Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 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 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.76393 | −0.513249 | −0.256625 | − | 0.966511i | \(-0.582610\pi\) | ||||
−0.256625 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23607 | 0.563327 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23607 | 0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.23607 | −0.860804 | −0.430402 | − | 0.902637i | \(-0.641628\pi\) | ||||
−0.430402 | + | 0.902637i | \(0.641628\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.23607 | 0.197929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.70820 | 0.579124 | 0.289562 | − | 0.957159i | \(-0.406490\pi\) | ||||
0.289562 | + | 0.957159i | \(0.406490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.23607 | −0.493496 | −0.246748 | − | 0.969080i | \(-0.579362\pi\) | ||||
−0.246748 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.47214 | −1.16374 | −0.581869 | − | 0.813283i | \(-0.697678\pi\) | ||||
−0.581869 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23607 | −0.436351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.52786 | 0.198911 | 0.0994555 | − | 0.995042i | \(-0.468290\pi\) | ||||
0.0994555 | + | 0.995042i | \(0.468290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47214 | −0.572598 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.23607 | −0.407706 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.47214 | −0.302019 | −0.151010 | − | 0.988532i | \(-0.548252\pi\) | ||||
−0.151010 | + | 0.988532i | \(0.548252\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.94427 | −0.586777 | −0.293389 | − | 0.955993i | \(-0.594783\pi\) | ||||
−0.293389 | + | 0.955993i | \(0.594783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.47214 | 0.991589 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.4721 | −1.19341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47214 | 0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.76393 | −0.296325 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.29180 | −0.454929 | −0.227465 | − | 0.973786i | \(-0.573044\pi\) | ||||
−0.227465 | + | 0.973786i | \(0.573044\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.1803 | −1.84593 | −0.922967 | − | 0.384879i | \(-0.874243\pi\) | ||||
−0.922967 | + | 0.384879i | \(0.874243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.23607 | 0.325237 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4721 | −1.24102 | −0.620512 | − | 0.784197i | \(-0.713075\pi\) | ||||
−0.620512 | + | 0.784197i | \(0.713075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.41641 | 0.730760 | 0.365380 | − | 0.930858i | \(-0.380939\pi\) | ||||
0.365380 | + | 0.930858i | \(0.380939\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.23607 | 0.315808 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.94427 | −0.864675 | −0.432338 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432338 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.47214 | −0.811483 | −0.405742 | − | 0.913988i | \(-0.632987\pi\) | ||||
−0.405742 | + | 0.913988i | \(0.632987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.23607 | −0.496986 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.05573 | −0.0993145 | −0.0496573 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496573 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.47214 | −0.230528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.23607 | 0.114275 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.4721 | 1.32666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.70820 | 0.334357 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.23607 | −0.284920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.70820 | 0.848210 | 0.424105 | − | 0.905613i | \(-0.360589\pi\) | ||||
0.424105 | + | 0.905613i | \(0.360589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.23607 | −0.280603 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.94427 | 0.251546 | 0.125773 | − | 0.992059i | \(-0.459859\pi\) | ||||
0.125773 | + | 0.992059i | \(0.459859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4721 | 1.56679 | 0.783393 | − | 0.621527i | \(-0.213487\pi\) | ||||
0.783393 | + | 0.621527i | \(0.213487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.47214 | 0.208191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.76393 | 0.229532 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.47214 | 0.286377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.4721 | −1.02176 | −0.510879 | − | 0.859653i | \(-0.670680\pi\) | ||||
−0.510879 | + | 0.859653i | \(0.670680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.47214 | −0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4164 | −1.38998 | −0.694990 | − | 0.719019i | \(-0.744591\pi\) | ||||
−0.694990 | + | 0.719019i | \(0.744591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.47214 | −0.671884 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6525 | −1.14767 | −0.573835 | − | 0.818971i | \(-0.694545\pi\) | ||||
−0.573835 | + | 0.818971i | \(0.694545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.23607 | −0.251928 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.9443 | −1.93025 | −0.965123 | − | 0.261797i | \(-0.915685\pi\) | ||||
−0.965123 | + | 0.261797i | \(0.915685\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.9443 | −1.74442 | −0.872210 | − | 0.489131i | \(-0.837314\pi\) | ||||
−0.872210 | + | 0.489131i | \(0.837314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.23607 | −0.244624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.52786 | 0.114841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.4721 | 1.08170 | 0.540849 | − | 0.841120i | \(-0.318103\pi\) | ||||
0.540849 | + | 0.841120i | \(0.318103\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.52786 | −0.262224 | −0.131112 | − | 0.991368i | \(-0.541855\pi\) | ||||
