Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,4,Mod(1,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, 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("688.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.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: | \(40.5933140839\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.847740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.1 |
$q$-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 | ||||||||
\(3\) | −9.49653 | −1.82761 | −0.913804 | − | 0.406154i | \(-0.866870\pi\) | ||||
−0.913804 | + | 0.406154i | \(0.866870\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.98245 | 0.266759 | 0.133379 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133379 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.0720 | 1.40776 | 0.703878 | − | 0.710321i | \(-0.251450\pi\) | ||||
0.703878 | + | 0.710321i | \(0.251450\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 63.1842 | 2.34015 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.8506 | 1.01008 | 0.505040 | − | 0.863096i | \(-0.331478\pi\) | ||||
0.505040 | + | 0.863096i | \(0.331478\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 89.5430 | 1.91037 | 0.955183 | − | 0.296016i | \(-0.0956581\pi\) | ||||
0.955183 | + | 0.296016i | \(0.0956581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −28.3230 | −0.487531 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −28.8042 | −0.410944 | −0.205472 | − | 0.978663i | \(-0.565873\pi\) | ||||
−0.205472 | + | 0.978663i | \(0.565873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.8677 | 0.710799 | 0.355400 | − | 0.934714i | \(-0.384345\pi\) | ||||
0.355400 | + | 0.934714i | \(0.384345\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −247.594 | −2.57283 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.63139 | −0.0238558 | −0.0119279 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119279 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −116.105 | −0.928840 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −343.624 | −2.44928 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 173.812 | 1.11297 | 0.556486 | − | 0.830857i | \(-0.312149\pi\) | ||||
0.556486 | + | 0.830857i | \(0.312149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −57.9476 | −0.335732 | −0.167866 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167866 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −349.953 | −1.84603 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 77.7586 | 0.375531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52.0754 | 0.231382 | 0.115691 | − | 0.993285i | \(-0.463092\pi\) | ||||
0.115691 | + | 0.993285i | \(0.463092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −850.348 | −3.49140 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 142.704 | 0.543577 | 0.271788 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271788 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.0000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 188.444 | 0.624257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 106.853 | 0.331618 | 0.165809 | − | 0.986158i | \(-0.446976\pi\) | ||||
0.165809 | + | 0.986158i | \(0.446976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 336.750 | 0.981779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 273.540 | 0.751045 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 244.652 | 0.634067 | 0.317033 | − | 0.948414i | \(-0.397313\pi\) | ||||
0.317033 | + | 0.948414i | \(0.397313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 109.905 | 0.269448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −559.039 | −1.29906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 127.799 | 0.281999 | 0.141000 | − | 0.990010i | \(-0.454968\pi\) | ||||
0.141000 | + | 0.990010i | \(0.454968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −443.613 | −0.931128 | −0.465564 | − | 0.885014i | \(-0.654149\pi\) | ||||
−0.465564 | + | 0.885014i | \(0.654149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1647.34 | 3.29437 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 267.058 | 0.509607 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 117.896 | 0.214975 | 0.107487 | − | 0.994206i | \(-0.465720\pi\) | ||||
0.107487 | + | 0.994206i | \(0.465720\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.9891 | 0.0435991 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −816.799 | −1.36530 | −0.682650 | − | 0.730746i | \(-0.739173\pi\) | ||||
−0.682650 | + | 0.730746i | \(0.739173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −620.953 | −0.995576 | −0.497788 | − | 0.867299i | \(-0.665854\pi\) | ||||
−0.497788 | + | 0.867299i | \(0.665854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1102.59 | 1.69756 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 960.770 | 1.42195 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −377.771 | −0.538007 | −0.269003 | − | 0.963139i | \(-0.586694\pi\) | ||||
−0.269003 | + | 0.963139i | \(0.586694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1557.27 | 2.13617 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1453.23 | 1.92184 | 0.960919 | − | 0.276829i | \(-0.0892835\pi\) | ||||
0.960919 | + | 0.276829i | \(0.0892835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −85.9072 | −0.109623 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1650.62 | −2.03408 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 627.993 | 0.747945 | 0.373973 | − | 0.927440i | \(-0.377995\pi\) | ||||
0.373973 | + | 0.927440i | \(0.377995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2334.57 | 2.68933 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 550.302 | 0.613587 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 175.570 | 0.189612 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −817.163 | −0.855365 | −0.427682 | − | 0.903929i | \(-0.640670\pi\) | ||||
−0.427682 | + | 0.903929i | \(0.640670\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2328.38 | 2.36374 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 513.438 | 0.505832 | 0.252916 | − | 0.967488i | \(-0.418610\pi\) | ||||
0.252916 | + | 0.967488i | \(0.418610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −689.788 | −0.659872 | −0.329936 | − | 0.944003i | \(-0.607027\pi\) | ||||
−0.329936 | + | 0.944003i | \(0.607027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −738.437 | −0.686325 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −320.710 | −0.289759 | −0.144879 | − | 0.989449i | \(-0.546279\pi\) | ||||
