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: | \(3\) |
Coefficient field: | 3.3.2700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.61323\) 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 | ||||||||
\(5\) | 2.61323 | 1.16867 | 0.584336 | − | 0.811512i | \(-0.301355\pi\) | ||||
0.584336 | + | 0.811512i | \(0.301355\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.61323 | −0.826376 | ||||||||
\(11\) | −3.55780 | −1.07272 | −0.536359 | − | 0.843990i | \(-0.680201\pi\) | ||||
−0.536359 | + | 0.843990i | \(0.680201\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.61323 | −0.674733 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.95529 | −1.92944 | −0.964721 | − | 0.263276i | \(-0.915197\pi\) | ||||
−0.964721 | + | 0.263276i | \(0.915197\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.17103 | −0.498068 | −0.249034 | − | 0.968495i | \(-0.580113\pi\) | ||||
−0.249034 | + | 0.968495i | \(0.580113\pi\) | |||||||
\(20\) | 2.61323 | 0.584336 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.55780 | 0.758525 | ||||||||
\(23\) | −2.55780 | −0.533338 | −0.266669 | − | 0.963788i | \(-0.585923\pi\) | ||||
−0.266669 | + | 0.963788i | \(0.585923\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.82897 | 0.365794 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 2.61323 | 0.477108 | ||||||||
\(31\) | −0.828970 | −0.148887 | −0.0744437 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744437 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.55780 | 0.619333 | ||||||||
\(34\) | 7.95529 | 1.36432 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.78426 | 1.27972 | 0.639862 | − | 0.768490i | \(-0.278991\pi\) | ||||
0.639862 | + | 0.768490i | \(0.278991\pi\) | |||||||
\(38\) | 2.17103 | 0.352188 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −2.61323 | −0.413188 | ||||||||
\(41\) | 11.7843 | 1.84039 | 0.920196 | − | 0.391458i | \(-0.128029\pi\) | ||||
0.920196 | + | 0.391458i | \(0.128029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.773540 | −0.117964 | −0.0589819 | − | 0.998259i | \(-0.518785\pi\) | ||||
−0.0589819 | + | 0.998259i | \(0.518785\pi\) | |||||||
\(44\) | −3.55780 | −0.536359 | ||||||||
\(45\) | 2.61323 | 0.389557 | ||||||||
\(46\) | 2.55780 | 0.377127 | ||||||||
\(47\) | −2.94457 | −0.429510 | −0.214755 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214755 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.82897 | −0.258655 | ||||||||
\(51\) | 7.95529 | 1.11396 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 12.5685 | 1.72642 | 0.863209 | − | 0.504846i | \(-0.168451\pi\) | ||||
0.863209 | + | 0.504846i | \(0.168451\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −9.29735 | −1.25365 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.17103 | 0.287560 | ||||||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | 4.78426 | 0.622858 | 0.311429 | − | 0.950269i | \(-0.399192\pi\) | ||||
0.311429 | + | 0.950269i | \(0.399192\pi\) | |||||||
\(60\) | −2.61323 | −0.337367 | ||||||||
\(61\) | 6.72883 | 0.861538 | 0.430769 | − | 0.902462i | \(-0.358242\pi\) | ||||
0.430769 | + | 0.902462i | \(0.358242\pi\) | |||||||
\(62\) | 0.828970 | 0.105279 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.61323 | 0.324131 | ||||||||
\(66\) | −3.55780 | −0.437935 | ||||||||
\(67\) | 14.5131 | 1.77306 | 0.886528 | − | 0.462675i | \(-0.153110\pi\) | ||||
0.886528 | + | 0.462675i | \(0.153110\pi\) | |||||||
\(68\) | −7.95529 | −0.964721 | ||||||||
\(69\) | 2.55780 | 0.307923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.82897 | −0.929128 | −0.464564 | − | 0.885540i | \(-0.653789\pi\) | ||||
−0.464564 | + | 0.885540i | \(0.653789\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 10.5578 | 1.23570 | 0.617849 | − | 0.786297i | \(-0.288004\pi\) | ||||
0.617849 | + | 0.786297i | \(0.288004\pi\) | |||||||
\(74\) | −7.78426 | −0.904902 | ||||||||
\(75\) | −1.82897 | −0.211191 | ||||||||
\(76\) | −2.17103 | −0.249034 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −2.39749 | −0.269739 | −0.134869 | − | 0.990863i | \(-0.543061\pi\) | ||||
−0.134869 | + | 0.990863i | \(0.543061\pi\) | |||||||
\(80\) | 2.61323 | 0.292168 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.7843 | −1.30135 | ||||||||
\(83\) | 15.5131 | 1.70278 | 0.851391 | − | 0.524531i | \(-0.175759\pi\) | ||||
0.851391 | + | 0.524531i | \(0.175759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.7890 | −2.25488 | ||||||||
\(86\) | 0.773540 | 0.0834130 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | 3.55780 | 0.379263 | ||||||||
\(89\) | 4.21574 | 0.446868 | 0.223434 | − | 0.974719i | \(-0.428273\pi\) | ||||
0.223434 | + | 0.974719i | \(0.428273\pi\) | |||||||
\(90\) | −2.61323 | −0.275459 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.55780 | −0.266669 | ||||||||
\(93\) | 0.828970 | 0.0859602 | ||||||||
\(94\) | 2.94457 | 0.303709 | ||||||||
\(95\) | −5.67340 | −0.582079 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 10.9553 | 1.11234 | 0.556171 | − | 0.831068i | \(-0.312270\pi\) | ||||
0.556171 | + | 0.831068i | \(0.312270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.55780 | −0.357572 | ||||||||
\(100\) | 1.82897 | 0.182897 | ||||||||
\(101\) | 10.3421 | 1.02907 | 0.514537 | − | 0.857468i | \(-0.327964\pi\) | ||||
0.514537 | + | 0.857468i | \(0.327964\pi\) | |||||||
\(102\) | −7.95529 | −0.787691 | ||||||||
\(103\) | −3.22646 | −0.317913 | −0.158956 | − | 0.987286i | \(-0.550813\pi\) | ||||
−0.158956 | + | 0.987286i | \(0.550813\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.5685 | −1.22076 | ||||||||
\(107\) | 8.28663 | 0.801099 | 0.400549 | − | 0.916275i | \(-0.368819\pi\) | ||||
0.400549 | + | 0.916275i | \(0.368819\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 9.29735 | 0.886467 | ||||||||
\(111\) | −7.78426 | −0.738849 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.1817 | −1.61632 | −0.808161 | − | 0.588961i | \(-0.799537\pi\) | ||||
−0.808161 | + | 0.588961i | \(0.799537\pi\) | |||||||
\(114\) | −2.17103 | −0.203336 | ||||||||
\(115\) | −6.68412 | −0.623297 | ||||||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −4.78426 | −0.440427 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.61323 | 0.238554 | ||||||||
\(121\) | 1.65794 | 0.150722 | ||||||||
\(122\) | −6.72883 | −0.609200 | ||||||||
\(123\) | −11.7843 | −1.06255 | ||||||||
\(124\) | −0.828970 | −0.0744437 | ||||||||
\(125\) | −8.28663 | −0.741179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2973 | 1.71236 | 0.856181 | − | 0.516675i | \(-0.172831\pi\) | ||||
0.856181 | + | 0.516675i | \(0.172831\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.773540 | 0.0681064 | ||||||||
\(130\) | −2.61323 | −0.229195 | ||||||||
