Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(305,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.cn (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 305.4 | ||
Character | \(\chi\) | \(=\) | 624.305 |
Dual form | 624.2.cn.f.401.4 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.31722 | + | 1.12469i | −0.760498 | + | 0.649341i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.72616 | + | 1.72616i | 0.771963 | + | 0.771963i | 0.978449 | − | 0.206486i | \(-0.0662029\pi\) |
−0.206486 | + | 0.978449i | \(0.566203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.574711 | − | 2.14485i | 0.217220 | − | 0.810677i | −0.768153 | − | 0.640266i | \(-0.778824\pi\) |
0.985373 | − | 0.170411i | \(-0.0545094\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.470140 | − | 2.96293i | 0.156713 | − | 0.987644i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.47004 | − | 5.48627i | −0.443234 | − | 1.65417i | −0.720557 | − | 0.693396i | \(-0.756114\pi\) |
0.277323 | − | 0.960777i | \(-0.410553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.76028 | − | 2.31967i | 0.765564 | − | 0.643360i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.21513 | − | 0.332337i | −1.08834 | − | 0.0858091i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40933 | − | 2.44104i | −0.341813 | − | 0.592038i | 0.642956 | − | 0.765903i | \(-0.277708\pi\) |
−0.984770 | + | 0.173865i | \(0.944374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.85833 | + | 2.10563i | 1.80282 | + | 0.483065i | 0.994414 | − | 0.105553i | \(-0.0336613\pi\) |
0.808411 | + | 0.588618i | \(0.200328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.65527 | + | 3.47161i | 0.361210 | + | 0.757568i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.84516 | + | 3.19592i | −0.384743 | + | 0.666395i | −0.991734 | − | 0.128314i | \(-0.959043\pi\) |
0.606990 | + | 0.794709i | \(0.292377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.959270i | 0.191854i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.71311 | + | 4.43160i | 0.522137 | + | 0.852861i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.95737 | − | 1.13009i | −0.363475 | − | 0.209853i | 0.307129 | − | 0.951668i | \(-0.400632\pi\) |
−0.670604 | + | 0.741815i | \(0.733965\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13483 | + | 3.13483i | −0.563031 | + | 0.563031i | −0.930167 | − | 0.367136i | \(-0.880338\pi\) |
0.367136 | + | 0.930167i | \(0.380338\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.10673 | + | 5.57328i | 1.41120 | + | 0.970184i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.69440 | − | 2.71031i | 0.793499 | − | 0.458127i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.36333 | − | 1.97300i | 1.21052 | − | 0.324359i | 0.403557 | − | 0.914955i | \(-0.367774\pi\) |
0.806968 | + | 0.590596i | \(0.201107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.02699 | + | 6.15998i | −0.164449 | + | 0.986386i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.02869 | + | 1.88333i | −1.09770 | + | 0.294127i | −0.761826 | − | 0.647781i | \(-0.775697\pi\) |
−0.335870 | + | 0.941908i | \(0.609030\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.416760 | − | 0.240616i | 0.0635553 | − | 0.0366937i | −0.467886 | − | 0.883789i | \(-0.654984\pi\) |
0.531441 | + | 0.847095i | \(0.321651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.92604 | − | 4.30296i | 0.883402 | − | 0.641448i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.57953 | − | 9.57953i | 1.39732 | − | 1.39732i | 0.589685 | − | 0.807633i | \(-0.299252\pi\) |
0.807633 | − | 0.589685i | \(-0.200748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.79209 | + | 1.03466i | 0.256013 | + | 0.147809i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.60181 | + | 1.63032i | 0.644383 | + | 0.228290i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.617097i | 0.0847648i | 0.999101 | + | 0.0423824i | \(0.0134948\pi\) | ||||
−0.999101 | + | 0.0423824i | \(0.986505\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.93266 | − | 12.0077i | 0.934800 | − | 1.61912i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.7193 | + | 6.06461i | −1.68472 | + | 0.803277i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.94720 | + | 0.521752i | 0.253504 | + | 0.0679263i | 0.383333 | − | 0.923610i | \(-0.374776\pi\) |
−0.129829 | + | 0.991536i | \(0.541443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.667748 | + | 1.15657i | 0.0854964 | + | 0.148084i | 0.905603 | − | 0.424127i | \(-0.139419\pi\) |
−0.820106 | + | 0.572211i | \(0.806086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.08485 | − | 2.71121i | −0.766619 | − | 0.341580i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.76881 | + | 0.760564i | 1.08764 | + | 0.0943364i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.667631 | + | 2.49163i | 0.0815641 | + | 0.304401i | 0.994641 | − | 0.103385i | \(-0.0329674\pi\) |
−0.913077 | + | 0.407787i | \(0.866301\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.16393 | − | 6.28497i | −0.140121 | − | 0.756621i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.81372 | + | 6.76890i | −0.215249 | + | 0.803320i | 0.770830 | + | 0.637041i | \(0.219842\pi\) |
−0.986079 | + | 0.166279i | \(0.946825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.75039 | − | 6.75039i | −0.790073 | − | 0.790073i | 0.191432 | − | 0.981506i | \(-0.438687\pi\) |
−0.981506 | + | 0.191432i | \(0.938687\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.07888 | − | 1.26357i | −0.124579 | − | 0.145904i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.6121 | −1.43728 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.372617 | 0.0419226 | 0.0209613 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209613 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.55794 | − | 2.78599i | −0.950882 | − | 0.309554i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.99123 | + | 4.99123i | 0.547858 | + | 0.547858i | 0.925821 | − | 0.377963i | \(-0.123375\pi\) |
−0.377963 | + | 0.925821i | \(0.623375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.78089 | − | 6.64636i | 0.193164 | − | 0.720899i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.84930 | − | 0.712863i | 0.412688 | − | 0.0764269i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.17011 | + | 8.09895i | 0.230031 | + | 0.858487i | 0.980326 | + | 0.197384i | \(0.0632446\pi\) |
−0.750295 | + | 0.661103i | \(0.770089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38898 | − | 7.25352i | −0.355261 | − | 0.760376i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.603546 | − | 7.65497i | 0.0625849 | − | 0.793783i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.93009 | + | 17.1994i | 1.01881 | + | 1.76462i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.03688 | + | 0.813729i | 0.308348 | + | 0.0826217i | 0.409675 | − | 0.912232i | \(-0.365642\pi\) |
−0.101327 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.9466 | + | 1.77632i | −1.70319 | + | 0.178527i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.672751 | − | 1.16524i | 0.0669412 | − | 0.115946i | −0.830612 | − | 0.556851i | \(-0.812009\pi\) |
0.897553 | + | 0.440906i | \(0.145343\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.0519i | − | 0.990446i | −0.868766 | − | 0.495223i | \(-0.835086\pi\) | ||
0.868766 | − | 0.495223i | \(-0.164914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.13530 | + | 8.84983i | −0.305974 | + | 0.863655i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9381 | − | 7.46982i | −1.25077 | − | 0.722135i | −0.279511 | − | 0.960143i | \(-0.590172\pi\) |
−0.971263 | + | 0.238008i | \(0.923506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.96629 | + | 5.96629i | −0.571467 | + | 0.571467i | −0.932538 | − | 0.361071i | \(-0.882411\pi\) |
0.361071 | + | 0.932538i | \(0.382411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.48012 | + | 10.8803i | −0.709981 | + | 1.03272i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.1400 | + | 8.74110i | −1.42425 | + | 0.822294i | −0.996659 | − | 0.0816760i | \(-0.973973\pi\) |
