Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(257,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Character | \(\chi\) | \(=\) | 504.257 |
Dual form | 504.2.bs.a.353.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70597 | + | 0.299447i | −0.984942 | + | 0.172886i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.76701 | + | 3.06054i | 0.790229 | + | 1.36872i | 0.925825 | + | 0.377952i | \(0.123372\pi\) |
−0.135596 | + | 0.990764i | \(0.543295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.34480 | + | 2.27849i | 0.508287 | + | 0.861188i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82066 | − | 1.02170i | 0.940221 | − | 0.340565i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.57467 | − | 0.909136i | −0.474781 | − | 0.274115i | 0.243458 | − | 0.969911i | \(-0.421718\pi\) |
−0.718239 | + | 0.695796i | \(0.755052\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.78280 | − | 1.60665i | −0.771809 | − | 0.445604i | 0.0617107 | − | 0.998094i | \(-0.480344\pi\) |
−0.833519 | + | 0.552490i | \(0.813678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.93093 | − | 4.69207i | −1.01496 | − | 1.21149i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.93434 | + | 5.08242i | 0.711682 | + | 1.23267i | 0.964225 | + | 0.265083i | \(0.0853995\pi\) |
−0.252544 | + | 0.967585i | \(0.581267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09143 | − | 1.20749i | −0.479807 | − | 0.277017i | 0.240529 | − | 0.970642i | \(-0.422679\pi\) |
−0.720336 | + | 0.693625i | \(0.756012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.97648 | − | 3.48434i | −0.649520 | − | 0.760344i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.33308 | + | 1.92436i | −0.694996 | + | 0.401256i | −0.805481 | − | 0.592622i | \(-0.798093\pi\) |
0.110485 | + | 0.993878i | \(0.464760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.74462 | + | 6.48586i | −0.748923 | + | 1.29717i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50602 | + | 2.58762i | −0.867184 | + | 0.497988i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.79110 | − | 3.34349i | 1.07538 | − | 0.620871i | 0.145734 | − | 0.989324i | \(-0.453446\pi\) |
0.929647 | + | 0.368452i | \(0.120112\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.87236i | 0.875102i | 0.899193 | + | 0.437551i | \(0.144154\pi\) | ||||
−0.899193 | + | 0.437551i | \(0.855846\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.95858 | + | 1.07943i | 0.515022 | + | 0.187904i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.59714 | + | 8.14192i | −0.777059 | + | 1.37624i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.905385 | + | 1.56817i | −0.148844 | + | 0.257806i | −0.930801 | − | 0.365527i | \(-0.880889\pi\) |
0.781956 | + | 0.623333i | \(0.214222\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.22847 | + | 1.90759i | 0.837225 | + | 0.305459i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.03152 | + | 8.71485i | −0.785792 | + | 1.36103i | 0.142733 | + | 0.989761i | \(0.454411\pi\) |
−0.928525 | + | 0.371270i | \(0.878922\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.36232 | − | 4.09166i | −0.360251 | − | 0.623973i | 0.627751 | − | 0.778414i | \(-0.283976\pi\) |
−0.988002 | + | 0.154441i | \(0.950642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.11107 | + | 6.82742i | 1.20913 | + | 1.01777i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.92151 | 1.15547 | 0.577736 | − | 0.816224i | \(-0.303936\pi\) | ||||
0.577736 | + | 0.816224i | \(0.303936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.38302 | + | 6.12823i | −0.483289 | + | 0.875461i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.52781 | − | 7.79178i | −0.914076 | − | 1.09107i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.26517 | + | 1.30780i | −0.311146 | + | 0.179640i | −0.647439 | − | 0.762117i | \(-0.724160\pi\) |
0.336293 | + | 0.941757i | \(0.390827\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.42580i | − | 0.866454i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.92950 | + | 1.43366i | 0.520474 | + | 0.189893i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.81208 | 1.14724 | 0.573618 | − | 0.819123i | \(-0.305540\pi\) | ||||
0.573618 | + | 0.819123i | \(0.305540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.3744i | − | 1.32830i | −0.747599 | − | 0.664151i | \(-0.768793\pi\) | ||
0.747599 | − | 0.664151i | \(-0.231207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.12115 | + | 5.05287i | 0.771193 | + | 0.636602i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 11.3558i | − | 1.40852i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.84769 | −0.958748 | −0.479374 | − | 0.877611i | \(-0.659136\pi\) | ||||
−0.479374 | + | 0.877611i | \(0.659136\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.10990 | − | 4.28098i | 0.615159 | − | 0.515369i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.62952i | − | 0.905458i | −0.891648 | − | 0.452729i | \(-0.850451\pi\) | ||
0.891648 | − | 0.452729i | \(-0.149549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7672 | + | 6.79382i | −1.37725 | + | 0.795156i | −0.991828 | − | 0.127584i | \(-0.959278\pi\) |
−0.385423 | + | 0.922740i | \(0.625945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.44602 | − | 12.1860i | 0.513383 | − | 1.40712i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0461599 | − | 4.81048i | −0.00526041 | − | 0.548205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.84254 | −0.207301 | −0.103651 | − | 0.994614i | \(-0.533052\pi\) | ||||
−0.103651 | + | 0.994614i | \(0.533052\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.91227 | − | 5.76372i | 0.768031 | − | 0.640413i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.61748 | + | 9.72975i | 0.616598 | + | 1.06798i | 0.990102 | + | 0.140351i | \(0.0448230\pi\) |
−0.373504 | + | 0.927629i | \(0.621844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3700 | + | 17.9613i | −1.12478 | + | 1.94818i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.87824 | + | 7.43803i | −0.951848 | + | 0.797440i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.89792 | − | 11.9475i | 0.731178 | − | 1.26644i | −0.225202 | − | 0.974312i | \(-0.572304\pi\) |
0.956380 | − | 0.292125i | \(-0.0943624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0815748 | − | 8.50119i | −0.00855137 | − | 0.891167i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.45902 | − | 8.31210i | −0.151293 | − | 0.861925i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.53455i | − | 0.875627i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.7982 | − | 7.96638i | 1.40099 | − | 0.808863i | 0.406497 | − | 0.913652i | \(-0.366750\pi\) |
0.994494 | + | 0.104789i | \(0.0334168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.37048 | − | 0.955533i | −0.539753 | − | 0.0960346i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56250 | − | 9.63453i | 0.553489 | − | 0.958671i | −0.444530 | − | 0.895764i | \(-0.646629\pi\) |
0.998019 | − | 0.0629076i | \(-0.0200373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.522237 | − | 0.301514i | 0.0514576 | − | 0.0297091i | −0.474050 | − | 0.880498i | \(-0.657209\pi\) |
0.525508 | + | 0.850789i | \(0.323875\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.40451 | − | 15.2665i | 0.527426 | − | 1.48985i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3342 | + | 6.54381i | 1.09572 | + | 0.632614i | 0.935094 | − | 0.354401i | \(-0.115315\pi\) |
0.160627 | + | 0.987015i | \(0.448649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.37061 | − | 2.37396i | −0.131280 | − | 0.227384i | 0.792890 | − | 0.609365i | \(-0.208575\pi\) |
−0.924170 | + | 0.381981i | \(0.875242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.07497 | − | 2.94637i | 0.102032 | − | 0.279657i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.65125 | + | 3.84010i | 0.625697 | + | 0.361246i | 0.779084 | − | 0.626920i | \(-0.215685\pi\) |
