Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(323,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.b (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: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Root | \(-1.02187 - 0.977642i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.323 |
Dual form | 324.2.b.b.323.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35760 | − | 0.396143i | −0.959966 | − | 0.280116i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.68614 | + | 1.07561i | 0.843070 | + | 0.537803i | ||||
\(5\) | − | 2.52434i | − | 1.12892i | −0.825461 | − | 0.564459i | \(-0.809085\pi\) | ||
0.825461 | − | 0.564459i | \(-0.190915\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.27582i | − | 0.482215i | −0.970498 | − | 0.241107i | \(-0.922489\pi\) | ||
0.970498 | − | 0.241107i | \(-0.0775106\pi\) | |||||||
\(8\) | −1.86301 | − | 2.12819i | −0.658672 | − | 0.752430i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | + | 3.42703i | −0.316228 | + | 1.08372i | ||||
\(11\) | −0.505408 | −0.152386 | −0.0761931 | − | 0.997093i | \(-0.524277\pi\) | ||||
−0.0761931 | + | 0.997093i | \(0.524277\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.37228 | −0.657952 | −0.328976 | − | 0.944338i | \(-0.606704\pi\) | ||||
−0.328976 | + | 0.944338i | \(0.606704\pi\) | |||||||
\(14\) | −0.505408 | + | 1.73205i | −0.135076 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.68614 | + | 3.62725i | 0.421535 | + | 0.906812i | ||||
\(17\) | − | 0.792287i | − | 0.192158i | −0.995374 | − | 0.0960789i | \(-0.969370\pi\) | ||
0.995374 | − | 0.0960789i | \(-0.0306301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.70285i | − | 1.07891i | −0.842015 | − | 0.539454i | \(-0.818631\pi\) | ||
0.842015 | − | 0.539454i | \(-0.181369\pi\) | |||||||
\(20\) | 2.71519 | − | 4.25639i | 0.607136 | − | 0.951757i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.686141 | + | 0.200214i | 0.146286 | + | 0.0426858i | ||||
\(23\) | −3.22060 | −0.671542 | −0.335771 | − | 0.941944i | \(-0.608997\pi\) | ||||
−0.335771 | + | 0.941944i | \(0.608997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.37228 | −0.274456 | ||||||||
\(26\) | 3.22060 | + | 0.939764i | 0.631612 | + | 0.184303i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.37228 | − | 2.15121i | 0.259337 | − | 0.406541i | ||||
\(29\) | − | 2.52434i | − | 0.468758i | −0.972145 | − | 0.234379i | \(-0.924694\pi\) | ||
0.972145 | − | 0.234379i | \(-0.0753056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.12989i | − | 1.46017i | −0.683356 | − | 0.730086i | \(-0.739480\pi\) | ||
0.683356 | − | 0.730086i | \(-0.260520\pi\) | |||||||
\(32\) | −0.852189 | − | 5.59230i | −0.150647 | − | 0.988588i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.313859 | + | 1.07561i | −0.0538264 | + | 0.184465i | ||||
\(35\) | −3.22060 | −0.544381 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.74456 | −1.10880 | −0.554400 | − | 0.832251i | \(-0.687052\pi\) | ||||
−0.554400 | + | 0.832251i | \(0.687052\pi\) | |||||||
\(38\) | −1.86301 | + | 6.38458i | −0.302219 | + | 1.03572i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.37228 | + | 4.70285i | −0.849432 | + | 0.743587i | ||||
\(41\) | 6.78073i | 1.05897i | 0.848319 | + | 0.529486i | \(0.177615\pi\) | ||||
−0.848319 | + | 0.529486i | \(0.822385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.72946i | − | 1.17873i | −0.807866 | − | 0.589366i | \(-0.799378\pi\) | ||
0.807866 | − | 0.589366i | \(-0.200622\pi\) | |||||||
\(44\) | −0.852189 | − | 0.543620i | −0.128472 | − | 0.0819538i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.37228 | + | 1.27582i | 0.644658 | + | 0.188110i | ||||
\(47\) | −1.19897 | −0.174888 | −0.0874439 | − | 0.996169i | \(-0.527870\pi\) | ||||
−0.0874439 | + | 0.996169i | \(0.527870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.37228 | 0.767469 | ||||||||
\(50\) | 1.86301 | + | 0.543620i | 0.263469 | + | 0.0768795i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | − | 2.55164i | −0.554700 | − | 0.353849i | ||||
\(53\) | − | 1.87953i | − | 0.258173i | −0.991633 | − | 0.129086i | \(-0.958796\pi\) | ||
0.991633 | − | 0.129086i | \(-0.0412045\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.27582i | 0.172032i | ||||||||
\(56\) | −2.71519 | + | 2.37686i | −0.362833 | + | 0.317621i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.00000 | + | 3.42703i | −0.131306 | + | 0.449992i | ||||
\(59\) | 12.3770 | 1.61135 | 0.805674 | − | 0.592359i | \(-0.201803\pi\) | ||||
0.805674 | + | 0.592359i | \(0.201803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.37228 | −0.303739 | −0.151870 | − | 0.988401i | \(-0.548529\pi\) | ||||
−0.151870 | + | 0.988401i | \(0.548529\pi\) | |||||||
\(62\) | −3.22060 | + | 11.0371i | −0.409017 | + | 1.40172i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.05842 | + | 7.92967i | −0.132303 | + | 0.991209i | ||||
\(65\) | 5.98844i | 0.742774i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72946i | 0.944304i | 0.881517 | + | 0.472152i | \(0.156523\pi\) | ||||
−0.881517 | + | 0.472152i | \(0.843477\pi\) | |||||||
\(68\) | 0.852189 | − | 1.33591i | 0.103343 | − | 0.162003i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.37228 | + | 1.27582i | 0.522588 | + | 0.152490i | ||||
\(71\) | 11.8716 | 1.40890 | 0.704450 | − | 0.709754i | \(-0.251194\pi\) | ||||
0.704450 | + | 0.709754i | \(0.251194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.37228 | 0.394696 | 0.197348 | − | 0.980334i | \(-0.436767\pi\) | ||||
0.197348 | + | 0.980334i | \(0.436767\pi\) | |||||||
\(74\) | 9.15640 | + | 2.67181i | 1.06441 | + | 0.310592i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.05842 | − | 7.92967i | 0.580241 | − | 0.909596i | ||||
\(77\) | 0.644810i | 0.0734829i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.88067i | 1.11166i | 0.831295 | + | 0.555831i | \(0.187600\pi\) | ||||
−0.831295 | + | 0.555831i | \(0.812400\pi\) | |||||||
\(80\) | 9.15640 | − | 4.25639i | 1.02372 | − | 0.475879i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.68614 | − | 9.20550i | 0.296635 | − | 1.01658i | ||||
\(83\) | 7.64018 | 0.838618 | 0.419309 | − | 0.907844i | \(-0.362272\pi\) | ||||
0.419309 | + | 0.907844i | \(0.362272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | −3.06198 | + | 10.4935i | −0.330181 | + | 1.13154i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.941578 | + | 1.07561i | 0.100373 | + | 0.114660i | ||||
\(89\) | 11.9769i | 1.26955i | 0.772698 | + | 0.634773i | \(0.218907\pi\) | ||||
−0.772698 | + | 0.634773i | \(0.781093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02661i | 0.317274i | ||||||||
\(92\) | −5.43039 | − | 3.46410i | −0.566157 | − | 0.361158i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.62772 | + | 0.474964i | 0.167886 | + | 0.0489888i | ||||
\(95\) | −11.8716 | −1.21800 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4891 | 1.06501 | 0.532505 | − | 0.846427i | \(-0.321251\pi\) | ||||
0.532505 | + | 0.846427i | \(0.321251\pi\) | |||||||
\(98\) | −7.29339 | − | 2.12819i | −0.736744 | − | 0.214980i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.31386 | − | 1.47603i | −0.231386 | − | 0.147603i | ||||
\(101\) | − | 1.23472i | − | 0.122859i | −0.998111 | − | 0.0614295i | \(-0.980434\pi\) | ||
0.998111 | − | 0.0614295i | \(-0.0195659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.474964i | − | 0.0467996i | −0.999726 | − | 0.0233998i | \(-0.992551\pi\) | ||
0.999726 | − | 0.0233998i | \(-0.00744907\pi\) | |||||||
\(104\) | 4.41957 | + | 5.04868i | 0.433375 | + | 0.495063i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.744563 | + | 2.55164i | −0.0723183 | + | 0.247837i | ||||
\(107\) | −12.5652 | −1.21472 | −0.607360 | − | 0.794427i | \(-0.707771\pi\) | ||||
−0.607360 | + | 0.794427i | \(0.707771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4891 | 1.29202 | 0.646012 | − | 0.763327i | \(-0.276436\pi\) | ||||
