Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, 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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.826865.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 668) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.69135\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.48567 | 1.69542 | 0.847712 | − | 0.530457i | \(-0.177979\pi\) | ||||
0.847712 | + | 0.530457i | \(0.177979\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62500 | 0.489957 | 0.244979 | − | 0.969528i | \(-0.421219\pi\) | ||||
0.244979 | + | 0.969528i | \(0.421219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.38270 | 0.938192 | 0.469096 | − | 0.883147i | \(-0.344580\pi\) | ||||
0.469096 | + | 0.883147i | \(0.344580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.30425 | 1.28647 | 0.643235 | − | 0.765669i | \(-0.277592\pi\) | ||||
0.643235 | + | 0.765669i | \(0.277592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.97394 | 1.59993 | 0.799966 | − | 0.600045i | \(-0.204851\pi\) | ||||
0.799966 | + | 0.600045i | \(0.204851\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.132692 | −0.0276682 | −0.0138341 | − | 0.999904i | \(-0.504404\pi\) | ||||
−0.0138341 | + | 0.999904i | \(0.504404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.86837 | 1.46112 | 0.730560 | − | 0.682849i | \(-0.239259\pi\) | ||||
0.730560 | + | 0.682849i | \(0.239259\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5868 | 1.90145 | 0.950726 | − | 0.310031i | \(-0.100339\pi\) | ||||
0.950726 | + | 0.310031i | \(0.100339\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.97134 | −1.51643 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.72133 | 0.282985 | 0.141493 | − | 0.989939i | \(-0.454810\pi\) | ||||
0.141493 | + | 0.989939i | \(0.454810\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.40828 | −1.31315 | −0.656576 | − | 0.754259i | \(-0.727996\pi\) | ||||
−0.656576 | + | 0.754259i | \(0.727996\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.76540 | −1.03171 | −0.515857 | − | 0.856675i | \(-0.672526\pi\) | ||||
−0.515857 | + | 0.856675i | \(0.672526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.208543 | −0.0304191 | −0.0152095 | − | 0.999884i | \(-0.504842\pi\) | ||||
−0.0152095 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.1212 | 1.87446 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.68695 | −1.19324 | −0.596622 | − | 0.802522i | \(-0.703491\pi\) | ||||
−0.596622 | + | 0.802522i | \(0.703491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.25001 | −0.438231 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.8152 | −1.79859 | −0.899293 | − | 0.437347i | \(-0.855918\pi\) | ||||
−0.899293 | + | 0.437347i | \(0.855918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.06741 | −0.392742 | −0.196371 | − | 0.980530i | \(-0.562916\pi\) | ||||
−0.196371 | + | 0.980530i | \(0.562916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.76540 | −0.839145 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.51019 | 0.917515 | 0.458758 | − | 0.888561i | \(-0.348295\pi\) | ||||
0.458758 | + | 0.888561i | \(0.348295\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.06752 | −0.245370 | −0.122685 | − | 0.992446i | \(-0.539150\pi\) | ||||
−0.122685 | + | 0.992446i | \(0.539150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.43694 | 0.636346 | 0.318173 | − | 0.948033i | \(-0.396931\pi\) | ||||
0.318173 | + | 0.948033i | \(0.396931\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.28924 | 0.830686 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.5256 | −1.97178 | −0.985892 | − | 0.167383i | \(-0.946468\pi\) | ||||
−0.985892 | + | 0.167383i | \(0.946468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1481 | 1.33343 | 0.666714 | − | 0.745314i | \(-0.267700\pi\) | ||||
0.666714 | + | 0.745314i | \(0.267700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.6085 | −1.15065 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8020 | 1.14501 | 0.572506 | − | 0.819900i | \(-0.305971\pi\) | ||||
0.572506 | + | 0.819900i | \(0.305971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.1737 | 1.59063 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.9479 | −1.43102 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.21809 | −0.428282 | −0.214141 | − | 0.976803i | \(-0.568695\pi\) | ||||
−0.214141 | + | 0.976803i | \(0.568695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.33291 | 0.232133 | 0.116066 | − | 0.993241i | \(-0.462971\pi\) | ||||
0.116066 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.3121 | −1.11461 | −0.557307 | − | 0.830306i | \(-0.688165\pi\) | ||||
−0.557307 | + | 0.830306i | \(0.688165\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0942 | −1.07251 | −0.536257 | − | 0.844055i | \(-0.680162\pi\) | ||||
