Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.43 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19557 | 0.845399 | 0.422699 | − | 0.906270i | \(-0.361083\pi\) | ||||
0.422699 | + | 0.906270i | \(0.361083\pi\) | |||||||
\(3\) | −0.378969 | −0.218798 | −0.109399 | − | 0.993998i | \(-0.534893\pi\) | ||||
−0.109399 | + | 0.993998i | \(0.534893\pi\) | |||||||
\(4\) | −0.570603 | −0.285301 | ||||||||
\(5\) | 0.0302315 | 0.0135199 | 0.00675996 | − | 0.999977i | \(-0.497848\pi\) | ||||
0.00675996 | + | 0.999977i | \(0.497848\pi\) | |||||||
\(6\) | −0.453085 | −0.184971 | ||||||||
\(7\) | 3.94410 | 1.49073 | 0.745365 | − | 0.666656i | \(-0.232275\pi\) | ||||
0.745365 | + | 0.666656i | \(0.232275\pi\) | |||||||
\(8\) | −3.07335 | −1.08659 | ||||||||
\(9\) | −2.85638 | −0.952128 | ||||||||
\(10\) | 0.0361440 | 0.0114297 | ||||||||
\(11\) | 1.87601 | 0.565639 | 0.282819 | − | 0.959173i | \(-0.408730\pi\) | ||||
0.282819 | + | 0.959173i | \(0.408730\pi\) | |||||||
\(12\) | 0.216240 | 0.0624232 | ||||||||
\(13\) | 0.677227 | 0.187829 | 0.0939145 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939145 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(14\) | 4.71547 | 1.26026 | ||||||||
\(15\) | −0.0114568 | −0.00295813 | ||||||||
\(16\) | −2.53321 | −0.633302 | ||||||||
\(17\) | −4.16638 | −1.01050 | −0.505248 | − | 0.862974i | \(-0.668599\pi\) | ||||
−0.505248 | + | 0.862974i | \(0.668599\pi\) | |||||||
\(18\) | −3.41502 | −0.804927 | ||||||||
\(19\) | −3.45637 | −0.792946 | −0.396473 | − | 0.918046i | \(-0.629766\pi\) | ||||
−0.396473 | + | 0.918046i | \(0.629766\pi\) | |||||||
\(20\) | −0.0172502 | −0.00385725 | ||||||||
\(21\) | −1.49469 | −0.326168 | ||||||||
\(22\) | 2.24291 | 0.478190 | ||||||||
\(23\) | 6.14590 | 1.28151 | 0.640755 | − | 0.767746i | \(-0.278622\pi\) | ||||
0.640755 | + | 0.767746i | \(0.278622\pi\) | |||||||
\(24\) | 1.16470 | 0.237744 | ||||||||
\(25\) | −4.99909 | −0.999817 | ||||||||
\(26\) | 0.809675 | 0.158790 | ||||||||
\(27\) | 2.21938 | 0.427121 | ||||||||
\(28\) | −2.25052 | −0.425307 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.0136974 | −0.00250080 | ||||||||
\(31\) | −3.10222 | −0.557174 | −0.278587 | − | 0.960411i | \(-0.589866\pi\) | ||||
−0.278587 | + | 0.960411i | \(0.589866\pi\) | |||||||
\(32\) | 3.11805 | 0.551199 | ||||||||
\(33\) | −0.710949 | −0.123760 | ||||||||
\(34\) | −4.98122 | −0.854272 | ||||||||
\(35\) | 0.119236 | 0.0201546 | ||||||||
\(36\) | 1.62986 | 0.271643 | ||||||||
\(37\) | −4.04246 | −0.664576 | −0.332288 | − | 0.943178i | \(-0.607821\pi\) | ||||
−0.332288 | + | 0.943178i | \(0.607821\pi\) | |||||||
\(38\) | −4.13235 | −0.670356 | ||||||||
\(39\) | −0.256648 | −0.0410965 | ||||||||
\(40\) | −0.0929118 | −0.0146906 | ||||||||
\(41\) | −6.63153 | −1.03567 | −0.517835 | − | 0.855480i | \(-0.673262\pi\) | ||||
−0.517835 | + | 0.855480i | \(0.673262\pi\) | |||||||
\(42\) | −1.78701 | −0.275742 | ||||||||
\(43\) | −3.15900 | −0.481743 | −0.240872 | − | 0.970557i | \(-0.577433\pi\) | ||||
−0.240872 | + | 0.970557i | \(0.577433\pi\) | |||||||
\(44\) | −1.07046 | −0.161378 | ||||||||
\(45\) | −0.0863527 | −0.0128727 | ||||||||
\(46\) | 7.34788 | 1.08339 | ||||||||
\(47\) | 1.79205 | 0.261397 | 0.130698 | − | 0.991422i | \(-0.458278\pi\) | ||||
0.130698 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(48\) | 0.960006 | 0.138565 | ||||||||
\(49\) | 8.55594 | 1.22228 | ||||||||
\(50\) | −5.97678 | −0.845244 | ||||||||
\(51\) | 1.57893 | 0.221094 | ||||||||
\(52\) | −0.386428 | −0.0535879 | ||||||||
\(53\) | 5.84228 | 0.802499 | 0.401249 | − | 0.915969i | \(-0.368576\pi\) | ||||
0.401249 | + | 0.915969i | \(0.368576\pi\) | |||||||
\(54\) | 2.65344 | 0.361087 | ||||||||
\(55\) | 0.0567146 | 0.00764739 | ||||||||
\(56\) | −12.1216 | −1.61982 | ||||||||
\(57\) | 1.30986 | 0.173495 | ||||||||
\(58\) | −1.19557 | −0.156987 | ||||||||
\(59\) | −7.81490 | −1.01741 | −0.508707 | − | 0.860940i | \(-0.669876\pi\) | ||||
−0.508707 | + | 0.860940i | \(0.669876\pi\) | |||||||
\(60\) | 0.00653727 | 0.000843957 0 | ||||||||
\(61\) | 6.45746 | 0.826793 | 0.413397 | − | 0.910551i | \(-0.364342\pi\) | ||||
0.413397 | + | 0.910551i | \(0.364342\pi\) | |||||||
\(62\) | −3.70893 | −0.471034 | ||||||||
\(63\) | −11.2659 | −1.41937 | ||||||||
\(64\) | 8.79428 | 1.09929 | ||||||||
\(65\) | 0.0204736 | 0.00253943 | ||||||||
\(66\) | −0.849993 | −0.104627 | ||||||||
\(67\) | −13.0351 | −1.59249 | −0.796243 | − | 0.604977i | \(-0.793182\pi\) | ||||
−0.796243 | + | 0.604977i | \(0.793182\pi\) | |||||||
\(68\) | 2.37735 | 0.288296 | ||||||||
\(69\) | −2.32910 | −0.280391 | ||||||||
\(70\) | 0.142555 | 0.0170386 | ||||||||
\(71\) | 1.57776 | 0.187246 | 0.0936231 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936231 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(72\) | 8.77865 | 1.03457 | ||||||||
\(73\) | 0.772201 | 0.0903793 | 0.0451897 | − | 0.998978i | \(-0.485611\pi\) | ||||
0.0451897 | + | 0.998978i | \(0.485611\pi\) | |||||||
\(74\) | −4.83306 | −0.561832 | ||||||||
\(75\) | 1.89450 | 0.218758 | ||||||||
\(76\) | 1.97222 | 0.226229 | ||||||||
\(77\) | 7.39918 | 0.843215 | ||||||||
\(78\) | −0.306841 | −0.0347430 | ||||||||
\(79\) | −7.96706 | −0.896364 | −0.448182 | − | 0.893942i | \(-0.647928\pi\) | ||||
−0.448182 | + | 0.893942i | \(0.647928\pi\) | |||||||
\(80\) | −0.0765826 | −0.00856219 | ||||||||
\(81\) | 7.72807 | 0.858675 | ||||||||
\(82\) | −7.92848 | −0.875555 | ||||||||
\(83\) | −10.1333 | −1.11228 | −0.556140 | − | 0.831089i | \(-0.687718\pi\) | ||||
−0.556140 | + | 0.831089i | \(0.687718\pi\) | |||||||
\(84\) | 0.852874 | 0.0930562 | ||||||||
\(85\) | −0.125956 | −0.0136618 | ||||||||
\(86\) | −3.77682 | −0.407265 | ||||||||
\(87\) | 0.378969 | 0.0406297 | ||||||||
\(88\) | −5.76563 | −0.614619 | ||||||||
\(89\) | −7.68535 | −0.814646 | −0.407323 | − | 0.913284i | \(-0.633538\pi\) | ||||
−0.407323 | + | 0.913284i | \(0.633538\pi\) | |||||||
\(90\) | −0.103241 | −0.0108826 | ||||||||
\(91\) | 2.67105 | 0.280002 | ||||||||
\(92\) | −3.50687 | −0.365616 | ||||||||
\(93\) | 1.17564 | 0.121908 | ||||||||
\(94\) | 2.14253 | 0.220985 | ||||||||
\(95\) | −0.104491 | −0.0107206 | ||||||||
\(96\) | −1.18164 | −0.120601 | ||||||||
\(97\) | 4.70310 | 0.477527 | 0.238763 | − | 0.971078i | \(-0.423258\pi\) | ||||
0.238763 | + | 0.971078i | \(0.423258\pi\) | |||||||
\(98\) | 10.2293 | 1.03331 | ||||||||
\(99\) | −5.35861 | −0.538560 | ||||||||
\(100\) | 2.85249 | 0.285249 | ||||||||
\(101\) | −10.3987 | −1.03471 | −0.517356 | − | 0.855770i | \(-0.673084\pi\) | ||||
−0.517356 | + | 0.855770i | \(0.673084\pi\) | |||||||
\(102\) | 1.88773 | 0.186913 | ||||||||
\(103\) | 12.0298 | 1.18533 | 0.592666 | − | 0.805448i | \(-0.298075\pi\) | ||||
0.592666 | + | 0.805448i | \(0.298075\pi\) | |||||||
\(104\) | −2.08135 | −0.204093 | ||||||||
\(105\) | −0.0451867 | −0.00440977 | ||||||||
\(106\) | 6.98488 | 0.678431 | ||||||||
\(107\) | −18.8308 | −1.82045 | −0.910223 | − | 0.414119i | \(-0.864090\pi\) | ||||
−0.910223 | + | 0.414119i | \(0.864090\pi\) | |||||||
\(108\) | −1.26639 | −0.121858 | ||||||||
\(109\) | −0.644546 | −0.0617363 | −0.0308681 | − | 0.999523i | \(-0.509827\pi\) | ||||
−0.0308681 | + | 0.999523i | \(0.509827\pi\) | |||||||