−0.144879 | + | 0.989449i | \(0.546279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1691.51 | −1.48640 | −0.743200 | − | 0.669069i | \(-0.766693\pi\) | ||||
−0.743200 | + | 0.669069i | \(0.766693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −494.535 | −0.422876 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 856.360 | 0.712916 | 0.356458 | − | 0.934311i | \(-0.383984\pi\) | ||||
0.356458 | + | 0.934311i | \(0.383984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.84801 | −0.00636374 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5657.70 | 4.47055 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −750.984 | −0.578509 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.9674 | 0.0202610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1355.19 | −0.993445 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −719.084 | −0.514535 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2233.72 | 1.56071 | 0.780357 | − | 0.625335i | \(-0.215038\pi\) | ||||
0.780357 | + | 0.625335i | \(0.215038\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −408.351 | −0.278708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2051.51 | 1.36825 | 0.684126 | − | 0.729364i | \(-0.260184\pi\) | ||||
0.684126 | + | 0.729364i | \(0.260184\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1534.80 | 1.00063 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1024.84 | −0.653367 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2594.49 | 1.61797 | 0.808986 | − | 0.587827i | \(-0.200017\pi\) | ||||
0.808986 | + | 0.587827i | \(0.200017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1140.44 | −0.695905 | −0.347953 | − | 0.937512i | \(-0.613123\pi\) | ||||
−0.347953 | + | 0.937512i | \(0.613123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1014.73 | −0.606068 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3299.71 | 1.92962 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 518.388 | 0.296895 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3197.96 | −1.79431 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2112.03 | −1.16124 | −0.580618 | − | 0.814176i | \(-0.697189\pi\) | ||||
−0.580618 | + | 0.814176i | \(0.697189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1351.31 | 0.728265 | 0.364132 | − | 0.931347i | \(-0.381366\pi\) | ||||
0.364132 | + | 0.931347i | \(0.381366\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1819.97 | −0.961672 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −172.826 | −0.0895595 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1506.02 | −0.765562 | −0.382781 | − | 0.923839i | \(-0.625034\pi\) | ||||
−0.382781 | + | 0.923839i | \(0.625034\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2323.35 | −1.15883 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −68.6057 | −0.0335832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1258.30 | 0.604647 | 0.302323 | − | 0.953205i | \(-0.402238\pi\) | ||||
0.302323 | + | 0.953205i | \(0.402238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1043.72 | −0.492445 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2764.50 | −1.28098 | −0.640489 | − | 0.767967i | \(-0.721268\pi\) | ||||
−0.640489 | + | 0.767967i | \(0.721268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5820.95 | 2.64950 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3719.51 | 1.66338 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1004.21 | 0.441322 | 0.220661 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220661 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3027.09 | −1.30758 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1213.64 | −0.515384 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2666.39 | −1.11338 | −0.556692 | − | 0.830719i | \(-0.687930\pi\) | ||||
−0.556692 | + | 0.830719i | \(0.687930\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3016.21 | 1.23863 | 0.619317 | − | 0.785141i | \(-0.287409\pi\) | ||||
0.619317 | + | 0.785141i | \(0.287409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4212.79 | 1.70174 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 155.312 | 0.0617232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1061.45 | −0.415086 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8958.98 | −3.44799 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1413.15 | −0.535352 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1246.60 | −0.464934 | −0.232467 | − | 0.972604i | \(-0.574680\pi\) | ||||
−0.232467 | + | 0.972604i | \(0.574680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2536.12 | −0.931362 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4931.17 | −1.78341 | −0.891704 | − | 0.452619i | \(-0.850490\pi\) | ||||
−0.891704 | + | 0.452619i | \(0.850490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −552.461 | −0.196799 | −0.0983993 | − | 0.995147i | \(-0.531372\pi\) | ||||
−0.0983993 | + | 0.995147i | \(0.531372\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1119.60 | −0.392889 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4531.64 | 1.56679 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 425.609 | 0.145004 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −166.262 | −0.0558263 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2169.31 | 0.717964 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2302.22 | −0.751145 | −0.375572 | − | 0.926793i | \(-0.622554\pi\) | ||||
−0.375572 | + | 0.926793i | \(0.622554\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7756.76 | 2.49523 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 128.246 | 0.0406803 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1510.81 | −0.472629 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5896.90 | 1.81952 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2579.21 | −0.785053 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2558.41 | −0.768269 | −0.384135 | − | 0.923277i | \(-0.625500\pi\) | ||||
−0.384135 | + | 0.923277i | \(0.625500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7336.00 | −2.17363 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3622.76 | −1.05926 | −0.529628 | − | 0.848230i | \(-0.677669\pi\) | ||||
−0.529628 | + | 0.848230i | \(0.677669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1155.46 | 0.333428 | 0.166714 | − | 0.986005i | \(-0.446684\pi\) | ||||
