Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), 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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.2 | ||
Root | \(-0.445042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.z.1351.5 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | 3.35690i | 1.26879i | 0.773010 | + | 0.634394i | \(0.218750\pi\) | ||||
−0.773010 | + | 0.634394i | \(0.781250\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.69202i | 0.510164i | 0.966919 | + | 0.255082i | \(0.0821024\pi\) | ||||
−0.966919 | + | 0.255082i | \(0.917898\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.35690 | 0.897168 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.939001 | −0.227741 | −0.113871 | − | 0.993496i | \(-0.536325\pi\) | ||||
−0.113871 | + | 0.993496i | \(0.536325\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 4.85086i | 1.11286i | 0.830894 | + | 0.556431i | \(0.187830\pi\) | ||||
−0.830894 | + | 0.556431i | \(0.812170\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 3.35690i | 0.732535i | ||||||||
\(22\) | 1.69202 | 0.360740 | ||||||||
\(23\) | −4.04892 | −0.844258 | −0.422129 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422129 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 3.35690i | − 0.634394i | ||||||||
\(29\) | −8.12498 | −1.50877 | −0.754386 | − | 0.656432i | \(-0.772065\pi\) | ||||
−0.754386 | + | 0.656432i | \(0.772065\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 4.08815i | − 0.734253i | −0.930171 | − | 0.367126i | \(-0.880342\pi\) | ||||
0.930171 | − | 0.367126i | \(-0.119658\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 1.69202i | 0.294543i | ||||||||
\(34\) | 0.939001i | 0.161037i | ||||||||
\(35\) | −3.35690 | −0.567419 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 11.6310i | 1.91213i | 0.293157 | + | 0.956064i | \(0.405294\pi\) | ||||
−0.293157 | + | 0.956064i | \(0.594706\pi\) | |||||||
\(38\) | 4.85086 | 0.786913 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | − 3.86294i | − 0.603289i | −0.953420 | − | 0.301645i | \(-0.902464\pi\) | ||||
0.953420 | − | 0.301645i | \(-0.0975356\pi\) | |||||||
\(42\) | 3.35690 | 0.517980 | ||||||||
\(43\) | −4.02177 | −0.613314 | −0.306657 | − | 0.951820i | \(-0.599210\pi\) | ||||
−0.306657 | + | 0.951820i | \(0.599210\pi\) | |||||||
\(44\) | − 1.69202i | − 0.255082i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 4.04892i | 0.596980i | ||||||||
\(47\) | − 1.27413i | − 0.185850i | −0.995673 | − | 0.0929252i | \(-0.970378\pi\) | ||||
0.995673 | − | 0.0929252i | \(-0.0296218\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.26875 | −0.609821 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −0.939001 | −0.131486 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.74094 | 0.788579 | 0.394289 | − | 0.918986i | \(-0.370991\pi\) | ||||
0.394289 | + | 0.918986i | \(0.370991\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | −1.69202 | −0.228152 | ||||||||
\(56\) | −3.35690 | −0.448584 | ||||||||
\(57\) | 4.85086i | 0.642511i | ||||||||
\(58\) | 8.12498i | 1.06686i | ||||||||
\(59\) | 0.417895i | 0.0544053i | 0.999630 | + | 0.0272026i | \(0.00865994\pi\) | ||||
−0.999630 | + | 0.0272026i | \(0.991340\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | 0.198062 | 0.0253593 | 0.0126796 | − | 0.999920i | \(-0.495964\pi\) | ||||
0.0126796 | + | 0.999920i | \(0.495964\pi\) | |||||||
\(62\) | −4.08815 | −0.519195 | ||||||||
\(63\) | 3.35690i | 0.422929i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.69202 | 0.208273 | ||||||||
\(67\) | − 8.93900i | − 1.09207i | −0.837761 | − | 0.546036i | \(-0.816136\pi\) | ||||
0.837761 | − | 0.546036i | \(-0.183864\pi\) | |||||||
\(68\) | 0.939001 | 0.113871 | ||||||||
\(69\) | −4.04892 | −0.487432 | ||||||||
\(70\) | 3.35690i | 0.401226i | ||||||||
\(71\) | 5.15883i | 0.612241i | 0.951993 | + | 0.306120i | \(0.0990310\pi\) | ||||
−0.951993 | + | 0.306120i | \(0.900969\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 11.5308i | − 1.34958i | −0.738011 | − | 0.674789i | \(-0.764235\pi\) | ||||
0.738011 | − | 0.674789i | \(-0.235765\pi\) | |||||||
\(74\) | 11.6310 | 1.35208 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | − 4.85086i | − 0.556431i | ||||||||
\(77\) | −5.67994 | −0.647289 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.94869 | −0.556771 | −0.278386 | − | 0.960469i | \(-0.589799\pi\) | ||||
−0.278386 | + | 0.960469i | \(0.589799\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.86294 | −0.426590 | ||||||||
\(83\) | − 13.1739i | − 1.44602i | −0.690836 | − | 0.723012i | \(-0.742757\pi\) | ||||
0.690836 | − | 0.723012i | \(-0.257243\pi\) | |||||||
\(84\) | − 3.35690i | − 0.366267i | ||||||||
\(85\) | − 0.939001i | − 0.101849i | ||||||||
\(86\) | 4.02177i | 0.433679i | ||||||||
\(87\) | −8.12498 | −0.871089 | ||||||||
\(88\) | −1.69202 | −0.180370 | ||||||||
\(89\) | − 9.47650i | − 1.00451i | −0.864720 | − | 0.502254i | \(-0.832504\pi\) | ||||
0.864720 | − | 0.502254i | \(-0.167496\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.04892 | 0.422129 | ||||||||
\(93\) | − 4.08815i | − 0.423921i | ||||||||
\(94\) | −1.27413 | −0.131416 | ||||||||
\(95\) | −4.85086 | −0.497687 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | − 15.4547i | − 1.56919i | −0.620009 | − | 0.784595i | \(-0.712871\pi\) | ||||
0.620009 | − | 0.784595i | \(-0.287129\pi\) | |||||||
\(98\) | 4.26875i | 0.431209i | ||||||||
\(99\) | 1.69202i | 0.170055i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.38404 | −0.535732 | −0.267866 | − | 0.963456i | \(-0.586318\pi\) | ||||
−0.267866 | + | 0.963456i | \(0.586318\pi\) | |||||||
\(102\) | 0.939001i | 0.0929750i | ||||||||
\(103\) | −4.08575 | −0.402581 | −0.201291 | − | 0.979532i | \(-0.564514\pi\) | ||||
−0.201291 | + | 0.979532i | \(0.564514\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.35690 | −0.327599 | ||||||||
\(106\) | − 5.74094i | − 0.557609i | ||||||||
\(107\) | −16.1196 | −1.55834 | −0.779171 | − | 0.626812i | \(-0.784359\pi\) | ||||
−0.779171 | + | 0.626812i | \(0.784359\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 14.2325i | 1.36323i | 0.731713 | + | 0.681613i | \(0.238721\pi\) | ||||
−0.731713 | + | 0.681613i | \(0.761279\pi\) | |||||||
\(110\) | 1.69202i | 0.161328i | ||||||||
\(111\) | 11.6310i | 1.10397i | ||||||||
\(112\) | 3.35690i | 0.317197i | ||||||||
\(113\) | −13.3274 | −1.25373 | −0.626866 | − | 0.779127i | \(-0.715663\pi\) | ||||
−0.626866 | + | 0.779127i | \(0.715663\pi\) | |||||||
\(114\) | 4.85086 | 0.454324 | ||||||||
\(115\) | − 4.04892i | − 0.377563i | ||||||||
\(116\) | 8.12498 | 0.754386 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.417895 | 0.0384703 | ||||||||
\(119\) | − 3.15213i | − 0.288955i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 8.13706 | 0.739733 | ||||||||
\(122\) | − 0.198062i | − 0.0179317i | ||||||||
\(123\) | − 3.86294i | − 0.348309i | ||||||||
\(124\) | 4.08815i | 0.367126i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 3.35690 | 0.299056 | ||||||||
\(127\) | 12.8509 | 1.14033 | 0.570164 | − | 0.821531i | \(-0.306879\pi\) | ||||
0.570164 | + | 0.821531i | \(0.306879\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.02177 | −0.354097 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.570024 | −0.0498032 | −0.0249016 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249016 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(132\) | − 1.69202i | − 0.147272i | ||||||||
\(133\) | −16.2838 | −1.41199 | ||||||||
\(134\) | −8.93900 | −0.772212 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 0.939001i | − 0.0805187i | ||||||||
\(137\) | 21.5405i | 1.84033i | 0.391533 | + | 0.920164i | \(0.371945\pi\) | ||||
−0.391533 | + | 0.920164i | \(0.628055\pi\) | |||||||
\(138\) | 4.04892i | 0.344667i | ||||||||
\(139\) | 7.09783 | 0.602030 | 0.301015 | − | 0.953619i | \(-0.402674\pi\) | ||||
0.301015 | + | 0.953619i | \(0.402674\pi\) | |||||||
\(140\) | 3.35690 | 0.283709 | ||||||||
\(141\) | − 1.27413i | − 0.107301i | ||||||||
\(142\) | 5.15883 | 0.432920 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 8.12498i | − 0.674743i | ||||||||
\(146\) | −11.5308 | −0.954295 | ||||||||
\(147\) | −4.26875 | −0.352081 | ||||||||
\(148\) | − 11.6310i | − 0.956064i | ||||||||
\(149\) | 1.14914i | 0.0941416i | 0.998892 | + | 0.0470708i | \(0.0149886\pi\) | ||||
−0.998892 | + | 0.0470708i | \(0.985011\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 0.0217703i | 0.00177164i | 1.00000 | 0.000885819i | \(0.000281965\pi\) | |||||
−1.00000 | 0.000885819i | \(0.999718\pi\) | ||||||||
\(152\) | −4.85086 | −0.393456 | ||||||||
\(153\) | −0.939001 | −0.0759137 | ||||||||
\(154\) | 5.67994i | 0.457703i | ||||||||
\(155\) | 4.08815 | 0.328368 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1588 | −0.810763 | −0.405382 | − | 0.914148i | \(-0.632861\pi\) | ||||
−0.405382 | + | 0.914148i | \(0.632861\pi\) | |||||||
\(158\) | 4.94869i | 0.393697i | ||||||||
\(159\) | 5.74094 | 0.455286 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | − 13.5918i | − 1.07118i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 19.1511i | 1.50003i | 0.661422 | + | 0.750014i | \(0.269953\pi\) | ||||
−0.661422 | + | 0.750014i | \(0.730047\pi\) | |||||||
\(164\) | 3.86294i | 0.301645i | ||||||||
\(165\) | −1.69202 | −0.131724 | ||||||||
\(166\) | −13.1739 | −1.02249 | ||||||||
\(167\) | − 15.2174i | − 1.17756i | −0.808293 | − | 0.588780i | \(-0.799608\pi\) | ||||
0.808293 | − | 0.588780i | \(-0.200392\pi\) | |||||||
\(168\) | −3.35690 | −0.258990 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.939001 | −0.0720181 | ||||||||
\(171\) | 4.85086i | 0.370954i | ||||||||
\(172\) | 4.02177 | 0.306657 | ||||||||
\(173\) | −21.8213 | −1.65904 | −0.829522 | − | 0.558474i | \(-0.811387\pi\) | ||||
−0.829522 | + | 0.558474i | \(0.811387\pi\) | |||||||
\(174\) | 8.12498i | 0.615953i | ||||||||
\(175\) | − 3.35690i | − 0.253757i | ||||||||
\(176\) | 1.69202i | 0.127541i | ||||||||
\(177\) | 0.417895i | 0.0314109i | ||||||||
\(178\) | −9.47650 | −0.710294 | ||||||||
\(179\) | 20.2513 | 1.51365 | 0.756826 | − | 0.653616i | \(-0.226749\pi\) | ||||
0.756826 | + | 0.653616i | \(0.226749\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −14.4969 | −1.07755 | −0.538775 | − | 0.842450i | \(-0.681113\pi\) | ||||
−0.538775 | + | 0.842450i | \(0.681113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.198062 | 0.0146412 | ||||||||
\(184\) | − 4.04892i | − 0.298490i | ||||||||
\(185\) | −11.6310 | −0.855130 | ||||||||
\(186\) | −4.08815 | −0.299757 | ||||||||
\(187\) | − 1.58881i | − 0.116185i | ||||||||
\(188\) | 1.27413i | 0.0929252i | ||||||||
\(189\) | 3.35690i | 0.244178i | ||||||||
\(190\) | 4.85086i | 0.351918i | ||||||||
\(191\) | −10.1806 | −0.736643 | −0.368321 | − | 0.929699i | \(-0.620067\pi\) | ||||
−0.368321 | + | 0.929699i | \(0.620067\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 27.6407i | 1.98962i | 0.101741 | + | 0.994811i | \(0.467559\pi\) | ||||
−0.101741 | + | 0.994811i | \(0.532441\pi\) | |||||||
\(194\) | −15.4547 | −1.10958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.26875 | 0.304911 | ||||||||
\(197\) | 13.0261i | 0.928070i | 0.885817 | + | 0.464035i | \(0.153599\pi\) | ||||
−0.885817 | + | 0.464035i | \(0.846401\pi\) | |||||||
\(198\) | 1.69202 | 0.120247 | ||||||||
\(199\) | −6.67563 | −0.473223 | −0.236611 | − | 0.971604i | \(-0.576037\pi\) | ||||
−0.236611 | + | 0.971604i | \(0.576037\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | − 8.93900i | − 0.630509i | ||||||||
\(202\) | 5.38404i | 0.378820i | ||||||||
\(203\) | − 27.2747i | − 1.91431i | ||||||||
\(204\) | 0.939001 | 0.0657432 | ||||||||
\(205\) | 3.86294 | 0.269799 | ||||||||
\(206\) | 4.08575i | 0.284668i | ||||||||
\(207\) | −4.04892 | −0.281419 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.20775 | −0.567742 | ||||||||
\(210\) | 3.35690i | 0.231648i | ||||||||
\(211\) | −11.3056 | −0.778309 | −0.389154 | − | 0.921173i | \(-0.627233\pi\) | ||||
−0.389154 | + | 0.921173i | \(0.627233\pi\) | |||||||
\(212\) | −5.74094 | −0.394289 | ||||||||
\(213\) | 5.15883i | 0.353477i | ||||||||
\(214\) | 16.1196i | 1.10191i | ||||||||
\(215\) | − 4.02177i | − 0.274282i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 13.7235 | 0.931611 | ||||||||
\(218\) | 14.2325 | 0.963947 | ||||||||
\(219\) | − 11.5308i | − 0.779179i | ||||||||
\(220\) | 1.69202 | 0.114076 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.6310 | 0.780623 | ||||||||
\(223\) | − 18.0911i | − 1.21147i | −0.795666 | − | 0.605736i | \(-0.792879\pi\) | ||||
0.795666 | − | 0.605736i | \(-0.207121\pi\) | |||||||
\(224\) | 3.35690 | 0.224292 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 13.3274i | 0.886523i | ||||||||
\(227\) | 9.37196i | 0.622039i | 0.950404 | + | 0.311019i | \(0.100670\pi\) | ||||
−0.950404 | + | 0.311019i | \(0.899330\pi\) | |||||||
\(228\) | − 4.85086i | − 0.321256i | ||||||||
\(229\) | 21.2664i | 1.40532i | 0.711526 | + | 0.702660i | \(0.248005\pi\) | ||||
−0.711526 | + | 0.702660i | \(0.751995\pi\) | |||||||
\(230\) | −4.04892 | −0.266978 | ||||||||
\(231\) | −5.67994 | −0.373713 | ||||||||
\(232\) | − 8.12498i | − 0.533431i | ||||||||
\(233\) | −2.03146 | −0.133085 | −0.0665427 | − | 0.997784i | \(-0.521197\pi\) | ||||
−0.0665427 | + | 0.997784i | \(0.521197\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.27413 | 0.0831149 | ||||||||
\(236\) | − 0.417895i | − 0.0272026i | ||||||||
\(237\) | −4.94869 | −0.321452 | ||||||||
\(238\) | −3.15213 | −0.204322 | ||||||||
\(239\) | 11.9903i | 0.775589i | 0.921746 | + | 0.387794i | \(0.126763\pi\) | ||||
−0.921746 | + | 0.387794i | \(0.873237\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 21.7627i | 1.40186i | 0.713230 | + | 0.700930i | \(0.247231\pi\) | ||||
−0.713230 | + | 0.700930i | \(0.752769\pi\) | |||||||
\(242\) | − 8.13706i | − 0.523070i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.198062 | −0.0126796 | ||||||||
\(245\) | − 4.26875i | − 0.272720i | ||||||||
\(246\) | −3.86294 | −0.246292 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.08815 | 0.259598 | ||||||||
\(249\) | − 13.1739i | − 0.834862i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −13.7506 | −0.867932 | −0.433966 | − | 0.900929i | \(-0.642886\pi\) | ||||
−0.433966 | + | 0.900929i | \(0.642886\pi\) | |||||||
\(252\) | − 3.35690i | − 0.211465i | ||||||||
\(253\) | − 6.85086i | − 0.430710i | ||||||||
\(254\) | − 12.8509i | − 0.806334i | ||||||||
\(255\) | − 0.939001i | − 0.0588025i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.1782 | 1.50820 | 0.754098 | − | 0.656762i | \(-0.228075\pi\) | ||||
0.754098 | + | 0.656762i | \(0.228075\pi\) | |||||||
\(258\) | 4.02177i | 0.250384i | ||||||||
\(259\) | −39.0441 | −2.42608 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.12498 | −0.502924 | ||||||||
\(262\) | 0.570024i | 0.0352162i | ||||||||
\(263\) | 0.960771 | 0.0592437 | 0.0296218 | − | 0.999561i | \(-0.490570\pi\) | ||||
0.0296218 | + | 0.999561i | \(0.490570\pi\) | |||||||
\(264\) | −1.69202 | −0.104137 | ||||||||
\(265\) | 5.74094i | 0.352663i | ||||||||
\(266\) | 16.2838i | 0.998425i | ||||||||
\(267\) | − 9.47650i | − 0.579952i | ||||||||
\(268\) | 8.93900i | 0.546036i | ||||||||
\(269\) | 10.0761 | 0.614348 | 0.307174 | − | 0.951653i | \(-0.400617\pi\) | ||||
0.307174 | + | 0.951653i | \(0.400617\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 14.9584i | − 0.908657i | −0.890834 | − | 0.454328i | \(-0.849879\pi\) | ||||
0.890834 | − | 0.454328i | \(-0.150121\pi\) | |||||||
\(272\) | −0.939001 | −0.0569353 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.5405 | 1.30131 | ||||||||
\(275\) | − 1.69202i | − 0.102033i | ||||||||
\(276\) | 4.04892 | 0.243716 | ||||||||
\(277\) | 13.0465 | 0.783890 | 0.391945 | − | 0.919989i | \(-0.371802\pi\) | ||||
0.391945 | + | 0.919989i | \(0.371802\pi\) | |||||||
\(278\) | − 7.09783i | − 0.425700i | ||||||||
\(279\) | − 4.08815i | − 0.244751i | ||||||||
\(280\) | − 3.35690i | − 0.200613i | ||||||||
\(281\) | 16.2881i | 0.971668i | 0.874051 | + | 0.485834i | \(0.161484\pi\) | ||||
−0.874051 | + | 0.485834i | \(0.838516\pi\) | |||||||
\(282\) | −1.27413 | −0.0758731 | ||||||||
\(283\) | 12.3773 | 0.735756 | 0.367878 | − | 0.929874i | \(-0.380084\pi\) | ||||
0.367878 | + | 0.929874i | \(0.380084\pi\) | |||||||
\(284\) | − 5.15883i | − 0.306120i | ||||||||
\(285\) | −4.85086 | −0.287340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9675 | 0.765446 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −16.1183 | −0.948134 | ||||||||
\(290\) | −8.12498 | −0.477115 | ||||||||
\(291\) | − 15.4547i | − 0.905972i | ||||||||
\(292\) | 11.5308i | 0.674789i | ||||||||
\(293\) | − 1.73663i | − 0.101455i | −0.998713 | − | 0.0507274i | \(-0.983846\pi\) | ||||
0.998713 | − | 0.0507274i | \(-0.0161540\pi\) | |||||||
\(294\) | 4.26875i | 0.248959i | ||||||||
\(295\) | −0.417895 | −0.0243308 | ||||||||
\(296\) | −11.6310 | −0.676039 | ||||||||
\(297\) | 1.69202i | 0.0981810i | ||||||||
\(298\) | 1.14914 | 0.0665682 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − 13.5007i | − 0.778165i | ||||||||
\(302\) | 0.0217703 | 0.00125274 | ||||||||
\(303\) | −5.38404 | −0.309305 | ||||||||
\(304\) | 4.85086i | 0.278216i | ||||||||
\(305\) | 0.198062i | 0.0113410i | ||||||||
\(306\) | 0.939001i | 0.0536791i | ||||||||
\(307\) | 25.4403i | 1.45195i | 0.687720 | + | 0.725976i | \(0.258612\pi\) | ||||
−0.687720 | + | 0.725976i | \(0.741388\pi\) | |||||||
\(308\) | 5.67994 | 0.323645 | ||||||||
\(309\) | −4.08575 | −0.232430 | ||||||||
\(310\) | − 4.08815i | − 0.232191i | ||||||||
\(311\) | 10.0325 | 0.568892 | 0.284446 | − | 0.958692i | \(-0.408190\pi\) | ||||
0.284446 | + | 0.958692i | \(0.408190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.3274 | −1.26202 | −0.631008 | − | 0.775776i | \(-0.717359\pi\) | ||||
−0.631008 | + | 0.775776i | \(0.717359\pi\) | |||||||
\(314\) | 10.1588i | 0.573296i | ||||||||
\(315\) | −3.35690 | −0.189140 | ||||||||
\(316\) | 4.94869 | 0.278386 | ||||||||
\(317\) | 5.33811i | 0.299818i | 0.988700 | + | 0.149909i | \(0.0478981\pi\) | ||||
−0.988700 | + | 0.149909i | \(0.952102\pi\) | |||||||
\(318\) | − 5.74094i | − 0.321936i | ||||||||
\(319\) | − 13.7476i | − 0.769720i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | −16.1196 | −0.899709 | ||||||||
\(322\) | −13.5918 | −0.757441 | ||||||||
\(323\) | − 4.55496i | − 0.253445i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.1511 | 1.06068 | ||||||||
\(327\) | 14.2325i | 0.787059i | ||||||||
\(328\) | 3.86294 | 0.213295 | ||||||||
\(329\) | 4.27711 | 0.235805 | ||||||||
\(330\) | 1.69202i | 0.0931427i | ||||||||
\(331\) | 4.49827i | 0.247247i | 0.992329 | + | 0.123624i | \(0.0394516\pi\) | ||||
−0.992329 | + | 0.123624i | \(0.960548\pi\) | |||||||
\(332\) | 13.1739i | 0.723012i | ||||||||
\(333\) | 11.6310i | 0.637376i | ||||||||
\(334\) | −15.2174 | −0.832661 | ||||||||
\(335\) | 8.93900 | 0.488390 | ||||||||
\(336\) | 3.35690i | 0.183134i | ||||||||
\(337\) | 11.5676 | 0.630129 | 0.315064 | − | 0.949070i | \(-0.397974\pi\) | ||||
0.315064 | + | 0.949070i | \(0.397974\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.3274 | −0.723843 | ||||||||
\(340\) | 0.939001i | 0.0509245i | ||||||||
\(341\) | 6.91723 | 0.374589 | ||||||||
\(342\) | 4.85086 | 0.262304 | ||||||||
\(343\) | 9.16852i | 0.495054i | ||||||||
\(344\) | − 4.02177i | − 0.216839i | ||||||||
\(345\) | − 4.04892i | − 0.217986i | ||||||||
\(346\) | 21.8213i | 1.17312i | ||||||||
\(347\) | 27.1226 | 1.45602 | 0.728008 | − | 0.685568i | \(-0.240446\pi\) | ||||
0.728008 | + | 0.685568i | \(0.240446\pi\) | |||||||
\(348\) | 8.12498 | 0.435545 | ||||||||
\(349\) | 12.8562i | 0.688178i | 0.938937 | + | 0.344089i | \(0.111812\pi\) | ||||
−0.938937 | + | 0.344089i | \(0.888188\pi\) | |||||||
\(350\) | −3.35690 | −0.179434 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.69202 | 0.0901850 | ||||||||
\(353\) | − 24.6262i | − 1.31072i | −0.755316 | − | 0.655361i | \(-0.772516\pi\) | ||||
0.755316 | − | 0.655361i | \(-0.227484\pi\) | |||||||
\(354\) | 0.417895 | 0.0222109 | ||||||||
\(355\) | −5.15883 | −0.273802 | ||||||||
\(356\) | 9.47650i | 0.502254i | ||||||||
\(357\) | − 3.15213i | − 0.166828i | ||||||||
\(358\) | − 20.2513i | − 1.07031i | ||||||||
\(359\) | − 23.8629i | − 1.25944i | −0.776823 | − | 0.629719i | \(-0.783170\pi\) | ||||
0.776823 | − | 0.629719i | \(-0.216830\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −4.53079 | −0.238463 | ||||||||
\(362\) | 14.4969i | 0.761942i | ||||||||
\(363\) | 8.13706 | 0.427085 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5308 | 0.603549 | ||||||||
\(366\) | − 0.198062i | − 0.0103529i | ||||||||
\(367\) | 33.1933 | 1.73267 | 0.866337 | − | 0.499459i | \(-0.166468\pi\) | ||||
0.866337 | + | 0.499459i | \(0.166468\pi\) | |||||||
\(368\) | −4.04892 | −0.211064 | ||||||||
\(369\) | − 3.86294i | − 0.201096i | ||||||||
\(370\) | 11.6310i | 0.604668i | ||||||||
\(371\) | 19.2717i | 1.00054i | ||||||||
\(372\) | 4.08815i | 0.211960i | ||||||||
\(373\) | −10.8465 | −0.561613 | −0.280806 | − | 0.959764i | \(-0.590602\pi\) | ||||
−0.280806 | + | 0.959764i | \(0.590602\pi\) | |||||||
\(374\) | −1.58881 | −0.0821554 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | 1.27413 | 0.0657081 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.35690 | 0.172660 | ||||||||
\(379\) | 6.09485i | 0.313071i | 0.987672 | + | 0.156536i | \(0.0500326\pi\) | ||||
−0.987672 | + | 0.156536i | \(0.949967\pi\) | |||||||
\(380\) | 4.85086 | 0.248844 | ||||||||
\(381\) | 12.8509 | 0.658369 | ||||||||
\(382\) | 10.1806i | 0.520885i | ||||||||
\(383\) | 7.95407i | 0.406434i | 0.979134 | + | 0.203217i | \(0.0651397\pi\) | ||||
−0.979134 | + | 0.203217i | \(0.934860\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 5.67994i | − 0.289477i | ||||||||
\(386\) | 27.6407 | 1.40688 | ||||||||
\(387\) | −4.02177 | −0.204438 | ||||||||
\(388\) | 15.4547i | 0.784595i | ||||||||
\(389\) | −1.50365 | −0.0762380 | −0.0381190 | − | 0.999273i | \(-0.512137\pi\) | ||||
−0.0381190 | + | 0.999273i | \(0.512137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.80194 | 0.192272 | ||||||||
\(392\) | − 4.26875i | − 0.215604i | ||||||||
\(393\) | −0.570024 | −0.0287539 | ||||||||
\(394\) | 13.0261 | 0.656245 | ||||||||
\(395\) | − 4.94869i | − 0.248996i | ||||||||
\(396\) | − 1.69202i | − 0.0850273i | ||||||||
\(397\) | 34.9627i | 1.75473i | 0.479826 | + | 0.877364i | \(0.340700\pi\) | ||||
−0.479826 | + | 0.877364i | \(0.659300\pi\) | |||||||
\(398\) | 6.67563i | 0.334619i | ||||||||
\(399\) | −16.2838 | −0.815210 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 31.1148i | − 1.55380i | −0.629624 | − | 0.776900i | \(-0.716791\pi\) | ||||
0.629624 | − | 0.776900i | \(-0.283209\pi\) | |||||||
\(402\) | −8.93900 | −0.445837 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.38404 | 0.267866 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −27.2747 | −1.35362 | ||||||||
\(407\) | −19.6799 | −0.975498 | ||||||||
\(408\) | − 0.939001i | − 0.0464875i | ||||||||
\(409\) | 32.7318i | 1.61849i | 0.587474 | + | 0.809243i | \(0.300122\pi\) | ||||
−0.587474 | + | 0.809243i | \(0.699878\pi\) | |||||||
\(410\) | − 3.86294i | − 0.190777i | ||||||||
\(411\) | 21.5405i | 1.06251i | ||||||||
\(412\) | 4.08575 | 0.201291 | ||||||||
\(413\) | −1.40283 | −0.0690287 | ||||||||
\(414\) | 4.04892i | 0.198993i | ||||||||
\(415\) | 13.1739 | 0.646681 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.09783 | 0.347582 | ||||||||
\(418\) | 8.20775i | 0.401454i | ||||||||
\(419\) | 13.0694 | 0.638480 | 0.319240 | − | 0.947674i | \(-0.396572\pi\) | ||||
0.319240 | + | 0.947674i | \(0.396572\pi\) | |||||||
\(420\) | 3.35690 | 0.163800 | ||||||||
\(421\) | − 16.4789i | − 0.803132i | −0.915830 | − | 0.401566i | \(-0.868466\pi\) | ||||
0.915830 | − | 0.401566i | \(-0.131534\pi\) | |||||||
\(422\) | 11.3056i | 0.550347i | ||||||||
\(423\) | − 1.27413i | − 0.0619502i | ||||||||
\(424\) | 5.74094i | 0.278805i | ||||||||
\(425\) | 0.939001 | 0.0455482 | ||||||||
\(426\) | 5.15883 | 0.249946 | ||||||||
\(427\) | 0.664874i | 0.0321755i | ||||||||
\(428\) | 16.1196 | 0.779171 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.02177 | −0.193947 | ||||||||
\(431\) | 41.0640i | 1.97798i | 0.147974 | + | 0.988991i | \(0.452725\pi\) | ||||
−0.147974 | + | 0.988991i | \(0.547275\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 6.04593 | 0.290549 | 0.145275 | − | 0.989391i | \(-0.453593\pi\) | ||||
0.145275 | + | 0.989391i | \(0.453593\pi\) | |||||||
\(434\) | − 13.7235i | − 0.658748i | ||||||||
\(435\) | − 8.12498i | − 0.389563i | ||||||||
\(436\) | − 14.2325i | − 0.681613i | ||||||||
\(437\) | − 19.6407i | − 0.939543i | ||||||||
\(438\) | −11.5308 | −0.550963 | ||||||||
\(439\) | 26.2543 | 1.25305 | 0.626524 | − | 0.779402i | \(-0.284477\pi\) | ||||
0.626524 | + | 0.779402i | \(0.284477\pi\) | |||||||
\(440\) | − 1.69202i | − 0.0806640i | ||||||||
\(441\) | −4.26875 | −0.203274 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.3846 | −1.87122 | −0.935610 | − | 0.353035i | \(-0.885150\pi\) | ||||
−0.935610 | + | 0.353035i | \(0.885150\pi\) | |||||||
\(444\) | − 11.6310i | − 0.551984i | ||||||||
\(445\) | 9.47650 | 0.449229 | ||||||||
\(446\) | −18.0911 | −0.856640 | ||||||||
\(447\) | 1.14914i | 0.0543527i | ||||||||
\(448\) | − 3.35690i | − 0.158598i | ||||||||
\(449\) | − 9.39075i | − 0.443177i | −0.975140 | − | 0.221588i | \(-0.928876\pi\) | ||||
0.975140 | − | 0.221588i | \(-0.0711241\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 6.53617 | 0.307776 | ||||||||
\(452\) | 13.3274 | 0.626866 | ||||||||
\(453\) | 0.0217703i | 0.00102286i | ||||||||
\(454\) | 9.37196 | 0.439848 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.85086 | −0.227162 | ||||||||
\(457\) | 2.66487i | 0.124658i | 0.998056 | + | 0.0623288i | \(0.0198527\pi\) | ||||
−0.998056 | + | 0.0623288i | \(0.980147\pi\) | |||||||
\(458\) | 21.2664 | 0.993712 | ||||||||
\(459\) | −0.939001 | −0.0438288 | ||||||||
\(460\) | 4.04892i | 0.188782i | ||||||||
\(461\) | 24.5284i | 1.14240i | 0.820810 | + | 0.571201i | \(0.193522\pi\) | ||||
−0.820810 | + | 0.571201i | \(0.806478\pi\) | |||||||
\(462\) | 5.67994i | 0.264255i | ||||||||
\(463\) | − 4.50498i | − 0.209364i | −0.994506 | − | 0.104682i | \(-0.966618\pi\) | ||||
0.994506 | − | 0.104682i | \(-0.0333825\pi\) | |||||||
\(464\) | −8.12498 | −0.377193 | ||||||||
\(465\) | 4.08815 | 0.189583 | ||||||||
\(466\) | 2.03146i | 0.0941055i | ||||||||
\(467\) | −21.3317 | −0.987112 | −0.493556 | − | 0.869714i | \(-0.664303\pi\) | ||||
−0.493556 | + | 0.869714i | \(0.664303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.0073 | 1.38561 | ||||||||
\(470\) | − 1.27413i | − 0.0587711i | ||||||||
\(471\) | −10.1588 | −0.468094 | ||||||||
\(472\) | −0.417895 | −0.0192352 | ||||||||
\(473\) | − 6.80492i | − 0.312891i | ||||||||
\(474\) | 4.94869i | 0.227301i | ||||||||
\(475\) | − 4.85086i | − 0.222572i | ||||||||
\(476\) | 3.15213i | 0.144478i | ||||||||
\(477\) | 5.74094 | 0.262860 | ||||||||
\(478\) | 11.9903 | 0.548424 | ||||||||
\(479\) | − 32.9517i | − 1.50560i | −0.658249 | − | 0.752800i | \(-0.728703\pi\) | ||||
0.658249 | − | 0.752800i | \(-0.271297\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 21.7627 | 0.991264 | ||||||||
\(483\) | − 13.5918i | − 0.618448i | ||||||||
\(484\) | −8.13706 | −0.369867 | ||||||||
\(485\) | 15.4547 | 0.701763 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 9.33034i | 0.422798i | 0.977400 | + | 0.211399i | \(0.0678020\pi\) | ||||
−0.977400 | + | 0.211399i | \(0.932198\pi\) | |||||||
\(488\) | 0.198062i | 0.00896586i | ||||||||
\(489\) | 19.1511i | 0.866041i | ||||||||
\(490\) | −4.26875 | −0.192842 | ||||||||
\(491\) | 20.4349 | 0.922213 | 0.461107 | − | 0.887345i | \(-0.347453\pi\) | ||||
0.461107 | + | 0.887345i | \(0.347453\pi\) | |||||||
\(492\) | 3.86294i | 0.174155i | ||||||||
\(493\) | 7.62937 | 0.343609 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.69202 | −0.0760507 | ||||||||
\(496\) | − 4.08815i | − 0.183563i | ||||||||
\(497\) | −17.3177 | −0.776804 | ||||||||
\(498\) | −13.1739 | −0.590337 | ||||||||
\(499\) | − 3.54958i | − 0.158901i | −0.996839 | − | 0.0794505i | \(-0.974683\pi\) | ||||
0.996839 | − | 0.0794505i | \(-0.0253166\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − 15.2174i | − 0.679865i | ||||||||
\(502\) | 13.7506i | 0.613721i | ||||||||
\(503\) | −19.8146 | −0.883490 | −0.441745 | − | 0.897141i | \(-0.645640\pi\) | ||||
−0.441745 | + | 0.897141i | \(0.645640\pi\) | |||||||
\(504\) | −3.35690 | −0.149528 | ||||||||
\(505\) | − 5.38404i | − 0.239587i | ||||||||
\(506\) | −6.85086 | −0.304558 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.8509 | −0.570164 | ||||||||
\(509\) | − 32.4325i | − 1.43754i | −0.695246 | − | 0.718772i | \(-0.744704\pi\) | ||||
0.695246 | − | 0.718772i | \(-0.255296\pi\) | |||||||
\(510\) | −0.939001 | −0.0415797 | ||||||||
\(511\) | 38.7077 | 1.71233 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 4.85086i | 0.214170i | ||||||||
\(514\) | − 24.1782i | − 1.06646i | ||||||||
\(515\) | − 4.08575i | − 0.180040i | ||||||||
\(516\) | 4.02177 | 0.177049 | ||||||||
\(517\) | 2.15585 | 0.0948142 | ||||||||
\(518\) | 39.0441i | 1.71550i | ||||||||
\(519\) | −21.8213 | −0.957849 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.87694 | 0.345095 | 0.172547 | − | 0.985001i | \(-0.444800\pi\) | ||||
0.172547 | + | 0.985001i | \(0.444800\pi\) | |||||||
\(522\) | 8.12498i | 0.355621i | ||||||||
\(523\) | −23.4276 | −1.02442 | −0.512208 | − | 0.858861i | \(-0.671172\pi\) | ||||
−0.512208 | + | 0.858861i | \(0.671172\pi\) | |||||||
\(524\) | 0.570024 | 0.0249016 | ||||||||
\(525\) | − 3.35690i | − 0.146507i | ||||||||
\(526\) | − 0.960771i | − 0.0418916i | ||||||||
\(527\) | 3.83877i | 0.167220i | ||||||||
\(528\) | 1.69202i | 0.0736358i | ||||||||
\(529\) | −6.60627 | −0.287229 | ||||||||
\(530\) | 5.74094 | 0.249370 | ||||||||
\(531\) | 0.417895i | 0.0181351i | ||||||||
\(532\) | 16.2838 | 0.705993 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.47650 | −0.410088 | ||||||||
\(535\) | − 16.1196i | − 0.696911i | ||||||||
\(536\) | 8.93900 | 0.386106 | ||||||||
\(537\) | 20.2513 | 0.873908 | ||||||||
\(538\) | − 10.0761i | − 0.434410i | ||||||||
\(539\) | − 7.22282i | − 0.311109i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 1.21552i | − 0.0522593i | −0.999659 | − | 0.0261297i | \(-0.991682\pi\) | ||||
0.999659 | − | 0.0261297i | \(-0.00831828\pi\) | |||||||
\(542\) | −14.9584 | −0.642517 | ||||||||
\(543\) | −14.4969 | −0.622123 | ||||||||
\(544\) | 0.939001i | 0.0402593i | ||||||||
\(545\) | −14.2325 | −0.609654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1371 | −0.647214 | −0.323607 | − | 0.946192i | \(-0.604896\pi\) | ||||
−0.323607 | + | 0.946192i | \(0.604896\pi\) | |||||||
\(548\) | − 21.5405i | − 0.920164i | ||||||||
\(549\) | 0.198062 | 0.00845309 | ||||||||
\(550\) | −1.69202 | −0.0721480 | ||||||||
\(551\) | − 39.4131i | − 1.67905i | ||||||||
\(552\) | − 4.04892i | − 0.172333i | ||||||||
\(553\) | − 16.6122i | − 0.706424i | ||||||||
\(554\) | − 13.0465i | − 0.554294i | ||||||||
\(555\) | −11.6310 | −0.493709 | ||||||||
\(556\) | −7.09783 | −0.301015 | ||||||||
\(557\) | 0.147817i | 0.00626321i | 0.999995 | + | 0.00313160i | \(0.000996822\pi\) | ||||
−0.999995 | + | 0.00313160i | \(0.999003\pi\) | |||||||
\(558\) | −4.08815 | −0.173065 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.35690 | −0.141855 | ||||||||
\(561\) | − 1.58881i | − 0.0670796i | ||||||||
\(562\) | 16.2881 | 0.687073 | ||||||||
\(563\) | −40.6945 | −1.71507 | −0.857535 | − | 0.514426i | \(-0.828005\pi\) | ||||
−0.857535 | + | 0.514426i | \(0.828005\pi\) | |||||||
\(564\) | 1.27413i | 0.0536504i | ||||||||
\(565\) | − 13.3274i | − 0.560686i | ||||||||
\(566\) | − 12.3773i | − 0.520258i | ||||||||
\(567\) | 3.35690i | 0.140976i | ||||||||
\(568\) | −5.15883 | −0.216460 | ||||||||
\(569\) | 26.2433 | 1.10017 | 0.550087 | − | 0.835107i | \(-0.314594\pi\) | ||||
0.550087 | + | 0.835107i | \(0.314594\pi\) | |||||||
\(570\) | 4.85086i | 0.203180i | ||||||||
\(571\) | −2.31575 | −0.0969110 | −0.0484555 | − | 0.998825i | \(-0.515430\pi\) | ||||
−0.0484555 | + | 0.998825i | \(0.515430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.1806 | −0.425301 | ||||||||
\(574\) | − 12.9675i | − 0.541252i | ||||||||
\(575\) | 4.04892 | 0.168852 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 14.5241i | 0.604646i | 0.953206 | + | 0.302323i | \(0.0977621\pi\) | ||||
−0.953206 | + | 0.302323i | \(0.902238\pi\) | |||||||
\(578\) | 16.1183i | 0.670432i | ||||||||
\(579\) | 27.6407i | 1.14871i | ||||||||
\(580\) | 8.12498i | 0.337372i | ||||||||
\(581\) | 44.2234 | 1.83470 | ||||||||
\(582\) | −15.4547 | −0.640619 | ||||||||
\(583\) | 9.71379i | 0.402304i | ||||||||
\(584\) | 11.5308 | 0.477148 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.73663 | −0.0717394 | ||||||||
\(587\) | 32.9028i | 1.35804i | 0.734119 | + | 0.679021i | \(0.237596\pi\) | ||||
−0.734119 | + | 0.679021i | \(0.762404\pi\) | |||||||
\(588\) | 4.26875 | 0.176040 | ||||||||
\(589\) | 19.8310 | 0.817122 | ||||||||
\(590\) | 0.417895i | 0.0172045i | ||||||||
\(591\) | 13.0261i | 0.535821i | ||||||||
\(592\) | 11.6310i | 0.478032i | ||||||||
\(593\) | − 36.0146i | − 1.47894i | −0.673188 | − | 0.739471i | \(-0.735076\pi\) | ||||
0.673188 | − | 0.739471i | \(-0.264924\pi\) | |||||||
\(594\) | 1.69202 | 0.0694245 | ||||||||
\(595\) | 3.15213 | 0.129225 | ||||||||
\(596\) | − 1.14914i | − 0.0470708i | ||||||||
\(597\) | −6.67563 | −0.273215 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.4644 | −1.20388 | −0.601942 | − | 0.798540i | \(-0.705606\pi\) | ||||
−0.601942 | + | 0.798540i | \(0.705606\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | −28.4004 | −1.15848 | −0.579239 | − | 0.815158i | \(-0.696650\pi\) | ||||
−0.579239 | + | 0.815158i | \(0.696650\pi\) | |||||||
\(602\) | −13.5007 | −0.550246 | ||||||||
\(603\) | − 8.93900i | − 0.364024i | ||||||||
\(604\) | − 0.0217703i | 0 0.000885819i | ||||||||
\(605\) | 8.13706i | 0.330819i | ||||||||
\(606\) | 5.38404i | 0.218712i | ||||||||
\(607\) | 15.6450 | 0.635012 | 0.317506 | − | 0.948256i | \(-0.397155\pi\) | ||||
0.317506 | + | 0.948256i | \(0.397155\pi\) | |||||||
\(608\) | 4.85086 | 0.196728 | ||||||||
\(609\) | − 27.2747i | − 1.10523i | ||||||||
\(610\) | 0.198062 | 0.00801931 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.939001 | 0.0379569 | ||||||||
\(613\) | 17.6329i | 0.712188i | 0.934450 | + | 0.356094i | \(0.115892\pi\) | ||||
−0.934450 | + | 0.356094i | \(0.884108\pi\) | |||||||
\(614\) | 25.4403 | 1.02669 | ||||||||
\(615\) | 3.86294 | 0.155769 | ||||||||
\(616\) | − 5.67994i | − 0.228851i | ||||||||
\(617\) | − 10.8582i | − 0.437133i | −0.975822 | − | 0.218566i | \(-0.929862\pi\) | ||||
0.975822 | − | 0.218566i | \(-0.0701380\pi\) | |||||||
\(618\) | 4.08575i | 0.164353i | ||||||||
\(619\) | − 34.2083i | − 1.37495i | −0.726208 | − | 0.687475i | \(-0.758719\pi\) | ||||
0.726208 | − | 0.687475i | \(-0.241281\pi\) | |||||||
\(620\) | −4.08815 | −0.164184 | ||||||||
\(621\) | −4.04892 | −0.162477 | ||||||||
\(622\) | − 10.0325i | − 0.402268i | ||||||||
