Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,4,Mod(1,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.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: | \(47.2015280046\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.1 |
$q$-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 | ||||||||
\(3\) | −0.898979 | −0.173009 | −0.0865043 | − | 0.996251i | \(-0.527570\pi\) | ||||
−0.0865043 | + | 0.996251i | \(0.527570\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.4949 | 1.53858 | 0.769290 | − | 0.638900i | \(-0.220610\pi\) | ||||
0.769290 | + | 0.638900i | \(0.220610\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.1918 | −0.970068 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60612 | −0.0714342 | −0.0357171 | − | 0.999362i | \(-0.511372\pi\) | ||||
−0.0357171 | + | 0.999362i | \(0.511372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33.1918 | 0.708135 | 0.354068 | − | 0.935220i | \(-0.384798\pi\) | ||||
0.354068 | + | 0.935220i | \(0.384798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −119.576 | −1.70596 | −0.852980 | − | 0.521944i | \(-0.825207\pi\) | ||||
−0.852980 | + | 0.521944i | \(0.825207\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −143.192 | −1.72897 | −0.864486 | − | 0.502657i | \(-0.832356\pi\) | ||||
−0.864486 | + | 0.502657i | \(0.832356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −25.6163 | −0.266188 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 113.889 | 1.03250 | 0.516249 | − | 0.856439i | \(-0.327328\pi\) | ||||
0.516249 | + | 0.856439i | \(0.327328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 47.8184 | 0.340839 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −67.6163 | −0.432967 | −0.216483 | − | 0.976286i | \(-0.569459\pi\) | ||||
−0.216483 | + | 0.976286i | \(0.569459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −117.394 | −0.680147 | −0.340074 | − | 0.940399i | \(-0.610452\pi\) | ||||
−0.340074 | + | 0.940399i | \(0.610452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.34285 | 0.0123587 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 256.384 | 1.13917 | 0.569584 | − | 0.821933i | \(-0.307104\pi\) | ||||
0.569584 | + | 0.821933i | \(0.307104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −29.8388 | −0.122514 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 245.959 | 0.936887 | 0.468444 | − | 0.883493i | \(-0.344815\pi\) | ||||
0.468444 | + | 0.883493i | \(0.344815\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −369.262 | −1.30958 | −0.654790 | − | 0.755811i | \(-0.727243\pi\) | ||||
−0.654790 | + | 0.755811i | \(0.727243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −76.3133 | −0.236839 | −0.118420 | − | 0.992964i | \(-0.537783\pi\) | ||||
−0.118420 | + | 0.992964i | \(0.537783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 468.959 | 1.36723 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 107.496 | 0.295146 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −40.4245 | −0.104769 | −0.0523843 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523843 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 128.727 | 0.299127 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −457.980 | −1.01057 | −0.505287 | − | 0.862951i | \(-0.668613\pi\) | ||||
−0.505287 | + | 0.862951i | \(0.668613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −477.233 | −1.00169 | −0.500847 | − | 0.865536i | \(-0.666978\pi\) | ||||
−0.500847 | + | 0.865536i | \(0.666978\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −746.334 | −1.49253 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −602.252 | −1.09816 | −0.549081 | − | 0.835769i | \(-0.685022\pi\) | ||||
−0.549081 | + | 0.835769i | \(0.685022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −102.384 | −0.178631 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1091.98 | 1.82527 | 0.912633 | − | 0.408780i | \(-0.134046\pi\) | ||||
0.912633 | + | 0.408780i | \(0.134046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −117.878 | −0.188993 | −0.0944967 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944967 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −74.2612 | −0.109907 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −858.624 | −1.22282 | −0.611410 | − | 0.791314i | \(-0.709397\pi\) | ||||
−0.611410 | + | 0.791314i | \(0.709397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 664.192 | 0.911100 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −565.748 | −0.748180 | −0.374090 | − | 0.927392i | \(-0.622045\pi\) | ||||
−0.374090 | + | 0.927392i | \(0.622045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 60.7857 | 0.0749070 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −625.151 | −0.744560 | −0.372280 | − | 0.928120i | \(-0.621424\pi\) | ||||
−0.372280 | + | 0.928120i | \(0.621424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 945.798 | 1.08952 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 105.535 | 0.117671 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −805.959 | −0.843637 | −0.421818 | − | 0.906680i | \(-0.638608\pi\) | ||||
−0.421818 | + | 0.906680i | \(0.638608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 68.2591 | 0.0692960 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −260.988 | −0.257121 | −0.128561 | − | 0.991702i | \(-0.541036\pi\) | ||||
−0.128561 | + | 0.991702i | \(0.541036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1640.01 | −1.56888 | −0.784441 | − | 0.620203i | \(-0.787050\pi\) | ||||
−0.784441 | + | 0.620203i | \(0.787050\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 679.001 | 0.613472 | 0.306736 | − | 0.951795i | \(-0.400763\pi\) | ||||
