Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(1049,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1050.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.d (of order \(2\), degree \(1\), not 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.3 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.d.1049.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.618034 | − | 1.61803i | 0.356822 | − | 0.934172i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | − | 1.61803i | 0.252311 | − | 0.660560i | ||||
\(7\) | 0.381966 | − | 2.61803i | 0.144370 | − | 0.989524i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.23607 | − | 2.00000i | −0.745356 | − | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214i | 1.34840i | 0.738549 | + | 0.674200i | \(0.235511\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0.618034 | − | 1.61803i | 0.178411 | − | 0.467086i | ||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 0.381966 | − | 2.61803i | 0.102085 | − | 0.699699i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.23607i | − | 1.26993i | −0.772540 | − | 0.634967i | \(-0.781014\pi\) | ||
0.772540 | − | 0.634967i | \(-0.218986\pi\) | |||||||
\(18\) | −2.23607 | − | 2.00000i | −0.527046 | − | 0.471405i | ||||
\(19\) | − | 8.47214i | − | 1.94364i | −0.235722 | − | 0.971821i | \(-0.575745\pi\) | ||
0.235722 | − | 0.971821i | \(-0.424255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | − | 2.23607i | −0.872872 | − | 0.487950i | ||||
\(22\) | 4.47214i | 0.953463i | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0.618034 | − | 1.61803i | 0.126156 | − | 0.330280i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | −4.61803 | + | 2.38197i | −0.888741 | + | 0.458410i | ||||
\(28\) | 0.381966 | − | 2.61803i | 0.0721848 | − | 0.494762i | ||||
\(29\) | 7.70820i | 1.43138i | 0.698419 | + | 0.715689i | \(0.253887\pi\) | ||||
−0.698419 | + | 0.715689i | \(0.746113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.76393i | − | 0.496417i | −0.968707 | − | 0.248208i | \(-0.920158\pi\) | ||
0.968707 | − | 0.248208i | \(-0.0798418\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.23607 | + | 2.76393i | 1.25964 | + | 0.481139i | ||||
\(34\) | − | 5.23607i | − | 0.897978i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.23607 | − | 2.00000i | −0.372678 | − | 0.333333i | ||||
\(37\) | − | 0.763932i | − | 0.125590i | −0.998026 | − | 0.0627948i | \(-0.979999\pi\) | ||
0.998026 | − | 0.0627948i | \(-0.0200014\pi\) | |||||||
\(38\) | − | 8.47214i | − | 1.37436i | ||||||
\(39\) | 0.763932 | − | 2.00000i | 0.122327 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.47214 | −0.386083 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(42\) | −4.00000 | − | 2.23607i | −0.617213 | − | 0.345033i | ||||
\(43\) | − | 4.94427i | − | 0.753994i | −0.926214 | − | 0.376997i | \(-0.876957\pi\) | ||
0.926214 | − | 0.376997i | \(-0.123043\pi\) | |||||||
\(44\) | 4.47214i | 0.674200i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 6.47214i | 0.944058i | 0.881583 | + | 0.472029i | \(0.156478\pi\) | ||||
−0.881583 | + | 0.472029i | \(0.843522\pi\) | |||||||
\(48\) | 0.618034 | − | 1.61803i | 0.0892055 | − | 0.233543i | ||||
\(49\) | −6.70820 | − | 2.00000i | −0.958315 | − | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.47214 | − | 3.23607i | −1.18634 | − | 0.453140i | ||||
\(52\) | 1.23607 | 0.171412 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | −4.61803 | + | 2.38197i | −0.628435 | + | 0.324145i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.381966 | − | 2.61803i | 0.0510424 | − | 0.349850i | ||||
\(57\) | −13.7082 | − | 5.23607i | −1.81570 | − | 0.693534i | ||||
\(58\) | 7.70820i | 1.01214i | ||||||||
\(59\) | −4.47214 | −0.582223 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23607i | 0.926484i | 0.886232 | + | 0.463242i | \(0.153314\pi\) | ||||
−0.886232 | + | 0.463242i | \(0.846686\pi\) | |||||||
\(62\) | − | 2.76393i | − | 0.351020i | ||||||
\(63\) | −6.09017 | + | 5.09017i | −0.767289 | + | 0.641301i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.23607 | + | 2.76393i | 0.890698 | + | 0.340217i | ||||
\(67\) | 12.0000i | 1.46603i | 0.680211 | + | 0.733017i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733017i | \(0.738112\pi\) | |||||||
\(68\) | − | 5.23607i | − | 0.634967i | ||||||
\(69\) | 2.47214 | − | 6.47214i | 0.297610 | − | 0.779154i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.23607i | − | 0.858763i | −0.903123 | − | 0.429382i | \(-0.858732\pi\) | ||
0.903123 | − | 0.429382i | \(-0.141268\pi\) | |||||||
\(72\) | −2.23607 | − | 2.00000i | −0.263523 | − | 0.235702i | ||||
\(73\) | 11.2361 | 1.31508 | 0.657541 | − | 0.753419i | \(-0.271597\pi\) | ||||
0.657541 | + | 0.753419i | \(0.271597\pi\) | |||||||
\(74\) | − | 0.763932i | − | 0.0888053i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 8.47214i | − | 0.971821i | ||||||
\(77\) | 11.7082 | + | 1.70820i | 1.33427 | + | 0.194668i | ||||
\(78\) | 0.763932 | − | 2.00000i | 0.0864983 | − | 0.226455i | ||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | −2.47214 | −0.273002 | ||||||||
\(83\) | 14.6525i | 1.60832i | 0.594414 | + | 0.804159i | \(0.297384\pi\) | ||||
−0.594414 | + | 0.804159i | \(0.702616\pi\) | |||||||
\(84\) | −4.00000 | − | 2.23607i | −0.436436 | − | 0.243975i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.94427i | − | 0.533155i | ||||||
\(87\) | 12.4721 | + | 4.76393i | 1.33715 | + | 0.510747i | ||||
\(88\) | 4.47214i | 0.476731i | ||||||||
\(89\) | 5.52786 | 0.585952 | 0.292976 | − | 0.956120i | \(-0.405354\pi\) | ||||
0.292976 | + | 0.956120i | \(0.405354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.472136 | − | 3.23607i | 0.0494933 | − | 0.339232i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | −4.47214 | − | 1.70820i | −0.463739 | − | 0.177132i | ||||
\(94\) | 6.47214i | 0.667550i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.618034 | − | 1.61803i | 0.0630778 | − | 0.165140i | ||||
\(97\) | 0.763932 | 0.0775655 | 0.0387828 | − | 0.999248i | \(-0.487652\pi\) | ||||
0.0387828 | + | 0.999248i | \(0.487652\pi\) | |||||||
\(98\) | −6.70820 | − | 2.00000i | −0.677631 | − | 0.202031i | ||||
\(99\) | 8.94427 | − | 10.0000i | 0.898933 | − | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4721 | −1.24102 | −0.620512 | − | 0.784197i | \(-0.713075\pi\) | ||||
−0.620512 | + | 0.784197i | \(0.713075\pi\) | |||||||
\(102\) | −8.47214 | − | 3.23607i | −0.838866 | − | 0.320418i | ||||
\(103\) | 14.6525 | 1.44375 | 0.721876 | − | 0.692023i | \(-0.243280\pi\) | ||||
0.721876 | + | 0.692023i | \(0.243280\pi\) | |||||||
\(104\) | 1.23607 | 0.121206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.472136 | −0.0458579 | ||||||||
\(107\) | 11.4164 | 1.10367 | 0.551833 | − | 0.833955i | \(-0.313929\pi\) | ||||
0.551833 | + | 0.833955i | \(0.313929\pi\) | |||||||
\(108\) | −4.61803 | + | 2.38197i | −0.444371 | + | 0.229205i | ||||
\(109\) | −4.47214 | −0.428353 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.23607 | − | 0.472136i | −0.117322 | − | 0.0448132i | ||||
\(112\) | 0.381966 | − | 2.61803i | 0.0360924 | − | 0.247381i | ||||
\(113\) | 2.94427 | 0.276974 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(114\) | −13.7082 | − | 5.23607i | −1.28389 | − | 0.490403i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.70820i | 0.715689i | ||||||||
\(117\) | −2.76393 | − | 2.47214i | −0.255526 | − | 0.228549i | ||||
\(118\) | −4.47214 | −0.411693 | ||||||||
\(119\) | −13.7082 | − | 2.00000i | −1.25663 | − | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 7.23607i | 0.655123i | ||||||||
\(123\) | −1.52786 | + | 4.00000i | −0.137763 | + | 0.360668i | ||||
\(124\) | − | 2.76393i | − | 0.248208i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.09017 | + | 5.09017i | −0.542555 | + | 0.453468i | ||||
\(127\) | 0.291796i | 0.0258927i | 0.999916 | + | 0.0129464i | \(0.00412107\pi\) | ||||
−0.999916 | + | 0.0129464i | \(0.995879\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.00000 | − | 3.05573i | −0.704361 | − | 0.269042i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.41641 | 0.473234 | 0.236617 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236617 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(132\) | 7.23607 | + | 2.76393i | 0.629819 | + | 0.240569i | ||||
