Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.a (trivial) |
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: | yes |
Analytic conductor: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.143376304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.116918\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0.486391 | 0.280818 | 0.140409 | − | 0.990094i | \(-0.455158\pi\) | ||||
0.140409 | + | 0.990094i | \(0.455158\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80495 | 0.682207 | 0.341103 | − | 0.940026i | \(-0.389199\pi\) | ||||
0.341103 | + | 0.940026i | \(0.389199\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.76342 | −0.921141 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.90652 | 0.876350 | 0.438175 | − | 0.898890i | \(-0.355625\pi\) | ||||
0.438175 | + | 0.898890i | \(0.355625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.25256 | 0.624747 | 0.312373 | − | 0.949959i | \(-0.398876\pi\) | ||||
0.312373 | + | 0.949959i | \(0.398876\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.14477 | −0.520184 | −0.260092 | − | 0.965584i | \(-0.583753\pi\) | ||||
−0.260092 | + | 0.965584i | \(0.583753\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.339824 | −0.0779610 | −0.0389805 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389805 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.877911 | 0.191576 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.80328 | −0.539491 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.60395 | −1.04063 | −0.520313 | − | 0.853975i | \(-0.674185\pi\) | ||||
−0.520313 | + | 0.853975i | \(0.674185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92083 | −1.06341 | −0.531706 | − | 0.846929i | \(-0.678449\pi\) | ||||
−0.531706 | + | 0.846929i | \(0.678449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41371 | 0.246095 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.98088 | 1.47645 | 0.738224 | − | 0.674556i | \(-0.235665\pi\) | ||||
0.738224 | + | 0.674556i | \(0.235665\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.09562 | 0.175440 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.89222 | 0.295515 | 0.147757 | − | 0.989024i | \(-0.452795\pi\) | ||||
0.147757 | + | 0.989024i | \(0.452795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.47322 | −1.44465 | −0.722327 | − | 0.691552i | \(-0.756927\pi\) | ||||
−0.722327 | + | 0.691552i | \(0.756927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.83384 | −1.14268 | −0.571342 | − | 0.820712i | \(-0.693577\pi\) | ||||
−0.571342 | + | 0.820712i | \(0.693577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.74216 | −0.534594 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.04320 | −0.146077 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.47764 | −0.889772 | −0.444886 | − | 0.895587i | \(-0.646756\pi\) | ||||
−0.444886 | + | 0.895587i | \(0.646756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.165287 | −0.0218928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.17914 | −0.674267 | −0.337134 | − | 0.941457i | \(-0.609457\pi\) | ||||
−0.337134 | + | 0.941457i | \(0.609457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.12565 | −1.16842 | −0.584210 | − | 0.811602i | \(-0.698596\pi\) | ||||
−0.584210 | + | 0.811602i | \(0.698596\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.98784 | −0.628409 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.25423 | −1.13058 | −0.565292 | − | 0.824891i | \(-0.691236\pi\) | ||||
−0.565292 | + | 0.824891i | \(0.691236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.486391 | −0.0585546 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.60255 | 0.546222 | 0.273111 | − | 0.961982i | \(-0.411947\pi\) | ||||
0.273111 | + | 0.961982i | \(0.411947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3300 | 1.32608 | 0.663038 | − | 0.748585i | \(-0.269267\pi\) | ||||
0.663038 | + | 0.748585i | \(0.269267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.24613 | 0.597852 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.94972 | −0.894414 | −0.447207 | − | 0.894431i | \(-0.647581\pi\) | ||||
−0.447207 | + | 0.894431i | \(0.647581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.92678 | 0.769643 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.37849 | 0.590366 | 0.295183 | − | 0.955441i | \(-0.404619\pi\) | ||||
0.295183 | + | 0.955441i | \(0.404619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.72571 | −0.292227 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.9258 | 1.37014 | 0.685069 | − | 0.728479i | \(-0.259772\pi\) | ||||
0.685069 | + | 0.728479i | \(0.259772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.06575 | 0.426206 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.87984 | −0.298625 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.43210 | 0.246942 | 0.123471 | − | 0.992348i | \(-0.460597\pi\) | ||||
0.123471 | + | 0.992348i | \(0.460597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.03196 | −0.807242 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.89635 | 0.288198 | 0.144099 | − | 0.989563i | \(-0.453972\pi\) | ||||
0.144099 | + | 0.989563i | \(0.453972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3524 | 1.02005 | 0.510027 | − | 0.860159i | \(-0.329636\pi\) | ||||
0.510027 | + | 0.860159i | \(0.329636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.2395 | −1.47326 | −0.736630 | − | 0.676296i | \(-0.763584\pi\) | ||||
−0.736630 | + | 0.676296i | \(0.763584\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00555 | −0.671010 | −0.335505 | − | 0.942038i | \(-0.608907\pi\) | ||||
