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 | 1.10 | ||
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 | ||||||||
\(3\) | −1.57318 | −0.908277 | −0.454138 | − | 0.890931i | \(-0.650053\pi\) | ||||
−0.454138 | + | 0.890931i | \(0.650053\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.10446 | −1.83557 | −0.917785 | − | 0.397078i | \(-0.870024\pi\) | ||||
−0.917785 | + | 0.397078i | \(0.870024\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.99696 | −1.51071 | −0.755354 | − | 0.655317i | \(-0.772535\pi\) | ||||
−0.755354 | + | 0.655317i | \(0.772535\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.525101 | −0.175034 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59278 | −1.68629 | −0.843144 | − | 0.537689i | \(-0.819298\pi\) | ||||
−0.843144 | + | 0.537689i | \(0.819298\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.327083 | 0.0907165 | 0.0453583 | − | 0.998971i | \(-0.485557\pi\) | ||||
0.0453583 | + | 0.998971i | \(0.485557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.45706 | 1.66720 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.21729 | 0.295237 | 0.147618 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147618 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.28794 | 1.37214 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.458737 | 0.0956534 | 0.0478267 | − | 0.998856i | \(-0.484770\pi\) | ||||
0.0478267 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.8466 | 2.36931 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.54562 | 1.06726 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.71079 | −0.503381 | −0.251691 | − | 0.967808i | \(-0.580987\pi\) | ||||
−0.251691 | + | 0.967808i | \(0.580987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.456065 | 0.0819117 | 0.0409559 | − | 0.999161i | \(-0.486960\pi\) | ||||
0.0409559 | + | 0.999161i | \(0.486960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.79846 | 1.53162 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.4053 | 2.77301 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0670418 | 0.0110216 | 0.00551080 | − | 0.999985i | \(-0.498246\pi\) | ||||
0.00551080 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.514561 | −0.0823957 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.54655 | −0.241531 | −0.120766 | − | 0.992681i | \(-0.538535\pi\) | ||||
−0.120766 | + | 0.992681i | \(0.538535\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.95138 | 1.36507 | 0.682536 | − | 0.730852i | \(-0.260877\pi\) | ||||
0.682536 | + | 0.730852i | \(0.260877\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.15525 | 0.321286 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.548674 | −0.0800323 | −0.0400162 | − | 0.999199i | \(-0.512741\pi\) | ||||
−0.0400162 | + | 0.999199i | \(0.512741\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.97566 | 1.28224 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.91502 | −0.268157 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.96699 | −0.819629 | −0.409815 | − | 0.912169i | \(-0.634407\pi\) | ||||
−0.409815 | + | 0.912169i | \(0.634407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.9553 | 3.09530 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.57318 | −0.208373 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.29820 | 0.559578 | 0.279789 | − | 0.960062i | \(-0.409736\pi\) | ||||
0.279789 | + | 0.960062i | \(0.409736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.43055 | 0.183163 | 0.0915815 | − | 0.995798i | \(-0.470808\pi\) | ||||
0.0915815 | + | 0.995798i | \(0.470808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.09880 | 0.264425 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.34250 | −0.166516 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.85776 | 0.349131 | 0.174565 | − | 0.984646i | \(-0.444148\pi\) | ||||
0.174565 | + | 0.984646i | \(0.444148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.721677 | −0.0868797 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.48446 | 0.650886 | 0.325443 | − | 0.945562i | \(-0.394487\pi\) | ||||
0.325443 | + | 0.945562i | \(0.394487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.0364 | −1.87691 | −0.938457 | − | 0.345395i | \(-0.887745\pi\) | ||||
−0.938457 | + | 0.345395i | \(0.887745\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.6368 | −2.15199 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.3541 | 2.54749 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.14897 | −0.794330 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.71197 | 0.407442 | 0.203721 | − | 0.979029i | \(-0.434696\pi\) | ||||
0.203721 | + | 0.979029i | \(0.434696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.99633 | −0.541928 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.26457 | 0.457209 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.84532 | −0.407603 | −0.203801 | − | 0.979012i | \(-0.565330\pi\) | ||||
−0.203801 | + | 0.979012i | \(0.565330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.30734 | −0.137046 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.717473 | −0.0743985 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.10446 | −0.421108 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.85022 | −0.695535 | −0.347767 | − | 0.937581i | \(-0.613060\pi\) | ||||
−0.347767 | + | 0.937581i | \(0.613060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.93677 | 0.295157 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.15331 | 0.114759 | 0.0573795 | − | 0.998352i | \(-0.481725\pi\) | ||||
0.0573795 | + | 0.998352i | \(0.481725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.32912 | 0.328028 | 0.164014 | − | 0.986458i | \(-0.447556\pi\) | ||||
0.164014 | + | 0.986458i | \(0.447556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.8086 | −2.51866 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.16106 | 0.498938 | 0.249469 | − | 0.968383i | \(-0.419744\pi\) | ||||
0.249469 | + | 0.968383i | \(0.419744\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.0741 | 1.92275 | 0.961374 | − | 0.275246i | \(-0.0887593\pi\) | ||||
0.961374 | + | 0.275246i | \(0.0887593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.105469 | −0.0100107 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5486 | −1.27454 | −0.637271 | − | 0.770639i | \(-0.719937\pi\) | ||||