0.646012 | + | 0.763327i | \(0.276436\pi\) | |||||||
\(110\) | 0.505408 | − | 1.73205i | 0.0481888 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.62772 | − | 2.15121i | 0.437278 | − | 0.203271i | ||||
\(113\) | − | 7.27806i | − | 0.684662i | −0.939579 | − | 0.342331i | \(-0.888784\pi\) | ||
0.939579 | − | 0.342331i | \(-0.111216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.12989i | 0.758116i | ||||||||
\(116\) | 2.71519 | − | 4.25639i | 0.252099 | − | 0.395196i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8030 | − | 4.90307i | −1.54684 | − | 0.451364i | ||||
\(119\) | −1.01082 | −0.0926614 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7446 | −0.976778 | ||||||||
\(122\) | 3.22060 | + | 0.939764i | 0.291580 | + | 0.0850822i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.74456 | − | 13.7081i | 0.785285 | − | 1.23103i | ||||
\(125\) | − | 9.15759i | − | 0.819080i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.65492i | 0.679265i | 0.940558 | + | 0.339632i | \(0.110303\pi\) | ||||
−0.940558 | + | 0.339632i | \(0.889697\pi\) | |||||||
\(128\) | 4.57820 | − | 10.3460i | 0.404660 | − | 0.914467i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.37228 | − | 8.12989i | 0.208063 | − | 0.713038i | ||||
\(131\) | −7.64018 | −0.667525 | −0.333763 | − | 0.942657i | \(-0.608318\pi\) | ||||
−0.333763 | + | 0.942657i | \(0.608318\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | −0.520266 | ||||||||
\(134\) | 3.06198 | − | 10.4935i | 0.264514 | − | 0.906500i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.68614 | + | 1.47603i | −0.144585 | + | 0.126569i | ||||
\(137\) | 5.49111i | 0.469137i | 0.972100 | + | 0.234568i | \(0.0753677\pi\) | ||||
−0.972100 | + | 0.234568i | \(0.924632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3844i | 1.30489i | 0.757838 | + | 0.652443i | \(0.226256\pi\) | ||||
−0.757838 | + | 0.652443i | \(0.773744\pi\) | |||||||
\(140\) | −5.43039 | − | 3.46410i | −0.458952 | − | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.1168 | − | 4.70285i | −1.35250 | − | 0.394655i | ||||
\(143\) | 1.19897 | 0.100263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.37228 | −0.529189 | ||||||||
\(146\) | −4.57820 | − | 1.33591i | −0.378895 | − | 0.110560i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.3723 | − | 7.25450i | −0.934796 | − | 0.596316i | ||||
\(149\) | − | 12.9166i | − | 1.05817i | −0.848568 | − | 0.529086i | \(-0.822535\pi\) | ||
0.848568 | − | 0.529086i | \(-0.177465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.02661i | − | 0.246302i | −0.992388 | − | 0.123151i | \(-0.960700\pi\) | ||
0.992388 | − | 0.123151i | \(-0.0392999\pi\) | |||||||
\(152\) | −10.0086 | + | 8.76144i | −0.811804 | + | 0.710647i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.255437 | − | 0.875393i | 0.0205837 | − | 0.0705411i | ||||
\(155\) | −20.5226 | −1.64841 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8614 | 0.946643 | 0.473322 | − | 0.880890i | \(-0.343055\pi\) | ||||
0.473322 | + | 0.880890i | \(0.343055\pi\) | |||||||
\(158\) | 3.91416 | − | 13.4140i | 0.311394 | − | 1.06716i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.1168 | + | 2.15121i | −1.11603 | + | 0.170068i | ||||
\(161\) | 4.10891i | 0.323828i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.75079i | − | 0.137132i | −0.997647 | − | 0.0685660i | \(-0.978158\pi\) | ||
0.997647 | − | 0.0685660i | \(-0.0218424\pi\) | |||||||
\(164\) | −7.29339 | + | 11.4333i | −0.569518 | + | 0.892787i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.3723 | − | 3.02661i | −0.805045 | − | 0.234910i | ||||
\(167\) | 17.4901 | 1.35343 | 0.676714 | − | 0.736246i | \(-0.263403\pi\) | ||||
0.676714 | + | 0.736246i | \(0.263403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.37228 | −0.567099 | ||||||||
\(170\) | 2.71519 | + | 0.792287i | 0.208246 | + | 0.0607656i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.31386 | − | 13.0330i | 0.633926 | − | 0.993754i | ||||
\(173\) | − | 17.6704i | − | 1.34345i | −0.740799 | − | 0.671726i | \(-0.765553\pi\) | ||
0.740799 | − | 0.671726i | \(-0.234447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.75079i | 0.132347i | ||||||||
\(176\) | −0.852189 | − | 1.83324i | −0.0642362 | − | 0.138186i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.74456 | − | 16.2598i | 0.355620 | − | 1.21872i | ||||
\(179\) | 8.83915 | 0.660669 | 0.330334 | − | 0.943864i | \(-0.392838\pi\) | ||||
0.330334 | + | 0.943864i | \(0.392838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | −0.297318 | −0.148659 | − | 0.988889i | \(-0.547496\pi\) | ||||
−0.148659 | + | 0.988889i | \(0.547496\pi\) | |||||||
\(182\) | 1.19897 | − | 4.10891i | 0.0888736 | − | 0.304573i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | + | 6.85407i | 0.442326 | + | 0.505289i | ||||
\(185\) | 17.0256i | 1.25174i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.400428i | 0.0292822i | ||||||||
\(188\) | −2.02163 | − | 1.28962i | −0.147443 | − | 0.0940552i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.1168 | + | 4.70285i | 1.16924 | + | 0.341181i | ||||
\(191\) | 15.0922 | 1.09203 | 0.546017 | − | 0.837774i | \(-0.316144\pi\) | ||||
0.546017 | + | 0.837774i | \(0.316144\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.74456 | 0.557466 | 0.278733 | − | 0.960369i | \(-0.410086\pi\) | ||||
0.278733 | + | 0.960369i | \(0.410086\pi\) | |||||||
\(194\) | −14.2400 | − | 4.15520i | −1.02237 | − | 0.298326i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.05842 | + | 5.77846i | 0.647030 | + | 0.412747i | ||||
\(197\) | − | 23.9538i | − | 1.70663i | −0.521392 | − | 0.853317i | \(-0.674587\pi\) | ||
0.521392 | − | 0.853317i | \(-0.325413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9073i | 0.914973i | 0.889217 | + | 0.457486i | \(0.151250\pi\) | ||||
−0.889217 | + | 0.457486i | \(0.848750\pi\) | |||||||
\(200\) | 2.55657 | + | 2.92048i | 0.180777 | + | 0.206509i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.489125 | + | 1.67625i | −0.0344147 | + | 0.117940i | ||||
\(203\) | −3.22060 | −0.226042 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.1168 | 1.19549 | ||||||||
\(206\) | −0.188154 | + | 0.644810i | −0.0131093 | + | 0.0449261i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | − | 8.60485i | −0.277350 | − | 0.596639i | ||||
\(209\) | 2.37686i | 0.164411i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.5356i | − | 1.20720i | −0.797287 | − | 0.603600i | \(-0.793732\pi\) | ||
0.797287 | − | 0.603600i | \(-0.206268\pi\) | |||||||
\(212\) | 2.02163 | − | 3.16915i | 0.138846 | − | 0.217658i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.0584 | + | 4.97760i | 1.16609 | + | 0.340262i | ||||
\(215\) | −19.5118 | −1.33069 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.3723 | −0.704116 | ||||||||
\(218\) | −18.3128 | − | 5.34363i | −1.24030 | − | 0.361916i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.37228 | + | 2.15121i | −0.0925192 | + | 0.145035i | ||||
\(221\) | 1.87953i | 0.126431i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.12989i | 0.544418i | 0.962238 | + | 0.272209i | \(0.0877541\pi\) | ||||
−0.962238 | + | 0.272209i | \(0.912246\pi\) | |||||||
\(224\) | −7.13477 | + | 1.08724i | −0.476712 | + | 0.0726443i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.88316 | + | 9.88067i | −0.191785 | + | 0.657253i | ||||
\(227\) | 14.3986 | 0.955671 | 0.477835 | − | 0.878449i | \(-0.341422\pi\) | ||||
0.477835 | + | 0.878449i | \(0.341422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.62772 | 0.239726 | 0.119863 | − | 0.992790i | \(-0.461754\pi\) | ||||
0.119863 | + | 0.992790i | \(0.461754\pi\) | |||||||
\(230\) | 3.22060 | − | 11.0371i | 0.212360 | − | 0.727766i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.37228 | + | 4.70285i | −0.352708 | + | 0.308758i | ||||
