Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [57,2,Mod(56,57)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(57, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("57.56");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.455147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 56.1 | ||
Root | \(-0.707107 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 57.56 |
Dual form | 57.2.d.a.56.2 |
$q$-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 \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(40\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 0.707107 | − | 1.58114i | 0.408248 | − | 0.912871i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(6\) | −1.00000 | + | 2.23607i | −0.408248 | + | 0.912871i | ||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −2.00000 | − | 2.23607i | −0.666667 | − | 0.745356i | ||||
\(10\) | 3.16228i | 1.00000i | ||||||||
\(11\) | 2.23607i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.16228i | 0.877058i | 0.898717 | + | 0.438529i | \(0.144500\pi\) | ||||
−0.898717 | + | 0.438529i | \(0.855500\pi\) | |||||||
\(14\) | −1.41421 | −0.377964 | ||||||||
\(15\) | −3.53553 | − | 1.58114i | −0.912871 | − | 0.408248i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 6.70820i | 1.62698i | 0.581580 | + | 0.813489i | \(0.302435\pi\) | ||||
−0.581580 | + | 0.813489i | \(0.697565\pi\) | |||||||
\(18\) | 2.82843 | + | 3.16228i | 0.666667 | + | 0.745356i | ||||
\(19\) | 3.00000 | − | 3.16228i | 0.688247 | − | 0.725476i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.707107 | − | 1.58114i | 0.154303 | − | 0.345033i | ||||
\(22\) | − | 3.16228i | − | 0.674200i | ||||||
\(23\) | − | 4.47214i | − | 0.932505i | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||
0.884652 | − | 0.466252i | \(-0.154396\pi\) | |||||||
\(24\) | 2.00000 | − | 4.47214i | 0.408248 | − | 0.912871i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4.47214i | − | 0.877058i | ||||||
\(27\) | −4.94975 | + | 1.58114i | −0.952579 | + | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.65685 | 1.05045 | 0.525226 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(30\) | 5.00000 | + | 2.23607i | 0.912871 | + | 0.408248i | ||||
\(31\) | − | 3.16228i | − | 0.567962i | −0.958830 | − | 0.283981i | \(-0.908345\pi\) | ||
0.958830 | − | 0.283981i | \(-0.0916552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.53553 | + | 1.58114i | 0.615457 | + | 0.275241i | ||||
\(34\) | − | 9.48683i | − | 1.62698i | ||||||
\(35\) | − | 2.23607i | − | 0.377964i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.48683i | 1.55963i | 0.626013 | + | 0.779813i | \(0.284686\pi\) | ||||
−0.626013 | + | 0.779813i | \(0.715314\pi\) | |||||||
\(38\) | −4.24264 | + | 4.47214i | −0.688247 | + | 0.725476i | ||||
\(39\) | 5.00000 | + | 2.23607i | 0.800641 | + | 0.358057i | ||||
\(40\) | − | 6.32456i | − | 1.00000i | ||||||
\(41\) | −9.89949 | −1.54604 | −0.773021 | − | 0.634381i | \(-0.781255\pi\) | ||||
−0.773021 | + | 0.634381i | \(0.781255\pi\) | |||||||
\(42\) | −1.00000 | + | 2.23607i | −0.154303 | + | 0.345033i | ||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.00000 | + | 4.47214i | −0.745356 | + | 0.666667i | ||||
\(46\) | 6.32456i | 0.932505i | ||||||||
\(47\) | − | 2.23607i | − | 0.326164i | −0.986613 | − | 0.163082i | \(-0.947856\pi\) | ||
0.986613 | − | 0.163082i | \(-0.0521435\pi\) | |||||||
\(48\) | −2.82843 | + | 6.32456i | −0.408248 | + | 0.912871i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.6066 | + | 4.74342i | 1.48522 | + | 0.664211i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264 | 0.582772 | 0.291386 | − | 0.956606i | \(-0.405884\pi\) | ||||
0.291386 | + | 0.956606i | \(0.405884\pi\) | |||||||
\(54\) | 7.00000 | − | 2.23607i | 0.952579 | − | 0.304290i | ||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | −2.87868 | − | 6.97948i | −0.381290 | − | 0.924455i | ||||
\(58\) | −8.00000 | −1.05045 | ||||||||
\(59\) | 1.41421 | 0.184115 | 0.0920575 | − | 0.995754i | \(-0.470656\pi\) | ||||
0.0920575 | + | 0.995754i | \(0.470656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 4.47214i | 0.567962i | ||||||||
\(63\) | −2.00000 | − | 2.23607i | −0.251976 | − | 0.281718i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 7.07107 | 0.877058 | ||||||||
\(66\) | −5.00000 | − | 2.23607i | −0.615457 | − | 0.275241i | ||||
\(67\) | 6.32456i | 0.772667i | 0.922359 | + | 0.386334i | \(0.126259\pi\) | ||||
−0.922359 | + | 0.386334i | \(0.873741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.07107 | − | 3.16228i | −0.851257 | − | 0.380693i | ||||
\(70\) | 3.16228i | 0.377964i | ||||||||
\(71\) | −4.24264 | −0.503509 | −0.251754 | − | 0.967791i | \(-0.581008\pi\) | ||||
−0.251754 | + | 0.967791i | \(0.581008\pi\) | |||||||
\(72\) | −5.65685 | − | 6.32456i | −0.666667 | − | 0.745356i | ||||
\(73\) | −3.00000 | −0.351123 | −0.175562 | − | 0.984468i | \(-0.556174\pi\) | ||||
−0.175562 | + | 0.984468i | \(0.556174\pi\) | |||||||
\(74\) | − | 13.4164i | − | 1.55963i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23607i | 0.254824i | ||||||||
\(78\) | −7.07107 | − | 3.16228i | −0.800641 | − | 0.358057i | ||||
\(79\) | − | 12.6491i | − | 1.42314i | −0.702617 | − | 0.711568i | \(-0.747985\pi\) | ||
0.702617 | − | 0.711568i | \(-0.252015\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | 14.0000 | 1.54604 | ||||||||
\(83\) | 8.94427i | 0.981761i | 0.871227 | + | 0.490881i | \(0.163325\pi\) | ||||
−0.871227 | + | 0.490881i | \(0.836675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.0000 | 1.62698 | ||||||||
\(86\) | 7.07107 | 0.762493 | ||||||||
\(87\) | 4.00000 | − | 8.94427i | 0.428845 | − | 0.958927i | ||||
\(88\) | 6.32456i | 0.674200i | ||||||||
\(89\) | −12.7279 | −1.34916 | −0.674579 | − | 0.738203i | \(-0.735675\pi\) | ||||
−0.674579 | + | 0.738203i | \(0.735675\pi\) | |||||||
\(90\) | 7.07107 | − | 6.32456i | 0.745356 | − | 0.666667i | ||||
\(91\) | 3.16228i | 0.331497i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.00000 | − | 2.23607i | −0.518476 | − | 0.231869i | ||||
\(94\) | 3.16228i | 0.326164i | ||||||||
\(95\) | −7.07107 | − | 6.70820i | −0.725476 | − | 0.688247i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.16228i | 0.321081i | 0.987029 | + | 0.160540i | \(0.0513237\pi\) | ||||
−0.987029 | + | 0.160540i | \(0.948676\pi\) | |||||||
\(98\) | 8.48528 | 0.857143 | ||||||||
\(99\) | 5.00000 | − | 4.47214i | 0.502519 | − | 0.449467i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.94427i | − | 0.889988i | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||
0.895533 | − | 0.444994i | \(-0.146794\pi\) | |||||||
\(102\) | −15.0000 | − | 6.70820i | −1.48522 | − | 0.664211i | ||||
\(103\) | − | 6.32456i | − | 0.623177i | −0.950217 | − | 0.311588i | \(-0.899139\pi\) | ||
0.950217 | − | 0.311588i | \(-0.100861\pi\) | |||||||
\(104\) | 8.94427i | 0.877058i | ||||||||
\(105\) | −3.53553 | − | 1.58114i | −0.345033 | − | 0.154303i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 8.48528 | 0.820303 | 0.410152 | − | 0.912017i | \(-0.365476\pi\) | ||||
0.410152 | + | 0.912017i | \(0.365476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.32456i | 0.605783i | 0.953025 | + | 0.302891i | \(0.0979519\pi\) | ||||
−0.953025 | + | 0.302891i | \(0.902048\pi\) | |||||||
\(110\) | −7.07107 | −0.674200 | ||||||||
\(111\) | 15.0000 | + | 6.70820i | 1.42374 | + | 0.636715i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 5.65685 | 0.532152 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(114\) | 4.07107 | + | 9.87048i | 0.381290 | + | 0.924455i | ||||
\(115\) | −10.0000 | −0.932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.07107 | − | 6.32456i | 0.653720 | − | 0.584705i | ||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | 6.70820i | 0.614940i | ||||||||
