Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.16053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | ||||||||
\(5\) | 1.16053 | 0.519005 | 0.259503 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259503 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.16053 | −0.366992 | ||||||||
\(11\) | 1.51929 | 0.458084 | 0.229042 | − | 0.973417i | \(-0.426441\pi\) | ||||
0.229042 | + | 0.973417i | \(0.426441\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.16053 | −0.299648 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.84035 | 1.41649 | 0.708247 | − | 0.705965i | \(-0.249486\pi\) | ||||
0.708247 | + | 0.705965i | \(0.249486\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.45774 | −0.334428 | −0.167214 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167214 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(20\) | 1.16053 | 0.259503 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.51929 | −0.323914 | ||||||||
\(23\) | 5.77880 | 1.20496 | 0.602482 | − | 0.798133i | \(-0.294179\pi\) | ||||
0.602482 | + | 0.798133i | \(0.294179\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.65317 | −0.730633 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.59771 | 0.668079 | 0.334039 | − | 0.942559i | \(-0.391588\pi\) | ||||
0.334039 | + | 0.942559i | \(0.391588\pi\) | |||||||
\(30\) | 1.16053 | 0.211883 | ||||||||
\(31\) | 7.29809 | 1.31078 | 0.655388 | − | 0.755292i | \(-0.272505\pi\) | ||||
0.655388 | + | 0.755292i | \(0.272505\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.51929 | −0.264475 | ||||||||
\(34\) | −5.84035 | −1.00161 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.95648 | 0.321643 | 0.160821 | − | 0.986984i | \(-0.448586\pi\) | ||||
0.160821 | + | 0.986984i | \(0.448586\pi\) | |||||||
\(38\) | 1.45774 | 0.236476 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.16053 | −0.183496 | ||||||||
\(41\) | −9.88388 | −1.54360 | −0.771801 | − | 0.635864i | \(-0.780644\pi\) | ||||
−0.771801 | + | 0.635864i | \(0.780644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.77880 | −0.271265 | −0.135632 | − | 0.990759i | \(-0.543307\pi\) | ||||
−0.135632 | + | 0.990759i | \(0.543307\pi\) | |||||||
\(44\) | 1.51929 | 0.229042 | ||||||||
\(45\) | 1.16053 | 0.173002 | ||||||||
\(46\) | −5.77880 | −0.852038 | ||||||||
\(47\) | −11.5867 | −1.69009 | −0.845045 | − | 0.534695i | \(-0.820426\pi\) | ||||
−0.845045 | + | 0.534695i | \(0.820426\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.65317 | 0.516636 | ||||||||
\(51\) | −5.84035 | −0.817813 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 9.58667 | 1.31683 | 0.658415 | − | 0.752655i | \(-0.271227\pi\) | ||||
0.658415 | + | 0.752655i | \(0.271227\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.76319 | 0.237748 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.45774 | 0.193082 | ||||||||
\(58\) | −3.59771 | −0.472403 | ||||||||
\(59\) | 0.0156151 | 0.00203291 | 0.00101645 | − | 0.999999i | \(-0.499676\pi\) | ||||
0.00101645 | + | 0.999999i | \(0.499676\pi\) | |||||||
\(60\) | −1.16053 | −0.149824 | ||||||||
\(61\) | 9.20988 | 1.17920 | 0.589602 | − | 0.807694i | \(-0.299284\pi\) | ||||
0.589602 | + | 0.807694i | \(0.299284\pi\) | |||||||
\(62\) | −7.29809 | −0.926859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.16053 | 0.143946 | ||||||||
\(66\) | 1.51929 | 0.187012 | ||||||||
\(67\) | 4.07842 | 0.498259 | 0.249129 | − | 0.968470i | \(-0.419856\pi\) | ||||
0.249129 | + | 0.968470i | \(0.419856\pi\) | |||||||
\(68\) | 5.84035 | 0.708247 | ||||||||
\(69\) | −5.77880 | −0.695686 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.358761 | −0.0425771 | −0.0212885 | − | 0.999773i | \(-0.506777\pi\) | ||||
−0.0212885 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.53491 | 0.413730 | 0.206865 | − | 0.978370i | \(-0.433674\pi\) | ||||
0.206865 | + | 0.978370i | \(0.433674\pi\) | |||||||
\(74\) | −1.95648 | −0.227436 | ||||||||
\(75\) | 3.65317 | 0.421831 | ||||||||
\(76\) | −1.45774 | −0.167214 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 10.2374 | 1.15180 | 0.575900 | − | 0.817520i | \(-0.304652\pi\) | ||||
0.575900 | + | 0.817520i | \(0.304652\pi\) | |||||||
\(80\) | 1.16053 | 0.129751 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.88388 | 1.09149 | ||||||||
\(83\) | −7.33579 | −0.805208 | −0.402604 | − | 0.915374i | \(-0.631895\pi\) | ||||
−0.402604 | + | 0.915374i | \(0.631895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.77792 | 0.735168 | ||||||||
\(86\) | 1.77880 | 0.191813 | ||||||||
\(87\) | −3.59771 | −0.385715 | ||||||||
\(88\) | −1.51929 | −0.161957 | ||||||||
\(89\) | −9.20406 | −0.975628 | −0.487814 | − | 0.872948i | \(-0.662206\pi\) | ||||
−0.487814 | + | 0.872948i | \(0.662206\pi\) | |||||||
\(90\) | −1.16053 | −0.122331 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.77880 | 0.602482 | ||||||||
\(93\) | −7.29809 | −0.756777 | ||||||||
\(94\) | 11.5867 | 1.19507 | ||||||||
\(95\) | −1.69175 | −0.173570 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 5.19543 | 0.527516 | 0.263758 | − | 0.964589i | \(-0.415038\pi\) | ||||
0.263758 | + | 0.964589i | \(0.415038\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.51929 | 0.152695 | ||||||||
\(100\) | −3.65317 | −0.365317 | ||||||||
\(101\) | 12.0273 | 1.19676 | 0.598379 | − | 0.801213i | \(-0.295812\pi\) | ||||
0.598379 | + | 0.801213i | \(0.295812\pi\) | |||||||
\(102\) | 5.84035 | 0.578281 | ||||||||
\(103\) | −7.81128 | −0.769669 | −0.384834 | − | 0.922986i | \(-0.625741\pi\) | ||||
−0.384834 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.58667 | −0.931140 | ||||||||
\(107\) | −5.10480 | −0.493500 | −0.246750 | − | 0.969079i | \(-0.579363\pi\) | ||||
−0.246750 | + | 0.969079i | \(0.579363\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.20037 | 0.593888 | 0.296944 | − | 0.954895i | \(-0.404033\pi\) | ||||
0.296944 | + | 0.954895i | \(0.404033\pi\) | |||||||
\(110\) | −1.76319 | −0.168113 | ||||||||
\(111\) | −1.95648 | −0.185700 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.0659 | −1.60542 | −0.802710 | − | 0.596369i | \(-0.796609\pi\) | ||||
−0.802710 | + | 0.596369i | \(0.796609\pi\) | |||||||
\(114\) | −1.45774 | −0.136530 | ||||||||
\(115\) | 6.70648 | 0.625382 | ||||||||
\(116\) | 3.59771 | 0.334039 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −0.0156151 | −0.00143748 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.16053 | 0.105942 | ||||||||
\(121\) | −8.69175 | −0.790159 | ||||||||
\(122\) | −9.20988 | −0.833824 | ||||||||
\(123\) | 9.88388 | 0.891199 | ||||||||
\(124\) | 7.29809 | 0.655388 | ||||||||
\(125\) | −10.0423 | −0.898208 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1651 | 1.52316 | 0.761578 | − | 0.648073i | \(-0.224425\pi\) | ||||