−0.131112 | + | 0.991368i | \(0.541855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.47214 | −0.330590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.23607 | 0.384963 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.4721 | −1.05831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.23607 | −0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.76393 | −0.344706 | −0.172353 | − | 0.985035i | \(-0.555137\pi\) | ||||
−0.172353 | + | 0.985035i | \(0.555137\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.76393 | −0.486878 | −0.243439 | − | 0.969916i | \(-0.578276\pi\) | ||||
−0.243439 | + | 0.969916i | \(0.578276\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.23607 | −0.0885167 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.41641 | 0.670891 | 0.335446 | − | 0.942060i | \(-0.391113\pi\) | ||||
0.335446 | + | 0.942060i | \(0.391113\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.52786 | 0.108307 | 0.0541537 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541537 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.47214 | −0.174371 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.94427 | 0.627765 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.70820 | −0.258992 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.47214 | 0.171825 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.23607 | 0.223844 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8885 | 0.956127 | 0.478063 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.94427 | −0.338776 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.23607 | 0.220698 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.9443 | 0.878714 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.47214 | 0.572494 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.52786 | −0.371844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.41641 | −0.496639 | −0.248320 | − | 0.968678i | \(-0.579878\pi\) | ||||
−0.248320 | + | 0.968678i | \(0.579878\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0557 | −0.733794 | −0.366897 | − | 0.930261i | \(-0.619580\pi\) | ||||
−0.366897 | + | 0.930261i | \(0.619580\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.47214 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4721 | −0.689016 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.9443 | −1.50313 | −0.751565 | − | 0.659659i | \(-0.770701\pi\) | ||||
−0.751565 | + | 0.659659i | \(0.770701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.47214 | −0.161264 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.9443 | 0.840821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.2361 | −0.726801 | −0.363400 | − | 0.931633i | \(-0.618384\pi\) | ||||
−0.363400 | + | 0.931633i | \(0.618384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.94427 | −0.189657 | −0.0948286 | − | 0.995494i | \(-0.530230\pi\) | ||||
−0.0948286 | + | 0.995494i | \(0.530230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.47214 | −0.221827 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.23607 | 0.0786491 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.70820 | −0.107821 | −0.0539104 | − | 0.998546i | \(-0.517169\pi\) | ||||
−0.0539104 | + | 0.998546i | \(0.517169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.47214 | 0.280056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.8885 | −0.991100 | −0.495550 | − | 0.868579i | \(-0.665033\pi\) | ||||
−0.495550 | + | 0.868579i | \(0.665033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.9443 | 1.05287 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.76393 | −0.171083 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.8885 | −1.34971 | −0.674853 | − | 0.737952i | \(-0.735793\pi\) | ||||
−0.674853 | + | 0.737952i | \(0.735793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.47214 | 0.520439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.29180 | −0.262654 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.70820 | −0.469977 | −0.234989 | − | 0.971998i | \(-0.575505\pi\) | ||||
−0.234989 | + | 0.971998i | \(0.575505\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.52786 | −0.0928111 | −0.0464056 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464056 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.23607 | 0.195142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4721 | 1.47039 | 0.735194 | − | 0.677857i | \(-0.237091\pi\) | ||||
0.735194 | + | 0.677857i | \(0.237091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.23607 | 0.312358 | 0.156179 | − | 0.987729i | \(-0.450082\pi\) | ||||
0.156179 | + | 0.987729i | \(0.450082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.70820 | −0.101542 | −0.0507711 | − | 0.998710i | \(-0.516168\pi\) | ||||
−0.0507711 | + | 0.998710i | \(0.516168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1803 | −1.06575 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.94427 | 0.172006 | 0.0860031 | − | 0.996295i | \(-0.472591\pi\) | ||||
0.0860031 | + | 0.996295i | \(0.472591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.52786 | −0.0889557 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.23607 | 0.187776 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.05573 | 0.176717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4721 | 0.603604 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.4721 | −0.716505 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.47214 | 0.256074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47214 | −0.141092 | −0.0705461 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705461 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.41641 | 0.421905 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7639 | −0.723776 | −0.361888 | − | 0.932222i | \(-0.617868\pi\) | ||||
−0.361888 | + | 0.932222i | \(0.617868\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.9443 | 1.74907 | 0.874537 | − | 0.484959i | \(-0.161166\pi\) | ||||
0.874537 | + | 0.484959i | \(0.161166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.23607 | 0.182332 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.3607 | 0.806576 | 0.403288 | − | 0.915073i | \(-0.367867\pi\) | ||||
