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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 8 x^{10} + 4 x^{9} + 36 x^{8} - 128 x^{7} + 232 x^{6} + 104 x^{5} + 324 x^{4} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.1 | ||
Root | \(-1.15765 + 1.15765i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.i.2431.12 |
$q$-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 | ||||||||
\(7\) | − | 5.16275i | − | 1.95134i | −0.219251 | − | 0.975668i | \(-0.570361\pi\) | ||
0.219251 | − | 0.975668i | \(-0.429639\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.48246i | 1.35151i | 0.737126 | + | 0.675756i | \(0.236183\pi\) | ||||
−0.737126 | + | 0.675756i | \(0.763817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.15254i | − | 0.319658i | −0.987145 | − | 0.159829i | \(-0.948906\pi\) | ||
0.987145 | − | 0.159829i | \(-0.0510943\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.995591 | 0.241466 | 0.120733 | − | 0.992685i | \(-0.461475\pi\) | ||||
0.120733 | + | 0.992685i | \(0.461475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.36000 | + | 2.77676i | −0.770837 | + | 0.637032i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.16275i | 1.12660i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.60109i | 0.542365i | 0.962528 | + | 0.271182i | \(0.0874147\pi\) | ||||
−0.962528 | + | 0.271182i | \(0.912585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.93774i | − | 1.84539i | −0.385528 | − | 0.922696i | \(-0.625981\pi\) | ||
0.385528 | − | 0.922696i | \(-0.374019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14440 | −0.385145 | −0.192573 | − | 0.981283i | \(-0.561683\pi\) | ||||
−0.192573 | + | 0.981283i | \(0.561683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.48246i | − | 0.780295i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.16275i | 0.872664i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.02135i | 1.15430i | 0.816637 | + | 0.577152i | \(0.195836\pi\) | ||||
−0.816637 | + | 0.577152i | \(0.804164\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.15254i | 0.184555i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.4810i | − | 1.79304i | −0.443005 | − | 0.896519i | \(-0.646088\pi\) | ||
0.443005 | − | 0.896519i | \(-0.353912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.55725i | 0.542476i | 0.962512 | + | 0.271238i | \(0.0874330\pi\) | ||||
−0.962512 | + | 0.271238i | \(0.912567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.00441i | − | 0.729968i | −0.931014 | − | 0.364984i | \(-0.881074\pi\) | ||
0.931014 | − | 0.364984i | \(-0.118926\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.6540 | −2.80772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.995591 | −0.139411 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.43460i | 0.746500i | 0.927731 | + | 0.373250i | \(0.121757\pi\) | ||||
−0.927731 | + | 0.373250i | \(0.878243\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.48246i | − | 0.604414i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.36000 | − | 2.77676i | 0.445043 | − | 0.367791i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.77199 | −0.621260 | −0.310630 | − | 0.950531i | \(-0.600540\pi\) | ||||
−0.310630 | + | 0.950531i | \(0.600540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.92520 | −0.374534 | −0.187267 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187267 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.16275i | − | 0.650446i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.15254i | 0.142955i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.46269 | −1.03388 | −0.516941 | − | 0.856021i | \(-0.672929\pi\) | ||||
−0.516941 | + | 0.856021i | \(0.672929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.60109i | − | 0.313134i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.99040 | 0.829607 | 0.414804 | − | 0.909911i | \(-0.363850\pi\) | ||||
0.414804 | + | 0.909911i | \(0.363850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.86881 | 0.452810 | 0.226405 | − | 0.974033i | \(-0.427303\pi\) | ||||
0.226405 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.1418 | 2.63725 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8235 | −1.44276 | −0.721379 | − | 0.692540i | \(-0.756491\pi\) | ||||
−0.721379 | + | 0.692540i | \(0.756491\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.3095i | 1.57067i | 0.619072 | + | 0.785335i | \(0.287509\pi\) | ||||
−0.619072 | + | 0.785335i | \(0.712491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.995591 | −0.107987 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.93774i | 1.06544i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0067i | 1.06071i | 0.847775 | + | 0.530356i | \(0.177942\pi\) | ||||
−0.847775 | + | 0.530356i | \(0.822058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.95029 | −0.623760 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.14440 | 0.222364 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.36000 | − | 2.77676i | 0.344729 | − | 0.284889i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.9863i | 1.62316i | 0.584242 | + | 0.811580i | \(0.301392\pi\) | ||||
−0.584242 | + | 0.811580i | \(0.698608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.48246i | 0.450504i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7451 | 1.36769 | 0.683844 | − | 0.729628i | \(-0.260307\pi\) | ||||
0.683844 | + | 0.729628i | \(0.260307\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.725070 | −0.0714433 | −0.0357216 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357216 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.16275i | − | 0.503833i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.03391 | −0.293299 | −0.146650 | − | 0.989189i | \(-0.546849\pi\) | ||||
−0.146650 | + | 0.989189i | \(0.546849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.9561i | − | 1.62410i | −0.583588 | − | 0.812050i | \(-0.698352\pi\) | ||
0.583588 | − | 0.812050i | \(-0.301648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.02135i | − | 0.666437i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.73087i | − | 0.915403i | −0.889106 | − | 0.457702i | \(-0.848673\pi\) | ||
