Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,3,Mod(1441,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.1441");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.s (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(45.7766844125\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1441.12 | ||
Root | \(1.31896 + 2.28450i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1441 |
Dual form | 1680.3.s.c.1441.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.69736 | + | 2.03600i | 0.956766 | + | 0.290857i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.03112 | 0.184647 | 0.0923235 | − | 0.995729i | \(-0.470571\pi\) | ||||
0.0923235 | + | 0.995729i | \(0.470571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.0174i | 1.38596i | 0.720958 | + | 0.692978i | \(0.243702\pi\) | ||||
−0.720958 | + | 0.692978i | \(0.756298\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.07289i | − | 0.0631109i | −0.999502 | − | 0.0315555i | \(-0.989954\pi\) | ||
0.999502 | − | 0.0315555i | \(-0.0100461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.7852i | 1.51501i | 0.652828 | + | 0.757506i | \(0.273583\pi\) | ||||
−0.652828 | + | 0.757506i | \(0.726417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.52646 | + | 11.6002i | −0.167927 | + | 0.552389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.8710 | −1.08135 | −0.540674 | − | 0.841232i | \(-0.681831\pi\) | ||||
−0.540674 | + | 0.841232i | \(0.681831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.4300 | −1.32517 | −0.662587 | − | 0.748985i | \(-0.730542\pi\) | ||||
−0.662587 | + | 0.748985i | \(0.730542\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 44.0899i | − | 1.42225i | −0.703064 | − | 0.711127i | \(-0.748185\pi\) | ||
0.703064 | − | 0.711127i | \(-0.251815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.51800i | 0.106606i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.55264 | + | 14.9758i | −0.130075 | + | 0.427879i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.2832 | 1.00765 | 0.503827 | − | 0.863804i | \(-0.331925\pi\) | ||||
0.503827 | + | 0.863804i | \(0.331925\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −31.2071 | −0.800182 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 49.9206i | − | 1.21758i | −0.793333 | − | 0.608788i | \(-0.791656\pi\) | ||
0.793333 | − | 0.608788i | \(-0.208344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.58871 | 0.222993 | 0.111497 | − | 0.993765i | \(-0.464436\pi\) | ||||
0.111497 | + | 0.993765i | \(0.464436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 55.6978i | 1.18506i | 0.805549 | + | 0.592529i | \(0.201871\pi\) | ||||
−0.805549 | + | 0.592529i | \(0.798129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.7094 | + | 27.2717i | 0.830804 | + | 0.556565i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85829 | 0.0364371 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 57.4656 | 1.08426 | 0.542128 | − | 0.840296i | \(-0.317619\pi\) | ||||
0.542128 | + | 0.840296i | \(0.317619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.54171i | 0.0825766i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −49.8575 | −0.874693 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 101.697i | 1.72368i | 0.507178 | + | 0.861841i | \(0.330689\pi\) | ||||
−0.507178 | + | 0.861841i | \(0.669311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31.9530i | 0.523819i | 0.965092 | + | 0.261910i | \(0.0843523\pi\) | ||||
−0.965092 | + | 0.261910i | \(0.915648\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.0921 | − | 6.10801i | −0.318922 | − | 0.0969525i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −40.2882 | −0.619819 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −95.7318 | −1.42883 | −0.714416 | − | 0.699721i | \(-0.753308\pi\) | ||||
−0.714416 | + | 0.699721i | \(0.753308\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 43.0778i | − | 0.624316i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 25.8039 | 0.363435 | 0.181718 | − | 0.983351i | \(-0.441834\pi\) | ||||
0.181718 | + | 0.983351i | \(0.441834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 95.6803i | 1.31069i | 0.755330 | + | 0.655345i | \(0.227477\pi\) | ||||
−0.755330 | + | 0.655345i | \(0.772523\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.6031 | + | 4.13536i | 0.176664 | + | 0.0537059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −28.1212 | −0.355965 | −0.177982 | − | 0.984034i | \(-0.556957\pi\) | ||||
−0.177982 | + | 0.984034i | \(0.556957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 103.374i | − | 1.24547i | −0.782435 | − | 0.622733i | \(-0.786022\pi\) | ||
0.782435 | − | 0.622733i | \(-0.213978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.39905 | 0.0282241 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 66.5628i | − | 0.765090i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 29.3629i | − | 0.329920i | −0.986300 | − | 0.164960i | \(-0.947250\pi\) | ||
0.986300 | − | 0.164960i | \(-0.0527496\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −36.6835 | + | 120.669i | −0.403116 | + | 1.32604i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 76.3659 | 0.821138 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −64.3658 | −0.677534 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 67.6473i | 0.697395i | 0.937235 | + | 0.348697i | \(0.113376\pi\) | ||||
−0.937235 | + | 0.348697i | \(0.886624\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.09335 | −0.0615490 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 73.3301i | − | 0.726040i | −0.931781 | − | 0.363020i | \(-0.881746\pi\) | ||
0.931781 | − | 0.363020i | \(-0.118254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 57.3431i | − | 0.556729i | −0.960476 | − | 0.278365i | \(-0.910208\pi\) | ||
0.960476 | − | 0.278365i | \(-0.0897923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.9388 | − | 7.88540i | −0.247036 | − | 0.0750991i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 39.8399 | 0.372336 | 0.186168 | − | 0.982518i | \(-0.440393\pi\) | ||||
0.186168 | + | 0.982518i | \(0.440393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −185.052 | −1.69773 | −0.848863 | − | 0.528613i | \(-0.822712\pi\) | ||||
−0.848863 | + | 0.528613i | \(0.822712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 64.5764i | 0.581770i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −120.716 | −1.06829 | −0.534143 | − | 0.845394i | \(-0.679366\pi\) | ||||
−0.534143 | + | 0.845394i | \(0.679366\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 55.6132i | − | 0.483593i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 54.0523i | − | 0.461986i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.18440 | − | 7.18551i | 0.0183563 | − | 0.0603824i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −116.875 | −0.965906 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 86.4651 | 0.702968 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 83.5096 | 0.657556 | 0.328778 | − | 0.944407i | \(-0.393363\pi\) | ||||
0.328778 | + | 0.944407i | \(0.393363\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.6081i | 0.128745i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 198.248i | − | 1.51334i | −0.653796 | − | 0.756671i | \(-0.726825\pi\) | ||
0.653796 | − | 0.756671i | \(-0.273175\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −58.6068 | + | 192.785i | −0.440653 | + | 1.44951i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −24.1635 | −0.176376 | −0.0881880 | − | 0.996104i | \(-0.528108\pi\) | ||||
−0.0881880 | + | 0.996104i | \(0.528108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 61.6370i | 0.443432i | 0.975111 | + | 0.221716i | \(0.0711658\pi\) | ||||
−0.975111 | + | 0.221716i | \(0.928834\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −96.4714 | −0.684194 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 36.5955i | 0.255913i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 85.9322i | − | 0.592636i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −47.2360 | + | 70.5107i | −0.321333 | + | 0.479665i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −28.8271 | −0.193470 | −0.0967351 | − | 0.995310i | \(-0.530840\pi\) | ||||
−0.0967351 | + | 0.995310i | \(0.530840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −248.311 | −1.64445 | −0.822223 | − | 0.569166i | \(-0.807266\pi\) | ||||
−0.822223 | + | 0.569166i | \(0.807266\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.21866i | 0.0210370i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 98.5879 | 0.636051 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 41.3848i | − | 0.263597i | −0.991277 | − | 0.131799i | \(-0.957925\pi\) | ||
0.991277 | − | 0.131799i | \(-0.0420752\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 99.5334i | 0.625996i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −166.570 | − | 50.6374i | −1.03460 | − | 0.314518i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 51.8103 | 0.317855 | 0.158927 | − | 0.987290i | \(-0.449196\pi\) | ||||
0.158927 | + | 0.987290i | \(0.449196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.86648 | −0.0476756 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 41.9711i | 0.251324i | 0.992073 | + | 0.125662i | \(0.0401055\pi\) | ||||
−0.992073 | + | 0.125662i | \(0.959895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −155.628 | −0.920876 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 86.3557i | − | 0.505004i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 98.0199i | 0.566589i | 0.959033 | + | 0.283295i | \(0.0914274\pi\) | ||||
−0.959033 | + | 0.283295i | \(0.908573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.4868 | − | 10.1800i | −0.191353 | − | 0.0581715i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −176.145 | −0.995168 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −68.5830 | −0.383145 | −0.191573 | − | 0.981478i | \(-0.561359\pi\) | ||||
−0.191573 | + | 0.981478i | \(0.561359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 105.124i | 0.580798i | 0.956906 | + | 0.290399i | \(0.0937880\pi\) | ||||
−0.956906 | + | 0.290399i | \(0.906212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −55.3442 | −0.302427 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 83.3678i | 0.450637i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.17916i | − | 0.0116532i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5794 | − | 34.8005i | 0.0559755 | − | 0.184130i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −229.803 | −1.20316 | −0.601579 | − | 0.798813i | \(-0.705461\pi\) | ||||
−0.601579 | + | 0.798813i | \(0.705461\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 111.530 | 0.577877 | 0.288939 | − | 0.957348i | \(-0.406698\pi\) | ||||
0.288939 | + | 0.957348i | \(0.406698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 69.7812i | − | 0.357852i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −172.865 | −0.877486 | −0.438743 | − | 0.898613i | \(-0.644576\pi\) | ||||
−0.438743 | + | 0.898613i | \(0.644576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 117.944i | 0.592685i | 0.955082 | + | 0.296343i | \(0.0957670\pi\) | ||||
−0.955082 | + | 0.296343i | \(0.904233\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 165.812i | − | 0.824937i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −257.380 | − | 78.2437i | −1.26788 | − | 0.385437i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 111.626 | 0.544517 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 74.6130 | 0.360449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 58.4662i | 0.279742i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 391.940 | 1.85754 | 0.928769 | − | 0.370660i | \(-0.120869\pi\) | ||||
0.928769 | + | 0.370660i | \(0.120869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 44.6936i | 0.209829i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.4410i | 0.0997256i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 89.7670 | − | 295.286i | 0.413673 | − | 1.36076i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −165.723 | −0.756727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3306 | 0.0874690 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 96.2512i | − | 0.431620i | −0.976435 | − | 0.215810i | \(-0.930761\pi\) | ||
0.976435 | − | 0.215810i | \(-0.0692391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 91.6962i | − | 0.403948i | −0.979391 | − | 0.201974i | \(-0.935264\pi\) | ||
0.979391 | − | 0.201974i | \(-0.0647357\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 323.972i | 1.41472i | 0.706852 | + | 0.707361i | \(0.250115\pi\) | ||||
−0.706852 | + | 0.707361i | \(0.749885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.16265 | + | 23.5613i | −0.0310071 | + | 0.101997i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 182.918 | 0.785055 | 0.392528 | − | 0.919740i | \(-0.371601\pi\) | ||||
0.392528 | + | 0.919740i | \(0.371601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −124.544 | −0.529974 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 48.7074i | − | 0.205516i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 42.9240 | 0.179598 | 0.0897992 | − | 0.995960i | \(-0.471377\pi\) | ||||
0.0897992 | + | 0.995960i | \(0.471377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 99.8942i | − | 0.414499i | −0.978288 | − | 0.207249i | \(-0.933549\pi\) | ||
0.978288 | − | 0.207249i | \(-0.0664511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −60.9814 | + | 91.0290i | −0.248904 | + | 0.371547i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −518.636 | −2.09974 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 179.048 | 0.719070 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 404.945i | 1.61333i | 0.591011 | + | 0.806663i | \(0.298729\pi\) | ||||
−0.591011 | + | 0.806663i | \(0.701271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −50.5159 | −0.199668 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.15527i | 0.0162952i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 102.697i | 0.399600i | 0.979837 | + | 0.199800i | \(0.0640292\pi\) | ||||
−0.979837 | + | 0.199800i | \(0.935971\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 249.699 | + | 75.9087i | 0.964090 | + | 0.293084i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 115.290 | 0.441725 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −281.479 | −1.07026 | −0.535132 | − | 0.844769i | \(-0.679738\pi\) | ||||
−0.535132 | + | 0.844769i | \(0.679738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 128.497i | 0.484894i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 50.8581 | 0.190480 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 176.412i | − | 0.655808i | −0.944711 | − | 0.327904i | \(-0.893658\pi\) | ||
0.944711 | − | 0.327904i | \(-0.106342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 306.041i | 1.12930i | 0.825330 | + | 0.564651i | \(0.190989\pi\) | ||||
−0.825330 | + | 0.564651i | \(0.809011\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −209.005 | − | 63.5378i | −0.765588 | − | 0.232739i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.1556 | −0.0369294 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 43.7993 | 0.158120 | 0.0790601 | − | 0.996870i | \(-0.474808\pi\) | ||||
0.0790601 | + | 0.996870i | \(0.474808\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 132.270i | 0.474084i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 499.502 | 1.77759 | 0.888794 | − | 0.458307i | \(-0.151544\pi\) | ||||
0.888794 | + | 0.458307i | \(0.151544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 122.672i | 0.433470i | 0.976231 | + | 0.216735i | \(0.0695407\pi\) | ||||
−0.976231 | + | 0.216735i | \(0.930459\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 111.485i | − | 0.391175i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 101.639 | − | 334.337i | 0.354141 | − | 1.16494i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 287.849 | 0.996017 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −117.169 | −0.402641 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 123.871i | 0.422769i | 0.977403 | + | 0.211385i | \(0.0677972\pi\) | ||||
−0.977403 | + | 0.211385i | \(0.932203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −227.402 | −0.770854 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 10.5540i | − | 0.0355353i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 448.112i | − | 1.49870i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 64.2191 | + | 19.5226i | 0.213352 | + | 0.0648593i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 127.011 | 0.419180 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −71.4490 | −0.234259 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 225.577i | 0.734778i | 0.930067 | + | 0.367389i | \(0.119748\pi\) | ||||
−0.930067 | + | 0.367389i | \(0.880252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 99.3211 | 0.321428 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 52.9648i | 0.170305i | 0.996368 | + | 0.0851525i | \(0.0271377\pi\) | ||||
−0.996368 | + | 0.0851525i | \(0.972862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 374.563i | − | 1.19669i | −0.801240 | − | 0.598343i | \(-0.795826\pi\) | ||
0.801240 | − | 0.598343i | \(-0.204174\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.6579 | − | 44.9273i | 0.0433585 | − | 0.142626i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0550 | 0.0380283 | 0.0190142 | − | 0.999819i | \(-0.493947\pi\) | ||||
0.0190142 | + | 0.999819i | \(0.493947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −78.0559 | −0.244689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 69.0048i | 0.214968i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.8833 | 0.0956138 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 90.0872i | − | 0.277191i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 320.520i | − | 0.980183i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −113.401 | + | 373.028i | −0.344683 | + | 1.13382i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 376.184 | 1.13651 | 0.568254 | − | 0.822853i | \(-0.307619\pi\) | ||||
0.568254 | + | 0.822853i | \(0.307619\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −111.850 | −0.335885 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 214.063i | − | 0.638993i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −108.973 | −0.323363 | −0.161682 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161682 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 209.087i | − | 0.616775i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 89.5516i | − | 0.262615i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 217.120 | + | 265.533i | 0.633004 | + | 0.774148i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 96.3250 | 0.279203 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 206.351 | 0.594671 | 0.297335 | − | 0.954773i | \(-0.403902\pi\) | ||||
0.297335 | + | 0.954773i | \(0.403902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 373.475i | 1.07013i | 0.844811 | + | 0.535064i | \(0.179713\pi\) | ||||
−0.844811 | + | 0.535064i | \(0.820287\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 93.6213 | 0.266727 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 646.142i | − | 1.83043i | −0.402964 | − | 0.915216i | \(-0.632020\pi\) | ||
0.402964 | − | 0.915216i | \(-0.367980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 57.6992i | 0.162533i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.4457 | + | 3.78349i | 0.0348618 | + | 0.0105980i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −175.261 | −0.488192 | −0.244096 | − | 0.969751i | \(-0.578491\pi\) | ||||
−0.244096 | + | 0.969751i | \(0.578491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −467.590 | −1.29526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 202.433i | − | 0.557666i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −213.948 | −0.586158 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 106.477i | − | 0.290127i | −0.989422 | − | 0.145063i | \(-0.953661\pi\) | ||
0.989422 | − | 0.145063i | \(-0.0463386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 149.762i | 0.405859i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 384.868 | + | 117.000i | 1.03738 | + | 0.315364i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 223.324 | 0.598723 | 0.299362 | − | 0.954140i | \(-0.403226\pi\) | ||||
0.299362 | + | 0.954140i | \(0.403226\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 692.411i | − | 1.83663i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −119.075 | −0.314183 | −0.157092 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157092 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 144.643i | 0.379640i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 494.637i | 1.29148i | 0.763557 | + | 0.645740i | \(0.223451\pi\) | ||||
−0.763557 | + | 0.645740i | \(0.776549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.24694 | + | 30.4175i | −0.0240180 | + | 0.0790065i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.7661 | −0.0743311 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −270.578 | −0.695574 | −0.347787 | − | 0.937574i | \(-0.613067\pi\) | ||||
−0.347787 | + | 0.937574i | \(0.613067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6837i | 0.0682448i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 343.375 | 0.873728 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 62.8810i | − | 0.159192i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.1881i | 0.0936727i | 0.998903 | + | 0.0468364i | \(0.0149139\pi\) | ||||
−0.998903 | + | 0.0468364i | \(0.985086\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −333.914 | − | 101.510i | −0.836877 | − | 0.254411i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.7102 | −0.0915467 | −0.0457733 | − | 0.998952i | \(-0.514575\pi\) | ||||
−0.0457733 | + | 0.998952i | \(0.514575\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 794.386 | 1.97118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 75.7266 | 0.186060 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 495.325i | 1.21106i | 0.795821 | + | 0.605532i | \(0.207040\pi\) | ||||
−0.795821 | + | 0.605532i | \(0.792960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 41.8524i | − | 0.101831i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −207.056 | + | 681.104i | −0.501346 | + | 1.64916i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 231.151 | 0.556989 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −106.758 | −0.256016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 269.297i | 0.642713i | 0.946958 | + | 0.321357i | \(0.104139\pi\) | ||||
−0.946958 | + | 0.321357i | \(0.895861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 756.722 | 1.79744 | 0.898719 | − | 0.438524i | \(-0.144499\pi\) | ||||
0.898719 | + | 0.438524i | \(0.144499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 167.093i | − | 0.395020i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.36443i | 0.0126222i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −65.0563 | + | 214.001i | −0.152357 | + | 0.501173i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −63.3853 | −0.147751 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −185.182 | −0.429657 | −0.214828 | − | 0.976652i | \(-0.568919\pi\) | ||||
−0.214828 | + | 0.976652i | \(0.568919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 642.846i | 1.48463i | 0.670049 | + | 0.742317i | \(0.266273\pi\) | ||||
−0.670049 | + | 0.742317i | \(0.733727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 148.839 | 0.342158 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 715.918i | − | 1.63826i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 464.239i | 1.05749i | 0.848780 | + | 0.528745i | \(0.177337\pi\) | ||||
−0.848780 | + | 0.528745i | \(0.822663\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −122.128 | − | 81.8151i | −0.276935 | − | 0.185522i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 115.228 | 0.260109 | 0.130054 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130054 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 65.6575 | 0.147545 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 49.9299i | − | 0.111700i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 333.955 | 0.743774 | 0.371887 | − | 0.928278i | \(-0.378711\pi\) | ||||
0.371887 | + | 0.928278i | \(0.378711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 101.395i | − | 0.224822i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 430.088i | − | 0.949421i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −269.825 | − | 82.0269i | −0.593022 | − | 0.180279i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 354.152 | 0.774949 | 0.387474 | − | 0.921880i | \(-0.373348\pi\) | ||||
0.387474 | + | 0.921880i | \(0.373348\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.57488 | −0.0121457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 128.906i | − | 0.279623i | −0.990178 | − | 0.139811i | \(-0.955350\pi\) | ||
0.990178 | − | 0.139811i | \(-0.0446497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 302.175 | 0.652645 | 0.326322 | − | 0.945259i | \(-0.394190\pi\) | ||||
0.326322 | + | 0.945259i | \(0.394190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 170.759i | 0.367224i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 808.227i | − | 1.73068i | −0.501186 | − | 0.865339i | \(-0.667103\pi\) | ||
0.501186 | − | 0.865339i | \(-0.332897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −641.151 | − | 194.910i | −1.36706 | − | 0.415587i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.6805 | 0.152188 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.4758 | 0.0411750 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 143.926i | − | 0.303003i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −172.397 | −0.361419 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 48.8836i | 0.102053i | 0.998697 | + | 0.0510267i | \(0.0162494\pi\) | ||||
−0.998697 | + | 0.0510267i | \(0.983751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 671.748i | 1.39657i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 87.7066 | − | 288.508i | 0.181587 | − | 0.597325i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −151.264 | −0.311884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −334.433 | −0.686720 | −0.343360 | − | 0.939204i | \(-0.611565\pi\) | ||||
−0.343360 | + | 0.939204i | \(0.611565\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 89.7381i | 0.183514i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 549.151 | 1.11843 | 0.559217 | − | 0.829021i | \(-0.311102\pi\) | ||||
0.559217 | + | 0.829021i | \(0.311102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.2310i | 0.0836329i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 13.6251i | − | 0.0275255i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 172.818 | + | 52.5368i | 0.347722 | + | 0.105708i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 462.450 | 0.926754 | 0.463377 | − | 0.886161i | \(-0.346638\pi\) | ||||
0.463377 | + | 0.886161i | \(0.346638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72.6961 | −0.145102 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 676.817i | 1.34556i | 0.739842 | + | 0.672781i | \(0.234900\pi\) | ||||
−0.739842 | + | 0.672781i | \(0.765100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 163.971 | 0.324695 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 269.556i | − | 0.531668i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 31.5959i | − | 0.0620744i | −0.999518 | − | 0.0310372i | \(-0.990119\pi\) | ||
0.999518 | − | 0.0310372i | \(-0.00988104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −194.805 | + | 640.806i | −0.381224 | + | 1.25402i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 149.572 | 0.291564 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 128.223 | 0.248977 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 113.129i | 0.218817i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −169.775 | −0.327120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 793.420i | 1.52288i | 0.648236 | + | 0.761440i | \(0.275507\pi\) | ||||
−0.648236 | + | 0.761440i | \(0.724493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 593.508i | 1.13481i | 0.823438 | + | 0.567407i | \(0.192053\pi\) | ||||
−0.823438 | + | 0.567407i | \(0.807947\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.6323 | − | 58.0009i | 0.0335853 | − | 0.110478i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.3034 | −0.0897597 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 89.5666 | 0.169313 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 305.092i | − | 0.574561i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 899.442 | 1.68751 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 89.0848i | 0.166514i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 118.789i | − | 0.221209i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 82.6855 | + | 55.3920i | 0.153405 | + | 0.102768i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 217.690 | 0.402385 | 0.201192 | − | 0.979552i | \(-0.435518\pi\) | ||||
0.201192 | + | 0.979552i | \(0.435518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −182.081 | −0.335324 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 413.789i | − | 0.759246i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 137.891 | 0.252085 | 0.126043 | − | 0.992025i | \(-0.459772\pi\) | ||||
0.126043 | + | 0.992025i | \(0.459772\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 95.8589i | − | 0.174606i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1106.22i | − | 2.00766i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −188.338 | − | 57.2549i | −0.340575 | − | 0.103535i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −144.397 | −0.260175 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −316.337 | −0.567930 | −0.283965 | − | 0.958835i | \(-0.591650\pi\) | ||||
−0.283965 | + | 0.958835i | \(0.591650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 172.764i | 0.309059i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.77441 | 0.00672800 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 151.482i | − | 0.269063i | −0.990909 | − | 0.134531i | \(-0.957047\pi\) | ||
0.990909 | − | 0.134531i | \(-0.0429529\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 269.930i | − | 0.477752i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 60.2763 | + | 18.3240i | 0.106307 | + | 0.0323175i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −213.993 | −0.376086 | −0.188043 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188043 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 204.492 | 0.358129 | 0.179065 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179065 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 398.031i | − | 0.694643i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 124.355 | 0.216270 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 957.823i | − | 1.66001i | −0.557759 | − | 0.830003i | \(-0.688339\pi\) | ||
0.557759 | − | 0.830003i | \(-0.311661\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 193.176i | 0.333638i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 210.469 | − | 692.331i | 0.362253 | − | 1.19162i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 116.719 | 0.200205 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 120.865 | 0.206606 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 981.279i | − | 1.67168i | −0.548969 | − | 0.835842i | \(-0.684980\pi\) | ||
0.548969 | − | 0.835842i | \(-0.315020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1269.14 | 2.15473 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 299.410i | − | 0.506617i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 708.384i | − | 1.19458i | −0.802026 | − | 0.597288i | \(-0.796245\pi\) | ||
0.802026 | − | 0.597288i | \(-0.203755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0673 | + | 4.88446i | 0.0270038 | + | 0.00820918i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −204.286 | −0.342187 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 928.994 | 1.55091 | 0.775454 | − | 0.631404i | \(-0.217521\pi\) | ||||
0.775454 | + | 0.631404i | \(0.217521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 466.882i | − | 0.776842i | −0.921482 | − | 0.388421i | \(-0.873021\pi\) | ||
0.921482 | − | 0.388421i | \(-0.126979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 287.195 | 0.476277 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 261.339i | − | 0.431966i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 988.757i | − | 1.62892i | −0.580216 | − | 0.814462i | \(-0.697032\pi\) | ||
0.580216 | − | 0.814462i | \(-0.302968\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 135.522 | − | 445.795i | 0.222532 | − | 0.732012i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1003.53 | −1.64244 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 469.962 | 0.766660 | 0.383330 | − | 0.923612i | \(-0.374777\pi\) | ||||
0.383330 | + | 0.923612i | \(0.374777\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 193.342i | 0.314377i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1081.72 | 1.75320 | 0.876598 | − | 0.481223i | \(-0.159807\pi\) | ||||
0.876598 | + | 0.481223i | \(0.159807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 553.956i | 0.894921i | 0.894304 | + | 0.447461i | \(0.147672\pi\) | ||||
−0.894304 | + | 0.447461i | \(0.852328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 129.234i | 0.208105i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 59.7829 | − | 196.654i | 0.0959598 | − | 0.315657i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −101.266 | −0.161509 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 40.0006i | − | 0.0635940i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 77.8822 | 0.123427 | 0.0617133 | − | 0.998094i | \(-0.480344\pi\) | ||||
0.0617133 | + | 0.998094i | \(0.480344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 678.861i | 1.07245i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 186.733i | 0.294068i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −491.366 | + | 733.479i | −0.771375 | + | 1.15146i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −77.4117 | −0.121145 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −360.619 | −0.562589 | −0.281294 | − | 0.959622i | \(-0.590764\pi\) | ||||
−0.281294 | + | 0.959622i | \(0.590764\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 793.158i | − | 1.23353i | −0.787148 | − | 0.616764i | \(-0.788443\pi\) | ||
0.787148 | − | 0.616764i | \(-0.211557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.1369 | −0.0575766 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 405.244i | 0.626344i | 0.949696 | + | 0.313172i | \(0.101392\pi\) | ||||
−0.949696 | + | 0.313172i | \(0.898608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 206.559i | 0.318273i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 511.450 | + | 155.481i | 0.785638 | + | 0.238834i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 493.508 | 0.755755 | 0.377877 | − | 0.925856i | \(-0.376654\pi\) | ||||
0.377877 | + | 0.925856i | \(0.376654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 443.295 | 0.676787 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 287.041i | − | 0.436896i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1120.88 | 1.70088 | 0.850441 | − | 0.526070i | \(-0.176335\pi\) | ||||
0.850441 | + | 0.526070i | \(0.176335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1134.48i | 1.71631i | 0.513393 | + | 0.858154i | \(0.328388\pi\) | ||||
−0.513393 | + | 0.858154i | \(0.671612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.4817i | 0.0505002i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −431.081 | − | 131.049i | −0.648242 | − | 0.197066i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 955.794 | 1.43297 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 166.712 | 0.249196 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.9002i | 0.0967216i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −763.267 | −1.13413 | −0.567063 | − | 0.823674i | \(-0.691920\pi\) | ||||
−0.567063 | + | 0.823674i | \(0.691920\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9808i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 456.611i | − | 0.674463i | −0.941422 | − | 0.337232i | \(-0.890509\pi\) | ||
0.941422 | − | 0.337232i | \(-0.109491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −137.730 | + | 453.058i | −0.202842 | + | 0.667244i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 158.822 | 0.233219 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 219.276 | 0.321049 | 0.160524 | − | 0.987032i | \(-0.448681\pi\) | ||||
0.160524 | + | 0.987032i | \(0.448681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 54.0313i | − | 0.0788777i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −561.135 | −0.816791 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1035.38i | 1.50273i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 396.801i | − | 0.574242i | −0.957894 | − | 0.287121i | \(-0.907302\pi\) | ||
0.957894 | − | 0.287121i | \(-0.0926982\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40.8094 | − | 12.4061i | −0.0588880 | − | 0.0179020i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −137.825 | −0.198309 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.5591 | −0.0768424 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 316.823i | 0.453252i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −493.156 | −0.703503 | −0.351752 | − | 0.936093i | \(-0.614414\pi\) | ||||
−0.351752 | + | 0.936093i | \(0.614414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1073.21i | 1.52661i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 215.717i | − | 0.305981i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 149.300 | − | 491.118i | 0.211174 | − | 0.694651i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 859.326 | 1.21202 | 0.606012 | − | 0.795455i | \(-0.292768\pi\) | ||||
0.606012 | + | 0.795455i | \(0.292768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 84.3637 | 0.118655 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1096.56i | 1.53795i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −81.8300 | −0.114448 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 74.3466i | 0.103691i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 385.539i | 0.536216i | 0.963389 | + | 0.268108i | \(0.0863983\pi\) | ||||
−0.963389 | + | 0.268108i | \(0.913602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 116.751 | − | 384.048i | 0.161929 | − | 0.532660i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 173.022 | 0.239311 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 192.150 | 0.265035 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 114.722i | 0.157802i | 0.996882 | + | 0.0789012i | \(0.0251412\pi\) | ||||
−0.996882 | + | 0.0789012i | \(0.974859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.2876i | − | 0.0140733i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 140.433i | − | 0.191586i | −0.995401 | − | 0.0957932i | \(-0.969461\pi\) | ||
0.995401 | − | 0.0957932i | \(-0.0305388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −157.667 | − | 105.623i | −0.214513 | − | 0.143705i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −194.442 | −0.263830 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.8609 | 0.0688239 | 0.0344120 | − | 0.999408i | \(-0.489044\pi\) | ||||
0.0344120 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 898.304i | − | 1.21229i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −930.694 | −1.25262 | −0.626309 | − | 0.779575i | \(-0.715435\pi\) | ||||
−0.626309 | + | 0.779575i | \(0.715435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 64.4593i | − | 0.0865225i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 310.121i | 0.415155i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 266.822 | + | 81.1142i | 0.356238 | + | 0.108297i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 446.702 | 0.594809 | 0.297404 | − | 0.954752i | \(-0.403879\pi\) | ||||
0.297404 | + | 0.954752i | \(0.403879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −701.385 | −0.931455 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 555.241i | − | 0.735419i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.2042 | 0.0359369 | 0.0179684 | − | 0.999839i | \(-0.494280\pi\) | ||||
0.0179684 | + | 0.999839i | \(0.494280\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 87.4961i | − | 0.115278i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 333.536i | 0.438287i | 0.975693 | + | 0.219143i | \(0.0703262\pi\) | ||||
−0.975693 | + | 0.219143i | \(0.929674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1239.36 | − | 376.767i | −1.62433 | − | 0.493796i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.19714 | −0.00940802 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1832.32 | −2.38895 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 56.3903i | − | 0.0733294i | −0.999328 | − | 0.0366647i | \(-0.988327\pi\) | ||
0.999328 | − | 0.0366647i | \(-0.0116734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −177.877 | −0.230709 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 296.398i | − | 0.383438i | −0.981450 | − | 0.191719i | \(-0.938594\pi\) | ||
0.981450 | − | 0.191719i | \(-0.0614063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 220.449i | 0.284451i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −131.478 | + | 432.492i | −0.169212 | + | 0.556618i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1436.98 | 1.84464 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.4107 | 0.0671072 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 199.688i | 0.255030i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 92.5392 | 0.117884 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 226.427i | − | 0.287709i | −0.989599 | − | 0.143854i | \(-0.954050\pi\) | ||
0.989599 | − | 0.143854i | \(-0.0459497\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 487.537i | − | 0.617917i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −808.481 | − | 245.779i | −1.02210 | − | 0.310719i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −575.711 | −0.725991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −222.563 | −0.279954 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 305.282i | − | 0.383038i | −0.981489 | − | 0.191519i | \(-0.938659\pi\) | ||
0.981489 | − | 0.191519i | \(-0.0613414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.7573 | 0.0747901 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 88.0887i | 0.109973i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 194.338i | 0.242015i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 113.229 | − | 372.462i | 0.140657 | − | 0.462686i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 305.555 | 0.378631 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 592.651 | 0.732573 | 0.366286 | − | 0.930502i | \(-0.380629\pi\) | ||||
0.366286 | + | 0.930502i | \(0.380629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 731.348i | − | 0.901785i | −0.892578 | − | 0.450893i | \(-0.851106\pi\) | ||
0.892578 | − | 0.450893i | \(-0.148894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −530.078 | −0.652003 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 115.851i | 0.142149i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 276.013i | 0.337838i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 110.051 | − | 362.008i | 0.134372 | − | 0.442012i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 268.560 | 0.327114 | 0.163557 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163557 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1213.35 | −1.47430 | −0.737151 | − | 0.675728i | \(-0.763830\pi\) | ||||
−0.737151 | + | 0.675728i | \(0.763830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 17.5900i | − | 0.0213212i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1238.49 | 1.49757 | 0.748785 | − | 0.662813i | \(-0.230637\pi\) | ||||
0.748785 | + | 0.662813i | \(0.230637\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 873.056i | − | 1.05314i | −0.850131 | − | 0.526572i | \(-0.823477\pi\) | ||
0.850131 | − | 0.526572i | \(-0.176523\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 75.8626i | 0.0912908i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.2594 | − | 43.6765i | 0.0351253 | − | 0.0524328i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −93.8503 | −0.112396 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −229.098 | −0.273713 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 100.572i | 0.119871i | 0.998202 | + | 0.0599355i | \(0.0190895\pi\) | ||||
−0.998202 | + | 0.0599355i | \(0.980910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 635.869 | 0.756086 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 865.163i | 1.02629i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 347.995i | − | 0.411828i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −782.752 | − | 237.957i | −0.924146 | − | 0.280941i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −212.474 | −0.250264 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −927.271 | −1.08963 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1162.30i | 1.36260i | 0.732003 | + | 0.681302i | \(0.238586\pi\) | ||||
−0.732003 | + | 0.681302i | \(0.761414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 193.097 | 0.225845 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 87.8213i | − | 0.102475i | −0.998686 | − | 0.0512376i | \(-0.983683\pi\) | ||
0.998686 | − | 0.0512376i | \(-0.0163166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 200.580i | 0.233504i | 0.993161 | + | 0.116752i | \(0.0372482\pi\) | ||||
−0.993161 | + | 0.116752i | \(0.962752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 579.088 | + | 176.043i | 0.672576 | + | 0.204464i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 617.914 | 0.716007 | 0.358004 | − | 0.933720i | \(-0.383458\pi\) | ||||
0.358004 | + | 0.933720i | \(0.383458\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −219.179 | −0.253386 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 498.569i | 0.575051i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −57.1175 | −0.0657278 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1724.84i | − | 1.98030i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 202.942i | − | 0.232465i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.7632 | − | 74.8788i | 0.0260151 | − | 0.0855758i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −638.649 | −0.728220 | −0.364110 | − | 0.931356i | \(-0.618627\pi\) | ||||
−0.364110 | + | 0.931356i | \(0.618627\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −214.551 | −0.244086 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 148.009i | 0.168001i | 0.996466 | + | 0.0840003i | \(0.0267697\pi\) | ||||
−0.996466 | + | 0.0840003i | \(0.973230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 784.505 | 0.888454 | 0.444227 | − | 0.895914i | \(-0.353478\pi\) | ||||
0.444227 | + | 0.895914i | \(0.353478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 393.872i | − | 0.445053i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1466.40i | − | 1.65321i | −0.562783 | − | 0.826605i | \(-0.690269\pi\) | ||
0.562783 | − | 0.826605i | \(-0.309731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 559.294 | + | 170.026i | 0.629127 | + | 0.191255i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.2800 | 0.0205163 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1603.27 | −1.79538 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 153.356i | − | 0.171348i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 776.152 | 0.865276 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1694.38i | 1.88473i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 61.6540i | − | 0.0684284i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.8142 | + | 111.231i | −0.0374465 | + | 0.123179i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −235.065 | −0.259741 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −488.454 | −0.538538 | −0.269269 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269269 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 219.990i | 0.242013i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1329.44 | −1.45932 | −0.729658 | − | 0.683812i | \(-0.760321\pi\) | ||||
−0.729658 | + | 0.683812i | \(0.760321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 209.964i | − | 0.229971i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 123.753i | − | 0.135250i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 403.633 | − | 1327.74i | 0.440167 | − | 1.44791i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1369.52 | −1.49023 | −0.745113 | − | 0.666938i | \(-0.767605\pi\) | ||||
−0.745113 | + | 0.666938i | \(0.767605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −390.710 | −0.424224 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 464.920i | 0.503705i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −186.416 | −0.201531 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 172.029i | 0.185576i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 909.289i | 0.978783i | 0.872064 | + | 0.489391i | \(0.162781\pi\) | ||||
−0.872064 | + | 0.489391i | \(0.837219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −785.022 | + | 1171.83i | −0.843203 | + | 1.25868i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −91.7378 | −0.0983256 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.87274 | 0.00521149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 184.883i | 0.197313i | 0.995122 | + | 0.0986566i | \(0.0314545\pi\) | ||||
−0.995122 | + | 0.0986566i | \(0.968545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 648.762 | 0.690907 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 884.454i | 0.939909i | 0.882691 | + | 0.469955i | \(0.155730\pi\) | ||||
−0.882691 | + | 0.469955i | \(0.844270\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1241.58i | 1.31662i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 77.8163 | + | 23.6562i | 0.0823453 | + | 0.0250330i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 651.331 | 0.687784 | 0.343892 | − | 0.939009i | \(-0.388255\pi\) | ||||
0.343892 | + | 0.939009i | \(0.388255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1723.91 | −1.81656 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.8798i | 0.0219557i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1622.61 | 1.70263 | 0.851316 | − | 0.524654i | \(-0.175805\pi\) | ||||
0.851316 | + | 0.524654i | \(0.175805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 513.855i | − | 0.538069i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 135.197i | − | 0.141271i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −161.832 | − | 49.1970i | −0.168751 | − | 0.0513003i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −982.915 | −1.02280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −119.520 | −0.124112 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 249.389i | 0.258435i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1491.24 | 1.54213 | 0.771067 | − | 0.636754i | \(-0.219724\pi\) | ||||
0.771067 | + | 0.636754i | \(0.219724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.4914i | 0.0552027i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1739.36i | 1.79130i | 0.444756 | + | 0.895652i | \(0.353291\pi\) | ||||
−0.444756 | + | 0.895652i | \(0.646709\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −125.493 | + | 412.806i | −0.128975 | + | 0.424261i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 156.036 | 0.160036 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −62.8973 | −0.0643780 | −0.0321890 | − | 0.999482i | \(-0.510248\pi\) | ||||
−0.0321890 | + | 0.999482i | \(0.510248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 59.6395i | − | 0.0609188i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 555.156 | 0.565909 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1214.68i | − | 1.23569i | −0.786299 | − | 0.617846i | \(-0.788006\pi\) | ||
0.786299 | − | 0.617846i | \(-0.211994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 386.537i | − | 0.392424i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −646.104 | − | 196.416i | −0.654614 | − | 0.199003i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −238.481 | −0.241133 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −114.216 | −0.115253 | −0.0576266 | − | 0.998338i | \(-0.518353\pi\) | ||||
−0.0576266 | + | 0.998338i | \(0.518353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 651.570i | 0.656163i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −263.732 | −0.265057 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 178.000i | − | 0.178536i | −0.996008 | − | 0.0892678i | \(-0.971547\pi\) | ||
0.996008 | − | 0.0892678i | \(-0.0284527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 193.729i | − | 0.193923i |
(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 | 1680.3.s.c.1441.12 | 12 | ||
4.3 | odd | 2 | 105.3.h.a.76.11 | ✓ | 12 | ||
7.6 | odd | 2 | inner | 1680.3.s.c.1441.3 | 12 | ||
12.11 | even | 2 | 315.3.h.d.181.1 | 12 | |||
20.3 | even | 4 | 525.3.e.c.349.23 | 24 | |||
20.7 | even | 4 | 525.3.e.c.349.10 | 24 | |||
20.19 | odd | 2 | 525.3.h.d.76.2 | 12 | |||
28.27 | even | 2 | 105.3.h.a.76.12 | yes | 12 | ||
84.83 | odd | 2 | 315.3.h.d.181.2 | 12 | |||
140.27 | odd | 4 | 525.3.e.c.349.24 | 24 | |||
140.83 | odd | 4 | 525.3.e.c.349.9 | 24 | |||
140.139 | even | 2 | 525.3.h.d.76.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.11 | ✓ | 12 | 4.3 | odd | 2 | ||
105.3.h.a.76.12 | yes | 12 | 28.27 | even | 2 | ||
315.3.h.d.181.1 | 12 | 12.11 | even | 2 | |||
315.3.h.d.181.2 | 12 | 84.83 | odd | 2 | |||
525.3.e.c.349.9 | 24 | 140.83 | odd | 4 | |||
525.3.e.c.349.10 | 24 | 20.7 | even | 4 | |||
525.3.e.c.349.23 | 24 | 20.3 | even | 4 | |||
525.3.e.c.349.24 | 24 | 140.27 | odd | 4 | |||
525.3.h.d.76.1 | 12 | 140.139 | even | 2 | |||
525.3.h.d.76.2 | 12 | 20.19 | odd | 2 | |||
1680.3.s.c.1441.3 | 12 | 7.6 | odd | 2 | inner | ||
1680.3.s.c.1441.12 | 12 | 1.1 | even | 1 | trivial |