\(120\) | −10.0000 | − | 4.47214i | −0.912871 | − | 0.408248i | ||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | 1.41421 | 0.128037 | ||||||||
\(123\) | −7.00000 | + | 15.6525i | −0.631169 | + | 1.41134i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 2.82843 | + | 3.16228i | 0.251976 | + | 0.281718i | ||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | −3.53553 | + | 7.90569i | −0.311286 | + | 0.696058i | ||||
\(130\) | −10.0000 | −0.877058 | ||||||||
\(131\) | − | 2.23607i | − | 0.195366i | −0.995218 | − | 0.0976831i | \(-0.968857\pi\) | ||
0.995218 | − | 0.0976831i | \(-0.0311432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | − | 3.16228i | 0.260133 | − | 0.274204i | ||||
\(134\) | − | 8.94427i | − | 0.772667i | ||||||
\(135\) | 3.53553 | + | 11.0680i | 0.304290 | + | 0.952579i | ||||
\(136\) | 18.9737i | 1.62698i | ||||||||
\(137\) | 2.23607i | 0.191040i | 0.995428 | + | 0.0955201i | \(0.0304514\pi\) | ||||
−0.995428 | + | 0.0955201i | \(0.969549\pi\) | |||||||
\(138\) | 10.0000 | + | 4.47214i | 0.851257 | + | 0.380693i | ||||
\(139\) | −7.00000 | −0.593732 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.53553 | − | 1.58114i | −0.297746 | − | 0.133156i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −7.07107 | −0.591312 | ||||||||
\(144\) | 8.00000 | + | 8.94427i | 0.666667 | + | 0.745356i | ||||
\(145\) | − | 12.6491i | − | 1.05045i | ||||||
\(146\) | 4.24264 | 0.351123 | ||||||||
\(147\) | −4.24264 | + | 9.48683i | −0.349927 | + | 0.782461i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1803i | 0.915929i | 0.888970 | + | 0.457965i | \(0.151421\pi\) | ||||
−0.888970 | + | 0.457965i | \(0.848579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.8114i | − | 1.28671i | −0.765567 | − | 0.643356i | \(-0.777541\pi\) | ||
0.765567 | − | 0.643356i | \(-0.222459\pi\) | |||||||
\(152\) | 8.48528 | − | 8.94427i | 0.688247 | − | 0.725476i | ||||
\(153\) | 15.0000 | − | 13.4164i | 1.21268 | − | 1.08465i | ||||
\(154\) | − | 3.16228i | − | 0.254824i | ||||||
\(155\) | −7.07107 | −0.567962 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00000 | 0.319235 | 0.159617 | − | 0.987179i | \(-0.448974\pi\) | ||||
0.159617 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(158\) | 17.8885i | 1.42314i | ||||||||
\(159\) | 3.00000 | − | 6.70820i | 0.237915 | − | 0.531995i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.47214i | − | 0.352454i | ||||||
\(162\) | 1.41421 | − | 12.6491i | 0.111111 | − | 0.993808i | ||||
\(163\) | −18.0000 | −1.40987 | −0.704934 | − | 0.709273i | \(-0.749024\pi\) | ||||
−0.704934 | + | 0.709273i | \(0.749024\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.53553 | − | 7.90569i | 0.275241 | − | 0.615457i | ||||
\(166\) | − | 12.6491i | − | 0.981761i | ||||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 2.00000 | − | 4.47214i | 0.154303 | − | 0.345033i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | −21.2132 | −1.62698 | ||||||||
\(171\) | −13.0711 | − | 0.383649i | −0.999570 | − | 0.0293383i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.82843 | −0.215041 | −0.107521 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107521 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(174\) | −5.65685 | + | 12.6491i | −0.428845 | + | 0.958927i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 8.94427i | − | 0.674200i | ||||||
\(177\) | 1.00000 | − | 2.23607i | 0.0751646 | − | 0.168073i | ||||
\(178\) | 18.0000 | 1.34916 | ||||||||
\(179\) | −5.65685 | −0.422813 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.9737i | − | 1.41030i | −0.709057 | − | 0.705151i | \(-0.750879\pi\) | ||
0.709057 | − | 0.705151i | \(-0.249121\pi\) | |||||||
\(182\) | − | 4.47214i | − | 0.331497i | ||||||
\(183\) | −0.707107 | + | 1.58114i | −0.0522708 | + | 0.116881i | ||||
\(184\) | − | 12.6491i | − | 0.932505i | ||||||
\(185\) | 21.2132 | 1.55963 | ||||||||
\(186\) | 7.07107 | + | 3.16228i | 0.518476 | + | 0.231869i | ||||
\(187\) | −15.0000 | −1.09691 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.94975 | + | 1.58114i | −0.360041 | + | 0.115011i | ||||
\(190\) | 10.0000 | + | 9.48683i | 0.725476 | + | 0.688247i | ||||
\(191\) | 11.1803i | 0.808981i | 0.914542 | + | 0.404491i | \(0.132551\pi\) | ||||
−0.914542 | + | 0.404491i | \(0.867449\pi\) | |||||||
\(192\) | 5.65685 | − | 12.6491i | 0.408248 | − | 0.912871i | ||||
\(193\) | 6.32456i | 0.455251i | 0.973749 | + | 0.227626i | \(0.0730963\pi\) | ||||
−0.973749 | + | 0.227626i | \(0.926904\pi\) | |||||||
\(194\) | − | 4.47214i | − | 0.321081i | ||||||
\(195\) | 5.00000 | − | 11.1803i | 0.358057 | − | 0.800641i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −7.07107 | + | 6.32456i | −0.502519 | + | 0.449467i | ||||
\(199\) | −3.00000 | −0.212664 | −0.106332 | − | 0.994331i | \(-0.533911\pi\) | ||||
−0.106332 | + | 0.994331i | \(0.533911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0000 | + | 4.47214i | 0.705346 | + | 0.315440i | ||||
\(202\) | 12.6491i | 0.889988i | ||||||||
\(203\) | 5.65685 | 0.397033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.1359i | 1.54604i | ||||||||
\(206\) | 8.94427i | 0.623177i | ||||||||
\(207\) | −10.0000 | + | 8.94427i | −0.695048 | + | 0.621670i | ||||
\(208\) | − | 12.6491i | − | 0.877058i | ||||||
\(209\) | 7.07107 | + | 6.70820i | 0.489116 | + | 0.464016i | ||||
\(210\) | 5.00000 | + | 2.23607i | 0.345033 | + | 0.154303i | ||||
\(211\) | 22.1359i | 1.52390i | 0.647635 | + | 0.761951i | \(0.275758\pi\) | ||||
−0.647635 | + | 0.761951i | \(0.724242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | + | 6.70820i | −0.205557 | + | 0.459639i | ||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 11.1803i | 0.762493i | ||||||||
\(216\) | −14.0000 | + | 4.47214i | −0.952579 | + | 0.304290i | ||||
\(217\) | − | 3.16228i | − | 0.214669i | ||||||
\(218\) | − | 8.94427i | − | 0.605783i | ||||||
\(219\) | −2.12132 | + | 4.74342i | −0.143346 | + | 0.320530i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.2132 | −1.42695 | ||||||||
\(222\) | −21.2132 | − | 9.48683i | −1.42374 | − | 0.636715i | ||||
\(223\) | 3.16228i | 0.211762i | 0.994379 | + | 0.105881i | \(0.0337662\pi\) | ||||
−0.994379 | + | 0.105881i | \(0.966234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | 1.41421 | 0.0938647 | 0.0469323 | − | 0.998898i | \(-0.485055\pi\) | ||||
0.0469323 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | −0.0660819 | −0.0330409 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330409 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(230\) | 14.1421 | 0.932505 | ||||||||
\(231\) | 3.53553 | + | 1.58114i | 0.232621 | + | 0.104031i | ||||
\(232\) | 16.0000 | 1.05045 | ||||||||
\(233\) | − | 20.1246i | − | 1.31841i | −0.751965 | − | 0.659204i | \(-0.770894\pi\) | ||
0.751965 | − | 0.659204i | \(-0.229106\pi\) | |||||||
\(234\) | −10.0000 | + | 8.94427i | −0.653720 | + | 0.584705i | ||||
\(235\) | −5.00000 | −0.326164 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.0000 | − | 8.94427i | −1.29914 | − | 0.580993i | ||||
\(238\) | − | 9.48683i | − | 0.614940i | ||||||
\(239\) | 15.6525i | 1.01247i | 0.862394 | + | 0.506237i | \(0.168964\pi\) | ||||
−0.862394 | + | 0.506237i | \(0.831036\pi\) | |||||||
\(240\) | 14.1421 | + | 6.32456i | 0.912871 | + | 0.408248i | ||||
\(241\) | − | 3.16228i | − | 0.203700i | −0.994800 | − | 0.101850i | \(-0.967524\pi\) | ||
0.994800 | − | 0.101850i | \(-0.0324762\pi\) | |||||||
\(242\) | −8.48528 | −0.545455 | ||||||||
\(243\) | 13.4350 | + | 7.90569i | 0.861858 | + | 0.507151i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.4164i | 0.857143i | ||||||||
\(246\) | 9.89949 | − | 22.1359i | 0.631169 | − | 1.41134i | ||||
\(247\) | 10.0000 | + | 9.48683i | 0.636285 | + | 0.603633i | ||||
\(248\) | − | 8.94427i | − | 0.567962i | ||||||