0.166714 | + | 0.986005i | \(0.446684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9123.98 | −2.59876 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 527.800 | 0.148401 | 0.0742003 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0742003 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 318.683 | 0.0884620 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3587.51 | 0.983266 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1341.41 | 0.363048 | 0.181524 | − | 0.983387i | \(-0.441897\pi\) | ||||
0.181524 | + | 0.983387i | \(0.441897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3738.93 | −0.999361 | −0.499680 | − | 0.866210i | \(-0.666549\pi\) | ||||
−0.499680 | + | 0.866210i | \(0.666549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5510.79 | −1.45480 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1004.34 | 0.261898 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5271.19 | 1.35789 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13800.6 | −3.51237 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1741.62 | 0.437969 | 0.218985 | − | 0.975728i | \(-0.429726\pi\) | ||||
0.218985 | + | 0.975728i | \(0.429726\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −96.9684 | −0.0240963 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 815.821 | 0.200348 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4121.68 | 1.00040 | 0.500200 | − | 0.865910i | \(-0.333260\pi\) | ||||
0.500200 | + | 0.865910i | \(0.333260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1357.71 | 0.325730 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10982.2 | 2.60452 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4315.46 | −1.01180 | −0.505898 | − | 0.862593i | \(-0.668839\pi\) | ||||
−0.505898 | + | 0.862593i | \(0.668839\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 729.663 | 0.169143 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5963.76 | −1.36695 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5195.44 | 1.17759 | 0.588794 | − | 0.808283i | \(-0.299603\pi\) | ||||
0.588794 | + | 0.808283i | \(0.299603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7874.15 | 1.76502 | 0.882510 | − | 0.470294i | \(-0.155852\pi\) | ||||
0.882510 | + | 0.470294i | \(0.155852\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22170.3 | −4.91504 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4278.54 | −0.938202 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −175.471 | −0.0380615 | −0.0190307 | − | 0.999819i | \(-0.506058\pi\) | ||||
−0.0190307 | + | 0.999819i | \(0.506058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3661.37 | −0.785665 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7263.01 | 1.54190 | 0.770951 | − | 0.636894i | \(-0.219781\pi\) | ||||
0.770951 | + | 0.636894i | \(0.219781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2314.68 | −0.486196 | −0.243098 | − | 0.970002i | \(-0.578164\pi\) | ||||
−0.243098 | + | 0.970002i | \(0.578164\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1667.31 | −0.346536 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3720.58 | 0.765224 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4083.32 | −0.831125 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7760.22 | 1.56327 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8723.52 | 1.73936 | 0.869681 | − | 0.493614i | \(-0.164324\pi\) | ||||
0.869681 | + | 0.493614i | \(0.164324\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 381.153 | 0.0752258 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12662.8 | −2.47397 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −235.623 | −0.0455733 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1121.10 | 0.214681 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4875.88 | −0.924462 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1323.06 | −0.248387 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1579.68 | −0.293672 | −0.146836 | − | 0.989161i | \(-0.546909\pi\) | ||||
−0.146836 | + | 0.989161i | \(0.546909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6550.59 | 1.20599 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5604.24 | 1.02182 | 0.510912 | − | 0.859633i | \(-0.329308\pi\) | ||||
0.510912 | + | 0.859633i | \(0.329308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3429.86 | 0.619384 | 0.309692 | − | 0.950837i | \(-0.399774\pi\) | ||||
0.309692 | + | 0.950837i | \(0.399774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4913.11 | 0.878802 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4493.00 | 0.796064 | 0.398032 | − | 0.917372i | \(-0.369693\pi\) | ||||
0.398032 | + | 0.917372i | \(0.369693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6405.09 | 1.12419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3045.63 | 0.529566 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1695.64 | −0.292098 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10396.4 | −1.77442 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16063.5 | 2.71656 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2785.86 | 0.466837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4433.87 | −0.736277 | −0.368139 | − | 0.929771i | \(-0.620005\pi\) | ||||
−0.368139 | + | 0.929771i | \(0.620005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3290.34 | 0.541470 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 351.620 | 0.0573463 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6498.33 | 1.05040 | 0.525202 | − | 0.850977i | \(-0.323990\pi\) | ||||
0.525202 | + | 0.850977i | \(0.323990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8132.45 | −1.30293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2135.41 | −0.339116 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −162.945 | −0.0256507 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 74.5289 | 0.0116304 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11973.6 | 1.85237 | 0.926187 | − | 0.377064i | \(-0.123066\pi\) | ||||
0.926187 | + | 0.377064i | \(0.123066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5611.30 | 0.860648 | 0.430324 | − | 0.902674i | \(-0.358399\pi\) | ||||
0.430324 | + | 0.902674i | \(0.358399\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30769.1 | −4.67902 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2022.00 | −0.304874 | −0.152437 | − | 0.988313i | \(-0.548712\pi\) | ||||
−0.152437 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2436.07 | −0.364206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7131.74 | 1.05729 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10135.3 | −1.49003 | −0.745014 | − | 0.667049i | \(-0.767557\pi\) | ||||
