Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.34 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 3.26778 | 1.88665 | 0.943327 | − | 0.331864i | \(-0.107678\pi\) | ||||
0.943327 | + | 0.331864i | \(0.107678\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.595639 | 0.266378 | 0.133189 | − | 0.991091i | \(-0.457478\pi\) | ||||
0.133189 | + | 0.991091i | \(0.457478\pi\) | |||||||
\(6\) | −3.26778 | −1.33407 | ||||||||
\(7\) | −2.99147 | −1.13067 | −0.565336 | − | 0.824861i | \(-0.691253\pi\) | ||||
−0.565336 | + | 0.824861i | \(0.691253\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.67840 | 2.55947 | ||||||||
\(10\) | −0.595639 | −0.188358 | ||||||||
\(11\) | 0.495097 | 0.149277 | 0.0746387 | − | 0.997211i | \(-0.476220\pi\) | ||||
0.0746387 | + | 0.997211i | \(0.476220\pi\) | |||||||
\(12\) | 3.26778 | 0.943327 | ||||||||
\(13\) | −2.84715 | −0.789657 | −0.394828 | − | 0.918755i | \(-0.629196\pi\) | ||||
−0.394828 | + | 0.918755i | \(0.629196\pi\) | |||||||
\(14\) | 2.99147 | 0.799505 | ||||||||
\(15\) | 1.94642 | 0.502563 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.90375 | −0.461727 | −0.230863 | − | 0.972986i | \(-0.574155\pi\) | ||||
−0.230863 | + | 0.972986i | \(0.574155\pi\) | |||||||
\(18\) | −7.67840 | −1.80982 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.595639 | 0.133189 | ||||||||
\(21\) | −9.77549 | −2.13319 | ||||||||
\(22\) | −0.495097 | −0.105555 | ||||||||
\(23\) | −8.88616 | −1.85289 | −0.926446 | − | 0.376427i | \(-0.877153\pi\) | ||||
−0.926446 | + | 0.376427i | \(0.877153\pi\) | |||||||
\(24\) | −3.26778 | −0.667033 | ||||||||
\(25\) | −4.64521 | −0.929043 | ||||||||
\(26\) | 2.84715 | 0.558372 | ||||||||
\(27\) | 15.2880 | 2.94217 | ||||||||
\(28\) | −2.99147 | −0.565336 | ||||||||
\(29\) | −0.0817407 | −0.0151789 | −0.00758943 | − | 0.999971i | \(-0.502416\pi\) | ||||
−0.00758943 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(30\) | −1.94642 | −0.355366 | ||||||||
\(31\) | −4.72927 | −0.849403 | −0.424701 | − | 0.905334i | \(-0.639621\pi\) | ||||
−0.424701 | + | 0.905334i | \(0.639621\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.61787 | 0.281635 | ||||||||
\(34\) | 1.90375 | 0.326490 | ||||||||
\(35\) | −1.78184 | −0.301186 | ||||||||
\(36\) | 7.67840 | 1.27973 | ||||||||
\(37\) | −1.10528 | −0.181706 | −0.0908532 | − | 0.995864i | \(-0.528959\pi\) | ||||
−0.0908532 | + | 0.995864i | \(0.528959\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −9.30386 | −1.48981 | ||||||||
\(40\) | −0.595639 | −0.0941788 | ||||||||
\(41\) | 8.82027 | 1.37749 | 0.688747 | − | 0.725002i | \(-0.258161\pi\) | ||||
0.688747 | + | 0.725002i | \(0.258161\pi\) | |||||||
\(42\) | 9.77549 | 1.50839 | ||||||||
\(43\) | 4.95602 | 0.755786 | 0.377893 | − | 0.925849i | \(-0.376649\pi\) | ||||
0.377893 | + | 0.925849i | \(0.376649\pi\) | |||||||
\(44\) | 0.495097 | 0.0746387 | ||||||||
\(45\) | 4.57355 | 0.681785 | ||||||||
\(46\) | 8.88616 | 1.31019 | ||||||||
\(47\) | −2.10145 | −0.306528 | −0.153264 | − | 0.988185i | \(-0.548979\pi\) | ||||
−0.153264 | + | 0.988185i | \(0.548979\pi\) | |||||||
\(48\) | 3.26778 | 0.471664 | ||||||||
\(49\) | 1.94892 | 0.278417 | ||||||||
\(50\) | 4.64521 | 0.656932 | ||||||||
\(51\) | −6.22104 | −0.871119 | ||||||||
\(52\) | −2.84715 | −0.394828 | ||||||||
\(53\) | 0.933659 | 0.128248 | 0.0641240 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641240 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(54\) | −15.2880 | −2.08043 | ||||||||
\(55\) | 0.294899 | 0.0397642 | ||||||||
\(56\) | 2.99147 | 0.399753 | ||||||||
\(57\) | −3.26778 | −0.432828 | ||||||||
\(58\) | 0.0817407 | 0.0107331 | ||||||||
\(59\) | 10.6946 | 1.39232 | 0.696160 | − | 0.717886i | \(-0.254890\pi\) | ||||
0.696160 | + | 0.717886i | \(0.254890\pi\) | |||||||
\(60\) | 1.94642 | 0.251282 | ||||||||
\(61\) | 6.78989 | 0.869357 | 0.434678 | − | 0.900586i | \(-0.356862\pi\) | ||||
0.434678 | + | 0.900586i | \(0.356862\pi\) | |||||||
\(62\) | 4.72927 | 0.600618 | ||||||||
\(63\) | −22.9697 | −2.89391 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.69587 | −0.210347 | ||||||||
\(66\) | −1.61787 | −0.199146 | ||||||||
\(67\) | −3.28824 | −0.401723 | −0.200861 | − | 0.979620i | \(-0.564374\pi\) | ||||
−0.200861 | + | 0.979620i | \(0.564374\pi\) | |||||||
\(68\) | −1.90375 | −0.230863 | ||||||||
\(69\) | −29.0380 | −3.49577 | ||||||||
\(70\) | 1.78184 | 0.212971 | ||||||||
\(71\) | −13.8027 | −1.63808 | −0.819039 | − | 0.573738i | \(-0.805493\pi\) | ||||
−0.819039 | + | 0.573738i | \(0.805493\pi\) | |||||||
\(72\) | −7.67840 | −0.904908 | ||||||||
\(73\) | 10.0079 | 1.17133 | 0.585667 | − | 0.810552i | \(-0.300833\pi\) | ||||
0.585667 | + | 0.810552i | \(0.300833\pi\) | |||||||
\(74\) | 1.10528 | 0.128486 | ||||||||
\(75\) | −15.1795 | −1.75278 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −1.48107 | −0.168784 | ||||||||
\(78\) | 9.30386 | 1.05345 | ||||||||
\(79\) | −3.99429 | −0.449393 | −0.224697 | − | 0.974429i | \(-0.572139\pi\) | ||||
−0.224697 | + | 0.974429i | \(0.572139\pi\) | |||||||
\(80\) | 0.595639 | 0.0665945 | ||||||||
\(81\) | 26.9226 | 2.99140 | ||||||||
\(82\) | −8.82027 | −0.974036 | ||||||||
\(83\) | −10.3525 | −1.13634 | −0.568170 | − | 0.822911i | \(-0.692348\pi\) | ||||
−0.568170 | + | 0.822911i | \(0.692348\pi\) | |||||||
\(84\) | −9.77549 | −1.06659 | ||||||||
\(85\) | −1.13395 | −0.122994 | ||||||||
\(86\) | −4.95602 | −0.534421 | ||||||||
\(87\) | −0.267111 | −0.0286373 | ||||||||
\(88\) | −0.495097 | −0.0527775 | ||||||||
\(89\) | −11.0506 | −1.17137 | −0.585683 | − | 0.810540i | \(-0.699173\pi\) | ||||
−0.585683 | + | 0.810540i | \(0.699173\pi\) | |||||||
\(90\) | −4.57355 | −0.482095 | ||||||||
\(91\) | 8.51717 | 0.892842 | ||||||||
\(92\) | −8.88616 | −0.926446 | ||||||||
\(93\) | −15.4542 | −1.60253 | ||||||||
\(94\) | 2.10145 | 0.216748 | ||||||||
\(95\) | −0.595639 | −0.0611113 | ||||||||
\(96\) | −3.26778 | −0.333517 | ||||||||
\(97\) | −6.88378 | −0.698942 | −0.349471 | − | 0.936947i | \(-0.613639\pi\) | ||||
−0.349471 | + | 0.936947i | \(0.613639\pi\) | |||||||
\(98\) | −1.94892 | −0.196871 | ||||||||
\(99\) | 3.80155 | 0.382070 | ||||||||
\(100\) | −4.64521 | −0.464521 | ||||||||
\(101\) | −14.4083 | −1.43368 | −0.716840 | − | 0.697238i | \(-0.754412\pi\) | ||||
−0.716840 | + | 0.697238i | \(0.754412\pi\) | |||||||
\(102\) | 6.22104 | 0.615974 | ||||||||
\(103\) | −18.8307 | −1.85545 | −0.927723 | − | 0.373269i | \(-0.878237\pi\) | ||||
−0.927723 | + | 0.373269i | \(0.878237\pi\) | |||||||
\(104\) | 2.84715 | 0.279186 | ||||||||
\(105\) | −5.82266 | −0.568234 | ||||||||
\(106\) | −0.933659 | −0.0906850 | ||||||||
\(107\) | −8.60229 | −0.831614 | −0.415807 | − | 0.909453i | \(-0.636501\pi\) | ||||
−0.415807 | + | 0.909453i | \(0.636501\pi\) | |||||||
\(108\) | 15.2880 | 1.47109 | ||||||||
\(109\) | 15.8524 | 1.51838 | 0.759190 | − | 0.650869i | \(-0.225595\pi\) | ||||
0.759190 | + | 0.650869i | \(0.225595\pi\) | |||||||
\(110\) | −0.294899 | −0.0281175 | ||||||||
\(111\) | −3.61180 | −0.342817 | ||||||||
\(112\) | −2.99147 | −0.282668 | ||||||||
