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 | 251.3 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.c.251.1 |
$q$-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 | ||||||||
\(3\) | −0.618034 | + | 1.61803i | −0.356822 | + | 0.934172i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.61803 | − | 0.618034i | −0.660560 | − | 0.252311i | ||||
\(7\) | −0.381966 | + | 2.61803i | −0.144370 | + | 0.989524i | ||||
\(8\) | − | 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 | \(0.235511\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0.618034 | − | 1.61803i | 0.178411 | − | 0.467086i | ||||
\(13\) | 3.23607i | 0.897524i | 0.893651 | + | 0.448762i | \(0.148135\pi\) | ||||
−0.893651 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(14\) | −2.61803 | − | 0.381966i | −0.699699 | − | 0.102085i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | 2.00000 | − | 2.23607i | 0.471405 | − | 0.527046i | ||||
\(19\) | 0.472136i | 0.108315i | 0.998532 | + | 0.0541577i | \(0.0172474\pi\) | ||||
−0.998532 | + | 0.0541577i | \(0.982753\pi\) | |||||||
\(20\) | 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 | \(-0.136929\pi\) | |||||||
\(24\) | 1.61803 | + | 0.618034i | 0.330280 | + | 0.126156i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.23607 | −0.634645 | ||||||||
\(27\) | 4.61803 | − | 2.38197i | 0.888741 | − | 0.458410i | ||||
\(28\) | 0.381966 | − | 2.61803i | 0.0721848 | − | 0.494762i | ||||
\(29\) | − | 5.70820i | − | 1.05999i | −0.848002 | − | 0.529993i | \(-0.822194\pi\) | ||
0.848002 | − | 0.529993i | \(-0.177806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.23607i | 1.29964i | 0.760090 | + | 0.649818i | \(0.225155\pi\) | ||||
−0.760090 | + | 0.649818i | \(0.774845\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −7.23607 | − | 2.76393i | −1.25964 | − | 0.481139i | ||||
\(34\) | − | 0.763932i | − | 0.131013i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.23607 | + | 2.00000i | 0.372678 | + | 0.333333i | ||||
\(37\) | −5.23607 | −0.860804 | −0.430402 | − | 0.902637i | \(-0.641628\pi\) | ||||
−0.430402 | + | 0.902637i | \(0.641628\pi\) | |||||||
\(38\) | −0.472136 | −0.0765906 | ||||||||
\(39\) | −5.23607 | − | 2.00000i | −0.838442 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.47214 | 1.01078 | 0.505389 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505389 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(42\) | 2.23607 | − | 4.00000i | 0.345033 | − | 0.617213i | ||||
\(43\) | −12.9443 | −1.97398 | −0.986991 | − | 0.160773i | \(-0.948601\pi\) | ||||
−0.986991 | + | 0.160773i | \(0.948601\pi\) | |||||||
\(44\) | − | 4.47214i | − | 0.674200i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | −2.47214 | −0.360598 | −0.180299 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(48\) | −0.618034 | + | 1.61803i | −0.0892055 | + | 0.233543i | ||||
\(49\) | −6.70820 | − | 2.00000i | −0.958315 | − | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.472136 | − | 1.23607i | 0.0661123 | − | 0.173084i | ||||
\(52\) | − | 3.23607i | − | 0.448762i | ||||||
\(53\) | − | 8.47214i | − | 1.16374i | −0.813283 | − | 0.581869i | \(-0.802322\pi\) | ||
0.813283 | − | 0.581869i | \(-0.197678\pi\) | |||||||
\(54\) | 2.38197 | + | 4.61803i | 0.324145 | + | 0.628435i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.61803 | + | 0.381966i | 0.349850 | + | 0.0510424i | ||||
\(57\) | −0.763932 | − | 0.291796i | −0.101185 | − | 0.0386493i | ||||
\(58\) | 5.70820 | 0.749524 | ||||||||
\(59\) | −4.47214 | −0.582223 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.76393i | − | 0.353885i | −0.984221 | − | 0.176943i | \(-0.943379\pi\) | ||
0.984221 | − | 0.176943i | \(-0.0566207\pi\) | |||||||
\(62\) | −7.23607 | −0.918982 | ||||||||
\(63\) | 6.09017 | − | 5.09017i | 0.767289 | − | 0.641301i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.76393 | − | 7.23607i | 0.340217 | − | 0.890698i | ||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0.763932 | 0.0926404 | ||||||||
\(69\) | 6.47214 | + | 2.47214i | 0.779154 | + | 0.297610i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.76393i | 0.328018i | 0.986459 | + | 0.164009i | \(0.0524427\pi\) | ||||
−0.986459 | + | 0.164009i | \(0.947557\pi\) | |||||||
\(72\) | −2.00000 | + | 2.23607i | −0.235702 | + | 0.263523i | ||||
\(73\) | − | 6.76393i | − | 0.791658i | −0.918324 | − | 0.395829i | \(-0.870457\pi\) | ||
0.918324 | − | 0.395829i | \(-0.129543\pi\) | |||||||
\(74\) | − | 5.23607i | − | 0.608681i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.472136i | − | 0.0541577i | ||||||
\(77\) | −11.7082 | − | 1.70820i | −1.33427 | − | 0.194668i | ||||
\(78\) | 2.00000 | − | 5.23607i | 0.226455 | − | 0.592868i | ||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 6.47214i | 0.714728i | ||||||||
\(83\) | 16.6525 | 1.82785 | 0.913923 | − | 0.405887i | \(-0.133037\pi\) | ||||
0.913923 | + | 0.405887i | \(0.133037\pi\) | |||||||
\(84\) | 4.00000 | + | 2.23607i | 0.436436 | + | 0.243975i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 12.9443i | − | 1.39582i | ||||||
\(87\) | 9.23607 | + | 3.52786i | 0.990210 | + | 0.378227i | ||||
\(88\) | 4.47214 | 0.476731 | ||||||||
\(89\) | −14.4721 | −1.53404 | −0.767022 | − | 0.641621i | \(-0.778262\pi\) | ||||
−0.767022 | + | 0.641621i | \(0.778262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.47214 | − | 1.23607i | −0.888121 | − | 0.129575i | ||||
\(92\) | 4.00000i | 0.417029i | ||||||||
\(93\) | −11.7082 | − | 4.47214i | −1.21408 | − | 0.463739i | ||||
\(94\) | − | 2.47214i | − | 0.254981i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.61803 | − | 0.618034i | −0.165140 | − | 0.0630778i | ||||
\(97\) | 5.23607i | 0.531642i | 0.964022 | + | 0.265821i | \(0.0856430\pi\) | ||||
−0.964022 | + | 0.265821i | \(0.914357\pi\) | |||||||
\(98\) | 2.00000 | − | 6.70820i | 0.202031 | − | 0.677631i | ||||
\(99\) | 8.94427 | − | 10.0000i | 0.898933 | − | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.52786 | −0.351036 | −0.175518 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175518 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(102\) | 1.23607 | + | 0.472136i | 0.122389 | + | 0.0467484i | ||||
\(103\) | 16.6525i | 1.64082i | 0.571778 | + | 0.820409i | \(0.306254\pi\) | ||||