−0.745014 | + | 0.667049i | \(0.767557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3393.59 | −0.494765 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −256.097 | −0.0370292 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1851.96 | −0.265579 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4379.58 | 0.622922 | 0.311461 | − | 0.950259i | \(-0.399182\pi\) | ||||
0.311461 | + | 0.950259i | \(0.399182\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9016.64 | 1.27205 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6378.57 | 0.892612 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4392.98 | 0.609813 | 0.304906 | − | 0.952382i | \(-0.401375\pi\) | ||||
0.304906 | + | 0.952382i | \(0.401375\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6828.81 | 0.940369 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15563.7 | 2.12618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 878.629 | 0.119082 | 0.0595411 | − | 0.998226i | \(-0.481036\pi\) | ||||
0.0595411 | + | 0.998226i | \(0.481036\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21212.6 | −2.85237 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5061.60 | −0.675289 | −0.337644 | − | 0.941274i | \(-0.609630\pi\) | ||||
−0.337644 | + | 0.941274i | \(0.609630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2865.45 | 0.379317 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2716.92 | 0.356870 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3417.17 | −0.445392 | −0.222696 | − | 0.974888i | \(-0.571486\pi\) | ||||
−0.222696 | + | 0.974888i | \(0.571486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 75.7952 | 0.00980339 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19482.2 | −2.50063 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1126.68 | −0.143518 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7634.34 | 0.965130 | 0.482565 | − | 0.875860i | \(-0.339705\pi\) | ||||
0.482565 | + | 0.875860i | \(0.339705\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14575.3 | −1.82876 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8402.74 | −1.04642 | −0.523208 | − | 0.852205i | \(-0.675265\pi\) | ||||
−0.523208 | + | 0.852205i | \(0.675265\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5188.80 | −0.641372 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4644.48 | 0.569842 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1919.01 | 0.233714 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11792.8 | −1.42571 | −0.712857 | − | 0.701310i | \(-0.752599\pi\) | ||||
−0.712857 | + | 0.701310i | \(0.752599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24638.7 | −2.95702 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3331.97 | 0.396986 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4334.19 | 0.512667 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10830.2 | 1.27184 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10631.9 | 1.23962 | 0.619811 | − | 0.784751i | \(-0.287209\pi\) | ||||
0.619811 | + | 0.784751i | \(0.287209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3136.52 | −0.363099 | −0.181550 | − | 0.983382i | \(-0.558111\pi\) | ||||
−0.181550 | + | 0.983382i | \(0.558111\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6751.39 | 0.776037 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3344.31 | 0.381701 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11565.9 | −1.31080 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31335.8 | −3.52659 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 170.380 | 0.0190416 | 0.00952080 | − | 0.999955i | \(-0.496969\pi\) | ||||
0.00952080 | + | 0.999955i | \(0.496969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2093.65 | 0.232365 | 0.116183 | − | 0.993228i | \(-0.462934\pi\) | ||||
0.116183 | + | 0.993228i | \(0.462934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4922.89 | −0.542608 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −154.904 | −0.0169567 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10860.1 | 1.18070 | 0.590348 | − | 0.807149i | \(-0.298990\pi\) | ||||
0.590348 | + | 0.807149i | \(0.298990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21277.3 | 2.29751 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8256.28 | −0.885480 | −0.442740 | − | 0.896650i | \(-0.645994\pi\) | ||||
−0.442740 | + | 0.896650i | \(0.645994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1872.96 | 0.199521 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20057.0 | 2.12229 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6792.03 | −0.713888 | −0.356944 | − | 0.934126i | \(-0.616181\pi\) | ||||
−0.356944 | + | 0.934126i | \(0.616181\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5258.73 | 0.549056 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12832.8 | −1.33098 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6962.74 | 0.717403 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4004.62 | 0.409908 | 0.204954 | − | 0.978772i | \(-0.434295\pi\) | ||||
0.204954 | + | 0.978772i | \(0.434295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9897.82 | 1.00652 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1164.36 | 0.117635 | 0.0588175 | − | 0.998269i | \(-0.481267\pi\) | ||||
0.0588175 | + | 0.998269i | \(0.481267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2566.99 | −0.257664 | −0.128832 | − | 0.991666i | \(-0.541123\pi\) | ||||
−0.128832 | + | 0.991666i | \(0.541123\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1641.25 | 0.163680 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7654.43 | 0.758469 | 0.379234 | − | 0.925301i | \(-0.376187\pi\) | ||||
0.379234 | + | 0.925301i | \(0.376187\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3073.79 | 0.302632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14301.9 | 1.39915 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1584.58 | 0.154036 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6834.84 | −0.660218 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15458.1 | 1.48381 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8754.20 | 0.835051 | 0.417526 | − | 0.908665i | \(-0.362897\pi\) | ||||
0.417526 | + | 0.908665i | \(0.362897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4662.98 | 0.442024 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 651.517 | 0.0613769 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2437.15 | −0.228176 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9406.39 | 0.875245 | 0.437623 | − | 0.899159i | \(-0.355821\pi\) | ||||
