Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.40459\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | −2.40459 | −1.38829 | −0.694144 | − | 0.719836i | \(-0.744217\pi\) | ||||
−0.694144 | + | 0.719836i | \(0.744217\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.489610 | −0.218960 | −0.109480 | − | 0.993989i | \(-0.534919\pi\) | ||||
−0.109480 | + | 0.993989i | \(0.534919\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.26722 | 1.61286 | 0.806429 | − | 0.591331i | \(-0.201397\pi\) | ||||
0.806429 | + | 0.591331i | \(0.201397\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.78204 | 0.927346 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.593113 | −0.178830 | −0.0894152 | − | 0.995994i | \(-0.528500\pi\) | ||||
−0.0894152 | + | 0.995994i | \(0.528500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.15631 | −0.320704 | −0.160352 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160352 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17731 | 0.303980 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.567069 | −0.137534 | −0.0687672 | − | 0.997633i | \(-0.521907\pi\) | ||||
−0.0687672 | + | 0.997633i | \(0.521907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.2609 | −2.23911 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.283453 | −0.0591040 | −0.0295520 | − | 0.999563i | \(-0.509408\pi\) | ||||
−0.0295520 | + | 0.999563i | \(0.509408\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.76028 | −0.952056 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.524106 | 0.100864 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.84950 | 1.45762 | 0.728808 | − | 0.684718i | \(-0.240075\pi\) | ||||
0.728808 | + | 0.684718i | \(0.240075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.45614 | −0.261531 | −0.130765 | − | 0.991413i | \(-0.541743\pi\) | ||||
−0.130765 | + | 0.991413i | \(0.541743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42619 | 0.248268 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.08928 | −0.353152 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2044 | −1.67759 | −0.838796 | − | 0.544446i | \(-0.816740\pi\) | ||||
−0.838796 | + | 0.544446i | \(0.816740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.78046 | 0.445229 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.80512 | −0.281912 | −0.140956 | − | 0.990016i | \(-0.545018\pi\) | ||||
−0.140956 | + | 0.990016i | \(0.545018\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9526 | −1.67025 | −0.835126 | − | 0.550059i | \(-0.814605\pi\) | ||||
−0.835126 | + | 0.550059i | \(0.814605\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.36212 | −0.203052 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.268056 | −0.0391000 | −0.0195500 | − | 0.999809i | \(-0.506223\pi\) | ||||
−0.0195500 | + | 0.999809i | \(0.506223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.2092 | 1.60131 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.36357 | 0.190937 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.290395 | 0.0391568 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.40459 | 0.318495 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.12660 | −0.927804 | −0.463902 | − | 0.885887i | \(-0.653551\pi\) | ||||
−0.463902 | + | 0.885887i | \(0.653551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.60308 | −0.461327 | −0.230664 | − | 0.973034i | \(-0.574090\pi\) | ||||
−0.230664 | + | 0.973034i | \(0.574090\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.8716 | 1.49568 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.566143 | 0.0702214 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0044 | 1.58874 | 0.794369 | − | 0.607436i | \(-0.207802\pi\) | ||||
0.794369 | + | 0.607436i | \(0.207802\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.681587 | 0.0820534 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.30469 | 0.629551 | 0.314776 | − | 0.949166i | \(-0.398071\pi\) | ||||
0.314776 | + | 0.949166i | \(0.398071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.82454 | 0.798752 | 0.399376 | − | 0.916787i | \(-0.369227\pi\) | ||||
0.399376 | + | 0.916787i | \(0.369227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.4465 | 1.32173 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.53095 | −0.288428 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.03777 | 0.679302 | 0.339651 | − | 0.940552i | \(-0.389691\pi\) | ||||
0.339651 | + | 0.940552i | \(0.389691\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.60638 | −1.06738 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18.1576 | −1.99305 | −0.996526 | − | 0.0832803i | \(-0.973460\pi\) | ||||
−0.996526 | + | 0.0832803i | \(0.973460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.277643 | 0.0301146 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.8748 | −2.02359 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2560 | 1.19314 | 0.596568 | − | 0.802563i | \(-0.296531\pi\) | ||||
0.596568 | + | 0.802563i | \(0.296531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.93425 | −0.517250 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.50142 | 0.363080 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.489610 | 0.0502330 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.7957 | 1.70534 | 0.852671 | − | 0.522448i | \(-0.174981\pi\) | ||||
0.852671 | + | 0.522448i | \(0.174981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.65006 | −0.165838 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.59077 | −0.655807 | −0.327903 | − | 0.944711i | \(-0.606342\pi\) | ||||
−0.327903 | + | 0.944711i | \(0.606342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.34526 | 0.329618 | 0.164809 | − | 0.986325i | \(-0.447299\pi\) | ||||
0.164809 | + | 0.986325i | \(0.447299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.02385 | 0.490277 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.55246 | −0.923471 | −0.461736 | − | 0.887018i | \(-0.652773\pi\) | ||||
−0.461736 | + | 0.887018i | \(0.652773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.195040 | 0.0186815 | 0.00934074 | − | 0.999956i | \(-0.497027\pi\) | ||||
0.00934074 | + | 0.999956i | \(0.497027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.5373 | 2.32898 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8267 | −1.30070 | −0.650352 | − | 0.759633i | \(-0.725379\pi\) | ||||