0.889106 | − | 0.457702i | \(-0.151327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.60109i | − | 0.242553i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.15254i | − | 0.106553i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.13999i | − | 0.471182i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09241 | −0.826583 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4810i | 1.03521i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.70373 | 0.328653 | 0.164327 | − | 0.986406i | \(-0.447455\pi\) | ||||
0.164327 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.55725i | − | 0.313199i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.37756i | − | 0.207728i | −0.994592 | − | 0.103864i | \(-0.966879\pi\) | ||
0.994592 | − | 0.103864i | \(-0.0331207\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.3357 | + | 17.3469i | 1.24306 | + | 1.50416i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.36587 | 0.800180 | 0.400090 | − | 0.916476i | \(-0.368979\pi\) | ||||
0.400090 | + | 0.916476i | \(0.368979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7808i | 1.33851i | 0.743033 | + | 0.669254i | \(0.233386\pi\) | ||||
−0.743033 | + | 0.669254i | \(0.766614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00441i | 0.421447i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.16622 | 0.432021 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.93774i | 0.825284i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.6540 | 1.62104 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.43760 | −0.445466 | −0.222733 | − | 0.974880i | \(-0.571498\pi\) | ||||
−0.222733 | + | 0.974880i | \(0.571498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.41557 | −0.440713 | −0.220357 | − | 0.975419i | \(-0.570722\pi\) | ||||
−0.220357 | + | 0.975419i | \(0.570722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.995591 | 0.0804887 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.14440 | 0.172242 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4933 | 1.63554 | 0.817772 | − | 0.575542i | \(-0.195209\pi\) | ||||
0.817772 | + | 0.575542i | \(0.195209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.43460i | − | 0.430992i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.4288 | 1.05834 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.99765i | 0.156468i | 0.996935 | + | 0.0782342i | \(0.0249282\pi\) | ||||
−0.996935 | + | 0.0782342i | \(0.975072\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.48246i | 0.348959i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.57140 | −0.508510 | −0.254255 | − | 0.967137i | \(-0.581830\pi\) | ||||
−0.254255 | + | 0.967137i | \(0.581830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6716 | 0.897819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.36000 | + | 2.77676i | −0.256946 | + | 0.212344i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.5228i | 1.56032i | 0.625579 | + | 0.780160i | \(0.284863\pi\) | ||||
−0.625579 | + | 0.780160i | \(0.715137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.16275i | − | 0.390267i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.77199 | 0.358685 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7469 | −0.952746 | −0.476373 | − | 0.879243i | \(-0.658049\pi\) | ||||
−0.476373 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4121i | 1.51722i | 0.651545 | + | 0.758610i | \(0.274121\pi\) | ||||
−0.651545 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.92520 | 0.216237 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 7.02135i | − | 0.516220i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.46269i | 0.326344i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.16275i | 0.375535i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.85573i | 0.496063i | 0.968752 | + | 0.248032i | \(0.0797837\pi\) | ||||
−0.968752 | + | 0.248032i | \(0.920216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.6986i | 1.48992i | 0.667109 | + | 0.744960i | \(0.267531\pi\) | ||||
−0.667109 | + | 0.744960i | \(0.732469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1.15254i | − | 0.0825353i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.77774 | −0.411647 | −0.205824 | − | 0.978589i | \(-0.565987\pi\) | ||||
−0.205824 | + | 0.978589i | \(0.565987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.45943i | 0.457897i | 0.973439 | + | 0.228948i | \(0.0735287\pi\) | ||||
−0.973439 | + | 0.228948i | \(0.926471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.46269 | 0.596912 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −51.3061 | −3.60098 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4810i | 0.801871i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.60109i | 0.180788i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.4467 | − | 15.0611i | −0.860956 | − | 1.04180i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.4870 | −1.27270 | −0.636349 | − | 0.771402i | \(-0.719556\pi\) | ||||
−0.636349 | + | 0.771402i | \(0.719556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.99040 | −0.478974 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.55725i | − | 0.242603i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.0710i | 0.751548i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.86881 | −0.261430 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.14746i | − | 0.0771866i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8114 | 0.857917 | 0.428958 | − | 0.903324i | \(-0.358881\pi\) | ||||
0.428958 | + | 0.903324i | \(0.358881\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.8133 | 1.77966 | 0.889829 | − | 0.456294i | \(-0.150823\pi\) | ||||
0.889829 | + | 0.456294i | \(0.150823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.85061 | −0.452701 | −0.226350 | − | 0.974046i | \(-0.572679\pi\) | ||||
−0.226350 | + | 0.974046i | \(0.572679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.1418 | −1.52262 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.33196 | −0.414820 | −0.207410 | − | 0.978254i | \(-0.566503\pi\) | ||||
−0.207410 | + | 0.978254i | \(0.566503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.00441i | 0.326452i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.8235 | 0.832977 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8565i | 0.896304i | 0.893957 | + | 0.448152i | \(0.147918\pi\) | ||||
−0.893957 | + | 0.448152i | \(0.852082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.30041i | 0.341430i | 0.985320 | + | 0.170715i | \(0.0546077\pi\) | ||||
−0.985320 | + | 0.170715i | \(0.945392\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.6540 | 1.25565 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.20033 | + | 3.87255i | 0.203632 | + | 0.246404i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.3095i | − | 0.906826i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.4249i | 0.910493i | 0.890366 | + | 0.455246i | \(0.150449\pi\) | ||||
−0.890366 | + | 0.455246i | \(0.849551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6593 | −0.733012 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.995591 | 0.0623463 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7940i | 1.17234i | 0.810189 | + | 0.586169i | \(0.199365\pi\) | ||||
−0.810189 | + | 0.586169i | \(0.800635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.2495 | 2.25243 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 9.93774i | − | 0.615131i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.48658i | − | 0.461643i | −0.972996 | − | 0.230821i | \(-0.925859\pi\) | ||
0.972996 | − | 0.230821i | \(-0.0741413\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.43460i | − | 0.333845i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.0067i | − | 0.612402i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.70524i | 0.469797i | 0.972020 | + | 0.234898i | \(0.0754757\pi\) | ||||
−0.972020 | + | 0.234898i | \(0.924524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1502i | 0.981053i | 0.871426 | + | 0.490527i | \(0.163196\pi\) | ||||
−0.871426 | + | 0.490527i | \(0.836804\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.95029 | 0.360128 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.48246i | 0.270302i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0926 | −1.02699 | −0.513496 | − | 0.858092i | \(-0.671650\pi\) | ||||
−0.513496 | + | 0.858092i | \(0.671650\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.14440 | −0.128382 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.3099i | − | 0.853660i | −0.904332 | − | 0.426830i | \(-0.859630\pi\) | ||
0.904332 | − | 0.426830i | \(-0.140370\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0771i | 1.07457i | 0.843401 | + | 0.537285i | \(0.180550\pi\) | ||||
−0.843401 | + | 0.537285i | \(0.819450\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.36000 | + | 2.77676i | −0.199029 | + | 0.164481i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −59.2738 | −3.49882 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0088 | −0.941694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 15.9863i | − | 0.937132i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.33637i | − | 0.311754i | −0.987776 | − | 0.155877i | \(-0.950180\pi\) | ||
0.987776 | − | 0.155877i | \(-0.0498203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.77199 | 0.277836 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.48246i | − | 0.260098i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.99787 | 0.173371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.3652 | 1.05855 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.7451 | −0.789635 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.92520 | 0.167497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.91660 | −0.280605 | −0.140303 | − | 0.990109i | \(-0.544808\pi\) | ||||
−0.140303 | + | 0.990109i | \(0.544808\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.725070 | 0.0412478 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3870i | 0.872518i | 0.899821 | + | 0.436259i | \(0.143697\pi\) | ||||
−0.899821 | + | 0.436259i | \(0.856303\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.3545 | −1.82878 | −0.914391 | − | 0.404832i | \(-0.867330\pi\) | ||||
−0.914391 | + | 0.404832i | \(0.867330\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.16275i | 0.290888i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.44342i | 0.193402i | 0.995313 | + | 0.0967009i | \(0.0308290\pi\) | ||||
−0.995313 | + | 0.0967009i | \(0.969171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 44.5455 | 2.49407 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.03391 | 0.169336 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.34519 | + | 2.76451i | −0.186131 | + | 0.153822i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.15254i | − | 0.0639316i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.9561i | 0.937674i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.8365 | −1.42441 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.6438 | −1.24462 | −0.622309 | − | 0.782772i | \(-0.713805\pi\) | ||||
−0.622309 | + | 0.782772i | \(0.713805\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.02135i | 0.384768i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.46269 | 0.462366 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.77848i | − | 0.205827i | −0.994690 | − | 0.102913i | \(-0.967184\pi\) | ||
0.994690 | − | 0.102913i | \(-0.0328165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.73087i | 0.528508i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.61217i | − | 0.520528i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 65.3295i | 3.52746i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.60109i | 0.140038i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.3008i | − | 0.982440i | −0.871036 | − | 0.491220i | \(-0.836551\pi\) | ||
0.871036 | − | 0.491220i | \(-0.163449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3080 | 1.62235 | 0.811176 | − | 0.584802i | \(-0.198828\pi\) | ||||
0.811176 | + | 0.584802i | \(0.198828\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.15254i | 0.0615182i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5930 | 0.670259 | 0.335130 | − | 0.942172i | \(-0.391220\pi\) | ||||
0.335130 | + | 0.942172i | \(0.391220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.99040 | −0.371012 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.13999i | 0.272037i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 19.1724i | − | 1.01188i | −0.862568 | − | 0.505941i | \(-0.831145\pi\) | ||
0.862568 | − | 0.505941i | \(-0.168855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.57923 | − | 18.6598i | 0.188381 | − | 0.982096i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.09241 | 0.477228 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.86881 | −0.202503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.6933i | 1.44558i | 0.691070 | + | 0.722788i | \(0.257140\pi\) | ||||