\(113\) | 1.67460 | 0.157533 | 0.0787664 | − | 0.996893i | \(-0.474902\pi\) | ||||
0.0787664 | + | 0.996893i | \(0.474902\pi\) | |||||||
\(114\) | 3.26778 | 0.306056 | ||||||||
\(115\) | −5.29294 | −0.493570 | ||||||||
\(116\) | −0.0817407 | −0.00758943 | ||||||||
\(117\) | −21.8615 | −2.02110 | ||||||||
\(118\) | −10.6946 | −0.984519 | ||||||||
\(119\) | 5.69502 | 0.522061 | ||||||||
\(120\) | −1.94642 | −0.177683 | ||||||||
\(121\) | −10.7549 | −0.977716 | ||||||||
\(122\) | −6.78989 | −0.614728 | ||||||||
\(123\) | 28.8227 | 2.59886 | ||||||||
\(124\) | −4.72927 | −0.424701 | ||||||||
\(125\) | −5.74507 | −0.513854 | ||||||||
\(126\) | 22.9697 | 2.04631 | ||||||||
\(127\) | −19.0429 | −1.68978 | −0.844892 | − | 0.534937i | \(-0.820335\pi\) | ||||
−0.844892 | + | 0.534937i | \(0.820335\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 16.1952 | 1.42591 | ||||||||
\(130\) | 1.69587 | 0.148738 | ||||||||
\(131\) | −3.50230 | −0.305997 | −0.152999 | − | 0.988226i | \(-0.548893\pi\) | ||||
−0.152999 | + | 0.988226i | \(0.548893\pi\) | |||||||
\(132\) | 1.61787 | 0.140817 | ||||||||
\(133\) | 2.99147 | 0.259394 | ||||||||
\(134\) | 3.28824 | 0.284061 | ||||||||
\(135\) | 9.10612 | 0.783730 | ||||||||
\(136\) | 1.90375 | 0.163245 | ||||||||
\(137\) | −8.32344 | −0.711119 | −0.355560 | − | 0.934654i | \(-0.615710\pi\) | ||||
−0.355560 | + | 0.934654i | \(0.615710\pi\) | |||||||
\(138\) | 29.0380 | 2.47188 | ||||||||
\(139\) | 9.07860 | 0.770036 | 0.385018 | − | 0.922909i | \(-0.374195\pi\) | ||||
0.385018 | + | 0.922909i | \(0.374195\pi\) | |||||||
\(140\) | −1.78184 | −0.150593 | ||||||||
\(141\) | −6.86708 | −0.578313 | ||||||||
\(142\) | 13.8027 | 1.15830 | ||||||||
\(143\) | −1.40962 | −0.117878 | ||||||||
\(144\) | 7.67840 | 0.639866 | ||||||||
\(145\) | −0.0486880 | −0.00404332 | ||||||||
\(146\) | −10.0079 | −0.828258 | ||||||||
\(147\) | 6.36865 | 0.525277 | ||||||||
\(148\) | −1.10528 | −0.0908532 | ||||||||
\(149\) | −21.6964 | −1.77744 | −0.888721 | − | 0.458449i | \(-0.848405\pi\) | ||||
−0.888721 | + | 0.458449i | \(0.848405\pi\) | |||||||
\(150\) | 15.1795 | 1.23940 | ||||||||
\(151\) | −5.30999 | −0.432121 | −0.216060 | − | 0.976380i | \(-0.569321\pi\) | ||||
−0.216060 | + | 0.976380i | \(0.569321\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −14.6177 | −1.18177 | ||||||||
\(154\) | 1.48107 | 0.119348 | ||||||||
\(155\) | −2.81694 | −0.226262 | ||||||||
\(156\) | −9.30386 | −0.744905 | ||||||||
\(157\) | −10.6815 | −0.852476 | −0.426238 | − | 0.904611i | \(-0.640161\pi\) | ||||
−0.426238 | + | 0.904611i | \(0.640161\pi\) | |||||||
\(158\) | 3.99429 | 0.317769 | ||||||||
\(159\) | 3.05099 | 0.241960 | ||||||||
\(160\) | −0.595639 | −0.0470894 | ||||||||
\(161\) | 26.5827 | 2.09501 | ||||||||
\(162\) | −26.9226 | −2.11524 | ||||||||
\(163\) | −3.40812 | −0.266944 | −0.133472 | − | 0.991053i | \(-0.542613\pi\) | ||||
−0.133472 | + | 0.991053i | \(0.542613\pi\) | |||||||
\(164\) | 8.82027 | 0.688747 | ||||||||
\(165\) | 0.963666 | 0.0750213 | ||||||||
\(166\) | 10.3525 | 0.803513 | ||||||||
\(167\) | 0.313528 | 0.0242616 | 0.0121308 | − | 0.999926i | \(-0.496139\pi\) | ||||
0.0121308 | + | 0.999926i | \(0.496139\pi\) | |||||||
\(168\) | 9.77549 | 0.754195 | ||||||||
\(169\) | −4.89375 | −0.376442 | ||||||||
\(170\) | 1.13395 | 0.0869698 | ||||||||
\(171\) | −7.67840 | −0.587182 | ||||||||
\(172\) | 4.95602 | 0.377893 | ||||||||
\(173\) | −0.365104 | −0.0277583 | −0.0138792 | − | 0.999904i | \(-0.504418\pi\) | ||||
−0.0138792 | + | 0.999904i | \(0.504418\pi\) | |||||||
\(174\) | 0.267111 | 0.0202496 | ||||||||
\(175\) | 13.8960 | 1.05044 | ||||||||
\(176\) | 0.495097 | 0.0373194 | ||||||||
\(177\) | 34.9477 | 2.62683 | ||||||||
\(178\) | 11.0506 | 0.828280 | ||||||||
\(179\) | −0.0604155 | −0.00451566 | −0.00225783 | − | 0.999997i | \(-0.500719\pi\) | ||||
−0.00225783 | + | 0.999997i | \(0.500719\pi\) | |||||||
\(180\) | 4.57355 | 0.340892 | ||||||||
\(181\) | 22.5406 | 1.67543 | 0.837715 | − | 0.546107i | \(-0.183891\pi\) | ||||
0.837715 | + | 0.546107i | \(0.183891\pi\) | |||||||
\(182\) | −8.51717 | −0.631335 | ||||||||
\(183\) | 22.1879 | 1.64018 | ||||||||
\(184\) | 8.88616 | 0.655096 | ||||||||
\(185\) | −0.658346 | −0.0484025 | ||||||||
\(186\) | 15.4542 | 1.13316 | ||||||||
\(187\) | −0.942541 | −0.0689254 | ||||||||
\(188\) | −2.10145 | −0.153264 | ||||||||
\(189\) | −45.7336 | −3.32663 | ||||||||
\(190\) | 0.595639 | 0.0432122 | ||||||||
\(191\) | 2.41398 | 0.174670 | 0.0873348 | − | 0.996179i | \(-0.472165\pi\) | ||||
0.0873348 | + | 0.996179i | \(0.472165\pi\) | |||||||
\(192\) | 3.26778 | 0.235832 | ||||||||
\(193\) | 17.3804 | 1.25107 | 0.625535 | − | 0.780196i | \(-0.284881\pi\) | ||||
0.625535 | + | 0.780196i | \(0.284881\pi\) | |||||||
\(194\) | 6.88378 | 0.494227 | ||||||||
\(195\) | −5.54174 | −0.396852 | ||||||||
\(196\) | 1.94892 | 0.139209 | ||||||||
\(197\) | 1.96372 | 0.139909 | 0.0699545 | − | 0.997550i | \(-0.477715\pi\) | ||||
0.0699545 | + | 0.997550i | \(0.477715\pi\) | |||||||
\(198\) | −3.80155 | −0.270165 | ||||||||
\(199\) | 6.83514 | 0.484530 | 0.242265 | − | 0.970210i | \(-0.422110\pi\) | ||||
0.242265 | + | 0.970210i | \(0.422110\pi\) | |||||||
\(200\) | 4.64521 | 0.328466 | ||||||||
\(201\) | −10.7453 | −0.757912 | ||||||||
\(202\) | 14.4083 | 1.01376 | ||||||||
\(203\) | 0.244525 | 0.0171623 | ||||||||
\(204\) | −6.22104 | −0.435560 | ||||||||
\(205\) | 5.25370 | 0.366934 | ||||||||
\(206\) | 18.8307 | 1.31200 | ||||||||
\(207\) | −68.2315 | −4.74241 | ||||||||
\(208\) | −2.84715 | −0.197414 | ||||||||
\(209\) | −0.495097 | −0.0342466 | ||||||||
\(210\) | 5.82266 | 0.401802 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 0.933659 | 0.0641240 | ||||||||
\(213\) | −45.1042 | −3.09049 | ||||||||
\(214\) | 8.60229 | 0.588040 | ||||||||
\(215\) | 2.95200 | 0.201325 | ||||||||
\(216\) | −15.2880 | −1.04021 | ||||||||
\(217\) | 14.1475 | 0.960395 | ||||||||
\(218\) | −15.8524 | −1.07366 | ||||||||
\(219\) | 32.7036 | 2.20990 | ||||||||
\(220\) | 0.294899 | 0.0198821 | ||||||||
\(221\) | 5.42026 | 0.364606 | ||||||||
\(222\) | 3.61180 | 0.242408 | ||||||||
\(223\) | 5.67181 | 0.379813 | 0.189906 | − | 0.981802i | \(-0.439182\pi\) | ||||
0.189906 | + | 0.981802i | \(0.439182\pi\) | |||||||
\(224\) | 2.99147 | 0.199876 | ||||||||
\(225\) | −35.6678 | −2.37785 | ||||||||
\(226\) | −1.67460 | −0.111393 | ||||||||
\(227\) | 21.6723 | 1.43844 | 0.719220 | − | 0.694782i | \(-0.244499\pi\) | ||||
0.719220 | + | 0.694782i | \(0.244499\pi\) | |||||||
\(228\) | −3.26778 | −0.216414 | ||||||||
\(229\) | −11.7675 | −0.777616 | −0.388808 | − | 0.921319i | \(-0.627113\pi\) | ||||
−0.388808 | + | 0.921319i | \(0.627113\pi\) | |||||||
\(230\) | 5.29294 | 0.349006 | ||||||||
\(231\) | −4.83982 | −0.318436 | ||||||||
\(232\) | 0.0817407 | 0.00536654 | ||||||||
\(233\) | 18.8101 | 1.23229 | 0.616147 | − | 0.787631i | \(-0.288693\pi\) | ||||
0.616147 | + | 0.787631i | \(0.288693\pi\) | |||||||
\(234\) | 21.8615 | 1.42913 | ||||||||
\(235\) | −1.25171 | −0.0816523 | ||||||||
\(236\) | 10.6946 | 0.696160 | ||||||||
\(237\) | −13.0525 | −0.847850 | ||||||||
