Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.17 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.f.757.18 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.796644 | − | 1.16849i | 0.563313 | − | 0.826244i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.730716 | − | 1.86173i | −0.365358 | − | 0.930867i | ||||
\(5\) | 2.52623i | 1.12976i | 0.825172 | + | 0.564882i | \(0.191078\pi\) | ||||
−0.825172 | + | 0.564882i | \(0.808922\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.75753 | − | 0.629309i | −0.974934 | − | 0.222494i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.95186 | + | 2.01251i | 0.933461 | + | 0.636410i | ||||
\(11\) | − | 5.70432i | − | 1.71992i | −0.510364 | − | 0.859958i | \(-0.670489\pi\) | ||
0.510364 | − | 0.859958i | \(-0.329511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.06046i | − | 0.848818i | −0.905471 | − | 0.424409i | \(-0.860482\pi\) | ||
0.905471 | − | 0.424409i | \(-0.139518\pi\) | |||||||
\(14\) | 0.796644 | − | 1.16849i | 0.212912 | − | 0.312291i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.93211 | + | 2.72080i | −0.733027 | + | 0.680199i | ||||
\(17\) | 5.49926 | 1.33377 | 0.666883 | − | 0.745163i | \(-0.267628\pi\) | ||||
0.666883 | + | 0.745163i | \(0.267628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.28486i | 1.67126i | 0.549291 | + | 0.835631i | \(0.314898\pi\) | ||||
−0.549291 | + | 0.835631i | \(0.685102\pi\) | |||||||
\(20\) | 4.70317 | − | 1.84596i | 1.05166 | − | 0.412768i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.66541 | − | 4.54431i | −1.42107 | − | 0.968851i | ||||
\(23\) | −0.539732 | −0.112542 | −0.0562710 | − | 0.998416i | \(-0.517921\pi\) | ||||
−0.0562710 | + | 0.998416i | \(0.517921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.38184 | −0.276367 | ||||||||
\(26\) | −3.57610 | − | 2.43809i | −0.701331 | − | 0.478150i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.730716 | − | 1.86173i | −0.138092 | − | 0.351835i | ||||
\(29\) | − | 8.35116i | − | 1.55077i | −0.631488 | − | 0.775386i | \(-0.717555\pi\) | ||
0.631488 | − | 0.775386i | \(-0.282445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.74848 | 1.21206 | 0.606032 | − | 0.795441i | \(-0.292761\pi\) | ||||
0.606032 | + | 0.795441i | \(0.292761\pi\) | |||||||
\(32\) | 0.843365 | + | 5.59363i | 0.149087 | + | 0.988824i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.38095 | − | 6.42580i | 0.751327 | − | 1.10202i | ||||
\(35\) | 2.52623i | 0.427011i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.2711i | − | 1.68855i | −0.535908 | − | 0.844277i | \(-0.680031\pi\) | ||
0.535908 | − | 0.844277i | \(-0.319969\pi\) | |||||||
\(38\) | 8.51226 | + | 5.80345i | 1.38087 | + | 0.941443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.58978 | − | 6.96615i | 0.251366 | − | 1.10145i | ||||
\(41\) | −5.58370 | −0.872028 | −0.436014 | − | 0.899940i | \(-0.643610\pi\) | ||||
−0.436014 | + | 0.899940i | \(0.643610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.98332i | 0.607451i | 0.952760 | + | 0.303725i | \(0.0982305\pi\) | ||||
−0.952760 | + | 0.303725i | \(0.901770\pi\) | |||||||
\(44\) | −10.6199 | + | 4.16824i | −1.60101 | + | 0.628385i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.429975 | + | 0.630669i | −0.0633963 | + | 0.0929871i | ||||
\(47\) | −4.83840 | −0.705754 | −0.352877 | − | 0.935670i | \(-0.614797\pi\) | ||||
−0.352877 | + | 0.935670i | \(0.614797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.10083 | + | 1.61466i | −0.155681 | + | 0.228347i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.69776 | + | 2.23632i | −0.790137 | + | 0.310122i | ||||
\(53\) | − | 11.1320i | − | 1.52910i | −0.644562 | − | 0.764552i | \(-0.722960\pi\) | ||
0.644562 | − | 0.764552i | \(-0.277040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4104 | 1.94310 | ||||||||
\(56\) | −2.75753 | − | 0.629309i | −0.368490 | − | 0.0840950i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.75821 | − | 6.65291i | −1.28132 | − | 0.873569i | ||||
\(59\) | − | 10.1647i | − | 1.32333i | −0.749798 | − | 0.661666i | \(-0.769850\pi\) | ||
0.749798 | − | 0.661666i | \(-0.230150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.14075i | − | 0.530169i | −0.964225 | − | 0.265084i | \(-0.914600\pi\) | ||
0.964225 | − | 0.265084i | \(-0.0853998\pi\) | |||||||
\(62\) | 5.37614 | − | 7.88550i | 0.682770 | − | 1.00146i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.20794 | + | 3.47068i | 0.900993 | + | 0.433835i | ||||
\(65\) | 7.73142 | 0.958964 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.96348i | − | 0.728555i | −0.931290 | − | 0.364278i | \(-0.881316\pi\) | ||
0.931290 | − | 0.364278i | \(-0.118684\pi\) | |||||||
\(68\) | −4.01839 | − | 10.2382i | −0.487302 | − | 1.24156i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.95186 | + | 2.01251i | 0.352815 | + | 0.240541i | ||||
\(71\) | 4.93014 | 0.585100 | 0.292550 | − | 0.956250i | \(-0.405496\pi\) | ||||
0.292550 | + | 0.956250i | \(0.405496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66798 | 1.01451 | 0.507255 | − | 0.861796i | \(-0.330660\pi\) | ||||
0.507255 | + | 0.861796i | \(0.330660\pi\) | |||||||
\(74\) | −12.0016 | − | 8.18239i | −1.39516 | − | 0.951183i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.5625 | − | 5.32317i | 1.55572 | − | 0.610609i | ||||
\(77\) | − | 5.70432i | − | 0.650067i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0532 | 1.35609 | 0.678044 | − | 0.735021i | \(-0.262828\pi\) | ||||
0.678044 | + | 0.735021i | \(0.262828\pi\) | |||||||
\(80\) | −6.87336 | − | 7.40718i | −0.768465 | − | 0.828148i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.44823 | + | 6.52448i | −0.491224 | + | 0.720508i | ||||
\(83\) | 5.83393i | 0.640357i | 0.947357 | + | 0.320178i | \(0.103743\pi\) | ||||
−0.947357 | + | 0.320178i | \(0.896257\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8924i | 1.50684i | ||||||||
\(86\) | 4.65445 | + | 3.17329i | 0.501902 | + | 0.342185i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.58978 | + | 15.7298i | −0.382672 | + | 1.67681i | ||||
\(89\) | −9.28810 | −0.984537 | −0.492268 | − | 0.870444i | \(-0.663832\pi\) | ||||
−0.492268 | + | 0.870444i | \(0.663832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.06046i | − | 0.320823i | ||||||
\(92\) | 0.394391 | + | 1.00484i | 0.0411181 | + | 0.104762i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.85449 | + | 5.65360i | −0.397560 | + | 0.583125i | ||||
\(95\) | −18.4032 | −1.88813 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3500 | 1.25395 | 0.626974 | − | 0.779040i | \(-0.284293\pi\) | ||||
0.626974 | + | 0.779040i | \(0.284293\pi\) | |||||||
\(98\) | 0.796644 | − | 1.16849i | 0.0804732 | − | 0.118035i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00973 | + | 2.57261i | 0.100973 | + | 0.257261i | ||||
\(101\) | − | 9.33719i | − | 0.929085i | −0.885551 | − | 0.464542i | \(-0.846219\pi\) | ||
0.885551 | − | 0.464542i | \(-0.153781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.28802 | −0.718110 | −0.359055 | − | 0.933316i | \(-0.616901\pi\) | ||||
−0.359055 | + | 0.933316i | \(0.616901\pi\) | |||||||
\(104\) | −1.92597 | + | 8.43930i | −0.188857 | + | 0.827541i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.0076 | − | 8.86828i | −1.26341 | − | 0.861364i | ||||
\(107\) | 7.31179i | 0.706858i | 0.935461 | + | 0.353429i | \(0.114984\pi\) | ||||
−0.935461 | + | 0.353429i | \(0.885016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9330i | 1.52611i | 0.646336 | + | 0.763053i | \(0.276300\pi\) | ||||
−0.646336 | + | 0.763053i | \(0.723700\pi\) | |||||||
\(110\) | 11.4800 | − | 16.8384i | 1.09457 | − | 1.60548i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.93211 | + | 2.72080i | −0.277058 | + | 0.257091i | ||||
\(113\) | 6.91459 | 0.650470 | 0.325235 | − | 0.945633i | \(-0.394557\pi\) | ||||
0.325235 | + | 0.945633i | \(0.394557\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.36349i | − | 0.127146i | ||||||