0.306736 | + | 0.951795i | \(0.400763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −840.220 | −0.738335 | −0.369168 | − | 0.929363i | \(-0.620357\pi\) | ||||
−0.369168 | + | 0.929363i | \(0.620357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −230.484 | −0.197086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1609.15 | 1.33961 | 0.669806 | − | 0.742536i | \(-0.266377\pi\) | ||||
0.669806 | + | 0.742536i | \(0.266377\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −869.355 | −0.686939 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3407.29 | −2.62476 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1324.21 | −0.994897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −221.112 | −0.162090 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1149.60 | −0.803234 | −0.401617 | − | 0.915808i | \(-0.631552\pi\) | ||||
−0.401617 | + | 0.915808i | \(0.631552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 331.959 | 0.226569 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2436.99 | −1.62535 | −0.812673 | − | 0.582719i | \(-0.801989\pi\) | ||||
−0.812673 | + | 0.582719i | \(0.801989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4080.24 | −2.66016 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 764.465 | 0.476735 | 0.238367 | − | 0.971175i | \(-0.423388\pi\) | ||||
0.238367 | + | 0.971175i | \(0.423388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2547.35 | −1.55441 | −0.777207 | − | 0.629245i | \(-0.783364\pi\) | ||||
−0.777207 | + | 0.629245i | \(0.783364\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 68.6041 | 0.0409752 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −86.5020 | −0.0505850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −421.585 | −0.236542 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2565.76 | 1.41070 | 0.705352 | − | 0.708857i | \(-0.250789\pi\) | ||||
0.705352 | + | 0.708857i | \(0.250789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 524.949 | 0.282912 | 0.141456 | − | 0.989945i | \(-0.454822\pi\) | ||||
0.141456 | + | 0.989945i | \(0.454822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3131.90 | 1.65490 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3569.59 | 1.81455 | 0.907275 | − | 0.420537i | \(-0.138158\pi\) | ||||
0.907275 | + | 0.420537i | \(0.138158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 36.3408 | 0.0181259 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3245.25 | 1.58858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1450.96 | −0.697227 | −0.348613 | − | 0.937267i | \(-0.613347\pi\) | ||||
−0.348613 | + | 0.937267i | \(0.613347\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3281.38 | 1.52048 | 0.760242 | − | 0.649640i | \(-0.225080\pi\) | ||||
0.760242 | + | 0.649640i | \(0.225080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1095.30 | −0.498544 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3750.46 | 1.67722 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1387.01 | −0.609553 | −0.304776 | − | 0.952424i | \(-0.598582\pi\) | ||||
−0.304776 | + | 0.952424i | \(0.598582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 411.714 | 0.174838 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3009.90 | −1.25682 | −0.628409 | − | 0.777883i | \(-0.716293\pi\) | ||||
−0.628409 | + | 0.777883i | \(0.716293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2304.14 | −0.946217 | −0.473109 | − | 0.881004i | \(-0.656868\pi\) | ||||
−0.473109 | + | 0.881004i | \(0.656868\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 429.022 | 0.173302 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 311.628 | 0.121864 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1362.58 | 0.524408 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −166.647 | −0.0631317 | −0.0315658 | − | 0.999502i | \(-0.510049\pi\) | ||||
−0.0315658 | + | 0.999502i | \(0.510049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −484.669 | −0.180763 | −0.0903815 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903815 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2088.10 | −0.755182 | −0.377591 | − | 0.925973i | \(-0.623247\pi\) | ||||
−0.377591 | + | 0.925973i | \(0.623247\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3401.93 | 1.21184 | 0.605921 | − | 0.795524i | \(-0.292805\pi\) | ||||
0.605921 | + | 0.795524i | \(0.292805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 541.412 | 0.189991 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1926.72 | −0.666154 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2982.96 | −1.00159 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 373.176 | 0.123508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2246.24 | 0.732879 | 0.366439 | − | 0.930442i | \(-0.380577\pi\) | ||||
0.366439 | + | 0.930442i | \(0.380577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −981.665 | −0.315787 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3345.13 | −1.04646 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 105.969 | 0.0326975 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3968.93 | −1.20805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1129.63 | −0.339217 | −0.169608 | − | 0.985512i | \(-0.554250\pi\) | ||||
−0.169608 | + | 0.985512i | \(0.554250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1693.88 | −0.495273 | −0.247637 | − | 0.968853i | \(-0.579654\pi\) | ||||
−0.247637 | + | 0.968853i | \(0.579654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5250.72 | −1.51518 | −0.757592 | − | 0.652728i | \(-0.773624\pi\) | ||||
−0.757592 | + | 0.652728i | \(0.773624\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 66.7593 | 0.0190149 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6042.60 | 1.69899 | 0.849493 | − | 0.527600i | \(-0.176908\pi\) | ||||