\(249\) | 14.1421 | + | 6.32456i | 0.896221 | + | 0.400802i | ||||
\(250\) | 15.8114i | 1.00000i | ||||||||
\(251\) | − | 6.70820i | − | 0.423418i | −0.977333 | − | 0.211709i | \(-0.932097\pi\) | ||
0.977333 | − | 0.211709i | \(-0.0679029\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | 0.628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.6066 | − | 23.7171i | 0.664211 | − | 1.48522i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.6274 | −1.41146 | −0.705730 | − | 0.708481i | \(-0.749381\pi\) | ||||
−0.705730 | + | 0.708481i | \(0.749381\pi\) | |||||||
\(258\) | 5.00000 | − | 11.1803i | 0.311286 | − | 0.696058i | ||||
\(259\) | 9.48683i | 0.589483i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.3137 | − | 12.6491i | −0.700301 | − | 0.782960i | ||||
\(262\) | 3.16228i | 0.195366i | ||||||||
\(263\) | − | 29.0689i | − | 1.79246i | −0.443585 | − | 0.896232i | \(-0.646294\pi\) | ||
0.443585 | − | 0.896232i | \(-0.353706\pi\) | |||||||
\(264\) | 10.0000 | + | 4.47214i | 0.615457 | + | 0.275241i | ||||
\(265\) | − | 9.48683i | − | 0.582772i | ||||||
\(266\) | −4.24264 | + | 4.47214i | −0.260133 | + | 0.274204i | ||||
\(267\) | −9.00000 | + | 20.1246i | −0.550791 | + | 1.23161i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.2132 | 1.29339 | 0.646696 | − | 0.762748i | \(-0.276150\pi\) | ||||
0.646696 | + | 0.762748i | \(0.276150\pi\) | |||||||
\(270\) | −5.00000 | − | 15.6525i | −0.304290 | − | 0.952579i | ||||
\(271\) | 6.00000 | 0.364474 | 0.182237 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182237 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(272\) | − | 26.8328i | − | 1.62698i | ||||||
\(273\) | 5.00000 | + | 2.23607i | 0.302614 | + | 0.135333i | ||||
\(274\) | − | 3.16228i | − | 0.191040i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0000 | 1.14160 | 0.570800 | − | 0.821089i | \(-0.306633\pi\) | ||||
0.570800 | + | 0.821089i | \(0.306633\pi\) | |||||||
\(278\) | 9.89949 | 0.593732 | ||||||||
\(279\) | −7.07107 | + | 6.32456i | −0.423334 | + | 0.378641i | ||||
\(280\) | − | 6.32456i | − | 0.377964i | ||||||
\(281\) | −14.1421 | −0.843649 | −0.421825 | − | 0.906677i | \(-0.638610\pi\) | ||||
−0.421825 | + | 0.906677i | \(0.638610\pi\) | |||||||
\(282\) | 5.00000 | + | 2.23607i | 0.297746 | + | 0.133156i | ||||
\(283\) | 25.0000 | 1.48610 | 0.743048 | − | 0.669238i | \(-0.233379\pi\) | ||||
0.743048 | + | 0.669238i | \(0.233379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.6066 | + | 6.43692i | −0.924455 | + | 0.381290i | ||||
\(286\) | 10.0000 | 0.591312 | ||||||||
\(287\) | −9.89949 | −0.584349 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.0000 | −1.64706 | ||||||||
\(290\) | 17.8885i | 1.05045i | ||||||||
\(291\) | 5.00000 | + | 2.23607i | 0.293105 | + | 0.131081i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.7990 | −1.15667 | −0.578335 | − | 0.815800i | \(-0.696297\pi\) | ||||
−0.578335 | + | 0.815800i | \(0.696297\pi\) | |||||||
\(294\) | 6.00000 | − | 13.4164i | 0.349927 | − | 0.782461i | ||||
\(295\) | − | 3.16228i | − | 0.184115i | ||||||
\(296\) | 26.8328i | 1.55963i | ||||||||
\(297\) | −3.53553 | − | 11.0680i | −0.205152 | − | 0.642229i | ||||
\(298\) | − | 15.8114i | − | 0.915929i | ||||||
\(299\) | 14.1421 | 0.817861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00000 | −0.288195 | ||||||||
\(302\) | 22.3607i | 1.28671i | ||||||||
\(303\) | −14.1421 | − | 6.32456i | −0.812444 | − | 0.363336i | ||||
\(304\) | −12.0000 | + | 12.6491i | −0.688247 | + | 0.725476i | ||||
\(305\) | 2.23607i | 0.128037i | ||||||||
\(306\) | −21.2132 | + | 18.9737i | −1.21268 | + | 1.08465i | ||||
\(307\) | − | 18.9737i | − | 1.08288i | −0.840738 | − | 0.541442i | \(-0.817879\pi\) | ||
0.840738 | − | 0.541442i | \(-0.182121\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0000 | − | 4.47214i | −0.568880 | − | 0.254411i | ||||
\(310\) | 10.0000 | 0.567962 | ||||||||
\(311\) | − | 24.5967i | − | 1.39475i | −0.716705 | − | 0.697377i | \(-0.754350\pi\) | ||
0.716705 | − | 0.697377i | \(-0.245650\pi\) | |||||||
\(312\) | 14.1421 | + | 6.32456i | 0.800641 | + | 0.358057i | ||||
\(313\) | 20.0000 | 1.13047 | 0.565233 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565233 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(314\) | −5.65685 | −0.319235 | ||||||||
\(315\) | −5.00000 | + | 4.47214i | −0.281718 | + | 0.251976i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.41421 | −0.0794301 | −0.0397151 | − | 0.999211i | \(-0.512645\pi\) | ||||
−0.0397151 | + | 0.999211i | \(0.512645\pi\) | |||||||
\(318\) | −4.24264 | + | 9.48683i | −0.237915 | + | 0.531995i | ||||
\(319\) | 12.6491i | 0.708214i | ||||||||
\(320\) | − | 17.8885i | − | 1.00000i | ||||||
\(321\) | 6.00000 | − | 13.4164i | 0.334887 | − | 0.748831i | ||||
\(322\) | 6.32456i | 0.352454i | ||||||||
\(323\) | 21.2132 | + | 20.1246i | 1.18033 | + | 1.11976i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.4558 | 1.40987 | ||||||||
\(327\) | 10.0000 | + | 4.47214i | 0.553001 | + | 0.247310i | ||||
\(328\) | −28.0000 | −1.54604 | ||||||||
\(329\) | − | 2.23607i | − | 0.123278i | ||||||
\(330\) | −5.00000 | + | 11.1803i | −0.275241 | + | 0.615457i | ||||
\(331\) | − | 12.6491i | − | 0.695258i | −0.937632 | − | 0.347629i | \(-0.886987\pi\) | ||
0.937632 | − | 0.347629i | \(-0.113013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.2132 | − | 18.9737i | 1.16248 | − | 1.03975i | ||||
\(334\) | −28.0000 | −1.53209 | ||||||||
\(335\) | 14.1421 | 0.772667 | ||||||||
\(336\) | −2.82843 | + | 6.32456i | −0.154303 | + | 0.345033i | ||||
\(337\) | 22.1359i | 1.20582i | 0.797809 | + | 0.602911i | \(0.205993\pi\) | ||||
−0.797809 | + | 0.602911i | \(0.794007\pi\) | |||||||
\(338\) | −4.24264 | −0.230769 | ||||||||
\(339\) | 4.00000 | − | 8.94427i | 0.217250 | − | 0.485786i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.07107 | 0.382920 | ||||||||
\(342\) | 18.4853 | + | 0.542561i | 0.999570 | + | 0.0293383i | ||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −14.1421 | −0.762493 | ||||||||
\(345\) | −7.07107 | + | 15.8114i | −0.380693 | + | 0.851257i | ||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | 2.23607i | 0.120038i | 0.998197 | + | 0.0600192i | \(0.0191162\pi\) | ||||
−0.998197 | + | 0.0600192i | \(0.980884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.00000 | −0.374701 | −0.187351 | − | 0.982293i | \(-0.559990\pi\) | ||||
−0.187351 | + | 0.982293i | \(0.559990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 15.6525i | −0.266880 | − | 0.835467i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.94427i | − | 0.476056i | −0.971258 | − | 0.238028i | \(-0.923499\pi\) | ||
0.971258 | − | 0.238028i | \(-0.0765009\pi\) | |||||||
\(354\) | −1.41421 | + | 3.16228i | −0.0751646 | + | 0.168073i | ||||
\(355\) | 9.48683i | 0.503509i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.6066 | + | 4.74342i | 0.561361 | + | 0.251048i | ||||
\(358\) | 8.00000 | 0.422813 | ||||||||
\(359\) | − | 20.1246i | − | 1.06214i | −0.847329 | − | 0.531068i | \(-0.821791\pi\) | ||
0.847329 | − | 0.531068i | \(-0.178209\pi\) | |||||||
\(360\) | −14.1421 | + | 12.6491i | −0.745356 | + | 0.666667i | ||||
\(361\) | −1.00000 | − | 18.9737i | −0.0526316 | − | 0.998614i | ||||
\(362\) | 26.8328i | 1.41030i | ||||||||
\(363\) | 4.24264 | − | 9.48683i | 0.222681 | − | 0.497930i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.70820i | 0.351123i | ||||||||
\(366\) | 1.00000 | − | 2.23607i | 0.0522708 | − | 0.116881i | ||||
\(367\) | −10.0000 | −0.521996 | −0.260998 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(368\) | 17.8885i | 0.932505i | ||||||||
\(369\) | 19.7990 | + | 22.1359i | 1.03069 | + | 1.15235i | ||||
\(370\) | −30.0000 | −1.55963 | ||||||||
