Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [430,2,Mod(1,430)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(430, 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("430.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.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: | \(3.43356728692\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 430.1 |
$q$-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 | ||||||||
\(3\) | 2.24914 | 1.29854 | 0.649271 | − | 0.760557i | \(-0.275074\pi\) | ||||
0.649271 | + | 0.760557i | \(0.275074\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.24914 | −0.918208 | ||||||||
\(7\) | 0.778457 | 0.294229 | 0.147115 | − | 0.989119i | \(-0.453001\pi\) | ||||
0.147115 | + | 0.989119i | \(0.453001\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.05863 | 0.686211 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.19051 | 1.56500 | 0.782498 | − | 0.622653i | \(-0.213945\pi\) | ||||
0.782498 | + | 0.622653i | \(0.213945\pi\) | |||||||
\(12\) | 2.24914 | 0.649271 | ||||||||
\(13\) | −3.83709 | −1.06422 | −0.532109 | − | 0.846676i | \(-0.678600\pi\) | ||||
−0.532109 | + | 0.846676i | \(0.678600\pi\) | |||||||
\(14\) | −0.778457 | −0.208051 | ||||||||
\(15\) | −2.24914 | −0.580726 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.30777 | 1.28732 | 0.643662 | − | 0.765310i | \(-0.277414\pi\) | ||||
0.643662 | + | 0.765310i | \(0.277414\pi\) | |||||||
\(18\) | −2.05863 | −0.485224 | ||||||||
\(19\) | 3.71982 | 0.853386 | 0.426693 | − | 0.904396i | \(-0.359678\pi\) | ||||
0.426693 | + | 0.904396i | \(0.359678\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.75086 | 0.382069 | ||||||||
\(22\) | −5.19051 | −1.10662 | ||||||||
\(23\) | 7.30777 | 1.52378 | 0.761888 | − | 0.647709i | \(-0.224273\pi\) | ||||
0.761888 | + | 0.647709i | \(0.224273\pi\) | |||||||
\(24\) | −2.24914 | −0.459104 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.83709 | 0.752515 | ||||||||
\(27\) | −2.11727 | −0.407468 | ||||||||
\(28\) | 0.778457 | 0.147115 | ||||||||
\(29\) | −9.52588 | −1.76891 | −0.884456 | − | 0.466624i | \(-0.845470\pi\) | ||||
−0.884456 | + | 0.466624i | \(0.845470\pi\) | |||||||
\(30\) | 2.24914 | 0.410635 | ||||||||
\(31\) | −0.412050 | −0.0740064 | −0.0370032 | − | 0.999315i | \(-0.511781\pi\) | ||||
−0.0370032 | + | 0.999315i | \(0.511781\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 11.6742 | 2.03221 | ||||||||
\(34\) | −5.30777 | −0.910276 | ||||||||
\(35\) | −0.778457 | −0.131583 | ||||||||
\(36\) | 2.05863 | 0.343106 | ||||||||
\(37\) | −10.8647 | −1.78614 | −0.893072 | − | 0.449914i | \(-0.851455\pi\) | ||||
−0.893072 | + | 0.449914i | \(0.851455\pi\) | |||||||
\(38\) | −3.71982 | −0.603435 | ||||||||
\(39\) | −8.63016 | −1.38193 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.66119 | 1.35265 | 0.676325 | − | 0.736603i | \(-0.263571\pi\) | ||||
0.676325 | + | 0.736603i | \(0.263571\pi\) | |||||||
\(42\) | −1.75086 | −0.270163 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 5.19051 | 0.782498 | ||||||||
\(45\) | −2.05863 | −0.306883 | ||||||||
\(46\) | −7.30777 | −1.07747 | ||||||||
\(47\) | 2.24914 | 0.328071 | 0.164035 | − | 0.986454i | \(-0.447549\pi\) | ||||
0.164035 | + | 0.986454i | \(0.447549\pi\) | |||||||
\(48\) | 2.24914 | 0.324635 | ||||||||
\(49\) | −6.39400 | −0.913429 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 11.9379 | 1.67164 | ||||||||
\(52\) | −3.83709 | −0.532109 | ||||||||
\(53\) | −4.05520 | −0.557024 | −0.278512 | − | 0.960433i | \(-0.589841\pi\) | ||||
−0.278512 | + | 0.960433i | \(0.589841\pi\) | |||||||
\(54\) | 2.11727 | 0.288123 | ||||||||
\(55\) | −5.19051 | −0.699888 | ||||||||
\(56\) | −0.778457 | −0.104026 | ||||||||
\(57\) | 8.36641 | 1.10816 | ||||||||
\(58\) | 9.52588 | 1.25081 | ||||||||
\(59\) | 10.6155 | 1.38203 | 0.691013 | − | 0.722842i | \(-0.257165\pi\) | ||||
0.691013 | + | 0.722842i | \(0.257165\pi\) | |||||||
\(60\) | −2.24914 | −0.290363 | ||||||||
\(61\) | 10.5845 | 1.35521 | 0.677604 | − | 0.735427i | \(-0.263018\pi\) | ||||
0.677604 | + | 0.735427i | \(0.263018\pi\) | |||||||
\(62\) | 0.412050 | 0.0523304 | ||||||||
\(63\) | 1.60256 | 0.201903 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.83709 | 0.475932 | ||||||||
\(66\) | −11.6742 | −1.43699 | ||||||||
\(67\) | −13.9690 | −1.70658 | −0.853290 | − | 0.521436i | \(-0.825396\pi\) | ||||
−0.853290 | + | 0.521436i | \(0.825396\pi\) | |||||||
\(68\) | 5.30777 | 0.643662 | ||||||||
\(69\) | 16.4362 | 1.97869 | ||||||||
\(70\) | 0.778457 | 0.0930434 | ||||||||
\(71\) | 1.19051 | 0.141287 | 0.0706436 | − | 0.997502i | \(-0.477495\pi\) | ||||
0.0706436 | + | 0.997502i | \(0.477495\pi\) | |||||||
\(72\) | −2.05863 | −0.242612 | ||||||||
\(73\) | −9.85170 | −1.15305 | −0.576527 | − | 0.817078i | \(-0.695592\pi\) | ||||
−0.576527 | + | 0.817078i | \(0.695592\pi\) | |||||||
\(74\) | 10.8647 | 1.26299 | ||||||||
\(75\) | 2.24914 | 0.259708 | ||||||||
\(76\) | 3.71982 | 0.426693 | ||||||||
\(77\) | 4.04059 | 0.460468 | ||||||||
\(78\) | 8.63016 | 0.977173 | ||||||||
\(79\) | 4.08623 | 0.459737 | 0.229868 | − | 0.973222i | \(-0.426170\pi\) | ||||
0.229868 | + | 0.973222i | \(0.426170\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | −8.66119 | −0.956469 | ||||||||
\(83\) | −10.0552 | −1.10370 | −0.551851 | − | 0.833943i | \(-0.686078\pi\) | ||||
−0.551851 | + | 0.833943i | \(0.686078\pi\) | |||||||
\(84\) | 1.75086 | 0.191034 | ||||||||
\(85\) | −5.30777 | −0.575709 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | −21.4250 | −2.29701 | ||||||||
\(88\) | −5.19051 | −0.553310 | ||||||||
\(89\) | −12.9820 | −1.37608 | −0.688042 | − | 0.725671i | \(-0.741530\pi\) | ||||
−0.688042 | + | 0.725671i | \(0.741530\pi\) | |||||||
\(90\) | 2.05863 | 0.216999 | ||||||||
\(91\) | −2.98701 | −0.313124 | ||||||||
\(92\) | 7.30777 | 0.761888 | ||||||||
\(93\) | −0.926759 | −0.0961004 | ||||||||
\(94\) | −2.24914 | −0.231981 | ||||||||
\(95\) | −3.71982 | −0.381646 | ||||||||
\(96\) | −2.24914 | −0.229552 | ||||||||
\(97\) | −10.8647 | −1.10314 | −0.551571 | − | 0.834128i | \(-0.685971\pi\) | ||||
−0.551571 | + | 0.834128i | \(0.685971\pi\) | |||||||
\(98\) | 6.39400 | 0.645892 | ||||||||
\(99\) | 10.6854 | 1.07392 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.809493 | −0.0805475 | −0.0402738 | − | 0.999189i | \(-0.512823\pi\) | ||||
−0.0402738 | + | 0.999189i | \(0.512823\pi\) | |||||||
\(102\) | −11.9379 | −1.18203 | ||||||||
\(103\) | −1.05863 | −0.104310 | −0.0521551 | − | 0.998639i | \(-0.516609\pi\) | ||||
−0.0521551 | + | 0.998639i | \(0.516609\pi\) | |||||||
\(104\) | 3.83709 | 0.376258 | ||||||||
\(105\) | −1.75086 | −0.170866 | ||||||||
\(106\) | 4.05520 | 0.393875 | ||||||||
\(107\) | −9.64315 | −0.932238 | −0.466119 | − | 0.884722i | \(-0.654348\pi\) | ||||
−0.466119 | + | 0.884722i | \(0.654348\pi\) | |||||||
\(108\) | −2.11727 | −0.203734 | ||||||||
\(109\) | 3.05863 | 0.292964 | 0.146482 | − | 0.989213i | \(-0.453205\pi\) | ||||
0.146482 | + | 0.989213i | \(0.453205\pi\) | |||||||
\(110\) | 5.19051 | 0.494895 | ||||||||
\(111\) | −24.4362 | −2.31938 | ||||||||
\(112\) | 0.778457 | 0.0735573 | ||||||||
