.28541i | 0.201821i | ||||||||
\(266\) | 0.752472 | + | 0.332474i | 0.0461370 | + | 0.0203853i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.69458 | + | 4.66714i | −0.164597 | + | 0.285091i | ||||
\(269\) | −1.06611 | − | 1.84656i | −0.0650019 | − | 0.112587i | 0.831693 | − | 0.555236i | \(-0.187372\pi\) |
−0.896695 | + | 0.442649i | \(0.854039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5382 | − | 13.5898i | −1.42984 | − | 0.825520i | −0.432735 | − | 0.901521i | \(-0.642451\pi\) |
−0.997108 | + | 0.0760010i | \(0.975785\pi\) | |||||||
\(272\) | −6.14775 | −0.372762 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.49469 | −0.573595 | ||||||||
\(275\) | −2.09005 | − | 1.20669i | −0.126035 | − | 0.0727663i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00742 | + | 8.67311i | 0.300867 | + | 0.521117i | 0.976333 | − | 0.216275i | \(-0.0693907\pi\) |
−0.675466 | + | 0.737391i | \(0.736057\pi\) | |||||||
\(278\) | 6.60098 | − | 11.4332i | 0.395901 | − | 0.685720i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.16211 | − | 0.773269i | 0.428018 | − | 0.0462117i | ||||
\(281\) | 28.1787i | 1.68100i | 0.541813 | + | 0.840499i | \(0.317738\pi\) | ||||
−0.541813 | + | 0.840499i | \(0.682262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.7390 | − | 13.7057i | 1.41114 | − | 0.814721i | 0.415642 | − | 0.909528i | \(-0.363557\pi\) |
0.995496 | + | 0.0948077i | \(0.0302236\pi\) | |||||||
\(284\) | 8.34383 | − | 4.81731i | 0.495115 | − | 0.285855i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.193887i | − | 0.0114648i | ||||||
\(287\) | −9.18198 | + | 6.71089i | −0.541995 | + | 0.396131i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3974 | + | 18.0089i | −0.611613 | + | 1.05934i | ||||
\(290\) | 5.67955 | + | 9.83727i | 0.333515 | + | 0.577664i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.50213 | − | 1.44461i | −0.146426 | − | 0.0845393i | ||||
\(293\) | 6.42673 | 0.375454 | 0.187727 | − | 0.982221i | \(-0.439888\pi\) | ||||
0.187727 | + | 0.982221i | \(0.439888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.5722 | 1.72176 | ||||||||
\(296\) | −3.82803 | − | 2.21011i | −0.222499 | − | 0.128460i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.87830 | − | 11.9136i | −0.398449 | − | 0.690134i | ||||
\(299\) | −0.504628 | + | 0.874041i | −0.0291834 | + | 0.0505471i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.76358 | + | 6.40509i | −0.505124 | + | 0.369183i | ||||
\(302\) | − | 20.8365i | − | 1.19900i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.269276 | + | 0.155466i | −0.0154440 | + | 0.00891660i | ||||
\(305\) | −22.3434 | + | 12.9000i | −1.27938 | + | 0.738651i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.7703i | 1.24250i | 0.783614 | + | 0.621248i | \(0.213374\pi\) | ||||
−0.783614 | + | 0.621248i | \(0.786626\pi\) | |||||||
\(308\) | −2.63046 | + | 0.284003i | −0.149885 | + | 0.0161826i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.17133 | + | 3.76085i | −0.123323 | + | 0.213602i | ||||
\(311\) | 6.47129 | + | 11.2086i | 0.366953 | + | 0.635582i | 0.989088 | − | 0.147329i | \(-0.0470676\pi\) |
−0.622134 | + | 0.782910i | \(0.713734\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.55581 | − | 0.898250i | −0.0879398 | − | 0.0507721i | 0.455385 | − | 0.890294i | \(-0.349502\pi\) |
−0.543325 | + | 0.839522i | \(0.682835\pi\) | |||||||
\(314\) | −15.6308 | −0.882098 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.2069 | −0.855455 | ||||||||
\(317\) | −25.0485 | − | 14.4617i | −1.40686 | − | 0.812252i | −0.411777 | − | 0.911285i | \(-0.635092\pi\) |
−0.995084 | + | 0.0990327i | \(0.968425\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.08596 | − | 3.61299i | −0.116791 | − | 0.202288i | ||||
\(320\) | −1.36138 | + | 2.35797i | −0.0761033 | + | 0.131815i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.5973 | + | 5.56600i | 0.702019 | + | 0.310181i | ||||
\(323\) | 1.91154i | 0.106361i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.405234 | − | 0.233962i | 0.0224784 | − | 0.0129779i | ||||
\(326\) | 4.39752 | − | 2.53891i | 0.243556 | − | 0.140617i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4.29859i | − | 0.237350i | ||||||
\(329\) | 2.06490 | + | 19.1253i | 0.113841 | + | 1.05441i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8278 | + | 30.8786i | −0.979904 | + | 1.69724i | −0.317204 | + | 0.948357i | \(0.602744\pi\) |
−0.662700 | + | 0.748885i | \(0.730589\pi\) | |||||||
\(332\) | 5.04416 | + | 8.73673i | 0.276834 | + | 0.479491i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.71688 | − | 1.56859i | −0.148661 | − | 0.0858294i | ||||
\(335\) | 14.6733 | 0.801690 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.6472 | 1.01578 | 0.507890 | − | 0.861422i | \(-0.330426\pi\) | ||||
0.507890 | + | 0.861422i | \(0.330426\pi\) | |||||||
\(338\) | −11.2258 | − | 6.48120i | −0.610602 | − | 0.352531i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.36940 | + | 14.4962i | 0.453895 | + | 0.786169i | ||||
\(341\) | 0.797476 | − | 1.38127i | 0.0431857 | − | 0.0747999i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.87243 | + | 17.5646i | 0.317081 | + | 0.948398i | ||||
\(344\) | − | 4.10271i | − | 0.221203i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.9202 | + | 8.61420i | −0.802116 | + | 0.463102i | ||||
\(347\) | 26.9301 | − | 15.5481i | 1.44569 | − | 0.834667i | 0.447465 | − | 0.894301i | \(-0.352327\pi\) |
0.998220 | + | 0.0596342i | \(0.0189934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.5679i | 0.726272i | 0.931736 | + | 0.363136i | \(0.118294\pi\) | ||||
−0.931736 | + | 0.363136i | \(0.881706\pi\) | |||||||
\(350\) | −3.76774 | − | 5.15511i | −0.201394 | − | 0.275552i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 0.975985 | + | 1.69046i | 0.0519465 | + | 0.0899739i | 0.890829 | − | 0.454338i | \(-0.150124\pi\) |
−0.838883 | + | 0.544312i | \(0.816791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.7182 | − | 13.1163i | −1.20576 | − | 0.696144i | ||||
\(356\) | 11.3591 | 0.602031 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6278 | 0.614548 | ||||||||
\(359\) | −1.05983 | − | 0.611893i | −0.0559357 | − | 0.0322945i | 0.471771 | − | 0.881721i | \(-0.343615\pi\) |
−0.527707 | + | 0.849426i | \(0.676948\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.45166 | − | 16.3708i | −0.497456 | − | 0.861619i | ||||
\(362\) | −5.19698 | + | 9.00143i | −0.273147 | + | 0.473105i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.207319 | − | 0.469217i | 0.0108665 | − | 0.0245936i | ||||
\(365\) | 7.86662i | 0.411758i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6347 | − | 11.9134i | 1.07712 | − | 0.621877i | 0.147004 | − | 0.989136i | \(-0.453037\pi\) |
0.930119 | + | 0.367259i | \(0.119704\pi\) | |||||||
\(368\) | −4.50799 | + | 2.60269i | −0.234995 | + | 0.135675i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.0352i | 0.625679i | ||||||||
\(371\) | 1.29024 | − | 2.92015i | 0.0669862 | − | 0.151607i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.5452 | + | 18.2648i | −0.546008 | + | 0.945714i | 0.452535 | + | 0.891747i | \(0.350520\pi\) |
−0.998543 | + | 0.0539668i | \(0.982813\pi\) | |||||||
\(374\) | −3.07388 | − | 5.32411i | −0.158946 | − | 0.275303i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.29661 | − | 3.63535i | −0.324723 | − | 0.187479i | ||||
\(377\) | 0.808881 | 0.0416595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.6286 | −1.52192 | −0.760961 | − | 0.648798i | \(-0.775272\pi\) | ||||
−0.760961 | + | 0.648798i | \(0.775272\pi\) | |||||||
\(380\) | 0.733171 | + | 0.423296i | 0.0376109 | + | 0.0217146i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.91542 | + | 15.4420i | 0.456152 | + | 0.790079i | ||||
\(383\) | 2.05855 | − | 3.56551i | 0.105187 | − | 0.182189i | −0.808628 | − | 0.588321i | \(-0.799789\pi\) |
0.913815 | + | 0.406132i | \(0.133123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.25072 | + | 5.81593i | 0.216637 | + | 0.296407i | ||||
\(386\) | 15.3307i | 0.780312i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.86514 | − | 3.38624i | 0.297758 | − | 0.171910i | ||||
\(389\) | −29.0363 | + | 16.7641i | −1.47220 | + | 0.849975i | −0.999511 | − | 0.0312539i | \(-0.990050\pi\) |
−0.472689 | + | 0.881229i | \(0.656717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.0014i | 1.61838i | ||||||||
\(392\) | −6.66953 | − | 2.12540i | −0.336862 | − | 0.107349i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.7753 | − | 20.3954i | 0.593232 | − | 1.02751i | ||||
\(395\) | 20.7023 | + | 35.8575i | 1.04165 | + | 1.80418i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.46549 | + | 0.846104i | 0.0735511 | + | 0.0424647i | 0.536325 | − | 0.844012i | \(-0.319812\pi\) |
−0.462773 | + | 0.886477i | \(0.653146\pi\) | |||||||
\(398\) | 13.2339 | 0.663357 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.41339 | 0.120669 | ||||||||
\(401\) | −32.1813 | − | 18.5799i | −1.60706 | − | 0.927835i | −0.990024 | − | 0.140897i | \(-0.955001\pi\) |
−0.617033 | − | 0.786937i | \(-0.711665\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.154620 | + | 0.267810i | 0.00770219 | + | 0.0133406i | ||||
\(404\) | 6.35755 | − | 11.0116i | 0.316300 | − | 0.547848i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.18484 | − | 10.9741i | −0.0588024 | − | 0.544634i | ||||
\(407\) | − | 4.42022i | − | 0.219102i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.23682 | + | 1.29143i | −0.110604 | + | 0.0638570i | −0.554281 | − | 0.832329i | \(-0.687007\pi\) |
0.443678 | + | 0.896186i | \(0.353673\pi\) | |||||||
\(410\) | −10.1360 | + | 5.85199i | −0.500579 | + | 0.289009i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.17194i | 0.107004i | ||||||||
\(413\) | −26.2845 | − | 11.6136i | −1.29338 | − | 0.571468i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.7340 | − | 23.7880i | 0.674175 | − | 1.16771i | ||||
\(416\) | 0.0969436 | + | 0.167911i | 0.00475305 | + | 0.00823252i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.269276 | − | 0.155466i | −0.0131707 | − | 0.00760410i | ||||
\(419\) | 22.0871 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.60120 | −0.175512 | −0.0877559 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877559 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(422\) | −0.811764 | − | 0.468672i | −0.0395161 | − | 0.0228146i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.603325 | + | 1.04499i | 0.0293000 | + | 0.0507492i | ||||
\(425\) | 7.41845 | − | 12.8491i | 0.359847 | − | 0.623274i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.9255 | − | 2.69112i | 1.20623 | − | 0.130232i | ||||
\(428\) | 5.07730i | 0.245421i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.67408 | + | 5.58533i | −0.466526 | + | 0.269349i | ||||
\(431\) | −2.29763 | + | 1.32654i | −0.110673 | + | 0.0638970i | −0.554315 | − | 0.832307i | \(-0.687020\pi\) |
0.443642 | + | 0.896204i | \(0.353686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.3112i | 1.02415i | 0.858940 | + | 0.512076i | \(0.171123\pi\) | ||||
−0.858940 | + | 0.512076i | \(0.828877\pi\) | |||||||
\(434\) | 3.40689 | − | 2.49002i | 0.163536 | − | 0.119525i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.813357 | + | 1.40878i | −0.0389527 | + | 0.0674681i | ||||
\(437\) | 0.809261 | + | 1.40168i | 0.0387122 | + | 0.0670515i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1839 | + | 6.45704i | 0.533780 | + | 0.308178i | 0.742554 | − | 0.669786i | \(-0.233614\pi\) |
−0.208775 | + | 0.977964i | \(0.566948\pi\) | |||||||
\(440\) | −2.72275 | −0.129802 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.19197 | 0.0566962 | ||||||||
\(443\) | 20.9687 | + | 12.1063i | 0.996251 | + | 0.575186i | 0.907137 | − | 0.420836i | \(-0.138263\pi\) |
0.0891141 | + | 0.996021i | \(0.471596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4640 | − | 26.7845i | −0.733064 | − | 1.26970i | ||||
\(446\) | 5.43749 | − | 9.41801i | 0.257473 | − | 0.445956i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.13605 | − | 1.56119i | 0.100919 | − | 0.0737591i | ||||
