Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05077 | −0.743009 | −0.371504 | − | 0.928431i | \(-0.621158\pi\) | ||||
−0.371504 | + | 0.928431i | \(0.621158\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.895876 | −0.447938 | ||||||||
\(5\) | −3.10634 | −1.38920 | −0.694599 | − | 0.719398i | \(-0.744418\pi\) | ||||
−0.694599 | + | 0.719398i | \(0.744418\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.07400 | 1.16186 | 0.580932 | − | 0.813952i | \(-0.302688\pi\) | ||||
0.580932 | + | 0.813952i | \(0.302688\pi\) | |||||||
\(8\) | 3.04291 | 1.07583 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.26406 | 1.03219 | ||||||||
\(11\) | 3.20654 | 0.966809 | 0.483404 | − | 0.875397i | \(-0.339400\pi\) | ||||
0.483404 | + | 0.875397i | \(0.339400\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0429964 | −0.0119251 | −0.00596253 | − | 0.999982i | \(-0.501898\pi\) | ||||
−0.00596253 | + | 0.999982i | \(0.501898\pi\) | |||||||
\(14\) | −3.23008 | −0.863276 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.40566 | −0.351414 | ||||||||
\(17\) | 4.01221 | 0.973104 | 0.486552 | − | 0.873652i | \(-0.338254\pi\) | ||||
0.486552 | + | 0.873652i | \(0.338254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.31997 | −1.67932 | −0.839658 | − | 0.543116i | \(-0.817244\pi\) | ||||
−0.839658 | + | 0.543116i | \(0.817244\pi\) | |||||||
\(20\) | 2.78289 | 0.622274 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.36935 | −0.718347 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.64934 | 0.929869 | ||||||||
\(26\) | 0.0451795 | 0.00886042 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.75393 | −0.520443 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.714345 | 0.128300 | 0.0641501 | − | 0.997940i | \(-0.479566\pi\) | ||||
0.0641501 | + | 0.997940i | \(0.479566\pi\) | |||||||
\(32\) | −4.60879 | −0.814727 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.21592 | −0.723025 | ||||||||
\(35\) | −9.54890 | −1.61406 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.91091 | −1.13615 | −0.568074 | − | 0.822978i | \(-0.692311\pi\) | ||||
−0.568074 | + | 0.822978i | \(0.692311\pi\) | |||||||
\(38\) | 7.69163 | 1.24775 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.45231 | −1.49454 | ||||||||
\(41\) | 5.11513 | 0.798848 | 0.399424 | − | 0.916766i | \(-0.369210\pi\) | ||||
0.399424 | + | 0.916766i | \(0.369210\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.9603 | −1.82393 | −0.911967 | − | 0.410263i | \(-0.865437\pi\) | ||||
−0.911967 | + | 0.410263i | \(0.865437\pi\) | |||||||
\(44\) | −2.87266 | −0.433070 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05077 | 0.154928 | ||||||||
\(47\) | 5.42059 | 0.790675 | 0.395337 | − | 0.918536i | \(-0.370628\pi\) | ||||
0.395337 | + | 0.918536i | \(0.370628\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.44951 | 0.349929 | ||||||||
\(50\) | −4.88541 | −0.690901 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0385194 | 0.00534168 | ||||||||
\(53\) | −2.84097 | −0.390237 | −0.195119 | − | 0.980780i | \(-0.562509\pi\) | ||||
−0.195119 | + | 0.980780i | \(0.562509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.96061 | −1.34309 | ||||||||
\(56\) | 9.35392 | 1.24997 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.05077 | 0.137973 | ||||||||
\(59\) | 10.8989 | 1.41892 | 0.709458 | − | 0.704748i | \(-0.248940\pi\) | ||||
0.709458 | + | 0.704748i | \(0.248940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.48818 | −1.08680 | −0.543400 | − | 0.839474i | \(-0.682863\pi\) | ||||
−0.543400 | + | 0.839474i | \(0.682863\pi\) | |||||||
\(62\) | −0.750615 | −0.0953281 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.65411 | 0.956763 | ||||||||
\(65\) | 0.133561 | 0.0165662 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.06291 | 0.374194 | 0.187097 | − | 0.982341i | \(-0.440092\pi\) | ||||
0.187097 | + | 0.982341i | \(0.440092\pi\) | |||||||
\(68\) | −3.59444 | −0.435890 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.0337 | 1.19926 | ||||||||
\(71\) | 3.65634 | 0.433927 | 0.216964 | − | 0.976180i | \(-0.430385\pi\) | ||||
0.216964 | + | 0.976180i | \(0.430385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.89771 | 1.15844 | 0.579220 | − | 0.815172i | \(-0.303357\pi\) | ||||
0.579220 | + | 0.815172i | \(0.303357\pi\) | |||||||
\(74\) | 7.26180 | 0.844168 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.55778 | 0.752229 | ||||||||
\(77\) | 9.85692 | 1.12330 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.31014 | 0.372419 | 0.186210 | − | 0.982510i | \(-0.440380\pi\) | ||||
0.186210 | + | 0.982510i | \(0.440380\pi\) | |||||||
\(80\) | 4.36644 | 0.488183 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.37484 | −0.593551 | ||||||||
\(83\) | −12.8843 | −1.41423 | −0.707115 | − | 0.707098i | \(-0.750004\pi\) | ||||
−0.707115 | + | 0.707098i | \(0.750004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4633 | −1.35183 | ||||||||
\(86\) | 12.5676 | 1.35520 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.75721 | 1.04012 | ||||||||
\(89\) | −6.29940 | −0.667735 | −0.333867 | − | 0.942620i | \(-0.608354\pi\) | ||||
−0.333867 | + | 0.942620i | \(0.608354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.132171 | −0.0138553 | ||||||||
\(92\) | 0.895876 | 0.0934015 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.69581 | −0.587478 | ||||||||
\(95\) | 22.7383 | 2.33290 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.736499 | −0.0747801 | −0.0373901 | − | 0.999301i | \(-0.511904\pi\) | ||||
−0.0373901 | + | 0.999301i | \(0.511904\pi\) | |||||||
\(98\) | −2.57387 | −0.260001 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.16523 | −0.416523 | ||||||||
\(101\) | 7.08667 | 0.705150 | 0.352575 | − | 0.935784i | \(-0.385306\pi\) | ||||
0.352575 | + | 0.935784i | \(0.385306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0369 | 0.988963 | 0.494481 | − | 0.869188i | \(-0.335358\pi\) | ||||
0.494481 | + | 0.869188i | \(0.335358\pi\) | |||||||
\(104\) | −0.130834 | −0.0128293 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.98522 | 0.289950 | ||||||||
\(107\) | −19.2040 | −1.85652 | −0.928261 | − | 0.371929i | \(-0.878696\pi\) | ||||
−0.928261 | + | 0.371929i | \(0.878696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5333 | −1.29625 | −0.648127 | − | 0.761533i | \(-0.724447\pi\) | ||||
−0.648127 | + | 0.761533i | \(0.724447\pi\) | |||||||
\(110\) | 10.4663 | 0.997926 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.32099 | −0.408295 | ||||||||
\(113\) | 15.6808 | 1.47512 | 0.737562 | − | 0.675280i | \(-0.235977\pi\) | ||||