\(133\) | −22.1803 | − | 3.23607i | −1.92328 | − | 0.280603i | ||||
\(134\) | 12.0000i | 1.03664i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 5.23607i | − | 0.448989i | ||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | 2.47214 | − | 6.47214i | 0.210442 | − | 0.550945i | ||||
\(139\) | 11.5279i | 0.977781i | 0.872345 | + | 0.488890i | \(0.162598\pi\) | ||||
−0.872345 | + | 0.488890i | \(0.837402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4721 | + | 4.00000i | 0.881913 | + | 0.336861i | ||||
\(142\) | − | 7.23607i | − | 0.607237i | ||||||
\(143\) | 5.52786i | 0.462263i | ||||||||
\(144\) | −2.23607 | − | 2.00000i | −0.186339 | − | 0.166667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.2361 | 0.929904 | ||||||||
\(147\) | −7.38197 | + | 9.61803i | −0.608854 | + | 0.793282i | ||||
\(148\) | − | 0.763932i | − | 0.0627948i | ||||||
\(149\) | 4.29180i | 0.351598i | 0.984426 | + | 0.175799i | \(0.0562508\pi\) | ||||
−0.984426 | + | 0.175799i | \(0.943749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.9443 | 1.70442 | 0.852210 | − | 0.523199i | \(-0.175262\pi\) | ||||
0.852210 | + | 0.523199i | \(0.175262\pi\) | |||||||
\(152\) | − | 8.47214i | − | 0.687181i | ||||||
\(153\) | −10.4721 | + | 11.7082i | −0.846622 | + | 0.946552i | ||||
\(154\) | 11.7082 | + | 1.70820i | 0.943474 | + | 0.137651i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.763932 | − | 2.00000i | 0.0611635 | − | 0.160128i | ||||
\(157\) | −9.23607 | −0.737118 | −0.368559 | − | 0.929604i | \(-0.620149\pi\) | ||||
−0.368559 | + | 0.929604i | \(0.620149\pi\) | |||||||
\(158\) | 8.94427 | 0.711568 | ||||||||
\(159\) | −0.291796 | + | 0.763932i | −0.0231409 | + | 0.0605838i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.52786 | − | 10.4721i | 0.120413 | − | 0.825320i | ||||
\(162\) | 1.00000 | + | 8.94427i | 0.0785674 | + | 0.702728i | ||||
\(163\) | − | 10.4721i | − | 0.820241i | −0.912031 | − | 0.410120i | \(-0.865487\pi\) | ||
0.912031 | − | 0.410120i | \(-0.134513\pi\) | |||||||
\(164\) | −2.47214 | −0.193041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.6525i | 1.13725i | ||||||||
\(167\) | 0.944272i | 0.0730700i | 0.999332 | + | 0.0365350i | \(0.0116320\pi\) | ||||
−0.999332 | + | 0.0365350i | \(0.988368\pi\) | |||||||
\(168\) | −4.00000 | − | 2.23607i | −0.308607 | − | 0.172516i | ||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.9443 | + | 18.9443i | −1.29576 | + | 1.44870i | ||||
\(172\) | − | 4.94427i | − | 0.376997i | ||||||
\(173\) | − | 9.41641i | − | 0.715916i | −0.933738 | − | 0.357958i | \(-0.883473\pi\) | ||
0.933738 | − | 0.357958i | \(-0.116527\pi\) | |||||||
\(174\) | 12.4721 | + | 4.76393i | 0.945510 | + | 0.361153i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.47214i | 0.337100i | ||||||||
\(177\) | −2.76393 | + | 7.23607i | −0.207750 | + | 0.543896i | ||||
\(178\) | 5.52786 | 0.414331 | ||||||||
\(179\) | 14.9443i | 1.11699i | 0.829509 | + | 0.558494i | \(0.188620\pi\) | ||||
−0.829509 | + | 0.558494i | \(0.811380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.1803i | − | 1.20268i | −0.798995 | − | 0.601338i | \(-0.794635\pi\) | ||
0.798995 | − | 0.601338i | \(-0.205365\pi\) | |||||||
\(182\) | 0.472136 | − | 3.23607i | 0.0349970 | − | 0.239873i | ||||
\(183\) | 11.7082 | + | 4.47214i | 0.865495 | + | 0.330590i | ||||
\(184\) | 4.00000 | 0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.47214 | − | 1.70820i | −0.327913 | − | 0.125252i | ||||
\(187\) | 23.4164 | 1.71238 | ||||||||
\(188\) | 6.47214i | 0.472029i | ||||||||
\(189\) | 4.47214 | + | 13.0000i | 0.325300 | + | 0.945611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.23607i | 0.523584i | 0.965124 | + | 0.261792i | \(0.0843134\pi\) | ||||
−0.965124 | + | 0.261792i | \(0.915687\pi\) | |||||||
\(192\) | 0.618034 | − | 1.61803i | 0.0446028 | − | 0.116772i | ||||
\(193\) | − | 6.00000i | − | 0.431889i | −0.976406 | − | 0.215945i | \(-0.930717\pi\) | ||
0.976406 | − | 0.215945i | \(-0.0692831\pi\) | |||||||
\(194\) | 0.763932 | 0.0548471 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.70820 | − | 2.00000i | −0.479157 | − | 0.142857i | ||||
\(197\) | 3.52786 | 0.251350 | 0.125675 | − | 0.992071i | \(-0.459890\pi\) | ||||
0.125675 | + | 0.992071i | \(0.459890\pi\) | |||||||
\(198\) | 8.94427 | − | 10.0000i | 0.635642 | − | 0.710669i | ||||
\(199\) | 22.1803i | 1.57232i | 0.618021 | + | 0.786161i | \(0.287935\pi\) | ||||
−0.618021 | + | 0.786161i | \(0.712065\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.4164 | + | 7.41641i | 1.36953 | + | 0.523113i | ||||
\(202\) | −12.4721 | −0.877536 | ||||||||
\(203\) | 20.1803 | + | 2.94427i | 1.41638 | + | 0.206647i | ||||
\(204\) | −8.47214 | − | 3.23607i | −0.593168 | − | 0.226570i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.6525 | 1.02089 | ||||||||
\(207\) | −8.94427 | − | 8.00000i | −0.621670 | − | 0.556038i | ||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | 37.8885 | 2.62081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | −0.472136 | −0.0324264 | ||||||||
\(213\) | −11.7082 | − | 4.47214i | −0.802233 | − | 0.306426i | ||||
\(214\) | 11.4164 | 0.780410 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.61803 | + | 2.38197i | −0.314217 | + | 0.162072i | ||||
\(217\) | −7.23607 | − | 1.05573i | −0.491216 | − | 0.0716675i | ||||
\(218\) | −4.47214 | −0.302891 | ||||||||
\(219\) | 6.94427 | − | 18.1803i | 0.469250 | − | 1.22851i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.47214i | − | 0.435363i | ||||||
\(222\) | −1.23607 | − | 0.472136i | −0.0829595 | − | 0.0316877i | ||||
\(223\) | −17.7082 | −1.18583 | −0.592915 | − | 0.805265i | \(-0.702023\pi\) | ||||
−0.592915 | + | 0.805265i | \(0.702023\pi\) | |||||||
\(224\) | 0.381966 | − | 2.61803i | 0.0255212 | − | 0.174925i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.94427 | 0.195850 | ||||||||
\(227\) | − | 0.763932i | − | 0.0507039i | −0.999679 | − | 0.0253520i | \(-0.991929\pi\) | ||
0.999679 | − | 0.0253520i | \(-0.00807065\pi\) | |||||||
\(228\) | −13.7082 | − | 5.23607i | −0.907848 | − | 0.346767i | ||||
\(229\) | 8.76393i | 0.579137i | 0.957157 | + | 0.289568i | \(0.0935118\pi\) | ||||
−0.957157 | + | 0.289568i | \(0.906488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.0000 | − | 17.8885i | 0.657952 | − | 1.17698i | ||||
\(232\) | 7.70820i | 0.506068i | ||||||||
\(233\) | −11.5279 | −0.755215 | −0.377608 | − | 0.925966i | \(-0.623253\pi\) | ||||
−0.377608 | + | 0.925966i | \(0.623253\pi\) | |||||||
\(234\) | −2.76393 | − | 2.47214i | −0.180684 | − | 0.161609i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.47214 | −0.291111 | ||||||||
\(237\) | 5.52786 | − | 14.4721i | 0.359073 | − | 0.940066i | ||||
\(238\) | −13.7082 | − | 2.00000i | −0.888571 | − | 0.129641i | ||||
\(239\) | − | 0.180340i | − | 0.0116652i | −0.999983 | − | 0.00583261i | \(-0.998143\pi\) | ||
0.999983 | − | 0.00583261i | \(-0.00185659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.8885i | 1.15230i | 0.817343 | + | 0.576151i | \(0.195446\pi\) | ||||
−0.817343 | + | 0.576151i | \(0.804554\pi\) | |||||||
\(242\) | −9.00000 | −0.578542 | ||||||||
\(243\) | 15.0902 | + | 3.90983i | 0.968035 | + | 0.250816i | ||||
\(244\) | 7.23607i | 0.463242i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.52786 | + | 4.00000i | −0.0974131 | + | 0.255031i | ||||
\(247\) | − | 10.4721i | − | 0.666326i | ||||||
\(248\) | − | 2.76393i | − | 0.175510i | ||||||
\(249\) | 23.7082 | + | 9.05573i | 1.50245 | + | 0.573883i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.4721 | −0.787234 | −0.393617 | − | 0.919274i | \(-0.628776\pi\) | ||||
−0.393617 | + | 0.919274i | \(0.628776\pi\) | |||||||
\(252\) | −6.09017 | + | 5.09017i | −0.383645 | + | 0.320651i | ||||
\(253\) | 17.8885i | 1.12464i | ||||||||
\(254\) | 0.291796i | 0.0183089i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.1803i | − | 0.884545i | −0.896881 | − | 0.442273i | \(-0.854172\pi\) | ||
