Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.907672 | −0.524045 | −0.262022 | − | 0.965062i | \(-0.584389\pi\) | ||||
−0.262022 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31635 | 0.588689 | 0.294344 | − | 0.955699i | \(-0.404899\pi\) | ||||
0.294344 | + | 0.955699i | \(0.404899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.29510 | −0.867468 | −0.433734 | − | 0.901041i | \(-0.642804\pi\) | ||||
−0.433734 | + | 0.901041i | \(0.642804\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17613 | −0.725377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.212653 | 0.0641172 | 0.0320586 | − | 0.999486i | \(-0.489794\pi\) | ||||
0.0320586 | + | 0.999486i | \(0.489794\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.06499 | 1.68213 | 0.841063 | − | 0.540937i | \(-0.181930\pi\) | ||||
0.841063 | + | 0.540937i | \(0.181930\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.19481 | −0.308499 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.799701 | 0.193956 | 0.0969780 | − | 0.995287i | \(-0.469082\pi\) | ||||
0.0969780 | + | 0.995287i | \(0.469082\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.08320 | 0.454592 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.602634 | 0.125658 | 0.0628289 | − | 0.998024i | \(-0.479988\pi\) | ||||
0.0628289 | + | 0.998024i | \(0.479988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.26723 | −0.653446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.69823 | 0.904175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.49105 | −1.39105 | −0.695526 | − | 0.718501i | \(-0.744829\pi\) | ||||
−0.695526 | + | 0.718501i | \(0.744829\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.42670 | −0.256242 | −0.128121 | − | 0.991759i | \(-0.540895\pi\) | ||||
−0.128121 | + | 0.991759i | \(0.540895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.193019 | −0.0336003 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.02116 | −0.510668 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.32189 | −1.36811 | −0.684055 | − | 0.729431i | \(-0.739785\pi\) | ||||
−0.684055 | + | 0.729431i | \(0.739785\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.50502 | −0.881509 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.745533 | 0.116433 | 0.0582164 | − | 0.998304i | \(-0.481459\pi\) | ||||
0.0582164 | + | 0.998304i | \(0.481459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.77416 | 1.33805 | 0.669023 | − | 0.743242i | \(-0.266713\pi\) | ||||
0.669023 | + | 0.743242i | \(0.266713\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.86455 | −0.427021 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.64327 | −1.40662 | −0.703308 | − | 0.710885i | \(-0.748294\pi\) | ||||
−0.703308 | + | 0.710885i | \(0.748294\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.73250 | −0.247500 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.725867 | −0.101642 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.32363 | −1.28070 | −0.640350 | − | 0.768083i | \(-0.721211\pi\) | ||||
−0.640350 | + | 0.768083i | \(0.721211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.279925 | 0.0377451 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.907672 | −0.120224 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.5563 | 1.37431 | 0.687157 | − | 0.726509i | \(-0.258858\pi\) | ||||
0.687157 | + | 0.726509i | \(0.258858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47197 | 0.572577 | 0.286289 | − | 0.958143i | \(-0.407578\pi\) | ||||
0.286289 | + | 0.958143i | \(0.407578\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.99445 | 0.629241 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.98364 | 0.990249 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.17038 | 0.265155 | 0.132577 | − | 0.991173i | \(-0.457675\pi\) | ||||
0.132577 | + | 0.991173i | \(0.457675\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.546994 | −0.0658503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3644 | 1.23002 | 0.615012 | − | 0.788518i | \(-0.289151\pi\) | ||||
0.615012 | + | 0.788518i | \(0.289151\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.30094 | 0.737469 | 0.368735 | − | 0.929535i | \(-0.379791\pi\) | ||||
0.368735 | + | 0.929535i | \(0.379791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.96557 | 0.342435 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.488060 | −0.0556196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.26394 | 0.251549 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.03828 | 0.882316 | 0.441158 | − | 0.897430i | \(-0.354568\pi\) | ||||
0.441158 | + | 0.897430i | \(0.354568\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.05269 | 0.114180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.79942 | 0.728974 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3703 | 1.09925 | 0.549626 | − | 0.835411i | \(-0.314770\pi\) | ||||
0.549626 | + | 0.835411i | \(0.314770\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.9198 | −1.45919 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.29497 | 0.134283 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.31635 | 0.135054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.60934 | 0.772612 | 0.386306 | − | 0.922371i | \(-0.373751\pi\) | ||||
0.386306 | + | 0.922371i | \(0.373751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.462760 | −0.0465091 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.90950 | −0.886528 | −0.443264 | − | 0.896391i | \(-0.646180\pi\) | ||||
−0.443264 | + | 0.896391i | \(0.646180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4376 | −1.22551 | −0.612756 | − | 0.790272i | \(-0.709939\pi\) | ||||
−0.612756 | + | 0.790272i | \(0.709939\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.74222 | 0.267613 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.09598 | −0.395973 | −0.197986 | − | 0.980205i | \(-0.563440\pi\) | ||||
−0.197986 | + | 0.980205i | \(0.563440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.21166 | −0.594969 | −0.297484 | − | 0.954727i | \(-0.596148\pi\) | ||||
−0.297484 | + | 0.954727i | \(0.596148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.55355 | 0.716951 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.0711 | −1.04148 | −0.520740 | − | 0.853716i | \(-0.674344\pi\) | ||||