\(110\) | 0.0678065 | 0.00646510 | ||||||||
\(111\) | 1.53197 | 0.145408 | ||||||||
\(112\) | −9.99123 | −0.944082 | ||||||||
\(113\) | 11.6268 | 1.09376 | 0.546880 | − | 0.837211i | \(-0.315815\pi\) | ||||
0.546880 | + | 0.837211i | \(0.315815\pi\) | |||||||
\(114\) | 1.56603 | 0.146672 | ||||||||
\(115\) | 0.185800 | 0.0173259 | ||||||||
\(116\) | 0.570603 | 0.0529791 | ||||||||
\(117\) | −1.93442 | −0.178837 | ||||||||
\(118\) | −9.34329 | −0.860120 | ||||||||
\(119\) | −16.4326 | −1.50638 | ||||||||
\(120\) | 0.0352106 | 0.00321428 | ||||||||
\(121\) | −7.48058 | −0.680053 | ||||||||
\(122\) | 7.72037 | 0.698970 | ||||||||
\(123\) | 2.51314 | 0.226602 | ||||||||
\(124\) | 1.77013 | 0.158963 | ||||||||
\(125\) | −0.302287 | −0.0270374 | ||||||||
\(126\) | −13.4692 | −1.19993 | ||||||||
\(127\) | −4.49114 | −0.398524 | −0.199262 | − | 0.979946i | \(-0.563855\pi\) | ||||
−0.199262 | + | 0.979946i | \(0.563855\pi\) | |||||||
\(128\) | 4.27810 | 0.378135 | ||||||||
\(129\) | 1.19716 | 0.105404 | ||||||||
\(130\) | 0.0244777 | 0.00214683 | ||||||||
\(131\) | 8.42874 | 0.736423 | 0.368211 | − | 0.929742i | \(-0.379970\pi\) | ||||
0.368211 | + | 0.929742i | \(0.379970\pi\) | |||||||
\(132\) | 0.405670 | 0.0353090 | ||||||||
\(133\) | −13.6323 | −1.18207 | ||||||||
\(134\) | −15.5844 | −1.34629 | ||||||||
\(135\) | 0.0670953 | 0.00577464 | ||||||||
\(136\) | 12.8047 | 1.09800 | ||||||||
\(137\) | −21.2023 | −1.81143 | −0.905716 | − | 0.423885i | \(-0.860666\pi\) | ||||
−0.905716 | + | 0.423885i | \(0.860666\pi\) | |||||||
\(138\) | −2.78462 | −0.237042 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | −0.0680364 | −0.00575012 | ||||||||
\(141\) | −0.679130 | −0.0571930 | ||||||||
\(142\) | 1.88633 | 0.158298 | ||||||||
\(143\) | 1.27049 | 0.106243 | ||||||||
\(144\) | 7.23581 | 0.602984 | ||||||||
\(145\) | −0.0302315 | −0.00251059 | ||||||||
\(146\) | 0.923224 | 0.0764066 | ||||||||
\(147\) | −3.24243 | −0.267431 | ||||||||
\(148\) | 2.30664 | 0.189605 | ||||||||
\(149\) | 4.97969 | 0.407952 | 0.203976 | − | 0.978976i | \(-0.434614\pi\) | ||||
0.203976 | + | 0.978976i | \(0.434614\pi\) | |||||||
\(150\) | 2.26501 | 0.184937 | ||||||||
\(151\) | −18.4816 | −1.50401 | −0.752004 | − | 0.659158i | \(-0.770913\pi\) | ||||
−0.752004 | + | 0.659158i | \(0.770913\pi\) | |||||||
\(152\) | 10.6226 | 0.861609 | ||||||||
\(153\) | 11.9008 | 0.962122 | ||||||||
\(154\) | 8.84627 | 0.712853 | ||||||||
\(155\) | −0.0937845 | −0.00753295 | ||||||||
\(156\) | 0.146444 | 0.0117249 | ||||||||
\(157\) | 5.86492 | 0.468072 | 0.234036 | − | 0.972228i | \(-0.424807\pi\) | ||||
0.234036 | + | 0.972228i | \(0.424807\pi\) | |||||||
\(158\) | −9.52521 | −0.757785 | ||||||||
\(159\) | −2.21404 | −0.175585 | ||||||||
\(160\) | 0.0942634 | 0.00745217 | ||||||||
\(161\) | 24.2401 | 1.91039 | ||||||||
\(162\) | 9.23948 | 0.725922 | ||||||||
\(163\) | 9.25562 | 0.724956 | 0.362478 | − | 0.931992i | \(-0.381931\pi\) | ||||
0.362478 | + | 0.931992i | \(0.381931\pi\) | |||||||
\(164\) | 3.78397 | 0.295478 | ||||||||
\(165\) | −0.0214930 | −0.00167323 | ||||||||
\(166\) | −12.1152 | −0.940319 | ||||||||
\(167\) | −15.6357 | −1.20993 | −0.604965 | − | 0.796252i | \(-0.706813\pi\) | ||||
−0.604965 | + | 0.796252i | \(0.706813\pi\) | |||||||
\(168\) | 4.59370 | 0.354412 | ||||||||
\(169\) | −12.5414 | −0.964720 | ||||||||
\(170\) | −0.150590 | −0.0115497 | ||||||||
\(171\) | 9.87272 | 0.754986 | ||||||||
\(172\) | 1.80254 | 0.137442 | ||||||||
\(173\) | −21.0242 | −1.59844 | −0.799221 | − | 0.601038i | \(-0.794754\pi\) | ||||
−0.799221 | + | 0.601038i | \(0.794754\pi\) | |||||||
\(174\) | 0.453085 | 0.0343483 | ||||||||
\(175\) | −19.7169 | −1.49046 | ||||||||
\(176\) | −4.75233 | −0.358220 | ||||||||
\(177\) | 2.96160 | 0.222608 | ||||||||
\(178\) | −9.18841 | −0.688700 | ||||||||
\(179\) | 1.91109 | 0.142841 | 0.0714207 | − | 0.997446i | \(-0.477247\pi\) | ||||
0.0714207 | + | 0.997446i | \(0.477247\pi\) | |||||||
\(180\) | 0.0492731 | 0.00367260 | ||||||||
\(181\) | 20.3001 | 1.50890 | 0.754448 | − | 0.656359i | \(-0.227904\pi\) | ||||
0.754448 | + | 0.656359i | \(0.227904\pi\) | |||||||
\(182\) | 3.19344 | 0.236714 | ||||||||
\(183\) | −2.44717 | −0.180900 | ||||||||
\(184\) | −18.8885 | −1.39248 | ||||||||
\(185\) | −0.122210 | −0.00898502 | ||||||||
\(186\) | 1.40557 | 0.103061 | ||||||||
\(187\) | −7.81619 | −0.571576 | ||||||||
\(188\) | −1.02255 | −0.0745769 | ||||||||
\(189\) | 8.75348 | 0.636722 | ||||||||
\(190\) | −0.124927 | −0.00906316 | ||||||||
\(191\) | −13.1332 | −0.950285 | −0.475143 | − | 0.879909i | \(-0.657604\pi\) | ||||
−0.475143 | + | 0.879909i | \(0.657604\pi\) | |||||||
\(192\) | −3.33276 | −0.240521 | ||||||||
\(193\) | 15.8725 | 1.14253 | 0.571264 | − | 0.820766i | \(-0.306453\pi\) | ||||
0.571264 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(194\) | 5.62290 | 0.403701 | ||||||||
\(195\) | −0.00775884 | −0.000555622 0 | ||||||||
\(196\) | −4.88204 | −0.348717 | ||||||||
\(197\) | −19.2357 | −1.37049 | −0.685245 | − | 0.728313i | \(-0.740305\pi\) | ||||
−0.685245 | + | 0.728313i | \(0.740305\pi\) | |||||||
\(198\) | −6.40661 | −0.455298 | ||||||||
\(199\) | 1.62911 | 0.115485 | 0.0577423 | − | 0.998332i | \(-0.481610\pi\) | ||||
0.0577423 | + | 0.998332i | \(0.481610\pi\) | |||||||
\(200\) | 15.3639 | 1.08639 | ||||||||
\(201\) | 4.93988 | 0.348432 | ||||||||
\(202\) | −12.4324 | −0.874744 | ||||||||
\(203\) | −3.94410 | −0.276822 | ||||||||
\(204\) | −0.900941 | −0.0630785 | ||||||||
\(205\) | −0.200481 | −0.0140022 | ||||||||
\(206\) | 14.3825 | 1.00208 | ||||||||
\(207\) | −17.5551 | −1.22016 | ||||||||
\(208\) | −1.71556 | −0.118952 | ||||||||
\(209\) | −6.48420 | −0.448521 | ||||||||
\(210\) | −0.0540240 | −0.00372801 | ||||||||
\(211\) | 11.7265 | 0.807285 | 0.403642 | − | 0.914917i | \(-0.367744\pi\) | ||||
0.403642 | + | 0.914917i | \(0.367744\pi\) | |||||||
\(212\) | −3.33362 | −0.228954 | ||||||||
\(213\) | −0.597923 | −0.0409690 | ||||||||
\(214\) | −22.5137 | −1.53900 | ||||||||
\(215\) | −0.0955013 | −0.00651313 | ||||||||
\(216\) | −6.82094 | −0.464106 | ||||||||
\(217\) | −12.2355 | −0.830597 | ||||||||
\(218\) | −0.770602 | −0.0521918 | ||||||||
\(219\) | −0.292640 | −0.0197748 | ||||||||
\(220\) | −0.0323615 | −0.00218181 | ||||||||
\(221\) | −2.82159 | −0.189801 | ||||||||
\(222\) | 1.83158 | 0.122927 | ||||||||
\(223\) | −22.6519 | −1.51688 | −0.758441 | − | 0.651742i | \(-0.774039\pi\) | ||||
−0.758441 | + | 0.651742i | \(0.774039\pi\) | |||||||
\(224\) | 12.2979 | 0.821690 | ||||||||
\(225\) | 14.2793 | 0.951954 | ||||||||
\(226\) | 13.9007 | 0.924663 | ||||||||
\(227\) | 10.7530 | 0.713705 | 0.356852 | − | 0.934161i | \(-0.383850\pi\) | ||||
0.356852 | + | 0.934161i | \(0.383850\pi\) | |||||||
\(228\) | −0.747407 | −0.0494983 | ||||||||
\(229\) | 7.38393 | 0.487944 | 0.243972 | − | 0.969782i | \(-0.421550\pi\) | ||||
0.243972 | + | 0.969782i | \(0.421550\pi\) | |||||||
\(230\) | 0.222137 | 0.0146473 | ||||||||
\(231\) | −2.80406 | −0.184493 | ||||||||
\(232\) | 3.07335 | 0.201775 | ||||||||
\(233\) | 15.9135 | 1.04253 | 0.521265 | − | 0.853395i | \(-0.325460\pi\) | ||||
0.521265 | + | 0.853395i | \(0.325460\pi\) | |||||||