0.896881 | − | 0.442273i | \(-0.145828\pi\) | |||||||
\(258\) | −8.00000 | − | 3.05573i | −0.498058 | − | 0.190241i | ||||
\(259\) | −2.00000 | − | 0.291796i | −0.124274 | − | 0.0181313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4164 | − | 17.2361i | 0.954252 | − | 1.06689i | ||||
\(262\) | 5.41641 | 0.334627 | ||||||||
\(263\) | 12.9443 | 0.798178 | 0.399089 | − | 0.916912i | \(-0.369326\pi\) | ||||
0.399089 | + | 0.916912i | \(0.369326\pi\) | |||||||
\(264\) | 7.23607 | + | 2.76393i | 0.445349 | + | 0.170108i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −22.1803 | − | 3.23607i | −1.35996 | − | 0.198416i | ||||
\(267\) | 3.41641 | − | 8.94427i | 0.209081 | − | 0.547381i | ||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | −4.47214 | −0.272671 | −0.136335 | − | 0.990663i | \(-0.543533\pi\) | ||||
−0.136335 | + | 0.990663i | \(0.543533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.7082i | 1.92614i | 0.269258 | + | 0.963068i | \(0.413222\pi\) | ||||
−0.269258 | + | 0.963068i | \(0.586778\pi\) | |||||||
\(272\) | − | 5.23607i | − | 0.317483i | ||||||
\(273\) | −4.94427 | − | 2.76393i | −0.299241 | − | 0.167281i | ||||
\(274\) | 3.52786 | 0.213126 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.47214 | − | 6.47214i | 0.148805 | − | 0.389577i | ||||
\(277\) | 17.1246i | 1.02892i | 0.857515 | + | 0.514459i | \(0.172007\pi\) | ||||
−0.857515 | + | 0.514459i | \(0.827993\pi\) | |||||||
\(278\) | 11.5279i | 0.691395i | ||||||||
\(279\) | −5.52786 | + | 6.18034i | −0.330945 | + | 0.370007i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | 10.4721 | + | 4.00000i | 0.623607 | + | 0.238197i | ||||
\(283\) | −13.2361 | −0.786803 | −0.393401 | − | 0.919367i | \(-0.628702\pi\) | ||||
−0.393401 | + | 0.919367i | \(0.628702\pi\) | |||||||
\(284\) | − | 7.23607i | − | 0.429382i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.52786i | 0.326869i | ||||||||
\(287\) | −0.944272 | + | 6.47214i | −0.0557386 | + | 0.382038i | ||||
\(288\) | −2.23607 | − | 2.00000i | −0.131762 | − | 0.117851i | ||||
\(289\) | −10.4164 | −0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.472136 | − | 1.23607i | 0.0276771 | − | 0.0724596i | ||||
\(292\) | 11.2361 | 0.657541 | ||||||||
\(293\) | − | 2.58359i | − | 0.150935i | −0.997148 | − | 0.0754675i | \(-0.975955\pi\) | ||
0.997148 | − | 0.0754675i | \(-0.0240449\pi\) | |||||||
\(294\) | −7.38197 | + | 9.61803i | −0.430525 | + | 0.560935i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 0.763932i | − | 0.0444026i | ||||||
\(297\) | −10.6525 | − | 20.6525i | −0.618119 | − | 1.19838i | ||||
\(298\) | 4.29180i | 0.248617i | ||||||||
\(299\) | 4.94427 | 0.285935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9443 | − | 1.88854i | −0.746095 | − | 0.108854i | ||||
\(302\) | 20.9443 | 1.20521 | ||||||||
\(303\) | −7.70820 | + | 20.1803i | −0.442825 | + | 1.15933i | ||||
\(304\) | − | 8.47214i | − | 0.485910i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.4721 | + | 11.7082i | −0.598652 | + | 0.669313i | ||||
\(307\) | −18.1803 | −1.03761 | −0.518803 | − | 0.854894i | \(-0.673622\pi\) | ||||
−0.518803 | + | 0.854894i | \(0.673622\pi\) | |||||||
\(308\) | 11.7082 | + | 1.70820i | 0.667137 | + | 0.0973340i | ||||
\(309\) | 9.05573 | − | 23.7082i | 0.515162 | − | 1.34871i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.5279 | 0.993914 | 0.496957 | − | 0.867775i | \(-0.334451\pi\) | ||||
0.496957 | + | 0.867775i | \(0.334451\pi\) | |||||||
\(312\) | 0.763932 | − | 2.00000i | 0.0432491 | − | 0.113228i | ||||
\(313\) | 5.70820 | 0.322647 | 0.161323 | − | 0.986902i | \(-0.448424\pi\) | ||||
0.161323 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(314\) | −9.23607 | −0.521221 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.94427 | 0.503155 | ||||||||
\(317\) | −10.9443 | −0.614692 | −0.307346 | − | 0.951598i | \(-0.599441\pi\) | ||||
−0.307346 | + | 0.951598i | \(0.599441\pi\) | |||||||
\(318\) | −0.291796 | + | 0.763932i | −0.0163631 | + | 0.0428392i | ||||
\(319\) | −34.4721 | −1.93007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.05573 | − | 18.4721i | 0.393812 | − | 1.03101i | ||||
\(322\) | 1.52786 | − | 10.4721i | 0.0851445 | − | 0.583589i | ||||
\(323\) | −44.3607 | −2.46829 | ||||||||
\(324\) | 1.00000 | + | 8.94427i | 0.0555556 | + | 0.496904i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 10.4721i | − | 0.579998i | ||||||
\(327\) | −2.76393 | + | 7.23607i | −0.152846 | + | 0.400155i | ||||
\(328\) | −2.47214 | −0.136501 | ||||||||
\(329\) | 16.9443 | + | 2.47214i | 0.934168 | + | 0.136293i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.05573 | 0.167958 | 0.0839790 | − | 0.996468i | \(-0.473237\pi\) | ||||
0.0839790 | + | 0.996468i | \(0.473237\pi\) | |||||||
\(332\) | 14.6525i | 0.804159i | ||||||||
\(333\) | −1.52786 | + | 1.70820i | −0.0837264 | + | 0.0936090i | ||||
\(334\) | 0.944272i | 0.0516683i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00000 | − | 2.23607i | −0.218218 | − | 0.121988i | ||||
\(337\) | − | 21.4164i | − | 1.16663i | −0.812247 | − | 0.583313i | \(-0.801756\pi\) | ||
0.812247 | − | 0.583313i | \(-0.198244\pi\) | |||||||
\(338\) | −11.4721 | −0.624002 | ||||||||
\(339\) | 1.81966 | − | 4.76393i | 0.0988304 | − | 0.258741i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3607 | 0.669368 | ||||||||
\(342\) | −16.9443 | + | 18.9443i | −0.916241 | + | 1.02439i | ||||
\(343\) | −7.79837 | + | 16.7984i | −0.421073 | + | 0.907027i | ||||
\(344\) | − | 4.94427i | − | 0.266577i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 9.41641i | − | 0.506229i | ||||||
\(347\) | 2.47214 | 0.132711 | 0.0663556 | − | 0.997796i | \(-0.478863\pi\) | ||||
0.0663556 | + | 0.997796i | \(0.478863\pi\) | |||||||
\(348\) | 12.4721 | + | 4.76393i | 0.668577 | + | 0.255374i | ||||
\(349\) | − | 20.1803i | − | 1.08023i | −0.841592 | − | 0.540114i | \(-0.818381\pi\) | ||
0.841592 | − | 0.540114i | \(-0.181619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.70820 | + | 2.94427i | −0.304681 | + | 0.157154i | ||||
\(352\) | 4.47214i | 0.238366i | ||||||||
\(353\) | − | 27.7082i | − | 1.47476i | −0.675479 | − | 0.737379i | \(-0.736063\pi\) | ||
0.675479 | − | 0.737379i | \(-0.263937\pi\) | |||||||
\(354\) | −2.76393 | + | 7.23607i | −0.146901 | + | 0.384593i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.52786 | 0.292976 | ||||||||
\(357\) | −11.7082 | + | 20.9443i | −0.619664 | + | 1.10849i | ||||
\(358\) | 14.9443i | 0.789829i | ||||||||
\(359\) | 12.1803i | 0.642854i | 0.946934 | + | 0.321427i | \(0.104162\pi\) | ||||
−0.946934 | + | 0.321427i | \(0.895838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −52.7771 | −2.77774 | ||||||||
\(362\) | − | 16.1803i | − | 0.850420i | ||||||
\(363\) | −5.56231 | + | 14.5623i | −0.291945 | + | 0.764323i | ||||
\(364\) | 0.472136 | − | 3.23607i | 0.0247466 | − | 0.169616i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.7082 | + | 4.47214i | 0.611998 | + | 0.233762i | ||||
\(367\) | −8.18034 | −0.427010 | −0.213505 | − | 0.976942i | \(-0.568488\pi\) | ||||
−0.213505 | + | 0.976942i | \(0.568488\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 5.52786 | + | 4.94427i | 0.287769 | + | 0.257389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.180340 | + | 1.23607i | −0.00936278 | + | 0.0641735i | ||||
\(372\) | −4.47214 | − | 1.70820i | −0.231869 | − | 0.0885662i | ||||
\(373\) | − | 32.1803i | − | 1.66623i | −0.553096 | − | 0.833117i | \(-0.686554\pi\) | ||
0.553096 | − | 0.833117i | \(-0.313446\pi\) | |||||||
\(374\) | 23.4164 | 1.21083 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.47214i | 0.333775i | ||||||||
\(377\) | 9.52786i | 0.490710i | ||||||||
\(378\) | 4.47214 | + | 13.0000i | 0.230022 | + | 0.668648i | ||||
\(379\) | 17.8885 | 0.918873 | 0.459436 | − | 0.888211i | \(-0.348051\pi\) | ||||
0.459436 | + | 0.888211i | \(0.348051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.472136 | + | 0.180340i | 0.0241883 | + | 0.00923909i | ||||
\(382\) | 7.23607i | 0.370229i | ||||||||
\(383\) | − | 13.8885i | − | 0.709671i | −0.934929 | − | 0.354836i | \(-0.884537\pi\) | ||