\(113\) | 1.91377 | 0.180032 | 0.0900161 | − | 0.995940i | \(-0.471308\pi\) | ||||
0.0900161 | + | 0.995940i | \(0.471308\pi\) | |||||||
\(114\) | −8.36641 | −0.783586 | ||||||||
\(115\) | −7.30777 | −0.681453 | ||||||||
\(116\) | −9.52588 | −0.884456 | ||||||||
\(117\) | −7.89916 | −0.730278 | ||||||||
\(118\) | −10.6155 | −0.977240 | ||||||||
\(119\) | 4.13187 | 0.378768 | ||||||||
\(120\) | 2.24914 | 0.205318 | ||||||||
\(121\) | 15.9414 | 1.44922 | ||||||||
\(122\) | −10.5845 | −0.958277 | ||||||||
\(123\) | 19.4802 | 1.75647 | ||||||||
\(124\) | −0.412050 | −0.0370032 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.60256 | −0.142767 | ||||||||
\(127\) | 2.61555 | 0.232092 | 0.116046 | − | 0.993244i | \(-0.462978\pi\) | ||||
0.116046 | + | 0.993244i | \(0.462978\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.24914 | 0.198026 | ||||||||
\(130\) | −3.83709 | −0.336535 | ||||||||
\(131\) | −3.93793 | −0.344058 | −0.172029 | − | 0.985092i | \(-0.555032\pi\) | ||||
−0.172029 | + | 0.985092i | \(0.555032\pi\) | |||||||
\(132\) | 11.6742 | 1.01611 | ||||||||
\(133\) | 2.89572 | 0.251091 | ||||||||
\(134\) | 13.9690 | 1.20673 | ||||||||
\(135\) | 2.11727 | 0.182225 | ||||||||
\(136\) | −5.30777 | −0.455138 | ||||||||
\(137\) | −0.855136 | −0.0730592 | −0.0365296 | − | 0.999333i | \(-0.511630\pi\) | ||||
−0.0365296 | + | 0.999333i | \(0.511630\pi\) | |||||||
\(138\) | −16.4362 | −1.39914 | ||||||||
\(139\) | 2.80949 | 0.238298 | 0.119149 | − | 0.992876i | \(-0.461983\pi\) | ||||
0.119149 | + | 0.992876i | \(0.461983\pi\) | |||||||
\(140\) | −0.778457 | −0.0657916 | ||||||||
\(141\) | 5.05863 | 0.426014 | ||||||||
\(142\) | −1.19051 | −0.0999052 | ||||||||
\(143\) | −19.9164 | −1.66550 | ||||||||
\(144\) | 2.05863 | 0.171553 | ||||||||
\(145\) | 9.52588 | 0.791081 | ||||||||
\(146\) | 9.85170 | 0.815332 | ||||||||
\(147\) | −14.3810 | −1.18613 | ||||||||
\(148\) | −10.8647 | −0.893072 | ||||||||
\(149\) | −13.2913 | −1.08887 | −0.544435 | − | 0.838803i | \(-0.683256\pi\) | ||||
−0.544435 | + | 0.838803i | \(0.683256\pi\) | |||||||
\(150\) | −2.24914 | −0.183642 | ||||||||
\(151\) | −5.05863 | −0.411666 | −0.205833 | − | 0.978587i | \(-0.565990\pi\) | ||||
−0.205833 | + | 0.978587i | \(0.565990\pi\) | |||||||
\(152\) | −3.71982 | −0.301718 | ||||||||
\(153\) | 10.9268 | 0.883376 | ||||||||
\(154\) | −4.04059 | −0.325600 | ||||||||
\(155\) | 0.412050 | 0.0330967 | ||||||||
\(156\) | −8.63016 | −0.690965 | ||||||||
\(157\) | 19.3630 | 1.54533 | 0.772667 | − | 0.634812i | \(-0.218922\pi\) | ||||
0.772667 | + | 0.634812i | \(0.218922\pi\) | |||||||
\(158\) | −4.08623 | −0.325083 | ||||||||
\(159\) | −9.12070 | −0.723319 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.68879 | 0.448339 | ||||||||
\(162\) | 10.9379 | 0.859365 | ||||||||
\(163\) | −17.2311 | −1.34964 | −0.674822 | − | 0.737981i | \(-0.735779\pi\) | ||||
−0.674822 | + | 0.737981i | \(0.735779\pi\) | |||||||
\(164\) | 8.66119 | 0.676325 | ||||||||
\(165\) | −11.6742 | −0.908834 | ||||||||
\(166\) | 10.0552 | 0.780435 | ||||||||
\(167\) | −11.8061 | −0.913580 | −0.456790 | − | 0.889575i | \(-0.651001\pi\) | ||||
−0.456790 | + | 0.889575i | \(0.651001\pi\) | |||||||
\(168\) | −1.75086 | −0.135082 | ||||||||
\(169\) | 1.72326 | 0.132559 | ||||||||
\(170\) | 5.30777 | 0.407088 | ||||||||
\(171\) | 7.65775 | 0.585603 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 1.39400 | 0.105984 | 0.0529921 | − | 0.998595i | \(-0.483124\pi\) | ||||
0.0529921 | + | 0.998595i | \(0.483124\pi\) | |||||||
\(174\) | 21.4250 | 1.62423 | ||||||||
\(175\) | 0.778457 | 0.0588458 | ||||||||
\(176\) | 5.19051 | 0.391249 | ||||||||
\(177\) | 23.8759 | 1.79462 | ||||||||
\(178\) | 12.9820 | 0.973039 | ||||||||
\(179\) | 17.7750 | 1.32857 | 0.664284 | − | 0.747481i | \(-0.268737\pi\) | ||||
0.664284 | + | 0.747481i | \(0.268737\pi\) | |||||||
\(180\) | −2.05863 | −0.153441 | ||||||||
\(181\) | −18.5389 | −1.37798 | −0.688992 | − | 0.724769i | \(-0.741946\pi\) | ||||
−0.688992 | + | 0.724769i | \(0.741946\pi\) | |||||||
\(182\) | 2.98701 | 0.221412 | ||||||||
\(183\) | 23.8061 | 1.75979 | ||||||||
\(184\) | −7.30777 | −0.538736 | ||||||||
\(185\) | 10.8647 | 0.798788 | ||||||||
\(186\) | 0.926759 | 0.0679533 | ||||||||
\(187\) | 27.5500 | 2.01466 | ||||||||
\(188\) | 2.24914 | 0.164035 | ||||||||
\(189\) | −1.64820 | −0.119889 | ||||||||
\(190\) | 3.71982 | 0.269864 | ||||||||
\(191\) | 14.4216 | 1.04351 | 0.521755 | − | 0.853095i | \(-0.325277\pi\) | ||||
0.521755 | + | 0.853095i | \(0.325277\pi\) | |||||||
\(192\) | 2.24914 | 0.162318 | ||||||||
\(193\) | 20.9414 | 1.50739 | 0.753696 | − | 0.657223i | \(-0.228269\pi\) | ||||
0.753696 | + | 0.657223i | \(0.228269\pi\) | |||||||
\(194\) | 10.8647 | 0.780039 | ||||||||
\(195\) | 8.63016 | 0.618018 | ||||||||
\(196\) | −6.39400 | −0.456715 | ||||||||
\(197\) | 9.22154 | 0.657008 | 0.328504 | − | 0.944503i | \(-0.393456\pi\) | ||||
0.328504 | + | 0.944503i | \(0.393456\pi\) | |||||||
\(198\) | −10.6854 | −0.759375 | ||||||||
\(199\) | −13.6888 | −0.970372 | −0.485186 | − | 0.874411i | \(-0.661248\pi\) | ||||
−0.485186 | + | 0.874411i | \(0.661248\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −31.4182 | −2.21607 | ||||||||
\(202\) | 0.809493 | 0.0569557 | ||||||||
\(203\) | −7.41549 | −0.520465 | ||||||||
\(204\) | 11.9379 | 0.835822 | ||||||||
\(205\) | −8.66119 | −0.604924 | ||||||||
\(206\) | 1.05863 | 0.0737585 | ||||||||
\(207\) | 15.0440 | 1.04563 | ||||||||
\(208\) | −3.83709 | −0.266054 | ||||||||
\(209\) | 19.3078 | 1.33555 | ||||||||
\(210\) | 1.75086 | 0.120821 | ||||||||
\(211\) | 4.88617 | 0.336378 | 0.168189 | − | 0.985755i | \(-0.446208\pi\) | ||||
0.168189 | + | 0.985755i | \(0.446208\pi\) | |||||||
\(212\) | −4.05520 | −0.278512 | ||||||||
\(213\) | 2.67762 | 0.183467 | ||||||||
\(214\) | 9.64315 | 0.659192 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 2.11727 | 0.144062 | ||||||||
\(217\) | −0.320763 | −0.0217748 | ||||||||
\(218\) | −3.05863 | −0.207157 | ||||||||
\(219\) | −22.1579 | −1.49729 | ||||||||
\(220\) | −5.19051 | −0.349944 | ||||||||
\(221\) | −20.3664 | −1.36999 | ||||||||
\(222\) | 24.4362 | 1.64005 | ||||||||
\(223\) | −17.5569 | −1.17570 | −0.587849 | − | 0.808971i | \(-0.700025\pi\) | ||||
−0.587849 | + | 0.808971i | \(0.700025\pi\) | |||||||
\(224\) | −0.778457 | −0.0520129 | ||||||||
\(225\) | 2.05863 | 0.137242 | ||||||||
\(226\) | −1.91377 | −0.127302 | ||||||||
\(227\) | −3.61211 | −0.239744 | −0.119872 | − | 0.992789i | \(-0.538248\pi\) | ||||
−0.119872 | + | 0.992789i | \(0.538248\pi\) | |||||||
\(228\) | 8.36641 | 0.554079 | ||||||||
\(229\) | 5.26719 | 0.348065 | 0.174033 | − | 0.984740i | \(-0.444320\pi\) | ||||
0.174033 | + | 0.984740i | \(0.444320\pi\) | |||||||
\(230\) | 7.30777 | 0.481860 | ||||||||
\(231\) | 9.08785 | 0.597937 | ||||||||
\(232\) | 9.52588 | 0.625405 | ||||||||
\(233\) | 26.6707 | 1.74726 | 0.873629 | − | 0.486592i | \(-0.161760\pi\) | ||||
0.873629 | + | 0.486592i | \(0.161760\pi\) | |||||||
\(234\) | 7.89916 | 0.516384 | ||||||||
\(235\) | −2.24914 | −0.146718 | ||||||||
\(236\) | 10.6155 | 0.691013 | ||||||||
\(237\) | 9.19051 | 0.596988 | ||||||||
\(238\) | −4.13187 | −0.267830 | ||||||||