−0.650352 | + | 0.759633i | \(0.725379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.138781 | 0.0129414 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.21691 | −0.297403 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.41981 | −0.221823 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6482 | −0.968020 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.34057 | 0.391376 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.77874 | 0.427423 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5583 | 1.20311 | 0.601553 | − | 0.798833i | \(-0.294549\pi\) | ||||
0.601553 | + | 0.798833i | \(0.294549\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.3364 | 2.31879 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3534 | 0.991953 | 0.495977 | − | 0.868336i | \(-0.334810\pi\) | ||||
0.495977 | + | 0.868336i | \(0.334810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.26722 | −0.370015 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.256608 | −0.0220853 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.2091 | 0.872223 | 0.436112 | − | 0.899893i | \(-0.356355\pi\) | ||||
0.436112 | + | 0.899893i | \(0.356355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.848744 | 0.0719895 | 0.0359947 | − | 0.999352i | \(-0.488540\pi\) | ||||
0.0359947 | + | 0.999352i | \(0.488540\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.644564 | 0.0542821 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.685825 | 0.0573516 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.84320 | −0.319160 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.9534 | −2.22308 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.7506 | 1.61803 | 0.809015 | − | 0.587788i | \(-0.200001\pi\) | ||||
0.809015 | + | 0.587788i | \(0.200001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.9990 | −1.46474 | −0.732368 | − | 0.680909i | \(-0.761585\pi\) | ||||
−0.732368 | + | 0.680909i | \(0.761585\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.57761 | −0.127542 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.712942 | 0.0572649 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.29269 | −0.422402 | −0.211201 | − | 0.977443i | \(-0.567738\pi\) | ||||
−0.211201 | + | 0.977443i | \(0.567738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.40459 | −0.190696 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.20956 | −0.0953263 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.9884 | −1.80059 | −0.900296 | − | 0.435278i | \(-0.856650\pi\) | ||||
−0.900296 | + | 0.435278i | \(0.856650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.698279 | −0.0543609 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0882 | −1.39971 | −0.699855 | − | 0.714285i | \(-0.746752\pi\) | ||||
−0.699855 | + | 0.714285i | \(0.746752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6629 | −0.897149 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.78204 | −0.212748 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3205 | 0.784651 | 0.392325 | − | 0.919827i | \(-0.371671\pi\) | ||||
0.392325 | + | 0.919827i | \(0.371671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.3132 | −1.53553 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.1365 | 1.28806 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7825 | −0.880666 | −0.440333 | − | 0.897834i | \(-0.645140\pi\) | ||||
−0.440333 | + | 0.897834i | \(0.645140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7511 | −0.799125 | −0.399562 | − | 0.916706i | \(-0.630838\pi\) | ||||
−0.399562 | + | 0.916706i | \(0.630838\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.66392 | 0.640456 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.99618 | 0.367326 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.336336 | 0.0245953 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23648 | 0.162680 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.9185 | −1.29654 | −0.648268 | − | 0.761412i | \(-0.724506\pi\) | ||||
−0.648268 | + | 0.761412i | \(0.724506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.7314 | −1.06039 | −0.530195 | − | 0.847876i | \(-0.677881\pi\) | ||||
−0.530195 | + | 0.847876i | \(0.677881\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.36134 | −0.0974876 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.16837 | 0.581973 | 0.290986 | − | 0.956727i | \(-0.406017\pi\) | ||||
0.290986 | + | 0.956727i | \(0.406017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.2015 | −1.85738 | −0.928688 | − | 0.370861i | \(-0.879062\pi\) | ||||
−0.928688 | + | 0.370861i | \(0.879062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −31.2702 | −2.20563 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.4956 | 2.35093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.883805 | 0.0617276 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.788577 | −0.0548099 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.593113 | 0.0410265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.1902 | −1.66532 | −0.832661 | − | 0.553782i | \(-0.813184\pi\) | ||||
−0.832661 | + | 0.553782i | \(0.813184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.7556 | −0.873999 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.36249 | 0.365719 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.21368 | −0.421812 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.4102 | −1.10890 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.655709 | 0.0441078 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.32596 | −0.222723 | −0.111361 | − | 0.993780i | \(-0.535521\pi\) | ||||
−0.111361 | + | 0.993780i | \(0.535521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.2433 | −0.882886 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7421 | −0.912096 | −0.456048 | − | 0.889955i | \(-0.650735\pi\) | ||||
−0.456048 | + | 0.889955i | \(0.650735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.4253 | −1.87840 | −0.939200 | − | 0.343371i | \(-0.888431\pi\) | ||||
−0.939200 | + | 0.343371i | \(0.888431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.08588 | 0.400422 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.2345 | −1.65316 | −0.826582 | − | 0.562816i | \(-0.809718\pi\) | ||||
