Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(191,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.h (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: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.5 | ||
Root | \(-0.599676 - 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.191 |
Dual form | 960.2.h.g.191.6 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.468213 | − | 1.66757i | 0.270323 | − | 0.962770i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.936426i | 0.353936i | 0.984217 | + | 0.176968i | \(0.0566289\pi\) | ||||
−0.984217 | + | 0.176968i | \(0.943371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.56155 | − | 1.56155i | −0.853851 | − | 0.520518i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.27156 | −1.28792 | −0.643962 | − | 0.765058i | \(-0.722710\pi\) | ||||
−0.643962 | + | 0.765058i | \(0.722710\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.12311 | −0.866194 | −0.433097 | − | 0.901347i | \(-0.642579\pi\) | ||||
−0.433097 | + | 0.901347i | \(0.642579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.66757 | − | 0.468213i | −0.430564 | − | 0.120892i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.27156i | 0.979963i | 0.871733 | + | 0.489981i | \(0.162996\pi\) | ||||
−0.871733 | + | 0.489981i | \(0.837004\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.56155 | + | 0.438447i | 0.340759 | + | 0.0956770i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.60669 | −1.58610 | −0.793052 | − | 0.609154i | \(-0.791509\pi\) | ||||
−0.793052 | + | 0.609154i | \(0.791509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.80335 | + | 3.54042i | −0.731954 | + | 0.681354i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.12311i | − | 0.951337i | −0.879625 | − | 0.475668i | \(-0.842206\pi\) | ||
0.879625 | − | 0.475668i | \(-0.157794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.39871i | − | 0.430820i | −0.976524 | − | 0.215410i | \(-0.930891\pi\) | ||
0.976524 | − | 0.215410i | \(-0.0691088\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 7.12311i | −0.348155 | + | 1.23997i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.936426 | 0.158285 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.12311 | 0.513435 | 0.256718 | − | 0.966486i | \(-0.417359\pi\) | ||||
0.256718 | + | 0.966486i | \(0.417359\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.46228 | + | 5.20798i | −0.234152 | + | 0.833945i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.12311i | − | 1.11244i | −0.831034 | − | 0.556221i | \(-0.812251\pi\) | ||
0.831034 | − | 0.556221i | \(-0.187749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.46228i | − | 0.222995i | −0.993765 | − | 0.111498i | \(-0.964435\pi\) | ||
0.993765 | − | 0.111498i | \(-0.0355648\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.56155 | + | 2.56155i | −0.232783 | + | 0.381854i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.936426 | 0.136592 | 0.0682959 | − | 0.997665i | \(-0.478244\pi\) | ||||
0.0682959 | + | 0.997665i | \(0.478244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.12311 | 0.874729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.33513 | − | 0.936426i | −0.467012 | − | 0.131126i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24621i | 0.583262i | 0.956531 | + | 0.291631i | \(0.0941979\pi\) | ||||
−0.956531 | + | 0.291631i | \(0.905802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.27156i | 0.575977i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.12311 | + | 2.00000i | 0.943478 | + | 0.264906i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.19612 | −0.936855 | −0.468427 | − | 0.883502i | \(-0.655179\pi\) | ||||
−0.468427 | + | 0.883502i | \(0.655179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.12311 | 0.655946 | 0.327973 | − | 0.944687i | \(-0.393634\pi\) | ||||
0.327973 | + | 0.944687i | \(0.393634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.46228 | − | 2.39871i | 0.184230 | − | 0.302209i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.12311i | 0.387374i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.20798i | − | 0.636257i | −0.948048 | − | 0.318128i | \(-0.896946\pi\) | ||
0.948048 | − | 0.318128i | \(-0.103054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.56155 | + | 12.6847i | −0.428761 | + | 1.52705i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.67026 | −0.791615 | −0.395807 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395807 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.24621 | −0.965146 | −0.482573 | − | 0.875856i | \(-0.660298\pi\) | ||||
−0.482573 | + | 0.875856i | \(0.660298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.468213 | + | 1.66757i | −0.0540646 | + | 0.192554i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.06897i | 1.02034i | 0.860074 | + | 0.510169i | \(0.170417\pi\) | ||||
−0.860074 | + | 0.510169i | \(0.829583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.12311 | + | 8.00000i | 0.458123 | + | 0.888889i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.68213 | −0.513931 | −0.256965 | − | 0.966421i | \(-0.582723\pi\) | ||||
−0.256965 | + | 0.966421i | \(0.582723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.54312 | − | 2.39871i | −0.915918 | − | 0.257168i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.24621i | 0.662097i | 0.943614 | + | 0.331049i | \(0.107402\pi\) | ||||
−0.943614 | + | 0.331049i | \(0.892598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.92456i | − | 0.306577i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | − | 1.12311i | −0.414781 | − | 0.116461i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.27156 | 0.438253 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.9418 | + | 6.67026i | 1.09969 | + | 0.670387i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.12311i | − | 0.907783i | −0.891057 | − | 0.453891i | \(-0.850035\pi\) | ||
0.891057 | − | 0.453891i | \(-0.149965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.4041i | − | 1.22221i | −0.791549 | − | 0.611106i | \(-0.790725\pi\) | ||
0.791549 | − | 0.611106i | \(-0.209275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.438447 | − | 1.56155i | 0.0427881 | − | 0.152392i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.936426 | 0.0905278 | 0.0452639 | − | 0.998975i | \(-0.485587\pi\) | ||||
0.0452639 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.12311 | 0.873835 | 0.436918 | − | 0.899502i | \(-0.356070\pi\) | ||||
0.436918 | + | 0.899502i | \(0.356070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.46228 | − | 5.20798i | 0.138793 | − | 0.494320i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.0000i | − | 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.60669i | 0.709328i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.00000 | + | 4.87689i | 0.739600 | + | 0.450869i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.87285 | 0.171684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.24621 | 0.658746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.8782 | − | 3.33513i | −1.07103 | − | 0.300719i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.68213i | − | 0.415472i | −0.978185 | − | 0.207736i | \(-0.933391\pi\) | ||