0.403288 | + | 0.915073i | \(0.367867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.94427 | −0.500783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.94427 | −0.499221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.47214 | −0.248836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23607 | 0.0685647 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.47214 | −0.468510 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.88854 | 0.543524 | 0.271762 | − | 0.962365i | \(-0.412394\pi\) | ||||
0.271762 | + | 0.962365i | \(0.412394\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.23607 | −0.286935 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.47214 | 0.135067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7082 | 0.855680 | 0.427840 | − | 0.903854i | \(-0.359275\pi\) | ||||
0.427840 | + | 0.903854i | \(0.359275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.05573 | −0.0573393 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.9443 | −0.700972 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.47214 | −0.133095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.88854 | −0.530845 | −0.265422 | − | 0.964132i | \(-0.585511\pi\) | ||||
−0.265422 | + | 0.964132i | \(0.585511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9443 | 1.01406 | 0.507032 | − | 0.861927i | \(-0.330743\pi\) | ||||
0.507032 | + | 0.861927i | \(0.330743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.23607 | 0.0659764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.8885 | 1.69726 | 0.848628 | − | 0.528990i | \(-0.177429\pi\) | ||||
0.848628 | + | 0.528990i | \(0.177429\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.94427 | 0.262415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.4721 | 0.765947 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2361 | 0.593017 | 0.296508 | − | 0.955030i | \(-0.404178\pi\) | ||||
0.296508 | + | 0.955030i | \(0.404178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.527864 | −0.0277057 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.47214 | −0.443452 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7639 | −0.666272 | −0.333136 | − | 0.942879i | \(-0.608107\pi\) | ||||
−0.333136 | + | 0.942879i | \(0.608107\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.70820 | 0.193041 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.4164 | 1.42339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.23607 | 0.0640012 | 0.0320006 | − | 0.999488i | \(-0.489812\pi\) | ||||
0.0320006 | + | 0.999488i | \(0.489812\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.41641 | −0.175954 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.8885 | 1.32284 | 0.661421 | − | 0.750014i | \(-0.269954\pi\) | ||||
0.661421 | + | 0.750014i | \(0.269954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.4721 | 0.533709 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.23607 | −0.164499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.05573 | 0.256336 | 0.128168 | − | 0.991752i | \(-0.459090\pi\) | ||||
0.128168 | + | 0.991752i | \(0.459090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0557 | −0.559112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.70820 | 0.489714 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9443 | −0.651297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.3607 | 1.72451 | 0.862257 | − | 0.506472i | \(-0.169051\pi\) | ||||
0.862257 | + | 0.506472i | \(0.169051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.23607 | −0.162006 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.7639 | −1.33653 | −0.668263 | − | 0.743925i | \(-0.732962\pi\) | ||||
−0.668263 | + | 0.743925i | \(0.732962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.94427 | −0.246292 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9443 | −0.839896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3050 | 1.54793 | 0.773965 | − | 0.633228i | \(-0.218271\pi\) | ||||
0.773965 | + | 0.633228i | \(0.218271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.94427 | 0.145230 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.94427 | −0.243292 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.4721 | 0.904584 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.70820 | −0.474277 | −0.237138 | − | 0.971476i | \(-0.576209\pi\) | ||||
−0.237138 | + | 0.971476i | \(0.576209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.47214 | 0.120199 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47214 | −0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4721 | 0.700356 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.36068 | 0.402720 | 0.201360 | − | 0.979517i | \(-0.435464\pi\) | ||||
0.201360 | + | 0.979517i | \(0.435464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5967 | −0.653418 | −0.326709 | − | 0.945125i | \(-0.605940\pi\) | ||||
−0.326709 | + | 0.945125i | \(0.605940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.76393 | 0.132520 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.47214 | 0.118258 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.94427 | −0.235977 | −0.117989 | − | 0.993015i | \(-0.537645\pi\) | ||||
−0.117989 | + | 0.993015i | \(0.537645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3607 | 1.15741 | 0.578705 | − | 0.815537i | \(-0.303558\pi\) | ||||
0.578705 | + | 0.815537i | \(0.303558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.29180 | 0.203451 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.4721 | −0.589912 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.0689 | −1.13588 | −0.567940 | − | 0.823070i | \(-0.692260\pi\) | ||||
−0.567940 | + | 0.823070i | \(0.692260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.94427 | −0.420239 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | 0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.88854 | −0.369011 | −0.184505 | − | 0.982832i | \(-0.559068\pi\) | ||||