−0.826582 | + | 0.562816i | \(0.809718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.131243 | 0.00856136 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.5183 | −0.943067 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4760 | 1.25980 | 0.629900 | − | 0.776676i | \(-0.283096\pi\) | ||||
0.629900 | + | 0.776676i | \(0.283096\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.36949 | 0.410295 | 0.205147 | − | 0.978731i | \(-0.434233\pi\) | ||||
0.205147 | + | 0.978731i | \(0.434233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.5270 | 1.38096 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.48813 | −0.350624 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.15631 | 0.0735745 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.6615 | 2.76693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0762 | −0.888479 | −0.444240 | − | 0.895908i | \(-0.646526\pi\) | ||||
−0.444240 | + | 0.895908i | \(0.646526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.168120 | 0.0105696 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.667616 | −0.0418077 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6236 | 1.47360 | 0.736801 | − | 0.676110i | \(-0.236336\pi\) | ||||
0.736801 | + | 0.676110i | \(0.236336\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −43.5444 | −2.70572 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.8376 | 1.35171 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.3321 | −1.56204 | −0.781022 | − | 0.624503i | \(-0.785301\pi\) | ||||
−0.781022 | + | 0.624503i | \(0.785301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.489610 | −0.0300765 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.0661 | −1.65642 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0059 | 0.610072 | 0.305036 | − | 0.952341i | \(-0.401331\pi\) | ||||
0.305036 | + | 0.952341i | \(0.401331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.45285 | −0.513474 | −0.256737 | − | 0.966481i | \(-0.582647\pi\) | ||||
−0.256737 | + | 0.966481i | \(0.582647\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.8648 | 0.718092 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.82339 | 0.170257 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6319 | 0.819063 | 0.409531 | − | 0.912296i | \(-0.365692\pi\) | ||||
0.409531 | + | 0.912296i | \(0.365692\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.05104 | −0.242530 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.21933 | 0.490324 | 0.245162 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245162 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9266 | −1.06562 | −0.532812 | − | 0.846234i | \(-0.678865\pi\) | ||||
−0.532812 | + | 0.846234i | \(0.678865\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.17731 | −0.0697379 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.70284 | −0.454684 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6784 | −0.981084 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −40.3867 | −2.36751 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.3915 | 1.48339 | 0.741694 | − | 0.670739i | \(-0.234023\pi\) | ||||
0.741694 | + | 0.670739i | \(0.234023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.48926 | 0.203152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.310854 | −0.0180376 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.327760 | 0.0189549 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.7370 | −2.69388 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.8481 | 0.910449 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.76411 | 0.101012 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.58449 | −0.375797 | −0.187898 | − | 0.982188i | \(-0.560168\pi\) | ||||
−0.187898 | + | 0.982188i | \(0.560168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.04397 | −0.457605 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.50525 | 0.198765 | 0.0993823 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993823 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0456 | 0.624337 | 0.312168 | − | 0.950027i | \(-0.398945\pi\) | ||||
0.312168 | + | 0.950027i | \(0.398945\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.81245 | −0.327494 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.51919 | −0.478486 | −0.239243 | − | 0.970960i | \(-0.576899\pi\) | ||||
−0.239243 | + | 0.970960i | \(0.576899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.65565 | −0.260666 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.9697 | 1.28204 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.567069 | 0.0315525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.50438 | 0.305328 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.468992 | −0.0259353 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.14386 | −0.0630628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8010 | 0.868503 | 0.434252 | − | 0.900792i | \(-0.357013\pi\) | ||||
0.434252 | + | 0.900792i | \(0.357013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −28.3890 | −1.55571 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.36708 | −0.347871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.91933 | −0.322446 | −0.161223 | − | 0.986918i | \(-0.551544\pi\) | ||||
−0.161223 | + | 0.986918i | \(0.551544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.2474 | 1.80575 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.863657 | 0.0467697 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9615 | 0.969829 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.333712 | −0.0179665 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.3477 | −1.79020 | −0.895100 | − | 0.445865i | \(-0.852896\pi\) | ||||
−0.895100 | + | 0.445865i | \(0.852896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.4860 | 0.882475 | 0.441238 | − | 0.897390i | \(-0.354540\pi\) | ||||
0.441238 | + | 0.897390i | \(0.354540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.606031 | −0.0323475 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.5765 | −1.41453 | −0.707263 | − | 0.706950i | \(-0.750071\pi\) | ||||
−0.707263 | + | 0.706950i | \(0.750071\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.59723 | −0.137847 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.81864 | 0.307955 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.3425 | 1.39030 | 0.695152 | − | 0.718863i | \(-0.255337\pi\) | ||||
