Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(97,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.x (of order \(4\), degree \(2\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Character | \(\chi\) | \(=\) | 280.97 |
Dual form | 280.2.x.a.153.1 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.16993 | − | 2.16993i | −1.25281 | − | 1.25281i | −0.954456 | − | 0.298351i | \(-0.903563\pi\) |
−0.298351 | − | 0.954456i | \(-0.596437\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.272751 | + | 2.21937i | 0.121978 | + | 0.992533i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.63589 | + | 2.07939i | −0.618310 | + | 0.785934i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.41716i | 2.13905i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56986 | 0.774841 | 0.387420 | − | 0.921903i | \(-0.373366\pi\) | ||||
0.387420 | + | 0.921903i | \(0.373366\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.35447 | + | 1.35447i | 0.375661 | + | 0.375661i | 0.869534 | − | 0.493873i | \(-0.164419\pi\) |
−0.493873 | + | 0.869534i | \(0.664419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.22402 | − | 5.40772i | 1.09064 | − | 1.39627i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.10000 | − | 2.10000i | 0.509325 | − | 0.509325i | −0.404994 | − | 0.914319i | \(-0.632726\pi\) |
0.914319 | + | 0.404994i | \(0.132726\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.43874 | 1.01832 | 0.509159 | − | 0.860673i | \(-0.329957\pi\) | ||||
0.509159 | + | 0.860673i | \(0.329957\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.06189 | − | 0.962346i | 1.75925 | − | 0.210001i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.78997 | + | 5.78997i | −1.20729 | + | 1.20729i | −0.235391 | + | 0.971901i | \(0.575637\pi\) |
−0.971901 | + | 0.235391i | \(0.924363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.85121 | + | 1.21067i | −0.970243 | + | 0.242135i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.41498 | − | 7.41498i | 1.42701 | − | 1.42701i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.28527i | 0.795754i | 0.917439 | + | 0.397877i | \(0.130253\pi\) | ||||
−0.917439 | + | 0.397877i | \(0.869747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.70587i | 1.74323i | 0.490194 | + | 0.871613i | \(0.336926\pi\) | ||||
−0.490194 | + | 0.871613i | \(0.663074\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.57640 | − | 5.57640i | −0.970726 | − | 0.970726i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.06112 | − | 3.06350i | −0.855486 | − | 0.517826i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.183701 | + | 0.183701i | 0.0302002 | + | 0.0302002i | 0.722046 | − | 0.691845i | \(-0.243202\pi\) |
−0.691845 | + | 0.722046i | \(0.743202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.87819i | − | 0.941263i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.81823i | 0.596307i | 0.954518 | + | 0.298153i | \(0.0963707\pi\) | ||||
−0.954518 | + | 0.298153i | \(0.903629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.86065 | − | 5.86065i | 0.893741 | − | 0.893741i | −0.101132 | − | 0.994873i | \(-0.532246\pi\) |
0.994873 | + | 0.101132i | \(0.0322464\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.2421 | + | 1.75029i | −2.12308 | + | 0.260918i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.83004 | + | 1.83004i | −0.266939 | + | 0.266939i | −0.827866 | − | 0.560926i | \(-0.810445\pi\) |
0.560926 | + | 0.827866i | \(0.310445\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.64770 | − | 6.80331i | −0.235386 | − | 0.971902i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.11369 | −1.27617 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.38616 | + | 2.38616i | −0.327764 | + | 0.327764i | −0.851736 | − | 0.523972i | \(-0.824450\pi\) |
0.523972 | + | 0.851736i | \(0.324450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.700932 | + | 5.70346i | 0.0945136 | + | 0.769055i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.63174 | − | 9.63174i | −1.27576 | − | 1.27576i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.34515 | −0.826068 | −0.413034 | − | 0.910716i | \(-0.635531\pi\) | ||||
−0.413034 | + | 0.910716i | \(0.635531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.62046i | − | 1.10374i | −0.833931 | − | 0.551868i | \(-0.813915\pi\) | ||
0.833931 | − | 0.551868i | \(-0.186085\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.3438 | − | 10.4978i | −1.68116 | − | 1.32260i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.63663 | + | 3.37550i | −0.327034 | + | 0.418679i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.68908 | + | 6.68908i | 0.817201 | + | 0.817201i | 0.985702 | − | 0.168501i | \(-0.0538925\pi\) |
−0.168501 | + | 0.985702i | \(0.553892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25.1276 | 3.02501 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.04557 | −0.717477 | −0.358739 | − | 0.933438i | \(-0.616793\pi\) | ||||
−0.358739 | + | 0.933438i | \(0.616793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.88962 | + | 1.88962i | 0.221164 | + | 0.221164i | 0.808988 | − | 0.587825i | \(-0.200015\pi\) |
−0.587825 | + | 0.808988i | \(0.700015\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.1538 | + | 7.89970i | 1.51888 | + | 0.912179i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.20401 | + | 5.34372i | −0.479092 | + | 0.608974i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.2456i | − | 1.37774i | −0.724887 | − | 0.688868i | \(-0.758108\pi\) | ||
0.724887 | − | 0.688868i | \(-0.241892\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.9285 | −1.43650 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.08951 | − | 2.08951i | −0.229354 | − | 0.229354i | 0.583069 | − | 0.812423i | \(-0.301852\pi\) |
−0.812423 | + | 0.583069i | \(0.801852\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.23346 | + | 4.08790i | 0.567648 | + | 0.443395i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.29871 | − | 9.29871i | 0.996927 | − | 0.996927i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1525 | 1.07616 | 0.538081 | − | 0.842893i | \(-0.319150\pi\) | ||||
0.538081 | + | 0.842893i | \(0.319150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.03222 | + | 0.600696i | −0.527520 | + | 0.0629700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.0610 | − | 21.0610i | 2.18393 | − | 2.18393i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.21067 | + | 9.85121i | 0.124212 | + | 1.01071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.15926 | − | 7.15926i | 0.726913 | − | 0.726913i | −0.243091 | − | 0.970004i | \(-0.578161\pi\) |
0.970004 | + | 0.243091i | \(0.0781613\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.4912i | 1.65743i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.12506i | 0.111947i | 0.998432 | + | 0.0559737i | \(0.0178263\pi\) | ||||
−0.998432 | + | 0.0559737i | \(0.982174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.56743 | − | 1.56743i | −0.154443 | − | 0.154443i | 0.625656 | − | 0.780099i | \(-0.284831\pi\) |
−0.780099 | + | 0.625656i | \(0.784831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.33469 | + | 17.6298i | 0.423023 | + | 1.72050i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.145240 | − | 0.145240i | −0.0140409 | − | 0.0140409i | 0.700051 | − | 0.714092i | \(-0.253160\pi\) |
−0.714092 | + | 0.700051i | \(0.753160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.51130i | − | 0.623669i | −0.950136 | − | 0.311835i | \(-0.899057\pi\) | ||
0.950136 | − | 0.311835i | \(-0.100943\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.797233i | − | 0.0756700i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.49203 | + | 7.49203i | −0.704791 | + | 0.704791i | −0.965435 | − | 0.260644i | \(-0.916065\pi\) |
