Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(239,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("672.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.j (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Root | \(-1.19877 - 0.750295i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.239 |
Dual form | 672.2.j.d.239.3 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.67298 | − | 0.448478i | −0.965896 | − | 0.258929i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.896956 | −0.401131 | −0.200565 | − | 0.979680i | \(-0.564278\pi\) | ||||
−0.200565 | + | 0.979680i | \(0.564278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.59774 | + | 1.50059i | 0.865912 | + | 0.500197i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.84951i | − | 0.512961i | −0.966549 | − | 0.256480i | \(-0.917437\pi\) | ||
0.966549 | − | 0.256480i | \(-0.0825629\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50059 | + | 0.402265i | 0.387451 | + | 0.103864i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.12397i | − | 1.00021i | −0.865965 | − | 0.500104i | \(-0.833295\pi\) | ||
0.865965 | − | 0.500104i | \(-0.166705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.654037 | 0.150046 | 0.0750232 | − | 0.997182i | \(-0.476097\pi\) | ||||
0.0750232 | + | 0.997182i | \(0.476097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.448478 | − | 1.67298i | 0.0978659 | − | 0.365075i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.12515 | −1.48570 | −0.742848 | − | 0.669460i | \(-0.766525\pi\) | ||||
−0.742848 | + | 0.669460i | \(0.766525\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.19547 | −0.839094 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67298 | − | 3.67549i | −0.706866 | − | 0.707348i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.79627 | −1.44773 | −0.723866 | − | 0.689941i | \(-0.757637\pi\) | ||||
−0.723866 | + | 0.689941i | \(0.757637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.896956i | − | 0.151613i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6919i | 1.75774i | 0.477060 | + | 0.878871i | \(0.341703\pi\) | ||||
−0.477060 | + | 0.878871i | \(0.658297\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.829463 | + | 3.09419i | −0.132820 | + | 0.495467i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.1263i | − | 1.58147i | −0.612161 | − | 0.790733i | \(-0.709699\pi\) | ||
0.612161 | − | 0.790733i | \(-0.290301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.19547 | 0.182308 | 0.0911538 | − | 0.995837i | \(-0.470945\pi\) | ||||
0.0911538 | + | 0.995837i | \(0.470945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.33005 | − | 1.34596i | −0.347344 | − | 0.200644i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.59019 | −1.39887 | −0.699436 | − | 0.714695i | \(-0.746565\pi\) | ||||
−0.699436 | + | 0.714695i | \(0.746565\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.84951 | + | 6.89932i | −0.258983 | + | 0.966098i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.24793 | −1.13294 | −0.566470 | − | 0.824082i | \(-0.691691\pi\) | ||||
−0.566470 | + | 0.824082i | \(0.691691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.09419 | − | 0.293321i | −0.144929 | − | 0.0388513i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.89932i | − | 0.898215i | −0.893478 | − | 0.449107i | \(-0.851742\pi\) | ||
0.893478 | − | 0.449107i | \(-0.148258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.54143i | − | 0.581471i | −0.956803 | − | 0.290735i | \(-0.906100\pi\) | ||
0.956803 | − | 0.290735i | \(-0.0939000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50059 | + | 2.59774i | −0.189057 | + | 0.327284i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.65893i | 0.205764i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.49646 | 0.671499 | 0.335750 | − | 0.941951i | \(-0.391010\pi\) | ||||
0.335750 | + | 0.941951i | \(0.391010\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.9202 | + | 3.19547i | 1.43503 | + | 0.384689i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.12397 | 0.489425 | 0.244712 | − | 0.969596i | \(-0.421306\pi\) | ||||
0.244712 | + | 0.969596i | \(0.421306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.01894 | + | 1.88158i | 0.810478 | + | 0.217266i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.3839i | − | 1.50580i | −0.658134 | − | 0.752901i | \(-0.728654\pi\) | ||
0.658134 | − | 0.752901i | \(-0.271346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.49646 | + | 7.79627i | 0.499606 | + | 0.866253i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.3533i | − | 1.46572i | −0.680380 | − | 0.732860i | \(-0.738185\pi\) | ||
0.680380 | − | 0.732860i | \(-0.261815\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.69901i | 0.401214i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.0430 | + | 3.49646i | 1.39836 | + | 0.374859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.7142i | 1.45370i | 0.686798 | + | 0.726849i | \(0.259016\pi\) | ||||
−0.686798 | + | 0.726849i | \(0.740984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.84951 | 0.193881 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.586642 | −0.0601882 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.99291 | −0.913092 | −0.456546 | − | 0.889700i | \(-0.650914\pi\) | ||||
−0.456546 | + | 0.889700i | \(0.650914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.35097 | 0.731449 | 0.365725 | − | 0.930723i | \(-0.380821\pi\) | ||||
0.365725 | + | 0.930723i | \(0.380821\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3839i | 1.31875i | 0.751814 | + | 0.659375i | \(0.229179\pi\) | ||||
−0.751814 | + | 0.659375i | \(0.770821\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.402265 | + | 1.50059i | −0.0392570 | + | 0.146443i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.79391i | 0.173424i | 0.996233 | + | 0.0867120i | \(0.0276360\pi\) | ||||
−0.996233 | + | 0.0867120i | \(0.972364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.30807i | − | 0.508421i | −0.967149 | − | 0.254211i | \(-0.918184\pi\) | ||
0.967149 | − | 0.254211i | \(-0.0818156\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.79509 | − | 17.8874i | 0.455130 | − | 1.69780i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.00118i | − | 0.282327i | −0.989986 | − | 0.141164i | \(-0.954916\pi\) | ||
0.989986 | − | 0.141164i | \(-0.0450844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.39094 | 0.595958 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.77535 | − | 4.80453i | 0.256581 | − | 0.444179i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.12397 | 0.378043 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.54143 | + | 16.9412i | −0.409487 | + | 1.52753i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.24793 | 0.737717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.1884i | − | 1.25902i | −0.776994 | − | 0.629508i | \(-0.783257\pi\) | ||
0.776994 | − | 0.629508i | \(-0.216743\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 0.536142i | −0.176090 | − | 0.0472047i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9412i | 1.48016i | 0.672521 | + | 0.740078i | \(0.265211\pi\) | ||||
−0.672521 | + | 0.740078i | \(0.734789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.654037i | 0.0567122i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.29450 | + | 3.29675i | 0.283546 | + | 0.283739i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8358i | 1.01120i | 0.862769 | + | 0.505598i | \(0.168728\pi\) | ||||
−0.862769 | + | 0.505598i | \(0.831272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0450 | −0.936823 | −0.468411 | − | 0.883510i | \(-0.655173\pi\) | ||||
−0.468411 | + | 0.883510i | \(0.655173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0442 | + | 4.30099i | 1.35117 | + | 0.362208i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.99291 | 0.580730 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.67298 | + | 0.448478i | 0.137985 | + | 0.0369898i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.66011 | 0.381771 | 0.190885 | − | 0.981612i | \(-0.438864\pi\) | ||||
0.190885 | + | 0.981612i | \(0.438864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5793i | 1.02369i | 0.859078 | + | 0.511845i | \(0.171038\pi\) | ||||
−0.859078 | + | 0.511845i | \(0.828962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.18838 | − | 10.7130i | 0.500301 | − | 0.866092i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.5343i | − | 1.55901i | −0.626396 | − | 0.779505i | \(-0.715471\pi\) | ||
0.626396 | − | 0.779505i | \(-0.284529\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.7986 | + | 3.69901i | 1.09430 | + | 0.293351i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.12515i | − | 0.561540i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.19547 | −0.720245 | −0.360122 | − | 0.932905i | \(-0.617265\pi\) | ||||
−0.360122 | + | 0.932905i | \(0.617265\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.8358 | 0.915878 | 0.457939 | − | 0.888984i | \(-0.348588\pi\) | ||||
0.457939 | + | 0.888984i | \(0.348588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.57932 | 0.736871 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.69901 | + | 0.981441i | 0.129927 | + | 0.0750527i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.3557 | −1.47159 | −0.735793 | − | 0.677206i | \(-0.763190\pi\) | ||||
−0.735793 | + | 0.677206i | \(0.763190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.19547i | − | 0.317148i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.09419 | + | 11.5424i | −0.232574 | + | 0.867582i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7019i | 1.09888i | 0.835535 | + | 0.549438i | \(0.185158\pi\) | ||||
−0.835535 | + | 0.549438i | \(0.814842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.54143i | − | 0.337562i | −0.985654 | − | 0.168781i | \(-0.946017\pi\) | ||
0.985654 | − | 0.168781i | \(-0.0539831\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.03673 | + | 7.59774i | −0.150560 | + | 0.561641i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.59019i | − | 0.705084i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.67549 | − | 3.67298i | 0.267352 | − | 0.267170i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.70943 | −0.123690 | −0.0618449 | − | 0.998086i | \(-0.519698\pi\) | ||||
−0.0618449 | + | 0.998086i | \(0.519698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1884 | 1.16527 | 0.582633 | − | 0.812736i | \(-0.302023\pi\) | ||||
0.582633 | + | 0.812736i | \(0.302023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.743992 | − | 2.77535i | 0.0532783 | − | 0.198747i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.59019 | 0.683272 | 0.341636 | − | 0.939832i | \(-0.389019\pi\) | ||||
0.341636 | + | 0.939832i | \(0.389019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3909i | 1.02015i | 0.860131 | + | 0.510073i | \(0.170382\pi\) | ||||
−0.860131 | + | 0.510073i | \(0.829618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.19547 | − | 2.46504i | −0.648598 | − | 0.173870i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.79627i | − | 0.547191i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.08287i | 0.634375i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.5092 | − | 10.6919i | −1.28648 | − | 0.743140i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8874 | −1.09373 | −0.546867 | − | 0.837220i | \(-0.684180\pi\) | ||||
−0.546867 | + | 0.837220i | \(0.684180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.89932 | − | 1.84951i | −0.472733 | − | 0.126726i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.07228 | −0.0731292 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.0379 | + | 2.69087i | 0.678298 | + | 0.181832i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.62730 | −0.513068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00709i | 0.603159i | 0.953441 | + | 0.301580i | \(0.0975139\pi\) | ||||
−0.953441 | + | 0.301580i | \(0.902486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.8987 | − | 6.29568i | −0.726581 | − | 0.419712i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 22.9435i | − | 1.52282i | −0.648274 | − | 0.761408i | \(-0.724509\pi\) | ||
0.648274 | − | 0.761408i | \(-0.275491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9324i | 0.722432i | 0.932482 | + | 0.361216i | \(0.117638\pi\) | ||||
−0.932482 | + | 0.361216i | \(0.882362\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.24793i | − | 0.540340i | −0.962813 | − | 0.270170i | \(-0.912920\pi\) | ||
0.962813 | − | 0.270170i | \(-0.0870799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.60197 | 0.561131 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.00236 | + | 22.3909i | −0.389895 | + | 1.45445i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.87958 | −0.315634 | −0.157817 | − | 0.987468i | \(-0.550446\pi\) | ||||
−0.157817 | + | 0.987468i | \(0.550446\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.99291 | −0.321622 | −0.160811 | − | 0.986985i | \(-0.551411\pi\) | ||||
−0.160811 | + | 0.986985i | \(0.551411\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.02603 | − | 15.0596i | −0.258270 | − | 0.966073i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.896956 | 0.0573044 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.20965i | − | 0.0769679i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.98868 | + | 22.3399i | −0.379517 | + | 1.41573i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1078i | 0.701116i | 0.936541 | + | 0.350558i | \(0.114008\pi\) | ||||
−0.936541 | + | 0.350558i | \(0.885992\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.65893 | − | 6.18838i | 0.103886 | − | 0.387532i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4686i | 0.715390i | 0.933838 | + | 0.357695i | \(0.116437\pi\) | ||||
−0.933838 | + | 0.357695i | \(0.883563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6919 | −0.664364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.2527 | − | 11.6990i | −1.25361 | − | 0.724151i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.3719 | −0.762884 | −0.381442 | − | 0.924393i | \(-0.624572\pi\) | ||||
−0.381442 | + | 0.924393i | \(0.624572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.39803 | 0.454457 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.15049 | − | 22.9435i | 0.376404 | − | 1.40412i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.7374 | 1.50827 | 0.754134 | − | 0.656721i | \(-0.228057\pi\) | ||||
0.754134 | + | 0.656721i | \(0.228057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.7819i | − | 1.26241i | −0.775616 | − | 0.631205i | \(-0.782561\pi\) | ||
0.775616 | − | 0.631205i | \(-0.217439\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.09419 | − | 0.829463i | −0.187269 | − | 0.0502014i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.60906i | 0.0966790i | 0.998831 | + | 0.0483395i | \(0.0153929\pi\) | ||||
−0.998831 | + | 0.0483395i | \(0.984607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.66011i | − | 0.277999i | −0.990292 | − | 0.138999i | \(-0.955611\pi\) | ||
0.990292 | − | 0.138999i | \(-0.0443886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7369 | −0.816574 | −0.408287 | − | 0.912854i | \(-0.633874\pi\) | ||||
−0.408287 | + | 0.912854i | \(0.633874\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.981441 | + | 0.263096i | 0.0581356 | + | 0.0155845i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1263 | 0.597738 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.00708757 | −0.000416916 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.0450 | + | 4.03312i | 0.881952 | + | 0.236426i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.3557 | −1.13077 | −0.565386 | − | 0.824826i | \(-0.691273\pi\) | ||||
−0.565386 | + | 0.824826i | \(0.691273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.18838i | 0.360302i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.1780i | 0.762104i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.19547i | 0.0689058i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.2980 | − | 3.29675i | −0.706504 | − | 0.189393i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.07347i | 0.233246i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.8198 | 1.75898 | 0.879489 | − | 0.475920i | \(-0.157885\pi\) | ||||
0.879489 | + | 0.475920i | \(0.157885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00236 | − | 22.3909i | 0.341462 | − | 1.27378i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00236 | −0.340363 | −0.170181 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170181 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7748 | −0.778597 | −0.389299 | − | 0.921112i | \(-0.627283\pi\) | ||||
−0.389299 | + | 0.921112i | \(0.627283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.34596 | − | 2.33005i | 0.0758364 | − | 0.131284i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.75679 | 0.211003 | 0.105501 | − | 0.994419i | \(-0.466355\pi\) | ||||
0.105501 | + | 0.994419i | \(0.466355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.804530 | − | 3.00118i | 0.0449045 | − | 0.167510i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.69722i | − | 0.150078i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.75955i | 0.430423i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.38055 | + | 8.88031i | −0.131645 | + | 0.491082i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.59019i | − | 0.528724i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.20256 | 0.340923 | 0.170462 | − | 0.985364i | \(-0.445474\pi\) | ||||
0.170462 | + | 0.985364i | \(0.445474\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.0442 | + | 27.7748i | −0.879217 | + | 1.52205i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.93008 | −0.269359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5793 | −0.794186 | −0.397093 | − | 0.917778i | \(-0.629981\pi\) | ||||
−0.397093 | + | 0.917778i | \(0.629981\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.34596 | + | 5.02092i | −0.0731027 | + | 0.272699i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.6919 | − | 2.86620i | −0.575634 | − | 0.154311i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.41690i | 0.451843i | 0.974146 | + | 0.225921i | \(0.0725393\pi\) | ||||
−0.974146 | + | 0.225921i | \(0.927461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.9253i | − | 1.38775i | −0.720096 | − | 0.693874i | \(-0.755902\pi\) | ||
0.720096 | − | 0.693874i | \(-0.244098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.79784 | + | 6.79321i | −0.362842 | + | 0.362594i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.7142i | − | 0.729931i | −0.931021 | − | 0.364965i | \(-0.881081\pi\) | ||
0.931021 | − | 0.364965i | \(-0.118919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.69901 | −0.196323 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.89932 | − | 1.84951i | −0.365151 | − | 0.0978863i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.3055 | 1.38835 | 0.694176 | − | 0.719805i | \(-0.255769\pi\) | ||||
0.694176 | + | 0.719805i | \(0.255769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5722 | −0.977486 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.4028 | − | 4.93326i | −0.965896 | − | 0.258929i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.38173 | 0.281693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.7748i | − | 1.03224i | −0.856518 | − | 0.516118i | \(-0.827377\pi\) | ||
0.856518 | − | 0.516118i | \(-0.172623\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.1955 | − | 26.3055i | 0.791045 | − | 1.36941i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.24793i | − | 0.428211i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.77479i | − | 0.195451i | −0.995213 | − | 0.0977257i | \(-0.968843\pi\) | ||
0.995213 | − | 0.0977257i | \(-0.0311568\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7986 | − | 3.69901i | −0.712558 | − | 0.191016i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.4193i | 0.742630i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.59350 | 0.441418 | 0.220709 | − | 0.975340i | \(-0.429163\pi\) | ||||
0.220709 | + | 0.975340i | \(0.429163\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.36318 | + | 23.7369i | −0.325995 | + | 1.21608i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8381 | −0.911485 | −0.455743 | − | 0.890112i | \(-0.650626\pi\) | ||||
−0.455743 | + | 0.890112i | \(0.650626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.10552 | + | 1.79391i | 0.157862 | + | 0.0911896i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.79627 | −0.395287 | −0.197643 | − | 0.980274i | \(-0.563329\pi\) | ||||
−0.197643 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.3839i | 1.48601i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.59774 | − | 28.3422i | 0.383255 | − | 1.42968i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0047i | 0.604023i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2263i | 1.11550i | 0.830007 | + | 0.557752i | \(0.188336\pi\) | ||||
−0.830007 | + | 0.557752i | \(0.811664\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.293321 | − | 1.09419i | 0.0146844 | − | 0.0547781i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.24675i | − | 0.262010i | −0.991382 | − | 0.131005i | \(-0.958180\pi\) | ||
0.991382 | − | 0.131005i | \(-0.0418204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.03312 | − | 6.99291i | −0.200407 | − | 0.347481i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.1657 | 1.39271 | 0.696353 | − | 0.717699i | \(-0.254805\pi\) | ||||
0.696353 | + | 0.717699i | \(0.254805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.30807 | − | 19.8010i | 0.261828 | − | 0.976711i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.89932 | 0.339493 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.9774i | 0.587945i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.4780 | + | 4.95343i | 0.904874 | + | 0.242570i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.23921i | − | 0.109393i | −0.998503 | − | 0.0546963i | \(-0.982581\pi\) | ||
0.998503 | − | 0.0546963i | \(-0.0174191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.99291i | 0.340814i | 0.985374 | + | 0.170407i | \(0.0545082\pi\) | ||||
−0.985374 | + | 0.170407i | \(0.945492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.9128 | − | 14.3909i | −1.21130 | − | 0.699711i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.3020i | 0.839269i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.54143 | 0.219775 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.80966 | 0.472515 | 0.236257 | − | 0.971691i | \(-0.424079\pi\) | ||||
0.236257 | + | 0.971691i | \(0.424079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.3839 | −1.12376 | −0.561878 | − | 0.827220i | \(-0.689921\pi\) | ||||
−0.561878 | + | 0.827220i | \(0.689921\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.6990 | − | 3.13617i | −0.560925 | − | 0.150368i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.66011 | −0.222923 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.3768i | − | 0.972530i | −0.873811 | − | 0.486265i | \(-0.838359\pi\) | ||
0.873811 | − | 0.486265i | \(-0.161641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.59774 | − | 1.50059i | −0.123702 | − | 0.0714567i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 36.5668i | − | 1.73734i | −0.495389 | − | 0.868671i | \(-0.664974\pi\) | ||
0.495389 | − | 0.868671i | \(-0.335026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.3010i | − | 0.583123i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.79627 | − | 2.08995i | −0.368751 | − | 0.0988515i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.1804i | 0.905178i | 0.891719 | + | 0.452589i | \(0.149499\pi\) | ||||
−0.891719 | + | 0.452589i | \(0.850501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.64155 | − | 21.0450i | 0.265063 | − | 0.988779i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.65893 | −0.0777717 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.5935 | −0.963323 | −0.481662 | − | 0.876357i | \(-0.659967\pi\) | ||||
−0.481662 | + | 0.876357i | \(0.659967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.1576 | + | 15.1472i | −0.707495 | + | 0.707013i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.69087 | 0.125326 | 0.0626631 | − | 0.998035i | \(-0.480041\pi\) | ||||
0.0626631 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.78188i | − | 0.222233i | −0.993807 | − | 0.111116i | \(-0.964557\pi\) | ||
0.993807 | − | 0.111116i | \(-0.0354427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.8341i | 1.10291i | 0.834204 | + | 0.551456i | \(0.185927\pi\) | ||||
−0.834204 | + | 0.551456i | \(0.814073\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.49646i | 0.253803i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.76072 | + | 32.6806i | −0.403673 | + | 1.50584i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.74399 | −0.125903 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.4259 | − | 12.3768i | −0.981026 | − | 0.566693i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5925 | 0.712442 | 0.356221 | − | 0.934402i | \(-0.384065\pi\) | ||||
0.356221 | + | 0.934402i | \(0.384065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.7748 | 0.901653 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.19547 | + | 11.9202i | −0.145399 | + | 0.542390i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.06624 | 0.366269 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2026i | 0.734208i | 0.930180 | + | 0.367104i | \(0.119651\pi\) | ||||
−0.930180 | + | 0.367104i | \(0.880349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3839 | + | 4.12397i | 0.695682 | + | 0.186492i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.62299i | − | 0.298891i | −0.988770 | − | 0.149446i | \(-0.952251\pi\) | ||
0.988770 | − | 0.149446i | \(-0.0477489\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.1516i | 1.44803i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.12397i | 0.184985i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.2713 | −0.952232 | −0.476116 | − | 0.879383i | \(-0.657956\pi\) | ||||
−0.476116 | + | 0.879383i | \(0.657956\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.8010 | − | 5.30807i | −0.884643 | − | 0.237147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07228 | −0.0478108 | −0.0239054 | − | 0.999714i | \(-0.507610\pi\) | ||||
−0.0239054 | + | 0.999714i | \(0.507610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.59350 | −0.293407 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.0260 | − | 4.29611i | −0.711741 | − | 0.190797i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.78755 | −0.0792320 | −0.0396160 | − | 0.999215i | \(-0.512613\pi\) | ||||
−0.0396160 | + | 0.999215i | \(0.512613\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.00000i | − | 0.265424i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.40226 | − | 2.40390i | −0.106063 | − | 0.106135i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 12.0047i | − | 0.528991i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.3817 | + | 8.68060i | 1.42140 | + | 0.381036i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.95304i | 0.392240i | 0.980580 | + | 0.196120i | \(0.0628342\pi\) | ||||
−0.980580 | + | 0.196120i | \(0.937166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.25601 | −0.0549214 | −0.0274607 | − | 0.999623i | \(-0.508742\pi\) | ||||
−0.0274607 | + | 0.999623i | \(0.508742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.88158 | + | 7.01894i | −0.0821187 | + | 0.306332i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.7677 | 1.20729 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3531 | − | 17.9226i | 0.449284 | − | 0.777775i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.7287 | −0.811231 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.60906i | − | 0.0695657i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.59350 | − | 24.5961i | 0.284530 | − | 1.06140i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 44.3768i | − | 1.90791i | −0.299956 | − | 0.953953i | \(-0.596972\pi\) | ||
0.299956 | − | 0.953953i | \(-0.403028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.03673 | + | 7.59774i | −0.0874046 | + | 0.326050i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.76111i | 0.203943i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.80453 | 0.290941 | 0.145470 | − | 0.989363i | \(-0.453530\pi\) | ||||
0.145470 | + | 0.989363i | \(0.453530\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.81483 | − | 11.7974i | 0.290850 | − | 0.503503i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.09905 | −0.217227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3839 | 0.569139 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.30099 | + | 16.0442i | −0.182567 | + | 0.681039i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 46.6087 | 1.97487 | 0.987436 | − | 0.158017i | \(-0.0505101\pi\) | ||||
0.987436 | + | 0.158017i | \(0.0505101\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.21103i | − | 0.0935166i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.89932i | 0.290772i | 0.989375 | + | 0.145386i | \(0.0464423\pi\) | ||||
−0.989375 | + | 0.145386i | \(0.953558\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.69193i | 0.113250i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.79627 | + | 4.49646i | −0.327413 | + | 0.188833i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.75798i | − | 0.283309i | −0.989916 | − | 0.141655i | \(-0.954758\pi\) | ||
0.989916 | − | 0.141655i | \(-0.0452422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1955 | −0.719608 | −0.359804 | − | 0.933028i | \(-0.617156\pi\) | ||||
−0.359804 | + | 0.933028i | \(0.617156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.85984 | + | 0.766640i | 0.119471 | + | 0.0320268i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.8933 | 1.24664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.1586 | −1.13063 | −0.565315 | − | 0.824875i | \(-0.691245\pi\) | ||||
−0.565315 | + | 0.824875i | \(0.691245\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.0829 | − | 7.26013i | −1.12553 | − | 0.301721i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3533 | 0.553990 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.48937 | + | 4.30945i | −0.102923 | + | 0.178174i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.5313i | 1.09507i | 0.836784 | + | 0.547533i | \(0.184433\pi\) | ||||
−0.836784 | + | 0.547533i | \(0.815567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0442 | − | 4.30099i | −0.659970 | − | 0.176919i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.9644i | 1.14836i | 0.818728 | + | 0.574181i | \(0.194679\pi\) | ||||
−0.818728 | + | 0.574181i | \(0.805321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.69901 | −0.151645 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.45402 | − | 24.0758i | 0.264145 | − | 0.985356i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.0391 | 1.43166 | 0.715829 | − | 0.698275i | \(-0.246049\pi\) | ||||
0.715829 | + | 0.698275i | \(0.246049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.37677 | 0.260114 | 0.130057 | − | 0.991507i | \(-0.458484\pi\) | ||||
0.130057 | + | 0.991507i | \(0.458484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.2783 | + | 8.24793i | 0.581459 | + | 0.335882i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.86651 | −0.401131 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.60197i | − | 0.349143i | −0.984644 | − | 0.174572i | \(-0.944146\pi\) | ||
0.984644 | − | 0.174572i | \(-0.0558541\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.49646 | + | 13.0430i | −0.141684 | + | 0.528530i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.7371i | 0.717567i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2939i | 0.779273i | 0.920969 | + | 0.389637i | \(0.127399\pi\) | ||||
−0.920969 | + | 0.389637i | \(0.872601\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.07347 | − | 15.1955i | 0.164258 | − | 0.612741i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0758i | 0.405638i | 0.979216 | + | 0.202819i | \(0.0650102\pi\) | ||||
−0.979216 | + | 0.202819i | \(0.934990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.7298 | 0.672428 | 0.336214 | − | 0.941786i | \(-0.390853\pi\) | ||||
0.336214 | + | 0.941786i | \(0.390853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.1705 | + | 26.1884i | 1.05019 | + | 1.05090i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.7142 | −0.549446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.5793 | 0.543173 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.0931 | 1.75811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.7819i | − | 0.827314i | −0.910433 | − | 0.413657i | \(-0.864251\pi\) | ||
0.910433 | − | 0.413657i | \(-0.135749\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.5793 | + | 7.12515i | 1.05643 | + | 0.283199i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.7264i | 0.505030i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.84951i | 0.0732801i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.7130 | + | 6.18838i | 0.423799 | + | 0.244809i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 37.6051i | − | 1.48531i | −0.669672 | − | 0.742657i | \(-0.733565\pi\) | ||
0.669672 | − | 0.742657i | \(-0.266435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.7369 | 1.01496 | 0.507482 | − | 0.861662i | \(-0.330576\pi\) | ||||
0.507482 | + | 0.861662i | \(0.330576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.79391 | + | 0.480896i | 0.0706352 | + | 0.0189352i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.8476 | 1.64520 | 0.822599 | − | 0.568622i | \(-0.192523\pi\) | ||||
0.822599 | + | 0.568622i | \(0.192523\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0418 | 0.392968 | 0.196484 | − | 0.980507i | \(-0.437048\pi\) | ||||
0.196484 | + | 0.980507i | \(0.437048\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 15.1955i | − | 0.593736i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.5864 | − | 9.00354i | −0.608084 | − | 0.351262i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.5843i | 1.89257i | 0.323327 | + | 0.946287i | \(0.395199\pi\) | ||||
−0.323327 | + | 0.946287i | \(0.604801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.164668i | 0.00640485i | 0.999995 | + | 0.00320242i | \(0.00101936\pi\) | ||||
−0.999995 | + | 0.00320242i | \(0.998981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.7603 | + | 3.42068i | 0.495570 | + | 0.132848i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.586642i | − | 0.0227490i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.5496 | 2.15089 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.03948 | − | 15.0687i | 0.156175 | − | 0.582589i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.00709 | 0.270103 | 0.135052 | − | 0.990839i | \(-0.456880\pi\) | ||||
0.135052 | + | 0.990839i | \(0.456880\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.4099 | + | 15.4204i | 0.593127 | + | 0.593531i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.27869 | 0.241310 | 0.120655 | − | 0.992695i | \(-0.461501\pi\) | ||||
0.120655 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.99291i | − | 0.345116i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.2897 | + | 38.3841i | −0.394301 | + | 1.47088i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 30.2945i | − | 1.15919i | −0.814906 | − | 0.579593i | \(-0.803211\pi\) | ||
0.814906 | − | 0.579593i | \(-0.196789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.6161i | − | 0.405622i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.90293 | − | 18.2897i | 0.187058 | − | 0.697794i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.2546i | 0.581154i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6469 | 0.595238 | 0.297619 | − | 0.954685i | \(-0.403807\pi\) | ||||
0.297619 | + | 0.954685i | \(0.403807\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.90686 | 0.375788 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.7606 | −1.58180 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.69901 | + | 13.7986i | −0.139910 | + | 0.521912i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.45402 | −0.243765 | −0.121882 | − | 0.992545i | \(-0.538893\pi\) | ||||
−0.121882 | + | 0.992545i | \(0.538893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.99291i | 0.263743i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.3909 | − | 3.85779i | −0.541994 | − | 0.145293i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.35097i | 0.276462i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0900i | 0.679383i | 0.940537 | + | 0.339691i | \(0.110323\pi\) | ||||
−0.940537 | + | 0.339691i | \(0.889677\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.0837 | − | 34.7677i | 0.753197 | − | 1.30389i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.16344 | + | 2.18838i | 0.304869 | + | 0.0817267i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.83339 | 0.217549 | 0.108774 | − | 0.994066i | \(-0.465307\pi\) | ||||
0.108774 | + | 0.994066i | \(0.465307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.3839 | −0.498441 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.35305 | + | 2.23921i | 0.310653 | + | 0.0832771i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.7090 | 1.21478 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.22521i | − | 0.156704i | −0.996926 | − | 0.0783521i | \(-0.975034\pi\) | ||
0.996926 | − | 0.0783521i | \(-0.0249658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.0184116 | + | 27.0000i | −0.000681912 | + | 1.00000i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.93008i | − | 0.182346i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.6101i | − | 1.61078i | −0.592747 | − | 0.805388i | \(-0.701957\pi\) | ||
0.592747 | − | 0.805388i | \(-0.298043\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.50059 | − | 0.402265i | −0.0553501 | − | 0.0148378i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.97735 | 0.219880 | 0.109940 | − | 0.993938i | \(-0.464934\pi\) | ||||
0.109940 | + | 0.993938i | \(0.464934\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.542499 | + | 2.02371i | −0.0199292 | + | 0.0743430i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.9770 | −1.83348 | −0.916740 | − | 0.399485i | \(-0.869189\pi\) | ||||
−0.916740 | + | 0.399485i | \(0.869189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.17991 | −0.153140 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.0379 | − | 34.6884i | 0.733148 | − | 1.26918i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.79391 | −0.0655481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.7974i | 1.16031i | 0.814508 | + | 0.580153i | \(0.197007\pi\) | ||||
−0.814508 | + | 0.580153i | \(0.802993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.98159 | − | 18.5831i | 0.181539 | − | 0.677206i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 11.2831i | − | 0.410634i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0900i | 1.23902i | 0.784989 | + | 0.619510i | \(0.212669\pi\) | ||||
−0.784989 | + | 0.619510i | \(0.787331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.806113i | 0.0292216i | 0.999893 | + | 0.0146108i | \(0.00465092\pi\) | ||||
−0.999893 | + | 0.0146108i | \(0.995349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.30807 | 0.192165 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.55071 | + | 9.60906i | −0.200686 | + | 0.347416i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.7603 | −0.460749 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.7748 | −0.640975 | −0.320488 | − | 0.947253i | \(-0.603847\pi\) | ||||
−0.320488 | + | 0.947253i | \(0.603847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.14341 | − | 19.1867i | 0.185235 | − | 0.690993i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.3928 | −0.625576 | −0.312788 | − | 0.949823i | \(-0.601263\pi\) | ||||
−0.312788 | + | 0.949823i | \(0.601263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.8874 | + | 4.79509i | 0.641707 | + | 0.172023i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 6.62299i | − | 0.237293i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.6356 | + | 28.6551i | 1.02335 | + | 1.02405i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.5214i | 0.625367i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0450 | −0.678880 | −0.339440 | − | 0.940628i | \(-0.610238\pi\) | ||||
−0.339440 | + | 0.940628i | \(0.610238\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.6980 | + | 5.54852i | 0.736867 | + | 0.197533i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00118 | 0.106710 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.39941 | −0.298272 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.3768 | − | 3.31785i | −0.438959 | − | 0.117672i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.2333 | −1.46056 | −0.730279 | − | 0.683149i | \(-0.760610\pi\) | ||||
−0.730279 | + | 0.683149i | \(0.760610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.5496i | 1.39916i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.5793 | + | 35.6257i | −0.727135 | + | 1.25877i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.39094i | 0.225251i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.3853 | − | 11.0942i | −1.45683 | − | 0.390534i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 37.5041i | − | 1.31857i | −0.751891 | − | 0.659287i | \(-0.770858\pi\) | ||
0.751891 | − | 0.659287i | \(-0.229142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.9097 | −1.85791 | −0.928956 | − | 0.370190i | \(-0.879292\pi\) | ||||
−0.928956 | + | 0.370190i | \(0.879292\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.32021 | + | 34.7677i | −0.326874 | + | 1.21936i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.24793 | 0.288912 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.781882 | 0.0273546 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.80453 | + | 2.77535i | 0.167884 | + | 0.0969787i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.0161 | −1.08247 | −0.541235 | − | 0.840871i | \(-0.682043\pi\) | ||||
−0.541235 | + | 0.840871i | \(0.682043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 42.1657i | − | 1.46981i | −0.678173 | − | 0.734903i | \(-0.737228\pi\) | ||
0.678173 | − | 0.734903i | \(-0.262772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.7067i | 0.928682i | 0.885656 | + | 0.464341i | \(0.153709\pi\) | ||||
−0.885656 | + | 0.464341i | \(0.846291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 49.3233i | − | 1.71307i | −0.516089 | − | 0.856535i | \(-0.672613\pi\) | ||
0.516089 | − | 0.856535i | \(-0.327387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.721627 | − | 2.69193i | 0.0250330 | − | 0.0933819i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.12397i | 0.142887i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.6161 | −0.367387 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.3387 | −1.59979 | −0.799895 | − | 0.600140i | \(-0.795111\pi\) | ||||
−0.799895 | + | 0.600140i | \(0.795111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.7819 | 1.09593 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.08995 | + | 7.79627i | −0.0719819 | + | 0.268518i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.59223 | −0.295582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000i | 0.377964i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.9816 | + | 6.16070i | 0.788726 | + | 0.211435i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 76.1815i | − | 2.61147i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.84951i | − | 0.0633259i | −0.999499 | − | 0.0316630i | \(-0.989920\pi\) | ||
0.999499 | − | 0.0316630i | \(-0.0100803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.52394 | − | 0.880309i | −0.0521177 | − | 0.0301059i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 55.5617i | − | 1.89795i | −0.315348 | − | 0.948976i | \(-0.602121\pi\) | ||
0.315348 | − | 0.948976i | \(-0.397879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9621 | −0.749338 | −0.374669 | − | 0.927159i | \(-0.622244\pi\) | ||||
−0.374669 | + | 0.927159i | \(0.622244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.9412 | − | 4.54143i | −0.577353 | − | 0.154772i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.0344 | 0.784099 | 0.392049 | − | 0.919944i | \(-0.371766\pi\) | ||||
0.392049 | + | 0.919944i | \(0.371766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.3612 | 0.590299 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.0118574 | + | 0.00317862i | 0.000402698 | + | 0.000107952i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.1657i | − | 0.344453i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.3612 | − | 13.4947i | −0.790657 | − | 0.456726i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.24793i | 0.278831i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.6778i | 0.833308i | 0.909065 | + | 0.416654i | \(0.136797\pi\) | ||||
−0.909065 | + | 0.416654i | \(0.863203\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.3817 | + | 8.68060i | 1.09221 | + | 0.292789i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3987i | 0.552485i | 0.961088 | + | 0.276242i | \(0.0890893\pi\) | ||||
−0.961088 | + | 0.276242i | \(0.910911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.2783 | −0.615115 | −0.307558 | − | 0.951529i | \(-0.599512\pi\) | ||||
−0.307558 | + | 0.951529i | \(0.599512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.77535 | − | 10.3531i | 0.0932925 | − | 0.348014i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.6696 | −0.962629 | −0.481315 | − | 0.876548i | \(-0.659841\pi\) | ||||
−0.481315 | + | 0.876548i | \(0.659841\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.1884 | 0.475863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.27233 | −0.209896 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13.1870i | − | 0.440793i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.91005 | − | 22.0466i | 0.197331 | − | 0.736113i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.0142i | 1.13318i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.536142 | − | 2.00000i | 0.0178417 | − | 0.0665558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.07347i | 0.135407i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.87322 | −0.195017 | −0.0975086 | − | 0.995235i | \(-0.531087\pi\) | ||||
−0.0975086 | + | 0.995235i | \(0.531087\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.0959 | + | 11.0308i | 0.633371 | + | 0.365869i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.4548 | −1.34033 | −0.670164 | − | 0.742213i | \(-0.733776\pi\) | ||||
−0.670164 | + | 0.742213i | \(0.733776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.82686 | − | 6.81483i | 0.0603941 | − | 0.225291i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.9412 | −0.559446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.3697i | − | 0.902842i | −0.892311 | − | 0.451421i | \(-0.850917\pi\) | ||
0.892311 | − | 0.451421i | \(-0.149083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.5609 | − | 13.8220i | −1.69899 | − | 0.455450i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.62730i | − | 0.251056i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 44.8577i | − | 1.47491i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.0837 | + | 34.7677i | −0.659635 | + | 1.14192i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 23.3043i | − | 0.764590i | −0.924040 | − | 0.382295i | \(-0.875134\pi\) | ||
0.924040 | − | 0.382295i | \(-0.124866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.654037 | −0.0214352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.0418 | + | 2.69193i | 0.328755 | + | 0.0881297i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.7535 | 1.52737 | 0.763686 | − | 0.645588i | \(-0.223388\pi\) | ||||
0.763686 | + | 0.645588i | \(0.223388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.0450 | + | 6.17769i | 0.752044 | + | 0.201601i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.4441 | −1.67703 | −0.838515 | − | 0.544879i | \(-0.816576\pi\) | ||||
−0.838515 | + | 0.544879i | \(0.816576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 72.1516i | 2.34958i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.29675 | + | 3.29450i | −0.107243 | + | 0.107170i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 16.4959i | − | 0.536043i | −0.963413 | − | 0.268022i | \(-0.913630\pi\) | ||
0.963413 | − | 0.268022i | \(-0.0863699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.0970i | 0.360225i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.28505 | − | 1.68484i | −0.203807 | − | 0.0546346i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3249i | 0.690783i | 0.938459 | + | 0.345391i | \(0.112254\pi\) | ||||
−0.938459 | + | 0.345391i | \(0.887746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.53328 | 0.0496158 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.8358 | −0.382196 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.69193 | + | 4.66011i | −0.0867461 | + | 0.150170i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.5203 | −0.467424 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2026i | 0.521039i | 0.965469 | + | 0.260520i | \(0.0838939\pi\) | ||||
−0.965469 | + | 0.260520i | \(0.916106\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.20965 | + | 4.51241i | −0.0388594 | + | 0.144959i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.175328i | 0.00562655i | 0.999996 | + | 0.00281328i | \(0.000895495\pi\) | ||||
−0.999996 | + | 0.00281328i | \(0.999105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.0450i | − | 0.354086i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.47999 | − | 12.9816i | 0.111449 | − | 0.415744i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 46.6087i | − | 1.49114i | −0.666425 | − | 0.745572i | \(-0.732176\pi\) | ||
0.666425 | − | 0.745572i | \(-0.267824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.96524 | − | 13.7890i | 0.254311 | − | 0.440248i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.4373 | −1.28975 | −0.644875 | − | 0.764288i | \(-0.723091\pi\) | ||||
−0.644875 | + | 0.764288i | \(0.723091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.60197 | −0.274082 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.30099 | + | 16.0442i | −0.136902 | + | 0.510693i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.51790 | −0.270853 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.6020i | 0.527379i | 0.964608 | + | 0.263690i | \(0.0849394\pi\) | ||||
−0.964608 | + | 0.263690i | \(0.915061\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.3768 | − | 2.78171i | −0.329297 | − | 0.0882749i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 12.9080i | − | 0.409212i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3091i | 0.991570i | 0.868445 | + | 0.495785i | \(0.165120\pi\) | ||||
−0.868445 | + | 0.495785i | \(0.834880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.2980 | − | 39.2713i | 1.24333 | − | 1.24249i |
(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 | 672.2.j.d.239.1 | 12 | ||
3.2 | odd | 2 | inner | 672.2.j.d.239.4 | 12 | ||
4.3 | odd | 2 | 168.2.j.d.155.10 | yes | 12 | ||
8.3 | odd | 2 | inner | 672.2.j.d.239.2 | 12 | ||
8.5 | even | 2 | 168.2.j.d.155.4 | yes | 12 | ||
12.11 | even | 2 | 168.2.j.d.155.3 | ✓ | 12 | ||
24.5 | odd | 2 | 168.2.j.d.155.9 | yes | 12 | ||
24.11 | even | 2 | inner | 672.2.j.d.239.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.j.d.155.3 | ✓ | 12 | 12.11 | even | 2 | ||
168.2.j.d.155.4 | yes | 12 | 8.5 | even | 2 | ||
168.2.j.d.155.9 | yes | 12 | 24.5 | odd | 2 | ||
168.2.j.d.155.10 | yes | 12 | 4.3 | odd | 2 | ||
672.2.j.d.239.1 | 12 | 1.1 | even | 1 | trivial | ||
672.2.j.d.239.2 | 12 | 8.3 | odd | 2 | inner | ||
672.2.j.d.239.3 | 12 | 24.11 | even | 2 | inner | ||
672.2.j.d.239.4 | 12 | 3.2 | odd | 2 | inner |