\(371\) | 4.24264 | 0.220267 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.6491i | − | 0.654946i | −0.944861 | − | 0.327473i | \(-0.893803\pi\) | ||
0.944861 | − | 0.327473i | \(-0.106197\pi\) | |||||||
\(374\) | 21.2132 | 1.09691 | ||||||||
\(375\) | −17.6777 | − | 7.90569i | −0.912871 | − | 0.408248i | ||||
\(376\) | − | 6.32456i | − | 0.326164i | ||||||
\(377\) | 17.8885i | 0.921307i | ||||||||
\(378\) | 7.00000 | − | 2.23607i | 0.360041 | − | 0.115011i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 15.8114i | − | 0.808981i | ||||||
\(383\) | −32.5269 | −1.66205 | −0.831024 | − | 0.556237i | \(-0.812245\pi\) | ||||
−0.831024 | + | 0.556237i | \(0.812245\pi\) | |||||||
\(384\) | −8.00000 | + | 17.8885i | −0.408248 | + | 0.912871i | ||||
\(385\) | 5.00000 | 0.254824 | ||||||||
\(386\) | − | 8.94427i | − | 0.455251i | ||||||
\(387\) | 10.0000 | + | 11.1803i | 0.508329 | + | 0.568329i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.23607i | 0.113373i | 0.998392 | + | 0.0566866i | \(0.0180536\pi\) | ||||
−0.998392 | + | 0.0566866i | \(0.981946\pi\) | |||||||
\(390\) | −7.07107 | + | 15.8114i | −0.358057 | + | 0.800641i | ||||
\(391\) | 30.0000 | 1.51717 | ||||||||
\(392\) | −16.9706 | −0.857143 | ||||||||
\(393\) | −3.53553 | − | 1.58114i | −0.178344 | − | 0.0797579i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.2843 | −1.42314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0000 | −0.752828 | −0.376414 | − | 0.926451i | \(-0.622843\pi\) | ||||
−0.376414 | + | 0.926451i | \(0.622843\pi\) | |||||||
\(398\) | 4.24264 | 0.212664 | ||||||||
\(399\) | −2.87868 | − | 6.97948i | −0.144114 | − | 0.349411i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.2843 | 1.41245 | 0.706225 | − | 0.707988i | \(-0.250397\pi\) | ||||
0.706225 | + | 0.707988i | \(0.250397\pi\) | |||||||
\(402\) | −14.1421 | − | 6.32456i | −0.705346 | − | 0.315440i | ||||
\(403\) | 10.0000 | 0.498135 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.0000 | + | 2.23607i | 0.993808 | + | 0.111111i | ||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | −21.2132 | −1.05150 | ||||||||
\(408\) | 30.0000 | + | 13.4164i | 1.48522 | + | 0.664211i | ||||
\(409\) | − | 3.16228i | − | 0.156365i | −0.996939 | − | 0.0781823i | \(-0.975088\pi\) | ||
0.996939 | − | 0.0781823i | \(-0.0249116\pi\) | |||||||
\(410\) | − | 31.3050i | − | 1.54604i | ||||||
\(411\) | 3.53553 | + | 1.58114i | 0.174395 | + | 0.0779918i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.41421 | 0.0695889 | ||||||||
\(414\) | 14.1421 | − | 12.6491i | 0.695048 | − | 0.621670i | ||||
\(415\) | 20.0000 | 0.981761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.94975 | + | 11.0680i | −0.242390 | + | 0.542001i | ||||
\(418\) | −10.0000 | − | 9.48683i | −0.489116 | − | 0.464016i | ||||
\(419\) | − | 22.3607i | − | 1.09239i | −0.837658 | − | 0.546195i | \(-0.816076\pi\) | ||
0.837658 | − | 0.546195i | \(-0.183924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1359i | 1.07884i | 0.842037 | + | 0.539420i | \(0.181356\pi\) | ||||
−0.842037 | + | 0.539420i | \(0.818644\pi\) | |||||||
\(422\) | − | 31.3050i | − | 1.52390i | ||||||
\(423\) | −5.00000 | + | 4.47214i | −0.243108 | + | 0.217443i | ||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.24264 | − | 9.48683i | 0.205557 | − | 0.459639i | ||||
\(427\) | −1.00000 | −0.0483934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.00000 | + | 11.1803i | −0.241402 | + | 0.539792i | ||||
\(430\) | − | 15.8114i | − | 0.762493i | ||||||
\(431\) | 4.24264 | 0.204361 | 0.102180 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(432\) | 19.7990 | − | 6.32456i | 0.952579 | − | 0.304290i | ||||
\(433\) | − | 18.9737i | − | 0.911816i | −0.890027 | − | 0.455908i | \(-0.849315\pi\) | ||
0.890027 | − | 0.455908i | \(-0.150685\pi\) | |||||||
\(434\) | 4.47214i | 0.214669i | ||||||||
\(435\) | −20.0000 | − | 8.94427i | −0.958927 | − | 0.428845i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.1421 | − | 13.4164i | −0.676510 | − | 0.641794i | ||||
\(438\) | 3.00000 | − | 6.70820i | 0.143346 | − | 0.320530i | ||||
\(439\) | − | 6.32456i | − | 0.301855i | −0.988545 | − | 0.150927i | \(-0.951774\pi\) | ||
0.988545 | − | 0.150927i | \(-0.0482259\pi\) | |||||||
\(440\) | 14.1421 | 0.674200 | ||||||||
\(441\) | 12.0000 | + | 13.4164i | 0.571429 | + | 0.638877i | ||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | 11.1803i | 0.531194i | 0.964084 | + | 0.265597i | \(0.0855691\pi\) | ||||
−0.964084 | + | 0.265597i | \(0.914431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.4605i | 1.34916i | ||||||||
\(446\) | − | 4.47214i | − | 0.211762i | ||||||
\(447\) | 17.6777 | + | 7.90569i | 0.836125 | + | 0.373927i | ||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | 5.65685 | 0.266963 | 0.133482 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133482 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22.1359i | − | 1.04234i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.0000 | − | 11.1803i | −1.17460 | − | 0.525298i | ||||
\(454\) | −2.00000 | −0.0938647 | ||||||||
\(455\) | 7.07107 | 0.331497 | ||||||||
\(456\) | −8.14214 | − | 19.7410i | −0.381290 | − | 0.924455i | ||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 1.41421 | 0.0660819 | ||||||||
\(459\) | −10.6066 | − | 33.2039i | −0.495074 | − | 1.54983i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.5967i | 1.14558i | 0.819700 | + | 0.572792i | \(0.194140\pi\) | ||||
−0.819700 | + | 0.572792i | \(0.805860\pi\) | |||||||
\(462\) | −5.00000 | − | 2.23607i | −0.232621 | − | 0.104031i | ||||
\(463\) | −5.00000 | −0.232370 | −0.116185 | − | 0.993228i | \(-0.537067\pi\) | ||||
−0.116185 | + | 0.993228i | \(0.537067\pi\) | |||||||
\(464\) | −22.6274 | −1.05045 | ||||||||
\(465\) | −5.00000 | + | 11.1803i | −0.231869 | + | 0.518476i | ||||
\(466\) | 28.4605i | 1.31841i | ||||||||
\(467\) | − | 2.23607i | − | 0.103473i | −0.998661 | − | 0.0517364i | \(-0.983524\pi\) | ||
0.998661 | − | 0.0517364i | \(-0.0164756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.32456i | 0.292041i | ||||||||
\(470\) | 7.07107 | 0.326164 | ||||||||
\(471\) | 2.82843 | − | 6.32456i | 0.130327 | − | 0.291420i | ||||
\(472\) | 4.00000 | 0.184115 | ||||||||
\(473\) | − | 11.1803i | − | 0.514073i | ||||||
\(474\) | 28.2843 | + | 12.6491i | 1.29914 | + | 0.580993i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.48528 | − | 9.48683i | −0.388514 | − | 0.434372i | ||||
\(478\) | − | 22.1359i | − | 1.01247i | ||||||
\(479\) | 22.3607i | 1.02169i | 0.859674 | + | 0.510843i | \(0.170667\pi\) | ||||
−0.859674 | + | 0.510843i | \(0.829333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.0000 | −1.36788 | ||||||||
\(482\) | 4.47214i | 0.203700i | ||||||||
\(483\) | −7.07107 | − | 3.16228i | −0.321745 | − | 0.143889i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.07107 | 0.321081 | ||||||||
\(486\) | −19.0000 | − | 11.1803i | −0.861858 | − | 0.507151i | ||||
\(487\) | 28.4605i | 1.28967i | 0.764323 | + | 0.644834i | \(0.223074\pi\) | ||||
−0.764323 | + | 0.644834i | \(0.776926\pi\) | |||||||
\(488\) | −2.82843 | −0.128037 | ||||||||
\(489\) | −12.7279 | + | 28.4605i | −0.575577 | + | 1.28703i | ||||
\(490\) | − | 18.9737i | − | 0.857143i | ||||||
\(491\) | 31.3050i | 1.41277i | 0.707826 | + | 0.706386i | \(0.249676\pi\) | ||||
−0.707826 | + | 0.706386i | \(0.750324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.9473i | 1.70906i | ||||||||
\(494\) | −14.1421 | − | 13.4164i | −0.636285 | − | 0.603633i | ||||
\(495\) | −10.0000 | − | 11.1803i | −0.449467 | − | 0.502519i | ||||
\(496\) | 12.6491i | 0.567962i | ||||||||
\(497\) | −4.24264 | −0.190308 | ||||||||
\(498\) | −20.0000 | − | 8.94427i | −0.896221 | − | 0.400802i | ||||
\(499\) | 17.0000 | 0.761025 | 0.380512 | − | 0.924776i | \(-0.375748\pi\) | ||||