\(234\) | −2.31274 | −0.151189 | ||||||||
\(235\) | 0.0541762 | 0.00353407 | ||||||||
\(236\) | 4.45920 | 0.290269 | ||||||||
\(237\) | 3.01926 | 0.196122 | ||||||||
\(238\) | −19.6464 | −1.27349 | ||||||||
\(239\) | −24.1341 | −1.56111 | −0.780553 | − | 0.625089i | \(-0.785063\pi\) | ||||
−0.780553 | + | 0.625089i | \(0.785063\pi\) | |||||||
\(240\) | 0.0290224 | 0.00187339 | ||||||||
\(241\) | −18.1709 | −1.17049 | −0.585247 | − | 0.810855i | \(-0.699002\pi\) | ||||
−0.585247 | + | 0.810855i | \(0.699002\pi\) | |||||||
\(242\) | −8.94359 | −0.574916 | ||||||||
\(243\) | −9.58685 | −0.614997 | ||||||||
\(244\) | −3.68464 | −0.235885 | ||||||||
\(245\) | 0.258659 | 0.0165251 | ||||||||
\(246\) | 3.00465 | 0.191569 | ||||||||
\(247\) | −2.34075 | −0.148938 | ||||||||
\(248\) | 9.53418 | 0.605421 | ||||||||
\(249\) | 3.84022 | 0.243364 | ||||||||
\(250\) | −0.361407 | −0.0228574 | ||||||||
\(251\) | −9.09251 | −0.573914 | −0.286957 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286957 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(252\) | 6.42833 | 0.404947 | ||||||||
\(253\) | 11.5298 | 0.724872 | ||||||||
\(254\) | −5.36949 | −0.336912 | ||||||||
\(255\) | 0.0477333 | 0.00298918 | ||||||||
\(256\) | −12.4738 | −0.779611 | ||||||||
\(257\) | 20.6452 | 1.28781 | 0.643907 | − | 0.765104i | \(-0.277312\pi\) | ||||
0.643907 | + | 0.765104i | \(0.277312\pi\) | |||||||
\(258\) | 1.43130 | 0.0891086 | ||||||||
\(259\) | −15.9439 | −0.990704 | ||||||||
\(260\) | −0.0116823 | −0.000724504 0 | ||||||||
\(261\) | 2.85638 | 0.176806 | ||||||||
\(262\) | 10.0772 | 0.622571 | ||||||||
\(263\) | −8.88540 | −0.547898 | −0.273949 | − | 0.961744i | \(-0.588330\pi\) | ||||
−0.273949 | + | 0.961744i | \(0.588330\pi\) | |||||||
\(264\) | 2.18499 | 0.134477 | ||||||||
\(265\) | 0.176621 | 0.0108497 | ||||||||
\(266\) | −16.2984 | −0.999320 | ||||||||
\(267\) | 2.91251 | 0.178243 | ||||||||
\(268\) | 7.43784 | 0.454338 | ||||||||
\(269\) | 9.39241 | 0.572665 | 0.286333 | − | 0.958130i | \(-0.407564\pi\) | ||||
0.286333 | + | 0.958130i | \(0.407564\pi\) | |||||||
\(270\) | 0.0802174 | 0.00488187 | ||||||||
\(271\) | −12.0112 | −0.729628 | −0.364814 | − | 0.931080i | \(-0.618867\pi\) | ||||
−0.364814 | + | 0.931080i | \(0.618867\pi\) | |||||||
\(272\) | 10.5543 | 0.639949 | ||||||||
\(273\) | −1.01225 | −0.0612639 | ||||||||
\(274\) | −25.3489 | −1.53138 | ||||||||
\(275\) | −9.37834 | −0.565535 | ||||||||
\(276\) | 1.32899 | 0.0799960 | ||||||||
\(277\) | −15.5181 | −0.932390 | −0.466195 | − | 0.884682i | \(-0.654376\pi\) | ||||
−0.466195 | + | 0.884682i | \(0.654376\pi\) | |||||||
\(278\) | −1.19557 | −0.0717058 | ||||||||
\(279\) | 8.86111 | 0.530501 | ||||||||
\(280\) | −0.366454 | −0.0218998 | ||||||||
\(281\) | 20.3300 | 1.21279 | 0.606395 | − | 0.795164i | \(-0.292615\pi\) | ||||
0.606395 | + | 0.795164i | \(0.292615\pi\) | |||||||
\(282\) | −0.811950 | −0.0483509 | ||||||||
\(283\) | 8.62730 | 0.512840 | 0.256420 | − | 0.966565i | \(-0.417457\pi\) | ||||
0.256420 | + | 0.966565i | \(0.417457\pi\) | |||||||
\(284\) | −0.900277 | −0.0534216 | ||||||||
\(285\) | 0.0395989 | 0.00234564 | ||||||||
\(286\) | 1.51896 | 0.0898180 | ||||||||
\(287\) | −26.1554 | −1.54391 | ||||||||
\(288\) | −8.90636 | −0.524812 | ||||||||
\(289\) | 0.358757 | 0.0211034 | ||||||||
\(290\) | −0.0361440 | −0.00212245 | ||||||||
\(291\) | −1.78232 | −0.104482 | ||||||||
\(292\) | −0.440620 | −0.0257853 | ||||||||
\(293\) | 15.3786 | 0.898427 | 0.449213 | − | 0.893424i | \(-0.351704\pi\) | ||||
0.449213 | + | 0.893424i | \(0.351704\pi\) | |||||||
\(294\) | −3.87657 | −0.226086 | ||||||||
\(295\) | −0.236256 | −0.0137554 | ||||||||
\(296\) | 12.4239 | 0.722123 | ||||||||
\(297\) | 4.16359 | 0.241596 | ||||||||
\(298\) | 5.95359 | 0.344882 | ||||||||
\(299\) | 4.16217 | 0.240705 | ||||||||
\(300\) | −1.08100 | −0.0624118 | ||||||||
\(301\) | −12.4594 | −0.718150 | ||||||||
\(302\) | −22.0961 | −1.27149 | ||||||||
\(303\) | 3.94079 | 0.226392 | ||||||||
\(304\) | 8.75571 | 0.502174 | ||||||||
\(305\) | 0.195219 | 0.0111782 | ||||||||
\(306\) | 14.2283 | 0.813376 | ||||||||
\(307\) | −3.69798 | −0.211055 | −0.105527 | − | 0.994416i | \(-0.533653\pi\) | ||||
−0.105527 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(308\) | −4.22199 | −0.240570 | ||||||||
\(309\) | −4.55892 | −0.259348 | ||||||||
\(310\) | −0.112126 | −0.00636835 | ||||||||
\(311\) | 25.1148 | 1.42413 | 0.712064 | − | 0.702114i | \(-0.247760\pi\) | ||||
0.712064 | + | 0.702114i | \(0.247760\pi\) | |||||||
\(312\) | 0.788767 | 0.0446552 | ||||||||
\(313\) | 31.9991 | 1.80870 | 0.904348 | − | 0.426797i | \(-0.140358\pi\) | ||||
0.904348 | + | 0.426797i | \(0.140358\pi\) | |||||||
\(314\) | 7.01195 | 0.395707 | ||||||||
\(315\) | −0.340584 | −0.0191897 | ||||||||
\(316\) | 4.54603 | 0.255734 | ||||||||
\(317\) | 32.4190 | 1.82083 | 0.910417 | − | 0.413691i | \(-0.135761\pi\) | ||||
0.910417 | + | 0.413691i | \(0.135761\pi\) | |||||||
\(318\) | −2.64705 | −0.148439 | ||||||||
\(319\) | −1.87601 | −0.105037 | ||||||||
\(320\) | 0.265864 | 0.0148623 | ||||||||
\(321\) | 7.13629 | 0.398309 | ||||||||
\(322\) | 28.9808 | 1.61504 | ||||||||
\(323\) | 14.4006 | 0.801269 | ||||||||
\(324\) | −4.40966 | −0.244981 | ||||||||
\(325\) | −3.38552 | −0.187795 | ||||||||
\(326\) | 11.0658 | 0.612877 | ||||||||
\(327\) | 0.244262 | 0.0135077 | ||||||||
\(328\) | 20.3810 | 1.12535 | ||||||||
\(329\) | 7.06802 | 0.389672 | ||||||||
\(330\) | −0.0256965 | −0.00141455 | ||||||||
\(331\) | 29.3420 | 1.61278 | 0.806392 | − | 0.591381i | \(-0.201417\pi\) | ||||
0.806392 | + | 0.591381i | \(0.201417\pi\) | |||||||
\(332\) | 5.78212 | 0.317335 | ||||||||
\(333\) | 11.5468 | 0.632762 | ||||||||
\(334\) | −18.6937 | −1.02287 | ||||||||
\(335\) | −0.394069 | −0.0215303 | ||||||||
\(336\) | 3.78636 | 0.206563 | ||||||||
\(337\) | −30.6442 | −1.66929 | −0.834647 | − | 0.550785i | \(-0.814328\pi\) | ||||
−0.834647 | + | 0.550785i | \(0.814328\pi\) | |||||||
\(338\) | −14.9941 | −0.815573 | ||||||||
\(339\) | −4.40620 | −0.239312 | ||||||||
\(340\) | 0.0718708 | 0.00389774 | ||||||||
\(341\) | −5.81979 | −0.315159 | ||||||||
\(342\) | 11.8036 | 0.638264 | ||||||||
\(343\) | 6.13681 | 0.331356 | ||||||||
\(344\) | 9.70871 | 0.523458 | ||||||||
\(345\) | −0.0704122 | −0.00379087 | ||||||||
\(346\) | −25.1360 | −1.35132 | ||||||||
\(347\) | 15.9639 | 0.856987 | 0.428494 | − | 0.903545i | \(-0.359044\pi\) | ||||
0.428494 | + | 0.903545i | \(0.359044\pi\) | |||||||
\(348\) | −0.216240 | −0.0115917 | ||||||||
\(349\) | −20.3707 | −1.09042 | −0.545209 | − | 0.838300i | \(-0.683550\pi\) | ||||
−0.545209 | + | 0.838300i | \(0.683550\pi\) | |||||||
\(350\) | −23.5730 | −1.26003 | ||||||||
\(351\) | 1.50303 | 0.0802257 | ||||||||
\(352\) | 5.84951 | 0.311780 | ||||||||
\(353\) | −17.6373 | −0.938738 | −0.469369 | − | 0.883002i | \(-0.655519\pi\) | ||||
−0.469369 | + | 0.883002i | \(0.655519\pi\) | |||||||
\(354\) | 3.54081 | 0.188192 | ||||||||
\(355\) | 0.0476981 | 0.00253155 | ||||||||
\(356\) | 4.38528 | 0.232420 | ||||||||
\(357\) | 6.22746 | 0.329592 | ||||||||
\(358\) | 2.28485 | 0.120758 | ||||||||
\(359\) | 31.2874 | 1.65129 | 0.825644 | − | 0.564192i | \(-0.190812\pi\) | ||||