−0.536257 | + | 0.844055i | \(0.680162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.77633 | −0.265924 | −0.132962 | − | 0.991121i | \(-0.542449\pi\) | ||||
−0.132962 | + | 0.991121i | \(0.542449\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2579 | 1.62348 | 0.811742 | − | 0.584017i | \(-0.198520\pi\) | ||||
0.811742 | + | 0.584017i | \(0.198520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.265384 | 0.0247472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.7931 | 2.18111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.35936 | −0.759942 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.31768 | −0.738075 | −0.369037 | − | 0.929415i | \(-0.620313\pi\) | ||||
−0.369037 | + | 0.929415i | \(0.620313\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.84309 | 0.510513 | 0.255257 | − | 0.966873i | \(-0.417840\pi\) | ||||
0.255257 | + | 0.966873i | \(0.417840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 31.2828 | 2.71256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6762 | −1.16843 | −0.584217 | − | 0.811598i | \(-0.698598\pi\) | ||||
−0.584217 | + | 0.811598i | \(0.698598\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2998 | 0.873618 | 0.436809 | − | 0.899554i | \(-0.356109\pi\) | ||||
0.436809 | + | 0.899554i | \(0.356109\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.49690 | 0.459674 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.7367 | −1.30687 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.84309 | 0.642531 | 0.321266 | − | 0.946989i | \(-0.395892\pi\) | ||||
0.321266 | + | 0.946989i | \(0.395892\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5232 | −1.26326 | −0.631632 | − | 0.775268i | \(-0.717615\pi\) | ||||
−0.631632 | + | 0.775268i | \(0.717615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.1737 | −1.70071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4174 | 1.39006 | 0.695030 | − | 0.718980i | \(-0.255391\pi\) | ||||
0.695030 | + | 0.718980i | \(0.255391\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.595212 | −0.0469093 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.9912 | 1.87914 | 0.939568 | − | 0.342363i | \(-0.111227\pi\) | ||||
0.939568 | + | 0.342363i | \(0.111227\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.55733 | −0.119795 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.68232 | 0.127904 | 0.0639522 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639522 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.48567 | −0.339085 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.760672 | 0.0568553 | 0.0284276 | − | 0.999596i | \(-0.490950\pi\) | ||||
0.0284276 | + | 0.999596i | \(0.490950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.35665 | −0.472486 | −0.236243 | − | 0.971694i | \(-0.575916\pi\) | ||||
−0.236243 | + | 0.971694i | \(0.575916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.44267 | −0.253110 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.61943 | 0.630315 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1989 | −0.810327 | −0.405163 | − | 0.914244i | \(-0.632785\pi\) | ||||
−0.405163 | + | 0.914244i | \(0.632785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9471 | −1.07592 | −0.537959 | − | 0.842971i | \(-0.680804\pi\) | ||||
−0.537959 | + | 0.842971i | \(0.680804\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0775 | −1.28797 | −0.643984 | − | 0.765039i | \(-0.722720\pi\) | ||||
−0.643984 | + | 0.765039i | \(0.722720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.67617 | −0.260596 | −0.130298 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130298 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 35.2949 | 2.47722 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8166 | 1.17452 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.3327 | 0.783899 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.2297 | −0.704243 | −0.352122 | − | 0.935954i | \(-0.614540\pi\) | ||||
−0.352122 | + | 0.935954i | \(0.614540\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.5308 | 0.922793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.4891 | 3.22377 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9427 | 1.20696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1032 | −1.48014 | −0.740070 | − | 0.672530i | \(-0.765208\pi\) | ||||
−0.740070 | + | 0.672530i | \(0.765208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.2050 | −1.47380 | −0.736898 | − | 0.676003i | \(-0.763710\pi\) | ||||
−0.736898 | + | 0.676003i | \(0.763710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.66030 | 0.109716 | 0.0548580 | − | 0.998494i | \(-0.482529\pi\) | ||||
0.0548580 | + | 0.998494i | \(0.482529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.0524 | 1.24817 | 0.624083 | − | 0.781358i | \(-0.285473\pi\) | ||||