0.849493 | + | 0.527600i | \(0.176908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 771.886 | 0.211559 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 385.416 | 0.104312 | 0.0521559 | − | 0.998639i | \(-0.483391\pi\) | ||||
0.0521559 | + | 0.998639i | \(0.483391\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4858.73 | 1.29866 | 0.649332 | − | 0.760505i | \(-0.275049\pi\) | ||||
0.649332 | + | 0.760505i | \(0.275049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1888.19 | −0.498467 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4752.80 | −1.22435 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 508.596 | 0.129442 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3784.74 | −0.951757 | −0.475878 | − | 0.879511i | \(-0.657870\pi\) | ||||
−0.475878 | + | 0.879511i | \(0.657870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −296.808 | −0.0737556 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3702.36 | −0.898626 | −0.449313 | − | 0.893374i | \(-0.648331\pi\) | ||||
−0.449313 | + | 0.893374i | \(0.648331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7305.63 | 1.75270 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1771.00 | 0.420007 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3517.77 | 0.824771 | 0.412385 | − | 0.911009i | \(-0.364696\pi\) | ||||
0.412385 | + | 0.911009i | \(0.364696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 561.998 | 0.128815 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5564.09 | −1.26115 | −0.630573 | − | 0.776130i | \(-0.717180\pi\) | ||||
−0.630573 | + | 0.776130i | \(0.717180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2585.39 | −0.579525 | −0.289762 | − | 0.957099i | \(-0.593576\pi\) | ||||
−0.289762 | + | 0.957099i | \(0.593576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −850.253 | −0.188497 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 884.433 | 0.191843 | 0.0959213 | − | 0.995389i | \(-0.469420\pi\) | ||||
0.0959213 | + | 0.995389i | \(0.469420\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3074.76 | 0.659789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3165.55 | 0.672032 | 0.336016 | − | 0.941856i | \(-0.390920\pi\) | ||||
0.336016 | + | 0.941856i | \(0.390920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4425.40 | 0.929550 | 0.464775 | − | 0.885429i | \(-0.346135\pi\) | ||||
0.464775 | + | 0.885429i | \(0.346135\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7008.58 | 1.44148 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9385.30 | 1.91030 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 724.541 | 0.145956 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2871.70 | −0.572582 | −0.286291 | − | 0.958143i | \(-0.592422\pi\) | ||||
−0.286291 | + | 0.958143i | \(0.592422\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −124.621 | −0.0243475 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3780.18 | 0.731148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10522.1 | −2.01489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 234.623 | 0.0444842 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3145.45 | 0.584757 | 0.292379 | − | 0.956303i | \(-0.405553\pi\) | ||||
0.292379 | + | 0.956303i | \(0.405553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1474.33 | 0.271430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −306.614 | −0.0559052 | −0.0279526 | − | 0.999609i | \(-0.508899\pi\) | ||||
−0.0279526 | + | 0.999609i | \(0.508899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3120.66 | 0.563547 | 0.281773 | − | 0.959481i | \(-0.409077\pi\) | ||||
0.281773 | + | 0.959481i | \(0.409077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8131.12 | 1.44066 | 0.720330 | − | 0.693632i | \(-0.243990\pi\) | ||||
0.720330 | + | 0.693632i | \(0.243990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 176.216 | 0.0309286 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −610.408 | −0.106136 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17122.2 | 2.94956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 755.341 | 0.127738 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2174.54 | −0.364396 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7877.80 | −1.30817 | −0.654083 | − | 0.756423i | \(-0.726945\pi\) | ||||
−0.654083 | + | 0.756423i | \(0.726945\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6715.16 | −1.10507 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2169.15 | 0.350627 | 0.175313 | − | 0.984513i | \(-0.443906\pi\) | ||||
0.175313 | + | 0.984513i | \(0.443906\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1446.59 | −0.231765 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 305.943 | 0.0485857 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3589.19 | 0.565009 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 325.475 | 0.0503527 | 0.0251764 | − | 0.999683i | \(-0.491985\pi\) | ||||
0.0251764 | + | 0.999683i | \(0.491985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9311.11 | 1.42812 | 0.714058 | − | 0.700087i | \(-0.246855\pi\) | ||||
0.714058 | + | 0.700087i | \(0.246855\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1587.18 | 0.241360 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3144.94 | −0.474188 | −0.237094 | − | 0.971487i | \(-0.576195\pi\) | ||||
−0.237094 | + | 0.971487i | \(0.576195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3063.09 | 0.454106 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −570.424 | −0.0838603 | −0.0419302 | − | 0.999121i | \(-0.513351\pi\) | ||||
