Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, 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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0220317756\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.173832 | −0.100362 | −0.0501809 | − | 0.998740i | \(-0.515980\pi\) | ||||
−0.0501809 | + | 0.998740i | \(0.515980\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.31890 | −0.589829 | −0.294914 | − | 0.955524i | \(-0.595291\pi\) | ||||
−0.294914 | + | 0.955524i | \(0.595291\pi\) | |||||||
\(6\) | 0.173832 | 0.0709665 | ||||||||
\(7\) | −4.23696 | −1.60142 | −0.800710 | − | 0.599053i | \(-0.795544\pi\) | ||||
−0.800710 | + | 0.599053i | \(0.795544\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.96978 | −0.989927 | ||||||||
\(10\) | 1.31890 | 0.417072 | ||||||||
\(11\) | −3.61787 | −1.09083 | −0.545414 | − | 0.838167i | \(-0.683628\pi\) | ||||
−0.545414 | + | 0.838167i | \(0.683628\pi\) | |||||||
\(12\) | −0.173832 | −0.0501809 | ||||||||
\(13\) | 3.62079 | 1.00423 | 0.502113 | − | 0.864802i | \(-0.332556\pi\) | ||||
0.502113 | + | 0.864802i | \(0.332556\pi\) | |||||||
\(14\) | 4.23696 | 1.13237 | ||||||||
\(15\) | 0.229266 | 0.0591963 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.39360 | 1.55068 | 0.775338 | − | 0.631546i | \(-0.217579\pi\) | ||||
0.775338 | + | 0.631546i | \(0.217579\pi\) | |||||||
\(18\) | 2.96978 | 0.699984 | ||||||||
\(19\) | −6.69433 | −1.53578 | −0.767892 | − | 0.640579i | \(-0.778694\pi\) | ||||
−0.767892 | + | 0.640579i | \(0.778694\pi\) | |||||||
\(20\) | −1.31890 | −0.294914 | ||||||||
\(21\) | 0.736518 | 0.160721 | ||||||||
\(22\) | 3.61787 | 0.771332 | ||||||||
\(23\) | −9.21759 | −1.92200 | −0.961000 | − | 0.276548i | \(-0.910809\pi\) | ||||
−0.961000 | + | 0.276548i | \(0.910809\pi\) | |||||||
\(24\) | 0.173832 | 0.0354833 | ||||||||
\(25\) | −3.26051 | −0.652102 | ||||||||
\(26\) | −3.62079 | −0.710094 | ||||||||
\(27\) | 1.03774 | 0.199713 | ||||||||
\(28\) | −4.23696 | −0.800710 | ||||||||
\(29\) | −6.74803 | −1.25308 | −0.626539 | − | 0.779390i | \(-0.715529\pi\) | ||||
−0.626539 | + | 0.779390i | \(0.715529\pi\) | |||||||
\(30\) | −0.229266 | −0.0418581 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.628900 | 0.109478 | ||||||||
\(34\) | −6.39360 | −1.09649 | ||||||||
\(35\) | 5.58811 | 0.944563 | ||||||||
\(36\) | −2.96978 | −0.494964 | ||||||||
\(37\) | 10.0326 | 1.64935 | 0.824676 | − | 0.565605i | \(-0.191357\pi\) | ||||
0.824676 | + | 0.565605i | \(0.191357\pi\) | |||||||
\(38\) | 6.69433 | 1.08596 | ||||||||
\(39\) | −0.629408 | −0.100786 | ||||||||
\(40\) | 1.31890 | 0.208536 | ||||||||
\(41\) | −8.49568 | −1.32680 | −0.663401 | − | 0.748264i | \(-0.730888\pi\) | ||||
−0.663401 | + | 0.748264i | \(0.730888\pi\) | |||||||
\(42\) | −0.736518 | −0.113647 | ||||||||
\(43\) | −12.1935 | −1.85949 | −0.929746 | − | 0.368202i | \(-0.879974\pi\) | ||||
−0.929746 | + | 0.368202i | \(0.879974\pi\) | |||||||
\(44\) | −3.61787 | −0.545414 | ||||||||
\(45\) | 3.91684 | 0.583888 | ||||||||
\(46\) | 9.21759 | 1.35906 | ||||||||
\(47\) | 1.87213 | 0.273078 | 0.136539 | − | 0.990635i | \(-0.456402\pi\) | ||||
0.136539 | + | 0.990635i | \(0.456402\pi\) | |||||||
\(48\) | −0.173832 | −0.0250905 | ||||||||
\(49\) | 10.9518 | 1.56454 | ||||||||
\(50\) | 3.26051 | 0.461106 | ||||||||
\(51\) | −1.11141 | −0.155629 | ||||||||
\(52\) | 3.62079 | 0.502113 | ||||||||
\(53\) | −6.92618 | −0.951384 | −0.475692 | − | 0.879612i | \(-0.657802\pi\) | ||||
−0.475692 | + | 0.879612i | \(0.657802\pi\) | |||||||
\(54\) | −1.03774 | −0.141218 | ||||||||
\(55\) | 4.77159 | 0.643402 | ||||||||
\(56\) | 4.23696 | 0.566187 | ||||||||
\(57\) | 1.16369 | 0.154134 | ||||||||
\(58\) | 6.74803 | 0.886059 | ||||||||
\(59\) | −12.6522 | −1.64718 | −0.823590 | − | 0.567186i | \(-0.808032\pi\) | ||||
−0.823590 | + | 0.567186i | \(0.808032\pi\) | |||||||
\(60\) | 0.229266 | 0.0295982 | ||||||||
\(61\) | −6.60424 | −0.845587 | −0.422793 | − | 0.906226i | \(-0.638950\pi\) | ||||
−0.422793 | + | 0.906226i | \(0.638950\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 12.5828 | 1.58529 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.77544 | −0.592321 | ||||||||
\(66\) | −0.628900 | −0.0774123 | ||||||||
\(67\) | −4.94181 | −0.603739 | −0.301869 | − | 0.953349i | \(-0.597611\pi\) | ||||
−0.301869 | + | 0.953349i | \(0.597611\pi\) | |||||||
\(68\) | 6.39360 | 0.775338 | ||||||||
\(69\) | 1.60231 | 0.192895 | ||||||||
\(70\) | −5.58811 | −0.667907 | ||||||||
\(71\) | −2.79897 | −0.332176 | −0.166088 | − | 0.986111i | \(-0.553114\pi\) | ||||
−0.166088 | + | 0.986111i | \(0.553114\pi\) | |||||||
\(72\) | 2.96978 | 0.349992 | ||||||||
\(73\) | 0.608398 | 0.0712076 | 0.0356038 | − | 0.999366i | \(-0.488665\pi\) | ||||
0.0356038 | + | 0.999366i | \(0.488665\pi\) | |||||||
\(74\) | −10.0326 | −1.16627 | ||||||||
\(75\) | 0.566780 | 0.0654462 | ||||||||
\(76\) | −6.69433 | −0.767892 | ||||||||
\(77\) | 15.3287 | 1.74687 | ||||||||
\(78\) | 0.629408 | 0.0712664 | ||||||||
\(79\) | −14.7478 | −1.65926 | −0.829631 | − | 0.558312i | \(-0.811449\pi\) | ||||
−0.829631 | + | 0.558312i | \(0.811449\pi\) | |||||||
\(80\) | −1.31890 | −0.147457 | ||||||||
\(81\) | 8.72896 | 0.969884 | ||||||||
\(82\) | 8.49568 | 0.938191 | ||||||||
\(83\) | −14.4747 | −1.58881 | −0.794403 | − | 0.607391i | \(-0.792216\pi\) | ||||
−0.794403 | + | 0.607391i | \(0.792216\pi\) | |||||||
\(84\) | 0.736518 | 0.0803607 | ||||||||
\(85\) | −8.43250 | −0.914633 | ||||||||
\(86\) | 12.1935 | 1.31486 | ||||||||
\(87\) | 1.17302 | 0.125761 | ||||||||
\(88\) | 3.61787 | 0.385666 | ||||||||
\(89\) | 13.4900 | 1.42994 | 0.714970 | − | 0.699155i | \(-0.246440\pi\) | ||||
0.714970 | + | 0.699155i | \(0.246440\pi\) | |||||||
\(90\) | −3.91684 | −0.412871 | ||||||||
\(91\) | −15.3411 | −1.60819 | ||||||||
\(92\) | −9.21759 | −0.961000 | ||||||||
\(93\) | −0.173832 | −0.0180255 | ||||||||
\(94\) | −1.87213 | −0.193096 | ||||||||
\(95\) | 8.82913 | 0.905850 | ||||||||
\(96\) | 0.173832 | 0.0177416 | ||||||||
\(97\) | −1.00000 | −0.101535 | ||||||||
\(98\) | −10.9518 | −1.10630 | ||||||||
\(99\) | 10.7443 | 1.07984 | ||||||||
\(100\) | −3.26051 | −0.326051 | ||||||||
\(101\) | −13.9642 | −1.38949 | −0.694743 | − | 0.719258i | \(-0.744482\pi\) | ||||
−0.694743 | + | 0.719258i | \(0.744482\pi\) | |||||||
\(102\) | 1.11141 | 0.110046 | ||||||||
\(103\) | 2.32597 | 0.229184 | 0.114592 | − | 0.993413i | \(-0.463444\pi\) | ||||
0.114592 | + | 0.993413i | \(0.463444\pi\) | |||||||
\(104\) | −3.62079 | −0.355047 | ||||||||
\(105\) | −0.971391 | −0.0947981 | ||||||||
\(106\) | 6.92618 | 0.672730 | ||||||||
\(107\) | −12.6743 | −1.22527 | −0.612635 | − | 0.790366i | \(-0.709890\pi\) | ||||
−0.612635 | + | 0.790366i | \(0.709890\pi\) | |||||||
\(108\) | 1.03774 | 0.0998564 | ||||||||
\(109\) | −18.1590 | −1.73932 | −0.869658 | − | 0.493655i | \(-0.835661\pi\) | ||||
−0.869658 | + | 0.493655i | \(0.835661\pi\) | |||||||
\(110\) | −4.77159 | −0.454954 | ||||||||
\(111\) | −1.74399 | −0.165532 | ||||||||
\(112\) | −4.23696 | −0.400355 | ||||||||
\(113\) | 13.0026 | 1.22318 | 0.611591 | − | 0.791174i | \(-0.290530\pi\) | ||||
