Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(111,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.111");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.r (of order \(4\), 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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 111.13 | ||
Character | \(\chi\) | \(=\) | 320.111 |
Dual form | 320.3.r.a.271.13 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 2.05924 | − | 2.05924i | 0.686413 | − | 0.686413i | −0.275025 | − | 0.961437i | \(-0.588686\pi\) |
0.961437 | + | 0.275025i | \(0.0886860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58114 | − | 1.58114i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.3931 | −1.48474 | −0.742368 | − | 0.669993i | \(-0.766297\pi\) | ||||
−0.742368 | + | 0.669993i | \(0.766297\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.519079i | 0.0576755i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.0477 | − | 14.0477i | −1.27706 | − | 1.27706i | −0.942304 | − | 0.334759i | \(-0.891345\pi\) |
−0.334759 | − | 0.942304i | \(-0.608655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.77323 | − | 9.77323i | −0.751787 | − | 0.751787i | 0.223026 | − | 0.974813i | \(-0.428407\pi\) |
−0.974813 | + | 0.223026i | \(0.928407\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.51188i | − | 0.434125i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.10104 | 0.417709 | 0.208854 | − | 0.977947i | \(-0.433027\pi\) | ||||
0.208854 | + | 0.977947i | \(0.433027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.6198 | − | 16.6198i | 0.874727 | − | 0.874727i | −0.118256 | − | 0.992983i | \(-0.537730\pi\) |
0.992983 | + | 0.118256i | \(0.0377303\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.4020 | + | 21.4020i | −1.01914 | + | 1.01914i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.8307 | −1.07959 | −0.539797 | − | 0.841795i | \(-0.681499\pi\) | ||||
−0.539797 | + | 0.841795i | \(0.681499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19.6020 | + | 19.6020i | 0.726002 | + | 0.726002i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.2993 | + | 11.2993i | 0.389631 | + | 0.389631i | 0.874556 | − | 0.484925i | \(-0.161153\pi\) |
−0.484925 | + | 0.874556i | \(0.661153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.04353i | − | 0.227211i | −0.993526 | − | 0.113605i | \(-0.963760\pi\) | ||
0.993526 | − | 0.113605i | \(-0.0362399\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −57.8551 | −1.75318 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.4330 | + | 16.4330i | −0.469515 | + | 0.469515i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2634 | − | 11.2634i | 0.304417 | − | 0.304417i | −0.538322 | − | 0.842739i | \(-0.680942\pi\) |
0.842739 | + | 0.538322i | \(0.180942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −40.2508 | −1.03207 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 62.6084i | − | 1.52704i | −0.645787 | − | 0.763518i | \(-0.723471\pi\) | ||
0.645787 | − | 0.763518i | \(-0.276529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 37.0749 | + | 37.0749i | 0.862206 | + | 0.862206i | 0.991594 | − | 0.129388i | \(-0.0413013\pi\) |
−0.129388 | + | 0.991594i | \(0.541301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.820736 | + | 0.820736i | 0.0182386 | + | 0.0182386i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.176089i | − | 0.00374658i | −0.999998 | − | 0.00187329i | \(-0.999404\pi\) | ||
0.999998 | − | 0.00187329i | \(-0.000596286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 59.0176 | 1.20444 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.6227 | − | 14.6227i | 0.286720 | − | 0.286720i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32.3810 | + | 32.3810i | −0.610963 | + | 0.610963i | −0.943197 | − | 0.332234i | \(-0.892198\pi\) |
0.332234 | + | 0.943197i | \(0.392198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −44.4227 | −0.807686 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 68.4483i | − | 1.20085i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25.8843 | − | 25.8843i | −0.438718 | − | 0.438718i | 0.452863 | − | 0.891580i | \(-0.350403\pi\) |
−0.891580 | + | 0.452863i | \(0.850403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.8700 | − | 36.8700i | −0.604426 | − | 0.604426i | 0.337058 | − | 0.941484i | \(-0.390568\pi\) |
−0.941484 | + | 0.337058i | \(0.890568\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.39487i | − | 0.0856328i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −30.9057 | −0.475472 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8767 | − | 12.8767i | 0.192190 | − | 0.192190i | −0.604452 | − | 0.796642i | \(-0.706608\pi\) |
0.796642 | + | 0.604452i | \(0.206608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −51.1323 | + | 51.1323i | −0.741047 | + | 0.741047i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 64.6644 | 0.910767 | 0.455383 | − | 0.890295i | \(-0.349502\pi\) | ||||
0.455383 | + | 0.890295i | \(0.349502\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 19.2006i | − | 0.263022i | −0.991315 | − | 0.131511i | \(-0.958017\pi\) | ||
0.991315 | − | 0.131511i | \(-0.0419828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.2962 | − | 10.2962i | −0.137283 | − | 0.137283i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 146.000 | + | 146.000i | 1.89610 | + | 1.89610i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 48.9106i | 0.619121i | 0.950880 | + | 0.309561i | \(0.100182\pi\) | ||||
−0.950880 | + | 0.309561i | \(0.899818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 76.0588 | 0.938998 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.5930 | − | 18.5930i | 0.224012 | − | 0.224012i | −0.586174 | − | 0.810185i | \(-0.699366\pi\) |
0.810185 | + | 0.586174i | \(0.199366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2277 | − | 11.2277i | 0.132091 | − | 0.132091i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 46.5359 | 0.534895 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 43.4973i | − | 0.488734i | −0.969683 | − | 0.244367i | \(-0.921420\pi\) | ||
0.969683 | − | 0.244367i | \(-0.0785801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 101.575 | + | 101.575i | 1.11620 | + | 1.11620i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.5043 | − | 14.5043i | −0.155960 | − | 0.155960i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 52.5565i | − | 0.553226i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −115.574 | −1.19148 | −0.595741 | − | 0.803177i | \(-0.703141\pi\) | ||||
−0.595741 | + | 0.803177i | \(0.703141\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.29186 | − | 7.29186i | 0.0736552 | − | 0.0736552i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 90.9433 | − | 90.9433i | 0.900428 | − | 0.900428i | −0.0950446 | − | 0.995473i | \(-0.530299\pi\) |
0.995473 | + | 0.0950446i | \(0.0302994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −41.0401 | −0.398447 | −0.199224 | − | 0.979954i | \(-0.563842\pi\) | ||||
−0.199224 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 67.6790i | 0.644562i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 91.4653 | + | 91.4653i | 0.854816 | + | 0.854816i | 0.990722 | − | 0.135906i | \(-0.0433946\pi\) |
−0.135906 | + | 0.990722i | \(0.543395\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 76.9281 | + | 76.9281i | 0.705762 | + | 0.705762i | 0.965641 | − | 0.259879i | \(-0.0836827\pi\) |
−0.259879 | + | 0.965641i | \(0.583683\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 46.3881i | − | 0.417911i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 37.6147 | 0.332873 | 0.166437 | − | 0.986052i | \(-0.446774\pi\) | ||||
