Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), 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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.361 |
Dual form | 1960.2.q.r.961.1 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.68614 | + | 2.92048i | −0.973494 | + | 1.68614i | −0.288675 | + | 0.957427i | \(0.593215\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.18614 | − | 7.25061i | −1.39538 | − | 2.41687i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.313859 | + | 0.543620i | −0.0946322 | + | 0.163908i | −0.909455 | − | 0.415802i | \(-0.863501\pi\) |
0.814823 | + | 0.579710i | \(0.196834\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37228 | 0.380602 | 0.190301 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190301 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.37228 | 0.870719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.68614 | − | 4.65253i | 0.651485 | − | 1.12840i | −0.331278 | − | 0.943533i | \(-0.607480\pi\) |
0.982763 | − | 0.184872i | \(-0.0591869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.37228 | + | 5.84096i | 0.773654 | + | 1.34001i | 0.935548 | + | 0.353200i | \(0.114907\pi\) |
−0.161893 | + | 0.986808i | \(0.551760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.37228 | − | 5.84096i | −0.703169 | − | 1.21792i | −0.967348 | − | 0.253451i | \(-0.918434\pi\) |
0.264179 | − | 0.964474i | \(-0.414899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.1168 | 3.48659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.37228 | 0.254826 | 0.127413 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127413 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.05842 | − | 1.83324i | −0.184248 | − | 0.319126i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.31386 | + | 4.00772i | −0.370514 | + | 0.641749i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.74456 | 0.740976 | 0.370488 | − | 0.928837i | \(-0.379190\pi\) | ||||
0.370488 | + | 0.928837i | \(0.379190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.74456 | 0.418542 | 0.209271 | − | 0.977858i | \(-0.432891\pi\) | ||||
0.209271 | + | 0.977858i | \(0.432891\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.18614 | + | 7.25061i | −0.624033 | + | 1.08086i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.05842 | + | 8.76144i | 0.737847 | + | 1.27799i | 0.953463 | + | 0.301510i | \(0.0974906\pi\) |
−0.215616 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.05842 | + | 15.6896i | 1.26843 | + | 2.19699i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.372281 | − | 0.644810i | 0.0511368 | − | 0.0885715i | −0.839324 | − | 0.543632i | \(-0.817049\pi\) |
0.890461 | + | 0.455060i | \(0.150382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.627719 | 0.0846416 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22.7446 | −3.01259 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.37228 | + | 7.57301i | 0.559813 | + | 0.969625i | 0.997512 | + | 0.0705031i | \(0.0224605\pi\) |
−0.437698 | + | 0.899122i | \(0.644206\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.686141 | − | 1.18843i | −0.0851053 | − | 0.147407i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.7446 | 2.73812 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | + | 5.19615i | −0.351123 | + | 0.608164i | −0.986447 | − | 0.164083i | \(-0.947534\pi\) |
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.68614 | − | 2.92048i | −0.194699 | − | 0.337228i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.05842 | + | 1.83324i | 0.119082 | + | 0.206256i | 0.919404 | − | 0.393314i | \(-0.128672\pi\) |
−0.800322 | + | 0.599570i | \(0.795338\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −17.9891 | + | 31.1581i | −1.99879 | + | 3.46201i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4891 | −1.48062 | −0.740312 | − | 0.672264i | \(-0.765322\pi\) | ||||
−0.740312 | + | 0.672264i | \(0.765322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.37228 | −0.582706 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.31386 | + | 4.00772i | −0.248072 | + | 0.429673i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.62772 | + | 2.81929i | 0.172538 | + | 0.298844i | 0.939306 | − | 0.343079i | \(-0.111470\pi\) |
−0.766769 | + | 0.641924i | \(0.778137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.4891 | − | 23.3639i | −1.39876 | − | 2.42272i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.37228 | − | 5.84096i | 0.345989 | − | 0.599270i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.8614 | −1.91509 | −0.957543 | − | 0.288291i | \(-0.906913\pi\) | ||||
−0.957543 | + | 0.288291i | \(0.906913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.25544 | 0.528191 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.68614 | − | 9.84868i | −0.560272 | − | 0.970420i | −0.997472 | − | 0.0710555i | \(-0.977363\pi\) |
0.437200 | − | 0.899364i | \(-0.355970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.37228 | + | 2.37686i | 0.132663 | + | 0.229780i | 0.924702 | − | 0.380691i | \(-0.124314\pi\) |
−0.792039 | + | 0.610470i | \(0.790980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.68614 | − | 4.65253i | 0.257286 | − | 0.445632i | −0.708228 | − | 0.705984i | \(-0.750505\pi\) |
0.965514 | + | 0.260352i | \(0.0838386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.74456 | −0.640166 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37228 | + | 5.84096i | −0.314467 | + | 0.544673i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.74456 | − | 9.94987i | −0.531085 | − | 0.919866i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.30298 | + | 9.18504i | 0.482090 | + | 0.835004i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00000 | + | 13.8564i | −0.721336 | + | 1.24939i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.62772 | + | 8.01544i | −0.407448 | + | 0.705720i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.37228 | + | 5.84096i | 0.294638 | + | 0.510327i | 0.974901 | − | 0.222641i | \(-0.0714677\pi\) |
−0.680263 | + | 0.732968i | \(0.738134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.05842 | − | 15.6896i | −0.779625 | − | 1.35035i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.62772 | + | 2.81929i | −0.139065 | + | 0.240868i | −0.927143 | − | 0.374707i | \(-0.877743\pi\) |
