Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −2.41806 | −1.39606 | −0.698032 | − | 0.716066i | \(-0.745941\pi\) | ||||
−0.698032 | + | 0.716066i | \(0.745941\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.877422 | 0.392395 | 0.196198 | − | 0.980564i | \(-0.437141\pi\) | ||||
0.196198 | + | 0.980564i | \(0.437141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.89114 | 1.09275 | 0.546374 | − | 0.837541i | \(-0.316008\pi\) | ||||
0.546374 | + | 0.837541i | \(0.316008\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.84699 | 0.948997 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.81257 | 0.546510 | 0.273255 | − | 0.961942i | \(-0.411900\pi\) | ||||
0.273255 | + | 0.961942i | \(0.411900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.69719 | −1.02542 | −0.512709 | − | 0.858563i | \(-0.671358\pi\) | ||||
−0.512709 | + | 0.858563i | \(0.671358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.12166 | −0.547809 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.52490 | −1.33998 | −0.669992 | − | 0.742368i | \(-0.733703\pi\) | ||||
−0.669992 | + | 0.742368i | \(0.733703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.24113 | −0.743566 | −0.371783 | − | 0.928320i | \(-0.621253\pi\) | ||||
−0.371783 | + | 0.928320i | \(0.621253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.99093 | −1.52555 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.45930 | −0.512799 | −0.256400 | − | 0.966571i | \(-0.582536\pi\) | ||||
−0.256400 | + | 0.966571i | \(0.582536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23013 | −0.846026 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.369983 | 0.0712033 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.86650 | 0.532296 | 0.266148 | − | 0.963932i | \(-0.414249\pi\) | ||||
0.266148 | + | 0.963932i | \(0.414249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.81129 | −1.40295 | −0.701474 | − | 0.712695i | \(-0.747474\pi\) | ||||
−0.701474 | + | 0.712695i | \(0.747474\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.38289 | −0.762963 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53675 | 0.428789 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.93159 | 0.810749 | 0.405374 | − | 0.914151i | \(-0.367141\pi\) | ||||
0.405374 | + | 0.914151i | \(0.367141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.94002 | 1.43155 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.1443 | 1.89663 | 0.948314 | − | 0.317333i | \(-0.102787\pi\) | ||||
0.948314 | + | 0.317333i | \(0.102787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.06072 | 0.924251 | 0.462126 | − | 0.886814i | \(-0.347087\pi\) | ||||
0.462126 | + | 0.886814i | \(0.347087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.49801 | 0.372382 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.72506 | 0.689221 | 0.344610 | − | 0.938746i | \(-0.388011\pi\) | ||||
0.344610 | + | 0.938746i | \(0.388011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.35868 | 0.194097 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.3595 | 1.87071 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.39504 | −0.191623 | −0.0958115 | − | 0.995399i | \(-0.530545\pi\) | ||||
−0.0958115 | + | 0.995399i | \(0.530545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.59039 | 0.214448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.83723 | 1.03807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.45080 | −1.10020 | −0.550100 | − | 0.835098i | \(-0.685411\pi\) | ||||
−0.550100 | + | 0.835098i | \(0.685411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.2787 | 1.70017 | 0.850084 | − | 0.526648i | \(-0.176551\pi\) | ||||
0.850084 | + | 0.526648i | \(0.176551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.23105 | 1.03701 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.24400 | −0.402369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.83863 | −1.07981 | −0.539906 | − | 0.841726i | \(-0.681540\pi\) | ||||
−0.539906 | + | 0.841726i | \(0.681540\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.94672 | 0.715901 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.13219 | −0.371723 | −0.185861 | − | 0.982576i | \(-0.559508\pi\) | ||||
−0.185861 | + | 0.982576i | \(0.559508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.61295 | 1.12511 | 0.562556 | − | 0.826759i | \(-0.309818\pi\) | ||||
0.562556 | + | 0.826759i | \(0.309818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.2287 | 1.18111 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.24039 | 0.597197 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.251676 | 0.0283157 | 0.0141579 | − | 0.999900i | \(-0.495493\pi\) | ||||
0.0141579 | + | 0.999900i | \(0.495493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.43561 | −1.04840 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.82717 | 0.200558 | 0.100279 | − | 0.994959i | \(-0.468026\pi\) | ||||
0.100279 | + | 0.994959i | \(0.468026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.84767 | −0.525804 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.93136 | −0.743120 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65191 | 0.387102 | 0.193551 | − | 0.981090i | \(-0.437999\pi\) | ||||
0.193551 | + | 0.981090i | \(0.437999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.6891 | −1.12052 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.8881 | 1.95861 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.84384 | −0.291772 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3340 | 1.15080 | 0.575399 | − | 0.817873i | \(-0.304847\pi\) | ||||
0.575399 | + | 0.817873i | \(0.304847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.16037 | 0.518636 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.02240 | 0.798259 | 0.399129 | − | 0.916895i | \(-0.369312\pi\) | ||||
0.399129 | + | 0.916895i | \(0.369312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.398605 | −0.0392757 | −0.0196379 | − | 0.999807i | \(-0.506251\pi\) | ||||
−0.0196379 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.13400 | −0.598617 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.81810 | −0.465783 | −0.232891 | − | 0.972503i | \(-0.574819\pi\) | ||||
−0.232891 | + | 0.972503i | \(0.574819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.3186 | −1.17990 | −0.589952 | − | 0.807439i | \(-0.700853\pi\) | ||||
