Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(1,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1500.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23607 | −1.22312 | −0.611559 | − | 0.791199i | \(-0.709457\pi\) | ||||
−0.611559 | + | 0.791199i | \(0.709457\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | −0.372689 | −0.186344 | − | 0.982485i | \(-0.559664\pi\) | ||||
−0.186344 | + | 0.982485i | \(0.559664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.381966 | 0.0926404 | 0.0463202 | − | 0.998927i | \(-0.485251\pi\) | ||||
0.0463202 | + | 0.998927i | \(0.485251\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.85410 | 1.34302 | 0.671512 | − | 0.740994i | \(-0.265645\pi\) | ||||
0.671512 | + | 0.740994i | \(0.265645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.85410 | 1.01215 | 0.506075 | − | 0.862489i | \(-0.331096\pi\) | ||||
0.506075 | + | 0.862489i | \(0.331096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.61803 | 1.36824 | 0.684120 | − | 0.729370i | \(-0.260187\pi\) | ||||
0.684120 | + | 0.729370i | \(0.260187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23607 | −0.215172 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.47214 | −0.698430 | −0.349215 | − | 0.937043i | \(-0.613552\pi\) | ||||
−0.349215 | + | 0.937043i | \(0.613552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70820 | 0.870493 | 0.435246 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435246 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.09017 | 1.32594 | 0.662969 | − | 0.748647i | \(-0.269296\pi\) | ||||
0.662969 | + | 0.748647i | \(0.269296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.381966 | 0.0534859 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.09017 | −0.699189 | −0.349594 | − | 0.936901i | \(-0.613681\pi\) | ||||
−0.349594 | + | 0.936901i | \(0.613681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.85410 | 0.775395 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2361 | 1.46281 | 0.731406 | − | 0.681943i | \(-0.238865\pi\) | ||||
0.731406 | + | 0.681943i | \(0.238865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.56231 | −0.712180 | −0.356090 | − | 0.934452i | \(-0.615890\pi\) | ||||
−0.356090 | + | 0.934452i | \(0.615890\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.23607 | −0.407706 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.7082 | −1.91906 | −0.959531 | − | 0.281602i | \(-0.909134\pi\) | ||||
−0.959531 | + | 0.281602i | \(0.909134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.85410 | 0.584365 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.52786 | 0.656037 | 0.328018 | − | 0.944671i | \(-0.393619\pi\) | ||||
0.328018 | + | 0.944671i | \(0.393619\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.52786 | −0.412905 | −0.206453 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206453 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8541 | 1.55871 | 0.779354 | − | 0.626584i | \(-0.215547\pi\) | ||||
0.779354 | + | 0.626584i | \(0.215547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.32624 | −0.694395 | −0.347197 | − | 0.937792i | \(-0.612867\pi\) | ||||
−0.347197 | + | 0.937792i | \(0.612867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.47214 | 0.908308 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.76393 | −0.292976 | −0.146488 | − | 0.989212i | \(-0.546797\pi\) | ||||
−0.146488 | + | 0.989212i | \(0.546797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.61803 | 0.789953 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | −1.21842 | −0.609208 | − | 0.793011i | \(-0.708512\pi\) | ||||
−0.609208 | + | 0.793011i | \(0.708512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.23607 | −0.124230 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.763932 | 0.0760141 | 0.0380070 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380070 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.29180 | −0.225817 | −0.112909 | − | 0.993605i | \(-0.536017\pi\) | ||||
−0.112909 | + | 0.993605i | \(0.536017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.3820 | −1.39036 | −0.695179 | − | 0.718837i | \(-0.744675\pi\) | ||||
−0.695179 | + | 0.718837i | \(0.744675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.61803 | 0.154980 | 0.0774898 | − | 0.996993i | \(-0.475309\pi\) | ||||
0.0774898 | + | 0.996993i | \(0.475309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.67376 | 0.157454 | 0.0787271 | − | 0.996896i | \(-0.474914\pi\) | ||||
0.0787271 | + | 0.996896i | \(0.474914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.23607 | −0.113310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.47214 | −0.403239 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.41641 | −0.835571 | −0.417786 | − | 0.908546i | \(-0.637194\pi\) | ||||
−0.417786 | + | 0.908546i | \(0.637194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.70820 | 0.502579 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9443 | 0.956205 | 0.478103 | − | 0.878304i | \(-0.341325\pi\) | ||||
