Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70774 | −1.91466 | −0.957330 | − | 0.288998i | \(-0.906678\pi\) | ||||
−0.957330 | + | 0.288998i | \(0.906678\pi\) | |||||||
\(3\) | 1.77949 | 1.02739 | 0.513694 | − | 0.857973i | \(-0.328277\pi\) | ||||
0.513694 | + | 0.857973i | \(0.328277\pi\) | |||||||
\(4\) | 5.33184 | 2.66592 | ||||||||
\(5\) | 1.68400 | 0.753109 | 0.376555 | − | 0.926394i | \(-0.377109\pi\) | ||||
0.376555 | + | 0.926394i | \(0.377109\pi\) | |||||||
\(6\) | −4.81839 | −1.96710 | ||||||||
\(7\) | −4.00894 | −1.51524 | −0.757618 | − | 0.652698i | \(-0.773637\pi\) | ||||
−0.757618 | + | 0.652698i | \(0.773637\pi\) | |||||||
\(8\) | −9.02175 | −3.18967 | ||||||||
\(9\) | 0.166582 | 0.0555273 | ||||||||
\(10\) | −4.55984 | −1.44195 | ||||||||
\(11\) | 0.0938184 | 0.0282873 | 0.0141436 | − | 0.999900i | \(-0.495498\pi\) | ||||
0.0141436 | + | 0.999900i | \(0.495498\pi\) | |||||||
\(12\) | 9.48796 | 2.73894 | ||||||||
\(13\) | 5.04814 | 1.40010 | 0.700051 | − | 0.714093i | \(-0.253161\pi\) | ||||
0.700051 | + | 0.714093i | \(0.253161\pi\) | |||||||
\(14\) | 10.8552 | 2.90116 | ||||||||
\(15\) | 2.99667 | 0.773736 | ||||||||
\(16\) | 13.7649 | 3.44121 | ||||||||
\(17\) | −5.54971 | −1.34600 | −0.673001 | − | 0.739641i | \(-0.734995\pi\) | ||||
−0.673001 | + | 0.739641i | \(0.734995\pi\) | |||||||
\(18\) | −0.451060 | −0.106316 | ||||||||
\(19\) | 2.65112 | 0.608210 | 0.304105 | − | 0.952639i | \(-0.401643\pi\) | ||||
0.304105 | + | 0.952639i | \(0.401643\pi\) | |||||||
\(20\) | 8.97884 | 2.00773 | ||||||||
\(21\) | −7.13386 | −1.55674 | ||||||||
\(22\) | −0.254035 | −0.0541605 | ||||||||
\(23\) | 5.90283 | 1.23082 | 0.615412 | − | 0.788206i | \(-0.288990\pi\) | ||||
0.615412 | + | 0.788206i | \(0.288990\pi\) | |||||||
\(24\) | −16.0541 | −3.27703 | ||||||||
\(25\) | −2.16413 | −0.432826 | ||||||||
\(26\) | −13.6690 | −2.68072 | ||||||||
\(27\) | −5.04204 | −0.970340 | ||||||||
\(28\) | −21.3750 | −4.03950 | ||||||||
\(29\) | 6.91321 | 1.28375 | 0.641876 | − | 0.766809i | \(-0.278157\pi\) | ||||
0.641876 | + | 0.766809i | \(0.278157\pi\) | |||||||
\(30\) | −8.11419 | −1.48144 | ||||||||
\(31\) | −7.88387 | −1.41598 | −0.707992 | − | 0.706220i | \(-0.750399\pi\) | ||||
−0.707992 | + | 0.706220i | \(0.750399\pi\) | |||||||
\(32\) | −19.2281 | −3.39908 | ||||||||
\(33\) | 0.166949 | 0.0290620 | ||||||||
\(34\) | 15.0272 | 2.57714 | ||||||||
\(35\) | −6.75107 | −1.14114 | ||||||||
\(36\) | 0.888189 | 0.148031 | ||||||||
\(37\) | −9.02474 | −1.48366 | −0.741829 | − | 0.670589i | \(-0.766042\pi\) | ||||
−0.741829 | + | 0.670589i | \(0.766042\pi\) | |||||||
\(38\) | −7.17855 | −1.16451 | ||||||||
\(39\) | 8.98311 | 1.43845 | ||||||||
\(40\) | −15.1927 | −2.40217 | ||||||||
\(41\) | −9.16330 | −1.43107 | −0.715533 | − | 0.698578i | \(-0.753816\pi\) | ||||
−0.715533 | + | 0.698578i | \(0.753816\pi\) | |||||||
\(42\) | 19.3166 | 2.98062 | ||||||||
\(43\) | 1.20217 | 0.183330 | 0.0916650 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916650 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(44\) | 0.500225 | 0.0754117 | ||||||||
\(45\) | 0.280525 | 0.0418181 | ||||||||
\(46\) | −15.9833 | −2.35661 | ||||||||
\(47\) | 4.52270 | 0.659703 | 0.329852 | − | 0.944033i | \(-0.393001\pi\) | ||||
0.329852 | + | 0.944033i | \(0.393001\pi\) | |||||||
\(48\) | 24.4944 | 3.53546 | ||||||||
\(49\) | 9.07159 | 1.29594 | ||||||||
\(50\) | 5.85990 | 0.828715 | ||||||||
\(51\) | −9.87565 | −1.38287 | ||||||||
\(52\) | 26.9159 | 3.73256 | ||||||||
\(53\) | 7.33830 | 1.00799 | 0.503996 | − | 0.863706i | \(-0.331862\pi\) | ||||
0.503996 | + | 0.863706i | \(0.331862\pi\) | |||||||
\(54\) | 13.6525 | 1.85787 | ||||||||
\(55\) | 0.157990 | 0.0213034 | ||||||||
\(56\) | 36.1677 | 4.83311 | ||||||||
\(57\) | 4.71765 | 0.624868 | ||||||||
\(58\) | −18.7192 | −2.45795 | ||||||||
\(59\) | −10.0866 | −1.31316 | −0.656580 | − | 0.754256i | \(-0.727998\pi\) | ||||
−0.656580 | + | 0.754256i | \(0.727998\pi\) | |||||||
\(60\) | 15.9778 | 2.06272 | ||||||||
\(61\) | −12.3760 | −1.58459 | −0.792293 | − | 0.610140i | \(-0.791113\pi\) | ||||
−0.792293 | + | 0.610140i | \(0.791113\pi\) | |||||||
\(62\) | 21.3474 | 2.71113 | ||||||||
\(63\) | −0.667817 | −0.0841370 | ||||||||
\(64\) | 24.5350 | 3.06687 | ||||||||
\(65\) | 8.50108 | 1.05443 | ||||||||
\(66\) | −0.452053 | −0.0556439 | ||||||||
\(67\) | 1.44119 | 0.176069 | 0.0880346 | − | 0.996117i | \(-0.471941\pi\) | ||||
0.0880346 | + | 0.996117i | \(0.471941\pi\) | |||||||
\(68\) | −29.5902 | −3.58834 | ||||||||
\(69\) | 10.5040 | 1.26453 | ||||||||
\(70\) | 18.2801 | 2.18489 | ||||||||
\(71\) | 10.0688 | 1.19495 | 0.597475 | − | 0.801887i | \(-0.296171\pi\) | ||||
0.597475 | + | 0.801887i | \(0.296171\pi\) | |||||||
\(72\) | −1.50286 | −0.177114 | ||||||||
\(73\) | 6.99331 | 0.818505 | 0.409252 | − | 0.912421i | \(-0.365790\pi\) | ||||
0.409252 | + | 0.912421i | \(0.365790\pi\) | |||||||
\(74\) | 24.4366 | 2.84070 | ||||||||
\(75\) | −3.85105 | −0.444681 | ||||||||
\(76\) | 14.1354 | 1.62144 | ||||||||
\(77\) | −0.376112 | −0.0428619 | ||||||||
\(78\) | −24.3239 | −2.75414 | ||||||||
\(79\) | −14.1156 | −1.58813 | −0.794067 | − | 0.607830i | \(-0.792040\pi\) | ||||
−0.794067 | + | 0.607830i | \(0.792040\pi\) | |||||||
\(80\) | 23.1801 | 2.59161 | ||||||||
\(81\) | −9.47200 | −1.05244 | ||||||||
\(82\) | 24.8118 | 2.74001 | ||||||||
\(83\) | 1.54231 | 0.169290 | 0.0846450 | − | 0.996411i | \(-0.473024\pi\) | ||||
0.0846450 | + | 0.996411i | \(0.473024\pi\) | |||||||
\(84\) | −38.0366 | −4.15014 | ||||||||
\(85\) | −9.34573 | −1.01369 | ||||||||
\(86\) | −3.25517 | −0.351014 | ||||||||
\(87\) | 12.3020 | 1.31891 | ||||||||
\(88\) | −0.846406 | −0.0902272 | ||||||||
\(89\) | 0.446210 | 0.0472982 | 0.0236491 | − | 0.999720i | \(-0.492472\pi\) | ||||
0.0236491 | + | 0.999720i | \(0.492472\pi\) | |||||||
\(90\) | −0.759587 | −0.0800675 | ||||||||
\(91\) | −20.2377 | −2.12149 | ||||||||
\(92\) | 31.4729 | 3.28128 | ||||||||
\(93\) | −14.0293 | −1.45477 | ||||||||
\(94\) | −12.2463 | −1.26311 | ||||||||
\(95\) | 4.46450 | 0.458048 | ||||||||
\(96\) | −34.2162 | −3.49218 | ||||||||
\(97\) | −0.217281 | −0.0220615 | −0.0110308 | − | 0.999939i | \(-0.503511\pi\) | ||||
−0.0110308 | + | 0.999939i | \(0.503511\pi\) | |||||||
\(98\) | −24.5635 | −2.48129 | ||||||||
\(99\) | 0.0156284 | 0.00157072 | ||||||||
\(100\) | −11.5388 | −1.15388 | ||||||||
\(101\) | 4.12847 | 0.410798 | 0.205399 | − | 0.978678i | \(-0.434151\pi\) | ||||
0.205399 | + | 0.978678i | \(0.434151\pi\) | |||||||
\(102\) | 26.7407 | 2.64772 | ||||||||
\(103\) | 16.8605 | 1.66131 | 0.830657 | − | 0.556784i | \(-0.187965\pi\) | ||||
0.830657 | + | 0.556784i | \(0.187965\pi\) | |||||||
\(104\) | −45.5431 | −4.46586 | ||||||||
\(105\) | −12.0135 | −1.17239 | ||||||||
\(106\) | −19.8702 | −1.92996 | ||||||||
\(107\) | −10.5140 | −1.01642 | −0.508211 | − | 0.861233i | \(-0.669693\pi\) | ||||
−0.508211 | + | 0.861233i | \(0.669693\pi\) | |||||||
\(108\) | −26.8833 | −2.58685 | ||||||||
\(109\) | −15.0308 | −1.43969 | −0.719844 | − | 0.694136i | \(-0.755787\pi\) | ||||
−0.719844 | + | 0.694136i | \(0.755787\pi\) | |||||||
