Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56879 | −1.81641 | −0.908204 | − | 0.418527i | \(-0.862546\pi\) | ||||
−0.908204 | + | 0.418527i | \(0.862546\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.59868 | 2.29934 | ||||||||
\(5\) | 3.14567 | 1.40679 | 0.703394 | − | 0.710800i | \(-0.251667\pi\) | ||||
0.703394 | + | 0.710800i | \(0.251667\pi\) | |||||||
\(6\) | −2.56879 | −1.04870 | ||||||||
\(7\) | −0.137684 | −0.0520397 | −0.0260198 | − | 0.999661i | \(-0.508283\pi\) | ||||
−0.0260198 | + | 0.999661i | \(0.508283\pi\) | |||||||
\(8\) | −6.67546 | −2.36013 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.08058 | −2.55530 | ||||||||
\(11\) | 0.886329 | 0.267238 | 0.133619 | − | 0.991033i | \(-0.457340\pi\) | ||||
0.133619 | + | 0.991033i | \(0.457340\pi\) | |||||||
\(12\) | 4.59868 | 1.32752 | ||||||||
\(13\) | 0.153446 | 0.0425583 | 0.0212791 | − | 0.999774i | \(-0.493226\pi\) | ||||
0.0212791 | + | 0.999774i | \(0.493226\pi\) | |||||||
\(14\) | 0.353681 | 0.0945254 | ||||||||
\(15\) | 3.14567 | 0.812210 | ||||||||
\(16\) | 7.95050 | 1.98763 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.56879 | −0.605470 | ||||||||
\(19\) | 6.70747 | 1.53880 | 0.769400 | − | 0.638768i | \(-0.220555\pi\) | ||||
0.769400 | + | 0.638768i | \(0.220555\pi\) | |||||||
\(20\) | 14.4660 | 3.23468 | ||||||||
\(21\) | −0.137684 | −0.0300451 | ||||||||
\(22\) | −2.27679 | −0.485414 | ||||||||
\(23\) | 7.75524 | 1.61708 | 0.808540 | − | 0.588442i | \(-0.200258\pi\) | ||||
0.808540 | + | 0.588442i | \(0.200258\pi\) | |||||||
\(24\) | −6.67546 | −1.36262 | ||||||||
\(25\) | 4.89527 | 0.979053 | ||||||||
\(26\) | −0.394171 | −0.0773033 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.633165 | −0.119657 | ||||||||
\(29\) | 4.03660 | 0.749577 | 0.374789 | − | 0.927110i | \(-0.377715\pi\) | ||||
0.374789 | + | 0.927110i | \(0.377715\pi\) | |||||||
\(30\) | −8.08058 | −1.47530 | ||||||||
\(31\) | −6.23265 | −1.11942 | −0.559709 | − | 0.828690i | \(-0.689087\pi\) | ||||
−0.559709 | + | 0.828690i | \(0.689087\pi\) | |||||||
\(32\) | −7.07224 | −1.25021 | ||||||||
\(33\) | 0.886329 | 0.154290 | ||||||||
\(34\) | −2.56879 | −0.440544 | ||||||||
\(35\) | −0.433109 | −0.0732088 | ||||||||
\(36\) | 4.59868 | 0.766447 | ||||||||
\(37\) | 8.71769 | 1.43318 | 0.716589 | − | 0.697495i | \(-0.245702\pi\) | ||||
0.716589 | + | 0.697495i | \(0.245702\pi\) | |||||||
\(38\) | −17.2301 | −2.79509 | ||||||||
\(39\) | 0.153446 | 0.0245710 | ||||||||
\(40\) | −20.9988 | −3.32021 | ||||||||
\(41\) | 4.00646 | 0.625705 | 0.312852 | − | 0.949802i | \(-0.398716\pi\) | ||||
0.312852 | + | 0.949802i | \(0.398716\pi\) | |||||||
\(42\) | 0.353681 | 0.0545742 | ||||||||
\(43\) | 1.85994 | 0.283638 | 0.141819 | − | 0.989893i | \(-0.454705\pi\) | ||||
0.141819 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(44\) | 4.07594 | 0.614471 | ||||||||
\(45\) | 3.14567 | 0.468929 | ||||||||
\(46\) | −19.9216 | −2.93728 | ||||||||
\(47\) | −8.83188 | −1.28826 | −0.644131 | − | 0.764915i | \(-0.722781\pi\) | ||||
−0.644131 | + | 0.764915i | \(0.722781\pi\) | |||||||
\(48\) | 7.95050 | 1.14756 | ||||||||
\(49\) | −6.98104 | −0.997292 | ||||||||
\(50\) | −12.5749 | −1.77836 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0.705650 | 0.0978560 | ||||||||
\(53\) | −1.81352 | −0.249107 | −0.124553 | − | 0.992213i | \(-0.539750\pi\) | ||||
−0.124553 | + | 0.992213i | \(0.539750\pi\) | |||||||
\(54\) | −2.56879 | −0.349568 | ||||||||
\(55\) | 2.78810 | 0.375947 | ||||||||
\(56\) | 0.919105 | 0.122821 | ||||||||
\(57\) | 6.70747 | 0.888426 | ||||||||
\(58\) | −10.3692 | −1.36154 | ||||||||
\(59\) | 1.89769 | 0.247058 | 0.123529 | − | 0.992341i | \(-0.460579\pi\) | ||||
0.123529 | + | 0.992341i | \(0.460579\pi\) | |||||||
\(60\) | 14.4660 | 1.86755 | ||||||||
\(61\) | −6.28907 | −0.805233 | −0.402617 | − | 0.915369i | \(-0.631899\pi\) | ||||
−0.402617 | + | 0.915369i | \(0.631899\pi\) | |||||||
\(62\) | 16.0104 | 2.03332 | ||||||||
\(63\) | −0.137684 | −0.0173466 | ||||||||
\(64\) | 2.26609 | 0.283261 | ||||||||
\(65\) | 0.482691 | 0.0598705 | ||||||||
\(66\) | −2.27679 | −0.280254 | ||||||||
\(67\) | −12.1576 | −1.48529 | −0.742643 | − | 0.669688i | \(-0.766428\pi\) | ||||
−0.742643 | + | 0.669688i | \(0.766428\pi\) | |||||||
\(68\) | 4.59868 | 0.557672 | ||||||||
\(69\) | 7.75524 | 0.933621 | ||||||||
\(70\) | 1.11257 | 0.132977 | ||||||||
\(71\) | 7.83419 | 0.929747 | 0.464873 | − | 0.885377i | \(-0.346100\pi\) | ||||
0.464873 | + | 0.885377i | \(0.346100\pi\) | |||||||
\(72\) | −6.67546 | −0.786711 | ||||||||
\(73\) | 0.0892372 | 0.0104444 | 0.00522221 | − | 0.999986i | \(-0.498338\pi\) | ||||
0.00522221 | + | 0.999986i | \(0.498338\pi\) | |||||||
\(74\) | −22.3939 | −2.60324 | ||||||||
\(75\) | 4.89527 | 0.565257 | ||||||||
\(76\) | 30.8455 | 3.53822 | ||||||||
\(77\) | −0.122033 | −0.0139070 | ||||||||
\(78\) | −0.394171 | −0.0446311 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 25.0097 | 2.79617 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.2918 | −1.13654 | ||||||||
\(83\) | 6.29504 | 0.690970 | 0.345485 | − | 0.938424i | \(-0.387714\pi\) | ||||
0.345485 | + | 0.938424i | \(0.387714\pi\) | |||||||
\(84\) | −0.633165 | −0.0690840 | ||||||||
\(85\) | 3.14567 | 0.341196 | ||||||||
\(86\) | −4.77778 | −0.515202 | ||||||||
\(87\) | 4.03660 | 0.432769 | ||||||||
\(88\) | −5.91665 | −0.630717 | ||||||||
\(89\) | −9.08666 | −0.963184 | −0.481592 | − | 0.876396i | \(-0.659941\pi\) | ||||
−0.481592 | + | 0.876396i | \(0.659941\pi\) | |||||||
\(90\) | −8.08058 | −0.851767 | ||||||||
\(91\) | −0.0211271 | −0.00221472 | ||||||||
\(92\) | 35.6639 | 3.71822 | ||||||||
\(93\) | −6.23265 | −0.646296 | ||||||||
\(94\) | 22.6872 | 2.34001 | ||||||||
\(95\) | 21.0995 | 2.16477 | ||||||||
\(96\) | −7.07224 | −0.721807 | ||||||||
\(97\) | −16.3940 | −1.66456 | −0.832280 | − | 0.554355i | \(-0.812965\pi\) | ||||
−0.832280 | + | 0.554355i | \(0.812965\pi\) | |||||||
\(98\) | 17.9328 | 1.81149 | ||||||||
\(99\) | 0.886329 | 0.0890794 | ||||||||
\(100\) | 22.5118 | 2.25118 | ||||||||
\(101\) | 13.6640 | 1.35962 | 0.679809 | − | 0.733389i | \(-0.262063\pi\) | ||||
0.679809 | + | 0.733389i | \(0.262063\pi\) | |||||||
\(102\) | −2.56879 | −0.254348 | ||||||||
\(103\) | 6.32754 | 0.623471 | 0.311736 | − | 0.950169i | \(-0.399090\pi\) | ||||
0.311736 | + | 0.950169i | \(0.399090\pi\) | |||||||
\(104\) | −1.02432 | −0.100443 | ||||||||
\(105\) | −0.433109 | −0.0422671 | ||||||||
\(106\) | 4.65856 | 0.452479 | ||||||||
\(107\) | −10.5763 | −1.02245 | −0.511226 | − | 0.859446i | \(-0.670809\pi\) | ||||
−0.511226 | + | 0.859446i | \(0.670809\pi\) | |||||||
\(108\) | 4.59868 | 0.442508 | ||||||||
\(109\) | 4.47043 | 0.428190 | 0.214095 | − | 0.976813i | \(-0.431320\pi\) | ||||
0.214095 | + | 0.976813i | \(0.431320\pi\) | |||||||
\(110\) | −7.16204 | −0.682874 | ||||||||
\(111\) | 8.71769 | 0.827446 | ||||||||
\(112\) | −1.09466 | −0.103435 | ||||||||
\(113\) | 11.7239 | 1.10289 | 0.551447 | − | 0.834210i | \(-0.314076\pi\) | ||||
0.551447 | + | 0.834210i | \(0.314076\pi\) | |||||||
\(114\) | −17.2301 | −1.61375 | ||||||||