−0.335505 | + | 0.942038i | \(0.608907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.36822 | 0.414613 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.48460 | −0.610020 | −0.305010 | − | 0.952349i | \(-0.598660\pi\) | ||||
−0.305010 | + | 0.952349i | \(0.598660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.22477 | −0.575480 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.87121 | −0.354873 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.55212 | −0.232011 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.920357 | 0.0829858 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.28324 | −0.557547 | −0.278774 | − | 0.960357i | \(-0.589928\pi\) | ||||
−0.278774 | + | 0.960357i | \(0.589928\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.60769 | −0.405684 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.90426 | 0.690598 | 0.345299 | − | 0.938493i | \(-0.387777\pi\) | ||||
0.345299 | + | 0.938493i | \(0.387777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.613365 | −0.0531855 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.28955 | 0.708224 | 0.354112 | − | 0.935203i | \(-0.384783\pi\) | ||||
0.354112 | + | 0.935203i | \(0.384783\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.97515 | 0.761262 | 0.380631 | − | 0.924727i | \(-0.375707\pi\) | ||||
0.380631 | + | 0.924727i | \(0.375707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.81031 | −0.320886 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.54711 | 0.547497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.82015 | −0.150124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.39792 | 0.442215 | 0.221107 | − | 0.975249i | \(-0.429033\pi\) | ||||
0.221107 | + | 0.975249i | \(0.429033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6083 | −1.83984 | −0.919919 | − | 0.392108i | \(-0.871746\pi\) | ||||
−0.919919 | + | 0.392108i | \(0.871746\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.92692 | 0.479163 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.00033 | −0.638496 | −0.319248 | − | 0.947671i | \(-0.603430\pi\) | ||||
−0.319248 | + | 0.947671i | \(0.603430\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.15066 | −0.249864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.80495 | −0.142250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.6504 | −1.46081 | −0.730404 | − | 0.683015i | \(-0.760668\pi\) | ||||
−0.730404 | + | 0.683015i | \(0.760668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.13547 | −0.242630 | −0.121315 | − | 0.992614i | \(-0.538711\pi\) | ||||
−0.121315 | + | 0.992614i | \(0.538711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.92599 | −0.609692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.939078 | 0.0718131 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.56301 | −0.575005 | −0.287503 | − | 0.957780i | \(-0.592825\pi\) | ||||
−0.287503 | + | 0.957780i | \(0.592825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.51909 | −0.189346 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.73608 | −0.727709 | −0.363855 | − | 0.931456i | \(-0.618539\pi\) | ||||
−0.363855 | + | 0.931456i | \(0.618539\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.260581 | 0.0193688 | 0.00968440 | − | 0.999953i | \(-0.496917\pi\) | ||||
0.00968440 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.43863 | −0.328113 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.23384 | −0.455863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.05977 | −0.368044 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.1730 | 1.31495 | 0.657476 | − | 0.753475i | \(-0.271624\pi\) | ||||
0.657476 | + | 0.753475i | \(0.271624\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.15073 | 0.154813 | 0.0774063 | − | 0.997000i | \(-0.475336\pi\) | ||||
0.0774063 | + | 0.997000i | \(0.475336\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.0886 | 1.92998 | 0.964992 | − | 0.262279i | \(-0.0844742\pi\) | ||||
0.964992 | + | 0.262279i | \(0.0844742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2178 | 1.00787 | 0.503937 | − | 0.863741i | \(-0.331884\pi\) | ||||
0.503937 | + | 0.863741i | \(0.331884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50117 | −0.317488 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.1148 | −0.709922 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.76342 | 0.192071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.987706 | −0.0683211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89855 | −0.130701 | −0.0653506 | − | 0.997862i | \(-0.520817\pi\) | ||||
−0.0653506 | + | 0.997862i | \(0.520817\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.23864 | 0.153389 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6868 | −0.725467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.51081 | 0.372386 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.83122 | −0.324983 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5574 | −1.37663 | −0.688313 | − | 0.725414i | \(-0.741648\pi\) | ||||
−0.688313 | + | 0.725414i | \(0.741648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.67464 | 0.509384 | 0.254692 | − | 0.967022i | \(-0.418026\pi\) | ||||
0.254692 | + | 0.967022i | \(0.418026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.50379 | 0.561946 | 0.280973 | − | 0.959716i | \(-0.409343\pi\) | ||||
0.280973 | + | 0.959716i | \(0.409343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.55167 | 0.167887 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.37058 | 0.155302 | 0.0776511 | − | 0.996981i | \(-0.475258\pi\) | ||||