\(238\) | −5.69502 | −0.369153 | ||||||||
\(239\) | 1.98719 | 0.128541 | 0.0642703 | − | 0.997933i | \(-0.479528\pi\) | ||||
0.0642703 | + | 0.997933i | \(0.479528\pi\) | |||||||
\(240\) | 1.94642 | 0.125641 | ||||||||
\(241\) | −16.8906 | −1.08802 | −0.544010 | − | 0.839079i | \(-0.683095\pi\) | ||||
−0.544010 | + | 0.839079i | \(0.683095\pi\) | |||||||
\(242\) | 10.7549 | 0.691350 | ||||||||
\(243\) | 42.1132 | 2.70156 | ||||||||
\(244\) | 6.78989 | 0.434678 | ||||||||
\(245\) | 1.16085 | 0.0741642 | ||||||||
\(246\) | −28.8227 | −1.83767 | ||||||||
\(247\) | 2.84715 | 0.181160 | ||||||||
\(248\) | 4.72927 | 0.300309 | ||||||||
\(249\) | −33.8299 | −2.14388 | ||||||||
\(250\) | 5.74507 | 0.363350 | ||||||||
\(251\) | −30.2392 | −1.90868 | −0.954341 | − | 0.298719i | \(-0.903441\pi\) | ||||
−0.954341 | + | 0.298719i | \(0.903441\pi\) | |||||||
\(252\) | −22.9697 | −1.44696 | ||||||||
\(253\) | −4.39951 | −0.276595 | ||||||||
\(254\) | 19.0429 | 1.19486 | ||||||||
\(255\) | −3.70549 | −0.232047 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.61342 | 0.537290 | 0.268645 | − | 0.963239i | \(-0.413424\pi\) | ||||
0.268645 | + | 0.963239i | \(0.413424\pi\) | |||||||
\(258\) | −16.1952 | −1.00827 | ||||||||
\(259\) | 3.30641 | 0.205450 | ||||||||
\(260\) | −1.69587 | −0.105174 | ||||||||
\(261\) | −0.627638 | −0.0388498 | ||||||||
\(262\) | 3.50230 | 0.216373 | ||||||||
\(263\) | 2.64067 | 0.162831 | 0.0814154 | − | 0.996680i | \(-0.474056\pi\) | ||||
0.0814154 | + | 0.996680i | \(0.474056\pi\) | |||||||
\(264\) | −1.61787 | −0.0995730 | ||||||||
\(265\) | 0.556124 | 0.0341624 | ||||||||
\(266\) | −2.99147 | −0.183419 | ||||||||
\(267\) | −36.1111 | −2.20996 | ||||||||
\(268\) | −3.28824 | −0.200861 | ||||||||
\(269\) | 9.86437 | 0.601441 | 0.300721 | − | 0.953712i | \(-0.402773\pi\) | ||||
0.300721 | + | 0.953712i | \(0.402773\pi\) | |||||||
\(270\) | −9.10612 | −0.554181 | ||||||||
\(271\) | 9.89556 | 0.601113 | 0.300556 | − | 0.953764i | \(-0.402828\pi\) | ||||
0.300556 | + | 0.953764i | \(0.402828\pi\) | |||||||
\(272\) | −1.90375 | −0.115432 | ||||||||
\(273\) | 27.8323 | 1.68448 | ||||||||
\(274\) | 8.32344 | 0.502837 | ||||||||
\(275\) | −2.29983 | −0.138685 | ||||||||
\(276\) | −29.0380 | −1.74788 | ||||||||
\(277\) | −15.4663 | −0.929278 | −0.464639 | − | 0.885500i | \(-0.653816\pi\) | ||||
−0.464639 | + | 0.885500i | \(0.653816\pi\) | |||||||
\(278\) | −9.07860 | −0.544498 | ||||||||
\(279\) | −36.3132 | −2.17402 | ||||||||
\(280\) | 1.78184 | 0.106485 | ||||||||
\(281\) | 12.1275 | 0.723467 | 0.361734 | − | 0.932281i | \(-0.382185\pi\) | ||||
0.361734 | + | 0.932281i | \(0.382185\pi\) | |||||||
\(282\) | 6.86708 | 0.408929 | ||||||||
\(283\) | 22.4200 | 1.33273 | 0.666364 | − | 0.745626i | \(-0.267850\pi\) | ||||
0.666364 | + | 0.745626i | \(0.267850\pi\) | |||||||
\(284\) | −13.8027 | −0.819039 | ||||||||
\(285\) | −1.94642 | −0.115296 | ||||||||
\(286\) | 1.40962 | 0.0833523 | ||||||||
\(287\) | −26.3856 | −1.55749 | ||||||||
\(288\) | −7.67840 | −0.452454 | ||||||||
\(289\) | −13.3757 | −0.786808 | ||||||||
\(290\) | 0.0486880 | 0.00285906 | ||||||||
\(291\) | −22.4947 | −1.31866 | ||||||||
\(292\) | 10.0079 | 0.585667 | ||||||||
\(293\) | 31.7772 | 1.85644 | 0.928221 | − | 0.372029i | \(-0.121338\pi\) | ||||
0.928221 | + | 0.372029i | \(0.121338\pi\) | |||||||
\(294\) | −6.36865 | −0.371427 | ||||||||
\(295\) | 6.37013 | 0.370883 | ||||||||
\(296\) | 1.10528 | 0.0642429 | ||||||||
\(297\) | 7.56903 | 0.439200 | ||||||||
\(298\) | 21.6964 | 1.25684 | ||||||||
\(299\) | 25.3002 | 1.46315 | ||||||||
\(300\) | −15.1795 | −0.876391 | ||||||||
\(301\) | −14.8258 | −0.854545 | ||||||||
\(302\) | 5.30999 | 0.305556 | ||||||||
\(303\) | −47.0832 | −2.70486 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 4.04433 | 0.231577 | ||||||||
\(306\) | 14.6177 | 0.835640 | ||||||||
\(307\) | −31.2263 | −1.78218 | −0.891089 | − | 0.453828i | \(-0.850058\pi\) | ||||
−0.891089 | + | 0.453828i | \(0.850058\pi\) | |||||||
\(308\) | −1.48107 | −0.0843918 | ||||||||
\(309\) | −61.5347 | −3.50059 | ||||||||
\(310\) | 2.81694 | 0.159991 | ||||||||
\(311\) | 3.56826 | 0.202338 | 0.101169 | − | 0.994869i | \(-0.467742\pi\) | ||||
0.101169 | + | 0.994869i | \(0.467742\pi\) | |||||||
\(312\) | 9.30386 | 0.526727 | ||||||||
\(313\) | −9.21005 | −0.520583 | −0.260291 | − | 0.965530i | \(-0.583819\pi\) | ||||
−0.260291 | + | 0.965530i | \(0.583819\pi\) | |||||||
\(314\) | 10.6815 | 0.602792 | ||||||||
\(315\) | −13.6817 | −0.770875 | ||||||||
\(316\) | −3.99429 | −0.224697 | ||||||||
\(317\) | −29.0885 | −1.63377 | −0.816887 | − | 0.576798i | \(-0.804302\pi\) | ||||
−0.816887 | + | 0.576798i | \(0.804302\pi\) | |||||||
\(318\) | −3.05099 | −0.171091 | ||||||||
\(319\) | −0.0404696 | −0.00226586 | ||||||||
\(320\) | 0.595639 | 0.0332972 | ||||||||
\(321\) | −28.1104 | −1.56897 | ||||||||
\(322\) | −26.5827 | −1.48140 | ||||||||
\(323\) | 1.90375 | 0.105927 | ||||||||
\(324\) | 26.9226 | 1.49570 | ||||||||
\(325\) | 13.2256 | 0.733625 | ||||||||
\(326\) | 3.40812 | 0.188758 | ||||||||
\(327\) | 51.8020 | 2.86466 | ||||||||
\(328\) | −8.82027 | −0.487018 | ||||||||
\(329\) | 6.28644 | 0.346583 | ||||||||
\(330\) | −0.963666 | −0.0530481 | ||||||||
\(331\) | −11.4134 | −0.627336 | −0.313668 | − | 0.949533i | \(-0.601558\pi\) | ||||
−0.313668 | + | 0.949533i | \(0.601558\pi\) | |||||||
\(332\) | −10.3525 | −0.568170 | ||||||||
\(333\) | −8.48675 | −0.465071 | ||||||||
\(334\) | −0.313528 | −0.0171555 | ||||||||
\(335\) | −1.95861 | −0.107010 | ||||||||
\(336\) | −9.77549 | −0.533296 | ||||||||
\(337\) | −10.7156 | −0.583715 | −0.291858 | − | 0.956462i | \(-0.594273\pi\) | ||||
−0.291858 | + | 0.956462i | \(0.594273\pi\) | |||||||
\(338\) | 4.89375 | 0.266185 | ||||||||
\(339\) | 5.47222 | 0.297210 | ||||||||
\(340\) | −1.13395 | −0.0614969 | ||||||||
\(341\) | −2.34145 | −0.126797 | ||||||||
\(342\) | 7.67840 | 0.415200 | ||||||||
\(343\) | 15.1102 | 0.815873 | ||||||||
\(344\) | −4.95602 | −0.267211 | ||||||||
\(345\) | −17.2962 | −0.931195 | ||||||||
\(346\) | 0.365104 | 0.0196281 | ||||||||
\(347\) | −7.44385 | −0.399607 | −0.199803 | − | 0.979836i | \(-0.564030\pi\) | ||||
−0.199803 | + | 0.979836i | \(0.564030\pi\) | |||||||
\(348\) | −0.267111 | −0.0143186 | ||||||||
\(349\) | 27.2479 | 1.45855 | 0.729273 | − | 0.684223i | \(-0.239858\pi\) | ||||
0.729273 | + | 0.684223i | \(0.239858\pi\) | |||||||
\(350\) | −13.8960 | −0.742775 | ||||||||
\(351\) | −43.5271 | −2.32331 | ||||||||
\(352\) | −0.495097 | −0.0263888 | ||||||||
\(353\) | −4.62222 | −0.246016 | −0.123008 | − | 0.992406i | \(-0.539254\pi\) | ||||
−0.123008 | + | 0.992406i | \(0.539254\pi\) | |||||||
\(354\) | −34.9477 | −1.85745 | ||||||||
\(355\) | −8.22142 | −0.436348 | ||||||||
\(356\) | −11.0506 | −0.585683 | ||||||||
\(357\) | 18.6101 | 0.984949 | ||||||||
\(358\) | 0.0604155 | 0.00319306 | ||||||||
\(359\) | 28.0275 | 1.47923 | 0.739617 | − | 0.673028i | \(-0.235007\pi\) | ||||
0.739617 | + | 0.673028i | \(0.235007\pi\) | |||||||
\(360\) | −4.57355 | −0.241047 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −22.5406 | −1.18471 | ||||||||