0.260644 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.4293 | − | 11.2709i | −1.34554 | − | 1.05101i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.69183 | + | 8.69183i | −0.803560 | + | 0.803560i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.931334 | + | 7.80209i | 0.0853753 | + | 0.715217i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.39584 | −0.399622 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.28527 | − | 8.28527i | 0.747057 | − | 0.747057i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.01011 | − | 10.4364i | −0.358675 | − | 0.933463i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.78578 | + | 6.78578i | 0.602141 | + | 0.602141i | 0.940880 | − | 0.338740i | \(-0.110001\pi\) |
−0.338740 | + | 0.940880i | \(0.610001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.4344 | −2.23937 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.37853i | 0.732036i | 0.930608 | + | 0.366018i | \(0.119279\pi\) | ||||
−0.930608 | + | 0.366018i | \(0.880721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.26131 | + | 9.22986i | −0.629636 | + | 0.800330i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.4790 | + | 14.4342i | 1.59042 | + | 1.24229i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.56986 | + | 7.56986i | 0.646736 | + | 0.646736i | 0.952203 | − | 0.305466i | \(-0.0988124\pi\) |
−0.305466 | + | 0.952203i | \(0.598812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2432 | −0.953636 | −0.476818 | − | 0.879002i | \(-0.658210\pi\) | ||||
−0.476818 | + | 0.879002i | \(0.658210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.94212 | 0.668847 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.48078 | + | 3.48078i | 0.291078 | + | 0.291078i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.51060 | + | 1.16881i | −0.789812 | + | 0.0970646i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.1873 | + | 18.3381i | −0.922713 | + | 1.51250i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.0067i | − | 1.47516i | −0.675258 | − | 0.737581i | \(-0.735968\pi\) | ||
0.675258 | − | 0.737581i | \(-0.264032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1231 | 0.986563 | 0.493282 | − | 0.869870i | \(-0.335797\pi\) | ||||
0.493282 | + | 0.869870i | \(0.335797\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.4760 | + | 13.4760i | 1.08947 | + | 1.08947i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.5409 | + | 2.64729i | −1.73021 | + | 0.212635i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6764 | − | 11.6764i | 0.931876 | − | 0.931876i | −0.0659475 | − | 0.997823i | \(-0.521007\pi\) |
0.997823 | + | 0.0659475i | \(0.0210070\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.3556 | 0.821249 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.56781 | − | 21.5114i | −0.202371 | − | 1.69533i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5217 | − | 10.5217i | 0.824123 | − | 0.824123i | −0.162574 | − | 0.986696i | \(-0.551980\pi\) |
0.986696 | + | 0.162574i | \(0.0519796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.8551 | − | 13.8971i | 0.845070 | − | 1.08188i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.06283 | − | 9.06283i | 0.701303 | − | 0.701303i | −0.263387 | − | 0.964690i | \(-0.584840\pi\) |
0.964690 | + | 0.263387i | \(0.0848398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.33084i | − | 0.717757i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 28.4841i | 2.17823i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.99321 | − | 9.99321i | −0.759770 | − | 0.759770i | 0.216511 | − | 0.976280i | \(-0.430532\pi\) |
−0.976280 | + | 0.216511i | \(0.930532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.41862 | − | 12.0681i | 0.409609 | − | 0.912261i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.7685 | + | 13.7685i | 1.03490 | + | 1.03490i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8694i | 1.11139i | 0.831386 | + | 0.555695i | \(0.187548\pi\) | ||||
−0.831386 | + | 0.555695i | \(0.812452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2095i | 1.05618i | 0.849188 | + | 0.528090i | \(0.177092\pi\) | ||||
−0.849188 | + | 0.528090i | \(0.822908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.7058 | + | 18.7058i | −1.38277 | + | 1.38277i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.357595 | + | 0.457804i | −0.0262909 | + | 0.0336584i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.39670 | − | 5.39670i | 0.394646 | − | 0.394646i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.28849 | + | 27.5488i | 0.239202 | + | 2.00388i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.04143 | −0.0753549 | −0.0376775 | − | 0.999290i | \(-0.511996\pi\) | ||||
−0.0376775 | + | 0.999290i | \(0.511996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0690260 | − | 0.0690260i | 0.00496860 | − | 0.00496860i | −0.704618 | − | 0.709587i | \(-0.748882\pi\) |
0.709587 | + | 0.704618i | \(0.248882\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.0459 | − | 1.60328i | 0.934234 | − | 0.114813i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.7945 | + | 12.7945i | 0.911571 | + | 0.911571i | 0.996396 | − | 0.0848244i | \(-0.0270329\pi\) |
−0.0848244 | + | 0.996396i | \(0.527033\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.09793 | 0.290494 | 0.145247 | − | 0.989395i | \(-0.453602\pi\) | ||||
0.145247 | + | 0.989395i | \(0.453602\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 29.0296i | − | 2.04759i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.91073 | − | 7.01025i | −0.625411 | − | 0.492023i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.47406 | + | 1.04143i | −0.591854 | + | 0.0727364i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −37.1551 | − | 37.1551i | −2.58246 | − | 2.58246i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.4069 | 0.789033 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.7179 | 1.97702 | 0.988510 | − | 0.151154i | \(-0.0482988\pi\) | ||||
0.988510 | + | 0.151154i | \(0.0482988\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.1184 | + | 13.1184i | 0.898861 | + | 0.898861i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.6055 | + | 11.4085i | 0.996084 | + | 0.778050i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.1823 | − | 15.8778i | −1.37006 | − | 1.07785i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 8.20069i | − | 0.554151i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.68876 | 0.382668 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.69411 | + | 3.69411i | 0.247376 | + | 0.247376i | 0.819893 | − | 0.572517i | \(-0.194033\pi\) |
−0.572517 | + | 0.819893i | \(0.694033\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.76908 | − | 31.1310i | −0.517939 | − | 2.07540i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.85781 | + | 7.85781i | −0.521541 | + | 0.521541i | −0.918037 | − | 0.396495i | \(-0.870226\pi\) |
0.396495 | + | 0.918037i | \(0.370226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.48513 | −0.626795 | −0.313397 | − | 0.949622i | \(-0.601467\pi\) | ||||
−0.313397 | + | 0.949622i | \(0.601467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.7179 | − | 2.47309i | 1.36314 | − | 0.162717i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.6024 | + | 13.6024i | −0.891126 | + | 0.891126i | −0.994629 | − | 0.103503i | \(-0.966995\pi\) |
0.103503 | + | 0.994629i | \(0.466995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.56069 | − | 3.56240i | −0.297507 | − | 0.232385i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.5720 | + | 26.5720i | −1.72604 | + | 1.72604i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.7581i | − | 1.21336i | −0.794946 | − | 0.606680i | \(-0.792501\pi\) | ||