\(116\) | −15.5476 | + | 6.10233i | −1.44356 | + | 0.566587i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.8773 | − | 8.09766i | −1.09340 | − | 0.745450i | ||||
\(119\) | 5.49926 | 0.504116 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.5393 | −1.95811 | ||||||||
\(122\) | −4.83840 | − | 3.29870i | −0.438049 | − | 0.298651i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.93122 | − | 12.5639i | −0.442837 | − | 1.12827i | ||||
\(125\) | 9.14031i | 0.817534i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6103 | −1.56267 | −0.781333 | − | 0.624115i | \(-0.785460\pi\) | ||||
−0.781333 | + | 0.624115i | \(0.785460\pi\) | |||||||
\(128\) | 9.79760 | − | 5.65748i | 0.865994 | − | 0.500055i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.15919 | − | 9.03405i | 0.540196 | − | 0.792338i | ||||
\(131\) | 10.7551i | 0.939675i | 0.882753 | + | 0.469838i | \(0.155688\pi\) | ||||
−0.882753 | + | 0.469838i | \(0.844312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.28486i | 0.631678i | ||||||||
\(134\) | −6.96824 | − | 4.75077i | −0.601964 | − | 0.410404i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.1644 | − | 3.46073i | −1.30033 | − | 0.296755i | ||||
\(137\) | 1.56413 | 0.133633 | 0.0668164 | − | 0.997765i | \(-0.478716\pi\) | ||||
0.0668164 | + | 0.997765i | \(0.478716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2728i | 0.956149i | 0.878319 | + | 0.478074i | \(0.158665\pi\) | ||||
−0.878319 | + | 0.478074i | \(0.841335\pi\) | |||||||
\(140\) | 4.70317 | − | 1.84596i | 0.397490 | − | 0.156012i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.92757 | − | 5.76080i | 0.329594 | − | 0.483436i | ||||
\(143\) | −17.4578 | −1.45990 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0970 | 1.75201 | ||||||||
\(146\) | 6.90529 | − | 10.1284i | 0.571486 | − | 0.838233i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.1220 | + | 7.50523i | −1.57182 | + | 0.616926i | ||||
\(149\) | 6.48749i | 0.531476i | 0.964045 | + | 0.265738i | \(0.0856156\pi\) | ||||
−0.964045 | + | 0.265738i | \(0.914384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.383325 | −0.0311945 | −0.0155973 | − | 0.999878i | \(-0.504965\pi\) | ||||
−0.0155973 | + | 0.999878i | \(0.504965\pi\) | |||||||
\(152\) | 4.58443 | − | 20.0882i | 0.371846 | − | 1.62937i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.66541 | − | 4.54431i | −0.537114 | − | 0.366191i | ||||
\(155\) | 17.0482i | 1.36935i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.66658i | 0.691669i | 0.938296 | + | 0.345834i | \(0.112404\pi\) | ||||
−0.938296 | + | 0.345834i | \(0.887596\pi\) | |||||||
\(158\) | 9.60210 | − | 14.0840i | 0.763902 | − | 1.12046i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.1308 | + | 2.13053i | −1.11714 | + | 0.168433i | ||||
\(161\) | −0.539732 | −0.0425369 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25.0771i | 1.96419i | 0.188382 | + | 0.982096i | \(0.439676\pi\) | ||||
−0.188382 | + | 0.982096i | \(0.560324\pi\) | |||||||
\(164\) | 4.08010 | + | 10.3954i | 0.318602 | + | 0.811742i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.81686 | + | 4.64756i | 0.529091 | + | 0.360721i | ||||
\(167\) | −8.75411 | −0.677414 | −0.338707 | − | 0.940892i | \(-0.609989\pi\) | ||||
−0.338707 | + | 0.940892i | \(0.609989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.63361 | 0.279508 | ||||||||
\(170\) | 16.2330 | + | 11.0673i | 1.24502 | + | 0.848822i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.41588 | − | 2.91067i | 0.565456 | − | 0.221937i | ||||
\(173\) | 9.29760i | 0.706883i | 0.935457 | + | 0.353442i | \(0.114989\pi\) | ||||
−0.935457 | + | 0.353442i | \(0.885011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.38184 | −0.104457 | ||||||||
\(176\) | 15.5203 | + | 16.7257i | 1.16989 | + | 1.26075i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.39931 | + | 10.8530i | −0.554602 | + | 0.813467i | ||||
\(179\) | 7.65495i | 0.572158i | 0.958206 | + | 0.286079i | \(0.0923520\pi\) | ||||
−0.958206 | + | 0.286079i | \(0.907648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.50424i | − | 0.186138i | −0.995660 | − | 0.0930692i | \(-0.970332\pi\) | ||
0.995660 | − | 0.0930692i | \(-0.0296678\pi\) | |||||||
\(182\) | −3.57610 | − | 2.43809i | −0.265078 | − | 0.180724i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.48833 | + | 0.339658i | 0.109721 | + | 0.0250400i | ||||
\(185\) | 25.9471 | 1.90767 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 31.3695i | − | 2.29397i | ||||||
\(188\) | 3.53550 | + | 9.00782i | 0.257853 | + | 0.656963i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.6608 | + | 21.5039i | −1.06361 | + | 1.56006i | ||||
\(191\) | −3.20627 | −0.231997 | −0.115999 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.115999 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9544 | 0.788518 | 0.394259 | − | 0.918999i | \(-0.371001\pi\) | ||||
0.394259 | + | 0.918999i | \(0.371001\pi\) | |||||||
\(194\) | 9.83853 | − | 14.4308i | 0.706365 | − | 1.03607i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.730716 | − | 1.86173i | −0.0521940 | − | 0.132981i | ||||
\(197\) | − | 7.87749i | − | 0.561248i | −0.959818 | − | 0.280624i | \(-0.909459\pi\) | ||
0.959818 | − | 0.280624i | \(-0.0905414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.00753 | 0.0714217 | 0.0357109 | − | 0.999362i | \(-0.488630\pi\) | ||||
0.0357109 | + | 0.999362i | \(0.488630\pi\) | |||||||
\(200\) | 3.81046 | + | 0.869603i | 0.269440 | + | 0.0614902i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.9104 | − | 7.43842i | −0.767651 | − | 0.523365i | ||||
\(203\) | − | 8.35116i | − | 0.586137i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 14.1057i | − | 0.985186i | ||||||
\(206\) | −5.80596 | + | 8.51594i | −0.404520 | + | 0.593334i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.32688 | + | 8.97359i | 0.577365 | + | 0.622206i | ||||
\(209\) | 41.5552 | 2.87443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2709i | 1.12014i | 0.828446 | + | 0.560069i | \(0.189225\pi\) | ||||
−0.828446 | + | 0.560069i | \(0.810775\pi\) | |||||||
\(212\) | −20.7249 | + | 8.13436i | −1.42339 | + | 0.558670i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.54372 | + | 5.82490i | 0.584037 | + | 0.398182i | ||||
\(215\) | −10.0628 | −0.686276 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.74848 | 0.458117 | ||||||||
\(218\) | 18.6175 | + | 12.6929i | 1.26094 | + | 0.859674i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.5299 | − | 26.8284i | −0.709927 | − | 1.80877i | ||||
\(221\) | − | 16.8302i | − | 1.13212i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.78339 | 0.186390 | 0.0931949 | − | 0.995648i | \(-0.470292\pi\) | ||||
0.0931949 | + | 0.995648i | \(0.470292\pi\) | |||||||
\(224\) | 0.843365 | + | 5.59363i | 0.0563497 | + | 0.373740i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.50847 | − | 8.07959i | 0.366418 | − | 0.537447i | ||||
\(227\) | − | 11.4440i | − | 0.759565i | −0.925076 | − | 0.379782i | \(-0.875999\pi\) | ||
0.925076 | − | 0.379782i | \(-0.124001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.54391i | 0.300270i | 0.988666 | + | 0.150135i | \(0.0479708\pi\) | ||||
−0.988666 | + | 0.150135i | \(0.952029\pi\) | |||||||
\(230\) | −1.59322 | − | 1.08621i | −0.105054 | − | 0.0716229i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.25546 | + | 23.0286i | −0.345038 | + | 1.51190i | ||||
\(233\) | −16.0188 | −1.04943 | −0.524715 | − | 0.851278i | \(-0.675828\pi\) | ||||
−0.524715 | + | 0.851278i | \(0.675828\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.2229i | − | 0.797335i | ||||||
\(236\) | −18.9240 | + | 7.42752i | −1.23185 | + | 0.483490i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.38095 | − | 6.42580i | 0.283975 | − | 0.416523i | ||||
\(239\) | −19.2968 | −1.24821 | −0.624104 | − | 0.781341i | \(-0.714536\pi\) | ||||