−0.691070 | + | 0.722788i | \(0.742860\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 11.4810i | − | 0.597679i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.0575 | 1.45667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.3563i | − | 1.52001i | −0.649915 | − | 0.760007i | \(-0.725195\pi\) | ||
0.649915 | − | 0.760007i | \(-0.274805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.4537 | −0.589894 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5516 | 0.901567 | 0.450783 | − | 0.892633i | \(-0.351145\pi\) | ||||
0.450783 | + | 0.892633i | \(0.351145\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.70373 | −0.189748 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.5033 | −1.09877 | −0.549383 | − | 0.835571i | \(-0.685137\pi\) | ||||
−0.549383 | + | 0.835571i | \(0.685137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.1418 | −1.17942 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.55725i | 0.180825i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.5202 | 0.685502 | 0.342751 | − | 0.939426i | \(-0.388641\pi\) | ||||
0.342751 | + | 0.939426i | \(0.388641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58962i | 0.130963i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.37756i | 0.119932i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.8235 | 0.645221 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.7409 | −0.990767 | −0.495383 | − | 0.868674i | \(-0.664972\pi\) | ||||
−0.495383 | + | 0.868674i | \(0.664972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.3357 | − | 17.3469i | −0.717683 | − | 0.868429i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0148i | 0.649927i | 0.945727 | + | 0.324963i | \(0.105352\pi\) | ||||
−0.945727 | + | 0.324963i | \(0.894648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.47151i | 0.123115i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.4729 | −1.56005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.21274i | − | 0.356647i | −0.983972 | − | 0.178323i | \(-0.942933\pi\) | ||
0.983972 | − | 0.178323i | \(-0.0570673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.36587 | −0.461984 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.6366i | 1.21229i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14.3095i | − | 0.702425i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 15.7808i | − | 0.772788i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.8697i | − | 1.11726i | −0.829417 | − | 0.558630i | \(-0.811327\pi\) | ||
0.829417 | − | 0.558630i | \(-0.188673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 0.690374i | − | 0.0336468i | −0.999858 | − | 0.0168234i | \(-0.994645\pi\) | ||
0.999858 | − | 0.0168234i | \(-0.00535530\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.00441i | − | 0.243323i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.995591 | 0.0482932 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.1021i | 0.730842i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.16622 | −0.249428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5189 | −0.843854 | −0.421927 | − | 0.906630i | \(-0.638646\pi\) | ||||
−0.421927 | + | 0.906630i | \(0.638646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.74698i | − | 0.324239i | −0.986771 | − | 0.162120i | \(-0.948167\pi\) | ||
0.986771 | − | 0.162120i | \(-0.0518330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 9.93774i | − | 0.476478i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.22260 | − | 8.73967i | −0.345504 | − | 0.418075i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0047 | −1.28887 | −0.644433 | − | 0.764661i | \(-0.722906\pi\) | ||||
−0.644433 | + | 0.764661i | \(0.722906\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.6540 | −0.935905 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3626i | 1.20501i | 0.798113 | + | 0.602507i | \(0.205832\pi\) | ||||
−0.798113 | + | 0.602507i | \(0.794168\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 10.0067i | − | 0.474365i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.43760 | 0.257190 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.1395i | 0.761671i | 0.924643 | + | 0.380836i | \(0.124364\pi\) | ||||
−0.924643 | + | 0.380836i | \(0.875636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 51.4633 | 2.42331 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.41557 | 0.254446 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.95029 | 0.278954 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.8033 | −1.11347 | −0.556735 | − | 0.830690i | \(-0.687946\pi\) | ||||
−0.556735 | + | 0.830690i | \(0.687946\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.995591 | −0.0464702 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2704 | −1.08381 | −0.541905 | − | 0.840440i | \(-0.682297\pi\) | ||||
−0.541905 | + | 0.840440i | \(0.682297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.25723i | − | 0.430220i | −0.976590 | − | 0.215110i | \(-0.930989\pi\) | ||
0.976590 | − | 0.215110i | \(-0.0690110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.14440 | −0.0994440 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 39.5695i | − | 1.83106i | −0.402253 | − | 0.915529i | \(-0.631773\pi\) | ||
0.402253 | − | 0.915529i | \(-0.368227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.6908i | 2.01745i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.4933 | −0.944282 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.9452 | −0.733162 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.36000 | + | 2.77676i | −0.154167 | + | 0.127406i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.43460i | 0.248833i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.06286i | 0.322711i | 0.986896 | + | 0.161355i | \(0.0515865\pi\) | ||||
−0.986896 | + | 0.161355i | \(0.948414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.09241 | 0.368982 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.4288 | −0.611031 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 15.9863i | − | 0.725899i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2623 | 0.465031 | 0.232515 | − | 0.972593i | \(-0.425304\pi\) | ||||
0.232515 | + | 0.972593i | \(0.425304\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.99765i | − | 0.0903370i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4753i | 0.788647i | 0.918972 | + | 0.394324i | \(0.129021\pi\) | ||||
