Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 17 x^{10} + 49 x^{9} + 106 x^{8} - 277 x^{7} - 317 x^{6} + 644 x^{5} + 537 x^{4} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.54171\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 2.54171 | 1.46745 | 0.733727 | − | 0.679444i | \(-0.237779\pi\) | ||||
0.733727 | + | 0.679444i | \(0.237779\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.59809 | 0.714688 | 0.357344 | − | 0.933973i | \(-0.383682\pi\) | ||||
0.357344 | + | 0.933973i | \(0.383682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13408 | −0.806608 | −0.403304 | − | 0.915066i | \(-0.632138\pi\) | ||||
−0.403304 | + | 0.915066i | \(0.632138\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.46027 | 1.15342 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.04529 | −1.52121 | −0.760605 | − | 0.649215i | \(-0.775098\pi\) | ||||
−0.760605 | + | 0.649215i | \(0.775098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.30452 | −0.361810 | −0.180905 | − | 0.983501i | \(-0.557903\pi\) | ||||
−0.180905 | + | 0.983501i | \(0.557903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.06188 | 1.04877 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.38632 | 0.336231 | 0.168116 | − | 0.985767i | \(-0.446232\pi\) | ||||
0.168116 | + | 0.985767i | \(0.446232\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.89363 | −0.893260 | −0.446630 | − | 0.894719i | \(-0.647376\pi\) | ||||
−0.446630 | + | 0.894719i | \(0.647376\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.42421 | −1.18366 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.19413 | −1.50008 | −0.750039 | − | 0.661393i | \(-0.769966\pi\) | ||||
−0.750039 | + | 0.661393i | \(0.769966\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44611 | −0.489221 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.16987 | 0.225141 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.67098 | −0.681684 | −0.340842 | − | 0.940121i | \(-0.610712\pi\) | ||||
−0.340842 | + | 0.940121i | \(0.610712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.32640 | −0.238229 | −0.119115 | − | 0.992881i | \(-0.538006\pi\) | ||||
−0.119115 | + | 0.992881i | \(0.538006\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.8236 | −2.23231 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.41046 | −0.576473 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.51613 | −0.249250 | −0.124625 | − | 0.992204i | \(-0.539773\pi\) | ||||
−0.124625 | + | 0.992204i | \(0.539773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.31572 | −0.530940 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.98934 | −1.40390 | −0.701949 | − | 0.712227i | \(-0.747687\pi\) | ||||
−0.701949 | + | 0.712227i | \(0.747687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.23204 | −0.950377 | −0.475188 | − | 0.879884i | \(-0.657620\pi\) | ||||
−0.475188 | + | 0.879884i | \(0.657620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.52983 | 0.824338 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.82639 | 0.995731 | 0.497866 | − | 0.867254i | \(-0.334117\pi\) | ||||
0.497866 | + | 0.867254i | \(0.334117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.44568 | −0.349384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.52361 | 0.493404 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.91183 | 0.399970 | 0.199985 | − | 0.979799i | \(-0.435911\pi\) | ||||
0.199985 | + | 0.979799i | \(0.435911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.06282 | −1.08719 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.89647 | −1.31082 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.42567 | 1.22712 | 0.613559 | − | 0.789649i | \(-0.289737\pi\) | ||||
0.613559 | + | 0.789649i | \(0.289737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4693 | 1.46849 | 0.734244 | − | 0.678886i | \(-0.237537\pi\) | ||||
0.734244 | + | 0.678886i | \(0.237537\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.38451 | −0.930360 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.08475 | −0.258581 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.381738 | −0.0466367 | −0.0233184 | − | 0.999728i | \(-0.507423\pi\) | ||||
−0.0233184 | + | 0.999728i | \(0.507423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.2854 | −2.20130 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60686 | 0.190699 | 0.0953497 | − | 0.995444i | \(-0.469603\pi\) | ||||
0.0953497 | + | 0.995444i | \(0.469603\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.1431 | 1.53828 | 0.769142 | − | 0.639078i | \(-0.220684\pi\) | ||||
0.769142 | + | 0.639078i | \(0.220684\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.21728 | −0.717910 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.7671 | 1.22702 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.64917 | −0.185546 | −0.0927732 | − | 0.995687i | \(-0.529573\pi\) | ||||
−0.0927732 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.40734 | −0.823038 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.795405 | −0.0873070 | −0.0436535 | − | 0.999047i | \(-0.513900\pi\) | ||||
−0.0436535 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.21546 | 0.240301 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.33055 | −1.00034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.551016 | −0.0584076 | −0.0292038 | − | 0.999573i | \(-0.509297\pi\) | ||||
−0.0292038 | + | 0.999573i | \(0.509297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.78397 | 0.291839 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.37133 | −0.349590 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.22238 | −0.638403 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.66229 | −0.777988 | −0.388994 | − | 0.921240i | \(-0.627177\pi\) | ||||
−0.388994 | + | 0.921240i | \(0.627177\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.4580 | −1.75460 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.08961 | 0.804946 | 0.402473 | − | 0.915432i | \(-0.368151\pi\) | ||||
0.402473 | + | 0.915432i | \(0.368151\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.8314 | 1.65845 | 0.829223 | − | 0.558918i | \(-0.188783\pi\) | ||||
0.829223 | + | 0.558918i | \(0.188783\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.66839 | −0.845948 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.9663 | −1.06015 | −0.530075 | − | 0.847951i | \(-0.677836\pi\) | ||||