0.624083 | + | 0.781358i | \(0.285473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.417085 | 0.0272076 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.68706 | −0.367865 | −0.183933 | − | 0.982939i | \(-0.558883\pi\) | ||||
−0.183933 | + | 0.982939i | \(0.558883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9721 | −1.02885 | −0.514427 | − | 0.857534i | \(-0.671995\pi\) | ||||
−0.514427 | + | 0.857534i | \(0.671995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.2425 | −1.67657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.5908 | 1.50104 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.9878 | 1.95593 | 0.977967 | − | 0.208760i | \(-0.0669429\pi\) | ||||
0.977967 | + | 0.208760i | \(0.0669429\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.215625 | −0.0135562 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.32611 | 0.207477 | 0.103739 | − | 0.994605i | \(-0.466919\pi\) | ||||
0.103739 | + | 0.994605i | \(0.466919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.72133 | 0.479780 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.47433 | −0.522549 | −0.261275 | − | 0.965265i | \(-0.584143\pi\) | ||||
−0.261275 | + | 0.965265i | \(0.584143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.3739 | 1.06727 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.94140 | 0.179340 | 0.0896702 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896702 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7654 | 0.775443 | 0.387721 | − | 0.921777i | \(-0.373262\pi\) | ||||
0.387721 | + | 0.921777i | \(0.373262\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.62500 | −0.0979915 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.54097 | −0.393009 | −0.196505 | − | 0.980503i | \(-0.562959\pi\) | ||||
−0.196505 | + | 0.980503i | \(0.562959\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.83281 | −0.347956 | −0.173978 | − | 0.984750i | \(-0.555662\pi\) | ||||
−0.173978 | + | 0.984750i | \(0.555662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.70270 | 0.398434 | 0.199217 | − | 0.979955i | \(-0.436160\pi\) | ||||
0.199217 | + | 0.979955i | \(0.436160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.7168 | −2.22635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1350 | 0.655003 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.113390 | 0.00662433 | 0.00331217 | − | 0.999995i | \(-0.498946\pi\) | ||||
0.00331217 | + | 0.999995i | \(0.498946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.6304 | 1.60870 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.448857 | −0.0259581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.3474 | −1.74919 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.13482 | 0.351279 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.7204 | −1.12550 | −0.562751 | − | 0.826627i | \(-0.690257\pi\) | ||||
−0.562751 | + | 0.826627i | \(0.690257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2858 | 1.60394 | 0.801970 | − | 0.597364i | \(-0.203785\pi\) | ||||
0.801970 | + | 0.597364i | \(0.203785\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.95285 | −0.166905 | −0.0834526 | − | 0.996512i | \(-0.526595\pi\) | ||||
−0.0834526 | + | 0.996512i | \(0.526595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.5101 | 1.32046 | 0.660230 | − | 0.751064i | \(-0.270459\pi\) | ||||
0.660230 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7861 | 0.715886 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.9915 | 2.05826 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.38270 | −0.187638 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.935453 | −0.0515732 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.53388 | −0.194240 | −0.0971198 | − | 0.995273i | \(-0.530963\pi\) | ||||
−0.0971198 | + | 0.995273i | \(0.530963\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0204 | −0.820651 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.7676 | −1.67602 | −0.838008 | − | 0.545657i | \(-0.816280\pi\) | ||||
−0.838008 | + | 0.545657i | \(0.816280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.2037 | 0.931631 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 27.4579 | 1.48259 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.95468 | −0.480713 | −0.240356 | − | 0.970685i | \(-0.577264\pi\) | ||||
−0.240356 | + | 0.970685i | \(0.577264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.10711 | 0.166320 | 0.0831599 | − | 0.996536i | \(-0.473499\pi\) | ||||
0.0831599 | + | 0.996536i | \(0.473499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0170 | 0.639600 | 0.319800 | − | 0.947485i | \(-0.396384\pi\) | ||||
0.319800 | + | 0.947485i | \(0.396384\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.13504 | 0.219465 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7949 | 1.51974 | 0.759869 | − | 0.650077i | \(-0.225263\pi\) | ||||