−0.918972 | + | 0.394324i | \(0.870979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.89392i | − | 0.445600i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.48246i | − | 0.201471i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 36.0897i | − | 1.61884i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 14.4274i | − | 0.645858i | −0.946423 | − | 0.322929i | \(-0.895333\pi\) | ||
0.946423 | − | 0.322929i | \(-0.104667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.57140 | 0.293588 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.05709i | 0.270073i | 0.990841 | + | 0.135036i | \(0.0431151\pi\) | ||||
−0.990841 | + | 0.135036i | \(0.956885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7451 | −0.611649 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6716 | −0.518356 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.3218i | 1.74291i | 0.490476 | + | 0.871455i | \(0.336823\pi\) | ||||
−0.490476 | + | 0.871455i | \(0.663177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 19.9737i | − | 0.883585i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.36000 | − | 2.77676i | 0.148348 | − | 0.122597i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.725070 | 0.0319504 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.4320 | 0.986560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.5228i | − | 0.900852i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.48802i | − | 0.328056i | −0.986456 | − | 0.164028i | \(-0.947551\pi\) | ||
0.986456 | − | 0.164028i | \(-0.0524487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.7456 | 1.56305 | 0.781524 | − | 0.623876i | \(-0.214443\pi\) | ||||
0.781524 | + | 0.623876i | \(0.214443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.16275i | 0.225321i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.13494 | −0.0929995 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2343 | 0.705840 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.77199 | −0.207087 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.2324 | −0.573159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.03391 | 0.131167 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.7469 | 0.550068 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 88.0982i | − | 3.79466i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.5821 | −0.454962 | −0.227481 | − | 0.973783i | \(-0.573049\pi\) | ||||
−0.227481 | + | 0.973783i | \(0.573049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 20.4121i | − | 0.875967i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9561i | 0.726319i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1571 | 1.33218 | 0.666091 | − | 0.745870i | \(-0.267966\pi\) | ||||
0.666091 | + | 0.745870i | \(0.267966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.92520 | −0.124845 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.5947 | + | 33.3908i | 1.17557 | + | 1.42250i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 66.2046i | 2.81531i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.02135i | 0.298040i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.3752 | −0.736210 | −0.368105 | − | 0.929784i | \(-0.619993\pi\) | ||||
−0.368105 | + | 0.929784i | \(0.619993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.09989 | 0.173407 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 4.46269i | − | 0.188415i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.92442 | 0.249684 | 0.124842 | − | 0.992177i | \(-0.460158\pi\) | ||||
0.124842 | + | 0.992177i | \(0.460158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.73087i | 0.409381i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.16275i | − | 0.216815i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 13.0381i | − | 0.546586i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.36120i | 0.266208i | 0.991102 | + | 0.133104i | \(0.0424944\pi\) | ||||
−0.991102 | + | 0.133104i | \(0.957506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.85573i | − | 0.286402i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.60109i | 0.108473i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5592 | −0.606107 | −0.303053 | − | 0.952974i | \(-0.598006\pi\) | ||||
−0.303053 | + | 0.952974i | \(0.598006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 20.6986i | − | 0.860206i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 73.8763 | 3.06490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.3604 | −1.00890 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.15254i | 0.0476518i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.2481i | 1.78504i | 0.451008 | + | 0.892520i | \(0.351065\pi\) | ||||
−0.451008 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.20518 | − | 5.95447i | 0.296884 | − | 0.245350i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.77774 | 0.237665 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.4861 | 1.70363 | 0.851815 | − | 0.523842i | \(-0.175502\pi\) | ||||
0.851815 | + | 0.523842i | \(0.175502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.13999i | 0.210719i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 6.45943i | − | 0.264367i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.196021 | 0.00800921 | 0.00400461 | − | 0.999992i | \(-0.498725\pi\) | ||||
0.00400461 | + | 0.999992i | \(0.498725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9285i | 0.608946i | 0.952521 | + | 0.304473i | \(0.0984804\pi\) | ||||
−0.952521 | + | 0.304473i | \(0.901520\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.46269 | −0.344627 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.09241 | 0.369659 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.83703 | −0.155740 | −0.0778702 | − | 0.996964i | \(-0.524812\pi\) | ||||
−0.0778702 | + | 0.996964i | \(0.524812\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51.3061 | 2.07903 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.76780 | −0.233340 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.6488 | 0.995556 | 0.497778 | − | 0.867304i | \(-0.334149\pi\) | ||||
0.497778 | + | 0.867304i | \(0.334149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 11.4810i | − | 0.462960i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.7863 | 1.11864 | 0.559318 | − | 0.828953i | \(-0.311063\pi\) | ||||
0.559318 | + | 0.828953i | \(0.311063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 49.1726i | − | 1.97641i | −0.153123 | − | 0.988207i | \(-0.548933\pi\) | ||