−0.589952 | + | 0.807439i | \(0.700853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.9249 | −1.13186 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.5143 | 1.36539 | 0.682694 | − | 0.730705i | \(-0.260808\pi\) | ||||
0.682694 | + | 0.730705i | \(0.260808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.15784 | −0.201220 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.5259 | −0.973118 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.9732 | −1.46427 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.71460 | −0.701327 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.3657 | −2.64782 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.09872 | −0.724372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5119 | 1.11025 | 0.555124 | − | 0.831767i | \(-0.312671\pi\) | ||||
0.555124 | + | 0.831767i | \(0.312671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.6552 | −1.29031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9192 | 0.954016 | 0.477008 | − | 0.878899i | \(-0.341721\pi\) | ||||
0.477008 | + | 0.878899i | \(0.341721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.37055 | −0.812530 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.324632 | 0.0279398 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.2321 | −0.874189 | −0.437095 | − | 0.899416i | \(-0.643993\pi\) | ||||
−0.437095 | + | 0.899416i | \(0.643993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0747 | −1.19380 | −0.596901 | − | 0.802315i | \(-0.703601\pi\) | ||||
−0.596901 | + | 0.802315i | \(0.703601\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4255 | −0.962197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.70142 | −0.560401 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.51513 | 0.208870 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.28537 | −0.270972 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.6740 | 1.36599 | 0.682995 | − | 0.730423i | \(-0.260677\pi\) | ||||
0.682995 | + | 0.730423i | \(0.260677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.91103 | −0.155517 | −0.0777586 | − | 0.996972i | \(-0.524776\pi\) | ||||
−0.0777586 | + | 0.996972i | \(0.524776\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.7293 | −1.27164 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.85380 | −0.550510 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2750 | 0.979654 | 0.489827 | − | 0.871820i | \(-0.337060\pi\) | ||||
0.489827 | + | 0.871820i | \(0.337060\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.37327 | 0.267518 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.11018 | −0.560360 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.44567 | 0.113234 | 0.0566170 | − | 0.998396i | \(-0.481969\pi\) | ||||
0.0566170 | + | 0.998396i | \(0.481969\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.84565 | −0.299383 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0957 | −1.24552 | −0.622762 | − | 0.782411i | \(-0.713990\pi\) | ||||
−0.622762 | + | 0.782411i | \(0.713990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.669243 | 0.0514803 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.22747 | −0.705642 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5761 | 0.880113 | 0.440057 | − | 0.897970i | \(-0.354958\pi\) | ||||
0.440057 | + | 0.897970i | \(0.354958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2299 | −0.924493 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.4345 | 1.53595 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.4469 | 1.37879 | 0.689395 | − | 0.724386i | \(-0.257877\pi\) | ||||
0.689395 | + | 0.724386i | \(0.257877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.30694 | 0.394462 | 0.197231 | − | 0.980357i | \(-0.436805\pi\) | ||||
0.197231 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −32.1087 | −2.37354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.32709 | 0.318134 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0143 | −0.732315 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.06967 | 0.0778072 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.03520 | 0.0749044 | 0.0374522 | − | 0.999298i | \(-0.488076\pi\) | ||||
0.0374522 | + | 0.999298i | \(0.488076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1227 | 1.16054 | 0.580268 | − | 0.814425i | \(-0.302948\pi\) | ||||
0.580268 | + | 0.814425i | \(0.302948\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.84417 | 0.561733 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7147 | 1.19088 | 0.595438 | − | 0.803401i | \(-0.296978\pi\) | ||||
0.595438 | + | 0.803401i | \(0.296978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.914111 | 0.0647996 | 0.0323998 | − | 0.999475i | \(-0.489685\pi\) | ||||
0.0323998 | + | 0.999475i | \(0.489685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3723 | 1.50749 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.28746 | 0.581665 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6557 | 0.744228 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.00160 | −0.486645 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.87477 | −0.406366 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.300114 | −0.0206607 | −0.0103303 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103303 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.57381 | 0.518949 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.31781 | 0.362672 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.5835 | −1.53307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.2447 | −1.57073 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.4266 | 1.37404 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.48842 | 0.568426 | 0.284213 | − | 0.958761i | \(-0.408268\pi\) | ||||
0.284213 | + | 0.958761i | \(0.408268\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0431 | −0.802876 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1657 | 0.741095 | 0.370548 | − | 0.928814i | \(-0.379170\pi\) | ||||
0.370548 | + | 0.928814i | \(0.379170\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.26396 | 0.413934 | 0.206967 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206967 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.6715 | −0.833726 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1058 | −0.858586 | −0.429293 | − | 0.903165i | \(-0.641237\pi\) | ||||