\(110\) | −0.427797 | −0.0407888 | ||||||||
\(111\) | −16.0594 | −1.52429 | ||||||||
\(112\) | −55.1825 | −5.21425 | ||||||||
\(113\) | −3.79135 | −0.356660 | −0.178330 | − | 0.983971i | \(-0.557069\pi\) | ||||
−0.178330 | + | 0.983971i | \(0.557069\pi\) | |||||||
\(114\) | −12.7741 | −1.19641 | ||||||||
\(115\) | 9.94038 | 0.926945 | ||||||||
\(116\) | 36.8601 | 3.42238 | ||||||||
\(117\) | 0.840929 | 0.0777439 | ||||||||
\(118\) | 27.3118 | 2.51425 | ||||||||
\(119\) | 22.2484 | 2.03951 | ||||||||
\(120\) | −27.0352 | −2.46796 | ||||||||
\(121\) | −10.9912 | −0.999200 | ||||||||
\(122\) | 33.5110 | 3.03394 | ||||||||
\(123\) | −16.3060 | −1.47026 | ||||||||
\(124\) | −42.0355 | −3.77490 | ||||||||
\(125\) | −12.0644 | −1.07907 | ||||||||
\(126\) | 1.80827 | 0.161094 | ||||||||
\(127\) | 21.7732 | 1.93206 | 0.966030 | − | 0.258429i | \(-0.0832047\pi\) | ||||
0.966030 | + | 0.258429i | \(0.0832047\pi\) | |||||||
\(128\) | −27.9780 | −2.47293 | ||||||||
\(129\) | 2.13926 | 0.188351 | ||||||||
\(130\) | −23.0187 | −2.01887 | ||||||||
\(131\) | −15.8265 | −1.38276 | −0.691382 | − | 0.722489i | \(-0.742998\pi\) | ||||
−0.691382 | + | 0.722489i | \(0.742998\pi\) | |||||||
\(132\) | 0.890144 | 0.0774771 | ||||||||
\(133\) | −10.6282 | −0.921581 | ||||||||
\(134\) | −3.90236 | −0.337113 | ||||||||
\(135\) | −8.49081 | −0.730773 | ||||||||
\(136\) | 50.0681 | 4.29331 | ||||||||
\(137\) | 16.9467 | 1.44786 | 0.723928 | − | 0.689875i | \(-0.242335\pi\) | ||||
0.723928 | + | 0.689875i | \(0.242335\pi\) | |||||||
\(138\) | −28.4421 | −2.42115 | ||||||||
\(139\) | −21.0409 | −1.78466 | −0.892331 | − | 0.451381i | \(-0.850932\pi\) | ||||
−0.892331 | + | 0.451381i | \(0.850932\pi\) | |||||||
\(140\) | −35.9956 | −3.04219 | ||||||||
\(141\) | 8.04809 | 0.677771 | ||||||||
\(142\) | −27.2638 | −2.28792 | ||||||||
\(143\) | 0.473608 | 0.0396051 | ||||||||
\(144\) | 2.29298 | 0.191081 | ||||||||
\(145\) | 11.6419 | 0.966805 | ||||||||
\(146\) | −18.9360 | −1.56716 | ||||||||
\(147\) | 16.1428 | 1.33144 | ||||||||
\(148\) | −48.1185 | −3.95532 | ||||||||
\(149\) | −17.2812 | −1.41573 | −0.707866 | − | 0.706346i | \(-0.750342\pi\) | ||||
−0.707866 | + | 0.706346i | \(0.750342\pi\) | |||||||
\(150\) | 10.4276 | 0.851412 | ||||||||
\(151\) | −10.7563 | −0.875335 | −0.437667 | − | 0.899137i | \(-0.644195\pi\) | ||||
−0.437667 | + | 0.899137i | \(0.644195\pi\) | |||||||
\(152\) | −23.9178 | −1.93999 | ||||||||
\(153\) | −0.924481 | −0.0747399 | ||||||||
\(154\) | 1.01841 | 0.0820660 | ||||||||
\(155\) | −13.2765 | −1.06639 | ||||||||
\(156\) | 47.8965 | 3.83479 | ||||||||
\(157\) | 2.33412 | 0.186283 | 0.0931416 | − | 0.995653i | \(-0.470309\pi\) | ||||
0.0931416 | + | 0.995653i | \(0.470309\pi\) | |||||||
\(158\) | 38.2215 | 3.04074 | ||||||||
\(159\) | 13.0584 | 1.03560 | ||||||||
\(160\) | −32.3802 | −2.55988 | ||||||||
\(161\) | −23.6641 | −1.86499 | ||||||||
\(162\) | 25.6477 | 2.01507 | ||||||||
\(163\) | −5.51055 | −0.431619 | −0.215810 | − | 0.976435i | \(-0.569239\pi\) | ||||
−0.215810 | + | 0.976435i | \(0.569239\pi\) | |||||||
\(164\) | −48.8573 | −3.81511 | ||||||||
\(165\) | 0.281142 | 0.0218869 | ||||||||
\(166\) | −4.17616 | −0.324133 | ||||||||
\(167\) | −14.0507 | −1.08727 | −0.543637 | − | 0.839320i | \(-0.682953\pi\) | ||||
−0.543637 | + | 0.839320i | \(0.682953\pi\) | |||||||
\(168\) | 64.3600 | 4.96548 | ||||||||
\(169\) | 12.4837 | 0.960285 | ||||||||
\(170\) | 25.3058 | 1.94087 | ||||||||
\(171\) | 0.441629 | 0.0337722 | ||||||||
\(172\) | 6.40981 | 0.488743 | ||||||||
\(173\) | 19.1340 | 1.45473 | 0.727365 | − | 0.686251i | \(-0.240745\pi\) | ||||
0.727365 | + | 0.686251i | \(0.240745\pi\) | |||||||
\(174\) | −33.3105 | −2.52527 | ||||||||
\(175\) | 8.67587 | 0.655834 | ||||||||
\(176\) | 1.29140 | 0.0973426 | ||||||||
\(177\) | −17.9489 | −1.34913 | ||||||||
\(178\) | −1.20822 | −0.0905599 | ||||||||
\(179\) | −4.38187 | −0.327516 | −0.163758 | − | 0.986501i | \(-0.552362\pi\) | ||||
−0.163758 | + | 0.986501i | \(0.552362\pi\) | |||||||
\(180\) | 1.49571 | 0.111484 | ||||||||
\(181\) | 26.0463 | 1.93600 | 0.968002 | − | 0.250943i | \(-0.0807407\pi\) | ||||
0.968002 | + | 0.250943i | \(0.0807407\pi\) | |||||||
\(182\) | 54.7983 | 4.06192 | ||||||||
\(183\) | −22.0230 | −1.62799 | ||||||||
\(184\) | −53.2538 | −3.92592 | ||||||||
\(185\) | −15.1977 | −1.11736 | ||||||||
\(186\) | 37.9875 | 2.78538 | ||||||||
\(187\) | −0.520665 | −0.0380748 | ||||||||
\(188\) | 24.1143 | 1.75872 | ||||||||
\(189\) | 20.2132 | 1.47030 | ||||||||
\(190\) | −12.0887 | −0.877007 | ||||||||
\(191\) | 6.65810 | 0.481763 | 0.240882 | − | 0.970555i | \(-0.422563\pi\) | ||||
0.240882 | + | 0.970555i | \(0.422563\pi\) | |||||||
\(192\) | 43.6597 | 3.15087 | ||||||||
\(193\) | −24.0136 | −1.72854 | −0.864269 | − | 0.503030i | \(-0.832219\pi\) | ||||
−0.864269 | + | 0.503030i | \(0.832219\pi\) | |||||||
\(194\) | 0.588340 | 0.0422403 | ||||||||
\(195\) | 15.1276 | 1.08331 | ||||||||
\(196\) | 48.3683 | 3.45488 | ||||||||
\(197\) | −8.03481 | −0.572457 | −0.286228 | − | 0.958161i | \(-0.592402\pi\) | ||||
−0.286228 | + | 0.958161i | \(0.592402\pi\) | |||||||
\(198\) | −0.0423177 | −0.00300739 | ||||||||
\(199\) | −2.16019 | −0.153132 | −0.0765658 | − | 0.997065i | \(-0.524396\pi\) | ||||
−0.0765658 | + | 0.997065i | \(0.524396\pi\) | |||||||
\(200\) | 19.5243 | 1.38057 | ||||||||
\(201\) | 2.56458 | 0.180892 | ||||||||
\(202\) | −11.1788 | −0.786538 | ||||||||
\(203\) | −27.7146 | −1.94519 | ||||||||
\(204\) | −52.6554 | −3.68662 | ||||||||
\(205\) | −15.4310 | −1.07775 | ||||||||
\(206\) | −45.6538 | −3.18085 | ||||||||
\(207\) | 0.983304 | 0.0683444 | ||||||||
\(208\) | 69.4869 | 4.81805 | ||||||||
\(209\) | 0.248724 | 0.0172046 | ||||||||
\(210\) | 32.5293 | 2.24473 | ||||||||
\(211\) | 2.62997 | 0.181055 | 0.0905274 | − | 0.995894i | \(-0.471145\pi\) | ||||
0.0905274 | + | 0.995894i | \(0.471145\pi\) | |||||||
\(212\) | 39.1266 | 2.68723 | ||||||||
\(213\) | 17.9174 | 1.22768 | ||||||||
\(214\) | 28.4690 | 1.94610 | ||||||||
\(215\) | 2.02447 | 0.138067 | ||||||||
\(216\) | 45.4880 | 3.09507 | ||||||||
\(217\) | 31.6059 | 2.14555 | ||||||||
\(218\) | 40.6994 | 2.75651 | ||||||||
\(219\) | 12.4445 | 0.840923 | ||||||||
\(220\) | 0.842380 | 0.0567933 | ||||||||
\(221\) | −28.0157 | −1.88454 | ||||||||
\(222\) | 43.4847 | 2.91850 | ||||||||
\(223\) | −5.44876 | −0.364876 | −0.182438 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182438 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(224\) | 77.0843 | 5.15041 | ||||||||
\(225\) | −0.360505 | −0.0240337 | ||||||||
\(226\) | 10.2660 | 0.682882 | ||||||||
\(227\) | 1.27000 | 0.0842931 | 0.0421466 | − | 0.999111i | \(-0.486580\pi\) | ||||
0.0421466 | + | 0.999111i | \(0.486580\pi\) | |||||||
\(228\) | 25.1537 | 1.66585 | ||||||||
\(229\) | 9.72188 | 0.642440 | 0.321220 | − | 0.947005i | \(-0.395907\pi\) | ||||
0.321220 | + | 0.947005i | \(0.395907\pi\) | |||||||
\(230\) | −26.9159 | −1.77478 | ||||||||
\(231\) | −0.669287 | −0.0440359 | ||||||||
\(232\) | −62.3693 | −4.09474 | ||||||||