0.478103 | + | 0.878304i | \(0.341325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.9443 | −1.64268 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4721 | 1.40731 | 0.703655 | − | 0.710542i | \(-0.251550\pi\) | ||||
0.703655 | + | 0.710542i | \(0.251550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.14590 | 0.436469 | 0.218235 | − | 0.975896i | \(-0.429970\pi\) | ||||
0.218235 | + | 0.975896i | \(0.429970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.09017 | 0.765530 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.47214 | 0.286377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.1246 | 1.89444 | 0.947221 | − | 0.320581i | \(-0.103878\pi\) | ||||
0.947221 | + | 0.320581i | \(0.103878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.85410 | −0.476400 | −0.238200 | − | 0.971216i | \(-0.576557\pi\) | ||||
−0.238200 | + | 0.971216i | \(0.576557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.381966 | 0.0308801 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7639 | −1.17829 | −0.589145 | − | 0.808027i | \(-0.700535\pi\) | ||||
−0.589145 | + | 0.808027i | \(0.700535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.09017 | −0.403677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.7082 | −1.23798 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.76393 | −0.216488 | −0.108244 | − | 0.994124i | \(-0.534523\pi\) | ||||
−0.108244 | + | 0.994124i | \(0.534523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.85410 | 0.607769 | 0.303884 | − | 0.952709i | \(-0.401716\pi\) | ||||
0.303884 | + | 0.952709i | \(0.401716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.85410 | 0.447674 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.8885 | 1.81621 | 0.908106 | − | 0.418740i | \(-0.137528\pi\) | ||||
0.908106 | + | 0.418740i | \(0.137528\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.2361 | 0.844555 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.8885 | −1.78551 | −0.892757 | − | 0.450539i | \(-0.851232\pi\) | ||||
−0.892757 | + | 0.450539i | \(0.851232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5623 | −1.30540 | −0.652698 | − | 0.757618i | \(-0.726363\pi\) | ||||
−0.652698 | + | 0.757618i | \(0.726363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.56231 | −0.411177 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.472136 | −0.0345260 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.23607 | −0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9443 | 0.936615 | 0.468307 | − | 0.883566i | \(-0.344864\pi\) | ||||
0.468307 | + | 0.883566i | \(0.344864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1246 | 1.52058 | 0.760291 | − | 0.649582i | \(-0.225056\pi\) | ||||
0.760291 | + | 0.649582i | \(0.225056\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.0344 | 1.64114 | 0.820568 | − | 0.571549i | \(-0.193657\pi\) | ||||
0.820568 | + | 0.571549i | \(0.193657\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7984 | −0.836365 | −0.418182 | − | 0.908363i | \(-0.637333\pi\) | ||||
−0.418182 | + | 0.908363i | \(0.637333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.7082 | −1.10797 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.4164 | −1.92425 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.85410 | 0.337383 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.23607 | −0.500529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5623 | 0.864825 | 0.432412 | − | 0.901676i | \(-0.357662\pi\) | ||||
0.432412 | + | 0.901676i | \(0.357662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.52786 | 0.378763 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.6525 | −1.67352 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.52786 | −0.238391 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.8328 | 1.79686 | 0.898429 | − | 0.439119i | \(-0.144709\pi\) | ||||
0.898429 | + | 0.439119i | \(0.144709\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9098 | 0.790483 | 0.395242 | − | 0.918577i | \(-0.370661\pi\) | ||||
0.395242 | + | 0.918577i | \(0.370661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.14590 | −0.207887 | −0.103943 | − | 0.994583i | \(-0.533146\pi\) | ||||
−0.103943 | + | 0.994583i | \(0.533146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.4164 | −0.878938 | −0.439469 | − | 0.898258i | \(-0.644833\pi\) | ||||
−0.439469 | + | 0.898258i | \(0.644833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8541 | 0.899921 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.763932 | 0.0494147 | 0.0247073 | − | 0.999695i | \(-0.492135\pi\) | ||||
0.0247073 | + | 0.999695i | \(0.492135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2705 | 0.790413 | 0.395207 | − | 0.918592i | \(-0.370673\pi\) | ||||
0.395207 | + | 0.918592i | \(0.370673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.32624 | −0.400909 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1803 | 0.895055 | 0.447528 | − | 0.894270i | \(-0.352305\pi\) | ||||
0.447528 | + | 0.894270i | \(0.352305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.38197 | −0.585231 | −0.292615 | − | 0.956230i | \(-0.594526\pi\) | ||||