0.611591 | + | 0.791174i | \(0.290530\pi\) | |||||||
\(114\) | −1.16369 | −0.108989 | ||||||||
\(115\) | 12.1571 | 1.13365 | ||||||||
\(116\) | −6.74803 | −0.626539 | ||||||||
\(117\) | −10.7529 | −0.994110 | ||||||||
\(118\) | 12.6522 | 1.16473 | ||||||||
\(119\) | −27.0894 | −2.48328 | ||||||||
\(120\) | −0.229266 | −0.0209291 | ||||||||
\(121\) | 2.08896 | 0.189906 | ||||||||
\(122\) | 6.60424 | 0.597920 | ||||||||
\(123\) | 1.47682 | 0.133160 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 10.8948 | 0.974457 | ||||||||
\(126\) | −12.5828 | −1.12097 | ||||||||
\(127\) | 8.34281 | 0.740305 | 0.370152 | − | 0.928971i | \(-0.379306\pi\) | ||||
0.370152 | + | 0.928971i | \(0.379306\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.11962 | 0.186622 | ||||||||
\(130\) | 4.77544 | 0.418834 | ||||||||
\(131\) | 15.3536 | 1.34145 | 0.670727 | − | 0.741705i | \(-0.265982\pi\) | ||||
0.670727 | + | 0.741705i | \(0.265982\pi\) | |||||||
\(132\) | 0.628900 | 0.0547388 | ||||||||
\(133\) | 28.3636 | 2.45943 | ||||||||
\(134\) | 4.94181 | 0.426908 | ||||||||
\(135\) | −1.36867 | −0.117796 | ||||||||
\(136\) | −6.39360 | −0.548247 | ||||||||
\(137\) | 5.54086 | 0.473387 | 0.236694 | − | 0.971584i | \(-0.423936\pi\) | ||||
0.236694 | + | 0.971584i | \(0.423936\pi\) | |||||||
\(138\) | −1.60231 | −0.136398 | ||||||||
\(139\) | 6.11248 | 0.518454 | 0.259227 | − | 0.965816i | \(-0.416532\pi\) | ||||
0.259227 | + | 0.965816i | \(0.416532\pi\) | |||||||
\(140\) | 5.58811 | 0.472282 | ||||||||
\(141\) | −0.325436 | −0.0274066 | ||||||||
\(142\) | 2.79897 | 0.234884 | ||||||||
\(143\) | −13.0995 | −1.09544 | ||||||||
\(144\) | −2.96978 | −0.247482 | ||||||||
\(145\) | 8.89995 | 0.739101 | ||||||||
\(146\) | −0.608398 | −0.0503514 | ||||||||
\(147\) | −1.90377 | −0.157021 | ||||||||
\(148\) | 10.0326 | 0.824676 | ||||||||
\(149\) | −4.93241 | −0.404078 | −0.202039 | − | 0.979377i | \(-0.564757\pi\) | ||||
−0.202039 | + | 0.979377i | \(0.564757\pi\) | |||||||
\(150\) | −0.566780 | −0.0462774 | ||||||||
\(151\) | −0.674030 | −0.0548518 | −0.0274259 | − | 0.999624i | \(-0.508731\pi\) | ||||
−0.0274259 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(152\) | 6.69433 | 0.542982 | ||||||||
\(153\) | −18.9876 | −1.53506 | ||||||||
\(154\) | −15.3287 | −1.23523 | ||||||||
\(155\) | −1.31890 | −0.105936 | ||||||||
\(156\) | −0.629408 | −0.0503929 | ||||||||
\(157\) | 11.6883 | 0.932830 | 0.466415 | − | 0.884566i | \(-0.345545\pi\) | ||||
0.466415 | + | 0.884566i | \(0.345545\pi\) | |||||||
\(158\) | 14.7478 | 1.17328 | ||||||||
\(159\) | 1.20399 | 0.0954826 | ||||||||
\(160\) | 1.31890 | 0.104268 | ||||||||
\(161\) | 39.0545 | 3.07793 | ||||||||
\(162\) | −8.72896 | −0.685812 | ||||||||
\(163\) | 11.1027 | 0.869630 | 0.434815 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434815 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(164\) | −8.49568 | −0.663401 | ||||||||
\(165\) | −0.829455 | −0.0645730 | ||||||||
\(166\) | 14.4747 | 1.12346 | ||||||||
\(167\) | −9.06043 | −0.701117 | −0.350558 | − | 0.936541i | \(-0.614008\pi\) | ||||
−0.350558 | + | 0.936541i | \(0.614008\pi\) | |||||||
\(168\) | −0.736518 | −0.0568236 | ||||||||
\(169\) | 0.110086 | 0.00846817 | ||||||||
\(170\) | 8.43250 | 0.646743 | ||||||||
\(171\) | 19.8807 | 1.52032 | ||||||||
\(172\) | −12.1935 | −0.929746 | ||||||||
\(173\) | −12.6604 | −0.962555 | −0.481277 | − | 0.876568i | \(-0.659827\pi\) | ||||
−0.481277 | + | 0.876568i | \(0.659827\pi\) | |||||||
\(174\) | −1.17302 | −0.0889265 | ||||||||
\(175\) | 13.8146 | 1.04429 | ||||||||
\(176\) | −3.61787 | −0.272707 | ||||||||
\(177\) | 2.19936 | 0.165314 | ||||||||
\(178\) | −13.4900 | −1.01112 | ||||||||
\(179\) | 9.89983 | 0.739948 | 0.369974 | − | 0.929042i | \(-0.379367\pi\) | ||||
0.369974 | + | 0.929042i | \(0.379367\pi\) | |||||||
\(180\) | 3.91684 | 0.291944 | ||||||||
\(181\) | −4.97321 | −0.369655 | −0.184828 | − | 0.982771i | \(-0.559173\pi\) | ||||
−0.184828 | + | 0.982771i | \(0.559173\pi\) | |||||||
\(182\) | 15.3411 | 1.13716 | ||||||||
\(183\) | 1.14803 | 0.0848647 | ||||||||
\(184\) | 9.21759 | 0.679530 | ||||||||
\(185\) | −13.2320 | −0.972836 | ||||||||
\(186\) | 0.173832 | 0.0127460 | ||||||||
\(187\) | −23.1312 | −1.69152 | ||||||||
\(188\) | 1.87213 | 0.136539 | ||||||||
\(189\) | −4.39685 | −0.319824 | ||||||||
\(190\) | −8.82913 | −0.640532 | ||||||||
\(191\) | 9.19255 | 0.665150 | 0.332575 | − | 0.943077i | \(-0.392083\pi\) | ||||
0.332575 | + | 0.943077i | \(0.392083\pi\) | |||||||
\(192\) | −0.173832 | −0.0125452 | ||||||||
\(193\) | 3.43888 | 0.247536 | 0.123768 | − | 0.992311i | \(-0.460502\pi\) | ||||
0.123768 | + | 0.992311i | \(0.460502\pi\) | |||||||
\(194\) | 1.00000 | 0.0717958 | ||||||||
\(195\) | 0.830124 | 0.0594464 | ||||||||
\(196\) | 10.9518 | 0.782272 | ||||||||
\(197\) | 23.5917 | 1.68084 | 0.840419 | − | 0.541938i | \(-0.182309\pi\) | ||||
0.840419 | + | 0.541938i | \(0.182309\pi\) | |||||||
\(198\) | −10.7443 | −0.763563 | ||||||||
\(199\) | 3.42905 | 0.243079 | 0.121540 | − | 0.992587i | \(-0.461217\pi\) | ||||
0.121540 | + | 0.992587i | \(0.461217\pi\) | |||||||
\(200\) | 3.26051 | 0.230553 | ||||||||
\(201\) | 0.859045 | 0.0605923 | ||||||||
\(202\) | 13.9642 | 0.982515 | ||||||||
\(203\) | 28.5911 | 2.00670 | ||||||||
\(204\) | −1.11141 | −0.0778144 | ||||||||
\(205\) | 11.2049 | 0.782586 | ||||||||
\(206\) | −2.32597 | −0.162058 | ||||||||
\(207\) | 27.3742 | 1.90264 | ||||||||
\(208\) | 3.62079 | 0.251056 | ||||||||
\(209\) | 24.2192 | 1.67528 | ||||||||
\(210\) | 0.971391 | 0.0670324 | ||||||||
\(211\) | 6.88052 | 0.473674 | 0.236837 | − | 0.971549i | \(-0.423889\pi\) | ||||
0.236837 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(212\) | −6.92618 | −0.475692 | ||||||||
\(213\) | 0.486550 | 0.0333378 | ||||||||
\(214\) | 12.6743 | 0.866396 | ||||||||
\(215\) | 16.0820 | 1.09678 | ||||||||
\(216\) | −1.03774 | −0.0706091 | ||||||||
\(217\) | −4.23696 | −0.287623 | ||||||||
\(218\) | 18.1590 | 1.22988 | ||||||||
\(219\) | −0.105759 | −0.00714653 | ||||||||
\(220\) | 4.77159 | 0.321701 | ||||||||
\(221\) | 23.1499 | 1.55723 | ||||||||
\(222\) | 1.74399 | 0.117049 | ||||||||
\(223\) | 4.06475 | 0.272196 | 0.136098 | − | 0.990695i | \(-0.456544\pi\) | ||||
0.136098 | + | 0.990695i | \(0.456544\pi\) | |||||||
\(224\) | 4.23696 | 0.283094 | ||||||||
\(225\) | 9.68301 | 0.645534 | ||||||||
\(226\) | −13.0026 | −0.864921 | ||||||||
\(227\) | 0.866799 | 0.0575315 | 0.0287657 | − | 0.999586i | \(-0.490842\pi\) | ||||
0.0287657 | + | 0.999586i | \(0.490842\pi\) | |||||||
\(228\) | 1.16369 | 0.0770671 | ||||||||
\(229\) | 15.1554 | 1.00150 | 0.500748 | − | 0.865593i | \(-0.333059\pi\) | ||||
0.500748 | + | 0.865593i | \(0.333059\pi\) | |||||||
\(230\) | −12.1571 | −0.801612 | ||||||||
\(231\) | −2.66462 | −0.175319 | ||||||||
\(232\) | 6.74803 | 0.443030 | ||||||||
\(233\) | 5.38639 | 0.352874 | 0.176437 | − | 0.984312i | \(-0.443543\pi\) | ||||
0.176437 | + | 0.984312i | \(0.443543\pi\) | |||||||
\(234\) | 10.7529 | 0.702942 | ||||||||
\(235\) | −2.46915 | −0.161069 | ||||||||
\(236\) | −12.6522 | −0.823590 | ||||||||