−0.530075 | + | 0.847951i | \(0.677836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8382 | 1.70859 | 0.854296 | − | 0.519786i | \(-0.173988\pi\) | ||||
0.854296 | + | 0.519786i | \(0.173988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.85356 | −0.365763 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50047 | 0.423369 | 0.211684 | − | 0.977338i | \(-0.432105\pi\) | ||||
0.211684 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.4969 | −1.07209 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.51401 | −0.417320 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.95852 | −0.271207 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.4549 | 1.31408 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.8482 | −2.06016 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8996 | −1.06433 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.7104 | −1.83775 | −0.918877 | − | 0.394543i | \(-0.870903\pi\) | ||||
−0.918877 | + | 0.394543i | \(0.870903\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.8400 | −1.39463 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.27198 | −0.722727 | −0.361363 | − | 0.932425i | \(-0.617689\pi\) | ||||
−0.361363 | + | 0.932425i | \(0.617689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.30934 | 0.720511 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.86956 | 0.160906 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.0707 | 1.80019 | 0.900096 | − | 0.435692i | \(-0.143496\pi\) | ||||
0.900096 | + | 0.435692i | \(0.143496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.97751 | −0.591825 | −0.295912 | − | 0.955215i | \(-0.595624\pi\) | ||||
−0.295912 | + | 0.955215i | \(0.595624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.3507 | 1.46119 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.58170 | 0.550389 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.86656 | −0.487191 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.21621 | −0.512704 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.52562 | −0.124984 | −0.0624920 | − | 0.998045i | \(-0.519905\pi\) | ||||
−0.0624920 | + | 0.998045i | \(0.519905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.20585 | 0.260889 | 0.130444 | − | 0.991456i | \(-0.458360\pi\) | ||||
0.130444 | + | 0.991456i | \(0.458360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.79703 | 0.387817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.11971 | −0.170259 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.55587 | −0.203981 | −0.101990 | − | 0.994785i | \(-0.532521\pi\) | ||||
−0.101990 | + | 0.994785i | \(0.532521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.40101 | 0.586938 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3529 | 1.20998 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.41086 | 0.658790 | 0.329395 | − | 0.944192i | \(-0.393155\pi\) | ||||
0.329395 | + | 0.944192i | \(0.393155\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.4933 | −1.59540 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.2059 | −1.56358 | −0.781788 | − | 0.623544i | \(-0.785692\pi\) | ||||
−0.781788 | + | 0.623544i | \(0.785692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2982 | −0.869093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.4730 | −1.03031 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.5098 | 1.63536 | 0.817682 | − | 0.575671i | \(-0.195259\pi\) | ||||
0.817682 | + | 0.575671i | \(0.195259\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.22019 | 0.394610 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.9573 | 1.80074 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.80625 | 0.135006 | 0.0675029 | − | 0.997719i | \(-0.478497\pi\) | ||||
0.0675029 | + | 0.997719i | \(0.478497\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.3324 | −1.36264 | −0.681318 | − | 0.731988i | \(-0.738593\pi\) | ||||
−0.681318 | + | 0.731988i | \(0.738593\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.1515 | 2.15494 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42291 | −0.178136 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.99437 | −0.511479 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.49660 | −0.181601 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4495 | 1.11789 | 0.558944 | − | 0.829206i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829206i | \(0.311207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1402 | −0.801890 | −0.400945 | − | 0.916102i | \(-0.631318\pi\) | ||||
−0.400945 | + | 0.916102i | \(0.631318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.29882 | −0.379456 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.47432 | −0.318782 | −0.159391 | − | 0.987216i | \(-0.550953\pi\) | ||||
−0.159391 | + | 0.987216i | \(0.550953\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.09932 | 0.645034 | 0.322517 | − | 0.946564i | \(-0.395471\pi\) | ||||
0.322517 | + | 0.946564i | \(0.395471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.970265 | −0.0684372 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.83418 | 0.549852 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.3658 | −1.00335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.8936 | −1.73023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.6445 | 1.35884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.452599 | 0.0311582 | 0.0155791 | − | 0.999879i | \(-0.495041\pi\) | ||||
0.0155791 | + | 0.999879i | \(0.495041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.08417 | 0.279843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.95936 | −0.679223 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.83066 | 0.192157 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 33.4059 | 2.25736 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.80849 | −0.121652 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3626 | 0.693932 | 0.346966 | − | 0.937878i | \(-0.387212\pi\) | ||||
0.346966 | + | 0.937878i | \(0.387212\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.46418 | −0.564279 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.9433 | −1.92103 | −0.960516 | − | 0.278224i | \(-0.910254\pi\) | ||||
−0.960516 | + | 0.278224i | \(0.910254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8134 | −1.04498 | −0.522489 | − | 0.852646i | \(-0.674997\pi\) | ||||