0.978185 | − | 0.207736i | \(-0.0666095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.43845 | − | 0.684658i | −0.214693 | − | 0.0602808i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6121 | 1.53878 | 0.769388 | − | 0.638782i | \(-0.220562\pi\) | ||||
0.769388 | + | 0.638782i | \(0.220562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.54042 | + | 3.80335i | 0.304711 | + | 0.327340i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.24621i | − | 0.704521i | −0.935902 | − | 0.352261i | \(-0.885413\pi\) | ||
0.935902 | − | 0.352261i | \(-0.114587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8664i | 1.17613i | 0.808813 | + | 0.588066i | \(0.200110\pi\) | ||||
−0.808813 | + | 0.588066i | \(0.799890\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.438447 | − | 1.56155i | 0.0369239 | − | 0.131506i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.3405 | 1.11559 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.12311 | −0.425451 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.86692 | − | 10.2107i | 0.236459 | − | 0.842163i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 14.0000i | − | 1.14692i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.14441i | 0.500025i | 0.968243 | + | 0.250013i | \(0.0804347\pi\) | ||||
−0.968243 | + | 0.250013i | \(0.919565\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.12311 | + | 5.12311i | −0.252488 | + | 0.414179i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.39871 | −0.192669 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.3693 | −1.70546 | −0.852729 | − | 0.522354i | \(-0.825054\pi\) | ||||
−0.852729 | + | 0.522354i | \(0.825054\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.08084 | + | 1.98813i | 0.561547 | + | 0.157669i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.12311i | − | 0.561379i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 24.1671i | − | 1.89291i | −0.322834 | − | 0.946456i | \(-0.604636\pi\) | ||
0.322834 | − | 0.946456i | \(-0.395364\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.12311 | + | 2.00000i | 0.554533 | + | 0.155700i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.80928 | −0.217389 | −0.108694 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108694 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.24621 | −0.249709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.67026 | − | 10.9418i | 0.510088 | − | 0.836742i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.936426i | − | 0.0707872i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.36932 | + | 12.0000i | −0.253253 | + | 0.901975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6875 | 1.09780 | 0.548899 | − | 0.835889i | \(-0.315047\pi\) | ||||
0.548899 | + | 0.835889i | \(0.315047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.24621 | −0.315618 | −0.157809 | − | 0.987470i | \(-0.550443\pi\) | ||||
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.39871 | − | 8.54312i | 0.177317 | − | 0.631525i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.12311i | − | 0.229615i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.54312i | 0.624735i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.31534 | − | 3.56155i | −0.241156 | − | 0.259065i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.72197 | 0.558742 | 0.279371 | − | 0.960183i | \(-0.409874\pi\) | ||||
0.279371 | + | 0.960183i | \(0.409874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2462 | 1.16943 | 0.584714 | − | 0.811240i | \(-0.301207\pi\) | ||||
0.584714 | + | 0.811240i | \(0.301207\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.20798 | + | 1.46228i | 0.372952 | + | 0.104716i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.2462i | − | 0.872506i | −0.899824 | − | 0.436253i | \(-0.856305\pi\) | ||
0.899824 | − | 0.436253i | \(-0.143695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.6121i | 1.24849i | 0.781230 | + | 0.624244i | \(0.214593\pi\) | ||||
−0.781230 | + | 0.624244i | \(0.785407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.68466 | − | 2.43845i | −0.612569 | − | 0.171995i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.79741 | 0.336712 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.12311 | −0.497499 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.4849 | + | 11.8782i | 1.35430 | + | 0.825595i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 18.2462i | − | 1.26212i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.34700i | − | 0.0927313i | −0.998925 | − | 0.0463656i | \(-0.985236\pi\) | ||
0.998925 | − | 0.0463656i | \(-0.0147639\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.12311 | + | 11.1231i | −0.213992 | + | 0.762143i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.46228 | −0.0997266 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24621 | 0.152483 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.86098 | + | 13.7511i | −0.260901 | + | 0.929213i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.24621i | 0.420166i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.0227i | − | 1.20689i | −0.797406 | − | 0.603443i | \(-0.793795\pi\) | ||
0.797406 | − | 0.603443i | \(-0.206205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.56155 | + | 1.56155i | 0.170770 | + | 0.104104i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.65840 | 0.574678 | 0.287339 | − | 0.957829i | \(-0.407229\pi\) | ||||
0.287339 | + | 0.957829i | \(0.407229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.246211 | −0.0162701 | −0.00813505 | − | 0.999967i | \(-0.502589\pi\) | ||||
−0.00813505 | + | 0.999967i | \(0.502589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.67026 | − | 1.87285i | −0.438871 | − | 0.123225i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.936426i | − | 0.0610857i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.1231 | + | 4.24621i | 0.982351 | + | 0.275821i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8319 | 1.34751 | 0.673753 | − | 0.738957i | \(-0.264681\pi\) | ||||
0.673753 | + | 0.738957i | \(0.264681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3693 | −0.732362 | −0.366181 | − | 0.930544i | \(-0.619335\pi\) | ||||
−0.366181 | + | 0.930544i | \(0.619335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2710 | − | 3.12985i | 0.979636 | − | 0.200780i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.12311i | − | 0.391191i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.3405i | − | 0.848837i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.19224 | + | 7.80776i | −0.138927 | + | 0.494797i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.1035 | −1.58452 | −0.792259 | − | 0.610184i | \(-0.791095\pi\) | ||||