\(131\) | 19.4082 | 1.69570 | 0.847852 | − | 0.530234i | \(-0.177896\pi\) | ||||
0.847852 | + | 0.530234i | \(0.177896\pi\) | |||||||
\(132\) | 3.55780 | 0.309667 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.5131 | −1.25374 | ||||||||
\(135\) | −2.61323 | −0.224911 | ||||||||
\(136\) | 7.95529 | 0.682160 | ||||||||
\(137\) | −0.215740 | −0.0184319 | −0.00921597 | − | 0.999958i | \(-0.502934\pi\) | ||||
−0.00921597 | + | 0.999958i | \(0.502934\pi\) | |||||||
\(138\) | −2.55780 | −0.217734 | ||||||||
\(139\) | −3.44220 | −0.291964 | −0.145982 | − | 0.989287i | \(-0.546634\pi\) | ||||
−0.145982 | + | 0.989287i | \(0.546634\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.94457 | 0.247978 | ||||||||
\(142\) | 7.82897 | 0.656993 | ||||||||
\(143\) | −3.55780 | −0.297518 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.83969 | −0.651051 | ||||||||
\(146\) | −10.5578 | −0.873770 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.78426 | 0.639862 | ||||||||
\(149\) | −9.44220 | −0.773535 | −0.386768 | − | 0.922177i | \(-0.626408\pi\) | ||||
−0.386768 | + | 0.922177i | \(0.626408\pi\) | |||||||
\(150\) | 1.82897 | 0.149335 | ||||||||
\(151\) | −6.44220 | −0.524259 | −0.262129 | − | 0.965033i | \(-0.584425\pi\) | ||||
−0.262129 | + | 0.965033i | \(0.584425\pi\) | |||||||
\(152\) | 2.17103 | 0.176094 | ||||||||
\(153\) | −7.95529 | −0.643147 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.16629 | −0.174001 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 6.83969 | 0.545867 | 0.272933 | − | 0.962033i | \(-0.412006\pi\) | ||||
0.272933 | + | 0.962033i | \(0.412006\pi\) | |||||||
\(158\) | 2.39749 | 0.190734 | ||||||||
\(159\) | −12.5685 | −0.996748 | ||||||||
\(160\) | −2.61323 | −0.206594 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −12.6239 | −0.988784 | −0.494392 | − | 0.869239i | \(-0.664609\pi\) | ||||
−0.494392 | + | 0.869239i | \(0.664609\pi\) | |||||||
\(164\) | 11.7843 | 0.920196 | ||||||||
\(165\) | 9.29735 | 0.723798 | ||||||||
\(166\) | −15.5131 | −1.20405 | ||||||||
\(167\) | 3.71811 | 0.287716 | 0.143858 | − | 0.989598i | \(-0.454049\pi\) | ||||
0.143858 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 20.7890 | 1.59444 | ||||||||
\(171\) | −2.17103 | −0.166023 | ||||||||
\(172\) | −0.773540 | −0.0589819 | ||||||||
\(173\) | 13.2866 | 1.01016 | 0.505082 | − | 0.863071i | \(-0.331462\pi\) | ||||
0.505082 | + | 0.863071i | \(0.331462\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.55780 | −0.268179 | ||||||||
\(177\) | −4.78426 | −0.359607 | ||||||||
\(178\) | −4.21574 | −0.315983 | ||||||||
\(179\) | −14.7950 | −1.10583 | −0.552914 | − | 0.833238i | \(-0.686484\pi\) | ||||
−0.552914 | + | 0.833238i | \(0.686484\pi\) | |||||||
\(180\) | 2.61323 | 0.194779 | ||||||||
\(181\) | −1.95529 | −0.145336 | −0.0726678 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726678 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.72883 | −0.497409 | ||||||||
\(184\) | 2.55780 | 0.188564 | ||||||||
\(185\) | 20.3421 | 1.49558 | ||||||||
\(186\) | −0.828970 | −0.0607830 | ||||||||
\(187\) | 28.3033 | 2.06974 | ||||||||
\(188\) | −2.94457 | −0.214755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.67340 | 0.411592 | ||||||||
\(191\) | −4.11086 | −0.297451 | −0.148726 | − | 0.988878i | \(-0.547517\pi\) | ||||
−0.148726 | + | 0.988878i | \(0.547517\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −10.1817 | −0.732898 | −0.366449 | − | 0.930438i | \(-0.619427\pi\) | ||||
−0.366449 | + | 0.930438i | \(0.619427\pi\) | |||||||
\(194\) | −10.9553 | −0.786544 | ||||||||
\(195\) | −2.61323 | −0.187137 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.44220 | −0.672729 | −0.336364 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336364 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(198\) | 3.55780 | 0.252842 | ||||||||
\(199\) | 13.2419 | 0.938695 | 0.469347 | − | 0.883014i | \(-0.344489\pi\) | ||||
0.469347 | + | 0.883014i | \(0.344489\pi\) | |||||||
\(200\) | −1.82897 | −0.129328 | ||||||||
\(201\) | −14.5131 | −1.02367 | ||||||||
\(202\) | −10.3421 | −0.727665 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.95529 | 0.556982 | ||||||||
\(205\) | 30.7950 | 2.15081 | ||||||||
\(206\) | 3.22646 | 0.224798 | ||||||||
\(207\) | −2.55780 | −0.177779 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 7.72409 | 0.534286 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.33134 | 0.0916532 | 0.0458266 | − | 0.998949i | \(-0.485408\pi\) | ||||
0.0458266 | + | 0.998949i | \(0.485408\pi\) | |||||||
\(212\) | 12.5685 | 0.863209 | ||||||||
\(213\) | 7.82897 | 0.536432 | ||||||||
\(214\) | −8.28663 | −0.566462 | ||||||||
\(215\) | −2.02144 | −0.137861 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.00000 | −0.270914 | ||||||||
\(219\) | −10.5578 | −0.713430 | ||||||||
\(220\) | −9.29735 | −0.626827 | ||||||||
\(221\) | −7.95529 | −0.535131 | ||||||||
\(222\) | 7.78426 | 0.522445 | ||||||||
\(223\) | 22.3528 | 1.49685 | 0.748426 | − | 0.663218i | \(-0.230810\pi\) | ||||
0.748426 | + | 0.663218i | \(0.230810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.82897 | 0.121931 | ||||||||
\(226\) | 17.1817 | 1.14291 | ||||||||
\(227\) | −19.8551 | −1.31783 | −0.658916 | − | 0.752216i | \(-0.728985\pi\) | ||||
−0.658916 | + | 0.752216i | \(0.728985\pi\) | |||||||
\(228\) | 2.17103 | 0.143780 | ||||||||
\(229\) | −19.1156 | −1.26319 | −0.631597 | − | 0.775297i | \(-0.717600\pi\) | ||||
−0.631597 | + | 0.775297i | \(0.717600\pi\) | |||||||
\(230\) | 6.68412 | 0.440738 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −21.0709 | −1.38040 | −0.690200 | − | 0.723619i | \(-0.742477\pi\) | ||||
−0.690200 | + | 0.723619i | \(0.742477\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −7.69484 | −0.501956 | ||||||||
\(236\) | 4.78426 | 0.311429 | ||||||||
\(237\) | 2.39749 | 0.155734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.39749 | 0.478504 | 0.239252 | − | 0.970958i | \(-0.423098\pi\) | ||||
0.239252 | + | 0.970958i | \(0.423098\pi\) | |||||||
\(240\) | −2.61323 | −0.168683 | ||||||||
\(241\) | 21.6239 | 1.39292 | 0.696461 | − | 0.717595i | \(-0.254757\pi\) | ||||
0.696461 | + | 0.717595i | \(0.254757\pi\) | |||||||
\(242\) | −1.65794 | −0.106576 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.72883 | 0.430769 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.7843 | 0.751337 | ||||||||
\(247\) | −2.17103 | −0.138139 | ||||||||
\(248\) | 0.828970 | 0.0526397 | ||||||||
\(249\) | −15.5131 | −0.983102 | ||||||||
\(250\) | 8.28663 | 0.524092 | ||||||||
\(251\) | −25.9660 | −1.63896 | −0.819480 | − | 0.573108i | \(-0.805738\pi\) | ||||