−0.0419302 | + | 0.999121i | \(0.513351\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13644.9 | 1.98934 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1190.44 | 0.172126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1629.17 | 0.231722 | 0.115861 | − | 0.993265i | \(-0.463037\pi\) | ||||
0.115861 | + | 0.993265i | \(0.463037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6442.12 | −0.908844 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1151.89 | −0.161195 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6985.76 | 0.969728 | 0.484864 | − | 0.874589i | \(-0.338869\pi\) | ||||
0.484864 | + | 0.874589i | \(0.338869\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2244.31 | −0.306599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11101.3 | 1.50458 | 0.752291 | − | 0.658831i | \(-0.228949\pi\) | ||||
0.752291 | + | 0.658831i | \(0.228949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1033.47 | 0.138967 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6608.71 | 0.881695 | 0.440848 | − | 0.897582i | \(-0.354678\pi\) | ||||
0.440848 | + | 0.897582i | \(0.354678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9671.66 | 1.27038 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 503.208 | 0.0655878 | 0.0327939 | − | 0.999462i | \(-0.489560\pi\) | ||||
0.0327939 | + | 0.999462i | \(0.489560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13618.3 | −1.76140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2190.80 | 0.281199 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1885.18 | −0.238323 | −0.119162 | − | 0.992875i | \(-0.538021\pi\) | ||||
−0.119162 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3668.05 | 0.460231 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13212.7 | −1.64541 | −0.822706 | − | 0.568467i | \(-0.807537\pi\) | ||||
−0.822706 | + | 0.568467i | \(0.807537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3896.52 | −0.481636 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −668.167 | −0.0813755 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8441.37 | −1.02054 | −0.510268 | − | 0.860016i | \(-0.670454\pi\) | ||||
−0.510268 | + | 0.860016i | \(0.670454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −687.239 | −0.0824793 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13050.1 | −1.55485 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2290.02 | 0.268927 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12823.2 | 1.49512 | 0.747559 | − | 0.664195i | \(-0.231226\pi\) | ||||
0.747559 | + | 0.664195i | \(0.231226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2474.24 | −0.286431 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1998.78 | 0.229750 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13598.7 | −1.54119 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 77.7635 | 0.00875165 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12461.3 | 1.39267 | 0.696334 | − | 0.717718i | \(-0.254813\pi\) | ||||
0.696334 | + | 0.717718i | \(0.254813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12063.0 | 1.33883 | 0.669414 | − | 0.742890i | \(-0.266545\pi\) | ||||
0.669414 | + | 0.742890i | \(0.266545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16307.9 | −1.78516 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16480.7 | 1.79176 | 0.895879 | − | 0.444299i | \(-0.146547\pi\) | ||||
0.895879 | + | 0.444299i | \(0.146547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12282.9 | −1.32630 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2159.19 | −0.231572 | −0.115786 | − | 0.993274i | \(-0.536939\pi\) | ||||
−0.115786 | + | 0.993274i | \(0.536939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2306.56 | −0.244064 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5552.38 | 0.583592 | 0.291796 | − | 0.956481i | \(-0.405747\pi\) | ||||
0.291796 | + | 0.956481i | \(0.405747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −641.000 | −0.0669257 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −471.918 | −0.0489463 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16667.9 | −1.70611 | −0.853055 | − | 0.521820i | \(-0.825253\pi\) | ||||
−0.853055 | + | 0.521820i | \(0.825253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5717.91 | −0.581457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15255.5 | 1.54126 | 0.770629 | − | 0.637284i | \(-0.219942\pi\) | ||||
0.770629 | + | 0.637284i | \(0.219942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6806.85 | 0.683242 | 0.341621 | − | 0.939838i | \(-0.389024\pi\) | ||||
0.341621 | + | 0.939838i | \(0.389024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6455.78 | −0.639696 | −0.319848 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319848 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17161.1 | −1.68961 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3208.99 | −0.313933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 962.343 | 0.0935488 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1058.79 | 0.101633 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8481.34 | 0.809024 | 0.404512 | − | 0.914533i | \(-0.367441\pi\) | ||||
0.404512 | + | 0.914533i | \(0.367441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8509.84 | 0.806685 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2917.41 | −0.274838 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10966.2 | −1.02038 | −0.510191 | − | 0.860061i | \(-0.670425\pi\) | ||||
−0.510191 | + | 0.860061i | \(0.670425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1304.38 | 0.120626 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6784.15 | 0.623553 | 0.311777 | − | 0.950155i | \(-0.399076\pi\) | ||||