\(233\) | −1.09875 | −0.0719818 | −0.0359909 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359909 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(234\) | −2.27701 | −0.148853 | ||||||||
\(235\) | 7.61624 | 0.496829 | ||||||||
\(236\) | −53.7800 | −3.50078 | ||||||||
\(237\) | −25.1186 | −1.63163 | ||||||||
\(238\) | −60.2430 | −3.90497 | ||||||||
\(239\) | 5.28448 | 0.341825 | 0.170912 | − | 0.985286i | \(-0.445329\pi\) | ||||
0.170912 | + | 0.985286i | \(0.445329\pi\) | |||||||
\(240\) | 41.2487 | 2.66259 | ||||||||
\(241\) | −6.33784 | −0.408256 | −0.204128 | − | 0.978944i | \(-0.565436\pi\) | ||||
−0.204128 | + | 0.978944i | \(0.565436\pi\) | |||||||
\(242\) | 29.7613 | 1.91313 | ||||||||
\(243\) | −1.72920 | −0.110929 | ||||||||
\(244\) | −65.9870 | −4.22438 | ||||||||
\(245\) | 15.2766 | 0.975986 | ||||||||
\(246\) | 44.1523 | 2.81505 | ||||||||
\(247\) | 13.3832 | 0.851555 | ||||||||
\(248\) | 71.1263 | 4.51652 | ||||||||
\(249\) | 2.74452 | 0.173927 | ||||||||
\(250\) | 32.6673 | 2.06606 | ||||||||
\(251\) | −19.1093 | −1.20617 | −0.603085 | − | 0.797677i | \(-0.706062\pi\) | ||||
−0.603085 | + | 0.797677i | \(0.706062\pi\) | |||||||
\(252\) | −3.56069 | −0.224303 | ||||||||
\(253\) | 0.553793 | 0.0348167 | ||||||||
\(254\) | −58.9562 | −3.69924 | ||||||||
\(255\) | −16.6306 | −1.04145 | ||||||||
\(256\) | 26.6872 | 1.66795 | ||||||||
\(257\) | 27.4215 | 1.71051 | 0.855253 | − | 0.518210i | \(-0.173402\pi\) | ||||
0.855253 | + | 0.518210i | \(0.173402\pi\) | |||||||
\(258\) | −5.79255 | −0.360628 | ||||||||
\(259\) | 36.1796 | 2.24809 | ||||||||
\(260\) | 45.3264 | 2.81103 | ||||||||
\(261\) | 1.15162 | 0.0712832 | ||||||||
\(262\) | 42.8539 | 2.64752 | ||||||||
\(263\) | −6.59506 | −0.406669 | −0.203335 | − | 0.979109i | \(-0.565178\pi\) | ||||
−0.203335 | + | 0.979109i | \(0.565178\pi\) | |||||||
\(264\) | −1.50617 | −0.0926984 | ||||||||
\(265\) | 12.3577 | 0.759129 | ||||||||
\(266\) | 28.7784 | 1.76451 | ||||||||
\(267\) | 0.794026 | 0.0485936 | ||||||||
\(268\) | 7.68419 | 0.469387 | ||||||||
\(269\) | −23.5132 | −1.43363 | −0.716813 | − | 0.697265i | \(-0.754400\pi\) | ||||
−0.716813 | + | 0.697265i | \(0.754400\pi\) | |||||||
\(270\) | 22.9909 | 1.39918 | ||||||||
\(271\) | −12.8936 | −0.783228 | −0.391614 | − | 0.920130i | \(-0.628083\pi\) | ||||
−0.391614 | + | 0.920130i | \(0.628083\pi\) | |||||||
\(272\) | −76.3910 | −4.63188 | ||||||||
\(273\) | −36.0127 | −2.17959 | ||||||||
\(274\) | −45.8873 | −2.77215 | ||||||||
\(275\) | −0.203035 | −0.0122435 | ||||||||
\(276\) | 56.0057 | 3.37115 | ||||||||
\(277\) | −26.8167 | −1.61126 | −0.805630 | − | 0.592419i | \(-0.798173\pi\) | ||||
−0.805630 | + | 0.592419i | \(0.798173\pi\) | |||||||
\(278\) | 56.9731 | 3.41702 | ||||||||
\(279\) | −1.31331 | −0.0786258 | ||||||||
\(280\) | 60.9065 | 3.63986 | ||||||||
\(281\) | 23.5836 | 1.40688 | 0.703439 | − | 0.710755i | \(-0.251647\pi\) | ||||
0.703439 | + | 0.710755i | \(0.251647\pi\) | |||||||
\(282\) | −21.7921 | −1.29770 | ||||||||
\(283\) | −20.5806 | −1.22339 | −0.611694 | − | 0.791095i | \(-0.709512\pi\) | ||||
−0.611694 | + | 0.791095i | \(0.709512\pi\) | |||||||
\(284\) | 53.6854 | 3.18564 | ||||||||
\(285\) | 7.94454 | 0.470594 | ||||||||
\(286\) | −1.28241 | −0.0758303 | ||||||||
\(287\) | 36.7351 | 2.16840 | ||||||||
\(288\) | −3.20306 | −0.188742 | ||||||||
\(289\) | 13.7993 | 0.811722 | ||||||||
\(290\) | −31.5231 | −1.85110 | ||||||||
\(291\) | −0.386649 | −0.0226658 | ||||||||
\(292\) | 37.2872 | 2.18207 | ||||||||
\(293\) | 13.5061 | 0.789036 | 0.394518 | − | 0.918888i | \(-0.370912\pi\) | ||||
0.394518 | + | 0.918888i | \(0.370912\pi\) | |||||||
\(294\) | −43.7105 | −2.54925 | ||||||||
\(295\) | −16.9858 | −0.988953 | ||||||||
\(296\) | 81.4190 | 4.73238 | ||||||||
\(297\) | −0.473036 | −0.0274483 | ||||||||
\(298\) | 46.7930 | 2.71065 | ||||||||
\(299\) | 29.7983 | 1.72328 | ||||||||
\(300\) | −20.5332 | −1.18548 | ||||||||
\(301\) | −4.81945 | −0.277788 | ||||||||
\(302\) | 29.1252 | 1.67597 | ||||||||
\(303\) | 7.34656 | 0.422049 | ||||||||
\(304\) | 36.4923 | 2.09298 | ||||||||
\(305\) | −20.8413 | −1.19337 | ||||||||
\(306\) | 2.50325 | 0.143101 | ||||||||
\(307\) | −33.4839 | −1.91103 | −0.955515 | − | 0.294943i | \(-0.904699\pi\) | ||||
−0.955515 | + | 0.294943i | \(0.904699\pi\) | |||||||
\(308\) | −2.00537 | −0.114267 | ||||||||
\(309\) | 30.0031 | 1.70682 | ||||||||
\(310\) | 35.9492 | 2.04178 | ||||||||
\(311\) | 22.1081 | 1.25364 | 0.626818 | − | 0.779166i | \(-0.284357\pi\) | ||||
0.626818 | + | 0.779166i | \(0.284357\pi\) | |||||||
\(312\) | −81.0434 | −4.58818 | ||||||||
\(313\) | −18.0176 | −1.01842 | −0.509208 | − | 0.860644i | \(-0.670062\pi\) | ||||
−0.509208 | + | 0.860644i | \(0.670062\pi\) | |||||||
\(314\) | −6.32019 | −0.356669 | ||||||||
\(315\) | −1.12461 | −0.0633644 | ||||||||
\(316\) | −75.2624 | −4.23384 | ||||||||
\(317\) | −19.2900 | −1.08343 | −0.541716 | − | 0.840561i | \(-0.682225\pi\) | ||||
−0.541716 | + | 0.840561i | \(0.682225\pi\) | |||||||
\(318\) | −35.3588 | −1.98282 | ||||||||
\(319\) | 0.648586 | 0.0363138 | ||||||||
\(320\) | 41.3170 | 2.30969 | ||||||||
\(321\) | −18.7095 | −1.04426 | ||||||||
\(322\) | 64.0761 | 3.57082 | ||||||||
\(323\) | −14.7130 | −0.818652 | ||||||||
\(324\) | −50.5032 | −2.80573 | ||||||||
\(325\) | −10.9248 | −0.606001 | ||||||||
\(326\) | 14.9211 | 0.826404 | ||||||||
\(327\) | −26.7471 | −1.47912 | ||||||||
\(328\) | 82.6690 | 4.56463 | ||||||||
\(329\) | −18.1312 | −0.999606 | ||||||||
\(330\) | −0.761260 | −0.0419060 | ||||||||
\(331\) | −33.5686 | −1.84509 | −0.922547 | − | 0.385884i | \(-0.873897\pi\) | ||||
−0.922547 | + | 0.385884i | \(0.873897\pi\) | |||||||
\(332\) | 8.22333 | 0.451314 | ||||||||
\(333\) | −1.50336 | −0.0823836 | ||||||||
\(334\) | 38.0455 | 2.08176 | ||||||||
\(335\) | 2.42697 | 0.132599 | ||||||||
\(336\) | −98.1966 | −5.35706 | ||||||||
\(337\) | −10.2885 | −0.560451 | −0.280226 | − | 0.959934i | \(-0.590409\pi\) | ||||
−0.280226 | + | 0.959934i | \(0.590409\pi\) | |||||||
\(338\) | −33.8026 | −1.83862 | ||||||||
\(339\) | −6.74666 | −0.366428 | ||||||||
\(340\) | −49.8300 | −2.70241 | ||||||||
\(341\) | −0.739651 | −0.0400544 | ||||||||
\(342\) | −1.19582 | −0.0646623 | ||||||||
\(343\) | −8.30489 | −0.448422 | ||||||||
\(344\) | −10.8457 | −0.584762 | ||||||||
\(345\) | 17.6888 | 0.952333 | ||||||||
\(346\) | −51.8098 | −2.78531 | ||||||||
\(347\) | 3.97595 | 0.213440 | 0.106720 | − | 0.994289i | \(-0.465965\pi\) | ||||
0.106720 | + | 0.994289i | \(0.465965\pi\) | |||||||
\(348\) | 65.5922 | 3.51611 | ||||||||
\(349\) | −32.8052 | −1.75602 | −0.878010 | − | 0.478642i | \(-0.841129\pi\) | ||||
−0.878010 | + | 0.478642i | \(0.841129\pi\) | |||||||
\(350\) | −23.4920 | −1.25570 | ||||||||
\(351\) | −25.4529 | −1.35858 | ||||||||
\(352\) | −1.80395 | −0.0961508 | ||||||||
\(353\) | 1.29076 | 0.0687003 | 0.0343502 | − | 0.999410i | \(-0.489064\pi\) | ||||
0.0343502 | + | 0.999410i | \(0.489064\pi\) | |||||||
\(354\) | 48.6010 | 2.58312 | ||||||||
\(355\) | 16.9560 | 0.899929 | ||||||||
\(356\) | 2.37912 | 0.126093 | ||||||||
\(357\) | 39.5909 | 2.09537 | ||||||||
\(358\) | 11.8649 | 0.627082 | ||||||||
\(359\) | 21.0048 | 1.10859 | 0.554294 | − | 0.832321i | \(-0.312988\pi\) | ||||