0.166437 | + | 0.986052i | \(0.446774\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39.2608 | + | 39.2608i | −0.341398 | + | 0.341398i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.07308 | − | 5.07308i | 0.0433597 | − | 0.0433597i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −73.8022 | −0.620187 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 273.675i | 2.26178i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −128.926 | − | 128.926i | −1.04818 | − | 1.04818i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90569 | − | 7.90569i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 76.6673i | − | 0.603680i | −0.953359 | − | 0.301840i | \(-0.902399\pi\) | ||
0.953359 | − | 0.301840i | \(-0.0976008\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 152.692 | 1.18366 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4149 | − | 12.4149i | 0.0947700 | − | 0.0947700i | −0.658132 | − | 0.752902i | \(-0.728653\pi\) |
0.752902 | + | 0.658132i | \(0.228653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −172.732 | + | 172.732i | −1.29874 | + | 1.29874i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 61.9871 | 0.459164 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 31.3649i | − | 0.228941i | −0.993427 | − | 0.114470i | \(-0.963483\pi\) | ||
0.993427 | − | 0.114470i | \(-0.0365171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.05252 | − | 9.05252i | −0.0651260 | − | 0.0651260i | 0.673794 | − | 0.738920i | \(-0.264664\pi\) |
−0.738920 | + | 0.673794i | \(0.764664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.362609 | − | 0.362609i | −0.00257170 | − | 0.00257170i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 274.583i | 1.92016i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 35.7315 | 0.246424 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 121.531 | − | 121.531i | 0.826743 | − | 0.826743i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 165.486 | − | 165.486i | 1.11064 | − | 1.11064i | 0.117581 | − | 0.993063i | \(-0.462486\pi\) |
0.993063 | − | 0.117581i | \(-0.0375141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 192.683 | 1.27605 | 0.638024 | − | 0.770016i | \(-0.279752\pi\) | ||||
0.638024 | + | 0.770016i | \(0.279752\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.68600i | 0.0240915i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.1368 | − | 11.1368i | −0.0718503 | − | 0.0718503i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.5629 | − | 65.5629i | −0.417598 | − | 0.417598i | 0.466777 | − | 0.884375i | \(-0.345415\pi\) |
−0.884375 | + | 0.466777i | \(0.845415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 133.360i | 0.838745i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 258.069 | 1.60291 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −164.309 | + | 164.309i | −1.00803 | + | 1.00803i | −0.00806604 | + | 0.999967i | \(0.502568\pi\) |
−0.999967 | + | 0.00806604i | \(0.997432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −91.4769 | + | 91.4769i | −0.554406 | + | 0.554406i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −107.045 | −0.640987 | −0.320494 | − | 0.947251i | \(-0.603849\pi\) | ||||
−0.320494 | + | 0.947251i | \(0.603849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.0320i | 0.130367i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.62700 | + | 8.62700i | 0.0504503 | + | 0.0504503i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −216.322 | − | 216.322i | −1.25042 | − | 1.25042i | −0.955533 | − | 0.294886i | \(-0.904718\pi\) |
−0.294886 | − | 0.955533i | \(-0.595282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 51.9657i | 0.296947i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −106.604 | −0.602283 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 149.660 | − | 149.660i | 0.836091 | − | 0.836091i | −0.152251 | − | 0.988342i | \(-0.548652\pi\) |
0.988342 | + | 0.152251i | \(0.0486522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 117.050 | − | 117.050i | 0.646684 | − | 0.646684i | −0.305506 | − | 0.952190i | \(-0.598826\pi\) |
0.952190 | + | 0.305506i | \(0.0988256\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −151.848 | −0.829771 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 35.6180i | − | 0.192530i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −99.7533 | − | 99.7533i | −0.533440 | − | 0.533440i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −203.727 | − | 203.727i | −1.07792 | − | 1.07792i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 264.175i | − | 1.38312i | −0.722321 | − | 0.691558i | \(-0.756925\pi\) | ||
0.722321 | − | 0.691558i | \(-0.243075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −350.764 | −1.81743 | −0.908715 | − | 0.417418i | \(-0.862935\pi\) | ||||
−0.908715 | + | 0.417418i | \(0.862935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −63.6421 | + | 63.6421i | −0.326370 | + | 0.326370i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 165.437 | − | 165.437i | 0.839782 | − | 0.839782i | −0.149048 | − | 0.988830i | \(-0.547621\pi\) |
0.988830 | + | 0.149048i | \(0.0476208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 140.603 | 0.706547 | 0.353274 | − | 0.935520i | \(-0.385068\pi\) | ||||
0.353274 | + | 0.935520i | \(0.385068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 53.0324i | − | 0.263843i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −117.435 | − | 117.435i | −0.578499 | − | 0.578499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −98.9926 | − | 98.9926i | −0.482891 | − | 0.482891i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 12.8891i | − | 0.0622661i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −466.940 | −2.23416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −280.563 | + | 280.563i | −1.32968 | + | 1.32968i | −0.424040 | + | 0.905643i | \(0.639388\pi\) |
−0.905643 | + | 0.424040i | \(0.860612\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 133.159 | − | 133.159i | 0.625162 | − | 0.625162i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 117.241 | 0.545307 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 73.2044i | 0.337348i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −39.5386 | − | 39.5386i | −0.180542 | − | 0.180542i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −69.4001 | − | 69.4001i | −0.314028 | − | 0.314028i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 227.136i | − | 1.01855i | −0.860604 | − | 0.509275i | \(-0.829914\pi\) | ||
0.860604 | − | 0.509275i | \(-0.170086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.59540 | 0.0115351 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.8393 | + | 16.8393i | −0.0741820 | + | 0.0741820i | −0.743224 | − | 0.669042i | \(-0.766704\pi\) |
0.669042 | + | 0.743224i | \(0.266704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −186.956 | + | 186.956i | −0.816400 | + | 0.816400i | −0.985584 | − | 0.169184i | \(-0.945887\pi\) |
0.169184 | + | 0.985584i | \(0.445887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 601.296 | 2.60302 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 43.8154i | 0.188049i | 0.995570 | + | 0.0940245i | \(0.0299732\pi\) | ||||
−0.995570 | + | 0.0940245i | \(0.970027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.278421 | − | 0.278421i | −0.00118477 | − | 0.00118477i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 100.719 | + | 100.719i | 0.424973 | + | 0.424973i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 101.703i | − | 0.425534i | −0.977103 | − | 0.212767i | \(-0.931752\pi\) | ||
