Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
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: | \( x^{8} - 4x^{7} - 4x^{6} + 22x^{5} + 3x^{4} - 28x^{3} + 7x^{2} + 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.47489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.47489 | −1.42888 | −0.714438 | − | 0.699699i | \(-0.753318\pi\) | ||||
−0.714438 | + | 0.699699i | \(0.753318\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.86363 | 1.28065 | 0.640327 | − | 0.768102i | \(-0.278799\pi\) | ||||
0.640327 | + | 0.768102i | \(0.278799\pi\) | |||||||
\(6\) | 2.47489 | 1.01037 | ||||||||
\(7\) | 1.77068 | 0.669253 | 0.334627 | − | 0.942351i | \(-0.391390\pi\) | ||||
0.334627 | + | 0.942351i | \(0.391390\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.12506 | 1.04169 | ||||||||
\(10\) | −2.86363 | −0.905560 | ||||||||
\(11\) | 0.764511 | 0.230509 | 0.115254 | − | 0.993336i | \(-0.463232\pi\) | ||||
0.115254 | + | 0.993336i | \(0.463232\pi\) | |||||||
\(12\) | −2.47489 | −0.714438 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.77068 | −0.473234 | ||||||||
\(15\) | −7.08716 | −1.82990 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.468182 | 0.113551 | 0.0567754 | − | 0.998387i | \(-0.481918\pi\) | ||||
0.0567754 | + | 0.998387i | \(0.481918\pi\) | |||||||
\(18\) | −3.12506 | −0.736584 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.86363 | 0.640327 | ||||||||
\(21\) | −4.38223 | −0.956280 | ||||||||
\(22\) | −0.764511 | −0.162994 | ||||||||
\(23\) | −3.33675 | −0.695760 | −0.347880 | − | 0.937539i | \(-0.613098\pi\) | ||||
−0.347880 | + | 0.937539i | \(0.613098\pi\) | |||||||
\(24\) | 2.47489 | 0.505184 | ||||||||
\(25\) | 3.20038 | 0.640076 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.309515 | −0.0595661 | ||||||||
\(28\) | 1.77068 | 0.334627 | ||||||||
\(29\) | 3.54830 | 0.658904 | 0.329452 | − | 0.944172i | \(-0.393136\pi\) | ||||
0.329452 | + | 0.944172i | \(0.393136\pi\) | |||||||
\(30\) | 7.08716 | 1.29393 | ||||||||
\(31\) | −2.73715 | −0.491607 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.89208 | −0.329368 | ||||||||
\(34\) | −0.468182 | −0.0802925 | ||||||||
\(35\) | 5.07057 | 0.857082 | ||||||||
\(36\) | 3.12506 | 0.520844 | ||||||||
\(37\) | −5.74198 | −0.943976 | −0.471988 | − | 0.881605i | \(-0.656463\pi\) | ||||
−0.471988 | + | 0.881605i | \(0.656463\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.86363 | −0.452780 | ||||||||
\(41\) | −9.46441 | −1.47809 | −0.739046 | − | 0.673655i | \(-0.764723\pi\) | ||||
−0.739046 | + | 0.673655i | \(0.764723\pi\) | |||||||
\(42\) | 4.38223 | 0.676192 | ||||||||
\(43\) | 6.78094 | 1.03408 | 0.517042 | − | 0.855960i | \(-0.327033\pi\) | ||||
0.517042 | + | 0.855960i | \(0.327033\pi\) | |||||||
\(44\) | 0.764511 | 0.115254 | ||||||||
\(45\) | 8.94902 | 1.33404 | ||||||||
\(46\) | 3.33675 | 0.491977 | ||||||||
\(47\) | −1.37434 | −0.200467 | −0.100234 | − | 0.994964i | \(-0.531959\pi\) | ||||
−0.100234 | + | 0.994964i | \(0.531959\pi\) | |||||||
\(48\) | −2.47489 | −0.357219 | ||||||||
\(49\) | −3.86470 | −0.552100 | ||||||||
\(50\) | −3.20038 | −0.452602 | ||||||||
\(51\) | −1.15870 | −0.162250 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.55237 | −1.31212 | −0.656060 | − | 0.754709i | \(-0.727778\pi\) | ||||
−0.656060 | + | 0.754709i | \(0.727778\pi\) | |||||||
\(54\) | 0.309515 | 0.0421196 | ||||||||
\(55\) | 2.18928 | 0.295202 | ||||||||
\(56\) | −1.77068 | −0.236617 | ||||||||
\(57\) | −2.47489 | −0.327807 | ||||||||
\(58\) | −3.54830 | −0.465915 | ||||||||
\(59\) | 5.76584 | 0.750649 | 0.375324 | − | 0.926894i | \(-0.377531\pi\) | ||||
0.375324 | + | 0.926894i | \(0.377531\pi\) | |||||||
\(60\) | −7.08716 | −0.914948 | ||||||||
\(61\) | −2.36516 | −0.302828 | −0.151414 | − | 0.988470i | \(-0.548383\pi\) | ||||
−0.151414 | + | 0.988470i | \(0.548383\pi\) | |||||||
\(62\) | 2.73715 | 0.347618 | ||||||||
\(63\) | 5.53348 | 0.697153 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.89208 | 0.232899 | ||||||||
\(67\) | −1.49066 | −0.182112 | −0.0910562 | − | 0.995846i | \(-0.529024\pi\) | ||||
−0.0910562 | + | 0.995846i | \(0.529024\pi\) | |||||||
\(68\) | 0.468182 | 0.0567754 | ||||||||
\(69\) | 8.25808 | 0.994156 | ||||||||
\(70\) | −5.07057 | −0.606049 | ||||||||
\(71\) | −2.41091 | −0.286122 | −0.143061 | − | 0.989714i | \(-0.545695\pi\) | ||||
−0.143061 | + | 0.989714i | \(0.545695\pi\) | |||||||
\(72\) | −3.12506 | −0.368292 | ||||||||
\(73\) | −12.1769 | −1.42520 | −0.712598 | − | 0.701573i | \(-0.752482\pi\) | ||||
−0.712598 | + | 0.701573i | \(0.752482\pi\) | |||||||
\(74\) | 5.74198 | 0.667492 | ||||||||
\(75\) | −7.92058 | −0.914590 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 1.35370 | 0.154269 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.31247 | −1.04773 | −0.523867 | − | 0.851800i | \(-0.675511\pi\) | ||||
−0.523867 | + | 0.851800i | \(0.675511\pi\) | |||||||
\(80\) | 2.86363 | 0.320164 | ||||||||
\(81\) | −8.60917 | −0.956575 | ||||||||
\(82\) | 9.46441 | 1.04517 | ||||||||
\(83\) | −3.26881 | −0.358798 | −0.179399 | − | 0.983776i | \(-0.557415\pi\) | ||||
−0.179399 | + | 0.983776i | \(0.557415\pi\) | |||||||
\(84\) | −4.38223 | −0.478140 | ||||||||
\(85\) | 1.34070 | 0.145419 | ||||||||
\(86\) | −6.78094 | −0.731208 | ||||||||
\(87\) | −8.78165 | −0.941492 | ||||||||
\(88\) | −0.764511 | −0.0814971 | ||||||||
\(89\) | −14.5129 | −1.53837 | −0.769184 | − | 0.639027i | \(-0.779337\pi\) | ||||
−0.769184 | + | 0.639027i | \(0.779337\pi\) | |||||||
\(90\) | −8.94902 | −0.943310 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.33675 | −0.347880 | ||||||||
\(93\) | 6.77413 | 0.702445 | ||||||||
\(94\) | 1.37434 | 0.141752 | ||||||||
\(95\) | 2.86363 | 0.293802 | ||||||||
\(96\) | 2.47489 | 0.252592 | ||||||||
\(97\) | −2.74409 | −0.278620 | −0.139310 | − | 0.990249i | \(-0.544488\pi\) | ||||
−0.139310 | + | 0.990249i | \(0.544488\pi\) | |||||||
\(98\) | 3.86470 | 0.390394 | ||||||||
\(99\) | 2.38914 | 0.240118 | ||||||||
\(100\) | 3.20038 | 0.320038 | ||||||||
\(101\) | 13.3665 | 1.33002 | 0.665009 | − | 0.746835i | \(-0.268428\pi\) | ||||
0.665009 | + | 0.746835i | \(0.268428\pi\) | |||||||
\(102\) | 1.15870 | 0.114728 | ||||||||
\(103\) | −7.96934 | −0.785242 | −0.392621 | − | 0.919700i | \(-0.628432\pi\) | ||||
−0.392621 | + | 0.919700i | \(0.628432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.5491 | −1.22466 | ||||||||
\(106\) | 9.55237 | 0.927808 | ||||||||
\(107\) | 5.93502 | 0.573760 | 0.286880 | − | 0.957966i | \(-0.407382\pi\) | ||||
0.286880 | + | 0.957966i | \(0.407382\pi\) | |||||||
\(108\) | −0.309515 | −0.0297831 | ||||||||
\(109\) | 2.85280 | 0.273249 | 0.136624 | − | 0.990623i | \(-0.456375\pi\) | ||||
0.136624 | + | 0.990623i | \(0.456375\pi\) | |||||||
\(110\) | −2.18928 | −0.208739 | ||||||||
\(111\) | 14.2107 | 1.34882 | ||||||||
\(112\) | 1.77068 | 0.167313 | ||||||||
\(113\) | −18.2867 | −1.72027 | −0.860135 | − | 0.510066i | \(-0.829621\pi\) | ||||
−0.860135 | + | 0.510066i | \(0.829621\pi\) | |||||||
\(114\) | 2.47489 | 0.231794 | ||||||||
\(115\) | −9.55522 | −0.891029 | ||||||||
\(116\) | 3.54830 | 0.329452 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.76584 | −0.530789 | ||||||||
\(119\) | 0.828999 | 0.0759943 | ||||||||
\(120\) | 7.08716 | 0.646966 | ||||||||
\(121\) | −10.4155 | −0.946866 | ||||||||
\(122\) | 2.36516 | 0.214132 | ||||||||
\(123\) | 23.4233 | 2.11201 | ||||||||
\(124\) | −2.73715 | −0.245803 | ||||||||
\(125\) | −5.15345 | −0.460938 | ||||||||
\(126\) | −5.53348 | −0.492961 | ||||||||
\(127\) | −14.0132 | −1.24347 | −0.621734 | − | 0.783228i | \(-0.713572\pi\) | ||||
−0.621734 | + | 0.783228i | \(0.713572\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −16.7821 | −1.47758 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9283 | 1.30429 | 0.652146 | − | 0.758094i | \(-0.273869\pi\) | ||||
0.652146 | + | 0.758094i | \(0.273869\pi\) | |||||||
\(132\) | −1.89208 | −0.164684 | ||||||||
\(133\) | 1.77068 | 0.153537 | ||||||||
\(134\) | 1.49066 | 0.128773 | ||||||||
\(135\) | −0.886336 | −0.0762836 | ||||||||
\(136\) | −0.468182 | −0.0401463 | ||||||||
\(137\) | 9.46492 | 0.808643 | 0.404321 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404321 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(138\) | −8.25808 | −0.702974 | ||||||||
\(139\) | −21.9657 | −1.86311 | −0.931554 | − | 0.363604i | \(-0.881546\pi\) | ||||
−0.931554 | + | 0.363604i | \(0.881546\pi\) | |||||||
\(140\) | 5.07057 | 0.428541 | ||||||||
\(141\) | 3.40132 | 0.286443 | ||||||||
\(142\) | 2.41091 | 0.202319 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.12506 | 0.260422 | ||||||||
\(145\) | 10.1610 | 0.843828 | ||||||||
\(146\) | 12.1769 | 1.00777 | ||||||||
\(147\) | 9.56469 | 0.788882 | ||||||||
\(148\) | −5.74198 | −0.471988 | ||||||||
\(149\) | −5.84283 | −0.478663 | −0.239332 | − | 0.970938i | \(-0.576928\pi\) | ||||
−0.239332 | + | 0.970938i | \(0.576928\pi\) | |||||||
\(150\) | 7.92058 | 0.646712 | ||||||||
\(151\) | 5.37075 | 0.437065 | 0.218533 | − | 0.975830i | \(-0.429873\pi\) | ||||
0.218533 | + | 0.975830i | \(0.429873\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 1.46310 | 0.118284 | ||||||||
\(154\) | −1.35370 | −0.109084 | ||||||||
\(155\) | −7.83819 | −0.629578 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3174 | 0.983039 | 0.491519 | − | 0.870867i | \(-0.336442\pi\) | ||||
0.491519 | + | 0.870867i | \(0.336442\pi\) | |||||||
\(158\) | 9.31247 | 0.740860 | ||||||||
\(159\) | 23.6410 | 1.87486 | ||||||||
\(160\) | −2.86363 | −0.226390 | ||||||||
\(161\) | −5.90831 | −0.465640 | ||||||||
\(162\) | 8.60917 | 0.676401 | ||||||||
\(163\) | 3.62592 | 0.284004 | 0.142002 | − | 0.989866i | \(-0.454646\pi\) | ||||
0.142002 | + | 0.989866i | \(0.454646\pi\) | |||||||
\(164\) | −9.46441 | −0.739046 | ||||||||
\(165\) | −5.41821 | −0.421807 | ||||||||
\(166\) | 3.26881 | 0.253709 | ||||||||
\(167\) | 0.0446192 | 0.00345274 | 0.00172637 | − | 0.999999i | \(-0.499450\pi\) | ||||
0.00172637 | + | 0.999999i | \(0.499450\pi\) | |||||||
\(168\) | 4.38223 | 0.338096 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.34070 | −0.102827 | ||||||||
\(171\) | 3.12506 | 0.238979 | ||||||||
\(172\) | 6.78094 | 0.517042 | ||||||||
\(173\) | −14.5771 | −1.10827 | −0.554137 | − | 0.832425i | \(-0.686952\pi\) | ||||
−0.554137 | + | 0.832425i | \(0.686952\pi\) | |||||||
\(174\) | 8.78165 | 0.665735 | ||||||||
\(175\) | 5.66684 | 0.428373 | ||||||||
\(176\) | 0.764511 | 0.0576271 | ||||||||
\(177\) | −14.2698 | −1.07258 | ||||||||
\(178\) | 14.5129 | 1.08779 | ||||||||
\(179\) | −11.7631 | −0.879214 | −0.439607 | − | 0.898190i | \(-0.644882\pi\) | ||||
−0.439607 | + | 0.898190i | \(0.644882\pi\) | |||||||
\(180\) | 8.94902 | 0.667021 | ||||||||
\(181\) | 16.7531 | 1.24525 | 0.622625 | − | 0.782520i | \(-0.286066\pi\) | ||||
0.622625 | + | 0.782520i | \(0.286066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.85350 | 0.432703 | ||||||||
\(184\) | 3.33675 | 0.245988 | ||||||||
\(185\) | −16.4429 | −1.20891 | ||||||||
\(186\) | −6.77413 | −0.496704 | ||||||||
\(187\) | 0.357930 | 0.0261744 | ||||||||
\(188\) | −1.37434 | −0.100234 | ||||||||
\(189\) | −0.548051 | −0.0398648 | ||||||||
\(190\) | −2.86363 | −0.207750 | ||||||||
\(191\) | 23.9089 | 1.72999 | 0.864995 | − | 0.501780i | \(-0.167321\pi\) | ||||
0.864995 | + | 0.501780i | \(0.167321\pi\) | |||||||
\(192\) | −2.47489 | −0.178610 | ||||||||
\(193\) | 21.8221 | 1.57079 | 0.785393 | − | 0.618997i | \(-0.212461\pi\) | ||||
0.785393 | + | 0.618997i | \(0.212461\pi\) | |||||||
\(194\) | 2.74409 | 0.197014 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.86470 | −0.276050 | ||||||||
\(197\) | −3.14538 | −0.224099 | −0.112049 | − | 0.993703i | \(-0.535742\pi\) | ||||
−0.112049 | + | 0.993703i | \(0.535742\pi\) | |||||||
\(198\) | −2.38914 | −0.169789 | ||||||||
\(199\) | 6.98844 | 0.495397 | 0.247699 | − | 0.968837i | \(-0.420326\pi\) | ||||
0.247699 | + | 0.968837i | \(0.420326\pi\) | |||||||
\(200\) | −3.20038 | −0.226301 | ||||||||
\(201\) | 3.68920 | 0.260216 | ||||||||
\(202\) | −13.3665 | −0.940465 | ||||||||
\(203\) | 6.28290 | 0.440973 | ||||||||
\(204\) | −1.15870 | −0.0811250 | ||||||||
\(205\) | −27.1026 | −1.89293 | ||||||||
\(206\) | 7.96934 | 0.555250 | ||||||||
\(207\) | −10.4276 | −0.724765 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.764511 | 0.0528823 | ||||||||
\(210\) | 12.5491 | 0.865969 | ||||||||
\(211\) | 18.2813 | 1.25854 | 0.629268 | − | 0.777188i | \(-0.283355\pi\) | ||||
0.629268 | + | 0.777188i | \(0.283355\pi\) | |||||||
\(212\) | −9.55237 | −0.656060 | ||||||||
\(213\) | 5.96673 | 0.408833 | ||||||||
\(214\) | −5.93502 | −0.405710 | ||||||||
\(215\) | 19.4181 | 1.32430 | ||||||||
\(216\) | 0.309515 | 0.0210598 | ||||||||
\(217\) | −4.84661 | −0.329009 | ||||||||
\(218\) | −2.85280 | −0.193216 | ||||||||
\(219\) | 30.1364 | 2.03643 | ||||||||
\(220\) | 2.18928 | 0.147601 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.2107 | −0.953763 | ||||||||
\(223\) | −12.1425 | −0.813119 | −0.406560 | − | 0.913624i | \(-0.633272\pi\) | ||||
−0.406560 | + | 0.913624i | \(0.633272\pi\) | |||||||
\(224\) | −1.77068 | −0.118308 | ||||||||
\(225\) | 10.0014 | 0.666759 | ||||||||
\(226\) | 18.2867 | 1.21642 | ||||||||
\(227\) | 22.4289 | 1.48866 | 0.744328 | − | 0.667814i | \(-0.232770\pi\) | ||||
0.744328 | + | 0.667814i | \(0.232770\pi\) | |||||||
\(228\) | −2.47489 | −0.163903 | ||||||||
\(229\) | −9.13113 | −0.603402 | −0.301701 | − | 0.953403i | \(-0.597554\pi\) | ||||
−0.301701 | + | 0.953403i | \(0.597554\pi\) | |||||||
\(230\) | 9.55522 | 0.630052 | ||||||||
\(231\) | −3.35026 | −0.220431 | ||||||||
\(232\) | −3.54830 | −0.232958 | ||||||||
\(233\) | 14.0387 | 0.919708 | 0.459854 | − | 0.887994i | \(-0.347902\pi\) | ||||
0.459854 | + | 0.887994i | \(0.347902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.93559 | −0.256729 | ||||||||
\(236\) | 5.76584 | 0.375324 | ||||||||
\(237\) | 23.0473 | 1.49708 | ||||||||
\(238\) | −0.828999 | −0.0537361 | ||||||||
\(239\) | 14.0823 | 0.910907 | 0.455453 | − | 0.890260i | \(-0.349477\pi\) | ||||
0.455453 | + | 0.890260i | \(0.349477\pi\) | |||||||
\(240\) | −7.08716 | −0.457474 | ||||||||
\(241\) | 30.4199 | 1.95951 | 0.979757 | − | 0.200188i | \(-0.0641554\pi\) | ||||
0.979757 | + | 0.200188i | \(0.0641554\pi\) | |||||||
\(242\) | 10.4155 | 0.669535 | ||||||||
\(243\) | 22.2353 | 1.42639 | ||||||||
\(244\) | −2.36516 | −0.151414 | ||||||||
\(245\) | −11.0671 | −0.707049 | ||||||||
\(246\) | −23.4233 | −1.49342 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.73715 | 0.173809 | ||||||||
\(249\) | 8.08992 | 0.512678 | ||||||||
\(250\) | 5.15345 | 0.325933 | ||||||||
\(251\) | −4.08765 | −0.258010 | −0.129005 | − | 0.991644i | \(-0.541178\pi\) | ||||
−0.129005 | + | 0.991644i | \(0.541178\pi\) | |||||||
\(252\) | 5.53348 | 0.348576 | ||||||||
\(253\) | −2.55098 | −0.160379 | ||||||||
\(254\) | 14.0132 | 0.879265 | ||||||||
\(255\) | −3.31808 | −0.207786 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.37406 | −0.272846 | −0.136423 | − | 0.990651i | \(-0.543561\pi\) | ||||
−0.136423 | + | 0.990651i | \(0.543561\pi\) | |||||||
\(258\) | 16.7821 | 1.04481 | ||||||||
\(259\) | −10.1672 | −0.631759 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0887 | 0.686372 | ||||||||
\(262\) | −14.9283 | −0.922273 | ||||||||
\(263\) | −17.3927 | −1.07248 | −0.536241 | − | 0.844065i | \(-0.680156\pi\) | ||||
−0.536241 | + | 0.844065i | \(0.680156\pi\) | |||||||
\(264\) | 1.89208 | 0.116449 | ||||||||
\(265\) | −27.3545 | −1.68037 | ||||||||
\(266\) | −1.77068 | −0.108567 | ||||||||
\(267\) | 35.9179 | 2.19814 | ||||||||
\(268\) | −1.49066 | −0.0910562 | ||||||||
\(269\) | −16.5567 | −1.00948 | −0.504739 | − | 0.863272i | \(-0.668411\pi\) | ||||
−0.504739 | + | 0.863272i | \(0.668411\pi\) | |||||||
\(270\) | 0.886336 | 0.0539407 | ||||||||
\(271\) | 25.6049 | 1.55539 | 0.777694 | − | 0.628643i | \(-0.216389\pi\) | ||||
0.777694 | + | 0.628643i | \(0.216389\pi\) | |||||||
\(272\) | 0.468182 | 0.0283877 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.46492 | −0.571797 | ||||||||
\(275\) | 2.44672 | 0.147543 | ||||||||
\(276\) | 8.25808 | 0.497078 | ||||||||
\(277\) | −32.6858 | −1.96390 | −0.981951 | − | 0.189136i | \(-0.939431\pi\) | ||||
−0.981951 | + | 0.189136i | \(0.939431\pi\) | |||||||
\(278\) | 21.9657 | 1.31742 | ||||||||
\(279\) | −8.55376 | −0.512100 | ||||||||
\(280\) | −5.07057 | −0.303024 | ||||||||
\(281\) | 16.1688 | 0.964551 | 0.482275 | − | 0.876020i | \(-0.339810\pi\) | ||||
0.482275 | + | 0.876020i | \(0.339810\pi\) | |||||||
\(282\) | −3.40132 | −0.202546 | ||||||||
\(283\) | −25.2008 | −1.49803 | −0.749017 | − | 0.662551i | \(-0.769474\pi\) | ||||
−0.749017 | + | 0.662551i | \(0.769474\pi\) | |||||||
\(284\) | −2.41091 | −0.143061 | ||||||||
\(285\) | −7.08716 | −0.419807 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.7584 | −0.989218 | ||||||||
\(288\) | −3.12506 | −0.184146 | ||||||||
\(289\) | −16.7808 | −0.987106 | ||||||||
\(290\) | −10.1610 | −0.596676 | ||||||||
\(291\) | 6.79131 | 0.398114 | ||||||||
\(292\) | −12.1769 | −0.712598 | ||||||||
\(293\) | −31.1586 | −1.82030 | −0.910151 | − | 0.414276i | \(-0.864035\pi\) | ||||
−0.910151 | + | 0.414276i | \(0.864035\pi\) | |||||||
\(294\) | −9.56469 | −0.557824 | ||||||||
\(295\) | 16.5112 | 0.961322 | ||||||||
\(296\) | 5.74198 | 0.333746 | ||||||||
\(297\) | −0.236627 | −0.0137305 | ||||||||
\(298\) | 5.84283 | 0.338466 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.92058 | −0.457295 | ||||||||
\(301\) | 12.0069 | 0.692064 | ||||||||
\(302\) | −5.37075 | −0.309052 | ||||||||
\(303\) | −33.0806 | −1.90043 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −6.77295 | −0.387818 | ||||||||
\(306\) | −1.46310 | −0.0836397 | ||||||||
\(307\) | 33.0592 | 1.88679 | 0.943395 | − | 0.331671i | \(-0.107612\pi\) | ||||
0.943395 | + | 0.331671i | \(0.107612\pi\) | |||||||
\(308\) | 1.35370 | 0.0771343 | ||||||||
\(309\) | 19.7232 | 1.12201 | ||||||||
\(310\) | 7.83819 | 0.445179 | ||||||||
\(311\) | −7.30371 | −0.414155 | −0.207078 | − | 0.978324i | \(-0.566395\pi\) | ||||
−0.207078 | + | 0.978324i | \(0.566395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6996 | 0.774347 | 0.387173 | − | 0.922007i | \(-0.373451\pi\) | ||||
0.387173 | + | 0.922007i | \(0.373451\pi\) | |||||||
\(314\) | −12.3174 | −0.695113 | ||||||||
\(315\) | 15.8458 | 0.892812 | ||||||||
\(316\) | −9.31247 | −0.523867 | ||||||||
\(317\) | −9.54433 | −0.536063 | −0.268031 | − | 0.963410i | \(-0.586373\pi\) | ||||
−0.268031 | + | 0.963410i | \(0.586373\pi\) | |||||||
\(318\) | −23.6410 | −1.32572 | ||||||||
\(319\) | 2.71272 | 0.151883 | ||||||||
\(320\) | 2.86363 | 0.160082 | ||||||||
\(321\) | −14.6885 | −0.819833 | ||||||||
\(322\) | 5.90831 | 0.329257 | ||||||||
\(323\) | 0.468182 | 0.0260503 | ||||||||
\(324\) | −8.60917 | −0.478287 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.62592 | −0.200821 | ||||||||
\(327\) | −7.06035 | −0.390438 | ||||||||
\(328\) | 9.46441 | 0.522584 | ||||||||
\(329\) | −2.43350 | −0.134163 | ||||||||
\(330\) | 5.41821 | 0.298263 | ||||||||
\(331\) | 7.65204 | 0.420594 | 0.210297 | − | 0.977638i | \(-0.432557\pi\) | ||||
0.210297 | + | 0.977638i | \(0.432557\pi\) | |||||||
\(332\) | −3.26881 | −0.179399 | ||||||||
\(333\) | −17.9440 | −0.983328 | ||||||||
\(334\) | −0.0446192 | −0.00244146 | ||||||||
\(335\) | −4.26869 | −0.233223 | ||||||||
\(336\) | −4.38223 | −0.239070 | ||||||||
\(337\) | −20.7810 | −1.13201 | −0.566007 | − | 0.824400i | \(-0.691513\pi\) | ||||
−0.566007 | + | 0.824400i | \(0.691513\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 45.2576 | 2.45805 | ||||||||
\(340\) | 1.34070 | 0.0727097 | ||||||||
\(341\) | −2.09258 | −0.113320 | ||||||||
\(342\) | −3.12506 | −0.168984 | ||||||||
\(343\) | −19.2379 | −1.03875 | ||||||||
\(344\) | −6.78094 | −0.365604 | ||||||||
\(345\) | 23.6481 | 1.27317 | ||||||||
\(346\) | 14.5771 | 0.783668 | ||||||||
\(347\) | −29.8422 | −1.60202 | −0.801008 | − | 0.598654i | \(-0.795702\pi\) | ||||
−0.801008 | + | 0.598654i | \(0.795702\pi\) | |||||||
\(348\) | −8.78165 | −0.470746 | ||||||||
\(349\) | −8.47281 | −0.453539 | −0.226770 | − | 0.973948i | \(-0.572816\pi\) | ||||
−0.226770 | + | 0.973948i | \(0.572816\pi\) | |||||||
\(350\) | −5.66684 | −0.302906 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.764511 | −0.0407485 | ||||||||
\(353\) | −10.1193 | −0.538595 | −0.269298 | − | 0.963057i | \(-0.586792\pi\) | ||||
−0.269298 | + | 0.963057i | \(0.586792\pi\) | |||||||
\(354\) | 14.2698 | 0.758432 | ||||||||
\(355\) | −6.90395 | −0.366424 | ||||||||
\(356\) | −14.5129 | −0.769184 | ||||||||
\(357\) | −2.05168 | −0.108586 | ||||||||
\(358\) | 11.7631 | 0.621698 | ||||||||
\(359\) | 35.0123 | 1.84788 | 0.923939 | − | 0.382539i | \(-0.124950\pi\) | ||||
0.923939 | + | 0.382539i | \(0.124950\pi\) | |||||||
\(360\) | −8.94902 | −0.471655 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.7531 | −0.880525 | ||||||||
\(363\) | 25.7772 | 1.35295 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.8701 | −1.82518 | ||||||||
\(366\) | −5.85350 | −0.305968 | ||||||||
\(367\) | 6.95348 | 0.362969 | 0.181484 | − | 0.983394i | \(-0.441910\pi\) | ||||
0.181484 | + | 0.983394i | \(0.441910\pi\) | |||||||
\(368\) | −3.33675 | −0.173940 | ||||||||
\(369\) | −29.5769 | −1.53971 | ||||||||
\(370\) | 16.4429 | 0.854826 | ||||||||
\(371\) | −16.9142 | −0.878140 | ||||||||
\(372\) | 6.77413 | 0.351222 | ||||||||
\(373\) | 1.25498 | 0.0649805 | 0.0324903 | − | 0.999472i | \(-0.489656\pi\) | ||||
0.0324903 | + | 0.999472i | \(0.489656\pi\) | |||||||
\(374\) | −0.357930 | −0.0185081 | ||||||||
\(375\) | 12.7542 | 0.658624 | ||||||||
\(376\) | 1.37434 | 0.0708759 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.548051 | 0.0281887 | ||||||||
\(379\) | −12.7877 | −0.656862 | −0.328431 | − | 0.944528i | \(-0.606520\pi\) | ||||
−0.328431 | + | 0.944528i | \(0.606520\pi\) | |||||||
\(380\) | 2.86363 | 0.146901 | ||||||||
\(381\) | 34.6810 | 1.77676 | ||||||||
\(382\) | −23.9089 | −1.22329 | ||||||||
\(383\) | 3.94739 | 0.201702 | 0.100851 | − | 0.994902i | \(-0.467843\pi\) | ||||
0.100851 | + | 0.994902i | \(0.467843\pi\) | |||||||
\(384\) | 2.47489 | 0.126296 | ||||||||
\(385\) | 3.87650 | 0.197565 | ||||||||
\(386\) | −21.8221 | −1.11071 | ||||||||
\(387\) | 21.1909 | 1.07719 | ||||||||
\(388\) | −2.74409 | −0.139310 | ||||||||
\(389\) | 14.1388 | 0.716864 | 0.358432 | − | 0.933556i | \(-0.383311\pi\) | ||||
0.358432 | + | 0.933556i | \(0.383311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.56221 | −0.0790042 | ||||||||
\(392\) | 3.86470 | 0.195197 | ||||||||
\(393\) | −36.9458 | −1.86367 | ||||||||
\(394\) | 3.14538 | 0.158462 | ||||||||
\(395\) | −26.6675 | −1.34179 | ||||||||
\(396\) | 2.38914 | 0.120059 | ||||||||
\(397\) | −12.9324 | −0.649061 | −0.324530 | − | 0.945875i | \(-0.605206\pi\) | ||||
−0.324530 | + | 0.945875i | \(0.605206\pi\) | |||||||
\(398\) | −6.98844 | −0.350299 | ||||||||
\(399\) | −4.38223 | −0.219386 | ||||||||
\(400\) | 3.20038 | 0.160019 | ||||||||
\(401\) | 1.92157 | 0.0959584 | 0.0479792 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479792 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(402\) | −3.68920 | −0.184001 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 13.3665 | 0.665009 | ||||||||
\(405\) | −24.6535 | −1.22504 | ||||||||
\(406\) | −6.28290 | −0.311815 | ||||||||
\(407\) | −4.38980 | −0.217595 | ||||||||
\(408\) | 1.15870 | 0.0573641 | ||||||||
\(409\) | 6.18073 | 0.305617 | 0.152809 | − | 0.988256i | \(-0.451168\pi\) | ||||
0.152809 | + | 0.988256i | \(0.451168\pi\) | |||||||
\(410\) | 27.1026 | 1.33850 | ||||||||
\(411\) | −23.4246 | −1.15545 | ||||||||
\(412\) | −7.96934 | −0.392621 | ||||||||
\(413\) | 10.2095 | 0.502374 | ||||||||
\(414\) | 10.4276 | 0.512486 | ||||||||
\(415\) | −9.36065 | −0.459496 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 54.3626 | 2.66215 | ||||||||
\(418\) | −0.764511 | −0.0373934 | ||||||||
\(419\) | 8.84081 | 0.431902 | 0.215951 | − | 0.976404i | \(-0.430715\pi\) | ||||
0.215951 | + | 0.976404i | \(0.430715\pi\) | |||||||
\(420\) | −12.5491 | −0.612332 | ||||||||
\(421\) | −27.8790 | −1.35874 | −0.679369 | − | 0.733797i | \(-0.737746\pi\) | ||||
−0.679369 | + | 0.733797i | \(0.737746\pi\) | |||||||
\(422\) | −18.2813 | −0.889919 | ||||||||
\(423\) | −4.29488 | −0.208824 | ||||||||
\(424\) | 9.55237 | 0.463904 | ||||||||
\(425\) | 1.49836 | 0.0726812 | ||||||||
\(426\) | −5.96673 | −0.289089 | ||||||||
\(427\) | −4.18794 | −0.202669 | ||||||||
\(428\) | 5.93502 | 0.286880 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.4181 | −0.936425 | ||||||||
\(431\) | −22.1378 | −1.06634 | −0.533169 | − | 0.846009i | \(-0.678999\pi\) | ||||
−0.533169 | + | 0.846009i | \(0.678999\pi\) | |||||||
\(432\) | −0.309515 | −0.0148915 | ||||||||
\(433\) | −34.0289 | −1.63532 | −0.817662 | − | 0.575699i | \(-0.804730\pi\) | ||||
−0.817662 | + | 0.575699i | \(0.804730\pi\) | |||||||
\(434\) | 4.84661 | 0.232645 | ||||||||
\(435\) | −25.1474 | −1.20573 | ||||||||
\(436\) | 2.85280 | 0.136624 | ||||||||
\(437\) | −3.33675 | −0.159618 | ||||||||
\(438\) | −30.1364 | −1.43997 | ||||||||
\(439\) | −16.2942 | −0.777680 | −0.388840 | − | 0.921305i | \(-0.627124\pi\) | ||||
−0.388840 | + | 0.921305i | \(0.627124\pi\) | |||||||
\(440\) | −2.18928 | −0.104370 | ||||||||
\(441\) | −12.0774 | −0.575116 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.2769 | 0.915873 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(444\) | 14.2107 | 0.674412 | ||||||||
\(445\) | −41.5597 | −1.97012 | ||||||||
\(446\) | 12.1425 | 0.574962 | ||||||||
\(447\) | 14.4603 | 0.683950 | ||||||||
\(448\) | 1.77068 | 0.0836567 | ||||||||
\(449\) | 7.67409 | 0.362163 | 0.181081 | − | 0.983468i | \(-0.442040\pi\) | ||||
0.181081 | + | 0.983468i | \(0.442040\pi\) | |||||||
\(450\) | −10.0014 | −0.471470 | ||||||||
\(451\) | −7.23564 | −0.340713 | ||||||||
\(452\) | −18.2867 | −0.860135 | ||||||||
\(453\) | −13.2920 | −0.624512 | ||||||||
\(454\) | −22.4289 | −1.05264 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.47489 | 0.115897 | ||||||||
\(457\) | −6.41003 | −0.299848 | −0.149924 | − | 0.988697i | \(-0.547903\pi\) | ||||
−0.149924 | + | 0.988697i | \(0.547903\pi\) | |||||||
\(458\) | 9.13113 | 0.426670 | ||||||||
\(459\) | −0.144909 | −0.00676378 | ||||||||
\(460\) | −9.55522 | −0.445514 | ||||||||
\(461\) | 12.3507 | 0.575227 | 0.287614 | − | 0.957747i | \(-0.407138\pi\) | ||||
0.287614 | + | 0.957747i | \(0.407138\pi\) | |||||||
\(462\) | 3.35026 | 0.155868 | ||||||||
\(463\) | 3.56113 | 0.165500 | 0.0827498 | − | 0.996570i | \(-0.473630\pi\) | ||||
0.0827498 | + | 0.996570i | \(0.473630\pi\) | |||||||
\(464\) | 3.54830 | 0.164726 | ||||||||
\(465\) | 19.3986 | 0.899589 | ||||||||
\(466\) | −14.0387 | −0.650332 | ||||||||
\(467\) | −14.1047 | −0.652689 | −0.326345 | − | 0.945251i | \(-0.605817\pi\) | ||||
−0.326345 | + | 0.945251i | \(0.605817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.63947 | −0.121879 | ||||||||
\(470\) | 3.93559 | 0.181535 | ||||||||
\(471\) | −30.4843 | −1.40464 | ||||||||
\(472\) | −5.76584 | −0.265394 | ||||||||
\(473\) | 5.18410 | 0.238365 | ||||||||
\(474\) | −23.0473 | −1.05860 | ||||||||
\(475\) | 3.20038 | 0.146844 | ||||||||
\(476\) | 0.828999 | 0.0379971 | ||||||||
\(477\) | −29.8518 | −1.36682 | ||||||||
\(478\) | −14.0823 | −0.644108 | ||||||||
\(479\) | −8.23436 | −0.376238 | −0.188119 | − | 0.982146i | \(-0.560239\pi\) | ||||
−0.188119 | + | 0.982146i | \(0.560239\pi\) | |||||||
\(480\) | 7.08716 | 0.323483 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −30.4199 | −1.38559 | ||||||||
\(483\) | 14.6224 | 0.665342 | ||||||||
\(484\) | −10.4155 | −0.473433 | ||||||||
\(485\) | −7.85806 | −0.356816 | ||||||||
\(486\) | −22.2353 | −1.00861 | ||||||||
\(487\) | −17.2786 | −0.782970 | −0.391485 | − | 0.920184i | \(-0.628039\pi\) | ||||
−0.391485 | + | 0.920184i | \(0.628039\pi\) | |||||||
\(488\) | 2.36516 | 0.107066 | ||||||||
\(489\) | −8.97374 | −0.405806 | ||||||||
\(490\) | 11.0671 | 0.499959 | ||||||||
\(491\) | −7.80350 | −0.352167 | −0.176083 | − | 0.984375i | \(-0.556343\pi\) | ||||
−0.176083 | + | 0.984375i | \(0.556343\pi\) | |||||||
\(492\) | 23.4233 | 1.05601 | ||||||||
\(493\) | 1.66125 | 0.0748190 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.84162 | 0.307508 | ||||||||
\(496\) | −2.73715 | −0.122902 | ||||||||
\(497\) | −4.26894 | −0.191488 | ||||||||
\(498\) | −8.08992 | −0.362518 | ||||||||
\(499\) | −7.14315 | −0.319771 | −0.159886 | − | 0.987136i | \(-0.551113\pi\) | ||||
−0.159886 | + | 0.987136i | \(0.551113\pi\) | |||||||
\(500\) | −5.15345 | −0.230469 | ||||||||
\(501\) | −0.110428 | −0.00493354 | ||||||||
\(502\) | 4.08765 | 0.182441 | ||||||||
\(503\) | 19.4259 | 0.866158 | 0.433079 | − | 0.901356i | \(-0.357427\pi\) | ||||
0.433079 | + | 0.901356i | \(0.357427\pi\) | |||||||
\(504\) | −5.53348 | −0.246481 | ||||||||
\(505\) | 38.2768 | 1.70329 | ||||||||
\(506\) | 2.55098 | 0.113405 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.0132 | −0.621734 | ||||||||
\(509\) | −21.1831 | −0.938923 | −0.469462 | − | 0.882953i | \(-0.655552\pi\) | ||||
−0.469462 | + | 0.882953i | \(0.655552\pi\) | |||||||
\(510\) | 3.31808 | 0.146927 | ||||||||
\(511\) | −21.5613 | −0.953817 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.309515 | −0.0136654 | ||||||||
\(514\) | 4.37406 | 0.192931 | ||||||||
\(515\) | −22.8212 | −1.00562 | ||||||||
\(516\) | −16.7821 | −0.738789 | ||||||||
\(517\) | −1.05069 | −0.0462095 | ||||||||
\(518\) | 10.1672 | 0.446721 | ||||||||
\(519\) | 36.0766 | 1.58359 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.4233 | 1.72716 | 0.863582 | − | 0.504208i | \(-0.168215\pi\) | ||||
0.863582 | + | 0.504208i | \(0.168215\pi\) | |||||||
\(522\) | −11.0887 | −0.485338 | ||||||||
\(523\) | −24.0725 | −1.05261 | −0.526307 | − | 0.850294i | \(-0.676424\pi\) | ||||
−0.526307 | + | 0.850294i | \(0.676424\pi\) | |||||||
\(524\) | 14.9283 | 0.652146 | ||||||||
\(525\) | −14.0248 | −0.612092 | ||||||||
\(526\) | 17.3927 | 0.758359 | ||||||||
\(527\) | −1.28148 | −0.0558223 | ||||||||
\(528\) | −1.89208 | −0.0823421 | ||||||||
\(529\) | −11.8661 | −0.515917 | ||||||||
\(530\) | 27.3545 | 1.18820 | ||||||||
\(531\) | 18.0186 | 0.781941 | ||||||||
\(532\) | 1.77068 | 0.0767686 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −35.9179 | −1.55432 | ||||||||
\(535\) | 16.9957 | 0.734789 | ||||||||
\(536\) | 1.49066 | 0.0643865 | ||||||||
\(537\) | 29.1123 | 1.25629 | ||||||||
\(538\) | 16.5567 | 0.713809 | ||||||||
\(539\) | −2.95460 | −0.127264 | ||||||||
\(540\) | −0.886336 | −0.0381418 | ||||||||
\(541\) | −31.8834 | −1.37078 | −0.685388 | − | 0.728178i | \(-0.740368\pi\) | ||||
−0.685388 | + | 0.728178i | \(0.740368\pi\) | |||||||
\(542\) | −25.6049 | −1.09983 | ||||||||
\(543\) | −41.4621 | −1.77931 | ||||||||
\(544\) | −0.468182 | −0.0200731 | ||||||||
\(545\) | 8.16936 | 0.349937 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.6236 | 1.82245 | 0.911227 | − | 0.411904i | \(-0.135136\pi\) | ||||
0.911227 | + | 0.411904i | \(0.135136\pi\) | |||||||
\(548\) | 9.46492 | 0.404321 | ||||||||
\(549\) | −7.39127 | −0.315452 | ||||||||
\(550\) | −2.44672 | −0.104329 | ||||||||
\(551\) | 3.54830 | 0.151163 | ||||||||
\(552\) | −8.25808 | −0.351487 | ||||||||
\(553\) | −16.4894 | −0.701200 | ||||||||
\(554\) | 32.6858 | 1.38869 | ||||||||
\(555\) | 40.6943 | 1.72738 | ||||||||
\(556\) | −21.9657 | −0.931554 | ||||||||
\(557\) | −7.79893 | −0.330451 | −0.165226 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165226 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(558\) | 8.55376 | 0.362110 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5.07057 | 0.214271 | ||||||||
\(561\) | −0.885836 | −0.0374000 | ||||||||
\(562\) | −16.1688 | −0.682040 | ||||||||
\(563\) | −22.6549 | −0.954788 | −0.477394 | − | 0.878689i | \(-0.658419\pi\) | ||||
−0.477394 | + | 0.878689i | \(0.658419\pi\) | |||||||
\(564\) | 3.40132 | 0.143222 | ||||||||
\(565\) | −52.3664 | −2.20307 | ||||||||
\(566\) | 25.2008 | 1.05927 | ||||||||
\(567\) | −15.2441 | −0.640191 | ||||||||
\(568\) | 2.41091 | 0.101159 | ||||||||
\(569\) | 29.6724 | 1.24393 | 0.621965 | − | 0.783045i | \(-0.286335\pi\) | ||||
0.621965 | + | 0.783045i | \(0.286335\pi\) | |||||||
\(570\) | 7.08716 | 0.296848 | ||||||||
\(571\) | −13.9581 | −0.584128 | −0.292064 | − | 0.956399i | \(-0.594342\pi\) | ||||
−0.292064 | + | 0.956399i | \(0.594342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −59.1719 | −2.47194 | ||||||||
\(574\) | 16.7584 | 0.699483 | ||||||||
\(575\) | −10.6789 | −0.445340 | ||||||||
\(576\) | 3.12506 | 0.130211 | ||||||||
\(577\) | −15.4839 | −0.644603 | −0.322301 | − | 0.946637i | \(-0.604456\pi\) | ||||
−0.322301 | + | 0.946637i | \(0.604456\pi\) | |||||||
\(578\) | 16.7808 | 0.697989 | ||||||||
\(579\) | −54.0071 | −2.24446 | ||||||||
\(580\) | 10.1610 | 0.421914 | ||||||||
\(581\) | −5.78800 | −0.240127 | ||||||||
\(582\) | −6.79131 | −0.281509 | ||||||||
\(583\) | −7.30289 | −0.302455 | ||||||||
\(584\) | 12.1769 | 0.503883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.1586 | 1.28715 | ||||||||
\(587\) | 29.6279 | 1.22288 | 0.611438 | − | 0.791293i | \(-0.290592\pi\) | ||||
0.611438 | + | 0.791293i | \(0.290592\pi\) | |||||||
\(588\) | 9.56469 | 0.394441 | ||||||||
\(589\) | −2.73715 | −0.112782 | ||||||||
\(590\) | −16.5112 | −0.679757 | ||||||||
\(591\) | 7.78445 | 0.320210 | ||||||||
\(592\) | −5.74198 | −0.235994 | ||||||||
\(593\) | 42.1120 | 1.72933 | 0.864666 | − | 0.502348i | \(-0.167530\pi\) | ||||
0.864666 | + | 0.502348i | \(0.167530\pi\) | |||||||
\(594\) | 0.236627 | 0.00970893 | ||||||||
\(595\) | 2.37395 | 0.0973224 | ||||||||
\(596\) | −5.84283 | −0.239332 | ||||||||
\(597\) | −17.2956 | −0.707862 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.9276 | −0.855077 | −0.427538 | − | 0.903997i | \(-0.640619\pi\) | ||||
−0.427538 | + | 0.903997i | \(0.640619\pi\) | |||||||
\(600\) | 7.92058 | 0.323356 | ||||||||
\(601\) | 25.8107 | 1.05284 | 0.526420 | − | 0.850224i | \(-0.323534\pi\) | ||||
0.526420 | + | 0.850224i | \(0.323534\pi\) | |||||||
\(602\) | −12.0069 | −0.489363 | ||||||||
\(603\) | −4.65839 | −0.189704 | ||||||||
\(604\) | 5.37075 | 0.218533 | ||||||||
\(605\) | −29.8262 | −1.21261 | ||||||||
\(606\) | 33.0806 | 1.34381 | ||||||||
\(607\) | 4.65459 | 0.188924 | 0.0944620 | − | 0.995528i | \(-0.469887\pi\) | ||||
0.0944620 | + | 0.995528i | \(0.469887\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −15.5495 | −0.630096 | ||||||||
\(610\) | 6.77295 | 0.274229 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.46310 | 0.0591422 | ||||||||
\(613\) | −10.0995 | −0.407916 | −0.203958 | − | 0.978980i | \(-0.565381\pi\) | ||||
−0.203958 | + | 0.978980i | \(0.565381\pi\) | |||||||
\(614\) | −33.0592 | −1.33416 | ||||||||
\(615\) | 67.0758 | 2.70476 | ||||||||
\(616\) | −1.35370 | −0.0545422 | ||||||||
\(617\) | 43.7568 | 1.76158 | 0.880791 | − | 0.473504i | \(-0.157011\pi\) | ||||
0.880791 | + | 0.473504i | \(0.157011\pi\) | |||||||
\(618\) | −19.7232 | −0.793384 | ||||||||
\(619\) | −44.1459 | −1.77437 | −0.887186 | − | 0.461412i | \(-0.847343\pi\) | ||||
−0.887186 | + | 0.461412i | \(0.847343\pi\) | |||||||
\(620\) | −7.83819 | −0.314789 | ||||||||
\(621\) | 1.03277 | 0.0414437 | ||||||||
\(622\) | 7.30371 | 0.292852 | ||||||||
\(623\) | −25.6978 | −1.02956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7595 | −1.23038 | ||||||||
\(626\) | −13.6996 | −0.547546 | ||||||||
\(627\) | −1.89208 | −0.0755623 | ||||||||
\(628\) | 12.3174 | 0.491519 | ||||||||
\(629\) | −2.68829 | −0.107189 | ||||||||
\(630\) | −15.8458 | −0.631313 | ||||||||
\(631\) | −0.00599428 | −0.000238628 0 | −0.000119314 | − | 1.00000i | \(-0.500038\pi\) | ||||
−0.000119314 | 1.00000i | \(0.500038\pi\) | ||||||||
\(632\) | 9.31247 | 0.370430 | ||||||||
\(633\) | −45.2441 | −1.79829 | ||||||||
\(634\) | 9.54433 | 0.379054 | ||||||||
\(635\) | −40.1286 | −1.59245 | ||||||||
\(636\) | 23.6410 | 0.937428 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.71272 | −0.107397 | ||||||||
\(639\) | −7.53424 | −0.298050 | ||||||||
\(640\) | −2.86363 | −0.113195 | ||||||||
\(641\) | −11.7773 | −0.465176 | −0.232588 | − | 0.972575i | \(-0.574719\pi\) | ||||
−0.232588 | + | 0.972575i | \(0.574719\pi\) | |||||||
\(642\) | 14.6885 | 0.579709 | ||||||||
\(643\) | −24.8665 | −0.980640 | −0.490320 | − | 0.871542i | \(-0.663120\pi\) | ||||
−0.490320 | + | 0.871542i | \(0.663120\pi\) | |||||||
\(644\) | −5.90831 | −0.232820 | ||||||||
\(645\) | −48.0576 | −1.89227 | ||||||||
\(646\) | −0.468182 | −0.0184204 | ||||||||
\(647\) | −35.0553 | −1.37816 | −0.689082 | − | 0.724683i | \(-0.741986\pi\) | ||||
−0.689082 | + | 0.724683i | \(0.741986\pi\) | |||||||
\(648\) | 8.60917 | 0.338200 | ||||||||
\(649\) | 4.40805 | 0.173031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.9948 | 0.470114 | ||||||||
\(652\) | 3.62592 | 0.142002 | ||||||||
\(653\) | 28.2767 | 1.10655 | 0.553277 | − | 0.832997i | \(-0.313377\pi\) | ||||
0.553277 | + | 0.832997i | \(0.313377\pi\) | |||||||
\(654\) | 7.06035 | 0.276082 | ||||||||
\(655\) | 42.7491 | 1.67035 | ||||||||
\(656\) | −9.46441 | −0.369523 | ||||||||
\(657\) | −38.0535 | −1.48461 | ||||||||
\(658\) | 2.43350 | 0.0948679 | ||||||||
\(659\) | −8.23201 | −0.320673 | −0.160337 | − | 0.987062i | \(-0.551258\pi\) | ||||
−0.160337 | + | 0.987062i | \(0.551258\pi\) | |||||||
\(660\) | −5.41821 | −0.210903 | ||||||||
\(661\) | 17.1371 | 0.666556 | 0.333278 | − | 0.942829i | \(-0.391845\pi\) | ||||
0.333278 | + | 0.942829i | \(0.391845\pi\) | |||||||
\(662\) | −7.65204 | −0.297405 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.26881 | 0.126854 | ||||||||
\(665\) | 5.07057 | 0.196628 | ||||||||
\(666\) | 17.9440 | 0.695318 | ||||||||
\(667\) | −11.8398 | −0.458439 | ||||||||
\(668\) | 0.0446192 | 0.00172637 | ||||||||
\(669\) | 30.0512 | 1.16185 | ||||||||
\(670\) | 4.26869 | 0.164914 | ||||||||
\(671\) | −1.80819 | −0.0698044 | ||||||||
\(672\) | 4.38223 | 0.169048 | ||||||||
\(673\) | 13.7359 | 0.529479 | 0.264739 | − | 0.964320i | \(-0.414714\pi\) | ||||
0.264739 | + | 0.964320i | \(0.414714\pi\) | |||||||
\(674\) | 20.7810 | 0.800455 | ||||||||
\(675\) | −0.990565 | −0.0381268 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.07430 | 0.118155 | 0.0590774 | − | 0.998253i | \(-0.481184\pi\) | ||||
0.0590774 | + | 0.998253i | \(0.481184\pi\) | |||||||
\(678\) | −45.2576 | −1.73811 | ||||||||
\(679\) | −4.85890 | −0.186468 | ||||||||
\(680\) | −1.34070 | −0.0514135 | ||||||||
\(681\) | −55.5089 | −2.12710 | ||||||||
\(682\) | 2.09258 | 0.0801290 | ||||||||
\(683\) | −32.0415 | −1.22603 | −0.613016 | − | 0.790070i | \(-0.710044\pi\) | ||||
−0.613016 | + | 0.790070i | \(0.710044\pi\) | |||||||
\(684\) | 3.12506 | 0.119490 | ||||||||
\(685\) | 27.1040 | 1.03559 | ||||||||
\(686\) | 19.2379 | 0.734506 | ||||||||
\(687\) | 22.5985 | 0.862187 | ||||||||
\(688\) | 6.78094 | 0.258521 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −23.6481 | −0.900267 | ||||||||
\(691\) | −3.10166 | −0.117993 | −0.0589964 | − | 0.998258i | \(-0.518790\pi\) | ||||
−0.0589964 | + | 0.998258i | \(0.518790\pi\) | |||||||
\(692\) | −14.5771 | −0.554137 | ||||||||
\(693\) | 4.23040 | 0.160700 | ||||||||
\(694\) | 29.8422 | 1.13280 | ||||||||
\(695\) | −62.9017 | −2.38600 | ||||||||
\(696\) | 8.78165 | 0.332868 | ||||||||
\(697\) | −4.43106 | −0.167839 | ||||||||
\(698\) | 8.47281 | 0.320701 | ||||||||
\(699\) | −34.7443 | −1.31415 | ||||||||
\(700\) | 5.66684 | 0.214187 | ||||||||
\(701\) | −3.93054 | −0.148454 | −0.0742272 | − | 0.997241i | \(-0.523649\pi\) | ||||
−0.0742272 | + | 0.997241i | \(0.523649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.74198 | −0.216563 | ||||||||
\(704\) | 0.764511 | 0.0288136 | ||||||||
\(705\) | 9.74013 | 0.366835 | ||||||||
\(706\) | 10.1193 | 0.380844 | ||||||||
\(707\) | 23.6678 | 0.890119 | ||||||||
\(708\) | −14.2698 | −0.536292 | ||||||||
\(709\) | 36.5498 | 1.37266 | 0.686328 | − | 0.727293i | \(-0.259222\pi\) | ||||
0.686328 | + | 0.727293i | \(0.259222\pi\) | |||||||
\(710\) | 6.90395 | 0.259101 | ||||||||
\(711\) | −29.1020 | −1.09141 | ||||||||
\(712\) | 14.5129 | 0.543896 | ||||||||
\(713\) | 9.13318 | 0.342040 | ||||||||
\(714\) | 2.05168 | 0.0767822 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.7631 | −0.439607 | ||||||||
\(717\) | −34.8520 | −1.30157 | ||||||||
\(718\) | −35.0123 | −1.30665 | ||||||||
\(719\) | 42.2264 | 1.57478 | 0.787389 | − | 0.616456i | \(-0.211432\pi\) | ||||
0.787389 | + | 0.616456i | \(0.211432\pi\) | |||||||
\(720\) | 8.94902 | 0.333510 | ||||||||
\(721\) | −14.1111 | −0.525526 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −75.2857 | −2.79990 | ||||||||
\(724\) | 16.7531 | 0.622625 | ||||||||
\(725\) | 11.3559 | 0.421748 | ||||||||
\(726\) | −25.7772 | −0.956683 | ||||||||
\(727\) | −17.3320 | −0.642809 | −0.321405 | − | 0.946942i | \(-0.604155\pi\) | ||||
−0.321405 | + | 0.946942i | \(0.604155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.2022 | −1.08156 | ||||||||
\(730\) | 34.8701 | 1.29060 | ||||||||
\(731\) | 3.17472 | 0.117421 | ||||||||
\(732\) | 5.85350 | 0.216352 | ||||||||
\(733\) | −2.27653 | −0.0840856 | −0.0420428 | − | 0.999116i | \(-0.513387\pi\) | ||||
−0.0420428 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(734\) | −6.95348 | −0.256658 | ||||||||
\(735\) | 27.3897 | 1.01029 | ||||||||
\(736\) | 3.33675 | 0.122994 | ||||||||
\(737\) | −1.13962 | −0.0419785 | ||||||||
\(738\) | 29.5769 | 1.08874 | ||||||||
\(739\) | 30.6823 | 1.12867 | 0.564334 | − | 0.825547i | \(-0.309133\pi\) | ||||
0.564334 | + | 0.825547i | \(0.309133\pi\) | |||||||
\(740\) | −16.4429 | −0.604453 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.9142 | 0.620939 | ||||||||
\(743\) | −3.84335 | −0.140999 | −0.0704995 | − | 0.997512i | \(-0.522459\pi\) | ||||
−0.0704995 | + | 0.997512i | \(0.522459\pi\) | |||||||
\(744\) | −6.77413 | −0.248352 | ||||||||
\(745\) | −16.7317 | −0.613002 | ||||||||
\(746\) | −1.25498 | −0.0459482 | ||||||||
\(747\) | −10.2152 | −0.373755 | ||||||||
\(748\) | 0.357930 | 0.0130872 | ||||||||
\(749\) | 10.5090 | 0.383991 | ||||||||
\(750\) | −12.7542 | −0.465717 | ||||||||
\(751\) | 8.93762 | 0.326139 | 0.163069 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163069 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(752\) | −1.37434 | −0.0501168 | ||||||||
\(753\) | 10.1165 | 0.368665 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.3798 | 0.559730 | ||||||||
\(756\) | −0.548051 | −0.0199324 | ||||||||
\(757\) | −10.4195 | −0.378703 | −0.189351 | − | 0.981909i | \(-0.560638\pi\) | ||||
−0.189351 | + | 0.981909i | \(0.560638\pi\) | |||||||
\(758\) | 12.7877 | 0.464472 | ||||||||
\(759\) | 6.31339 | 0.229161 | ||||||||
\(760\) | −2.86363 | −0.103875 | ||||||||
\(761\) | −45.1809 | −1.63781 | −0.818903 | − | 0.573932i | \(-0.805417\pi\) | ||||
−0.818903 | + | 0.573932i | \(0.805417\pi\) | |||||||
\(762\) | −34.6810 | −1.25636 | ||||||||
\(763\) | 5.05139 | 0.182873 | ||||||||
\(764\) | 23.9089 | 0.864995 | ||||||||
\(765\) | 4.18977 | 0.151482 | ||||||||
\(766\) | −3.94739 | −0.142625 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.47489 | −0.0893048 | ||||||||
\(769\) | −31.0575 | −1.11996 | −0.559981 | − | 0.828506i | \(-0.689191\pi\) | ||||
−0.559981 | + | 0.828506i | \(0.689191\pi\) | |||||||
\(770\) | −3.87650 | −0.139699 | ||||||||
\(771\) | 10.8253 | 0.389864 | ||||||||
\(772\) | 21.8221 | 0.785393 | ||||||||
\(773\) | 10.6459 | 0.382906 | 0.191453 | − | 0.981502i | \(-0.438680\pi\) | ||||
0.191453 | + | 0.981502i | \(0.438680\pi\) | |||||||
\(774\) | −21.1909 | −0.761690 | ||||||||
\(775\) | −8.75992 | −0.314666 | ||||||||
\(776\) | 2.74409 | 0.0985071 | ||||||||
\(777\) | 25.1627 | 0.902705 | ||||||||
\(778\) | −14.1388 | −0.506900 | ||||||||
\(779\) | −9.46441 | −0.339098 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.84317 | −0.0659536 | ||||||||
\(782\) | 1.56221 | 0.0558644 | ||||||||
\(783\) | −1.09825 | −0.0392483 | ||||||||
\(784\) | −3.86470 | −0.138025 | ||||||||
\(785\) | 35.2726 | 1.25893 | ||||||||
\(786\) | 36.9458 | 1.31781 | ||||||||
\(787\) | 13.9279 | 0.496477 | 0.248238 | − | 0.968699i | \(-0.420148\pi\) | ||||
0.248238 | + | 0.968699i | \(0.420148\pi\) | |||||||
\(788\) | −3.14538 | −0.112049 | ||||||||
\(789\) | 43.0450 | 1.53244 | ||||||||
\(790\) | 26.6675 | 0.948786 | ||||||||
\(791\) | −32.3799 | −1.15130 | ||||||||
\(792\) | −2.38914 | −0.0848945 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.9324 | 0.458955 | ||||||||
\(795\) | 67.6992 | 2.40104 | ||||||||
\(796\) | 6.98844 | 0.247699 | ||||||||
\(797\) | −43.3987 | −1.53726 | −0.768631 | − | 0.639693i | \(-0.779062\pi\) | ||||
−0.768631 | + | 0.639693i | \(0.779062\pi\) | |||||||
\(798\) | 4.38223 | 0.155129 | ||||||||
\(799\) | −0.643439 | −0.0227632 | ||||||||
\(800\) | −3.20038 | −0.113151 | ||||||||
\(801\) | −45.3539 | −1.60250 | ||||||||
\(802\) | −1.92157 | −0.0678529 | ||||||||
\(803\) | −9.30935 | −0.328520 | ||||||||
\(804\) | 3.68920 | 0.130108 | ||||||||
\(805\) | −16.9192 | −0.596324 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.9759 | 1.44242 | ||||||||
\(808\) | −13.3665 | −0.470233 | ||||||||
\(809\) | 21.9861 | 0.772991 | 0.386495 | − | 0.922291i | \(-0.373685\pi\) | ||||
0.386495 | + | 0.922291i | \(0.373685\pi\) | |||||||
\(810\) | 24.6535 | 0.866235 | ||||||||
\(811\) | −34.1994 | −1.20090 | −0.600452 | − | 0.799661i | \(-0.705013\pi\) | ||||
−0.600452 | + | 0.799661i | \(0.705013\pi\) | |||||||
\(812\) | 6.28290 | 0.220487 | ||||||||
\(813\) | −63.3693 | −2.22246 | ||||||||
\(814\) | 4.38980 | 0.153863 | ||||||||
\(815\) | 10.3833 | 0.363711 | ||||||||
\(816\) | −1.15870 | −0.0405625 | ||||||||
\(817\) | 6.78094 | 0.237235 | ||||||||
\(818\) | −6.18073 | −0.216104 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.1026 | −0.946463 | ||||||||
\(821\) | 21.6637 | 0.756067 | 0.378033 | − | 0.925792i | \(-0.376600\pi\) | ||||
0.378033 | + | 0.925792i | \(0.376600\pi\) | |||||||
\(822\) | 23.4246 | 0.817027 | ||||||||
\(823\) | −34.3177 | −1.19624 | −0.598121 | − | 0.801406i | \(-0.704086\pi\) | ||||
−0.598121 | + | 0.801406i | \(0.704086\pi\) | |||||||
\(824\) | 7.96934 | 0.277625 | ||||||||
\(825\) | −6.05537 | −0.210821 | ||||||||
\(826\) | −10.2095 | −0.355232 | ||||||||
\(827\) | 48.1657 | 1.67489 | 0.837444 | − | 0.546524i | \(-0.184049\pi\) | ||||
0.837444 | + | 0.546524i | \(0.184049\pi\) | |||||||
\(828\) | −10.4276 | −0.362382 | ||||||||
\(829\) | 35.0387 | 1.21695 | 0.608473 | − | 0.793575i | \(-0.291783\pi\) | ||||
0.608473 | + | 0.793575i | \(0.291783\pi\) | |||||||
\(830\) | 9.36065 | 0.324913 | ||||||||
\(831\) | 80.8937 | 2.80617 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.80938 | −0.0626914 | ||||||||
\(834\) | −54.3626 | −1.88242 | ||||||||
\(835\) | 0.127773 | 0.00442177 | ||||||||
\(836\) | 0.764511 | 0.0264411 | ||||||||
\(837\) | 0.847188 | 0.0292831 | ||||||||
\(838\) | −8.84081 | −0.305401 | ||||||||
\(839\) | 39.5247 | 1.36454 | 0.682272 | − | 0.731098i | \(-0.260992\pi\) | ||||
0.682272 | + | 0.731098i | \(0.260992\pi\) | |||||||
\(840\) | 12.5491 | 0.432984 | ||||||||
\(841\) | −16.4095 | −0.565846 | ||||||||
\(842\) | 27.8790 | 0.960772 | ||||||||
\(843\) | −40.0160 | −1.37822 | ||||||||
\(844\) | 18.2813 | 0.629268 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.29488 | 0.147661 | ||||||||
\(847\) | −18.4425 | −0.633693 | ||||||||
\(848\) | −9.55237 | −0.328030 | ||||||||
\(849\) | 62.3692 | 2.14051 | ||||||||
\(850\) | −1.49836 | −0.0513933 | ||||||||
\(851\) | 19.1596 | 0.656781 | ||||||||
\(852\) | 5.96673 | 0.204417 | ||||||||
\(853\) | 29.7468 | 1.01851 | 0.509256 | − | 0.860615i | \(-0.329921\pi\) | ||||
0.509256 | + | 0.860615i | \(0.329921\pi\) | |||||||
\(854\) | 4.18794 | 0.143308 | ||||||||
\(855\) | 8.94902 | 0.306050 | ||||||||
\(856\) | −5.93502 | −0.202855 | ||||||||
\(857\) | −52.6321 | −1.79788 | −0.898939 | − | 0.438074i | \(-0.855661\pi\) | ||||
−0.898939 | + | 0.438074i | \(0.855661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.3911 | −0.763974 | −0.381987 | − | 0.924168i | \(-0.624760\pi\) | ||||
−0.381987 | + | 0.924168i | \(0.624760\pi\) | |||||||
\(860\) | 19.4181 | 0.662152 | ||||||||
\(861\) | 41.4752 | 1.41347 | ||||||||
\(862\) | 22.1378 | 0.754015 | ||||||||
\(863\) | −16.1610 | −0.550128 | −0.275064 | − | 0.961426i | \(-0.588699\pi\) | ||||
−0.275064 | + | 0.961426i | \(0.588699\pi\) | |||||||
\(864\) | 0.309515 | 0.0105299 | ||||||||
\(865\) | −41.7434 | −1.41932 | ||||||||
\(866\) | 34.0289 | 1.15635 | ||||||||
\(867\) | 41.5306 | 1.41045 | ||||||||
\(868\) | −4.84661 | −0.164505 | ||||||||
\(869\) | −7.11948 | −0.241512 | ||||||||
\(870\) | 25.1474 | 0.852577 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.85280 | −0.0966080 | ||||||||
\(873\) | −8.57545 | −0.290235 | ||||||||
\(874\) | 3.33675 | 0.112867 | ||||||||
\(875\) | −9.12509 | −0.308484 | ||||||||
\(876\) | 30.1364 | 1.01821 | ||||||||
\(877\) | 7.90458 | 0.266919 | 0.133459 | − | 0.991054i | \(-0.457391\pi\) | ||||
0.133459 | + | 0.991054i | \(0.457391\pi\) | |||||||
\(878\) | 16.2942 | 0.549903 | ||||||||
\(879\) | 77.1139 | 2.60099 | ||||||||
\(880\) | 2.18928 | 0.0738005 | ||||||||
\(881\) | 48.9018 | 1.64754 | 0.823771 | − | 0.566922i | \(-0.191866\pi\) | ||||
0.823771 | + | 0.566922i | \(0.191866\pi\) | |||||||
\(882\) | 12.0774 | 0.406668 | ||||||||
\(883\) | 3.81146 | 0.128266 | 0.0641329 | − | 0.997941i | \(-0.479572\pi\) | ||||
0.0641329 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40.8635 | −1.37361 | ||||||||
\(886\) | −19.2769 | −0.647620 | ||||||||
\(887\) | 30.7116 | 1.03119 | 0.515597 | − | 0.856831i | \(-0.327570\pi\) | ||||
0.515597 | + | 0.856831i | \(0.327570\pi\) | |||||||
\(888\) | −14.2107 | −0.476881 | ||||||||
\(889\) | −24.8128 | −0.832195 | ||||||||
\(890\) | 41.5597 | 1.39308 | ||||||||
\(891\) | −6.58180 | −0.220499 | ||||||||
\(892\) | −12.1425 | −0.406560 | ||||||||
\(893\) | −1.37434 | −0.0459904 | ||||||||
\(894\) | −14.4603 | −0.483626 | ||||||||
\(895\) | −33.6851 | −1.12597 | ||||||||
\(896\) | −1.77068 | −0.0591542 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.67409 | −0.256088 | ||||||||
\(899\) | −9.71224 | −0.323921 | ||||||||
\(900\) | 10.0014 | 0.333380 | ||||||||
\(901\) | −4.47225 | −0.148992 | ||||||||
\(902\) | 7.23564 | 0.240920 | ||||||||
\(903\) | −29.7156 | −0.988874 | ||||||||
\(904\) | 18.2867 | 0.608208 | ||||||||
\(905\) | 47.9748 | 1.59474 | ||||||||
\(906\) | 13.2920 | 0.441597 | ||||||||
\(907\) | −19.8204 | −0.658125 | −0.329063 | − | 0.944308i | \(-0.606733\pi\) | ||||
−0.329063 | + | 0.944308i | \(0.606733\pi\) | |||||||
\(908\) | 22.4289 | 0.744328 | ||||||||
\(909\) | 41.7712 | 1.38546 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.87384 | 0.227741 | 0.113870 | − | 0.993496i | \(-0.463675\pi\) | ||||
0.113870 | + | 0.993496i | \(0.463675\pi\) | |||||||
\(912\) | −2.47489 | −0.0819517 | ||||||||
\(913\) | −2.49904 | −0.0827060 | ||||||||
\(914\) | 6.41003 | 0.212025 | ||||||||
\(915\) | 16.7623 | 0.554144 | ||||||||
\(916\) | −9.13113 | −0.301701 | ||||||||
\(917\) | 26.4332 | 0.872901 | ||||||||
\(918\) | 0.144909 | 0.00478272 | ||||||||
\(919\) | −25.0260 | −0.825532 | −0.412766 | − | 0.910837i | \(-0.635437\pi\) | ||||
−0.412766 | + | 0.910837i | \(0.635437\pi\) | |||||||
\(920\) | 9.55522 | 0.315026 | ||||||||
\(921\) | −81.8179 | −2.69599 | ||||||||
\(922\) | −12.3507 | −0.406747 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.35026 | −0.110215 | ||||||||
\(925\) | −18.3765 | −0.604216 | ||||||||
\(926\) | −3.56113 | −0.117026 | ||||||||
\(927\) | −24.9047 | −0.817977 | ||||||||
\(928\) | −3.54830 | −0.116479 | ||||||||
\(929\) | −52.0702 | −1.70837 | −0.854184 | − | 0.519971i | \(-0.825943\pi\) | ||||
−0.854184 | + | 0.519971i | \(0.825943\pi\) | |||||||
\(930\) | −19.3986 | −0.636106 | ||||||||
\(931\) | −3.86470 | −0.126660 | ||||||||
\(932\) | 14.0387 | 0.459854 | ||||||||
\(933\) | 18.0759 | 0.591777 | ||||||||
\(934\) | 14.1047 | 0.461521 | ||||||||
\(935\) | 1.02498 | 0.0335204 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.3297 | −0.696812 | −0.348406 | − | 0.937344i | \(-0.613277\pi\) | ||||
−0.348406 | + | 0.937344i | \(0.613277\pi\) | |||||||
\(938\) | 2.63947 | 0.0861818 | ||||||||
\(939\) | −33.9049 | −1.10645 | ||||||||
\(940\) | −3.93559 | −0.128365 | ||||||||
\(941\) | −53.3220 | −1.73825 | −0.869124 | − | 0.494594i | \(-0.835317\pi\) | ||||
−0.869124 | + | 0.494594i | \(0.835317\pi\) | |||||||
\(942\) | 30.4843 | 0.993231 | ||||||||
\(943\) | 31.5804 | 1.02840 | ||||||||
\(944\) | 5.76584 | 0.187662 | ||||||||
\(945\) | −1.56941 | −0.0510531 | ||||||||
\(946\) | −5.18410 | −0.168550 | ||||||||
\(947\) | −26.0970 | −0.848039 | −0.424020 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424020 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(948\) | 23.0473 | 0.748542 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.20038 | −0.103834 | ||||||||
\(951\) | 23.6211 | 0.765968 | ||||||||
\(952\) | −0.828999 | −0.0268680 | ||||||||
\(953\) | 17.9036 | 0.579954 | 0.289977 | − | 0.957034i | \(-0.406352\pi\) | ||||
0.289977 | + | 0.957034i | \(0.406352\pi\) | |||||||
\(954\) | 29.8518 | 0.966486 | ||||||||
\(955\) | 68.4664 | 2.21552 | ||||||||
\(956\) | 14.0823 | 0.455453 | ||||||||
\(957\) | −6.71366 | −0.217022 | ||||||||
\(958\) | 8.23436 | 0.266040 | ||||||||
\(959\) | 16.7593 | 0.541187 | ||||||||
\(960\) | −7.08716 | −0.228737 | ||||||||
\(961\) | −23.5080 | −0.758323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.5473 | 0.597679 | ||||||||
\(964\) | 30.4199 | 0.979757 | ||||||||
\(965\) | 62.4903 | 2.01164 | ||||||||
\(966\) | −14.6224 | −0.470468 | ||||||||
\(967\) | 52.6412 | 1.69283 | 0.846414 | − | 0.532525i | \(-0.178757\pi\) | ||||
0.846414 | + | 0.532525i | \(0.178757\pi\) | |||||||
\(968\) | 10.4155 | 0.334768 | ||||||||
\(969\) | −1.15870 | −0.0372227 | ||||||||
\(970\) | 7.85806 | 0.252307 | ||||||||
\(971\) | 25.3264 | 0.812763 | 0.406382 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406382 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(972\) | 22.2353 | 0.713197 | ||||||||
\(973\) | −38.8942 | −1.24689 | ||||||||
\(974\) | 17.2786 | 0.553643 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.36516 | −0.0757069 | ||||||||
\(977\) | −55.5077 | −1.77585 | −0.887924 | − | 0.459990i | \(-0.847853\pi\) | ||||
−0.887924 | + | 0.459990i | \(0.847853\pi\) | |||||||
\(978\) | 8.97374 | 0.286948 | ||||||||
\(979\) | −11.0953 | −0.354607 | ||||||||
\(980\) | −11.0671 | −0.353525 | ||||||||
\(981\) | 8.91517 | 0.284640 | ||||||||
\(982\) | 7.80350 | 0.249020 | ||||||||
\(983\) | 4.80383 | 0.153218 | 0.0766092 | − | 0.997061i | \(-0.475591\pi\) | ||||
0.0766092 | + | 0.997061i | \(0.475591\pi\) | |||||||
\(984\) | −23.4233 | −0.746708 | ||||||||
\(985\) | −9.00720 | −0.286993 | ||||||||
\(986\) | −1.66125 | −0.0529050 | ||||||||
\(987\) | 6.02265 | 0.191703 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.6263 | −0.719475 | ||||||||
\(990\) | −6.84162 | −0.217441 | ||||||||
\(991\) | 0.0302006 | 0.000959354 0 | 0.000479677 | − | 1.00000i | \(-0.499847\pi\) | ||||
0.000479677 | 1.00000i | \(0.499847\pi\) | ||||||||
\(992\) | 2.73715 | 0.0869046 | ||||||||
\(993\) | −18.9379 | −0.600977 | ||||||||
\(994\) | 4.26894 | 0.135403 | ||||||||
\(995\) | 20.0123 | 0.634433 | ||||||||
\(996\) | 8.08992 | 0.256339 | ||||||||
\(997\) | 14.6989 | 0.465519 | 0.232760 | − | 0.972534i | \(-0.425224\pi\) | ||||
0.232760 | + | 0.972534i | \(0.425224\pi\) | |||||||
\(998\) | 7.14315 | 0.226113 | ||||||||
\(999\) | 1.77723 | 0.0562290 |
(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 | 6422.2.a.bg.1.2 | 8 | ||
13.2 | odd | 12 | 494.2.m.a.381.4 | yes | 16 | ||
13.7 | odd | 12 | 494.2.m.a.153.4 | ✓ | 16 | ||
13.12 | even | 2 | 6422.2.a.bh.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.a.153.4 | ✓ | 16 | 13.7 | odd | 12 | ||
494.2.m.a.381.4 | yes | 16 | 13.2 | odd | 12 | ||
6422.2.a.bg.1.2 | 8 | 1.1 | even | 1 | trivial | ||
6422.2.a.bh.1.2 | 8 | 13.12 | even | 2 |