0.695152 | + | 0.718863i | \(0.255337\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.6046 | 1.34389 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.34137 | −0.174895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.93086 | 0.413987 | 0.206994 | − | 0.978342i | \(-0.433632\pi\) | ||||
0.206994 | + | 0.978342i | \(0.433632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.02191 | −0.261430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.26722 | 0.221543 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.1490 | −1.04328 | −0.521638 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521638 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.4909 | −0.593387 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.07649 | −0.467463 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.74775 | 0.141142 | 0.0705712 | − | 0.997507i | \(-0.477518\pi\) | ||||
0.0705712 | + | 0.997507i | \(0.477518\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.6022 | −1.67026 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.5199 | 0.946321 | 0.473160 | − | 0.880976i | \(-0.343113\pi\) | ||||
0.473160 | + | 0.880976i | \(0.343113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.23918 | 0.0631543 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.4705 | −1.54890 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.0162 | 0.812052 | 0.406026 | − | 0.913861i | \(-0.366914\pi\) | ||||
0.406026 | + | 0.913861i | \(0.366914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.160737 | 0.00812883 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.3003 | −1.37712 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.95615 | −0.148740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7822 | −1.34416 | −0.672080 | − | 0.740479i | \(-0.734599\pi\) | ||||
−0.672080 | + | 0.740479i | \(0.734599\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2609 | 0.513688 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0341 | 0.551018 | 0.275509 | − | 0.961299i | \(-0.411154\pi\) | ||||
0.275509 | + | 0.961299i | \(0.411154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.68376 | 0.0838739 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.70338 | 0.233713 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.05236 | 0.300004 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.49748 | −0.271833 | −0.135916 | − | 0.990720i | \(-0.543398\pi\) | ||||
−0.135916 | + | 0.990720i | \(0.543398\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.5487 | −1.21090 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −30.4108 | −1.49642 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.89014 | 0.436400 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.04088 | −0.0999422 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.5023 | −0.903897 | −0.451949 | − | 0.892044i | \(-0.649271\pi\) | ||||
−0.451949 | + | 0.892044i | \(0.649271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.2312 | −1.37591 | −0.687953 | − | 0.725755i | \(-0.741490\pi\) | ||||
−0.687953 | + | 0.725755i | \(0.741490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.745743 | −0.0362593 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.69941 | 0.130940 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.3751 | −0.744055 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.64913 | −0.0796206 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.69590 | −0.129857 | −0.0649285 | − | 0.997890i | \(-0.520682\pi\) | ||||
−0.0649285 | + | 0.997890i | \(0.520682\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3997 | 0.932291 | 0.466145 | − | 0.884708i | \(-0.345642\pi\) | ||||
0.466145 | + | 0.884708i | \(0.345642\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.24130 | 0.443087 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.283453 | 0.0135594 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.3458 | −1.73469 | −0.867344 | − | 0.497708i | \(-0.834175\pi\) | ||||
−0.867344 | + | 0.497708i | \(0.834175\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.1844 | 1.48497 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.9977 | −0.950120 | −0.475060 | − | 0.879953i | \(-0.657574\pi\) | ||||
−0.475060 | + | 0.879953i | \(0.657574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.51106 | −0.261249 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −47.4920 | −2.24629 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.85329 | −0.465006 | −0.232503 | − | 0.972596i | \(-0.574691\pi\) | ||||
−0.232503 | + | 0.972596i | \(0.574691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.07064 | 0.0504145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 43.2801 | 2.03348 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.41586 | 0.113257 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.0250 | 1.12384 | 0.561922 | − | 0.827190i | \(-0.310062\pi\) | ||||
0.561922 | + | 0.827190i | \(0.310062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.297204 | −0.0138723 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0400 | 1.21280 | 0.606401 | − | 0.795159i | \(-0.292613\pi\) | ||||
0.606401 | + | 0.795159i | \(0.292613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1893 | 0.566483 | 0.283241 | − | 0.959049i | \(-0.408590\pi\) | ||||
0.283241 | + | 0.959049i | \(0.408590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.71433 | −0.0795002 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.9943 | 0.555030 | 0.277515 | − | 0.960721i | \(-0.410489\pi\) | ||||
0.277515 | + | 0.960721i | \(0.410489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.4925 | 2.56241 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7267 | 0.586416 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.49612 | 0.298692 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.76028 | 0.218417 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.78204 | 0.127381 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.4019 | 1.70894 | 0.854469 | − | 0.519503i | \(-0.173883\pi\) | ||||
0.854469 | + | 0.519503i | \(0.173883\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7995 | 0.538010 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.90848 | 0.132341 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.22334 | −0.373403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.58556 | −0.253106 | −0.126553 | − | 0.991960i | \(-0.540391\pi\) | ||||
