Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.11492689.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 9x^{3} + 13x^{2} + 18x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.42642\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.42642 | −0.637915 | −0.318958 | − | 0.947769i | \(-0.603333\pi\) | ||||
−0.318958 | + | 0.947769i | \(0.603333\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.31394 | −1.63052 | −0.815259 | − | 0.579097i | \(-0.803405\pi\) | ||||
−0.815259 | + | 0.579097i | \(0.803405\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.42642 | −0.451074 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.09185 | −1.13487 | −0.567437 | − | 0.823417i | \(-0.692065\pi\) | ||||
−0.567437 | + | 0.823417i | \(0.692065\pi\) | |||||||
\(14\) | −4.31394 | −1.15295 | ||||||||
\(15\) | 1.42642 | 0.368301 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.94918 | 0.715281 | 0.357641 | − | 0.933859i | \(-0.383581\pi\) | ||||
0.357641 | + | 0.933859i | \(0.383581\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.11248 | 0.484635 | 0.242318 | − | 0.970197i | \(-0.422092\pi\) | ||||
0.242318 | + | 0.970197i | \(0.422092\pi\) | |||||||
\(20\) | −1.42642 | −0.318958 | ||||||||
\(21\) | 4.31394 | 0.941380 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −8.99021 | −1.87459 | −0.937294 | − | 0.348540i | \(-0.886678\pi\) | ||||
−0.937294 | + | 0.348540i | \(0.886678\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.96532 | −0.593064 | ||||||||
\(26\) | −4.09185 | −0.802478 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.31394 | −0.815259 | ||||||||
\(29\) | −0.364765 | −0.0677353 | −0.0338676 | − | 0.999426i | \(-0.510782\pi\) | ||||
−0.0338676 | + | 0.999426i | \(0.510782\pi\) | |||||||
\(30\) | 1.42642 | 0.260428 | ||||||||
\(31\) | 6.51827 | 1.17072 | 0.585358 | − | 0.810775i | \(-0.300954\pi\) | ||||
0.585358 | + | 0.810775i | \(0.300954\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 2.94918 | 0.505780 | ||||||||
\(35\) | 6.15350 | 1.04013 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.86689 | 1.45771 | 0.728854 | − | 0.684669i | \(-0.240053\pi\) | ||||
0.728854 | + | 0.684669i | \(0.240053\pi\) | |||||||
\(38\) | 2.11248 | 0.342689 | ||||||||
\(39\) | 4.09185 | 0.655220 | ||||||||
\(40\) | −1.42642 | −0.225537 | ||||||||
\(41\) | −7.50136 | −1.17152 | −0.585758 | − | 0.810486i | \(-0.699203\pi\) | ||||
−0.585758 | + | 0.810486i | \(0.699203\pi\) | |||||||
\(42\) | 4.31394 | 0.665656 | ||||||||
\(43\) | −9.40579 | −1.43437 | −0.717185 | − | 0.696883i | \(-0.754570\pi\) | ||||
−0.717185 | + | 0.696883i | \(0.754570\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.42642 | −0.212638 | ||||||||
\(46\) | −8.99021 | −1.32553 | ||||||||
\(47\) | 11.3095 | 1.64965 | 0.824827 | − | 0.565385i | \(-0.191272\pi\) | ||||
0.824827 | + | 0.565385i | \(0.191272\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.6101 | 1.65859 | ||||||||
\(50\) | −2.96532 | −0.419360 | ||||||||
\(51\) | −2.94918 | −0.412968 | ||||||||
\(52\) | −4.09185 | −0.567437 | ||||||||
\(53\) | 0.972256 | 0.133550 | 0.0667748 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667748 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.42642 | −0.192339 | ||||||||
\(56\) | −4.31394 | −0.576475 | ||||||||
\(57\) | −2.11248 | −0.279804 | ||||||||
\(58\) | −0.364765 | −0.0478961 | ||||||||
\(59\) | −3.18742 | −0.414966 | −0.207483 | − | 0.978239i | \(-0.566527\pi\) | ||||
−0.207483 | + | 0.978239i | \(0.566527\pi\) | |||||||
\(60\) | 1.42642 | 0.184150 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 6.51827 | 0.827821 | ||||||||
\(63\) | −4.31394 | −0.543506 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.83670 | 0.723954 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 1.61461 | 0.197256 | 0.0986278 | − | 0.995124i | \(-0.468555\pi\) | ||||
0.0986278 | + | 0.995124i | \(0.468555\pi\) | |||||||
\(68\) | 2.94918 | 0.357641 | ||||||||
\(69\) | 8.99021 | 1.08229 | ||||||||
\(70\) | 6.15350 | 0.735485 | ||||||||
\(71\) | 16.3409 | 1.93931 | 0.969655 | − | 0.244476i | \(-0.0786160\pi\) | ||||
0.969655 | + | 0.244476i | \(0.0786160\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.11959 | −0.248080 | −0.124040 | − | 0.992277i | \(-0.539585\pi\) | ||||
−0.124040 | + | 0.992277i | \(0.539585\pi\) | |||||||
\(74\) | 8.86689 | 1.03076 | ||||||||
\(75\) | 2.96532 | 0.342406 | ||||||||
\(76\) | 2.11248 | 0.242318 | ||||||||
\(77\) | −4.31394 | −0.491620 | ||||||||
\(78\) | 4.09185 | 0.463311 | ||||||||
\(79\) | 12.7706 | 1.43680 | 0.718400 | − | 0.695630i | \(-0.244875\pi\) | ||||
0.718400 | + | 0.695630i | \(0.244875\pi\) | |||||||
\(80\) | −1.42642 | −0.159479 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.50136 | −0.828387 | ||||||||
\(83\) | −16.6242 | −1.82474 | −0.912370 | − | 0.409367i | \(-0.865750\pi\) | ||||
−0.912370 | + | 0.409367i | \(0.865750\pi\) | |||||||
\(84\) | 4.31394 | 0.470690 | ||||||||
\(85\) | −4.20677 | −0.456289 | ||||||||
\(86\) | −9.40579 | −1.01425 | ||||||||
\(87\) | 0.364765 | 0.0391070 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 6.82510 | 0.723459 | 0.361730 | − | 0.932283i | \(-0.382186\pi\) | ||||
0.361730 | + | 0.932283i | \(0.382186\pi\) | |||||||
\(90\) | −1.42642 | −0.150358 | ||||||||
\(91\) | 17.6520 | 1.85043 | ||||||||
\(92\) | −8.99021 | −0.937294 | ||||||||
\(93\) | −6.51827 | −0.675913 | ||||||||
\(94\) | 11.3095 | 1.16648 | ||||||||
\(95\) | −3.01328 | −0.309156 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 18.5432 | 1.88277 | 0.941386 | − | 0.337331i | \(-0.109524\pi\) | ||||
0.941386 | + | 0.337331i | \(0.109524\pi\) | |||||||
\(98\) | 11.6101 | 1.17280 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −2.96532 | −0.296532 | ||||||||
\(101\) | 14.5291 | 1.44570 | 0.722850 | − | 0.691005i | \(-0.242832\pi\) | ||||
0.722850 | + | 0.691005i | \(0.242832\pi\) | |||||||
\(102\) | −2.94918 | −0.292012 | ||||||||
\(103\) | −7.60056 | −0.748905 | −0.374452 | − | 0.927246i | \(-0.622169\pi\) | ||||
−0.374452 | + | 0.927246i | \(0.622169\pi\) | |||||||
\(104\) | −4.09185 | −0.401239 | ||||||||
\(105\) | −6.15350 | −0.600521 | ||||||||
\(106\) | 0.972256 | 0.0944338 | ||||||||
\(107\) | −5.61705 | −0.543021 | −0.271511 | − | 0.962435i | \(-0.587523\pi\) | ||||
−0.271511 | + | 0.962435i | \(0.587523\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.3889 | 1.09086 | 0.545429 | − | 0.838157i | \(-0.316367\pi\) | ||||
0.545429 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(110\) | −1.42642 | −0.136004 | ||||||||
\(111\) | −8.86689 | −0.841608 | ||||||||
\(112\) | −4.31394 | −0.407629 | ||||||||
\(113\) | −11.2470 | −1.05803 | −0.529014 | − | 0.848613i | \(-0.677438\pi\) | ||||
−0.529014 | + | 0.848613i | \(0.677438\pi\) | |||||||
\(114\) | −2.11248 | −0.197852 | ||||||||
\(115\) | 12.8238 | 1.19583 | ||||||||
\(116\) | −0.364765 | −0.0338676 | ||||||||
\(117\) | −4.09185 | −0.378292 | ||||||||
\(118\) | −3.18742 | −0.293426 | ||||||||
\(119\) | −12.7226 | −1.16628 | ||||||||