0.759869 | + | 0.650077i | \(0.225263\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.6359 | 1.55978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8739 | −0.569165 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.28255 | 0.380146 | 0.190073 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190073 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −38.9668 | −2.02306 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2500 | 1.30740 | 0.653698 | − | 0.756756i | \(-0.273217\pi\) | ||||
0.653698 | + | 0.756756i | \(0.273217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.6163 | 1.37081 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2733 | −0.784535 | −0.392268 | − | 0.919851i | \(-0.628309\pi\) | ||||
−0.392268 | + | 0.919851i | \(0.628309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.83494 | −0.144859 | −0.0724293 | − | 0.997374i | \(-0.523075\pi\) | ||||
−0.0724293 | + | 0.997374i | \(0.523075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.5785 | −0.742988 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8121 | 0.903110 | 0.451555 | − | 0.892243i | \(-0.350869\pi\) | ||||
0.451555 | + | 0.892243i | \(0.350869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.703831 | −0.0355942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.0512 | 1.76362 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5585 | 0.931425 | 0.465712 | − | 0.884936i | \(-0.345798\pi\) | ||||
0.465712 | + | 0.884936i | \(0.345798\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8040 | −0.988967 | −0.494483 | − | 0.869187i | \(-0.664643\pi\) | ||||
−0.494483 | + | 0.869187i | \(0.664643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.8121 | 1.78393 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.79717 | 0.138651 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2604 | 1.19960 | 0.599799 | − | 0.800151i | \(-0.295247\pi\) | ||||
0.599799 | + | 0.800151i | \(0.295247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −61.9704 | −3.04937 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.2962 | −1.19265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5947 | 0.810704 | 0.405352 | − | 0.914161i | \(-0.367149\pi\) | ||||
0.405352 | + | 0.914161i | \(0.367149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1760 | −1.17827 | −0.589134 | − | 0.808035i | \(-0.700531\pi\) | ||||
−0.589134 | + | 0.808035i | \(0.700531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.30425 | −0.257294 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.7594 | −0.665864 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.233761 | −0.0112598 | −0.00562992 | − | 0.999984i | \(-0.501792\pi\) | ||||
−0.00562992 | + | 0.999984i | \(0.501792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0595 | 1.49263 | 0.746313 | − | 0.665595i | \(-0.231822\pi\) | ||||
0.746313 | + | 0.665595i | \(0.231822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.925386 | −0.0442672 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.3994 | −0.973610 | −0.486805 | − | 0.873511i | \(-0.661838\pi\) | ||||
−0.486805 | + | 0.873511i | \(0.661838\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.445779 | −0.0211796 | −0.0105898 | − | 0.999944i | \(-0.503371\pi\) | ||||
−0.0105898 | + | 0.999944i | \(0.503371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.6041 | −1.02413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8874 | −1.12732 | −0.563659 | − | 0.826007i | \(-0.690607\pi\) | ||||
−0.563659 | + | 0.826007i | \(0.690607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6635 | −0.643389 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.3474 | −1.42271 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.8064 | 0.552280 | 0.276140 | − | 0.961117i | \(-0.410945\pi\) | ||||
0.276140 | + | 0.961117i | \(0.410945\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0913 | −0.656295 | −0.328148 | − | 0.944626i | \(-0.606424\pi\) | ||||
−0.328148 | + | 0.944626i | \(0.606424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6663 | 0.681602 | 0.340801 | − | 0.940135i | \(-0.389302\pi\) | ||||
0.340801 | + | 0.940135i | \(0.389302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.8445 | −1.42731 | −0.713656 | − | 0.700496i | \(-0.752962\pi\) | ||||
−0.713656 | + | 0.700496i | \(0.752962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.6882 | 1.55558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.9938 | −0.505496 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.97394 | −0.319987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.40615 | −0.201322 | −0.100661 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100661 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.82275 | 0.265495 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.43618 | 0.383067 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.2128 | 1.09719 | 0.548594 | − | 0.836089i | \(-0.315163\pi\) | ||||