−0.819480 | + | 0.573108i | \(0.805738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.10014 | 0.572121 | ||||||||
\(254\) | −19.2973 | −1.21082 | ||||||||
\(255\) | 20.7890 | 1.30186 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.1156 | −0.693372 | −0.346686 | − | 0.937981i | \(-0.612693\pi\) | ||||
−0.346686 | + | 0.937981i | \(0.612693\pi\) | |||||||
\(258\) | −0.773540 | −0.0481585 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.61323 | 0.162066 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | −19.4082 | −1.19904 | ||||||||
\(263\) | 8.44694 | 0.520861 | 0.260430 | − | 0.965493i | \(-0.416136\pi\) | ||||
0.260430 | + | 0.965493i | \(0.416136\pi\) | |||||||
\(264\) | −3.55780 | −0.218967 | ||||||||
\(265\) | 32.8444 | 2.01762 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.21574 | −0.257999 | ||||||||
\(268\) | 14.5131 | 0.886528 | ||||||||
\(269\) | 11.2312 | 0.684778 | 0.342389 | − | 0.939558i | \(-0.388764\pi\) | ||||
0.342389 | + | 0.939558i | \(0.388764\pi\) | |||||||
\(270\) | 2.61323 | 0.159036 | ||||||||
\(271\) | −13.7890 | −0.837622 | −0.418811 | − | 0.908073i | \(-0.637553\pi\) | ||||
−0.418811 | + | 0.908073i | \(0.637553\pi\) | |||||||
\(272\) | −7.95529 | −0.482360 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.215740 | 0.0130334 | ||||||||
\(275\) | −6.50711 | −0.392394 | ||||||||
\(276\) | 2.55780 | 0.153961 | ||||||||
\(277\) | 20.2973 | 1.21955 | 0.609775 | − | 0.792575i | \(-0.291260\pi\) | ||||
0.609775 | + | 0.792575i | \(0.291260\pi\) | |||||||
\(278\) | 3.44220 | 0.206449 | ||||||||
\(279\) | −0.828970 | −0.0496291 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1370 | 1.14162 | 0.570810 | − | 0.821082i | \(-0.306629\pi\) | ||||
0.570810 | + | 0.821082i | \(0.306629\pi\) | |||||||
\(282\) | −2.94457 | −0.175347 | ||||||||
\(283\) | 0.326600 | 0.0194144 | 0.00970718 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970718 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(284\) | −7.82897 | −0.464564 | ||||||||
\(285\) | 5.67340 | 0.336063 | ||||||||
\(286\) | 3.55780 | 0.210377 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 46.2866 | 2.72274 | ||||||||
\(290\) | 7.83969 | 0.460362 | ||||||||
\(291\) | −10.9553 | −0.642210 | ||||||||
\(292\) | 10.5578 | 0.617849 | ||||||||
\(293\) | 8.61323 | 0.503190 | 0.251595 | − | 0.967833i | \(-0.419045\pi\) | ||||
0.251595 | + | 0.967833i | \(0.419045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.5024 | 0.727916 | ||||||||
\(296\) | −7.78426 | −0.452451 | ||||||||
\(297\) | 3.55780 | 0.206444 | ||||||||
\(298\) | 9.44220 | 0.546972 | ||||||||
\(299\) | −2.55780 | −0.147921 | ||||||||
\(300\) | −1.82897 | −0.105596 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.44220 | 0.370707 | ||||||||
\(303\) | −10.3421 | −0.594136 | ||||||||
\(304\) | −2.17103 | −0.124517 | ||||||||
\(305\) | 17.5840 | 1.00686 | ||||||||
\(306\) | 7.95529 | 0.454774 | ||||||||
\(307\) | 28.1710 | 1.60781 | 0.803903 | − | 0.594761i | \(-0.202753\pi\) | ||||
0.803903 | + | 0.594761i | \(0.202753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.22646 | 0.183547 | ||||||||
\(310\) | 2.16629 | 0.123037 | ||||||||
\(311\) | −24.2372 | −1.37436 | −0.687182 | − | 0.726485i | \(-0.741153\pi\) | ||||
−0.687182 | + | 0.726485i | \(0.741153\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 22.0554 | 1.24665 | 0.623323 | − | 0.781964i | \(-0.285782\pi\) | ||||
0.623323 | + | 0.781964i | \(0.285782\pi\) | |||||||
\(314\) | −6.83969 | −0.385986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.39749 | −0.134869 | ||||||||
\(317\) | 8.48691 | 0.476672 | 0.238336 | − | 0.971183i | \(-0.423398\pi\) | ||||
0.238336 | + | 0.971183i | \(0.423398\pi\) | |||||||
\(318\) | 12.5685 | 0.704808 | ||||||||
\(319\) | 10.6734 | 0.597596 | ||||||||
\(320\) | 2.61323 | 0.146084 | ||||||||
\(321\) | −8.28663 | −0.462515 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.2712 | 0.960994 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.82897 | 0.101453 | ||||||||
\(326\) | 12.6239 | 0.699176 | ||||||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | −11.7843 | −0.650677 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −9.29735 | −0.511802 | ||||||||
\(331\) | −29.0262 | −1.59542 | −0.797712 | − | 0.603039i | \(-0.793956\pi\) | ||||
−0.797712 | + | 0.603039i | \(0.793956\pi\) | |||||||
\(332\) | 15.5131 | 0.851391 | ||||||||
\(333\) | 7.78426 | 0.426575 | ||||||||
\(334\) | −3.71811 | −0.203446 | ||||||||
\(335\) | 37.9260 | 2.07212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.7950 | −0.969354 | −0.484677 | − | 0.874693i | \(-0.661063\pi\) | ||||
−0.484677 | + | 0.874693i | \(0.661063\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 17.1817 | 0.933185 | ||||||||
\(340\) | −20.7890 | −1.12744 | ||||||||
\(341\) | 2.94931 | 0.159714 | ||||||||
\(342\) | 2.17103 | 0.117396 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.773540 | 0.0417065 | ||||||||
\(345\) | 6.68412 | 0.359861 | ||||||||
\(346\) | −13.2866 | −0.714294 | ||||||||
\(347\) | −11.3528 | −0.609449 | −0.304725 | − | 0.952441i | \(-0.598564\pi\) | ||||
−0.304725 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(348\) | 3.00000 | 0.160817 | ||||||||
\(349\) | 14.8999 | 0.797571 | 0.398786 | − | 0.917044i | \(-0.369432\pi\) | ||||
0.398786 | + | 0.917044i | \(0.369432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.55780 | 0.189631 | ||||||||
\(353\) | −13.1370 | −0.699214 | −0.349607 | − | 0.936896i | \(-0.613685\pi\) | ||||
−0.349607 | + | 0.936896i | \(0.613685\pi\) | |||||||
\(354\) | 4.78426 | 0.254281 | ||||||||
\(355\) | −20.4589 | −1.08585 | ||||||||
\(356\) | 4.21574 | 0.223434 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.7950 | 0.781939 | ||||||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | −2.61323 | −0.137729 | ||||||||
\(361\) | −14.2866 | −0.751928 | ||||||||
\(362\) | 1.95529 | 0.102768 | ||||||||
\(363\) | −1.65794 | −0.0870193 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.5900 | 1.44412 | ||||||||
\(366\) | 6.72883 | 0.351722 | ||||||||
\(367\) | 1.71337 | 0.0894372 | 0.0447186 | − | 0.999000i | \(-0.485761\pi\) | ||||
0.0447186 | + | 0.999000i | \(0.485761\pi\) | |||||||
\(368\) | −2.55780 | −0.133335 | ||||||||
\(369\) | 11.7843 | 0.613464 | ||||||||
\(370\) | −20.3421 | −1.05753 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.828970 | 0.0429801 | ||||||||
\(373\) | 25.9767 | 1.34502 | 0.672512 | − | 0.740086i | \(-0.265215\pi\) | ||||
0.672512 | + | 0.740086i | \(0.265215\pi\) | |||||||
\(374\) | −28.3033 | −1.46353 | ||||||||
\(375\) | 8.28663 | 0.427920 | ||||||||
\(376\) | 2.94457 | 0.151855 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.4529 | −0.742397 | −0.371198 | − | 0.928554i | \(-0.621053\pi\) | ||||