0.761578 | + | 0.648073i | \(0.224425\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.77880 | 0.156615 | ||||||||
\(130\) | −1.16053 | −0.101785 | ||||||||
\(131\) | −12.9127 | −1.12819 | −0.564093 | − | 0.825711i | \(-0.690774\pi\) | ||||
−0.564093 | + | 0.825711i | \(0.690774\pi\) | |||||||
\(132\) | −1.51929 | −0.132237 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.07842 | −0.352322 | ||||||||
\(135\) | −1.16053 | −0.0998826 | ||||||||
\(136\) | −5.84035 | −0.500806 | ||||||||
\(137\) | 10.4348 | 0.891503 | 0.445751 | − | 0.895157i | \(-0.352937\pi\) | ||||
0.445751 | + | 0.895157i | \(0.352937\pi\) | |||||||
\(138\) | 5.77880 | 0.491924 | ||||||||
\(139\) | −20.7071 | −1.75635 | −0.878176 | − | 0.478337i | \(-0.841240\pi\) | ||||
−0.878176 | + | 0.478337i | \(0.841240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5867 | 0.975774 | ||||||||
\(142\) | 0.358761 | 0.0301065 | ||||||||
\(143\) | 1.51929 | 0.127050 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.17526 | 0.346736 | ||||||||
\(146\) | −3.53491 | −0.292551 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.95648 | 0.160821 | ||||||||
\(149\) | −2.50736 | −0.205411 | −0.102706 | − | 0.994712i | \(-0.532750\pi\) | ||||
−0.102706 | + | 0.994712i | \(0.532750\pi\) | |||||||
\(150\) | −3.65317 | −0.298280 | ||||||||
\(151\) | 1.67614 | 0.136402 | 0.0682010 | − | 0.997672i | \(-0.478274\pi\) | ||||
0.0682010 | + | 0.997672i | \(0.478274\pi\) | |||||||
\(152\) | 1.45774 | 0.118238 | ||||||||
\(153\) | 5.84035 | 0.472165 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.46967 | 0.680300 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 10.8551 | 0.866330 | 0.433165 | − | 0.901315i | \(-0.357397\pi\) | ||||
0.433165 | + | 0.901315i | \(0.357397\pi\) | |||||||
\(158\) | −10.2374 | −0.814446 | ||||||||
\(159\) | −9.58667 | −0.760273 | ||||||||
\(160\) | −1.16053 | −0.0917481 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 8.00699 | 0.627156 | 0.313578 | − | 0.949563i | \(-0.398472\pi\) | ||||
0.313578 | + | 0.949563i | \(0.398472\pi\) | |||||||
\(164\) | −9.88388 | −0.771801 | ||||||||
\(165\) | −1.76319 | −0.137264 | ||||||||
\(166\) | 7.33579 | 0.569368 | ||||||||
\(167\) | −0.339091 | −0.0262397 | −0.0131198 | − | 0.999914i | \(-0.504176\pi\) | ||||
−0.0131198 | + | 0.999914i | \(0.504176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −6.77792 | −0.519842 | ||||||||
\(171\) | −1.45774 | −0.111476 | ||||||||
\(172\) | −1.77880 | −0.135632 | ||||||||
\(173\) | 2.22577 | 0.169222 | 0.0846112 | − | 0.996414i | \(-0.473035\pi\) | ||||
0.0846112 | + | 0.996414i | \(0.473035\pi\) | |||||||
\(174\) | 3.59771 | 0.272742 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.51929 | 0.114521 | ||||||||
\(177\) | −0.0156151 | −0.00117370 | ||||||||
\(178\) | 9.20406 | 0.689873 | ||||||||
\(179\) | −6.45280 | −0.482305 | −0.241152 | − | 0.970487i | \(-0.577525\pi\) | ||||
−0.241152 | + | 0.970487i | \(0.577525\pi\) | |||||||
\(180\) | 1.16053 | 0.0865009 | ||||||||
\(181\) | −0.0238555 | −0.00177317 | −0.000886584 | − | 1.00000i | \(-0.500282\pi\) | ||||
−0.000886584 | 1.00000i | \(0.500282\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.20988 | −0.680814 | ||||||||
\(184\) | −5.77880 | −0.426019 | ||||||||
\(185\) | 2.27055 | 0.166934 | ||||||||
\(186\) | 7.29809 | 0.535122 | ||||||||
\(187\) | 8.87321 | 0.648873 | ||||||||
\(188\) | −11.5867 | −0.845045 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.69175 | 0.122733 | ||||||||
\(191\) | 9.20164 | 0.665808 | 0.332904 | − | 0.942961i | \(-0.391972\pi\) | ||||
0.332904 | + | 0.942961i | \(0.391972\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 23.2522 | 1.67373 | 0.836863 | − | 0.547412i | \(-0.184387\pi\) | ||||
0.836863 | + | 0.547412i | \(0.184387\pi\) | |||||||
\(194\) | −5.19543 | −0.373010 | ||||||||
\(195\) | −1.16053 | −0.0831074 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.7521 | 1.54978 | 0.774888 | − | 0.632098i | \(-0.217806\pi\) | ||||
0.774888 | + | 0.632098i | \(0.217806\pi\) | |||||||
\(198\) | −1.51929 | −0.107971 | ||||||||
\(199\) | 17.4902 | 1.23985 | 0.619924 | − | 0.784661i | \(-0.287163\pi\) | ||||
0.619924 | + | 0.784661i | \(0.287163\pi\) | |||||||
\(200\) | 3.65317 | 0.258318 | ||||||||
\(201\) | −4.07842 | −0.287670 | ||||||||
\(202\) | −12.0273 | −0.846236 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.84035 | −0.408907 | ||||||||
\(205\) | −11.4706 | −0.801138 | ||||||||
\(206\) | 7.81128 | 0.544238 | ||||||||
\(207\) | 5.77880 | 0.401654 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −2.21473 | −0.153196 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.87070 | 0.335313 | 0.167656 | − | 0.985845i | \(-0.446380\pi\) | ||||
0.167656 | + | 0.985845i | \(0.446380\pi\) | |||||||
\(212\) | 9.58667 | 0.658415 | ||||||||
\(213\) | 0.358761 | 0.0245819 | ||||||||
\(214\) | 5.10480 | 0.348957 | ||||||||
\(215\) | −2.06435 | −0.140788 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.20037 | −0.419942 | ||||||||
\(219\) | −3.53491 | −0.238867 | ||||||||
\(220\) | 1.76319 | 0.118874 | ||||||||
\(221\) | 5.84035 | 0.392865 | ||||||||
\(222\) | 1.95648 | 0.131310 | ||||||||
\(223\) | −8.01165 | −0.536500 | −0.268250 | − | 0.963349i | \(-0.586445\pi\) | ||||
−0.268250 | + | 0.963349i | \(0.586445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.65317 | −0.243544 | ||||||||
\(226\) | 17.0659 | 1.13520 | ||||||||
\(227\) | −23.8532 | −1.58319 | −0.791595 | − | 0.611046i | \(-0.790749\pi\) | ||||
−0.791595 | + | 0.611046i | \(0.790749\pi\) | |||||||
\(228\) | 1.45774 | 0.0965411 | ||||||||
\(229\) | 14.4935 | 0.957759 | 0.478879 | − | 0.877881i | \(-0.341043\pi\) | ||||
0.478879 | + | 0.877881i | \(0.341043\pi\) | |||||||
\(230\) | −6.70648 | −0.442212 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.59771 | −0.236202 | ||||||||
\(233\) | 17.0723 | 1.11844 | 0.559222 | − | 0.829018i | \(-0.311100\pi\) | ||||
0.559222 | + | 0.829018i | \(0.311100\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −13.4467 | −0.877166 | ||||||||
\(236\) | 0.0156151 | 0.00101645 | ||||||||
\(237\) | −10.2374 | −0.664992 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.8943 | −1.28685 | −0.643427 | − | 0.765507i | \(-0.722488\pi\) | ||||
−0.643427 | + | 0.765507i | \(0.722488\pi\) | |||||||
\(240\) | −1.16053 | −0.0749120 | ||||||||
\(241\) | −6.03374 | −0.388667 | −0.194334 | − | 0.980936i | \(-0.562254\pi\) | ||||
−0.194334 | + | 0.980936i | \(0.562254\pi\) | |||||||
\(242\) | 8.69175 | 0.558727 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.20988 | 0.589602 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.88388 | −0.630173 | ||||||||
\(247\) | −1.45774 | −0.0927537 | ||||||||
\(248\) | −7.29809 | −0.463429 | ||||||||