0.554294 | + | 0.832321i | \(0.312988\pi\) | |||||||
\(360\) | −2.53082 | −0.133386 | ||||||||
\(361\) | −11.9715 | −0.630081 | ||||||||
\(362\) | −70.5265 | −3.70679 | ||||||||
\(363\) | −19.5587 | −1.02657 | ||||||||
\(364\) | −107.904 | −5.65571 | ||||||||
\(365\) | 11.7768 | 0.616424 | ||||||||
\(366\) | 59.6325 | 3.11704 | ||||||||
\(367\) | 18.1579 | 0.947834 | 0.473917 | − | 0.880570i | \(-0.342840\pi\) | ||||
0.473917 | + | 0.880570i | \(0.342840\pi\) | |||||||
\(368\) | 81.2515 | 4.23553 | ||||||||
\(369\) | −1.52644 | −0.0794633 | ||||||||
\(370\) | 41.1514 | 2.13936 | ||||||||
\(371\) | −29.4188 | −1.52735 | ||||||||
\(372\) | −74.8018 | −3.87829 | ||||||||
\(373\) | −3.95098 | −0.204574 | −0.102287 | − | 0.994755i | \(-0.532616\pi\) | ||||
−0.102287 | + | 0.994755i | \(0.532616\pi\) | |||||||
\(374\) | 1.40982 | 0.0729002 | ||||||||
\(375\) | −21.4685 | −1.10863 | ||||||||
\(376\) | −40.8027 | −2.10424 | ||||||||
\(377\) | 34.8988 | 1.79738 | ||||||||
\(378\) | −54.7321 | −2.81511 | ||||||||
\(379\) | 25.1821 | 1.29352 | 0.646759 | − | 0.762694i | \(-0.276124\pi\) | ||||
0.646759 | + | 0.762694i | \(0.276124\pi\) | |||||||
\(380\) | 23.8040 | 1.22112 | ||||||||
\(381\) | 38.7452 | 1.98498 | ||||||||
\(382\) | −18.0284 | −0.922412 | ||||||||
\(383\) | −30.1525 | −1.54072 | −0.770359 | − | 0.637610i | \(-0.779923\pi\) | ||||
−0.770359 | + | 0.637610i | \(0.779923\pi\) | |||||||
\(384\) | −49.7866 | −2.54066 | ||||||||
\(385\) | −0.633374 | −0.0322797 | ||||||||
\(386\) | 65.0226 | 3.30956 | ||||||||
\(387\) | 0.200261 | 0.0101798 | ||||||||
\(388\) | −1.15851 | −0.0588143 | ||||||||
\(389\) | −11.3353 | −0.574722 | −0.287361 | − | 0.957822i | \(-0.592778\pi\) | ||||
−0.287361 | + | 0.957822i | \(0.592778\pi\) | |||||||
\(390\) | −40.9615 | −2.07417 | ||||||||
\(391\) | −32.7590 | −1.65669 | ||||||||
\(392\) | −81.8417 | −4.13363 | ||||||||
\(393\) | −28.1630 | −1.42064 | ||||||||
\(394\) | 21.7562 | 1.09606 | ||||||||
\(395\) | −23.7708 | −1.19604 | ||||||||
\(396\) | 0.0833284 | 0.00418741 | ||||||||
\(397\) | −35.4022 | −1.77678 | −0.888392 | − | 0.459087i | \(-0.848177\pi\) | ||||
−0.888392 | + | 0.459087i | \(0.848177\pi\) | |||||||
\(398\) | 5.84922 | 0.293195 | ||||||||
\(399\) | −18.9128 | −0.946822 | ||||||||
\(400\) | −29.7890 | −1.48945 | ||||||||
\(401\) | −4.12490 | −0.205988 | −0.102994 | − | 0.994682i | \(-0.532842\pi\) | ||||
−0.102994 | + | 0.994682i | \(0.532842\pi\) | |||||||
\(402\) | −6.94421 | −0.346346 | ||||||||
\(403\) | −39.7989 | −1.98252 | ||||||||
\(404\) | 22.0123 | 1.09515 | ||||||||
\(405\) | −15.9509 | −0.792605 | ||||||||
\(406\) | 75.0440 | 3.72437 | ||||||||
\(407\) | −0.846687 | −0.0419687 | ||||||||
\(408\) | 89.0957 | 4.41089 | ||||||||
\(409\) | 1.91853 | 0.0948651 | 0.0474326 | − | 0.998874i | \(-0.484896\pi\) | ||||
0.0474326 | + | 0.998874i | \(0.484896\pi\) | |||||||
\(410\) | 41.7832 | 2.06352 | ||||||||
\(411\) | 30.1565 | 1.48751 | ||||||||
\(412\) | 89.8975 | 4.42893 | ||||||||
\(413\) | 40.4365 | 1.98975 | ||||||||
\(414\) | −2.66253 | −0.130856 | ||||||||
\(415\) | 2.59725 | 0.127494 | ||||||||
\(416\) | −97.0662 | −4.75906 | ||||||||
\(417\) | −37.4420 | −1.83354 | ||||||||
\(418\) | −0.673480 | −0.0329410 | ||||||||
\(419\) | 11.5308 | 0.563314 | 0.281657 | − | 0.959515i | \(-0.409116\pi\) | ||||
0.281657 | + | 0.959515i | \(0.409116\pi\) | |||||||
\(420\) | −64.0538 | −3.12551 | ||||||||
\(421\) | −17.1584 | −0.836248 | −0.418124 | − | 0.908390i | \(-0.637312\pi\) | ||||
−0.418124 | + | 0.908390i | \(0.637312\pi\) | |||||||
\(422\) | −7.12128 | −0.346658 | ||||||||
\(423\) | 0.753400 | 0.0366315 | ||||||||
\(424\) | −66.2043 | −3.21517 | ||||||||
\(425\) | 12.0103 | 0.582585 | ||||||||
\(426\) | −48.5156 | −2.35059 | ||||||||
\(427\) | 49.6147 | 2.40102 | ||||||||
\(428\) | −56.0587 | −2.70970 | ||||||||
\(429\) | 0.842780 | 0.0406898 | ||||||||
\(430\) | −5.48172 | −0.264352 | ||||||||
\(431\) | 30.3698 | 1.46286 | 0.731430 | − | 0.681916i | \(-0.238853\pi\) | ||||
0.731430 | + | 0.681916i | \(0.238853\pi\) | |||||||
\(432\) | −69.4029 | −3.33915 | ||||||||
\(433\) | −21.3831 | −1.02760 | −0.513802 | − | 0.857909i | \(-0.671764\pi\) | ||||
−0.513802 | + | 0.857909i | \(0.671764\pi\) | |||||||
\(434\) | −85.5806 | −4.10800 | ||||||||
\(435\) | 20.7166 | 0.993284 | ||||||||
\(436\) | −80.1417 | −3.83809 | ||||||||
\(437\) | 15.6491 | 0.748599 | ||||||||
\(438\) | −33.6965 | −1.61008 | ||||||||
\(439\) | 24.3736 | 1.16329 | 0.581644 | − | 0.813444i | \(-0.302410\pi\) | ||||
0.581644 | + | 0.813444i | \(0.302410\pi\) | |||||||
\(440\) | −1.42535 | −0.0679509 | ||||||||
\(441\) | 1.51116 | 0.0719602 | ||||||||
\(442\) | 75.8592 | 3.60825 | ||||||||
\(443\) | 20.5892 | 0.978224 | 0.489112 | − | 0.872221i | \(-0.337321\pi\) | ||||
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(444\) | −85.6264 | −4.06365 | ||||||||
\(445\) | 0.751419 | 0.0356207 | ||||||||
\(446\) | 14.7538 | 0.698613 | ||||||||
\(447\) | −30.7517 | −1.45451 | ||||||||
\(448\) | −98.3591 | −4.64703 | ||||||||
\(449\) | 13.4653 | 0.635467 | 0.317733 | − | 0.948180i | \(-0.397078\pi\) | ||||
0.317733 | + | 0.948180i | \(0.397078\pi\) | |||||||
\(450\) | 0.976153 | 0.0460163 | ||||||||
\(451\) | −0.859686 | −0.0404810 | ||||||||
\(452\) | −20.2149 | −0.950827 | ||||||||
\(453\) | −19.1407 | −0.899309 | ||||||||
\(454\) | −3.43884 | −0.161393 | ||||||||
\(455\) | −34.0803 | −1.59771 | ||||||||
\(456\) | −42.5614 | −1.99312 | ||||||||
\(457\) | 9.25597 | 0.432976 | 0.216488 | − | 0.976285i | \(-0.430540\pi\) | ||||
0.216488 | + | 0.976285i | \(0.430540\pi\) | |||||||
\(458\) | −26.3243 | −1.23005 | ||||||||
\(459\) | 27.9818 | 1.30608 | ||||||||
\(460\) | 53.0005 | 2.47116 | ||||||||
\(461\) | 19.2416 | 0.896173 | 0.448086 | − | 0.893990i | \(-0.352106\pi\) | ||||
0.448086 | + | 0.893990i | \(0.352106\pi\) | |||||||
\(462\) | 1.81225 | 0.0843137 | ||||||||
\(463\) | 6.78623 | 0.315383 | 0.157691 | − | 0.987488i | \(-0.449595\pi\) | ||||
0.157691 | + | 0.987488i | \(0.449595\pi\) | |||||||
\(464\) | 95.1593 | 4.41766 | ||||||||
\(465\) | −23.6253 | −1.09560 | ||||||||
\(466\) | 2.97514 | 0.137821 | ||||||||
\(467\) | 27.8902 | 1.29060 | 0.645302 | − | 0.763928i | \(-0.276732\pi\) | ||||
0.645302 | + | 0.763928i | \(0.276732\pi\) | |||||||
\(468\) | 4.48370 | 0.207259 | ||||||||
\(469\) | −5.77764 | −0.266787 | ||||||||
\(470\) | −20.6228 | −0.951258 | ||||||||
\(471\) | 4.15354 | 0.191385 | ||||||||
\(472\) | 90.9986 | 4.18855 | ||||||||
\(473\) | 0.112786 | 0.00518591 | ||||||||
\(474\) | 68.0147 | 3.12402 | ||||||||
\(475\) | −5.73738 | −0.263249 | ||||||||
\(476\) | 118.625 | 5.43718 | ||||||||
\(477\) | 1.22243 | 0.0559711 | ||||||||
\(478\) | −14.3090 | −0.654478 | ||||||||
\(479\) | 4.21852 | 0.192749 | 0.0963745 | − | 0.995345i | \(-0.469275\pi\) | ||||
0.0963745 | + | 0.995345i | \(0.469275\pi\) | |||||||
\(480\) | −57.6202 | −2.62999 | ||||||||
\(481\) | −45.5582 | −2.07727 | ||||||||
\(482\) | 17.1612 | 0.781672 | ||||||||
\(483\) | −42.1100 | −1.91607 | ||||||||
\(484\) | −58.6033 | −2.66379 | ||||||||
\(485\) | −0.365902 | −0.0166147 | ||||||||