−0.153387 | + | 0.988166i | \(0.549018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.7792 | − | 6.80070i | −1.09841 | − | 0.634168i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.49083 | − | 1.68864i | −0.877428 | − | 0.156115i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.63415 | + | 13.5207i | −0.699821 | + | 1.23944i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.84694 | − | 6.66310i | −0.349722 | − | 0.605736i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.97398 | − | 16.3739i | 0.538656 | − | 1.47639i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.79697 | −0.786825 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9246 | 1.59055 | 0.795277 | − | 0.606246i | \(-0.207325\pi\) | ||||
0.795277 | + | 0.606246i | \(0.207325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.25529 | + | 6.27286i | 0.462702 | + | 0.552295i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.48534 | + | 14.6970i | 0.741367 | + | 1.28409i | 0.951873 | + | 0.306493i | \(0.0991556\pi\) |
−0.210506 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0613082 | − | 6.38913i | −0.00531609 | − | 0.554008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.8817 | − | 9.21852i | −1.36688 | − | 0.793404i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.81631 | + | 2.78070i | 0.411485 | + | 0.237571i | 0.691428 | − | 0.722446i | \(-0.256982\pi\) |
−0.279943 | + | 0.960017i | \(0.590315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4503 | + | 7.18817i | 1.05602 | + | 0.609693i | 0.924328 | − | 0.381598i | \(-0.124626\pi\) |
0.131690 | + | 0.991291i | \(0.457960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5139 | + | 2.37208i | −1.13807 | + | 0.199765i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.92132 | + | 5.05988i | 0.244293 | + | 0.423129i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.4658 | + | 11.8159i | 1.69959 | + | 0.981261i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.93626 | − | 11.4676i | 0.324657 | − | 0.945832i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.56086 | + | 3.21056i | −0.455563 | + | 0.263019i | −0.710177 | − | 0.704023i | \(-0.751385\pi\) |
0.254614 | + | 0.967043i | \(0.418052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.99627 | + | 13.8499i | −0.650727 | + | 1.12709i | 0.332220 | + | 0.943202i | \(0.392202\pi\) |
−0.982947 | + | 0.183890i | \(0.941131\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.4695 | + | 11.3378i | 1.08894 | + | 0.916607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.9121 | + | 8.60949i | −1.19777 | + | 0.691531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9271i | 1.11151i | 0.831348 | + | 0.555753i | \(0.187570\pi\) | ||||
−0.831348 | + | 0.555753i | \(0.812430\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.47270 | − | 2.90937i | 0.275403 | − | 0.230728i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.86696 | − | 5.00652i | −0.698814 | − | 0.394569i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.79498 | − | 13.5013i | 0.610550 | − | 1.05750i | −0.380598 | − | 0.924740i | \(-0.624282\pi\) |
0.991148 | − | 0.132762i | \(-0.0423847\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.92419 | + | 10.9622i | 0.149798 | + | 0.853407i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.58728 | − | 11.4095i | 0.509739 | − | 0.882893i | −0.490198 | − | 0.871611i | \(-0.663075\pi\) |
0.999936 | − | 0.0112821i | \(-0.00359127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33736 | − | 2.31638i | −0.102874 | − | 0.178183i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.13291 | − | 1.26911i | −0.545467 | − | 0.0970513i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2080 | −0.852132 | −0.426066 | − | 0.904692i | \(-0.640101\pi\) | ||||
−0.426066 | + | 0.904692i | \(0.640101\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.8137 | + | 0.190127i | −1.49778 | + | 0.0143722i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.0331 | + | 2.63875i | −1.12996 | + | 0.198341i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.22783 | + | 5.32769i | −0.689721 | + | 0.398210i | −0.803507 | − | 0.595295i | \(-0.797035\pi\) |
0.113787 | + | 0.993505i | \(0.463702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.8897i | − | 0.883754i | −0.897076 | − | 0.441877i | \(-0.854313\pi\) | ||
0.897076 | − | 0.441877i | \(-0.145687\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.10658 | + | 17.6984i | 0.229645 | + | 1.30830i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.39928 | −0.470484 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.6709i | − | 0.780330i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.9556 | − | 6.78708i | −0.869639 | − | 0.493688i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.223967i | − | 0.0162057i | −0.999967 | − | 0.00810283i | \(-0.997421\pi\) | ||
0.999967 | − | 0.00810283i | \(-0.00257924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.0745 | 1.87688 | 0.938442 | − | 0.345437i | \(-0.112269\pi\) | ||||
0.938442 | + | 0.345437i | \(0.112269\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.40047 | + | 19.3727i | 0.243513 | + | 1.38731i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.56289i | 0.111352i | 0.998449 | + | 0.0556758i | \(0.0177313\pi\) | ||||
−0.998449 | + | 0.0556758i | \(0.982269\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4725 | − | 7.77832i | 0.955037 | − | 0.551391i | 0.0603949 | − | 0.998175i | \(-0.480764\pi\) |
0.894642 | + | 0.446784i | \(0.147431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.3879 | − | 2.34997i | 0.944311 | − | 0.165754i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.4060 | + | 8.69863i | 1.08129 | + | 0.610524i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.5629 | −2.48382 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.43540 | + | 8.83336i | −0.516796 | + | 0.613961i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.19554 | + | 3.80279i | 0.151869 | + | 0.263045i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98216 | − | 12.0935i | 0.480672 | − | 0.832548i | −0.519082 | − | 0.854724i | \(-0.673726\pi\) |
0.999754 | + | 0.0221763i | \(0.00705950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.28464 | + | 13.0157i | 0.156541 | + | 0.891823i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.34848 | − | 14.4600i | 0.569361 | − | 0.986163i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1016 | + | 6.55236i | −0.753628 | + | 0.444803i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.0402 | − | 15.1137i | 1.21904 | − | 1.02129i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 18.8578i | − | 1.26851i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4242 | − | 12.3693i | 1.43467 | − | 0.828307i | 0.437198 | − | 0.899366i | \(-0.355971\pi\) |
0.997472 | + | 0.0710586i | \(0.0226377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.93571 | + | 22.1203i | −0.262381 | + | 1.47469i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.12076 | + | 5.40532i | −0.207132 | + | 0.358764i | −0.950810 | − | 0.309775i | \(-0.899746\pi\) |
0.743678 | + | 0.668538i | \(0.233080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.7329 | + | 7.92870i | −0.907496 | + | 0.523943i | −0.879625 | − | 0.475668i | \(-0.842206\pi\) |
−0.0278714 | + | 0.999612i | \(0.508873\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.51923 | + | 8.19270i | 0.0999581 | + | 0.539040i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.94574 | − | 1.70072i | −0.192982 | − | 0.111418i | 0.400396 | − | 0.916342i | \(-0.368873\pi\) |
−0.593378 | + | 0.804924i | \(0.702206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9974 | + | 24.2441i | 0.913087 | + | 1.58151i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.14331 | − | 0.551742i | 0.204180 | − | 0.0358395i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3482 | − | 9.43864i | −1.05748 | − | 0.610535i | −0.132744 | − | 0.991150i | \(-0.542379\pi\) |
−0.924733 | + | 0.380615i | \(0.875712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.68610 | − | 5.59227i | −0.623937 | − | 0.360230i | 0.154463 | − | 0.987999i | \(-0.450635\pi\) |