\(233\) | 4.84630i | 0.317491i | 0.987320 | + | 0.158746i | \(0.0507450\pi\) | ||||
−0.987320 | + | 0.158746i | \(0.949255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.02661i | 0.197434i | ||||||||
\(236\) | 20.8694 | + | 13.3128i | 1.35848 | + | 0.866589i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.37228 | + | 0.400428i | 0.0889518 | + | 0.0259559i | ||||
\(239\) | −12.0597 | −0.780080 | −0.390040 | − | 0.920798i | \(-0.627539\pi\) | ||||
−0.390040 | + | 0.920798i | \(0.627539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.48913 | −0.418001 | −0.209001 | − | 0.977916i | \(-0.567021\pi\) | ||||
−0.209001 | + | 0.977916i | \(0.567021\pi\) | |||||||
\(242\) | 14.5868 | + | 4.25639i | 0.937674 | + | 0.273611i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | − | 2.55164i | −0.256074 | − | 0.163352i | ||||
\(245\) | − | 13.5615i | − | 0.866409i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1565i | 0.709871i | ||||||||
\(248\) | −17.3020 | + | 15.1460i | −1.09868 | + | 0.961774i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.62772 | + | 12.4323i | −0.229437 | + | 0.786289i | ||||
\(251\) | 11.1780 | 0.705551 | 0.352776 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352776 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.62772 | 0.102334 | ||||||||
\(254\) | 3.03245 | − | 10.3923i | 0.190273 | − | 0.652071i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.3139 | + | 12.2321i | −0.644616 | + | 0.764506i | ||||
\(257\) | 14.9985i | 0.935584i | 0.883839 | + | 0.467792i | \(0.154950\pi\) | ||||
−0.883839 | + | 0.467792i | \(0.845050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.60485i | 0.534680i | ||||||||
\(260\) | −6.44121 | + | 10.0974i | −0.399467 | + | 0.626211i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3723 | + | 3.02661i | 0.640802 | + | 0.186984i | ||||
\(263\) | −27.9746 | −1.72499 | −0.862494 | − | 0.506067i | \(-0.831099\pi\) | ||||
−0.862494 | + | 0.506067i | \(0.831099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.74456 | −0.291456 | ||||||||
\(266\) | 8.14558 | + | 2.37686i | 0.499438 | + | 0.145735i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.31386 | + | 13.0330i | −0.507850 | + | 0.796115i | ||||
\(269\) | 21.4843i | 1.30992i | 0.755663 | + | 0.654961i | \(0.227315\pi\) | ||||
−0.755663 | + | 0.654961i | \(0.772685\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 29.9679i | − | 1.82042i | −0.414146 | − | 0.910211i | \(-0.635920\pi\) | ||
0.414146 | − | 0.910211i | \(-0.364080\pi\) | |||||||
\(272\) | 2.87382 | − | 1.33591i | 0.174251 | − | 0.0810013i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.17527 | − | 7.45471i | 0.131413 | − | 0.450356i | ||||
\(275\) | 0.693562 | 0.0418234 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.37228 | 0.382873 | 0.191437 | − | 0.981505i | \(-0.438685\pi\) | ||||
0.191437 | + | 0.981505i | \(0.438685\pi\) | |||||||
\(278\) | 6.09442 | − | 20.8858i | 0.365519 | − | 1.25265i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.00000 | + | 6.85407i | 0.358569 | + | 0.409609i | ||||
\(281\) | 23.0140i | 1.37290i | 0.727177 | + | 0.686450i | \(0.240832\pi\) | ||||
−0.727177 | + | 0.686450i | \(0.759168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.88067i | − | 0.587345i | −0.955906 | − | 0.293673i | \(-0.905122\pi\) | ||
0.955906 | − | 0.293673i | \(-0.0948775\pi\) | |||||||
\(284\) | 20.0172 | + | 12.7692i | 1.18780 | + | 0.757711i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.62772 | − | 0.474964i | −0.0962490 | − | 0.0280852i | ||||
\(287\) | 8.65099 | 0.510652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3723 | 0.963075 | ||||||||
\(290\) | 8.65099 | + | 2.52434i | 0.508004 | + | 0.148234i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.68614 | + | 3.62725i | 0.332756 | + | 0.212269i | ||||
\(293\) | − | 23.3089i | − | 1.36172i | −0.732412 | − | 0.680862i | \(-0.761605\pi\) | ||
0.732412 | − | 0.680862i | \(-0.238395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 31.2437i | − | 1.81908i | ||||||
\(296\) | 12.5652 | + | 14.3537i | 0.730335 | + | 0.834294i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.11684 | + | 17.5356i | −0.296411 | + | 1.01581i | ||||
\(299\) | 7.64018 | 0.441843 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.86141 | −0.568402 | ||||||||
\(302\) | −1.19897 | + | 4.10891i | −0.0689930 | + | 0.236441i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.0584 | − | 7.92967i | 0.978368 | − | 0.454798i | ||||
\(305\) | 5.98844i | 0.342897i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.20128i | 0.0685609i | 0.999412 | + | 0.0342805i | \(0.0109140\pi\) | ||||
−0.999412 | + | 0.0342805i | \(0.989086\pi\) | |||||||
\(308\) | −0.693562 | + | 1.08724i | −0.0395194 | + | 0.0619513i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.8614 | + | 8.12989i | 1.58242 | + | 0.461747i | ||||
\(311\) | 19.1355 | 1.08507 | 0.542536 | − | 0.840032i | \(-0.317464\pi\) | ||||
0.542536 | + | 0.840032i | \(0.317464\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.4891 | −1.04507 | −0.522534 | − | 0.852619i | \(-0.675013\pi\) | ||||
−0.522534 | + | 0.852619i | \(0.675013\pi\) | |||||||
\(314\) | −16.1030 | − | 4.69882i | −0.908746 | − | 0.265170i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.6277 | + | 16.6602i | −0.597856 | + | 0.937210i | ||||
\(317\) | 32.5214i | 1.82659i | 0.407303 | + | 0.913293i | \(0.366469\pi\) | ||||
−0.407303 | + | 0.913293i | \(0.633531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.27582i | 0.0714323i | ||||||||
\(320\) | 20.0172 | + | 2.67181i | 1.11899 | + | 0.149359i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.62772 | − | 5.57825i | 0.0907092 | − | 0.310864i | ||||
\(323\) | −3.72601 | −0.207321 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.25544 | 0.180579 | ||||||||
\(326\) | −0.693562 | + | 2.37686i | −0.0384129 | + | 0.131642i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.4307 | − | 12.6325i | 0.796802 | − | 0.697515i | ||||
\(329\) | 1.52967i | 0.0843335i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 27.7422i | − | 1.52485i | −0.647078 | − | 0.762424i | \(-0.724009\pi\) | ||
0.647078 | − | 0.762424i | \(-0.275991\pi\) | |||||||
\(332\) | 12.8824 | + | 8.21782i | 0.707014 | + | 0.451012i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.7446 | − | 6.92860i | −1.29924 | − | 0.379116i | ||||
\(335\) | 19.5118 | 1.06604 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.7446 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(338\) | 10.0086 | + | 2.92048i | 0.544395 | + | 0.158853i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.37228 | − | 2.15121i | −0.182888 | − | 0.116666i | ||||
\(341\) | 4.10891i | 0.222510i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.7848i | − | 0.852300i | ||||||
\(344\) | −16.4498 | + | 14.4000i | −0.886913 | + | 0.776397i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.00000 | + | 23.9892i | −0.376322 | + | 1.28967i | ||||
\(347\) | −6.94661 | −0.372914 | −0.186457 | − | 0.982463i | \(-0.559700\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.62772 | −0.301245 | −0.150622 | − | 0.988591i | \(-0.548128\pi\) | ||||
−0.150622 | + | 0.988591i | \(0.548128\pi\) | |||||||
\(350\) | 0.693562 | − | 2.37686i | 0.0370725 | − | 0.127049i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.430703 | + | 2.82639i | 0.0229566 | + | 0.150647i | ||||
\(353\) | − | 8.36530i | − | 0.445240i | −0.974905 | − | 0.222620i | \(-0.928539\pi\) | ||
0.974905 | − | 0.222620i | \(-0.0714609\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 29.9679i | − | 1.59053i | ||||||
\(356\) | −12.8824 | + | 20.1947i | −0.682766 | + | 1.07032i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | − | 3.50157i | −0.634220 | − | 0.185064i | ||||
\(359\) | −1.38712 | −0.0732096 | −0.0366048 | − | 0.999330i | \(-0.511654\pi\) | ||||
