Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.251");
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.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: | \(8.38429221223\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.c.251.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.61803 | − | 0.618034i | 0.934172 | − | 0.356822i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | + | 1.61803i | 0.252311 | + | 0.660560i | ||||
\(7\) | −2.61803 | + | 0.381966i | −0.989524 | + | 0.144370i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.23607 | − | 2.00000i | 0.745356 | − | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.47214i | − | 1.34840i | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||
0.738549 | − | 0.674200i | \(-0.235511\pi\) | |||||||
\(12\) | −1.61803 | + | 0.618034i | −0.467086 | + | 0.178411i | ||||
\(13\) | − | 1.23607i | − | 0.342824i | −0.985199 | − | 0.171412i | \(-0.945167\pi\) | ||
0.985199 | − | 0.171412i | \(-0.0548329\pi\) | |||||||
\(14\) | −0.381966 | − | 2.61803i | −0.102085 | − | 0.699699i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.23607 | −1.26993 | −0.634967 | − | 0.772540i | \(-0.718986\pi\) | ||||
−0.634967 | + | 0.772540i | \(0.718986\pi\) | |||||||
\(18\) | 2.00000 | + | 2.23607i | 0.471405 | + | 0.527046i | ||||
\(19\) | − | 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 | ||||
\(22\) | 4.47214 | 0.953463 | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | −0.618034 | − | 1.61803i | −0.126156 | − | 0.330280i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | 2.38197 | − | 4.61803i | 0.458410 | − | 0.888741i | ||||
\(28\) | 2.61803 | − | 0.381966i | 0.494762 | − | 0.0721848i | ||||
\(29\) | 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 | \(0.0798418\pi\) | ||||
−0.968707 | + | 0.248208i | \(0.920158\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −2.76393 | − | 7.23607i | −0.481139 | − | 1.25964i | ||||
\(34\) | − | 5.23607i | − | 0.897978i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.23607 | + | 2.00000i | −0.372678 | + | 0.333333i | ||||
\(37\) | −0.763932 | −0.125590 | −0.0627948 | − | 0.998026i | \(-0.520001\pi\) | ||||
−0.0627948 | + | 0.998026i | \(0.520001\pi\) | |||||||
\(38\) | 8.47214 | 1.37436 | ||||||||
\(39\) | −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 | \(0.561835\pi\) | |||||||
\(42\) | −2.23607 | − | 4.00000i | −0.345033 | − | 0.617213i | ||||
\(43\) | 4.94427 | 0.753994 | 0.376997 | − | 0.926214i | \(-0.376957\pi\) | ||||
0.376997 | + | 0.926214i | \(0.376957\pi\) | |||||||
\(44\) | 4.47214i | 0.674200i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 6.47214 | 0.944058 | 0.472029 | − | 0.881583i | \(-0.343522\pi\) | ||||
0.472029 | + | 0.881583i | \(0.343522\pi\) | |||||||
\(48\) | 1.61803 | − | 0.618034i | 0.233543 | − | 0.0892055i | ||||
\(49\) | 6.70820 | − | 2.00000i | 0.958315 | − | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.47214 | + | 3.23607i | −1.18634 | + | 0.453140i | ||||
\(52\) | 1.23607i | 0.171412i | ||||||||
\(53\) | 0.472136i | 0.0648529i | 0.999474 | + | 0.0324264i | \(0.0103235\pi\) | ||||
−0.999474 | + | 0.0324264i | \(0.989677\pi\) | |||||||
\(54\) | 4.61803 | + | 2.38197i | 0.628435 | + | 0.324145i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.381966 | + | 2.61803i | 0.0510424 | + | 0.349850i | ||||
\(57\) | −5.23607 | − | 13.7082i | −0.693534 | − | 1.81570i | ||||
\(58\) | −7.70820 | −1.01214 | ||||||||
\(59\) | 4.47214 | 0.582223 | 0.291111 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291111 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.23607i | − | 0.926484i | −0.886232 | − | 0.463242i | \(-0.846686\pi\) | ||
0.886232 | − | 0.463242i | \(-0.153314\pi\) | |||||||
\(62\) | −2.76393 | −0.351020 | ||||||||
\(63\) | −5.09017 | + | 6.09017i | −0.641301 | + | 0.767289i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.23607 | − | 2.76393i | 0.890698 | − | 0.340217i | ||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 5.23607 | 0.634967 | ||||||||
\(69\) | −2.47214 | − | 6.47214i | −0.297610 | − | 0.779154i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.23607i | 0.858763i | 0.903123 | + | 0.429382i | \(0.141268\pi\) | ||||
−0.903123 | + | 0.429382i | \(0.858732\pi\) | |||||||
\(72\) | −2.00000 | − | 2.23607i | −0.235702 | − | 0.263523i | ||||
\(73\) | − | 11.2361i | − | 1.31508i | −0.753419 | − | 0.657541i | \(-0.771597\pi\) | ||
0.753419 | − | 0.657541i | \(-0.228403\pi\) | |||||||
\(74\) | − | 0.763932i | − | 0.0888053i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.47214i | 0.971821i | ||||||||
\(77\) | 1.70820 | + | 11.7082i | 0.194668 | + | 1.33427i | ||||
\(78\) | 2.00000 | − | 0.763932i | 0.226455 | − | 0.0864983i | ||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | − | 2.47214i | − | 0.273002i | ||||||
\(83\) | −14.6525 | −1.60832 | −0.804159 | − | 0.594414i | \(-0.797384\pi\) | ||||
−0.804159 | + | 0.594414i | \(0.797384\pi\) | |||||||
\(84\) | 4.00000 | − | 2.23607i | 0.436436 | − | 0.243975i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.94427i | 0.533155i | ||||||||
\(87\) | 4.76393 | + | 12.4721i | 0.510747 | + | 1.33715i | ||||
\(88\) | −4.47214 | −0.476731 | ||||||||
\(89\) | −5.52786 | −0.585952 | −0.292976 | − | 0.956120i | \(-0.594646\pi\) | ||||
−0.292976 | + | 0.956120i | \(0.594646\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.472136 | + | 3.23607i | 0.0494933 | + | 0.339232i | ||||
\(92\) | 4.00000i | 0.417029i | ||||||||
\(93\) | 1.70820 | + | 4.47214i | 0.177132 | + | 0.463739i | ||||
\(94\) | 6.47214i | 0.667550i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.618034 | + | 1.61803i | 0.0630778 | + | 0.165140i | ||||
\(97\) | 0.763932i | 0.0775655i | 0.999248 | + | 0.0387828i | \(0.0123480\pi\) | ||||
−0.999248 | + | 0.0387828i | \(0.987652\pi\) | |||||||
\(98\) | 2.00000 | + | 6.70820i | 0.202031 | + | 0.677631i | ||||
\(99\) | −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 | \(0.713075\pi\) | |||||||
\(102\) | −3.23607 | − | 8.47214i | −0.320418 | − | 0.838866i | ||||
\(103\) | − | 14.6525i | − | 1.44375i | −0.692023 | − | 0.721876i | \(-0.743280\pi\) | ||
0.692023 | − | 0.721876i | \(-0.256720\pi\) | |||||||
\(104\) | −1.23607 | −0.121206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.472136 | −0.0458579 | ||||||||
\(107\) | 11.4164i | 1.10367i | 0.833955 | + | 0.551833i | \(0.186071\pi\) | ||||
−0.833955 | + | 0.551833i | \(0.813929\pi\) | |||||||
\(108\) | −2.38197 | + | 4.61803i | −0.229205 | + | 0.444371i | ||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.23607 | + | 0.472136i | −0.117322 | + | 0.0448132i | ||||
\(112\) | −2.61803 | + | 0.381966i | −0.247381 | + | 0.0360924i | ||||
\(113\) | − | 2.94427i | − | 0.276974i | −0.990364 | − | 0.138487i | \(-0.955776\pi\) | ||
0.990364 | − | 0.138487i | \(-0.0442239\pi\) | |||||||
\(114\) | 13.7082 | − | 5.23607i | 1.28389 | − | 0.490403i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.70820i | − | 0.715689i | ||||||
\(117\) | −2.47214 | − | 2.76393i | −0.228549 | − | 0.255526i | ||||
\(118\) | 4.47214i | 0.411693i | ||||||||
\(119\) | 13.7082 | − | 2.00000i | 1.25663 | − | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 7.23607 | 0.655123 | ||||||||
\(123\) | −4.00000 | + | 1.52786i | −0.360668 | + | 0.137763i | ||||
\(124\) | − | 2.76393i | − | 0.248208i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.09017 | − | 5.09017i | −0.542555 | − | 0.453468i | ||||