\(115\) | 24.3955 | 2.27489 | ||||||||
\(116\) | 18.5630 | 1.72353 | ||||||||
\(117\) | 0.153446 | 0.0141861 | ||||||||
\(118\) | −4.87477 | −0.448759 | ||||||||
\(119\) | −0.137684 | −0.0126215 | ||||||||
\(120\) | −20.9988 | −1.91692 | ||||||||
\(121\) | −10.2144 | −0.928584 | ||||||||
\(122\) | 16.1553 | 1.46263 | ||||||||
\(123\) | 4.00646 | 0.361251 | ||||||||
\(124\) | −28.6620 | −2.57392 | ||||||||
\(125\) | −0.329457 | −0.0294675 | ||||||||
\(126\) | 0.353681 | 0.0315085 | ||||||||
\(127\) | 9.39492 | 0.833665 | 0.416832 | − | 0.908983i | \(-0.363140\pi\) | ||||
0.416832 | + | 0.908983i | \(0.363140\pi\) | |||||||
\(128\) | 8.32337 | 0.735689 | ||||||||
\(129\) | 1.85994 | 0.163758 | ||||||||
\(130\) | −1.23993 | −0.108749 | ||||||||
\(131\) | 17.4924 | 1.52832 | 0.764158 | − | 0.645029i | \(-0.223155\pi\) | ||||
0.764158 | + | 0.645029i | \(0.223155\pi\) | |||||||
\(132\) | 4.07594 | 0.354765 | ||||||||
\(133\) | −0.923512 | −0.0800787 | ||||||||
\(134\) | 31.2303 | 2.69789 | ||||||||
\(135\) | 3.14567 | 0.270737 | ||||||||
\(136\) | −6.67546 | −0.572416 | ||||||||
\(137\) | −6.18726 | −0.528614 | −0.264307 | − | 0.964439i | \(-0.585143\pi\) | ||||
−0.264307 | + | 0.964439i | \(0.585143\pi\) | |||||||
\(138\) | −19.9216 | −1.69584 | ||||||||
\(139\) | −13.4519 | −1.14098 | −0.570488 | − | 0.821306i | \(-0.693246\pi\) | ||||
−0.570488 | + | 0.821306i | \(0.693246\pi\) | |||||||
\(140\) | −1.99173 | −0.168332 | ||||||||
\(141\) | −8.83188 | −0.743778 | ||||||||
\(142\) | −20.1244 | −1.68880 | ||||||||
\(143\) | 0.136004 | 0.0113732 | ||||||||
\(144\) | 7.95050 | 0.662542 | ||||||||
\(145\) | 12.6978 | 1.05450 | ||||||||
\(146\) | −0.229232 | −0.0189713 | ||||||||
\(147\) | −6.98104 | −0.575787 | ||||||||
\(148\) | 40.0899 | 3.29537 | ||||||||
\(149\) | 7.97695 | 0.653497 | 0.326749 | − | 0.945111i | \(-0.394047\pi\) | ||||
0.326749 | + | 0.945111i | \(0.394047\pi\) | |||||||
\(150\) | −12.5749 | −1.02674 | ||||||||
\(151\) | 6.34255 | 0.516150 | 0.258075 | − | 0.966125i | \(-0.416912\pi\) | ||||
0.258075 | + | 0.966125i | \(0.416912\pi\) | |||||||
\(152\) | −44.7755 | −3.63177 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0.313478 | 0.0252608 | ||||||||
\(155\) | −19.6059 | −1.57478 | ||||||||
\(156\) | 0.705650 | 0.0564972 | ||||||||
\(157\) | −4.96083 | −0.395918 | −0.197959 | − | 0.980210i | \(-0.563431\pi\) | ||||
−0.197959 | + | 0.980210i | \(0.563431\pi\) | |||||||
\(158\) | −2.56879 | −0.204362 | ||||||||
\(159\) | −1.81352 | −0.143822 | ||||||||
\(160\) | −22.2470 | −1.75878 | ||||||||
\(161\) | −1.06777 | −0.0841523 | ||||||||
\(162\) | −2.56879 | −0.201823 | ||||||||
\(163\) | −17.8809 | −1.40054 | −0.700272 | − | 0.713877i | \(-0.746938\pi\) | ||||
−0.700272 | + | 0.713877i | \(0.746938\pi\) | |||||||
\(164\) | 18.4244 | 1.43871 | ||||||||
\(165\) | 2.78810 | 0.217053 | ||||||||
\(166\) | −16.1706 | −1.25508 | ||||||||
\(167\) | −0.248750 | −0.0192489 | −0.00962443 | − | 0.999954i | \(-0.503064\pi\) | ||||
−0.00962443 | + | 0.999954i | \(0.503064\pi\) | |||||||
\(168\) | 0.919105 | 0.0709105 | ||||||||
\(169\) | −12.9765 | −0.998189 | ||||||||
\(170\) | −8.08058 | −0.619752 | ||||||||
\(171\) | 6.70747 | 0.512933 | ||||||||
\(172\) | 8.55325 | 0.652179 | ||||||||
\(173\) | −20.4864 | −1.55755 | −0.778774 | − | 0.627304i | \(-0.784158\pi\) | ||||
−0.778774 | + | 0.627304i | \(0.784158\pi\) | |||||||
\(174\) | −10.3692 | −0.786085 | ||||||||
\(175\) | −0.674000 | −0.0509496 | ||||||||
\(176\) | 7.04676 | 0.531169 | ||||||||
\(177\) | 1.89769 | 0.142639 | ||||||||
\(178\) | 23.3417 | 1.74954 | ||||||||
\(179\) | 20.3027 | 1.51750 | 0.758748 | − | 0.651384i | \(-0.225811\pi\) | ||||
0.758748 | + | 0.651384i | \(0.225811\pi\) | |||||||
\(180\) | 14.4660 | 1.07823 | ||||||||
\(181\) | 6.39501 | 0.475337 | 0.237669 | − | 0.971346i | \(-0.423617\pi\) | ||||
0.237669 | + | 0.971346i | \(0.423617\pi\) | |||||||
\(182\) | 0.0542711 | 0.00402284 | ||||||||
\(183\) | −6.28907 | −0.464902 | ||||||||
\(184\) | −51.7698 | −3.81652 | ||||||||
\(185\) | 27.4230 | 2.01618 | ||||||||
\(186\) | 16.0104 | 1.17394 | ||||||||
\(187\) | 0.886329 | 0.0648148 | ||||||||
\(188\) | −40.6150 | −2.96215 | ||||||||
\(189\) | −0.137684 | −0.0100150 | ||||||||
\(190\) | −54.2002 | −3.93210 | ||||||||
\(191\) | 6.78820 | 0.491177 | 0.245588 | − | 0.969374i | \(-0.421019\pi\) | ||||
0.245588 | + | 0.969374i | \(0.421019\pi\) | |||||||
\(192\) | 2.26609 | 0.163541 | ||||||||
\(193\) | 0.0206068 | 0.00148331 | 0.000741653 | − | 1.00000i | \(-0.499764\pi\) | ||||
0.000741653 | 1.00000i | \(0.499764\pi\) | ||||||||
\(194\) | 42.1128 | 3.02352 | ||||||||
\(195\) | 0.482691 | 0.0345663 | ||||||||
\(196\) | −32.1036 | −2.29311 | ||||||||
\(197\) | 5.35940 | 0.381841 | 0.190921 | − | 0.981605i | \(-0.438853\pi\) | ||||
0.190921 | + | 0.981605i | \(0.438853\pi\) | |||||||
\(198\) | −2.27679 | −0.161805 | ||||||||
\(199\) | −18.6041 | −1.31881 | −0.659405 | − | 0.751788i | \(-0.729192\pi\) | ||||
−0.659405 | + | 0.751788i | \(0.729192\pi\) | |||||||
\(200\) | −32.6782 | −2.31070 | ||||||||
\(201\) | −12.1576 | −0.857530 | ||||||||
\(202\) | −35.0999 | −2.46962 | ||||||||
\(203\) | −0.555775 | −0.0390078 | ||||||||
\(204\) | 4.59868 | 0.321972 | ||||||||
\(205\) | 12.6030 | 0.880234 | ||||||||
\(206\) | −16.2541 | −1.13248 | ||||||||
\(207\) | 7.75524 | 0.539026 | ||||||||
\(208\) | 1.21997 | 0.0845899 | ||||||||
\(209\) | 5.94502 | 0.411226 | ||||||||
\(210\) | 1.11257 | 0.0767744 | ||||||||
\(211\) | 12.3382 | 0.849400 | 0.424700 | − | 0.905334i | \(-0.360380\pi\) | ||||
0.424700 | + | 0.905334i | \(0.360380\pi\) | |||||||
\(212\) | −8.33981 | −0.572781 | ||||||||
\(213\) | 7.83419 | 0.536790 | ||||||||
\(214\) | 27.1684 | 1.85719 | ||||||||
\(215\) | 5.85075 | 0.399018 | ||||||||
\(216\) | −6.67546 | −0.454208 | ||||||||
\(217\) | 0.858137 | 0.0582541 | ||||||||
\(218\) | −11.4836 | −0.777767 | ||||||||
\(219\) | 0.0892372 | 0.00603009 | ||||||||
\(220\) | 12.8216 | 0.864431 | ||||||||
\(221\) | 0.153446 | 0.0103219 | ||||||||
\(222\) | −22.3939 | −1.50298 | ||||||||
\(223\) | 2.52511 | 0.169094 | 0.0845469 | − | 0.996419i | \(-0.473056\pi\) | ||||
0.0845469 | + | 0.996419i | \(0.473056\pi\) | |||||||
\(224\) | 0.973735 | 0.0650604 | ||||||||
\(225\) | 4.89527 | 0.326351 | ||||||||
\(226\) | −30.1163 | −2.00331 | ||||||||
\(227\) | −11.0846 | −0.735711 | −0.367855 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367855 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(228\) | 30.8455 | 2.04279 | ||||||||
\(229\) | −9.95351 | −0.657746 | −0.328873 | − | 0.944374i | \(-0.606669\pi\) | ||||
−0.328873 | + | 0.944374i | \(0.606669\pi\) | |||||||
\(230\) | −62.6668 | −4.13213 | ||||||||
\(231\) | −0.122033 | −0.00802920 | ||||||||
\(232\) | −26.9462 | −1.76910 | ||||||||
\(233\) | −19.2676 | −1.26226 | −0.631131 | − | 0.775676i | \(-0.717409\pi\) | ||||
−0.631131 | + | 0.775676i | \(0.717409\pi\) | |||||||
\(234\) | −0.394171 | −0.0257678 | ||||||||
\(235\) | −27.7822 | −1.81231 | ||||||||
\(236\) | 8.72687 | 0.568071 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0.353681 | 0.0229258 | ||||||||