0.380512 | + | 0.924776i | \(0.375748\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.0000 | − | 31.3050i | 0.625474 | − | 1.39860i | ||||
\(502\) | 9.48683i | 0.423418i | ||||||||
\(503\) | 40.2492i | 1.79462i | 0.441397 | + | 0.897312i | \(0.354483\pi\) | ||||
−0.441397 | + | 0.897312i | \(0.645517\pi\) | |||||||
\(504\) | −5.65685 | − | 6.32456i | −0.251976 | − | 0.281718i | ||||
\(505\) | −20.0000 | −0.889988 | ||||||||
\(506\) | −14.1421 | −0.628695 | ||||||||
\(507\) | 2.12132 | − | 4.74342i | 0.0942111 | − | 0.210663i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8701 | 1.19099 | 0.595497 | − | 0.803357i | \(-0.296955\pi\) | ||||
0.595497 | + | 0.803357i | \(0.296955\pi\) | |||||||
\(510\) | −15.0000 | + | 33.5410i | −0.664211 | + | 1.48522i | ||||
\(511\) | −3.00000 | −0.132712 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −9.84924 | + | 20.3959i | −0.434855 | + | 0.900501i | ||||
\(514\) | 32.0000 | 1.41146 | ||||||||
\(515\) | −14.1421 | −0.623177 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.00000 | 0.219900 | ||||||||
\(518\) | − | 13.4164i | − | 0.589483i | ||||||
\(519\) | −2.00000 | + | 4.47214i | −0.0877903 | + | 0.196305i | ||||
\(520\) | 20.0000 | 0.877058 | ||||||||
\(521\) | 31.1127 | 1.36307 | 0.681536 | − | 0.731785i | \(-0.261312\pi\) | ||||
0.681536 | + | 0.731785i | \(0.261312\pi\) | |||||||
\(522\) | 16.0000 | + | 17.8885i | 0.700301 | + | 0.782960i | ||||
\(523\) | 37.9473i | 1.65932i | 0.558268 | + | 0.829660i | \(0.311466\pi\) | ||||
−0.558268 | + | 0.829660i | \(0.688534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.1096i | 1.79246i | ||||||||
\(527\) | 21.2132 | 0.924062 | ||||||||
\(528\) | −14.1421 | − | 6.32456i | −0.615457 | − | 0.275241i | ||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 13.4164i | 0.582772i | ||||||||
\(531\) | −2.82843 | − | 3.16228i | −0.122743 | − | 0.137231i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 31.3050i | − | 1.35597i | ||||||
\(534\) | 12.7279 | − | 28.4605i | 0.550791 | − | 1.23161i | ||||
\(535\) | − | 18.9737i | − | 0.820303i | ||||||
\(536\) | 17.8885i | 0.772667i | ||||||||
\(537\) | −4.00000 | + | 8.94427i | −0.172613 | + | 0.385974i | ||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | − | 13.4164i | − | 0.577886i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.00000 | 0.128980 | 0.0644900 | − | 0.997918i | \(-0.479458\pi\) | ||||
0.0644900 | + | 0.997918i | \(0.479458\pi\) | |||||||
\(542\) | −8.48528 | −0.364474 | ||||||||
\(543\) | −30.0000 | − | 13.4164i | −1.28742 | − | 0.575753i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1421 | 0.605783 | ||||||||
\(546\) | −7.07107 | − | 3.16228i | −0.302614 | − | 0.135333i | ||||
\(547\) | − | 22.1359i | − | 0.946465i | −0.880938 | − | 0.473232i | \(-0.843087\pi\) | ||
0.880938 | − | 0.473232i | \(-0.156913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.00000 | + | 2.23607i | 0.0853579 | + | 0.0954331i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9706 | − | 17.8885i | 0.722970 | − | 0.762078i | ||||
\(552\) | −20.0000 | − | 8.94427i | −0.851257 | − | 0.380693i | ||||
\(553\) | − | 12.6491i | − | 0.537895i | ||||||
\(554\) | −26.8701 | −1.14160 | ||||||||
\(555\) | 15.0000 | − | 33.5410i | 0.636715 | − | 1.42374i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.23607i | 0.0947452i | 0.998877 | + | 0.0473726i | \(0.0150848\pi\) | ||||
−0.998877 | + | 0.0473726i | \(0.984915\pi\) | |||||||
\(558\) | 10.0000 | − | 8.94427i | 0.423334 | − | 0.378641i | ||||
\(559\) | − | 15.8114i | − | 0.668750i | ||||||
\(560\) | 8.94427i | 0.377964i | ||||||||
\(561\) | −10.6066 | + | 23.7171i | −0.447811 | + | 1.00134i | ||||
\(562\) | 20.0000 | 0.843649 | ||||||||
\(563\) | −18.3848 | −0.774826 | −0.387413 | − | 0.921906i | \(-0.626631\pi\) | ||||
−0.387413 | + | 0.921906i | \(0.626631\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.6491i | − | 0.532152i | ||||||
\(566\) | −35.3553 | −1.48610 | ||||||||
\(567\) | −1.00000 | + | 8.94427i | −0.0419961 | + | 0.375624i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | −1.41421 | −0.0592869 | −0.0296435 | − | 0.999561i | \(-0.509437\pi\) | ||||
−0.0296435 | + | 0.999561i | \(0.509437\pi\) | |||||||
\(570\) | 22.0711 | − | 9.10318i | 0.924455 | − | 0.381290i | ||||
\(571\) | 26.0000 | 1.08807 | 0.544033 | − | 0.839064i | \(-0.316897\pi\) | ||||
0.544033 | + | 0.839064i | \(0.316897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.6777 | + | 7.90569i | 0.738495 | + | 0.330265i | ||||
\(574\) | 14.0000 | 0.584349 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −16.0000 | − | 17.8885i | −0.666667 | − | 0.745356i | ||||
\(577\) | −45.0000 | −1.87337 | −0.936687 | − | 0.350167i | \(-0.886125\pi\) | ||||
−0.936687 | + | 0.350167i | \(0.886125\pi\) | |||||||
\(578\) | 39.5980 | 1.64706 | ||||||||
\(579\) | 10.0000 | + | 4.47214i | 0.415586 | + | 0.185856i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.94427i | 0.371071i | ||||||||
\(582\) | −7.07107 | − | 3.16228i | −0.293105 | − | 0.131081i | ||||
\(583\) | 9.48683i | 0.392904i | ||||||||
\(584\) | −8.48528 | −0.351123 | ||||||||
\(585\) | −14.1421 | − | 15.8114i | −0.584705 | − | 0.653720i | ||||
\(586\) | 28.0000 | 1.15667 | ||||||||
\(587\) | − | 38.0132i | − | 1.56897i | −0.620147 | − | 0.784485i | \(-0.712927\pi\) | ||
0.620147 | − | 0.784485i | \(-0.287073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | − | 9.48683i | −0.412043 | − | 0.390898i | ||||
\(590\) | 4.47214i | 0.184115i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 37.9473i | − | 1.55963i | ||||||
\(593\) | 13.4164i | 0.550946i | 0.961309 | + | 0.275473i | \(0.0888344\pi\) | ||||
−0.961309 | + | 0.275473i | \(0.911166\pi\) | |||||||
\(594\) | 5.00000 | + | 15.6525i | 0.205152 | + | 0.642229i | ||||
\(595\) | 15.0000 | 0.614940 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.12132 | + | 4.74342i | −0.0868199 | + | 0.194135i | ||||
\(598\) | −20.0000 | −0.817861 | ||||||||
\(599\) | 14.1421 | 0.577832 | 0.288916 | − | 0.957354i | \(-0.406705\pi\) | ||||
0.288916 | + | 0.957354i | \(0.406705\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.1096i | − | 1.67690i | −0.544982 | − | 0.838448i | \(-0.683463\pi\) | ||
0.544982 | − | 0.838448i | \(-0.316537\pi\) | |||||||
\(602\) | 7.07107 | 0.288195 | ||||||||
\(603\) | 14.1421 | − | 12.6491i | 0.575912 | − | 0.515112i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 13.4164i | − | 0.545455i | ||||||
\(606\) | 20.0000 | + | 8.94427i | 0.812444 | + | 0.363336i | ||||
\(607\) | 15.8114i | 0.641764i | 0.947119 | + | 0.320882i | \(0.103979\pi\) | ||||
−0.947119 | + | 0.320882i | \(0.896021\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | − | 8.94427i | 0.162088 | − | 0.362440i | ||||
\(610\) | − | 3.16228i | − | 0.128037i | ||||||
\(611\) | 7.07107 | 0.286065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.0000 | 1.33286 | 0.666429 | − | 0.745569i | \(-0.267822\pi\) | ||||
0.666429 | + | 0.745569i | \(0.267822\pi\) | |||||||
\(614\) | 26.8328i | 1.08288i | ||||||||
\(615\) | 35.0000 | + | 15.6525i | 1.41134 | + | 0.631169i | ||||
\(616\) | 6.32456i | 0.254824i | ||||||||
\(617\) | − | 15.6525i | − | 0.630145i | −0.949068 | − | 0.315072i | \(-0.897971\pi\) | ||
0.949068 | − | 0.315072i | \(-0.102029\pi\) | |||||||
\(618\) | 14.1421 | + | 6.32456i | 0.568880 | + | 0.254411i | ||||
\(619\) | 32.0000 | 1.28619 | 0.643094 | − | 0.765787i | \(-0.277650\pi\) | ||||
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.07107 | + | 22.1359i | 0.283752 | + | 0.888285i | ||||
\(622\) | 34.7851i | 1.39475i | ||||||||
\(623\) | −12.7279 | −0.509933 | ||||||||
\(624\) | −20.0000 | − | 8.94427i | −0.800641 | − | 0.358057i | ||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | −28.2843 | −1.13047 | ||||||||