−0.371198 | + | 0.928554i | \(0.621053\pi\) | |||||||
\(380\) | −5.67340 | −0.291039 | ||||||||
\(381\) | −19.2973 | −0.988633 | ||||||||
\(382\) | 4.11086 | 0.210330 | ||||||||
\(383\) | 20.4529 | 1.04510 | 0.522548 | − | 0.852610i | \(-0.324982\pi\) | ||||
0.522548 | + | 0.852610i | \(0.324982\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.1817 | 0.518237 | ||||||||
\(387\) | −0.773540 | −0.0393213 | ||||||||
\(388\) | 10.9553 | 0.556171 | ||||||||
\(389\) | 23.3975 | 1.18630 | 0.593150 | − | 0.805092i | \(-0.297884\pi\) | ||||
0.593150 | + | 0.805092i | \(0.297884\pi\) | |||||||
\(390\) | 2.61323 | 0.132326 | ||||||||
\(391\) | 20.3480 | 1.02904 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.4082 | −0.979015 | ||||||||
\(394\) | 9.44220 | 0.475691 | ||||||||
\(395\) | −6.26519 | −0.315236 | ||||||||
\(396\) | −3.55780 | −0.178786 | ||||||||
\(397\) | 22.4684 | 1.12766 | 0.563828 | − | 0.825892i | \(-0.309328\pi\) | ||||
0.563828 | + | 0.825892i | \(0.309328\pi\) | |||||||
\(398\) | −13.2419 | −0.663757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.82897 | 0.0914485 | ||||||||
\(401\) | 2.89986 | 0.144812 | 0.0724060 | − | 0.997375i | \(-0.476932\pi\) | ||||
0.0724060 | + | 0.997375i | \(0.476932\pi\) | |||||||
\(402\) | 14.5131 | 0.723847 | ||||||||
\(403\) | −0.828970 | −0.0412939 | ||||||||
\(404\) | 10.3421 | 0.514537 | ||||||||
\(405\) | 2.61323 | 0.129852 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.6948 | −1.37278 | ||||||||
\(408\) | −7.95529 | −0.393846 | ||||||||
\(409\) | 5.27591 | 0.260877 | 0.130438 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130438 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(410\) | −30.7950 | −1.52086 | ||||||||
\(411\) | 0.215740 | 0.0106417 | ||||||||
\(412\) | −3.22646 | −0.158956 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.55780 | 0.125709 | ||||||||
\(415\) | 40.5393 | 1.98999 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 3.44220 | 0.168565 | ||||||||
\(418\) | −7.72409 | −0.377798 | ||||||||
\(419\) | −3.22646 | −0.157623 | −0.0788114 | − | 0.996890i | \(-0.525113\pi\) | ||||
−0.0788114 | + | 0.996890i | \(0.525113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.5792 | 1.68529 | 0.842644 | − | 0.538470i | \(-0.180998\pi\) | ||||
0.842644 | + | 0.538470i | \(0.180998\pi\) | |||||||
\(422\) | −1.33134 | −0.0648086 | ||||||||
\(423\) | −2.94457 | −0.143170 | ||||||||
\(424\) | −12.5685 | −0.610381 | ||||||||
\(425\) | −14.5500 | −0.705778 | ||||||||
\(426\) | −7.82897 | −0.379315 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.28663 | 0.400549 | ||||||||
\(429\) | 3.55780 | 0.171772 | ||||||||
\(430\) | 2.02144 | 0.0974824 | ||||||||
\(431\) | 12.4529 | 0.599836 | 0.299918 | − | 0.953965i | \(-0.403041\pi\) | ||||
0.299918 | + | 0.953965i | \(0.403041\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −5.62869 | −0.270498 | −0.135249 | − | 0.990812i | \(-0.543183\pi\) | ||||
−0.135249 | + | 0.990812i | \(0.543183\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.83969 | 0.375884 | ||||||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | 5.55306 | 0.265639 | ||||||||
\(438\) | 10.5578 | 0.504471 | ||||||||
\(439\) | 12.5238 | 0.597729 | 0.298864 | − | 0.954296i | \(-0.403392\pi\) | ||||
0.298864 | + | 0.954296i | \(0.403392\pi\) | |||||||
\(440\) | 9.29735 | 0.443234 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.95529 | 0.378395 | ||||||||
\(443\) | −8.50237 | −0.403960 | −0.201980 | − | 0.979390i | \(-0.564738\pi\) | ||||
−0.201980 | + | 0.979390i | \(0.564738\pi\) | |||||||
\(444\) | −7.78426 | −0.369425 | ||||||||
\(445\) | 11.0167 | 0.522242 | ||||||||
\(446\) | −22.3528 | −1.05843 | ||||||||
\(447\) | 9.44220 | 0.446601 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.9153 | −1.64776 | −0.823878 | − | 0.566767i | \(-0.808194\pi\) | ||||
−0.823878 | + | 0.566767i | \(0.808194\pi\) | |||||||
\(450\) | −1.82897 | −0.0862185 | ||||||||
\(451\) | −41.9260 | −1.97422 | ||||||||
\(452\) | −17.1817 | −0.808161 | ||||||||
\(453\) | 6.44220 | 0.302681 | ||||||||
\(454\) | 19.8551 | 0.931848 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.17103 | −0.101668 | ||||||||
\(457\) | 1.83969 | 0.0860570 | 0.0430285 | − | 0.999074i | \(-0.486299\pi\) | ||||
0.0430285 | + | 0.999074i | \(0.486299\pi\) | |||||||
\(458\) | 19.1156 | 0.893213 | ||||||||
\(459\) | 7.95529 | 0.371321 | ||||||||
\(460\) | −6.68412 | −0.311649 | ||||||||
\(461\) | −23.4577 | −1.09253 | −0.546266 | − | 0.837612i | \(-0.683951\pi\) | ||||
−0.546266 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4529 | −1.04348 | −0.521738 | − | 0.853106i | \(-0.674716\pi\) | ||||
−0.521738 | + | 0.853106i | \(0.674716\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 2.16629 | 0.100459 | ||||||||
\(466\) | 21.0709 | 0.976090 | ||||||||
\(467\) | 8.98928 | 0.415974 | 0.207987 | − | 0.978132i | \(-0.433309\pi\) | ||||
0.207987 | + | 0.978132i | \(0.433309\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.69484 | 0.354936 | ||||||||
\(471\) | −6.83969 | −0.315156 | ||||||||
\(472\) | −4.78426 | −0.220213 | ||||||||
\(473\) | 2.75210 | 0.126542 | ||||||||
\(474\) | −2.39749 | −0.110120 | ||||||||
\(475\) | −3.97075 | −0.182190 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.5685 | 0.575473 | ||||||||
\(478\) | −7.39749 | −0.338353 | ||||||||
\(479\) | 35.5178 | 1.62285 | 0.811426 | − | 0.584456i | \(-0.198692\pi\) | ||||
0.811426 | + | 0.584456i | \(0.198692\pi\) | |||||||
\(480\) | 2.61323 | 0.119277 | ||||||||
\(481\) | 7.78426 | 0.354932 | ||||||||
\(482\) | −21.6239 | −0.984944 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.65794 | 0.0753609 | ||||||||
\(485\) | 28.6287 | 1.29996 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 18.0107 | 0.816144 | 0.408072 | − | 0.912950i | \(-0.366201\pi\) | ||||
0.408072 | + | 0.912950i | \(0.366201\pi\) | |||||||
\(488\) | −6.72883 | −0.304600 | ||||||||
\(489\) | 12.6239 | 0.570875 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8504 | −0.579931 | −0.289965 | − | 0.957037i | \(-0.593644\pi\) | ||||
−0.289965 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(492\) | −11.7843 | −0.531275 | ||||||||
\(493\) | 23.8659 | 1.07486 | ||||||||
\(494\) | 2.17103 | 0.0976792 | ||||||||
\(495\) | −9.29735 | −0.417885 | ||||||||
\(496\) | −0.828970 | −0.0372219 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.5131 | 0.695158 | ||||||||
\(499\) | 3.00474 | 0.134511 | 0.0672553 | − | 0.997736i | \(-0.478576\pi\) | ||||
0.0672553 | + | 0.997736i | \(0.478576\pi\) | |||||||
\(500\) | −8.28663 | −0.370589 | ||||||||
\(501\) | −3.71811 | −0.166113 | ||||||||
\(502\) | 25.9660 | 1.15892 | ||||||||