0.788078 | + | 0.615576i | \(0.211076\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.74456 | −0.572066 | −0.286033 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286033 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34.1168 | −2.87316 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.430703 | + | 0.746000i | −0.0360172 | + | 0.0623837i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.686141 | − | 1.18843i | −0.0569809 | − | 0.0986938i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.74456 | + | 6.48577i | 0.306767 | + | 0.531335i | 0.977653 | − | 0.210225i | \(-0.0674196\pi\) |
−0.670887 | + | 0.741560i | \(0.734086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05842 | − | 1.83324i | 0.0861332 | − | 0.149187i | −0.819740 | − | 0.572735i | \(-0.805882\pi\) |
0.905874 | + | 0.423548i | \(0.139216\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.9783 | −3.63628 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.74456 | − | 6.48577i | 0.298849 | − | 0.517621i | −0.677024 | − | 0.735961i | \(-0.736731\pi\) |
0.975873 | + | 0.218340i | \(0.0700641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.25544 | + | 2.17448i | 0.0995627 | + | 0.172448i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.62772 | + | 4.55134i | 0.205819 | + | 0.356489i | 0.950393 | − | 0.311051i | \(-0.100681\pi\) |
−0.744574 | + | 0.667539i | \(0.767348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.05842 | + | 1.83324i | −0.0823980 | + | 0.142718i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3723 | 0.880014 | 0.440007 | − | 0.897994i | \(-0.354976\pi\) | ||||
0.440007 | + | 0.897994i | \(0.354976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1168 | −0.855142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 28.2337 | − | 48.9022i | 2.15908 | − | 3.73964i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.68614 | + | 4.65253i | 0.204223 | + | 0.353725i | 0.949885 | − | 0.312599i | \(-0.101200\pi\) |
−0.745662 | + | 0.666325i | \(0.767866\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.4891 | + | 23.3639i | 1.01390 | + | 1.75613i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.4891 | + | 19.8997i | −0.858738 | + | 1.48738i | 0.0143962 | + | 0.999896i | \(0.495417\pi\) |
−0.873134 | + | 0.487481i | \(0.837916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2337 | 1.35530 | 0.677650 | − | 0.735385i | \(-0.262999\pi\) | ||||
0.677650 | + | 0.735385i | \(0.262999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.4891 | −2.17990 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | − | 1.73205i | 0.0735215 | − | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.68614 | + | 2.92048i | 0.123303 | + | 0.213567i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4307 | + | 21.5306i | 0.899454 | + | 1.55790i | 0.828193 | + | 0.560443i | \(0.189369\pi\) |
0.0712608 | + | 0.997458i | \(0.477298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.37228 | − | 4.10891i | 0.170761 | − | 0.295766i | −0.767925 | − | 0.640539i | \(-0.778711\pi\) |
0.938686 | + | 0.344773i | \(0.112044\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.62772 | 0.331398 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.2337 | 1.86907 | 0.934536 | − | 0.355867i | \(-0.115815\pi\) | ||||
0.934536 | + | 0.355867i | \(0.115815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.74456 | + | 11.6819i | 0.475725 | + | 0.823979i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.37228 | − | 4.10891i | −0.165687 | − | 0.286979i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −28.2337 | + | 48.9022i | −1.96238 | + | 3.39894i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.23369 | −0.292850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.62772 | −0.593957 | −0.296978 | − | 0.954884i | \(-0.595979\pi\) | ||||
−0.296978 | + | 0.954884i | \(0.595979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.4891 | + | 23.3639i | −0.924260 | + | 1.60086i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.37228 | − | 2.37686i | −0.0935888 | − | 0.162101i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.1168 | − | 17.5229i | −0.683633 | − | 1.18409i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.68614 | − | 6.38458i | 0.247957 | − | 0.429474i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3723 | 0.761544 | 0.380772 | − | 0.924669i | \(-0.375658\pi\) | ||||
0.380772 | + | 0.924669i | \(0.375658\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.37228 | 0.558152 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.43070 | + | 7.67420i | −0.294076 | + | 0.509355i | −0.974770 | − | 0.223214i | \(-0.928345\pi\) |
0.680693 | + | 0.732568i | \(0.261679\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.1168 | + | 19.2549i | 0.734622 | + | 1.27240i | 0.954889 | + | 0.296963i | \(0.0959737\pi\) |
−0.220267 | + | 0.975440i | \(0.570693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.37228 | + | 11.0371i | 0.417462 | + | 0.723065i | 0.995683 | − | 0.0928145i | \(-0.0295863\pi\) |
−0.578221 | + | 0.815880i | \(0.696253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.05842 | − | 8.76144i | 0.329975 | − | 0.571534i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.13859 | −0.463701 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3723 | 1.25309 | 0.626544 | − | 0.779386i | \(-0.284469\pi\) | ||||
0.626544 | + | 0.779386i | \(0.284469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | − | 22.5167i | 0.837404 | − | 1.45043i | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) |
0.892058 | − | 0.451920i | \(-0.149261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −33.4891 | − | 58.0049i | −2.14833 | − | 3.72101i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.62772 | + | 8.01544i | 0.294455 | + | 0.510010i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.7446 | − | 39.3947i | 1.44138 | − | 2.49654i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.74456 | 0.425713 | 0.212857 | − | 0.977083i | \(-0.431723\pi\) | ||||
0.212857 | + | 0.977083i | \(0.431723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.23369 | 0.266170 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.05842 | − | 15.6896i | 0.567260 | − | 0.982524i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.255437 | − | 0.442430i | −0.0159337 | − | 0.0275981i | 0.857949 | − | 0.513736i | \(-0.171739\pi\) |
−0.873882 | + | 0.486137i | \(0.838405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.74456 | − | 9.94987i | −0.355580 | − | 0.615882i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.11684 | − | 10.5947i | 0.377181 | − | 0.653296i | −0.613470 | − | 0.789718i | \(-0.710227\pi\) |