0.437623 | + | 0.899159i | \(0.355821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11949.5 | −1.10506 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6362.18 | −0.584768 | −0.292384 | − | 0.956301i | \(-0.594449\pi\) | ||||
−0.292384 | + | 0.956301i | \(0.594449\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5006.53 | −0.457369 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6944.27 | 0.630549 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21295.6 | −1.92201 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11574.8 | −1.03840 | −0.519198 | − | 0.854654i | \(-0.673769\pi\) | ||||
−0.519198 | + | 0.854654i | \(0.673769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26253.2 | 2.34113 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11443.5 | −1.01439 | −0.507196 | − | 0.861831i | \(-0.669318\pi\) | ||||
−0.507196 | + | 0.861831i | \(0.669318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1531.31 | 0.134935 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −55278.8 | −4.84225 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17397.9 | −1.51502 | −0.757511 | − | 0.652822i | \(-0.773585\pi\) | ||||
−0.757511 | + | 0.652822i | \(0.773585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16189.5 | −1.40153 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20228.4 | −1.74095 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2057.26 | −0.176027 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3937.58 | 0.334961 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9536.53 | −0.806565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23236.4 | −1.95394 | −0.976972 | − | 0.213369i | \(-0.931556\pi\) | ||||
−0.976972 | + | 0.213369i | \(0.931556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6523.69 | 0.545432 | 0.272716 | − | 0.962095i | \(-0.412078\pi\) | ||||
0.272716 | + | 0.962095i | \(0.412078\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28746.9 | 2.38975 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1669.13 | 0.137967 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12160.1 | −0.999431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8074.85 | 0.659922 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12778.2 | 1.03843 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −956.502 | −0.0772957 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25321.5 | 2.03483 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12409.5 | 0.991675 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13311.4 | −1.05786 | −0.528930 | − | 0.848666i | \(-0.677406\pi\) | ||||
−0.528930 | + | 0.848666i | \(0.677406\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28643.5 | −2.26374 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5044.86 | −0.396510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24529.8 | 1.91740 | 0.958700 | − | 0.284420i | \(-0.0918010\pi\) | ||||
0.958700 | + | 0.284420i | \(0.0918010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28029.3 | −2.17898 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10231.9 | 0.791099 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9849.25 | −0.757383 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1474.93 | −0.112806 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1732.87 | −0.131821 | −0.0659104 | − | 0.997826i | \(-0.520995\pi\) | ||||
−0.0659104 | + | 0.997826i | \(0.520995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3850.35 | 0.291328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10080.1 | 0.758615 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13482.0 | −1.00924 | −0.504618 | − | 0.863343i | \(-0.668366\pi\) | ||||
−0.504618 | + | 0.863343i | \(0.668366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2554.05 | 0.190177 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 40601.1 | 3.00721 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23053.6 | 1.69852 | 0.849261 | − | 0.527973i | \(-0.177048\pi\) | ||||
0.849261 | + | 0.527973i | \(0.177048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8791.94 | −0.644363 | −0.322181 | − | 0.946678i | \(-0.604416\pi\) | ||||
−0.322181 | + | 0.946678i | \(0.604416\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13420.1 | 0.978414 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 305.518 | 0.0221582 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12464.3 | −0.899302 | −0.449651 | − | 0.893204i | \(-0.648452\pi\) | ||||
−0.449651 | + | 0.893204i | \(0.648452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11838.4 | 0.849718 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37888.6 | 2.70548 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9015.58 | 0.640458 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16873.8 | 1.19256 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24395.5 | 1.71535 | 0.857674 | − | 0.514193i | \(-0.171909\pi\) | ||||
0.857674 | + | 0.514193i | \(0.171909\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3411.24 | −0.238638 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46829.0 | 3.25937 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8779.99 | −0.608012 | −0.304006 | − | 0.952670i | \(-0.598324\pi\) | ||||
−0.304006 | + | 0.952670i | \(0.598324\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2239.77 | −0.154322 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5246.46 | 0.359671 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14440.3 | 0.985001 | 0.492501 | − | 0.870312i | \(-0.336083\pi\) | ||||
0.492501 | + | 0.870312i | \(0.336083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7456.08 | 0.506056 | 0.253028 | − | 0.967459i | \(-0.418573\pi\) | ||||
0.253028 | + | 0.967459i | \(0.418573\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7449.16 | 0.503074 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 80.4290 | 0.00540480 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6832.01 | 0.456842 | 0.228421 | − | 0.973563i | \(-0.426644\pi\) | ||||
0.228421 | + | 0.973563i | \(0.426644\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −43034.9 | −2.86348 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9567.89 | 0.633512 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12239.8 | 0.806460 | 0.403230 | − | 0.915099i | \(-0.367887\pi\) | ||||
0.403230 | + | 0.915099i | \(0.367887\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4041.81 | −0.265010 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4307.99 | 0.281091 | 0.140546 | − | 0.990074i | \(-0.455114\pi\) | ||||