\(249\) | 7.33579 | 0.464887 | ||||||||
\(250\) | 10.0423 | 0.635129 | ||||||||
\(251\) | 10.5817 | 0.667913 | 0.333957 | − | 0.942588i | \(-0.391616\pi\) | ||||
0.333957 | + | 0.942588i | \(0.391616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.77969 | 0.551974 | ||||||||
\(254\) | −17.1651 | −1.07703 | ||||||||
\(255\) | −6.77792 | −0.424450 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.27512 | −0.141918 | −0.0709592 | − | 0.997479i | \(-0.522606\pi\) | ||||
−0.0709592 | + | 0.997479i | \(0.522606\pi\) | |||||||
\(258\) | −1.77880 | −0.110743 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.16053 | 0.0719731 | ||||||||
\(261\) | 3.59771 | 0.222693 | ||||||||
\(262\) | 12.9127 | 0.797748 | ||||||||
\(263\) | 14.9853 | 0.924031 | 0.462016 | − | 0.886872i | \(-0.347126\pi\) | ||||
0.462016 | + | 0.886872i | \(0.347126\pi\) | |||||||
\(264\) | 1.51929 | 0.0935060 | ||||||||
\(265\) | 11.1256 | 0.683442 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.20406 | 0.563279 | ||||||||
\(268\) | 4.07842 | 0.249129 | ||||||||
\(269\) | −4.34656 | −0.265014 | −0.132507 | − | 0.991182i | \(-0.542303\pi\) | ||||
−0.132507 | + | 0.991182i | \(0.542303\pi\) | |||||||
\(270\) | 1.16053 | 0.0706277 | ||||||||
\(271\) | −5.32195 | −0.323285 | −0.161643 | − | 0.986849i | \(-0.551679\pi\) | ||||
−0.161643 | + | 0.986849i | \(0.551679\pi\) | |||||||
\(272\) | 5.84035 | 0.354124 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4348 | −0.630387 | ||||||||
\(275\) | −5.55023 | −0.334691 | ||||||||
\(276\) | −5.77880 | −0.347843 | ||||||||
\(277\) | −22.0052 | −1.32216 | −0.661082 | − | 0.750314i | \(-0.729902\pi\) | ||||
−0.661082 | + | 0.750314i | \(0.729902\pi\) | |||||||
\(278\) | 20.7071 | 1.24193 | ||||||||
\(279\) | 7.29809 | 0.436925 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.6348 | 1.29062 | 0.645311 | − | 0.763920i | \(-0.276728\pi\) | ||||
0.645311 | + | 0.763920i | \(0.276728\pi\) | |||||||
\(282\) | −11.5867 | −0.689976 | ||||||||
\(283\) | −16.2530 | −0.966143 | −0.483072 | − | 0.875581i | \(-0.660479\pi\) | ||||
−0.483072 | + | 0.875581i | \(0.660479\pi\) | |||||||
\(284\) | −0.358761 | −0.0212885 | ||||||||
\(285\) | 1.69175 | 0.100211 | ||||||||
\(286\) | −1.51929 | −0.0898376 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 17.1097 | 1.00646 | ||||||||
\(290\) | −4.17526 | −0.245180 | ||||||||
\(291\) | −5.19543 | −0.304561 | ||||||||
\(292\) | 3.53491 | 0.206865 | ||||||||
\(293\) | −4.43020 | −0.258815 | −0.129407 | − | 0.991592i | \(-0.541307\pi\) | ||||
−0.129407 | + | 0.991592i | \(0.541307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0181218 | 0.00105509 | ||||||||
\(296\) | −1.95648 | −0.113718 | ||||||||
\(297\) | −1.51929 | −0.0881583 | ||||||||
\(298\) | 2.50736 | 0.145248 | ||||||||
\(299\) | 5.77880 | 0.334197 | ||||||||
\(300\) | 3.65317 | 0.210916 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.67614 | −0.0964508 | ||||||||
\(303\) | −12.0273 | −0.690949 | ||||||||
\(304\) | −1.45774 | −0.0836070 | ||||||||
\(305\) | 10.6884 | 0.612014 | ||||||||
\(306\) | −5.84035 | −0.333871 | ||||||||
\(307\) | −3.75611 | −0.214372 | −0.107186 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107186 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.81128 | 0.444368 | ||||||||
\(310\) | −8.46967 | −0.481045 | ||||||||
\(311\) | 28.1348 | 1.59538 | 0.797688 | − | 0.603070i | \(-0.206056\pi\) | ||||
0.797688 | + | 0.603070i | \(0.206056\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 33.5490 | 1.89630 | 0.948150 | − | 0.317823i | \(-0.102952\pi\) | ||||
0.948150 | + | 0.317823i | \(0.102952\pi\) | |||||||
\(314\) | −10.8551 | −0.612588 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2374 | 0.575900 | ||||||||
\(317\) | 16.4714 | 0.925128 | 0.462564 | − | 0.886586i | \(-0.346930\pi\) | ||||
0.462564 | + | 0.886586i | \(0.346930\pi\) | |||||||
\(318\) | 9.58667 | 0.537594 | ||||||||
\(319\) | 5.46598 | 0.306036 | ||||||||
\(320\) | 1.16053 | 0.0648757 | ||||||||
\(321\) | 5.10480 | 0.284922 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.51371 | −0.473716 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.65317 | −0.202641 | ||||||||
\(326\) | −8.00699 | −0.443466 | ||||||||
\(327\) | −6.20037 | −0.342881 | ||||||||
\(328\) | 9.88388 | 0.545746 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.76319 | 0.0970602 | ||||||||
\(331\) | −1.98477 | −0.109093 | −0.0545465 | − | 0.998511i | \(-0.517371\pi\) | ||||
−0.0545465 | + | 0.998511i | \(0.517371\pi\) | |||||||
\(332\) | −7.33579 | −0.402604 | ||||||||
\(333\) | 1.95648 | 0.107214 | ||||||||
\(334\) | 0.339091 | 0.0185543 | ||||||||
\(335\) | 4.73314 | 0.258599 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.3707 | 1.05519 | 0.527594 | − | 0.849496i | \(-0.323094\pi\) | ||||
0.527594 | + | 0.849496i | \(0.323094\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 17.0659 | 0.926890 | ||||||||
\(340\) | 6.77792 | 0.367584 | ||||||||
\(341\) | 11.0879 | 0.600445 | ||||||||
\(342\) | 1.45774 | 0.0788255 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.77880 | 0.0959065 | ||||||||
\(345\) | −6.70648 | −0.361065 | ||||||||
\(346\) | −2.22577 | −0.119658 | ||||||||
\(347\) | 15.3921 | 0.826293 | 0.413146 | − | 0.910665i | \(-0.364430\pi\) | ||||
0.413146 | + | 0.910665i | \(0.364430\pi\) | |||||||
\(348\) | −3.59771 | −0.192858 | ||||||||
\(349\) | 29.0585 | 1.55546 | 0.777732 | − | 0.628596i | \(-0.216370\pi\) | ||||
0.777732 | + | 0.628596i | \(0.216370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.51929 | −0.0809785 | ||||||||
\(353\) | 17.8955 | 0.952483 | 0.476242 | − | 0.879314i | \(-0.341999\pi\) | ||||
0.476242 | + | 0.879314i | \(0.341999\pi\) | |||||||
\(354\) | 0.0156151 | 0.000829931 0 | ||||||||
\(355\) | −0.416353 | −0.0220977 | ||||||||
\(356\) | −9.20406 | −0.487814 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.45280 | 0.341041 | ||||||||
\(359\) | −9.71445 | −0.512709 | −0.256354 | − | 0.966583i | \(-0.582521\pi\) | ||||
−0.256354 | + | 0.966583i | \(0.582521\pi\) | |||||||
\(360\) | −1.16053 | −0.0611654 | ||||||||
\(361\) | −16.8750 | −0.888158 | ||||||||
\(362\) | 0.0238555 | 0.00125382 | ||||||||
\(363\) | 8.69175 | 0.456199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.10237 | 0.214728 | ||||||||
\(366\) | 9.20988 | 0.481408 | ||||||||
\(367\) | 4.84530 | 0.252922 | 0.126461 | − | 0.991972i | \(-0.459638\pi\) | ||||
0.126461 | + | 0.991972i | \(0.459638\pi\) | |||||||
\(368\) | 5.77880 | 0.301241 | ||||||||
\(369\) | −9.88388 | −0.514534 | ||||||||
\(370\) | −2.27055 | −0.118040 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.29809 | −0.378389 | ||||||||
\(373\) | 15.1001 | 0.781856 | 0.390928 | − | 0.920421i | \(-0.372154\pi\) | ||||