\(363\) | −35.1446 | −1.84461 | ||||||||
\(364\) | 8.51717 | 0.446421 | ||||||||
\(365\) | 5.96108 | 0.312017 | ||||||||
\(366\) | −22.1879 | −1.15978 | ||||||||
\(367\) | 12.8611 | 0.671345 | 0.335672 | − | 0.941979i | \(-0.391037\pi\) | ||||
0.335672 | + | 0.941979i | \(0.391037\pi\) | |||||||
\(368\) | −8.88616 | −0.463223 | ||||||||
\(369\) | 67.7255 | 3.52565 | ||||||||
\(370\) | 0.658346 | 0.0342258 | ||||||||
\(371\) | −2.79302 | −0.145006 | ||||||||
\(372\) | −15.4542 | −0.801265 | ||||||||
\(373\) | 18.6028 | 0.963215 | 0.481608 | − | 0.876387i | \(-0.340053\pi\) | ||||
0.481608 | + | 0.876387i | \(0.340053\pi\) | |||||||
\(374\) | 0.942541 | 0.0487376 | ||||||||
\(375\) | −18.7736 | −0.969466 | ||||||||
\(376\) | 2.10145 | 0.108374 | ||||||||
\(377\) | 0.232728 | 0.0119861 | ||||||||
\(378\) | 45.7336 | 2.35228 | ||||||||
\(379\) | 27.9555 | 1.43598 | 0.717989 | − | 0.696055i | \(-0.245063\pi\) | ||||
0.717989 | + | 0.696055i | \(0.245063\pi\) | |||||||
\(380\) | −0.595639 | −0.0305556 | ||||||||
\(381\) | −62.2280 | −3.18804 | ||||||||
\(382\) | −2.41398 | −0.123510 | ||||||||
\(383\) | 27.7445 | 1.41768 | 0.708839 | − | 0.705371i | \(-0.249219\pi\) | ||||
0.708839 | + | 0.705371i | \(0.249219\pi\) | |||||||
\(384\) | −3.26778 | −0.166758 | ||||||||
\(385\) | −0.882184 | −0.0449602 | ||||||||
\(386\) | −17.3804 | −0.884640 | ||||||||
\(387\) | 38.0543 | 1.93441 | ||||||||
\(388\) | −6.88378 | −0.349471 | ||||||||
\(389\) | 14.6916 | 0.744892 | 0.372446 | − | 0.928054i | \(-0.378519\pi\) | ||||
0.372446 | + | 0.928054i | \(0.378519\pi\) | |||||||
\(390\) | 5.54174 | 0.280617 | ||||||||
\(391\) | 16.9170 | 0.855530 | ||||||||
\(392\) | −1.94892 | −0.0984354 | ||||||||
\(393\) | −11.4448 | −0.577312 | ||||||||
\(394\) | −1.96372 | −0.0989306 | ||||||||
\(395\) | −2.37916 | −0.119708 | ||||||||
\(396\) | 3.80155 | 0.191035 | ||||||||
\(397\) | −2.97296 | −0.149208 | −0.0746042 | − | 0.997213i | \(-0.523769\pi\) | ||||
−0.0746042 | + | 0.997213i | \(0.523769\pi\) | |||||||
\(398\) | −6.83514 | −0.342614 | ||||||||
\(399\) | 9.77549 | 0.489386 | ||||||||
\(400\) | −4.64521 | −0.232261 | ||||||||
\(401\) | 37.9993 | 1.89760 | 0.948798 | − | 0.315883i | \(-0.102301\pi\) | ||||
0.948798 | + | 0.315883i | \(0.102301\pi\) | |||||||
\(402\) | 10.7453 | 0.535925 | ||||||||
\(403\) | 13.4649 | 0.670737 | ||||||||
\(404\) | −14.4083 | −0.716840 | ||||||||
\(405\) | 16.0361 | 0.796842 | ||||||||
\(406\) | −0.244525 | −0.0121356 | ||||||||
\(407\) | −0.547219 | −0.0271247 | ||||||||
\(408\) | 6.22104 | 0.307987 | ||||||||
\(409\) | −7.73451 | −0.382447 | −0.191224 | − | 0.981547i | \(-0.561246\pi\) | ||||
−0.191224 | + | 0.981547i | \(0.561246\pi\) | |||||||
\(410\) | −5.25370 | −0.259462 | ||||||||
\(411\) | −27.1992 | −1.34164 | ||||||||
\(412\) | −18.8307 | −0.927723 | ||||||||
\(413\) | −31.9927 | −1.57426 | ||||||||
\(414\) | 68.2315 | 3.35339 | ||||||||
\(415\) | −6.16638 | −0.302696 | ||||||||
\(416\) | 2.84715 | 0.139593 | ||||||||
\(417\) | 29.6669 | 1.45279 | ||||||||
\(418\) | 0.495097 | 0.0242160 | ||||||||
\(419\) | −28.8403 | −1.40894 | −0.704470 | − | 0.709734i | \(-0.748815\pi\) | ||||
−0.704470 | + | 0.709734i | \(0.748815\pi\) | |||||||
\(420\) | −5.82266 | −0.284117 | ||||||||
\(421\) | −14.2895 | −0.696426 | −0.348213 | − | 0.937415i | \(-0.613211\pi\) | ||||
−0.348213 | + | 0.937415i | \(0.613211\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −16.1358 | −0.784548 | ||||||||
\(424\) | −0.933659 | −0.0453425 | ||||||||
\(425\) | 8.84332 | 0.428964 | ||||||||
\(426\) | 45.1042 | 2.18530 | ||||||||
\(427\) | −20.3118 | −0.982956 | ||||||||
\(428\) | −8.60229 | −0.415807 | ||||||||
\(429\) | −4.60631 | −0.222395 | ||||||||
\(430\) | −2.95200 | −0.142358 | ||||||||
\(431\) | 18.3478 | 0.883782 | 0.441891 | − | 0.897069i | \(-0.354308\pi\) | ||||
0.441891 | + | 0.897069i | \(0.354308\pi\) | |||||||
\(432\) | 15.2880 | 0.735543 | ||||||||
\(433\) | 6.45669 | 0.310289 | 0.155144 | − | 0.987892i | \(-0.450416\pi\) | ||||
0.155144 | + | 0.987892i | \(0.450416\pi\) | |||||||
\(434\) | −14.1475 | −0.679102 | ||||||||
\(435\) | −0.159102 | −0.00762834 | ||||||||
\(436\) | 15.8524 | 0.759190 | ||||||||
\(437\) | 8.88616 | 0.425083 | ||||||||
\(438\) | −32.7036 | −1.56264 | ||||||||
\(439\) | −33.6109 | −1.60416 | −0.802082 | − | 0.597215i | \(-0.796274\pi\) | ||||
−0.802082 | + | 0.597215i | \(0.796274\pi\) | |||||||
\(440\) | −0.294899 | −0.0140588 | ||||||||
\(441\) | 14.9646 | 0.712599 | ||||||||
\(442\) | −5.42026 | −0.257815 | ||||||||
\(443\) | −23.1564 | −1.10019 | −0.550097 | − | 0.835101i | \(-0.685409\pi\) | ||||
−0.550097 | + | 0.835101i | \(0.685409\pi\) | |||||||
\(444\) | −3.61180 | −0.171409 | ||||||||
\(445\) | −6.58219 | −0.312026 | ||||||||
\(446\) | −5.67181 | −0.268568 | ||||||||
\(447\) | −70.8992 | −3.35342 | ||||||||
\(448\) | −2.99147 | −0.141334 | ||||||||
\(449\) | 10.3057 | 0.486355 | 0.243178 | − | 0.969982i | \(-0.421810\pi\) | ||||
0.243178 | + | 0.969982i | \(0.421810\pi\) | |||||||
\(450\) | 35.6678 | 1.68140 | ||||||||
\(451\) | 4.36689 | 0.205629 | ||||||||
\(452\) | 1.67460 | 0.0787664 | ||||||||
\(453\) | −17.3519 | −0.815263 | ||||||||
\(454\) | −21.6723 | −1.01713 | ||||||||
\(455\) | 5.07316 | 0.237833 | ||||||||
\(456\) | 3.26778 | 0.153028 | ||||||||
\(457\) | −12.5752 | −0.588243 | −0.294122 | − | 0.955768i | \(-0.595027\pi\) | ||||
−0.294122 | + | 0.955768i | \(0.595027\pi\) | |||||||
\(458\) | 11.7675 | 0.549858 | ||||||||
\(459\) | −29.1045 | −1.35848 | ||||||||
\(460\) | −5.29294 | −0.246785 | ||||||||
\(461\) | 41.3655 | 1.92658 | 0.963292 | − | 0.268458i | \(-0.0865139\pi\) | ||||
0.963292 | + | 0.268458i | \(0.0865139\pi\) | |||||||
\(462\) | 4.83982 | 0.225169 | ||||||||
\(463\) | 1.50708 | 0.0700399 | 0.0350199 | − | 0.999387i | \(-0.488851\pi\) | ||||
0.0350199 | + | 0.999387i | \(0.488851\pi\) | |||||||
\(464\) | −0.0817407 | −0.00379472 | ||||||||
\(465\) | −9.20514 | −0.426878 | ||||||||
\(466\) | −18.8101 | −0.871363 | ||||||||
\(467\) | −35.0388 | −1.62140 | −0.810702 | − | 0.585459i | \(-0.800914\pi\) | ||||
−0.810702 | + | 0.585459i | \(0.800914\pi\) | |||||||
\(468\) | −21.8615 | −1.01055 | ||||||||
\(469\) | 9.83670 | 0.454216 | ||||||||
\(470\) | 1.25171 | 0.0577369 | ||||||||
\(471\) | −34.9048 | −1.60833 | ||||||||
\(472\) | −10.6946 | −0.492260 | ||||||||
\(473\) | 2.45371 | 0.112822 | ||||||||
\(474\) | 13.0525 | 0.599520 | ||||||||
\(475\) | 4.64521 | 0.213137 | ||||||||
\(476\) | 5.69502 | 0.261031 | ||||||||
\(477\) | 7.16901 | 0.328246 | ||||||||
\(478\) | −1.98719 | −0.0908919 | ||||||||
\(479\) | −14.0967 | −0.644096 | −0.322048 | − | 0.946723i | \(-0.604371\pi\) | ||||
−0.322048 | + | 0.946723i | \(0.604371\pi\) | |||||||
\(480\) | −1.94642 | −0.0888414 | ||||||||
\(481\) | 3.14689 | 0.143486 | ||||||||
\(482\) | 16.8906 | 0.769346 | ||||||||
\(483\) | 86.8665 | 3.95256 | ||||||||
\(484\) | −10.7549 | −0.488858 | ||||||||
\(485\) | −4.10025 | −0.186183 | ||||||||
\(486\) | −42.1132 | −1.91029 | ||||||||
\(487\) | −17.0378 | −0.772057 | −0.386029 | − | 0.922487i | \(-0.626153\pi\) | ||||