0.0776511 | + | 0.996981i | \(0.475258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.86667 | −0.251167 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.298079 | 0.0192811 | 0.00964057 | − | 0.999954i | \(-0.496931\pi\) | ||||
0.00964057 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.7779 | 1.91817 | 0.959083 | − | 0.283126i | \(-0.0913714\pi\) | ||||
0.959083 | + | 0.283126i | \(0.0913714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7790 | 0.755620 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.765472 | −0.0487058 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.61605 | 0.165785 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.1766 | −0.642341 | −0.321171 | − | 0.947021i | \(-0.604076\pi\) | ||||
−0.321171 | + | 0.947021i | \(0.604076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.90652 | −0.182732 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.2919 | −1.76480 | −0.882400 | − | 0.470501i | \(-0.844073\pi\) | ||||
−0.882400 | + | 0.470501i | \(0.844073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.2100 | 1.00724 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4861 | 0.958564 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.9182 | −1.53652 | −0.768260 | − | 0.640138i | \(-0.778877\pi\) | ||||
−0.768260 | + | 0.640138i | \(0.778877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.28701 | 0.384759 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8948 | 1.57883 | 0.789416 | − | 0.613859i | \(-0.210384\pi\) | ||||
0.789416 | + | 0.613859i | \(0.210384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.49603 | −0.212369 | −0.106184 | − | 0.994346i | \(-0.533863\pi\) | ||||
−0.106184 | + | 0.994346i | \(0.533863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.97754 | 0.119686 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.38317 | 0.0831064 | 0.0415532 | − | 0.999136i | \(-0.486769\pi\) | ||||
0.0415532 | + | 0.999136i | \(0.486769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.3618 | 0.979553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3144 | 0.913582 | 0.456791 | − | 0.889574i | \(-0.348999\pi\) | ||||
0.456791 | + | 0.889574i | \(0.348999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8266 | −0.703019 | −0.351510 | − | 0.936184i | \(-0.614332\pi\) | ||||
−0.351510 | + | 0.936184i | \(0.614332\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.41536 | 0.201602 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3999 | −0.729409 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.18295 | 0.0693458 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.4274 | −1.83601 | −0.918005 | − | 0.396569i | \(-0.870201\pi\) | ||||
−0.918005 | + | 0.396569i | \(0.870201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.14779 | −0.472783 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.25256 | −0.130269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0987 | −0.985552 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.40876 | 0.0809311 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.43504 | −0.0819018 | −0.0409509 | − | 0.999161i | \(-0.513039\pi\) | ||||
−0.0409509 | + | 0.999161i | \(0.513039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.03532 | 0.286449 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9698 | −1.18909 | −0.594544 | − | 0.804063i | \(-0.702667\pi\) | ||||
−0.594544 | + | 0.804063i | \(0.702667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.535929 | 0.0302925 | 0.0151463 | − | 0.999885i | \(-0.495179\pi\) | ||||
0.0151463 | + | 0.999885i | \(0.495179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.61790 | −0.371698 | −0.185849 | − | 0.982578i | \(-0.559504\pi\) | ||||
−0.185849 | + | 0.982578i | \(0.559504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2880 | −0.911953 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.41236 | −0.413718 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.728845 | 0.0405540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.40744 | −0.188432 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.1397 | −0.779546 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.81617 | 0.0998255 | 0.0499127 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499127 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.8180 | −1.36002 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.3308 | −0.889593 | −0.444796 | − | 0.895632i | \(-0.646724\pi\) | ||||
−0.444796 | + | 0.895632i | \(0.646724\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.15405 | −0.171304 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2090 | −0.931922 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.3891 | −1.04691 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.1771 | −0.653700 | −0.326850 | − | 0.945076i | \(-0.605987\pi\) | ||||
−0.326850 | + | 0.945076i | \(0.605987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0364 | 0.644293 | 0.322147 | − | 0.946690i | \(-0.395596\pi\) | ||||
0.322147 | + | 0.946690i | \(0.395596\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.31454 | −0.337045 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.0447 | −1.59912 | −0.799559 | − | 0.600588i | \(-0.794933\pi\) | ||||
−0.799559 | + | 0.600588i | \(0.794933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.88292 | −0.0996547 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.6859 | 1.56676 | 0.783380 | − | 0.621543i | \(-0.213494\pi\) | ||||