\(120\) | 1.42642 | 0.130214 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 7.50136 | 0.676375 | ||||||||
\(124\) | 6.51827 | 0.585358 | ||||||||
\(125\) | 11.3619 | 1.01624 | ||||||||
\(126\) | −4.31394 | −0.384317 | ||||||||
\(127\) | −0.825867 | −0.0732838 | −0.0366419 | − | 0.999328i | \(-0.511666\pi\) | ||||
−0.0366419 | + | 0.999328i | \(0.511666\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.40579 | 0.828134 | ||||||||
\(130\) | 5.83670 | 0.511913 | ||||||||
\(131\) | 6.22740 | 0.544091 | 0.272045 | − | 0.962284i | \(-0.412300\pi\) | ||||
0.272045 | + | 0.962284i | \(0.412300\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −9.11311 | −0.790207 | ||||||||
\(134\) | 1.61461 | 0.139481 | ||||||||
\(135\) | 1.42642 | 0.122767 | ||||||||
\(136\) | 2.94918 | 0.252890 | ||||||||
\(137\) | 12.8830 | 1.10067 | 0.550336 | − | 0.834943i | \(-0.314500\pi\) | ||||
0.550336 | + | 0.834943i | \(0.314500\pi\) | |||||||
\(138\) | 8.99021 | 0.765297 | ||||||||
\(139\) | 5.84201 | 0.495513 | 0.247756 | − | 0.968822i | \(-0.420307\pi\) | ||||
0.247756 | + | 0.968822i | \(0.420307\pi\) | |||||||
\(140\) | 6.15350 | 0.520066 | ||||||||
\(141\) | −11.3095 | −0.952428 | ||||||||
\(142\) | 16.3409 | 1.37130 | ||||||||
\(143\) | −4.09185 | −0.342178 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.520309 | 0.0432093 | ||||||||
\(146\) | −2.11959 | −0.175419 | ||||||||
\(147\) | −11.6101 | −0.957586 | ||||||||
\(148\) | 8.86689 | 0.728854 | ||||||||
\(149\) | 7.92855 | 0.649532 | 0.324766 | − | 0.945794i | \(-0.394714\pi\) | ||||
0.324766 | + | 0.945794i | \(0.394714\pi\) | |||||||
\(150\) | 2.96532 | 0.242117 | ||||||||
\(151\) | 2.10164 | 0.171029 | 0.0855146 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855146 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(152\) | 2.11248 | 0.171345 | ||||||||
\(153\) | 2.94918 | 0.238427 | ||||||||
\(154\) | −4.31394 | −0.347628 | ||||||||
\(155\) | −9.29780 | −0.746818 | ||||||||
\(156\) | 4.09185 | 0.327610 | ||||||||
\(157\) | 8.26312 | 0.659469 | 0.329735 | − | 0.944074i | \(-0.393041\pi\) | ||||
0.329735 | + | 0.944074i | \(0.393041\pi\) | |||||||
\(158\) | 12.7706 | 1.01597 | ||||||||
\(159\) | −0.972256 | −0.0771049 | ||||||||
\(160\) | −1.42642 | −0.112769 | ||||||||
\(161\) | 38.7833 | 3.05655 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 7.18533 | 0.562798 | 0.281399 | − | 0.959591i | \(-0.409202\pi\) | ||||
0.281399 | + | 0.959591i | \(0.409202\pi\) | |||||||
\(164\) | −7.50136 | −0.585758 | ||||||||
\(165\) | 1.42642 | 0.111047 | ||||||||
\(166\) | −16.6242 | −1.29029 | ||||||||
\(167\) | 3.88059 | 0.300289 | 0.150144 | − | 0.988664i | \(-0.452026\pi\) | ||||
0.150144 | + | 0.988664i | \(0.452026\pi\) | |||||||
\(168\) | 4.31394 | 0.332828 | ||||||||
\(169\) | 3.74322 | 0.287940 | ||||||||
\(170\) | −4.20677 | −0.322645 | ||||||||
\(171\) | 2.11248 | 0.161545 | ||||||||
\(172\) | −9.40579 | −0.717185 | ||||||||
\(173\) | 6.99265 | 0.531642 | 0.265821 | − | 0.964022i | \(-0.414357\pi\) | ||||
0.265821 | + | 0.964022i | \(0.414357\pi\) | |||||||
\(174\) | 0.364765 | 0.0276528 | ||||||||
\(175\) | 12.7922 | 0.967002 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 3.18742 | 0.239581 | ||||||||
\(178\) | 6.82510 | 0.511563 | ||||||||
\(179\) | 22.3105 | 1.66757 | 0.833783 | − | 0.552093i | \(-0.186171\pi\) | ||||
0.833783 | + | 0.552093i | \(0.186171\pi\) | |||||||
\(180\) | −1.42642 | −0.106319 | ||||||||
\(181\) | −16.3574 | −1.21584 | −0.607919 | − | 0.793999i | \(-0.707995\pi\) | ||||
−0.607919 | + | 0.793999i | \(0.707995\pi\) | |||||||
\(182\) | 17.6520 | 1.30845 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −8.99021 | −0.662767 | ||||||||
\(185\) | −12.6479 | −0.929894 | ||||||||
\(186\) | −6.51827 | −0.477943 | ||||||||
\(187\) | 2.94918 | 0.215665 | ||||||||
\(188\) | 11.3095 | 0.824827 | ||||||||
\(189\) | 4.31394 | 0.313793 | ||||||||
\(190\) | −3.01328 | −0.218607 | ||||||||
\(191\) | −23.6912 | −1.71424 | −0.857118 | − | 0.515119i | \(-0.827748\pi\) | ||||
−0.857118 | + | 0.515119i | \(0.827748\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −12.7713 | −0.919300 | −0.459650 | − | 0.888100i | \(-0.652025\pi\) | ||||
−0.459650 | + | 0.888100i | \(0.652025\pi\) | |||||||
\(194\) | 18.5432 | 1.33132 | ||||||||
\(195\) | −5.83670 | −0.417975 | ||||||||
\(196\) | 11.6101 | 0.829294 | ||||||||
\(197\) | 15.2901 | 1.08937 | 0.544687 | − | 0.838639i | \(-0.316648\pi\) | ||||
0.544687 | + | 0.838639i | \(0.316648\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 6.97937 | 0.494755 | 0.247377 | − | 0.968919i | \(-0.420431\pi\) | ||||
0.247377 | + | 0.968919i | \(0.420431\pi\) | |||||||
\(200\) | −2.96532 | −0.209680 | ||||||||
\(201\) | −1.61461 | −0.113886 | ||||||||
\(202\) | 14.5291 | 1.02226 | ||||||||
\(203\) | 1.57358 | 0.110444 | ||||||||
\(204\) | −2.94918 | −0.206484 | ||||||||
\(205\) | 10.7001 | 0.747328 | ||||||||
\(206\) | −7.60056 | −0.529556 | ||||||||
\(207\) | −8.99021 | −0.624863 | ||||||||
\(208\) | −4.09185 | −0.283719 | ||||||||
\(209\) | 2.11248 | 0.146123 | ||||||||
\(210\) | −6.15350 | −0.424632 | ||||||||
\(211\) | −16.9302 | −1.16553 | −0.582763 | − | 0.812642i | \(-0.698028\pi\) | ||||
−0.582763 | + | 0.812642i | \(0.698028\pi\) | |||||||
\(212\) | 0.972256 | 0.0667748 | ||||||||
\(213\) | −16.3409 | −1.11966 | ||||||||
\(214\) | −5.61705 | −0.383974 | ||||||||
\(215\) | 13.4166 | 0.915006 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −28.1195 | −1.90887 | ||||||||
\(218\) | 11.3889 | 0.771353 | ||||||||
\(219\) | 2.11959 | 0.143229 | ||||||||
\(220\) | −1.42642 | −0.0961693 | ||||||||
\(221\) | −12.0676 | −0.811754 | ||||||||
\(222\) | −8.86689 | −0.595107 | ||||||||
\(223\) | −0.523168 | −0.0350339 | −0.0175169 | − | 0.999847i | \(-0.505576\pi\) | ||||
−0.0175169 | + | 0.999847i | \(0.505576\pi\) | |||||||
\(224\) | −4.31394 | −0.288238 | ||||||||
\(225\) | −2.96532 | −0.197688 | ||||||||
\(226\) | −11.2470 | −0.748138 | ||||||||
\(227\) | 11.7126 | 0.777394 | 0.388697 | − | 0.921366i | \(-0.372925\pi\) | ||||
0.388697 | + | 0.921366i | \(0.372925\pi\) | |||||||
\(228\) | −2.11248 | −0.139902 | ||||||||
\(229\) | 16.3317 | 1.07923 | 0.539615 | − | 0.841912i | \(-0.318570\pi\) | ||||
0.539615 | + | 0.841912i | \(0.318570\pi\) | |||||||
\(230\) | 12.8238 | 0.845578 | ||||||||
\(231\) | 4.31394 | 0.283837 | ||||||||
\(232\) | −0.364765 | −0.0239480 | ||||||||
\(233\) | 3.84287 | 0.251755 | 0.125877 | − | 0.992046i | \(-0.459825\pi\) | ||||
0.125877 | + | 0.992046i | \(0.459825\pi\) | |||||||
\(234\) | −4.09185 | −0.267493 | ||||||||
\(235\) | −16.1321 | −1.05234 | ||||||||
\(236\) | −3.18742 | −0.207483 | ||||||||
\(237\) | −12.7706 | −0.829537 | ||||||||
\(238\) | −12.7226 | −0.824683 | ||||||||
\(239\) | −25.2682 | −1.63446 | −0.817232 | − | 0.576309i | \(-0.804493\pi\) | ||||
−0.817232 | + | 0.576309i | \(0.804493\pi\) | |||||||
\(240\) | 1.42642 | 0.0920751 | ||||||||
\(241\) | 2.81712 | 0.181467 | 0.0907334 | − | 0.995875i | \(-0.471079\pi\) | ||||