−0.522489 | + | 0.852646i | \(0.674997\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.3667 | 1.80060 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.37375 | −0.0899975 | −0.0449987 | − | 0.998987i | \(-0.514328\pi\) | ||||
−0.0449987 | + | 0.998987i | \(0.514328\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.9092 | 0.711637 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.19171 | −0.272281 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.55257 | 0.423850 | 0.211925 | − | 0.977286i | \(-0.432027\pi\) | ||||
0.211925 | + | 0.977286i | \(0.432027\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1044 | 0.779714 | 0.389857 | − | 0.920875i | \(-0.372524\pi\) | ||||
0.389857 | + | 0.920875i | \(0.372524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3369 | −1.43291 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.90843 | −0.249700 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.07934 | 0.323191 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.02169 | −0.128119 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.2964 | 2.28194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.63105 | 0.352630 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.95959 | 0.434127 | 0.217064 | − | 0.976157i | \(-0.430352\pi\) | ||||
0.217064 | + | 0.976157i | \(0.430352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.23555 | 0.201047 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.7026 | −0.786270 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.55435 | −0.342496 | −0.171248 | − | 0.985228i | \(-0.554780\pi\) | ||||
−0.171248 | + | 0.985228i | \(0.554780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.65337 | 0.285854 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.40052 | −0.0857105 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.82631 | 0.233294 | 0.116647 | − | 0.993173i | \(-0.462785\pi\) | ||||
0.116647 | + | 0.993173i | \(0.462785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.73772 | −0.591524 | −0.295762 | − | 0.955262i | \(-0.595574\pi\) | ||||
−0.295762 | + | 0.955262i | \(0.595574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.07602 | 0.428260 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.3413 | 0.744208 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.183259 | 0.0110110 | 0.00550548 | − | 0.999985i | \(-0.498248\pi\) | ||||
0.00550548 | + | 0.999985i | \(0.498248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.58971 | −0.274779 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9547 | −1.36937 | −0.684683 | − | 0.728841i | \(-0.740059\pi\) | ||||
−0.684683 | + | 0.728841i | \(0.740059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.52082 | 0.149847 | 0.0749235 | − | 0.997189i | \(-0.476129\pi\) | ||||
0.0749235 | + | 0.997189i | \(0.476129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.8155 | −0.936827 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.1840 | 1.13240 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0781 | −0.886948 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.4753 | −1.14166 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.5994 | −1.37869 | −0.689344 | − | 0.724434i | \(-0.742101\pi\) | ||||
−0.689344 | + | 0.724434i | \(0.742101\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0631 | 0.877006 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.90232 | −0.342488 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.38492 | 0.542744 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.2997 | 0.766581 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.5614 | 1.18122 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.3289 | 1.04951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.97689 | −0.455265 | −0.227632 | − | 0.973747i | \(-0.573098\pi\) | ||||
−0.227632 | + | 0.973747i | \(0.573098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 42.7805 | 2.43369 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.3344 | 0.586012 | 0.293006 | − | 0.956111i | \(-0.405344\pi\) | ||||
0.293006 | + | 0.956111i | \(0.405344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.34392 | −0.189010 | −0.0945048 | − | 0.995524i | \(-0.530127\pi\) | ||||
−0.0945048 | + | 0.995524i | \(0.530127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.8011 | −0.664917 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.85428 | 0.328809 | 0.164405 | − | 0.986393i | \(-0.447430\pi\) | ||||
0.164405 | + | 0.986393i | \(0.447430\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.5211 | 1.03698 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.8731 | −1.55572 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.39781 | −0.300342 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.19100 | 0.177005 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 45.3395 | 2.50728 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.5681 | −0.803165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.39239 | −0.186463 | −0.0932313 | − | 0.995644i | \(-0.529720\pi\) | ||||
−0.0932313 | + | 0.995644i | \(0.529720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.24622 | −0.287491 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.610052 | −0.0333307 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6012 | 1.17669 | 0.588347 | − | 0.808608i | \(-0.299779\pi\) | ||||
0.588347 | + | 0.808608i | \(0.299779\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.4389 | 0.621274 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.69208 | 0.362397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1579 | 1.08842 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.2217 | −1.57324 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.1731 | −1.35136 | −0.675680 | − | 0.737195i | \(-0.736150\pi\) | ||||
−0.675680 | + | 0.737195i | \(0.736150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1278 | 1.02389 | 0.511945 | − | 0.859019i | \(-0.328925\pi\) | ||||
0.511945 | + | 0.859019i | \(0.328925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.52612 | −0.0814584 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.2057 | −1.07544 | −0.537721 | − | 0.843123i | \(-0.680714\pi\) | ||||
−0.537721 | + | 0.843123i | \(0.680714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.56791 | 0.136291 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.51969 | −0.397984 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.81237 | −0.465099 | −0.232549 | − | 0.972585i | \(-0.574707\pi\) | ||||