−0.427596 | + | 0.903970i | \(0.640639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.70173 | + | 2.33162i | −0.811440 | + | 0.217425i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.57530 | − | 9.26909i | −0.515437 | − | 0.856927i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.04561 | + | 1.61992i | −0.554200 | + | 0.148498i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.4119 | + | 10.6301i | −1.67380 | + | 0.966372i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.14017 | − | 10.3859i | 0.643807 | − | 0.936462i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.97495 | − | 6.97495i | 0.623859 | − | 0.623859i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.06716 | + | 0.616127i | 0.0946954 | + | 0.0546724i | 0.546600 | − | 0.837394i | \(-0.315922\pi\) |
−0.451904 | + | 0.892066i | \(0.649255\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.278346 | + | 0.785671i | −0.0245070 | + | 0.0691745i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.17983i | 0.627305i | 0.949538 | + | 0.313652i | \(0.101553\pi\) | ||||
−0.949538 | + | 0.313652i | \(0.898447\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.03253 | − | 15.6448i | 0.783220 | − | 1.35658i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.96640 | + | 12.3329i | −0.255307 | + | 1.06145i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6202 | + | 3.11363i | 0.992783 | + | 0.266015i | 0.718419 | − | 0.695611i | \(-0.244866\pi\) |
0.274364 | + | 0.961626i | \(0.411533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.16445 | − | 2.01689i | −0.0987677 | − | 0.171071i | 0.812407 | − | 0.583091i | \(-0.198157\pi\) |
−0.911175 | + | 0.412020i | \(0.864823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.84434 | + | 23.3924i | −0.155322 | + | 1.96999i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.7841 | − | 11.7336i | −1.40355 | − | 0.981215i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.42803 | − | 5.32947i | −0.118591 | − | 0.442588i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.52425 | + | 0.652667i | −0.290676 | + | 0.0538311i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.04901 | − | 18.8432i | 0.413631 | − | 1.54369i | −0.373930 | − | 0.927457i | \(-0.621990\pi\) |
0.787562 | − | 0.616236i | \(-0.211343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.712411 | − | 0.712411i | −0.0579752 | − | 0.0579752i | 0.677525 | − | 0.735500i | \(-0.263053\pi\) |
−0.735500 | + | 0.677525i | \(0.763053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.89521 | + | 3.02813i | −0.638290 | + | 0.244810i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.8224 | −0.869279 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0306 | 1.35919 | 0.679594 | − | 0.733588i | \(-0.262156\pi\) | ||||
0.679594 | + | 0.733588i | \(0.262156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.694044 | − | 0.812853i | −0.0550413 | − | 0.0644635i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.79433 | + | 5.79433i | 0.456657 | + | 0.456657i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.57138 | + | 9.59651i | −0.201406 | + | 0.751657i | 0.789109 | + | 0.614253i | \(0.210542\pi\) |
−0.990515 | + | 0.137404i | \(0.956124\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.37313 | + | 23.6139i | 0.340448 | + | 1.83834i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.68928 | − | 10.0365i | −0.208102 | − | 0.776649i | −0.988481 | − | 0.151342i | \(-0.951640\pi\) |
0.780379 | − | 0.625307i | \(-0.215026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.23828 | − | 12.8059i | 0.172175 | − | 0.985066i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.93336 | − | 22.2938i | 0.759623 | − | 1.70485i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.65624 | + | 11.5289i | 0.506064 | + | 0.876529i | 0.999975 | + | 0.00701675i | \(0.00223352\pi\) |
−0.493911 | + | 0.869512i | \(0.664433\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.05749 | + | 0.551303i | 0.155532 | + | 0.0416746i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.15171 | + | 1.50274i | −0.236897 | + | 0.112953i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.225490 | + | 0.390560i | −0.0168539 | + | 0.0291918i | −0.874329 | − | 0.485333i | \(-0.838698\pi\) |
0.857475 | + | 0.514525i | \(0.172032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.572791i | − | 0.0425752i | −0.999773 | − | 0.0212876i | \(-0.993223\pi\) | ||
0.999773 | − | 0.0212876i | \(-0.00677657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.18036 | − | 0.772452i | −0.161177 | − | 0.0571013i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.1160 | + | 9.30459i | 1.18487 | + | 0.684087i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3204 | + | 11.3204i | −0.827830 | + | 0.827830i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.0644 | − | 3.27232i | 0.804814 | − | 0.238026i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.87896 | − | 4.54892i | 0.570102 | − | 0.329148i | −0.187088 | − | 0.982343i | \(-0.559905\pi\) |
0.757190 | + | 0.653195i | \(0.226572\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.9688 | + | 3.74292i | −1.00549 | + | 0.269421i | −0.723745 | − | 0.690067i | \(-0.757581\pi\) |
−0.281748 | + | 0.959488i | \(0.590914\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.4059 | + | 8.86037i | −0.888402 | + | 0.634504i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.22190 | − | 1.66715i | 0.443292 | − | 0.118780i | −0.0302668 | − | 0.999542i | \(-0.509636\pi\) |
0.473559 | + | 0.880762i | \(0.342969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.683303 | − | 0.394505i | 0.0484381 | − | 0.0279657i | −0.475585 | − | 0.879670i | \(-0.657764\pi\) |
0.524023 | + | 0.851704i | \(0.324430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.68173 | − | 2.53115i | −0.259689 | − | 0.178534i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.54880 | + | 3.54880i | −0.249077 | + | 0.249077i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3836 | − | 8.88172i | −1.07444 | − | 0.620326i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.60181 | + | 6.96963i | 0.597867 | + | 0.484423i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 46.2083i | − | 3.19629i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5246 | + | 19.9611i | −0.793383 | + | 1.37418i | 0.130478 | + | 0.991451i | \(0.458349\pi\) |
−0.923861 | + | 0.382729i | \(0.874984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.22385 | − | 10.9560i | −0.357932 | − | 0.750693i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.13474 | + | 0.304052i | 0.0773885 | + | 0.0207362i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.92211 | + | 8.52535i | 0.334135 | + | 0.578738i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.4839 | + | 1.29965i | 1.11388 | + | 0.0878221i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.55254 | − | 3.46875i | −0.642574 | − | 0.233334i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.35292 | − | 12.5133i | −0.224528 | − | 0.837950i | −0.982593 | − | 0.185771i | \(-0.940522\pi\) |
0.758065 | − | 0.652179i | \(-0.226145\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.84225 | + | 0.450991i | 0.189483 | + | 0.0300661i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.62037 | + | 9.77935i | −0.173920 | + | 0.649079i | 0.822813 | + | 0.568312i | \(0.192403\pi\) |
−0.996733 | + | 0.0807663i | \(0.974263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.04210 | + | 6.04210i | 0.399273 | + | 0.399273i | 0.877977 | − | 0.478703i | \(-0.158893\pi\) |
−0.478703 | + | 0.877977i | \(0.658893\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.6129 | − | 14.1847i | 1.09305 | − | 0.933284i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.52224 | 0.623823 | 0.311911 | − | 0.950111i | \(-0.399031\pi\) | ||||
0.311911 | + | 0.950111i | \(0.399031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.0716 | 2.15736 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.490818 | + | 0.419079i | −0.0318821 | + | 0.0272221i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.346997 | − | 0.346997i | −0.0224454 | − | 0.0224454i | 0.695795 | − | 0.718240i | \(-0.255052\pi\) |
