Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(239,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("672.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.j (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.239 |
Dual form | 672.2.j.c.239.2 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.618034 | − | 1.61803i | −0.356822 | − | 0.934172i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.47214i | − | 1.34840i | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||
0.738549 | − | 0.674200i | \(-0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607i | 0.897524i | 0.893651 | + | 0.448762i | \(0.148135\pi\) | ||||
−0.893651 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.763932 | + | 2.00000i | 0.197246 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.76393 | −0.634089 | −0.317045 | − | 0.948411i | \(-0.602691\pi\) | ||||
−0.317045 | + | 0.948411i | \(0.602691\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.61803 | + | 0.618034i | −0.353084 | + | 0.134866i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.47214 | −1.76656 | −0.883281 | − | 0.468844i | \(-0.844671\pi\) | ||||
−0.883281 | + | 0.468844i | \(0.844671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.61803 | + | 2.38197i | 0.888741 | + | 0.458410i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94427i | 1.60644i | 0.595683 | + | 0.803219i | \(0.296881\pi\) | ||||
−0.595683 | + | 0.803219i | \(0.703119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.23607 | + | 2.76393i | −1.25964 | + | 0.481139i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23607i | 0.208934i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.47214i | 0.406417i | 0.979136 | + | 0.203208i | \(0.0651369\pi\) | ||||
−0.979136 | + | 0.203208i | \(0.934863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.23607 | − | 2.00000i | 0.838442 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.47214i | − | 0.698430i | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||
0.937043 | − | 0.349215i | \(-0.113552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.47214 | −1.29199 | −0.645994 | − | 0.763342i | \(-0.723557\pi\) | ||||
−0.645994 | + | 0.763342i | \(0.723557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.76393 | − | 2.47214i | 0.412023 | − | 0.368524i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.47214 | 0.944058 | 0.472029 | − | 0.881583i | \(-0.343522\pi\) | ||||
0.472029 | + | 0.881583i | \(0.343522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.23607 | + | 1.23607i | −0.453140 | + | 0.173084i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.52786 | −0.209868 | −0.104934 | − | 0.994479i | \(-0.533463\pi\) | ||||
−0.104934 | + | 0.994479i | \(0.533463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.52786i | 0.745377i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.70820 | + | 4.47214i | 0.226257 | + | 0.592349i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.23607i | 0.421300i | 0.977562 | + | 0.210650i | \(0.0675581\pi\) | ||||
−0.977562 | + | 0.210650i | \(0.932442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.70820i | − | 0.218713i | −0.994003 | − | 0.109357i | \(-0.965121\pi\) | ||
0.994003 | − | 0.109357i | \(-0.0348790\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | + | 2.23607i | 0.251976 | + | 0.281718i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.00000i | − | 0.496139i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.94427 | −0.848378 | −0.424189 | − | 0.905574i | \(-0.639441\pi\) | ||||
−0.424189 | + | 0.905574i | \(0.639441\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.23607 | + | 13.7082i | 0.630349 | + | 1.65027i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9443 | −1.29885 | −0.649423 | − | 0.760427i | \(-0.724990\pi\) | ||||
−0.649423 | + | 0.760427i | \(0.724990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.47214 | 0.991589 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.14590 | + | 5.61803i | 0.247787 | + | 0.648715i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.47214 | −0.509647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.9443i | − | 1.45634i | −0.685394 | − | 0.728172i | \(-0.740370\pi\) | ||
0.685394 | − | 0.728172i | \(-0.259630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.76393i | − | 0.961967i | −0.876730 | − | 0.480983i | \(-0.840280\pi\) | ||
0.876730 | − | 0.480983i | \(-0.159720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.47214i | 0.268141i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23607 | 0.339232 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.4721 | − | 5.52786i | 1.50069 | − | 0.573213i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.41641 | 0.350516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4721 | 1.26635 | 0.633177 | − | 0.774007i | \(-0.281751\pi\) | ||||
0.633177 | + | 0.774007i | \(0.281751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.94427 | + | 10.0000i | 0.898933 | + | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.7082 | −1.96104 | −0.980520 | − | 0.196420i | \(-0.937068\pi\) | ||||
−0.980520 | + | 0.196420i | \(0.937068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.4721i | − | 1.03185i | −0.856634 | − | 0.515925i | \(-0.827448\pi\) | ||
0.856634 | − | 0.515925i | \(-0.172552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | − | 0.763932i | 0.195180 | − | 0.0745521i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000i | 0.193347i | 0.995316 | + | 0.0966736i | \(0.0308203\pi\) | ||||
−0.995316 | + | 0.0966736i | \(0.969180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 19.4164i | − | 1.85975i | −0.367870 | − | 0.929877i | \(-0.619913\pi\) | ||
0.367870 | − | 0.929877i | \(-0.380087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | − | 1.52786i | 0.379663 | − | 0.145018i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.94427i | 0.465118i | 0.972582 | + | 0.232559i | \(0.0747099\pi\) | ||||
−0.972582 | + | 0.232559i | \(0.925290\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.4721 | 0.976532 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.47214 | − | 7.23607i | −0.598349 | − | 0.668975i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.23607 | + | 2.76393i | −0.652454 | + | 0.249215i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.944272i | 0.0837906i | 0.999122 | + | 0.0418953i | \(0.0133396\pi\) | ||||
−0.999122 | + | 0.0418953i | \(0.986660\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.23607 | + | 13.7082i | 0.461010 | + | 1.20694i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.23607i | − | 0.632218i | −0.948723 | − | 0.316109i | \(-0.897623\pi\) | ||