−0.232549 | + | 0.972585i | \(0.574707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.83963 | −0.202086 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 36.7401 | 1.92836 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0039 | 1.09939 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3718 | 1.22000 | 0.610000 | − | 0.792401i | \(-0.291169\pi\) | ||||
0.610000 | + | 0.792401i | \(0.291169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.1055 | −1.61929 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.21409 | −0.322619 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.5810 | −1.06565 | −0.532823 | − | 0.846227i | \(-0.678869\pi\) | ||||
−0.532823 | + | 0.846227i | \(0.678869\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.2452 | −1.56185 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.78888 | 0.246640 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6588 | −0.804340 | −0.402170 | − | 0.915565i | \(-0.631744\pi\) | ||||
−0.402170 | + | 0.915565i | \(0.631744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −52.6399 | −2.69682 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8618 | −0.912697 | −0.456349 | − | 0.889801i | \(-0.650843\pi\) | ||||
−0.456349 | + | 0.889801i | \(0.650843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.2067 | 0.876937 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.5645 | −1.09619 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.193458 | 0.00980869 | 0.00490435 | − | 0.999988i | \(-0.498439\pi\) | ||||
0.00490435 | + | 0.999988i | \(0.498439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.97335 | −0.504374 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.0250 | −1.06057 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.63553 | −0.132608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.91134 | −0.346870 | −0.173435 | − | 0.984845i | \(-0.555487\pi\) | ||||
−0.173435 | + | 0.984845i | \(0.555487\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.1199 | 1.05732 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0625622 | 0.00312421 | 0.00156210 | − | 0.999999i | \(-0.499503\pi\) | ||||
0.00156210 | + | 0.999999i | \(0.499503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.73033 | 0.0861937 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.8376 | −0.588216 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.64931 | 0.379162 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.7758 | −1.86789 | −0.933946 | − | 0.357413i | \(-0.883659\pi\) | ||||
−0.933946 | + | 0.357413i | \(0.883659\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 53.5555 | 2.64170 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.1152 | −0.989803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.27113 | −0.0623973 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.7348 | −0.868476 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.50796 | 0.464494 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46623 | 0.168934 | 0.0844670 | − | 0.996426i | \(-0.473081\pi\) | ||||
0.0844670 | + | 0.996426i | \(0.473081\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.6211 | 1.14850 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.39108 | −0.164492 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.4764 | −1.18449 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.7287 | 0.807671 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.25683 | −0.108707 | −0.0543537 | − | 0.998522i | \(-0.517310\pi\) | ||||
−0.0543537 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.6218 | −1.47159 | −0.735794 | − | 0.677205i | \(-0.763191\pi\) | ||||
−0.735794 | + | 0.677205i | \(0.763191\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.9111 | −0.714931 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.0113 | 1.33996 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.8888 | 0.901515 | 0.450757 | − | 0.892646i | \(-0.351154\pi\) | ||||
0.450757 | + | 0.892646i | \(0.351154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.46273 | −0.402987 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.3435 | −1.20411 | −0.602053 | − | 0.798456i | \(-0.705650\pi\) | ||||
−0.602053 | + | 0.798456i | \(0.705650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.880575 | −0.0417432 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.87769 | −0.183408 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.3032 | 1.19413 | 0.597067 | − | 0.802192i | \(-0.296333\pi\) | ||||
0.597067 | + | 0.802192i | \(0.296333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45.3538 | 2.13563 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.14834 | 0.382842 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.44903 | 0.208574 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.4337 | −1.18974 | −0.594869 | − | 0.803823i | \(-0.702796\pi\) | ||||
−0.594869 | + | 0.803823i | \(0.702796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.62181 | 0.0756996 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.02340 | 0.420261 | 0.210131 | − | 0.977673i | \(-0.432611\pi\) | ||||
0.210131 | + | 0.977673i | \(0.432611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7729 | 0.593606 | 0.296803 | − | 0.954939i | \(-0.404080\pi\) | ||||
0.296803 | + | 0.954939i | \(0.404080\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.38769 | −0.249848 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6856 | 0.494469 | 0.247235 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247235 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.814661 | 0.0376175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.49627 | −0.299332 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.4424 | 1.44572 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.52423 | 0.437002 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0757 | 0.461335 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.54775 | 0.0707187 | 0.0353594 | − | 0.999375i | \(-0.488742\pi\) | ||||
0.0353594 | + | 0.999375i | \(0.488742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.97783 | 0.0901813 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 39.0225 | 1.77558 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.2450 | −0.556019 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.1077 | −1.09242 | −0.546212 | − | 0.837647i | \(-0.683931\pi\) | ||||