\(239\) | 16.5390 | 1.06982 | 0.534911 | − | 0.844909i | \(-0.320345\pi\) | ||||
0.534911 | + | 0.844909i | \(0.320345\pi\) | |||||||
\(240\) | 25.0097 | 1.61437 | ||||||||
\(241\) | 26.3974 | 1.70041 | 0.850203 | − | 0.526454i | \(-0.176479\pi\) | ||||
0.850203 | + | 0.526454i | \(0.176479\pi\) | |||||||
\(242\) | 26.2387 | 1.68669 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −28.9214 | −1.85150 | ||||||||
\(245\) | −21.9601 | −1.40298 | ||||||||
\(246\) | −10.2918 | −0.656179 | ||||||||
\(247\) | 1.02924 | 0.0654887 | ||||||||
\(248\) | 41.6058 | 2.64197 | ||||||||
\(249\) | 6.29504 | 0.398932 | ||||||||
\(250\) | 0.846305 | 0.0535250 | ||||||||
\(251\) | 1.40438 | 0.0886437 | 0.0443219 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443219 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(252\) | −0.633165 | −0.0398857 | ||||||||
\(253\) | 6.87369 | 0.432145 | ||||||||
\(254\) | −24.1336 | −1.51428 | ||||||||
\(255\) | 3.14567 | 0.196990 | ||||||||
\(256\) | −25.9132 | −1.61957 | ||||||||
\(257\) | −11.3803 | −0.709881 | −0.354941 | − | 0.934889i | \(-0.615499\pi\) | ||||
−0.354941 | + | 0.934889i | \(0.615499\pi\) | |||||||
\(258\) | −4.77778 | −0.297452 | ||||||||
\(259\) | −1.20029 | −0.0745822 | ||||||||
\(260\) | 2.21974 | 0.137663 | ||||||||
\(261\) | 4.03660 | 0.249859 | ||||||||
\(262\) | −44.9342 | −2.77605 | ||||||||
\(263\) | −18.9971 | −1.17141 | −0.585705 | − | 0.810525i | \(-0.699182\pi\) | ||||
−0.585705 | + | 0.810525i | \(0.699182\pi\) | |||||||
\(264\) | −5.91665 | −0.364145 | ||||||||
\(265\) | −5.70475 | −0.350440 | ||||||||
\(266\) | 2.37231 | 0.145456 | ||||||||
\(267\) | −9.08666 | −0.556095 | ||||||||
\(268\) | −55.9089 | −3.41518 | ||||||||
\(269\) | −8.23267 | −0.501955 | −0.250977 | − | 0.967993i | \(-0.580752\pi\) | ||||
−0.250977 | + | 0.967993i | \(0.580752\pi\) | |||||||
\(270\) | −8.08058 | −0.491768 | ||||||||
\(271\) | −0.135088 | −0.00820603 | −0.00410301 | − | 0.999992i | \(-0.501306\pi\) | ||||
−0.00410301 | + | 0.999992i | \(0.501306\pi\) | |||||||
\(272\) | 7.95050 | 0.482070 | ||||||||
\(273\) | −0.0211271 | −0.00127867 | ||||||||
\(274\) | 15.8938 | 0.960178 | ||||||||
\(275\) | 4.33881 | 0.261640 | ||||||||
\(276\) | 35.6639 | 2.14671 | ||||||||
\(277\) | −23.2923 | −1.39950 | −0.699749 | − | 0.714388i | \(-0.746705\pi\) | ||||
−0.699749 | + | 0.714388i | \(0.746705\pi\) | |||||||
\(278\) | 34.5551 | 2.07248 | ||||||||
\(279\) | −6.23265 | −0.373139 | ||||||||
\(280\) | 2.89121 | 0.172783 | ||||||||
\(281\) | 25.7854 | 1.53823 | 0.769113 | − | 0.639113i | \(-0.220698\pi\) | ||||
0.769113 | + | 0.639113i | \(0.220698\pi\) | |||||||
\(282\) | 22.6872 | 1.35101 | ||||||||
\(283\) | 18.9333 | 1.12547 | 0.562735 | − | 0.826637i | \(-0.309749\pi\) | ||||
0.562735 | + | 0.826637i | \(0.309749\pi\) | |||||||
\(284\) | 36.0269 | 2.13780 | ||||||||
\(285\) | 21.0995 | 1.24983 | ||||||||
\(286\) | −0.349365 | −0.0206584 | ||||||||
\(287\) | −0.551626 | −0.0325615 | ||||||||
\(288\) | −7.07224 | −0.416736 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −32.6180 | −1.91540 | ||||||||
\(291\) | −16.3940 | −0.961035 | ||||||||
\(292\) | 0.410374 | 0.0240153 | ||||||||
\(293\) | 7.36864 | 0.430481 | 0.215240 | − | 0.976561i | \(-0.430946\pi\) | ||||
0.215240 | + | 0.976561i | \(0.430946\pi\) | |||||||
\(294\) | 17.9328 | 1.04586 | ||||||||
\(295\) | 5.96952 | 0.347559 | ||||||||
\(296\) | −58.1946 | −3.38249 | ||||||||
\(297\) | 0.886329 | 0.0514300 | ||||||||
\(298\) | −20.4911 | −1.18702 | ||||||||
\(299\) | 1.19001 | 0.0688201 | ||||||||
\(300\) | 22.5118 | 1.29972 | ||||||||
\(301\) | −0.256084 | −0.0147604 | ||||||||
\(302\) | −16.2927 | −0.937539 | ||||||||
\(303\) | 13.6640 | 0.784976 | ||||||||
\(304\) | 53.3278 | 3.05856 | ||||||||
\(305\) | −19.7834 | −1.13279 | ||||||||
\(306\) | −2.56879 | −0.146848 | ||||||||
\(307\) | −24.2984 | −1.38678 | −0.693391 | − | 0.720561i | \(-0.743884\pi\) | ||||
−0.693391 | + | 0.720561i | \(0.743884\pi\) | |||||||
\(308\) | −0.561192 | −0.0319769 | ||||||||
\(309\) | 6.32754 | 0.359961 | ||||||||
\(310\) | 50.3634 | 2.86045 | ||||||||
\(311\) | −6.81598 | −0.386499 | −0.193249 | − | 0.981150i | \(-0.561903\pi\) | ||||
−0.193249 | + | 0.981150i | \(0.561903\pi\) | |||||||
\(312\) | −1.02432 | −0.0579909 | ||||||||
\(313\) | 22.8625 | 1.29226 | 0.646131 | − | 0.763226i | \(-0.276386\pi\) | ||||
0.646131 | + | 0.763226i | \(0.276386\pi\) | |||||||
\(314\) | 12.7433 | 0.719148 | ||||||||
\(315\) | −0.433109 | −0.0244029 | ||||||||
\(316\) | 4.59868 | 0.258696 | ||||||||
\(317\) | 10.9591 | 0.615525 | 0.307762 | − | 0.951463i | \(-0.400420\pi\) | ||||
0.307762 | + | 0.951463i | \(0.400420\pi\) | |||||||
\(318\) | 4.65856 | 0.261239 | ||||||||
\(319\) | 3.57775 | 0.200316 | ||||||||
\(320\) | 7.12838 | 0.398489 | ||||||||
\(321\) | −10.5763 | −0.590313 | ||||||||
\(322\) | 2.74288 | 0.152855 | ||||||||
\(323\) | 6.70747 | 0.373214 | ||||||||
\(324\) | 4.59868 | 0.255482 | ||||||||
\(325\) | 0.751160 | 0.0416668 | ||||||||
\(326\) | 45.9324 | 2.54396 | ||||||||
\(327\) | 4.47043 | 0.247215 | ||||||||
\(328\) | −26.7450 | −1.47675 | ||||||||
\(329\) | 1.21601 | 0.0670408 | ||||||||
\(330\) | −7.16204 | −0.394258 | ||||||||
\(331\) | 24.6789 | 1.35647 | 0.678236 | − | 0.734844i | \(-0.262745\pi\) | ||||
0.678236 | + | 0.734844i | \(0.262745\pi\) | |||||||
\(332\) | 28.9489 | 1.58878 | ||||||||
\(333\) | 8.71769 | 0.477726 | ||||||||
\(334\) | 0.638987 | 0.0349638 | ||||||||
\(335\) | −38.2438 | −2.08948 | ||||||||
\(336\) | −1.09466 | −0.0597185 | ||||||||
\(337\) | 18.1589 | 0.989181 | 0.494590 | − | 0.869126i | \(-0.335318\pi\) | ||||
0.494590 | + | 0.869126i | \(0.335318\pi\) | |||||||
\(338\) | 33.3338 | 1.81312 | ||||||||
\(339\) | 11.7239 | 0.636756 | ||||||||
\(340\) | 14.4660 | 0.784526 | ||||||||
\(341\) | −5.52418 | −0.299151 | ||||||||
\(342\) | −17.2301 | −0.931696 | ||||||||
\(343\) | 1.92497 | 0.103938 | ||||||||
\(344\) | −12.4159 | −0.669422 | ||||||||
\(345\) | 24.3955 | 1.31341 | ||||||||
\(346\) | 52.6251 | 2.82914 | ||||||||
\(347\) | 4.94297 | 0.265353 | 0.132676 | − | 0.991159i | \(-0.457643\pi\) | ||||
0.132676 | + | 0.991159i | \(0.457643\pi\) | |||||||
\(348\) | 18.5630 | 0.995082 | ||||||||
\(349\) | −10.9480 | −0.586032 | −0.293016 | − | 0.956108i | \(-0.594659\pi\) | ||||
−0.293016 | + | 0.956108i | \(0.594659\pi\) | |||||||
\(350\) | 1.73137 | 0.0925454 | ||||||||
\(351\) | 0.153446 | 0.00819035 | ||||||||
\(352\) | −6.26833 | −0.334103 | ||||||||
\(353\) | −6.40755 | −0.341039 | −0.170520 | − | 0.985354i | \(-0.554545\pi\) | ||||
−0.170520 | + | 0.985354i | \(0.554545\pi\) | |||||||
\(354\) | −4.87477 | −0.259091 | ||||||||
\(355\) | 24.6438 | 1.30796 | ||||||||
\(356\) | −41.7866 | −2.21469 | ||||||||
\(357\) | −0.137684 | −0.00728702 | ||||||||
\(358\) | −52.1534 | −2.75639 | ||||||||
\(359\) | −26.0161 | −1.37308 | −0.686538 | − | 0.727094i | \(-0.740870\pi\) | ||||
−0.686538 | + | 0.727094i | \(0.740870\pi\) | |||||||
\(360\) | −20.9988 | −1.10674 | ||||||||
\(361\) | 25.9902 | 1.36790 | ||||||||
\(362\) | −16.4274 | −0.863407 | ||||||||
\(363\) | −10.2144 | −0.536118 | ||||||||