−0.571778 | + | 0.820409i | \(0.693746\pi\) | |||||||
\(104\) | 3.23607 | 0.317323 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.47214 | 0.822887 | ||||||||
\(107\) | − | 15.4164i | − | 1.49036i | −0.666863 | − | 0.745180i | \(-0.732363\pi\) | ||
0.666863 | − | 0.745180i | \(-0.267637\pi\) | |||||||
\(108\) | −4.61803 | + | 2.38197i | −0.444371 | + | 0.229205i | ||||
\(109\) | −4.47214 | −0.428353 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.23607 | − | 8.47214i | 0.307154 | − | 0.804140i | ||||
\(112\) | −0.381966 | + | 2.61803i | −0.0360924 | + | 0.247381i | ||||
\(113\) | 14.9443i | 1.40584i | 0.711269 | + | 0.702919i | \(0.248121\pi\) | ||||
−0.711269 | + | 0.702919i | \(0.751879\pi\) | |||||||
\(114\) | 0.291796 | − | 0.763932i | 0.0273292 | − | 0.0715488i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.70820i | 0.529993i | ||||||||
\(117\) | 6.47214 | − | 7.23607i | 0.598349 | − | 0.668975i | ||||
\(118\) | − | 4.47214i | − | 0.411693i | ||||||
\(119\) | 0.291796 | − | 2.00000i | 0.0267489 | − | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 2.76393 | 0.250235 | ||||||||
\(123\) | −4.00000 | + | 10.4721i | −0.360668 | + | 0.944241i | ||||
\(124\) | − | 7.23607i | − | 0.649818i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.09017 | + | 6.09017i | 0.453468 | + | 0.542555i | ||||
\(127\) | 13.7082 | 1.21641 | 0.608203 | − | 0.793781i | \(-0.291891\pi\) | ||||
0.608203 | + | 0.793781i | \(0.291891\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 8.00000 | − | 20.9443i | 0.704361 | − | 1.84404i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.4164 | −1.87116 | −0.935580 | − | 0.353114i | \(-0.885123\pi\) | ||||
−0.935580 | + | 0.353114i | \(0.885123\pi\) | |||||||
\(132\) | 7.23607 | + | 2.76393i | 0.629819 | + | 0.240569i | ||||
\(133\) | −1.23607 | − | 0.180340i | −0.107181 | − | 0.0156375i | ||||
\(134\) | 12.0000i | 1.03664i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.763932i | 0.0655066i | ||||||||
\(137\) | 12.4721i | 1.06557i | 0.846252 | + | 0.532783i | \(0.178854\pi\) | ||||
−0.846252 | + | 0.532783i | \(0.821146\pi\) | |||||||
\(138\) | −2.47214 | + | 6.47214i | −0.210442 | + | 0.550945i | ||||
\(139\) | 20.4721i | 1.73642i | 0.496194 | + | 0.868212i | \(0.334731\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.52786 | − | 4.00000i | 0.128669 | − | 0.336861i | ||||
\(142\) | −2.76393 | −0.231944 | ||||||||
\(143\) | −14.4721 | −1.21022 | ||||||||
\(144\) | −2.23607 | − | 2.00000i | −0.186339 | − | 0.166667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.76393 | 0.559787 | ||||||||
\(147\) | 7.38197 | − | 9.61803i | 0.608854 | − | 0.793282i | ||||
\(148\) | 5.23607 | 0.430402 | ||||||||
\(149\) | 17.7082i | 1.45071i | 0.688374 | + | 0.725356i | \(0.258325\pi\) | ||||
−0.688374 | + | 0.725356i | \(0.741675\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | 0.472136 | 0.0382953 | ||||||||
\(153\) | 1.70820 | + | 1.52786i | 0.138100 | + | 0.123520i | ||||
\(154\) | 1.70820 | − | 11.7082i | 0.137651 | − | 0.943474i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.23607 | + | 2.00000i | 0.419221 | + | 0.160128i | ||||
\(157\) | − | 4.76393i | − | 0.380203i | −0.981764 | − | 0.190102i | \(-0.939118\pi\) | ||
0.981764 | − | 0.190102i | \(-0.0608817\pi\) | |||||||
\(158\) | 8.94427i | 0.711568i | ||||||||
\(159\) | 13.7082 | + | 5.23607i | 1.08713 | + | 0.415247i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4721 | + | 1.52786i | 0.825320 | + | 0.120413i | ||||
\(162\) | −8.94427 | + | 1.00000i | −0.702728 | + | 0.0785674i | ||||
\(163\) | 1.52786 | 0.119672 | 0.0598358 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598358 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(164\) | −6.47214 | −0.505389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6525i | 1.29248i | ||||||||
\(167\) | −16.9443 | −1.31119 | −0.655594 | − | 0.755114i | \(-0.727582\pi\) | ||||
−0.655594 | + | 0.755114i | \(0.727582\pi\) | |||||||
\(168\) | −2.23607 | + | 4.00000i | −0.172516 | + | 0.308607i | ||||
\(169\) | 2.52786 | 0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.944272 | − | 1.05573i | 0.0722103 | − | 0.0807335i | ||||
\(172\) | 12.9443 | 0.986991 | ||||||||
\(173\) | −17.4164 | −1.32414 | −0.662072 | − | 0.749440i | \(-0.730323\pi\) | ||||
−0.662072 | + | 0.749440i | \(0.730323\pi\) | |||||||
\(174\) | −3.52786 | + | 9.23607i | −0.267447 | + | 0.700185i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.47214i | 0.337100i | ||||||||
\(177\) | 2.76393 | − | 7.23607i | 0.207750 | − | 0.543896i | ||||
\(178\) | − | 14.4721i | − | 1.08473i | ||||||
\(179\) | − | 2.94427i | − | 0.220065i | −0.993928 | − | 0.110033i | \(-0.964904\pi\) | ||
0.993928 | − | 0.110033i | \(-0.0350955\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.18034i | − | 0.459381i | −0.973264 | − | 0.229691i | \(-0.926229\pi\) | ||
0.973264 | − | 0.229691i | \(-0.0737714\pi\) | |||||||
\(182\) | 1.23607 | − | 8.47214i | 0.0916235 | − | 0.627996i | ||||
\(183\) | 4.47214 | + | 1.70820i | 0.330590 | + | 0.126274i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.47214 | − | 11.7082i | 0.327913 | − | 0.858487i | ||||
\(187\) | − | 3.41641i | − | 0.249832i | ||||||
\(188\) | 2.47214 | 0.180299 | ||||||||
\(189\) | 4.47214 | + | 13.0000i | 0.325300 | + | 0.945611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.76393i | − | 0.199991i | −0.994988 | − | 0.0999956i | \(-0.968117\pi\) | ||
0.994988 | − | 0.0999956i | \(-0.0318829\pi\) | |||||||
\(192\) | 0.618034 | − | 1.61803i | 0.0446028 | − | 0.116772i | ||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | −5.23607 | −0.375928 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70820 | + | 2.00000i | 0.479157 | + | 0.142857i | ||||
\(197\) | 12.4721i | 0.888603i | 0.895877 | + | 0.444301i | \(0.146548\pi\) | ||||
−0.895877 | + | 0.444301i | \(0.853452\pi\) | |||||||
\(198\) | 10.0000 | + | 8.94427i | 0.710669 | + | 0.635642i | ||||
\(199\) | − | 0.180340i | − | 0.0127840i | −0.999980 | − | 0.00639198i | \(-0.997965\pi\) | ||
0.999980 | − | 0.00639198i | \(-0.00203464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41641 | + | 19.4164i | −0.523113 | + | 1.36953i | ||||
\(202\) | − | 3.52786i | − | 0.248220i | ||||||
