Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | 1.41351 | 0.816093 | 0.408046 | − | 0.912961i | \(-0.366210\pi\) | ||||
0.408046 | + | 0.912961i | \(0.366210\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.774385 | −0.346315 | −0.173158 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173158 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.47209 | −0.556400 | −0.278200 | − | 0.960523i | \(-0.589738\pi\) | ||||
−0.278200 | + | 0.960523i | \(0.589738\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00198 | −0.333992 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.39960 | 0.421995 | 0.210998 | − | 0.977487i | \(-0.432329\pi\) | ||||
0.210998 | + | 0.977487i | \(0.432329\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.835705 | −0.231783 | −0.115891 | − | 0.993262i | \(-0.536972\pi\) | ||||
−0.115891 | + | 0.993262i | \(0.536972\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.09460 | −0.282626 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.36245 | 1.54312 | 0.771561 | − | 0.636156i | \(-0.219476\pi\) | ||||
0.771561 | + | 0.636156i | \(0.219476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08083 | −0.454074 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.70029 | −0.563050 | −0.281525 | − | 0.959554i | \(-0.590840\pi\) | ||||
−0.281525 | + | 0.959554i | \(0.590840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.40033 | −0.880066 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.34850 | −1.17889 | −0.589443 | − | 0.807810i | \(-0.700653\pi\) | ||||
−0.589443 | + | 0.807810i | \(0.700653\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.44981 | 1.51763 | 0.758815 | − | 0.651306i | \(-0.225779\pi\) | ||||
0.758815 | + | 0.651306i | \(0.225779\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.97835 | 0.344387 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.13997 | 0.192690 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.59928 | −0.920516 | −0.460258 | − | 0.887785i | \(-0.652243\pi\) | ||||
−0.460258 | + | 0.887785i | \(0.652243\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.18128 | −0.189156 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.34120 | 1.30268 | 0.651338 | − | 0.758788i | \(-0.274208\pi\) | ||||
0.651338 | + | 0.758788i | \(0.274208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.34849 | 0.358141 | 0.179071 | − | 0.983836i | \(-0.442691\pi\) | ||||
0.179071 | + | 0.983836i | \(0.442691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.775916 | 0.115667 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.0033 | −1.89672 | −0.948360 | − | 0.317196i | \(-0.897259\pi\) | ||||
−0.948360 | + | 0.317196i | \(0.897259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.83294 | −0.690420 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.99342 | 1.25933 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.78665 | 0.932219 | 0.466109 | − | 0.884727i | \(-0.345655\pi\) | ||||
0.466109 | + | 0.884727i | \(0.345655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.08383 | −0.146143 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.41351 | 0.187225 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.23753 | −1.20262 | −0.601312 | − | 0.799014i | \(-0.705355\pi\) | ||||
−0.601312 | + | 0.799014i | \(0.705355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.97256 | −0.764707 | −0.382354 | − | 0.924016i | \(-0.624886\pi\) | ||||
−0.382354 | + | 0.924016i | \(0.624886\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.47501 | 0.185833 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.647158 | 0.0802700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.612758 | −0.0748603 | −0.0374301 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374301 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.81690 | −0.459501 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.89595 | −0.343686 | −0.171843 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171843 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.61320 | 0.422893 | 0.211447 | − | 0.977390i | \(-0.432183\pi\) | ||||
0.211447 | + | 0.977390i | \(0.432183\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.21993 | −0.718215 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.06034 | −0.234798 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.99011 | −0.554457 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.51099 | −1.04397 | −0.521983 | − | 0.852956i | \(-0.674808\pi\) | ||||
−0.521983 | + | 0.852956i | \(0.674808\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.92699 | −0.534407 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.97369 | −0.962080 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.80314 | 0.191133 | 0.0955663 | − | 0.995423i | \(-0.469534\pi\) | ||||
0.0955663 | + | 0.995423i | \(0.469534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23024 | 0.128964 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.9439 | 1.23853 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.774385 | −0.0794502 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7277 | −1.19077 | −0.595386 | − | 0.803440i | \(-0.703001\pi\) | ||||
−0.595386 | + | 0.803440i | \(0.703001\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.40237 | −0.140943 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.05786 | −0.304269 | −0.152134 | − | 0.988360i | \(-0.548615\pi\) | ||||
−0.152134 | + | 0.988360i | \(0.548615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1125 | 1.48908 | 0.744541 | − | 0.667576i | \(-0.232668\pi\) | ||||
0.744541 | + | 0.667576i | \(0.232668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.61136 | 0.157253 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.1798 | 1.08079 | 0.540395 | − | 0.841411i | \(-0.318275\pi\) | ||||
0.540395 | + | 0.841411i | \(0.318275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4747 | 1.48221 | 0.741103 | − | 0.671391i | \(-0.234303\pi\) | ||||
0.741103 | + | 0.671391i | \(0.234303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.91466 | −0.751226 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.23795 | −0.774961 | −0.387480 | − | 0.921878i | \(-0.626655\pi\) | ||||