−0.0366048 | + | 0.999330i | \(0.511654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11684 | −0.164044 | ||||||||
\(362\) | 5.43039 | + | 1.58457i | 0.285415 | + | 0.0832834i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.25544 | + | 5.10328i | −0.170631 | + | 0.267485i | ||||
\(365\) | − | 8.51278i | − | 0.445579i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.37910i | 0.332987i | 0.986043 | + | 0.166493i | \(0.0532444\pi\) | ||||
−0.986043 | + | 0.166493i | \(0.946756\pi\) | |||||||
\(368\) | −5.43039 | − | 11.6819i | −0.283079 | − | 0.608962i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.74456 | − | 23.1138i | 0.350633 | − | 1.20163i | ||||
\(371\) | −2.39794 | −0.124495 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8614 | −1.02838 | −0.514192 | − | 0.857675i | \(-0.671908\pi\) | ||||
−0.514192 | + | 0.857675i | \(0.671908\pi\) | |||||||
\(374\) | 0.158627 | − | 0.543620i | 0.00820241 | − | 0.0281099i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.23369 | + | 2.55164i | 0.115194 | + | 0.131591i | ||||
\(377\) | 5.98844i | 0.308420i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.45364i | 0.331501i | 0.986168 | + | 0.165751i | \(0.0530047\pi\) | ||||
−0.986168 | + | 0.165751i | \(0.946995\pi\) | |||||||
\(380\) | −20.0172 | − | 12.7692i | −1.02686 | − | 0.655044i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.4891 | − | 5.97868i | −1.04831 | − | 0.305896i | ||||
\(383\) | 8.65099 | 0.442045 | 0.221023 | − | 0.975269i | \(-0.429061\pi\) | ||||
0.221023 | + | 0.975269i | \(0.429061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.62772 | 0.0829562 | ||||||||
\(386\) | −10.5140 | − | 3.06796i | −0.535148 | − | 0.156155i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.6861 | + | 11.2822i | 0.897878 | + | 0.572766i | ||||
\(389\) | − | 31.5268i | − | 1.59847i | −0.601018 | − | 0.799235i | \(-0.705238\pi\) | ||
0.601018 | − | 0.799235i | \(-0.294762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.55164i | 0.129042i | ||||||||
\(392\) | −10.0086 | − | 11.4333i | −0.505510 | − | 0.577467i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.48913 | + | 32.5196i | −0.478055 | + | 1.63831i | ||||
\(395\) | 24.9422 | 1.25498 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7446 | −0.940763 | −0.470381 | − | 0.882463i | \(-0.655884\pi\) | ||||
−0.470381 | + | 0.882463i | \(0.655884\pi\) | |||||||
\(398\) | 5.11313 | − | 17.5229i | 0.256298 | − | 0.878343i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.31386 | − | 4.97760i | −0.115693 | − | 0.248880i | ||||
\(401\) | 4.60625i | 0.230025i | 0.993364 | + | 0.115012i | \(0.0366908\pi\) | ||||
−0.993364 | + | 0.115012i | \(0.963309\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.2864i | 0.960723i | ||||||||
\(404\) | 1.32807 | − | 2.08191i | 0.0660740 | − | 0.103579i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.37228 | + | 1.27582i | 0.216993 | + | 0.0633179i | ||||
\(407\) | 3.40876 | 0.168966 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7446 | 0.679625 | 0.339812 | − | 0.940493i | \(-0.389636\pi\) | ||||
0.339812 | + | 0.940493i | \(0.389636\pi\) | |||||||
\(410\) | −23.2378 | − | 6.78073i | −1.14763 | − | 0.334876i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.510875 | − | 0.800857i | 0.0251690 | − | 0.0394554i | ||||
\(413\) | − | 15.7908i | − | 0.777016i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 19.2864i | − | 0.946731i | ||||||
\(416\) | 2.02163 | + | 13.2665i | 0.0991187 | + | 0.650444i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.941578 | − | 3.22682i | 0.0460541 | − | 0.157829i | ||||
\(419\) | −26.9638 | −1.31727 | −0.658634 | − | 0.752464i | \(-0.728865\pi\) | ||||
−0.658634 | + | 0.752464i | \(0.728865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.6060 | −0.516903 | −0.258452 | − | 0.966024i | \(-0.583212\pi\) | ||||
−0.258452 | + | 0.966024i | \(0.583212\pi\) | |||||||
\(422\) | −6.94661 | + | 23.8063i | −0.338156 | + | 1.15887i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.00000 | + | 3.50157i | −0.194257 | + | 0.170051i | ||||
\(425\) | 1.08724i | 0.0527389i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.02661i | 0.146468i | ||||||||
\(428\) | −21.1866 | − | 13.5152i | −1.02409 | − | 0.653280i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.4891 | + | 7.72946i | 1.27742 | + | 0.372748i | ||||
\(431\) | −31.1952 | −1.50262 | −0.751310 | − | 0.659949i | \(-0.770578\pi\) | ||||
−0.751310 | + | 0.659949i | \(0.770578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.62772 | −0.414622 | −0.207311 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207311 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(434\) | 14.0814 | + | 4.10891i | 0.675928 | + | 0.197234i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.7446 | + | 14.5090i | 1.08927 | + | 0.694855i | ||||
\(437\) | 15.1460i | 0.724533i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.52818i | − | 0.311573i | −0.987791 | − | 0.155786i | \(-0.950209\pi\) | ||
0.987791 | − | 0.155786i | \(-0.0497912\pi\) | |||||||
\(440\) | 2.71519 | − | 2.37686i | 0.129442 | − | 0.113312i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.744563 | − | 2.55164i | 0.0354152 | − | 0.121369i | ||||
\(443\) | −12.3770 | −0.588049 | −0.294025 | − | 0.955798i | \(-0.594995\pi\) | ||||
−0.294025 | + | 0.955798i | \(0.594995\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.2337 | 1.43321 | ||||||||
\(446\) | 3.22060 | − | 11.0371i | 0.152500 | − | 0.522623i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.1168 | + | 1.35036i | 0.477976 | + | 0.0637984i | ||||
\(449\) | − | 19.4024i | − | 0.915657i | −0.889041 | − | 0.457828i | \(-0.848627\pi\) | ||
0.889041 | − | 0.457828i | \(-0.151373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.42703i | − | 0.161373i | ||||||
\(452\) | 7.82833 | − | 12.2718i | 0.368214 | − | 0.577218i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.5475 | − | 5.70393i | −0.917412 | − | 0.267698i | ||||
\(455\) | 7.64018 | 0.358177 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.9783 | 1.87010 | 0.935052 | − | 0.354511i | \(-0.115353\pi\) | ||||
0.935052 | + | 0.354511i | \(0.115353\pi\) | |||||||
\(458\) | −4.92498 | − | 1.43710i | −0.230129 | − | 0.0671511i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.74456 | + | 13.7081i | −0.407717 | + | 0.639145i | ||||
\(461\) | − | 0.349857i | − | 0.0162944i | −0.999967 | − | 0.00814722i | \(-0.997407\pi\) | ||
0.999967 | − | 0.00814722i | \(-0.00259337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.77739i | 0.222024i | 0.993819 | + | 0.111012i | \(0.0354092\pi\) | ||||
−0.993819 | + | 0.111012i | \(0.964591\pi\) | |||||||
\(464\) | 9.15640 | − | 4.25639i | 0.425075 | − | 0.197598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.91983 | − | 6.57932i | 0.0889343 | − | 0.304781i | ||||
\(467\) | 5.11313 | 0.236608 | 0.118304 | − | 0.992977i | \(-0.462254\pi\) | ||||
0.118304 | + | 0.992977i | \(0.462254\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.86141 | 0.455357 | ||||||||
\(470\) | 1.19897 | − | 4.10891i | 0.0553044 | − | 0.189530i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.0584 | − | 26.3407i | −1.06135 | − | 1.21243i | ||||
\(473\) | 3.90653i | 0.179623i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.45364i | 0.296113i | ||||||||
\(476\) | −1.70438 | − | 1.08724i | −0.0781201 | − | 0.0498336i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.3723 | + | 4.77739i | 0.748851 | + | 0.218513i | ||||
\(479\) | −13.0706 | −0.597209 | −0.298605 | − | 0.954377i | \(-0.596521\pi\) | ||||
−0.298605 | + | 0.954377i | \(0.596521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | 0.729537 | ||||||||
\(482\) | 8.80962 | + | 2.57062i | 0.401267 | + | 0.117089i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.1168 | − | 11.5569i | −0.823493 | − | 0.525315i | ||||