−0.637271 | + | 0.770639i | \(0.719937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.88287 | −0.175578 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.171752 | −0.0158784 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.86547 | −0.446017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.2792 | 1.84356 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.43301 | 0.219377 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −28.1015 | −2.51347 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.08976 | −0.540379 | −0.270190 | − | 0.962807i | \(-0.587086\pi\) | ||||
−0.270190 | + | 0.962807i | \(0.587086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.0821 | −1.23986 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.53677 | −0.309009 | −0.154505 | − | 0.987992i | \(-0.549378\pi\) | ||||
−0.154505 | + | 0.987992i | \(0.549378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.99696 | −0.346580 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.7618 | −1.95902 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4890 | −0.981568 | −0.490784 | − | 0.871281i | \(-0.663290\pi\) | ||||
−0.490784 | + | 0.871281i | \(0.663290\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3300 | 1.30027 | 0.650136 | − | 0.759818i | \(-0.274712\pi\) | ||||
0.650136 | + | 0.759818i | \(0.274712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.863164 | 0.0726915 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.82930 | −0.152974 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.1263 | 0.923991 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.1203 | −1.16463 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.3751 | −0.931886 | −0.465943 | − | 0.884815i | \(-0.654285\pi\) | ||||
−0.465943 | + | 0.884815i | \(0.654285\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.817869 | −0.0665572 | −0.0332786 | − | 0.999446i | \(-0.510595\pi\) | ||||
−0.0332786 | + | 0.999446i | \(0.510595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.639201 | −0.0516764 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.87190 | −0.150355 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.21581 | 0.416267 | 0.208134 | − | 0.978100i | \(-0.433261\pi\) | ||||
0.208134 | + | 0.978100i | \(0.433261\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.38716 | 0.744450 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.83355 | −0.144504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.59696 | 0.125083 | 0.0625416 | − | 0.998042i | \(-0.480079\pi\) | ||||
0.0625416 | + | 0.998042i | \(0.480079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −36.1129 | −2.81139 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.60733 | −0.743437 | −0.371719 | − | 0.928345i | \(-0.621231\pi\) | ||||
−0.371719 | + | 0.928345i | \(0.621231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8930 | −0.991771 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.525101 | −0.0401555 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.33646 | 0.709838 | 0.354919 | − | 0.934897i | \(-0.384508\pi\) | ||||
0.354919 | + | 0.934897i | \(0.384508\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −47.3502 | −3.57934 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.76185 | −0.508252 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.2905 | 1.74081 | 0.870405 | − | 0.492336i | \(-0.163857\pi\) | ||||
0.870405 | + | 0.492336i | \(0.163857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.48778 | 0.705221 | 0.352611 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352611 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.25051 | −0.166363 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.275170 | −0.0202309 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.80805 | −0.497854 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.1656 | −1.61231 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.1823 | −0.953840 | −0.476920 | − | 0.878947i | \(-0.658247\pi\) | ||||
−0.476920 | + | 0.878947i | \(0.658247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.75206 | 0.126116 | 0.0630579 | − | 0.998010i | \(-0.479915\pi\) | ||||
0.0630579 | + | 0.998010i | \(0.479915\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.11199 | 0.151243 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1443 | 1.22148 | 0.610740 | − | 0.791831i | \(-0.290872\pi\) | ||||
0.610740 | + | 0.791831i | \(0.290872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.4873 | −1.52320 | −0.761598 | − | 0.648050i | \(-0.775585\pi\) | ||||
−0.761598 | + | 0.648050i | \(0.775585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.49577 | −0.317107 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.8349 | 0.760462 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.34776 | 0.443347 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.240883 | −0.0167425 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.59278 | −0.386861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9611 | 1.37418 | 0.687091 | − | 0.726572i | \(-0.258888\pi\) | ||||
0.687091 | + | 0.726572i | \(0.258888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.62805 | −0.591185 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −36.7405 | −2.50568 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.82287 | −0.123745 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.2281 | 1.70476 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.398156 | 0.0267828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.61741 | 0.577064 | 0.288532 | − | 0.957470i | \(-0.406833\pi\) | ||||
0.288532 | + | 0.957470i | \(0.406833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.22064 | −0.414710 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7063 | 0.976089 | 0.488044 | − | 0.872819i | \(-0.337710\pi\) | ||||
0.488044 | + | 0.872819i | \(0.337710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8146 | −0.846810 | −0.423405 | − | 0.905941i | \(-0.639165\pi\) | ||||
−0.423405 | + | 0.905941i | \(0.639165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35.1671 | −2.31382 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.57316 | −0.168574 | −0.0842868 | − | 0.996442i | \(-0.526861\pi\) | ||||