−0.292615 | + | 0.956230i | \(0.594526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.47214 | −0.402159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.47214 | 0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.6180 | 1.08637 | 0.543187 | − | 0.839612i | \(-0.317217\pi\) | ||||
0.543187 | + | 0.839612i | \(0.317217\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.76393 | −0.169150 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.1246 | −1.77576 | −0.887879 | − | 0.460076i | \(-0.847822\pi\) | ||||
−0.887879 | + | 0.460076i | \(0.847822\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2705 | 1.10985 | 0.554927 | − | 0.831899i | \(-0.312746\pi\) | ||||
0.554927 | + | 0.831899i | \(0.312746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4164 | −0.926282 | −0.463141 | − | 0.886285i | \(-0.653278\pi\) | ||||
−0.463141 | + | 0.886285i | \(0.653278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.61803 | 0.456080 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7639 | −1.59660 | −0.798301 | − | 0.602258i | \(-0.794268\pi\) | ||||
−0.798301 | + | 0.602258i | \(0.794268\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.18034 | −0.248495 | −0.124248 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124248 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4721 | 0.854263 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8541 | −0.991418 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0344 | 1.11200 | 0.556002 | − | 0.831181i | \(-0.312335\pi\) | ||||
0.556002 | + | 0.831181i | \(0.312335\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.23607 | −0.0717239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.4721 | −1.06472 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.763932 | 0.0438867 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.1803 | −1.38004 | −0.690022 | − | 0.723788i | \(-0.742399\pi\) | ||||
−0.690022 | + | 0.723788i | \(0.742399\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.29180 | −0.130376 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.2918 | −0.810413 | −0.405207 | − | 0.914225i | \(-0.632800\pi\) | ||||
−0.405207 | + | 0.914225i | \(0.632800\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.7082 | −0.887880 | −0.443940 | − | 0.896056i | \(-0.646420\pi\) | ||||
−0.443940 | + | 0.896056i | \(0.646420\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.8328 | −1.84407 | −0.922037 | − | 0.387101i | \(-0.873476\pi\) | ||||
−0.922037 | + | 0.387101i | \(0.873476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4721 | −0.586327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.3820 | −0.802723 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.23607 | 0.124418 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.61803 | 0.0894775 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.4164 | −1.62178 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.0344 | 1.32105 | 0.660526 | − | 0.750803i | \(-0.270333\pi\) | ||||
0.660526 | + | 0.750803i | \(0.270333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1803 | 0.990346 | 0.495173 | − | 0.868794i | \(-0.335105\pi\) | ||||
0.495173 | + | 0.868794i | \(0.335105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.67376 | 0.0909063 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.41641 | −0.509927 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.50658 | 0.456657 | 0.228329 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228329 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.85410 | −0.259834 | −0.129917 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129917 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8541 | 1.21640 | 0.608201 | − | 0.793783i | \(-0.291892\pi\) | ||||
0.608201 | + | 0.793783i | \(0.291892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.23607 | −0.0654197 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4721 | −0.552698 | −0.276349 | − | 0.961057i | \(-0.589125\pi\) | ||||
−0.276349 | + | 0.961057i | \(0.589125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2705 | 0.803711 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.47214 | −0.497158 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4164 | −1.01353 | −0.506764 | − | 0.862085i | \(-0.669158\pi\) | ||||
−0.506764 | + | 0.862085i | \(0.669158\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.47214 | −0.232810 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4721 | 0.855191 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.5279 | −1.11467 | −0.557335 | − | 0.830288i | \(-0.688176\pi\) | ||||
−0.557335 | + | 0.830288i | \(0.688176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.41641 | −0.482417 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.2148 | −1.08402 | −0.542012 | − | 0.840371i | \(-0.682337\pi\) | ||||
−0.542012 | + | 0.840371i | \(0.682337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.70820 | 0.290164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.65248 | 0.337294 | 0.168647 | − | 0.985677i | \(-0.446060\pi\) | ||||