\(364\) | −0.0971567 | −0.00509240 | ||||||||
\(365\) | 0.280711 | 0.0146931 | ||||||||
\(366\) | 16.1553 | 0.844451 | ||||||||
\(367\) | 7.02332 | 0.366614 | 0.183307 | − | 0.983056i | \(-0.441320\pi\) | ||||
0.183307 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(368\) | 61.6580 | 3.21415 | ||||||||
\(369\) | 4.00646 | 0.208568 | ||||||||
\(370\) | −70.4439 | −3.66221 | ||||||||
\(371\) | 0.249693 | 0.0129634 | ||||||||
\(372\) | −28.6620 | −1.48605 | ||||||||
\(373\) | −20.5593 | −1.06452 | −0.532260 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532260 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(374\) | −2.27679 | −0.117730 | ||||||||
\(375\) | −0.329457 | −0.0170131 | ||||||||
\(376\) | 58.9569 | 3.04047 | ||||||||
\(377\) | 0.619400 | 0.0319007 | ||||||||
\(378\) | 0.353681 | 0.0181914 | ||||||||
\(379\) | −28.3640 | −1.45696 | −0.728480 | − | 0.685067i | \(-0.759773\pi\) | ||||
−0.728480 | + | 0.685067i | \(0.759773\pi\) | |||||||
\(380\) | 97.0300 | 4.97753 | ||||||||
\(381\) | 9.39492 | 0.481317 | ||||||||
\(382\) | −17.4375 | −0.892178 | ||||||||
\(383\) | −0.877959 | −0.0448616 | −0.0224308 | − | 0.999748i | \(-0.507141\pi\) | ||||
−0.0224308 | + | 0.999748i | \(0.507141\pi\) | |||||||
\(384\) | 8.32337 | 0.424750 | ||||||||
\(385\) | −0.383877 | −0.0195642 | ||||||||
\(386\) | −0.0529344 | −0.00269429 | ||||||||
\(387\) | 1.85994 | 0.0945458 | ||||||||
\(388\) | −75.3909 | −3.82739 | ||||||||
\(389\) | 18.5261 | 0.939313 | 0.469657 | − | 0.882849i | \(-0.344378\pi\) | ||||
0.469657 | + | 0.882849i | \(0.344378\pi\) | |||||||
\(390\) | −1.23993 | −0.0627864 | ||||||||
\(391\) | 7.75524 | 0.392199 | ||||||||
\(392\) | 46.6017 | 2.35374 | ||||||||
\(393\) | 17.4924 | 0.882374 | ||||||||
\(394\) | −13.7672 | −0.693580 | ||||||||
\(395\) | 3.14567 | 0.158276 | ||||||||
\(396\) | 4.07594 | 0.204824 | ||||||||
\(397\) | 7.78973 | 0.390955 | 0.195478 | − | 0.980708i | \(-0.437374\pi\) | ||||
0.195478 | + | 0.980708i | \(0.437374\pi\) | |||||||
\(398\) | 47.7900 | 2.39550 | ||||||||
\(399\) | −0.923512 | −0.0462334 | ||||||||
\(400\) | 38.9198 | 1.94599 | ||||||||
\(401\) | 30.5551 | 1.52585 | 0.762923 | − | 0.646489i | \(-0.223763\pi\) | ||||
0.762923 | + | 0.646489i | \(0.223763\pi\) | |||||||
\(402\) | 31.2303 | 1.55762 | ||||||||
\(403\) | −0.956376 | −0.0476405 | ||||||||
\(404\) | 62.8363 | 3.12622 | ||||||||
\(405\) | 3.14567 | 0.156310 | ||||||||
\(406\) | 1.42767 | 0.0708541 | ||||||||
\(407\) | 7.72673 | 0.383000 | ||||||||
\(408\) | −6.67546 | −0.330485 | ||||||||
\(409\) | 39.4597 | 1.95116 | 0.975579 | − | 0.219651i | \(-0.0704918\pi\) | ||||
0.975579 | + | 0.219651i | \(0.0704918\pi\) | |||||||
\(410\) | −32.3745 | −1.59886 | ||||||||
\(411\) | −6.18726 | −0.305195 | ||||||||
\(412\) | 29.0983 | 1.43357 | ||||||||
\(413\) | −0.261282 | −0.0128568 | ||||||||
\(414\) | −19.9216 | −0.979092 | ||||||||
\(415\) | 19.8021 | 0.972049 | ||||||||
\(416\) | −1.08521 | −0.0532067 | ||||||||
\(417\) | −13.4519 | −0.658742 | ||||||||
\(418\) | −15.2715 | −0.746954 | ||||||||
\(419\) | −3.10743 | −0.151808 | −0.0759039 | − | 0.997115i | \(-0.524184\pi\) | ||||
−0.0759039 | + | 0.997115i | \(0.524184\pi\) | |||||||
\(420\) | −1.99173 | −0.0971865 | ||||||||
\(421\) | −11.1773 | −0.544748 | −0.272374 | − | 0.962192i | \(-0.587809\pi\) | ||||
−0.272374 | + | 0.962192i | \(0.587809\pi\) | |||||||
\(422\) | −31.6943 | −1.54286 | ||||||||
\(423\) | −8.83188 | −0.429421 | ||||||||
\(424\) | 12.1061 | 0.587925 | ||||||||
\(425\) | 4.89527 | 0.237455 | ||||||||
\(426\) | −20.1244 | −0.975029 | ||||||||
\(427\) | 0.865905 | 0.0419041 | ||||||||
\(428\) | −48.6372 | −2.35097 | ||||||||
\(429\) | 0.136004 | 0.00656632 | ||||||||
\(430\) | −15.0294 | −0.724780 | ||||||||
\(431\) | 7.74831 | 0.373223 | 0.186611 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186611 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(432\) | 7.95050 | 0.382519 | ||||||||
\(433\) | −12.6430 | −0.607584 | −0.303792 | − | 0.952738i | \(-0.598253\pi\) | ||||
−0.303792 | + | 0.952738i | \(0.598253\pi\) | |||||||
\(434\) | −2.20437 | −0.105813 | ||||||||
\(435\) | 12.6978 | 0.608814 | ||||||||
\(436\) | 20.5581 | 0.984554 | ||||||||
\(437\) | 52.0180 | 2.48836 | ||||||||
\(438\) | −0.229232 | −0.0109531 | ||||||||
\(439\) | 24.0391 | 1.14733 | 0.573663 | − | 0.819092i | \(-0.305522\pi\) | ||||
0.573663 | + | 0.819092i | \(0.305522\pi\) | |||||||
\(440\) | −18.6119 | −0.887286 | ||||||||
\(441\) | −6.98104 | −0.332431 | ||||||||
\(442\) | −0.394171 | −0.0187488 | ||||||||
\(443\) | −8.61339 | −0.409235 | −0.204617 | − | 0.978842i | \(-0.565595\pi\) | ||||
−0.204617 | + | 0.978842i | \(0.565595\pi\) | |||||||
\(444\) | 40.0899 | 1.90258 | ||||||||
\(445\) | −28.5837 | −1.35500 | ||||||||
\(446\) | −6.48648 | −0.307144 | ||||||||
\(447\) | 7.97695 | 0.377297 | ||||||||
\(448\) | −0.312005 | −0.0147408 | ||||||||
\(449\) | −41.1657 | −1.94273 | −0.971365 | − | 0.237592i | \(-0.923642\pi\) | ||||
−0.971365 | + | 0.237592i | \(0.923642\pi\) | |||||||
\(450\) | −12.5749 | −0.592787 | ||||||||
\(451\) | 3.55104 | 0.167212 | ||||||||
\(452\) | 53.9146 | 2.53593 | ||||||||
\(453\) | 6.34255 | 0.297999 | ||||||||
\(454\) | 28.4740 | 1.33635 | ||||||||
\(455\) | −0.0664589 | −0.00311564 | ||||||||
\(456\) | −44.7755 | −2.09680 | ||||||||
\(457\) | −39.5093 | −1.84817 | −0.924084 | − | 0.382190i | \(-0.875170\pi\) | ||||
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(458\) | 25.5685 | 1.19474 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 112.187 | 5.23074 | ||||||||
\(461\) | 28.8203 | 1.34229 | 0.671147 | − | 0.741324i | \(-0.265802\pi\) | ||||
0.671147 | + | 0.741324i | \(0.265802\pi\) | |||||||
\(462\) | 0.313478 | 0.0145843 | ||||||||
\(463\) | 21.6787 | 1.00749 | 0.503747 | − | 0.863851i | \(-0.331954\pi\) | ||||
0.503747 | + | 0.863851i | \(0.331954\pi\) | |||||||
\(464\) | 32.0930 | 1.48988 | ||||||||
\(465\) | −19.6059 | −0.909201 | ||||||||
\(466\) | 49.4944 | 2.29278 | ||||||||
\(467\) | −7.24370 | −0.335198 | −0.167599 | − | 0.985855i | \(-0.553601\pi\) | ||||
−0.167599 | + | 0.985855i | \(0.553601\pi\) | |||||||
\(468\) | 0.705650 | 0.0326187 | ||||||||
\(469\) | 1.67391 | 0.0772938 | ||||||||
\(470\) | 71.3667 | 3.29190 | ||||||||
\(471\) | −4.96083 | −0.228583 | ||||||||
\(472\) | −12.6680 | −0.583090 | ||||||||
\(473\) | 1.64851 | 0.0757988 | ||||||||
\(474\) | −2.56879 | −0.117988 | ||||||||
\(475\) | 32.8349 | 1.50657 | ||||||||
\(476\) | −0.633165 | −0.0290211 | ||||||||
\(477\) | −1.81352 | −0.0830355 | ||||||||
\(478\) | −42.4853 | −1.94323 | ||||||||
\(479\) | −13.3885 | −0.611737 | −0.305869 | − | 0.952074i | \(-0.598947\pi\) | ||||
−0.305869 | + | 0.952074i | \(0.598947\pi\) | |||||||
\(480\) | −22.2470 | −1.01543 | ||||||||
\(481\) | 1.33770 | 0.0609936 | ||||||||
\(482\) | −67.8094 | −3.08863 | ||||||||
\(483\) | −1.06777 | −0.0485854 | ||||||||
\(484\) | −46.9729 | −2.13513 | ||||||||
\(485\) | −51.5702 | −2.34168 | ||||||||
\(486\) | −2.56879 | −0.116523 | ||||||||
\(487\) | 8.61232 | 0.390261 | 0.195131 | − | 0.980777i | \(-0.437487\pi\) | ||||