0.794946 | − | 0.606680i | \(-0.207499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.78395i | − | 0.179330i | −0.995972 | − | 0.0896649i | \(-0.971420\pi\) | ||
0.995972 | − | 0.0896649i | \(-0.0285796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.80885 | + | 5.80885i | 0.372638 | + | 0.372638i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.6497 | − | 5.51247i | 0.935933 | − | 0.352179i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.01213 | + | 6.01213i | 0.382543 | + | 0.382543i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.06817i | 0.574672i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 28.3562i | − | 1.78983i | −0.446241 | − | 0.894913i | \(-0.647237\pi\) | ||
0.446241 | − | 0.894913i | \(-0.352763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8794 | + | 14.8794i | −0.935458 | + | 0.935458i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.48577 | − | 20.2267i | −0.155665 | − | 1.26664i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.9740 | + | 17.9740i | −1.12119 | + | 1.12119i | −0.129626 | + | 0.991563i | \(0.541378\pi\) |
−0.991563 | + | 0.129626i | \(0.958622\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.682499 | + | 0.0814698i | −0.0424084 | + | 0.00506229i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.4992 | −1.70216 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.986652 | − | 0.986652i | 0.0608396 | − | 0.0608396i | −0.676032 | − | 0.736872i | \(-0.736302\pi\) |
0.736872 | + | 0.676032i | \(0.236302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.94659 | − | 4.64494i | −0.365296 | − | 0.285336i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.0301 | − | 22.0301i | −1.34822 | − | 1.34822i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.65510 | −0.161884 | −0.0809422 | − | 0.996719i | \(-0.525793\pi\) | ||||
−0.0809422 | + | 0.996719i | \(0.525793\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.573473i | − | 0.0348360i | −0.999848 | − | 0.0174180i | \(-0.994455\pi\) | ||
0.999848 | − | 0.0174180i | \(-0.00554460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.2230 | + | 9.61609i | 0.739771 | + | 0.581992i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.4669 | + | 3.11125i | −0.751783 | + | 0.187616i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.98543 | + | 6.98543i | 0.419714 | + | 0.419714i | 0.885105 | − | 0.465391i | \(-0.154086\pi\) |
−0.465391 | + | 0.885105i | \(0.654086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −62.2841 | −3.72885 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2936 | 1.38958 | 0.694789 | − | 0.719213i | \(-0.255498\pi\) | ||||
0.694789 | + | 0.719213i | \(0.255498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.27105 | + | 9.27105i | 0.551107 | + | 0.551107i | 0.926760 | − | 0.375653i | \(-0.122582\pi\) |
−0.375653 | + | 0.926760i | \(0.622582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.7493 | − | 24.0035i | 1.11061 | − | 1.42184i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.93957 | − | 6.24621i | −0.468658 | − | 0.368702i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17999i | 0.481176i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.0701 | −1.82136 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3951 | − | 11.3951i | −0.665707 | − | 0.665707i | 0.291012 | − | 0.956719i | \(-0.406008\pi\) |
−0.956719 | + | 0.291012i | \(0.906008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.73065 | − | 14.0822i | −0.100762 | − | 0.819899i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.0554 | − | 19.0554i | 1.10571 | − | 1.10571i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.6846 | −0.907066 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.59915 | + | 21.7740i | 0.149813 | + | 1.25503i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.44129 | − | 2.44129i | 0.140249 | − | 0.140249i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.1320 | − | 2.35124i | 1.09549 | − | 0.134632i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7022 | − | 12.7022i | 0.724953 | − | 0.724953i | −0.244657 | − | 0.969610i | \(-0.578675\pi\) |
0.969610 | + | 0.244657i | \(0.0786753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.80241i | 0.386976i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 12.2723i | − | 0.695896i | −0.937514 | − | 0.347948i | \(-0.886879\pi\) | ||
0.937514 | − | 0.347948i | \(-0.113121\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9640 | + | 11.9640i | 0.676246 | + | 0.676246i | 0.959149 | − | 0.282903i | \(-0.0912974\pi\) |
−0.282903 | + | 0.959149i | \(0.591297\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.6590 | − | 32.4780i | 1.10766 | − | 1.82993i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.9944 | − | 18.9944i | −1.06683 | − | 1.06683i | −0.997600 | − | 0.0692338i | \(-0.977945\pi\) |
−0.0692338 | − | 0.997600i | \(-0.522055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0125i | 0.616583i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.630320i | 0.0351811i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.32136 | − | 9.32136i | 0.518654 | − | 0.518654i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.21062 | − | 4.93099i | −0.455443 | − | 0.273522i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1290 | + | 14.1290i | −0.781337 | + | 0.781337i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.811611 | − | 6.79913i | −0.0447455 | − | 0.374848i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.8309 | −1.30986 | −0.654931 | − | 0.755689i | \(-0.727302\pi\) | ||||
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.17884 | + | 1.17884i | −0.0645998 | + | 0.0645998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.0211 | + | 16.6700i | −0.711418 | + | 0.910779i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.26895 | + | 8.26895i | 0.450439 | + | 0.450439i | 0.895500 | − | 0.445061i | \(-0.146818\pi\) |
−0.445061 | + | 0.895500i | \(0.646818\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32.5143 | 1.76593 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.9427i | 1.35072i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8422 | + | 7.70330i | 0.909392 | + | 0.415939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.85359 | + | 55.7675i | 0.368985 | + | 3.00242i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0104 | + | 12.0104i | 0.644754 | + | 0.644754i | 0.951720 | − | 0.306966i | \(-0.0993139\pi\) |
−0.306966 | + | 0.951720i | \(0.599314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0227 | 0.697092 | 0.348546 | − | 0.937292i | \(-0.386676\pi\) | ||||
0.348546 | + | 0.937292i | \(0.386676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0867 | 1.07215 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.48642 | + | 9.48642i | 0.504911 | + | 0.504911i | 0.912960 | − | 0.408049i | \(-0.133791\pi\) |
−0.408049 | + | 0.912960i | \(0.633791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.64894 | − | 13.4174i | −0.0875165 | − | 0.712120i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.9090 | − | 18.9509i | 0.789070 | − | 1.00299i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.36637i | − | 0.494338i | −0.968972 | − | 0.247169i | \(-0.920500\pi\) | ||
0.968972 | − | 0.247169i | \(-0.0795003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.702427 | 0.0369698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.53865 | + | 9.53865i | 0.500649 | + | 0.500649i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.67838 | + | 4.70918i | −0.192535 | + | 0.246490i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.22951 | − | 1.22951i | 0.0641798 | − | 0.0641798i | −0.674288 | − | 0.738468i | \(-0.735549\pi\) |