−0.387480 | + | 0.921878i | \(0.626655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.09107 | 0.194993 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.837358 | 0.0774138 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.36613 | −0.858592 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.04112 | −0.821920 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.7904 | 1.06310 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.27947 | 0.651096 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0740 | −1.24887 | −0.624435 | − | 0.781077i | \(-0.714671\pi\) | ||||
−0.624435 | + | 0.781077i | \(0.714671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.31962 | 0.292276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.7337 | 1.81151 | 0.905757 | − | 0.423797i | \(-0.139303\pi\) | ||||
0.905757 | + | 0.423797i | \(0.139303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.47209 | −0.127647 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.38058 | 0.377020 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.82954 | −0.412616 | −0.206308 | − | 0.978487i | \(-0.566145\pi\) | ||||
−0.206308 | + | 0.978487i | \(0.566145\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7093 | −1.16281 | −0.581404 | − | 0.813615i | \(-0.697496\pi\) | ||||
−0.581404 | + | 0.813615i | \(0.697496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.3803 | −1.54790 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.16965 | −0.0978113 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.91618 | 0.408266 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.83143 | −0.563446 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.69242 | 0.302495 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1346 | −1.47577 | −0.737887 | − | 0.674924i | \(-0.764176\pi\) | ||||
−0.737887 | + | 0.674924i | \(0.764176\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.37503 | −0.515391 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.54340 | −0.525579 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.90415 | −0.790438 | −0.395219 | − | 0.918587i | \(-0.629331\pi\) | ||||
−0.395219 | + | 0.918587i | \(0.629331\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.59303 | 0.760777 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.97509 | 0.313281 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.76671 | 0.451684 | 0.225842 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.53201 | −0.119267 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.40558 | −0.418297 | −0.209148 | − | 0.977884i | \(-0.567069\pi\) | ||||
−0.209148 | + | 0.977884i | \(0.567069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3016 | −0.946277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00198 | −0.0766231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.553258 | 0.0420634 | 0.0210317 | − | 0.999779i | \(-0.493305\pi\) | ||||
0.0210317 | + | 0.999779i | \(0.493305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.47770 | 0.489668 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.0574 | −0.981453 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7371 | −0.877274 | −0.438637 | − | 0.898664i | \(-0.644539\pi\) | ||||
−0.438637 | + | 0.898664i | \(0.644539\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.3407 | −1.88356 | −0.941780 | − | 0.336229i | \(-0.890848\pi\) | ||||
−0.941780 | + | 0.336229i | \(0.890848\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.44229 | −0.624072 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.33600 | 0.318789 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.90488 | 0.651190 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.32742 | 0.605731 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2615 | −1.53843 | −0.769215 | − | 0.638990i | \(-0.779352\pi\) | ||||
−0.769215 | + | 0.638990i | \(0.779352\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0245 | 0.865543 | 0.432772 | − | 0.901504i | \(-0.357536\pi\) | ||||
0.432772 | + | 0.901504i | \(0.357536\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.914767 | 0.0655078 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.64779 | −0.616129 | −0.308065 | − | 0.951365i | \(-0.599681\pi\) | ||||
−0.308065 | + | 0.951365i | \(0.599681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4299 | −1.44824 | −0.724118 | − | 0.689677i | \(-0.757753\pi\) | ||||
−0.724118 | + | 0.689677i | \(0.757753\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.866142 | −0.0610929 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.34559 | 0.655932 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.45930 | −0.451137 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.70563 | 0.188054 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.39960 | 0.0968123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9071 | 0.819720 | 0.409860 | − | 0.912148i | \(-0.365577\pi\) | ||||
0.409860 | + | 0.912148i | \(0.365577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.09347 | −0.280480 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.81863 | −0.124030 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.4389 | −0.844409 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.10731 | 0.345120 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.31714 | −0.357669 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.7338 | −1.79023 | −0.895115 | − | 0.445836i | \(-0.852907\pi\) | ||||
−0.895115 | + | 0.445836i | \(0.852907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.40903 | 0.293935 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.425128 | 0.0282167 | 0.0141084 | − | 0.999900i | \(-0.495509\pi\) | ||||
0.0141084 | + | 0.999900i | \(0.495509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.0592 | −1.85421 | −0.927103 | − | 0.374808i | \(-0.877709\pi\) | ||||
−0.927103 | + | 0.374808i | \(0.877709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.91232 | −0.191617 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.00268 | 0.524273 | 0.262137 | − | 0.965031i | \(-0.415573\pi\) | ||||
0.262137 | + | 0.965031i | \(0.415573\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0695 | 0.656863 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.41351 | −0.0918176 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.62206 | 0.493030 | 0.246515 | − | 0.969139i | \(-0.420715\pi\) | ||||
0.246515 | + | 0.969139i | \(0.420715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2953 | 0.856428 | 0.428214 | − | 0.903677i | \(-0.359143\pi\) | ||||
0.428214 | + | 0.903677i | \(0.359143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.91697 | 0.636174 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.74255 | 0.239103 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.835705 | −0.0531747 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.4439 | −0.851974 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7163 | −1.24448 | −0.622241 | − | 0.782826i | \(-0.713778\pi\) | ||||
−0.622241 | + | 0.782826i | \(0.713778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.77933 | −0.237604 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.96437 | −0.436126 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0729 | −0.815465 | −0.407733 | − | 0.913101i | \(-0.633680\pi\) | ||||
−0.407733 | + | 0.913101i | \(0.633680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24267 | 0.512175 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.36105 | 0.393739 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.2542 | −1.18726 | −0.593632 | − | 0.804736i | \(-0.702307\pi\) | ||||
−0.593632 | + | 0.804736i | \(0.702307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.25548 | −0.322842 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.54877 | 0.155982 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.44576 | −0.271063 | −0.135531 | − | 0.990773i | \(-0.543274\pi\) | ||||
−0.135531 | + | 0.990773i | \(0.543274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4799 | 1.12257 | 0.561286 | − | 0.827622i | \(-0.310307\pi\) | ||||
0.561286 | + | 0.827622i | \(0.310307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73896 | 0.105247 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.15870 | −0.371383 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.2490 | −1.69732 | −0.848658 | − | 0.528942i | \(-0.822589\pi\) | ||||
−0.848658 | + | 0.528942i | \(0.822589\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.46652 | −0.506877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.95595 | 0.176337 | 0.0881686 | − | 0.996106i | \(-0.471899\pi\) | ||||
0.0881686 | + | 0.996106i | \(0.471899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.626007 | −0.0372123 | −0.0186061 | − | 0.999827i | \(-0.505923\pi\) | ||||
−0.0186061 | + | 0.999827i | \(0.505923\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.09460 | −0.0648388 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.2790 | −0.724808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.4808 | 1.38122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.5773 | −0.971780 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.3828 | 1.77498 | 0.887491 | − | 0.460825i | \(-0.152446\pi\) | ||||
0.887491 | + | 0.460825i | \(0.152446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.15340 | 0.416487 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.91733 | −0.459410 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.25665 | 0.130505 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.45720 | −0.199270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.32234 | −0.248312 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.62506 | 0.264830 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.2374 | 1.09794 | 0.548969 | − | 0.835842i | \(-0.315020\pi\) | ||||
0.548969 | + | 0.835842i | \(0.315020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.3618 | 1.21523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.8570 | −0.842462 | −0.421231 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421231 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9584 | 0.675929 | 0.337964 | − | 0.941159i | \(-0.390262\pi\) | ||||
0.337964 | + | 0.941159i | \(0.390262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.14222 | −0.0643569 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.6436 | −1.38412 | −0.692062 | − | 0.721838i | \(-0.743298\pi\) | ||||
−0.692062 | + | 0.721838i | \(0.743298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.88535 | −0.497484 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8028 | 0.882025 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.36245 | 0.354016 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.67738 | 0.203984 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.8737 | 1.20962 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.1420 | 1.05533 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.4370 | −1.78290 | −0.891450 | − | 0.453120i | \(-0.850311\pi\) | ||||
−0.891450 | + | 0.453120i | \(0.850311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.61035 | 0.307445 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.474510 | 0.0259253 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.30322 | 0.452305 | 0.226153 | − | 0.974092i | \(-0.427385\pi\) | ||||
0.226153 | + | 0.974092i | \(0.427385\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.6445 | −0.632440 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.8263 | 0.640433 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4192 | 0.940549 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.95575 | 0.159132 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.5566 | 0.888807 | 0.444403 | − | 0.895827i | \(-0.353416\pi\) | ||||
0.444403 | + | 0.895827i | \(0.353416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.19901 | 0.492412 | 0.246206 | − | 0.969218i | \(-0.420816\pi\) | ||||
0.246206 | + | 0.969218i | \(0.420816\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.72746 | 0.252333 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.47278 | −0.291287 | −0.145643 | − | 0.989337i | \(-0.546525\pi\) | ||||
−0.145643 | + | 0.989337i | \(0.546525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.24258 | 0.119024 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.2392 | −0.700691 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.379156 | 0.0200111 | 0.0100055 | − | 0.999950i | \(-0.496815\pi\) | ||||
0.0100055 | + | 0.999950i | \(0.496815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.7798 | −0.670763 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.79801 | −0.146454 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.8330 | 1.50507 | 0.752535 | − | 0.658552i | \(-0.228831\pi\) | ||||