−0.0842868 | + | 0.996442i | \(0.526861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.25201 | 0.146905 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.57318 | 0.102189 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.55062 | 0.164986 | 0.0824930 | − | 0.996592i | \(-0.473712\pi\) | ||||
0.0824930 | + | 0.996592i | \(0.473712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.1862 | 1.30031 | 0.650154 | − | 0.759803i | \(-0.274704\pi\) | ||||
0.650154 | + | 0.759803i | \(0.274704\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.39025 | −0.345784 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −36.8402 | −2.35364 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.327083 | 0.0208118 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.83961 | −0.370070 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.67050 | −0.547277 | −0.273639 | − | 0.961833i | \(-0.588227\pi\) | ||||
−0.273639 | + | 0.961833i | \(0.588227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.56562 | −0.161299 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.86013 | 0.492220 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.1081 | 1.75334 | 0.876669 | − | 0.481095i | \(-0.159761\pi\) | ||||
0.876669 | + | 0.481095i | \(0.159761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.267963 | −0.0166504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.42344 | 0.0881086 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.2321 | −0.630936 | −0.315468 | − | 0.948936i | \(-0.602162\pi\) | ||||
−0.315468 | + | 0.948936i | \(0.602162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.4913 | 1.50449 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.04938 | 0.370216 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.04045 | −0.307322 | −0.153661 | − | 0.988124i | \(-0.549106\pi\) | ||||
−0.153661 | + | 0.988124i | \(0.549106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6297 | 0.645710 | 0.322855 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322855 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.05668 | 0.124476 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −66.2553 | −3.99535 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.79054 | −0.227751 | −0.113876 | − | 0.993495i | \(-0.536327\pi\) | ||||
−0.113876 | + | 0.993495i | \(0.536327\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.239480 | −0.0143373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5635 | 1.34602 | 0.673012 | − | 0.739632i | \(-0.265000\pi\) | ||||
0.673012 | + | 0.739632i | \(0.265000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.59292 | −0.332465 | −0.166232 | − | 0.986087i | \(-0.553160\pi\) | ||||
−0.166232 | + | 0.986087i | \(0.553160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.45706 | 0.382483 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.18151 | 0.364883 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5182 | −0.912835 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.7766 | 0.631738 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.38464 | −0.372994 | −0.186497 | − | 0.982455i | \(-0.559714\pi\) | ||||
−0.186497 | + | 0.982455i | \(0.559714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.6418 | −1.02714 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −31.0155 | −1.79970 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.150045 | 0.00867734 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.7783 | −2.06222 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.81437 | −0.104233 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.87162 | −0.336208 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3165 | 0.702938 | 0.351469 | − | 0.936200i | \(-0.385682\pi\) | ||||
0.351469 | + | 0.936200i | \(0.385682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.23731 | −0.297940 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.26184 | 0.468486 | 0.234243 | − | 0.972178i | \(-0.424739\pi\) | ||||
0.234243 | + | 0.972178i | \(0.424739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8083 | 1.34573 | 0.672863 | − | 0.739767i | \(-0.265064\pi\) | ||||
0.672863 | + | 0.739767i | \(0.265064\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.61446 | −0.485370 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.3381 | −1.36696 | −0.683482 | − | 0.729968i | \(-0.739535\pi\) | ||||
−0.683482 | + | 0.729968i | \(0.739535\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.1609 | 0.848845 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.11928 | −0.453174 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.21729 | 0.0677320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.87481 | 0.214936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.5802 | −1.74639 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.19303 | 0.120905 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.3429 | 1.33801 | 0.669003 | − | 0.743260i | \(-0.266721\pi\) | ||||
0.669003 | + | 0.743260i | \(0.266721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0352037 | −0.00192915 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.7295 | −0.640854 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9317 | 0.704433 | 0.352217 | − | 0.935918i | \(-0.385428\pi\) | ||||
0.352217 | + | 0.935918i | \(0.385428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.3144 | 1.15764 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.55067 | −0.138127 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.89664 | −0.426379 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.96209 | 0.159474 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.39723 | 0.128690 | 0.0643449 | − | 0.997928i | \(-0.479504\pi\) | ||||
0.0643449 | + | 0.997928i | \(0.479504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.1153 | 1.29086 | 0.645432 | − | 0.763818i | \(-0.276678\pi\) | ||||
0.645432 | + | 0.763818i | \(0.276678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.81388 | 0.0968177 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.4944 | −1.19726 | −0.598628 | − | 0.801027i | \(-0.704287\pi\) | ||||
−0.598628 | + | 0.801027i | \(0.704287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.5107 | −1.19475 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.65426 | 0.405106 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.62800 | 0.297034 | 0.148517 | − | 0.988910i | \(-0.452550\pi\) | ||||