0.168647 | + | 0.985677i | \(0.446060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85410 | 0.0937660 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9443 | 0.552065 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.29180 | −0.315776 | −0.157888 | − | 0.987457i | \(-0.550469\pi\) | ||||
−0.157888 | + | 0.987457i | \(0.550469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.9443 | −0.948400 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3607 | 0.916889 | 0.458444 | − | 0.888723i | \(-0.348407\pi\) | ||||
0.458444 | + | 0.888723i | \(0.348407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.47214 | −0.122539 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.5623 | −1.06619 | −0.533094 | − | 0.846056i | \(-0.678971\pi\) | ||||
−0.533094 | + | 0.846056i | \(0.678971\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.4721 | 0.812511 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.3607 | −1.78919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.14590 | 0.251996 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.81966 | 0.284309 | 0.142155 | − | 0.989844i | \(-0.454597\pi\) | ||||
0.142155 | + | 0.989844i | \(0.454597\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.3262 | −0.990640 | −0.495320 | − | 0.868711i | \(-0.664949\pi\) | ||||
−0.495320 | + | 0.868711i | \(0.664949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.09017 | 0.441979 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | 0.871081 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.52786 | −0.362604 | −0.181302 | − | 0.983427i | \(-0.558031\pi\) | ||||
−0.181302 | + | 0.983427i | \(0.558031\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.4164 | −1.31755 | −0.658774 | − | 0.752341i | \(-0.728925\pi\) | ||||
−0.658774 | + | 0.752341i | \(0.728925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.4164 | 1.35934 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4164 | −0.735785 | −0.367893 | − | 0.929868i | \(-0.619921\pi\) | ||||
−0.367893 | + | 0.929868i | \(0.619921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7984 | 0.988161 | 0.494080 | − | 0.869416i | \(-0.335505\pi\) | ||||
0.494080 | + | 0.869416i | \(0.335505\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.1246 | 1.09376 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.81966 | −0.274647 | −0.137323 | − | 0.990526i | \(-0.543850\pi\) | ||||
−0.137323 | + | 0.990526i | \(0.543850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.52786 | 0.260297 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.85410 | −0.275050 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.12461 | 0.239719 | 0.119860 | − | 0.992791i | \(-0.461756\pi\) | ||||
0.119860 | + | 0.992791i | \(0.461756\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.381966 | 0.0178286 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.1803 | −0.939892 | −0.469946 | − | 0.882695i | \(-0.655727\pi\) | ||||
−0.469946 | + | 0.882695i | \(0.655727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.9443 | 1.43810 | 0.719051 | − | 0.694957i | \(-0.244577\pi\) | ||||
0.719051 | + | 0.694957i | \(0.244577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.74265 | 0.265738 | 0.132869 | − | 0.991134i | \(-0.457581\pi\) | ||||
0.132869 | + | 0.991134i | \(0.457581\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.8328 | 2.34724 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.7639 | −0.680286 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.05573 | −0.324423 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.09017 | −0.233063 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.1246 | −0.508296 | −0.254148 | − | 0.967165i | \(-0.581795\pi\) | ||||
−0.254148 | + | 0.967165i | \(0.581795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.7082 | −0.714748 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.7639 | 0.487760 | 0.243880 | − | 0.969805i | \(-0.421580\pi\) | ||||
0.243880 | + | 0.969805i | \(0.421580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.76393 | −0.124989 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.8328 | −1.48172 | −0.740862 | − | 0.671657i | \(-0.765583\pi\) | ||||
−0.740862 | + | 0.671657i | \(0.765583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.23607 | 0.145745 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.8885 | −0.802411 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.6869 | −1.28420 | −0.642101 | − | 0.766620i | \(-0.721937\pi\) | ||||
−0.642101 | + | 0.766620i | \(0.721937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.85410 | 0.350895 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.9443 | −1.46891 | −0.734456 | − | 0.678656i | \(-0.762563\pi\) | ||||
−0.734456 | + | 0.678656i | \(0.762563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.8885 | 1.32479 | 0.662393 | − | 0.749156i | \(-0.269541\pi\) | ||||