0.140546 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21923.8 | −1.42357 | −0.711786 | − | 0.702396i | \(-0.752113\pi\) | ||||
−0.711786 | + | 0.702396i | \(0.752113\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 904.210 | 0.0584295 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16373.0 | 1.05292 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12368.5 | 0.791583 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20600.9 | −1.31216 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1499.99 | −0.0950850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13249.3 | −0.835891 | −0.417945 | − | 0.908472i | \(-0.637250\pi\) | ||||
−0.417945 | + | 0.908472i | \(0.637250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21863.1 | 1.37280 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6661.97 | 0.416334 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30153.6 | 1.87556 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −51608.8 | −3.19501 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6897.79 | −0.425033 | −0.212517 | − | 0.977157i | \(-0.568166\pi\) | ||||
−0.212517 | + | 0.977157i | \(0.568166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 570.068 | 0.0349631 | 0.0174816 | − | 0.999847i | \(-0.494435\pi\) | ||||
0.0174816 | + | 0.999847i | \(0.494435\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1217.89 | −0.0743477 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15788.1 | −0.959341 | −0.479670 | − | 0.877449i | \(-0.659244\pi\) | ||||
−0.479670 | + | 0.877449i | \(0.659244\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4709.46 | 0.284842 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14347.5 | 0.863782 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21960.3 | 1.31604 | 0.658019 | − | 0.753001i | \(-0.271394\pi\) | ||||
0.658019 | + | 0.753001i | \(0.271394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6118.52 | 0.364993 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39234.4 | −2.32980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12142.6 | 0.717766 | 0.358883 | − | 0.933383i | \(-0.383158\pi\) | ||||
0.358883 | + | 0.933383i | \(0.383158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3554.01 | 0.209130 | 0.104565 | − | 0.994518i | \(-0.466655\pi\) | ||||
0.104565 | + | 0.994518i | \(0.466655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24493.6 | 1.43477 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4577.47 | 0.266927 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −457.369 | −0.0265508 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24296.1 | 1.40410 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16347.4 | −0.940514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20271.0 | 1.16106 | 0.580528 | − | 0.814240i | \(-0.302846\pi\) | ||||
0.580528 | + | 0.814240i | \(0.302846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 39896.5 | 2.27499 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26668.2 | 1.51395 | 0.756973 | − | 0.653447i | \(-0.226678\pi\) | ||||
0.756973 | + | 0.653447i | \(0.226678\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21305.1 | −1.20415 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34403.7 | 1.93591 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5584.15 | 0.312843 | 0.156421 | − | 0.987690i | \(-0.450004\pi\) | ||||
0.156421 | + | 0.987690i | \(0.450004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7737.95 | 0.431608 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10972.9 | −0.609377 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21906.9 | 1.21130 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2702.39 | 0.148776 | 0.0743878 | − | 0.997229i | \(-0.476300\pi\) | ||||
0.0743878 | + | 0.997229i | \(0.476300\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 60705.4 | 3.32757 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3401.31 | −0.185639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4110.48 | −0.223379 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5012.27 | −0.271218 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19885.1 | −1.07140 | −0.535700 | − | 0.844408i | \(-0.679952\pi\) | ||||
−0.535700 | + | 0.844408i | \(0.679952\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3065.56 | 0.164466 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3026.38 | −0.161674 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13386.4 | 0.712088 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7798.56 | −0.413090 | −0.206545 | − | 0.978437i | \(-0.566222\pi\) | ||||
−0.206545 | + | 0.978437i | \(0.566222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23869.1 | −1.25902 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 152.483 | 0.00800916 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9841.24 | 0.514744 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12738.7 | −0.663509 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1118.09 | −0.0579939 | −0.0289970 | − | 0.999579i | \(-0.509231\pi\) | ||||
−0.0289970 | + | 0.999579i | \(0.509231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17984.2 | −0.928939 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35506.9 | 1.82644 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20180.5 | −1.03377 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1741.54 | 0.0888449 | 0.0444225 | − | 0.999013i | \(-0.485855\pi\) | ||||
0.0444225 | + | 0.999013i | \(0.485855\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10287.2 | 0.522642 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1238.58 | −0.0626683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9461.10 | −0.476744 | −0.238372 | − | 0.971174i | \(-0.576614\pi\) | ||||
−0.238372 | + | 0.971174i | \(0.576614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9537.77 | −0.478648 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4344.54 | 0.217141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30605.3 | −1.52346 | −0.761728 | − | 0.647897i | \(-0.775649\pi\) | ||||
−0.761728 | + | 0.647897i | \(0.775649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50058.1 | −2.48169 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14556.5 | −0.718745 | −0.359373 | − | 0.933194i | \(-0.617009\pi\) | ||||