0.737562 | + | 0.675280i | \(0.235977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.10634 | 0.289668 | ||||||||
\(116\) | 0.895876 | 0.0831800 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.4523 | −1.05427 | ||||||||
\(119\) | 12.3336 | 1.13062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.718091 | −0.0652810 | ||||||||
\(122\) | 8.91915 | 0.807502 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.639964 | −0.0574705 | ||||||||
\(125\) | 1.08926 | 0.0974263 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.23438 | 0.553212 | 0.276606 | − | 0.960983i | \(-0.410790\pi\) | ||||
0.276606 | + | 0.960983i | \(0.410790\pi\) | |||||||
\(128\) | 1.17486 | 0.103843 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.140343 | −0.0123089 | ||||||||
\(131\) | 14.7195 | 1.28605 | 0.643025 | − | 0.765845i | \(-0.277679\pi\) | ||||
0.643025 | + | 0.765845i | \(0.277679\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.5016 | −1.95114 | ||||||||
\(134\) | −3.21842 | −0.278029 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.2088 | 1.04690 | ||||||||
\(137\) | −14.3504 | −1.22604 | −0.613021 | − | 0.790067i | \(-0.710046\pi\) | ||||
−0.613021 | + | 0.790067i | \(0.710046\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.86612 | −0.582377 | −0.291188 | − | 0.956666i | \(-0.594051\pi\) | ||||
−0.291188 | + | 0.956666i | \(0.594051\pi\) | |||||||
\(140\) | 8.55463 | 0.722998 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.84198 | −0.322412 | ||||||||
\(143\) | −0.137870 | −0.0115292 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.10634 | 0.257967 | ||||||||
\(146\) | −10.4002 | −0.860731 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.19132 | 0.508923 | ||||||||
\(149\) | −2.26630 | −0.185662 | −0.0928312 | − | 0.995682i | \(-0.529592\pi\) | ||||
−0.0928312 | + | 0.995682i | \(0.529592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.1474 | 1.39543 | 0.697716 | − | 0.716375i | \(-0.254200\pi\) | ||||
0.697716 | + | 0.716375i | \(0.254200\pi\) | |||||||
\(152\) | −22.2740 | −1.80666 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.3574 | −0.834622 | ||||||||
\(155\) | −2.21900 | −0.178234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.3834 | −1.46715 | −0.733576 | − | 0.679608i | \(-0.762150\pi\) | ||||
−0.733576 | + | 0.679608i | \(0.762150\pi\) | |||||||
\(158\) | −3.47820 | −0.276711 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.3165 | 1.13182 | ||||||||
\(161\) | −3.07400 | −0.242266 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5756 | 0.984995 | 0.492497 | − | 0.870314i | \(-0.336084\pi\) | ||||
0.492497 | + | 0.870314i | \(0.336084\pi\) | |||||||
\(164\) | −4.58252 | −0.357834 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.5384 | 1.05079 | ||||||||
\(167\) | −5.05267 | −0.390988 | −0.195494 | − | 0.980705i | \(-0.562631\pi\) | ||||
−0.195494 | + | 0.980705i | \(0.562631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9982 | −0.999858 | ||||||||
\(170\) | 13.0961 | 1.00442 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.7150 | 0.817009 | ||||||||
\(173\) | 9.98395 | 0.759066 | 0.379533 | − | 0.925178i | \(-0.376085\pi\) | ||||
0.379533 | + | 0.925178i | \(0.376085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.2921 | 1.08038 | ||||||||
\(176\) | −4.50729 | −0.339750 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.61924 | 0.496133 | ||||||||
\(179\) | −7.70479 | −0.575883 | −0.287942 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287942 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2801 | −1.13576 | −0.567881 | − | 0.823111i | \(-0.692236\pi\) | ||||
−0.567881 | + | 0.823111i | \(0.692236\pi\) | |||||||
\(182\) | 0.138882 | 0.0102946 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.04291 | −0.224326 | ||||||||
\(185\) | 21.4676 | 1.57833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.8653 | 0.940806 | ||||||||
\(188\) | −4.85618 | −0.354173 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.8928 | −1.73337 | ||||||||
\(191\) | −8.19768 | −0.593163 | −0.296582 | − | 0.955007i | \(-0.595847\pi\) | ||||
−0.296582 | + | 0.955007i | \(0.595847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6875 | 1.05723 | 0.528615 | − | 0.848862i | \(-0.322712\pi\) | ||||
0.528615 | + | 0.848862i | \(0.322712\pi\) | |||||||
\(194\) | 0.773893 | 0.0555623 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.19445 | −0.156747 | ||||||||
\(197\) | 6.90137 | 0.491702 | 0.245851 | − | 0.969308i | \(-0.420933\pi\) | ||||
0.245851 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1987 | 1.00652 | 0.503259 | − | 0.864136i | \(-0.332134\pi\) | ||||
0.503259 | + | 0.864136i | \(0.332134\pi\) | |||||||
\(200\) | 14.1475 | 1.00038 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.44648 | −0.523932 | ||||||||
\(203\) | −3.07400 | −0.215753 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.8893 | −1.10976 | ||||||||
\(206\) | −10.5465 | −0.734808 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0604381 | 0.00419063 | ||||||||
\(209\) | −23.4718 | −1.62358 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9150 | 0.889102 | 0.444551 | − | 0.895754i | \(-0.353363\pi\) | ||||
0.444551 | + | 0.895754i | \(0.353363\pi\) | |||||||
\(212\) | 2.54516 | 0.174802 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.1791 | 1.37941 | ||||||||
\(215\) | 37.1529 | 2.53380 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.19590 | 0.149067 | ||||||||
\(218\) | 14.2204 | 0.963128 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.92346 | 0.601620 | ||||||||
\(221\) | −0.172511 | −0.0116043 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.99684 | −0.468543 | −0.234271 | − | 0.972171i | \(-0.575270\pi\) | ||||
−0.234271 | + | 0.972171i | \(0.575270\pi\) | |||||||
\(224\) | −14.1674 | −0.946603 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.4769 | −1.09603 | ||||||||
\(227\) | −20.8089 | −1.38114 | −0.690569 | − | 0.723267i | \(-0.742640\pi\) | ||||
−0.690569 | + | 0.723267i | \(0.742640\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.58224 | 0.567131 | 0.283565 | − | 0.958953i | \(-0.408483\pi\) | ||||
0.283565 | + | 0.958953i | \(0.408483\pi\) | |||||||
\(230\) | −3.26406 | −0.215226 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.04291 | −0.199777 | ||||||||
\(233\) | −20.1645 | −1.32102 | −0.660511 | − | 0.750817i | \(-0.729660\pi\) | ||||
−0.660511 | + | 0.750817i | \(0.729660\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.8382 | −1.09840 | ||||||||