−0.386029 | + | 0.922487i | \(0.626153\pi\) | |||||||
\(488\) | −6.78989 | −0.307364 | ||||||||
\(489\) | −11.1370 | −0.503631 | ||||||||
\(490\) | −1.16085 | −0.0524420 | ||||||||
\(491\) | 0.328562 | 0.0148278 | 0.00741391 | − | 0.999973i | \(-0.497640\pi\) | ||||
0.00741391 | + | 0.999973i | \(0.497640\pi\) | |||||||
\(492\) | 28.8227 | 1.29943 | ||||||||
\(493\) | 0.155614 | 0.00700849 | ||||||||
\(494\) | −2.84715 | −0.128099 | ||||||||
\(495\) | 2.26435 | 0.101775 | ||||||||
\(496\) | −4.72927 | −0.212351 | ||||||||
\(497\) | 41.2904 | 1.85213 | ||||||||
\(498\) | 33.8299 | 1.51595 | ||||||||
\(499\) | 1.49375 | 0.0668694 | 0.0334347 | − | 0.999441i | \(-0.489355\pi\) | ||||
0.0334347 | + | 0.999441i | \(0.489355\pi\) | |||||||
\(500\) | −5.74507 | −0.256927 | ||||||||
\(501\) | 1.02454 | 0.0457732 | ||||||||
\(502\) | 30.2392 | 1.34964 | ||||||||
\(503\) | 19.7560 | 0.880877 | 0.440438 | − | 0.897783i | \(-0.354823\pi\) | ||||
0.440438 | + | 0.897783i | \(0.354823\pi\) | |||||||
\(504\) | 22.9697 | 1.02315 | ||||||||
\(505\) | −8.58215 | −0.381901 | ||||||||
\(506\) | 4.39951 | 0.195582 | ||||||||
\(507\) | −15.9917 | −0.710216 | ||||||||
\(508\) | −19.0429 | −0.844892 | ||||||||
\(509\) | −9.61557 | −0.426203 | −0.213101 | − | 0.977030i | \(-0.568356\pi\) | ||||
−0.213101 | + | 0.977030i | \(0.568356\pi\) | |||||||
\(510\) | 3.70549 | 0.164082 | ||||||||
\(511\) | −29.9383 | −1.32439 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −15.2880 | −0.674981 | ||||||||
\(514\) | −8.61342 | −0.379922 | ||||||||
\(515\) | −11.2163 | −0.494250 | ||||||||
\(516\) | 16.1952 | 0.712953 | ||||||||
\(517\) | −1.04042 | −0.0457577 | ||||||||
\(518\) | −3.30641 | −0.145275 | ||||||||
\(519\) | −1.19308 | −0.0523704 | ||||||||
\(520\) | 1.69587 | 0.0743689 | ||||||||
\(521\) | −32.5266 | −1.42502 | −0.712508 | − | 0.701664i | \(-0.752441\pi\) | ||||
−0.712508 | + | 0.701664i | \(0.752441\pi\) | |||||||
\(522\) | 0.627638 | 0.0274709 | ||||||||
\(523\) | 1.88304 | 0.0823395 | 0.0411697 | − | 0.999152i | \(-0.486892\pi\) | ||||
0.0411697 | + | 0.999152i | \(0.486892\pi\) | |||||||
\(524\) | −3.50230 | −0.152999 | ||||||||
\(525\) | 45.4092 | 1.98182 | ||||||||
\(526\) | −2.64067 | −0.115139 | ||||||||
\(527\) | 9.00335 | 0.392192 | ||||||||
\(528\) | 1.61787 | 0.0704087 | ||||||||
\(529\) | 55.9638 | 2.43321 | ||||||||
\(530\) | −0.556124 | −0.0241565 | ||||||||
\(531\) | 82.1175 | 3.56360 | ||||||||
\(532\) | 2.99147 | 0.129697 | ||||||||
\(533\) | −25.1126 | −1.08775 | ||||||||
\(534\) | 36.1111 | 1.56268 | ||||||||
\(535\) | −5.12386 | −0.221524 | ||||||||
\(536\) | 3.28824 | 0.142030 | ||||||||
\(537\) | −0.197425 | −0.00851950 | ||||||||
\(538\) | −9.86437 | −0.425283 | ||||||||
\(539\) | 0.964905 | 0.0415614 | ||||||||
\(540\) | 9.10612 | 0.391865 | ||||||||
\(541\) | −0.671178 | −0.0288562 | −0.0144281 | − | 0.999896i | \(-0.504593\pi\) | ||||
−0.0144281 | + | 0.999896i | \(0.504593\pi\) | |||||||
\(542\) | −9.89556 | −0.425051 | ||||||||
\(543\) | 73.6578 | 3.16096 | ||||||||
\(544\) | 1.90375 | 0.0816226 | ||||||||
\(545\) | 9.44228 | 0.404463 | ||||||||
\(546\) | −27.8323 | −1.19111 | ||||||||
\(547\) | 9.52062 | 0.407073 | 0.203536 | − | 0.979067i | \(-0.434757\pi\) | ||||
0.203536 | + | 0.979067i | \(0.434757\pi\) | |||||||
\(548\) | −8.32344 | −0.355560 | ||||||||
\(549\) | 52.1355 | 2.22509 | ||||||||
\(550\) | 2.29983 | 0.0980652 | ||||||||
\(551\) | 0.0817407 | 0.00348227 | ||||||||
\(552\) | 29.0380 | 1.23594 | ||||||||
\(553\) | 11.9488 | 0.508116 | ||||||||
\(554\) | 15.4663 | 0.657099 | ||||||||
\(555\) | −2.15133 | −0.0913189 | ||||||||
\(556\) | 9.07860 | 0.385018 | ||||||||
\(557\) | 8.07247 | 0.342041 | 0.171021 | − | 0.985267i | \(-0.445293\pi\) | ||||
0.171021 | + | 0.985267i | \(0.445293\pi\) | |||||||
\(558\) | 36.3132 | 1.53726 | ||||||||
\(559\) | −14.1105 | −0.596811 | ||||||||
\(560\) | −1.78184 | −0.0752965 | ||||||||
\(561\) | −3.08002 | −0.130038 | ||||||||
\(562\) | −12.1275 | −0.511569 | ||||||||
\(563\) | −30.9043 | −1.30246 | −0.651230 | − | 0.758880i | \(-0.725747\pi\) | ||||
−0.651230 | + | 0.758880i | \(0.725747\pi\) | |||||||
\(564\) | −6.86708 | −0.289156 | ||||||||
\(565\) | 0.997455 | 0.0419633 | ||||||||
\(566\) | −22.4200 | −0.942381 | ||||||||
\(567\) | −80.5382 | −3.38229 | ||||||||
\(568\) | 13.8027 | 0.579148 | ||||||||
\(569\) | 30.3513 | 1.27239 | 0.636196 | − | 0.771527i | \(-0.280507\pi\) | ||||
0.636196 | + | 0.771527i | \(0.280507\pi\) | |||||||
\(570\) | 1.94642 | 0.0815265 | ||||||||
\(571\) | −45.8428 | −1.91846 | −0.959231 | − | 0.282624i | \(-0.908795\pi\) | ||||
−0.959231 | + | 0.282624i | \(0.908795\pi\) | |||||||
\(572\) | −1.40962 | −0.0589390 | ||||||||
\(573\) | 7.88836 | 0.329541 | ||||||||
\(574\) | 26.3856 | 1.10131 | ||||||||
\(575\) | 41.2781 | 1.72142 | ||||||||
\(576\) | 7.67840 | 0.319933 | ||||||||
\(577\) | 23.9754 | 0.998107 | 0.499053 | − | 0.866571i | \(-0.333681\pi\) | ||||
0.499053 | + | 0.866571i | \(0.333681\pi\) | |||||||
\(578\) | 13.3757 | 0.556357 | ||||||||
\(579\) | 56.7954 | 2.36034 | ||||||||
\(580\) | −0.0486880 | −0.00202166 | ||||||||
\(581\) | 30.9694 | 1.28483 | ||||||||
\(582\) | 22.4947 | 0.932435 | ||||||||
\(583\) | 0.462252 | 0.0191445 | ||||||||
\(584\) | −10.0079 | −0.414129 | ||||||||
\(585\) | −13.0216 | −0.538376 | ||||||||
\(586\) | −31.7772 | −1.31270 | ||||||||
\(587\) | 8.49237 | 0.350517 | 0.175259 | − | 0.984522i | \(-0.443924\pi\) | ||||
0.175259 | + | 0.984522i | \(0.443924\pi\) | |||||||
\(588\) | 6.36865 | 0.262639 | ||||||||
\(589\) | 4.72927 | 0.194866 | ||||||||
\(590\) | −6.37013 | −0.262254 | ||||||||
\(591\) | 6.41699 | 0.263960 | ||||||||
\(592\) | −1.10528 | −0.0454266 | ||||||||
\(593\) | −38.2367 | −1.57019 | −0.785097 | − | 0.619372i | \(-0.787387\pi\) | ||||
−0.785097 | + | 0.619372i | \(0.787387\pi\) | |||||||
\(594\) | −7.56903 | −0.310561 | ||||||||
\(595\) | 3.39217 | 0.139066 | ||||||||
\(596\) | −21.6964 | −0.888721 | ||||||||
\(597\) | 22.3357 | 0.914141 | ||||||||
\(598\) | −25.3002 | −1.03460 | ||||||||
\(599\) | 18.7729 | 0.767038 | 0.383519 | − | 0.923533i | \(-0.374712\pi\) | ||||
0.383519 | + | 0.923533i | \(0.374712\pi\) | |||||||
\(600\) | 15.1795 | 0.619702 | ||||||||
\(601\) | 39.4013 | 1.60721 | 0.803607 | − | 0.595160i | \(-0.202912\pi\) | ||||
0.803607 | + | 0.595160i | \(0.202912\pi\) | |||||||
\(602\) | 14.8258 | 0.604255 | ||||||||
\(603\) | −25.2484 | −1.02820 | ||||||||
\(604\) | −5.30999 | −0.216060 | ||||||||
\(605\) | −6.40603 | −0.260442 | ||||||||
\(606\) | 47.0832 | 1.91262 | ||||||||
\(607\) | −38.0332 | −1.54372 | −0.771860 | − | 0.635793i | \(-0.780673\pi\) | ||||
−0.771860 | + | 0.635793i | \(0.780673\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0.799055 | 0.0323793 | ||||||||
\(610\) | −4.04433 | −0.163750 | ||||||||
\(611\) | 5.98314 | 0.242052 | ||||||||
\(612\) | −14.6177 | −0.590887 | ||||||||
\(613\) | −10.1886 | −0.411514 | −0.205757 | − | 0.978603i | \(-0.565966\pi\) | ||||
−0.205757 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(614\) | 31.2263 | 1.26019 | ||||||||
\(615\) | 17.1679 | 0.692278 | ||||||||
