Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(257,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bs (of order \(6\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.15 | ||
Character | \(\chi\) | \(=\) | 504.257 |
Dual form | 504.2.bs.a.353.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.690387 | + | 1.58851i | 0.398595 | + | 0.917127i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.10442 | + | 1.91291i | 0.493912 | + | 0.855480i | 0.999975 | − | 0.00701597i | \(-0.00223327\pi\) |
−0.506064 | + | 0.862496i | \(0.668900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.234181 | + | 2.63537i | 0.0885120 | + | 0.996075i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.04673 | + | 2.19337i | −0.682244 | + | 0.731125i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.157541 | + | 0.0909565i | 0.0475005 | + | 0.0274244i | 0.523562 | − | 0.851987i | \(-0.324603\pi\) |
−0.476062 | + | 0.879412i | \(0.657936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50424 | − | 1.44582i | −0.694551 | − | 0.400999i | 0.110763 | − | 0.993847i | \(-0.464670\pi\) |
−0.805315 | + | 0.592847i | \(0.798004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.27620 | + | 3.07503i | −0.587713 | + | 0.793970i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.98511 | − | 3.43832i | −0.481461 | − | 0.833915i | 0.518313 | − | 0.855191i | \(-0.326560\pi\) |
−0.999774 | + | 0.0212765i | \(0.993227\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.867067 | + | 0.500601i | 0.198919 | + | 0.114846i | 0.596151 | − | 0.802872i | \(-0.296696\pi\) |
−0.397232 | + | 0.917718i | \(0.630029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.02463 | + | 2.19142i | −0.878247 | + | 0.478208i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.86112 | − | 2.80657i | 1.01361 | − | 0.585210i | 0.101365 | − | 0.994849i | \(-0.467679\pi\) |
0.912247 | + | 0.409640i | \(0.134346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0605124 | − | 0.104811i | 0.0121025 | − | 0.0209621i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.89724 | − | 1.73697i | −0.942473 | − | 0.334281i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.703311 | − | 0.406057i | 0.130602 | − | 0.0754028i | −0.433276 | − | 0.901261i | \(-0.642642\pi\) |
0.563877 | + | 0.825859i | \(0.309309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.96637i | 1.43080i | 0.698714 | + | 0.715401i | \(0.253756\pi\) | ||||
−0.698714 | + | 0.715401i | \(0.746244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0357208 | + | 0.313051i | −0.00621820 | + | 0.0544952i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.78259 | + | 3.35852i | −0.808405 | + | 0.567693i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.25614 | − | 2.17569i | 0.206507 | − | 0.357681i | −0.744105 | − | 0.668063i | \(-0.767124\pi\) |
0.950612 | + | 0.310382i | \(0.100457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.567810 | − | 4.97619i | 0.0909224 | − | 0.796828i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.612906 | − | 1.06158i | 0.0957198 | − | 0.165792i | −0.814189 | − | 0.580600i | \(-0.802818\pi\) |
0.909909 | + | 0.414808i | \(0.136151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.47716 | + | 9.48671i | 0.835259 | + | 1.44671i | 0.893820 | + | 0.448426i | \(0.148015\pi\) |
−0.0585613 | + | 0.998284i | \(0.518651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.45618 | − | 1.49281i | −0.962431 | − | 0.222535i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.15102 | 1.04308 | 0.521542 | − | 0.853226i | \(-0.325357\pi\) | ||||
0.521542 | + | 0.853226i | \(0.325357\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.89032 | + | 1.23430i | −0.984331 | + | 0.176329i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.09131 | − | 5.52715i | 0.572898 | − | 0.773955i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.75586 | − | 1.01374i | 0.241186 | − | 0.139249i | −0.374536 | − | 0.927212i | \(-0.622198\pi\) |
0.615722 | + | 0.787964i | \(0.288865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.401817i | 0.0541810i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.196598 | + | 1.72295i | −0.0260401 | + | 0.228211i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.55821 | −0.853806 | −0.426903 | − | 0.904297i | \(-0.640396\pi\) | ||||
−0.426903 | + | 0.904297i | \(0.640396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.05143i | 1.03088i | 0.856926 | + | 0.515440i | \(0.172372\pi\) | ||||
−0.856926 | + | 0.515440i | \(0.827628\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.25965 | − | 4.88024i | −0.788642 | − | 0.614852i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.38719i | − | 0.792233i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.89011 | 0.841761 | 0.420880 | − | 0.907116i | \(-0.361721\pi\) | ||||
0.420880 | + | 0.907116i | \(0.361721\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.81431 | + | 5.78431i | 0.940733 | + | 0.696350i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.4168i | − | 1.35492i | −0.735560 | − | 0.677460i | \(-0.763081\pi\) | ||
0.735560 | − | 0.677460i | \(-0.236919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1861 | + | 5.88094i | −1.19219 | + | 0.688312i | −0.958803 | − | 0.284072i | \(-0.908315\pi\) |
−0.233388 | + | 0.972384i | \(0.574981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.208270 | + | 0.0237647i | 0.0240489 | + | 0.00274411i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.202811 | + | 0.436479i | −0.0231124 | + | 0.0497414i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7100 | 1.42999 | 0.714994 | − | 0.699130i | \(-0.246429\pi\) | ||||
0.714994 | + | 0.699130i | \(0.246429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.621788 | − | 8.97850i | −0.0690875 | − | 0.997611i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.19085 | + | 12.4549i | 0.789298 | + | 1.36710i | 0.926397 | + | 0.376547i | \(0.122889\pi\) |
−0.137099 | + | 0.990557i | \(0.543778\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.38480 | − | 7.59470i | 0.475598 | − | 0.823760i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.13058 | + | 0.836880i | 0.121211 | + | 0.0897230i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.11375 | − | 12.3214i | 0.754055 | − | 1.30606i | −0.191787 | − | 0.981437i | \(-0.561428\pi\) |
0.945843 | − | 0.324626i | \(-0.105238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.22383 | − | 6.93818i | 0.337949 | − | 0.727319i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.6547 | + | 5.49988i | −1.31223 | + | 0.570311i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.21150i | 0.226895i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.01040 | − | 1.73805i | 0.305659 | − | 0.176473i | −0.339323 | − | 0.940670i | \(-0.610198\pi\) |
0.644982 | + | 0.764197i | \(0.276865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.521946 | + | 0.159384i | −0.0524576 | + | 0.0160187i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.75282 | − | 8.23212i | 0.472923 | − | 0.819126i | −0.526597 | − | 0.850115i | \(-0.676532\pi\) |
0.999520 | + | 0.0309887i | \(0.00986560\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.26167 | − | 4.19253i | 0.715514 | − | 0.413102i | −0.0975856 | − | 0.995227i | \(-0.531112\pi\) |
0.813099 | + | 0.582125i | \(0.197779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.63688 | − | 5.27852i | −0.842873 | − | 0.515130i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7310 | − | 7.35026i | −1.23075 | − | 0.710576i | −0.263567 | − | 0.964641i | \(-0.584899\pi\) |
−0.967187 | + | 0.254065i | \(0.918232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.35648 | + | 14.4738i | 0.800405 | + | 1.38634i | 0.919350 | + | 0.393442i | \(0.128716\pi\) |
−0.118944 | + | 0.992901i | \(0.537951\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.32333 | + | 0.493315i | 0.410352 | + | 0.0468234i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.19493 | − | 0.689894i | −0.112410 | − | 0.0648998i | 0.442741 | − | 0.896650i | \(-0.354006\pi\) |