0.825644 | + | 0.564192i | \(0.190812\pi\) | |||||||
\(360\) | 0.265392 | 0.0139874 | ||||||||
\(361\) | −7.05349 | −0.371236 | ||||||||
\(362\) | 24.2703 | 1.27562 | ||||||||
\(363\) | 2.83490 | 0.148794 | ||||||||
\(364\) | −1.52411 | −0.0798851 | ||||||||
\(365\) | 0.0233448 | 0.00122192 | ||||||||
\(366\) | −2.92578 | −0.152933 | ||||||||
\(367\) | 0.0122125 | 0.000637487 0 | 0.000318744 | − | 1.00000i | \(-0.499899\pi\) | ||||
0.000318744 | 1.00000i | \(0.499899\pi\) | ||||||||
\(368\) | −15.5689 | −0.811582 | ||||||||
\(369\) | 18.9422 | 0.986091 | ||||||||
\(370\) | −0.146111 | −0.00759593 | ||||||||
\(371\) | 23.0426 | 1.19631 | ||||||||
\(372\) | −0.670824 | −0.0347806 | ||||||||
\(373\) | −35.0219 | −1.81336 | −0.906682 | − | 0.421814i | \(-0.861394\pi\) | ||||
−0.906682 | + | 0.421814i | \(0.861394\pi\) | |||||||
\(374\) | −9.34483 | −0.483210 | ||||||||
\(375\) | 0.114557 | 0.00591571 | ||||||||
\(376\) | −5.50758 | −0.284032 | ||||||||
\(377\) | −0.677227 | −0.0348790 | ||||||||
\(378\) | 10.4654 | 0.538284 | ||||||||
\(379\) | 11.0529 | 0.567749 | 0.283874 | − | 0.958861i | \(-0.408380\pi\) | ||||
0.283874 | + | 0.958861i | \(0.408380\pi\) | |||||||
\(380\) | 0.0596230 | 0.00305859 | ||||||||
\(381\) | 1.70200 | 0.0871961 | ||||||||
\(382\) | −15.7017 | −0.803370 | ||||||||
\(383\) | −2.19567 | −0.112194 | −0.0560968 | − | 0.998425i | \(-0.517866\pi\) | ||||
−0.0560968 | + | 0.998425i | \(0.517866\pi\) | |||||||
\(384\) | −1.62127 | −0.0827349 | ||||||||
\(385\) | 0.223688 | 0.0114002 | ||||||||
\(386\) | 18.9768 | 0.965892 | ||||||||
\(387\) | 9.02332 | 0.458681 | ||||||||
\(388\) | −2.68360 | −0.136239 | ||||||||
\(389\) | 32.7752 | 1.66177 | 0.830884 | − | 0.556446i | \(-0.187835\pi\) | ||||
0.830884 | + | 0.556446i | \(0.187835\pi\) | |||||||
\(390\) | −0.00927627 | −0.000469722 0 | ||||||||
\(391\) | −25.6062 | −1.29496 | ||||||||
\(392\) | −26.2954 | −1.32812 | ||||||||
\(393\) | −3.19423 | −0.161127 | ||||||||
\(394\) | −22.9977 | −1.15861 | ||||||||
\(395\) | −0.240856 | −0.0121188 | ||||||||
\(396\) | 3.05764 | 0.153652 | ||||||||
\(397\) | −35.4390 | −1.77863 | −0.889316 | − | 0.457294i | \(-0.848819\pi\) | ||||
−0.889316 | + | 0.457294i | \(0.848819\pi\) | |||||||
\(398\) | 1.94772 | 0.0976305 | ||||||||
\(399\) | 5.16621 | 0.258634 | ||||||||
\(400\) | 12.6637 | 0.633186 | ||||||||
\(401\) | −6.03871 | −0.301559 | −0.150779 | − | 0.988567i | \(-0.548178\pi\) | ||||
−0.150779 | + | 0.988567i | \(0.548178\pi\) | |||||||
\(402\) | 5.90599 | 0.294564 | ||||||||
\(403\) | −2.10090 | −0.104654 | ||||||||
\(404\) | 5.93354 | 0.295205 | ||||||||
\(405\) | 0.233631 | 0.0116092 | ||||||||
\(406\) | −4.71547 | −0.234025 | ||||||||
\(407\) | −7.58370 | −0.375910 | ||||||||
\(408\) | −4.85259 | −0.240239 | ||||||||
\(409\) | 6.65664 | 0.329149 | 0.164575 | − | 0.986365i | \(-0.447375\pi\) | ||||
0.164575 | + | 0.986365i | \(0.447375\pi\) | |||||||
\(410\) | −0.239690 | −0.0118374 | ||||||||
\(411\) | 8.03499 | 0.396337 | ||||||||
\(412\) | −6.86424 | −0.338177 | ||||||||
\(413\) | −30.8228 | −1.51669 | ||||||||
\(414\) | −20.9884 | −1.03152 | ||||||||
\(415\) | −0.306346 | −0.0150379 | ||||||||
\(416\) | 2.11163 | 0.103531 | ||||||||
\(417\) | 0.378969 | 0.0185582 | ||||||||
\(418\) | −7.75234 | −0.379179 | ||||||||
\(419\) | −23.1709 | −1.13197 | −0.565987 | − | 0.824414i | \(-0.691505\pi\) | ||||
−0.565987 | + | 0.824414i | \(0.691505\pi\) | |||||||
\(420\) | 0.0257836 | 0.00125811 | ||||||||
\(421\) | −6.12806 | −0.298663 | −0.149332 | − | 0.988787i | \(-0.547712\pi\) | ||||
−0.149332 | + | 0.988787i | \(0.547712\pi\) | |||||||
\(422\) | 14.0199 | 0.682477 | ||||||||
\(423\) | −5.11877 | −0.248883 | ||||||||
\(424\) | −17.9553 | −0.871989 | ||||||||
\(425\) | 20.8281 | 1.01031 | ||||||||
\(426\) | −0.714861 | −0.0346351 | ||||||||
\(427\) | 25.4689 | 1.23253 | ||||||||
\(428\) | 10.7449 | 0.519376 | ||||||||
\(429\) | −0.481474 | −0.0232458 | ||||||||
\(430\) | −0.114179 | −0.00550619 | ||||||||
\(431\) | 14.7821 | 0.712031 | 0.356015 | − | 0.934480i | \(-0.384135\pi\) | ||||
0.356015 | + | 0.934480i | \(0.384135\pi\) | |||||||
\(432\) | −5.62216 | −0.270496 | ||||||||
\(433\) | −2.25372 | −0.108307 | −0.0541534 | − | 0.998533i | \(-0.517246\pi\) | ||||
−0.0541534 | + | 0.998533i | \(0.517246\pi\) | |||||||
\(434\) | −14.6284 | −0.702185 | ||||||||
\(435\) | 0.0114568 | 0.000549310 0 | ||||||||
\(436\) | 0.367779 | 0.0176134 | ||||||||
\(437\) | −21.2425 | −1.01617 | ||||||||
\(438\) | −0.349873 | −0.0167176 | ||||||||
\(439\) | 13.8210 | 0.659640 | 0.329820 | − | 0.944044i | \(-0.393012\pi\) | ||||
0.329820 | + | 0.944044i | \(0.393012\pi\) | |||||||
\(440\) | −0.174304 | −0.00830960 | ||||||||
\(441\) | −24.4391 | −1.16376 | ||||||||
\(442\) | −3.37342 | −0.160457 | ||||||||
\(443\) | −12.5364 | −0.595621 | −0.297811 | − | 0.954625i | \(-0.596256\pi\) | ||||
−0.297811 | + | 0.954625i | \(0.596256\pi\) | |||||||
\(444\) | −0.874143 | −0.0414850 | ||||||||
\(445\) | −0.232340 | −0.0110140 | ||||||||
\(446\) | −27.0820 | −1.28237 | ||||||||
\(447\) | −1.88715 | −0.0892590 | ||||||||
\(448\) | 34.6855 | 1.63874 | ||||||||
\(449\) | 3.08640 | 0.145656 | 0.0728280 | − | 0.997345i | \(-0.476798\pi\) | ||||
0.0728280 | + | 0.997345i | \(0.476798\pi\) | |||||||
\(450\) | 17.0720 | 0.804780 | ||||||||
\(451\) | −12.4408 | −0.585816 | ||||||||
\(452\) | −6.63430 | −0.312051 | ||||||||
\(453\) | 7.00393 | 0.329073 | ||||||||
\(454\) | 12.8561 | 0.603365 | ||||||||
\(455\) | 0.0807499 | 0.00378561 | ||||||||
\(456\) | −4.02564 | −0.188518 | ||||||||
\(457\) | 4.70253 | 0.219975 | 0.109987 | − | 0.993933i | \(-0.464919\pi\) | ||||
0.109987 | + | 0.993933i | \(0.464919\pi\) | |||||||
\(458\) | 8.82803 | 0.412507 | ||||||||
\(459\) | −9.24681 | −0.431604 | ||||||||
\(460\) | −0.106018 | −0.00494311 | ||||||||
\(461\) | 37.7987 | 1.76046 | 0.880231 | − | 0.474545i | \(-0.157387\pi\) | ||||
0.880231 | + | 0.474545i | \(0.157387\pi\) | |||||||
\(462\) | −3.35246 | −0.155970 | ||||||||
\(463\) | 10.8225 | 0.502966 | 0.251483 | − | 0.967862i | \(-0.419082\pi\) | ||||
0.251483 | + | 0.967862i | \(0.419082\pi\) | |||||||
\(464\) | 2.53321 | 0.117601 | ||||||||
\(465\) | 0.0355414 | 0.00164819 | ||||||||
\(466\) | 19.0258 | 0.881353 | ||||||||
\(467\) | −10.5603 | −0.488671 | −0.244335 | − | 0.969691i | \(-0.578570\pi\) | ||||
−0.244335 | + | 0.969691i | \(0.578570\pi\) | |||||||
\(468\) | 1.10379 | 0.0510225 | ||||||||
\(469\) | −51.4116 | −2.37397 | ||||||||
\(470\) | 0.0647717 | 0.00298770 | ||||||||
\(471\) | −2.22262 | −0.102413 | ||||||||
\(472\) | 24.0179 | 1.10551 | ||||||||
\(473\) | −5.92633 | −0.272493 | ||||||||
\(474\) | 3.60975 | 0.165802 | ||||||||
\(475\) | 17.2787 | 0.792801 | ||||||||
\(476\) | 9.37651 | 0.429772 | ||||||||
\(477\) | −16.6878 | −0.764081 | ||||||||
\(478\) | −28.8541 | −1.31976 | ||||||||
\(479\) | −13.5504 | −0.619134 | −0.309567 | − | 0.950878i | \(-0.600184\pi\) | ||||
−0.309567 | + | 0.950878i | \(0.600184\pi\) | |||||||
\(480\) | −0.0357229 | −0.00163052 | ||||||||
\(481\) | −2.73766 | −0.124827 | ||||||||
\(482\) | −21.7247 | −0.989533 | ||||||||
\(483\) | −9.18623 | −0.417988 | ||||||||
\(484\) | 4.26844 | 0.194020 | ||||||||
\(485\) | 0.142181 | 0.00645613 | ||||||||