0.752535 | + | 0.658552i | \(0.228831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.35769 | −0.435084 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.99060 | −0.518686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.11790 | −0.161439 | −0.0807193 | − | 0.996737i | \(-0.525722\pi\) | ||||
−0.0807193 | + | 0.996737i | \(0.525722\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2896 | 0.531355 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.30547 | 0.273246 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0258 | 1.38822 | 0.694112 | − | 0.719867i | \(-0.255797\pi\) | ||||
0.694112 | + | 0.719867i | \(0.255797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.8939 | −1.01919 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.3908 | 1.29741 | 0.648704 | − | 0.761041i | \(-0.275311\pi\) | ||||
0.648704 | + | 0.761041i | \(0.275311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.59550 | 0.0813141 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.35313 | −0.119616 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.9565 | 1.31605 | 0.658023 | − | 0.752998i | \(-0.271393\pi\) | ||||
0.658023 | + | 0.752998i | \(0.271393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.1805 | −0.868854 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.3074 | 1.47836 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.774385 | 0.0389635 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.53535 | 0.127246 | 0.0636228 | − | 0.997974i | \(-0.479735\pi\) | ||||
0.0636228 | + | 0.997974i | \(0.479735\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.08083 | −0.104172 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.882963 | 0.0440931 | 0.0220465 | − | 0.999757i | \(-0.492982\pi\) | ||||
0.0220465 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.06155 | −0.351761 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.86427 | 0.192017 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.83675 | −0.388453 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.3123 | −1.39995 | −0.699976 | − | 0.714166i | \(-0.746806\pi\) | ||||
−0.699976 | + | 0.714166i | \(0.746806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.82663 | −0.336733 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.5985 | 0.669139 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.36517 | 0.361542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.3783 | −0.948960 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.3791 | 0.897878 | 0.448939 | − | 0.893562i | \(-0.351802\pi\) | ||||
0.448939 | + | 0.893562i | \(0.351802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.3246 | 1.28298 | 0.641492 | − | 0.767129i | \(-0.278316\pi\) | ||||
0.641492 | + | 0.767129i | \(0.278316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.0290 | 0.633490 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.9969 | −1.35805 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.79217 | 0.425483 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.65332 | −0.0798231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.1995 | −1.93634 | −0.968172 | − | 0.250287i | \(-0.919475\pi\) | ||||
−0.968172 | + | 0.250287i | \(0.919475\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.80403 | −0.230867 | −0.115434 | − | 0.993315i | \(-0.536826\pi\) | ||||
−0.115434 | + | 0.993315i | \(0.536826\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.94909 | 0.333183 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.70029 | −0.129172 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5989 | −0.649041 | −0.324520 | − | 0.945879i | \(-0.605203\pi\) | ||||
−0.324520 | + | 0.945879i | \(0.605203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.84249 | 0.230595 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.9050 | −1.13576 | −0.567881 | − | 0.823111i | \(-0.692236\pi\) | ||||
−0.567881 | + | 0.823111i | \(0.692236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.39633 | −0.0661922 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.21928 | 0.246864 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.2670 | 0.767685 | 0.383843 | − | 0.923399i | \(-0.374601\pi\) | ||||
0.383843 | + | 0.923399i | \(0.374601\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6743 | 0.549723 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.6335 | −1.20437 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.952677 | −0.0446622 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.2972 | 1.83825 | 0.919123 | − | 0.393971i | \(-0.128899\pi\) | ||||
0.919123 | + | 0.393971i | \(0.128899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.9915 | −1.67994 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.40539 | 0.0654555 | 0.0327278 | − | 0.999464i | \(-0.489581\pi\) | ||||
0.0327278 | + | 0.999464i | \(0.489581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.8190 | 1.01402 | 0.507008 | − | 0.861941i | \(-0.330751\pi\) | ||||
0.507008 | + | 0.861941i | \(0.330751\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.24919 | −0.428921 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2835 | 0.568411 | 0.284205 | − | 0.958763i | \(-0.408270\pi\) | ||||
0.284205 | + | 0.958763i | \(0.408270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.902037 | 0.0416522 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.9997 | −0.645070 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.28694 | 0.151134 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.40033 | −0.201901 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.80007 | −0.311354 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.8810 | 0.542857 | 0.271429 | − | 0.962459i | \(-0.412504\pi\) | ||||
0.271429 | + | 0.962459i | \(0.412504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.67935 | 0.213360 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.61884 | 0.255666 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.08178 | 0.412383 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.3298 | −0.921229 | −0.460615 | − | 0.887600i | \(-0.652371\pi\) | ||||