0.990651 | + | 0.136422i | \(0.0435602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.744563 | −0.0457381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9783 | −0.671858 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | + | 5.19615i | −0.182913 | + | 0.316815i | −0.942871 | − | 0.333157i | \(-0.891886\pi\) |
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.74456 | − | 11.6819i | −0.409703 | − | 0.709626i | 0.585153 | − | 0.810923i | \(-0.301034\pi\) |
−0.994856 | + | 0.101296i | \(0.967701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.313859 | − | 0.543620i | −0.0189264 | − | 0.0327815i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4891 | − | 18.1677i | 0.630230 | − | 1.09159i | −0.357274 | − | 0.934000i | \(-0.616294\pi\) |
0.987504 | − | 0.157592i | \(-0.0503729\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 66.9783 | 4.00988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6060 | −1.28890 | −0.644452 | − | 0.764645i | \(-0.722914\pi\) | ||||
−0.644452 | + | 0.764645i | \(0.722914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0584 | + | 22.6179i | −0.776243 | + | 1.34449i | 0.157851 | + | 0.987463i | \(0.449543\pi\) |
−0.934093 | + | 0.357029i | \(0.883790\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.3723 | + | 19.6974i | 0.673636 | + | 1.16677i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.93070 | − | 10.2723i | −0.348865 | − | 0.604252i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.8030 | − | 55.0844i | 1.86432 | − | 3.22910i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.88316 | −0.460539 | −0.230269 | − | 0.973127i | \(-0.573961\pi\) | ||||
−0.230269 | + | 0.973127i | \(0.573961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.68614 | + | 9.84868i | −0.329943 | + | 0.571479i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.62772 | − | 8.01544i | −0.267628 | − | 0.463545i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1168 | − | 17.5229i | −0.581198 | − | 1.00666i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.37228 | − | 7.57301i | 0.250356 | − | 0.433629i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8832 | −0.792354 | −0.396177 | − | 0.918174i | \(-0.629663\pi\) | ||||
−0.396177 | + | 0.918174i | \(0.629663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 38.3505 | 2.18169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.627719 | + | 1.08724i | −0.0355947 | + | 0.0616518i | −0.883274 | − | 0.468857i | \(-0.844666\pi\) |
0.847679 | + | 0.530509i | \(0.177999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0584 | + | 17.4217i | 0.568536 | + | 0.984733i | 0.996711 | + | 0.0810370i | \(0.0258232\pi\) |
−0.428175 | + | 0.903696i | \(0.640843\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.00000 | − | 12.1244i | −0.393159 | − | 0.680972i | 0.599705 | − | 0.800221i | \(-0.295285\pi\) |
−0.992864 | + | 0.119249i | \(0.961951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.430703 | + | 0.746000i | −0.0241148 | + | 0.0417680i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.25544 | −0.516588 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.2337 | 2.01610 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.686141 | + | 1.18843i | −0.0380602 | + | 0.0659223i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.05842 | + | 15.6896i | 0.500932 | + | 0.867639i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | − | 10.3923i | −0.329790 | − | 0.571213i | 0.652680 | − | 0.757634i | \(-0.273645\pi\) |
−0.982470 | + | 0.186421i | \(0.940311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.37228 | − | 14.5012i | 0.458798 | − | 0.794662i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.4891 | 0.843746 | 0.421873 | − | 0.906655i | \(-0.361373\pi\) | ||||
0.421873 | + | 0.906655i | \(0.361373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.37228 | + | 5.84096i | −0.183157 | + | 0.317238i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.51087 | − | 4.34896i | −0.135971 | − | 0.235510i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.3723 | − | 19.6974i | −0.612263 | − | 1.06047i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.62772 | − | 11.4795i | 0.355795 | − | 0.616254i | −0.631459 | − | 0.775409i | \(-0.717544\pi\) |
0.987254 | + | 0.159155i | \(0.0508769\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.48913 | 0.186769 | 0.0933843 | − | 0.995630i | \(-0.470231\pi\) | ||||
0.0933843 | + | 0.995630i | \(0.470231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.8614 | 1.32700 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4307 | − | 23.2627i | 0.714844 | − | 1.23815i | −0.248175 | − | 0.968715i | \(-0.579831\pi\) |
0.963020 | − | 0.269431i | \(-0.0868357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2446 | + | 22.9403i | −0.697082 | + | 1.20738i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −35.7663 | −1.87724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.43070 | + | 7.67420i | −0.231281 | + | 0.400590i | −0.958185 | − | 0.286148i | \(-0.907625\pi\) |
0.726904 | + | 0.686739i | \(0.240958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.8614 | − | 34.4010i | −1.03394 | − | 1.79084i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.62772 | + | 16.6757i | 0.498504 | + | 0.863435i | 0.999999 | − | 0.00172614i | \(-0.000549447\pi\) |
−0.501494 | + | 0.865161i | \(0.667216\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.68614 | + | 2.92048i | −0.0870719 | + | 0.150813i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.88316 | 0.0969875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.4891 | + | 23.3639i | −0.691069 | + | 1.19697i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.74456 | + | 4.75372i | 0.140241 | + | 0.242904i | 0.927587 | − | 0.373607i | \(-0.121879\pi\) |
−0.787347 | + | 0.616511i | \(0.788546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4891 | − | 19.8997i | −0.584025 | − | 1.01156i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.43070 | − | 9.40625i | 0.275348 | − | 0.476916i | −0.694875 | − | 0.719130i | \(-0.744540\pi\) |
0.970223 | + | 0.242214i | \(0.0778737\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.2337 | −1.83242 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.7446 | −1.14731 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.05842 | − | 1.83324i | 0.0532550 | − | 0.0922403i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.6861 | + | 32.3653i | 0.937831 | + | 1.62437i | 0.769507 | + | 0.638638i | \(0.220502\pi\) |