\(486\) | −11.4618 | −0.519917 | ||||||||
\(487\) | 22.5007 | 1.01960 | 0.509801 | − | 0.860292i | \(-0.329719\pi\) | ||||
0.509801 | + | 0.860292i | \(0.329719\pi\) | |||||||
\(488\) | −19.8460 | −0.898387 | ||||||||
\(489\) | −3.50759 | −0.158619 | ||||||||
\(490\) | 0.309246 | 0.0139703 | ||||||||
\(491\) | 34.7873 | 1.56993 | 0.784965 | − | 0.619540i | \(-0.212681\pi\) | ||||
0.784965 | + | 0.619540i | \(0.212681\pi\) | |||||||
\(492\) | −1.43400 | −0.0646499 | ||||||||
\(493\) | 4.16638 | 0.187645 | ||||||||
\(494\) | −2.79854 | −0.125912 | ||||||||
\(495\) | −0.161999 | −0.00728130 | ||||||||
\(496\) | 7.85855 | 0.352860 | ||||||||
\(497\) | 6.22287 | 0.279134 | ||||||||
\(498\) | 4.59127 | 0.205740 | ||||||||
\(499\) | 4.67908 | 0.209464 | 0.104732 | − | 0.994500i | \(-0.466601\pi\) | ||||
0.104732 | + | 0.994500i | \(0.466601\pi\) | |||||||
\(500\) | 0.172486 | 0.00771380 | ||||||||
\(501\) | 5.92545 | 0.264730 | ||||||||
\(502\) | −10.8708 | −0.485186 | ||||||||
\(503\) | 3.31304 | 0.147721 | 0.0738606 | − | 0.997269i | \(-0.476468\pi\) | ||||
0.0738606 | + | 0.997269i | \(0.476468\pi\) | |||||||
\(504\) | 34.6239 | 1.54227 | ||||||||
\(505\) | −0.314369 | −0.0139892 | ||||||||
\(506\) | 13.7847 | 0.612805 | ||||||||
\(507\) | 4.75278 | 0.211078 | ||||||||
\(508\) | 2.56266 | 0.113700 | ||||||||
\(509\) | 21.6383 | 0.959099 | 0.479550 | − | 0.877515i | \(-0.340800\pi\) | ||||
0.479550 | + | 0.877515i | \(0.340800\pi\) | |||||||
\(510\) | 0.0570687 | 0.00252705 | ||||||||
\(511\) | 3.04564 | 0.134731 | ||||||||
\(512\) | −23.4695 | −1.03722 | ||||||||
\(513\) | −7.67102 | −0.338684 | ||||||||
\(514\) | 24.6829 | 1.08872 | ||||||||
\(515\) | 0.363679 | 0.0160256 | ||||||||
\(516\) | −0.683104 | −0.0300720 | ||||||||
\(517\) | 3.36190 | 0.147856 | ||||||||
\(518\) | −19.0621 | −0.837540 | ||||||||
\(519\) | 7.96752 | 0.349735 | ||||||||
\(520\) | −0.0629224 | −0.00275933 | ||||||||
\(521\) | 18.6397 | 0.816619 | 0.408310 | − | 0.912843i | \(-0.366118\pi\) | ||||
0.408310 | + | 0.912843i | \(0.366118\pi\) | |||||||
\(522\) | 3.41502 | 0.149471 | ||||||||
\(523\) | −17.3550 | −0.758881 | −0.379441 | − | 0.925216i | \(-0.623884\pi\) | ||||
−0.379441 | + | 0.925216i | \(0.623884\pi\) | |||||||
\(524\) | −4.80946 | −0.210102 | ||||||||
\(525\) | 7.47209 | 0.326109 | ||||||||
\(526\) | −10.6232 | −0.463192 | ||||||||
\(527\) | 12.9250 | 0.563023 | ||||||||
\(528\) | 1.80098 | 0.0783777 | ||||||||
\(529\) | 14.7721 | 0.642267 | ||||||||
\(530\) | 0.211163 | 0.00917234 | ||||||||
\(531\) | 22.3224 | 0.968708 | ||||||||
\(532\) | 7.77862 | 0.337246 | ||||||||
\(533\) | −4.49105 | −0.194529 | ||||||||
\(534\) | 3.48212 | 0.150686 | ||||||||
\(535\) | −0.569284 | −0.0246123 | ||||||||
\(536\) | 40.0612 | 1.73038 | ||||||||
\(537\) | −0.724243 | −0.0312534 | ||||||||
\(538\) | 11.2293 | 0.484130 | ||||||||
\(539\) | 16.0511 | 0.691368 | ||||||||
\(540\) | −0.0382847 | −0.00164751 | ||||||||
\(541\) | 13.1985 | 0.567447 | 0.283724 | − | 0.958906i | \(-0.408430\pi\) | ||||
0.283724 | + | 0.958906i | \(0.408430\pi\) | |||||||
\(542\) | −14.3603 | −0.616826 | ||||||||
\(543\) | −7.69311 | −0.330143 | ||||||||
\(544\) | −12.9910 | −0.556985 | ||||||||
\(545\) | −0.0194856 | −0.000834670 0 | ||||||||
\(546\) | −1.21021 | −0.0517924 | ||||||||
\(547\) | 0.526453 | 0.0225095 | 0.0112547 | − | 0.999937i | \(-0.496417\pi\) | ||||
0.0112547 | + | 0.999937i | \(0.496417\pi\) | |||||||
\(548\) | 12.0981 | 0.516804 | ||||||||
\(549\) | −18.4450 | −0.787213 | ||||||||
\(550\) | −11.2125 | −0.478103 | ||||||||
\(551\) | 3.45637 | 0.147246 | ||||||||
\(552\) | 7.15814 | 0.304671 | ||||||||
\(553\) | −31.4229 | −1.33624 | ||||||||
\(554\) | −18.5530 | −0.788241 | ||||||||
\(555\) | 0.0463136 | 0.00196590 | ||||||||
\(556\) | 0.570603 | 0.0241989 | ||||||||
\(557\) | −28.2681 | −1.19776 | −0.598878 | − | 0.800840i | \(-0.704387\pi\) | ||||
−0.598878 | + | 0.800840i | \(0.704387\pi\) | |||||||
\(558\) | 10.5941 | 0.448485 | ||||||||
\(559\) | −2.13936 | −0.0904854 | ||||||||
\(560\) | −0.302050 | −0.0127639 | ||||||||
\(561\) | 2.96209 | 0.125059 | ||||||||
\(562\) | 24.3061 | 1.02529 | ||||||||
\(563\) | 19.1250 | 0.806023 | 0.403012 | − | 0.915195i | \(-0.367963\pi\) | ||||
0.403012 | + | 0.915195i | \(0.367963\pi\) | |||||||
\(564\) | 0.387513 | 0.0163172 | ||||||||
\(565\) | 0.351496 | 0.0147876 | ||||||||
\(566\) | 10.3146 | 0.433554 | ||||||||
\(567\) | 30.4803 | 1.28005 | ||||||||
\(568\) | −4.84902 | −0.203460 | ||||||||
\(569\) | −10.0202 | −0.420067 | −0.210033 | − | 0.977694i | \(-0.567357\pi\) | ||||
−0.210033 | + | 0.977694i | \(0.567357\pi\) | |||||||
\(570\) | 0.0473434 | 0.00198300 | ||||||||
\(571\) | −32.3114 | −1.35219 | −0.676095 | − | 0.736815i | \(-0.736329\pi\) | ||||
−0.676095 | + | 0.736815i | \(0.736329\pi\) | |||||||
\(572\) | −0.724943 | −0.0303114 | ||||||||
\(573\) | 4.97707 | 0.207920 | ||||||||
\(574\) | −31.2708 | −1.30522 | ||||||||
\(575\) | −30.7239 | −1.28128 | ||||||||
\(576\) | −25.1198 | −1.04666 | ||||||||
\(577\) | −31.8860 | −1.32743 | −0.663716 | − | 0.747984i | \(-0.731022\pi\) | ||||
−0.663716 | + | 0.747984i | \(0.731022\pi\) | |||||||
\(578\) | 0.428921 | 0.0178408 | ||||||||
\(579\) | −6.01518 | −0.249982 | ||||||||
\(580\) | 0.0172502 | 0.000716274 0 | ||||||||
\(581\) | −39.9670 | −1.65811 | ||||||||
\(582\) | −2.13090 | −0.0883287 | ||||||||
\(583\) | 10.9602 | 0.453925 | ||||||||
\(584\) | −2.37324 | −0.0982055 | ||||||||
\(585\) | −0.0584804 | −0.00241787 | ||||||||
\(586\) | 18.3862 | 0.759529 | ||||||||
\(587\) | 26.9417 | 1.11200 | 0.556001 | − | 0.831182i | \(-0.312335\pi\) | ||||
0.556001 | + | 0.831182i | \(0.312335\pi\) | |||||||
\(588\) | 1.85014 | 0.0762985 | ||||||||
\(589\) | 10.7224 | 0.441809 | ||||||||
\(590\) | −0.282462 | −0.0116288 | ||||||||
\(591\) | 7.28974 | 0.299860 | ||||||||
\(592\) | 10.2404 | 0.420877 | ||||||||
\(593\) | 4.92949 | 0.202430 | 0.101215 | − | 0.994865i | \(-0.467727\pi\) | ||||
0.101215 | + | 0.994865i | \(0.467727\pi\) | |||||||
\(594\) | 4.97788 | 0.204245 | ||||||||
\(595\) | −0.496783 | −0.0203661 | ||||||||
\(596\) | −2.84143 | −0.116389 | ||||||||
\(597\) | −0.617382 | −0.0252677 | ||||||||
\(598\) | 4.97619 | 0.203491 | ||||||||
\(599\) | 1.56201 | 0.0638219 | 0.0319110 | − | 0.999491i | \(-0.489841\pi\) | ||||
0.0319110 | + | 0.999491i | \(0.489841\pi\) | |||||||
\(600\) | −5.82244 | −0.237700 | ||||||||
\(601\) | −0.516815 | −0.0210813 | −0.0105407 | − | 0.999944i | \(-0.503355\pi\) | ||||
−0.0105407 | + | 0.999944i | \(0.503355\pi\) | |||||||
\(602\) | −14.8962 | −0.607123 | ||||||||
\(603\) | 37.2331 | 1.51625 | ||||||||
\(604\) | 10.5456 | 0.429096 | ||||||||
\(605\) | −0.226149 | −0.00919426 | ||||||||
\(606\) | 4.71151 | 0.191392 | ||||||||
\(607\) | 20.1693 | 0.818648 | 0.409324 | − | 0.912389i | \(-0.365765\pi\) | ||||
0.409324 | + | 0.912389i | \(0.365765\pi\) | |||||||
\(608\) | −10.7772 | −0.437071 | ||||||||
\(609\) | 1.49469 | 0.0605679 | ||||||||
\(610\) | 0.233398 | 0.00945002 | ||||||||
\(611\) | 1.21362 | 0.0490979 | ||||||||
\(612\) | −6.79062 | −0.274495 | ||||||||
\(613\) | 31.3265 | 1.26527 | 0.632633 | − | 0.774452i | \(-0.281974\pi\) | ||||
0.632633 | + | 0.774452i | \(0.281974\pi\) | |||||||