0.934929 | − | 0.354836i | \(-0.115463\pi\) | |||||||
\(384\) | 0.618034 | − | 1.61803i | 0.0315389 | − | 0.0825700i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.00000i | − | 0.305392i | ||||||
\(387\) | −9.88854 | + | 11.0557i | −0.502663 | + | 0.561994i | ||||
\(388\) | 0.763932 | 0.0387828 | ||||||||
\(389\) | − | 30.1803i | − | 1.53020i | −0.643909 | − | 0.765102i | \(-0.722689\pi\) | ||
0.643909 | − | 0.765102i | \(-0.277311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.9443i | − | 1.05920i | ||||||
\(392\) | −6.70820 | − | 2.00000i | −0.338815 | − | 0.101015i | ||||
\(393\) | 3.34752 | − | 8.76393i | 0.168860 | − | 0.442082i | ||||
\(394\) | 3.52786 | 0.177731 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.94427 | − | 10.0000i | 0.449467 | − | 0.502519i | ||||
\(397\) | 23.1246 | 1.16059 | 0.580295 | − | 0.814406i | \(-0.302937\pi\) | ||||
0.580295 | + | 0.814406i | \(0.302937\pi\) | |||||||
\(398\) | 22.1803i | 1.11180i | ||||||||
\(399\) | −18.9443 | + | 33.8885i | −0.948400 | + | 1.69655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4721i | 0.722704i | 0.932429 | + | 0.361352i | \(0.117685\pi\) | ||||
−0.932429 | + | 0.361352i | \(0.882315\pi\) | |||||||
\(402\) | 19.4164 | + | 7.41641i | 0.968402 | + | 0.369897i | ||||
\(403\) | − | 3.41641i | − | 0.170183i | ||||||
\(404\) | −12.4721 | −0.620512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.1803 | + | 2.94427i | 1.00153 | + | 0.146122i | ||||
\(407\) | 3.41641 | 0.169345 | ||||||||
\(408\) | −8.47214 | − | 3.23607i | −0.419433 | − | 0.160209i | ||||
\(409\) | − | 7.41641i | − | 0.366718i | −0.983046 | − | 0.183359i | \(-0.941303\pi\) | ||
0.983046 | − | 0.183359i | \(-0.0586970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.18034 | − | 5.70820i | 0.107548 | − | 0.281565i | ||||
\(412\) | 14.6525 | 0.721876 | ||||||||
\(413\) | −1.70820 | + | 11.7082i | −0.0840552 | + | 0.576123i | ||||
\(414\) | −8.94427 | − | 8.00000i | −0.439587 | − | 0.393179i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.23607 | 0.0606032 | ||||||||
\(417\) | 18.6525 | + | 7.12461i | 0.913416 | + | 0.348894i | ||||
\(418\) | 37.8885 | 1.85319 | ||||||||
\(419\) | −36.8328 | −1.79940 | −0.899700 | − | 0.436508i | \(-0.856215\pi\) | ||||
−0.899700 | + | 0.436508i | \(0.856215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.52786 | −0.171938 | −0.0859688 | − | 0.996298i | \(-0.527399\pi\) | ||||
−0.0859688 | + | 0.996298i | \(0.527399\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 12.9443 | − | 14.4721i | 0.629372 | − | 0.703659i | ||||
\(424\) | −0.472136 | −0.0229289 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −11.7082 | − | 4.47214i | −0.567264 | − | 0.216676i | ||||
\(427\) | 18.9443 | + | 2.76393i | 0.916778 | + | 0.133756i | ||||
\(428\) | 11.4164 | 0.551833 | ||||||||
\(429\) | 8.94427 | + | 3.41641i | 0.431834 | + | 0.164946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.5967i | − | 1.90731i | −0.300905 | − | 0.953654i | \(-0.597289\pi\) | ||
0.300905 | − | 0.953654i | \(-0.402711\pi\) | |||||||
\(432\) | −4.61803 | + | 2.38197i | −0.222185 | + | 0.114602i | ||||
\(433\) | −26.6525 | −1.28084 | −0.640418 | − | 0.768026i | \(-0.721239\pi\) | ||||
−0.640418 | + | 0.768026i | \(0.721239\pi\) | |||||||
\(434\) | −7.23607 | − | 1.05573i | −0.347342 | − | 0.0506766i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.47214 | −0.214176 | ||||||||
\(437\) | − | 33.8885i | − | 1.62111i | ||||||
\(438\) | 6.94427 | − | 18.1803i | 0.331810 | − | 0.868690i | ||||
\(439\) | − | 10.1803i | − | 0.485881i | −0.970041 | − | 0.242941i | \(-0.921888\pi\) | ||
0.970041 | − | 0.242941i | \(-0.0781120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0000 | + | 17.8885i | 0.523810 | + | 0.851835i | ||||
\(442\) | − | 6.47214i | − | 0.307848i | ||||||
\(443\) | 18.4721 | 0.877638 | 0.438819 | − | 0.898576i | \(-0.355397\pi\) | ||||
0.438819 | + | 0.898576i | \(0.355397\pi\) | |||||||
\(444\) | −1.23607 | − | 0.472136i | −0.0586612 | − | 0.0224066i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.7082 | −0.838508 | ||||||||
\(447\) | 6.94427 | + | 2.65248i | 0.328453 | + | 0.125458i | ||||
\(448\) | 0.381966 | − | 2.61803i | 0.0180462 | − | 0.123690i | ||||
\(449\) | 10.4721i | 0.494211i | 0.968989 | + | 0.247105i | \(0.0794794\pi\) | ||||
−0.968989 | + | 0.247105i | \(0.920521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 11.0557i | − | 0.520594i | ||||||
\(452\) | 2.94427 | 0.138487 | ||||||||
\(453\) | 12.9443 | − | 33.8885i | 0.608175 | − | 1.59222i | ||||
\(454\) | − | 0.763932i | − | 0.0358531i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.7082 | − | 5.23607i | −0.641945 | − | 0.245201i | ||||
\(457\) | − | 26.9443i | − | 1.26040i | −0.776433 | − | 0.630200i | \(-0.782973\pi\) | ||
0.776433 | − | 0.630200i | \(-0.217027\pi\) | |||||||
\(458\) | 8.76393i | 0.409512i | ||||||||
\(459\) | 12.4721 | + | 24.1803i | 0.582149 | + | 1.12864i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.94427 | −0.323427 | −0.161713 | − | 0.986838i | \(-0.551702\pi\) | ||||
−0.161713 | + | 0.986838i | \(0.551702\pi\) | |||||||
\(462\) | 10.0000 | − | 17.8885i | 0.465242 | − | 0.832250i | ||||
\(463\) | − | 22.1803i | − | 1.03081i | −0.856947 | − | 0.515404i | \(-0.827642\pi\) | ||
0.856947 | − | 0.515404i | \(-0.172358\pi\) | |||||||
\(464\) | 7.70820i | 0.357844i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.5279 | −0.534018 | ||||||||
\(467\) | 33.7082i | 1.55983i | 0.625886 | + | 0.779915i | \(0.284738\pi\) | ||||
−0.625886 | + | 0.779915i | \(0.715262\pi\) | |||||||
\(468\) | −2.76393 | − | 2.47214i | −0.127763 | − | 0.114275i | ||||
\(469\) | 31.4164 | + | 4.58359i | 1.45067 | + | 0.211651i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.70820 | + | 14.9443i | −0.263020 | + | 0.688596i | ||||
\(472\) | −4.47214 | −0.205847 | ||||||||
\(473\) | 22.1115 | 1.01669 | ||||||||
\(474\) | 5.52786 | − | 14.4721i | 0.253903 | − | 0.664727i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.7082 | − | 2.00000i | −0.628314 | − | 0.0916698i | ||||
\(477\) | 1.05573 | + | 0.944272i | 0.0483385 | + | 0.0432352i | ||||
\(478\) | − | 0.180340i | − | 0.00824855i | ||||||
\(479\) | −37.8885 | −1.73117 | −0.865586 | − | 0.500761i | \(-0.833054\pi\) | ||||
−0.865586 | + | 0.500761i | \(0.833054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.944272i | − | 0.0430551i | ||||||
\(482\) | 17.8885i | 0.814801i | ||||||||
\(483\) | −16.0000 | − | 8.94427i | −0.728025 | − | 0.406978i | ||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.0902 | + | 3.90983i | 0.684504 | + | 0.177353i | ||||
\(487\) | − | 17.5967i | − | 0.797385i | −0.917085 | − | 0.398692i | \(-0.869464\pi\) | ||
0.917085 | − | 0.398692i | \(-0.130536\pi\) | |||||||
\(488\) | 7.23607i | 0.327561i | ||||||||
\(489\) | −16.9443 | − | 6.47214i | −0.766246 | − | 0.292680i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4164i | 0.605474i | 0.953074 | + | 0.302737i | \(0.0979004\pi\) | ||||
−0.953074 | + | 0.302737i | \(0.902100\pi\) | |||||||
\(492\) | −1.52786 | + | 4.00000i | −0.0688814 | + | 0.180334i | ||||
\(493\) | 40.3607 | 1.81775 | ||||||||
\(494\) | − | 10.4721i | − | 0.471164i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.76393i | − | 0.124104i | ||||||
\(497\) | −18.9443 | − | 2.76393i | −0.849767 | − | 0.123979i | ||||
\(498\) | 23.7082 | + | 9.05573i | 1.06239 | + | 0.405797i | ||||
\(499\) | −17.8885 | −0.800801 | −0.400401 | − | 0.916340i | \(-0.631129\pi\) | ||||
−0.400401 | + | 0.916340i | \(0.631129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52786 | + | 0.583592i | 0.0682599 | + | 0.0260730i | ||||
\(502\) | −12.4721 | −0.556659 | ||||||||
\(503\) | − | 28.3607i | − | 1.26454i | −0.774748 | − | 0.632270i | \(-0.782123\pi\) | ||
0.774748 | − | 0.632270i | \(-0.217877\pi\) | |||||||
\(504\) | −6.09017 | + | 5.09017i | −0.271278 | + | 0.226734i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.8885i | 0.795243i | ||||||||
\(507\) | −7.09017 | + | 18.5623i | −0.314886 | + | 0.824381i | ||||
\(508\) | 0.291796i | 0.0129464i | ||||||||
\(509\) | −15.5279 | −0.688260 | −0.344130 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344130 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.29180 | − | 29.4164i | 0.189858 | − | 1.30131i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 20.1803 | + | 39.1246i | 0.890984 | + | 1.72739i | ||||
\(514\) | − | 14.1803i | − | 0.625468i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.00000 | − | 3.05573i | −0.352180 | − | 0.134521i | ||||
\(517\) | −28.9443 | −1.27297 | ||||||||
\(518\) | −2.00000 | − | 0.291796i | −0.0878750 | − | 0.0128208i | ||||
\(519\) | −15.2361 | − | 5.81966i | −0.668789 | − | 0.255455i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.9443 | −1.61856 | −0.809279 | − | 0.587425i | \(-0.800142\pi\) | ||||
−0.809279 | + | 0.587425i | \(0.800142\pi\) | |||||||
\(522\) | 15.4164 | − | 17.2361i | 0.674758 | − | 0.754402i | ||||
\(523\) | 42.5410 | 1.86019 | 0.930094 | − | 0.367320i | \(-0.119725\pi\) | ||||
0.930094 | + | 0.367320i | \(0.119725\pi\) | |||||||
\(524\) | 5.41641 | 0.236617 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.9443 | 0.564397 | ||||||||
\(527\) | −14.4721 | −0.630416 | ||||||||
\(528\) | 7.23607 | + | 2.76393i | 0.314909 | + | 0.120285i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | + | 8.94427i | 0.433963 | + | 0.388148i | ||||
\(532\) | −22.1803 | − | 3.23607i | −0.961640 | − | 0.140301i | ||||
\(533\) | −3.05573 | −0.132358 | ||||||||
\(534\) | 3.41641 | − | 8.94427i | 0.147842 | − | 0.387056i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0000i | 0.518321i | ||||||||
\(537\) | 24.1803 | + | 9.23607i | 1.04346 | + | 0.398566i | ||||
\(538\) | −4.47214 | −0.192807 | ||||||||
\(539\) | 8.94427 | − | 30.0000i | 0.385257 | − | 1.29219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.9443 | 1.33040 | 0.665199 | − | 0.746666i | \(-0.268347\pi\) | ||||
0.665199 | + | 0.746666i | \(0.268347\pi\) | |||||||
\(542\) | 31.7082i | 1.36198i | ||||||||
\(543\) | −26.1803 | − | 10.0000i | −1.12351 | − | 0.429141i | ||||
\(544\) | − | 5.23607i | − | 0.224495i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.94427 | − | 2.76393i | −0.211595 | − | 0.118285i | ||||
\(547\) | 35.4164i | 1.51430i | 0.653243 | + | 0.757148i | \(0.273408\pi\) | ||||
−0.653243 | + | 0.757148i | \(0.726592\pi\) | |||||||
\(548\) | 3.52786 | 0.150703 | ||||||||
\(549\) | 14.4721 | − | 16.1803i | 0.617656 | − | 0.690560i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.3050 | 2.78208 | ||||||||
\(552\) | 2.47214 | − | 6.47214i | 0.105221 | − | 0.275472i | ||||
\(553\) | 3.41641 | − | 23.4164i | 0.145280 | − | 0.995767i | ||||
\(554\) | 17.1246i | 0.727555i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.5279i | 0.488890i | ||||||||
\(557\) | −7.52786 | −0.318966 | −0.159483 | − | 0.987201i | \(-0.550983\pi\) | ||||
−0.159483 | + | 0.987201i | \(0.550983\pi\) | |||||||
\(558\) | −5.52786 | + | 6.18034i | −0.234013 | + | 0.261635i | ||||
\(559\) | − | 6.11146i | − | 0.258487i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4721 | − | 37.8885i | 0.611014 | − | 1.59966i | ||||
\(562\) | 20.0000i | 0.843649i | ||||||||
\(563\) | 40.1803i | 1.69340i | 0.532071 | + | 0.846700i | \(0.321414\pi\) | ||||
−0.532071 | + | 0.846700i | \(0.678586\pi\) | |||||||
\(564\) | 10.4721 | + | 4.00000i | 0.440956 | + | 0.168430i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.2361 | −0.556353 | ||||||||
\(567\) | 23.7984 | + | 0.798374i | 0.999438 | + | 0.0335286i | ||||
\(568\) | − | 7.23607i | − | 0.303619i | ||||||
\(569\) | − | 9.52786i | − | 0.399429i | −0.979854 | − | 0.199714i | \(-0.935999\pi\) | ||
0.979854 | − | 0.199714i | \(-0.0640014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.8328 | 0.788129 | 0.394064 | − | 0.919083i | \(-0.371069\pi\) | ||||
0.394064 | + | 0.919083i | \(0.371069\pi\) | |||||||
\(572\) | 5.52786i | 0.231132i | ||||||||
\(573\) | 11.7082 | + | 4.47214i | 0.489117 | + | 0.186826i | ||||
\(574\) | −0.944272 | + | 6.47214i | −0.0394131 | + | 0.270142i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.23607 | − | 2.00000i | −0.0931695 | − | 0.0833333i | ||||
\(577\) | −8.18034 | −0.340552 | −0.170276 | − | 0.985396i | \(-0.554466\pi\) | ||||
−0.170276 | + | 0.985396i | \(0.554466\pi\) | |||||||
\(578\) | −10.4164 | −0.433265 | ||||||||
\(579\) | −9.70820 | − | 3.70820i | −0.403459 | − | 0.154108i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.3607 | + | 5.59675i | 1.59147 | + | 0.232192i | ||||
\(582\) | 0.472136 | − | 1.23607i | 0.0195707 | − | 0.0512367i | ||||
\(583\) | − | 2.11146i | − | 0.0874476i | ||||||
\(584\) | 11.2361 | 0.464952 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 2.58359i | − | 0.106727i | ||||||
\(587\) | 10.2918i | 0.424788i | 0.977184 | + | 0.212394i | \(0.0681260\pi\) | ||||
−0.977184 | + | 0.212394i | \(0.931874\pi\) | |||||||
\(588\) | −7.38197 | + | 9.61803i | −0.304427 | + | 0.396641i | ||||
\(589\) | −23.4164 | −0.964856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.18034 | − | 5.70820i | 0.0896872 | − | 0.234804i | ||||
\(592\) | − | 0.763932i | − | 0.0313974i | ||||||
\(593\) | − | 29.0132i | − | 1.19143i | −0.803197 | − | 0.595714i | \(-0.796869\pi\) | ||
0.803197 | − | 0.595714i | \(-0.203131\pi\) | |||||||
\(594\) | −10.6525 | − | 20.6525i | −0.437076 | − | 0.847381i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.29180i | 0.175799i | ||||||||
\(597\) | 35.8885 | + | 13.7082i | 1.46882 | + | 0.561039i | ||||
\(598\) | 4.94427 | 0.202186 | ||||||||
\(599\) | − | 36.7639i | − | 1.50213i | −0.660226 | − | 0.751067i | \(-0.729540\pi\) | ||
0.660226 | − | 0.751067i | \(-0.270460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.52786i | 0.225486i | 0.993624 | + | 0.112743i | \(0.0359637\pi\) | ||||
−0.993624 | + | 0.112743i | \(0.964036\pi\) | |||||||
\(602\) | −12.9443 | − | 1.88854i | −0.527569 | − | 0.0769713i | ||||
\(603\) | 24.0000 | − | 26.8328i | 0.977356 | − | 1.09272i | ||||
\(604\) | 20.9443 | 0.852210 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.70820 | + | 20.1803i | −0.313124 | + | 0.819770i | ||||
\(607\) | −19.2361 | −0.780768 | −0.390384 | − | 0.920652i | \(-0.627658\pi\) | ||||
−0.390384 | + | 0.920652i | \(0.627658\pi\) | |||||||
\(608\) | − | 8.47214i | − | 0.343590i | ||||||
\(609\) | 17.2361 | − | 30.8328i | 0.698441 | − | 1.24941i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000i | 0.323645i | ||||||||
\(612\) | −10.4721 | + | 11.7082i | −0.423311 | + | 0.473276i | ||||
\(613\) | 38.0689i | 1.53759i | 0.639497 | + | 0.768794i | \(0.279143\pi\) | ||||
−0.639497 | + | 0.768794i | \(0.720857\pi\) | |||||||
\(614\) | −18.1803 | −0.733699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.7082 | + | 1.70820i | 0.471737 | + | 0.0688255i | ||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 9.05573 | − | 23.7082i | 0.364275 | − | 0.953684i | ||||
\(619\) | − | 14.0000i | − | 0.562708i | −0.959604 | − | 0.281354i | \(-0.909217\pi\) | ||
0.959604 | − | 0.281354i | \(-0.0907834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4721 | + | 9.52786i | −0.741261 | + | 0.382340i | ||||
\(622\) | 17.5279 | 0.702803 | ||||||||
\(623\) | 2.11146 | − | 14.4721i | 0.0845937 | − | 0.579814i | ||||
\(624\) | 0.763932 | − | 2.00000i | 0.0305818 | − | 0.0800641i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.70820 | 0.228146 | ||||||||
\(627\) | 23.4164 | − | 61.3050i | 0.935161 | − | 2.44828i | ||||
\(628\) | −9.23607 | −0.368559 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.88854 | −0.234419 | −0.117210 | − | 0.993107i | \(-0.537395\pi\) | ||||
−0.117210 | + | 0.993107i | \(0.537395\pi\) | |||||||
\(632\) | 8.94427 | 0.355784 | ||||||||
\(633\) | −4.94427 | + | 12.9443i | −0.196517 | + | 0.514489i | ||||
\(634\) | −10.9443 | −0.434653 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.291796 | + | 0.763932i | −0.0115705 | + | 0.0302919i | ||||
\(637\) | −8.29180 | − | 2.47214i | −0.328533 | − | 0.0979496i | ||||
\(638\) | −34.4721 | −1.36476 | ||||||||
\(639\) | −14.4721 | + | 16.1803i | −0.572509 | + | 0.640084i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.4164i | 0.924893i | 0.886647 | + | 0.462446i | \(0.153028\pi\) | ||||