0.148517 | + | 0.988910i | \(0.452550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −31.9029 | −1.67447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 65.8206 | 3.44521 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1345 | −1.20761 | −0.603806 | − | 0.797131i | \(-0.706350\pi\) | ||||
−0.603806 | + | 0.797131i | \(0.706350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.812096 | 0.0422760 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.8498 | 1.23822 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4809 | 0.956905 | 0.478453 | − | 0.878113i | \(-0.341198\pi\) | ||||
0.478453 | + | 0.878113i | \(0.341198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 44.2087 | 2.28293 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.886654 | −0.0456650 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.6326 | −1.21392 | −0.606962 | − | 0.794731i | \(-0.707612\pi\) | ||||
−0.606962 | + | 0.794731i | \(0.707612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.58030 | 0.490814 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.7925 | 1.47123 | 0.735615 | − | 0.677400i | \(-0.236893\pi\) | ||||
0.735615 | + | 0.677400i | \(0.236893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −91.7515 | −4.67609 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.70037 | −0.238933 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.7952 | −1.40927 | −0.704635 | − | 0.709570i | \(-0.748889\pi\) | ||||
−0.704635 | + | 0.709570i | \(0.748889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.558418 | 0.0282404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.56399 | 0.280666 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.10446 | 0.206518 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.4482 | −1.57834 | −0.789169 | − | 0.614176i | \(-0.789489\pi\) | ||||
−0.789169 | + | 0.614176i | \(0.789489\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.28794 | 0.314791 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0651 | 0.602502 | 0.301251 | − | 0.953545i | \(-0.402596\pi\) | ||||
0.301251 | + | 0.953545i | \(0.402596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.149171 | 0.00743074 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.3426 | 1.45805 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.374950 | −0.0185856 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1415 | −0.550913 | −0.275457 | − | 0.961313i | \(-0.588829\pi\) | ||||
−0.275457 | + | 0.961313i | \(0.588829\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0742 | 0.891535 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.1797 | −0.845359 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.2356 | −0.747888 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.1168 | −1.18101 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.5351 | 1.88256 | 0.941281 | − | 0.337623i | \(-0.109623\pi\) | ||||
0.941281 | + | 0.337623i | \(0.109623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.6715 | −1.39737 | −0.698683 | − | 0.715432i | \(-0.746230\pi\) | ||||
−0.698683 | + | 0.715432i | \(0.746230\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.288109 | 0.0140083 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.4207 | 0.699509 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.71784 | −0.276706 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.87783 | 0.138943 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.4598 | −1.41903 | −0.709515 | − | 0.704690i | \(-0.751086\pi\) | ||||
−0.709515 | + | 0.704690i | \(0.751086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.1873 | 1.64294 | 0.821469 | − | 0.570253i | \(-0.193155\pi\) | ||||
0.821469 | + | 0.570253i | \(0.193155\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.5037 | −0.839240 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.458737 | 0.0219444 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.24743 | −0.250446 | −0.125223 | − | 0.992129i | \(-0.539965\pi\) | ||||
−0.125223 | + | 0.992129i | \(0.539965\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.71313 | −0.224435 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8133 | 0.703801 | 0.351901 | − | 0.936037i | \(-0.385536\pi\) | ||||
0.351901 | + | 0.936037i | \(0.385536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7829 | 0.748183 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.8951 | 0.846410 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0530 | 0.757589 | 0.378794 | − | 0.925481i | \(-0.376339\pi\) | ||||
0.378794 | + | 0.925481i | \(0.376339\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.64953 | 0.407291 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.28666 | 0.0604524 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.36591 | 0.251558 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.9869 | −0.560723 | −0.280362 | − | 0.959894i | \(-0.590454\pi\) | ||||
−0.280362 | + | 0.959894i | \(0.590454\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.75064 | 0.315093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.84746 | −0.412067 | −0.206034 | − | 0.978545i | \(-0.566056\pi\) | ||||
−0.206034 | + | 0.978545i | \(0.566056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4226 | 0.949121 | 0.474560 | − | 0.880223i | \(-0.342607\pi\) | ||||
0.474560 | + | 0.880223i | \(0.342607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.94484 | 0.136564 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.59247 | 0.0736907 | 0.0368454 | − | 0.999321i | \(-0.488269\pi\) | ||||
0.0368454 | + | 0.999321i | \(0.488269\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4223 | −0.527434 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.20542 | −0.378086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.0631 | −2.30190 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.8466 | 0.543558 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.13327 | 0.143463 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.82798 | 0.0835226 | 0.0417613 | − | 0.999128i | \(-0.486703\pi\) | ||||
0.0417613 | + | 0.999128i | \(0.486703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0219282 | 0.000999841 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.88451 | 0.131250 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.1165 | 1.27670 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.7337 | 0.486392 | 0.243196 | − | 0.969977i | \(-0.421804\pi\) | ||||