−0.792259 | + | 0.610184i | \(0.791095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.4924 | 2.04278 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.936426 | + | 3.33513i | −0.0586413 | + | 0.208854i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.49242i | 0.155473i | 0.996974 | + | 0.0777365i | \(0.0247693\pi\) | ||||
−0.996974 | + | 0.0777365i | \(0.975231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.92456i | 0.181723i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.00000 | + | 13.1231i | −0.495188 | + | 0.812300i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0981 | −0.930989 | −0.465494 | − | 0.885051i | \(-0.654123\pi\) | ||||
−0.465494 | + | 0.885051i | \(0.654123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.24621 | 0.260843 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4160 | + | 2.92456i | 0.637447 | + | 0.178980i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0000i | 0.853595i | 0.904347 | + | 0.426798i | \(0.140358\pi\) | ||||
−0.904347 | + | 0.426798i | \(0.859642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.7738i | − | 1.93012i | −0.262032 | − | 0.965059i | \(-0.584392\pi\) | ||
0.262032 | − | 0.965059i | \(-0.415608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.87689 | − | 1.36932i | −0.295163 | − | 0.0828748i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.27156 | 0.257585 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.36932 | 0.0822743 | 0.0411371 | − | 0.999154i | \(-0.486902\pi\) | ||||
0.0411371 | + | 0.999154i | \(0.486902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.74571 | + | 6.14441i | −0.224250 | + | 0.367856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6155i | 1.64740i | 0.567023 | + | 0.823702i | \(0.308095\pi\) | ||||
−0.567023 | + | 0.823702i | \(0.691905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.38684i | − | 0.260770i | −0.991463 | − | 0.130385i | \(-0.958379\pi\) | ||
0.991463 | − | 0.130385i | \(-0.0416214\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | − | 7.12311i | 0.118470 | − | 0.421936i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.67026 | 0.393733 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.80928 | + | 10.0054i | −0.164683 | + | 0.586527i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.4924i | − | 1.78139i | −0.454605 | − | 0.890693i | \(-0.650220\pi\) | ||
0.454605 | − | 0.890693i | \(-0.349780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.19612i | 0.418974i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.2462 | − | 15.1231i | 0.942701 | − | 0.877532i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.7565 | 1.37387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.36932 | 0.0789261 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.2134 | − | 4.27156i | −0.873986 | − | 0.245395i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.12311i | − | 0.293348i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.13254i | − | 0.464149i | −0.972698 | − | 0.232074i | \(-0.925449\pi\) | ||
0.972698 | − | 0.232074i | \(-0.0745513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.6847 | − | 5.80776i | −1.17671 | − | 0.330392i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1617 | 0.803035 | 0.401517 | − | 0.915851i | \(-0.368483\pi\) | ||||
0.401517 | + | 0.915851i | \(0.368483\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4924 | 0.593067 | 0.296533 | − | 0.955022i | \(-0.404169\pi\) | ||||
0.296533 | + | 0.955022i | \(0.404169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.39871 | − | 1.46228i | −0.135152 | − | 0.0823901i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.7386i | 1.83878i | 0.393342 | + | 0.919392i | \(0.371319\pi\) | ||||
−0.393342 | + | 0.919392i | \(0.628681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.8836i | 1.22525i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.438447 | − | 1.56155i | 0.0244717 | − | 0.0871574i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.54312 | 0.475352 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.12311 | 0.173239 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.27156 | − | 15.2134i | 0.236218 | − | 0.841302i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.876894i | 0.0483448i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 28.0281i | − | 1.54056i | −0.637705 | − | 0.770281i | \(-0.720116\pi\) | ||
0.637705 | − | 0.770281i | \(-0.279884\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00000 | − | 4.87689i | −0.438397 | − | 0.267252i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.20798 | −0.284543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.4924 | −1.87892 | −0.939461 | − | 0.342656i | \(-0.888674\pi\) | ||||
−0.939461 | + | 0.342656i | \(0.888674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.3459 | − | 6.55498i | −1.26798 | − | 0.356018i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2462i | 0.554863i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.2888i | 0.663534i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.6847 | + | 3.56155i | 0.682919 | + | 0.191748i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.8718 | −1.28150 | −0.640752 | − | 0.767748i | \(-0.721377\pi\) | ||||
−0.640752 | + | 0.767748i | \(0.721377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.8782 | − | 11.0571i | 0.634014 | − | 0.590184i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.75379i | 0.199794i | 0.994998 | + | 0.0998970i | \(0.0318513\pi\) | ||||
−0.994998 | + | 0.0998970i | \(0.968149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.67026i | 0.354021i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.876894 | − | 3.12311i | 0.0464102 | − | 0.165292i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.05171 | −0.0555069 | −0.0277535 | − | 0.999615i | \(-0.508835\pi\) | ||||
−0.0277535 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.753789 | 0.0396731 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.39277 | − | 12.0835i | 0.178074 | − | 0.634221i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.24621i | 0.431626i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.5658i | 1.38672i | 0.720590 | + | 0.693361i | \(0.243871\pi\) | ||||
−0.720590 | + | 0.693361i | \(0.756129\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.1231 | + | 18.2462i | −0.579046 | + | 0.949860i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.97626 | −0.206437 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.876894 | 0.0454039 | 0.0227019 | − | 0.999742i | \(-0.492773\pi\) | ||||
0.0227019 | + | 0.999742i | \(0.492773\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.66757 | + | 0.468213i | 0.0861127 | + | 0.0241784i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0000i | 0.824042i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1035i | 1.28948i | 0.764402 | + | 0.644740i | \(0.223034\pi\) | ||||
−0.764402 | + | 0.644740i | \(0.776966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.80776 | − | 2.19224i | −0.400004 | − | 0.112312i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.68213 | −0.239246 | −0.119623 | − | 0.992819i | \(-0.538169\pi\) | ||||