−0.886647 | + | 0.462446i | \(0.846972\pi\) | |||||||
\(642\) | 7.05573 | − | 18.4721i | 0.278467 | − | 0.729037i | ||||
\(643\) | 12.2918 | 0.484741 | 0.242371 | − | 0.970184i | \(-0.422075\pi\) | ||||
0.242371 | + | 0.970184i | \(0.422075\pi\) | |||||||
\(644\) | 1.52786 | − | 10.4721i | 0.0602063 | − | 0.412660i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.3607 | −1.74535 | ||||||||
\(647\) | − | 34.8328i | − | 1.36942i | −0.728816 | − | 0.684710i | \(-0.759929\pi\) | ||
0.728816 | − | 0.684710i | \(-0.240071\pi\) | |||||||
\(648\) | 1.00000 | + | 8.94427i | 0.0392837 | + | 0.351364i | ||||
\(649\) | − | 20.0000i | − | 0.785069i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.18034 | + | 11.0557i | −0.242227 | + | 0.433308i | ||||
\(652\) | − | 10.4721i | − | 0.410120i | ||||||
\(653\) | −23.8885 | −0.934831 | −0.467415 | − | 0.884038i | \(-0.654815\pi\) | ||||
−0.467415 | + | 0.884038i | \(0.654815\pi\) | |||||||
\(654\) | −2.76393 | + | 7.23607i | −0.108078 | + | 0.282953i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.47214 | −0.0965207 | ||||||||
\(657\) | −25.1246 | − | 22.4721i | −0.980204 | − | 0.876722i | ||||
\(658\) | 16.9443 | + | 2.47214i | 0.660556 | + | 0.0963739i | ||||
\(659\) | 31.5279i | 1.22815i | 0.789247 | + | 0.614076i | \(0.210471\pi\) | ||||
−0.789247 | + | 0.614076i | \(0.789529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.2918i | 0.711468i | 0.934587 | + | 0.355734i | \(0.115769\pi\) | ||||
−0.934587 | + | 0.355734i | \(0.884231\pi\) | |||||||
\(662\) | 3.05573 | 0.118764 | ||||||||
\(663\) | −10.4721 | − | 4.00000i | −0.406704 | − | 0.155347i | ||||
\(664\) | 14.6525i | 0.568626i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.52786 | + | 1.70820i | −0.0592035 | + | 0.0661916i | ||||
\(667\) | 30.8328i | 1.19385i | ||||||||
\(668\) | 0.944272i | 0.0365350i | ||||||||
\(669\) | −10.9443 | + | 28.6525i | −0.423130 | + | 1.10777i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.3607 | −1.24927 | ||||||||
\(672\) | −4.00000 | − | 2.23607i | −0.154303 | − | 0.0862582i | ||||
\(673\) | 19.5279i | 0.752744i | 0.926469 | + | 0.376372i | \(0.122829\pi\) | ||||
−0.926469 | + | 0.376372i | \(0.877171\pi\) | |||||||
\(674\) | − | 21.4164i | − | 0.824929i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.4721 | −0.441236 | ||||||||
\(677\) | − | 18.0000i | − | 0.691796i | −0.938272 | − | 0.345898i | \(-0.887574\pi\) | ||
0.938272 | − | 0.345898i | \(-0.112426\pi\) | |||||||
\(678\) | 1.81966 | − | 4.76393i | 0.0698836 | − | 0.182958i | ||||
\(679\) | 0.291796 | − | 2.00000i | 0.0111981 | − | 0.0767530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23607 | − | 0.472136i | −0.0473662 | − | 0.0180923i | ||||
\(682\) | 12.3607 | 0.473315 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | −16.9443 | + | 18.9443i | −0.647880 | + | 0.724352i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.79837 | + | 16.7984i | −0.297743 | + | 0.641365i | ||||
\(687\) | 14.1803 | + | 5.41641i | 0.541014 | + | 0.206649i | ||||
\(688\) | − | 4.94427i | − | 0.188499i | ||||||
\(689\) | −0.583592 | −0.0222331 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.0557i | − | 0.800998i | −0.916297 | − | 0.400499i | \(-0.868837\pi\) | ||
0.916297 | − | 0.400499i | \(-0.131163\pi\) | |||||||
\(692\) | − | 9.41641i | − | 0.357958i | ||||||
\(693\) | −22.7639 | − | 27.2361i | −0.864730 | − | 1.03461i | ||||
\(694\) | 2.47214 | 0.0938410 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.4721 | + | 4.76393i | 0.472755 | + | 0.180576i | ||||
\(697\) | 12.9443i | 0.490299i | ||||||||
\(698\) | − | 20.1803i | − | 0.763837i | ||||||
\(699\) | −7.12461 | + | 18.6525i | −0.269478 | + | 0.705501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.0689i | − | 1.66446i | −0.554431 | − | 0.832229i | \(-0.687064\pi\) | ||
0.554431 | − | 0.832229i | \(-0.312936\pi\) | |||||||
\(702\) | −5.70820 | + | 2.94427i | −0.215442 | + | 0.111124i | ||||
\(703\) | −6.47214 | −0.244101 | ||||||||
\(704\) | 4.47214i | 0.168550i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 27.7082i | − | 1.04281i | ||||||
\(707\) | −4.76393 | + | 32.6525i | −0.179166 | + | 1.22802i | ||||
\(708\) | −2.76393 | + | 7.23607i | −0.103875 | + | 0.271948i | ||||
\(709\) | 15.5279 | 0.583161 | 0.291581 | − | 0.956546i | \(-0.405819\pi\) | ||||
0.291581 | + | 0.956546i | \(0.405819\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0000 | − | 17.8885i | −0.750059 | − | 0.670873i | ||||
\(712\) | 5.52786 | 0.207165 | ||||||||
\(713\) | − | 11.0557i | − | 0.414040i | ||||||
\(714\) | −11.7082 | + | 20.9443i | −0.438169 | + | 0.783820i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.9443i | 0.558494i | ||||||||
\(717\) | −0.291796 | − | 0.111456i | −0.0108973 | − | 0.00416241i | ||||
\(718\) | 12.1803i | 0.454566i | ||||||||
\(719\) | 34.4721 | 1.28559 | 0.642797 | − | 0.766037i | \(-0.277774\pi\) | ||||
0.642797 | + | 0.766037i | \(0.277774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.59675 | − | 38.3607i | 0.208434 | − | 1.42863i | ||||
\(722\) | −52.7771 | −1.96416 | ||||||||
\(723\) | 28.9443 | + | 11.0557i | 1.07645 | + | 0.411167i | ||||
\(724\) | − | 16.1803i | − | 0.601338i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.56231 | + | 14.5623i | −0.206437 | + | 0.540458i | ||||
\(727\) | 26.2918 | 0.975109 | 0.487554 | − | 0.873093i | \(-0.337889\pi\) | ||||
0.487554 | + | 0.873093i | \(0.337889\pi\) | |||||||
\(728\) | 0.472136 | − | 3.23607i | 0.0174985 | − | 0.119937i | ||||
\(729\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | 11.7082 | + | 4.47214i | 0.432748 | + | 0.165295i | ||||
\(733\) | −20.0689 | −0.741261 | −0.370631 | − | 0.928780i | \(-0.620858\pi\) | ||||
−0.370631 | + | 0.928780i | \(0.620858\pi\) | |||||||
\(734\) | −8.18034 | −0.301942 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | −53.6656 | −1.97680 | ||||||||
\(738\) | 5.52786 | + | 4.94427i | 0.203483 | + | 0.182001i | ||||
\(739\) | −8.94427 | −0.329020 | −0.164510 | − | 0.986375i | \(-0.552604\pi\) | ||||
−0.164510 | + | 0.986375i | \(0.552604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9443 | − | 6.47214i | −0.622463 | − | 0.237760i | ||||
\(742\) | −0.180340 | + | 1.23607i | −0.00662049 | + | 0.0453775i | ||||
\(743\) | −10.4721 | −0.384185 | −0.192093 | − | 0.981377i | \(-0.561527\pi\) | ||||
−0.192093 | + | 0.981377i | \(0.561527\pi\) | |||||||
\(744\) | −4.47214 | − | 1.70820i | −0.163956 | − | 0.0626258i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 32.1803i | − | 1.17821i | ||||||
\(747\) | 29.3050 | − | 32.7639i | 1.07221 | − | 1.19877i | ||||
\(748\) | 23.4164 | 0.856189 | ||||||||
\(749\) | 4.36068 | − | 29.8885i | 0.159336 | − | 1.09210i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.58359 | 0.313220 | 0.156610 | − | 0.987661i | \(-0.449943\pi\) | ||||
0.156610 | + | 0.987661i | \(0.449943\pi\) | |||||||
\(752\) | 6.47214i | 0.236015i | ||||||||
\(753\) | −7.70820 | + | 20.1803i | −0.280903 | + | 0.735412i | ||||
\(754\) | 9.52786i | 0.346984i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.47214 | + | 13.0000i | 0.162650 | + | 0.472805i | ||||
\(757\) | 2.65248i | 0.0964059i | 0.998838 | + | 0.0482029i | \(0.0153494\pi\) | ||||
−0.998838 | + | 0.0482029i | \(0.984651\pi\) | |||||||
\(758\) | 17.8885 | 0.649741 | ||||||||
\(759\) | 28.9443 | + | 11.0557i | 1.05061 | + | 0.401298i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.88854 | −0.213460 | −0.106730 | − | 0.994288i | \(-0.534038\pi\) | ||||
−0.106730 | + | 0.994288i | \(0.534038\pi\) | |||||||
\(762\) | 0.472136 | + | 0.180340i | 0.0171037 | + | 0.00653302i | ||||
\(763\) | −1.70820 | + | 11.7082i | −0.0618411 | + | 0.423865i | ||||
\(764\) | 7.23607i | 0.261792i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 13.8885i | − | 0.501813i | ||||||
\(767\) | −5.52786 | −0.199600 | ||||||||
\(768\) | 0.618034 | − | 1.61803i | 0.0223014 | − | 0.0583858i | ||||
\(769\) | 36.0000i | 1.29819i | 0.760706 | + | 0.649097i | \(0.224853\pi\) | ||||
−0.760706 | + | 0.649097i | \(0.775147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.9443 | − | 8.76393i | −0.826318 | − | 0.315625i | ||||
\(772\) | − | 6.00000i | − | 0.215945i | ||||||
\(773\) | 10.5836i | 0.380665i | 0.981720 | + | 0.190333i | \(0.0609567\pi\) | ||||
−0.981720 | + | 0.190333i | \(0.939043\pi\) | |||||||
\(774\) | −9.88854 | + | 11.0557i | −0.355436 | + | 0.397390i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.763932 | 0.0274236 | ||||||||
\(777\) | −1.70820 | + | 3.05573i | −0.0612815 | + | 0.109624i | ||||
\(778\) | − | 30.1803i | − | 1.08202i | ||||||
\(779\) | 20.9443i | 0.750406i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.3607 | 1.15796 | ||||||||
\(782\) | − | 20.9443i | − | 0.748966i | ||||||
\(783\) | −18.3607 | − | 35.5967i | −0.656157 | − | 1.27212i | ||||
\(784\) | −6.70820 | − | 2.00000i | −0.239579 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.34752 | − | 8.76393i | 0.119402 | − | 0.312599i | ||||
\(787\) | 36.2918 | 1.29366 | 0.646831 | − | 0.762633i | \(-0.276094\pi\) | ||||
0.646831 | + | 0.762633i | \(0.276094\pi\) | |||||||
\(788\) | 3.52786 | 0.125675 | ||||||||
\(789\) | 8.00000 | − | 20.9443i | 0.284808 | − | 0.745636i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.12461 | − | 7.70820i | 0.0399866 | − | 0.274072i | ||||
\(792\) | 8.94427 | − | 10.0000i | 0.317821 | − | 0.355335i | ||||
\(793\) | 8.94427i | 0.317620i | ||||||||
\(794\) | 23.1246 | 0.820662 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.1803i | 0.786161i | ||||||||
\(797\) | − | 21.4164i | − | 0.758608i | −0.925272 | − | 0.379304i | \(-0.876163\pi\) | ||
0.925272 | − | 0.379304i | \(-0.123837\pi\) | |||||||
\(798\) | −18.9443 | + | 33.8885i | −0.670620 | + | 1.19964i | ||||
\(799\) | 33.8885 | 1.19889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.3607 | − | 11.0557i | −0.436743 | − | 0.390635i | ||||
\(802\) | 14.4721i | 0.511029i | ||||||||
\(803\) | 50.2492i | 1.77326i | ||||||||
\(804\) | 19.4164 | + | 7.41641i | 0.684764 | + | 0.261557i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3.41641i | − | 0.120338i | ||||||
\(807\) | −2.76393 | + | 7.23607i | −0.0972950 | + | 0.254722i | ||||
\(808\) | −12.4721 | −0.438768 | ||||||||
\(809\) | − | 36.3607i | − | 1.27837i | −0.769052 | − | 0.639187i | \(-0.779271\pi\) | ||
0.769052 | − | 0.639187i | \(-0.220729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.8328i | 1.29338i | 0.762755 | + | 0.646688i | \(0.223846\pi\) | ||||
−0.762755 | + | 0.646688i | \(0.776154\pi\) | |||||||
\(812\) | 20.1803 | + | 2.94427i | 0.708191 | + | 0.103324i | ||||
\(813\) | 51.3050 | + | 19.5967i | 1.79934 | + | 0.687288i | ||||
\(814\) | 3.41641 | 0.119745 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.47214 | − | 3.23607i | −0.296584 | − | 0.113285i | ||||
\(817\) | −41.8885 | −1.46549 | ||||||||
\(818\) | − | 7.41641i | − | 0.259309i | ||||||
\(819\) | −7.52786 | + | 6.29180i | −0.263045 | + | 0.219853i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 31.7082i | − | 1.10662i | −0.832974 | − | 0.553312i | \(-0.813364\pi\) | ||
0.832974 | − | 0.553312i | \(-0.186636\pi\) | |||||||
\(822\) | 2.18034 | − | 5.70820i | 0.0760481 | − | 0.199096i | ||||
\(823\) | − | 22.1803i | − | 0.773158i | −0.922256 | − | 0.386579i | \(-0.873657\pi\) | ||
0.922256 | − | 0.386579i | \(-0.126343\pi\) | |||||||
\(824\) | 14.6525 | 0.510443 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.70820 | + | 11.7082i | −0.0594360 | + | 0.407381i | ||||
\(827\) | −38.8328 | −1.35035 | −0.675175 | − | 0.737658i | \(-0.735932\pi\) | ||||
−0.675175 | + | 0.737658i | \(0.735932\pi\) | |||||||
\(828\) | −8.94427 | − | 8.00000i | −0.310835 | − | 0.278019i | ||||
\(829\) | − | 7.81966i | − | 0.271588i | −0.990737 | − | 0.135794i | \(-0.956641\pi\) | ||
0.990737 | − | 0.135794i | \(-0.0433585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.7082 | + | 10.5836i | 0.961187 | + | 0.367141i | ||||
\(832\) | 1.23607 | 0.0428529 | ||||||||
\(833\) | −10.4721 | + | 35.1246i | −0.362838 | + | 1.21700i | ||||
\(834\) | 18.6525 | + | 7.12461i | 0.645882 | + | 0.246705i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 37.8885 | 1.31040 | ||||||||
\(837\) | 6.58359 | + | 12.7639i | 0.227562 | + | 0.441186i | ||||
\(838\) | −36.8328 | −1.27237 | ||||||||
\(839\) | −5.52786 | −0.190843 | −0.0954215 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954215 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.4164 | −1.04884 | ||||||||
\(842\) | −3.52786 | −0.121578 | ||||||||
\(843\) | 32.3607 | + | 12.3607i | 1.11456 | + | 0.425724i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.9443 | − | 14.4721i | 0.445033 | − | 0.497562i | ||||
\(847\) | −3.43769 | + | 23.5623i | −0.118121 | + | 0.809610i | ||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | −8.18034 | + | 21.4164i | −0.280749 | + | 0.735009i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.05573i | − | 0.104749i | ||||||
\(852\) | −11.7082 | − | 4.47214i | −0.401116 | − | 0.153213i | ||||
\(853\) | −7.70820 | −0.263924 | −0.131962 | − | 0.991255i | \(-0.542128\pi\) | ||||
−0.131962 | + | 0.991255i | \(0.542128\pi\) | |||||||
\(854\) | 18.9443 | + | 2.76393i | 0.648260 | + | 0.0945798i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.4164 | 0.390205 | ||||||||
\(857\) | 11.3475i | 0.387624i | 0.981039 | + | 0.193812i | \(0.0620852\pi\) | ||||
−0.981039 | + | 0.193812i | \(0.937915\pi\) | |||||||
\(858\) | 8.94427 | + | 3.41641i | 0.305352 | + | 0.116634i | ||||
\(859\) | 17.0557i | 0.581934i | 0.956733 | + | 0.290967i | \(0.0939770\pi\) | ||||
−0.956733 | + | 0.290967i | \(0.906023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.88854 | + | 5.52786i | 0.337001 | + | 0.188389i | ||||
\(862\) | − | 39.5967i | − | 1.34867i | ||||||
\(863\) | −30.4721 | −1.03728 | −0.518642 | − | 0.854992i | \(-0.673562\pi\) | ||||
−0.518642 | + | 0.854992i | \(0.673562\pi\) | |||||||
\(864\) | −4.61803 | + | 2.38197i | −0.157109 | + | 0.0810361i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26.6525 | −0.905688 | ||||||||
\(867\) | −6.43769 | + | 16.8541i | −0.218636 | + | 0.572395i | ||||
\(868\) | −7.23607 | − | 1.05573i | −0.245608 | − | 0.0358337i | ||||
\(869\) | 40.0000i | 1.35691i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.8328i | 0.502591i | ||||||||
\(872\) | −4.47214 | −0.151446 | ||||||||
\(873\) | −1.70820 | − | 1.52786i | −0.0578139 | − | 0.0517104i | ||||
\(874\) | − | 33.8885i | − | 1.14630i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.94427 | − | 18.1803i | 0.234625 | − | 0.614257i | ||||
\(877\) | − | 38.6525i | − | 1.30520i | −0.757702 | − | 0.652601i | \(-0.773678\pi\) | ||
0.757702 | − | 0.652601i | \(-0.226322\pi\) | |||||||
\(878\) | − | 10.1803i | − | 0.343570i | ||||||
\(879\) | −4.18034 | − | 1.59675i | −0.140999 | − | 0.0538570i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.4164 | 0.519392 | 0.259696 | − | 0.965690i | \(-0.416378\pi\) | ||||
0.259696 | + | 0.965690i | \(0.416378\pi\) | |||||||
\(882\) | 11.0000 | + | 17.8885i | 0.370389 | + | 0.602339i | ||||
\(883\) | − | 13.8885i | − | 0.467387i | −0.972310 | − | 0.233693i | \(-0.924919\pi\) | ||
0.972310 | − | 0.233693i | \(-0.0750812\pi\) | |||||||
\(884\) | − | 6.47214i | − | 0.217681i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.4721 | 0.620584 | ||||||||
\(887\) | 17.5279i | 0.588528i | 0.955724 | + | 0.294264i | \(0.0950745\pi\) | ||||
−0.955724 | + | 0.294264i | \(0.904925\pi\) | |||||||
\(888\) | −1.23607 | − | 0.472136i | −0.0414797 | − | 0.0158438i | ||||
\(889\) | 0.763932 | + | 0.111456i | 0.0256215 | + | 0.00373812i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.0000 | + | 4.47214i | −1.34005 | + | 0.149822i | ||||
\(892\) | −17.7082 | −0.592915 | ||||||||
\(893\) | 54.8328 | 1.83491 | ||||||||
\(894\) | 6.94427 | + | 2.65248i | 0.232251 | + | 0.0887121i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.381966 | − | 2.61803i | 0.0127606 | − | 0.0874624i | ||||
\(897\) | 3.05573 | − | 8.00000i | 0.102028 | − | 0.267112i | ||||
\(898\) | 10.4721i | 0.349460i | ||||||||
\(899\) | 21.3050 | 0.710560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.47214i | 0.0823588i | ||||||||