\(503\) | −33.9106 | −1.51200 | −0.755999 | − | 0.654573i | \(-0.772849\pi\) | ||||
−0.755999 | + | 0.654573i | \(0.772849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.0262 | 1.20265 | ||||||||
\(506\) | −9.10014 | −0.404551 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 19.2973 | 0.856181 | ||||||||
\(509\) | −25.1925 | −1.11664 | −0.558318 | − | 0.829627i | \(-0.688553\pi\) | ||||
−0.558318 | + | 0.829627i | \(0.688553\pi\) | |||||||
\(510\) | −20.7890 | −0.920552 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.17103 | 0.0958533 | ||||||||
\(514\) | 11.1156 | 0.490288 | ||||||||
\(515\) | −8.43148 | −0.371535 | ||||||||
\(516\) | 0.773540 | 0.0340532 | ||||||||
\(517\) | 10.4762 | 0.460742 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.2866 | −0.583218 | ||||||||
\(520\) | −2.61323 | −0.114598 | ||||||||
\(521\) | 39.2574 | 1.71990 | 0.859948 | − | 0.510381i | \(-0.170496\pi\) | ||||
0.859948 | + | 0.510381i | \(0.170496\pi\) | |||||||
\(522\) | 3.00000 | 0.131306 | ||||||||
\(523\) | 13.6794 | 0.598157 | 0.299079 | − | 0.954228i | \(-0.403321\pi\) | ||||
0.299079 | + | 0.954228i | \(0.403321\pi\) | |||||||
\(524\) | 19.4082 | 0.847852 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.44694 | −0.368304 | ||||||||
\(527\) | 6.59470 | 0.287270 | ||||||||
\(528\) | 3.55780 | 0.154833 | ||||||||
\(529\) | −16.4577 | −0.715550 | ||||||||
\(530\) | −32.8444 | −1.42667 | ||||||||
\(531\) | 4.78426 | 0.207619 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7843 | 0.510433 | ||||||||
\(534\) | 4.21574 | 0.182433 | ||||||||
\(535\) | 21.6549 | 0.936222 | ||||||||
\(536\) | −14.5131 | −0.626870 | ||||||||
\(537\) | 14.7950 | 0.638450 | ||||||||
\(538\) | −11.2312 | −0.484211 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.61323 | −0.112456 | ||||||||
\(541\) | −3.35278 | −0.144147 | −0.0720736 | − | 0.997399i | \(-0.522962\pi\) | ||||
−0.0720736 | + | 0.997399i | \(0.522962\pi\) | |||||||
\(542\) | 13.7890 | 0.592288 | ||||||||
\(543\) | 1.95529 | 0.0839095 | ||||||||
\(544\) | 7.95529 | 0.341080 | ||||||||
\(545\) | 10.4529 | 0.447754 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.899860 | −0.0384752 | −0.0192376 | − | 0.999815i | \(-0.506124\pi\) | ||||
−0.0192376 | + | 0.999815i | \(0.506124\pi\) | |||||||
\(548\) | −0.215740 | −0.00921597 | ||||||||
\(549\) | 6.72883 | 0.287179 | ||||||||
\(550\) | 6.50711 | 0.277464 | ||||||||
\(551\) | 6.51309 | 0.277467 | ||||||||
\(552\) | −2.55780 | −0.108867 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.2973 | −0.862352 | ||||||||
\(555\) | −20.3421 | −0.863472 | ||||||||
\(556\) | −3.44220 | −0.145982 | ||||||||
\(557\) | 9.71337 | 0.411569 | 0.205784 | − | 0.978597i | \(-0.434025\pi\) | ||||
0.205784 | + | 0.978597i | \(0.434025\pi\) | |||||||
\(558\) | 0.828970 | 0.0350931 | ||||||||
\(559\) | −0.773540 | −0.0327173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.3033 | −1.19497 | ||||||||
\(562\) | −19.1370 | −0.807247 | ||||||||
\(563\) | −35.1710 | −1.48228 | −0.741141 | − | 0.671349i | \(-0.765715\pi\) | ||||
−0.741141 | + | 0.671349i | \(0.765715\pi\) | |||||||
\(564\) | 2.94457 | 0.123989 | ||||||||
\(565\) | −44.8999 | −1.88895 | ||||||||
\(566\) | −0.326600 | −0.0137280 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.82897 | 0.328496 | ||||||||
\(569\) | −12.0661 | −0.505839 | −0.252920 | − | 0.967487i | \(-0.581391\pi\) | ||||
−0.252920 | + | 0.967487i | \(0.581391\pi\) | |||||||
\(570\) | −5.67340 | −0.237633 | ||||||||
\(571\) | 31.1370 | 1.30304 | 0.651522 | − | 0.758630i | \(-0.274131\pi\) | ||||
0.651522 | + | 0.758630i | \(0.274131\pi\) | |||||||
\(572\) | −3.55780 | −0.148759 | ||||||||
\(573\) | 4.11086 | 0.171734 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.67814 | −0.195092 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −28.7395 | −1.19644 | −0.598222 | − | 0.801331i | \(-0.704126\pi\) | ||||
−0.598222 | + | 0.801331i | \(0.704126\pi\) | |||||||
\(578\) | −46.2866 | −1.92527 | ||||||||
\(579\) | 10.1817 | 0.423139 | ||||||||
\(580\) | −7.83969 | −0.325525 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.9553 | 0.454111 | ||||||||
\(583\) | −44.7163 | −1.85196 | ||||||||
\(584\) | −10.5578 | −0.436885 | ||||||||
\(585\) | 2.61323 | 0.108044 | ||||||||
\(586\) | −8.61323 | −0.355809 | ||||||||
\(587\) | 12.7628 | 0.526778 | 0.263389 | − | 0.964690i | \(-0.415160\pi\) | ||||
0.263389 | + | 0.964690i | \(0.415160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.79972 | 0.0741561 | ||||||||
\(590\) | −12.5024 | −0.514714 | ||||||||
\(591\) | 9.44220 | 0.388400 | ||||||||
\(592\) | 7.78426 | 0.319931 | ||||||||
\(593\) | 23.3528 | 0.958984 | 0.479492 | − | 0.877546i | \(-0.340821\pi\) | ||||
0.479492 | + | 0.877546i | \(0.340821\pi\) | |||||||
\(594\) | −3.55780 | −0.145978 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.44220 | −0.386768 | ||||||||
\(597\) | −13.2419 | −0.541956 | ||||||||
\(598\) | 2.55780 | 0.104596 | ||||||||
\(599\) | 2.89986 | 0.118485 | 0.0592425 | − | 0.998244i | \(-0.481131\pi\) | ||||
0.0592425 | + | 0.998244i | \(0.481131\pi\) | |||||||
\(600\) | 1.82897 | 0.0746674 | ||||||||
\(601\) | 31.5947 | 1.28877 | 0.644387 | − | 0.764699i | \(-0.277112\pi\) | ||||
0.644387 | + | 0.764699i | \(0.277112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.5131 | 0.591019 | ||||||||
\(604\) | −6.44220 | −0.262129 | ||||||||
\(605\) | 4.33258 | 0.176144 | ||||||||
\(606\) | 10.3421 | 0.420117 | ||||||||
\(607\) | 41.9600 | 1.70311 | 0.851553 | − | 0.524269i | \(-0.175661\pi\) | ||||
0.851553 | + | 0.524269i | \(0.175661\pi\) | |||||||
\(608\) | 2.17103 | 0.0880469 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.5840 | −0.711954 | ||||||||
\(611\) | −2.94457 | −0.119125 | ||||||||
\(612\) | −7.95529 | −0.321574 | ||||||||
\(613\) | −18.0214 | −0.727879 | −0.363940 | − | 0.931423i | \(-0.618569\pi\) | ||||
−0.363940 | + | 0.931423i | \(0.618569\pi\) | |||||||
\(614\) | −28.1710 | −1.13689 | ||||||||
\(615\) | −30.7950 | −1.24177 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.551821 | 0.0222155 | 0.0111077 | − | 0.999938i | \(-0.496464\pi\) | ||||
0.0111077 | + | 0.999938i | \(0.496464\pi\) | |||||||
\(618\) | −3.22646 | −0.129787 | ||||||||
\(619\) | −40.3421 | −1.62148 | −0.810742 | − | 0.585403i | \(-0.800936\pi\) | ||||
−0.810742 | + | 0.585403i | \(0.800936\pi\) | |||||||
\(620\) | −2.16629 | −0.0870003 | ||||||||
\(621\) | 2.55780 | 0.102641 | ||||||||
\(622\) | 24.2372 | 0.971822 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −30.7997 | −1.23199 | ||||||||
\(626\) | −22.0554 | −0.881512 | ||||||||
\(627\) | −7.72409 | −0.308470 | ||||||||
\(628\) | 6.83969 | 0.272933 | ||||||||