0.948723 | − | 0.316109i | \(-0.102377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.76393i | 0.239663i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.70820 | − | 2.94427i | −0.491284 | − | 0.253403i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.944272i | − | 0.0806746i | −0.999186 | − | 0.0403373i | \(-0.987157\pi\) | ||
0.999186 | − | 0.0403373i | \(-0.0128432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6525 | 1.75172 | 0.875860 | − | 0.482565i | \(-0.160295\pi\) | ||||
0.875860 | + | 0.482565i | \(0.160295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | − | 10.4721i | −0.336861 | − | 0.881913i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.4721 | 1.21022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.618034 | + | 1.61803i | 0.0509746 | + | 0.133453i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.41641 | 0.279883 | 0.139942 | − | 0.990160i | \(-0.455309\pi\) | ||||
0.139942 | + | 0.990160i | \(0.455309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.94427i | − | 0.727875i | −0.931423 | − | 0.363937i | \(-0.881432\pi\) | ||
0.931423 | − | 0.363937i | \(-0.118568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | + | 4.47214i | 0.323381 | + | 0.361551i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 11.0557i | − | 0.888017i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.70820i | 0.774799i | 0.921912 | + | 0.387400i | \(0.126627\pi\) | ||||
−0.921912 | + | 0.387400i | \(0.873373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.944272 | + | 2.47214i | 0.0748856 | + | 0.196053i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.47214i | 0.667698i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.472136 | 0.0369805 | 0.0184903 | − | 0.999829i | \(-0.494114\pi\) | ||||
0.0184903 | + | 0.999829i | \(0.494114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.94427 | − | 3.41641i | 0.696311 | − | 0.265967i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.9443 | −1.31119 | −0.655594 | − | 0.755114i | \(-0.727582\pi\) | ||||
−0.655594 | + | 0.755114i | \(0.727582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.52786 | 0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.18034 | − | 5.52786i | 0.472622 | − | 0.422726i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.29180 | −0.326299 | −0.163150 | − | 0.986601i | \(-0.552165\pi\) | ||||
−0.163150 | + | 0.986601i | \(0.552165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.47214i | 0.262469i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.23607 | − | 2.00000i | 0.393567 | − | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2.94427i | − | 0.220065i | −0.993928 | − | 0.110033i | \(-0.964904\pi\) | ||
0.993928 | − | 0.110033i | \(-0.0350955\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.7639i | − | 0.948736i | −0.880327 | − | 0.474368i | \(-0.842677\pi\) | ||
0.880327 | − | 0.474368i | \(-0.157323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.76393 | + | 1.05573i | −0.204316 | + | 0.0780417i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.05573i | − | 0.224662i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.94427 | −0.654070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.38197 | − | 4.61803i | 0.173263 | − | 0.335913i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | −0.144715 | −0.0723575 | − | 0.997379i | \(-0.523052\pi\) | ||||
−0.0723575 | + | 0.997379i | \(0.523052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.4721 | −1.47362 | −0.736808 | − | 0.676102i | \(-0.763668\pi\) | ||||
−0.736808 | + | 0.676102i | \(0.763668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.47214 | + | 2.47214i | −0.463479 | + | 0.177033i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5279 | 0.963820 | 0.481910 | − | 0.876221i | \(-0.339943\pi\) | ||||
0.481910 | + | 0.876221i | \(0.339943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.52786i | 0.108307i | 0.998533 | + | 0.0541537i | \(0.0172461\pi\) | ||||
−0.998533 | + | 0.0541537i | \(0.982754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.29180 | + | 11.2361i | 0.302720 | + | 0.792531i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.52786i | 0.386083i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9443 | − | 16.9443i | 1.31672 | − | 1.17771i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.3607i | 0.855006i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.9443 | 1.85492 | 0.927460 | − | 0.373922i | \(-0.121987\pi\) | ||||
0.927460 | + | 0.373922i | \(0.121987\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.76393 | + | 17.7082i | 0.463457 | + | 1.21335i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.4721 | 0.714194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.94427 | 0.607177 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.23607 | − | 13.7082i | −0.353821 | − | 0.926315i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214 | 0.435363 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.4164i | 1.83594i | 0.396652 | + | 0.917969i | \(0.370172\pi\) | ||||
−0.396652 | + | 0.917969i | \(0.629828\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.76393 | − | 6.94427i | 0.517595 | − | 0.462951i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7082i | 0.909845i | 0.890531 | + | 0.454923i | \(0.150333\pi\) | ||||
−0.890531 | + | 0.454923i | \(0.849667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.7082i | − | 1.17019i | −0.810964 | − | 0.585096i | \(-0.801057\pi\) | ||
0.810964 | − | 0.585096i | \(-0.198943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.76393 | + | 7.23607i | 0.181853 | + | 0.476098i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0000i | 1.04819i | 0.851658 | + | 0.524097i | \(0.175597\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.9443 | + | 8.00000i | −1.36048 | + | 0.519656i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.4164 | 0.867835 | 0.433918 | − | 0.900953i | \(-0.357131\pi\) | ||||
0.433918 | + | 0.900953i | \(0.357131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4721 | −0.803401 | −0.401700 | − | 0.915771i | \(-0.631581\pi\) | ||||
−0.401700 | + | 0.915771i | \(0.631581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.0902 | + | 3.90983i | −0.968035 | + | 0.250816i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.23607 | 0.0789695 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.94427i | − | 0.569110i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.1803 | + | 5.41641i | −0.898643 | + | 0.343251i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.7082i | 1.37021i | 0.728444 | + | 0.685105i | \(0.240244\pi\) | ||||