\(485\) | − | 26.4781i | − | 1.20231i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.8752i | 1.94286i | 0.237325 | + | 0.971430i | \(0.423729\pi\) | ||||
−0.237325 | + | 0.971430i | \(0.576271\pi\) | |||||||
\(488\) | 4.41957 | + | 5.04868i | 0.200065 | + | 0.228543i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.37228 | + | 18.4110i | −0.242695 | + | 0.831724i | ||||
\(491\) | 13.7641 | 0.621166 | 0.310583 | − | 0.950546i | \(-0.399476\pi\) | ||||
0.310583 | + | 0.950546i | \(0.399476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | −0.0900755 | ||||||||
\(494\) | 4.41957 | − | 15.1460i | 0.198846 | − | 0.681452i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.4891 | − | 13.7081i | 1.32410 | − | 0.615513i | ||||
\(497\) | − | 15.1460i | − | 0.679392i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.42703i | − | 0.153415i | −0.997054 | − | 0.0767076i | \(-0.975559\pi\) | ||
0.997054 | − | 0.0767076i | \(-0.0244408\pi\) | |||||||
\(500\) | 9.84996 | − | 15.4410i | 0.440504 | − | 0.690542i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.1753 | − | 4.42810i | −0.677305 | − | 0.197636i | ||||
\(503\) | −19.3236 | −0.861597 | −0.430799 | − | 0.902448i | \(-0.641768\pi\) | ||||
−0.430799 | + | 0.902448i | \(0.641768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.11684 | −0.138698 | ||||||||
\(506\) | −2.20979 | − | 0.644810i | −0.0982370 | − | 0.0286653i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.23369 | + | 12.9073i | −0.365311 | + | 0.572668i | ||||
\(509\) | 14.7962i | 0.655829i | 0.944707 | + | 0.327914i | \(0.106346\pi\) | ||||
−0.944707 | + | 0.327914i | \(0.893654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.30243i | − | 0.190328i | ||||||
\(512\) | 18.8477 | − | 12.5205i | 0.832960 | − | 0.553333i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.94158 | − | 20.3620i | 0.262072 | − | 0.898129i | ||||
\(515\) | −1.19897 | −0.0528329 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.605969 | 0.0266505 | ||||||||
\(518\) | 3.40876 | − | 11.6819i | 0.149772 | − | 0.513274i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.7446 | − | 11.1565i | 0.558886 | − | 0.489245i | ||||
\(521\) | 26.0357i | 1.14064i | 0.821421 | + | 0.570322i | \(0.193181\pi\) | ||||
−0.821421 | + | 0.570322i | \(0.806819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40571i | 0.411283i | 0.978627 | + | 0.205641i | \(0.0659281\pi\) | ||||
−0.978627 | + | 0.205641i | \(0.934072\pi\) | |||||||
\(524\) | −12.8824 | − | 8.21782i | −0.562771 | − | 0.358997i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37.9783 | + | 11.0820i | 1.65593 | + | 0.483196i | ||||
\(527\) | −6.44121 | −0.280583 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6277 | −0.549031 | ||||||||
\(530\) | 6.44121 | + | 1.87953i | 0.279788 | + | 0.0816415i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.1168 | − | 6.45364i | −0.438621 | − | 0.279801i | ||||
\(533\) | − | 16.0858i | − | 0.696753i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.7187i | 1.37132i | ||||||||
\(536\) | 16.4498 | − | 14.4000i | 0.710523 | − | 0.621986i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.51087 | − | 29.1671i | 0.366930 | − | 1.25748i | ||||
\(539\) | −2.71519 | −0.116952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.97825 | −0.386005 | −0.193003 | − | 0.981198i | \(-0.561823\pi\) | ||||
−0.193003 | + | 0.981198i | \(0.561823\pi\) | |||||||
\(542\) | −11.8716 | + | 40.6844i | −0.509929 | + | 1.74754i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.43070 | + | 0.675178i | −0.189965 | + | 0.0289480i | ||||
\(545\) | − | 34.0511i | − | 1.45859i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2385i | 0.950848i | 0.879757 | + | 0.475424i | \(0.157705\pi\) | ||||
−0.879757 | + | 0.475424i | \(0.842295\pi\) | |||||||
\(548\) | −5.90627 | + | 9.25878i | −0.252303 | + | 0.395515i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.941578 | − | 0.274750i | −0.0401490 | − | 0.0117154i | ||||
\(551\) | −11.8716 | −0.505747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6060 | 0.536060 | ||||||||
\(554\) | −8.65099 | − | 2.52434i | −0.367545 | − | 0.107249i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.5475 | + | 25.9402i | −0.701772 | + | 1.10011i | ||||
\(557\) | 7.22316i | 0.306055i | 0.988222 | + | 0.153027i | \(0.0489023\pi\) | ||||
−0.988222 | + | 0.153027i | \(0.951098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.3365i | 0.775549i | ||||||||
\(560\) | −5.43039 | − | 11.6819i | −0.229476 | − | 0.493651i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.11684 | − | 31.2437i | 0.384571 | − | 1.31794i | ||||
\(563\) | −15.7858 | −0.665290 | −0.332645 | − | 0.943052i | \(-0.607941\pi\) | ||||
−0.332645 | + | 0.943052i | \(0.607941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.3723 | −0.772928 | ||||||||
\(566\) | −3.91416 | + | 13.4140i | −0.164525 | + | 0.563831i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.1168 | − | 25.2651i | −0.928002 | − | 1.06010i | ||||
\(569\) | 25.3909i | 1.06444i | 0.846606 | + | 0.532220i | \(0.178642\pi\) | ||||
−0.846606 | + | 0.532220i | \(0.821358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.22789i | 0.176932i | 0.996079 | + | 0.0884659i | \(0.0281964\pi\) | ||||
−0.996079 | + | 0.0884659i | \(0.971804\pi\) | |||||||
\(572\) | 2.02163 | + | 1.28962i | 0.0845287 | + | 0.0539217i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.7446 | − | 3.42703i | −0.490209 | − | 0.143042i | ||||
\(575\) | 4.41957 | 0.184309 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.8397 | 1.32550 | 0.662751 | − | 0.748840i | \(-0.269389\pi\) | ||||
0.662751 | + | 0.748840i | \(0.269389\pi\) | |||||||
\(578\) | −22.2270 | − | 6.48577i | −0.924520 | − | 0.269773i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.7446 | − | 6.85407i | −0.446144 | − | 0.284600i | ||||
\(581\) | − | 9.74749i | − | 0.404394i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.949929i | 0.0393420i | ||||||||
\(584\) | −6.28258 | − | 7.17687i | −0.259975 | − | 0.296981i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.23369 | + | 31.6442i | −0.381440 | + | 1.30721i | ||||
\(587\) | 3.91416 | 0.161555 | 0.0807774 | − | 0.996732i | \(-0.474260\pi\) | ||||
0.0807774 | + | 0.996732i | \(0.474260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.2337 | −1.57539 | ||||||||
\(590\) | −12.3770 | + | 42.4164i | −0.509553 | + | 1.74626i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.3723 | − | 24.4642i | −0.467398 | − | 1.00547i | ||||
\(593\) | − | 8.80773i | − | 0.361690i | −0.983512 | − | 0.180845i | \(-0.942117\pi\) | ||
0.983512 | − | 0.180845i | \(-0.0578833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.55164i | 0.104607i | ||||||||
\(596\) | 13.8932 | − | 21.7793i | 0.569089 | − | 0.892114i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.3723 | − | 3.02661i | −0.424154 | − | 0.123767i | ||||
\(599\) | −0.188154 | −0.00768776 | −0.00384388 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384388 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9783 | 0.651766 | 0.325883 | − | 0.945410i | \(-0.394338\pi\) | ||||
0.325883 | + | 0.945410i | \(0.394338\pi\) | |||||||
\(602\) | 13.3878 | + | 3.90653i | 0.545647 | + | 0.159218i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.25544 | − | 5.10328i | 0.132462 | − | 0.207650i | ||||
\(605\) | 27.1229i | 1.10270i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.97653i | − | 0.161403i | −0.996738 | − | 0.0807013i | \(-0.974284\pi\) | ||
0.996738 | − | 0.0807013i | \(-0.0257160\pi\) | |||||||
\(608\) | −26.2998 | + | 4.00772i | −1.06660 | + | 0.162535i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.37228 | − | 8.12989i | 0.0960509 | − | 0.329170i | ||||