−0.520740 | + | 0.853716i | \(0.674344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.793276 | 0.0739733 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.1982 | −1.22018 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.83540 | −0.168251 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9548 | −0.995889 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.676700 | −0.0610160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8825 | −0.973365 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9148 | 1.05727 | 0.528633 | − | 0.848850i | \(-0.322705\pi\) | ||||
0.528633 | + | 0.848850i | \(0.322705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.96406 | −0.701196 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.73112 | −0.238619 | −0.119309 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119309 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.29510 | −0.199011 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.18451 | 0.532278 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.3863 | −1.82715 | −0.913577 | − | 0.406666i | \(-0.866691\pi\) | ||||
−0.913577 | + | 0.406666i | \(0.866691\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.13598 | −0.435628 | −0.217814 | − | 0.975990i | \(-0.569893\pi\) | ||||
−0.217814 | + | 0.975990i | \(0.569893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.75293 | 0.737130 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.28974 | 0.107853 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.86083 | −0.818897 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.57254 | 0.129701 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3694 | −1.34103 | −0.670515 | − | 0.741896i | \(-0.733927\pi\) | ||||
−0.670515 | + | 0.741896i | \(0.733927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.7389 | 1.52495 | 0.762475 | − | 0.647017i | \(-0.223984\pi\) | ||||
0.762475 | + | 0.647017i | \(0.223984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.74026 | −0.140691 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.87803 | −0.150847 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.2865 | −1.77866 | −0.889328 | − | 0.457270i | \(-0.848827\pi\) | ||||
−0.889328 | + | 0.457270i | \(0.848827\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.46280 | 0.671144 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.38311 | −0.109004 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.68612 | 0.523697 | 0.261849 | − | 0.965109i | \(-0.415668\pi\) | ||||
0.261849 | + | 0.965109i | \(0.415668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.254080 | −0.0197801 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.87917 | −0.609709 | −0.304854 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304854 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.7841 | 1.82955 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.17613 | −0.166413 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.4446 | −0.870115 | −0.435058 | − | 0.900403i | \(-0.643272\pi\) | ||||
−0.435058 | + | 0.900403i | \(0.643272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.49863 | 0.566843 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.58167 | −0.720202 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.16670 | −0.236690 | −0.118345 | − | 0.992973i | \(-0.537759\pi\) | ||||
−0.118345 | + | 0.992973i | \(0.537759\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7792 | −1.09853 | −0.549264 | − | 0.835649i | \(-0.685092\pi\) | ||||
−0.549264 | + | 0.835649i | \(0.685092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.05909 | −0.300056 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.9545 | −0.805391 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.170059 | 0.0124359 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.7829 | −0.784343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.50227 | −0.398131 | −0.199065 | − | 0.979986i | \(-0.563791\pi\) | ||||
−0.199065 | + | 0.979986i | \(0.563791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2497 | 1.09769 | 0.548847 | − | 0.835923i | \(-0.315067\pi\) | ||||
0.548847 | + | 0.835923i | \(0.315067\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.24653 | −0.518935 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.14603 | 0.224146 | 0.112073 | − | 0.993700i | \(-0.464251\pi\) | ||||
0.112073 | + | 0.993700i | \(0.464251\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7138 | −1.11392 | −0.556962 | − | 0.830538i | \(-0.688033\pi\) | ||||
−0.556962 | + | 0.830538i | \(0.688033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.97000 | −0.138953 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.1927 | 1.20669 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.981381 | 0.0685426 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.31141 | −0.0911493 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.212653 | 0.0147095 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.51341 | 0.517245 | 0.258622 | − | 0.965979i | \(-0.416731\pi\) | ||||
0.258622 | + | 0.965979i | \(0.416731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.40745 | −0.644588 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.5498 | 0.787693 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.27442 | 0.222282 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.71919 | −0.386467 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.85018 | 0.326259 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.84169 | −0.458153 | −0.229077 | − | 0.973408i | \(-0.573571\pi\) | ||||
−0.229077 | + | 0.973408i | \(0.573571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.10991 | 0.473994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.8344 | −1.91380 | −0.956902 | − | 0.290410i | \(-0.906208\pi\) | ||||
−0.956902 | + | 0.290410i | \(0.906208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.7678 | −1.50454 | −0.752271 | − | 0.658854i | \(-0.771041\pi\) | ||||
−0.752271 | + | 0.658854i | \(0.771041\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.442998 | 0.0291471 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.41156 | 0.485547 | 0.242774 | − | 0.970083i | \(-0.421943\pi\) | ||||
0.242774 | + | 0.970083i | \(0.421943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.6939 | −0.828059 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.907672 | 0.0589597 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.06663 | −0.586472 | −0.293236 | − | 0.956040i | \(-0.594732\pi\) | ||||