\(239\) | 6.20350 | 0.401271 | 0.200635 | − | 0.979666i | \(-0.435699\pi\) | ||||
0.200635 | + | 0.979666i | \(0.435699\pi\) | |||||||
\(240\) | −2.24914 | −0.145181 | ||||||||
\(241\) | 11.9233 | 0.768049 | 0.384024 | − | 0.923323i | \(-0.374538\pi\) | ||||
0.384024 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(242\) | −15.9414 | −1.02475 | ||||||||
\(243\) | −18.2491 | −1.17068 | ||||||||
\(244\) | 10.5845 | 0.677604 | ||||||||
\(245\) | 6.39400 | 0.408498 | ||||||||
\(246\) | −19.4802 | −1.24201 | ||||||||
\(247\) | −14.2733 | −0.908188 | ||||||||
\(248\) | 0.412050 | 0.0261652 | ||||||||
\(249\) | −22.6155 | −1.43320 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −7.20512 | −0.454783 | −0.227391 | − | 0.973803i | \(-0.573020\pi\) | ||||
−0.227391 | + | 0.973803i | \(0.573020\pi\) | |||||||
\(252\) | 1.60256 | 0.100952 | ||||||||
\(253\) | 37.9311 | 2.38470 | ||||||||
\(254\) | −2.61555 | −0.164114 | ||||||||
\(255\) | −11.9379 | −0.747582 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.20350 | −0.511720 | −0.255860 | − | 0.966714i | \(-0.582359\pi\) | ||||
−0.255860 | + | 0.966714i | \(0.582359\pi\) | |||||||
\(258\) | −2.24914 | −0.140025 | ||||||||
\(259\) | −8.45769 | −0.525536 | ||||||||
\(260\) | 3.83709 | 0.237966 | ||||||||
\(261\) | −19.6103 | −1.21385 | ||||||||
\(262\) | 3.93793 | 0.243286 | ||||||||
\(263\) | 1.43010 | 0.0881835 | 0.0440917 | − | 0.999027i | \(-0.485961\pi\) | ||||
0.0440917 | + | 0.999027i | \(0.485961\pi\) | |||||||
\(264\) | −11.6742 | −0.718496 | ||||||||
\(265\) | 4.05520 | 0.249109 | ||||||||
\(266\) | −2.89572 | −0.177548 | ||||||||
\(267\) | −29.1982 | −1.78690 | ||||||||
\(268\) | −13.9690 | −0.853290 | ||||||||
\(269\) | 21.0518 | 1.28355 | 0.641774 | − | 0.766894i | \(-0.278199\pi\) | ||||
0.641774 | + | 0.766894i | \(0.278199\pi\) | |||||||
\(270\) | −2.11727 | −0.128853 | ||||||||
\(271\) | 21.9069 | 1.33075 | 0.665375 | − | 0.746510i | \(-0.268272\pi\) | ||||
0.665375 | + | 0.746510i | \(0.268272\pi\) | |||||||
\(272\) | 5.30777 | 0.321831 | ||||||||
\(273\) | −6.71821 | −0.406604 | ||||||||
\(274\) | 0.855136 | 0.0516607 | ||||||||
\(275\) | 5.19051 | 0.312999 | ||||||||
\(276\) | 16.4362 | 0.989344 | ||||||||
\(277\) | 20.9414 | 1.25824 | 0.629122 | − | 0.777306i | \(-0.283414\pi\) | ||||
0.629122 | + | 0.777306i | \(0.283414\pi\) | |||||||
\(278\) | −2.80949 | −0.168502 | ||||||||
\(279\) | −0.848260 | −0.0507840 | ||||||||
\(280\) | 0.778457 | 0.0465217 | ||||||||
\(281\) | 27.3871 | 1.63378 | 0.816890 | − | 0.576794i | \(-0.195697\pi\) | ||||
0.816890 | + | 0.576794i | \(0.195697\pi\) | |||||||
\(282\) | −5.05863 | −0.301237 | ||||||||
\(283\) | 9.64315 | 0.573225 | 0.286613 | − | 0.958047i | \(-0.407471\pi\) | ||||
0.286613 | + | 0.958047i | \(0.407471\pi\) | |||||||
\(284\) | 1.19051 | 0.0706436 | ||||||||
\(285\) | −8.36641 | −0.495583 | ||||||||
\(286\) | 19.9164 | 1.17768 | ||||||||
\(287\) | 6.74237 | 0.397989 | ||||||||
\(288\) | −2.05863 | −0.121306 | ||||||||
\(289\) | 11.1725 | 0.657204 | ||||||||
\(290\) | −9.52588 | −0.559379 | ||||||||
\(291\) | −24.4362 | −1.43248 | ||||||||
\(292\) | −9.85170 | −0.576527 | ||||||||
\(293\) | −6.99656 | −0.408744 | −0.204372 | − | 0.978893i | \(-0.565515\pi\) | ||||
−0.204372 | + | 0.978893i | \(0.565515\pi\) | |||||||
\(294\) | 14.3810 | 0.838718 | ||||||||
\(295\) | −10.6155 | −0.618061 | ||||||||
\(296\) | 10.8647 | 0.631497 | ||||||||
\(297\) | −10.9897 | −0.637686 | ||||||||
\(298\) | 13.2913 | 0.769947 | ||||||||
\(299\) | −28.0406 | −1.62163 | ||||||||
\(300\) | 2.24914 | 0.129854 | ||||||||
\(301\) | 0.778457 | 0.0448695 | ||||||||
\(302\) | 5.05863 | 0.291092 | ||||||||
\(303\) | −1.82066 | −0.104594 | ||||||||
\(304\) | 3.71982 | 0.213347 | ||||||||
\(305\) | −10.5845 | −0.606067 | ||||||||
\(306\) | −10.9268 | −0.624641 | ||||||||
\(307\) | −27.4638 | −1.56744 | −0.783721 | − | 0.621113i | \(-0.786681\pi\) | ||||
−0.783721 | + | 0.621113i | \(0.786681\pi\) | |||||||
\(308\) | 4.04059 | 0.230234 | ||||||||
\(309\) | −2.38101 | −0.135451 | ||||||||
\(310\) | −0.412050 | −0.0234029 | ||||||||
\(311\) | 6.29478 | 0.356944 | 0.178472 | − | 0.983945i | \(-0.442885\pi\) | ||||
0.178472 | + | 0.983945i | \(0.442885\pi\) | |||||||
\(312\) | 8.63016 | 0.488586 | ||||||||
\(313\) | −10.9966 | −0.621562 | −0.310781 | − | 0.950481i | \(-0.600591\pi\) | ||||
−0.310781 | + | 0.950481i | \(0.600591\pi\) | |||||||
\(314\) | −19.3630 | −1.09272 | ||||||||
\(315\) | −1.60256 | −0.0902939 | ||||||||
\(316\) | 4.08623 | 0.229868 | ||||||||
\(317\) | 8.10084 | 0.454988 | 0.227494 | − | 0.973779i | \(-0.426947\pi\) | ||||
0.227494 | + | 0.973779i | \(0.426947\pi\) | |||||||
\(318\) | 9.12070 | 0.511464 | ||||||||
\(319\) | −49.4441 | −2.76834 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −21.6888 | −1.21055 | ||||||||
\(322\) | −5.68879 | −0.317024 | ||||||||
\(323\) | 19.7440 | 1.09858 | ||||||||
\(324\) | −10.9379 | −0.607663 | ||||||||
\(325\) | −3.83709 | −0.212843 | ||||||||
\(326\) | 17.2311 | 0.954342 | ||||||||
\(327\) | 6.87930 | 0.380426 | ||||||||
\(328\) | −8.66119 | −0.478234 | ||||||||
\(329\) | 1.75086 | 0.0965280 | ||||||||
\(330\) | 11.6742 | 0.642642 | ||||||||
\(331\) | −2.28973 | −0.125855 | −0.0629274 | − | 0.998018i | \(-0.520044\pi\) | ||||
−0.0629274 | + | 0.998018i | \(0.520044\pi\) | |||||||
\(332\) | −10.0552 | −0.551851 | ||||||||
\(333\) | −22.3664 | −1.22567 | ||||||||
\(334\) | 11.8061 | 0.645999 | ||||||||
\(335\) | 13.9690 | 0.763206 | ||||||||
\(336\) | 1.75086 | 0.0955172 | ||||||||
\(337\) | 15.8827 | 0.865188 | 0.432594 | − | 0.901589i | \(-0.357598\pi\) | ||||
0.432594 | + | 0.901589i | \(0.357598\pi\) | |||||||
\(338\) | −1.72326 | −0.0937331 | ||||||||
\(339\) | 4.30434 | 0.233779 | ||||||||
\(340\) | −5.30777 | −0.287854 | ||||||||
\(341\) | −2.13875 | −0.115820 | ||||||||
\(342\) | −7.65775 | −0.414084 | ||||||||
\(343\) | −10.4267 | −0.562987 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | −16.4362 | −0.884896 | ||||||||
\(346\) | −1.39400 | −0.0749421 | ||||||||
\(347\) | 16.6922 | 0.896086 | 0.448043 | − | 0.894012i | \(-0.352121\pi\) | ||||
0.448043 | + | 0.894012i | \(0.352121\pi\) | |||||||
\(348\) | −21.4250 | −1.14850 | ||||||||
\(349\) | −23.2603 | −1.24510 | −0.622548 | − | 0.782582i | \(-0.713902\pi\) | ||||
−0.622548 | + | 0.782582i | \(0.713902\pi\) | |||||||
\(350\) | −0.778457 | −0.0416103 | ||||||||
\(351\) | 8.12414 | 0.433635 | ||||||||
\(352\) | −5.19051 | −0.276655 | ||||||||
\(353\) | −17.8681 | −0.951024 | −0.475512 | − | 0.879709i | \(-0.657737\pi\) | ||||
−0.475512 | + | 0.879709i | \(0.657737\pi\) | |||||||
\(354\) | −23.8759 | −1.26899 | ||||||||
\(355\) | −1.19051 | −0.0631856 | ||||||||
\(356\) | −12.9820 | −0.688042 | ||||||||
\(357\) | 9.29317 | 0.491846 | ||||||||
\(358\) | −17.7750 | −0.939439 | ||||||||
\(359\) | 1.53275 | 0.0808957 | 0.0404478 | − | 0.999182i | \(-0.487122\pi\) | ||||
0.0404478 | + | 0.999182i | \(0.487122\pi\) | |||||||
\(360\) | 2.05863 | 0.108499 | ||||||||
\(361\) | −5.16291 | −0.271732 | ||||||||
\(362\) | 18.5389 | 0.974381 | ||||||||
\(363\) | 35.8544 | 1.88187 | ||||||||
\(364\) | −2.98701 | −0.156562 | ||||||||