\(627\) | 15.6066 | − | 6.43692i | 0.623268 | − | 0.257066i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −63.6396 | −2.53748 | ||||||||
\(630\) | 7.07107 | − | 6.32456i | 0.281718 | − | 0.251976i | ||||
\(631\) | −33.0000 | −1.31371 | −0.656855 | − | 0.754017i | \(-0.728113\pi\) | ||||
−0.656855 | + | 0.754017i | \(0.728113\pi\) | |||||||
\(632\) | − | 35.7771i | − | 1.42314i | ||||||
\(633\) | 35.0000 | + | 15.6525i | 1.39113 | + | 0.622130i | ||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 18.9737i | − | 0.751764i | ||||||
\(638\) | − | 17.8885i | − | 0.708214i | ||||||
\(639\) | 8.48528 | + | 9.48683i | 0.335673 | + | 0.375293i | ||||
\(640\) | 25.2982i | 1.00000i | ||||||||
\(641\) | −35.3553 | −1.39645 | −0.698226 | − | 0.715877i | \(-0.746027\pi\) | ||||
−0.698226 | + | 0.715877i | \(0.746027\pi\) | |||||||
\(642\) | −8.48528 | + | 18.9737i | −0.334887 | + | 0.748831i | ||||
\(643\) | −7.00000 | −0.276053 | −0.138027 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.6777 | + | 7.90569i | 0.696058 | + | 0.311286i | ||||
\(646\) | −30.0000 | − | 28.4605i | −1.18033 | − | 1.11976i | ||||
\(647\) | 6.70820i | 0.263727i | 0.991268 | + | 0.131863i | \(0.0420960\pi\) | ||||
−0.991268 | + | 0.131863i | \(0.957904\pi\) | |||||||
\(648\) | −2.82843 | + | 25.2982i | −0.111111 | + | 0.993808i | ||||
\(649\) | 3.16228i | 0.124130i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.00000 | − | 2.23607i | −0.195965 | − | 0.0876384i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.4853i | 1.66258i | 0.555840 | + | 0.831289i | \(0.312397\pi\) | ||||
−0.555840 | + | 0.831289i | \(0.687603\pi\) | |||||||
\(654\) | −14.1421 | − | 6.32456i | −0.553001 | − | 0.247310i | ||||
\(655\) | −5.00000 | −0.195366 | ||||||||
\(656\) | 39.5980 | 1.54604 | ||||||||
\(657\) | 6.00000 | + | 6.70820i | 0.234082 | + | 0.261712i | ||||
\(658\) | 3.16228i | 0.123278i | ||||||||
\(659\) | −14.1421 | −0.550899 | −0.275450 | − | 0.961315i | \(-0.588827\pi\) | ||||
−0.275450 | + | 0.961315i | \(0.588827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 25.2982i | − | 0.983987i | −0.870599 | − | 0.491993i | \(-0.836268\pi\) | ||
0.870599 | − | 0.491993i | \(-0.163732\pi\) | |||||||
\(662\) | 17.8885i | 0.695258i | ||||||||
\(663\) | −15.0000 | + | 33.5410i | −0.582552 | + | 1.30263i | ||||
\(664\) | 25.2982i | 0.981761i | ||||||||
\(665\) | −7.07107 | − | 6.70820i | −0.274204 | − | 0.260133i | ||||
\(666\) | −30.0000 | + | 26.8328i | −1.16248 | + | 1.03975i | ||||
\(667\) | − | 25.2982i | − | 0.979551i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.00000 | + | 2.23607i | 0.193311 | + | 0.0864514i | ||||
\(670\) | −20.0000 | −0.772667 | ||||||||
\(671\) | − | 2.23607i | − | 0.0863224i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.1359i | 0.853278i | 0.904422 | + | 0.426639i | \(0.140302\pi\) | ||||
−0.904422 | + | 0.426639i | \(0.859698\pi\) | |||||||
\(674\) | − | 31.3050i | − | 1.20582i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.7696 | 1.41317 | 0.706584 | − | 0.707629i | \(-0.250235\pi\) | ||||
0.706584 | + | 0.707629i | \(0.250235\pi\) | |||||||
\(678\) | −5.65685 | + | 12.6491i | −0.217250 | + | 0.485786i | ||||
\(679\) | 3.16228i | 0.121357i | ||||||||
\(680\) | 42.4264 | 1.62698 | ||||||||
\(681\) | 1.00000 | − | 2.23607i | 0.0383201 | − | 0.0856863i | ||||
\(682\) | −10.0000 | −0.382920 | ||||||||
\(683\) | 4.24264 | 0.162340 | 0.0811701 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811701 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.00000 | 0.191040 | ||||||||
\(686\) | 18.3848 | 0.701934 | ||||||||
\(687\) | −0.707107 | + | 1.58114i | −0.0269778 | + | 0.0603242i | ||||
\(688\) | 20.0000 | 0.762493 | ||||||||
\(689\) | 13.4164i | 0.511124i | ||||||||
\(690\) | 10.0000 | − | 22.3607i | 0.380693 | − | 0.851257i | ||||
\(691\) | −43.0000 | −1.63580 | −0.817899 | − | 0.575362i | \(-0.804861\pi\) | ||||
−0.817899 | + | 0.575362i | \(0.804861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.00000 | − | 4.47214i | 0.189934 | − | 0.169882i | ||||
\(694\) | − | 3.16228i | − | 0.120038i | ||||||
\(695\) | 15.6525i | 0.593732i | ||||||||
\(696\) | 11.3137 | − | 25.2982i | 0.428845 | − | 0.958927i | ||||
\(697\) | − | 66.4078i | − | 2.51538i | ||||||
\(698\) | 9.89949 | 0.374701 | ||||||||
\(699\) | −31.8198 | − | 14.2302i | −1.20354 | − | 0.538237i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 7.07107 | + | 22.1359i | 0.266880 | + | 0.835467i | ||||
\(703\) | 30.0000 | + | 28.4605i | 1.13147 | + | 1.07341i | ||||
\(704\) | 17.8885i | 0.674200i | ||||||||
\(705\) | −3.53553 | + | 7.90569i | −0.133156 | + | 0.297746i | ||||
\(706\) | 12.6491i | 0.476056i | ||||||||
\(707\) | − | 8.94427i | − | 0.336384i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0000 | −1.20179 | −0.600893 | − | 0.799330i | \(-0.705188\pi\) | ||||
−0.600893 | + | 0.799330i | \(0.705188\pi\) | |||||||
\(710\) | − | 13.4164i | − | 0.503509i | ||||||
\(711\) | −28.2843 | + | 25.2982i | −1.06074 | + | 0.948757i | ||||
\(712\) | −36.0000 | −1.34916 | ||||||||
\(713\) | −14.1421 | −0.529627 | ||||||||
\(714\) | −15.0000 | − | 6.70820i | −0.561361 | − | 0.251048i | ||||
\(715\) | 15.8114i | 0.591312i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.7487 | + | 11.0680i | 0.924259 | + | 0.413341i | ||||
\(718\) | 28.4605i | 1.06214i | ||||||||
\(719\) | − | 33.5410i | − | 1.25087i | −0.780277 | − | 0.625434i | \(-0.784922\pi\) | ||
0.780277 | − | 0.625434i | \(-0.215078\pi\) | |||||||
\(720\) | 20.0000 | − | 17.8885i | 0.745356 | − | 0.666667i | ||||
\(721\) | − | 6.32456i | − | 0.235539i | ||||||
\(722\) | 1.41421 | + | 26.8328i | 0.0526316 | + | 0.998614i | ||||
\(723\) | −5.00000 | − | 2.23607i | −0.185952 | − | 0.0831603i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.00000 | + | 13.4164i | −0.222681 | + | 0.497930i | ||||
\(727\) | −49.0000 | −1.81731 | −0.908655 | − | 0.417548i | \(-0.862889\pi\) | ||||
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | 8.94427i | 0.331497i | ||||||||
\(729\) | 22.0000 | − | 15.6525i | 0.814815 | − | 0.579721i | ||||
\(730\) | − | 9.48683i | − | 0.351123i | ||||||
\(731\) | − | 33.5410i | − | 1.24056i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.00000 | −0.295487 | −0.147743 | − | 0.989026i | \(-0.547201\pi\) | ||||
−0.147743 | + | 0.989026i | \(0.547201\pi\) | |||||||
\(734\) | 14.1421 | 0.521996 | ||||||||
\(735\) | 21.2132 | + | 9.48683i | 0.782461 | + | 0.349927i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.1421 | −0.520932 | ||||||||
\(738\) | −28.0000 | − | 31.3050i | −1.03069 | − | 1.15235i | ||||
\(739\) | 47.0000 | 1.72892 | 0.864461 | − | 0.502699i | \(-0.167660\pi\) | ||||
0.864461 | + | 0.502699i | \(0.167660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.0711 | − | 9.10318i | 0.810801 | − | 0.334414i | ||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | 45.2548 | 1.66024 | 0.830119 | − | 0.557586i | \(-0.188272\pi\) | ||||
0.830119 | + | 0.557586i | \(0.188272\pi\) | |||||||
\(744\) | −14.1421 | − | 6.32456i | −0.518476 | − | 0.231869i | ||||
\(745\) | 25.0000 | 0.915929 | ||||||||
\(746\) | 17.8885i | 0.654946i | ||||||||
\(747\) | 20.0000 | − | 17.8885i | 0.731762 | − | 0.654508i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.48528 | 0.310045 | ||||||||
\(750\) | 25.0000 | + | 11.1803i | 0.912871 | + | 0.408248i | ||||
\(751\) | 31.6228i | 1.15393i | 0.816768 | + | 0.576966i | \(0.195763\pi\) | ||||
−0.816768 | + | 0.576966i | \(0.804237\pi\) | |||||||
\(752\) | 8.94427i | 0.326164i | ||||||||
\(753\) | −10.6066 | − | 4.74342i | −0.386526 | − | 0.172860i | ||||
\(754\) | − | 25.2982i | − | 0.921307i | ||||||
\(755\) | −35.3553 | −1.28671 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.0000 | 1.85363 | 0.926813 | − | 0.375523i | \(-0.122537\pi\) | ||||