\(127\) | 0.291796 | 0.0258927 | 0.0129464 | − | 0.999916i | \(-0.495879\pi\) | ||||
0.0129464 | + | 0.999916i | \(0.495879\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 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 | \(0.423961\pi\) | |||||||
\(132\) | 2.76393 | + | 7.23607i | 0.240569 | + | 0.629819i | ||||
\(133\) | 3.23607 | + | 22.1803i | 0.280603 | + | 1.92328i | ||||
\(134\) | 12.0000i | 1.03664i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.23607i | 0.448989i | ||||||||
\(137\) | 3.52786i | 0.301406i | 0.988579 | + | 0.150703i | \(0.0481537\pi\) | ||||
−0.988579 | + | 0.150703i | \(0.951846\pi\) | |||||||
\(138\) | 6.47214 | − | 2.47214i | 0.550945 | − | 0.210442i | ||||
\(139\) | 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 | ||||
\(142\) | −7.23607 | −0.607237 | ||||||||
\(143\) | −5.52786 | −0.462263 | ||||||||
\(144\) | 2.23607 | − | 2.00000i | 0.186339 | − | 0.166667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.2361 | 0.929904 | ||||||||
\(147\) | 9.61803 | − | 7.38197i | 0.793282 | − | 0.608854i | ||||
\(148\) | 0.763932 | 0.0627948 | ||||||||
\(149\) | 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 | \(0.175262\pi\) | |||||||
\(152\) | −8.47214 | −0.687181 | ||||||||
\(153\) | −11.7082 | + | 10.4721i | −0.946552 | + | 0.846622i | ||||
\(154\) | −11.7082 | + | 1.70820i | −0.943474 | + | 0.137651i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.763932 | + | 2.00000i | 0.0611635 | + | 0.160128i | ||||
\(157\) | − | 9.23607i | − | 0.737118i | −0.929604 | − | 0.368559i | \(-0.879851\pi\) | ||
0.929604 | − | 0.368559i | \(-0.120149\pi\) | |||||||
\(158\) | − | 8.94427i | − | 0.711568i | ||||||
\(159\) | 0.291796 | + | 0.763932i | 0.0231409 | + | 0.0605838i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.52786 | + | 10.4721i | 0.120413 | + | 0.825320i | ||||
\(162\) | 8.94427 | + | 1.00000i | 0.702728 | + | 0.0785674i | ||||
\(163\) | 10.4721 | 0.820241 | 0.410120 | − | 0.912031i | \(-0.365487\pi\) | ||||
0.410120 | + | 0.912031i | \(0.365487\pi\) | |||||||
\(164\) | 2.47214 | 0.193041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.6525i | − | 1.13725i | ||||||
\(167\) | 0.944272 | 0.0730700 | 0.0365350 | − | 0.999332i | \(-0.488368\pi\) | ||||
0.0365350 | + | 0.999332i | \(0.488368\pi\) | |||||||
\(168\) | 2.23607 | + | 4.00000i | 0.172516 | + | 0.308607i | ||||
\(169\) | 11.4721 | 0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.9443 | − | 18.9443i | −1.29576 | − | 1.44870i | ||||
\(172\) | −4.94427 | −0.376997 | ||||||||
\(173\) | 9.41641 | 0.715916 | 0.357958 | − | 0.933738i | \(-0.383473\pi\) | ||||
0.357958 | + | 0.933738i | \(0.383473\pi\) | |||||||
\(174\) | −12.4721 | + | 4.76393i | −0.945510 | + | 0.361153i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.47214i | − | 0.337100i | ||||||
\(177\) | 7.23607 | − | 2.76393i | 0.543896 | − | 0.207750i | ||||
\(178\) | − | 5.52786i | − | 0.414331i | ||||||
\(179\) | 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 | \(0.205365\pi\) | ||||
−0.798995 | + | 0.601338i | \(0.794635\pi\) | |||||||
\(182\) | −3.23607 | + | 0.472136i | −0.239873 | + | 0.0349970i | ||||
\(183\) | −4.47214 | − | 11.7082i | −0.330590 | − | 0.865495i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.47214 | + | 1.70820i | −0.327913 | + | 0.125252i | ||||
\(187\) | 23.4164i | 1.71238i | ||||||||
\(188\) | −6.47214 | −0.472029 | ||||||||
\(189\) | −4.47214 | + | 13.0000i | −0.325300 | + | 0.945611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.23607i | − | 0.523584i | −0.965124 | − | 0.261792i | \(-0.915687\pi\) | ||
0.965124 | − | 0.261792i | \(-0.0843134\pi\) | |||||||
\(192\) | −1.61803 | + | 0.618034i | −0.116772 | + | 0.0446028i | ||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | −0.763932 | −0.0548471 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.70820 | + | 2.00000i | −0.479157 | + | 0.142857i | ||||
\(197\) | 3.52786i | 0.251350i | 0.992071 | + | 0.125675i | \(0.0401096\pi\) | ||||
−0.992071 | + | 0.125675i | \(0.959890\pi\) | |||||||
\(198\) | 10.0000 | − | 8.94427i | 0.710669 | − | 0.635642i | ||||
\(199\) | 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 | ||||
\(202\) | − | 12.4721i | − | 0.877536i | ||||||
\(203\) | −2.94427 | − | 20.1803i | −0.206647 | − | 1.41638i | ||||
\(204\) | 8.47214 | − | 3.23607i | 0.593168 | − | 0.226570i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.6525 | 1.02089 | ||||||||
\(207\) | −8.00000 | − | 8.94427i | −0.556038 | − | 0.621670i | ||||
\(208\) | − | 1.23607i | − | 0.0857059i | ||||||
\(209\) | −37.8885 | −2.62081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | − | 0.472136i | − | 0.0324264i | ||||||
\(213\) | 4.47214 | + | 11.7082i | 0.306426 | + | 0.802233i | ||||
\(214\) | −11.4164 | −0.780410 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.61803 | − | 2.38197i | −0.314217 | − | 0.162072i | ||||
\(217\) | −1.05573 | − | 7.23607i | −0.0716675 | − | 0.491216i | ||||
\(218\) | 4.47214i | 0.302891i | ||||||||
\(219\) | −6.94427 | − | 18.1803i | −0.469250 | − | 1.22851i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214i | 0.435363i | ||||||||
\(222\) | −0.472136 | − | 1.23607i | −0.0316877 | − | 0.0829595i | ||||
\(223\) | 17.7082i | 1.18583i | 0.805265 | + | 0.592915i | \(0.202023\pi\) | ||||
−0.805265 | + | 0.592915i | \(0.797977\pi\) | |||||||
\(224\) | −0.381966 | − | 2.61803i | −0.0255212 | − | 0.174925i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.94427 | 0.195850 | ||||||||
\(227\) | −0.763932 | −0.0507039 | −0.0253520 | − | 0.999679i | \(-0.508071\pi\) | ||||
−0.0253520 | + | 0.999679i | \(0.508071\pi\) | |||||||
\(228\) | 5.23607 | + | 13.7082i | 0.346767 | + | 0.907848i | ||||
\(229\) | 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 | ||||
\(232\) | 7.70820 | 0.506068 | ||||||||
\(233\) | 11.5279i | 0.755215i | 0.925966 | + | 0.377608i | \(0.123253\pi\) | ||||
−0.925966 | + | 0.377608i | \(0.876747\pi\) | |||||||
\(234\) | 2.76393 | − | 2.47214i | 0.180684 | − | 0.161609i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.47214 | −0.291111 | ||||||||
\(237\) | −14.4721 | + | 5.52786i | −0.940066 | + | 0.359073i | ||||
\(238\) | 2.00000 | + | 13.7082i | 0.129641 | + | 0.888571i | ||||
\(239\) | − | 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 | \(-0.804554\pi\) | ||
0.817343 | − | 0.576151i | \(-0.195446\pi\) | |||||||
\(242\) | − | 9.00000i | − | 0.578542i | ||||||
\(243\) | −3.90983 | − | 15.0902i | −0.250816 | − | 0.968035i | ||||
\(244\) | 7.23607i | 0.463242i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.52786 | − | 4.00000i | −0.0974131 | − | 0.255031i | ||||
\(247\) | −10.4721 | −0.666326 | ||||||||
\(248\) | 2.76393 | 0.175510 | ||||||||
\(249\) | −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 | \(0.628776\pi\) | |||||||
\(252\) | 5.09017 | − | 6.09017i | 0.320651 | − | 0.383645i | ||||
\(253\) | −17.8885 | −1.12464 | ||||||||
\(254\) | 0.291796i | 0.0183089i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.1803 | −0.884545 | −0.442273 | − | 0.896881i | \(-0.645828\pi\) | ||||
−0.442273 | + | 0.896881i | \(0.645828\pi\) | |||||||
\(258\) | 3.05573 | + | 8.00000i | 0.190241 | + | 0.498058i | ||||
\(259\) | 2.00000 | − | 0.291796i | 0.124274 | − | 0.0181313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4164 | + | 17.2361i | 0.954252 | + | 1.06689i | ||||
\(262\) | 5.41641i | 0.334627i | ||||||||