\(365\) | 9.85170 | 0.515661 | ||||||||
\(366\) | −23.8061 | −1.24436 | ||||||||
\(367\) | 0.234533 | 0.0122425 | 0.00612125 | − | 0.999981i | \(-0.498052\pi\) | ||||
0.00612125 | + | 0.999981i | \(0.498052\pi\) | |||||||
\(368\) | 7.30777 | 0.380944 | ||||||||
\(369\) | 17.8302 | 0.928204 | ||||||||
\(370\) | −10.8647 | −0.564828 | ||||||||
\(371\) | −3.15680 | −0.163893 | ||||||||
\(372\) | −0.926759 | −0.0480502 | ||||||||
\(373\) | 4.74742 | 0.245812 | 0.122906 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122906 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(374\) | −27.5500 | −1.42458 | ||||||||
\(375\) | −2.24914 | −0.116145 | ||||||||
\(376\) | −2.24914 | −0.115991 | ||||||||
\(377\) | 36.5517 | 1.88251 | ||||||||
\(378\) | 1.64820 | 0.0847743 | ||||||||
\(379\) | 14.2897 | 0.734014 | 0.367007 | − | 0.930218i | \(-0.380383\pi\) | ||||
0.367007 | + | 0.930218i | \(0.380383\pi\) | |||||||
\(380\) | −3.71982 | −0.190823 | ||||||||
\(381\) | 5.88273 | 0.301382 | ||||||||
\(382\) | −14.4216 | −0.737873 | ||||||||
\(383\) | 3.71982 | 0.190074 | 0.0950371 | − | 0.995474i | \(-0.469703\pi\) | ||||
0.0950371 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(384\) | −2.24914 | −0.114776 | ||||||||
\(385\) | −4.04059 | −0.205927 | ||||||||
\(386\) | −20.9414 | −1.06589 | ||||||||
\(387\) | 2.05863 | 0.104646 | ||||||||
\(388\) | −10.8647 | −0.551571 | ||||||||
\(389\) | −22.6087 | −1.14631 | −0.573153 | − | 0.819449i | \(-0.694280\pi\) | ||||
−0.573153 | + | 0.819449i | \(0.694280\pi\) | |||||||
\(390\) | −8.63016 | −0.437005 | ||||||||
\(391\) | 38.7880 | 1.96159 | ||||||||
\(392\) | 6.39400 | 0.322946 | ||||||||
\(393\) | −8.85696 | −0.446774 | ||||||||
\(394\) | −9.22154 | −0.464575 | ||||||||
\(395\) | −4.08623 | −0.205601 | ||||||||
\(396\) | 10.6854 | 0.536959 | ||||||||
\(397\) | −8.20855 | −0.411975 | −0.205988 | − | 0.978555i | \(-0.566041\pi\) | ||||
−0.205988 | + | 0.978555i | \(0.566041\pi\) | |||||||
\(398\) | 13.6888 | 0.686157 | ||||||||
\(399\) | 6.51289 | 0.326052 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −36.5370 | −1.82457 | −0.912287 | − | 0.409552i | \(-0.865685\pi\) | ||||
−0.912287 | + | 0.409552i | \(0.865685\pi\) | |||||||
\(402\) | 31.4182 | 1.56700 | ||||||||
\(403\) | 1.58107 | 0.0787589 | ||||||||
\(404\) | −0.809493 | −0.0402738 | ||||||||
\(405\) | 10.9379 | 0.543510 | ||||||||
\(406\) | 7.41549 | 0.368024 | ||||||||
\(407\) | −56.3932 | −2.79531 | ||||||||
\(408\) | −11.9379 | −0.591016 | ||||||||
\(409\) | 34.6302 | 1.71235 | 0.856175 | − | 0.516685i | \(-0.172834\pi\) | ||||
0.856175 | + | 0.516685i | \(0.172834\pi\) | |||||||
\(410\) | 8.66119 | 0.427746 | ||||||||
\(411\) | −1.92332 | −0.0948704 | ||||||||
\(412\) | −1.05863 | −0.0521551 | ||||||||
\(413\) | 8.26375 | 0.406632 | ||||||||
\(414\) | −15.0440 | −0.739374 | ||||||||
\(415\) | 10.0552 | 0.493590 | ||||||||
\(416\) | 3.83709 | 0.188129 | ||||||||
\(417\) | 6.31894 | 0.309440 | ||||||||
\(418\) | −19.3078 | −0.944374 | ||||||||
\(419\) | 34.6803 | 1.69424 | 0.847122 | − | 0.531399i | \(-0.178334\pi\) | ||||
0.847122 | + | 0.531399i | \(0.178334\pi\) | |||||||
\(420\) | −1.75086 | −0.0854332 | ||||||||
\(421\) | 9.46381 | 0.461238 | 0.230619 | − | 0.973044i | \(-0.425925\pi\) | ||||
0.230619 | + | 0.973044i | \(0.425925\pi\) | |||||||
\(422\) | −4.88617 | −0.237855 | ||||||||
\(423\) | 4.63016 | 0.225126 | ||||||||
\(424\) | 4.05520 | 0.196938 | ||||||||
\(425\) | 5.30777 | 0.257465 | ||||||||
\(426\) | −2.67762 | −0.129731 | ||||||||
\(427\) | 8.23959 | 0.398742 | ||||||||
\(428\) | −9.64315 | −0.466119 | ||||||||
\(429\) | −44.7949 | −2.16272 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | −18.8172 | −0.906394 | −0.453197 | − | 0.891410i | \(-0.649717\pi\) | ||||
−0.453197 | + | 0.891410i | \(0.649717\pi\) | |||||||
\(432\) | −2.11727 | −0.101867 | ||||||||
\(433\) | −9.11888 | −0.438226 | −0.219113 | − | 0.975700i | \(-0.570316\pi\) | ||||
−0.219113 | + | 0.975700i | \(0.570316\pi\) | |||||||
\(434\) | 0.320763 | 0.0153971 | ||||||||
\(435\) | 21.4250 | 1.02725 | ||||||||
\(436\) | 3.05863 | 0.146482 | ||||||||
\(437\) | 27.1836 | 1.30037 | ||||||||
\(438\) | 22.1579 | 1.05874 | ||||||||
\(439\) | −21.8827 | −1.04441 | −0.522203 | − | 0.852821i | \(-0.674890\pi\) | ||||
−0.522203 | + | 0.852821i | \(0.674890\pi\) | |||||||
\(440\) | 5.19051 | 0.247448 | ||||||||
\(441\) | −13.1629 | −0.626805 | ||||||||
\(442\) | 20.3664 | 0.968731 | ||||||||
\(443\) | 34.6397 | 1.64578 | 0.822891 | − | 0.568199i | \(-0.192360\pi\) | ||||
0.822891 | + | 0.568199i | \(0.192360\pi\) | |||||||
\(444\) | −24.4362 | −1.15969 | ||||||||
\(445\) | 12.9820 | 0.615404 | ||||||||
\(446\) | 17.5569 | 0.831344 | ||||||||
\(447\) | −29.8941 | −1.41394 | ||||||||
\(448\) | 0.778457 | 0.0367786 | ||||||||
\(449\) | −34.7405 | −1.63951 | −0.819754 | − | 0.572716i | \(-0.805890\pi\) | ||||
−0.819754 | + | 0.572716i | \(0.805890\pi\) | |||||||
\(450\) | −2.05863 | −0.0970449 | ||||||||
\(451\) | 44.9560 | 2.11689 | ||||||||
\(452\) | 1.91377 | 0.0900161 | ||||||||
\(453\) | −11.3776 | −0.534565 | ||||||||
\(454\) | 3.61211 | 0.169525 | ||||||||
\(455\) | 2.98701 | 0.140033 | ||||||||
\(456\) | −8.36641 | −0.391793 | ||||||||
\(457\) | 28.4914 | 1.33277 | 0.666386 | − | 0.745607i | \(-0.267840\pi\) | ||||
0.666386 | + | 0.745607i | \(0.267840\pi\) | |||||||
\(458\) | −5.26719 | −0.246119 | ||||||||
\(459\) | −11.2380 | −0.524544 | ||||||||
\(460\) | −7.30777 | −0.340727 | ||||||||
\(461\) | −20.3112 | −0.945987 | −0.472994 | − | 0.881066i | \(-0.656827\pi\) | ||||
−0.472994 | + | 0.881066i | \(0.656827\pi\) | |||||||
\(462\) | −9.08785 | −0.422805 | ||||||||
\(463\) | 39.5665 | 1.83881 | 0.919405 | − | 0.393313i | \(-0.128671\pi\) | ||||
0.919405 | + | 0.393313i | \(0.128671\pi\) | |||||||
\(464\) | −9.52588 | −0.442228 | ||||||||
\(465\) | 0.926759 | 0.0429774 | ||||||||
\(466\) | −26.6707 | −1.23550 | ||||||||
\(467\) | 7.48024 | 0.346144 | 0.173072 | − | 0.984909i | \(-0.444631\pi\) | ||||
0.173072 | + | 0.984909i | \(0.444631\pi\) | |||||||
\(468\) | −7.89916 | −0.365139 | ||||||||
\(469\) | −10.8742 | −0.502126 | ||||||||
\(470\) | 2.24914 | 0.103745 | ||||||||
\(471\) | 43.5500 | 2.00668 | ||||||||
\(472\) | −10.6155 | −0.488620 | ||||||||
\(473\) | 5.19051 | 0.238660 | ||||||||
\(474\) | −9.19051 | −0.422134 | ||||||||
\(475\) | 3.71982 | 0.170677 | ||||||||
\(476\) | 4.13187 | 0.189384 | ||||||||
\(477\) | −8.34816 | −0.382236 | ||||||||
\(478\) | −6.20350 | −0.283741 | ||||||||
\(479\) | −6.14648 | −0.280840 | −0.140420 | − | 0.990092i | \(-0.544845\pi\) | ||||
−0.140420 | + | 0.990092i | \(0.544845\pi\) | |||||||
\(480\) | 2.24914 | 0.102659 | ||||||||
\(481\) | 41.6888 | 1.90085 | ||||||||
\(482\) | −11.9233 | −0.543092 | ||||||||
\(483\) | 12.7949 | 0.582187 | ||||||||
\(484\) | 15.9414 | 0.724608 | ||||||||
\(485\) | 10.8647 | 0.493340 | ||||||||
\(486\) | 18.2491 | 0.827798 | ||||||||
\(487\) | 39.3561 | 1.78339 | 0.891697 | − | 0.452632i | \(-0.149515\pi\) | ||||
0.891697 | + | 0.452632i | \(0.149515\pi\) | |||||||
\(488\) | −10.5845 | −0.479138 | ||||||||
\(489\) | −38.7552 | −1.75257 | ||||||||
\(490\) | −6.39400 | −0.288852 | ||||||||