−0.293236 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.888982 | 0.0572644 | 0.0286322 | − | 0.999590i | \(-0.490885\pi\) | ||||
0.0286322 | + | 0.999590i | \(0.490885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1496 | −1.03600 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.28057 | −0.145700 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.06499 | 0.385906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.29612 | −0.462373 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.90246 | 0.561919 | 0.280959 | − | 0.959720i | \(-0.409347\pi\) | ||||
0.280959 | + | 0.959720i | \(0.409347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.128152 | 0.00805682 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.955494 | −0.0598353 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.73303 | −0.482373 | −0.241187 | − | 0.970479i | \(-0.577537\pi\) | ||||
−0.241187 | + | 0.970479i | \(0.577537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.0996 | 1.18679 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.3015 | 1.00904 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0240 | 0.803095 | 0.401548 | − | 0.915838i | \(-0.368472\pi\) | ||||
0.401548 | + | 0.915838i | \(0.368472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2731 | −0.753933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.41285 | −0.576057 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.05414 | 0.552041 | 0.276020 | − | 0.961152i | \(-0.410984\pi\) | ||||
0.276020 | + | 0.961152i | \(0.410984\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4755 | −1.06156 | −0.530780 | − | 0.847510i | \(-0.678101\pi\) | ||||
−0.530780 | + | 0.847510i | \(0.678101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6346 | 0.764681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.694784 | −0.0418971 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1324 | 1.02938 | 0.514692 | − | 0.857375i | \(-0.327906\pi\) | ||||
0.514692 | + | 0.857375i | \(0.327906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.10468 | 0.185872 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.99487 | −0.417279 | −0.208639 | − | 0.977993i | \(-0.566904\pi\) | ||||
−0.208639 | + | 0.977993i | \(0.566904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.6513 | −0.930371 | −0.465185 | − | 0.885213i | \(-0.654012\pi\) | ||||
−0.465185 | + | 0.885213i | \(0.654012\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.19481 | −0.0707746 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.71108 | −0.101002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3605 | −0.962381 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.90679 | −0.404883 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.782121 | 0.0456920 | 0.0228460 | − | 0.999739i | \(-0.492727\pi\) | ||||
0.0228460 | + | 0.999739i | \(0.492727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.8958 | 0.809043 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.999091 | 0.0579731 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.65497 | 0.211372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1376 | −1.16071 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.08691 | 0.464581 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.88667 | 0.337070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.1179 | −1.83307 | −0.916533 | − | 0.399959i | \(-0.869024\pi\) | ||||
−0.916533 | + | 0.399959i | \(0.869024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2893 | 0.642223 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5891 | 0.770569 | 0.385285 | − | 0.922798i | \(-0.374103\pi\) | ||||
0.385285 | + | 0.922798i | \(0.374103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.1834 | −1.87563 | −0.937817 | − | 0.347130i | \(-0.887156\pi\) | ||||
−0.937817 | + | 0.347130i | \(0.887156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.57443 | 0.370427 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.60751 | 0.0902869 | 0.0451434 | − | 0.998981i | \(-0.485626\pi\) | ||||
0.0451434 | + | 0.998981i | \(0.485626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.59299 | −0.0891903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.71780 | 0.207508 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.799701 | 0.0444966 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.8157 | −1.09918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.63815 | 0.311790 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.1323 | 1.22019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.2000 | −0.945398 | −0.472699 | − | 0.881224i | \(-0.656720\pi\) | ||||
−0.472699 | + | 0.881224i | \(0.656720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1095 | 0.992395 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.85698 | 0.156094 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.43131 | 0.295863 | 0.147931 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147931 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0489 | 0.545782 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.303391 | −0.0164295 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0420 | 1.08217 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.720035 | −0.0387654 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.39695 | −0.450772 | −0.225386 | − | 0.974270i | \(-0.572364\pi\) | ||||
−0.225386 | + | 0.974270i | \(0.572364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.2473 | −0.816168 | −0.408084 | − | 0.912944i | \(-0.633803\pi\) | ||||
−0.408084 | + | 0.912944i | \(0.633803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.4947 | 1.52094 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.60997 | 0.511487 | 0.255744 | − | 0.966745i | \(-0.417680\pi\) | ||||
0.255744 | + | 0.966745i | \(0.417680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.6431 | 0.724101 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.66594 | 0.0881709 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.27060 | 0.330950 | 0.165475 | − | 0.986214i | \(-0.447084\pi\) | ||||