−0.718240 | + | 0.695795i | \(0.755052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.84098 | + | 25.5309i | −0.440667 | + | 1.64459i | 0.286464 | + | 0.958091i | \(0.407520\pi\) |
−0.727131 | + | 0.686499i | \(0.759147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.4061 | − | 5.95528i | 0.924149 | − | 0.382031i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.30744 | + | 4.87943i | 0.0835293 | + | 0.311736i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5756 | − | 12.4166i | 1.69096 | − | 0.790049i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.1881 | − | 0.960958i | −0.772392 | − | 0.0608983i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.74616 | + | 11.6847i | 0.425814 | + | 0.737531i | 0.996496 | − | 0.0836399i | \(-0.0266545\pi\) |
−0.570682 | + | 0.821171i | \(0.693321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.2461 | + | 5.42494i | 1.27286 | + | 0.341063i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.12928 | + | 10.7577i | 0.321208 | + | 0.673671i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.24981 | + | 2.16473i | −0.0779610 | + | 0.135032i | −0.902370 | − | 0.430962i | \(-0.858174\pi\) |
0.824409 | + | 0.565994i | \(0.191508\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.9271i | − | 1.05180i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.26862 | + | 5.26827i | −0.264221 | + | 0.326098i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.32134 | − | 4.80433i | −0.513116 | − | 0.296248i | 0.220998 | − | 0.975274i | \(-0.429069\pi\) |
−0.734114 | + | 0.679027i | \(0.762402\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.06521 | + | 1.06521i | −0.0654353 | + | 0.0654353i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9673 | − | 8.22740i | −0.732388 | − | 0.503509i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4109 | + | 8.32012i | −0.878646 | + | 0.507286i | −0.870212 | − | 0.492678i | \(-0.836018\pi\) |
−0.00843422 | + | 0.999964i | \(0.502685\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.2838 | + | 8.11452i | −1.83961 | + | 0.492922i | −0.998826 | − | 0.0484469i | \(-0.984573\pi\) |
−0.840785 | + | 0.541369i | \(0.817906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6220 | + | 5.74293i | 0.763918 | + | 0.347578i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.26281 | − | 1.41017i | 0.317360 | − | 0.0850362i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.36855 | + | 3.67688i | −0.382649 | + | 0.220923i | −0.678970 | − | 0.734166i | \(-0.737573\pi\) |
0.296321 | + | 0.955088i | \(0.404240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.81447 | + | 10.7621i | 0.467840 | + | 0.644309i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.52193 | + | 5.52193i | −0.329411 | + | 0.329411i | −0.852362 | − | 0.522952i | \(-0.824831\pi\) |
0.522952 | + | 0.852362i | \(0.324831\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.91761 | − | 5.14859i | −0.530097 | − | 0.306052i | 0.210959 | − | 0.977495i | \(-0.432341\pi\) |
−0.741056 | + | 0.671443i | \(0.765675\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.4241 | − | 11.4871i | −1.92064 | − | 0.680440i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.1578i | 0.953768i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.52756 | − | 7.84197i | 0.266327 | − | 0.461292i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.91543 | + | 2.34369i | −0.288148 | + | 0.137390i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.2842 | − | 7.31077i | −1.59396 | − | 0.427100i | −0.650748 | − | 0.759294i | \(-0.725544\pi\) |
−0.943211 | + | 0.332194i | \(0.892211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.46056 | + | 4.26182i | 0.143259 | + | 0.248133i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.3246 | − | 21.3995i | 1.17935 | − | 1.24172i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.32030 | + | 13.1018i | 0.134187 | + | 0.757696i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.276570 | − | 1.03217i | −0.0159412 | − | 0.0594934i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.424372 | + | 2.29151i | 0.0243796 | + | 0.131644i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.843792 | + | 3.14907i | −0.0483154 | + | 0.180315i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0722051 | + | 0.0722051i | 0.00412096 | + | 0.00412096i | 0.709164 | − | 0.705043i | \(-0.249072\pi\) |
−0.705043 | + | 0.709164i | \(0.749072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.3053 | + | 13.2406i | 0.643137 | + | 0.753232i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0161 | 1.13501 | 0.567504 | − | 0.823370i | \(-0.307909\pi\) | ||||
0.567504 | + | 0.823370i | \(0.307909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.626697 | 0.0354230 | 0.0177115 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177115 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.82345 | − | 15.1834i | −0.328114 | − | 0.855489i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.4492 | + | 14.4492i | 0.811546 | + | 0.811546i | 0.984866 | − | 0.173320i | \(-0.0554493\pi\) |
−0.173320 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.32256 | + | 12.4000i | −0.186028 | + | 0.694265i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.4436 | − | 4.71197i | 1.42012 | − | 0.262997i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.93508 | − | 22.1500i | −0.330236 | − | 1.23246i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.22519 | + | 2.64785i | 0.123431 | + | 0.146876i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.14869 | − | 14.5692i | 0.0635226 | − | 0.805677i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0412 | − | 26.0521i | −0.829248 | − | 1.43630i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.05445 | + | 2.42613i | 0.497678 | + | 0.133352i | 0.498922 | − | 0.866647i | \(-0.333729\pi\) |
−0.00124426 | + | 0.999999i | \(0.500396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.38407 | − | 22.7446i | −0.130646 | − | 1.24640i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.14852 | + | 5.45340i | −0.172022 | + | 0.297951i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.6022i | − | 1.12227i | −0.827724 | − | 0.561136i | \(-0.810365\pi\) | ||
0.827724 | − | 0.561136i | \(-0.189635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1117 | − | 28.5418i | 0.549194 | − | 1.55018i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8068 | + | 12.5902i | 1.18091 | + | 0.681796i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2401 | − | 14.2401i | 0.768893 | − | 0.768893i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.83974 | − | 12.8580i | 0.475916 | − | 0.692252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7808 | − | 11.9978i | 1.11557 | − | 0.644076i | 0.175306 | − | 0.984514i | \(-0.443909\pi\) |
0.940267 | + | 0.340437i | \(0.110575\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.5949 | + | 7.92992i | −1.58418 | + | 0.424479i | −0.940216 | − | 0.340579i | \(-0.889377\pi\) |
−0.643961 | + | 0.765058i | \(0.722710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.7688 | + | 5.93894i | 0.948427 | + | 0.316997i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.6149 | + | 7.66733i | −1.52302 | + | 0.408091i | −0.920733 | − | 0.390193i | \(-0.872408\pi\) |
−0.602282 | + | 0.798283i | \(0.705742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8150 | + | 8.55343i | −0.786298 | + | 0.453969i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.14150 | − | 8.93324i | 0.325043 | − | 0.472797i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.69605 | + | 9.69605i | −0.511738 | + | 0.511738i | −0.915059 | − | 0.403321i | \(-0.867856\pi\) |
0.403321 | + | 0.915059i | \(0.367856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.8652 | + | 23.5935i | 2.15080 | + | 1.24176i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.2969 | − | 34.7098i | 0.645420 | − | 1.82179i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 23.3045i | − | 1.21981i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.92261 | − | 10.2583i | 0.309158 | − | 0.535477i | −0.669020 | − | 0.743244i | \(-0.733286\pi\) |
0.978178 | + | 0.207767i | \(0.0666195\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.27572 | + | 21.7110i | 0.118469 | + | 1.13023i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.32358 | + | 0.354652i | 0.0687169 | + | 0.0184126i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5599 | + | 21.7543i | 0.650325 | + | 1.12640i | 0.983044 | + | 0.183369i | \(0.0587004\pi\) |
−0.332719 | + | 0.943026i | \(0.607966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34288 | + | 17.0322i | −0.0693463 | + | 0.879540i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.02434 | + | 1.42109i | −0.413274 | + | 0.0731901i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.78147 | + | 29.0409i | 0.399707 | + | 1.49173i | 0.813612 | + | 0.581408i | \(0.197498\pi\) |
−0.413904 | + | 0.910320i | \(0.635835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.09864 | + | 0.388654i | −0.107517 | + | 0.0199113i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.42225 | − | 12.7720i | 0.174869 | − | 0.652620i | −0.821705 | − | 0.569913i | \(-0.806977\pi\) |
0.996574 | − | 0.0827069i | \(-0.0263565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.7705 | − | 21.7705i | −1.10953 | − | 1.10953i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.516995 | − | 1.34795i | −0.0262803 | − | 0.0685204i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.5709 | 1.80352 | 0.901759 | − | 0.432239i | \(-0.142276\pi\) | ||||
0.901759 | + | 0.432239i | \(0.142276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4018 | 0.526042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.07509 | − | 9.45742i | −0.407334 | − | 0.477064i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.643197 | + | 0.643197i | 0.0323627 | + | 0.0323627i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0698912 | − | 0.260837i | 0.00350774 | − | 0.0130911i | −0.964150 | − | 0.265359i | \(-0.914510\pi\) |
0.967658 | + | 0.252268i | \(0.0811763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.69774 | + | 30.7665i | 0.285244 | + | 1.54025i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.32674 | + | 12.4156i | 0.166130 | + | 0.620004i | 0.997893 | + | 0.0648745i | \(0.0206647\pi\) |
−0.831764 | + | 0.555130i | \(0.812669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.38124 | + | 15.9248i | −0.0688043 | + | 0.793268i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.96332 | − | 19.5814i | −0.495081 | − | 0.973010i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.6488 | − | 37.4968i | −1.07309 | − | 1.85865i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0337 | − | 3.76033i | −0.693924 | − | 0.185936i | −0.105417 | − | 0.994428i | \(-0.533618\pi\) |
−0.588508 | + | 0.808492i | \(0.700284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.8083 | + | 8.96782i | −0.927743 | + | 0.442350i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.23816 | − | 3.87660i | 0.110133 | − | 0.190755i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2313i | 0.845853i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.80223 | + | 1.34704i | 0.186196 | + | 0.0659650i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.4856 | + | 16.4462i | 1.39161 | + | 0.803448i | 0.993494 | − | 0.113887i | \(-0.0363301\pi\) |
0.398118 | + | 0.917334i | \(0.369663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6319 | + | 12.6319i | −0.615641 | + | 0.615641i | −0.944410 | − | 0.328769i | \(-0.893366\pi\) |
0.328769 | + | 0.944410i | \(0.393366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.8798 | − | 32.8872i | −1.16107 | − | 1.59903i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.34161 | − | 1.35193i | 0.113585 | − | 0.0655782i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.86444 | − | 0.767524i | 0.138620 | − | 0.0371431i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 35.3050 | − | 3.42110i | 1.70454 | − | 0.165172i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.3199 | + | 5.71266i | −1.02694 | + | 0.275169i | −0.732693 | − | 0.680559i | \(-0.761737\pi\) |
−0.294252 | + | 0.955728i | \(0.595070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.4780 | − | 18.7512i | 1.56079 | − | 0.901125i | 0.563618 | − | 0.826035i | \(-0.309409\pi\) |
0.997177 | − | 0.0750900i | \(-0.0239244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.87503 | + | 5.41399i | 0.377579 | + | 0.259581i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.2293 | + | 21.2293i | −1.01554 | + | 1.01554i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.7404 | − | 10.8198i | −0.894431 | − | 0.516400i | −0.0190419 | − | 0.999819i | \(-0.506062\pi\) |
−0.875389 | + | 0.483419i | \(0.839395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.90817 | − | 4.82340i | 0.186103 | − | 0.229686i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 7.66009i | − | 0.363942i | −0.983304 | − | 0.181971i | \(-0.941752\pi\) | ||
0.983304 | − | 0.181971i | \(-0.0582477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2341 | + | 17.7260i | −0.485145 | + | 0.840295i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.5421 | + | 30.4992i | 0.687817 | + | 1.44256i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.38164 | + | 2.24585i | 0.395554 | + | 0.105988i | 0.451113 | − | 0.892467i | \(-0.351027\pi\) |
−0.0555585 | + | 0.998455i | \(0.517694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6649 | + | 35.7927i | 0.973073 | + | 1.68541i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.73964 | + | 0.137160i | 0.0817356 | + | 0.00644434i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.67083 | − | 18.3707i | 0.312733 | − | 0.861231i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2516 | + | 38.2595i | 0.479550 | + | 1.78970i | 0.603439 | + | 0.797409i | \(0.293796\pi\) |
−0.123890 | + | 0.992296i | \(0.539537\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.99402 | − | 12.8684i | 0.326453 | − | 0.600645i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.25094 | + | 8.40062i | −0.104837 | + | 0.391256i | −0.998327 | − | 0.0578275i | \(-0.981583\pi\) |
0.893490 | + | 0.449083i | \(0.148249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.9840 | − | 13.9840i | −0.649893 | − | 0.649893i | 0.303074 | − | 0.952967i | \(-0.401987\pi\) |
−0.952967 | + | 0.303074i | \(0.901987\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.2555 | − | 12.1719i | 0.661085 | − | 0.564458i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4617 | −1.36333 | −0.681663 | − | 0.731666i | \(-0.738743\pi\) | ||||
−0.681663 | + | 0.731666i | \(0.738743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.72787 | 0.264489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.4330 | + | 19.1541i | −1.03366 | + | 0.882576i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.93274 | − | 1.93274i | −0.0888675 | − | 0.0888675i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.01987 | + | 7.53826i | −0.0926780 | + | 0.345879i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.82842 | + | 0.290122i | 0.0837175 | + | 0.0132838i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.50742 | + | 31.7501i | 0.388714 | + | 1.45070i | 0.832228 | + | 0.554433i | \(0.187065\pi\) |
−0.443514 | + | 0.896267i | \(0.646268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7481 | − | 22.5265i | 0.718054 | − | 1.02712i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.1492 | − | 1.11558i | −0.643813 | − | 0.0507606i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.83752 | + | 6.64677i | 0.174253 | + | 0.301814i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0631 | − | 2.96434i | −0.501316 | − | 0.134327i | −0.000705427 | − | 1.00000i | \(-0.500225\pi\) |
−0.500611 | + | 0.865672i | \(0.666891\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.40604 | − | 15.5327i | −0.334913 | − | 0.702414i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.607370 | + | 1.05200i | −0.0274102 | + | 0.0474759i | −0.879405 | − | 0.476074i | \(-0.842059\pi\) |
