Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.3 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.b.1609.15 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.71974 | − | 1.42915i | −0.769093 | − | 0.639137i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.37984i | − | 0.521530i | −0.965402 | − | 0.260765i | \(-0.916025\pi\) | ||
0.965402 | − | 0.260765i | \(-0.0839748\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.21525 | 0.969434 | 0.484717 | − | 0.874671i | \(-0.338923\pi\) | ||||
0.484717 | + | 0.874671i | \(0.338923\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24439i | 0.345131i | 0.984998 | + | 0.172565i | \(0.0552056\pi\) | ||||
−0.984998 | + | 0.172565i | \(0.944794\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.42915 | + | 1.71974i | −0.369006 | + | 0.444036i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00989i | 1.21508i | 0.794291 | + | 0.607538i | \(0.207843\pi\) | ||||
−0.794291 | + | 0.607538i | \(0.792157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.139104 | −0.0319127 | −0.0159564 | − | 0.999873i | \(-0.505079\pi\) | ||||
−0.0159564 | + | 0.999873i | \(0.505079\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.37984 | −0.301105 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.01041i | − | 0.210685i | −0.994436 | − | 0.105342i | \(-0.966406\pi\) | ||
0.994436 | − | 0.105342i | \(-0.0335938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.915034 | + | 4.91556i | 0.183007 | + | 0.983112i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.55341 | 1.58833 | 0.794164 | − | 0.607703i | \(-0.207909\pi\) | ||||
0.794164 | + | 0.607703i | \(0.207909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.37797 | 0.247490 | 0.123745 | − | 0.992314i | \(-0.460509\pi\) | ||||
0.123745 | + | 0.992314i | \(0.460509\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.21525i | − | 0.559703i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.97200 | + | 2.37297i | −0.333329 | + | 0.401105i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.04284i | − | 0.829038i | −0.910041 | − | 0.414519i | \(-0.863950\pi\) | ||
0.910041 | − | 0.414519i | \(-0.136050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.24439 | 0.199261 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.647462 | −0.101117 | −0.0505583 | − | 0.998721i | \(-0.516100\pi\) | ||||
−0.0505583 | + | 0.998721i | \(0.516100\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.78726i | 1.49254i | 0.665642 | + | 0.746272i | \(0.268158\pi\) | ||||
−0.665642 | + | 0.746272i | \(0.731842\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.71974 | + | 1.42915i | 0.256364 | + | 0.213046i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.18464i | 0.464528i | 0.972653 | + | 0.232264i | \(0.0746134\pi\) | ||||
−0.972653 | + | 0.232264i | \(0.925387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.09605 | 0.728007 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.00989 | 0.701524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.68009i | 0.368138i | 0.982913 | + | 0.184069i | \(0.0589271\pi\) | ||||
−0.982913 | + | 0.184069i | \(0.941073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.52940 | − | 4.59509i | −0.745584 | − | 0.619601i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.139104i | 0.0184248i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.87278 | 1.28533 | 0.642664 | − | 0.766149i | \(-0.277829\pi\) | ||||
0.642664 | + | 0.766149i | \(0.277829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9260 | 1.65501 | 0.827503 | − | 0.561462i | \(-0.189761\pi\) | ||||
0.827503 | + | 0.561462i | \(0.189761\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.37984i | 0.173843i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.77842 | − | 2.14003i | 0.220586 | − | 0.265438i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.01041 | −0.121639 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.7434 | −1.86840 | −0.934201 | − | 0.356747i | \(-0.883886\pi\) | ||||
−0.934201 | + | 0.356747i | \(0.883886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0722i | 1.88111i | 0.339640 | + | 0.940556i | \(0.389695\pi\) | ||||
−0.339640 | + | 0.940556i | \(0.610305\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.91556 | − | 0.915034i | 0.567600 | − | 0.105659i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.43652i | − | 0.505589i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.22583 | 0.137917 | 0.0689585 | − | 0.997620i | \(-0.478032\pi\) | ||||
0.0689585 | + | 0.997620i | \(0.478032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.38678i | − | 0.371747i | −0.982574 | − | 0.185874i | \(-0.940488\pi\) | ||
0.982574 | − | 0.185874i | \(-0.0595115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.15990 | − | 8.61572i | 0.776600 | − | 0.934506i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.55341i | − | 0.917022i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.10216 | 0.222829 | 0.111414 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111414 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.71705 | 0.179996 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.37797i | − | 0.142889i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.239224 | + | 0.198802i | 0.0245439 | + | 0.0203966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.14957i | 0.827464i | 0.910399 | + | 0.413732i | \(0.135775\pi\) | ||||
−0.910399 | + | 0.413732i | \(0.864225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.21525 | −0.323145 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.04519 | −0.502015 | −0.251008 | − | 0.967985i | \(-0.580762\pi\) | ||||
−0.251008 | + | 0.967985i | \(0.580762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.5579i | − | 1.63150i | −0.578406 | − | 0.815749i | \(-0.696325\pi\) | ||
0.578406 | − | 0.815749i | \(-0.303675\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.37297 | + | 1.97200i | 0.231578 | + | 0.192448i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.9770i | − | 1.06118i | −0.847627 | − | 0.530592i | \(-0.821970\pi\) | ||
0.847627 | − | 0.530592i | \(-0.178030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.71636 | 0.451745 | 0.225873 | − | 0.974157i | \(-0.427477\pi\) | ||||
0.225873 | + | 0.974157i | \(0.427477\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.04284 | −0.478646 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.35021i | − | 0.879594i | −0.898097 | − | 0.439797i | \(-0.855050\pi\) | ||