\(614\) | −4.42121 | −0.178426 | ||||||||
\(615\) | 0.0759759 | 0.00306365 | ||||||||
\(616\) | −22.7402 | −0.916231 | ||||||||
\(617\) | 26.6442 | 1.07265 | 0.536327 | − | 0.844010i | \(-0.319811\pi\) | ||||
0.536327 | + | 0.844010i | \(0.319811\pi\) | |||||||
\(618\) | −5.45053 | −0.219252 | ||||||||
\(619\) | 21.6375 | 0.869686 | 0.434843 | − | 0.900506i | \(-0.356804\pi\) | ||||
0.434843 | + | 0.900506i | \(0.356804\pi\) | |||||||
\(620\) | 0.0535137 | 0.00214916 | ||||||||
\(621\) | 13.6401 | 0.547359 | ||||||||
\(622\) | 30.0266 | 1.20396 | ||||||||
\(623\) | −30.3118 | −1.21442 | ||||||||
\(624\) | 0.650142 | 0.0260265 | ||||||||
\(625\) | 24.9863 | 0.999452 | ||||||||
\(626\) | 38.2573 | 1.52907 | ||||||||
\(627\) | 2.45731 | 0.0981353 | ||||||||
\(628\) | −3.34654 | −0.133541 | ||||||||
\(629\) | 16.8424 | 0.671552 | ||||||||
\(630\) | −0.407193 | −0.0162230 | ||||||||
\(631\) | 28.5404 | 1.13618 | 0.568088 | − | 0.822968i | \(-0.307683\pi\) | ||||
0.568088 | + | 0.822968i | \(0.307683\pi\) | |||||||
\(632\) | 24.4855 | 0.973982 | ||||||||
\(633\) | −4.44397 | −0.176632 | ||||||||
\(634\) | 38.7594 | 1.53933 | ||||||||
\(635\) | −0.135774 | −0.00538802 | ||||||||
\(636\) | 1.26334 | 0.0500946 | ||||||||
\(637\) | 5.79432 | 0.229579 | ||||||||
\(638\) | −2.24291 | −0.0887977 | ||||||||
\(639\) | −4.50670 | −0.178282 | ||||||||
\(640\) | 0.129333 | 0.00511235 | ||||||||
\(641\) | 30.7200 | 1.21337 | 0.606684 | − | 0.794943i | \(-0.292499\pi\) | ||||
0.606684 | + | 0.794943i | \(0.292499\pi\) | |||||||
\(642\) | 8.53197 | 0.336730 | ||||||||
\(643\) | −25.9826 | −1.02465 | −0.512327 | − | 0.858791i | \(-0.671216\pi\) | ||||
−0.512327 | + | 0.858791i | \(0.671216\pi\) | |||||||
\(644\) | −13.8315 | −0.545036 | ||||||||
\(645\) | 0.0361920 | 0.00142506 | ||||||||
\(646\) | 17.2170 | 0.677392 | ||||||||
\(647\) | 12.8682 | 0.505903 | 0.252951 | − | 0.967479i | \(-0.418599\pi\) | ||||
0.252951 | + | 0.967479i | \(0.418599\pi\) | |||||||
\(648\) | −23.7510 | −0.933029 | ||||||||
\(649\) | −14.6608 | −0.575489 | ||||||||
\(650\) | −4.04764 | −0.158761 | ||||||||
\(651\) | 4.63685 | 0.181733 | ||||||||
\(652\) | −5.28128 | −0.206831 | ||||||||
\(653\) | 41.8671 | 1.63839 | 0.819194 | − | 0.573517i | \(-0.194421\pi\) | ||||
0.819194 | + | 0.573517i | \(0.194421\pi\) | |||||||
\(654\) | 0.292034 | 0.0114194 | ||||||||
\(655\) | 0.254813 | 0.00995638 | ||||||||
\(656\) | 16.7990 | 0.655892 | ||||||||
\(657\) | −2.20570 | −0.0860527 | ||||||||
\(658\) | 8.45034 | 0.329429 | ||||||||
\(659\) | −10.1048 | −0.393625 | −0.196813 | − | 0.980441i | \(-0.563059\pi\) | ||||
−0.196813 | + | 0.980441i | \(0.563059\pi\) | |||||||
\(660\) | 0.0122640 | 0.000477375 0 | ||||||||
\(661\) | 2.13762 | 0.0831438 | 0.0415719 | − | 0.999136i | \(-0.486763\pi\) | ||||
0.0415719 | + | 0.999136i | \(0.486763\pi\) | |||||||
\(662\) | 35.0806 | 1.36345 | ||||||||
\(663\) | 1.06929 | 0.0415279 | ||||||||
\(664\) | 31.1433 | 1.20859 | ||||||||
\(665\) | −0.412124 | −0.0159815 | ||||||||
\(666\) | 13.8051 | 0.534936 | ||||||||
\(667\) | −6.14590 | −0.237970 | ||||||||
\(668\) | 8.92179 | 0.345195 | ||||||||
\(669\) | 8.58435 | 0.331890 | ||||||||
\(670\) | −0.471139 | −0.0182017 | ||||||||
\(671\) | 12.1143 | 0.467666 | ||||||||
\(672\) | −4.66053 | −0.179784 | ||||||||
\(673\) | 41.5513 | 1.60169 | 0.800843 | − | 0.598874i | \(-0.204385\pi\) | ||||
0.800843 | + | 0.598874i | \(0.204385\pi\) | |||||||
\(674\) | −36.6374 | −1.41122 | ||||||||
\(675\) | −11.0949 | −0.427043 | ||||||||
\(676\) | 7.15614 | 0.275236 | ||||||||
\(677\) | −17.3113 | −0.665326 | −0.332663 | − | 0.943046i | \(-0.607947\pi\) | ||||
−0.332663 | + | 0.943046i | \(0.607947\pi\) | |||||||
\(678\) | −5.26794 | −0.202314 | ||||||||
\(679\) | 18.5495 | 0.711864 | ||||||||
\(680\) | 0.387106 | 0.0148448 | ||||||||
\(681\) | −4.07507 | −0.156157 | ||||||||
\(682\) | −6.95799 | −0.266435 | ||||||||
\(683\) | 26.2315 | 1.00372 | 0.501861 | − | 0.864948i | \(-0.332649\pi\) | ||||
0.501861 | + | 0.864948i | \(0.332649\pi\) | |||||||
\(684\) | −5.63340 | −0.215399 | ||||||||
\(685\) | −0.640976 | −0.0244904 | ||||||||
\(686\) | 7.33701 | 0.280128 | ||||||||
\(687\) | −2.79828 | −0.106761 | ||||||||
\(688\) | 8.00241 | 0.305089 | ||||||||
\(689\) | 3.95655 | 0.150733 | ||||||||
\(690\) | −0.0841831 | −0.00320479 | ||||||||
\(691\) | 35.4542 | 1.34874 | 0.674371 | − | 0.738393i | \(-0.264415\pi\) | ||||
0.674371 | + | 0.738393i | \(0.264415\pi\) | |||||||
\(692\) | 11.9965 | 0.456037 | ||||||||
\(693\) | −21.1349 | −0.802848 | ||||||||
\(694\) | 19.0860 | 0.724496 | ||||||||
\(695\) | −0.0302315 | −0.00114675 | ||||||||
\(696\) | −1.16470 | −0.0441479 | ||||||||
\(697\) | 27.6295 | 1.04654 | ||||||||
\(698\) | −24.3547 | −0.921837 | ||||||||
\(699\) | −6.03072 | −0.228103 | ||||||||
\(700\) | 11.2505 | 0.425230 | ||||||||
\(701\) | −25.3920 | −0.959042 | −0.479521 | − | 0.877530i | \(-0.659190\pi\) | ||||
−0.479521 | + | 0.877530i | \(0.659190\pi\) | |||||||
\(702\) | 1.79698 | 0.0678227 | ||||||||
\(703\) | 13.9722 | 0.526973 | ||||||||
\(704\) | 16.4982 | 0.621798 | ||||||||
\(705\) | −0.0205311 | −0.000773245 0 | ||||||||
\(706\) | −21.0867 | −0.793608 | ||||||||
\(707\) | −41.0136 | −1.54248 | ||||||||
\(708\) | −1.68990 | −0.0635102 | ||||||||
\(709\) | −25.3437 | −0.951801 | −0.475901 | − | 0.879499i | \(-0.657878\pi\) | ||||
−0.475901 | + | 0.879499i | \(0.657878\pi\) | |||||||
\(710\) | 0.0570267 | 0.00214017 | ||||||||
\(711\) | 22.7570 | 0.853453 | ||||||||
\(712\) | 23.6197 | 0.885188 | ||||||||
\(713\) | −19.0659 | −0.714024 | ||||||||
\(714\) | 7.44538 | 0.278637 | ||||||||
\(715\) | 0.0384087 | 0.00143640 | ||||||||
\(716\) | −1.09047 | −0.0407529 | ||||||||
\(717\) | 9.14607 | 0.341566 | ||||||||
\(718\) | 37.4064 | 1.39600 | ||||||||
\(719\) | 25.0797 | 0.935313 | 0.467657 | − | 0.883910i | \(-0.345098\pi\) | ||||
0.467657 | + | 0.883910i | \(0.345098\pi\) | |||||||
\(720\) | 0.218749 | 0.00815230 | ||||||||
\(721\) | 47.4468 | 1.76701 | ||||||||
\(722\) | −8.43297 | −0.313843 | ||||||||
\(723\) | 6.88621 | 0.256101 | ||||||||
\(724\) | −11.5833 | −0.430490 | ||||||||
\(725\) | 4.99909 | 0.185661 | ||||||||
\(726\) | 3.38934 | 0.125790 | ||||||||
\(727\) | 51.2949 | 1.90242 | 0.951211 | − | 0.308540i | \(-0.0998405\pi\) | ||||
0.951211 | + | 0.308540i | \(0.0998405\pi\) | |||||||
\(728\) | −8.20907 | −0.304248 | ||||||||
\(729\) | −19.5511 | −0.724115 | ||||||||
\(730\) | 0.0279104 | 0.00103301 | ||||||||
\(731\) | 13.1616 | 0.486800 | ||||||||
\(732\) | 1.39636 | 0.0516111 | ||||||||
\(733\) | −32.0511 | −1.18384 | −0.591918 | − | 0.805998i | \(-0.701629\pi\) | ||||
−0.591918 | + | 0.805998i | \(0.701629\pi\) | |||||||
\(734\) | 0.0146009 | 0.000538931 0 | ||||||||
\(735\) | −0.0980235 | −0.00361565 | ||||||||
\(736\) | 19.1633 | 0.706367 | ||||||||
\(737\) | −24.4539 | −0.900772 | ||||||||
\(738\) | 22.6468 | 0.833640 | ||||||||
\(739\) | 9.53180 | 0.350633 | 0.175316 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175316 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(740\) | 0.0697331 | 0.00256344 | ||||||||
\(741\) | 0.887070 | 0.0325873 | ||||||||
\(742\) | 27.5491 | 1.01136 | ||||||||