0.0907334 | + | 0.995875i | \(0.471079\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −16.5609 | −1.05804 | ||||||||
\(246\) | 7.50136 | 0.478269 | ||||||||
\(247\) | −8.64394 | −0.550001 | ||||||||
\(248\) | 6.51827 | 0.413911 | ||||||||
\(249\) | 16.6242 | 1.05351 | ||||||||
\(250\) | 11.3619 | 0.718590 | ||||||||
\(251\) | −13.3675 | −0.843748 | −0.421874 | − | 0.906654i | \(-0.638628\pi\) | ||||
−0.421874 | + | 0.906654i | \(0.638628\pi\) | |||||||
\(252\) | −4.31394 | −0.271753 | ||||||||
\(253\) | −8.99021 | −0.565209 | ||||||||
\(254\) | −0.825867 | −0.0518195 | ||||||||
\(255\) | 4.20677 | 0.263438 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.44578 | 0.526833 | 0.263417 | − | 0.964682i | \(-0.415151\pi\) | ||||
0.263417 | + | 0.964682i | \(0.415151\pi\) | |||||||
\(258\) | 9.40579 | 0.585579 | ||||||||
\(259\) | −38.2513 | −2.37682 | ||||||||
\(260\) | 5.83670 | 0.361977 | ||||||||
\(261\) | −0.364765 | −0.0225784 | ||||||||
\(262\) | 6.22740 | 0.384730 | ||||||||
\(263\) | 8.47107 | 0.522349 | 0.261174 | − | 0.965292i | \(-0.415890\pi\) | ||||
0.261174 | + | 0.965292i | \(0.415890\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −1.38685 | −0.0851933 | ||||||||
\(266\) | −9.11311 | −0.558761 | ||||||||
\(267\) | −6.82510 | −0.417689 | ||||||||
\(268\) | 1.61461 | 0.0986278 | ||||||||
\(269\) | −20.0276 | −1.22110 | −0.610552 | − | 0.791976i | \(-0.709053\pi\) | ||||
−0.610552 | + | 0.791976i | \(0.709053\pi\) | |||||||
\(270\) | 1.42642 | 0.0868093 | ||||||||
\(271\) | −1.79328 | −0.108934 | −0.0544669 | − | 0.998516i | \(-0.517346\pi\) | ||||
−0.0544669 | + | 0.998516i | \(0.517346\pi\) | |||||||
\(272\) | 2.94918 | 0.178820 | ||||||||
\(273\) | −17.6520 | −1.06835 | ||||||||
\(274\) | 12.8830 | 0.778293 | ||||||||
\(275\) | −2.96532 | −0.178816 | ||||||||
\(276\) | 8.99021 | 0.541147 | ||||||||
\(277\) | −7.31639 | −0.439599 | −0.219800 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219800 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(278\) | 5.84201 | 0.350380 | ||||||||
\(279\) | 6.51827 | 0.390239 | ||||||||
\(280\) | 6.15350 | 0.367742 | ||||||||
\(281\) | 11.7126 | 0.698716 | 0.349358 | − | 0.936989i | \(-0.386400\pi\) | ||||
0.349358 | + | 0.936989i | \(0.386400\pi\) | |||||||
\(282\) | −11.3095 | −0.673468 | ||||||||
\(283\) | −7.94841 | −0.472484 | −0.236242 | − | 0.971694i | \(-0.575916\pi\) | ||||
−0.236242 | + | 0.971694i | \(0.575916\pi\) | |||||||
\(284\) | 16.3409 | 0.969655 | ||||||||
\(285\) | 3.01328 | 0.178492 | ||||||||
\(286\) | −4.09185 | −0.241956 | ||||||||
\(287\) | 32.3605 | 1.91018 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −8.30234 | −0.488373 | ||||||||
\(290\) | 0.520309 | 0.0305536 | ||||||||
\(291\) | −18.5432 | −1.08702 | ||||||||
\(292\) | −2.11959 | −0.124040 | ||||||||
\(293\) | 27.6790 | 1.61702 | 0.808512 | − | 0.588480i | \(-0.200273\pi\) | ||||
0.808512 | + | 0.588480i | \(0.200273\pi\) | |||||||
\(294\) | −11.6101 | −0.677116 | ||||||||
\(295\) | 4.54660 | 0.264713 | ||||||||
\(296\) | 8.86689 | 0.515378 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 7.92855 | 0.459289 | ||||||||
\(299\) | 36.7866 | 2.12742 | ||||||||
\(300\) | 2.96532 | 0.171203 | ||||||||
\(301\) | 40.5761 | 2.33877 | ||||||||
\(302\) | 2.10164 | 0.120936 | ||||||||
\(303\) | −14.5291 | −0.834675 | ||||||||
\(304\) | 2.11248 | 0.121159 | ||||||||
\(305\) | −1.42642 | −0.0816767 | ||||||||
\(306\) | 2.94918 | 0.168593 | ||||||||
\(307\) | −5.87220 | −0.335144 | −0.167572 | − | 0.985860i | \(-0.553593\pi\) | ||||
−0.167572 | + | 0.985860i | \(0.553593\pi\) | |||||||
\(308\) | −4.31394 | −0.245810 | ||||||||
\(309\) | 7.60056 | 0.432380 | ||||||||
\(310\) | −9.29780 | −0.528080 | ||||||||
\(311\) | −2.20840 | −0.125227 | −0.0626135 | − | 0.998038i | \(-0.519944\pi\) | ||||
−0.0626135 | + | 0.998038i | \(0.519944\pi\) | |||||||
\(312\) | 4.09185 | 0.231655 | ||||||||
\(313\) | 5.90919 | 0.334007 | 0.167004 | − | 0.985956i | \(-0.446591\pi\) | ||||
0.167004 | + | 0.985956i | \(0.446591\pi\) | |||||||
\(314\) | 8.26312 | 0.466315 | ||||||||
\(315\) | 6.15350 | 0.346711 | ||||||||
\(316\) | 12.7706 | 0.718400 | ||||||||
\(317\) | −6.50059 | −0.365110 | −0.182555 | − | 0.983196i | \(-0.558437\pi\) | ||||
−0.182555 | + | 0.983196i | \(0.558437\pi\) | |||||||
\(318\) | −0.972256 | −0.0545214 | ||||||||
\(319\) | −0.364765 | −0.0204229 | ||||||||
\(320\) | −1.42642 | −0.0797394 | ||||||||
\(321\) | 5.61705 | 0.313513 | ||||||||
\(322\) | 38.7833 | 2.16131 | ||||||||
\(323\) | 6.23007 | 0.346651 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 12.1336 | 0.673053 | ||||||||
\(326\) | 7.18533 | 0.397958 | ||||||||
\(327\) | −11.3889 | −0.629807 | ||||||||
\(328\) | −7.50136 | −0.414193 | ||||||||
\(329\) | −48.7884 | −2.68979 | ||||||||
\(330\) | 1.42642 | 0.0785219 | ||||||||
\(331\) | −12.1572 | −0.668222 | −0.334111 | − | 0.942534i | \(-0.608436\pi\) | ||||
−0.334111 | + | 0.942534i | \(0.608436\pi\) | |||||||
\(332\) | −16.6242 | −0.912370 | ||||||||
\(333\) | 8.86689 | 0.485903 | ||||||||
\(334\) | 3.88059 | 0.212336 | ||||||||
\(335\) | −2.30311 | −0.125832 | ||||||||
\(336\) | 4.31394 | 0.235345 | ||||||||
\(337\) | −5.19798 | −0.283152 | −0.141576 | − | 0.989927i | \(-0.545217\pi\) | ||||
−0.141576 | + | 0.989927i | \(0.545217\pi\) | |||||||
\(338\) | 3.74322 | 0.203605 | ||||||||
\(339\) | 11.2470 | 0.610852 | ||||||||
\(340\) | −4.20677 | −0.228144 | ||||||||
\(341\) | 6.51827 | 0.352984 | ||||||||
\(342\) | 2.11248 | 0.114230 | ||||||||
\(343\) | −19.8878 | −1.07384 | ||||||||
\(344\) | −9.40579 | −0.507126 | ||||||||
\(345\) | −12.8238 | −0.690412 | ||||||||
\(346\) | 6.99265 | 0.375927 | ||||||||
\(347\) | 13.3297 | 0.715575 | 0.357787 | − | 0.933803i | \(-0.383531\pi\) | ||||
0.357787 | + | 0.933803i | \(0.383531\pi\) | |||||||
\(348\) | 0.364765 | 0.0195535 | ||||||||
\(349\) | −14.1748 | −0.758758 | −0.379379 | − | 0.925241i | \(-0.623862\pi\) | ||||
−0.379379 | + | 0.925241i | \(0.623862\pi\) | |||||||
\(350\) | 12.7922 | 0.683773 | ||||||||
\(351\) | 4.09185 | 0.218407 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 33.0438 | 1.75874 | 0.879371 | − | 0.476138i | \(-0.157964\pi\) | ||||
0.879371 | + | 0.476138i | \(0.157964\pi\) | |||||||
\(354\) | 3.18742 | 0.169409 | ||||||||
\(355\) | −23.3090 | −1.23712 | ||||||||
\(356\) | 6.82510 | 0.361730 | ||||||||
\(357\) | 12.7226 | 0.673351 | ||||||||
\(358\) | 22.3105 | 1.17915 | ||||||||
\(359\) | 0.876687 | 0.0462698 | 0.0231349 | − | 0.999732i | \(-0.492635\pi\) | ||||
0.0231349 | + | 0.999732i | \(0.492635\pi\) | |||||||
\(360\) | −1.42642 | −0.0751790 | ||||||||
\(361\) | −14.5374 | −0.765128 | ||||||||
\(362\) | −16.3574 | −0.859727 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 17.6520 | 0.925217 | ||||||||
\(365\) | 3.02343 | 0.158254 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | −37.2181 | −1.94277 | −0.971386 | − | 0.237507i | \(-0.923670\pi\) | ||||
−0.971386 | + | 0.237507i | \(0.923670\pi\) | |||||||
