Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1365,2,Mod(274,1365)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1365, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1365.274");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1365 = 3 \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1365.f (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: | \(10.8995798759\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - x^{6} + x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.1 | ||
Root | \(-0.587785 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1365.274 |
Dual form | 1365.2.f.c.274.7 |
$q$-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 \(\left(\mathbb{Z}/1365\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(547\) | \(911\) | \(976\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.61803i | − | 1.14412i | −0.820211 | − | 0.572061i | \(-0.806144\pi\) | ||
0.820211 | − | 0.572061i | \(-0.193856\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | −1.90211 | − | 1.17557i | −0.850651 | − | 0.525731i | ||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.90211 | + | 3.07768i | −0.601501 | + | 0.973249i | ||||
\(11\) | −4.80423 | −1.44853 | −0.724264 | − | 0.689522i | \(-0.757820\pi\) | ||||
−0.724264 | + | 0.689522i | \(0.757820\pi\) | |||||||
\(12\) | 0.618034i | 0.178411i | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | −1.17557 | + | 1.90211i | −0.303531 | + | 0.491123i | ||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 3.24669i | 0.787438i | 0.919231 | + | 0.393719i | \(0.128812\pi\) | ||||
−0.919231 | + | 0.393719i | \(0.871188\pi\) | |||||||
\(18\) | 1.61803i | 0.381374i | ||||||||
\(19\) | 0.891491 | 0.204522 | 0.102261 | − | 0.994758i | \(-0.467392\pi\) | ||||
0.102261 | + | 0.994758i | \(0.467392\pi\) | |||||||
\(20\) | 1.17557 | + | 0.726543i | 0.262866 | + | 0.162460i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 7.77340i | 1.65729i | ||||||||
\(23\) | − | 1.41164i | − | 0.294347i | −0.989111 | − | 0.147173i | \(-0.952982\pi\) | ||
0.989111 | − | 0.147173i | \(-0.0470176\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 2.23607 | + | 4.47214i | 0.447214 | + | 0.894427i | ||||
\(26\) | −1.61803 | −0.317323 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 0.618034i | − | 0.116797i | ||||||
\(29\) | −0.459650 | −0.0853548 | −0.0426774 | − | 0.999089i | \(-0.513589\pi\) | ||||
−0.0426774 | + | 0.999089i | \(0.513589\pi\) | |||||||
\(30\) | 3.07768 | + | 1.90211i | 0.561906 | + | 0.347277i | ||||
\(31\) | 0.340519 | 0.0611591 | 0.0305795 | − | 0.999532i | \(-0.490265\pi\) | ||||
0.0305795 | + | 0.999532i | \(0.490265\pi\) | |||||||
\(32\) | 3.38197i | 0.597853i | ||||||||
\(33\) | 4.80423i | 0.836308i | ||||||||
\(34\) | 5.25325 | 0.900926 | ||||||||
\(35\) | 1.17557 | − | 1.90211i | 0.198708 | − | 0.321516i | ||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | − | 1.71592i | − | 0.282096i | −0.990003 | − | 0.141048i | \(-0.954953\pi\) | ||
0.990003 | − | 0.141048i | \(-0.0450471\pi\) | |||||||
\(38\) | − | 1.44246i | − | 0.233998i | ||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −2.62866 | + | 4.25325i | −0.415627 | + | 0.672499i | ||||
\(41\) | −3.07768 | −0.480653 | −0.240327 | − | 0.970692i | \(-0.577255\pi\) | ||||
−0.240327 | + | 0.970692i | \(0.577255\pi\) | |||||||
\(42\) | − | 1.61803i | − | 0.249668i | ||||||
\(43\) | 11.8885i | 1.81298i | 0.422232 | + | 0.906488i | \(0.361247\pi\) | ||||
−0.422232 | + | 0.906488i | \(0.638753\pi\) | |||||||
\(44\) | 2.96917 | 0.447620 | ||||||||
\(45\) | 1.90211 | + | 1.17557i | 0.283550 | + | 0.175244i | ||||
\(46\) | −2.28408 | −0.336769 | ||||||||
\(47\) | − | 4.50953i | − | 0.657782i | −0.944368 | − | 0.328891i | \(-0.893325\pi\) | ||
0.944368 | − | 0.328891i | \(-0.106675\pi\) | |||||||
\(48\) | 4.85410i | 0.700629i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 7.23607 | − | 3.61803i | 1.02333 | − | 0.511667i | ||||
\(51\) | 3.24669 | 0.454627 | ||||||||
\(52\) | 0.618034i | 0.0857059i | ||||||||
\(53\) | 0.405074i | 0.0556412i | 0.999613 | + | 0.0278206i | \(0.00885671\pi\) | ||||
−0.999613 | + | 0.0278206i | \(0.991143\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | 9.13818 | + | 5.64771i | 1.23219 | + | 0.761537i | ||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | − | 0.891491i | − | 0.118081i | ||||||
\(58\) | 0.743729i | 0.0976563i | ||||||||
\(59\) | −8.94241 | −1.16420 | −0.582101 | − | 0.813116i | \(-0.697769\pi\) | ||||
−0.582101 | + | 0.813116i | \(0.697769\pi\) | |||||||
\(60\) | 0.726543 | − | 1.17557i | 0.0937962 | − | 0.151765i | ||||
\(61\) | −10.3138 | −1.32054 | −0.660270 | − | 0.751028i | \(-0.729558\pi\) | ||||
−0.660270 | + | 0.751028i | \(0.729558\pi\) | |||||||
\(62\) | − | 0.550972i | − | 0.0699735i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | −1.17557 | + | 1.90211i | −0.145812 | + | 0.235928i | ||||
\(66\) | 7.77340 | 0.956840 | ||||||||
\(67\) | 8.24367i | 1.00712i | 0.863959 | + | 0.503562i | \(0.167978\pi\) | ||||
−0.863959 | + | 0.503562i | \(0.832022\pi\) | |||||||
\(68\) | − | 2.00656i | − | 0.243332i | ||||||
\(69\) | −1.41164 | −0.169941 | ||||||||
\(70\) | −3.07768 | − | 1.90211i | −0.367854 | − | 0.227346i | ||||
\(71\) | 7.57763 | 0.899299 | 0.449649 | − | 0.893205i | \(-0.351549\pi\) | ||||
0.449649 | + | 0.893205i | \(0.351549\pi\) | |||||||
\(72\) | 2.23607i | 0.263523i | ||||||||
\(73\) | − | 2.48276i | − | 0.290585i | −0.989389 | − | 0.145292i | \(-0.953588\pi\) | ||
0.989389 | − | 0.145292i | \(-0.0464123\pi\) | |||||||
\(74\) | −2.77642 | −0.322752 | ||||||||
\(75\) | 4.47214 | − | 2.23607i | 0.516398 | − | 0.258199i | ||||
\(76\) | −0.550972 | −0.0632008 | ||||||||
\(77\) | − | 4.80423i | − | 0.547492i | ||||||
\(78\) | 1.61803i | 0.183206i | ||||||||
\(79\) | 9.07112 | 1.02058 | 0.510290 | − | 0.860002i | \(-0.329538\pi\) | ||||
0.510290 | + | 0.860002i | \(0.329538\pi\) | |||||||
\(80\) | 9.23305 | + | 5.70634i | 1.03229 | + | 0.637988i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.97980i | 0.549927i | ||||||||
\(83\) | 3.83035i | 0.420436i | 0.977655 | + | 0.210218i | \(0.0674173\pi\) | ||||
−0.977655 | + | 0.210218i | \(0.932583\pi\) | |||||||
\(84\) | −0.618034 | −0.0674330 | ||||||||
\(85\) | 3.81671 | − | 6.17557i | 0.413981 | − | 0.669835i | ||||
\(86\) | 19.2360 | 2.07427 | ||||||||
\(87\) | 0.459650i | 0.0492796i | ||||||||
\(88\) | 10.7426i | 1.14516i | ||||||||
\(89\) | −15.2935 | −1.62111 | −0.810556 | − | 0.585661i | \(-0.800835\pi\) | ||||
−0.810556 | + | 0.585661i | \(0.800835\pi\) | |||||||
\(90\) | 1.90211 | − | 3.07768i | 0.200500 | − | 0.324416i | ||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0.872441i | 0.0909582i | ||||||||
\(93\) | − | 0.340519i | − | 0.0353102i | ||||||
\(94\) | −7.29657 | −0.752583 | ||||||||
\(95\) | −1.69572 | − | 1.04801i | −0.173977 | − | 0.107524i | ||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | − | 10.4893i | − | 1.06503i | −0.846421 | − | 0.532515i | \(-0.821247\pi\) | ||
0.846421 | − | 0.532515i | \(-0.178753\pi\) | |||||||
\(98\) | 1.61803i | 0.163446i | ||||||||
\(99\) | 4.80423 | 0.482843 | ||||||||
\(100\) | −1.38197 | − | 2.76393i | −0.138197 | − | 0.276393i | ||||
\(101\) | 2.46151 | 0.244930 | 0.122465 | − | 0.992473i | \(-0.460920\pi\) | ||||
0.122465 | + | 0.992473i | \(0.460920\pi\) | |||||||
\(102\) | − | 5.25325i | − | 0.520150i | ||||||
\(103\) | 4.66906i | 0.460056i | 0.973184 | + | 0.230028i | \(0.0738818\pi\) | ||||
−0.973184 | + | 0.230028i | \(0.926118\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | −1.90211 | − | 1.17557i | −0.185627 | − | 0.114724i | ||||
\(106\) | 0.655423 | 0.0636604 | ||||||||
\(107\) | − | 6.28949i | − | 0.608028i | −0.952668 | − | 0.304014i | \(-0.901673\pi\) | ||
0.952668 | − | 0.304014i | \(-0.0983270\pi\) | |||||||
\(108\) | − | 0.618034i | − | 0.0594703i | ||||||
\(109\) | 3.92045 | 0.375511 | 0.187756 | − | 0.982216i | \(-0.439879\pi\) | ||||
0.187756 | + | 0.982216i | \(0.439879\pi\) | |||||||
\(110\) | 9.13818 | − | 14.7859i | 0.871291 | − | 1.40978i | ||||
\(111\) | −1.71592 | −0.162868 | ||||||||
\(112\) | − | 4.85410i | − | 0.458670i | ||||||
\(113\) | 2.43841i | 0.229386i | 0.993401 | + | 0.114693i | \(0.0365884\pi\) | ||||
−0.993401 | + | 0.114693i | \(0.963412\pi\) | |||||||
\(114\) | −1.44246 | −0.135099 | ||||||||
\(115\) | −1.65948 | + | 2.68510i | −0.154747 | + | 0.250386i | ||||
\(116\) | 0.284079 | 0.0263761 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 14.4691i | 1.33199i | ||||||||
\(119\) | −3.24669 | −0.297624 | ||||||||
\(120\) | 4.25325 | + | 2.62866i | 0.388267 | + | 0.239962i | ||||
\(121\) | 12.0806 | 1.09824 | ||||||||
\(122\) | 16.6880i | 1.51086i | ||||||||
\(123\) | 3.07768i | 0.277505i | ||||||||
\(124\) | −0.210453 | −0.0188992 | ||||||||
\(125\) | 1.00406 | − | 11.1352i | 0.0898056 | − | 0.995959i | ||||
\(126\) | −1.61803 | −0.144146 | ||||||||
\(127\) | − | 13.3974i | − | 1.18882i | −0.804161 | − | 0.594412i | \(-0.797385\pi\) | ||
0.804161 | − | 0.594412i | \(-0.202615\pi\) | |||||||
\(128\) | 13.6180i | 1.20368i | ||||||||
\(129\) | 11.8885 | 1.04672 | ||||||||
\(130\) | 3.07768 | + | 1.90211i | 0.269931 | + | 0.166826i | ||||
\(131\) | −20.5593 | −1.79627 | −0.898137 | − | 0.439716i | \(-0.855079\pi\) | ||||
−0.898137 | + | 0.439716i | \(0.855079\pi\) | |||||||
\(132\) | − | 2.96917i | − | 0.258434i | ||||||
\(133\) | 0.891491i | 0.0773021i | ||||||||
\(134\) | 13.3385 | 1.15227 | ||||||||
\(135\) | 1.17557 | − | 1.90211i | 0.101177 | − | 0.163708i | ||||
\(136\) | 7.25982 | 0.622524 | ||||||||
\(137\) | − | 4.74258i | − | 0.405186i | −0.979263 | − | 0.202593i | \(-0.935063\pi\) | ||
0.979263 | − | 0.202593i | \(-0.0649368\pi\) | |||||||
\(138\) | 2.28408i | 0.194434i | ||||||||
\(139\) | −14.9069 | −1.26439 | −0.632193 | − | 0.774811i | \(-0.717845\pi\) | ||||
−0.632193 | + | 0.774811i | \(0.717845\pi\) | |||||||
\(140\) | −0.726543 | + | 1.17557i | −0.0614041 | + | 0.0993538i | ||||
\(141\) | −4.50953 | −0.379771 | ||||||||
\(142\) | − | 12.2609i | − | 1.02891i | ||||||
\(143\) | 4.80423i | 0.401750i | ||||||||
\(144\) | 4.85410 | 0.404508 | ||||||||
\(145\) | 0.874305 | + | 0.540350i | 0.0726071 | + | 0.0448737i | ||||
\(146\) | −4.01719 | −0.332465 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 1.06050i | 0.0871724i | ||||||||
\(149\) | 9.09372 | 0.744986 | 0.372493 | − | 0.928035i | \(-0.378503\pi\) | ||||
0.372493 | + | 0.928035i | \(0.378503\pi\) | |||||||
\(150\) | −3.61803 | − | 7.23607i | −0.295411 | − | 0.590822i | ||||
\(151\) | −12.9864 | −1.05682 | −0.528408 | − | 0.848991i | \(-0.677211\pi\) | ||||
−0.528408 | + | 0.848991i | \(0.677211\pi\) | |||||||
\(152\) | − | 1.99344i | − | 0.161689i | ||||||
\(153\) | − | 3.24669i | − | 0.262479i | ||||||
\(154\) | −7.77340 | −0.626399 | ||||||||
\(155\) | −0.647706 | − | 0.400305i | −0.0520250 | − | 0.0321532i | ||||
\(156\) | 0.618034 | 0.0494823 | ||||||||
\(157\) | 2.55703i | 0.204073i | 0.994781 | + | 0.102036i | \(0.0325358\pi\) | ||||
−0.994781 | + | 0.102036i | \(0.967464\pi\) | |||||||
\(158\) | − | 14.6774i | − | 1.16767i | ||||||
\(159\) | 0.405074 | 0.0321245 | ||||||||
\(160\) | 3.97574 | − | 6.43288i | 0.314310 | − | 0.508564i | ||||
\(161\) | 1.41164 | 0.111253 | ||||||||
\(162\) | − | 1.61803i | − | 0.127125i | ||||||
\(163\) | − | 25.2136i | − | 1.97488i | −0.157999 | − | 0.987439i | \(-0.550504\pi\) | ||
0.157999 | − | 0.987439i | \(-0.449496\pi\) | |||||||
\(164\) | 1.90211 | 0.148530 | ||||||||
\(165\) | 5.64771 | − | 9.13818i | 0.439673 | − | 0.711406i | ||||
\(166\) | 6.19764 | 0.481030 | ||||||||
\(167\) | − | 14.4068i | − | 1.11483i | −0.830235 | − | 0.557414i | \(-0.811794\pi\) | ||
0.830235 | − | 0.557414i | \(-0.188206\pi\) | |||||||
\(168\) | − | 2.23607i | − | 0.172516i | ||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −9.99228 | − | 6.17557i | −0.766373 | − | 0.473645i | ||||
\(171\) | −0.891491 | −0.0681741 | ||||||||
\(172\) | − | 7.34748i | − | 0.560240i | ||||||
\(173\) | 10.0659i | 0.765297i | 0.923894 | + | 0.382648i | \(0.124988\pi\) | ||||
−0.923894 | + | 0.382648i | \(0.875012\pi\) | |||||||
\(174\) | 0.743729 | 0.0563819 | ||||||||
\(175\) | −4.47214 | + | 2.23607i | −0.338062 | + | 0.169031i | ||||
\(176\) | 23.3202 | 1.75783 | ||||||||
\(177\) | 8.94241i | 0.672152i | ||||||||
\(178\) | 24.7455i | 1.85475i | ||||||||
\(179\) | −8.15910 | −0.609840 | −0.304920 | − | 0.952378i | \(-0.598630\pi\) | ||||
−0.304920 | + | 0.952378i | \(0.598630\pi\) | |||||||
\(180\) | −1.17557 | − | 0.726543i | −0.0876219 | − | 0.0541533i | ||||
\(181\) | −20.5509 | −1.52753 | −0.763767 | − | 0.645492i | \(-0.776652\pi\) | ||||
−0.763767 | + | 0.645492i | \(0.776652\pi\) | |||||||
\(182\) | − | 1.61803i | − | 0.119937i | ||||||
\(183\) | 10.3138i | 0.762414i | ||||||||
\(184\) | −3.15652 | −0.232702 | ||||||||
\(185\) | −2.01719 | + | 3.26388i | −0.148306 | + | 0.239965i | ||||
\(186\) | −0.550972 | −0.0403992 | ||||||||
\(187\) | − | 15.5978i | − | 1.14063i | ||||||
\(188\) | 2.78704i | 0.203266i | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −1.69572 | + | 2.74373i | −0.123020 | + | 0.199051i | ||||
\(191\) | 14.8310 | 1.07313 | 0.536567 | − | 0.843858i | \(-0.319721\pi\) | ||||
0.536567 | + | 0.843858i | \(0.319721\pi\) | |||||||
\(192\) | 4.23607i | 0.305712i | ||||||||
\(193\) | 4.38447i | 0.315601i | 0.987471 | + | 0.157801i | \(0.0504403\pi\) | ||||
−0.987471 | + | 0.157801i | \(0.949560\pi\) | |||||||
\(194\) | −16.9721 | −1.21852 | ||||||||
\(195\) | 1.90211 | + | 1.17557i | 0.136213 | + | 0.0841844i | ||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | − | 5.40321i | − | 0.384963i | −0.981301 | − | 0.192481i | \(-0.938347\pi\) | ||
0.981301 | − | 0.192481i | \(-0.0616535\pi\) | |||||||
\(198\) | − | 7.77340i | − | 0.552432i | ||||||
\(199\) | 11.5692 | 0.820119 | 0.410059 | − | 0.912059i | \(-0.365508\pi\) | ||||
0.410059 | + | 0.912059i | \(0.365508\pi\) | |||||||
\(200\) | 10.0000 | − | 5.00000i | 0.707107 | − | 0.353553i | ||||
\(201\) | 8.24367 | 0.581464 | ||||||||
\(202\) | − | 3.98281i | − | 0.280230i | ||||||
\(203\) | − | 0.459650i | − | 0.0322611i | ||||||
\(204\) | −2.00656 | −0.140488 | ||||||||
\(205\) | 5.85410 | + | 3.61803i | 0.408868 | + | 0.252694i | ||||
\(206\) | 7.55470 | 0.526361 | ||||||||
\(207\) | 1.41164i | 0.0981157i | ||||||||
\(208\) | 4.85410i | 0.336571i | ||||||||
\(209\) | −4.28293 | −0.296256 | ||||||||
\(210\) | −1.90211 | + | 3.07768i | −0.131258 | + | 0.212380i | ||||
\(211\) | −10.7653 | −0.741113 | −0.370556 | − | 0.928810i | \(-0.620833\pi\) | ||||
−0.370556 | + | 0.928810i | \(0.620833\pi\) | |||||||
\(212\) | − | 0.250349i | − | 0.0171941i | ||||||
\(213\) | − | 7.57763i | − | 0.519210i | ||||||
\(214\) | −10.1766 | −0.695659 | ||||||||
\(215\) | 13.9757 | − | 22.6132i | 0.953138 | − | 1.54221i | ||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 0.340519i | 0.0231160i | ||||||||
\(218\) | − | 6.34342i | − | 0.429631i | ||||||
\(219\) | −2.48276 | −0.167769 | ||||||||
\(220\) | −5.64771 | − | 3.49047i | −0.380768 | − | 0.235328i | ||||
\(221\) | 3.24669 | 0.218396 | ||||||||
\(222\) | 2.77642i | 0.186341i | ||||||||
\(223\) | 9.65948i | 0.646847i | 0.946254 | + | 0.323423i | \(0.104834\pi\) | ||||
−0.946254 | + | 0.323423i | \(0.895166\pi\) | |||||||
\(224\) | −3.38197 | −0.225967 | ||||||||
\(225\) | −2.23607 | − | 4.47214i | −0.149071 | − | 0.298142i | ||||
\(226\) | 3.94542 | 0.262446 | ||||||||
\(227\) | 27.8250i | 1.84681i | 0.383825 | + | 0.923406i | \(0.374607\pi\) | ||||
−0.383825 | + | 0.923406i | \(0.625393\pi\) | |||||||
\(228\) | 0.550972i | 0.0364890i | ||||||||
\(229\) | −8.53026 | −0.563695 | −0.281848 | − | 0.959459i | \(-0.590947\pi\) | ||||
−0.281848 | + | 0.959459i | \(0.590947\pi\) | |||||||
\(230\) | 4.34458 | + | 2.68510i | 0.286473 | + | 0.177050i | ||||
\(231\) | −4.80423 | −0.316095 | ||||||||
\(232\) | 1.02781i | 0.0674789i | ||||||||
\(233\) | − | 21.1471i | − | 1.38540i | −0.721228 | − | 0.692698i | \(-0.756422\pi\) | ||
0.721228 | − | 0.692698i | \(-0.243578\pi\) | |||||||
\(234\) | 1.61803 | 0.105774 | ||||||||
\(235\) | −5.30127 | + | 8.57763i | −0.345816 | + | 0.559543i | ||||
\(236\) | 5.52671 | 0.359758 | ||||||||
\(237\) | − | 9.07112i | − | 0.589233i | ||||||
\(238\) | 5.25325i | 0.340518i | ||||||||
\(239\) | −18.1840 | −1.17623 | −0.588113 | − | 0.808779i | \(-0.700129\pi\) | ||||
−0.588113 | + | 0.808779i | \(0.700129\pi\) | |||||||
\(240\) | 5.70634 | − | 9.23305i | 0.368343 | − | 0.595991i | ||||
\(241\) | −11.7022 | −0.753803 | −0.376901 | − | 0.926253i | \(-0.623010\pi\) | ||||
−0.376901 | + | 0.926253i | \(0.623010\pi\) | |||||||
\(242\) | − | 19.5468i | − | 1.25652i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.37425 | 0.408069 | ||||||||
\(245\) | 1.90211 | + | 1.17557i | 0.121522 | + | 0.0751044i | ||||
\(246\) | 4.97980 | 0.317500 | ||||||||
\(247\) | − | 0.891491i | − | 0.0567242i | ||||||
\(248\) | − | 0.761425i | − | 0.0483505i | ||||||
\(249\) | 3.83035 | 0.242739 | ||||||||
\(250\) | −18.0171 | − | 1.62460i | −1.13950 | − | 0.102749i | ||||
\(251\) | 6.64185 | 0.419230 | 0.209615 | − | 0.977784i | \(-0.432779\pi\) | ||||
0.209615 | + | 0.977784i | \(0.432779\pi\) | |||||||
\(252\) | 0.618034i | 0.0389325i | ||||||||
\(253\) | 6.78183i | 0.426370i | ||||||||
\(254\) | −21.6774 | −1.36016 | ||||||||
\(255\) | −6.17557 | − | 3.81671i | −0.386729 | − | 0.239012i | ||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | − | 16.4358i | − | 1.02524i | −0.858617 | − | 0.512618i | \(-0.828676\pi\) | ||
0.858617 | − | 0.512618i | \(-0.171324\pi\) | |||||||
\(258\) | − | 19.2360i | − | 1.19758i | ||||||
\(259\) | 1.71592 | 0.106622 | ||||||||
\(260\) | 0.726543 | − | 1.17557i | 0.0450583 | − | 0.0729058i | ||||
\(261\) | 0.459650 | 0.0284516 | ||||||||
\(262\) | 33.2656i | 2.05516i | ||||||||
\(263\) | 27.9057i | 1.72074i | 0.509673 | + | 0.860368i | \(0.329766\pi\) | ||||
−0.509673 | + | 0.860368i | \(0.670234\pi\) | |||||||
\(264\) | 10.7426 | 0.661160 | ||||||||
\(265\) | 0.476193 | − | 0.770497i | 0.0292523 | − | 0.0473312i | ||||
\(266\) | 1.44246 | 0.0884431 | ||||||||
\(267\) | 15.2935i | 0.935950i | ||||||||
\(268\) | − | 5.09487i | − | 0.311219i | ||||||
\(269\) | −27.3788 | −1.66932 | −0.834659 | − | 0.550768i | \(-0.814335\pi\) | ||||
−0.834659 | + | 0.550768i | \(0.814335\pi\) | |||||||
\(270\) | −3.07768 | − | 1.90211i | −0.187302 | − | 0.115759i | ||||
\(271\) | −3.10600 | −0.188676 | −0.0943381 | − | 0.995540i | \(-0.530073\pi\) | ||||
−0.0943381 | + | 0.995540i | \(0.530073\pi\) | |||||||
\(272\) | − | 15.7598i | − | 0.955576i | ||||||
\(273\) | − | 1.00000i | − | 0.0605228i | ||||||
\(274\) | −7.67365 | −0.463582 | ||||||||
\(275\) | −10.7426 | − | 21.4852i | −0.647802 | − | 1.29560i | ||||
\(276\) | 0.872441 | 0.0525148 | ||||||||
\(277\) | 30.2146i | 1.81542i | 0.419599 | + | 0.907710i | \(0.362171\pi\) | ||||
−0.419599 | + | 0.907710i | \(0.637829\pi\) | |||||||
\(278\) | 24.1198i | 1.44661i | ||||||||
\(279\) | −0.340519 | −0.0203864 | ||||||||
\(280\) | −4.25325 | − | 2.62866i | −0.254181 | − | 0.157092i | ||||
\(281\) | −0.922959 | −0.0550591 | −0.0275296 | − | 0.999621i | \(-0.508764\pi\) | ||||
−0.0275296 | + | 0.999621i | \(0.508764\pi\) | |||||||
\(282\) | 7.29657i | 0.434504i | ||||||||
\(283\) | 16.7953i | 0.998376i | 0.866494 | + | 0.499188i | \(0.166368\pi\) | ||||
−0.866494 | + | 0.499188i | \(0.833632\pi\) | |||||||
\(284\) | −4.68323 | −0.277899 | ||||||||
\(285\) | −1.04801 | + | 1.69572i | −0.0620788 | + | 0.100446i | ||||
\(286\) | 7.77340 | 0.459651 | ||||||||
\(287\) | − | 3.07768i | − | 0.181670i | ||||||
\(288\) | − | 3.38197i | − | 0.199284i | ||||||
\(289\) | 6.45901 | 0.379942 | ||||||||
\(290\) | 0.874305 | − | 1.41466i | 0.0513410 | − | 0.0830715i | ||||
\(291\) | −10.4893 | −0.614895 | ||||||||
\(292\) | 1.53443i | 0.0897956i | ||||||||
\(293\) | − | 5.53066i | − | 0.323104i | −0.986864 | − | 0.161552i | \(-0.948350\pi\) | ||
0.986864 | − | 0.161552i | \(-0.0516500\pi\) | |||||||
\(294\) | 1.61803 | 0.0943657 | ||||||||
\(295\) | 17.0095 | + | 10.5124i | 0.990330 | + | 0.612057i | ||||
\(296\) | −3.83692 | −0.223016 | ||||||||
\(297\) | − | 4.80423i | − | 0.278769i | ||||||
\(298\) | − | 14.7139i | − | 0.852356i | ||||||
\(299\) | −1.41164 | −0.0816372 | ||||||||
\(300\) | −2.76393 | + | 1.38197i | −0.159576 | + | 0.0797878i | ||||
\(301\) | −11.8885 | −0.685240 | ||||||||
\(302\) | 21.0124i | 1.20913i | ||||||||
\(303\) | − | 2.46151i | − | 0.141410i | ||||||
\(304\) | −4.32739 | −0.248193 | ||||||||
\(305\) | 19.6179 | + | 12.1245i | 1.12332 | + | 0.694249i | ||||
\(306\) | −5.25325 | −0.300309 | ||||||||
\(307\) | − | 31.3957i | − | 1.79185i | −0.444208 | − | 0.895923i | \(-0.646515\pi\) | ||
0.444208 | − | 0.895923i | \(-0.353485\pi\) | |||||||
\(308\) | 2.96917i | 0.169184i | ||||||||
\(309\) | 4.66906 | 0.265614 | ||||||||
\(310\) | −0.647706 | + | 1.04801i | −0.0367873 | + | 0.0595230i | ||||
\(311\) | 2.73362 | 0.155009 | 0.0775046 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775046 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(312\) | 2.23607i | 0.126592i | ||||||||
\(313\) | 2.92489i | 0.165325i | 0.996578 | + | 0.0826624i | \(0.0263423\pi\) | ||||
−0.996578 | + | 0.0826624i | \(0.973658\pi\) | |||||||
\(314\) | 4.13736 | 0.233485 | ||||||||
\(315\) | −1.17557 | + | 1.90211i | −0.0662359 | + | 0.107172i | ||||
\(316\) | −5.60626 | −0.315377 | ||||||||
\(317\) | 0.810148i | 0.0455024i | 0.999741 | + | 0.0227512i | \(0.00724256\pi\) | ||||
−0.999741 | + | 0.0227512i | \(0.992757\pi\) | |||||||
\(318\) | − | 0.655423i | − | 0.0367543i | ||||||
\(319\) | 2.20826 | 0.123639 | ||||||||
\(320\) | 8.05748 | + | 4.97980i | 0.450427 | + | 0.278379i | ||||
\(321\) | −6.28949 | −0.351045 | ||||||||
\(322\) | − | 2.28408i | − | 0.127287i | ||||||
\(323\) | 2.89440i | 0.161049i | ||||||||
\(324\) | −0.618034 | −0.0343352 | ||||||||
\(325\) | 4.47214 | − | 2.23607i | 0.248069 | − | 0.124035i | ||||
\(326\) | −40.7964 | −2.25950 | ||||||||
\(327\) | − | 3.92045i | − | 0.216801i | ||||||
\(328\) | 6.88191i | 0.379990i | ||||||||
\(329\) | 4.50953 | 0.248618 | ||||||||
\(330\) | −14.7859 | − | 9.13818i | −0.813936 | − | 0.503040i | ||||
\(331\) | −5.02278 | −0.276077 | −0.138038 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138038 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(332\) | − | 2.36729i | − | 0.129922i | ||||||
\(333\) | 1.71592i | 0.0940319i | ||||||||
\(334\) | −23.3106 | −1.27550 | ||||||||
\(335\) | 9.69102 | − | 15.6804i | 0.529477 | − | 0.856712i | ||||
\(336\) | −4.85410 | −0.264813 | ||||||||
\(337\) | − | 14.9881i | − | 0.816455i | −0.912880 | − | 0.408227i | \(-0.866147\pi\) | ||
0.912880 | − | 0.408227i | \(-0.133853\pi\) | |||||||
\(338\) | 1.61803i | 0.0880094i | ||||||||
\(339\) | 2.43841 | 0.132436 | ||||||||
\(340\) | −2.35886 | + | 3.81671i | −0.127927 | + | 0.206990i | ||||
\(341\) | −1.63593 | −0.0885907 | ||||||||
\(342\) | 1.44246i | 0.0779995i | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 26.5834 | 1.43328 | ||||||||
\(345\) | 2.68510 | + | 1.65948i | 0.144561 | + | 0.0893434i | ||||
\(346\) | 16.2870 | 0.875594 | ||||||||
\(347\) | − | 3.88544i | − | 0.208581i | −0.994547 | − | 0.104291i | \(-0.966743\pi\) | ||
0.994547 | − | 0.104291i | \(-0.0332572\pi\) | |||||||
\(348\) | − | 0.284079i | − | 0.0152282i | ||||||
\(349\) | −33.1267 | −1.77323 | −0.886616 | − | 0.462507i | \(-0.846950\pi\) | ||||
−0.886616 | + | 0.462507i | \(0.846950\pi\) | |||||||
\(350\) | 3.61803 | + | 7.23607i | 0.193392 | + | 0.386784i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | − | 16.2477i | − | 0.866007i | ||||||
\(353\) | − | 6.16721i | − | 0.328248i | −0.986440 | − | 0.164124i | \(-0.947520\pi\) | ||
0.986440 | − | 0.164124i | \(-0.0524796\pi\) | |||||||
\(354\) | 14.4691 | 0.769025 | ||||||||
\(355\) | −14.4135 | − | 8.90803i | −0.764989 | − | 0.472789i | ||||
\(356\) | 9.45193 | 0.500951 | ||||||||
\(357\) | 3.24669i | 0.171833i | ||||||||
\(358\) | 13.2017i | 0.697731i | ||||||||
\(359\) | 4.35926 | 0.230073 | 0.115036 | − | 0.993361i | \(-0.463302\pi\) | ||||
0.115036 | + | 0.993361i | \(0.463302\pi\) | |||||||
\(360\) | 2.62866 | − | 4.25325i | 0.138542 | − | 0.224166i | ||||
\(361\) | −18.2052 | −0.958171 | ||||||||
\(362\) | 33.2520i | 1.74769i | ||||||||
\(363\) | − | 12.0806i | − | 0.634066i | ||||||
\(364\) | −0.618034 | −0.0323938 | ||||||||
\(365\) | −2.91866 | + | 4.72249i | −0.152769 | + | 0.247186i | ||||
\(366\) | 16.6880 | 0.872296 | ||||||||
\(367\) | − | 35.6921i | − | 1.86311i | −0.363600 | − | 0.931555i | \(-0.618453\pi\) | ||
0.363600 | − | 0.931555i | \(-0.381547\pi\) | |||||||
\(368\) | 6.85224i | 0.357198i | ||||||||
\(369\) | 3.07768 | 0.160218 | ||||||||
\(370\) | 5.28106 | + | 3.26388i | 0.274549 | + | 0.169681i | ||||
\(371\) | −0.405074 | −0.0210304 | ||||||||
\(372\) | 0.210453i | 0.0109115i | ||||||||
\(373\) | − | 11.6759i | − | 0.604556i | −0.953220 | − | 0.302278i | \(-0.902253\pi\) | ||
0.953220 | − | 0.302278i | \(-0.0977471\pi\) | |||||||
\(374\) | −25.2378 | −1.30502 | ||||||||
\(375\) | −11.1352 | − | 1.00406i | −0.575017 | − | 0.0518493i | ||||
\(376\) | −10.0836 | −0.520022 | ||||||||
\(377\) | 0.459650i | 0.0236732i | ||||||||
\(378\) | 1.61803i | 0.0832227i | ||||||||
\(379\) | −20.0941 | −1.03217 | −0.516083 | − | 0.856539i | \(-0.672610\pi\) | ||||
−0.516083 | + | 0.856539i | \(0.672610\pi\) | |||||||
\(380\) | 1.04801 | + | 0.647706i | 0.0537618 | + | 0.0332266i | ||||
\(381\) | −13.3974 | −0.686367 | ||||||||
\(382\) | − | 23.9971i | − | 1.22780i | ||||||
\(383\) | 0.874948i | 0.0447078i | 0.999750 | + | 0.0223539i | \(0.00711605\pi\) | ||||
−0.999750 | + | 0.0223539i | \(0.992884\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | −5.64771 | + | 9.13818i | −0.287834 | + | 0.465725i | ||||
\(386\) | 7.09423 | 0.361087 | ||||||||
\(387\) | − | 11.8885i | − | 0.604325i | ||||||
\(388\) | 6.48276i | 0.329112i | ||||||||
\(389\) | −32.7010 | −1.65801 | −0.829004 | − | 0.559243i | \(-0.811092\pi\) | ||||
−0.829004 | + | 0.559243i | \(0.811092\pi\) | |||||||
\(390\) | 1.90211 | − | 3.07768i | 0.0963172 | − | 0.155845i | ||||
\(391\) | 4.58315 | 0.231780 | ||||||||
\(392\) | 2.23607i | 0.112938i | ||||||||
\(393\) | 20.5593i | 1.03708i | ||||||||
\(394\) | −8.74258 | −0.440445 | ||||||||
\(395\) | −17.2543 | − | 10.6637i | −0.868158 | − | 0.536551i | ||||
\(396\) | −2.96917 | −0.149207 | ||||||||
\(397\) | − | 37.1937i | − | 1.86670i | −0.358971 | − | 0.933349i | \(-0.616872\pi\) | ||
0.358971 | − | 0.933349i | \(-0.383128\pi\) | |||||||
\(398\) | − | 18.7194i | − | 0.938316i | ||||||
\(399\) | 0.891491 | 0.0446304 | ||||||||
\(400\) | −10.8541 | − | 21.7082i | −0.542705 | − | 1.08541i | ||||
\(401\) | −3.69636 | −0.184587 | −0.0922937 | − | 0.995732i | \(-0.529420\pi\) | ||||
−0.0922937 | + | 0.995732i | \(0.529420\pi\) | |||||||
\(402\) | − | 13.3385i | − | 0.665266i | ||||||
\(403\) | − | 0.340519i | − | 0.0169625i | ||||||
\(404\) | −1.52130 | −0.0756875 | ||||||||
\(405\) | −1.90211 | − | 1.17557i | −0.0945168 | − | 0.0584146i | ||||
\(406\) | −0.743729 | −0.0369106 | ||||||||
\(407\) | 8.24367i | 0.408624i | ||||||||
\(408\) | − | 7.25982i | − | 0.359415i | ||||||
\(409\) | 5.50837 | 0.272372 | 0.136186 | − | 0.990683i | \(-0.456516\pi\) | ||||
0.136186 | + | 0.990683i | \(0.456516\pi\) | |||||||
\(410\) | 5.85410 | − | 9.47214i | 0.289113 | − | 0.467795i | ||||
\(411\) | −4.74258 | −0.233934 | ||||||||
\(412\) | − | 2.88564i | − | 0.142165i | ||||||
\(413\) | − | 8.94241i | − | 0.440027i | ||||||
\(414\) | 2.28408 | 0.112256 | ||||||||
\(415\) | 4.50285 | − | 7.28576i | 0.221036 | − | 0.357644i | ||||
\(416\) | 3.38197 | 0.165815 | ||||||||
\(417\) | 14.9069i | 0.729993i | ||||||||
\(418\) | 6.92992i | 0.338953i | ||||||||
\(419\) | 24.5229 | 1.19802 | 0.599012 | − | 0.800740i | \(-0.295560\pi\) | ||||
0.599012 | + | 0.800740i | \(0.295560\pi\) | |||||||
\(420\) | 1.17557 | + | 0.726543i | 0.0573620 | + | 0.0354516i | ||||
\(421\) | −6.91531 | −0.337032 | −0.168516 | − | 0.985699i | \(-0.553897\pi\) | ||||
−0.168516 | + | 0.985699i | \(0.553897\pi\) | |||||||
\(422\) | 17.4186i | 0.847924i | ||||||||
\(423\) | 4.50953i | 0.219261i | ||||||||
\(424\) | 0.905773 | 0.0439882 | ||||||||
\(425\) | −14.5196 | + | 7.25982i | −0.704306 | + | 0.352153i | ||||
\(426\) | −12.2609 | −0.594041 | ||||||||
\(427\) | − | 10.3138i | − | 0.499117i | ||||||
\(428\) | 3.88712i | 0.187891i | ||||||||
\(429\) | 4.80423 | 0.231950 | ||||||||
\(430\) | −36.5890 | − | 22.6132i | −1.76448 | − | 1.09051i | ||||
\(431\) | 6.75428 | 0.325342 | 0.162671 | − | 0.986680i | \(-0.447989\pi\) | ||||
0.162671 | + | 0.986680i | \(0.447989\pi\) | |||||||
\(432\) | − | 4.85410i | − | 0.233543i | ||||||
\(433\) | − | 26.2842i | − | 1.26314i | −0.775320 | − | 0.631568i | \(-0.782412\pi\) | ||
0.775320 | − | 0.631568i | \(-0.217588\pi\) | |||||||
\(434\) | 0.550972 | 0.0264475 | ||||||||
\(435\) | 0.540350 | − | 0.874305i | 0.0259078 | − | 0.0419197i | ||||
\(436\) | −2.42297 | −0.116039 | ||||||||
\(437\) | − | 1.25846i | − | 0.0602005i | ||||||
\(438\) | 4.01719i | 0.191949i | ||||||||
\(439\) | 21.6867 | 1.03505 | 0.517526 | − | 0.855668i | \(-0.326853\pi\) | ||||
0.517526 | + | 0.855668i | \(0.326853\pi\) | |||||||
\(440\) | 12.6287 | − | 20.4336i | 0.602048 | − | 0.974133i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 5.25325i | − | 0.249872i | ||||||
\(443\) | 30.0870i | 1.42948i | 0.699391 | + | 0.714739i | \(0.253455\pi\) | ||||
−0.699391 | + | 0.714739i | \(0.746545\pi\) | |||||||
\(444\) | 1.06050 | 0.0503290 | ||||||||
\(445\) | 29.0901 | + | 17.9786i | 1.37900 | + | 0.852269i | ||||
\(446\) | 15.6294 | 0.740072 | ||||||||
\(447\) | − | 9.09372i | − | 0.430118i | ||||||
\(448\) | − | 4.23607i | − | 0.200135i | ||||||
\(449\) | 37.4141 | 1.76568 | 0.882840 | − | 0.469673i | \(-0.155628\pi\) | ||||
0.882840 | + | 0.469673i | \(0.155628\pi\) | |||||||
\(450\) | −7.23607 | + | 3.61803i | −0.341112 | + | 0.170556i | ||||
\(451\) | 14.7859 | 0.696240 | ||||||||
\(452\) | − | 1.50702i | − | 0.0708842i | ||||||
\(453\) | 12.9864i | 0.610152i | ||||||||
\(454\) | 45.0218 | 2.11298 | ||||||||
\(455\) | −1.90211 | − | 1.17557i | −0.0891724 | − | 0.0551116i | ||||
\(456\) | −1.99344 | −0.0933512 | ||||||||
\(457\) | − | 8.26452i | − | 0.386598i | −0.981140 | − | 0.193299i | \(-0.938081\pi\) | ||
0.981140 | − | 0.193299i | \(-0.0619187\pi\) | |||||||
\(458\) | 13.8022i | 0.644937i | ||||||||
\(459\) | −3.24669 | −0.151542 | ||||||||
\(460\) | 1.02562 | − | 1.65948i | 0.0478196 | − | 0.0773737i | ||||
\(461\) | 0.874815 | 0.0407442 | 0.0203721 | − | 0.999792i | \(-0.493515\pi\) | ||||
0.0203721 | + | 0.999792i | \(0.493515\pi\) | |||||||
\(462\) | 7.77340i | 0.361651i | ||||||||
\(463\) | 20.4850i | 0.952020i | 0.879440 | + | 0.476010i | \(0.157917\pi\) | ||||
−0.879440 | + | 0.476010i | \(0.842083\pi\) | |||||||
\(464\) | 2.23119 | 0.103580 | ||||||||
\(465\) | −0.400305 | + | 0.647706i | −0.0185637 | + | 0.0300367i | ||||
\(466\) | −34.2168 | −1.58506 | ||||||||
\(467\) | − | 12.7298i | − | 0.589063i | −0.955642 | − | 0.294532i | \(-0.904836\pi\) | ||
0.955642 | − | 0.294532i | \(-0.0951636\pi\) | |||||||
\(468\) | − | 0.618034i | − | 0.0285686i | ||||||
\(469\) | −8.24367 | −0.380657 | ||||||||
\(470\) | 13.8789 | + | 8.57763i | 0.640186 | + | 0.395656i | ||||
\(471\) | 2.55703 | 0.117822 | ||||||||
\(472\) | 19.9958i | 0.920383i | ||||||||
\(473\) | − | 57.1149i | − | 2.62615i | ||||||
\(474\) | −14.6774 | −0.674154 | ||||||||
\(475\) | 1.99344 | + | 3.98687i | 0.0914651 | + | 0.182930i | ||||
\(476\) | 2.00656 | 0.0919707 | ||||||||
\(477\) | − | 0.405074i | − | 0.0185471i | ||||||
\(478\) | 29.4223i | 1.34575i | ||||||||
\(479\) | −24.9962 | −1.14210 | −0.571052 | − | 0.820914i | \(-0.693464\pi\) | ||||
−0.571052 | + | 0.820914i | \(0.693464\pi\) | |||||||
\(480\) | −6.43288 | − | 3.97574i | −0.293620 | − | 0.181467i | ||||
\(481\) | −1.71592 | −0.0782393 | ||||||||
\(482\) | 18.9345i | 0.862443i | ||||||||
\(483\) | − | 1.41164i | − | 0.0642318i | ||||||
\(484\) | −7.46621 | −0.339373 | ||||||||
\(485\) | −12.3309 | + | 19.9519i | −0.559919 | + | 0.905968i | ||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | 27.6813i | 1.25436i | 0.778874 | + | 0.627180i | \(0.215791\pi\) | ||||
−0.778874 | + | 0.627180i | \(0.784209\pi\) | |||||||
\(488\) | 23.0622i | 1.04398i | ||||||||
\(489\) | −25.2136 | −1.14020 | ||||||||
\(490\) | 1.90211 | − | 3.07768i | 0.0859287 | − | 0.139036i | ||||
\(491\) | 5.75969 | 0.259931 | 0.129966 | − | 0.991518i | \(-0.458513\pi\) | ||||
0.129966 | + | 0.991518i | \(0.458513\pi\) | |||||||
\(492\) | − | 1.90211i | − | 0.0857539i | ||||||
\(493\) | − | 1.49234i | − | 0.0672116i | ||||||
\(494\) | −1.44246 | −0.0648995 | ||||||||
\(495\) | −9.13818 | − | 5.64771i | −0.410731 | − | 0.253846i | ||||
\(496\) | −1.65292 | −0.0742181 | ||||||||
\(497\) | 7.57763i | 0.339903i | ||||||||
\(498\) | − | 6.19764i | − | 0.277723i | ||||||
\(499\) | 35.2238 | 1.57683 | 0.788416 | − | 0.615143i | \(-0.210902\pi\) | ||||
0.788416 | + | 0.615143i | \(0.210902\pi\) | |||||||
\(500\) | −0.620541 | + | 6.88191i | −0.0277515 | + | 0.307768i | ||||
\(501\) | −14.4068 | −0.643646 | ||||||||
\(502\) | − | 10.7467i | − | 0.479651i | ||||||
\(503\) | 23.1576i | 1.03254i | 0.856425 | + | 0.516272i | \(0.172681\pi\) | ||||
−0.856425 | + | 0.516272i | \(0.827319\pi\) | |||||||
\(504\) | −2.23607 | −0.0996024 | ||||||||
\(505\) | −4.68208 | − | 2.89368i | −0.208350 | − | 0.128767i | ||||
\(506\) | 10.9732 | 0.487820 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | 8.28002i | 0.367367i | ||||||||
\(509\) | −7.23722 | −0.320784 | −0.160392 | − | 0.987053i | \(-0.551276\pi\) | ||||
−0.160392 | + | 0.987053i | \(0.551276\pi\) | |||||||
\(510\) | −6.17557 | + | 9.99228i | −0.273459 | + | 0.442466i | ||||
\(511\) | 2.48276 | 0.109831 | ||||||||
\(512\) | 5.29180i | 0.233867i | ||||||||
\(513\) | 0.891491i | 0.0393603i | ||||||||
\(514\) | −26.5937 | −1.17300 | ||||||||
\(515\) | 5.48881 | − | 8.88108i | 0.241866 | − | 0.391347i | ||||
\(516\) | −7.34748 | −0.323455 | ||||||||
\(517\) | 21.6648i | 0.952816i | ||||||||
\(518\) | − | 2.77642i | − | 0.121989i | ||||||
\(519\) | 10.0659 | 0.441844 | ||||||||
\(520\) | 4.25325 | + | 2.62866i | 0.186518 | + | 0.115274i | ||||
\(521\) | −16.2953 | −0.713910 | −0.356955 | − | 0.934122i | \(-0.616185\pi\) | ||||
−0.356955 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(522\) | − | 0.743729i | − | 0.0325521i | ||||||
\(523\) | 22.1147i | 0.967010i | 0.875342 | + | 0.483505i | \(0.160637\pi\) | ||||
−0.875342 | + | 0.483505i | \(0.839363\pi\) | |||||||
\(524\) | 12.7063 | 0.555079 | ||||||||
\(525\) | 2.23607 | + | 4.47214i | 0.0975900 | + | 0.195180i | ||||
\(526\) | 45.1523 | 1.96873 | ||||||||
\(527\) | 1.10556i | 0.0481590i | ||||||||
\(528\) | − | 23.3202i | − | 1.01488i | ||||||
\(529\) | 21.0073 | 0.913360 | ||||||||
\(530\) | −1.24669 | − | 0.770497i | −0.0541527 | − | 0.0334682i | ||||
\(531\) | 8.94241 | 0.388067 | ||||||||
\(532\) | − | 0.550972i | − | 0.0238877i | ||||||
\(533\) | 3.07768i | 0.133309i | ||||||||
\(534\) | 24.7455 | 1.07084 | ||||||||
\(535\) | −7.39374 | + | 11.9633i | −0.319659 | + | 0.517220i | ||||
\(536\) | 18.4334 | 0.796202 | ||||||||
\(537\) | 8.15910i | 0.352091i | ||||||||
\(538\) | 44.2999i | 1.90990i | ||||||||
\(539\) | 4.80423 | 0.206933 | ||||||||
\(540\) | −0.726543 | + | 1.17557i | −0.0312654 | + | 0.0505885i | ||||
\(541\) | −13.0517 | −0.561138 | −0.280569 | − | 0.959834i | \(-0.590523\pi\) | ||||
−0.280569 | + | 0.959834i | \(0.590523\pi\) | |||||||
\(542\) | 5.02562i | 0.215869i | ||||||||
\(543\) | 20.5509i | 0.881922i | ||||||||
\(544\) | −10.9802 | −0.470772 | ||||||||
\(545\) | −7.45714 | − | 4.60877i | −0.319429 | − | 0.197418i | ||||
\(546\) | −1.61803 | −0.0692455 | ||||||||
\(547\) | − | 21.3283i | − | 0.911933i | −0.889997 | − | 0.455966i | \(-0.849294\pi\) | ||
0.889997 | − | 0.455966i | \(-0.150706\pi\) | |||||||
\(548\) | 2.93107i | 0.125209i | ||||||||
\(549\) | 10.3138 | 0.440180 | ||||||||
\(550\) | −34.7637 | + | 17.3819i | −1.48233 | + | 0.741165i | ||||
\(551\) | −0.409774 | −0.0174569 | ||||||||
\(552\) | 3.15652i | 0.134350i | ||||||||
\(553\) | 9.07112i | 0.385743i | ||||||||
\(554\) | 48.8882 | 2.07706 | ||||||||
\(555\) | 3.26388 | + | 2.01719i | 0.138544 | + | 0.0856248i | ||||
\(556\) | 9.21296 | 0.390717 | ||||||||
\(557\) | 18.4676i | 0.782496i | 0.920285 | + | 0.391248i | \(0.127957\pi\) | ||||
−0.920285 | + | 0.391248i | \(0.872043\pi\) | |||||||
\(558\) | 0.550972i | 0.0233245i | ||||||||
\(559\) | 11.8885 | 0.502829 | ||||||||
\(560\) | −5.70634 | + | 9.23305i | −0.241137 | + | 0.390168i | ||||
\(561\) | −15.5978 | −0.658541 | ||||||||
\(562\) | 1.49338i | 0.0629944i | ||||||||
\(563\) | − | 3.69475i | − | 0.155715i | −0.996964 | − | 0.0778575i | \(-0.975192\pi\) | ||
0.996964 | − | 0.0778575i | \(-0.0248079\pi\) | |||||||
\(564\) | 2.78704 | 0.117356 | ||||||||
\(565\) | 2.86652 | − | 4.63812i | 0.120595 | − | 0.195127i | ||||
\(566\) | 27.1753 | 1.14226 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 16.9441i | − | 0.710958i | ||||||
\(569\) | 31.4370 | 1.31791 | 0.658954 | − | 0.752183i | \(-0.270999\pi\) | ||||
0.658954 | + | 0.752183i | \(0.270999\pi\) | |||||||
\(570\) | 2.74373 | + | 1.69572i | 0.114922 | + | 0.0710258i | ||||
\(571\) | 32.3772 | 1.35494 | 0.677471 | − | 0.735549i | \(-0.263076\pi\) | ||||
0.677471 | + | 0.735549i | \(0.263076\pi\) | |||||||
\(572\) | − | 2.96917i | − | 0.124147i | ||||||
\(573\) | − | 14.8310i | − | 0.619574i | ||||||
\(574\) | −4.97980 | −0.207853 | ||||||||
\(575\) | 6.31304 | − | 3.15652i | 0.263272 | − | 0.131636i | ||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | − | 26.6939i | − | 1.11128i | −0.831422 | − | 0.555642i | \(-0.812473\pi\) | ||
0.831422 | − | 0.555642i | \(-0.187527\pi\) | |||||||
\(578\) | − | 10.4509i | − | 0.434700i | ||||||
\(579\) | 4.38447 | 0.182212 | ||||||||
\(580\) | −0.540350 | − | 0.333955i | −0.0224368 | − | 0.0138667i | ||||
\(581\) | −3.83035 | −0.158910 | ||||||||
\(582\) | 16.9721i | 0.703515i | ||||||||
\(583\) | − | 1.94607i | − | 0.0805979i | ||||||
\(584\) | −5.55161 | −0.229727 | ||||||||
\(585\) | 1.17557 | − | 1.90211i | 0.0486039 | − | 0.0786427i | ||||
\(586\) | −8.94879 | −0.369671 | ||||||||
\(587\) | − | 25.0174i | − | 1.03258i | −0.856414 | − | 0.516289i | \(-0.827313\pi\) | ||
0.856414 | − | 0.516289i | \(-0.172687\pi\) | |||||||
\(588\) | − | 0.618034i | − | 0.0254873i | ||||||
\(589\) | 0.303570 | 0.0125084 | ||||||||
\(590\) | 17.0095 | − | 27.5219i | 0.700269 | − | 1.13306i | ||||
\(591\) | −5.40321 | −0.222258 | ||||||||
\(592\) | 8.32926i | 0.342330i | ||||||||
\(593\) | 30.4293i | 1.24958i | 0.780792 | + | 0.624791i | \(0.214816\pi\) | ||||
−0.780792 | + | 0.624791i | \(0.785184\pi\) | |||||||
\(594\) | −7.77340 | −0.318947 | ||||||||
\(595\) | 6.17557 | + | 3.81671i | 0.253174 | + | 0.156470i | ||||
\(596\) | −5.62023 | −0.230213 | ||||||||
\(597\) | − | 11.5692i | − | 0.473496i | ||||||
\(598\) | 2.28408i | 0.0934029i | ||||||||
\(599\) | 45.6159 | 1.86382 | 0.931908 | − | 0.362694i | \(-0.118143\pi\) | ||||
0.931908 | + | 0.362694i | \(0.118143\pi\) | |||||||
\(600\) | −5.00000 | − | 10.0000i | −0.204124 | − | 0.408248i | ||||
\(601\) | 30.8212 | 1.25722 | 0.628611 | − | 0.777720i | \(-0.283624\pi\) | ||||
0.628611 | + | 0.777720i | \(0.283624\pi\) | |||||||
\(602\) | 19.2360i | 0.783999i | ||||||||
\(603\) | − | 8.24367i | − | 0.335708i | ||||||
\(604\) | 8.02601 | 0.326574 | ||||||||
\(605\) | −22.9786 | − | 14.2016i | −0.934215 | − | 0.577376i | ||||
\(606\) | −3.98281 | −0.161791 | ||||||||
\(607\) | − | 45.7895i | − | 1.85854i | −0.369403 | − | 0.929269i | \(-0.620438\pi\) | ||
0.369403 | − | 0.929269i | \(-0.379562\pi\) | |||||||
\(608\) | 3.01499i | 0.122274i | ||||||||
\(609\) | −0.459650 | −0.0186259 | ||||||||
\(610\) | 19.6179 | − | 31.7425i | 0.794306 | − | 1.28521i | ||||
\(611\) | −4.50953 | −0.182436 | ||||||||
\(612\) | 2.00656i | 0.0811106i | ||||||||
\(613\) | − | 42.3482i | − | 1.71043i | −0.518276 | − | 0.855214i | \(-0.673426\pi\) | ||
0.518276 | − | 0.855214i | \(-0.326574\pi\) | |||||||
\(614\) | −50.7993 | −2.05009 | ||||||||
\(615\) | 3.61803 | − | 5.85410i | 0.145893 | − | 0.236060i | ||||
\(616\) | −10.7426 | −0.432831 | ||||||||
\(617\) | 20.2302i | 0.814438i | 0.913331 | + | 0.407219i | \(0.133501\pi\) | ||||
−0.913331 | + | 0.407219i | \(0.866499\pi\) | |||||||
\(618\) | − | 7.55470i | − | 0.303895i | ||||||
\(619\) | 42.9807 | 1.72754 | 0.863771 | − | 0.503885i | \(-0.168097\pi\) | ||||
0.863771 | + | 0.503885i | \(0.168097\pi\) | |||||||
\(620\) | 0.400305 | + | 0.247402i | 0.0160766 | + | 0.00993590i | ||||
\(621\) | 1.41164 | 0.0566471 | ||||||||
\(622\) | − | 4.42309i | − | 0.177350i | ||||||
\(623\) | − | 15.2935i | − | 0.612723i | ||||||
\(624\) | 4.85410 | 0.194320 | ||||||||
\(625\) | −15.0000 | + | 20.0000i | −0.600000 | + | 0.800000i | ||||
\(626\) | 4.73258 | 0.189152 | ||||||||
\(627\) | 4.28293i | 0.171044i | ||||||||
\(628\) | − | 1.58033i | − | 0.0630620i | ||||||
\(629\) | 5.57106 | 0.222133 | ||||||||
\(630\) | 3.07768 | + | 1.90211i | 0.122618 | + | 0.0757820i | ||||
\(631\) | −33.9944 | −1.35329 | −0.676647 | − | 0.736307i | \(-0.736568\pi\) | ||||
−0.676647 | + | 0.736307i | \(0.736568\pi\) | |||||||
\(632\) | − | 20.2836i | − | 0.806840i | ||||||
\(633\) | 10.7653i | 0.427882i | ||||||||
\(634\) | 1.31085 | 0.0520604 | ||||||||
\(635\) | −15.7495 | + | 25.4833i | −0.625001 | + | 1.01127i | ||||
\(636\) | −0.250349 | −0.00992700 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | − | 3.57304i | − | 0.141458i | ||||||
\(639\) | −7.57763 | −0.299766 | ||||||||
\(640\) | 16.0090 | − | 25.9030i | 0.632810 | − | 1.02391i | ||||
\(641\) | −4.61668 | −0.182348 | −0.0911739 | − | 0.995835i | \(-0.529062\pi\) | ||||
−0.0911739 | + | 0.995835i | \(0.529062\pi\) | |||||||
\(642\) | 10.1766i | 0.401639i | ||||||||
\(643\) | 15.0975i | 0.595386i | 0.954662 | + | 0.297693i | \(0.0962171\pi\) | ||||
−0.954662 | + | 0.297693i | \(0.903783\pi\) | |||||||
\(644\) | −0.872441 | −0.0343790 | ||||||||
\(645\) | −22.6132 | − | 13.9757i | −0.890395 | − | 0.550294i | ||||
\(646\) | 4.68323 | 0.184259 | ||||||||
\(647\) | 24.3079i | 0.955642i | 0.878457 | + | 0.477821i | \(0.158573\pi\) | ||||
−0.878457 | + | 0.477821i | \(0.841427\pi\) | |||||||
\(648\) | − | 2.23607i | − | 0.0878410i | ||||||
\(649\) | 42.9613 | 1.68638 | ||||||||
\(650\) | −3.61803 | − | 7.23607i | −0.141911 | − | 0.283822i | ||||
\(651\) | 0.340519 | 0.0133460 | ||||||||
\(652\) | 15.5828i | 0.610271i | ||||||||
\(653\) | − | 36.8251i | − | 1.44108i | −0.693415 | − | 0.720539i | \(-0.743895\pi\) | ||
0.693415 | − | 0.720539i | \(-0.256105\pi\) | |||||||
\(654\) | −6.34342 | −0.248048 | ||||||||
\(655\) | 39.1061 | + | 24.1689i | 1.52800 | + | 0.944357i | ||||
\(656\) | 14.9394 | 0.583285 | ||||||||
\(657\) | 2.48276i | 0.0968616i | ||||||||
\(658\) | − | 7.29657i | − | 0.284450i | ||||||
\(659\) | −26.7208 | −1.04090 | −0.520448 | − | 0.853893i | \(-0.674235\pi\) | ||||
−0.520448 | + | 0.853893i | \(0.674235\pi\) | |||||||
\(660\) | −3.49047 | + | 5.64771i | −0.135867 | + | 0.219837i | ||||
\(661\) | 27.8739 | 1.08417 | 0.542084 | − | 0.840324i | \(-0.317636\pi\) | ||||
0.542084 | + | 0.840324i | \(0.317636\pi\) | |||||||
\(662\) | 8.12703i | 0.315866i | ||||||||
\(663\) | − | 3.24669i | − | 0.126091i | ||||||
\(664\) | 8.56493 | 0.332384 | ||||||||
\(665\) | 1.04801 | − | 1.69572i | 0.0406401 | − | 0.0657571i | ||||
\(666\) | 2.77642 | 0.107584 | ||||||||
\(667\) | 0.648859i | 0.0251239i | ||||||||
\(668\) | 8.90387i | 0.344501i | ||||||||
\(669\) | 9.65948 | 0.373457 | ||||||||
\(670\) | −25.3714 | − | 15.6804i | −0.980183 | − | 0.605787i | ||||
\(671\) | 49.5496 | 1.91284 | ||||||||
\(672\) | 3.38197i | 0.130462i | ||||||||
\(673\) | 2.24554i | 0.0865591i | 0.999063 | + | 0.0432795i | \(0.0137806\pi\) | ||||
−0.999063 | + | 0.0432795i | \(0.986219\pi\) | |||||||
\(674\) | −24.2513 | −0.934124 | ||||||||
\(675\) | −4.47214 | + | 2.23607i | −0.172133 | + | 0.0860663i | ||||
\(676\) | 0.618034 | 0.0237705 | ||||||||
\(677\) | − | 3.64602i | − | 0.140128i | −0.997542 | − | 0.0700640i | \(-0.977680\pi\) | ||
0.997542 | − | 0.0700640i | \(-0.0223204\pi\) | |||||||
\(678\) | − | 3.94542i | − | 0.151523i | ||||||
\(679\) | 10.4893 | 0.402543 | ||||||||
\(680\) | −13.8090 | − | 8.53443i | −0.529551 | − | 0.327280i | ||||
\(681\) | 27.8250 | 1.06626 | ||||||||
\(682\) | 2.64699i | 0.101359i | ||||||||
\(683\) | 16.3180i | 0.624391i | 0.950018 | + | 0.312196i | \(0.101064\pi\) | ||||
−0.950018 | + | 0.312196i | \(0.898936\pi\) | |||||||
\(684\) | 0.550972 | 0.0210669 | ||||||||
\(685\) | −5.57523 | + | 9.02092i | −0.213019 | + | 0.344671i | ||||
\(686\) | −1.61803 | −0.0617768 | ||||||||
\(687\) | 8.53026i | 0.325450i | ||||||||
\(688\) | − | 57.7079i | − | 2.20009i | ||||||
\(689\) | 0.405074 | 0.0154321 | ||||||||
\(690\) | 2.68510 | − | 4.34458i | 0.102220 | − | 0.165395i | ||||
\(691\) | 25.9174 | 0.985946 | 0.492973 | − | 0.870045i | \(-0.335910\pi\) | ||||
0.492973 | + | 0.870045i | \(0.335910\pi\) | |||||||
\(692\) | − | 6.22107i | − | 0.236490i | ||||||
\(693\) | 4.80423i | 0.182497i | ||||||||
\(694\) | −6.28677 | −0.238642 | ||||||||
\(695\) | 28.3546 | + | 17.5241i | 1.07555 | + | 0.664727i | ||||
\(696\) | 1.02781 | 0.0389589 | ||||||||
\(697\) | − | 9.99228i | − | 0.378485i | ||||||
\(698\) | 53.6001i | 2.02879i | ||||||||
\(699\) | −21.1471 | −0.799858 | ||||||||
\(700\) | 2.76393 | − | 1.38197i | 0.104467 | − | 0.0522334i | ||||
\(701\) | 3.27417 | 0.123664 | 0.0618318 | − | 0.998087i | \(-0.480306\pi\) | ||||
0.0618318 | + | 0.998087i | \(0.480306\pi\) | |||||||
\(702\) | − | 1.61803i | − | 0.0610688i | ||||||
\(703\) | − | 1.52973i | − | 0.0576948i | ||||||
\(704\) | 20.3510 | 0.767008 | ||||||||
\(705\) | 8.57763 | + | 5.30127i | 0.323052 | + | 0.199657i | ||||
\(706\) | −9.97876 | −0.375555 | ||||||||
\(707\) | 2.46151i | 0.0925748i | ||||||||
\(708\) | − | 5.52671i | − | 0.207707i | ||||||
\(709\) | 25.4583 | 0.956105 | 0.478052 | − | 0.878331i | \(-0.341343\pi\) | ||||
0.478052 | + | 0.878331i | \(0.341343\pi\) | |||||||
\(710\) | −14.4135 | + | 23.3215i | −0.540929 | + | 0.875242i | ||||
\(711\) | −9.07112 | −0.340194 | ||||||||
\(712\) | 34.1974i | 1.28160i | ||||||||
\(713\) | − | 0.480690i | − | 0.0180020i | ||||||
\(714\) | 5.25325 | 0.196598 | ||||||||
\(715\) | 5.64771 | − | 9.13818i | 0.211212 | − | 0.341749i | ||||
\(716\) | 5.04260 | 0.188451 | ||||||||
\(717\) | 18.1840i | 0.679094i | ||||||||
\(718\) | − | 7.05342i | − | 0.263231i | ||||||
\(719\) | 31.3560 | 1.16938 | 0.584690 | − | 0.811257i | \(-0.301216\pi\) | ||||
0.584690 | + | 0.811257i | \(0.301216\pi\) | |||||||
\(720\) | −9.23305 | − | 5.70634i | −0.344095 | − | 0.212663i | ||||
\(721\) | −4.66906 | −0.173885 | ||||||||
\(722\) | 29.4567i | 1.09626i | ||||||||
\(723\) | 11.7022i | 0.435208i | ||||||||
\(724\) | 12.7011 | 0.472034 | ||||||||
\(725\) | −1.02781 | − | 2.05562i | −0.0381718 | − | 0.0763436i | ||||
\(726\) | −19.5468 | −0.725450 | ||||||||
\(727\) | 31.0101i | 1.15010i | 0.818118 | + | 0.575050i | \(0.195017\pi\) | ||||
−0.818118 | + | 0.575050i | \(0.804983\pi\) | |||||||
\(728\) | − | 2.23607i | − | 0.0828742i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 7.64114 | + | 4.72249i | 0.282811 | + | 0.174787i | ||||
\(731\) | −38.5982 | −1.42761 | ||||||||
\(732\) | − | 6.37425i | − | 0.235599i | ||||||
\(733\) | 2.45901i | 0.0908255i | 0.998968 | + | 0.0454127i | \(0.0144603\pi\) | ||||
−0.998968 | + | 0.0454127i | \(0.985540\pi\) | |||||||
\(734\) | −57.7510 | −2.13163 | ||||||||
\(735\) | 1.17557 | − | 1.90211i | 0.0433616 | − | 0.0701605i | ||||
\(736\) | 4.77411 | 0.175976 | ||||||||
\(737\) | − | 39.6045i | − | 1.45885i | ||||||
\(738\) | − | 4.97980i | − | 0.183309i | ||||||
\(739\) | 8.78416 | 0.323130 | 0.161565 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161565 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(740\) | 1.24669 | − | 2.01719i | 0.0458292 | − | 0.0741532i | ||||
\(741\) | −0.891491 | −0.0327498 | ||||||||
\(742\) | 0.655423i | 0.0240614i | ||||||||
\(743\) | 8.51627i | 0.312432i | 0.987723 | + | 0.156216i | \(0.0499296\pi\) | ||||
−0.987723 | + | 0.156216i | \(0.950070\pi\) | |||||||
\(744\) | −0.761425 | −0.0279152 | ||||||||
\(745\) | −17.2973 | − | 10.6903i | −0.633723 | − | 0.391662i | ||||
\(746\) | −18.8920 | −0.691686 | ||||||||
\(747\) | − | 3.83035i | − | 0.140145i | ||||||
\(748\) | 9.63999i | 0.352473i | ||||||||
\(749\) | 6.28949 | 0.229813 | ||||||||
\(750\) | −1.62460 | + | 18.0171i | −0.0593219 | + | 0.657890i | ||||
\(751\) | 33.0460 | 1.20587 | 0.602933 | − | 0.797791i | \(-0.293998\pi\) | ||||
0.602933 | + | 0.797791i | \(0.293998\pi\) | |||||||
\(752\) | 21.8897i | 0.798235i | ||||||||
\(753\) | − | 6.64185i | − | 0.242043i | ||||||
\(754\) | 0.743729 | 0.0270850 | ||||||||
\(755\) | 24.7015 | + | 15.2664i | 0.898981 | + | 0.555601i | ||||
\(756\) | 0.618034 | 0.0224777 | ||||||||
\(757\) | − | 29.7676i | − | 1.08192i | −0.841048 | − | 0.540961i | \(-0.818061\pi\) | ||
0.841048 | − | 0.540961i | \(-0.181939\pi\) | |||||||
\(758\) | 32.5130i | 1.18092i | ||||||||
\(759\) | 6.78183 | 0.246165 | ||||||||
\(760\) | −2.34342 | + | 3.79174i | −0.0850049 | + | 0.137541i | ||||
\(761\) | 14.2403 | 0.516209 | 0.258104 | − | 0.966117i | \(-0.416902\pi\) | ||||
0.258104 | + | 0.966117i | \(0.416902\pi\) | |||||||
\(762\) | 21.6774i | 0.785289i | ||||||||
\(763\) | 3.92045i | 0.141930i | ||||||||
\(764\) | −9.16606 | −0.331616 | ||||||||
\(765\) | −3.81671 | + | 6.17557i | −0.137994 | + | 0.223278i | ||||
\(766\) | 1.41570 | 0.0511512 | ||||||||
\(767\) | 8.94241i | 0.322892i | ||||||||
\(768\) | − | 13.5623i | − | 0.489388i | ||||||
\(769\) | 38.0129 | 1.37078 | 0.685390 | − | 0.728176i | \(-0.259632\pi\) | ||||
0.685390 | + | 0.728176i | \(0.259632\pi\) | |||||||
\(770\) | 14.7859 | + | 9.13818i | 0.532846 | + | 0.329317i | ||||
\(771\) | −16.4358 | −0.591920 | ||||||||
\(772\) | − | 2.70975i | − | 0.0975262i | ||||||
\(773\) | − | 39.9492i | − | 1.43687i | −0.695593 | − | 0.718436i | \(-0.744858\pi\) | ||
0.695593 | − | 0.718436i | \(-0.255142\pi\) | |||||||
\(774\) | −19.2360 | −0.691422 | ||||||||
\(775\) | 0.761425 | + | 1.52285i | 0.0273512 | + | 0.0547024i | ||||
\(776\) | −23.4548 | −0.841980 | ||||||||
\(777\) | − | 1.71592i | − | 0.0615583i | ||||||
\(778\) | 52.9114i | 1.89696i | ||||||||
\(779\) | −2.74373 | −0.0983043 | ||||||||
\(780\) | −1.17557 | − | 0.726543i | −0.0420922 | − | 0.0260144i | ||||
\(781\) | −36.4046 | −1.30266 | ||||||||
\(782\) | − | 7.41570i | − | 0.265185i | ||||||
\(783\) | − | 0.459650i | − | 0.0164265i | ||||||
\(784\) | 4.85410 | 0.173361 | ||||||||
\(785\) | 3.00597 | − | 4.86375i | 0.107287 | − | 0.173595i | ||||
\(786\) | 33.2656 | 1.18655 | ||||||||
\(787\) | − | 40.2577i | − | 1.43503i | −0.696541 | − | 0.717517i | \(-0.745279\pi\) | ||
0.696541 | − | 0.717517i | \(-0.254721\pi\) | |||||||
\(788\) | 3.33937i | 0.118960i | ||||||||
\(789\) | 27.9057 | 0.993468 | ||||||||
\(790\) | −17.2543 | + | 27.9180i | −0.613880 | + | 0.993279i | ||||
\(791\) | −2.43841 | −0.0866998 | ||||||||
\(792\) | − | 10.7426i | − | 0.381721i | ||||||
\(793\) | 10.3138i | 0.366252i | ||||||||
\(794\) | −60.1806 | −2.13573 | ||||||||
\(795\) | −0.770497 | − | 0.476193i | −0.0273267 | − | 0.0168888i | ||||
\(796\) | −7.15016 | −0.253431 | ||||||||
\(797\) | 15.9645i | 0.565493i | 0.959195 | + | 0.282747i | \(0.0912455\pi\) | ||||
−0.959195 | + | 0.282747i | \(0.908754\pi\) | |||||||
\(798\) | − | 1.44246i | − | 0.0510627i | ||||||
\(799\) | 14.6410 | 0.517962 | ||||||||
\(800\) | −15.1246 | + | 7.56231i | −0.534736 | + | 0.267368i | ||||
\(801\) | 15.2935 | 0.540371 | ||||||||
\(802\) | 5.98084i | 0.211191i | ||||||||
\(803\) | 11.9277i | 0.420920i | ||||||||
\(804\) | −5.09487 | −0.179682 | ||||||||
\(805\) | −2.68510 | − | 1.65948i | −0.0946372 | − | 0.0584890i | ||||
\(806\) | −0.550972 | −0.0194072 | ||||||||
\(807\) | 27.3788i | 0.963781i | ||||||||
\(808\) | − | 5.50411i | − | 0.193634i | ||||||
\(809\) | 31.1877 | 1.09650 | 0.548251 | − | 0.836314i | \(-0.315294\pi\) | ||||
0.548251 | + | 0.836314i | \(0.315294\pi\) | |||||||
\(810\) | −1.90211 | + | 3.07768i | −0.0668334 | + | 0.108139i | ||||
\(811\) | 43.7661 | 1.53684 | 0.768418 | − | 0.639948i | \(-0.221044\pi\) | ||||
0.768418 | + | 0.639948i | \(0.221044\pi\) | |||||||
\(812\) | 0.284079i | 0.00996922i | ||||||||
\(813\) | 3.10600i | 0.108932i | ||||||||
\(814\) | 13.3385 | 0.467516 | ||||||||
\(815\) | −29.6403 | + | 47.9590i | −1.03826 | + | 1.67993i | ||||
\(816\) | −15.7598 | −0.551702 | ||||||||
\(817\) | 10.5985i | 0.370794i | ||||||||
\(818\) | − | 8.91273i | − | 0.311626i | ||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | −3.61803 | − | 2.23607i | −0.126347 | − | 0.0780869i | ||||
\(821\) | −29.9442 | −1.04506 | −0.522529 | − | 0.852621i | \(-0.675011\pi\) | ||||
−0.522529 | + | 0.852621i | \(0.675011\pi\) | |||||||
\(822\) | 7.67365i | 0.267649i | ||||||||
\(823\) | 10.1764i | 0.354728i | 0.984145 | + | 0.177364i | \(0.0567570\pi\) | ||||
−0.984145 | + | 0.177364i | \(0.943243\pi\) | |||||||
\(824\) | 10.4403 | 0.363707 | ||||||||
\(825\) | −21.4852 | + | 10.7426i | −0.748017 | + | 0.374008i | ||||
\(826\) | −14.4691 | −0.503445 | ||||||||
\(827\) | − | 36.8304i | − | 1.28072i | −0.768075 | − | 0.640360i | \(-0.778785\pi\) | ||
0.768075 | − | 0.640360i | \(-0.221215\pi\) | |||||||
\(828\) | − | 0.872441i | − | 0.0303194i | ||||||
\(829\) | −18.6901 | −0.649133 | −0.324567 | − | 0.945863i | \(-0.605218\pi\) | ||||
−0.324567 | + | 0.945863i | \(0.605218\pi\) | |||||||
\(830\) | −11.7886 | − | 7.28576i | −0.409189 | − | 0.252892i | ||||
\(831\) | 30.2146 | 1.04813 | ||||||||
\(832\) | 4.23607i | 0.146859i | ||||||||
\(833\) | − | 3.24669i | − | 0.112491i | ||||||
\(834\) | 24.1198 | 0.835202 | ||||||||
\(835\) | −16.9362 | + | 27.4033i | −0.586100 | + | 0.948330i | ||||
\(836\) | 2.64699 | 0.0915482 | ||||||||
\(837\) | 0.340519i | 0.0117701i | ||||||||
\(838\) | − | 39.6789i | − | 1.37069i | ||||||
\(839\) | −42.0400 | −1.45138 | −0.725692 | − | 0.688020i | \(-0.758480\pi\) | ||||
−0.725692 | + | 0.688020i | \(0.758480\pi\) | |||||||
\(840\) | −2.62866 | + | 4.25325i | −0.0906972 | + | 0.146751i | ||||
\(841\) | −28.7887 | −0.992715 | ||||||||
\(842\) | 11.1892i | 0.385606i | ||||||||
\(843\) | 0.922959i | 0.0317884i | ||||||||
\(844\) | 6.65331 | 0.229016 | ||||||||
\(845\) | 1.90211 | + | 1.17557i | 0.0654347 | + | 0.0404409i | ||||
\(846\) | 7.29657 | 0.250861 | ||||||||
\(847\) | 12.0806i | 0.415094i | ||||||||
\(848\) | − | 1.96627i | − | 0.0675220i | ||||||
\(849\) | 16.7953 | 0.576413 | ||||||||
\(850\) | 11.7466 | + | 23.4933i | 0.402906 | + | 0.805812i | ||||
\(851\) | −2.42226 | −0.0830340 | ||||||||
\(852\) | 4.68323i | 0.160445i | ||||||||
\(853\) | 33.0029i | 1.13000i | 0.825092 | + | 0.564998i | \(0.191123\pi\) | ||||
−0.825092 | + | 0.564998i | \(0.808877\pi\) | |||||||
\(854\) | −16.6880 | −0.571052 | ||||||||
\(855\) | 1.69572 | + | 1.04801i | 0.0579923 | + | 0.0358412i | ||||
\(856\) | −14.0637 | −0.480688 | ||||||||
\(857\) | − | 6.77951i | − | 0.231583i | −0.993274 | − | 0.115792i | \(-0.963059\pi\) | ||
0.993274 | − | 0.115792i | \(-0.0369405\pi\) | |||||||
\(858\) | − | 7.77340i | − | 0.265380i | ||||||
\(859\) | 47.5032 | 1.62079 | 0.810395 | − | 0.585884i | \(-0.199253\pi\) | ||||
0.810395 | + | 0.585884i | \(0.199253\pi\) | |||||||
\(860\) | −8.63748 | + | 13.9757i | −0.294536 | + | 0.476569i | ||||
\(861\) | −3.07768 | −0.104887 | ||||||||
\(862\) | − | 10.9287i | − | 0.372231i | ||||||
\(863\) | 35.7993i | 1.21862i | 0.792931 | + | 0.609311i | \(0.208554\pi\) | ||||
−0.792931 | + | 0.609311i | \(0.791446\pi\) | |||||||
\(864\) | −3.38197 | −0.115057 | ||||||||
\(865\) | 11.8332 | − | 19.1465i | 0.402340 | − | 0.651000i | ||||
\(866\) | −42.5287 | −1.44518 | ||||||||
\(867\) | − | 6.45901i | − | 0.219359i | ||||||
\(868\) | − | 0.210453i | − | 0.00714323i | ||||||
\(869\) | −43.5797 | −1.47834 | ||||||||
\(870\) | −1.41466 | − | 0.874305i | −0.0479613 | − | 0.0296417i | ||||
\(871\) | 8.24367 | 0.279326 | ||||||||
\(872\) | − | 8.76640i | − | 0.296868i | ||||||
\(873\) | 10.4893i | 0.355010i | ||||||||
\(874\) | −2.03624 | −0.0688767 | ||||||||
\(875\) | 11.1352 | + | 1.00406i | 0.376437 | + | 0.0339433i | ||||
\(876\) | 1.53443 | 0.0518435 | ||||||||
\(877\) | 0.361560i | 0.0122090i | 0.999981 | + | 0.00610451i | \(0.00194314\pi\) | ||||
−0.999981 | + | 0.00610451i | \(0.998057\pi\) | |||||||
\(878\) | − | 35.0899i | − | 1.18423i | ||||||
\(879\) | −5.53066 | −0.186544 | ||||||||
\(880\) | −44.3577 | − | 27.4145i | −1.49530 | − | 0.924144i | ||||
\(881\) | −15.8057 | −0.532506 | −0.266253 | − | 0.963903i | \(-0.585786\pi\) | ||||
−0.266253 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(882\) | − | 1.61803i | − | 0.0544820i | ||||||
\(883\) | − | 16.0987i | − | 0.541765i | −0.962612 | − | 0.270883i | \(-0.912684\pi\) | ||
0.962612 | − | 0.270883i | \(-0.0873156\pi\) | |||||||
\(884\) | −2.00656 | −0.0674881 | ||||||||
\(885\) | 10.5124 | − | 17.0095i | 0.353371 | − | 0.571767i | ||||
\(886\) | 48.6819 | 1.63550 | ||||||||
\(887\) | 23.3425i | 0.783764i | 0.920015 | + | 0.391882i | \(0.128176\pi\) | ||||
−0.920015 | + | 0.391882i | \(0.871824\pi\) | |||||||
\(888\) | 3.83692i | 0.128758i | ||||||||
\(889\) | 13.3974 | 0.449333 | ||||||||
\(890\) | 29.0901 | − | 47.0687i | 0.975101 | − | 1.57775i | ||||
\(891\) | −4.80423 | −0.160948 | ||||||||
\(892\) | − | 5.96989i | − | 0.199887i | ||||||
\(893\) | − | 4.02020i | − | 0.134531i | ||||||
\(894\) | −14.7139 | −0.492108 | ||||||||
\(895\) | 15.5195 | + | 9.59159i | 0.518760 | + | 0.320612i | ||||
\(896\) | −13.6180 | −0.454947 | ||||||||
\(897\) | 1.41164i | 0.0471332i | ||||||||
\(898\) | − | 60.5373i | − | 2.02016i | ||||||
\(899\) | −0.156520 | −0.00522022 | ||||||||
\(900\) | 1.38197 | + | 2.76393i | 0.0460655 | + | 0.0921311i | ||||
\(901\) | −1.31515 | −0.0438140 | ||||||||
\(902\) | − | 23.9241i | − | 0.796584i | ||||||
\(903\) | 11.8885i | 0.395624i | ||||||||
\(904\) | 5.45244 | 0.181346 | ||||||||
\(905\) | 39.0901 | + | 24.1590i | 1.29940 | + | 0.803072i | ||||
\(906\) | 21.0124 | 0.698089 | ||||||||
\(907\) | 43.6032i | 1.44782i | 0.689894 | + | 0.723910i | \(0.257657\pi\) | ||||
−0.689894 | + | 0.723910i | \(0.742343\pi\) | |||||||
\(908\) | − | 17.1968i | − | 0.570696i | ||||||
\(909\) | −2.46151 | −0.0816433 | ||||||||
\(910\) | −1.90211 | + | 3.07768i | −0.0630544 | + | 0.102024i | ||||
\(911\) | −42.3998 | −1.40477 | −0.702385 | − | 0.711798i | \(-0.747881\pi\) | ||||
−0.702385 | + | 0.711798i | \(0.747881\pi\) | |||||||
\(912\) | 4.32739i | 0.143294i | ||||||||
\(913\) | − | 18.4019i | − | 0.609013i | ||||||
\(914\) | −13.3723 | −0.442315 | ||||||||
\(915\) | 12.1245 | − | 19.6179i | 0.400825 | − | 0.648548i | ||||
\(916\) | 5.27199 | 0.174191 | ||||||||
\(917\) | − | 20.5593i | − | 0.678928i | ||||||
\(918\) | 5.25325i | 0.173383i | ||||||||
\(919\) | 6.50432 | 0.214558 | 0.107279 | − | 0.994229i | \(-0.465786\pi\) | ||||
0.107279 | + | 0.994229i | \(0.465786\pi\) | |||||||
\(920\) | 6.00406 | + | 3.71071i | 0.197948 | + | 0.122339i | ||||
\(921\) | −31.3957 | −1.03452 | ||||||||
\(922\) | − | 1.41548i | − | 0.0466164i | ||||||
\(923\) | − | 7.57763i | − | 0.249421i | ||||||
\(924\) | 2.96917 | 0.0976787 | ||||||||
\(925\) | 7.67383 | − | 3.83692i | 0.252314 | − | 0.126157i | ||||
\(926\) | 33.1455 | 1.08923 | ||||||||
\(927\) | − | 4.66906i | − | 0.153352i | ||||||
\(928\) | − | 1.55452i | − | 0.0510296i | ||||||
\(929\) | −44.7854 | −1.46936 | −0.734681 | − | 0.678412i | \(-0.762668\pi\) | ||||
−0.734681 | + | 0.678412i | \(0.762668\pi\) | |||||||
\(930\) | 1.04801 | + | 0.647706i | 0.0343656 | + | 0.0212391i | ||||
\(931\) | −0.891491 | −0.0292175 | ||||||||
\(932\) | 13.0697i | 0.428111i | ||||||||
\(933\) | − | 2.73362i | − | 0.0894946i | ||||||
\(934\) | −20.5972 | −0.673961 | ||||||||
\(935\) | −18.3363 | + | 29.6688i | −0.599663 | + | 0.970275i | ||||
\(936\) | 2.23607 | 0.0730882 | ||||||||
\(937\) | 9.80796i | 0.320412i | 0.987084 | + | 0.160206i | \(0.0512158\pi\) | ||||
−0.987084 | + | 0.160206i | \(0.948784\pi\) | |||||||
\(938\) | 13.3385i | 0.435519i | ||||||||
\(939\) | 2.92489 | 0.0954503 | ||||||||
\(940\) | 3.27636 | − | 5.30127i | 0.106863 | − | 0.172908i | ||||
\(941\) | 6.56164 | 0.213903 | 0.106952 | − | 0.994264i | \(-0.465891\pi\) | ||||
0.106952 | + | 0.994264i | \(0.465891\pi\) | |||||||
\(942\) | − | 4.13736i | − | 0.134802i | ||||||
\(943\) | 4.34458i | 0.141479i | ||||||||
\(944\) | 43.4074 | 1.41279 | ||||||||
\(945\) | 1.90211 | + | 1.17557i | 0.0618757 | + | 0.0382413i | ||||
\(946\) | −92.4139 | −3.00463 | ||||||||
\(947\) | 19.7936i | 0.643206i | 0.946875 | + | 0.321603i | \(0.104222\pi\) | ||||
−0.946875 | + | 0.321603i | \(0.895778\pi\) | |||||||
\(948\) | 5.60626i | 0.182083i | ||||||||
\(949\) | −2.48276 | −0.0805937 | ||||||||
\(950\) | 6.45089 | − | 3.22545i | 0.209295 | − | 0.104647i | ||||
\(951\) | 0.810148 | 0.0262708 | ||||||||
\(952\) | 7.25982i | 0.235292i | ||||||||
\(953\) | − | 15.0734i | − | 0.488275i | −0.969741 | − | 0.244138i | \(-0.921495\pi\) | ||
0.969741 | − | 0.244138i | \(-0.0785049\pi\) | |||||||
\(954\) | −0.655423 | −0.0212201 | ||||||||
\(955\) | −28.2102 | − | 17.4349i | −0.912862 | − | 0.564179i | ||||
\(956\) | 11.2383 | 0.363474 | ||||||||
\(957\) | − | 2.20826i | − | 0.0713829i | ||||||
\(958\) | 40.4446i | 1.30671i | ||||||||
\(959\) | 4.74258 | 0.153146 | ||||||||
\(960\) | 4.97980 | − | 8.05748i | 0.160722 | − | 0.260054i | ||||
\(961\) | −30.8840 | −0.996260 | ||||||||
\(962\) | 2.77642i | 0.0895153i | ||||||||
\(963\) | 6.28949i | 0.202676i | ||||||||
\(964\) | 7.23234 | 0.232938 | ||||||||
\(965\) | 5.15426 | − | 8.33976i | 0.165921 | − | 0.268467i | ||||
\(966\) | −2.28408 | −0.0734890 | ||||||||
\(967\) | 2.83139i | 0.0910514i | 0.998963 | + | 0.0455257i | \(0.0144963\pi\) | ||||
−0.998963 | + | 0.0455257i | \(0.985504\pi\) | |||||||
\(968\) | − | 27.0130i | − | 0.868231i | ||||||
\(969\) | 2.89440 | 0.0929814 | ||||||||
\(970\) | 32.2828 | + | 19.9519i | 1.03654 | + | 0.640616i | ||||
\(971\) | −2.43707 | −0.0782093 | −0.0391047 | − | 0.999235i | \(-0.512451\pi\) | ||||
−0.0391047 | + | 0.999235i | \(0.512451\pi\) | |||||||
\(972\) | 0.618034i | 0.0198234i | ||||||||
\(973\) | − | 14.9069i | − | 0.477893i | ||||||
\(974\) | 44.7893 | 1.43514 | ||||||||
\(975\) | −2.23607 | − | 4.47214i | −0.0716115 | − | 0.143223i | ||||
\(976\) | 50.0640 | 1.60251 | ||||||||
\(977\) | − | 51.3238i | − | 1.64199i | −0.570934 | − | 0.820996i | \(-0.693419\pi\) | ||
0.570934 | − | 0.820996i | \(-0.306581\pi\) | |||||||
\(978\) | 40.7964i | 1.30452i | ||||||||
\(979\) | 73.4737 | 2.34823 | ||||||||
\(980\) | −1.17557 | − | 0.726543i | −0.0375522 | − | 0.0232085i | ||||
\(981\) | −3.92045 | −0.125170 | ||||||||
\(982\) | − | 9.31938i | − | 0.297393i | ||||||
\(983\) | − | 10.8569i | − | 0.346283i | −0.984897 | − | 0.173141i | \(-0.944608\pi\) | ||
0.984897 | − | 0.173141i | \(-0.0553917\pi\) | |||||||
\(984\) | 6.88191 | 0.219387 | ||||||||
\(985\) | −6.35185 | + | 10.2775i | −0.202387 | + | 0.327469i | ||||
\(986\) | −2.41466 | −0.0768983 | ||||||||
\(987\) | − | 4.50953i | − | 0.143540i | ||||||
\(988\) | 0.550972i | 0.0175288i | ||||||||
\(989\) | 16.7822 | 0.533644 | ||||||||
\(990\) | −9.13818 | + | 14.7859i | −0.290430 | + | 0.469926i | ||||
\(991\) | −5.95012 | −0.189012 | −0.0945060 | − | 0.995524i | \(-0.530127\pi\) | ||||
−0.0945060 | + | 0.995524i | \(0.530127\pi\) | |||||||
\(992\) | 1.15163i | 0.0365641i | ||||||||
\(993\) | 5.02278i | 0.159393i | ||||||||
\(994\) | 12.2609 | 0.388891 | ||||||||
\(995\) | −22.0059 | − | 13.6004i | −0.697635 | − | 0.431162i | ||||
\(996\) | −2.36729 | −0.0750104 | ||||||||
\(997\) | 3.66128i | 0.115954i | 0.998318 | + | 0.0579769i | \(0.0184650\pi\) | ||||
−0.998318 | + | 0.0579769i | \(0.981535\pi\) | |||||||
\(998\) | − | 56.9932i | − | 1.80409i | ||||||
\(999\) | 1.71592 | 0.0542893 |
(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 | 1365.2.f.c.274.1 | ✓ | 8 | |
5.2 | odd | 4 | 6825.2.a.bm.1.3 | 4 | |||
5.3 | odd | 4 | 6825.2.a.be.1.1 | 4 | |||
5.4 | even | 2 | inner | 1365.2.f.c.274.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1365.2.f.c.274.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1365.2.f.c.274.7 | yes | 8 | 5.4 | even | 2 | inner | |
6825.2.a.be.1.1 | 4 | 5.3 | odd | 4 | |||
6825.2.a.bm.1.3 | 4 | 5.2 | odd | 4 |