−0.429293 | + | 0.903165i | \(0.641237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.14587 | 0.270447 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.608566 | −0.0395306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.4793 | −1.26001 | −0.630006 | − | 0.776590i | \(-0.716948\pi\) | ||||
−0.630006 | + | 0.776590i | \(0.716948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3358 | 1.37436 | 0.687180 | − | 0.726487i | \(-0.258848\pi\) | ||||
0.687180 | + | 0.726487i | \(0.258848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.7059 | 1.39243 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.19214 | 0.0761629 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.9831 | 0.762465 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.41820 | −0.279992 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0562 | 0.697859 | 0.348929 | − | 0.937149i | \(-0.386545\pi\) | ||||
0.348929 | + | 0.937149i | \(0.386545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.45765 | −0.280250 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.7219 | 0.734056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.9376 | 1.55556 | 0.777781 | − | 0.628535i | \(-0.216345\pi\) | ||||
0.777781 | + | 0.628535i | \(0.216345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.2579 | 0.885944 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.16091 | 0.505148 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.4803 | −1.26287 | −0.631436 | − | 0.775428i | \(-0.717534\pi\) | ||||
−0.631436 | + | 0.775428i | \(0.717534\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.22404 | −0.0751919 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.83053 | −0.540420 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.3651 | −1.18071 | −0.590356 | − | 0.807143i | \(-0.701013\pi\) | ||||
−0.590356 | + | 0.807143i | \(0.701013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.00825 | 0.304230 | 0.152115 | − | 0.988363i | \(-0.451392\pi\) | ||||
0.152115 | + | 0.988363i | \(0.451392\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.8468 | 1.56432 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.66740 | −0.462362 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.09507 | 0.185965 | 0.0929825 | − | 0.995668i | \(-0.470360\pi\) | ||||
0.0929825 | + | 0.995668i | \(0.470360\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.2387 | −1.33139 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0408 | −1.19553 | −0.597767 | − | 0.801670i | \(-0.703945\pi\) | ||||
−0.597767 | + | 0.801670i | \(0.703945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1114 | 1.19550 | 0.597749 | − | 0.801683i | \(-0.296062\pi\) | ||||
0.597749 | + | 0.801683i | \(0.296062\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.87656 | 0.407332 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.1110 | 2.07254 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5245 | 0.795559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.4063 | −1.60659 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.8533 | 1.04300 | 0.521500 | − | 0.853252i | \(-0.325373\pi\) | ||||
0.521500 | + | 0.853252i | \(0.325373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.41492 | −0.431714 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.670620 | 0.0389133 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.09251 | 0.525833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.5224 | 1.00997 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.3986 | −1.11442 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.6511 | 0.667137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.7019 | 1.69517 | 0.847587 | − | 0.530656i | \(-0.178054\pi\) | ||||
0.847587 | + | 0.530656i | \(0.178054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.963849 | 0.0548315 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7601 | 0.893671 | 0.446836 | − | 0.894616i | \(-0.352551\pi\) | ||||
0.446836 | + | 0.894616i | \(0.352551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.0224 | −1.69697 | −0.848484 | − | 0.529221i | \(-0.822484\pi\) | ||||
−0.848484 | + | 0.529221i | \(0.822484\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.22210 | 0.406919 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.05026 | 0.0589884 | 0.0294942 | − | 0.999565i | \(-0.490610\pi\) | ||||
0.0294942 | + | 0.999565i | \(0.490610\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.19573 | 0.290905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6504 | 0.650263 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.9069 | 0.996367 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.6396 | 0.867530 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.7869 | 1.64722 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.6608 | 0.753145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9827 | 0.658630 | 0.329315 | − | 0.944220i | \(-0.393182\pi\) | ||||
0.329315 | + | 0.944220i | \(0.393182\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0402 | 0.769398 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.75521 | −0.423713 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.8991 | 0.757130 | 0.378565 | − | 0.925575i | \(-0.376418\pi\) | ||||
0.378565 | + | 0.925575i | \(0.376418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −35.0963 | −1.90617 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.1585 | −0.766725 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.3098 | −0.880648 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.21779 | 0.280916 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.07712 | −0.165189 | −0.0825943 | − | 0.996583i | \(-0.526321\pi\) | ||||
−0.0825943 | + | 0.996583i | \(0.526321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.6214 | 1.79971 | 0.899857 | − | 0.436185i | \(-0.143671\pi\) | ||||
0.899857 | + | 0.436185i | \(0.143671\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.36790 | −0.0730131 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.8629 | −1.16365 | −0.581823 | − | 0.813315i | \(-0.697660\pi\) | ||||
−0.581823 | + | 0.813315i | \(0.697660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.74825 | −0.145862 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 38.6242 | 2.04421 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.0907 | −1.79924 | −0.899619 | − | 0.436675i | \(-0.856156\pi\) | ||||