\(263\) | − | 12.9443i | − | 0.798178i | −0.916912 | − | 0.399089i | \(-0.869326\pi\) | ||
0.916912 | − | 0.399089i | \(-0.130674\pi\) | |||||||
\(264\) | −7.23607 | + | 2.76393i | −0.445349 | + | 0.170108i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −22.1803 | + | 3.23607i | −1.35996 | + | 0.198416i | ||||
\(267\) | −8.94427 | + | 3.41641i | −0.547381 | + | 0.209081i | ||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | 4.47214 | 0.272671 | 0.136335 | − | 0.990663i | \(-0.456467\pi\) | ||||
0.136335 | + | 0.990663i | \(0.456467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.7082i | − | 1.92614i | −0.269258 | − | 0.963068i | \(-0.586778\pi\) | ||
0.269258 | − | 0.963068i | \(-0.413222\pi\) | |||||||
\(272\) | −5.23607 | −0.317483 | ||||||||
\(273\) | 2.76393 | + | 4.94427i | 0.167281 | + | 0.299241i | ||||
\(274\) | −3.52786 | −0.213126 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.47214 | + | 6.47214i | 0.148805 | + | 0.389577i | ||||
\(277\) | 17.1246 | 1.02892 | 0.514459 | − | 0.857515i | \(-0.327993\pi\) | ||||
0.514459 | + | 0.857515i | \(0.327993\pi\) | |||||||
\(278\) | −11.5279 | −0.691395 | ||||||||
\(279\) | 5.52786 | + | 6.18034i | 0.330945 | + | 0.370007i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.0000i | − | 1.19310i | −0.802576 | − | 0.596550i | \(-0.796538\pi\) | ||
0.802576 | − | 0.596550i | \(-0.203462\pi\) | |||||||
\(282\) | 4.00000 | + | 10.4721i | 0.238197 | + | 0.623607i | ||||
\(283\) | 13.2361i | 0.786803i | 0.919367 | + | 0.393401i | \(0.128702\pi\) | ||||
−0.919367 | + | 0.393401i | \(0.871298\pi\) | |||||||
\(284\) | − | 7.23607i | − | 0.429382i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5.52786i | − | 0.326869i | ||||||
\(287\) | 6.47214 | − | 0.944272i | 0.382038 | − | 0.0557386i | ||||
\(288\) | 2.00000 | + | 2.23607i | 0.117851 | + | 0.131762i | ||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.472136 | + | 1.23607i | 0.0276771 | + | 0.0724596i | ||||
\(292\) | 11.2361i | 0.657541i | ||||||||
\(293\) | 2.58359 | 0.150935 | 0.0754675 | − | 0.997148i | \(-0.475955\pi\) | ||||
0.0754675 | + | 0.997148i | \(0.475955\pi\) | |||||||
\(294\) | 7.38197 | + | 9.61803i | 0.430525 | + | 0.560935i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.763932i | 0.0444026i | ||||||||
\(297\) | −20.6525 | − | 10.6525i | −1.19838 | − | 0.618119i | ||||
\(298\) | −4.29180 | −0.248617 | ||||||||
\(299\) | −4.94427 | −0.285935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9443 | + | 1.88854i | −0.746095 | + | 0.108854i | ||||
\(302\) | 20.9443i | 1.20521i | ||||||||
\(303\) | −20.1803 | + | 7.70820i | −1.15933 | + | 0.442825i | ||||
\(304\) | − | 8.47214i | − | 0.485910i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.4721 | − | 11.7082i | −0.598652 | − | 0.669313i | ||||
\(307\) | − | 18.1803i | − | 1.03761i | −0.854894 | − | 0.518803i | \(-0.826378\pi\) | ||
0.854894 | − | 0.518803i | \(-0.173622\pi\) | |||||||
\(308\) | −1.70820 | − | 11.7082i | −0.0973340 | − | 0.667137i | ||||
\(309\) | −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 | \(0.334451\pi\) | |||||||
\(312\) | −2.00000 | + | 0.763932i | −0.113228 | + | 0.0432491i | ||||
\(313\) | − | 5.70820i | − | 0.322647i | −0.986902 | − | 0.161323i | \(-0.948424\pi\) | ||
0.986902 | − | 0.161323i | \(-0.0515762\pi\) | |||||||
\(314\) | 9.23607 | 0.521221 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.94427 | 0.503155 | ||||||||
\(317\) | − | 10.9443i | − | 0.614692i | −0.951598 | − | 0.307346i | \(-0.900559\pi\) | ||
0.951598 | − | 0.307346i | \(-0.0994408\pi\) | |||||||
\(318\) | −0.763932 | + | 0.291796i | −0.0428392 | + | 0.0163631i | ||||
\(319\) | 34.4721 | 1.93007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.05573 | + | 18.4721i | 0.393812 | + | 1.03101i | ||||
\(322\) | −10.4721 | + | 1.52786i | −0.583589 | + | 0.0851445i | ||||
\(323\) | 44.3607i | 2.46829i | ||||||||
\(324\) | −1.00000 | + | 8.94427i | −0.0555556 | + | 0.496904i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.4721i | 0.579998i | ||||||||
\(327\) | 7.23607 | − | 2.76393i | 0.400155 | − | 0.152846i | ||||
\(328\) | 2.47214i | 0.136501i | ||||||||
\(329\) | −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 | \(0.473237\pi\) | |||||||
\(332\) | 14.6525 | 0.804159 | ||||||||
\(333\) | −1.70820 | + | 1.52786i | −0.0936090 | + | 0.0837264i | ||||
\(334\) | 0.944272i | 0.0516683i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00000 | + | 2.23607i | −0.218218 | + | 0.121988i | ||||
\(337\) | −21.4164 | −1.16663 | −0.583313 | − | 0.812247i | \(-0.698244\pi\) | ||||
−0.583313 | + | 0.812247i | \(0.698244\pi\) | |||||||
\(338\) | 11.4721i | 0.624002i | ||||||||
\(339\) | −1.81966 | − | 4.76393i | −0.0988304 | − | 0.258741i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3607 | 0.669368 | ||||||||
\(342\) | 18.9443 | − | 16.9443i | 1.02439 | − | 0.916241i | ||||
\(343\) | −16.7984 | + | 7.79837i | −0.907027 | + | 0.421073i | ||||
\(344\) | − | 4.94427i | − | 0.266577i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.41641i | 0.506229i | ||||||||
\(347\) | 2.47214i | 0.132711i | 0.997796 | + | 0.0663556i | \(0.0211372\pi\) | ||||
−0.997796 | + | 0.0663556i | \(0.978863\pi\) | |||||||
\(348\) | −4.76393 | − | 12.4721i | −0.255374 | − | 0.668577i | ||||
\(349\) | − | 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 | ||||
\(352\) | 4.47214 | 0.238366 | ||||||||
\(353\) | 27.7082 | 1.47476 | 0.737379 | − | 0.675479i | \(-0.236063\pi\) | ||||
0.737379 | + | 0.675479i | \(0.236063\pi\) | |||||||
\(354\) | 2.76393 | + | 7.23607i | 0.146901 | + | 0.384593i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.52786 | 0.292976 | ||||||||
\(357\) | 20.9443 | − | 11.7082i | 1.10849 | − | 0.619664i | ||||
\(358\) | −14.9443 | −0.789829 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | −16.1803 | −0.850420 | ||||||||
\(363\) | −14.5623 | + | 5.56231i | −0.764323 | + | 0.291945i | ||||
\(364\) | −0.472136 | − | 3.23607i | −0.0247466 | − | 0.169616i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.7082 | − | 4.47214i | 0.611998 | − | 0.233762i | ||||
\(367\) | − | 8.18034i | − | 0.427010i | −0.976942 | − | 0.213505i | \(-0.931512\pi\) | ||
0.976942 | − | 0.213505i | \(-0.0684880\pi\) | |||||||
\(368\) | − | 4.00000i | − | 0.208514i | ||||||
\(369\) | −5.52786 | + | 4.94427i | −0.287769 | + | 0.257389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.180340 | − | 1.23607i | −0.00936278 | − | 0.0641735i | ||||
\(372\) | −1.70820 | − | 4.47214i | −0.0885662 | − | 0.231869i | ||||
\(373\) | 32.1803 | 1.66623 | 0.833117 | − | 0.553096i | \(-0.186554\pi\) | ||||
0.833117 | + | 0.553096i | \(0.186554\pi\) | |||||||
\(374\) | −23.4164 | −1.21083 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 6.47214i | − | 0.333775i | ||||||
\(377\) | 9.52786 | 0.490710 | ||||||||
\(378\) | −13.0000 | − | 4.47214i | −0.668648 | − | 0.230022i | ||||
\(379\) | −17.8885 | −0.918873 | −0.459436 | − | 0.888211i | \(-0.651949\pi\) | ||||
−0.459436 | + | 0.888211i | \(0.651949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.472136 | − | 0.180340i | 0.0241883 | − | 0.00923909i | ||||
\(382\) | 7.23607 | 0.370229 | ||||||||
\(383\) | 13.8885 | 0.709671 | 0.354836 | − | 0.934929i | \(-0.384537\pi\) | ||||
0.354836 | + | 0.934929i | \(0.384537\pi\) | |||||||
\(384\) | −0.618034 | − | 1.61803i | −0.0315389 | − | 0.0825700i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000i | 0.305392i | ||||||||