\(491\) | −1.29317 | −0.0583598 | −0.0291799 | − | 0.999574i | \(-0.509290\pi\) | ||||
−0.0291799 | + | 0.999574i | \(0.509290\pi\) | |||||||
\(492\) | 19.4802 | 0.878237 | ||||||||
\(493\) | −50.5612 | −2.27716 | ||||||||
\(494\) | 14.2733 | 0.642186 | ||||||||
\(495\) | −10.6854 | −0.480271 | ||||||||
\(496\) | −0.412050 | −0.0185016 | ||||||||
\(497\) | 0.926759 | 0.0415708 | ||||||||
\(498\) | 22.6155 | 1.01343 | ||||||||
\(499\) | −25.7750 | −1.15385 | −0.576924 | − | 0.816798i | \(-0.695747\pi\) | ||||
−0.576924 | + | 0.816798i | \(0.695747\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −26.5535 | −1.18632 | ||||||||
\(502\) | 7.20512 | 0.321580 | ||||||||
\(503\) | 23.0518 | 1.02783 | 0.513914 | − | 0.857842i | \(-0.328195\pi\) | ||||
0.513914 | + | 0.857842i | \(0.328195\pi\) | |||||||
\(504\) | −1.60256 | −0.0713836 | ||||||||
\(505\) | 0.809493 | 0.0360219 | ||||||||
\(506\) | −37.9311 | −1.68624 | ||||||||
\(507\) | 3.87586 | 0.172133 | ||||||||
\(508\) | 2.61555 | 0.116046 | ||||||||
\(509\) | 15.1690 | 0.672355 | 0.336178 | − | 0.941799i | \(-0.390866\pi\) | ||||
0.336178 | + | 0.941799i | \(0.390866\pi\) | |||||||
\(510\) | 11.9379 | 0.528620 | ||||||||
\(511\) | −7.66912 | −0.339262 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.87586 | −0.347728 | ||||||||
\(514\) | 8.20350 | 0.361841 | ||||||||
\(515\) | 1.05863 | 0.0466490 | ||||||||
\(516\) | 2.24914 | 0.0990129 | ||||||||
\(517\) | 11.6742 | 0.513430 | ||||||||
\(518\) | 8.45769 | 0.371610 | ||||||||
\(519\) | 3.13531 | 0.137625 | ||||||||
\(520\) | −3.83709 | −0.168268 | ||||||||
\(521\) | −36.7665 | −1.61077 | −0.805385 | − | 0.592752i | \(-0.798042\pi\) | ||||
−0.805385 | + | 0.592752i | \(0.798042\pi\) | |||||||
\(522\) | 19.6103 | 0.858319 | ||||||||
\(523\) | 12.8026 | 0.559819 | 0.279910 | − | 0.960026i | \(-0.409695\pi\) | ||||
0.279910 | + | 0.960026i | \(0.409695\pi\) | |||||||
\(524\) | −3.93793 | −0.172029 | ||||||||
\(525\) | 1.75086 | 0.0764138 | ||||||||
\(526\) | −1.43010 | −0.0623551 | ||||||||
\(527\) | −2.18707 | −0.0952702 | ||||||||
\(528\) | 11.6742 | 0.508053 | ||||||||
\(529\) | 30.4036 | 1.32189 | ||||||||
\(530\) | −4.05520 | −0.176146 | ||||||||
\(531\) | 21.8535 | 0.948362 | ||||||||
\(532\) | 2.89572 | 0.125546 | ||||||||
\(533\) | −33.2338 | −1.43951 | ||||||||
\(534\) | 29.1982 | 1.26353 | ||||||||
\(535\) | 9.64315 | 0.416910 | ||||||||
\(536\) | 13.9690 | 0.603367 | ||||||||
\(537\) | 39.9785 | 1.72520 | ||||||||
\(538\) | −21.0518 | −0.907606 | ||||||||
\(539\) | −33.1881 | −1.42951 | ||||||||
\(540\) | 2.11727 | 0.0911126 | ||||||||
\(541\) | −10.7328 | −0.461440 | −0.230720 | − | 0.973020i | \(-0.574108\pi\) | ||||
−0.230720 | + | 0.973020i | \(0.574108\pi\) | |||||||
\(542\) | −21.9069 | −0.940982 | ||||||||
\(543\) | −41.6965 | −1.78937 | ||||||||
\(544\) | −5.30777 | −0.227569 | ||||||||
\(545\) | −3.05863 | −0.131017 | ||||||||
\(546\) | 6.71821 | 0.287513 | ||||||||
\(547\) | 7.76547 | 0.332027 | 0.166014 | − | 0.986123i | \(-0.446910\pi\) | ||||
0.166014 | + | 0.986123i | \(0.446910\pi\) | |||||||
\(548\) | −0.855136 | −0.0365296 | ||||||||
\(549\) | 21.7896 | 0.929959 | ||||||||
\(550\) | −5.19051 | −0.221324 | ||||||||
\(551\) | −35.4346 | −1.50956 | ||||||||
\(552\) | −16.4362 | −0.699572 | ||||||||
\(553\) | 3.18096 | 0.135268 | ||||||||
\(554\) | −20.9414 | −0.889713 | ||||||||
\(555\) | 24.4362 | 1.03726 | ||||||||
\(556\) | 2.80949 | 0.119149 | ||||||||
\(557\) | −32.0388 | −1.35753 | −0.678763 | − | 0.734357i | \(-0.737484\pi\) | ||||
−0.678763 | + | 0.734357i | \(0.737484\pi\) | |||||||
\(558\) | 0.848260 | 0.0359097 | ||||||||
\(559\) | −3.83709 | −0.162292 | ||||||||
\(560\) | −0.778457 | −0.0328958 | ||||||||
\(561\) | 61.9639 | 2.61612 | ||||||||
\(562\) | −27.3871 | −1.15526 | ||||||||
\(563\) | −5.31733 | −0.224099 | −0.112049 | − | 0.993703i | \(-0.535741\pi\) | ||||
−0.112049 | + | 0.993703i | \(0.535741\pi\) | |||||||
\(564\) | 5.05863 | 0.213007 | ||||||||
\(565\) | −1.91377 | −0.0805129 | ||||||||
\(566\) | −9.64315 | −0.405332 | ||||||||
\(567\) | −8.51471 | −0.357584 | ||||||||
\(568\) | −1.19051 | −0.0499526 | ||||||||
\(569\) | 8.95779 | 0.375530 | 0.187765 | − | 0.982214i | \(-0.439876\pi\) | ||||
0.187765 | + | 0.982214i | \(0.439876\pi\) | |||||||
\(570\) | 8.36641 | 0.350430 | ||||||||
\(571\) | −29.3251 | −1.22722 | −0.613608 | − | 0.789611i | \(-0.710282\pi\) | ||||
−0.613608 | + | 0.789611i | \(0.710282\pi\) | |||||||
\(572\) | −19.9164 | −0.832748 | ||||||||
\(573\) | 32.4362 | 1.35504 | ||||||||
\(574\) | −6.74237 | −0.281421 | ||||||||
\(575\) | 7.30777 | 0.304755 | ||||||||
\(576\) | 2.05863 | 0.0857764 | ||||||||
\(577\) | −32.1706 | −1.33928 | −0.669641 | − | 0.742685i | \(-0.733552\pi\) | ||||
−0.669641 | + | 0.742685i | \(0.733552\pi\) | |||||||
\(578\) | −11.1725 | −0.464713 | ||||||||
\(579\) | 47.1001 | 1.95741 | ||||||||
\(580\) | 9.52588 | 0.395541 | ||||||||
\(581\) | −7.82754 | −0.324741 | ||||||||
\(582\) | 24.4362 | 1.01291 | ||||||||
\(583\) | −21.0485 | −0.871741 | ||||||||
\(584\) | 9.85170 | 0.407666 | ||||||||
\(585\) | 7.89916 | 0.326590 | ||||||||
\(586\) | 6.99656 | 0.289025 | ||||||||
\(587\) | −27.9785 | −1.15480 | −0.577398 | − | 0.816462i | \(-0.695932\pi\) | ||||
−0.577398 | + | 0.816462i | \(0.695932\pi\) | |||||||
\(588\) | −14.3810 | −0.593063 | ||||||||
\(589\) | −1.53275 | −0.0631560 | ||||||||
\(590\) | 10.6155 | 0.437035 | ||||||||
\(591\) | 20.7405 | 0.853152 | ||||||||
\(592\) | −10.8647 | −0.446536 | ||||||||
\(593\) | −4.06025 | −0.166735 | −0.0833673 | − | 0.996519i | \(-0.526567\pi\) | ||||
−0.0833673 | + | 0.996519i | \(0.526567\pi\) | |||||||
\(594\) | 10.9897 | 0.450912 | ||||||||
\(595\) | −4.13187 | −0.169390 | ||||||||
\(596\) | −13.2913 | −0.544435 | ||||||||
\(597\) | −30.7880 | −1.26007 | ||||||||
\(598\) | 28.0406 | 1.14666 | ||||||||
\(599\) | 29.9639 | 1.22429 | 0.612146 | − | 0.790745i | \(-0.290306\pi\) | ||||
0.612146 | + | 0.790745i | \(0.290306\pi\) | |||||||
\(600\) | −2.24914 | −0.0918208 | ||||||||
\(601\) | −12.9706 | −0.529081 | −0.264541 | − | 0.964375i | \(-0.585220\pi\) | ||||
−0.264541 | + | 0.964375i | \(0.585220\pi\) | |||||||
\(602\) | −0.778457 | −0.0317275 | ||||||||
\(603\) | −28.7570 | −1.17107 | ||||||||
\(604\) | −5.05863 | −0.205833 | ||||||||
\(605\) | −15.9414 | −0.648109 | ||||||||
\(606\) | 1.82066 | 0.0739594 | ||||||||
\(607\) | 15.0518 | 0.610932 | 0.305466 | − | 0.952203i | \(-0.401188\pi\) | ||||
0.305466 | + | 0.952203i | \(0.401188\pi\) | |||||||
\(608\) | −3.71982 | −0.150859 | ||||||||
\(609\) | −16.6785 | −0.675846 | ||||||||
\(610\) | 10.5845 | 0.428554 | ||||||||
\(611\) | −8.63016 | −0.349139 | ||||||||
\(612\) | 10.9268 | 0.441688 | ||||||||
\(613\) | −17.0682 | −0.689378 | −0.344689 | − | 0.938717i | \(-0.612016\pi\) | ||||
−0.344689 | + | 0.938717i | \(0.612016\pi\) | |||||||
\(614\) | 27.4638 | 1.10835 | ||||||||
\(615\) | −19.4802 | −0.785519 | ||||||||
\(616\) | −4.04059 | −0.162800 | ||||||||
\(617\) | 48.6639 | 1.95913 | 0.979567 | − | 0.201119i | \(-0.0644579\pi\) | ||||
0.979567 | + | 0.201119i | \(0.0644579\pi\) | |||||||
\(618\) | 2.38101 | 0.0957785 | ||||||||