0.165475 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.94335 | 0.521891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.29423 | 0.434140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.9952 | −1.93113 | −0.965566 | − | 0.260158i | \(-0.916225\pi\) | ||||
−0.965566 | + | 0.260158i | \(0.916225\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.62238 | −0.0844576 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.3987 | 1.11097 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.8082 | 0.559629 | 0.279815 | − | 0.960054i | \(-0.409727\pi\) | ||||
0.279815 | + | 0.960054i | \(0.409727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.87779 | 0.510087 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.4331 | −2.33993 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00285 | 0.411079 | 0.205539 | − | 0.978649i | \(-0.434105\pi\) | ||||
0.205539 | + | 0.978649i | \(0.434105\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.8147 | −0.554055 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.55079 | −0.334730 | −0.167365 | − | 0.985895i | \(-0.553526\pi\) | ||||
−0.167365 | + | 0.985895i | \(0.553526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.642456 | −0.0327426 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.0937 | −0.970588 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.8079 | −0.902895 | −0.451448 | − | 0.892298i | \(-0.649092\pi\) | ||||
−0.451448 | + | 0.892298i | \(0.649092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.481927 | 0.0243721 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.47896 | 0.125047 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.31635 | −0.0662327 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.3653 | 1.67456 | 0.837279 | − | 0.546776i | \(-0.184145\pi\) | ||||
0.837279 | + | 0.546776i | \(0.184145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.08320 | 0.104291 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.9966 | −1.14839 | −0.574197 | − | 0.818717i | \(-0.694686\pi\) | ||||
−0.574197 | + | 0.818717i | \(0.694686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.65291 | −0.431032 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.98013 | 0.148084 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.76967 | −0.0877193 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.76368 | 0.284996 | 0.142498 | − | 0.989795i | \(-0.454487\pi\) | ||||
0.142498 | + | 0.989795i | \(0.454487\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.4117 | 0.957511 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.2278 | −1.19217 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5812 | 0.519409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.66179 | 0.228289 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.2053 | −1.42677 | −0.713386 | − | 0.700771i | \(-0.752840\pi\) | ||||
−0.713386 | + | 0.700771i | \(0.752840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.41774 | −0.458992 | −0.229496 | − | 0.973310i | \(-0.573708\pi\) | ||||
−0.229496 | + | 0.973310i | \(0.573708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.9850 | 1.02033 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.61281 | −0.126740 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2636 | −0.496692 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.17066 | −0.0565199 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.6086 | 0.896345 | 0.448173 | − | 0.893947i | \(-0.352075\pi\) | ||||
0.448173 | + | 0.893947i | \(0.352075\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.0750803 | −0.00360813 | −0.00180406 | − | 0.999998i | \(-0.500574\pi\) | ||||
−0.00180406 | + | 0.999998i | \(0.500574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.95040 | 0.429139 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.602634 | 0.0288279 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2730 | −0.872125 | −0.436062 | − | 0.899916i | \(-0.643627\pi\) | ||||
−0.436062 | + | 0.899916i | \(0.643627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.77014 | 0.179531 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7909 | −0.702738 | −0.351369 | − | 0.936237i | \(-0.614284\pi\) | ||||
−0.351369 | + | 0.936237i | \(0.614284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.6509 | 0.647117 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.8580 | 0.702760 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.82066 | 0.274694 | 0.137347 | − | 0.990523i | \(-0.456143\pi\) | ||||
0.137347 | + | 0.990523i | \(0.456143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.158540 | 0.00746534 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.0088 | −0.799143 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.3233 | −0.859009 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.45912 | 0.348923 | 0.174461 | − | 0.984664i | \(-0.444182\pi\) | ||||
0.174461 | + | 0.984664i | \(0.444182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.75718 | 0.175370 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.0021 | 1.44391 | 0.721957 | − | 0.691938i | \(-0.243243\pi\) | ||||
0.721957 | + | 0.691938i | \(0.243243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.65186 | 0.216190 | 0.108095 | − | 0.994141i | \(-0.465525\pi\) | ||||
0.108095 | + | 0.994141i | \(0.465525\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.70464 | 0.0790506 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.1669 | −0.701842 | −0.350921 | − | 0.936405i | \(-0.614131\pi\) | ||||
−0.350921 | + | 0.936405i | \(0.614131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.98125 | −0.230013 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.2288 | 0.932096 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.86585 | 0.0857917 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.26723 | −0.149911 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.2894 | 0.928990 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.1452 | −0.554930 | −0.277465 | − | 0.960736i | \(-0.589494\pi\) | ||||
−0.277465 | + | 0.960736i | \(0.589494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −50.4722 | −2.30133 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.25541 | 0.0571230 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0165 | 0.454828 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.1953 | −0.733880 | −0.366940 | − | 0.930245i | \(-0.619595\pi\) | ||||