−0.359373 | + | 0.933194i | \(0.617009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6299.03 | −0.309770 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 91821.1 | 4.49740 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8361.55 | −0.407910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17528.3 | 0.851685 | 0.425843 | − | 0.904797i | \(-0.359978\pi\) | ||||
0.425843 | + | 0.904797i | \(0.359978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16539.4 | −0.800436 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4030.22 | 0.194271 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37789.1 | −1.81436 | −0.907179 | − | 0.420744i | \(-0.861769\pi\) | ||||
−0.907179 | + | 0.420744i | \(0.861769\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 920.864 | 0.0440385 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3292.90 | 0.156856 | 0.0784281 | − | 0.996920i | \(-0.475010\pi\) | ||||
0.0784281 | + | 0.996920i | \(0.475010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44101.2 | −2.09249 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5427.98 | −0.256534 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11443.5 | 0.538722 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28023.9 | −1.31413 | −0.657065 | − | 0.753834i | \(-0.728202\pi\) | ||||
−0.657065 | + | 0.753834i | \(0.728202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39141.6 | −1.82834 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22131.0 | 1.02975 | 0.514875 | − | 0.857265i | \(-0.327838\pi\) | ||||
0.514875 | + | 0.857265i | \(0.327838\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6728.01 | 0.311841 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12893.5 | −0.595306 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8400.67 | 0.386374 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30099.6 | −1.37906 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −59726.2 | −2.72598 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4491.63 | −0.204220 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5390.88 | −0.244173 | −0.122087 | − | 0.992519i | \(-0.538959\pi\) | ||||
−0.122087 | + | 0.992519i | \(0.538959\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 40981.9 | 1.84917 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22327.0 | 1.00361 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39722.4 | −1.77880 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6929.27 | −0.309127 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43815.4 | 1.94733 | 0.973664 | − | 0.227986i | \(-0.0732142\pi\) | ||||
0.973664 | + | 0.227986i | \(0.0732142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3077.80 | −0.136276 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39679.2 | 1.75031 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22882.5 | −1.00561 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −204.613 | −0.00895860 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49338.6 | −2.15217 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19752.4 | −0.858415 | −0.429208 | − | 0.903206i | \(-0.641207\pi\) | ||||
−0.429208 | + | 0.903206i | \(0.641207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21280.3 | −0.921398 | −0.460699 | − | 0.887556i | \(-0.652401\pi\) | ||||
−0.460699 | + | 0.887556i | \(0.652401\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −74777.1 | −3.22577 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3752.81 | 0.161295 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2531.31 | 0.108396 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 147508. | 6.29345 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19716.5 | −0.838136 | −0.419068 | − | 0.907955i | \(-0.637643\pi\) | ||||
−0.419068 | + | 0.907955i | \(0.637643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16269.0 | −0.689065 | −0.344532 | − | 0.938774i | \(-0.611963\pi\) | ||||
−0.344532 | + | 0.938774i | \(0.611963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 40631.3 | 1.71467 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27410.0 | 1.15253 | 0.576263 | − | 0.817264i | \(-0.304510\pi\) | ||||
0.576263 | + | 0.817264i | \(0.304510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25392.8 | −1.06385 | −0.531923 | − | 0.846792i | \(-0.678531\pi\) | ||||
−0.531923 | + | 0.846792i | \(0.678531\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1666.37 | 0.0695615 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9699.82 | −0.403456 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8244.99 | −0.341712 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19912.2 | 0.822302 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20579.5 | 0.846823 | 0.423412 | − | 0.905937i | \(-0.360832\pi\) | ||||
0.423412 | + | 0.905937i | \(0.360832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5821.76 | 0.238704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −68973.4 | −2.81799 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17360.7 | 0.706777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 703.094 | 0.0285225 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21981.4 | 0.888575 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −137.031 | −0.00551980 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6873.98 | 0.275921 | 0.137961 | − | 0.990438i | \(-0.455945\pi\) | ||||
0.137961 | + | 0.990438i | \(0.455945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11093.3 | 0.443721 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20623.8 | −0.822049 | −0.411025 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411025 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40959.1 | −1.62690 | −0.813450 | − | 0.581635i | \(-0.802413\pi\) | ||||
−0.813450 | + | 0.581635i | \(0.802413\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −35332.7 | −1.39853 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33784.0 | −1.33258 | −0.666292 | − | 0.745691i | \(-0.732120\pi\) | ||||
−0.666292 | + | 0.745691i | \(0.732120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2995.01 | 0.117727 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38777.4 | 1.51897 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13921.1 | −0.543430 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10556.8 | 0.410680 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −51631.8 | −2.00169 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18748.0 | −0.724340 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37125.7 | −1.42947 | −0.714736 | − | 0.699395i | \(-0.753453\pi\) | ||||