−0.546212 | + | 0.837647i | \(0.683931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.3779 | 0.966744 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8426 | 0.579579 | 0.289790 | − | 0.957090i | \(-0.406415\pi\) | ||||
0.289790 | + | 0.957090i | \(0.406415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.08914 | −0.229204 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.8995 | −1.25399 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.42918 | −0.153820 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.2582 | −1.39931 | −0.699656 | − | 0.714480i | \(-0.746663\pi\) | ||||
−0.699656 | + | 0.714480i | \(0.746663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −51.3574 | −2.29448 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.4896 | −1.80534 | −0.902671 | − | 0.430331i | \(-0.858397\pi\) | ||||
−0.902671 | + | 0.430331i | \(0.858397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.9279 | 0.575285 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.7167 | −1.27536 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.6633 | 0.516969 | 0.258484 | − | 0.966015i | \(-0.416777\pi\) | ||||
0.258484 | + | 0.966015i | \(0.416777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0485 | −1.24079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.55504 | −0.201110 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.8981 | 1.18527 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.4411 | −1.51472 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 54.6717 | 2.39982 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.9667 | −0.962380 | −0.481190 | − | 0.876616i | \(-0.659795\pi\) | ||||
−0.481190 | + | 0.876616i | \(0.659795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.0482 | 1.05155 | 0.525777 | − | 0.850623i | \(-0.323775\pi\) | ||||
0.525777 | + | 0.850623i | \(0.323775\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.2682 | 0.579072 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.83882 | −0.0801001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.7554 | 1.25024 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.6154 | 1.41539 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7268 | 0.507945 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.5251 | −0.757676 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.59097 | 0.198115 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.3392 | 0.531486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.8332 | 1.15365 | 0.576824 | − | 0.816868i | \(-0.304292\pi\) | ||||
0.576824 | + | 0.816868i | \(0.304292\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.5955 | −1.99961 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.5071 | 1.22111 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0363 | 0.557391 | 0.278696 | − | 0.960379i | \(-0.410098\pi\) | ||||
0.278696 | + | 0.960379i | \(0.410098\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.6867 | 1.69379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.2934 | 0.608921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.51947 | 0.149663 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.15833 | −0.261407 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.3232 | 1.83566 | 0.917831 | − | 0.396972i | \(-0.129939\pi\) | ||||
0.917831 | + | 0.396972i | \(0.129939\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.12985 | 0.343856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.7776 | −0.750572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3743 | 0.479368 | 0.239684 | − | 0.970851i | \(-0.422956\pi\) | ||||
0.239684 | + | 0.970851i | \(0.422956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.19216 | 0.302577 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.8079 | 0.663869 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.3860 | −1.48346 | −0.741729 | − | 0.670700i | \(-0.765994\pi\) | ||||
−0.741729 | + | 0.670700i | \(0.765994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3697 | −1.14539 | −0.572693 | − | 0.819770i | \(-0.694101\pi\) | ||||
−0.572693 | + | 0.819770i | \(0.694101\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.2681 | 1.64045 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.5976 | 0.733870 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.8609 | 1.74269 | 0.871347 | − | 0.490667i | \(-0.163247\pi\) | ||||
0.871347 | + | 0.490667i | \(0.163247\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.3151 | −1.17674 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.69746 | 0.0704225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.6910 | −0.608439 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.21379 | −0.298254 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.28935 | 0.259589 | 0.129795 | − | 0.991541i | \(-0.458568\pi\) | ||||
0.129795 | + | 0.991541i | \(0.458568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.16453 | 0.212801 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.3724 | −0.467798 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.2028 | −1.24028 | −0.620141 | − | 0.784491i | \(-0.712925\pi\) | ||||
−0.620141 | + | 0.784491i | \(0.712925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.72798 | −0.193828 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.1278 | 0.946558 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.5651 | −0.921984 | −0.460992 | − | 0.887404i | \(-0.652506\pi\) | ||||
−0.460992 | + | 0.887404i | \(0.652506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.8820 | −0.729422 | −0.364711 | − | 0.931121i | \(-0.618832\pi\) | ||||
−0.364711 | + | 0.931121i | \(0.618832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.32092 | −0.0537919 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.1002 | 0.939159 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.12709 | −0.0457472 | −0.0228736 | − | 0.999738i | \(-0.507282\pi\) | ||||
−0.0228736 | + | 0.999738i | \(0.507282\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.9122 | 0.806882 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.90520 | −0.360266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.96703 | −0.321785 | −0.160893 | − | 0.986972i | \(-0.551437\pi\) | ||||