−0.555151 | + | 0.831750i | \(0.687339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7374 | + | 6.19926i | 1.00127 | + | 0.578084i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.29674 | − | 2.53353i | 0.767034 | − | 0.234225i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.59636 | − | 6.03669i | 0.788027 | − | 0.553383i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.48345 | − | 9.49762i | −0.498496 | − | 0.863420i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.10948 | + | 0.240703i | 0.190205 | + | 0.0217035i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3115 | 1.01173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.9684 | −1.06202 | −0.531012 | − | 0.847364i | \(-0.678188\pi\) | ||||
−0.531012 | + | 0.847364i | \(0.678188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.2884 | + | 15.2500i | −0.993887 | + | 1.34269i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.67698 | − | 6.36872i | −0.321259 | − | 0.556438i | 0.659489 | − | 0.751714i | \(-0.270773\pi\) |
−0.980748 | + | 0.195277i | \(0.937439\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.11622 | + | 2.40227i | −0.0967884 | + | 0.208303i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.08593 | − | 11.2863i | −0.179528 | − | 0.971373i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.2302 | − | 8.21582i | −1.21577 | − | 0.701925i | −0.251760 | − | 0.967790i | \(-0.581009\pi\) |
−0.964010 | + | 0.265865i | \(0.914343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2110 | − | 6.47266i | −0.950903 | − | 0.549004i | −0.0575417 | − | 0.998343i | \(-0.518326\pi\) |
−0.893361 | + | 0.449339i | \(0.851660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.93697 | + | 11.3595i | 0.415768 | + | 0.956639i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.263014 | − | 0.455554i | −0.0219944 | − | 0.0380953i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.55350 | + | 0.896914i | 0.129011 | + | 0.0744847i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.71769 | − | 10.0932i | −0.554066 | − | 0.832473i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1947 | − | 7.61797i | 1.08095 | − | 0.624088i | 0.149799 | − | 0.988716i | \(-0.452137\pi\) |
0.931153 | + | 0.364628i | \(0.118804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.83125 | − | 11.8321i | 0.555919 | − | 0.962880i | −0.441912 | − | 0.897058i | \(-0.645700\pi\) |
0.997831 | − | 0.0658217i | \(-0.0209669\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.6045 | + | 2.68321i | 0.938169 | + | 0.216925i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2390 | + | 8.79822i | −1.22402 | + | 0.706690i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.8151i | − | 0.942951i | −0.881879 | − | 0.471475i | \(-0.843722\pi\) | ||
0.881879 | − | 0.471475i | \(-0.156278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.82257 | + | 2.08932i | 0.223844 | + | 0.165694i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.53471 | + | 12.1536i | 0.672630 | + | 0.957836i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.35998 | + | 7.55170i | −0.341500 | + | 0.591495i | −0.984711 | − | 0.174194i | \(-0.944268\pi\) |
0.643212 | + | 0.765688i | \(0.277601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.638290 | + | 0.277409i | −0.0496908 | + | 0.0215963i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.89862 | + | 15.4129i | −0.688596 | + | 1.19268i | 0.283696 | + | 0.958914i | \(0.408439\pi\) |
−0.972292 | + | 0.233769i | \(0.924894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.31918 | − | 4.01695i | −0.178399 | − | 0.308996i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.87266 | + | 0.877207i | −0.219678 | + | 0.0670817i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.1203 | 1.45369 | 0.726845 | − | 0.686802i | \(-0.240986\pi\) | ||||
0.726845 | + | 0.686802i | \(0.240986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.290385 | + | 0.134928i | 0.0219511 | + | 0.0101996i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.52771 | − | 10.4178i | −0.340323 | − | 0.783049i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.31891 | − | 3.07088i | 0.397554 | − | 0.229528i | −0.287874 | − | 0.957668i | \(-0.592948\pi\) |
0.685428 | + | 0.728140i | \(0.259615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.1208i | − | 0.826604i | −0.910594 | − | 0.413302i | \(-0.864375\pi\) | ||
0.910594 | − | 0.413302i | \(-0.135625\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7898 | + | 5.55861i | −0.945448 | + | 0.410904i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.54920 | 0.407986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.722236i | − | 0.0528151i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.43073 | − | 13.3128i | 0.249549 | − | 0.968362i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 14.9352i | − | 1.08067i | −0.841450 | − | 0.540336i | \(-0.818297\pi\) | ||
0.841450 | − | 0.540336i | \(-0.181703\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4277 | −0.894569 | −0.447284 | − | 0.894392i | \(-0.647609\pi\) | ||||
−0.447284 | + | 0.894392i | \(0.647609\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.1461 | − | 4.40963i | 0.726578 | − | 0.315780i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1512i | 1.15073i | 0.817897 | + | 0.575364i | \(0.195140\pi\) | ||||
−0.817897 | + | 0.575364i | \(0.804860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.5762 | + | 12.4571i | −1.52950 | + | 0.883057i | −0.530117 | + | 0.847925i | \(0.677852\pi\) |
−0.999383 | + | 0.0351325i | \(0.988815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.75684 | + | 10.9450i | 0.335522 | + | 0.772001i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.23481 | + | 1.75839i | 0.0866667 | + | 0.123415i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.70762 | 0.189108 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.79354 | + | 16.4065i | −0.263669 | + | 1.14033i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0910659 | + | 0.157731i | 0.00629916 | + | 0.0109105i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.78631 | − | 10.0222i | 0.398346 | − | 0.689955i | −0.595176 | − | 0.803595i | \(-0.702918\pi\) |
0.993522 | + | 0.113640i | \(0.0362510\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.1356 | − | 7.88198i | 1.24263 | − | 0.540065i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0982 | + | 20.9546i | −0.825088 | + | 1.42909i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.9943 | + | 1.86557i | −1.42519 | + | 0.126643i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3743 | − | 12.1206i | −1.10647 | − | 0.819033i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.4805i | 0.772262i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9653 | + | 8.06285i | −0.935183 | + | 0.539928i | −0.888447 | − | 0.458979i | \(-0.848215\pi\) |
−0.0467358 | + | 0.998907i | \(0.514882\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.106036 | + | 0.347246i | 0.00706909 | + | 0.0231497i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.90180 | + | 17.1504i | −0.657206 | + | 1.13831i | 0.324130 | + | 0.946012i | \(0.394928\pi\) |
−0.981336 | + | 0.192301i | \(0.938405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5101 | − | 7.80006i | 0.892772 | − | 0.515442i | 0.0179241 | − | 0.999839i | \(-0.494294\pi\) |
0.874848 | + | 0.484397i | \(0.160961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.833370 | − | 0.0208270i | −0.0548317 | − | 0.00137031i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6450 | + | 6.14590i | 0.697378 | + | 0.402631i | 0.806370 | − | 0.591411i | \(-0.201429\pi\) |
−0.108992 | + | 0.994043i | \(0.534762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.89773 | + | 13.6793i | 0.515191 | + | 0.892337i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.77483 | + | 20.1900i | 0.569987 | + | 1.31148i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8058 | − | 7.97079i | −0.893024 | − | 0.515588i | −0.0180934 | − | 0.999836i | \(-0.505760\pi\) |
−0.874930 | + | 0.484249i | \(0.839093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9156 | + | 10.3436i | 1.15405 | + | 0.666290i | 0.949870 | − | 0.312644i | \(-0.101215\pi\) |
0.204178 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8332 | − | 7.18636i | 0.887398 | − | 0.461005i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.97092 | − | 11.8174i | −0.637019 | − | 0.754985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.44756 | − | 2.50725i | −0.0921062 | − | 0.159533i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.8203 | + | 20.0215i | −0.939198 | + | 1.26881i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.66566 | −0.483852 | −0.241926 | − | 0.970295i | \(-0.577779\pi\) | ||||
−0.241926 | + | 0.970295i | \(0.577779\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.02110 | 0.0641961 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.0915 | + | 1.72202i | 0.945064 | + | 0.107837i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.96487 | − | 10.3315i | −0.372078 | − | 0.644459i | 0.617807 | − | 0.786330i | \(-0.288021\pi\) |
−0.989885 | + | 0.141871i | \(0.954688\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.02791 | + | 2.80087i | 0.374556 | + | 0.174038i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.548853 | + | 2.37371i | −0.0339732 | + | 0.146929i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.69006 | + | 3.86251i | 0.412527 | + | 0.238172i | 0.691875 | − | 0.722018i | \(-0.256785\pi\) |
−0.279348 | + | 0.960190i | \(0.590118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.87841 | + | 2.23920i | 0.238249 | + | 0.137553i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.4839 | + | 2.79374i | 1.49839 | + | 0.170974i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.98739 | + | 8.63841i | 0.304086 | + | 0.526693i | 0.977058 | − | 0.212976i | \(-0.0683155\pi\) |
−0.672971 | + | 0.739669i | \(0.734982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.61508 | + | 2.08717i | 0.219600 | + | 0.126786i | 0.605765 | − | 0.795643i | \(-0.292867\pi\) |
−0.386165 | + | 0.922430i | \(0.626200\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.2471 | + | 0.331061i | 0.801749 | + | 0.0200367i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0190664 | − | 0.0110080i | 0.00114975 | − | 0.000663807i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.22504 | + | 3.85387i | −0.133689 | + | 0.231557i | −0.925096 | − | 0.379733i | \(-0.876016\pi\) |
0.791407 | + | 0.611290i | \(0.209349\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.4732 | − | 16.3050i | −1.04610 | − | 0.976156i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.5472 | + | 14.1723i | −1.46436 | + | 0.845451i | −0.999209 | − | 0.0397785i | \(-0.987335\pi\) |
−0.465155 | + | 0.885229i | \(0.654001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5963i | 0.689329i | 0.938726 | + | 0.344664i | \(0.112007\pi\) | ||||
−0.938726 | + | 0.344664i | \(0.887993\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.51299 | + | 1.52679i | −0.208091 | + | 0.0904392i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.94119 | + | 1.36663i | 0.173613 | + | 0.0806696i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.618645 | − | 1.07152i | 0.0363909 | − | 0.0630308i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.83925 | + | 3.58212i | 0.283682 | + | 0.209987i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.4199 | + | 24.9760i | −0.842418 | + | 1.45911i | 0.0454266 | + | 0.998968i | \(0.485535\pi\) |
−0.887845 | + | 0.460143i | \(0.847798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.24302 | − | 12.5453i | −0.421705 | − | 0.730414i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.613528 | − | 0.719081i | −0.0356005 | − | 0.0417253i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2312 | −0.938675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.7183 | + | 16.6559i | −1.36710 | + | 0.960031i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.3581 | + | 1.86655i | 0.939748 | + | 0.107230i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.4017 | + | 8.89216i | −0.881898 | + | 0.509164i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.8117i | − | 0.617059i | −0.951215 | − | 0.308529i | \(-0.900163\pi\) | ||
0.951215 | − | 0.308529i | \(-0.0998368\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6732 | + | 8.64077i | 0.664067 | + | 0.491556i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1832 | 0.974370 | 0.487185 | − | 0.873299i | \(-0.338024\pi\) | ||||
0.487185 | + | 0.873299i | \(0.338024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.14399i | − | 0.516849i | −0.966031 | − | 0.258425i | \(-0.916797\pi\) | ||
0.966031 | − | 0.258425i | \(-0.0832033\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.42218 | − | 17.3640i | 0.136474 | − | 0.978351i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.13698i | − | 0.0638589i | −0.999490 | − | 0.0319295i | \(-0.989835\pi\) | ||
0.999490 | − | 0.0319295i | \(-0.0101652\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.147734 | 0.00827152 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.88663 | − | 25.2979i | 0.161116 | − | 1.41199i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.97500i | − | 0.221175i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.303075 | + | 0.174981i | −0.0168116 | + | 0.00970618i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.2226 | + | 23.2669i | −0.952414 | + | 1.28666i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.67463 | + | 18.8456i | 0.0923254 | + | 1.03899i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.04788 | −0.332421 | −0.166211 | − | 0.986090i | \(-0.553153\pi\) | ||||
−0.166211 | + | 0.986090i | \(0.553153\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.20113 | + | 7.20823i | 0.120621 | + | 0.395008i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.60957 | + | 13.1802i | 0.415755 | + | 0.720110i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.6873 | − | 30.6353i | 0.963490 | − | 1.66881i | 0.249871 | − | 0.968279i | \(-0.419612\pi\) |
0.713619 | − | 0.700534i | \(-0.247055\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.270938 | − | 2.37446i | 0.0147153 | − | 0.128963i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.724593 | + | 1.25503i | −0.0392389 | + | 0.0679638i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.86643 | − | 17.8695i | −0.262762 | − | 0.964861i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.43460 | + | 21.3364i | −0.131074 | + | 1.14871i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 23.2102i | − | 1.24599i | −0.782225 | − | 0.622995i | \(-0.785916\pi\) | ||
0.782225 | − | 0.622995i | \(-0.214084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7248 | + | 7.34667i | −0.681144 | + | 0.393258i | −0.800286 | − | 0.599619i | \(-0.795319\pi\) |
0.119142 | + | 0.992877i | \(0.461986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.75250 | + | 11.4303i | 0.520550 | + | 0.610107i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.73122 | + | 11.6588i | −0.358267 | + | 0.620536i | −0.987671 | − | 0.156542i | \(-0.949965\pi\) |
0.629405 | + | 0.777078i | \(0.283299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.8392 | − | 12.6089i | 1.15911 | − | 0.669211i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.5242 | + | 9.48774i | 0.821626 | + | 0.502145i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5004 | − | 7.79444i | −0.712522 | − | 0.411375i | 0.0994721 | − | 0.995040i | \(-0.468285\pi\) |
−0.811994 | + | 0.583666i | \(0.801618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.99880 | − | 15.5864i | −0.473621 | − | 0.820335i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.3014 | − | 15.2676i | 0.593168 | − | 0.801339i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.4994 | − | 12.9901i | −1.17767 | − | 0.679930i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.50847 | − | 4.33501i | −0.391939 | − | 0.226286i | 0.291061 | − | 0.956704i | \(-0.405992\pi\) |
−0.683000 | + | 0.730419i | \(0.739325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.07400 | + | 3.51711i | 0.0559101 | + | 0.183093i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.08278 | + | 4.38993i | 0.160050 | + | 0.227914i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0489 | + | 20.8693i | 0.623868 | + | 1.08057i | 0.988759 | + | 0.149521i | \(0.0477730\pi\) |
−0.364891 | + | 0.931050i | \(0.618894\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.80933 | + | 17.9685i | 0.403272 | + | 0.927888i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.34835 | −0.120946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0778 | 0.517662 | 0.258831 | − | 0.965923i | \(-0.416663\pi\) | ||||
0.258831 | + | 0.965923i | \(0.416663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.26283 | − | 19.0119i | −0.423318 | − | 0.974011i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.35238 | + | 4.07444i | 0.120201 | + | 0.208194i | 0.919847 | − | 0.392278i | \(-0.128313\pi\) |
−0.799646 | + | 0.600472i | \(0.794979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.05893 | + | 0.0940978i | −0.0539683 | + | 0.00479567i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.0182 | − | 7.40329i | −1.62758 | − | 0.376330i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6198 | − | 10.7502i | −0.944062 | − | 0.545055i | −0.0528309 | − | 0.998603i | \(-0.516824\pi\) |
−0.891231 | + | 0.453549i | \(0.850158\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.2997 | − | 11.1427i | −0.976030 | − | 0.563511i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.57823 | − | 10.2378i | 0.382271 | − | 0.516429i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0372 | + | 24.3131i | 0.706288 | + | 1.22333i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7548 | − | 13.7148i | −1.19222 | − | 0.688327i | −0.233408 | − | 0.972379i | \(-0.574988\pi\) |
−0.958809 | + | 0.284052i | \(0.908321\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.58666 | − | 0.114626i | −0.229620 | − | 0.00573849i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.3138 | − | 14.6150i | 1.26411 | − | 0.729836i | 0.290245 | − | 0.956952i | \(-0.406263\pi\) |
0.973868 | + | 0.227116i | \(0.0729298\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5180 | − | 19.9497i | 0.573751 | − | 0.993766i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.4884 | − | 11.1055i | 0.819313 | − | 0.551835i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.395786 | − | 0.228507i | 0.0196184 | − | 0.0113267i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 31.5884i | − | 1.56195i | −0.624564 | − | 0.780974i | \(-0.714723\pi\) | ||
0.624564 | − | 0.780974i | \(-0.285277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.22655 | − | 28.2770i | 0.159154 | − | 1.39480i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.53581 | − | 17.2833i | −0.0755721 | − | 0.850455i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.8834 | + | 27.5109i | −0.779687 | + | 1.35046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.54197 | − | 22.2774i | 0.124481 | − | 1.09093i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.80176 | − | 11.7810i | 0.332288 | − | 0.575539i | −0.650672 | − | 0.759359i | \(-0.725513\pi\) |
0.982960 | + | 0.183819i | \(0.0588462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.8629 | − | 25.7432i | −0.724372 | − | 1.25465i | −0.959232 | − | 0.282620i | \(-0.908797\pi\) |
0.234860 | − | 0.972029i | \(-0.424537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.6362 | + | 15.6849i | −0.711637 | + | 0.762624i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.480496 | −0.0233075 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.2185 | + | 1.88549i | −1.02683 | + | 0.0912453i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.542071 | − | 0.732310i | 0.0261714 | − | 0.0353562i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.6467 | − | 12.4977i | 1.04268 | − | 0.601994i | 0.122091 | − | 0.992519i | \(-0.461040\pi\) |
0.920592 | + | 0.390525i | \(0.127707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.7778i | 0.902401i | 0.892423 | + | 0.451201i | \(0.149004\pi\) | ||||
−0.892423 | + | 0.451201i | \(0.850996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.352240 | + | 3.08697i | −0.0168886 | + | 0.148009i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.61988 | 0.268836 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.10574i | − | 0.100502i | −0.998737 | − | 0.0502508i | \(-0.983998\pi\) | ||
0.998737 | − | 0.0502508i | \(-0.0160021\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.3953 | − | 17.6393i | 0.542635 | − | 0.839969i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.4467i | 0.638874i | 0.947608 | + | 0.319437i | \(0.103494\pi\) | ||||
−0.947608 | + | 0.319437i | \(0.896506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.4263 | 1.48975 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.2107 | + | 15.7006i | 1.00323 | + | 0.742612i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.42429i | − | 0.350374i | −0.984535 | − | 0.175187i | \(-0.943947\pi\) | ||
0.984535 | − | 0.175187i | \(-0.0560530\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.193116 | − | 0.111496i | 0.00909347 | − | 0.00525012i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.5116 | + | 2.68280i | 1.10467 | + | 0.126049i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.8326 | − | 1.49576i | 0.789124 | − | 0.0701222i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.278018 | −0.0130051 | −0.00650257 | − | 0.999979i | \(-0.502070\pi\) | ||||
−0.00650257 | + | 0.999979i | \(0.502070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.74930 | + | 20.2863i | 0.175002 | + | 0.946886i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.98573 | + | 6.90348i | 0.185634 | + | 0.321527i | 0.943790 | − | 0.330546i | \(-0.107233\pi\) |
−0.758156 | + | 0.652073i | \(0.773900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4572 | − | 21.5765i | 0.578936 | − | 1.00275i | −0.416666 | − | 0.909060i | \(-0.636801\pi\) |
0.995602 | − | 0.0936870i | \(-0.0298653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.4969 | − | 18.1331i | −1.13601 | − | 0.840901i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.4485 | + | 31.9538i | −0.853695 | + | 1.47864i | 0.0241548 | + | 0.999708i | \(0.492311\pi\) |
−0.877850 | + | 0.478935i | \(0.841023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.61353 | + | 18.1580i | 0.0745059 | + | 0.838457i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.7685 | − | 8.15702i | 0.864806 | − | 0.375856i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.99273i | 0.0916259i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.104937 | − | 0.0605852i | 0.00481483 | − | 0.00277984i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.37024 | + | 5.92612i | −0.0627392 | + | 0.271338i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.70584 | − | 2.95461i | 0.0779420 | − | 0.135000i | −0.824420 | − | 0.565979i | \(-0.808498\pi\) |
0.902362 | + | 0.430979i | \(0.141832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.29133 | + | 3.63230i | −0.286860 | + | 0.165619i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.4138 | + | 21.9482i | −0.610350 | + | 0.998676i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.64948 | + | 3.83908i | 0.301938 | + | 0.174324i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.17122 | − | 2.02861i | −0.0530729 | − | 0.0919249i | 0.838268 | − | 0.545258i | \(-0.183568\pi\) |
−0.891341 | + | 0.453333i | \(0.850235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.0060 | − | 1.71227i | −0.678596 | − | 0.0774315i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.65365 | + | 2.68678i | 0.210016 | + | 0.121253i | 0.601319 | − | 0.799009i | \(-0.294642\pi\) |
−0.391303 | + | 0.920262i | \(0.627975\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.79230 | − | 1.61214i | −0.125759 | − | 0.0726070i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.881335 | − | 0.822411i | −0.0396131 | − | 0.0369646i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.0873 | − | 2.67358i | 1.34960 | − | 0.119927i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6906 | + | 28.9090i | 0.747175 | + | 1.29415i | 0.949171 | + | 0.314759i | \(0.101924\pi\) |
−0.201996 | + | 0.979386i | \(0.564743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.6270 | − | 3.49471i | −1.36831 | − | 0.156132i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.01630 | −0.268254 | −0.134127 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134127 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.9964 | 0.934328 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.77982 | − | 6.45730i | 0.212279 | − | 0.286779i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.01991 | − | 8.69473i | −0.222503 | − | 0.385387i | 0.733064 | − | 0.680160i | \(-0.238090\pi\) |
−0.955568 | + | 0.294772i | \(0.904756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8838 | − | 25.4669i | −0.791133 | − | 1.12659i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.37670 | − | 3.95764i | −0.149085 | − | 0.174734i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0399 | + | 9.26062i | 0.706801 | + | 0.408072i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.12658 | + | 0.650432i | 0.0495470 | + | 0.0286059i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.2004 | + | 30.3728i | 0.579434 | + | 1.33322i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8007 | − | 18.7074i | −0.473188 | − | 0.819586i | 0.526341 | − | 0.850274i | \(-0.323564\pi\) |
−0.999529 | + | 0.0306875i | \(0.990230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.6105 | + | 6.70332i | 0.507692 | + | 0.293116i | 0.731884 | − | 0.681429i | \(-0.238641\pi\) |
−0.224193 | + | 0.974545i | \(0.571974\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0138560 | + | 0.554433i | −0.000604724 | + | 0.0241974i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.3909 | − | 15.8142i | 1.19317 | − | 0.688875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.25363 | − | 7.36750i | 0.184940 | − | 0.320326i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.4229 | − | 14.3846i | 0.582504 | − | 0.624239i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.06973 | + | 1.77231i | −0.132965 | + | 0.0767672i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 32.4711i | − | 1.40385i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.55023 | + | 6.32905i | 0.368970 | + | 0.273119i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.19778 | − | 0.432265i | −0.0515919 | − | 0.0186190i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.53805 | − | 7.86013i | 0.195106 | − | 0.337933i | −0.751829 | − | 0.659358i | \(-0.770828\pi\) |
0.946935 | + | 0.321424i | \(0.104162\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.6655 | − | 7.67767i | 0.758101 | − | 0.329480i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4581 | + | 31.9704i | −0.790659 | + | 1.36946i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.5359 | + | 23.4448i | 0.578752 | + | 1.00243i | 0.995623 | + | 0.0934620i | \(0.0297934\pi\) |
−0.416871 | + | 0.908966i | \(0.636873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.6598 | − | 16.4791i | −0.753702 | − | 0.703311i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.813090 | 0.0346388 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.97644 | + | 33.4956i | 0.126571 | + | 1.42438i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.83110 | + | 8.81497i | 0.162621 | + | 0.374175i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.8690 | − | 13.7808i | 1.01136 | − | 0.583911i | 0.0997727 | − | 0.995010i | \(-0.468188\pi\) |
0.911591 | + | 0.411099i | \(0.134855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31.6760i | − | 1.33975i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.14728 | − | 0.498623i | 0.0484382 | − | 0.0210519i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.8466 | 0.583563 | 0.291781 | − | 0.956485i | \(-0.405752\pi\) | ||||
0.291781 | + | 0.956485i | \(0.405752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.04773i | − | 0.128219i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.5160 | − | 3.74123i | 0.987580 | − | 0.157117i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.1497i | 0.509342i | 0.967028 | + | 0.254671i | \(0.0819672\pi\) | ||||
−0.967028 | + | 0.254671i | \(0.918033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.3010 | −1.93764 | −0.968819 | − | 0.247771i | \(-0.920302\pi\) | ||||
−0.968819 | + | 0.247771i | \(0.920302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.7247 | − | 10.3111i | 0.991113 | − | 0.430750i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.679329i | − | 0.0283300i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.6284 | + | 6.13630i | −0.442465 | + | 0.255457i | −0.704643 | − | 0.709562i | \(-0.748893\pi\) |
0.262178 | + | 0.965020i | \(0.415559\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.57996 | − | 19.7416i | −0.356571 | − | 0.820433i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.1393 | + | 21.8672i | −1.29188 | + | 0.907206i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.368827 | 0.0152752 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.0095 | + | 13.0729i | 0.579222 | + | 0.540496i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9875 | − | 20.7630i | −0.494778 | − | 0.856980i | 0.505204 | − | 0.863000i | \(-0.331417\pi\) |
−0.999982 | + | 0.00601986i | \(0.998084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.98798 | + | 6.90738i | −0.164322 | + | 0.284614i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.6564 | + | 11.1506i | −1.05536 | + | 0.458675i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4912 | − | 26.8315i | 0.636146 | − | 1.10184i | −0.350125 | − | 0.936703i | \(-0.613861\pi\) |
0.986271 | − | 0.165134i | \(-0.0528056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0416 | + | 9.77702i | 0.862623 | + | 0.400819i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.6841 | − | 25.6739i | −1.41953 | − | 1.05076i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 24.7558i | − | 1.01150i | −0.862681 | − | 0.505748i | \(-0.831217\pi\) | ||
0.862681 | − | 0.505748i | \(-0.168783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.67329 | + | 4.43017i | −0.313000 | + | 0.180711i | −0.648268 | − | 0.761412i | \(-0.724506\pi\) |
0.335268 | + | 0.942123i | \(0.391173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.1022 | + | 15.1126i | −0.574286 | + | 0.615432i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1121 | − | 20.9787i | 0.492426 | − | 0.852907i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2943 | + | 6.52076i | −0.458421 | + | 0.264670i | −0.711380 | − | 0.702807i | \(-0.751930\pi\) |
0.252959 | + | 0.967477i | \(0.418596\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.94073 | + | 3.17548i | −0.0786422 | + | 0.128677i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.9079 | − | 10.3391i | −0.724475 | − | 0.418276i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.90775 | + | 10.2325i | 0.238612 | + | 0.413288i | 0.960316 | − | 0.278914i | \(-0.0899743\pi\) |
−0.721704 | + | 0.692201i | \(0.756641\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.86931 | + | 4.30108i | 0.0753778 | + | 0.173436i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7906 | − | 7.96200i | −0.555188 | − | 0.320538i | 0.196024 | − | 0.980599i | \(-0.437197\pi\) |
−0.751212 | + | 0.660061i | \(0.770530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.7802 | + | 15.4616i | 1.07639 | + | 0.621453i | 0.929920 | − | 0.367762i | \(-0.119876\pi\) |
0.146468 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.6810 | + | 5.30078i | −1.15093 | + | 0.212713i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.1372 | + | 15.8619i | 1.36768 | + | 0.635494i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1901 | + | 21.1139i | 0.487605 | + | 0.844556i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.187686 | + | 0.253555i | −0.00749547 | + | 0.0101260i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.97429 | −0.397701 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.925450 | 0.0368416 | 0.0184208 | − | 0.999830i | \(-0.494136\pi\) | ||||
0.0184208 | + | 0.999830i | \(0.494136\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.9151 | + | 2.27243i | 0.791556 | + | 0.0903208i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.2181 | − | 22.8945i | −0.524546 | − | 0.908540i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.0396 | + | 6.87119i | 0.754377 | + | 0.272247i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 25.0412 | + | 23.3670i | 0.990616 | + | 0.924385i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.7464 | − | 17.1741i | −1.17491 | − | 0.678336i | −0.220080 | − | 0.975482i | \(-0.570632\pi\) |
−0.954832 | + | 0.297146i | \(0.903965\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8373 | − | 6.83426i | −0.466817 | − | 0.269517i | 0.248089 | − | 0.968737i | \(-0.420197\pi\) |
−0.714906 | + | 0.699220i | \(0.753531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41.6391 | − | 4.75124i | −1.63954 | − | 0.187080i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.1075 | − | 31.3630i | −0.711877 | − | 1.23301i | −0.964152 | − | 0.265352i | \(-0.914512\pi\) |
0.252274 | − | 0.967656i | \(-0.418822\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.03319 | − | 0.596512i | −0.0405562 | − | 0.0234151i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4577 | − | 32.0617i | −0.684221 | − | 1.25660i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.6333 | + | 18.2635i | −1.23791 | + | 0.714705i | −0.968666 | − | 0.248368i | \(-0.920106\pi\) |
−0.269240 | + | 0.963073i | \(0.586773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.12186 | − | 14.0675i | 0.317347 | − | 0.549662i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.94907 | − | 34.3786i | 0.310123 | − | 1.34124i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5178 | + | 11.2686i | −0.760305 | + | 0.438962i | −0.829405 | − | 0.558648i | \(-0.811320\pi\) |
0.0691004 | + | 0.997610i | \(0.477987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.49643i | − | 0.0582045i | −0.999576 | − | 0.0291022i | \(-0.990735\pi\) | ||
0.999576 | − | 0.0291022i | \(-0.00926484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.2369 | + | 7.92599i | −0.708262 | + | 0.307820i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.82811 | + | 0.517890i | −0.226004 | + | 0.0200829i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.27925 | − | 3.94778i | 0.0882529 | − | 0.152859i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.4494 | − | 16.6175i | −0.867942 | − | 0.642469i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.732330 | + | 1.26843i | −0.0282713 | + | 0.0489673i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.9366 | + | 24.1389i | 0.537215 | + | 0.930484i | 0.999053 | + | 0.0435197i | \(0.0138571\pi\) |
−0.461837 | + | 0.886965i | \(0.652810\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.478397 | + | 0.408174i | −0.0184135 | + | 0.0157106i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.2688 | −1.20176 | −0.600880 | − | 0.799340i | \(-0.705183\pi\) | ||||
−0.600880 | + | 0.799340i | \(0.705183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.28538 | + | 7.52648i | 0.202834 | + | 0.288840i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.0797 | − | 3.88868i | −1.30594 | − | 0.149015i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.06769 | + | 4.65788i | −0.308701 | + | 0.178229i | −0.646345 | − | 0.763045i | \(-0.723703\pi\) |
0.337644 | + | 0.941274i | \(0.390370\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.2949i | − | 1.38676i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.7177 | + | 16.0759i | 0.828581 | + | 0.613333i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.86279 | −0.223354 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.5515i | 1.84699i | 0.383615 | + | 0.923493i | \(0.374679\pi\) | ||||
−0.383615 | + | 0.923493i | \(0.625321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.542264 | − | 1.33820i | −0.0205989 | − | 0.0508338i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 28.5942i | − | 1.08464i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.86675 | −0.184341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.41365 | + | 21.1528i | −0.0912925 | + | 0.800071i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.9812i | 0.867987i | 0.900916 | + | 0.433994i | \(0.142896\pi\) | ||||
−0.900916 | + | 0.433994i | \(0.857104\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.17831 | − | 1.25765i | 0.0821564 | − | 0.0474330i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.2772 | + | 21.9896i | −0.613033 | + | 0.828177i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.8077 | + | 10.5976i | 0.857771 | + | 0.398564i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.6865 | 1.15246 | 0.576228 | − | 0.817289i | \(-0.304524\pi\) | ||||
0.576228 | + | 0.817289i | \(0.304524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −26.0140 | + | 27.8778i | −0.975600 | + | 1.04550i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.3582 | + | 38.7255i | 0.837319 | + | 1.45028i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.580956 | − | 1.00625i | 0.0217265 | − | 0.0376315i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.13032 | − | 27.4336i | 0.116904 | − | 1.02453i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.44166 | + | 4.22907i | −0.0910584 | + | 0.157718i | −0.907957 | − | 0.419064i | \(-0.862358\pi\) |
0.816898 | + | 0.576782i | \(0.195692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.7494 | + | 18.1554i | 0.474812 | + | 0.676141i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.06218 | + | 35.6003i | −0.151074 | + | 1.32399i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 0.0982859i | − | 0.00365025i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.7779 | + | 18.9243i | −1.21567 | + | 0.701865i | −0.963988 | − | 0.265946i | \(-0.914316\pi\) |
−0.251678 | + | 0.967811i | \(0.580982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.9658 | + | 17.0127i | 0.776513 | + | 0.630102i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.7456 | − | 37.6644i | 0.804289 | − | 1.39307i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1113 | + | 23.1583i | −1.48155 | + | 0.855370i | −0.999781 | − | 0.0209305i | \(-0.993337\pi\) |
−0.481764 | + | 0.876301i | \(0.660004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8882 | − | 23.9975i | 0.438504 | − | 0.885161i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.08548 | + | 0.626700i | 0.0399840 | + | 0.0230848i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.15606 | + | 8.93056i | 0.189669 | + | 0.328516i | 0.945140 | − | 0.326666i | \(-0.105925\pi\) |
−0.755471 | + | 0.655182i | \(0.772592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.98342 | − | 4.03045i | 0.109599 | − | 0.148062i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.9984 | + | 12.7008i | 0.807042 | + | 0.465946i | 0.845928 | − | 0.533298i | \(-0.179047\pi\) |
−0.0388856 | + | 0.999244i | \(0.512381\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.1450 | + | 16.8269i | 1.06779 | + | 0.616489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −42.0360 | − | 9.71963i | −1.53802 | − | 0.355623i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.3893 | − | 35.2722i | 0.598851 | − | 1.28882i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8653 | + | 46.5321i | 0.980329 | + | 1.69798i | 0.661091 | + | 0.750306i | \(0.270094\pi\) |
0.319238 | + | 0.947675i | \(0.396573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.29228 | − | 12.1770i | −0.192861 | − | 0.443754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.1783 | 1.09830 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3821 | 1.03157 | 0.515783 | − | 0.856719i | \(-0.327501\pi\) | ||||
0.515783 | + | 0.856719i | \(0.327501\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.704956 | + | 1.62203i | 0.0255883 | + | 0.0588760i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5592 | + | 20.0211i | 0.419021 | + | 0.725765i | 0.995841 | − | 0.0911059i | \(-0.0290402\pi\) |