\(237\) | 2.56364 | 0.166527 | ||||||||
\(238\) | 27.0894 | 1.75595 | ||||||||
\(239\) | −17.6518 | −1.14180 | −0.570901 | − | 0.821019i | \(-0.693406\pi\) | ||||
−0.570901 | + | 0.821019i | \(0.693406\pi\) | |||||||
\(240\) | 0.229266 | 0.0147991 | ||||||||
\(241\) | −3.92400 | −0.252767 | −0.126383 | − | 0.991981i | \(-0.540337\pi\) | ||||
−0.126383 | + | 0.991981i | \(0.540337\pi\) | |||||||
\(242\) | −2.08896 | −0.134284 | ||||||||
\(243\) | −4.63058 | −0.297052 | ||||||||
\(244\) | −6.60424 | −0.422793 | ||||||||
\(245\) | −14.4443 | −0.922813 | ||||||||
\(246\) | −1.47682 | −0.0941586 | ||||||||
\(247\) | −24.2387 | −1.54227 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 2.51617 | 0.159456 | ||||||||
\(250\) | −10.8948 | −0.689045 | ||||||||
\(251\) | −27.8382 | −1.75713 | −0.878567 | − | 0.477619i | \(-0.841500\pi\) | ||||
−0.878567 | + | 0.477619i | \(0.841500\pi\) | |||||||
\(252\) | 12.5828 | 0.792644 | ||||||||
\(253\) | 33.3480 | 2.09657 | ||||||||
\(254\) | −8.34281 | −0.523474 | ||||||||
\(255\) | 1.46584 | 0.0917943 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.99512 | 0.124452 | 0.0622262 | − | 0.998062i | \(-0.480180\pi\) | ||||
0.0622262 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(258\) | −2.11962 | −0.131962 | ||||||||
\(259\) | −42.5078 | −2.64131 | ||||||||
\(260\) | −4.77544 | −0.296160 | ||||||||
\(261\) | 20.0402 | 1.24046 | ||||||||
\(262\) | −15.3536 | −0.948551 | ||||||||
\(263\) | 2.99842 | 0.184890 | 0.0924451 | − | 0.995718i | \(-0.470532\pi\) | ||||
0.0924451 | + | 0.995718i | \(0.470532\pi\) | |||||||
\(264\) | −0.628900 | −0.0387061 | ||||||||
\(265\) | 9.13491 | 0.561153 | ||||||||
\(266\) | −28.3636 | −1.73908 | ||||||||
\(267\) | −2.34500 | −0.143511 | ||||||||
\(268\) | −4.94181 | −0.301869 | ||||||||
\(269\) | 4.42303 | 0.269677 | 0.134838 | − | 0.990868i | \(-0.456948\pi\) | ||||
0.134838 | + | 0.990868i | \(0.456948\pi\) | |||||||
\(270\) | 1.36867 | 0.0832946 | ||||||||
\(271\) | 27.8927 | 1.69436 | 0.847181 | − | 0.531304i | \(-0.178298\pi\) | ||||
0.847181 | + | 0.531304i | \(0.178298\pi\) | |||||||
\(272\) | 6.39360 | 0.387669 | ||||||||
\(273\) | 2.66677 | 0.161400 | ||||||||
\(274\) | −5.54086 | −0.334735 | ||||||||
\(275\) | 11.7961 | 0.711331 | ||||||||
\(276\) | 1.60231 | 0.0964477 | ||||||||
\(277\) | −8.08413 | −0.485728 | −0.242864 | − | 0.970060i | \(-0.578087\pi\) | ||||
−0.242864 | + | 0.970060i | \(0.578087\pi\) | |||||||
\(278\) | −6.11248 | −0.366602 | ||||||||
\(279\) | −2.96978 | −0.177796 | ||||||||
\(280\) | −5.58811 | −0.333953 | ||||||||
\(281\) | −32.6934 | −1.95032 | −0.975162 | − | 0.221494i | \(-0.928907\pi\) | ||||
−0.975162 | + | 0.221494i | \(0.928907\pi\) | |||||||
\(282\) | 0.325436 | 0.0193794 | ||||||||
\(283\) | −7.15089 | −0.425076 | −0.212538 | − | 0.977153i | \(-0.568173\pi\) | ||||
−0.212538 | + | 0.977153i | \(0.568173\pi\) | |||||||
\(284\) | −2.79897 | −0.166088 | ||||||||
\(285\) | −1.53478 | −0.0909127 | ||||||||
\(286\) | 13.0995 | 0.774591 | ||||||||
\(287\) | 35.9958 | 2.12477 | ||||||||
\(288\) | 2.96978 | 0.174996 | ||||||||
\(289\) | 23.8781 | 1.40460 | ||||||||
\(290\) | −8.89995 | −0.522623 | ||||||||
\(291\) | 0.173832 | 0.0101902 | ||||||||
\(292\) | 0.608398 | 0.0356038 | ||||||||
\(293\) | −0.212267 | −0.0124008 | −0.00620039 | − | 0.999981i | \(-0.501974\pi\) | ||||
−0.00620039 | + | 0.999981i | \(0.501974\pi\) | |||||||
\(294\) | 1.90377 | 0.111030 | ||||||||
\(295\) | 16.6870 | 0.971554 | ||||||||
\(296\) | −10.0326 | −0.583134 | ||||||||
\(297\) | −3.75440 | −0.217852 | ||||||||
\(298\) | 4.93241 | 0.285727 | ||||||||
\(299\) | −33.3749 | −1.93012 | ||||||||
\(300\) | 0.566780 | 0.0327231 | ||||||||
\(301\) | 51.6633 | 2.97783 | ||||||||
\(302\) | 0.674030 | 0.0387861 | ||||||||
\(303\) | 2.42741 | 0.139451 | ||||||||
\(304\) | −6.69433 | −0.383946 | ||||||||
\(305\) | 8.71032 | 0.498751 | ||||||||
\(306\) | 18.9876 | 1.08545 | ||||||||
\(307\) | −7.50586 | −0.428382 | −0.214191 | − | 0.976792i | \(-0.568711\pi\) | ||||
−0.214191 | + | 0.976792i | \(0.568711\pi\) | |||||||
\(308\) | 15.3287 | 0.873437 | ||||||||
\(309\) | −0.404327 | −0.0230014 | ||||||||
\(310\) | 1.31890 | 0.0749083 | ||||||||
\(311\) | −26.5197 | −1.50379 | −0.751897 | − | 0.659281i | \(-0.770861\pi\) | ||||
−0.751897 | + | 0.659281i | \(0.770861\pi\) | |||||||
\(312\) | 0.629408 | 0.0356332 | ||||||||
\(313\) | −16.5080 | −0.933086 | −0.466543 | − | 0.884499i | \(-0.654501\pi\) | ||||
−0.466543 | + | 0.884499i | \(0.654501\pi\) | |||||||
\(314\) | −11.6883 | −0.659611 | ||||||||
\(315\) | −16.5955 | −0.935049 | ||||||||
\(316\) | −14.7478 | −0.829631 | ||||||||
\(317\) | 6.43940 | 0.361673 | 0.180836 | − | 0.983513i | \(-0.442120\pi\) | ||||
0.180836 | + | 0.983513i | \(0.442120\pi\) | |||||||
\(318\) | −1.20399 | −0.0675164 | ||||||||
\(319\) | 24.4135 | 1.36689 | ||||||||
\(320\) | −1.31890 | −0.0737286 | ||||||||
\(321\) | 2.20319 | 0.122970 | ||||||||
\(322\) | −39.0545 | −2.17642 | ||||||||
\(323\) | −42.8009 | −2.38150 | ||||||||
\(324\) | 8.72896 | 0.484942 | ||||||||
\(325\) | −11.8056 | −0.654857 | ||||||||
\(326\) | −11.1027 | −0.614921 | ||||||||
\(327\) | 3.15661 | 0.174561 | ||||||||
\(328\) | 8.49568 | 0.469095 | ||||||||
\(329\) | −7.93214 | −0.437313 | ||||||||
\(330\) | 0.829455 | 0.0456600 | ||||||||
\(331\) | 16.8284 | 0.924974 | 0.462487 | − | 0.886626i | \(-0.346957\pi\) | ||||
0.462487 | + | 0.886626i | \(0.346957\pi\) | |||||||
\(332\) | −14.4747 | −0.794403 | ||||||||
\(333\) | −29.7947 | −1.63274 | ||||||||
\(334\) | 9.06043 | 0.495764 | ||||||||
\(335\) | 6.51774 | 0.356102 | ||||||||
\(336\) | 0.736518 | 0.0401804 | ||||||||
\(337\) | −27.0110 | −1.47138 | −0.735691 | − | 0.677318i | \(-0.763142\pi\) | ||||
−0.735691 | + | 0.677318i | \(0.763142\pi\) | |||||||
\(338\) | −0.110086 | −0.00598790 | ||||||||
\(339\) | −2.26027 | −0.122761 | ||||||||
\(340\) | −8.43250 | −0.457317 | ||||||||
\(341\) | −3.61787 | −0.195918 | ||||||||
\(342\) | −19.8807 | −1.07503 | ||||||||
\(343\) | −16.7436 | −0.904071 | ||||||||
\(344\) | 12.1935 | 0.657430 | ||||||||
\(345\) | −2.11328 | −0.113775 | ||||||||
\(346\) | 12.6604 | 0.680629 | ||||||||
\(347\) | 9.78225 | 0.525138 | 0.262569 | − | 0.964913i | \(-0.415430\pi\) | ||||
0.262569 | + | 0.964913i | \(0.415430\pi\) | |||||||
\(348\) | 1.17302 | 0.0628806 | ||||||||
\(349\) | −22.8126 | −1.22113 | −0.610565 | − | 0.791966i | \(-0.709058\pi\) | ||||
−0.610565 | + | 0.791966i | \(0.709058\pi\) | |||||||
\(350\) | −13.8146 | −0.738424 | ||||||||
\(351\) | 3.75743 | 0.200557 | ||||||||
\(352\) | 3.61787 | 0.192833 | ||||||||
\(353\) | 3.05550 | 0.162628 | 0.0813140 | − | 0.996689i | \(-0.474088\pi\) | ||||
0.0813140 | + | 0.996689i | \(0.474088\pi\) | |||||||
\(354\) | −2.19936 | −0.116895 | ||||||||
\(355\) | 3.69155 | 0.195927 | ||||||||
\(356\) | 13.4900 | 0.714970 | ||||||||
\(357\) | 4.70900 | 0.249227 | ||||||||
\(358\) | −9.89983 | −0.523222 | ||||||||
\(359\) | 31.3452 | 1.65434 | 0.827168 | − | 0.561954i | \(-0.189950\pi\) | ||||
0.827168 | + | 0.561954i | \(0.189950\pi\) | |||||||
\(360\) | −3.91684 | −0.206435 | ||||||||
\(361\) | 25.8140 | 1.35863 | ||||||||
\(362\) | 4.97321 | 0.261386 | ||||||||
\(363\) | −0.363128 | −0.0190593 | ||||||||
\(364\) | −15.3411 | −0.804093 | ||||||||
\(365\) | −0.802415 | −0.0420003 | ||||||||
\(366\) | −1.14803 | −0.0600084 | ||||||||
\(367\) | 0.529997 | 0.0276656 | 0.0138328 | − | 0.999904i | \(-0.495597\pi\) | ||||
0.0138328 | + | 0.999904i | \(0.495597\pi\) | |||||||
\(368\) | −9.21759 | −0.480500 | ||||||||
\(369\) | 25.2303 | 1.31344 | ||||||||
\(370\) | 13.2320 | 0.687899 | ||||||||
\(371\) | 29.3459 | 1.52356 | ||||||||
\(372\) | −0.173832 | −0.00901276 | ||||||||
\(373\) | −23.4992 | −1.21674 | −0.608371 | − | 0.793652i | \(-0.708177\pi\) | ||||
−0.608371 | + | 0.793652i | \(0.708177\pi\) | |||||||
\(374\) | 23.1312 | 1.19609 | ||||||||
\(375\) | −1.89386 | −0.0977983 | ||||||||
\(376\) | −1.87213 | −0.0965478 | ||||||||
\(377\) | −24.4332 | −1.25837 | ||||||||
\(378\) | 4.39685 | 0.226150 | ||||||||
\(379\) | −19.6438 | −1.00904 | −0.504518 | − | 0.863401i | \(-0.668330\pi\) | ||||
−0.504518 | + | 0.863401i | \(0.668330\pi\) | |||||||
\(380\) | 8.82913 | 0.452925 | ||||||||
\(381\) | −1.45025 | −0.0742983 | ||||||||
\(382\) | −9.19255 | −0.470332 | ||||||||
\(383\) | −9.46299 | −0.483536 | −0.241768 | − | 0.970334i | \(-0.577727\pi\) | ||||
−0.241768 | + | 0.970334i | \(0.577727\pi\) | |||||||
\(384\) | 0.173832 | 0.00887082 | ||||||||
\(385\) | −20.2170 | −1.03036 | ||||||||
\(386\) | −3.43888 | −0.175034 | ||||||||
\(387\) | 36.2121 | 1.84076 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 31.2880 | 1.58637 | 0.793183 | − | 0.608983i | \(-0.208422\pi\) | ||||
0.793183 | + | 0.608983i | \(0.208422\pi\) | |||||||
\(390\) | −0.830124 | −0.0420350 | ||||||||
\(391\) | −58.9336 | −2.98040 | ||||||||
\(392\) | −10.9518 | −0.553150 | ||||||||
\(393\) | −2.66895 | −0.134631 | ||||||||
\(394\) | −23.5917 | −1.18853 | ||||||||
\(395\) | 19.4509 | 0.978680 | ||||||||
\(396\) | 10.7443 | 0.539920 | ||||||||
\(397\) | 3.82153 | 0.191797 | 0.0958985 | − | 0.995391i | \(-0.469428\pi\) | ||||
0.0958985 | + | 0.995391i | \(0.469428\pi\) | |||||||
\(398\) | −3.42905 | −0.171883 | ||||||||
\(399\) | −4.93049 | −0.246833 | ||||||||
\(400\) | −3.26051 | −0.163026 | ||||||||
\(401\) | −12.8041 | −0.639408 | −0.319704 | − | 0.947518i | \(-0.603583\pi\) | ||||
−0.319704 | + | 0.947518i | \(0.603583\pi\) | |||||||
\(402\) | −0.859045 | −0.0428452 | ||||||||
\(403\) | 3.62079 | 0.180364 | ||||||||
\(404\) | −13.9642 | −0.694743 | ||||||||
\(405\) | −11.5126 | −0.572065 | ||||||||
\(406\) | −28.5911 | −1.41895 | ||||||||
\(407\) | −36.2967 | −1.79916 | ||||||||
\(408\) | 1.11141 | 0.0550231 | ||||||||
\(409\) | −21.2957 | −1.05300 | −0.526502 | − | 0.850174i | \(-0.676497\pi\) | ||||
−0.526502 | + | 0.850174i | \(0.676497\pi\) | |||||||
\(410\) | −11.2049 | −0.553372 | ||||||||
\(411\) | −0.963177 | −0.0475100 | ||||||||
\(412\) | 2.32597 | 0.114592 | ||||||||
\(413\) | 53.6069 | 2.63782 | ||||||||
\(414\) | −27.3742 | −1.34537 | ||||||||
\(415\) | 19.0907 | 0.937124 | ||||||||
\(416\) | −3.62079 | −0.177524 | ||||||||
\(417\) | −1.06254 | −0.0520330 | ||||||||
\(418\) | −24.2192 | −1.18460 | ||||||||
\(419\) | 4.03517 | 0.197131 | 0.0985654 | − | 0.995131i | \(-0.468575\pi\) | ||||
0.0985654 | + | 0.995131i | \(0.468575\pi\) | |||||||
\(420\) | −0.971391 | −0.0473990 | ||||||||
\(421\) | 7.42421 | 0.361834 | 0.180917 | − | 0.983498i | \(-0.442093\pi\) | ||||
0.180917 | + | 0.983498i | \(0.442093\pi\) | |||||||
\(422\) | −6.88052 | −0.334938 | ||||||||
\(423\) | −5.55982 | −0.270328 | ||||||||
\(424\) | 6.92618 | 0.336365 | ||||||||
\(425\) | −20.8464 | −1.01120 | ||||||||
\(426\) | −0.486550 | −0.0235734 | ||||||||
\(427\) | 27.9819 | 1.35414 | ||||||||
\(428\) | −12.6743 | −0.612635 | ||||||||
\(429\) | 2.27711 | 0.109940 | ||||||||
\(430\) | −16.0820 | −0.775542 | ||||||||
\(431\) | 11.4262 | 0.550380 | 0.275190 | − | 0.961390i | \(-0.411259\pi\) | ||||
0.275190 | + | 0.961390i | \(0.411259\pi\) | |||||||
\(432\) | 1.03774 | 0.0499282 | ||||||||
\(433\) | −20.6999 | −0.994773 | −0.497386 | − | 0.867529i | \(-0.665707\pi\) | ||||
−0.497386 | + | 0.867529i | \(0.665707\pi\) | |||||||
\(434\) | 4.23696 | 0.203380 | ||||||||
\(435\) | −1.54709 | −0.0741775 | ||||||||
\(436\) | −18.1590 | −0.869658 | ||||||||
\(437\) | 61.7056 | 2.95178 | ||||||||
\(438\) | 0.105759 | 0.00505336 | ||||||||
\(439\) | 12.7594 | 0.608974 | 0.304487 | − | 0.952517i | \(-0.401515\pi\) | ||||
0.304487 | + | 0.952517i | \(0.401515\pi\) | |||||||
\(440\) | −4.77159 | −0.227477 | ||||||||
\(441\) | −32.5245 | −1.54878 | ||||||||
\(442\) | −23.1499 | −1.10113 | ||||||||
\(443\) | −13.3180 | −0.632757 | −0.316379 | − | 0.948633i | \(-0.602467\pi\) | ||||
−0.316379 | + | 0.948633i | \(0.602467\pi\) | |||||||
\(444\) | −1.74399 | −0.0827660 | ||||||||
\(445\) | −17.7920 | −0.843420 | ||||||||
\(446\) | −4.06475 | −0.192471 | ||||||||
\(447\) | 0.857409 | 0.0405541 | ||||||||
\(448\) | −4.23696 | −0.200177 | ||||||||
\(449\) | −24.1592 | −1.14014 | −0.570072 | − | 0.821594i | \(-0.693085\pi\) | ||||
−0.570072 | + | 0.821594i | \(0.693085\pi\) | |||||||
\(450\) | −9.68301 | −0.456461 | ||||||||
\(451\) | 30.7362 | 1.44731 | ||||||||
\(452\) | 13.0026 | 0.611591 | ||||||||
\(453\) | 0.117168 | 0.00550502 | ||||||||
\(454\) | −0.866799 | −0.0406809 | ||||||||
\(455\) | 20.2333 | 0.948554 | ||||||||
\(456\) | −1.16369 | −0.0544947 | ||||||||
\(457\) | 23.1157 | 1.08131 | 0.540653 | − | 0.841246i | \(-0.318177\pi\) | ||||
0.540653 | + | 0.841246i | \(0.318177\pi\) | |||||||
\(458\) | −15.1554 | −0.708164 | ||||||||
\(459\) | 6.63488 | 0.309690 | ||||||||
\(460\) | 12.1571 | 0.566825 | ||||||||
\(461\) | −15.7824 | −0.735059 | −0.367529 | − | 0.930012i | \(-0.619796\pi\) | ||||
−0.367529 | + | 0.930012i | \(0.619796\pi\) | |||||||
\(462\) | 2.66462 | 0.123970 | ||||||||
\(463\) | 11.8773 | 0.551984 | 0.275992 | − | 0.961160i | \(-0.410994\pi\) | ||||
0.275992 | + | 0.961160i | \(0.410994\pi\) | |||||||
\(464\) | −6.74803 | −0.313269 | ||||||||
\(465\) | 0.229266 | 0.0106320 | ||||||||
\(466\) | −5.38639 | −0.249520 | ||||||||
\(467\) | −27.1256 | −1.25522 | −0.627611 | − | 0.778527i | \(-0.715967\pi\) | ||||
−0.627611 | + | 0.778527i | \(0.715967\pi\) | |||||||
\(468\) | −10.7529 | −0.497055 | ||||||||
\(469\) | 20.9383 | 0.966839 | ||||||||
\(470\) | 2.46915 | 0.113893 | ||||||||
\(471\) | −2.03180 | −0.0936206 | ||||||||
\(472\) | 12.6522 | 0.582366 | ||||||||
\(473\) | 44.1145 | 2.02839 | ||||||||
\(474\) | −2.56364 | −0.117752 | ||||||||
\(475\) | 21.8269 | 1.00149 | ||||||||
\(476\) | −27.0894 | −1.24164 | ||||||||
\(477\) | 20.5692 | 0.941801 | ||||||||
\(478\) | 17.6518 | 0.807376 | ||||||||
\(479\) | 16.3194 | 0.745652 | 0.372826 | − | 0.927901i | \(-0.378389\pi\) | ||||
0.372826 | + | 0.927901i | \(0.378389\pi\) | |||||||
\(480\) | −0.229266 | −0.0104645 | ||||||||
\(481\) | 36.3260 | 1.65632 | ||||||||
\(482\) | 3.92400 | 0.178733 | ||||||||
\(483\) | −6.78892 | −0.308907 | ||||||||
\(484\) | 2.08896 | 0.0949529 | ||||||||
\(485\) | 1.31890 | 0.0598880 | ||||||||
\(486\) | 4.63058 | 0.210048 | ||||||||
\(487\) | 14.9165 | 0.675931 | 0.337966 | − | 0.941158i | \(-0.390261\pi\) | ||||