0.662393 | + | 0.749156i | \(0.269541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4164 | 0.505032 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.85410 | 0.258465 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.2361 | −0.494162 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.8885 | 1.04859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.8885 | 1.30944 | 0.654720 | − | 0.755871i | \(-0.272786\pi\) | ||||
0.654720 | + | 0.755871i | \(0.272786\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.8885 | 1.74420 | 0.872102 | − | 0.489324i | \(-0.162756\pi\) | ||||
0.872102 | + | 0.489324i | \(0.162756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.90983 | 0.126754 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.562306 | 0.0244481 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2361 | 0.487604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.8885 | −1.03087 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.29180 | −0.184861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2705 | −0.699524 | −0.349762 | − | 0.936839i | \(-0.613738\pi\) | ||||
−0.349762 | + | 0.936839i | \(0.613738\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.5623 | −0.753671 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.8328 | 1.91691 | 0.958456 | − | 0.285239i | \(-0.0920730\pi\) | ||||
0.958456 | + | 0.285239i | \(0.0920730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.56231 | −0.237393 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 49.5967 | 2.11289 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.8328 | −1.90649 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3607 | 0.438996 | 0.219498 | − | 0.975613i | \(-0.429558\pi\) | ||||
0.219498 | + | 0.975613i | \(0.429558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.472136 | −0.0199336 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.38197 | −0.268968 | −0.134484 | − | 0.990916i | \(-0.542938\pi\) | ||||
−0.134484 | + | 0.990916i | \(0.542938\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.23607 | −0.135902 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.3050 | −1.06084 | −0.530419 | − | 0.847735i | \(-0.677966\pi\) | ||||
−0.530419 | + | 0.847735i | \(0.677966\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.8885 | −1.58559 | −0.792793 | − | 0.609491i | \(-0.791374\pi\) | ||||
−0.792793 | + | 0.609491i | \(0.791374\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.9443 | 0.540755 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.1246 | 0.962690 | 0.481345 | − | 0.876531i | \(-0.340148\pi\) | ||||
0.481345 | + | 0.876531i | \(0.340148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.1246 | 0.877909 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.4721 | 0.849327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.29180 | 0.260580 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.0344 | −0.537989 | −0.268994 | − | 0.963142i | \(-0.586691\pi\) | ||||
−0.268994 | + | 0.963142i | \(0.586691\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.5967 | 1.83758 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.0344 | 0.947510 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5066 | 0.842104 | 0.421052 | − | 0.907036i | \(-0.361661\pi\) | ||||
0.421052 | + | 0.907036i | \(0.361661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.7984 | −0.482875 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.8328 | 1.34151 | 0.670756 | − | 0.741678i | \(-0.265970\pi\) | ||||
0.670756 | + | 0.741678i | \(0.265970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.8541 | −0.524330 | −0.262165 | − | 0.965023i | \(-0.584436\pi\) | ||||
−0.262165 | + | 0.965023i | \(0.584436\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.7082 | −0.639688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −48.2492 | −1.95838 | −0.979188 | − | 0.202956i | \(-0.934945\pi\) | ||||
−0.979188 | + | 0.202956i | \(0.934945\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −27.4164 | −1.11097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.59675 | −0.306830 | −0.153415 | − | 0.988162i | \(-0.549027\pi\) | ||||
−0.153415 | + | 0.988162i | \(0.549027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.4508 | −1.38694 | −0.693469 | − | 0.720486i | \(-0.743919\pi\) | ||||
−0.693469 | + | 0.720486i | \(0.743919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7984 | 0.956537 | 0.478269 | − | 0.878214i | \(-0.341265\pi\) | ||||
0.478269 | + | 0.878214i | \(0.341265\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.85410 | 0.194788 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.94427 | 0.358345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.23607 | −0.288981 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.763932 | 0.0304600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.3050 | −1.16661 | −0.583306 | − | 0.812253i | \(-0.698241\pi\) | ||||
−0.583306 | + | 0.812253i | \(0.698241\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5623 | 0.499307 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.52786 | 0.218679 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.7771 | −1.65010 | −0.825048 | − | 0.565063i | \(-0.808852\pi\) | ||||