−0.126553 | + | 0.991960i | \(0.540391\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 55.2777 | 2.49974 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.376459 | −0.0169893 | −0.00849467 | − | 0.999964i | \(-0.502704\pi\) | ||||
−0.00849467 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.45121 | −0.200472 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.807889 | 0.0363119 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.6363 | 1.01538 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.55394 | 0.203862 | 0.101931 | − | 0.994791i | \(-0.467498\pi\) | ||||
0.101931 | + | 0.994791i | \(0.467498\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.4948 | 1.94320 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.1855 | 0.944616 | 0.472308 | − | 0.881433i | \(-0.343421\pi\) | ||||
0.472308 | + | 0.881433i | \(0.343421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.22691 | 0.143596 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.0446 | 1.24550 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.8635 | 1.05773 | 0.528865 | − | 0.848706i | \(-0.322618\pi\) | ||||
0.528865 | + | 0.848706i | \(0.322618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.1218 | 1.28827 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.524106 | −0.0231398 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.63787 | −0.0721733 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.158988 | 0.00699227 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.8165 | −1.08932 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.2098 | 1.41114 | 0.705568 | − | 0.708642i | \(-0.250692\pi\) | ||||
0.705568 | + | 0.708642i | \(0.250692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.73250 | −0.119484 | −0.0597420 | − | 0.998214i | \(-0.519028\pi\) | ||||
−0.0597420 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 48.8448 | 2.13176 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.825732 | 0.0359695 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9197 | −0.996507 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.8265 | −0.860396 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.08728 | 0.0904103 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.67698 | 0.202204 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.3321 | 1.22262 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.64831 | −0.286363 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.6113 | −0.929143 | −0.464572 | − | 0.885536i | \(-0.653792\pi\) | ||||
−0.464572 | + | 0.885536i | \(0.653792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.8520 | 1.10942 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0954939 | −0.00409051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0368 | −0.600168 | −0.300084 | − | 0.953913i | \(-0.597015\pi\) | ||||
−0.300084 | + | 0.953913i | \(0.597015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0239 | −0.427810 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.84950 | −0.334400 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.7645 | 1.09562 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.0137 | −0.509955 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.4768 | 0.740517 | 0.370258 | − | 0.928929i | \(-0.379269\pi\) | ||||
0.370258 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.6646 | 0.535656 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.808749 | −0.0341454 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.49829 | 0.231725 | 0.115863 | − | 0.993265i | \(-0.463037\pi\) | ||||
0.115863 | + | 0.993265i | \(0.463037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.76968 | 0.284803 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −40.9925 | −1.72152 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.659955 | −0.0276668 | −0.0138334 | − | 0.999904i | \(-0.504403\pi\) | ||||
−0.0138334 | + | 0.999904i | \(0.504403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.4557 | 1.69302 | 0.846509 | − | 0.532374i | \(-0.178700\pi\) | ||||
0.846509 | + | 0.532374i | \(0.178700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.0866 | 1.79997 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.34931 | 0.0562703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.5897 | −0.440855 | −0.220428 | − | 0.975403i | \(-0.570745\pi\) | ||||
−0.220428 | + | 0.975403i | \(0.570745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.4230 | 1.47213 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −77.4824 | −3.21451 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.593113 | −0.0245642 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.57503 | 0.0651196 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.2330 | −1.08275 | −0.541376 | − | 0.840780i | \(-0.682097\pi\) | ||||
−0.541376 | + | 0.840780i | \(0.682097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.45614 | 0.0599993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6416 | −0.807946 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.9710 | 1.76461 | 0.882304 | − | 0.470680i | \(-0.155991\pi\) | ||||
0.882304 | + | 0.470680i | \(0.155991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.18476 | 0.0485705 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 63.0038 | 2.57858 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.4694 | −0.836355 | −0.418178 | − | 0.908365i | \(-0.637331\pi\) | ||||
−0.418178 | + | 0.908365i | \(0.637331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.64710 | 0.352723 | 0.176361 | − | 0.984325i | \(-0.443567\pi\) | ||||
0.176361 | + | 0.984325i | \(0.443567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 36.1787 | 1.47331 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.21348 | 0.211958 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.5194 | −1.19815 | −0.599077 | − | 0.800691i | \(-0.704466\pi\) | ||||
−0.599077 | + | 0.800691i | \(0.704466\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −80.5430 | −3.26377 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.309957 | 0.0125395 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.6360 | −0.591144 | −0.295572 | − | 0.955320i | \(-0.595510\pi\) | ||||