−0.728444 | + | 0.685105i | \(0.759756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.8885i | 2.38203i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | − | 1.52786i | 0.250490 | − | 0.0956786i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 25.4164i | − | 1.58543i | −0.609591 | − | 0.792716i | \(-0.708666\pi\) | ||
0.609591 | − | 0.792716i | \(-0.291334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.47214 | 0.153611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0000 | −0.863277 | −0.431638 | − | 0.902047i | \(-0.642064\pi\) | ||||
−0.431638 | + | 0.902047i | \(0.642064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.88854 | 0.116012 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.70820 | + | 3.70820i | −0.594132 | + | 0.226938i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.18034 | −0.376822 | −0.188411 | − | 0.982090i | \(-0.560334\pi\) | ||||
−0.188411 | + | 0.982090i | \(0.560334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.52786i | − | 0.335794i | −0.985805 | − | 0.167897i | \(-0.946302\pi\) | ||
0.985805 | − | 0.167897i | \(-0.0536976\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | − | 5.23607i | −0.121046 | − | 0.316901i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.5279i | 0.936365i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.0000i | − | 0.721010i | −0.932757 | − | 0.360505i | \(-0.882604\pi\) | ||
0.932757 | − | 0.360505i | \(-0.117396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.8885 | − | 20.0000i | −1.07096 | − | 1.19737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.8885i | − | 1.06714i | −0.845756 | − | 0.533571i | \(-0.820850\pi\) | ||
0.845756 | − | 0.533571i | \(-0.179150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23607 | −0.0734766 | −0.0367383 | − | 0.999325i | \(-0.511697\pi\) | ||||
−0.0367383 | + | 0.999325i | \(0.511697\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.11146 | − | 5.52786i | −0.125072 | − | 0.327442i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.47214 | −0.263982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.70820 | − | 20.1803i | −0.451863 | − | 1.18299i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1246 | −0.649907 | −0.324953 | − | 0.945730i | \(-0.605349\pi\) | ||||
−0.324953 | + | 0.945730i | \(0.605349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.00000i | − | 0.232889i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.6525 | − | 20.6525i | 0.618119 | − | 1.19838i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 27.4164i | − | 1.58553i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.47214i | 0.488326i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.1803 | + | 31.8885i | 0.699742 | + | 1.83195i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.11146i | 0.120902i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.1246 | −1.31979 | −0.659896 | − | 0.751357i | \(-0.729400\pi\) | ||||
−0.659896 | + | 0.751357i | \(0.729400\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.9443 | + | 6.47214i | −0.963926 | + | 0.368187i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3607 | −1.38137 | −0.690684 | − | 0.723157i | \(-0.742690\pi\) | ||||
−0.690684 | + | 0.723157i | \(0.742690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.9443 | −0.844700 | −0.422350 | − | 0.906433i | \(-0.638795\pi\) | ||||
−0.422350 | + | 0.906433i | \(0.638795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.47214 | − | 2.76393i | −0.139289 | − | 0.155730i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.47214 | −0.363511 | −0.181756 | − | 0.983344i | \(-0.558178\pi\) | ||||
−0.181756 | + | 0.983344i | \(0.558178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.23607 | − | 1.23607i | 0.180620 | − | 0.0689906i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.52786i | 0.307579i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 11.2361i | − | 0.623265i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.4164 | + | 12.0000i | −1.73733 | + | 0.663602i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.47214i | − | 0.356820i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3607 | −0.789334 | −0.394667 | − | 0.918824i | \(-0.629140\pi\) | ||||
−0.394667 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.94427 | − | 5.52786i | −0.270944 | − | 0.302925i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.58359 | 0.468972 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.52786 | −0.410069 | −0.205034 | − | 0.978755i | \(-0.565731\pi\) | ||||
−0.205034 | + | 0.978755i | \(0.565731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.00000 | − | 3.05573i | 0.434500 | − | 0.165964i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0000 | 2.16612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.47214 | − | 16.9443i | −0.348448 | − | 0.912249i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4721i | 0.884271i | 0.896948 | + | 0.442135i | \(0.145779\pi\) | ||||
−0.896948 | + | 0.442135i | \(0.854221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.180340i | 0.00965337i | 0.999988 | + | 0.00482669i | \(0.00153639\pi\) | ||||
−0.999988 | + | 0.00482669i | \(0.998464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.70820 | + | 14.9443i | −0.411433 | + | 0.797666i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.5279i | 0.613566i | 0.951779 | + | 0.306783i | \(0.0992526\pi\) | ||||
−0.951779 | + | 0.306783i | \(0.900747\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5279 | 0.717984 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.23607 | + | 3.23607i | 0.0654197 | + | 0.171271i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4164 | 0.708091 | 0.354045 | − | 0.935228i | \(-0.384806\pi\) | ||||
0.354045 | + | 0.935228i | \(0.384806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.56231 | + | 14.5623i | 0.291945 | + | 0.764323i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.4721 | −0.548137 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.47214i | 0.337843i | 0.985630 | + | 0.168921i | \(0.0540284\pi\) | ||||
−0.985630 | + | 0.168921i | \(0.945972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.94427 | + | 10.0000i | 0.465620 | + | 0.520579i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52786i | 0.0793227i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.88854i | − | 0.0977851i | −0.998804 | − | 0.0488925i | \(-0.984431\pi\) | ||