−0.825048 | + | 0.565063i | \(0.808852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.65248 | −0.183476 | −0.0917379 | − | 0.995783i | \(-0.529242\pi\) | ||||
−0.0917379 | + | 0.995783i | \(0.529242\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0557 | −0.749158 | −0.374579 | − | 0.927195i | \(-0.622213\pi\) | ||||
−0.374579 | + | 0.927195i | \(0.622213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8885 | −0.545173 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.6525 | −0.966207 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 46.6869 | 1.82700 | 0.913500 | − | 0.406838i | \(-0.133369\pi\) | ||||
0.913500 | + | 0.406838i | \(0.133369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.52786 | −0.137635 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.0689 | 1.24923 | 0.624613 | − | 0.780934i | \(-0.285257\pi\) | ||||
0.624613 | + | 0.780934i | \(0.285257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.2016 | 0.707961 | 0.353981 | − | 0.935253i | \(-0.384828\pi\) | ||||
0.353981 | + | 0.935253i | \(0.384828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.1246 | 1.59235 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.8328 | 1.03742 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.87539 | 0.265421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.88854 | −0.304081 | −0.152041 | − | 0.988374i | \(-0.548584\pi\) | ||||
−0.152041 | + | 0.988374i | \(0.548584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.97871 | −0.268214 | −0.134107 | − | 0.990967i | \(-0.542817\pi\) | ||||
−0.134107 | + | 0.990967i | \(0.542817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.8328 | 1.49027 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.9098 | 0.456386 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.3262 | −0.739498 | −0.369749 | − | 0.929132i | \(-0.620556\pi\) | ||||
−0.369749 | + | 0.929132i | \(0.620556\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.14590 | −0.120023 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.56231 | −0.173558 | −0.0867791 | − | 0.996228i | \(-0.527657\pi\) | ||||
−0.0867791 | + | 0.996228i | \(0.527657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.70820 | −0.0647028 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.4164 | −0.507455 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.88854 | −0.0713293 | −0.0356647 | − | 0.999364i | \(-0.511355\pi\) | ||||
−0.0356647 | + | 0.999364i | \(0.511355\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.7082 | 0.441583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.47214 | −0.0929742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6180 | 0.473880 | 0.236940 | − | 0.971524i | \(-0.423855\pi\) | ||||
0.236940 | + | 0.971524i | \(0.423855\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.8541 | 0.519569 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.9787 | 1.38486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.763932 | 0.0285296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.7639 | 0.774364 | 0.387182 | − | 0.922003i | \(-0.373449\pi\) | ||||
0.387182 | + | 0.922003i | \(0.373449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.41641 | 0.276201 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.2705 | 0.456345 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.8328 | −0.698470 | −0.349235 | − | 0.937035i | \(-0.613559\pi\) | ||||
−0.349235 | + | 0.937035i | \(0.613559\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.18034 | 0.0806428 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1803 | 0.376019 | 0.188010 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188010 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.4164 | 0.715213 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5623 | −0.462112 | −0.231056 | − | 0.972940i | \(-0.574218\pi\) | ||||
−0.231056 | + | 0.972940i | \(0.574218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.41641 | −0.272082 | −0.136041 | − | 0.990703i | \(-0.543438\pi\) | ||||
−0.136041 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.32624 | −0.231465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.5410 | 1.70057 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.90983 | 0.325124 | 0.162562 | − | 0.986698i | \(-0.448024\pi\) | ||||
0.162562 | + | 0.986698i | \(0.448024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.1803 | 0.516760 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.4853 | 1.58050 | 0.790250 | − | 0.612785i | \(-0.209951\pi\) | ||||
0.790250 | + | 0.612785i | \(0.209951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | −0.217786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5279 | −0.490385 | −0.245192 | − | 0.969474i | \(-0.578851\pi\) | ||||
−0.245192 | + | 0.969474i | \(0.578851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.23607 | −0.189558 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.14590 | −0.0773831 | −0.0386915 | − | 0.999251i | \(-0.512319\pi\) | ||||