0.337966 | + | 0.941158i | \(0.390261\pi\) | |||||||
\(488\) | 6.60424 | 0.298960 | ||||||||
\(489\) | −1.93000 | −0.0872777 | ||||||||
\(490\) | 14.4443 | 0.652527 | ||||||||
\(491\) | −16.6762 | −0.752585 | −0.376292 | − | 0.926501i | \(-0.622801\pi\) | ||||
−0.376292 | + | 0.926501i | \(0.622801\pi\) | |||||||
\(492\) | 1.47682 | 0.0665802 | ||||||||
\(493\) | −43.1442 | −1.94312 | ||||||||
\(494\) | 24.2387 | 1.09055 | ||||||||
\(495\) | −14.1706 | −0.636921 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 11.8591 | 0.531953 | ||||||||
\(498\) | −2.51617 | −0.112752 | ||||||||
\(499\) | 31.1702 | 1.39537 | 0.697686 | − | 0.716404i | \(-0.254213\pi\) | ||||
0.697686 | + | 0.716404i | \(0.254213\pi\) | |||||||
\(500\) | 10.8948 | 0.487229 | ||||||||
\(501\) | 1.57499 | 0.0703654 | ||||||||
\(502\) | 27.8382 | 1.24248 | ||||||||
\(503\) | 4.86875 | 0.217087 | 0.108543 | − | 0.994092i | \(-0.465381\pi\) | ||||
0.108543 | + | 0.994092i | \(0.465381\pi\) | |||||||
\(504\) | −12.5828 | −0.560484 | ||||||||
\(505\) | 18.4173 | 0.819558 | ||||||||
\(506\) | −33.3480 | −1.48250 | ||||||||
\(507\) | −0.0191365 | −0.000849881 0 | ||||||||
\(508\) | 8.34281 | 0.370152 | ||||||||
\(509\) | −1.43778 | −0.0637286 | −0.0318643 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318643 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(510\) | −1.46584 | −0.0649084 | ||||||||
\(511\) | −2.57776 | −0.114033 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.94696 | −0.306716 | ||||||||
\(514\) | −1.99512 | −0.0880011 | ||||||||
\(515\) | −3.06771 | −0.135179 | ||||||||
\(516\) | 2.11962 | 0.0933110 | ||||||||
\(517\) | −6.77312 | −0.297881 | ||||||||
\(518\) | 42.5078 | 1.86768 | ||||||||
\(519\) | 2.20079 | 0.0966038 | ||||||||
\(520\) | 4.77544 | 0.209417 | ||||||||
\(521\) | −39.4832 | −1.72979 | −0.864896 | − | 0.501951i | \(-0.832616\pi\) | ||||
−0.864896 | + | 0.501951i | \(0.832616\pi\) | |||||||
\(522\) | −20.0402 | −0.877134 | ||||||||
\(523\) | 37.3384 | 1.63270 | 0.816348 | − | 0.577560i | \(-0.195995\pi\) | ||||
0.816348 | + | 0.577560i | \(0.195995\pi\) | |||||||
\(524\) | 15.3536 | 0.670727 | ||||||||
\(525\) | −2.40142 | −0.104807 | ||||||||
\(526\) | −2.99842 | −0.130737 | ||||||||
\(527\) | 6.39360 | 0.278510 | ||||||||
\(528\) | 0.628900 | 0.0273694 | ||||||||
\(529\) | 61.9639 | 2.69408 | ||||||||
\(530\) | −9.13491 | −0.396795 | ||||||||
\(531\) | 37.5744 | 1.63059 | ||||||||
\(532\) | 28.3636 | 1.22972 | ||||||||
\(533\) | −30.7610 | −1.33241 | ||||||||
\(534\) | 2.34500 | 0.101478 | ||||||||
\(535\) | 16.7161 | 0.722699 | ||||||||
\(536\) | 4.94181 | 0.213454 | ||||||||
\(537\) | −1.72091 | −0.0742626 | ||||||||
\(538\) | −4.42303 | −0.190690 | ||||||||
\(539\) | −39.6222 | −1.70665 | ||||||||
\(540\) | −1.36867 | −0.0588982 | ||||||||
\(541\) | −12.4064 | −0.533393 | −0.266697 | − | 0.963781i | \(-0.585932\pi\) | ||||
−0.266697 | + | 0.963781i | \(0.585932\pi\) | |||||||
\(542\) | −27.8927 | −1.19810 | ||||||||
\(543\) | 0.864501 | 0.0370993 | ||||||||
\(544\) | −6.39360 | −0.274123 | ||||||||
\(545\) | 23.9498 | 1.02590 | ||||||||
\(546\) | −2.66677 | −0.114127 | ||||||||
\(547\) | 24.6365 | 1.05338 | 0.526690 | − | 0.850057i | \(-0.323433\pi\) | ||||
0.526690 | + | 0.850057i | \(0.323433\pi\) | |||||||
\(548\) | 5.54086 | 0.236694 | ||||||||
\(549\) | 19.6132 | 0.837070 | ||||||||
\(550\) | −11.7961 | −0.502987 | ||||||||
\(551\) | 45.1735 | 1.92446 | ||||||||
\(552\) | −1.60231 | −0.0681988 | ||||||||
\(553\) | 62.4860 | 2.65717 | ||||||||
\(554\) | 8.08413 | 0.343462 | ||||||||
\(555\) | 2.30014 | 0.0976356 | ||||||||
\(556\) | 6.11248 | 0.259227 | ||||||||
\(557\) | −21.7501 | −0.921580 | −0.460790 | − | 0.887509i | \(-0.652434\pi\) | ||||
−0.460790 | + | 0.887509i | \(0.652434\pi\) | |||||||
\(558\) | 2.96978 | 0.125721 | ||||||||
\(559\) | −44.1501 | −1.86735 | ||||||||
\(560\) | 5.58811 | 0.236141 | ||||||||
\(561\) | 4.02094 | 0.169764 | ||||||||
\(562\) | 32.6934 | 1.37909 | ||||||||
\(563\) | −25.3959 | −1.07031 | −0.535154 | − | 0.844754i | \(-0.679747\pi\) | ||||
−0.535154 | + | 0.844754i | \(0.679747\pi\) | |||||||
\(564\) | −0.325436 | −0.0137033 | ||||||||
\(565\) | −17.1491 | −0.721468 | ||||||||
\(566\) | 7.15089 | 0.300574 | ||||||||
\(567\) | −36.9842 | −1.55319 | ||||||||
\(568\) | 2.79897 | 0.117442 | ||||||||
\(569\) | −22.3151 | −0.935497 | −0.467749 | − | 0.883862i | \(-0.654935\pi\) | ||||
−0.467749 | + | 0.883862i | \(0.654935\pi\) | |||||||
\(570\) | 1.53478 | 0.0642850 | ||||||||
\(571\) | 25.2273 | 1.05573 | 0.527866 | − | 0.849328i | \(-0.322992\pi\) | ||||
0.527866 | + | 0.849328i | \(0.322992\pi\) | |||||||
\(572\) | −13.0995 | −0.547718 | ||||||||
\(573\) | −1.59796 | −0.0667557 | ||||||||
\(574\) | −35.9958 | −1.50244 | ||||||||
\(575\) | 30.0540 | 1.25334 | ||||||||
\(576\) | −2.96978 | −0.123741 | ||||||||
\(577\) | −39.4406 | −1.64193 | −0.820967 | − | 0.570975i | \(-0.806565\pi\) | ||||
−0.820967 | + | 0.570975i | \(0.806565\pi\) | |||||||
\(578\) | −23.8781 | −0.993200 | ||||||||
\(579\) | −0.597786 | −0.0248432 | ||||||||
\(580\) | 8.89995 | 0.369550 | ||||||||
\(581\) | 61.3288 | 2.54435 | ||||||||
\(582\) | −0.173832 | −0.00720556 | ||||||||
\(583\) | 25.0580 | 1.03780 | ||||||||
\(584\) | −0.608398 | −0.0251757 | ||||||||
\(585\) | 14.1820 | 0.586355 | ||||||||
\(586\) | 0.212267 | 0.00876867 | ||||||||
\(587\) | −27.7266 | −1.14440 | −0.572200 | − | 0.820114i | \(-0.693910\pi\) | ||||
−0.572200 | + | 0.820114i | \(0.693910\pi\) | |||||||
\(588\) | −1.90377 | −0.0785103 | ||||||||
\(589\) | −6.69433 | −0.275835 | ||||||||
\(590\) | −16.6870 | −0.686992 | ||||||||
\(591\) | −4.10098 | −0.168692 | ||||||||
\(592\) | 10.0326 | 0.412338 | ||||||||
\(593\) | 8.88644 | 0.364922 | 0.182461 | − | 0.983213i | \(-0.441594\pi\) | ||||
0.182461 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(594\) | 3.75440 | 0.154045 | ||||||||
\(595\) | 35.7282 | 1.46471 | ||||||||
\(596\) | −4.93241 | −0.202039 | ||||||||
\(597\) | −0.596079 | −0.0243959 | ||||||||
\(598\) | 33.3749 | 1.36480 | ||||||||
\(599\) | −28.1985 | −1.15216 | −0.576079 | − | 0.817394i | \(-0.695418\pi\) | ||||
−0.576079 | + | 0.817394i | \(0.695418\pi\) | |||||||
\(600\) | −0.566780 | −0.0231387 | ||||||||
\(601\) | 33.4749 | 1.36547 | 0.682736 | − | 0.730665i | \(-0.260790\pi\) | ||||
0.682736 | + | 0.730665i | \(0.260790\pi\) | |||||||
\(602\) | −51.6633 | −2.10564 | ||||||||
\(603\) | 14.6761 | 0.597658 | ||||||||
\(604\) | −0.674030 | −0.0274259 | ||||||||
\(605\) | −2.75513 | −0.112012 | ||||||||
\(606\) | −2.42741 | −0.0986070 | ||||||||
\(607\) | −23.2609 | −0.944132 | −0.472066 | − | 0.881563i | \(-0.656492\pi\) | ||||
−0.472066 | + | 0.881563i | \(0.656492\pi\) | |||||||
\(608\) | 6.69433 | 0.271491 | ||||||||
\(609\) | −4.97004 | −0.201396 | ||||||||
\(610\) | −8.71032 | −0.352671 | ||||||||
\(611\) | 6.77858 | 0.274232 | ||||||||
\(612\) | −18.9876 | −0.767528 | ||||||||
\(613\) | 24.3093 | 0.981845 | 0.490922 | − | 0.871203i | \(-0.336660\pi\) | ||||
0.490922 | + | 0.871203i | \(0.336660\pi\) | |||||||
\(614\) | 7.50586 | 0.302912 | ||||||||