\(629\) | −61.9260 | −2.46915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.5131 | −1.09528 | −0.547639 | − | 0.836714i | \(-0.684473\pi\) | ||||
−0.547639 | + | 0.836714i | \(0.684473\pi\) | |||||||
\(632\) | 2.39749 | 0.0953670 | ||||||||
\(633\) | −1.33134 | −0.0529160 | ||||||||
\(634\) | −8.48691 | −0.337058 | ||||||||
\(635\) | 50.4284 | 2.00119 | ||||||||
\(636\) | −12.5685 | −0.498374 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.6734 | −0.422564 | ||||||||
\(639\) | −7.82897 | −0.309709 | ||||||||
\(640\) | −2.61323 | −0.103297 | ||||||||
\(641\) | −2.23120 | −0.0881271 | −0.0440635 | − | 0.999029i | \(-0.514030\pi\) | ||||
−0.0440635 | + | 0.999029i | \(0.514030\pi\) | |||||||
\(642\) | 8.28663 | 0.327047 | ||||||||
\(643\) | −16.7134 | −0.659111 | −0.329555 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329555 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.02144 | 0.0795941 | ||||||||
\(646\) | −17.2712 | −0.679525 | ||||||||
\(647\) | −26.7950 | −1.05342 | −0.526710 | − | 0.850045i | \(-0.676574\pi\) | ||||
−0.526710 | + | 0.850045i | \(0.676574\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −17.0214 | −0.668150 | ||||||||
\(650\) | −1.82897 | −0.0717381 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.6239 | −0.494392 | ||||||||
\(653\) | −24.9707 | −0.977181 | −0.488590 | − | 0.872513i | \(-0.662489\pi\) | ||||
−0.488590 | + | 0.872513i | \(0.662489\pi\) | |||||||
\(654\) | 4.00000 | 0.156412 | ||||||||
\(655\) | 50.7181 | 1.98172 | ||||||||
\(656\) | 11.7843 | 0.460098 | ||||||||
\(657\) | 10.5578 | 0.411899 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8999 | −0.814143 | −0.407071 | − | 0.913396i | \(-0.633450\pi\) | ||||
−0.407071 | + | 0.913396i | \(0.633450\pi\) | |||||||
\(660\) | 9.29735 | 0.361899 | ||||||||
\(661\) | −47.7163 | −1.85595 | −0.927974 | − | 0.372645i | \(-0.878451\pi\) | ||||
−0.927974 | + | 0.372645i | \(0.878451\pi\) | |||||||
\(662\) | 29.0262 | 1.12813 | ||||||||
\(663\) | 7.95529 | 0.308958 | ||||||||
\(664\) | −15.5131 | −0.602025 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.78426 | −0.301634 | ||||||||
\(667\) | 7.67340 | 0.297115 | ||||||||
\(668\) | 3.71811 | 0.143858 | ||||||||
\(669\) | −22.3528 | −0.864208 | ||||||||
\(670\) | −37.9260 | −1.46521 | ||||||||
\(671\) | −23.9398 | −0.924187 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6025 | 0.447244 | 0.223622 | − | 0.974676i | \(-0.428212\pi\) | ||||
0.223622 | + | 0.974676i | \(0.428212\pi\) | |||||||
\(674\) | 17.7950 | 0.685437 | ||||||||
\(675\) | −1.82897 | −0.0703971 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 8.33732 | 0.320429 | 0.160215 | − | 0.987082i | \(-0.448781\pi\) | ||||
0.160215 | + | 0.987082i | \(0.448781\pi\) | |||||||
\(678\) | −17.1817 | −0.659861 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.7890 | 0.797222 | ||||||||
\(681\) | 19.8551 | 0.760851 | ||||||||
\(682\) | −2.94931 | −0.112935 | ||||||||
\(683\) | −32.5393 | −1.24508 | −0.622540 | − | 0.782588i | \(-0.713899\pi\) | ||||
−0.622540 | + | 0.782588i | \(0.713899\pi\) | |||||||
\(684\) | −2.17103 | −0.0830114 | ||||||||
\(685\) | −0.563779 | −0.0215409 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.1156 | 0.729306 | ||||||||
\(688\) | −0.773540 | −0.0294909 | ||||||||
\(689\) | 12.5685 | 0.478822 | ||||||||
\(690\) | −6.68412 | −0.254460 | ||||||||
\(691\) | −32.3128 | −1.22924 | −0.614619 | − | 0.788824i | \(-0.710690\pi\) | ||||
−0.614619 | + | 0.788824i | \(0.710690\pi\) | |||||||
\(692\) | 13.2866 | 0.505082 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.3528 | 0.430946 | ||||||||
\(695\) | −8.99526 | −0.341210 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | −93.7472 | −3.55093 | ||||||||
\(698\) | −14.8999 | −0.563968 | ||||||||
\(699\) | 21.0709 | 0.796974 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.7657 | −0.973158 | −0.486579 | − | 0.873637i | \(-0.661755\pi\) | ||||
−0.486579 | + | 0.873637i | \(0.661755\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −16.8999 | −0.637390 | ||||||||
\(704\) | −3.55780 | −0.134090 | ||||||||
\(705\) | 7.69484 | 0.289804 | ||||||||
\(706\) | 13.1370 | 0.494419 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.78426 | −0.179803 | ||||||||
\(709\) | −7.12158 | −0.267457 | −0.133728 | − | 0.991018i | \(-0.542695\pi\) | ||||
−0.133728 | + | 0.991018i | \(0.542695\pi\) | |||||||
\(710\) | 20.4589 | 0.767809 | ||||||||
\(711\) | −2.39749 | −0.0899129 | ||||||||
\(712\) | −4.21574 | −0.157992 | ||||||||
\(713\) | 2.12034 | 0.0794074 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.29735 | −0.347701 | ||||||||
\(716\) | −14.7950 | −0.552914 | ||||||||
\(717\) | −7.39749 | −0.276264 | ||||||||
\(718\) | 18.0000 | 0.671754 | ||||||||
\(719\) | 13.7783 | 0.513843 | 0.256922 | − | 0.966432i | \(-0.417292\pi\) | ||||
0.256922 | + | 0.966432i | \(0.417292\pi\) | |||||||
\(720\) | 2.61323 | 0.0973893 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.2866 | 0.531693 | ||||||||
\(723\) | −21.6239 | −0.804203 | ||||||||
\(724\) | −1.95529 | −0.0726678 | ||||||||
\(725\) | −5.48691 | −0.203779 | ||||||||
\(726\) | 1.65794 | 0.0615319 | ||||||||
\(727\) | −9.62395 | −0.356933 | −0.178466 | − | 0.983946i | \(-0.557114\pi\) | ||||
−0.178466 | + | 0.983946i | \(0.557114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.5900 | −1.02115 | ||||||||
\(731\) | 6.15374 | 0.227604 | ||||||||
\(732\) | −6.72883 | −0.248705 | ||||||||
\(733\) | −26.0369 | −0.961695 | −0.480847 | − | 0.876804i | \(-0.659671\pi\) | ||||
−0.480847 | + | 0.876804i | \(0.659671\pi\) | |||||||
\(734\) | −1.71337 | −0.0632417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.55780 | 0.0942818 | ||||||||
\(737\) | −51.6347 | −1.90199 | ||||||||
\(738\) | −11.7843 | −0.433785 | ||||||||
\(739\) | 44.7056 | 1.64452 | 0.822260 | − | 0.569112i | \(-0.192713\pi\) | ||||
0.822260 | + | 0.569112i | \(0.192713\pi\) | |||||||
\(740\) | 20.3421 | 0.747789 | ||||||||
\(741\) | 2.17103 | 0.0797548 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.1972 | 1.14451 | 0.572257 | − | 0.820074i | \(-0.306068\pi\) | ||||
0.572257 | + | 0.820074i | \(0.306068\pi\) | |||||||
\(744\) | −0.828970 | −0.0303915 | ||||||||
\(745\) | −24.6746 | −0.904009 | ||||||||
\(746\) | −25.9767 | −0.951076 | ||||||||
\(747\) | 15.5131 | 0.567594 | ||||||||
\(748\) | 28.3033 | 1.03487 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.28663 | −0.302585 | ||||||||
\(751\) | −4.17577 | −0.152376 | −0.0761880 | − | 0.997093i | \(-0.524275\pi\) | ||||
−0.0761880 | + | 0.997093i | \(0.524275\pi\) | |||||||
\(752\) | −2.94457 | −0.107377 | ||||||||
\(753\) | 25.9660 | 0.946254 | ||||||||
\(754\) | 3.00000 | 0.109254 | ||||||||