\(203\) | 14.9443 | + | 2.18034i | 1.04888 | + | 0.153030i | ||||
\(204\) | −0.472136 | + | 1.23607i | −0.0330561 | + | 0.0865421i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.6525 | −1.16023 | ||||||||
\(207\) | −8.00000 | + | 8.94427i | −0.556038 | + | 0.621670i | ||||
\(208\) | 3.23607i | 0.224381i | ||||||||
\(209\) | −2.11146 | −0.146052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 8.47214i | 0.581869i | ||||||||
\(213\) | −4.47214 | − | 1.70820i | −0.306426 | − | 0.117044i | ||||
\(214\) | 15.4164 | 1.05384 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.38197 | − | 4.61803i | −0.162072 | − | 0.314217i | ||||
\(217\) | −18.9443 | − | 2.76393i | −1.28602 | − | 0.187628i | ||||
\(218\) | − | 4.47214i | − | 0.302891i | ||||||
\(219\) | 10.9443 | + | 4.18034i | 0.739545 | + | 0.282481i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.47214i | − | 0.166294i | ||||||
\(222\) | 8.47214 | + | 3.23607i | 0.568613 | + | 0.217191i | ||||
\(223\) | 4.29180i | 0.287400i | 0.989621 | + | 0.143700i | \(0.0459000\pi\) | ||||
−0.989621 | + | 0.143700i | \(0.954100\pi\) | |||||||
\(224\) | −2.61803 | − | 0.381966i | −0.174925 | − | 0.0255212i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.9443 | −0.994078 | ||||||||
\(227\) | −5.23607 | −0.347530 | −0.173765 | − | 0.984787i | \(-0.555593\pi\) | ||||
−0.173765 | + | 0.984787i | \(0.555593\pi\) | |||||||
\(228\) | 0.763932 | + | 0.291796i | 0.0505926 | + | 0.0193247i | ||||
\(229\) | 13.2361i | 0.874664i | 0.899300 | + | 0.437332i | \(0.144077\pi\) | ||||
−0.899300 | + | 0.437332i | \(0.855923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.0000 | − | 17.8885i | 0.657952 | − | 1.17698i | ||||
\(232\) | −5.70820 | −0.374762 | ||||||||
\(233\) | 20.4721i | 1.34117i | 0.741831 | + | 0.670587i | \(0.233958\pi\) | ||||
−0.741831 | + | 0.670587i | \(0.766042\pi\) | |||||||
\(234\) | 7.23607 | + | 6.47214i | 0.473037 | + | 0.423097i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.47214 | 0.291111 | ||||||||
\(237\) | −5.52786 | + | 14.4721i | −0.359073 | + | 0.940066i | ||||
\(238\) | 2.00000 | + | 0.291796i | 0.129641 | + | 0.0189143i | ||||
\(239\) | 22.1803i | 1.43473i | 0.696699 | + | 0.717363i | \(0.254651\pi\) | ||||
−0.696699 | + | 0.717363i | \(0.745349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.8885i | 1.15230i | 0.817343 | + | 0.576151i | \(0.195446\pi\) | ||||
−0.817343 | + | 0.576151i | \(0.804554\pi\) | |||||||
\(242\) | − | 9.00000i | − | 0.578542i | ||||||
\(243\) | −15.0902 | − | 3.90983i | −0.968035 | − | 0.250816i | ||||
\(244\) | 2.76393i | 0.176943i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.4721 | − | 4.00000i | −0.667679 | − | 0.255031i | ||||
\(247\) | −1.52786 | −0.0972157 | ||||||||
\(248\) | 7.23607 | 0.459491 | ||||||||
\(249\) | −10.2918 | + | 26.9443i | −0.652216 | + | 1.70752i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.52786 | −0.222677 | −0.111338 | − | 0.993783i | \(-0.535514\pi\) | ||||
−0.111338 | + | 0.993783i | \(0.535514\pi\) | |||||||
\(252\) | −6.09017 | + | 5.09017i | −0.383645 | + | 0.320651i | ||||
\(253\) | 17.8885 | 1.12464 | ||||||||
\(254\) | 13.7082i | 0.860129i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.18034 | 0.510276 | 0.255138 | − | 0.966905i | \(-0.417879\pi\) | ||||
0.255138 | + | 0.966905i | \(0.417879\pi\) | |||||||
\(258\) | 20.9443 | + | 8.00000i | 1.30393 | + | 0.498058i | ||||
\(259\) | 2.00000 | − | 13.7082i | 0.124274 | − | 0.851786i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4164 | + | 12.7639i | −0.706658 | + | 0.790068i | ||||
\(262\) | − | 21.4164i | − | 1.32311i | ||||||
\(263\) | 4.94427i | 0.304877i | 0.988313 | + | 0.152438i | \(0.0487126\pi\) | ||||
−0.988313 | + | 0.152438i | \(0.951287\pi\) | |||||||
\(264\) | −2.76393 | + | 7.23607i | −0.170108 | + | 0.445349i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.180340 | − | 1.23607i | 0.0110573 | − | 0.0757882i | ||||
\(267\) | 8.94427 | − | 23.4164i | 0.547381 | − | 1.43306i | ||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | −4.47214 | −0.272671 | −0.136335 | − | 0.990663i | \(-0.543533\pi\) | ||||
−0.136335 | + | 0.990663i | \(0.543533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.2918i | − | 1.11115i | −0.831467 | − | 0.555574i | \(-0.812499\pi\) | ||
0.831467 | − | 0.555574i | \(-0.187501\pi\) | |||||||
\(272\) | −0.763932 | −0.0463202 | ||||||||
\(273\) | 7.23607 | − | 12.9443i | 0.437947 | − | 0.783423i | ||||
\(274\) | −12.4721 | −0.753469 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.47214 | − | 2.47214i | −0.389577 | − | 0.148805i | ||||
\(277\) | −23.1246 | −1.38942 | −0.694712 | − | 0.719288i | \(-0.744468\pi\) | ||||
−0.694712 | + | 0.719288i | \(0.744468\pi\) | |||||||
\(278\) | −20.4721 | −1.22784 | ||||||||
\(279\) | 14.4721 | − | 16.1803i | 0.866424 | − | 0.968692i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.0000i | − | 1.19310i | −0.802576 | − | 0.596550i | \(-0.796538\pi\) | ||
0.802576 | − | 0.596550i | \(-0.203462\pi\) | |||||||
\(282\) | 4.00000 | + | 1.52786i | 0.238197 | + | 0.0909830i | ||||
\(283\) | 8.76393i | 0.520962i | 0.965479 | + | 0.260481i | \(0.0838811\pi\) | ||||
−0.965479 | + | 0.260481i | \(0.916119\pi\) | |||||||
\(284\) | − | 2.76393i | − | 0.164009i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 14.4721i | − | 0.855755i | ||||||
\(287\) | −2.47214 | + | 16.9443i | −0.145926 | + | 1.00019i | ||||
\(288\) | 2.00000 | − | 2.23607i | 0.117851 | − | 0.131762i | ||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.47214 | − | 3.23607i | −0.496645 | − | 0.189702i | ||||
\(292\) | 6.76393i | 0.395829i | ||||||||
\(293\) | 29.4164 | 1.71852 | 0.859262 | − | 0.511535i | \(-0.170923\pi\) | ||||
0.859262 | + | 0.511535i | \(0.170923\pi\) | |||||||
\(294\) | 9.61803 | + | 7.38197i | 0.560935 | + | 0.430525i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.23607i | 0.304340i | ||||||||
\(297\) | 10.6525 | + | 20.6525i | 0.618119 | + | 1.19838i | ||||
\(298\) | −17.7082 | −1.02581 | ||||||||
\(299\) | 12.9443 | 0.748587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.94427 | − | 33.8885i | 0.284983 | − | 1.95330i | ||||
\(302\) | 3.05573i | 0.175837i | ||||||||
\(303\) | 2.18034 | − | 5.70820i | 0.125257 | − | 0.327928i | ||||