−0.295572 | + | 0.955320i | \(0.595510\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.12519 | −0.0856958 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.60037 | −0.225462 | −0.112731 | − | 0.993626i | \(-0.535960\pi\) | ||||
−0.112731 | + | 0.993626i | \(0.535960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0552 | −0.404151 | −0.202075 | − | 0.979370i | \(-0.564769\pi\) | ||||
−0.202075 | + | 0.979370i | \(0.564769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.148559 | −0.00596148 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.0319 | 1.92436 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.4617 | 0.858468 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.42619 | −0.0569567 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.78659 | 0.230726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9043 | 1.70799 | 0.853996 | − | 0.520280i | \(-0.174172\pi\) | ||||
0.853996 | + | 0.520280i | \(0.174172\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58.1675 | 2.31195 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.63829 | −0.263433 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.9613 | −0.513546 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.7579 | 0.583812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.7730 | −0.544003 | −0.272001 | − | 0.962297i | \(-0.587686\pi\) | ||||
−0.272001 | + | 0.962297i | \(0.587686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.2396 | −1.31084 | −0.655421 | − | 0.755263i | \(-0.727509\pi\) | ||||
−0.655421 | + | 0.755263i | \(0.727509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.8946 | −0.507724 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.8612 | −1.48848 | −0.744238 | − | 0.667914i | \(-0.767187\pi\) | ||||
−0.744238 | + | 0.667914i | \(0.767187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.22688 | 0.165920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.9413 | 0.585597 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.1029 | 0.943219 | 0.471610 | − | 0.881807i | \(-0.343673\pi\) | ||||
0.471610 | + | 0.881807i | \(0.343673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.55875 | −0.217199 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.9861 | 0.740720 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.9261 | −1.82798 | −0.913991 | − | 0.405735i | \(-0.867016\pi\) | ||||
−0.913991 | + | 0.405735i | \(0.867016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8119 | 0.459431 | 0.229715 | − | 0.973258i | \(-0.426220\pi\) | ||||
0.229715 | + | 0.973258i | \(0.426220\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.57671 | −0.0612343 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.08928 | 0.0810186 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.22496 | −0.0861509 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.99757 | 0.309204 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.13704 | 0.0824994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.1703 | −1.04734 | −0.523668 | − | 0.851922i | \(-0.675437\pi\) | ||||
−0.523668 | + | 0.851922i | \(0.675437\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.49489 | −0.0960285 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.4682 | −0.940390 | −0.470195 | − | 0.882563i | \(-0.655816\pi\) | ||||
−0.470195 | + | 0.882563i | \(0.655816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 71.6709 | 2.75048 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.0441 | 1.26625 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.7130 | −1.09867 | −0.549337 | − | 0.835601i | \(-0.685120\pi\) | ||||
−0.549337 | + | 0.835601i | \(0.685120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.99849 | −0.190982 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 68.3512 | 2.60776 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.15631 | −0.0440520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.2097 | −0.882938 | −0.441469 | − | 0.897276i | \(-0.645543\pi\) | ||||
−0.441469 | + | 0.897276i | \(0.645543\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.04119 | −0.267473 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.415554 | −0.0157629 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.02363 | 0.0387726 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 60.6785 | 2.29507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2814 | 0.539402 | 0.269701 | − | 0.962944i | \(-0.413075\pi\) | ||||
0.269701 | + | 0.962944i | \(0.413075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2044 | 0.384866 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.315585 | −0.0118856 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.1243 | −1.05772 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5116 | −0.544993 | −0.272497 | − | 0.962157i | \(-0.587849\pi\) | ||||
−0.272497 | + | 0.962157i | \(0.587849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.7973 | 0.629948 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.412747 | 0.0154575 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.335787 | −0.0125577 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.8318 | −1.74897 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.2609 | 1.83712 | 0.918561 | − | 0.395280i | \(-0.129353\pi\) | ||||
0.918561 | + | 0.395280i | \(0.129353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.2750 | 0.531627 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.3160 | −0.569608 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37.3658 | −1.38773 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.9463 | −0.665593 | −0.332796 | − | 0.942999i | \(-0.607992\pi\) | ||||
−0.332796 | + | 0.942999i | \(0.607992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.9445 | −0.849798 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.21086 | 0.229717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7118 | −0.543393 | −0.271697 | − | 0.962383i | \(-0.587585\pi\) | ||||
−0.271697 | + | 0.962383i | \(0.587585\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.1967 | 0.486767 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.71307 | −0.284115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6777 | −0.503141 | −0.251570 | − | 0.967839i | \(-0.580947\pi\) | ||||
−0.251570 | + | 0.967839i | \(0.580947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.78046 | −0.102143 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.9122 | 1.24412 | 0.622059 | − | 0.782971i | \(-0.286296\pi\) | ||||
0.622059 | + | 0.782971i | \(0.286296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.67008 | −0.354284 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.5151 | −1.84825 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.7625 | −1.48943 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4999 | 0.748050 | 0.374025 | − | 0.927419i | \(-0.377977\pi\) | ||||
0.374025 | + | 0.927419i | \(0.377977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.8473 | 1.23347 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.81249 | 0.320719 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.6654 | −1.15090 | −0.575450 | − | 0.817837i | \(-0.695173\pi\) | ||||
−0.575450 | + | 0.817837i | \(0.695173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.404258 | −0.0146736 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6218 | −0.457540 | −0.228770 | − | 0.973480i | \(-0.573470\pi\) | ||||
−0.228770 | + | 0.973480i | \(0.573470\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.832281 | 0.0301306 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.772413 | 0.0279266 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.24058 | 0.297550 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.2496 | −1.70386 | −0.851932 | − | 0.523652i | \(-0.824569\pi\) | ||||
−0.851932 | + | 0.523652i | \(0.824569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −56.8051 | −2.04579 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.3017 | 1.41358 | 0.706791 | − | 0.707422i | \(-0.250142\pi\) | ||||
0.706791 | + | 0.707422i | \(0.250142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.93165 | 0.248992 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 104.706 | 3.75632 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.80512 | 0.0646751 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.14628 | −0.112583 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.11397 | 0.147021 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.59135 | 0.0924894 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7525 | 0.597163 | 0.298581 | − | 0.954384i | \(-0.403487\pi\) | ||||
0.298581 | + | 0.954384i | \(0.403487\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 60.9133 | 2.16857 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.0015 | −2.09785 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.16629 | 0.147949 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.17731 | 0.0417549 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.4218 | 1.53808 | 0.769039 | − | 0.639202i | \(-0.220735\pi\) | ||||
0.769039 | + | 0.639202i | \(0.220735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.152006 | 0.00537759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.3147 | 1.10645 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.04773 | −0.142841 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.592211 | 0.0208727 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.0601 | −0.846956 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.1872 | −1.48322 | −0.741611 | − | 0.670831i | \(-0.765938\pi\) | ||||
−0.741611 | + | 0.670831i | \(0.765938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.39281 | 0.189367 | 0.0946837 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946837 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.3256 | 0.712850 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.2554 | 0.394258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9526 | 0.383182 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.7273 | −0.479669 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.9182 | 1.32335 | 0.661677 | − | 0.749789i | \(-0.269845\pi\) | ||||
0.661677 | + | 0.749789i | \(0.269845\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.2072 | −1.47125 | −0.735625 | − | 0.677389i | \(-0.763111\pi\) | ||||
−0.735625 | + | 0.677389i | \(0.763111\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.78908 | −0.236365 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.53128 | 0.331435 | 0.165718 | − | 0.986173i | \(-0.447006\pi\) | ||||
0.165718 | + | 0.986173i | \(0.447006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.77654 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.7791 | −1.13710 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.35637 | −0.220235 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.85619 | 0.306481 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.763173 | −0.0263791 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.60525 | −0.331610 | −0.165805 | − | 0.986159i | \(-0.553022\pi\) | ||||
−0.165805 | + | 0.986159i | \(0.553022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.6147 | 1.12464 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.7641 | −0.680712 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.71030 | 0.196440 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.4383 | −1.56128 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.1060 | 1.47939 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.89246 | 0.0991523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.76954 | −0.129066 | −0.0645332 | − | 0.997916i | \(-0.520556\pi\) | ||||
−0.0645332 | + | 0.997916i | \(0.520556\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.36212 | 0.0465834 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.8511 | −1.08801 | −0.544007 | − | 0.839081i | \(-0.683094\pi\) | ||||
−0.544007 | + | 0.839081i | \(0.683094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.7453 | −1.56081 | −0.780404 | − | 0.625275i | \(-0.784987\pi\) | ||||
−0.780404 | + | 0.625275i | \(0.784987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.5222 | 0.631233 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2650 | 0.485586 | 0.242793 | − | 0.970078i | \(-0.421936\pi\) | ||||