0.390928 | + | 0.920421i | \(0.372154\pi\) | |||||||
\(374\) | −8.87321 | −0.458823 | ||||||||
\(375\) | 10.0423 | 0.518581 | ||||||||
\(376\) | 11.5867 | 0.597537 | ||||||||
\(377\) | 3.59771 | 0.185292 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.30508 | 0.375237 | 0.187618 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187618 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(380\) | −1.69175 | −0.0867850 | ||||||||
\(381\) | −17.1651 | −0.879395 | ||||||||
\(382\) | −9.20164 | −0.470797 | ||||||||
\(383\) | 8.36800 | 0.427585 | 0.213792 | − | 0.976879i | \(-0.431418\pi\) | ||||
0.213792 | + | 0.976879i | \(0.431418\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.2522 | −1.18350 | ||||||||
\(387\) | −1.77880 | −0.0904216 | ||||||||
\(388\) | 5.19543 | 0.263758 | ||||||||
\(389\) | 11.8042 | 0.598497 | 0.299248 | − | 0.954175i | \(-0.403264\pi\) | ||||
0.299248 | + | 0.954175i | \(0.403264\pi\) | |||||||
\(390\) | 1.16053 | 0.0587658 | ||||||||
\(391\) | 33.7503 | 1.70682 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9127 | 0.651358 | ||||||||
\(394\) | −21.7521 | −1.09586 | ||||||||
\(395\) | 11.8809 | 0.597791 | ||||||||
\(396\) | 1.51929 | 0.0763473 | ||||||||
\(397\) | −6.64950 | −0.333729 | −0.166864 | − | 0.985980i | \(-0.553364\pi\) | ||||
−0.166864 | + | 0.985980i | \(0.553364\pi\) | |||||||
\(398\) | −17.4902 | −0.876706 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.65317 | −0.182658 | ||||||||
\(401\) | −2.59619 | −0.129647 | −0.0648237 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648237 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(402\) | 4.07842 | 0.203413 | ||||||||
\(403\) | 7.29809 | 0.363544 | ||||||||
\(404\) | 12.0273 | 0.598379 | ||||||||
\(405\) | 1.16053 | 0.0576673 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.97246 | 0.147339 | ||||||||
\(408\) | 5.84035 | 0.289141 | ||||||||
\(409\) | 9.20824 | 0.455318 | 0.227659 | − | 0.973741i | \(-0.426893\pi\) | ||||
0.227659 | + | 0.973741i | \(0.426893\pi\) | |||||||
\(410\) | 11.4706 | 0.566490 | ||||||||
\(411\) | −10.4348 | −0.514709 | ||||||||
\(412\) | −7.81128 | −0.384834 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.77880 | −0.284013 | ||||||||
\(415\) | −8.51342 | −0.417907 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 20.7071 | 1.01403 | ||||||||
\(418\) | 2.21473 | 0.108326 | ||||||||
\(419\) | −10.5383 | −0.514830 | −0.257415 | − | 0.966301i | \(-0.582871\pi\) | ||||
−0.257415 | + | 0.966301i | \(0.582871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6400 | 0.859720 | 0.429860 | − | 0.902895i | \(-0.358563\pi\) | ||||
0.429860 | + | 0.902895i | \(0.358563\pi\) | |||||||
\(422\) | −4.87070 | −0.237102 | ||||||||
\(423\) | −11.5867 | −0.563363 | ||||||||
\(424\) | −9.58667 | −0.465570 | ||||||||
\(425\) | −21.3358 | −1.03494 | ||||||||
\(426\) | −0.358761 | −0.0173820 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.10480 | −0.246750 | ||||||||
\(429\) | −1.51929 | −0.0733521 | ||||||||
\(430\) | 2.06435 | 0.0995520 | ||||||||
\(431\) | −9.42944 | −0.454200 | −0.227100 | − | 0.973871i | \(-0.572924\pi\) | ||||
−0.227100 | + | 0.973871i | \(0.572924\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.4316 | −0.741595 | −0.370798 | − | 0.928714i | \(-0.620916\pi\) | ||||
−0.370798 | + | 0.928714i | \(0.620916\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.17526 | −0.200188 | ||||||||
\(436\) | 6.20037 | 0.296944 | ||||||||
\(437\) | −8.42398 | −0.402974 | ||||||||
\(438\) | 3.53491 | 0.168904 | ||||||||
\(439\) | 27.0938 | 1.29311 | 0.646557 | − | 0.762865i | \(-0.276208\pi\) | ||||
0.646557 | + | 0.762865i | \(0.276208\pi\) | |||||||
\(440\) | −1.76319 | −0.0840566 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.84035 | −0.277797 | ||||||||
\(443\) | 34.8250 | 1.65458 | 0.827292 | − | 0.561771i | \(-0.189880\pi\) | ||||
0.827292 | + | 0.561771i | \(0.189880\pi\) | |||||||
\(444\) | −1.95648 | −0.0928502 | ||||||||
\(445\) | −10.6816 | −0.506356 | ||||||||
\(446\) | 8.01165 | 0.379363 | ||||||||
\(447\) | 2.50736 | 0.118594 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.9556 | −0.988954 | −0.494477 | − | 0.869191i | \(-0.664640\pi\) | ||||
−0.494477 | + | 0.869191i | \(0.664640\pi\) | |||||||
\(450\) | 3.65317 | 0.172212 | ||||||||
\(451\) | −15.0165 | −0.707099 | ||||||||
\(452\) | −17.0659 | −0.802710 | ||||||||
\(453\) | −1.67614 | −0.0787518 | ||||||||
\(454\) | 23.8532 | 1.11948 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.45774 | −0.0682649 | ||||||||
\(457\) | 37.8171 | 1.76901 | 0.884505 | − | 0.466531i | \(-0.154496\pi\) | ||||
0.884505 | + | 0.466531i | \(0.154496\pi\) | |||||||
\(458\) | −14.4935 | −0.677238 | ||||||||
\(459\) | −5.84035 | −0.272604 | ||||||||
\(460\) | 6.70648 | 0.312691 | ||||||||
\(461\) | −24.0146 | −1.11847 | −0.559235 | − | 0.829009i | \(-0.688905\pi\) | ||||
−0.559235 | + | 0.829009i | \(0.688905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8594 | 0.829996 | 0.414998 | − | 0.909822i | \(-0.363782\pi\) | ||||
0.414998 | + | 0.909822i | \(0.363782\pi\) | |||||||
\(464\) | 3.59771 | 0.167020 | ||||||||
\(465\) | −8.46967 | −0.392771 | ||||||||
\(466\) | −17.0723 | −0.790860 | ||||||||
\(467\) | −36.2355 | −1.67678 | −0.838390 | − | 0.545070i | \(-0.816503\pi\) | ||||
−0.838390 | + | 0.545070i | \(0.816503\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13.4467 | 0.620250 | ||||||||
\(471\) | −10.8551 | −0.500176 | ||||||||
\(472\) | −0.0156151 | −0.000718741 0 | ||||||||
\(473\) | −2.70252 | −0.124262 | ||||||||
\(474\) | 10.2374 | 0.470221 | ||||||||
\(475\) | 5.32536 | 0.244344 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.58667 | 0.438944 | ||||||||
\(478\) | 19.8943 | 0.909943 | ||||||||
\(479\) | −23.8606 | −1.09022 | −0.545110 | − | 0.838364i | \(-0.683512\pi\) | ||||
−0.545110 | + | 0.838364i | \(0.683512\pi\) | |||||||
\(480\) | 1.16053 | 0.0529708 | ||||||||
\(481\) | 1.95648 | 0.0892076 | ||||||||
\(482\) | 6.03374 | 0.274829 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.69175 | −0.395080 | ||||||||
\(485\) | 6.02946 | 0.273784 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −34.0551 | −1.54318 | −0.771592 | − | 0.636118i | \(-0.780539\pi\) | ||||
−0.771592 | + | 0.636118i | \(0.780539\pi\) | |||||||
\(488\) | −9.20988 | −0.416912 | ||||||||
\(489\) | −8.00699 | −0.362088 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.02422 | −0.226740 | −0.113370 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113370 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(492\) | 9.88388 | 0.445600 | ||||||||
\(493\) | 21.0119 | 0.946330 | ||||||||
\(494\) | 1.45774 | 0.0655868 | ||||||||
\(495\) | 1.76319 | 0.0792493 | ||||||||