\(616\) | 1.48107 | 0.0596740 | ||||||||
\(617\) | 7.87871 | 0.317185 | 0.158593 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158593 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(618\) | 61.5347 | 2.47529 | ||||||||
\(619\) | −11.3787 | −0.457348 | −0.228674 | − | 0.973503i | \(-0.573439\pi\) | ||||
−0.228674 | + | 0.973503i | \(0.573439\pi\) | |||||||
\(620\) | −2.81694 | −0.113131 | ||||||||
\(621\) | −135.851 | −5.45153 | ||||||||
\(622\) | −3.56826 | −0.143074 | ||||||||
\(623\) | 33.0577 | 1.32443 | ||||||||
\(624\) | −9.30386 | −0.372452 | ||||||||
\(625\) | 19.8041 | 0.792163 | ||||||||
\(626\) | 9.21005 | 0.368108 | ||||||||
\(627\) | −1.61787 | −0.0646115 | ||||||||
\(628\) | −10.6815 | −0.426238 | ||||||||
\(629\) | 2.10417 | 0.0838987 | ||||||||
\(630\) | 13.6817 | 0.545091 | ||||||||
\(631\) | 8.36517 | 0.333012 | 0.166506 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166506 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(632\) | 3.99429 | 0.158884 | ||||||||
\(633\) | −3.26778 | −0.129883 | ||||||||
\(634\) | 29.0885 | 1.15525 | ||||||||
\(635\) | −11.3427 | −0.450121 | ||||||||
\(636\) | 3.05099 | 0.120980 | ||||||||
\(637\) | −5.54887 | −0.219854 | ||||||||
\(638\) | 0.0404696 | 0.00160221 | ||||||||
\(639\) | −105.982 | −4.19260 | ||||||||
\(640\) | −0.595639 | −0.0235447 | ||||||||
\(641\) | 46.8610 | 1.85090 | 0.925450 | − | 0.378871i | \(-0.123688\pi\) | ||||
0.925450 | + | 0.378871i | \(0.123688\pi\) | |||||||
\(642\) | 28.1104 | 1.10943 | ||||||||
\(643\) | 13.5912 | 0.535985 | 0.267992 | − | 0.963421i | \(-0.413640\pi\) | ||||
0.267992 | + | 0.963421i | \(0.413640\pi\) | |||||||
\(644\) | 26.5827 | 1.04751 | ||||||||
\(645\) | 9.64648 | 0.379830 | ||||||||
\(646\) | −1.90375 | −0.0749020 | ||||||||
\(647\) | 29.5982 | 1.16363 | 0.581813 | − | 0.813323i | \(-0.302344\pi\) | ||||
0.581813 | + | 0.813323i | \(0.302344\pi\) | |||||||
\(648\) | −26.9226 | −1.05762 | ||||||||
\(649\) | 5.29488 | 0.207842 | ||||||||
\(650\) | −13.2256 | −0.518751 | ||||||||
\(651\) | 46.2309 | 1.81193 | ||||||||
\(652\) | −3.40812 | −0.133472 | ||||||||
\(653\) | 24.0933 | 0.942845 | 0.471423 | − | 0.881907i | \(-0.343741\pi\) | ||||
0.471423 | + | 0.881907i | \(0.343741\pi\) | |||||||
\(654\) | −51.8020 | −2.02562 | ||||||||
\(655\) | −2.08611 | −0.0815110 | ||||||||
\(656\) | 8.82027 | 0.344374 | ||||||||
\(657\) | 76.8444 | 2.99799 | ||||||||
\(658\) | −6.28644 | −0.245071 | ||||||||
\(659\) | 20.5042 | 0.798729 | 0.399365 | − | 0.916792i | \(-0.369231\pi\) | ||||
0.399365 | + | 0.916792i | \(0.369231\pi\) | |||||||
\(660\) | 0.963666 | 0.0375107 | ||||||||
\(661\) | −43.2392 | −1.68181 | −0.840905 | − | 0.541183i | \(-0.817977\pi\) | ||||
−0.840905 | + | 0.541183i | \(0.817977\pi\) | |||||||
\(662\) | 11.4134 | 0.443593 | ||||||||
\(663\) | 17.7122 | 0.687885 | ||||||||
\(664\) | 10.3525 | 0.401757 | ||||||||
\(665\) | 1.78184 | 0.0690968 | ||||||||
\(666\) | 8.48675 | 0.328855 | ||||||||
\(667\) | 0.726361 | 0.0281248 | ||||||||
\(668\) | 0.313528 | 0.0121308 | ||||||||
\(669\) | 18.5342 | 0.716575 | ||||||||
\(670\) | 1.95861 | 0.0756676 | ||||||||
\(671\) | 3.36166 | 0.129775 | ||||||||
\(672\) | 9.77549 | 0.377098 | ||||||||
\(673\) | −22.0677 | −0.850649 | −0.425325 | − | 0.905041i | \(-0.639840\pi\) | ||||
−0.425325 | + | 0.905041i | \(0.639840\pi\) | |||||||
\(674\) | 10.7156 | 0.412749 | ||||||||
\(675\) | −71.0159 | −2.73340 | ||||||||
\(676\) | −4.89375 | −0.188221 | ||||||||
\(677\) | −2.07471 | −0.0797375 | −0.0398688 | − | 0.999205i | \(-0.512694\pi\) | ||||
−0.0398688 | + | 0.999205i | \(0.512694\pi\) | |||||||
\(678\) | −5.47222 | −0.210159 | ||||||||
\(679\) | 20.5927 | 0.790274 | ||||||||
\(680\) | 1.13395 | 0.0434849 | ||||||||
\(681\) | 70.8203 | 2.71384 | ||||||||
\(682\) | 2.34145 | 0.0896588 | ||||||||
\(683\) | −42.4940 | −1.62599 | −0.812994 | − | 0.582272i | \(-0.802164\pi\) | ||||
−0.812994 | + | 0.582272i | \(0.802164\pi\) | |||||||
\(684\) | −7.67840 | −0.293591 | ||||||||
\(685\) | −4.95777 | −0.189427 | ||||||||
\(686\) | −15.1102 | −0.576909 | ||||||||
\(687\) | −38.4535 | −1.46709 | ||||||||
\(688\) | 4.95602 | 0.188946 | ||||||||
\(689\) | −2.65827 | −0.101272 | ||||||||
\(690\) | 17.2962 | 0.658455 | ||||||||
\(691\) | 16.9513 | 0.644858 | 0.322429 | − | 0.946594i | \(-0.395501\pi\) | ||||
0.322429 | + | 0.946594i | \(0.395501\pi\) | |||||||
\(692\) | −0.365104 | −0.0138792 | ||||||||
\(693\) | −11.3722 | −0.431996 | ||||||||
\(694\) | 7.44385 | 0.282565 | ||||||||
\(695\) | 5.40757 | 0.205121 | ||||||||
\(696\) | 0.267111 | 0.0101248 | ||||||||
\(697\) | −16.7916 | −0.636026 | ||||||||
\(698\) | −27.2479 | −1.03135 | ||||||||
\(699\) | 61.4675 | 2.32491 | ||||||||
\(700\) | 13.8960 | 0.525221 | ||||||||
\(701\) | 47.9954 | 1.81276 | 0.906380 | − | 0.422464i | \(-0.138835\pi\) | ||||
0.906380 | + | 0.422464i | \(0.138835\pi\) | |||||||
\(702\) | 43.5271 | 1.64283 | ||||||||
\(703\) | 1.10528 | 0.0416863 | ||||||||
\(704\) | 0.495097 | 0.0186597 | ||||||||
\(705\) | −4.09030 | −0.154050 | ||||||||
\(706\) | 4.62222 | 0.173959 | ||||||||
\(707\) | 43.1021 | 1.62102 | ||||||||
\(708\) | 34.9477 | 1.31341 | ||||||||
\(709\) | 45.8860 | 1.72329 | 0.861643 | − | 0.507514i | \(-0.169436\pi\) | ||||
0.861643 | + | 0.507514i | \(0.169436\pi\) | |||||||
\(710\) | 8.22142 | 0.308544 | ||||||||
\(711\) | −30.6698 | −1.15021 | ||||||||
\(712\) | 11.0506 | 0.414140 | ||||||||
\(713\) | 42.0251 | 1.57385 | ||||||||
\(714\) | −18.6101 | −0.696464 | ||||||||
\(715\) | −0.839622 | −0.0314001 | ||||||||
\(716\) | −0.0604155 | −0.00225783 | ||||||||
\(717\) | 6.49370 | 0.242512 | ||||||||
\(718\) | −28.0275 | −1.04598 | ||||||||
\(719\) | 10.0234 | 0.373810 | 0.186905 | − | 0.982378i | \(-0.440154\pi\) | ||||
0.186905 | + | 0.982378i | \(0.440154\pi\) | |||||||
\(720\) | 4.57355 | 0.170446 | ||||||||
\(721\) | 56.3316 | 2.09790 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −55.1948 | −2.05272 | ||||||||
\(724\) | 22.5406 | 0.837715 | ||||||||
\(725\) | 0.379703 | 0.0141018 | ||||||||
\(726\) | 35.1446 | 1.30434 | ||||||||
\(727\) | 11.7520 | 0.435859 | 0.217930 | − | 0.975965i | \(-0.430070\pi\) | ||||
0.217930 | + | 0.975965i | \(0.430070\pi\) | |||||||
\(728\) | −8.51717 | −0.315667 | ||||||||
\(729\) | 56.8489 | 2.10551 | ||||||||
\(730\) | −5.96108 | −0.220630 | ||||||||
\(731\) | −9.43501 | −0.348967 | ||||||||
\(732\) | 22.1879 | 0.820088 | ||||||||
\(733\) | −33.3254 | −1.23090 | −0.615451 | − | 0.788175i | \(-0.711026\pi\) | ||||
−0.615451 | + | 0.788175i | \(0.711026\pi\) | |||||||
\(734\) | −12.8611 | −0.474712 | ||||||||
\(735\) | 3.79342 | 0.139922 | ||||||||
\(736\) | 8.88616 | 0.327548 | ||||||||
\(737\) | −1.62800 | −0.0599681 | ||||||||
\(738\) | −67.7255 | −2.49301 | ||||||||
\(739\) | 49.0404 | 1.80398 | 0.901989 | − | 0.431758i | \(-0.142107\pi\) | ||||
0.901989 | + | 0.431758i | \(0.142107\pi\) | |||||||
\(740\) | −0.658346 | −0.0242013 | ||||||||
\(741\) | 9.30386 | 0.341786 | ||||||||
\(742\) | 2.79302 | 0.102535 | ||||||||
\(743\) | 20.6653 | 0.758137 | 0.379068 | − | 0.925369i | \(-0.376245\pi\) | ||||