0.195131 | + | 0.980777i | \(0.437487\pi\) | |||||||
\(488\) | 41.9825 | 1.90046 | ||||||||
\(489\) | −17.8809 | −0.808604 | ||||||||
\(490\) | 56.4108 | 2.54838 | ||||||||
\(491\) | 26.6586 | 1.20308 | 0.601542 | − | 0.798841i | \(-0.294553\pi\) | ||||
0.601542 | + | 0.798841i | \(0.294553\pi\) | |||||||
\(492\) | 18.4244 | 0.830638 | ||||||||
\(493\) | 4.03660 | 0.181799 | ||||||||
\(494\) | −2.64389 | −0.118954 | ||||||||
\(495\) | 2.78810 | 0.125316 | ||||||||
\(496\) | −49.5527 | −2.22498 | ||||||||
\(497\) | −1.07864 | −0.0483837 | ||||||||
\(498\) | −16.1706 | −0.724623 | ||||||||
\(499\) | −6.29777 | −0.281927 | −0.140963 | − | 0.990015i | \(-0.545020\pi\) | ||||
−0.140963 | + | 0.990015i | \(0.545020\pi\) | |||||||
\(500\) | −1.51507 | −0.0677558 | ||||||||
\(501\) | −0.248750 | −0.0111133 | ||||||||
\(502\) | −3.60756 | −0.161013 | ||||||||
\(503\) | 17.6609 | 0.787460 | 0.393730 | − | 0.919226i | \(-0.371185\pi\) | ||||
0.393730 | + | 0.919226i | \(0.371185\pi\) | |||||||
\(504\) | 0.919105 | 0.0409402 | ||||||||
\(505\) | 42.9825 | 1.91269 | ||||||||
\(506\) | −17.6571 | −0.784952 | ||||||||
\(507\) | −12.9765 | −0.576305 | ||||||||
\(508\) | 43.2043 | 1.91688 | ||||||||
\(509\) | −5.36610 | −0.237848 | −0.118924 | − | 0.992903i | \(-0.537944\pi\) | ||||
−0.118924 | + | 0.992903i | \(0.537944\pi\) | |||||||
\(510\) | −8.08058 | −0.357814 | ||||||||
\(511\) | −0.0122865 | −0.000543525 0 | ||||||||
\(512\) | 49.9187 | 2.20612 | ||||||||
\(513\) | 6.70747 | 0.296142 | ||||||||
\(514\) | 29.2335 | 1.28943 | ||||||||
\(515\) | 19.9044 | 0.877092 | ||||||||
\(516\) | 8.55325 | 0.376536 | ||||||||
\(517\) | −7.82795 | −0.344273 | ||||||||
\(518\) | 3.08328 | 0.135472 | ||||||||
\(519\) | −20.4864 | −0.899251 | ||||||||
\(520\) | −3.22219 | −0.141302 | ||||||||
\(521\) | −6.54100 | −0.286566 | −0.143283 | − | 0.989682i | \(-0.545766\pi\) | ||||
−0.143283 | + | 0.989682i | \(0.545766\pi\) | |||||||
\(522\) | −10.3692 | −0.453846 | ||||||||
\(523\) | 24.4974 | 1.07120 | 0.535599 | − | 0.844473i | \(-0.320086\pi\) | ||||
0.535599 | + | 0.844473i | \(0.320086\pi\) | |||||||
\(524\) | 80.4418 | 3.51412 | ||||||||
\(525\) | −0.674000 | −0.0294158 | ||||||||
\(526\) | 48.7995 | 2.12776 | ||||||||
\(527\) | −6.23265 | −0.271499 | ||||||||
\(528\) | 7.04676 | 0.306671 | ||||||||
\(529\) | 37.1437 | 1.61494 | ||||||||
\(530\) | 14.6543 | 0.636543 | ||||||||
\(531\) | 1.89769 | 0.0823528 | ||||||||
\(532\) | −4.24694 | −0.184128 | ||||||||
\(533\) | 0.614776 | 0.0266289 | ||||||||
\(534\) | 23.3417 | 1.01009 | ||||||||
\(535\) | −33.2697 | −1.43837 | ||||||||
\(536\) | 81.1575 | 3.50547 | ||||||||
\(537\) | 20.3027 | 0.876127 | ||||||||
\(538\) | 21.1480 | 0.911755 | ||||||||
\(539\) | −6.18750 | −0.266514 | ||||||||
\(540\) | 14.4660 | 0.622515 | ||||||||
\(541\) | −42.9711 | −1.84747 | −0.923737 | − | 0.383028i | \(-0.874881\pi\) | ||||
−0.923737 | + | 0.383028i | \(0.874881\pi\) | |||||||
\(542\) | 0.347013 | 0.0149055 | ||||||||
\(543\) | 6.39501 | 0.274436 | ||||||||
\(544\) | −7.07224 | −0.303220 | ||||||||
\(545\) | 14.0625 | 0.602372 | ||||||||
\(546\) | 0.0542711 | 0.00232259 | ||||||||
\(547\) | 9.48682 | 0.405627 | 0.202814 | − | 0.979217i | \(-0.434991\pi\) | ||||
0.202814 | + | 0.979217i | \(0.434991\pi\) | |||||||
\(548\) | −28.4532 | −1.21546 | ||||||||
\(549\) | −6.28907 | −0.268411 | ||||||||
\(550\) | −11.1455 | −0.475246 | ||||||||
\(551\) | 27.0754 | 1.15345 | ||||||||
\(552\) | −51.7698 | −2.20347 | ||||||||
\(553\) | −0.137684 | −0.00585492 | ||||||||
\(554\) | 59.8330 | 2.54206 | ||||||||
\(555\) | 27.4230 | 1.16404 | ||||||||
\(556\) | −61.8610 | −2.62349 | ||||||||
\(557\) | −16.5982 | −0.703290 | −0.351645 | − | 0.936133i | \(-0.614378\pi\) | ||||
−0.351645 | + | 0.936133i | \(0.614378\pi\) | |||||||
\(558\) | 16.0104 | 0.677773 | ||||||||
\(559\) | 0.285400 | 0.0120711 | ||||||||
\(560\) | −3.44344 | −0.145512 | ||||||||
\(561\) | 0.886329 | 0.0374208 | ||||||||
\(562\) | −66.2372 | −2.79405 | ||||||||
\(563\) | 12.6343 | 0.532471 | 0.266236 | − | 0.963908i | \(-0.414220\pi\) | ||||
0.266236 | + | 0.963908i | \(0.414220\pi\) | |||||||
\(564\) | −40.6150 | −1.71020 | ||||||||
\(565\) | 36.8796 | 1.55154 | ||||||||
\(566\) | −48.6357 | −2.04431 | ||||||||
\(567\) | −0.137684 | −0.00578219 | ||||||||
\(568\) | −52.2968 | −2.19433 | ||||||||
\(569\) | 24.9192 | 1.04467 | 0.522334 | − | 0.852741i | \(-0.325062\pi\) | ||||
0.522334 | + | 0.852741i | \(0.325062\pi\) | |||||||
\(570\) | −54.2002 | −2.27020 | ||||||||
\(571\) | 6.28106 | 0.262854 | 0.131427 | − | 0.991326i | \(-0.458044\pi\) | ||||
0.131427 | + | 0.991326i | \(0.458044\pi\) | |||||||
\(572\) | 0.625437 | 0.0261509 | ||||||||
\(573\) | 6.78820 | 0.283581 | ||||||||
\(574\) | 1.41701 | 0.0591449 | ||||||||
\(575\) | 37.9640 | 1.58321 | ||||||||
\(576\) | 2.26609 | 0.0944204 | ||||||||
\(577\) | −33.9537 | −1.41351 | −0.706756 | − | 0.707457i | \(-0.749842\pi\) | ||||
−0.706756 | + | 0.707457i | \(0.749842\pi\) | |||||||
\(578\) | −2.56879 | −0.106848 | ||||||||
\(579\) | 0.0206068 | 0.000856388 0 | ||||||||
\(580\) | 58.3932 | 2.42465 | ||||||||
\(581\) | −0.866727 | −0.0359579 | ||||||||
\(582\) | 42.1128 | 1.74563 | ||||||||
\(583\) | −1.60738 | −0.0665708 | ||||||||
\(584\) | −0.595700 | −0.0246502 | ||||||||
\(585\) | 0.482691 | 0.0199568 | ||||||||
\(586\) | −18.9285 | −0.781929 | ||||||||
\(587\) | 33.7214 | 1.39183 | 0.695916 | − | 0.718124i | \(-0.254999\pi\) | ||||
0.695916 | + | 0.718124i | \(0.254999\pi\) | |||||||
\(588\) | −32.1036 | −1.32393 | ||||||||
\(589\) | −41.8053 | −1.72256 | ||||||||
\(590\) | −15.3344 | −0.631309 | ||||||||
\(591\) | 5.35940 | 0.220456 | ||||||||
\(592\) | 69.3100 | 2.84862 | ||||||||
\(593\) | −31.6351 | −1.29910 | −0.649549 | − | 0.760320i | \(-0.725042\pi\) | ||||
−0.649549 | + | 0.760320i | \(0.725042\pi\) | |||||||
\(594\) | −2.27679 | −0.0934179 | ||||||||
\(595\) | −0.433109 | −0.0177558 | ||||||||
\(596\) | 36.6834 | 1.50261 | ||||||||
\(597\) | −18.6041 | −0.761415 | ||||||||
\(598\) | −3.05689 | −0.125005 | ||||||||
\(599\) | −10.0084 | −0.408931 | −0.204465 | − | 0.978874i | \(-0.565546\pi\) | ||||
−0.204465 | + | 0.978874i | \(0.565546\pi\) | |||||||
\(600\) | −32.6782 | −1.33408 | ||||||||
\(601\) | 39.2087 | 1.59936 | 0.799679 | − | 0.600428i | \(-0.205003\pi\) | ||||
0.799679 | + | 0.600428i | \(0.205003\pi\) | |||||||
\(602\) | 0.657825 | 0.0268109 | ||||||||
\(603\) | −12.1576 | −0.495095 | ||||||||
\(604\) | 29.1674 | 1.18680 | ||||||||
\(605\) | −32.1312 | −1.30632 | ||||||||
\(606\) | −35.0999 | −1.42584 | ||||||||
\(607\) | −1.91002 | −0.0775251 | −0.0387626 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387626 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(608\) | −47.4368 | −1.92382 | ||||||||
\(609\) | −0.555775 | −0.0225211 | ||||||||
\(610\) | 50.8193 | 2.05761 | ||||||||
\(611\) | −1.35522 | −0.0548262 | ||||||||
\(612\) | 4.59868 | 0.185891 | ||||||||
\(613\) | −10.1587 | −0.410305 | −0.205152 | − | 0.978730i | \(-0.565769\pi\) | ||||
−0.205152 | + | 0.978730i | \(0.565769\pi\) | |||||||
\(614\) | 62.4175 | 2.51896 | ||||||||