−0.624104 | + | 0.781341i | \(0.714536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.1358 | −1.42589 | −0.712947 | − | 0.701218i | \(-0.752640\pi\) | ||||
−0.712947 | + | 0.701218i | \(0.752640\pi\) | |||||||
\(242\) | −17.1591 | + | 25.1683i | −1.10303 | + | 1.61788i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.70897 | + | 3.02571i | −0.493516 | + | 0.193701i | ||||
\(245\) | 2.52623i | 0.161395i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.2950 | 1.41860 | ||||||||
\(248\) | −18.6091 | − | 4.24688i | −1.18168 | − | 0.269677i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.6803 | + | 7.28158i | 0.675483 | + | 0.460527i | ||||
\(251\) | 7.94172i | 0.501277i | 0.968081 | + | 0.250638i | \(0.0806405\pi\) | ||||
−0.968081 | + | 0.250638i | \(0.919360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.07881i | 0.193563i | ||||||||
\(254\) | −14.0292 | + | 20.5774i | −0.880269 | + | 1.29114i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.19452 | − | 15.9553i | 0.0746576 | − | 0.997209i | ||||
\(257\) | 7.02501 | 0.438208 | 0.219104 | − | 0.975701i | \(-0.429687\pi\) | ||||
0.219104 | + | 0.975701i | \(0.429687\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 10.2711i | − | 0.638213i | ||||||
\(260\) | −5.64947 | − | 14.3938i | −0.350365 | − | 0.892668i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.5671 | + | 8.56797i | 0.776401 | + | 0.529331i | ||||
\(263\) | 19.4695 | 1.20054 | 0.600270 | − | 0.799798i | \(-0.295060\pi\) | ||||
0.600270 | + | 0.799798i | \(0.295060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.1221 | 1.72753 | ||||||||
\(266\) | 8.51226 | + | 5.80345i | 0.521920 | + | 0.355832i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.1024 | + | 4.35761i | −0.678188 | + | 0.266184i | ||||
\(269\) | − | 15.4258i | − | 0.940526i | −0.882526 | − | 0.470263i | \(-0.844159\pi\) | ||
0.882526 | − | 0.470263i | \(-0.155841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.28198 | 0.442349 | 0.221174 | − | 0.975234i | \(-0.429011\pi\) | ||||
0.221174 | + | 0.975234i | \(0.429011\pi\) | |||||||
\(272\) | −16.1244 | + | 14.9624i | −0.977686 | + | 0.907227i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.24606 | − | 1.82766i | 0.0752770 | − | 0.110413i | ||||
\(275\) | 7.88244i | 0.475329i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.43449i | 0.146275i | 0.997322 | + | 0.0731373i | \(0.0233011\pi\) | ||||
−0.997322 | + | 0.0731373i | \(0.976699\pi\) | |||||||
\(278\) | 13.1721 | + | 8.98043i | 0.790012 | + | 0.538611i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.58978 | − | 6.96615i | 0.0950075 | − | 0.416307i | ||||
\(281\) | 18.1555 | 1.08307 | 0.541534 | − | 0.840679i | \(-0.317844\pi\) | ||||
0.541534 | + | 0.840679i | \(0.317844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.2909i | 1.86005i | 0.367496 | + | 0.930025i | \(0.380215\pi\) | ||||
−0.367496 | + | 0.930025i | \(0.619785\pi\) | |||||||
\(284\) | −3.60253 | − | 9.17862i | −0.213771 | − | 0.544651i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.9077 | + | 20.3992i | −0.822378 | + | 1.20623i | ||||
\(287\) | −5.58370 | −0.329596 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.2418 | 0.778931 | ||||||||
\(290\) | 16.8068 | − | 24.6515i | 0.986928 | − | 1.44759i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.33383 | − | 16.1375i | −0.370659 | − | 0.944374i | ||||
\(293\) | 18.3419i | 1.07155i | 0.844362 | + | 0.535773i | \(0.179980\pi\) | ||||
−0.844362 | + | 0.535773i | \(0.820020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.6784 | 1.49505 | ||||||||
\(296\) | −6.46368 | + | 28.3228i | −0.375694 | + | 1.64623i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.58053 | + | 5.16822i | 0.439129 | + | 0.299387i | ||||
\(299\) | 1.65183i | 0.0955276i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.98332i | 0.229595i | ||||||||
\(302\) | −0.305373 | + | 0.447909i | −0.0175723 | + | 0.0257743i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −19.8206 | − | 21.3600i | −1.13679 | − | 1.22508i | ||||
\(305\) | 10.4605 | 0.598966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.5811i | − | 1.40292i | −0.712709 | − | 0.701460i | \(-0.752532\pi\) | ||
0.712709 | − | 0.701460i | \(-0.247468\pi\) | |||||||
\(308\) | −10.6199 | + | 4.16824i | −0.605126 | + | 0.237507i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 19.9206 | + | 13.5814i | 1.13141 | + | 0.771370i | ||||
\(311\) | 6.95251 | 0.394240 | 0.197120 | − | 0.980379i | \(-0.436841\pi\) | ||||
0.197120 | + | 0.980379i | \(0.436841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.81498 | −0.554775 | −0.277388 | − | 0.960758i | \(-0.589469\pi\) | ||||
−0.277388 | + | 0.960758i | \(0.589469\pi\) | |||||||
\(314\) | 10.1268 | + | 6.90418i | 0.571487 | + | 0.389626i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.80745 | − | 22.4398i | −0.495458 | − | 1.26234i | ||||
\(317\) | − | 6.69289i | − | 0.375910i | −0.982178 | − | 0.187955i | \(-0.939814\pi\) | ||
0.982178 | − | 0.187955i | \(-0.0601860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −47.6377 | −2.66720 | ||||||||
\(320\) | −8.76773 | + | 18.2089i | −0.490131 | + | 1.01791i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.429975 | + | 0.630669i | −0.0239616 | + | 0.0351458i | ||||
\(323\) | 40.0613i | 2.22907i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.22905i | 0.234586i | ||||||||
\(326\) | 29.3022 | + | 19.9775i | 1.62290 | + | 1.10645i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.3972 | + | 3.51388i | 0.850170 | + | 0.194021i | ||||
\(329\) | −4.83840 | −0.266750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.10916i | − | 0.115930i | −0.998319 | − | 0.0579651i | \(-0.981539\pi\) | ||
0.998319 | − | 0.0579651i | \(-0.0184612\pi\) | |||||||
\(332\) | 10.8612 | − | 4.26294i | 0.596087 | − | 0.233959i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.97391 | + | 10.2291i | −0.381596 | + | 0.559709i | ||||
\(335\) | 15.0651 | 0.823096 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.53954 | −0.301758 | −0.150879 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150879 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(338\) | 2.89469 | − | 4.24582i | 0.157451 | − | 0.230942i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.8639 | − | 10.1514i | 1.40267 | − | 0.550536i | ||||
\(341\) | − | 38.4955i | − | 2.08465i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.50674 | − | 10.9841i | 0.135154 | − | 0.592224i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.8641 | + | 7.40688i | 0.584058 | + | 0.398196i | ||||
\(347\) | − | 9.63790i | − | 0.517389i | −0.965959 | − | 0.258695i | \(-0.916708\pi\) | ||
0.965959 | − | 0.258695i | \(-0.0832924\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.04565i | 0.430674i | 0.976540 | + | 0.215337i | \(0.0690850\pi\) | ||||
−0.976540 | + | 0.215337i | \(0.930915\pi\) | |||||||
\(350\) | −1.10083 | + | 1.61466i | −0.0588420 | + | 0.0863070i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 31.9079 | − | 4.81082i | 1.70070 | − | 0.256418i | ||||
\(353\) | −27.2775 | −1.45184 | −0.725918 | − | 0.687782i | \(-0.758585\pi\) | ||||
−0.725918 | + | 0.687782i | \(0.758585\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4547i | 0.661025i | ||||||||
\(356\) | 6.78696 | + | 17.2920i | 0.359708 | + | 0.916473i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.94470 | + | 6.09827i | 0.472742 | + | 0.322304i | ||||
\(359\) | 7.36413 | 0.388664 | 0.194332 | − | 0.980936i | \(-0.437746\pi\) | ||||
0.194332 | + | 0.980936i | \(0.437746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −34.0692 | −1.79312 | ||||||||
\(362\) | −2.92616 | − | 1.99499i | −0.153796 | − | 0.104854i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.69776 | + | 2.23632i | −0.298644 | + | 0.117215i | ||||
\(365\) | 21.8973i | 1.14616i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8746 | 1.14185 | 0.570923 | − | 0.821003i | \(-0.306585\pi\) | ||||
0.570923 | + | 0.821003i | \(0.306585\pi\) | |||||||
\(368\) | 1.58255 | − | 1.46850i | 0.0824963 | − | 0.0765510i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.6706 | − | 30.3188i | 1.07461 | − | 1.57620i | ||||
\(371\) | − | 11.1320i | − | 0.577947i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.99106i | 0.465539i | 0.972532 | + | 0.232770i | \(0.0747788\pi\) | ||||
−0.972532 | + | 0.232770i | \(0.925221\pi\) | |||||||
\(374\) | −36.6548 | − | 24.9903i | −1.89538 | − | 1.29222i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.3420 | + | 3.04485i | 0.688063 | + | 0.157026i | ||||
\(377\) | −25.5584 | −1.31632 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.9165i | − | 1.48534i | −0.669656 | − | 0.742671i | \(-0.733558\pi\) | ||
0.669656 | − | 0.742671i | \(-0.266442\pi\) | |||||||
\(380\) | 13.4475 | + | 34.2619i | 0.689844 | + | 1.75760i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.55425 | + | 3.74647i | −0.130687 | + | 0.191686i | ||||
\(383\) | −12.5404 | −0.640786 | −0.320393 | − | 0.947285i | \(-0.603815\pi\) | ||||
−0.320393 | + | 0.947285i | \(0.603815\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4104 | 0.734423 | ||||||||
\(386\) | 8.72680 | − | 12.8001i | 0.444182 | − | 0.651509i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.02431 | − | 22.9924i | −0.458140 | − | 1.16726i | ||||
\(389\) | 7.50374i | 0.380455i | 0.981740 | + | 0.190227i | \(0.0609225\pi\) | ||||
−0.981740 | + | 0.190227i | \(0.939077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.96813 | −0.150105 | ||||||||
\(392\) | −2.75753 | − | 0.629309i | −0.139276 | − | 0.0317849i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.20474 | − | 6.27556i | −0.463728 | − | 0.316158i | ||||
\(395\) | 30.4491i | 1.53206i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.6639i | − | 1.38841i | −0.719778 | − | 0.694205i | \(-0.755756\pi\) | ||
0.719778 | − | 0.694205i | \(-0.244244\pi\) | |||||||
\(398\) | 0.802641 | − | 1.17728i | 0.0402327 | − | 0.0590117i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.05170 | − | 3.75970i | 0.202585 | − | 0.187985i | ||||
\(401\) | 35.8414 | 1.78983 | 0.894916 | − | 0.446234i | \(-0.147235\pi\) | ||||
0.894916 | + | 0.446234i | \(0.147235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.6534i | − | 1.02882i | ||||||
\(404\) | −17.3834 | + | 6.82283i | −0.864855 | + | 0.339449i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.75821 | − | 6.65291i | −0.484292 | − | 0.330178i | ||||
\(407\) | −58.5894 | −2.90417 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4056 | 0.910097 | 0.455048 | − | 0.890467i | \(-0.349622\pi\) | ||||
0.455048 | + | 0.890467i | \(0.349622\pi\) | |||||||
\(410\) | −16.4823 | − | 11.2372i | −0.814004 | − | 0.554968i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.32547 | + | 13.5684i | 0.262367 | + | 0.668465i | ||||
\(413\) | − | 10.1647i | − | 0.500173i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.7378 | −0.723452 | ||||||||
\(416\) | 17.1191 | − | 2.58108i | 0.839331 | − | 0.126548i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.1047 | − | 48.5566i | 1.61920 | − | 2.37498i | ||||
\(419\) | 0.0173724i | 0.000848699i | 1.00000 | 0.000424349i | \(0.000135075\pi\) | |||||
−1.00000 | 0.000424349i | \(0.999865\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.03437i | 0.0504121i | 0.999682 | + | 0.0252060i | \(0.00802418\pi\) | ||||
−0.999682 | + | 0.0252060i | \(0.991976\pi\) | |||||||
\(422\) | 19.0124 | + | 12.9622i | 0.925507 | + | 0.630988i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.00550 | + | 30.6970i | −0.340217 | + | 1.49078i | ||||
\(425\) | −7.59908 | −0.368609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.14075i | − | 0.200385i | ||||||
\(428\) | 13.6126 | − | 5.34284i | 0.657991 | − | 0.258256i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.01646 | + | 11.7582i | −0.386588 | + | 0.567031i | ||||
\(431\) | −10.1392 | −0.488390 | −0.244195 | − | 0.969726i | \(-0.578524\pi\) | ||||
−0.244195 | + | 0.969726i | \(0.578524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.5806 | −1.61378 | −0.806890 | − | 0.590701i | \(-0.798851\pi\) | ||||
−0.806890 | + | 0.590701i | \(0.798851\pi\) | |||||||
\(434\) | 5.37614 | − | 7.88550i | 0.258063 | − | 0.378516i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.6630 | − | 11.6425i | 1.42060 | − | 0.557575i | ||||
\(437\) | − | 3.93188i | − | 0.188087i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.92098 | −0.187138 | −0.0935692 | − | 0.995613i | \(-0.529828\pi\) | ||||
−0.0935692 | + | 0.995613i | \(0.529828\pi\) | |||||||
\(440\) | −39.7372 | − | 9.06861i | −1.89439 | − | 0.432329i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.6659 | − | 13.4077i | −0.935411 | − | 0.637740i | ||||
\(443\) | 34.6306i | 1.64535i | 0.568514 | + | 0.822674i | \(0.307519\pi\) | ||||
−0.568514 | + | 0.822674i | \(0.692481\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 23.4639i | − | 1.11229i | ||||||
\(446\) | 2.21737 | − | 3.25235i | 0.104996 | − | 0.154003i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.20794 | + | 3.47068i | 0.340543 | + | 0.163974i | ||||
\(449\) | 17.7862 | 0.839383 | 0.419691 | − | 0.907667i | \(-0.362138\pi\) | ||||
0.419691 | + | 0.907667i | \(0.362138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.8512i | 1.49982i | ||||||||
\(452\) | −5.05260 | − | 12.8731i | −0.237654 | − | 0.605501i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.3721 | − | 9.11679i | −0.627586 | − | 0.427872i | ||||
\(455\) | 7.73142 | 0.362454 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5852 | 0.541933 | 0.270966 | − | 0.962589i | \(-0.412657\pi\) | ||||
0.270966 | + | 0.962589i | \(0.412657\pi\) | |||||||
\(458\) | 5.30949 | + | 3.61988i | 0.248096 | + | 0.169146i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.53845 | + | 0.996322i | −0.118356 | + | 0.0464538i | ||||
\(461\) | 12.5948i | 0.586596i | 0.956021 | + | 0.293298i | \(0.0947529\pi\) | ||||
−0.956021 | + | 0.293298i | \(0.905247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.16107 | −0.146907 | −0.0734537 | − | 0.997299i | \(-0.523402\pi\) | ||||
−0.0734537 | + | 0.997299i | \(0.523402\pi\) | |||||||
\(464\) | 22.7218 | + | 24.4865i | 1.05483 | + | 1.13676i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.7613 | + | 18.7178i | −0.591157 | + | 0.867085i | ||||
\(467\) | − | 20.8974i | − | 0.967015i | −0.875340 | − | 0.483507i | \(-0.839363\pi\) | ||
0.875340 | − | 0.483507i | \(-0.160637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.96348i | − | 0.275368i | ||||||
\(470\) | −14.2823 | − | 9.73732i | −0.658794 | − | 0.449149i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.39674 | + | 28.0295i | −0.294434 | + | 1.29016i | ||||
\(473\) | 22.7221 | 1.04476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10.0665i | − | 0.461882i | ||||||
\(476\) | −4.01839 | − | 10.2382i | −0.184183 | − | 0.469265i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.3727 | + | 22.5481i | −0.703131 | + | 1.03132i | ||||
\(479\) | −28.2766 | −1.29199 | −0.645996 | − | 0.763341i | \(-0.723558\pi\) | ||||
−0.645996 | + | 0.763341i | \(0.723558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.4341 | −1.43327 | ||||||||
\(482\) | −17.6344 | + | 25.8654i | −0.803224 | + | 1.17814i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.7391 | + | 40.1004i | 0.715412 | + | 1.82274i | ||||
\(485\) | 31.1988i | 1.41667i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.8879 | −1.21841 | −0.609203 | − | 0.793014i | \(-0.708511\pi\) | ||||
−0.609203 | + | 0.793014i | \(0.708511\pi\) | |||||||
\(488\) | −2.60581 | + | 11.4182i | −0.117960 | + | 0.516879i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.95186 | + | 2.01251i | 0.133352 | + | 0.0909158i | ||||
\(491\) | 6.00142i | 0.270840i | 0.990788 | + | 0.135420i | \(0.0432384\pi\) | ||||
−0.990788 | + | 0.135420i | \(0.956762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 45.9252i | − | 2.06837i | ||||||
\(494\) | 17.7612 | − | 26.0514i | 0.799114 | − | 1.17211i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.7873 | + | 18.3613i | −0.888475 | + | 0.824445i | ||||
\(497\) | 4.93014 | 0.221147 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3124i | − | 0.819777i | −0.912136 | − | 0.409888i | \(-0.865568\pi\) | ||
0.912136 | − | 0.409888i | \(-0.134432\pi\) | |||||||
\(500\) | 17.0168 | − | 6.67897i | 0.761016 | − | 0.298693i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.27978 | + | 6.32672i | 0.414177 | + | 0.282375i | ||||
\(503\) | 6.95874 | 0.310275 | 0.155137 | − | 0.987893i | \(-0.450418\pi\) | ||||
0.155137 | + | 0.987893i | \(0.450418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.5879 | 1.04965 | ||||||||
\(506\) | 3.59754 | + | 2.45271i | 0.159930 | + | 0.109036i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.8682 | + | 32.7858i | 0.570932 | + | 1.45463i | ||||
\(509\) | 15.2426i | 0.675618i | 0.941215 | + | 0.337809i | \(0.109686\pi\) | ||||
−0.941215 | + | 0.337809i | \(0.890314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.66798 | 0.383449 | ||||||||
\(512\) | −17.6920 | − | 14.1065i | −0.781882 | − | 0.623426i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.59644 | − | 8.20862i | 0.246848 | − | 0.362067i | ||||
\(515\) | − | 18.4112i | − | 0.811295i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.5998i | 1.21384i | ||||||||
\(518\) | −12.0016 | − | 8.18239i | −0.527320 | − | 0.359513i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −21.3196 | − | 4.86545i | −0.934927 | − | 0.213364i | ||||
\(521\) | 13.0764 | 0.572887 | 0.286444 | − | 0.958097i | \(-0.407527\pi\) | ||||
0.286444 | + | 0.958097i | \(0.407527\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.9123i | − | 1.04561i | −0.852452 | − | 0.522806i | \(-0.824885\pi\) | ||
0.852452 | − | 0.522806i | \(-0.175115\pi\) | |||||||
\(524\) | 20.0231 | − | 7.85891i | 0.874713 | − | 0.343318i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.5103 | − | 22.7498i | 0.676279 | − | 0.991939i | ||||
\(527\) | 37.1116 | 1.61661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7087 | −0.987334 | ||||||||
\(530\) | 22.4033 | − | 32.8603i | 0.973138 | − | 1.42736i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.5625 | − | 5.32317i | 0.588008 | − | 0.230789i | ||||
\(533\) | 17.0887i | 0.740193i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.4713 | −0.798583 | ||||||||
\(536\) | −3.75287 | + | 16.4445i | −0.162099 | + | 0.710293i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.0248 | − | 12.2889i | −0.777104 | − | 0.529810i | ||||
\(539\) | − | 5.70432i | − | 0.245702i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.9717i | − | 0.600689i | −0.953831 | − | 0.300345i | \(-0.902898\pi\) | ||
0.953831 | − | 0.300345i | \(-0.0971017\pi\) | |||||||
\(542\) | 5.80115 | − | 8.50889i | 0.249181 | − | 0.365488i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.63788 | + | 30.7608i | 0.198847 | + | 1.31886i | ||||
\(545\) | −40.2504 | −1.72414 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.5760i | 0.922522i | 0.887264 | + | 0.461261i | \(0.152603\pi\) | ||||
−0.887264 | + | 0.461261i | \(0.847397\pi\) | |||||||
\(548\) | −1.14294 | − | 2.91200i | −0.0488238 | − | 0.124394i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.21051 | + | 6.27950i | 0.392738 | + | 0.267759i | ||||
\(551\) | 60.8371 | 2.59175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0532 | 0.512553 | ||||||||
\(554\) | 2.84467 | + | 1.93942i | 0.120858 | + | 0.0823983i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.9870 | − | 8.23723i | 0.890047 | − | 0.349337i | ||||
\(557\) | 0.679074i | 0.0287733i | 0.999897 | + | 0.0143866i | \(0.00457957\pi\) | ||||
−0.999897 | + | 0.0143866i | \(0.995420\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1908 | 0.515615 | ||||||||
\(560\) | −6.87336 | − | 7.40718i | −0.290452 | − | 0.313010i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.4635 | − | 21.2145i | 0.610106 | − | 0.894878i | ||||
\(563\) | 15.8429i | 0.667698i | 0.942626 | + | 0.333849i | \(0.108348\pi\) | ||||
−0.942626 | + | 0.333849i | \(0.891652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.4678i | 0.734877i | ||||||||
\(566\) | 36.5629 | + | 24.9277i | 1.53686 | + | 1.04779i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.5950 | − | 3.10258i | −0.570434 | − | 0.130182i | ||||
\(569\) | 3.24267 | 0.135940 | 0.0679698 | − | 0.997687i | \(-0.478348\pi\) | ||||
0.0679698 | + | 0.997687i | \(0.478348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.38251i | 0.0578563i | 0.999581 | + | 0.0289281i | \(0.00920939\pi\) | ||||
−0.999581 | + | 0.0289281i | \(0.990791\pi\) | |||||||
\(572\) | 12.7567 | + | 32.5018i | 0.533385 | + | 1.35897i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.44823 | + | 6.52448i | −0.185665 | + | 0.272326i | ||||
\(575\) | 0.745822 | 0.0311029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.57598 | −0.315392 | −0.157696 | − | 0.987488i | \(-0.550407\pi\) | ||||
−0.157696 | + | 0.987488i | \(0.550407\pi\) | |||||||
\(578\) | 10.5490 | − | 15.4729i | 0.438782 | − | 0.643587i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.4159 | − | 39.2769i | −0.640110 | − | 1.63089i | ||||
\(581\) | 5.83393i | 0.242032i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −63.5007 | −2.62993 | ||||||||
\(584\) | −23.9022 | − | 5.45484i | −0.989080 | − | 0.225723i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.4323 | + | 14.6120i | 0.885358 | + | 0.603615i | ||||
\(587\) | − | 5.03970i | − | 0.208011i | −0.994577 | − | 0.104005i | \(-0.966834\pi\) | ||
0.994577 | − | 0.104005i | \(-0.0331659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.1618i | 2.02568i | ||||||||
\(590\) | 20.4565 | − | 30.0048i | 0.842183 | − | 1.23528i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.9455 | + | 30.1159i | 1.14855 | + | 1.23776i | ||||
\(593\) | −7.94121 | −0.326106 | −0.163053 | − | 0.986617i | \(-0.552134\pi\) | ||||
−0.163053 | + | 0.986617i | \(0.552134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8924i | 0.569532i | ||||||||
\(596\) | 12.0780 | − | 4.74051i | 0.494733 | − | 0.194179i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.93014 | + | 1.31592i | 0.0789291 | + | 0.0538119i | ||||
\(599\) | −33.0131 | −1.34888 | −0.674439 | − | 0.738331i | \(-0.735614\pi\) | ||||
−0.674439 | + | 0.738331i | \(0.735614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4038 | 1.64810 | 0.824052 | − | 0.566513i | \(-0.191708\pi\) | ||||
0.824052 | + | 0.566513i | \(0.191708\pi\) | |||||||
\(602\) | 4.65445 | + | 3.17329i | 0.189701 | + | 0.129334i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.280101 | + | 0.713648i | 0.0113972 | + | 0.0290379i | ||||
\(605\) | − | 54.4131i | − | 2.21221i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.544975 | 0.0221199 | 0.0110599 | − | 0.999939i | \(-0.496479\pi\) | ||||
0.0110599 | + | 0.999939i | \(0.496479\pi\) | |||||||
\(608\) | −40.7489 | + | 6.14380i | −1.65258 | + | 0.249164i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.33328 | − | 12.2229i | 0.337405 | − | 0.494892i | ||||
\(611\) | 14.8077i | 0.599056i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.75425i | 0.111243i | 0.998452 | + | 0.0556215i | \(0.0177140\pi\) | ||||
−0.998452 | + | 0.0556215i | \(0.982286\pi\) | |||||||
\(614\) | −28.7227 | − | 19.5824i | −1.15915 | − | 0.790283i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.58978 | + | 15.7298i | −0.144636 | + | 0.633773i | ||||
\(617\) | 32.6720 | 1.31533 | 0.657664 | − | 0.753312i | \(-0.271545\pi\) | ||||
0.657664 | + | 0.753312i | \(0.271545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.4789i | − | 0.421183i | −0.977574 | − | 0.210591i | \(-0.932461\pi\) | ||
0.977574 | − | 0.210591i | \(-0.0675389\pi\) | |||||||
\(620\) | 31.7392 | − | 12.4574i | 1.27468 | − | 0.500301i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.53867 | − | 8.12390i | 0.222081 | − | 0.325739i | ||||
\(623\) | −9.28810 | −0.372120 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9997 | −1.19999 | ||||||||
\(626\) | −7.81904 | + | 11.4687i | −0.312512 | + | 0.458380i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.1349 | − | 6.33281i | 0.643852 | − | 0.252707i | ||||
\(629\) | − | 56.4832i | − | 2.25213i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.94128 | −0.316138 | −0.158069 | − | 0.987428i | \(-0.550527\pi\) | ||||
−0.158069 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(632\) | −33.2370 | − | 7.58518i | −1.32210 | − | 0.301722i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.82055 | − | 5.33185i | −0.310594 | − | 0.211755i | ||||
\(635\) | − | 44.4878i | − | 1.76544i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.06046i | − | 0.121260i | ||||||
\(638\) | −37.9503 | + | 55.6639i | −1.50247 | + | 2.20376i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.2921 | + | 24.7510i | 0.564944 | + | 0.978369i | ||||
\(641\) | 17.5222 | 0.692084 | 0.346042 | − | 0.938219i | \(-0.387525\pi\) | ||||
0.346042 | + | 0.938219i | \(0.387525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.7998i | 1.37237i | 0.727426 | + | 0.686186i | \(0.240716\pi\) | ||||
−0.727426 | + | 0.686186i | \(0.759284\pi\) | |||||||
\(644\) | 0.394391 | + | 1.00484i | 0.0155412 | + | 0.0395962i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 46.8111 | + | 31.9146i | 1.84176 | + | 1.25566i | ||||
\(647\) | 24.4054 | 0.959474 | 0.479737 | − | 0.877412i | \(-0.340732\pi\) | ||||
0.479737 | + | 0.877412i | \(0.340732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.9827 | −2.27602 | ||||||||
\(650\) | 4.94158 | + | 3.36905i | 0.193825 | + | 0.132145i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 46.6869 | − | 18.3243i | 1.82840 | − | 0.717633i | ||||
\(653\) | 20.9374i | 0.819345i | 0.912233 | + | 0.409673i | \(0.134357\pi\) | ||||
−0.912233 | + | 0.409673i | \(0.865643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.1698 | −1.06161 | ||||||||
\(656\) | 16.3720 | − | 15.1921i | 0.639220 | − | 0.593153i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.85449 | + | 5.65360i | −0.150264 | + | 0.220400i | ||||
\(659\) | − | 27.6061i | − | 1.07538i | −0.843143 | − | 0.537690i | \(-0.819297\pi\) | ||
0.843143 | − | 0.537690i | \(-0.180703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.2679i | − | 1.21618i | −0.793868 | − | 0.608090i | \(-0.791936\pi\) | ||
0.793868 | − | 0.608090i | \(-0.208064\pi\) | |||||||
\(662\) | −2.46453 | − | 1.68025i | −0.0957865 | − | 0.0653049i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.67134 | − | 16.0872i | 0.142476 | − | 0.624305i | ||||
\(665\) | −18.4032 | −0.713647 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50739i | 0.174527i | ||||||||
\(668\) | 6.39677 | + | 16.2978i | 0.247498 | + | 0.630582i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.0015 | − | 17.6034i | 0.463660 | − | 0.680078i | ||||
\(671\) | −23.6201 | −0.911846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7023 | 0.720923 | 0.360461 | − | 0.932774i | \(-0.382619\pi\) | ||||
0.360461 | + | 0.932774i | \(0.382619\pi\) | |||||||
\(674\) | −4.41304 | + | 6.47287i | −0.169984 | + | 0.249326i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.65514 | − | 6.76481i | −0.102121 | − | 0.260185i | ||||
\(677\) | − | 1.58757i | − | 0.0610152i | −0.999535 | − | 0.0305076i | \(-0.990288\pi\) | ||
0.999535 | − | 0.0305076i | \(-0.00971238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.3500 | 0.473948 | ||||||||
\(680\) | 8.74260 | − | 38.3087i | 0.335264 | − | 1.46907i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −44.9814 | − | 30.6672i | −1.72243 | − | 1.17431i | ||||
\(683\) | 34.1798i | 1.30785i | 0.756557 | + | 0.653927i | \(0.226880\pi\) | ||||
−0.756557 | + | 0.653927i | \(0.773120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.95135i | 0.150974i | ||||||||
\(686\) | 0.796644 | − | 1.16849i | 0.0304160 | − | 0.0446130i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.8378 | − | 11.6795i | −0.413187 | − | 0.445278i | ||||
\(689\) | −34.0691 | −1.29793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.5718i | 1.50538i | 0.658373 | + | 0.752692i | \(0.271245\pi\) | ||||
−0.658373 | + | 0.752692i | \(0.728755\pi\) | |||||||
\(692\) | 17.3097 | − | 6.79390i | 0.658014 | − | 0.258265i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.2617 | − | 7.67798i | −0.427490 | − | 0.291452i | ||||
\(695\) | −28.4778 | −1.08022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.7062 | −1.16308 | ||||||||
\(698\) | 9.40123 | + | 6.40952i | 0.355842 | + | 0.242604i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00973 | + | 2.57261i | 0.0381642 | + | 0.0972356i | ||||
\(701\) | − | 30.2500i | − | 1.14253i | −0.820767 | − | 0.571263i | \(-0.806454\pi\) | ||
0.820767 | − | 0.571263i | \(-0.193546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 74.8233 | 2.82202 | ||||||||
\(704\) | 19.7978 | − | 41.1164i | 0.746159 | − | 1.54963i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.7305 | + | 31.8734i | −0.817837 | + | 1.19957i | ||||
\(707\) | − | 9.33719i | − | 0.351161i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 51.5735i | − | 1.93688i | −0.249244 | − | 0.968441i | \(-0.580182\pi\) | ||
0.249244 | − | 0.968441i | \(-0.419818\pi\) | |||||||
\(710\) | 14.5531 | + | 9.92194i | 0.546168 | + | 0.372364i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.6122 | + | 5.84509i | 0.959858 | + | 0.219054i | ||||
\(713\) | −3.64237 | −0.136408 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 44.1025i | − | 1.64934i | ||||||
\(716\) | 14.2515 | − | 5.59359i | 0.532603 | − | 0.209042i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.86659 | − | 8.60488i | 0.218939 | − | 0.321131i | ||||
\(719\) | 11.2028 | 0.417795 | 0.208898 | − | 0.977938i | \(-0.433012\pi\) | ||||
0.208898 | + | 0.977938i | \(0.433012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.28802 | −0.271420 | ||||||||
\(722\) | −27.1411 | + | 39.8094i | −1.01009 | + | 1.48155i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.66222 | + | 1.82989i | −0.173270 | + | 0.0680072i | ||||
\(725\) | 11.5399i | 0.428583i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.814724 | −0.0302164 | −0.0151082 | − | 0.999886i | \(-0.504809\pi\) | ||||
−0.0151082 | + | 0.999886i | \(0.504809\pi\) | |||||||
\(728\) | −1.92597 | + | 8.43930i | −0.0713813 | + | 0.312781i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.5867 | + | 17.4444i | 0.947005 | + | 0.645645i | ||||
\(731\) | 21.9053i | 0.810197i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7283i | 0.470131i | 0.971980 | + | 0.235066i | \(0.0755305\pi\) | ||||
−0.971980 | + | 0.235066i | \(0.924470\pi\) | |||||||
\(734\) | 17.4263 | − | 25.5602i | 0.643217 | − | 0.943444i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.455191 | − | 3.01906i | −0.0167786 | − | 0.111284i | ||||
\(737\) | −34.0176 | −1.25305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.13395i | 0.335998i | 0.985787 | + | 0.167999i | \(0.0537305\pi\) | ||||
−0.985787 | + | 0.167999i | \(0.946269\pi\) | |||||||
\(740\) | −18.9599 | − | 48.3066i | −0.696981 | − | 1.77578i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.0076 | − | 8.86828i | −0.477525 | − | 0.325565i | ||||
\(743\) | 15.4112 | 0.565383 | 0.282692 | − | 0.959211i | \(-0.408773\pi\) | ||||
0.282692 | + | 0.959211i | \(0.408773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.3889 | −0.600442 | ||||||||
\(746\) | 10.5059 | + | 7.16267i | 0.384649 | + | 0.262244i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −58.4017 | + | 22.9222i | −2.13538 | + | 0.838119i | ||||
\(749\) | 7.31179i | 0.267167i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.7526 | 1.48708 | 0.743542 | − | 0.668690i | \(-0.233144\pi\) | ||||
0.743542 | + | 0.668690i | \(0.233144\pi\) | |||||||