−0.899619 | + | 0.436675i | \(0.856156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.49508 | −0.447110 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.6543 | 0.979098 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.43462 | 0.441488 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2588 | −1.31850 | −0.659248 | − | 0.751926i | \(-0.729125\pi\) | ||||
−0.659248 | + | 0.751926i | \(0.729125\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 34.5748 | 1.79989 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.03324 | −0.209396 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.58372 | 0.340892 | 0.170446 | − | 0.985367i | \(-0.445479\pi\) | ||||
0.170446 | + | 0.985367i | \(0.445479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.5832 | 1.01127 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.5980 | −0.545826 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.88202 | −0.507605 | −0.253803 | − | 0.967256i | \(-0.581681\pi\) | ||||
−0.253803 | + | 0.967256i | \(0.581681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.2544 | −1.54998 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.7773 | 1.87923 | 0.939615 | − | 0.342233i | \(-0.111183\pi\) | ||||
0.939615 | + | 0.342233i | \(0.111183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.59803 | 0.234337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.2548 | 0.877112 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8853 | −0.653308 | −0.326654 | − | 0.945144i | \(-0.605921\pi\) | ||||
−0.326654 | + | 0.945144i | \(0.605921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5874 | 0.687143 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.4033 | −1.33187 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.220826 | 0.0111110 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.80575 | −0.241194 | −0.120597 | − | 0.992702i | \(-0.538481\pi\) | ||||
−0.120597 | + | 0.992702i | \(0.538481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.6585 | 1.13434 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.39828 | 0.369452 | 0.184726 | − | 0.982790i | \(-0.440860\pi\) | ||||
0.184726 | + | 0.982790i | \(0.440860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.8798 | 1.43861 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.27902 | −0.411388 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.93885 | 0.443082 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7161 | 0.579323 | 0.289662 | − | 0.957129i | \(-0.406457\pi\) | ||||
0.289662 | + | 0.957129i | \(0.406457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.7418 | 1.22042 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.4324 | −1.20224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.60320 | 0.0786980 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.0334 | 1.66662 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9433 | 0.827734 | 0.413867 | − | 0.910337i | \(-0.364178\pi\) | ||||
0.413867 | + | 0.910337i | \(0.364178\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2552 | 0.743493 | 0.371747 | − | 0.928334i | \(-0.378759\pi\) | ||||
0.371747 | + | 0.928334i | \(0.378759\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.4522 | 0.654069 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.3710 | 1.13366 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.3906 | 1.85785 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.2044 | 0.782356 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2726 | −0.880158 | −0.440079 | − | 0.897959i | \(-0.645050\pi\) | ||||
−0.440079 | + | 0.897959i | \(0.645050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.76978 | 0.469506 | 0.234753 | − | 0.972055i | \(-0.424572\pi\) | ||||
0.234753 | + | 0.972055i | \(0.424572\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.08173 | −0.291597 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.97091 | 0.381300 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4162 | 1.16532 | 0.582660 | − | 0.812716i | \(-0.302012\pi\) | ||||
0.582660 | + | 0.812716i | \(0.302012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.86815 | 0.184198 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3693 | 1.20533 | 0.602667 | − | 0.797993i | \(-0.294105\pi\) | ||||
0.602667 | + | 0.797993i | \(0.294105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.20427 | 0.151897 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −40.3187 | −1.90701 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.5235 | −1.72365 | −0.861825 | − | 0.507207i | \(-0.830678\pi\) | ||||
−0.861825 | + | 0.507207i | \(0.830678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.0125 | 1.03653 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.62097 | 0.217112 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.37885 | −0.439687 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.5234 | 1.66171 | 0.830857 | − | 0.556485i | \(-0.187850\pi\) | ||||
0.830857 | + | 0.556485i | \(0.187850\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.04412 | −0.0954114 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.3542 | 1.69318 | 0.846591 | − | 0.532244i | \(-0.178651\pi\) | ||||
0.846591 | + | 0.532244i | \(0.178651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9330 | −0.879892 | −0.439946 | − | 0.898024i | \(-0.645002\pi\) | ||||
−0.439946 | + | 0.898024i | \(0.645002\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.5729 | 0.768548 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.70155 | 0.402660 | 0.201330 | − | 0.979523i | \(-0.435474\pi\) | ||||
0.201330 | + | 0.979523i | \(0.435474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.5537 | −1.17996 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.6817 | −1.36766 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.9855 | 0.505113 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7104 | 0.629076 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.97166 | −0.181850 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.9779 | −1.09558 | −0.547790 | − | 0.836616i | \(-0.684531\pi\) | ||||