0.738468 | + | 0.674288i | \(0.235549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.5022 | −1.27553 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.05824 | − | 8.86524i | −0.0549412 | − | 0.460260i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.68837 | + | 6.68837i | −0.346311 | + | 0.346311i | −0.858733 | − | 0.512423i | \(-0.828748\pi\) |
0.512423 | + | 0.858733i | \(0.328748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.9446 | + | 31.3479i | −0.720098 | + | 1.61880i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.80425 | + | 5.80425i | −0.298934 | + | 0.298934i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0350675i | 0.00180130i | 1.00000 | 0.000900649i | \(0.000286685\pi\) | |||||
−1.00000 | 0.000900649i | \(0.999713\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 29.4493i | − | 1.50873i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.5450 | + | 20.5450i | 1.04980 | + | 1.04980i | 0.998693 | + | 0.0511048i | \(0.0162743\pi\) |
0.0511048 | + | 0.998693i | \(0.483726\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.0064 | − | 7.87275i | −0.662865 | − | 0.401233i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 37.6087 | + | 37.6087i | 1.91176 | + | 1.91176i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11.6510i | − | 0.590730i | −0.955385 | − | 0.295365i | \(-0.904559\pi\) | ||
0.955385 | − | 0.295365i | \(-0.0954412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.3179i | 1.22981i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.1808 | − | 18.1808i | 0.917100 | − | 0.917100i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.1775 | − | 3.34000i | 1.36745 | − | 0.168054i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.22472 | − | 4.22472i | 0.212033 | − | 0.212033i | −0.593098 | − | 0.805131i | \(-0.702095\pi\) |
0.805131 | + | 0.593098i | \(0.202095\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 35.7846 | − | 4.27160i | 1.79147 | − | 0.213848i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.26395 | −0.212932 | −0.106466 | − | 0.994316i | \(-0.533953\pi\) | ||||
−0.106466 | + | 0.994316i | \(0.533953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1463 | + | 13.1463i | −0.654863 | + | 0.654863i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.52625 | − | 28.6930i | −0.175221 | − | 1.42577i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.472084 | + | 0.472084i | 0.0234003 | + | 0.0234003i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.3610 | −1.25402 | −0.627011 | − | 0.779010i | \(-0.715722\pi\) | ||||
−0.627011 | + | 0.779010i | \(0.715722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 32.8521i | − | 1.62047i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3800 | − | 13.1940i | 0.510766 | − | 0.649235i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.06748 | − | 5.20732i | 0.199665 | − | 0.255617i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.3969 | + | 24.3969i | 1.19472 | + | 1.19472i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.597961 | −0.0292123 | −0.0146061 | − | 0.999893i | \(-0.504649\pi\) | ||||
−0.0146061 | + | 0.999893i | \(0.504649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.94725 | −0.484799 | −0.242400 | − | 0.970176i | \(-0.577935\pi\) | ||||
−0.242400 | + | 0.970176i | \(0.577935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.7437 | − | 11.7437i | −0.570998 | − | 0.570998i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.64514 | + | 12.7300i | −0.370844 | + | 0.617494i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.9253 | + | 14.1022i | 0.867464 | + | 0.682451i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 15.1061i | − | 0.729329i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.29543 | −0.158735 | −0.0793677 | − | 0.996845i | \(-0.525290\pi\) | ||||
−0.0793677 | + | 0.996845i | \(0.525290\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.8212 | − | 14.8212i | −0.712260 | − | 0.712260i | 0.254747 | − | 0.967008i | \(-0.418008\pi\) |
−0.967008 | + | 0.254747i | \(0.918008\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.1735 | + | 18.1011i | 1.11109 | + | 0.867879i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.7002 | + | 25.7002i | −1.22941 | + | 1.22941i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.93710 | −0.187907 | −0.0939537 | − | 0.995577i | \(-0.529951\pi\) | ||||
−0.0939537 | + | 0.995577i | \(0.529951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.6580 | − | 10.5735i | 2.07895 | − | 0.503502i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.0246 | − | 23.0246i | 1.09393 | − | 1.09393i | 0.0988281 | − | 0.995105i | \(-0.468491\pi\) |
0.995105 | − | 0.0988281i | \(-0.0315094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.76910 | + | 22.5321i | 0.131268 | + | 1.06813i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −39.0731 | + | 39.0731i | −1.84810 | + | 1.84810i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.44923i | 0.445937i | 0.974826 | + | 0.222968i | \(0.0715747\pi\) | ||||
−0.974826 | + | 0.222968i | \(0.928425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.81229i | 0.462043i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26.3062 | − | 26.3062i | −1.23597 | − | 1.23597i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.70571 | − | 11.0045i | −0.126846 | − | 0.515900i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8997 | − | 17.8997i | −0.837313 | − | 0.837313i | 0.151191 | − | 0.988505i | \(-0.451689\pi\) |
−0.988505 | + | 0.151191i | \(0.951689\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 31.1429i | − | 1.45363i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.91063i | 0.415009i | 0.978234 | + | 0.207505i | \(0.0665342\pi\) | ||||
−0.978234 | + | 0.207505i | \(0.933466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.48151 | − | 1.48151i | 0.0688518 | − | 0.0688518i | −0.671842 | − | 0.740694i | \(-0.734497\pi\) |
0.740694 | + | 0.671842i | \(0.234497\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 52.4867 | + | 40.9978i | 2.43401 | + | 1.90123i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.836995 | + | 0.836995i | −0.0387315 | + | 0.0387315i | −0.726207 | − | 0.687476i | \(-0.758719\pi\) |
0.687476 | + | 0.726207i | \(0.258719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.8518 | + | 2.96656i | −1.14755 | + | 0.136983i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −50.6737 | −2.33492 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.0610 | − | 15.0610i | 0.692507 | − | 0.692507i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.5333 | + | 5.37386i | −0.988015 | + | 0.246570i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.3123 | − | 15.3123i | −0.701104 | − | 0.701104i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.6142 | 1.07896 | 0.539479 | − | 0.841999i | \(-0.318621\pi\) | ||||
0.539479 | + | 0.841999i | \(0.318621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.497632i | 0.0226901i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −41.1061 | + | 52.2500i | −1.87039 | + | 2.37746i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.8417 | + | 13.9364i | 0.810152 | + | 0.632817i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7931 | + | 22.7931i | 1.03285 | + | 1.03285i | 0.999442 | + | 0.0334131i | \(0.0106377\pi\) |
0.0334131 | + | 0.999442i | \(0.489362\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.6626 | −2.06493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.02524 | 0.226786 | 0.113393 | − | 0.993550i | \(-0.463828\pi\) | ||||
0.113393 | + | 0.993550i | \(0.463828\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.99907 | + | 8.99907i | 0.405298 | + | 0.405298i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −36.6000 | + | 4.49799i | −1.64505 | + | 0.202170i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.88992 | − | 12.5711i | 0.443623 | − | 0.563890i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9254i | 0.489089i | 0.969638 | + | 0.244544i | \(0.0786384\pi\) | ||||
−0.969638 | + | 0.244544i | \(0.921362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.3313 | −1.75719 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.4112 | − | 13.4112i | −0.597974 | − | 0.597974i | 0.341799 | − | 0.939773i | \(-0.388964\pi\) |
−0.939773 | + | 0.341799i | \(0.888964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.49692 | + | 0.306861i | −0.111111 | + | 0.0136551i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.2472 | + | 20.2472i | −0.899211 | + | 0.899211i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.1376 | 1.77907 | 0.889533 | − | 0.456871i | \(-0.151030\pi\) | ||||
0.889533 | + | 0.456871i | \(0.151030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.02049 | + | 0.838034i | −0.310568 | + | 0.0370724i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.9132 | − | 32.9132i | 1.45315 | − | 1.45315i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.05119 | − | 3.90622i | 0.134451 | − | 0.172129i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.70295 | + | 4.70295i | −0.206835 | + | 0.206835i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.3691i | 1.90369i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.2753i | 0.844467i | 0.906487 | + | 0.422234i | \(0.138754\pi\) | ||||
−0.906487 | + | 0.422234i | \(0.861246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6573 | − | 10.6573i | −0.466013 | − | 0.466013i | 0.434607 | − | 0.900620i | \(-0.356887\pi\) |
−0.900620 | + | 0.434607i | \(0.856887\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −37.9448 | + | 14.4288i | −1.65605 | + | 0.629727i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.3823 | + | 20.3823i | 0.887869 | + | 0.887869i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 44.0474i | − | 1.91511i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 40.7178i | − | 1.76700i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.17166 | + | 5.17166i | −0.224009 | + | 0.224009i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.282727 | − | 0.361956i | 0.0122234 | − | 0.0156487i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.2655 | − | 32.2655i | 1.39236 | − | 1.39236i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.23435 | − | 17.4835i | −0.182386 | − | 0.753069i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8503 | 0.552479 | 0.276240 | − | 0.961089i | \(-0.410912\pi\) | ||||
0.276240 | + | 0.961089i | \(0.410912\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.8335 | − | 30.8335i | 1.32319 | − | 1.32319i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.4510 | − | 1.77597i | 0.619012 | − | 0.0760740i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.5300 | − | 26.5300i | −1.13434 | − | 1.13434i | −0.989447 | − | 0.144895i | \(-0.953716\pi\) |
−0.144895 | − | 0.989447i | \(-0.546284\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 55.3188 | 2.36095 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.0212i | 0.810330i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.4633 | + | 20.0325i | 1.08281 | + | 0.851868i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.76936 | − | 0.217446i | 0.0751050 | − | 0.00923009i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.9969 | − | 25.9969i | −1.10152 | − | 1.10152i | −0.994227 | − | 0.107298i | \(-0.965780\pi\) |
−0.107298 | − | 0.994227i | \(-0.534220\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8761 | 0.671488 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.4209 | −0.988830 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.11717 | + | 1.11717i | 0.0470833 | + | 0.0470833i | 0.730256 | − | 0.683173i | \(-0.239401\pi\) |
−0.683173 | + | 0.730256i | \(0.739401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.6711 | − | 14.5841i | −0.785497 | − | 0.613559i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.1496 | − | 26.8833i | 0.888199 | − | 1.12899i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.9125i | − | 0.960543i | −0.877120 | − | 0.480271i | \(-0.840538\pi\) | ||
0.877120 | − | 0.480271i | \(-0.159462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.1839 | 1.38870 | 0.694351 | − | 0.719636i | \(-0.255692\pi\) | ||||
0.694351 | + | 0.719636i | \(0.255692\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.25982 | + | 2.25982i | 0.0944052 | + | 0.0944052i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.0786 | − | 35.0981i | 0.879039 | − | 1.46369i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.4941 | − | 29.4941i | 1.22786 | − | 1.22786i | 0.263084 | − | 0.964773i | \(-0.415260\pi\) |
0.964773 | − | 0.263084i | \(-0.0847397\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.299563 | −0.0124494 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.76312 | − | 0.926682i | 0.322069 | − | 0.0384452i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.13207 | + | 6.13207i | −0.253965 | + | 0.253965i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.6611 | − | 16.9197i | −0.895576 | − | 0.699543i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.6733 | − | 14.6733i | 0.605634 | − | 0.605634i | −0.336168 | − | 0.941802i | \(-0.609131\pi\) |
0.941802 | + | 0.336168i | \(0.109131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.0819i | 1.77516i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 55.5263i | − | 2.28405i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.3914 | + | 21.3914i | 0.878439 | + | 0.878439i | 0.993373 | − | 0.114934i | \(-0.0366657\pi\) |
−0.114934 | + | 0.993373i | \(0.536666\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.0617 | + | 4.19501i | −0.699462 | + | 0.171979i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.89220 | − | 8.89220i | −0.363933 | − | 0.363933i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.4975i | 0.551494i | 0.961230 | + | 0.275747i | \(0.0889252\pi\) | ||||
−0.961230 | + | 0.275747i | \(0.911075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.3870i | 1.48426i | 0.670258 | + | 0.742128i | \(0.266183\pi\) | ||||
−0.670258 | + | 0.742128i | \(0.733817\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.9249 | + | 42.9249i | −1.74804 | + | 1.74804i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.19897 | − | 9.75600i | −0.0487451 | − | 0.396638i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.3687 | − | 29.3687i | 1.19204 | − | 1.19204i | 0.215545 | − | 0.976494i | \(-0.430847\pi\) |
0.976494 | − | 0.215545i | \(-0.0691529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.12391 | + | 34.5473i | 0.167109 | + | 1.39993i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.95747 | −0.200558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.4722 | + | 20.4722i | −0.826863 | + | 0.826863i | −0.987082 | − | 0.160218i | \(-0.948780\pi\) |
0.160218 | + | 0.987082i | \(0.448780\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.6479 | + | 16.1283i | 0.832604 | + | 0.650354i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.88024 | − | 5.88024i | −0.236729 | − | 0.236729i | 0.578765 | − | 0.815494i | \(-0.303535\pi\) |
−0.815494 | + | 0.578765i | \(0.803535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.3760 | −0.899368 | −0.449684 | − | 0.893188i | \(-0.648463\pi\) | ||||
−0.449684 | + | 0.893188i | \(0.648463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 85.8650i | 3.44564i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.6084 | + | 21.1109i | −0.665401 | + | 0.845792i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.0685 | − | 11.7465i | 0.882742 | − | 0.469859i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.7522 | − | 24.7522i | −0.988507 | − | 0.988507i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.771543 | 0.0307634 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0404 | −1.67360 | −0.836802 | − | 0.547506i | \(-0.815577\pi\) | ||||
−0.836802 | + | 0.547506i | \(0.815577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −62.3157 | − | 62.3157i | −2.47683 | − | 2.47683i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.2093 | + | 16.9110i | −0.524196 | + | 0.671092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.98311 | − | 11.4466i | 0.276681 | − | 0.453531i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 38.7954i | − | 1.53472i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.69064 | −0.0667764 | −0.0333882 | − | 0.999442i | \(-0.510630\pi\) | ||||
−0.0333882 | + | 0.999442i | \(0.510630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.492457 | − | 0.492457i | −0.0194206 | − | 0.0194206i | 0.697330 | − | 0.716750i | \(-0.254371\pi\) |
−0.716750 | + | 0.697330i | \(0.754371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.93726 | − | 56.4483i | −0.273154 | − | 2.22265i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.32851 | + | 6.32851i | −0.248799 | + | 0.248799i | −0.820478 | − | 0.571678i | \(-0.806293\pi\) |
0.571678 | + | 0.820478i | \(0.306293\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.3061 | −0.640071 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.34040 | + | 78.2476i | 0.366079 | + | 3.06677i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.3667 | − | 24.3667i | 0.953543 | − | 0.953543i | −0.0454247 | − | 0.998968i | \(-0.514464\pi\) |
0.998968 | + | 0.0454247i | \(0.0144641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.5951 | + | 2.28526i | −0.726569 | + | 0.0892923i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.1260 | + | 12.1260i | −0.473081 | + | 0.473081i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.7004i | 0.416829i | 0.978041 | + | 0.208414i | \(0.0668303\pi\) | ||||
−0.978041 | + | 0.208414i | \(0.933170\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 34.1408i | − | 1.32792i | −0.747766 | − | 0.663962i | \(-0.768874\pi\) | ||
0.747766 | − | 0.663962i | \(-0.231126\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.3442 | − | 12.3442i | −0.479409 | − | 0.479409i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.4650 | − | 13.5981i | −0.871156 | − | 0.527311i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.8116 | − | 24.8116i | −0.960707 | − | 0.960707i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 16.0319i | − | 0.619829i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 22.1533i | − | 0.855220i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2267 | + | 11.2267i | −0.432758 | + | 0.432758i | −0.889566 | − | 0.456808i | \(-0.848993\pi\) |
0.456808 | + | 0.889566i | \(0.348993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.9946 | + | 44.9488i | −1.03902 | + | 1.73008i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.84843 | − | 2.84843i | 0.109474 | − | 0.109474i | −0.650248 | − | 0.759722i | \(-0.725335\pi\) |
0.759722 | + | 0.650248i | \(0.225335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.17508 | + | 26.5987i | 0.121848 | + | 1.02076i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.1017 | 1.30678 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.5165 | − | 22.5165i | 0.861571 | − | 0.861571i | −0.129950 | − | 0.991521i | \(-0.541482\pi\) |
0.991521 | + | 0.129950i | \(0.0414816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.7356 | + | 18.8650i | −0.563019 | + | 0.720795i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.5820 | + | 20.5820i | 0.785253 | + | 0.785253i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.46394 | −0.246256 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.28794i | 0.277246i | 0.990345 | + | 0.138623i | \(0.0442677\pi\) | ||||
−0.990345 | + | 0.138623i | \(0.955732\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −34.2915 | − | 26.9778i | −1.30263 | − | 1.02480i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.06660 | − | 24.9528i | −0.116323 | − | 0.946515i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.01828 | + | 8.01828i | 0.303714 | + | 0.303714i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 59.0326 | 2.23282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.29057 | 0.313130 | 0.156565 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156565 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.815399 | + | 0.815399i | 0.0307534 | + | 0.0307534i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.16622 | + | 17.6265i | 0.0815847 | + | 0.663853i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.33943 | − | 1.84048i | −0.0879833 | − | 0.0692182i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8960i | 0.596987i | 0.954412 | + | 0.298493i | \(0.0964841\pi\) | ||||
−0.954412 | + | 0.298493i | \(0.903516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 78.5819 | 2.94705 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −56.1967 | − | 56.1967i | −2.10458 | − | 2.10458i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.77576 | + | 8.67454i | −0.253399 | + | 0.324409i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.7036 | + | 40.7036i | −1.52011 | + | 1.52011i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.3180 | −1.54090 | −0.770450 | − | 0.637500i | \(-0.779969\pi\) | ||||
−0.770450 | + | 0.637500i | \(0.779969\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.82344 | − | 0.695143i | 0.216876 | − | 0.0258885i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.04096 | + | 6.04096i | −0.224666 | + | 0.224666i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.18806 | − | 20.7887i | −0.192680 | − | 0.772075i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.27196 | + | 2.27196i | −0.0842625 | + | 0.0842625i | −0.747982 | − | 0.663719i | \(-0.768977\pi\) |
0.663719 | + | 0.747982i | \(0.268977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5758i | 0.502809i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 24.6147i | − | 0.910409i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.64097 | + | 4.64097i | 0.171418 | + | 0.171418i | 0.787602 | − | 0.616184i | \(-0.211322\pi\) |
−0.616184 | + | 0.787602i | \(0.711322\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −43.7503 | − | 19.8270i | −1.61376 | − | 0.731332i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.1900 | + | 17.1900i | 0.633201 | + | 0.633201i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.48628i | 0.0914592i | 0.998954 | + | 0.0457296i | \(0.0145613\pi\) | ||||
−0.998954 | + | 0.0457296i | \(0.985439\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 26.0917i | − | 0.958504i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.7230 | − | 11.7230i | 0.430075 | − | 0.430075i | −0.458579 | − | 0.888654i | \(-0.651641\pi\) |
0.888654 | + | 0.458579i | \(0.151641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.9634 | − | 4.91134i | 1.46415 | − | 0.179938i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.4087 | − | 13.4087i | 0.490600 | − | 0.490600i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.539608 | − | 0.0644129i | 0.0197168 | − | 0.00235359i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.4627 | −0.673714 | −0.336857 | − | 0.941556i | \(-0.609364\pi\) | ||||
−0.336857 | + | 0.941556i | \(0.609364\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −61.5308 | + | 61.5308i | −2.24231 | + | 2.24231i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.30659 | + | 26.9056i | 0.120339 | + | 0.979196i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.72346 | − | 2.72346i | −0.0989857 | − | 0.0989857i | 0.655880 | − | 0.754865i | \(-0.272298\pi\) |