0.998804 | − | 0.0488925i | \(-0.0155692\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.47214 | − | 16.9443i | −0.334220 | − | 0.874998i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.47214 | 0.229718 | 0.114859 | − | 0.993382i | \(-0.463358\pi\) | ||||
0.114859 | + | 0.993382i | \(0.463358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.52786 | − | 0.583592i | 0.0782748 | − | 0.0298983i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5279 | 1.10002 | 0.550011 | − | 0.835157i | \(-0.314623\pi\) | ||||
0.550011 | + | 0.835157i | \(0.314623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.52786 | 0.281726 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.9443 | − | 16.9443i | 0.962991 | − | 0.861326i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.0557 | −0.560548 | −0.280274 | − | 0.959920i | \(-0.590425\pi\) | ||||
−0.280274 | + | 0.959920i | \(0.590425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.9443i | 0.856909i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.7082 | + | 4.47214i | −0.590601 | + | 0.225589i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000i | 0.805047i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.2361i | 1.76845i | 0.467063 | + | 0.884224i | \(0.345312\pi\) | ||||
−0.467063 | + | 0.884224i | \(0.654688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.47214 | − | 1.70820i | 0.223887 | − | 0.0855172i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.8885i | − | 0.893311i | −0.894706 | − | 0.446656i | \(-0.852615\pi\) | ||
0.894706 | − | 0.446656i | \(-0.147385\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.9443 | −1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.23607 | + | 11.0557i | −0.0614207 | + | 0.549364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0557 | 0.548012 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.52786 | + | 0.583592i | −0.0753640 | + | 0.0287865i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.23607 | 0.159236 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.8328i | 0.531762i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.7639 | − | 33.4164i | −0.625052 | − | 1.63641i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.2918i | − | 1.08903i | −0.838753 | − | 0.544513i | \(-0.816715\pi\) | ||
0.838753 | − | 0.544513i | \(-0.183285\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.94427i | − | 0.435917i | −0.975958 | − | 0.217959i | \(-0.930060\pi\) | ||
0.975958 | − | 0.217959i | \(-0.0699398\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.4721 | + | 12.9443i | −0.703659 | + | 0.629372i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.94427i | 0.336847i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.70820 | −0.0826658 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.94427 | − | 23.4164i | −0.431834 | − | 1.13055i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.52786 | 0.169931 | 0.0849656 | − | 0.996384i | \(-0.472922\pi\) | ||||
0.0849656 | + | 0.996384i | \(0.472922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.3607 | −0.882358 | −0.441179 | − | 0.897419i | \(-0.645440\pi\) | ||||
−0.441179 | + | 0.897419i | \(0.645440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.4164 | 1.12016 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.88854i | − | 0.0901353i | −0.998984 | − | 0.0450676i | \(-0.985650\pi\) | ||
0.998984 | − | 0.0450676i | \(-0.0143503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.23607 | − | 2.00000i | 0.106479 | − | 0.0952381i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.9443i | − | 0.710024i | −0.934862 | − | 0.355012i | \(-0.884477\pi\) | ||
0.934862 | − | 0.355012i | \(-0.115523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.41641i | 0.351571i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.11146 | − | 5.52786i | −0.0998685 | − | 0.261459i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8885i | 1.03298i | 0.856292 | + | 0.516492i | \(0.172762\pi\) | ||||
−0.856292 | + | 0.516492i | \(0.827238\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | −0.941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4721 | + | 5.52786i | −0.679960 | + | 0.259722i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.41641 | −0.253369 | −0.126684 | − | 0.991943i | \(-0.540434\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.76393 | − | 9.23607i | 0.222361 | − | 0.431103i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1803 | −0.660444 | −0.330222 | − | 0.943903i | \(-0.607124\pi\) | ||||
−0.330222 | + | 0.943903i | \(0.607124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.94427i | − | 0.229780i | −0.993378 | − | 0.114890i | \(-0.963348\pi\) | ||
0.993378 | − | 0.114890i | \(-0.0366515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.8885 | + | 6.83282i | −0.829561 | + | 0.316864i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.7082i | 0.634340i | 0.948369 | + | 0.317170i | \(0.102733\pi\) | ||||
−0.948369 | + | 0.317170i | \(0.897267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.94427i | 0.320657i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.7082 | − | 6.00000i | 0.723796 | − | 0.276465i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.8885i | 1.74212i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.59675 | 0.440329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.41641 | − | 3.05573i | 0.156427 | − | 0.139912i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.5279 | −1.16640 | −0.583199 | − | 0.812329i | \(-0.698199\pi\) | ||||
−0.583199 | + | 0.812329i | \(0.698199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.7082 | − | 5.23607i | 0.623745 | − | 0.238249i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.4164 | −0.700023 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.88854i | − | 0.266835i | −0.991060 | − | 0.133418i | \(-0.957405\pi\) | ||
0.991060 | − | 0.133418i | \(-0.0425952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.291796 | − | 0.763932i | −0.0131955 | − | 0.0345462i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.88854i | − | 0.356005i | −0.984030 | − | 0.178002i | \(-0.943036\pi\) | ||
0.984030 | − | 0.178002i | \(-0.0569635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.0557 | − | 12.3607i | −0.496918 | − | 0.555571i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9443i | 0.490918i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.88854 | 0.353140 | 0.176570 | − | 0.984288i | \(-0.443500\pi\) | ||||
0.176570 | + | 0.984288i | \(0.443500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4721 | + | 27.4164i | 0.467861 | + | 1.22487i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.4164 | 1.75749 | 0.878745 | − | 0.477291i | \(-0.158381\pi\) | ||||