−0.547790 | + | 0.836616i | \(0.684531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2331 | −0.831356 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.1928 | 0.782299 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.94474 | 0.451567 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.37041 | −0.333985 | −0.166993 | − | 0.985958i | \(-0.553406\pi\) | ||||
−0.166993 | + | 0.985958i | \(0.553406\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.49572 | −0.158082 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.4776 | −1.24005 | −0.620023 | − | 0.784584i | \(-0.712877\pi\) | ||||
−0.620023 | + | 0.784584i | \(0.712877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.8371 | −0.713269 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.52782 | 0.203510 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.05560 | −0.406199 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.7649 | −1.19816 | −0.599082 | − | 0.800688i | \(-0.704468\pi\) | ||||
−0.599082 | + | 0.800688i | \(0.704468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.9204 | 1.73883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.279986 | 0.0124840 | 0.00624199 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624199 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.03903 | 0.313233 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.61827 | −0.0718698 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.4582 | −1.03977 | −0.519883 | − | 0.854237i | \(-0.674025\pi\) | ||||
−0.519883 | + | 0.854237i | \(0.674025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.7924 | 1.22946 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.19916 | −0.0529444 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.349745 | −0.0154116 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.56450 | 0.376666 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.9916 | −1.22870 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4150 | −0.500102 | −0.250051 | − | 0.968233i | \(-0.580447\pi\) | ||||
−0.250051 | + | 0.968233i | \(0.580447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.93823 | −0.0847530 | −0.0423765 | − | 0.999102i | \(-0.513493\pi\) | ||||
−0.0423765 | + | 0.999102i | \(0.513493\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.5726 | 1.29065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.1566 | 1.87993 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9518 | −0.737037 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.0594 | −1.04409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.9000 | −1.94483 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.22750 | −0.182771 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.6057 | −1.92488 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.46270 | 0.106076 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.1820 | 0.996671 | 0.498335 | − | 0.866984i | \(-0.333945\pi\) | ||||
0.498335 | + | 0.866984i | \(0.333945\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.8325 | −0.550694 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.8086 | −0.462988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0059 | 0.940903 | 0.470451 | − | 0.882426i | \(-0.344091\pi\) | ||||
0.470451 | + | 0.882426i | \(0.344091\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.8044 | 1.61345 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.29071 | −0.395797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.727630 | 0.0309420 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.4631 | −0.444135 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8515 | 1.34959 | 0.674795 | − | 0.738005i | \(-0.264232\pi\) | ||||
0.674795 | + | 0.738005i | \(0.264232\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.4077 | −0.947743 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.2150 | 1.02236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0243 | 0.843925 | 0.421963 | − | 0.906613i | \(-0.361341\pi\) | ||||
0.421963 | + | 0.906613i | \(0.361341\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.7351 | 0.535772 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.2797 | −1.14564 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.1337 | −1.13750 | −0.568752 | − | 0.822509i | \(-0.692574\pi\) | ||||
−0.568752 | + | 0.822509i | \(0.692574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.72437 | 0.281406 | 0.140703 | − | 0.990052i | \(-0.455064\pi\) | ||||
0.140703 | + | 0.990052i | \(0.455064\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.50317 | −0.104571 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.4032 | 0.433842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.3510 | −0.639069 | −0.319535 | − | 0.947575i | \(-0.603527\pi\) | ||||
−0.319535 | + | 0.947575i | \(0.603527\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.9856 | −1.62018 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.28260 | 0.219159 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.52860 | −0.104724 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.23564 | −0.381847 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.56946 | −0.188602 | −0.0943008 | − | 0.995544i | \(-0.530062\pi\) | ||||
−0.0943008 | + | 0.995544i | \(0.530062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.3174 | 1.04318 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.4172 | −1.66254 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.9698 | −0.573672 | −0.286836 | − | 0.957980i | \(-0.592603\pi\) | ||||
−0.286836 | + | 0.957980i | \(0.592603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.0153 | −0.574571 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.21037 | −0.0904644 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.33124 | −0.217829 | −0.108914 | − | 0.994051i | \(-0.534737\pi\) | ||||
−0.108914 | + | 0.994051i | \(0.534737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.0067 | 1.59111 | 0.795557 | − | 0.605878i | \(-0.207178\pi\) | ||||
0.795557 | + | 0.605878i | \(0.207178\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.1635 | −1.02474 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.76896 | −0.275197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2493 | 0.862481 | 0.431240 | − | 0.902237i | \(-0.358076\pi\) | ||||
0.431240 | + | 0.902237i | \(0.358076\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0395 | −0.812043 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.4695 | −0.706739 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8698 | 0.802532 | 0.401266 | − | 0.915962i | \(-0.368570\pi\) | ||||