\(615\) | −1.94777 | −0.0785418 | ||||||||
\(616\) | −15.3287 | −0.617613 | ||||||||
\(617\) | 10.9593 | 0.441205 | 0.220602 | − | 0.975364i | \(-0.429198\pi\) | ||||
0.220602 | + | 0.975364i | \(0.429198\pi\) | |||||||
\(618\) | 0.404327 | 0.0162644 | ||||||||
\(619\) | 35.1657 | 1.41343 | 0.706714 | − | 0.707499i | \(-0.250177\pi\) | ||||
0.706714 | + | 0.707499i | \(0.250177\pi\) | |||||||
\(620\) | −1.31890 | −0.0529682 | ||||||||
\(621\) | −9.56544 | −0.383848 | ||||||||
\(622\) | 26.5197 | 1.06334 | ||||||||
\(623\) | −57.1567 | −2.28993 | ||||||||
\(624\) | −0.629408 | −0.0251965 | ||||||||
\(625\) | 1.93348 | 0.0773392 | ||||||||
\(626\) | 16.5080 | 0.659791 | ||||||||
\(627\) | −4.21007 | −0.168134 | ||||||||
\(628\) | 11.6883 | 0.466415 | ||||||||
\(629\) | 64.1446 | 2.55761 | ||||||||
\(630\) | 16.5955 | 0.661179 | ||||||||
\(631\) | 1.14073 | 0.0454117 | 0.0227059 | − | 0.999742i | \(-0.492772\pi\) | ||||
0.0227059 | + | 0.999742i | \(0.492772\pi\) | |||||||
\(632\) | 14.7478 | 0.586638 | ||||||||
\(633\) | −1.19605 | −0.0475388 | ||||||||
\(634\) | −6.43940 | −0.255741 | ||||||||
\(635\) | −11.0033 | −0.436653 | ||||||||
\(636\) | 1.20399 | 0.0477413 | ||||||||
\(637\) | 39.6541 | 1.57115 | ||||||||
\(638\) | −24.4135 | −0.966538 | ||||||||
\(639\) | 8.31232 | 0.328830 | ||||||||
\(640\) | 1.31890 | 0.0521340 | ||||||||
\(641\) | −36.2581 | −1.43211 | −0.716055 | − | 0.698044i | \(-0.754054\pi\) | ||||
−0.716055 | + | 0.698044i | \(0.754054\pi\) | |||||||
\(642\) | −2.20319 | −0.0869531 | ||||||||
\(643\) | 14.2857 | 0.563374 | 0.281687 | − | 0.959506i | \(-0.409106\pi\) | ||||
0.281687 | + | 0.959506i | \(0.409106\pi\) | |||||||
\(644\) | 39.0545 | 1.53896 | ||||||||
\(645\) | −2.79556 | −0.110075 | ||||||||
\(646\) | 42.8009 | 1.68398 | ||||||||
\(647\) | 28.9194 | 1.13694 | 0.568470 | − | 0.822704i | \(-0.307536\pi\) | ||||
0.568470 | + | 0.822704i | \(0.307536\pi\) | |||||||
\(648\) | −8.72896 | −0.342906 | ||||||||
\(649\) | 45.7741 | 1.79679 | ||||||||
\(650\) | 11.8056 | 0.463054 | ||||||||
\(651\) | 0.736518 | 0.0288664 | ||||||||
\(652\) | 11.1027 | 0.434815 | ||||||||
\(653\) | −45.5471 | −1.78239 | −0.891197 | − | 0.453616i | \(-0.850134\pi\) | ||||
−0.891197 | + | 0.453616i | \(0.850134\pi\) | |||||||
\(654\) | −3.15661 | −0.123433 | ||||||||
\(655\) | −20.2499 | −0.791228 | ||||||||
\(656\) | −8.49568 | −0.331701 | ||||||||
\(657\) | −1.80681 | −0.0704904 | ||||||||
\(658\) | 7.93214 | 0.309227 | ||||||||
\(659\) | 43.4631 | 1.69308 | 0.846541 | − | 0.532324i | \(-0.178681\pi\) | ||||
0.846541 | + | 0.532324i | \(0.178681\pi\) | |||||||
\(660\) | −0.829455 | −0.0322865 | ||||||||
\(661\) | −17.5186 | −0.681396 | −0.340698 | − | 0.940173i | \(-0.610663\pi\) | ||||
−0.340698 | + | 0.940173i | \(0.610663\pi\) | |||||||
\(662\) | −16.8284 | −0.654056 | ||||||||
\(663\) | −4.02418 | −0.156286 | ||||||||
\(664\) | 14.4747 | 0.561728 | ||||||||
\(665\) | −37.4086 | −1.45065 | ||||||||
\(666\) | 29.7947 | 1.15452 | ||||||||
\(667\) | 62.2005 | 2.40841 | ||||||||
\(668\) | −9.06043 | −0.350558 | ||||||||
\(669\) | −0.706582 | −0.0273180 | ||||||||
\(670\) | −6.51774 | −0.251802 | ||||||||
\(671\) | 23.8933 | 0.922390 | ||||||||
\(672\) | −0.736518 | −0.0284118 | ||||||||
\(673\) | −29.5198 | −1.13790 | −0.568952 | − | 0.822371i | \(-0.692651\pi\) | ||||
−0.568952 | + | 0.822371i | \(0.692651\pi\) | |||||||
\(674\) | 27.0110 | 1.04042 | ||||||||
\(675\) | −3.38356 | −0.130233 | ||||||||
\(676\) | 0.110086 | 0.00423408 | ||||||||
\(677\) | −44.2751 | −1.70163 | −0.850815 | − | 0.525465i | \(-0.823891\pi\) | ||||
−0.850815 | + | 0.525465i | \(0.823891\pi\) | |||||||
\(678\) | 2.26027 | 0.0868051 | ||||||||
\(679\) | 4.23696 | 0.162599 | ||||||||
\(680\) | 8.43250 | 0.323372 | ||||||||
\(681\) | −0.150677 | −0.00577397 | ||||||||
\(682\) | 3.61787 | 0.138535 | ||||||||
\(683\) | −21.3490 | −0.816898 | −0.408449 | − | 0.912781i | \(-0.633930\pi\) | ||||
−0.408449 | + | 0.912781i | \(0.633930\pi\) | |||||||
\(684\) | 19.8807 | 0.760158 | ||||||||
\(685\) | −7.30782 | −0.279217 | ||||||||
\(686\) | 16.7436 | 0.639275 | ||||||||
\(687\) | −2.63449 | −0.100512 | ||||||||
\(688\) | −12.1935 | −0.464873 | ||||||||
\(689\) | −25.0782 | −0.955403 | ||||||||
\(690\) | 2.11328 | 0.0804513 | ||||||||
\(691\) | 14.9082 | 0.567135 | 0.283567 | − | 0.958952i | \(-0.408482\pi\) | ||||
0.283567 | + | 0.958952i | \(0.408482\pi\) | |||||||
\(692\) | −12.6604 | −0.481277 | ||||||||
\(693\) | −45.5230 | −1.72928 | ||||||||
\(694\) | −9.78225 | −0.371329 | ||||||||
\(695\) | −8.06174 | −0.305799 | ||||||||
\(696\) | −1.17302 | −0.0444633 | ||||||||
\(697\) | −54.3180 | −2.05744 | ||||||||
\(698\) | 22.8126 | 0.863470 | ||||||||
\(699\) | −0.936326 | −0.0354151 | ||||||||
\(700\) | 13.8146 | 0.522144 | ||||||||
\(701\) | −43.5750 | −1.64580 | −0.822902 | − | 0.568184i | \(-0.807646\pi\) | ||||
−0.822902 | + | 0.568184i | \(0.807646\pi\) | |||||||
\(702\) | −3.75743 | −0.141815 | ||||||||
\(703\) | −67.1617 | −2.53305 | ||||||||
\(704\) | −3.61787 | −0.136354 | ||||||||
\(705\) | 0.429216 | 0.0161652 | ||||||||
\(706\) | −3.05550 | −0.114995 | ||||||||
\(707\) | 59.1655 | 2.22515 | ||||||||
\(708\) | 2.19936 | 0.0826570 | ||||||||
\(709\) | 6.08427 | 0.228499 | 0.114250 | − | 0.993452i | \(-0.463554\pi\) | ||||
0.114250 | + | 0.993452i | \(0.463554\pi\) | |||||||
\(710\) | −3.69155 | −0.138541 | ||||||||
\(711\) | 43.7979 | 1.64255 | ||||||||
\(712\) | −13.4900 | −0.505560 | ||||||||
\(713\) | −9.21759 | −0.345201 | ||||||||
\(714\) | −4.70900 | −0.176230 | ||||||||
\(715\) | 17.2769 | 0.646120 | ||||||||
\(716\) | 9.89983 | 0.369974 | ||||||||
\(717\) | 3.06845 | 0.114593 | ||||||||
\(718\) | −31.3452 | −1.16979 | ||||||||
\(719\) | −5.71962 | −0.213306 | −0.106653 | − | 0.994296i | \(-0.534013\pi\) | ||||
−0.106653 | + | 0.994296i | \(0.534013\pi\) | |||||||
\(720\) | 3.91684 | 0.145972 | ||||||||
\(721\) | −9.85502 | −0.367020 | ||||||||
\(722\) | −25.8140 | −0.960699 | ||||||||
\(723\) | 0.682115 | 0.0253681 | ||||||||
\(724\) | −4.97321 | −0.184828 | ||||||||
\(725\) | 22.0020 | 0.817134 | ||||||||
\(726\) | 0.363128 | 0.0134770 | ||||||||
\(727\) | 8.17750 | 0.303287 | 0.151643 | − | 0.988435i | \(-0.451543\pi\) | ||||
0.151643 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(728\) | 15.3411 | 0.568579 | ||||||||
\(729\) | −25.3819 | −0.940071 | ||||||||
\(730\) | 0.802415 | 0.0296987 | ||||||||
\(731\) | −77.9604 | −2.88347 | ||||||||
\(732\) | 1.14803 | 0.0424323 | ||||||||
\(733\) | −37.5681 | −1.38761 | −0.693805 | − | 0.720163i | \(-0.744067\pi\) | ||||
−0.693805 | + | 0.720163i | \(0.744067\pi\) | |||||||
\(734\) | −0.529997 | −0.0195625 | ||||||||
\(735\) | 2.51088 | 0.0926152 | ||||||||
\(736\) | 9.21759 | 0.339765 | ||||||||
\(737\) | 17.8788 | 0.658575 | ||||||||
\(738\) | −25.2303 | −0.928741 | ||||||||
\(739\) | 14.9091 | 0.548441 | 0.274220 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274220 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(740\) | −13.2320 | −0.486418 | ||||||||
\(741\) | 4.21346 | 0.154785 | ||||||||
\(742\) | −29.3459 | −1.07732 | ||||||||