0.242793 | + | 0.970078i | \(0.421936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.05301 | −0.171807 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.1047 | 1.36203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.58108 | −0.121480 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0371 | −0.509514 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.7262 | 1.58144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.3919 | 0.689373 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.98368 | 0.168287 | 0.0841434 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841434 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −61.0561 | −2.05937 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.2448 | −1.18743 | −0.593713 | − | 0.804677i | \(-0.702339\pi\) | ||||
−0.593713 | + | 0.804677i | \(0.702339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.1327 | 0.576562 | 0.288281 | − | 0.957546i | \(-0.406916\pi\) | ||||
0.288281 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.39022 | −0.282034 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7821 | −0.429180 | −0.214590 | − | 0.976704i | \(-0.568841\pi\) | ||||
−0.214590 | + | 0.976704i | \(0.568841\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57.8563 | 1.94044 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.69767 | 0.190879 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.268056 | 0.00897016 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.76884 | 0.192831 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.788128 | −0.0263148 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.4300 | −0.381211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.567069 | −0.0188918 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 112.383 | 3.73988 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.26386 | 0.174977 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.2799 | −1.33747 | −0.668735 | − | 0.743501i | \(-0.733164\pi\) | ||||
−0.668735 | + | 0.743501i | \(0.733164\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.3358 | −0.608160 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.3166 | 1.36888 | 0.684440 | − | 0.729069i | \(-0.260047\pi\) | ||||
0.684440 | + | 0.729069i | \(0.260047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7695 | 0.356418 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.24195 | −0.140234 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.4476 | 1.59988 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.6644 | 1.86919 | 0.934593 | − | 0.355720i | \(-0.115764\pi\) | ||||
0.934593 | + | 0.355720i | \(0.115764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8330 | 0.521714 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.13389 | −0.201899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.5758 | 1.59716 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.30664 | 0.305670 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.3730 | 1.35740 | 0.678702 | − | 0.734414i | \(-0.262543\pi\) | ||||
0.678702 | + | 0.734414i | \(0.262543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.2092 | −0.367366 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.42868 | −0.275943 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.164674 | −0.00538540 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.98784 | 0.162946 | 0.0814728 | − | 0.996676i | \(-0.474038\pi\) | ||||
0.0814728 | + | 0.996676i | \(0.474038\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.5602 | −0.866760 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.1052 | −0.557612 | −0.278806 | − | 0.960347i | \(-0.589939\pi\) | ||||
−0.278806 | + | 0.960347i | \(0.589939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.511666 | 0.0166621 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.09500 | −0.0356204 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.775986 | −0.0252162 | −0.0126081 | − | 0.999921i | \(-0.504013\pi\) | ||||
−0.0126081 | + | 0.999921i | \(0.504013\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.89131 | −0.256163 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.4851 | 0.664276 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0180 | −0.778018 | −0.389009 | − | 0.921234i | \(-0.627182\pi\) | ||||
−0.389009 | + | 0.921234i | \(0.627182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.77308 | 0.283890 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.1949 | 0.361880 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.5645 | 1.40677 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8797 | −0.931602 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.5753 | −0.856378 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.21265 | 0.232183 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.13796 | 0.229541 | 0.114771 | − | 0.993392i | \(-0.463387\pi\) | ||||
0.114771 | + | 0.993392i | \(0.463387\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.36357 | −0.0438040 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.3344 | −0.460014 | −0.230007 | − | 0.973189i | \(-0.573875\pi\) | ||||
−0.230007 | + | 0.973189i | \(0.573875\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.62178 | 0.116109 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.2358 | −0.423884 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.5586 | −1.23360 | −0.616800 | − | 0.787120i | \(-0.711571\pi\) | ||||
−0.616800 | + | 0.787120i | \(0.711571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.67610 | −0.213369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.542610 | 0.0173242 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.3991 | −0.554944 | −0.277472 | − | 0.960734i | \(-0.589497\pi\) | ||||
−0.277472 | + | 0.960734i | \(0.589497\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.99932 | −0.127429 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.75050 | 0.0875493 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.10454 | 0.0987185 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.6058 | 1.51225 | 0.756123 | − | 0.654429i | \(-0.227091\pi\) | ||||
0.756123 | + | 0.654429i | \(0.227091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.9950 | −1.20573 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.8285 | 0.406692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.9178 | −1.61258 | −0.806292 | − | 0.591518i | \(-0.798529\pi\) | ||||
−0.806292 | + | 0.591518i | \(0.798529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.34818 | −0.169209 |
(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 | 4028.2.a.d.1.4 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.4 | ✓ | 19 | 1.1 | even | 1 | trivial |