Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9821011968.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 118x^{2} + 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.2 | ||
Root | \(-2.60808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.e.2431.5 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.60808i | − | 0.985763i | −0.870097 | − | 0.492881i | \(-0.835944\pi\) | ||
0.870097 | − | 0.492881i | \(-0.164056\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.74632i | 0.526536i | 0.964723 | + | 0.263268i | \(0.0848003\pi\) | ||||
−0.964723 | + | 0.263268i | \(0.915200\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.60808i | − | 0.723352i | −0.932304 | − | 0.361676i | \(-0.882205\pi\) | ||
0.932304 | − | 0.361676i | \(-0.117795\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.802094 | −0.194536 | −0.0972682 | − | 0.995258i | \(-0.531010\pi\) | ||||
−0.0972682 | + | 0.995258i | \(0.531010\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.197906 | + | 4.35440i | 0.0454027 | + | 0.998969i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.60808i | 0.569130i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.23017i | − | 0.256508i | −0.991741 | − | 0.128254i | \(-0.959063\pi\) | ||
0.991741 | − | 0.128254i | \(-0.0409372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.74632i | 0.324284i | 0.986767 | + | 0.162142i | \(0.0518402\pi\) | ||||
−0.986767 | + | 0.162142i | \(0.948160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.15874 | 1.46535 | 0.732676 | − | 0.680577i | \(-0.238271\pi\) | ||||
0.732676 | + | 0.680577i | \(0.238271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.74632i | − | 0.303996i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.60808i | 0.440846i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.97649i | − | 0.489332i | −0.969607 | − | 0.244666i | \(-0.921322\pi\) | ||
0.969607 | − | 0.244666i | \(-0.0786783\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.60808i | 0.417627i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.96249i | − | 1.08736i | −0.839293 | − | 0.543679i | \(-0.817031\pi\) | ||
0.839293 | − | 0.543679i | \(-0.182969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.97649i | − | 0.453910i | −0.973905 | − | 0.226955i | \(-0.927123\pi\) | ||
0.973905 | − | 0.226955i | \(-0.0728771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.93897i | 1.44975i | 0.688881 | + | 0.724874i | \(0.258102\pi\) | ||||
−0.688881 | + | 0.724874i | \(0.741898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.197906 | 0.0282722 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.802094 | 0.112316 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.23017i | 0.168976i | 0.996424 | + | 0.0844882i | \(0.0269255\pi\) | ||||
−0.996424 | + | 0.0844882i | \(0.973074\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.74632i | − | 0.235474i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.197906 | − | 4.35440i | −0.0262132 | − | 0.576755i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.60419 | 0.208848 | 0.104424 | − | 0.994533i | \(-0.466700\pi\) | ||||
0.104424 | + | 0.994533i | \(0.466700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1587 | 1.30069 | 0.650347 | − | 0.759638i | \(-0.274624\pi\) | ||||
0.650347 | + | 0.759638i | \(0.274624\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.60808i | − | 0.328588i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.60808i | 0.323493i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.35664 | −1.14310 | −0.571548 | − | 0.820569i | \(-0.693657\pi\) | ||||
−0.571548 | + | 0.820569i | \(0.693657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.23017i | 0.148095i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60419 | 0.190382 | 0.0951911 | − | 0.995459i | \(-0.469654\pi\) | ||||
0.0951911 | + | 0.995459i | \(0.469654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5650 | −1.23654 | −0.618271 | − | 0.785965i | \(-0.712167\pi\) | ||||
−0.618271 | + | 0.785965i | \(0.712167\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.55455 | 0.519039 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9608 | 1.90824 | 0.954121 | − | 0.299420i | \(-0.0967932\pi\) | ||||
0.954121 | + | 0.299420i | \(0.0967932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.72281i | 0.518396i | 0.965824 | + | 0.259198i | \(0.0834582\pi\) | ||||
−0.965824 | + | 0.259198i | \(0.916542\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.802094 | 0.0869993 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.74632i | − | 0.187225i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 12.5471i | − | 1.32999i | −0.746850 | − | 0.664993i | \(-0.768435\pi\) | ||
0.746850 | − | 0.664993i | \(-0.231565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.80209 | −0.713053 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.15874 | −0.846022 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.197906 | − | 4.35440i | −0.0203047 | − | 0.446752i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.85656i | − | 0.899247i | −0.893218 | − | 0.449624i | \(-0.851558\pi\) | ||
0.893218 | − | 0.449624i | \(-0.148442\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.74632i | 0.175512i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.3175 | −1.82266 | −0.911329 | − | 0.411680i | \(-0.864942\pi\) | ||||
−0.911329 | + | 0.411680i | \(0.864942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.39581 | 0.236066 | 0.118033 | − | 0.993010i | \(-0.462341\pi\) | ||||
0.118033 | + | 0.993010i | \(0.462341\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.60808i | − | 0.254523i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.75246 | −0.942806 | −0.471403 | − | 0.881918i | \(-0.656252\pi\) | ||||
−0.471403 | + | 0.881918i | \(0.656252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.75583i | 0.263961i | 0.991252 | + | 0.131980i | \(0.0421336\pi\) | ||||
−0.991252 | + | 0.131980i | \(0.957866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.97649i | 0.282516i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.4316i | − | 1.26354i | −0.775156 | − | 0.631770i | \(-0.782329\pi\) | ||