0.548594 | + | 0.836089i | \(0.315163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.9516 | 1.48709 | 0.743543 | − | 0.668689i | \(-0.233144\pi\) | ||||
0.743543 | + | 0.668689i | \(0.233144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.7358 | 1.87969 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.27422 | −0.416006 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.79619 | 0.438538 | 0.219269 | − | 0.975664i | \(-0.429633\pi\) | ||||
0.219269 | + | 0.975664i | \(0.429633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.0414 | −0.626075 | −0.313038 | − | 0.949741i | \(-0.601347\pi\) | ||||
−0.313038 | + | 0.949741i | \(0.601347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.66581 | −0.207626 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.9992 | 1.37402 | 0.687008 | − | 0.726650i | \(-0.258924\pi\) | ||||
0.687008 | + | 0.726650i | \(0.258924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.3883 | 1.07888 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.6242 | 0.996941 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.338883 | −0.0149040 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.3877 | −1.02463 | −0.512317 | − | 0.858796i | \(-0.671213\pi\) | ||||
−0.512317 | + | 0.858796i | \(0.671213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.2130 | −0.621490 | −0.310745 | − | 0.950493i | \(-0.600579\pi\) | ||||
−0.310745 | + | 0.950493i | \(0.600579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.1552 | 2.44616 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9824 | −0.999234 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.4427 | −1.23199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.1883 | 0.959285 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.3221 | 0.918407 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.61867 | −0.155579 | −0.0777893 | − | 0.996970i | \(-0.524786\pi\) | ||||
−0.0777893 | + | 0.996970i | \(0.524786\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.55267 | 0.237850 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1945 | 0.692426 | 0.346213 | − | 0.938156i | \(-0.387467\pi\) | ||||
0.346213 | + | 0.938156i | \(0.387467\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.8736 | 2.33769 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −78.6141 | −3.34301 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.39689 | 0.228674 | 0.114337 | − | 0.993442i | \(-0.463526\pi\) | ||||
0.114337 | + | 0.993442i | \(0.463526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.8853 | −0.967946 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.3990 | −1.61833 | −0.809163 | − | 0.587585i | \(-0.800079\pi\) | ||||
−0.809163 | + | 0.587585i | \(0.800079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5157 | −1.45209 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.14674 | 0.299607 | 0.149803 | − | 0.988716i | \(-0.452136\pi\) | ||||
0.149803 | + | 0.988716i | \(0.452136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.09003 | 0.380406 | 0.190203 | − | 0.981745i | \(-0.439085\pi\) | ||||
0.190203 | + | 0.981745i | \(0.439085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.132692 | 0.00553363 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.92103 | −0.246496 | −0.123248 | − | 0.992376i | \(-0.539331\pi\) | ||||
−0.123248 | + | 0.992376i | \(0.539331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 54.4924 | 2.26073 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.1163 | −0.584639 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.2003 | −1.12267 | −0.561337 | − | 0.827587i | \(-0.689713\pi\) | ||||
−0.561337 | + | 0.827587i | \(0.689713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 73.8320 | 3.04220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.3314 | −0.670648 | −0.335324 | − | 0.942103i | \(-0.608846\pi\) | ||||
−0.335324 | + | 0.942103i | \(0.608846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −47.5862 | −1.95084 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.6823 | 0.599902 | 0.299951 | − | 0.953955i | \(-0.403030\pi\) | ||||
0.299951 | + | 0.953955i | \(0.403030\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3773 | −0.831206 | −0.415603 | − | 0.909546i | \(-0.636430\pi\) | ||||
−0.415603 | + | 0.909546i | \(0.636430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.7187 | 0.679713 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.72706 | −0.0700992 | −0.0350496 | − | 0.999386i | \(-0.511159\pi\) | ||||
−0.0350496 | + | 0.999386i | \(0.511159\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.705437 | −0.0285389 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.43357 | −0.381018 | −0.190509 | − | 0.981685i | \(-0.561014\pi\) | ||||