\(743\) | 15.8842 | 0.582736 | 0.291368 | − | 0.956611i | \(-0.405890\pi\) | ||||
0.291368 | + | 0.956611i | \(0.405890\pi\) | |||||||
\(744\) | −3.61315 | −0.132465 | ||||||||
\(745\) | 0.150543 | 0.00551548 | ||||||||
\(746\) | −41.8713 | −1.53302 | ||||||||
\(747\) | 28.9447 | 1.05903 | ||||||||
\(748\) | 4.45994 | 0.163071 | ||||||||
\(749\) | −74.2708 | −2.71379 | ||||||||
\(750\) | 0.136962 | 0.00500113 | ||||||||
\(751\) | 8.01121 | 0.292333 | 0.146167 | − | 0.989260i | \(-0.453306\pi\) | ||||
0.146167 | + | 0.989260i | \(0.453306\pi\) | |||||||
\(752\) | −4.53963 | −0.165543 | ||||||||
\(753\) | 3.44578 | 0.125571 | ||||||||
\(754\) | −0.809675 | −0.0294866 | ||||||||
\(755\) | −0.558725 | −0.0203341 | ||||||||
\(756\) | −4.99476 | −0.181658 | ||||||||
\(757\) | 2.88914 | 0.105007 | 0.0525037 | − | 0.998621i | \(-0.483280\pi\) | ||||
0.0525037 | + | 0.998621i | \(0.483280\pi\) | |||||||
\(758\) | 13.2146 | 0.479974 | ||||||||
\(759\) | −4.36943 | −0.158600 | ||||||||
\(760\) | 0.321138 | 0.0116489 | ||||||||
\(761\) | −7.83742 | −0.284106 | −0.142053 | − | 0.989859i | \(-0.545370\pi\) | ||||
−0.142053 | + | 0.989859i | \(0.545370\pi\) | |||||||
\(762\) | 2.03487 | 0.0737155 | ||||||||
\(763\) | −2.54215 | −0.0920321 | ||||||||
\(764\) | 7.49384 | 0.271118 | ||||||||
\(765\) | 0.359778 | 0.0130078 | ||||||||
\(766\) | −2.62509 | −0.0948483 | ||||||||
\(767\) | −5.29246 | −0.191100 | ||||||||
\(768\) | 4.72717 | 0.170577 | ||||||||
\(769\) | −21.1905 | −0.764150 | −0.382075 | − | 0.924131i | \(-0.624790\pi\) | ||||
−0.382075 | + | 0.924131i | \(0.624790\pi\) | |||||||
\(770\) | 0.267436 | 0.00963772 | ||||||||
\(771\) | −7.82389 | −0.281771 | ||||||||
\(772\) | −9.05690 | −0.325965 | ||||||||
\(773\) | 44.9789 | 1.61778 | 0.808890 | − | 0.587961i | \(-0.200069\pi\) | ||||
0.808890 | + | 0.587961i | \(0.200069\pi\) | |||||||
\(774\) | 10.7880 | 0.387768 | ||||||||
\(775\) | 15.5082 | 0.557072 | ||||||||
\(776\) | −14.4542 | −0.518877 | ||||||||
\(777\) | 6.04223 | 0.216764 | ||||||||
\(778\) | 39.1852 | 1.40486 | ||||||||
\(779\) | 22.9210 | 0.821231 | ||||||||
\(780\) | 0.00442721 | 0.000158520 0 | ||||||||
\(781\) | 2.95991 | 0.105914 | ||||||||
\(782\) | −30.6141 | −1.09476 | ||||||||
\(783\) | −2.21938 | −0.0793143 | ||||||||
\(784\) | −21.6740 | −0.774071 | ||||||||
\(785\) | 0.177305 | 0.00632829 | ||||||||
\(786\) | −3.81894 | −0.136217 | ||||||||
\(787\) | −45.1149 | −1.60817 | −0.804087 | − | 0.594512i | \(-0.797345\pi\) | ||||
−0.804087 | + | 0.594512i | \(0.797345\pi\) | |||||||
\(788\) | 10.9760 | 0.391002 | ||||||||
\(789\) | 3.36729 | 0.119879 | ||||||||
\(790\) | −0.287961 | −0.0102452 | ||||||||
\(791\) | 45.8574 | 1.63050 | ||||||||
\(792\) | 16.4689 | 0.585195 | ||||||||
\(793\) | 4.37317 | 0.155296 | ||||||||
\(794\) | −42.3699 | −1.50365 | ||||||||
\(795\) | −0.0669337 | −0.00237389 | ||||||||
\(796\) | −0.929575 | −0.0329479 | ||||||||
\(797\) | 32.7739 | 1.16091 | 0.580455 | − | 0.814292i | \(-0.302875\pi\) | ||||
0.580455 | + | 0.814292i | \(0.302875\pi\) | |||||||
\(798\) | 6.17658 | 0.218649 | ||||||||
\(799\) | −7.46636 | −0.264141 | ||||||||
\(800\) | −15.5874 | −0.551099 | ||||||||
\(801\) | 21.9523 | 0.775647 | ||||||||
\(802\) | −7.21972 | −0.254937 | ||||||||
\(803\) | 1.44866 | 0.0511221 | ||||||||
\(804\) | −2.81871 | −0.0994081 | ||||||||
\(805\) | 0.732813 | 0.0258283 | ||||||||
\(806\) | −2.51179 | −0.0884739 | ||||||||
\(807\) | −3.55943 | −0.125298 | ||||||||
\(808\) | 31.9589 | 1.12431 | ||||||||
\(809\) | −17.5841 | −0.618223 | −0.309112 | − | 0.951026i | \(-0.600032\pi\) | ||||
−0.309112 | + | 0.951026i | \(0.600032\pi\) | |||||||
\(810\) | 0.279323 | 0.00981441 | ||||||||
\(811\) | −39.0338 | −1.37066 | −0.685330 | − | 0.728232i | \(-0.740342\pi\) | ||||
−0.685330 | + | 0.728232i | \(0.740342\pi\) | |||||||
\(812\) | 2.25052 | 0.0789776 | ||||||||
\(813\) | 4.55186 | 0.159641 | ||||||||
\(814\) | −9.06688 | −0.317794 | ||||||||
\(815\) | 0.279811 | 0.00980135 | ||||||||
\(816\) | −3.99975 | −0.140019 | ||||||||
\(817\) | 10.9187 | 0.381997 | ||||||||
\(818\) | 7.95850 | 0.278262 | ||||||||
\(819\) | −7.62955 | −0.266598 | ||||||||
\(820\) | 0.114395 | 0.00399484 | ||||||||
\(821\) | 0.794572 | 0.0277307 | 0.0138654 | − | 0.999904i | \(-0.495586\pi\) | ||||
0.0138654 | + | 0.999904i | \(0.495586\pi\) | |||||||
\(822\) | 9.60643 | 0.335063 | ||||||||
\(823\) | −37.6273 | −1.31161 | −0.655803 | − | 0.754932i | \(-0.727670\pi\) | ||||
−0.655803 | + | 0.754932i | \(0.727670\pi\) | |||||||
\(824\) | −36.9718 | −1.28797 | ||||||||
\(825\) | 3.55410 | 0.123738 | ||||||||
\(826\) | −36.8509 | −1.28221 | ||||||||
\(827\) | −40.2318 | −1.39900 | −0.699499 | − | 0.714634i | \(-0.746593\pi\) | ||||
−0.699499 | + | 0.714634i | \(0.746593\pi\) | |||||||
\(828\) | 10.0170 | 0.348113 | ||||||||
\(829\) | −13.0473 | −0.453152 | −0.226576 | − | 0.973994i | \(-0.572753\pi\) | ||||
−0.226576 | + | 0.973994i | \(0.572753\pi\) | |||||||
\(830\) | −0.366259 | −0.0127130 | ||||||||
\(831\) | 5.88086 | 0.204005 | ||||||||
\(832\) | 5.95573 | 0.206478 | ||||||||
\(833\) | −35.6474 | −1.23511 | ||||||||
\(834\) | 0.453085 | 0.0156890 | ||||||||
\(835\) | −0.472691 | −0.0163582 | ||||||||
\(836\) | 3.69990 | 0.127964 | ||||||||
\(837\) | −6.88501 | −0.237981 | ||||||||
\(838\) | −27.7026 | −0.956970 | ||||||||
\(839\) | −32.5161 | −1.12258 | −0.561289 | − | 0.827620i | \(-0.689695\pi\) | ||||
−0.561289 | + | 0.827620i | \(0.689695\pi\) | |||||||
\(840\) | 0.138874 | 0.00479162 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −7.32655 | −0.252490 | ||||||||
\(843\) | −7.70445 | −0.265355 | ||||||||
\(844\) | −6.69117 | −0.230319 | ||||||||
\(845\) | −0.379144 | −0.0130429 | ||||||||
\(846\) | −6.11987 | −0.210406 | ||||||||
\(847\) | −29.5042 | −1.01378 | ||||||||
\(848\) | −14.7997 | −0.508224 | ||||||||
\(849\) | −3.26948 | −0.112208 | ||||||||
\(850\) | 24.9016 | 0.854116 | ||||||||
\(851\) | −24.8446 | −0.851661 | ||||||||
\(852\) | 0.341176 | 0.0116885 | ||||||||
\(853\) | 22.5792 | 0.773097 | 0.386549 | − | 0.922269i | \(-0.373667\pi\) | ||||
0.386549 | + | 0.922269i | \(0.373667\pi\) | |||||||
\(854\) | 30.4499 | 1.04198 | ||||||||
\(855\) | 0.298467 | 0.0102074 | ||||||||
\(856\) | 57.8737 | 1.97808 | ||||||||
\(857\) | −2.88091 | −0.0984100 | −0.0492050 | − | 0.998789i | \(-0.515669\pi\) | ||||
−0.0492050 | + | 0.998789i | \(0.515669\pi\) | |||||||
\(858\) | −0.575638 | −0.0196520 | ||||||||
\(859\) | −29.2296 | −0.997302 | −0.498651 | − | 0.866803i | \(-0.666171\pi\) | ||||
−0.498651 | + | 0.866803i | \(0.666171\pi\) | |||||||
\(860\) | 0.0544933 | 0.00185821 | ||||||||
\(861\) | 9.91208 | 0.337803 | ||||||||
\(862\) | 17.6731 | 0.601950 | ||||||||
\(863\) | −13.0246 | −0.443362 | −0.221681 | − | 0.975119i | \(-0.571154\pi\) | ||||
−0.221681 | + | 0.975119i | \(0.571154\pi\) | |||||||
\(864\) | 6.92016 | 0.235429 | ||||||||
\(865\) | −0.635593 | −0.0216108 | ||||||||
\(866\) | −2.69449 | −0.0915624 | ||||||||
\(867\) | −0.135958 | −0.00461737 | ||||||||
\(868\) | 6.98158 | 0.236970 | ||||||||
\(869\) | −14.9463 | −0.507018 | ||||||||
\(870\) | 0.0136974 | 0.000464386 0 | ||||||||
\(871\) | −8.82770 | −0.299115 | ||||||||
\(872\) | 1.98091 | 0.0670821 | ||||||||