\(619\) | −14.5750 | −0.585817 | −0.292909 | − | 0.956140i | \(-0.594623\pi\) | ||||
−0.292909 | + | 0.956140i | \(0.594623\pi\) | |||||||
\(620\) | 0.412050 | 0.0165483 | ||||||||
\(621\) | −15.4725 | −0.620890 | ||||||||
\(622\) | −6.29478 | −0.252398 | ||||||||
\(623\) | −10.1059 | −0.404884 | ||||||||
\(624\) | −8.63016 | −0.345483 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.9966 | 0.439511 | ||||||||
\(627\) | 43.4259 | 1.73426 | ||||||||
\(628\) | 19.3630 | 0.772667 | ||||||||
\(629\) | −57.6673 | −2.29935 | ||||||||
\(630\) | 1.60256 | 0.0638474 | ||||||||
\(631\) | 9.09922 | 0.362234 | 0.181117 | − | 0.983462i | \(-0.442029\pi\) | ||||
0.181117 | + | 0.983462i | \(0.442029\pi\) | |||||||
\(632\) | −4.08623 | −0.162542 | ||||||||
\(633\) | 10.9897 | 0.436801 | ||||||||
\(634\) | −8.10084 | −0.321725 | ||||||||
\(635\) | −2.61555 | −0.103795 | ||||||||
\(636\) | −9.12070 | −0.361659 | ||||||||
\(637\) | 24.5344 | 0.972087 | ||||||||
\(638\) | 49.4441 | 1.95751 | ||||||||
\(639\) | 2.45082 | 0.0969529 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −7.38445 | −0.291668 | −0.145834 | − | 0.989309i | \(-0.546587\pi\) | ||||
−0.145834 | + | 0.989309i | \(0.546587\pi\) | |||||||
\(642\) | 21.6888 | 0.855988 | ||||||||
\(643\) | −1.47068 | −0.0579981 | −0.0289990 | − | 0.999579i | \(-0.509232\pi\) | ||||
−0.0289990 | + | 0.999579i | \(0.509232\pi\) | |||||||
\(644\) | 5.68879 | 0.224170 | ||||||||
\(645\) | −2.24914 | −0.0885598 | ||||||||
\(646\) | −19.7440 | −0.776817 | ||||||||
\(647\) | 49.1234 | 1.93124 | 0.965620 | − | 0.259959i | \(-0.0837090\pi\) | ||||
0.965620 | + | 0.259959i | \(0.0837090\pi\) | |||||||
\(648\) | 10.9379 | 0.429682 | ||||||||
\(649\) | 55.1001 | 2.16287 | ||||||||
\(650\) | 3.83709 | 0.150503 | ||||||||
\(651\) | −0.721442 | −0.0282755 | ||||||||
\(652\) | −17.2311 | −0.674822 | ||||||||
\(653\) | 7.30090 | 0.285706 | 0.142853 | − | 0.989744i | \(-0.454372\pi\) | ||||
0.142853 | + | 0.989744i | \(0.454372\pi\) | |||||||
\(654\) | −6.87930 | −0.269002 | ||||||||
\(655\) | 3.93793 | 0.153868 | ||||||||
\(656\) | 8.66119 | 0.338163 | ||||||||
\(657\) | −20.2810 | −0.791238 | ||||||||
\(658\) | −1.75086 | −0.0682556 | ||||||||
\(659\) | 19.3370 | 0.753262 | 0.376631 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376631 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(660\) | −11.6742 | −0.454417 | ||||||||
\(661\) | 28.5941 | 1.11218 | 0.556090 | − | 0.831122i | \(-0.312301\pi\) | ||||
0.556090 | + | 0.831122i | \(0.312301\pi\) | |||||||
\(662\) | 2.28973 | 0.0889928 | ||||||||
\(663\) | −45.8069 | −1.77899 | ||||||||
\(664\) | 10.0552 | 0.390217 | ||||||||
\(665\) | −2.89572 | −0.112291 | ||||||||
\(666\) | 22.3664 | 0.866681 | ||||||||
\(667\) | −69.6130 | −2.69542 | ||||||||
\(668\) | −11.8061 | −0.456790 | ||||||||
\(669\) | −39.4880 | −1.52669 | ||||||||
\(670\) | −13.9690 | −0.539668 | ||||||||
\(671\) | 54.9390 | 2.12090 | ||||||||
\(672\) | −1.75086 | −0.0675409 | ||||||||
\(673\) | −7.08279 | −0.273022 | −0.136511 | − | 0.990639i | \(-0.543589\pi\) | ||||
−0.136511 | + | 0.990639i | \(0.543589\pi\) | |||||||
\(674\) | −15.8827 | −0.611780 | ||||||||
\(675\) | −2.11727 | −0.0814936 | ||||||||
\(676\) | 1.72326 | 0.0662793 | ||||||||
\(677\) | −12.6155 | −0.484855 | −0.242427 | − | 0.970170i | \(-0.577944\pi\) | ||||
−0.242427 | + | 0.970170i | \(0.577944\pi\) | |||||||
\(678\) | −4.30434 | −0.165307 | ||||||||
\(679\) | −8.45769 | −0.324576 | ||||||||
\(680\) | 5.30777 | 0.203544 | ||||||||
\(681\) | −8.12414 | −0.311318 | ||||||||
\(682\) | 2.13875 | 0.0818970 | ||||||||
\(683\) | 0.967346 | 0.0370145 | 0.0185072 | − | 0.999829i | \(-0.494109\pi\) | ||||
0.0185072 | + | 0.999829i | \(0.494109\pi\) | |||||||
\(684\) | 7.65775 | 0.292802 | ||||||||
\(685\) | 0.855136 | 0.0326731 | ||||||||
\(686\) | 10.4267 | 0.398092 | ||||||||
\(687\) | 11.8466 | 0.451978 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 15.5602 | 0.592795 | ||||||||
\(690\) | 16.4362 | 0.625716 | ||||||||
\(691\) | 1.21199 | 0.0461063 | 0.0230532 | − | 0.999734i | \(-0.492661\pi\) | ||||
0.0230532 | + | 0.999734i | \(0.492661\pi\) | |||||||
\(692\) | 1.39400 | 0.0529921 | ||||||||
\(693\) | 8.31809 | 0.315978 | ||||||||
\(694\) | −16.6922 | −0.633628 | ||||||||
\(695\) | −2.80949 | −0.106570 | ||||||||
\(696\) | 21.4250 | 0.812114 | ||||||||
\(697\) | 45.9716 | 1.74130 | ||||||||
\(698\) | 23.2603 | 0.880416 | ||||||||
\(699\) | 59.9862 | 2.26889 | ||||||||
\(700\) | 0.778457 | 0.0294229 | ||||||||
\(701\) | 38.3336 | 1.44784 | 0.723919 | − | 0.689885i | \(-0.242339\pi\) | ||||
0.723919 | + | 0.689885i | \(0.242339\pi\) | |||||||
\(702\) | −8.12414 | −0.306626 | ||||||||
\(703\) | −40.4147 | −1.52427 | ||||||||
\(704\) | 5.19051 | 0.195625 | ||||||||
\(705\) | −5.05863 | −0.190519 | ||||||||
\(706\) | 17.8681 | 0.672476 | ||||||||
\(707\) | −0.630155 | −0.0236994 | ||||||||
\(708\) | 23.8759 | 0.897310 | ||||||||
\(709\) | 18.8647 | 0.708478 | 0.354239 | − | 0.935155i | \(-0.384740\pi\) | ||||
0.354239 | + | 0.935155i | \(0.384740\pi\) | |||||||
\(710\) | 1.19051 | 0.0446789 | ||||||||
\(711\) | 8.41205 | 0.315477 | ||||||||
\(712\) | 12.9820 | 0.486519 | ||||||||
\(713\) | −3.01117 | −0.112769 | ||||||||
\(714\) | −9.29317 | −0.347788 | ||||||||
\(715\) | 19.9164 | 0.744833 | ||||||||
\(716\) | 17.7750 | 0.664284 | ||||||||
\(717\) | 13.9525 | 0.521067 | ||||||||
\(718\) | −1.53275 | −0.0572019 | ||||||||
\(719\) | −43.2863 | −1.61431 | −0.807153 | − | 0.590342i | \(-0.798993\pi\) | ||||
−0.807153 | + | 0.590342i | \(0.798993\pi\) | |||||||
\(720\) | −2.05863 | −0.0767207 | ||||||||
\(721\) | −0.824101 | −0.0306911 | ||||||||
\(722\) | 5.16291 | 0.192144 | ||||||||
\(723\) | 26.8172 | 0.997343 | ||||||||
\(724\) | −18.5389 | −0.688992 | ||||||||
\(725\) | −9.52588 | −0.353782 | ||||||||
\(726\) | −35.8544 | −1.33068 | ||||||||
\(727\) | 35.9379 | 1.33286 | 0.666432 | − | 0.745566i | \(-0.267821\pi\) | ||||
0.666432 | + | 0.745566i | \(0.267821\pi\) | |||||||
\(728\) | 2.98701 | 0.110706 | ||||||||
\(729\) | −8.23109 | −0.304855 | ||||||||
\(730\) | −9.85170 | −0.364628 | ||||||||
\(731\) | 5.30777 | 0.196315 | ||||||||
\(732\) | 23.8061 | 0.879897 | ||||||||
\(733\) | −10.6922 | −0.394926 | −0.197463 | − | 0.980310i | \(-0.563270\pi\) | ||||
−0.197463 | + | 0.980310i | \(0.563270\pi\) | |||||||
\(734\) | −0.234533 | −0.00865676 | ||||||||
\(735\) | 14.3810 | 0.530452 | ||||||||
\(736\) | −7.30777 | −0.269368 | ||||||||
\(737\) | −72.5060 | −2.67079 | ||||||||
\(738\) | −17.8302 | −0.656339 | ||||||||
\(739\) | −6.10084 | −0.224423 | −0.112211 | − | 0.993684i | \(-0.535793\pi\) | ||||
−0.112211 | + | 0.993684i | \(0.535793\pi\) | |||||||
\(740\) | 10.8647 | 0.399394 | ||||||||
\(741\) | −32.1027 | −1.17932 | ||||||||
\(742\) | 3.15680 | 0.115890 | ||||||||
\(743\) | −24.7785 | −0.909033 | −0.454517 | − | 0.890738i | \(-0.650188\pi\) | ||||
−0.454517 | + | 0.890738i | \(0.650188\pi\) | |||||||
\(744\) | 0.926759 | 0.0339766 | ||||||||
\(745\) | 13.2913 | 0.486957 | ||||||||
\(746\) | −4.74742 | −0.173815 | ||||||||
\(747\) | −20.7000 | −0.757372 | ||||||||
\(748\) | 27.5500 | 1.00733 | ||||||||