−0.0386915 | + | 0.999251i | \(0.512319\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.38197 | −0.337883 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −51.9230 | −1.86754 | −0.933770 | − | 0.357874i | \(-0.883502\pi\) | ||||
−0.933770 | + | 0.357874i | \(0.883502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.47214 | −0.232187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.1803 | −0.938008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.83282 | −0.244497 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.47214 | 0.302769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7082 | 1.41544 | 0.707722 | − | 0.706491i | \(-0.249723\pi\) | ||||
0.707722 | + | 0.706491i | \(0.249723\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.6180 | 0.627219 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.41641 | −0.192585 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.7426 | −0.734742 | −0.367371 | − | 0.930074i | \(-0.619742\pi\) | ||||
−0.367371 | + | 0.930074i | \(0.619742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.47214 | 0.122835 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.76393 | −0.0976587 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.36068 | 0.153885 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.1246 | −1.02523 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.4164 | 1.73739 | 0.868694 | − | 0.495349i | \(-0.164960\pi\) | ||||
0.868694 | + | 0.495349i | \(0.164960\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.43769 | 0.0855990 | 0.0427995 | − | 0.999084i | \(-0.486372\pi\) | ||||
0.0427995 | + | 0.999084i | \(0.486372\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.2705 | 0.640775 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.4164 | 1.16909 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.5279 | 1.44933 | 0.724666 | − | 0.689100i | \(-0.241994\pi\) | ||||
0.724666 | + | 0.689100i | \(0.241994\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.7639 | 0.514638 | 0.257319 | − | 0.966326i | \(-0.417161\pi\) | ||||
0.257319 | + | 0.966326i | \(0.417161\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1459 | −0.561448 | −0.280724 | − | 0.959789i | \(-0.590575\pi\) | ||||
−0.280724 | + | 0.959789i | \(0.590575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.8541 | 1.31473 | 0.657364 | − | 0.753574i | \(-0.271672\pi\) | ||||
0.657364 | + | 0.753574i | \(0.271672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4164 | −0.534789 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.32624 | 0.0459514 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.61803 | 0.263318 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.0132 | 0.932598 | 0.466299 | − | 0.884627i | \(-0.345587\pi\) | ||||
0.466299 | + | 0.884627i | \(0.345587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.7639 | −0.921799 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.6525 | 1.05323 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.18034 | −0.143469 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.70820 | 0.332793 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2918 | 0.900214 | 0.450107 | − | 0.892975i | \(-0.351386\pi\) | ||||
0.450107 | + | 0.892975i | \(0.351386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.9098 | 1.19250 | 0.596249 | − | 0.802800i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802800i | \(0.296657\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.8328 | 0.915524 | 0.457762 | − | 0.889075i | \(-0.348651\pi\) | ||||
0.457762 | + | 0.889075i | \(0.348651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.4721 | 0.493209 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.5279 | −0.596655 | −0.298328 | − | 0.954464i | \(-0.596429\pi\) | ||||
−0.298328 | + | 0.954464i | \(0.596429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8541 | −0.572395 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1246 | −0.580913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0000 | −0.406138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.5410 | 1.16637 | 0.583184 | − | 0.812340i | \(-0.301807\pi\) | ||||
0.583184 | + | 0.812340i | \(0.301807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.0344 | 0.642016 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5836 | −0.558715 | −0.279358 | − | 0.960187i | \(-0.590122\pi\) | ||||
−0.279358 | + | 0.960187i | \(0.590122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.1115 | 0.340278 | 0.170139 | − | 0.985420i | \(-0.445578\pi\) | ||||
0.170139 | + | 0.985420i | \(0.445578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.9098 | −0.769237 | −0.384618 | − | 0.923076i | \(-0.625667\pi\) | ||||
−0.384618 | + | 0.923076i | \(0.625667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.4721 | 1.02200 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.23607 | −0.0414098 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.2148 | 1.78076 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.5410 | 2.15256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.94427 | −0.0647731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.4721 | −0.614714 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.7082 | 1.78335 | 0.891676 | − | 0.452675i | \(-0.149530\pi\) | ||||