\(304\) | 0.472136i | 0.0270789i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.52786 | + | 1.70820i | −0.0873422 | + | 0.0976515i | ||||
\(307\) | 4.18034i | 0.238585i | 0.992859 | + | 0.119292i | \(0.0380626\pi\) | ||||
−0.992859 | + | 0.119292i | \(0.961937\pi\) | |||||||
\(308\) | 11.7082 | + | 1.70820i | 0.667137 | + | 0.0973340i | ||||
\(309\) | −26.9443 | − | 10.2918i | −1.53281 | − | 0.585480i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4721 | 1.50110 | 0.750549 | − | 0.660815i | \(-0.229789\pi\) | ||||
0.750549 | + | 0.660815i | \(0.229789\pi\) | |||||||
\(312\) | −2.00000 | + | 5.23607i | −0.113228 | + | 0.296434i | ||||
\(313\) | 7.70820i | 0.435693i | 0.975983 | + | 0.217847i | \(0.0699033\pi\) | ||||
−0.975983 | + | 0.217847i | \(0.930097\pi\) | |||||||
\(314\) | 4.76393 | 0.268844 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.94427 | −0.503155 | ||||||||
\(317\) | 6.94427i | 0.390029i | 0.980800 | + | 0.195015i | \(0.0624754\pi\) | ||||
−0.980800 | + | 0.195015i | \(0.937525\pi\) | |||||||
\(318\) | −5.23607 | + | 13.7082i | −0.293624 | + | 0.768718i | ||||
\(319\) | 25.5279 | 1.42929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.9443 | + | 9.52786i | 1.39225 | + | 0.531794i | ||||
\(322\) | −1.52786 | + | 10.4721i | −0.0851445 | + | 0.583589i | ||||
\(323\) | − | 0.360680i | − | 0.0200688i | ||||||
\(324\) | −1.00000 | − | 8.94427i | −0.0555556 | − | 0.496904i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.52786i | 0.0846206i | ||||||||
\(327\) | 2.76393 | − | 7.23607i | 0.152846 | − | 0.400155i | ||||
\(328\) | − | 6.47214i | − | 0.357364i | ||||||
\(329\) | 0.944272 | − | 6.47214i | 0.0520594 | − | 0.356820i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.9443 | 1.15120 | 0.575601 | − | 0.817731i | \(-0.304768\pi\) | ||||
0.575601 | + | 0.817731i | \(0.304768\pi\) | |||||||
\(332\) | −16.6525 | −0.913923 | ||||||||
\(333\) | 11.7082 | + | 10.4721i | 0.641606 | + | 0.573870i | ||||
\(334\) | − | 16.9443i | − | 0.927149i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00000 | − | 2.23607i | −0.218218 | − | 0.121988i | ||||
\(337\) | 5.41641 | 0.295051 | 0.147525 | − | 0.989058i | \(-0.452869\pi\) | ||||
0.147525 | + | 0.989058i | \(0.452869\pi\) | |||||||
\(338\) | 2.52786i | 0.137498i | ||||||||
\(339\) | −24.1803 | − | 9.23607i | −1.31330 | − | 0.501634i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.3607 | −1.75243 | ||||||||
\(342\) | 1.05573 | + | 0.944272i | 0.0570872 | + | 0.0510604i | ||||
\(343\) | 7.79837 | − | 16.7984i | 0.421073 | − | 0.907027i | ||||
\(344\) | 12.9443i | 0.697908i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 17.4164i | − | 0.936312i | ||||||
\(347\) | − | 6.47214i | − | 0.347442i | −0.984795 | − | 0.173721i | \(-0.944421\pi\) | ||
0.984795 | − | 0.173721i | \(-0.0555792\pi\) | |||||||
\(348\) | −9.23607 | − | 3.52786i | −0.495105 | − | 0.189113i | ||||
\(349\) | 2.18034i | 0.116711i | 0.998296 | + | 0.0583555i | \(0.0185857\pi\) | ||||
−0.998296 | + | 0.0583555i | \(0.981414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.70820 | + | 14.9443i | 0.411433 | + | 0.797666i | ||||
\(352\) | −4.47214 | −0.238366 | ||||||||
\(353\) | 14.2918 | 0.760676 | 0.380338 | − | 0.924848i | \(-0.375808\pi\) | ||||
0.380338 | + | 0.924848i | \(0.375808\pi\) | |||||||
\(354\) | 7.23607 | + | 2.76393i | 0.384593 | + | 0.146901i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.4721 | 0.767022 | ||||||||
\(357\) | 3.05573 | + | 1.70820i | 0.161726 | + | 0.0904077i | ||||
\(358\) | 2.94427 | 0.155610 | ||||||||
\(359\) | − | 10.1803i | − | 0.537298i | −0.963238 | − | 0.268649i | \(-0.913423\pi\) | ||
0.963238 | − | 0.268649i | \(-0.0865771\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7771 | 0.988268 | ||||||||
\(362\) | 6.18034 | 0.324831 | ||||||||
\(363\) | 5.56231 | − | 14.5623i | 0.291945 | − | 0.764323i | ||||
\(364\) | 8.47214 | + | 1.23607i | 0.444061 | + | 0.0647876i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.70820 | + | 4.47214i | −0.0892892 | + | 0.233762i | ||||
\(367\) | 14.1803i | 0.740208i | 0.928990 | + | 0.370104i | \(0.120678\pi\) | ||||
−0.928990 | + | 0.370104i | \(0.879322\pi\) | |||||||
\(368\) | − | 4.00000i | − | 0.208514i | ||||||
\(369\) | −14.4721 | − | 12.9443i | −0.753389 | − | 0.673852i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.1803 | + | 3.23607i | 1.15155 | + | 0.168008i | ||||
\(372\) | 11.7082 | + | 4.47214i | 0.607042 | + | 0.231869i | ||||
\(373\) | 9.81966 | 0.508443 | 0.254221 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254221 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(374\) | 3.41641 | 0.176658 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.47214i | 0.127491i | ||||||||
\(377\) | 18.4721 | 0.951363 | ||||||||
\(378\) | −13.0000 | + | 4.47214i | −0.668648 | + | 0.230022i | ||||
\(379\) | 17.8885 | 0.918873 | 0.459436 | − | 0.888211i | \(-0.348051\pi\) | ||||
0.459436 | + | 0.888211i | \(0.348051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.47214 | + | 22.1803i | −0.434041 | + | 1.13633i | ||||
\(382\) | 2.76393 | 0.141415 | ||||||||
\(383\) | −21.8885 | −1.11845 | −0.559226 | − | 0.829015i | \(-0.688902\pi\) | ||||
−0.559226 | + | 0.829015i | \(0.688902\pi\) | |||||||
\(384\) | 1.61803 | + | 0.618034i | 0.0825700 | + | 0.0315389i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000i | 0.305392i | ||||||||
\(387\) | 28.9443 | + | 25.8885i | 1.47132 | + | 1.31599i | ||||
\(388\) | − | 5.23607i | − | 0.265821i | ||||||
\(389\) | − | 7.81966i | − | 0.396473i | −0.980154 | − | 0.198236i | \(-0.936479\pi\) | ||
0.980154 | − | 0.198236i | \(-0.0635213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.05573i | 0.154535i | ||||||||
\(392\) | −2.00000 | + | 6.70820i | −0.101015 | + | 0.338815i | ||||
\(393\) | 13.2361 | − | 34.6525i | 0.667671 | − | 1.74799i | ||||
\(394\) | −12.4721 | −0.628337 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.94427 | + | 10.0000i | −0.449467 | + | 0.502519i | ||||
\(397\) | − | 17.1246i | − | 0.859460i | −0.902958 | − | 0.429730i | \(-0.858609\pi\) | ||
0.902958 | − | 0.429730i | \(-0.141391\pi\) | |||||||
\(398\) | 0.180340 | 0.00903962 | ||||||||