−0.778400 | + | 0.627768i | \(0.783968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0662 | + | 11.9026i | −0.645747 | + | 0.763552i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.7335 | + | 0.474714i | −1.58017 | + | 0.0303284i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.88002 | + | 6.72039i | 0.246880 | + | 0.427608i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.4968 | − | 14.9165i | −0.791952 | − | 0.945296i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.4537 | −0.975431 | −0.487716 | − | 0.873003i | \(-0.662170\pi\) | ||||
−0.487716 | + | 0.873003i | \(0.662170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99801 | 0.439961 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.3124 | − | 33.7468i | 0.771032 | − | 2.11330i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.32238 | − | 9.21864i | −0.332001 | − | 0.575043i | 0.650903 | − | 0.759161i | \(-0.274390\pi\) |
−0.982904 | + | 0.184118i | \(0.941057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.79063 | + | 0.0459694i | −0.297675 | + | 0.00285640i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.9187 | − | 15.3476i | 0.799648 | − | 0.949994i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.60206 | + | 5.54375i | 0.592088 | + | 0.341842i | 0.765923 | − | 0.642933i | \(-0.222282\pi\) |
−0.173835 | + | 0.984775i | \(0.555616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00515 | − | 4.62178i | −0.491753 | − | 0.283913i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.18998 | + | 22.4477i | −0.501218 | + | 1.37378i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.14147 | + | 5.44119i | 0.191539 | + | 0.331755i | 0.945760 | − | 0.324865i | \(-0.105319\pi\) |
−0.754221 | + | 0.656620i | \(0.771986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.954533 | + | 0.551100i | 0.0579838 | + | 0.0334769i | 0.528712 | − | 0.848802i | \(-0.322675\pi\) |
−0.470728 | + | 0.882278i | \(0.656009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.68482 | + | 14.4783i | 0.162493 | + | 0.876269i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.7931 | − | 6.80873i | 0.711149 | − | 0.410582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.68081 | − | 13.3036i | 0.461495 | − | 0.799333i | −0.537541 | − | 0.843238i | \(-0.680647\pi\) |
0.999036 | + | 0.0439049i | \(0.0139798\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.97807 | + | 13.7433i | 0.298030 | + | 0.822790i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9133 | − | 10.9196i | 1.12827 | − | 0.651407i | 0.184771 | − | 0.982782i | \(-0.440846\pi\) |
0.943499 | + | 0.331374i | \(0.107512\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0785i | 0.658548i | 0.944234 | + | 0.329274i | \(0.106804\pi\) | ||||
−0.944234 | + | 0.329274i | \(0.893196\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.55565 | + | 14.5597i | 0.151384 | + | 0.862441i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.6231 | + | 0.255467i | −1.57151 | + | 0.0150797i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.72069 | + | 15.1047i | −0.512982 | + | 0.888511i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.1537 | + | 17.7222i | −1.24005 | + | 1.03889i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6330 | + | 21.8810i | −0.738027 | + | 1.27830i | 0.215355 | + | 0.976536i | \(0.430909\pi\) |
−0.953382 | + | 0.301765i | \(0.902424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5710 | + | 26.9698i | 0.906578 | + | 1.57024i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.44800 | + | 0.0219345i | 0.548228 | + | 0.00127277i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3671 | 0.715206 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.14596 | − | 10.8850i | 0.354247 | − | 0.627401i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.60442 | + | 18.1019i | −0.379414 | + | 1.03993i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.7512 | − | 18.3316i | 1.81807 | − | 1.04966i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2163i | 0.697219i | 0.937268 | + | 0.348610i | \(0.113346\pi\) | ||||
−0.937268 | + | 0.348610i | \(0.886654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.800634 | + | 0.670756i | −0.0455465 | + | 0.0381580i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.48967 | −0.538110 | −0.269055 | − | 0.963125i | \(-0.586711\pi\) | ||||
−0.269055 | + | 0.963125i | \(0.586711\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5513i | 0.765964i | 0.923756 | + | 0.382982i | \(0.125103\pi\) | ||||
−0.923756 | + | 0.382982i | \(0.874897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.64842 | + | 27.6625i | −0.261909 | + | 1.55861i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 15.8839i | − | 0.892131i | −0.895000 | − | 0.446065i | \(-0.852825\pi\) | ||
0.895000 | − | 0.446065i | \(-0.147175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.1588 | −0.680761 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.2954 | − | 7.76954i | −1.18859 | − | 0.433654i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 14.1727i | − | 0.788591i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.8410 | − | 12.0326i | 1.15605 | − | 0.667446i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.04909 | + | 3.63948i | 0.168615 | + | 0.201264i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.6529 | + | 18.0491i | 0.587311 | + | 0.995078i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9739 | 0.603183 | 0.301591 | − | 0.953437i | \(-0.402482\pi\) | ||||
0.301591 | + | 0.953437i | \(0.402482\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.951590 | + | 5.34831i | −0.0521468 | + | 0.293086i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.8669 | − | 24.0182i | −0.757630 | − | 1.31225i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.80751 | − | 4.86275i | 0.152935 | − | 0.264891i | −0.779370 | − | 0.626564i | \(-0.784461\pi\) |
0.932305 | + | 0.361673i | \(0.117794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.4967 | − | 4.55940i | −0.678730 | − | 0.247632i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.42964 | − | 7.67237i | 0.239879 | − | 0.415482i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5126 | + | 0.533054i | −0.999586 | + | 0.0287822i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.1313 | + | 8.07455i | 1.19151 | + | 0.434719i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4.82668i | − | 0.259110i | −0.991572 | − | 0.129555i | \(-0.958645\pi\) | ||
0.991572 | − | 0.129555i | \(-0.0413549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7167 | + | 13.1155i | −1.21600 | + | 0.702056i | −0.964059 | − | 0.265688i | \(-0.914401\pi\) |
−0.251937 | + | 0.967744i | \(0.581068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.6967 | + | 0.0387633i | 0.891206 | + | 0.00206903i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.4957 | + | 30.3034i | −0.931201 | + | 1.61289i | −0.149930 | + | 0.988697i | \(0.547905\pi\) |
−0.781271 | + | 0.624192i | \(0.785428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.3505 | − | 13.4814i | 1.23931 | − | 0.715519i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.97488 | − | 25.3519i | 0.475001 | − | 1.34177i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.6396 | + | 12.4936i | 1.14209 | + | 0.659388i | 0.946948 | − | 0.321386i | \(-0.104149\pi\) |
0.195146 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58394 | − | 11.4037i | −0.346523 | − | 0.600196i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.55801 | + | 10.2151i | 0.449179 | + | 0.536153i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −41.5855 | − | 24.0094i | −2.17669 | − | 1.25671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.3100 | − | 12.3034i | −1.11237 | − | 0.642230i | −0.172931 | − | 0.984934i | \(-0.555324\pi\) |
−0.939443 | + | 0.342704i | \(0.888657\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.28830 | + | 29.7223i | −0.275298 | + | 1.54728i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.02601 | − | 3.40245i | −0.312855 | − | 0.176646i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.21870 | + | 9.03905i | 0.270214 | + | 0.468024i | 0.968916 | − | 0.247388i | \(-0.0795723\pi\) |
−0.698703 | + | 0.715412i | \(0.746239\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.0074 | − | 2.63423i | 0.774977 | − | 0.136031i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.4873 | −1.10665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8728 | 1.63719 | 0.818597 | − | 0.574368i | \(-0.194752\pi\) | ||||
0.818597 | + | 0.574368i | \(0.194752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.5789 | + | 5.36749i | −1.56660 | + | 0.274985i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.3860 | − | 21.4531i | −0.632893 | − | 1.09620i | −0.986957 | − | 0.160982i | \(-0.948534\pi\) |
0.354065 | − | 0.935221i | \(-0.384799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.6411 | − | 8.64141i | 0.746180 | − | 0.440407i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8438 | − | 9.12763i | −0.551219 | − | 0.463983i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.9382 | + | 11.5113i | 1.01091 | + | 0.583647i | 0.911457 | − | 0.411395i | \(-0.134958\pi\) |
0.0994499 | + | 0.995043i | \(0.468292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.5608 | − | 11.2934i | −0.989232 | − | 0.571133i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.8767 | − | 22.5318i | −0.952204 | − | 1.13658i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.25577 | − | 5.63916i | −0.163816 | − | 0.283737i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9247 | + | 13.8129i | 1.20075 | + | 0.693251i | 0.960721 | − | 0.277515i | \(-0.0895109\pi\) |
0.240025 | + | 0.970767i | \(0.422844\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.01780 | + | 10.8813i | 0.101016 | + | 0.544747i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.61058 | − | 2.66192i | 0.230241 | − | 0.132930i | −0.380442 | − | 0.924805i | \(-0.624228\pi\) |
0.610683 | + | 0.791875i | \(0.290895\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.82817 | − | 13.5588i | 0.389949 | − | 0.675412i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.8541 | + | 10.9708i | 1.48346 | + | 0.545143i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85137 | − | 1.64624i | 0.141337 | − | 0.0816009i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.06575i | − | 0.349379i | −0.984624 | − | 0.174690i | \(-0.944108\pi\) | ||
0.984624 | − | 0.174690i | \(-0.0558922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.04915 | − | 3.30155i | −0.446362 | − | 0.162854i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.8505 | + | 20.0782i | 0.583124 | + | 0.987985i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.8522 | + | 34.3851i | −0.974507 | + | 1.68790i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.3923 | − | 8.53459i | −1.14552 | − | 0.417941i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.94504 | − | 3.36891i | 0.0950215 | − | 0.164582i | −0.814596 | − | 0.580029i | \(-0.803041\pi\) |
0.909618 | + | 0.415447i | \(0.136375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.18533 | − | 3.78510i | −0.106506 | − | 0.184475i | 0.807846 | − | 0.589393i | \(-0.200633\pi\) |
−0.914353 | + | 0.404919i | \(0.867300\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.3439 | − | 8.09338i | 1.08640 | − | 0.393514i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −43.9519 | −2.13198 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.6379 | − | 13.9515i | 1.14392 | − | 0.675158i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.49886 | − | 7.75722i | −0.313768 | − | 0.374522i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7505 | + | 6.20681i | −0.517834 | + | 0.298971i | −0.736048 | − | 0.676929i | \(-0.763310\pi\) |
0.218214 | + | 0.975901i | \(0.429977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.2979i | − | 1.21574i | −0.794036 | − | 0.607870i | \(-0.792024\pi\) | ||
0.794036 | − | 0.607870i | \(-0.207976\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.4523 | − | 14.0292i | −1.84365 | − | 0.672649i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.29455 | 0.444619 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 26.8362i | − | 1.28082i | −0.768033 | − | 0.640410i | \(-0.778764\pi\) | ||
0.768033 | − | 0.640410i | \(-0.221236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.28119 | + | 20.7421i | −0.156247 | + | 0.987718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0540i | 0.620213i | 0.950702 | + | 0.310107i | \(0.100365\pi\) | ||||
−0.950702 | + | 0.310107i | \(0.899635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 48.7546 | 2.31119 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.52526 | − | 7.14230i | 0.403231 | − | 0.337819i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.468645i | − | 0.0221167i | −0.999939 | − | 0.0110584i | \(-0.996480\pi\) | ||
0.999939 | − | 0.0110584i | \(-0.00352006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8460 | − | 9.14868i | 0.746158 | − | 0.430795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.49406 | − | 26.0220i | 0.446070 | − | 1.22262i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.8741 | − | 15.2713i | 1.21300 | − | 0.715930i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.12972 | −0.193180 | −0.0965901 | − | 0.995324i | \(-0.530794\pi\) | ||||
−0.0965901 | + | 0.995324i | \(0.530794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.3736 | − | 15.3085i | −1.23101 | − | 0.714542i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.9115 | − | 22.3633i | −0.601347 | − | 1.04156i | −0.992617 | − | 0.121288i | \(-0.961298\pi\) |
0.391271 | − | 0.920276i | \(-0.372036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.56402 | + | 4.44101i | −0.119160 | + | 0.206391i | −0.919435 | − | 0.393242i | \(-0.871353\pi\) |
0.800275 | + | 0.599633i | \(0.204687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.8615 | − | 19.1529i | 1.06017 | − | 0.888195i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.26091 | − | 2.18396i | 0.0583480 | − | 0.101062i | −0.835376 | − | 0.549679i | \(-0.814750\pi\) |
0.893724 | + | 0.448617i | \(0.148083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5536 | − | 17.8809i | −0.487319 | − | 0.825662i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.17044 | − | 23.7592i | −0.192164 | − | 1.09477i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.59070i | 0.395001i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.6632 | − | 9.04316i | 0.718677 | − | 0.414929i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.05312 | + | 6.00318i | −0.231366 | + | 0.274867i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.74622 | + | 9.95275i | −0.262552 | + | 0.454753i | −0.966919 | − | 0.255083i | \(-0.917897\pi\) |
0.704368 | + | 0.709835i | \(0.251231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.03900 | − | 2.90927i | 0.229759 | − | 0.132651i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.6260 | + | 5.88578i | 0.756507 | + | 0.267812i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.7629 | + | 28.1533i | 2.21421 | + | 1.27837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.8463 | − | 18.7864i | −0.491493 | − | 0.851292i | 0.508459 | − | 0.861086i | \(-0.330215\pi\) |
−0.999952 | + | 0.00979483i | \(0.996882\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.25506 | + | 25.3670i | −0.418528 | + | 1.14713i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3592 | − | 11.1771i | −0.873669 | − | 0.504413i | −0.00510349 | − | 0.999987i | \(-0.501624\pi\) |
−0.868566 | + | 0.495574i | \(0.834958\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.9861 | + | 19.6219i | 1.53066 | + | 0.883726i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.56521 | − | 18.1250i | −0.295084 | − | 0.814658i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.3838 | − | 10.2602i | 0.779769 | − | 0.460232i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.76231 | − | 15.1768i | −0.392255 | − | 0.679405i | 0.600492 | − | 0.799631i | \(-0.294972\pi\) |
−0.992747 | + | 0.120226i | \(0.961638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.82115 | + | 21.4368i | −0.349423 | + | 0.957725i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.60926 | 0.339280 | 0.169640 | − | 0.985506i | \(-0.445739\pi\) | ||||
0.169640 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.3159 | 1.74953 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.97514 | + | 3.55121i | 0.132130 | + | 0.157715i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.39373 | − | 5.87811i | −0.150424 | − | 0.260543i | 0.780959 | − | 0.624582i | \(-0.214731\pi\) |
−0.931384 | + | 0.364039i | \(0.881397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.3042 | − | 17.6752i | −1.38482 | − | 0.781905i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.5486 | + | 0.0291328i | 0.554032 | + | 0.00128624i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.84559 | + | 1.06555i | 0.0813265 | + | 0.0469539i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.4738 | − | 7.20174i | −0.548596 | − | 0.316732i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.1206 | − | 3.35622i | 0.839300 | − | 0.147322i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8435 | + | 23.9777i | 0.606497 | + | 1.05048i | 0.991813 | + | 0.127698i | \(0.0407590\pi\) |
−0.385316 | + | 0.922785i | \(0.625908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.834923 | − | 0.482043i | −0.0365086 | − | 0.0210783i | 0.481635 | − | 0.876372i | \(-0.340043\pi\) |
−0.518143 | + | 0.855294i | \(0.673377\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.7447 | − | 6.25752i | 1.47274 | − | 0.273101i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.7634 | + | 14.2972i | −1.07871 | + | 0.622794i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.09370 | + | 7.09049i | −0.177987 | + | 0.308282i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.8559 | − | 9.00327i | 1.07865 | − | 0.390709i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.0034 | − | 16.1678i | 1.21296 | − | 0.700304i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.2518i | 1.99964i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.1470 | − | 11.8521i | 0.610490 | − | 0.511457i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.8985 | − | 6.57430i | 0.469433 | − | 0.283175i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.36867 | − | 4.10266i | 0.101837 | − | 0.176387i | −0.810604 | − | 0.585594i | \(-0.800861\pi\) |
0.912442 | + | 0.409207i | \(0.134195\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.56034 | + | 20.2835i | 0.152789 | + | 0.870447i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.84374 | − | 8.38960i | 0.207483 | − | 0.359371i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.840875 | − | 1.45644i | −0.0359532 | − | 0.0622728i | 0.847489 | − | 0.530813i | \(-0.178113\pi\) |
−0.883442 | + | 0.468540i | \(0.844780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5994 | − | 29.2626i | −0.452373 | − | 1.24890i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.1489 | −0.687967 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.47784 | − | 4.19820i | −0.105369 | − | 0.178525i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.9170 | − | 1.91625i | 0.463400 | − | 0.0813402i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.14983 | + | 4.70530i | −0.345319 | + | 0.199370i | −0.662622 | − | 0.748954i | \(-0.730556\pi\) |
0.317303 | + | 0.948324i | \(0.397223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.1817i | 0.642117i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.19536 | + | 18.2042i | 0.134908 | + | 0.768580i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.0638 | −1.30918 | −0.654591 | − | 0.755983i | \(-0.727159\pi\) | ||||
−0.654591 | + | 0.755983i | \(0.727159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.1419i | 1.14187i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.4282 | + | 7.99849i | 0.941896 | + | 0.335905i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 20.1032i | − | 0.842769i | −0.906882 | − | 0.421384i | \(-0.861544\pi\) | ||
0.906882 | − | 0.421384i | \(-0.138456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.87413 | −0.329522 | −0.164761 | − | 0.986333i | \(-0.552685\pi\) | ||||
−0.164761 | + | 0.986333i | \(0.552685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0670662 | + | 0.382080i | 0.00280173 | + | 0.0159616i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 28.8239i | − | 1.20204i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.77842 | + | 1.60412i | −0.115667 | + | 0.0667805i | −0.556717 | − | 0.830702i | \(-0.687939\pi\) |
0.441050 | + | 0.897482i | \(0.354606\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −44.4823 | + | 7.80794i | −1.84862 | + | 0.324487i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6148 | + | 25.8839i | −0.606322 | + | 1.07385i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.75587 | 0.196968 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.6022 | − | 32.0309i | −0.479692 | − | 1.32432i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37708 | + | 4.11722i | 0.0981125 | + | 0.169936i | 0.910903 | − | 0.412620i | \(-0.135386\pi\) |
−0.812791 | + | 0.582556i | \(0.802053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.88332 | − | 10.1902i | 0.242418 | − | 0.419880i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.468004 | − | 2.66625i | −0.0192511 | − | 0.109675i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0354 | + | 22.5780i | −0.535300 | + | 0.927166i | 0.463849 | + | 0.885914i | \(0.346468\pi\) |
−0.999149 | + | 0.0412519i | \(0.986865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −54.8703 | + | 0.526519i | −2.24946 | + | 0.0215852i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6544 | + | 17.3039i | −0.845328 | + | 0.708200i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.5024i | − | 1.12372i | −0.827233 | − | 0.561859i | \(-0.810086\pi\) | ||
0.827233 | − | 0.561859i | \(-0.189914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.8647 | − | 15.5104i | 1.09584 | − | 0.632681i | 0.160712 | − | 0.987001i | \(-0.448621\pi\) |
0.935124 | + | 0.354320i | \(0.115288\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.1357 | + | 8.01795i | −0.901435 | + | 0.326516i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.5951 | − | 23.5475i | 0.552721 | − | 0.957340i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.9745 | + | 19.6152i | −1.37898 | + | 0.796156i | −0.992037 | − | 0.125947i | \(-0.959803\pi\) |
−0.386945 | + | 0.922103i | \(0.626470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.8869 | − | 10.2263i | −1.17056 | − | 0.414391i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.0440 | − | 12.7271i | −0.891803 | − | 0.514883i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5364 | − | 19.9817i | −0.465951 | − | 0.807051i | 0.533293 | − | 0.845931i | \(-0.320954\pi\) |
−0.999244 | + | 0.0388795i | \(0.987621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 60.6692 | − | 10.6492i | 2.44642 | − | 0.429418i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.15715 | + | 2.97748i | 0.207619 | + | 0.119869i | 0.600204 | − | 0.799847i | \(-0.295086\pi\) |
−0.392585 | + | 0.919716i | \(0.628419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0289 | − | 16.1825i | −1.12658 | − | 0.650429i | −0.183504 | − | 0.983019i | \(-0.558744\pi\) |
−0.943072 | + | 0.332590i | \(0.892078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0394 | − | 17.2960i | 0.402869 | − | 0.694063i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.4987 | − | 0.350230i | 1.46229 | − | 0.0140317i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.17879 | + | 5.50582i | 0.127152 | + | 0.220233i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.88426 | − | 5.83000i | −0.195059 | − | 0.232828i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.6268 | −0.423719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.6689 | −1.41996 | −0.709978 | − | 0.704224i | \(-0.751295\pi\) | ||||
−0.709978 | + | 0.704224i | \(0.751295\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.29000 | + | 22.7219i | −0.329498 | + | 0.903113i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.6729 | + | 54.8591i | 1.25690 | + | 2.17702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.2602 | − | 11.6183i | 0.763116 | − | 0.460333i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.79505 | − | 21.5203i | −0.308367 | − | 0.851330i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.5239 | + | 12.4268i | 0.850141 | + | 0.490829i | 0.860699 | − | 0.509115i | \(-0.170027\pi\) |
−0.0105572 | + | 0.999944i | \(0.503361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.8270 | − | 8.56038i | −0.584720 | − | 0.337588i | 0.178287 | − | 0.983979i | \(-0.442944\pi\) |
−0.763007 | + | 0.646390i | \(0.776278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.91224 | + | 27.1682i | −0.390294 | + | 1.06975i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.7208 | − | 28.9613i | −0.657363 | − | 1.13859i | −0.981296 | − | 0.192506i | \(-0.938339\pi\) |
0.323933 | − | 0.946080i | \(-0.394995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8761 | − | 8.01138i | −0.544686 | − | 0.314474i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.9770 | − | 14.5025i | 0.665379 | − | 0.568397i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.8837 | − | 13.2119i | 0.895508 | − | 0.517022i | 0.0197678 | − | 0.999805i | \(-0.493707\pi\) |
0.875740 | + | 0.482783i | \(0.160374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.9873 | + | 51.9395i | −1.17170 | + | 2.02944i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.2502 | + | 31.1856i | −1.02412 | + | 1.21667i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.8862 | − | 14.9454i | 1.00838 | − | 0.582191i | 0.0976658 | − | 0.995219i | \(-0.468862\pi\) |
0.910718 | + | 0.413029i | \(0.135529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.53368i | 0.176340i | 0.996105 | + | 0.0881699i | \(0.0281018\pi\) | ||||
−0.996105 | + | 0.0881699i | \(0.971898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.64692 | + | 32.1708i | 0.219308 | + | 1.24941i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.4459 | − | 11.4773i | 0.754079 | − | 0.445069i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.8682 | + | 22.2883i | −0.498257 | + | 0.863006i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.8451 | + | 27.5170i | −1.26986 | + | 1.06387i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.43172 | + | 16.3362i | −0.364107 | + | 0.630652i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.12239 | + | 7.14019i | 0.158907 | + | 0.275234i | 0.934475 | − | 0.356030i | \(-0.115870\pi\) |
−0.775568 | + | 0.631264i | \(0.782536\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0903455 | − | 38.9151i | 0.00347740 | − | 1.49784i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.51263 | 0.211867 | 0.105934 | − | 0.994373i | \(-0.466217\pi\) | ||||
0.105934 | + | 0.994373i | \(0.466217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.7071 | + | 20.7258i | 1.40869 | + | 0.795383i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.70532 | − | 10.1558i | 0.141988 | − | 0.389172i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0097 | + | 13.8620i | −0.918706 | + | 0.530415i | −0.883222 | − | 0.468955i | \(-0.844631\pi\) |
−0.0354840 | + | 0.999370i | \(0.511297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.6540i | 0.750942i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.0537 | − | 17.6384i | 0.803248 | − | 0.672947i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.40469 | 0.320193 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.1826i | 1.60470i | 0.596853 | + | 0.802351i | \(0.296418\pi\) | ||||
−0.596853 | + | 0.802351i | \(0.703582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.04505 | − | 13.5216i | −0.191645 | − | 0.513642i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 50.8061i | 1.92719i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.0568 | −2.23693 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.53461 | + | 2.01929i | 0.209338 | + | 0.0763764i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.07738i | 0.0406922i | 0.999793 | + | 0.0203461i | \(0.00647681\pi\) | ||||
−0.999793 | + | 0.0203461i | \(0.993523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.78710 | − | 2.18648i | 0.142833 | − | 0.0824648i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.1389 | − | 37.1683i | −1.17276 | − | 1.39984i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.4326 | − | 0.282426i | 1.10693 | − | 0.0106217i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9612 | −0.824769 | −0.412385 | − | 0.911010i | \(-0.635304\pi\) | ||||
−0.412385 | + | 0.911010i | \(0.635304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.19717 | + | 1.88251i | −0.194909 | + | 0.0705997i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.37617 | − | 16.2400i | −0.351140 | − | 0.608193i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.3240 | + | 17.8817i | −0.386095 | + | 0.668737i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.7159 | + | 11.2066i | 1.14711 | + | 0.418518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89267 | − | 10.2064i | 0.219760 | − | 0.380635i | −0.734975 | − | 0.678094i | \(-0.762806\pi\) |
0.954734 | + | 0.297460i | \(0.0961394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.38930 | + | 0.784436i | 0.0517403 | + | 0.0292139i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.1988 | + | 6.63977i | 0.676820 | + | 0.246936i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 50.0804i | 1.85994i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1963 | − | 5.88682i | 0.378159 | − | 0.218330i | −0.298858 | − | 0.954298i | \(-0.596606\pi\) |
0.677017 | + | 0.735967i | \(0.263272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.6084 | − | 23.3198i | 0.504016 | − | 0.863694i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8637 | − | 24.0127i | 0.512768 | − | 0.888140i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.9020 | + | 21.8828i | −1.39994 | + | 0.808258i | −0.994386 | − | 0.105812i | \(-0.966256\pi\) |
−0.405558 | + | 0.914069i | \(0.632923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 42.0525 | − | 8.21624i | 1.55113 | − | 0.303060i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.3575 | + | 7.13462i | 0.455195 | + | 0.262807i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.9728 | + | 24.2016i | 0.513998 | + | 0.890270i | 0.999868 | + | 0.0162393i | \(0.00516935\pi\) |
−0.485870 | + | 0.874031i | \(0.661497\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.63159 | − | 10.3029i | −0.317089 | − | 0.378487i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0951 | + | 17.9528i | 1.14077 | + | 0.658623i | 0.946621 | − | 0.322350i | \(-0.104473\pi\) |
0.194147 | + | 0.980972i | \(0.437806\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.6521 | − | 11.3462i | −0.719998 | − | 0.415691i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.7859 | + | 21.7050i | 0.943455 | + | 0.794144i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.332251 | + | 34.6250i | 0.0121402 | + | 1.26517i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.17516 | + | 2.03543i | 0.0428821 | + | 0.0742740i | 0.886670 | − | 0.462403i | \(-0.153013\pi\) |
−0.843788 | + | 0.536677i | \(0.819679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.3636 | − | 4.62758i | 0.960743 | − | 0.168638i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −56.5178 | −2.05689 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.88061 | 0.322771 | 0.161386 | − | 0.986891i | \(-0.448404\pi\) | ||||
0.161386 | + | 0.986891i | \(0.448404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.9384 | + | 2.09554i | −0.433336 | + | 0.0760632i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.4883 | + | 23.3624i | 0.488951 | + | 0.846888i | 0.999919 | − | 0.0127118i | \(-0.00404640\pi\) |