\(449\) | 6.97436i | 0.329140i | 0.986365 | + | 0.164570i | \(0.0526237\pi\) | ||||
−0.986365 | + | 0.164570i | \(0.947376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.72268 | − | 2.14929i | 0.175294 | − | 0.101206i | ||||
\(452\) | 7.86457 | − | 4.54061i | 0.369918 | − | 0.213572i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 7.74120i | − | 0.363312i | ||||||
\(455\) | −1.38864 | + | 0.149927i | −0.0651004 | + | 0.00702868i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0495834 | − | 0.0858810i | 0.00231941 | − | 0.00401734i | −0.864863 | − | 0.502007i | \(-0.832595\pi\) |
0.867183 | + | 0.497990i | \(0.165928\pi\) | |||||||
\(458\) | −2.56594 | − | 4.44434i | −0.119899 | − | 0.207671i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.2741 | + | 7.08648i | 0.572285 | + | 0.330409i | ||||
\(461\) | 30.2189 | 1.40744 | 0.703718 | − | 0.710480i | \(-0.251522\pi\) | ||||
0.703718 | + | 0.710480i | \(0.251522\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6191 | −1.46946 | −0.734731 | − | 0.678358i | \(-0.762692\pi\) | ||||
−0.734731 | + | 0.678358i | \(0.762692\pi\) | |||||||
\(464\) | 3.61299 | + | 2.08596i | 0.167729 | + | 0.0968382i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.54801 | + | 16.5376i | 0.442303 | + | 0.766091i | ||||
\(467\) | 12.6717 | − | 21.9481i | 0.586378 | − | 1.01564i | −0.408324 | − | 0.912837i | \(-0.633887\pi\) |
0.994702 | − | 0.102800i | \(-0.0327801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.0420 | − | 5.76250i | −0.602224 | − | 0.266088i | ||||
\(470\) | 19.7963i | 0.913135i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.40603 | − | 5.43057i | 0.432948 | − | 0.249962i | ||||
\(473\) | 3.55305 | − | 2.05135i | 0.163369 | − | 0.0943214i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.750400i | − | 0.0344307i | ||||||
\(476\) | −1.74598 | − | 16.1714i | −0.0800268 | − | 0.741217i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.21293 | + | 10.7611i | −0.284173 | + | 0.492202i | ||||
\(479\) | −16.3051 | − | 28.2413i | −0.745000 | − | 1.29038i | −0.950195 | − | 0.311657i | \(-0.899116\pi\) |
0.205194 | − | 0.978721i | \(-0.434217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.742205 | + | 0.428512i | 0.0338416 | + | 0.0195385i | ||||
\(482\) | 22.6145 | 1.03006 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −15.9693 | − | 9.21990i | −0.725130 | − | 0.418654i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.05532 | − | 3.55991i | −0.0931353 | − | 0.161315i | 0.815694 | − | 0.578484i | \(-0.196356\pi\) |
−0.908829 | + | 0.417169i | \(0.863022\pi\) | |||||||
\(488\) | −4.73784 | + | 8.20619i | −0.214472 | + | 0.371477i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.06811 | + | 18.6201i | 0.183779 | + | 0.841168i | ||||
\(491\) | − | 4.57385i | − | 0.206415i | −0.994660 | − | 0.103207i | \(-0.967089\pi\) | ||
0.994660 | − | 0.103207i | \(-0.0329106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.2117 | − | 12.8240i | 1.00037 | − | 0.577562i | ||||
\(494\) | 0.0522091 | − | 0.0301429i | 0.00234900 | − | 0.00135619i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.59495i | 0.0716155i | ||||||||
\(497\) | 15.0414 | + | 20.5800i | 0.674701 | + | 0.923140i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.3034 | + | 31.7024i | −0.819372 | + | 1.41919i | 0.0867728 | + | 0.996228i | \(0.472345\pi\) |
−0.906145 | + | 0.422967i | \(0.860989\pi\) | |||||||
\(500\) | 3.52136 | + | 6.09917i | 0.157480 | + | 0.272763i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.39080 | + | 3.11238i | 0.240603 | + | 0.138912i | ||||
\(503\) | −17.0391 | −0.759738 | −0.379869 | − | 0.925040i | \(-0.624031\pi\) | ||||
−0.379869 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.6201 | −1.54057 | ||||||||
\(506\) | −4.50799 | − | 2.60269i | −0.200405 | − | 0.115704i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.50310 | + | 2.60344i | 0.0666891 | + | 0.115509i | ||||
\(509\) | 5.96804 | − | 10.3370i | 0.264529 | − | 0.458177i | −0.702911 | − | 0.711278i | \(-0.748117\pi\) |
0.967440 | + | 0.253100i | \(0.0814502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.08938 | − | 6.99205i | 0.136666 | − | 0.309310i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.9359 | − | 12.6647i | 0.967552 | − | 0.558616i | ||||
\(515\) | 5.12138 | − | 2.95683i | 0.225675 | − | 0.130294i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.27069i | − | 0.319765i | ||||||
\(518\) | 4.72645 | − | 10.6972i | 0.207668 | − | 0.470006i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.263953 | − | 0.457181i | 0.0115751 | − | 0.0200487i | ||||
\(521\) | 21.4867 | + | 37.2161i | 0.941350 | + | 1.63047i | 0.762899 | + | 0.646518i | \(0.223775\pi\) |
0.178452 | + | 0.983949i | \(0.442891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1432 | − | 17.9806i | −1.36180 | − | 0.786235i | −0.371935 | − | 0.928259i | \(-0.621306\pi\) |
−0.989863 | + | 0.142024i | \(0.954639\pi\) | |||||||
\(524\) | 6.20844 | 0.271217 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.8723 | 1.04088 | ||||||||
\(527\) | 8.49170 | + | 4.90268i | 0.369904 | + | 0.213564i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.04798 | + | 3.54720i | 0.0890425 | + | 0.154226i | ||||
\(530\) | 1.64270 | − | 2.84525i | 0.0713545 | − | 0.123590i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.485424 | − | 0.664167i | −0.0210458 | − | 0.0287953i | ||||
\(533\) | 0.833440i | 0.0361003i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.9721 | − | 6.91212i | 0.517601 | − | 0.298837i | ||||
\(536\) | 4.66714 | − | 2.69458i | 0.201590 | − | 0.116388i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.13222i | 0.0919266i | ||||||||
\(539\) | −1.49412 | − | 6.83868i | −0.0643562 | − | 0.294563i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.56847 | + | 2.71667i | −0.0674337 | + | 0.116799i | −0.897771 | − | 0.440463i | \(-0.854814\pi\) |
0.830337 | + | 0.557261i | \(0.188148\pi\) | |||||||
\(542\) | 13.5898 | + | 23.5382i | 0.583731 | + | 1.01105i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.32411 | + | 3.07388i | 0.228269 | + | 0.131791i | ||||