\(749\) | −7.50677 | −0.274292 | ||||||||
\(750\) | 2.24914 | 0.0821270 | ||||||||
\(751\) | 19.3991 | 0.707882 | 0.353941 | − | 0.935268i | \(-0.384841\pi\) | ||||
0.353941 | + | 0.935268i | \(0.384841\pi\) | |||||||
\(752\) | 2.24914 | 0.0820177 | ||||||||
\(753\) | −16.2053 | −0.590555 | ||||||||
\(754\) | −36.5517 | −1.33113 | ||||||||
\(755\) | 5.05863 | 0.184103 | ||||||||
\(756\) | −1.64820 | −0.0599445 | ||||||||
\(757\) | −42.7191 | −1.55265 | −0.776325 | − | 0.630332i | \(-0.782919\pi\) | ||||
−0.776325 | + | 0.630332i | \(0.782919\pi\) | |||||||
\(758\) | −14.2897 | −0.519026 | ||||||||
\(759\) | 85.3123 | 3.09664 | ||||||||
\(760\) | 3.71982 | 0.134932 | ||||||||
\(761\) | −34.7191 | −1.25857 | −0.629283 | − | 0.777177i | \(-0.716651\pi\) | ||||
−0.629283 | + | 0.777177i | \(0.716651\pi\) | |||||||
\(762\) | −5.88273 | −0.213109 | ||||||||
\(763\) | 2.38101 | 0.0861985 | ||||||||
\(764\) | 14.4216 | 0.521755 | ||||||||
\(765\) | −10.9268 | −0.395058 | ||||||||
\(766\) | −3.71982 | −0.134403 | ||||||||
\(767\) | −40.7328 | −1.47078 | ||||||||
\(768\) | 2.24914 | 0.0811589 | ||||||||
\(769\) | 43.1234 | 1.55507 | 0.777534 | − | 0.628840i | \(-0.216470\pi\) | ||||
0.777534 | + | 0.628840i | \(0.216470\pi\) | |||||||
\(770\) | 4.04059 | 0.145613 | ||||||||
\(771\) | −18.4508 | −0.664490 | ||||||||
\(772\) | 20.9414 | 0.753696 | ||||||||
\(773\) | −0.747422 | −0.0268829 | −0.0134414 | − | 0.999910i | \(-0.504279\pi\) | ||||
−0.0134414 | + | 0.999910i | \(0.504279\pi\) | |||||||
\(774\) | −2.05863 | −0.0739960 | ||||||||
\(775\) | −0.412050 | −0.0148013 | ||||||||
\(776\) | 10.8647 | 0.390020 | ||||||||
\(777\) | −19.0225 | −0.682430 | ||||||||
\(778\) | 22.6087 | 0.810560 | ||||||||
\(779\) | 32.2181 | 1.15433 | ||||||||
\(780\) | 8.63016 | 0.309009 | ||||||||
\(781\) | 6.17934 | 0.221114 | ||||||||
\(782\) | −38.7880 | −1.38706 | ||||||||
\(783\) | 20.1688 | 0.720775 | ||||||||
\(784\) | −6.39400 | −0.228357 | ||||||||
\(785\) | −19.3630 | −0.691094 | ||||||||
\(786\) | 8.85696 | 0.315917 | ||||||||
\(787\) | −37.9260 | −1.35192 | −0.675958 | − | 0.736940i | \(-0.736270\pi\) | ||||
−0.675958 | + | 0.736940i | \(0.736270\pi\) | |||||||
\(788\) | 9.22154 | 0.328504 | ||||||||
\(789\) | 3.21649 | 0.114510 | ||||||||
\(790\) | 4.08623 | 0.145382 | ||||||||
\(791\) | 1.48979 | 0.0529707 | ||||||||
\(792\) | −10.6854 | −0.379687 | ||||||||
\(793\) | −40.6137 | −1.44224 | ||||||||
\(794\) | 8.20855 | 0.291311 | ||||||||
\(795\) | 9.12070 | 0.323478 | ||||||||
\(796\) | −13.6888 | −0.485186 | ||||||||
\(797\) | −8.63198 | −0.305760 | −0.152880 | − | 0.988245i | \(-0.548855\pi\) | ||||
−0.152880 | + | 0.988245i | \(0.548855\pi\) | |||||||
\(798\) | −6.51289 | −0.230554 | ||||||||
\(799\) | 11.9379 | 0.422334 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −26.7251 | −0.944284 | ||||||||
\(802\) | 36.5370 | 1.29017 | ||||||||
\(803\) | −51.1353 | −1.80453 | ||||||||
\(804\) | −31.4182 | −1.10803 | ||||||||
\(805\) | −5.68879 | −0.200503 | ||||||||
\(806\) | −1.58107 | −0.0556910 | ||||||||
\(807\) | 47.3484 | 1.66674 | ||||||||
\(808\) | 0.809493 | 0.0284779 | ||||||||
\(809\) | 49.3611 | 1.73545 | 0.867723 | − | 0.497048i | \(-0.165583\pi\) | ||||
0.867723 | + | 0.497048i | \(0.165583\pi\) | |||||||
\(810\) | −10.9379 | −0.384320 | ||||||||
\(811\) | 26.5991 | 0.934021 | 0.467011 | − | 0.884252i | \(-0.345331\pi\) | ||||
0.467011 | + | 0.884252i | \(0.345331\pi\) | |||||||
\(812\) | −7.41549 | −0.260233 | ||||||||
\(813\) | 49.2717 | 1.72803 | ||||||||
\(814\) | 56.3932 | 1.97658 | ||||||||
\(815\) | 17.2311 | 0.603579 | ||||||||
\(816\) | 11.9379 | 0.417911 | ||||||||
\(817\) | 3.71982 | 0.130140 | ||||||||
\(818\) | −34.6302 | −1.21081 | ||||||||
\(819\) | −6.14916 | −0.214869 | ||||||||
\(820\) | −8.66119 | −0.302462 | ||||||||
\(821\) | −50.6087 | −1.76625 | −0.883127 | − | 0.469133i | \(-0.844566\pi\) | ||||
−0.883127 | + | 0.469133i | \(0.844566\pi\) | |||||||
\(822\) | 1.92332 | 0.0670835 | ||||||||
\(823\) | −48.8103 | −1.70142 | −0.850711 | − | 0.525634i | \(-0.823828\pi\) | ||||
−0.850711 | + | 0.525634i | \(0.823828\pi\) | |||||||
\(824\) | 1.05863 | 0.0368792 | ||||||||
\(825\) | 11.6742 | 0.406443 | ||||||||
\(826\) | −8.26375 | −0.287533 | ||||||||
\(827\) | 47.2293 | 1.64232 | 0.821161 | − | 0.570696i | \(-0.193327\pi\) | ||||
0.821161 | + | 0.570696i | \(0.193327\pi\) | |||||||
\(828\) | 15.0440 | 0.522816 | ||||||||
\(829\) | −7.44147 | −0.258453 | −0.129226 | − | 0.991615i | \(-0.541249\pi\) | ||||
−0.129226 | + | 0.991615i | \(0.541249\pi\) | |||||||
\(830\) | −10.0552 | −0.349021 | ||||||||
\(831\) | 47.1001 | 1.63388 | ||||||||
\(832\) | −3.83709 | −0.133027 | ||||||||
\(833\) | −33.9379 | −1.17588 | ||||||||
\(834\) | −6.31894 | −0.218807 | ||||||||
\(835\) | 11.8061 | 0.408565 | ||||||||
\(836\) | 19.3078 | 0.667773 | ||||||||
\(837\) | 0.872420 | 0.0301553 | ||||||||
\(838\) | −34.6803 | −1.19801 | ||||||||
\(839\) | 16.5389 | 0.570985 | 0.285493 | − | 0.958381i | \(-0.407843\pi\) | ||||
0.285493 | + | 0.958381i | \(0.407843\pi\) | |||||||
\(840\) | 1.75086 | 0.0604104 | ||||||||
\(841\) | 61.7424 | 2.12905 | ||||||||
\(842\) | −9.46381 | −0.326144 | ||||||||
\(843\) | 61.5975 | 2.12153 | ||||||||
\(844\) | 4.88617 | 0.168189 | ||||||||
\(845\) | −1.72326 | −0.0592820 | ||||||||
\(846\) | −4.63016 | −0.159188 | ||||||||
\(847\) | 12.4097 | 0.426401 | ||||||||
\(848\) | −4.05520 | −0.139256 | ||||||||
\(849\) | 21.6888 | 0.744357 | ||||||||
\(850\) | −5.30777 | −0.182055 | ||||||||
\(851\) | −79.3967 | −2.72168 | ||||||||
\(852\) | 2.67762 | 0.0917337 | ||||||||
\(853\) | −34.8862 | −1.19448 | −0.597240 | − | 0.802063i | \(-0.703736\pi\) | ||||
−0.597240 | + | 0.802063i | \(0.703736\pi\) | |||||||
\(854\) | −8.23959 | −0.281953 | ||||||||
\(855\) | −7.65775 | −0.261890 | ||||||||
\(856\) | 9.64315 | 0.329596 | ||||||||
\(857\) | 10.0698 | 0.343978 | 0.171989 | − | 0.985099i | \(-0.444981\pi\) | ||||
0.171989 | + | 0.985099i | \(0.444981\pi\) | |||||||
\(858\) | 44.7949 | 1.52927 | ||||||||
\(859\) | −36.1560 | −1.23363 | −0.616814 | − | 0.787109i | \(-0.711577\pi\) | ||||
−0.616814 | + | 0.787109i | \(0.711577\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 15.1645 | 0.516806 | ||||||||
\(862\) | 18.8172 | 0.640917 | ||||||||
\(863\) | −38.3189 | −1.30439 | −0.652196 | − | 0.758050i | \(-0.726152\pi\) | ||||
−0.652196 | + | 0.758050i | \(0.726152\pi\) | |||||||
\(864\) | 2.11727 | 0.0720309 | ||||||||
\(865\) | −1.39400 | −0.0473976 | ||||||||
\(866\) | 9.11888 | 0.309872 | ||||||||
\(867\) | 25.1284 | 0.853406 | ||||||||
\(868\) | −0.320763 | −0.0108874 | ||||||||
\(869\) | 21.2096 | 0.719487 | ||||||||
\(870\) | −21.4250 | −0.726377 | ||||||||
\(871\) | 53.6002 | 1.81617 | ||||||||
\(872\) | −3.05863 | −0.103578 | ||||||||
\(873\) | −22.3664 | −0.756988 | ||||||||
\(874\) | −27.1836 | −0.919500 | ||||||||
\(875\) | −0.778457 | −0.0263167 | ||||||||
\(876\) | −22.1579 | −0.748644 | ||||||||
\(877\) | 34.5174 | 1.16557 | 0.582785 | − | 0.812627i | \(-0.301963\pi\) | ||||
0.582785 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(878\) | 21.8827 | 0.738506 | ||||||||
\(879\) | −15.7363 | −0.530771 | ||||||||