0.153123 | − | 0.988207i | \(-0.451067\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2.60109i | − | 0.104378i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.6623 | 2.06981 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.4467 | + | 15.0611i | 0.497073 | + | 0.601481i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.99040i | 0.278725i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.4304i | 0.574464i | 0.957861 | + | 0.287232i | \(0.0927350\pi\) | ||||
−0.957861 | + | 0.287232i | \(0.907265\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.4870 | 0.734792 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.70373 | −0.146978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.6521i | 0.897509i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.99040 | 0.276536 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.5888i | − | 0.931700i | −0.884864 | − | 0.465850i | \(-0.845749\pi\) | ||
0.884864 | − | 0.465850i | \(-0.154251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4984i | 1.04499i | 0.852641 | + | 0.522497i | \(0.174999\pi\) | ||||
−0.852641 | + | 0.522497i | \(0.825001\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.55725i | 0.140067i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5619i | 0.415229i | 0.978211 | + | 0.207615i | \(0.0665700\pi\) | ||||
−0.978211 | + | 0.207615i | \(0.933430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21.3902i | − | 0.839640i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 11.0710i | − | 0.433906i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3807 | −0.445362 | −0.222681 | − | 0.974891i | \(-0.571481\pi\) | ||||
−0.222681 | + | 0.974891i | \(0.571481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.37756i | 0.0928988i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.86881 | 0.150937 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.8293 | 1.55153 | 0.775765 | − | 0.631022i | \(-0.217364\pi\) | ||||
0.775765 | + | 0.631022i | \(0.217364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.0820i | 1.79238i | 0.443670 | + | 0.896190i | \(0.353676\pi\) | ||||
−0.443670 | + | 0.896190i | \(0.646324\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.14746i | 0.0445637i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.3357 | − | 17.3469i | −0.555915 | − | 0.672682i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.8490 | 1.00088 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.8114 | −0.495319 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 13.1121i | − | 0.506187i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.48259i | 0.0956967i | 0.998855 | + | 0.0478483i | \(0.0152364\pi\) | ||||
−0.998855 | + | 0.0478483i | \(0.984764\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 43.1610i | − | 1.65881i | −0.558645 | − | 0.829407i | \(-0.688679\pi\) | ||
0.558645 | − | 0.829407i | \(-0.311321\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 82.5331 | 3.16733 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.8133 | −1.02749 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.447502 | −0.0171232 | −0.00856159 | − | 0.999963i | \(-0.502725\pi\) | ||||
−0.00856159 | + | 0.999963i | \(0.502725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.36587 | −0.357851 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.85061 | 0.261367 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.26361 | 0.238625 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4.36401i | − | 0.166015i | −0.996549 | − | 0.0830075i | \(-0.973547\pi\) | ||
0.996549 | − | 0.0830075i | \(-0.0264525\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.1418 | 0.879085 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 15.7808i | − | 0.598599i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 11.4304i | − | 0.432958i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.33196 | 0.239497 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2254 | 1.02829 | 0.514145 | − | 0.857703i | \(-0.328109\pi\) | ||||
0.514145 | + | 0.857703i | \(0.328109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.4966 | − | 23.5918i | −0.735328 | − | 0.889780i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 5.00441i | − | 0.188477i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 70.9625i | − | 2.66882i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.9476 | −1.38760 | −0.693798 | − | 0.720169i | \(-0.744064\pi\) | ||||
−0.693798 | + | 0.720169i | \(0.744064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8235 | −0.480919 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.57777i | − | 0.208889i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.16622 | −0.193206 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 13.8565i | − | 0.517481i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 23.2685i | − | 0.867769i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.74336i | 0.139410i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.30041i | − | 0.197124i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 9.93774i | − | 0.369078i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.4621i | − | 1.09269i | −0.837561 | − | 0.546344i | \(-0.816019\pi\) | ||
0.837561 | − | 0.546344i | \(-0.183981\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.54157i | 0.130990i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5024 | 1.01582 | 0.507912 | − | 0.861409i | \(-0.330417\pi\) | ||||
0.507912 | + | 0.861409i | \(0.330417\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.6540 | −0.724949 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 37.9336i | − | 1.39730i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 34.8909i | − | 1.28348i | −0.766921 | − | 0.641741i | \(-0.778212\pi\) | ||
0.766921 | − | 0.641741i | \(-0.221788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.20033 | − | 3.87255i | −0.117567 | − | 0.142262i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.4237 | 0.382410 | 0.191205 | − | 0.981550i | \(-0.438761\pi\) | ||||
0.191205 | + | 0.981550i | \(0.438761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.43760 | 0.199218 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.3095i | 0.523556i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.6633i | 0.572325i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.4633 | −1.65898 | −0.829489 | − | 0.558523i | \(-0.811368\pi\) | ||||