0.977103 | − | 0.212767i | \(-0.0682475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101.753 | 0.422211 | 0.211105 | − | 0.977463i | \(-0.432294\pi\) | ||||
0.211105 | + | 0.977463i | \(0.432294\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.7952 | + | 19.7952i | −0.0814617 | + | 0.0814617i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 93.3149 | − | 93.3149i | 0.380877 | − | 0.380877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −324.859 | −1.31522 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 76.5747i | − | 0.307529i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −250.137 | − | 250.137i | −0.996562 | − | 0.996562i | 0.00343190 | − | 0.999994i | \(-0.498908\pi\) |
−0.999994 | + | 0.00343190i | \(0.998908\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 348.814 | + | 348.814i | 1.37871 | + | 1.37871i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 46.2412i | − | 0.181338i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.7854 | −0.119788 | −0.0598938 | − | 0.998205i | \(-0.519076\pi\) | ||||
−0.0598938 | + | 0.998205i | \(0.519076\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −117.062 | + | 117.062i | −0.451978 | + | 0.451978i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.86523 | + | 5.86523i | −0.0224721 | + | 0.0224721i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −33.6453 | −0.127929 | −0.0639644 | − | 0.997952i | \(-0.520374\pi\) | ||||
−0.0639644 | + | 0.997952i | \(0.520374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 102.398i | 0.386407i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −89.5713 | − | 89.5713i | −0.335473 | − | 0.335473i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 181.278 | + | 181.278i | 0.673897 | + | 0.673897i | 0.958612 | − | 0.284715i | \(-0.0918990\pi\) |
−0.284715 | + | 0.958612i | \(0.591899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 116.847i | 0.431172i | 0.976485 | + | 0.215586i | \(0.0691661\pi\) | ||||
−0.976485 | + | 0.215586i | \(0.930834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 418.333 | 1.53235 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −70.2385 | + | 70.2385i | −0.255413 | + | 0.255413i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −147.875 | + | 147.875i | −0.533845 | + | 0.533845i | −0.921714 | − | 0.387870i | \(-0.873211\pi\) |
0.387870 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.65615 | 0.0131045 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 483.500i | 1.72064i | 0.509754 | + | 0.860320i | \(0.329736\pi\) | ||||
−0.509754 | + | 0.860320i | \(0.670264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −63.7806 | − | 63.7806i | −0.225373 | − | 0.225373i | 0.585383 | − | 0.810757i | \(-0.300944\pi\) |
−0.810757 | + | 0.585383i | \(0.800944\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −108.226 | − | 108.226i | −0.379741 | − | 0.379741i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 650.699i | 2.26724i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −238.575 | −0.825520 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −237.994 | + | 237.994i | −0.817848 | + | 0.817848i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 175.050 | − | 175.050i | 0.597440 | − | 0.597440i | −0.342191 | − | 0.939631i | \(-0.611169\pi\) |
0.939631 | + | 0.342191i | \(0.111169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −81.8535 | −0.277469 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 550.727i | − | 1.85430i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 242.676 | + | 242.676i | 0.811625 | + | 0.811625i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −385.325 | − | 385.325i | −1.28015 | − | 1.28015i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 374.548i | − | 1.23613i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −116.593 | −0.382273 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 413.683 | − | 413.683i | 1.34750 | − | 1.34750i | 0.459133 | − | 0.888367i | \(-0.348160\pi\) |
0.888367 | − | 0.459133i | \(-0.151840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −84.5113 | + | 84.5113i | −0.273499 | + | 0.273499i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −363.740 | −1.16958 | −0.584791 | − | 0.811184i | \(-0.698823\pi\) | ||||
−0.584791 | + | 0.811184i | \(0.698823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 281.938i | 0.900760i | 0.892837 | + | 0.450380i | \(0.148712\pi\) | ||||
−0.892837 | + | 0.450380i | \(0.851288\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.53003 | − | 8.53003i | −0.0270795 | − | 0.0270795i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 271.946 | + | 271.946i | 0.857873 | + | 0.857873i | 0.991087 | − | 0.133215i | \(-0.0425299\pi\) |
−0.133215 | + | 0.991087i | \(0.542530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 317.458i | − | 0.995166i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 376.697 | 1.17351 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 118.018 | − | 118.018i | 0.365381 | − | 0.365381i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −48.8661 | + | 48.8661i | −0.150357 | + | 0.150357i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 316.826 | 0.968888 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.83012i | 0.00556267i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 87.1363 | + | 87.1363i | 0.263252 | + | 0.263252i | 0.826374 | − | 0.563122i | \(-0.190400\pi\) |
−0.563122 | + | 0.826374i | \(0.690400\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.84660 | + | 5.84660i | 0.0175574 | + | 0.0175574i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 40.7197i | − | 0.121551i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 480.244 | 1.42506 | 0.712528 | − | 0.701644i | \(-0.247550\pi\) | ||||
0.712528 | + | 0.701644i | \(0.247550\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 77.4576 | − | 77.4576i | 0.228488 | − | 0.228488i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −98.9453 | + | 98.9453i | −0.290162 | + | 0.290162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −104.114 | −0.303539 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 161.694i | 0.468680i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −108.368 | − | 108.368i | −0.312299 | − | 0.312299i | 0.533501 | − | 0.845800i | \(-0.320876\pi\) |
−0.845800 | + | 0.533501i | \(0.820876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 82.3704 | + | 82.3704i | 0.236018 | + | 0.236018i | 0.815199 | − | 0.579181i | \(-0.196627\pi\) |
−0.579181 | + | 0.815199i | \(0.696627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 383.151i | − | 1.09160i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −401.677 | −1.13790 | −0.568948 | − | 0.822373i | \(-0.692650\pi\) | ||||
−0.568948 | + | 0.822373i | \(0.692650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 102.243 | − | 102.243i | 0.288010 | − | 0.288010i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −151.976 | + | 151.976i | −0.425704 | + | 0.425704i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 276.390 | 0.769890 | 0.384945 | − | 0.922940i | \(-0.374220\pi\) | ||||
0.384945 | + | 0.922940i | \(0.374220\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 191.437i | − | 0.530295i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 563.563 | + | 563.563i | 1.55251 | + | 1.55251i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.3588 | − | 30.3588i | −0.0831748 | − | 0.0831748i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 669.742i | 1.82491i | 0.409177 | + | 0.912455i | \(0.365816\pi\) | ||||