\(755\) | −16.8349 | −0.612687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.38203 | −0.195613 | −0.0978066 | − | 0.995205i | \(-0.531183\pi\) | ||||
−0.0978066 | + | 0.995205i | \(0.531183\pi\) | |||||||
\(758\) | 14.4529 | 0.524954 | ||||||||
\(759\) | −9.10014 | −0.330314 | ||||||||
\(760\) | 5.67340 | 0.205796 | ||||||||
\(761\) | 53.1585 | 1.92699 | 0.963497 | − | 0.267720i | \(-0.0862703\pi\) | ||||
0.963497 | + | 0.267720i | \(0.0862703\pi\) | |||||||
\(762\) | 19.2973 | 0.699069 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.11086 | −0.148726 | ||||||||
\(765\) | −20.7890 | −0.751628 | ||||||||
\(766\) | −20.4529 | −0.738994 | ||||||||
\(767\) | 4.78426 | 0.172750 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −38.7764 | −1.39831 | −0.699157 | − | 0.714968i | \(-0.746441\pi\) | ||||
−0.699157 | + | 0.714968i | \(0.746441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1156 | 0.400319 | ||||||||
\(772\) | −10.1817 | −0.366449 | ||||||||
\(773\) | −10.2217 | −0.367650 | −0.183825 | − | 0.982959i | \(-0.558848\pi\) | ||||
−0.183825 | + | 0.982959i | \(0.558848\pi\) | |||||||
\(774\) | 0.773540 | 0.0278043 | ||||||||
\(775\) | −1.51616 | −0.0544621 | ||||||||
\(776\) | −10.9553 | −0.393272 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.3975 | −0.838841 | ||||||||
\(779\) | −25.5840 | −0.916641 | ||||||||
\(780\) | −2.61323 | −0.0935686 | ||||||||
\(781\) | 27.8539 | 0.996691 | ||||||||
\(782\) | −20.3480 | −0.727644 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.8737 | 0.637939 | ||||||||
\(786\) | 19.4082 | 0.692268 | ||||||||
\(787\) | 3.28663 | 0.117156 | 0.0585778 | − | 0.998283i | \(-0.481343\pi\) | ||||
0.0585778 | + | 0.998283i | \(0.481343\pi\) | |||||||
\(788\) | −9.44220 | −0.336364 | ||||||||
\(789\) | −8.44694 | −0.300719 | ||||||||
\(790\) | 6.26519 | 0.222905 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.55780 | 0.126421 | ||||||||
\(793\) | 6.72883 | 0.238948 | ||||||||
\(794\) | −22.4684 | −0.797373 | ||||||||
\(795\) | −32.8444 | −1.16487 | ||||||||
\(796\) | 13.2419 | 0.469347 | ||||||||
\(797\) | 36.4284 | 1.29036 | 0.645180 | − | 0.764030i | \(-0.276782\pi\) | ||||
0.645180 | + | 0.764030i | \(0.276782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.4249 | 0.828714 | ||||||||
\(800\) | −1.82897 | −0.0646639 | ||||||||
\(801\) | 4.21574 | 0.148956 | ||||||||
\(802\) | −2.89986 | −0.102398 | ||||||||
\(803\) | −37.5625 | −1.32555 | ||||||||
\(804\) | −14.5131 | −0.511837 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.828970 | 0.0291992 | ||||||||
\(807\) | −11.2312 | −0.395357 | ||||||||
\(808\) | −10.3421 | −0.363832 | ||||||||
\(809\) | 43.6656 | 1.53520 | 0.767600 | − | 0.640929i | \(-0.221451\pi\) | ||||
0.767600 | + | 0.640929i | \(0.221451\pi\) | |||||||
\(810\) | −2.61323 | −0.0918195 | ||||||||
\(811\) | 21.8891 | 0.768632 | 0.384316 | − | 0.923202i | \(-0.374437\pi\) | ||||
0.384316 | + | 0.923202i | \(0.374437\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.7890 | 0.483601 | ||||||||
\(814\) | 27.6948 | 0.970704 | ||||||||
\(815\) | −32.9893 | −1.15556 | ||||||||
\(816\) | 7.95529 | 0.278491 | ||||||||
\(817\) | 1.67938 | 0.0587540 | ||||||||
\(818\) | −5.27591 | −0.184468 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.7950 | 1.07541 | ||||||||
\(821\) | 48.3450 | 1.68725 | 0.843625 | − | 0.536932i | \(-0.180417\pi\) | ||||
0.843625 | + | 0.536932i | \(0.180417\pi\) | |||||||
\(822\) | −0.215740 | −0.00752481 | ||||||||
\(823\) | 28.2157 | 0.983539 | 0.491769 | − | 0.870725i | \(-0.336350\pi\) | ||||
0.491769 | + | 0.870725i | \(0.336350\pi\) | |||||||
\(824\) | 3.22646 | 0.112399 | ||||||||
\(825\) | 6.50711 | 0.226548 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2586 | 1.01742 | 0.508711 | − | 0.860937i | \(-0.330122\pi\) | ||||
0.508711 | + | 0.860937i | \(0.330122\pi\) | |||||||
\(828\) | −2.55780 | −0.0888897 | ||||||||
\(829\) | 44.0876 | 1.53123 | 0.765613 | − | 0.643302i | \(-0.222436\pi\) | ||||
0.765613 | + | 0.643302i | \(0.222436\pi\) | |||||||
\(830\) | −40.5393 | −1.40714 | ||||||||
\(831\) | −20.2973 | −0.704107 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.44220 | −0.119194 | ||||||||
\(835\) | 9.71628 | 0.336246 | ||||||||
\(836\) | 7.72409 | 0.267143 | ||||||||
\(837\) | 0.828970 | 0.0286534 | ||||||||
\(838\) | 3.22646 | 0.111456 | ||||||||
\(839\) | −39.9707 | −1.37994 | −0.689972 | − | 0.723836i | \(-0.742377\pi\) | ||||
−0.689972 | + | 0.723836i | \(0.742377\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −34.5792 | −1.19168 | ||||||||
\(843\) | −19.1370 | −0.659115 | ||||||||
\(844\) | 1.33134 | 0.0458266 | ||||||||
\(845\) | 2.61323 | 0.0898978 | ||||||||
\(846\) | 2.94457 | 0.101236 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.5685 | 0.431605 | ||||||||
\(849\) | −0.326600 | −0.0112089 | ||||||||
\(850\) | 14.5500 | 0.499060 | ||||||||
\(851\) | −19.9106 | −0.682526 | ||||||||
\(852\) | 7.82897 | 0.268216 | ||||||||
\(853\) | 7.10962 | 0.243429 | 0.121714 | − | 0.992565i | \(-0.461161\pi\) | ||||
0.121714 | + | 0.992565i | \(0.461161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.67340 | −0.194026 | ||||||||
\(856\) | −8.28663 | −0.283231 | ||||||||
\(857\) | −31.4344 | −1.07378 | −0.536889 | − | 0.843653i | \(-0.680401\pi\) | ||||
−0.536889 | + | 0.843653i | \(0.680401\pi\) | |||||||
\(858\) | −3.55780 | −0.121461 | ||||||||
\(859\) | −27.5685 | −0.940626 | −0.470313 | − | 0.882500i | \(-0.655859\pi\) | ||||
−0.470313 | + | 0.882500i | \(0.655859\pi\) | |||||||
\(860\) | −2.02144 | −0.0689305 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.4529 | −0.424148 | ||||||||
\(863\) | 14.2312 | 0.484436 | 0.242218 | − | 0.970222i | \(-0.422125\pi\) | ||||
0.242218 | + | 0.970222i | \(0.422125\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 34.7210 | 1.18055 | ||||||||
\(866\) | 5.62869 | 0.191271 | ||||||||
\(867\) | −46.2866 | −1.57198 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.52979 | 0.289353 | ||||||||
\(870\) | −7.83969 | −0.265790 | ||||||||
\(871\) | 14.5131 | 0.491757 | ||||||||
\(872\) | −4.00000 | −0.135457 | ||||||||
\(873\) | 10.9553 | 0.370780 | ||||||||
\(874\) | −5.55306 | −0.187835 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.5578 | −0.356715 | ||||||||
\(877\) | 36.1478 | 1.22062 | 0.610312 | − | 0.792161i | \(-0.291044\pi\) | ||||
0.610312 | + | 0.792161i | \(0.291044\pi\) | |||||||
\(878\) | −12.5238 | −0.422658 | ||||||||
\(879\) | −8.61323 | −0.290517 | ||||||||
\(880\) | −9.29735 | −0.313414 | ||||||||
\(881\) | −10.8939 | −0.367024 | −0.183512 | − | 0.983017i | \(-0.558747\pi\) | ||||