\(387\) | 11.0557 | − | 9.88854i | 0.561994 | − | 0.502663i | ||||
\(388\) | − | 0.763932i | − | 0.0387828i | ||||||
\(389\) | − | 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 | ||||||||
\(392\) | −2.00000 | − | 6.70820i | −0.101015 | − | 0.338815i | ||||
\(393\) | 8.76393 | − | 3.34752i | 0.442082 | − | 0.168860i | ||||
\(394\) | −3.52786 | −0.177731 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.94427 | + | 10.0000i | 0.449467 | + | 0.502519i | ||||
\(397\) | 23.1246i | 1.16059i | 0.814406 | + | 0.580295i | \(0.197063\pi\) | ||||
−0.814406 | + | 0.580295i | \(0.802937\pi\) | |||||||
\(398\) | −22.1803 | −1.11180 | ||||||||
\(399\) | 18.9443 | + | 33.8885i | 0.948400 | + | 1.69655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.4721i | − | 0.722704i | −0.932429 | − | 0.361352i | \(-0.882315\pi\) | ||
0.932429 | − | 0.361352i | \(-0.117685\pi\) | |||||||
\(402\) | 7.41641 | + | 19.4164i | 0.369897 | + | 0.968402i | ||||
\(403\) | 3.41641 | 0.170183 | ||||||||
\(404\) | 12.4721 | 0.620512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.1803 | − | 2.94427i | 1.00153 | − | 0.146122i | ||||
\(407\) | 3.41641i | 0.169345i | ||||||||
\(408\) | 3.23607 | + | 8.47214i | 0.160209 | + | 0.419433i | ||||
\(409\) | − | 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 | ||||
\(412\) | 14.6525i | 0.721876i | ||||||||
\(413\) | −11.7082 | + | 1.70820i | −0.576123 | + | 0.0840552i | ||||
\(414\) | 8.94427 | − | 8.00000i | 0.439587 | − | 0.393179i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.23607 | 0.0606032 | ||||||||
\(417\) | 7.12461 | + | 18.6525i | 0.348894 | + | 0.913416i | ||||
\(418\) | − | 37.8885i | − | 1.85319i | ||||||
\(419\) | 36.8328 | 1.79940 | 0.899700 | − | 0.436508i | \(-0.143785\pi\) | ||||
0.899700 | + | 0.436508i | \(0.143785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.52786 | −0.171938 | −0.0859688 | − | 0.996298i | \(-0.527399\pi\) | ||||
−0.0859688 | + | 0.996298i | \(0.527399\pi\) | |||||||
\(422\) | − | 8.00000i | − | 0.389434i | ||||||
\(423\) | 14.4721 | − | 12.9443i | 0.703659 | − | 0.629372i | ||||
\(424\) | 0.472136 | 0.0229289 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −11.7082 | + | 4.47214i | −0.567264 | + | 0.216676i | ||||
\(427\) | 2.76393 | + | 18.9443i | 0.133756 | + | 0.916778i | ||||
\(428\) | − | 11.4164i | − | 0.551833i | ||||||
\(429\) | −8.94427 | + | 3.41641i | −0.431834 | + | 0.164946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.5967i | 1.90731i | 0.300905 | + | 0.953654i | \(0.402711\pi\) | ||||
−0.300905 | + | 0.953654i | \(0.597289\pi\) | |||||||
\(432\) | 2.38197 | − | 4.61803i | 0.114602 | − | 0.222185i | ||||
\(433\) | 26.6525i | 1.28084i | 0.768026 | + | 0.640418i | \(0.221239\pi\) | ||||
−0.768026 | + | 0.640418i | \(0.778761\pi\) | |||||||
\(434\) | 7.23607 | − | 1.05573i | 0.347342 | − | 0.0506766i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.47214 | −0.214176 | ||||||||
\(437\) | −33.8885 | −1.62111 | ||||||||
\(438\) | 18.1803 | − | 6.94427i | 0.868690 | − | 0.331810i | ||||
\(439\) | − | 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 | ||||
\(442\) | −6.47214 | −0.307848 | ||||||||
\(443\) | − | 18.4721i | − | 0.877638i | −0.898576 | − | 0.438819i | \(-0.855397\pi\) | ||
0.898576 | − | 0.438819i | \(-0.144603\pi\) | |||||||
\(444\) | 1.23607 | − | 0.472136i | 0.0586612 | − | 0.0224066i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.7082 | −0.838508 | ||||||||
\(447\) | 2.65248 | + | 6.94427i | 0.125458 | + | 0.328453i | ||||
\(448\) | 2.61803 | − | 0.381966i | 0.123690 | − | 0.0180462i | ||||
\(449\) | 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 | ||||||||
\(452\) | 2.94427i | 0.138487i | ||||||||
\(453\) | 33.8885 | − | 12.9443i | 1.59222 | − | 0.608175i | ||||
\(454\) | − | 0.763932i | − | 0.0358531i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.7082 | + | 5.23607i | −0.641945 | + | 0.245201i | ||||
\(457\) | −26.9443 | −1.26040 | −0.630200 | − | 0.776433i | \(-0.717027\pi\) | ||||
−0.630200 | + | 0.776433i | \(0.717027\pi\) | |||||||
\(458\) | −8.76393 | −0.409512 | ||||||||
\(459\) | −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 | \(0.551702\pi\) | |||||||
\(462\) | −17.8885 | + | 10.0000i | −0.832250 | + | 0.465242i | ||||
\(463\) | 22.1803 | 1.03081 | 0.515404 | − | 0.856947i | \(-0.327642\pi\) | ||||
0.515404 | + | 0.856947i | \(0.327642\pi\) | |||||||
\(464\) | 7.70820i | 0.357844i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.5279 | −0.534018 | ||||||||
\(467\) | 33.7082 | 1.55983 | 0.779915 | − | 0.625886i | \(-0.215262\pi\) | ||||
0.779915 | + | 0.625886i | \(0.215262\pi\) | |||||||
\(468\) | 2.47214 | + | 2.76393i | 0.114275 | + | 0.127763i | ||||
\(469\) | −31.4164 | + | 4.58359i | −1.45067 | + | 0.211651i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.70820 | − | 14.9443i | −0.263020 | − | 0.688596i | ||||
\(472\) | − | 4.47214i | − | 0.205847i | ||||||
\(473\) | − | 22.1115i | − | 1.01669i | ||||||
\(474\) | −5.52786 | − | 14.4721i | −0.253903 | − | 0.664727i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.7082 | + | 2.00000i | −0.628314 | + | 0.0916698i | ||||
\(477\) | 0.944272 | + | 1.05573i | 0.0432352 | + | 0.0483385i | ||||
\(478\) | 0.180340 | 0.00824855 | ||||||||
\(479\) | 37.8885 | 1.73117 | 0.865586 | − | 0.500761i | \(-0.166946\pi\) | ||||
0.865586 | + | 0.500761i | \(0.166946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.944272i | 0.0430551i | ||||||||
\(482\) | 17.8885 | 0.814801 | ||||||||
\(483\) | 8.94427 | + | 16.0000i | 0.406978 | + | 0.728025i | ||||
\(484\) | 9.00000 | 0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.0902 | − | 3.90983i | 0.684504 | − | 0.177353i | ||||
\(487\) | −17.5967 | −0.797385 | −0.398692 | − | 0.917085i | \(-0.630536\pi\) | ||||
−0.398692 | + | 0.917085i | \(0.630536\pi\) | |||||||
\(488\) | −7.23607 | −0.327561 | ||||||||
\(489\) | 16.9443 | − | 6.47214i | 0.766246 | − | 0.292680i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.4164i | − | 0.605474i | −0.953074 | − | 0.302737i | \(-0.902100\pi\) | ||
0.953074 | − | 0.302737i | \(-0.0979004\pi\) | |||||||
\(492\) | 4.00000 | − | 1.52786i | 0.180334 | − | 0.0688814i | ||||
\(493\) | − | 40.3607i | − | 1.81775i | ||||||
\(494\) | − | 10.4721i | − | 0.471164i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.76393i | 0.124104i | ||||||||
\(497\) | −2.76393 | − | 18.9443i | −0.123979 | − | 0.849767i | ||||
\(498\) | −9.05573 | − | 23.7082i | −0.405797 | − | 1.06239i | ||||
\(499\) | 17.8885 | 0.800801 | 0.400401 | − | 0.916340i | \(-0.368871\pi\) | ||||
0.400401 | + | 0.916340i | \(0.368871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52786 | − | 0.583592i | 0.0682599 | − | 0.0260730i | ||||
\(502\) | − | 12.4721i | − | 0.556659i | ||||||
\(503\) | 28.3607 | 1.26454 | 0.632270 | − | 0.774748i | \(-0.282123\pi\) | ||||
0.632270 | + | 0.774748i | \(0.282123\pi\) | |||||||
\(504\) | 6.09017 | + | 5.09017i | 0.271278 | + | 0.226734i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 17.8885i | − | 0.795243i | ||||||
\(507\) | 18.5623 | − | 7.09017i | 0.824381 | − | 0.314886i | ||||
\(508\) | −0.291796 | −0.0129464 | ||||||||
\(509\) | 15.5279 | 0.688260 | 0.344130 | − | 0.938922i | \(-0.388174\pi\) | ||||
0.344130 | + | 0.938922i | \(0.388174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.29180 | + | 29.4164i | 0.189858 | + | 1.30131i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −39.1246 | − | 20.1803i | −1.72739 | − | 0.890984i | ||||