\(873\) | −13.4338 | −0.454667 | ||||||||
\(874\) | −25.3970 | −0.859067 | ||||||||
\(875\) | −1.19225 | −0.0403054 | ||||||||
\(876\) | 0.166981 | 0.00564177 | ||||||||
\(877\) | −21.9791 | −0.742182 | −0.371091 | − | 0.928597i | \(-0.621016\pi\) | ||||
−0.371091 | + | 0.928597i | \(0.621016\pi\) | |||||||
\(878\) | 16.5240 | 0.557659 | ||||||||
\(879\) | −5.82800 | −0.196574 | ||||||||
\(880\) | −0.143670 | −0.00484311 | ||||||||
\(881\) | 23.9173 | 0.805794 | 0.402897 | − | 0.915245i | \(-0.368003\pi\) | ||||
0.402897 | + | 0.915245i | \(0.368003\pi\) | |||||||
\(882\) | −29.2187 | −0.983845 | ||||||||
\(883\) | 1.71200 | 0.0576133 | 0.0288067 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288067 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(884\) | 1.61001 | 0.0541504 | ||||||||
\(885\) | 0.0895336 | 0.00300964 | ||||||||
\(886\) | −14.9882 | −0.503537 | ||||||||
\(887\) | −16.5012 | −0.554056 | −0.277028 | − | 0.960862i | \(-0.589350\pi\) | ||||
−0.277028 | + | 0.960862i | \(0.589350\pi\) | |||||||
\(888\) | −4.70826 | −0.157999 | ||||||||
\(889\) | −17.7135 | −0.594092 | ||||||||
\(890\) | −0.277779 | −0.00931118 | ||||||||
\(891\) | 14.4980 | 0.485700 | ||||||||
\(892\) | 12.9252 | 0.432769 | ||||||||
\(893\) | −6.19398 | −0.207274 | ||||||||
\(894\) | −2.25622 | −0.0754594 | ||||||||
\(895\) | 0.0577750 | 0.00193121 | ||||||||
\(896\) | 16.8733 | 0.563697 | ||||||||
\(897\) | −1.57733 | −0.0526656 | ||||||||
\(898\) | 3.69002 | 0.123137 | ||||||||
\(899\) | 3.10222 | 0.103465 | ||||||||
\(900\) | −8.14781 | −0.271594 | ||||||||
\(901\) | −24.3412 | −0.810922 | ||||||||
\(902\) | −14.8739 | −0.495248 | ||||||||
\(903\) | 4.72173 | 0.157129 | ||||||||
\(904\) | −35.7333 | −1.18847 | ||||||||
\(905\) | 0.613703 | 0.0204002 | ||||||||
\(906\) | 8.37372 | 0.278198 | ||||||||
\(907\) | −50.3022 | −1.67026 | −0.835128 | − | 0.550055i | \(-0.814607\pi\) | ||||
−0.835128 | + | 0.550055i | \(0.814607\pi\) | |||||||
\(908\) | −6.13572 | −0.203621 | ||||||||
\(909\) | 29.7027 | 0.985178 | ||||||||
\(910\) | 0.0965425 | 0.00320035 | ||||||||
\(911\) | −45.1616 | −1.49627 | −0.748135 | − | 0.663546i | \(-0.769051\pi\) | ||||
−0.748135 | + | 0.663546i | \(0.769051\pi\) | |||||||
\(912\) | −3.31814 | −0.109875 | ||||||||
\(913\) | −19.0103 | −0.629148 | ||||||||
\(914\) | 5.62222 | 0.185966 | ||||||||
\(915\) | −0.0739817 | −0.00244576 | ||||||||
\(916\) | −4.21329 | −0.139211 | ||||||||
\(917\) | 33.2438 | 1.09781 | ||||||||
\(918\) | −11.0552 | −0.364877 | ||||||||
\(919\) | −21.3789 | −0.705226 | −0.352613 | − | 0.935769i | \(-0.614707\pi\) | ||||
−0.352613 | + | 0.935769i | \(0.614707\pi\) | |||||||
\(920\) | −0.571027 | −0.0188262 | ||||||||
\(921\) | 1.40142 | 0.0461783 | ||||||||
\(922\) | 45.1912 | 1.48829 | ||||||||
\(923\) | 1.06851 | 0.0351703 | ||||||||
\(924\) | 1.60000 | 0.0526362 | ||||||||
\(925\) | 20.2086 | 0.664455 | ||||||||
\(926\) | 12.9392 | 0.425207 | ||||||||
\(927\) | −34.3618 | −1.12859 | ||||||||
\(928\) | −3.11805 | −0.102355 | ||||||||
\(929\) | 32.0168 | 1.05044 | 0.525218 | − | 0.850968i | \(-0.323984\pi\) | ||||
0.525218 | + | 0.850968i | \(0.323984\pi\) | |||||||
\(930\) | 0.0424924 | 0.00139338 | ||||||||
\(931\) | −29.5725 | −0.969201 | ||||||||
\(932\) | −9.08029 | −0.297435 | ||||||||
\(933\) | −9.51771 | −0.311596 | ||||||||
\(934\) | −12.6256 | −0.413121 | ||||||||
\(935\) | −0.236295 | −0.00772767 | ||||||||
\(936\) | 5.94514 | 0.194323 | ||||||||
\(937\) | −43.4092 | −1.41812 | −0.709058 | − | 0.705150i | \(-0.750880\pi\) | ||||
−0.709058 | + | 0.705150i | \(0.750880\pi\) | |||||||
\(938\) | −61.4664 | −2.00695 | ||||||||
\(939\) | −12.1266 | −0.395738 | ||||||||
\(940\) | −0.0309131 | −0.00100827 | ||||||||
\(941\) | −50.2495 | −1.63809 | −0.819043 | − | 0.573732i | \(-0.805495\pi\) | ||||
−0.819043 | + | 0.573732i | \(0.805495\pi\) | |||||||
\(942\) | −2.65731 | −0.0865797 | ||||||||
\(943\) | −40.7567 | −1.32722 | ||||||||
\(944\) | 19.7968 | 0.644330 | ||||||||
\(945\) | 0.264631 | 0.00860843 | ||||||||
\(946\) | −7.08536 | −0.230365 | ||||||||
\(947\) | 3.84195 | 0.124847 | 0.0624233 | − | 0.998050i | \(-0.480117\pi\) | ||||
0.0624233 | + | 0.998050i | \(0.480117\pi\) | |||||||
\(948\) | −1.72280 | −0.0559540 | ||||||||
\(949\) | 0.522956 | 0.0169759 | ||||||||
\(950\) | 20.6580 | 0.670233 | ||||||||
\(951\) | −12.2858 | −0.398394 | ||||||||
\(952\) | 50.5032 | 1.63682 | ||||||||
\(953\) | −25.9928 | −0.841991 | −0.420995 | − | 0.907063i | \(-0.638319\pi\) | ||||
−0.420995 | + | 0.907063i | \(0.638319\pi\) | |||||||
\(954\) | −19.9515 | −0.645953 | ||||||||
\(955\) | −0.397036 | −0.0128478 | ||||||||
\(956\) | 13.7710 | 0.445386 | ||||||||
\(957\) | 0.710949 | 0.0229817 | ||||||||
\(958\) | −16.2005 | −0.523415 | ||||||||
\(959\) | −83.6239 | −2.70036 | ||||||||
\(960\) | −0.100754 | −0.00325182 | ||||||||
\(961\) | −21.3763 | −0.689557 | ||||||||
\(962\) | −3.27308 | −0.105528 | ||||||||
\(963\) | 53.7881 | 1.73330 | ||||||||
\(964\) | 10.3684 | 0.333943 | ||||||||
\(965\) | 0.479849 | 0.0154469 | ||||||||
\(966\) | −10.9828 | −0.353366 | ||||||||
\(967\) | 45.5252 | 1.46399 | 0.731995 | − | 0.681309i | \(-0.238589\pi\) | ||||
0.731995 | + | 0.681309i | \(0.238589\pi\) | |||||||
\(968\) | 22.9904 | 0.738940 | ||||||||
\(969\) | −5.45736 | −0.175316 | ||||||||
\(970\) | 0.169988 | 0.00545800 | ||||||||
\(971\) | 7.92777 | 0.254414 | 0.127207 | − | 0.991876i | \(-0.459399\pi\) | ||||
0.127207 | + | 0.991876i | \(0.459399\pi\) | |||||||
\(972\) | 5.47028 | 0.175459 | ||||||||
\(973\) | −3.94410 | −0.126442 | ||||||||
\(974\) | 26.9012 | 0.861971 | ||||||||
\(975\) | 1.28300 | 0.0410890 | ||||||||
\(976\) | −16.3581 | −0.523610 | ||||||||
\(977\) | 17.7730 | 0.568608 | 0.284304 | − | 0.958734i | \(-0.408238\pi\) | ||||
0.284304 | + | 0.958734i | \(0.408238\pi\) | |||||||
\(978\) | −4.19358 | −0.134096 | ||||||||
\(979\) | −14.4178 | −0.460795 | ||||||||
\(980\) | −0.147591 | −0.00471463 | ||||||||
\(981\) | 1.84107 | 0.0587808 | ||||||||
\(982\) | 41.5908 | 1.32722 | ||||||||
\(983\) | −12.1055 | −0.386105 | −0.193052 | − | 0.981188i | \(-0.561839\pi\) | ||||
−0.193052 | + | 0.981188i | \(0.561839\pi\) | |||||||
\(984\) | −7.72375 | −0.246224 | ||||||||
\(985\) | −0.581525 | −0.0185289 | ||||||||
\(986\) | 4.98122 | 0.158634 | ||||||||
\(987\) | −2.67856 | −0.0852594 | ||||||||
\(988\) | 1.33564 | 0.0424923 | ||||||||
\(989\) | −19.4149 | −0.617359 | ||||||||
\(990\) | −0.193681 | −0.00615560 | ||||||||
\(991\) | 33.0534 | 1.04998 | 0.524988 | − | 0.851110i | \(-0.324070\pi\) | ||||
0.524988 | + | 0.851110i | \(0.324070\pi\) | |||||||
\(992\) | −9.67288 | −0.307114 | ||||||||
\(993\) | −11.1197 | −0.352873 | ||||||||
\(994\) | 7.43990 | 0.235979 | ||||||||
\(995\) | 0.0492504 | 0.00156134 | ||||||||
\(996\) | −2.19124 | −0.0694321 | ||||||||
\(997\) | −16.9351 | −0.536339 | −0.268169 | − | 0.963372i | \(-0.586419\pi\) | ||||
−0.268169 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(998\) | 5.59418 | 0.177081 | ||||||||
\(999\) | −8.97178 | −0.283854 |
(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 | 4031.2.a.c.1.43 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.43 | ✓ | 61 | 1.1 | even | 1 | trivial |