−0.409177 | + | 0.912455i | \(0.634184\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.4987 | 0.0880725 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 336.541 | − | 336.541i | 0.907118 | − | 0.907118i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −79.6410 | + | 79.6410i | −0.213515 | + | 0.213515i | −0.805759 | − | 0.592244i | \(-0.798242\pi\) |
0.592244 | + | 0.805759i | \(0.298242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −32.5594 | −0.0868251 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 220.861i | − | 0.585839i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 180.062 | + | 180.062i | 0.475097 | + | 0.475097i | 0.903559 | − | 0.428463i | \(-0.140945\pi\) |
−0.428463 | + | 0.903559i | \(0.640945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −157.876 | − | 157.876i | −0.414373 | − | 0.414373i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 146.777i | 0.383229i | 0.981470 | + | 0.191615i | \(0.0613724\pi\) | ||||
−0.981470 | + | 0.191615i | \(0.938628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 461.692 | 1.19920 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.2448 | + | 19.2448i | −0.0497281 | + | 0.0497281i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 343.044 | − | 343.044i | 0.881861 | − | 0.881861i | −0.111863 | − | 0.993724i | \(-0.535682\pi\) |
0.993724 | + | 0.111863i | \(0.0356818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −176.324 | −0.450956 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 51.1303i | − | 0.130103i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 77.3344 | + | 77.3344i | 0.195783 | + | 0.195783i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −40.3574 | − | 40.3574i | −0.101656 | − | 0.101656i | 0.654450 | − | 0.756106i | \(-0.272900\pi\) |
−0.756106 | + | 0.654450i | \(0.772900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 711.394i | 1.78294i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −451.974 | −1.12712 | −0.563559 | − | 0.826076i | \(-0.690568\pi\) | ||||
−0.563559 | + | 0.826076i | \(0.690568\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −68.8380 | + | 68.8380i | −0.170814 | + | 0.170814i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 120.260 | − | 120.260i | 0.296937 | − | 0.296937i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −316.450 | −0.777518 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 638.957i | − | 1.56224i | −0.624380 | − | 0.781121i | \(-0.714648\pi\) | ||
0.624380 | − | 0.781121i | \(-0.285352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −64.5878 | − | 64.5878i | −0.157148 | − | 0.157148i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 269.020 | + | 269.020i | 0.651380 | + | 0.651380i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 58.7962i | − | 0.141677i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.2826 | −0.0894066 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 244.970 | − | 244.970i | 0.584654 | − | 0.584654i | −0.351525 | − | 0.936179i | \(-0.614337\pi\) |
0.936179 | + | 0.351525i | \(0.114337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −168.087 | + | 168.087i | −0.399256 | + | 0.399256i | −0.877970 | − | 0.478715i | \(-0.841103\pi\) |
0.478715 | + | 0.877970i | \(0.341103\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0914041 | 0.000216085 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 35.5052i | − | 0.0835417i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 383.195 | + | 383.195i | 0.897413 | + | 0.897413i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 565.431 | + | 565.431i | 1.31802 | + | 1.31802i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 62.2481i | − | 0.144427i | −0.997389 | − | 0.0722135i | \(-0.976994\pi\) | ||
0.997389 | − | 0.0722135i | \(-0.0230063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 270.015 | 0.623590 | 0.311795 | − | 0.950149i | \(-0.399070\pi\) | ||||
0.311795 | + | 0.950149i | \(0.399070\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 73.5797 | − | 73.5797i | 0.169149 | − | 0.169149i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −412.681 | + | 412.681i | −0.944351 | + | 0.944351i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −501.545 | −1.14247 | −0.571236 | − | 0.820786i | \(-0.693536\pi\) | ||||
−0.571236 | + | 0.820786i | \(0.693536\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.6348i | 0.0694666i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 72.6881 | + | 72.6881i | 0.164081 | + | 0.164081i | 0.784372 | − | 0.620291i | \(-0.212985\pi\) |
−0.620291 | + | 0.784372i | \(0.712985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −68.7753 | − | 68.7753i | −0.154551 | − | 0.154551i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 681.550i | − | 1.52472i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 270.002 | 0.601342 | 0.300671 | − | 0.953728i | \(-0.402789\pi\) | ||||
0.300671 | + | 0.953728i | \(0.402789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −879.504 | + | 879.504i | −1.95012 | + | 1.95012i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 396.781 | − | 396.781i | 0.875896 | − | 0.875896i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 321.207 | 0.705950 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 764.553i | 1.67298i | 0.547980 | + | 0.836492i | \(0.315397\pi\) | ||||
−0.547980 | + | 0.836492i | \(0.684603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 139.195 | + | 139.195i | 0.303257 | + | 0.303257i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −117.608 | − | 117.608i | −0.255115 | − | 0.255115i | 0.567949 | − | 0.823064i | \(-0.307737\pi\) |
−0.823064 | + | 0.567949i | \(0.807737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 524.036i | 1.13183i | 0.824465 | + | 0.565914i | \(0.191476\pi\) | ||||
−0.824465 | + | 0.565914i | \(0.808524\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −45.8666 | −0.0986379 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 327.269 | − | 327.269i | 0.700789 | − | 0.700789i | −0.263791 | − | 0.964580i | \(-0.584973\pi\) |
0.964580 | + | 0.263791i | \(0.0849728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −133.830 | + | 133.830i | −0.285351 | + | 0.285351i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −270.019 | −0.573289 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1041.63i | − | 2.20218i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −83.0991 | − | 83.0991i | −0.174945 | − | 0.174945i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.8083 | − | 16.8083i | −0.0352375 | − | 0.0352375i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 257.109i | − | 0.536761i | −0.963313 | − | 0.268381i | \(-0.913512\pi\) | ||
0.963313 | − | 0.268381i | \(-0.0864885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −220.160 | −0.457713 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 531.425 | − | 531.425i | 1.10026 | − | 1.10026i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −182.738 | + | 182.738i | −0.376780 | + | 0.376780i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −538.554 | −1.10586 | −0.552930 | − | 0.833227i | \(-0.686490\pi\) | ||||
−0.552930 | + | 0.833227i | \(0.686490\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 676.705i | 1.38385i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.0314 | − | 31.0314i | −0.0632004 | − | 0.0632004i | 0.674800 | − | 0.738001i | \(-0.264230\pi\) |
−0.738001 | + | 0.674800i | \(0.764230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 80.2368 | + | 80.2368i | 0.162752 | + | 0.162752i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 23.0589i | − | 0.0465836i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −672.067 | −1.35225 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −160.845 | + | 160.845i | −0.322335 | + | 0.322335i | −0.849662 | − | 0.527327i | \(-0.823194\pi\) |
0.527327 | + | 0.849662i | \(0.323194\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −220.431 | + | 220.431i | −0.439982 | + | 0.439982i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 787.428 | 1.56546 | 0.782732 | − | 0.622359i | \(-0.213826\pi\) | ||||
0.782732 | + | 0.622359i | \(0.213826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 287.588i | − | 0.569481i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 45.3691 | + | 45.3691i | 0.0894854 | + | 0.0894854i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −108.575 | − | 108.575i | −0.213310 | − | 0.213310i | 0.592362 | − | 0.805672i | \(-0.298196\pi\) |
−0.805672 | + | 0.592362i | \(0.798196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 199.555i | 0.390518i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 651.565 | 1.27011 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −64.8900 | + | 64.8900i | −0.126000 | + | 0.126000i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.47364 | + | 2.47364i | −0.00478461 | + | 0.00478461i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −890.918 | −1.71661 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 294.967i | 0.566156i | 0.959097 | + | 0.283078i | \(0.0913555\pi\) | ||||
−0.959097 | + | 0.283078i | \(0.908645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −95.9563 | − | 95.9563i | −0.183473 | − | 0.183473i | 0.609394 | − | 0.792867i | \(-0.291413\pi\) |
−0.792867 | + | 0.609394i | \(0.791413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 107.010 | + | 107.010i | 0.203828 | + | 0.203828i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 50.0164i | − | 0.0949078i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 87.5627 | 0.165525 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.4360 | − | 13.4360i | 0.0253032 | − | 0.0253032i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −611.887 | + | 611.887i | −1.14800 | + | 1.14800i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 289.239 | 0.540633 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 616.372i | − | 1.14781i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −829.060 | − | 829.060i | −1.53815 | − | 1.53815i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 286.845 | + | 286.845i | 0.530212 | + | 0.530212i | 0.920635 | − | 0.390423i | \(-0.127671\pi\) |
−0.390423 | + | 0.920635i | \(0.627671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 482.067i | − | 0.887784i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 243.268 | 0.446363 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 285.464 | − | 285.464i | 0.521872 | − | 0.521872i | −0.396264 | − | 0.918136i | \(-0.629694\pi\) |
0.918136 | + | 0.396264i | \(0.129694\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.1384 | − | 19.1384i | 0.0348605 | − | 0.0348605i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 375.584 | 0.681641 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 508.335i | − | 0.919231i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −73.3460 | − | 73.3460i | −0.132155 | − | 0.132155i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 168.107 | + | 168.107i | 0.301808 | + | 0.301808i | 0.841721 | − | 0.539913i | \(-0.181543\pi\) |
−0.539913 | + | 0.841721i | \(0.681543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 724.682i | − | 1.29639i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −410.832 | −0.732320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 400.369 | − | 400.369i | 0.711136 | − | 0.711136i | −0.255637 | − | 0.966773i | \(-0.582285\pi\) |
0.966773 | + | 0.255637i | \(0.0822852\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 59.4740 | − | 59.4740i | 0.105264 | − | 0.105264i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −790.491 | −1.39416 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 741.052i | − | 1.30238i | −0.758916 | − | 0.651188i | \(-0.774271\pi\) | ||
0.758916 | − | 0.651188i | \(-0.225729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 91.1623 | + | 91.1623i | 0.159654 | + | 0.159654i | 0.782413 | − | 0.622760i | \(-0.213989\pi\) |
−0.622760 | + | 0.782413i | \(0.713989\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −544.000 | − | 544.000i | −0.949388 | − | 0.949388i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 124.153i | 0.215919i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −725.837 | −1.25795 | −0.628975 | − | 0.777426i | \(-0.716525\pi\) | ||||
−0.628975 | + | 0.777426i | \(0.716525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −722.306 | + | 722.306i | −1.24751 | + | 1.24751i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −193.240 | + | 193.240i | −0.332598 | + | 0.332598i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 909.757 | 1.56048 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 16.0425i | − | 0.0274231i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −327.120 | − | 327.120i | −0.557274 | − | 0.557274i | 0.371256 | − | 0.928530i | \(-0.378927\pi\) |
−0.928530 | + | 0.371256i | \(0.878927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −117.062 | − | 117.062i | −0.198747 | − | 0.198747i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 681.349i | − | 1.15287i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −195.537 | −0.329742 | −0.164871 | − | 0.986315i | \(-0.552721\pi\) | ||||
−0.164871 | + | 0.986315i | \(0.552721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −116.692 | + | 116.692i | −0.196120 | + | 0.196120i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 289.535 | − | 289.535i | 0.484983 | − | 0.484983i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −730.188 | −1.21901 | −0.609506 | − | 0.792782i | \(-0.708632\pi\) | ||||
−0.609506 | + | 0.792782i | \(0.708632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 477.101i | − | 0.793845i | −0.917852 | − | 0.396922i | \(-0.870078\pi\) | ||
0.917852 | − | 0.396922i | \(-0.129922\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.68403 | + | 6.68403i | 0.0110846 | + | 0.0110846i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 432.719 | + | 432.719i | 0.715238 | + | 0.715238i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 810.479i | − | 1.33522i | −0.744511 | − | 0.667610i | \(-0.767317\pi\) | ||
0.744511 | − | 0.667610i | \(-0.232683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −483.654 | −0.794178 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.72096 | + | 1.72096i | −0.00281663 | + | 0.00281663i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 306.486 | − | 306.486i | 0.499976 | − | 0.499976i | −0.411454 | − | 0.911431i | \(-0.634979\pi\) |
0.911431 | + | 0.411454i | \(0.134979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −407.699 | −0.662925 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 241.465i | 0.391353i | 0.980669 | + | 0.195676i | \(0.0626902\pi\) | ||||
−0.980669 | + | 0.195676i | \(0.937310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.0837 | + | 43.0837i | 0.0696022 | + | 0.0696022i | 0.741051 | − | 0.671449i | \(-0.234328\pi\) |