0.379068 | + | 0.925369i | \(0.376245\pi\) | |||||||
\(744\) | 15.4542 | 0.566580 | ||||||||
\(745\) | −12.9232 | −0.473471 | ||||||||
\(746\) | −18.6028 | −0.681096 | ||||||||
\(747\) | −79.4909 | −2.90842 | ||||||||
\(748\) | −0.942541 | −0.0344627 | ||||||||
\(749\) | 25.7335 | 0.940282 | ||||||||
\(750\) | 18.7736 | 0.685516 | ||||||||
\(751\) | −15.4919 | −0.565309 | −0.282655 | − | 0.959222i | \(-0.591215\pi\) | ||||
−0.282655 | + | 0.959222i | \(0.591215\pi\) | |||||||
\(752\) | −2.10145 | −0.0766321 | ||||||||
\(753\) | −98.8151 | −3.60102 | ||||||||
\(754\) | −0.232728 | −0.00847545 | ||||||||
\(755\) | −3.16284 | −0.115107 | ||||||||
\(756\) | −45.7336 | −1.66331 | ||||||||
\(757\) | 11.3261 | 0.411652 | 0.205826 | − | 0.978589i | \(-0.434012\pi\) | ||||
0.205826 | + | 0.978589i | \(0.434012\pi\) | |||||||
\(758\) | −27.9555 | −1.01539 | ||||||||
\(759\) | −14.3766 | −0.521839 | ||||||||
\(760\) | 0.595639 | 0.0216061 | ||||||||
\(761\) | −43.3859 | −1.57274 | −0.786370 | − | 0.617756i | \(-0.788042\pi\) | ||||
−0.786370 | + | 0.617756i | \(0.788042\pi\) | |||||||
\(762\) | 62.2280 | 2.25428 | ||||||||
\(763\) | −47.4219 | −1.71679 | ||||||||
\(764\) | 2.41398 | 0.0873348 | ||||||||
\(765\) | −8.70690 | −0.314798 | ||||||||
\(766\) | −27.7445 | −1.00245 | ||||||||
\(767\) | −30.4492 | −1.09946 | ||||||||
\(768\) | 3.26778 | 0.117916 | ||||||||
\(769\) | −6.40277 | −0.230890 | −0.115445 | − | 0.993314i | \(-0.536829\pi\) | ||||
−0.115445 | + | 0.993314i | \(0.536829\pi\) | |||||||
\(770\) | 0.882184 | 0.0317917 | ||||||||
\(771\) | 28.1468 | 1.01368 | ||||||||
\(772\) | 17.3804 | 0.625535 | ||||||||
\(773\) | −21.1472 | −0.760611 | −0.380305 | − | 0.924861i | \(-0.624181\pi\) | ||||
−0.380305 | + | 0.924861i | \(0.624181\pi\) | |||||||
\(774\) | −38.0543 | −1.36783 | ||||||||
\(775\) | 21.9685 | 0.789131 | ||||||||
\(776\) | 6.88378 | 0.247113 | ||||||||
\(777\) | 10.8046 | 0.387613 | ||||||||
\(778\) | −14.6916 | −0.526718 | ||||||||
\(779\) | −8.82027 | −0.316019 | ||||||||
\(780\) | −5.54174 | −0.198426 | ||||||||
\(781\) | −6.83367 | −0.244528 | ||||||||
\(782\) | −16.9170 | −0.604951 | ||||||||
\(783\) | −1.24965 | −0.0446588 | ||||||||
\(784\) | 1.94892 | 0.0696043 | ||||||||
\(785\) | −6.36232 | −0.227081 | ||||||||
\(786\) | 11.4448 | 0.408221 | ||||||||
\(787\) | 42.7108 | 1.52247 | 0.761237 | − | 0.648474i | \(-0.224592\pi\) | ||||
0.761237 | + | 0.648474i | \(0.224592\pi\) | |||||||
\(788\) | 1.96372 | 0.0699545 | ||||||||
\(789\) | 8.62914 | 0.307205 | ||||||||
\(790\) | 2.37916 | 0.0846466 | ||||||||
\(791\) | −5.00951 | −0.178118 | ||||||||
\(792\) | −3.80155 | −0.135082 | ||||||||
\(793\) | −19.3318 | −0.686493 | ||||||||
\(794\) | 2.97296 | 0.105506 | ||||||||
\(795\) | 1.81729 | 0.0644527 | ||||||||
\(796\) | 6.83514 | 0.242265 | ||||||||
\(797\) | −30.7253 | −1.08834 | −0.544172 | − | 0.838973i | \(-0.683156\pi\) | ||||
−0.544172 | + | 0.838973i | \(0.683156\pi\) | |||||||
\(798\) | −9.77549 | −0.346048 | ||||||||
\(799\) | 4.00064 | 0.141532 | ||||||||
\(800\) | 4.64521 | 0.164233 | ||||||||
\(801\) | −84.8512 | −2.99807 | ||||||||
\(802\) | −37.9993 | −1.34180 | ||||||||
\(803\) | 4.95487 | 0.174854 | ||||||||
\(804\) | −10.7453 | −0.378956 | ||||||||
\(805\) | 15.8337 | 0.558065 | ||||||||
\(806\) | −13.4649 | −0.474282 | ||||||||
\(807\) | 32.2346 | 1.13471 | ||||||||
\(808\) | 14.4083 | 0.506882 | ||||||||
\(809\) | −9.04409 | −0.317973 | −0.158987 | − | 0.987281i | \(-0.550823\pi\) | ||||
−0.158987 | + | 0.987281i | \(0.550823\pi\) | |||||||
\(810\) | −16.0361 | −0.563452 | ||||||||
\(811\) | 26.4572 | 0.929039 | 0.464520 | − | 0.885563i | \(-0.346227\pi\) | ||||
0.464520 | + | 0.885563i | \(0.346227\pi\) | |||||||
\(812\) | 0.244525 | 0.00858116 | ||||||||
\(813\) | 32.3365 | 1.13409 | ||||||||
\(814\) | 0.547219 | 0.0191800 | ||||||||
\(815\) | −2.03001 | −0.0711080 | ||||||||
\(816\) | −6.22104 | −0.217780 | ||||||||
\(817\) | −4.95602 | −0.173389 | ||||||||
\(818\) | 7.73451 | 0.270431 | ||||||||
\(819\) | 65.3982 | 2.28520 | ||||||||
\(820\) | 5.25370 | 0.183467 | ||||||||
\(821\) | −26.8504 | −0.937085 | −0.468543 | − | 0.883441i | \(-0.655221\pi\) | ||||
−0.468543 | + | 0.883441i | \(0.655221\pi\) | |||||||
\(822\) | 27.1992 | 0.948680 | ||||||||
\(823\) | 1.78159 | 0.0621025 | 0.0310512 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310512 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(824\) | 18.8307 | 0.655999 | ||||||||
\(825\) | −7.51535 | −0.261651 | ||||||||
\(826\) | 31.9927 | 1.11317 | ||||||||
\(827\) | 9.31898 | 0.324053 | 0.162026 | − | 0.986786i | \(-0.448197\pi\) | ||||
0.162026 | + | 0.986786i | \(0.448197\pi\) | |||||||
\(828\) | −68.2315 | −2.37121 | ||||||||
\(829\) | 9.01445 | 0.313085 | 0.156542 | − | 0.987671i | \(-0.449965\pi\) | ||||
0.156542 | + | 0.987671i | \(0.449965\pi\) | |||||||
\(830\) | 6.16638 | 0.214038 | ||||||||
\(831\) | −50.5404 | −1.75323 | ||||||||
\(832\) | −2.84715 | −0.0987071 | ||||||||
\(833\) | −3.71026 | −0.128553 | ||||||||
\(834\) | −29.6669 | −1.02728 | ||||||||
\(835\) | 0.186750 | 0.00646274 | ||||||||
\(836\) | −0.495097 | −0.0171233 | ||||||||
\(837\) | −72.3010 | −2.49909 | ||||||||
\(838\) | 28.8403 | 0.996270 | ||||||||
\(839\) | −32.4366 | −1.11984 | −0.559918 | − | 0.828548i | \(-0.689167\pi\) | ||||
−0.559918 | + | 0.828548i | \(0.689167\pi\) | |||||||
\(840\) | 5.82266 | 0.200901 | ||||||||
\(841\) | −28.9933 | −0.999770 | ||||||||
\(842\) | 14.2895 | 0.492447 | ||||||||
\(843\) | 39.6301 | 1.36493 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −2.91491 | −0.100276 | ||||||||
\(846\) | 16.1358 | 0.554759 | ||||||||
\(847\) | 32.1729 | 1.10548 | ||||||||
\(848\) | 0.933659 | 0.0320620 | ||||||||
\(849\) | 73.2635 | 2.51440 | ||||||||
\(850\) | −8.84332 | −0.303323 | ||||||||
\(851\) | 9.82166 | 0.336682 | ||||||||
\(852\) | −45.1042 | −1.54524 | ||||||||
\(853\) | −4.75390 | −0.162771 | −0.0813853 | − | 0.996683i | \(-0.525934\pi\) | ||||
−0.0813853 | + | 0.996683i | \(0.525934\pi\) | |||||||
\(854\) | 20.3118 | 0.695055 | ||||||||
\(855\) | −4.57355 | −0.156412 | ||||||||
\(856\) | 8.60229 | 0.294020 | ||||||||
\(857\) | −54.9257 | −1.87623 | −0.938113 | − | 0.346328i | \(-0.887428\pi\) | ||||
−0.938113 | + | 0.346328i | \(0.887428\pi\) | |||||||
\(858\) | 4.60631 | 0.157257 | ||||||||
\(859\) | −38.8642 | −1.32603 | −0.663015 | − | 0.748606i | \(-0.730723\pi\) | ||||
−0.663015 | + | 0.748606i | \(0.730723\pi\) | |||||||
\(860\) | 2.95200 | 0.100662 | ||||||||
\(861\) | −86.2224 | −2.93845 | ||||||||
\(862\) | −18.3478 | −0.624928 | ||||||||
\(863\) | 22.0537 | 0.750717 | 0.375359 | − | 0.926880i | \(-0.377520\pi\) | ||||
0.375359 | + | 0.926880i | \(0.377520\pi\) | |||||||
\(864\) | −15.2880 | −0.520107 | ||||||||
\(865\) | −0.217470 | −0.00739420 | ||||||||
\(866\) | −6.45669 | −0.219407 | ||||||||
\(867\) | −43.7090 | −1.48444 | ||||||||
\(868\) | 14.1475 | 0.480197 | ||||||||
\(869\) | −1.97756 | −0.0670843 | ||||||||
\(870\) | 0.159102 | 0.00539405 | ||||||||
\(871\) | 9.36212 | 0.317223 | ||||||||
\(872\) | −15.8524 | −0.536828 | ||||||||