0.401266 | + | 0.915962i | \(0.368570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.7661 | −1.03899 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7854 | 0.836789 | 0.418395 | − | 0.908265i | \(-0.362593\pi\) | ||||
0.418395 | + | 0.908265i | \(0.362593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.46068 | 0.380257 | 0.190128 | − | 0.981759i | \(-0.439110\pi\) | ||||
0.190128 | + | 0.981759i | \(0.439110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.909900 | −0.0365130 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.5582 | 0.423005 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0447 | 0.561786 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.2055 | 0.567314 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.2465 | −1.08639 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.06357 | −0.0821493 | −0.0410747 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410747 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.725691 | 0.0288436 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9782 | 0.435656 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.02331 | −0.199031 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.91732 | −0.352764 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.0857 | 1.82028 | 0.910138 | − | 0.414306i | \(-0.135976\pi\) | ||||
0.910138 | + | 0.414306i | \(0.135976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.7595 | 1.88345 | 0.941725 | − | 0.336383i | \(-0.109204\pi\) | ||||
0.941725 | + | 0.336383i | \(0.109204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.8588 | −0.506313 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.44393 | −0.331965 | −0.165983 | − | 0.986129i | \(-0.553080\pi\) | ||||
−0.165983 | + | 0.986129i | \(0.553080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.3177 | −0.601271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 54.6082 | 2.14026 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.60473 | −0.141064 | −0.0705320 | − | 0.997510i | \(-0.522470\pi\) | ||||
−0.0705320 | + | 0.997510i | \(0.522470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.58076 | 0.374351 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.3680 | 1.06773 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.14378 | −0.200373 | −0.100187 | − | 0.994969i | \(-0.531944\pi\) | ||||
−0.100187 | + | 0.994969i | \(0.531944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.81877 | −0.304115 | −0.152057 | − | 0.988372i | \(-0.548590\pi\) | ||||
−0.152057 | + | 0.988372i | \(0.548590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −49.3927 | −1.91825 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.22193 | −0.318833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.04959 | −0.272961 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.5255 | −0.793560 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0686 | 0.929158 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.5503 | 0.792157 | 0.396078 | − | 0.918217i | \(-0.370371\pi\) | ||||
0.396078 | + | 0.918217i | \(0.370371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.56508 | −0.0602399 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.4948 | −1.47948 | −0.739738 | − | 0.672895i | \(-0.765051\pi\) | ||||
−0.739738 | + | 0.672895i | \(0.765051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.7683 | 1.25753 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.9993 | −1.03462 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.9996 | 0.688735 | 0.344368 | − | 0.938835i | \(-0.388093\pi\) | ||||
0.344368 | + | 0.938835i | \(0.388093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.97789 | −0.343028 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.1466 | −0.577879 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.15772 | 0.196493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.55829 | −0.325573 | −0.162786 | − | 0.986661i | \(-0.552048\pi\) | ||||
−0.162786 | + | 0.986661i | \(0.552048\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.9193 | 0.566739 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.3495 | −0.468442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −67.0963 | −2.54145 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.6904 | 1.19864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.80365 | 0.332509 | 0.166255 | − | 0.986083i | \(-0.446833\pi\) | ||||
0.166255 | + | 0.986083i | \(0.446833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.9839 | −0.602845 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.0250 | −0.377562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.1939 | 0.872295 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.8018 | −0.818784 | −0.409392 | − | 0.912359i | \(-0.634259\pi\) | ||||
−0.409392 | + | 0.912359i | \(0.634259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.716519 | 0.0268716 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.2103 | 0.719431 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.87997 | −0.219899 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.1021 | 1.75906 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.8234 | 1.29869 | 0.649347 | − | 0.760492i | \(-0.275042\pi\) | ||||
0.649347 | + | 0.760492i | \(0.275042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.15242 | −0.0429185 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51.5912 | −1.91870 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.1257 | −0.450337 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.3070 | 0.382265 | 0.191133 | − | 0.981564i | \(-0.438784\pi\) | ||||
0.191133 | + | 0.981564i | \(0.438784\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1792 | −0.895526 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.4849 | −1.23848 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.83455 | −0.141632 | −0.0708162 | − | 0.997489i | \(-0.522560\pi\) | ||||
−0.0708162 | + | 0.997489i | \(0.522560\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.88265 | −0.106328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0206 | −0.590127 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.1903 | 0.853069 | 0.426535 | − | 0.904471i | \(-0.359734\pi\) | ||||