\(545\) | 4.42914 | 0.189723 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.97672 | 0.0845184 | 0.0422592 | − | 0.999107i | \(-0.486544\pi\) | ||||
0.0422592 | + | 0.999107i | \(0.486544\pi\) | |||||||
\(548\) | 8.22265 | + | 4.74735i | 0.351254 | + | 0.202797i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.20669 | + | 2.09005i | 0.0514535 | + | 0.0891202i | ||||
\(551\) | 0.648592 | − | 1.12339i | 0.0276310 | − | 0.0478582i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.31880 | − | 40.0012i | −0.183654 | − | 1.70102i | ||||
\(554\) | − | 10.0148i | − | 0.425490i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4332 | + | 6.60098i | −0.484877 | + | 0.279944i | ||||
\(557\) | 12.2471 | − | 7.07088i | 0.518927 | − | 0.299603i | −0.217568 | − | 0.976045i | \(-0.569813\pi\) |
0.736496 | + | 0.676442i | \(0.236479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.795462i | 0.0336445i | ||||||||
\(560\) | −6.58920 | − | 2.91138i | −0.278445 | − | 0.123028i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.0893 | − | 24.4034i | 0.594323 | − | 1.02940i | ||||
\(563\) | 3.39720 | + | 5.88412i | 0.143175 | + | 0.247986i | 0.928691 | − | 0.370856i | \(-0.120936\pi\) |
−0.785516 | + | 0.618842i | \(0.787602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.4133 | − | 12.3630i | −0.900864 | − | 0.520114i | ||||
\(566\) | −27.4114 | −1.15219 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.63462 | −0.404260 | ||||||||
\(569\) | −37.4383 | − | 21.6150i | −1.56949 | − | 0.906147i | −0.996228 | − | 0.0867776i | \(-0.972343\pi\) |
−0.573265 | − | 0.819370i | \(-0.694324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.3065 | − | 40.3680i | −0.975346 | − | 1.68935i | −0.678790 | − | 0.734333i | \(-0.737495\pi\) |
−0.296556 | − | 0.955015i | \(-0.595838\pi\) | |||||||
\(572\) | −0.0969436 | + | 0.167911i | −0.00405341 | + | 0.00702072i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.3073 | − | 1.22081i | 0.471957 | − | 0.0509556i | ||||
\(575\) | − | 12.5626i | − | 0.523896i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.6159 | − | 18.8308i | 1.35782 | − | 0.783936i | 0.368488 | − | 0.929633i | \(-0.379876\pi\) |
0.989329 | + | 0.145697i | \(0.0465423\pi\) | |||||||
\(578\) | 18.0089 | − | 10.3974i | 0.749070 | − | 0.432476i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 11.3591i | − | 0.471661i | ||||||
\(581\) | −21.5491 | + | 15.7497i | −0.894008 | + | 0.653409i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.603325 | + | 1.04499i | −0.0249872 | + | 0.0432790i | ||||
\(584\) | 1.44461 | + | 2.50213i | 0.0597783 | + | 0.103539i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.56571 | − | 3.21337i | −0.229918 | − | 0.132743i | ||||
\(587\) | −43.9834 | −1.81539 | −0.907694 | − | 0.419632i | \(-0.862159\pi\) | ||||
−0.907694 | + | 0.419632i | \(0.862159\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.495923 | 0.0204341 | ||||||||
\(590\) | −25.6103 | − | 14.7861i | −1.05436 | − | 0.608735i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.21011 | + | 3.82803i | 0.0908350 | + | 0.157331i | ||||
\(593\) | 9.09719 | − | 15.7568i | 0.373577 | − | 0.647054i | −0.616536 | − | 0.787327i | \(-0.711465\pi\) |
0.990113 | + | 0.140272i | \(0.0447978\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.7549 | + | 26.1324i | −1.46581 | + | 1.07132i | ||||
\(596\) | 13.7566i | 0.563492i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.874041 | − | 0.504628i | 0.0357422 | − | 0.0206358i | ||||
\(599\) | 28.8965 | − | 16.6834i | 1.18068 | − | 0.681665i | 0.224507 | − | 0.974472i | \(-0.427923\pi\) |
0.956171 | + | 0.292807i | \(0.0945894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 45.3210i | − | 1.84868i | −0.381566 | − | 0.924341i | \(-0.624615\pi\) | ||
0.381566 | − | 0.924341i | \(-0.375385\pi\) | |||||||
\(602\) | 10.7920 | − | 1.16518i | 0.439850 | − | 0.0474892i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.4182 | + | 18.0449i | −0.423912 | + | 0.734237i | ||||
\(605\) | −1.36138 | − | 2.35797i | −0.0553478 | − | 0.0958653i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.26548 | − | 3.04003i | −0.213719 | − | 0.123391i | 0.389319 | − | 0.921103i | \(-0.372710\pi\) |
−0.603039 | + | 0.797712i | \(0.706044\pi\) | |||||||
\(608\) | 0.310933 | 0.0126100 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.8000 | 1.04461 | ||||||||
\(611\) | 1.22083 | + | 0.704847i | 0.0493895 | + | 0.0285151i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8152 | − | 20.4645i | −0.477211 | − | 0.826554i | 0.522447 | − | 0.852671i | \(-0.325019\pi\) |
−0.999659 | + | 0.0261170i | \(0.991686\pi\) | |||||||
\(614\) | 10.8851 | − | 18.8536i | 0.439288 | − | 0.760870i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.42005 | + | 1.06928i | 0.0975066 | + | 0.0430825i | ||||
\(617\) | 22.4859i | 0.905248i | 0.891702 | + | 0.452624i | \(0.149512\pi\) | ||||
−0.891702 | + | 0.452624i | \(0.850488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.68075 | − | 3.27978i | 0.228329 | − | 0.131826i | −0.381472 | − | 0.924380i | \(-0.624583\pi\) |
0.609801 | + | 0.792555i | \(0.291249\pi\) | |||||||
\(620\) | 3.76085 | − | 2.17133i | 0.151040 | − | 0.0872027i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.9426i | − | 0.518950i | ||||||
\(623\) | 3.22601 | + | 29.8797i | 0.129248 | + | 1.19710i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6212 | − | 27.0568i | 0.624850 | − | 1.08227i | ||||
\(626\) | 0.898250 | + | 1.55581i | 0.0359013 | + | 0.0621828i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5367 | + | 7.81541i | 0.540172 | + | 0.311869i | ||||
\(629\) | 27.1744 | 1.08352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.60407 | −0.382332 | −0.191166 | − | 0.981558i | \(-0.561227\pi\) | ||||
−0.191166 | + | 0.981558i | \(0.561227\pi\) | |||||||
\(632\) | 13.1696 | + | 7.60345i | 0.523857 | + | 0.302449i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.4617 | + | 25.0485i | 0.574349 | + | 0.994801i | ||||