−0.671449 | + | 0.741051i | \(0.734328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −486.732 | − | 486.732i | −0.783788 | − | 0.783788i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 452.074i | 0.725641i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −961.541 | + | 961.541i | −1.53356 | + | 1.53356i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 79.9820 | − | 79.9820i | 0.127157 | − | 0.127157i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −327.143 | −0.518451 | −0.259225 | − | 0.965817i | \(-0.583467\pi\) | ||||
−0.259225 | + | 0.965817i | \(0.583467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1155.49i | 1.82542i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −121.222 | − | 121.222i | −0.190900 | − | 0.190900i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −576.792 | − | 576.792i | −0.905482 | − | 0.905482i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.5660i | 0.0525289i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −267.455 | −0.417246 | −0.208623 | − | 0.977996i | \(-0.566898\pi\) | ||||
−0.208623 | + | 0.977996i | \(0.566898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −324.978 | + | 324.978i | −0.505409 | + | 0.505409i | −0.913114 | − | 0.407704i | \(-0.866329\pi\) |
0.407704 | + | 0.913114i | \(0.366329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 241.427 | − | 241.427i | 0.374306 | − | 0.374306i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 893.197 | 1.38052 | 0.690261 | − | 0.723561i | \(-0.257496\pi\) | ||||
0.690261 | + | 0.723561i | \(0.257496\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 727.231i | 1.12054i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 150.745 | + | 150.745i | 0.231560 | + | 0.231560i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 249.337 | + | 249.337i | 0.381833 | + | 0.381833i | 0.871762 | − | 0.489929i | \(-0.162977\pi\) |
−0.489929 | + | 0.871762i | \(0.662977\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 39.2593i | − | 0.0599378i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.96663 | 0.0151699 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 505.483 | − | 505.483i | 0.767045 | − | 0.767045i | −0.210540 | − | 0.977585i | \(-0.567522\pi\) |
0.977585 | + | 0.210540i | \(0.0675223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 720.088 | − | 720.088i | 1.08939 | − | 1.08939i | 0.0938007 | − | 0.995591i | \(-0.470098\pi\) |
0.995591 | − | 0.0938007i | \(-0.0299016\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −285.823 | −0.431105 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 546.227i | 0.821394i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −280.569 | − | 280.569i | −0.420643 | − | 0.420643i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −467.728 | − | 467.728i | −0.699145 | − | 0.699145i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1035.88i | 1.54378i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 767.329 | 1.14016 | 0.570081 | − | 0.821588i | \(-0.306912\pi\) | ||||
0.570081 | + | 0.821588i | \(0.306912\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 98.0102 | − | 98.0102i | 0.145200 | − | 0.145200i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 650.823 | − | 650.823i | 0.961333 | − | 0.961333i | −0.0379464 | − | 0.999280i | \(-0.512082\pi\) |
0.999280 | + | 0.0379464i | \(0.0120816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1201.18 | 1.76904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 69.3523i | 0.101839i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 147.895 | + | 147.895i | 0.216537 | + | 0.216537i | 0.807038 | − | 0.590500i | \(-0.201070\pi\) |
−0.590500 | + | 0.807038i | \(0.701070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.5922 | − | 49.5922i | −0.0723974 | − | 0.0723974i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 769.972i | 1.12077i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 632.934 | 0.918627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 868.389 | − | 868.389i | 1.25671 | − | 1.25671i | 0.304061 | − | 0.952653i | \(-0.401657\pi\) |
0.952653 | − | 0.304061i | \(-0.0983426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −75.7854 | + | 75.7854i | −0.109358 | + | 0.109358i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.6266 | −0.0411893 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 444.585i | − | 0.637856i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 90.2263 | + | 90.2263i | 0.129079 | + | 0.129079i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 712.136 | + | 712.136i | 1.01589 | + | 1.01589i | 0.999872 | + | 0.0160148i | \(0.00509788\pi\) |
0.0160148 | + | 0.999872i | \(0.494902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 374.392i | − | 0.532563i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.14667 | −0.00162648 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −945.187 | + | 945.187i | −1.33690 | + | 1.33690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −553.104 | + | 553.104i | −0.780118 | + | 0.780118i | −0.979850 | − | 0.199732i | \(-0.935993\pi\) |
0.199732 | + | 0.979850i | \(0.435993\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.3885 | −0.0357081 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 174.896i | 0.245295i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 434.153 | + | 434.153i | 0.607207 | + | 0.607207i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −209.430 | − | 209.430i | −0.292092 | − | 0.292092i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1389.67i | 1.93278i | 0.257084 | + | 0.966389i | \(0.417238\pi\) | ||||
−0.257084 | + | 0.966389i | \(0.582762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 426.536 | 0.591589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 209.533 | − | 209.533i | 0.289811 | − | 0.289811i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 56.4965 | − | 56.4965i | 0.0779262 | − | 0.0779262i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 610.697 | 0.840023 | 0.420012 | − | 0.907519i | \(-0.362026\pi\) | ||||
0.420012 | + | 0.907519i | \(0.362026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 766.056i | 1.05083i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 263.270 | + | 263.270i | 0.360151 | + | 0.360151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −355.943 | − | 355.943i | −0.485597 | − | 0.485597i | 0.421316 | − | 0.906914i | \(-0.361568\pi\) |
−0.906914 | + | 0.421316i | \(0.861568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 384.315i | − | 0.522878i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −361.776 | −0.490876 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 429.694 | − | 429.694i | 0.581453 | − | 0.581453i | −0.353849 | − | 0.935302i | \(-0.615127\pi\) |
0.935302 | + | 0.353849i | \(0.115127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −668.961 | + | 668.961i | −0.902781 | + | 0.902781i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −362.510 | −0.487900 | −0.243950 | − | 0.969788i | \(-0.578443\pi\) | ||||
−0.243950 | + | 0.969788i | \(0.578443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 523.313i | − | 0.702433i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.65123 | + | 9.65123i | 0.0129200 | + | 0.0129200i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −950.612 | − | 950.612i | −1.26918 | − | 1.26918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 718.108i | 0.956202i | 0.878305 | + | 0.478101i | \(0.158675\pi\) | ||||
−0.878305 | + | 0.478101i | \(0.841325\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1030.18 | −1.36811 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 304.659 | − | 304.659i | 0.403522 | − | 0.403522i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −222.303 | + | 222.303i | −0.293664 | + | 0.293664i | −0.838526 | − | 0.544862i | \(-0.816582\pi\) |