0.311777 | + | 0.950155i | \(0.399076\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8085.26 | 0.738624 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31115.8 | 2.80832 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17785.8 | −1.59560 | −0.797799 | − | 0.602924i | \(-0.794002\pi\) | ||||
−0.797799 | + | 0.602924i | \(0.794002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2949.89 | −0.263057 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8440.25 | −0.748175 | −0.374087 | − | 0.927393i | \(-0.622044\pi\) | ||||
−0.374087 | + | 0.927393i | \(0.622044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 984.654 | 0.0862525 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10923.4 | 0.951222 | 0.475611 | − | 0.879656i | \(-0.342227\pi\) | ||||
0.475611 | + | 0.879656i | \(0.342227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3358.91 | −0.290782 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6847.20 | −0.589301 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 198.882 | 0.0169184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1246.90 | 0.105458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9879.76 | −0.830787 | −0.415394 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415394 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −105.197 | −0.00879531 | −0.00439766 | − | 0.999990i | \(-0.501400\pi\) | ||||
−0.00439766 | + | 0.999990i | \(0.501400\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14037.4 | 1.16030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 803.653 | 0.0660519 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11995.3 | 0.980325 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8163.84 | 0.663443 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2705.84 | 0.217440 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1222.17 | −0.0976668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19055.6 | 1.51435 | 0.757175 | − | 0.653212i | \(-0.226579\pi\) | ||||
0.757175 | + | 0.653212i | \(0.226579\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2071.37 | 0.163704 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3910.22 | 0.305647 | 0.152824 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152824 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12499.6 | 0.971712 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9682.11 | 0.748587 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24466.4 | −1.88141 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1727.52 | −0.131413 | −0.0657067 | − | 0.997839i | \(-0.520930\pi\) | ||||
−0.0657067 | + | 0.997839i | \(0.520930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12256.5 | −0.927360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −280.148 | −0.0210835 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20905.0 | −1.56491 | −0.782453 | − | 0.622709i | \(-0.786032\pi\) | ||||
−0.782453 | + | 0.622709i | \(0.786032\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18926.1 | 1.40180 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −256.523 | −0.0188998 | −0.00944990 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944990 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15793.4 | −1.15750 | −0.578749 | − | 0.815506i | \(-0.696459\pi\) | ||||
−0.578749 | + | 0.815506i | \(0.696459\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 149.812 | 0.0109223 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5923.65 | 0.427391 | 0.213696 | − | 0.976900i | \(-0.431450\pi\) | ||||
0.213696 | + | 0.976900i | \(0.431450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 435.708 | 0.0312736 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16120.9 | −1.15113 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 105.351 | 0.00748405 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11730.7 | 0.824832 | 0.412416 | − | 0.910996i | \(-0.364685\pi\) | ||||
0.412416 | + | 0.910996i | \(0.364685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16809.8 | 1.17596 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1877.16 | 0.130653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2781.00 | −0.192584 | −0.0962919 | − | 0.995353i | \(-0.530698\pi\) | ||||
−0.0962919 | + | 0.995353i | \(0.530698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3058.27 | −0.209659 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22999.7 | −1.56885 | −0.784425 | − | 0.620224i | \(-0.787042\pi\) | ||||
−0.784425 | + | 0.620224i | \(0.787042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2680.42 | −0.181925 | −0.0909624 | − | 0.995854i | \(-0.528994\pi\) | ||||
−0.0909624 | + | 0.995854i | \(0.528994\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15774.1 | 1.06529 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16977.3 | −1.13523 | −0.567617 | − | 0.823293i | \(-0.692135\pi\) | ||||
−0.567617 | + | 0.823293i | \(0.692135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1732.08 | 0.115250 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2532.98 | −0.167714 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24124.3 | 1.58951 | 0.794755 | − | 0.606930i | \(-0.207599\pi\) | ||||
0.794755 | + | 0.606930i | \(0.207599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12286.0 | −0.801644 | −0.400822 | − | 0.916156i | \(-0.631275\pi\) | ||||
−0.400822 | + | 0.916156i | \(0.631275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6240.17 | −0.405192 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5445.98 | 0.351915 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17813.6 | −1.14557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −335.477 | −0.0213679 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30657.2 | −1.94338 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8142.22 | −0.513687 | −0.256844 | − | 0.966453i | \(-0.582683\pi\) | ||||