\(368\) | −8.99021 | −0.468647 | ||||||||
\(369\) | −7.50136 | −0.390505 | ||||||||
\(370\) | −12.6479 | −0.657535 | ||||||||
\(371\) | −4.19426 | −0.217755 | ||||||||
\(372\) | −6.51827 | −0.337957 | ||||||||
\(373\) | −15.6612 | −0.810904 | −0.405452 | − | 0.914116i | \(-0.632886\pi\) | ||||
−0.405452 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(374\) | 2.94918 | 0.152498 | ||||||||
\(375\) | −11.3619 | −0.586726 | ||||||||
\(376\) | 11.3095 | 0.583241 | ||||||||
\(377\) | 1.49257 | 0.0768710 | ||||||||
\(378\) | 4.31394 | 0.221885 | ||||||||
\(379\) | 17.7746 | 0.913018 | 0.456509 | − | 0.889719i | \(-0.349100\pi\) | ||||
0.456509 | + | 0.889719i | \(0.349100\pi\) | |||||||
\(380\) | −3.01328 | −0.154578 | ||||||||
\(381\) | 0.825867 | 0.0423104 | ||||||||
\(382\) | −23.6912 | −1.21215 | ||||||||
\(383\) | 5.32233 | 0.271958 | 0.135979 | − | 0.990712i | \(-0.456582\pi\) | ||||
0.135979 | + | 0.990712i | \(0.456582\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 6.15350 | 0.313612 | ||||||||
\(386\) | −12.7713 | −0.650043 | ||||||||
\(387\) | −9.40579 | −0.478123 | ||||||||
\(388\) | 18.5432 | 0.941386 | ||||||||
\(389\) | 6.88145 | 0.348903 | 0.174452 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174452 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(390\) | −5.83670 | −0.295553 | ||||||||
\(391\) | −26.5137 | −1.34086 | ||||||||
\(392\) | 11.6101 | 0.586400 | ||||||||
\(393\) | −6.22740 | −0.314131 | ||||||||
\(394\) | 15.2901 | 0.770304 | ||||||||
\(395\) | −18.2162 | −0.916557 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 9.40172 | 0.471859 | 0.235929 | − | 0.971770i | \(-0.424187\pi\) | ||||
0.235929 | + | 0.971770i | \(0.424187\pi\) | |||||||
\(398\) | 6.97937 | 0.349844 | ||||||||
\(399\) | 9.11311 | 0.456226 | ||||||||
\(400\) | −2.96532 | −0.148266 | ||||||||
\(401\) | 14.8318 | 0.740665 | 0.370332 | − | 0.928899i | \(-0.379244\pi\) | ||||
0.370332 | + | 0.928899i | \(0.379244\pi\) | |||||||
\(402\) | −1.61461 | −0.0805292 | ||||||||
\(403\) | −26.6718 | −1.32862 | ||||||||
\(404\) | 14.5291 | 0.722850 | ||||||||
\(405\) | −1.42642 | −0.0708795 | ||||||||
\(406\) | 1.57358 | 0.0780954 | ||||||||
\(407\) | 8.86689 | 0.439516 | ||||||||
\(408\) | −2.94918 | −0.146006 | ||||||||
\(409\) | −34.9984 | −1.73056 | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||||
−0.865279 | + | 0.501291i | \(0.832859\pi\) | |||||||
\(410\) | 10.7001 | 0.528441 | ||||||||
\(411\) | −12.8830 | −0.635473 | ||||||||
\(412\) | −7.60056 | −0.374452 | ||||||||
\(413\) | 13.7503 | 0.676610 | ||||||||
\(414\) | −8.99021 | −0.441845 | ||||||||
\(415\) | 23.7131 | 1.16403 | ||||||||
\(416\) | −4.09185 | −0.200619 | ||||||||
\(417\) | −5.84201 | −0.286084 | ||||||||
\(418\) | 2.11248 | 0.103325 | ||||||||
\(419\) | −4.96323 | −0.242470 | −0.121235 | − | 0.992624i | \(-0.538685\pi\) | ||||
−0.121235 | + | 0.992624i | \(0.538685\pi\) | |||||||
\(420\) | −6.15350 | −0.300260 | ||||||||
\(421\) | 25.2941 | 1.23276 | 0.616379 | − | 0.787450i | \(-0.288599\pi\) | ||||
0.616379 | + | 0.787450i | \(0.288599\pi\) | |||||||
\(422\) | −16.9302 | −0.824151 | ||||||||
\(423\) | 11.3095 | 0.549885 | ||||||||
\(424\) | 0.972256 | 0.0472169 | ||||||||
\(425\) | −8.74526 | −0.424208 | ||||||||
\(426\) | −16.3409 | −0.791720 | ||||||||
\(427\) | −4.31394 | −0.208766 | ||||||||
\(428\) | −5.61705 | −0.271511 | ||||||||
\(429\) | 4.09185 | 0.197556 | ||||||||
\(430\) | 13.4166 | 0.647007 | ||||||||
\(431\) | 19.6236 | 0.945237 | 0.472618 | − | 0.881267i | \(-0.343309\pi\) | ||||
0.472618 | + | 0.881267i | \(0.343309\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 19.7824 | 0.950681 | 0.475341 | − | 0.879802i | \(-0.342325\pi\) | ||||
0.475341 | + | 0.879802i | \(0.342325\pi\) | |||||||
\(434\) | −28.1195 | −1.34978 | ||||||||
\(435\) | −0.520309 | −0.0249469 | ||||||||
\(436\) | 11.3889 | 0.545429 | ||||||||
\(437\) | −18.9916 | −0.908492 | ||||||||
\(438\) | 2.11959 | 0.101278 | ||||||||
\(439\) | 14.8754 | 0.709963 | 0.354981 | − | 0.934873i | \(-0.384487\pi\) | ||||
0.354981 | + | 0.934873i | \(0.384487\pi\) | |||||||
\(440\) | −1.42642 | −0.0680020 | ||||||||
\(441\) | 11.6101 | 0.552863 | ||||||||
\(442\) | −12.0676 | −0.573997 | ||||||||
\(443\) | 7.09855 | 0.337262 | 0.168631 | − | 0.985679i | \(-0.446065\pi\) | ||||
0.168631 | + | 0.985679i | \(0.446065\pi\) | |||||||
\(444\) | −8.86689 | −0.420804 | ||||||||
\(445\) | −9.73547 | −0.461506 | ||||||||
\(446\) | −0.523168 | −0.0247727 | ||||||||
\(447\) | −7.92855 | −0.375008 | ||||||||
\(448\) | −4.31394 | −0.203815 | ||||||||
\(449\) | −1.51664 | −0.0715747 | −0.0357874 | − | 0.999359i | \(-0.511394\pi\) | ||||
−0.0357874 | + | 0.999359i | \(0.511394\pi\) | |||||||
\(450\) | −2.96532 | −0.139787 | ||||||||
\(451\) | −7.50136 | −0.353225 | ||||||||
\(452\) | −11.2470 | −0.529014 | ||||||||
\(453\) | −2.10164 | −0.0987437 | ||||||||
\(454\) | 11.7126 | 0.549701 | ||||||||
\(455\) | −25.1792 | −1.18042 | ||||||||
\(456\) | −2.11248 | −0.0989258 | ||||||||
\(457\) | −33.1060 | −1.54863 | −0.774316 | − | 0.632800i | \(-0.781906\pi\) | ||||
−0.774316 | + | 0.632800i | \(0.781906\pi\) | |||||||
\(458\) | 16.3317 | 0.763131 | ||||||||
\(459\) | −2.94918 | −0.137656 | ||||||||
\(460\) | 12.8238 | 0.597914 | ||||||||
\(461\) | 15.4501 | 0.719584 | 0.359792 | − | 0.933032i | \(-0.382848\pi\) | ||||
0.359792 | + | 0.933032i | \(0.382848\pi\) | |||||||
\(462\) | 4.31394 | 0.200703 | ||||||||
\(463\) | 14.6657 | 0.681573 | 0.340786 | − | 0.940141i | \(-0.389307\pi\) | ||||
0.340786 | + | 0.940141i | \(0.389307\pi\) | |||||||
\(464\) | −0.364765 | −0.0169338 | ||||||||
\(465\) | 9.29780 | 0.431175 | ||||||||
\(466\) | 3.84287 | 0.178018 | ||||||||
\(467\) | −24.5598 | −1.13649 | −0.568246 | − | 0.822859i | \(-0.692378\pi\) | ||||
−0.568246 | + | 0.822859i | \(0.692378\pi\) | |||||||
\(468\) | −4.09185 | −0.189146 | ||||||||
\(469\) | −6.96532 | −0.321629 | ||||||||
\(470\) | −16.1321 | −0.744116 | ||||||||
\(471\) | −8.26312 | −0.380745 | ||||||||
\(472\) | −3.18742 | −0.146713 | ||||||||
\(473\) | −9.40579 | −0.432479 | ||||||||
\(474\) | −12.7706 | −0.586571 | ||||||||
\(475\) | −6.26417 | −0.287420 | ||||||||
\(476\) | −12.7226 | −0.583139 | ||||||||
\(477\) | 0.972256 | 0.0445165 | ||||||||
\(478\) | −25.2682 | −1.15574 | ||||||||
\(479\) | 35.0596 | 1.60191 | 0.800956 | − | 0.598723i | \(-0.204325\pi\) | ||||
0.800956 | + | 0.598723i | \(0.204325\pi\) | |||||||
\(480\) | 1.42642 | 0.0651070 | ||||||||
\(481\) | −36.2820 | −1.65432 | ||||||||
\(482\) | 2.81712 | 0.128316 | ||||||||
\(483\) | −38.7833 | −1.76470 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −26.4504 | −1.20105 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −34.8064 | −1.57723 | −0.788614 | − | 0.614889i | \(-0.789201\pi\) | ||||
−0.788614 | + | 0.614889i | \(0.789201\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −7.18533 | −0.324932 | ||||||||
\(490\) | −16.5609 | −0.748146 | ||||||||
\(491\) | −28.4117 | −1.28220 | −0.641102 | − | 0.767456i | \(-0.721522\pi\) | ||||