0.783380 | + | 0.621543i | \(0.213494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8845 | −0.993922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.24133 | −0.0651527 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4413 | 0.649428 | 0.324714 | − | 0.945812i | \(-0.394732\pi\) | ||||
0.324714 | + | 0.945812i | \(0.394732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.22900 | −0.272211 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6918 | −0.607008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5580 | −1.47867 | −0.739337 | − | 0.673335i | \(-0.764861\pi\) | ||||
−0.739337 | + | 0.673335i | \(0.764861\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.6232 | −0.650128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8436 | −0.762465 | −0.381233 | − | 0.924479i | \(-0.624500\pi\) | ||||
−0.381233 | + | 0.924479i | \(0.624500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.05611 | −0.156569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.00776 | 0.358080 | 0.179040 | − | 0.983842i | \(-0.442701\pi\) | ||||
0.179040 | + | 0.983842i | \(0.442701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.1785 | 1.33073 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.2715 | 1.48413 | 0.742063 | − | 0.670330i | \(-0.233847\pi\) | ||||
0.742063 | + | 0.670330i | \(0.233847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.14477 | 0.108466 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.84456 | 0.193932 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9288 | 1.65265 | 0.826324 | − | 0.563196i | \(-0.190428\pi\) | ||||
0.826324 | + | 0.563196i | \(0.190428\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.298335 | −0.0149354 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3403 | −1.21550 | −0.607749 | − | 0.794129i | \(-0.707927\pi\) | ||||
−0.607749 | + | 0.794129i | \(0.707927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3370 | −0.664363 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.1031 | 1.29389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.84661 | −0.289096 | −0.144548 | − | 0.989498i | \(-0.546173\pi\) | ||||
−0.144548 | + | 0.989498i | \(0.546173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.03196 | 0.198882 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.34809 | −0.459990 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.36543 | 0.213776 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0557 | 1.37061 | 0.685304 | − | 0.728257i | \(-0.259669\pi\) | ||||
0.685304 | + | 0.728257i | \(0.259669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0719 | −1.46561 | −0.732807 | − | 0.680437i | \(-0.761790\pi\) | ||||
−0.732807 | + | 0.680437i | \(0.761790\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.6482 | 1.05257 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.4713 | −0.797104 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.18445 | 0.153747 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.92111 | 0.477883 | 0.238941 | − | 0.971034i | \(-0.423200\pi\) | ||||
0.238941 | + | 0.971034i | \(0.423200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.82152 | 0.471992 | 0.235996 | − | 0.971754i | \(-0.424165\pi\) | ||||
0.235996 | + | 0.971754i | \(0.424165\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.339824 | 0.0162560 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.4026 | −1.16467 | −0.582336 | − | 0.812948i | \(-0.697861\pi\) | ||||
−0.582336 | + | 0.812948i | \(0.697861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.3412 | 0.492437 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.35646 | 0.397027 | 0.198514 | − | 0.980098i | \(-0.436389\pi\) | ||||
0.198514 | + | 0.980098i | \(0.436389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.62550 | 0.124182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4109 | 0.727286 | 0.363643 | − | 0.931538i | \(-0.381533\pi\) | ||||
0.363643 | + | 0.931538i | \(0.381533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.49978 | 0.258974 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.9965 | −0.516659 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.9314 | −1.07269 | −0.536343 | − | 0.844000i | \(-0.680195\pi\) | ||||
−0.536343 | + | 0.844000i | \(0.680195\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.01239 | 0.280634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.71207 | −0.452336 | −0.226168 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226168 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6091 | 0.632469 | 0.316234 | − | 0.948681i | \(-0.397581\pi\) | ||||
0.316234 | + | 0.948681i | \(0.397581\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.9381 | 1.61674 | 0.808371 | − | 0.588674i | \(-0.200350\pi\) | ||||
0.808371 | + | 0.588674i | \(0.200350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.7034 | −0.771292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.89129 | −0.179301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.5342 | −1.26602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.9005 | 0.819606 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.87962 | 0.314338 | 0.157169 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2299 | 0.922406 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.877911 | −0.0399463 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.8903 | −1.44509 | −0.722544 | − | 0.691325i | \(-0.757027\pi\) | ||||