−0.256844 | + | 0.966453i | \(0.582683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2019.32 | −0.126794 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15565.6 | 0.968182 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28600.9 | −1.77063 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6380.36 | 0.393150 | 0.196575 | − | 0.980489i | \(-0.437018\pi\) | ||||
0.196575 | + | 0.980489i | \(0.437018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18308.0 | 1.12286 | 0.561430 | − | 0.827524i | \(-0.310251\pi\) | ||||
0.561430 | + | 0.827524i | \(0.310251\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21497.9 | −1.30629 | −0.653145 | − | 0.757233i | \(-0.726551\pi\) | ||||
−0.653145 | + | 0.757233i | \(0.726551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1193.55 | 0.0721895 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3007.20 | 0.181047 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16035.4 | 0.960972 | 0.480486 | − | 0.877002i | \(-0.340460\pi\) | ||||
0.480486 | + | 0.877002i | \(0.340460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3087.43 | 0.183337 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12259.7 | −0.724688 | −0.362344 | − | 0.932044i | \(-0.618023\pi\) | ||||
−0.362344 | + | 0.932044i | \(0.618023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7515.22 | 0.442221 | 0.221111 | − | 0.975249i | \(-0.429032\pi\) | ||||
0.221111 | + | 0.975249i | \(0.429032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3567.99 | 0.209003 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7700.74 | −0.447037 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1015.51 | 0.0586874 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1243.73 | 0.0715552 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17438.7 | −0.998829 | −0.499415 | − | 0.866363i | \(-0.666452\pi\) | ||||
−0.499415 | + | 0.866363i | \(0.666452\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14679.1 | −0.833331 | −0.416665 | − | 0.909060i | \(-0.636801\pi\) | ||||
−0.416665 | + | 0.909060i | \(0.636801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22965.7 | −1.29800 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1522.77 | 0.0856866 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30494.6 | −1.70841 | −0.854204 | − | 0.519937i | \(-0.825955\pi\) | ||||
−0.854204 | + | 0.519937i | \(0.825955\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4720.29 | 0.262140 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1341.76 | −0.0741903 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13887.9 | −0.764576 | −0.382288 | − | 0.924043i | \(-0.624864\pi\) | ||||
−0.382288 | + | 0.924043i | \(0.624864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1945.04 | 0.106617 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29410.7 | −1.59829 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5432.17 | −0.293939 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11296.0 | 0.608622 | 0.304311 | − | 0.952573i | \(-0.401574\pi\) | ||||
0.304311 | + | 0.952573i | \(0.401574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36712.0 | −1.96959 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7436.82 | −0.395602 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24405.6 | −1.29277 | −0.646384 | − | 0.763013i | \(-0.723719\pi\) | ||||
−0.646384 | + | 0.763013i | \(0.723719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22489.0 | 1.18622 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13369.8 | −0.702251 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −346.481 | −0.0180468 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11883.4 | 0.616379 | 0.308189 | − | 0.951325i | \(-0.400277\pi\) | ||||
0.308189 | + | 0.951325i | \(0.400277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46731.9 | −2.41385 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4367.90 | −0.224680 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21154.5 | 1.07920 | 0.539599 | − | 0.841922i | \(-0.318576\pi\) | ||||
0.539599 | + | 0.841922i | \(0.318576\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16235.7 | −0.824861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44154.7 | 2.23409 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5806.54 | 0.292591 | 0.146296 | − | 0.989241i | \(-0.453265\pi\) | ||||
0.146296 | + | 0.989241i | \(0.453265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1569.54 | 0.0784462 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14389.0 | 0.716248 | 0.358124 | − | 0.933674i | \(-0.383416\pi\) | ||||
0.358124 | + | 0.933674i | \(0.383416\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4272.67 | 0.211822 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18366.0 | −0.906839 | −0.453420 | − | 0.891297i | \(-0.649796\pi\) | ||||
−0.453420 | + | 0.891297i | \(0.649796\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14818.0 | 0.725785 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19348.1 | 0.943876 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19355.0 | −0.940444 | −0.470222 | − | 0.882548i | \(-0.655826\pi\) | ||||
−0.470222 | + | 0.882548i | \(0.655826\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3402.41 | 0.164662 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 494.408 | 0.0237379 | 0.0118689 | − | 0.999930i | \(-0.496222\pi\) | ||||
0.0118689 | + | 0.999930i | \(0.496222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 266.824 | 0.0127604 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2310.20 | −0.110045 | −0.0550227 | − | 0.998485i | \(-0.517523\pi\) | ||||