0.898097 | − | 0.439797i | \(-0.144950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.44403 | + | 1.73764i | −0.134656 | + | 0.162036i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.24439i | − | 0.115044i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.91283 | 0.633698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.662180 | −0.0601982 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.647462i | 0.0583796i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.45147 | − | 9.76122i | 0.487594 | − | 0.873070i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.63486i | 0.411277i | 0.978628 | + | 0.205639i | \(0.0659271\pi\) | ||||
−0.978628 | + | 0.205639i | \(0.934073\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.78726 | 0.861720 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.2600 | −1.68275 | −0.841377 | − | 0.540448i | \(-0.818255\pi\) | ||||
−0.841377 | + | 0.540448i | \(0.818255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.191942i | 0.0166435i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.42915 | − | 1.71974i | 0.123002 | − | 0.148012i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 11.3789i | − | 0.972164i | −0.873913 | − | 0.486082i | \(-0.838426\pi\) | ||
0.873913 | − | 0.486082i | \(-0.161574\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.21532 | 0.272720 | 0.136360 | − | 0.990659i | \(-0.456460\pi\) | ||||
0.136360 | + | 0.990659i | \(0.456460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.18464 | 0.268195 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00101i | 0.334582i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.7097 | − | 12.2241i | −1.22157 | − | 1.01516i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.09605i | − | 0.420315i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.57555 | −0.702537 | −0.351268 | − | 0.936275i | \(-0.614250\pi\) | ||||
−0.351268 | + | 0.936275i | \(0.614250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5884 | 1.10581 | 0.552903 | − | 0.833245i | \(-0.313520\pi\) | ||||
0.552903 | + | 0.833245i | \(0.313520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.00989i | − | 0.405025i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.36975 | − | 1.96933i | −0.190343 | − | 0.158180i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.87121i | − | 0.308957i | −0.987996 | − | 0.154478i | \(-0.950630\pi\) | ||
0.987996 | − | 0.154478i | \(-0.0493697\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.68009 | 0.212545 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.39420 | −0.109878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.361794i | 0.0283379i | 0.999900 | + | 0.0141690i | \(0.00451027\pi\) | ||||
−0.999900 | + | 0.0141690i | \(0.995490\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.59509 | + | 5.52940i | −0.357727 | + | 0.430463i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.09311i | 0.0845877i | 0.999105 | + | 0.0422939i | \(0.0134666\pi\) | ||||
−0.999105 | + | 0.0422939i | \(0.986533\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4515 | 0.880885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.139104 | 0.0106376 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 16.2610i | − | 1.23630i | −0.786061 | − | 0.618149i | \(-0.787883\pi\) | ||
0.786061 | − | 0.618149i | \(-0.212117\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.78268 | − | 1.26260i | 0.512722 | − | 0.0954436i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.87278i | − | 0.742084i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1958 | 1.58425 | 0.792126 | − | 0.610358i | \(-0.208974\pi\) | ||||
0.792126 | + | 0.610358i | \(0.208974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.79730 | 0.207922 | 0.103961 | − | 0.994581i | \(-0.466848\pi\) | ||||
0.103961 | + | 0.994581i | \(0.466848\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.9260i | − | 0.955518i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.20700 | + | 8.67240i | −0.529869 | + | 0.637607i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.1080i | 1.17794i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.37984 | 0.100368 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.31561 | 0.674054 | 0.337027 | − | 0.941495i | \(-0.390579\pi\) | ||||
0.337027 | + | 0.941495i | \(0.390579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.5754i | − | 1.33708i | −0.743675 | − | 0.668542i | \(-0.766919\pi\) | ||
0.743675 | − | 0.668542i | \(-0.233081\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.14003 | − | 1.77842i | −0.153250 | − | 0.127355i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.70902i | − | 0.121763i | −0.998145 | − | 0.0608813i | \(-0.980609\pi\) | ||
0.998145 | − | 0.0608813i | \(-0.0193911\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4929 | 1.24004 | 0.620018 | − | 0.784587i | \(-0.287125\pi\) | ||||
0.620018 | + | 0.784587i | \(0.287125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 11.8023i | − | 0.828361i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.11347 | + | 0.925323i | 0.0777680 | + | 0.0646273i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.01041i | 0.0702282i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.447255 | −0.0309373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.86128 | 0.334664 | 0.167332 | − | 0.985901i | \(-0.446485\pi\) | ||||
0.167332 | + | 0.985901i | \(0.446485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.7434i | 1.07872i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.9875 | − | 16.8316i | 0.953940 | − | 1.14790i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.90137i | − | 0.129074i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.0722 | 1.08606 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.23424 | −0.419360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.732877i | 0.0490771i | 0.999699 | + | 0.0245385i | \(0.00781164\pi\) | ||||
−0.999699 | + | 0.0245385i | \(0.992188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.915034 | − | 4.91556i | −0.0610023 | − | 0.327704i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 4.36928i | − | 0.289999i | −0.989432 | − | 0.145000i | \(-0.953682\pi\) | ||
0.989432 | − | 0.145000i | \(-0.0463181\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.5903 | 1.36065 | 0.680323 | − | 0.732912i | \(-0.261840\pi\) | ||||
0.680323 | + | 0.732912i | \(0.261840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.43652 | −0.291902 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.59737i | − | 0.104647i | −0.998630 | − | 0.0523237i | \(-0.983337\pi\) | ||
0.998630 | − | 0.0523237i | \(-0.0166628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.55135 | − | 5.47677i | 0.296897 | − | 0.357265i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.22583i | − | 0.0796264i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.07220 | −0.198724 | −0.0993619 | − | 0.995051i | \(-0.531680\pi\) | ||||