\(399\) | 1.05573 | − | 1.88854i | 0.0528525 | − | 0.0945454i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.52786i | − | 0.276048i | −0.990429 | − | 0.138024i | \(-0.955925\pi\) | ||
0.990429 | − | 0.138024i | \(-0.0440752\pi\) | |||||||
\(402\) | −19.4164 | − | 7.41641i | −0.968402 | − | 0.369897i | ||||
\(403\) | −23.4164 | −1.16645 | ||||||||
\(404\) | 3.52786 | 0.175518 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.18034 | + | 14.9443i | −0.108208 | + | 0.741672i | ||||
\(407\) | − | 23.4164i | − | 1.16071i | ||||||
\(408\) | −1.23607 | − | 0.472136i | −0.0611945 | − | 0.0233742i | ||||
\(409\) | 19.4164i | 0.960080i | 0.877247 | + | 0.480040i | \(0.159378\pi\) | ||||
−0.877247 | + | 0.480040i | \(0.840622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.1803 | − | 7.70820i | −0.995423 | − | 0.380218i | ||||
\(412\) | − | 16.6525i | − | 0.820409i | ||||||
\(413\) | 1.70820 | − | 11.7082i | 0.0840552 | − | 0.576123i | ||||
\(414\) | −8.94427 | − | 8.00000i | −0.439587 | − | 0.393179i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.23607 | −0.158661 | ||||||||
\(417\) | −33.1246 | − | 12.6525i | −1.62212 | − | 0.619594i | ||||
\(418\) | − | 2.11146i | − | 0.103275i | ||||||
\(419\) | −16.8328 | −0.822337 | −0.411168 | − | 0.911559i | \(-0.634879\pi\) | ||||
−0.411168 | + | 0.911559i | \(0.634879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4721 | −0.607855 | −0.303927 | − | 0.952695i | \(-0.598298\pi\) | ||||
−0.303927 | + | 0.952695i | \(0.598298\pi\) | |||||||
\(422\) | − | 8.00000i | − | 0.389434i | ||||||
\(423\) | 5.52786 | + | 4.94427i | 0.268774 | + | 0.240399i | ||||
\(424\) | −8.47214 | −0.411443 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.70820 | − | 4.47214i | 0.0827628 | − | 0.216676i | ||||
\(427\) | 7.23607 | + | 1.05573i | 0.350178 | + | 0.0510903i | ||||
\(428\) | 15.4164i | 0.745180i | ||||||||
\(429\) | 8.94427 | − | 23.4164i | 0.431834 | − | 1.13055i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9.59675i | − | 0.462259i | −0.972923 | − | 0.231130i | \(-0.925758\pi\) | ||
0.972923 | − | 0.231130i | \(-0.0742421\pi\) | |||||||
\(432\) | 4.61803 | − | 2.38197i | 0.222185 | − | 0.114602i | ||||
\(433\) | − | 4.65248i | − | 0.223584i | −0.993732 | − | 0.111792i | \(-0.964341\pi\) | ||
0.993732 | − | 0.111792i | \(-0.0356590\pi\) | |||||||
\(434\) | 2.76393 | − | 18.9443i | 0.132673 | − | 0.909354i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.47214 | 0.214176 | ||||||||
\(437\) | 1.88854 | 0.0903413 | ||||||||
\(438\) | −4.18034 | + | 10.9443i | −0.199744 | + | 0.522938i | ||||
\(439\) | 12.1803i | 0.581336i | 0.956824 | + | 0.290668i | \(0.0938775\pi\) | ||||
−0.956824 | + | 0.290668i | \(0.906123\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0000 | + | 17.8885i | 0.523810 | + | 0.851835i | ||||
\(442\) | 2.47214 | 0.117588 | ||||||||
\(443\) | − | 9.52786i | − | 0.452682i | −0.974048 | − | 0.226341i | \(-0.927324\pi\) | ||
0.974048 | − | 0.226341i | \(-0.0726764\pi\) | |||||||
\(444\) | −3.23607 | + | 8.47214i | −0.153577 | + | 0.402070i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.29180 | −0.203222 | ||||||||
\(447\) | −28.6525 | − | 10.9443i | −1.35522 | − | 0.517646i | ||||
\(448\) | 0.381966 | − | 2.61803i | 0.0180462 | − | 0.123690i | ||||
\(449\) | 1.52786i | 0.0721044i | 0.999350 | + | 0.0360522i | \(0.0114783\pi\) | ||||
−0.999350 | + | 0.0360522i | \(0.988522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9443i | 1.36293i | ||||||||
\(452\) | − | 14.9443i | − | 0.702919i | ||||||
\(453\) | −1.88854 | + | 4.94427i | −0.0887315 | + | 0.232302i | ||||
\(454\) | − | 5.23607i | − | 0.245741i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.291796 | + | 0.763932i | −0.0136646 | + | 0.0357744i | ||||
\(457\) | −9.05573 | −0.423609 | −0.211805 | − | 0.977312i | \(-0.567934\pi\) | ||||
−0.211805 | + | 0.977312i | \(0.567934\pi\) | |||||||
\(458\) | −13.2361 | −0.618481 | ||||||||
\(459\) | −3.52786 | + | 1.81966i | −0.164667 | + | 0.0849345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.9443 | 0.509726 | 0.254863 | − | 0.966977i | \(-0.417970\pi\) | ||||
0.254863 | + | 0.966977i | \(0.417970\pi\) | |||||||
\(462\) | 17.8885 | + | 10.0000i | 0.832250 | + | 0.465242i | ||||
\(463\) | −0.180340 | −0.00838111 | −0.00419055 | − | 0.999991i | \(-0.501334\pi\) | ||||
−0.00419055 | + | 0.999991i | \(0.501334\pi\) | |||||||
\(464\) | − | 5.70820i | − | 0.264997i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4721 | −0.948353 | ||||||||
\(467\) | 20.2918 | 0.938992 | 0.469496 | − | 0.882935i | \(-0.344436\pi\) | ||||
0.469496 | + | 0.882935i | \(0.344436\pi\) | |||||||
\(468\) | −6.47214 | + | 7.23607i | −0.299175 | + | 0.334487i | ||||
\(469\) | −4.58359 | + | 31.4164i | −0.211651 | + | 1.45067i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.70820 | + | 2.94427i | 0.355175 | + | 0.135665i | ||||
\(472\) | 4.47214i | 0.205847i | ||||||||
\(473\) | − | 57.8885i | − | 2.66172i | ||||||
\(474\) | −14.4721 | − | 5.52786i | −0.664727 | − | 0.253903i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.291796 | + | 2.00000i | −0.0133745 | + | 0.0916698i | ||||
\(477\) | −16.9443 | + | 18.9443i | −0.775825 | + | 0.867399i | ||||
\(478\) | −22.1803 | −1.01451 | ||||||||
\(479\) | 2.11146 | 0.0964749 | 0.0482374 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482374 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.9443i | − | 0.772592i | ||||||
\(482\) | −17.8885 | −0.814801 | ||||||||
\(483\) | −8.94427 | + | 16.0000i | −0.406978 | + | 0.728025i | ||||
\(484\) | 9.00000 | 0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.90983 | − | 15.0902i | 0.177353 | − | 0.684504i | ||||
\(487\) | 31.5967 | 1.43179 | 0.715893 | − | 0.698210i | \(-0.246020\pi\) | ||||
0.715893 | + | 0.698210i | \(0.246020\pi\) | |||||||
\(488\) | −2.76393 | −0.125117 | ||||||||
\(489\) | −0.944272 | + | 2.47214i | −0.0427015 | + | 0.111794i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4164i | 0.605474i | 0.953074 | + | 0.302737i | \(0.0979004\pi\) | ||||
−0.953074 | + | 0.302737i | \(0.902100\pi\) | |||||||
\(492\) | 4.00000 | − | 10.4721i | 0.180334 | − | 0.472120i | ||||
\(493\) | 4.36068i | 0.196395i | ||||||||
\(494\) | − | 1.52786i | − | 0.0687419i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.23607i | 0.324909i | ||||||||