0.878745 | + | 0.477291i | \(0.158381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.3607 | 1.08404 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.56231 | − | 4.09017i | −0.0693844 | − | 0.181651i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.1246 | 1.55687 | 0.778436 | − | 0.627725i | \(-0.216014\pi\) | ||||
0.778436 | + | 0.627725i | \(0.216014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.47214i | − | 0.374785i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.7639 | − | 6.58359i | −0.563541 | − | 0.290673i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.9443i | 0.570393i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 28.9443i | − | 1.27297i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.65248 | + | 6.94427i | 0.116431 | + | 0.304820i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4164i | 1.46400i | 0.681305 | + | 0.732000i | \(0.261413\pi\) | ||||
−0.681305 | + | 0.732000i | \(0.738587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2918 | −0.537483 | −0.268741 | − | 0.963212i | \(-0.586608\pi\) | ||||
−0.268741 | + | 0.963212i | \(0.586608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.61803 | − | 2.14590i | 0.245191 | − | 0.0936547i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.8885 | 0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.7771 | 2.12074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.47214 | − | 7.23607i | −0.280867 | − | 0.314019i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.4721 | 0.626858 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.47214i | − | 0.106880i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.76393 | + | 1.81966i | −0.205579 | + | 0.0785241i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.47214i | 0.192629i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.94427i | 0.384544i | 0.981342 | + | 0.192272i | \(0.0615856\pi\) | ||||
−0.981342 | + | 0.192272i | \(0.938414\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.6525 | + | 7.88854i | −0.886283 | + | 0.338530i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0000i | 1.02805i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.5279 | −1.00598 | −0.502989 | − | 0.864293i | \(-0.667767\pi\) | ||||
−0.502989 | + | 0.864293i | \(0.667767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.41641 | + | 3.81966i | 0.145809 | + | 0.163019i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9443 | −0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.94427 | + | 1.88854i | −0.209873 | + | 0.0801642i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.47214 | −0.274233 | −0.137117 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137117 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 27.4164i | − | 1.15959i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.52786 | + | 14.4721i | 0.233387 | + | 0.611014i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 32.1803i | − | 1.35624i | −0.734951 | − | 0.678120i | \(-0.762795\pi\) | ||
0.734951 | − | 0.678120i | \(-0.237205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.11146i | − | 0.257111i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.94427 | − | 1.00000i | −0.375624 | − | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.8885i | 0.917615i | 0.888536 | + | 0.458808i | \(0.151723\pi\) | ||||
−0.888536 | + | 0.458808i | \(0.848277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.4721 | 1.35892 | 0.679458 | − | 0.733714i | \(-0.262215\pi\) | ||||
0.679458 | + | 0.733714i | \(0.262215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.23607 | + | 3.23607i | 0.0516375 | + | 0.135189i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.4164 | 1.22675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9443 | 1.12170 | 0.560852 | − | 0.827916i | \(-0.310474\pi\) | ||||
0.560852 | + | 0.827916i | \(0.310474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.6525 | + | 33.1246i | 0.525819 | + | 1.37661i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.76393 | −0.363589 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.83282i | 0.282986i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.00000 | + | 8.94427i | 0.330759 | + | 0.369800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2918i | 0.424788i | 0.977184 | + | 0.212394i | \(0.0681260\pi\) | ||||
−0.977184 | + | 0.212394i | \(0.931874\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.7214i | − | 1.01863i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.36068 | − | 21.8885i | −0.343912 | − | 0.900374i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.4164i | − | 0.715206i | −0.933874 | − | 0.357603i | \(-0.883594\pi\) | ||
0.933874 | − | 0.357603i | \(-0.116406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.47214 | 0.101348 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.47214 | − | 0.944272i | 0.101178 | − | 0.0386465i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.9443 | −0.774042 | −0.387021 | − | 0.922071i | \(-0.626496\pi\) | ||||
−0.387021 | + | 0.922071i | \(0.626496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4721 | 0.671912 | 0.335956 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335956 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.5279 | − | 13.8885i | 0.632344 | − | 0.565585i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.1246 | 0.452280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.47214i | 0.262696i | 0.991336 | + | 0.131348i | \(0.0419305\pi\) | ||||
−0.991336 | + | 0.131348i | \(0.958069\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.9443i | 0.847315i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27.4164i | − | 1.10734i | −0.832737 | − | 0.553669i | \(-0.813227\pi\) | ||
0.832737 | − | 0.553669i | \(-0.186773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.94427 | − | 3.41641i | 0.360668 | − | 0.137763i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.0000i | − | 1.28827i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) | ||
0.764911 | − | 0.644136i | \(-0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1246 | 1.41178 | 0.705889 | − | 0.708323i | \(-0.250548\pi\) | ||||
0.705889 | + | 0.708323i | \(0.250548\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.1246 | − | 20.1803i | −1.57002 | − | 0.809809i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | − | 7.63932i | 0.798723 | − | 0.305085i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.94427 | 0.197141 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.6525 | − | 43.5967i | −0.661876 | − | 1.73282i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.16718i | − | 0.0463183i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.23607i | − | 0.128218i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.4721 | − | 21.8885i | 0.968103 | − | 0.865897i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 40.0000i | − | 1.57991i | −0.613168 | − | 0.789953i | \(-0.710105\pi\) | ||
0.613168 | − | 0.789953i | \(-0.289895\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.81966 | 0.387250 | 0.193625 | − | 0.981076i | \(-0.437976\pi\) | ||||
0.193625 | + | 0.981076i | \(0.437976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.47214 | − | 16.9443i | −0.254840 | − | 0.667180i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.4721 | 0.568081 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.52786 | − | 14.4721i | −0.216654 | − | 0.567208i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.8328 | −1.67618 | −0.838089 | − | 0.545534i | \(-0.816327\pi\) | ||||
−0.838089 | + | 0.545534i | \(0.816327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.94427i | 0.349482i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.9443 | + | 16.9443i | −0.739086 | + | 0.661059i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.63932i | − | 0.0638588i | −0.999490 | − | 0.0319294i | \(-0.989835\pi\) | ||
0.999490 | − | 0.0319294i | \(-0.0101652\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.12461i | 0.199324i | 0.995021 | + | 0.0996621i | \(0.0317762\pi\) | ||||
−0.995021 | + | 0.0996621i | \(0.968224\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.00000 | − | 10.4721i | −0.155347 | − | 0.406704i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.41641i | − | 0.132483i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.3607 | − | 16.9443i | 1.71508 | − | 0.655103i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.63932 | −0.294913 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.05573 | 0.194884 | 0.0974420 | − | 0.995241i | \(-0.468934\pi\) | ||||
0.0974420 | + | 0.995241i | \(0.468934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.0344 | − | 8.27051i | −0.617166 | − | 0.318332i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.81966 | 0.0699352 | 0.0349676 | − | 0.999388i | \(-0.488867\pi\) | ||||
0.0349676 | + | 0.999388i | \(0.488867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 12.4721i | − | 0.478637i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.1803 | − | 8.47214i | 0.849952 | − | 0.324653i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0557i | 0.958731i | 0.877615 | + | 0.479365i | \(0.159133\pi\) | ||||
−0.877615 | + | 0.479365i | \(0.840867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.16718i | 0.0445958i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.6525 | + | 10.9443i | −1.09316 | + | 0.417550i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.94427i | − | 0.188362i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.6525 | 1.08999 | 0.544996 | − | 0.838439i | \(-0.316531\pi\) | ||||
0.544996 | + | 0.838439i | \(0.316531\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0000 | − | 8.94427i | 0.379869 | − | 0.339765i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.5279 | −0.968327 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.94427 | −0.338788 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.8885 | − | 9.88854i | 0.979195 | − | 0.374019i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.8885 | 1.12887 | 0.564437 | − | 0.825476i | \(-0.309093\pi\) | ||||
0.564437 | + | 0.825476i | \(0.309093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.83282i | − | 0.257705i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.94427 | + | 12.9443i | 0.186212 | + | 0.487509i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.7082i | 0.741203i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.52786i | − | 0.0573801i | −0.999588 | − | 0.0286901i | \(-0.990866\pi\) | ||
0.999588 | − | 0.0286901i | \(-0.00913359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.8885 | + | 28.9443i | 0.970896 | + | 1.08550i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 75.7771i | − | 2.83787i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.8885 | −0.668994 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.29180 | − | 21.7082i | −0.309663 | − | 0.810708i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.3607 | −0.460976 | −0.230488 | − | 0.973075i | \(-0.574032\pi\) | ||||
−0.230488 | + | 0.973075i | \(0.574032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4721 | −0.390003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.70820 | + | 20.1803i | 0.286671 | + | 0.750515i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.4164i | 0.571763i | 0.958265 | + | 0.285881i | \(0.0922864\pi\) | ||||
−0.958265 | + | 0.285881i | \(0.907714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.9443i | 0.626707i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5410i | 0.906443i | 0.891398 | + | 0.453222i | \(0.149725\pi\) | ||||
−0.891398 | + | 0.453222i | \(0.850275\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.763932 | − | 2.00000i | −0.0281781 | − | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.0557i | 1.14395i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.47214 | 0.164510 | 0.0822551 | − | 0.996611i | \(-0.473788\pi\) | ||||
0.0822551 | + | 0.996611i | \(0.473788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.4721 | + | 5.52786i | −0.531647 | + | 0.203071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3050 | −0.561484 | −0.280742 | − | 0.959783i | \(-0.590581\pi\) | ||||
−0.280742 | + | 0.959783i | \(0.590581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.22291 | −0.154716 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.5279 | + | 19.5967i | 0.641311 | + | 0.717008i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00000 | 0.0730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26.8328i | − | 0.979143i | −0.871963 | − | 0.489572i | \(-0.837153\pi\) | ||
0.871963 | − | 0.489572i | \(-0.162847\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.1246 | − | 13.4164i | 1.28001 | − | 0.488921i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.0557i | 0.402359i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35.4164i | − | 1.28723i | −0.765349 | − | 0.643616i | \(-0.777434\pi\) | ||
0.765349 | − | 0.643616i | \(-0.222566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 61.3050 | − | 23.4164i | 2.22523 | − | 0.849962i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3050i | 0.409804i | 0.978782 | + | 0.204902i | \(0.0656876\pi\) | ||||