\(486\) | 4.68223 | 0.212390 | ||||||||
\(487\) | −1.58960 | −0.0720316 | −0.0360158 | − | 0.999351i | \(-0.511467\pi\) | ||||
−0.0360158 | + | 0.999351i | \(0.511467\pi\) | |||||||
\(488\) | 111.653 | 5.05431 | ||||||||
\(489\) | −9.80596 | −0.443441 | ||||||||
\(490\) | −41.3650 | −1.86868 | ||||||||
\(491\) | −1.19870 | −0.0540968 | −0.0270484 | − | 0.999634i | \(-0.508611\pi\) | ||||
−0.0270484 | + | 0.999634i | \(0.508611\pi\) | |||||||
\(492\) | −86.9410 | −3.91960 | ||||||||
\(493\) | −38.3663 | −1.72793 | ||||||||
\(494\) | −36.2383 | −1.63044 | ||||||||
\(495\) | 0.0263184 | 0.00118292 | ||||||||
\(496\) | −108.520 | −4.87270 | ||||||||
\(497\) | −40.3653 | −1.81063 | ||||||||
\(498\) | −7.43143 | −0.333010 | ||||||||
\(499\) | 37.3369 | 1.67143 | 0.835716 | − | 0.549163i | \(-0.185053\pi\) | ||||
0.835716 | + | 0.549163i | \(0.185053\pi\) | |||||||
\(500\) | −64.3256 | −2.87673 | ||||||||
\(501\) | −25.0030 | −1.11705 | ||||||||
\(502\) | 51.7430 | 2.30941 | ||||||||
\(503\) | −19.2479 | −0.858223 | −0.429112 | − | 0.903251i | \(-0.641173\pi\) | ||||
−0.429112 | + | 0.903251i | \(0.641173\pi\) | |||||||
\(504\) | 6.02488 | 0.268369 | ||||||||
\(505\) | 6.95235 | 0.309376 | ||||||||
\(506\) | −1.49953 | −0.0666621 | ||||||||
\(507\) | 22.2146 | 0.986586 | ||||||||
\(508\) | 116.091 | 5.15072 | ||||||||
\(509\) | −25.9922 | −1.15208 | −0.576041 | − | 0.817421i | \(-0.695403\pi\) | ||||
−0.576041 | + | 0.817421i | \(0.695403\pi\) | |||||||
\(510\) | 45.0314 | 1.99402 | ||||||||
\(511\) | −28.0358 | −1.24023 | ||||||||
\(512\) | −16.3059 | −0.720624 | ||||||||
\(513\) | −13.3671 | −0.590170 | ||||||||
\(514\) | −74.2502 | −3.27504 | ||||||||
\(515\) | 28.3932 | 1.25115 | ||||||||
\(516\) | 11.4062 | 0.502129 | ||||||||
\(517\) | 0.424312 | 0.0186612 | ||||||||
\(518\) | −97.9650 | −4.30433 | ||||||||
\(519\) | 34.0487 | 1.49457 | ||||||||
\(520\) | −76.6947 | −3.36328 | ||||||||
\(521\) | −28.2433 | −1.23736 | −0.618680 | − | 0.785643i | \(-0.712332\pi\) | ||||
−0.618680 | + | 0.785643i | \(0.712332\pi\) | |||||||
\(522\) | −3.11827 | −0.136483 | ||||||||
\(523\) | 19.8619 | 0.868501 | 0.434251 | − | 0.900792i | \(-0.357013\pi\) | ||||
0.434251 | + | 0.900792i | \(0.357013\pi\) | |||||||
\(524\) | −84.3842 | −3.68634 | ||||||||
\(525\) | 15.4386 | 0.673797 | ||||||||
\(526\) | 17.8577 | 0.778633 | ||||||||
\(527\) | 43.7532 | 1.90592 | ||||||||
\(528\) | 2.29803 | 0.100009 | ||||||||
\(529\) | 11.8433 | 0.514928 | ||||||||
\(530\) | −33.4615 | −1.45347 | ||||||||
\(531\) | −1.68024 | −0.0729162 | ||||||||
\(532\) | −56.6679 | −2.45686 | ||||||||
\(533\) | −46.2576 | −2.00364 | ||||||||
\(534\) | −2.15001 | −0.0930402 | ||||||||
\(535\) | −17.7055 | −0.765477 | ||||||||
\(536\) | −13.0021 | −0.561603 | ||||||||
\(537\) | −7.79748 | −0.336486 | ||||||||
\(538\) | 63.6676 | 2.74491 | ||||||||
\(539\) | 0.851082 | 0.0366587 | ||||||||
\(540\) | −45.2717 | −1.94818 | ||||||||
\(541\) | 13.1432 | 0.565071 | 0.282535 | − | 0.959257i | \(-0.408825\pi\) | ||||
0.282535 | + | 0.959257i | \(0.408825\pi\) | |||||||
\(542\) | 34.9124 | 1.49962 | ||||||||
\(543\) | 46.3491 | 1.98903 | ||||||||
\(544\) | 106.710 | 4.57517 | ||||||||
\(545\) | −25.3119 | −1.08424 | ||||||||
\(546\) | 97.5130 | 4.17317 | ||||||||
\(547\) | −0.493534 | −0.0211020 | −0.0105510 | − | 0.999944i | \(-0.503359\pi\) | ||||
−0.0105510 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(548\) | 90.3573 | 3.85987 | ||||||||
\(549\) | −2.06162 | −0.0879878 | ||||||||
\(550\) | 0.549766 | 0.0234421 | ||||||||
\(551\) | 18.3278 | 0.780790 | ||||||||
\(552\) | −94.7646 | −4.03345 | ||||||||
\(553\) | 56.5888 | 2.40640 | ||||||||
\(554\) | 72.6126 | 3.08501 | ||||||||
\(555\) | −27.0441 | −1.14796 | ||||||||
\(556\) | −112.187 | −4.75777 | ||||||||
\(557\) | 0.533101 | 0.0225882 | 0.0112941 | − | 0.999936i | \(-0.496405\pi\) | ||||
0.0112941 | + | 0.999936i | \(0.496405\pi\) | |||||||
\(558\) | 3.55610 | 0.150542 | ||||||||
\(559\) | 6.06874 | 0.256681 | ||||||||
\(560\) | −92.9275 | −3.92690 | ||||||||
\(561\) | −0.926517 | −0.0391176 | ||||||||
\(562\) | −63.8581 | −2.69369 | ||||||||
\(563\) | −22.4495 | −0.946134 | −0.473067 | − | 0.881026i | \(-0.656853\pi\) | ||||
−0.473067 | + | 0.881026i | \(0.656853\pi\) | |||||||
\(564\) | 42.9111 | 1.80689 | ||||||||
\(565\) | −6.38464 | −0.268604 | ||||||||
\(566\) | 55.7268 | 2.34237 | ||||||||
\(567\) | 37.9727 | 1.59470 | ||||||||
\(568\) | −90.8385 | −3.81150 | ||||||||
\(569\) | −9.91094 | −0.415488 | −0.207744 | − | 0.978183i | \(-0.566612\pi\) | ||||
−0.207744 | + | 0.978183i | \(0.566612\pi\) | |||||||
\(570\) | −21.5117 | −0.901027 | ||||||||
\(571\) | 9.03093 | 0.377933 | 0.188966 | − | 0.981984i | \(-0.439486\pi\) | ||||
0.188966 | + | 0.981984i | \(0.439486\pi\) | |||||||
\(572\) | 2.52520 | 0.105584 | ||||||||
\(573\) | 11.8480 | 0.494958 | ||||||||
\(574\) | −99.4690 | −4.15176 | ||||||||
\(575\) | −12.7745 | −0.532733 | ||||||||
\(576\) | 4.08708 | 0.170295 | ||||||||
\(577\) | −0.0902827 | −0.00375852 | −0.00187926 | − | 0.999998i | \(-0.500598\pi\) | ||||
−0.00187926 | + | 0.999998i | \(0.500598\pi\) | |||||||
\(578\) | −37.3648 | −1.55417 | ||||||||
\(579\) | −42.7320 | −1.77588 | ||||||||
\(580\) | 62.0726 | 2.57743 | ||||||||
\(581\) | −6.18301 | −0.256514 | ||||||||
\(582\) | 1.04694 | 0.0433972 | ||||||||
\(583\) | 0.688467 | 0.0285134 | ||||||||
\(584\) | −63.0919 | −2.61076 | ||||||||
\(585\) | 1.41613 | 0.0585496 | ||||||||
\(586\) | −36.5710 | −1.51073 | ||||||||
\(587\) | −1.90877 | −0.0787836 | −0.0393918 | − | 0.999224i | \(-0.512542\pi\) | ||||
−0.0393918 | + | 0.999224i | \(0.512542\pi\) | |||||||
\(588\) | 86.0709 | 3.54950 | ||||||||
\(589\) | −20.9011 | −0.861215 | ||||||||
\(590\) | 45.9932 | 1.89351 | ||||||||
\(591\) | −14.2979 | −0.588135 | ||||||||
\(592\) | −124.224 | −5.10559 | ||||||||
\(593\) | 10.5040 | 0.431347 | 0.215674 | − | 0.976466i | \(-0.430805\pi\) | ||||
0.215674 | + | 0.976466i | \(0.430805\pi\) | |||||||
\(594\) | 1.28086 | 0.0525542 | ||||||||
\(595\) | 37.4665 | 1.53598 | ||||||||
\(596\) | −92.1407 | −3.77423 | ||||||||
\(597\) | −3.84403 | −0.157326 | ||||||||
\(598\) | −80.6859 | −3.29949 | ||||||||
\(599\) | 3.47252 | 0.141884 | 0.0709418 | − | 0.997480i | \(-0.477400\pi\) | ||||
0.0709418 | + | 0.997480i | \(0.477400\pi\) | |||||||
\(600\) | 34.7432 | 1.41839 | ||||||||
\(601\) | −0.00276960 | −0.000112974 0 | −5.64872e−5 | − | 1.00000i | \(-0.500018\pi\) | ||||
−5.64872e−5 | 1.00000i | \(0.500018\pi\) | ||||||||
\(602\) | 13.0498 | 0.531870 | ||||||||
\(603\) | 0.240076 | 0.00977665 | ||||||||
\(604\) | −57.3509 | −2.33357 | ||||||||
\(605\) | −18.5092 | −0.752507 | ||||||||
\(606\) | −19.8926 | −0.808080 | ||||||||
\(607\) | 15.6679 | 0.635940 | 0.317970 | − | 0.948101i | \(-0.396999\pi\) | ||||
0.317970 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(608\) | −50.9761 | −2.06735 | ||||||||
\(609\) | −49.3179 | −1.99846 | ||||||||
\(610\) | 56.4327 | 2.28489 | ||||||||
\(611\) | 22.8312 | 0.923652 | ||||||||
\(612\) | −4.92919 | −0.199251 | ||||||||
\(613\) | 16.3145 | 0.658937 | 0.329469 | − | 0.944167i | \(-0.393130\pi\) | ||||