0.775156 | − | 0.631770i | \(-0.217671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23017i | 0.114714i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.60808i | − | 0.241117i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.09193i | 0.191767i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.95036 | 0.722760 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.96249i | 0.627786i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.5650 | −1.11497 | −0.557483 | − | 0.830189i | \(-0.688233\pi\) | ||||
−0.557483 | + | 0.830189i | \(0.688233\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.97649i | 0.262065i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3029i | 1.33702i | 0.743703 | + | 0.668510i | \(0.233068\pi\) | ||||
−0.743703 | + | 0.668510i | \(0.766932\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3566 | − | 0.516154i | 0.984746 | − | 0.0447562i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.56502 | −0.731759 | −0.365880 | − | 0.930662i | \(-0.619232\pi\) | ||||
−0.365880 | + | 0.930662i | \(0.619232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.9250i | − | 1.18110i | −0.807001 | − | 0.590550i | \(-0.798911\pi\) | ||
0.807001 | − | 0.590550i | \(-0.201089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.93897i | − | 0.837013i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.55455 | 0.380871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.74632i | − | 0.145024i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.197906 | −0.0163230 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.60419 | 0.622959 | 0.311480 | − | 0.950253i | \(-0.399175\pi\) | ||||
0.311480 | + | 0.950253i | \(0.399175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5154 | −1.09987 | −0.549933 | − | 0.835209i | \(-0.685347\pi\) | ||||
−0.549933 | + | 0.835209i | \(0.685347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.802094 | −0.0648455 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.15874 | −0.655326 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3566 | 1.22559 | 0.612797 | − | 0.790240i | \(-0.290044\pi\) | ||||
0.612797 | + | 0.790240i | \(0.290044\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.23017i | − | 0.0975586i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.20838 | −0.252856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.0727i | − | 1.10226i | −0.834419 | − | 0.551130i | \(-0.814197\pi\) | ||
0.834419 | − | 0.551130i | \(-0.185803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.74632i | 0.135951i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.19791 | −0.402226 | −0.201113 | − | 0.979568i | \(-0.564456\pi\) | ||||
−0.201113 | + | 0.979568i | \(0.564456\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.19791 | 0.476762 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.197906 | + | 4.35440i | 0.0151342 | + | 0.332990i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.1404i | − | 1.68331i | −0.540019 | − | 0.841653i | \(-0.681583\pi\) | ||
0.540019 | − | 0.841653i | \(-0.318417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.60808i | − | 0.197153i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.60419 | −0.120578 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.93969i | − | 0.515823i | −0.966169 | − | 0.257911i | \(-0.916966\pi\) | ||
0.966169 | − | 0.257911i | \(-0.0830343\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.1587 | −0.750956 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.97649i | 0.218836i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.40071i | − | 0.102430i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.60808i | 0.189710i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00951i | 0.0730455i | 0.999333 | + | 0.0365228i | \(0.0116281\pi\) | ||||
−0.999333 | + | 0.0365228i | \(0.988372\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 26.9654i | − | 1.94101i | −0.241079 | − | 0.970505i | \(-0.577501\pi\) | ||
0.241079 | − | 0.970505i | \(-0.422499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 2.60808i | − | 0.186769i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1979 | 0.797818 | 0.398909 | − | 0.916991i | \(-0.369389\pi\) | ||||
0.398909 | + | 0.916991i | \(0.369389\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.95298i | − | 0.421995i | −0.977487 | − | 0.210998i | \(-0.932329\pi\) | ||
0.977487 | − | 0.210998i | \(-0.0676713\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.35664 | 0.659967 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.55455 | 0.319667 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.96249i | 0.486281i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.23017i | − | 0.0855025i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.60419 | + | 0.345607i | −0.525993 | + | 0.0239061i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.35664 | 0.0933953 | 0.0466976 | − | 0.998909i | \(-0.485130\pi\) | ||||
0.0466976 | + | 0.998909i | \(0.485130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.60419 | −0.109917 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.97649i | 0.202995i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 21.2787i | − | 1.44449i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5650 | 0.713918 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.09193i | 0.140718i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.812566 | −0.0544135 | −0.0272067 | − | 0.999630i | \(-0.508661\pi\) | ||||
−0.0272067 | + | 0.999630i | \(0.508661\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.3279 | 1.48196 | 0.740979 | − | 0.671528i | \(-0.234362\pi\) | ||||
0.740979 | + | 0.671528i | \(0.234362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8021 | −1.11031 | −0.555157 | − | 0.831746i | \(-0.687342\pi\) | ||||
−0.555157 | + | 0.831746i | \(0.687342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.55455 | −0.299667 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5049 | 1.67088 | 0.835441 | − | 0.549580i | \(-0.185212\pi\) | ||||
0.835441 | + | 0.549580i | \(0.185212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.93897i | − | 0.648347i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9608 | −1.10172 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.36320i | 0.540970i | 0.962724 | + | 0.270485i | \(0.0871841\pi\) | ||||
−0.962724 | + | 0.270485i | \(0.912816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 26.8632i | − | 1.73041i | −0.501416 | − | 0.865207i | \(-0.667187\pi\) | ||