\(743\) | −23.6468 | −0.867516 | −0.433758 | − | 0.901029i | \(-0.642813\pi\) | ||||
−0.433758 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(744\) | 0.173832 | 0.00637298 | ||||||||
\(745\) | 6.50534 | 0.238337 | ||||||||
\(746\) | 23.4992 | 0.860367 | ||||||||
\(747\) | 42.9868 | 1.57280 | ||||||||
\(748\) | −23.1312 | −0.845760 | ||||||||
\(749\) | 53.7004 | 1.96217 | ||||||||
\(750\) | 1.89386 | 0.0691539 | ||||||||
\(751\) | −41.4838 | −1.51377 | −0.756883 | − | 0.653551i | \(-0.773279\pi\) | ||||
−0.756883 | + | 0.653551i | \(0.773279\pi\) | |||||||
\(752\) | 1.87213 | 0.0682696 | ||||||||
\(753\) | 4.83917 | 0.176349 | ||||||||
\(754\) | 24.4332 | 0.889803 | ||||||||
\(755\) | 0.888976 | 0.0323531 | ||||||||
\(756\) | −4.39685 | −0.159912 | ||||||||
\(757\) | 9.85862 | 0.358318 | 0.179159 | − | 0.983820i | \(-0.442662\pi\) | ||||
0.179159 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(758\) | 19.6438 | 0.713496 | ||||||||
\(759\) | −5.79695 | −0.210416 | ||||||||
\(760\) | −8.82913 | −0.320266 | ||||||||
\(761\) | 11.4352 | 0.414526 | 0.207263 | − | 0.978285i | \(-0.433544\pi\) | ||||
0.207263 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(762\) | 1.45025 | 0.0525369 | ||||||||
\(763\) | 76.9389 | 2.78537 | ||||||||
\(764\) | 9.19255 | 0.332575 | ||||||||
\(765\) | 25.0427 | 0.905421 | ||||||||
\(766\) | 9.46299 | 0.341912 | ||||||||
\(767\) | −45.8110 | −1.65414 | ||||||||
\(768\) | −0.173832 | −0.00627262 | ||||||||
\(769\) | −11.0578 | −0.398754 | −0.199377 | − | 0.979923i | \(-0.563892\pi\) | ||||
−0.199377 | + | 0.979923i | \(0.563892\pi\) | |||||||
\(770\) | 20.2170 | 0.728572 | ||||||||
\(771\) | −0.346816 | −0.0124903 | ||||||||
\(772\) | 3.43888 | 0.123768 | ||||||||
\(773\) | −38.2248 | −1.37485 | −0.687426 | − | 0.726255i | \(-0.741259\pi\) | ||||
−0.687426 | + | 0.726255i | \(0.741259\pi\) | |||||||
\(774\) | −36.2121 | −1.30162 | ||||||||
\(775\) | −3.26051 | −0.117121 | ||||||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | 7.38921 | 0.265086 | ||||||||
\(778\) | −31.2880 | −1.12173 | ||||||||
\(779\) | 56.8729 | 2.03768 | ||||||||
\(780\) | 0.830124 | 0.0297232 | ||||||||
\(781\) | 10.1263 | 0.362347 | ||||||||
\(782\) | 58.9336 | 2.10746 | ||||||||
\(783\) | −7.00268 | −0.250256 | ||||||||
\(784\) | 10.9518 | 0.391136 | ||||||||
\(785\) | −15.4157 | −0.550210 | ||||||||
\(786\) | 2.66895 | 0.0951983 | ||||||||
\(787\) | 43.0967 | 1.53623 | 0.768116 | − | 0.640311i | \(-0.221195\pi\) | ||||
0.768116 | + | 0.640311i | \(0.221195\pi\) | |||||||
\(788\) | 23.5917 | 0.840419 | ||||||||
\(789\) | −0.521220 | −0.0185559 | ||||||||
\(790\) | −19.4509 | −0.692031 | ||||||||
\(791\) | −55.0915 | −1.95883 | ||||||||
\(792\) | −10.7443 | −0.381781 | ||||||||
\(793\) | −23.9126 | −0.849160 | ||||||||
\(794\) | −3.82153 | −0.135621 | ||||||||
\(795\) | −1.58794 | −0.0563184 | ||||||||
\(796\) | 3.42905 | 0.121540 | ||||||||
\(797\) | −0.876194 | −0.0310364 | −0.0155182 | − | 0.999880i | \(-0.504940\pi\) | ||||
−0.0155182 | + | 0.999880i | \(0.504940\pi\) | |||||||
\(798\) | 4.93049 | 0.174538 | ||||||||
\(799\) | 11.9697 | 0.423456 | ||||||||
\(800\) | 3.26051 | 0.115276 | ||||||||
\(801\) | −40.0625 | −1.41554 | ||||||||
\(802\) | 12.8041 | 0.452130 | ||||||||
\(803\) | −2.20110 | −0.0776753 | ||||||||
\(804\) | 0.859045 | 0.0302962 | ||||||||
\(805\) | −51.5089 | −1.81545 | ||||||||
\(806\) | −3.62079 | −0.127537 | ||||||||
\(807\) | −0.768863 | −0.0270653 | ||||||||
\(808\) | 13.9642 | 0.491257 | ||||||||
\(809\) | −29.1068 | −1.02334 | −0.511671 | − | 0.859181i | \(-0.670973\pi\) | ||||
−0.511671 | + | 0.859181i | \(0.670973\pi\) | |||||||
\(810\) | 11.5126 | 0.404511 | ||||||||
\(811\) | −52.0320 | −1.82709 | −0.913545 | − | 0.406738i | \(-0.866666\pi\) | ||||
−0.913545 | + | 0.406738i | \(0.866666\pi\) | |||||||
\(812\) | 28.5911 | 1.00335 | ||||||||
\(813\) | −4.84864 | −0.170049 | ||||||||
\(814\) | 36.2967 | 1.27220 | ||||||||
\(815\) | −14.6433 | −0.512933 | ||||||||
\(816\) | −1.11141 | −0.0389072 | ||||||||
\(817\) | 81.6273 | 2.85578 | ||||||||
\(818\) | 21.2957 | 0.744587 | ||||||||
\(819\) | 45.5598 | 1.59199 | ||||||||
\(820\) | 11.2049 | 0.391293 | ||||||||
\(821\) | 2.04825 | 0.0714843 | 0.0357421 | − | 0.999361i | \(-0.488620\pi\) | ||||
0.0357421 | + | 0.999361i | \(0.488620\pi\) | |||||||
\(822\) | 0.963177 | 0.0335947 | ||||||||
\(823\) | 4.36551 | 0.152172 | 0.0760861 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760861 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(824\) | −2.32597 | −0.0810289 | ||||||||
\(825\) | −2.05054 | −0.0713905 | ||||||||
\(826\) | −53.6069 | −1.86522 | ||||||||
\(827\) | −8.08686 | −0.281208 | −0.140604 | − | 0.990066i | \(-0.544904\pi\) | ||||
−0.140604 | + | 0.990066i | \(0.544904\pi\) | |||||||
\(828\) | 27.3742 | 0.951320 | ||||||||
\(829\) | −16.9502 | −0.588705 | −0.294352 | − | 0.955697i | \(-0.595104\pi\) | ||||
−0.294352 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(830\) | −19.0907 | −0.662647 | ||||||||
\(831\) | 1.40528 | 0.0487486 | ||||||||
\(832\) | 3.62079 | 0.125528 | ||||||||
\(833\) | 70.0215 | 2.42610 | ||||||||
\(834\) | 1.06254 | 0.0367929 | ||||||||
\(835\) | 11.9498 | 0.413539 | ||||||||
\(836\) | 24.2192 | 0.837638 | ||||||||
\(837\) | 1.03774 | 0.0358695 | ||||||||
\(838\) | −4.03517 | −0.139393 | ||||||||
\(839\) | −31.3851 | −1.08354 | −0.541768 | − | 0.840528i | \(-0.682245\pi\) | ||||
−0.541768 | + | 0.840528i | \(0.682245\pi\) | |||||||
\(840\) | 0.971391 | 0.0335162 | ||||||||
\(841\) | 16.5359 | 0.570202 | ||||||||
\(842\) | −7.42421 | −0.255855 | ||||||||
\(843\) | 5.68315 | 0.195738 | ||||||||
\(844\) | 6.88052 | 0.236837 | ||||||||
\(845\) | −0.145192 | −0.00499477 | ||||||||
\(846\) | 5.55982 | 0.191151 | ||||||||
\(847\) | −8.85085 | −0.304119 | ||||||||
\(848\) | −6.92618 | −0.237846 | ||||||||
\(849\) | 1.24305 | 0.0426615 | ||||||||
\(850\) | 20.8464 | 0.715026 | ||||||||
\(851\) | −92.4766 | −3.17006 | ||||||||
\(852\) | 0.486550 | 0.0166689 | ||||||||
\(853\) | 24.3909 | 0.835127 | 0.417564 | − | 0.908648i | \(-0.362884\pi\) | ||||
0.417564 | + | 0.908648i | \(0.362884\pi\) | |||||||
\(854\) | −27.9819 | −0.957521 | ||||||||
\(855\) | −26.2206 | −0.896725 | ||||||||
\(856\) | 12.6743 | 0.433198 | ||||||||
\(857\) | 6.00163 | 0.205012 | 0.102506 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102506 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(858\) | −2.27711 | −0.0777394 | ||||||||
\(859\) | 55.9301 | 1.90831 | 0.954156 | − | 0.299310i | \(-0.0967566\pi\) | ||||
0.954156 | + | 0.299310i | \(0.0967566\pi\) | |||||||
\(860\) | 16.0820 | 0.548391 | ||||||||
\(861\) | −6.25722 | −0.213246 | ||||||||
\(862\) | −11.4262 | −0.389177 | ||||||||
\(863\) | 19.5488 | 0.665449 | 0.332725 | − | 0.943024i | \(-0.392032\pi\) | ||||
0.332725 | + | 0.943024i | \(0.392032\pi\) | |||||||
\(864\) | −1.03774 | −0.0353046 | ||||||||
\(865\) | 16.6978 | 0.567742 | ||||||||
\(866\) | 20.6999 | 0.703411 | ||||||||
\(867\) | −4.15078 | −0.140968 | ||||||||
\(868\) | −4.23696 | −0.143812 | ||||||||
\(869\) | 53.3557 | 1.80997 | ||||||||