−0.119623 | + | 0.992819i | \(0.538169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.28343 | + | 3.74571i | −0.116073 | + | 0.190405i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.7386i | 1.45711i | 0.684989 | + | 0.728553i | \(0.259807\pi\) | ||||
−0.684989 | + | 0.728553i | \(0.740193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.2134i | 0.769374i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.24621 | − | 29.3693i | 0.415966 | − | 1.48149i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.06897 | 0.456309 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.1231 | −1.16052 | −0.580258 | − | 0.814433i | \(-0.697048\pi\) | ||||
−0.580258 | + | 0.814433i | \(0.697048\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.87285 | + | 6.67026i | −0.0937599 | + | 0.333931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.0000i | − | 1.19850i | −0.800561 | − | 0.599251i | \(-0.795465\pi\) | ||
0.800561 | − | 0.599251i | \(-0.204535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.49141i | 0.373174i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.00000 | − | 4.12311i | 0.397523 | − | 0.204879i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.3405 | −0.661265 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.630683 | 0.0311853 | 0.0155926 | − | 0.999878i | \(-0.495037\pi\) | ||||
0.0155926 | + | 0.999878i | \(0.495037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.7511 | − | 3.86098i | −0.678292 | − | 0.190448i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.73863i | − | 0.331586i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.68213i | 0.229837i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.1231 | + | 6.49242i | 1.13234 | + | 0.317935i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.14441 | −0.300174 | −0.150087 | − | 0.988673i | \(-0.547955\pi\) | ||||
−0.150087 | + | 0.988673i | \(0.547955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.630683 | 0.0307376 | 0.0153688 | − | 0.999882i | \(-0.495108\pi\) | ||||
0.0153688 | + | 0.999882i | \(0.495108\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.39871 | − | 1.46228i | −0.116629 | − | 0.0710985i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000i | 0.0970143i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.79741i | 0.232163i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.24621 | − | 22.2462i | 0.301570 | − | 1.07406i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0453 | −1.73624 | −0.868121 | − | 0.496353i | \(-0.834672\pi\) | ||||
−0.868121 | + | 0.496353i | \(0.834672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.39871 | + | 8.54312i | −0.115009 | + | 0.409611i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 32.4924i | − | 1.55432i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.9009i | − | 1.42709i | −0.700608 | − | 0.713546i | \(-0.747088\pi\) | ||
0.700608 | − | 0.713546i | \(-0.252912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.6847 | − | 9.56155i | −0.746888 | − | 0.455312i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.7446 | −1.22316 | −0.611582 | − | 0.791181i | \(-0.709467\pi\) | ||||
−0.611582 | + | 0.791181i | \(0.709467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.24621 | 0.296099 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.3459 | − | 6.55498i | −1.10422 | − | 0.310040i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.63068i | 0.124150i | 0.998071 | + | 0.0620748i | \(0.0197717\pi\) | ||||
−0.998071 | + | 0.0620748i | \(0.980228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.4268i | 1.43274i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.2462 | + | 2.87689i | 0.481409 | + | 0.135168i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.92456 | −0.137105 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.08084 | + | 7.60669i | 0.330505 | + | 0.355050i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15.8617i | − | 0.738755i | −0.929279 | − | 0.369377i | \(-0.879571\pi\) | ||
0.929279 | − | 0.369377i | \(-0.120429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.936426i | − | 0.0435194i | −0.999763 | − | 0.0217597i | \(-0.993073\pi\) | ||
0.999763 | − | 0.0217597i | \(-0.00692688\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.12311 | + | 4.00000i | −0.0520828 | + | 0.185496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1498 | −0.747324 | −0.373662 | − | 0.927565i | \(-0.621898\pi\) | ||||
−0.373662 | + | 0.927565i | \(0.621898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.87689 | 0.225194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0054 | + | 35.6347i | −0.461024 | + | 1.64196i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.24621i | 0.287201i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.27156i | − | 0.195993i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.63068 | − | 10.8769i | 0.303598 | − | 0.498019i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9354 | −1.04794 | −0.523971 | − | 0.851736i | \(-0.675550\pi\) | ||||
−0.523971 | + | 0.851736i | \(0.675550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.75379 | −0.444734 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.8782 | − | 3.33513i | −0.540479 | − | 0.151754i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000i | 0.272446i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.3287i | − | 0.694608i | −0.937753 | − | 0.347304i | \(-0.887097\pi\) | ||
0.937753 | − | 0.347304i | \(-0.112903\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −40.3002 | − | 11.3153i | −1.82244 | − | 0.511697i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.6638 | 0.842285 | 0.421143 | − | 0.906994i | \(-0.361629\pi\) | ||||
0.421143 | + | 0.906994i | \(0.361629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2462 | −0.461466 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.67026 | − | 10.9418i | 0.299806 | − | 0.491798i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.24621i | − | 0.280181i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.57756i | − | 0.0706212i | −0.999376 | − | 0.0353106i | \(-0.988758\pi\) | ||
0.999376 | − | 0.0353106i | \(-0.0112421\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.31534 | + | 4.68466i | −0.0587651 | + | 0.209295i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8955 | 0.887097 | 0.443549 | − | 0.896250i | \(-0.353719\pi\) | ||||
0.443549 | + | 0.896250i | \(0.353719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.12311 | −0.405973 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.51992 | + | 5.41327i | −0.0675020 | + | 0.240412i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.87689i | 0.127516i | 0.997965 | + | 0.0637581i | \(0.0203086\pi\) | ||||