0.168323 | + | 0.985732i | \(0.446165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.802985 | − | 1.39081i | −0.0400991 | − | 0.0694537i | 0.845279 | − | 0.534325i | \(-0.179434\pi\) |
−0.885378 | + | 0.464871i | \(0.846101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.48913 | + | 9.50744i | −0.273433 | + | 0.473600i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.9783 | 1.78777 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.25544 | −0.0622297 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.74456 | + | 9.94987i | −0.284050 | + | 0.491990i | −0.972378 | − | 0.233410i | \(-0.925012\pi\) |
0.688328 | + | 0.725399i | \(0.258345\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.48913 | − | 9.50744i | −0.270759 | − | 0.468968i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.74456 | + | 11.6819i | 0.331078 | + | 0.573443i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.3723 | − | 19.6974i | 0.556903 | − | 0.964584i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.4891 | 1.83146 | 0.915732 | − | 0.401790i | \(-0.131612\pi\) | ||||
0.915732 | + | 0.401790i | \(0.131612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6060 | 1.05301 | 0.526505 | − | 0.850172i | \(-0.323502\pi\) | ||||
0.526505 | + | 0.850172i | \(0.323502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 42.3505 | − | 73.3533i | 2.05915 | − | 3.56656i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.68614 | + | 4.65253i | 0.130297 | + | 0.225681i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.45245 | − | 2.51572i | −0.0701251 | − | 0.121460i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.31386 | + | 10.9359i | −0.304128 | + | 0.526765i | −0.977067 | − | 0.212933i | \(-0.931698\pi\) |
0.672939 | + | 0.739698i | \(0.265032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9783 | 0.815923 | 0.407961 | − | 0.912999i | \(-0.366240\pi\) | ||||
0.407961 | + | 0.912999i | \(0.366240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.62772 | 0.221882 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.7446 | − | 39.3947i | 1.08802 | − | 1.88451i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1168 | + | 24.4511i | 0.673760 | + | 1.16699i | 0.976830 | + | 0.214018i | \(0.0686553\pi\) |
−0.303069 | + | 0.952968i | \(0.598011\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.62772 | + | 4.55134i | 0.124847 | + | 0.216241i | 0.921673 | − | 0.387968i | \(-0.126823\pi\) |
−0.796826 | + | 0.604208i | \(0.793489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.62772 | − | 2.81929i | 0.0771613 | − | 0.133647i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.2554 | −1.19454 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.116844 | −0.00551421 | −0.00275710 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275710 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.48913 | + | 2.57924i | −0.0701202 | + | 0.121452i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.56930 | + | 6.18220i | 0.167700 | + | 0.290465i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.37228 | − | 14.5012i | −0.391639 | − | 0.678338i | 0.601027 | − | 0.799229i | \(-0.294758\pi\) |
−0.992666 | + | 0.120890i | \(0.961425\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 48.6644 | − | 84.2892i | 2.27146 | − | 3.93428i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7446 | 0.593573 | 0.296787 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296787 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4891 | −1.37048 | −0.685238 | − | 0.728319i | \(-0.740302\pi\) | ||||
−0.685238 | + | 0.728319i | \(0.740302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.4891 | + | 23.3639i | −0.625543 | + | 1.08347i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8030 | − | 27.3716i | −0.731275 | − | 1.26661i | −0.956339 | − | 0.292261i | \(-0.905592\pi\) |
0.225064 | − | 0.974344i | \(-0.427741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6277 | + | 21.8719i | 0.581855 | + | 1.00780i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.861407 | + | 1.49200i | −0.0396075 | + | 0.0686022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.74456 | −0.309462 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.23369 | −0.285421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.11684 | + | 10.5947i | −0.279486 | + | 0.484083i | −0.971257 | − | 0.238033i | \(-0.923497\pi\) |
0.691771 | + | 0.722117i | \(0.256831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.37228 | + | 2.37686i | 0.0625706 | + | 0.108376i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.43070 | + | 16.3345i | 0.428226 | + | 0.741709i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.11684 | − | 3.66648i | 0.0959234 | − | 0.166144i | −0.814070 | − | 0.580766i | \(-0.802753\pi\) |
0.909994 | + | 0.414622i | \(0.136086\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.7228 | −0.801453 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8832 | 0.807056 | 0.403528 | − | 0.914967i | \(-0.367784\pi\) | ||||
0.403528 | + | 0.914967i | \(0.367784\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.68614 | − | 6.38458i | 0.166015 | − | 0.287547i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.62772 | − | 4.55134i | −0.118107 | − | 0.204568i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.56930 | − | 2.71810i | −0.0702514 | − | 0.121679i | 0.828760 | − | 0.559604i | \(-0.189047\pi\) |
−0.899011 | + | 0.437925i | \(0.855713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.1753 | + | 33.2125i | −0.856688 | + | 1.48383i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6277 | 0.563042 | 0.281521 | − | 0.959555i | \(-0.409161\pi\) | ||||
0.281521 | + | 0.959555i | \(0.409161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.7446 | − | 32.4665i | 0.832475 | − | 1.44189i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.48913 | + | 4.31129i | 0.110329 | + | 0.191095i | 0.915903 | − | 0.401400i | \(-0.131476\pi\) |
−0.805574 | + | 0.592495i | \(0.798143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 61.0951 | + | 105.820i | 2.69741 | + | 4.67206i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.68614 | + | 9.84868i | −0.250561 | + | 0.433985i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.35053 | −0.279296 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.1168 | −0.795241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0000 | + | 25.9808i | −0.657162 | + | 1.13824i | 0.324185 | + | 0.945994i | \(0.394910\pi\) |