\(496\) | 7.29809 | 0.327694 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.33579 | −0.328725 | ||||||||
\(499\) | 24.1863 | 1.08273 | 0.541363 | − | 0.840789i | \(-0.317908\pi\) | ||||
0.541363 | + | 0.840789i | \(0.317908\pi\) | |||||||
\(500\) | −10.0423 | −0.449104 | ||||||||
\(501\) | 0.339091 | 0.0151495 | ||||||||
\(502\) | −10.5817 | −0.472286 | ||||||||
\(503\) | 31.6915 | 1.41305 | 0.706527 | − | 0.707686i | \(-0.250261\pi\) | ||||
0.706527 | + | 0.707686i | \(0.250261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9580 | 0.621124 | ||||||||
\(506\) | −8.77969 | −0.390305 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 17.1651 | 0.761578 | ||||||||
\(509\) | −36.1410 | −1.60192 | −0.800960 | − | 0.598717i | \(-0.795677\pi\) | ||||
−0.800960 | + | 0.598717i | \(0.795677\pi\) | |||||||
\(510\) | 6.77792 | 0.300131 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.45774 | 0.0643607 | ||||||||
\(514\) | 2.27512 | 0.100351 | ||||||||
\(515\) | −9.06524 | −0.399462 | ||||||||
\(516\) | 1.77880 | 0.0783074 | ||||||||
\(517\) | −17.6035 | −0.774203 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.22577 | −0.0977006 | ||||||||
\(520\) | −1.16053 | −0.0508927 | ||||||||
\(521\) | −11.5089 | −0.504212 | −0.252106 | − | 0.967700i | \(-0.581123\pi\) | ||||
−0.252106 | + | 0.967700i | \(0.581123\pi\) | |||||||
\(522\) | −3.59771 | −0.157468 | ||||||||
\(523\) | 12.6798 | 0.554450 | 0.277225 | − | 0.960805i | \(-0.410585\pi\) | ||||
0.277225 | + | 0.960805i | \(0.410585\pi\) | |||||||
\(524\) | −12.9127 | −0.564093 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.9853 | −0.653389 | ||||||||
\(527\) | 42.6235 | 1.85671 | ||||||||
\(528\) | −1.51929 | −0.0661187 | ||||||||
\(529\) | 10.3945 | 0.451937 | ||||||||
\(530\) | −11.1256 | −0.483267 | ||||||||
\(531\) | 0.0156151 | 0.000677636 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.88388 | −0.428118 | ||||||||
\(534\) | −9.20406 | −0.398298 | ||||||||
\(535\) | −5.92429 | −0.256129 | ||||||||
\(536\) | −4.07842 | −0.176161 | ||||||||
\(537\) | 6.45280 | 0.278459 | ||||||||
\(538\) | 4.34656 | 0.187393 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.16053 | −0.0499413 | ||||||||
\(541\) | −4.65014 | −0.199925 | −0.0999626 | − | 0.994991i | \(-0.531872\pi\) | ||||
−0.0999626 | + | 0.994991i | \(0.531872\pi\) | |||||||
\(542\) | 5.32195 | 0.228597 | ||||||||
\(543\) | 0.0238555 | 0.00102374 | ||||||||
\(544\) | −5.84035 | −0.250403 | ||||||||
\(545\) | 7.19572 | 0.308231 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.7916 | 0.760715 | 0.380357 | − | 0.924840i | \(-0.375801\pi\) | ||||
0.380357 | + | 0.924840i | \(0.375801\pi\) | |||||||
\(548\) | 10.4348 | 0.445751 | ||||||||
\(549\) | 9.20988 | 0.393068 | ||||||||
\(550\) | 5.55023 | 0.236663 | ||||||||
\(551\) | −5.24453 | −0.223424 | ||||||||
\(552\) | 5.77880 | 0.245962 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.0052 | 0.934911 | ||||||||
\(555\) | −2.27055 | −0.0963795 | ||||||||
\(556\) | −20.7071 | −0.878176 | ||||||||
\(557\) | 30.6373 | 1.29814 | 0.649072 | − | 0.760727i | \(-0.275157\pi\) | ||||
0.649072 | + | 0.760727i | \(0.275157\pi\) | |||||||
\(558\) | −7.29809 | −0.308953 | ||||||||
\(559\) | −1.77880 | −0.0752353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.87321 | −0.374627 | ||||||||
\(562\) | −21.6348 | −0.912608 | ||||||||
\(563\) | 18.3741 | 0.774375 | 0.387188 | − | 0.922001i | \(-0.373447\pi\) | ||||
0.387188 | + | 0.922001i | \(0.373447\pi\) | |||||||
\(564\) | 11.5867 | 0.487887 | ||||||||
\(565\) | −19.8055 | −0.833222 | ||||||||
\(566\) | 16.2530 | 0.683166 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.358761 | 0.0150533 | ||||||||
\(569\) | −17.9394 | −0.752057 | −0.376028 | − | 0.926608i | \(-0.622710\pi\) | ||||
−0.376028 | + | 0.926608i | \(0.622710\pi\) | |||||||
\(570\) | −1.69175 | −0.0708597 | ||||||||
\(571\) | −18.6495 | −0.780457 | −0.390229 | − | 0.920718i | \(-0.627604\pi\) | ||||
−0.390229 | + | 0.920718i | \(0.627604\pi\) | |||||||
\(572\) | 1.51929 | 0.0635248 | ||||||||
\(573\) | −9.20164 | −0.384404 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.1109 | −0.880386 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 36.3523 | 1.51337 | 0.756683 | − | 0.653782i | \(-0.226819\pi\) | ||||
0.756683 | + | 0.653782i | \(0.226819\pi\) | |||||||
\(578\) | −17.1097 | −0.711672 | ||||||||
\(579\) | −23.2522 | −0.966327 | ||||||||
\(580\) | 4.17526 | 0.173368 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.19543 | 0.215357 | ||||||||
\(583\) | 14.5650 | 0.603219 | ||||||||
\(584\) | −3.53491 | −0.146276 | ||||||||
\(585\) | 1.16053 | 0.0479821 | ||||||||
\(586\) | 4.43020 | 0.183010 | ||||||||
\(587\) | 18.7622 | 0.774398 | 0.387199 | − | 0.921996i | \(-0.373443\pi\) | ||||
0.387199 | + | 0.921996i | \(0.373443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.6387 | −0.438360 | ||||||||
\(590\) | −0.0181218 | −0.000746061 0 | ||||||||
\(591\) | −21.7521 | −0.894764 | ||||||||
\(592\) | 1.95648 | 0.0804106 | ||||||||
\(593\) | 12.0975 | 0.496783 | 0.248391 | − | 0.968660i | \(-0.420098\pi\) | ||||
0.248391 | + | 0.968660i | \(0.420098\pi\) | |||||||
\(594\) | 1.51929 | 0.0623373 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.50736 | −0.102706 | ||||||||
\(597\) | −17.4902 | −0.715827 | ||||||||
\(598\) | −5.77880 | −0.236313 | ||||||||
\(599\) | −19.3009 | −0.788613 | −0.394307 | − | 0.918979i | \(-0.629015\pi\) | ||||
−0.394307 | + | 0.918979i | \(0.629015\pi\) | |||||||
\(600\) | −3.65317 | −0.149140 | ||||||||
\(601\) | −17.6854 | −0.721402 | −0.360701 | − | 0.932682i | \(-0.617462\pi\) | ||||
−0.360701 | + | 0.932682i | \(0.617462\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.07842 | 0.166086 | ||||||||
\(604\) | 1.67614 | 0.0682010 | ||||||||
\(605\) | −10.0870 | −0.410097 | ||||||||
\(606\) | 12.0273 | 0.488574 | ||||||||
\(607\) | −33.1514 | −1.34557 | −0.672786 | − | 0.739837i | \(-0.734903\pi\) | ||||
−0.672786 | + | 0.739837i | \(0.734903\pi\) | |||||||
\(608\) | 1.45774 | 0.0591191 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.6884 | −0.432759 | ||||||||
\(611\) | −11.5867 | −0.468747 | ||||||||
\(612\) | 5.84035 | 0.236082 | ||||||||
\(613\) | −28.6489 | −1.15712 | −0.578558 | − | 0.815641i | \(-0.696384\pi\) | ||||
−0.578558 | + | 0.815641i | \(0.696384\pi\) | |||||||
\(614\) | 3.75611 | 0.151584 | ||||||||
\(615\) | 11.4706 | 0.462537 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.2380 | −0.895270 | −0.447635 | − | 0.894216i | \(-0.647734\pi\) | ||||
−0.447635 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(618\) | −7.81128 | −0.314216 | ||||||||
\(619\) | −38.5778 | −1.55057 | −0.775286 | − | 0.631611i | \(-0.782394\pi\) | ||||
−0.775286 | + | 0.631611i | \(0.782394\pi\) | |||||||