−0.641102 | + | 0.767456i | \(0.721522\pi\) | |||||||
\(492\) | 7.50136 | 0.338188 | ||||||||
\(493\) | −1.07576 | −0.0484497 | ||||||||
\(494\) | −8.64394 | −0.388909 | ||||||||
\(495\) | −1.42642 | −0.0641129 | ||||||||
\(496\) | 6.51827 | 0.292679 | ||||||||
\(497\) | −70.4938 | −3.16208 | ||||||||
\(498\) | 16.6242 | 0.744947 | ||||||||
\(499\) | −21.4703 | −0.961143 | −0.480571 | − | 0.876956i | \(-0.659571\pi\) | ||||
−0.480571 | + | 0.876956i | \(0.659571\pi\) | |||||||
\(500\) | 11.3619 | 0.508120 | ||||||||
\(501\) | −3.88059 | −0.173372 | ||||||||
\(502\) | −13.3675 | −0.596620 | ||||||||
\(503\) | −20.3715 | −0.908321 | −0.454161 | − | 0.890920i | \(-0.650061\pi\) | ||||
−0.454161 | + | 0.890920i | \(0.650061\pi\) | |||||||
\(504\) | −4.31394 | −0.192158 | ||||||||
\(505\) | −20.7246 | −0.922234 | ||||||||
\(506\) | −8.99021 | −0.399663 | ||||||||
\(507\) | −3.74322 | −0.166242 | ||||||||
\(508\) | −0.825867 | −0.0366419 | ||||||||
\(509\) | 12.9596 | 0.574424 | 0.287212 | − | 0.957867i | \(-0.407272\pi\) | ||||
0.287212 | + | 0.957867i | \(0.407272\pi\) | |||||||
\(510\) | 4.20677 | 0.186279 | ||||||||
\(511\) | 9.14381 | 0.404498 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.11248 | −0.0932681 | ||||||||
\(514\) | 8.44578 | 0.372527 | ||||||||
\(515\) | 10.8416 | 0.477738 | ||||||||
\(516\) | 9.40579 | 0.414067 | ||||||||
\(517\) | 11.3095 | 0.497389 | ||||||||
\(518\) | −38.2513 | −1.68067 | ||||||||
\(519\) | −6.99265 | −0.306943 | ||||||||
\(520\) | 5.83670 | 0.255956 | ||||||||
\(521\) | 9.51995 | 0.417077 | 0.208538 | − | 0.978014i | \(-0.433129\pi\) | ||||
0.208538 | + | 0.978014i | \(0.433129\pi\) | |||||||
\(522\) | −0.364765 | −0.0159654 | ||||||||
\(523\) | 11.1623 | 0.488093 | 0.244047 | − | 0.969763i | \(-0.421525\pi\) | ||||
0.244047 | + | 0.969763i | \(0.421525\pi\) | |||||||
\(524\) | 6.22740 | 0.272045 | ||||||||
\(525\) | −12.7922 | −0.558299 | ||||||||
\(526\) | 8.47107 | 0.369356 | ||||||||
\(527\) | 19.2235 | 0.837391 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 57.8238 | 2.51408 | ||||||||
\(530\) | −1.38685 | −0.0602408 | ||||||||
\(531\) | −3.18742 | −0.138322 | ||||||||
\(532\) | −9.11311 | −0.395103 | ||||||||
\(533\) | 30.6944 | 1.32952 | ||||||||
\(534\) | −6.82510 | −0.295351 | ||||||||
\(535\) | 8.01229 | 0.346401 | ||||||||
\(536\) | 1.61461 | 0.0697404 | ||||||||
\(537\) | −22.3105 | −0.962769 | ||||||||
\(538\) | −20.0276 | −0.863452 | ||||||||
\(539\) | 11.6101 | 0.500083 | ||||||||
\(540\) | 1.42642 | 0.0613834 | ||||||||
\(541\) | 45.3700 | 1.95061 | 0.975304 | − | 0.220867i | \(-0.0708886\pi\) | ||||
0.975304 | + | 0.220867i | \(0.0708886\pi\) | |||||||
\(542\) | −1.79328 | −0.0770279 | ||||||||
\(543\) | 16.3574 | 0.701964 | ||||||||
\(544\) | 2.94918 | 0.126445 | ||||||||
\(545\) | −16.2454 | −0.695874 | ||||||||
\(546\) | −17.6520 | −0.755436 | ||||||||
\(547\) | −26.5826 | −1.13659 | −0.568294 | − | 0.822826i | \(-0.692396\pi\) | ||||
−0.568294 | + | 0.822826i | \(0.692396\pi\) | |||||||
\(548\) | 12.8830 | 0.550336 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −2.96532 | −0.126442 | ||||||||
\(551\) | −0.770559 | −0.0328269 | ||||||||
\(552\) | 8.99021 | 0.382649 | ||||||||
\(553\) | −55.0915 | −2.34273 | ||||||||
\(554\) | −7.31639 | −0.310844 | ||||||||
\(555\) | 12.6479 | 0.536875 | ||||||||
\(556\) | 5.84201 | 0.247756 | ||||||||
\(557\) | 27.0180 | 1.14479 | 0.572394 | − | 0.819979i | \(-0.306015\pi\) | ||||
0.572394 | + | 0.819979i | \(0.306015\pi\) | |||||||
\(558\) | 6.51827 | 0.275940 | ||||||||
\(559\) | 38.4871 | 1.62783 | ||||||||
\(560\) | 6.15350 | 0.260033 | ||||||||
\(561\) | −2.94918 | −0.124514 | ||||||||
\(562\) | 11.7126 | 0.494067 | ||||||||
\(563\) | −14.6292 | −0.616546 | −0.308273 | − | 0.951298i | \(-0.599751\pi\) | ||||
−0.308273 | + | 0.951298i | \(0.599751\pi\) | |||||||
\(564\) | −11.3095 | −0.476214 | ||||||||
\(565\) | 16.0429 | 0.674932 | ||||||||
\(566\) | −7.94841 | −0.334097 | ||||||||
\(567\) | −4.31394 | −0.181169 | ||||||||
\(568\) | 16.3409 | 0.685650 | ||||||||
\(569\) | −9.87823 | −0.414117 | −0.207059 | − | 0.978329i | \(-0.566389\pi\) | ||||
−0.207059 | + | 0.978329i | \(0.566389\pi\) | |||||||
\(570\) | 3.01328 | 0.126213 | ||||||||
\(571\) | 37.4785 | 1.56842 | 0.784212 | − | 0.620492i | \(-0.213067\pi\) | ||||
0.784212 | + | 0.620492i | \(0.213067\pi\) | |||||||
\(572\) | −4.09185 | −0.171089 | ||||||||
\(573\) | 23.6912 | 0.989715 | ||||||||
\(574\) | 32.3605 | 1.35070 | ||||||||
\(575\) | 26.6588 | 1.11175 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.9372 | −0.621845 | −0.310922 | − | 0.950435i | \(-0.600638\pi\) | ||||
−0.310922 | + | 0.950435i | \(0.600638\pi\) | |||||||
\(578\) | −8.30234 | −0.345332 | ||||||||
\(579\) | 12.7713 | 0.530758 | ||||||||
\(580\) | 0.520309 | 0.0216047 | ||||||||
\(581\) | 71.7157 | 2.97527 | ||||||||
\(582\) | −18.5432 | −0.768639 | ||||||||
\(583\) | 0.972256 | 0.0402667 | ||||||||
\(584\) | −2.11959 | −0.0877094 | ||||||||
\(585\) | 5.83670 | 0.241318 | ||||||||
\(586\) | 27.6790 | 1.14341 | ||||||||
\(587\) | 20.6681 | 0.853066 | 0.426533 | − | 0.904472i | \(-0.359735\pi\) | ||||
0.426533 | + | 0.904472i | \(0.359735\pi\) | |||||||
\(588\) | −11.6101 | −0.478793 | ||||||||
\(589\) | 13.7697 | 0.567370 | ||||||||
\(590\) | 4.54660 | 0.187181 | ||||||||
\(591\) | −15.2901 | −0.628951 | ||||||||
\(592\) | 8.86689 | 0.364427 | ||||||||
\(593\) | 32.2729 | 1.32529 | 0.662644 | − | 0.748935i | \(-0.269434\pi\) | ||||
0.662644 | + | 0.748935i | \(0.269434\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 18.1478 | 0.743987 | ||||||||
\(596\) | 7.92855 | 0.324766 | ||||||||
\(597\) | −6.97937 | −0.285647 | ||||||||
\(598\) | 36.7866 | 1.50431 | ||||||||
\(599\) | −7.86626 | −0.321407 | −0.160703 | − | 0.987003i | \(-0.551376\pi\) | ||||
−0.160703 | + | 0.987003i | \(0.551376\pi\) | |||||||
\(600\) | 2.96532 | 0.121059 | ||||||||
\(601\) | 47.2616 | 1.92784 | 0.963921 | − | 0.266188i | \(-0.0857642\pi\) | ||||
0.963921 | + | 0.266188i | \(0.0857642\pi\) | |||||||
\(602\) | 40.5761 | 1.65376 | ||||||||
\(603\) | 1.61461 | 0.0657518 | ||||||||
\(604\) | 2.10164 | 0.0855146 | ||||||||
\(605\) | −1.42642 | −0.0579923 | ||||||||
\(606\) | −14.5291 | −0.590205 | ||||||||
\(607\) | 19.5408 | 0.793135 | 0.396568 | − | 0.918006i | \(-0.370201\pi\) | ||||
0.396568 | + | 0.918006i | \(0.370201\pi\) | |||||||
\(608\) | 2.11248 | 0.0856723 | ||||||||
\(609\) | −1.57358 | −0.0637646 | ||||||||
\(610\) | −1.42642 | −0.0577541 | ||||||||
\(611\) | −46.2766 | −1.87215 | ||||||||
\(612\) | 2.94918 | 0.119214 | ||||||||
\(613\) | −28.7176 | −1.15989 | −0.579947 | − | 0.814654i | \(-0.696927\pi\) | ||||
−0.579947 | + | 0.814654i | \(0.696927\pi\) | |||||||
\(614\) | −5.87220 | −0.236983 | ||||||||
\(615\) | −10.7001 | −0.431470 | ||||||||
\(616\) | −4.31394 | −0.173814 | ||||||||
\(617\) | −28.3734 | −1.14227 | −0.571136 | − | 0.820856i | \(-0.693497\pi\) | ||||
−0.571136 | + | 0.820856i | \(0.693497\pi\) | |||||||
