Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.o (of order \(8\), 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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 671.3 | ||
Character | \(\chi\) | \(=\) | 768.671 |
Dual form | 768.2.o.b.95.3 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
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 | ||||||||
\(3\) | −1.25135 | − | 1.19755i | −0.722465 | − | 0.691408i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.18808 | + | 0.906333i | 0.978540 | + | 0.405324i | 0.813884 | − | 0.581027i | \(-0.197349\pi\) |
0.164655 | + | 0.986351i | \(0.447349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.93241 | + | 1.93241i | −0.730381 | + | 0.730381i | −0.970695 | − | 0.240314i | \(-0.922750\pi\) |
0.240314 | + | 0.970695i | \(0.422750\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.131733 | + | 2.99711i | 0.0439110 | + | 0.999035i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.42447 | − | 0.590036i | −0.429495 | − | 0.177903i | 0.157454 | − | 0.987526i | \(-0.449671\pi\) |
−0.586949 | + | 0.809624i | \(0.699671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.110405 | + | 0.266541i | 0.0306208 | + | 0.0739252i | 0.938450 | − | 0.345414i | \(-0.112262\pi\) |
−0.907829 | + | 0.419340i | \(0.862262\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.65266 | − | 3.75448i | −0.426716 | − | 0.969402i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.17031 | −1.49652 | −0.748260 | − | 0.663406i | \(-0.769110\pi\) | ||||
−0.748260 | + | 0.663406i | \(0.769110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.34269 | + | 3.04144i | −1.68453 | + | 0.697755i | −0.999526 | − | 0.0307845i | \(-0.990199\pi\) |
−0.685004 | + | 0.728540i | \(0.740199\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.73227 | − | 0.103949i | 1.03267 | − | 0.0226836i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.85295 | − | 1.85295i | 0.386366 | − | 0.386366i | −0.487023 | − | 0.873389i | \(-0.661917\pi\) |
0.873389 | + | 0.487023i | \(0.161917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.430727 | + | 0.430727i | 0.0861453 | + | 0.0861453i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.42435 | − | 3.90817i | 0.659017 | − | 0.752128i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.11574 | − | 5.10784i | −0.392882 | − | 0.948501i | −0.989309 | − | 0.145834i | \(-0.953413\pi\) |
0.596427 | − | 0.802667i | \(-0.296587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.42046i | 0.614332i | 0.951656 | + | 0.307166i | \(0.0993807\pi\) | ||||
−0.951656 | + | 0.307166i | \(0.900619\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.07591 | + | 2.44422i | 0.187292 | + | 0.425485i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.97967 | + | 2.47686i | −1.01075 | + | 0.418666i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.52377 | + | 6.09293i | −0.414906 | + | 1.00167i | 0.568895 | + | 0.822410i | \(0.307371\pi\) |
−0.983801 | + | 0.179262i | \(0.942629\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.181042 | − | 0.465751i | 0.0289900 | − | 0.0745798i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.753641 | − | 0.753641i | −0.117699 | − | 0.117699i | 0.645804 | − | 0.763503i | \(-0.276522\pi\) |
−0.763503 | + | 0.645804i | \(0.776522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.57129 | + | 3.79343i | −0.239619 | + | 0.578492i | −0.997243 | − | 0.0741989i | \(-0.976360\pi\) |
0.757624 | + | 0.652691i | \(0.226360\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.42813 | + | 6.67731i | −0.361965 | + | 0.995394i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.54798i | 0.225796i | 0.993607 | + | 0.112898i | \(0.0360133\pi\) | ||||
−0.993607 | + | 0.112898i | \(0.963987\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 0.468394i | − | 0.0669135i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.72119 | + | 7.38927i | 1.08118 | + | 1.03471i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.12700 | + | 12.3777i | −0.704248 | + | 1.70020i | 0.00964932 | + | 0.999953i | \(0.496928\pi\) |
−0.713897 | + | 0.700251i | \(0.753072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.58210 | − | 2.58210i | −0.348170 | − | 0.348170i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.8305 | + | 4.98737i | 1.69945 | + | 0.660593i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.08775 | − | 7.45449i | 0.401991 | − | 0.970492i | −0.585191 | − | 0.810895i | \(-0.698981\pi\) |
0.987182 | − | 0.159597i | \(-0.0510195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.28571 | − | 1.77520i | 0.548728 | − | 0.227291i | −0.0910552 | − | 0.995846i | \(-0.529024\pi\) |
0.639784 | + | 0.768555i | \(0.279024\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.04619 | − | 5.53707i | −0.761748 | − | 0.697605i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.683277i | 0.0847501i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.531731 | + | 1.28371i | 0.0649613 | + | 0.156831i | 0.953026 | − | 0.302887i | \(-0.0979506\pi\) |
−0.888065 | + | 0.459718i | \(0.847951\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.53768 | + | 0.0996750i | −0.546272 | + | 0.0119995i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.72539 | + | 8.72539i | 1.03551 | + | 1.03551i | 0.999346 | + | 0.0361678i | \(0.0115151\pi\) |
0.0361678 | + | 0.999346i | \(0.488485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.73022 | + | 2.73022i | −0.319548 | + | 0.319548i | −0.848593 | − | 0.529046i | \(-0.822550\pi\) |
0.529046 | + | 0.848593i | \(0.322550\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0231699 | − | 1.05481i | −0.00267543 | − | 0.121799i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.89285 | − | 1.61247i | 0.443632 | − | 0.183758i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.76080 | −0.310614 | −0.155307 | − | 0.987866i | \(-0.549637\pi\) | ||||
−0.155307 | + | 0.987866i | \(0.549637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.96529 | + | 0.789635i | −0.996144 | + | 0.0877372i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.53133 | − | 6.11116i | −0.277849 | − | 0.670787i | 0.721927 | − | 0.691970i | \(-0.243257\pi\) |
−0.999776 | + | 0.0211827i | \(0.993257\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.5011 | − | 5.59235i | −1.46440 | − | 0.606576i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.46939 | + | 8.92538i | −0.371958 | + | 0.956901i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.14369 | − | 4.14369i | 0.439230 | − | 0.439230i | −0.452523 | − | 0.891753i | \(-0.649476\pi\) |
0.891753 | + | 0.452523i | \(0.149476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.728413 | − | 0.301719i | −0.0763585 | − | 0.0316287i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.09618 | − | 4.28017i | 0.424754 | − | 0.443833i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.8230 | −1.93120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.3656 | −1.05246 | −0.526232 | − | 0.850341i | \(-0.676396\pi\) | ||||
−0.526232 | + | 0.850341i | \(0.676396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.58075 | − | 4.34703i | 0.158872 | − | 0.436893i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5700 | + | 4.37825i | 1.05176 | + | 0.435652i | 0.840519 | − | 0.541783i | \(-0.182250\pi\) |
0.211238 | + | 0.977435i | \(0.432250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4823 | + | 10.4823i | −1.03285 | + | 1.03285i | −0.0334101 | + | 0.999442i | \(0.510637\pi\) |
−0.999442 | + | 0.0334101i | \(0.989363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.4488 | + | 4.06156i | 1.01970 | + | 0.396368i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.39578 | + | 3.89186i | 0.908325 | + | 0.376240i | 0.787415 | − | 0.616423i | \(-0.211419\pi\) |
0.120910 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00588 | − | 7.25683i | −0.287911 | − | 0.695078i | 0.712064 | − | 0.702114i | \(-0.247760\pi\) |
−0.999975 | + | 0.00703600i | \(0.997760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4547 | − | 4.60201i | 0.992318 | − | 0.436803i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.6372 | 1.28288 | 0.641438 | − | 0.767175i | \(-0.278338\pi\) | ||||