−0.184505 | + | 0.982832i | \(0.559068\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.58359 | −0.120330 | −0.0601649 | − | 0.998188i | \(-0.519163\pi\) | ||||
−0.0601649 | + | 0.998188i | \(0.519163\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.0689 | 1.58332 | 0.791658 | − | 0.610965i | \(-0.209218\pi\) | ||||
0.791658 | + | 0.610965i | \(0.209218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5279 | −0.811093 | −0.405546 | − | 0.914074i | \(-0.632919\pi\) | ||||
−0.405546 | + | 0.914074i | \(0.632919\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4164 | −0.802506 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.4721 | −0.481509 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.47214 | −0.387912 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.34752 | 0.427099 | 0.213550 | − | 0.976932i | \(-0.431497\pi\) | ||||
0.213550 | + | 0.976932i | \(0.431497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.47214 | −0.295104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.00000 | −0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.1803 | 0.825527 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.4164 | 1.42361 | 0.711807 | − | 0.702375i | \(-0.247877\pi\) | ||||
0.711807 | + | 0.702375i | \(0.247877\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.6525 | −0.662608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7639 | 0.576028 | 0.288014 | − | 0.957626i | \(-0.407005\pi\) | ||||
0.288014 | + | 0.957626i | \(0.407005\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.3607 | 0.556697 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.23607 | −0.145450 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3607 | −0.553340 | −0.276670 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276670 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.9443 | −1.11443 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.8885 | −0.975962 | −0.487981 | − | 0.872854i | \(-0.662266\pi\) | ||||
−0.487981 | + | 0.872854i | \(0.662266\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4721 | 0.555003 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.4721 | −0.509495 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.5967 | 1.31185 | 0.655926 | − | 0.754825i | \(-0.272278\pi\) | ||||
0.655926 | + | 0.754825i | \(0.272278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.4164 | −1.21283 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.41641 | −0.326806 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.9443 | −1.00714 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.59675 | −0.420441 | −0.210221 | − | 0.977654i | \(-0.567418\pi\) | ||||
−0.210221 | + | 0.977654i | \(0.567418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8885 | 0.957119 | 0.478560 | − | 0.878055i | \(-0.341159\pi\) | ||||
0.478560 | + | 0.878055i | \(0.341159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.23607 | −0.141234 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.8885 | 0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.52786 | 0.0663037 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.58359 | 0.198537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.94427 | 0.386695 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.4721 | 0.624519 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2361 | 0.483972 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.52786 | −0.151395 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.47214 | 0.362906 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.58359 | −0.367008 | −0.183504 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183504 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.47214 | −0.190866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.76393 | −0.117747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.8885 | −1.78128 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.23607 | 0.222259 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.8328 | −1.22169 | −0.610843 | − | 0.791752i | \(-0.709169\pi\) | ||||
−0.610843 | + | 0.791752i | \(0.709169\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4721 | −0.611014 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.8328 | −1.29945 | −0.649724 | − | 0.760170i | \(-0.725116\pi\) | ||||
−0.649724 | + | 0.760170i | \(0.725116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.05573 | 0.0444148 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.23607 | −0.135902 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.0132 | −1.88705 | −0.943525 | − | 0.331302i | \(-0.892512\pi\) | ||||
−0.943525 | + | 0.331302i | \(0.892512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3607 | −0.852068 | −0.426034 | − | 0.904707i | \(-0.640090\pi\) | ||||
−0.426034 | + | 0.904707i | \(0.640090\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.76393 | −0.199016 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.47214 | 0.103095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.76393 | −0.281099 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.4164 | −1.13547 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.23607 | −0.0511051 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5836 | −0.519380 | −0.259690 | − | 0.965692i | \(-0.583620\pi\) | ||||
−0.259690 | + | 0.965692i | \(0.583620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.41641 | 0.387339 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.8328 | 0.526981 | 0.263490 | − | 0.964662i | \(-0.415126\pi\) | ||||
0.263490 | + | 0.964662i | \(0.415126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4721 | −0.593300 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.52786 | 0.0625313 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3607 | −0.668479 | −0.334240 | − | 0.942488i | \(-0.608479\pi\) | ||||
−0.334240 | + | 0.942488i | \(0.608479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.58359 | 0.268550 | 0.134275 | − | 0.990944i | \(-0.457129\pi\) | ||||
0.134275 | + | 0.990944i | \(0.457129\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.47214 | −0.100673 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.527864 | 0.0214607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4164 | 0.625733 | 0.312866 | − | 0.949797i | \(-0.398711\pi\) | ||||
0.312866 | + | 0.949797i | \(0.398711\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.94427 | 0.362440 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.05573 | 0.123622 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3607 | 0.418464 | 0.209232 | − | 0.977866i | \(-0.432904\pi\) | ||||
0.209232 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.70820 | −0.149529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.36068 | −0.256071 | −0.128036 | − | 0.991770i | \(-0.540867\pi\) | ||||
−0.128036 | + | 0.991770i | \(0.540867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.583592 | −0.0234565 | −0.0117283 | − | 0.999931i | \(-0.503733\pi\) | ||||
−0.0117283 | + | 0.999931i | \(0.503733\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.47214 | 0.0992034 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8885 | 0.556433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.23607 | 0.129236 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.4164 | 0.933673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.7771 | −1.74274 | −0.871369 | − | 0.490628i | \(-0.836767\pi\) | ||||
−0.871369 | + | 0.490628i | \(0.836767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.8885 | 0.552020 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.29180 | 0.170047 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.94427 | −0.195592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.5410 | 1.36429 | 0.682144 | − | 0.731218i | \(-0.261048\pi\) | ||||
0.682144 | + | 0.731218i | \(0.261048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.5967 | −1.71929 | −0.859644 | − | 0.510894i | \(-0.829315\pi\) | ||||
−0.859644 | + | 0.510894i | \(0.829315\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.23607 | 0.127420 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.8885 | −1.48955 | −0.744776 | − | 0.667314i | \(-0.767444\pi\) | ||||
−0.744776 | + | 0.667314i | \(0.767444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.94427 | 0.194080 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.9443 | 0.507326 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.5279 | −0.764184 | −0.382092 | − | 0.924124i | \(-0.624796\pi\) | ||||
−0.382092 | + | 0.924124i | \(0.624796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.70820 | −0.379331 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.47214 | 0.330530 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0000 | 0.623272 | 0.311636 | − | 0.950202i | \(-0.399123\pi\) | ||||
0.311636 | + | 0.950202i | \(0.399123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.5279 | 1.53746 | 0.768728 | − | 0.639576i | \(-0.220890\pi\) | ||||
0.768728 | + | 0.639576i | \(0.220890\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.52786 | −0.214684 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.23607 | 0.125489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.83282 | −0.264568 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.41641 | −0.286735 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.4721 | −0.558691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.65248 | 0.179340 | 0.0896699 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896699 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.4164 | 0.669367 | 0.334683 | − | 0.942331i | \(-0.391371\pi\) | ||||
0.334683 | + | 0.942331i | \(0.391371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 58.8328 | 2.25780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0557 | −0.423656 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.94427 | −0.112495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.47214 | −0.170623 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.4721 | −0.398957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.3607 | −1.68756 | −0.843780 | − | 0.536689i | \(-0.819675\pi\) | ||||
−0.843780 | + | 0.536689i | \(0.819675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.4721 | −0.397804 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.4721 | −0.700688 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.5836 | −0.628148 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.9443 | −0.867832 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.58359 | −0.0975809 | −0.0487905 | − | 0.998809i | \(-0.515537\pi\) | ||||
−0.0487905 | + | 0.998809i | \(0.515537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.23607 | −0.197482 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.47214 | −0.0931060 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.3607 | 1.51792 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.47214 | −0.167955 | −0.0839773 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839773 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.9443 | 0.485448 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.88854 | −0.370329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.2361 | −0.419619 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.7082 | 0.660405 | 0.330202 | − | 0.943910i | \(-0.392883\pi\) | ||||
0.330202 | + | 0.943910i | \(0.392883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.94427 | −0.109499 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.76393 | −0.102650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.2361 | 0.416723 | 0.208361 | − | 0.978052i | \(-0.433187\pi\) | ||||
0.208361 | + | 0.978052i | \(0.433187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.4721 | 0.535271 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.8885 | −0.882343 | −0.441172 | − | 0.897423i | \(-0.645437\pi\) | ||||
−0.441172 | + | 0.897423i | \(0.645437\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.47214 | −0.128072 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9443 | 0.917590 | 0.458795 | − | 0.888542i | \(-0.348281\pi\) | ||||
0.458795 | + | 0.888542i | \(0.348281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.23607 | 0.0454081 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.8328 | −1.13115 | −0.565573 | − | 0.824698i | \(-0.691345\pi\) | ||||
−0.565573 | + | 0.824698i | \(0.691345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4721 | 0.456944 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.9443 | 1.05760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8885 | 0.798724 | 0.399362 | − | 0.916793i | \(-0.369232\pi\) | ||||
0.399362 | + | 0.916793i | \(0.369232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.70820 | −0.0622504 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.94427 | 0.325515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.9443 | 0.833924 | 0.416962 | − | 0.908924i | \(-0.363095\pi\) | ||||
0.416962 | + | 0.908924i | \(0.363095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.3050 | 0.554804 | 0.277402 | − | 0.960754i | \(-0.410527\pi\) | ||||
0.277402 | + | 0.960754i | \(0.410527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.4164 | 0.992541 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.47214 | 0.161690 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.88854 | 0.0681914 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8885 | −0.572212 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3607 | −0.660388 | −0.330194 | − | 0.943913i | \(-0.607114\pi\) | ||||
−0.330194 | + | 0.943913i | \(0.607114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.9443 | 0.607872 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.70820 | 0.132860 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | −0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.76393 | −0.0987749 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.4164 | 0.621618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | 0.712923 | 0.356462 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356462 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.8885 | −0.779253 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.41641 | 0.121473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.52786 | −0.196300 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.47214 | 0.300476 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.0557 | −0.745832 | −0.372916 | − | 0.927865i | \(-0.621642\pi\) | ||||
−0.372916 | + | 0.927865i | \(0.621642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.0557 | −0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.29180 | −0.151643 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.4164 | 0.967504 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.70820 | −0.271342 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.05573 | 0.177750 | 0.0888750 | − | 0.996043i | \(-0.471673\pi\) | ||||
0.0888750 | + | 0.996043i | \(0.471673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0557 | 0.809596 | 0.404798 | − | 0.914406i | \(-0.367342\pi\) | ||||
0.404798 | + | 0.914406i | \(0.367342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.52786 | −0.0535845 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.6525 | 0.513254 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.23607 | −0.113216 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00000 | −0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.47214 | 0.295680 | 0.147840 | − | 0.989011i | \(-0.452768\pi\) | ||||
0.147840 | + | 0.989011i | \(0.452768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.7082 | −0.617269 | −0.308635 | − | 0.951181i | \(-0.599872\pi\) | ||||
−0.308635 | + | 0.951181i | \(0.599872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.23607 | 0.112665 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.0557 | −0.940820 | −0.470410 | − | 0.882448i | \(-0.655894\pi\) | ||||
−0.470410 | + | 0.882448i | \(0.655894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.47214 | −0.294249 | −0.147125 | − | 0.989118i | \(-0.547002\pi\) | ||||
−0.147125 | + | 0.989118i | \(0.547002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.4721 | 0.848929 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.5279 | −0.538009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.9443 | 0.863232 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.7214 | 1.68205 | 0.841024 | − | 0.540998i | \(-0.181953\pi\) | ||||
0.841024 | + | 0.540998i | \(0.181953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.23607 | 0.180340 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.4721 | 0.394653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.70820 | 0.0586946 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.70820 | −0.0586254 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.9443 | −0.443724 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.94427 | −0.100810 | −0.0504050 | − | 0.998729i | \(-0.516051\pi\) | ||||
−0.0504050 | + | 0.998729i | \(0.516051\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.3607 | 0.627189 | 0.313594 | − | 0.949557i | \(-0.398467\pi\) | ||||
0.313594 | + | 0.949557i | \(0.398467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.9443 | 0.851088 | 0.425544 | − | 0.904938i | \(-0.360083\pi\) | ||||
0.425544 | + | 0.904938i | \(0.360083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.8328 | −1.32188 | −0.660942 | − | 0.750437i | \(-0.729843\pi\) | ||||
−0.660942 | + | 0.750437i | \(0.729843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.9443 | 0.780129 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.00000 | 0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.8885 | 1.42097 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.05573 | −0.103539 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.1803 | −0.615311 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.23607 | 0.109399 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.4853 | −1.33332 | −0.666662 | − | 0.745360i | \(-0.732277\pi\) | ||||
−0.666662 | + | 0.745360i | \(0.732277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.94427 | 0.0993078 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.52786 | 0.118857 | 0.0594284 | − | 0.998233i | \(-0.481072\pi\) | ||||
0.0594284 | + | 0.998233i | \(0.481072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0689 | 1.14651 | 0.573255 | − | 0.819377i | \(-0.305681\pi\) | ||||
0.573255 | + | 0.819377i | \(0.305681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.52786 | −0.0513586 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.00000 | −0.268614 | −0.134307 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134307 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.9443 | 0.434137 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.23607 | 0.108412 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.47214 | 0.0827269 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.4721 | −0.483750 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.05573 | 0.102028 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0557 | 0.368729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.8885 | 1.26225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4721 | 0.348491 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.52786 | 0.117270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.9443 | 1.89080 | 0.945402 | − | 0.325907i | \(-0.105670\pi\) | ||||
0.945402 | + | 0.325907i | \(0.105670\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.4721 | −0.413675 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8885 | −0.592674 | −0.296337 | − | 0.955083i | \(-0.595765\pi\) | ||||
−0.296337 | + | 0.955083i | \(0.595765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.47214 | 0.147844 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.4164 | −1.03746 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.0000 | 1.58337 | 0.791687 | − | 0.610927i | \(-0.209203\pi\) | ||||
0.791687 | + | 0.610927i | \(0.209203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.47214 | −0.0814596 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.11146 | −0.201161 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.23607 | −0.172161 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.41641 | 0.243587 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.8328 | 1.33968 | 0.669841 | − | 0.742505i | \(-0.266362\pi\) | ||||
0.669841 | + | 0.742505i | \(0.266362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.47214 | 0.113795 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.7639 | −0.417872 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.4721 | 0.473289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3050 | 0.761340 | 0.380670 | − | 0.924711i | \(-0.375693\pi\) | ||||
0.380670 | + | 0.924711i | \(0.375693\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.9443 | 1.00983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.6525 | −0.412459 | −0.206229 | − | 0.978504i | \(-0.566119\pi\) | ||||
−0.206229 | + | 0.978504i | \(0.566119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.16718 | 0.298525 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.23607 | 0.105269 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.7771 | −0.902634 | −0.451317 | − | 0.892364i | \(-0.649046\pi\) | ||||
−0.451317 | + | 0.892364i | \(0.649046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4721 | 0.339940 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.3607 | 0.465677 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.8885 | 0.385108 | 0.192554 | − | 0.981286i | \(-0.438323\pi\) | ||||
0.192554 | + | 0.981286i | \(0.438323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.76393 | 0.154157 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.94427 | −0.289127 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.52786 | −0.307671 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.94427 | −0.288225 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.76393 | 0.217739 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.70820 | −0.0549321 | −0.0274661 | − | 0.999623i | \(-0.508744\pi\) | ||||
−0.0274661 | + | 0.999623i | \(0.508744\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.47214 | −0.143666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | 0.770197 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.7771 | −1.91637 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.23607 | 0.0395859 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.3050 | −0.361677 | −0.180839 | − | 0.983513i | \(-0.557881\pi\) | ||||
−0.180839 | + | 0.983513i | \(0.557881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.8885 | −0.443880 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.47214 | −0.270494 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.8328 | 0.855834 | 0.427917 | − | 0.903818i | \(-0.359248\pi\) | ||||
0.427917 | + | 0.903818i | \(0.359248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.41641 | −0.300032 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | −0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.8885 | −1.33063 | −0.665317 | − | 0.746561i | \(-0.731703\pi\) | ||||
−0.665317 | + | 0.746561i | \(0.731703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.88854 | 0.313803 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.52786 | −0.0484365 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.4164 | 1.43835 | 0.719176 | − | 0.694828i | \(-0.244519\pi\) | ||||
0.719176 | + | 0.694828i | \(0.244519\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.23607 | −0.165662 |
(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 | 4560.2.a.bk.1.1 | 2 | ||
4.3 | odd | 2 | 2280.2.a.m.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 6840.2.a.bc.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.m.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
4560.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6840.2.a.bc.1.2 | 2 | 12.11 | even | 2 |