\(620\) | 8.46967 | 0.340150 | ||||||||
\(621\) | −5.77880 | −0.231895 | ||||||||
\(622\) | −28.1348 | −1.12810 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 6.61146 | 0.264459 | ||||||||
\(626\) | −33.5490 | −1.34089 | ||||||||
\(627\) | 2.21473 | 0.0884478 | ||||||||
\(628\) | 10.8551 | 0.433165 | ||||||||
\(629\) | 11.4265 | 0.455605 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.5419 | 1.73337 | 0.866687 | − | 0.498852i | \(-0.166245\pi\) | ||||
0.866687 | + | 0.498852i | \(0.166245\pi\) | |||||||
\(632\) | −10.2374 | −0.407223 | ||||||||
\(633\) | −4.87070 | −0.193593 | ||||||||
\(634\) | −16.4714 | −0.654164 | ||||||||
\(635\) | 19.9206 | 0.790527 | ||||||||
\(636\) | −9.58667 | −0.380136 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.46598 | −0.216400 | ||||||||
\(639\) | −0.358761 | −0.0141924 | ||||||||
\(640\) | −1.16053 | −0.0458740 | ||||||||
\(641\) | 12.2184 | 0.482598 | 0.241299 | − | 0.970451i | \(-0.422427\pi\) | ||||
0.241299 | + | 0.970451i | \(0.422427\pi\) | |||||||
\(642\) | −5.10480 | −0.201471 | ||||||||
\(643\) | 26.4417 | 1.04276 | 0.521380 | − | 0.853325i | \(-0.325417\pi\) | ||||
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.06435 | 0.0812839 | ||||||||
\(646\) | 8.51371 | 0.334967 | ||||||||
\(647\) | −8.39591 | −0.330077 | −0.165039 | − | 0.986287i | \(-0.552775\pi\) | ||||
−0.165039 | + | 0.986287i | \(0.552775\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.0237238 | 0.000931242 0 | ||||||||
\(650\) | 3.65317 | 0.143289 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00699 | 0.313578 | ||||||||
\(653\) | −23.3820 | −0.915007 | −0.457503 | − | 0.889208i | \(-0.651256\pi\) | ||||
−0.457503 | + | 0.889208i | \(0.651256\pi\) | |||||||
\(654\) | 6.20037 | 0.242454 | ||||||||
\(655\) | −14.9856 | −0.585534 | ||||||||
\(656\) | −9.88388 | −0.385901 | ||||||||
\(657\) | 3.53491 | 0.137910 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.7625 | −1.78266 | −0.891328 | − | 0.453359i | \(-0.850225\pi\) | ||||
−0.891328 | + | 0.453359i | \(0.850225\pi\) | |||||||
\(660\) | −1.76319 | −0.0686319 | ||||||||
\(661\) | −0.169046 | −0.00657512 | −0.00328756 | − | 0.999995i | \(-0.501046\pi\) | ||||
−0.00328756 | + | 0.999995i | \(0.501046\pi\) | |||||||
\(662\) | 1.98477 | 0.0771404 | ||||||||
\(663\) | −5.84035 | −0.226821 | ||||||||
\(664\) | 7.33579 | 0.284684 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.95648 | −0.0758119 | ||||||||
\(667\) | 20.7905 | 0.805010 | ||||||||
\(668\) | −0.339091 | −0.0131198 | ||||||||
\(669\) | 8.01165 | 0.309748 | ||||||||
\(670\) | −4.73314 | −0.182857 | ||||||||
\(671\) | 13.9925 | 0.540175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.1905 | 1.81906 | 0.909530 | − | 0.415639i | \(-0.136442\pi\) | ||||
0.909530 | + | 0.415639i | \(0.136442\pi\) | |||||||
\(674\) | −19.3707 | −0.746131 | ||||||||
\(675\) | 3.65317 | 0.140610 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 32.7187 | 1.25748 | 0.628742 | − | 0.777614i | \(-0.283570\pi\) | ||||
0.628742 | + | 0.777614i | \(0.283570\pi\) | |||||||
\(678\) | −17.0659 | −0.655410 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.77792 | −0.259921 | ||||||||
\(681\) | 23.8532 | 0.914055 | ||||||||
\(682\) | −11.0879 | −0.424579 | ||||||||
\(683\) | −17.9035 | −0.685060 | −0.342530 | − | 0.939507i | \(-0.611284\pi\) | ||||
−0.342530 | + | 0.939507i | \(0.611284\pi\) | |||||||
\(684\) | −1.45774 | −0.0557380 | ||||||||
\(685\) | 12.1099 | 0.462695 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4935 | −0.552962 | ||||||||
\(688\) | −1.77880 | −0.0678162 | ||||||||
\(689\) | 9.58667 | 0.365223 | ||||||||
\(690\) | 6.70648 | 0.255311 | ||||||||
\(691\) | 7.03858 | 0.267760 | 0.133880 | − | 0.990998i | \(-0.457256\pi\) | ||||
0.133880 | + | 0.990998i | \(0.457256\pi\) | |||||||
\(692\) | 2.22577 | 0.0846112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.3921 | −0.584277 | ||||||||
\(695\) | −24.0312 | −0.911557 | ||||||||
\(696\) | 3.59771 | 0.136371 | ||||||||
\(697\) | −57.7254 | −2.18650 | ||||||||
\(698\) | −29.0585 | −1.09988 | ||||||||
\(699\) | −17.0723 | −0.645734 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.7808 | −1.38919 | −0.694596 | − | 0.719400i | \(-0.744417\pi\) | ||||
−0.694596 | + | 0.719400i | \(0.744417\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −2.85203 | −0.107566 | ||||||||
\(704\) | 1.51929 | 0.0572605 | ||||||||
\(705\) | 13.4467 | 0.506432 | ||||||||
\(706\) | −17.8955 | −0.673507 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.0156151 | −0.000586850 0 | ||||||||
\(709\) | −23.0021 | −0.863863 | −0.431932 | − | 0.901906i | \(-0.642168\pi\) | ||||
−0.431932 | + | 0.901906i | \(0.642168\pi\) | |||||||
\(710\) | 0.416353 | 0.0156255 | ||||||||
\(711\) | 10.2374 | 0.383933 | ||||||||
\(712\) | 9.20406 | 0.344937 | ||||||||
\(713\) | 42.1742 | 1.57944 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.76319 | 0.0659394 | ||||||||
\(716\) | −6.45280 | −0.241152 | ||||||||
\(717\) | 19.8943 | 0.742966 | ||||||||
\(718\) | 9.71445 | 0.362540 | ||||||||
\(719\) | 4.66817 | 0.174093 | 0.0870467 | − | 0.996204i | \(-0.472257\pi\) | ||||
0.0870467 | + | 0.996204i | \(0.472257\pi\) | |||||||
\(720\) | 1.16053 | 0.0432505 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.8750 | 0.628022 | ||||||||
\(723\) | 6.03374 | 0.224397 | ||||||||
\(724\) | −0.0238555 | −0.000886584 0 | ||||||||
\(725\) | −13.1431 | −0.488121 | ||||||||
\(726\) | −8.69175 | −0.322581 | ||||||||
\(727\) | 25.6085 | 0.949767 | 0.474883 | − | 0.880049i | \(-0.342490\pi\) | ||||
0.474883 | + | 0.880049i | \(0.342490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.10237 | −0.151836 | ||||||||
\(731\) | −10.3888 | −0.384245 | ||||||||
\(732\) | −9.20988 | −0.340407 | ||||||||
\(733\) | 1.84962 | 0.0683174 | 0.0341587 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341587 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(734\) | −4.84530 | −0.178843 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.77880 | −0.213009 | ||||||||
\(737\) | 6.19631 | 0.228244 | ||||||||
\(738\) | 9.88388 | 0.363831 | ||||||||
\(739\) | −23.9488 | −0.880973 | −0.440486 | − | 0.897759i | \(-0.645194\pi\) | ||||
−0.440486 | + | 0.897759i | \(0.645194\pi\) | |||||||
\(740\) | 2.27055 | 0.0834671 | ||||||||
\(741\) | 1.45774 | 0.0535514 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.4754 | −0.384305 | −0.192153 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192153 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(744\) | 7.29809 | 0.267561 | ||||||||
\(745\) | −2.90988 | −0.106610 | ||||||||
\(746\) | −15.1001 | −0.552855 | ||||||||
\(747\) | −7.33579 | −0.268403 | ||||||||
\(748\) | 8.87321 | 0.324437 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.0423 | −0.366692 | ||||||||