−0.997965 | + | 0.0637581i | \(0.979691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.72197i | − | 0.341600i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.1231 | − | 16.2462i | −0.667701 | − | 0.717288i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.4041 | −0.546590 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.33513 | + | 0.936426i | 0.146396 | + | 0.0411046i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7538i | 0.953051i | 0.879161 | + | 0.476525i | \(0.158104\pi\) | ||||
−0.879161 | + | 0.476525i | \(0.841896\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.641132i | 0.0280348i | 0.999902 | + | 0.0140174i | \(0.00446202\pi\) | ||||
−0.999902 | + | 0.0140174i | \(0.995538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.56155 | − | 0.438447i | −0.0681518 | − | 0.0191354i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.79741 | −0.208979 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.8617 | 1.51573 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.4332 | + | 11.2371i | 0.799934 | + | 0.487649i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.2462i | 0.963590i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.936426i | − | 0.0404852i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.87689 | − | 24.4924i | 0.296760 | − | 1.05693i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.1552 | −1.12658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9848 | −1.67609 | −0.838045 | − | 0.545602i | \(-0.816301\pi\) | ||||
−0.838045 | + | 0.545602i | \(0.816301\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.98813 | + | 7.08084i | −0.0853189 | + | 0.303868i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.12311i | − | 0.390791i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.2188i | − | 1.07828i | −0.842217 | − | 0.539139i | \(-0.818750\pi\) | ||
0.842217 | − | 0.539139i | \(-0.181250\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.1231 | − | 8.00000i | −0.560080 | − | 0.341432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.8836 | 0.932275 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.49242 | −0.361135 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.20798 | − | 1.46228i | −0.221067 | − | 0.0620703i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.7538i | 0.836995i | 0.908218 | + | 0.418497i | \(0.137443\pi\) | ||||
−0.908218 | + | 0.418497i | \(0.862557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.56685i | 0.193157i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.2462 | + | 4.00000i | 0.601476 | + | 0.168880i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.1606 | −1.52399 | −0.761994 | − | 0.647584i | \(-0.775779\pi\) | ||||
−0.761994 | + | 0.647584i | \(0.775779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | −0.588984 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.49141 | + | 3.86098i | −0.314610 | + | 0.162146i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.87689i | 0.204450i | 0.994761 | + | 0.102225i | \(0.0325962\pi\) | ||||
−0.994761 | + | 0.102225i | \(0.967404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.7909i | − | 0.702679i | −0.936248 | − | 0.351339i | \(-0.885726\pi\) | ||
0.936248 | − | 0.351339i | \(-0.114274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.61553 | − | 12.8769i | 0.151041 | − | 0.537940i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.60669 | 0.317221 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.7538 | −0.655839 | −0.327919 | − | 0.944706i | \(-0.606347\pi\) | ||||
−0.327919 | + | 0.944706i | \(0.606347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.60669 | − | 27.0916i | 0.316123 | − | 1.12589i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.38447i | − | 0.181899i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.1379i | − | 0.751197i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.87689 | − | 8.00000i | 0.201635 | − | 0.330759i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.0335 | 1.56981 | 0.784904 | − | 0.619617i | \(-0.212712\pi\) | ||||
0.784904 | + | 0.619617i | \(0.212712\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.2462 | 0.422188 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.4214 | − | 5.73384i | −0.840023 | − | 0.235859i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.24621i | 0.338631i | 0.985562 | + | 0.169316i | \(0.0541557\pi\) | ||||
−0.985562 | + | 0.169316i | \(0.945844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.87285i | − | 0.0767795i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.3693 | + | 8.24621i | 1.20201 | + | 0.337495i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.8665 | −1.50632 | −0.753162 | − | 0.657836i | \(-0.771472\pi\) | ||||
−0.753162 | + | 0.657836i | \(0.771472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8769 | 0.606841 | 0.303421 | − | 0.952857i | \(-0.401871\pi\) | ||||
0.303421 | + | 0.952857i | \(0.401871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.13254 | + | 13.3405i | −0.331183 | + | 0.543268i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7.24621i | − | 0.294600i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4903i | 1.19698i | 0.801132 | + | 0.598488i | \(0.204232\pi\) | ||||
−0.801132 | + | 0.598488i | \(0.795768\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.24621 | − | 8.00000i | 0.0910211 | − | 0.324176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.92456 | −0.118315 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.876894 | −0.0354174 | −0.0177087 | − | 0.999843i | \(-0.505637\pi\) | ||||
−0.0177087 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.33513 | + | 11.8782i | −0.134486 | + | 0.478977i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0000i | 0.563619i | 0.959470 | + | 0.281809i | \(0.0909346\pi\) | ||||
−0.959470 | + | 0.281809i | \(0.909065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.3061i | − | 0.816171i | −0.912944 | − | 0.408085i | \(-0.866197\pi\) | ||
0.912944 | − | 0.408085i | \(-0.133803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.9309 | − | 26.9309i | 1.16096 | − | 1.08070i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.84912 | −0.234340 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.4268 | − | 8.54312i | −1.21513 | − | 0.341179i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.24621i | − | 0.249053i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1315i | 1.19951i | 0.800182 | + | 0.599757i | \(0.204736\pi\) | ||||
−0.800182 | + | 0.599757i | \(0.795264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.24621 | − | 0.630683i | −0.0892789 | − | 0.0250674i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.68213 | −0.185805 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.1231 | −0.757685 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.0862 | + | 10.4160i | 0.675921 | + | 0.412049i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.6155i | 1.88070i | 0.340208 | + | 0.940350i | \(0.389502\pi\) | ||||
−0.340208 | + | 0.940350i | \(0.610498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.4214i | 0.805340i | 0.915345 | + | 0.402670i | \(0.131918\pi\) | ||||