0.926813 | + | 0.375523i | \(0.122537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.07107 | − | 15.8114i | 0.256664 | − | 0.573917i | ||||
\(760\) | −20.0000 | − | 18.9737i | −0.725476 | − | 0.688247i | ||||
\(761\) | 29.0689i | 1.05375i | 0.849944 | + | 0.526873i | \(0.176636\pi\) | ||||
−0.849944 | + | 0.526873i | \(0.823364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.32456i | 0.228964i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.0000 | − | 33.5410i | −1.08465 | − | 1.21268i | ||||
\(766\) | 46.0000 | 1.66205 | ||||||||
\(767\) | 4.47214i | 0.161479i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.00000 | 0.252426 | 0.126213 | − | 0.992003i | \(-0.459718\pi\) | ||||
0.126213 | + | 0.992003i | \(0.459718\pi\) | |||||||
\(770\) | −7.07107 | −0.254824 | ||||||||
\(771\) | −16.0000 | + | 35.7771i | −0.576226 | + | 1.28848i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3848 | −0.661254 | −0.330627 | − | 0.943761i | \(-0.607260\pi\) | ||||
−0.330627 | + | 0.943761i | \(0.607260\pi\) | |||||||
\(774\) | −14.1421 | − | 15.8114i | −0.508329 | − | 0.568329i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.94427i | 0.321081i | ||||||||
\(777\) | 15.0000 | + | 6.70820i | 0.538122 | + | 0.240655i | ||||
\(778\) | − | 3.16228i | − | 0.113373i | ||||||
\(779\) | −29.6985 | + | 31.3050i | −1.06406 | + | 1.12162i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.48683i | − | 0.339466i | ||||||
\(782\) | −42.4264 | −1.51717 | ||||||||
\(783\) | −28.0000 | + | 8.94427i | −1.00064 | + | 0.319642i | ||||
\(784\) | 24.0000 | 0.857143 | ||||||||
\(785\) | − | 8.94427i | − | 0.319235i | ||||||
\(786\) | 5.00000 | + | 2.23607i | 0.178344 | + | 0.0797579i | ||||
\(787\) | − | 25.2982i | − | 0.901784i | −0.892578 | − | 0.450892i | \(-0.851106\pi\) | ||
0.892578 | − | 0.450892i | \(-0.148894\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −45.9619 | − | 20.5548i | −1.63629 | − | 0.731770i | ||||
\(790\) | 40.0000 | 1.42314 | ||||||||
\(791\) | 5.65685 | 0.201135 | ||||||||
\(792\) | 14.1421 | − | 12.6491i | 0.502519 | − | 0.449467i | ||||
\(793\) | − | 3.16228i | − | 0.112296i | ||||||
\(794\) | 21.2132 | 0.752828 | ||||||||
\(795\) | −15.0000 | − | 6.70820i | −0.531995 | − | 0.237915i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.7990 | 0.701316 | 0.350658 | − | 0.936504i | \(-0.385958\pi\) | ||||
0.350658 | + | 0.936504i | \(0.385958\pi\) | |||||||
\(798\) | 4.07107 | + | 9.87048i | 0.144114 | + | 0.349411i | ||||
\(799\) | 15.0000 | 0.530662 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4558 | + | 28.4605i | 0.899438 | + | 1.00560i | ||||
\(802\) | −40.0000 | −1.41245 | ||||||||
\(803\) | − | 6.70820i | − | 0.236727i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0000 | −0.352454 | ||||||||
\(806\) | −14.1421 | −0.498135 | ||||||||
\(807\) | 15.0000 | − | 33.5410i | 0.528025 | − | 1.18070i | ||||
\(808\) | − | 25.2982i | − | 0.889988i | ||||||
\(809\) | 2.23607i | 0.0786160i | 0.999227 | + | 0.0393080i | \(0.0125153\pi\) | ||||
−0.999227 | + | 0.0393080i | \(0.987485\pi\) | |||||||
\(810\) | −28.2843 | − | 3.16228i | −0.993808 | − | 0.111111i | ||||
\(811\) | 47.4342i | 1.66564i | 0.553545 | + | 0.832819i | \(0.313275\pi\) | ||||
−0.553545 | + | 0.832819i | \(0.686725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.24264 | − | 9.48683i | 0.148796 | − | 0.332718i | ||||
\(814\) | 30.0000 | 1.05150 | ||||||||
\(815\) | 40.2492i | 1.40987i | ||||||||
\(816\) | −42.4264 | − | 18.9737i | −1.48522 | − | 0.664211i | ||||
\(817\) | −15.0000 | + | 15.8114i | −0.524784 | + | 0.553170i | ||||
\(818\) | 4.47214i | 0.156365i | ||||||||
\(819\) | 7.07107 | − | 6.32456i | 0.247083 | − | 0.220998i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 51.4296i | − | 1.79490i | −0.441112 | − | 0.897452i | \(-0.645416\pi\) | ||
0.441112 | − | 0.897452i | \(-0.354584\pi\) | |||||||
\(822\) | −5.00000 | − | 2.23607i | −0.174395 | − | 0.0779918i | ||||
\(823\) | −23.0000 | −0.801730 | −0.400865 | − | 0.916137i | \(-0.631290\pi\) | ||||
−0.400865 | + | 0.916137i | \(0.631290\pi\) | |||||||
\(824\) | − | 17.8885i | − | 0.623177i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.00000 | −0.0695889 | ||||||||
\(827\) | 25.4558 | 0.885186 | 0.442593 | − | 0.896723i | \(-0.354059\pi\) | ||||
0.442593 | + | 0.896723i | \(0.354059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9737i | 0.658983i | 0.944159 | + | 0.329491i | \(0.106877\pi\) | ||||
−0.944159 | + | 0.329491i | \(0.893123\pi\) | |||||||
\(830\) | −28.2843 | −0.981761 | ||||||||
\(831\) | 13.4350 | − | 30.0416i | 0.466056 | − | 1.04213i | ||||
\(832\) | 25.2982i | 0.877058i | ||||||||
\(833\) | − | 40.2492i | − | 1.39455i | ||||||
\(834\) | 7.00000 | − | 15.6525i | 0.242390 | − | 0.542001i | ||||
\(835\) | − | 44.2719i | − | 1.53209i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.00000 | + | 15.6525i | 0.172825 | + | 0.541029i | ||||
\(838\) | 31.6228i | 1.09239i | ||||||||
\(839\) | 19.7990 | 0.683537 | 0.341769 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341769 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(840\) | −10.0000 | − | 4.47214i | −0.345033 | − | 0.154303i | ||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | − | 31.3050i | − | 1.07884i | ||||||
\(843\) | −10.0000 | + | 22.3607i | −0.344418 | + | 0.770143i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.70820i | − | 0.230769i | ||||||
\(846\) | 7.07107 | − | 6.32456i | 0.243108 | − | 0.217443i | ||||
\(847\) | 6.00000 | 0.206162 | ||||||||
\(848\) | −16.9706 | −0.582772 | ||||||||
\(849\) | 17.6777 | − | 39.5285i | 0.606696 | − | 1.35661i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.4264 | 1.45436 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.0000 | 0.958702 | 0.479351 | − | 0.877623i | \(-0.340872\pi\) | ||||
0.479351 | + | 0.877623i | \(0.340872\pi\) | |||||||
\(854\) | 1.41421 | 0.0483934 | ||||||||
\(855\) | −0.857864 | + | 29.2278i | −0.0293383 | + | 0.999570i | ||||
\(856\) | 24.0000 | 0.820303 | ||||||||
\(857\) | 1.41421 | 0.0483086 | 0.0241543 | − | 0.999708i | \(-0.492311\pi\) | ||||
0.0241543 | + | 0.999708i | \(0.492311\pi\) | |||||||
\(858\) | 7.07107 | − | 15.8114i | 0.241402 | − | 0.539792i | ||||
\(859\) | 13.0000 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.00000 | + | 15.6525i | −0.238559 | + | 0.533435i | ||||
\(862\) | −6.00000 | −0.204361 | ||||||||
\(863\) | 38.1838 | 1.29979 | 0.649895 | − | 0.760024i | \(-0.274813\pi\) | ||||
0.649895 | + | 0.760024i | \(0.274813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.32456i | 0.215041i | ||||||||
\(866\) | 26.8328i | 0.911816i | ||||||||
\(867\) | −19.7990 | + | 44.2719i | −0.672409 | + | 1.50355i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.2843 | 0.959478 | ||||||||
\(870\) | 28.2843 | + | 12.6491i | 0.958927 | + | 0.428845i | ||||
\(871\) | −20.0000 | −0.677674 | ||||||||
\(872\) | 17.8885i | 0.605783i | ||||||||
\(873\) | 7.07107 | − | 6.32456i | 0.239319 | − | 0.214054i | ||||
\(874\) | 20.0000 | + | 18.9737i | 0.676510 | + | 0.641794i | ||||
\(875\) | − | 11.1803i | − | 0.377964i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.6228i | 1.06783i | 0.845540 | + | 0.533913i | \(0.179279\pi\) | ||||
−0.845540 | + | 0.533913i | \(0.820721\pi\) | |||||||
\(878\) | 8.94427i | 0.301855i | ||||||||
\(879\) | −14.0000 | + | 31.3050i | −0.472208 | + | 1.05589i | ||||
\(880\) | −20.0000 | −0.674200 | ||||||||
\(881\) | − | 6.70820i | − | 0.226005i | −0.993595 | − | 0.113003i | \(-0.963953\pi\) | ||
0.993595 | − | 0.113003i | \(-0.0360468\pi\) | |||||||
\(882\) | −16.9706 | − | 18.9737i | −0.571429 | − | 0.638877i | ||||
\(883\) | −33.0000 | −1.11054 | −0.555269 | − | 0.831671i | \(-0.687385\pi\) | ||||
−0.555269 | + | 0.831671i | \(0.687385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.00000 | − | 2.23607i | −0.168073 | − | 0.0751646i | ||||