\(615\) | 12.6030 | 0.508203 | ||||||||
\(616\) | 0.814629 | 0.0328223 | ||||||||
\(617\) | 6.58019 | 0.264909 | 0.132454 | − | 0.991189i | \(-0.457714\pi\) | ||||
0.132454 | + | 0.991189i | \(0.457714\pi\) | |||||||
\(618\) | −16.2541 | −0.653837 | ||||||||
\(619\) | −20.5201 | −0.824771 | −0.412386 | − | 0.911009i | \(-0.635304\pi\) | ||||
−0.412386 | + | 0.911009i | \(0.635304\pi\) | |||||||
\(620\) | −90.1612 | −3.62096 | ||||||||
\(621\) | 7.75524 | 0.311207 | ||||||||
\(622\) | 17.5088 | 0.702040 | ||||||||
\(623\) | 1.25109 | 0.0501238 | ||||||||
\(624\) | 1.21997 | 0.0488380 | ||||||||
\(625\) | −25.5127 | −1.02051 | ||||||||
\(626\) | −58.7289 | −2.34728 | ||||||||
\(627\) | 5.94502 | 0.237421 | ||||||||
\(628\) | −22.8133 | −0.910349 | ||||||||
\(629\) | 8.71769 | 0.347597 | ||||||||
\(630\) | 1.11257 | 0.0443257 | ||||||||
\(631\) | 22.7532 | 0.905792 | 0.452896 | − | 0.891563i | \(-0.350391\pi\) | ||||
0.452896 | + | 0.891563i | \(0.350391\pi\) | |||||||
\(632\) | −6.67546 | −0.265536 | ||||||||
\(633\) | 12.3382 | 0.490401 | ||||||||
\(634\) | −28.1516 | −1.11804 | ||||||||
\(635\) | 29.5534 | 1.17279 | ||||||||
\(636\) | −8.33981 | −0.330695 | ||||||||
\(637\) | −1.07121 | −0.0424430 | ||||||||
\(638\) | −9.19049 | −0.363855 | ||||||||
\(639\) | 7.83419 | 0.309916 | ||||||||
\(640\) | 26.1826 | 1.03496 | ||||||||
\(641\) | 34.8738 | 1.37743 | 0.688715 | − | 0.725032i | \(-0.258175\pi\) | ||||
0.688715 | + | 0.725032i | \(0.258175\pi\) | |||||||
\(642\) | 27.1684 | 1.07225 | ||||||||
\(643\) | 36.3233 | 1.43245 | 0.716225 | − | 0.697870i | \(-0.245868\pi\) | ||||
0.716225 | + | 0.697870i | \(0.245868\pi\) | |||||||
\(644\) | −4.91035 | −0.193495 | ||||||||
\(645\) | 5.85075 | 0.230373 | ||||||||
\(646\) | −17.2301 | −0.677909 | ||||||||
\(647\) | 13.9056 | 0.546687 | 0.273343 | − | 0.961917i | \(-0.411870\pi\) | ||||
0.273343 | + | 0.961917i | \(0.411870\pi\) | |||||||
\(648\) | −6.67546 | −0.262237 | ||||||||
\(649\) | 1.68198 | 0.0660234 | ||||||||
\(650\) | −1.92957 | −0.0756840 | ||||||||
\(651\) | 0.858137 | 0.0336330 | ||||||||
\(652\) | −82.2287 | −3.22032 | ||||||||
\(653\) | −37.4461 | −1.46538 | −0.732690 | − | 0.680562i | \(-0.761736\pi\) | ||||
−0.732690 | + | 0.680562i | \(0.761736\pi\) | |||||||
\(654\) | −11.4836 | −0.449044 | ||||||||
\(655\) | 55.0253 | 2.15002 | ||||||||
\(656\) | 31.8534 | 1.24367 | ||||||||
\(657\) | 0.0892372 | 0.00348148 | ||||||||
\(658\) | −3.12367 | −0.121773 | ||||||||
\(659\) | −28.9304 | −1.12697 | −0.563485 | − | 0.826126i | \(-0.690540\pi\) | ||||
−0.563485 | + | 0.826126i | \(0.690540\pi\) | |||||||
\(660\) | 12.8216 | 0.499080 | ||||||||
\(661\) | 21.5071 | 0.836529 | 0.418264 | − | 0.908325i | \(-0.362639\pi\) | ||||
0.418264 | + | 0.908325i | \(0.362639\pi\) | |||||||
\(662\) | −63.3948 | −2.46391 | ||||||||
\(663\) | 0.153446 | 0.00595935 | ||||||||
\(664\) | −42.0223 | −1.63078 | ||||||||
\(665\) | −2.90507 | −0.112654 | ||||||||
\(666\) | −22.3939 | −0.867746 | ||||||||
\(667\) | 31.3048 | 1.21213 | ||||||||
\(668\) | −1.14392 | −0.0442597 | ||||||||
\(669\) | 2.52511 | 0.0976264 | ||||||||
\(670\) | 98.2403 | 3.79535 | ||||||||
\(671\) | −5.57418 | −0.215189 | ||||||||
\(672\) | 0.973735 | 0.0375626 | ||||||||
\(673\) | −28.6479 | −1.10430 | −0.552148 | − | 0.833746i | \(-0.686192\pi\) | ||||
−0.552148 | + | 0.833746i | \(0.686192\pi\) | |||||||
\(674\) | −46.6465 | −1.79676 | ||||||||
\(675\) | 4.89527 | 0.188419 | ||||||||
\(676\) | −59.6746 | −2.29518 | ||||||||
\(677\) | −5.18671 | −0.199341 | −0.0996707 | − | 0.995020i | \(-0.531779\pi\) | ||||
−0.0996707 | + | 0.995020i | \(0.531779\pi\) | |||||||
\(678\) | −30.1163 | −1.15661 | ||||||||
\(679\) | 2.25720 | 0.0866232 | ||||||||
\(680\) | −20.9988 | −0.805269 | ||||||||
\(681\) | −11.0846 | −0.424763 | ||||||||
\(682\) | 14.1904 | 0.543380 | ||||||||
\(683\) | 3.48378 | 0.133303 | 0.0666516 | − | 0.997776i | \(-0.478768\pi\) | ||||
0.0666516 | + | 0.997776i | \(0.478768\pi\) | |||||||
\(684\) | 30.8455 | 1.17941 | ||||||||
\(685\) | −19.4631 | −0.743647 | ||||||||
\(686\) | −4.94484 | −0.188795 | ||||||||
\(687\) | −9.95351 | −0.379750 | ||||||||
\(688\) | 14.7874 | 0.563765 | ||||||||
\(689\) | −0.278278 | −0.0106016 | ||||||||
\(690\) | −62.6668 | −2.38568 | ||||||||
\(691\) | −13.1216 | −0.499169 | −0.249584 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249584 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(692\) | −94.2102 | −3.58133 | ||||||||
\(693\) | −0.122033 | −0.00463566 | ||||||||
\(694\) | −12.6975 | −0.481989 | ||||||||
\(695\) | −42.3153 | −1.60511 | ||||||||
\(696\) | −26.9462 | −1.02139 | ||||||||
\(697\) | 4.00646 | 0.151756 | ||||||||
\(698\) | 28.1231 | 1.06447 | ||||||||
\(699\) | −19.2676 | −0.728767 | ||||||||
\(700\) | −3.09951 | −0.117151 | ||||||||
\(701\) | −33.0949 | −1.24998 | −0.624988 | − | 0.780634i | \(-0.714896\pi\) | ||||
−0.624988 | + | 0.780634i | \(0.714896\pi\) | |||||||
\(702\) | −0.394171 | −0.0148770 | ||||||||
\(703\) | 58.4736 | 2.20537 | ||||||||
\(704\) | 2.00850 | 0.0756982 | ||||||||
\(705\) | −27.7822 | −1.04634 | ||||||||
\(706\) | 16.4596 | 0.619467 | ||||||||
\(707\) | −1.88131 | −0.0707541 | ||||||||
\(708\) | 8.72687 | 0.327976 | ||||||||
\(709\) | 6.41526 | 0.240930 | 0.120465 | − | 0.992718i | \(-0.461561\pi\) | ||||
0.120465 | + | 0.992718i | \(0.461561\pi\) | |||||||
\(710\) | −63.3047 | −2.37578 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 60.6577 | 2.27324 | ||||||||
\(713\) | −48.3357 | −1.81019 | ||||||||
\(714\) | 0.353681 | 0.0132362 | ||||||||
\(715\) | 0.427823 | 0.0159997 | ||||||||
\(716\) | 93.3657 | 3.48924 | ||||||||
\(717\) | 16.5390 | 0.617662 | ||||||||
\(718\) | 66.8298 | 2.49407 | ||||||||
\(719\) | 13.4629 | 0.502081 | 0.251040 | − | 0.967977i | \(-0.419227\pi\) | ||||
0.251040 | + | 0.967977i | \(0.419227\pi\) | |||||||
\(720\) | 25.0097 | 0.932056 | ||||||||
\(721\) | −0.871202 | −0.0324452 | ||||||||
\(722\) | −66.7633 | −2.48467 | ||||||||
\(723\) | 26.3974 | 0.981730 | ||||||||
\(724\) | 29.4086 | 1.09296 | ||||||||
\(725\) | 19.7602 | 0.733876 | ||||||||
\(726\) | 26.2387 | 0.973810 | ||||||||
\(727\) | −24.5117 | −0.909090 | −0.454545 | − | 0.890724i | \(-0.650198\pi\) | ||||
−0.454545 | + | 0.890724i | \(0.650198\pi\) | |||||||
\(728\) | 0.141033 | 0.00522704 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.721088 | −0.0266887 | ||||||||
\(731\) | 1.85994 | 0.0687922 | ||||||||
\(732\) | −28.9214 | −1.06897 | ||||||||
\(733\) | 46.4494 | 1.71565 | 0.857824 | − | 0.513944i | \(-0.171816\pi\) | ||||
0.857824 | + | 0.513944i | \(0.171816\pi\) | |||||||
\(734\) | −18.0414 | −0.665921 | ||||||||
\(735\) | −21.9601 | −0.810010 | ||||||||
\(736\) | −54.8469 | −2.02168 | ||||||||
\(737\) | −10.7756 | −0.396925 | ||||||||
\(738\) | −10.2918 | −0.378845 | ||||||||
\(739\) | −25.7210 | −0.946163 | −0.473081 | − | 0.881019i | \(-0.656858\pi\) | ||||
−0.473081 | + | 0.881019i | \(0.656858\pi\) | |||||||
\(740\) | 126.110 | 4.63588 | ||||||||
\(741\) | 1.02924 | 0.0378099 | ||||||||
\(742\) | −0.641410 | −0.0235469 | ||||||||
\(743\) | −40.1614 | −1.47338 | −0.736689 | − | 0.676232i | \(-0.763612\pi\) | ||||