0.329469 | + | 0.944167i | \(0.393130\pi\) | |||||||
\(614\) | 90.6657 | 3.65897 | ||||||||
\(615\) | −27.4594 | −1.10727 | ||||||||
\(616\) | 3.39319 | 0.136716 | ||||||||
\(617\) | −16.2169 | −0.652868 | −0.326434 | − | 0.945220i | \(-0.605847\pi\) | ||||
−0.326434 | + | 0.945220i | \(0.605847\pi\) | |||||||
\(618\) | −81.2405 | −3.26797 | ||||||||
\(619\) | −4.20536 | −0.169028 | −0.0845138 | − | 0.996422i | \(-0.526934\pi\) | ||||
−0.0845138 | + | 0.996422i | \(0.526934\pi\) | |||||||
\(620\) | −70.7880 | −2.84291 | ||||||||
\(621\) | −29.7623 | −1.19432 | ||||||||
\(622\) | −59.8630 | −2.40029 | ||||||||
\(623\) | −1.78883 | −0.0716679 | ||||||||
\(624\) | 123.651 | 4.95001 | ||||||||
\(625\) | −9.49588 | −0.379835 | ||||||||
\(626\) | 48.7870 | 1.94992 | ||||||||
\(627\) | 0.442602 | 0.0176758 | ||||||||
\(628\) | 12.4452 | 0.496616 | ||||||||
\(629\) | 50.0847 | 1.99701 | ||||||||
\(630\) | 3.04514 | 0.121321 | ||||||||
\(631\) | −8.04819 | −0.320394 | −0.160197 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160197 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(632\) | 127.348 | 5.06563 | ||||||||
\(633\) | 4.68001 | 0.186014 | ||||||||
\(634\) | 52.2322 | 2.07440 | ||||||||
\(635\) | 36.6662 | 1.45505 | ||||||||
\(636\) | 69.6254 | 2.76083 | ||||||||
\(637\) | 45.7947 | 1.81445 | ||||||||
\(638\) | −1.75620 | −0.0695287 | ||||||||
\(639\) | 1.67729 | 0.0663524 | ||||||||
\(640\) | −47.1151 | −1.86239 | ||||||||
\(641\) | −32.9370 | −1.30093 | −0.650467 | − | 0.759535i | \(-0.725427\pi\) | ||||
−0.650467 | + | 0.759535i | \(0.725427\pi\) | |||||||
\(642\) | 50.6603 | 1.99940 | ||||||||
\(643\) | −20.4066 | −0.804757 | −0.402379 | − | 0.915473i | \(-0.631816\pi\) | ||||
−0.402379 | + | 0.915473i | \(0.631816\pi\) | |||||||
\(644\) | −126.173 | −4.97192 | ||||||||
\(645\) | 3.60252 | 0.141849 | ||||||||
\(646\) | 39.8389 | 1.56744 | ||||||||
\(647\) | 16.0600 | 0.631382 | 0.315691 | − | 0.948862i | \(-0.397764\pi\) | ||||
0.315691 | + | 0.948862i | \(0.397764\pi\) | |||||||
\(648\) | 85.4540 | 3.35695 | ||||||||
\(649\) | −0.946306 | −0.0371458 | ||||||||
\(650\) | 29.5816 | 1.16029 | ||||||||
\(651\) | 56.2424 | 2.20431 | ||||||||
\(652\) | −29.3814 | −1.15066 | ||||||||
\(653\) | 18.3918 | 0.719727 | 0.359863 | − | 0.933005i | \(-0.382823\pi\) | ||||
0.359863 | + | 0.933005i | \(0.382823\pi\) | |||||||
\(654\) | 72.4241 | 2.83201 | ||||||||
\(655\) | −26.6518 | −1.04137 | ||||||||
\(656\) | −126.131 | −4.92461 | ||||||||
\(657\) | 1.16496 | 0.0454494 | ||||||||
\(658\) | 49.0946 | 1.91391 | ||||||||
\(659\) | 30.8481 | 1.20167 | 0.600835 | − | 0.799373i | \(-0.294835\pi\) | ||||
0.600835 | + | 0.799373i | \(0.294835\pi\) | |||||||
\(660\) | 1.49901 | 0.0583488 | ||||||||
\(661\) | −0.320457 | −0.0124643 | −0.00623216 | − | 0.999981i | \(-0.501984\pi\) | ||||
−0.00623216 | + | 0.999981i | \(0.501984\pi\) | |||||||
\(662\) | 90.8948 | 3.53273 | ||||||||
\(663\) | −49.8536 | −1.93616 | ||||||||
\(664\) | −13.9143 | −0.539980 | ||||||||
\(665\) | −17.8979 | −0.694052 | ||||||||
\(666\) | 4.07070 | 0.157736 | ||||||||
\(667\) | 40.8075 | 1.58007 | ||||||||
\(668\) | −74.9160 | −2.89859 | ||||||||
\(669\) | −9.69600 | −0.374869 | ||||||||
\(670\) | −6.57159 | −0.253883 | ||||||||
\(671\) | −1.16110 | −0.0448237 | ||||||||
\(672\) | 137.171 | 5.29147 | ||||||||
\(673\) | −4.89177 | −0.188564 | −0.0942819 | − | 0.995546i | \(-0.530055\pi\) | ||||
−0.0942819 | + | 0.995546i | \(0.530055\pi\) | |||||||
\(674\) | 27.8586 | 1.07307 | ||||||||
\(675\) | 10.9116 | 0.419989 | ||||||||
\(676\) | 66.5611 | 2.56004 | ||||||||
\(677\) | −2.37378 | −0.0912319 | −0.0456159 | − | 0.998959i | \(-0.514525\pi\) | ||||
−0.0456159 | + | 0.998959i | \(0.514525\pi\) | |||||||
\(678\) | 18.2682 | 0.701585 | ||||||||
\(679\) | 0.871066 | 0.0334284 | ||||||||
\(680\) | 84.3149 | 3.23333 | ||||||||
\(681\) | 2.25996 | 0.0866018 | ||||||||
\(682\) | 2.00278 | 0.0766905 | ||||||||
\(683\) | 21.2261 | 0.812194 | 0.406097 | − | 0.913830i | \(-0.366890\pi\) | ||||
0.406097 | + | 0.913830i | \(0.366890\pi\) | |||||||
\(684\) | 2.35470 | 0.0900341 | ||||||||
\(685\) | 28.5384 | 1.09039 | ||||||||
\(686\) | 22.4875 | 0.858575 | ||||||||
\(687\) | 17.3000 | 0.660036 | ||||||||
\(688\) | 16.5478 | 0.630877 | ||||||||
\(689\) | 37.0447 | 1.41129 | ||||||||
\(690\) | −47.8966 | −1.82339 | ||||||||
\(691\) | 10.7654 | 0.409535 | 0.204767 | − | 0.978811i | \(-0.434356\pi\) | ||||
0.204767 | + | 0.978811i | \(0.434356\pi\) | |||||||
\(692\) | 102.019 | 3.87820 | ||||||||
\(693\) | −0.0626535 | −0.00238001 | ||||||||
\(694\) | −10.7658 | −0.408665 | ||||||||
\(695\) | −35.4329 | −1.34405 | ||||||||
\(696\) | −110.985 | −4.20689 | ||||||||
\(697\) | 50.8537 | 1.92622 | ||||||||
\(698\) | 88.8278 | 3.36218 | ||||||||
\(699\) | −1.95522 | −0.0739533 | ||||||||
\(700\) | 46.2584 | 1.74840 | ||||||||
\(701\) | 36.7220 | 1.38697 | 0.693486 | − | 0.720470i | \(-0.256074\pi\) | ||||
0.693486 | + | 0.720470i | \(0.256074\pi\) | |||||||
\(702\) | 68.9198 | 2.60121 | ||||||||
\(703\) | −23.9257 | −0.902376 | ||||||||
\(704\) | 2.30183 | 0.0867535 | ||||||||
\(705\) | 13.5530 | 0.510436 | ||||||||
\(706\) | −3.49504 | −0.131538 | ||||||||
\(707\) | −16.5508 | −0.622456 | ||||||||
\(708\) | −95.7010 | −3.59666 | ||||||||
\(709\) | 2.13423 | 0.0801527 | 0.0400763 | − | 0.999197i | \(-0.487240\pi\) | ||||
0.0400763 | + | 0.999197i | \(0.487240\pi\) | |||||||
\(710\) | −45.9123 | −1.72306 | ||||||||
\(711\) | −2.35141 | −0.0881848 | ||||||||
\(712\) | −4.02560 | −0.150866 | ||||||||
\(713\) | −46.5371 | −1.74283 | ||||||||
\(714\) | −107.202 | −4.01192 | ||||||||
\(715\) | 0.797558 | 0.0298270 | ||||||||
\(716\) | −23.3634 | −0.873132 | ||||||||
\(717\) | 9.40367 | 0.351187 | ||||||||
\(718\) | −56.8754 | −2.12257 | ||||||||
\(719\) | 12.5831 | 0.469270 | 0.234635 | − | 0.972084i | \(-0.424611\pi\) | ||||
0.234635 | + | 0.972084i | \(0.424611\pi\) | |||||||
\(720\) | 3.86138 | 0.143905 | ||||||||
\(721\) | −67.5927 | −2.51728 | ||||||||
\(722\) | 32.4158 | 1.20639 | ||||||||
\(723\) | −11.2781 | −0.419438 | ||||||||
\(724\) | 138.875 | 5.16123 | ||||||||
\(725\) | −14.9611 | −0.555641 | ||||||||
\(726\) | 52.9599 | 1.96553 | ||||||||
\(727\) | −8.80514 | −0.326565 | −0.163282 | − | 0.986579i | \(-0.552208\pi\) | ||||
−0.163282 | + | 0.986579i | \(0.552208\pi\) | |||||||
\(728\) | 182.579 | 6.76684 | ||||||||
\(729\) | 25.3389 | 0.938477 | ||||||||
\(730\) | −31.8884 | −1.18024 | ||||||||
\(731\) | −6.67172 | −0.246762 | ||||||||
\(732\) | −117.423 | −4.34008 | ||||||||
\(733\) | −39.7274 | −1.46737 | −0.733683 | − | 0.679492i | \(-0.762200\pi\) | ||||
−0.733683 | + | 0.679492i | \(0.762200\pi\) | |||||||
\(734\) | −49.1668 | −1.81478 | ||||||||
\(735\) | 27.1845 | 1.00272 | ||||||||
\(736\) | −113.500 | −4.18367 | ||||||||
\(737\) | 0.135210 | 0.00498052 | ||||||||
\(738\) | 4.13320 | 0.152145 | ||||||||
\(739\) | 39.4916 | 1.45272 | 0.726362 | − | 0.687313i | \(-0.241210\pi\) | ||||
0.726362 | + | 0.687313i | \(0.241210\pi\) | |||||||
\(740\) | −81.0318 | −2.97879 | ||||||||
\(741\) | 23.8153 | 0.874878 | ||||||||