0.501416 | − | 0.865207i | \(-0.332813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.197906 | −0.0126437 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3566 | − | 0.516154i | 0.722606 | − | 0.0328421i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.72281i | − | 0.299296i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.10144i | − | 0.195761i | −0.995198 | − | 0.0978805i | \(-0.968794\pi\) | ||
0.995198 | − | 0.0978805i | \(-0.0312063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.14827 | 0.135060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.802094 | −0.0502291 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.6155i | − | 1.09882i | −0.835552 | − | 0.549412i | \(-0.814852\pi\) | ||
0.835552 | − | 0.549412i | \(-0.185148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.76293 | −0.482365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.74632i | 0.108095i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 17.6155i | − | 1.08622i | −0.839663 | − | 0.543108i | \(-0.817247\pi\) | ||
0.839663 | − | 0.543108i | \(-0.182753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.23017i | − | 0.0755686i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.5471i | 0.767867i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.2839i | 0.809932i | 0.914332 | + | 0.404966i | \(0.132717\pi\) | ||||
−0.914332 | + | 0.404966i | \(0.867283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.6338i | − | 1.37490i | −0.726230 | − | 0.687452i | \(-0.758729\pi\) | ||
0.726230 | − | 0.687452i | \(-0.241271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.80209 | 0.411681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.74632i | 0.105307i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3175 | −0.619917 | −0.309959 | − | 0.950750i | \(-0.600315\pi\) | ||||
−0.309959 | + | 0.950750i | \(0.600315\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.15874 | 0.488451 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.5043i | − | 1.64077i | −0.571811 | − | 0.820386i | \(-0.693759\pi\) | ||
0.571811 | − | 0.820386i | \(-0.306241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.884560i | − | 0.0525817i | −0.999654 | − | 0.0262908i | \(-0.991630\pi\) | ||
0.999654 | − | 0.0262908i | \(-0.00836959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.197906 | + | 4.35440i | 0.0117229 | + | 0.257933i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.1587 | −1.07188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3566 | −0.962156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.85656i | 0.519181i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.26248i | − | 0.132175i | −0.997814 | − | 0.0660876i | \(-0.978948\pi\) | ||
0.997814 | − | 0.0660876i | \(-0.0210517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.60419 | −0.0933995 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.74632i | − | 0.101332i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.20838 | −0.185545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.76293 | −0.447448 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.3175 | 1.05231 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1587 | −0.581688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3958 | 0.821612 | 0.410806 | − | 0.911723i | \(-0.365247\pi\) | ||||
0.410806 | + | 0.911723i | \(0.365247\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.39581 | −0.136293 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.06770i | 0.457478i | 0.973488 | + | 0.228739i | \(0.0734602\pi\) | ||||
−0.973488 | + | 0.228739i | \(0.926540\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1692 | −0.687844 | −0.343922 | − | 0.938998i | \(-0.611756\pi\) | ||||
−0.343922 | + | 0.938998i | \(0.611756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.60808i | 0.146949i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.9257i | − | 0.613648i | −0.951766 | − | 0.306824i | \(-0.900734\pi\) | ||
0.951766 | − | 0.306824i | \(-0.0992662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.04964 | −0.170747 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.75246 | 0.544329 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.158739 | − | 3.49264i | −0.00883247 | − | 0.194336i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.60808i | − | 0.144670i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.75583i | − | 0.152398i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.9217 | 1.42911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.59372 | 0.417388 | 0.208694 | − | 0.977981i | \(-0.433079\pi\) | ||||
0.208694 | + | 0.977981i | \(0.433079\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.97649i | − | 0.163111i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.35664 | 0.511208 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0383i | 1.47287i | 0.676508 | + | 0.736435i | \(0.263492\pi\) | ||||
−0.676508 | + | 0.736435i | \(0.736508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.4316i | 0.729505i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2478i | 0.771561i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.7727i | − | 1.01363i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.23017i | − | 0.0662300i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.8359i | 1.70904i | 0.519416 | + | 0.854521i | \(0.326150\pi\) | ||||
−0.519416 | + | 0.854521i | \(0.673850\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.14827 | −0.329109 | −0.164555 | − | 0.986368i | \(-0.552619\pi\) | ||||
−0.164555 | + | 0.986368i | \(0.552619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.60808i | 0.139209i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.79162 | 0.148583 | 0.0742915 | − | 0.997237i | \(-0.476330\pi\) | ||||
0.0742915 | + | 0.997237i | \(0.476330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.60419 | −0.0851415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.09193i | − | 0.110717i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.43754i | 0.128648i | 0.997929 | + | 0.0643241i | \(0.0204891\pi\) | ||||
−0.997929 | + | 0.0643241i | \(0.979511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9217 | + | 1.72352i | −0.995877 | + | 0.0907117i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.95036 | −0.417286 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5650 | 0.552999 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 29.0573i | − | 1.51678i | −0.651801 | − | 0.758390i | \(-0.725986\pi\) | ||