\(514\) | − | 14.1803i | − | 0.625468i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.00000 | + | 3.05573i | −0.352180 | + | 0.134521i | ||||
\(517\) | − | 28.9443i | − | 1.27297i | ||||||
\(518\) | 0.291796 | + | 2.00000i | 0.0128208 | + | 0.0878750i | ||||
\(519\) | 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 | \(0.800142\pi\) | |||||||
\(522\) | −17.2361 | + | 15.4164i | −0.754402 | + | 0.674758i | ||||
\(523\) | − | 42.5410i | − | 1.86019i | −0.367320 | − | 0.930094i | \(-0.619725\pi\) | ||
0.367320 | − | 0.930094i | \(-0.380275\pi\) | |||||||
\(524\) | −5.41641 | −0.236617 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.9443 | 0.564397 | ||||||||
\(527\) | − | 14.4721i | − | 0.630416i | ||||||
\(528\) | −2.76393 | − | 7.23607i | −0.120285 | − | 0.314909i | ||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | − | 8.94427i | 0.433963 | − | 0.388148i | ||||
\(532\) | −3.23607 | − | 22.1803i | −0.140301 | − | 0.961640i | ||||
\(533\) | 3.05573i | 0.132358i | ||||||||
\(534\) | −3.41641 | − | 8.94427i | −0.147842 | − | 0.387056i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.0000i | − | 0.518321i | ||||||
\(537\) | 9.23607 | + | 24.1803i | 0.398566 | + | 1.04346i | ||||
\(538\) | 4.47214i | 0.192807i | ||||||||
\(539\) | −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 | \(0.268347\pi\) | |||||||
\(542\) | 31.7082 | 1.36198 | ||||||||
\(543\) | 10.0000 | + | 26.1803i | 0.429141 | + | 1.12351i | ||||
\(544\) | − | 5.23607i | − | 0.224495i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.94427 | + | 2.76393i | −0.211595 | + | 0.118285i | ||||
\(547\) | 35.4164 | 1.51430 | 0.757148 | − | 0.653243i | \(-0.226592\pi\) | ||||
0.757148 | + | 0.653243i | \(0.226592\pi\) | |||||||
\(548\) | − | 3.52786i | − | 0.150703i | ||||||
\(549\) | −14.4721 | − | 16.1803i | −0.617656 | − | 0.690560i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.3050 | 2.78208 | ||||||||
\(552\) | −6.47214 | + | 2.47214i | −0.275472 | + | 0.105221i | ||||
\(553\) | 23.4164 | − | 3.41641i | 0.995767 | − | 0.145280i | ||||
\(554\) | 17.1246i | 0.727555i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 11.5279i | − | 0.488890i | ||||||
\(557\) | − | 7.52786i | − | 0.318966i | −0.987201 | − | 0.159483i | \(-0.949017\pi\) | ||
0.987201 | − | 0.159483i | \(-0.0509827\pi\) | |||||||
\(558\) | −6.18034 | + | 5.52786i | −0.261635 | + | 0.234013i | ||||
\(559\) | − | 6.11146i | − | 0.258487i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4721 | + | 37.8885i | 0.611014 | + | 1.59966i | ||||
\(562\) | 20.0000 | 0.843649 | ||||||||
\(563\) | −40.1803 | −1.69340 | −0.846700 | − | 0.532071i | \(-0.821414\pi\) | ||||
−0.846700 | + | 0.532071i | \(0.821414\pi\) | |||||||
\(564\) | −10.4721 | + | 4.00000i | −0.440956 | + | 0.168430i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.2361 | −0.556353 | ||||||||
\(567\) | 0.798374 | + | 23.7984i | 0.0335286 | + | 0.999438i | ||||
\(568\) | 7.23607 | 0.303619 | ||||||||
\(569\) | − | 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 | \(0.371069\pi\) | |||||||
\(572\) | 5.52786 | 0.231132 | ||||||||
\(573\) | −4.47214 | − | 11.7082i | −0.186826 | − | 0.489117i | ||||
\(574\) | 0.944272 | + | 6.47214i | 0.0394131 | + | 0.270142i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.23607 | + | 2.00000i | −0.0931695 | + | 0.0833333i | ||||
\(577\) | − | 8.18034i | − | 0.340552i | −0.985396 | − | 0.170276i | \(-0.945534\pi\) | ||
0.985396 | − | 0.170276i | \(-0.0544659\pi\) | |||||||
\(578\) | 10.4164i | 0.433265i | ||||||||
\(579\) | 9.70820 | − | 3.70820i | 0.403459 | − | 0.154108i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.3607 | − | 5.59675i | 1.59147 | − | 0.232192i | ||||
\(582\) | −1.23607 | + | 0.472136i | −0.0512367 | + | 0.0195707i | ||||
\(583\) | 2.11146 | 0.0874476 | ||||||||
\(584\) | −11.2361 | −0.464952 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.58359i | 0.106727i | ||||||||
\(587\) | 10.2918 | 0.424788 | 0.212394 | − | 0.977184i | \(-0.431874\pi\) | ||||
0.212394 | + | 0.977184i | \(0.431874\pi\) | |||||||
\(588\) | −9.61803 | + | 7.38197i | −0.396641 | + | 0.304427i | ||||
\(589\) | 23.4164 | 0.964856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.18034 | + | 5.70820i | 0.0896872 | + | 0.234804i | ||||
\(592\) | −0.763932 | −0.0313974 | ||||||||
\(593\) | 29.0132 | 1.19143 | 0.595714 | − | 0.803197i | \(-0.296869\pi\) | ||||
0.595714 | + | 0.803197i | \(0.296869\pi\) | |||||||
\(594\) | 10.6525 | − | 20.6525i | 0.437076 | − | 0.847381i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 4.29180i | − | 0.175799i | ||||||
\(597\) | 13.7082 | + | 35.8885i | 0.561039 | + | 1.46882i | ||||
\(598\) | − | 4.94427i | − | 0.202186i | ||||||
\(599\) | − | 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 | \(-0.964036\pi\) | ||
0.993624 | − | 0.112743i | \(-0.0359637\pi\) | |||||||
\(602\) | −1.88854 | − | 12.9443i | −0.0769713 | − | 0.527569i | ||||
\(603\) | 26.8328 | − | 24.0000i | 1.09272 | − | 0.977356i | ||||
\(604\) | −20.9443 | −0.852210 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.70820 | − | 20.1803i | −0.313124 | − | 0.819770i | ||||
\(607\) | − | 19.2361i | − | 0.780768i | −0.920652 | − | 0.390384i | \(-0.872342\pi\) | ||
0.920652 | − | 0.390384i | \(-0.127658\pi\) | |||||||
\(608\) | 8.47214 | 0.343590 | ||||||||
\(609\) | −17.2361 | − | 30.8328i | −0.698441 | − | 1.24941i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8.00000i | − | 0.323645i | ||||||
\(612\) | 11.7082 | − | 10.4721i | 0.473276 | − | 0.423311i | ||||
\(613\) | −38.0689 | −1.53759 | −0.768794 | − | 0.639497i | \(-0.779143\pi\) | ||||
−0.768794 | + | 0.639497i | \(0.779143\pi\) | |||||||
\(614\) | 18.1803 | 0.733699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.7082 | − | 1.70820i | 0.471737 | − | 0.0688255i | ||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 23.7082 | − | 9.05573i | 0.953684 | − | 0.364275i | ||||
\(619\) | − | 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 | ||||
\(622\) | 17.5279i | 0.702803i | ||||||||
\(623\) | 14.4721 | − | 2.11146i | 0.579814 | − | 0.0845937i | ||||
\(624\) | −0.763932 | − | 2.00000i | −0.0305818 | − | 0.0800641i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.70820 | 0.228146 | ||||||||
\(627\) | −61.3050 | + | 23.4164i | −2.44828 | + | 0.935161i | ||||
\(628\) | 9.23607i | 0.368559i | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.88854 | −0.234419 | −0.117210 | − | 0.993107i | \(-0.537395\pi\) | ||||
−0.117210 | + | 0.993107i | \(0.537395\pi\) | |||||||
\(632\) | 8.94427i | 0.355784i | ||||||||
\(633\) | −12.9443 | + | 4.94427i | −0.514489 | + | 0.196517i | ||||
\(634\) | 10.9443 | 0.434653 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.291796 | − | 0.763932i | −0.0115705 | − | 0.0302919i | ||||
\(637\) | −2.47214 | − | 8.29180i | −0.0979496 | − | 0.328533i | ||||
\(638\) | 34.4721i | 1.36476i | ||||||||
\(639\) | 14.4721 | + | 16.1803i | 0.572509 | + | 0.640084i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.4164i | − | 0.924893i | −0.886647 | − | 0.462446i | \(-0.846972\pi\) | ||
0.886647 | − | 0.462446i | \(-0.153028\pi\) | |||||||
\(642\) | −18.4721 | + | 7.05573i | −0.729037 | + | 0.278467i | ||||
\(643\) | − | 12.2918i | − | 0.484741i | −0.970184 | − | 0.242371i | \(-0.922075\pi\) | ||
0.970184 | − | 0.242371i | \(-0.0779250\pi\) | |||||||