−0.722544 | + | 0.691325i | \(0.757027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.07136 | −0.410221 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1719 | −1.00061 | −0.500303 | − | 0.865851i | \(-0.666778\pi\) | ||||
−0.500303 | + | 0.865851i | \(0.666778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0192 | 0.541317 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.30737 | 0.372636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5721 | −0.518037 | −0.259019 | − | 0.965872i | \(-0.583399\pi\) | ||||
−0.259019 | + | 0.965872i | \(0.583399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.52506 | −0.0681349 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.2532 | −1.75021 | −0.875106 | − | 0.483931i | \(-0.839208\pi\) | ||||
−0.875106 | + | 0.483931i | \(0.839208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.85513 | −0.171212 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.61391 | −0.160184 | −0.0800919 | − | 0.996787i | \(-0.525521\pi\) | ||||
−0.0800919 | + | 0.996787i | \(0.525521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4501 | 0.904658 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.952620 | 0.0420592 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.7692 | −1.00139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.67858 | −0.161472 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.64494 | 0.334931 | 0.167465 | − | 0.985878i | \(-0.446442\pi\) | ||||
0.167465 | + | 0.985878i | \(0.446442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.62852 | 0.246118 | 0.123059 | − | 0.992399i | \(-0.460730\pi\) | ||||
0.123059 | + | 0.992399i | \(0.460730\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6988 | 0.553170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3122 | 0.621095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.26233 | 0.184622 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.73554 | −0.204354 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.8767 | −0.468492 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.537263 | 0.0230987 | 0.0115494 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115494 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.126744 | 0.00543911 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.7590 | 1.78548 | 0.892742 | − | 0.450568i | \(-0.148778\pi\) | ||||
0.892742 | + | 0.450568i | \(0.148778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.2181 | 1.07628 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.90435 | 0.0811282 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3488 | −0.610175 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5405 | 0.955071 | 0.477535 | − | 0.878613i | \(-0.341530\pi\) | ||||
0.477535 | + | 0.878613i | \(0.341530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.3390 | −0.902542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.03208 | −0.128015 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.5366 | −1.32911 | −0.664554 | − | 0.747240i | \(-0.731378\pi\) | ||||
−0.664554 | + | 0.747240i | \(0.731378\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.5025 | 0.525055 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.49650 | 0.104659 | 0.0523294 | − | 0.998630i | \(-0.483335\pi\) | ||||
0.0523294 | + | 0.998630i | \(0.483335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.6658 | 1.82736 | 0.913678 | − | 0.406440i | \(-0.133230\pi\) | ||||
0.913678 | + | 0.406440i | \(0.133230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.83919 | 0.369262 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.7402 | −1.40462 | −0.702312 | − | 0.711869i | \(-0.747849\pi\) | ||||
−0.702312 | + | 0.711869i | \(0.747849\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.04609 | 0.0434742 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.70790 | 0.402751 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8274 | −0.779752 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8050 | −0.569795 | −0.284898 | − | 0.958558i | \(-0.591960\pi\) | ||||
−0.284898 | + | 0.958558i | \(0.591960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.01204 | 0.0829047 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.1757 | 0.541974 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.3336 | −1.77950 | −0.889749 | − | 0.456450i | \(-0.849121\pi\) | ||||
−0.889749 | + | 0.456450i | \(0.849121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.91541 | 0.283029 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.2077 | 1.11168 | 0.555838 | − | 0.831290i | \(-0.312397\pi\) | ||||
0.555838 | + | 0.831290i | \(0.312397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.6299 | 1.61654 | 0.808269 | − | 0.588813i | \(-0.200405\pi\) | ||||
0.808269 | + | 0.588813i | \(0.200405\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.5734 | 1.04143 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10233 | −0.0447421 | −0.0223711 | − | 0.999750i | \(-0.507122\pi\) | ||||
−0.0223711 | + | 0.999750i | \(0.507122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.91976 | −0.199359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.6462 | −0.713887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6705 | 0.552145 | 0.276073 | − | 0.961137i | \(-0.410967\pi\) | ||||
0.276073 | + | 0.961137i | \(0.410967\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.9011 | −0.801187 | −0.400594 | − | 0.916256i | \(-0.631196\pi\) | ||||
−0.400594 | + | 0.916256i | \(0.631196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1024 | 1.29030 | 0.645151 | − | 0.764055i | \(-0.276794\pi\) | ||||