0.651801 | − | 0.758390i | \(-0.274014\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.96249i | − | 0.362453i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.20838 | 0.166571 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.2699i | − | 0.894200i | −0.894484 | − | 0.447100i | \(-0.852457\pi\) | ||
0.894484 | − | 0.447100i | \(-0.147543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.55455 | 0.234571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.59372 | 0.390063 | 0.195032 | − | 0.980797i | \(-0.437519\pi\) | ||||
0.195032 | + | 0.980797i | \(0.437519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5650 | 0.643726 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.55455 | −0.232121 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.97649i | − | 0.151303i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.18743 | −0.0602053 | −0.0301026 | − | 0.999547i | \(-0.509583\pi\) | ||||
−0.0301026 | + | 0.999547i | \(0.509583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.986710i | 0.0499001i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 15.3029i | − | 0.771929i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.9608 | −0.853392 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.3566 | + | 0.516154i | −0.568543 | + | 0.0258400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.4418i | − | 0.571378i | −0.958322 | − | 0.285689i | \(-0.907778\pi\) | ||
0.958322 | − | 0.285689i | \(-0.0922225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 21.2787i | − | 1.05997i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.19791 | 0.257651 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.22945i | 0.209133i | 0.994518 | + | 0.104567i | \(0.0333455\pi\) | ||||
−0.994518 | + | 0.104567i | \(0.966654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.56502 | 0.422481 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.18386i | − | 0.205874i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.72281i | − | 0.231834i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.9250i | 0.681909i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.1316i | − | 0.885788i | −0.896574 | − | 0.442894i | \(-0.853952\pi\) | ||
0.896574 | − | 0.442894i | \(-0.146048\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.44562i | 0.460351i | 0.973149 | + | 0.230176i | \(0.0739301\pi\) | ||||
−0.973149 | + | 0.230176i | \(0.926070\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.93897i | 0.483249i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.802094 | −0.0389073 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 26.4948i | − | 1.28217i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.55455 | −0.219896 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.60419 | 0.0772711 | 0.0386355 | − | 0.999253i | \(-0.487699\pi\) | ||||
0.0386355 | + | 0.999253i | \(0.487699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.884560i | − | 0.0425093i | −0.999774 | − | 0.0212546i | \(-0.993234\pi\) | ||
0.999774 | − | 0.0212546i | \(-0.00676607\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.74632i | 0.0837297i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.35664 | − | 0.243457i | 0.256243 | − | 0.0116461i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.197906 | 0.00942408 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.4639i | − | 0.687202i | −0.939116 | − | 0.343601i | \(-0.888353\pi\) | ||
0.939116 | − | 0.343601i | \(-0.111647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.5471i | 0.594788i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.60419 | −0.359666 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.3844i | 1.57551i | 0.615990 | + | 0.787754i | \(0.288756\pi\) | ||||
−0.615990 | + | 0.787754i | \(0.711244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.1587 | 0.572533 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.5154 | 0.635008 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.80209 | 0.318887 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.35664 | −0.344129 | −0.172065 | − | 0.985086i | \(-0.555044\pi\) | ||||
−0.172065 | + | 0.985086i | \(0.555044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.802094 | 0.0374386 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.6350 | −1.42681 | −0.713406 | − | 0.700751i | \(-0.752848\pi\) | ||||
−0.713406 | + | 0.700751i | \(0.752848\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.1779i | − | 0.705379i | −0.935740 | − | 0.352689i | \(-0.885267\pi\) | ||
0.935740 | − | 0.352689i | \(-0.114733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.15874 | 0.378352 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.7271i | 0.635215i | 0.948222 | + | 0.317608i | \(0.102879\pi\) | ||||
−0.948222 | + | 0.317608i | \(0.897121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.4029i | 1.12682i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.3566 | −0.707597 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.19791 | 0.239000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.197906 | + | 4.35440i | 0.00908053 | + | 0.199794i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.23017i | 0.0563255i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 14.2706i | − | 0.652039i | −0.945363 | − | 0.326020i | \(-0.894292\pi\) | ||
0.945363 | − | 0.326020i | \(-0.105708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.76293 | −0.353959 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.20838 | 0.145986 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.85656i | 0.402155i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.7525 | 0.532555 | 0.266277 | − | 0.963896i | \(-0.414206\pi\) | ||||
0.266277 | + | 0.963896i | \(0.414206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0727i | 0.636390i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.23896i | 0.236431i | 0.992988 | + | 0.118216i | \(0.0377174\pi\) | ||||
−0.992988 | + | 0.118216i | \(0.962283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.40071i | − | 0.0630850i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 1.74632i | − | 0.0784913i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.18386i | − | 0.187672i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6618i | 0.656352i | 0.944617 | + | 0.328176i | \(0.106434\pi\) | ||||