0.544862 | + | 0.838526i | \(0.316582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1436.58 | 1.89273 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1319.68i | 1.73414i | 0.498191 | + | 0.867068i | \(0.333998\pi\) | ||||
−0.498191 | + | 0.867068i | \(0.666002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −799.525 | − | 799.525i | −1.04787 | − | 1.04787i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.82808 | + | 5.82808i | 0.00761841 | + | 0.00761841i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 505.947i | 0.659644i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1346.98 | 1.75160 | 0.875800 | − | 0.482674i | \(-0.160334\pi\) | ||||
0.875800 | + | 0.482674i | \(0.160334\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.3945 | + | 63.3945i | −0.0822237 | + | 0.0822237i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 543.589 | − | 543.589i | 0.703220 | − | 0.703220i | −0.261881 | − | 0.965100i | \(-0.584343\pi\) |
0.965100 | + | 0.261881i | \(0.0843426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.2176 | −0.0454421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 482.118i | 0.620487i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1040.54 | − | 1040.54i | −1.33574 | − | 1.33574i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −908.386 | − | 908.386i | −1.16311 | − | 1.16311i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 442.979i | 0.565745i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −207.328 | −0.264112 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.2661 | + | 31.2661i | −0.0397283 | + | 0.0397283i | −0.726692 | − | 0.686964i | \(-0.758943\pi\) |
0.686964 | + | 0.726692i | \(0.258943\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −69.2837 | + | 69.2837i | −0.0878120 | + | 0.0878120i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −390.935 | −0.494229 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 720.677i | 0.908799i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 210.861 | + | 210.861i | 0.265234 | + | 0.265234i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 270.786 | + | 270.786i | 0.339756 | + | 0.339756i | 0.856275 | − | 0.516519i | \(-0.172773\pi\) |
−0.516519 | + | 0.856275i | \(0.672773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.25042i | − | 0.00156498i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.5785 | 0.0281880 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −269.724 | + | 269.724i | −0.335895 | + | 0.335895i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 408.043 | − | 408.043i | 0.506886 | − | 0.506886i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 746.590 | 0.925143 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 544.465i | − | 0.673010i | −0.941682 | − | 0.336505i | \(-0.890755\pi\) | ||
0.941682 | − | 0.336505i | \(-0.109245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −451.927 | − | 451.927i | −0.557246 | − | 0.557246i | 0.371276 | − | 0.928522i | \(-0.378920\pi\) |
−0.928522 | + | 0.371276i | \(0.878920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 240.617 | + | 240.617i | 0.295962 | + | 0.295962i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 519.592i | 0.637536i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1232.35 | 1.50839 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −52.7253 | + | 52.7253i | −0.0643776 | + | 0.0643776i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 433.211 | − | 433.211i | 0.527663 | − | 0.527663i | −0.392212 | − | 0.919875i | \(-0.628290\pi\) |
0.919875 | + | 0.392212i | \(0.128290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 787.997 | 0.957469 | 0.478734 | − | 0.877960i | \(-0.341096\pi\) | ||||
0.478734 | + | 0.877960i | \(0.341096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 289.275i | 0.350637i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 994.198 | + | 994.198i | 1.20217 | + | 1.20217i | 0.973504 | + | 0.228671i | \(0.0734379\pi\) |
0.228671 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 886.683 | + | 886.683i | 1.06958 | + | 1.06958i | 0.997391 | + | 0.0721910i | \(0.0229991\pi\) |
0.0721910 | + | 0.997391i | \(0.477001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 609.019i | 0.732875i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 419.086 | 0.503105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −169.253 | + | 169.253i | −0.202698 | + | 0.202698i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 138.068 | − | 138.068i | 0.164955 | − | 0.164955i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 306.867 | 0.365753 | 0.182876 | − | 0.983136i | \(-0.441459\pi\) | ||||
0.182876 | + | 0.983136i | \(0.441459\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 585.652i | − | 0.696376i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 995.641 | + | 995.641i | 1.18107 | + | 1.18107i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.8356 | + | 34.8356i | 0.0412256 | + | 0.0412256i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2844.35i | − | 3.35814i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −262.679 | −0.309398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −279.678 | + | 279.678i | −0.328647 | + | 0.328647i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 423.675 | − | 423.675i | 0.496688 | − | 0.496688i | −0.413718 | − | 0.910405i | \(-0.635770\pi\) |
0.910405 | + | 0.413718i | \(0.135770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 27.2810 | 0.0319076 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 811.440i | 0.946838i | 0.880837 | + | 0.473419i | \(0.156980\pi\) | ||||
−0.880837 | + | 0.473419i | \(0.843020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 992.394 | + | 992.394i | 1.15529 | + | 1.15529i | 0.985476 | + | 0.169814i | \(0.0543166\pi\) |
0.169814 | + | 0.985476i | \(0.445683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1339.94 | + | 1339.94i | 1.55626 | + | 1.55626i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1479.18i | − | 1.71399i | −0.515322 | − | 0.856997i | \(-0.672328\pi\) | ||
0.515322 | − | 0.856997i | \(-0.327672\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −684.071 | −0.790834 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −491.283 | + | 491.283i | −0.566647 | + | 0.566647i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 687.081 | − | 687.081i | 0.790657 | − | 0.790657i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −251.694 | −0.288971 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 59.9919i | − | 0.0687193i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 82.1651 | + | 82.1651i | 0.0939029 | + | 0.0939029i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 491.849 | + | 491.849i | 0.560831 | + | 0.560831i | 0.929544 | − | 0.368712i | \(-0.120201\pi\) |
−0.368712 | + | 0.929544i | \(0.620201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 720.939i | − | 0.820181i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −508.703 | −0.577416 | −0.288708 | − | 0.957417i | \(-0.593226\pi\) | ||||
−0.288708 | + | 0.957417i | \(0.593226\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −432.055 | + | 432.055i | −0.489304 | + | 0.489304i | −0.908086 | − | 0.418783i | \(-0.862457\pi\) |
0.418783 | + | 0.908086i | \(0.362457\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −168.556 | + | 168.556i | −0.190459 | + | 0.190459i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 147.316 | 0.166083 | 0.0830417 | − | 0.996546i | \(-0.473537\pi\) | ||||