\(497\) | −7.23607 | − | 1.05573i | −0.324582 | − | 0.0473559i | ||||
\(498\) | −26.9443 | − | 10.2918i | −1.20740 | − | 0.461186i | ||||
\(499\) | −17.8885 | −0.800801 | −0.400401 | − | 0.916340i | \(-0.631129\pi\) | ||||
−0.400401 | + | 0.916340i | \(0.631129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4721 | − | 27.4164i | 0.467861 | − | 1.22487i | ||||
\(502\) | − | 3.52786i | − | 0.157456i | ||||||
\(503\) | −16.3607 | −0.729487 | −0.364743 | − | 0.931108i | \(-0.618843\pi\) | ||||
−0.364743 | + | 0.931108i | \(0.618843\pi\) | |||||||
\(504\) | −5.09017 | − | 6.09017i | −0.226734 | − | 0.271278i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.8885i | 0.795243i | ||||||||
\(507\) | −1.56231 | + | 4.09017i | −0.0693844 | + | 0.181651i | ||||
\(508\) | −13.7082 | −0.608203 | ||||||||
\(509\) | 24.4721 | 1.08471 | 0.542354 | − | 0.840150i | \(-0.317533\pi\) | ||||
0.542354 | + | 0.840150i | \(0.317533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7082 | + | 2.58359i | 0.783365 | + | 0.114291i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.12461 | + | 2.18034i | 0.0496528 | + | 0.0962644i | ||||
\(514\) | 8.18034i | 0.360819i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.00000 | + | 20.9443i | −0.352180 | + | 0.922020i | ||||
\(517\) | − | 11.0557i | − | 0.486230i | ||||||
\(518\) | 13.7082 | + | 2.00000i | 0.602304 | + | 0.0878750i | ||||
\(519\) | 10.7639 | − | 28.1803i | 0.472484 | − | 1.23698i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0557 | −0.834847 | −0.417423 | − | 0.908712i | \(-0.637067\pi\) | ||||
−0.417423 | + | 0.908712i | \(0.637067\pi\) | |||||||
\(522\) | −12.7639 | − | 11.4164i | −0.558662 | − | 0.499683i | ||||
\(523\) | 24.5410i | 1.07310i | 0.843867 | + | 0.536552i | \(0.180273\pi\) | ||||
−0.843867 | + | 0.536552i | \(0.819727\pi\) | |||||||
\(524\) | 21.4164 | 0.935580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.94427 | −0.215580 | ||||||||
\(527\) | − | 5.52786i | − | 0.240798i | ||||||
\(528\) | −7.23607 | − | 2.76393i | −0.314909 | − | 0.120285i | ||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | + | 8.94427i | 0.433963 | + | 0.388148i | ||||
\(532\) | 1.23607 | + | 0.180340i | 0.0535903 | + | 0.00781873i | ||||
\(533\) | 20.9443i | 0.907197i | ||||||||
\(534\) | 23.4164 | + | 8.94427i | 1.01333 | + | 0.387056i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.0000i | − | 0.518321i | ||||||
\(537\) | 4.76393 | + | 1.81966i | 0.205579 | + | 0.0785241i | ||||
\(538\) | − | 4.47214i | − | 0.192807i | ||||||
\(539\) | 8.94427 | − | 30.0000i | 0.385257 | − | 1.29219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0557 | 0.561310 | 0.280655 | − | 0.959809i | \(-0.409448\pi\) | ||||
0.280655 | + | 0.959809i | \(0.409448\pi\) | |||||||
\(542\) | 18.2918 | 0.785700 | ||||||||
\(543\) | 10.0000 | + | 3.81966i | 0.429141 | + | 0.163917i | ||||
\(544\) | − | 0.763932i | − | 0.0327533i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.9443 | + | 7.23607i | 0.553964 | + | 0.309675i | ||||
\(547\) | 8.58359 | 0.367008 | 0.183504 | − | 0.983019i | \(-0.441256\pi\) | ||||
0.183504 | + | 0.983019i | \(0.441256\pi\) | |||||||
\(548\) | − | 12.4721i | − | 0.532783i | ||||||
\(549\) | −5.52786 | + | 6.18034i | −0.235923 | + | 0.263770i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.69505 | 0.114813 | ||||||||
\(552\) | 2.47214 | − | 6.47214i | 0.105221 | − | 0.275472i | ||||
\(553\) | −3.41641 | + | 23.4164i | −0.145280 | + | 0.995767i | ||||
\(554\) | − | 23.1246i | − | 0.982471i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 20.4721i | − | 0.868212i | ||||||
\(557\) | − | 16.4721i | − | 0.697947i | −0.937133 | − | 0.348973i | \(-0.886530\pi\) | ||
0.937133 | − | 0.348973i | \(-0.113470\pi\) | |||||||
\(558\) | 16.1803 | + | 14.4721i | 0.684968 | + | 0.612654i | ||||
\(559\) | − | 41.8885i | − | 1.77170i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.52786 | + | 2.11146i | 0.233387 | + | 0.0891457i | ||||
\(562\) | 20.0000 | 0.843649 | ||||||||
\(563\) | −17.8197 | −0.751009 | −0.375505 | − | 0.926821i | \(-0.622531\pi\) | ||||
−0.375505 | + | 0.926821i | \(0.622531\pi\) | |||||||
\(564\) | −1.52786 | + | 4.00000i | −0.0643347 | + | 0.168430i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.76393 | −0.368376 | ||||||||
\(567\) | −23.7984 | − | 0.798374i | −0.999438 | − | 0.0335286i | ||||
\(568\) | 2.76393 | 0.115972 | ||||||||
\(569\) | − | 18.4721i | − | 0.774392i | −0.921997 | − | 0.387196i | \(-0.873444\pi\) | ||
0.921997 | − | 0.387196i | \(-0.126556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.8328 | −1.45771 | −0.728854 | − | 0.684669i | \(-0.759947\pi\) | ||||
−0.728854 | + | 0.684669i | \(0.759947\pi\) | |||||||
\(572\) | 14.4721 | 0.605110 | ||||||||
\(573\) | 4.47214 | + | 1.70820i | 0.186826 | + | 0.0713612i | ||||
\(574\) | −16.9443 | − | 2.47214i | −0.707240 | − | 0.103185i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.23607 | + | 2.00000i | 0.0931695 | + | 0.0833333i | ||||
\(577\) | 14.1803i | 0.590335i | 0.955445 | + | 0.295168i | \(0.0953755\pi\) | ||||
−0.955445 | + | 0.295168i | \(0.904625\pi\) | |||||||
\(578\) | − | 16.4164i | − | 0.682833i | ||||||
\(579\) | −3.70820 | + | 9.70820i | −0.154108 | + | 0.403459i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.36068 | + | 43.5967i | −0.263885 | + | 1.80870i | ||||
\(582\) | 3.23607 | − | 8.47214i | 0.134139 | − | 0.351181i | ||||
\(583\) | 37.8885 | 1.56918 | ||||||||
\(584\) | −6.76393 | −0.279893 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.4164i | 1.21518i | ||||||||
\(587\) | 23.7082 | 0.978542 | 0.489271 | − | 0.872132i | \(-0.337263\pi\) | ||||
0.489271 | + | 0.872132i | \(0.337263\pi\) | |||||||
\(588\) | −7.38197 | + | 9.61803i | −0.304427 | + | 0.396641i | ||||
\(589\) | −3.41641 | −0.140771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1803 | − | 7.70820i | −0.830108 | − | 0.317073i | ||||
\(592\) | −5.23607 | −0.215201 | ||||||||
\(593\) | −47.0132 | −1.93060 | −0.965299 | − | 0.261145i | \(-0.915900\pi\) | ||||
−0.965299 | + | 0.261145i | \(0.915900\pi\) | |||||||
\(594\) | −20.6525 | + | 10.6525i | −0.847381 | + | 0.437076i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 17.7082i | − | 0.725356i | ||||||