\(236\) | −9.76406 | −0.635586 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.9598 | −0.840057 | ||||||||
\(239\) | −19.3093 | −1.24901 | −0.624507 | − | 0.781019i | \(-0.714700\pi\) | ||||
−0.624507 | + | 0.781019i | \(0.714700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.32842 | −0.278818 | −0.139409 | − | 0.990235i | \(-0.544520\pi\) | ||||
−0.139409 | + | 0.990235i | \(0.544520\pi\) | |||||||
\(242\) | 0.754551 | 0.0485044 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.60435 | 0.486819 | ||||||||
\(245\) | −7.60900 | −0.486121 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.314732 | 0.0200259 | ||||||||
\(248\) | 2.17369 | 0.138029 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.14456 | −0.0723886 | ||||||||
\(251\) | −7.41999 | −0.468345 | −0.234173 | − | 0.972195i | \(-0.575238\pi\) | ||||
−0.234173 | + | 0.972195i | \(0.575238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.20654 | −0.201594 | ||||||||
\(254\) | −6.55092 | −0.411041 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.5427 | −1.03392 | ||||||||
\(257\) | 24.9240 | 1.55472 | 0.777359 | − | 0.629057i | \(-0.216559\pi\) | ||||
0.777359 | + | 0.629057i | \(0.216559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.2442 | −1.32005 | ||||||||
\(260\) | −0.119654 | −0.00742065 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.4669 | −0.955547 | ||||||||
\(263\) | 8.09672 | 0.499265 | 0.249633 | − | 0.968341i | \(-0.419690\pi\) | ||||
0.249633 | + | 0.968341i | \(0.419690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.82502 | 0.542117 | ||||||||
\(266\) | 23.6441 | 1.44971 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.74398 | −0.167615 | ||||||||
\(269\) | −10.3743 | −0.632533 | −0.316267 | − | 0.948670i | \(-0.602429\pi\) | ||||
−0.316267 | + | 0.948670i | \(0.602429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.9369 | −1.94003 | −0.970014 | − | 0.243050i | \(-0.921852\pi\) | ||||
−0.970014 | + | 0.243050i | \(0.921852\pi\) | |||||||
\(272\) | −5.63979 | −0.341962 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.0791 | 0.910960 | ||||||||
\(275\) | 14.9083 | 0.899005 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8274 | 1.61190 | 0.805951 | − | 0.591982i | \(-0.201655\pi\) | ||||
0.805951 | + | 0.591982i | \(0.201655\pi\) | |||||||
\(278\) | 7.21473 | 0.432711 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −29.0564 | −1.73645 | ||||||||
\(281\) | 1.09966 | 0.0656000 | 0.0328000 | − | 0.999462i | \(-0.489558\pi\) | ||||
0.0328000 | + | 0.999462i | \(0.489558\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.7079 | −0.993182 | −0.496591 | − | 0.867985i | \(-0.665415\pi\) | ||||
−0.496591 | + | 0.867985i | \(0.665415\pi\) | |||||||
\(284\) | −3.27562 | −0.194372 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.144870 | 0.00856633 | ||||||||
\(287\) | 15.7239 | 0.928154 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.902157 | −0.0530681 | ||||||||
\(290\) | −3.26406 | −0.191672 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.86712 | −0.518909 | ||||||||
\(293\) | −2.31072 | −0.134994 | −0.0674970 | − | 0.997719i | \(-0.521501\pi\) | ||||
−0.0674970 | + | 0.997719i | \(0.521501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.8557 | −1.97115 | ||||||||
\(296\) | −21.0293 | −1.22230 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.38137 | 0.137949 | ||||||||
\(299\) | 0.0429964 | 0.00248655 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.7661 | −2.11916 | ||||||||
\(302\) | −18.0180 | −1.03682 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.2894 | 0.590135 | ||||||||
\(305\) | 26.3672 | 1.50978 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.2607 | −1.27049 | −0.635243 | − | 0.772312i | \(-0.719100\pi\) | ||||
−0.635243 | + | 0.772312i | \(0.719100\pi\) | |||||||
\(308\) | −8.83058 | −0.503169 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.33166 | 0.132430 | ||||||||
\(311\) | −16.0897 | −0.912361 | −0.456181 | − | 0.889887i | \(-0.650783\pi\) | ||||
−0.456181 | + | 0.889887i | \(0.650783\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.19668 | 0.519827 | 0.259914 | − | 0.965632i | \(-0.416306\pi\) | ||||
0.259914 | + | 0.965632i | \(0.416306\pi\) | |||||||
\(314\) | 19.3167 | 1.09011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.96547 | −0.166821 | ||||||||
\(317\) | −2.73116 | −0.153397 | −0.0766986 | − | 0.997054i | \(-0.524438\pi\) | ||||
−0.0766986 | + | 0.997054i | \(0.524438\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.20654 | −0.179532 | ||||||||
\(320\) | −23.7762 | −1.32913 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.23008 | 0.180005 | ||||||||
\(323\) | −29.3693 | −1.63415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.199905 | −0.0110887 | ||||||||
\(326\) | −13.2141 | −0.731860 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.5649 | 0.859426 | ||||||||
\(329\) | 16.6629 | 0.918657 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6627 | −1.35559 | −0.677794 | − | 0.735252i | \(-0.737064\pi\) | ||||
−0.677794 | + | 0.735252i | \(0.737064\pi\) | |||||||
\(332\) | 11.5427 | 0.633487 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.30921 | 0.290507 | ||||||||
\(335\) | −9.51443 | −0.519829 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.08897 | −0.277214 | −0.138607 | − | 0.990347i | \(-0.544262\pi\) | ||||
−0.138607 | + | 0.990347i | \(0.544262\pi\) | |||||||
\(338\) | 13.6581 | 0.742903 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.1656 | 0.605537 | ||||||||
\(341\) | 2.29058 | 0.124042 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.9882 | −0.755294 | ||||||||
\(344\) | −36.3942 | −1.96224 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.4909 | −0.563992 | ||||||||
\(347\) | 26.6514 | 1.43072 | 0.715360 | − | 0.698756i | \(-0.246263\pi\) | ||||
0.715360 | + | 0.698756i | \(0.246263\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.2848 | −1.78170 | −0.890848 | − | 0.454301i | \(-0.849889\pi\) | ||||
−0.890848 | + | 0.454301i | \(0.849889\pi\) | |||||||
\(350\) | −15.0178 | −0.802733 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.7783 | −0.787685 | ||||||||
\(353\) | 28.5065 | 1.51725 | 0.758623 | − | 0.651530i | \(-0.225873\pi\) | ||||
0.758623 | + | 0.651530i | \(0.225873\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.3578 | −0.602811 | ||||||||
\(356\) | 5.64348 | 0.299104 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.09599 | 0.427886 | ||||||||
\(359\) | −12.3505 | −0.651832 | −0.325916 | − | 0.945399i | \(-0.605673\pi\) | ||||
−0.325916 | + | 0.945399i | \(0.605673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.5819 | 1.82010 | ||||||||
\(362\) | 16.0559 | 0.843881 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.118409 | 0.00620631 | ||||||||
\(365\) | −30.7456 | −1.60930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7884 | −1.03294 | −0.516472 | − | 0.856304i | \(-0.672755\pi\) | ||||
−0.516472 | + | 0.856304i | \(0.672755\pi\) | |||||||
\(368\) | 1.40566 | 0.0732748 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22.5576 | −1.17272 | ||||||||
\(371\) | −8.73316 | −0.453403 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.00491154 | 0.000254310 0 | 0.000127155 | − | 1.00000i | \(-0.499960\pi\) | ||||
0.000127155 | 1.00000i | \(0.499960\pi\) | ||||||||
\(374\) | −13.5185 | −0.699027 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.4944 | 0.850632 | ||||||||
\(377\) | 0.0429964 | 0.00221443 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3054 | −1.50532 | −0.752658 | − | 0.658411i | \(-0.771229\pi\) | ||||
−0.752658 | + | 0.658411i | \(0.771229\pi\) | |||||||
\(380\) | −20.3707 | −1.04499 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.61390 | 0.440726 | ||||||||
\(383\) | −2.27253 | −0.116121 | −0.0580604 | − | 0.998313i | \(-0.518492\pi\) | ||||
−0.0580604 | + | 0.998313i | \(0.518492\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.6189 | −1.56049 | ||||||||
\(386\) | −15.4332 | −0.785531 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.659811 | 0.0334968 | ||||||||
\(389\) | −29.8019 | −1.51101 | −0.755507 | − | 0.655140i | \(-0.772609\pi\) | ||||
−0.755507 | + | 0.655140i | \(0.772609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.01221 | −0.202906 | ||||||||
\(392\) | 7.45362 | 0.376465 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.25178 | −0.365339 | ||||||||
\(395\) | −10.2824 | −0.517364 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.7498 | −0.690081 | −0.345040 | − | 0.938588i | \(-0.612135\pi\) | ||||
−0.345040 | + | 0.938588i | \(0.612135\pi\) | |||||||
\(398\) | −14.9196 | −0.747852 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.53537 | −0.326769 | ||||||||
\(401\) | −11.4510 | −0.571836 | −0.285918 | − | 0.958254i | \(-0.592299\pi\) | ||||
−0.285918 | + | 0.958254i | \(0.592299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0307143 | −0.00152999 | ||||||||
\(404\) | −6.34877 | −0.315863 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.23008 | 0.160306 | ||||||||
\(407\) | −22.1601 | −1.09844 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.99053 | −0.345660 | −0.172830 | − | 0.984952i | \(-0.555291\pi\) | ||||
−0.172830 | + | 0.984952i | \(0.555291\pi\) | |||||||
\(410\) | 16.6961 | 0.824560 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.99179 | −0.442994 | ||||||||
\(413\) | 33.5033 | 1.64859 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.0229 | 1.96464 | ||||||||
\(416\) | 0.198161 | 0.00971566 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24.6635 | 1.20633 | ||||||||
\(419\) | 18.8803 | 0.922364 | 0.461182 | − | 0.887305i | \(-0.347425\pi\) | ||||
0.461182 | + | 0.887305i | \(0.347425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.75470 | 0.280467 | 0.140233 | − | 0.990118i | \(-0.455215\pi\) | ||||
0.140233 | + | 0.990118i | \(0.455215\pi\) | |||||||
\(422\) | −13.5707 | −0.660611 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.64482 | −0.419829 | ||||||||
\(425\) | 18.6541 | 0.904859 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.0927 | −1.26271 | ||||||||
\(428\) | 17.2044 | 0.831607 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −39.0392 | −1.88264 | ||||||||
\(431\) | 19.6675 | 0.947350 | 0.473675 | − | 0.880700i | \(-0.342927\pi\) | ||||
0.473675 | + | 0.880700i | \(0.342927\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5240 | −1.22660 | −0.613302 | − | 0.789849i | \(-0.710159\pi\) | ||||
−0.613302 | + | 0.789849i | \(0.710159\pi\) | |||||||
\(434\) | −2.30739 | −0.110758 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.1241 | 0.580641 | ||||||||
\(437\) | 7.31997 | 0.350162 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.99635 | −0.429372 | −0.214686 | − | 0.976683i | \(-0.568873\pi\) | ||||
−0.214686 | + | 0.976683i | \(0.568873\pi\) | |||||||
\(440\) | −30.3092 | −1.44493 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.181270 | 0.00862211 | ||||||||
\(443\) | −1.63232 | −0.0775541 | −0.0387770 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387770 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.5681 | 0.927615 | ||||||||
\(446\) | 7.35209 | 0.348131 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.5288 | 1.11163 | ||||||||
\(449\) | −36.0363 | −1.70066 | −0.850329 | − | 0.526251i | \(-0.823597\pi\) | ||||
−0.850329 | + | 0.526251i | \(0.823597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.4019 | 0.772334 | ||||||||
\(452\) | −14.0480 | −0.660764 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.8655 | 1.02620 | ||||||||
\(455\) | 0.410568 | 0.0192477 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.27483 | −0.199968 | −0.0999841 | − | 0.994989i | \(-0.531879\pi\) | ||||
−0.0999841 | + | 0.994989i | \(0.531879\pi\) | |||||||
\(458\) | −9.01799 | −0.421383 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.78289 | −0.129753 | ||||||||
\(461\) | 23.0578 | 1.07391 | 0.536954 | − | 0.843612i | \(-0.319575\pi\) | ||||
0.536954 | + | 0.843612i | \(0.319575\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.6421 | 1.60996 | 0.804978 | − | 0.593305i | \(-0.202177\pi\) | ||||
0.804978 | + | 0.593305i | \(0.202177\pi\) | |||||||
\(464\) | 1.40566 | 0.0652559 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.1883 | 0.981531 | ||||||||
\(467\) | −6.60876 | −0.305817 | −0.152908 | − | 0.988240i | \(-0.548864\pi\) | ||||
−0.152908 | + | 0.988240i | \(0.548864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.41539 | 0.434762 | ||||||||
\(470\) | 17.6931 | 0.816123 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 33.1644 | 1.52651 | ||||||||
\(473\) | −38.3513 | −1.76340 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.0330 | −1.56154 | ||||||||
\(476\) | −11.0493 | −0.506445 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.2897 | 0.928029 | ||||||||
\(479\) | −14.1027 | −0.644368 | −0.322184 | − | 0.946677i | \(-0.604417\pi\) | ||||
−0.322184 | + | 0.946677i | \(0.604417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.297144 | 0.0135486 | ||||||||
\(482\) | 4.54819 | 0.207164 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.643321 | 0.0292418 | ||||||||
\(485\) | 2.28781 | 0.103884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.1971 | −0.733962 | −0.366981 | − | 0.930228i | \(-0.619609\pi\) | ||||
−0.366981 | + | 0.930228i | \(0.619609\pi\) | |||||||
\(488\) | −25.8287 | −1.16921 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.99533 | 0.361192 | ||||||||
\(491\) | 35.1704 | 1.58722 | 0.793609 | − | 0.608428i | \(-0.208200\pi\) | ||||
0.793609 | + | 0.608428i | \(0.208200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.01221 | −0.180701 | ||||||||
\(494\) | −0.330712 | −0.0148794 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00412 | −0.0450864 | ||||||||
\(497\) | 11.2396 | 0.504165 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0912 | −1.30230 | −0.651150 | − | 0.758949i | \(-0.725713\pi\) | ||||
−0.651150 | + | 0.758949i | \(0.725713\pi\) | |||||||
\(500\) | −0.975841 | −0.0436409 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.79672 | 0.347985 | ||||||||
\(503\) | −42.0281 | −1.87394 | −0.936970 | − | 0.349411i | \(-0.886382\pi\) | ||||
−0.936970 | + | 0.349411i | \(0.886382\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.0136 | −0.979592 | ||||||||
\(506\) | 3.36935 | 0.149786 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.58523 | −0.247804 | ||||||||
\(509\) | 1.26068 | 0.0558787 | 0.0279394 | − | 0.999610i | \(-0.491105\pi\) | ||||
0.0279394 | + | 0.999610i | \(0.491105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.4256 | 1.34595 | ||||||||
\(512\) | 15.0329 | 0.664368 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.1895 | −1.15517 | ||||||||
\(515\) | −31.1779 | −1.37386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.3814 | 0.764431 | ||||||||
\(518\) | 22.3228 | 0.980808 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.406415 | 0.0178225 | ||||||||
\(521\) | 27.7996 | 1.21792 | 0.608961 | − | 0.793200i | \(-0.291587\pi\) | ||||
0.608961 | + | 0.793200i | \(0.291587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.2875 | 1.49929 | 0.749644 | − | 0.661842i | \(-0.230225\pi\) | ||||
0.749644 | + | 0.661842i | \(0.230225\pi\) | |||||||
\(524\) | −13.1869 | −0.576070 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.50782 | −0.370958 | ||||||||
\(527\) | 2.86610 | 0.124849 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −9.27310 | −0.402798 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.1586 | 0.873988 | ||||||||
\(533\) | −0.219932 | −0.00952631 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.6542 | 2.57908 | ||||||||
\(536\) | 9.32015 | 0.402569 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.9011 | 0.469978 | ||||||||
\(539\) | 7.85444 | 0.338315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.2929 | 1.68933 | 0.844666 | − | 0.535293i | \(-0.179799\pi\) | ||||
0.844666 | + | 0.535293i | \(0.179799\pi\) | |||||||
\(542\) | 33.5584 | 1.44146 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.4914 | −0.792814 | ||||||||
\(545\) | 42.0390 | 1.80075 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.1700 | −1.07619 | −0.538095 | − | 0.842884i | \(-0.680856\pi\) | ||||
−0.538095 | + | 0.842884i | \(0.680856\pi\) | |||||||
\(548\) | 12.8562 | 0.549190 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.6653 | −0.667969 | ||||||||
\(551\) | 7.31997 | 0.311841 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1754 | 0.432701 | ||||||||
\(554\) | −28.1895 | −1.19766 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.15119 | 0.260869 | ||||||||
\(557\) | 18.8437 | 0.798433 | 0.399217 | − | 0.916857i | \(-0.369282\pi\) | ||||
0.399217 | + | 0.916857i | \(0.369282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.514251 | 0.0217505 | ||||||||
\(560\) | 13.4225 | 0.567203 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.15549 | −0.0487414 | ||||||||
\(563\) | −18.4647 | −0.778196 | −0.389098 | − | 0.921196i | \(-0.627213\pi\) | ||||
−0.389098 | + | 0.921196i | \(0.627213\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.7098 | −2.04924 | ||||||||
\(566\) | 17.5562 | 0.737943 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1259 | 0.466832 | ||||||||
\(569\) | 24.5751 | 1.03024 | 0.515121 | − | 0.857117i | \(-0.327747\pi\) | ||||
0.515121 | + | 0.857117i | \(0.327747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1662 | 1.34612 | 0.673058 | − | 0.739590i | \(-0.264981\pi\) | ||||
0.673058 | + | 0.739590i | \(0.264981\pi\) | |||||||
\(572\) | 0.123514 | 0.00516438 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.5223 | −0.689626 | ||||||||
\(575\) | −4.64934 | −0.193891 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.94261 | 0.164133 | 0.0820664 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820664 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(578\) | 0.947962 | 0.0394300 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.78289 | −0.115553 | ||||||||
\(581\) | −39.6063 | −1.64314 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.10969 | −0.377285 | ||||||||
\(584\) | 30.1178 | 1.24628 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.42805 | 0.100302 | ||||||||
\(587\) | 31.9270 | 1.31777 | 0.658885 | − | 0.752244i | \(-0.271029\pi\) | ||||
0.658885 | + | 0.752244i | \(0.271029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.22898 | −0.215456 | ||||||||
\(590\) | 35.5746 | 1.46458 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.71436 | 0.399258 | ||||||||
\(593\) | −9.21942 | −0.378596 | −0.189298 | − | 0.981920i | \(-0.560621\pi\) | ||||
−0.189298 | + | 0.981920i | \(0.560621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38.3122 | −1.57065 | ||||||||
\(596\) | 2.03032 | 0.0831652 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.0451795 | −0.00184753 | ||||||||
\(599\) | −26.7668 | −1.09366 | −0.546831 | − | 0.837243i | \(-0.684166\pi\) | ||||
−0.546831 | + | 0.837243i | \(0.684166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6788 | −0.925088 | −0.462544 | − | 0.886596i | \(-0.653063\pi\) | ||||
−0.462544 | + | 0.886596i | \(0.653063\pi\) | |||||||
\(602\) | 38.6329 | 1.57456 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.3619 | −0.625067 | ||||||||
\(605\) | 2.23064 | 0.0906882 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7375 | −1.20701 | −0.603503 | − | 0.797360i | \(-0.706229\pi\) | ||||
−0.603503 | + | 0.797360i | \(0.706229\pi\) | |||||||
\(608\) | 33.7362 | 1.36818 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27.7059 | −1.12178 | ||||||||
\(611\) | −0.233066 | −0.00942884 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4654 | −0.422695 | −0.211347 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211347 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(614\) | 23.3910 | 0.943982 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 29.9937 | 1.20848 | ||||||||
\(617\) | 1.84782 | 0.0743905 | 0.0371953 | − | 0.999308i | \(-0.488158\pi\) | ||||
0.0371953 | + | 0.999308i | \(0.488158\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.67510 | 0.187908 | 0.0939540 | − | 0.995577i | \(-0.470049\pi\) | ||||
0.0939540 | + | 0.995577i | \(0.470049\pi\) | |||||||
\(620\) | 1.98795 | 0.0798378 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.9066 | 0.677892 | ||||||||
\(623\) | −19.3644 | −0.775817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.6303 | −1.06521 | ||||||||
\(626\) | −9.66363 | −0.386236 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.4692 | 0.657193 | ||||||||
\(629\) | −27.7281 | −1.10559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.2191 | −1.68072 | −0.840358 | − | 0.542031i | \(-0.817655\pi\) | ||||
−0.840358 | + | 0.542031i | \(0.817655\pi\) | |||||||
\(632\) | 10.0724 | 0.400660 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.86983 | 0.113975 | ||||||||
\(635\) | −19.3661 | −0.768520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.105320 | −0.00417293 | ||||||||
\(638\) | 3.36935 | 0.133394 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.64950 | −0.144259 | ||||||||
\(641\) | 29.1294 | 1.15054 | 0.575271 | − | 0.817963i | \(-0.304897\pi\) | ||||
0.575271 | + | 0.817963i | \(0.304897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8177 | 0.544916 | 0.272458 | − | 0.962168i | \(-0.412163\pi\) | ||||
0.272458 | + | 0.962168i | \(0.412163\pi\) | |||||||
\(644\) | 2.75393 | 0.108520 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.8604 | 1.21419 | ||||||||
\(647\) | −42.2780 | −1.66212 | −0.831059 | − | 0.556184i | \(-0.812265\pi\) | ||||
−0.831059 | + | 0.556184i | \(0.812265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.9478 | 1.37182 | ||||||||
\(650\) | 0.210055 | 0.00823903 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.2661 | −0.441216 | ||||||||
\(653\) | −29.2866 | −1.14607 | −0.573037 | − | 0.819529i | \(-0.694235\pi\) | ||||
−0.573037 | + | 0.819529i | \(0.694235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.7238 | −1.78658 | ||||||||
\(656\) | −7.19010 | −0.280726 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.5090 | −0.682570 | ||||||||
\(659\) | 6.15767 | 0.239869 | 0.119934 | − | 0.992782i | \(-0.461732\pi\) | ||||
0.119934 | + | 0.992782i | \(0.461732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9869 | −0.816295 | −0.408148 | − | 0.912916i | \(-0.633825\pi\) | ||||
−0.408148 | + | 0.912916i | \(0.633825\pi\) | |||||||
\(662\) | 25.9150 | 1.00721 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −39.2056 | −1.52147 | ||||||||
\(665\) | 69.8976 | 2.71051 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 4.52657 | 0.175138 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.99751 | 0.386237 | ||||||||
\(671\) | −27.2177 | −1.05073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9550 | 0.730660 | 0.365330 | − | 0.930878i | \(-0.380956\pi\) | ||||
0.365330 | + | 0.930878i | \(0.380956\pi\) | |||||||
\(674\) | 5.34736 | 0.205972 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.6447 | 0.447874 | ||||||||
\(677\) | 2.63505 | 0.101273 | 0.0506366 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506366 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.26400 | −0.0868844 | ||||||||
\(680\) | −37.9247 | −1.45434 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.40688 | −0.0921641 | ||||||||
\(683\) | −18.5862 | −0.711180 | −0.355590 | − | 0.934642i | \(-0.615720\pi\) | ||||
−0.355590 | + | 0.934642i | \(0.615720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.5774 | 1.70321 | ||||||||
\(686\) | 14.6985 | 0.561190 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.8121 | 0.640956 | ||||||||
\(689\) | 0.122152 | 0.00465360 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.6567 | 1.66078 | 0.830389 | − | 0.557184i | \(-0.188118\pi\) | ||||
0.830389 | + | 0.557184i | \(0.188118\pi\) | |||||||
\(692\) | −8.94438 | −0.340014 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.0045 | −1.06304 | ||||||||
\(695\) | 21.3285 | 0.809036 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.5230 | 0.777363 | ||||||||
\(698\) | 34.9748 | 1.32382 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.8039 | −0.483944 | ||||||||
\(701\) | 22.0312 | 0.832107 | 0.416054 | − | 0.909340i | \(-0.363413\pi\) | ||||
0.416054 | + | 0.909340i | \(0.363413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.5877 | 1.90795 | ||||||||
\(704\) | 24.5432 | 0.925007 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.9538 | −1.12733 | ||||||||
\(707\) | 21.7844 | 0.819288 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.9056 | −1.27335 | −0.636676 | − | 0.771131i | \(-0.719691\pi\) | ||||
−0.636676 | + | 0.771131i | \(0.719691\pi\) | |||||||
\(710\) | 11.9345 | 0.447894 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −19.1685 | −0.718369 | ||||||||
\(713\) | −0.714345 | −0.0267524 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.428270 | 0.0160164 | ||||||||
\(716\) | 6.90253 | 0.257960 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.9775 | 0.484317 | ||||||||
\(719\) | 10.7651 | 0.401472 | 0.200736 | − | 0.979645i | \(-0.435667\pi\) | ||||
0.200736 | + | 0.979645i | \(0.435667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.8534 | 1.14904 | ||||||||
\(722\) | −36.3378 | −1.35235 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.6891 | 0.508750 | ||||||||
\(725\) | −4.64934 | −0.172672 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.9953 | 1.81714 | 0.908568 | − | 0.417737i | \(-0.137177\pi\) | ||||
0.908568 | + | 0.417737i | \(0.137177\pi\) | |||||||
\(728\) | −0.402185 | −0.0149060 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 32.3067 | 1.19572 | ||||||||
\(731\) | −47.9874 | −1.77488 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.4364 | 1.12420 | 0.562098 | − | 0.827071i | \(-0.309995\pi\) | ||||
0.562098 | + | 0.827071i | \(0.309995\pi\) | |||||||
\(734\) | 20.7931 | 0.767487 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.60879 | 0.169882 | ||||||||
\(737\) | 9.82134 | 0.361774 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.83114 | 0.104145 | 0.0520727 | − | 0.998643i | \(-0.483417\pi\) | ||||
0.0520727 | + | 0.998643i | \(0.483417\pi\) | |||||||
\(740\) | −19.2323 | −0.706995 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.17657 | 0.336883 | ||||||||
\(743\) | −18.5983 | −0.682307 | −0.341153 | − | 0.940008i | \(-0.610818\pi\) | ||||
−0.341153 | + | 0.940008i | \(0.610818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.03989 | 0.257922 | ||||||||
\(746\) | −0.00516091 | −0.000188954 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.5257 | −0.421422 | ||||||||
\(749\) | −59.0332 | −2.15703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.7942 | −0.904752 | −0.452376 | − | 0.891827i | \(-0.649424\pi\) | ||||
−0.452376 | + | 0.891827i | \(0.649424\pi\) | |||||||
\(752\) | −7.61948 | −0.277854 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0451795 | −0.00164534 | ||||||||
\(755\) | −53.2655 | −1.93853 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.63450 | −0.0957527 | −0.0478763 | − | 0.998853i | \(-0.515245\pi\) | ||||
−0.0478763 | + | 0.998853i | \(0.515245\pi\) | |||||||
\(758\) | 30.7933 | 1.11846 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 69.1906 | 2.50981 | ||||||||
\(761\) | −22.7357 | −0.824168 | −0.412084 | − | 0.911146i | \(-0.635199\pi\) | ||||
−0.412084 | + | 0.911146i | \(0.635199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.6014 | −1.50607 | ||||||||
\(764\) | 7.34410 | 0.265700 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.38791 | 0.0862788 | ||||||||
\(767\) | −0.468613 | −0.0169206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.477039 | 0.0172025 | 0.00860123 | − | 0.999963i | \(-0.497262\pi\) | ||||
0.00860123 | + | 0.999963i | \(0.497262\pi\) | |||||||
\(770\) | 32.1736 | 1.15946 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.1582 | −0.473573 | ||||||||
\(773\) | −4.06587 | −0.146239 | −0.0731197 | − | 0.997323i | \(-0.523296\pi\) | ||||
−0.0731197 | + | 0.997323i | \(0.523296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.32123 | 0.119302 | ||||||||
\(776\) | −2.24110 | −0.0804507 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.3150 | 1.12270 | ||||||||
\(779\) | −37.4426 | −1.34152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7242 | 0.419525 | ||||||||
\(782\) | 4.21592 | 0.150761 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.44316 | −0.122970 | ||||||||
\(785\) | 57.1049 | 2.03816 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.2517 | −0.793188 | −0.396594 | − | 0.917994i | \(-0.629808\pi\) | ||||
−0.396594 | + | 0.917994i | \(0.629808\pi\) | |||||||
\(788\) | −6.18277 | −0.220252 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.8045 | 0.384406 | ||||||||
\(791\) | 48.2028 | 1.71389 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.364961 | 0.0129601 | ||||||||
\(794\) | 14.4479 | 0.512736 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.7203 | −0.450858 | ||||||||
\(797\) | −55.3496 | −1.96058 | −0.980291 | − | 0.197559i | \(-0.936699\pi\) | ||||
−0.980291 | + | 0.197559i | \(0.936699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.7486 | 0.769409 | ||||||||
\(800\) | −21.4279 | −0.757589 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0324 | 0.424879 | ||||||||
\(803\) | 31.7374 | 1.11999 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.54890 | 0.336555 | ||||||||
\(806\) | 0.0322737 | 0.00113679 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21.5641 | 0.758621 | ||||||||
\(809\) | −10.4303 | −0.366711 | −0.183356 | − | 0.983047i | \(-0.558696\pi\) | ||||
−0.183356 | + | 0.983047i | \(0.558696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.7760 | −1.01046 | −0.505232 | − | 0.862984i | \(-0.668593\pi\) | ||||
−0.505232 | + | 0.862984i | \(0.668593\pi\) | |||||||
\(812\) | 2.75393 | 0.0966439 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.2853 | 0.816148 | ||||||||
\(815\) | −39.0640 | −1.36835 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 87.5493 | 3.06296 | ||||||||
\(818\) | 7.34546 | 0.256828 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.2349 | 0.497103 | ||||||||
\(821\) | −19.8123 | −0.691453 | −0.345727 | − | 0.938335i | \(-0.612368\pi\) | ||||
−0.345727 | + | 0.938335i | \(0.612368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.5275 | −0.645828 | −0.322914 | − | 0.946428i | \(-0.604662\pi\) | ||||
−0.322914 | + | 0.946428i | \(0.604662\pi\) | |||||||
\(824\) | 30.5413 | 1.06396 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.2043 | −1.22492 | ||||||||
\(827\) | −6.68508 | −0.232463 | −0.116232 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116232 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.6286 | 1.13324 | 0.566620 | − | 0.823980i | \(-0.308251\pi\) | ||||
0.566620 | + | 0.823980i | \(0.308251\pi\) | |||||||
\(830\) | −42.0549 | −1.45975 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.329099 | −0.0114095 | ||||||||
\(833\) | 9.82794 | 0.340518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.6953 | 0.543159 | ||||||||
\(836\) | 21.0278 | 0.727262 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.8389 | −0.685325 | ||||||||
\(839\) | 14.7983 | 0.510894 | 0.255447 | − | 0.966823i | \(-0.417777\pi\) | ||||
0.255447 | + | 0.966823i | \(0.417777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −6.04688 | −0.208389 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.5702 | −0.398262 | ||||||||
\(845\) | 40.3767 | 1.38900 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.20742 | −0.0758477 | ||||||||
\(848\) | 3.99343 | 0.137135 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.6013 | −0.672318 | ||||||||
\(851\) | 6.91091 | 0.236903 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.3532 | 0.559922 | 0.279961 | − | 0.960011i | \(-0.409679\pi\) | ||||
0.279961 | + | 0.960011i | \(0.409679\pi\) | |||||||
\(854\) | 27.4175 | 0.938208 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −58.4361 | −1.99730 | ||||||||
\(857\) | −47.5474 | −1.62419 | −0.812094 | − | 0.583527i | \(-0.801672\pi\) | ||||
−0.812094 | + | 0.583527i | \(0.801672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.87247 | 0.200366 | 0.100183 | − | 0.994969i | \(-0.468057\pi\) | ||||
0.100183 | + | 0.994969i | \(0.468057\pi\) | |||||||
\(860\) | −33.2843 | −1.13499 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.6661 | −0.703889 | ||||||||
\(863\) | −30.9619 | −1.05396 | −0.526978 | − | 0.849879i | \(-0.676675\pi\) | ||||
−0.526978 | + | 0.849879i | \(0.676675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.0135 | −1.05449 | ||||||||
\(866\) | 26.8199 | 0.911377 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.96725 | −0.0667729 | ||||||||
\(869\) | 10.6141 | 0.360058 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.131694 | −0.00446228 | ||||||||
\(872\) | −41.1805 | −1.39455 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.69163 | −0.260173 | ||||||||