\(611\) | 2.84429 | 0.115068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.23369 | 0.170997 | 0.0854985 | − | 0.996338i | \(-0.472752\pi\) | ||||
0.0854985 | + | 0.996338i | \(0.472752\pi\) | |||||||
\(614\) | 0.475881 | − | 1.63086i | 0.0192050 | − | 0.0658162i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.37228 | − | 1.20128i | 0.0552908 | − | 0.0484011i | ||||
\(617\) | − | 4.90120i | − | 0.197315i | −0.995121 | − | 0.0986574i | \(-0.968545\pi\) | ||
0.995121 | − | 0.0986574i | \(-0.0314548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.33117i | 0.375052i | 0.982260 | + | 0.187526i | \(0.0600468\pi\) | ||||
−0.982260 | + | 0.187526i | \(0.939953\pi\) | |||||||
\(620\) | −34.6040 | − | 22.0742i | −1.38973 | − | 0.886522i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.9783 | − | 7.58039i | −1.04163 | − | 0.303946i | ||||
\(623\) | 15.2804 | 0.612194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9783 | −1.19913 | ||||||||
\(626\) | 25.1008 | + | 7.32435i | 1.00323 | + | 0.292740i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0000 | + | 12.7582i | 0.798087 | + | 0.509108i | ||||
\(629\) | 5.34363i | 0.213064i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 42.8752i | − | 1.70683i | −0.521228 | − | 0.853417i | \(-0.674526\pi\) | ||
0.521228 | − | 0.853417i | \(-0.325474\pi\) | |||||||
\(632\) | 21.0280 | − | 18.4077i | 0.836449 | − | 0.732221i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.8832 | − | 44.1510i | 0.511655 | − | 1.75346i | ||||
\(635\) | 19.3236 | 0.766834 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.7446 | −0.504958 | ||||||||
\(638\) | 0.505408 | − | 1.73205i | 0.0200093 | − | 0.0685725i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.1168 | − | 11.5569i | −1.03236 | − | 0.456827i | ||||
\(641\) | − | 20.9321i | − | 0.826768i | −0.910557 | − | 0.413384i | \(-0.864347\pi\) | ||
0.910557 | − | 0.413384i | \(-0.135653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.9466i | 1.41760i | 0.705412 | + | 0.708798i | \(0.250762\pi\) | ||||
−0.705412 | + | 0.708798i | \(0.749238\pi\) | |||||||
\(644\) | −4.41957 | + | 6.92820i | −0.174156 | + | 0.273009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.05842 | + | 1.47603i | 0.199021 | + | 0.0580738i | ||||
\(647\) | 46.0993 | 1.81235 | 0.906174 | − | 0.422904i | \(-0.138989\pi\) | ||||
0.906174 | + | 0.422904i | \(0.138989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.25544 | −0.245547 | ||||||||
\(650\) | −4.41957 | − | 1.28962i | −0.173350 | − | 0.0505831i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.88316 | − | 2.95207i | 0.0737501 | − | 0.115612i | ||||
\(653\) | 4.40387i | 0.172337i | 0.996281 | + | 0.0861683i | \(0.0274623\pi\) | ||||
−0.996281 | + | 0.0861683i | \(0.972538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.2864i | 0.753581i | ||||||||
\(656\) | −24.5954 | + | 11.4333i | −0.960288 | + | 0.446394i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.605969 | − | 2.07668i | 0.0236231 | − | 0.0809573i | ||||
\(659\) | 12.0597 | 0.469781 | 0.234891 | − | 0.972022i | \(-0.424527\pi\) | ||||
0.234891 | + | 0.972022i | \(0.424527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6277 | 0.607848 | 0.303924 | − | 0.952696i | \(-0.401703\pi\) | ||||
0.303924 | + | 0.952696i | \(0.401703\pi\) | |||||||
\(662\) | −10.9899 | + | 37.6627i | −0.427134 | + | 1.46380i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.2337 | − | 16.2598i | −0.552374 | − | 0.631002i | ||||
\(665\) | 15.1460i | 0.587338i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.12989i | 0.314791i | ||||||||
\(668\) | 29.4908 | + | 18.8125i | 1.14103 | + | 0.727878i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.4891 | − | 7.72946i | −1.02336 | − | 0.298615i | ||||
\(671\) | 1.19897 | 0.0462857 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.8614 | 1.15107 | 0.575536 | − | 0.817776i | \(-0.304793\pi\) | ||||
0.575536 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(674\) | 21.3748 | + | 6.23711i | 0.823326 | + | 0.240244i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4307 | − | 7.92967i | −0.478104 | − | 0.304987i | ||||
\(677\) | 3.51900i | 0.135246i | 0.997711 | + | 0.0676232i | \(0.0215416\pi\) | ||||
−0.997711 | + | 0.0676232i | \(0.978458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.3822i | − | 0.513563i | ||||||
\(680\) | 3.72601 | + | 4.25639i | 0.142886 | + | 0.163225i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.62772 | − | 5.57825i | 0.0623286 | − | 0.213602i | ||||
\(683\) | −20.0172 | −0.765936 | −0.382968 | − | 0.923762i | \(-0.625098\pi\) | ||||
−0.382968 | + | 0.923762i | \(0.625098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8614 | 0.529617 | ||||||||
\(686\) | −6.25305 | + | 21.4294i | −0.238743 | + | 0.818179i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.0367 | − | 13.0330i | 1.06889 | − | 0.496877i | ||||
\(689\) | 4.45877i | 0.169866i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.0872i | − | 0.764155i | −0.924130 | − | 0.382077i | \(-0.875209\pi\) | ||
0.924130 | − | 0.382077i | \(-0.124791\pi\) | |||||||
\(692\) | 19.0064 | − | 29.7947i | 0.722513 | − | 1.13263i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.43070 | + | 2.75186i | 0.357985 | + | 0.104459i | ||||
\(695\) | 38.8354 | 1.47311 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.37228 | 0.203490 | ||||||||
\(698\) | 7.64018 | + | 2.22938i | 0.289185 | + | 0.0843834i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.88316 | + | 2.95207i | −0.0711766 | + | 0.111578i | ||||
\(701\) | 32.7615i | 1.23738i | 0.785634 | + | 0.618692i | \(0.212337\pi\) | ||||
−0.785634 | + | 0.618692i | \(0.787663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.7187i | 1.19629i | ||||||||
\(704\) | 0.534935 | − | 4.00772i | 0.0201611 | − | 0.151047i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.31386 | + | 11.3567i | −0.124719 | + | 0.427415i | ||||
\(707\) | −1.57528 | −0.0592444 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8614 | 0.896134 | 0.448067 | − | 0.894000i | \(-0.352113\pi\) | ||||
0.448067 | + | 0.894000i | \(0.352113\pi\) | |||||||
\(710\) | −11.8716 | + | 40.6844i | −0.445533 | + | 1.52686i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.4891 | − | 22.3130i | 0.955245 | − | 0.836215i | ||||
\(713\) | 26.1831i | 0.980566i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.02661i | − | 0.113189i | ||||||
\(716\) | 14.9040 | + | 9.50744i | 0.556990 | + | 0.355310i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.88316 | + | 0.549500i | 0.0702788 | + | 0.0205072i | ||||
\(719\) | 16.2912 | 0.607558 | 0.303779 | − | 0.952743i | \(-0.401752\pi\) | ||||
0.303779 | + | 0.952743i | \(0.401752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.605969 | −0.0225675 | ||||||||
\(722\) | 4.23142 | + | 1.23472i | 0.157477 | + | 0.0459514i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.74456 | − | 4.30243i | −0.250660 | − | 0.159898i | ||||
\(725\) | 3.46410i | 0.128654i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.0978i | 1.41297i | 0.707728 | + | 0.706485i | \(0.249720\pi\) | ||||
−0.707728 | + | 0.706485i | \(0.750280\pi\) | |||||||
\(728\) | 6.44121 | − | 5.63858i | 0.238727 | − | 0.208980i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.37228 | + | 11.5569i | −0.124814 | + | 0.427741i | ||||
\(731\) | −6.12395 | −0.226503 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.372281 | 0.0137505 | 0.00687526 | − | 0.999976i | \(-0.497812\pi\) | ||||
0.00687526 | + | 0.999976i | \(0.497812\pi\) | |||||||
\(734\) | 2.52704 | − | 8.66025i | 0.0932748 | − | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.74456 | + | 18.0106i | 0.101166 | + | 0.663878i | ||||
\(737\) | − | 3.90653i | − | 0.143899i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.45364i | − | 0.237401i | −0.992930 | − | 0.118700i | \(-0.962127\pi\) | ||
0.992930 | − | 0.118700i | \(-0.0378728\pi\) | |||||||
\(740\) | −18.3128 | + | 28.7075i | −0.673192 | + | 1.05531i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.25544 | + | 0.949929i | 0.119511 | + | 0.0348730i | ||||
\(743\) | −21.1571 | −0.776179 | −0.388089 | − | 0.921622i | \(-0.626865\pi\) | ||||
−0.388089 | + | 0.921622i | \(0.626865\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.6060 | −1.19459 | ||||||||
\(746\) | 26.9638 | + | 7.86797i | 0.987215 | + | 0.288067i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.430703 | + | 0.675178i | −0.0157481 | + | 0.0246870i | ||||
\(749\) | 16.0309i | 0.585756i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 21.6890i | − | 0.791441i | −0.918371 | − | 0.395721i | \(-0.870495\pi\) | ||
0.918371 | − | 0.395721i | \(-0.129505\pi\) | |||||||
\(752\) | −2.02163 | − | 4.34896i | −0.0737213 | − | 0.158590i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.37228 | − | 8.12989i | 0.0863934 | − | 0.296073i | ||||
\(755\) | −7.64018 | −0.278054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0000 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(758\) | 2.55657 | − | 8.76144i | 0.0928587 | − | 0.318230i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.1168 | + | 25.2651i | 0.802262 | + | 0.916460i | ||||
\(761\) | 17.3754i | 0.629858i | 0.949115 | + | 0.314929i | \(0.101981\pi\) | ||||
−0.949115 | + | 0.314929i | \(0.898019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 17.2097i | − | 0.623033i | ||||||
\(764\) | 25.4476 | + | 16.2333i | 0.920661 | + | 0.587299i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.7446 | − | 3.42703i | −0.424348 | − | 0.123824i | ||||
\(767\) | −29.3617 | −1.06019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.09509 | 0.291917 | 0.145958 | − | 0.989291i | \(-0.453373\pi\) | ||||
0.145958 | + | 0.989291i | \(0.453373\pi\) | |||||||
\(770\) | −2.20979 | − | 0.644810i | −0.0796352 | − | 0.0232373i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.0584 | + | 8.33010i | 0.469983 | + | 0.299807i | ||||
\(773\) | 0.699713i | 0.0251669i | 0.999921 | + | 0.0125835i | \(0.00400555\pi\) | ||||
−0.999921 | + | 0.0125835i | \(0.995994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.1565i | 0.400753i | ||||||||
\(776\) | −19.5413 | − | 22.3229i | −0.701492 | − | 0.801345i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.4891 | + | 42.8007i | −0.447757 | + | 1.53448i | ||||
\(779\) | 31.8888 | 1.14253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | 1.01082 | − | 3.46410i | 0.0361467 | − | 0.123876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.05842 | + | 19.4866i | 0.323515 | + | 0.695950i | ||||
\(785\) | − | 29.9422i | − | 1.06868i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.7453i | 1.23854i | 0.785180 | + | 0.619268i | \(0.212571\pi\) | ||||
−0.785180 | + | 0.619268i | \(0.787429\pi\) | |||||||
\(788\) | 25.7648 | − | 40.3894i | 0.917834 | − | 1.43881i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.8614 | − | 9.88067i | −1.20473 | − | 0.351539i | ||||
\(791\) | −9.28550 | −0.330154 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.62772 | 0.199846 | ||||||||
\(794\) | 25.4476 | + | 7.42554i | 0.903100 | + | 0.263522i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.8832 | + | 21.7635i | −0.492075 | + | 0.771386i | ||||
\(797\) | 23.8989i | 0.846541i | 0.906003 | + | 0.423270i | \(0.139118\pi\) | ||||
−0.906003 | + | 0.423270i | \(0.860882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.949929i | 0.0336061i | ||||||||
\(800\) | 1.16944 | + | 7.67420i | 0.0413461 | + | 0.271324i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.82473 | − | 6.25343i | 0.0644336 | − | 0.220816i | ||||
\(803\) | −1.70438 | −0.0601462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3723 | 0.365575 | ||||||||
\(806\) | 7.64018 | − | 26.1831i | 0.269114 | − | 0.922262i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.62772 | + | 2.30029i | −0.0924428 | + | 0.0809238i | ||||
\(809\) | − | 35.8381i | − | 1.26000i | −0.776595 | − | 0.630000i | \(-0.783055\pi\) | ||
0.776595 | − | 0.630000i | \(-0.216945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.20128i | − | 0.0421828i | −0.999778 | − | 0.0210914i | \(-0.993286\pi\) | ||
0.999778 | − | 0.0210914i | \(-0.00671410\pi\) | |||||||
\(812\) | −5.43039 | − | 3.46410i | −0.190569 | − | 0.121566i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.62772 | − | 1.35036i | −0.162201 | − | 0.0473300i | ||||
\(815\) | −4.41957 | −0.154811 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.3505 | −1.27174 | ||||||||
\(818\) | −18.6596 | − | 5.44482i | −0.652417 | − | 0.190374i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.8614 | + | 18.4110i | 1.00788 | + | 0.642940i | ||||
\(821\) | 18.2603i | 0.637288i | 0.947874 | + | 0.318644i | \(0.103227\pi\) | ||||
−0.947874 | + | 0.318644i | \(0.896773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 14.0340i | − | 0.489195i | −0.969625 | − | 0.244598i | \(-0.921344\pi\) | ||
0.969625 | − | 0.244598i | \(-0.0786559\pi\) | |||||||
\(824\) | −1.01082 | + | 0.884861i | −0.0352135 | + | 0.0308256i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.25544 | + | 21.4376i | −0.217655 | + | 0.745909i | ||||
\(827\) | −47.4864 | −1.65126 | −0.825632 | − | 0.564210i | \(-0.809181\pi\) | ||||
−0.825632 | + | 0.564210i | \(0.809181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.2337 | −1.67523 | −0.837613 | − | 0.546265i | \(-0.816049\pi\) | ||||
−0.837613 | + | 0.546265i | \(0.816049\pi\) | |||||||
\(830\) | −7.64018 | + | 26.1831i | −0.265194 | + | 0.908830i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.51087 | − | 18.8114i | 0.0870489 | − | 0.652169i | ||||
\(833\) | − | 4.25639i | − | 0.147475i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 44.1510i | − | 1.52791i | ||||||
\(836\) | −2.55657 | + | 4.00772i | −0.0884207 | + | 0.138610i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.6060 | + | 10.6815i | 1.26453 | + | 0.368987i | ||||
\(839\) | −42.6205 | −1.47142 | −0.735711 | − | 0.677296i | \(-0.763152\pi\) | ||||
−0.735711 | + | 0.677296i | \(0.763152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.6277 | 0.780266 | ||||||||
\(842\) | 14.3986 | + | 4.20149i | 0.496210 | + | 0.144793i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.8614 | − | 29.5675i | 0.649236 | − | 1.01775i | ||||
\(845\) | 18.6101i | 0.640208i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7081i | 0.471017i | ||||||||
\(848\) | 6.81751 | − | 3.16915i | 0.234114 | − | 0.108829i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.430703 | − | 1.47603i | 0.0147730 | − | 0.0506276i | ||||
\(851\) | 21.7216 | 0.744605 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.6060 | 1.52728 | 0.763640 | − | 0.645643i | \(-0.223410\pi\) | ||||
0.763640 | + | 0.645643i | \(0.223410\pi\) | |||||||
\(854\) | 1.19897 | − | 4.10891i | 0.0410279 | − | 0.140604i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.4090 | + | 26.7411i | 0.800102 | + | 0.913992i | ||||
\(857\) | − | 37.5701i | − | 1.28337i | −0.766968 | − | 0.641685i | \(-0.778236\pi\) | ||
0.766968 | − | 0.641685i | \(-0.221764\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.82532i | 0.0622791i | 0.999515 | + | 0.0311396i | \(0.00991364\pi\) | ||||
−0.999515 | + | 0.0311396i | \(0.990086\pi\) | |||||||
\(860\) | −32.8996 | − | 20.9870i | −1.12187 | − | 0.715650i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.3505 | + | 12.3578i | 1.44246 | + | 0.420908i | ||||
\(863\) | 40.0344 | 1.36279 | 0.681393 | − | 0.731918i | \(-0.261375\pi\) | ||||
0.681393 | + | 0.731918i | \(0.261375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.6060 | −1.51665 | ||||||||
\(866\) | 11.7130 | + | 3.41781i | 0.398023 | + | 0.116142i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −17.4891 | − | 11.1565i | −0.593620 | − | 0.378676i | ||||