\(870\) | 1.54709 | 0.0524514 | ||||||||
\(871\) | −17.8932 | −0.606290 | ||||||||
\(872\) | 18.1590 | 0.614941 | ||||||||
\(873\) | 2.96978 | 0.100512 | ||||||||
\(874\) | −61.7056 | −2.08722 | ||||||||
\(875\) | −46.1606 | −1.56051 | ||||||||
\(876\) | −0.105759 | −0.00357326 | ||||||||
\(877\) | −11.9413 | −0.403228 | −0.201614 | − | 0.979465i | \(-0.564619\pi\) | ||||
−0.201614 | + | 0.979465i | \(0.564619\pi\) | |||||||
\(878\) | −12.7594 | −0.430610 | ||||||||
\(879\) | 0.0368988 | 0.00124456 | ||||||||
\(880\) | 4.77159 | 0.160850 | ||||||||
\(881\) | −45.4310 | −1.53061 | −0.765304 | − | 0.643669i | \(-0.777412\pi\) | ||||
−0.765304 | + | 0.643669i | \(0.777412\pi\) | |||||||
\(882\) | 32.5245 | 1.09516 | ||||||||
\(883\) | 22.5467 | 0.758757 | 0.379378 | − | 0.925242i | \(-0.376138\pi\) | ||||
0.379378 | + | 0.925242i | \(0.376138\pi\) | |||||||
\(884\) | 23.1499 | 0.778614 | ||||||||
\(885\) | −2.90073 | −0.0975069 | ||||||||
\(886\) | 13.3180 | 0.447427 | ||||||||
\(887\) | −22.4420 | −0.753530 | −0.376765 | − | 0.926309i | \(-0.622964\pi\) | ||||
−0.376765 | + | 0.926309i | \(0.622964\pi\) | |||||||
\(888\) | 1.74399 | 0.0585244 | ||||||||
\(889\) | −35.3481 | −1.18554 | ||||||||
\(890\) | 17.7920 | 0.596388 | ||||||||
\(891\) | −31.5802 | −1.05798 | ||||||||
\(892\) | 4.06475 | 0.136098 | ||||||||
\(893\) | −12.5327 | −0.419389 | ||||||||
\(894\) | −0.857409 | −0.0286761 | ||||||||
\(895\) | −13.0569 | −0.436443 | ||||||||
\(896\) | 4.23696 | 0.141547 | ||||||||
\(897\) | 5.80162 | 0.193710 | ||||||||
\(898\) | 24.1592 | 0.806204 | ||||||||
\(899\) | −6.74803 | −0.225059 | ||||||||
\(900\) | 9.68301 | 0.322767 | ||||||||
\(901\) | −44.2832 | −1.47529 | ||||||||
\(902\) | −30.7362 | −1.02340 | ||||||||
\(903\) | −8.98073 | −0.298860 | ||||||||
\(904\) | −13.0026 | −0.432460 | ||||||||
\(905\) | 6.55915 | 0.218033 | ||||||||
\(906\) | −0.117168 | −0.00389264 | ||||||||
\(907\) | −11.1784 | −0.371171 | −0.185586 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(908\) | 0.866799 | 0.0287657 | ||||||||
\(909\) | 41.4705 | 1.37549 | ||||||||
\(910\) | −20.2333 | −0.670729 | ||||||||
\(911\) | 18.0496 | 0.598011 | 0.299006 | − | 0.954251i | \(-0.403345\pi\) | ||||
0.299006 | + | 0.954251i | \(0.403345\pi\) | |||||||
\(912\) | 1.16369 | 0.0385335 | ||||||||
\(913\) | 52.3676 | 1.73311 | ||||||||
\(914\) | −23.1157 | −0.764599 | ||||||||
\(915\) | −1.51413 | −0.0500556 | ||||||||
\(916\) | 15.1554 | 0.500748 | ||||||||
\(917\) | −65.0527 | −2.14823 | ||||||||
\(918\) | −6.63488 | −0.218984 | ||||||||
\(919\) | 46.3061 | 1.52750 | 0.763749 | − | 0.645514i | \(-0.223357\pi\) | ||||
0.763749 | + | 0.645514i | \(0.223357\pi\) | |||||||
\(920\) | −12.1571 | −0.400806 | ||||||||
\(921\) | 1.30476 | 0.0429932 | ||||||||
\(922\) | 15.7824 | 0.519765 | ||||||||
\(923\) | −10.1345 | −0.333580 | ||||||||
\(924\) | −2.66462 | −0.0876597 | ||||||||
\(925\) | −32.7115 | −1.07555 | ||||||||
\(926\) | −11.8773 | −0.390312 | ||||||||
\(927\) | −6.90761 | −0.226876 | ||||||||
\(928\) | 6.74803 | 0.221515 | ||||||||
\(929\) | 37.4875 | 1.22993 | 0.614963 | − | 0.788556i | \(-0.289171\pi\) | ||||
0.614963 | + | 0.788556i | \(0.289171\pi\) | |||||||
\(930\) | −0.229266 | −0.00751794 | ||||||||
\(931\) | −73.3150 | −2.40280 | ||||||||
\(932\) | 5.38639 | 0.176437 | ||||||||
\(933\) | 4.60996 | 0.150923 | ||||||||
\(934\) | 27.1256 | 0.887576 | ||||||||
\(935\) | 30.5077 | 0.997708 | ||||||||
\(936\) | 10.7529 | 0.351471 | ||||||||
\(937\) | −39.8737 | −1.30262 | −0.651309 | − | 0.758812i | \(-0.725780\pi\) | ||||
−0.651309 | + | 0.758812i | \(0.725780\pi\) | |||||||
\(938\) | −20.9383 | −0.683658 | ||||||||
\(939\) | 2.86961 | 0.0936462 | ||||||||
\(940\) | −2.46915 | −0.0805347 | ||||||||
\(941\) | −0.123850 | −0.00403740 | −0.00201870 | − | 0.999998i | \(-0.500643\pi\) | ||||
−0.00201870 | + | 0.999998i | \(0.500643\pi\) | |||||||
\(942\) | 2.03180 | 0.0661998 | ||||||||
\(943\) | 78.3097 | 2.55011 | ||||||||
\(944\) | −12.6522 | −0.411795 | ||||||||
\(945\) | 5.79900 | 0.188641 | ||||||||
\(946\) | −44.1145 | −1.43429 | ||||||||
\(947\) | −33.0353 | −1.07350 | −0.536751 | − | 0.843741i | \(-0.680349\pi\) | ||||
−0.536751 | + | 0.843741i | \(0.680349\pi\) | |||||||
\(948\) | 2.56364 | 0.0832633 | ||||||||
\(949\) | 2.20288 | 0.0715085 | ||||||||
\(950\) | −21.8269 | −0.708159 | ||||||||
\(951\) | −1.11937 | −0.0362981 | ||||||||
\(952\) | 27.0894 | 0.877973 | ||||||||
\(953\) | 45.1825 | 1.46361 | 0.731803 | − | 0.681516i | \(-0.238679\pi\) | ||||
0.731803 | + | 0.681516i | \(0.238679\pi\) | |||||||
\(954\) | −20.5692 | −0.665954 | ||||||||
\(955\) | −12.1240 | −0.392324 | ||||||||
\(956\) | −17.6518 | −0.570901 | ||||||||
\(957\) | −4.24384 | −0.137184 | ||||||||
\(958\) | −16.3194 | −0.527256 | ||||||||
\(959\) | −23.4764 | −0.758091 | ||||||||
\(960\) | 0.229266 | 0.00739954 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −36.3260 | −1.17120 | ||||||||
\(963\) | 37.6399 | 1.21293 | ||||||||
\(964\) | −3.92400 | −0.126383 | ||||||||
\(965\) | −4.53553 | −0.146004 | ||||||||
\(966\) | 6.78892 | 0.218430 | ||||||||
\(967\) | 15.5107 | 0.498789 | 0.249395 | − | 0.968402i | \(-0.419768\pi\) | ||||
0.249395 | + | 0.968402i | \(0.419768\pi\) | |||||||
\(968\) | −2.08896 | −0.0671418 | ||||||||
\(969\) | 7.44015 | 0.239012 | ||||||||
\(970\) | −1.31890 | −0.0423472 | ||||||||
\(971\) | 11.5909 | 0.371969 | 0.185985 | − | 0.982553i | \(-0.440453\pi\) | ||||
0.185985 | + | 0.982553i | \(0.440453\pi\) | |||||||
\(972\) | −4.63058 | −0.148526 | ||||||||
\(973\) | −25.8983 | −0.830262 | ||||||||
\(974\) | −14.9165 | −0.477955 | ||||||||
\(975\) | 2.05219 | 0.0657227 | ||||||||
\(976\) | −6.60424 | −0.211397 | ||||||||
\(977\) | 43.9247 | 1.40527 | 0.702637 | − | 0.711548i | \(-0.252006\pi\) | ||||
0.702637 | + | 0.711548i | \(0.252006\pi\) | |||||||
\(978\) | 1.93000 | 0.0617147 | ||||||||
\(979\) | −48.8051 | −1.55982 | ||||||||
\(980\) | −14.4443 | −0.461406 | ||||||||
\(981\) | 53.9283 | 1.72180 | ||||||||
\(982\) | 16.6762 | 0.532158 | ||||||||
\(983\) | 41.1580 | 1.31274 | 0.656368 | − | 0.754441i | \(-0.272092\pi\) | ||||
0.656368 | + | 0.754441i | \(0.272092\pi\) | |||||||
\(984\) | −1.47682 | −0.0470793 | ||||||||
\(985\) | −31.1150 | −0.991406 | ||||||||
\(986\) | 43.1442 | 1.37399 | ||||||||
\(987\) | 1.37886 | 0.0438895 | ||||||||
\(988\) | −24.2387 | −0.771137 | ||||||||
\(989\) | 112.395 | 3.57394 | ||||||||
\(990\) | 14.1706 | 0.450371 | ||||||||
\(991\) | −10.7951 | −0.342919 | −0.171459 | − | 0.985191i | \(-0.554848\pi\) | ||||
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −2.92532 | −0.0928321 | ||||||||
\(994\) | −11.8591 | −0.376148 | ||||||||
\(995\) | −4.52257 | −0.143375 | ||||||||
\(996\) | 2.51617 | 0.0797278 | ||||||||
\(997\) | −33.1731 | −1.05060 | −0.525301 | − | 0.850917i | \(-0.676047\pi\) | ||||
−0.525301 | + | 0.850917i | \(0.676047\pi\) | |||||||
\(998\) | −31.1702 | −0.986677 | ||||||||
\(999\) | 10.4112 | 0.329397 |
(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 | 6014.2.a.l.1.20 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.l.1.20 | ✓ | 38 | 1.1 | even | 1 | trivial |