Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.79755\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | 0.797548 | 0.356674 | 0.178337 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178337 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.52438 | −1.71006 | −0.855028 | − | 0.518581i | \(-0.826460\pi\) | ||||
−0.855028 | + | 0.518581i | \(0.826460\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.797548 | 0.252207 | ||||||||
\(11\) | 0.726837 | 0.219150 | 0.109575 | − | 0.993979i | \(-0.465051\pi\) | ||||
0.109575 | + | 0.993979i | \(0.465051\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.52438 | −1.20919 | ||||||||
\(15\) | 0.797548 | 0.205926 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.987094 | 0.239406 | 0.119703 | − | 0.992810i | \(-0.461806\pi\) | ||||
0.119703 | + | 0.992810i | \(0.461806\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.78344 | 0.409149 | 0.204574 | − | 0.978851i | \(-0.434419\pi\) | ||||
0.204574 | + | 0.978851i | \(0.434419\pi\) | |||||||
\(20\) | 0.797548 | 0.178337 | ||||||||
\(21\) | −4.52438 | −0.987302 | ||||||||
\(22\) | 0.726837 | 0.154962 | ||||||||
\(23\) | −5.45739 | −1.13794 | −0.568972 | − | 0.822357i | \(-0.692659\pi\) | ||||
−0.568972 | + | 0.822357i | \(0.692659\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.36392 | −0.872784 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.52438 | −0.855028 | ||||||||
\(29\) | 2.41751 | 0.448920 | 0.224460 | − | 0.974483i | \(-0.427938\pi\) | ||||
0.224460 | + | 0.974483i | \(0.427938\pi\) | |||||||
\(30\) | 0.797548 | 0.145612 | ||||||||
\(31\) | −0.500062 | −0.0898137 | −0.0449069 | − | 0.998991i | \(-0.514299\pi\) | ||||
−0.0449069 | + | 0.998991i | \(0.514299\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.726837 | 0.126526 | ||||||||
\(34\) | 0.987094 | 0.169285 | ||||||||
\(35\) | −3.60841 | −0.609933 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.242893 | 0.0399314 | 0.0199657 | − | 0.999801i | \(-0.493644\pi\) | ||||
0.0199657 | + | 0.999801i | \(0.493644\pi\) | |||||||
\(38\) | 1.78344 | 0.289312 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.797548 | 0.126103 | ||||||||
\(41\) | −11.0069 | −1.71899 | −0.859495 | − | 0.511144i | \(-0.829222\pi\) | ||||
−0.859495 | + | 0.511144i | \(0.829222\pi\) | |||||||
\(42\) | −4.52438 | −0.698128 | ||||||||
\(43\) | −6.15290 | −0.938309 | −0.469154 | − | 0.883116i | \(-0.655441\pi\) | ||||
−0.469154 | + | 0.883116i | \(0.655441\pi\) | |||||||
\(44\) | 0.726837 | 0.109575 | ||||||||
\(45\) | 0.797548 | 0.118891 | ||||||||
\(46\) | −5.45739 | −0.804648 | ||||||||
\(47\) | 6.55388 | 0.955981 | 0.477991 | − | 0.878365i | \(-0.341365\pi\) | ||||
0.477991 | + | 0.878365i | \(0.341365\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 13.4701 | 1.92429 | ||||||||
\(50\) | −4.36392 | −0.617151 | ||||||||
\(51\) | 0.987094 | 0.138221 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −0.739743 | −0.101611 | −0.0508057 | − | 0.998709i | \(-0.516179\pi\) | ||||
−0.0508057 | + | 0.998709i | \(0.516179\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.579687 | 0.0781650 | ||||||||
\(56\) | −4.52438 | −0.604596 | ||||||||
\(57\) | 1.78344 | 0.236222 | ||||||||
\(58\) | 2.41751 | 0.317434 | ||||||||
\(59\) | −2.94509 | −0.383417 | −0.191709 | − | 0.981452i | \(-0.561403\pi\) | ||||
−0.191709 | + | 0.981452i | \(0.561403\pi\) | |||||||
\(60\) | 0.797548 | 0.102963 | ||||||||
\(61\) | −11.9494 | −1.52997 | −0.764985 | − | 0.644048i | \(-0.777254\pi\) | ||||
−0.764985 | + | 0.644048i | \(0.777254\pi\) | |||||||
\(62\) | −0.500062 | −0.0635079 | ||||||||
\(63\) | −4.52438 | −0.570019 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.797548 | −0.0989236 | ||||||||
\(66\) | 0.726837 | 0.0894674 | ||||||||
\(67\) | 0.738580 | 0.0902319 | 0.0451160 | − | 0.998982i | \(-0.485634\pi\) | ||||
0.0451160 | + | 0.998982i | \(0.485634\pi\) | |||||||
\(68\) | 0.987094 | 0.119703 | ||||||||
\(69\) | −5.45739 | −0.656993 | ||||||||
\(70\) | −3.60841 | −0.431288 | ||||||||
\(71\) | −0.256125 | −0.0303965 | −0.0151982 | − | 0.999885i | \(-0.504838\pi\) | ||||
−0.0151982 | + | 0.999885i | \(0.504838\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.07464 | −0.945065 | −0.472532 | − | 0.881313i | \(-0.656660\pi\) | ||||
−0.472532 | + | 0.881313i | \(0.656660\pi\) | |||||||
\(74\) | 0.242893 | 0.0282358 | ||||||||
\(75\) | −4.36392 | −0.503902 | ||||||||
\(76\) | 1.78344 | 0.204574 | ||||||||
\(77\) | −3.28849 | −0.374758 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 1.16693 | 0.131290 | 0.0656452 | − | 0.997843i | \(-0.479089\pi\) | ||||
0.0656452 | + | 0.997843i | \(0.479089\pi\) | |||||||
\(80\) | 0.797548 | 0.0891686 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.0069 | −1.21551 | ||||||||
\(83\) | −8.73755 | −0.959071 | −0.479535 | − | 0.877523i | \(-0.659195\pi\) | ||||
−0.479535 | + | 0.877523i | \(0.659195\pi\) | |||||||
\(84\) | −4.52438 | −0.493651 | ||||||||
\(85\) | 0.787255 | 0.0853898 | ||||||||
\(86\) | −6.15290 | −0.663485 | ||||||||
\(87\) | 2.41751 | 0.259184 | ||||||||
\(88\) | 0.726837 | 0.0774811 | ||||||||
\(89\) | 2.51500 | 0.266589 | 0.133295 | − | 0.991076i | \(-0.457444\pi\) | ||||
0.133295 | + | 0.991076i | \(0.457444\pi\) | |||||||
\(90\) | 0.797548 | 0.0840689 | ||||||||
\(91\) | 4.52438 | 0.474284 | ||||||||
\(92\) | −5.45739 | −0.568972 | ||||||||
\(93\) | −0.500062 | −0.0518540 | ||||||||
\(94\) | 6.55388 | 0.675981 | ||||||||
\(95\) | 1.42238 | 0.145933 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.1954 | −1.03519 | −0.517594 | − | 0.855626i | \(-0.673172\pi\) | ||||
−0.517594 | + | 0.855626i | \(0.673172\pi\) | |||||||
\(98\) | 13.4701 | 1.36068 | ||||||||
\(99\) | 0.726837 | 0.0730499 | ||||||||
\(100\) | −4.36392 | −0.436392 | ||||||||
\(101\) | 9.95897 | 0.990954 | 0.495477 | − | 0.868621i | \(-0.334993\pi\) | ||||
0.495477 | + | 0.868621i | \(0.334993\pi\) | |||||||
\(102\) | 0.987094 | 0.0977369 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −3.60841 | −0.352145 | ||||||||
\(106\) | −0.739743 | −0.0718501 | ||||||||
\(107\) | −0.884089 | −0.0854681 | −0.0427340 | − | 0.999086i | \(-0.513607\pi\) | ||||
−0.0427340 | + | 0.999086i | \(0.513607\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −13.9459 | −1.33578 | −0.667888 | − | 0.744262i | \(-0.732801\pi\) | ||||
−0.667888 | + | 0.744262i | \(0.732801\pi\) | |||||||
\(110\) | 0.579687 | 0.0552710 | ||||||||
\(111\) | 0.242893 | 0.0230544 | ||||||||
\(112\) | −4.52438 | −0.427514 | ||||||||
\(113\) | 8.78961 | 0.826857 | 0.413428 | − | 0.910537i | \(-0.364331\pi\) | ||||
0.413428 | + | 0.910537i | \(0.364331\pi\) | |||||||
\(114\) | 1.78344 | 0.167034 | ||||||||
\(115\) | −4.35253 | −0.405876 | ||||||||
\(116\) | 2.41751 | 0.224460 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −2.94509 | −0.271117 | ||||||||
\(119\) | −4.46599 | −0.409397 | ||||||||
\(120\) | 0.797548 | 0.0728058 | ||||||||
\(121\) | −10.4717 | −0.951973 | ||||||||
\(122\) | −11.9494 | −1.08185 | ||||||||
\(123\) | −11.0069 | −0.992459 | ||||||||
\(124\) | −0.500062 | −0.0449069 | ||||||||
\(125\) | −7.46817 | −0.667974 | ||||||||
\(126\) | −4.52438 | −0.403064 | ||||||||
\(127\) | 14.9261 | 1.32448 | 0.662238 | − | 0.749294i | \(-0.269607\pi\) | ||||
0.662238 | + | 0.749294i | \(0.269607\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.15290 | −0.541733 | ||||||||
\(130\) | −0.797548 | −0.0699496 | ||||||||
\(131\) | 6.85518 | 0.598940 | 0.299470 | − | 0.954106i | \(-0.403190\pi\) | ||||
0.299470 | + | 0.954106i | \(0.403190\pi\) | |||||||
\(132\) | 0.726837 | 0.0632630 | ||||||||
\(133\) | −8.06896 | −0.699668 | ||||||||
\(134\) | 0.738580 | 0.0638036 | ||||||||
\(135\) | 0.797548 | 0.0686420 | ||||||||
\(136\) | 0.987094 | 0.0846426 | ||||||||
\(137\) | 3.70447 | 0.316494 | 0.158247 | − | 0.987400i | \(-0.449416\pi\) | ||||
0.158247 | + | 0.987400i | \(0.449416\pi\) | |||||||
\(138\) | −5.45739 | −0.464564 | ||||||||
\(139\) | −17.2252 | −1.46102 | −0.730511 | − | 0.682901i | \(-0.760718\pi\) | ||||
−0.730511 | + | 0.682901i | \(0.760718\pi\) | |||||||
\(140\) | −3.60841 | −0.304967 | ||||||||
\(141\) | 6.55388 | 0.551936 | ||||||||
\(142\) | −0.256125 | −0.0214936 | ||||||||
\(143\) | −0.726837 | −0.0607812 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.92808 | 0.160118 | ||||||||
\(146\) | −8.07464 | −0.668262 | ||||||||
\(147\) | 13.4701 | 1.11099 | ||||||||
\(148\) | 0.242893 | 0.0199657 | ||||||||
\(149\) | −16.4849 | −1.35049 | −0.675247 | − | 0.737591i | \(-0.735963\pi\) | ||||
−0.675247 | + | 0.737591i | \(0.735963\pi\) | |||||||
\(150\) | −4.36392 | −0.356312 | ||||||||
\(151\) | −5.22890 | −0.425522 | −0.212761 | − | 0.977104i | \(-0.568246\pi\) | ||||
−0.212761 | + | 0.977104i | \(0.568246\pi\) | |||||||
\(152\) | 1.78344 | 0.144656 | ||||||||
\(153\) | 0.987094 | 0.0798018 | ||||||||
\(154\) | −3.28849 | −0.264994 | ||||||||
\(155\) | −0.398823 | −0.0320342 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 13.1212 | 1.04719 | 0.523593 | − | 0.851968i | \(-0.324591\pi\) | ||||
0.523593 | + | 0.851968i | \(0.324591\pi\) | |||||||
\(158\) | 1.16693 | 0.0928363 | ||||||||
\(159\) | −0.739743 | −0.0586654 | ||||||||
\(160\) | 0.797548 | 0.0630517 | ||||||||
\(161\) | 24.6913 | 1.94595 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.05386 | 0.160871 | 0.0804354 | − | 0.996760i | \(-0.474369\pi\) | ||||
0.0804354 | + | 0.996760i | \(0.474369\pi\) | |||||||
\(164\) | −11.0069 | −0.859495 | ||||||||
\(165\) | 0.579687 | 0.0451286 | ||||||||
\(166\) | −8.73755 | −0.678165 | ||||||||
\(167\) | 6.47667 | 0.501180 | 0.250590 | − | 0.968093i | \(-0.419375\pi\) | ||||
0.250590 | + | 0.968093i | \(0.419375\pi\) | |||||||
\(168\) | −4.52438 | −0.349064 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.787255 | 0.0603797 | ||||||||
\(171\) | 1.78344 | 0.136383 | ||||||||
\(172\) | −6.15290 | −0.469154 | ||||||||
\(173\) | −3.56976 | −0.271404 | −0.135702 | − | 0.990750i | \(-0.543329\pi\) | ||||
−0.135702 | + | 0.990750i | \(0.543329\pi\) | |||||||
\(174\) | 2.41751 | 0.183271 | ||||||||
\(175\) | 19.7440 | 1.49251 | ||||||||
\(176\) | 0.726837 | 0.0547874 | ||||||||
\(177\) | −2.94509 | −0.221366 | ||||||||
\(178\) | 2.51500 | 0.188507 | ||||||||
\(179\) | −5.40943 | −0.404319 | −0.202160 | − | 0.979353i | \(-0.564796\pi\) | ||||
−0.202160 | + | 0.979353i | \(0.564796\pi\) | |||||||
\(180\) | 0.797548 | 0.0594457 | ||||||||
\(181\) | −6.80871 | −0.506087 | −0.253044 | − | 0.967455i | \(-0.581432\pi\) | ||||
−0.253044 | + | 0.967455i | \(0.581432\pi\) | |||||||
\(182\) | 4.52438 | 0.335370 | ||||||||
\(183\) | −11.9494 | −0.883328 | ||||||||
\(184\) | −5.45739 | −0.402324 | ||||||||
\(185\) | 0.193719 | 0.0142425 | ||||||||
\(186\) | −0.500062 | −0.0366663 | ||||||||
\(187\) | 0.717457 | 0.0524656 | ||||||||
\(188\) | 6.55388 | 0.477991 | ||||||||
\(189\) | −4.52438 | −0.329101 | ||||||||
\(190\) | 1.42238 | 0.103190 | ||||||||
\(191\) | 27.2893 | 1.97458 | 0.987291 | − | 0.158924i | \(-0.0508024\pi\) | ||||
0.987291 | + | 0.158924i | \(0.0508024\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 0.595016 | 0.0428302 | 0.0214151 | − | 0.999771i | \(-0.493183\pi\) | ||||
0.0214151 | + | 0.999771i | \(0.493183\pi\) | |||||||
\(194\) | −10.1954 | −0.731988 | ||||||||
\(195\) | −0.797548 | −0.0571136 | ||||||||
\(196\) | 13.4701 | 0.962147 | ||||||||
\(197\) | −15.9865 | −1.13899 | −0.569497 | − | 0.821994i | \(-0.692862\pi\) | ||||
−0.569497 | + | 0.821994i | \(0.692862\pi\) | |||||||
\(198\) | 0.726837 | 0.0516540 | ||||||||
\(199\) | −11.5511 | −0.818836 | −0.409418 | − | 0.912347i | \(-0.634268\pi\) | ||||
−0.409418 | + | 0.912347i | \(0.634268\pi\) | |||||||
\(200\) | −4.36392 | −0.308576 | ||||||||
\(201\) | 0.738580 | 0.0520954 | ||||||||
\(202\) | 9.95897 | 0.700710 | ||||||||
\(203\) | −10.9377 | −0.767678 | ||||||||
\(204\) | 0.987094 | 0.0691104 | ||||||||
\(205\) | −8.77853 | −0.613119 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −5.45739 | −0.379315 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 1.29627 | 0.0896648 | ||||||||
\(210\) | −3.60841 | −0.249004 | ||||||||
\(211\) | −24.7761 | −1.70565 | −0.852827 | − | 0.522194i | \(-0.825114\pi\) | ||||
−0.852827 | + | 0.522194i | \(0.825114\pi\) | |||||||
\(212\) | −0.739743 | −0.0508057 | ||||||||
\(213\) | −0.256125 | −0.0175494 | ||||||||
\(214\) | −0.884089 | −0.0604351 | ||||||||
\(215\) | −4.90723 | −0.334671 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.26247 | 0.153587 | ||||||||
\(218\) | −13.9459 | −0.944536 | ||||||||
\(219\) | −8.07464 | −0.545633 | ||||||||
\(220\) | 0.579687 | 0.0390825 | ||||||||
\(221\) | −0.987094 | −0.0663991 | ||||||||
\(222\) | 0.242893 | 0.0163019 | ||||||||
\(223\) | 2.06150 | 0.138048 | 0.0690241 | − | 0.997615i | \(-0.478011\pi\) | ||||
0.0690241 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(224\) | −4.52438 | −0.302298 | ||||||||
\(225\) | −4.36392 | −0.290928 | ||||||||
\(226\) | 8.78961 | 0.584676 | ||||||||
\(227\) | 19.0225 | 1.26257 | 0.631283 | − | 0.775552i | \(-0.282528\pi\) | ||||
0.631283 | + | 0.775552i | \(0.282528\pi\) | |||||||
\(228\) | 1.78344 | 0.118111 | ||||||||
\(229\) | 15.9093 | 1.05132 | 0.525658 | − | 0.850696i | \(-0.323819\pi\) | ||||
0.525658 | + | 0.850696i | \(0.323819\pi\) | |||||||
\(230\) | −4.35253 | −0.286997 | ||||||||
\(231\) | −3.28849 | −0.216367 | ||||||||
\(232\) | 2.41751 | 0.158717 | ||||||||
\(233\) | −15.4747 | −1.01378 | −0.506890 | − | 0.862011i | \(-0.669205\pi\) | ||||
−0.506890 | + | 0.862011i | \(0.669205\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 5.22703 | 0.340974 | ||||||||
\(236\) | −2.94509 | −0.191709 | ||||||||
\(237\) | 1.16693 | 0.0758005 | ||||||||
\(238\) | −4.46599 | −0.289487 | ||||||||
\(239\) | −9.91541 | −0.641375 | −0.320687 | − | 0.947185i | \(-0.603914\pi\) | ||||
−0.320687 | + | 0.947185i | \(0.603914\pi\) | |||||||
\(240\) | 0.797548 | 0.0514815 | ||||||||
\(241\) | −24.1212 | −1.55379 | −0.776893 | − | 0.629633i | \(-0.783205\pi\) | ||||
−0.776893 | + | 0.629633i | \(0.783205\pi\) | |||||||
\(242\) | −10.4717 | −0.673147 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.9494 | −0.764985 | ||||||||
\(245\) | 10.7430 | 0.686346 | ||||||||
\(246\) | −11.0069 | −0.701775 | ||||||||
\(247\) | −1.78344 | −0.113477 | ||||||||
\(248\) | −0.500062 | −0.0317540 | ||||||||
\(249\) | −8.73755 | −0.553720 | ||||||||
\(250\) | −7.46817 | −0.472329 | ||||||||
\(251\) | 1.25196 | 0.0790232 | 0.0395116 | − | 0.999219i | \(-0.487420\pi\) | ||||
0.0395116 | + | 0.999219i | \(0.487420\pi\) | |||||||
\(252\) | −4.52438 | −0.285009 | ||||||||
\(253\) | −3.96663 | −0.249380 | ||||||||
\(254\) | 14.9261 | 0.936546 | ||||||||
\(255\) | 0.787255 | 0.0492998 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.1530 | −1.25711 | −0.628553 | − | 0.777766i | \(-0.716353\pi\) | ||||
−0.628553 | + | 0.777766i | \(0.716353\pi\) | |||||||
\(258\) | −6.15290 | −0.383063 | ||||||||
\(259\) | −1.09894 | −0.0682850 | ||||||||
\(260\) | −0.797548 | −0.0494618 | ||||||||
\(261\) | 2.41751 | 0.149640 | ||||||||
\(262\) | 6.85518 | 0.423514 | ||||||||
\(263\) | −13.0656 | −0.805659 | −0.402829 | − | 0.915275i | \(-0.631973\pi\) | ||||
−0.402829 | + | 0.915275i | \(0.631973\pi\) | |||||||
\(264\) | 0.726837 | 0.0447337 | ||||||||
\(265\) | −0.589980 | −0.0362422 | ||||||||
\(266\) | −8.06896 | −0.494740 | ||||||||
\(267\) | 2.51500 | 0.153915 | ||||||||
\(268\) | 0.738580 | 0.0451160 | ||||||||
\(269\) | 27.1939 | 1.65804 | 0.829020 | − | 0.559219i | \(-0.188899\pi\) | ||||
0.829020 | + | 0.559219i | \(0.188899\pi\) | |||||||
\(270\) | 0.797548 | 0.0485372 | ||||||||
\(271\) | 1.66544 | 0.101168 | 0.0505842 | − | 0.998720i | \(-0.483892\pi\) | ||||
0.0505842 | + | 0.998720i | \(0.483892\pi\) | |||||||
\(272\) | 0.987094 | 0.0598514 | ||||||||
\(273\) | 4.52438 | 0.273828 | ||||||||
\(274\) | 3.70447 | 0.223795 | ||||||||
\(275\) | −3.17186 | −0.191270 | ||||||||
\(276\) | −5.45739 | −0.328496 | ||||||||
\(277\) | −29.8720 | −1.79483 | −0.897417 | − | 0.441183i | \(-0.854559\pi\) | ||||
−0.897417 | + | 0.441183i | \(0.854559\pi\) | |||||||
\(278\) | −17.2252 | −1.03310 | ||||||||
\(279\) | −0.500062 | −0.0299379 | ||||||||
\(280\) | −3.60841 | −0.215644 | ||||||||
\(281\) | −8.28440 | −0.494206 | −0.247103 | − | 0.968989i | \(-0.579479\pi\) | ||||
−0.247103 | + | 0.968989i | \(0.579479\pi\) | |||||||
\(282\) | 6.55388 | 0.390278 | ||||||||
\(283\) | 0.106605 | 0.00633701 | 0.00316850 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00316850 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(284\) | −0.256125 | −0.0151982 | ||||||||
\(285\) | 1.42238 | 0.0842544 | ||||||||
\(286\) | −0.726837 | −0.0429788 | ||||||||
\(287\) | 49.7995 | 2.93957 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0256 | −0.942685 | ||||||||
\(290\) | 1.92808 | 0.113221 | ||||||||
\(291\) | −10.1954 | −0.597666 | ||||||||
\(292\) | −8.07464 | −0.472532 | ||||||||
\(293\) | −2.52246 | −0.147364 | −0.0736819 | − | 0.997282i | \(-0.523475\pi\) | ||||
−0.0736819 | + | 0.997282i | \(0.523475\pi\) | |||||||
\(294\) | 13.4701 | 0.785590 | ||||||||
\(295\) | −2.34885 | −0.136755 | ||||||||
\(296\) | 0.242893 | 0.0141179 | ||||||||
\(297\) | 0.726837 | 0.0421754 | ||||||||
\(298\) | −16.4849 | −0.954944 | ||||||||
\(299\) | 5.45739 | 0.315609 | ||||||||
\(300\) | −4.36392 | −0.251951 | ||||||||
\(301\) | 27.8381 | 1.60456 | ||||||||
\(302\) | −5.22890 | −0.300889 | ||||||||
\(303\) | 9.95897 | 0.572128 | ||||||||
\(304\) | 1.78344 | 0.102287 | ||||||||
\(305\) | −9.53025 | −0.545701 | ||||||||
\(306\) | 0.987094 | 0.0564284 | ||||||||
\(307\) | 22.0445 | 1.25815 | 0.629073 | − | 0.777347i | \(-0.283435\pi\) | ||||
0.629073 | + | 0.777347i | \(0.283435\pi\) | |||||||
\(308\) | −3.28849 | −0.187379 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −0.398823 | −0.0226516 | ||||||||
\(311\) | 0.982492 | 0.0557120 | 0.0278560 | − | 0.999612i | \(-0.491132\pi\) | ||||
0.0278560 | + | 0.999612i | \(0.491132\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −3.79254 | −0.214367 | −0.107183 | − | 0.994239i | \(-0.534183\pi\) | ||||
−0.107183 | + | 0.994239i | \(0.534183\pi\) | |||||||
\(314\) | 13.1212 | 0.740472 | ||||||||
\(315\) | −3.60841 | −0.203311 | ||||||||
\(316\) | 1.16693 | 0.0656452 | ||||||||
\(317\) | 14.9328 | 0.838708 | 0.419354 | − | 0.907823i | \(-0.362257\pi\) | ||||
0.419354 | + | 0.907823i | \(0.362257\pi\) | |||||||
\(318\) | −0.739743 | −0.0414827 | ||||||||
\(319\) | 1.75713 | 0.0983806 | ||||||||
\(320\) | 0.797548 | 0.0445843 | ||||||||
\(321\) | −0.884089 | −0.0493450 | ||||||||
\(322\) | 24.6913 | 1.37599 | ||||||||
\(323\) | 1.76042 | 0.0979525 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.36392 | 0.242067 | ||||||||
\(326\) | 2.05386 | 0.113753 | ||||||||
\(327\) | −13.9459 | −0.771210 | ||||||||
\(328\) | −11.0069 | −0.607755 | ||||||||
\(329\) | −29.6523 | −1.63478 | ||||||||
\(330\) | 0.579687 | 0.0319107 | ||||||||
\(331\) | −10.1335 | −0.556990 | −0.278495 | − | 0.960438i | \(-0.589836\pi\) | ||||
−0.278495 | + | 0.960438i | \(0.589836\pi\) | |||||||
\(332\) | −8.73755 | −0.479535 | ||||||||
\(333\) | 0.242893 | 0.0133105 | ||||||||
\(334\) | 6.47667 | 0.354388 | ||||||||
\(335\) | 0.589053 | 0.0321834 | ||||||||
\(336\) | −4.52438 | −0.246825 | ||||||||
\(337\) | 19.9561 | 1.08708 | 0.543538 | − | 0.839384i | \(-0.317084\pi\) | ||||
0.543538 | + | 0.839384i | \(0.317084\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 8.78961 | 0.477386 | ||||||||
\(340\) | 0.787255 | 0.0426949 | ||||||||
\(341\) | −0.363463 | −0.0196826 | ||||||||
\(342\) | 1.78344 | 0.0964373 | ||||||||
\(343\) | −29.2730 | −1.58059 | ||||||||
\(344\) | −6.15290 | −0.331742 | ||||||||
\(345\) | −4.35253 | −0.234332 | ||||||||
\(346\) | −3.56976 | −0.191912 | ||||||||
\(347\) | 3.81997 | 0.205067 | 0.102533 | − | 0.994730i | \(-0.467305\pi\) | ||||
0.102533 | + | 0.994730i | \(0.467305\pi\) | |||||||
\(348\) | 2.41751 | 0.129592 | ||||||||
\(349\) | 11.6084 | 0.621381 | 0.310690 | − | 0.950511i | \(-0.399440\pi\) | ||||
0.310690 | + | 0.950511i | \(0.399440\pi\) | |||||||
\(350\) | 19.7440 | 1.05536 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0.726837 | 0.0387405 | ||||||||
\(353\) | 10.4353 | 0.555416 | 0.277708 | − | 0.960666i | \(-0.410425\pi\) | ||||
0.277708 | + | 0.960666i | \(0.410425\pi\) | |||||||
\(354\) | −2.94509 | −0.156530 | ||||||||
\(355\) | −0.204272 | −0.0108416 | ||||||||
\(356\) | 2.51500 | 0.133295 | ||||||||
\(357\) | −4.46599 | −0.236365 | ||||||||
\(358\) | −5.40943 | −0.285897 | ||||||||
\(359\) | 5.73178 | 0.302512 | 0.151256 | − | 0.988495i | \(-0.451668\pi\) | ||||
0.151256 | + | 0.988495i | \(0.451668\pi\) | |||||||
\(360\) | 0.797548 | 0.0420345 | ||||||||
\(361\) | −15.8193 | −0.832597 | ||||||||
\(362\) | −6.80871 | −0.357858 | ||||||||
\(363\) | −10.4717 | −0.549622 | ||||||||
\(364\) | 4.52438 | 0.237142 | ||||||||
\(365\) | −6.43991 | −0.337080 | ||||||||
\(366\) | −11.9494 | −0.624608 | ||||||||
\(367\) | 5.52511 | 0.288408 | 0.144204 | − | 0.989548i | \(-0.453938\pi\) | ||||
0.144204 | + | 0.989548i | \(0.453938\pi\) | |||||||
\(368\) | −5.45739 | −0.284486 | ||||||||
\(369\) | −11.0069 | −0.572997 | ||||||||
\(370\) | 0.193719 | 0.0100710 | ||||||||
\(371\) | 3.34688 | 0.173761 | ||||||||
\(372\) | −0.500062 | −0.0259270 | ||||||||
\(373\) | 27.1285 | 1.40466 | 0.702330 | − | 0.711852i | \(-0.252143\pi\) | ||||
0.702330 | + | 0.711852i | \(0.252143\pi\) | |||||||
\(374\) | 0.717457 | 0.0370988 | ||||||||
\(375\) | −7.46817 | −0.385655 | ||||||||
\(376\) | 6.55388 | 0.337990 | ||||||||
\(377\) | −2.41751 | −0.124508 | ||||||||
\(378\) | −4.52438 | −0.232709 | ||||||||
\(379\) | −31.7844 | −1.63265 | −0.816327 | − | 0.577590i | \(-0.803993\pi\) | ||||
−0.816327 | + | 0.577590i | \(0.803993\pi\) | |||||||
\(380\) | 1.42238 | 0.0729664 | ||||||||
\(381\) | 14.9261 | 0.764687 | ||||||||
\(382\) | 27.2893 | 1.39624 | ||||||||
\(383\) | −22.4750 | −1.14842 | −0.574210 | − | 0.818708i | \(-0.694691\pi\) | ||||
−0.574210 | + | 0.818708i | \(0.694691\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.62273 | −0.133667 | ||||||||
\(386\) | 0.595016 | 0.0302855 | ||||||||
\(387\) | −6.15290 | −0.312770 | ||||||||
\(388\) | −10.1954 | −0.517594 | ||||||||
\(389\) | −1.87542 | −0.0950874 | −0.0475437 | − | 0.998869i | \(-0.515139\pi\) | ||||
−0.0475437 | + | 0.998869i | \(0.515139\pi\) | |||||||
\(390\) | −0.797548 | −0.0403854 | ||||||||
\(391\) | −5.38696 | −0.272430 | ||||||||
\(392\) | 13.4701 | 0.680341 | ||||||||
\(393\) | 6.85518 | 0.345798 | ||||||||
\(394\) | −15.9865 | −0.805390 | ||||||||
\(395\) | 0.930686 | 0.0468279 | ||||||||
\(396\) | 0.726837 | 0.0365249 | ||||||||
\(397\) | 1.42324 | 0.0714303 | 0.0357152 | − | 0.999362i | \(-0.488629\pi\) | ||||
0.0357152 | + | 0.999362i | \(0.488629\pi\) | |||||||
\(398\) | −11.5511 | −0.579005 | ||||||||
\(399\) | −8.06896 | −0.403953 | ||||||||
\(400\) | −4.36392 | −0.218196 | ||||||||
\(401\) | 16.9059 | 0.844241 | 0.422120 | − | 0.906540i | \(-0.361286\pi\) | ||||
0.422120 | + | 0.906540i | \(0.361286\pi\) | |||||||
\(402\) | 0.738580 | 0.0368370 | ||||||||
\(403\) | 0.500062 | 0.0249099 | ||||||||
\(404\) | 9.95897 | 0.495477 | ||||||||
\(405\) | 0.797548 | 0.0396305 | ||||||||
\(406\) | −10.9377 | −0.542831 | ||||||||
\(407\) | 0.176544 | 0.00875095 | ||||||||
\(408\) | 0.987094 | 0.0488685 | ||||||||
\(409\) | −10.3569 | −0.512113 | −0.256057 | − | 0.966662i | \(-0.582423\pi\) | ||||
−0.256057 | + | 0.966662i | \(0.582423\pi\) | |||||||
\(410\) | −8.77853 | −0.433541 | ||||||||
\(411\) | 3.70447 | 0.182728 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 13.3247 | 0.655666 | ||||||||
\(414\) | −5.45739 | −0.268216 | ||||||||
\(415\) | −6.96861 | −0.342076 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −17.2252 | −0.843521 | ||||||||
\(418\) | 1.29627 | 0.0634026 | ||||||||
\(419\) | 17.3634 | 0.848255 | 0.424128 | − | 0.905602i | \(-0.360581\pi\) | ||||
0.424128 | + | 0.905602i | \(0.360581\pi\) | |||||||
\(420\) | −3.60841 | −0.176073 | ||||||||
\(421\) | −26.7985 | −1.30608 | −0.653039 | − | 0.757324i | \(-0.726506\pi\) | ||||
−0.653039 | + | 0.757324i | \(0.726506\pi\) | |||||||
\(422\) | −24.7761 | −1.20608 | ||||||||
\(423\) | 6.55388 | 0.318660 | ||||||||
\(424\) | −0.739743 | −0.0359251 | ||||||||
\(425\) | −4.30760 | −0.208949 | ||||||||
\(426\) | −0.256125 | −0.0124093 | ||||||||
\(427\) | 54.0639 | 2.61633 | ||||||||
\(428\) | −0.884089 | −0.0427340 | ||||||||
\(429\) | −0.726837 | −0.0350920 | ||||||||
\(430\) | −4.90723 | −0.236648 | ||||||||
\(431\) | 14.2900 | 0.688324 | 0.344162 | − | 0.938910i | \(-0.388163\pi\) | ||||
0.344162 | + | 0.938910i | \(0.388163\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 14.9149 | 0.716763 | 0.358382 | − | 0.933575i | \(-0.383329\pi\) | ||||
0.358382 | + | 0.933575i | \(0.383329\pi\) | |||||||
\(434\) | 2.26247 | 0.108602 | ||||||||
\(435\) | 1.92808 | 0.0924442 | ||||||||
\(436\) | −13.9459 | −0.667888 | ||||||||
\(437\) | −9.73292 | −0.465589 | ||||||||
\(438\) | −8.07464 | −0.385821 | ||||||||
\(439\) | 1.51504 | 0.0723090 | 0.0361545 | − | 0.999346i | \(-0.488489\pi\) | ||||
0.0361545 | + | 0.999346i | \(0.488489\pi\) | |||||||
\(440\) | 0.579687 | 0.0276355 | ||||||||
\(441\) | 13.4701 | 0.641431 | ||||||||
\(442\) | −0.987094 | −0.0469513 | ||||||||
\(443\) | −0.0224802 | −0.00106807 | −0.000534034 | − | 1.00000i | \(-0.500170\pi\) | ||||
−0.000534034 | 1.00000i | \(0.500170\pi\) | ||||||||
\(444\) | 0.242893 | 0.0115272 | ||||||||
\(445\) | 2.00583 | 0.0950855 | ||||||||
\(446\) | 2.06150 | 0.0976149 | ||||||||
\(447\) | −16.4849 | −0.779708 | ||||||||
\(448\) | −4.52438 | −0.213757 | ||||||||
\(449\) | 4.30909 | 0.203358 | 0.101679 | − | 0.994817i | \(-0.467578\pi\) | ||||
0.101679 | + | 0.994817i | \(0.467578\pi\) | |||||||
\(450\) | −4.36392 | −0.205717 | ||||||||
\(451\) | −8.00022 | −0.376716 | ||||||||
\(452\) | 8.78961 | 0.413428 | ||||||||
\(453\) | −5.22890 | −0.245675 | ||||||||
\(454\) | 19.0225 | 0.892770 | ||||||||
\(455\) | 3.60841 | 0.169165 | ||||||||
\(456\) | 1.78344 | 0.0835172 | ||||||||
\(457\) | 19.5132 | 0.912789 | 0.456394 | − | 0.889778i | \(-0.349141\pi\) | ||||
0.456394 | + | 0.889778i | \(0.349141\pi\) | |||||||
\(458\) | 15.9093 | 0.743393 | ||||||||
\(459\) | 0.987094 | 0.0460736 | ||||||||
\(460\) | −4.35253 | −0.202938 | ||||||||
\(461\) | −37.7225 | −1.75691 | −0.878457 | − | 0.477822i | \(-0.841426\pi\) | ||||
−0.878457 | + | 0.477822i | \(0.841426\pi\) | |||||||
\(462\) | −3.28849 | −0.152994 | ||||||||
\(463\) | 18.3765 | 0.854028 | 0.427014 | − | 0.904245i | \(-0.359566\pi\) | ||||
0.427014 | + | 0.904245i | \(0.359566\pi\) | |||||||
\(464\) | 2.41751 | 0.112230 | ||||||||
\(465\) | −0.398823 | −0.0184950 | ||||||||
\(466\) | −15.4747 | −0.716850 | ||||||||
\(467\) | 14.3930 | 0.666028 | 0.333014 | − | 0.942922i | \(-0.391934\pi\) | ||||
0.333014 | + | 0.942922i | \(0.391934\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −3.34162 | −0.154302 | ||||||||
\(470\) | 5.22703 | 0.241105 | ||||||||
\(471\) | 13.1212 | 0.604593 | ||||||||
\(472\) | −2.94509 | −0.135559 | ||||||||
\(473\) | −4.47216 | −0.205630 | ||||||||
\(474\) | 1.16693 | 0.0535991 | ||||||||
\(475\) | −7.78278 | −0.357098 | ||||||||
\(476\) | −4.46599 | −0.204699 | ||||||||
\(477\) | −0.739743 | −0.0338705 | ||||||||
\(478\) | −9.91541 | −0.453520 | ||||||||
\(479\) | 7.31044 | 0.334023 | 0.167011 | − | 0.985955i | \(-0.446588\pi\) | ||||
0.167011 | + | 0.985955i | \(0.446588\pi\) | |||||||
\(480\) | 0.797548 | 0.0364029 | ||||||||
\(481\) | −0.242893 | −0.0110750 | ||||||||
\(482\) | −24.1212 | −1.09869 | ||||||||
\(483\) | 24.6913 | 1.12349 | ||||||||
\(484\) | −10.4717 | −0.475987 | ||||||||
\(485\) | −8.13133 | −0.369225 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 13.9513 | 0.632196 | 0.316098 | − | 0.948727i | \(-0.397627\pi\) | ||||
0.316098 | + | 0.948727i | \(0.397627\pi\) | |||||||
\(488\) | −11.9494 | −0.540926 | ||||||||
\(489\) | 2.05386 | 0.0928788 | ||||||||
\(490\) | 10.7430 | 0.485320 | ||||||||
\(491\) | 31.1091 | 1.40393 | 0.701967 | − | 0.712209i | \(-0.252305\pi\) | ||||
0.701967 | + | 0.712209i | \(0.252305\pi\) | |||||||
\(492\) | −11.0069 | −0.496230 | ||||||||
\(493\) | 2.38631 | 0.107474 | ||||||||
\(494\) | −1.78344 | −0.0802407 | ||||||||
\(495\) | 0.579687 | 0.0260550 | ||||||||
\(496\) | −0.500062 | −0.0224534 | ||||||||
\(497\) | 1.15881 | 0.0519797 | ||||||||
\(498\) | −8.73755 | −0.391539 | ||||||||
\(499\) | 9.53910 | 0.427029 | 0.213514 | − | 0.976940i | \(-0.431509\pi\) | ||||
0.213514 | + | 0.976940i | \(0.431509\pi\) | |||||||
\(500\) | −7.46817 | −0.333987 | ||||||||
\(501\) | 6.47667 | 0.289356 | ||||||||
\(502\) | 1.25196 | 0.0558778 | ||||||||
\(503\) | −17.6243 | −0.785830 | −0.392915 | − | 0.919575i | \(-0.628533\pi\) | ||||
−0.392915 | + | 0.919575i | \(0.628533\pi\) | |||||||
\(504\) | −4.52438 | −0.201532 | ||||||||
\(505\) | 7.94275 | 0.353448 | ||||||||
\(506\) | −3.96663 | −0.176338 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 14.9261 | 0.662238 | ||||||||
\(509\) | 1.14732 | 0.0508542 | 0.0254271 | − | 0.999677i | \(-0.491905\pi\) | ||||
0.0254271 | + | 0.999677i | \(0.491905\pi\) | |||||||
\(510\) | 0.787255 | 0.0348602 | ||||||||
\(511\) | 36.5328 | 1.61611 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.78344 | 0.0787407 | ||||||||
\(514\) | −20.1530 | −0.888909 | ||||||||
\(515\) | −0.797548 | −0.0351442 | ||||||||
\(516\) | −6.15290 | −0.270866 | ||||||||
\(517\) | 4.76360 | 0.209503 | ||||||||
\(518\) | −1.09894 | −0.0482848 | ||||||||
\(519\) | −3.56976 | −0.156695 | ||||||||
\(520\) | −0.797548 | −0.0349748 | ||||||||
\(521\) | 2.61627 | 0.114621 | 0.0573105 | − | 0.998356i | \(-0.481748\pi\) | ||||
0.0573105 | + | 0.998356i | \(0.481748\pi\) | |||||||
\(522\) | 2.41751 | 0.105811 | ||||||||
\(523\) | 36.4244 | 1.59273 | 0.796364 | − | 0.604817i | \(-0.206754\pi\) | ||||
0.796364 | + | 0.604817i | \(0.206754\pi\) | |||||||
\(524\) | 6.85518 | 0.299470 | ||||||||
\(525\) | 19.7440 | 0.861701 | ||||||||
\(526\) | −13.0656 | −0.569687 | ||||||||
\(527\) | −0.493608 | −0.0215019 | ||||||||
\(528\) | 0.726837 | 0.0316315 | ||||||||
\(529\) | 6.78312 | 0.294918 | ||||||||
\(530\) | −0.589980 | −0.0256271 | ||||||||
\(531\) | −2.94509 | −0.127806 | ||||||||
\(532\) | −8.06896 | −0.349834 | ||||||||
\(533\) | 11.0069 | 0.476762 | ||||||||
\(534\) | 2.51500 | 0.108835 | ||||||||
\(535\) | −0.705103 | −0.0304843 | ||||||||
\(536\) | 0.738580 | 0.0319018 | ||||||||
\(537\) | −5.40943 | −0.233434 | ||||||||
\(538\) | 27.1939 | 1.17241 | ||||||||
\(539\) | 9.79053 | 0.421708 | ||||||||
\(540\) | 0.797548 | 0.0343210 | ||||||||
\(541\) | 35.3850 | 1.52132 | 0.760661 | − | 0.649150i | \(-0.224875\pi\) | ||||
0.760661 | + | 0.649150i | \(0.224875\pi\) | |||||||
\(542\) | 1.66544 | 0.0715368 | ||||||||
\(543\) | −6.80871 | −0.292190 | ||||||||
\(544\) | 0.987094 | 0.0423213 | ||||||||
\(545\) | −11.1225 | −0.476436 | ||||||||
\(546\) | 4.52438 | 0.193626 | ||||||||
\(547\) | 29.1934 | 1.24822 | 0.624109 | − | 0.781337i | \(-0.285462\pi\) | ||||
0.624109 | + | 0.781337i | \(0.285462\pi\) | |||||||
\(548\) | 3.70447 | 0.158247 | ||||||||
\(549\) | −11.9494 | −0.509990 | ||||||||
\(550\) | −3.17186 | −0.135248 | ||||||||
\(551\) | 4.31148 | 0.183675 | ||||||||
\(552\) | −5.45739 | −0.232282 | ||||||||
\(553\) | −5.27966 | −0.224514 | ||||||||
\(554\) | −29.8720 | −1.26914 | ||||||||
\(555\) | 0.193719 | 0.00822292 | ||||||||
\(556\) | −17.2252 | −0.730511 | ||||||||
\(557\) | −11.5853 | −0.490887 | −0.245443 | − | 0.969411i | \(-0.578934\pi\) | ||||
−0.245443 | + | 0.969411i | \(0.578934\pi\) | |||||||
\(558\) | −0.500062 | −0.0211693 | ||||||||
\(559\) | 6.15290 | 0.260240 | ||||||||
\(560\) | −3.60841 | −0.152483 | ||||||||
\(561\) | 0.717457 | 0.0302910 | ||||||||
\(562\) | −8.28440 | −0.349456 | ||||||||
\(563\) | 40.2228 | 1.69519 | 0.847595 | − | 0.530644i | \(-0.178050\pi\) | ||||
0.847595 | + | 0.530644i | \(0.178050\pi\) | |||||||
\(564\) | 6.55388 | 0.275968 | ||||||||
\(565\) | 7.01013 | 0.294918 | ||||||||
\(566\) | 0.106605 | 0.00448094 | ||||||||
\(567\) | −4.52438 | −0.190006 | ||||||||
\(568\) | −0.256125 | −0.0107468 | ||||||||
\(569\) | −9.88422 | −0.414368 | −0.207184 | − | 0.978302i | \(-0.566430\pi\) | ||||
−0.207184 | + | 0.978302i | \(0.566430\pi\) | |||||||
\(570\) | 1.42238 | 0.0595768 | ||||||||
\(571\) | −9.62620 | −0.402844 | −0.201422 | − | 0.979505i | \(-0.564556\pi\) | ||||
−0.201422 | + | 0.979505i | \(0.564556\pi\) | |||||||
\(572\) | −0.726837 | −0.0303906 | ||||||||
\(573\) | 27.2893 | 1.14003 | ||||||||
\(574\) | 49.7995 | 2.07859 | ||||||||
\(575\) | 23.8156 | 0.993179 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.8517 | −0.743177 | −0.371589 | − | 0.928397i | \(-0.621187\pi\) | ||||
−0.371589 | + | 0.928397i | \(0.621187\pi\) | |||||||
\(578\) | −16.0256 | −0.666579 | ||||||||
\(579\) | 0.595016 | 0.0247280 | ||||||||
\(580\) | 1.92808 | 0.0800591 | ||||||||
\(581\) | 39.5320 | 1.64007 | ||||||||
\(582\) | −10.1954 | −0.422614 | ||||||||
\(583\) | −0.537672 | −0.0222681 | ||||||||
\(584\) | −8.07464 | −0.334131 | ||||||||
\(585\) | −0.797548 | −0.0329745 | ||||||||
\(586\) | −2.52246 | −0.104202 | ||||||||
\(587\) | −40.7854 | −1.68339 | −0.841697 | − | 0.539950i | \(-0.818443\pi\) | ||||
−0.841697 | + | 0.539950i | \(0.818443\pi\) | |||||||
\(588\) | 13.4701 | 0.555496 | ||||||||
\(589\) | −0.891829 | −0.0367472 | ||||||||
\(590\) | −2.34885 | −0.0967005 | ||||||||
\(591\) | −15.9865 | −0.657598 | ||||||||
\(592\) | 0.242893 | 0.00998286 | ||||||||
\(593\) | −11.4018 | −0.468215 | −0.234107 | − | 0.972211i | \(-0.575217\pi\) | ||||
−0.234107 | + | 0.972211i | \(0.575217\pi\) | |||||||
\(594\) | 0.726837 | 0.0298225 | ||||||||
\(595\) | −3.56184 | −0.146021 | ||||||||
\(596\) | −16.4849 | −0.675247 | ||||||||
\(597\) | −11.5511 | −0.472755 | ||||||||
\(598\) | 5.45739 | 0.223169 | ||||||||
\(599\) | 32.6152 | 1.33262 | 0.666311 | − | 0.745674i | \(-0.267872\pi\) | ||||
0.666311 | + | 0.745674i | \(0.267872\pi\) | |||||||
\(600\) | −4.36392 | −0.178156 | ||||||||
\(601\) | −33.9546 | −1.38504 | −0.692518 | − | 0.721400i | \(-0.743499\pi\) | ||||
−0.692518 | + | 0.721400i | \(0.743499\pi\) | |||||||
\(602\) | 27.8381 | 1.13460 | ||||||||
\(603\) | 0.738580 | 0.0300773 | ||||||||
\(604\) | −5.22890 | −0.212761 | ||||||||
\(605\) | −8.35169 | −0.339544 | ||||||||
\(606\) | 9.95897 | 0.404555 | ||||||||
\(607\) | −20.1260 | −0.816889 | −0.408444 | − | 0.912783i | \(-0.633929\pi\) | ||||
−0.408444 | + | 0.912783i | \(0.633929\pi\) | |||||||
\(608\) | 1.78344 | 0.0723280 | ||||||||
\(609\) | −10.9377 | −0.443219 | ||||||||
\(610\) | −9.53025 | −0.385869 | ||||||||
\(611\) | −6.55388 | −0.265142 | ||||||||
\(612\) | 0.987094 | 0.0399009 | ||||||||
\(613\) | 41.6300 | 1.68142 | 0.840711 | − | 0.541485i | \(-0.182138\pi\) | ||||
0.840711 | + | 0.541485i | \(0.182138\pi\) | |||||||
\(614\) | 22.0445 | 0.889643 | ||||||||
\(615\) | −8.77853 | −0.353985 | ||||||||
\(616\) | −3.28849 | −0.132497 | ||||||||
\(617\) | 3.23796 | 0.130355 | 0.0651776 | − | 0.997874i | \(-0.479239\pi\) | ||||
0.0651776 | + | 0.997874i | \(0.479239\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 18.3610 | 0.737989 | 0.368995 | − | 0.929431i | \(-0.379702\pi\) | ||||
0.368995 | + | 0.929431i | \(0.379702\pi\) | |||||||
\(620\) | −0.398823 | −0.0160171 | ||||||||
\(621\) | −5.45739 | −0.218998 | ||||||||
\(622\) | 0.982492 | 0.0393943 | ||||||||
\(623\) | −11.3788 | −0.455883 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 15.8634 | 0.634535 | ||||||||
\(626\) | −3.79254 | −0.151580 | ||||||||
\(627\) | 1.29627 | 0.0517680 | ||||||||
\(628\) | 13.1212 | 0.523593 | ||||||||
\(629\) | 0.239759 | 0.00955980 | ||||||||
\(630\) | −3.60841 | −0.143763 | ||||||||
\(631\) | 22.8885 | 0.911178 | 0.455589 | − | 0.890190i | \(-0.349429\pi\) | ||||
0.455589 | + | 0.890190i | \(0.349429\pi\) | |||||||
\(632\) | 1.16693 | 0.0464182 | ||||||||
\(633\) | −24.7761 | −0.984760 | ||||||||
\(634\) | 14.9328 | 0.593056 | ||||||||
\(635\) | 11.9043 | 0.472406 | ||||||||
\(636\) | −0.739743 | −0.0293327 | ||||||||
\(637\) | −13.4701 | −0.533703 | ||||||||
\(638\) | 1.75713 | 0.0695656 | ||||||||
\(639\) | −0.256125 | −0.0101322 | ||||||||
\(640\) | 0.797548 | 0.0315258 | ||||||||
\(641\) | −16.0348 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(642\) | −0.884089 | −0.0348922 | ||||||||
\(643\) | −21.9170 | −0.864322 | −0.432161 | − | 0.901796i | \(-0.642249\pi\) | ||||
−0.432161 | + | 0.901796i | \(0.642249\pi\) | |||||||
\(644\) | 24.6913 | 0.972975 | ||||||||
\(645\) | −4.90723 | −0.193222 | ||||||||
\(646\) | 1.76042 | 0.0692629 | ||||||||
\(647\) | −3.37893 | −0.132839 | −0.0664197 | − | 0.997792i | \(-0.521158\pi\) | ||||
−0.0664197 | + | 0.997792i | \(0.521158\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.14060 | −0.0840258 | ||||||||
\(650\) | 4.36392 | 0.171167 | ||||||||
\(651\) | 2.26247 | 0.0886733 | ||||||||
\(652\) | 2.05386 | 0.0804354 | ||||||||
\(653\) | −1.86127 | −0.0728372 | −0.0364186 | − | 0.999337i | \(-0.511595\pi\) | ||||
−0.0364186 | + | 0.999337i | \(0.511595\pi\) | |||||||
\(654\) | −13.9459 | −0.545328 | ||||||||
\(655\) | 5.46733 | 0.213626 | ||||||||
\(656\) | −11.0069 | −0.429747 | ||||||||
\(657\) | −8.07464 | −0.315022 | ||||||||
\(658\) | −29.6523 | −1.15597 | ||||||||
\(659\) | 3.66110 | 0.142616 | 0.0713082 | − | 0.997454i | \(-0.477283\pi\) | ||||
0.0713082 | + | 0.997454i | \(0.477283\pi\) | |||||||
\(660\) | 0.579687 | 0.0225643 | ||||||||
\(661\) | 30.4869 | 1.18580 | 0.592902 | − | 0.805275i | \(-0.297982\pi\) | ||||
0.592902 | + | 0.805275i | \(0.297982\pi\) | |||||||
\(662\) | −10.1335 | −0.393851 | ||||||||
\(663\) | −0.987094 | −0.0383356 | ||||||||
\(664\) | −8.73755 | −0.339083 | ||||||||
\(665\) | −6.43538 | −0.249553 | ||||||||
\(666\) | 0.242893 | 0.00941193 | ||||||||
\(667\) | −13.1933 | −0.510846 | ||||||||
\(668\) | 6.47667 | 0.250590 | ||||||||
\(669\) | 2.06150 | 0.0797022 | ||||||||
\(670\) | 0.589053 | 0.0227571 | ||||||||
\(671\) | −8.68530 | −0.335292 | ||||||||
\(672\) | −4.52438 | −0.174532 | ||||||||
\(673\) | 34.7610 | 1.33994 | 0.669970 | − | 0.742389i | \(-0.266307\pi\) | ||||
0.669970 | + | 0.742389i | \(0.266307\pi\) | |||||||
\(674\) | 19.9561 | 0.768679 | ||||||||
\(675\) | −4.36392 | −0.167967 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −21.6936 | −0.833753 | −0.416876 | − | 0.908963i | \(-0.636875\pi\) | ||||
−0.416876 | + | 0.908963i | \(0.636875\pi\) | |||||||
\(678\) | 8.78961 | 0.337563 | ||||||||
\(679\) | 46.1280 | 1.77023 | ||||||||
\(680\) | 0.787255 | 0.0301898 | ||||||||
\(681\) | 19.0225 | 0.728943 | ||||||||
\(682\) | −0.363463 | −0.0139177 | ||||||||
\(683\) | 34.4730 | 1.31907 | 0.659536 | − | 0.751673i | \(-0.270753\pi\) | ||||
0.659536 | + | 0.751673i | \(0.270753\pi\) | |||||||
\(684\) | 1.78344 | 0.0681915 | ||||||||
\(685\) | 2.95449 | 0.112885 | ||||||||
\(686\) | −29.2730 | −1.11765 | ||||||||
\(687\) | 15.9093 | 0.606978 | ||||||||
\(688\) | −6.15290 | −0.234577 | ||||||||
\(689\) | 0.739743 | 0.0281819 | ||||||||
\(690\) | −4.35253 | −0.165698 | ||||||||
\(691\) | −5.39903 | −0.205389 | −0.102694 | − | 0.994713i | \(-0.532746\pi\) | ||||
−0.102694 | + | 0.994713i | \(0.532746\pi\) | |||||||
\(692\) | −3.56976 | −0.135702 | ||||||||
\(693\) | −3.28849 | −0.124919 | ||||||||
\(694\) | 3.81997 | 0.145004 | ||||||||
\(695\) | −13.7379 | −0.521109 | ||||||||
\(696\) | 2.41751 | 0.0916354 | ||||||||
\(697\) | −10.8649 | −0.411536 | ||||||||
\(698\) | 11.6084 | 0.439383 | ||||||||
\(699\) | −15.4747 | −0.585306 | ||||||||
\(700\) | 19.7440 | 0.746255 | ||||||||
\(701\) | 34.9808 | 1.32121 | 0.660604 | − | 0.750735i | \(-0.270300\pi\) | ||||
0.660604 | + | 0.750735i | \(0.270300\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 0.433185 | 0.0163379 | ||||||||
\(704\) | 0.726837 | 0.0273937 | ||||||||
\(705\) | 5.22703 | 0.196861 | ||||||||
\(706\) | 10.4353 | 0.392739 | ||||||||
\(707\) | −45.0582 | −1.69459 | ||||||||
\(708\) | −2.94509 | −0.110683 | ||||||||
\(709\) | −25.2093 | −0.946756 | −0.473378 | − | 0.880859i | \(-0.656966\pi\) | ||||
−0.473378 | + | 0.880859i | \(0.656966\pi\) | |||||||
\(710\) | −0.204272 | −0.00766620 | ||||||||
\(711\) | 1.16693 | 0.0437635 | ||||||||
\(712\) | 2.51500 | 0.0942535 | ||||||||
\(713\) | 2.72903 | 0.102203 | ||||||||
\(714\) | −4.46599 | −0.167136 | ||||||||
\(715\) | −0.579687 | −0.0216791 | ||||||||
\(716\) | −5.40943 | −0.202160 | ||||||||
\(717\) | −9.91541 | −0.370298 | ||||||||
\(718\) | 5.73178 | 0.213908 | ||||||||
\(719\) | −25.2591 | −0.942006 | −0.471003 | − | 0.882132i | \(-0.656108\pi\) | ||||
−0.471003 | + | 0.882132i | \(0.656108\pi\) | |||||||
\(720\) | 0.797548 | 0.0297229 | ||||||||
\(721\) | 4.52438 | 0.168497 | ||||||||
\(722\) | −15.8193 | −0.588735 | ||||||||
\(723\) | −24.1212 | −0.897079 | ||||||||
\(724\) | −6.80871 | −0.253044 | ||||||||
\(725\) | −10.5498 | −0.391810 | ||||||||
\(726\) | −10.4717 | −0.388642 | ||||||||
\(727\) | 1.00734 | 0.0373601 | 0.0186800 | − | 0.999826i | \(-0.494054\pi\) | ||||
0.0186800 | + | 0.999826i | \(0.494054\pi\) | |||||||
\(728\) | 4.52438 | 0.167685 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.43991 | −0.238352 | ||||||||
\(731\) | −6.07349 | −0.224636 | ||||||||
\(732\) | −11.9494 | −0.441664 | ||||||||
\(733\) | 36.6669 | 1.35432 | 0.677161 | − | 0.735835i | \(-0.263210\pi\) | ||||
0.677161 | + | 0.735835i | \(0.263210\pi\) | |||||||
\(734\) | 5.52511 | 0.203935 | ||||||||
\(735\) | 10.7430 | 0.396262 | ||||||||
\(736\) | −5.45739 | −0.201162 | ||||||||
\(737\) | 0.536827 | 0.0197743 | ||||||||
\(738\) | −11.0069 | −0.405170 | ||||||||
\(739\) | 23.2457 | 0.855108 | 0.427554 | − | 0.903990i | \(-0.359375\pi\) | ||||
0.427554 | + | 0.903990i | \(0.359375\pi\) | |||||||
\(740\) | 0.193719 | 0.00712125 | ||||||||
\(741\) | −1.78344 | −0.0655163 | ||||||||
\(742\) | 3.34688 | 0.122868 | ||||||||
\(743\) | 27.3497 | 1.00336 | 0.501681 | − | 0.865052i | \(-0.332715\pi\) | ||||
0.501681 | + | 0.865052i | \(0.332715\pi\) | |||||||
\(744\) | −0.500062 | −0.0183332 | ||||||||
\(745\) | −13.1475 | −0.481687 | ||||||||
\(746\) | 27.1285 | 0.993244 | ||||||||
\(747\) | −8.73755 | −0.319690 | ||||||||
\(748\) | 0.717457 | 0.0262328 | ||||||||
\(749\) | 3.99996 | 0.146155 | ||||||||
\(750\) | −7.46817 | −0.272699 | ||||||||
\(751\) | 28.4157 | 1.03690 | 0.518451 | − | 0.855107i | \(-0.326509\pi\) | ||||
0.518451 | + | 0.855107i | \(0.326509\pi\) | |||||||
\(752\) | 6.55388 | 0.238995 | ||||||||
\(753\) | 1.25196 | 0.0456240 | ||||||||
\(754\) | −2.41751 | −0.0880404 | ||||||||
\(755\) | −4.17030 | −0.151773 | ||||||||
\(756\) | −4.52438 | −0.164550 | ||||||||
\(757\) | −17.9350 | −0.651859 | −0.325930 | − | 0.945394i | \(-0.605677\pi\) | ||||
−0.325930 | + | 0.945394i | \(0.605677\pi\) | |||||||
\(758\) | −31.7844 | −1.15446 | ||||||||
\(759\) | −3.96663 | −0.143980 | ||||||||
\(760\) | 1.42238 | 0.0515951 | ||||||||
\(761\) | −0.407740 | −0.0147806 | −0.00739028 | − | 0.999973i | \(-0.502352\pi\) | ||||
−0.00739028 | + | 0.999973i | \(0.502352\pi\) | |||||||
\(762\) | 14.9261 | 0.540715 | ||||||||
\(763\) | 63.0966 | 2.28425 | ||||||||
\(764\) | 27.2893 | 0.987291 | ||||||||
\(765\) | 0.787255 | 0.0284633 | ||||||||
\(766\) | −22.4750 | −0.812055 | ||||||||
\(767\) | 2.94509 | 0.106341 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −11.7330 | −0.423104 | −0.211552 | − | 0.977367i | \(-0.567852\pi\) | ||||
−0.211552 | + | 0.977367i | \(0.567852\pi\) | |||||||
\(770\) | −2.62273 | −0.0945165 | ||||||||
\(771\) | −20.1530 | −0.725791 | ||||||||
\(772\) | 0.595016 | 0.0214151 | ||||||||
\(773\) | −14.7850 | −0.531779 | −0.265890 | − | 0.964003i | \(-0.585666\pi\) | ||||
−0.265890 | + | 0.964003i | \(0.585666\pi\) | |||||||
\(774\) | −6.15290 | −0.221162 | ||||||||
\(775\) | 2.18223 | 0.0783880 | ||||||||
\(776\) | −10.1954 | −0.365994 | ||||||||
\(777\) | −1.09894 | −0.0394244 | ||||||||
\(778\) | −1.87542 | −0.0672370 | ||||||||
\(779\) | −19.6301 | −0.703323 | ||||||||
\(780\) | −0.797548 | −0.0285568 | ||||||||
\(781\) | −0.186161 | −0.00666138 | ||||||||
\(782\) | −5.38696 | −0.192637 | ||||||||
\(783\) | 2.41751 | 0.0863947 | ||||||||
\(784\) | 13.4701 | 0.481073 | ||||||||
\(785\) | 10.4648 | 0.373504 | ||||||||
\(786\) | 6.85518 | 0.244516 | ||||||||
\(787\) | −4.69636 | −0.167407 | −0.0837036 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837036 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(788\) | −15.9865 | −0.569497 | ||||||||
\(789\) | −13.0656 | −0.465147 | ||||||||
\(790\) | 0.930686 | 0.0331123 | ||||||||
\(791\) | −39.7676 | −1.41397 | ||||||||
\(792\) | 0.726837 | 0.0258270 | ||||||||
\(793\) | 11.9494 | 0.424337 | ||||||||
\(794\) | 1.42324 | 0.0505089 | ||||||||
\(795\) | −0.589980 | −0.0209244 | ||||||||
\(796\) | −11.5511 | −0.409418 | ||||||||
\(797\) | −34.0542 | −1.20626 | −0.603131 | − | 0.797642i | \(-0.706080\pi\) | ||||
−0.603131 | + | 0.797642i | \(0.706080\pi\) | |||||||
\(798\) | −8.06896 | −0.285638 | ||||||||
\(799\) | 6.46930 | 0.228867 | ||||||||
\(800\) | −4.36392 | −0.154288 | ||||||||
\(801\) | 2.51500 | 0.0888630 | ||||||||
\(802\) | 16.9059 | 0.596968 | ||||||||
\(803\) | −5.86894 | −0.207111 | ||||||||
\(804\) | 0.738580 | 0.0260477 | ||||||||
\(805\) | 19.6925 | 0.694070 | ||||||||
\(806\) | 0.500062 | 0.0176139 | ||||||||
\(807\) | 27.1939 | 0.957270 | ||||||||
\(808\) | 9.95897 | 0.350355 | ||||||||
\(809\) | −45.7412 | −1.60817 | −0.804087 | − | 0.594512i | \(-0.797345\pi\) | ||||
−0.804087 | + | 0.594512i | \(0.797345\pi\) | |||||||
\(810\) | 0.797548 | 0.0280230 | ||||||||
\(811\) | −9.34669 | −0.328207 | −0.164103 | − | 0.986443i | \(-0.552473\pi\) | ||||
−0.164103 | + | 0.986443i | \(0.552473\pi\) | |||||||
\(812\) | −10.9377 | −0.383839 | ||||||||
\(813\) | 1.66544 | 0.0584096 | ||||||||
\(814\) | 0.176544 | 0.00618786 | ||||||||
\(815\) | 1.63805 | 0.0573785 | ||||||||
\(816\) | 0.987094 | 0.0345552 | ||||||||
\(817\) | −10.9733 | −0.383908 | ||||||||
\(818\) | −10.3569 | −0.362119 | ||||||||
\(819\) | 4.52438 | 0.158095 | ||||||||
\(820\) | −8.77853 | −0.306560 | ||||||||
\(821\) | −26.8650 | −0.937595 | −0.468797 | − | 0.883306i | \(-0.655313\pi\) | ||||
−0.468797 | + | 0.883306i | \(0.655313\pi\) | |||||||
\(822\) | 3.70447 | 0.129208 | ||||||||
\(823\) | 24.7424 | 0.862467 | 0.431234 | − | 0.902240i | \(-0.358078\pi\) | ||||
0.431234 | + | 0.902240i | \(0.358078\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −3.17186 | −0.110430 | ||||||||
\(826\) | 13.3247 | 0.463626 | ||||||||
\(827\) | −27.9021 | −0.970250 | −0.485125 | − | 0.874445i | \(-0.661226\pi\) | ||||
−0.485125 | + | 0.874445i | \(0.661226\pi\) | |||||||
\(828\) | −5.45739 | −0.189657 | ||||||||
\(829\) | 38.3360 | 1.33146 | 0.665732 | − | 0.746191i | \(-0.268119\pi\) | ||||
0.665732 | + | 0.746191i | \(0.268119\pi\) | |||||||
\(830\) | −6.96861 | −0.241884 | ||||||||
\(831\) | −29.8720 | −1.03625 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 13.2962 | 0.460687 | ||||||||
\(834\) | −17.2252 | −0.596459 | ||||||||
\(835\) | 5.16546 | 0.178758 | ||||||||
\(836\) | 1.29627 | 0.0448324 | ||||||||
\(837\) | −0.500062 | −0.0172847 | ||||||||
\(838\) | 17.3634 | 0.599807 | ||||||||
\(839\) | 23.2516 | 0.802735 | 0.401367 | − | 0.915917i | \(-0.368535\pi\) | ||||
0.401367 | + | 0.915917i | \(0.368535\pi\) | |||||||
\(840\) | −3.60841 | −0.124502 | ||||||||
\(841\) | −23.1557 | −0.798471 | ||||||||
\(842\) | −26.7985 | −0.923537 | ||||||||
\(843\) | −8.28440 | −0.285330 | ||||||||
\(844\) | −24.7761 | −0.852827 | ||||||||
\(845\) | 0.797548 | 0.0274365 | ||||||||
\(846\) | 6.55388 | 0.225327 | ||||||||
\(847\) | 47.3780 | 1.62793 | ||||||||
\(848\) | −0.739743 | −0.0254029 | ||||||||
\(849\) | 0.106605 | 0.00365867 | ||||||||
\(850\) | −4.30760 | −0.147749 | ||||||||
\(851\) | −1.32556 | −0.0454398 | ||||||||
\(852\) | −0.256125 | −0.00877471 | ||||||||
\(853\) | 7.32715 | 0.250877 | 0.125438 | − | 0.992101i | \(-0.459966\pi\) | ||||
0.125438 | + | 0.992101i | \(0.459966\pi\) | |||||||
\(854\) | 54.0639 | 1.85003 | ||||||||
\(855\) | 1.42238 | 0.0486443 | ||||||||
\(856\) | −0.884089 | −0.0302175 | ||||||||
\(857\) | −14.7087 | −0.502439 | −0.251220 | − | 0.967930i | \(-0.580832\pi\) | ||||
−0.251220 | + | 0.967930i | \(0.580832\pi\) | |||||||
\(858\) | −0.726837 | −0.0248138 | ||||||||
\(859\) | 24.5352 | 0.837130 | 0.418565 | − | 0.908187i | \(-0.362533\pi\) | ||||
0.418565 | + | 0.908187i | \(0.362533\pi\) | |||||||
\(860\) | −4.90723 | −0.167335 | ||||||||
\(861\) | 49.7995 | 1.69716 | ||||||||
\(862\) | 14.2900 | 0.486718 | ||||||||
\(863\) | −7.54013 | −0.256669 | −0.128335 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128335 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.84706 | −0.0968029 | ||||||||
\(866\) | 14.9149 | 0.506828 | ||||||||
\(867\) | −16.0256 | −0.544259 | ||||||||
\(868\) | 2.26247 | 0.0767933 | ||||||||
\(869\) | 0.848171 | 0.0287722 | ||||||||
\(870\) | 1.92808 | 0.0653680 | ||||||||
\(871\) | −0.738580 | −0.0250258 | ||||||||
\(872\) | −13.9459 | −0.472268 | ||||||||
\(873\) | −10.1954 | −0.345063 | ||||||||
\(874\) | −9.73292 | −0.329221 | ||||||||
\(875\) | 33.7889 | 1.14227 | ||||||||
\(876\) | −8.07464 | −0.272817 | ||||||||
\(877\) | 4.62436 | 0.156154 | 0.0780768 | − | 0.996947i | \(-0.475122\pi\) | ||||
0.0780768 | + | 0.996947i | \(0.475122\pi\) | |||||||
\(878\) | 1.51504 | 0.0511302 | ||||||||
\(879\) | −2.52246 | −0.0850805 | ||||||||
\(880\) | 0.579687 | 0.0195412 | ||||||||
\(881\) | −42.9887 | −1.44833 | −0.724163 | − | 0.689629i | \(-0.757774\pi\) | ||||
−0.724163 | + | 0.689629i | \(0.757774\pi\) | |||||||
\(882\) | 13.4701 | 0.453560 | ||||||||
\(883\) | −7.23511 | −0.243481 | −0.121740 | − | 0.992562i | \(-0.538848\pi\) | ||||
−0.121740 | + | 0.992562i | \(0.538848\pi\) | |||||||
\(884\) | −0.987094 | −0.0331996 | ||||||||
\(885\) | −2.34885 | −0.0789556 | ||||||||
\(886\) | −0.0224802 | −0.000755238 0 | ||||||||
\(887\) | 37.8766 | 1.27177 | 0.635886 | − | 0.771783i | \(-0.280635\pi\) | ||||
0.635886 | + | 0.771783i | \(0.280635\pi\) | |||||||
\(888\) | 0.242893 | 0.00815097 | ||||||||
\(889\) | −67.5314 | −2.26493 | ||||||||
\(890\) | 2.00583 | 0.0672356 | ||||||||
\(891\) | 0.726837 | 0.0243500 | ||||||||
\(892\) | 2.06150 | 0.0690241 | ||||||||
\(893\) | 11.6884 | 0.391139 | ||||||||
\(894\) | −16.4849 | −0.551337 | ||||||||
\(895\) | −4.31428 | −0.144210 | ||||||||
\(896\) | −4.52438 | −0.151149 | ||||||||
\(897\) | 5.45739 | 0.182217 | ||||||||
\(898\) | 4.30909 | 0.143796 | ||||||||
\(899\) | −1.20890 | −0.0403192 | ||||||||
\(900\) | −4.36392 | −0.145464 | ||||||||
\(901\) | −0.730196 | −0.0243263 | ||||||||
\(902\) | −8.00022 | −0.266378 | ||||||||
\(903\) | 27.8381 | 0.926394 | ||||||||
\(904\) | 8.78961 | 0.292338 | ||||||||
\(905\) | −5.43027 | −0.180508 | ||||||||
\(906\) | −5.22890 | −0.173719 | ||||||||
\(907\) | 7.01925 | 0.233071 | 0.116535 | − | 0.993187i | \(-0.462821\pi\) | ||||
0.116535 | + | 0.993187i | \(0.462821\pi\) | |||||||
\(908\) | 19.0225 | 0.631283 | ||||||||
\(909\) | 9.95897 | 0.330318 | ||||||||
\(910\) | 3.60841 | 0.119618 | ||||||||
\(911\) | 37.9417 | 1.25706 | 0.628532 | − | 0.777783i | \(-0.283656\pi\) | ||||
0.628532 | + | 0.777783i | \(0.283656\pi\) | |||||||
\(912\) | 1.78344 | 0.0590556 | ||||||||
\(913\) | −6.35077 | −0.210180 | ||||||||
\(914\) | 19.5132 | 0.645439 | ||||||||
\(915\) | −9.53025 | −0.315060 | ||||||||
\(916\) | 15.9093 | 0.525658 | ||||||||
\(917\) | −31.0155 | −1.02422 | ||||||||
\(918\) | 0.987094 | 0.0325790 | ||||||||
\(919\) | 30.1113 | 0.993279 | 0.496639 | − | 0.867957i | \(-0.334567\pi\) | ||||
0.496639 | + | 0.867957i | \(0.334567\pi\) | |||||||
\(920\) | −4.35253 | −0.143499 | ||||||||
\(921\) | 22.0445 | 0.726391 | ||||||||
\(922\) | −37.7225 | −1.24233 | ||||||||
\(923\) | 0.256125 | 0.00843047 | ||||||||
\(924\) | −3.28849 | −0.108183 | ||||||||
\(925\) | −1.05997 | −0.0348515 | ||||||||
\(926\) | 18.3765 | 0.603889 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 2.41751 | 0.0793586 | ||||||||
\(929\) | −7.98142 | −0.261862 | −0.130931 | − | 0.991392i | \(-0.541797\pi\) | ||||
−0.130931 | + | 0.991392i | \(0.541797\pi\) | |||||||
\(930\) | −0.398823 | −0.0130779 | ||||||||
\(931\) | 24.0230 | 0.787323 | ||||||||
\(932\) | −15.4747 | −0.506890 | ||||||||
\(933\) | 0.982492 | 0.0321653 | ||||||||
\(934\) | 14.3930 | 0.470953 | ||||||||
\(935\) | 0.572206 | 0.0187131 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 42.9781 | 1.40403 | 0.702017 | − | 0.712160i | \(-0.252283\pi\) | ||||
0.702017 | + | 0.712160i | \(0.252283\pi\) | |||||||
\(938\) | −3.34162 | −0.109108 | ||||||||
\(939\) | −3.79254 | −0.123765 | ||||||||
\(940\) | 5.22703 | 0.170487 | ||||||||
\(941\) | −4.88484 | −0.159241 | −0.0796207 | − | 0.996825i | \(-0.525371\pi\) | ||||
−0.0796207 | + | 0.996825i | \(0.525371\pi\) | |||||||
\(942\) | 13.1212 | 0.427512 | ||||||||
\(943\) | 60.0690 | 1.95612 | ||||||||
\(944\) | −2.94509 | −0.0958544 | ||||||||
\(945\) | −3.60841 | −0.117382 | ||||||||
\(946\) | −4.47216 | −0.145402 | ||||||||
\(947\) | 7.34327 | 0.238624 | 0.119312 | − | 0.992857i | \(-0.461931\pi\) | ||||
0.119312 | + | 0.992857i | \(0.461931\pi\) | |||||||
\(948\) | 1.16693 | 0.0379003 | ||||||||
\(949\) | 8.07464 | 0.262114 | ||||||||
\(950\) | −7.78278 | −0.252507 | ||||||||
\(951\) | 14.9328 | 0.484228 | ||||||||
\(952\) | −4.46599 | −0.144744 | ||||||||
\(953\) | 40.4781 | 1.31121 | 0.655607 | − | 0.755102i | \(-0.272413\pi\) | ||||
0.655607 | + | 0.755102i | \(0.272413\pi\) | |||||||
\(954\) | −0.739743 | −0.0239500 | ||||||||
\(955\) | 21.7645 | 0.704282 | ||||||||
\(956\) | −9.91541 | −0.320687 | ||||||||
\(957\) | 1.75713 | 0.0568001 | ||||||||
\(958\) | 7.31044 | 0.236190 | ||||||||
\(959\) | −16.7605 | −0.541224 | ||||||||
\(960\) | 0.797548 | 0.0257407 | ||||||||
\(961\) | −30.7499 | −0.991933 | ||||||||
\(962\) | −0.242893 | −0.00783120 | ||||||||
\(963\) | −0.884089 | −0.0284894 | ||||||||
\(964\) | −24.1212 | −0.776893 | ||||||||
\(965\) | 0.474554 | 0.0152764 | ||||||||
\(966\) | 24.6913 | 0.794431 | ||||||||
\(967\) | −36.9299 | −1.18759 | −0.593793 | − | 0.804618i | \(-0.702370\pi\) | ||||
−0.593793 | + | 0.804618i | \(0.702370\pi\) | |||||||
\(968\) | −10.4717 | −0.336573 | ||||||||
\(969\) | 1.76042 | 0.0565529 | ||||||||
\(970\) | −8.13133 | −0.261081 | ||||||||
\(971\) | −7.92569 | −0.254347 | −0.127174 | − | 0.991880i | \(-0.540591\pi\) | ||||
−0.127174 | + | 0.991880i | \(0.540591\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 77.9334 | 2.49843 | ||||||||
\(974\) | 13.9513 | 0.447030 | ||||||||
\(975\) | 4.36392 | 0.139757 | ||||||||
\(976\) | −11.9494 | −0.382492 | ||||||||
\(977\) | 2.74275 | 0.0877483 | 0.0438741 | − | 0.999037i | \(-0.486030\pi\) | ||||
0.0438741 | + | 0.999037i | \(0.486030\pi\) | |||||||
\(978\) | 2.05386 | 0.0656752 | ||||||||
\(979\) | 1.82799 | 0.0584229 | ||||||||
\(980\) | 10.7430 | 0.343173 | ||||||||
\(981\) | −13.9459 | −0.445258 | ||||||||
\(982\) | 31.1091 | 0.992731 | ||||||||
\(983\) | −25.6816 | −0.819115 | −0.409557 | − | 0.912284i | \(-0.634317\pi\) | ||||
−0.409557 | + | 0.912284i | \(0.634317\pi\) | |||||||
\(984\) | −11.0069 | −0.350887 | ||||||||
\(985\) | −12.7500 | −0.406250 | ||||||||
\(986\) | 2.38631 | 0.0759955 | ||||||||
\(987\) | −29.6523 | −0.943842 | ||||||||
\(988\) | −1.78344 | −0.0567387 | ||||||||
\(989\) | 33.5788 | 1.06774 | ||||||||
\(990\) | 0.579687 | 0.0184237 | ||||||||
\(991\) | 31.4969 | 1.00053 | 0.500267 | − | 0.865871i | \(-0.333235\pi\) | ||||
0.500267 | + | 0.865871i | \(0.333235\pi\) | |||||||
\(992\) | −0.500062 | −0.0158770 | ||||||||
\(993\) | −10.1335 | −0.321578 | ||||||||
\(994\) | 1.15881 | 0.0367552 | ||||||||
\(995\) | −9.21256 | −0.292058 | ||||||||
\(996\) | −8.73755 | −0.276860 | ||||||||
\(997\) | 34.4563 | 1.09124 | 0.545620 | − | 0.838032i | \(-0.316294\pi\) | ||||
0.545620 | + | 0.838032i | \(0.316294\pi\) | |||||||
\(998\) | 9.53910 | 0.301955 | ||||||||
\(999\) | 0.242893 | 0.00768481 |
(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 | 8034.2.a.q.1.6 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.q.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial |