Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.2 | ||
Root | \(0.264658 - 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.h.1217.5 |
$q$-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 \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.24914i | − 1.29854i | −0.760557 | − | 0.649271i | \(-0.775074\pi\) | ||||
0.760557 | − | 0.649271i | \(-0.224926\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.47068i | − 0.657710i | −0.944380 | − | 0.328855i | \(-0.893337\pi\) | ||||
0.944380 | − | 0.328855i | \(-0.106663\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.47068 | 0.555866 | 0.277933 | − | 0.960600i | \(-0.410351\pi\) | ||||
0.277933 | + | 0.960600i | \(0.410351\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.05863 | −0.686211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77846i | 1.44076i | 0.693580 | + | 0.720380i | \(0.256032\pi\) | ||||
−0.693580 | + | 0.720380i | \(0.743968\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.49828i | 1.24760i | 0.781585 | + | 0.623799i | \(0.214412\pi\) | ||||
−0.781585 | + | 0.623799i | \(0.785588\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.30777 | −0.854063 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.71982 | 0.417119 | 0.208559 | − | 0.978010i | \(-0.433123\pi\) | ||||
0.208559 | + | 0.978010i | \(0.433123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 3.30777i | − 0.721815i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.83709 | 0.567418 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2.11727i | − 0.407468i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.80605i | 1.44955i | 0.688987 | + | 0.724774i | \(0.258056\pi\) | ||||
−0.688987 | + | 0.724774i | \(0.741944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.13187 | 0.742107 | 0.371053 | − | 0.928612i | \(-0.378997\pi\) | ||||
0.371053 | + | 0.928612i | \(0.378997\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.7474 | 1.87089 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.16291i | − 0.365598i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.30777i | − 0.543795i | −0.962326 | − | 0.271897i | \(-0.912349\pi\) | ||||
0.962326 | − | 0.271897i | \(-0.0876511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.1173 | 1.62006 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.80605 | 1.53145 | 0.765724 | − | 0.643169i | \(-0.222381\pi\) | ||||
0.765724 | + | 0.643169i | \(0.222381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.83709i | − 0.280154i | −0.990141 | − | 0.140077i | \(-0.955265\pi\) | ||||
0.990141 | − | 0.140077i | \(-0.0447350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.02760i | 0.451328i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.14486 | 0.750456 | 0.375228 | − | 0.926933i | \(-0.377564\pi\) | ||||
0.375228 | + | 0.926933i | \(0.377564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.83709 | −0.691013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.86813i | − 0.541646i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8647i | 1.76710i | 0.468336 | + | 0.883550i | \(0.344854\pi\) | ||||
−0.468336 | + | 0.883550i | \(0.655146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.02760 | 0.947601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.24914 | −0.297906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.05863i | − 1.17933i | −0.807647 | − | 0.589667i | \(-0.799259\pi\) | ||||
0.807647 | − | 0.589667i | \(-0.200741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.91033i | 1.14085i | 0.821349 | + | 0.570426i | \(0.193222\pi\) | ||||
−0.821349 | + | 0.570426i | \(0.806778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.02760 | −0.381441 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.61555 | 0.820558 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.92332i | 0.723649i | 0.932246 | + | 0.361824i | \(0.117846\pi\) | ||||
−0.932246 | + | 0.361824i | \(0.882154\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 8.99656i | − 1.08306i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.05520 | −0.718619 | −0.359310 | − | 0.933218i | \(-0.616988\pi\) | ||||
−0.359310 | + | 0.933218i | \(0.616988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.335371 | 0.0392522 | 0.0196261 | − | 0.999807i | \(-0.493752\pi\) | ||||
0.0196261 | + | 0.999807i | \(0.493752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 6.38101i | − 0.736816i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.02760i | 0.800869i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.366407 | 0.0412240 | 0.0206120 | − | 0.999788i | \(-0.493439\pi\) | ||||
0.0206120 | + | 0.999788i | \(0.493439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 18.0552i | − 1.98182i | −0.134544 | − | 0.990908i | \(-0.542957\pi\) | ||||
0.134544 | − | 0.990908i | \(-0.457043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.52932i | − 0.274343i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.5569 | 1.88230 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.36641 | −0.250839 | −0.125419 | − | 0.992104i | \(-0.540028\pi\) | ||||
−0.125419 | + | 0.992104i | \(0.540028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.61555i | 0.693498i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 9.29317i | − 0.963656i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.47068 | −0.150889 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.05863 | −0.716696 | −0.358348 | − | 0.933588i | \(-0.616660\pi\) | ||||
−0.358348 | + | 0.933588i | \(0.616660\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 9.83709i | − 0.988665i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.94137i | 0.690692i | 0.938475 | + | 0.345346i | \(0.112238\pi\) | ||||
−0.938475 | + | 0.345346i | \(0.887762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.824101 | 0.0812010 | 0.0406005 | − | 0.999175i | \(-0.487073\pi\) | ||||
0.0406005 | + | 0.999175i | \(0.487073\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.86469 | −0.474745 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.4396i | − 1.10591i | −0.833210 | − | 0.552956i | \(-0.813500\pi\) | ||||
0.833210 | − | 0.552956i | \(-0.186500\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 4.13187i | − 0.395762i | −0.980226 | − | 0.197881i | \(-0.936594\pi\) | ||||
0.980226 | − | 0.197881i | \(-0.0634059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.43965 | −0.706140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.92332 | −0.745363 | −0.372682 | − | 0.927959i | \(-0.621562\pi\) | ||||
−0.372682 | + | 0.927959i | \(0.621562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.88273i | − 0.548568i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 9.26031i | − 0.856116i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.52932 | 0.231862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.8337 | −1.07579 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 22.0552i | − 1.98865i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.5259i | − 1.03091i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.19051 | −0.105640 | −0.0528202 | − | 0.998604i | \(-0.516821\pi\) | ||||
−0.0528202 | + | 0.998604i | \(0.516821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.13187 | −0.363791 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.39744i | 0.209466i | 0.994500 | + | 0.104733i | \(0.0333987\pi\) | ||||
−0.994500 | + | 0.104733i | \(0.966601\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.47068i | − 0.127524i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.11383 | −0.267996 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.39400 | 0.802584 | 0.401292 | − | 0.915950i | \(-0.368561\pi\) | ||||
0.401292 | + | 0.915950i | \(0.368561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2181i | 1.03633i | 0.855282 | + | 0.518163i | \(0.173384\pi\) | ||||
−0.855282 | + | 0.518163i | \(0.826616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 11.5715i | − 0.974498i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.4948 | −1.79749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4802 | 0.953382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.8793i | 0.897309i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 16.8190i | − 1.37787i | −0.724823 | − | 0.688935i | \(-0.758079\pi\) | ||||
0.724823 | − | 0.688935i | \(-0.241921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.17590 | −0.583966 | −0.291983 | − | 0.956423i | \(-0.594315\pi\) | ||||
−0.291983 | + | 0.956423i | \(0.594315\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.54049 | −0.286231 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.07668i | − 0.488091i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6742i | 1.25094i | 0.780250 | + | 0.625468i | \(0.215092\pi\) | ||||
−0.780250 | + | 0.625468i | \(0.784908\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.9345 | 2.29465 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.88273 | 0.463624 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.32238i | 0.730185i | 0.930971 | + | 0.365093i | \(0.118963\pi\) | ||||
−0.930971 | + | 0.365093i | \(0.881037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 15.8061i | − 1.23050i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.3043 | 1.57120 | 0.785598 | − | 0.618737i | \(-0.212355\pi\) | ||||
0.785598 | + | 0.618737i | \(0.212355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.23453 | −0.556503 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.05863i | 0.157428i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.560352i | − 0.0426028i | −0.999773 | − | 0.0213014i | \(-0.993219\pi\) | ||||
0.999773 | − | 0.0213014i | \(-0.00678096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.17246 | 0.315408 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.3741 | −1.53141 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.36641i | 0.326361i | 0.986596 | + | 0.163180i | \(0.0521752\pi\) | ||||
−0.986596 | + | 0.163180i | \(0.947825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.05863i | − 0.376005i | −0.982169 | − | 0.188003i | \(-0.939799\pi\) | ||||
0.982169 | − | 0.188003i | \(-0.0602013\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.0406 | 1.48144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.86469 | −0.357659 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.21811i | 0.600967i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 3.11383i | − 0.226498i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.46725 | 0.178524 | 0.0892618 | − | 0.996008i | \(-0.471549\pi\) | ||||
0.0892618 | + | 0.996008i | \(0.471549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2491 | 0.881712 | 0.440856 | − | 0.897578i | \(-0.354675\pi\) | ||||
0.440856 | + | 0.897578i | \(0.354675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 14.8793i | − 1.06553i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.23109i | 0.0877119i | 0.999038 | + | 0.0438559i | \(0.0139643\pi\) | ||||
−0.999038 | + | 0.0438559i | \(0.986036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.0276 | 1.91594 | 0.957968 | − | 0.286876i | \(-0.0926167\pi\) | ||||
0.957968 | + | 0.286876i | \(0.0926167\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.3224 | 0.939688 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4802i | 0.805755i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 14.4216i | − 1.00725i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.23453 | −0.572340 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.77846 | 0.330533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.325819i | 0.0224303i | 0.999937 | + | 0.0112152i | \(0.00356997\pi\) | ||||
−0.999937 | + | 0.0112152i | \(0.996430\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.6190i | 0.933157i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.70178 | −0.184260 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.07668 | 0.412512 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 0.754297i | − 0.0509707i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.73625i | 0.520397i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4182 | −1.56820 | −0.784098 | − | 0.620637i | \(-0.786874\pi\) | ||||
−0.784098 | + | 0.620637i | \(0.786874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.84053 | −0.389369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 23.8466i | − 1.58276i | −0.611326 | − | 0.791379i | \(-0.709364\pi\) | ||||
0.611326 | − | 0.791379i | \(-0.290636\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.9690i | 0.923095i | 0.887115 | + | 0.461548i | \(0.152706\pi\) | ||||
−0.887115 | + | 0.461548i | \(0.847294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.8061 | 1.03996 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8337 | 0.840761 | 0.420380 | − | 0.907348i | \(-0.361897\pi\) | ||||
0.420380 | + | 0.907348i | \(0.361897\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7.56647i | − 0.493582i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.824101i | − 0.0535311i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.2587 | −1.56916 | −0.784582 | − | 0.620025i | \(-0.787123\pi\) | ||||
−0.784582 | + | 0.620025i | \(0.787123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0698 | −1.67930 | −0.839652 | − | 0.543125i | \(-0.817241\pi\) | ||||
−0.839652 | + | 0.543125i | \(0.817241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.2491i | 1.17068i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.11383i | 0.454486i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.49828 | 0.286219 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −40.6087 | −2.57347 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 23.3319i | − 1.47270i | −0.676602 | − | 0.736349i | \(-0.736548\pi\) | ||||
0.676602 | − | 0.736349i | \(-0.263452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.1138i | 1.20168i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.68879 | −0.356246 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.82410 | 0.176163 | 0.0880813 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880813 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.86469i | − 0.302277i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 16.0698i | − 0.994696i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.08967 | 0.437168 | 0.218584 | − | 0.975818i | \(-0.429856\pi\) | ||||
0.218584 | + | 0.975818i | \(0.429856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.9199 | 1.16224 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.32238i | 0.325724i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 20.8647i | − 1.27214i | −0.771630 | − | 0.636071i | \(-0.780558\pi\) | ||||
0.771630 | − | 0.636071i | \(-0.219442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0620710 | −0.00377055 | −0.00188527 | − | 0.999998i | \(-0.500600\pi\) | ||||
−0.00188527 | + | 0.999998i | \(0.500600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.8793 | 0.900536 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.5569i | 0.817513i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7.82248i | − 0.470007i | −0.971994 | − | 0.235004i | \(-0.924490\pi\) | ||||
0.971994 | − | 0.235004i | \(-0.0755102\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.50601 | −0.509242 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.6448 | −1.23156 | −0.615782 | − | 0.787917i | \(-0.711160\pi\) | ||||
−0.615782 | + | 0.787917i | \(0.711160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.3871i | − 1.27133i | −0.771964 | − | 0.635666i | \(-0.780725\pi\) | ||||
0.771964 | − | 0.635666i | \(-0.219275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.30777i | 0.195936i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4216 | 0.851280 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0422 | −0.826012 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.8759i | 0.930659i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.6087i | 1.43765i | 0.695189 | + | 0.718827i | \(0.255321\pi\) | ||||
−0.695189 | + | 0.718827i | \(0.744679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3224 | −0.775659 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.1173 | 0.587063 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.9931i | 1.04057i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.70178i | − 0.155728i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6121 | 0.896892 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1043 | 0.750349 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 10.4216i | − 0.594792i | −0.954754 | − | 0.297396i | \(-0.903882\pi\) | ||||
0.954754 | − | 0.297396i | \(-0.0961182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.85352i | − 0.105443i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.91377 | 0.448749 | 0.224374 | − | 0.974503i | \(-0.427966\pi\) | ||||
0.224374 | + | 0.974503i | \(0.427966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7846 | 1.00524 | 0.502622 | − | 0.864506i | \(-0.332369\pi\) | ||||
0.502622 | + | 0.864506i | \(0.332369\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.45264i | 0.250878i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 30.0552i | − 1.68807i | −0.536290 | − | 0.844034i | \(-0.680175\pi\) | ||||
0.536290 | − | 0.844034i | \(-0.319825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.3009 | −2.08845 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.7294 | −1.43607 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.71982i | − 0.0956936i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7620i | 0.707910i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.29317 | −0.513913 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.56647 | 0.417153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.8095i | 1.03386i | 0.856027 | + | 0.516932i | \(0.172926\pi\) | ||||
−0.856027 | + | 0.516932i | \(0.827074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.80949i | 0.373158i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.71133 | 0.475951 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.2017 | 1.64519 | 0.822595 | − | 0.568628i | \(-0.192525\pi\) | ||||
0.822595 | + | 0.568628i | \(0.192525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.8207i | 0.967886i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.7440i | 1.06920i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4086 | −0.939977 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.2311 | −0.712338 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 9.36802i | − 0.502902i | −0.967870 | − | 0.251451i | \(-0.919092\pi\) | ||||
0.967870 | − | 0.251451i | \(-0.0809077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 21.3173i | − 1.14109i | −0.821266 | − | 0.570545i | \(-0.806732\pi\) | ||||
0.821266 | − | 0.570545i | \(-0.193268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.52406 | 0.508357 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4362 | 0.981260 | 0.490630 | − | 0.871368i | \(-0.336767\pi\) | ||||
0.490630 | + | 0.871368i | \(0.336767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.90528i | 0.472643i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 5.68879i | − 0.301083i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 37.1932 | 1.96298 | 0.981491 | − | 0.191510i | \(-0.0613386\pi\) | ||||
0.981491 | + | 0.191510i | \(0.0613386\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.6155i | 1.39695i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.493225i | − 0.0258166i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6121 | −0.606147 | −0.303074 | − | 0.952967i | \(-0.598013\pi\) | ||||
−0.303074 | + | 0.952967i | \(0.598013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.1871 | −1.05090 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9199i | 0.982271i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6087i | 1.27419i | 0.770786 | + | 0.637094i | \(0.219864\pi\) | ||||
−0.770786 | + | 0.637094i | \(0.780136\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.9233 | −1.33867 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −35.1138 | −1.80845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.05863i | 0.0543783i | 0.999630 | + | 0.0271892i | \(0.00865565\pi\) | ||||
−0.999630 | + | 0.0271892i | \(0.991344\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.67762i | 0.137179i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.4837 | −0.944472 | −0.472236 | − | 0.881472i | \(-0.656553\pi\) | ||||
−0.472236 | + | 0.881472i | \(0.656553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3354 | 0.526739 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.78189i | 0.192245i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.46725i | 0.125094i | 0.998042 | + | 0.0625472i | \(0.0199224\pi\) | ||||
−0.998042 | + | 0.0625472i | \(0.980078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.87930 | 0.347901 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.39218 | 0.272000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 0.538868i | − 0.0271134i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6.91721i | − 0.347165i | −0.984819 | − | 0.173582i | \(-0.944466\pi\) | ||||
0.984819 | − | 0.173582i | \(-0.0555343\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.30777 | −0.165596 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.8578 | 1.04159 | 0.520795 | − | 0.853682i | \(-0.325636\pi\) | ||||
0.520795 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5863i | 0.925851i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.0862i | 0.799331i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8061 | 0.783477 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.9820 | 1.23528 | 0.617639 | − | 0.786462i | \(-0.288089\pi\) | ||||
0.617639 | + | 0.786462i | \(0.288089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 21.1284i | − 1.04219i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 13.3224i | − 0.655552i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.5535 | −1.30346 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.4802 | 1.34571 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 31.6742i | − 1.54738i | −0.633561 | − | 0.773692i | \(-0.718408\pi\) | ||||
0.633561 | − | 0.773692i | \(-0.281592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5941i | 1.88096i | 0.339850 | + | 0.940480i | \(0.389624\pi\) | ||||
−0.339850 | + | 0.940480i | \(0.610376\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.5914 | −0.514971 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.87930 | 0.236681 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1043i | 0.634160i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 48.3449i | 2.33411i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.4948 | −1.80606 | −0.903032 | − | 0.429574i | \(-0.858664\pi\) | ||||
−0.903032 | + | 0.429574i | \(0.858664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4182 | 0.644836 | 0.322418 | − | 0.946597i | \(-0.395504\pi\) | ||||
0.322418 | + | 0.946597i | \(0.395504\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 25.8207i | − 1.23801i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.00000i | − 0.191346i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.3043 | −1.73271 | −0.866356 | − | 0.499427i | \(-0.833544\pi\) | ||||
−0.866356 | + | 0.499427i | \(0.833544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.95779 | 0.474181 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9215i | 1.32659i | 0.748358 | + | 0.663295i | \(0.230843\pi\) | ||||
−0.748358 | + | 0.663295i | \(0.769157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.48024i | 0.164979i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.8284 | −1.78922 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2086 | −0.576157 | −0.288079 | − | 0.957607i | \(-0.593016\pi\) | ||||
−0.288079 | + | 0.957607i | \(0.593016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.8578i | 2.20645i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.1396i | 0.758305i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.72938 | 0.456120 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.42666 | 0.207070 | 0.103535 | − | 0.994626i | \(-0.466985\pi\) | ||||
0.103535 | + | 0.994626i | \(0.466985\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3.64133i | − 0.169963i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.96553i | − 0.324417i | −0.986757 | − | 0.162208i | \(-0.948138\pi\) | ||||
0.986757 | − | 0.162208i | \(-0.0518617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.7501 | 1.42908 | 0.714539 | − | 0.699595i | \(-0.246636\pi\) | ||||
0.714539 | + | 0.699595i | \(0.246636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.6673 | −0.633806 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.16635i | 0.239070i | 0.992830 | + | 0.119535i | \(0.0381404\pi\) | ||||
−0.992830 | + | 0.119535i | \(0.961860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.71133i | 0.402252i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.2534 | 1.62439 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.77846 | 0.403634 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.83709i | − 0.130175i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 26.4837i | − 1.21260i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3776 | 1.06815 | 0.534074 | − | 0.845437i | \(-0.320660\pi\) | ||||
0.534074 | + | 0.845437i | \(0.320660\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.8793 | 0.678437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 13.2311i | − 0.602036i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3810i | 0.471378i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.9018 | −1.89875 | −0.949377 | − | 0.314140i | \(-0.898284\pi\) | ||||
−0.949377 | + | 0.314140i | \(0.898284\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.9673 | 0.948176 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.90528i | 0.221372i | 0.993855 | + | 0.110686i | \(0.0353048\pi\) | ||||
−0.993855 | + | 0.110686i | \(0.964695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4250i | 0.604633i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.4672 | −0.650254 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.90528 | −0.399456 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5.77502i | − 0.258525i | −0.991610 | − | 0.129263i | \(-0.958739\pi\) | ||||
0.991610 | − | 0.129263i | \(-0.0412610\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 45.6673i | − 2.04026i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.3776 | −1.39906 | −0.699529 | − | 0.714605i | \(-0.746607\pi\) | ||||
−0.699529 | + | 0.714605i | \(0.746607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2086 | 0.454275 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.2715i | 0.722642i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2603i | 0.765050i | 0.923945 | + | 0.382525i | \(0.124945\pi\) | ||||
−0.923945 | + | 0.382525i | \(0.875055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.493225 | 0.0218190 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.11727 | −0.0934796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.21199i | − 0.0534067i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.5845i | 1.08123i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.26031 | −0.0553215 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.8939 | 0.827757 | 0.413878 | − | 0.910332i | \(-0.364174\pi\) | ||||
0.413878 | + | 0.910332i | \(0.364174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.2017i | 1.75790i | 0.476917 | + | 0.878948i | \(0.341754\pi\) | ||||
−0.476917 | + | 0.878948i | \(0.658246\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 9.38445i | − 0.409571i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.10610 | 0.309546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.6484i | 0.809272i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.1104i | 1.91063i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.8241 | −0.727369 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.82066 | 0.423793 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 23.1138i | − 0.995583i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 22.4052i | − 0.963274i | −0.876371 | − | 0.481637i | \(-0.840042\pi\) | ||||
0.876371 | − | 0.481637i | \(-0.159958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.3776 | −0.488259 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.07668 | −0.260296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 37.9931i | − 1.62447i | −0.583331 | − | 0.812234i | \(-0.698251\pi\) | ||||
0.583331 | − | 0.812234i | \(-0.301749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 18.3431i | − 0.782865i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.80605 | 0.332549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.538868 | 0.0229150 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.9414i | 0.464435i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.1775i | 0.685463i | 0.939433 | + | 0.342732i | \(0.111352\pi\) | ||||
−0.939433 | + | 0.342732i | \(0.888648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.26375 | 0.349519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.4837 | 0.780381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 9.59750i | − 0.404486i | −0.979335 | − | 0.202243i | \(-0.935177\pi\) | ||||
0.979335 | − | 0.202243i | \(-0.0648232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6527i | 0.490233i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.0862 | −0.675558 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.9018 | −1.00202 | −0.501009 | − | 0.865442i | \(-0.667037\pi\) | ||||
−0.501009 | + | 0.865442i | \(0.667037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1725i | 1.51377i | 0.653548 | + | 0.756885i | \(0.273280\pi\) | ||||
−0.653548 | + | 0.756885i | \(0.726720\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5.54918i | − 0.231820i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.3484 | 0.473259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5699 | −0.523292 | −0.261646 | − | 0.965164i | \(-0.584265\pi\) | ||||
−0.261646 | + | 0.965164i | \(0.584265\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 27.5500i | − 1.14494i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 26.5535i | − 1.10162i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −61.4734 | −2.54597 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.6190 | −0.563076 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.107714i | 0.00444585i | 0.999998 | + | 0.00222292i | \(0.000707579\pi\) | ||||
−0.999998 | + | 0.00222292i | \(0.999292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4.13187i | − 0.170251i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.76891 | 0.113898 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.7846 | 1.05885 | 0.529423 | − | 0.848358i | \(-0.322409\pi\) | ||||
0.529423 | + | 0.848358i | \(0.322409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.71982i | − 0.152498i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 60.7889i | − 2.48792i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.6336 | 0.965642 | 0.482821 | − | 0.875719i | \(-0.339612\pi\) | ||||
0.482821 | + | 0.875719i | \(0.339612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.3415 | −1.44161 | −0.720805 | − | 0.693138i | \(-0.756228\pi\) | ||||
−0.720805 | + | 0.693138i | \(0.756228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 12.1939i | − 0.496576i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.4036i | 0.707555i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.8432 | 1.17071 | 0.585355 | − | 0.810777i | \(-0.300955\pi\) | ||||
0.585355 | + | 0.810777i | \(0.300955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.8207 | 1.04631 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.1430i | 0.936267i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 27.7604i | − 1.12123i | −0.828076 | − | 0.560616i | \(-0.810564\pi\) | ||||
0.828076 | − | 0.560616i | \(-0.189436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −32.4362 | −1.30795 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.5370 | −1.30989 | −0.654946 | − | 0.755676i | \(-0.727309\pi\) | ||||
−0.654946 | + | 0.755676i | \(0.727309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.20855i | 0.249543i | 0.992186 | + | 0.124771i | \(0.0398198\pi\) | ||||
−0.992186 | + | 0.124771i | \(0.960180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 8.46907i | − 0.339852i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.48024 | −0.139433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.76547 | −0.110619 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 10.7474i | − 0.429211i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5.68879i | − 0.226827i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.67256 | 0.106393 | 0.0531965 | − | 0.998584i | \(-0.483059\pi\) | ||||
0.0531965 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.732814 | 0.0291267 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.75086i | 0.0694807i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 21.7586i | − 0.862107i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.4654 | 0.493125 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6639 | −0.974164 | −0.487082 | − | 0.873356i | \(-0.661939\pi\) | ||||
−0.487082 | + | 0.873356i | \(0.661939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.5405i | 1.00722i | 0.863932 | + | 0.503609i | \(0.167995\pi\) | ||||
−0.863932 | + | 0.503609i | \(0.832005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.07668i | 0.239269i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.7535 | −0.855220 | −0.427610 | − | 0.903963i | \(-0.640644\pi\) | ||||
−0.427610 | + | 0.903963i | \(0.640644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.2863 | 1.69914 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 13.6673i | − 0.535664i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.37940i | 0.367044i | 0.983016 | + | 0.183522i | \(0.0587499\pi\) | ||||
−0.983016 | + | 0.183522i | \(0.941250\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.52588 | 0.137767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.690407 | −0.0269353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.8138i | 1.55092i | 0.631394 | + | 0.775462i | \(0.282483\pi\) | ||||
−0.631394 | + | 0.775462i | \(0.717517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19.1138i | − 0.743442i | −0.928345 | − | 0.371721i | \(-0.878768\pi\) | ||||
0.928345 | − | 0.371721i | \(-0.121232\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.3999 | 0.675757 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.16291 | −0.0838740 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.2242i | 1.20901i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 52.6707i | 2.03637i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.5776 | −1.64369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1138 | −0.813878 | −0.406939 | − | 0.913455i | \(-0.633404\pi\) | ||||
−0.406939 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 6.00688i | − 0.231205i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 36.3855i | − 1.39841i | −0.714922 | − | 0.699204i | \(-0.753538\pi\) | ||||
0.714922 | − | 0.699204i | \(-0.246462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.3810 | −0.398387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −53.6344 | −2.05528 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 12.6087i | − 0.482457i | −0.970468 | − | 0.241229i | \(-0.922450\pi\) | ||||
0.970468 | − | 0.241229i | \(-0.0775504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 13.8156i | − 0.527867i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.4182 | 1.19868 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.8690 | −2.20463 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8405i | 0.640644i | 0.947309 | + | 0.320322i | \(0.103791\pi\) | ||||
−0.947309 | + | 0.320322i | \(0.896209\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 14.4672i | − 0.549565i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.9690 | 0.681602 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8647 | 0.638796 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 28.8647i | − 1.09176i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 33.9311i | − 1.28156i | −0.767725 | − | 0.640779i | \(-0.778611\pi\) | ||||
0.767725 | − | 0.640779i | \(-0.221389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.30777 | −0.124755 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.0180 | −0.640937 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.2086i | 0.383932i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 30.8984i | − 1.16041i | −0.814469 | − | 0.580207i | \(-0.802972\pi\) | ||||
0.814469 | − | 0.580207i | \(-0.197028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.754297 | −0.0282884 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.5275 | 0.618960 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.6121i | 1.18223i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 54.5612i | 2.03763i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.8122 | −0.999925 | −0.499963 | − | 0.866047i | \(-0.666653\pi\) | ||||
−0.499963 | + | 0.866047i | \(0.666653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.21199 | 0.0451369 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 58.6347i | 2.18065i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.1465i | 0.822500i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.1897 | 1.11968 | 0.559838 | − | 0.828602i | \(-0.310863\pi\) | ||||
0.559838 | + | 0.828602i | \(0.310863\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.23109 | 0.304855 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3.15947i | − 0.116857i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.8207i | 1.39694i | 0.715640 | + | 0.698469i | \(0.246135\pi\) | ||||
−0.715640 | + | 0.698469i | \(0.753865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.0000 | 0.590169 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.3043 | −1.04260 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 39.3803i | − 1.44863i | −0.689471 | − | 0.724313i | \(-0.742157\pi\) | ||||
0.689471 | − | 0.724313i | \(-0.257843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 10.1173i | − 0.371667i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.9854 | 0.513074 | 0.256537 | − | 0.966534i | \(-0.417418\pi\) | ||||
0.256537 | + | 0.966534i | \(0.417418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.7355 | −0.906238 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.1690i | 1.35994i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 16.8241i | − 0.614739i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0777 | −0.915100 | −0.457550 | − | 0.889184i | \(-0.651273\pi\) | ||||
−0.457550 | + | 0.889184i | \(0.651273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.4768 | −1.91236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.5535i | 0.384080i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 24.6137i | − 0.894601i | −0.894384 | − | 0.447301i | \(-0.852385\pi\) | ||||
0.894384 | − | 0.447301i | \(-0.147615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 42.9897 | 1.56043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.8010 | 1.37029 | 0.685143 | − | 0.728409i | \(-0.259740\pi\) | ||||
0.685143 | + | 0.728409i | \(0.259740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6.07668i | − 0.219991i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.20693i | 0.188257i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.7483 | 1.47134 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.98357 | 0.360017 | 0.180008 | − | 0.983665i | \(-0.442388\pi\) | ||||
0.180008 | + | 0.983665i | \(0.442388\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 6.35180i | − 0.228754i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 12.5896i | − 0.452815i | −0.974033 | − | 0.226408i | \(-0.927302\pi\) | ||||
0.974033 | − | 0.226408i | \(-0.0726981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7225 | 0.421085 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.9414 | −0.392519 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 9.80605i | − 0.351338i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 28.9345i | − 1.03536i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.5275 | 0.590645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.0518 | 0.822753 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.2603i | 1.04302i | 0.853246 | + | 0.521509i | \(0.174631\pi\) | ||||
−0.853246 | + | 0.521509i | \(0.825369\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 15.9457i | − 0.567681i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.6527 | −0.414322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.0812 | −1.42332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 42.5535i | − 1.50922i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.8578i | 1.65979i | 0.557920 | + | 0.829894i | \(0.311599\pi\) | ||||
−0.557920 | + | 0.829894i | \(0.688401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.84826 | 0.313029 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.87156 | 0.172128 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.60256i | 0.0565530i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.65164i | − 0.304930i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.9276 | −1.65193 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.6681 | 0.796967 | 0.398483 | − | 0.917176i | \(-0.369537\pi\) | ||||
0.398483 | + | 0.917176i | \(0.369537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7620i | 1.15043i | 0.818002 | + | 0.575215i | \(0.195082\pi\) | ||||
−0.818002 | + | 0.575215i | \(0.804918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.139606i | 0.00489621i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7103 | 0.480250 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.83709 | −0.0642717 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 13.6190i | − 0.475886i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.20006i | − 0.111683i | −0.998440 | − | 0.0558414i | \(-0.982216\pi\) | ||||
0.998440 | − | 0.0558414i | \(-0.0177841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.4741 | −0.853114 | −0.426557 | − | 0.904461i | \(-0.640274\pi\) | ||||
−0.426557 | + | 0.904461i | \(0.640274\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.4914 | 1.06157 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 24.5681i | − 0.854316i | −0.904177 | − | 0.427158i | \(-0.859515\pi\) | ||||
0.904177 | − | 0.427158i | \(-0.140485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 11.2380i | − 0.390311i | −0.980772 | − | 0.195155i | \(-0.937479\pi\) | ||||
0.980772 | − | 0.195155i | \(-0.0625211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5939 | −0.610324 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.31894 | −0.288234 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 29.8613i | − 1.03339i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 8.74828i | − 0.302385i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.94480 | 0.0671421 | 0.0335711 | − | 0.999436i | \(-0.489312\pi\) | ||||
0.0335711 | + | 0.999436i | \(0.489312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.9345 | −1.10119 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.4330i | 1.59924i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6397i | 0.366017i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.4036 | −0.597993 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48.1027 | −1.65088 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 13.2311i | − 0.453556i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8207i | 1.02104i | 0.859866 | + | 0.510520i | \(0.170547\pi\) | ||||
−0.859866 | + | 0.510520i | \(0.829453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.02760 | 0.103542 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.49828 | 0.221977 | 0.110989 | − | 0.993822i | \(-0.464598\pi\) | ||||
0.110989 | + | 0.993822i | \(0.464598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21.0422i | − 0.717951i | −0.933347 | − | 0.358975i | \(-0.883126\pi\) | ||||
0.933347 | − | 0.358975i | \(-0.116874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 32.4362i | − 1.10542i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.80605 | −0.265721 | −0.132861 | − | 0.991135i | \(-0.542416\pi\) | ||||
−0.132861 | + | 0.991135i | \(0.542416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.824101 | −0.0280203 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.5829i | 1.07261i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75086i | 0.0593938i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.6448 | −0.902823 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.5311 | 0.491804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 16.9509i | − 0.573046i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.32582i | − 0.146073i | −0.997329 | − | 0.0730363i | \(-0.976731\pi\) | ||||
0.997329 | − | 0.0730363i | \(-0.0232689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 55.3484 | 1.86685 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.65775 | −0.190615 | −0.0953073 | − | 0.995448i | \(-0.530383\pi\) | ||||
−0.0953073 | + | 0.995448i | \(0.530383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.6578i | 0.661536i | 0.943712 | + | 0.330768i | \(0.107308\pi\) | ||||
−0.943712 | + | 0.330768i | \(0.892692\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29.9639i | 1.00723i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.7811 | −1.36930 | −0.684648 | − | 0.728874i | \(-0.740044\pi\) | ||||
−0.684648 | + | 0.728874i | \(0.740044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.75086 | −0.0587219 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 52.2664i | − 1.75099i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.14486i | − 0.172166i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.42160 | 0.214650 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.4691 | 1.35122 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.2536i | 1.07572i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.1250i | 0.737091i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.07668 | −0.202219 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.43965 | −0.247302 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.1475i | 1.23346i | 0.787173 | + | 0.616732i | \(0.211544\pi\) | ||||
−0.787173 | + | 0.616732i | \(0.788456\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 14.2897i | − 0.473960i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.4070 | −0.676114 | −0.338057 | − | 0.941126i | \(-0.609770\pi\) | ||||
−0.338057 | + | 0.941126i | \(0.609770\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 86.2760 | 2.85532 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 29.4734i | − 0.974359i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.52588i | 0.116435i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.9536 | −1.74678 | −0.873389 | − | 0.487023i | \(-0.838083\pi\) | ||||
−0.873389 | + | 0.487023i | \(0.838083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.4396 | −0.772363 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 27.2380i | − 0.896549i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.38445i | − 0.308559i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.69652 | −0.0557210 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.8984 | 1.86678 | 0.933388 | − | 0.358869i | \(-0.116837\pi\) | ||||
0.933388 | + | 0.358869i | \(0.116837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.83709i | 0.158529i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 17.7992i | − 0.582719i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0862 | 0.395262 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.9148 | −1.33663 | −0.668315 | − | 0.743879i | \(-0.732984\pi\) | ||||
−0.668315 | + | 0.743879i | \(0.732984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 40.0000i | − 1.30535i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.59644i | 0.0846416i | 0.999104 | + | 0.0423208i | \(0.0134752\pi\) | ||||
−0.999104 | + | 0.0423208i | \(0.986525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.2242 | 1.27732 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.57946 | −0.148970 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.7586i | 0.837042i | 0.908207 | + | 0.418521i | \(0.137451\pi\) | ||||
−0.908207 | + | 0.418521i | \(0.862549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50859i | 0.0489711i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −67.5984 | −2.19203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.25602 | −0.0730795 | −0.0365398 | − | 0.999332i | \(-0.511634\pi\) | ||||
−0.0365398 | + | 0.999332i | \(0.511634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3.62854i | − 0.117417i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 83.8950i | 2.71194i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8156 | 0.446129 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9276 | −0.449278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.5500i | 0.758889i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 18.0146i | − 0.579911i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0449 | 1.44855 | 0.724273 | − | 0.689513i | \(-0.242176\pi\) | ||||
0.724273 | + | 0.689513i | \(0.242176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.86813 | −0.124262 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 17.5760i | − 0.564041i | −0.959408 | − | 0.282021i | \(-0.908995\pi\) | ||||
0.959408 | − | 0.282021i | \(-0.0910047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.9690i | 0.576059i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.7036 | 0.919251 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.9042 | −0.508821 | −0.254410 | − | 0.967096i | \(-0.581881\pi\) | ||||
−0.254410 | + | 0.967096i | \(0.581881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 11.3078i | − 0.361398i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.50601i | 0.271576i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.7294 | 1.33096 | 0.665480 | − | 0.746416i | \(-0.268227\pi\) | ||||
0.665480 | + | 0.746416i | \(0.268227\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.81055 | 0.0576889 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 17.0180i | − 0.541690i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 7.34836i | − 0.233664i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.193945 | 0.00616087 | 0.00308044 | − | 0.999995i | \(-0.499019\pi\) | ||||
0.00308044 | + | 0.999995i | \(0.499019\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.3052 | 1.34251 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 39.7490i | − 1.26013i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 40.6949i | − 1.28882i | −0.764680 | − | 0.644410i | \(-0.777103\pi\) | ||||
0.764680 | − | 0.644410i | \(-0.222897\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.00344 | −0.221579 |
(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 | 2432.2.c.h.1217.2 | yes | 6 | |
4.3 | odd | 2 | 2432.2.c.e.1217.5 | yes | 6 | ||
8.3 | odd | 2 | 2432.2.c.e.1217.2 | ✓ | 6 | ||
8.5 | even | 2 | inner | 2432.2.c.h.1217.5 | yes | 6 | |
16.3 | odd | 4 | 4864.2.a.bg.1.1 | 3 | |||
16.5 | even | 4 | 4864.2.a.bh.1.1 | 3 | |||
16.11 | odd | 4 | 4864.2.a.bb.1.3 | 3 | |||
16.13 | even | 4 | 4864.2.a.ba.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.e.1217.2 | ✓ | 6 | 8.3 | odd | 2 | ||
2432.2.c.e.1217.5 | yes | 6 | 4.3 | odd | 2 | ||
2432.2.c.h.1217.2 | yes | 6 | 1.1 | even | 1 | trivial | |
2432.2.c.h.1217.5 | yes | 6 | 8.5 | even | 2 | inner | |
4864.2.a.ba.1.3 | 3 | 16.13 | even | 4 | |||
4864.2.a.bb.1.3 | 3 | 16.11 | odd | 4 | |||
4864.2.a.bg.1.1 | 3 | 16.3 | odd | 4 | |||
4864.2.a.bh.1.1 | 3 | 16.5 | even | 4 |