−0.736689 | + | 0.676232i | \(0.763612\pi\) | |||||||
\(744\) | 41.6058 | 1.52534 | ||||||||
\(745\) | 25.0929 | 0.919332 | ||||||||
\(746\) | 52.8125 | 1.93360 | ||||||||
\(747\) | 6.29504 | 0.230323 | ||||||||
\(748\) | 4.07594 | 0.149031 | ||||||||
\(749\) | 1.45619 | 0.0532081 | ||||||||
\(750\) | 0.846305 | 0.0309027 | ||||||||
\(751\) | −34.8498 | −1.27169 | −0.635844 | − | 0.771818i | \(-0.719348\pi\) | ||||
−0.635844 | + | 0.771818i | \(0.719348\pi\) | |||||||
\(752\) | −70.2179 | −2.56058 | ||||||||
\(753\) | 1.40438 | 0.0511785 | ||||||||
\(754\) | −1.59111 | −0.0579448 | ||||||||
\(755\) | 19.9516 | 0.726113 | ||||||||
\(756\) | −0.633165 | −0.0230280 | ||||||||
\(757\) | 23.6413 | 0.859259 | 0.429629 | − | 0.903005i | \(-0.358644\pi\) | ||||
0.429629 | + | 0.903005i | \(0.358644\pi\) | |||||||
\(758\) | 72.8611 | 2.64643 | ||||||||
\(759\) | 6.87369 | 0.249499 | ||||||||
\(760\) | −140.849 | −5.10913 | ||||||||
\(761\) | −23.9851 | −0.869458 | −0.434729 | − | 0.900561i | \(-0.643156\pi\) | ||||
−0.434729 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(762\) | −24.1336 | −0.874267 | ||||||||
\(763\) | −0.615507 | −0.0222829 | ||||||||
\(764\) | 31.2168 | 1.12938 | ||||||||
\(765\) | 3.14567 | 0.113732 | ||||||||
\(766\) | 2.25529 | 0.0814870 | ||||||||
\(767\) | 0.291193 | 0.0105144 | ||||||||
\(768\) | −25.9132 | −0.935061 | ||||||||
\(769\) | 5.09074 | 0.183577 | 0.0917884 | − | 0.995779i | \(-0.470742\pi\) | ||||
0.0917884 | + | 0.995779i | \(0.470742\pi\) | |||||||
\(770\) | 0.986100 | 0.0355366 | ||||||||
\(771\) | −11.3803 | −0.409850 | ||||||||
\(772\) | 0.0947639 | 0.00341063 | ||||||||
\(773\) | −39.5891 | −1.42392 | −0.711960 | − | 0.702220i | \(-0.752192\pi\) | ||||
−0.711960 | + | 0.702220i | \(0.752192\pi\) | |||||||
\(774\) | −4.77778 | −0.171734 | ||||||||
\(775\) | −30.5105 | −1.09597 | ||||||||
\(776\) | 109.438 | 3.92858 | ||||||||
\(777\) | −1.20029 | −0.0430600 | ||||||||
\(778\) | −47.5898 | −1.70618 | ||||||||
\(779\) | 26.8732 | 0.962834 | ||||||||
\(780\) | 2.21974 | 0.0794796 | ||||||||
\(781\) | 6.94366 | 0.248464 | ||||||||
\(782\) | −19.9216 | −0.712394 | ||||||||
\(783\) | 4.03660 | 0.144256 | ||||||||
\(784\) | −55.5028 | −1.98224 | ||||||||
\(785\) | −15.6052 | −0.556972 | ||||||||
\(786\) | −44.9342 | −1.60275 | ||||||||
\(787\) | 13.0925 | 0.466697 | 0.233348 | − | 0.972393i | \(-0.425032\pi\) | ||||
0.233348 | + | 0.972393i | \(0.425032\pi\) | |||||||
\(788\) | 24.6461 | 0.877983 | ||||||||
\(789\) | −18.9971 | −0.676313 | ||||||||
\(790\) | −8.08058 | −0.287494 | ||||||||
\(791\) | −1.61420 | −0.0573943 | ||||||||
\(792\) | −5.91665 | −0.210239 | ||||||||
\(793\) | −0.965034 | −0.0342693 | ||||||||
\(794\) | −20.0102 | −0.710134 | ||||||||
\(795\) | −5.70475 | −0.202327 | ||||||||
\(796\) | −85.5543 | −3.03239 | ||||||||
\(797\) | −18.4655 | −0.654082 | −0.327041 | − | 0.945010i | \(-0.606052\pi\) | ||||
−0.327041 | + | 0.945010i | \(0.606052\pi\) | |||||||
\(798\) | 2.37231 | 0.0839788 | ||||||||
\(799\) | −8.83188 | −0.312449 | ||||||||
\(800\) | −34.6205 | −1.22402 | ||||||||
\(801\) | −9.08666 | −0.321061 | ||||||||
\(802\) | −78.4895 | −2.77156 | ||||||||
\(803\) | 0.0790935 | 0.00279115 | ||||||||
\(804\) | −55.9089 | −1.97175 | ||||||||
\(805\) | −3.35887 | −0.118384 | ||||||||
\(806\) | 2.45673 | 0.0865346 | ||||||||
\(807\) | −8.23267 | −0.289804 | ||||||||
\(808\) | −91.2135 | −3.20888 | ||||||||
\(809\) | −49.5903 | −1.74350 | −0.871751 | − | 0.489949i | \(-0.837015\pi\) | ||||
−0.871751 | + | 0.489949i | \(0.837015\pi\) | |||||||
\(810\) | −8.08058 | −0.283922 | ||||||||
\(811\) | 17.5640 | 0.616756 | 0.308378 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308378 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(812\) | −2.55583 | −0.0896921 | ||||||||
\(813\) | −0.135088 | −0.00473775 | ||||||||
\(814\) | −19.8484 | −0.695684 | ||||||||
\(815\) | −56.2476 | −1.97027 | ||||||||
\(816\) | 7.95050 | 0.278323 | ||||||||
\(817\) | 12.4755 | 0.436461 | ||||||||
\(818\) | −101.364 | −3.54410 | ||||||||
\(819\) | −0.0211271 | −0.000738240 0 | ||||||||
\(820\) | 57.9573 | 2.02396 | ||||||||
\(821\) | −37.4516 | −1.30707 | −0.653535 | − | 0.756896i | \(-0.726715\pi\) | ||||
−0.653535 | + | 0.756896i | \(0.726715\pi\) | |||||||
\(822\) | 15.8938 | 0.554359 | ||||||||
\(823\) | −0.551602 | −0.0192276 | −0.00961382 | − | 0.999954i | \(-0.503060\pi\) | ||||
−0.00961382 | + | 0.999954i | \(0.503060\pi\) | |||||||
\(824\) | −42.2393 | −1.47147 | ||||||||
\(825\) | 4.33881 | 0.151058 | ||||||||
\(826\) | 0.671178 | 0.0233533 | ||||||||
\(827\) | −23.1491 | −0.804971 | −0.402486 | − | 0.915426i | \(-0.631854\pi\) | ||||
−0.402486 | + | 0.915426i | \(0.631854\pi\) | |||||||
\(828\) | 35.6639 | 1.23941 | ||||||||
\(829\) | 25.0048 | 0.868454 | 0.434227 | − | 0.900803i | \(-0.357022\pi\) | ||||
0.434227 | + | 0.900803i | \(0.357022\pi\) | |||||||
\(830\) | −50.8675 | −1.76564 | ||||||||
\(831\) | −23.2923 | −0.808001 | ||||||||
\(832\) | 0.347723 | 0.0120551 | ||||||||
\(833\) | −6.98104 | −0.241879 | ||||||||
\(834\) | 34.5551 | 1.19655 | ||||||||
\(835\) | −0.782487 | −0.0270791 | ||||||||
\(836\) | 27.3393 | 0.945548 | ||||||||
\(837\) | −6.23265 | −0.215432 | ||||||||
\(838\) | 7.98232 | 0.275745 | ||||||||
\(839\) | 11.0268 | 0.380687 | 0.190343 | − | 0.981718i | \(-0.439040\pi\) | ||||
0.190343 | + | 0.981718i | \(0.439040\pi\) | |||||||
\(840\) | 2.89121 | 0.0997561 | ||||||||
\(841\) | −12.7059 | −0.438134 | ||||||||
\(842\) | 28.7121 | 0.989484 | ||||||||
\(843\) | 25.7854 | 0.888095 | ||||||||
\(844\) | 56.7396 | 1.95306 | ||||||||
\(845\) | −40.8197 | −1.40424 | ||||||||
\(846\) | 22.6872 | 0.780003 | ||||||||
\(847\) | 1.40636 | 0.0483232 | ||||||||
\(848\) | −14.4184 | −0.495131 | ||||||||
\(849\) | 18.9333 | 0.649790 | ||||||||
\(850\) | −12.5749 | −0.431316 | ||||||||
\(851\) | 67.6077 | 2.31756 | ||||||||
\(852\) | 36.0269 | 1.23426 | ||||||||
\(853\) | 39.0814 | 1.33812 | 0.669061 | − | 0.743207i | \(-0.266696\pi\) | ||||
0.669061 | + | 0.743207i | \(0.266696\pi\) | |||||||
\(854\) | −2.22433 | −0.0761149 | ||||||||
\(855\) | 21.0995 | 0.721588 | ||||||||
\(856\) | 70.6019 | 2.41312 | ||||||||
\(857\) | −42.7467 | −1.46020 | −0.730099 | − | 0.683341i | \(-0.760526\pi\) | ||||
−0.730099 | + | 0.683341i | \(0.760526\pi\) | |||||||
\(858\) | −0.349365 | −0.0119271 | ||||||||
\(859\) | 42.2640 | 1.44203 | 0.721014 | − | 0.692920i | \(-0.243676\pi\) | ||||
0.721014 | + | 0.692920i | \(0.243676\pi\) | |||||||
\(860\) | 26.9057 | 0.917478 | ||||||||
\(861\) | −0.551626 | −0.0187994 | ||||||||
\(862\) | −19.9038 | −0.677925 | ||||||||
\(863\) | −10.1925 | −0.346958 | −0.173479 | − | 0.984838i | \(-0.555501\pi\) | ||||
−0.173479 | + | 0.984838i | \(0.555501\pi\) | |||||||
\(864\) | −7.07224 | −0.240602 | ||||||||
\(865\) | −64.4434 | −2.19114 | ||||||||
\(866\) | 32.4772 | 1.10362 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 3.94630 | 0.133946 | ||||||||
\(869\) | 0.886329 | 0.0300666 | ||||||||
\(870\) | −32.6180 | −1.10585 | ||||||||
\(871\) | −1.86553 | −0.0632112 | ||||||||