−0.183512 | + | 0.983017i | \(0.558747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.2681 | 1.89357 | 0.946786 | − | 0.321863i | \(-0.104309\pi\) | ||||
0.946786 | + | 0.321863i | \(0.104309\pi\) | |||||||
\(884\) | −7.95529 | −0.267565 | ||||||||
\(885\) | −12.5024 | −0.420263 | ||||||||
\(886\) | 8.50237 | 0.285643 | ||||||||
\(887\) | −28.1632 | −0.945628 | −0.472814 | − | 0.881162i | \(-0.656762\pi\) | ||||
−0.472814 | + | 0.881162i | \(0.656762\pi\) | |||||||
\(888\) | 7.78426 | 0.261223 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.0167 | −0.369281 | ||||||||
\(891\) | −3.55780 | −0.119191 | ||||||||
\(892\) | 22.3528 | 0.748426 | ||||||||
\(893\) | 6.39275 | 0.213925 | ||||||||
\(894\) | −9.44220 | −0.315794 | ||||||||
\(895\) | −38.6627 | −1.29235 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.55780 | 0.0854025 | ||||||||
\(898\) | 34.9153 | 1.16514 | ||||||||
\(899\) | 2.48691 | 0.0829431 | ||||||||
\(900\) | 1.82897 | 0.0609657 | ||||||||
\(901\) | −99.9862 | −3.33102 | ||||||||
\(902\) | 41.9260 | 1.39598 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.1817 | 0.571456 | ||||||||
\(905\) | −5.10962 | −0.169850 | ||||||||
\(906\) | −6.44220 | −0.214028 | ||||||||
\(907\) | −26.4469 | −0.878156 | −0.439078 | − | 0.898449i | \(-0.644695\pi\) | ||||
−0.439078 | + | 0.898449i | \(0.644695\pi\) | |||||||
\(908\) | −19.8551 | −0.658916 | ||||||||
\(909\) | 10.3421 | 0.343024 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.0000 | 1.52405 | 0.762024 | − | 0.647549i | \(-0.224206\pi\) | ||||
0.762024 | + | 0.647549i | \(0.224206\pi\) | |||||||
\(912\) | 2.17103 | 0.0718900 | ||||||||
\(913\) | −55.1925 | −1.82660 | ||||||||
\(914\) | −1.83969 | −0.0608515 | ||||||||
\(915\) | −17.5840 | −0.581308 | ||||||||
\(916\) | −19.1156 | −0.631597 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.95529 | −0.262564 | ||||||||
\(919\) | 2.54234 | 0.0838641 | 0.0419320 | − | 0.999120i | \(-0.486649\pi\) | ||||
0.0419320 | + | 0.999120i | \(0.486649\pi\) | |||||||
\(920\) | 6.68412 | 0.220369 | ||||||||
\(921\) | −28.1710 | −0.928267 | ||||||||
\(922\) | 23.4577 | 0.772537 | ||||||||
\(923\) | −7.82897 | −0.257694 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.2372 | 0.468116 | ||||||||
\(926\) | 22.4529 | 0.737849 | ||||||||
\(927\) | −3.22646 | −0.105971 | ||||||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | −5.88914 | −0.193216 | −0.0966082 | − | 0.995322i | \(-0.530799\pi\) | ||||
−0.0966082 | + | 0.995322i | \(0.530799\pi\) | |||||||
\(930\) | −2.16629 | −0.0710354 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.0709 | −0.690200 | ||||||||
\(933\) | 24.2372 | 0.793490 | ||||||||
\(934\) | −8.98928 | −0.294138 | ||||||||
\(935\) | 73.9631 | 2.41885 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 21.3635 | 0.697915 | 0.348958 | − | 0.937139i | \(-0.386536\pi\) | ||||
0.348958 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.0554 | −0.719752 | ||||||||
\(940\) | −7.69484 | −0.250978 | ||||||||
\(941\) | −17.9446 | −0.584976 | −0.292488 | − | 0.956269i | \(-0.594483\pi\) | ||||
−0.292488 | + | 0.956269i | \(0.594483\pi\) | |||||||
\(942\) | 6.83969 | 0.222849 | ||||||||
\(943\) | −30.1418 | −0.981551 | ||||||||
\(944\) | 4.78426 | 0.155714 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.75210 | −0.0894785 | ||||||||
\(947\) | 45.6441 | 1.48324 | 0.741618 | − | 0.670823i | \(-0.234059\pi\) | ||||
0.741618 | + | 0.670823i | \(0.234059\pi\) | |||||||
\(948\) | 2.39749 | 0.0778668 | ||||||||
\(949\) | 10.5578 | 0.342721 | ||||||||
\(950\) | 3.97075 | 0.128828 | ||||||||
\(951\) | −8.48691 | −0.275207 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.8444 | 1.80898 | 0.904489 | − | 0.426496i | \(-0.140252\pi\) | ||||
0.904489 | + | 0.426496i | \(0.140252\pi\) | |||||||
\(954\) | −12.5685 | −0.406921 | ||||||||
\(955\) | −10.7426 | −0.347623 | ||||||||
\(956\) | 7.39749 | 0.239252 | ||||||||
\(957\) | −10.6734 | −0.345022 | ||||||||
\(958\) | −35.5178 | −1.14753 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.61323 | −0.0843416 | ||||||||
\(961\) | −30.3128 | −0.977833 | ||||||||
\(962\) | −7.78426 | −0.250975 | ||||||||
\(963\) | 8.28663 | 0.267033 | ||||||||
\(964\) | 21.6239 | 0.696461 | ||||||||
\(965\) | −26.6073 | −0.856518 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.2419 | −1.03683 | −0.518415 | − | 0.855129i | \(-0.673478\pi\) | ||||
−0.518415 | + | 0.855129i | \(0.673478\pi\) | |||||||
\(968\) | −1.65794 | −0.0532882 | ||||||||
\(969\) | −17.2712 | −0.554830 | ||||||||
\(970\) | −28.6287 | −0.919212 | ||||||||
\(971\) | 42.7764 | 1.37276 | 0.686381 | − | 0.727242i | \(-0.259198\pi\) | ||||
0.686381 | + | 0.727242i | \(0.259198\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.0107 | −0.577101 | ||||||||
\(975\) | −1.82897 | −0.0585739 | ||||||||
\(976\) | 6.72883 | 0.215385 | ||||||||
\(977\) | 11.1156 | 0.355620 | 0.177810 | − | 0.984065i | \(-0.443099\pi\) | ||||
0.177810 | + | 0.984065i | \(0.443099\pi\) | |||||||
\(978\) | −12.6239 | −0.403669 | ||||||||
\(979\) | −14.9988 | −0.479362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00000 | 0.127710 | ||||||||
\(982\) | 12.8504 | 0.410073 | ||||||||
\(983\) | −12.5131 | −0.399106 | −0.199553 | − | 0.979887i | \(-0.563949\pi\) | ||||
−0.199553 | + | 0.979887i | \(0.563949\pi\) | |||||||
\(984\) | 11.7843 | 0.375668 | ||||||||
\(985\) | −24.6746 | −0.786199 | ||||||||
\(986\) | −23.8659 | −0.760044 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.17103 | −0.0690697 | ||||||||
\(989\) | 1.97856 | 0.0629146 | ||||||||
\(990\) | 9.29735 | 0.295489 | ||||||||
\(991\) | −44.9707 | −1.42854 | −0.714271 | − | 0.699869i | \(-0.753242\pi\) | ||||
−0.714271 | + | 0.699869i | \(0.753242\pi\) | |||||||
\(992\) | 0.828970 | 0.0263198 | ||||||||
\(993\) | 29.0262 | 0.921118 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.6042 | 1.09703 | ||||||||
\(996\) | −15.5131 | −0.491551 | ||||||||
\(997\) | 18.1770 | 0.575672 | 0.287836 | − | 0.957680i | \(-0.407064\pi\) | ||||
0.287836 | + | 0.957680i | \(0.407064\pi\) | |||||||
\(998\) | −3.00474 | −0.0951134 | ||||||||
\(999\) | −7.78426 | −0.246283 |
(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.bv.1.2 | 3 | ||
7.2 | even | 3 | 546.2.i.k.235.2 | yes | 6 | ||
7.4 | even | 3 | 546.2.i.k.79.2 | ✓ | 6 | ||
7.6 | odd | 2 | 3822.2.a.bw.1.2 | 3 | |||
21.2 | odd | 6 | 1638.2.j.q.235.2 | 6 | |||
21.11 | odd | 6 | 1638.2.j.q.1171.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.k.79.2 | ✓ | 6 | 7.4 | even | 3 | ||
546.2.i.k.235.2 | yes | 6 | 7.2 | even | 3 | ||
1638.2.j.q.235.2 | 6 | 21.2 | odd | 6 | |||
1638.2.j.q.1171.2 | 6 | 21.11 | odd | 6 | |||
3822.2.a.bv.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3822.2.a.bw.1.2 | 3 | 7.6 | odd | 2 |