\(618\) | 7.60056 | 0.305739 | ||||||||
\(619\) | −26.0718 | −1.04791 | −0.523956 | − | 0.851745i | \(-0.675544\pi\) | ||||
−0.523956 | + | 0.851745i | \(0.675544\pi\) | |||||||
\(620\) | −9.29780 | −0.373409 | ||||||||
\(621\) | 8.99021 | 0.360765 | ||||||||
\(622\) | −2.20840 | −0.0885489 | ||||||||
\(623\) | −29.4431 | −1.17961 | ||||||||
\(624\) | 4.09185 | 0.163805 | ||||||||
\(625\) | −1.38027 | −0.0552108 | ||||||||
\(626\) | 5.90919 | 0.236179 | ||||||||
\(627\) | −2.11248 | −0.0843642 | ||||||||
\(628\) | 8.26312 | 0.329735 | ||||||||
\(629\) | 26.1501 | 1.04267 | ||||||||
\(630\) | 6.15350 | 0.245162 | ||||||||
\(631\) | 5.50399 | 0.219110 | 0.109555 | − | 0.993981i | \(-0.465057\pi\) | ||||
0.109555 | + | 0.993981i | \(0.465057\pi\) | |||||||
\(632\) | 12.7706 | 0.507986 | ||||||||
\(633\) | 16.9302 | 0.672916 | ||||||||
\(634\) | −6.50059 | −0.258172 | ||||||||
\(635\) | 1.17803 | 0.0467489 | ||||||||
\(636\) | −0.972256 | −0.0385524 | ||||||||
\(637\) | −47.5068 | −1.88229 | ||||||||
\(638\) | −0.364765 | −0.0144412 | ||||||||
\(639\) | 16.3409 | 0.646437 | ||||||||
\(640\) | −1.42642 | −0.0563843 | ||||||||
\(641\) | 23.5007 | 0.928223 | 0.464111 | − | 0.885777i | \(-0.346374\pi\) | ||||
0.464111 | + | 0.885777i | \(0.346374\pi\) | |||||||
\(642\) | 5.61705 | 0.221687 | ||||||||
\(643\) | −18.8775 | −0.744454 | −0.372227 | − | 0.928142i | \(-0.621406\pi\) | ||||
−0.372227 | + | 0.928142i | \(0.621406\pi\) | |||||||
\(644\) | 38.7833 | 1.52827 | ||||||||
\(645\) | −13.4166 | −0.528279 | ||||||||
\(646\) | 6.23007 | 0.245119 | ||||||||
\(647\) | 8.49828 | 0.334102 | 0.167051 | − | 0.985948i | \(-0.446576\pi\) | ||||
0.167051 | + | 0.985948i | \(0.446576\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.18742 | −0.125117 | ||||||||
\(650\) | 12.1336 | 0.475921 | ||||||||
\(651\) | 28.1195 | 1.10209 | ||||||||
\(652\) | 7.18533 | 0.281399 | ||||||||
\(653\) | 12.8312 | 0.502122 | 0.251061 | − | 0.967971i | \(-0.419220\pi\) | ||||
0.251061 | + | 0.967971i | \(0.419220\pi\) | |||||||
\(654\) | −11.3889 | −0.445341 | ||||||||
\(655\) | −8.88290 | −0.347084 | ||||||||
\(656\) | −7.50136 | −0.292879 | ||||||||
\(657\) | −2.11959 | −0.0826932 | ||||||||
\(658\) | −48.7884 | −1.90197 | ||||||||
\(659\) | −35.2902 | −1.37471 | −0.687356 | − | 0.726321i | \(-0.741229\pi\) | ||||
−0.687356 | + | 0.726321i | \(0.741229\pi\) | |||||||
\(660\) | 1.42642 | 0.0555234 | ||||||||
\(661\) | 21.9543 | 0.853923 | 0.426962 | − | 0.904270i | \(-0.359584\pi\) | ||||
0.426962 | + | 0.904270i | \(0.359584\pi\) | |||||||
\(662\) | −12.1572 | −0.472504 | ||||||||
\(663\) | 12.0676 | 0.468667 | ||||||||
\(664\) | −16.6242 | −0.645143 | ||||||||
\(665\) | 12.9991 | 0.504085 | ||||||||
\(666\) | 8.86689 | 0.343585 | ||||||||
\(667\) | 3.27932 | 0.126976 | ||||||||
\(668\) | 3.88059 | 0.150144 | ||||||||
\(669\) | 0.523168 | 0.0202268 | ||||||||
\(670\) | −2.30311 | −0.0889769 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 4.31394 | 0.166414 | ||||||||
\(673\) | −29.7526 | −1.14688 | −0.573439 | − | 0.819248i | \(-0.694391\pi\) | ||||
−0.573439 | + | 0.819248i | \(0.694391\pi\) | |||||||
\(674\) | −5.19798 | −0.200219 | ||||||||
\(675\) | 2.96532 | 0.114135 | ||||||||
\(676\) | 3.74322 | 0.143970 | ||||||||
\(677\) | 44.6102 | 1.71451 | 0.857255 | − | 0.514892i | \(-0.172168\pi\) | ||||
0.857255 | + | 0.514892i | \(0.172168\pi\) | |||||||
\(678\) | 11.2470 | 0.431938 | ||||||||
\(679\) | −79.9942 | −3.06989 | ||||||||
\(680\) | −4.20677 | −0.161322 | ||||||||
\(681\) | −11.7126 | −0.448829 | ||||||||
\(682\) | 6.51827 | 0.249597 | ||||||||
\(683\) | 31.9359 | 1.22199 | 0.610997 | − | 0.791633i | \(-0.290769\pi\) | ||||
0.610997 | + | 0.791633i | \(0.290769\pi\) | |||||||
\(684\) | 2.11248 | 0.0807726 | ||||||||
\(685\) | −18.3766 | −0.702135 | ||||||||
\(686\) | −19.8878 | −0.759320 | ||||||||
\(687\) | −16.3317 | −0.623094 | ||||||||
\(688\) | −9.40579 | −0.358593 | ||||||||
\(689\) | −3.97832 | −0.151562 | ||||||||
\(690\) | −12.8238 | −0.488195 | ||||||||
\(691\) | 49.0636 | 1.86647 | 0.933235 | − | 0.359268i | \(-0.116974\pi\) | ||||
0.933235 | + | 0.359268i | \(0.116974\pi\) | |||||||
\(692\) | 6.99265 | 0.265821 | ||||||||
\(693\) | −4.31394 | −0.163873 | ||||||||
\(694\) | 13.3297 | 0.505988 | ||||||||
\(695\) | −8.33317 | −0.316095 | ||||||||
\(696\) | 0.364765 | 0.0138264 | ||||||||
\(697\) | −22.1229 | −0.837963 | ||||||||
\(698\) | −14.1748 | −0.536523 | ||||||||
\(699\) | −3.84287 | −0.145351 | ||||||||
\(700\) | 12.7922 | 0.483501 | ||||||||
\(701\) | −45.0157 | −1.70022 | −0.850109 | − | 0.526606i | \(-0.823464\pi\) | ||||
−0.850109 | + | 0.526606i | \(0.823464\pi\) | |||||||
\(702\) | 4.09185 | 0.154437 | ||||||||
\(703\) | 18.7311 | 0.706457 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 16.1321 | 0.607568 | ||||||||
\(706\) | 33.0438 | 1.24362 | ||||||||
\(707\) | −62.6778 | −2.35724 | ||||||||
\(708\) | 3.18742 | 0.119790 | ||||||||
\(709\) | −35.8338 | −1.34577 | −0.672884 | − | 0.739748i | \(-0.734945\pi\) | ||||
−0.672884 | + | 0.739748i | \(0.734945\pi\) | |||||||
\(710\) | −23.3090 | −0.874773 | ||||||||
\(711\) | 12.7706 | 0.478933 | ||||||||
\(712\) | 6.82510 | 0.255781 | ||||||||
\(713\) | −58.6006 | −2.19461 | ||||||||
\(714\) | 12.7226 | 0.476131 | ||||||||
\(715\) | 5.83670 | 0.218280 | ||||||||
\(716\) | 22.3105 | 0.833783 | ||||||||
\(717\) | 25.2682 | 0.943658 | ||||||||
\(718\) | 0.876687 | 0.0327177 | ||||||||
\(719\) | 29.7875 | 1.11089 | 0.555443 | − | 0.831554i | \(-0.312549\pi\) | ||||
0.555443 | + | 0.831554i | \(0.312549\pi\) | |||||||
\(720\) | −1.42642 | −0.0531596 | ||||||||
\(721\) | 32.7884 | 1.22110 | ||||||||
\(722\) | −14.5374 | −0.541028 | ||||||||
\(723\) | −2.81712 | −0.104770 | ||||||||
\(724\) | −16.3574 | −0.607919 | ||||||||
\(725\) | 1.08165 | 0.0401713 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 18.5459 | 0.687829 | 0.343914 | − | 0.939001i | \(-0.388247\pi\) | ||||
0.343914 | + | 0.939001i | \(0.388247\pi\) | |||||||
\(728\) | 17.6520 | 0.654227 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.02343 | 0.111902 | ||||||||
\(731\) | −27.7394 | −1.02598 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 10.0302 | 0.370475 | 0.185238 | − | 0.982694i | \(-0.440695\pi\) | ||||
0.185238 | + | 0.982694i | \(0.440695\pi\) | |||||||
\(734\) | −37.2181 | −1.37375 | ||||||||
\(735\) | 16.5609 | 0.610859 | ||||||||
\(736\) | −8.99021 | −0.331383 | ||||||||
\(737\) | 1.61461 | 0.0594748 | ||||||||
\(738\) | −7.50136 | −0.276129 | ||||||||
\(739\) | −32.5413 | −1.19705 | −0.598526 | − | 0.801103i | \(-0.704247\pi\) | ||||
−0.598526 | + | 0.801103i | \(0.704247\pi\) | |||||||
\(740\) | −12.6479 | −0.464947 | ||||||||
\(741\) | 8.64394 | 0.317543 | ||||||||
\(742\) | −4.19426 | −0.153976 | ||||||||
\(743\) | −3.08415 | −0.113146 | −0.0565732 | − | 0.998398i | \(-0.518017\pi\) | ||||
−0.0565732 | + | 0.998398i | \(0.518017\pi\) | |||||||
\(744\) | −6.51827 | −0.238971 | ||||||||
\(745\) | −11.3095 | −0.414346 | ||||||||