\(875\) | 3.34839 | 0.113196 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6154 | −0.594830 | −0.297415 | − | 0.954748i | \(-0.596124\pi\) | ||||
−0.297415 | + | 0.954748i | \(0.596124\pi\) | |||||||
\(878\) | 9.45312 | 0.319027 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.0012 | 0.471980 | ||||||||
\(881\) | 4.21972 | 0.142166 | 0.0710831 | − | 0.997470i | \(-0.477354\pi\) | ||||
0.0710831 | + | 0.997470i | \(0.477354\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.73658 | 0.226704 | 0.113352 | − | 0.993555i | \(-0.463841\pi\) | ||||
0.113352 | + | 0.993555i | \(0.463841\pi\) | |||||||
\(884\) | 0.154548 | 0.00519801 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.71520 | 0.0576234 | ||||||||
\(887\) | −56.2580 | −1.88896 | −0.944479 | − | 0.328571i | \(-0.893433\pi\) | ||||
−0.944479 | + | 0.328571i | \(0.893433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1645 | 0.642757 | ||||||||
\(890\) | −20.5616 | −0.689226 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.26829 | 0.209878 | ||||||||
\(893\) | −39.6786 | −1.32779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.9337 | 0.800015 | ||||||||
\(896\) | 3.61151 | 0.120652 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.8660 | 1.26360 | ||||||||
\(899\) | −0.714345 | −0.0238247 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3986 | −0.379742 | ||||||||
\(902\) | −17.2346 | −0.573851 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 47.7152 | 1.58698 | ||||||||
\(905\) | 47.4652 | 1.57780 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.6879 | 1.08538 | 0.542691 | − | 0.839932i | \(-0.317405\pi\) | ||||
0.542691 | + | 0.839932i | \(0.317405\pi\) | |||||||
\(908\) | 18.6422 | 0.618664 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.431414 | −0.0143012 | ||||||||
\(911\) | 27.6041 | 0.914565 | 0.457283 | − | 0.889321i | \(-0.348823\pi\) | ||||
0.457283 | + | 0.889321i | \(0.348823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.3139 | −1.36729 | ||||||||
\(914\) | 4.49188 | 0.148578 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.68862 | −0.254039 | ||||||||
\(917\) | 45.2479 | 1.49422 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.4419 | 0.443409 | 0.221704 | − | 0.975114i | \(-0.428838\pi\) | ||||
0.221704 | + | 0.975114i | \(0.428838\pi\) | |||||||
\(920\) | 9.45231 | 0.311633 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.2285 | −0.797923 | ||||||||
\(923\) | −0.157209 | −0.00517461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.1312 | −1.05647 | ||||||||
\(926\) | −36.4010 | −1.19621 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.60879 | 0.151291 | ||||||||
\(929\) | −29.7370 | −0.975640 | −0.487820 | − | 0.872944i | \(-0.662208\pi\) | ||||
−0.487820 | + | 0.872944i | \(0.662208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.9303 | −0.587642 | ||||||||
\(932\) | 18.0649 | 0.591735 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.94431 | 0.227225 | ||||||||
\(935\) | −39.9641 | −1.30696 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.43663 | −0.0469325 | −0.0234663 | − | 0.999725i | \(-0.507470\pi\) | ||||
−0.0234663 | + | 0.999725i | \(0.507470\pi\) | |||||||
\(938\) | −9.89344 | −0.323032 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.0849 | 0.492016 | ||||||||
\(941\) | −6.73354 | −0.219507 | −0.109754 | − | 0.993959i | \(-0.535006\pi\) | ||||
−0.109754 | + | 0.993959i | \(0.535006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.11513 | −0.166571 | ||||||||
\(944\) | −15.3201 | −0.498627 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.2985 | 1.31022 | ||||||||
\(947\) | 14.0154 | 0.455440 | 0.227720 | − | 0.973727i | \(-0.426873\pi\) | ||||
0.227720 | + | 0.973727i | \(0.426873\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.425566 | −0.0138144 | ||||||||
\(950\) | 35.7610 | 1.16024 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 37.5299 | 1.21635 | ||||||||
\(953\) | 12.8306 | 0.415624 | 0.207812 | − | 0.978169i | \(-0.433366\pi\) | ||||
0.207812 | + | 0.978169i | \(0.433366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.4648 | 0.824021 | ||||||||
\(956\) | 17.2987 | 0.559481 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.8187 | 0.478771 | ||||||||
\(959\) | −44.1134 | −1.42449 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4897 | −0.983539 | ||||||||
\(962\) | −0.312231 | −0.0100667 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.87773 | 0.124893 | ||||||||
\(965\) | −45.6244 | −1.46870 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6661 | 0.986156 | 0.493078 | − | 0.869985i | \(-0.335872\pi\) | ||||
0.493078 | + | 0.869985i | \(0.335872\pi\) | |||||||
\(968\) | −2.18509 | −0.0702313 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.40397 | −0.0771870 | ||||||||
\(971\) | 12.6876 | 0.407166 | 0.203583 | − | 0.979058i | \(-0.434741\pi\) | ||||
0.203583 | + | 0.979058i | \(0.434741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.1065 | −0.676643 | ||||||||
\(974\) | 17.0195 | 0.545340 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.9315 | 0.381916 | ||||||||
\(977\) | 34.7063 | 1.11035 | 0.555177 | − | 0.831732i | \(-0.312650\pi\) | ||||
0.555177 | + | 0.831732i | \(0.312650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.1993 | −0.645572 | ||||||||
\(980\) | 6.81671 | 0.217752 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36.9561 | −1.17932 | ||||||||
\(983\) | −59.0415 | −1.88313 | −0.941566 | − | 0.336828i | \(-0.890646\pi\) | ||||
−0.941566 | + | 0.336828i | \(0.890646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.4380 | −0.683072 | ||||||||
\(986\) | 4.21592 | 0.134262 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.281961 | −0.00897037 | ||||||||
\(989\) | 11.9603 | 0.380317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.1877 | −1.53073 | −0.765367 | − | 0.643594i | \(-0.777442\pi\) | ||||
−0.765367 | + | 0.643594i | \(0.777442\pi\) | |||||||
\(992\) | −3.29227 | −0.104530 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.8103 | −0.374599 | ||||||||
\(995\) | −44.1059 | −1.39825 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0886 | 1.20628 | 0.603139 | − | 0.797636i | \(-0.293916\pi\) | ||||
0.603139 | + | 0.797636i | \(0.293916\pi\) | |||||||
\(998\) | 30.5682 | 0.967620 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.u.1.8 | yes | 22 | |
3.2 | odd | 2 | 6003.2.a.t.1.15 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.15 | ✓ | 22 | 3.2 | odd | 2 | ||
6003.2.a.u.1.8 | yes | 22 | 1.1 | even | 1 | trivial |