\(869\) | − | 4.99377i | − | 0.169402i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 18.3365i | − | 0.621307i | ||||||
\(872\) | −25.1303 | − | 28.7075i | −0.851020 | − | 0.972158i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.00000 | − | 20.5622i | 0.202953 | − | 0.695527i | ||||
\(875\) | −11.6834 | −0.394972 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6277 | 0.730316 | 0.365158 | − | 0.930946i | \(-0.381015\pi\) | ||||
0.365158 | + | 0.930946i | \(0.381015\pi\) | |||||||
\(878\) | −2.58609 | + | 8.86263i | −0.0872765 | + | 0.299099i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.62772 | + | 2.15121i | −0.156000 | + | 0.0725174i | ||||
\(881\) | − | 52.9562i | − | 1.78414i | −0.451898 | − | 0.892070i | \(-0.649253\pi\) | ||
0.451898 | − | 0.892070i | \(-0.350747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.0127i | − | 0.673481i | −0.941597 | − | 0.336741i | \(-0.890675\pi\) | ||
0.941597 | − | 0.336741i | \(-0.109325\pi\) | |||||||
\(884\) | −2.02163 | + | 3.16915i | −0.0679949 | + | 0.106590i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.8030 | + | 4.90307i | 0.564507 | + | 0.164722i | ||||
\(887\) | −19.5118 | −0.655141 | −0.327571 | − | 0.944827i | \(-0.606230\pi\) | ||||
−0.327571 | + | 0.944827i | \(0.606230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.76631 | 0.327552 | ||||||||
\(890\) | −41.0452 | − | 11.9769i | −1.37584 | − | 0.401466i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.74456 | + | 13.7081i | −0.292790 | + | 0.458982i | ||||
\(893\) | 5.63858i | 0.188688i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22.3130i | − | 0.745841i | ||||||
\(896\) | −13.1997 | − | 5.84096i | −0.440970 | − | 0.195133i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.68614 | + | 26.3407i | −0.256490 | + | 0.878999i | ||||
\(899\) | −20.5226 | −0.684467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.48913 | −0.0496100 | ||||||||
\(902\) | −1.35760 | + | 4.65253i | −0.0452030 | + | 0.154912i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.4891 | + | 13.5591i | −0.515161 | + | 0.450968i | ||||
\(905\) | 10.0974i | 0.335647i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.8934i | 0.992593i | 0.868153 | + | 0.496297i | \(0.165307\pi\) | ||||
−0.868153 | + | 0.496297i | \(0.834693\pi\) | |||||||
\(908\) | 24.2781 | + | 15.4873i | 0.805698 | + | 0.513963i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.3723 | − | 3.02661i | −0.343838 | − | 0.100331i | ||||
\(911\) | 35.8029 | 1.18620 | 0.593102 | − | 0.805127i | \(-0.297903\pi\) | ||||
0.593102 | + | 0.805127i | \(0.297903\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.86141 | −0.127794 | ||||||||
\(914\) | −54.2744 | − | 15.8371i | −1.79524 | − | 0.523846i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.11684 | + | 3.90200i | 0.202106 | + | 0.128926i | ||||
\(917\) | 9.74749i | 0.321891i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36.9711i | − | 1.21956i | −0.792570 | − | 0.609781i | \(-0.791257\pi\) | ||
0.792570 | − | 0.609781i | \(-0.208743\pi\) | |||||||
\(920\) | 17.3020 | − | 15.1460i | 0.570429 | − | 0.499350i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.138593 | + | 0.474964i | −0.00456433 | + | 0.0156421i | ||||
\(923\) | −28.1628 | −0.926989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.25544 | 0.304317 | ||||||||
\(926\) | 1.89253 | − | 6.48577i | 0.0621925 | − | 0.213136i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.1168 | + | 2.15121i | −0.463408 | + | 0.0706170i | ||||
\(929\) | − | 18.5552i | − | 0.608777i | −0.952548 | − | 0.304389i | \(-0.901548\pi\) | ||
0.952548 | − | 0.304389i | \(-0.0984521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 25.2651i | − | 0.828029i | ||||||
\(932\) | −5.21271 | + | 8.17154i | −0.170748 | + | 0.267668i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.94158 | − | 2.02554i | −0.227135 | − | 0.0662775i | ||||
\(935\) | 1.01082 | 0.0330572 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.7228 | 1.49370 | 0.746850 | − | 0.664993i | \(-0.231565\pi\) | ||||
0.746850 | + | 0.664993i | \(0.231565\pi\) | |||||||
\(938\) | −13.3878 | − | 3.90653i | −0.437128 | − | 0.127553i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.25544 | + | 5.10328i | −0.106181 | + | 0.166451i | ||||
\(941\) | 13.5065i | 0.440301i | 0.975466 | + | 0.220150i | \(0.0706548\pi\) | ||||
−0.975466 | + | 0.220150i | \(0.929345\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 21.8380i | − | 0.711144i | ||||||
\(944\) | 20.8694 | + | 44.8945i | 0.679240 | + | 1.46119i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.54755 | − | 5.30350i | 0.0503151 | − | 0.172432i | ||||
\(947\) | −6.57031 | −0.213506 | −0.106753 | − | 0.994286i | \(-0.534045\pi\) | ||||
−0.106753 | + | 0.994286i | \(0.534045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | 2.55657 | − | 8.76144i | 0.0829460 | − | 0.284259i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.88316 | + | 2.15121i | 0.0610334 | + | 0.0697212i | ||||
\(953\) | − | 10.2997i | − | 0.333641i | −0.985987 | − | 0.166821i | \(-0.946650\pi\) | ||
0.985987 | − | 0.166821i | \(-0.0533500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38.0978i | − | 1.23282i | ||||||
\(956\) | −20.3344 | − | 12.9715i | −0.657663 | − | 0.419530i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.7446 | + | 5.17782i | 0.573301 | + | 0.167288i | ||||
\(959\) | 7.00567 | 0.226225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −35.0951 | −1.13210 | ||||||||
\(962\) | −21.7216 | − | 6.33830i | −0.700331 | − | 0.204355i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.9416 | − | 6.97975i | −0.352404 | − | 0.224802i | ||||
\(965\) | − | 19.5499i | − | 0.629333i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 46.8517i | − | 1.50665i | −0.657648 | − | 0.753325i | \(-0.728449\pi\) | ||
0.657648 | − | 0.753325i | \(-0.271551\pi\) | |||||||
\(968\) | 20.0172 | + | 22.8665i | 0.643376 | + | 0.734958i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.4891 | + | 35.9466i | −0.336786 | + | 1.15418i | ||||
\(971\) | 37.0019 | 1.18745 | 0.593724 | − | 0.804669i | \(-0.297657\pi\) | ||||
0.593724 | + | 0.804669i | \(0.297657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.6277 | 0.629236 | ||||||||
\(974\) | 16.9847 | − | 58.2072i | 0.544226 | − | 1.86508i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 8.60485i | −0.128037 | − | 0.275435i | ||||
\(977\) | − | 54.6882i | − | 1.74963i | −0.484455 | − | 0.874816i | \(-0.660982\pi\) | ||
0.484455 | − | 0.874816i | \(-0.339018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.05321i | − | 0.193461i | ||||||
\(980\) | 14.5868 | − | 22.8665i | 0.465958 | − | 0.730444i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.6861 | − | 5.45257i | −0.596299 | − | 0.173998i | ||||
\(983\) | 34.4158 | 1.09769 | 0.548847 | − | 0.835923i | \(-0.315067\pi\) | ||||
0.548847 | + | 0.835923i | \(0.315067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −60.4674 | −1.92665 | ||||||||
\(986\) | 2.71519 | + | 0.792287i | 0.0864694 | + | 0.0252316i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | + | 18.8114i | −0.381771 | + | 0.598471i | ||||
\(989\) | 24.8935i | 0.791568i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7.65492i | − | 0.243167i | −0.992581 | − | 0.121583i | \(-0.961203\pi\) | ||
0.992581 | − | 0.121583i | \(-0.0387972\pi\) | |||||||
\(992\) | −45.4647 | + | 6.92820i | −1.44351 | + | 0.219971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | + | 20.5622i | −0.190308 | + | 0.652194i | ||||
\(995\) | 32.5823 | 1.03293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.1386 | −0.764477 | −0.382238 | − | 0.924064i | \(-0.624847\pi\) | ||||
−0.382238 | + | 0.924064i | \(0.624847\pi\) | |||||||
\(998\) | −1.35760 | + | 4.65253i | −0.0429740 | + | 0.147273i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))