\(872\) | −29.8422 | −1.01058 | ||||||||
\(873\) | −16.3940 | −0.554854 | ||||||||
\(874\) | −133.623 | −4.51988 | ||||||||
\(875\) | 0.0453610 | 0.00153348 | ||||||||
\(876\) | 0.410374 | 0.0138652 | ||||||||
\(877\) | −29.6015 | −0.999571 | −0.499786 | − | 0.866149i | \(-0.666588\pi\) | ||||
−0.499786 | + | 0.866149i | \(0.666588\pi\) | |||||||
\(878\) | −61.7515 | −2.08401 | ||||||||
\(879\) | 7.36864 | 0.248538 | ||||||||
\(880\) | 22.1668 | 0.747243 | ||||||||
\(881\) | 18.6139 | 0.627117 | 0.313559 | − | 0.949569i | \(-0.398479\pi\) | ||||
0.313559 | + | 0.949569i | \(0.398479\pi\) | |||||||
\(882\) | 17.9328 | 0.603830 | ||||||||
\(883\) | −20.1737 | −0.678899 | −0.339449 | − | 0.940624i | \(-0.610241\pi\) | ||||
−0.339449 | + | 0.940624i | \(0.610241\pi\) | |||||||
\(884\) | 0.705650 | 0.0237336 | ||||||||
\(885\) | 5.96952 | 0.200663 | ||||||||
\(886\) | 22.1260 | 0.743337 | ||||||||
\(887\) | 32.5535 | 1.09304 | 0.546521 | − | 0.837446i | \(-0.315952\pi\) | ||||
0.546521 | + | 0.837446i | \(0.315952\pi\) | |||||||
\(888\) | −58.1946 | −1.95288 | ||||||||
\(889\) | −1.29353 | −0.0433837 | ||||||||
\(890\) | 73.4254 | 2.46123 | ||||||||
\(891\) | 0.886329 | 0.0296931 | ||||||||
\(892\) | 11.6122 | 0.388804 | ||||||||
\(893\) | −59.2396 | −1.98238 | ||||||||
\(894\) | −20.4911 | −0.685325 | ||||||||
\(895\) | 63.8657 | 2.13480 | ||||||||
\(896\) | −1.14600 | −0.0382850 | ||||||||
\(897\) | 1.19001 | 0.0397333 | ||||||||
\(898\) | 105.746 | 3.52879 | ||||||||
\(899\) | −25.1587 | −0.839090 | ||||||||
\(900\) | 22.5118 | 0.750392 | ||||||||
\(901\) | −1.81352 | −0.0604172 | ||||||||
\(902\) | −9.12188 | −0.303725 | ||||||||
\(903\) | −0.256084 | −0.00852193 | ||||||||
\(904\) | −78.2626 | −2.60298 | ||||||||
\(905\) | 20.1166 | 0.668699 | ||||||||
\(906\) | −16.2927 | −0.541288 | ||||||||
\(907\) | −48.4169 | −1.60766 | −0.803829 | − | 0.594860i | \(-0.797207\pi\) | ||||
−0.803829 | + | 0.594860i | \(0.797207\pi\) | |||||||
\(908\) | −50.9745 | −1.69165 | ||||||||
\(909\) | 13.6640 | 0.453206 | ||||||||
\(910\) | 0.170719 | 0.00565928 | ||||||||
\(911\) | 25.5200 | 0.845517 | 0.422758 | − | 0.906242i | \(-0.361062\pi\) | ||||
0.422758 | + | 0.906242i | \(0.361062\pi\) | |||||||
\(912\) | 53.3278 | 1.76586 | ||||||||
\(913\) | 5.57947 | 0.184654 | ||||||||
\(914\) | 101.491 | 3.35703 | ||||||||
\(915\) | −19.7834 | −0.654018 | ||||||||
\(916\) | −45.7730 | −1.51238 | ||||||||
\(917\) | −2.40842 | −0.0795331 | ||||||||
\(918\) | −2.56879 | −0.0847827 | ||||||||
\(919\) | 45.6377 | 1.50545 | 0.752724 | − | 0.658337i | \(-0.228740\pi\) | ||||
0.752724 | + | 0.658337i | \(0.228740\pi\) | |||||||
\(920\) | −162.851 | −5.36904 | ||||||||
\(921\) | −24.2984 | −0.800659 | ||||||||
\(922\) | −74.0332 | −2.43815 | ||||||||
\(923\) | 1.20213 | 0.0395684 | ||||||||
\(924\) | −0.561192 | −0.0184619 | ||||||||
\(925\) | 42.6754 | 1.40316 | ||||||||
\(926\) | −55.6880 | −1.83002 | ||||||||
\(927\) | 6.32754 | 0.207824 | ||||||||
\(928\) | −28.5478 | −0.937127 | ||||||||
\(929\) | 28.5673 | 0.937262 | 0.468631 | − | 0.883394i | \(-0.344747\pi\) | ||||
0.468631 | + | 0.883394i | \(0.344747\pi\) | |||||||
\(930\) | 50.3634 | 1.65148 | ||||||||
\(931\) | −46.8252 | −1.53463 | ||||||||
\(932\) | −88.6055 | −2.90237 | ||||||||
\(933\) | −6.81598 | −0.223145 | ||||||||
\(934\) | 18.6075 | 0.608857 | ||||||||
\(935\) | 2.78810 | 0.0911806 | ||||||||
\(936\) | −1.02432 | −0.0334811 | ||||||||
\(937\) | −28.4968 | −0.930951 | −0.465476 | − | 0.885061i | \(-0.654117\pi\) | ||||
−0.465476 | + | 0.885061i | \(0.654117\pi\) | |||||||
\(938\) | −4.29991 | −0.140397 | ||||||||
\(939\) | 22.8625 | 0.746088 | ||||||||
\(940\) | −127.762 | −4.16712 | ||||||||
\(941\) | −17.4581 | −0.569119 | −0.284559 | − | 0.958658i | \(-0.591847\pi\) | ||||
−0.284559 | + | 0.958658i | \(0.591847\pi\) | |||||||
\(942\) | 12.7433 | 0.415200 | ||||||||
\(943\) | 31.0711 | 1.01181 | ||||||||
\(944\) | 15.0876 | 0.491059 | ||||||||
\(945\) | −0.433109 | −0.0140890 | ||||||||
\(946\) | −4.23469 | −0.137682 | ||||||||
\(947\) | −45.4816 | −1.47795 | −0.738976 | − | 0.673731i | \(-0.764690\pi\) | ||||
−0.738976 | + | 0.673731i | \(0.764690\pi\) | |||||||
\(948\) | 4.59868 | 0.149358 | ||||||||
\(949\) | 0.0136931 | 0.000444497 0 | ||||||||
\(950\) | −84.3459 | −2.73654 | ||||||||
\(951\) | 10.9591 | 0.355373 | ||||||||
\(952\) | 0.919105 | 0.0297884 | ||||||||
\(953\) | 40.1735 | 1.30135 | 0.650674 | − | 0.759357i | \(-0.274486\pi\) | ||||
0.650674 | + | 0.759357i | \(0.274486\pi\) | |||||||
\(954\) | 4.65856 | 0.150826 | ||||||||
\(955\) | 21.3535 | 0.690982 | ||||||||
\(956\) | 76.0577 | 2.45988 | ||||||||
\(957\) | 3.57775 | 0.115652 | ||||||||
\(958\) | 34.3923 | 1.11116 | ||||||||
\(959\) | 0.851888 | 0.0275089 | ||||||||
\(960\) | 7.12838 | 0.230067 | ||||||||
\(961\) | 7.84593 | 0.253094 | ||||||||
\(962\) | −3.43626 | −0.110789 | ||||||||
\(963\) | −10.5763 | −0.340817 | ||||||||
\(964\) | 121.393 | 3.90981 | ||||||||
\(965\) | 0.0648221 | 0.00208670 | ||||||||
\(966\) | 2.74288 | 0.0882509 | ||||||||
\(967\) | 31.9226 | 1.02656 | 0.513281 | − | 0.858221i | \(-0.328430\pi\) | ||||
0.513281 | + | 0.858221i | \(0.328430\pi\) | |||||||
\(968\) | 68.1860 | 2.19158 | ||||||||
\(969\) | 6.70747 | 0.215475 | ||||||||
\(970\) | 132.473 | 4.25346 | ||||||||
\(971\) | −14.9843 | −0.480869 | −0.240434 | − | 0.970665i | \(-0.577290\pi\) | ||||
−0.240434 | + | 0.970665i | \(0.577290\pi\) | |||||||
\(972\) | 4.59868 | 0.147503 | ||||||||
\(973\) | 1.85211 | 0.0593760 | ||||||||
\(974\) | −22.1232 | −0.708874 | ||||||||
\(975\) | 0.751160 | 0.0240564 | ||||||||
\(976\) | −50.0013 | −1.60050 | ||||||||
\(977\) | −8.88467 | −0.284246 | −0.142123 | − | 0.989849i | \(-0.545393\pi\) | ||||
−0.142123 | + | 0.989849i | \(0.545393\pi\) | |||||||
\(978\) | 45.9324 | 1.46876 | ||||||||
\(979\) | −8.05377 | −0.257399 | ||||||||
\(980\) | −100.987 | −3.22592 | ||||||||
\(981\) | 4.47043 | 0.142730 | ||||||||
\(982\) | −68.4803 | −2.18529 | ||||||||
\(983\) | 33.4795 | 1.06783 | 0.533915 | − | 0.845538i | \(-0.320720\pi\) | ||||
0.533915 | + | 0.845538i | \(0.320720\pi\) | |||||||
\(984\) | −26.7450 | −0.852600 | ||||||||
\(985\) | 16.8589 | 0.537170 | ||||||||
\(986\) | −10.3692 | −0.330222 | ||||||||
\(987\) | 1.21601 | 0.0387060 | ||||||||
\(988\) | 4.73313 | 0.150581 | ||||||||
\(989\) | 14.4242 | 0.458664 | ||||||||
\(990\) | −7.16204 | −0.227625 | ||||||||
\(991\) | −52.5256 | −1.66853 | −0.834265 | − | 0.551364i | \(-0.814108\pi\) | ||||
−0.834265 | + | 0.551364i | \(0.814108\pi\) | |||||||
\(992\) | 44.0788 | 1.39950 | ||||||||
\(993\) | 24.6789 | 0.783160 | ||||||||
\(994\) | 2.77081 | 0.0878847 | ||||||||
\(995\) | −58.5224 | −1.85529 | ||||||||
\(996\) | 28.9489 | 0.917280 | ||||||||
\(997\) | 10.5707 | 0.334776 | 0.167388 | − | 0.985891i | \(-0.446467\pi\) | ||||
0.167388 | + | 0.985891i | \(0.446467\pi\) | |||||||
\(998\) | 16.1776 | 0.512094 | ||||||||
\(999\) | 8.71769 | 0.275815 |
(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 | 4029.2.a.k.1.2 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.2 | ✓ | 31 | 1.1 | even | 1 | trivial |