0.243196 | + | 0.969977i | \(0.421804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.51230 | −0.113610 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6342 | −0.660433 | −0.330217 | − | 0.943905i | \(-0.607122\pi\) | ||||
−0.330217 | + | 0.943905i | \(0.607122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.29983 | −0.148617 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0539 | −0.541781 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.9212 | −0.983299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.7058 | −1.37458 | −0.687289 | − | 0.726384i | \(-0.741199\pi\) | ||||
−0.687289 | + | 0.726384i | \(0.741199\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.1141 | 0.675247 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.1039 | 0.940975 | 0.470488 | − | 0.882407i | \(-0.344078\pi\) | ||||
0.470488 | + | 0.882407i | \(0.344078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.73373 | −0.210648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.2831 | 0.900802 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.3917 | −1.56871 | −0.784355 | − | 0.620313i | \(-0.787006\pi\) | ||||
−0.784355 | + | 0.620313i | \(0.787006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 64.0967 | 2.83547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.54562 | 0.244845 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.6642 | −0.602118 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.06861 | 0.134957 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.6879 | −0.644729 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.6559 | −1.64973 | −0.824867 | − | 0.565327i | \(-0.808750\pi\) | ||||
−0.824867 | + | 0.565327i | \(0.808750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.6908 | −0.642382 | −0.321191 | − | 0.947014i | \(-0.604083\pi\) | ||||
−0.321191 | + | 0.947014i | \(0.604083\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 74.4905 | 3.25103 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.555165 | 0.0241834 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7896 | −0.990850 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.25699 | −0.0979449 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.505851 | −0.0219108 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.1833 | −0.915836 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.6401 | −1.58114 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −50.1989 | −2.16222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.52639 | 0.151611 | 0.0758057 | − | 0.997123i | \(-0.475847\pi\) | ||||
0.0758057 | + | 0.997123i | \(0.475847\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.9260 | −0.640536 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −82.3932 | −3.52934 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.70442 | −0.0728757 | −0.0364379 | − | 0.999336i | \(-0.511601\pi\) | ||||
−0.0364379 | + | 0.999336i | \(0.511601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.751182 | −0.0320597 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.71079 | −0.115484 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.99696 | 0.169968 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.432893 | 0.0183753 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.10169 | 0.173794 | 0.0868971 | − | 0.996217i | \(-0.472305\pi\) | ||||
0.0868971 | + | 0.996217i | \(0.472305\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.92784 | 0.123835 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7103 | 0.452189 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.2141 | 1.31552 | 0.657758 | − | 0.753229i | \(-0.271505\pi\) | ||||
0.657758 | + | 0.753229i | \(0.271505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.6096 | 2.33951 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.5741 | 1.20000 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.8722 | −1.75537 | −0.877687 | − | 0.479234i | \(-0.840915\pi\) | ||||
−0.877687 | + | 0.479234i | \(0.840915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2242 | 0.427868 | 0.213934 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213934 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7382 | 0.866351 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.43447 | 0.226633 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.7283 | 1.07108 | 0.535542 | − | 0.844509i | \(-0.320107\pi\) | ||||
0.535542 | + | 0.844509i | \(0.320107\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.75630 | −0.114548 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.8366 | −0.615526 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.3721 | 1.38213 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.704947 | 0.0291460 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.5875 | −1.22121 | −0.610603 | − | 0.791937i | \(-0.709073\pi\) | ||||
−0.610603 | + | 0.791937i | \(0.709073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.456065 | 0.0187918 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.9711 | −1.10944 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.7882 | 1.05899 | 0.529497 | − | 0.848312i | \(-0.322381\pi\) | ||||
0.529497 | + | 0.848312i | \(0.322381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.9701 | 0.818694 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.8035 | 1.38348 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.29197 | −0.134506 | −0.0672532 | − | 0.997736i | \(-0.521424\pi\) | ||||
−0.0672532 | + | 0.997736i | \(0.521424\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.9851 | 1.63103 | 0.815514 | − | 0.578738i | \(-0.196454\pi\) | ||||
0.815514 | + | 0.578738i | \(0.196454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.50061 | −0.0611096 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −83.2351 | −3.38399 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.3498 | −0.825971 | −0.412986 | − | 0.910738i | \(-0.635514\pi\) | ||||
−0.412986 | + | 0.910738i | \(0.635514\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.0453 | −0.690710 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.179462 | −0.00726025 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.75369 | −0.393948 | −0.196974 | − | 0.980409i | \(-0.563111\pi\) | ||||