−0.510968 | + | 0.859600i | \(0.670713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.56585 | − | 6.31541i | 0.129092 | − | 0.228633i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.8992 | + | 61.2579i | −0.394061 | + | 2.21478i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.5222 | − | 14.1579i | −0.885446 | − | 0.511213i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.88232 | − | 4.55086i | −0.284244 | − | 0.164108i | 0.351099 | − | 0.936338i | \(-0.385808\pi\) |
−0.635343 | + | 0.772230i | \(0.719141\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.8403 | + | 14.1329i | 0.426419 | + | 0.508985i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.46864 | + | 11.2040i | 0.232661 | + | 0.402980i | 0.958590 | − | 0.284789i | \(-0.0919235\pi\) |
−0.725929 | + | 0.687769i | \(0.758590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.6015 | − | 18.2451i | −1.13516 | − | 0.655384i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.15890 | − | 1.51296i | 0.292699 | − | 0.0542772i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.0462 | − | 12.1510i | 0.754057 | − | 0.435355i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.93628 | + | 12.0140i | −0.248199 | + | 0.429894i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.4431 | + | 30.0510i | −0.623366 | + | 1.07394i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.6245 | + | 24.6093i | −1.52134 | + | 0.878343i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.8566i | − | 0.886043i | −0.896511 | − | 0.443022i | \(-0.853906\pi\) | ||
0.896511 | − | 0.443022i | \(-0.146094\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.0409 | − | 6.58216i | −0.642272 | − | 0.234331i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.194975 | + | 20.3190i | 0.00693250 | + | 0.722460i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.6680 | + | 28.8697i | −0.591896 | + | 1.02519i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.0405 | + | 5.48749i | 0.533432 | + | 0.194621i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.71671 | + | 11.6337i | −0.237918 | + | 0.412086i | −0.960117 | − | 0.279600i | \(-0.909798\pi\) |
0.722199 | + | 0.691686i | \(0.243132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2444 | + | 40.2605i | 0.822328 | + | 1.42431i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.24994 | − | 40.7476i | 0.256164 | − | 1.43974i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.7060 | 0.871857 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.345294 | − | 35.9843i | −0.0121700 | − | 1.26828i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.98860 | − | 8.34180i | −0.246011 | − | 0.293645i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.38524 | − | 5.41857i | 0.329967 | − | 0.190507i | −0.325859 | − | 0.945418i | \(-0.605654\pi\) |
0.655827 | + | 0.754912i | \(0.272320\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.3334i | − | 1.24072i | −0.784316 | − | 0.620361i | \(-0.786986\pi\) | ||
0.784316 | − | 0.620361i | \(-0.213014\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.79343 | − | 0.654327i | −0.0628983 | − | 0.0229483i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 55.0951 | 1.92990 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.4099i | 0.399182i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.91573 | − | 23.8956i | −0.311541 | − | 0.834981i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2156i | 0.670631i | 0.942106 | + | 0.335315i | \(0.108843\pi\) | ||||
−0.942106 | + | 0.335315i | \(0.891157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.8148 | 1.03928 | 0.519639 | − | 0.854386i | \(-0.326066\pi\) | ||||
0.519639 | + | 0.854386i | \(0.326066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.0798 | + | 15.1469i | −0.629456 | + | 0.527347i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.356137i | − | 0.0123841i | −0.999981 | − | 0.00619205i | \(-0.998029\pi\) | ||
0.999981 | − | 0.00619205i | \(-0.00197100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5571 | + | 10.1366i | −0.609783 | + | 0.352058i | −0.772880 | − | 0.634552i | \(-0.781185\pi\) |
0.163098 | + | 0.986610i | \(0.447851\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.11951 | + | 24.9955i | −0.316352 | + | 0.867083i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.0732 | + | 0.788324i | −1.42310 | + | 0.0273138i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.5590 | 1.61124 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.6078 | − | 21.9550i | −0.435791 | − | 0.758875i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.662663 | + | 1.14777i | 0.0228777 | + | 0.0396253i | 0.877238 | − | 0.480056i | \(-0.159384\pi\) |
−0.854360 | + | 0.519682i | \(0.826051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.85791 | − | 13.6103i | 0.270962 | − | 0.469321i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.9956 | + | 24.2920i | −0.998662 | + | 0.836661i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.72626 | − | 8.18612i | 0.162588 | − | 0.281611i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0084 | − | 17.7258i | 0.343894 | − | 0.609064i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.31743 | − | 18.8996i | −0.113854 | − | 0.648632i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.96914i | − | 0.238899i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.7558 | − | 24.1077i | 1.42969 | − | 0.825432i | 0.432594 | − | 0.901589i | \(-0.357598\pi\) |
0.997096 | + | 0.0761571i | \(0.0242650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.71972 | − | 24.0731i | −0.298208 | − | 0.823282i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.4387 | + | 18.0803i | −0.356578 | + | 0.617611i | −0.987387 | − | 0.158328i | \(-0.949390\pi\) |
0.630809 | + | 0.775938i | \(0.282723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8727 | − | 6.85469i | 0.405090 | − | 0.233879i | −0.283588 | − | 0.958946i | \(-0.591525\pi\) |
0.688678 | + | 0.725067i | \(0.258191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 45.3417 | − | 8.40803i | 1.54524 | − | 0.286545i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.1125 | − | 16.2307i | −0.956959 | − | 0.552501i | −0.0617233 | − | 0.998093i | \(-0.519660\pi\) |
−0.895236 | + | 0.445593i | \(0.852993\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8047 | − | 34.3027i | −0.673379 | − | 1.16633i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.3542 | − | 28.3795i | 0.351646 | − | 0.963819i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.90139 | + | 1.67512i | 0.0984228 | + | 0.0568244i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8385 | + | 12.6085i | 0.739970 | + | 0.427222i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.7808 | − | 36.5680i | 1.04177 | − | 1.23764i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.8302 | − | 20.0438i | −0.399933 | − | 0.677604i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.9669 | − | 18.9953i | −0.370326 | − | 0.641424i | 0.619289 | − | 0.785163i | \(-0.287421\pi\) |
−0.989616 | + | 0.143739i | \(0.954087\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.9993 | − | 41.1112i | 0.505913 | − | 1.38665i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.8019 | −0.734526 | −0.367263 | − | 0.930117i | \(-0.619705\pi\) | ||||
−0.367263 | + | 0.930117i | \(0.619705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4085 | −0.821411 | −0.410705 | − | 0.911768i | \(-0.634717\pi\) | ||||
−0.410705 | + | 0.911768i | \(0.634717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.6397 | − | 41.3469i | −1.16440 | − | 1.38986i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8722 | − | 29.2235i | −0.566513 | − | 0.981230i | −0.996907 | − | 0.0785887i | \(-0.974959\pi\) |
0.430394 | − | 0.902641i | \(-0.358375\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.1051 | + | 40.8411i | 0.808458 | + | 1.36977i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.1246 | + | 2.79176i | −0.540193 | + | 0.0935274i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.5673 | − | 9.56513i | −0.554403 | − | 0.320085i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.6113 | − | 18.8281i | −1.09007 | − | 0.629355i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.0978 | + | 3.70328i | −0.704436 | + | 0.123649i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.2907 | + | 28.2164i | 0.543326 | + | 0.941068i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2936 | − | 7.67505i | −0.442873 | − | 0.255693i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.22533 | + | 20.4099i | −0.240444 | + | 0.679198i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.3889 | − | 21.0092i | 1.20961 | − | 0.698368i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.52832 | + | 13.0394i | −0.249974 | + | 0.432967i | −0.963518 | − | 0.267643i | \(-0.913755\pi\) |
0.713544 | + | 0.700610i | \(0.247089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.84637 | − | 32.8589i | 0.193912 | − | 1.08986i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.5047 | + | 12.4157i | −0.712481 | + | 0.411351i | −0.811979 | − | 0.583686i | \(-0.801610\pi\) |
0.0994977 | + | 0.995038i | \(0.468276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 20.4282i | − | 0.676075i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −48.6772 | + | 40.7809i | −1.60922 | + | 1.34817i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.0759 | + | 39.0983i | −0.729012 | + | 1.29114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0689 | + | 20.9039i | −0.398115 | + | 0.689555i | −0.993493 | − | 0.113890i | \(-0.963669\pi\) |
0.595378 | + | 0.803445i | \(0.297002\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.65813 | − | 20.8406i | −0.120539 | − | 0.686720i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2580 | + | 21.2314i | −0.403476 | + | 0.698840i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.78064 | − | 11.7444i | −0.222946 | − | 0.386154i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.16500 | − | 1.38404i | 0.0382636 | − | 0.0454577i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6620 | −0.874752 | −0.437376 | − | 0.899279i | \(-0.644092\pi\) | ||||
−0.437376 | + | 0.899279i | \(0.644092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.4751 | − | 8.73180i | 0.474403 | − | 0.286173i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.1891 | − | 2.84166i | 0.530007 | − | 0.0930317i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.6586 | − | 18.8555i | 1.06805 | − | 0.616640i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.17165i | − | 0.266956i | −0.991052 | − | 0.133478i | \(-0.957385\pi\) | ||
0.991052 | − | 0.133478i | \(-0.0426146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.05790 | − | 23.1181i | −0.132424 | − | 0.754430i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0272 | 1.04406 | 0.522028 | − | 0.852928i | \(-0.325176\pi\) | ||||
0.522028 | + | 0.852928i | \(0.325176\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 38.7298i | − | 1.26122i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.353392 | − | 48.5833i | −0.0114958 | − | 1.58042i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.9002i | 0.581678i | 0.956772 | + | 0.290839i | \(0.0939344\pi\) | ||||
−0.956772 | + | 0.290839i | \(0.906066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.6611 | 1.41730 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.75640 | + | 27.0975i | 0.154237 | + | 0.878697i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.2737i | − | 0.365191i | −0.983188 | − | 0.182596i | \(-0.941550\pi\) | ||
0.983188 | − | 0.182596i | \(-0.0584499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.685459 | − | 0.395750i | 0.0221809 | − | 0.0128062i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7425 | − | 3.64091i | 0.670510 | − | 0.117694i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.141185 | + | 14.7134i | 0.00455911 | + | 0.475120i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.26007 | 0.234196 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.6558 | + | 6.87776i | 1.24567 | + | 0.221633i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.0738 | + | 79.8022i | 1.48317 | + | 2.56892i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.3313 | − | 26.5546i | 0.493022 | − | 0.853939i | −0.506946 | − | 0.861978i | \(-0.669226\pi\) |
0.999968 | + | 0.00803913i | \(0.00255896\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.24398 | + | 24.1782i | 0.136336 | + | 0.776716i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.0807 | + | 33.0488i | −0.612330 | + | 1.06059i | 0.378517 | + | 0.925595i | \(0.376434\pi\) |
−0.990847 | + | 0.134992i | \(0.956899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.364967 | + | 38.0345i | 0.0117003 | + | 1.21933i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −31.9510 | + | 26.7680i | −1.02325 | + | 0.857261i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.6991i | 0.982151i | 0.871117 | + | 0.491076i | \(0.163396\pi\) | ||||
−0.871117 | + | 0.491076i | \(0.836604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.7239 | + | 12.5423i | −0.694299 | + | 0.400854i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.29148 | − | 5.29580i | −0.200872 | − | 0.169082i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9028 | − | 22.3484i | 0.411536 | − | 0.712802i | −0.583522 | − | 0.812098i | \(-0.698326\pi\) |
0.995058 | + | 0.0992957i | \(0.0316590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.78330 | + | 2.76164i | −0.152409 | + | 0.0879932i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.5782 | − | 27.6012i | −0.750502 | − | 0.878556i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7476 | + | 9.09191i | 0.500746 | + | 0.289106i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4388 | − | 19.8126i | −0.363366 | − | 0.629369i | 0.625146 | − | 0.780508i | \(-0.285039\pi\) |
−0.988513 | + | 0.151139i | \(0.951706\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.7212 | + | 3.28612i | −0.594100 | + | 0.104282i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 47.6118 | + | 27.4887i | 1.50940 | + | 0.871450i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.9753 | − | 20.7704i | −1.13935 | − | 0.657804i | −0.193080 | − | 0.981183i | \(-0.561848\pi\) |
−0.946269 | + | 0.323379i | \(0.895181\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0218440 | − | 9.40901i | 0.000691115 | − | 0.297688i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.bs.a.257.1 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bs.a.1097.3 | 48 | |||
4.3 | odd | 2 | 1008.2.ca.e.257.24 | 48 | |||
7.3 | odd | 6 | 504.2.cx.a.185.7 | yes | 48 | ||
9.2 | odd | 6 | 504.2.cx.a.425.7 | yes | 48 | ||
9.7 | even | 3 | 1512.2.cx.a.89.3 | 48 | |||
12.11 | even | 2 | 3024.2.ca.e.2609.3 | 48 | |||
21.17 | even | 6 | 1512.2.cx.a.17.3 | 48 | |||
28.3 | even | 6 | 1008.2.df.e.689.18 | 48 | |||
36.7 | odd | 6 | 3024.2.df.e.1601.3 | 48 | |||
36.11 | even | 6 | 1008.2.df.e.929.18 | 48 | |||
63.38 | even | 6 | inner | 504.2.bs.a.353.1 | yes | 48 | |
63.52 | odd | 6 | 1512.2.bs.a.521.3 | 48 | |||
84.59 | odd | 6 | 3024.2.df.e.17.3 | 48 | |||
252.115 | even | 6 | 3024.2.ca.e.2033.3 | 48 | |||
252.227 | odd | 6 | 1008.2.ca.e.353.24 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bs.a.353.1 | yes | 48 | 63.38 | even | 6 | inner | |
504.2.cx.a.185.7 | yes | 48 | 7.3 | odd | 6 | ||
504.2.cx.a.425.7 | yes | 48 | 9.2 | odd | 6 | ||
1008.2.ca.e.257.24 | 48 | 4.3 | odd | 2 | |||
1008.2.ca.e.353.24 | 48 | 252.227 | odd | 6 | |||
1008.2.df.e.689.18 | 48 | 28.3 | even | 6 | |||
1008.2.df.e.929.18 | 48 | 36.11 | even | 6 | |||
1512.2.bs.a.521.3 | 48 | 63.52 | odd | 6 | |||
1512.2.bs.a.1097.3 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.17.3 | 48 | 21.17 | even | 6 | |||
1512.2.cx.a.89.3 | 48 | 9.7 | even | 3 | |||
3024.2.ca.e.2033.3 | 48 | 252.115 | even | 6 | |||
3024.2.ca.e.2609.3 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.17.3 | 48 | 84.59 | odd | 6 | |||
3024.2.df.e.1601.3 | 48 | 36.7 | odd | 6 |