0.426535 | + | 0.904471i | \(0.359734\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.9758 | −1.06445 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.71053 | 0.0994396 | 0.0497198 | − | 0.998763i | \(-0.484167\pi\) | ||||
0.0497198 | + | 0.998763i | \(0.484167\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6302 | 0.536008 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.20194 | 0.190329 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.9298 | −0.508983 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.7344 | −0.974256 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.67678 | −0.0610242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6147 | −0.749254 | −0.374627 | − | 0.927176i | \(-0.622229\pi\) | ||||
−0.374627 | + | 0.927176i | \(0.622229\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.7788 | 0.391247 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5508 | 0.889968 | 0.444984 | − | 0.895539i | \(-0.353209\pi\) | ||||
0.444984 | + | 0.895539i | \(0.353209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.6146 | −1.28934 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.8013 | −0.498986 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.2443 | 1.12816 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.6604 | 1.64655 | 0.823277 | − | 0.567639i | \(-0.192143\pi\) | ||||
0.823277 | + | 0.567639i | \(0.192143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −60.3004 | −2.17167 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.27916 | −0.297781 | −0.148890 | − | 0.988854i | \(-0.547570\pi\) | ||||
−0.148890 | + | 0.988854i | \(0.547570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.0428 | 1.18693 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34.4764 | −1.23683 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.3614 | −1.41027 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.67731 | −0.203150 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.06056 | 0.0379013 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7704 | 0.384412 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.10988 | −0.0395628 | −0.0197814 | − | 0.999804i | \(-0.506297\pi\) | ||||
−0.0197814 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.5226 | 1.76305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.9628 | 1.49202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.0940 | −1.74338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.95979 | 0.104973 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.23483 | 0.150005 | 0.0750027 | − | 0.997183i | \(-0.476103\pi\) | ||||
0.0750027 | + | 0.997183i | \(0.476103\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.1055 | −0.923546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.3970 | 0.367359 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.4241 | 0.614884 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.23863 | −0.219883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.8259 | 1.64835 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.13975 | 0.110388 | 0.0551938 | − | 0.998476i | \(-0.482422\pi\) | ||||
0.0551938 | + | 0.998476i | \(0.482422\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.2914 | 0.958329 | 0.479165 | − | 0.877725i | \(-0.340940\pi\) | ||||
0.479165 | + | 0.877725i | \(0.340940\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.1102 | −0.424724 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.26847 | 0.0444325 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.6436 | −0.687242 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.4318 | −1.06337 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.7072 | 1.17639 | 0.588195 | − | 0.808719i | \(-0.299839\pi\) | ||||
0.588195 | + | 0.808719i | \(0.299839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.9615 | −1.91584 | −0.957919 | − | 0.287040i | \(-0.907329\pi\) | ||||
−0.957919 | + | 0.287040i | \(0.907329\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.5402 | 0.645487 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.5563 | 1.27119 | 0.635594 | − | 0.772024i | \(-0.280755\pi\) | ||||
0.635594 | + | 0.772024i | \(0.280755\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.26003 | −0.252151 | −0.126076 | − | 0.992021i | \(-0.540238\pi\) | ||||
−0.126076 | + | 0.992021i | \(0.540238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.48406 | −0.259619 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.50658 | −0.260087 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1227 | −0.488738 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.89004 | −0.0998946 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.5396 | 1.84839 | 0.924197 | − | 0.381916i | \(-0.124736\pi\) | ||||
0.924197 | + | 0.381916i | \(0.124736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7832 | −0.716661 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.4598 | 1.66904 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.587209 | 0.0202006 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.3040 | −0.766373 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48.6305 | −1.66899 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.1283 | −0.415751 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.02428 | −0.206267 | −0.103134 | − | 0.994667i | \(-0.532887\pi\) | ||||
−0.103134 | + | 0.994667i | \(0.532887\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.09638 | −0.276890 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.27674 | −0.146090 | −0.0730452 | − | 0.997329i | \(-0.523272\pi\) | ||||
−0.0730452 | + | 0.997329i | \(0.523272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.7405 | 1.73124 | 0.865622 | − | 0.500698i | \(-0.166923\pi\) | ||||
0.865622 | + | 0.500698i | \(0.166923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −84.9003 | −2.89339 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.9238 | −0.610133 | −0.305066 | − | 0.952331i | \(-0.598679\pi\) | ||||
−0.305066 | + | 0.952331i | \(0.598679\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.1571 | 0.345352 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.7030 | −1.11065 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.456180 | 0.0154748 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.6781 | 1.10726 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.2679 | 1.09210 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.4145 | −0.791555 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.8516 | −1.04179 | −0.520893 | − | 0.853622i | \(-0.674401\pi\) | ||||