−0.0993619 | + | 0.995051i | \(0.531680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.3067 | 1.75898 | 0.879490 | − | 0.475917i | \(-0.157884\pi\) | ||||
0.879490 | + | 0.475917i | \(0.157884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.76389 | − | 7.28304i | −0.559904 | − | 0.465296i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.173100i | − | 0.0110141i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.38678 | −0.214629 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.06807 | −0.0674161 | −0.0337080 | − | 0.999432i | \(-0.510732\pi\) | ||||
−0.0337080 | + | 0.999432i | \(0.510732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.24871i | − | 0.204245i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.61572 | − | 7.15990i | −0.539537 | − | 0.448370i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.76072i | − | 0.608857i | −0.952535 | − | 0.304429i | \(-0.901535\pi\) | ||
0.952535 | − | 0.304429i | \(-0.0984655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.95831 | −0.432368 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.55341 | −0.529443 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.09365i | − | 0.437413i | −0.975791 | − | 0.218707i | \(-0.929816\pi\) | ||
0.975791 | − | 0.218707i | \(-0.0701838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.83026 | − | 4.60906i | 0.235291 | − | 0.283133i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.10216i | − | 0.128650i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.4888 | −1.49311 | −0.746555 | − | 0.665324i | \(-0.768293\pi\) | ||||
−0.746555 | + | 0.665324i | \(0.768293\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6330 | −0.828148 | −0.414074 | − | 0.910243i | \(-0.635894\pi\) | ||||
−0.414074 | + | 0.910243i | \(0.635894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.71705i | − | 0.103921i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.94206 | + | 15.8047i | 0.177413 | + | 0.953062i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.9812i | 1.56106i | 0.625120 | + | 0.780528i | \(0.285050\pi\) | ||||
−0.625120 | + | 0.780528i | \(0.714950\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.37797 | −0.0824967 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.41129 | −0.203501 | −0.101750 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101750 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1212i | 0.958304i | 0.877732 | + | 0.479152i | \(0.159056\pi\) | ||||
−0.877732 | + | 0.479152i | \(0.840944\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.198802 | − | 0.239224i | 0.0117760 | − | 0.0141704i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.893392i | 0.0527353i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.09896 | −0.476409 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.14957 | 0.477736 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.8616i | 1.91979i | 0.280353 | + | 0.959897i | \(0.409548\pi\) | ||||
−0.280353 | + | 0.959897i | \(0.590452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.9787 | − | 14.1097i | −0.988536 | − | 0.821501i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.21525i | 0.186568i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.25734 | 0.0727137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5048 | 0.778406 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.04519i | 0.289839i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.2294 | − | 18.4733i | −1.27285 | − | 1.05778i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.5637i | − | 1.34485i | −0.740164 | − | 0.672427i | \(-0.765252\pi\) | ||
0.740164 | − | 0.672427i | \(-0.234748\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5579 | −0.941946 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8330 | 1.35145 | 0.675723 | − | 0.737155i | \(-0.263831\pi\) | ||||
0.675723 | + | 0.737155i | \(0.263831\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8108i | 1.11977i | 0.828570 | + | 0.559885i | \(0.189155\pi\) | ||||
−0.828570 | + | 0.559885i | \(0.810845\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.97200 | − | 2.37297i | 0.111110 | − | 0.133702i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7.70559i | − | 0.432789i | −0.976306 | − | 0.216394i | \(-0.930570\pi\) | ||
0.976306 | − | 0.216394i | \(-0.0694297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.5013 | 1.53978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.9770 | −0.612675 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.696897i | − | 0.0387764i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.11686 | + | 1.13866i | −0.339302 | + | 0.0631613i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.71636i | − | 0.260815i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.39429 | 0.242265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.9273 | −0.875444 | −0.437722 | − | 0.899110i | \(-0.644215\pi\) | ||||
−0.437722 | + | 0.899110i | \(0.644215\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.04284i | 0.276346i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.42915 | − | 1.71974i | 0.0780831 | − | 0.0939596i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.3453i | 1.87091i | 0.353451 | + | 0.935453i | \(0.385008\pi\) | ||||
−0.353451 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.35021 | −0.507834 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.43051 | 0.239925 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.6906i | − | 0.901207i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.73764 | + | 1.44403i | 0.0935515 | + | 0.0777439i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.4834i | 0.992242i | 0.868253 | + | 0.496121i | \(0.165243\pi\) | ||||
−0.868253 | + | 0.496121i | \(0.834757\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.4357 | 0.933312 | 0.466656 | − | 0.884439i | \(-0.345459\pi\) | ||||
0.466656 | + | 0.884439i | \(0.345459\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.24439 | −0.0664205 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0673i | 0.961627i | 0.876823 | + | 0.480813i | \(0.159659\pi\) | ||||
−0.876823 | + | 0.480813i | \(0.840341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0747 | + | 22.4998i | 1.43697 | + | 1.19417i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6.91283i | − | 0.365866i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.7760 | 1.04374 | 0.521868 | − | 0.853026i | \(-0.325235\pi\) | ||||
0.521868 | + | 0.853026i | \(0.325235\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9806 | −0.998982 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.662180i | 0.0347554i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.9697 | − | 27.6401i | 1.20229 | − | 1.44675i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.9318i | − | 0.727233i | −0.931549 | − | 0.363616i | \(-0.881542\pi\) | ||
0.931549 | − | 0.363616i | \(-0.118458\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.647462 | 0.0337055 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.69809 | 0.191995 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.3171i | 1.36265i | 0.731983 | + | 0.681323i | \(0.238595\pi\) | ||||
−0.731983 | + | 0.681323i | \(0.761405\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.76122 | − | 5.45147i | −0.504067 | − | 0.281513i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.6438i | 0.548181i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0224 | −1.23395 | −0.616975 | − | 0.786983i | \(-0.711642\pi\) | ||||
−0.616975 | + | 0.786983i | \(0.711642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.63486 | 0.237451 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 29.2552i | − | 1.49487i | −0.664334 | − | 0.747436i | \(-0.731285\pi\) | ||
0.664334 | − | 0.747436i | \(-0.268715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.34048 | + | 7.62968i | −0.323141 | + | 0.388845i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 9.78726i | − | 0.497514i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.43519 | −0.427681 | −0.213841 | − | 0.976869i | \(-0.568597\pi\) | ||||
−0.213841 | + | 0.976869i | \(0.568597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.06203 | 0.255998 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.2600i | 0.971539i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.10812 | − | 1.75191i | −0.106071 | − | 0.0881479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0271i | 0.954943i | 0.878647 | + | 0.477471i | \(0.158447\pi\) | ||||
−0.878647 | + | 0.477471i | \(0.841553\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.191942 | 0.00960910 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.8977 | −1.69277 | −0.846386 | − | 0.532570i | \(-0.821226\pi\) | ||||
−0.846386 | + | 0.532570i | \(0.821226\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.71472i | 0.0854165i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.71974 | − | 1.42915i | −0.0854547 | − | 0.0710153i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.2140i | − | 0.803698i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.06819 | −0.250606 | −0.125303 | − | 0.992119i | \(-0.539990\pi\) | ||||
−0.125303 | + | 0.992119i | \(0.539990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.3789 | −0.561279 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13.6228i | − | 0.670337i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.84023 | + | 5.82439i | −0.237598 | + | 0.285908i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.21532i | − | 0.157455i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.14074 | −0.348848 | −0.174424 | − | 0.984671i | \(-0.555806\pi\) | ||||
−0.174424 | + | 0.984671i | \(0.555806\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6859 | 1.30059 | 0.650295 | − | 0.759681i | \(-0.274645\pi\) | ||||
0.650295 | + | 0.759681i | \(0.274645\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.18464i | − | 0.154843i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.6264 | + | 4.58422i | −1.19456 | + | 0.222367i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 17.8358i | − | 0.863135i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00101 | 0.193171 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.8374 | 1.24454 | 0.622272 | − | 0.782801i | \(-0.286210\pi\) | ||||
0.622272 | + | 0.782801i | \(0.286210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.2078i | − | 0.730838i | −0.930843 | − | 0.365419i | \(-0.880926\pi\) | ||
0.930843 | − | 0.365419i | \(-0.119074\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2241 | + | 14.7097i | −0.586103 | + | 0.705275i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.140552i | 0.00672352i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.5804 | −1.12543 | −0.562715 | − | 0.826651i | \(-0.690243\pi\) | ||||
−0.562715 | + | 0.826651i | \(0.690243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.09605 | −0.242669 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 17.7399i | − | 0.842849i | −0.906864 | − | 0.421424i | \(-0.861530\pi\) | ||
0.906864 | − | 0.421424i | \(-0.138470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.61518 | − | 3.00432i | −0.171376 | − | 0.142418i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.57555i | 0.405610i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2690 | 0.531815 | 0.265907 | − | 0.963999i | \(-0.414328\pi\) | ||||
0.265907 | + | 0.963999i | \(0.414328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.08175 | −0.0980258 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 13.5884i | − | 0.638438i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.95289 | − | 2.45393i | −0.138434 | − | 0.115042i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7.40159i | − | 0.346232i | −0.984901 | − | 0.173116i | \(-0.944617\pi\) | ||
0.984901 | − | 0.173116i | \(-0.0553835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.00989 | −0.233841 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.4254 | −0.671858 | −0.335929 | − | 0.941887i | \(-0.609050\pi\) | ||||
−0.335929 | + | 0.941887i | \(0.609050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.6194i | − | 0.725893i | −0.931810 | − | 0.362947i | \(-0.881771\pi\) | ||
0.931810 | − | 0.362947i | \(-0.118229\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.96933 | + | 2.36975i | −0.0913254 | + | 0.109894i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.9400i | − | 0.783888i | −0.919989 | − | 0.391944i | \(-0.871803\pi\) | ||
0.919989 | − | 0.391944i | \(-0.128197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.37984 | 0.0637150 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.87121 | −0.178376 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.4685i | 1.44692i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.127285 | − | 0.683776i | −0.00584025 | − | 0.0313738i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.68009i | − | 0.122713i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.32582 | −0.151961 | −0.0759803 | − | 0.997109i | \(-0.524209\pi\) | ||||
−0.0759803 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.27525 | 0.286127 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.39420i | 0.0634383i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.6470 | − | 14.0152i | 0.528863 | − | 0.636396i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.4222i | − | 1.06136i | −0.847572 | − | 0.530680i | \(-0.821937\pi\) | ||
0.847572 | − | 0.530680i | \(-0.178063\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.361794 | 0.0163609 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.5478 | 1.51399 | 0.756996 | − | 0.653419i | \(-0.226666\pi\) | ||||
0.756996 | + | 0.653419i | \(0.226666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.8516i | 1.92994i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.52940 | + | 4.59509i | 0.248528 | + | 0.206534i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.7234i | 0.974428i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.9695 | 1.78928 | 0.894640 | − | 0.446787i | \(-0.147432\pi\) | ||||
0.894640 | + | 0.446787i | \(0.147432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.09311 | 0.0488367 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.72475i | 0.389017i | 0.980901 | + | 0.194509i | \(0.0623113\pi\) | ||||
−0.980901 | + | 0.194509i | \(0.937689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.67643 | + | 7.21036i | 0.386096 | + | 0.320857i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.4515i | − | 0.508579i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0080 | 0.842514 | 0.421257 | − | 0.906941i | \(-0.361589\pi\) | ||||
0.421257 | + | 0.906941i | \(0.361589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.1771 | 0.981056 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.139104i | − | 0.00614161i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.6638 | + | 28.4753i | −1.04275 | + | 1.25477i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2394i | 0.450329i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.2610 | −0.713777 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.0434 | −1.27242 | −0.636208 | − | 0.771518i | \(-0.719498\pi\) | ||||
−0.636208 | + | 0.771518i | \(0.719498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.3180i | 1.63180i | 0.578190 | + | 0.815902i | \(0.303759\pi\) | ||||
−0.578190 | + | 0.815902i | \(0.696241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.26260 | − | 6.78268i | −0.0551044 | − | 0.296020i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.90346i | 0.300719i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.9791 | 0.955612 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.87278 | −0.428442 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.805693i | − | 0.0348984i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.6878 | + | 18.8776i | −0.678242 | + | 0.816149i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 21.1958i | − | 0.914668i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.3851 | 0.705754 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.14688 | −0.393255 | −0.196627 | − | 0.980478i | \(-0.562999\pi\) | ||||
−0.196627 | + | 0.980478i | \(0.562999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.79730i | − | 0.120044i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.11093 | − | 6.74041i | −0.347434 | − | 0.288727i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.7131i | − | 0.629088i | −0.949243 | − | 0.314544i | \(-0.898148\pi\) | ||
0.949243 | − | 0.314544i | \(-0.101852\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.9260 | −0.551668 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.18982 | −0.0506879 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.69145i | − | 0.0719278i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.67240 | + | 7.20700i | 0.368123 | + | 0.305920i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.112803i | − | 0.00477962i | −0.999997 | − | 0.00238981i | \(-0.999239\pi\) | ||
0.999997 | − | 0.00238981i | \(-0.000760701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.1791 | −0.515123 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.1080 | 0.680081 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.3205i | 1.78359i | 0.452435 | + | 0.891797i | \(0.350555\pi\) | ||||
−0.452435 | + | 0.891797i | \(0.649445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3629 | + | 16.0800i | −0.562181 | + | 0.676489i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.37984i | − | 0.0579478i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.67609 | 0.154110 | 0.0770548 | − | 0.997027i | \(-0.475448\pi\) | ||||
0.0770548 | + | 0.997027i | \(0.475448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.1635 | −1.13676 | −0.568378 | − | 0.822768i | \(-0.692429\pi\) | ||||
−0.568378 | + | 0.822768i | \(0.692429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.31561i | − | 0.389165i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.96672 | − | 0.924558i | 0.207126 | − | 0.0385567i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3776i | 0.723439i | 0.932287 | + | 0.361719i | \(0.117810\pi\) | ||||
−0.932287 | + | 0.361719i | \(0.882190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.5754 | −0.771966 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.67321 | −0.193877 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.61715i | 0.356886i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.77842 | + | 2.14003i | −0.0735287 | + | 0.0884792i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 16.3397i | − | 0.674413i | −0.941431 | − | 0.337206i | \(-0.890518\pi\) | ||
0.941431 | − | 0.337206i | \(-0.109482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.191681 | −0.00789809 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.70902 | −0.0702997 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0886i | 1.72837i | 0.503171 | + | 0.864187i | \(0.332167\pi\) | ||||
−0.503171 | + | 0.864187i | \(0.667833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.8883 | − | 9.87951i | −0.487373 | − | 0.405020i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 17.4929i | − | 0.715935i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.2137 | 1.84738 | 0.923690 | − | 0.383140i | \(-0.125157\pi\) | ||||
0.923690 | + | 0.383140i | \(0.125157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.2577 | −1.23424 | −0.617120 | − | 0.786869i | \(-0.711700\pi\) | ||||
−0.617120 | + | 0.786869i | \(0.711700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.13878 | + | 0.946357i | 0.0462980 | + | 0.0384749i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.53779i | − | 0.387127i | −0.981088 | − | 0.193563i | \(-0.937995\pi\) | ||
0.981088 | − | 0.193563i | \(-0.0620045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.8023 | −0.478254 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.96293 | −0.160323 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.34523i | 0.337061i | 0.985696 | + | 0.168530i | \(0.0539021\pi\) | ||||
−0.985696 | + | 0.168530i | \(0.946098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.925323 | − | 1.11347i | 0.0373126 | − | 0.0448994i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.24011i | 0.0499250i | 0.999688 | + | 0.0249625i | \(0.00794663\pi\) | ||||
−0.999688 | + | 0.0249625i | \(0.992053\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.78730 | 0.272805 | 0.136402 | − | 0.990654i | \(-0.456446\pi\) | ||||
0.136402 | + | 0.990654i | \(0.456446\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.01041 | 0.0405463 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.90065i | − | 0.116212i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.3254 | + | 8.99581i | −0.933017 | + | 0.359832i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.447255i | 0.0178617i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.2641 | 1.00734 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5565 | 1.53491 | 0.767456 | − | 0.641102i | \(-0.221522\pi\) | ||||
0.767456 | + | 0.641102i | \(0.221522\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 4.86128i | − | 0.193218i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.62393 | − | 7.97077i | 0.262863 | − | 0.316310i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.34145i | 0.251258i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.7434 | 0.622801 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.5577 | −1.72043 | −0.860213 | − | 0.509935i | \(-0.829669\pi\) | ||||
−0.860213 | + | 0.509935i | \(0.829669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.88593i | 0.271554i | 0.990739 | + | 0.135777i | \(0.0433531\pi\) | ||||
−0.990739 | + | 0.135777i | \(0.956647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.8316 | − | 13.9875i | −0.662743 | − | 0.550758i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.4769i | 1.23749i | 0.785593 | + | 0.618743i | \(0.212358\pi\) | ||||
−0.785593 | + | 0.618743i | \(0.787642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.7435 | 1.24604 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.90137 | −0.0745206 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47.5114i | − | 1.85927i | −0.368487 | − | 0.929633i | \(-0.620124\pi\) | ||
0.368487 | − | 0.929633i | \(-0.379876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.1223 | + | 27.5255i | 1.29419 | + | 1.07551i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 16.0722i | − | 0.627037i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.3074 | 0.635246 | 0.317623 | − | 0.948217i | \(-0.397115\pi\) | ||||
0.317623 | + | 0.948217i | \(0.397115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.7121 | −1.58352 | −0.791758 | − | 0.610834i | \(-0.790834\pi\) | ||||
−0.791758 | + | 0.610834i | \(0.790834\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.23424i | 0.242118i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.274314 | − | 0.330090i | 0.0106375 | − | 0.0128004i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.64243i | − | 0.334636i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.732877 | 0.0283347 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.5603 | 1.60442 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 47.3035i | − | 1.82341i | −0.410840 | − | 0.911707i | \(-0.634765\pi\) | ||
0.410840 | − | 0.911707i | \(-0.365235\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.91556 | + | 0.915034i | −0.189200 | + | 0.0352197i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.7091i | 1.56458i | 0.622915 | + | 0.782290i | \(0.285948\pi\) | ||||
−0.622915 | + | 0.782290i | \(0.714052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.2451 | 0.431547 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.36928 | −0.167431 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.5106i | − | 0.670025i | −0.942214 | − | 0.335013i | \(-0.891259\pi\) | ||
0.942214 | − | 0.335013i | \(-0.108741\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.2622 | + | 19.5688i | −0.621346 | + | 0.747684i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 20.5903i | − | 0.785569i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.33507 | −0.127056 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5338 | −0.476809 | −0.238404 | − | 0.971166i | \(-0.576624\pi\) | ||||
−0.238404 | + | 0.971166i | \(0.576624\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.43652i | 0.168530i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.52952 | − | 4.59519i | −0.209747 | − | 0.174305i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.24371i | − | 0.122864i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.59737 | −0.0604182 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.49750 | −0.0943292 | −0.0471646 | − | 0.998887i | \(-0.515019\pi\) | ||||
−0.0471646 | + | 0.998887i | \(0.515019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.701482i | 0.0264569i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.47677 | − | 4.55135i | −0.206267 | − | 0.171414i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.96155i | 0.261816i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.8977 | 0.935052 | 0.467526 | − | 0.883979i | \(-0.345145\pi\) | ||||
0.467526 | + | 0.883979i | \(0.345145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.22583 | −0.0459723 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.39231i | − | 0.0521423i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.71807 | − | 6.88072i | 0.213844 | − | 0.257324i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.07220i | 0.114733i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.4342 | −1.13500 | −0.567502 | − | 0.823372i | \(-0.692090\pi\) | ||||
−0.567502 | + | 0.823372i | \(0.692090\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.8472 | −0.850875 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 27.3067i | − | 1.01555i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.82667 | + | 42.0448i | 0.290675 | + | 1.56150i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.7716i | − | 1.10417i | −0.833789 | − | 0.552083i | \(-0.813833\pi\) | ||
0.833789 | − | 0.552083i | \(-0.186167\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.0331 | −1.81355 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.43162i | − | 0.200621i | −0.994956 | − | 0.100311i | \(-0.968016\pi\) | ||
0.994956 | − | 0.100311i | \(-0.0319837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.28304 | + | 8.76389i | −0.268639 | + | 0.323261i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.21525i | 0.118435i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.2870 | −1.18770 | −0.593848 | − | 0.804577i | \(-0.702392\pi\) | ||||
−0.593848 | + | 0.804577i | \(0.702392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.173100 | −0.00635898 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 36.8619i | − | 1.35233i | −0.736749 | − | 0.676166i | \(-0.763640\pi\) | ||
0.736749 | − | 0.676166i | \(-0.236360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.7478 | + | 12.2558i | 0.540316 | + | 0.449017i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.38678i | 0.123916i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.1464 | −0.553439 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1860 | 0.846070 | 0.423035 | − | 0.906113i | \(-0.360965\pi\) | ||||
0.423035 | + | 0.906113i | \(0.360965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06807i | 0.0389227i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.3685 | − | 19.4199i | −0.850468 | − | 0.706762i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.4866i | 0.599217i | 0.954062 | + | 0.299608i | \(0.0968560\pi\) | ||||
−0.954062 | + | 0.299608i | \(0.903144\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.24871 | −0.117921 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.23550 | −0.226037 | −0.113018 | − | 0.993593i | \(-0.536052\pi\) | ||||
−0.113018 | + | 0.993593i | \(0.536052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 6.50781i | − | 0.235599i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.15990 | + | 8.61572i | −0.258867 | + | 0.311502i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2856i | 0.443606i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.7662 | 1.07340 | 0.536699 | − | 0.843774i | \(-0.319671\pi\) | ||||
0.536699 | + | 0.843774i | \(0.319671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.76072 | −0.351524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.47745i | − | 0.340880i | −0.985368 | − | 0.170440i | \(-0.945481\pi\) | ||
0.985368 | − | 0.170440i | \(-0.0545189\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.26089 | + | 6.77348i | 0.0452924 | + | 0.243310i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.95831i | 0.249628i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0900648 | 0.00322691 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.6191 | −1.81129 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.55341i | 0.305674i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.53256 | + | 6.65750i | −0.197466 | + | 0.237616i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5181i | 0.517514i | 0.965942 | + | 0.258757i | \(0.0833130\pi\) | ||||
−0.965942 | + | 0.258757i | \(0.916687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.09365 | −0.252541 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9018 | −0.458734 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0850i | 0.571194i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.60906 | − | 3.83026i | −0.163467 | − | 0.135845i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.78303i | 0.240267i | 0.992758 | + | 0.120134i | \(0.0383323\pi\) | ||||
−0.992758 | + | 0.120134i | \(0.961668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.9547 | −0.564437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.10216 | −0.0742763 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.6762i | 1.82361i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.39766 | + | 1.99253i | 0.0845066 | + | 0.0702273i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.4888i | 0.862047i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.2675 | −1.48605 | −0.743024 | − | 0.669265i | \(-0.766609\pi\) | ||||
−0.743024 | + | 0.669265i | \(0.766609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.30209 | 0.151067 | 0.0755335 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755335 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6330i | 0.478131i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.517060 | − | 0.622193i | 0.0181118 | − | 0.0217945i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.36145i | − | 0.0476311i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.71705 | −0.0599987 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.4813 | −1.30811 | −0.654053 | − | 0.756449i | \(-0.726933\pi\) | ||||
−0.654053 | + | 0.756449i | \(0.726933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.0654i | 1.08287i | 0.840742 | + | 0.541435i | \(0.182119\pi\) | ||||
−0.840742 | + | 0.541435i | \(0.817881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.8047 | − | 2.94206i | 0.550250 | − | 0.102429i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.35419i | − | 0.220957i | −0.993879 | − | 0.110478i | \(-0.964762\pi\) | ||
0.993879 | − | 0.110478i | \(-0.0352383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.20436 | 0.250218 | 0.125109 | − | 0.992143i | \(-0.460072\pi\) | ||||
0.125109 | + | 0.992143i | \(0.460072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.9812 | 0.901276 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.5306i | 0.884583i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.56223 | − | 1.87988i | 0.0540632 | − | 0.0650558i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.37797i | 0.0476295i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.9943 | −0.655755 | −0.327877 | − | 0.944720i | \(-0.606333\pi\) | ||||
−0.327877 | + | 0.944720i | \(0.606333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.1609 | 1.52279 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.41129i | 0.117491i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.6936 | − | 16.3660i | −0.677482 | − | 0.563006i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.913701i | 0.0313951i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.1212 | 0.553277 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.09533 | −0.174666 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.4748i | 1.07768i | 0.842409 | + | 0.538838i | \(0.181136\pi\) | ||||
−0.842409 | + | 0.538838i | \(0.818864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.239224 | − | 0.198802i | −0.00818129 | − | 0.00679888i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.2795i | − | 0.658576i | −0.944230 | − | 0.329288i | \(-0.893191\pi\) | ||
0.944230 | − | 0.329288i | \(-0.106809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1150 | 1.30047 | 0.650233 | − | 0.759735i | \(-0.274671\pi\) | ||||
0.650233 | + | 0.759735i | \(0.274671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.893392 | 0.0304467 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 35.9823i | − | 1.22485i | −0.790528 | − | 0.612425i | \(-0.790194\pi\) | ||
0.790528 | − | 0.612425i | \(-0.209806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.2394 | + | 27.9647i | −0.790164 | + | 0.950827i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.09896i | 0.275055i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.94136 | 0.133701 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.24439 | −0.0421645 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.14957i | − | 0.275821i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.4689 | − | 7.52215i | −0.455332 | − | 0.254295i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.2807i | 0.684830i | 0.939549 | + | 0.342415i | \(0.111245\pi\) | ||||
−0.939549 | + | 0.342415i | \(0.888755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.8616 | 1.10839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.4240 | 1.53037 | 0.765187 | − | 0.643809i | \(-0.222647\pi\) | ||||
0.765187 | + | 0.643809i | \(0.222647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.80229i | 0.296221i | 0.988971 | + | 0.148110i | \(0.0473191\pi\) | ||||
−0.988971 | + | 0.148110i | \(0.952681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.1097 | + | 16.9787i | −0.474294 | + | 0.570731i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.08114i | 0.103455i | 0.998661 | + | 0.0517273i | \(0.0164726\pi\) | ||||
−0.998661 | + | 0.0517273i | \(0.983527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.39536 | 0.214493 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.21525 | 0.107715 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 0.442998i | − | 0.0148244i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.4514 | − | 30.2921i | −1.21844 | − | 1.01255i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.25734i | − | 0.0419813i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.7863 | 0.393096 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.4269 | −0.447316 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 13.5048i | − | 0.449413i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.81064 | − | 3.99777i | −0.159911 | − | 0.132890i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.6761i | 1.98151i | 0.135659 | + | 0.990756i | \(0.456685\pi\) | ||||
−0.135659 | + | 0.990756i | \(0.543315\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.04519 | 0.167338 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.00185 | 0.0994557 | 0.0497279 | − | 0.998763i | \(-0.484165\pi\) | ||||
0.0497279 | + | 0.998763i | \(0.484165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.8893i | − | 0.360385i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.4733 | + | 22.2294i | −0.610707 | + | 0.734882i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.5757i | 0.877607i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0779 | 0.827244 | 0.413622 | − | 0.910449i | \(-0.364264\pi\) | ||||
0.413622 | + | 0.910449i | \(0.364264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.5637 | −0.776452 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 19.5909i | − | 0.644843i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.7884 | − | 4.61437i | 0.815037 | − | 0.151720i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.5579i | 0.543833i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.9759 | 1.08191 | 0.540953 | − | 0.841053i | \(-0.318064\pi\) | ||||
0.540953 | + | 0.841053i | \(0.318064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.708883 | −0.0232327 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 23.8330i | − | 0.780258i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.0209 | − | 27.7017i | 0.752863 | − | 0.905942i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.0273i | 1.11162i | 0.831308 | + | 0.555812i | \(0.187593\pi\) | ||||
−0.831308 | + | 0.555812i | \(0.812407\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.8108 | 0.646500 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.6448 | −1.32498 | −0.662492 | − | 0.749069i | \(-0.730501\pi\) | ||||
−0.662492 | + | 0.749069i | \(0.730501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.654200i | 0.0213037i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.37297 | − | 1.97200i | −0.0771927 | − | 0.0641492i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.2683i | − | 1.30854i | −0.756260 | − | 0.654272i | \(-0.772975\pi\) | ||
0.756260 | − | 0.654272i | \(-0.227025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0001 | −0.649230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.70559 | −0.249871 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.1148i | − | 0.781155i | −0.920570 | − | 0.390578i | \(-0.872275\pi\) | ||
0.920570 | − | 0.390578i | \(-0.127725\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.0205 | − | 13.3135i | −0.518410 | − | 0.430813i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 27.5013i | − | 0.888992i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.7010 | −0.507012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1012 | −0.938749 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.9770i | 0.353728i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.5471 | + | 31.9448i | −0.854580 | + | 1.02834i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.5601i | 0.339591i | 0.985479 | + | 0.169795i | \(0.0543107\pi\) | ||||
−0.985479 | + | 0.169795i | \(0.945689\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.696897 | −0.0223876 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.52267 | −0.241414 | −0.120707 | − | 0.992688i | \(-0.538516\pi\) | ||||
−0.120707 | + | 0.992688i | \(0.538516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.43662i | − | 0.142232i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.13866 | + | 6.11686i | 0.0364662 | + | 0.195896i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14.9046i | − | 0.476841i | −0.971162 | − | 0.238421i | \(-0.923370\pi\) | ||
0.971162 | − | 0.238421i | \(-0.0766297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.75898 | 0.216018 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.71636 | −0.150582 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 11.6522i | − | 0.371648i | −0.982583 | − | 0.185824i | \(-0.940505\pi\) | ||
0.982583 | − | 0.185824i | \(-0.0594954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.44245 | + | 2.93907i | −0.0778230 | + | 0.0936467i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.39429i | − | 0.139872i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.88912 | 0.314456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7682 | 0.373830 | 0.186915 | − | 0.982376i | \(-0.440151\pi\) | ||||
0.186915 | + | 0.982376i | \(0.440151\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.9273i | 0.505438i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.0832 | − | 25.0000i | −0.953703 | − | 0.792554i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 34.8434i | − | 1.10350i | −0.834009 | − | 0.551751i | \(-0.813960\pi\) | ||
0.834009 | − | 0.551751i | \(-0.186040\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.04284 | 0.159549 |
(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 | 4020.2.g.b.1609.3 | ✓ | 24 | |
5.4 | even | 2 | inner | 4020.2.g.b.1609.15 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.b.1609.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
4020.2.g.b.1609.15 | yes | 24 | 5.4 | even | 2 | inner |