−0.0550227 | + | 0.998485i | \(0.517523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23942.0 | −1.13599 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15201.2 | −0.715623 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24590.9 | 1.15315 | 0.576573 | − | 0.817045i | \(-0.304389\pi\) | ||||
0.576573 | + | 0.817045i | \(0.304389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3328.34 | 0.155470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22102.6 | 1.02843 | 0.514214 | − | 0.857662i | \(-0.328084\pi\) | ||||
0.514214 | + | 0.857662i | \(0.328084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6567.61 | −0.303232 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35219.3 | −1.61985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2845.83 | −0.130386 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3233.30 | −0.147572 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29715.0 | −1.34590 | −0.672952 | − | 0.739686i | \(-0.734974\pi\) | ||||
−0.672952 | + | 0.739686i | \(0.734974\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3162.40 | −0.142693 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45852.6 | 2.06110 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15840.2 | −0.709335 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1237.06 | 0.0549799 | 0.0274899 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274899 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9125.20 | 0.404038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16373.9 | 0.722274 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 307.203 | 0.0135006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5002.00 | 0.218189 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4675.39 | −0.203186 | −0.101593 | − | 0.994826i | \(-0.532394\pi\) | ||||
−0.101593 | + | 0.994826i | \(0.532394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3243.36 | −0.140431 | −0.0702156 | − | 0.997532i | \(-0.522369\pi\) | ||||
−0.0702156 | + | 0.997532i | \(0.522369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2324.21 | 0.100263 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 52875.3 | 2.26423 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24772.2 | −1.05691 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33551.4 | 1.42625 | 0.713126 | − | 0.701036i | \(-0.247279\pi\) | ||||
0.713126 | + | 0.701036i | \(0.247279\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6365.66 | −0.269615 | −0.134807 | − | 0.990872i | \(-0.543042\pi\) | ||||
−0.134807 | + | 0.990872i | \(0.543042\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18980.7 | 0.798094 | 0.399047 | − | 0.916930i | \(-0.369341\pi\) | ||||
0.399047 | + | 0.916930i | \(0.369341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33674.2 | 1.41080 | 0.705400 | − | 0.708809i | \(-0.250767\pi\) | ||||
0.705400 | + | 0.708809i | \(0.250767\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −795.087 | −0.0331904 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −56076.0 | −2.33244 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5613.58 | −0.231821 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4639.47 | −0.190909 | −0.0954544 | − | 0.995434i | \(-0.530430\pi\) | ||||
−0.0954544 | + | 0.995434i | \(0.530430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19817.0 | −0.812540 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2845.77 | −0.116267 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37733.2 | −1.53073 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3978.34 | −0.160820 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29199.2 | 1.17619 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1646.37 | 0.0660850 | 0.0330425 | − | 0.999454i | \(-0.489480\pi\) | ||||
0.0330425 | + | 0.999454i | \(0.489480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46767.8 | 1.86413 | 0.932064 | − | 0.362295i | \(-0.118007\pi\) | ||||
0.932064 | + | 0.362295i | \(0.118007\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11466.7 | 0.455460 | 0.227730 | − | 0.973724i | \(-0.426870\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6300.57 | −0.249388 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42704.1 | 1.68443 | 0.842216 | − | 0.539140i | \(-0.181250\pi\) | ||||
0.842216 | + | 0.539140i | \(0.181250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8437.19 | −0.330498 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2237.68 | 0.0873511 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19989.9 | −0.777647 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21109.6 | 0.818385 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18376.9 | 0.707574 | 0.353787 | − | 0.935326i | \(-0.384894\pi\) | ||||
0.353787 | + | 0.935326i | \(0.384894\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2581.60 | 0.0990616 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7024.26 | −0.268619 | −0.134310 | − | 0.990939i | \(-0.542882\pi\) | ||||
−0.134310 | + | 0.990939i | \(0.542882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41747.1 | −1.59106 | −0.795528 | − | 0.605917i | \(-0.792806\pi\) | ||||
−0.795528 | + | 0.605917i | \(0.792806\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5863.18 | −0.221946 | −0.110973 | − | 0.993823i | \(-0.535397\pi\) | ||||
−0.110973 | + | 0.993823i | \(0.535397\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32757.8 | −1.23584 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1730.97 | −0.0650836 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10927.4 | 0.409488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3398.30 | −0.126495 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7937.74 | 0.294481 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4833.78 | 0.178731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9459.14 | 0.348594 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13945.6 | −0.510536 | −0.255268 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255268 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6835.75 | 0.249425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38202.8 | −1.38937 | −0.694685 | − | 0.719314i | \(-0.744456\pi\) | ||||