−0.829489 | + | 0.558523i | \(0.811368\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 14.4249i | − | 0.525673i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.41557 | 0.197093 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.18584 | 0.115791 | 0.0578957 | − | 0.998323i | \(-0.481561\pi\) | ||||
0.0578957 | + | 0.998323i | \(0.481561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.6593 | 0.423205 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.31177 | 0.337552 | 0.168776 | − | 0.985654i | \(-0.446019\pi\) | ||||
0.168776 | + | 0.985654i | \(0.446019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −87.5401 | −3.16916 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.995591 | −0.0359957 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.49992i | 0.198591i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.315250 | 0.0113682 | 0.00568410 | − | 0.999984i | \(-0.498191\pi\) | ||||
0.00568410 | + | 0.999984i | \(0.498191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 18.7940i | − | 0.676850i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.7998i | 1.57537i | 0.616080 | + | 0.787684i | \(0.288720\pi\) | ||||
−0.616080 | + | 0.787684i | \(0.711280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.14440 | −0.0770290 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.2495 | −1.30044 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.8801 | + | 38.5763i | 1.14222 | + | 1.38214i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.3341i | 1.12122i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.93774i | 0.355146i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4933 | −0.731438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.6022 | −0.484866 | −0.242433 | − | 0.970168i | \(-0.577946\pi\) | ||||
−0.242433 | + | 0.970168i | \(0.577946\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.48658i | 0.266529i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.2381 | −1.78626 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.37142i | 0.119723i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.43460i | 0.192745i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 30.0201i | − | 1.06337i | −0.846943 | − | 0.531683i | \(-0.821560\pi\) | ||
0.846943 | − | 0.531683i | \(-0.178440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.98234i | − | 0.176263i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0067i | 0.353571i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.3418i | 0.611978i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.4288 | −0.473302 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 7.70524i | − | 0.271237i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.8299 | 0.697180 | 0.348590 | − | 0.937275i | \(-0.386660\pi\) | ||||
0.348590 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.7040 | −1.32397 | −0.661983 | − | 0.749519i | \(-0.730285\pi\) | ||||
−0.661983 | + | 0.749519i | \(0.730285\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.1502i | − | 0.566411i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.99765i | − | 0.0699748i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.87763 | − | 11.9524i | −0.345575 | − | 0.418161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.95029 | −0.207920 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.3399 | 0.430666 | 0.215333 | − | 0.976541i | \(-0.430916\pi\) | ||||
0.215333 | + | 0.976541i | \(0.430916\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.2739i | − | 0.532416i | −0.963916 | − | 0.266208i | \(-0.914229\pi\) | ||
0.963916 | − | 0.266208i | \(-0.0857709\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.48246i | − | 0.156059i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.8582 | −1.28168 | −0.640842 | − | 0.767673i | \(-0.721415\pi\) | ||||
−0.640842 | + | 0.767673i | \(0.721415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.0555i | − | 0.939678i | −0.882752 | − | 0.469839i | \(-0.844312\pi\) | ||
0.882752 | − | 0.469839i | \(-0.155688\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.0926 | 0.592934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.5673 | −0.677968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.57140 | 0.227413 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.14440 | 0.0741212 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.19899 | 0.0413937 | 0.0206968 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206968 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −69.7587 | −2.40547 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.3099i | 0.492861i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6716 | −0.401517 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.9419i | 1.61294i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 18.0771i | − | 0.620403i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.2632 | −0.626054 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.9746 | −0.855113 | −0.427556 | − | 0.903989i | \(-0.640625\pi\) | ||||
−0.427556 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.36000 | − | 2.77676i | 0.114910 | − | 0.0949631i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.2060i | 1.33925i | 0.742698 | + | 0.669626i | \(0.233546\pi\) | ||||
−0.742698 | + | 0.669626i | \(0.766454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.14872i | − | 0.243911i | −0.992536 | − | 0.121956i | \(-0.961083\pi\) | ||
0.992536 | − | 0.121956i | \(-0.0389165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 59.2738 | 2.02005 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1320 | 1.26399 | 0.631993 | − | 0.774974i | \(-0.282237\pi\) | ||||
0.631993 | + | 0.774974i | \(0.282237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 20.5228i | − | 0.697797i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0088 | 0.543687 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 57.4808i | − | 1.94990i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.75362i | 0.330489i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.9863i | 0.541053i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.16275i | 0.174533i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 24.3162i | − | 0.821100i | −0.911838 | − | 0.410550i | \(-0.865337\pi\) | ||
0.911838 | − | 0.410550i | \(-0.134663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.33637i | 0.179991i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.0694 | −1.65319 | −0.826595 | − | 0.562797i | \(-0.809725\pi\) | ||||