\(751\) | −23.5849 | −0.860624 | −0.430312 | − | 0.902680i | \(-0.641596\pi\) | ||||
−0.430312 | + | 0.902680i | \(0.641596\pi\) | |||||||
\(752\) | −11.5867 | −0.422522 | ||||||||
\(753\) | −10.5817 | −0.385620 | ||||||||
\(754\) | −3.59771 | −0.131021 | ||||||||
\(755\) | 1.94521 | 0.0707934 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.6602 | −0.678218 | −0.339109 | − | 0.940747i | \(-0.610126\pi\) | ||||
−0.339109 | + | 0.940747i | \(0.610126\pi\) | |||||||
\(758\) | −7.30508 | −0.265332 | ||||||||
\(759\) | −8.77969 | −0.318682 | ||||||||
\(760\) | 1.69175 | 0.0613663 | ||||||||
\(761\) | −27.1786 | −0.985222 | −0.492611 | − | 0.870250i | \(-0.663957\pi\) | ||||
−0.492611 | + | 0.870250i | \(0.663957\pi\) | |||||||
\(762\) | 17.1651 | 0.621826 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.20164 | 0.332904 | ||||||||
\(765\) | 6.77792 | 0.245056 | ||||||||
\(766\) | −8.36800 | −0.302348 | ||||||||
\(767\) | 0.0156151 | 0.000563827 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −30.8339 | −1.11190 | −0.555949 | − | 0.831217i | \(-0.687645\pi\) | ||||
−0.555949 | + | 0.831217i | \(0.687645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.27512 | 0.0819366 | ||||||||
\(772\) | 23.2522 | 0.836863 | ||||||||
\(773\) | −14.0245 | −0.504425 | −0.252213 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252213 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(774\) | 1.77880 | 0.0639377 | ||||||||
\(775\) | −26.6612 | −0.957697 | ||||||||
\(776\) | −5.19543 | −0.186505 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.8042 | −0.423201 | ||||||||
\(779\) | 14.4081 | 0.516224 | ||||||||
\(780\) | −1.16053 | −0.0415537 | ||||||||
\(781\) | −0.545062 | −0.0195039 | ||||||||
\(782\) | −33.7503 | −1.20691 | ||||||||
\(783\) | −3.59771 | −0.128572 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.5977 | 0.449630 | ||||||||
\(786\) | −12.9127 | −0.460580 | ||||||||
\(787\) | −24.7524 | −0.882328 | −0.441164 | − | 0.897426i | \(-0.645434\pi\) | ||||
−0.441164 | + | 0.897426i | \(0.645434\pi\) | |||||||
\(788\) | 21.7521 | 0.774888 | ||||||||
\(789\) | −14.9853 | −0.533490 | ||||||||
\(790\) | −11.8809 | −0.422702 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.51929 | −0.0539857 | ||||||||
\(793\) | 9.20988 | 0.327053 | ||||||||
\(794\) | 6.64950 | 0.235982 | ||||||||
\(795\) | −11.1256 | −0.394586 | ||||||||
\(796\) | 17.4902 | 0.619924 | ||||||||
\(797\) | 17.5536 | 0.621782 | 0.310891 | − | 0.950446i | \(-0.399373\pi\) | ||||
0.310891 | + | 0.950446i | \(0.399373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.6703 | −2.39400 | ||||||||
\(800\) | 3.65317 | 0.129159 | ||||||||
\(801\) | −9.20406 | −0.325209 | ||||||||
\(802\) | 2.59619 | 0.0916745 | ||||||||
\(803\) | 5.37056 | 0.189523 | ||||||||
\(804\) | −4.07842 | −0.143835 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.29809 | −0.257064 | ||||||||
\(807\) | 4.34656 | 0.153006 | ||||||||
\(808\) | −12.0273 | −0.423118 | ||||||||
\(809\) | −0.153431 | −0.00539434 | −0.00269717 | − | 0.999996i | \(-0.500859\pi\) | ||||
−0.00269717 | + | 0.999996i | \(0.500859\pi\) | |||||||
\(810\) | −1.16053 | −0.0407769 | ||||||||
\(811\) | 41.7585 | 1.46634 | 0.733169 | − | 0.680046i | \(-0.238040\pi\) | ||||
0.733169 | + | 0.680046i | \(0.238040\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.32195 | 0.186649 | ||||||||
\(814\) | −2.97246 | −0.104185 | ||||||||
\(815\) | 9.29236 | 0.325497 | ||||||||
\(816\) | −5.84035 | −0.204453 | ||||||||
\(817\) | 2.59303 | 0.0907185 | ||||||||
\(818\) | −9.20824 | −0.321959 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.4706 | −0.400569 | ||||||||
\(821\) | −50.4865 | −1.76199 | −0.880996 | − | 0.473124i | \(-0.843126\pi\) | ||||
−0.880996 | + | 0.473124i | \(0.843126\pi\) | |||||||
\(822\) | 10.4348 | 0.363954 | ||||||||
\(823\) | −52.6062 | −1.83374 | −0.916868 | − | 0.399190i | \(-0.869292\pi\) | ||||
−0.916868 | + | 0.399190i | \(0.869292\pi\) | |||||||
\(824\) | 7.81128 | 0.272119 | ||||||||
\(825\) | 5.55023 | 0.193234 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.35509 | 0.0818946 | 0.0409473 | − | 0.999161i | \(-0.486962\pi\) | ||||
0.0409473 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(828\) | 5.77880 | 0.200827 | ||||||||
\(829\) | 1.43169 | 0.0497248 | 0.0248624 | − | 0.999691i | \(-0.492085\pi\) | ||||
0.0248624 | + | 0.999691i | \(0.492085\pi\) | |||||||
\(830\) | 8.51342 | 0.295505 | ||||||||
\(831\) | 22.0052 | 0.763351 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.7071 | −0.717028 | ||||||||
\(835\) | −0.393526 | −0.0136185 | ||||||||
\(836\) | −2.21473 | −0.0765981 | ||||||||
\(837\) | −7.29809 | −0.252259 | ||||||||
\(838\) | 10.5383 | 0.364040 | ||||||||
\(839\) | −22.5382 | −0.778105 | −0.389053 | − | 0.921216i | \(-0.627198\pi\) | ||||
−0.389053 | + | 0.921216i | \(0.627198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.0565 | −0.553671 | ||||||||
\(842\) | −17.6400 | −0.607914 | ||||||||
\(843\) | −21.6348 | −0.745141 | ||||||||
\(844\) | 4.87070 | 0.167656 | ||||||||
\(845\) | 1.16053 | 0.0399235 | ||||||||
\(846\) | 11.5867 | 0.398358 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.58667 | 0.329208 | ||||||||
\(849\) | 16.2530 | 0.557803 | ||||||||
\(850\) | 21.3358 | 0.731812 | ||||||||
\(851\) | 11.3061 | 0.387567 | ||||||||
\(852\) | 0.358761 | 0.0122909 | ||||||||
\(853\) | 4.09925 | 0.140356 | 0.0701779 | − | 0.997534i | \(-0.477643\pi\) | ||||
0.0701779 | + | 0.997534i | \(0.477643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.69175 | −0.0578567 | ||||||||
\(856\) | 5.10480 | 0.174479 | ||||||||
\(857\) | 11.8622 | 0.405204 | 0.202602 | − | 0.979261i | \(-0.435060\pi\) | ||||
0.202602 | + | 0.979261i | \(0.435060\pi\) | |||||||
\(858\) | 1.51929 | 0.0518678 | ||||||||
\(859\) | −44.5980 | −1.52166 | −0.760831 | − | 0.648950i | \(-0.775209\pi\) | ||||
−0.760831 | + | 0.648950i | \(0.775209\pi\) | |||||||
\(860\) | −2.06435 | −0.0703939 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.42944 | 0.321168 | ||||||||
\(863\) | 9.83022 | 0.334625 | 0.167312 | − | 0.985904i | \(-0.446491\pi\) | ||||
0.167312 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 2.58308 | 0.0878273 | ||||||||
\(866\) | 15.4316 | 0.524387 | ||||||||
\(867\) | −17.1097 | −0.581077 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.5536 | 0.527621 | ||||||||
\(870\) | 4.17526 | 0.141555 | ||||||||
\(871\) | 4.07842 | 0.138192 | ||||||||
\(872\) | −6.20037 | −0.209971 | ||||||||
\(873\) | 5.19543 | 0.175839 | ||||||||
\(874\) | 8.42398 | 0.284945 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.53491 | −0.119433 | ||||||||
\(877\) | −38.3415 | −1.29470 | −0.647350 | − | 0.762193i | \(-0.724123\pi\) | ||||
−0.647350 | + | 0.762193i | \(0.724123\pi\) | |||||||
\(878\) | −27.0938 | −0.914370 | ||||||||
\(879\) | 4.43020 | 0.149427 | ||||||||
\(880\) | 1.76319 | 0.0594370 | ||||||||
\(881\) | 14.2467 | 0.479983 | 0.239992 | − | 0.970775i | \(-0.422855\pi\) | ||||
0.239992 | + | 0.970775i | \(0.422855\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.1329 | −1.82172 | −0.910858 | − | 0.412720i | \(-0.864579\pi\) | ||||
−0.910858 | + | 0.412720i | \(0.864579\pi\) | |||||||
\(884\) | 5.84035 | 0.196432 | ||||||||
\(885\) | −0.0181218 | −0.000609156 0 | ||||||||
\(886\) | −34.8250 | −1.16997 | ||||||||
\(887\) | −8.85788 | −0.297419 | −0.148709 | − | 0.988881i | \(-0.547512\pi\) | ||||
−0.148709 | + | 0.988881i | \(0.547512\pi\) | |||||||
\(888\) | 1.95648 | 0.0656550 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.6816 | 0.358048 | ||||||||
\(891\) | 1.51929 | 0.0508982 | ||||||||
\(892\) | −8.01165 | −0.268250 | ||||||||
\(893\) | 16.8903 | 0.565214 | ||||||||
\(894\) | −2.50736 | −0.0838588 | ||||||||
\(895\) | −7.48867 | −0.250319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.77880 | −0.192949 | ||||||||
\(898\) | 20.9556 | 0.699296 | ||||||||
\(899\) | 26.2565 | 0.875702 | ||||||||
\(900\) | −3.65317 | −0.121772 | ||||||||
\(901\) | 55.9896 | 1.86528 | ||||||||
\(902\) | 15.0165 | 0.499995 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.0659 | 0.567602 | ||||||||
\(905\) | −0.0276851 | −0.000920284 0 | ||||||||
\(906\) | 1.67614 | 0.0556859 | ||||||||
\(907\) | −13.1980 | −0.438232 | −0.219116 | − | 0.975699i | \(-0.570317\pi\) | ||||
−0.219116 | + | 0.975699i | \(0.570317\pi\) | |||||||
\(908\) | −23.8532 | −0.791595 | ||||||||
\(909\) | 12.0273 | 0.398919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.6427 | −1.28029 | −0.640146 | − | 0.768254i | \(-0.721126\pi\) | ||||
−0.640146 | + | 0.768254i | \(0.721126\pi\) | |||||||
\(912\) | 1.45774 | 0.0482705 | ||||||||
\(913\) | −11.1452 | −0.368853 | ||||||||
\(914\) | −37.8171 | −1.25088 | ||||||||
\(915\) | −10.6884 | −0.353346 | ||||||||
\(916\) | 14.4935 | 0.478879 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.84035 | 0.192760 | ||||||||
\(919\) | −10.5294 | −0.347334 | −0.173667 | − | 0.984804i | \(-0.555562\pi\) | ||||
−0.173667 | + | 0.984804i | \(0.555562\pi\) | |||||||
\(920\) | −6.70648 | −0.221106 | ||||||||
\(921\) | 3.75611 | 0.123768 | ||||||||
\(922\) | 24.0146 | 0.790878 | ||||||||
\(923\) | −0.358761 | −0.0118088 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.14733 | −0.235003 | ||||||||
\(926\) | −17.8594 | −0.586896 | ||||||||
\(927\) | −7.81128 | −0.256556 | ||||||||
\(928\) | −3.59771 | −0.118101 | ||||||||
\(929\) | −33.7331 | −1.10675 | −0.553373 | − | 0.832933i | \(-0.686660\pi\) | ||||
−0.553373 | + | 0.832933i | \(0.686660\pi\) | |||||||
\(930\) | 8.46967 | 0.277731 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.0723 | 0.559222 | ||||||||
\(933\) | −28.1348 | −0.921091 | ||||||||
\(934\) | 36.2355 | 1.18566 | ||||||||
\(935\) | 10.2976 | 0.336769 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −6.05885 | −0.197934 | −0.0989669 | − | 0.995091i | \(-0.531554\pi\) | ||||
−0.0989669 | + | 0.995091i | \(0.531554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.5490 | −1.09483 | ||||||||
\(940\) | −13.4467 | −0.438583 | ||||||||
\(941\) | 48.1109 | 1.56837 | 0.784185 | − | 0.620527i | \(-0.213081\pi\) | ||||
0.784185 | + | 0.620527i | \(0.213081\pi\) | |||||||
\(942\) | 10.8551 | 0.353678 | ||||||||
\(943\) | −57.1170 | −1.85998 | ||||||||
\(944\) | 0.0156151 | 0.000508227 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.70252 | 0.0878665 | ||||||||
\(947\) | −46.8777 | −1.52332 | −0.761660 | − | 0.647977i | \(-0.775615\pi\) | ||||
−0.761660 | + | 0.647977i | \(0.775615\pi\) | |||||||
\(948\) | −10.2374 | −0.332496 | ||||||||
\(949\) | 3.53491 | 0.114748 | ||||||||
\(950\) | −5.32536 | −0.172778 | ||||||||
\(951\) | −16.4714 | −0.534123 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.3401 | −1.11238 | −0.556192 | − | 0.831054i | \(-0.687738\pi\) | ||||
−0.556192 | + | 0.831054i | \(0.687738\pi\) | |||||||
\(954\) | −9.58667 | −0.310380 | ||||||||
\(955\) | 10.6788 | 0.345558 | ||||||||
\(956\) | −19.8943 | −0.643427 | ||||||||
\(957\) | −5.46598 | −0.176690 | ||||||||
\(958\) | 23.8606 | 0.770902 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.16053 | −0.0374560 | ||||||||
\(961\) | 22.2622 | 0.718134 | ||||||||
\(962\) | −1.95648 | −0.0630793 | ||||||||
\(963\) | −5.10480 | −0.164500 | ||||||||
\(964\) | −6.03374 | −0.194334 | ||||||||
\(965\) | 26.9849 | 0.868673 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.9586 | −0.384564 | −0.192282 | − | 0.981340i | \(-0.561589\pi\) | ||||
−0.192282 | + | 0.981340i | \(0.561589\pi\) | |||||||
\(968\) | 8.69175 | 0.279363 | ||||||||
\(969\) | 8.51371 | 0.273500 | ||||||||
\(970\) | −6.02946 | −0.193594 | ||||||||
\(971\) | 5.64697 | 0.181220 | 0.0906100 | − | 0.995886i | \(-0.471118\pi\) | ||||
0.0906100 | + | 0.995886i | \(0.471118\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.0551 | 1.09120 | ||||||||
\(975\) | 3.65317 | 0.116995 | ||||||||
\(976\) | 9.20988 | 0.294801 | ||||||||
\(977\) | 54.2348 | 1.73512 | 0.867562 | − | 0.497329i | \(-0.165686\pi\) | ||||
0.867562 | + | 0.497329i | \(0.165686\pi\) | |||||||
\(978\) | 8.00699 | 0.256035 | ||||||||
\(979\) | −13.9837 | −0.446919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.20037 | 0.197963 | ||||||||
\(982\) | 5.02422 | 0.160329 | ||||||||
\(983\) | −35.0175 | −1.11688 | −0.558442 | − | 0.829543i | \(-0.688601\pi\) | ||||
−0.558442 | + | 0.829543i | \(0.688601\pi\) | |||||||
\(984\) | −9.88388 | −0.315087 | ||||||||
\(985\) | 25.2440 | 0.804342 | ||||||||
\(986\) | −21.0119 | −0.669156 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.45774 | −0.0463768 | ||||||||
\(989\) | −10.2793 | −0.326864 | ||||||||
\(990\) | −1.76319 | −0.0560377 | ||||||||
\(991\) | −12.4835 | −0.396552 | −0.198276 | − | 0.980146i | \(-0.563534\pi\) | ||||
−0.198276 | + | 0.980146i | \(0.563534\pi\) | |||||||
\(992\) | −7.29809 | −0.231715 | ||||||||
\(993\) | 1.98477 | 0.0629848 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.2980 | 0.643488 | ||||||||
\(996\) | 7.33579 | 0.232443 | ||||||||
\(997\) | 59.4282 | 1.88211 | 0.941054 | − | 0.338255i | \(-0.109837\pi\) | ||||
0.941054 | + | 0.338255i | \(0.109837\pi\) | |||||||
\(998\) | −24.1863 | −0.765603 | ||||||||
\(999\) | −1.95648 | −0.0619001 |
(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 | 3822.2.a.bx.1.4 | ✓ | 4 | |
7.6 | odd | 2 | 3822.2.a.by.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bx.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3822.2.a.by.1.1 | yes | 4 | 7.6 | odd | 2 |