0.0830417 | + | 0.996546i | \(0.473537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 796.815i | 0.896305i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1068.45 | − | 1068.45i | −1.19916 | − | 1.19916i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.92657 | − | 2.92657i | −0.00327723 | − | 0.00327723i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 473.267i | − | 0.528790i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 999.455 | 1.11422 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 79.5869 | − | 79.5869i | 0.0885282 | − | 0.0885282i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −229.939 | + | 229.939i | −0.255204 | + | 0.255204i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1586.95 | −1.75742 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 370.144i | − | 0.408999i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1011.19 | − | 1011.19i | −1.11487 | − | 1.11487i | −0.992483 | − | 0.122386i | \(-0.960945\pi\) |
−0.122386 | − | 0.992483i | \(-0.539055\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47.2068 | + | 47.2068i | 0.0519326 | + | 0.0519326i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 486.973i | − | 0.534547i | −0.963621 | − | 0.267274i | \(-0.913877\pi\) | ||
0.963621 | − | 0.267274i | \(-0.0861227\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −522.377 | −0.572154 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −240.093 | + | 240.093i | −0.262397 | + | 0.262397i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −129.030 | + | 129.030i | −0.140708 | + | 0.140708i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −277.022 | −0.301438 | −0.150719 | − | 0.988577i | \(-0.548159\pi\) | ||||
−0.150719 | + | 0.988577i | \(0.548159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1703.74i | − | 1.84988i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −631.980 | − | 631.980i | −0.684702 | − | 0.684702i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56.3171 | − | 56.3171i | −0.0608833 | − | 0.0608833i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 21.3030i | − | 0.0229806i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1669.27 | −1.79685 | −0.898425 | − | 0.439128i | \(-0.855287\pi\) | ||||
−0.898425 | + | 0.439128i | \(0.855287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 980.861 | − | 980.861i | 1.05356 | − | 1.05356i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −749.027 | + | 749.027i | −0.802815 | + | 0.802815i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −315.448 | −0.337377 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1122.11i | 1.19755i | 0.800917 | + | 0.598776i | \(0.204346\pi\) | ||||
−0.800917 | + | 0.598776i | \(0.795654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 580.577 | + | 580.577i | 0.618293 | + | 0.618293i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 696.516 | + | 696.516i | 0.740187 | + | 0.740187i | 0.972614 | − | 0.232427i | \(-0.0746667\pi\) |
−0.232427 | + | 0.972614i | \(0.574667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1554.61i | 1.64858i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −644.241 | −0.681737 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 65.1524 | − | 65.1524i | 0.0687988 | − | 0.0687988i | −0.671870 | − | 0.740669i | \(-0.734509\pi\) |
0.740669 | + | 0.671870i | \(0.234509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −187.652 | + | 187.652i | −0.197736 | + | 0.197736i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1120.00 | 1.17771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.49818i | 0.00996661i | 0.999988 | + | 0.00498331i | \(0.00158624\pi\) | ||||
−0.999988 | + | 0.00498331i | \(0.998414\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −417.698 | − | 417.698i | −0.437380 | − | 0.437380i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −653.722 | − | 653.722i | −0.683095 | − | 0.683095i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 325.980i | 0.339916i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 911.389 | 0.948375 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −47.4777 | + | 47.4777i | −0.0493019 | + | 0.0493019i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −554.606 | + | 554.606i | −0.574722 | + | 0.574722i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1278.80 | 1.32244 | 0.661222 | − | 0.750190i | \(-0.270038\pi\) | ||||
0.661222 | + | 0.750190i | \(0.270038\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 486.055i | − | 0.501604i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.2611 | − | 37.2611i | −0.0383739 | − | 0.0383739i | 0.687659 | − | 0.726033i | \(-0.258638\pi\) |
−0.726033 | + | 0.687659i | \(0.758638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 94.0842 | + | 94.0842i | 0.0966949 | + | 0.0966949i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 201.254i | 0.206414i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1006.12 | 1.02980 | 0.514902 | − | 0.857249i | \(-0.327828\pi\) | ||||
0.514902 | + | 0.857249i | \(0.327828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −611.037 | + | 611.037i | −0.624144 | + | 0.624144i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.9318 | + | 39.9318i | −0.0407052 | + | 0.0407052i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1218.44 | −1.23951 | −0.619754 | − | 0.784796i | \(-0.712767\pi\) | ||||
−0.619754 | + | 0.784796i | \(0.712767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 523.158i | − | 0.531125i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.76865 | + | 3.76865i | 0.00381829 | + | 0.00381829i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −920.594 | − | 920.594i | −0.930833 | − | 0.930833i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 247.969i | − | 0.250221i | −0.992143 | − | 0.125110i | \(-0.960071\pi\) | ||
0.992143 | − | 0.125110i | \(-0.0399285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 358.869 | 0.361398 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 222.313 | − | 222.313i | 0.223430 | − | 0.223430i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 113.625 | − | 113.625i | 0.113967 | − | 0.113967i | −0.647823 | − | 0.761791i | \(-0.724321\pi\) |
0.761791 | + | 0.647823i | \(0.224321\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 441.572 | 0.442014 |
(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 | 320.3.r.a.111.13 | 32 | ||
4.3 | odd | 2 | 80.3.r.a.51.6 | yes | 32 | ||
8.3 | odd | 2 | 640.3.r.a.351.13 | 32 | |||
8.5 | even | 2 | 640.3.r.b.351.4 | 32 | |||
16.3 | odd | 4 | 640.3.r.b.31.4 | 32 | |||
16.5 | even | 4 | 80.3.r.a.11.6 | ✓ | 32 | ||
16.11 | odd | 4 | inner | 320.3.r.a.271.13 | 32 | ||
16.13 | even | 4 | 640.3.r.a.31.13 | 32 | |||
20.3 | even | 4 | 400.3.k.h.99.3 | 32 | |||
20.7 | even | 4 | 400.3.k.g.99.14 | 32 | |||
20.19 | odd | 2 | 400.3.r.f.51.11 | 32 | |||
80.37 | odd | 4 | 400.3.k.h.299.3 | 32 | |||
80.53 | odd | 4 | 400.3.k.g.299.14 | 32 | |||
80.69 | even | 4 | 400.3.r.f.251.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.r.a.11.6 | ✓ | 32 | 16.5 | even | 4 | ||
80.3.r.a.51.6 | yes | 32 | 4.3 | odd | 2 | ||
320.3.r.a.111.13 | 32 | 1.1 | even | 1 | trivial | ||
320.3.r.a.271.13 | 32 | 16.11 | odd | 4 | inner | ||
400.3.k.g.99.14 | 32 | 20.7 | even | 4 | |||
400.3.k.g.299.14 | 32 | 80.53 | odd | 4 | |||
400.3.k.h.99.3 | 32 | 20.3 | even | 4 | |||
400.3.k.h.299.3 | 32 | 80.37 | odd | 4 | |||
400.3.r.f.51.11 | 32 | 20.19 | odd | 2 | |||
400.3.r.f.251.11 | 32 | 80.69 | even | 4 | |||
640.3.r.a.31.13 | 32 | 16.13 | even | 4 | |||
640.3.r.a.351.13 | 32 | 8.3 | odd | 2 | |||
640.3.r.b.31.4 | 32 | 16.3 | odd | 4 | |||
640.3.r.b.351.4 | 32 | 8.5 | even | 2 |