Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.43025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 21x^{2} + 10x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(4.07314\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.07314 | 1.53950 | 0.769751 | − | 0.638344i | \(-0.220380\pi\) | ||||
0.769751 | + | 0.638344i | \(0.220380\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.13537 | 1.14695 | 0.573473 | − | 0.819224i | \(-0.305596\pi\) | ||||
0.573473 | + | 0.819224i | \(0.305596\pi\) | |||||||
\(14\) | 4.07314 | 1.08859 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.97245 | −1.44853 | −0.724266 | − | 0.689521i | \(-0.757821\pi\) | ||||
−0.724266 | + | 0.689521i | \(0.757821\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.35441 | 1.22839 | 0.614193 | − | 0.789156i | \(-0.289482\pi\) | ||||
0.614193 | + | 0.789156i | \(0.289482\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 4.07314 | 0.888832 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.33676 | 0.695763 | 0.347881 | − | 0.937539i | \(-0.386901\pi\) | ||||
0.347881 | + | 0.937539i | \(0.386901\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.13537 | 0.811014 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.07314 | 0.769751 | ||||||||
\(29\) | −2.45511 | −0.455902 | −0.227951 | − | 0.973673i | \(-0.573203\pi\) | ||||
−0.227951 | + | 0.973673i | \(0.573203\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −4.92724 | −0.884959 | −0.442480 | − | 0.896779i | \(-0.645901\pi\) | ||||
−0.442480 | + | 0.896779i | \(0.645901\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.97245 | −1.02427 | ||||||||
\(35\) | 4.07314 | 0.688487 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.14590 | 0.352783 | 0.176392 | − | 0.984320i | \(-0.443557\pi\) | ||||
0.176392 | + | 0.984320i | \(0.443557\pi\) | |||||||
\(38\) | 5.35441 | 0.868601 | ||||||||
\(39\) | 4.13537 | 0.662190 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −7.10782 | −1.11006 | −0.555028 | − | 0.831832i | \(-0.687292\pi\) | ||||
−0.555028 | + | 0.831832i | \(0.687292\pi\) | |||||||
\(42\) | 4.07314 | 0.628499 | ||||||||
\(43\) | −11.6807 | −1.78128 | −0.890641 | − | 0.454707i | \(-0.849744\pi\) | ||||
−0.890641 | + | 0.454707i | \(0.849744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 3.33676 | 0.491979 | ||||||||
\(47\) | −4.01091 | −0.585051 | −0.292526 | − | 0.956258i | \(-0.594496\pi\) | ||||
−0.292526 | + | 0.956258i | \(0.594496\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 9.59048 | 1.37007 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −5.97245 | −0.836310 | ||||||||
\(52\) | 4.13537 | 0.573473 | ||||||||
\(53\) | −1.63506 | −0.224593 | −0.112297 | − | 0.993675i | \(-0.535821\pi\) | ||||
−0.112297 | + | 0.993675i | \(0.535821\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.07314 | 0.544296 | ||||||||
\(57\) | 5.35441 | 0.709209 | ||||||||
\(58\) | −2.45511 | −0.322371 | ||||||||
\(59\) | −6.56293 | −0.854421 | −0.427210 | − | 0.904152i | \(-0.640504\pi\) | ||||
−0.427210 | + | 0.904152i | \(0.640504\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 4.14628 | 0.530877 | 0.265439 | − | 0.964128i | \(-0.414483\pi\) | ||||
0.265439 | + | 0.964128i | \(0.414483\pi\) | |||||||
\(62\) | −4.92724 | −0.625761 | ||||||||
\(63\) | 4.07314 | 0.513168 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.13537 | 0.512930 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0517 | 1.59452 | 0.797260 | − | 0.603636i | \(-0.206282\pi\) | ||||
0.797260 | + | 0.603636i | \(0.206282\pi\) | |||||||
\(68\) | −5.97245 | −0.724266 | ||||||||
\(69\) | 3.33676 | 0.401699 | ||||||||
\(70\) | 4.07314 | 0.486834 | ||||||||
\(71\) | −13.1810 | −1.56429 | −0.782146 | − | 0.623095i | \(-0.785875\pi\) | ||||
−0.782146 | + | 0.623095i | \(0.785875\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 2.14590 | 0.249456 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 5.35441 | 0.614193 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.13537 | 0.468239 | ||||||||
\(79\) | 4.97182 | 0.559374 | 0.279687 | − | 0.960091i | \(-0.409769\pi\) | ||||
0.279687 | + | 0.960091i | \(0.409769\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.10782 | −0.784928 | ||||||||
\(83\) | −10.4721 | −1.14947 | −0.574733 | − | 0.818341i | \(-0.694894\pi\) | ||||
−0.574733 | + | 0.818341i | \(0.694894\pi\) | |||||||
\(84\) | 4.07314 | 0.444416 | ||||||||
\(85\) | −5.97245 | −0.647803 | ||||||||
\(86\) | −11.6807 | −1.25956 | ||||||||
\(87\) | −2.45511 | −0.263215 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.5800 | 1.43947 | 0.719736 | − | 0.694248i | \(-0.244263\pi\) | ||||
0.719736 | + | 0.694248i | \(0.244263\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 16.8440 | 1.76573 | ||||||||
\(92\) | 3.33676 | 0.347881 | ||||||||
\(93\) | −4.92724 | −0.510931 | ||||||||
\(94\) | −4.01091 | −0.413694 | ||||||||
\(95\) | 5.35441 | 0.549351 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 8.43808 | 0.856757 | 0.428379 | − | 0.903599i | \(-0.359085\pi\) | ||||
0.428379 | + | 0.903599i | \(0.359085\pi\) | |||||||
\(98\) | 9.59048 | 0.968785 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.97245 | −0.196266 | −0.0981329 | − | 0.995173i | \(-0.531287\pi\) | ||||
−0.0981329 | + | 0.995173i | \(0.531287\pi\) | |||||||
\(102\) | −5.97245 | −0.591360 | ||||||||
\(103\) | 9.35441 | 0.921718 | 0.460859 | − | 0.887473i | \(-0.347541\pi\) | ||||
0.460859 | + | 0.887473i | \(0.347541\pi\) | |||||||
\(104\) | 4.13537 | 0.405507 | ||||||||
\(105\) | 4.07314 | 0.397498 | ||||||||
\(106\) | −1.63506 | −0.158811 | ||||||||
\(107\) | −8.34767 | −0.807000 | −0.403500 | − | 0.914980i | \(-0.632206\pi\) | ||||
−0.403500 | + | 0.914980i | \(0.632206\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −14.4721 | −1.38618 | −0.693090 | − | 0.720851i | \(-0.743751\pi\) | ||||
−0.693090 | + | 0.720851i | \(0.743751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.14590 | 0.203680 | ||||||||
\(112\) | 4.07314 | 0.384876 | ||||||||
\(113\) | 13.0735 | 1.22985 | 0.614927 | − | 0.788584i | \(-0.289185\pi\) | ||||
0.614927 | + | 0.788584i | \(0.289185\pi\) | |||||||
\(114\) | 5.35441 | 0.501487 | ||||||||
\(115\) | 3.33676 | 0.311155 | ||||||||
\(116\) | −2.45511 | −0.227951 | ||||||||
\(117\) | 4.13537 | 0.382315 | ||||||||
\(118\) | −6.56293 | −0.604167 | ||||||||
\(119\) | −24.3266 | −2.23002 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.14628 | 0.375387 | ||||||||
\(123\) | −7.10782 | −0.640891 | ||||||||
\(124\) | −4.92724 | −0.442480 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.07314 | 0.362864 | ||||||||
\(127\) | −19.5007 | −1.73041 | −0.865203 | − | 0.501421i | \(-0.832811\pi\) | ||||
−0.865203 | + | 0.501421i | \(0.832811\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.6807 | −1.02842 | ||||||||
\(130\) | 4.13537 | 0.362696 | ||||||||
\(131\) | 15.7252 | 1.37392 | 0.686960 | − | 0.726695i | \(-0.258945\pi\) | ||||
0.686960 | + | 0.726695i | \(0.258945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.8093 | 1.89110 | ||||||||
\(134\) | 13.0517 | 1.12750 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −5.97245 | −0.512133 | ||||||||
\(137\) | −3.74628 | −0.320066 | −0.160033 | − | 0.987112i | \(-0.551160\pi\) | ||||
−0.160033 | + | 0.987112i | \(0.551160\pi\) | |||||||
\(138\) | 3.33676 | 0.284044 | ||||||||
\(139\) | −13.7473 | −1.16603 | −0.583015 | − | 0.812461i | \(-0.698127\pi\) | ||||
−0.583015 | + | 0.812461i | \(0.698127\pi\) | |||||||
\(140\) | 4.07314 | 0.344243 | ||||||||
\(141\) | −4.01091 | −0.337779 | ||||||||
\(142\) | −13.1810 | −1.10612 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.45511 | −0.203886 | ||||||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 9.59048 | 0.791010 | ||||||||
\(148\) | 2.14590 | 0.176392 | ||||||||
\(149\) | −6.02755 | −0.493796 | −0.246898 | − | 0.969041i | \(-0.579411\pi\) | ||||
−0.246898 | + | 0.969041i | \(0.579411\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 14.8551 | 1.20889 | 0.604446 | − | 0.796646i | \(-0.293395\pi\) | ||||
0.604446 | + | 0.796646i | \(0.293395\pi\) | |||||||
\(152\) | 5.35441 | 0.434300 | ||||||||
\(153\) | −5.97245 | −0.482844 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.92724 | −0.395766 | ||||||||
\(156\) | 4.13537 | 0.331095 | ||||||||
\(157\) | −4.45133 | −0.355254 | −0.177627 | − | 0.984098i | \(-0.556842\pi\) | ||||
−0.177627 | + | 0.984098i | \(0.556842\pi\) | |||||||
\(158\) | 4.97182 | 0.395537 | ||||||||
\(159\) | −1.63506 | −0.129669 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 13.5911 | 1.07113 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −18.2991 | −1.43329 | −0.716647 | − | 0.697436i | \(-0.754324\pi\) | ||||
−0.716647 | + | 0.697436i | \(0.754324\pi\) | |||||||
\(164\) | −7.10782 | −0.555028 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.4721 | −0.812795 | ||||||||
\(167\) | −12.9552 | −1.00250 | −0.501251 | − | 0.865302i | \(-0.667127\pi\) | ||||
−0.501251 | + | 0.865302i | \(0.667127\pi\) | |||||||
\(168\) | 4.07314 | 0.314250 | ||||||||
\(169\) | 4.10132 | 0.315486 | ||||||||
\(170\) | −5.97245 | −0.458066 | ||||||||
\(171\) | 5.35441 | 0.409462 | ||||||||
\(172\) | −11.6807 | −0.890641 | ||||||||
\(173\) | 10.3439 | 0.786431 | 0.393216 | − | 0.919446i | \(-0.371363\pi\) | ||||
0.393216 | + | 0.919446i | \(0.371363\pi\) | |||||||
\(174\) | −2.45511 | −0.186121 | ||||||||
\(175\) | 4.07314 | 0.307901 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.56293 | −0.493300 | ||||||||
\(178\) | 13.5800 | 1.01786 | ||||||||
\(179\) | 4.88816 | 0.365358 | 0.182679 | − | 0.983173i | \(-0.441523\pi\) | ||||
0.182679 | + | 0.983173i | \(0.441523\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 16.8440 | 1.24856 | ||||||||
\(183\) | 4.14628 | 0.306502 | ||||||||
\(184\) | 3.33676 | 0.245989 | ||||||||
\(185\) | 2.14590 | 0.157770 | ||||||||
\(186\) | −4.92724 | −0.361283 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.01091 | −0.292526 | ||||||||
\(189\) | 4.07314 | 0.296277 | ||||||||
\(190\) | 5.35441 | 0.388450 | ||||||||
\(191\) | 24.0701 | 1.74165 | 0.870827 | − | 0.491590i | \(-0.163584\pi\) | ||||
0.870827 | + | 0.491590i | \(0.163584\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −15.1116 | −1.08776 | −0.543878 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543878 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(194\) | 8.43808 | 0.605819 | ||||||||
\(195\) | 4.13537 | 0.296140 | ||||||||
\(196\) | 9.59048 | 0.685034 | ||||||||
\(197\) | 17.0515 | 1.21487 | 0.607433 | − | 0.794371i | \(-0.292199\pi\) | ||||
0.607433 | + | 0.794371i | \(0.292199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.40990 | 0.383498 | 0.191749 | − | 0.981444i | \(-0.438584\pi\) | ||||
0.191749 | + | 0.981444i | \(0.438584\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 13.0517 | 0.920597 | ||||||||
\(202\) | −1.97245 | −0.138781 | ||||||||
\(203\) | −10.0000 | −0.701862 | ||||||||
\(204\) | −5.97245 | −0.418155 | ||||||||
\(205\) | −7.10782 | −0.496432 | ||||||||
\(206\) | 9.35441 | 0.651753 | ||||||||
\(207\) | 3.33676 | 0.231921 | ||||||||
\(208\) | 4.13537 | 0.286737 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.07314 | 0.281073 | ||||||||
\(211\) | 25.8545 | 1.77990 | 0.889948 | − | 0.456062i | \(-0.150740\pi\) | ||||
0.889948 | + | 0.456062i | \(0.150740\pi\) | |||||||
\(212\) | −1.63506 | −0.112297 | ||||||||
\(213\) | −13.1810 | −0.903145 | ||||||||
\(214\) | −8.34767 | −0.570635 | ||||||||
\(215\) | −11.6807 | −0.796614 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −20.0694 | −1.36240 | ||||||||
\(218\) | −14.4721 | −0.980177 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.6983 | −1.66139 | ||||||||
\(222\) | 2.14590 | 0.144023 | ||||||||
\(223\) | −9.74729 | −0.652727 | −0.326363 | − | 0.945244i | \(-0.605823\pi\) | ||||
−0.326363 | + | 0.945244i | \(0.605823\pi\) | |||||||
\(224\) | 4.07314 | 0.272148 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 13.0735 | 0.869638 | ||||||||
\(227\) | −19.1599 | −1.27169 | −0.635844 | − | 0.771818i | \(-0.719348\pi\) | ||||
−0.635844 | + | 0.771818i | \(0.719348\pi\) | |||||||
\(228\) | 5.35441 | 0.354605 | ||||||||
\(229\) | 19.2028 | 1.26896 | 0.634478 | − | 0.772941i | \(-0.281215\pi\) | ||||
0.634478 | + | 0.772941i | \(0.281215\pi\) | |||||||
\(230\) | 3.33676 | 0.220020 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.45511 | −0.161186 | ||||||||
\(233\) | 5.83746 | 0.382425 | 0.191212 | − | 0.981549i | \(-0.438758\pi\) | ||||
0.191212 | + | 0.981549i | \(0.438758\pi\) | |||||||
\(234\) | 4.13537 | 0.270338 | ||||||||
\(235\) | −4.01091 | −0.261643 | ||||||||
\(236\) | −6.56293 | −0.427210 | ||||||||
\(237\) | 4.97182 | 0.322955 | ||||||||
\(238\) | −24.3266 | −1.57686 | ||||||||
\(239\) | −15.1246 | −0.978330 | −0.489165 | − | 0.872191i | \(-0.662698\pi\) | ||||
−0.489165 | + | 0.872191i | \(0.662698\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 20.4902 | 1.31989 | 0.659944 | − | 0.751315i | \(-0.270580\pi\) | ||||
0.659944 | + | 0.751315i | \(0.270580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.14628 | 0.265439 | ||||||||
\(245\) | 9.59048 | 0.612713 | ||||||||
\(246\) | −7.10782 | −0.453178 | ||||||||
\(247\) | 22.1425 | 1.40889 | ||||||||
\(248\) | −4.92724 | −0.312880 | ||||||||
\(249\) | −10.4721 | −0.663645 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.6300 | 0.923434 | 0.461717 | − | 0.887027i | \(-0.347234\pi\) | ||||
0.461717 | + | 0.887027i | \(0.347234\pi\) | |||||||
\(252\) | 4.07314 | 0.256584 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −19.5007 | −1.22358 | ||||||||
\(255\) | −5.97245 | −0.374009 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.4164 | 1.33592 | 0.667959 | − | 0.744198i | \(-0.267168\pi\) | ||||
0.667959 | + | 0.744198i | \(0.267168\pi\) | |||||||
\(258\) | −11.6807 | −0.727206 | ||||||||
\(259\) | 8.74055 | 0.543111 | ||||||||
\(260\) | 4.13537 | 0.256465 | ||||||||
\(261\) | −2.45511 | −0.151967 | ||||||||
\(262\) | 15.7252 | 0.971508 | ||||||||
\(263\) | 30.3270 | 1.87004 | 0.935022 | − | 0.354590i | \(-0.115380\pi\) | ||||
0.935022 | + | 0.354590i | \(0.115380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.63506 | −0.100441 | ||||||||
\(266\) | 21.8093 | 1.33721 | ||||||||
\(267\) | 13.5800 | 0.831080 | ||||||||
\(268\) | 13.0517 | 0.797260 | ||||||||
\(269\) | −10.5796 | −0.645048 | −0.322524 | − | 0.946561i | \(-0.604531\pi\) | ||||
−0.322524 | + | 0.946561i | \(0.604531\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −0.825542 | −0.0501481 | −0.0250740 | − | 0.999686i | \(-0.507982\pi\) | ||||
−0.0250740 | + | 0.999686i | \(0.507982\pi\) | |||||||
\(272\) | −5.97245 | −0.362133 | ||||||||
\(273\) | 16.8440 | 1.01944 | ||||||||
\(274\) | −3.74628 | −0.226321 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.33676 | 0.200849 | ||||||||
\(277\) | −26.7321 | −1.60618 | −0.803089 | − | 0.595859i | \(-0.796812\pi\) | ||||
−0.803089 | + | 0.595859i | \(0.796812\pi\) | |||||||
\(278\) | −13.7473 | −0.824508 | ||||||||
\(279\) | −4.92724 | −0.294986 | ||||||||
\(280\) | 4.07314 | 0.243417 | ||||||||
\(281\) | −6.94427 | −0.414261 | −0.207130 | − | 0.978313i | \(-0.566412\pi\) | ||||
−0.207130 | + | 0.978313i | \(0.566412\pi\) | |||||||
\(282\) | −4.01091 | −0.238846 | ||||||||
\(283\) | 5.57895 | 0.331634 | 0.165817 | − | 0.986157i | \(-0.446974\pi\) | ||||
0.165817 | + | 0.986157i | \(0.446974\pi\) | |||||||
\(284\) | −13.1810 | −0.782146 | ||||||||
\(285\) | 5.35441 | 0.317168 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.9512 | −1.70893 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 18.6701 | 1.09824 | ||||||||
\(290\) | −2.45511 | −0.144169 | ||||||||
\(291\) | 8.43808 | 0.494649 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | −7.87175 | −0.459873 | −0.229936 | − | 0.973206i | \(-0.573852\pi\) | ||||
−0.229936 | + | 0.973206i | \(0.573852\pi\) | |||||||
\(294\) | 9.59048 | 0.559328 | ||||||||
\(295\) | −6.56293 | −0.382108 | ||||||||
\(296\) | 2.14590 | 0.124728 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.02755 | −0.349167 | ||||||||
\(299\) | 13.7988 | 0.798003 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −47.5769 | −2.74229 | ||||||||
\(302\) | 14.8551 | 0.854816 | ||||||||
\(303\) | −1.97245 | −0.113314 | ||||||||
\(304\) | 5.35441 | 0.307097 | ||||||||
\(305\) | 4.14628 | 0.237415 | ||||||||
\(306\) | −5.97245 | −0.341422 | ||||||||
\(307\) | 20.5463 | 1.17264 | 0.586319 | − | 0.810080i | \(-0.300576\pi\) | ||||
0.586319 | + | 0.810080i | \(0.300576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.35441 | 0.532154 | ||||||||
\(310\) | −4.92724 | −0.279849 | ||||||||
\(311\) | 12.8198 | 0.726945 | 0.363472 | − | 0.931605i | \(-0.381591\pi\) | ||||
0.363472 | + | 0.931605i | \(0.381591\pi\) | |||||||
\(312\) | 4.13537 | 0.234119 | ||||||||
\(313\) | −1.36053 | −0.0769019 | −0.0384509 | − | 0.999260i | \(-0.512242\pi\) | ||||
−0.0384509 | + | 0.999260i | \(0.512242\pi\) | |||||||
\(314\) | −4.45133 | −0.251203 | ||||||||
\(315\) | 4.07314 | 0.229496 | ||||||||
\(316\) | 4.97182 | 0.279687 | ||||||||
\(317\) | −25.1197 | −1.41087 | −0.705433 | − | 0.708777i | \(-0.749247\pi\) | ||||
−0.705433 | + | 0.708777i | \(0.749247\pi\) | |||||||
\(318\) | −1.63506 | −0.0916898 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −8.34767 | −0.465922 | ||||||||
\(322\) | 13.5911 | 0.757403 | ||||||||
\(323\) | −31.9790 | −1.77936 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.13537 | 0.229389 | ||||||||
\(326\) | −18.2991 | −1.01349 | ||||||||
\(327\) | −14.4721 | −0.800311 | ||||||||
\(328\) | −7.10782 | −0.392464 | ||||||||
\(329\) | −16.3370 | −0.900688 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.64683 | 0.255413 | 0.127706 | − | 0.991812i | \(-0.459238\pi\) | ||||
0.127706 | + | 0.991812i | \(0.459238\pi\) | |||||||
\(332\) | −10.4721 | −0.574733 | ||||||||
\(333\) | 2.14590 | 0.117594 | ||||||||
\(334\) | −12.9552 | −0.708876 | ||||||||
\(335\) | 13.0517 | 0.713091 | ||||||||
\(336\) | 4.07314 | 0.222208 | ||||||||
\(337\) | 19.3613 | 1.05468 | 0.527339 | − | 0.849655i | \(-0.323190\pi\) | ||||
0.527339 | + | 0.849655i | \(0.323190\pi\) | |||||||
\(338\) | 4.10132 | 0.223082 | ||||||||
\(339\) | 13.0735 | 0.710056 | ||||||||
\(340\) | −5.97245 | −0.323901 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.35441 | 0.289534 | ||||||||
\(343\) | 10.5514 | 0.569722 | ||||||||
\(344\) | −11.6807 | −0.629779 | ||||||||
\(345\) | 3.33676 | 0.179645 | ||||||||
\(346\) | 10.3439 | 0.556091 | ||||||||
\(347\) | 28.0150 | 1.50393 | 0.751963 | − | 0.659206i | \(-0.229107\pi\) | ||||
0.751963 | + | 0.659206i | \(0.229107\pi\) | |||||||
\(348\) | −2.45511 | −0.131608 | ||||||||
\(349\) | −25.7300 | −1.37730 | −0.688648 | − | 0.725096i | \(-0.741796\pi\) | ||||
−0.688648 | + | 0.725096i | \(0.741796\pi\) | |||||||
\(350\) | 4.07314 | 0.217719 | ||||||||
\(351\) | 4.13537 | 0.220730 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.66702 | −0.354850 | −0.177425 | − | 0.984134i | \(-0.556777\pi\) | ||||
−0.177425 | + | 0.984134i | \(0.556777\pi\) | |||||||
\(354\) | −6.56293 | −0.348816 | ||||||||
\(355\) | −13.1810 | −0.699573 | ||||||||
\(356\) | 13.5800 | 0.719736 | ||||||||
\(357\) | −24.3266 | −1.28750 | ||||||||
\(358\) | 4.88816 | 0.258347 | ||||||||
\(359\) | −8.83329 | −0.466203 | −0.233102 | − | 0.972452i | \(-0.574887\pi\) | ||||
−0.233102 | + | 0.972452i | \(0.574887\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 9.66974 | 0.508934 | ||||||||
\(362\) | −8.00000 | −0.420471 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.8440 | 0.882864 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 4.14628 | 0.216730 | ||||||||
\(367\) | 12.0341 | 0.628173 | 0.314086 | − | 0.949394i | \(-0.398302\pi\) | ||||
0.314086 | + | 0.949394i | \(0.398302\pi\) | |||||||
\(368\) | 3.33676 | 0.173941 | ||||||||
\(369\) | −7.10782 | −0.370018 | ||||||||
\(370\) | 2.14590 | 0.111560 | ||||||||
\(371\) | −6.65984 | −0.345762 | ||||||||
\(372\) | −4.92724 | −0.255466 | ||||||||
\(373\) | −31.8273 | −1.64796 | −0.823978 | − | 0.566622i | \(-0.808250\pi\) | ||||
−0.823978 | + | 0.566622i | \(0.808250\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −4.01091 | −0.206847 | ||||||||
\(377\) | −10.1528 | −0.522895 | ||||||||
\(378\) | 4.07314 | 0.209500 | ||||||||
\(379\) | −15.6153 | −0.802102 | −0.401051 | − | 0.916056i | \(-0.631355\pi\) | ||||
−0.401051 | + | 0.916056i | \(0.631355\pi\) | |||||||
\(380\) | 5.35441 | 0.274676 | ||||||||
\(381\) | −19.5007 | −0.999051 | ||||||||
\(382\) | 24.0701 | 1.23153 | ||||||||
\(383\) | −0.346664 | −0.0177137 | −0.00885684 | − | 0.999961i | \(-0.502819\pi\) | ||||
−0.00885684 | + | 0.999961i | \(0.502819\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.1116 | −0.769160 | ||||||||
\(387\) | −11.6807 | −0.593761 | ||||||||
\(388\) | 8.43808 | 0.428379 | ||||||||
\(389\) | −1.93714 | −0.0982171 | −0.0491086 | − | 0.998793i | \(-0.515638\pi\) | ||||
−0.0491086 | + | 0.998793i | \(0.515638\pi\) | |||||||
\(390\) | 4.13537 | 0.209403 | ||||||||
\(391\) | −19.9286 | −1.00783 | ||||||||
\(392\) | 9.59048 | 0.484392 | ||||||||
\(393\) | 15.7252 | 0.793233 | ||||||||
\(394\) | 17.0515 | 0.859041 | ||||||||
\(395\) | 4.97182 | 0.250160 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.9205 | 1.55186 | 0.775928 | − | 0.630822i | \(-0.217282\pi\) | ||||
0.775928 | + | 0.630822i | \(0.217282\pi\) | |||||||
\(398\) | 5.40990 | 0.271174 | ||||||||
\(399\) | 21.8093 | 1.09183 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 32.1885 | 1.60742 | 0.803708 | − | 0.595024i | \(-0.202858\pi\) | ||||
0.803708 | + | 0.595024i | \(0.202858\pi\) | |||||||
\(402\) | 13.0517 | 0.650960 | ||||||||
\(403\) | −20.3760 | −1.01500 | ||||||||
\(404\) | −1.97245 | −0.0981329 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.0000 | −0.496292 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.97245 | −0.295680 | ||||||||
\(409\) | −5.39249 | −0.266641 | −0.133321 | − | 0.991073i | \(-0.542564\pi\) | ||||
−0.133321 | + | 0.991073i | \(0.542564\pi\) | |||||||
\(410\) | −7.10782 | −0.351030 | ||||||||
\(411\) | −3.74628 | −0.184790 | ||||||||
\(412\) | 9.35441 | 0.460859 | ||||||||
\(413\) | −26.7317 | −1.31538 | ||||||||
\(414\) | 3.33676 | 0.163993 | ||||||||
\(415\) | −10.4721 | −0.514057 | ||||||||
\(416\) | 4.13537 | 0.202753 | ||||||||
\(417\) | −13.7473 | −0.673208 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.67453 | 0.277219 | 0.138610 | − | 0.990347i | \(-0.455737\pi\) | ||||
0.138610 | + | 0.990347i | \(0.455737\pi\) | |||||||
\(420\) | 4.07314 | 0.198749 | ||||||||
\(421\) | −7.43870 | −0.362540 | −0.181270 | − | 0.983433i | \(-0.558021\pi\) | ||||
−0.181270 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(422\) | 25.8545 | 1.25858 | ||||||||
\(423\) | −4.01091 | −0.195017 | ||||||||
\(424\) | −1.63506 | −0.0794057 | ||||||||
\(425\) | −5.97245 | −0.289706 | ||||||||
\(426\) | −13.1810 | −0.638620 | ||||||||
\(427\) | 16.8884 | 0.817287 | ||||||||
\(428\) | −8.34767 | −0.403500 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.6807 | −0.563291 | ||||||||
\(431\) | 29.1599 | 1.40458 | 0.702292 | − | 0.711889i | \(-0.252160\pi\) | ||||
0.702292 | + | 0.711889i | \(0.252160\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 23.0918 | 1.10972 | 0.554861 | − | 0.831943i | \(-0.312772\pi\) | ||||
0.554861 | + | 0.831943i | \(0.312772\pi\) | |||||||
\(434\) | −20.0694 | −0.963360 | ||||||||
\(435\) | −2.45511 | −0.117713 | ||||||||
\(436\) | −14.4721 | −0.693090 | ||||||||
\(437\) | 17.8664 | 0.854666 | ||||||||
\(438\) | −6.00000 | −0.286691 | ||||||||
\(439\) | −37.6709 | −1.79793 | −0.898967 | − | 0.438017i | \(-0.855681\pi\) | ||||
−0.898967 | + | 0.438017i | \(0.855681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.59048 | 0.456690 | ||||||||
\(442\) | −24.6983 | −1.17478 | ||||||||
\(443\) | −16.9796 | −0.806724 | −0.403362 | − | 0.915041i | \(-0.632158\pi\) | ||||
−0.403362 | + | 0.915041i | \(0.632158\pi\) | |||||||
\(444\) | 2.14590 | 0.101840 | ||||||||
\(445\) | 13.5800 | 0.643752 | ||||||||
\(446\) | −9.74729 | −0.461547 | ||||||||
\(447\) | −6.02755 | −0.285093 | ||||||||
\(448\) | 4.07314 | 0.192438 | ||||||||
\(449\) | −7.13877 | −0.336899 | −0.168450 | − | 0.985710i | \(-0.553876\pi\) | ||||
−0.168450 | + | 0.985710i | \(0.553876\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.0735 | 0.614927 | ||||||||
\(453\) | 14.8551 | 0.697954 | ||||||||
\(454\) | −19.1599 | −0.899219 | ||||||||
\(455\) | 16.8440 | 0.789657 | ||||||||
\(456\) | 5.35441 | 0.250743 | ||||||||
\(457\) | 16.3266 | 0.763727 | 0.381864 | − | 0.924219i | \(-0.375282\pi\) | ||||
0.381864 | + | 0.924219i | \(0.375282\pi\) | |||||||
\(458\) | 19.2028 | 0.897287 | ||||||||
\(459\) | −5.97245 | −0.278770 | ||||||||
\(460\) | 3.33676 | 0.155577 | ||||||||
\(461\) | −22.0636 | −1.02761 | −0.513803 | − | 0.857908i | \(-0.671764\pi\) | ||||
−0.513803 | + | 0.857908i | \(0.671764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.7592 | −1.10418 | −0.552092 | − | 0.833783i | \(-0.686170\pi\) | ||||
−0.552092 | + | 0.833783i | \(0.686170\pi\) | |||||||
\(464\) | −2.45511 | −0.113976 | ||||||||
\(465\) | −4.92724 | −0.228495 | ||||||||
\(466\) | 5.83746 | 0.270415 | ||||||||
\(467\) | −2.59785 | −0.120214 | −0.0601070 | − | 0.998192i | \(-0.519144\pi\) | ||||
−0.0601070 | + | 0.998192i | \(0.519144\pi\) | |||||||
\(468\) | 4.13537 | 0.191158 | ||||||||
\(469\) | 53.1615 | 2.45477 | ||||||||
\(470\) | −4.01091 | −0.185009 | ||||||||
\(471\) | −4.45133 | −0.205106 | ||||||||
\(472\) | −6.56293 | −0.302083 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.97182 | 0.228363 | ||||||||
\(475\) | 5.35441 | 0.245677 | ||||||||
\(476\) | −24.3266 | −1.11501 | ||||||||
\(477\) | −1.63506 | −0.0748644 | ||||||||
\(478\) | −15.1246 | −0.691784 | ||||||||
\(479\) | −17.4382 | −0.796773 | −0.398386 | − | 0.917218i | \(-0.630430\pi\) | ||||
−0.398386 | + | 0.917218i | \(0.630430\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 8.87409 | 0.404624 | ||||||||
\(482\) | 20.4902 | 0.933302 | ||||||||
\(483\) | 13.5911 | 0.618417 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.43808 | 0.383153 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.4734 | 0.927737 | 0.463869 | − | 0.885904i | \(-0.346461\pi\) | ||||
0.463869 | + | 0.885904i | \(0.346461\pi\) | |||||||
\(488\) | 4.14628 | 0.187693 | ||||||||
\(489\) | −18.2991 | −0.827513 | ||||||||
\(490\) | 9.59048 | 0.433254 | ||||||||
\(491\) | −4.92112 | −0.222087 | −0.111044 | − | 0.993816i | \(-0.535419\pi\) | ||||
−0.111044 | + | 0.993816i | \(0.535419\pi\) | |||||||
\(492\) | −7.10782 | −0.320445 | ||||||||
\(493\) | 14.6630 | 0.660388 | ||||||||
\(494\) | 22.1425 | 0.996238 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.92724 | −0.221240 | ||||||||
\(497\) | −53.6879 | −2.40823 | ||||||||
\(498\) | −10.4721 | −0.469268 | ||||||||
\(499\) | −26.1766 | −1.17182 | −0.585912 | − | 0.810375i | \(-0.699264\pi\) | ||||
−0.585912 | + | 0.810375i | \(0.699264\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −12.9552 | −0.578795 | ||||||||
\(502\) | 14.6300 | 0.652967 | ||||||||
\(503\) | −8.89931 | −0.396800 | −0.198400 | − | 0.980121i | \(-0.563575\pi\) | ||||
−0.198400 | + | 0.980121i | \(0.563575\pi\) | |||||||
\(504\) | 4.07314 | 0.181432 | ||||||||
\(505\) | −1.97245 | −0.0877728 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.10132 | 0.182146 | ||||||||
\(508\) | −19.5007 | −0.865203 | ||||||||
\(509\) | 15.7605 | 0.698573 | 0.349287 | − | 0.937016i | \(-0.386424\pi\) | ||||
0.349287 | + | 0.937016i | \(0.386424\pi\) | |||||||
\(510\) | −5.97245 | −0.264464 | ||||||||
\(511\) | −24.4388 | −1.08111 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.35441 | 0.236403 | ||||||||
\(514\) | 21.4164 | 0.944637 | ||||||||
\(515\) | 9.35441 | 0.412205 | ||||||||
\(516\) | −11.6807 | −0.514212 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.74055 | 0.384038 | ||||||||
\(519\) | 10.3439 | 0.454046 | ||||||||
\(520\) | 4.13537 | 0.181348 | ||||||||
\(521\) | −32.7269 | −1.43379 | −0.716895 | − | 0.697181i | \(-0.754437\pi\) | ||||
−0.716895 | + | 0.697181i | \(0.754437\pi\) | |||||||
\(522\) | −2.45511 | −0.107457 | ||||||||
\(523\) | 17.0224 | 0.744339 | 0.372170 | − | 0.928165i | \(-0.378614\pi\) | ||||
0.372170 | + | 0.928165i | \(0.378614\pi\) | |||||||
\(524\) | 15.7252 | 0.686960 | ||||||||
\(525\) | 4.07314 | 0.177766 | ||||||||
\(526\) | 30.3270 | 1.32232 | ||||||||
\(527\) | 29.4277 | 1.28189 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.8660 | −0.515914 | ||||||||
\(530\) | −1.63506 | −0.0710226 | ||||||||
\(531\) | −6.56293 | −0.284807 | ||||||||
\(532\) | 21.8093 | 0.945552 | ||||||||
\(533\) | −29.3935 | −1.27317 | ||||||||
\(534\) | 13.5800 | 0.587662 | ||||||||
\(535\) | −8.34767 | −0.360901 | ||||||||
\(536\) | 13.0517 | 0.563748 | ||||||||
\(537\) | 4.88816 | 0.210940 | ||||||||
\(538\) | −10.5796 | −0.456118 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −16.4864 | −0.708805 | −0.354403 | − | 0.935093i | \(-0.615316\pi\) | ||||
−0.354403 | + | 0.935093i | \(0.615316\pi\) | |||||||
\(542\) | −0.825542 | −0.0354601 | ||||||||
\(543\) | −8.00000 | −0.343313 | ||||||||
\(544\) | −5.97245 | −0.256067 | ||||||||
\(545\) | −14.4721 | −0.619918 | ||||||||
\(546\) | 16.8440 | 0.720855 | ||||||||
\(547\) | −9.60124 | −0.410520 | −0.205260 | − | 0.978708i | \(-0.565804\pi\) | ||||
−0.205260 | + | 0.978708i | \(0.565804\pi\) | |||||||
\(548\) | −3.74628 | −0.160033 | ||||||||
\(549\) | 4.14628 | 0.176959 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.1457 | −0.560024 | ||||||||
\(552\) | 3.33676 | 0.142022 | ||||||||
\(553\) | 20.2509 | 0.861158 | ||||||||
\(554\) | −26.7321 | −1.13574 | ||||||||
\(555\) | 2.14590 | 0.0910883 | ||||||||
\(556\) | −13.7473 | −0.583015 | ||||||||
\(557\) | 26.3891 | 1.11814 | 0.559071 | − | 0.829120i | \(-0.311158\pi\) | ||||
0.559071 | + | 0.829120i | \(0.311158\pi\) | |||||||
\(558\) | −4.92724 | −0.208587 | ||||||||
\(559\) | −48.3039 | −2.04304 | ||||||||
\(560\) | 4.07314 | 0.172122 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.94427 | −0.292926 | ||||||||
\(563\) | −37.7994 | −1.59305 | −0.796527 | − | 0.604603i | \(-0.793332\pi\) | ||||
−0.796527 | + | 0.604603i | \(0.793332\pi\) | |||||||
\(564\) | −4.01091 | −0.168890 | ||||||||
\(565\) | 13.0735 | 0.550007 | ||||||||
\(566\) | 5.57895 | 0.234501 | ||||||||
\(567\) | 4.07314 | 0.171056 | ||||||||
\(568\) | −13.1810 | −0.553061 | ||||||||
\(569\) | −2.43305 | −0.101999 | −0.0509994 | − | 0.998699i | \(-0.516241\pi\) | ||||
−0.0509994 | + | 0.998699i | \(0.516241\pi\) | |||||||
\(570\) | 5.35441 | 0.224272 | ||||||||
\(571\) | −24.7058 | −1.03391 | −0.516953 | − | 0.856014i | \(-0.672934\pi\) | ||||
−0.516953 | + | 0.856014i | \(0.672934\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0701 | 1.00554 | ||||||||
\(574\) | −28.9512 | −1.20840 | ||||||||
\(575\) | 3.33676 | 0.139153 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −24.5082 | −1.02029 | −0.510145 | − | 0.860088i | \(-0.670408\pi\) | ||||
−0.510145 | + | 0.860088i | \(0.670408\pi\) | |||||||
\(578\) | 18.6701 | 0.776575 | ||||||||
\(579\) | −15.1116 | −0.628017 | ||||||||
\(580\) | −2.45511 | −0.101943 | ||||||||
\(581\) | −42.6545 | −1.76961 | ||||||||
\(582\) | 8.43808 | 0.349770 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 4.13537 | 0.170977 | ||||||||
\(586\) | −7.87175 | −0.325179 | ||||||||
\(587\) | −11.8768 | −0.490207 | −0.245104 | − | 0.969497i | \(-0.578822\pi\) | ||||
−0.245104 | + | 0.969497i | \(0.578822\pi\) | |||||||
\(588\) | 9.59048 | 0.395505 | ||||||||
\(589\) | −26.3825 | −1.08707 | ||||||||
\(590\) | −6.56293 | −0.270191 | ||||||||
\(591\) | 17.0515 | 0.701404 | ||||||||
\(592\) | 2.14590 | 0.0881959 | ||||||||
\(593\) | −11.2190 | −0.460711 | −0.230355 | − | 0.973107i | \(-0.573989\pi\) | ||||
−0.230355 | + | 0.973107i | \(0.573989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.3266 | −0.997294 | ||||||||
\(596\) | −6.02755 | −0.246898 | ||||||||
\(597\) | 5.40990 | 0.221413 | ||||||||
\(598\) | 13.7988 | 0.564273 | ||||||||
\(599\) | 6.34011 | 0.259050 | 0.129525 | − | 0.991576i | \(-0.458655\pi\) | ||||
0.129525 | + | 0.991576i | \(0.458655\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −23.6054 | −0.962883 | −0.481441 | − | 0.876478i | \(-0.659887\pi\) | ||||
−0.481441 | + | 0.876478i | \(0.659887\pi\) | |||||||
\(602\) | −47.5769 | −1.93909 | ||||||||
\(603\) | 13.0517 | 0.531507 | ||||||||
\(604\) | 14.8551 | 0.604446 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.97245 | −0.0801252 | ||||||||
\(607\) | −8.08916 | −0.328329 | −0.164164 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164164 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(608\) | 5.35441 | 0.217150 | ||||||||
\(609\) | −10.0000 | −0.405220 | ||||||||
\(610\) | 4.14628 | 0.167878 | ||||||||
\(611\) | −16.5866 | −0.671022 | ||||||||
\(612\) | −5.97245 | −0.241422 | ||||||||
\(613\) | 21.1675 | 0.854946 | 0.427473 | − | 0.904028i | \(-0.359404\pi\) | ||||
0.427473 | + | 0.904028i | \(0.359404\pi\) | |||||||
\(614\) | 20.5463 | 0.829181 | ||||||||
\(615\) | −7.10782 | −0.286615 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2579 | −0.533742 | −0.266871 | − | 0.963732i | \(-0.585990\pi\) | ||||
−0.266871 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(618\) | 9.35441 | 0.376290 | ||||||||
\(619\) | −9.73537 | −0.391298 | −0.195649 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195649 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(620\) | −4.92724 | −0.197883 | ||||||||
\(621\) | 3.33676 | 0.133900 | ||||||||
\(622\) | 12.8198 | 0.514027 | ||||||||
\(623\) | 55.3131 | 2.21607 | ||||||||
\(624\) | 4.13537 | 0.165547 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.36053 | −0.0543778 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.45133 | −0.177627 | ||||||||
\(629\) | −12.8163 | −0.511018 | ||||||||
\(630\) | 4.07314 | 0.162278 | ||||||||
\(631\) | −21.4545 | −0.854090 | −0.427045 | − | 0.904230i | \(-0.640445\pi\) | ||||
−0.427045 | + | 0.904230i | \(0.640445\pi\) | |||||||
\(632\) | 4.97182 | 0.197769 | ||||||||
\(633\) | 25.8545 | 1.02762 | ||||||||
\(634\) | −25.1197 | −0.997632 | ||||||||
\(635\) | −19.5007 | −0.773862 | ||||||||
\(636\) | −1.63506 | −0.0648344 | ||||||||
\(637\) | 39.6602 | 1.57140 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.1810 | −0.521431 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.1315 | −1.54560 | −0.772801 | − | 0.634649i | \(-0.781145\pi\) | ||||
−0.772801 | + | 0.634649i | \(0.781145\pi\) | |||||||
\(642\) | −8.34767 | −0.329456 | ||||||||
\(643\) | 44.8729 | 1.76961 | 0.884807 | − | 0.465957i | \(-0.154290\pi\) | ||||
0.884807 | + | 0.465957i | \(0.154290\pi\) | |||||||
\(644\) | 13.5911 | 0.535565 | ||||||||
\(645\) | −11.6807 | −0.459925 | ||||||||
\(646\) | −31.9790 | −1.25820 | ||||||||
\(647\) | 10.3752 | 0.407892 | 0.203946 | − | 0.978982i | \(-0.434623\pi\) | ||||
0.203946 | + | 0.978982i | \(0.434623\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.13537 | 0.162203 | ||||||||
\(651\) | −20.0694 | −0.786580 | ||||||||
\(652\) | −18.2991 | −0.716647 | ||||||||
\(653\) | −37.2988 | −1.45962 | −0.729808 | − | 0.683652i | \(-0.760391\pi\) | ||||
−0.729808 | + | 0.683652i | \(0.760391\pi\) | |||||||
\(654\) | −14.4721 | −0.565905 | ||||||||
\(655\) | 15.7252 | 0.614436 | ||||||||
\(656\) | −7.10782 | −0.277514 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −16.3370 | −0.636883 | ||||||||
\(659\) | 2.58058 | 0.100525 | 0.0502626 | − | 0.998736i | \(-0.483994\pi\) | ||||
0.0502626 | + | 0.998736i | \(0.483994\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.146283 | −0.00568975 | −0.00284487 | − | 0.999996i | \(-0.500906\pi\) | ||||
−0.00284487 | + | 0.999996i | \(0.500906\pi\) | |||||||
\(662\) | 4.64683 | 0.180604 | ||||||||
\(663\) | −24.6983 | −0.959203 | ||||||||
\(664\) | −10.4721 | −0.406398 | ||||||||
\(665\) | 21.8093 | 0.845728 | ||||||||
\(666\) | 2.14590 | 0.0831519 | ||||||||
\(667\) | −8.19211 | −0.317200 | ||||||||
\(668\) | −12.9552 | −0.501251 | ||||||||
\(669\) | −9.74729 | −0.376852 | ||||||||
\(670\) | 13.0517 | 0.504231 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.07314 | 0.157125 | ||||||||
\(673\) | −5.21502 | −0.201024 | −0.100512 | − | 0.994936i | \(-0.532048\pi\) | ||||
−0.100512 | + | 0.994936i | \(0.532048\pi\) | |||||||
\(674\) | 19.3613 | 0.745770 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 4.10132 | 0.157743 | ||||||||
\(677\) | −28.8694 | −1.10954 | −0.554770 | − | 0.832004i | \(-0.687194\pi\) | ||||
−0.554770 | + | 0.832004i | \(0.687194\pi\) | |||||||
\(678\) | 13.0735 | 0.502086 | ||||||||
\(679\) | 34.3695 | 1.31898 | ||||||||
\(680\) | −5.97245 | −0.229033 | ||||||||
\(681\) | −19.1599 | −0.734210 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.40479 | 0.245073 | 0.122536 | − | 0.992464i | \(-0.460897\pi\) | ||||
0.122536 | + | 0.992464i | \(0.460897\pi\) | |||||||
\(684\) | 5.35441 | 0.204731 | ||||||||
\(685\) | −3.74628 | −0.143138 | ||||||||
\(686\) | 10.5514 | 0.402854 | ||||||||
\(687\) | 19.2028 | 0.732632 | ||||||||
\(688\) | −11.6807 | −0.445321 | ||||||||
\(689\) | −6.76159 | −0.257596 | ||||||||
\(690\) | 3.33676 | 0.127028 | ||||||||
\(691\) | 19.1515 | 0.728556 | 0.364278 | − | 0.931290i | \(-0.381316\pi\) | ||||
0.364278 | + | 0.931290i | \(0.381316\pi\) | |||||||
\(692\) | 10.3439 | 0.393216 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0150 | 1.06344 | ||||||||
\(695\) | −13.7473 | −0.521464 | ||||||||
\(696\) | −2.45511 | −0.0930606 | ||||||||
\(697\) | 42.4511 | 1.60795 | ||||||||
\(698\) | −25.7300 | −0.973896 | ||||||||
\(699\) | 5.83746 | 0.220793 | ||||||||
\(700\) | 4.07314 | 0.153950 | ||||||||
\(701\) | 39.8810 | 1.50628 | 0.753142 | − | 0.657858i | \(-0.228537\pi\) | ||||
0.753142 | + | 0.657858i | \(0.228537\pi\) | |||||||
\(702\) | 4.13537 | 0.156080 | ||||||||
\(703\) | 11.4900 | 0.433355 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.01091 | −0.151060 | ||||||||
\(706\) | −6.66702 | −0.250917 | ||||||||
\(707\) | −8.03406 | −0.302152 | ||||||||
\(708\) | −6.56293 | −0.246650 | ||||||||
\(709\) | 18.0361 | 0.677359 | 0.338679 | − | 0.940902i | \(-0.390020\pi\) | ||||
0.338679 | + | 0.940902i | \(0.390020\pi\) | |||||||
\(710\) | −13.1810 | −0.494673 | ||||||||
\(711\) | 4.97182 | 0.186458 | ||||||||
\(712\) | 13.5800 | 0.508930 | ||||||||
\(713\) | −16.4410 | −0.615722 | ||||||||
\(714\) | −24.3266 | −0.910401 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.88816 | 0.182679 | ||||||||
\(717\) | −15.1246 | −0.564839 | ||||||||
\(718\) | −8.83329 | −0.329656 | ||||||||
\(719\) | −7.58297 | −0.282797 | −0.141399 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141399 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 38.1018 | 1.41899 | ||||||||
\(722\) | 9.66974 | 0.359871 | ||||||||
\(723\) | 20.4902 | 0.762038 | ||||||||
\(724\) | −8.00000 | −0.297318 | ||||||||
\(725\) | −2.45511 | −0.0911804 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.9840 | 1.03787 | 0.518934 | − | 0.854814i | \(-0.326329\pi\) | ||||
0.518934 | + | 0.854814i | \(0.326329\pi\) | |||||||
\(728\) | 16.8440 | 0.624279 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 69.7621 | 2.58024 | ||||||||
\(732\) | 4.14628 | 0.153251 | ||||||||
\(733\) | 13.7223 | 0.506844 | 0.253422 | − | 0.967356i | \(-0.418444\pi\) | ||||
0.253422 | + | 0.967356i | \(0.418444\pi\) | |||||||
\(734\) | 12.0341 | 0.444185 | ||||||||
\(735\) | 9.59048 | 0.353750 | ||||||||
\(736\) | 3.33676 | 0.122995 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −7.10782 | −0.261643 | ||||||||
\(739\) | 46.6495 | 1.71603 | 0.858014 | − | 0.513626i | \(-0.171698\pi\) | ||||
0.858014 | + | 0.513626i | \(0.171698\pi\) | |||||||
\(740\) | 2.14590 | 0.0788848 | ||||||||
\(741\) | 22.1425 | 0.813425 | ||||||||
\(742\) | −6.65984 | −0.244490 | ||||||||
\(743\) | −26.3399 | −0.966316 | −0.483158 | − | 0.875533i | \(-0.660510\pi\) | ||||
−0.483158 | + | 0.875533i | \(0.660510\pi\) | |||||||
\(744\) | −4.92724 | −0.180642 | ||||||||
\(745\) | −6.02755 | −0.220832 | ||||||||
\(746\) | −31.8273 | −1.16528 | ||||||||
\(747\) | −10.4721 | −0.383155 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.0012 | −1.24238 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 4.47864 | 0.163428 | 0.0817140 | − | 0.996656i | \(-0.473961\pi\) | ||||
0.0817140 | + | 0.996656i | \(0.473961\pi\) | |||||||
\(752\) | −4.01091 | −0.146263 | ||||||||
\(753\) | 14.6300 | 0.533145 | ||||||||
\(754\) | −10.1528 | −0.369743 | ||||||||
\(755\) | 14.8551 | 0.540633 | ||||||||
\(756\) | 4.07314 | 0.148139 | ||||||||
\(757\) | 19.1027 | 0.694300 | 0.347150 | − | 0.937810i | \(-0.387150\pi\) | ||||
0.347150 | + | 0.937810i | \(0.387150\pi\) | |||||||
\(758\) | −15.6153 | −0.567172 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.35441 | 0.194225 | ||||||||
\(761\) | −2.98637 | −0.108256 | −0.0541279 | − | 0.998534i | \(-0.517238\pi\) | ||||
−0.0541279 | + | 0.998534i | \(0.517238\pi\) | |||||||
\(762\) | −19.5007 | −0.706436 | ||||||||
\(763\) | −58.9471 | −2.13403 | ||||||||
\(764\) | 24.0701 | 0.870827 | ||||||||
\(765\) | −5.97245 | −0.215934 | ||||||||
\(766\) | −0.346664 | −0.0125255 | ||||||||
\(767\) | −27.1402 | −0.979975 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −13.9222 | −0.502048 | −0.251024 | − | 0.967981i | \(-0.580767\pi\) | ||||
−0.251024 | + | 0.967981i | \(0.580767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.4164 | 0.771293 | ||||||||
\(772\) | −15.1116 | −0.543878 | ||||||||
\(773\) | −6.00378 | −0.215941 | −0.107971 | − | 0.994154i | \(-0.534435\pi\) | ||||
−0.107971 | + | 0.994154i | \(0.534435\pi\) | |||||||
\(774\) | −11.6807 | −0.419852 | ||||||||
\(775\) | −4.92724 | −0.176992 | ||||||||
\(776\) | 8.43808 | 0.302909 | ||||||||
\(777\) | 8.74055 | 0.313565 | ||||||||
\(778\) | −1.93714 | −0.0694500 | ||||||||
\(779\) | −38.0582 | −1.36358 | ||||||||
\(780\) | 4.13537 | 0.148070 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −19.9286 | −0.712647 | ||||||||
\(783\) | −2.45511 | −0.0877384 | ||||||||
\(784\) | 9.59048 | 0.342517 | ||||||||
\(785\) | −4.45133 | −0.158875 | ||||||||
\(786\) | 15.7252 | 0.560900 | ||||||||
\(787\) | 37.5915 | 1.33999 | 0.669996 | − | 0.742365i | \(-0.266296\pi\) | ||||
0.669996 | + | 0.742365i | \(0.266296\pi\) | |||||||
\(788\) | 17.0515 | 0.607433 | ||||||||
\(789\) | 30.3270 | 1.07967 | ||||||||
\(790\) | 4.97182 | 0.176890 | ||||||||
\(791\) | 53.2503 | 1.89336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.1464 | 0.608888 | ||||||||
\(794\) | 30.9205 | 1.09733 | ||||||||
\(795\) | −1.63506 | −0.0579897 | ||||||||
\(796\) | 5.40990 | 0.191749 | ||||||||
\(797\) | −23.2442 | −0.823352 | −0.411676 | − | 0.911330i | \(-0.635056\pi\) | ||||
−0.411676 | + | 0.911330i | \(0.635056\pi\) | |||||||
\(798\) | 21.8093 | 0.772040 | ||||||||
\(799\) | 23.9549 | 0.847465 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 13.5800 | 0.479824 | ||||||||
\(802\) | 32.1885 | 1.13661 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 13.0517 | 0.460298 | ||||||||
\(805\) | 13.5911 | 0.479023 | ||||||||
\(806\) | −20.3760 | −0.717714 | ||||||||
\(807\) | −10.5796 | −0.372419 | ||||||||
\(808\) | −1.97245 | −0.0693905 | ||||||||
\(809\) | 18.4239 | 0.647751 | 0.323875 | − | 0.946100i | \(-0.395014\pi\) | ||||
0.323875 | + | 0.946100i | \(0.395014\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −7.93987 | −0.278806 | −0.139403 | − | 0.990236i | \(-0.544518\pi\) | ||||
−0.139403 | + | 0.990236i | \(0.544518\pi\) | |||||||
\(812\) | −10.0000 | −0.350931 | ||||||||
\(813\) | −0.825542 | −0.0289530 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.2991 | −0.640988 | ||||||||
\(816\) | −5.97245 | −0.209077 | ||||||||
\(817\) | −62.5430 | −2.18810 | ||||||||
\(818\) | −5.39249 | −0.188544 | ||||||||
\(819\) | 16.8440 | 0.588576 | ||||||||
\(820\) | −7.10782 | −0.248216 | ||||||||
\(821\) | 44.5280 | 1.55404 | 0.777019 | − | 0.629477i | \(-0.216731\pi\) | ||||
0.777019 | + | 0.629477i | \(0.216731\pi\) | |||||||
\(822\) | −3.74628 | −0.130667 | ||||||||
\(823\) | 5.97283 | 0.208200 | 0.104100 | − | 0.994567i | \(-0.466804\pi\) | ||||
0.104100 | + | 0.994567i | \(0.466804\pi\) | |||||||
\(824\) | 9.35441 | 0.325876 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.7317 | −0.930116 | ||||||||
\(827\) | 20.7865 | 0.722818 | 0.361409 | − | 0.932407i | \(-0.382296\pi\) | ||||
0.361409 | + | 0.932407i | \(0.382296\pi\) | |||||||
\(828\) | 3.33676 | 0.115960 | ||||||||
\(829\) | −32.2573 | −1.12034 | −0.560171 | − | 0.828377i | \(-0.689264\pi\) | ||||
−0.560171 | + | 0.828377i | \(0.689264\pi\) | |||||||
\(830\) | −10.4721 | −0.363493 | ||||||||
\(831\) | −26.7321 | −0.927327 | ||||||||
\(832\) | 4.13537 | 0.143368 | ||||||||
\(833\) | −57.2786 | −1.98459 | ||||||||
\(834\) | −13.7473 | −0.476030 | ||||||||
\(835\) | −12.9552 | −0.448333 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.92724 | −0.170310 | ||||||||
\(838\) | 5.67453 | 0.196023 | ||||||||
\(839\) | −42.2497 | −1.45862 | −0.729311 | − | 0.684183i | \(-0.760159\pi\) | ||||
−0.729311 | + | 0.684183i | \(0.760159\pi\) | |||||||
\(840\) | 4.07314 | 0.140537 | ||||||||
\(841\) | −22.9724 | −0.792153 | ||||||||
\(842\) | −7.43870 | −0.256355 | ||||||||
\(843\) | −6.94427 | −0.239173 | ||||||||
\(844\) | 25.8545 | 0.889948 | ||||||||
\(845\) | 4.10132 | 0.141090 | ||||||||
\(846\) | −4.01091 | −0.137898 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.63506 | −0.0561483 | ||||||||
\(849\) | 5.57895 | 0.191469 | ||||||||
\(850\) | −5.97245 | −0.204853 | ||||||||
\(851\) | 7.16035 | 0.245454 | ||||||||
\(852\) | −13.1810 | −0.451572 | ||||||||
\(853\) | 27.3214 | 0.935469 | 0.467734 | − | 0.883869i | \(-0.345070\pi\) | ||||
0.467734 | + | 0.883869i | \(0.345070\pi\) | |||||||
\(854\) | 16.8884 | 0.577909 | ||||||||
\(855\) | 5.35441 | 0.183117 | ||||||||
\(856\) | −8.34767 | −0.285318 | ||||||||
\(857\) | 32.2432 | 1.10141 | 0.550703 | − | 0.834701i | \(-0.314360\pi\) | ||||
0.550703 | + | 0.834701i | \(0.314360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.6148 | 0.805726 | 0.402863 | − | 0.915260i | \(-0.368015\pi\) | ||||
0.402863 | + | 0.915260i | \(0.368015\pi\) | |||||||
\(860\) | −11.6807 | −0.398307 | ||||||||
\(861\) | −28.9512 | −0.986653 | ||||||||
\(862\) | 29.1599 | 0.993191 | ||||||||
\(863\) | 9.45085 | 0.321711 | 0.160855 | − | 0.986978i | \(-0.448575\pi\) | ||||
0.160855 | + | 0.986978i | \(0.448575\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 10.3439 | 0.351703 | ||||||||
\(866\) | 23.0918 | 0.784691 | ||||||||
\(867\) | 18.6701 | 0.634071 | ||||||||
\(868\) | −20.0694 | −0.681198 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.45511 | −0.0832359 | ||||||||
\(871\) | 53.9737 | 1.82883 | ||||||||
\(872\) | −14.4721 | −0.490088 | ||||||||
\(873\) | 8.43808 | 0.285586 | ||||||||
\(874\) | 17.8664 | 0.604340 | ||||||||
\(875\) | 4.07314 | 0.137697 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −7.78551 | −0.262898 | −0.131449 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131449 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(878\) | −37.6709 | −1.27133 | ||||||||
\(879\) | −7.87175 | −0.265508 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.10705 | −0.0372975 | −0.0186488 | − | 0.999826i | \(-0.505936\pi\) | ||||
−0.0186488 | + | 0.999826i | \(0.505936\pi\) | |||||||
\(882\) | 9.59048 | 0.322928 | ||||||||
\(883\) | −16.6595 | −0.560635 | −0.280318 | − | 0.959907i | \(-0.590440\pi\) | ||||
−0.280318 | + | 0.959907i | \(0.590440\pi\) | |||||||
\(884\) | −24.6983 | −0.830694 | ||||||||
\(885\) | −6.56293 | −0.220610 | ||||||||
\(886\) | −16.9796 | −0.570440 | ||||||||
\(887\) | −7.34977 | −0.246781 | −0.123391 | − | 0.992358i | \(-0.539377\pi\) | ||||
−0.123391 | + | 0.992358i | \(0.539377\pi\) | |||||||
\(888\) | 2.14590 | 0.0720116 | ||||||||
\(889\) | −79.4291 | −2.66397 | ||||||||
\(890\) | 13.5800 | 0.455201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.74729 | −0.326363 | ||||||||
\(893\) | −21.4761 | −0.718669 | ||||||||
\(894\) | −6.02755 | −0.201592 | ||||||||
\(895\) | 4.88816 | 0.163393 | ||||||||
\(896\) | 4.07314 | 0.136074 | ||||||||
\(897\) | 13.7988 | 0.460727 | ||||||||
\(898\) | −7.13877 | −0.238224 | ||||||||
\(899\) | 12.0969 | 0.403455 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 9.76532 | 0.325330 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.5769 | −1.58326 | ||||||||
\(904\) | 13.0735 | 0.434819 | ||||||||
\(905\) | −8.00000 | −0.265929 | ||||||||
\(906\) | 14.8551 | 0.493528 | ||||||||
\(907\) | 57.3678 | 1.90487 | 0.952433 | − | 0.304747i | \(-0.0985719\pi\) | ||||
0.952433 | + | 0.304747i | \(0.0985719\pi\) | |||||||
\(908\) | −19.1599 | −0.635844 | ||||||||
\(909\) | −1.97245 | −0.0654219 | ||||||||
\(910\) | 16.8440 | 0.558372 | ||||||||
\(911\) | 16.1252 | 0.534253 | 0.267126 | − | 0.963661i | \(-0.413926\pi\) | ||||
0.267126 | + | 0.963661i | \(0.413926\pi\) | |||||||
\(912\) | 5.35441 | 0.177302 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.3266 | 0.540037 | ||||||||
\(915\) | 4.14628 | 0.137072 | ||||||||
\(916\) | 19.2028 | 0.634478 | ||||||||
\(917\) | 64.0511 | 2.11515 | ||||||||
\(918\) | −5.97245 | −0.197120 | ||||||||
\(919\) | 40.7506 | 1.34424 | 0.672120 | − | 0.740443i | \(-0.265384\pi\) | ||||
0.672120 | + | 0.740443i | \(0.265384\pi\) | |||||||
\(920\) | 3.33676 | 0.110010 | ||||||||
\(921\) | 20.5463 | 0.677023 | ||||||||
\(922\) | −22.0636 | −0.726627 | ||||||||
\(923\) | −54.5082 | −1.79416 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.14590 | 0.0705567 | ||||||||
\(926\) | −23.7592 | −0.780776 | ||||||||
\(927\) | 9.35441 | 0.307239 | ||||||||
\(928\) | −2.45511 | −0.0805929 | ||||||||
\(929\) | −58.3454 | −1.91425 | −0.957126 | − | 0.289673i | \(-0.906453\pi\) | ||||
−0.957126 | + | 0.289673i | \(0.906453\pi\) | |||||||
\(930\) | −4.92724 | −0.161571 | ||||||||
\(931\) | 51.3514 | 1.68297 | ||||||||
\(932\) | 5.83746 | 0.191212 | ||||||||
\(933\) | 12.8198 | 0.419702 | ||||||||
\(934\) | −2.59785 | −0.0850041 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.13537 | 0.135169 | ||||||||
\(937\) | −28.0130 | −0.915145 | −0.457573 | − | 0.889172i | \(-0.651281\pi\) | ||||
−0.457573 | + | 0.889172i | \(0.651281\pi\) | |||||||
\(938\) | 53.1615 | 1.73578 | ||||||||
\(939\) | −1.36053 | −0.0443993 | ||||||||
\(940\) | −4.01091 | −0.130821 | ||||||||
\(941\) | 13.4906 | 0.439780 | 0.219890 | − | 0.975525i | \(-0.429430\pi\) | ||||
0.219890 | + | 0.975525i | \(0.429430\pi\) | |||||||
\(942\) | −4.45133 | −0.145032 | ||||||||
\(943\) | −23.7171 | −0.772335 | ||||||||
\(944\) | −6.56293 | −0.213605 | ||||||||
\(945\) | 4.07314 | 0.132499 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.5192 | −1.18671 | −0.593357 | − | 0.804939i | \(-0.702198\pi\) | ||||
−0.593357 | + | 0.804939i | \(0.702198\pi\) | |||||||
\(948\) | 4.97182 | 0.161477 | ||||||||
\(949\) | −24.8122 | −0.805439 | ||||||||
\(950\) | 5.35441 | 0.173720 | ||||||||
\(951\) | −25.1197 | −0.814563 | ||||||||
\(952\) | −24.3266 | −0.788430 | ||||||||
\(953\) | −30.9398 | −1.00224 | −0.501119 | − | 0.865378i | \(-0.667078\pi\) | ||||
−0.501119 | + | 0.865378i | \(0.667078\pi\) | |||||||
\(954\) | −1.63506 | −0.0529371 | ||||||||
\(955\) | 24.0701 | 0.778891 | ||||||||
\(956\) | −15.1246 | −0.489165 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.4382 | −0.563404 | ||||||||
\(959\) | −15.2591 | −0.492743 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −6.72227 | −0.216847 | ||||||||
\(962\) | 8.87409 | 0.286112 | ||||||||
\(963\) | −8.34767 | −0.269000 | ||||||||
\(964\) | 20.4902 | 0.659944 | ||||||||
\(965\) | −15.1116 | −0.486460 | ||||||||
\(966\) | 13.5911 | 0.437287 | ||||||||
\(967\) | −31.3913 | −1.00947 | −0.504737 | − | 0.863273i | \(-0.668411\pi\) | ||||
−0.504737 | + | 0.863273i | \(0.668411\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.9790 | −1.02731 | ||||||||
\(970\) | 8.43808 | 0.270930 | ||||||||
\(971\) | 35.9982 | 1.15524 | 0.577619 | − | 0.816306i | \(-0.303982\pi\) | ||||
0.577619 | + | 0.816306i | \(0.303982\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −55.9947 | −1.79511 | ||||||||
\(974\) | 20.4734 | 0.656009 | ||||||||
\(975\) | 4.13537 | 0.132438 | ||||||||
\(976\) | 4.14628 | 0.132719 | ||||||||
\(977\) | 58.7239 | 1.87874 | 0.939371 | − | 0.342902i | \(-0.111410\pi\) | ||||
0.939371 | + | 0.342902i | \(0.111410\pi\) | |||||||
\(978\) | −18.2991 | −0.585140 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 9.59048 | 0.306357 | ||||||||
\(981\) | −14.4721 | −0.462060 | ||||||||
\(982\) | −4.92112 | −0.157039 | ||||||||
\(983\) | −43.9957 | −1.40325 | −0.701623 | − | 0.712548i | \(-0.747541\pi\) | ||||
−0.701623 | + | 0.712548i | \(0.747541\pi\) | |||||||
\(984\) | −7.10782 | −0.226589 | ||||||||
\(985\) | 17.0515 | 0.543305 | ||||||||
\(986\) | 14.6630 | 0.466965 | ||||||||
\(987\) | −16.3370 | −0.520012 | ||||||||
\(988\) | 22.1425 | 0.704447 | ||||||||
\(989\) | −38.9756 | −1.23935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.8969 | −1.29913 | −0.649567 | − | 0.760305i | \(-0.725050\pi\) | ||||
−0.649567 | + | 0.760305i | \(0.725050\pi\) | |||||||
\(992\) | −4.92724 | −0.156440 | ||||||||
\(993\) | 4.64683 | 0.147463 | ||||||||
\(994\) | −53.6879 | −1.70288 | ||||||||
\(995\) | 5.40990 | 0.171505 | ||||||||
\(996\) | −10.4721 | −0.331822 | ||||||||
\(997\) | 30.7616 | 0.974230 | 0.487115 | − | 0.873338i | \(-0.338049\pi\) | ||||
0.487115 | + | 0.873338i | \(0.338049\pi\) | |||||||
\(998\) | −26.1766 | −0.828604 | ||||||||
\(999\) | 2.14590 | 0.0678932 |
(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 | 3630.2.a.bt.1.4 | 4 | ||
11.3 | even | 5 | 330.2.m.e.31.1 | ✓ | 8 | ||
11.4 | even | 5 | 330.2.m.e.181.1 | yes | 8 | ||
11.10 | odd | 2 | 3630.2.a.br.1.1 | 4 | |||
33.14 | odd | 10 | 990.2.n.k.361.1 | 8 | |||
33.26 | odd | 10 | 990.2.n.k.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.e.31.1 | ✓ | 8 | 11.3 | even | 5 | ||
330.2.m.e.181.1 | yes | 8 | 11.4 | even | 5 | ||
990.2.n.k.181.1 | 8 | 33.26 | odd | 10 | |||
990.2.n.k.361.1 | 8 | 33.14 | odd | 10 | |||
3630.2.a.br.1.1 | 4 | 11.10 | odd | 2 | |||
3630.2.a.bt.1.4 | 4 | 1.1 | even | 1 | trivial |