\(902\) | − | 11.0557i | − | 0.368115i | ||||||
\(903\) | −11.0557 | + | 19.7771i | −0.367912 | + | 0.658140i | ||||
\(904\) | 2.94427 | 0.0979250 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.9443 | − | 33.8885i | 0.430045 | − | 1.12587i | ||||
\(907\) | 17.5279i | 0.582003i | 0.956723 | + | 0.291002i | \(0.0939885\pi\) | ||||
−0.956723 | + | 0.291002i | \(0.906012\pi\) | |||||||
\(908\) | − | 0.763932i | − | 0.0253520i | ||||||
\(909\) | 27.8885 | + | 24.9443i | 0.925005 | + | 0.827349i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.6525i | 1.67819i | 0.543984 | + | 0.839096i | \(0.316915\pi\) | ||||
−0.543984 | + | 0.839096i | \(0.683085\pi\) | |||||||
\(912\) | −13.7082 | − | 5.23607i | −0.453924 | − | 0.173384i | ||||
\(913\) | −65.5279 | −2.16866 | ||||||||
\(914\) | − | 26.9443i | − | 0.891237i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.76393i | 0.289568i | ||||||||
\(917\) | 2.06888 | − | 14.1803i | 0.0683206 | − | 0.468276i | ||||
\(918\) | 12.4721 | + | 24.1803i | 0.411642 | + | 0.798070i | ||||
\(919\) | 44.7214 | 1.47522 | 0.737611 | − | 0.675226i | \(-0.235954\pi\) | ||||
0.737611 | + | 0.675226i | \(0.235954\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2361 | + | 29.4164i | −0.370241 | + | 0.969304i | ||||
\(922\) | −6.94427 | −0.228697 | ||||||||
\(923\) | − | 8.94427i | − | 0.294404i | ||||||
\(924\) | 10.0000 | − | 17.8885i | 0.328976 | − | 0.588490i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 22.1803i | − | 0.728891i | ||||||
\(927\) | −32.7639 | − | 29.3050i | −1.07611 | − | 0.962501i | ||||
\(928\) | 7.70820i | 0.253034i | ||||||||
\(929\) | −37.8885 | −1.24308 | −0.621541 | − | 0.783381i | \(-0.713493\pi\) | ||||
−0.621541 | + | 0.783381i | \(0.713493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.9443 | + | 56.8328i | −0.555326 | + | 1.86262i | ||||
\(932\) | −11.5279 | −0.377608 | ||||||||
\(933\) | 10.8328 | − | 28.3607i | 0.354650 | − | 0.928487i | ||||
\(934\) | 33.7082i | 1.10297i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.76393 | − | 2.47214i | −0.0903419 | − | 0.0808043i | ||||
\(937\) | 42.0689 | 1.37433 | 0.687165 | − | 0.726501i | \(-0.258855\pi\) | ||||
0.687165 | + | 0.726501i | \(0.258855\pi\) | |||||||
\(938\) | 31.4164 | + | 4.58359i | 1.02578 | + | 0.149660i | ||||
\(939\) | 3.52786 | − | 9.23607i | 0.115127 | − | 0.301408i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.0000 | 0.717180 | 0.358590 | − | 0.933495i | \(-0.383258\pi\) | ||||
0.358590 | + | 0.933495i | \(0.383258\pi\) | |||||||
\(942\) | −5.70820 | + | 14.9443i | −0.185983 | + | 0.486911i | ||||
\(943\) | −9.88854 | −0.322015 | ||||||||
\(944\) | −4.47214 | −0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.1115 | 0.718905 | ||||||||
\(947\) | 60.3607 | 1.96146 | 0.980729 | − | 0.195372i | \(-0.0625913\pi\) | ||||
0.980729 | + | 0.195372i | \(0.0625913\pi\) | |||||||
\(948\) | 5.52786 | − | 14.4721i | 0.179537 | − | 0.470033i | ||||
\(949\) | 13.8885 | 0.450841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.76393 | + | 17.7082i | −0.219336 | + | 0.574228i | ||||
\(952\) | −13.7082 | − | 2.00000i | −0.444285 | − | 0.0648204i | ||||
\(953\) | −22.5836 | −0.731554 | −0.365777 | − | 0.930702i | \(-0.619197\pi\) | ||||
−0.365777 | + | 0.930702i | \(0.619197\pi\) | |||||||
\(954\) | 1.05573 | + | 0.944272i | 0.0341805 | + | 0.0305719i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 0.180340i | − | 0.00583261i | ||||||
\(957\) | −21.3050 | + | 55.7771i | −0.688691 | + | 1.80302i | ||||
\(958\) | −37.8885 | −1.22412 | ||||||||
\(959\) | 1.34752 | − | 9.23607i | 0.0435138 | − | 0.298248i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3607 | 0.753570 | ||||||||
\(962\) | − | 0.944272i | − | 0.0304445i | ||||||
\(963\) | −25.5279 | − | 22.8328i | −0.822624 | − | 0.735777i | ||||
\(964\) | 17.8885i | 0.576151i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.0000 | − | 8.94427i | −0.514792 | − | 0.287777i | ||||
\(967\) | 39.4853i | 1.26976i | 0.772610 | + | 0.634881i | \(0.218951\pi\) | ||||
−0.772610 | + | 0.634881i | \(0.781049\pi\) | |||||||
\(968\) | −9.00000 | −0.289271 | ||||||||
\(969\) | −27.4164 | + | 71.7771i | −0.880742 | + | 2.30581i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.0000 | −1.86131 | −0.930654 | − | 0.365900i | \(-0.880761\pi\) | ||||
−0.930654 | + | 0.365900i | \(0.880761\pi\) | |||||||
\(972\) | 15.0902 | + | 3.90983i | 0.484017 | + | 0.125408i | ||||
\(973\) | 30.1803 | + | 4.40325i | 0.967537 | + | 0.141162i | ||||
\(974\) | − | 17.5967i | − | 0.563836i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.23607i | 0.231621i | ||||||||
\(977\) | 1.41641 | 0.0453149 | 0.0226575 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226575 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(978\) | −16.9443 | − | 6.47214i | −0.541818 | − | 0.206956i | ||||
\(979\) | 24.7214i | 0.790098i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | + | 8.94427i | 0.319275 | + | 0.285569i | ||||
\(982\) | 13.4164i | 0.428135i | ||||||||
\(983\) | − | 12.5836i | − | 0.401354i | −0.979657 | − | 0.200677i | \(-0.935686\pi\) | ||
0.979657 | − | 0.200677i | \(-0.0643142\pi\) | |||||||
\(984\) | −1.52786 | + | 4.00000i | −0.0487065 | + | 0.127515i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 40.3607 | 1.28535 | ||||||||
\(987\) | 14.4721 | − | 25.8885i | 0.460653 | − | 0.824041i | ||||
\(988\) | − | 10.4721i | − | 0.333163i | ||||||
\(989\) | − | 19.7771i | − | 0.628875i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5279 | 0.556791 | 0.278395 | − | 0.960467i | \(-0.410197\pi\) | ||||
0.278395 | + | 0.960467i | \(0.410197\pi\) | |||||||
\(992\) | − | 2.76393i | − | 0.0877549i | ||||||
\(993\) | 1.88854 | − | 4.94427i | 0.0599311 | − | 0.156902i | ||||
\(994\) | −18.9443 | − | 2.76393i | −0.600876 | − | 0.0876666i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 23.7082 | + | 9.05573i | 0.751223 | + | 0.286942i | ||||
\(997\) | 25.2361 | 0.799234 | 0.399617 | − | 0.916682i | \(-0.369143\pi\) | ||||
0.399617 | + | 0.916682i | \(0.369143\pi\) | |||||||
\(998\) | −17.8885 | −0.566252 | ||||||||
\(999\) | 1.81966 | + | 3.52786i | 0.0575715 | + | 0.111617i |
(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 | 1050.2.d.d.1049.3 | 4 | ||
3.2 | odd | 2 | 1050.2.d.a.1049.4 | 4 | |||
5.2 | odd | 4 | 210.2.b.a.41.3 | yes | 4 | ||
5.3 | odd | 4 | 1050.2.b.c.251.2 | 4 | |||
5.4 | even | 2 | 1050.2.d.c.1049.2 | 4 | |||
7.6 | odd | 2 | 1050.2.d.f.1049.2 | 4 | |||
15.2 | even | 4 | 210.2.b.b.41.2 | yes | 4 | ||
15.8 | even | 4 | 1050.2.b.a.251.3 | 4 | |||
15.14 | odd | 2 | 1050.2.d.f.1049.1 | 4 | |||
20.7 | even | 4 | 1680.2.f.i.881.4 | 4 | |||
21.20 | even | 2 | 1050.2.d.c.1049.1 | 4 | |||
35.13 | even | 4 | 1050.2.b.a.251.1 | 4 | |||
35.27 | even | 4 | 210.2.b.b.41.4 | yes | 4 | ||
35.34 | odd | 2 | 1050.2.d.a.1049.3 | 4 | |||
60.47 | odd | 4 | 1680.2.f.e.881.2 | 4 | |||
105.62 | odd | 4 | 210.2.b.a.41.1 | ✓ | 4 | ||
105.83 | odd | 4 | 1050.2.b.c.251.4 | 4 | |||
105.104 | even | 2 | inner | 1050.2.d.d.1049.4 | 4 | ||
140.27 | odd | 4 | 1680.2.f.e.881.1 | 4 | |||
420.167 | even | 4 | 1680.2.f.i.881.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.b.a.41.1 | ✓ | 4 | 105.62 | odd | 4 | ||
210.2.b.a.41.3 | yes | 4 | 5.2 | odd | 4 | ||
210.2.b.b.41.2 | yes | 4 | 15.2 | even | 4 | ||
210.2.b.b.41.4 | yes | 4 | 35.27 | even | 4 | ||
1050.2.b.a.251.1 | 4 | 35.13 | even | 4 | |||
1050.2.b.a.251.3 | 4 | 15.8 | even | 4 | |||
1050.2.b.c.251.2 | 4 | 5.3 | odd | 4 | |||
1050.2.b.c.251.4 | 4 | 105.83 | odd | 4 | |||
1050.2.d.a.1049.3 | 4 | 35.34 | odd | 2 | |||
1050.2.d.a.1049.4 | 4 | 3.2 | odd | 2 | |||
1050.2.d.c.1049.1 | 4 | 21.20 | even | 2 | |||
1050.2.d.c.1049.2 | 4 | 5.4 | even | 2 | |||
1050.2.d.d.1049.3 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.d.d.1049.4 | 4 | 105.104 | even | 2 | inner | ||
1050.2.d.f.1049.1 | 4 | 15.14 | odd | 2 | |||
1050.2.d.f.1049.2 | 4 | 7.6 | odd | 2 | |||
1680.2.f.e.881.1 | 4 | 140.27 | odd | 4 | |||
1680.2.f.e.881.2 | 4 | 60.47 | odd | 4 | |||
1680.2.f.i.881.3 | 4 | 420.167 | even | 4 | |||
1680.2.f.i.881.4 | 4 | 20.7 | even | 4 |