\(644\) | −1.52786 | − | 10.4721i | −0.0602063 | − | 0.412660i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.3607 | −1.74535 | ||||||||
\(647\) | −34.8328 | −1.36942 | −0.684710 | − | 0.728816i | \(-0.740071\pi\) | ||||
−0.684710 | + | 0.728816i | \(0.740071\pi\) | |||||||
\(648\) | −8.94427 | − | 1.00000i | −0.351364 | − | 0.0392837i | ||||
\(649\) | − | 20.0000i | − | 0.785069i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.18034 | − | 11.0557i | −0.242227 | − | 0.433308i | ||||
\(652\) | −10.4721 | −0.410120 | ||||||||
\(653\) | 23.8885i | 0.934831i | 0.884038 | + | 0.467415i | \(0.154815\pi\) | ||||
−0.884038 | + | 0.467415i | \(0.845185\pi\) | |||||||
\(654\) | 2.76393 | + | 7.23607i | 0.108078 | + | 0.282953i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.47214 | −0.0965207 | ||||||||
\(657\) | −22.4721 | − | 25.1246i | −0.876722 | − | 0.980204i | ||||
\(658\) | −2.47214 | − | 16.9443i | −0.0963739 | − | 0.660556i | ||||
\(659\) | 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 | \(-0.884231\pi\) | ||
0.934587 | − | 0.355734i | \(-0.115769\pi\) | |||||||
\(662\) | 3.05573i | 0.118764i | ||||||||
\(663\) | 4.00000 | + | 10.4721i | 0.155347 | + | 0.406704i | ||||
\(664\) | 14.6525i | 0.568626i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.52786 | − | 1.70820i | −0.0592035 | − | 0.0661916i | ||||
\(667\) | 30.8328 | 1.19385 | ||||||||
\(668\) | −0.944272 | −0.0365350 | ||||||||
\(669\) | 10.9443 | + | 28.6525i | 0.423130 | + | 1.10777i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.3607 | −1.24927 | ||||||||
\(672\) | −2.23607 | − | 4.00000i | −0.0862582 | − | 0.154303i | ||||
\(673\) | −19.5279 | −0.752744 | −0.376372 | − | 0.926469i | \(-0.622829\pi\) | ||||
−0.376372 | + | 0.926469i | \(0.622829\pi\) | |||||||
\(674\) | − | 21.4164i | − | 0.824929i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.4721 | −0.441236 | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 4.76393 | − | 1.81966i | 0.182958 | − | 0.0698836i | ||||
\(679\) | −0.291796 | − | 2.00000i | −0.0111981 | − | 0.0767530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23607 | + | 0.472136i | −0.0473662 | + | 0.0180923i | ||||
\(682\) | 12.3607i | 0.473315i | ||||||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | 16.9443 | + | 18.9443i | 0.647880 | + | 0.724352i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.79837 | − | 16.7984i | −0.297743 | − | 0.641365i | ||||
\(687\) | 5.41641 | + | 14.1803i | 0.206649 | + | 0.541014i | ||||
\(688\) | 4.94427 | 0.188499 | ||||||||
\(689\) | 0.583592 | 0.0222331 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0557i | 0.800998i | 0.916297 | + | 0.400499i | \(0.131163\pi\) | ||||
−0.916297 | + | 0.400499i | \(0.868837\pi\) | |||||||
\(692\) | −9.41641 | −0.357958 | ||||||||
\(693\) | 27.2361 | + | 22.7639i | 1.03461 | + | 0.864730i | ||||
\(694\) | −2.47214 | −0.0938410 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.4721 | − | 4.76393i | 0.472755 | − | 0.180576i | ||||
\(697\) | 12.9443 | 0.490299 | ||||||||
\(698\) | 20.1803 | 0.763837 | ||||||||
\(699\) | 7.12461 | + | 18.6525i | 0.269478 | + | 0.705501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.0689i | 1.66446i | 0.554431 | + | 0.832229i | \(0.312936\pi\) | ||||
−0.554431 | + | 0.832229i | \(0.687064\pi\) | |||||||
\(702\) | 2.94427 | − | 5.70820i | 0.111124 | − | 0.215442i | ||||
\(703\) | 6.47214i | 0.244101i | ||||||||
\(704\) | 4.47214i | 0.168550i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.7082i | 1.04281i | ||||||||
\(707\) | 32.6525 | − | 4.76393i | 1.22802 | − | 0.179166i | ||||
\(708\) | −7.23607 | + | 2.76393i | −0.271948 | + | 0.103875i | ||||
\(709\) | −15.5279 | −0.583161 | −0.291581 | − | 0.956546i | \(-0.594181\pi\) | ||||
−0.291581 | + | 0.956546i | \(0.594181\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0000 | + | 17.8885i | −0.750059 | + | 0.670873i | ||||
\(712\) | 5.52786i | 0.207165i | ||||||||
\(713\) | 11.0557 | 0.414040 | ||||||||
\(714\) | 11.7082 | + | 20.9443i | 0.438169 | + | 0.783820i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 14.9443i | − | 0.558494i | ||||||
\(717\) | −0.111456 | − | 0.291796i | −0.00416241 | − | 0.0108973i | ||||
\(718\) | −12.1803 | −0.454566 | ||||||||
\(719\) | −34.4721 | −1.28559 | −0.642797 | − | 0.766037i | \(-0.722226\pi\) | ||||
−0.642797 | + | 0.766037i | \(0.722226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.59675 | + | 38.3607i | 0.208434 | + | 1.42863i | ||||
\(722\) | − | 52.7771i | − | 1.96416i | ||||||
\(723\) | −11.0557 | − | 28.9443i | −0.411167 | − | 1.07645i | ||||
\(724\) | − | 16.1803i | − | 0.601338i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.56231 | − | 14.5623i | −0.206437 | − | 0.540458i | ||||
\(727\) | 26.2918i | 0.975109i | 0.873093 | + | 0.487554i | \(0.162111\pi\) | ||||
−0.873093 | + | 0.487554i | \(0.837889\pi\) | |||||||
\(728\) | 3.23607 | − | 0.472136i | 0.119937 | − | 0.0174985i | ||||
\(729\) | −15.6525 | − | 22.0000i | −0.579721 | − | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | 4.47214 | + | 11.7082i | 0.165295 | + | 0.432748i | ||||
\(733\) | 20.0689i | 0.741261i | 0.928780 | + | 0.370631i | \(0.120858\pi\) | ||||
−0.928780 | + | 0.370631i | \(0.879142\pi\) | |||||||
\(734\) | 8.18034 | 0.301942 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | − | 53.6656i | − | 1.97680i | ||||||
\(738\) | −4.94427 | − | 5.52786i | −0.182001 | − | 0.203483i | ||||
\(739\) | 8.94427 | 0.329020 | 0.164510 | − | 0.986375i | \(-0.447396\pi\) | ||||
0.164510 | + | 0.986375i | \(0.447396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9443 | + | 6.47214i | −0.622463 | + | 0.237760i | ||||
\(742\) | 1.23607 | − | 0.180340i | 0.0453775 | − | 0.00662049i | ||||
\(743\) | 10.4721i | 0.384185i | 0.981377 | + | 0.192093i | \(0.0615274\pi\) | ||||
−0.981377 | + | 0.192093i | \(0.938473\pi\) | |||||||
\(744\) | 4.47214 | − | 1.70820i | 0.163956 | − | 0.0626258i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.1803i | 1.17821i | ||||||||
\(747\) | −32.7639 | + | 29.3050i | −1.19877 | + | 1.07221i | ||||
\(748\) | − | 23.4164i | − | 0.856189i | ||||||
\(749\) | −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 | \(0.449943\pi\) | |||||||
\(752\) | 6.47214 | 0.236015 | ||||||||
\(753\) | −20.1803 | + | 7.70820i | −0.735412 | + | 0.280903i | ||||
\(754\) | 9.52786i | 0.346984i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.47214 | − | 13.0000i | 0.162650 | − | 0.472805i | ||||
\(757\) | 2.65248 | 0.0964059 | 0.0482029 | − | 0.998838i | \(-0.484651\pi\) | ||||
0.0482029 | + | 0.998838i | \(0.484651\pi\) | |||||||
\(758\) | − | 17.8885i | − | 0.649741i | ||||||
\(759\) | −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 | \(0.534038\pi\) | |||||||
\(762\) | 0.180340 | + | 0.472136i | 0.00653302 | + | 0.0171037i | ||||
\(763\) | −11.7082 | + | 1.70820i | −0.423865 | + | 0.0618411i | ||||
\(764\) | 7.23607i | 0.261792i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.8885i | 0.501813i | ||||||||
\(767\) | − | 5.52786i | − | 0.199600i | ||||||
\(768\) | 1.61803 | − | 0.618034i | 0.0583858 | − | 0.0223014i | ||||
\(769\) | 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 | ||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | −10.5836 | −0.380665 | −0.190333 | − | 0.981720i | \(-0.560957\pi\) | ||||
−0.190333 | + | 0.981720i | \(0.560957\pi\) | |||||||
\(774\) | 9.88854 | + | 11.0557i | 0.355436 | + | 0.397390i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.763932 | 0.0274236 | ||||||||