−0.944617 | + | 0.328176i | \(0.893566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.19791 | 0.232225 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6155i | 0.785435i | 0.919659 | + | 0.392718i | \(0.128465\pi\) | ||||
−0.919659 | + | 0.392718i | \(0.871535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3175 | 0.815117 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.19791 | −0.275259 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.1359i | 1.20278i | 0.798956 | + | 0.601390i | \(0.205386\pi\) | ||||
−0.798956 | + | 0.601390i | \(0.794614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.5544i | 1.21894i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.197906 | − | 4.35440i | −0.00873775 | − | 0.192252i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.39581 | −0.105572 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.3566 | −0.763344 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.1404i | 0.971857i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.3970i | − | 1.76982i | −0.465757 | − | 0.884912i | \(-0.654218\pi\) | ||
0.465757 | − | 0.884912i | \(-0.345782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3776 | −0.759869 | −0.379934 | − | 0.925013i | \(-0.624053\pi\) | ||||
−0.379934 | + | 0.925013i | \(0.624053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.60808i | 0.113826i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.54408 | −0.285065 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4867 | 0.934204 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.60419 | 0.0696159 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.1587 | −0.786542 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.75246 | 0.421635 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.345607i | 0.0148863i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.6350 | 1.23111 | 0.615556 | − | 0.788093i | \(-0.288931\pi\) | ||||
0.615556 | + | 0.788093i | \(0.288931\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.93969i | 0.297810i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.75583i | − | 0.118047i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3175 | 0.697685 | 0.348842 | − | 0.937181i | \(-0.386575\pi\) | ||||
0.348842 | + | 0.937181i | \(0.386575\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.1587 | 0.433564 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.60419 | + | 0.345607i | −0.323949 | + | 0.0147233i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 44.2353i | − | 1.88107i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 2.97649i | − | 0.126345i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.4867 | 0.952792 | 0.476396 | − | 0.879231i | \(-0.341943\pi\) | ||||
0.476396 | + | 0.879231i | \(0.341943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.76293 | −0.328337 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.40071i | 0.0591382i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.1196 | 0.805794 | 0.402897 | − | 0.915245i | \(-0.368003\pi\) | ||||
0.402897 | + | 0.915245i | \(0.368003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4316i | 0.565072i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.60808i | − | 0.109529i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3008i | 1.22835i | 0.789169 | + | 0.614176i | \(0.210512\pi\) | ||||
−0.789169 | + | 0.614176i | \(0.789488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 26.0808i | − | 1.09145i | −0.837965 | − | 0.545724i | \(-0.816255\pi\) | ||
0.837965 | − | 0.545724i | \(-0.183745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.00951i | − | 0.0421729i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.23017i | − | 0.0513015i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.75246 | −0.239478 | −0.119739 | − | 0.992805i | \(-0.538206\pi\) | ||||
−0.119739 | + | 0.992805i | \(0.538206\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.9654i | 1.12064i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.3175 | 0.511015 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.14827 | −0.0889721 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.60808i | 0.107831i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.48007i | − | 0.0610888i | −0.999533 | − | 0.0305444i | \(-0.990276\pi\) | ||
0.999533 | − | 0.0305444i | \(-0.00972410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.61466 | + | 35.5264i | 0.0665309 | + | 1.46384i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.1979 | −0.460620 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.14827 | 0.0882188 | 0.0441094 | − | 0.999027i | \(-0.485955\pi\) | ||||
0.0441094 | + | 0.999027i | \(0.485955\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.09193i | − | 0.0857607i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.95298i | 0.243639i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.3175 | −1.48389 | −0.741946 | − | 0.670460i | \(-0.766097\pi\) | ||||
−0.741946 | + | 0.670460i | \(0.766097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.1867i | − | 0.782643i | −0.920254 | − | 0.391322i | \(-0.872018\pi\) | ||
0.920254 | − | 0.391322i | \(-0.127982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.35664 | −0.381032 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.95036 | −0.323228 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7734 | −0.640223 | −0.320111 | − | 0.947380i | \(-0.603720\pi\) | ||||
−0.320111 | + | 0.947380i | \(0.603720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.55455 | −0.184560 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.9217 | 1.04868 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.6741 | −0.794630 | −0.397315 | − | 0.917682i | \(-0.630058\pi\) | ||||
−0.397315 | + | 0.917682i | \(0.630058\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 6.96249i | − | 0.280755i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.40628 | 0.0968733 | 0.0484367 | − | 0.998826i | \(-0.484576\pi\) | ||||
0.0484367 | + | 0.998826i | \(0.484576\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.6205i | − | 0.949388i | −0.880151 | − | 0.474694i | \(-0.842559\pi\) | ||
0.880151 | − | 0.474694i | \(-0.157441\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.23017i | 0.0493649i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.7238 | −1.31105 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.60419 | − | 0.345607i | 0.303682 | − | 0.0138022i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.38742i | 0.0951929i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.64419i | 0.264501i | 0.991216 | + | 0.132251i | \(0.0422203\pi\) | ||||
−0.991216 | + | 0.132251i | \(0.957780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.35664 | −0.0539218 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.5650 | 0.498628 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.516154i | − | 0.0204508i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.60419 | 0.0634607 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9514i | 1.22251i | 0.791435 | + | 0.611253i | \(0.209334\pi\) | ||||
−0.791435 | + | 0.611253i | \(0.790666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4088i | 0.528792i | 0.964414 | + | 0.264396i | \(0.0851726\pi\) | ||||
−0.964414 | + | 0.264396i | \(0.914827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.97649i | − | 0.117199i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.1271i | 0.909222i | 0.890690 | + | 0.454611i | \(0.150222\pi\) | ||||
−0.890690 | + | 0.454611i | \(0.849778\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.80143i | 0.109966i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.2787i | 0.833977i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.9321 | −0.701739 | −0.350869 | − | 0.936424i | \(-0.614114\pi\) | ||||
−0.350869 | + | 0.936424i | \(0.614114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 15.3029i | − | 0.597933i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.5650 | −0.412181 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.9217 | −1.47722 | −0.738609 | − | 0.674134i | \(-0.764517\pi\) | ||||
−0.738609 | + | 0.674134i | \(0.764517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.295496i | 0.0114935i | 0.999983 | + | 0.00574674i | \(0.00182925\pi\) | ||||
−0.999983 | + | 0.00574674i | \(0.998171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.09193i | − | 0.0812438i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3566 | + | 0.516154i | −0.440392 | + | 0.0200156i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.14827 | 0.0831812 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.812566 | 0.0314156 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7404i | 0.684861i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.4896i | 1.52221i | 0.648626 | + | 0.761107i | \(0.275344\pi\) | ||||
−0.648626 | + | 0.761107i | \(0.724656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.1361i | 0.504862i | 0.967615 | + | 0.252431i | \(0.0812301\pi\) | ||||
−0.967615 | + | 0.252431i | \(0.918770\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.0986 | −0.886444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.3279 | −0.855609 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.5958 | −1.89773 | −0.948865 | − | 0.315682i | \(-0.897767\pi\) | ||||
−0.948865 | + | 0.315682i | \(0.897767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.56502 | 0.327253 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.8021 | 0.641040 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.20838 | 0.122229 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.2913i | − | 1.07625i | −0.842865 | − | 0.538125i | \(-0.819133\pi\) | ||
0.842865 | − | 0.538125i | \(-0.180867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.55455 | 0.173013 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.9250i | 0.528204i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.58457i | 0.211531i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.5049 | −0.964684 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.18743 | −0.0448488 | −0.0224244 | − | 0.999749i | \(-0.507138\pi\) | ||||
−0.0224244 | + | 0.999749i | \(0.507138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.9608 | − | 0.589064i | 0.488827 | − | 0.0222170i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.93897i | 0.374323i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.7735i | 1.79671i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.74198 | −0.290756 | −0.145378 | − | 0.989376i | \(-0.546440\pi\) | ||||
−0.145378 | + | 0.989376i | \(0.546440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.9608 | 0.636081 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 10.0366i | − | 0.375874i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.55455 | −0.170331 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.36320i | − | 0.312329i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 36.9044i | − | 1.37630i | −0.725568 | − | 0.688150i | \(-0.758423\pi\) | ||
0.725568 | − | 0.688150i | \(-0.241577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.24847i | − | 0.232705i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.8632i | 0.999054i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.74632i | 0.0648567i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.147748i | 0.00547968i | 0.999996 | + | 0.00273984i | \(0.000872119\pi\) | ||||
−0.999996 | + | 0.00273984i | \(0.999128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.38742i | 0.0883021i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.5650 | 1.12894 | 0.564472 | − | 0.825452i | \(-0.309080\pi\) | ||||
0.564472 | + | 0.825452i | \(0.309080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.197906 | 0.00729986 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 16.3397i | − | 0.601881i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 38.0324i | − | 1.39904i | −0.714611 | − | 0.699522i | \(-0.753396\pi\) | ||
0.714611 | − | 0.699522i | \(-0.246604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.3566 | + | 0.516154i | −0.417197 | + | 0.0189614i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.0783 | −0.369738 | −0.184869 | − | 0.982763i | \(-0.559186\pi\) | ||||
−0.184869 | + | 0.982763i | \(0.559186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.60419 | −0.278596 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.72281i | 0.172799i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.4352i | 0.929382i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3070 | −0.376108 | −0.188054 | − | 0.982159i | \(-0.560218\pi\) | ||||