\(746\) | −15.6612 | −0.573396 | ||||||||
\(747\) | −16.6242 | −0.608247 | ||||||||
\(748\) | 2.94918 | 0.107833 | ||||||||
\(749\) | 24.2317 | 0.885406 | ||||||||
\(750\) | −11.3619 | −0.414878 | ||||||||
\(751\) | −41.4041 | −1.51086 | −0.755428 | − | 0.655232i | \(-0.772571\pi\) | ||||
−0.755428 | + | 0.655232i | \(0.772571\pi\) | |||||||
\(752\) | 11.3095 | 0.412413 | ||||||||
\(753\) | 13.3675 | 0.487138 | ||||||||
\(754\) | 1.49257 | 0.0543560 | ||||||||
\(755\) | −2.99783 | −0.109102 | ||||||||
\(756\) | 4.31394 | 0.156897 | ||||||||
\(757\) | 2.33562 | 0.0848894 | 0.0424447 | − | 0.999099i | \(-0.486485\pi\) | ||||
0.0424447 | + | 0.999099i | \(0.486485\pi\) | |||||||
\(758\) | 17.7746 | 0.645601 | ||||||||
\(759\) | 8.99021 | 0.326324 | ||||||||
\(760\) | −3.01328 | −0.109303 | ||||||||
\(761\) | −10.1231 | −0.366961 | −0.183481 | − | 0.983023i | \(-0.558736\pi\) | ||||
−0.183481 | + | 0.983023i | \(0.558736\pi\) | |||||||
\(762\) | 0.825867 | 0.0299180 | ||||||||
\(763\) | −49.1310 | −1.77866 | ||||||||
\(764\) | −23.6912 | −0.857118 | ||||||||
\(765\) | −4.20677 | −0.152096 | ||||||||
\(766\) | 5.32233 | 0.192304 | ||||||||
\(767\) | 13.0424 | 0.470935 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 45.6436 | 1.64595 | 0.822975 | − | 0.568078i | \(-0.192313\pi\) | ||||
0.822975 | + | 0.568078i | \(0.192313\pi\) | |||||||
\(770\) | 6.15350 | 0.221757 | ||||||||
\(771\) | −8.44578 | −0.304167 | ||||||||
\(772\) | −12.7713 | −0.459650 | ||||||||
\(773\) | −9.19035 | −0.330554 | −0.165277 | − | 0.986247i | \(-0.552852\pi\) | ||||
−0.165277 | + | 0.986247i | \(0.552852\pi\) | |||||||
\(774\) | −9.40579 | −0.338084 | ||||||||
\(775\) | −19.3288 | −0.694310 | ||||||||
\(776\) | 18.5432 | 0.665661 | ||||||||
\(777\) | 38.2513 | 1.37226 | ||||||||
\(778\) | 6.88145 | 0.246712 | ||||||||
\(779\) | −15.8465 | −0.567758 | ||||||||
\(780\) | −5.83670 | −0.208987 | ||||||||
\(781\) | 16.3409 | 0.584724 | ||||||||
\(782\) | −26.5137 | −0.948129 | ||||||||
\(783\) | 0.364765 | 0.0130357 | ||||||||
\(784\) | 11.6101 | 0.414647 | ||||||||
\(785\) | −11.7867 | −0.420685 | ||||||||
\(786\) | −6.22740 | −0.222124 | ||||||||
\(787\) | 1.90275 | 0.0678257 | 0.0339129 | − | 0.999425i | \(-0.489203\pi\) | ||||
0.0339129 | + | 0.999425i | \(0.489203\pi\) | |||||||
\(788\) | 15.2901 | 0.544687 | ||||||||
\(789\) | −8.47107 | −0.301578 | ||||||||
\(790\) | −18.2162 | −0.648103 | ||||||||
\(791\) | 48.5189 | 1.72513 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −4.09185 | −0.145306 | ||||||||
\(794\) | 9.40172 | 0.333654 | ||||||||
\(795\) | 1.38685 | 0.0491864 | ||||||||
\(796\) | 6.97937 | 0.247377 | ||||||||
\(797\) | −30.7964 | −1.09086 | −0.545432 | − | 0.838155i | \(-0.683635\pi\) | ||||
−0.545432 | + | 0.838155i | \(0.683635\pi\) | |||||||
\(798\) | 9.11311 | 0.322601 | ||||||||
\(799\) | 33.3536 | 1.17997 | ||||||||
\(800\) | −2.96532 | −0.104840 | ||||||||
\(801\) | 6.82510 | 0.241153 | ||||||||
\(802\) | 14.8318 | 0.523729 | ||||||||
\(803\) | −2.11959 | −0.0747988 | ||||||||
\(804\) | −1.61461 | −0.0569428 | ||||||||
\(805\) | −55.3213 | −1.94982 | ||||||||
\(806\) | −26.6718 | −0.939473 | ||||||||
\(807\) | 20.0276 | 0.705005 | ||||||||
\(808\) | 14.5291 | 0.511132 | ||||||||
\(809\) | −24.4553 | −0.859802 | −0.429901 | − | 0.902876i | \(-0.641452\pi\) | ||||
−0.429901 | + | 0.902876i | \(0.641452\pi\) | |||||||
\(810\) | −1.42642 | −0.0501194 | ||||||||
\(811\) | −30.8476 | −1.08321 | −0.541603 | − | 0.840635i | \(-0.682182\pi\) | ||||
−0.541603 | + | 0.840635i | \(0.682182\pi\) | |||||||
\(812\) | 1.57358 | 0.0552218 | ||||||||
\(813\) | 1.79328 | 0.0628930 | ||||||||
\(814\) | 8.86689 | 0.310784 | ||||||||
\(815\) | −10.2493 | −0.359018 | ||||||||
\(816\) | −2.94918 | −0.103242 | ||||||||
\(817\) | −19.8695 | −0.695147 | ||||||||
\(818\) | −34.9984 | −1.22369 | ||||||||
\(819\) | 17.6520 | 0.616811 | ||||||||
\(820\) | 10.7001 | 0.373664 | ||||||||
\(821\) | −18.7136 | −0.653108 | −0.326554 | − | 0.945179i | \(-0.605888\pi\) | ||||
−0.326554 | + | 0.945179i | \(0.605888\pi\) | |||||||
\(822\) | −12.8830 | −0.449347 | ||||||||
\(823\) | 14.4025 | 0.502041 | 0.251020 | − | 0.967982i | \(-0.419234\pi\) | ||||
0.251020 | + | 0.967982i | \(0.419234\pi\) | |||||||
\(824\) | −7.60056 | −0.264778 | ||||||||
\(825\) | 2.96532 | 0.103239 | ||||||||
\(826\) | 13.7503 | 0.478436 | ||||||||
\(827\) | −21.1576 | −0.735721 | −0.367861 | − | 0.929881i | \(-0.619910\pi\) | ||||
−0.367861 | + | 0.929881i | \(0.619910\pi\) | |||||||
\(828\) | −8.99021 | −0.312431 | ||||||||
\(829\) | −14.4749 | −0.502734 | −0.251367 | − | 0.967892i | \(-0.580880\pi\) | ||||
−0.251367 | + | 0.967892i | \(0.580880\pi\) | |||||||
\(830\) | 23.7131 | 0.823093 | ||||||||
\(831\) | 7.31639 | 0.253803 | ||||||||
\(832\) | −4.09185 | −0.141859 | ||||||||
\(833\) | 34.2403 | 1.18636 | ||||||||
\(834\) | −5.84201 | −0.202292 | ||||||||
\(835\) | −5.53536 | −0.191559 | ||||||||
\(836\) | 2.11248 | 0.0730615 | ||||||||
\(837\) | −6.51827 | −0.225304 | ||||||||
\(838\) | −4.96323 | −0.171452 | ||||||||
\(839\) | −52.6999 | −1.81940 | −0.909702 | − | 0.415262i | \(-0.863690\pi\) | ||||
−0.909702 | + | 0.415262i | \(0.863690\pi\) | |||||||
\(840\) | −6.15350 | −0.212316 | ||||||||
\(841\) | −28.8669 | −0.995412 | ||||||||
\(842\) | 25.2941 | 0.871692 | ||||||||
\(843\) | −11.7126 | −0.403404 | ||||||||
\(844\) | −16.9302 | −0.582763 | ||||||||
\(845\) | −5.33942 | −0.183682 | ||||||||
\(846\) | 11.3095 | 0.388827 | ||||||||
\(847\) | −4.31394 | −0.148229 | ||||||||
\(848\) | 0.972256 | 0.0333874 | ||||||||
\(849\) | 7.94841 | 0.272789 | ||||||||
\(850\) | −8.74526 | −0.299960 | ||||||||
\(851\) | −79.7152 | −2.73260 | ||||||||
\(852\) | −16.3409 | −0.559831 | ||||||||
\(853\) | −28.3406 | −0.970362 | −0.485181 | − | 0.874414i | \(-0.661246\pi\) | ||||
−0.485181 | + | 0.874414i | \(0.661246\pi\) | |||||||
\(854\) | −4.31394 | −0.147620 | ||||||||
\(855\) | −3.01328 | −0.103052 | ||||||||
\(856\) | −5.61705 | −0.191987 | ||||||||
\(857\) | 51.9454 | 1.77442 | 0.887210 | − | 0.461366i | \(-0.152640\pi\) | ||||
0.887210 | + | 0.461366i | \(0.152640\pi\) | |||||||
\(858\) | 4.09185 | 0.139693 | ||||||||
\(859\) | 36.6638 | 1.25095 | 0.625476 | − | 0.780243i | \(-0.284905\pi\) | ||||
0.625476 | + | 0.780243i | \(0.284905\pi\) | |||||||
\(860\) | 13.4166 | 0.457503 | ||||||||
\(861\) | −32.3605 | −1.10284 | ||||||||
\(862\) | 19.6236 | 0.668383 | ||||||||
\(863\) | −26.9352 | −0.916885 | −0.458443 | − | 0.888724i | \(-0.651593\pi\) | ||||
−0.458443 | + | 0.888724i | \(0.651593\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −9.97448 | −0.339142 | ||||||||
\(866\) | 19.7824 | 0.672233 | ||||||||
\(867\) | 8.30234 | 0.281962 | ||||||||
\(868\) | −28.1195 | −0.954437 | ||||||||
\(869\) | 12.7706 | 0.433212 | ||||||||
\(870\) | −0.520309 | −0.0176401 | ||||||||
\(871\) | −6.60672 | −0.223860 | ||||||||
\(872\) | 11.3889 | 0.385676 | ||||||||
\(873\) | 18.5432 | 0.627591 | ||||||||
\(874\) | −18.9916 | −0.642401 | ||||||||