−0.754865 | + | 0.655880i | \(0.772298\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 64.5743 | 2.34390 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.4733i | − | 0.488406i | −0.969724 | − | 0.244203i | \(-0.921474\pi\) | ||
0.969724 | − | 0.244203i | \(-0.0785263\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5395 | + | 10.6518i | 0.490163 | + | 0.385621i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.2327 | + | 33.5839i | −0.948446 | + | 1.21423i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.59429 | − | 8.59429i | −0.310322 | − | 0.310322i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.2864 | 0.479121 | 0.239561 | − | 0.970881i | \(-0.422997\pi\) | ||||
0.239561 | + | 0.970881i | \(0.422997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 78.0046 | 2.80927 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.232304 | + | 0.232304i | 0.00835541 | + | 0.00835541i | 0.711272 | − | 0.702917i | \(-0.248119\pi\) |
−0.702917 | + | 0.711272i | \(0.748119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7506 | − | 47.0853i | −0.422095 | − | 1.69135i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.65776 | + | 1.30419i | 0.0594717 | + | 0.0467875i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.9481i | 0.607229i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.5362 | −0.555931 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31.7752 | + | 31.7752i | 1.13555 | + | 1.13555i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.0989 | + | 22.7294i | 1.03859 | + | 0.811249i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.0984 | + | 32.0984i | −1.14419 | + | 1.14419i | −0.156509 | + | 0.987676i | \(0.550024\pi\) |
−0.987676 | + | 0.156509i | \(0.949976\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.28192 | −0.152441 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.32266 | − | 27.8350i | −0.118140 | − | 0.989699i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6761 | − | 11.6761i | 0.414631 | − | 0.414631i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.82449 | + | 22.9828i | 0.100174 | + | 0.815117i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.3730 | − | 31.3730i | 1.11129 | − | 1.11129i | 0.118313 | − | 0.992976i | \(-0.462251\pi\) |
0.992976 | − | 0.118313i | \(-0.0377485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.68619i | 0.271918i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 65.1501i | 2.30197i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.85606 | + | 4.85606i | 0.171367 | + | 0.171367i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 47.0413 | − | 11.5662i | 1.65799 | − | 0.407654i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.76138 | + | 5.76138i | 0.202810 | + | 0.202810i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.8681i | 1.54232i | 0.636642 | + | 0.771160i | \(0.280323\pi\) | ||||
−0.636642 | + | 0.771160i | \(0.719677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.3680i | 0.715217i | 0.933872 | + | 0.357609i | \(0.116408\pi\) | ||||
−0.933872 | + | 0.357609i | \(0.883592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.24439 | + | 1.24439i | −0.0436428 | + | 0.0436428i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.2213 | + | 20.4817i | 0.918494 | + | 0.717444i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0139 | − | 26.0139i | 0.910112 | − | 0.910112i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.85476 | − | 32.2926i | −0.134696 | − | 1.12839i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.15818 | 0.0753209 | 0.0376604 | − | 0.999291i | \(-0.488009\pi\) | ||||
0.0376604 | + | 0.999291i | \(0.488009\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0905 | − | 24.0905i | 0.839741 | − | 0.839741i | −0.149083 | − | 0.988825i | \(-0.547632\pi\) |
0.988825 | + | 0.149083i | \(0.0476322\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 33.8035 | + | 20.3011i | 1.17689 | + | 0.706794i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0992 | − | 24.0992i | −0.838011 | − | 0.838011i | 0.150586 | − | 0.988597i | \(-0.451884\pi\) |
−0.988597 | + | 0.150586i | \(0.951884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.8499 | 0.932536 | 0.466268 | − | 0.884643i | \(-0.345598\pi\) | ||||
0.466268 | + | 0.884643i | \(0.345598\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 30.3157i | − | 1.05164i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.7471 | − | 10.8268i | −0.614902 | − | 0.375126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.5857 | + | 17.6419i | 0.781610 | + | 0.610522i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 71.9689 | + | 71.9689i | 2.48761 | + | 2.48761i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1545 | 0.557717 | 0.278858 | − | 0.960332i | \(-0.410044\pi\) | ||||
0.278858 | + | 0.960332i | \(0.410044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6365 | 0.366775 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −50.5454 | − | 50.5454i | −1.74087 | − | 1.74087i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.7086 | − | 2.54500i | 0.712397 | − | 0.0875506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.19113 | − | 9.14066i | 0.247090 | − | 0.314077i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 40.2350i | − | 1.38086i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.12724 | −0.0729208 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.00773 | − | 2.00773i | −0.0687435 | − | 0.0687435i | 0.671899 | − | 0.740643i | \(-0.265479\pi\) |
−0.740643 | + | 0.671899i | \(0.765479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −63.2168 | + | 7.76908i | −2.16197 | + | 0.265697i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.9532 | + | 23.9532i | −0.818225 | + | 0.818225i | −0.985851 | − | 0.167626i | \(-0.946390\pi\) |
0.167626 | + | 0.985851i | \(0.446390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0499 | 0.957049 | 0.478525 | − | 0.878074i | \(-0.341172\pi\) | ||||
0.478525 | + | 0.878074i | \(0.341172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.67445 | + | 30.7821i | 0.125225 | + | 1.04905i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.191578 | − | 0.191578i | 0.00652139 | − | 0.00652139i | −0.703839 | − | 0.710360i | \(-0.748532\pi\) |
0.710360 | + | 0.703839i | \(0.248532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.4530 | − | 24.9043i | 0.661421 | − | 0.846772i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.7500 | − | 17.7500i | 0.602821 | − | 0.602821i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 31.4694i | − | 1.06753i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.1203i | 0.613982i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45.9421 | + | 45.9421i | 1.55490 | + | 1.55490i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.2615 | + | 8.73433i | 0.955413 | + | 0.295274i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.2975 | + | 41.2975i | 1.39452 | + | 1.39452i | 0.814863 | + | 0.579653i | \(0.196812\pi\) |
0.579653 | + | 0.814863i | \(0.303188\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 49.4529i | 1.66801i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24.7259i | − | 0.833037i | −0.909127 | − | 0.416519i | \(-0.863250\pi\) | ||
0.909127 | − | 0.416519i | \(-0.136750\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2632 | − | 12.2632i | 0.412688 | − | 0.412688i | −0.469986 | − | 0.882674i | \(-0.655741\pi\) |
0.882674 | + | 0.469986i | \(0.155741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.8020 | + | 34.3128i | −0.900940 | + | 1.15341i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0519 | + | 14.0519i | −0.471816 | + | 0.471816i | −0.902502 | − | 0.430686i | \(-0.858272\pi\) |