0.851995 | + | 0.523550i | \(0.175393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.37070i | 0.286922i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.3187 | − | 26.1863i | −1.45262 | − | 1.17699i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4759 | + | 7.78031i | 0.604477 | + | 0.348995i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.3336 | + | 21.3336i | −0.955024 | + | 0.955024i | −0.999031 | − | 0.0440068i | \(-0.985988\pi\) |
0.0440068 | + | 0.999031i | \(0.485988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.8304 | + | 10.1957i | 0.662571 | + | 0.455510i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.6423 | − | 11.3405i | 0.875808 | − | 0.505648i | 0.00653389 | − | 0.999979i | \(-0.497920\pi\) |
0.869274 | + | 0.494331i | \(0.164587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.17267 | − | 0.850114i | 0.141182 | − | 0.0378296i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4543 | + | 19.3855i | 0.508705 | + | 0.860941i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.3215 | − | 5.17719i | 0.856412 | − | 0.229475i | 0.196209 | − | 0.980562i | \(-0.437137\pi\) |
0.660203 | + | 0.751087i | \(0.270470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.3581 | + | 10.5991i | −0.812114 | + | 0.468874i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.9892 | + | 40.5378i | 0.529334 | + | 1.78979i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.3513 | − | 17.3513i | 0.764588 | − | 0.764588i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −66.6382 | − | 38.4736i | −2.93075 | − | 1.69207i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.7342 | − | 7.69995i | −0.954027 | − | 0.337990i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.4238i | 0.850973i | 0.904965 | + | 0.425486i | \(0.139897\pi\) | ||||
−0.904965 | + | 0.425486i | \(0.860103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1755 | − | 17.6244i | 0.444942 | − | 0.770663i | −0.553106 | − | 0.833111i | \(-0.686557\pi\) |
0.998048 | + | 0.0624482i | \(0.0198908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.33021 | + | 1.58785i | −0.145342 | + | 0.0692996i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0702 | + | 3.23421i | 0.525788 | + | 0.140884i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.69074 | + | 8.12459i | 0.203945 | + | 0.353243i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.46137 | − | 5.52414i | 0.106814 | − | 0.239727i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.0324 | + | 21.5027i | −0.651127 | + | 0.931387i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.43915 | − | 35.2274i | −0.408090 | − | 1.52301i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.142239 | − | 0.768060i | −0.00613808 | − | 0.0331442i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.04200 | − | 11.3529i | 0.131028 | − | 0.489003i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.28291 | + | 5.28291i | 0.227130 | + | 0.227130i | 0.811493 | − | 0.584363i | \(-0.198655\pi\) |
−0.584363 | + | 0.811493i | \(0.698655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.644213 | + | 0.754492i | 0.0276458 | + | 0.0323784i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.5976 | −0.882303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.2518 | −0.652122 | −0.326061 | − | 0.945349i | \(-0.605721\pi\) | ||||
−0.326061 | + | 0.945349i | \(0.605721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.74078 | − | 1.43474i | 0.159653 | − | 0.0612332i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.0021 | − | 13.0021i | −0.553910 | − | 0.553910i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.214147 | − | 0.799207i | 0.00910645 | − | 0.0339857i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −31.6931 | + | 5.86935i | −1.34530 | + | 0.249140i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.77202 | − | 6.61326i | −0.0750828 | − | 0.280213i | 0.918169 | − | 0.396188i | \(-0.129667\pi\) |
−0.993252 | + | 0.115975i | \(0.963001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.592223 | − | 1.63091i | 0.0250484 | − | 0.0689803i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.17951 | − | 27.6434i | 0.0920190 | − | 1.16711i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.52928 | + | 16.5052i | 0.401611 | + | 0.695611i | 0.993921 | − | 0.110099i | \(-0.0351169\pi\) |
−0.592309 | + | 0.805711i | \(0.701784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.2227 | − | 11.0456i | −1.73425 | − | 0.464692i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.8939 | + | 16.7544i | −0.457499 | + | 0.703617i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.18974 | + | 5.52479i | −0.133721 | + | 0.231611i | −0.925108 | − | 0.379704i | \(-0.876026\pi\) |
0.791387 | + | 0.611315i | \(0.209359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.64342i | 0.194321i | 0.995269 | + | 0.0971605i | \(0.0309760\pi\) | ||||
−0.995269 | + | 0.0971605i | \(0.969024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.26220 | + | 14.8533i | −0.219832 | + | 0.620507i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.06575 | − | 1.77001i | −0.127851 | − | 0.0738145i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.3269 | + | 16.3269i | −0.679699 | + | 0.679699i | −0.959932 | − | 0.280233i | \(-0.909588\pi\) |
0.280233 | + | 0.959932i | \(0.409588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1903 | − | 20.6408i | 0.589729 | − | 0.857802i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5739 | − | 7.83692i | 0.563142 | − | 0.325130i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.38556 | − | 0.907159i | 0.140216 | − | 0.0375707i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.37607 | − | 25.6238i | 0.263618 | − | 1.05941i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.6852 | + | 4.73874i | −0.729948 | + | 0.195589i | −0.604606 | − | 0.796525i | \(-0.706669\pi\) |
−0.125342 | + | 0.992114i | \(0.540003\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.2353 | + | 18.0337i | −1.28703 | + | 0.743066i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.32059 | + | 9.19373i | −0.259994 | + | 0.378179i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.8285 | + | 11.8285i | −0.485739 | + | 0.485739i | −0.906959 | − | 0.421220i | \(-0.861602\pi\) |
0.421220 | + | 0.906959i | \(0.361602\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.2319 | − | 7.63947i | −0.542457 | − | 0.313188i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.456364 | + | 1.28816i | −0.0186777 | + | 0.0527207i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.6793i | 1.49867i | 0.662188 | + | 0.749337i | \(0.269628\pi\) | ||||
−0.662188 | + | 0.749337i | \(0.730372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.04984 | + | 3.55043i | −0.0836147 | + | 0.144825i | −0.904800 | − | 0.425837i | \(-0.859980\pi\) |
0.821185 | + | 0.570662i | \(0.193313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.69642 | − | 0.806729i | 0.313422 | − | 0.0328525i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −50.1311 | − | 13.4326i | −2.03812 | − | 0.546112i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.15357 | − | 7.19419i | −0.168588 | − | 0.292003i | 0.769336 | − | 0.638845i | \(-0.220587\pi\) |
−0.937924 | + | 0.346842i | \(0.887254\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.683249 | − | 8.66585i | 0.0276866 | − | 0.351158i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.22084 | − | 48.6635i | 0.170757 | − | 1.96872i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.42881 | − | 5.33239i | −0.0577091 | − | 0.215373i | 0.931050 | − | 0.364892i | \(-0.118894\pi\) |
−0.988759 | + | 0.149519i | \(0.952227\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.2528 | − | 5.60260i | 1.21991 | − | 0.225919i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.17063 | − | 23.0291i | 0.248420 | − | 0.927117i | −0.723213 | − | 0.690625i | \(-0.757336\pi\) |
0.971633 | − | 0.236492i | \(-0.0759978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.4317 | − | 19.4317i | −0.781028 | − | 0.781028i | 0.198976 | − | 0.980004i | \(-0.436238\pi\) |
−0.980004 | + | 0.198976i | \(0.936238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.1692 | + | 0.493838i | −0.769232 | + | 0.0198170i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.6182 | 0.745923 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.8762 | 1.15505 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 51.9701 | + | 60.8665i | 2.07548 | + | 2.43077i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.1935 | − | 15.1935i | −0.605806 | − | 0.605806i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.00162 | − | 11.2022i | 0.119493 | − | 0.445953i | −0.880091 | − | 0.474805i | \(-0.842519\pi\) |
0.999584 | + | 0.0288524i | \(0.00918527\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.26971 | − | 39.2548i | −0.288945 | − | 1.56024i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.778561 | + | 2.90563i | 0.0308963 | + | 0.115306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.34674 | − | 1.30109i | 0.291089 | − | 0.0515512i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.2031 | + | 8.55626i | 0.759662 | + | 0.338480i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.29977 | − | 16.1077i | −0.367319 | − | 0.636215i | 0.621826 | − | 0.783155i | \(-0.286391\pi\) |
−0.989145 | + | 0.146940i | \(0.953058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.9091 | − | 7.74616i | −1.14006 | − | 0.305479i | −0.361086 | − | 0.932532i | \(-0.617594\pi\) |
−0.778976 | + | 0.627054i | \(0.784261\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.83667 | + | 0.875726i | −0.0723186 | + | 0.0344817i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.6735 | + | 18.4871i | −0.419619 | + | 0.726802i | −0.995901 | − | 0.0904492i | \(-0.971170\pi\) |
0.576282 | + | 0.817251i | \(0.304503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.4499i | − | 0.449447i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0719 | − | 5.69391i | −0.629907 | − | 0.223162i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.3357 | − | 10.5861i | −0.717533 | − | 0.414268i | 0.0963112 | − | 0.995351i | \(-0.469296\pi\) |
−0.813844 | + | 0.581084i | \(0.802629\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.3936 | + | 12.3936i | −0.484256 | + | 0.484256i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.1746 | + | 16.8273i | −0.904126 | + | 0.656496i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.9228 | + | 17.8533i | −1.20458 | + | 0.695464i | −0.961570 | − | 0.274559i | \(-0.911468\pi\) |
−0.243010 | + | 0.970024i | \(0.578135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7357 | + | 4.75228i | −0.689840 | + | 0.184842i | −0.586675 | − | 0.809822i | \(-0.699564\pi\) |
−0.103165 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.4841 | − | 6.17455i | 0.640189 | − | 0.239800i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 42.5971 | − | 11.4139i | 1.65184 | − | 0.442610i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.22336 | − | 4.17041i | 0.279690 | − | 0.161479i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.4901 | + | 12.7117i | 0.714868 | + | 0.491464i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.36366 | − | 5.36366i | 0.207062 | − | 0.207062i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8577 | − | 14.9289i | −0.996740 | − | 0.575468i | −0.0894579 | − | 0.995991i | \(-0.528513\pi\) |
−0.907282 | + | 0.420522i | \(0.861847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.25110 | + | 2.60260i | −0.163625 | + | 0.100174i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.5956i | 0.829988i | 0.909824 | + | 0.414994i | \(0.136216\pi\) | ||||
−0.909824 | + | 0.414994i | \(0.863784\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.49065 | − | 6.04599i | 0.133959 | − | 0.232024i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.54715 | − | 15.8287i | −0.289207 | − | 0.606556i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.6457 | + | 9.01534i | 1.28742 | + | 0.344962i | 0.836679 | − | 0.547694i | \(-0.184494\pi\) |
0.450738 | + | 0.892656i | \(0.351161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6838 | + | 25.4330i | 0.561038 | + | 0.971746i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7543 | − | 1.16328i | −0.562911 | − | 0.0443820i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.43146 | + | 1.70336i | 0.0545343 | + | 0.0648929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.05147 | + | 26.3164i | 0.268250 | + | 1.00112i | 0.960231 | + | 0.279208i | \(0.0900718\pi\) |
−0.691980 | + | 0.721916i | \(0.743262\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.92944 | + | 37.3687i | −0.225241 | + | 1.41952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.47145 | − | 5.49152i | 0.0558152 | − | 0.208305i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5030 | + | 14.5030i | 0.549342 | + | 0.549342i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.5429 | + | 10.7096i | −0.474416 | + | 0.405073i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.80915 | 0.294948 | 0.147474 | − | 0.989066i | \(-0.452886\pi\) | ||||
0.147474 | + | 0.989066i | \(0.452886\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 62.0179 | 2.33905 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −43.5627 | + | 37.1954i | −1.64066 | + | 1.40086i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.11262 | − | 2.11262i | −0.0794534 | − | 0.0794534i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.07769 | − | 30.1463i | 0.303364 | − | 1.13217i | −0.630981 | − | 0.775799i | \(-0.717347\pi\) |
0.934345 | − | 0.356371i | \(-0.115986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.175182 | − | 1.10404i | 0.00656984 | − | 0.0414047i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.23438 | − | 15.8029i | −0.158579 | − | 0.591824i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.71785 | − | 49.2261i | −0.326029 | − | 1.84095i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.847337 | + | 0.0668072i | 0.0316444 | + | 0.00249496i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.01546 | + | 3.49089i | 0.0751641 | + | 0.130188i | 0.901158 | − | 0.433492i | \(-0.142719\pi\) |
−0.825993 | + | 0.563680i | \(0.809385\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.5599 | − | 5.77695i | −0.802932 | − | 0.215145i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.7033 | − | 41.3238i | −0.732773 | − | 1.53685i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.08406 | − | 1.87765i | 0.0402611 | − | 0.0697342i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5507i | 0.984711i | 0.870394 | + | 0.492356i | \(0.163864\pi\) | ||||
−0.870394 | + | 0.492356i | \(0.836136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2781 | + | 24.0468i | −0.454745 | + | 0.890622i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.17471 | − | 0.678217i | −0.0434481 | − | 0.0250848i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7035 | − | 15.7035i | 0.580021 | − | 0.580021i | −0.354888 | − | 0.934909i | \(-0.615481\pi\) |
0.934909 | + | 0.354888i | \(0.115481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.21004 | − | 4.95682i | −0.265946 | − | 0.182835i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.6883 | − | 7.32561i | 0.467380 | − | 0.269842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.55841 | − | 1.75732i | 0.241255 | − | 0.0646441i | −0.136165 | − | 0.990686i | \(-0.543478\pi\) |
0.377420 | + | 0.926042i | \(0.376811\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.0410 | + | 46.2447i | −0.772962 | + | 1.69884i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.6931 | − | 10.9037i | 1.49288 | − | 0.400017i | 0.582174 | − | 0.813064i | \(-0.302202\pi\) |
0.910709 | + | 0.413047i | \(0.135536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.2418 | − | 23.8110i | 1.51098 | − | 0.872366i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.1352 | − | 12.4421i | 0.626946 | − | 0.455232i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.4573 | + | 23.4573i | −0.857112 | + | 0.857112i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.3813 | + | 18.1180i | 1.14512 | + | 0.661135i | 0.947693 | − | 0.319183i | \(-0.103408\pi\) |
0.197426 | + | 0.980318i | \(0.436742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0278 | − | 7.80397i | −0.802739 | − | 0.284392i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.45947i | − | 0.0895093i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.17824 | + | 5.50487i | −0.115515 | + | 0.200078i | −0.917986 | − | 0.396614i | \(-0.870185\pi\) |
0.802470 | + | 0.596692i | \(0.203519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.7700 | + | 15.6248i | −1.18948 | + | 0.567145i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.0411 | − | 5.63796i | −0.762741 | − | 0.204376i | −0.143579 | − | 0.989639i | \(-0.545861\pi\) |
−0.619162 | + | 0.785263i | \(0.712528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.36791 | + | 16.2257i | 0.339141 | + | 0.587410i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.8554 | − | 8.40137i | −0.681720 | − | 0.303752i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.58512 | − | 3.07669i | 0.237775 | − | 0.111093i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.69721 | − | 13.7982i | −0.133325 | − | 0.497575i | 0.866674 | − | 0.498874i | \(-0.166253\pi\) |
−0.999999 | + | 0.00129915i | \(0.999586\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.788382 | − | 4.25708i | −0.0283929 | − | 0.153315i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.17937 | + | 8.13353i | −0.0783866 | + | 0.292543i | −0.993980 | − | 0.109563i | \(-0.965055\pi\) |
0.915593 | + | 0.402106i | \(0.131722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.00714 | − | 3.00714i | −0.108020 | − | 0.108020i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.0378 | + | 22.2968i | 0.682978 | + | 0.799893i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.1994 | −2.12104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.8022 | 1.42424 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.302456 | − | 11.7404i | −0.0108089 | − | 0.419566i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.3975 | + | 29.3975i | 1.04924 | + | 1.04924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.57267 | + | 31.9936i | −0.305583 | + | 1.14045i | 0.626860 | + | 0.779132i | \(0.284340\pi\) |
−0.932443 | + | 0.361318i | \(0.882327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.3644 | − | 3.03058i | 0.582589 | − | 0.107891i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0472 | + | 37.4967i | 0.357238 | + | 1.33323i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.52604 | + | 1.64351i | 0.160724 | + | 0.0583628i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.205084 | − | 2.60115i | 0.00727359 | − | 0.0922532i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.4840 | + | 47.6037i | 0.973534 | + | 1.68621i | 0.684691 | + | 0.728834i | \(0.259937\pi\) |
0.288843 | + | 0.957376i | \(0.406729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.8847 | − | 9.88323i | −1.30489 | − | 0.349644i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.0169 | − | 2.62224i | 0.883928 | − | 0.0926523i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.1111 | + | 46.9578i | −0.956730 | + | 1.65711i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.0039i | 0.705045i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.62473 | − | 27.1672i | 0.338806 | − | 0.956331i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.7137 | − | 16.0005i | −0.974361 | − | 0.562547i | −0.0737978 | − | 0.997273i | \(-0.523512\pi\) |
−0.900563 | + | 0.434726i | \(0.856845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.5566 | − | 34.5566i | 1.21344 | − | 1.21344i | 0.243559 | − | 0.969886i | \(-0.421685\pi\) |
0.969886 | − | 0.243559i | \(-0.0783148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.7641 | − | 44.7486i | 1.07895 | − | 1.56940i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.0037 | + | 12.1265i | −0.735729 | + | 0.424773i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.78169 | − | 1.01330i | 0.132304 | − | 0.0354509i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −23.0850 | + | 6.63114i | −0.806655 | + | 0.231711i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.31469 | + | 1.69202i | −0.220384 | + | 0.0590518i | −0.367321 | − | 0.930094i | \(-0.619725\pi\) |
0.146937 | + | 0.989146i | \(0.453058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.88316 | − | 5.70605i | 0.344505 | − | 0.198900i | −0.317757 | − | 0.948172i | \(-0.602930\pi\) |
0.662263 | + | 0.749272i | \(0.269596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.34628 | + | 7.77654i | −0.186134 | + | 0.270744i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1511 | − | 16.1511i | 0.561628 | − | 0.561628i | −0.368142 | − | 0.929770i | \(-0.620006\pi\) |
0.929770 | + | 0.368142i | \(0.120006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.4973 | + | 6.06059i | 0.364585 | + | 0.210493i | 0.671090 | − | 0.741376i | \(-0.265826\pi\) |
−0.306505 | + | 0.951869i | \(0.599160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.25343 | − | 12.0059i | 0.147550 | − | 0.416481i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.83274i | − | 0.202092i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6825 | − | 21.9668i | 0.438897 | − | 0.760192i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.3974 | − | 5.38717i | −0.774168 | − | 0.186208i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.4519 | + | 8.69547i | 1.12036 | + | 0.300201i | 0.771031 | − | 0.636798i | \(-0.219741\pi\) |
0.349334 | + | 0.936998i | \(0.386408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.9458 | − | 20.6907i | −0.411924 | − | 0.713473i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.06313 | − | 13.4841i | 0.0366163 | − | 0.464416i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.9686 | − | 18.2414i | 0.893348 | − | 0.627522i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2185 | + | 45.5999i | 0.419831 | + | 1.56683i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.5370 | − | 3.24774i | 0.601869 | − | 0.111462i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.28102 | + | 27.1731i | −0.249590 | + | 0.931483i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0421 | + | 14.0421i | 0.480792 | + | 0.480792i | 0.905385 | − | 0.424592i | \(-0.139583\pi\) |
−0.424592 | + | 0.905385i | \(0.639583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 55.6292 | − | 21.3360i | 1.90248 | − | 0.729677i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.0059 | 0.990824 | 0.495412 | − | 0.868658i | \(-0.335017\pi\) | ||||
0.495412 | + | 0.868658i | \(0.335017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0160 | 0.375859 | 0.187930 | − | 0.982182i | \(-0.439822\pi\) | ||||
0.187930 | + | 0.982182i | \(0.439822\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.1726 | − | 21.2835i | −0.619320 | − | 0.725338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.8394 | − | 21.8394i | −0.743422 | − | 0.743422i | 0.229813 | − | 0.973235i | \(-0.426189\pi\) |
−0.973235 | + | 0.229813i | \(0.926189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.41108 | + | 31.3906i | −0.285985 | + | 1.06731i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.85599 | + | 15.4217i | 0.0969946 | + | 0.523749i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.547762 | − | 2.04428i | −0.0185816 | − | 0.0693473i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.62261 | + | 5.32892i | 0.258282 | + | 0.180563i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.83878 | − | 8.61550i | 0.129923 | − | 0.291590i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.9516 | − | 18.9688i | −0.370233 | − | 0.641263i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.5387 | + | 13.8098i | 1.74034 | + | 0.466322i | 0.982522 | − | 0.186146i | \(-0.0595996\pi\) |
0.757816 | + | 0.652468i | \(0.226266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.1616 | − | 21.0564i | 1.48954 | − | 0.710214i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.5586 | − | 40.8048i | 0.793711 | − | 1.37475i | −0.129943 | − | 0.991521i | \(-0.541480\pi\) |