−0.460615 | + | 0.887600i | \(0.652371\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.15133 | 0.368616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.7077 | −0.708880 | −0.354440 | − | 0.935079i | \(-0.615328\pi\) | ||||
−0.354440 | + | 0.935079i | \(0.615328\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.3920 | −1.81916 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.08597 | 0.0488108 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.26311 | 0.191227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.223546 | 0.0100073 | 0.00500365 | − | 0.999987i | \(-0.498407\pi\) | ||||
0.00500365 | + | 0.999987i | \(0.498407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.64087 | −0.341369 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7343 | 1.14744 | 0.573719 | − | 0.819052i | \(-0.305500\pi\) | ||||
0.573719 | + | 0.819052i | \(0.305500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.36796 | 0.105373 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.3885 | −0.772250 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.59995 | −0.203889 | −0.101945 | − | 0.994790i | \(-0.532506\pi\) | ||||
−0.101945 | + | 0.994790i | \(0.532506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.31897 | −0.235297 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.65685 | −0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7029 | −0.515692 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.1994 | −0.800407 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.782038 | 0.0343276 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.57999 | 0.332085 | 0.166043 | − | 0.986119i | \(-0.446901\pi\) | ||||
0.166043 | + | 0.986119i | \(0.446901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.70634 | −0.424429 | −0.212214 | − | 0.977223i | \(-0.568068\pi\) | ||||
−0.212214 | + | 0.977223i | \(0.568068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.15632 | 0.399615 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.7615 | 2.34189 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7084 | −0.682975 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.25580 | 0.401667 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.97078 | −0.301938 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.65746 | −0.374294 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.5906 | −0.715937 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.76418 | −0.291354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.3492 | 1.64876 | 0.824381 | − | 0.566035i | \(-0.191523\pi\) | ||||
0.824381 | + | 0.566035i | \(0.191523\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.8195 | −1.53716 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.9834 | −0.513311 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.3424 | 0.869779 | 0.434890 | − | 0.900484i | \(-0.356787\pi\) | ||||
0.434890 | + | 0.900484i | \(0.356787\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.98437 | 0.255406 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.34850 | −0.270455 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.47209 | 0.0625998 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.12899 | 0.260161 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0353 | −0.425210 | −0.212605 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212605 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.96264 | −0.0830110 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.5872 | 0.531431 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.7118 | −1.29435 | −0.647173 | − | 0.762343i | \(-0.724049\pi\) | ||||
−0.647173 | + | 0.762343i | \(0.724049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.37934 | 0.268381 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.34591 | 0.308499 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.40944 | 0.310620 | 0.155310 | − | 0.987866i | \(-0.450362\pi\) | ||||
0.155310 | + | 0.987866i | \(0.450362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.2464 | 1.51686 | 0.758431 | − | 0.651753i | \(-0.225966\pi\) | ||||
0.758431 | + | 0.651753i | \(0.225966\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.0535 | −1.25550 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.8822 | 0.495521 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.1738 | −1.46430 | −0.732152 | − | 0.681141i | \(-0.761484\pi\) | ||||
−0.732152 | + | 0.681141i | \(0.761484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.9968 | 0.706364 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.0011 | 0.580863 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.49860 | 0.393392 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.648437 | −0.0268096 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.4899 | −1.05208 | −0.526040 | − | 0.850460i | \(-0.676324\pi\) | ||||
−0.526040 | + | 0.850460i | \(0.676324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.44981 | 0.348168 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.2238 | −0.502819 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.7445 | −1.87850 | −0.939252 | − | 0.343229i | \(-0.888479\pi\) | ||||
−0.939252 | + | 0.343229i | \(0.888479\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.25299 | 0.297344 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.8779 | −1.18189 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.7399 | 1.29686 | 0.648429 | − | 0.761275i | \(-0.275426\pi\) | ||||
0.648429 | + | 0.761275i | \(0.275426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3510 | 0.911717 | 0.455859 | − | 0.890052i | \(-0.349332\pi\) | ||||
0.455859 | + | 0.890052i | \(0.349332\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.613969 | 0.0250028 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00131 | 0.284644 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.53011 | 0.305638 | 0.152819 | − | 0.988254i | \(-0.451165\pi\) | ||||
0.152819 | + | 0.988254i | \(0.451165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.2101 | 0.535301 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.8669 | 0.439627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.9095 | −1.24842 | −0.624211 | − | 0.781256i | \(-0.714580\pi\) | ||||
−0.624211 | + | 0.781256i | \(0.714580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.13031 | −0.368170 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2291 | 0.935170 | 0.467585 | − | 0.883948i | \(-0.345124\pi\) | ||||