−0.915345 | + | 0.402670i | \(0.868082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.684658 | + | 2.43845i | −0.0269584 | + | 0.0960138i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.63043 | −0.142727 | −0.0713634 | − | 0.997450i | \(-0.522735\pi\) | ||||
−0.0713634 | + | 0.997450i | \(0.522735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.7386 | 1.20660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.05171 | − | 3.74571i | 0.0412196 | − | 0.146806i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.9848i | 1.05600i | 0.849245 | + | 0.527999i | \(0.177058\pi\) | ||||
−0.849245 | + | 0.527999i | \(0.822942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.6121i | − | 0.688161i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.1231 | + | 12.8769i | 0.824091 | + | 0.502375i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.9764 | −1.05085 | −0.525425 | − | 0.850840i | \(-0.676094\pi\) | ||||
−0.525425 | + | 0.850840i | \(0.676094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.1080 | 1.79339 | 0.896696 | − | 0.442647i | \(-0.145961\pi\) | ||||
0.896696 | + | 0.442647i | \(0.145961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4160 | + | 2.92456i | 0.404523 | + | 0.113580i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00000i | 0.155113i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.9699i | 1.50892i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.0540 | − | 8.43845i | −1.16195 | − | 0.326249i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.8836 | −0.844809 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4924 | −0.404453 | −0.202227 | − | 0.979339i | \(-0.564818\pi\) | ||||
−0.202227 | + | 0.979339i | \(0.564818\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.80335 | − | 3.54042i | 0.146391 | − | 0.136271i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.4924i | 1.32565i | 0.748774 | + | 0.662826i | \(0.230643\pi\) | ||||
−0.748774 | + | 0.662826i | \(0.769357\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.61856i | − | 0.215620i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.05398 | − | 14.4384i | 0.155349 | − | 0.553282i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.1606 | 1.38365 | 0.691823 | − | 0.722067i | \(-0.256808\pi\) | ||||
0.691823 | + | 0.722067i | \(0.256808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.24621 | −0.315072 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.115279 | + | 0.410574i | −0.00439818 | + | 0.0156644i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.2614i | − | 0.505218i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.0798i | 1.10625i | 0.833100 | + | 0.553123i | \(0.186564\pi\) | ||||
−0.833100 | + | 0.553123i | \(0.813436\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.24621 | + | 10.2462i | −0.237274 | + | 0.389221i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.8664 | 0.525982 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.2462 | −0.539614 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.6757 | + | 4.68213i | 0.630731 | + | 0.177094i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.4924i | 1.90707i | 0.301278 | + | 0.953536i | \(0.402587\pi\) | ||||
−0.301278 | + | 0.953536i | \(0.597413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3405i | 0.503148i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.56155 | − | 0.438447i | −0.0588115 | − | 0.0165129i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.54312 | 0.321297 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.4924 | 0.994944 | 0.497472 | − | 0.867480i | \(-0.334262\pi\) | ||||
0.497472 | + | 0.867480i | \(0.334262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1617 | − | 23.2306i | 0.531104 | − | 0.871217i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.2462i | 0.683326i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 13.3405i | − | 0.498907i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.75379 | − | 34.7386i | 0.364262 | − | 1.29734i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.84912 | 0.218135 | 0.109068 | − | 0.994034i | \(-0.465213\pi\) | ||||
0.109068 | + | 0.994034i | \(0.465213\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6155 | 0.432585 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.32326 | + | 18.9591i | −0.197974 | + | 0.705096i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.12311i | 0.190267i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.5658i | − | 0.985270i | −0.870236 | − | 0.492635i | \(-0.836034\pi\) | ||
0.870236 | − | 0.492635i | \(-0.163966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.93087 | − | 26.9309i | 0.0715137 | − | 0.997440i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.92456 | −0.108169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.1231 | 1.29730 | 0.648651 | − | 0.761086i | \(-0.275334\pi\) | ||||
0.648651 | + | 0.761086i | \(0.275334\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.2107 | − | 2.86692i | −0.376627 | − | 0.105748i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.2462i | 0.819450i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18.6638i | − | 0.686559i | −0.939233 | − | 0.343279i | \(-0.888462\pi\) | ||
0.939233 | − | 0.343279i | \(-0.111538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.2462 | − | 6.24621i | −0.817235 | − | 0.229460i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.4041 | 0.455062 | 0.227531 | − | 0.973771i | \(-0.426935\pi\) | ||||
0.227531 | + | 0.973771i | \(0.426935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0000 | −0.512920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.9935 | + | 7.31140i | 0.438820 | + | 0.267510i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.876894i | 0.0320410i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15.7392i | − | 0.574333i | −0.957881 | − | 0.287166i | \(-0.907287\pi\) | ||
0.957881 | − | 0.287166i | \(-0.0927133\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.7538 | + | 41.8617i | −0.428332 | + | 1.52553i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.14441 | 0.223618 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.1231 | −0.695041 | −0.347521 | − | 0.937672i | \(-0.612976\pi\) | ||||
−0.347521 | + | 0.937672i | \(0.612976\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.2134 | − | 54.1833i | 0.552211 | − | 1.96673i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 51.2311i | − | 1.85712i | −0.371177 | − | 0.928562i | \(-0.621046\pi\) | ||
0.371177 | − | 0.928562i | \(-0.378954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.54312i | 0.309282i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.12311 | + | 3.12311i | 0.185226 | + | 0.112916i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.4742 | 0.811498 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.9848 | −0.973098 | −0.486549 | − | 0.873653i | \(-0.661745\pi\) | ||||
−0.486549 | + | 0.873653i | \(0.661745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.15628 | + | 1.16699i | 0.149685 | + | 0.0420279i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.2462i | 0.584336i | 0.956367 | + | 0.292168i | \(0.0943766\pi\) | ||||