−0.366940 | + | 0.930245i | \(0.619595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.06880 | −0.274441 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.3465 | −1.23413 | −0.617064 | − | 0.786913i | \(-0.711678\pi\) | ||||
−0.617064 | + | 0.786913i | \(0.711678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.99060 | −0.269803 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.609153 | −0.0273794 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.7873 | −1.06701 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.743094 | −0.0332655 | −0.0166327 | − | 0.999862i | \(-0.505295\pi\) | ||||
−0.0166327 | + | 0.999862i | \(0.505295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.15171 | 0.319515 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.5285 | 1.22743 | 0.613717 | − | 0.789526i | \(-0.289674\pi\) | ||||
0.613717 | + | 0.789526i | \(0.289674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.7280 | −0.521889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.5882 | −0.958765 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.9392 | 1.37136 | 0.685678 | − | 0.727905i | \(-0.259506\pi\) | ||||
0.685678 | + | 0.727905i | \(0.259506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4613 | −0.639731 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.69823 | 0.207432 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.3722 | −0.721445 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.05067 | −0.0901882 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3879 | 0.455980 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5475 | 0.724961 | 0.362481 | − | 0.931991i | \(-0.381930\pi\) | ||||
0.362481 | + | 0.931991i | \(0.381930\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.6976 | 1.12368 | 0.561838 | − | 0.827247i | \(-0.310095\pi\) | ||||
0.561838 | + | 0.827247i | \(0.310095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.80630 | −0.297051 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.14093 | −0.0496998 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6368 | −0.984210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.9719 | −0.996896 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.52165 | 0.195855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.39173 | −0.233105 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.87432 | 0.124036 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.368420 | −0.0158690 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.0660 | 1.55060 | 0.775298 | − | 0.631595i | \(-0.217600\pi\) | ||||
0.775298 | + | 0.631595i | \(0.217600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4147 | 0.575678 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.17670 | −0.350251 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.8682 | −0.892260 | −0.446130 | − | 0.894968i | \(-0.647198\pi\) | ||||
−0.446130 | + | 0.894968i | \(0.647198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.73160 | −0.415334 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.49105 | −0.319129 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.29510 | 0.0975977 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.94310 | 0.422061 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.68520 | 0.0714043 | 0.0357021 | − | 0.999362i | \(-0.488633\pi\) | ||||
0.0357021 | + | 0.999362i | \(0.488633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.2152 | 2.25076 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.154357 | −0.00651698 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.2814 | −0.939049 | −0.469524 | − | 0.882920i | \(-0.655575\pi\) | ||||
−0.469524 | + | 0.882920i | \(0.655575\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.5734 | −0.613107 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.19597 | −0.218210 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6477 | 0.781753 | 0.390877 | − | 0.920443i | \(-0.372172\pi\) | ||||
0.390877 | + | 0.920443i | \(0.372172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1853 | 1.13767 | 0.568835 | − | 0.822452i | \(-0.307394\pi\) | ||||
0.568835 | + | 0.822452i | \(0.307394\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.99426 | 0.208638 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.96894 | −0.0821105 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9785 | 1.41454 | 0.707272 | − | 0.706941i | \(-0.249925\pi\) | ||||
0.707272 | + | 0.706941i | \(0.249925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.8417 | −0.575241 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.4487 | −0.765380 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.98269 | −0.0821148 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.3734 | −0.718303 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.5660 | 1.50924 | 0.754620 | − | 0.656163i | \(-0.227821\pi\) | ||||
0.754620 | + | 0.656163i | \(0.227821\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.42670 | −0.0587860 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.85557 | −0.117462 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.9967 | 1.60140 | 0.800701 | − | 0.599064i | \(-0.204461\pi\) | ||||
0.800701 | + | 0.599064i | \(0.204461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.41602 | −0.0990473 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2630 | 0.583746 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.2090 | 0.621422 | 0.310711 | − | 0.950504i | \(-0.399433\pi\) | ||||
0.310711 | + | 0.950504i | \(0.399433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.28586 | −0.174824 | −0.0874119 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874119 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.72304 | −0.192337 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.4203 | −0.586269 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.48618 | −0.303855 | −0.151927 | − | 0.988392i | \(-0.548548\pi\) | ||||
−0.151927 | + | 0.988392i | \(0.548548\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.6054 | −0.632361 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.4863 | −2.36610 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1938 | 0.573281 | 0.286640 | − | 0.958038i | \(-0.407461\pi\) | ||||
0.286640 | + | 0.958038i | \(0.407461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.890773 | −0.0359194 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.2773 | −0.655298 | −0.327649 | − | 0.944800i | \(-0.606256\pi\) | ||||