−0.196974 | + | 0.980409i | \(0.563111\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.98618 | −0.402682 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.5216 | 1.30927 | 0.654635 | − | 0.755945i | \(-0.272822\pi\) | ||||
0.654635 | + | 0.755945i | \(0.272822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.57754 | −0.143793 | −0.0718967 | − | 0.997412i | \(-0.522905\pi\) | ||||
−0.0718967 | + | 0.997412i | \(0.522905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.54398 | 0.102087 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3696 | 0.615769 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 56.1085 | 2.24434 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.79846 | 0.351377 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0816094 | 0.00325398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.08973 | −0.0831910 | −0.0415955 | − | 0.999135i | \(-0.513244\pi\) | ||||
−0.0415955 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.4025 | −1.24814 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.9952 | 0.991904 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.93579 | 0.116320 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.87990 | −0.113927 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.6336 | −1.88141 | −0.940706 | − | 0.339223i | \(-0.889836\pi\) | ||||
−0.940706 | + | 0.339223i | \(0.889836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.5481 | −0.810338 | −0.405169 | − | 0.914242i | \(-0.632787\pi\) | ||||
−0.405169 | + | 0.914242i | \(0.632787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 57.7995 | 2.27585 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.2271 | 1.50286 | 0.751431 | − | 0.659811i | \(-0.229364\pi\) | ||||
0.751431 | + | 0.659811i | \(0.229364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0389 | −0.943609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.86771 | 0.112394 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.5122 | 1.42883 | 0.714416 | − | 0.699721i | \(-0.246692\pi\) | ||||
0.714416 | + | 0.699721i | \(0.246692\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5165 | 0.567208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.42071 | 0.328523 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.1347 | 1.68029 | 0.840145 | − | 0.542362i | \(-0.182470\pi\) | ||||
0.840145 | + | 0.542362i | \(0.182470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.743732 | 0.0289278 | 0.0144639 | − | 0.999895i | \(-0.495396\pi\) | ||||
0.0144639 | + | 0.999895i | \(0.495396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.626371 | −0.0243262 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.4053 | 0.636172 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.24354 | −0.0481501 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.5567 | −0.524134 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00074 | −0.308865 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.5488 | 0.637908 | 0.318954 | − | 0.947770i | \(-0.396668\pi\) | ||||
0.318954 | + | 0.947770i | \(0.396668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 65.6966 | 2.52866 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.7688 | −0.875075 | −0.437538 | − | 0.899200i | \(-0.644149\pi\) | ||||
−0.437538 | + | 0.899200i | \(0.644149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.3800 | 1.05075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.1356 | −0.886559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.80440 | −0.0690434 | −0.0345217 | − | 0.999404i | \(-0.510991\pi\) | ||||
−0.0345217 | + | 0.999404i | \(0.510991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 47.1559 | 1.80174 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1596 | 0.769137 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.95170 | −0.0743539 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.8270 | −1.43901 | −0.719503 | − | 0.694490i | \(-0.755630\pi\) | ||||
−0.719503 | + | 0.694490i | \(0.755630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.7382 | −0.445896 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −62.9212 | −2.38674 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.88261 | −0.0713088 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.04805 | 0.153111 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.2393 | −0.802198 | −0.401099 | − | 0.916035i | \(-0.631372\pi\) | ||||
−0.401099 | + | 0.916035i | \(0.631372\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0670418 | 0.00252853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.54282 | −0.133430 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.60975 | −0.173367 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.0595 | −1.01624 | −0.508121 | − | 0.861286i | \(-0.669660\pi\) | ||||
−0.508121 | + | 0.861286i | \(0.669660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.525101 | 0.0196928 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.209214 | 0.00783513 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.50830 | 0.280794 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.01259 | −0.149853 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.1345 | −1.42218 | −0.711088 | − | 0.703103i | \(-0.751797\pi\) | ||||
−0.711088 | + | 0.703103i | \(0.751797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.3063 | −0.495554 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.7566 | −1.18104 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32.1136 | −1.19267 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.39871 | 0.348579 | 0.174289 | − | 0.984694i | \(-0.444237\pi\) | ||||
0.174289 | + | 0.984694i | \(0.444237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9267 | 1.10840 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8964 | 0.403019 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.07265 | −0.0765552 | −0.0382776 | − | 0.999267i | \(-0.512187\pi\) | ||||
−0.0382776 | + | 0.999267i | \(0.512187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 57.9564 | 2.13775 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.9828 | −0.588734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.6647 | 1.27516 | 0.637582 | − | 0.770383i | \(-0.279935\pi\) | ||||