−0.956367 | + | 0.292168i | \(0.905623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.39871i | 0.0861641i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.87689 | + | 1.36932i | 0.174958 | + | 0.0491240i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.4268 | 1.09015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.4924 | 1.01954 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.1379 | + | 19.4849i | 0.648197 | + | 0.696335i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.3693i | 0.762704i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 13.9817i | − | 0.498392i | −0.968453 | − | 0.249196i | \(-0.919834\pi\) | ||
0.968453 | − | 0.249196i | \(-0.0801664\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.06913 | + | 25.1771i | −0.251668 | + | 0.896328i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1100 | 0.466137 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0000 | −0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.98813 | − | 7.08084i | 0.0705118 | − | 0.251131i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 36.7386i | − | 1.30135i | −0.759357 | − | 0.650675i | \(-0.774486\pi\) | ||
0.759357 | − | 0.650675i | \(-0.225514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.87285i | − | 0.0662568i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.75379 | − | 16.0000i | 0.344633 | − | 0.565332i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.2242 | 1.24303 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.12311 | −0.251056 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.3459 | + | 6.55498i | 0.821815 | + | 0.230746i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.2462i | 1.62593i | 0.582312 | + | 0.812965i | \(0.302148\pi\) | ||||
−0.582312 | + | 0.812965i | \(0.697852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.9246i | − | 0.910337i | −0.890405 | − | 0.455169i | \(-0.849579\pi\) | ||
0.890405 | − | 0.455169i | \(-0.150421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52.9848 | − | 14.8769i | −1.85826 | − | 0.521755i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.1671 | −0.846536 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.24621 | 0.218527 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.56685 | + | 7.49141i | −0.159579 | + | 0.261771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 29.2311i | − | 1.02017i | −0.860124 | − | 0.510085i | \(-0.829614\pi\) | ||
0.860124 | − | 0.510085i | \(-0.170386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.8071i | 1.63159i | 0.578338 | + | 0.815797i | \(0.303701\pi\) | ||||
−0.578338 | + | 0.815797i | \(0.696299\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | − | 7.12311i | 0.0696311 | − | 0.247995i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.2252 | 0.459887 | 0.229943 | − | 0.973204i | \(-0.426146\pi\) | ||||
0.229943 | + | 0.973204i | \(0.426146\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.1231 | 0.594710 | 0.297355 | − | 0.954767i | \(-0.403896\pi\) | ||||
0.297355 | + | 0.954767i | \(0.403896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.641132 | − | 2.28343i | 0.0222406 | − | 0.0792112i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 12.2462i | − | 0.424306i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.80928i | 0.0972191i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.49242 | + | 9.12311i | 0.293541 | + | 0.315341i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.5647 | 1.67664 | 0.838320 | − | 0.545179i | \(-0.183538\pi\) | ||||
0.838320 | + | 0.545179i | \(0.183538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75379 | 0.0949582 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.0507 | + | 12.9300i | 1.58607 | + | 0.445331i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.24621i | 0.111673i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.78554i | 0.233154i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.31534 | − | 2.05398i | −0.251062 | − | 0.0704923i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.7565 | −0.814362 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.8617 | −1.70723 | −0.853617 | − | 0.520902i | \(-0.825596\pi\) | ||||
−0.853617 | + | 0.520902i | \(0.825596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.9418 | − | 6.67026i | −0.374202 | − | 0.228118i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.7386i | − | 0.981693i | −0.871246 | − | 0.490847i | \(-0.836688\pi\) | ||
0.871246 | − | 0.490847i | \(-0.163312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37.3923i | − | 1.27581i | −0.770115 | − | 0.637905i | \(-0.779801\pi\) | ||
0.770115 | − | 0.637905i | \(-0.220199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.12311 | − | 11.1231i | 0.106435 | − | 0.379074i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.6175 | −0.940110 | −0.470055 | − | 0.882637i | \(-0.655766\pi\) | ||||
−0.470055 | + | 0.882637i | \(0.655766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.08677 | − | 21.6784i | 0.206718 | − | 0.736236i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 38.7386i | − | 1.31412i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2651i | 0.551121i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.3693 | + | 9.36932i | 0.520173 | + | 0.317103i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.936426 | −0.0316570 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.61553 | 0.122088 | 0.0610439 | − | 0.998135i | \(-0.480557\pi\) | ||||
0.0610439 | + | 0.998135i | \(0.480557\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −50.8481 | − | 14.2770i | −1.71506 | − | 0.481550i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 25.3693i | − | 0.854714i | −0.904083 | − | 0.427357i | \(-0.859445\pi\) | ||
0.904083 | − | 0.427357i | \(-0.140555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.8265i | − | 0.364342i | −0.983267 | − | 0.182171i | \(-0.941688\pi\) | ||
0.983267 | − | 0.182171i | \(-0.0583125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | + | 3.36932i | 0.403376 | + | 0.113258i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.4774 | 1.79560 | 0.897798 | − | 0.440408i | \(-0.145166\pi\) | ||||
0.897798 | + | 0.440408i | \(0.145166\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.38447 | 0.147050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.6121 | − | 34.1725i | −0.590027 | − | 1.14482i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.00000i | 0.133855i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14.6875i | − | 0.490950i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.1231 | − | 39.6155i | 0.371390 | − | 1.32272i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.2888 | −0.409855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.49242 | 0.282924 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.641132 | − | 2.28343i | 0.0213355 | − | 0.0759877i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.24621i | 0.141149i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.8653i | 1.19089i | 0.803397 | + | 0.595444i | \(0.203024\pi\) | ||||