\(635\) | 4.09256 | − | 7.08852i | 0.162408 | − | 0.281299i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.29314 | + | 0.412087i | 0.0512359 | + | 0.0163275i | ||||
\(638\) | 4.17192i | 0.165168i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.35797 | − | 1.36138i | 0.0932071 | − | 0.0538131i | ||||
\(641\) | −25.3563 | + | 14.6395i | −1.00151 | + | 0.578224i | −0.908696 | − | 0.417459i | \(-0.862921\pi\) |
−0.0928182 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6438i | 0.656368i | 0.944614 | + | 0.328184i | \(0.106437\pi\) | ||||
−0.944614 | + | 0.328184i | \(0.893563\pi\) | |||||||
\(644\) | −8.12656 | − | 11.1189i | −0.320231 | − | 0.438147i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.955768 | − | 1.65544i | 0.0376042 | − | 0.0651324i | ||||
\(647\) | −20.7616 | − | 35.9602i | −0.816223 | − | 1.41374i | −0.908446 | − | 0.418001i | \(-0.862731\pi\) |
0.0922233 | − | 0.995738i | \(-0.470603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.40603 | + | 5.43057i | 0.369219 | + | 0.213169i | ||||
\(650\) | −0.467924 | −0.0183535 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.07782 | −0.198863 | ||||||||
\(653\) | −30.7284 | − | 17.7410i | −1.20249 | − | 0.694260i | −0.241385 | − | 0.970429i | \(-0.577602\pi\) |
−0.961109 | + | 0.276169i | \(0.910935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.45202 | − | 14.6393i | −0.330248 | − | 0.572006i | ||||
\(656\) | −2.14929 | + | 3.72268i | −0.0839158 | + | 0.145346i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.77440 | − | 17.5954i | 0.303078 | − | 0.685942i | ||||
\(659\) | 1.37768i | 0.0536668i | 0.999640 | + | 0.0268334i | \(0.00854237\pi\) | ||||
−0.999640 | + | 0.0268334i | \(0.991458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.1453 | − | 11.6309i | 0.783561 | − | 0.452389i | −0.0541298 | − | 0.998534i | \(-0.517238\pi\) |
0.837691 | + | 0.546145i | \(0.183905\pi\) | |||||||
\(662\) | 30.8786 | − | 17.8278i | 1.20013 | − | 0.692896i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 10.0883i | − | 0.391502i | ||||||
\(665\) | −0.905243 | + | 2.04880i | −0.0351038 | + | 0.0794489i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.8582 | − | 18.8070i | 0.420431 | − | 0.728208i | ||||
\(668\) | 1.56859 | + | 2.71688i | 0.0606905 | + | 0.105119i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.7075 | − | 7.33666i | −0.490933 | − | 0.283440i | ||||
\(671\) | −9.47569 | −0.365805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.3559 | −1.70979 | −0.854896 | − | 0.518799i | \(-0.826379\pi\) | ||||
−0.854896 | + | 0.518799i | \(0.826379\pi\) | |||||||
\(674\) | −16.1490 | − | 9.32362i | −0.622036 | − | 0.359133i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.48120 | + | 11.2258i | 0.249277 | + | 0.431761i | ||||
\(677\) | −16.3344 | + | 28.2920i | −0.627781 | + | 1.08735i | 0.360214 | + | 0.932870i | \(0.382704\pi\) |
−0.987996 | + | 0.154480i | \(0.950630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5731 | + | 14.4664i | 0.405759 | + | 0.555168i | ||||
\(680\) | − | 16.7388i | − | 0.641904i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.38127 | + | 0.797476i | −0.0528915 | + | 0.0305369i | ||||
\(683\) | 13.7043 | − | 7.91217i | 0.524380 | − | 0.302751i | −0.214345 | − | 0.976758i | \(-0.568762\pi\) |
0.738725 | + | 0.674007i | \(0.235428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 25.8517i | − | 0.987743i | ||||||
\(686\) | 3.69662 | − | 18.1476i | 0.141138 | − | 0.692878i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.05135 | + | 3.55305i | −0.0782072 | + | 0.135459i | ||||
\(689\) | −0.116977 | − | 0.202610i | −0.00445647 | − | 0.00771882i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.4940 | + | 15.2963i | 1.00788 | + | 0.581899i | 0.910570 | − | 0.413355i | \(-0.135643\pi\) |
0.0973085 | + | 0.995254i | \(0.468977\pi\) | |||||||
\(692\) | 17.2284 | 0.654925 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.0962 | −1.18040 | ||||||||
\(695\) | 31.1299 | + | 17.9729i | 1.18082 | + | 0.681749i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2133 | + | 22.8861i | 0.500490 | + | 0.866874i | ||||
\(698\) | 6.78394 | − | 11.7501i | 0.256776 | − | 0.444749i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.685408 | + | 6.34832i | 0.0259060 | + | 0.239944i | ||||
\(701\) | 6.04929i | 0.228479i | 0.993453 | + | 0.114239i | \(0.0364431\pi\) | ||||
−0.993453 | + | 0.114239i | \(0.963557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19026 | − | 0.687196i | 0.0448914 | − | 0.0259181i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.95197i | − | 0.0734634i | ||||||
\(707\) | 30.7712 | + | 13.5960i | 1.15727 | + | 0.511330i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.64611 | − | 11.5114i | 0.249600 | − | 0.432320i | −0.713815 | − | 0.700334i | \(-0.753034\pi\) |
0.963415 | + | 0.268015i | \(0.0863675\pi\) | |||||||
\(710\) | 13.1163 | + | 22.7182i | 0.492248 | + | 0.852598i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.83727 | − | 5.67955i | −0.368667 | − | 0.212850i | ||||
\(713\) | 8.30233 | 0.310925 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.527907 | 0.0197426 | ||||||||
\(716\) | −10.0700 | − | 5.81389i | −0.376332 | − | 0.217275i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.611893 | + | 1.05983i | 0.0228356 | + | 0.0395525i | ||||
\(719\) | 5.80479 | − | 10.0542i | 0.216482 | − | 0.374958i | −0.737248 | − | 0.675622i | \(-0.763875\pi\) |
0.953730 | + | 0.300664i | \(0.0972084\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.71321 | + | 0.616837i | −0.212771 | + | 0.0229722i | ||||
\(722\) | 18.9033i | 0.703509i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.00143 | − | 5.19698i | 0.334536 | − | 0.193144i | ||||
\(725\) | −8.71952 | + | 5.03422i | −0.323835 | + | 0.186966i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.0147i | − | 0.593953i | −0.954885 | − | 0.296977i | \(-0.904022\pi\) | ||
0.954885 | − | 0.296977i | \(-0.0959783\pi\) | |||||||
\(728\) | −0.414152 | + | 0.302694i | −0.0153495 | + | 0.0112186i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.93331 | − | 6.81269i | 0.145578 | − | 0.252149i | ||||
\(731\) | 12.6112 | + | 21.8433i | 0.466443 | + | 0.807902i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.5271 | + | 10.1193i | 0.647377 | + | 0.373763i | 0.787450 | − | 0.616378i | \(-0.211401\pi\) |
−0.140074 | + | 0.990141i | \(0.544734\pi\) | |||||||
\(734\) | −23.8269 | −0.879467 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.20538 | 0.191873 | ||||||||
\(737\) | 4.66714 | + | 2.69458i | 0.171916 | + | 0.0992560i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.78566 | − | 10.0211i | −0.212829 | − | 0.368630i | 0.739770 | − | 0.672860i | \(-0.234934\pi\) |
−0.952599 | + | 0.304229i | \(0.901601\pi\) | |||||||
\(740\) | 6.01759 | − | 10.4228i | 0.221211 | − | 0.383149i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.57746 | + | 1.88380i | −0.0946216 | + | 0.0691566i | ||||
\(743\) | 9.50531i | 0.348716i | 0.984682 | + | 0.174358i | \(0.0557850\pi\) | ||||
−0.984682 | + | 0.174358i | \(0.944215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.4377 | − | 18.7279i | 1.18842 | − | 0.686137i | ||||
\(746\) | 18.2648 | − | 10.5452i | 0.668720 | − | 0.386086i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.14775i | 0.224784i | ||||||||
\(749\) | −13.3557 | + | 1.44197i | −0.488005 | + | 0.0526884i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5445 | + | 23.4597i | −0.494245 | + | 0.856057i | −0.999978 | − | 0.00663281i | \(-0.997889\pi\) |
0.505733 | + | 0.862690i | \(0.331222\pi\) | |||||||
\(752\) | 3.63535 | + | 6.29661i | 0.132567 | + | 0.229614i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.700511 | − | 0.404440i | −0.0255111 | − | 0.0147289i | ||||
\(755\) | 56.7325 | 2.06471 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.9214 | 1.74173 | 0.870867 | − | 0.491518i | \(-0.163558\pi\) | ||||
0.870867 | + | 0.491518i | \(0.163558\pi\) | |||||||
\(758\) | 25.6592 | + | 14.8143i | 0.931983 | + | 0.538081i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.423296 | − | 0.733171i | −0.0153546 | − | 0.0265949i | ||||
\(761\) | −8.27095 | + | 14.3257i | −0.299822 | + | 0.519306i | −0.976095 | − | 0.217345i | \(-0.930260\pi\) |
0.676273 | + | 0.736651i | \(0.263594\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.93673 | − | 1.73941i | −0.142519 | − | 0.0629709i | ||||
\(764\) | − | 17.8308i | − | 0.645097i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.56551 | + | 2.05855i | −0.128827 | + | 0.0743783i | ||||
\(767\) | −1.82371 | + | 1.05292i | −0.0658503 | + | 0.0380187i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.14692i | − | 0.185603i | −0.995685 | − | 0.0928013i | \(-0.970418\pi\) | ||
0.995685 | − | 0.0928013i | \(-0.0295821\pi\) | |||||||
\(770\) | −0.773269 | − | 7.16211i | −0.0278667 | − | 0.258104i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.66535 | − | 13.2768i | 0.275882 | − | 0.477842i | ||||
\(773\) | 2.10953 | + | 3.65382i | 0.0758746 | + | 0.131419i | 0.901466 | − | 0.432849i | \(-0.142492\pi\) |
−0.825592 | + | 0.564268i | \(0.809158\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.33353 | − | 1.92462i | −0.119744 | − | 0.0691343i | ||||
\(776\) | −6.77249 | −0.243118 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.5283 | 1.20205 | ||||||||
\(779\) | 1.15750 | + | 0.668285i | 0.0414719 | + | 0.0239438i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.81731 | − | 8.34383i | −0.172377 | − | 0.298566i | ||||
\(782\) | 16.0007 | − | 27.7140i | 0.572183 | − | 0.991050i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.71329 | + | 5.17542i | 0.168332 | + | 0.184836i | ||||
\(785\) | − | 42.5588i | − | 1.51899i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.2097 | + | 17.4416i | −1.07686 | + | 0.621724i | −0.930047 | − | 0.367440i | \(-0.880234\pi\) |
−0.146811 | + | 0.989165i | \(0.546901\pi\) | |||||||
\(788\) | −20.3954 | + | 11.7753i | −0.726557 | + | 0.419478i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 41.4046i | − | 1.47311i | ||||||
\(791\) | 14.1775 | + | 19.3979i | 0.504093 | + | 0.689711i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918607 | − | 1.59107i | 0.0326207 | − | 0.0565007i | ||||
\(794\) | −0.846104 | − | 1.46549i | −0.0300271 | − | 0.0520085i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.4609 | − | 6.61697i | −0.406222 | − | 0.234532i | ||||
\(797\) | 17.4825 | 0.619262 | 0.309631 | − | 0.950857i | \(-0.399795\pi\) | ||||
0.309631 | + | 0.950857i | \(0.399795\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.6984 | 1.58132 | ||||||||
\(800\) | −2.09005 | − | 1.20669i | −0.0738945 | − | 0.0426630i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.5799 | + | 32.1813i | 0.656078 | + | 1.13636i | ||||
\(803\) | −1.44461 | + | 2.50213i | −0.0509791 | + | 0.0882984i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.1548 | + | 34.2993i | −0.534138 | + | 1.20889i | ||||
\(806\) | − | 0.309241i | − | 0.0108925i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.0116 | + | 6.35755i | −0.387387 | + | 0.223658i | ||||
\(809\) | 22.8674 | − | 13.2025i | 0.803975 | − | 0.464175i | −0.0408842 | − | 0.999164i | \(-0.513017\pi\) |
0.844859 | + | 0.534989i | \(0.179684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.4016i | − | 1.10266i | −0.834287 | − | 0.551330i | \(-0.814121\pi\) | ||
0.834287 | − | 0.551330i | \(-0.185879\pi\) | |||||||
\(812\) | −4.46094 | + | 10.0962i | −0.156548 | + | 0.354309i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.21011 | + | 3.82803i | −0.0774644 | + | 0.134172i | ||||
\(815\) | 6.91283 | + | 11.9734i | 0.242146 | + | 0.419409i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.10476 | + | 0.637833i | 0.0386506 | + | 0.0223149i | ||||
\(818\) | 2.58286 | 0.0903075 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.7040 | 0.408721 | ||||||||
\(821\) | 46.8857 | + | 27.0695i | 1.63632 | + | 0.944731i | 0.982084 | + | 0.188444i | \(0.0603443\pi\) |
0.654239 | + | 0.756288i | \(0.272989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.6961 | − | 23.7223i | −0.477416 | − | 0.826909i | 0.522249 | − | 0.852793i | \(-0.325093\pi\) |
−0.999665 | + | 0.0258842i | \(0.991760\pi\) | |||||||
\(824\) | 1.08597 | − | 1.88096i | 0.0378316 | − | 0.0655262i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.9563 | + | 23.1999i | 0.589984 | + | 0.807229i | ||||
\(827\) | 25.1390i | 0.874168i | 0.899421 | + | 0.437084i | \(0.143989\pi\) | ||||
−0.899421 | + | 0.437084i | \(0.856011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.4945 | + | 11.8325i | −0.711804 | + | 0.410960i | −0.811729 | − | 0.584035i | \(-0.801473\pi\) |
0.0999244 | + | 0.994995i | \(0.468140\pi\) | |||||||
\(830\) | −23.7880 | + | 13.7340i | −0.825693 | + | 0.476714i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.193887i | − | 0.00672183i | ||||||
\(833\) | 42.0425 | − | 9.18547i | 1.45669 | − | 0.318258i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.27088 | − | 7.39738i | 0.147800 | − | 0.255997i | ||||
\(836\) | 0.155466 | + | 0.269276i | 0.00537691 | + | 0.00931309i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.1280 | − | 11.0435i | −0.660765 | − | 0.381493i | ||||
\(839\) | 5.46018 | 0.188506 | 0.0942532 | − | 0.995548i | \(-0.469954\pi\) | ||||
0.0942532 | + | 0.995548i | \(0.469954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5951 | 0.399832 | ||||||||
\(842\) | 3.11873 | + | 1.80060i | 0.107479 | + | 0.0620528i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.468672 | + | 0.811764i | 0.0161324 | + | 0.0279421i | ||||
\(845\) | 17.6467 | − | 30.5650i | 0.607066 | − | 1.05147i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.284003 | + | 2.63046i | 0.00975845 | + | 0.0903838i | ||||
\(848\) | − | 1.20665i | − | 0.0414365i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.8491 | + | 7.41845i | −0.440721 | + | 0.254451i | ||||
\(851\) | 19.9263 | − | 11.5045i | 0.683065 | − | 0.394368i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.29168i | − | 0.318141i | −0.987267 | − | 0.159071i | \(-0.949150\pi\) | ||
0.987267 | − | 0.159071i | \(-0.0508497\pi\) | |||||||
\(854\) | −22.9316 | − | 10.1322i | −0.784705 | − | 0.346715i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.53865 | − | 4.39707i | 0.0867693 | − | 0.150289i | ||||
\(857\) | 7.51046 | + | 13.0085i | 0.256552 | + | 0.444362i | 0.965316 | − | 0.261084i | \(-0.0840801\pi\) |
−0.708764 | + | 0.705446i | \(0.750747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.6855 | + | 16.5616i | 0.978737 | + | 0.565074i | 0.901889 | − | 0.431969i | \(-0.142181\pi\) |
0.0768486 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(860\) | 11.1707 | 0.380916 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.65307 | 0.0903640 | ||||||||
\(863\) | −8.04372 | − | 4.64405i | −0.273812 | − | 0.158085i | 0.356807 | − | 0.934178i | \(-0.383865\pi\) |
−0.630619 | + | 0.776093i | \(0.717199\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.4543 | − | 40.6241i | −0.797471 | − | 1.38126i | ||||
\(866\) | 10.6556 | − | 18.4561i | 0.362092 | − | 0.627162i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.19546 | + | 0.452971i | −0.142403 | + | 0.0153748i | ||||
\(869\) | 15.2069i | 0.515859i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.904899 | + | 0.522443i | −0.0306613 | + | 0.0177023i | ||||
\(872\) | 1.40878 | − | 0.813357i | 0.0477071 | − | 0.0275437i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.61852i | − | 0.0547473i | ||||||
\(875\) | −15.0436 | + | 10.9950i | −0.508566 | + | 0.371698i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.74463 | − | 13.4141i | 0.261518 | − | 0.452962i | −0.705128 | − | 0.709080i | \(-0.749110\pi\) |
0.966645 | + | 0.256118i | \(0.0824437\pi\) | |||||||
\(878\) | −6.45704 | − | 11.1839i | −0.217915 | − | 0.377439i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.35797 | + | 1.36138i | 0.0794873 | + | 0.0458920i | ||||
\(881\) | −33.5368 | −1.12988 | −0.564942 | − | 0.825130i | \(-0.691102\pi\) | ||||
−0.564942 | + | 0.825130i | \(0.691102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5616 | 0.624648 | 0.312324 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312324 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(884\) | −1.03228 | − | 0.595985i | −0.0347192 | − | 0.0200451i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.1063 | − | 20.9687i | −0.406718 | − | 0.704456i | ||||
\(887\) | −11.7850 | + | 20.4122i | −0.395701 | + | 0.685375i | −0.993190 | − | 0.116502i | \(-0.962832\pi\) |
0.597489 | + | 0.801877i | \(0.296165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.42137 | + | 4.69322i | −0.215366 | + | 0.157406i | ||||
\(890\) | 30.9280i | 1.03671i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.41801 | + | 5.43749i | −0.315338 | + | 0.182061i | ||||
\(893\) | 1.95782 | − | 1.13035i | 0.0655159 | − | 0.0378256i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.6596i | 1.05826i | ||||||||
\(896\) | −2.63046 | + | 0.284003i | −0.0878776 | + | 0.00948787i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.48718 | − | 6.03997i | 0.116369 | − | 0.201557i | ||||
\(899\) | −3.32700 | − | 5.76254i | −0.110962 | − | 0.192191i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.42433 | − | 3.70909i | −0.214026 | − | 0.123568i | ||||
\(902\) | −4.29859 | −0.143127 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.08122 | −0.302037 | ||||||||
\(905\) | −24.5087 | − | 14.1501i | −0.814696 | − | 0.470365i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.6867 | + | 44.4907i | 0.852913 | + | 1.47729i | 0.878568 | + | 0.477618i | \(0.158500\pi\) |
−0.0256543 | + | 0.999671i | \(0.508167\pi\) | |||||||
\(908\) | −3.87060 | + | 6.70408i | −0.128450 | + | 0.222483i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.27756 | + | 0.564479i | 0.0423507 | + | 0.0187123i | ||||
\(911\) | − | 14.4547i | − | 0.478906i | −0.970908 | − | 0.239453i | \(-0.923032\pi\) | ||
0.970908 | − | 0.239453i | \(-0.0769681\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.73673 | − | 5.04416i | 0.289144 | − | 0.166937i | ||||