−0.327649 | + | 0.944800i | \(0.606256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3928 | 0.699075 | 0.349538 | − | 0.936922i | \(-0.386339\pi\) | ||||
0.349538 | + | 0.936922i | \(0.386339\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.83131 | 0.113617 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.8009 | −0.953565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.01091 | 0.0804365 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.193019 | −0.00770843 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.65503 | −0.265353 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.1128 | −0.721060 | −0.360530 | − | 0.932748i | \(-0.617404\pi\) | ||||
−0.360530 | + | 0.932748i | \(0.617404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.81972 | −0.271059 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.6840 | 0.622401 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.5076 | −0.416326 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.5542 | −0.892231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.6608 | −1.44801 | −0.724007 | − | 0.689793i | \(-0.757702\pi\) | ||||
−0.724007 | + | 0.689793i | \(0.757702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.4423 | 1.63432 | 0.817162 | − | 0.576408i | \(-0.195546\pi\) | ||||
0.817162 | + | 0.576408i | \(0.195546\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4835 | −0.412786 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.39252 | 0.251316 | 0.125658 | − | 0.992074i | \(-0.459896\pi\) | ||||
0.125658 | + | 0.992074i | \(0.459896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.24483 | 0.0881171 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.97210 | −0.116486 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.1607 | −1.68901 | −0.844504 | − | 0.535549i | \(-0.820105\pi\) | ||||
−0.844504 | + | 0.535549i | \(0.820105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.59510 | −0.140472 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.7117 | −0.534943 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.63245 | 0.297318 | 0.148659 | − | 0.988889i | \(-0.452504\pi\) | ||||
0.148659 | + | 0.988889i | \(0.452504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.4839 | 0.680046 | 0.340023 | − | 0.940417i | \(-0.389565\pi\) | ||||
0.340023 | + | 0.940417i | \(0.389565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.40238 | −0.170974 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.02116 | −0.117155 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.51436 | −0.174797 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.21001 | 0.240093 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.950976 | 0.0367120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.76960 | −0.183855 | −0.0919273 | − | 0.995766i | \(-0.529303\pi\) | ||||
−0.0919273 | + | 0.995766i | \(0.529303\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.3502 | −0.590829 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.3659 | −1.43609 | −0.718044 | − | 0.695997i | \(-0.754962\pi\) | ||||
−0.718044 | + | 0.695997i | \(0.754962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.4642 | −0.670216 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.1722 | 1.00292 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.07054 | −0.0409630 | −0.0204815 | − | 0.999790i | \(-0.506520\pi\) | ||||
−0.0204815 | + | 0.999790i | \(0.506520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.1518 | −1.07563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.6657 | 0.788447 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −56.5477 | −2.15430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.0167153 | −0.000635881 0 | −0.000317941 | − | 1.00000i | \(-0.500101\pi\) | ||||
−0.000317941 | 1.00000i | \(0.500101\pi\) | ||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.06208 | 0.0403451 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.76074 | −0.256450 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.596204 | 0.0225828 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.72727 | −0.254449 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.76635 | −0.255562 | −0.127781 | − | 0.991802i | \(-0.540785\pi\) | ||||
−0.127781 | + | 0.991802i | \(0.540785\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.32189 | −0.313866 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.5219 | 0.433940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.4482 | 0.769035 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9997 | −0.563326 | −0.281663 | − | 0.959513i | \(-0.590886\pi\) | ||||
−0.281663 | + | 0.959513i | \(0.590886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.17613 | 0.0816113 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.859776 | −0.0321989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.69774 | 0.0634919 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.22953 | 0.307338 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.53208 | −0.0944306 | −0.0472153 | − | 0.998885i | \(-0.515035\pi\) | ||||
−0.0472153 | + | 0.998885i | \(0.515035\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.5455 | 1.06309 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.806905 | −0.0300091 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.4750 | 0.908977 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6961 | 0.693400 | 0.346700 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346700 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.86674 | 0.291361 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.01670 | 0.259522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.5545 | −1.64566 | −0.822829 | − | 0.568289i | \(-0.807606\pi\) | ||||
−0.822829 | + | 0.568289i | \(0.807606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.07001 | 0.0763536 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.461538 | 0.0170010 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.5839 | 1.01469 | 0.507346 | − | 0.861743i | \(-0.330627\pi\) | ||||
0.507346 | + | 0.861743i | \(0.330627\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.50502 | −0.202232 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1685 | −0.849971 | −0.424985 | − | 0.905200i | \(-0.639721\pi\) | ||||