−0.981347 | + | 0.192244i | \(0.938423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2337 | + | 28.1176i | 0.709850 | + | 1.22950i | 0.964913 | + | 0.262571i | \(0.0845704\pi\) |
−0.255063 | + | 0.966924i | \(0.582096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.4891 | + | 37.2203i | 0.936081 | + | 1.62134i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2446 | + | 19.4762i | −0.488894 | + | 0.846789i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −66.9783 | −2.90661 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.51087 | 0.282017 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.37228 | − | 2.37686i | 0.0593289 | − | 0.102761i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −38.7446 | − | 67.1076i | −1.67195 | − | 2.89590i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.1753 | − | 17.6241i | −0.437469 | − | 0.757718i | 0.560025 | − | 0.828476i | \(-0.310792\pi\) |
−0.997494 | + | 0.0707576i | \(0.977458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.7446 | + | 53.2511i | −1.31938 | + | 2.28523i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.37228 | −0.230123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9783 | 0.640424 | 0.320212 | − | 0.947346i | \(-0.396246\pi\) | ||||
0.320212 | + | 0.947346i | \(0.396246\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.6060 | − | 63.4034i | 1.56230 | − | 2.70599i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.62772 | + | 8.01544i | 0.197147 | + | 0.341469i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.37228 | + | 5.84096i | 0.143145 | + | 0.247935i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.1168 | − | 33.1113i | 0.810007 | − | 1.40297i | −0.102852 | − | 0.994697i | \(-0.532797\pi\) |
0.912859 | − | 0.408276i | \(-0.133870\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.76631 | 0.159298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.3723 | −0.480138 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.74456 | + | 4.75372i | −0.115670 | + | 0.200345i | −0.918047 | − | 0.396471i | \(-0.870235\pi\) |
0.802378 | + | 0.596817i | \(0.203568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.00000 | − | 1.73205i | −0.0420703 | − | 0.0728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.4891 | − | 18.1677i | −0.439727 | − | 0.761630i | 0.557941 | − | 0.829880i | \(-0.311591\pi\) |
−0.997668 | + | 0.0682510i | \(0.978258\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | − | 17.3205i | 0.418487 | − | 0.724841i | −0.577301 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916910i | \(0.0292272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −83.8397 | −3.50245 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.74456 | 0.281268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.80298 | − | 15.2472i | 0.366473 | − | 0.634750i | −0.622538 | − | 0.782589i | \(-0.713899\pi\) |
0.989011 | + | 0.147839i | \(0.0472319\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.00000 | + | 13.8564i | 0.332469 | + | 0.575853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.233688 | + | 0.404759i | 0.00967837 | + | 0.0167634i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.74456 | + | 9.94987i | −0.237508 | + | 0.411377i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.9783 | −0.453121 | −0.226560 | − | 0.973997i | \(-0.572748\pi\) | ||||
−0.226560 | + | 0.973997i | \(0.572748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.9565 | −2.22324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.2337 | + | 76.6150i | −1.81953 | + | 3.15152i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.6861 | − | 21.9730i | −0.520957 | − | 0.902325i | −0.999703 | − | 0.0243710i | \(-0.992242\pi\) |
0.478746 | − | 0.877954i | \(-0.341092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.9783 | − | 46.7277i | −1.10415 | − | 1.91244i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.80298 | + | 6.58696i | −0.155386 | + | 0.269136i | −0.933199 | − | 0.359359i | \(-0.882995\pi\) |
0.777814 | + | 0.628495i | \(0.216329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.4891 | −1.61080 | −0.805398 | − | 0.592735i | \(-0.798048\pi\) | ||||
−0.805398 | + | 0.592735i | \(0.798048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.4891 | −1.36378 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.30298 | − | 9.18504i | 0.215597 | − | 0.373425i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.80298 | − | 13.5152i | −0.316713 | − | 0.548564i | 0.663087 | − | 0.748542i | \(-0.269246\pi\) |
−0.979800 | + | 0.199979i | \(0.935913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.94158 | + | 12.0232i | 0.280826 | + | 0.486405i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7446 | − | 27.2704i | 0.635917 | − | 1.10144i | −0.350403 | − | 0.936599i | \(-0.613955\pi\) |
0.986320 | − | 0.164841i | \(-0.0527112\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0000 | 0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.627719 | + | 1.08724i | −0.0252301 | + | 0.0436999i | −0.878365 | − | 0.477991i | \(-0.841365\pi\) |
0.853135 | + | 0.521691i | \(0.174699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −61.0951 | − | 105.820i | −2.45166 | − | 4.24640i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.13859 | − | 12.3644i | 0.285088 | − | 0.493787i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.7446 | 0.428414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.37228 | −0.134248 | −0.0671242 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671242 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.5475 | − | 25.1971i | 0.578213 | − | 1.00149i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | − | 6.92820i | −0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.4891 | − | 58.0049i | −1.32481 | − | 2.29464i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | + | 1.73205i | −0.0394976 | + | 0.0684119i | −0.885098 | − | 0.465404i | \(-0.845909\pi\) |
0.845601 | + | 0.533816i | \(0.179242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6277 | −0.497989 | −0.248994 | − | 0.968505i | \(-0.580100\pi\) | ||||
−0.248994 | + | 0.968505i | \(0.580100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.25544 | 0.364432 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.00000 | + | 13.8564i | −0.314512 | + | 0.544752i | −0.979334 | − | 0.202251i | \(-0.935174\pi\) |