−0.978782 | + | 0.204902i | \(0.934312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.4164 | −0.702921 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.94427 | − | 5.52786i | −0.178761 | − | 0.199860i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.4721 | −0.378127 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.3607 | −0.806347 | −0.403173 | − | 0.915124i | \(-0.632093\pi\) | ||||
−0.403173 | + | 0.915124i | \(0.632093\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.1246 | + | 15.7082i | −1.48107 | + | 0.565717i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.6525 | 0.886688 | 0.443344 | − | 0.896352i | \(-0.353792\pi\) | ||||
0.443344 | + | 0.896352i | \(0.353792\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 31.0557i | − | 1.11555i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.52786 | − | 4.00000i | −0.0548118 | − | 0.143499i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.3607i | 0.442867i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.9443i | 1.75136i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 12.0000i | − | 0.428298i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.1246 | −0.824303 | −0.412152 | − | 0.911115i | \(-0.635223\pi\) | ||||
−0.412152 | + | 0.911115i | \(0.635223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.65248 | + | 22.6525i | 0.308036 | + | 0.806449i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.94427 | 0.175798 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.52786 | 0.196300 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.16718 | − | 3.05573i | −0.0413958 | − | 0.108376i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.0689 | 1.13594 | 0.567969 | − | 0.823050i | \(-0.307729\pi\) | ||||
0.567969 | + | 0.823050i | \(0.307729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.9443i | − | 0.457935i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0000 | + | 13.4164i | 0.423999 | + | 0.474045i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 37.8885i | − | 1.33706i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 10.4721i | − | 0.369094i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.81966 | + | 10.0000i | 0.134458 | + | 0.352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.7214i | 1.71295i | 0.516187 | + | 0.856476i | \(0.327351\pi\) | ||||
−0.516187 | + | 0.856476i | \(0.672649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0689 | −0.564255 | −0.282127 | − | 0.959377i | \(-0.591040\pi\) | ||||
−0.282127 | + | 0.959377i | \(0.591040\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.94427 | + | 3.41641i | −0.313689 | + | 0.119819i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.583592 | −0.0204423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.4164 | 0.819236 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.23607 | + | 6.47214i | −0.252849 | + | 0.226155i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.4721 | −0.784283 | −0.392141 | − | 0.919905i | \(-0.628266\pi\) | ||||
−0.392141 | + | 0.919905i | \(0.628266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8328i | 1.07476i | 0.843339 | + | 0.537382i | \(0.180587\pi\) | ||||
−0.843339 | + | 0.537382i | \(0.819413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.1246 | − | 9.59675i | 0.874727 | − | 0.334116i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.00000i | 0.0695468i | 0.999395 | + | 0.0347734i | \(0.0110710\pi\) | ||||
−0.999395 | + | 0.0347734i | \(0.988929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.65248i | − | 0.231050i | −0.993305 | − | 0.115525i | \(-0.963145\pi\) | ||
0.993305 | − | 0.115525i | \(-0.0368550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.4164 | + | 7.41641i | −0.673548 | + | 0.257272i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.9443 | 0.724806 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.3050 | + | 41.3050i | −0.736407 | + | 1.42771i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.7771 | 0.544686 | 0.272343 | − | 0.962200i | \(-0.412202\pi\) | ||||
0.272343 | + | 0.962200i | \(0.412202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9443 | + | 11.0557i | −0.996894 | + | 0.380780i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.12461 | −0.107490 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000i | 0.309244i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.763932 | + | 2.00000i | 0.0262181 | + | 0.0686398i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 20.9443i | − | 0.717960i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.1246i | 0.723293i | 0.932315 | + | 0.361646i | \(0.117785\pi\) | ||||
−0.932315 | + | 0.361646i | \(0.882215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.63932 | + | 6.83282i | −0.261259 | + | 0.233677i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 23.3050i | − | 0.796082i | −0.917368 | − | 0.398041i | \(-0.869690\pi\) | ||
0.917368 | − | 0.398041i | \(-0.130310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0689 | −1.50361 | −0.751805 | − | 0.659385i | \(-0.770817\pi\) | ||||
−0.751805 | + | 0.659385i | \(0.770817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.76393 | + | 7.23607i | 0.0941946 | + | 0.246605i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.7214 | −1.31809 | −0.659045 | − | 0.752103i | \(-0.729039\pi\) | ||||
−0.659045 | + | 0.752103i | \(0.729039\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.30495 | 0.180374 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.03444 | − | 21.0344i | −0.272864 | − | 0.714367i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −57.8885 | −1.96373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 22.4721i | − | 0.761439i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.8885 | + | 24.9443i | −0.943884 | + | 0.844236i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 10.4721i | − | 0.354023i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.58359i | 0.154777i | 0.997001 | + | 0.0773885i | \(0.0246582\pi\) | ||||
−0.997001 | + | 0.0773885i | \(0.975342\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.87539 | + | 18.0000i | 0.231901 | + | 0.607125i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.4164i | − | 0.452010i | −0.974126 | − | 0.226005i | \(-0.927433\pi\) | ||
0.974126 | − | 0.226005i | \(-0.0725666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9443 | 0.502915 | 0.251457 | − | 0.967868i | \(-0.419090\pi\) | ||||
0.251457 | + | 0.967868i | \(0.419090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.47214 | + | 2.47214i | −0.217558 | + | 0.0830999i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.8885 | 1.00356 | 0.501780 | − | 0.864996i | \(-0.332679\pi\) | ||||