0.467585 | + | 0.883948i | \(0.345124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2358 | 0.853541 | 0.426770 | − | 0.904360i | \(-0.359651\pi\) | ||||
0.426770 | + | 0.904360i | \(0.359651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.2752 | 0.612971 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.65439 | −0.106346 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.3645 | 0.654581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.97835 | 0.0790078 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.6251 | −1.42047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.55045 | 0.181151 | 0.0905754 | − | 0.995890i | \(-0.471129\pi\) | ||||
0.0905754 | + | 0.995890i | \(0.471129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8309 | 0.668968 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.8987 | 0.432503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.03891 | 0.160028 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.90168 | 0.114789 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.74444 | 0.266389 | 0.133195 | − | 0.991090i | \(-0.457476\pi\) | ||||
0.133195 | + | 0.991090i | \(0.457476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.5024 | −0.769101 | −0.384550 | − | 0.923104i | \(-0.625644\pi\) | ||||
−0.384550 | + | 0.923104i | \(0.625644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.57066 | −0.101220 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.2044 | 0.558431 | 0.279216 | − | 0.960228i | \(-0.409926\pi\) | ||||
0.279216 | + | 0.960228i | \(0.409926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9288 | −0.507501 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.5826 | −0.689116 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.6061 | −0.532448 | −0.266224 | − | 0.963911i | \(-0.585776\pi\) | ||||
−0.266224 | + | 0.963911i | \(0.585776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0559 | −0.627355 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.62034 | −0.141243 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.41489 | −0.171980 | −0.0859898 | − | 0.996296i | \(-0.527405\pi\) | ||||
−0.0859898 | + | 0.996296i | \(0.527405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.65776 | −0.103375 | −0.0516874 | − | 0.998663i | \(-0.516460\pi\) | ||||
−0.0516874 | + | 0.998663i | \(0.516460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.51585 | −0.291891 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.13997 | 0.0442061 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.1428 | 0.663772 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.7887 | −1.46099 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.35918 | −0.322703 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6678 | 1.41344 | 0.706721 | − | 0.707493i | \(-0.250174\pi\) | ||||
0.706721 | + | 0.707493i | \(0.250174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.8920 | 0.958094 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.3390 | 0.973857 | 0.486929 | − | 0.873442i | \(-0.338117\pi\) | ||||
0.486929 | + | 0.873442i | \(0.338117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.2643 | 0.662545 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.600924 | 0.0230275 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.2600 | 0.507381 | 0.253691 | − | 0.967285i | \(-0.418355\pi\) | ||||
0.253691 | + | 0.967285i | \(0.418355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.73993 | 0.142895 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.6621 | −1.51320 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.67164 | −0.216072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2345 | 0.617589 | 0.308794 | − | 0.951129i | \(-0.400074\pi\) | ||||
0.308794 | + | 0.951129i | \(0.400074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.06442 | 0.0784207 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.6163 | 0.402699 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.0705 | 2.01019 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.3119 | 0.427856 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.1937 | −1.14040 | −0.570201 | − | 0.821506i | \(-0.693135\pi\) | ||||
−0.570201 | + | 0.821506i | \(0.693135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.59928 | −0.211181 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.2334 | 0.536062 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.50147 | 0.169295 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9202 | −0.560341 | −0.280170 | − | 0.959950i | \(-0.590391\pi\) | ||||
−0.280170 | + | 0.959950i | \(0.590391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00198 | 0.0375771 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.8169 | −0.854501 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.905761 | 0.0338736 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.7739 | 0.402358 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.8157 | 1.63405 | 0.817024 | − | 0.576603i | \(-0.195622\pi\) | ||||
0.817024 | + | 0.576603i | \(0.195622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.2471 | −0.828525 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7932 | 0.698925 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.9355 | 1.03750 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5631 | 0.985172 | 0.492586 | − | 0.870264i | \(-0.336052\pi\) | ||||
0.492586 | + | 0.870264i | \(0.336052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.9881 | 1.07363 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9421 | 0.552655 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.0462 | 1.70075 | 0.850377 | − | 0.526174i | \(-0.176374\pi\) | ||||
0.850377 | + | 0.526174i | \(0.176374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.29015 | 0.195130 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.857615 | −0.0315907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.31308 | −0.305801 | −0.152901 | − | 0.988242i | \(-0.548861\pi\) | ||||
−0.152901 | + | 0.988242i | \(0.548861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.18128 | −0.0433955 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.6836 | 0.905553 | 0.452777 | − | 0.891624i | \(-0.350434\pi\) | ||||