\(886\) | − | 15.8114i | − | 0.531194i | ||||||
\(887\) | −32.5269 | −1.09215 | −0.546073 | − | 0.837737i | \(-0.683878\pi\) | ||||
−0.546073 | + | 0.837737i | \(0.683878\pi\) | |||||||
\(888\) | 42.4264 | + | 18.9737i | 1.42374 | + | 0.636715i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 40.2492i | − | 1.34916i | ||||||
\(891\) | −20.0000 | − | 2.23607i | −0.670025 | − | 0.0749111i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.07107 | − | 6.70820i | −0.236624 | − | 0.224481i | ||||
\(894\) | −25.0000 | − | 11.1803i | −0.836125 | − | 0.373927i | ||||
\(895\) | 12.6491i | 0.422813i | ||||||||
\(896\) | −11.3137 | −0.377964 | ||||||||
\(897\) | 10.0000 | − | 22.3607i | 0.333890 | − | 0.746601i | ||||
\(898\) | −8.00000 | −0.266963 | ||||||||
\(899\) | − | 17.8885i | − | 0.596616i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.4605i | 0.948157i | ||||||||
\(902\) | 31.3050i | 1.04234i | ||||||||
\(903\) | −3.53553 | + | 7.90569i | −0.117655 | + | 0.263085i | ||||
\(904\) | 16.0000 | 0.532152 | ||||||||
\(905\) | −42.4264 | −1.41030 | ||||||||
\(906\) | 35.3553 | + | 15.8114i | 1.17460 | + | 0.525298i | ||||
\(907\) | − | 15.8114i | − | 0.525009i | −0.964931 | − | 0.262504i | \(-0.915452\pi\) | ||
0.964931 | − | 0.262504i | \(-0.0845484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.0000 | + | 17.8885i | −0.663358 | + | 0.593326i | ||||
\(910\) | −10.0000 | −0.331497 | ||||||||
\(911\) | −53.7401 | −1.78049 | −0.890245 | − | 0.455483i | \(-0.849467\pi\) | ||||
−0.890245 | + | 0.455483i | \(0.849467\pi\) | |||||||
\(912\) | 11.5147 | + | 27.9179i | 0.381290 | + | 0.924455i | ||||
\(913\) | −20.0000 | −0.661903 | ||||||||
\(914\) | 15.5563 | 0.514558 | ||||||||
\(915\) | 3.53553 | + | 1.58114i | 0.116881 | + | 0.0522708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.23607i | − | 0.0738415i | ||||||
\(918\) | 15.0000 | + | 46.9574i | 0.495074 | + | 1.54983i | ||||
\(919\) | −18.0000 | −0.593765 | −0.296883 | − | 0.954914i | \(-0.595947\pi\) | ||||
−0.296883 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(920\) | −28.2843 | −0.932505 | ||||||||
\(921\) | −30.0000 | − | 13.4164i | −0.988534 | − | 0.442086i | ||||
\(922\) | − | 34.7851i | − | 1.14558i | ||||||
\(923\) | − | 13.4164i | − | 0.441606i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.07107 | 0.232370 | ||||||||
\(927\) | −14.1421 | + | 12.6491i | −0.464489 | + | 0.415451i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.7214i | 1.46726i | 0.679549 | + | 0.733630i | \(0.262175\pi\) | ||||
−0.679549 | + | 0.733630i | \(0.737825\pi\) | |||||||
\(930\) | 7.07107 | − | 15.8114i | 0.231869 | − | 0.518476i | ||||
\(931\) | −18.0000 | + | 18.9737i | −0.589926 | + | 0.621837i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.8909 | − | 17.3925i | −1.27323 | − | 0.569406i | ||||
\(934\) | 3.16228i | 0.103473i | ||||||||
\(935\) | 33.5410i | 1.09691i | ||||||||
\(936\) | 20.0000 | − | 17.8885i | 0.653720 | − | 0.584705i | ||||
\(937\) | 21.0000 | 0.686040 | 0.343020 | − | 0.939328i | \(-0.388550\pi\) | ||||
0.343020 | + | 0.939328i | \(0.388550\pi\) | |||||||
\(938\) | − | 8.94427i | − | 0.292041i | ||||||
\(939\) | 14.1421 | − | 31.6228i | 0.461511 | − | 1.03197i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.2843 | −0.922041 | −0.461020 | − | 0.887390i | \(-0.652517\pi\) | ||||
−0.461020 | + | 0.887390i | \(0.652517\pi\) | |||||||
\(942\) | −4.00000 | + | 8.94427i | −0.130327 | + | 0.291420i | ||||
\(943\) | 44.2719i | 1.44169i | ||||||||
\(944\) | −5.65685 | −0.184115 | ||||||||
\(945\) | 3.53553 | + | 11.0680i | 0.115011 | + | 0.360041i | ||||
\(946\) | 15.8114i | 0.514073i | ||||||||
\(947\) | 58.1378i | 1.88922i | 0.328190 | + | 0.944612i | \(0.393561\pi\) | ||||
−0.328190 | + | 0.944612i | \(0.606439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 9.48683i | − | 0.307956i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00000 | + | 2.23607i | −0.0324272 | + | 0.0725095i | ||||
\(952\) | 18.9737i | 0.614940i | ||||||||
\(953\) | 25.4558 | 0.824596 | 0.412298 | − | 0.911049i | \(-0.364726\pi\) | ||||
0.412298 | + | 0.911049i | \(0.364726\pi\) | |||||||
\(954\) | 12.0000 | + | 13.4164i | 0.388514 | + | 0.434372i | ||||
\(955\) | 25.0000 | 0.808981 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.0000 | + | 8.94427i | 0.646508 | + | 0.289127i | ||||
\(958\) | − | 31.6228i | − | 1.02169i | ||||||
\(959\) | 2.23607i | 0.0722064i | ||||||||
\(960\) | −28.2843 | − | 12.6491i | −0.912871 | − | 0.408248i | ||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | 42.4264 | 1.36788 | ||||||||
\(963\) | −16.9706 | − | 18.9737i | −0.546869 | − | 0.611418i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.1421 | 0.455251 | ||||||||
\(966\) | 10.0000 | + | 4.47214i | 0.321745 | + | 0.143889i | ||||
\(967\) | −26.0000 | −0.836104 | −0.418052 | − | 0.908423i | \(-0.637287\pi\) | ||||
−0.418052 | + | 0.908423i | \(0.637287\pi\) | |||||||
\(968\) | 16.9706 | 0.545455 | ||||||||
\(969\) | 46.8198 | − | 19.3108i | 1.50407 | − | 0.620351i | ||||
\(970\) | −10.0000 | −0.321081 | ||||||||
\(971\) | 16.9706 | 0.544611 | 0.272306 | − | 0.962211i | \(-0.412214\pi\) | ||||
0.272306 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.00000 | −0.224410 | ||||||||
\(974\) | − | 40.2492i | − | 1.28967i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.00000 | 0.128037 | ||||||||
\(977\) | 24.0416 | 0.769160 | 0.384580 | − | 0.923092i | \(-0.374346\pi\) | ||||
0.384580 | + | 0.923092i | \(0.374346\pi\) | |||||||
\(978\) | 18.0000 | − | 40.2492i | 0.575577 | − | 1.28703i | ||||
\(979\) | − | 28.4605i | − | 0.909601i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1421 | − | 12.6491i | 0.451524 | − | 0.403855i | ||||
\(982\) | − | 44.2719i | − | 1.41277i | ||||||
\(983\) | −48.0833 | −1.53362 | −0.766809 | − | 0.641875i | \(-0.778157\pi\) | ||||
−0.766809 | + | 0.641875i | \(0.778157\pi\) | |||||||
\(984\) | −19.7990 | + | 44.2719i | −0.631169 | + | 1.41134i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 53.6656i | − | 1.70906i | ||||||
\(987\) | −3.53553 | − | 1.58114i | −0.112537 | − | 0.0503282i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.3607i | 0.711028i | ||||||||
\(990\) | 14.1421 | + | 15.8114i | 0.449467 | + | 0.502519i | ||||
\(991\) | 28.4605i | 0.904078i | 0.891998 | + | 0.452039i | \(0.149303\pi\) | ||||
−0.891998 | + | 0.452039i | \(0.850697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0000 | − | 8.94427i | −0.634681 | − | 0.283838i | ||||
\(994\) | 6.00000 | 0.190308 | ||||||||
\(995\) | 6.70820i | 0.212664i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.0000 | 0.791758 | 0.395879 | − | 0.918303i | \(-0.370440\pi\) | ||||
0.395879 | + | 0.918303i | \(0.370440\pi\) | |||||||
\(998\) | −24.0416 | −0.761025 | ||||||||
\(999\) | −15.0000 | − | 46.9574i | −0.474579 | − | 1.48567i |
(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 | 57.2.d.a.56.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 57.2.d.a.56.3 | yes | 4 | |
4.3 | odd | 2 | 912.2.f.f.113.2 | 4 | |||
12.11 | even | 2 | 912.2.f.f.113.4 | 4 | |||
19.18 | odd | 2 | inner | 57.2.d.a.56.4 | yes | 4 | |
57.56 | even | 2 | inner | 57.2.d.a.56.2 | yes | 4 | |
76.75 | even | 2 | 912.2.f.f.113.3 | 4 | |||
228.227 | odd | 2 | 912.2.f.f.113.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.d.a.56.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
57.2.d.a.56.2 | yes | 4 | 57.56 | even | 2 | inner | |
57.2.d.a.56.3 | yes | 4 | 3.2 | odd | 2 | inner | |
57.2.d.a.56.4 | yes | 4 | 19.18 | odd | 2 | inner | |
912.2.f.f.113.1 | 4 | 228.227 | odd | 2 | |||
912.2.f.f.113.2 | 4 | 4.3 | odd | 2 | |||
912.2.f.f.113.3 | 4 | 76.75 | even | 2 | |||
912.2.f.f.113.4 | 4 | 12.11 | even | 2 |