0.645151 | + | 0.764055i | \(0.276794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.80328 | 0.112492 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.3305 | 0.934717 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.480411 | −0.0191858 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.2620 | −0.768024 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3065 | −1.28610 | −0.643051 | − | 0.765823i | \(-0.722332\pi\) | ||||
−0.643051 | + | 0.765823i | \(0.722332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.923435 | −0.0367033 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.42942 | −0.333986 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.7188 | −0.503148 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.6696 | −0.737407 | −0.368703 | − | 0.929547i | \(-0.620198\pi\) | ||||
−0.368703 | + | 0.929547i | \(0.620198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.9459 | −0.786590 | −0.393295 | − | 0.919412i | \(-0.628665\pi\) | ||||
−0.393295 | + | 0.919412i | \(0.628665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.6920 | 1.01006 | 0.505029 | − | 0.863102i | \(-0.331482\pi\) | ||||
0.505029 | + | 0.863102i | \(0.331482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.0533 | −0.590894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.19796 | −0.203724 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.7648 | 0.577791 | 0.288896 | − | 0.957361i | \(-0.406712\pi\) | ||||
0.288896 | + | 0.957361i | \(0.406712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.3096 | −1.22150 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.53869 | −0.371574 | −0.185787 | − | 0.982590i | \(-0.559484\pi\) | ||||
−0.185787 | + | 0.982590i | \(0.559484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2912 | 0.516968 | 0.258484 | − | 0.966016i | \(-0.416777\pi\) | ||||
0.258484 | + | 0.966016i | \(0.416777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.34986 | −0.0912611 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.60395 | 0.216986 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.99894 | −0.386581 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.5239 | −1.02395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.1517 | −0.429868 | −0.214934 | − | 0.976629i | \(-0.568954\pi\) | ||||
−0.214934 | + | 0.976629i | \(0.568954\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.0771 | −1.04066 | −0.520328 | − | 0.853966i | \(-0.674190\pi\) | ||||
−0.520328 | + | 0.853966i | \(0.674190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.38981 | 0.168466 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.73287 | 0.143044 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.8752 | −0.913561 | −0.456780 | − | 0.889579i | \(-0.650997\pi\) | ||||
−0.456780 | + | 0.889579i | \(0.650997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.13616 | 0.157805 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.5912 | −0.555882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5350 | −1.42790 | −0.713950 | − | 0.700197i | \(-0.753096\pi\) | ||||
−0.713950 | + | 0.700197i | \(0.753096\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.4973 | −0.550706 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.05838 | −0.153722 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.15303 | 0.0436116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.8587 | 1.73206 | 0.866030 | − | 0.499992i | \(-0.166664\pi\) | ||||
0.866030 | + | 0.499992i | \(0.166664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.05192 | −0.115105 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.22777 | 0.196611 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2917 | 0.386515 | 0.193257 | − | 0.981148i | \(-0.438095\pi\) | ||||
0.193257 | + | 0.981148i | \(0.438095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.9685 | 0.823881 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.92083 | 0.221737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.144983 | 0.00541449 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.2862 | 0.570080 | 0.285040 | − | 0.958516i | \(-0.407993\pi\) | ||||
0.285040 | + | 0.958516i | \(0.407993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.6856 | 0.695887 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.4837 | 0.538655 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5486 | −0.687930 | −0.343965 | − | 0.938982i | \(-0.611770\pi\) | ||||
−0.343965 | + | 0.938982i | \(0.611770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.0512 | −0.557451 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3179 | 0.751485 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.6045 | 1.09347 | 0.546734 | − | 0.837307i | \(-0.315871\pi\) | ||||
0.546734 | + | 0.837307i | \(0.315871\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.8976 | −0.990787 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.2455 | −1.62760 | −0.813799 | − | 0.581147i | \(-0.802604\pi\) | ||||
−0.813799 | + | 0.581147i | \(0.802604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.372319 | −0.0136775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.33740 | 0.0857509 | 0.0428755 | − | 0.999080i | \(-0.486348\pi\) | ||||
0.0428755 | + | 0.999080i | \(0.486348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.8630 | −0.543810 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.5066 | −1.00507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.4606 | 1.25748 | 0.628742 | − | 0.777614i | \(-0.283570\pi\) | ||||