\(873\) | −52.8564 | −1.78892 | ||||||||
\(874\) | −8.88616 | −0.300579 | ||||||||
\(875\) | 17.1862 | 0.581000 | ||||||||
\(876\) | 32.7036 | 1.10495 | ||||||||
\(877\) | 30.4868 | 1.02947 | 0.514733 | − | 0.857351i | \(-0.327891\pi\) | ||||
0.514733 | + | 0.857351i | \(0.327891\pi\) | |||||||
\(878\) | 33.6109 | 1.13431 | ||||||||
\(879\) | 103.841 | 3.50247 | ||||||||
\(880\) | 0.294899 | 0.00994105 | ||||||||
\(881\) | −32.1836 | −1.08429 | −0.542147 | − | 0.840283i | \(-0.682389\pi\) | ||||
−0.542147 | + | 0.840283i | \(0.682389\pi\) | |||||||
\(882\) | −14.9646 | −0.503884 | ||||||||
\(883\) | −16.1616 | −0.543880 | −0.271940 | − | 0.962314i | \(-0.587665\pi\) | ||||
−0.271940 | + | 0.962314i | \(0.587665\pi\) | |||||||
\(884\) | 5.42026 | 0.182303 | ||||||||
\(885\) | 20.8162 | 0.699729 | ||||||||
\(886\) | 23.1564 | 0.777955 | ||||||||
\(887\) | −14.1693 | −0.475757 | −0.237879 | − | 0.971295i | \(-0.576452\pi\) | ||||
−0.237879 | + | 0.971295i | \(0.576452\pi\) | |||||||
\(888\) | 3.61180 | 0.121204 | ||||||||
\(889\) | 56.9663 | 1.91059 | ||||||||
\(890\) | 6.58219 | 0.220636 | ||||||||
\(891\) | 13.3293 | 0.446548 | ||||||||
\(892\) | 5.67181 | 0.189906 | ||||||||
\(893\) | 2.10145 | 0.0703224 | ||||||||
\(894\) | 70.8992 | 2.37122 | ||||||||
\(895\) | −0.0359858 | −0.00120287 | ||||||||
\(896\) | 2.99147 | 0.0999382 | ||||||||
\(897\) | 82.6756 | 2.76046 | ||||||||
\(898\) | −10.3057 | −0.343905 | ||||||||
\(899\) | 0.386574 | 0.0128930 | ||||||||
\(900\) | −35.6678 | −1.18893 | ||||||||
\(901\) | −1.77745 | −0.0592155 | ||||||||
\(902\) | −4.36689 | −0.145402 | ||||||||
\(903\) | −48.4475 | −1.61223 | ||||||||
\(904\) | −1.67460 | −0.0556963 | ||||||||
\(905\) | 13.4261 | 0.446298 | ||||||||
\(906\) | 17.3519 | 0.576478 | ||||||||
\(907\) | 31.5563 | 1.04781 | 0.523904 | − | 0.851777i | \(-0.324475\pi\) | ||||
0.523904 | + | 0.851777i | \(0.324475\pi\) | |||||||
\(908\) | 21.6723 | 0.719220 | ||||||||
\(909\) | −110.633 | −3.66945 | ||||||||
\(910\) | −5.07316 | −0.168174 | ||||||||
\(911\) | 12.4511 | 0.412525 | 0.206262 | − | 0.978497i | \(-0.433870\pi\) | ||||
0.206262 | + | 0.978497i | \(0.433870\pi\) | |||||||
\(912\) | −3.26778 | −0.108207 | ||||||||
\(913\) | −5.12552 | −0.169630 | ||||||||
\(914\) | 12.5752 | 0.415951 | ||||||||
\(915\) | 13.2160 | 0.436907 | ||||||||
\(916\) | −11.7675 | −0.388808 | ||||||||
\(917\) | 10.4770 | 0.345983 | ||||||||
\(918\) | 29.1045 | 0.960590 | ||||||||
\(919\) | −9.82004 | −0.323933 | −0.161967 | − | 0.986796i | \(-0.551784\pi\) | ||||
−0.161967 | + | 0.986796i | \(0.551784\pi\) | |||||||
\(920\) | 5.29294 | 0.174503 | ||||||||
\(921\) | −102.041 | −3.36235 | ||||||||
\(922\) | −41.3655 | −1.36230 | ||||||||
\(923\) | 39.2983 | 1.29352 | ||||||||
\(924\) | −4.83982 | −0.159218 | ||||||||
\(925\) | 5.13425 | 0.168813 | ||||||||
\(926\) | −1.50708 | −0.0495257 | ||||||||
\(927\) | −144.590 | −4.74895 | ||||||||
\(928\) | 0.0817407 | 0.00268327 | ||||||||
\(929\) | 13.3004 | 0.436373 | 0.218187 | − | 0.975907i | \(-0.429986\pi\) | ||||
0.218187 | + | 0.975907i | \(0.429986\pi\) | |||||||
\(930\) | 9.20514 | 0.301849 | ||||||||
\(931\) | −1.94892 | −0.0638733 | ||||||||
\(932\) | 18.8101 | 0.616147 | ||||||||
\(933\) | 11.6603 | 0.381741 | ||||||||
\(934\) | 35.0388 | 1.14651 | ||||||||
\(935\) | −0.561414 | −0.0183602 | ||||||||
\(936\) | 21.8615 | 0.714567 | ||||||||
\(937\) | 18.6557 | 0.609456 | 0.304728 | − | 0.952439i | \(-0.401434\pi\) | ||||
0.304728 | + | 0.952439i | \(0.401434\pi\) | |||||||
\(938\) | −9.83670 | −0.321180 | ||||||||
\(939\) | −30.0964 | −0.982160 | ||||||||
\(940\) | −1.25171 | −0.0408262 | ||||||||
\(941\) | −10.2926 | −0.335528 | −0.167764 | − | 0.985827i | \(-0.553655\pi\) | ||||
−0.167764 | + | 0.985827i | \(0.553655\pi\) | |||||||
\(942\) | 34.9048 | 1.13726 | ||||||||
\(943\) | −78.3783 | −2.55235 | ||||||||
\(944\) | 10.6946 | 0.348080 | ||||||||
\(945\) | −27.2407 | −0.886140 | ||||||||
\(946\) | −2.45371 | −0.0797770 | ||||||||
\(947\) | −28.6077 | −0.929627 | −0.464813 | − | 0.885409i | \(-0.653879\pi\) | ||||
−0.464813 | + | 0.885409i | \(0.653879\pi\) | |||||||
\(948\) | −13.0525 | −0.423925 | ||||||||
\(949\) | −28.4939 | −0.924952 | ||||||||
\(950\) | −4.64521 | −0.150711 | ||||||||
\(951\) | −95.0549 | −3.08237 | ||||||||
\(952\) | −5.69502 | −0.184577 | ||||||||
\(953\) | −1.65219 | −0.0535197 | −0.0267598 | − | 0.999642i | \(-0.508519\pi\) | ||||
−0.0267598 | + | 0.999642i | \(0.508519\pi\) | |||||||
\(954\) | −7.16901 | −0.232105 | ||||||||
\(955\) | 1.43786 | 0.0465281 | ||||||||
\(956\) | 1.98719 | 0.0642703 | ||||||||
\(957\) | −0.132246 | −0.00427490 | ||||||||
\(958\) | 14.0967 | 0.455445 | ||||||||
\(959\) | 24.8994 | 0.804042 | ||||||||
\(960\) | 1.94642 | 0.0628204 | ||||||||
\(961\) | −8.63397 | −0.278515 | ||||||||
\(962\) | −3.14689 | −0.101460 | ||||||||
\(963\) | −66.0518 | −2.12849 | ||||||||
\(964\) | −16.8906 | −0.544010 | ||||||||
\(965\) | 10.3525 | 0.333257 | ||||||||
\(966\) | −86.8665 | −2.79488 | ||||||||
\(967\) | −4.93976 | −0.158852 | −0.0794259 | − | 0.996841i | \(-0.525309\pi\) | ||||
−0.0794259 | + | 0.996841i | \(0.525309\pi\) | |||||||
\(968\) | 10.7549 | 0.345675 | ||||||||
\(969\) | 6.22104 | 0.199848 | ||||||||
\(970\) | 4.10025 | 0.131651 | ||||||||
\(971\) | 54.2923 | 1.74232 | 0.871161 | − | 0.490997i | \(-0.163367\pi\) | ||||
0.871161 | + | 0.490997i | \(0.163367\pi\) | |||||||
\(972\) | 42.1132 | 1.35078 | ||||||||
\(973\) | −27.1584 | −0.870658 | ||||||||
\(974\) | 17.0378 | 0.545927 | ||||||||
\(975\) | 43.2184 | 1.38410 | ||||||||
\(976\) | 6.78989 | 0.217339 | ||||||||
\(977\) | 26.1764 | 0.837458 | 0.418729 | − | 0.908111i | \(-0.362476\pi\) | ||||
0.418729 | + | 0.908111i | \(0.362476\pi\) | |||||||
\(978\) | 11.1370 | 0.356121 | ||||||||
\(979\) | −5.47114 | −0.174858 | ||||||||
\(980\) | 1.16085 | 0.0370821 | ||||||||
\(981\) | 121.721 | 3.88624 | ||||||||
\(982\) | −0.328562 | −0.0104848 | ||||||||
\(983\) | −10.0687 | −0.321141 | −0.160570 | − | 0.987024i | \(-0.551333\pi\) | ||||
−0.160570 | + | 0.987024i | \(0.551333\pi\) | |||||||
\(984\) | −28.8227 | −0.918834 | ||||||||
\(985\) | 1.16967 | 0.0372686 | ||||||||
\(986\) | −0.155614 | −0.00495575 | ||||||||
\(987\) | 20.5427 | 0.653882 | ||||||||
\(988\) | 2.84715 | 0.0905799 | ||||||||
\(989\) | −44.0400 | −1.40039 | ||||||||
\(990\) | −2.26435 | −0.0719659 | ||||||||
\(991\) | −52.6995 | −1.67406 | −0.837028 | − | 0.547160i | \(-0.815709\pi\) | ||||
−0.837028 | + | 0.547160i | \(0.815709\pi\) | |||||||
\(992\) | 4.72927 | 0.150155 | ||||||||
\(993\) | −37.2964 | −1.18357 | ||||||||
\(994\) | −41.2904 | −1.30965 | ||||||||
\(995\) | 4.07128 | 0.129068 | ||||||||
\(996\) | −33.8299 | −1.07194 | ||||||||
\(997\) | −26.1407 | −0.827885 | −0.413943 | − | 0.910303i | \(-0.635849\pi\) | ||||
−0.413943 | + | 0.910303i | \(0.635849\pi\) | |||||||
\(998\) | −1.49375 | −0.0472838 | ||||||||
\(999\) | −16.8974 | −0.534611 |
(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 | 8018.2.a.f.1.34 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.34 | ✓ | 34 | 1.1 | even | 1 | trivial |