−0.826595 | + | 0.562797i | \(0.809725\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.11482i | − | 0.172127i | −0.996290 | − | 0.0860636i | \(-0.972571\pi\) | ||
0.996290 | − | 0.0860636i | \(-0.0274288\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.77199 | −0.160409 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.37877 | −0.0798713 | −0.0399356 | − | 0.999202i | \(-0.512715\pi\) | ||||
−0.0399356 | + | 0.999202i | \(0.512715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19.1215i | − | 0.641313i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.48246i | 0.150168i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.8960 | + | 16.8148i | 0.465013 | + | 0.562687i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7469 | 0.426081 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.99787 | −0.100096 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.3105i | 0.710744i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.41064i | 0.180255i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.3652 | −0.611156 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 20.4121i | − | 0.678521i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.0637 | −0.699408 | −0.349704 | − | 0.936860i | \(-0.613718\pi\) | ||||
−0.349704 | + | 0.936860i | \(0.613718\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.7451 | 0.455896 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.9681 | 0.760967 | 0.380483 | − | 0.924788i | \(-0.375758\pi\) | ||||
0.380483 | + | 0.924788i | \(0.375758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −64.1416 | −2.12278 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.92520 | −0.0967042 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.2747 | −0.405347 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.8892i | 1.74465i | 0.488924 | + | 0.872326i | \(0.337389\pi\) | ||||
−0.488924 | + | 0.872326i | \(0.662611\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.91660 | 0.162008 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.05673i | − | 0.265191i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.02135i | 0.230861i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.725070 | −0.0238144 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −59.5452 | −1.95361 | −0.976807 | − | 0.214122i | \(-0.931311\pi\) | ||||
−0.976807 | + | 0.214122i | \(0.931311\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 66.0375 | − | 54.5744i | 2.16429 | − | 1.78860i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 15.3870i | − | 0.503749i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.46269i | − | 0.145946i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8671 | −0.714366 | −0.357183 | − | 0.934034i | \(-0.616263\pi\) | ||||
−0.357183 | + | 0.934034i | \(0.616263\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.3545 | 1.05585 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 18.7261i | − | 0.610452i | −0.952280 | − | 0.305226i | \(-0.901268\pi\) | ||
0.952280 | − | 0.305226i | \(-0.0987321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.8632 | 0.972481 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 5.16275i | − | 0.167944i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.3189i | 1.63514i | 0.575826 | + | 0.817572i | \(0.304680\pi\) | ||||
−0.575826 | + | 0.817572i | \(0.695320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.45897i | − | 0.144744i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.44342i | − | 0.111661i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.9031i | − | 1.00105i | −0.865722 | − | 0.500524i | \(-0.833141\pi\) | ||
0.865722 | − | 0.500524i | \(-0.166859\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 6.85573i | − | 0.221846i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44.5455 | −1.43995 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 48.3537i | − | 1.56142i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4016 | −0.851663 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.03391 | −0.0977664 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 20.6986i | − | 0.666313i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.6337i | − | 1.11375i | −0.830598 | − | 0.556873i | \(-0.812001\pi\) | ||
0.830598 | − | 0.556873i | \(-0.187999\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.34519 | − | 2.76451i | 0.107463 | − | 0.0888090i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.2909 | 0.651166 | 0.325583 | − | 0.945514i | \(-0.394439\pi\) | ||||
0.325583 | + | 0.945514i | \(0.394439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 81.4723 | 2.61188 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.15254i | 0.0369109i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.84740i | − | 0.187075i | −0.995616 | − | 0.0935374i | \(-0.970183\pi\) | ||
0.995616 | − | 0.0935374i | \(-0.0298175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.8548 | −1.43356 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 16.9561i | − | 0.541366i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.5915 | −0.624873 | −0.312436 | − | 0.949939i | \(-0.601145\pi\) | ||||
−0.312436 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.77774 | 0.184094 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.8365 | 0.822386 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.25273 | −0.294220 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.2215 | 0.832954 | 0.416477 | − | 0.909146i | \(-0.363265\pi\) | ||||
0.416477 | + | 0.909146i | \(0.363265\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.6438 | 0.718581 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6.45943i | − | 0.204778i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.3206 | −1.87870 | −0.939352 | − | 0.342955i | \(-0.888572\pi\) | ||||
−0.939352 | + | 0.342955i | \(0.888572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.02135i | − | 0.222146i |
(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.i.2431.1 | ✓ | 12 | |
4.3 | odd | 2 | 4560.2.d.k.2431.12 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.k.2431.1 | yes | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.i.2431.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.i.2431.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.i.2431.12 | yes | 12 | 76.75 | even | 2 | inner | |
4560.2.d.k.2431.1 | yes | 12 | 19.18 | odd | 2 | ||
4560.2.d.k.2431.12 | yes | 12 | 4.3 | odd | 2 |