0.628742 | + | 0.777614i | \(0.283570\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.94980 | −0.180381 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.5337 | 0.964384 | 0.482192 | − | 0.876066i | \(-0.339841\pi\) | ||||
0.482192 | + | 0.876066i | \(0.339841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.41371 | −0.0513143 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.2585 | −1.74937 | −0.874685 | − | 0.484691i | \(-0.838932\pi\) | ||||
−0.874685 | + | 0.484691i | \(0.838932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6447 | −0.457768 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.6663 | −0.421246 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6874 | 1.14268 | 0.571338 | − | 0.820715i | \(-0.306424\pi\) | ||||
0.571338 | + | 0.820715i | \(0.306424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.7609 | −0.495587 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.7906 | 0.927623 | 0.463811 | − | 0.885934i | \(-0.346481\pi\) | ||||
0.463811 | + | 0.885934i | \(0.346481\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.88441 | 0.282852 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.643021 | −0.0230386 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.3774 | 0.478682 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.7094 | 0.561408 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.2714 | −0.936475 | −0.468237 | − | 0.883603i | \(-0.655111\pi\) | ||||
−0.468237 | + | 0.883603i | \(0.655111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.1200 | −0.431482 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.7044 | −0.416159 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.5560 | −0.729967 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.81284 | 0.205901 | 0.102951 | − | 0.994686i | \(-0.467172\pi\) | ||||
0.102951 | + | 0.994686i | \(0.467172\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8018 | 0.594405 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.7196 | −1.26209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.9309 | 1.16211 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.5950 | 0.443364 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.5439 | 1.53092 | 0.765462 | − | 0.643481i | \(-0.222511\pi\) | ||||
0.765462 | + | 0.643481i | \(0.222511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.0230 | −0.387069 | −0.193535 | − | 0.981093i | \(-0.561995\pi\) | ||||
−0.193535 | + | 0.981093i | \(0.561995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.70044 | −0.0596369 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.21923 | 0.112627 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.2354 | −0.392596 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4664 | 0.644481 | 0.322240 | − | 0.946658i | \(-0.395564\pi\) | ||||
0.322240 | + | 0.946658i | \(0.395564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4960 | −0.400724 | −0.200362 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200362 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9089 | 0.483658 | 0.241829 | − | 0.970319i | \(-0.422253\pi\) | ||||
0.241829 | + | 0.970319i | \(0.422253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.63272 | 0.334558 | 0.167279 | − | 0.985910i | \(-0.446502\pi\) | ||||
0.167279 | + | 0.985910i | \(0.446502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.672759 | 0.0233378 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.02608 | 0.278087 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.5977 | 0.573701 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.697892 | 0.0240939 | 0.0120470 | − | 0.999927i | \(-0.496165\pi\) | ||||
0.0120470 | + | 0.999927i | \(0.496165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.40421 | 0.0829036 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.44880 | 0.256550 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.60644 | −0.158279 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.75236 | −0.197420 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.98088 | −0.307861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.2978 | 1.37977 | 0.689885 | − | 0.723919i | \(-0.257661\pi\) | ||||
0.689885 | + | 0.723919i | \(0.257661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.1828 | −1.64589 | −0.822947 | − | 0.568118i | \(-0.807672\pi\) | ||||
−0.822947 | + | 0.568118i | \(0.807672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.5268 | −1.89455 | −0.947276 | − | 0.320419i | \(-0.896176\pi\) | ||||
−0.947276 | + | 0.320419i | \(0.896176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.66120 | 0.0566135 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.8794 | 1.35751 | 0.678756 | − | 0.734364i | \(-0.262520\pi\) | ||||
0.678756 | + | 0.734364i | \(0.262520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.03122 | −0.204831 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.1061 | −0.783819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.8457 | −0.706328 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.72092 | −0.227469 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.8562 | 1.17701 | 0.588506 | − | 0.808493i | \(-0.299716\pi\) | ||||
0.588506 | + | 0.808493i | \(0.299716\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.2860 | −0.515584 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.94904 | −0.166737 | −0.0833687 | − | 0.996519i | \(-0.526568\pi\) | ||||
−0.0833687 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.95960 | −0.301515 | −0.150757 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150757 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.8125 | −0.967429 | −0.483714 | − | 0.875226i | \(-0.660713\pi\) | ||||