−0.714736 | + | 0.699395i | \(0.753453\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −82843.2 | −3.17887 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −108.651 | −0.00415499 | −0.00207749 | − | 0.999998i | \(-0.500661\pi\) | ||||
−0.00207749 | + | 0.999998i | \(0.500661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19622.4 | 0.747843 | 0.373921 | − | 0.927460i | \(-0.378013\pi\) | ||||
0.373921 | + | 0.927460i | \(0.378013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3619.64 | −0.137483 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26012.1 | 0.984668 | 0.492334 | − | 0.870406i | \(-0.336144\pi\) | ||||
0.492334 | + | 0.870406i | \(0.336144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58237.6 | 2.19710 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57386.2 | 2.15770 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6290.17 | 0.235714 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7952.40 | −0.297005 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2237.60 | 0.0832902 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10072.0 | −0.373660 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7047.01 | −0.260566 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10646.5 | −0.392353 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8995.70 | 0.330417 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42258.2 | 1.54703 | 0.773517 | − | 0.633776i | \(-0.218496\pi\) | ||||
0.773517 | + | 0.633776i | \(0.218496\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32441.2 | 1.18372 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6717.75 | −0.244313 | −0.122156 | − | 0.992511i | \(-0.538981\pi\) | ||||
−0.122156 | + | 0.992511i | \(0.538981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53552.4 | 1.94121 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12564.4 | 0.453954 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 53486.9 | 1.92616 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46824.2 | −1.68073 | −0.840364 | − | 0.542023i | \(-0.817659\pi\) | ||||
−0.840364 | + | 0.542023i | \(0.817659\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15001.5 | 0.536717 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −73138.7 | −2.60822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6046.21 | −0.214917 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −43583.7 | −1.54420 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14300.0 | 0.505025 | 0.252513 | − | 0.967594i | \(-0.418743\pi\) | ||||
0.252513 | + | 0.967594i | \(0.418743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19823.7 | 0.697848 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −53220.8 | −1.86749 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3165.73 | −0.110728 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44630.3 | 1.55604 | 0.778019 | − | 0.628241i | \(-0.216225\pi\) | ||||
0.778019 | + | 0.628241i | \(0.216225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32571.8 | −1.13199 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12069.3 | −0.418116 | −0.209058 | − | 0.977903i | \(-0.567040\pi\) | ||||
−0.209058 | + | 0.977903i | \(0.567040\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −375.511 | −0.0129675 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26719.7 | −0.919781 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23634.0 | −0.810984 | −0.405492 | − | 0.914099i | \(-0.632900\pi\) | ||||
−0.405492 | + | 0.914099i | \(0.632900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55602.0 | −1.90192 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42668.0 | −1.45489 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31376.9 | −1.06652 | −0.533262 | − | 0.845950i | \(-0.679034\pi\) | ||||
−0.533262 | + | 0.845950i | \(0.679034\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4214.67 | −0.142810 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −60826.2 | −2.05458 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67643.6 | 2.27771 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26433.1 | −0.887284 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20263.8 | −0.678080 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3717.93 | −0.124025 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32665.7 | −1.08631 | −0.543154 | − | 0.839633i | \(-0.682770\pi\) | ||||
−0.543154 | + | 0.839633i | \(0.682770\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16102.7 | 0.533842 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41567.8 | 1.37381 | 0.686907 | − | 0.726745i | \(-0.258968\pi\) | ||||
0.686907 | + | 0.726745i | \(0.258968\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29733.6 | −0.979665 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 98729.6 | 3.24295 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25363.2 | −0.830542 | −0.415271 | − | 0.909698i | \(-0.636313\pi\) | ||||
−0.415271 | + | 0.909698i | \(0.636313\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23141.9 | 0.755484 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −106877. | −3.47841 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3961.23 | 0.128528 | 0.0642642 | − | 0.997933i | \(-0.479530\pi\) | ||||
0.0642642 | + | 0.997933i | \(0.479530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14707.0 | −0.475740 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26456.0 | −0.853196 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −113.150 | −0.00363798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27940.2 | −0.895610 | −0.447805 | − | 0.894131i | \(-0.647794\pi\) | ||||
−0.447805 | + | 0.894131i | \(0.647794\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42106.4 | 1.34563 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1647.69 | −0.0524978 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15531.3 | −0.493363 | −0.246681 | − | 0.969097i | \(-0.579340\pi\) | ||||
−0.246681 | + | 0.969097i | \(0.579340\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17894.4 | −0.566719 |
(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 | 688.4.a.i.1.1 | 6 | ||
4.3 | odd | 2 | 43.4.a.b.1.4 | ✓ | 6 | ||
12.11 | even | 2 | 387.4.a.h.1.3 | 6 | |||
20.19 | odd | 2 | 1075.4.a.b.1.3 | 6 | |||
28.27 | even | 2 | 2107.4.a.c.1.4 | 6 | |||
172.171 | even | 2 | 1849.4.a.c.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.a.b.1.4 | ✓ | 6 | 4.3 | odd | 2 | ||
387.4.a.h.1.3 | 6 | 12.11 | even | 2 | |||
688.4.a.i.1.1 | 6 | 1.1 | even | 1 | trivial | ||
1075.4.a.b.1.3 | 6 | 20.19 | odd | 2 | |||
1849.4.a.c.1.3 | 6 | 172.171 | even | 2 | |||
2107.4.a.c.1.4 | 6 | 28.27 | even | 2 |