Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(369,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.c (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
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: | \( x^{12} + 24x^{10} + 188x^{8} + 530x^{6} + 508x^{4} + 80x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.6 | ||
Root | \(0.116918i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.369 |
Dual form | 460.2.c.a.369.7 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 0.486391i | − | 0.280818i | −0.990094 | − | 0.140409i | \(-0.955158\pi\) | ||
0.990094 | − | 0.140409i | \(-0.0448417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.52160 | + | 1.63852i | 0.680480 | + | 0.732767i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80495i | 0.682207i | 0.940026 | + | 0.341103i | \(0.110801\pi\) | ||||
−0.940026 | + | 0.341103i | \(0.889199\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.76342 | 0.921141 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.90652 | −0.876350 | −0.438175 | − | 0.898890i | \(-0.644375\pi\) | ||||
−0.438175 | + | 0.898890i | \(0.644375\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.25256i | 0.624747i | 0.949959 | + | 0.312373i | \(0.101124\pi\) | ||||
−0.949959 | + | 0.312373i | \(0.898876\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.796959 | − | 0.740092i | 0.205774 | − | 0.191091i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.14477i | 0.520184i | 0.965584 | + | 0.260092i | \(0.0837529\pi\) | ||||
−0.965584 | + | 0.260092i | \(0.916247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.339824 | −0.0779610 | −0.0389805 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389805 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.877911 | 0.191576 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.369473 | + | 4.98633i | −0.0738946 | + | 0.997266i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.80328i | − | 0.539491i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.60395 | 1.04063 | 0.520313 | − | 0.853975i | \(-0.325815\pi\) | ||||
0.520313 | + | 0.853975i | \(0.325815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.92083 | 1.06341 | 0.531706 | − | 0.846929i | \(-0.321551\pi\) | ||||
0.531706 | + | 0.846929i | \(0.321551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41371i | 0.246095i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.95744 | + | 2.74641i | −0.499898 | + | 0.464228i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.98088i | − | 1.47645i | −0.674556 | − | 0.738224i | \(-0.735665\pi\) | ||
0.674556 | − | 0.738224i | \(-0.264335\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.09562 | 0.175440 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.89222 | 0.295515 | 0.147757 | − | 0.989024i | \(-0.452795\pi\) | ||||
0.147757 | + | 0.989024i | \(0.452795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.47322i | 1.44465i | 0.691552 | + | 0.722327i | \(0.256927\pi\) | ||||
−0.691552 | + | 0.722327i | \(0.743073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.20482 | + | 4.52792i | 0.626818 | + | 0.674982i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.83384i | − | 1.14268i | −0.820712 | − | 0.571342i | \(-0.806423\pi\) | ||
0.820712 | − | 0.571342i | \(-0.193577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.74216 | 0.534594 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.04320 | 0.146077 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.47764i | − | 0.889772i | −0.895587 | − | 0.444886i | \(-0.853244\pi\) | ||
0.895587 | − | 0.444886i | \(-0.146756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.42256 | − | 4.76239i | −0.596338 | − | 0.642160i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.165287i | 0.0218928i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.17914 | −0.674267 | −0.337134 | − | 0.941457i | \(-0.609457\pi\) | ||||
−0.337134 | + | 0.941457i | \(0.609457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.12565 | −1.16842 | −0.584210 | − | 0.811602i | \(-0.698596\pi\) | ||||
−0.584210 | + | 0.811602i | \(0.698596\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.98784i | 0.628409i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.69085 | + | 3.42749i | −0.457794 | + | 0.425127i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.25423i | − | 1.13058i | −0.824891 | − | 0.565292i | \(-0.808764\pi\) | ||
0.824891 | − | 0.565292i | \(-0.191236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.486391 | 0.0585546 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.60255 | −0.546222 | −0.273111 | − | 0.961982i | \(-0.588053\pi\) | ||||
−0.273111 | + | 0.961982i | \(0.588053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3300i | 1.32608i | 0.748585 | + | 0.663038i | \(0.230733\pi\) | ||||
−0.748585 | + | 0.663038i | \(0.769267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.42531 | + | 0.179708i | 0.280050 | + | 0.0207509i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.24613i | − | 0.597852i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.94972 | −0.894414 | −0.447207 | − | 0.894431i | \(-0.647581\pi\) | ||||
−0.447207 | + | 0.894431i | \(0.647581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.92678 | 0.769643 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.37849i | − | 0.590366i | −0.955441 | − | 0.295183i | \(-0.904619\pi\) | ||
0.955441 | − | 0.295183i | \(-0.0953806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.51425 | + | 3.26348i | −0.381174 | + | 0.353975i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.72571i | − | 0.292227i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.9258 | −1.37014 | −0.685069 | − | 0.728479i | \(-0.740228\pi\) | ||||
−0.685069 | + | 0.728479i | \(0.740228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.06575 | −0.426206 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.87984i | − | 0.298625i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.517076 | − | 0.556807i | −0.0530508 | − | 0.0571272i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.43210i | − | 0.246942i | −0.992348 | − | 0.123471i | \(-0.960597\pi\) | ||
0.992348 | − | 0.123471i | \(-0.0394026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.03196 | −0.807242 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.89635 | 0.288198 | 0.144099 | − | 0.989563i | \(-0.453972\pi\) | ||||
0.144099 | + | 0.989563i | \(0.453972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.3524i | − | 1.02005i | −0.860159 | − | 0.510027i | \(-0.829636\pi\) | ||
0.860159 | − | 0.510027i | \(-0.170364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.33583 | + | 1.43847i | 0.130363 | + | 0.140380i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.2395i | − | 1.47326i | −0.676296 | − | 0.736630i | \(-0.736416\pi\) | ||
0.676296 | − | 0.736630i | \(-0.263584\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00555 | 0.671010 | 0.335505 | − | 0.942038i | \(-0.391093\pi\) | ||||
0.335505 | + | 0.942038i | \(0.391093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.36822 | −0.414613 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.48460i | − | 0.610020i | −0.952349 | − | 0.305010i | \(-0.901340\pi\) | ||
0.952349 | − | 0.305010i | \(-0.0986597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.63852 | + | 1.52160i | −0.152792 | + | 0.141890i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.22477i | 0.575480i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.87121 | −0.354873 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.55212 | −0.232011 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.920357i | − | 0.0829858i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.73237 | + | 6.98181i | −0.781047 | + | 0.624472i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.28324i | − | 0.557547i | −0.960357 | − | 0.278774i | \(-0.910072\pi\) | ||
0.960357 | − | 0.278774i | \(-0.0899279\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.60769 | 0.405684 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.90426 | −0.690598 | −0.345299 | − | 0.938493i | \(-0.612223\pi\) | ||||
−0.345299 | + | 0.938493i | \(0.612223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.613365i | − | 0.0531855i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.59321 | − | 4.26546i | 0.395321 | − | 0.367113i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.28955i | − | 0.708224i | −0.935203 | − | 0.354112i | \(-0.884783\pi\) | ||
0.935203 | − | 0.354112i | \(-0.115217\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.97515 | 0.761262 | 0.380631 | − | 0.924727i | \(-0.375707\pi\) | ||||
0.380631 | + | 0.924727i | \(0.375707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.81031 | −0.320886 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.54711i | − | 0.547497i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.52696 | + | 9.18216i | 0.708125 | + | 0.762537i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.82015i | − | 0.150124i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.39792 | −0.442215 | −0.221107 | − | 0.975249i | \(-0.570967\pi\) | ||||
−0.221107 | + | 0.975249i | \(0.570967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6083 | 1.83984 | 0.919919 | − | 0.392108i | \(-0.128254\pi\) | ||||
0.919919 | + | 0.392108i | \(0.128254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.92692i | 0.479163i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00913 | + | 9.70138i | 0.723631 | + | 0.779234i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00033i | 0.638496i | 0.947671 | + | 0.319248i | \(0.103430\pi\) | ||||
−0.947671 | + | 0.319248i | \(0.896570\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.15066 | −0.249864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.80495 | −0.142250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.6504i | 1.46081i | 0.683015 | + | 0.730404i | \(0.260668\pi\) | ||||
−0.683015 | + | 0.730404i | \(0.739332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.31638 | + | 2.15109i | −0.180330 | + | 0.167462i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.13547i | − | 0.242630i | −0.992614 | − | 0.121315i | \(-0.961289\pi\) | ||
0.992614 | − | 0.121315i | \(-0.0387111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.92599 | 0.609692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.939078 | −0.0718131 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.56301i | − | 0.575005i | −0.957780 | − | 0.287503i | \(-0.907175\pi\) | ||
0.957780 | − | 0.287503i | \(-0.0928250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.00007 | − | 0.666880i | −0.680342 | − | 0.0504114i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.51909i | 0.189346i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.73608 | −0.727709 | −0.363855 | − | 0.931456i | \(-0.618539\pi\) | ||||
−0.363855 | + | 0.931456i | \(0.618539\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.260581 | 0.0193688 | 0.00968440 | − | 0.999953i | \(-0.496917\pi\) | ||||
0.00968440 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.43863i | 0.328113i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7153 | − | 13.6653i | 1.08189 | − | 1.00469i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.23384i | − | 0.455863i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.05977 | 0.368044 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.1730 | −1.31495 | −0.657476 | − | 0.753475i | \(-0.728376\pi\) | ||||
−0.657476 | + | 0.753475i | \(0.728376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.15073i | 0.154813i | 0.997000 | + | 0.0774063i | \(0.0246639\pi\) | ||||
−0.997000 | + | 0.0774063i | \(0.975336\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.66710 | + | 1.79520i | 0.119383 | + | 0.128557i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 27.0886i | − | 1.92998i | −0.262279 | − | 0.964992i | \(-0.584474\pi\) | ||
0.262279 | − | 0.964992i | \(-0.415526\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2178 | 1.00787 | 0.503937 | − | 0.863741i | \(-0.331884\pi\) | ||||
0.503937 | + | 0.863741i | \(0.331884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50117 | −0.317488 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1148i | 0.709922i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.87920 | + | 3.10043i | 0.201092 | + | 0.216543i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.76342i | 0.192071i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.987706 | 0.0683211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.89855 | 0.130701 | 0.0653506 | − | 0.997862i | \(-0.479183\pi\) | ||||
0.0653506 | + | 0.997862i | \(0.479183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.23864i | 0.153389i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5220 | + | 14.4144i | −1.05859 | + | 0.983057i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6868i | 0.725467i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.51081 | 0.372386 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.83122 | −0.324983 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5574i | 1.37663i | 0.725414 | + | 0.688313i | \(0.241648\pi\) | ||||
−0.725414 | + | 0.688313i | \(0.758352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.02101 | + | 13.7793i | −0.0680674 | + | 0.918623i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.67464i | 0.509384i | 0.967022 | + | 0.254692i | \(0.0819740\pi\) | ||||
−0.967022 | + | 0.254692i | \(0.918026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.50379 | −0.561946 | −0.280973 | − | 0.959716i | \(-0.590657\pi\) | ||||
−0.280973 | + | 0.959716i | \(0.590657\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.55167 | −0.167887 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.37058i | 0.155302i | 0.996981 | + | 0.0776511i | \(0.0247420\pi\) | ||||
−0.996981 | + | 0.0776511i | \(0.975258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8359 | − | 11.9200i | 0.837320 | − | 0.777573i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.86667i | 0.251167i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.298079 | 0.0192811 | 0.00964057 | − | 0.999954i | \(-0.496931\pi\) | ||||
0.00964057 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.7779 | 1.91817 | 0.959083 | − | 0.283126i | \(-0.0913714\pi\) | ||||
0.959083 | + | 0.283126i | \(0.0913714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 11.7790i | − | 0.755620i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.69406 | + | 6.13159i | 0.363780 | + | 0.391733i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.765472i | − | 0.0487058i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.61605 | −0.165785 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1766 | 0.642341 | 0.321171 | − | 0.947021i | \(-0.395924\pi\) | ||||
0.321171 | + | 0.947021i | \(0.395924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.90652i | − | 0.182732i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.58733 | + | 1.70930i | 0.0994024 | + | 0.107040i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.2919i | 1.76480i | 0.470501 | + | 0.882400i | \(0.344073\pi\) | ||||
−0.470501 | + | 0.882400i | \(0.655927\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.2100 | 1.00724 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4861 | 0.958564 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.9182i | 1.53652i | 0.640138 | + | 0.768260i | \(0.278877\pi\) | ||||
−0.640138 | + | 0.768260i | \(0.721123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6137 | − | 9.85637i | 0.651996 | − | 0.605472i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.28701i | 0.384759i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.8948 | −1.57883 | −0.789416 | − | 0.613859i | \(-0.789616\pi\) | ||||
−0.789416 | + | 0.613859i | \(0.789616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.49603 | 0.212369 | 0.106184 | − | 0.994346i | \(-0.466137\pi\) | ||||
0.106184 | + | 0.994346i | \(0.466137\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.97754i | 0.119686i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.07388 | − | 14.4929i | 0.0647576 | − | 0.873954i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.38317i | − | 0.0831064i | −0.999136 | − | 0.0415532i | \(-0.986769\pi\) | ||
0.999136 | − | 0.0415532i | \(-0.0132306\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.3618 | 0.979553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3144 | 0.913582 | 0.456791 | − | 0.889574i | \(-0.348999\pi\) | ||||
0.456791 | + | 0.889574i | \(0.348999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8266i | 0.703019i | 0.936184 | + | 0.351510i | \(0.114332\pi\) | ||||
−0.936184 | + | 0.351510i | \(0.885668\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.270826 | + | 0.251501i | −0.0160423 | + | 0.0148976i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.41536i | 0.201602i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3999 | 0.729409 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.18295 | −0.0693458 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 31.4274i | − | 1.83601i | −0.396569 | − | 0.918005i | \(-0.629799\pi\) | ||
0.396569 | − | 0.918005i | \(-0.370201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.88058 | − | 8.48611i | −0.458825 | − | 0.494081i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.14779i | 0.472783i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.25256 | −0.130269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0987 | −0.985552 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.40876i | − | 0.0809311i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.8856 | − | 14.9525i | −0.795086 | − | 0.856180i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.43504i | − | 0.0819018i | −0.999161 | − | 0.0409509i | \(-0.986961\pi\) | ||
0.999161 | − | 0.0409509i | \(-0.0130387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.03532 | −0.286449 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9698 | 1.18909 | 0.594544 | − | 0.804063i | \(-0.297333\pi\) | ||||
0.594544 | + | 0.804063i | \(0.297333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.535929i | 0.0302925i | 0.999885 | + | 0.0151463i | \(0.00482139\pi\) | ||||
−0.999885 | + | 0.0151463i | \(0.995179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.17266 | + | 7.58949i | −0.460477 | + | 0.427619i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.61790i | 0.371698i | 0.982578 | + | 0.185849i | \(0.0595036\pi\) | ||||
−0.982578 | + | 0.185849i | \(0.940496\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2880 | −0.911953 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.41236 | −0.413718 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.728845i | − | 0.0405540i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2320 | − | 0.832259i | −0.623038 | − | 0.0461654i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.40744i | − | 0.188432i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.1397 | 0.779546 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.81617 | −0.0998255 | −0.0499127 | − | 0.998754i | \(-0.515894\pi\) | ||||
−0.0499127 | + | 0.998754i | \(0.515894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 24.8180i | − | 1.36002i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.1632 | − | 14.0812i | 0.828454 | − | 0.769339i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3308i | 0.889593i | 0.895632 | + | 0.444796i | \(0.146724\pi\) | ||||
−0.895632 | + | 0.444796i | \(0.853276\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.15405 | −0.171304 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2090 | −0.931922 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3891i | 1.04691i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.740092 | + | 0.796959i | 0.0398452 | + | 0.0429069i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.1771i | − | 0.653700i | −0.945076 | − | 0.326850i | \(-0.894013\pi\) | ||
0.945076 | − | 0.326850i | \(-0.105987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0364 | −0.644293 | −0.322147 | − | 0.946690i | \(-0.604404\pi\) | ||||
−0.322147 | + | 0.946690i | \(0.604404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.31454 | 0.337045 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 30.0447i | − | 1.59912i | −0.600588 | − | 0.799559i | \(-0.705067\pi\) | ||
0.600588 | − | 0.799559i | \(-0.294933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.00324 | − | 7.54135i | −0.371693 | − | 0.400254i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.88292i | 0.0996547i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.6859 | 1.56676 | 0.783380 | − | 0.621543i | \(-0.213494\pi\) | ||||
0.783380 | + | 0.621543i | \(0.213494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8845 | −0.993922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.24133i | 0.0651527i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.5644 | + | 17.2397i | −0.971705 | + | 0.902368i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4413i | 0.649428i | 0.945812 | + | 0.324714i | \(0.105268\pi\) | ||||
−0.945812 | + | 0.324714i | \(0.894732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.22900 | 0.272211 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.6918 | 0.607008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.5580i | − | 1.47867i | −0.673335 | − | 0.739337i | \(-0.735139\pi\) | ||
0.673335 | − | 0.739337i | \(-0.264861\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.39589 | + | 4.24735i | 0.175363 | + | 0.219332i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.6232i | 0.650128i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8436 | −0.762465 | −0.381233 | − | 0.924479i | \(-0.624500\pi\) | ||||
−0.381233 | + | 0.924479i | \(0.624500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.05611 | −0.156569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7.00776i | − | 0.358080i | −0.983842 | − | 0.179040i | \(-0.942701\pi\) | ||
0.983842 | − | 0.179040i | \(-0.0572991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.59587 | − | 7.98250i | 0.438086 | − | 0.406826i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.1785i | 1.33073i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.2715 | −1.48413 | −0.742063 | − | 0.670330i | \(-0.766153\pi\) | ||||
−0.742063 | + | 0.670330i | \(0.766153\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.14477 | −0.108466 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.84456i | 0.193932i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0963 | − | 13.0258i | −0.608630 | − | 0.655397i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.9288i | − | 1.65265i | −0.563196 | − | 0.826324i | \(-0.690428\pi\) | ||
0.563196 | − | 0.826324i | \(-0.309572\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.298335 | −0.0149354 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3403 | −1.21550 | −0.607749 | − | 0.794129i | \(-0.707927\pi\) | ||||
−0.607749 | + | 0.794129i | \(0.707927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.3370i | 0.664363i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.5398 | + | 11.3497i | 0.523726 | + | 0.563969i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.1031i | 1.29389i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.84661 | 0.289096 | 0.144548 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144548 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.03196 | −0.198882 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.34809i | − | 0.459990i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.81274 | − | 8.18390i | 0.432600 | − | 0.401732i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.36543i | − | 0.213776i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0557 | 1.37061 | 0.685304 | − | 0.728257i | \(-0.259669\pi\) | ||||
0.685304 | + | 0.728257i | \(0.259669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0719 | −1.46561 | −0.732807 | − | 0.680437i | \(-0.761790\pi\) | ||||
−0.732807 | + | 0.680437i | \(0.761790\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 21.6482i | − | 1.05257i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.6945 | − | 0.792436i | −0.518762 | − | 0.0384388i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 16.4713i | − | 0.797104i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.18445 | −0.153747 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.92111 | −0.477883 | −0.238941 | − | 0.971034i | \(-0.576800\pi\) | ||||
−0.238941 | + | 0.971034i | \(0.576800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.82152i | 0.471992i | 0.971754 | + | 0.235996i | \(0.0758353\pi\) | ||||
−0.971754 | + | 0.235996i | \(0.924165\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.46612 | − | 4.14743i | 0.214134 | − | 0.198854i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.339824i | − | 0.0162560i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.4026 | −1.16467 | −0.582336 | − | 0.812948i | \(-0.697861\pi\) | ||||
−0.582336 | + | 0.812948i | \(0.697861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.3412 | 0.492437 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8.35646i | − | 0.397027i | −0.980098 | − | 0.198514i | \(-0.936389\pi\) | ||
0.980098 | − | 0.198514i | \(-0.0636114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.6680 | − | 21.1792i | −0.932351 | − | 1.00399i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.62550i | 0.124182i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.4109 | −0.727286 | −0.363643 | − | 0.931538i | \(-0.618467\pi\) | ||||
−0.363643 | + | 0.931538i | \(0.618467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.49978 | −0.258974 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 10.9965i | − | 0.516659i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.18644 | − | 6.66180i | −0.290025 | − | 0.312310i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.9314i | 1.07269i | 0.844000 | + | 0.536343i | \(0.180195\pi\) | ||||
−0.844000 | + | 0.536343i | \(0.819805\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.01239 | 0.280634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.71207 | −0.452336 | −0.226168 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226168 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.6091i | − | 0.632469i | −0.948681 | − | 0.316234i | \(-0.897581\pi\) | ||
0.948681 | − | 0.316234i | \(-0.102419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.71866 | − | 4.38196i | 0.218823 | − | 0.203208i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.9381i | 1.61674i | 0.588674 | + | 0.808371i | \(0.299650\pi\) | ||||
−0.588674 | + | 0.808371i | \(0.700350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.7034 | 0.771292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.89129 | 0.179301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 27.5342i | − | 1.26602i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.125556 | − | 1.69447i | 0.00576090 | − | 0.0777478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 17.9005i | − | 0.819606i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.87962 | 0.314338 | 0.157169 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2299 | 0.922406 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.877911i | 0.0399463i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.98503 | − | 3.70068i | 0.180951 | − | 0.168039i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.8903i | − | 1.44509i | −0.691325 | − | 0.722544i | \(-0.742973\pi\) | ||
0.691325 | − | 0.722544i | \(-0.257027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.07136 | 0.410221 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.1719 | 1.00061 | 0.500303 | − | 0.865851i | \(-0.333222\pi\) | ||||
0.500303 | + | 0.865851i | \(0.333222\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0192i | 0.541317i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.2214 | − | 13.1605i | −0.549312 | − | 0.591520i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.30737i | − | 0.372636i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5721 | −0.518037 | −0.259019 | − | 0.965872i | \(-0.583399\pi\) | ||||
−0.259019 | + | 0.965872i | \(0.583399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.52506 | −0.0681349 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.2532i | 1.75021i | 0.483931 | + | 0.875106i | \(0.339208\pi\) | ||||
−0.483931 | + | 0.875106i | \(0.660792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.40709 | + | 4.74572i | 0.196113 | + | 0.211182i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.85513i | − | 0.171212i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.61391 | 0.160184 | 0.0800919 | − | 0.996787i | \(-0.474479\pi\) | ||||
0.0800919 | + | 0.996787i | \(0.474479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.4501 | −0.904658 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.952620i | 0.0420592i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.9626 | − | 15.7522i | 0.747461 | − | 0.694126i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.7692i | 1.00139i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.67858 | −0.161472 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.64494 | 0.334931 | 0.167465 | − | 0.985878i | \(-0.446442\pi\) | ||||
0.167465 | + | 0.985878i | \(0.446442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.62852i | − | 0.246118i | −0.992399 | − | 0.123059i | \(-0.960730\pi\) | ||
0.992399 | − | 0.123059i | \(-0.0392704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.324364 | + | 4.37755i | −0.0141564 | + | 0.191052i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6988i | 0.553170i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.3122 | −0.621095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.26233i | 0.184622i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.9702 | − | 23.1884i | 1.07956 | − | 1.00252i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.73554i | 0.204354i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.8767 | −0.468492 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.537263 | 0.0230987 | 0.0115494 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115494 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 0.126744i | − | 0.00543911i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.6596 | + | 11.4787i | 0.456609 | + | 0.491694i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.7590i | 1.78548i | 0.450568 | + | 0.892742i | \(0.351222\pi\) | ||||
−0.450568 | + | 0.892742i | \(0.648778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.2181 | −1.07628 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.90435 | −0.0811282 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.3488i | − | 0.610175i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.64668 | − | 7.15740i | −0.282136 | − | 0.303815i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 22.5405i | − | 0.955071i | −0.878613 | − | 0.477535i | \(-0.841530\pi\) | ||
0.878613 | − | 0.477535i | \(-0.158470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.3390 | −0.902542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.03208 | −0.128015 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.5366i | 1.32911i | 0.747240 | + | 0.664554i | \(0.231378\pi\) | ||||
−0.747240 | + | 0.664554i | \(0.768622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.6251 | − | 9.86696i | 0.447002 | − | 0.415106i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.5025i | 0.525055i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.49650 | −0.104659 | −0.0523294 | − | 0.998630i | \(-0.516665\pi\) | ||||
−0.0523294 | + | 0.998630i | \(0.516665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.6658 | −1.82736 | −0.913678 | − | 0.406440i | \(-0.866770\pi\) | ||||
−0.913678 | + | 0.406440i | \(0.866770\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.83919i | 0.369262i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.98633 | − | 0.369473i | −0.207944 | − | 0.0154081i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7402i | 1.40462i | 0.711869 | + | 0.702312i | \(0.247849\pi\) | ||||
−0.711869 | + | 0.702312i | \(0.752151\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.04609 | 0.0434742 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.70790 | 0.402751 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.8274i | 0.779752i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.1994 | + | 9.47160i | −0.421693 | + | 0.391602i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 13.8050i | − | 0.569795i | −0.958558 | − | 0.284898i | \(-0.908040\pi\) | ||
0.958558 | − | 0.284898i | \(-0.0919596\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.01204 | −0.0829047 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.1757 | −0.541974 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 43.3336i | − | 1.77950i | −0.456450 | − | 0.889749i | \(-0.650879\pi\) | ||
0.456450 | − | 0.889749i | \(-0.349121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.89042 | − | 6.34304i | −0.241484 | − | 0.260039i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 6.91541i | − | 0.283029i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.2077 | 1.11168 | 0.555838 | − | 0.831290i | \(-0.312397\pi\) | ||||
0.555838 | + | 0.831290i | \(0.312397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.6299 | 1.61654 | 0.808269 | − | 0.588813i | \(-0.200405\pi\) | ||||
0.808269 | + | 0.588813i | \(0.200405\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 25.5734i | − | 1.04143i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.88330 | − | 4.18168i | −0.157878 | − | 0.170010i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.10233i | − | 0.0447421i | −0.999750 | − | 0.0223711i | \(-0.992878\pi\) | ||
0.999750 | − | 0.0223711i | \(-0.00712152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.91976 | 0.199359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.6462 | 0.713887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6705i | 0.552145i | 0.961137 | + | 0.276073i | \(0.0890331\pi\) | ||||
−0.961137 | + | 0.276073i | \(0.910967\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.50802 | − | 1.40041i | 0.0608093 | − | 0.0564702i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.9011i | 0.801187i | 0.916256 | + | 0.400594i | \(0.131196\pi\) | ||||
−0.916256 | + | 0.400594i | \(0.868804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1024 | 1.29030 | 0.645151 | − | 0.764055i | \(-0.276794\pi\) | ||||
0.645151 | + | 0.764055i | \(0.276794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.80328 | 0.112492 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 23.3305i | − | 0.934717i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7270 | − | 3.68463i | −0.989079 | − | 0.147385i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.480411i | − | 0.0191858i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.2620 | 0.768024 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3065 | 1.28610 | 0.643051 | − | 0.765823i | \(-0.277668\pi\) | ||||
0.643051 | + | 0.765823i | \(0.277668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.923435i | − | 0.0367033i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2952 | − | 9.56057i | 0.408552 | − | 0.379400i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.42942i | 0.333986i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.7188 | −0.503148 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.6696 | −0.737407 | −0.368703 | − | 0.929547i | \(-0.620198\pi\) | ||||
−0.368703 | + | 0.929547i | \(0.620198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9459i | 0.786590i | 0.919412 | + | 0.393295i | \(0.128665\pi\) | ||||
−0.919412 | + | 0.393295i | \(0.871335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.01106 | + | 7.54978i | 0.276060 | + | 0.297272i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.6920i | 1.01006i | 0.863102 | + | 0.505029i | \(0.168518\pi\) | ||||
−0.863102 | + | 0.505029i | \(0.831482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0533 | 0.590894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.19796 | 0.203724 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.7648i | 0.577791i | 0.957361 | + | 0.288896i | \(0.0932880\pi\) | ||||
−0.957361 | + | 0.288896i | \(0.906712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0271 | − | 12.9513i | −0.469938 | − | 0.506047i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.3096i | 1.22150i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.53869 | −0.371574 | −0.185787 | − | 0.982590i | \(-0.559484\pi\) | ||||
−0.185787 | + | 0.982590i | \(0.559484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2912 | 0.516968 | 0.258484 | − | 0.966016i | \(-0.416777\pi\) | ||||
0.258484 | + | 0.966016i | \(0.416777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.34986i | 0.0912611i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.00501 | − | 0.933295i | 0.0389726 | − | 0.0361916i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.60395i | 0.216986i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.99894 | 0.386581 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.5239 | 1.02395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.1517i | − | 0.429868i | −0.976629 | − | 0.214934i | \(-0.931046\pi\) | ||
0.976629 | − | 0.214934i | \(-0.0689536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.9781 | + | 1.03574i | 0.538016 | + | 0.0398655i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0771i | 1.04066i | 0.853966 | + | 0.520328i | \(0.174190\pi\) | ||||
−0.853966 | + | 0.520328i | \(0.825810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.38981 | 0.168466 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.73287 | 0.143044 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8752i | 0.913561i | 0.889579 | + | 0.456780i | \(0.150997\pi\) | ||||
−0.889579 | + | 0.456780i | \(0.849003\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5826 | − | 12.6134i | 0.518963 | − | 0.481932i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.13616i | 0.157805i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5912 | 0.555882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5350 | 1.42790 | 0.713950 | − | 0.700197i | \(-0.246904\pi\) | ||||
0.713950 | + | 0.700197i | \(0.246904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 14.4973i | − | 0.550706i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6566 | + | 14.7059i | 0.518023 | + | 0.557828i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.05838i | 0.153722i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.15303 | 0.0436116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.8587 | 1.73206 | 0.866030 | − | 0.499992i | \(-0.166664\pi\) | ||||
0.866030 | + | 0.499992i | \(0.166664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.05192i | 0.115105i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.79776 | − | 6.24325i | −0.218356 | − | 0.235135i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.22777i | 0.196611i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.2917 | −0.386515 | −0.193257 | − | 0.981148i | \(-0.561905\pi\) | ||||
−0.193257 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.9685 | −0.823881 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.92083i | 0.221737i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7275 | − | 9.96207i | 0.401187 | − | 0.372560i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.144983i | − | 0.00541449i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.2862 | 0.570080 | 0.285040 | − | 0.958516i | \(-0.407993\pi\) | ||||
0.285040 | + | 0.958516i | \(0.407993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.6856 | 0.695887 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 14.4837i | − | 0.538655i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.07051 | + | 27.9431i | −0.0768967 | + | 1.03778i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.5486i | − | 0.687930i | −0.938982 | − | 0.343965i | \(-0.888230\pi\) | ||
0.938982 | − | 0.343965i | \(-0.111770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.0512 | 0.557451 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.3179 | −0.751485 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.6045i | 1.09347i | 0.837307 | + | 0.546734i | \(0.184129\pi\) | ||||
−0.837307 | + | 0.546734i | \(0.815871\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.98235 | − | 2.76954i | 0.110006 | − | 0.102156i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8976i | 0.990787i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.2455 | −1.62760 | −0.813799 | − | 0.581147i | \(-0.802604\pi\) | ||||
−0.813799 | + | 0.581147i | \(0.802604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.372319 | −0.0136775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.33740i | − | 0.0857509i | −0.999080 | − | 0.0428755i | \(-0.986348\pi\) | ||
0.999080 | − | 0.0428755i | \(-0.0136519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.21347 | − | 8.84458i | −0.300918 | − | 0.324040i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 14.8630i | − | 0.543810i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.5066 | 1.00507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.4606 | −1.25748 | −0.628742 | − | 0.777614i | \(-0.716430\pi\) | ||||
−0.628742 | + | 0.777614i | \(0.716430\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.94980i | − | 0.180381i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.4008 | + | 37.0441i | 1.25197 | + | 1.34817i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.5337i | − | 0.964384i | −0.876066 | − | 0.482192i | \(-0.839841\pi\) | ||
0.876066 | − | 0.482192i | \(-0.160159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.41371 | −0.0513143 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.2585 | −1.74937 | −0.874685 | − | 0.484691i | \(-0.838932\pi\) | ||||
−0.874685 | + | 0.484691i | \(0.838932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6447i | 0.457768i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.71135 | + | 9.01839i | −0.351115 | + | 0.326061i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.6663i | − | 0.421246i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.6874 | −1.14268 | −0.571338 | − | 0.820715i | \(-0.693576\pi\) | ||||
−0.571338 | + | 0.820715i | \(0.693576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.7609 | 0.495587 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.7906i | 0.927623i | 0.885934 | + | 0.463811i | \(0.153519\pi\) | ||||
−0.885934 | + | 0.463811i | \(0.846481\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.18759 | + | 29.5232i | −0.0785805 | + | 1.06051i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.88441i | − | 0.282852i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.643021 | −0.0230386 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.3774 | 0.478682 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 15.7094i | − | 0.561408i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.1087 | + | 12.1733i | −0.467868 | + | 0.434483i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 26.2714i | − | 0.936475i | −0.883603 | − | 0.468237i | \(-0.844889\pi\) | ||
0.883603 | − | 0.468237i | \(-0.155111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.1200 | 0.431482 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.7044 | 0.416159 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 20.5560i | − | 0.729967i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.79405 | − | 5.16241i | −0.170027 | − | 0.183092i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.81284i | − | 0.205901i | −0.994686 | − | 0.102951i | \(-0.967172\pi\) | ||
0.994686 | − | 0.102951i | \(-0.0328284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8018 | 0.594405 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.7196 | −1.26209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 32.9309i | − | 1.16211i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.74641 | − | 2.95744i | −0.0967982 | − | 0.104236i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.5950i | 0.443364i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.5439 | −1.53092 | −0.765462 | − | 0.643481i | \(-0.777489\pi\) | ||||
−0.765462 | + | 0.643481i | \(0.777489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0230 | 0.387069 | 0.193535 | − | 0.981093i | \(-0.438005\pi\) | ||||
0.193535 | + | 0.981093i | \(0.438005\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.70044i | − | 0.0596369i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.5589 | + | 28.3784i | −1.07043 | + | 0.994051i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.21923i | − | 0.112627i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.2354 | −0.392596 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4664 | 0.644481 | 0.322240 | − | 0.946658i | \(-0.395564\pi\) | ||||
0.322240 | + | 0.946658i | \(0.395564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4960i | 0.400724i | 0.979722 | + | 0.200362i | \(0.0642118\pi\) | ||||
−0.979722 | + | 0.200362i | \(0.935788\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.04921 | − | 0.522327i | −0.245422 | − | 0.0181851i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9089i | 0.483658i | 0.970319 | + | 0.241829i | \(0.0777474\pi\) | ||||
−0.970319 | + | 0.241829i | \(0.922253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.63272 | −0.334558 | −0.167279 | − | 0.985910i | \(-0.553498\pi\) | ||||
−0.167279 | + | 0.985910i | \(0.553498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.672759 | −0.0233378 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.02608i | 0.278087i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.13752 | − | 4.77093i | 0.177791 | − | 0.165105i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 16.5977i | − | 0.573701i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.697892 | 0.0240939 | 0.0120470 | − | 0.999927i | \(-0.496165\pi\) | ||||
0.0120470 | + | 0.999927i | \(0.496165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.40421 | 0.0829036 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 7.44880i | − | 0.256550i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0602 | + | 12.9869i | 0.414883 | + | 0.446762i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.60644i | − | 0.158279i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.75236 | 0.197420 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.98088 | 0.307861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.2978i | 1.37977i | 0.723919 | + | 0.689885i | \(0.242339\pi\) | ||||
−0.723919 | + | 0.689885i | \(0.757661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.42890 | − | 1.53869i | −0.0488673 | − | 0.0526222i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.1828i | 1.64589i | 0.568118 | + | 0.822947i | \(0.307672\pi\) | ||||
−0.568118 | + | 0.822947i | \(0.692328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.5268 | −1.89455 | −0.947276 | − | 0.320419i | \(-0.896176\pi\) | ||||
−0.947276 | + | 0.320419i | \(0.896176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.66120 | 0.0566135 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 39.8794i | − | 1.35751i | −0.734364 | − | 0.678756i | \(-0.762520\pi\) | ||
0.734364 | − | 0.678756i | \(-0.237480\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3921 | − | 11.5079i | 0.421345 | − | 0.391279i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 6.03122i | − | 0.204831i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.1061 | 0.783819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.8457 | 0.706328 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.72092i | − | 0.227469i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.6018 | − | 15.7615i | −0.426019 | − | 0.532836i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 34.8562i | − | 1.17701i | −0.808493 | − | 0.588506i | \(-0.799716\pi\) | ||
0.808493 | − | 0.588506i | \(-0.200284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.2860 | −0.515584 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.94904 | −0.166737 | −0.0833687 | − | 0.996519i | \(-0.526568\pi\) | ||||
−0.0833687 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.95960i | 0.301515i | 0.988571 | + | 0.150757i | \(0.0481712\pi\) | ||||
−0.988571 | + | 0.150757i | \(0.951829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.12757 | + | 3.83304i | −0.138747 | + | 0.128846i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 28.8125i | − | 0.967429i | −0.875226 | − | 0.483714i | \(-0.839287\pi\) | ||
0.875226 | − | 0.483714i | \(-0.160713\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.3409 | 0.380363 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.1329 | −0.674476 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.66213i | 0.0890847i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8144 | − | 15.9527i | −0.495191 | − | 0.533241i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.09562i | 0.0365818i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.1800 | 1.10662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.8931 | 0.462845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.31665i | 0.276761i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.396499 | + | 0.426966i | 0.0131801 | + | 0.0141928i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 29.2784i | − | 0.972174i | −0.873910 | − | 0.486087i | \(-0.838424\pi\) | ||
0.873910 | − | 0.486087i | \(-0.161576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.00385 | 0.265471 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.48369 | −0.281077 | −0.140539 | − | 0.990075i | \(-0.544883\pi\) | ||||
−0.140539 | + | 0.990075i | \(0.544883\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.6327i | 0.517367i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.27278 | + | 6.75382i | −0.240431 | + | 0.223274i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 14.2668i | − | 0.471131i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.73942 | −0.189326 | −0.0946630 | − | 0.995509i | \(-0.530177\pi\) | ||||
−0.0946630 | + | 0.995509i | \(0.530177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.697988 | −0.0229995 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.3675i | − | 0.341250i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.7816 | + | 3.31819i | 1.47241 | + | 0.109102i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 28.6081i | − | 0.939613i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.72127 | −0.187709 | −0.0938544 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938544 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.27167 | −0.0416775 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 10.1995i | − | 0.333917i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.2142 | − | 9.48540i | 0.334041 | − | 0.310206i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.6492i | − | 1.16461i | −0.812971 | − | 0.582304i | \(-0.802151\pi\) | ||
0.812971 | − | 0.582304i | \(-0.197849\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.260671 | 0.00850668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5212 | −0.636372 | −0.318186 | − | 0.948028i | \(-0.603074\pi\) | ||||
−0.318186 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.89222i | 0.0616191i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.69894 | + | 8.29052i | 0.250447 | + | 0.269691i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.7799i | 1.16269i | 0.813657 | + | 0.581345i | \(0.197473\pi\) | ||||
−0.813657 | + | 0.581345i | \(0.802527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.5215 | −0.828462 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.21889 | 0.104380 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.97808i | 0.323222i | 0.986855 | + | 0.161611i | \(0.0516689\pi\) | ||||
−0.986855 | + | 0.161611i | \(0.948331\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.6520 | − | 29.7768i | −0.894799 | − | 0.963554i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.92234i | 0.256093i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.9622 | 0.483155 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.05624 | 0.130847 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 42.1133i | − | 1.35708i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.52400 | + | 3.27254i | −0.113442 | + | 0.105347i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 58.6546i | − | 1.88620i | −0.332505 | − | 0.943102i | \(-0.607894\pi\) | ||
0.332505 | − | 0.943102i | \(-0.392106\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.354504 | −0.0113883 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.8684 | −1.27944 | −0.639719 | − | 0.768609i | \(-0.720949\pi\) | ||||
−0.639719 | + | 0.768609i | \(0.720949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.1997i | 0.519338i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.404803 | + | 5.46313i | −0.0129641 | + | 0.174960i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26.7860i | − | 0.856962i | −0.903551 | − | 0.428481i | \(-0.859049\pi\) | ||
0.903551 | − | 0.428481i | \(-0.140951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.5693 | 1.20072 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.3593 | 0.618095 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.5711i | 1.86813i | 0.357104 | + | 0.934065i | \(0.383764\pi\) | ||||
−0.357104 | + | 0.934065i | \(0.616236\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.3851 | − | 41.2180i | 1.41423 | − | 1.31331i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 6.87741i | − | 0.218910i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.47322 | −0.301231 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.9818 | −1.71479 | −0.857394 | − | 0.514661i | \(-0.827918\pi\) | ||||
−0.857394 | + | 0.514661i | \(0.827918\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.883366i | 0.0280328i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.6338 | + | 23.2961i | 0.685838 | + | 0.738536i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.592272i | 0.0187575i | 0.999956 | + | 0.00937873i | \(0.00298538\pi\) | ||||
−0.999956 | + | 0.00937873i | \(0.997015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.1759 | −0.796530 |
(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 | 460.2.c.a.369.6 | ✓ | 12 | |
3.2 | odd | 2 | 4140.2.f.b.829.5 | 12 | |||
4.3 | odd | 2 | 1840.2.e.f.369.7 | 12 | |||
5.2 | odd | 4 | 2300.2.a.o.1.3 | 6 | |||
5.3 | odd | 4 | 2300.2.a.n.1.4 | 6 | |||
5.4 | even | 2 | inner | 460.2.c.a.369.7 | yes | 12 | |
15.14 | odd | 2 | 4140.2.f.b.829.6 | 12 | |||
20.3 | even | 4 | 9200.2.a.cy.1.3 | 6 | |||
20.7 | even | 4 | 9200.2.a.cx.1.4 | 6 | |||
20.19 | odd | 2 | 1840.2.e.f.369.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
460.2.c.a.369.7 | yes | 12 | 5.4 | even | 2 | inner | |
1840.2.e.f.369.6 | 12 | 20.19 | odd | 2 | |||
1840.2.e.f.369.7 | 12 | 4.3 | odd | 2 | |||
2300.2.a.n.1.4 | 6 | 5.3 | odd | 4 | |||
2300.2.a.o.1.3 | 6 | 5.2 | odd | 4 | |||
4140.2.f.b.829.5 | 12 | 3.2 | odd | 2 | |||
4140.2.f.b.829.6 | 12 | 15.14 | odd | 2 | |||
9200.2.a.cx.1.4 | 6 | 20.7 | even | 4 | |||
9200.2.a.cy.1.3 | 6 | 20.3 | even | 4 |