−0.483714 | + | 0.875226i | \(0.660713\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.3409 | −0.380363 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.1329 | 0.674476 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.66213 | 0.0890847 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.09562 | −0.0365818 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.1800 | 1.10662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.8931 | 0.462845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.31665 | −0.276761 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.2784 | −0.972174 | −0.486087 | − | 0.873910i | \(-0.661576\pi\) | ||||
−0.486087 | + | 0.873910i | \(0.661576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00385 | −0.265471 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.48369 | 0.281077 | 0.140539 | − | 0.990075i | \(-0.455117\pi\) | ||||
0.140539 | + | 0.990075i | \(0.455117\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.6327 | 0.517367 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.2668 | 0.471131 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.73942 | −0.189326 | −0.0946630 | − | 0.995509i | \(-0.530177\pi\) | ||||
−0.0946630 | + | 0.995509i | \(0.530177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.697988 | −0.0229995 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3675 | 0.341250 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.6081 | −0.939613 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.72127 | 0.187709 | 0.0938544 | − | 0.995586i | \(-0.470081\pi\) | ||||
0.0938544 | + | 0.995586i | \(0.470081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.27167 | 0.0416775 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.1995 | −0.333917 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.6492 | 1.16461 | 0.582304 | − | 0.812971i | \(-0.302151\pi\) | ||||
0.582304 | + | 0.812971i | \(0.302151\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.260671 | 0.00850668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5212 | −0.636372 | −0.318186 | − | 0.948028i | \(-0.603074\pi\) | ||||
−0.318186 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.89222 | −0.0616191 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.7799 | 1.16269 | 0.581345 | − | 0.813657i | \(-0.302527\pi\) | ||||
0.581345 | + | 0.813657i | \(0.302527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.5215 | 0.828462 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.21889 | −0.104380 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.97808 | 0.323222 | 0.161611 | − | 0.986855i | \(-0.448331\pi\) | ||||
0.161611 | + | 0.986855i | \(0.448331\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.92234 | −0.256093 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.9622 | 0.483155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.05624 | 0.130847 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.1133 | 1.35708 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.6546 | −1.88620 | −0.943102 | − | 0.332505i | \(-0.892106\pi\) | ||||
−0.943102 | + | 0.332505i | \(0.892106\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.354504 | 0.0113883 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.8684 | 1.27944 | 0.639719 | − | 0.768609i | \(-0.279051\pi\) | ||||
0.639719 | + | 0.768609i | \(0.279051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.1997 | 0.519338 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.7860 | 0.856962 | 0.428481 | − | 0.903551i | \(-0.359049\pi\) | ||||
0.428481 | + | 0.903551i | \(0.359049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.5693 | 1.20072 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.3593 | 0.618095 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −58.5711 | −1.86813 | −0.934065 | − | 0.357104i | \(-0.883764\pi\) | ||||
−0.934065 | + | 0.357104i | \(0.883764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.87741 | −0.218910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.47322 | 0.301231 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.9818 | 1.71479 | 0.857394 | − | 0.514661i | \(-0.172082\pi\) | ||||
0.857394 | + | 0.514661i | \(0.172082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.883366 | 0.0280328 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.592272 | −0.0187575 | −0.00937873 | − | 0.999956i | \(-0.502985\pi\) | ||||
−0.00937873 | + | 0.999956i | \(0.502985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.1759 | −0.796530 |
(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 | 9200.2.a.cx.1.4 | 6 | ||
4.3 | odd | 2 | 2300.2.a.o.1.3 | 6 | |||
5.2 | odd | 4 | 1840.2.e.f.369.6 | 12 | |||
5.3 | odd | 4 | 1840.2.e.f.369.7 | 12 | |||
5.4 | even | 2 | 9200.2.a.cy.1.3 | 6 | |||
20.3 | even | 4 | 460.2.c.a.369.6 | ✓ | 12 | ||
20.7 | even | 4 | 460.2.c.a.369.7 | yes | 12 | ||
20.19 | odd | 2 | 2300.2.a.n.1.4 | 6 | |||
60.23 | odd | 4 | 4140.2.f.b.829.5 | 12 | |||
60.47 | odd | 4 | 4140.2.f.b.829.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.6 | ✓ | 12 | 20.3 | even | 4 | ||
460.2.c.a.369.7 | yes | 12 | 20.7 | even | 4 | ||
1840.2.e.f.369.6 | 12 | 5.2 | odd | 4 | |||
1840.2.e.f.369.7 | 12 | 5.3 | odd | 4 | |||
2300.2.a.n.1.4 | 6 | 20.19 | odd | 2 | |||
2300.2.a.o.1.3 | 6 | 4.3 | odd | 2 | |||
4140.2.f.b.829.5 | 12 | 60.23 | odd | 4 | |||
4140.2.f.b.829.6 | 12 | 60.47 | odd | 4 | |||
9200.2.a.cx.1.4 | 6 | 1.1 | even | 1 | trivial | ||
9200.2.a.cy.1.3 | 6 | 5.4 | even | 2 |