\(875\) | −49.0146 | −1.65700 | ||||||||
\(876\) | 2.11959 | 0.0716144 | ||||||||
\(877\) | 15.3005 | 0.516662 | 0.258331 | − | 0.966056i | \(-0.416827\pi\) | ||||
0.258331 | + | 0.966056i | \(0.416827\pi\) | |||||||
\(878\) | 14.8754 | 0.502020 | ||||||||
\(879\) | −27.6790 | −0.933589 | ||||||||
\(880\) | −1.42642 | −0.0480847 | ||||||||
\(881\) | 40.5694 | 1.36682 | 0.683409 | − | 0.730036i | \(-0.260497\pi\) | ||||
0.683409 | + | 0.730036i | \(0.260497\pi\) | |||||||
\(882\) | 11.6101 | 0.390933 | ||||||||
\(883\) | −8.39786 | −0.282610 | −0.141305 | − | 0.989966i | \(-0.545130\pi\) | ||||
−0.141305 | + | 0.989966i | \(0.545130\pi\) | |||||||
\(884\) | −12.0676 | −0.405877 | ||||||||
\(885\) | −4.54660 | −0.152832 | ||||||||
\(886\) | 7.09855 | 0.238481 | ||||||||
\(887\) | 36.8832 | 1.23842 | 0.619209 | − | 0.785227i | \(-0.287454\pi\) | ||||
0.619209 | + | 0.785227i | \(0.287454\pi\) | |||||||
\(888\) | −8.86689 | −0.297553 | ||||||||
\(889\) | 3.56274 | 0.119491 | ||||||||
\(890\) | −9.73547 | −0.326334 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −0.523168 | −0.0175169 | ||||||||
\(893\) | 23.8910 | 0.799481 | ||||||||
\(894\) | −7.92855 | −0.265170 | ||||||||
\(895\) | −31.8242 | −1.06377 | ||||||||
\(896\) | −4.31394 | −0.144119 | ||||||||
\(897\) | −36.7866 | −1.22827 | ||||||||
\(898\) | −1.51664 | −0.0506110 | ||||||||
\(899\) | −2.37764 | −0.0792987 | ||||||||
\(900\) | −2.96532 | −0.0988440 | ||||||||
\(901\) | 2.86736 | 0.0955255 | ||||||||
\(902\) | −7.50136 | −0.249768 | ||||||||
\(903\) | −40.5761 | −1.35029 | ||||||||
\(904\) | −11.2470 | −0.374069 | ||||||||
\(905\) | 23.3326 | 0.775601 | ||||||||
\(906\) | −2.10164 | −0.0698224 | ||||||||
\(907\) | 28.0051 | 0.929893 | 0.464947 | − | 0.885339i | \(-0.346074\pi\) | ||||
0.464947 | + | 0.885339i | \(0.346074\pi\) | |||||||
\(908\) | 11.7126 | 0.388697 | ||||||||
\(909\) | 14.5291 | 0.481900 | ||||||||
\(910\) | −25.1792 | −0.834683 | ||||||||
\(911\) | 2.41431 | 0.0799898 | 0.0399949 | − | 0.999200i | \(-0.487266\pi\) | ||||
0.0399949 | + | 0.999200i | \(0.487266\pi\) | |||||||
\(912\) | −2.11248 | −0.0699511 | ||||||||
\(913\) | −16.6242 | −0.550180 | ||||||||
\(914\) | −33.1060 | −1.09505 | ||||||||
\(915\) | 1.42642 | 0.0471561 | ||||||||
\(916\) | 16.3317 | 0.539615 | ||||||||
\(917\) | −26.8647 | −0.887150 | ||||||||
\(918\) | −2.94918 | −0.0973374 | ||||||||
\(919\) | −5.04284 | −0.166348 | −0.0831740 | − | 0.996535i | \(-0.526506\pi\) | ||||
−0.0831740 | + | 0.996535i | \(0.526506\pi\) | |||||||
\(920\) | 12.8238 | 0.422789 | ||||||||
\(921\) | 5.87220 | 0.193496 | ||||||||
\(922\) | 15.4501 | 0.508823 | ||||||||
\(923\) | −66.8646 | −2.20087 | ||||||||
\(924\) | 4.31394 | 0.141918 | ||||||||
\(925\) | −26.2932 | −0.864515 | ||||||||
\(926\) | 14.6657 | 0.481945 | ||||||||
\(927\) | −7.60056 | −0.249635 | ||||||||
\(928\) | −0.364765 | −0.0119740 | ||||||||
\(929\) | 27.4828 | 0.901682 | 0.450841 | − | 0.892604i | \(-0.351124\pi\) | ||||
0.450841 | + | 0.892604i | \(0.351124\pi\) | |||||||
\(930\) | 9.29780 | 0.304887 | ||||||||
\(931\) | 24.5261 | 0.803811 | ||||||||
\(932\) | 3.84287 | 0.125877 | ||||||||
\(933\) | 2.20840 | 0.0722999 | ||||||||
\(934\) | −24.5598 | −0.803621 | ||||||||
\(935\) | −4.20677 | −0.137576 | ||||||||
\(936\) | −4.09185 | −0.133746 | ||||||||
\(937\) | 34.7865 | 1.13642 | 0.568212 | − | 0.822882i | \(-0.307635\pi\) | ||||
0.568212 | + | 0.822882i | \(0.307635\pi\) | |||||||
\(938\) | −6.96532 | −0.227426 | ||||||||
\(939\) | −5.90919 | −0.192839 | ||||||||
\(940\) | −16.1321 | −0.526170 | ||||||||
\(941\) | 20.6215 | 0.672241 | 0.336121 | − | 0.941819i | \(-0.390885\pi\) | ||||
0.336121 | + | 0.941819i | \(0.390885\pi\) | |||||||
\(942\) | −8.26312 | −0.269227 | ||||||||
\(943\) | 67.4388 | 2.19611 | ||||||||
\(944\) | −3.18742 | −0.103742 | ||||||||
\(945\) | −6.15350 | −0.200174 | ||||||||
\(946\) | −9.40579 | −0.305809 | ||||||||
\(947\) | −46.2085 | −1.50157 | −0.750787 | − | 0.660544i | \(-0.770326\pi\) | ||||
−0.750787 | + | 0.660544i | \(0.770326\pi\) | |||||||
\(948\) | −12.7706 | −0.414768 | ||||||||
\(949\) | 8.67305 | 0.281539 | ||||||||
\(950\) | −6.26417 | −0.203237 | ||||||||
\(951\) | 6.50059 | 0.210796 | ||||||||
\(952\) | −12.7226 | −0.412342 | ||||||||
\(953\) | 15.6775 | 0.507844 | 0.253922 | − | 0.967225i | \(-0.418279\pi\) | ||||
0.253922 | + | 0.967225i | \(0.418279\pi\) | |||||||
\(954\) | 0.972256 | 0.0314779 | ||||||||
\(955\) | 33.7937 | 1.09354 | ||||||||
\(956\) | −25.2682 | −0.817232 | ||||||||
\(957\) | 0.364765 | 0.0117912 | ||||||||
\(958\) | 35.0596 | 1.13272 | ||||||||
\(959\) | −55.5767 | −1.79467 | ||||||||
\(960\) | 1.42642 | 0.0460376 | ||||||||
\(961\) | 11.4878 | 0.370576 | ||||||||
\(962\) | −36.2820 | −1.16978 | ||||||||
\(963\) | −5.61705 | −0.181007 | ||||||||
\(964\) | 2.81712 | 0.0907334 | ||||||||
\(965\) | 18.2173 | 0.586436 | ||||||||
\(966\) | −38.7833 | −1.24783 | ||||||||
\(967\) | 49.4316 | 1.58961 | 0.794807 | − | 0.606862i | \(-0.207572\pi\) | ||||
0.794807 | + | 0.606862i | \(0.207572\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −6.23007 | −0.200139 | ||||||||
\(970\) | −26.4504 | −0.849270 | ||||||||
\(971\) | 17.2880 | 0.554797 | 0.277399 | − | 0.960755i | \(-0.410528\pi\) | ||||
0.277399 | + | 0.960755i | \(0.410528\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −25.2021 | −0.807942 | ||||||||
\(974\) | −34.8064 | −1.11527 | ||||||||
\(975\) | −12.1336 | −0.388588 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | 16.2088 | 0.518566 | 0.259283 | − | 0.965801i | \(-0.416514\pi\) | ||||
0.259283 | + | 0.965801i | \(0.416514\pi\) | |||||||
\(978\) | −7.18533 | −0.229761 | ||||||||
\(979\) | 6.82510 | 0.218131 | ||||||||
\(980\) | −16.5609 | −0.529019 | ||||||||
\(981\) | 11.3889 | 0.363619 | ||||||||
\(982\) | −28.4117 | −0.906655 | ||||||||
\(983\) | 40.5441 | 1.29316 | 0.646578 | − | 0.762848i | \(-0.276200\pi\) | ||||
0.646578 | + | 0.762848i | \(0.276200\pi\) | |||||||
\(984\) | 7.50136 | 0.239135 | ||||||||
\(985\) | −21.8101 | −0.694929 | ||||||||
\(986\) | −1.07576 | −0.0342591 | ||||||||
\(987\) | 48.7884 | 1.55295 | ||||||||
\(988\) | −8.64394 | −0.275000 | ||||||||
\(989\) | 84.5600 | 2.68885 | ||||||||
\(990\) | −1.42642 | −0.0453347 | ||||||||
\(991\) | −49.2789 | −1.56539 | −0.782697 | − | 0.622403i | \(-0.786157\pi\) | ||||
−0.782697 | + | 0.622403i | \(0.786157\pi\) | |||||||
\(992\) | 6.51827 | 0.206955 | ||||||||
\(993\) | 12.1572 | 0.385798 | ||||||||
\(994\) | −70.4938 | −2.23593 | ||||||||
\(995\) | −9.95553 | −0.315611 | ||||||||
\(996\) | 16.6242 | 0.526757 | ||||||||
\(997\) | 5.09937 | 0.161499 | 0.0807494 | − | 0.996734i | \(-0.474269\pi\) | ||||
0.0807494 | + | 0.996734i | \(0.474269\pi\) | |||||||
\(998\) | −21.4703 | −0.679631 | ||||||||
\(999\) | −8.86689 | −0.280536 |
(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 | 4026.2.a.v.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.v.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |