Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(323,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.j (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.18 | ||
Character | \(\chi\) | \(=\) | 504.323 |
Dual form | 504.2.j.a.323.17 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.619645 | + | 1.27124i | 0.438155 | + | 0.898899i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.23208 | + | 1.57543i | −0.616040 | + | 0.787715i | ||||
\(5\) | 0.753720 | 0.337074 | 0.168537 | − | 0.985695i | \(-0.446096\pi\) | ||||
0.168537 | + | 0.985695i | \(0.446096\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −2.76619 | − | 0.590057i | −0.977997 | − | 0.208617i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.467039 | + | 0.958156i | 0.147691 | + | 0.302996i | ||||
\(11\) | 4.40413i | 1.32790i | 0.747779 | + | 0.663948i | \(0.231120\pi\) | ||||
−0.747779 | + | 0.663948i | \(0.768880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.28230i | 1.18770i | 0.804578 | + | 0.593848i | \(0.202392\pi\) | ||||
−0.804578 | + | 0.593848i | \(0.797608\pi\) | |||||||
\(14\) | 1.27124 | − | 0.619645i | 0.339752 | − | 0.165607i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.963957 | − | 3.88211i | −0.240989 | − | 0.970528i | ||||
\(17\) | 7.48403i | 1.81514i | 0.419897 | + | 0.907572i | \(0.362066\pi\) | ||||
−0.419897 | + | 0.907572i | \(0.637934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.157023 | 0.0360236 | 0.0180118 | − | 0.999838i | \(-0.494266\pi\) | ||||
0.0180118 | + | 0.999838i | \(0.494266\pi\) | |||||||
\(20\) | −0.928644 | + | 1.18743i | −0.207651 | + | 0.265518i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.59869 | + | 2.72900i | −1.19364 | + | 0.581824i | ||||
\(23\) | 2.84216 | 0.592631 | 0.296316 | − | 0.955090i | \(-0.404242\pi\) | ||||
0.296316 | + | 0.955090i | \(0.404242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.43191 | −0.886381 | ||||||||
\(26\) | −5.44381 | + | 2.65350i | −1.06762 | + | 0.520395i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.57543 | + | 1.23208i | 0.297728 | + | 0.232841i | ||||
\(29\) | 5.03950 | 0.935812 | 0.467906 | − | 0.883778i | \(-0.345009\pi\) | ||||
0.467906 | + | 0.883778i | \(0.345009\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.13728i | − | 1.64110i | −0.571572 | − | 0.820552i | \(-0.693666\pi\) | ||
0.571572 | − | 0.820552i | \(-0.306334\pi\) | |||||||
\(32\) | 4.33777 | − | 3.63095i | 0.766816 | − | 0.641867i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.51396 | + | 4.63744i | −1.63163 | + | 0.795315i | ||||
\(35\) | − | 0.753720i | − | 0.127402i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.38541i | − | 1.04975i | −0.851178 | − | 0.524877i | \(-0.824111\pi\) | ||
0.851178 | − | 0.524877i | \(-0.175889\pi\) | |||||||
\(38\) | 0.0972987 | + | 0.199614i | 0.0157839 | + | 0.0323816i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.08494 | − | 0.444738i | −0.329658 | − | 0.0703193i | ||||
\(41\) | 2.93539i | 0.458431i | 0.973376 | + | 0.229215i | \(0.0736160\pi\) | ||||
−0.973376 | + | 0.229215i | \(0.926384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50524 | 0.229547 | 0.114774 | − | 0.993392i | \(-0.463386\pi\) | ||||
0.114774 | + | 0.993392i | \(0.463386\pi\) | |||||||
\(44\) | −6.93840 | − | 5.42624i | −1.04600 | − | 0.818037i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76113 | + | 3.61306i | 0.259665 | + | 0.532716i | ||||
\(47\) | −6.17443 | −0.900634 | −0.450317 | − | 0.892869i | \(-0.648689\pi\) | ||||
−0.450317 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −2.74621 | − | 5.63400i | −0.388372 | − | 0.796767i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.74646 | − | 5.27613i | −0.935565 | − | 0.731668i | ||||
\(53\) | 10.5926 | 1.45501 | 0.727506 | − | 0.686102i | \(-0.240680\pi\) | ||||
0.727506 | + | 0.686102i | \(0.240680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.31948i | 0.447599i | ||||||||
\(56\) | −0.590057 | + | 2.76619i | −0.0788497 | + | 0.369648i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.12270 | + | 6.40639i | 0.410031 | + | 0.841201i | ||||
\(59\) | − | 6.17443i | − | 0.803843i | −0.915674 | − | 0.401921i | \(-0.868343\pi\) | ||
0.915674 | − | 0.401921i | \(-0.131657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.34822i | 1.19692i | 0.801154 | + | 0.598458i | \(0.204220\pi\) | ||||
−0.801154 | + | 0.598458i | \(0.795780\pi\) | |||||||
\(62\) | 11.6156 | − | 5.66187i | 1.47519 | − | 0.719058i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.30367 | + | 3.26443i | 0.912958 | + | 0.408053i | ||||
\(65\) | 3.22765i | 0.400341i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.5662 | 1.41304 | 0.706521 | − | 0.707692i | \(-0.250264\pi\) | ||||
0.706521 | + | 0.707692i | \(0.250264\pi\) | |||||||
\(68\) | −11.7906 | − | 9.22092i | −1.42982 | − | 1.11820i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.958156 | − | 0.467039i | 0.114522 | − | 0.0558219i | ||||
\(71\) | −2.69634 | −0.319997 | −0.159998 | − | 0.987117i | \(-0.551149\pi\) | ||||
−0.159998 | + | 0.987117i | \(0.551149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.74091 | 0.203758 | 0.101879 | − | 0.994797i | \(-0.467515\pi\) | ||||
0.101879 | + | 0.994797i | \(0.467515\pi\) | |||||||
\(74\) | 8.11736 | − | 3.95668i | 0.943623 | − | 0.459955i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.193465 | + | 0.247379i | −0.0221920 | + | 0.0283763i | ||||
\(77\) | 4.40413 | 0.501897 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.2700i | − | 1.38048i | −0.723581 | − | 0.690240i | \(-0.757505\pi\) | ||
0.723581 | − | 0.690240i | \(-0.242495\pi\) | |||||||
\(80\) | −0.726554 | − | 2.92603i | −0.0812312 | − | 0.327140i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.73157 | + | 1.81890i | −0.412083 | + | 0.200864i | ||||
\(83\) | 8.29068i | 0.910021i | 0.890486 | + | 0.455010i | \(0.150364\pi\) | ||||
−0.890486 | + | 0.455010i | \(0.849636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.64087i | 0.611838i | ||||||||
\(86\) | 0.932715 | + | 1.91352i | 0.100577 | + | 0.206340i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.59869 | − | 12.1827i | 0.277021 | − | 1.29868i | ||||
\(89\) | − | 5.13323i | − | 0.544121i | −0.962280 | − | 0.272061i | \(-0.912295\pi\) | ||
0.962280 | − | 0.272061i | \(-0.0877052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.28230 | 0.448907 | ||||||||
\(92\) | −3.50177 | + | 4.47762i | −0.365085 | + | 0.466825i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.82596 | − | 7.84916i | −0.394617 | − | 0.809579i | ||||
\(95\) | 0.118352 | 0.0121426 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.83722 | 0.592680 | 0.296340 | − | 0.955083i | \(-0.404234\pi\) | ||||
0.296340 | + | 0.955083i | \(0.404234\pi\) | |||||||
\(98\) | −0.619645 | − | 1.27124i | −0.0625936 | − | 0.128414i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.46046 | − | 6.98216i | 0.546046 | − | 0.698216i | ||||
\(101\) | −3.90513 | −0.388575 | −0.194287 | − | 0.980945i | \(-0.562239\pi\) | ||||
−0.194287 | + | 0.980945i | \(0.562239\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.9804i | − | 1.57459i | −0.616574 | − | 0.787297i | \(-0.711480\pi\) | ||
0.616574 | − | 0.787297i | \(-0.288520\pi\) | |||||||
\(104\) | 2.52680 | − | 11.8457i | 0.247773 | − | 1.16156i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.56368 | + | 13.4657i | 0.637521 | + | 1.30791i | ||||
\(107\) | − | 7.41901i | − | 0.717223i | −0.933487 | − | 0.358612i | \(-0.883250\pi\) | ||
0.933487 | − | 0.358612i | \(-0.116750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9803i | 1.05172i | 0.850572 | + | 0.525859i | \(0.176256\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(110\) | −4.21985 | + | 2.05690i | −0.402347 | + | 0.196118i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.88211 | + | 0.963957i | −0.366825 | + | 0.0910854i | ||||
\(113\) | − | 10.0685i | − | 0.947166i | −0.880749 | − | 0.473583i | \(-0.842960\pi\) | ||
0.880749 | − | 0.473583i | \(-0.157040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14219 | 0.199761 | ||||||||
\(116\) | −6.20907 | + | 7.93938i | −0.576498 | + | 0.737153i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.84916 | − | 3.82596i | 0.722574 | − | 0.352208i | ||||
\(119\) | 7.48403 | 0.686060 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.39637 | −0.763307 | ||||||||
\(122\) | −11.8838 | + | 5.79258i | −1.07591 | + | 0.524435i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.3951 | + | 11.2579i | 1.29272 | + | 1.01099i | ||||
\(125\) | −7.10902 | −0.635850 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.57353i | 0.139628i | 0.997560 | + | 0.0698142i | \(0.0222406\pi\) | ||||
−0.997560 | + | 0.0698142i | \(0.977759\pi\) | |||||||
\(128\) | 0.375826 | + | 11.3075i | 0.0332186 | + | 0.999448i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.10311 | + | 2.00000i | −0.359867 | + | 0.175412i | ||||
\(131\) | 2.80096i | 0.244721i | 0.992486 | + | 0.122361i | \(0.0390464\pi\) | ||||
−0.992486 | + | 0.122361i | \(0.960954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.157023i | − | 0.0136157i | ||||||
\(134\) | 7.16697 | + | 14.7034i | 0.619132 | + | 1.27018i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.41600 | − | 20.7023i | 0.378669 | − | 1.77521i | ||||
\(137\) | 14.3363i | 1.22483i | 0.790536 | + | 0.612416i | \(0.209802\pi\) | ||||
−0.790536 | + | 0.612416i | \(0.790198\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7353 | 1.24983 | 0.624915 | − | 0.780693i | \(-0.285134\pi\) | ||||
0.624915 | + | 0.780693i | \(0.285134\pi\) | |||||||
\(140\) | 1.18743 | + | 0.928644i | 0.100356 | + | 0.0784847i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.67077 | − | 3.42769i | −0.140208 | − | 0.287645i | ||||
\(143\) | −18.8598 | −1.57714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.79837 | 0.315438 | ||||||||
\(146\) | 1.07874 | + | 2.21310i | 0.0892775 | + | 0.183158i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0598 | + | 7.86733i | 0.826907 | + | 0.646691i | ||||
\(149\) | 9.30727 | 0.762481 | 0.381240 | − | 0.924476i | \(-0.375497\pi\) | ||||
0.381240 | + | 0.924476i | \(0.375497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7353i | 0.873625i | 0.899553 | + | 0.436812i | \(0.143893\pi\) | ||||
−0.899553 | + | 0.436812i | \(0.856107\pi\) | |||||||
\(152\) | −0.434357 | − | 0.0926527i | −0.0352310 | − | 0.00751513i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.72900 | + | 5.59869i | 0.219909 | + | 0.451155i | ||||
\(155\) | − | 6.88696i | − | 0.553174i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.8050i | − | 1.10176i | −0.834585 | − | 0.550879i | \(-0.814293\pi\) | ||
0.834585 | − | 0.550879i | \(-0.185707\pi\) | |||||||
\(158\) | 15.5980 | − | 7.60302i | 1.24091 | − | 0.604864i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.26946 | − | 2.73672i | 0.258474 | − | 0.216357i | ||||
\(161\) | − | 2.84216i | − | 0.223994i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.56294 | 0.435723 | 0.217861 | − | 0.975980i | \(-0.430092\pi\) | ||||
0.217861 | + | 0.975980i | \(0.430092\pi\) | |||||||
\(164\) | −4.62450 | − | 3.61663i | −0.361113 | − | 0.282412i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.5394 | + | 5.13728i | −0.818017 | + | 0.398730i | ||||
\(167\) | −25.5058 | −1.97370 | −0.986850 | − | 0.161638i | \(-0.948322\pi\) | ||||
−0.986850 | + | 0.161638i | \(0.948322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.33806 | −0.410620 | ||||||||
\(170\) | −7.17087 | + | 3.49533i | −0.549981 | + | 0.268080i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.85458 | + | 2.37140i | −0.141410 | + | 0.180818i | ||||
\(173\) | −4.05978 | −0.308659 | −0.154330 | − | 0.988019i | \(-0.549322\pi\) | ||||
−0.154330 | + | 0.988019i | \(0.549322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.43191i | 0.335021i | ||||||||
\(176\) | 17.0973 | − | 4.24539i | 1.28876 | − | 0.320009i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.52555 | − | 3.18078i | 0.489110 | − | 0.238410i | ||||
\(179\) | − | 24.3019i | − | 1.81641i | −0.418528 | − | 0.908204i | \(-0.637454\pi\) | ||
0.418528 | − | 0.908204i | \(-0.362546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.7424i | 1.69043i | 0.534428 | + | 0.845214i | \(0.320527\pi\) | ||||
−0.534428 | + | 0.845214i | \(0.679473\pi\) | |||||||
\(182\) | 2.65350 | + | 5.44381i | 0.196691 | + | 0.403522i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.86197 | − | 1.67704i | −0.579592 | − | 0.123633i | ||||
\(185\) | − | 4.81281i | − | 0.353845i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.9606 | −2.41032 | ||||||||
\(188\) | 7.60740 | − | 9.72739i | 0.554826 | − | 0.709442i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0733361 | + | 0.150453i | 0.00532036 | + | 0.0109150i | ||||
\(191\) | 9.59578 | 0.694326 | 0.347163 | − | 0.937805i | \(-0.387145\pi\) | ||||
0.347163 | + | 0.937805i | \(0.387145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.47075 | 0.537756 | 0.268878 | − | 0.963174i | \(-0.413347\pi\) | ||||
0.268878 | + | 0.963174i | \(0.413347\pi\) | |||||||
\(194\) | 3.61700 | + | 7.42048i | 0.259686 | + | 0.532759i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23208 | − | 1.57543i | 0.0880057 | − | 0.112531i | ||||
\(197\) | 23.0306 | 1.64086 | 0.820431 | − | 0.571746i | \(-0.193734\pi\) | ||||
0.820431 | + | 0.571746i | \(0.193734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.28608i | − | 0.162056i | −0.996712 | − | 0.0810279i | \(-0.974180\pi\) | ||
0.996712 | − | 0.0810279i | \(-0.0258203\pi\) | |||||||
\(200\) | 12.2595 | + | 2.61508i | 0.866878 | + | 0.184914i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.41979 | − | 4.96434i | −0.170256 | − | 0.349290i | ||||
\(203\) | − | 5.03950i | − | 0.353704i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.21246i | 0.154525i | ||||||||
\(206\) | 20.3148 | − | 9.90217i | 1.41540 | − | 0.689917i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.6244 | − | 4.12795i | 1.15269 | − | 0.286222i | ||||
\(209\) | 0.691552i | 0.0478356i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.6480 | −1.49031 | −0.745154 | − | 0.666893i | \(-0.767624\pi\) | ||||
−0.745154 | + | 0.666893i | \(0.767624\pi\) | |||||||
\(212\) | −13.0510 | + | 16.6880i | −0.896345 | + | 1.14613i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.43131 | − | 4.59715i | 0.644711 | − | 0.314255i | ||||
\(215\) | 1.13453 | 0.0773744 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.13728 | −0.620279 | ||||||||
\(218\) | −13.9585 | + | 6.80386i | −0.945389 | + | 0.460816i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.22961 | − | 4.08987i | −0.352580 | − | 0.275739i | ||||
\(221\) | −32.0488 | −2.15584 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.85664i | 0.392190i | 0.980585 | + | 0.196095i | \(0.0628260\pi\) | ||||
−0.980585 | + | 0.196095i | \(0.937174\pi\) | |||||||
\(224\) | −3.63095 | − | 4.33777i | −0.242603 | − | 0.289829i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.7995 | − | 6.23891i | 0.851407 | − | 0.415006i | ||||
\(227\) | 18.5005i | 1.22792i | 0.789336 | + | 0.613961i | \(0.210425\pi\) | ||||
−0.789336 | + | 0.613961i | \(0.789575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.16399i | − | 0.605573i | −0.953058 | − | 0.302787i | \(-0.902083\pi\) | ||
0.953058 | − | 0.302787i | \(-0.0979169\pi\) | |||||||
\(230\) | 1.32740 | + | 2.72323i | 0.0875262 | + | 0.179565i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.9402 | − | 2.97359i | −0.915221 | − | 0.195226i | ||||
\(233\) | − | 5.29278i | − | 0.346742i | −0.984857 | − | 0.173371i | \(-0.944534\pi\) | ||
0.984857 | − | 0.173371i | \(-0.0554659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.65380 | −0.303580 | ||||||||
\(236\) | 9.72739 | + | 7.60740i | 0.633199 | + | 0.495199i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.63744 | + | 9.51396i | 0.300601 | + | 0.616699i | ||||
\(239\) | 11.6411 | 0.753002 | 0.376501 | − | 0.926416i | \(-0.377127\pi\) | ||||
0.376501 | + | 0.926416i | \(0.377127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.2913 | −1.88682 | −0.943410 | − | 0.331628i | \(-0.892402\pi\) | ||||
−0.943410 | + | 0.331628i | \(0.892402\pi\) | |||||||
\(242\) | −5.20277 | − | 10.6738i | −0.334447 | − | 0.686136i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.7275 | − | 11.5178i | −0.942829 | − | 0.737349i | ||||
\(245\) | −0.753720 | −0.0481534 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.672421i | 0.0427851i | ||||||||
\(248\) | −5.39152 | + | 25.2755i | −0.342362 | + | 1.60500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.40507 | − | 9.03724i | −0.278601 | − | 0.571565i | ||||
\(251\) | 4.92371i | 0.310782i | 0.987853 | + | 0.155391i | \(0.0496637\pi\) | ||||
−0.987853 | + | 0.155391i | \(0.950336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.5172i | 0.786953i | ||||||||
\(254\) | −2.00033 | + | 0.975031i | −0.125512 | + | 0.0611789i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.1416 | + | 7.48438i | −0.883848 | + | 0.467774i | ||||
\(257\) | − | 23.7193i | − | 1.47957i | −0.672844 | − | 0.739784i | \(-0.734928\pi\) | ||
0.672844 | − | 0.739784i | \(-0.265072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.38541 | −0.396770 | ||||||||
\(260\) | −5.08494 | − | 3.97673i | −0.315355 | − | 0.246626i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.56068 | + | 1.73560i | −0.219980 | + | 0.107226i | ||||
\(263\) | 6.62803 | 0.408702 | 0.204351 | − | 0.978898i | \(-0.434492\pi\) | ||||
0.204351 | + | 0.978898i | \(0.434492\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.98389 | 0.490447 | ||||||||
\(266\) | 0.199614 | − | 0.0972987i | 0.0122391 | − | 0.00596577i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.2505 | + | 18.2218i | −0.870491 | + | 1.11307i | ||||
\(269\) | −21.7190 | −1.32423 | −0.662117 | − | 0.749401i | \(-0.730342\pi\) | ||||
−0.662117 | + | 0.749401i | \(0.730342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.09127i | 0.248527i | 0.992249 | + | 0.124263i | \(0.0396568\pi\) | ||||
−0.992249 | + | 0.124263i | \(0.960343\pi\) | |||||||
\(272\) | 29.0538 | − | 7.21428i | 1.76165 | − | 0.437430i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.2248 | + | 8.88340i | −1.10100 | + | 0.536666i | ||||
\(275\) | − | 19.5187i | − | 1.17702i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.31594i | − | 0.439572i | −0.975548 | − | 0.219786i | \(-0.929464\pi\) | ||
0.975548 | − | 0.219786i | \(-0.0705360\pi\) | |||||||
\(278\) | 9.13064 | + | 18.7320i | 0.547620 | + | 1.12347i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.444738 | + | 2.08494i | −0.0265782 | + | 0.124599i | ||||
\(281\) | − | 1.40887i | − | 0.0840459i | −0.999117 | − | 0.0420230i | \(-0.986620\pi\) | ||
0.999117 | − | 0.0420230i | \(-0.0133803\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0005 | 1.07002 | 0.535010 | − | 0.844846i | \(-0.320308\pi\) | ||||
0.535010 | + | 0.844846i | \(0.320308\pi\) | |||||||
\(284\) | 3.32211 | − | 4.24790i | 0.197131 | − | 0.252066i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.6864 | − | 23.9752i | −0.691030 | − | 1.41769i | ||||
\(287\) | 2.93539 | 0.173270 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −39.0107 | −2.29475 | ||||||||
\(290\) | 2.35364 | + | 4.82863i | 0.138211 | + | 0.283547i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.14494 | + | 2.74268i | −0.125523 | + | 0.160503i | ||||
\(293\) | −12.8759 | −0.752219 | −0.376110 | − | 0.926575i | \(-0.622738\pi\) | ||||
−0.376110 | + | 0.926575i | \(0.622738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.65380i | − | 0.270955i | ||||||
\(296\) | −3.76775 | + | 17.6633i | −0.218996 | + | 1.02666i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.76720 | + | 11.8317i | 0.334085 | + | 0.685394i | ||||
\(299\) | 12.1710i | 0.703866i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.50524i | − | 0.0867607i | ||||||
\(302\) | −13.6471 | + | 6.65206i | −0.785301 | + | 0.382783i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.151364 | − | 0.609582i | −0.00868131 | − | 0.0349619i | ||||
\(305\) | 7.04594i | 0.403450i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.0182 | −1.02835 | −0.514176 | − | 0.857685i | \(-0.671902\pi\) | ||||
−0.514176 | + | 0.857685i | \(0.671902\pi\) | |||||||
\(308\) | −5.42624 | + | 6.93840i | −0.309189 | + | 0.395352i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.75494 | − | 4.26747i | 0.497247 | − | 0.242376i | ||||
\(311\) | 3.68495 | 0.208954 | 0.104477 | − | 0.994527i | \(-0.466683\pi\) | ||||
0.104477 | + | 0.994527i | \(0.466683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.6789 | 1.67755 | 0.838777 | − | 0.544476i | \(-0.183271\pi\) | ||||
0.838777 | + | 0.544476i | \(0.183271\pi\) | |||||||
\(314\) | 17.5494 | − | 8.55419i | 0.990369 | − | 0.482741i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.3305 | + | 15.1176i | 1.08742 | + | 0.850431i | ||||
\(317\) | −12.2672 | −0.688995 | −0.344498 | − | 0.938787i | \(-0.611951\pi\) | ||||
−0.344498 | + | 0.938787i | \(0.611951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.1946i | 1.24266i | ||||||||
\(320\) | 5.50492 | + | 2.46046i | 0.307735 | + | 0.137544i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.61306 | − | 1.76113i | 0.201348 | − | 0.0981440i | ||||
\(323\) | 1.17517i | 0.0653881i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 18.9787i | − | 1.05275i | ||||||
\(326\) | 3.44705 | + | 7.07180i | 0.190914 | + | 0.391671i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.73205 | − | 8.11985i | 0.0956363 | − | 0.448344i | ||||
\(329\) | 6.17443i | 0.340408i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.587758 | 0.0323061 | 0.0161530 | − | 0.999870i | \(-0.494858\pi\) | ||||
0.0161530 | + | 0.999870i | \(0.494858\pi\) | |||||||
\(332\) | −13.0614 | − | 10.2148i | −0.716837 | − | 0.560609i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.8046 | − | 32.4239i | −0.864787 | − | 1.77416i | ||||
\(335\) | 8.71772 | 0.476300 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0318 | 1.74489 | 0.872443 | − | 0.488716i | \(-0.162535\pi\) | ||||
0.872443 | + | 0.488716i | \(0.162535\pi\) | |||||||
\(338\) | −3.30770 | − | 6.78594i | −0.179915 | − | 0.369106i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.88679 | − | 6.95000i | −0.481954 | − | 0.376917i | ||||
\(341\) | 40.2418 | 2.17921 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −4.16379 | − | 0.888178i | −0.224497 | − | 0.0478874i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.51562 | − | 5.16093i | −0.135241 | − | 0.277454i | ||||
\(347\) | 22.5357i | 1.20978i | 0.796309 | + | 0.604889i | \(0.206783\pi\) | ||||
−0.796309 | + | 0.604889i | \(0.793217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.66226i | 0.517209i | 0.965983 | + | 0.258605i | \(0.0832627\pi\) | ||||
−0.965983 | + | 0.258605i | \(0.916737\pi\) | |||||||
\(350\) | −5.63400 | + | 2.74621i | −0.301150 | + | 0.146791i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.9912 | + | 19.1041i | 0.852332 | + | 1.01825i | ||||
\(353\) | 8.41228i | 0.447741i | 0.974619 | + | 0.223870i | \(0.0718692\pi\) | ||||
−0.974619 | + | 0.223870i | \(0.928131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.03229 | −0.107863 | ||||||||
\(356\) | 8.08704 | + | 6.32455i | 0.428613 | + | 0.335201i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 30.8934 | − | 15.0585i | 1.63277 | − | 0.795869i | ||||
\(359\) | −20.2579 | −1.06917 | −0.534586 | − | 0.845114i | \(-0.679533\pi\) | ||||
−0.534586 | + | 0.845114i | \(0.679533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9753 | −0.998702 | ||||||||
\(362\) | −28.9109 | + | 14.0922i | −1.51952 | + | 0.740670i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.27613 | + | 6.74646i | −0.276544 | + | 0.353610i | ||||
\(365\) | 1.31216 | 0.0686814 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.5860i | 1.96197i | 0.194082 | + | 0.980985i | \(0.437827\pi\) | ||||
−0.194082 | + | 0.980985i | \(0.562173\pi\) | |||||||
\(368\) | −2.73972 | − | 11.0336i | −0.142818 | − | 0.575165i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.11822 | − | 2.98223i | 0.318071 | − | 0.155039i | ||||
\(371\) | − | 10.5926i | − | 0.549943i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 37.2643i | − | 1.92947i | −0.263215 | − | 0.964737i | \(-0.584783\pi\) | ||
0.263215 | − | 0.964737i | \(-0.415217\pi\) | |||||||
\(374\) | −20.4239 | − | 41.9007i | −1.05609 | − | 2.16664i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.0797 | + | 3.64327i | 0.880817 | + | 0.187887i | ||||
\(377\) | 21.5806i | 1.11146i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4549 | −0.691131 | −0.345565 | − | 0.938395i | \(-0.612313\pi\) | ||||
−0.345565 | + | 0.938395i | \(0.612313\pi\) | |||||||
\(380\) | −0.145819 | + | 0.186455i | −0.00748035 | + | 0.00956493i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.94598 | + | 12.1985i | 0.304223 | + | 0.624129i | ||||
\(383\) | 17.8814 | 0.913696 | 0.456848 | − | 0.889545i | \(-0.348978\pi\) | ||||
0.456848 | + | 0.889545i | \(0.348978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.31948 | 0.169177 | ||||||||
\(386\) | 4.62921 | + | 9.49708i | 0.235621 | + | 0.483389i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.19192 | + | 9.19613i | −0.365114 | + | 0.466863i | ||||
\(389\) | −7.56746 | −0.383685 | −0.191843 | − | 0.981426i | \(-0.561446\pi\) | ||||
−0.191843 | + | 0.981426i | \(0.561446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2708i | 1.07571i | ||||||||
\(392\) | 2.76619 | + | 0.590057i | 0.139714 | + | 0.0298024i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.2708 | + | 29.2773i | 0.718952 | + | 1.47497i | ||||
\(395\) | − | 9.24813i | − | 0.465324i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.422202i | 0.0211897i | 0.999944 | + | 0.0105948i | \(0.00337251\pi\) | ||||
−0.999944 | + | 0.0105948i | \(0.996627\pi\) | |||||||
\(398\) | 2.90614 | − | 1.41656i | 0.145672 | − | 0.0710056i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.27217 | + | 17.2051i | 0.213608 | + | 0.860257i | ||||
\(401\) | − | 3.67413i | − | 0.183477i | −0.995783 | − | 0.0917386i | \(-0.970758\pi\) | ||
0.995783 | − | 0.0917386i | \(-0.0292424\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.1285 | 1.94913 | ||||||||
\(404\) | 4.81143 | − | 6.15226i | 0.239378 | − | 0.306086i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.40639 | − | 3.12270i | 0.317944 | − | 0.154977i | ||||
\(407\) | 28.1222 | 1.39396 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2115 | 1.14773 | 0.573867 | − | 0.818949i | \(-0.305443\pi\) | ||||
0.573867 | + | 0.818949i | \(0.305443\pi\) | |||||||
\(410\) | −2.81256 | + | 1.37094i | −0.138902 | + | 0.0677060i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 25.1760 | + | 19.6891i | 1.24033 | + | 0.970013i | ||||
\(413\) | −6.17443 | −0.303824 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.24886i | 0.306744i | ||||||||
\(416\) | 15.5488 | + | 18.5756i | 0.762342 | + | 0.910744i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.879125 | + | 0.428516i | −0.0429994 | + | 0.0209594i | ||||
\(419\) | 29.5694i | 1.44456i | 0.691601 | + | 0.722279i | \(0.256906\pi\) | ||||
−0.691601 | + | 0.722279i | \(0.743094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 35.9658i | − | 1.75287i | −0.481525 | − | 0.876433i | \(-0.659917\pi\) | ||
0.481525 | − | 0.876433i | \(-0.340083\pi\) | |||||||
\(422\) | −13.4141 | − | 27.5197i | −0.652986 | − | 1.33964i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.3013 | − | 6.25026i | −1.42300 | − | 0.303540i | ||||
\(425\) | − | 33.1685i | − | 1.60891i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.34822 | 0.452392 | ||||||||
\(428\) | 11.6881 | + | 9.14082i | 0.564967 | + | 0.441838i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.703007 | + | 1.44226i | 0.0339020 | + | 0.0695518i | ||||
\(431\) | −26.0881 | −1.25662 | −0.628309 | − | 0.777964i | \(-0.716253\pi\) | ||||
−0.628309 | + | 0.777964i | \(0.716253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.4426 | 1.79938 | 0.899688 | − | 0.436533i | \(-0.143794\pi\) | ||||
0.899688 | + | 0.436533i | \(0.143794\pi\) | |||||||
\(434\) | −5.66187 | − | 11.6156i | −0.271778 | − | 0.557568i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.2986 | − | 13.5286i | −0.828454 | − | 0.647900i | ||||
\(437\) | 0.446286 | 0.0213487 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 32.9236i | − | 1.57136i | −0.618634 | − | 0.785679i | \(-0.712314\pi\) | ||
0.618634 | − | 0.785679i | \(-0.287686\pi\) | |||||||
\(440\) | 1.95869 | − | 9.18234i | 0.0933766 | − | 0.437751i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.8589 | − | 40.7416i | −0.944591 | − | 1.93788i | ||||
\(443\) | 3.82558i | 0.181759i | 0.995862 | + | 0.0908795i | \(0.0289678\pi\) | ||||
−0.995862 | + | 0.0908795i | \(0.971032\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3.86902i | − | 0.183409i | ||||||
\(446\) | −7.44517 | + | 3.62904i | −0.352539 | + | 0.171840i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.26443 | − | 7.30367i | 0.154230 | − | 0.345066i | ||||
\(449\) | − | 20.9883i | − | 0.990501i | −0.868750 | − | 0.495251i | \(-0.835076\pi\) | ||
0.868750 | − | 0.495251i | \(-0.164924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.9278 | −0.608748 | ||||||||
\(452\) | 15.8622 | + | 12.4052i | 0.746097 | + | 0.583492i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.5185 | + | 11.4638i | −1.10378 | + | 0.538021i | ||||
\(455\) | 3.22765 | 0.151315 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0953 | 0.752908 | 0.376454 | − | 0.926435i | \(-0.377143\pi\) | ||||
0.376454 | + | 0.926435i | \(0.377143\pi\) | |||||||
\(458\) | 11.6496 | − | 5.67842i | 0.544349 | − | 0.265335i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.63936 | + | 3.37488i | −0.123061 | + | 0.157354i | ||||
\(461\) | −28.0400 | −1.30595 | −0.652976 | − | 0.757378i | \(-0.726480\pi\) | ||||
−0.652976 | + | 0.757378i | \(0.726480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.7148i | − | 1.38097i | −0.723349 | − | 0.690483i | \(-0.757398\pi\) | ||
0.723349 | − | 0.690483i | \(-0.242602\pi\) | |||||||
\(464\) | −4.85786 | − | 19.5639i | −0.225521 | − | 0.908231i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.72838 | − | 3.27965i | 0.311686 | − | 0.151927i | ||||
\(467\) | 34.8049i | 1.61058i | 0.592882 | + | 0.805289i | \(0.297990\pi\) | ||||
−0.592882 | + | 0.805289i | \(0.702010\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.5662i | − | 0.534080i | ||||||
\(470\) | −2.88370 | − | 5.91607i | −0.133015 | − | 0.272888i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.64327 | + | 17.0797i | −0.167695 | + | 0.786156i | ||||
\(473\) | 6.62928i | 0.304815i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.695913 | −0.0319307 | ||||||||
\(476\) | −9.22092 | + | 11.7906i | −0.422640 | + | 0.540419i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.21337 | + | 14.7986i | 0.329932 | + | 0.676873i | ||||
\(479\) | 11.9604 | 0.546483 | 0.273241 | − | 0.961946i | \(-0.411904\pi\) | ||||
0.273241 | + | 0.961946i | \(0.411904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3442 | 1.24679 | ||||||||
\(482\) | −18.1502 | − | 37.2362i | −0.826720 | − | 1.69606i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.3450 | − | 13.2279i | 0.470228 | − | 0.601268i | ||||
\(485\) | 4.39963 | 0.199777 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1035i | 0.593775i | 0.954912 | + | 0.296888i | \(0.0959487\pi\) | ||||
−0.954912 | + | 0.296888i | \(0.904051\pi\) | |||||||
\(488\) | 5.51598 | − | 25.8590i | 0.249697 | − | 1.17058i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.467039 | − | 0.958156i | −0.0210987 | − | 0.0432851i | ||||
\(491\) | 4.69315i | 0.211799i | 0.994377 | + | 0.105899i | \(0.0337722\pi\) | ||||
−0.994377 | + | 0.105899i | \(0.966228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.7158i | 1.69863i | ||||||||
\(494\) | −0.854805 | + | 0.416662i | −0.0384595 | + | 0.0187465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −35.4719 | + | 8.80795i | −1.59274 | + | 0.395488i | ||||
\(497\) | 2.69634i | 0.120947i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7443 | 0.615278 | 0.307639 | − | 0.951503i | \(-0.400461\pi\) | ||||
0.307639 | + | 0.951503i | \(0.400461\pi\) | |||||||
\(500\) | 8.75888 | − | 11.1998i | 0.391709 | − | 0.500869i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.25919 | + | 3.05095i | −0.279361 | + | 0.136171i | ||||
\(503\) | 2.18114 | 0.0972521 | 0.0486261 | − | 0.998817i | \(-0.484516\pi\) | ||||
0.0486261 | + | 0.998817i | \(0.484516\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.94338 | −0.130979 | ||||||||
\(506\) | −15.9124 | + | 7.75625i | −0.707391 | + | 0.344807i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.47899 | − | 1.93872i | −0.109987 | − | 0.0860167i | ||||
\(509\) | 8.77140 | 0.388786 | 0.194393 | − | 0.980924i | \(-0.437726\pi\) | ||||
0.194393 | + | 0.980924i | \(0.437726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.74091i | − | 0.0770132i | ||||||
\(512\) | −18.2772 | − | 13.3396i | −0.807744 | − | 0.589533i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.1528 | − | 14.6975i | 1.32998 | − | 0.648281i | ||||
\(515\) | − | 12.0447i | − | 0.530755i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 27.1930i | − | 1.19595i | ||||||
\(518\) | −3.95668 | − | 8.11736i | −0.173847 | − | 0.356656i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.90450 | − | 8.92832i | 0.0835179 | − | 0.391533i | ||||
\(521\) | 7.64302i | 0.334847i | 0.985885 | + | 0.167423i | \(0.0535447\pi\) | ||||
−0.985885 | + | 0.167423i | \(0.946455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.0903 | −1.27203 | −0.636016 | − | 0.771676i | \(-0.719419\pi\) | ||||
−0.636016 | + | 0.771676i | \(0.719419\pi\) | |||||||
\(524\) | −4.41272 | − | 3.45101i | −0.192770 | − | 0.150758i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.10703 | + | 8.42579i | 0.179075 | + | 0.367382i | ||||
\(527\) | 68.3837 | 2.97884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.9221 | −0.648788 | ||||||||
\(530\) | 4.94718 | + | 10.1494i | 0.214892 | + | 0.440862i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.247379 | + | 0.193465i | 0.0107253 | + | 0.00838779i | ||||
\(533\) | −12.5702 | −0.544476 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.59186i | − | 0.241757i | ||||||
\(536\) | −31.9945 | − | 6.82475i | −1.38195 | − | 0.294784i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.4581 | − | 27.6100i | −0.580220 | − | 1.19035i | ||||
\(539\) | − | 4.40413i | − | 0.189699i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16.6902i | − | 0.717567i | −0.933421 | − | 0.358784i | \(-0.883192\pi\) | ||
0.933421 | − | 0.358784i | \(-0.116808\pi\) | |||||||
\(542\) | −5.20096 | + | 2.53513i | −0.223401 | + | 0.108893i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27.1741 | + | 32.4640i | 1.16508 | + | 1.39188i | ||||
\(545\) | 8.27605i | 0.354507i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.06961 | −0.259518 | −0.129759 | − | 0.991546i | \(-0.541420\pi\) | ||||
−0.129759 | + | 0.991546i | \(0.541420\pi\) | |||||||
\(548\) | −22.5858 | − | 17.6634i | −0.964818 | − | 0.754545i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24.8129 | − | 12.0947i | 1.05802 | − | 0.515718i | ||||
\(551\) | 0.791319 | 0.0337113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2700 | −0.521772 | ||||||||
\(554\) | 9.30029 | − | 4.53329i | 0.395131 | − | 0.192601i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.1550 | + | 23.2144i | −0.769945 | + | 0.984510i | ||||
\(557\) | −1.23215 | −0.0522079 | −0.0261039 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261039 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.44589i | 0.272632i | ||||||||
\(560\) | −2.92603 | + | 0.726554i | −0.123647 | + | 0.0307025i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.79100 | − | 0.872997i | 0.0755488 | − | 0.0368252i | ||||
\(563\) | − | 26.5142i | − | 1.11744i | −0.829356 | − | 0.558720i | \(-0.811293\pi\) | ||
0.829356 | − | 0.558720i | \(-0.188707\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 7.58885i | − | 0.319265i | ||||||
\(566\) | 11.1539 | + | 22.8829i | 0.468835 | + | 0.961840i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.45861 | + | 1.59100i | 0.312956 | + | 0.0667567i | ||||
\(569\) | − | 3.22646i | − | 0.135260i | −0.997710 | − | 0.0676301i | \(-0.978456\pi\) | ||
0.997710 | − | 0.0676301i | \(-0.0215438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.7231 | 0.867236 | 0.433618 | − | 0.901097i | \(-0.357237\pi\) | ||||
0.433618 | + | 0.901097i | \(0.357237\pi\) | |||||||
\(572\) | 23.2368 | − | 29.7123i | 0.971579 | − | 1.24233i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.81890 | + | 3.73157i | 0.0759194 | + | 0.155753i | ||||
\(575\) | −12.5962 | −0.525297 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.99870 | −0.291360 | −0.145680 | − | 0.989332i | \(-0.546537\pi\) | ||||
−0.145680 | + | 0.989332i | \(0.546537\pi\) | |||||||
\(578\) | −24.1728 | − | 49.5918i | −1.00545 | − | 2.06275i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.67990 | + | 5.98407i | −0.194322 | + | 0.248475i | ||||
\(581\) | 8.29068 | 0.343956 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.6514i | 1.93210i | ||||||||
\(584\) | −4.81569 | − | 1.02723i | −0.199275 | − | 0.0425073i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.97850 | − | 16.3683i | −0.329589 | − | 0.676169i | ||||
\(587\) | 6.59578i | 0.272237i | 0.990693 | + | 0.136119i | \(0.0434628\pi\) | ||||
−0.990693 | + | 0.136119i | \(0.956537\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.43477i | − | 0.0591185i | ||||||
\(590\) | 5.91607 | − | 2.88370i | 0.243561 | − | 0.118720i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.7889 | + | 6.15526i | −1.01882 | + | 0.252980i | ||||
\(593\) | 17.4761i | 0.717656i | 0.933404 | + | 0.358828i | \(0.116824\pi\) | ||||
−0.933404 | + | 0.358828i | \(0.883176\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.64087 | 0.231253 | ||||||||
\(596\) | −11.4673 | + | 14.6629i | −0.469719 | + | 0.600617i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.4722 | + | 7.54168i | −0.632704 | + | 0.308402i | ||||
\(599\) | 17.4691 | 0.713766 | 0.356883 | − | 0.934149i | \(-0.383839\pi\) | ||||
0.356883 | + | 0.934149i | \(0.383839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.47159 | −0.182400 | −0.0912001 | − | 0.995833i | \(-0.529070\pi\) | ||||
−0.0912001 | + | 0.995833i | \(0.529070\pi\) | |||||||
\(602\) | 1.91352 | − | 0.932715i | 0.0779891 | − | 0.0380146i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.9127 | − | 13.2267i | −0.688167 | − | 0.538188i | ||||
\(605\) | −6.32852 | −0.257291 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.5209i | − | 0.873507i | −0.899581 | − | 0.436754i | \(-0.856128\pi\) | ||
0.899581 | − | 0.436754i | \(-0.143872\pi\) | |||||||
\(608\) | 0.681131 | − | 0.570144i | 0.0276235 | − | 0.0231224i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.95705 | + | 4.36598i | −0.362661 | + | 0.176774i | ||||
\(611\) | − | 26.4408i | − | 1.06968i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.0467i | − | 1.05202i | −0.850480 | − | 0.526008i | \(-0.823688\pi\) | ||
0.850480 | − | 0.526008i | \(-0.176312\pi\) | |||||||
\(614\) | −11.1649 | − | 22.9053i | −0.450578 | − | 0.924385i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.1827 | − | 2.59869i | −0.490854 | − | 0.104704i | ||||
\(617\) | − | 18.3524i | − | 0.738838i | −0.929263 | − | 0.369419i | \(-0.879557\pi\) | ||
0.929263 | − | 0.369419i | \(-0.120443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.2386 | 1.01443 | 0.507213 | − | 0.861821i | \(-0.330676\pi\) | ||||
0.507213 | + | 0.861821i | \(0.330676\pi\) | |||||||
\(620\) | 10.8499 | + | 8.48528i | 0.435743 | + | 0.340777i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.28336 | + | 4.68444i | 0.0915545 | + | 0.187829i | ||||
\(623\) | −5.13323 | −0.205659 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.8013 | 0.672053 | ||||||||
\(626\) | 18.3904 | + | 37.7289i | 0.735029 | + | 1.50795i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.7488 | + | 17.0088i | 0.867871 | + | 0.678727i | ||||
\(629\) | 47.7886 | 1.90545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.3071i | 0.410320i | 0.978728 | + | 0.205160i | \(0.0657715\pi\) | ||||
−0.978728 | + | 0.205160i | \(0.934228\pi\) | |||||||
\(632\) | −7.23998 | + | 33.9411i | −0.287991 | + | 1.35011i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.60132 | − | 15.5945i | −0.301887 | − | 0.619337i | ||||
\(635\) | 1.18600i | 0.0470651i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.28230i | − | 0.169671i | ||||||
\(638\) | −28.2146 | + | 13.7528i | −1.11703 | + | 0.544478i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.283268 | + | 8.52267i | 0.0111971 | + | 0.336888i | ||||
\(641\) | 9.80081i | 0.387109i | 0.981090 | + | 0.193554i | \(0.0620016\pi\) | ||||
−0.981090 | + | 0.193554i | \(0.937998\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.91301 | 0.272622 | 0.136311 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136311 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(644\) | 4.47762 | + | 3.50177i | 0.176443 | + | 0.137989i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.49391 | + | 0.728187i | −0.0587773 | + | 0.0286501i | ||||
\(647\) | 34.5868 | 1.35975 | 0.679874 | − | 0.733329i | \(-0.262034\pi\) | ||||
0.679874 | + | 0.733329i | \(0.262034\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1930 | 1.06742 | ||||||||
\(650\) | 24.1264 | − | 11.7601i | 0.946317 | − | 0.461268i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.85398 | + | 8.76401i | −0.268423 | + | 0.343225i | ||||
\(653\) | −8.32949 | −0.325958 | −0.162979 | − | 0.986630i | \(-0.552110\pi\) | ||||
−0.162979 | + | 0.986630i | \(0.552110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.11114i | 0.0824891i | ||||||||
\(656\) | 11.3955 | − | 2.82959i | 0.444920 | − | 0.110477i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.84916 | + | 3.82596i | −0.305992 | + | 0.149151i | ||||
\(659\) | 43.5377i | 1.69599i | 0.530006 | + | 0.847994i | \(0.322190\pi\) | ||||
−0.530006 | + | 0.847994i | \(0.677810\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.15619i | 0.200552i | 0.994960 | + | 0.100276i | \(0.0319726\pi\) | ||||
−0.994960 | + | 0.100276i | \(0.968027\pi\) | |||||||
\(662\) | 0.364201 | + | 0.747178i | 0.0141551 | + | 0.0290399i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.89198 | − | 22.9336i | 0.189846 | − | 0.889998i | ||||
\(665\) | − | 0.118352i | − | 0.00458948i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.3231 | 0.554591 | ||||||||
\(668\) | 31.4252 | − | 40.1826i | 1.21588 | − | 1.55471i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.40189 | + | 11.0823i | 0.208693 | + | 0.428146i | ||||
\(671\) | −41.1708 | −1.58938 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.16066 | −0.121834 | −0.0609172 | − | 0.998143i | \(-0.519403\pi\) | ||||
−0.0609172 | + | 0.998143i | \(0.519403\pi\) | |||||||
\(674\) | 19.8484 | + | 40.7200i | 0.764531 | + | 1.56848i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.57692 | − | 8.40974i | 0.252958 | − | 0.323452i | ||||
\(677\) | 2.51349 | 0.0966012 | 0.0483006 | − | 0.998833i | \(-0.484619\pi\) | ||||
0.0483006 | + | 0.998833i | \(0.484619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.83722i | − | 0.224012i | ||||||
\(680\) | 3.32843 | − | 15.6037i | 0.127640 | − | 0.598376i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.9356 | + | 51.1568i | 0.954834 | + | 1.95889i | ||||
\(683\) | 1.45836i | 0.0558026i | 0.999611 | + | 0.0279013i | \(0.00888241\pi\) | ||||
−0.999611 | + | 0.0279013i | \(0.991118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8055i | 0.412859i | ||||||||
\(686\) | −1.27124 | + | 0.619645i | −0.0485360 | + | 0.0236582i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.45099 | − | 5.84351i | −0.0553184 | − | 0.222782i | ||||
\(689\) | 45.3608i | 1.72811i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.4386 | −1.80465 | −0.902325 | − | 0.431055i | \(-0.858141\pi\) | ||||
−0.902325 | + | 0.431055i | \(0.858141\pi\) | |||||||
\(692\) | 5.00197 | − | 6.39589i | 0.190146 | − | 0.243135i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.6482 | + | 13.9641i | −1.08747 | + | 0.530071i | ||||
\(695\) | 11.1063 | 0.421285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.9685 | −0.832117 | ||||||||
\(698\) | −12.2830 | + | 5.98717i | −0.464919 | + | 0.226618i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.98216 | − | 5.46046i | −0.263901 | − | 0.206386i | ||||
\(701\) | −17.9259 | −0.677051 | −0.338526 | − | 0.940957i | \(-0.609928\pi\) | ||||
−0.338526 | + | 0.940957i | \(0.609928\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.00266i | − | 0.0378160i | ||||||
\(704\) | −14.3770 | + | 32.1663i | −0.541852 | + | 1.21231i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6940 | + | 5.21263i | −0.402474 | + | 0.196180i | ||||
\(707\) | 3.90513i | 0.146868i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.5590i | 1.03500i | 0.855683 | + | 0.517501i | \(0.173138\pi\) | ||||
−0.855683 | + | 0.517501i | \(0.826862\pi\) | |||||||
\(710\) | −1.25930 | − | 2.58352i | −0.0472606 | − | 0.0969577i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.02890 | + | 14.1995i | −0.113513 | + | 0.532149i | ||||
\(713\) | − | 25.9696i | − | 0.972570i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.2150 | −0.531611 | ||||||||
\(716\) | 38.2859 | + | 29.9419i | 1.43081 | + | 1.11898i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.5527 | − | 25.7526i | −0.468464 | − | 0.961079i | ||||
\(719\) | −48.7684 | −1.81876 | −0.909378 | − | 0.415971i | \(-0.863442\pi\) | ||||
−0.909378 | + | 0.415971i | \(0.863442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9804 | −0.595141 | ||||||||
\(722\) | −11.7580 | − | 24.1221i | −0.437587 | − | 0.897733i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.8290 | − | 28.0204i | −1.33157 | − | 1.04137i | ||||
\(725\) | −22.3346 | −0.829486 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.4470i | − | 0.980864i | −0.871479 | − | 0.490432i | \(-0.836839\pi\) | ||
0.871479 | − | 0.490432i | \(-0.163161\pi\) | |||||||
\(728\) | −11.8457 | − | 2.52680i | −0.439030 | − | 0.0936494i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.813072 | + | 1.66806i | 0.0300931 | + | 0.0617377i | ||||
\(731\) | 11.2653i | 0.416661i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.5433i | 1.31282i | 0.754403 | + | 0.656411i | \(0.227926\pi\) | ||||
−0.754403 | + | 0.656411i | \(0.772074\pi\) | |||||||
\(734\) | −47.7806 | + | 23.2899i | −1.76361 | + | 0.859648i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.3286 | − | 10.3197i | 0.454439 | − | 0.380391i | ||||
\(737\) | 50.9393i | 1.87637i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.3506 | −1.00611 | −0.503054 | − | 0.864255i | \(-0.667790\pi\) | ||||
−0.503054 | + | 0.864255i | \(0.667790\pi\) | |||||||
\(740\) | 7.58225 | + | 5.92977i | 0.278729 | + | 0.217983i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.4657 | − | 6.56368i | 0.494343 | − | 0.240960i | ||||
\(743\) | −29.2925 | −1.07464 | −0.537319 | − | 0.843379i | \(-0.680563\pi\) | ||||
−0.537319 | + | 0.843379i | \(0.680563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.01508 | 0.257013 | ||||||||
\(746\) | 47.3718 | − | 23.0907i | 1.73440 | − | 0.845409i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 40.6102 | − | 51.9272i | 1.48485 | − | 1.89865i | ||||
\(749\) | −7.41901 | −0.271085 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.38966i | 0.160181i | 0.996788 | + | 0.0800904i | \(0.0255209\pi\) | ||||
−0.996788 | + | 0.0800904i | \(0.974479\pi\) | |||||||
\(752\) | 5.95189 | + | 23.9698i | 0.217043 | + | 0.874090i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27.4341 | + | 13.3723i | −0.999090 | + | 0.486992i | ||||
\(755\) | 8.09140i | 0.294476i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.60965i | 0.240232i | 0.992760 | + | 0.120116i | \(0.0383266\pi\) | ||||
−0.992760 | + | 0.120116i | \(0.961673\pi\) | |||||||
\(758\) | −8.33725 | − | 17.1043i | −0.302823 | − | 0.621257i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.327384 | − | 0.0698343i | −0.0118755 | − | 0.00253316i | ||||
\(761\) | − | 9.83905i | − | 0.356665i | −0.983970 | − | 0.178333i | \(-0.942930\pi\) | ||
0.983970 | − | 0.178333i | \(-0.0570703\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9803 | 0.397512 | ||||||||
\(764\) | −11.8228 | + | 15.1175i | −0.427733 | + | 0.546931i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.0801 | + | 22.7315i | 0.400341 | + | 0.821321i | ||||
\(767\) | 26.4408 | 0.954720 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.2643 | −0.550446 | −0.275223 | − | 0.961380i | \(-0.588752\pi\) | ||||
−0.275223 | + | 0.961380i | \(0.588752\pi\) | |||||||
\(770\) | 2.05690 | + | 4.21985i | 0.0741256 | + | 0.152073i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.20456 | + | 11.7696i | −0.331279 | + | 0.423599i | ||||
\(773\) | 50.1053 | 1.80216 | 0.901082 | − | 0.433650i | \(-0.142774\pi\) | ||||
0.901082 | + | 0.433650i | \(0.142774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.4956i | 1.45464i | ||||||||
\(776\) | −16.1469 | − | 3.44429i | −0.579639 | − | 0.123643i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.68914 | − | 9.62003i | −0.168114 | − | 0.344895i | ||||
\(779\) | 0.460925i | 0.0165143i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.8750i | − | 0.424922i | ||||||
\(782\) | −27.0402 | + | 13.1804i | −0.966956 | + | 0.471328i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.963957 | + | 3.88211i | 0.0344270 | + | 0.138647i | ||||
\(785\) | − | 10.4051i | − | 0.371374i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5548 | 0.661406 | 0.330703 | − | 0.943735i | \(-0.392714\pi\) | ||||
0.330703 | + | 0.943735i | \(0.392714\pi\) | |||||||
\(788\) | −28.3755 | + | 36.2831i | −1.01084 | + | 1.29253i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.7565 | − | 5.73056i | 0.418279 | − | 0.203884i | ||||
\(791\) | −10.0685 | −0.357995 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.0318 | −1.42157 | ||||||||
\(794\) | −0.536718 | + | 0.261615i | −0.0190474 | + | 0.00928438i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.60155 | + | 2.81663i | 0.127654 | + | 0.0998328i | ||||
\(797\) | −45.6932 | −1.61854 | −0.809268 | − | 0.587439i | \(-0.800136\pi\) | ||||
−0.809268 | + | 0.587439i | \(0.800136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 46.2096i | − | 1.63478i | ||||||
\(800\) | −19.2246 | + | 16.0920i | −0.679691 | + | 0.568939i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.67068 | − | 2.27665i | 0.164927 | − | 0.0803915i | ||||
\(803\) | 7.66718i | 0.270569i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 2.14219i | − | 0.0755024i | ||||||
\(806\) | 24.2458 | + | 49.7416i | 0.854022 | + | 1.75207i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.8023 | + | 2.30425i | 0.380025 | + | 0.0810632i | ||||
\(809\) | 34.1703i | 1.20136i | 0.799489 | + | 0.600681i | \(0.205104\pi\) | ||||
−0.799489 | + | 0.600681i | \(0.794896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5443 | −0.545834 | −0.272917 | − | 0.962038i | \(-0.587988\pi\) | ||||
−0.272917 | + | 0.962038i | \(0.587988\pi\) | |||||||
\(812\) | 7.93938 | + | 6.20907i | 0.278618 | + | 0.217896i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.4258 | + | 35.7499i | 0.610773 | + | 1.25303i | ||||
\(815\) | 4.19290 | 0.146871 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.236358 | 0.00826912 | ||||||||
\(818\) | 14.3829 | + | 29.5072i | 0.502885 | + | 1.03170i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.48558 | − | 2.72593i | −0.121722 | − | 0.0951936i | ||||
\(821\) | 21.3688 | 0.745775 | 0.372887 | − | 0.927877i | \(-0.378368\pi\) | ||||
0.372887 | + | 0.927877i | \(0.378368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.9533i | − | 1.21839i | −0.793019 | − | 0.609197i | \(-0.791492\pi\) | ||
0.793019 | − | 0.609197i | \(-0.208508\pi\) | |||||||
\(824\) | −9.42934 | + | 44.2049i | −0.328487 | + | 1.53995i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.82596 | − | 7.84916i | −0.133122 | − | 0.273107i | ||||
\(827\) | 7.96828i | 0.277084i | 0.990357 | + | 0.138542i | \(0.0442416\pi\) | ||||
−0.990357 | + | 0.138542i | \(0.955758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6279i | 0.612241i | 0.951993 | + | 0.306120i | \(0.0990310\pi\) | ||||
−0.951993 | + | 0.306120i | \(0.900969\pi\) | |||||||
\(830\) | −7.94377 | + | 3.87207i | −0.275732 | + | 0.134402i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.9792 | + | 31.2765i | −0.484643 | + | 1.08432i | ||||
\(833\) | − | 7.48403i | − | 0.259306i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.2243 | −0.665283 | ||||||||
\(836\) | −1.08949 | − | 0.852047i | −0.0376808 | − | 0.0294687i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −37.5897 | + | 18.3225i | −1.29851 | + | 0.632941i | ||||
\(839\) | −13.0585 | −0.450831 | −0.225415 | − | 0.974263i | \(-0.572374\pi\) | ||||
−0.225415 | + | 0.974263i | \(0.572374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.60344 | −0.124256 | ||||||||
\(842\) | 45.7210 | − | 22.2860i | 1.57565 | − | 0.768027i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.6720 | − | 34.1048i | 0.918089 | − | 1.17394i | ||||
\(845\) | −4.02341 | −0.138409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.39637i | 0.288503i | ||||||||
\(848\) | −10.2109 | − | 41.1218i | −0.350642 | − | 1.41213i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 42.1650 | − | 20.5527i | 1.44625 | − | 0.704952i | ||||
\(851\) | − | 18.1483i | − | 0.622117i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35.6157i | − | 1.21946i | −0.792610 | − | 0.609729i | \(-0.791278\pi\) | ||
0.792610 | − | 0.609729i | \(-0.208722\pi\) | |||||||
\(854\) | 5.79258 | + | 11.8838i | 0.198218 | + | 0.406655i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.37764 | + | 20.5224i | −0.149625 | + | 0.701442i | ||||
\(857\) | − | 48.8491i | − | 1.66865i | −0.551271 | − | 0.834327i | \(-0.685857\pi\) | ||
0.551271 | − | 0.834327i | \(-0.314143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.6213 | −1.35186 | −0.675930 | − | 0.736965i | \(-0.736258\pi\) | ||||
−0.675930 | + | 0.736965i | \(0.736258\pi\) | |||||||
\(860\) | −1.39783 | + | 1.78737i | −0.0476657 | + | 0.0609490i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.1653 | − | 33.1641i | −0.550594 | − | 1.12957i | ||||
\(863\) | −28.1238 | −0.957346 | −0.478673 | − | 0.877993i | \(-0.658882\pi\) | ||||
−0.478673 | + | 0.877993i | \(0.658882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.05994 | −0.104041 | ||||||||
\(866\) | 23.2011 | + | 47.5984i | 0.788406 | + | 1.61746i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.2579 | − | 14.3951i | 0.382117 | − | 0.488603i | ||||
\(869\) | 54.0386 | 1.83313 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.5301i | 1.67826i | ||||||||
\(872\) | 6.47898 | − | 30.3735i | 0.219406 | − | 1.02858i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.276539 | + | 0.567334i | 0.00935406 | + | 0.0191904i | ||||
\(875\) | 7.10902i | 0.240329i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.6093i | 0.628392i | 0.949358 | + | 0.314196i | \(0.101735\pi\) | ||||
−0.949358 | + | 0.314196i | \(0.898265\pi\) | |||||||
\(878\) | 41.8537 | − | 20.4010i | 1.41249 | − | 0.688499i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.8866 | − | 3.19984i | 0.434407 | − | 0.107867i | ||||
\(881\) | − | 46.6579i | − | 1.57195i | −0.618261 | − | 0.785973i | \(-0.712162\pi\) | ||
0.618261 | − | 0.785973i | \(-0.287838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2503 | 0.614173 | 0.307087 | − | 0.951682i | \(-0.400646\pi\) | ||||
0.307087 | + | 0.951682i | \(0.400646\pi\) | |||||||
\(884\) | 39.4867 | − | 50.4907i | 1.32808 | − | 1.69819i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.86322 | + | 2.37050i | −0.163383 | + | 0.0796387i | ||||
\(887\) | 3.18771 | 0.107033 | 0.0535163 | − | 0.998567i | \(-0.482957\pi\) | ||||
0.0535163 | + | 0.998567i | \(0.482957\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.57353 | 0.0527746 | ||||||||
\(890\) | 4.91844 | − | 2.39742i | 0.164866 | − | 0.0803617i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.22673 | − | 7.21585i | −0.308934 | − | 0.241605i | ||||
\(893\) | −0.969530 | −0.0324441 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18.3168i | − | 0.612264i | ||||||
\(896\) | 11.3075 | − | 0.375826i | 0.377756 | − | 0.0125555i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.6811 | − | 13.0053i | 0.890361 | − | 0.433993i | ||||
\(899\) | − | 46.0473i | − | 1.53576i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 79.2756i | 2.64105i | ||||||||
\(902\) | −8.01067 | − | 16.4343i | −0.266726 | − | 0.547203i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.94100 | + | 27.8515i | −0.197595 | + | 0.926326i | ||||
\(905\) | 17.1414i | 0.569799i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9992 | 0.962901 | 0.481451 | − | 0.876473i | \(-0.340110\pi\) | ||||
0.481451 | + | 0.876473i | \(0.340110\pi\) | |||||||
\(908\) | −29.1463 | − | 22.7941i | −0.967253 | − | 0.756449i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.00000 | + | 4.10311i | 0.0662994 | + | 0.136017i | ||||
\(911\) | −26.2517 | −0.869759 | −0.434880 | − | 0.900489i | \(-0.643209\pi\) | ||||
−0.434880 | + | 0.900489i | \(0.643209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.5133 | −1.20841 | ||||||||
\(914\) | 9.97340 | + | 20.4610i | 0.329891 | + | 0.676789i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.4372 | + | 11.2908i | 0.477019 | + | 0.373057i | ||||
\(917\) | 2.80096 | 0.0924958 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.3857i | − | 1.46415i | −0.681224 | − | 0.732075i | \(-0.738552\pi\) | ||
0.681224 | − | 0.732075i | \(-0.261448\pi\) | |||||||
\(920\) | −5.92573 | − | 1.26402i | −0.195365 | − | 0.0416734i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.3748 | − | 35.6454i | −0.572210 | − | 1.17392i | ||||
\(923\) | − | 11.5465i | − | 0.380059i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.2995i | 0.930482i | ||||||||
\(926\) | 37.7745 | − | 18.4126i | 1.24135 | − | 0.605077i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21.8602 | − | 18.2982i | 0.717595 | − | 0.600667i | ||||
\(929\) | − | 44.1182i | − | 1.44747i | −0.690078 | − | 0.723735i | \(-0.742424\pi\) | ||
0.690078 | − | 0.723735i | \(-0.257576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.157023 | −0.00514623 | ||||||||
\(932\) | 8.33841 | + | 6.52113i | 0.273134 | + | 0.213607i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −44.2452 | + | 21.5667i | −1.44775 | + | 0.705683i | ||||
\(935\) | −24.8431 | −0.812457 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.54976 | 0.148634 | 0.0743172 | − | 0.997235i | \(-0.476322\pi\) | ||||
0.0743172 | + | 0.997235i | \(0.476322\pi\) | |||||||
\(938\) | 14.7034 | − | 7.16697i | 0.480084 | − | 0.234010i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.73385 | − | 7.33173i | 0.187018 | − | 0.239135i | ||||
\(941\) | −33.4057 | −1.08899 | −0.544497 | − | 0.838763i | \(-0.683279\pi\) | ||||
−0.544497 | + | 0.838763i | \(0.683279\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.34284i | 0.271680i | ||||||||
\(944\) | −23.9698 | + | 5.95189i | −0.780152 | + | 0.193717i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.42738 | + | 4.10780i | −0.273998 | + | 0.133556i | ||||
\(947\) | − | 23.7401i | − | 0.771451i | −0.922614 | − | 0.385725i | \(-0.873951\pi\) | ||
0.922614 | − | 0.385725i | \(-0.126049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.45508i | 0.242002i | ||||||||
\(950\) | −0.431219 | − | 0.884669i | −0.0139906 | − | 0.0287025i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.7023 | − | 4.41600i | −0.670965 | − | 0.143124i | ||||
\(953\) | 14.0051i | 0.453670i | 0.973933 | + | 0.226835i | \(0.0728378\pi\) | ||||
−0.973933 | + | 0.226835i | \(0.927162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.23254 | 0.234039 | ||||||||
\(956\) | −14.3428 | + | 18.3398i | −0.463880 | + | 0.593151i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.41118 | + | 15.2044i | 0.239444 | + | 0.491233i | ||||
\(959\) | 14.3363 | 0.462943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −52.4899 | −1.69322 | ||||||||
\(962\) | 16.9437 | + | 34.7609i | 0.546287 | + | 1.12074i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 36.0893 | − | 46.1464i | 1.16236 | − | 1.48628i | ||||
\(965\) | 5.63086 | 0.181264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.5228i | 0.595652i | 0.954620 | + | 0.297826i | \(0.0962616\pi\) | ||||
−0.954620 | + | 0.297826i | \(0.903738\pi\) | |||||||
\(968\) | 23.2260 | + | 4.95434i | 0.746512 | + | 0.159239i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.72621 | + | 5.59297i | 0.0875333 | + | 0.179579i | ||||
\(971\) | − | 47.5729i | − | 1.52669i | −0.645993 | − | 0.763343i | \(-0.723557\pi\) | ||
0.645993 | − | 0.763343i | \(-0.276443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.7353i | − | 0.472391i | ||||||
\(974\) | −16.6576 | + | 8.11951i | −0.533744 | + | 0.260166i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.2908 | − | 9.01128i | 1.16164 | − | 0.288444i | ||||
\(977\) | − | 7.09500i | − | 0.226989i | −0.993539 | − | 0.113495i | \(-0.963796\pi\) | ||
0.993539 | − | 0.113495i | \(-0.0362045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.6074 | 0.722536 | ||||||||
\(980\) | 0.928644 | − | 1.18743i | 0.0296644 | − | 0.0379312i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.96610 | + | 2.90809i | −0.190386 | + | 0.0928008i | ||||
\(983\) | 9.29050 | 0.296321 | 0.148160 | − | 0.988963i | \(-0.452665\pi\) | ||||
0.148160 | + | 0.988963i | \(0.452665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.3586 | 0.553092 | ||||||||
\(986\) | −47.9456 | + | 23.3704i | −1.52690 | + | 0.744265i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.05935 | − | 0.828476i | −0.0337025 | − | 0.0263573i | ||||
\(989\) | 4.27814 | 0.136037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.4037i | − | 1.12464i | −0.826921 | − | 0.562319i | \(-0.809909\pi\) | ||
0.826921 | − | 0.562319i | \(-0.190091\pi\) | |||||||
\(992\) | −33.1770 | − | 39.6354i | −1.05337 | − | 1.25843i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.42769 | + | 1.67077i | −0.108720 | + | 0.0529938i | ||||
\(995\) | − | 1.72306i | − | 0.0546248i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 10.8948i | − | 0.345041i | −0.985006 | − | 0.172520i | \(-0.944809\pi\) | ||
0.985006 | − | 0.172520i | \(-0.0551911\pi\) | |||||||
\(998\) | 8.51657 | + | 17.4722i | 0.269587 | + | 0.553073i | ||||
\(999\) | 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 | 504.2.j.a.323.18 | yes | 24 | |
3.2 | odd | 2 | inner | 504.2.j.a.323.7 | ✓ | 24 | |
4.3 | odd | 2 | 2016.2.j.a.1583.16 | 24 | |||
8.3 | odd | 2 | inner | 504.2.j.a.323.8 | yes | 24 | |
8.5 | even | 2 | 2016.2.j.a.1583.10 | 24 | |||
12.11 | even | 2 | 2016.2.j.a.1583.9 | 24 | |||
24.5 | odd | 2 | 2016.2.j.a.1583.15 | 24 | |||
24.11 | even | 2 | inner | 504.2.j.a.323.17 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.j.a.323.7 | ✓ | 24 | 3.2 | odd | 2 | inner | |
504.2.j.a.323.8 | yes | 24 | 8.3 | odd | 2 | inner | |
504.2.j.a.323.17 | yes | 24 | 24.11 | even | 2 | inner | |
504.2.j.a.323.18 | yes | 24 | 1.1 | even | 1 | trivial | |
2016.2.j.a.1583.9 | 24 | 12.11 | even | 2 | |||
2016.2.j.a.1583.10 | 24 | 8.5 | even | 2 | |||
2016.2.j.a.1583.15 | 24 | 24.5 | odd | 2 | |||
2016.2.j.a.1583.16 | 24 | 4.3 | odd | 2 |