\(914\) | −0.0858810 | + | 0.0495834i | −0.00284069 | + | 0.00164007i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.13189i | 0.169562i | ||||||||
\(917\) | 1.76321 | + | 16.3311i | 0.0582264 | + | 0.539300i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.6474 | + | 39.2265i | −0.747070 | + | 1.29396i | 0.202151 | + | 0.979354i | \(0.435207\pi\) |
−0.949221 | + | 0.314609i | \(0.898127\pi\) | |||||||
\(920\) | −7.08648 | − | 12.2741i | −0.233634 | − | 0.404666i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.1703 | − | 15.1095i | −0.861874 | − | 0.497603i | ||||
\(923\) | 1.86803 | 0.0614869 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6677 | −0.350752 | ||||||||
\(926\) | 27.3829 | + | 15.8095i | 0.899858 | + | 0.519533i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.08596 | − | 3.61299i | −0.0684749 | − | 0.118602i | ||||
\(929\) | 29.6524 | − | 51.3595i | 0.972865 | − | 1.68505i | 0.286057 | − | 0.958212i | \(-0.407655\pi\) |
0.686808 | − | 0.726839i | \(-0.259011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.60921 | − | 1.46551i | 0.0527396 | − | 0.0480303i | ||||
\(932\) | − | 19.0960i | − | 0.625511i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.9481 | + | 12.6717i | −0.718164 | + | 0.414632i | ||||
\(935\) | 14.4962 | − | 8.36940i | 0.474078 | − | 0.273709i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.2633i | − | 1.25001i | −0.780621 | − | 0.625005i | \(-0.785097\pi\) | ||
0.780621 | − | 0.625005i | \(-0.214903\pi\) | |||||||
\(938\) | 8.41346 | + | 11.5115i | 0.274709 | + | 0.375863i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.89815 | − | 17.1441i | 0.322842 | − | 0.559179i | ||||
\(941\) | −2.04961 | − | 3.55002i | −0.0668152 | − | 0.115727i | 0.830683 | − | 0.556746i | \(-0.187950\pi\) |
−0.897498 | + | 0.441019i | \(0.854617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.3780 | + | 11.1879i | 0.631034 | + | 0.364328i | ||||
\(944\) | −10.8611 | −0.353500 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.10271 | −0.133391 | ||||||||
\(947\) | 19.3014 | + | 11.1437i | 0.627211 | + | 0.362120i | 0.779671 | − | 0.626189i | \(-0.215386\pi\) |
−0.152460 | + | 0.988310i | \(0.548720\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.280091 | − | 0.485131i | −0.00909213 | − | 0.0157480i | ||||
\(950\) | −0.375200 | + | 0.649866i | −0.0121731 | + | 0.0210844i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.57366 | + | 14.8779i | −0.213053 | + | 0.482194i | ||||
\(953\) | − | 6.17864i | − | 0.200146i | −0.994980 | − | 0.100073i | \(-0.968092\pi\) | ||
0.994980 | − | 0.100073i | \(-0.0319076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.0446 | + | 24.2745i | −1.36053 | + | 0.785504i | ||||
\(956\) | 10.7611 | − | 6.21293i | 0.348039 | − | 0.200941i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.6103i | 1.05359i | ||||||||
\(959\) | −10.1525 | + | 22.9776i | −0.327840 | + | 0.741987i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2281 | + | 24.6437i | −0.458970 | + | 0.794959i | ||||
\(962\) | −0.428512 | − | 0.742205i | −0.0138158 | − | 0.0239296i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.5847 | − | 11.3072i | −0.630781 | − | 0.364181i | ||||
\(965\) | −41.7417 | −1.34371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.02187 | 0.0650191 | 0.0325095 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325095 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(968\) | −0.866025 | − | 0.500000i | −0.0278351 | − | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.21990 | + | 15.9693i | 0.296033 | + | 0.512745i | ||||
\(971\) | −8.39201 | + | 14.5354i | −0.269313 | + | 0.466463i | −0.968684 | − | 0.248295i | \(-0.920130\pi\) |
0.699372 | + | 0.714758i | \(0.253463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.6107 | − | 28.2000i | −0.660750 | − | 0.904052i | ||||
\(974\) | 4.11063i | 0.131713i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.20619 | − | 4.73784i | 0.262674 | − | 0.151655i | ||||
\(977\) | −17.2826 | + | 9.97813i | −0.552920 | + | 0.319229i | −0.750299 | − | 0.661099i | \(-0.770090\pi\) |
0.197379 | + | 0.980327i | \(0.436757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.3591i | − | 0.363038i | ||||||
\(980\) | 5.78693 | − | 18.1595i | 0.184857 | − | 0.580084i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.28693 | + | 3.96107i | −0.0729787 | + | 0.126403i | ||||
\(983\) | −9.37668 | − | 16.2409i | −0.299070 | − | 0.518004i | 0.676854 | − | 0.736117i | \(-0.263343\pi\) |
−0.975923 | + | 0.218114i | \(0.930010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.5318 | + | 32.0613i | 1.76939 | + | 1.02156i | ||||
\(986\) | −25.6479 | −0.816796 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0602858 | −0.00191795 | ||||||||
\(989\) | 18.4950 | + | 10.6781i | 0.588106 | + | 0.339543i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.643923 | − | 1.11531i | −0.0204549 | − | 0.0354289i | 0.855617 | − | 0.517610i | \(-0.173178\pi\) |
−0.876072 | + | 0.482181i | \(0.839845\pi\) | |||||||
\(992\) | 0.797476 | − | 1.38127i | 0.0253199 | − | 0.0438553i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.73626 | − | 25.3435i | −0.0867889 | − | 0.803848i | ||||
\(995\) | 36.0327i | 1.14231i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0369 | + | 25.4247i | −1.39466 | + | 0.805208i | −0.993827 | − | 0.110942i | \(-0.964613\pi\) |
−0.400835 | + | 0.916150i | \(0.631280\pi\) | |||||||
\(998\) | 31.7024 | − | 18.3034i | 1.00352 | − | 0.579384i | ||||
\(999\) | 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 | 1386.2.r.d.89.1 | ✓ | 24 | |
3.2 | odd | 2 | inner | 1386.2.r.d.89.12 | yes | 24 | |
7.3 | odd | 6 | inner | 1386.2.r.d.1277.12 | yes | 24 | |
21.17 | even | 6 | inner | 1386.2.r.d.1277.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.d.89.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1386.2.r.d.89.12 | yes | 24 | 3.2 | odd | 2 | inner | |
1386.2.r.d.1277.1 | yes | 24 | 21.17 | even | 6 | inner | |
1386.2.r.d.1277.12 | yes | 24 | 7.3 | odd | 6 | inner |