0.452777 | + | 0.891624i | \(0.350434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.85935 | −0.104759 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.52980 | 0.348677 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.4577 | −0.601351 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0857 | 1.60871 | 0.804355 | − | 0.594149i | \(-0.202511\pi\) | ||||
0.804355 | + | 0.594149i | \(0.202511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.8693 | −1.01561 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0432 | 0.511083 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0793 | 1.38401 | 0.692007 | − | 0.721891i | \(-0.256727\pi\) | ||||
0.692007 | + | 0.721891i | \(0.256727\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.34213 | −0.193907 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0722 | −0.908866 | −0.454433 | − | 0.890781i | \(-0.650158\pi\) | ||||
−0.454433 | + | 0.890781i | \(0.650158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.7802 | −0.824699 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.93673 | 0.178488 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.71985 | 0.278748 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.9005 | −1.18642 | −0.593211 | − | 0.805047i | \(-0.702140\pi\) | ||||
−0.593211 | + | 0.805047i | \(0.702140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.4787 | −0.665495 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.3011 | −0.730178 | −0.365089 | − | 0.930973i | \(-0.618961\pi\) | ||||
−0.365089 | + | 0.930973i | \(0.618961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.1819 | −1.33561 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6511 | 0.417982 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.34120 | 0.298854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.05317 | −0.145034 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 35.9125 | 1.28341 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.66963 | 0.273741 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.2127 | 1.89683 | 0.948415 | − | 0.317032i | \(-0.102686\pi\) | ||||
0.948415 | + | 0.317032i | \(0.102686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.2161 | −0.968918 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.1270 | 0.431188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.99130 | 0.177246 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.42870 | −0.263469 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −48.2952 | −1.71070 | −0.855352 | − | 0.518048i | \(-0.826659\pi\) | ||||
−0.855352 | + | 0.518048i | \(0.826659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −82.7326 | −2.92687 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.80671 | −0.0638368 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.05703 | 0.178459 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.07825 | −0.108494 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.28415 | −0.221213 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.56100 | −0.336147 | −0.168073 | − | 0.985774i | \(-0.553755\pi\) | ||||
−0.168073 | + | 0.985774i | \(0.553755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4095 | 0.435756 | 0.217878 | − | 0.975976i | \(-0.430087\pi\) | ||||
0.217878 | + | 0.975976i | \(0.430087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.1215 | 0.916122 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.46566 | −0.156425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.34849 | 0.0821632 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.23267 | −0.0430730 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.0777 | −1.71282 | −0.856412 | − | 0.516292i | \(-0.827312\pi\) | ||||
−0.856412 | + | 0.516292i | \(0.827312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0206 | 0.349298 | 0.174649 | − | 0.984631i | \(-0.444121\pi\) | ||||
0.174649 | + | 0.984631i | \(0.444121\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.70541 | −0.303083 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.35349 | −0.186159 | −0.0930796 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930796 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5264 | 0.886569 | 0.443285 | − | 0.896381i | \(-0.353813\pi\) | ||||
0.443285 | + | 0.896381i | \(0.353813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39.9303 | −1.38517 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.7493 | −1.06540 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.18600 | 0.144863 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −47.7993 | −1.65219 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.4699 | −0.465032 | −0.232516 | − | 0.972593i | \(-0.574696\pi\) | ||||
−0.232516 | + | 0.972593i | \(0.574696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3034 | 0.389772 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.17828 | 0.143908 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.52617 | 0.327710 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.3094 | 0.457316 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.884870 | −0.0303687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.1197 | 0.518296 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.7172 | −1.77076 | −0.885382 | − | 0.464864i | \(-0.846103\pi\) | ||||
−0.885382 | + | 0.464864i | \(0.846103\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.775916 | 0.0265358 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.5215 | −1.00843 | −0.504217 | − | 0.863577i | \(-0.668219\pi\) | ||||
−0.504217 | + | 0.863577i | \(0.668219\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.6645 | 0.363869 | 0.181934 | − | 0.983311i | \(-0.441764\pi\) | ||||
0.181934 | + | 0.983311i | \(0.441764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.3566 | −0.591511 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7388 | 1.31869 | 0.659343 | − | 0.751843i | \(-0.270835\pi\) | ||||
0.659343 | + | 0.751843i | \(0.270835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.428434 | −0.0145672 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.1904 | 1.12721 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.39960 | −0.0474782 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.512085 | 0.0173513 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.7509 | 0.397709 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.7161 | −0.362269 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7011 | 0.530187 | 0.265094 | − | 0.964223i | \(-0.414597\pi\) | ||||