\(623\) | 31.8116 | 1.27451 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.3274i | 0.892381i | ||||||||
\(627\) | −8.20775 | −0.327786 | ||||||||
\(628\) | 10.1588 | 0.405382 | ||||||||
\(629\) | − 10.9215i | − 0.435470i | ||||||||
\(630\) | 3.35690i | 0.133742i | ||||||||
\(631\) | 31.9571i | 1.27219i | 0.771611 | + | 0.636095i | \(0.219451\pi\) | ||||
−0.771611 | + | 0.636095i | \(0.780549\pi\) | |||||||
\(632\) | − 4.94869i | − 0.196848i | ||||||||
\(633\) | −11.3056 | −0.449357 | ||||||||
\(634\) | 5.33811 | 0.212003 | ||||||||
\(635\) | 12.8509i | 0.509971i | ||||||||
\(636\) | −5.74094 | −0.227643 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.7476 | −0.544274 | ||||||||
\(639\) | 5.15883i | 0.204080i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 45.8297 | 1.81016 | 0.905082 | − | 0.425238i | \(-0.139810\pi\) | ||||
0.905082 | + | 0.425238i | \(0.139810\pi\) | |||||||
\(642\) | 16.1196i | 0.636190i | ||||||||
\(643\) | − 20.6418i | − 0.814032i | −0.913421 | − | 0.407016i | \(-0.866569\pi\) | ||||
0.913421 | − | 0.407016i | \(-0.133431\pi\) | |||||||
\(644\) | 13.5918i | 0.535592i | ||||||||
\(645\) | − 4.02177i | − 0.158357i | ||||||||
\(646\) | −4.55496 | −0.179212 | ||||||||
\(647\) | −1.40389 | −0.0551928 | −0.0275964 | − | 0.999619i | \(-0.508785\pi\) | ||||
−0.0275964 | + | 0.999619i | \(0.508785\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −0.707087 | −0.0277556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.7235 | 0.537866 | ||||||||
\(652\) | − 19.1511i | − 0.750014i | ||||||||
\(653\) | −4.54229 | −0.177753 | −0.0888767 | − | 0.996043i | \(-0.528328\pi\) | ||||
−0.0888767 | + | 0.996043i | \(0.528328\pi\) | |||||||
\(654\) | 14.2325 | 0.556535 | ||||||||
\(655\) | − 0.570024i | − 0.0222727i | ||||||||
\(656\) | − 3.86294i | − 0.150822i | ||||||||
\(657\) | − 11.5308i | − 0.449859i | ||||||||
\(658\) | − 4.27711i | − 0.166739i | ||||||||
\(659\) | 17.4161 | 0.678435 | 0.339217 | − | 0.940708i | \(-0.389838\pi\) | ||||
0.339217 | + | 0.940708i | \(0.389838\pi\) | |||||||
\(660\) | 1.69202 | 0.0658618 | ||||||||
\(661\) | 43.3682i | 1.68683i | 0.537263 | + | 0.843415i | \(0.319458\pi\) | ||||
−0.537263 | + | 0.843415i | \(0.680542\pi\) | |||||||
\(662\) | 4.49827 | 0.174830 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.1739 | 0.511246 | ||||||||
\(665\) | − 16.2838i | − 0.631459i | ||||||||
\(666\) | 11.6310 | 0.450693 | ||||||||
\(667\) | 32.8974 | 1.27379 | ||||||||
\(668\) | 15.2174i | 0.588780i | ||||||||
\(669\) | − 18.0911i | − 0.699443i | ||||||||
\(670\) | − 8.93900i | − 0.345344i | ||||||||
\(671\) | 0.335126i | 0.0129374i | ||||||||
\(672\) | 3.35690 | 0.129495 | ||||||||
\(673\) | 3.49875 | 0.134867 | 0.0674334 | − | 0.997724i | \(-0.478519\pi\) | ||||
0.0674334 | + | 0.997724i | \(0.478519\pi\) | |||||||
\(674\) | − 11.5676i | − 0.445568i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3284 | −0.512253 | −0.256126 | − | 0.966643i | \(-0.582446\pi\) | ||||
−0.256126 | + | 0.966643i | \(0.582446\pi\) | |||||||
\(678\) | 13.3274i | 0.511834i | ||||||||
\(679\) | 51.8799 | 1.99097 | ||||||||
\(680\) | 0.939001 | 0.0360090 | ||||||||
\(681\) | 9.37196i | 0.359134i | ||||||||
\(682\) | − 6.91723i | − 0.264874i | ||||||||
\(683\) | − 24.1739i | − 0.924989i | −0.886622 | − | 0.462494i | \(-0.846955\pi\) | ||||
0.886622 | − | 0.462494i | \(-0.153045\pi\) | |||||||
\(684\) | − 4.85086i | − 0.185477i | ||||||||
\(685\) | −21.5405 | −0.823020 | ||||||||
\(686\) | 9.16852 | 0.350056 | ||||||||
\(687\) | 21.2664i | 0.811362i | ||||||||
\(688\) | −4.02177 | −0.153329 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.04892 | −0.154140 | ||||||||
\(691\) | 37.8810i | 1.44106i | 0.693423 | + | 0.720530i | \(0.256102\pi\) | ||||
−0.693423 | + | 0.720530i | \(0.743898\pi\) | |||||||
\(692\) | 21.8213 | 0.829522 | ||||||||
\(693\) | −5.67994 | −0.215763 | ||||||||
\(694\) | − 27.1226i | − 1.02956i | ||||||||
\(695\) | 7.09783i | 0.269236i | ||||||||
\(696\) | − 8.12498i | − 0.307977i | ||||||||
\(697\) | 3.62730i | 0.137394i | ||||||||
\(698\) | 12.8562 | 0.486616 | ||||||||
\(699\) | −2.03146 | −0.0768368 | ||||||||
\(700\) | 3.35690i | 0.126879i | ||||||||
\(701\) | 21.5967 | 0.815696 | 0.407848 | − | 0.913050i | \(-0.366279\pi\) | ||||
0.407848 | + | 0.913050i | \(0.366279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −56.4204 | −2.12794 | ||||||||
\(704\) | − 1.69202i | − 0.0637705i | ||||||||
\(705\) | 1.27413 | 0.0479864 | ||||||||
\(706\) | −24.6262 | −0.926821 | ||||||||
\(707\) | − 18.0737i | − 0.679730i | ||||||||
\(708\) | − 0.417895i | − 0.0157054i | ||||||||
\(709\) | 41.3062i | 1.55129i | 0.631172 | + | 0.775643i | \(0.282574\pi\) | ||||
−0.631172 | + | 0.775643i | \(0.717426\pi\) | |||||||
\(710\) | 5.15883i | 0.193608i | ||||||||
\(711\) | −4.94869 | −0.185590 | ||||||||
\(712\) | 9.47650 | 0.355147 | ||||||||
\(713\) | 16.5526i | 0.619898i | ||||||||
\(714\) | −3.15213 | −0.117965 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.2513 | −0.756826 | ||||||||
\(717\) | 11.9903i | 0.447786i | ||||||||
\(718\) | −23.8629 | −0.890557 | ||||||||
\(719\) | 35.5338 | 1.32519 | 0.662593 | − | 0.748980i | \(-0.269456\pi\) | ||||
0.662593 | + | 0.748980i | \(0.269456\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − 13.7154i | − 0.510790i | ||||||||
\(722\) | 4.53079i | 0.168619i | ||||||||
\(723\) | 21.7627i | 0.809364i | ||||||||
\(724\) | 14.4969 | 0.538775 | ||||||||
\(725\) | 8.12498 | 0.301754 | ||||||||
\(726\) | − 8.13706i | − 0.301995i | ||||||||
\(727\) | −19.6635 | −0.729281 | −0.364640 | − | 0.931148i | \(-0.618808\pi\) | ||||
−0.364640 | + | 0.931148i | \(0.618808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 11.5308i | − 0.426774i | ||||||||
\(731\) | 3.77645 | 0.139677 | ||||||||
\(732\) | −0.198062 | −0.00732059 | ||||||||
\(733\) | 46.8702i | 1.73119i | 0.500743 | + | 0.865596i | \(0.333060\pi\) | ||||
−0.500743 | + | 0.865596i | \(0.666940\pi\) | |||||||
\(734\) | − 33.1933i | − 1.22519i | ||||||||
\(735\) | − 4.26875i | − 0.157455i | ||||||||
\(736\) | 4.04892i | 0.149245i | ||||||||
\(737\) | 15.1250 | 0.557136 | ||||||||
\(738\) | −3.86294 | −0.142197 | ||||||||
\(739\) | − 8.57779i | − 0.315539i | −0.987476 | − | 0.157770i | \(-0.949570\pi\) | ||||
0.987476 | − | 0.157770i | \(-0.0504303\pi\) | |||||||
\(740\) | 11.6310 | 0.427565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.2717 | 0.707488 | ||||||||
\(743\) | 44.9506i | 1.64908i | 0.565805 | + | 0.824539i | \(0.308565\pi\) | ||||
−0.565805 | + | 0.824539i | \(0.691435\pi\) | |||||||
\(744\) | 4.08815 | 0.149879 | ||||||||
\(745\) | −1.14914 | −0.0421014 | ||||||||
\(746\) | 10.8465i | 0.397120i | ||||||||
\(747\) | − 13.1739i | − 0.482008i | ||||||||
\(748\) | 1.58881i | 0.0580926i | ||||||||
\(749\) | − 54.1118i | − 1.97720i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −44.0374 | −1.60695 | −0.803474 | − | 0.595339i | \(-0.797018\pi\) | ||||
−0.803474 | + | 0.595339i | \(0.797018\pi\) | |||||||
\(752\) | − 1.27413i | − 0.0464626i | ||||||||
\(753\) | −13.7506 | −0.501101 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0217703 | −0.000792301 0 | ||||||||
\(756\) | − 3.35690i | − 0.122089i | ||||||||
\(757\) | −13.2798 | −0.482661 | −0.241331 | − | 0.970443i | \(-0.577584\pi\) | ||||
−0.241331 | + | 0.970443i | \(0.577584\pi\) | |||||||
\(758\) | 6.09485 | 0.221375 | ||||||||
\(759\) | − 6.85086i | − 0.248670i | ||||||||
\(760\) | − 4.85086i | − 0.175959i | ||||||||
\(761\) | 9.11231i | 0.330321i | 0.986267 | + | 0.165160i | \(0.0528142\pi\) | ||||
−0.986267 | + | 0.165160i | \(0.947186\pi\) | |||||||
\(762\) | − 12.8509i | − 0.465537i | ||||||||
\(763\) | −47.7770 | −1.72964 | ||||||||
\(764\) | 10.1806 | 0.368321 | ||||||||
\(765\) | − 0.939001i | − 0.0339497i | ||||||||
\(766\) | 7.95407 | 0.287392 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 31.7784i | 1.14596i | 0.819570 | + | 0.572979i | \(0.194212\pi\) | ||||
−0.819570 | + | 0.572979i | \(0.805788\pi\) | |||||||
\(770\) | −5.67994 | −0.204691 | ||||||||
\(771\) | 24.1782 | 0.870757 | ||||||||
\(772\) | − 27.6407i | − 0.994811i | ||||||||
\(773\) | − 7.11960i | − 0.256074i | −0.991769 | − | 0.128037i | \(-0.959132\pi\) | ||||
0.991769 | − | 0.128037i | \(-0.0408677\pi\) | |||||||
\(774\) | 4.02177i | 0.144560i | ||||||||
\(775\) | 4.08815i | 0.146851i | ||||||||
\(776\) | 15.4547 | 0.554792 | ||||||||
\(777\) | −39.0441 | −1.40070 | ||||||||
\(778\) | 1.50365i | 0.0539084i | ||||||||
\(779\) | 18.7385 | 0.671378 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.72886 | −0.312343 | ||||||||
\(782\) | − 3.80194i | − 0.135957i | ||||||||
\(783\) | −8.12498 | −0.290363 | ||||||||
\(784\) | −4.26875 | −0.152455 | ||||||||
\(785\) | − 10.1588i | − 0.362584i | ||||||||
\(786\) | 0.570024i | 0.0203321i | ||||||||
\(787\) | − 44.2121i | − 1.57599i | −0.615682 | − | 0.787995i | \(-0.711119\pi\) | ||||
0.615682 | − | 0.787995i | \(-0.288881\pi\) | |||||||
\(788\) | − 13.0261i | − 0.464035i | ||||||||
\(789\) | 0.960771 | 0.0342044 | ||||||||
\(790\) | −4.94869 | −0.176066 | ||||||||
\(791\) | − 44.7385i | − 1.59072i | ||||||||
\(792\) | −1.69202 | −0.0601234 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 34.9627 | 1.24078 | ||||||||
\(795\) | 5.74094i | 0.203610i | ||||||||
\(796\) | 6.67563 | 0.236611 | ||||||||
\(797\) | −19.2241 | −0.680954 | −0.340477 | − | 0.940253i | \(-0.610589\pi\) | ||||
−0.340477 | + | 0.940253i | \(0.610589\pi\) | |||||||
\(798\) | 16.2838i | 0.576441i | ||||||||
\(799\) | 1.19641i | 0.0423258i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 9.47650i | − 0.334836i | ||||||||
\(802\) | −31.1148 | −1.09870 | ||||||||
\(803\) | 19.5104 | 0.688505 | ||||||||
\(804\) | 8.93900i | 0.315254i | ||||||||
\(805\) | 13.5918 | 0.479048 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0761 | 0.354694 | ||||||||
\(808\) | − 5.38404i | − 0.189410i | ||||||||
\(809\) | 0.0988996 | 0.00347713 | 0.00173856 | − | 0.999998i | \(-0.499447\pi\) | ||||
0.00173856 | + | 0.999998i | \(0.499447\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 6.70304i | − 0.235376i | −0.993051 | − | 0.117688i | \(-0.962452\pi\) | ||||
0.993051 | − | 0.117688i | \(-0.0375482\pi\) | |||||||
\(812\) | 27.2747i | 0.957155i | ||||||||
\(813\) | − 14.9584i | − 0.524613i | ||||||||
\(814\) | 19.6799i | 0.689782i | ||||||||
\(815\) | −19.1511 | −0.670833 | ||||||||
\(816\) | −0.939001 | −0.0328716 | ||||||||
\(817\) | − 19.5090i | − 0.682534i | ||||||||
\(818\) | 32.7318 | 1.14444 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.86294 | −0.134900 | ||||||||
\(821\) | 23.7450i | 0.828706i | 0.910116 | + | 0.414353i | \(0.135992\pi\) | ||||
−0.910116 | + | 0.414353i | \(0.864008\pi\) | |||||||
\(822\) | 21.5405 | 0.751311 | ||||||||
\(823\) | −18.0049 | −0.627611 | −0.313806 | − | 0.949487i | \(-0.601604\pi\) | ||||
−0.313806 | + | 0.949487i | \(0.601604\pi\) | |||||||
\(824\) | − 4.08575i | − 0.142334i | ||||||||
\(825\) | − 1.69202i | − 0.0589086i | ||||||||
\(826\) | 1.40283i | 0.0488107i | ||||||||
\(827\) | 40.4566i | 1.40682i | 0.710787 | + | 0.703408i | \(0.248339\pi\) | ||||
−0.710787 | + | 0.703408i | \(0.751661\pi\) | |||||||
\(828\) | 4.04892 | 0.140710 | ||||||||
\(829\) | −8.56704 | −0.297546 | −0.148773 | − | 0.988871i | \(-0.547532\pi\) | ||||
−0.148773 | + | 0.988871i | \(0.547532\pi\) | |||||||
\(830\) | − 13.1739i | − 0.457273i | ||||||||
\(831\) | 13.0465 | 0.452579 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00836 | 0.138881 | ||||||||
\(834\) | − 7.09783i | − 0.245778i | ||||||||
\(835\) | 15.2174 | 0.526621 | ||||||||
\(836\) | 8.20775 | 0.283871 | ||||||||
\(837\) | − 4.08815i | − 0.141307i | ||||||||
\(838\) | − 13.0694i | − 0.451474i | ||||||||
\(839\) | − 6.75600i | − 0.233243i | −0.993176 | − | 0.116622i | \(-0.962794\pi\) | ||||
0.993176 | − | 0.116622i | \(-0.0372065\pi\) | |||||||
\(840\) | − 3.35690i | − 0.115824i | ||||||||
\(841\) | 37.0153 | 1.27639 | ||||||||
\(842\) | −16.4789 | −0.567900 | ||||||||
\(843\) | 16.2881i | 0.560993i | ||||||||
\(844\) | 11.3056 | 0.389154 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.27413 | −0.0438054 | ||||||||
\(847\) | 27.3153i | 0.938564i | ||||||||
\(848\) | 5.74094 | 0.197145 | ||||||||
\(849\) | 12.3773 | 0.424789 | ||||||||
\(850\) | − 0.939001i | − 0.0322075i | ||||||||
\(851\) | − 47.0930i | − 1.61433i | ||||||||
\(852\) | − 5.15883i | − 0.176739i | ||||||||
\(853\) | − 37.1269i | − 1.27120i | −0.772018 | − | 0.635600i | \(-0.780753\pi\) | ||||
0.772018 | − | 0.635600i | \(-0.219247\pi\) | |||||||
\(854\) | 0.664874 | 0.0227515 | ||||||||
\(855\) | −4.85086 | −0.165896 | ||||||||
\(856\) | − 16.1196i | − 0.550957i | ||||||||
\(857\) | 24.3937 | 0.833274 | 0.416637 | − | 0.909073i | \(-0.363209\pi\) | ||||
0.416637 | + | 0.909073i | \(0.363209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.9366 | 1.49910 | 0.749549 | − | 0.661949i | \(-0.230270\pi\) | ||||
0.749549 | + | 0.661949i | \(0.230270\pi\) | |||||||
\(860\) | 4.02177i | 0.137141i | ||||||||
\(861\) | 12.9675 | 0.441930 | ||||||||
\(862\) | 41.0640 | 1.39864 | ||||||||
\(863\) | − 16.3846i | − 0.557739i | −0.960329 | − | 0.278870i | \(-0.910040\pi\) | ||||
0.960329 | − | 0.278870i | \(-0.0899598\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 21.8213i | − 0.741947i | ||||||||
\(866\) | − 6.04593i | − 0.205449i | ||||||||
\(867\) | −16.1183 | −0.547405 | ||||||||
\(868\) | −13.7235 | −0.465805 | ||||||||
\(869\) | − 8.37329i | − 0.284044i | ||||||||
\(870\) | −8.12498 | −0.275463 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −14.2325 | −0.481973 | ||||||||
\(873\) | − 15.4547i | − 0.523063i | ||||||||
\(874\) | −19.6407 | −0.664357 | ||||||||
\(875\) | 3.35690 | 0.113484 | ||||||||
\(876\) | 11.5308i | 0.389589i | ||||||||
\(877\) | − 28.1347i | − 0.950040i | −0.879975 | − | 0.475020i | \(-0.842441\pi\) | ||||
0.879975 | − | 0.475020i | \(-0.157559\pi\) | |||||||
\(878\) | − 26.2543i | − 0.886039i | ||||||||
\(879\) | − 1.73663i | − 0.0585750i | ||||||||
\(880\) | −1.69202 | −0.0570380 | ||||||||
\(881\) | −39.1454 | −1.31884 | −0.659421 | − | 0.751773i | \(-0.729199\pi\) | ||||
−0.659421 | + | 0.751773i | \(0.729199\pi\) | |||||||
\(882\) | 4.26875i | 0.143736i | ||||||||
\(883\) | −46.2833 | −1.55756 | −0.778779 | − | 0.627298i | \(-0.784161\pi\) | ||||
−0.778779 | + | 0.627298i | \(0.784161\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.417895 | −0.0140474 | ||||||||
\(886\) | 39.3846i | 1.32315i | ||||||||
\(887\) | −3.08097 | −0.103449 | −0.0517244 | − | 0.998661i | \(-0.516472\pi\) | ||||
−0.0517244 | + | 0.998661i | \(0.516472\pi\) | |||||||
\(888\) | −11.6310 | −0.390312 | ||||||||
\(889\) | 43.1390i | 1.44684i | ||||||||
\(890\) | − 9.47650i | − 0.317653i | ||||||||
\(891\) | 1.69202i | 0.0566849i | ||||||||
\(892\) | 18.0911i | 0.605736i | ||||||||
\(893\) | 6.18060 | 0.206826 | ||||||||
\(894\) | 1.14914 | 0.0384332 | ||||||||
\(895\) | 20.2513i | 0.676926i | ||||||||
\(896\) | −3.35690 | −0.112146 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.39075 | −0.313373 | ||||||||
\(899\) | 33.2161i | 1.10782i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −5.39075 | −0.179592 | ||||||||
\(902\) | − 6.53617i | − 0.217631i | ||||||||
\(903\) | − 13.5007i | − 0.449274i | ||||||||
\(904\) | − 13.3274i | − 0.443261i | ||||||||
\(905\) | − 14.4969i | − 0.481895i | ||||||||
\(906\) | 0.0217703 | 0.000723269 0 | ||||||||
\(907\) | 2.61224 | 0.0867379 | 0.0433689 | − | 0.999059i | \(-0.486191\pi\) | ||||
0.0433689 | + | 0.999059i | \(0.486191\pi\) | |||||||
\(908\) | − 9.37196i | − 0.311019i | ||||||||
\(909\) | −5.38404 | −0.178577 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9302 | 0.825973 | 0.412987 | − | 0.910737i | \(-0.364486\pi\) | ||||
0.412987 | + | 0.910737i | \(0.364486\pi\) | |||||||
\(912\) | 4.85086i | 0.160628i | ||||||||
\(913\) | 22.2905 | 0.737709 | ||||||||
\(914\) | 2.66487 | 0.0881462 | ||||||||
\(915\) | 0.198062i | 0.00654774i | ||||||||
\(916\) | − 21.2664i | − 0.702660i | ||||||||
\(917\) | − 1.91351i | − 0.0631897i | ||||||||
\(918\) | 0.939001i | 0.0309917i | ||||||||
\(919\) | −54.4462 | −1.79602 | −0.898008 | − | 0.439980i | \(-0.854986\pi\) | ||||
−0.898008 | + | 0.439980i | \(0.854986\pi\) | |||||||
\(920\) | 4.04892 | 0.133489 | ||||||||
\(921\) | 25.4403i | 0.838285i | ||||||||
\(922\) | 24.5284 | 0.807800 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5.67994 | 0.186856 | ||||||||
\(925\) | − 11.6310i | − 0.382426i | ||||||||
\(926\) | −4.50498 | −0.148043 | ||||||||
\(927\) | −4.08575 | −0.134194 | ||||||||
\(928\) | 8.12498i | 0.266716i | ||||||||
\(929\) | 40.8267i | 1.33948i | 0.742596 | + | 0.669740i | \(0.233595\pi\) | ||||
−0.742596 | + | 0.669740i | \(0.766405\pi\) | |||||||
\(930\) | − 4.08815i | − 0.134056i | ||||||||
\(931\) | − 20.7071i | − 0.678647i | ||||||||
\(932\) | 2.03146 | 0.0665427 | ||||||||
\(933\) | 10.0325 | 0.328450 | ||||||||
\(934\) | 21.3317i | 0.697993i | ||||||||
\(935\) | 1.58881 | 0.0519596 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.9571 | −1.53402 | −0.767010 | − | 0.641635i | \(-0.778256\pi\) | ||||
−0.767010 | + | 0.641635i | \(0.778256\pi\) | |||||||
\(938\) | − 30.0073i | − 0.979773i | ||||||||
\(939\) | −22.3274 | −0.728626 | ||||||||
\(940\) | −1.27413 | −0.0415574 | ||||||||
\(941\) | − 35.8525i | − 1.16876i | −0.811481 | − | 0.584379i | \(-0.801338\pi\) | ||||
0.811481 | − | 0.584379i | \(-0.198662\pi\) | |||||||
\(942\) | 10.1588i | 0.330993i | ||||||||
\(943\) | 15.6407i | 0.509332i | ||||||||
\(944\) | 0.417895i | 0.0136013i | ||||||||
\(945\) | −3.35690 | −0.109200 | ||||||||
\(946\) | −6.80492 | −0.221247 | ||||||||
\(947\) | − 8.73019i | − 0.283693i | −0.989889 | − | 0.141846i | \(-0.954696\pi\) | ||||
0.989889 | − | 0.141846i | \(-0.0453039\pi\) | |||||||
\(948\) | 4.94869 | 0.160726 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.85086 | −0.157383 | ||||||||
\(951\) | 5.33811i | 0.173100i | ||||||||
\(952\) | 3.15213 | 0.102161 | ||||||||
\(953\) | −10.2107 | −0.330758 | −0.165379 | − | 0.986230i | \(-0.552885\pi\) | ||||
−0.165379 | + | 0.986230i | \(0.552885\pi\) | |||||||
\(954\) | − 5.74094i | − 0.185870i | ||||||||
\(955\) | − 10.1806i | − 0.329437i | ||||||||
\(956\) | − 11.9903i | − 0.387794i | ||||||||
\(957\) | − 13.7476i | − 0.444398i | ||||||||
\(958\) | −32.9517 | −1.06462 | ||||||||
\(959\) | −72.3092 | −2.33498 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 14.2871 | 0.460873 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.1196 | −0.519447 | ||||||||
\(964\) | − 21.7627i | − 0.700930i | ||||||||
\(965\) | −27.6407 | −0.889786 | ||||||||
\(966\) | −13.5918 | −0.437309 | ||||||||
\(967\) | 34.6907i | 1.11558i | 0.829983 | + | 0.557789i | \(0.188350\pi\) | ||||
−0.829983 | + | 0.557789i | \(0.811650\pi\) | |||||||
\(968\) | 8.13706i | 0.261535i | ||||||||
\(969\) | − 4.55496i | − 0.146326i | ||||||||
\(970\) | − 15.4547i | − 0.496221i | ||||||||
\(971\) | 34.8039 | 1.11691 | 0.558454 | − | 0.829535i | \(-0.311395\pi\) | ||||
0.558454 | + | 0.829535i | \(0.311395\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 23.8267i | 0.763849i | ||||||||
\(974\) | 9.33034 | 0.298963 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.198062 | 0.00633982 | ||||||||
\(977\) | − 23.3086i | − 0.745707i | −0.927890 | − | 0.372854i | \(-0.878379\pi\) | ||||
0.927890 | − | 0.372854i | \(-0.121621\pi\) | |||||||
\(978\) | 19.1511 | 0.612383 | ||||||||
\(979\) | 16.0344 | 0.512463 | ||||||||
\(980\) | 4.26875i | 0.136360i | ||||||||
\(981\) | 14.2325i | 0.454409i | ||||||||
\(982\) | − 20.4349i | − 0.652103i | ||||||||
\(983\) | 41.3639i | 1.31930i | 0.751571 | + | 0.659652i | \(0.229296\pi\) | ||||
−0.751571 | + | 0.659652i | \(0.770704\pi\) | |||||||
\(984\) | 3.86294 | 0.123146 | ||||||||
\(985\) | −13.0261 | −0.415045 | ||||||||
\(986\) | − 7.62937i | − 0.242969i | ||||||||
\(987\) | 4.27711 | 0.136142 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.2838 | 0.517795 | ||||||||
\(990\) | 1.69202i | 0.0537760i | ||||||||
\(991\) | 49.4209 | 1.56991 | 0.784953 | − | 0.619555i | \(-0.212687\pi\) | ||||
0.784953 | + | 0.619555i | \(0.212687\pi\) | |||||||
\(992\) | −4.08815 | −0.129799 | ||||||||
\(993\) | 4.49827i | 0.142748i | ||||||||
\(994\) | 17.3177i | 0.549283i | ||||||||
\(995\) | − 6.67563i | − 0.211632i | ||||||||
\(996\) | 13.1739i | 0.417431i | ||||||||
\(997\) | 44.1879 | 1.39944 | 0.699722 | − | 0.714415i | \(-0.253307\pi\) | ||||
0.699722 | + | 0.714415i | \(0.253307\pi\) | |||||||
\(998\) | −3.54958 | −0.112360 | ||||||||
\(999\) | 11.6310i | 0.367989i |
(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 | 5070.2.b.z.1351.2 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bp.1.2 | ✓ | 3 | ||
13.8 | odd | 4 | 5070.2.a.bw.1.2 | yes | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.z.1351.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bp.1.2 | ✓ | 3 | 13.5 | odd | 4 | ||
5070.2.a.bw.1.2 | yes | 3 | 13.8 | odd | 4 | ||
5070.2.b.z.1351.2 | 6 | 1.1 | even | 1 | trivial | ||
5070.2.b.z.1351.5 | 6 | 13.12 | even | 2 | inner |