−0.424985 | + | 0.905200i | \(0.639721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.5478 | −0.789449 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.4923 | −0.640011 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.40069 | 0.343494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.1753 | −1.28357 | −0.641783 | − | 0.766887i | \(-0.721805\pi\) | ||||
−0.641783 | + | 0.766887i | \(0.721805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.08052 | −0.294471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.6669 | 0.897721 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.2779 | −1.20950 | −0.604752 | − | 0.796414i | \(-0.706728\pi\) | ||||
−0.604752 | + | 0.796414i | \(0.706728\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.116320 | −0.00422214 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3808 | 0.412553 | 0.206277 | − | 0.978494i | \(-0.433865\pi\) | ||||
0.206277 | + | 0.978494i | \(0.433865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2564 | 0.516116 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.29078 | −0.0828234 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 64.0239 | 2.31177 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9211 | −1.04292 | −0.521461 | − | 0.853275i | \(-0.674613\pi\) | ||||
−0.521461 | + | 0.853275i | \(0.674613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.01906 | 0.252785 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.0244 | −1.61941 | −0.809707 | − | 0.586834i | \(-0.800374\pi\) | ||||
−0.809707 | + | 0.586834i | \(0.800374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.66134 | 0.167440 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.3362 | −0.621932 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.745533 | 0.0267115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.20401 | 0.0788657 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.1947 | −1.25776 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.3368 | −1.04707 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0180664 | 0.000643996 0 | 0.000321998 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000321998 | 1.00000i | \(0.499898\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.8215 | −0.420858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.4093 | 0.903450 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.1225 | 0.963147 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.1400 | 0.395095 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.4973 | −0.974005 | −0.487002 | − | 0.873401i | \(-0.661910\pi\) | ||||
−0.487002 | + | 0.873401i | \(0.661910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.71174 | −0.272822 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.5672 | −0.797371 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.33991 | 0.0472844 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.82065 | −0.0641695 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.21819 | −0.289294 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.2070 | 1.30813 | 0.654065 | − | 0.756439i | \(-0.273062\pi\) | ||||
0.654065 | + | 0.756439i | \(0.273062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6138 | 0.583390 | 0.291695 | − | 0.956511i | \(-0.405781\pi\) | ||||
0.291695 | + | 0.956511i | \(0.405781\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.8620 | 0.556305 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.80126 | 0.308295 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.77416 | 0.306969 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.2913 | 1.05846 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.4193 | 0.956941 | 0.478470 | − | 0.878104i | \(-0.341191\pi\) | ||||
0.478470 | + | 0.878104i | \(0.341191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.3656 | −0.675043 | −0.337522 | − | 0.941318i | \(-0.609589\pi\) | ||||
−0.337522 | + | 0.941318i | \(0.609589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.630637 | 0.0219559 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.8321 | 1.59374 | 0.796869 | − | 0.604152i | \(-0.206488\pi\) | ||||
0.796869 | + | 0.604152i | \(0.206488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.4776 | 0.433366 | 0.216683 | − | 0.976242i | \(-0.430476\pi\) | ||||
0.216683 | + | 0.976242i | \(0.430476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.5506 | −0.539443 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.38548 | −0.0480041 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.3717 | −0.358929 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.70295 | −0.231688 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.7591 | 0.716684 | 0.358342 | − | 0.933590i | \(-0.383342\pi\) | ||||
0.358342 | + | 0.933590i | \(0.383342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1158 | 0.935028 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.34905 | 0.218673 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.3082 | 1.07703 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.1424 | 0.863901 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.2062 | 0.487556 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.01505 | −0.171914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.7925 | 0.574964 | 0.287482 | − | 0.957786i | \(-0.407182\pi\) | ||||
0.287482 | + | 0.957786i | \(0.407182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.86455 | −0.0979654 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.3214 | 0.933283 | 0.466641 | − | 0.884447i | \(-0.345464\pi\) | ||||
0.466641 | + | 0.884447i | \(0.345464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.6749 | −1.18309 | −0.591546 | − | 0.806271i | \(-0.701482\pi\) | ||||
−0.591546 | + | 0.806271i | \(0.701482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.55310 | 0.0529294 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.12687 | 0.242602 | 0.121301 | − | 0.992616i | \(-0.461293\pi\) | ||||
0.121301 | + | 0.992616i | \(0.461293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0651 | −0.512227 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.8500 | 0.504331 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.212653 | −0.00721374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1634 | 0.446023 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.5589 | −0.560435 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.9766 | 0.844363 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.43655 | 0.0485087 | 0.0242544 | − | 0.999706i | \(-0.492279\pi\) | ||||