−0.520893 | + | 0.853622i | \(0.674401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.1702 | −1.45609 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5257 | 0.388310 | 0.194155 | − | 0.980971i | \(-0.437804\pi\) | ||||
0.194155 | + | 0.980971i | \(0.437804\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.0129 | 0.909057 | 0.454529 | − | 0.890732i | \(-0.349808\pi\) | ||||
0.454529 | + | 0.890732i | \(0.349808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.9297 | 0.602700 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.5969 | −1.29596 | −0.647978 | − | 0.761659i | \(-0.724385\pi\) | ||||
−0.647978 | + | 0.761659i | \(0.724385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.1735 | 1.21322 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.1027 | −0.572962 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3145 | −0.512481 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.1858 | 0.541030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.9862 | −0.734097 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.3911 | −0.746784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.70743 | 0.256772 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42.3701 | −1.40999 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.65643 | 0.154785 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.8510 | −1.42284 | −0.711422 | − | 0.702765i | \(-0.751948\pi\) | ||||
−0.711422 | + | 0.702765i | \(0.751948\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.8397 | 0.757545 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.3626 | −1.20475 | −0.602374 | − | 0.798214i | \(-0.705778\pi\) | ||||
−0.602374 | + | 0.798214i | \(0.705778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.31187 | 0.109607 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.1729 | −0.931367 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.5690 | 1.04250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.3256 | −1.42918 | −0.714591 | − | 0.699543i | \(-0.753387\pi\) | ||||
−0.714591 | + | 0.699543i | \(0.753387\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −71.8207 | −2.36657 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.5803 | 0.381171 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.8613 | −0.685915 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.13483 | −0.0372725 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.5898 | 0.413057 | 0.206529 | − | 0.978441i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978441i | \(0.433783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.40366 | −0.144324 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.1087 | −1.24762 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.78673 | −0.287357 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.3585 | −0.403734 | −0.201867 | − | 0.979413i | \(-0.564701\pi\) | ||||
−0.201867 | + | 0.979413i | \(0.564701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 72.5959 | 2.36908 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.4472 | 0.503564 | 0.251782 | − | 0.967784i | \(-0.418983\pi\) | ||||
0.251782 | + | 0.967784i | \(0.418983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.8666 | −0.972590 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.938555 | 0.0305312 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.98024 | −0.0968447 | −0.0484223 | − | 0.998827i | \(-0.515419\pi\) | ||||
−0.0484223 | + | 0.998827i | \(0.515419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.5410 | −1.15371 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.53958 | −0.0823516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.9731 | 1.48922 | 0.744608 | − | 0.667502i | \(-0.232637\pi\) | ||||
0.744608 | + | 0.667502i | \(0.232637\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.908307 | 0.0293921 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.5636 | −0.406123 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.5825 | −0.955268 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0162 | 0.968264 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.7171 | −0.442027 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.1464 | 0.455389 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.3403 | 1.55452 | 0.777260 | − | 0.629180i | \(-0.216609\pi\) | ||||
0.777260 | + | 0.629180i | \(0.216609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.2999 | −1.39099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.0021 | −1.82928 | −0.914642 | − | 0.404266i | \(-0.867527\pi\) | ||||
−0.914642 | + | 0.404266i | \(0.867527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.6920 | −1.30452 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37.8174 | −1.21113 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.6077 | 1.42713 | 0.713564 | − | 0.700590i | \(-0.247080\pi\) | ||||
0.713564 | + | 0.700590i | \(0.247080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.61934 | 0.211555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.0708 | −1.11972 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.95916 | 0.0943827 | 0.0471913 | − | 0.998886i | \(-0.484973\pi\) | ||||
0.0471913 | + | 0.998886i | \(0.484973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6659 | 0.467294 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.0326 | −1.05144 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.9051 | −0.473955 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.8424 | 0.598548 | 0.299274 | − | 0.954167i | \(-0.403256\pi\) | ||||
0.299274 | + | 0.954167i | \(0.403256\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.9749 | −0.919490 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.802061 | 0.0254270 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.28041 | 0.262243 | 0.131122 | − | 0.991366i | \(-0.458142\pi\) | ||||
0.131122 | + | 0.991366i | \(0.458142\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.82461 | 0.0577280 |
(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 | 6008.2.a.e.1.9 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.9 | ✓ | 50 | 1.1 | even | 1 | trivial |