0.641438 | + | 0.767175i | \(0.278338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.73378 | − | 2.37501i | 0.534678 | − | 0.221471i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.784308 | + | 0.366008i | −0.0725093 | + | 0.0338374i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.9235 | − | 11.9235i | 1.09303 | − | 1.09303i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.09719 | − | 6.09719i | −0.554290 | − | 0.554290i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0405404 | + | 1.84559i | 0.00365540 | + | 0.166411i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.97958 | − | 9.60756i | −0.355945 | − | 0.859326i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.75395i | − | 0.688052i | −0.938960 | − | 0.344026i | \(-0.888209\pi\) | ||
0.938960 | − | 0.344026i | \(-0.111791\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.50906 | − | 2.86519i | 0.573090 | − | 0.252266i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.16782 | − | 0.483728i | 0.102033 | − | 0.0422635i | −0.331083 | − | 0.943602i | \(-0.607414\pi\) |
0.433116 | + | 0.901338i | \(0.357414\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.31177 | − | 20.0664i | 0.720722 | − | 1.73998i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.0349 | − | 5.44780i | 0.949730 | − | 0.468872i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.54494 | − | 7.54494i | −0.644608 | − | 0.644608i | 0.307077 | − | 0.951685i | \(-0.400649\pi\) |
−0.951685 | + | 0.307077i | \(0.900649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.412435 | + | 0.995705i | −0.0349822 | + | 0.0844546i | −0.940405 | − | 0.340056i | \(-0.889554\pi\) |
0.905423 | + | 0.424511i | \(0.139554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.85379 | − | 1.93706i | 0.156117 | − | 0.163130i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.444824i | − | 0.0371980i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 13.0939i | − | 1.08739i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.560927 | + | 0.586123i | −0.0462645 | + | 0.0483426i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.458938 | − | 1.10798i | 0.0375977 | − | 0.0907689i | −0.903965 | − | 0.427606i | \(-0.859357\pi\) |
0.941563 | + | 0.336837i | \(0.109357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.80869 | + | 9.80869i | 0.798220 | + | 0.798220i | 0.982815 | − | 0.184595i | \(-0.0590974\pi\) |
−0.184595 | + | 0.982815i | \(0.559097\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.812833 | − | 18.4931i | −0.0657136 | − | 1.49508i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.10007 | + | 7.48424i | −0.249004 | + | 0.601148i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.28207 | + | 3.43055i | −0.660981 | + | 0.273787i | −0.687851 | − | 0.725852i | \(-0.741446\pi\) |
0.0268702 | + | 0.999639i | \(0.491446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.2386 | − | 9.34890i | 1.68433 | − | 0.741416i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.16129i | 0.564389i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.15049 | + | 2.77752i | 0.0901131 | + | 0.217552i | 0.962510 | − | 0.271246i | \(-0.0874355\pi\) |
−0.872397 | + | 0.488798i | \(0.837436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.138898 | + | 6.32329i | 0.0108132 | + | 0.492267i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.86833 | − | 1.86833i | −0.144576 | − | 0.144576i | 0.631114 | − | 0.775690i | \(-0.282598\pi\) |
−0.775690 | + | 0.631114i | \(0.782598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.13353 | − | 9.13353i | 0.702579 | − | 0.702579i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.0828 | − | 21.6062i | −0.771051 | − | 1.65227i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.59196 | − | 3.97312i | 0.729263 | − | 0.302071i | 0.0130138 | − | 0.999915i | \(-0.495857\pi\) |
0.716249 | + | 0.697845i | \(0.245857\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.66468 | −0.125838 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.7910 | + | 5.63040i | −0.961430 | + | 0.423207i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.00532113 | − | 0.0128464i | −0.000397720 | − | 0.000960181i | 0.923681 | − | 0.383163i | \(-0.125165\pi\) |
−0.924078 | + | 0.382203i | \(0.875165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.45181 | + | 3.91507i | 0.702547 | + | 0.291005i | 0.705217 | − | 0.708992i | \(-0.250850\pi\) |
−0.00266940 | + | 0.999996i | \(0.500850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.48879 | − | 2.91097i | −0.553588 | − | 0.215185i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.0444 | + | 11.0444i | −0.812004 | + | 0.812004i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.78944 | + | 3.64071i | 0.642748 | + | 0.266235i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.934943 | + | 14.1694i | 0.0680071 | + | 1.03067i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.77941 | 0.562898 | 0.281449 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281449 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.23528 | −0.448825 | −0.224413 | − | 0.974494i | \(-0.572046\pi\) | ||||
−0.224413 | + | 0.974494i | \(0.572046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.818261 | − | 0.855016i | 0.0585969 | − | 0.0612290i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.90773 | − | 2.86128i | −0.492156 | − | 0.203858i | 0.122781 | − | 0.992434i | \(-0.460819\pi\) |
−0.614937 | + | 0.788576i | \(0.710819\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4517 | − | 12.4517i | 0.882681 | − | 0.882681i | −0.111125 | − | 0.993806i | \(-0.535445\pi\) |
0.993806 | + | 0.111125i | \(0.0354455\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.871935 | − | 2.24315i | 0.0615015 | − | 0.158219i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.9589 | + | 5.78196i | 0.979721 | + | 0.405814i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.965978 | − | 2.33208i | −0.0674668 | − | 0.162879i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.79757 | + | 5.30938i | 0.402959 | + | 0.369028i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2540 | 0.847630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16851 | − | 0.484011i | 0.0804432 | − | 0.0333207i | −0.342099 | − | 0.939664i | \(-0.611138\pi\) |
0.422542 | + | 0.906343i | \(0.361138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.469362 | − | 21.3676i | −0.0321602 | − | 1.46408i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.87622 | + | 6.87622i | −0.468954 | + | 0.468954i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.60972 | − | 6.60972i | −0.448697 | − | 0.448697i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.68602 | − | 0.146866i | 0.451800 | − | 0.00992426i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.681233 | − | 1.64464i | −0.0458247 | − | 0.110631i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5047i | 0.703449i | 0.936104 | + | 0.351724i | \(0.114405\pi\) | ||||
−0.936104 | + | 0.351724i | \(0.885595\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.23419 | + | 1.34767i | −0.0822795 | + | 0.0898450i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.7869 | + | 6.95334i | −1.11418 | + | 0.461509i | −0.862376 | − | 0.506268i | \(-0.831025\pi\) |
−0.251806 | + | 0.967778i | \(0.581025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.87646 | + | 14.1870i | −0.388327 | + | 0.937505i | 0.601967 | + | 0.798521i | \(0.294384\pi\) |
−0.990295 | + | 0.138984i | \(0.955616\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.80233 | − | 2.64414i | −0.447560 | − | 0.173972i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.54073 | + | 2.54073i | 0.166449 | + | 0.166449i | 0.785416 | − | 0.618968i | \(-0.212449\pi\) |
−0.618968 | + | 0.785416i | \(0.712449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.40298 | + | 3.38711i | −0.0915206 | + | 0.220950i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.45471 | + | 3.30620i | 0.224408 | + | 0.214761i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6107i | 1.13914i | 0.821943 | + | 0.569570i | \(0.192890\pi\) | ||||