0.0242544 | + | 0.999706i | \(0.492279\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.709910 | −0.0239447 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1294 | 0.644486 | 0.322243 | − | 0.946657i | \(-0.395563\pi\) | ||||
0.322243 | + | 0.946657i | \(0.395563\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.2884 | 0.649107 | 0.324554 | − | 0.945867i | \(-0.394786\pi\) | ||||
0.324554 | + | 0.945867i | \(0.394786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.6128 | −0.423975 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.9315 | 1.13931 | 0.569654 | − | 0.821884i | \(-0.307077\pi\) | ||||
0.569654 | + | 0.821884i | \(0.307077\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.3457 | −0.917144 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.481432 | 0.0161286 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.64327 | −0.322700 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.16848 | −0.139337 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.31751 | −0.110769 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6875 | 0.356447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.45612 | −0.248399 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.2783 | 0.608265 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.4546 | −0.646692 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.81028 | −0.192927 | −0.0964636 | − | 0.995337i | \(-0.530753\pi\) | ||||
−0.0964636 | + | 0.995337i | \(0.530753\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.3882 | 0.643067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.2030 | −1.63017 | −0.815084 | − | 0.579342i | \(-0.803309\pi\) | ||||
−0.815084 | + | 0.579342i | \(0.803309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.70936 | 0.0565716 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.34317 | −0.176640 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.26820 | 0.206994 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.8208 | 0.521878 | 0.260939 | − | 0.965355i | \(-0.415968\pi\) | ||||
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.1525 | 0.960609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.8598 | 2.06906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.1895 | 0.893985 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27.0658 | 0.888958 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1185 | 1.02096 | 0.510482 | − | 0.859888i | \(-0.329467\pi\) | ||||
0.510482 | + | 0.859888i | \(0.329467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.73250 | −0.0567804 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3345 | −0.403813 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.223856 | 0.00732088 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.1811 | 0.920638 | 0.460319 | − | 0.887754i | \(-0.347735\pi\) | ||||
0.460319 | + | 0.887754i | \(0.347735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.1196 | 0.982916 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.1766 | −1.60311 | −0.801555 | − | 0.597920i | \(-0.795994\pi\) | ||||
−0.801555 | + | 0.597920i | \(0.795994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.449283 | 0.0146307 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.1941 | −0.461734 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.5513 | −1.48022 | −0.740109 | − | 0.672487i | \(-0.765226\pi\) | ||||
−0.740109 | + | 0.672487i | \(0.765226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.2151 | 1.24052 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.45909 | −0.0473144 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.4307 | −1.47165 | −0.735823 | − | 0.677174i | \(-0.763204\pi\) | ||||
−0.735823 | + | 0.677174i | \(0.763204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.24291 | −0.234375 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.44591 | 0.0467397 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.0838 | 1.58500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9645 | −0.934340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.91338 | 0.287230 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.0739 | 0.646200 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0778 | −0.420555 | −0.210277 | − | 0.977642i | \(-0.567437\pi\) | ||||
−0.210277 | + | 0.977642i | \(0.567437\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.725867 | −0.0233182 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.1513 | −0.646687 | −0.323344 | − | 0.946282i | \(-0.604807\pi\) | ||||
−0.323344 | + | 0.946282i | \(0.604807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7876 | 0.377894 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.9862 | 0.576018 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.8525 | −0.667131 | −0.333565 | − | 0.942727i | \(-0.608252\pi\) | ||||
−0.333565 | + | 0.942727i | \(0.608252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.20527 | 0.0704809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.5174 | 0.431577 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.3109 | 0.998664 | 0.499332 | − | 0.866411i | \(-0.333579\pi\) | ||||
0.499332 | + | 0.866411i | \(0.333579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.14128 | 0.131952 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.0889 | −0.639436 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.28760 | 0.168136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.7897 | −0.660407 | −0.330204 | − | 0.943910i | \(-0.607117\pi\) | ||||
−0.330204 | + | 0.943910i | \(0.607117\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.6120 | 0.495431 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.6849 | −0.655755 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.4444 | 1.66093 | 0.830465 | − | 0.557070i | \(-0.188075\pi\) | ||||
0.830465 | + | 0.557070i | \(0.188075\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.0981 | −1.23701 |
(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 | 6004.2.a.g.1.11 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.11 | ✓ | 27 | 1.1 | even | 1 | trivial |