−0.576821 | + | 0.816871i | \(0.695707\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.1870 | + | 25.4119i | −1.31006 | + | 0.919972i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.68351 | + | 25.1618i | 0.277798 | + | 0.909727i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.4233 | + | 9.48202i | 0.593013 | + | 0.342376i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.1698 | + | 13.3771i | 0.835524 | + | 0.482390i | 0.855740 | − | 0.517406i | \(-0.173102\pi\) |
−0.0202163 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.2936 | − | 16.6080i | 0.442742 | − | 0.598121i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.97203 | + | 6.87976i | 0.142864 | + | 0.247448i | 0.928574 | − | 0.371147i | \(-0.121035\pi\) |
−0.785710 | + | 0.618595i | \(0.787702\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.834960 | + | 0.482065i | 0.0299927 | + | 0.0173163i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.287626 | + | 11.5091i | −0.0103185 | + | 0.412886i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.06286 | − | 0.613643i | 0.0380809 | − | 0.0219860i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03843 | − | 1.79861i | 0.0371579 | − | 0.0643593i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.14959 | + | 0.766922i | −0.148294 | + | 0.0274076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.6013 | − | 13.0489i | 0.806676 | − | 0.465734i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.1939i | 0.434666i | 0.976097 | + | 0.217333i | \(0.0697358\pi\) | ||||
−0.976097 | + | 0.217333i | \(0.930264\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.51690 | + | 13.2939i | −0.0540031 | + | 0.473274i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.53829 | − | 3.31064i | 0.0546954 | − | 0.117713i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6410 | − | 20.1627i | 0.413382 | − | 0.715999i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.879389 | + | 7.70681i | −0.0311887 | + | 0.273332i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.30173 | − | 5.71876i | 0.116953 | − | 0.202569i | −0.801606 | − | 0.597853i | \(-0.796021\pi\) |
0.918559 | + | 0.395284i | \(0.129354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1956 | − | 24.5875i | −0.502204 | − | 0.869842i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.4655 | + | 40.8216i | 0.440445 | + | 1.44236i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.13964 | −0.0755062 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.8228 | + | 29.7488i | −0.487190 | + | 1.04851i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.2790 | + | 13.8864i | −0.361837 | + | 0.488823i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.57462 | + | 4.95056i | −0.301468 | + | 0.174052i | −0.643102 | − | 0.765780i | \(-0.722353\pi\) |
0.341634 | + | 0.939833i | \(0.389020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.1027i | − | 1.16239i | −0.813763 | − | 0.581197i | \(-0.802584\pi\) | ||
0.813763 | − | 0.581197i | \(-0.197416\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.819682 | + | 7.18355i | −0.0287475 | + | 0.251938i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.2610 | −0.674683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9675i | 0.383704i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.61971 | + | 21.2717i | 0.301197 | + | 0.743292i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4327i | 0.399004i | 0.979897 | + | 0.199502i | \(0.0639324\pi\) | ||||
−0.979897 | + | 0.199502i | \(0.936068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.9019 | −1.35603 | −0.678017 | − | 0.735047i | \(-0.737160\pi\) | ||||
−0.678017 | + | 0.735047i | \(0.737160\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0306495 | + | 0.0226874i | 0.00106708 | + | 0.000789874i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 8.05228i | − | 0.280005i | −0.990151 | − | 0.140003i | \(-0.955289\pi\) | ||
0.990151 | − | 0.140003i | \(-0.0447111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3389 | + | 6.54652i | −0.393816 | + | 0.227370i | −0.683812 | − | 0.729658i | \(-0.739679\pi\) |
0.289996 | + | 0.957028i | \(0.406346\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.65806 | − | 0.873826i | −0.265655 | − | 0.0303127i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.9220 | + | 21.2409i | 0.620960 | + | 0.735953i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.3113 | −1.36042 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.8374 | − | 39.0132i | 0.478290 | − | 1.34849i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.51797 | − | 9.55740i | −0.190501 | − | 0.329958i | 0.754915 | − | 0.655822i | \(-0.227678\pi\) |
−0.945416 | + | 0.325864i | \(0.894345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1702 | + | 24.5436i | −0.488629 | + | 0.846330i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −39.4600 | − | 29.2091i | −1.35907 | − | 1.00601i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.12271 | − | 8.87279i | 0.176227 | − | 0.305233i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.7456 | − | 16.6751i | 0.815908 | − | 0.572962i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.4209 | + | 8.00594i | −0.632202 | + | 0.274763i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 14.1017i | − | 0.483400i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.2134 | + | 11.6702i | −0.692092 | + | 0.399580i | −0.804395 | − | 0.594094i | \(-0.797511\pi\) |
0.112303 | + | 0.993674i | \(0.464177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.85064 | − | 4.52634i | −0.165888 | − | 0.154798i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.10606 | − | 15.7722i | 0.311057 | − | 0.538767i | −0.667534 | − | 0.744579i | \(-0.732650\pi\) |
0.978592 | + | 0.205812i | \(0.0659836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.9133 | − | 19.5799i | 1.15711 | − | 0.668057i | 0.206499 | − | 0.978447i | \(-0.433793\pi\) |
0.950609 | + | 0.310390i | \(0.100460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.140341 | + | 5.61562i | −0.00478282 | + | 0.191380i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.7847 | + | 13.1548i | 0.775601 | + | 0.447793i | 0.834869 | − | 0.550449i | \(-0.185543\pi\) |
−0.0592683 | + | 0.998242i | \(0.518877\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1168 | + | 36.5754i | 0.717994 | + | 1.24360i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.12923 | + | 0.242957i | 0.0723125 | + | 0.00825125i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.00235 | + | 1.15606i | 0.0679252 | + | 0.0392166i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.2545 | − | 9.96189i | −0.584646 | − | 0.337546i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.34927 | + | 10.1603i | −0.0795107 | + | 0.343872i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.64894 | + | 29.8100i | 0.0895506 | + | 1.00776i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.59833 | − | 6.23249i | −0.121507 | − | 0.210456i | 0.798855 | − | 0.601523i | \(-0.205439\pi\) |
−0.920362 | + | 0.391067i | \(0.872106\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.6299 | − | 5.66304i | −1.67397 | − | 0.191010i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.2133 | −1.25375 | −0.626874 | − | 0.779121i | \(-0.715666\pi\) | ||||
−0.626874 | + | 0.779121i | \(0.715666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.72629 | 0.327316 | 0.163658 | − | 0.986517i | \(-0.447671\pi\) | ||||
0.163658 | + | 0.986517i | \(0.447671\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.9278 | − | 20.1667i | 0.501793 | − | 0.677897i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.3493 | + | 17.9255i | 0.347496 | + | 0.601881i | 0.985804 | − | 0.167900i | \(-0.0536986\pi\) |
−0.638308 | + | 0.769781i | \(0.720365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.80277 | − | 31.5411i | −0.0940019 | − | 1.05786i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.718695 | − | 1.47104i | 0.0240772 | − | 0.0492817i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.20041 | + | 3.57981i | 0.207489 | + | 0.119794i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7486 | + | 6.78307i | 0.392713 | + | 0.226733i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.2058 | − | 25.7834i | −0.374151 | − | 0.860884i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.23480 | + | 5.60284i | 0.107887 | + | 0.186865i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.97115 | − | 4.02480i | −0.232243 | − | 0.134085i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42.8329 | − | 26.1778i | −1.42539 | − | 0.871142i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.2731 | − | 12.2821i | 0.707143 | − | 0.408269i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.495464 | + | 0.858169i | −0.0164516 | + | 0.0284950i | −0.874134 | − | 0.485685i | \(-0.838570\pi\) |
0.857682 | + | 0.514180i | \(0.171904\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.32839 | + | 27.2736i | 0.276235 | + | 0.904609i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2170 | − | 8.78552i | 0.504161 | − | 0.291077i | −0.226269 | − | 0.974065i | \(-0.572653\pi\) |
0.730430 | + | 0.682987i | \(0.239320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.61622i | 0.0865842i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.7584 | − | 18.3267i | −0.818488 | − | 0.605862i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.9228 | − | 11.1816i | 0.525818 | − | 0.369250i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.22417 | + | 15.9767i | −0.304277 | + | 0.527024i | −0.977100 | − | 0.212780i | \(-0.931748\pi\) |
0.672823 | + | 0.739804i | \(0.265082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.1746 | − | 7.46429i | 0.565921 | − | 0.245957i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.5066 | + | 28.5903i | −0.543322 | + | 0.941061i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.152024 | − | 0.263313i | −0.00499851 | − | 0.00865767i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.66690 | + | 24.5085i | −0.186125 | + | 0.804966i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.9425 | −0.687100 | −0.343550 | − | 0.939134i | \(-0.611629\pi\) | ||||
−0.343550 | + | 0.939134i | \(0.611629\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.59226 | − | 2.37908i | −0.216053 | − | 0.0779712i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.8631 | + | 27.2957i | 0.388380 | + | 0.893621i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.38157 | − | 0.797652i | 0.0451823 | − | 0.0260860i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 27.1677i | − | 0.887529i | −0.896143 | − | 0.443764i | \(-0.853643\pi\) | ||
0.896143 | − | 0.443764i | \(-0.146357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.5253 | − | 6.31290i | 0.474016 | − | 0.206014i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.85152 | −0.0929569 | −0.0464785 | − | 0.998919i | \(-0.514800\pi\) | ||||
−0.0464785 | + | 0.998919i | \(0.514800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.88064i | − | 0.224065i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 29.2551 | − | 8.14022i | 0.951670 | − | 0.264802i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 17.6279i | − | 0.572830i | −0.958106 | − | 0.286415i | \(-0.907536\pi\) | ||
0.958106 | − | 0.286415i | \(-0.0924635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.0112 | 1.10405 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.80610 | − | 0.784953i | 0.0585667 | − | 0.0254539i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.1766i | − | 1.52820i | −0.645097 | − | 0.764101i | \(-0.723183\pi\) | ||
0.645097 | − | 0.764101i | \(-0.276817\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.5697 | − | 16.4947i | 0.924493 | − | 0.533756i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.101994 | + | 0.234677i | 0.00329699 | + | 0.00758603i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.3193 | − | 39.4259i | 0.591560 | − | 1.27313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.4631 | −1.04720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.1788 | − | 12.8799i | 1.35919 | − | 0.415049i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.7255 | − | 23.7732i | −0.441838 | − | 0.765286i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.62809 | + | 6.28404i | −0.116672 | + | 0.202081i | −0.918447 | − | 0.395545i | \(-0.870556\pi\) |
0.801775 | + | 0.597626i | \(0.203889\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.31433 | − | 2.74429i | 0.202846 | − | 0.0881594i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.2653 | − | 17.7800i | 0.329429 | − | 0.570588i | −0.652970 | − | 0.757384i | \(-0.726477\pi\) |
0.982399 | + | 0.186796i | \(0.0598104\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.4324 | − | 31.0608i | 0.462683 | − | 0.995764i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.487198 | − | 0.360634i | −0.0156028 | − | 0.0115495i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.7499i | 1.43168i | 0.698267 | + | 0.715838i | \(0.253955\pi\) | ||||
−0.698267 | + | 0.715838i | \(0.746045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.24142 | − | 1.29408i | 0.0716360 | − | 0.0413591i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48.8500 | − | 11.2952i | −1.55966 | − | 0.360627i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.4550 | − | 23.3047i | 0.429146 | − | 0.743303i | −0.567651 | − | 0.823269i | \(-0.692148\pi\) |
0.996798 | + | 0.0799658i | \(0.0254811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.8959 | + | 17.8378i | −0.984425 | + | 0.568358i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.7802 | + | 15.6709i | −0.916084 | + | 0.498810i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.2502 | + | 30.7440i | 1.69326 | + | 0.977602i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8668 | + | 24.0181i | 0.440494 | + | 0.762959i | 0.997726 | − | 0.0673982i | \(-0.0214698\pi\) |
−0.557232 | + | 0.830357i | \(0.688136\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.17538 | − | 9.60711i | −0.132502 | − | 0.304873i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47.6585 | − | 27.5156i | −1.51088 | − | 0.872304i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4320 | + | 11.2191i | 0.615418 | + | 0.355312i | 0.775083 | − | 0.631859i | \(-0.217708\pi\) |
−0.159665 | + | 0.987171i | \(0.551041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.93071 | + | 8.47299i | −0.314194 | + | 0.268074i |
(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 | 504.2.bs.a.257.15 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bs.a.1097.7 | 48 | |||
4.3 | odd | 2 | 1008.2.ca.e.257.10 | 48 | |||
7.3 | odd | 6 | 504.2.cx.a.185.8 | yes | 48 | ||
9.2 | odd | 6 | 504.2.cx.a.425.8 | yes | 48 | ||
9.7 | even | 3 | 1512.2.cx.a.89.7 | 48 | |||
12.11 | even | 2 | 3024.2.ca.e.2609.7 | 48 | |||
21.17 | even | 6 | 1512.2.cx.a.17.7 | 48 | |||
28.3 | even | 6 | 1008.2.df.e.689.17 | 48 | |||
36.7 | odd | 6 | 3024.2.df.e.1601.7 | 48 | |||
36.11 | even | 6 | 1008.2.df.e.929.17 | 48 | |||
63.38 | even | 6 | inner | 504.2.bs.a.353.15 | yes | 48 | |
63.52 | odd | 6 | 1512.2.bs.a.521.7 | 48 | |||
84.59 | odd | 6 | 3024.2.df.e.17.7 | 48 | |||
252.115 | even | 6 | 3024.2.ca.e.2033.7 | 48 | |||
252.227 | odd | 6 | 1008.2.ca.e.353.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.15 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bs.a.353.15 | yes | 48 | 63.38 | even | 6 | inner | |
504.2.cx.a.185.8 | yes | 48 | 7.3 | odd | 6 | ||
504.2.cx.a.425.8 | yes | 48 | 9.2 | odd | 6 | ||
1008.2.ca.e.257.10 | 48 | 4.3 | odd | 2 | |||
1008.2.ca.e.353.10 | 48 | 252.227 | odd | 6 | |||
1008.2.df.e.689.17 | 48 | 28.3 | even | 6 | |||
1008.2.df.e.929.17 | 48 | 36.11 | even | 6 | |||
1512.2.bs.a.521.7 | 48 | 63.52 | odd | 6 | |||
1512.2.bs.a.1097.7 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.17.7 | 48 | 21.17 | even | 6 | |||
1512.2.cx.a.89.7 | 48 | 9.7 | even | 3 | |||
3024.2.ca.e.2033.7 | 48 | 252.115 | even | 6 | |||
3024.2.ca.e.2609.7 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.17.7 | 48 | 84.59 | odd | 6 | |||
3024.2.df.e.1601.7 | 48 | 36.7 | odd | 6 |