−0.160893 | + | 0.986972i | \(0.551437\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.5136 | −1.47237 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.1850 | 0.530809 | 0.265405 | − | 0.964137i | \(-0.414494\pi\) | ||||
0.265405 | + | 0.964137i | \(0.414494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1297 | 1.33160 | 0.665798 | − | 0.746132i | \(-0.268091\pi\) | ||||
0.665798 | + | 0.746132i | \(0.268091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.41619 | −0.337730 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.17592 | 0.0471121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.78604 | −0.271442 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 49.9305 | 1.99403 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.10184 | −0.0838058 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.8604 | −0.790631 | −0.395316 | − | 0.918545i | \(-0.629365\pi\) | ||||
−0.395316 | + | 0.918545i | \(0.629365\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.15037 | 0.0457232 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.0972 | −1.31342 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.19046 | 0.126410 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.56017 | 0.219957 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.7746 | −0.465070 | −0.232535 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232535 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.43202 | −0.293090 | −0.146545 | − | 0.989204i | \(-0.546815\pi\) | ||||
−0.146545 | + | 0.989204i | \(0.546815\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.3138 | −0.996729 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.7841 | −1.01368 | −0.506838 | − | 0.862041i | \(-0.669186\pi\) | ||||
−0.506838 | + | 0.862041i | \(0.669186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.5552 | −1.86670 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.19470 | 0.281982 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.13174 | −0.357352 | −0.178676 | − | 0.983908i | \(-0.557181\pi\) | ||||
−0.178676 | + | 0.983908i | \(0.557181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2194 | −0.516524 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 45.4787 | 1.77429 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.0069 | 1.36367 | 0.681837 | − | 0.731504i | \(-0.261181\pi\) | ||||
0.681837 | + | 0.731504i | \(0.261181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5112 | −0.797795 | −0.398897 | − | 0.916996i | \(-0.630607\pi\) | ||||
−0.398897 | + | 0.916996i | \(0.630607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.59664 | −0.178519 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.2791 | 0.514941 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.4095 | 1.02258 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.3387 | 1.01831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −57.8657 | −2.23388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.3968 | −1.09462 | −0.547308 | − | 0.836931i | \(-0.684347\pi\) | ||||
−0.547308 | + | 0.836931i | \(0.684347\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.86162 | −0.110144 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.4454 | −1.13168 | −0.565839 | − | 0.824516i | \(-0.691447\pi\) | ||||
−0.565839 | + | 0.824516i | \(0.691447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.3520 | 0.627531 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −73.5653 | −2.81903 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9146 | 0.647219 | 0.323609 | − | 0.946191i | \(-0.395104\pi\) | ||||
0.323609 | + | 0.946191i | \(0.395104\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.6729 | 1.28658 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.1930 | −1.53346 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.79855 | −0.144713 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.6037 | −0.859885 | −0.429942 | − | 0.902856i | \(-0.641466\pi\) | ||||
−0.429942 | + | 0.902856i | \(0.641466\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 37.2569 | 1.41527 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.1507 | −0.422970 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4621 | −0.472035 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.49167 | −0.132067 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9476 | 0.904487 | 0.452243 | − | 0.891895i | \(-0.350624\pi\) | ||||
0.452243 | + | 0.891895i | \(0.350624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.90325 | 0.222645 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.7280 | 1.04430 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.2639 | −0.649276 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.1930 | −1.35926 | −0.679629 | − | 0.733556i | \(-0.737859\pi\) | ||||
−0.679629 | + | 0.733556i | \(0.737859\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.70658 | −0.214014 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.54231 | 0.357362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.5182 | 0.393357 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.6547 | 0.621981 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.7318 | 0.847754 | 0.423877 | − | 0.905720i | \(-0.360669\pi\) | ||||
0.423877 | + | 0.905720i | \(0.360669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.9196 | −1.33772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.7659 | 1.14419 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.97960 | 0.333494 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1774 | −0.711250 | −0.355625 | − | 0.934629i | \(-0.615732\pi\) | ||||
−0.355625 | + | 0.934629i | \(0.615732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.5518 | −1.27970 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.63958 | −0.319547 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.1975 | −1.52166 | −0.760832 | − | 0.648949i | \(-0.775209\pi\) | ||||
−0.760832 | + | 0.648949i | \(0.775209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.93407 | −0.366424 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.92598 | 0.0709443 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.3856 | −0.455611 | −0.227806 | − | 0.973707i | \(-0.573155\pi\) | ||||
−0.227806 | + | 0.973707i | \(0.573155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.9102 | 0.474268 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.9274 | −1.20799 | −0.603994 | − | 0.796989i | \(-0.706425\pi\) | ||||