0.891676 | + | 0.452675i | \(0.149530\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.763932 | 0.0253380 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.0689 | −1.85764 | −0.928822 | − | 0.370525i | \(-0.879178\pi\) | ||||
−0.928822 | + | 0.370525i | \(0.879178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.81966 | 0.258793 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.4164 | −1.16955 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.25735 | −0.107450 | −0.0537251 | − | 0.998556i | \(-0.517109\pi\) | ||||
−0.0537251 | + | 0.998556i | \(0.517109\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.1803 | −0.796769 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.29180 | −0.0752725 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.4853 | −1.62356 | −0.811780 | − | 0.583964i | \(-0.801501\pi\) | ||||
−0.811780 | + | 0.583964i | \(0.801501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.3262 | 0.666166 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.2918 | −0.467892 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.5836 | −0.476425 | −0.238213 | − | 0.971213i | \(-0.576562\pi\) | ||||
−0.238213 | + | 0.971213i | \(0.576562\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.7082 | −0.512618 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.2918 | 1.24828 | 0.624138 | − | 0.781314i | \(-0.285450\pi\) | ||||
0.624138 | + | 0.781314i | \(0.285450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.7082 | −0.706916 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.2148 | −0.689388 | −0.344694 | − | 0.938715i | \(-0.612017\pi\) | ||||
−0.344694 | + | 0.938715i | \(0.612017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.8328 | −1.06468 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.7426 | −0.412775 | −0.206387 | − | 0.978470i | \(-0.566171\pi\) | ||||
−0.206387 | + | 0.978470i | \(0.566171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.4721 | −0.338516 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −53.3050 | −1.72131 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0344 | 0.872079 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.3820 | −0.463452 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.9443 | 0.609207 | 0.304603 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304603 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.23607 | 0.0718329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.5410 | −0.980108 | −0.490054 | − | 0.871692i | \(-0.663023\pi\) | ||||
−0.490054 | + | 0.871692i | \(0.663023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.6525 | −0.533854 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.7295 | −0.567217 | −0.283608 | − | 0.958940i | \(-0.591532\pi\) | ||||
−0.283608 | + | 0.958940i | \(0.591532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.41641 | 0.109189 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.61803 | 0.0516598 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.5066 | 1.54712 | 0.773560 | − | 0.633723i | \(-0.218474\pi\) | ||||
0.773560 | + | 0.633723i | \(0.218474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.4164 | −0.936335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7082 | 0.881070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.56231 | 0.176692 | 0.0883462 | − | 0.996090i | \(-0.471842\pi\) | ||||
0.0883462 | + | 0.996090i | \(0.471842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.0344 | 0.762710 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.00000 | 0.190022 | 0.0950110 | − | 0.995476i | \(-0.469711\pi\) | ||||
0.0950110 | + | 0.995476i | \(0.469711\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 1500.2.a.g.1.1 | yes | 2 | |
3.2 | odd | 2 | 4500.2.a.d.1.1 | 2 | |||
4.3 | odd | 2 | 6000.2.a.i.1.2 | 2 | |||
5.2 | odd | 4 | 1500.2.d.b.1249.1 | 4 | |||
5.3 | odd | 4 | 1500.2.d.b.1249.4 | 4 | |||
5.4 | even | 2 | 1500.2.a.c.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 4500.2.d.a.4249.1 | 4 | |||
15.8 | even | 4 | 4500.2.d.a.4249.4 | 4 | |||
15.14 | odd | 2 | 4500.2.a.h.1.2 | 2 | |||
20.3 | even | 4 | 6000.2.f.f.1249.1 | 4 | |||
20.7 | even | 4 | 6000.2.f.f.1249.4 | 4 | |||
20.19 | odd | 2 | 6000.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1500.2.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
1500.2.a.g.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1500.2.d.b.1249.1 | 4 | 5.2 | odd | 4 | |||
1500.2.d.b.1249.4 | 4 | 5.3 | odd | 4 | |||
4500.2.a.d.1.1 | 2 | 3.2 | odd | 2 | |||
4500.2.a.h.1.2 | 2 | 15.14 | odd | 2 | |||
4500.2.d.a.4249.1 | 4 | 15.2 | even | 4 | |||
4500.2.d.a.4249.4 | 4 | 15.8 | even | 4 | |||
6000.2.a.i.1.2 | 2 | 4.3 | odd | 2 | |||
6000.2.a.s.1.1 | 2 | 20.19 | odd | 2 | |||
6000.2.f.f.1249.1 | 4 | 20.3 | even | 4 | |||
6000.2.f.f.1249.4 | 4 | 20.7 | even | 4 |