−0.190509 | + | 0.981685i | \(0.561014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2934 | 0.776724 | 0.388362 | − | 0.921507i | \(-0.373041\pi\) | ||||
0.388362 | + | 0.921507i | \(0.373041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7698 | −0.473067 | −0.236533 | − | 0.971623i | \(-0.576011\pi\) | ||||
−0.236533 | + | 0.971623i | \(0.576011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.4543 | 1.94128 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.13038 | 0.364052 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7072 | 1.42148 | 0.710742 | − | 0.703453i | \(-0.248360\pi\) | ||||
0.710742 | + | 0.703453i | \(0.248360\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.6354 | 0.660154 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44.3852 | 1.75861 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.4396 | 1.28129 | 0.640644 | − | 0.767838i | \(-0.278667\pi\) | ||||
0.640644 | + | 0.767838i | \(0.278667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.8629 | 0.980496 | 0.490248 | − | 0.871583i | \(-0.336906\pi\) | ||||
0.490248 | + | 0.871583i | \(0.336906\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.5888 | 0.888056 | 0.444028 | − | 0.896013i | \(-0.353549\pi\) | ||||
0.444028 | + | 0.896013i | \(0.353549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.4498 | −0.881230 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.9597 | −0.898481 | −0.449241 | − | 0.893411i | \(-0.648305\pi\) | ||||
−0.449241 | + | 0.893411i | \(0.648305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.6862 | −0.456617 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.23673 | 0.0481760 | 0.0240880 | − | 0.999710i | \(-0.492332\pi\) | ||||
0.0240880 | + | 0.999710i | \(0.492332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5706 | 0.488940 | 0.244470 | − | 0.969657i | \(-0.421386\pi\) | ||||
0.244470 | + | 0.969657i | \(0.421386\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −62.5656 | −2.42619 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.04407 | −0.0404265 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.98455 | −0.192427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.5661 | −1.87208 | −0.936042 | − | 0.351888i | \(-0.885540\pi\) | ||||
−0.936042 | + | 0.351888i | \(0.885540\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.90041 | −0.149905 | −0.0749525 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749525 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.9210 | −0.726120 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2389 | 0.659626 | 0.329813 | − | 0.944046i | \(-0.393014\pi\) | ||||
0.329813 | + | 0.944046i | \(0.393014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.3523 | 1.04508 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.3853 | −1.11949 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.1641 | −0.995330 | −0.497665 | − | 0.867369i | \(-0.665809\pi\) | ||||
−0.497665 | + | 0.867369i | \(0.665809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.5996 | −0.781388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.5996 | −1.68933 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.0982 | −1.17456 | −0.587282 | − | 0.809382i | \(-0.699802\pi\) | ||||
−0.587282 | + | 0.809382i | \(0.699802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0045 | 0.452758 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4646 | 0.393564 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.23408 | −0.346793 | −0.173397 | − | 0.984852i | \(-0.555474\pi\) | ||||
−0.173397 | + | 0.984852i | \(0.555474\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.40479 | −0.0526097 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.9938 | −0.411145 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.3348 | −1.24318 | −0.621590 | − | 0.783343i | \(-0.713513\pi\) | ||||
−0.621590 | + | 0.783343i | \(0.713513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.7424 | −1.88974 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.86837 | −0.292224 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.10327 | 0.0780061 | 0.0390030 | − | 0.999239i | \(-0.487582\pi\) | ||||
0.0390030 | + | 0.999239i | \(0.487582\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.8854 | −1.32727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0965 | −1.25938 | −0.629691 | − | 0.776846i | \(-0.716818\pi\) | ||||
−0.629691 | + | 0.776846i | \(0.716818\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.2041 | 0.449543 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.1479 | −0.410081 | −0.205040 | − | 0.978754i | \(-0.565733\pi\) | ||||
−0.205040 | + | 0.978754i | \(0.565733\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.4849 | 0.861579 | 0.430789 | − | 0.902452i | \(-0.358235\pi\) | ||||