−0.603994 | + | 0.796989i | \(0.706425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.43808 | −0.0893245 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.75232 | −0.100702 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.4030 | 0.855125 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.8582 | −1.08954 | −0.544770 | − | 0.838586i | \(-0.683383\pi\) | ||||
−0.544770 | + | 0.838586i | \(0.683383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.54171 | −0.0926249 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.12325 | 0.186454 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.9563 | 1.63397 | 0.816983 | − | 0.576662i | \(-0.195645\pi\) | ||||
0.816983 | + | 0.576662i | \(0.195645\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 92.2548 | 3.34864 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.4840 | 1.21379 | 0.606897 | − | 0.794781i | \(-0.292414\pi\) | ||||
0.606897 | + | 0.794781i | \(0.292414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.0683 | −1.37816 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.66610 | 0.277168 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.2960 | −0.443984 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2470 | −1.27104 | −0.635520 | − | 0.772084i | \(-0.719214\pi\) | ||||
−0.635520 | + | 0.772084i | \(0.719214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6892 | 0.637062 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.6216 | −1.46106 | −0.730528 | − | 0.682883i | \(-0.760726\pi\) | ||||
−0.730528 | + | 0.682883i | \(0.760726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.24452 | 0.116547 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.22382 | 0.295028 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.0012 | 1.25405 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.10707 | −0.290094 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.29457 | −0.153475 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.08451 | −0.145783 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.6719 | −1.20027 | −0.600137 | − | 0.799897i | \(-0.704887\pi\) | ||||
−0.600137 | + | 0.799897i | \(0.704887\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.1175 | −0.502598 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.60438 | −0.341493 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.9619 | −0.531314 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.8275 | 0.419478 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.5850 | −0.374940 | −0.187470 | − | 0.982270i | \(-0.560029\pi\) | ||||
−0.187470 | + | 0.982270i | \(0.560029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.46355 | 0.334796 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.90667 | −0.0673687 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −66.3107 | −2.34006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.5353 | 0.864755 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.72535 | 0.342349 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.1819 | 1.27209 | 0.636045 | − | 0.771652i | \(-0.280569\pi\) | ||||
0.636045 | + | 0.771652i | \(0.280569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.59789 | 0.337027 | 0.168514 | − | 0.985699i | \(-0.446103\pi\) | ||||
0.168514 | + | 0.985699i | \(0.446103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.7504 | −0.868035 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.4413 | 0.470829 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.2653 | 0.848934 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.63327 | 0.336614 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.5397 | 0.821540 | 0.410770 | − | 0.911739i | \(-0.365260\pi\) | ||||
0.410770 | + | 0.911739i | \(0.365260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.7477 | 1.76895 | 0.884476 | − | 0.466586i | \(-0.154516\pi\) | ||||
0.884476 | + | 0.466586i | \(0.154516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 31.3680 | 1.09209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.6898 | 0.823773 | 0.411887 | − | 0.911235i | \(-0.364870\pi\) | ||||
0.411887 | + | 0.911235i | \(0.364870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.6980 | −0.961992 | −0.480996 | − | 0.876723i | \(-0.659725\pi\) | ||||
−0.480996 | + | 0.876723i | \(0.659725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.465790 | 0.0161581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.39050 | −0.117474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.2908 | −1.11747 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.55172 | −0.0536352 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4722 | 0.879397 | 0.439698 | − | 0.898146i | \(-0.355085\pi\) | ||||
0.439698 | + | 0.898146i | \(0.355085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5239 | −0.535307 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −58.3442 | −2.00948 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.0556 | −0.621131 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.8480 | −1.05995 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.40718 | 0.219894 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9072 | 0.373895 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.5546 | 1.76520 | 0.882598 | − | 0.470128i | \(-0.155792\pi\) | ||||
0.882598 | + | 0.470128i | \(0.155792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.5311 | −0.736348 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.96362 | −0.101235 | −0.0506176 | − | 0.998718i | \(-0.516119\pi\) | ||||
−0.0506176 | + | 0.998718i | \(0.516119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.4356 | 1.03845 | 0.519225 | − | 0.854637i | \(-0.326221\pi\) | ||||
0.519225 | + | 0.854637i | \(0.326221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.7601 | 1.66174 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.0957 | 1.16063 | 0.580315 | − | 0.814392i | \(-0.302929\pi\) | ||||
0.580315 | + | 0.814392i | \(0.302929\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.3747 | 1.16877 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.3242 | −1.30156 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.32055 | 0.282255 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.497987 | 0.0168736 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.5136 | −0.897349 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.3946 | 0.858496 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.76496 | −0.127134 | −0.0635669 | − | 0.997978i | \(-0.520248\pi\) | ||||