0.637582 | + | 0.770383i | \(0.279935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.514561 | −0.0189029 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.2067 | −0.447819 | −0.223909 | − | 0.974610i | \(-0.571882\pi\) | ||||
−0.223909 | + | 0.974610i | \(0.571882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.6887 | 1.71054 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.94916 | −0.0713161 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.6285 | −0.753750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2478 | 1.03078 | 0.515389 | − | 0.856956i | \(-0.327647\pi\) | ||||
0.515389 | + | 0.856956i | \(0.327647\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.6403 | 0.497079 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.35691 | 0.122170 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.67098 | 0.133424 | 0.0667120 | − | 0.997772i | \(-0.478749\pi\) | ||||
0.0667120 | + | 0.997772i | \(0.478749\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.03618 | 0.146504 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.8374 | −1.11786 | −0.558928 | − | 0.829216i | \(-0.688787\pi\) | ||||
−0.558928 | + | 0.829216i | \(0.688787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −80.2352 | −2.90471 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.62357 | 0.0948555 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.40587 | 0.0507629 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3452 | 0.661547 | 0.330773 | − | 0.943710i | \(-0.392690\pi\) | ||||
0.330773 | + | 0.943710i | \(0.392690\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.2192 | −1.59252 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.3154 | 1.45005 | 0.725023 | − | 0.688725i | \(-0.241829\pi\) | ||||
0.725023 | + | 0.688725i | \(0.241829\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.40281 | 0.194075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.421554 | 0.0151232 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.54655 | −0.0554110 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.6734 | −1.09758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.0330 | −0.537236 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.4081 | −0.764087 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.00664 | 0.285406 | 0.142703 | − | 0.989766i | \(-0.454421\pi\) | ||||
0.142703 | + | 0.989766i | \(0.454421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0969 | 0.573065 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.1531 | 1.92546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.467908 | 0.0166159 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.5292 | −1.36649 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.5703 | 1.25996 | 0.629982 | − | 0.776610i | \(-0.283062\pi\) | ||||
0.629982 | + | 0.776610i | \(0.283062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.667897 | −0.0236285 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.01918 | 0.0713442 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 89.6879 | 3.16502 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.52574 | 0.265248 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.92955 | 0.279133 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.4000 | −0.682069 | −0.341034 | − | 0.940051i | \(-0.610777\pi\) | ||||
−0.341034 | + | 0.940051i | \(0.610777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.2890 | −0.852901 | −0.426450 | − | 0.904511i | \(-0.640236\pi\) | ||||
−0.426450 | + | 0.904511i | \(0.640236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.7225 | −0.586483 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.55464 | −0.229599 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.95138 | 0.313169 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.686483 | 0.0239877 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.547649 | 0.0191131 | 0.00955654 | − | 0.999954i | \(-0.496958\pi\) | ||||
0.00955654 | + | 0.999954i | \(0.496958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4942 | 0.888671 | 0.444336 | − | 0.895860i | \(-0.353440\pi\) | ||||
0.444336 | + | 0.895860i | \(0.353440\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 104.232 | 3.62888 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.8677 | −1.69930 | −0.849648 | − | 0.527351i | \(-0.823185\pi\) | ||||
−0.849648 | + | 0.527351i | \(0.823185\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.4309 | 1.33476 | 0.667380 | − | 0.744717i | \(-0.267416\pi\) | ||||
0.667380 | + | 0.744717i | \(0.267416\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.96320 | 0.206861 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.9260 | 0.378564 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.4329 | 1.36463 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.52916 | 0.0874207 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.9842 | 0.758980 | 0.379490 | − | 0.925196i | \(-0.376099\pi\) | ||||
0.379490 | + | 0.925196i | \(0.376099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6516 | −0.746607 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.4964 | −1.22256 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.9188 | 1.82046 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −81.0551 | −2.78509 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.79868 | 0.301970 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0307546 | 0.00105425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.0540 | −0.583919 | −0.291960 | − | 0.956431i | \(-0.594307\pi\) | ||||
−0.291960 | + | 0.956431i | \(0.594307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.15525 | 0.0737081 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.4244 | −0.766004 | −0.383002 | − | 0.923747i | \(-0.625110\pi\) | ||||
−0.383002 | + | 0.923747i | \(0.625110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.6310 | 0.669801 | 0.334900 | − | 0.942254i | \(-0.391297\pi\) | ||||
0.334900 | + | 0.942254i | \(0.391297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.72463 | −0.331414 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.1648 | −0.788538 | −0.394269 | − | 0.918995i | \(-0.629002\pi\) | ||||