0.430789 | + | 0.902452i | \(0.358235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.6862 | −0.574697 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.7648 | −1.81837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1954 | 1.13834 | 0.569169 | − | 0.822221i | \(-0.307265\pi\) | ||||
0.569169 | + | 0.822221i | \(0.307265\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.0465 | 1.12990 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.3753 | −0.704208 | −0.352104 | − | 0.935961i | \(-0.614534\pi\) | ||||
−0.352104 | + | 0.935961i | \(0.614534\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.7008 | −1.25790 | −0.628951 | − | 0.777445i | \(-0.716515\pi\) | ||||
−0.628951 | + | 0.777445i | \(0.716515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4537 | −0.450855 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.7327 | −1.68742 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.6173 | −0.923785 | −0.461892 | − | 0.886936i | \(-0.652829\pi\) | ||||
−0.461892 | + | 0.886936i | \(0.652829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.4065 | 0.913808 | 0.456904 | − | 0.889516i | \(-0.348958\pi\) | ||||
0.456904 | + | 0.889516i | \(0.348958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.5868 | −0.380291 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.6389 | −2.10096 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.35973 | −0.120221 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.8348 | −1.24331 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.5483 | 1.23151 | 0.615757 | − | 0.787936i | \(-0.288850\pi\) | ||||
0.615757 | + | 0.787936i | \(0.288850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 77.4131 | 2.75249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3761 | −0.368467 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.1106 | −1.52706 | −0.763529 | − | 0.645774i | \(-0.776535\pi\) | ||||
−0.763529 | + | 0.645774i | \(0.776535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.10616 | −0.0391332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.83505 | 0.311782 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19042 | 0.0419569 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.4150 | −0.858386 | −0.429193 | − | 0.903213i | \(-0.641202\pi\) | ||||
−0.429193 | + | 0.903213i | \(0.641202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.1406 | −1.37441 | −0.687206 | − | 0.726463i | \(-0.741163\pi\) | ||||
−0.687206 | + | 0.726463i | \(0.741163\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47.9824 | −1.68075 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.1815 | −1.65067 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.3557 | −0.919822 | −0.459911 | − | 0.887965i | \(-0.652119\pi\) | ||||
−0.459911 | + | 0.887965i | \(0.652119\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0365 | 0.384709 | 0.192354 | − | 0.981326i | \(-0.438388\pi\) | ||||
0.192354 | + | 0.981326i | \(0.438388\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.5066 | 0.400123 | 0.200062 | − | 0.979783i | \(-0.435886\pi\) | ||||
0.200062 | + | 0.979783i | \(0.435886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.9151 | −0.622217 | −0.311108 | − | 0.950374i | \(-0.600700\pi\) | ||||
−0.311108 | + | 0.950374i | \(0.600700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 69.5983 | 2.41144 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | −0.0692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.8888 | −1.61878 | −0.809390 | − | 0.587271i | \(-0.800202\pi\) | ||||
−0.809390 | + | 0.587271i | \(0.800202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.9113 | 1.13487 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.11467 | 0.107148 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.4973 | −1.28842 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.228407 | −0.00782969 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.97457 | −0.273044 | −0.136522 | − | 0.990637i | \(-0.543592\pi\) | ||||
−0.136522 | + | 0.990637i | \(0.543592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.3453 | −1.30985 | −0.654925 | − | 0.755694i | \(-0.727300\pi\) | ||||
−0.654925 | + | 0.755694i | \(0.727300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.7156 | 1.90099 | 0.950497 | − | 0.310735i | \(-0.100575\pi\) | ||||
0.950497 | + | 0.310735i | \(0.100575\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.5096 | −1.20876 | −0.604381 | − | 0.796696i | \(-0.706579\pi\) | ||||
−0.604381 | + | 0.796696i | \(0.706579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.36464 | −0.114401 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.4792 | −0.966090 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.4047 | 0.860806 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 53.8281 | 1.81972 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.96237 | 0.0662646 | 0.0331323 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331323 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.9608 | 0.874642 | 0.437321 | − | 0.899305i | \(-0.355927\pi\) | ||||