\(742\) | 79.6584 | 2.92435 | ||||||||
\(743\) | 49.9068 | 1.83090 | 0.915452 | − | 0.402428i | \(-0.131833\pi\) | ||||
0.915452 | + | 0.402428i | \(0.131833\pi\) | |||||||
\(744\) | 126.568 | 4.64023 | ||||||||
\(745\) | −29.1016 | −1.06620 | ||||||||
\(746\) | 10.6982 | 0.391690 | ||||||||
\(747\) | 0.256920 | 0.00940022 | ||||||||
\(748\) | −2.77610 | −0.101504 | ||||||||
\(749\) | 42.1498 | 1.54012 | ||||||||
\(750\) | 58.1311 | 2.12265 | ||||||||
\(751\) | 11.1901 | 0.408334 | 0.204167 | − | 0.978936i | \(-0.434551\pi\) | ||||
0.204167 | + | 0.978936i | \(0.434551\pi\) | |||||||
\(752\) | 62.2543 | 2.27018 | ||||||||
\(753\) | −34.0048 | −1.23921 | ||||||||
\(754\) | −94.4969 | −3.44137 | ||||||||
\(755\) | −18.1136 | −0.659223 | ||||||||
\(756\) | 107.774 | 3.91969 | ||||||||
\(757\) | −7.37130 | −0.267914 | −0.133957 | − | 0.990987i | \(-0.542768\pi\) | ||||
−0.133957 | + | 0.990987i | \(0.542768\pi\) | |||||||
\(758\) | −68.1865 | −2.47665 | ||||||||
\(759\) | 0.985469 | 0.0357703 | ||||||||
\(760\) | −40.2776 | −1.46102 | ||||||||
\(761\) | 1.90260 | 0.0689691 | 0.0344846 | − | 0.999405i | \(-0.489021\pi\) | ||||
0.0344846 | + | 0.999405i | \(0.489021\pi\) | |||||||
\(762\) | −104.912 | −3.80056 | ||||||||
\(763\) | 60.2575 | 2.18147 | ||||||||
\(764\) | 35.4999 | 1.28434 | ||||||||
\(765\) | −1.55683 | −0.0562873 | ||||||||
\(766\) | 81.6449 | 2.94995 | ||||||||
\(767\) | −50.9184 | −1.83856 | ||||||||
\(768\) | 47.4895 | 1.71363 | ||||||||
\(769\) | 21.3282 | 0.769115 | 0.384558 | − | 0.923101i | \(-0.374354\pi\) | ||||
0.384558 | + | 0.923101i | \(0.374354\pi\) | |||||||
\(770\) | 1.71501 | 0.0618047 | ||||||||
\(771\) | 48.7963 | 1.75735 | ||||||||
\(772\) | −128.037 | −4.60815 | ||||||||
\(773\) | 25.2876 | 0.909530 | 0.454765 | − | 0.890611i | \(-0.349723\pi\) | ||||
0.454765 | + | 0.890611i | \(0.349723\pi\) | |||||||
\(774\) | −0.542253 | −0.0194909 | ||||||||
\(775\) | 17.0617 | 0.612875 | ||||||||
\(776\) | 1.96025 | 0.0703690 | ||||||||
\(777\) | 64.3813 | 2.30967 | ||||||||
\(778\) | 30.6930 | 1.10040 | ||||||||
\(779\) | −24.2930 | −0.870389 | ||||||||
\(780\) | 80.6579 | 2.88802 | ||||||||
\(781\) | 0.944641 | 0.0338019 | ||||||||
\(782\) | 88.7027 | 3.17200 | ||||||||
\(783\) | −34.8567 | −1.24568 | ||||||||
\(784\) | 124.869 | 4.45961 | ||||||||
\(785\) | 3.93067 | 0.140292 | ||||||||
\(786\) | 76.2581 | 2.72003 | ||||||||
\(787\) | −53.9186 | −1.92199 | −0.960996 | − | 0.276564i | \(-0.910804\pi\) | ||||
−0.960996 | + | 0.276564i | \(0.910804\pi\) | |||||||
\(788\) | −42.8403 | −1.52612 | ||||||||
\(789\) | −11.7358 | −0.417807 | ||||||||
\(790\) | 64.3651 | 2.29001 | ||||||||
\(791\) | 15.1993 | 0.540424 | ||||||||
\(792\) | −0.140996 | −0.00501007 | ||||||||
\(793\) | −62.4759 | −2.21858 | ||||||||
\(794\) | 95.8597 | 3.40193 | ||||||||
\(795\) | 21.9904 | 0.779920 | ||||||||
\(796\) | −11.5178 | −0.408237 | ||||||||
\(797\) | −16.0796 | −0.569568 | −0.284784 | − | 0.958592i | \(-0.591922\pi\) | ||||
−0.284784 | + | 0.958592i | \(0.591922\pi\) | |||||||
\(798\) | 51.2108 | 1.81284 | ||||||||
\(799\) | −25.0997 | −0.887962 | ||||||||
\(800\) | 41.6121 | 1.47121 | ||||||||
\(801\) | 0.0743305 | 0.00262634 | ||||||||
\(802\) | 11.1692 | 0.394397 | ||||||||
\(803\) | 0.656101 | 0.0231533 | ||||||||
\(804\) | 13.6739 | 0.482243 | ||||||||
\(805\) | −39.8504 | −1.40454 | ||||||||
\(806\) | 107.765 | 3.79585 | ||||||||
\(807\) | −41.8415 | −1.47289 | ||||||||
\(808\) | −37.2460 | −1.31031 | ||||||||
\(809\) | 13.4360 | 0.472386 | 0.236193 | − | 0.971706i | \(-0.424100\pi\) | ||||
0.236193 | + | 0.971706i | \(0.424100\pi\) | |||||||
\(810\) | 43.1908 | 1.51757 | ||||||||
\(811\) | 3.67845 | 0.129168 | 0.0645838 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645838 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(812\) | −147.770 | −5.18571 | ||||||||
\(813\) | −22.9440 | −0.804680 | ||||||||
\(814\) | 2.29261 | 0.0803558 | ||||||||
\(815\) | −9.27978 | −0.325057 | ||||||||
\(816\) | −135.937 | −4.75874 | ||||||||
\(817\) | 3.18711 | 0.111503 | ||||||||
\(818\) | −5.19487 | −0.181634 | ||||||||
\(819\) | −3.37123 | −0.117800 | ||||||||
\(820\) | −82.2758 | −2.87320 | ||||||||
\(821\) | −36.8656 | −1.28662 | −0.643309 | − | 0.765606i | \(-0.722439\pi\) | ||||
−0.643309 | + | 0.765606i | \(0.722439\pi\) | |||||||
\(822\) | −81.6559 | −2.84808 | ||||||||
\(823\) | 21.9538 | 0.765263 | 0.382631 | − | 0.923901i | \(-0.375018\pi\) | ||||
0.382631 | + | 0.923901i | \(0.375018\pi\) | |||||||
\(824\) | −152.111 | −5.29905 | ||||||||
\(825\) | −0.361299 | −0.0125788 | ||||||||
\(826\) | −109.491 | −3.80969 | ||||||||
\(827\) | −49.8488 | −1.73341 | −0.866707 | − | 0.498818i | \(-0.833768\pi\) | ||||
−0.866707 | + | 0.498818i | \(0.833768\pi\) | |||||||
\(828\) | 5.24282 | 0.182201 | ||||||||
\(829\) | −10.1842 | −0.353714 | −0.176857 | − | 0.984237i | \(-0.556593\pi\) | ||||
−0.176857 | + | 0.984237i | \(0.556593\pi\) | |||||||
\(830\) | −7.03267 | −0.244107 | ||||||||
\(831\) | −47.7200 | −1.65539 | ||||||||
\(832\) | 123.856 | 4.29393 | ||||||||
\(833\) | −50.3447 | −1.74434 | ||||||||
\(834\) | 101.383 | 3.51061 | ||||||||
\(835\) | −23.6614 | −0.818836 | ||||||||
\(836\) | 1.32616 | 0.0458661 | ||||||||
\(837\) | 39.7507 | 1.37399 | ||||||||
\(838\) | −31.2223 | −1.07856 | ||||||||
\(839\) | −23.1258 | −0.798391 | −0.399195 | − | 0.916866i | \(-0.630710\pi\) | ||||
−0.399195 | + | 0.916866i | \(0.630710\pi\) | |||||||
\(840\) | 108.382 | 3.73955 | ||||||||
\(841\) | 18.7925 | 0.648017 | ||||||||
\(842\) | 46.4604 | 1.60113 | ||||||||
\(843\) | 41.9667 | 1.44541 | ||||||||
\(844\) | 14.0226 | 0.482678 | ||||||||
\(845\) | 21.0226 | 0.723200 | ||||||||
\(846\) | −2.04001 | −0.0701369 | ||||||||
\(847\) | 44.0630 | 1.51402 | ||||||||
\(848\) | 101.011 | 3.46872 | ||||||||
\(849\) | −36.6229 | −1.25689 | ||||||||
\(850\) | −32.5207 | −1.11545 | ||||||||
\(851\) | −53.2715 | −1.82612 | ||||||||
\(852\) | 95.5326 | 3.27289 | ||||||||
\(853\) | −14.8711 | −0.509178 | −0.254589 | − | 0.967049i | \(-0.581940\pi\) | ||||
−0.254589 | + | 0.967049i | \(0.581940\pi\) | |||||||
\(854\) | −134.344 | −4.59714 | ||||||||
\(855\) | 0.743706 | 0.0254342 | ||||||||
\(856\) | 94.8543 | 3.24205 | ||||||||
\(857\) | −6.61504 | −0.225966 | −0.112983 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112983 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(858\) | −2.28203 | −0.0779072 | ||||||||
\(859\) | −40.4453 | −1.37998 | −0.689988 | − | 0.723821i | \(-0.742384\pi\) | ||||
−0.689988 | + | 0.723821i | \(0.742384\pi\) | |||||||
\(860\) | 10.7941 | 0.368077 | ||||||||
\(861\) | 65.3697 | 2.22779 | ||||||||
\(862\) | −82.2333 | −2.80088 | ||||||||
\(863\) | 2.84697 | 0.0969119 | 0.0484560 | − | 0.998825i | \(-0.484570\pi\) | ||||
0.0484560 | + | 0.998825i | \(0.484570\pi\) | |||||||
\(864\) | 96.9488 | 3.29827 | ||||||||
\(865\) | 32.2217 | 1.09557 | ||||||||
\(866\) | 57.8997 | 1.96751 | ||||||||
\(867\) | 24.5557 | 0.833954 | ||||||||
\(868\) | 168.518 | 5.71987 | ||||||||
\(869\) | −1.32431 | −0.0449240 | ||||||||
\(870\) | −56.0951 | −1.90180 | ||||||||
\(871\) | 7.27532 | 0.246515 | ||||||||