\(752\) | 14.1867 | − | 13.1643i | 0.517337 | − | 0.480053i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.3609 | + | 29.8646i | −0.741501 | + | 1.08760i | ||||
\(755\) | − | 0.968366i | − | 0.0352424i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.0085i | − | 0.945296i | −0.881251 | − | 0.472648i | \(-0.843298\pi\) | ||
0.881251 | − | 0.472648i | \(-0.156702\pi\) | |||||||
\(758\) | −33.7885 | − | 23.0362i | −1.22726 | − | 0.836712i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 50.7475 | + | 11.5813i | 1.84080 | + | 0.420099i | ||||
\(761\) | 10.3686 | 0.375861 | 0.187931 | − | 0.982182i | \(-0.439822\pi\) | ||||
0.187931 | + | 0.982182i | \(0.439822\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.9330i | 0.576814i | ||||||||
\(764\) | 2.34287 | + | 5.96922i | 0.0847620 | + | 0.215959i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.99027 | + | 14.6533i | −0.360963 | + | 0.529446i | ||||
\(767\) | −31.1086 | −1.12327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.7525 | −1.14502 | −0.572512 | − | 0.819896i | \(-0.694031\pi\) | ||||
−0.572512 | + | 0.819896i | \(0.694031\pi\) | |||||||
\(770\) | 11.4800 | − | 16.8384i | 0.413710 | − | 0.606813i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.00459 | − | 20.3943i | −0.288091 | − | 0.734006i | ||||
\(773\) | − | 16.3614i | − | 0.588478i | −0.955732 | − | 0.294239i | \(-0.904934\pi\) | ||
0.955732 | − | 0.294239i | \(-0.0950662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.32530 | −0.334975 | ||||||||
\(776\) | −34.0554 | − | 7.77194i | −1.22252 | − | 0.278997i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.76801 | + | 5.97781i | 0.314348 | + | 0.214315i | ||||
\(779\) | − | 40.6765i | − | 1.45739i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 28.1231i | − | 1.00632i | ||||||
\(782\) | −2.36454 | + | 3.46821i | −0.0845558 | + | 0.124023i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.93211 | + | 2.72080i | −0.104718 | + | 0.0971713i | ||||
\(785\) | −21.8938 | −0.781422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4664i | 0.907781i | 0.891058 | + | 0.453890i | \(0.149964\pi\) | ||||
−0.891058 | + | 0.453890i | \(0.850036\pi\) | |||||||
\(788\) | −14.6658 | + | 5.75621i | −0.522448 | + | 0.205057i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 35.5793 | + | 24.2571i | 1.26586 | + | 0.863029i | ||||
\(791\) | 6.91459 | 0.245854 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.6726 | −0.450016 | ||||||||
\(794\) | −32.3248 | − | 22.0383i | −1.14716 | − | 0.782108i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.736216 | − | 1.87575i | −0.0260945 | − | 0.0664841i | ||||
\(797\) | 27.4312i | 0.971664i | 0.874052 | + | 0.485832i | \(0.161483\pi\) | ||||
−0.874052 | + | 0.485832i | \(0.838517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.6076 | −0.941310 | ||||||||
\(800\) | −1.16539 | − | 7.72949i | −0.0412028 | − | 0.273279i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.5528 | − | 41.8801i | 1.00824 | − | 1.47884i | ||||
\(803\) | − | 49.4449i | − | 1.74487i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.36349i | − | 0.0480566i | ||||||
\(806\) | −24.1332 | − | 16.4534i | −0.850057 | − | 0.579548i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.87598 | + | 25.7476i | −0.206716 | + | 0.905796i | ||||
\(809\) | −23.8507 | −0.838546 | −0.419273 | − | 0.907860i | \(-0.637715\pi\) | ||||
−0.419273 | + | 0.907860i | \(0.637715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.8123i | − | 0.976622i | −0.872670 | − | 0.488311i | \(-0.837613\pi\) | ||
0.872670 | − | 0.488311i | \(-0.162387\pi\) | |||||||
\(812\) | −15.5476 | + | 6.10233i | −0.545615 | + | 0.214150i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −46.6749 | + | 68.4609i | −1.63596 | + | 2.39955i | ||||
\(815\) | −63.3506 | −2.21907 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.0179 | −1.01521 | ||||||||
\(818\) | 14.6627 | − | 21.5066i | 0.512669 | − | 0.751962i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.2611 | + | 10.3073i | −0.917077 | + | 0.359946i | ||||
\(821\) | 53.9215i | 1.88187i | 0.338583 | + | 0.940936i | \(0.390052\pi\) | ||||
−0.338583 | + | 0.940936i | \(0.609948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4932 | −0.400628 | −0.200314 | − | 0.979732i | \(-0.564196\pi\) | ||||
−0.200314 | + | 0.979732i | \(0.564196\pi\) | |||||||
\(824\) | 20.0969 | + | 4.58642i | 0.700110 | + | 0.159775i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.8773 | − | 8.09766i | −0.413265 | − | 0.281754i | ||||
\(827\) | 0.946387i | 0.0329091i | 0.999865 | + | 0.0164546i | \(0.00523788\pi\) | ||||
−0.999865 | + | 0.0164546i | \(0.994762\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.9151i | 1.49050i | 0.666783 | + | 0.745252i | \(0.267671\pi\) | ||||
−0.666783 | + | 0.745252i | \(0.732329\pi\) | |||||||
\(830\) | −11.7408 | + | 17.2210i | −0.407530 | + | 0.597748i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.6219 | − | 22.0596i | 0.368247 | − | 0.764778i | ||||
\(833\) | 5.49926 | 0.190538 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 22.1149i | − | 0.765318i | ||||||
\(836\) | −30.3650 | − | 77.3647i | −1.05020 | − | 2.67571i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.0202994 | + | 0.0138396i | 0.000701232 | + | 0.000478083i | ||||
\(839\) | 31.2098 | 1.07748 | 0.538741 | − | 0.842471i | \(-0.318900\pi\) | ||||
0.538741 | + | 0.842471i | \(0.318900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40.7419 | −1.40489 | ||||||||
\(842\) | 1.20865 | + | 0.824024i | 0.0416527 | + | 0.0283978i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.2922 | − | 11.8894i | 1.04270 | − | 0.409251i | ||||
\(845\) | 9.17933i | 0.315779i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.5393 | −0.740097 | ||||||||
\(848\) | 30.2880 | + | 32.6404i | 1.04010 | + | 1.12087i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.05376 | + | 8.87941i | −0.207642 | + | 0.304561i | ||||
\(851\) | 5.54363i | 0.190033i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.84389i | − | 0.302809i | −0.988472 | − | 0.151404i | \(-0.951620\pi\) | ||
0.988472 | − | 0.151404i | \(-0.0483796\pi\) | |||||||
\(854\) | −4.83840 | − | 3.29870i | −0.165567 | − | 0.112879i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.60138 | − | 20.1625i | 0.157272 | − | 0.689140i | ||||
\(857\) | 49.1414 | 1.67864 | 0.839319 | − | 0.543640i | \(-0.182954\pi\) | ||||
0.839319 | + | 0.543640i | \(0.182954\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.8201i | 1.49512i | 0.664193 | + | 0.747561i | \(0.268775\pi\) | ||||
−0.664193 | + | 0.747561i | \(0.731225\pi\) | |||||||
\(860\) | 7.35303 | + | 18.7342i | 0.250736 | + | 0.638832i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.07737 | + | 11.8476i | −0.275116 | + | 0.403529i | ||||
\(863\) | 31.5811 | 1.07503 | 0.537516 | − | 0.843253i | \(-0.319363\pi\) | ||||
0.537516 | + | 0.843253i | \(0.319363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.4879 | −0.798612 | ||||||||
\(866\) | −26.7518 | + | 39.2384i | −0.909063 | + | 1.33338i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.93122 | − | 12.5639i | −0.167377 | − | 0.426446i | ||||
\(869\) | − | 68.7552i | − | 2.33236i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.2510 | −0.618411 | ||||||||
\(872\) | 10.0268 | − | 43.9357i | 0.339550 | − | 1.48785i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.59434 | − | 3.13231i | −0.155406 | − | 0.105952i | ||||
\(875\) | 9.14031i | 0.308999i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.7451i | 1.13949i | 0.821821 | + | 0.569746i | \(0.192959\pi\) | ||||
−0.821821 | + | 0.569746i | \(0.807041\pi\) | |||||||
\(878\) | −3.12363 | + | 4.58161i | −0.105417 | + | 0.154622i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −42.2529 | + | 39.2078i | −1.42435 | + | 1.32170i | ||||
\(881\) | −8.58523 | −0.289244 | −0.144622 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144622 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.07348i | − | 0.271694i | −0.990730 | − | 0.135847i | \(-0.956624\pi\) | ||
0.990730 | − | 0.135847i | \(-0.0433756\pi\) | |||||||
\(884\) | −31.3334 | + | 12.2981i | −1.05386 | + | 0.413631i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.4653 | + | 27.5882i | 1.35946 | + | 0.926845i | ||||
\(887\) | 31.4397 | 1.05564 | 0.527821 | − | 0.849356i | \(-0.323009\pi\) | ||||
0.527821 | + | 0.849356i | \(0.323009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.6103 | −0.590632 | ||||||||
\(890\) | −27.4172 | − | 18.6924i | −0.919026 | − | 0.626569i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.03387 | − | 5.18194i | −0.0680990 | − | 0.173504i | ||||
\(893\) | − | 35.2471i | − | 1.17950i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.3382 | −0.646404 | ||||||||
\(896\) | 9.79760 | − | 5.65748i | 0.327315 | − | 0.189003i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.1693 | − | 20.7829i | 0.472835 | − | 0.693535i | ||||
\(899\) | − | 56.3577i | − | 1.87963i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 61.2180i | − | 2.03947i | ||||||
\(902\) | 37.2177 | + | 25.3741i | 1.23921 | + | 0.844865i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.0672 | − | 4.35141i | −0.634165 | − | 0.144726i | ||||
\(905\) | 6.32628 | 0.210293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 10.4183i | − | 0.345932i | −0.984928 | − | 0.172966i | \(-0.944665\pi\) | ||
0.984928 | − | 0.172966i | \(-0.0553352\pi\) | |||||||
\(908\) | −21.3057 | + | 8.36231i | −0.707054 | + | 0.277513i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.15919 | − | 9.03405i | 0.204175 | − | 0.299476i | ||||
\(911\) | −47.9123 | −1.58741 | −0.793703 | − | 0.608305i | \(-0.791850\pi\) | ||||
−0.793703 | + | 0.608305i | \(0.791850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.2786 | 1.10136 | ||||||||
\(914\) | 9.22928 | − | 13.5371i | 0.305277 | − | 0.447768i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.45955 | − | 3.32031i | 0.279511 | − | 0.109706i | ||||
\(917\) | 10.7551i | 0.355164i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.6472 | −1.24187 | −0.620933 | − | 0.783863i | \(-0.713246\pi\) | ||||
−0.620933 | + | 0.783863i | \(0.713246\pi\) | |||||||
\(920\) | −0.858055 | + | 3.75986i | −0.0282892 | + | 0.123959i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.7168 | + | 10.0335i | 0.484672 | + | 0.330437i | ||||
\(923\) | − | 15.0885i | − | 0.496644i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1929i | 0.466661i | ||||||||
\(926\) | −2.51825 | + | 3.69366i | −0.0827547 | + | 0.121381i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 46.7133 | − | 7.04308i | 1.53344 | − | 0.231200i | ||||
\(929\) | −44.8135 | −1.47028 | −0.735141 | − | 0.677914i | \(-0.762884\pi\) | ||||
−0.735141 | + | 0.677914i | \(0.762884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.28486i | 0.238752i | ||||||||
\(932\) | 11.7052 | + | 29.8228i | 0.383417 | + | 0.976880i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.4183 | − | 16.6478i | −0.798990 | − | 0.544732i | ||||
\(935\) | 79.2466 | 2.59164 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.2431 | 0.955330 | 0.477665 | − | 0.878542i | \(-0.341483\pi\) | ||||
0.477665 | + | 0.878542i | \(0.341483\pi\) | |||||||
\(938\) | −6.96824 | − | 4.75077i | −0.227521 | − | 0.155118i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −22.7558 | + | 8.93148i | −0.742213 | + | 0.291313i | ||||
\(941\) | 11.7936i | 0.384460i | 0.981350 | + | 0.192230i | \(0.0615719\pi\) | ||||
−0.981350 | + | 0.192230i | \(0.938428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.01371 | 0.0981398 | ||||||||
\(944\) | 27.6561 | + | 29.8040i | 0.900130 | + | 0.970039i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.1014 | − | 26.5505i | 0.588529 | − | 0.863230i | ||||
\(947\) | 14.5710i | 0.473493i | 0.971572 | + | 0.236746i | \(0.0760810\pi\) | ||||
−0.971572 | + | 0.236746i | \(0.923919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 26.5280i | − | 0.861134i | ||||||
\(950\) | −11.7626 | − | 8.01942i | −0.381628 | − | 0.260184i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.1644 | − | 3.46073i | −0.491480 | − | 0.112163i | ||||
\(953\) | 54.0151 | 1.74972 | 0.874860 | − | 0.484375i | \(-0.160953\pi\) | ||||
0.874860 | + | 0.484375i | \(0.160953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.09977i | − | 0.262102i | ||||||
\(956\) | 14.1005 | + | 35.9256i | 0.456043 | + | 1.16192i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.5264 | + | 33.0408i | −0.727795 | + | 1.06750i | ||||
\(959\) | 1.56413 | 0.0505084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5420 | 0.469097 | ||||||||
\(962\) | −25.0418 | + | 36.7303i | −0.807381 | + | 1.18423i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.1750 | + | 41.2110i | 0.520961 | + | 1.32732i | ||||
\(965\) | 27.6735i | 0.890840i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.1750 | 1.25978 | 0.629892 | − | 0.776683i | \(-0.283099\pi\) | ||||
0.629892 | + | 0.776683i | \(0.283099\pi\) | |||||||
\(968\) | 59.3951 | + | 13.5548i | 1.90903 | + | 0.435669i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.4554 | + | 24.8544i | 1.17051 | + | 0.798026i | ||||
\(971\) | − | 2.39896i | − | 0.0769864i | −0.999259 | − | 0.0384932i | \(-0.987744\pi\) | ||
0.999259 | − | 0.0384932i | \(-0.0122558\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2728i | 0.361390i | ||||||||
\(974\) | −21.4201 | + | 31.4181i | −0.686343 | + | 1.00670i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.2661 | + | 12.1411i | 0.360620 | + | 0.388628i | ||||
\(977\) | −15.7447 | −0.503717 | −0.251858 | − | 0.967764i | \(-0.581042\pi\) | ||||
−0.251858 | + | 0.967764i | \(0.581042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52.9823i | 1.69332i | ||||||||
\(980\) | 4.70317 | − | 1.84596i | 0.150237 | − | 0.0589669i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.01257 | + | 4.78100i | 0.223780 | + | 0.152568i | ||||
\(983\) | 14.5566 | 0.464285 | 0.232142 | − | 0.972682i | \(-0.425426\pi\) | ||||
0.232142 | + | 0.972682i | \(0.425426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.9004 | 0.634078 | ||||||||
\(986\) | −53.6629 | − | 36.5860i | −1.70898 | − | 1.16514i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.2913 | − | 41.5074i | −0.518296 | − | 1.32053i | ||||
\(989\) | − | 2.14993i | − | 0.0683637i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.2853 | −0.739681 | −0.369841 | − | 0.929095i | \(-0.620588\pi\) | ||||
−0.369841 | + | 0.929095i | \(0.620588\pi\) | |||||||
\(992\) | 5.69143 | + | 37.7485i | 0.180703 | + | 1.19852i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.92757 | − | 5.76080i | 0.124575 | − | 0.182721i | ||||
\(995\) | 2.54525i | 0.0806897i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.38107i | − | 0.0437390i | −0.999761 | − | 0.0218695i | \(-0.993038\pi\) | ||
0.999761 | − | 0.0218695i | \(-0.00696184\pi\) | |||||||
\(998\) | −21.3978 | − | 14.5885i | −0.677335 | − | 0.461790i | ||||
\(999\) | 0 | 0 |
(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 | 1512.2.c.f.757.17 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.f.757.8 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.g.3025.19 | 24 | |||
8.3 | odd | 2 | 6048.2.c.g.3025.6 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.f.757.18 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.g.3025.5 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.f.757.7 | ✓ | 24 | |
24.11 | even | 2 | 6048.2.c.g.3025.20 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.7 | ✓ | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.f.757.8 | yes | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.f.757.17 | yes | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.f.757.18 | yes | 24 | 8.5 | even | 2 | inner | |
6048.2.c.g.3025.5 | 24 | 12.11 | even | 2 | |||
6048.2.c.g.3025.6 | 24 | 8.3 | odd | 2 | |||
6048.2.c.g.3025.19 | 24 | 4.3 | odd | 2 | |||
6048.2.c.g.3025.20 | 24 | 24.11 | even | 2 |