−0.0635669 | + | 0.997978i | \(0.520248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −59.9826 | −2.02316 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.0494 | 0.742864 | 0.371432 | − | 0.928460i | \(-0.378867\pi\) | ||||
0.371432 | + | 0.928460i | \(0.378867\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7325 | 0.596746 | 0.298373 | − | 0.954449i | \(-0.403556\pi\) | ||||
0.298373 | + | 0.954449i | \(0.403556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.2859 | 1.28697 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.336822 | −0.0113094 | −0.00565468 | − | 0.999984i | \(-0.501800\pi\) | ||||
−0.00565468 | + | 0.999984i | \(0.501800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.1978 | 1.48235 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.3722 | 1.25201 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.5795 | −0.889448 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.88656 | 0.0964870 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.8537 | 0.796452 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.86920 | 0.162397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.03672 | 0.134483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.8039 | 1.12492 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.2968 | −0.973859 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9599 | −0.430327 | −0.215164 | − | 0.976578i | \(-0.569029\pi\) | ||||
−0.215164 | + | 0.976578i | \(0.569029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.9922 | 0.928443 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0769 | −0.797702 | −0.398851 | − | 0.917016i | \(-0.630591\pi\) | ||||
−0.398851 | + | 0.917016i | \(0.630591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.01304 | 0.132812 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 46.5867 | 1.54011 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.6531 | 0.582957 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3872 | −0.474592 | −0.237296 | − | 0.971437i | \(-0.576261\pi\) | ||||
−0.237296 | + | 0.971437i | \(0.576261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2749 | −0.668081 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.09619 | −0.0689969 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.70861 | 0.121938 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 58.2412 | 1.91289 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.60076 | 0.0853282 | 0.0426641 | − | 0.999089i | \(-0.486415\pi\) | ||||
0.0426641 | + | 0.999089i | \(0.486415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.52260 | 0.312091 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.2671 | 0.859945 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.1776 | −0.365548 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.2275 | −0.856815 | −0.428408 | − | 0.903586i | \(-0.640925\pi\) | ||||
−0.428408 | + | 0.903586i | \(0.640925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.49926 | −0.277363 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.8090 | −0.841350 | −0.420675 | − | 0.907211i | \(-0.638207\pi\) | ||||
−0.420675 | + | 0.907211i | \(0.638207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.6704 | 2.10596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.98979 | −0.129788 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.7228 | 1.61577 | 0.807886 | − | 0.589338i | \(-0.200611\pi\) | ||||
0.807886 | + | 0.589338i | \(0.200611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1455 | −0.556567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.8799 | 0.482513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.91565 | −0.256413 | −0.128207 | − | 0.991747i | \(-0.540922\pi\) | ||||
−0.128207 | + | 0.991747i | \(0.540922\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.6897 | 0.798941 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.0753 | 1.52173 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.9666 | −1.45205 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2407 | −0.943247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −37.9463 | −1.22280 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8031 | −0.573101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.7013 | 1.56613 | 0.783065 | − | 0.621940i | \(-0.213655\pi\) | ||||
0.783065 | + | 0.621940i | \(0.213655\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.7197 | −0.440739 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.5260 | −0.658711 | −0.329356 | − | 0.944206i | \(-0.606832\pi\) | ||||
−0.329356 | + | 0.944206i | \(0.606832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.8906 | 0.477371 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.11060 | 0.259747 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.7385 | 0.791455 | 0.395727 | − | 0.918368i | \(-0.370492\pi\) | ||||
0.395727 | + | 0.918368i | \(0.370492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.78004 | 0.0888503 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 61.7251 | 1.97073 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.6117 | 1.48668 | 0.743341 | − | 0.668913i | \(-0.233240\pi\) | ||||
0.743341 | + | 0.668913i | \(0.233240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.15037 | −0.227830 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −37.0278 | −1.17861 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.8341 | 1.42564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.2400 | −1.24650 | −0.623249 | − | 0.782023i | \(-0.714188\pi\) | ||||
−0.623249 | + | 0.782023i | \(0.714188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.62246 | −0.273625 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.5415 | 0.460998 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.4562 | −1.47128 | −0.735642 | − | 0.677371i | \(-0.763119\pi\) | ||||
−0.735642 | + | 0.677371i | \(0.763119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.77367 | −0.0561166 |
(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 | 4016.2.a.i.1.12 | 12 | ||
4.3 | odd | 2 | 2008.2.a.b.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.b.1.1 | ✓ | 12 | 4.3 | odd | 2 | ||
4016.2.a.i.1.12 | 12 | 1.1 | even | 1 | trivial |