\(777\) | 3.05573 | − | 1.70820i | 0.109624 | − | 0.0612815i | ||||
\(778\) | 30.1803 | 1.08202 | ||||||||
\(779\) | 20.9443i | 0.750406i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.3607 | 1.15796 | ||||||||
\(782\) | −20.9443 | −0.748966 | ||||||||
\(783\) | 35.5967 | + | 18.3607i | 1.27212 | + | 0.656157i | ||||
\(784\) | 6.70820 | − | 2.00000i | 0.239579 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.34752 | + | 8.76393i | 0.119402 | + | 0.312599i | ||||
\(787\) | 36.2918i | 1.29366i | 0.762633 | + | 0.646831i | \(0.223906\pi\) | ||||
−0.762633 | + | 0.646831i | \(0.776094\pi\) | |||||||
\(788\) | − | 3.52786i | − | 0.125675i | ||||||
\(789\) | −8.00000 | − | 20.9443i | −0.284808 | − | 0.745636i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.12461 | + | 7.70820i | 0.0399866 | + | 0.274072i | ||||
\(792\) | −10.0000 | + | 8.94427i | −0.355335 | + | 0.317821i | ||||
\(793\) | −8.94427 | −0.317620 | ||||||||
\(794\) | −23.1246 | −0.820662 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 22.1803i | − | 0.786161i | ||||||
\(797\) | −21.4164 | −0.758608 | −0.379304 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379304 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(798\) | −33.8885 | + | 18.9443i | −1.19964 | + | 0.670620i | ||||
\(799\) | −33.8885 | −1.19889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.3607 | + | 11.0557i | −0.436743 | + | 0.390635i | ||||
\(802\) | 14.4721 | 0.511029 | ||||||||
\(803\) | −50.2492 | −1.77326 | ||||||||
\(804\) | −19.4164 | + | 7.41641i | −0.684764 | + | 0.261557i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.41641i | 0.120338i | ||||||||
\(807\) | 7.23607 | − | 2.76393i | 0.254722 | − | 0.0972950i | ||||
\(808\) | 12.4721i | 0.438768i | ||||||||
\(809\) | − | 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 | \(-0.776154\pi\) | ||
0.762755 | − | 0.646688i | \(-0.223846\pi\) | |||||||
\(812\) | 2.94427 | + | 20.1803i | 0.103324 | + | 0.708191i | ||||
\(813\) | −19.5967 | − | 51.3050i | −0.687288 | − | 1.79934i | ||||
\(814\) | −3.41641 | −0.119745 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.47214 | + | 3.23607i | −0.296584 | + | 0.113285i | ||||
\(817\) | − | 41.8885i | − | 1.46549i | ||||||
\(818\) | 7.41641 | 0.259309 | ||||||||
\(819\) | 7.52786 | + | 6.29180i | 0.263045 | + | 0.219853i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.7082i | 1.10662i | 0.832974 | + | 0.553312i | \(0.186636\pi\) | ||||
−0.832974 | + | 0.553312i | \(0.813364\pi\) | |||||||
\(822\) | −5.70820 | + | 2.18034i | −0.199096 | + | 0.0760481i | ||||
\(823\) | 22.1803 | 0.773158 | 0.386579 | − | 0.922256i | \(-0.373657\pi\) | ||||
0.386579 | + | 0.922256i | \(0.373657\pi\) | |||||||
\(824\) | −14.6525 | −0.510443 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.70820 | − | 11.7082i | −0.0594360 | − | 0.407381i | ||||
\(827\) | − | 38.8328i | − | 1.35035i | −0.737658 | − | 0.675175i | \(-0.764068\pi\) | ||
0.737658 | − | 0.675175i | \(-0.235932\pi\) | |||||||
\(828\) | 8.00000 | + | 8.94427i | 0.278019 | + | 0.310835i | ||||
\(829\) | − | 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 | ||||
\(832\) | 1.23607i | 0.0428529i | ||||||||
\(833\) | −35.1246 | + | 10.4721i | −1.21700 | + | 0.362838i | ||||
\(834\) | −18.6525 | + | 7.12461i | −0.645882 | + | 0.246705i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 37.8885 | 1.31040 | ||||||||
\(837\) | 12.7639 | + | 6.58359i | 0.441186 | + | 0.227562i | ||||
\(838\) | 36.8328i | 1.27237i | ||||||||
\(839\) | 5.52786 | 0.190843 | 0.0954215 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954215 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.4164 | −1.04884 | ||||||||
\(842\) | − | 3.52786i | − | 0.121578i | ||||||
\(843\) | −12.3607 | − | 32.3607i | −0.425724 | − | 1.11456i | ||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.9443 | + | 14.4721i | 0.445033 | + | 0.497562i | ||||
\(847\) | 23.5623 | − | 3.43769i | 0.809610 | − | 0.118121i | ||||
\(848\) | 0.472136i | 0.0162132i | ||||||||
\(849\) | 8.18034 | + | 21.4164i | 0.280749 | + | 0.735009i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.05573i | 0.104749i | ||||||||
\(852\) | −4.47214 | − | 11.7082i | −0.153213 | − | 0.401116i | ||||
\(853\) | 7.70820i | 0.263924i | 0.991255 | + | 0.131962i | \(0.0421277\pi\) | ||||
−0.991255 | + | 0.131962i | \(0.957872\pi\) | |||||||
\(854\) | −18.9443 | + | 2.76393i | −0.648260 | + | 0.0945798i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.4164 | 0.390205 | ||||||||
\(857\) | 11.3475 | 0.387624 | 0.193812 | − | 0.981039i | \(-0.437915\pi\) | ||||
0.193812 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(858\) | −3.41641 | − | 8.94427i | −0.116634 | − | 0.305352i | ||||
\(859\) | 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 | ||||
\(862\) | −39.5967 | −1.34867 | ||||||||
\(863\) | 30.4721i | 1.03728i | 0.854992 | + | 0.518642i | \(0.173562\pi\) | ||||
−0.854992 | + | 0.518642i | \(0.826438\pi\) | |||||||
\(864\) | 4.61803 | + | 2.38197i | 0.157109 | + | 0.0810361i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26.6525 | −0.905688 | ||||||||
\(867\) | 16.8541 | − | 6.43769i | 0.572395 | − | 0.218636i | ||||
\(868\) | 1.05573 | + | 7.23607i | 0.0358337 | + | 0.245608i | ||||
\(869\) | 40.0000i | 1.35691i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.8328i | − | 0.502591i | ||||||
\(872\) | − | 4.47214i | − | 0.151446i | ||||||
\(873\) | 1.52786 | + | 1.70820i | 0.0517104 | + | 0.0578139i | ||||
\(874\) | − | 33.8885i | − | 1.14630i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.94427 | + | 18.1803i | 0.234625 | + | 0.614257i | ||||
\(877\) | −38.6525 | −1.30520 | −0.652601 | − | 0.757702i | \(-0.726322\pi\) | ||||
−0.652601 | + | 0.757702i | \(0.726322\pi\) | |||||||
\(878\) | 10.1803 | 0.343570 | ||||||||
\(879\) | 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 | \(0.416378\pi\) | |||||||
\(882\) | 17.8885 | + | 11.0000i | 0.602339 | + | 0.370389i | ||||
\(883\) | 13.8885 | 0.467387 | 0.233693 | − | 0.972310i | \(-0.424919\pi\) | ||||
0.233693 | + | 0.972310i | \(0.424919\pi\) | |||||||
\(884\) | − | 6.47214i | − | 0.217681i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.4721 | 0.620584 | ||||||||
\(887\) | 17.5279 | 0.588528 | 0.294264 | − | 0.955724i | \(-0.404925\pi\) | ||||
0.294264 | + | 0.955724i | \(0.404925\pi\) | |||||||
\(888\) | 0.472136 | + | 1.23607i | 0.0158438 | + | 0.0414797i | ||||
\(889\) | −0.763932 | + | 0.111456i | −0.0256215 | + | 0.00373812i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.0000 | − | 4.47214i | −1.34005 | − | 0.149822i | ||||
\(892\) | − | 17.7082i | − | 0.592915i | ||||||
\(893\) | − | 54.8328i | − | 1.83491i | ||||||
\(894\) | −6.94427 | + | 2.65248i | −0.232251 | + | 0.0887121i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.381966 | + | 2.61803i | 0.0127606 | + | 0.0874624i | ||||
\(897\) | −8.00000 | + | 3.05573i | −0.267112 | + | 0.102028i | ||||
\(898\) | −10.4721 | −0.349460 | ||||||||
\(899\) | −21.3050 | −0.710560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.47214i | − | 0.0823588i | ||||||
\(902\) | −11.0557 | −0.368115 | ||||||||
\(903\) | −19.7771 | + | 11.0557i | −0.658140 | + | 0.367912i | ||||
\(904\) | −2.94427 | −0.0979250 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.9443 | + | 33.8885i | 0.430045 | + | 1.12587i | ||||
\(907\) | 17.5279 | 0.582003 | 0.291002 | − | 0.956723i | \(-0.406012\pi\) | ||||