0.437321 | + | 0.899305i | \(0.355927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.1139 | 1.08072 | 0.540360 | − | 0.841434i | \(-0.318288\pi\) | ||||
0.540360 | + | 0.841434i | \(0.318288\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.96553 | −0.233880 | −0.116940 | − | 0.993139i | \(-0.537308\pi\) | ||||
−0.116940 | + | 0.993139i | \(0.537308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.3104 | −1.25135 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.45436 | −0.0486684 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.52134 | −0.0508529 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 83.3012 | 2.77825 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.0777 | −1.53507 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.7133 | 0.422604 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.2026 | 1.13568 | 0.567839 | − | 0.823140i | \(-0.307780\pi\) | ||||
0.567839 | + | 0.823140i | \(0.307780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5867 | 1.11278 | 0.556388 | − | 0.830922i | \(-0.312187\pi\) | ||||
0.556388 | + | 0.830922i | \(0.312187\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7407 | 0.653323 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.2102 | 0.865537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.8672 | 1.48003 | 0.740017 | − | 0.672588i | \(-0.234817\pi\) | ||||
0.740017 | + | 0.672588i | \(0.234817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.99381 | −0.230204 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.72133 | −0.0565971 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.6760 | 0.415887 | 0.207943 | − | 0.978141i | \(-0.433323\pi\) | ||||
0.207943 | + | 0.978141i | \(0.433323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 91.5068 | 2.99902 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.2389 | −0.563771 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.52060 | 0.115013 | 0.0575065 | − | 0.998345i | \(-0.481685\pi\) | ||||
0.0575065 | + | 0.998345i | \(0.481685\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.2981 | −1.77007 | −0.885034 | − | 0.465526i | \(-0.845865\pi\) | ||||
−0.885034 | + | 0.465526i | \(0.845865\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.11571 | 0.0363325 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.3015 | −1.14715 | −0.573573 | − | 0.819155i | \(-0.694443\pi\) | ||||
−0.573573 | + | 0.819155i | \(0.694443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3915 | 0.597015 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.2048 | −1.33475 | −0.667377 | − | 0.744720i | \(-0.732583\pi\) | ||||
−0.667377 | + | 0.744720i | \(0.732583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.3979 | 0.724778 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −61.3468 | −1.98099 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81.0812 | 2.61552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.8943 | 0.962330 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.5718 | −0.532913 | −0.266457 | − | 0.963847i | \(-0.585853\pi\) | ||||
−0.266457 | + | 0.963847i | \(0.585853\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.8901 | 1.34432 | 0.672158 | − | 0.740408i | \(-0.265368\pi\) | ||||
0.672158 | + | 0.740408i | \(0.265368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.2015 | 1.48115 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54.2586 | −1.73589 | −0.867944 | − | 0.496663i | \(-0.834559\pi\) | ||||
−0.867944 | + | 0.496663i | \(0.834559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5533 | 0.561007 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.0351 | 1.27692 | 0.638460 | − | 0.769655i | \(-0.279572\pi\) | ||||
0.638460 | + | 0.769655i | \(0.279572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.1550 | 1.15199 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.897714 | 0.0285456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.86359 | 0.218029 | 0.109015 | − | 0.994040i | \(-0.465230\pi\) | ||||
0.109015 | + | 0.994040i | \(0.465230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.35233 | 0.233085 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.6578 | 0.844260 | 0.422130 | − | 0.906535i | \(-0.361283\pi\) | ||||
0.422130 | + | 0.906535i | \(0.361283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6012.2.a.d.1.4 | 5 | ||
3.2 | odd | 2 | 668.2.a.b.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 2672.2.a.j.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.a.b.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
2672.2.a.j.1.4 | 5 | 12.11 | even | 2 | |||
6012.2.a.d.1.4 | 5 | 1.1 | even | 1 | trivial |