−0.694685 | + | 0.719314i | \(0.744456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1474.41 | 0.0534456 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −69441.7 | −2.50073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8586.98 | 0.308225 | 0.154112 | − | 0.988053i | \(-0.450748\pi\) | ||||
0.154112 | + | 0.988053i | \(0.450748\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2827.70 | −0.101168 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36244.7 | 1.29254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42954.9 | 1.52192 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50645.2 | 1.78861 | 0.894303 | − | 0.447461i | \(-0.147672\pi\) | ||||
0.894303 | + | 0.447461i | \(0.147672\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −67151.1 | −2.36390 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 275.640 | 0.00967208 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26068.7 | −0.908887 | −0.454444 | − | 0.890775i | \(-0.650162\pi\) | ||||
−0.454444 | + | 0.890775i | \(0.650162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2805.41 | −0.0974985 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4036.78 | −0.139846 | −0.0699230 | − | 0.997552i | \(-0.522275\pi\) | ||||
−0.0699230 | + | 0.997552i | \(0.522275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28012.0 | 0.967334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47790.1 | 1.63988 | 0.819942 | − | 0.572446i | \(-0.194005\pi\) | ||||
0.819942 | + | 0.572446i | \(0.194005\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3912.57 | −0.133833 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7309.71 | −0.249247 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49284.8 | 1.67523 | 0.837613 | − | 0.546264i | \(-0.183950\pi\) | ||||
0.837613 | + | 0.546264i | \(0.183950\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −158.415 | −0.00535092 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21783.4 | 0.733495 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16009.7 | −0.537400 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17784.3 | −0.595110 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19830.2 | 0.659459 | 0.329729 | − | 0.944076i | \(-0.393043\pi\) | ||||
0.329729 | + | 0.944076i | \(0.393043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15392.5 | −0.510299 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24538.6 | 0.811000 | 0.405500 | − | 0.914095i | \(-0.367097\pi\) | ||||
0.405500 | + | 0.914095i | \(0.367097\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −72586.5 | −2.39159 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15113.6 | 0.494909 | 0.247454 | − | 0.968900i | \(-0.420406\pi\) | ||||
0.247454 | + | 0.968900i | \(0.420406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1629.22 | 0.0531870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22006.9 | 0.716235 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13262.7 | −0.430330 | −0.215165 | − | 0.976578i | \(-0.569029\pi\) | ||||
−0.215165 | + | 0.976578i | \(0.569029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1954.87 | 0.0630436 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42054.8 | −1.35214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7053.73 | −0.226104 | −0.113052 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113052 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7081.98 | 0.226324 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38686.1 | −1.22889 | −0.614443 | − | 0.788961i | \(-0.710619\pi\) | ||||
−0.614443 | + | 0.788961i | \(0.710619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12259.8 | 0.388273 |
(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 | 800.4.a.s.1.1 | 2 | ||
4.3 | odd | 2 | 800.4.a.m.1.2 | 2 | |||
5.2 | odd | 4 | 800.4.c.i.449.3 | 4 | |||
5.3 | odd | 4 | 800.4.c.i.449.2 | 4 | |||
5.4 | even | 2 | 160.4.a.c.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 1600.4.a.cn.1.1 | 2 | |||
8.5 | even | 2 | 1600.4.a.cd.1.2 | 2 | |||
15.14 | odd | 2 | 1440.4.a.t.1.1 | 2 | |||
20.3 | even | 4 | 800.4.c.k.449.3 | 4 | |||
20.7 | even | 4 | 800.4.c.k.449.2 | 4 | |||
20.19 | odd | 2 | 160.4.a.g.1.1 | yes | 2 | ||
40.19 | odd | 2 | 320.4.a.o.1.2 | 2 | |||
40.29 | even | 2 | 320.4.a.s.1.1 | 2 | |||
60.59 | even | 2 | 1440.4.a.x.1.2 | 2 | |||
80.19 | odd | 4 | 1280.4.d.q.641.2 | 4 | |||
80.29 | even | 4 | 1280.4.d.x.641.3 | 4 | |||
80.59 | odd | 4 | 1280.4.d.q.641.3 | 4 | |||
80.69 | even | 4 | 1280.4.d.x.641.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
160.4.a.g.1.1 | yes | 2 | 20.19 | odd | 2 | ||
320.4.a.o.1.2 | 2 | 40.19 | odd | 2 | |||
320.4.a.s.1.1 | 2 | 40.29 | even | 2 | |||
800.4.a.m.1.2 | 2 | 4.3 | odd | 2 | |||
800.4.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
800.4.c.i.449.2 | 4 | 5.3 | odd | 4 | |||
800.4.c.i.449.3 | 4 | 5.2 | odd | 4 | |||
800.4.c.k.449.2 | 4 | 20.7 | even | 4 | |||
800.4.c.k.449.3 | 4 | 20.3 | even | 4 | |||
1280.4.d.q.641.2 | 4 | 80.19 | odd | 4 | |||
1280.4.d.q.641.3 | 4 | 80.59 | odd | 4 | |||
1280.4.d.x.641.2 | 4 | 80.69 | even | 4 | |||
1280.4.d.x.641.3 | 4 | 80.29 | even | 4 | |||
1440.4.a.t.1.1 | 2 | 15.14 | odd | 2 | |||
1440.4.a.x.1.2 | 2 | 60.59 | even | 2 | |||
1600.4.a.cd.1.2 | 2 | 8.5 | even | 2 | |||
1600.4.a.cn.1.1 | 2 | 8.3 | odd | 2 |