0.265094 | + | 0.964223i | \(0.414597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.9465 | 1.44855 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.7452 | −1.00214 | −0.501071 | − | 0.865406i | \(-0.667060\pi\) | ||||
−0.501071 | + | 0.865406i | \(0.667060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5309 | 0.892836 | 0.446418 | − | 0.894825i | \(-0.352700\pi\) | ||||
0.446418 | + | 0.894825i | \(0.352700\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1114 | 0.339892 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.2772 | −1.82245 | −0.911226 | − | 0.411907i | \(-0.864863\pi\) | ||||
−0.911226 | + | 0.411907i | \(0.864863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.7183 | 0.694870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.98415 | −0.233978 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0033 | −0.435137 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.08905 | 0.303814 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.18981 | 0.106504 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53.6436 | −1.78911 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.1798 | 1.43853 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.88680 | −0.162622 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.6235 | 0.652306 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8919 | −0.693704 | −0.346852 | − | 0.937920i | \(-0.612749\pi\) | ||||
−0.346852 | + | 0.937920i | \(0.612749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.06391 | 0.101624 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5884 | −0.450203 | −0.225102 | − | 0.974335i | \(-0.572271\pi\) | ||||
−0.225102 | + | 0.974335i | \(0.572271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.3116 | −0.440549 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.53758 | 0.216126 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.5220 | −1.00793 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.3308 | 1.85818 | 0.929090 | − | 0.369853i | \(-0.120592\pi\) | ||||
0.929090 | + | 0.369853i | \(0.120592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.1924 | 0.896020 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.42016 | 0.0796606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.6387 | 0.810114 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.1424 | −0.497342 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8760 | −0.914583 | −0.457291 | − | 0.889317i | \(-0.651180\pi\) | ||||
−0.457291 | + | 0.889317i | \(0.651180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.83294 | −0.158393 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.0006 | −0.687528 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.89581 | −0.225517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.95785 | −0.0966288 | −0.0483144 | − | 0.998832i | \(-0.515385\pi\) | ||||
−0.0483144 | + | 0.998832i | \(0.515385\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9034 | 0.551621 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.1216 | 1.07973 | 0.539867 | − | 0.841750i | \(-0.318475\pi\) | ||||
0.539867 | + | 0.841750i | \(0.318475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.5237 | −0.733472 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.44863 | −0.209774 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.44438 | 0.241910 | 0.120955 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120955 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.01957 | −0.0980194 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.8341 | −1.12957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0640 | −1.13584 | −0.567918 | − | 0.823085i | \(-0.692251\pi\) | ||||
−0.567918 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4646 | 0.532782 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.5596 | −0.405993 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.10955 | 0.229579 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.3992 | 1.30320 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.2019 | −0.360976 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.31160 | −0.299751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.1678 | −1.06660 | −0.533301 | − | 0.845925i | \(-0.679049\pi\) | ||||
−0.533301 | + | 0.845925i | \(0.679049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.99342 | 0.288910 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.16827 | −0.165858 | −0.0829288 | − | 0.996555i | \(-0.526427\pi\) | ||||
−0.0829288 | + | 0.996555i | \(0.526427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.1814 | 0.646986 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.19803 | 0.166470 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.8373 | −0.570665 | −0.285333 | − | 0.958429i | \(-0.592104\pi\) | ||||
−0.285333 | + | 0.958429i | \(0.592104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.52368 | 0.0806570 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.5053 | −0.495046 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.6358 | 0.977131 | 0.488566 | − | 0.872527i | \(-0.337520\pi\) | ||||
0.488566 | + | 0.872527i | \(0.337520\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.69672 | 0.213375 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.0575 | 0.861251 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.34160 | −0.201651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.890956 | 0.0283021 | 0.0141511 | − | 0.999900i | \(-0.495495\pi\) | ||||
0.0141511 | + | 0.999900i | \(0.495495\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −45.8502 | −1.45501 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.8206 | 0.501546 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.0416 | −0.666394 | −0.333197 | − | 0.942857i | \(-0.608127\pi\) | ||||
−0.333197 | + | 0.942857i | \(0.608127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.6743 | 1.00213 |
(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 | 6004.2.a.g.1.20 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.20 | ✓ | 27 | 1.1 | even | 1 | trivial |