\(880\) | −5.19051 | −0.174972 | ||||||||
\(881\) | −21.1303 | −0.711896 | −0.355948 | − | 0.934506i | \(-0.615842\pi\) | ||||
−0.355948 | + | 0.934506i | \(0.615842\pi\) | |||||||
\(882\) | 13.1629 | 0.443218 | ||||||||
\(883\) | −6.99838 | −0.235514 | −0.117757 | − | 0.993042i | \(-0.537570\pi\) | ||||
−0.117757 | + | 0.993042i | \(0.537570\pi\) | |||||||
\(884\) | −20.3664 | −0.684996 | ||||||||
\(885\) | −23.8759 | −0.802578 | ||||||||
\(886\) | −34.6397 | −1.16374 | ||||||||
\(887\) | 38.3216 | 1.28671 | 0.643357 | − | 0.765566i | \(-0.277541\pi\) | ||||
0.643357 | + | 0.765566i | \(0.277541\pi\) | |||||||
\(888\) | 24.4362 | 0.820026 | ||||||||
\(889\) | 2.03609 | 0.0682883 | ||||||||
\(890\) | −12.9820 | −0.435156 | ||||||||
\(891\) | −56.7734 | −1.90198 | ||||||||
\(892\) | −17.5569 | −0.587849 | ||||||||
\(893\) | 8.36641 | 0.279971 | ||||||||
\(894\) | 29.8941 | 0.999808 | ||||||||
\(895\) | −17.7750 | −0.594153 | ||||||||
\(896\) | −0.778457 | −0.0260064 | ||||||||
\(897\) | −63.0672 | −2.10575 | ||||||||
\(898\) | 34.7405 | 1.15931 | ||||||||
\(899\) | 3.92514 | 0.130911 | ||||||||
\(900\) | 2.05863 | 0.0686211 | ||||||||
\(901\) | −21.5241 | −0.717070 | ||||||||
\(902\) | −44.9560 | −1.49687 | ||||||||
\(903\) | 1.75086 | 0.0582650 | ||||||||
\(904\) | −1.91377 | −0.0636510 | ||||||||
\(905\) | 18.5389 | 0.616253 | ||||||||
\(906\) | 11.3776 | 0.377995 | ||||||||
\(907\) | −55.4829 | −1.84228 | −0.921140 | − | 0.389232i | \(-0.872741\pi\) | ||||
−0.921140 | + | 0.389232i | \(0.872741\pi\) | |||||||
\(908\) | −3.61211 | −0.119872 | ||||||||
\(909\) | −1.66645 | −0.0552726 | ||||||||
\(910\) | −2.98701 | −0.0990184 | ||||||||
\(911\) | −25.2717 | −0.837288 | −0.418644 | − | 0.908150i | \(-0.637495\pi\) | ||||
−0.418644 | + | 0.908150i | \(0.637495\pi\) | |||||||
\(912\) | 8.36641 | 0.277039 | ||||||||
\(913\) | −52.1916 | −1.72729 | ||||||||
\(914\) | −28.4914 | −0.942412 | ||||||||
\(915\) | −23.8061 | −0.787004 | ||||||||
\(916\) | 5.26719 | 0.174033 | ||||||||
\(917\) | −3.06551 | −0.101232 | ||||||||
\(918\) | 11.2380 | 0.370908 | ||||||||
\(919\) | 21.1741 | 0.698468 | 0.349234 | − | 0.937035i | \(-0.386442\pi\) | ||||
0.349234 | + | 0.937035i | \(0.386442\pi\) | |||||||
\(920\) | 7.30777 | 0.240930 | ||||||||
\(921\) | −61.7700 | −2.03539 | ||||||||
\(922\) | 20.3112 | 0.668914 | ||||||||
\(923\) | −4.56808 | −0.150360 | ||||||||
\(924\) | 9.08785 | 0.298968 | ||||||||
\(925\) | −10.8647 | −0.357229 | ||||||||
\(926\) | −39.5665 | −1.30023 | ||||||||
\(927\) | −2.17934 | −0.0715788 | ||||||||
\(928\) | 9.52588 | 0.312702 | ||||||||
\(929\) | −27.4948 | −0.902077 | −0.451038 | − | 0.892505i | \(-0.648946\pi\) | ||||
−0.451038 | + | 0.892505i | \(0.648946\pi\) | |||||||
\(930\) | −0.926759 | −0.0303896 | ||||||||
\(931\) | −23.7846 | −0.779508 | ||||||||
\(932\) | 26.6707 | 0.873629 | ||||||||
\(933\) | 14.1579 | 0.463507 | ||||||||
\(934\) | −7.48024 | −0.244761 | ||||||||
\(935\) | −27.5500 | −0.900983 | ||||||||
\(936\) | 7.89916 | 0.258192 | ||||||||
\(937\) | −39.7914 | −1.29993 | −0.649965 | − | 0.759964i | \(-0.725216\pi\) | ||||
−0.649965 | + | 0.759964i | \(0.725216\pi\) | |||||||
\(938\) | 10.8742 | 0.355057 | ||||||||
\(939\) | −24.7328 | −0.807125 | ||||||||
\(940\) | −2.24914 | −0.0733589 | ||||||||
\(941\) | 23.7079 | 0.772855 | 0.386428 | − | 0.922320i | \(-0.373709\pi\) | ||||
0.386428 | + | 0.922320i | \(0.373709\pi\) | |||||||
\(942\) | −43.5500 | −1.41894 | ||||||||
\(943\) | 63.2940 | 2.06114 | ||||||||
\(944\) | 10.6155 | 0.345507 | ||||||||
\(945\) | 1.64820 | 0.0536160 | ||||||||
\(946\) | −5.19051 | −0.168758 | ||||||||
\(947\) | 13.1932 | 0.428721 | 0.214360 | − | 0.976755i | \(-0.431233\pi\) | ||||
0.214360 | + | 0.976755i | \(0.431233\pi\) | |||||||
\(948\) | 9.19051 | 0.298494 | ||||||||
\(949\) | 37.8019 | 1.22710 | ||||||||
\(950\) | −3.71982 | −0.120687 | ||||||||
\(951\) | 18.2199 | 0.590822 | ||||||||
\(952\) | −4.13187 | −0.133915 | ||||||||
\(953\) | 26.6949 | 0.864733 | 0.432366 | − | 0.901698i | \(-0.357679\pi\) | ||||
0.432366 | + | 0.901698i | \(0.357679\pi\) | |||||||
\(954\) | 8.34816 | 0.270282 | ||||||||
\(955\) | −14.4216 | −0.466672 | ||||||||
\(956\) | 6.20350 | 0.200635 | ||||||||
\(957\) | −111.207 | −3.59481 | ||||||||
\(958\) | 6.14648 | 0.198584 | ||||||||
\(959\) | −0.665687 | −0.0214961 | ||||||||
\(960\) | −2.24914 | −0.0725907 | ||||||||
\(961\) | −30.8302 | −0.994523 | ||||||||
\(962\) | −41.6888 | −1.34410 | ||||||||
\(963\) | −19.8517 | −0.639712 | ||||||||
\(964\) | 11.9233 | 0.384024 | ||||||||
\(965\) | −20.9414 | −0.674126 | ||||||||
\(966\) | −12.7949 | −0.411669 | ||||||||
\(967\) | 14.6233 | 0.470253 | 0.235126 | − | 0.971965i | \(-0.424450\pi\) | ||||
0.235126 | + | 0.971965i | \(0.424450\pi\) | |||||||
\(968\) | −15.9414 | −0.512375 | ||||||||
\(969\) | 44.4070 | 1.42656 | ||||||||
\(970\) | −10.8647 | −0.348844 | ||||||||
\(971\) | −15.1836 | −0.487266 | −0.243633 | − | 0.969868i | \(-0.578339\pi\) | ||||
−0.243633 | + | 0.969868i | \(0.578339\pi\) | |||||||
\(972\) | −18.2491 | −0.585341 | ||||||||
\(973\) | 2.18707 | 0.0701142 | ||||||||
\(974\) | −39.3561 | −1.26105 | ||||||||
\(975\) | −8.63016 | −0.276386 | ||||||||
\(976\) | 10.5845 | 0.338802 | ||||||||
\(977\) | −8.27836 | −0.264848 | −0.132424 | − | 0.991193i | \(-0.542276\pi\) | ||||
−0.132424 | + | 0.991193i | \(0.542276\pi\) | |||||||
\(978\) | 38.7552 | 1.23925 | ||||||||
\(979\) | −67.3829 | −2.15357 | ||||||||
\(980\) | 6.39400 | 0.204249 | ||||||||
\(981\) | 6.29660 | 0.201035 | ||||||||
\(982\) | 1.29317 | 0.0412666 | ||||||||
\(983\) | 34.6803 | 1.10613 | 0.553065 | − | 0.833138i | \(-0.313458\pi\) | ||||
0.553065 | + | 0.833138i | \(0.313458\pi\) | |||||||
\(984\) | −19.4802 | −0.621007 | ||||||||
\(985\) | −9.22154 | −0.293823 | ||||||||
\(986\) | 50.5612 | 1.61020 | ||||||||
\(987\) | 3.93793 | 0.125346 | ||||||||
\(988\) | −14.2733 | −0.454094 | ||||||||
\(989\) | 7.30777 | 0.232374 | ||||||||
\(990\) | 10.6854 | 0.339603 | ||||||||
\(991\) | −30.6967 | −0.975114 | −0.487557 | − | 0.873091i | \(-0.662112\pi\) | ||||
−0.487557 | + | 0.873091i | \(0.662112\pi\) | |||||||
\(992\) | 0.412050 | 0.0130826 | ||||||||
\(993\) | −5.14992 | −0.163428 | ||||||||
\(994\) | −0.926759 | −0.0293950 | ||||||||
\(995\) | 13.6888 | 0.433964 | ||||||||
\(996\) | −22.6155 | −0.716601 | ||||||||
\(997\) | 52.1656 | 1.65210 | 0.826050 | − | 0.563596i | \(-0.190583\pi\) | ||||
0.826050 | + | 0.563596i | \(0.190583\pi\) | |||||||
\(998\) | 25.7750 | 0.815894 | ||||||||
\(999\) | 23.0034 | 0.727797 |
(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 | 430.2.a.h.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 3870.2.a.bn.1.3 | 3 | |||
4.3 | odd | 2 | 3440.2.a.n.1.1 | 3 | |||
5.2 | odd | 4 | 2150.2.b.t.1549.1 | 6 | |||
5.3 | odd | 4 | 2150.2.b.t.1549.6 | 6 | |||
5.4 | even | 2 | 2150.2.a.bf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
430.2.a.h.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2150.2.a.bf.1.1 | 3 | 5.4 | even | 2 | |||
2150.2.b.t.1549.1 | 6 | 5.2 | odd | 4 | |||
2150.2.b.t.1549.6 | 6 | 5.3 | odd | 4 | |||
3440.2.a.n.1.1 | 3 | 4.3 | odd | 2 | |||
3870.2.a.bn.1.3 | 3 | 3.2 | odd | 2 |