0.291002 | + | 0.956723i | \(0.406012\pi\) | |||||||
\(908\) | 0.763932 | 0.0253520 | ||||||||
\(909\) | −27.8885 | + | 24.9443i | −0.925005 | + | 0.827349i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.6525i | − | 1.67819i | −0.543984 | − | 0.839096i | \(-0.683085\pi\) | ||
0.543984 | − | 0.839096i | \(-0.316915\pi\) | |||||||
\(912\) | −5.23607 | − | 13.7082i | −0.173384 | − | 0.453924i | ||||
\(913\) | 65.5279i | 2.16866i | ||||||||
\(914\) | − | 26.9443i | − | 0.891237i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 8.76393i | − | 0.289568i | ||||||
\(917\) | −14.1803 | + | 2.06888i | −0.468276 | + | 0.0683206i | ||||
\(918\) | −24.1803 | − | 12.4721i | −0.798070 | − | 0.411642i | ||||
\(919\) | −44.7214 | −1.47522 | −0.737611 | − | 0.675226i | \(-0.764046\pi\) | ||||
−0.737611 | + | 0.675226i | \(0.764046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2361 | − | 29.4164i | −0.370241 | − | 0.969304i | ||||
\(922\) | − | 6.94427i | − | 0.228697i | ||||||
\(923\) | 8.94427 | 0.294404 | ||||||||
\(924\) | −10.0000 | − | 17.8885i | −0.328976 | − | 0.588490i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.1803i | 0.728891i | ||||||||
\(927\) | −29.3050 | − | 32.7639i | −0.962501 | − | 1.07611i | ||||
\(928\) | −7.70820 | −0.253034 | ||||||||
\(929\) | 37.8885 | 1.24308 | 0.621541 | − | 0.783381i | \(-0.286507\pi\) | ||||
0.621541 | + | 0.783381i | \(0.286507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.9443 | − | 56.8328i | −0.555326 | − | 1.86262i | ||||
\(932\) | − | 11.5279i | − | 0.377608i | ||||||
\(933\) | 28.3607 | − | 10.8328i | 0.928487 | − | 0.354650i | ||||
\(934\) | 33.7082i | 1.10297i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.76393 | + | 2.47214i | −0.0903419 | + | 0.0808043i | ||||
\(937\) | 42.0689i | 1.37433i | 0.726501 | + | 0.687165i | \(0.241145\pi\) | ||||
−0.726501 | + | 0.687165i | \(0.758855\pi\) | |||||||
\(938\) | −4.58359 | − | 31.4164i | −0.149660 | − | 1.02578i | ||||
\(939\) | −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 | \(0.383258\pi\) | |||||||
\(942\) | 14.9443 | − | 5.70820i | 0.486911 | − | 0.185983i | ||||
\(943\) | 9.88854i | 0.322015i | ||||||||
\(944\) | 4.47214 | 0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.1115 | 0.718905 | ||||||||
\(947\) | 60.3607i | 1.96146i | 0.195372 | + | 0.980729i | \(0.437409\pi\) | ||||
−0.195372 | + | 0.980729i | \(0.562591\pi\) | |||||||
\(948\) | 14.4721 | − | 5.52786i | 0.470033 | − | 0.179537i | ||||
\(949\) | −13.8885 | −0.450841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.76393 | − | 17.7082i | −0.219336 | − | 0.574228i | ||||
\(952\) | −2.00000 | − | 13.7082i | −0.0648204 | − | 0.444285i | ||||
\(953\) | 22.5836i | 0.731554i | 0.930702 | + | 0.365777i | \(0.119197\pi\) | ||||
−0.930702 | + | 0.365777i | \(0.880803\pi\) | |||||||
\(954\) | −1.05573 | + | 0.944272i | −0.0341805 | + | 0.0305719i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.180340i | 0.00583261i | ||||||||
\(957\) | 55.7771 | − | 21.3050i | 1.80302 | − | 0.688691i | ||||
\(958\) | 37.8885i | 1.22412i | ||||||||
\(959\) | −1.34752 | − | 9.23607i | −0.0435138 | − | 0.298248i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3607 | 0.753570 | ||||||||
\(962\) | −0.944272 | −0.0304445 | ||||||||
\(963\) | 22.8328 | + | 25.5279i | 0.735777 | + | 0.822624i | ||||
\(964\) | 17.8885i | 0.576151i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.0000 | + | 8.94427i | −0.514792 | + | 0.287777i | ||||
\(967\) | 39.4853 | 1.26976 | 0.634881 | − | 0.772610i | \(-0.281049\pi\) | ||||
0.634881 | + | 0.772610i | \(0.281049\pi\) | |||||||
\(968\) | 9.00000i | 0.289271i | ||||||||
\(969\) | 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 | \(0.880761\pi\) | |||||||
\(972\) | 3.90983 | + | 15.0902i | 0.125408 | + | 0.484017i | ||||
\(973\) | −4.40325 | − | 30.1803i | −0.141162 | − | 0.967537i | ||||
\(974\) | − | 17.5967i | − | 0.563836i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 7.23607i | − | 0.231621i | ||||||
\(977\) | 1.41641i | 0.0453149i | 0.999743 | + | 0.0226575i | \(0.00721271\pi\) | ||||
−0.999743 | + | 0.0226575i | \(0.992787\pi\) | |||||||
\(978\) | 6.47214 | + | 16.9443i | 0.206956 | + | 0.541818i | ||||
\(979\) | 24.7214i | 0.790098i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | − | 8.94427i | 0.319275 | − | 0.285569i | ||||
\(982\) | 13.4164 | 0.428135 | ||||||||
\(983\) | 12.5836 | 0.401354 | 0.200677 | − | 0.979657i | \(-0.435686\pi\) | ||||
0.200677 | + | 0.979657i | \(0.435686\pi\) | |||||||
\(984\) | 1.52786 | + | 4.00000i | 0.0487065 | + | 0.127515i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 40.3607 | 1.28535 | ||||||||
\(987\) | −25.8885 | + | 14.4721i | −0.824041 | + | 0.460653i | ||||
\(988\) | 10.4721 | 0.333163 | ||||||||
\(989\) | − | 19.7771i | − | 0.628875i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5279 | 0.556791 | 0.278395 | − | 0.960467i | \(-0.410197\pi\) | ||||
0.278395 | + | 0.960467i | \(0.410197\pi\) | |||||||
\(992\) | −2.76393 | −0.0877549 | ||||||||
\(993\) | 4.94427 | − | 1.88854i | 0.156902 | − | 0.0599311i | ||||
\(994\) | 18.9443 | − | 2.76393i | 0.600876 | − | 0.0876666i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 23.7082 | − | 9.05573i | 0.751223 | − | 0.286942i | ||||
\(997\) | 25.2361i | 0.799234i | 0.916682 | + | 0.399617i | \(0.130857\pi\) | ||||
−0.916682 | + | 0.399617i | \(0.869143\pi\) | |||||||
\(998\) | 17.8885i | 0.566252i | ||||||||
\(999\) | −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.b.c.251.4 | 4 | ||
3.2 | odd | 2 | 1050.2.b.a.251.1 | 4 | |||
5.2 | odd | 4 | 1050.2.d.c.1049.1 | 4 | |||
5.3 | odd | 4 | 1050.2.d.d.1049.4 | 4 | |||
5.4 | even | 2 | 210.2.b.a.41.1 | ✓ | 4 | ||
7.6 | odd | 2 | 1050.2.b.a.251.3 | 4 | |||
15.2 | even | 4 | 1050.2.d.f.1049.2 | 4 | |||
15.8 | even | 4 | 1050.2.d.a.1049.3 | 4 | |||
15.14 | odd | 2 | 210.2.b.b.41.4 | yes | 4 | ||
20.19 | odd | 2 | 1680.2.f.i.881.3 | 4 | |||
21.20 | even | 2 | inner | 1050.2.b.c.251.2 | 4 | ||
35.13 | even | 4 | 1050.2.d.f.1049.1 | 4 | |||
35.27 | even | 4 | 1050.2.d.a.1049.4 | 4 | |||
35.34 | odd | 2 | 210.2.b.b.41.2 | yes | 4 | ||
60.59 | even | 2 | 1680.2.f.e.881.1 | 4 | |||
105.62 | odd | 4 | 1050.2.d.d.1049.3 | 4 | |||
105.83 | odd | 4 | 1050.2.d.c.1049.2 | 4 | |||
105.104 | even | 2 | 210.2.b.a.41.3 | yes | 4 | ||
140.139 | even | 2 | 1680.2.f.e.881.2 | 4 | |||
420.419 | odd | 2 | 1680.2.f.i.881.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.b.a.41.1 | ✓ | 4 | 5.4 | even | 2 | ||
210.2.b.a.41.3 | yes | 4 | 105.104 | even | 2 | ||
210.2.b.b.41.2 | yes | 4 | 35.34 | odd | 2 | ||
210.2.b.b.41.4 | yes | 4 | 15.14 | odd | 2 | ||
1050.2.b.a.251.1 | 4 | 3.2 | odd | 2 | |||
1050.2.b.a.251.3 | 4 | 7.6 | odd | 2 | |||
1050.2.b.c.251.2 | 4 | 21.20 | even | 2 | inner | ||
1050.2.b.c.251.4 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.d.a.1049.3 | 4 | 15.8 | even | 4 | |||
1050.2.d.a.1049.4 | 4 | 35.27 | even | 4 | |||
1050.2.d.c.1049.1 | 4 | 5.2 | odd | 4 | |||
1050.2.d.c.1049.2 | 4 | 105.83 | odd | 4 | |||
1050.2.d.d.1049.3 | 4 | 105.62 | odd | 4 | |||
1050.2.d.d.1049.4 | 4 | 5.3 | odd | 4 | |||
1050.2.d.f.1049.1 | 4 | 35.13 | even | 4 | |||
1050.2.d.f.1049.2 | 4 | 15.2 | even | 4 | |||
1680.2.f.e.881.1 | 4 | 60.59 | even | 2 | |||
1680.2.f.e.881.2 | 4 | 140.139 | even | 2 | |||
1680.2.f.i.881.3 | 4 | 20.19 | odd | 2 | |||
1680.2.f.i.881.4 | 4 | 420.419 | odd | 2 |