\(597\) | 0.291796 | + | 0.111456i | 0.0119424 | + | 0.00456160i | ||||
\(598\) | 12.9443i | 0.529331i | ||||||||
\(599\) | − | 41.2361i | − | 1.68486i | −0.538806 | − | 0.842430i | \(-0.681124\pi\) | ||
0.538806 | − | 0.842430i | \(-0.318876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.4721i | − | 0.590331i | −0.955446 | − | 0.295165i | \(-0.904625\pi\) | ||
0.955446 | − | 0.295165i | \(-0.0953747\pi\) | |||||||
\(602\) | 33.8885 | + | 4.94427i | 1.38119 | + | 0.201513i | ||||
\(603\) | −26.8328 | − | 24.0000i | −1.09272 | − | 0.977356i | ||||
\(604\) | −3.05573 | −0.124336 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.70820 | + | 2.18034i | 0.231880 | + | 0.0885703i | ||||
\(607\) | − | 14.7639i | − | 0.599250i | −0.954057 | − | 0.299625i | \(-0.903139\pi\) | ||
0.954057 | − | 0.299625i | \(-0.0968615\pi\) | |||||||
\(608\) | −0.472136 | −0.0191476 | ||||||||
\(609\) | −12.7639 | + | 22.8328i | −0.517221 | + | 0.925232i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8.00000i | − | 0.323645i | ||||||
\(612\) | −1.70820 | − | 1.52786i | −0.0690501 | − | 0.0617602i | ||||
\(613\) | 20.0689 | 0.810575 | 0.405287 | − | 0.914189i | \(-0.367171\pi\) | ||||
0.405287 | + | 0.914189i | \(0.367171\pi\) | |||||||
\(614\) | −4.18034 | −0.168705 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.70820 | + | 11.7082i | −0.0688255 | + | 0.471737i | ||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 10.2918 | − | 26.9443i | 0.413997 | − | 1.08386i | ||||
\(619\) | − | 14.0000i | − | 0.562708i | −0.959604 | − | 0.281354i | \(-0.909217\pi\) | ||
0.959604 | − | 0.281354i | \(-0.0907834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.52786 | − | 18.4721i | −0.382340 | − | 0.741261i | ||||
\(622\) | 26.4721i | 1.06144i | ||||||||
\(623\) | 5.52786 | − | 37.8885i | 0.221469 | − | 1.51797i | ||||
\(624\) | −5.23607 | − | 2.00000i | −0.209610 | − | 0.0800641i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.70820 | −0.308082 | ||||||||
\(627\) | 1.30495 | − | 3.41641i | 0.0521148 | − | 0.136438i | ||||
\(628\) | 4.76393i | 0.190102i | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8885 | 1.18984 | 0.594922 | − | 0.803783i | \(-0.297183\pi\) | ||||
0.594922 | + | 0.803783i | \(0.297183\pi\) | |||||||
\(632\) | − | 8.94427i | − | 0.355784i | ||||||
\(633\) | 4.94427 | − | 12.9443i | 0.196517 | − | 0.514489i | ||||
\(634\) | −6.94427 | −0.275792 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.7082 | − | 5.23607i | −0.543566 | − | 0.207624i | ||||
\(637\) | 6.47214 | − | 21.7082i | 0.256435 | − | 0.860110i | ||||
\(638\) | 25.5279i | 1.01066i | ||||||||
\(639\) | 5.52786 | − | 6.18034i | 0.218679 | − | 0.244490i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.41641i | 0.134940i | 0.997721 | + | 0.0674700i | \(0.0214927\pi\) | ||||
−0.997721 | + | 0.0674700i | \(0.978507\pi\) | |||||||
\(642\) | −9.52786 | + | 24.9443i | −0.376035 | + | 0.984472i | ||||
\(643\) | − | 25.7082i | − | 1.01383i | −0.861995 | − | 0.506916i | \(-0.830785\pi\) | ||
0.861995 | − | 0.506916i | \(-0.169215\pi\) | |||||||
\(644\) | −10.4721 | − | 1.52786i | −0.412660 | − | 0.0602063i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.360680 | 0.0141908 | ||||||||
\(647\) | 18.8328 | 0.740394 | 0.370197 | − | 0.928953i | \(-0.379290\pi\) | ||||
0.370197 | + | 0.928953i | \(0.379290\pi\) | |||||||
\(648\) | 8.94427 | − | 1.00000i | 0.351364 | − | 0.0392837i | ||||
\(649\) | − | 20.0000i | − | 0.785069i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.1803 | − | 28.9443i | 0.634158 | − | 1.13442i | ||||
\(652\) | −1.52786 | −0.0598358 | ||||||||
\(653\) | − | 11.8885i | − | 0.465235i | −0.972568 | − | 0.232617i | \(-0.925271\pi\) | ||
0.972568 | − | 0.232617i | \(-0.0747290\pi\) | |||||||
\(654\) | 7.23607 | + | 2.76393i | 0.282953 | + | 0.108078i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.47214 | 0.252694 | ||||||||
\(657\) | −13.5279 | + | 15.1246i | −0.527772 | + | 0.590067i | ||||
\(658\) | 6.47214 | + | 0.944272i | 0.252310 | + | 0.0368116i | ||||
\(659\) | 40.4721i | 1.57657i | 0.615310 | + | 0.788285i | \(0.289031\pi\) | ||||
−0.615310 | + | 0.788285i | \(0.710969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 31.7082i | − | 1.23331i | −0.787235 | − | 0.616653i | \(-0.788488\pi\) | ||
0.787235 | − | 0.616653i | \(-0.211512\pi\) | |||||||
\(662\) | 20.9443i | 0.814022i | ||||||||
\(663\) | 4.00000 | + | 1.52786i | 0.155347 | + | 0.0593373i | ||||
\(664\) | − | 16.6525i | − | 0.646241i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4721 | + | 11.7082i | −0.405787 | + | 0.453684i | ||||
\(667\) | −22.8328 | −0.884090 | ||||||||
\(668\) | 16.9443 | 0.655594 | ||||||||
\(669\) | −6.94427 | − | 2.65248i | −0.268481 | − | 0.102551i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3607 | 0.477179 | ||||||||
\(672\) | 2.23607 | − | 4.00000i | 0.0862582 | − | 0.154303i | ||||
\(673\) | −28.4721 | −1.09752 | −0.548760 | − | 0.835980i | \(-0.684900\pi\) | ||||
−0.548760 | + | 0.835980i | \(0.684900\pi\) | |||||||
\(674\) | 5.41641i | 0.208632i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.52786 | −0.0972255 | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 9.23607 | − | 24.1803i | 0.354709 | − | 0.928640i | ||||
\(679\) | −13.7082 | − | 2.00000i | −0.526073 | − | 0.0767530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.23607 | − | 8.47214i | 0.124006 | − | 0.324653i | ||||
\(682\) | − | 32.3607i | − | 1.23915i | ||||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | −0.944272 | + | 1.05573i | −0.0361051 | + | 0.0403668i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.7984 | + | 7.79837i | 0.641365 | + | 0.297743i | ||||
\(687\) | −21.4164 | − | 8.18034i | −0.817087 | − | 0.312099i | ||||
\(688\) | −12.9443 | −0.493496 | ||||||||
\(689\) | 27.4164 | 1.04448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9443i | 1.48151i | 0.671775 | + | 0.740755i | \(0.265532\pi\) | ||||
−0.671775 | + | 0.740755i | \(0.734468\pi\) | |||||||
\(692\) | 17.4164 | 0.662072 | ||||||||
\(693\) | 22.7639 | + | 27.2361i | 0.864730 | + | 1.03461i | ||||
\(694\) | 6.47214 | 0.245679 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.52786 | − | 9.23607i | 0.133723 | − | 0.350092i | ||||