\(872\) | 135.604 | 4.59213 | ||||||||
\(873\) | −0.0361951 | −0.00122502 | ||||||||
\(874\) | −42.3737 | −1.43331 | ||||||||
\(875\) | 48.3655 | 1.63505 | ||||||||
\(876\) | 66.3522 | 2.24183 | ||||||||
\(877\) | 1.77809 | 0.0600420 | 0.0300210 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300210 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(878\) | −65.9972 | −2.22730 | ||||||||
\(879\) | 24.0340 | 0.810646 | ||||||||
\(880\) | 2.17472 | 0.0733097 | ||||||||
\(881\) | −37.3178 | −1.25727 | −0.628634 | − | 0.777702i | \(-0.716385\pi\) | ||||
−0.628634 | + | 0.777702i | \(0.716385\pi\) | |||||||
\(882\) | −4.09183 | −0.137779 | ||||||||
\(883\) | 23.7579 | 0.799516 | 0.399758 | − | 0.916621i | \(-0.369094\pi\) | ||||
0.399758 | + | 0.916621i | \(0.369094\pi\) | |||||||
\(884\) | −149.375 | −5.02404 | ||||||||
\(885\) | −30.2261 | −1.01604 | ||||||||
\(886\) | −55.7502 | −1.87297 | ||||||||
\(887\) | 33.9081 | 1.13852 | 0.569262 | − | 0.822156i | \(-0.307229\pi\) | ||||
0.569262 | + | 0.822156i | \(0.307229\pi\) | |||||||
\(888\) | 144.884 | 4.86200 | ||||||||
\(889\) | −87.2875 | −2.92753 | ||||||||
\(890\) | −2.03465 | −0.0682015 | ||||||||
\(891\) | −0.888647 | −0.0297708 | ||||||||
\(892\) | −29.0519 | −0.972730 | ||||||||
\(893\) | 11.9902 | 0.401238 | ||||||||
\(894\) | 83.2677 | 2.78489 | ||||||||
\(895\) | −7.37908 | −0.246655 | ||||||||
\(896\) | 112.162 | 3.74707 | ||||||||
\(897\) | 53.0257 | 1.77048 | ||||||||
\(898\) | −36.4605 | −1.21670 | ||||||||
\(899\) | −54.5028 | −1.81777 | ||||||||
\(900\) | −1.92216 | −0.0640719 | ||||||||
\(901\) | −40.7254 | −1.35676 | ||||||||
\(902\) | 2.32780 | 0.0775074 | ||||||||
\(903\) | −8.57615 | −0.285396 | ||||||||
\(904\) | 34.2046 | 1.13763 | ||||||||
\(905\) | 43.8620 | 1.45802 | ||||||||
\(906\) | 51.8280 | 1.72187 | ||||||||
\(907\) | 3.99263 | 0.132573 | 0.0662866 | − | 0.997801i | \(-0.478885\pi\) | ||||
0.0662866 | + | 0.997801i | \(0.478885\pi\) | |||||||
\(908\) | 6.77146 | 0.224719 | ||||||||
\(909\) | 0.687728 | 0.0228105 | ||||||||
\(910\) | 92.2806 | 3.05907 | ||||||||
\(911\) | 12.9365 | 0.428605 | 0.214302 | − | 0.976767i | \(-0.431252\pi\) | ||||
0.214302 | + | 0.976767i | \(0.431252\pi\) | |||||||
\(912\) | 64.9377 | 2.15030 | ||||||||
\(913\) | 0.144697 | 0.00478876 | ||||||||
\(914\) | −25.0627 | −0.829002 | ||||||||
\(915\) | −37.0868 | −1.22605 | ||||||||
\(916\) | 51.8355 | 1.71269 | ||||||||
\(917\) | 63.4473 | 2.09522 | ||||||||
\(918\) | −75.7675 | −2.50070 | ||||||||
\(919\) | 15.7623 | 0.519949 | 0.259975 | − | 0.965615i | \(-0.416286\pi\) | ||||
0.259975 | + | 0.965615i | \(0.416286\pi\) | |||||||
\(920\) | −89.6797 | −2.95665 | ||||||||
\(921\) | −59.5843 | −1.96337 | ||||||||
\(922\) | −52.1013 | −1.71587 | ||||||||
\(923\) | 50.8289 | 1.67305 | ||||||||
\(924\) | −3.56853 | −0.117396 | ||||||||
\(925\) | 19.5307 | 0.642166 | ||||||||
\(926\) | −18.3753 | −0.603851 | ||||||||
\(927\) | 2.80866 | 0.0922483 | ||||||||
\(928\) | −132.928 | −4.36357 | ||||||||
\(929\) | −15.3516 | −0.503669 | −0.251835 | − | 0.967770i | \(-0.581034\pi\) | ||||
−0.251835 | + | 0.967770i | \(0.581034\pi\) | |||||||
\(930\) | 63.9712 | 2.09770 | ||||||||
\(931\) | 24.0499 | 0.788204 | ||||||||
\(932\) | −5.85839 | −0.191898 | ||||||||
\(933\) | 39.3412 | 1.28797 | ||||||||
\(934\) | −75.5193 | −2.47107 | ||||||||
\(935\) | −0.876801 | −0.0286745 | ||||||||
\(936\) | −7.58665 | −0.247977 | ||||||||
\(937\) | 39.4822 | 1.28983 | 0.644914 | − | 0.764255i | \(-0.276893\pi\) | ||||
0.644914 | + | 0.764255i | \(0.276893\pi\) | |||||||
\(938\) | 15.6443 | 0.510805 | ||||||||
\(939\) | −32.0622 | −1.04631 | ||||||||
\(940\) | 40.6086 | 1.32451 | ||||||||
\(941\) | −60.8393 | −1.98330 | −0.991652 | − | 0.128945i | \(-0.958841\pi\) | ||||
−0.991652 | + | 0.128945i | \(0.958841\pi\) | |||||||
\(942\) | −11.2467 | −0.366437 | ||||||||
\(943\) | −54.0894 | −1.76139 | ||||||||
\(944\) | −138.840 | −4.51886 | ||||||||
\(945\) | 34.0391 | 1.10729 | ||||||||
\(946\) | −0.305395 | −0.00992925 | ||||||||
\(947\) | −0.622701 | −0.0202351 | −0.0101175 | − | 0.999949i | \(-0.503221\pi\) | ||||
−0.0101175 | + | 0.999949i | \(0.503221\pi\) | |||||||
\(948\) | −133.929 | −4.34980 | ||||||||
\(949\) | 35.3032 | 1.14599 | ||||||||
\(950\) | 15.5353 | 0.504032 | ||||||||
\(951\) | −34.3263 | −1.11311 | ||||||||
\(952\) | −200.720 | −6.50537 | ||||||||
\(953\) | −37.9909 | −1.23064 | −0.615322 | − | 0.788276i | \(-0.710974\pi\) | ||||
−0.615322 | + | 0.788276i | \(0.710974\pi\) | |||||||
\(954\) | −3.31001 | −0.107166 | ||||||||
\(955\) | 11.2123 | 0.362820 | ||||||||
\(956\) | 28.1760 | 0.911277 | ||||||||
\(957\) | 1.15415 | 0.0373084 | ||||||||
\(958\) | −11.4226 | −0.369049 | ||||||||
\(959\) | −67.9384 | −2.19385 | ||||||||
\(960\) | 73.5231 | 2.37295 | ||||||||
\(961\) | 31.1553 | 1.00501 | ||||||||
\(962\) | 123.360 | 3.97727 | ||||||||
\(963\) | −1.75143 | −0.0564392 | ||||||||
\(964\) | −33.7924 | −1.08838 | ||||||||
\(965\) | −40.4390 | −1.30178 | ||||||||
\(966\) | 114.023 | 3.66862 | ||||||||
\(967\) | −35.8008 | −1.15128 | −0.575638 | − | 0.817705i | \(-0.695246\pi\) | ||||
−0.575638 | + | 0.817705i | \(0.695246\pi\) | |||||||
\(968\) | 99.1599 | 3.18712 | ||||||||
\(969\) | −26.1816 | −0.841073 | ||||||||
\(970\) | 0.990766 | 0.0318116 | ||||||||
\(971\) | −26.5224 | −0.851145 | −0.425572 | − | 0.904924i | \(-0.639927\pi\) | ||||
−0.425572 | + | 0.904924i | \(0.639927\pi\) | |||||||
\(972\) | −9.21984 | −0.295727 | ||||||||
\(973\) | 84.3515 | 2.70419 | ||||||||
\(974\) | 4.30422 | 0.137916 | ||||||||
\(975\) | −19.4406 | −0.622598 | ||||||||
\(976\) | −170.354 | −5.45290 | ||||||||
\(977\) | −27.4097 | −0.876913 | −0.438456 | − | 0.898752i | \(-0.644475\pi\) | ||||
−0.438456 | + | 0.898752i | \(0.644475\pi\) | |||||||
\(978\) | 26.5520 | 0.849038 | ||||||||
\(979\) | 0.0418627 | 0.00133794 | ||||||||
\(980\) | 81.4524 | 2.60190 | ||||||||
\(981\) | −2.50386 | −0.0799420 | ||||||||
\(982\) | 3.24578 | 0.103577 | ||||||||
\(983\) | 9.75905 | 0.311265 | 0.155633 | − | 0.987815i | \(-0.450258\pi\) | ||||
0.155633 | + | 0.987815i | \(0.450258\pi\) | |||||||
\(984\) | 147.109 | 4.68965 | ||||||||
\(985\) | −13.5307 | −0.431122 | ||||||||
\(986\) | 103.886 | 3.30840 | ||||||||
\(987\) | −32.2643 | −1.02698 | ||||||||
\(988\) | 71.3573 | 2.27018 | ||||||||
\(989\) | 7.09623 | 0.225647 | ||||||||
\(990\) | −0.0712632 | −0.00226489 | ||||||||
\(991\) | 58.8446 | 1.86926 | 0.934630 | − | 0.355621i | \(-0.115731\pi\) | ||||
0.934630 | + | 0.355621i | \(0.115731\pi\) | |||||||
\(992\) | 151.592 | 4.81305 | ||||||||
\(993\) | −59.7349 | −1.89563 | ||||||||
\(994\) | 109.299 | 3.46675 | ||||||||
\(995\) | −3.63776 | −0.115325 | ||||||||
\(996\) | 14.6333 | 0.463675 | ||||||||
\(997\) | −17.7878 | −0.563346 | −0.281673 | − | 0.959510i | \(-0.590889\pi\) | ||||
−0.281673 | + | 0.959510i | \(0.590889\pi\) | |||||||
\(998\) | −101.099 | −3.20022 | ||||||||
\(999\) | 45.5031 | 1.43965 |
(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 | 4019.2.a.a.1.3 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.a.1.3 | ✓ | 149 | 1.1 | even | 1 | trivial |