0.923654 | − | 0.383226i | \(-0.125187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.4475i | − | 0.721765i | −0.932611 | − | 0.360882i | \(-0.882476\pi\) | ||
0.932611 | − | 0.360882i | \(-0.117524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.03433 | − | 2.84638i | −0.270071 | − | 0.0956801i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.6954 | − | 12.5259i | −0.728461 | − | 0.420577i | 0.0893977 | − | 0.995996i | \(-0.471506\pi\) |
−0.817859 | + | 0.575419i | \(0.804839\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93481 | − | 1.93481i | 0.0648914 | − | 0.0648914i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.70415 | + | 51.0467i | −0.0905924 | + | 1.71013i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 95.4501 | − | 55.1082i | 3.19412 | − | 1.84412i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.06340 | + | 0.284938i | −0.0355456 | + | 0.00952442i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.7918 | − | 14.6483i | −0.594052 | − | 0.489094i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.67867 | − | 2.59339i | 0.322802 | − | 0.0864944i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.50636 | − | 0.869695i | 0.0501840 | − | 0.0289738i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.52518 | + | 1.04854i | 0.0507548 | + | 0.0348933i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.988730 | − | 0.988730i | 0.0328665 | − | 0.0328665i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.8693 | − | 14.3583i | −0.825772 | − | 0.476760i | 0.0266307 | − | 0.999645i | \(-0.491522\pi\) |
−0.852403 | + | 0.522886i | \(0.824856\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.13624 | − | 2.54114i | −0.104022 | − | 0.0842843i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.6397i | − | 1.01514i | −0.861611 | − | 0.507569i | \(-0.830544\pi\) | ||
0.861611 | − | 0.507569i | \(-0.169456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0459 | − | 34.7205i | 0.663423 | − | 1.14908i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.43028 | − | 5.09703i | −0.0803424 | − | 0.168503i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.3997 | + | 4.12633i | 0.508542 | + | 0.136263i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.08612 | + | 8.80943i | 0.167776 | + | 0.290596i | 0.937638 | − | 0.347615i | \(-0.113008\pi\) |
−0.769862 | + | 0.638211i | \(0.779675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.176318 | − | 0.0139016i | −0.00580989 | − | 0.000458074i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.6952 | + | 22.8913i | 0.352037 | + | 0.753475i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.89264 | + | 7.06342i | 0.0622296 | + | 0.232244i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.7832 | − | 4.72581i | −0.978208 | − | 0.155216i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.27665 | + | 23.4248i | −0.205930 | + | 0.768542i | 0.783234 | + | 0.621727i | \(0.213569\pi\) |
−0.989164 | + | 0.146815i | \(0.953098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9042 | + | 11.9042i | 0.390145 | + | 0.390145i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.3656 | + | 22.5119i | −0.863171 | + | 0.737007i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39.0817 | −1.27811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1432 | 0.527376 | 0.263688 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263688 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.825499 | + | 0.704841i | −0.0269391 | + | 0.0230016i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.888058 | + | 0.888058i | 0.0289499 | + | 0.0289499i | 0.721434 | − | 0.692484i | \(-0.243484\pi\) |
−0.692484 | + | 0.721434i | \(0.743484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.95011 | − | 25.9382i | 0.226327 | − | 0.844663i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.7474 | + | 13.4503i | 0.805034 | + | 0.437539i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.622237 | + | 2.32222i | 0.0202200 | + | 0.0754620i | 0.975299 | − | 0.220891i | \(-0.0708964\pi\) |
−0.955079 | + | 0.296352i | \(0.904230\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.2916 | − | 2.97429i | −1.11315 | − | 0.0965496i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35.2836 | − | 2.78189i | −1.14415 | − | 0.0902090i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.06072 | + | 10.4975i | 0.196326 | + | 0.340046i | 0.947334 | − | 0.320246i | \(-0.103766\pi\) |
−0.751008 | + | 0.660293i | \(0.770432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4525 | + | 5.74819i | 0.694188 | + | 0.186007i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.56959 | − | 20.0703i | −0.309341 | − | 0.648782i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3565 | − | 23.1342i | 0.431305 | − | 0.747042i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.3457i | 0.365991i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.2153 | + | 34.8229i | −0.909225 | + | 1.12215i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.5732 | − | 17.6515i | −0.984187 | − | 0.568220i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.7092 | − | 10.7092i | 0.344386 | − | 0.344386i | −0.513628 | − | 0.858013i | \(-0.671699\pi\) |
0.858013 | + | 0.513628i | \(0.171699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32.7297 | + | 22.5013i | 1.05143 | + | 0.722846i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.1662 | − | 5.86945i | 0.326248 | − | 0.188360i | −0.327926 | − | 0.944703i | \(-0.606350\pi\) |
0.654174 | + | 0.756344i | \(0.273016\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.99516 | + | 1.33845i | −0.160137 | + | 0.0429087i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.90908 | − | 0.985156i | −0.189242 | − | 0.0315502i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.0380 | − | 4.29736i | 0.513100 | − | 0.137485i | 0.00702677 | − | 0.999975i | \(-0.497763\pi\) |
0.506073 | + | 0.862491i | \(0.331097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.2429 | − | 23.8116i | 1.31813 | − | 0.761021i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.8727 | + | 20.4827i | 0.474850 | + | 0.653963i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.9952 | + | 25.9952i | −0.829118 | + | 0.829118i | −0.987395 | − | 0.158277i | \(-0.949406\pi\) |
0.158277 | + | 0.987395i | \(0.449406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6178 | + | 7.86223i | 0.433899 | + | 0.250512i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 49.1132 | + | 17.3997i | 1.56329 | + | 0.553838i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.77591i | 0.0564706i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1294 | − | 21.0088i | 0.385304 | − | 0.667366i | −0.606508 | − | 0.795078i | \(-0.707430\pi\) |
0.991811 | + | 0.127712i | \(0.0407634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.6554 | + | 6.98771i | −0.465074 | + | 0.221748i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.86047 | + | 0.498512i | 0.0589809 | + | 0.0158039i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.5907 | − | 47.7884i | −0.873805 | − | 1.51347i | −0.858030 | − | 0.513599i | \(-0.828312\pi\) |
−0.0157748 | − | 0.999876i | \(-0.505021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.7210 | + | 27.2784i | 0.908693 | + | 0.863050i |
(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 | 624.2.cn.f.305.4 | 56 | ||
3.2 | odd | 2 | inner | 624.2.cn.f.305.6 | 56 | ||
4.3 | odd | 2 | 312.2.bp.a.305.11 | yes | 56 | ||
12.11 | even | 2 | 312.2.bp.a.305.9 | yes | 56 | ||
13.11 | odd | 12 | inner | 624.2.cn.f.401.6 | 56 | ||
39.11 | even | 12 | inner | 624.2.cn.f.401.4 | 56 | ||
52.11 | even | 12 | 312.2.bp.a.89.9 | ✓ | 56 | ||
156.11 | odd | 12 | 312.2.bp.a.89.11 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bp.a.89.9 | ✓ | 56 | 52.11 | even | 12 | ||
312.2.bp.a.89.11 | yes | 56 | 156.11 | odd | 12 | ||
312.2.bp.a.305.9 | yes | 56 | 12.11 | even | 2 | ||
312.2.bp.a.305.11 | yes | 56 | 4.3 | odd | 2 | ||
624.2.cn.f.305.4 | 56 | 1.1 | even | 1 | trivial | ||
624.2.cn.f.305.6 | 56 | 3.2 | odd | 2 | inner | ||
624.2.cn.f.401.4 | 56 | 39.11 | even | 12 | inner | ||
624.2.cn.f.401.6 | 56 | 13.11 | odd | 12 | inner |