0.664821 | + | 0.747002i | \(0.268508\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.51087 | + | 4.34896i | 0.0985605 | + | 0.170712i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | − | 5.19615i | −0.117399 | − | 0.203341i | 0.801337 | − | 0.598213i | \(-0.204122\pi\) |
−0.918736 | + | 0.394872i | \(0.870789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.37228 | − | 5.84096i | 0.131766 | − | 0.228225i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 50.2337 | 1.95980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.11684 | 0.238278 | 0.119139 | − | 0.992878i | \(-0.461987\pi\) | ||||
0.119139 | + | 0.992878i | \(0.461987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.62772 | − | 2.81929i | 0.0633109 | − | 0.109658i | −0.832633 | − | 0.553826i | \(-0.813167\pi\) |
0.895943 | + | 0.444168i | \(0.146501\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.4307 | + | 21.5306i | 0.482769 | + | 0.836180i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.62772 | − | 8.01544i | −0.179186 | − | 0.310359i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.1753 | + | 33.2125i | −0.741359 | + | 1.28407i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.48913 | −0.211905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7228 | −1.22282 | −0.611412 | − | 0.791312i | \(-0.709398\pi\) | ||||
−0.611412 | + | 0.791312i | \(0.709398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.05842 | + | 15.6896i | −0.348659 | + | 0.603895i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1753 | − | 31.4805i | −0.698532 | − | 1.20989i | −0.968975 | − | 0.247157i | \(-0.920504\pi\) |
0.270443 | − | 0.962736i | \(-0.412830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9416 | − | 25.8796i | −0.572563 | − | 0.991707i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0000 | + | 31.1769i | −0.688751 | + | 1.19295i | 0.283491 | + | 0.958975i | \(0.408507\pi\) |
−0.972242 | + | 0.233977i | \(0.924826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.25544 | 0.124384 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −74.9783 | −2.86060 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.510875 | − | 0.884861i | 0.0194628 | − | 0.0337105i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.74456 | + | 11.6819i | 0.256575 | + | 0.444401i | 0.965322 | − | 0.261061i | \(-0.0840725\pi\) |
−0.708747 | + | 0.705463i | \(0.750739\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.37228 | + | 5.84096i | 0.127918 | + | 0.221560i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.7446 | − | 22.0742i | 0.482735 | − | 0.836121i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −42.9783 | −1.62559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.8614 | 1.16562 | 0.582810 | − | 0.812609i | \(-0.301953\pi\) | ||||
0.582810 | + | 0.812609i | \(0.301953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.74456 | + | 11.6819i | −0.254376 | + | 0.440592i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.0584 | + | 29.5461i | 0.642457 | + | 1.11277i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.8030 | + | 29.1036i | 0.631049 | + | 1.09301i | 0.987338 | + | 0.158633i | \(0.0507088\pi\) |
−0.356288 | + | 0.934376i | \(0.615958\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.86141 | − | 15.3484i | 0.332329 | − | 0.575610i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 53.9565 | 2.02069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.861407 | 0.0322148 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.6644 | + | 56.5764i | −1.21987 | + | 2.11288i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.37228 | + | 12.7692i | 0.274940 | + | 0.476210i | 0.970120 | − | 0.242626i | \(-0.0780088\pi\) |
−0.695180 | + | 0.718836i | \(0.744675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.8397 | + | 75.9325i | 1.63041 | + | 2.82396i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.686141 | + | 1.18843i | −0.0254826 | + | 0.0441372i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 117.935 | 4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.37228 | − | 12.7692i | 0.272674 | − | 0.472285i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4307 | − | 33.6550i | −0.717689 | − | 1.24307i | −0.961913 | − | 0.273356i | \(-0.911866\pi\) |
0.244224 | − | 0.969719i | \(-0.421467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.25544 | + | 2.17448i | 0.0462446 | + | 0.0800980i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.80298 | + | 16.9793i | −0.360609 | + | 0.624592i | −0.988061 | − | 0.154062i | \(-0.950764\pi\) |
0.627453 | + | 0.778655i | \(0.284098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.2119 | −1.14660 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4891 | −1.08185 | −0.540926 | − | 0.841070i | \(-0.681926\pi\) | ||||
−0.540926 | + | 0.841070i | \(0.681926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.74456 | − | 6.48577i | 0.137190 | − | 0.237620i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 56.4674 | + | 97.8044i | 2.06603 | + | 3.57847i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4307 | − | 42.3152i | −0.891489 | − | 1.54410i | −0.838091 | − | 0.545531i | \(-0.816328\pi\) |
−0.0533984 | − | 0.998573i | \(-0.517005\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.3723 | + | 19.6974i | −0.414429 | + | 0.717812i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.11684 | −0.0770398 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.2337 | −1.38963 | −0.694814 | − | 0.719190i | \(-0.744513\pi\) | ||||
−0.694814 | + | 0.719190i | \(0.744513\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.13859 | + | 12.3644i | −0.259115 | + | 0.448800i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.4891 | − | 35.4882i | −0.742730 | − | 1.28645i | −0.951248 | − | 0.308428i | \(-0.900197\pi\) |
0.208518 | − | 0.978019i | \(-0.433136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.4891 | + | 38.9523i | 0.813096 | + | 1.40832i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.48913 | − | 9.50744i | 0.198201 | − | 0.343294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4891 | 0.702796 | 0.351398 | − | 0.936226i | \(-0.385706\pi\) | ||||
0.351398 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.72281 | 0.0620456 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.686141 | + | 1.18843i | −0.0246788 | + | 0.0427449i | −0.878101 | − | 0.478475i | \(-0.841190\pi\) |
0.853422 | + | 0.521220i | \(0.174523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | − | 6.92820i | −0.143684 | − | 0.248868i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | + | 27.7128i | 0.573259 | + | 0.992915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.51087 | + | 4.34896i | −0.0898462 | + | 0.155618i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.8614 | 0.888474 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.48913 | −0.267298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.94158 | + | 12.0232i | −0.247441 | + | 0.428580i | −0.962815 | − | 0.270162i | \(-0.912923\pi\) |
0.715374 | + | 0.698741i | \(0.246256\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.6277 | + | 35.7283i | 0.734366 | + | 1.27196i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | + | 10.3923i | 0.213066 | + | 0.369042i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.25544 | − | 2.17448i | 0.0445258 | − | 0.0771209i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.3723 | −0.757045 | −0.378523 | − | 0.925592i | \(-0.623568\pi\) | ||||
−0.378523 | + | 0.925592i | \(0.623568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.3505 | 1.92278 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.6277 | − | 23.6039i | 0.481512 | − | 0.834003i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.88316 | − | 3.26172i | −0.0664551 | − | 0.115104i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.1168 | − | 17.5229i | −0.356130 | − | 0.616835i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.31386 | + | 12.6680i | −0.257142 | + | 0.445382i | −0.965475 | − | 0.260496i | \(-0.916114\pi\) |
0.708333 | + | 0.705878i | \(0.249447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.25544 | −0.0440844 | −0.0220422 | − | 0.999757i | \(-0.507017\pi\) | ||||
−0.0220422 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.4891 | 1.59537 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.62772 | − | 4.55134i | 0.0920450 | − | 0.159427i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.25544 | + | 16.0309i | 0.323807 | + | 0.560850i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.94158 | + | 6.82701i | 0.137562 | + | 0.238264i | 0.926573 | − | 0.376114i | \(-0.122740\pi\) |
−0.789011 | + | 0.614379i | \(0.789407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | − | 6.92820i | 0.139431 | − | 0.241502i | −0.787850 | − | 0.615867i | \(-0.788806\pi\) |
0.927281 | + | 0.374365i | \(0.122139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.11684 | 0.0736990 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.2554 | 0.460937 | 0.230468 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230468 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1168 | − | 19.2549i | 0.386104 | − | 0.668752i | −0.605818 | − | 0.795603i | \(-0.707154\pi\) |
0.991922 | + | 0.126852i | \(0.0404873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.3723 | + | 61.2666i | 1.22705 | + | 2.12531i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.68614 | − | 9.84868i | −0.196777 | − | 0.340828i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −72.4674 | + | 125.517i | −2.50484 | + | 4.33851i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.7446 | 0.785230 | 0.392615 | − | 0.919703i | \(-0.371571\pi\) | ||||
0.392615 | + | 0.919703i | \(0.371571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.4307 | − | 63.0998i | 1.25474 | − | 2.17327i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.55842 | + | 9.62747i | 0.191216 | + | 0.331195i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.0367 | − | 76.2738i | −1.51133 | − | 2.61771i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.74456 | − | 11.6819i | 0.231201 | − | 0.400451i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5109 | 0.565322 | 0.282661 | − | 0.959220i | \(-0.408783\pi\) | ||||
0.282661 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −56.4674 | −1.93114 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.2337 | − | 21.1894i | −0.417408 | − | 0.722972i | 0.578270 | − | 0.815846i | \(-0.303728\pi\) |
−0.995678 | + | 0.0928736i | \(0.970395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.25544 | − | 2.17448i | −0.0427356 | − | 0.0740202i | 0.843866 | − | 0.536553i | \(-0.180274\pi\) |
−0.886602 | + | 0.462533i | \(0.846941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.68614 | − | 4.65253i | 0.0913315 | − | 0.158191i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.0000 | 1.35847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.32878 | −0.0450759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.74456 | − | 4.75372i | 0.0929960 | − | 0.161074i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 78.9565 | + | 136.757i | 2.67227 | + | 4.62851i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4891 | + | 45.8805i | 0.894474 | + | 1.54927i | 0.834454 | + | 0.551078i | \(0.185783\pi\) |
0.0600202 | + | 0.998197i | \(0.480883\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.2921 | − | 23.0226i | 0.448332 | − | 0.776533i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.7446 | 1.23796 | 0.618978 | − | 0.785408i | \(-0.287547\pi\) | ||||
0.618978 | + | 0.785408i | \(0.287547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.4891 | −1.12700 | −0.563499 | − | 0.826116i | \(-0.690545\pi\) | ||||
−0.563499 | + | 0.826116i | \(0.690545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.4891 | − | 23.3639i | 0.453432 | − | 0.785367i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.4891 | − | 51.0767i | −0.990148 | − | 1.71499i | −0.616339 | − | 0.787481i | \(-0.711385\pi\) |
−0.373808 | − | 0.927506i | \(-0.621948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.2921 | − | 19.5585i | −0.378300 | − | 0.655235i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.1168 | + | 59.0921i | −1.14168 | + | 1.97744i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.9783 | 0.768078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.2119 | 1.04214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.48913 | + | 9.50744i | −0.183073 | + | 0.317091i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | − | 3.46410i | −0.0666297 | − | 0.115406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.11684 | − | 15.7908i | −0.303054 | − | 0.524905i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.8614 | − | 39.5971i | 0.759101 | − | 1.31480i | −0.184209 | − | 0.982887i | \(-0.558972\pi\) |
0.943310 | − | 0.331914i | \(-0.107694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.2337 | 1.66615 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.9565 | 1.52261 | 0.761303 | − | 0.648396i | \(-0.224560\pi\) | ||||
0.761303 | + | 0.648396i | \(0.224560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.23369 | − | 7.33296i | 0.140115 | − | 0.242686i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.7446 | + | 25.5383i | 0.487440 | + | 0.844271i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.68614 | − | 16.7769i | −0.319516 | − | 0.553418i | 0.660871 | − | 0.750500i | \(-0.270187\pi\) |
−0.980387 | + | 0.197081i | \(0.936854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.4090 | − | 40.5455i | 0.771351 | − | 1.33602i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9783 | 0.361354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −47.6060 | + | 82.4560i | −1.56359 | + | 2.70821i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.1168 | − | 36.5754i | −0.692821 | − | 1.20000i | −0.970910 | − | 0.239446i | \(-0.923034\pi\) |
0.278089 | − | 0.960555i | \(-0.410299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.11684 | − | 3.66648i | −0.0693024 | − | 0.120035i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.68614 | − | 2.92048i | 0.0551427 | − | 0.0955100i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0951 | 1.14651 | 0.573253 | − | 0.819378i | \(-0.305681\pi\) | ||||
0.573253 | + | 0.819378i | \(0.305681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.8397 | −2.21386 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.11684 | + | 1.93443i | −0.0364081 | + | 0.0630606i | −0.883655 | − | 0.468138i | \(-0.844925\pi\) |
0.847247 | + | 0.531199i | \(0.178258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | − | 27.7128i | −0.521032 | − | 0.902453i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.0000 | + | 24.2487i | 0.454939 | + | 0.787977i | 0.998685 | − | 0.0512727i | \(-0.0163278\pi\) |
−0.543746 | + | 0.839250i | \(0.682994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.11684 | + | 7.13058i | −0.133638 | + | 0.231469i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.2119 | 1.53095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.7446 | 1.57899 | 0.789496 | − | 0.613756i | \(-0.210342\pi\) | ||||
0.789496 | + | 0.613756i | \(0.210342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4307 | − | 21.5306i | 0.402248 | − | 0.696714i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.45245 | − | 2.51572i | −0.0469511 | − | 0.0813217i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.4891 | − | 19.8997i | 0.370232 | − | 0.641260i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.74456 | −0.152733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2337 | 1.16520 | 0.582598 | − | 0.812760i | \(-0.302036\pi\) | ||||
0.582598 | + | 0.812760i | \(0.302036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −61.0951 | + | 105.820i | −1.96266 | + | 3.39942i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.25544 | + | 9.10268i | 0.168655 | + | 0.292119i | 0.937947 | − | 0.346778i | \(-0.112724\pi\) |
−0.769292 | + | 0.638897i | \(0.779391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.31386 | − | 4.00772i | −0.0741028 | − | 0.128350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.51087 | + | 6.08101i | −0.112323 | + | 0.194549i | −0.916706 | − | 0.399561i | \(-0.869162\pi\) |
0.804384 | + | 0.594110i | \(0.202496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.04350 | −0.0653105 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.9783 | −1.43605 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.31386 | + | 4.00772i | −0.0738007 | + | 0.127826i | −0.900564 | − | 0.434723i | \(-0.856846\pi\) |
0.826763 | + | 0.562550i | \(0.190180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1168 | − | 22.7190i | −0.417937 | − | 0.723889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.25544 | − | 16.0309i | −0.294306 | − | 0.509753i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.9783 | + | 46.7277i | −0.856992 | + | 1.48435i | 0.0177919 | + | 0.999842i | \(0.494336\pi\) |
−0.874784 | + | 0.484513i | \(0.838997\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.4674 | 1.28419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0584 | + | 20.8858i | −0.381894 | + | 0.661460i | −0.991333 | − | 0.131373i | \(-0.958061\pi\) |
0.609439 | + | 0.792833i | \(0.291395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.1168 | + | 31.3793i | 0.573192 | + | 0.992797i |
(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 | 1960.2.q.r.361.1 | 4 | ||
7.2 | even | 3 | inner | 1960.2.q.r.961.1 | 4 | ||
7.3 | odd | 6 | 280.2.a.c.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 1960.2.a.s.1.2 | 2 | |||
7.5 | odd | 6 | 1960.2.q.t.961.2 | 4 | |||
7.6 | odd | 2 | 1960.2.q.t.361.2 | 4 | |||
21.17 | even | 6 | 2520.2.a.x.1.2 | 2 | |||
28.3 | even | 6 | 560.2.a.h.1.2 | 2 | |||
28.11 | odd | 6 | 3920.2.a.bt.1.1 | 2 | |||
35.3 | even | 12 | 1400.2.g.i.449.1 | 4 | |||
35.4 | even | 6 | 9800.2.a.bu.1.1 | 2 | |||
35.17 | even | 12 | 1400.2.g.i.449.4 | 4 | |||
35.24 | odd | 6 | 1400.2.a.r.1.2 | 2 | |||
56.3 | even | 6 | 2240.2.a.bg.1.1 | 2 | |||
56.45 | odd | 6 | 2240.2.a.bk.1.2 | 2 | |||
84.59 | odd | 6 | 5040.2.a.by.1.1 | 2 | |||
140.3 | odd | 12 | 2800.2.g.r.449.4 | 4 | |||
140.59 | even | 6 | 2800.2.a.bk.1.1 | 2 | |||
140.87 | odd | 12 | 2800.2.g.r.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.c.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
560.2.a.h.1.2 | 2 | 28.3 | even | 6 | |||
1400.2.a.r.1.2 | 2 | 35.24 | odd | 6 | |||
1400.2.g.i.449.1 | 4 | 35.3 | even | 12 | |||
1400.2.g.i.449.4 | 4 | 35.17 | even | 12 | |||
1960.2.a.s.1.2 | 2 | 7.4 | even | 3 | |||
1960.2.q.r.361.1 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.q.r.961.1 | 4 | 7.2 | even | 3 | inner | ||
1960.2.q.t.361.2 | 4 | 7.6 | odd | 2 | |||
1960.2.q.t.961.2 | 4 | 7.5 | odd | 6 | |||
2240.2.a.bg.1.1 | 2 | 56.3 | even | 6 | |||
2240.2.a.bk.1.2 | 2 | 56.45 | odd | 6 | |||
2520.2.a.x.1.2 | 2 | 21.17 | even | 6 | |||
2800.2.a.bk.1.1 | 2 | 140.59 | even | 6 | |||
2800.2.g.r.449.1 | 4 | 140.87 | odd | 12 | |||
2800.2.g.r.449.4 | 4 | 140.3 | odd | 12 | |||
3920.2.a.bt.1.1 | 2 | 28.11 | odd | 6 | |||
5040.2.a.by.1.1 | 2 | 84.59 | odd | 6 | |||
9800.2.a.bu.1.1 | 2 | 35.4 | even | 6 |