−0.821943 | + | 0.569570i | \(0.807110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.18628i | − | 0.398493i | −0.979949 | − | 0.199247i | \(-0.936151\pi\) | ||
0.979949 | − | 0.199247i | \(-0.0638495\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.1643 | + | 9.74831i | 0.780341 | + | 0.625354i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.424521 | − | 1.02489i | 0.0271217 | − | 0.0654775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.62134 | − | 1.62134i | −0.103163 | − | 0.103163i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.15088 | + | 10.6786i | −0.263051 | + | 0.676727i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.18840 | + | 22.1828i | −0.579967 | + | 1.40016i | 0.312876 | + | 0.949794i | \(0.398708\pi\) |
−0.892842 | + | 0.450369i | \(0.851292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.73278 | + | 1.54617i | −0.234678 | + | 0.0972067i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.1975 | + | 23.1663i | 0.638589 | + | 1.45073i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.8836i | − | 0.741276i | −0.928777 | − | 0.370638i | \(-0.879139\pi\) | ||
0.928777 | − | 0.370638i | \(-0.120861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.89706 | − | 16.6510i | −0.428563 | − | 1.03464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0300 | − | 7.01395i | 0.930335 | − | 0.434153i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.6191 | − | 11.6191i | −0.716464 | − | 0.716464i | 0.251415 | − | 0.967879i | \(-0.419104\pi\) |
−0.967879 | + | 0.251415i | \(0.919104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.4366 | + | 22.4366i | −1.37827 | + | 1.37827i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.1475 | + | 0.222900i | −0.621015 | + | 0.0136413i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7480 | + | 5.69459i | −0.838228 | + | 0.347205i | −0.760155 | − | 0.649742i | \(-0.774877\pi\) |
−0.0780733 | + | 0.996948i | \(0.524877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.07297 | 0.429652 | 0.214826 | − | 0.976652i | \(-0.431081\pi\) | ||||
0.214826 | + | 0.976652i | \(0.431081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.550173 | + | 1.24987i | 0.0332980 | + | 0.0756455i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.359414 | − | 0.867703i | −0.0216735 | − | 0.0523245i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.13397 | + | 0.469705i | 0.0681335 | + | 0.0282218i | 0.416490 | − | 0.909140i | \(-0.363260\pi\) |
−0.348356 | + | 0.937362i | \(0.613260\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.2515 | + | 0.450587i | −0.613740 | + | 0.0269759i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0212 | + | 12.0212i | −0.717122 | + | 0.717122i | −0.968015 | − | 0.250893i | \(-0.919276\pi\) |
0.250893 | + | 0.968015i | \(0.419276\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8158 | − | 5.30848i | −0.761821 | − | 0.315557i | −0.0322666 | − | 0.999479i | \(-0.510273\pi\) |
−0.729555 | + | 0.683923i | \(0.760273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.5541 | + | 22.5415i | 1.39522 | + | 1.33524i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.91268 | 0.171930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.0727 | 1.23957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.9709 | + | 12.4133i | 0.760369 | + | 0.727682i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.7412 | − | 10.2481i | −1.44539 | − | 0.598702i | −0.484295 | − | 0.874905i | \(-0.660924\pi\) |
−0.961099 | + | 0.276203i | \(0.910924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.5125 | − | 13.5125i | 0.786729 | − | 0.786729i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.18386 | + | 3.54660i | −0.416850 | + | 0.205795i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.698461 | + | 0.289312i | 0.0403930 | + | 0.0167313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.29408 | − | 10.3668i | −0.247506 | − | 0.597533i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.98357 | − | 18.1369i | −0.458644 | − | 1.04194i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9864 | 0.629079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.664375 | − | 0.275193i | 0.0379179 | − | 0.0157061i | −0.363644 | − | 0.931538i | \(-0.618468\pi\) |
0.401562 | + | 0.915832i | \(0.368468\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.6701 | − | 0.563871i | 1.46032 | − | 0.0320775i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.60638 | − | 3.60638i | 0.204499 | − | 0.204499i | −0.597425 | − | 0.801924i | \(-0.703810\pi\) |
0.801924 | + | 0.597425i | \(0.203810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2233 | + | 23.2233i | 1.31266 | + | 1.31266i | 0.919449 | + | 0.393210i | \(0.128635\pi\) |
0.393210 | + | 0.919449i | \(0.371365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.21113 | − | 17.5954i | −0.462645 | − | 0.991389i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.42053 | − | 3.42947i | −0.0797850 | − | 0.192618i | 0.878954 | − | 0.476907i | \(-0.158242\pi\) |
−0.958738 | + | 0.284289i | \(0.908242\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.52434i | 0.477271i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.09666 | − | 16.1220i | −0.396097 | − | 0.899843i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.3067 | − | 18.7666i | 2.52093 | − | 1.04420i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0672520 | + | 0.162361i | −0.00373047 | + | 0.00900615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.92905 | + | 12.6805i | −0.272577 | + | 0.701233i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.99133 | − | 2.99133i | −0.164917 | − | 0.164917i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.25086 | − | 7.84826i | 0.178683 | − | 0.431380i | −0.809008 | − | 0.587798i | \(-0.799995\pi\) |
0.987691 | + | 0.156419i | \(0.0499949\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.5936 | − | 6.76138i | −1.01892 | − | 0.370521i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.29079i | 0.179795i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2771i | 1.32246i | 0.750183 | + | 0.661230i | \(0.229965\pi\) | ||||
−0.750183 | + | 0.661230i | \(0.770035\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.0648 | − | 16.3312i | −0.926833 | − | 0.886990i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.01819 | − | 4.87235i | 0.109291 | − | 0.263853i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6217 | − | 12.6217i | −0.681509 | − | 0.681509i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.0191 | − | 3.89455i | −0.539413 | − | 0.209676i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.37907 | − | 3.32937i | 0.0740325 | − | 0.178730i | −0.882531 | − | 0.470254i | \(-0.844162\pi\) |
0.956564 | + | 0.291524i | \(0.0941623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7378 | + | 4.44775i | −0.574782 | + | 0.238083i | −0.651089 | − | 0.759002i | \(-0.725687\pi\) |
0.0763062 | + | 0.997084i | \(0.475687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41975 | + | 0.481249i | 0.0757809 | + | 0.0256871i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.62531i | − | 0.299405i | −0.988731 | − | 0.149703i | \(-0.952168\pi\) | ||
0.988731 | − | 0.149703i | \(-0.0478316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.1838 | + | 27.0000i | 0.593572 | + | 1.43301i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.1996 | + | 0.641400i | −1.54540 | + | 0.0339465i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3781 | − | 22.3781i | −1.18107 | − | 1.18107i | −0.979467 | − | 0.201603i | \(-0.935385\pi\) |
−0.201603 | − | 0.979467i | \(-0.564615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.2298 | − | 31.2298i | 1.64367 | − | 1.64367i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.327984 | + | 14.9314i | 0.0172147 | + | 0.783696i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.44842 | + | 3.49945i | −0.442211 | + | 0.183170i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.0135 | −1.35789 | −0.678946 | − | 0.734188i | \(-0.737563\pi\) | ||||
−0.678946 | + | 0.734188i | \(0.737563\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.15946 | − | 2.35802i | 0.112417 | − | 0.122754i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0113 | − | 33.8262i | −0.727428 | − | 1.75617i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.7694 | + | 6.94611i | 0.868286 | + | 0.359656i | 0.771942 | − | 0.635692i | \(-0.219285\pi\) |
0.0963434 | + | 0.995348i | \(0.469285\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.52573 | + | 16.7881i | −0.336987 | + | 0.866936i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12786 | − | 1.12786i | 0.0580878 | − | 0.0580878i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.8673 | − | 4.91559i | −0.609582 | − | 0.252497i | 0.0564681 | − | 0.998404i | \(-0.482016\pi\) |
−0.666050 | + | 0.745907i | \(0.732016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.28576 | + | 9.70287i | −0.475724 | + | 0.497093i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.25906 | −0.268725 | −0.134363 | − | 0.990932i | \(-0.542899\pi\) | ||||
−0.134363 | + | 0.990932i | \(0.542899\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.97932 | 0.508593 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.5763 | − | 4.20960i | −0.588456 | − | 0.213986i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.9373 | + | 10.7436i | 1.31507 | + | 0.544721i | 0.926360 | − | 0.376639i | \(-0.122920\pi\) |
0.388712 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4333 | + | 11.4333i | −0.578204 | + | 0.578204i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.04064 | − | 0.793219i | −0.102937 | − | 0.0400126i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.04085 | − | 2.50220i | −0.303948 | − | 0.125899i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4580 | + | 34.9046i | 0.725624 | + | 1.75181i | 0.656654 | + | 0.754192i | \(0.271971\pi\) |
0.0689699 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.4315 | + | 15.1562i | −1.72373 | + | 0.758759i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.7191 | 1.58397 | 0.791987 | − | 0.610537i | \(-0.209046\pi\) | ||||
0.791987 | + | 0.610537i | \(0.209046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.911693 | + | 0.377635i | −0.0454146 | + | 0.0188114i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.3325 | − | 6.39776i | −1.01033 | − | 0.317907i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.19010 | − | 7.19010i | 0.356400 | − | 0.356400i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8308 | − | 17.8308i | −0.881677 | − | 0.881677i | 0.112028 | − | 0.993705i | \(-0.464265\pi\) |
−0.993705 | + | 0.112028i | \(0.964265\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.405863 | + | 18.4768i | 0.0200197 | + | 0.911393i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.43832 | + | 20.3719i | 0.415223 | + | 1.00244i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.6659i | − | 0.769011i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.70851 | − | 0.752059i | 0.0836660 | − | 0.0368285i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.10652 | − | 0.872548i | 0.102910 | − | 0.0426268i | −0.330634 | − | 0.943759i | \(-0.607263\pi\) |
0.433544 | + | 0.901132i | \(0.357263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.169965 | − | 0.410331i | 0.00828357 | − | 0.0199983i | −0.919684 | − | 0.392660i | \(-0.871555\pi\) |
0.927967 | + | 0.372662i | \(0.121555\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.63946 | + | 0.203920i | −0.225578 | + | 0.00991492i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.65772 | − | 2.65772i | −0.128918 | − | 0.128918i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.85132 | + | 11.7121i | −0.234772 | + | 0.566790i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.532700 | + | 0.556628i | −0.0257190 | + | 0.0268743i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.95351i | 0.142266i | 0.997467 | + | 0.0711329i | \(0.0226614\pi\) | ||||
−0.997467 | + | 0.0711329i | \(0.977339\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3472i | 1.50645i | 0.657764 | + | 0.753224i | \(0.271503\pi\) | ||||
−0.657764 | + | 0.753224i | \(0.728497\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.6807 | + | 16.3850i | −0.751830 | + | 0.785602i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.96999 | + | 19.2413i | −0.381256 | + | 0.920434i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.44392 | − | 7.44392i | −0.355279 | − | 0.355279i | 0.506791 | − | 0.862069i | \(-0.330832\pi\) |
−0.862069 | + | 0.506791i | \(0.830832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.40383 | − | 0.0617029i | 0.0668489 | − | 0.00293824i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.50021 | + | 8.45026i | −0.166300 | + | 0.401484i | −0.984957 | − | 0.172799i | \(-0.944719\pi\) |
0.818657 | + | 0.574283i | \(0.194719\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.8223 | − | 5.31117i | 0.607835 | − | 0.251773i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.90115 | + | 0.836857i | −0.0899213 | + | 0.0395820i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0900i | 1.13688i | 0.822725 | + | 0.568439i | \(0.192453\pi\) | ||||
−0.822725 | + | 0.568439i | \(0.807547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.628866 | + | 1.51822i | 0.0296121 | + | 0.0714901i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.527636 | − | 24.0205i | −0.0247905 | − | 1.12858i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.32037 | − | 1.32037i | −0.0618999 | − | 0.0618999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.8807 | + | 13.8807i | −0.649311 | + | 0.649311i | −0.952827 | − | 0.303515i | \(-0.901840\pi\) |
0.303515 | + | 0.952827i | \(0.401840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.1293 | + | 24.1146i | −0.986231 | + | 1.12557i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.4361 | − | 10.9502i | 1.23125 | − | 0.510001i | 0.330282 | − | 0.943882i | \(-0.392856\pi\) |
0.900970 | + | 0.433881i | \(0.142856\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7558 | 1.66171 | 0.830857 | − | 0.556485i | \(-0.187850\pi\) | ||||
0.830857 | + | 0.556485i | \(0.187850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.8420 | − | 5.65287i | 0.595535 | − | 0.262145i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.84875 | − | 4.46327i | −0.0855498 | − | 0.206536i | 0.875315 | − | 0.483553i | \(-0.160654\pi\) |
−0.960865 | + | 0.277018i | \(0.910654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.50818 | − | 1.45313i | −0.161993 | − | 0.0670995i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4720 | + | 5.62542i | 0.666834 | + | 0.259206i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.47652 | − | 4.47652i | 0.205831 | − | 0.205831i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.47273 | − | 1.85266i | −0.205223 | − | 0.0850060i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.7726 | − | 13.7356i | −1.72949 | − | 0.628911i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.8988 | 0.726433 | 0.363216 | − | 0.931705i | \(-0.381679\pi\) | ||||
0.363216 | + | 0.931705i | \(0.381679\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.90265 | −0.0867535 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.57603 | − | 8.96126i | 0.390223 | − | 0.407751i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.6807 | − | 9.39466i | −1.02988 | − | 0.426590i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4283 | + | 10.4283i | −0.472552 | + | 0.472552i | −0.902740 | − | 0.430187i | \(-0.858448\pi\) |
0.430187 | + | 0.902740i | \(0.358448\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.88657 | − | 4.85341i | 0.0853138 | − | 0.219479i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.306137 | − | 0.126806i | −0.0138158 | − | 0.00572268i | 0.375765 | − | 0.926715i | \(-0.377380\pi\) |
−0.389581 | + | 0.920992i | \(0.627380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0547 | + | 31.5169i | 0.587956 | + | 1.41945i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.39867 | − | 8.07896i | 0.332545 | − | 0.363122i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33.7220 | −1.51264 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.62549 | + | 2.33015i | −0.251831 | + | 0.104312i | −0.505028 | − | 0.863103i | \(-0.668518\pi\) |
0.253197 | + | 0.967415i | \(0.418518\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.100502 | + | 4.57535i | 0.00449012 | + | 0.204411i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.6198 | + | 10.6198i | −0.473513 | + | 0.473513i | −0.903050 | − | 0.429536i | \(-0.858677\pi\) |
0.429536 | + | 0.903050i | \(0.358677\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1599 | + | 19.1599i | 0.852605 | + | 0.852605i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.3671 | + | 0.491317i | −0.993358 | + | 0.0218202i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.01172 | + | 4.85673i | 0.0891681 | + | 0.215271i | 0.962172 | − | 0.272442i | \(-0.0878313\pi\) |
−0.873004 | + | 0.487713i | \(0.837831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.5518i | − | 0.466783i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.2575 | + | 39.1115i | −0.585332 | + | 1.72681i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.4366 | + | 13.4357i | −1.42933 | + | 0.592046i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.913364 | − | 2.20506i | 0.0401697 | − | 0.0969783i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.7609 | − | 6.51513i | −0.735721 | − | 0.285983i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.9974 | − | 19.9974i | −0.876102 | − | 0.876102i | 0.117027 | − | 0.993129i | \(-0.462664\pi\) |
−0.993129 | + | 0.117027i | \(0.962664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2948 | − | 36.9248i | 0.668793 | − | 1.61461i | −0.114839 | − | 0.993384i | \(-0.536635\pi\) |
0.783632 | − | 0.621225i | \(-0.213365\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.08309 | + | 1.99354i | 0.0909134 | + | 0.0870053i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 21.1053i | − | 0.919360i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1332i | 0.701443i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.7487 | + | 8.27232i | 0.987208 | + | 0.358988i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.117671 | − | 0.284082i | 0.00509688 | − | 0.0123050i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.0314 | + | 17.0314i | 0.736332 | + | 0.736332i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.00872561 | + | 0.0224476i | −0.000376538 | + | 0.000968684i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.276370 | + | 0.667216i | −0.0119041 | + | 0.0287390i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.6786 | − | 14.7786i | 1.53394 | − | 0.635380i | 0.553618 | − | 0.832771i | \(-0.313247\pi\) |
0.980325 | + | 0.197391i | \(0.0632468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.13898 | − | 16.2181i | −0.306363 | − | 0.695987i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.6029i | − | 0.796859i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4112 | − | 29.9634i | −0.530666 | − | 1.28114i | −0.931083 | − | 0.364808i | \(-0.881135\pi\) |
0.400416 | − | 0.916333i | \(-0.368865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.88502 | + | 12.6109i | 0.251167 | + | 0.538219i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.0704 | + | 31.0704i | 1.32364 | + | 1.32364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.33499 | − | 5.33499i | 0.226867 | − | 0.226867i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.0467 | − | 0.594111i | 1.14807 | − | 0.0252186i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.30090 | − | 3.85256i | 0.394092 | − | 0.163238i | −0.176832 | − | 0.984241i | \(-0.556585\pi\) |
0.570924 | + | 0.821003i | \(0.306585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.18458 | −0.0501025 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.63869 | − | 15.0816i | −0.280286 | − | 0.636746i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.24166 | + | 2.99763i | 0.0523297 | + | 0.126335i | 0.947882 | − | 0.318620i | \(-0.103220\pi\) |
−0.895553 | + | 0.444955i | \(0.853220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.8392 | + | 12.3598i | 1.25535 | + | 0.519981i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.7987 | − | 18.8505i | 0.663483 | − | 0.791646i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.3250 | + | 28.3250i | −1.18745 | + | 1.18745i | −0.209674 | + | 0.977771i | \(0.567240\pi\) |
−0.977771 | + | 0.209674i | \(0.932760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5476 | + | 15.5527i | 1.57132 | + | 0.650862i | 0.987008 | − | 0.160669i | \(-0.0513651\pi\) |
0.584310 | + | 0.811530i | \(0.301365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.73473 | − | 9.31626i | −0.406674 | − | 0.389192i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.59623 | 0.0665673 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.37886 | 0.223925 | 0.111962 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111962 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.80249 | + | 7.46708i | 0.324260 | + | 0.310321i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.7008 | + | 6.91770i | 0.692866 | + | 0.286994i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.6066 | − | 14.6066i | 0.604942 | − | 0.604942i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.04785 | + | 0.0900101i | −0.0846684 | + | 0.00372146i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.77252 | + | 0.734203i | 0.0731599 | + | 0.0303038i | 0.418963 | − | 0.908003i | \(-0.362394\pi\) |
−0.345803 | + | 0.938307i | \(0.612394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4031 | − | 25.1154i | −0.428653 | − | 1.03486i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.21743 | + | 11.8528i | 0.214616 | + | 0.487560i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.1664 | −0.992394 | −0.496197 | − | 0.868210i | \(-0.665271\pi\) | ||||
−0.496197 | + | 0.868210i | \(0.665271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.8964 | − | 15.2830i | 1.51260 | − | 0.626541i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.4931 | + | 0.669813i | −1.24800 | + | 0.0274136i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.6692 | − | 11.6692i | 0.476789 | − | 0.476789i | −0.427314 | − | 0.904103i | \(-0.640540\pi\) |
0.904103 | + | 0.427314i | \(0.140540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.80143 | − | 8.80143i | −0.359018 | − | 0.359018i | 0.504433 | − | 0.863451i | \(-0.331702\pi\) |
−0.863451 | + | 0.504433i | \(0.831702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.77738 | + | 1.76276i | −0.153827 | + | 0.0717852i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.81507 | − | 18.8672i | −0.317728 | − | 0.767062i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.9215i | 1.29565i | 0.761788 | + | 0.647826i | \(0.224322\pi\) | ||||
−0.761788 | + | 0.647826i | \(0.775678\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.5432 | − | 23.9517i | −0.427231 | − | 0.970573i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.412600 | + | 0.170905i | −0.0166920 | + | 0.00691406i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.35458 | + | 17.7555i | −0.297049 | + | 0.717139i | 0.702934 | + | 0.711255i | \(0.251873\pi\) |
−0.999983 | + | 0.00588391i | \(0.998127\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.58401 | + | 4.07504i | −0.0638736 | + | 0.164322i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5933 | + | 13.5933i | 0.547246 | + | 0.547246i | 0.925643 | − | 0.378397i | \(-0.123525\pi\) |
−0.378397 | + | 0.925643i | \(0.623525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.75210 | − | 9.05838i | 0.150810 | − | 0.364087i | −0.830362 | − | 0.557224i | \(-0.811866\pi\) |
0.981172 | + | 0.193137i | \(0.0618663\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.896498 | − | 13.5868i | −0.0359752 | − | 0.545219i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.0146i | 0.641611i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 27.6746i | − | 1.10699i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.3340 | − | 14.6749i | −0.612383 | − | 0.586058i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.5725 | − | 37.5953i | 0.620915 | − | 1.49902i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.39207 | + | 5.39207i | 0.214655 | + | 0.214655i | 0.806242 | − | 0.591587i | \(-0.201498\pi\) |
−0.591587 | + | 0.806242i | \(0.701498\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.04183 | − | 0.793682i | −0.0811556 | − | 0.0315460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.02766 | − | 16.9663i | 0.278884 | − | 0.673286i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.124846 | − | 0.0517131i | 0.00494659 | − | 0.00204895i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.0015 | + | 27.3003i | −0.989044 | + | 1.07999i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.82203i | − | 0.0719659i | −0.999352 | − | 0.0359830i | \(-0.988544\pi\) | ||
0.999352 | − | 0.0359830i | \(-0.0114562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4095 | + | 25.1308i | 0.410511 | + | 0.991062i | 0.985001 | + | 0.172550i | \(0.0552007\pi\) |
−0.574489 | + | 0.818512i | \(0.694799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.8392 | − | 0.369890i | 0.663041 | − | 0.0145644i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.3258 | + | 27.3258i | 1.07429 | + | 1.07429i | 0.997010 | + | 0.0772785i | \(0.0246231\pi\) |
0.0772785 | + | 0.997010i | \(0.475377\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.79684 | + | 8.79684i | −0.345306 | + | 0.345306i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.355554 | + | 16.1865i | 0.0139353 | + | 0.634400i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.5061 | + | 8.90811i | −0.841598 | + | 0.348601i | −0.761483 | − | 0.648184i | \(-0.775529\pi\) |
−0.0801145 | + | 0.996786i | \(0.525529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.99371 | 0.116974 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.54241 | − | 7.82309i | −0.333271 | − | 0.305208i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.2778 | + | 41.7123i | 0.673048 | + | 1.62488i | 0.776403 | + | 0.630237i | \(0.217042\pi\) |
−0.103355 | + | 0.994644i | \(0.532958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.7407 | − | 18.5322i | −1.74021 | − | 0.720819i | −0.998759 | − | 0.0498140i | \(-0.984137\pi\) |
−0.741453 | − | 0.671005i | \(-0.765863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.11709 | + | 2.87383i | −0.0433841 | + | 0.111610i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.3736 | − | 36.3736i | 1.41051 | − | 1.41051i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3849 | − | 5.54420i | −0.518265 | − | 0.214672i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.5800 | − | 13.1451i | 0.486370 | − | 0.508217i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.15231 | −0.276112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8139 | −0.416844 | −0.208422 | − | 0.978039i | \(-0.566833\pi\) | ||||
−0.208422 | + | 0.978039i | \(0.566833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.15831 | − | 0.208395i | 0.121564 | − | 0.00802114i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.7436 | + | 6.93541i | 0.643507 | + | 0.266549i | 0.680480 | − | 0.732767i | \(-0.261771\pi\) |
−0.0369727 | + | 0.999316i | \(0.511771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0305 | − | 20.0305i | 0.768701 | − | 0.768701i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.3332 | + | 11.4021i | 1.12405 | + | 0.436930i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.5660 | − | 18.0456i | −1.66701 | − | 0.690497i | −0.668428 | − | 0.743777i | \(-0.733032\pi\) |
−0.998580 | + | 0.0532798i | \(0.983032\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.67071 | − | 23.3472i | −0.369499 | − | 0.892049i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.3432 | − | 10.7155i | 0.928751 | − | 0.408822i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.86521 | −0.147253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.29763 | − | 2.19435i | 0.201531 | − | 0.0834771i | −0.279635 | − | 0.960106i | \(-0.590213\pi\) |
0.481166 | + | 0.876629i | \(0.340213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.34557 | + | 11.4549i | 0.203061 | + | 0.435135i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.80488 | + | 1.80488i | −0.0684630 | + | 0.0684630i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.65020 | + | 4.65020i | 0.176139 | + | 0.176139i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.136673 | − | 6.22199i | −0.00516943 | − | 0.235337i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.7184 | + | 33.1190i | 0.518135 | + | 1.25089i | 0.939047 | + | 0.343787i | \(0.111710\pi\) |
−0.420912 | + | 0.907101i | \(0.638290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 52.4144i | − | 1.97685i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.81186 | − | 2.55829i | 0.218887 | − | 0.0963508i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.8861 | + | 11.9650i | −1.08638 | + | 0.449991i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.39804 | − | 3.37516i | 0.0525044 | − | 0.126757i | −0.895451 | − | 0.445160i | \(-0.853147\pi\) |
0.947955 | + | 0.318403i | \(0.103147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.363688 | − | 8.27440i | −0.0136394 | − | 0.310314i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.33792 | + | 6.33792i | 0.237357 | + | 0.237357i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.403158 | − | 0.973311i | 0.0150773 | − | 0.0363998i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.0897 | − | 22.0371i | 0.787610 | − | 0.822989i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 25.3851i | − | 0.946706i | −0.880873 | − | 0.473353i | \(-0.843044\pi\) | ||
0.880873 | − | 0.473353i | \(-0.156956\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 40.5121i | − | 1.50875i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.40840 | + | 7.74117i | −0.275521 | + | 0.287897i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.28878 | − | 3.11138i | 0.0478640 | − | 0.115554i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.5294 | − | 32.5294i | −1.20645 | − | 1.20645i | −0.972169 | − | 0.234280i | \(-0.924727\pi\) |
−0.234280 | − | 0.972169i | \(-0.575273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.54764 | − | 26.7659i | −0.131394 | − | 0.991330i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.69534 | − | 23.4066i | 0.358595 | − | 0.865725i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.3419 | + | 10.9112i | −0.972961 | + | 0.403014i | −0.811814 | − | 0.583917i | \(-0.801519\pi\) |
−0.161147 | + | 0.986930i | \(0.551519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.75858 | + | 0.774099i | −0.0648661 | + | 0.0285531i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.14236i | − | 0.0789147i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.4201 | − | 32.3991i | −0.493668 | − | 1.19182i | −0.952840 | − | 0.303473i | \(-0.901854\pi\) |
0.459172 | − | 0.888347i | \(-0.348146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0872162 | + | 3.97050i | 0.00320397 | + | 0.145860i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.42669 | + | 5.42669i | 0.199086 | + | 0.199086i | 0.799608 | − | 0.600522i | \(-0.205041\pi\) |
−0.600522 | + | 0.799608i | \(0.705041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00839 | − | 2.00839i | 0.0735817 | − | 0.0735817i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.9823 | − | 8.39169i | 0.657939 | − | 0.307036i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.6771 | + | 10.6358i | −0.938222 | + | 0.388624i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.67683 | 0.134170 | 0.0670848 | − | 0.997747i | \(-0.478630\pi\) | ||||
0.0670848 | + | 0.997747i | \(0.478630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.0629 | − | 16.7547i | 1.38709 | − | 0.610576i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5723 | + | 30.3521i | 0.457552 | + | 1.10463i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.0816 | + | 5.41857i | 0.475458 | + | 0.196941i | 0.607526 | − | 0.794299i | \(-0.292162\pi\) |
−0.132068 | + | 0.991241i | \(0.542162\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.52262 | + | 2.53541i | 0.236756 | + | 0.0920296i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.8277 | − | 25.8277i | 0.936254 | − | 0.936254i | −0.0618325 | − | 0.998087i | \(-0.519694\pi\) |