−0.394269 | + | 0.918995i | \(0.629002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.3211 | −1.30296 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.4129 | 0.829107 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.59278 | 0.189722 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.934724 | 0.0316719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.59706 | 0.121742 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 112.320 | 3.79712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.9242 | −1.38191 | −0.690956 | − | 0.722897i | \(-0.742810\pi\) | ||||
−0.690956 | + | 0.722897i | \(0.742810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.0442 | 0.338782 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.6472 | −1.87480 | −0.937401 | − | 0.348253i | \(-0.886775\pi\) | ||||
−0.937401 | + | 0.348253i | \(0.886775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1100 | −0.373880 | −0.186940 | − | 0.982371i | \(-0.559857\pi\) | ||||
−0.186940 | + | 0.982371i | \(0.559857\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.7537 | 0.932931 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.3166 | 1.42085 | 0.710426 | − | 0.703772i | \(-0.248502\pi\) | ||||
0.710426 | + | 0.703772i | \(0.248502\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.3405 | 0.816355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.9826 | 1.33947 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.548674 | −0.0183607 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −95.5947 | −3.19538 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.236048 | −0.00788142 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.23630 | −0.0412328 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.26357 | −0.241985 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 56.2857 | 1.87307 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −38.9422 | −1.29448 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.7786 | 1.42044 | 0.710220 | − | 0.703980i | \(-0.248595\pi\) | ||||
0.710220 | + | 0.703980i | \(0.248595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.605606 | −0.0200867 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3474 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.7603 | −0.687064 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.23713 | 0.305370 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.1363 | 0.466823 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.5599 | −1.63483 | −0.817415 | − | 0.576049i | \(-0.804594\pi\) | ||||
−0.817415 | + | 0.576049i | \(0.804594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.3760 | −0.638462 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.79387 | 0.0590461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.794215 | 0.0261136 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.74812 | −0.0574159 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.6654 | −1.36700 | −0.683498 | − | 0.729952i | \(-0.739542\pi\) | ||||
−0.683498 | + | 0.729952i | \(0.739542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.97566 | 0.294165 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9974 | −0.425515 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.9434 | 0.913846 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6064 | −0.738518 | −0.369259 | − | 0.929326i | \(-0.620389\pi\) | ||||
−0.369259 | + | 0.929326i | \(0.620389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.4548 | −1.22229 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.4668 | 1.22138 | 0.610692 | − | 0.791868i | \(-0.290891\pi\) | ||||
0.610692 | + | 0.791868i | \(0.290891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.709462 | −0.0231033 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 90.9778 | 2.95951 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 58.3077 | 1.89474 | 0.947372 | − | 0.320135i | \(-0.103728\pi\) | ||||
0.947372 | + | 0.320135i | \(0.103728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.24522 | −0.170267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.2882 | 1.24158 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.4350 | 0.856312 | 0.428156 | − | 0.903705i | \(-0.359163\pi\) | ||||
0.428156 | + | 0.903705i | \(0.359163\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.1063 | 1.75084 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.8508 | −0.770986 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.9209 | 1.48286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7920 | −0.993290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.71007 | −0.0873309 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.19124 | −0.231494 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.9051 | 1.25111 | 0.625553 | − | 0.780182i | \(-0.284874\pi\) | ||||
0.625553 | + | 0.780182i | \(0.284874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.91502 | −0.0615194 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8772 | −0.862531 | −0.431266 | − | 0.902225i | \(-0.641933\pi\) | ||||
−0.431266 | + | 0.902225i | \(0.641933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −61.2732 | −1.96433 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.09578 | −0.195221 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.6472 | 0.468607 | 0.234303 | − | 0.972163i | \(-0.424719\pi\) | ||||
0.234303 | + | 0.972163i | \(0.424719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.5060 | 0.687335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5409 | −0.336545 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.5276 | −0.495255 | −0.247627 | − | 0.968855i | \(-0.579651\pi\) | ||||
−0.247627 | + | 0.968855i | \(0.579651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70.3680 | −2.24211 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.45003 | −0.109816 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.10633 | 0.130574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.8684 | −0.821738 | −0.410869 | − | 0.911694i | \(-0.634775\pi\) | ||||
−0.410869 | + | 0.911694i | \(0.634775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −38.2958 | −1.21528 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 88.1938 | 2.79593 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.1565 | 1.81017 | 0.905083 | − | 0.425235i | \(-0.139809\pi\) | ||||
0.905083 | + | 0.425235i | \(0.139809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.371788 | 0.0117629 |
(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.1.10 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.10 | ✓ | 27 | 1.1 | even | 1 | trivial |