−0.188054 | + | 0.982159i | \(0.560218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.10144i | 0.113023i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.5154 | 0.491875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.31748 | 0.0842302 | 0.0421151 | − | 0.999113i | \(-0.486590\pi\) | ||||
0.0421151 | + | 0.999113i | \(0.486590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.14827 | −0.0779772 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9426 | −1.44792 | −0.723959 | − | 0.689843i | \(-0.757680\pi\) | ||||
−0.723959 | + | 0.689843i | \(0.757680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.18743 | 0.260203 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.802094 | 0.0289998 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.18386i | − | 0.151070i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5049 | −0.559121 | −0.279561 | − | 0.960128i | \(-0.590189\pi\) | ||||
−0.279561 | + | 0.960128i | \(0.590189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6155i | 0.634406i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 32.5272i | − | 1.16992i | −0.811062 | − | 0.584960i | \(-0.801110\pi\) | ||
0.811062 | − | 0.584960i | \(-0.198890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.15874 | 0.293071 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.76293 | 0.278493 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.3175 | − | 1.37792i | 1.08624 | − | 0.0493689i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.80143i | 0.100243i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.74632i | − | 0.0624084i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3566 | −0.548102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03917 | 0.0370423 | 0.0185211 | − | 0.999828i | \(-0.494104\pi\) | ||||
0.0185211 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.6155i | 0.627127i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.0308 | −1.24555 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.4948i | − | 0.940859i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.23017i | 0.0436295i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.0991i | 1.10159i | 0.834641 | + | 0.550794i | \(0.185675\pi\) | ||||
−0.834641 | + | 0.550794i | \(0.814325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.97200i | − | 0.282029i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12.5471i | − | 0.443328i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 18.4499i | − | 0.651084i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.20838 | 0.113080 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 13.2839i | − | 0.467614i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.9007 | −0.418407 | −0.209204 | − | 0.977872i | \(-0.567087\pi\) | ||||
−0.209204 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.41675 | −0.0848637 | −0.0424319 | − | 0.999099i | \(-0.513511\pi\) | ||||
−0.0424319 | + | 0.999099i | \(0.513511\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.6338i | 0.793801i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.0727i | 0.492946i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9608 | − | 0.589064i | 0.453442 | − | 0.0206087i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.80209 | −0.237684 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.92167 | 0.276468 | 0.138234 | − | 0.990400i | \(-0.455857\pi\) | ||||
0.138234 | + | 0.990400i | \(0.455857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.6236i | 0.858323i | 0.903228 | + | 0.429162i | \(0.141191\pi\) | ||||
−0.903228 | + | 0.429162i | \(0.858809\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.74632i | − | 0.0607991i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.2496 | 1.26052 | 0.630261 | − | 0.776383i | \(-0.282948\pi\) | ||||
0.630261 | + | 0.776383i | \(0.282948\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.8955i | 0.968852i | 0.874832 | + | 0.484426i | \(0.160972\pi\) | ||||
−0.874832 | + | 0.484426i | \(0.839028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.3175 | 0.357909 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.158739 | −0.00549998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.19791 | 0.179881 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.15874 | −0.282007 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6825 | 0.817611 | 0.408806 | − | 0.912621i | \(-0.365945\pi\) | ||||
0.408806 | + | 0.912621i | \(0.365945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9504 | 0.894840 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.5043i | 0.947300i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.19791 | −0.213214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.7352i | − | 0.712470i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.884560i | 0.0303580i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.66158 | −0.125517 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.1091 | 1.20211 | 0.601056 | − | 0.799207i | \(-0.294747\pi\) | ||||
0.601056 | + | 0.799207i | \(0.294747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.197906 | − | 4.35440i | −0.00676823 | − | 0.148917i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0948i | 0.754745i | 0.926062 | + | 0.377372i | \(0.123172\pi\) | ||||
−0.926062 | + | 0.377372i | \(0.876828\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.8514i | 0.745559i | 0.927920 | + | 0.372780i | \(0.121595\pi\) | ||||
−0.927920 | + | 0.372780i | \(0.878405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.1587 | 0.618848 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.1692 | 1.36738 | 0.683688 | − | 0.729775i | \(-0.260375\pi\) | ||||
0.683688 | + | 0.729775i | \(0.260375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1404i | 0.752797i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3566 | 0.555501 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.6191i | 1.00476i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4029i | 0.826861i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.85656i | − | 0.299749i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.60808i | 0.0881693i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 14.8824i | − | 0.502544i | −0.967916 | − | 0.251272i | \(-0.919151\pi\) | ||
0.967916 | − | 0.251272i | \(-0.0808489\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.26248i | 0.0763114i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.9217 | 1.47976 | 0.739879 | − | 0.672740i | \(-0.234883\pi\) | ||||
0.739879 | + | 0.672740i | \(0.234883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.5051i | − | 0.824661i | −0.911034 | − | 0.412330i | \(-0.864715\pi\) | ||
0.911034 | − | 0.412330i | \(-0.135285\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.60419 | 0.0539242 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.3384 | 0.682897 | 0.341449 | − | 0.939900i | \(-0.389082\pi\) | ||||
0.341449 | + | 0.939900i | \(0.389082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.7706i | 1.09909i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.74632i | 0.0585040i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.2783 | + | 1.96698i | −1.44825 | + | 0.0658225i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.20838 | 0.107125 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.2478i | 0.475190i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.986710i | − | 0.0328721i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.76293 | 0.258334 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.93969i | 0.230683i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.06011 | −0.168018 | −0.0840091 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840091 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.3175 | −0.607552 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.8224 | 1.45190 | 0.725950 | − | 0.687747i | \(-0.241400\pi\) | ||||
0.725950 | + | 0.687747i | \(0.241400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.24754 | −0.272954 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.1587 | 0.335838 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.9112 | 1.31798 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.6633i | 1.50629i | 0.657853 | + | 0.753146i | \(0.271465\pi\) | ||||
−0.657853 | + | 0.753146i | \(0.728535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.3958 | −0.474358 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.18386i | − | 0.137713i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.97649i | − | 0.0978663i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.39581 | 0.0786888 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.37487 | −0.274770 | −0.137385 | − | 0.990518i | \(-0.543870\pi\) | ||||
−0.137385 | + | 0.990518i | \(0.543870\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0391666 | + | 0.861761i | 0.00128363 | + | 0.0282431i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 8.06770i | − | 0.264125i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.40071i | 0.0458083i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.890899 | −0.0291044 | −0.0145522 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145522 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.1692 | 0.397127 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.7148i | 0.968674i | 0.874882 | + | 0.484337i | \(0.160939\pi\) | ||||
−0.874882 | + | 0.484337i | \(0.839061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.56502 | −0.278915 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 2.60808i | − | 0.0848409i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.5315i | 1.34959i | 0.738005 | + | 0.674796i | \(0.235768\pi\) | ||||
−0.738005 | + | 0.674796i | \(0.764232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.5544i | 0.894455i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.9257i | 0.354290i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.9258i | − | 1.55247i | −0.630445 | − | 0.776234i | \(-0.717128\pi\) | ||
0.630445 | − | 0.776234i | \(-0.282872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.00951i | − | 0.0326670i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.04964 | 0.0985808 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.3383i | 0.721341i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.5650 | 1.14726 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.75246 | −0.314269 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.9654i | 0.868046i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.1772i | − | 0.745330i | −0.927966 | − | 0.372665i | \(-0.878444\pi\) | ||
0.927966 | − | 0.372665i | \(-0.121556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.158739 | + | 3.49264i | 0.00509943 | + | 0.112200i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.3384 | −1.42289 | −0.711444 | − | 0.702743i | \(-0.751958\pi\) | ||||
−0.711444 | + | 0.702743i | \(0.751958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.3175 | −1.16428 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.60808i | 0.0835255i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.69050i | 0.118070i | 0.998256 | + | 0.0590348i | \(0.0188023\pi\) | ||||
−0.998256 | + | 0.0590348i | \(0.981198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.9112 | 0.700285 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.75583i | 0.0879869i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.08881 | −0.257993 | −0.128996 | − | 0.991645i | \(-0.541176\pi\) | ||||
−0.128996 | + | 0.991645i | \(0.541176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.1979 | −0.356795 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.9217 | −0.825096 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.66158 | −0.116431 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.6042 | 0.876876 | 0.438438 | − | 0.898761i | \(-0.355532\pi\) | ||||
0.438438 | + | 0.898761i | \(0.355532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.59372 | −0.240979 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.95298i | 0.188722i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.2783 | −1.05393 | −0.526967 | − | 0.849886i | \(-0.676671\pi\) | ||||
−0.526967 | + | 0.849886i | \(0.676671\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.97649i | 0.0941719i |
(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 | 4560.2.d.e.2431.2 | ✓ | 6 | |
4.3 | odd | 2 | 4560.2.d.g.2431.5 | yes | 6 | ||
19.18 | odd | 2 | 4560.2.d.g.2431.2 | yes | 6 | ||
76.75 | even | 2 | inner | 4560.2.d.e.2431.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.e.2431.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
4560.2.d.e.2431.5 | yes | 6 | 76.75 | even | 2 | inner | |
4560.2.d.g.2431.2 | yes | 6 | 19.18 | odd | 2 | ||
4560.2.d.g.2431.5 | yes | 6 | 4.3 | odd | 2 |