−0.803397 | + | 0.595444i | \(0.796976\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.2462 | + | 23.3693i | −0.472517 | + | 0.775111i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.8944 | 1.38802 | 0.694012 | − | 0.719963i | \(-0.255841\pi\) | ||||
0.694012 | + | 0.719963i | \(0.255841\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.54312 | − | 2.39871i | −0.282427 | − | 0.0792988i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4924i | 0.544628i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 50.1423i | − | 1.65404i | −0.562172 | − | 0.827020i | \(-0.690034\pi\) | ||
0.562172 | − | 0.827020i | \(-0.309966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5616 | − | 3.80776i | −0.446868 | − | 0.125470i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.8319 | 0.685692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.12311 | −0.102687 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.3697 | + | 31.7738i | −0.636183 | + | 1.04359i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.8769i | 0.816184i | 0.912941 | + | 0.408092i | \(0.133806\pi\) | ||||
−0.912941 | + | 0.408092i | \(0.866194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.1552i | 0.857202i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.63068 | − | 23.6155i | 0.217079 | − | 0.773138i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.54312 | 0.279390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.4924 | 0.342773 | 0.171386 | − | 0.985204i | \(-0.445175\pi\) | ||||
0.171386 | + | 0.985204i | \(0.445175\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.91269 | − | 17.4968i | 0.160320 | − | 0.570987i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.12311i | 0.297405i | 0.988882 | + | 0.148702i | \(0.0475096\pi\) | ||||
−0.988882 | + | 0.148702i | \(0.952490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54.1833i | 1.76445i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.56155 | + | 3.31534i | −0.115857 | + | 0.107848i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5141 | −0.829096 | −0.414548 | − | 0.910027i | \(-0.636060\pi\) | ||||
−0.414548 | + | 0.910027i | \(0.636060\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.7538 | 0.836003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 54.5938 | + | 15.3287i | 1.77033 | + | 0.497066i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.4924i | − | 0.339883i | −0.985454 | − | 0.169941i | \(-0.945642\pi\) | ||
0.985454 | − | 0.169941i | \(-0.0543579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7.72197i | − | 0.249877i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.4924 | + | 10.2462i | 1.17963 | + | 0.331213i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.72197 | 0.249355 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2462 | 0.814394 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.39871 | − | 1.46228i | −0.0772972 | − | 0.0471213i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 16.2462i | − | 0.522984i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.6412i | − | 0.760250i | −0.924935 | − | 0.380125i | \(-0.875881\pi\) | ||
0.924935 | − | 0.380125i | \(-0.124119\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | − | 14.2462i | 0.128499 | − | 0.457654i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.5991 | 1.33498 | 0.667490 | − | 0.744619i | \(-0.267369\pi\) | ||||
0.667490 | + | 0.744619i | \(0.267369\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.9848 | −0.416275 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.46228 | − | 5.20798i | 0.0468304 | − | 0.166789i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 48.2462i | − | 1.54353i | −0.635906 | − | 0.771767i | \(-0.719373\pi\) | ||
0.635906 | − | 0.771767i | \(-0.280627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 26.6811i | − | 0.852730i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.3693 | − | 14.2462i | −0.746125 | − | 0.454847i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.03984 | −0.0969558 | −0.0484779 | − | 0.998824i | \(-0.515437\pi\) | ||||
−0.0484779 | + | 0.998824i | \(0.515437\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.2462 | −0.390197 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.46228 | + | 0.410574i | 0.0465449 | + | 0.0130687i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.1231i | 0.353694i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.7909i | − | 0.533382i | −0.963782 | − | 0.266691i | \(-0.914070\pi\) | ||
0.963782 | − | 0.266691i | \(-0.0859303\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46.7386 | − | 13.1231i | −1.48321 | − | 0.416449i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.6121 | 0.558341 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.61553 | −0.241186 | −0.120593 | − | 0.992702i | \(-0.538480\pi\) | ||||
−0.120593 | + | 0.992702i | \(0.538480\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8782 | + | 11.0571i | −0.375811 | + | 0.349831i |
(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 | 960.2.h.g.191.5 | 8 | ||
3.2 | odd | 2 | inner | 960.2.h.g.191.3 | 8 | ||
4.3 | odd | 2 | inner | 960.2.h.g.191.4 | 8 | ||
8.3 | odd | 2 | 60.2.e.a.11.6 | yes | 8 | ||
8.5 | even | 2 | 60.2.e.a.11.4 | yes | 8 | ||
12.11 | even | 2 | inner | 960.2.h.g.191.6 | 8 | ||
24.5 | odd | 2 | 60.2.e.a.11.5 | yes | 8 | ||
24.11 | even | 2 | 60.2.e.a.11.3 | ✓ | 8 | ||
40.3 | even | 4 | 300.2.h.b.299.6 | 8 | |||
40.13 | odd | 4 | 300.2.h.b.299.7 | 8 | |||
40.19 | odd | 2 | 300.2.e.c.251.3 | 8 | |||
40.27 | even | 4 | 300.2.h.a.299.3 | 8 | |||
40.29 | even | 2 | 300.2.e.c.251.5 | 8 | |||
40.37 | odd | 4 | 300.2.h.a.299.2 | 8 | |||
120.29 | odd | 2 | 300.2.e.c.251.4 | 8 | |||
120.53 | even | 4 | 300.2.h.a.299.1 | 8 | |||
120.59 | even | 2 | 300.2.e.c.251.6 | 8 | |||
120.77 | even | 4 | 300.2.h.b.299.8 | 8 | |||
120.83 | odd | 4 | 300.2.h.a.299.4 | 8 | |||
120.107 | odd | 4 | 300.2.h.b.299.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.e.a.11.3 | ✓ | 8 | 24.11 | even | 2 | ||
60.2.e.a.11.4 | yes | 8 | 8.5 | even | 2 | ||
60.2.e.a.11.5 | yes | 8 | 24.5 | odd | 2 | ||
60.2.e.a.11.6 | yes | 8 | 8.3 | odd | 2 | ||
300.2.e.c.251.3 | 8 | 40.19 | odd | 2 | |||
300.2.e.c.251.4 | 8 | 120.29 | odd | 2 | |||
300.2.e.c.251.5 | 8 | 40.29 | even | 2 | |||
300.2.e.c.251.6 | 8 | 120.59 | even | 2 | |||
300.2.h.a.299.1 | 8 | 120.53 | even | 4 | |||
300.2.h.a.299.2 | 8 | 40.37 | odd | 4 | |||
300.2.h.a.299.3 | 8 | 40.27 | even | 4 | |||
300.2.h.a.299.4 | 8 | 120.83 | odd | 4 | |||
300.2.h.b.299.5 | 8 | 120.107 | odd | 4 | |||
300.2.h.b.299.6 | 8 | 40.3 | even | 4 | |||
300.2.h.b.299.7 | 8 | 40.13 | odd | 4 | |||
300.2.h.b.299.8 | 8 | 120.77 | even | 4 | |||
960.2.h.g.191.3 | 8 | 3.2 | odd | 2 | inner | ||
960.2.h.g.191.4 | 8 | 4.3 | odd | 2 | inner | ||
960.2.h.g.191.5 | 8 | 1.1 | even | 1 | trivial | ||
960.2.h.g.191.6 | 8 | 12.11 | even | 2 | inner |