0.430686 | + | 0.902502i | \(0.358272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.2111 | + | 3.00944i | −0.845553 | + | 0.100933i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.2243 | −1.11305 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.12309 | + | 8.12309i | −0.271829 | + | 0.271829i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.0007 | + | 4.05564i | −1.10309 | + | 0.135565i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.0345 | + | 34.0345i | 1.13638 | + | 1.13638i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.5923 | −1.38718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0219i | 0.333876i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.6079 | − | 52.8879i | 1.38463 | − | 1.76000i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.5360 | + | 3.87565i | −1.04829 | + | 0.128831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.9592 | − | 30.9592i | −1.02798 | − | 1.02798i | −0.999597 | − | 0.0283860i | \(-0.990963\pi\) |
−0.0283860 | − | 0.999597i | \(-0.509037\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.21967 | −0.239461 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.1629 | 0.734289 | 0.367145 | − | 0.930164i | \(-0.380335\pi\) | ||||
0.367145 | + | 0.930164i | \(0.380335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.36974 | − | 5.36974i | −0.177712 | − | 0.177712i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.6170 | − | 36.4130i | −1.54111 | − | 1.20378i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.4222 | − | 13.7064i | −0.575332 | − | 0.452625i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.60542i | 0.184906i | 0.995717 | + | 0.0924529i | \(0.0294708\pi\) | ||||
−0.995717 | + | 0.0924529i | \(0.970529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55.1257 | −1.81645 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.18853 | − | 8.18853i | −0.269529 | − | 0.269529i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.11357 | − | 0.668769i | −0.0366140 | − | 0.0219890i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.0584 | − | 10.0584i | 0.330363 | − | 0.330363i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.8751 | 0.980170 | 0.490085 | − | 0.871675i | \(-0.336966\pi\) | ||||
0.490085 | + | 0.871675i | \(0.336966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.31371 | − | 30.1982i | −0.239697 | − | 0.989705i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.6299 | + | 26.6299i | −0.871824 | + | 0.871824i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.4492 | + | 10.5053i | 0.439837 | + | 0.343561i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6529 | − | 34.6529i | 1.13206 | − | 1.13206i | 0.142226 | − | 0.989834i | \(-0.454574\pi\) |
0.989834 | − | 0.142226i | \(-0.0454258\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 51.9220i | − | 1.69441i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 21.6170i | − | 0.704693i | −0.935870 | − | 0.352346i | \(-0.885384\pi\) | ||
0.935870 | − | 0.352346i | \(-0.114616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.1074 | − | 22.1074i | −0.719916 | − | 0.719916i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −60.2440 | + | 14.8123i | −1.95974 | + | 0.481845i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.95185 | + | 7.95185i | 0.258400 | + | 0.258400i | 0.824403 | − | 0.566003i | \(-0.191511\pi\) |
−0.566003 | + | 0.824403i | \(0.691511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.11887i | 0.166165i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82.4331i | 2.67308i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.7397 | + | 12.7397i | −0.412678 | + | 0.412678i | −0.882671 | − | 0.469992i | \(-0.844257\pi\) |
0.469992 | + | 0.882671i | \(0.344257\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.284050 | − | 2.31131i | −0.00919165 | − | 0.0747923i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.8964 | − | 23.8964i | 0.772459 | − | 0.772459i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.1241 | + | 3.35717i | −0.908176 | + | 0.108409i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63.2040 | −2.03884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.932029 | − | 0.932029i | 0.0300342 | − | 0.0300342i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.172021 | + | 0.134367i | 0.00553756 | + | 0.00432544i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.8492 | + | 11.8492i | 0.381045 | + | 0.381045i | 0.871478 | − | 0.490434i | \(-0.163162\pi\) |
−0.490434 | + | 0.871478i | \(0.663162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.4533 | −1.29955 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.5371i | 1.55763i | 0.627255 | + | 0.778814i | \(0.284179\pi\) | ||||
−0.627255 | + | 0.778814i | \(0.715821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.3927 | − | 23.3790i | 0.589642 | − | 0.749495i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.11656 | + | 28.5163i | 0.227912 | + | 0.913254i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.9303 | − | 18.9303i | −0.605635 | − | 0.605635i | 0.336167 | − | 0.941802i | \(-0.390869\pi\) |
−0.941802 | + | 0.336167i | \(0.890869\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.0904 | 0.833854 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.7840 | 1.33406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.97683 | − | 7.97683i | −0.254421 | − | 0.254421i | 0.568359 | − | 0.822781i | \(-0.307578\pi\) |
−0.822781 | + | 0.568359i | \(0.807578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.9061 | + | 31.8855i | −0.793573 | + | 1.01596i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.9925 | + | 16.5147i | −0.413555 | + | 0.525670i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 67.8660i | 2.15801i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.6706 | −1.57784 | −0.788920 | − | 0.614496i | \(-0.789359\pi\) | ||||
−0.788920 | + | 0.614496i | \(0.789359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 51.7112 | + | 51.7112i | 1.64100 | + | 1.64100i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.11771 | + | 9.09482i | 0.0354339 | + | 0.288325i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.4002 | + | 12.4002i | −0.392718 | + | 0.392718i | −0.875655 | − | 0.482937i | \(-0.839570\pi\) |
0.482937 | + | 0.875655i | \(0.339570\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.72427 | 0.0861922 |
(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 | 280.2.x.a.97.1 | ✓ | 24 | |
4.3 | odd | 2 | 560.2.bj.d.97.12 | 24 | |||
5.2 | odd | 4 | 1400.2.x.b.993.1 | 24 | |||
5.3 | odd | 4 | inner | 280.2.x.a.153.12 | yes | 24 | |
5.4 | even | 2 | 1400.2.x.b.657.12 | 24 | |||
7.6 | odd | 2 | inner | 280.2.x.a.97.12 | yes | 24 | |
20.3 | even | 4 | 560.2.bj.d.433.1 | 24 | |||
28.27 | even | 2 | 560.2.bj.d.97.1 | 24 | |||
35.13 | even | 4 | inner | 280.2.x.a.153.1 | yes | 24 | |
35.27 | even | 4 | 1400.2.x.b.993.12 | 24 | |||
35.34 | odd | 2 | 1400.2.x.b.657.1 | 24 | |||
140.83 | odd | 4 | 560.2.bj.d.433.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.x.a.97.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
280.2.x.a.97.12 | yes | 24 | 7.6 | odd | 2 | inner | |
280.2.x.a.153.1 | yes | 24 | 35.13 | even | 4 | inner | |
280.2.x.a.153.12 | yes | 24 | 5.3 | odd | 4 | inner | |
560.2.bj.d.97.1 | 24 | 28.27 | even | 2 | |||
560.2.bj.d.97.12 | 24 | 4.3 | odd | 2 | |||
560.2.bj.d.433.1 | 24 | 20.3 | even | 4 | |||
560.2.bj.d.433.12 | 24 | 140.83 | odd | 4 | |||
1400.2.x.b.657.1 | 24 | 35.34 | odd | 2 | |||
1400.2.x.b.657.12 | 24 | 5.4 | even | 2 | |||
1400.2.x.b.993.1 | 24 | 5.2 | odd | 4 | |||
1400.2.x.b.993.12 | 24 | 35.27 | even | 4 |