0.998087 | + | 0.0618325i | \(0.0196945\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.8317 | + | 8.21457i | 0.717957 | + | 0.297387i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.9823 | − | 41.2010i | 0.541688 | − | 1.48963i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.32783 | 0.0840532 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.8386 | −0.823580 | −0.411790 | − | 0.911279i | \(-0.635096\pi\) | ||||
−0.411790 | + | 0.911279i | \(0.635096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.2312 | + | 14.8704i | −0.512524 | + | 0.535546i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.07057 | + | 3.34294i | 0.290278 | + | 0.120237i | 0.523071 | − | 0.852289i | \(-0.324786\pi\) |
−0.232793 | + | 0.972526i | \(0.574786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.47328 | + | 1.47328i | −0.0529219 | + | 0.0529219i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.3098 | + | 29.0957i | −0.405738 | + | 1.04380i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.82591 | + | 3.24160i | 0.280392 | + | 0.116142i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.28079 | − | 17.5774i | −0.260527 | − | 0.628968i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.2073 | − | 9.22236i | −0.972311 | − | 0.329580i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.2311 | −0.757769 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.1792 | + | 9.60114i | −0.826249 | + | 0.342244i | −0.755417 | − | 0.655245i | \(-0.772566\pi\) |
−0.0708325 | + | 0.997488i | \(0.522566\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.625023 | + | 28.4540i | 0.0222514 | + | 1.01299i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.3525 | + | 26.3525i | −0.936989 | + | 0.936989i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.946326 | + | 0.946326i | 0.0336050 | + | 0.0336050i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 54.9449 | − | 1.20692i | 1.94870 | − | 0.0428052i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.64229 | − | 23.2785i | −0.341547 | − | 0.824568i | −0.997560 | − | 0.0698182i | \(-0.977758\pi\) |
0.656012 | − | 0.754750i | \(-0.272242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.55151i | − | 0.337908i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.9649 | + | 11.8732i | 0.458093 | + | 0.419519i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.50005 | − | 2.27819i | 0.194092 | − | 0.0803957i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.49052 | + | 15.6695i | −0.228761 | + | 0.552277i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0230 | + | 9.33801i | 0.845651 | + | 0.328713i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.9240 | + | 24.9240i | 0.876282 | + | 0.876282i | 0.993148 | − | 0.116866i | \(-0.0372847\pi\) |
−0.116866 | + | 0.993148i | \(0.537285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.09225 | + | 14.7080i | −0.213928 | + | 0.516467i | −0.994020 | − | 0.109197i | \(-0.965172\pi\) |
0.780092 | + | 0.625664i | \(0.215172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.85073 | − | 8.47026i | −0.310409 | − | 0.297065i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.12017i | 0.249409i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 32.6330i | − | 1.14168i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.808327 | − | 2.22288i | 0.0282452 | − | 0.0776737i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.49765 | + | 22.9294i | −0.331470 | + | 0.800240i | 0.667006 | + | 0.745053i | \(0.267576\pi\) |
−0.998476 | + | 0.0551876i | \(0.982424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2557 | + | 27.2557i | 0.950072 | + | 0.950072i | 0.998812 | − | 0.0487391i | \(-0.0155203\pi\) |
−0.0487391 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.589369 | + | 1.51621i | −0.0205192 | + | 0.0527878i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.6867 | − | 49.9420i | 0.719345 | − | 1.73665i | 0.0441379 | − | 0.999025i | \(-0.485946\pi\) |
0.675207 | − | 0.737628i | \(-0.264054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.359915 | − | 0.149082i | 0.0125004 | − | 0.00517782i | −0.376424 | − | 0.926447i | \(-0.622847\pi\) |
0.388925 | + | 0.921269i | \(0.372847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.856489 | − | 1.94575i | −0.0297113 | − | 0.0674973i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.89014i | 0.100137i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.39473 | − | 5.78138i | −0.0828730 | − | 0.200073i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.3677 | + | 11.7128i | 0.462057 | + | 0.404855i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.7697 | − | 27.7697i | −0.958717 | − | 0.958717i | 0.0404644 | − | 0.999181i | \(-0.487116\pi\) |
−0.999181 | + | 0.0404644i | \(0.987116\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.10756 | + | 1.10756i | −0.0381918 | + | 0.0381918i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.4386 | − | 0.646651i | 1.01392 | − | 0.0222718i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.2629 | − | 11.7069i | 0.972275 | − | 0.402729i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5645 | 0.809686 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.67982 | + | 21.9904i | 0.332211 | + | 0.754707i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.61346 | + | 15.9663i | 0.226706 | + | 0.547317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4516 | − | 8.47133i | −0.700250 | − | 0.290053i | 0.00401354 | − | 0.999992i | \(-0.498722\pi\) |
−0.704263 | + | 0.709939i | \(0.748722\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.47960 | − | 56.4145i | −0.0848007 | − | 1.92933i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.1734 | − | 13.1734i | 0.449996 | − | 0.449996i | −0.445357 | − | 0.895353i | \(-0.646923\pi\) |
0.895353 | + | 0.445357i | \(0.146923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.55122 | + | 3.12782i | 0.257644 | + | 0.106720i | 0.507767 | − | 0.861494i | \(-0.330471\pi\) |
−0.250123 | + | 0.968214i | \(0.580471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.64477 | − | 3.48809i | −0.124214 | − | 0.118874i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3590 | −0.658989 | −0.329494 | − | 0.944158i | \(-0.606878\pi\) | ||||
−0.329494 | + | 0.944158i | \(0.606878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.5889 | 0.836049 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.3692 | − | 25.2357i | −0.895547 | − | 0.857049i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.93268 | + | 1.62897i | 0.133407 | + | 0.0552591i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.283457 | + | 0.283457i | −0.00960456 | + | 0.00960456i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.36549 | − | 31.0667i | −0.0462147 | − | 1.05145i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.2559 | + | 10.8755i | 0.887611 | + | 0.367661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.24223 | + | 15.0701i | 0.210785 | + | 0.508880i | 0.993544 | − | 0.113444i | \(-0.0361884\pi\) |
−0.782759 | + | 0.622325i | \(0.786188\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.6871 | + | 42.4528i | 0.630299 | + | 1.43190i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6844 | −1.23593 | −0.617964 | − | 0.786207i | \(-0.712042\pi\) | ||||
−0.617964 | + | 0.786207i | \(0.712042\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.4178 | + | 4.72942i | −0.384240 | + | 0.159158i | −0.566438 | − | 0.824104i | \(-0.691679\pi\) |
0.182198 | + | 0.983262i | \(0.441679\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.0908 | + | 0.726874i | −1.11233 | + | 0.0244336i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.3135 | + | 34.3135i | −1.15213 | + | 1.15213i | −0.166009 | + | 0.986124i | \(0.553088\pi\) |
−0.986124 | + | 0.166009i | \(0.946912\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.9838 | + | 14.9838i | 0.502540 | + | 0.502540i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.2367 | + | 4.16503i | 0.443447 | + | 0.139534i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.70809 | − | 11.3663i | −0.157550 | − | 0.380360i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.0329316i | − | 0.00110078i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.527550 | − | 1.19847i | −0.0176144 | − | 0.0400159i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.4711 | − | 7.23678i | 0.582695 | − | 0.241360i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.6352 | − | 76.3741i | 1.05392 | − | 2.54439i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.04144 | + | 18.1149i | −0.234324 | + | 0.602825i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.1330 | + | 17.1330i | 0.569519 | + | 0.569519i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.32554 | + | 12.8570i | −0.176832 | + | 0.426910i | −0.987299 | − | 0.158875i | \(-0.949213\pi\) |
0.810467 | + | 0.585784i | \(0.199213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.7297 | + | 32.2562i | −0.389048 | + | 1.06987i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.5385i | 0.349157i | 0.984643 | + | 0.174579i | \(0.0558563\pi\) | ||||
−0.984643 | + | 0.174579i | \(0.944144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.1988i | 0.337530i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.7478 | − | 13.1568i | −0.454488 | − | 0.434950i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.32195 | + | 3.19147i | −0.0436546 | + | 0.105392i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.9849 | + | 11.9849i | 0.395346 | + | 0.395346i | 0.876588 | − | 0.481242i | \(-0.159814\pi\) |
−0.481242 | + | 0.876588i | \(0.659814\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.16092 | − | 0.451262i | −0.0382536 | − | 0.0148696i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.36235 | + | 3.28900i | −0.0448423 | + | 0.108259i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.71144 | + | 1.53733i | −0.122032 | + | 0.0505471i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.7974 | − | 30.0357i | −1.07721 | − | 0.986502i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 0.514845i | − | 0.0168915i | −0.999964 | − | 0.00844575i | \(-0.997312\pi\) | ||
0.999964 | − | 0.00844575i | \(-0.00268840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.42460 | + | 3.43928i | 0.0466892 | + | 0.112718i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.83166 | + | 0.193997i | −0.289136 | + | 0.00635117i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.9323 | + | 15.9323i | 0.521043 | + | 0.521043i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.6989 | + | 15.6989i | −0.512862 | + | 0.512862i | −0.915402 | − | 0.402540i | \(-0.868127\pi\) |
0.402540 | + | 0.915402i | \(0.368127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.24924 | − | 56.8715i | −0.0407675 | − | 1.85593i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.26022 | + | 3.42149i | −0.269275 | + | 0.111538i | −0.513236 | − | 0.858248i | \(-0.671553\pi\) |
0.243960 | + | 0.969785i | \(0.421553\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.79291 | −0.0909497 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.7965 | + | 31.8512i | −0.351210 | + | 1.03612i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.67384 | + | 4.04101i | 0.0543926 | + | 0.131315i | 0.948740 | − | 0.316058i | \(-0.102359\pi\) |
−0.894347 | + | 0.447373i | \(0.852359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.02914 | − | 0.426286i | −0.0334074 | − | 0.0138378i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.32939 | + | 5.99261i | −0.0755357 | + | 0.194324i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0579 | − | 32.0579i | 1.03846 | − | 1.03846i | 0.0392279 | − | 0.999230i | \(-0.487510\pi\) |
0.999230 | − | 0.0392279i | \(-0.0124898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.0220 | + | 7.05074i | 0.550819 | + | 0.228157i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.2083 | − | 10.6669i | 0.329989 | − | 0.344812i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.1598 | 0.941619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.3005 | 0.622596 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.4266 | + | 28.6728i | −0.335992 | + | 0.923970i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6433 | − | 5.65124i | −0.439193 | − | 0.181920i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.4258 | + | 37.4258i | −1.20353 | + | 1.20353i | −0.230448 | + | 0.973085i | \(0.574019\pi\) |
−0.973085 | + | 0.230448i | \(0.925981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −79.1684 | − | 30.7736i | −2.54326 | − | 0.988591i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.0754 | − | 13.7003i | −1.06144 | − | 0.439663i | −0.217478 | − | 0.976065i | \(-0.569783\pi\) |
−0.843962 | + | 0.536402i | \(0.819783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.12712 | − | 2.72110i | −0.0361337 | − | 0.0872344i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.278591 | − | 0.122632i | 0.00892206 | − | 0.00392735i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.7489 | −1.27168 | −0.635839 | − | 0.771821i | \(-0.719346\pi\) | ||||
−0.635839 | + | 0.771821i | \(0.719346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.34750 | + | 3.45765i | −0.266787 | + | 0.110507i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.3535 | − | 9.96489i | 0.681765 | − | 0.318155i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.8565 | − | 29.8565i | 0.952276 | − | 0.952276i | −0.0466360 | − | 0.998912i | \(-0.514850\pi\) |
0.998912 | + | 0.0466360i | \(0.0148501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.5214 | − | 12.5214i | −0.398965 | − | 0.398965i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.160912 | + | 7.32546i | 0.00512187 | + | 0.233172i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.11750 | + | 9.94053i | 0.130929 | + | 0.316091i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.2662i | 1.78736i | 0.448710 | + | 0.893678i | \(0.351884\pi\) | ||||
−0.448710 | + | 0.893678i | \(0.648116\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.4667 | + | 5.92782i | −0.427352 | + | 0.188114i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.5309 | − | 15.9600i | 1.22151 | − | 0.505966i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.8797 | + | 33.5085i | −0.439574 | + | 1.06122i | 0.536523 | + | 0.843886i | \(0.319738\pi\) |
−0.976096 | + | 0.217339i | \(0.930262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.1699 | + | 30.7277i | 0.479956 | + | 0.972181i |
(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 | 768.2.o.b.671.3 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.671.8 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.671.12 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.335.3 | 56 | |||
8.5 | even | 2 | 96.2.o.a.11.13 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.671.7 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.11.2 | ✓ | 56 | ||
24.11 | even | 2 | 384.2.o.a.335.8 | 56 | |||
32.3 | odd | 8 | inner | 768.2.o.b.95.8 | 56 | ||
32.13 | even | 8 | 384.2.o.a.47.8 | 56 | |||
32.19 | odd | 8 | 96.2.o.a.35.2 | yes | 56 | ||
32.29 | even | 8 | 768.2.o.a.95.7 | 56 | |||
96.29 | odd | 8 | 768.2.o.a.95.12 | 56 | |||
96.35 | even | 8 | inner | 768.2.o.b.95.3 | 56 | ||
96.77 | odd | 8 | 384.2.o.a.47.3 | 56 | |||
96.83 | even | 8 | 96.2.o.a.35.13 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.2 | ✓ | 56 | 24.5 | odd | 2 | ||
96.2.o.a.11.13 | yes | 56 | 8.5 | even | 2 | ||
96.2.o.a.35.2 | yes | 56 | 32.19 | odd | 8 | ||
96.2.o.a.35.13 | yes | 56 | 96.83 | even | 8 | ||
384.2.o.a.47.3 | 56 | 96.77 | odd | 8 | |||
384.2.o.a.47.8 | 56 | 32.13 | even | 8 | |||
384.2.o.a.335.3 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.335.8 | 56 | 24.11 | even | 2 | |||
768.2.o.a.95.7 | 56 | 32.29 | even | 8 | |||
768.2.o.a.95.12 | 56 | 96.29 | odd | 8 | |||
768.2.o.a.671.7 | 56 | 12.11 | even | 2 | |||
768.2.o.a.671.12 | 56 | 4.3 | odd | 2 | |||
768.2.o.b.95.3 | 56 | 96.35 | even | 8 | inner | ||
768.2.o.b.95.8 | 56 | 32.3 | odd | 8 | inner | ||
768.2.o.b.671.3 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.671.8 | 56 | 3.2 | odd | 2 | inner |