0.501780 | + | 0.864996i | \(0.332679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.944272 | 0.0316699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.0000 | − | 4.47214i | −1.34005 | − | 0.149822i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.8885 | −0.598617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.63932i | 0.121649i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.3607 | + | 16.9443i | −1.48116 | + | 0.565753i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.05573i | 0.101801i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.7082 | − | 5.23607i | 0.456180 | − | 0.174245i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.7771i | 0.524448i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.7214 | 1.55136 | 0.775679 | − | 0.631128i | \(-0.217408\pi\) | ||||
0.775679 | + | 0.631128i | \(0.217408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.0689 | − | 39.4164i | 1.46167 | − | 1.30736i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.63932 | −0.319365 | −0.159682 | − | 0.987168i | \(-0.551047\pi\) | ||||
−0.159682 | + | 0.987168i | \(0.551047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.1935 | −1.29712 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.41641 | − | 1.30495i | 0.112943 | − | 0.0431404i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.23607 | −0.238956 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.9443i | 1.48257i | 0.671188 | + | 0.741287i | \(0.265784\pi\) | ||||
−0.671188 | + | 0.741287i | \(0.734216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.2918 | + | 37.4164i | 0.470931 | + | 1.23291i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 35.4164i | − | 1.16575i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 8.58359i | − | 0.282227i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.9443 | + | 23.4164i | 0.687900 | + | 0.769096i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 37.0557i | − | 1.21576i | −0.794029 | − | 0.607880i | \(-0.792020\pi\) | ||
0.794029 | − | 0.607880i | \(-0.207980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.76393 | 0.0905842 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0557 | + | 39.4164i | 0.492902 | + | 1.29044i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.0557 | 0.361561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.41641 | −0.176946 | −0.0884732 | − | 0.996079i | \(-0.528199\pi\) | ||||
−0.0884732 | + | 0.996079i | \(0.528199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.23607 | + | 24.1803i | 0.301408 | + | 0.789096i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.0689 | −1.04542 | −0.522708 | − | 0.852512i | \(-0.675078\pi\) | ||||
−0.522708 | + | 0.852512i | \(0.675078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.8885i | 1.23382i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.94427 | + | 5.70820i | −0.0957772 | + | 0.185688i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.52786i | 0.244623i | 0.992492 | + | 0.122311i | \(0.0390306\pi\) | ||||
−0.992492 | + | 0.122311i | \(0.960969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.4164i | 0.889974i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000 | + | 10.4721i | 0.129709 | + | 0.339582i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.88854i | − | 0.0611759i | −0.999532 | − | 0.0305880i | \(-0.990262\pi\) | ||
0.999532 | − | 0.0305880i | \(-0.00973797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.47214 | 0.0799964 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.944272 | −0.0304921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −49.0000 | −1.58065 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | − | 4.47214i | −0.128898 | − | 0.144113i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.3050 | 0.814595 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.9443i | − | 0.544891i | −0.962171 | − | 0.272446i | \(-0.912168\pi\) | ||
0.962171 | − | 0.272446i | \(-0.0878325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.94427 | − | 3.41641i | 0.287331 | − | 0.109751i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 41.7082i | − | 1.33848i | −0.743046 | − | 0.669240i | \(-0.766620\pi\) | ||
0.743046 | − | 0.669240i | \(-0.233380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 20.6525i | − | 0.662088i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.1803 | + | 6.94427i | −0.582237 | + | 0.222395i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 9.88854i | − | 0.316363i | −0.987410 | − | 0.158181i | \(-0.949437\pi\) | ||
0.987410 | − | 0.158181i | \(-0.0505630\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.8328 | −0.857581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.8328 | + | 43.4164i | 1.23984 | + | 1.38618i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.0557 | −1.11810 | −0.559052 | − | 0.829133i | \(-0.688835\pi\) | ||||
−0.559052 | + | 0.829133i | \(0.688835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.7214 | −0.532787 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.4721 | + | 4.00000i | −0.333332 | + | 0.127321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 71.7771 | 2.28238 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000i | 1.27064i | 0.772248 | + | 0.635321i | \(0.219132\pi\) | ||||
−0.772248 | + | 0.635321i | \(0.780868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.87539 | + | 23.2361i | 0.281652 | + | 0.737374i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.88854i | − | 0.0598709i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.87539i | 0.0910645i | 0.998963 | + | 0.0455322i | \(0.0144984\pi\) | ||||
−0.998963 | + | 0.0455322i | \(0.985502\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.88854 | + | 11.4164i | −0.186305 | + | 0.361199i |
(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 | 672.2.j.c.239.1 | 4 | ||
3.2 | odd | 2 | 672.2.j.b.239.2 | 4 | |||
4.3 | odd | 2 | 168.2.j.a.155.2 | ✓ | 4 | ||
8.3 | odd | 2 | 672.2.j.b.239.1 | 4 | |||
8.5 | even | 2 | 168.2.j.c.155.2 | yes | 4 | ||
12.11 | even | 2 | 168.2.j.c.155.4 | yes | 4 | ||
24.5 | odd | 2 | 168.2.j.a.155.4 | yes | 4 | ||
24.11 | even | 2 | inner | 672.2.j.c.239.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.j.a.155.2 | ✓ | 4 | 4.3 | odd | 2 | ||
168.2.j.a.155.4 | yes | 4 | 24.5 | odd | 2 | ||
168.2.j.c.155.2 | yes | 4 | 8.5 | even | 2 | ||
168.2.j.c.155.4 | yes | 4 | 12.11 | even | 2 | ||
672.2.j.b.239.1 | 4 | 8.3 | odd | 2 | |||
672.2.j.b.239.2 | 4 | 3.2 | odd | 2 | |||
672.2.j.c.239.1 | 4 | 1.1 | even | 1 | trivial | ||
672.2.j.c.239.2 | 4 | 24.11 | even | 2 | inner |