\(697\) | −4.94427 | −0.187278 | ||||||||
\(698\) | −2.18034 | −0.0825271 | ||||||||
\(699\) | −33.1246 | − | 12.6525i | −1.25289 | − | 0.478561i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.0689i | − | 0.531374i | −0.964059 | − | 0.265687i | \(-0.914401\pi\) | ||
0.964059 | − | 0.265687i | \(-0.0855988\pi\) | |||||||
\(702\) | −14.9443 | + | 7.70820i | −0.564035 | + | 0.290927i | ||||
\(703\) | − | 2.47214i | − | 0.0932384i | ||||||
\(704\) | − | 4.47214i | − | 0.168550i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.2918i | 0.537879i | ||||||||
\(707\) | 1.34752 | − | 9.23607i | 0.0506789 | − | 0.347358i | ||||
\(708\) | −2.76393 | + | 7.23607i | −0.103875 | + | 0.271948i | ||||
\(709\) | −24.4721 | −0.919070 | −0.459535 | − | 0.888160i | \(-0.651984\pi\) | ||||
−0.459535 | + | 0.888160i | \(0.651984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0000 | − | 17.8885i | −0.750059 | − | 0.670873i | ||||
\(712\) | 14.4721i | 0.542366i | ||||||||
\(713\) | 28.9443 | 1.08397 | ||||||||
\(714\) | −1.70820 | + | 3.05573i | −0.0639279 | + | 0.114358i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.94427i | 0.110033i | ||||||||
\(717\) | −35.8885 | − | 13.7082i | −1.34028 | − | 0.511942i | ||||
\(718\) | 10.1803 | 0.379927 | ||||||||
\(719\) | −25.5279 | −0.952029 | −0.476014 | − | 0.879438i | \(-0.657919\pi\) | ||||
−0.476014 | + | 0.879438i | \(0.657919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.5967 | − | 6.36068i | −1.62363 | − | 0.236884i | ||||
\(722\) | 18.7771i | 0.698811i | ||||||||
\(723\) | −28.9443 | − | 11.0557i | −1.07645 | − | 0.411167i | ||||
\(724\) | 6.18034i | 0.229691i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.5623 | + | 5.56231i | 0.540458 | + | 0.206437i | ||||
\(727\) | 39.7082i | 1.47270i | 0.676603 | + | 0.736348i | \(0.263451\pi\) | ||||
−0.676603 | + | 0.736348i | \(0.736549\pi\) | |||||||
\(728\) | −1.23607 | + | 8.47214i | −0.0458117 | + | 0.313998i | ||||
\(729\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.88854 | 0.365741 | ||||||||
\(732\) | −4.47214 | − | 1.70820i | −0.165295 | − | 0.0631370i | ||||
\(733\) | − | 38.0689i | − | 1.40611i | −0.711137 | − | 0.703053i | \(-0.751820\pi\) | ||
0.711137 | − | 0.703053i | \(-0.248180\pi\) | |||||||
\(734\) | −14.1803 | −0.523406 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 53.6656i | 1.97680i | ||||||||
\(738\) | 12.9443 | − | 14.4721i | 0.476485 | − | 0.532727i | ||||
\(739\) | −8.94427 | −0.329020 | −0.164510 | − | 0.986375i | \(-0.552604\pi\) | ||||
−0.164510 | + | 0.986375i | \(0.552604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.944272 | − | 2.47214i | 0.0346887 | − | 0.0908162i | ||||
\(742\) | −3.23607 | + | 22.1803i | −0.118800 | + | 0.814266i | ||||
\(743\) | 1.52786i | 0.0560519i | 0.999607 | + | 0.0280259i | \(0.00892210\pi\) | ||||
−0.999607 | + | 0.0280259i | \(0.991078\pi\) | |||||||
\(744\) | −4.47214 | + | 11.7082i | −0.163956 | + | 0.429244i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.81966i | 0.359523i | ||||||||
\(747\) | −37.2361 | − | 33.3050i | −1.36240 | − | 1.21856i | ||||
\(748\) | 3.41641i | 0.124916i | ||||||||
\(749\) | 40.3607 | + | 5.88854i | 1.47475 | + | 0.215163i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.4164 | 1.29236 | 0.646182 | − | 0.763184i | \(-0.276365\pi\) | ||||
0.646182 | + | 0.763184i | \(0.276365\pi\) | |||||||
\(752\) | −2.47214 | −0.0901495 | ||||||||
\(753\) | 2.18034 | − | 5.70820i | 0.0794560 | − | 0.208019i | ||||
\(754\) | 18.4721i | 0.672716i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.47214 | − | 13.0000i | −0.162650 | − | 0.472805i | ||||
\(757\) | −28.6525 | −1.04139 | −0.520696 | − | 0.853742i | \(-0.674327\pi\) | ||||
−0.520696 | + | 0.853742i | \(0.674327\pi\) | |||||||
\(758\) | 17.8885i | 0.649741i | ||||||||
\(759\) | −11.0557 | + | 28.9443i | −0.401298 | + | 1.05061i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.8885 | 1.08346 | 0.541729 | − | 0.840553i | \(-0.317770\pi\) | ||||
0.541729 | + | 0.840553i | \(0.317770\pi\) | |||||||
\(762\) | −22.1803 | − | 8.47214i | −0.803509 | − | 0.306913i | ||||
\(763\) | 1.70820 | − | 11.7082i | 0.0618411 | − | 0.423865i | ||||
\(764\) | 2.76393i | 0.0999956i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 21.8885i | − | 0.790865i | ||||||
\(767\) | − | 14.4721i | − | 0.522559i | ||||||
\(768\) | −0.618034 | + | 1.61803i | −0.0223014 | + | 0.0583858i | ||||
\(769\) | 36.0000i | 1.29819i | 0.760706 | + | 0.649097i | \(0.224853\pi\) | ||||
−0.760706 | + | 0.649097i | \(0.775147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.05573 | + | 13.2361i | −0.182078 | + | 0.476685i | ||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | −37.4164 | −1.34577 | −0.672887 | − | 0.739745i | \(-0.734946\pi\) | ||||
−0.672887 | + | 0.739745i | \(0.734946\pi\) | |||||||
\(774\) | −25.8885 | + | 28.9443i | −0.930544 | + | 1.04038i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.23607 | 0.187964 | ||||||||
\(777\) | 20.9443 | + | 11.7082i | 0.751372 | + | 0.420029i | ||||
\(778\) | 7.81966 | 0.280348 | ||||||||
\(779\) | 3.05573i | 0.109483i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3607 | −0.442300 | ||||||||
\(782\) | −3.05573 | −0.109273 | ||||||||
\(783\) | −13.5967 | − | 26.3607i | −0.485908 | − | 0.942054i | ||||
\(784\) | −6.70820 | − | 2.00000i | −0.239579 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.6525 | + | 13.2361i | 1.23601 | + | 0.472115i | ||||
\(787\) | 49.7082i | 1.77191i | 0.463775 | + | 0.885953i | \(0.346495\pi\) | ||||
−0.463775 | + | 0.885953i | \(0.653505\pi\) | |||||||
\(788\) | − | 12.4721i | − | 0.444301i | ||||||
\(789\) | −8.00000 | − | 3.05573i | −0.284808 | − | 0.108787i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.1246 | − | 5.70820i | −1.39111 | − | 0.202960i | ||||
\(792\) | −10.0000 | − | 8.94427i | −0.355335 | − | 0.317821i | ||||
\(793\) | 8.94427 | 0.317620 | ||||||||
\(794\) | 17.1246 | 0.607730 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.180340i | 0.00639198i | ||||||||
\(797\) | 5.41641 | 0.191859 | 0.0959295 | − | 0.995388i | \(-0.469418\pi\) | ||||
0.0959295 | + | 0.995388i | \(0.469418\pi\) | |||||||
\(798\) | 1.88854 | + | 1.05573i | 0.0668537 | + | 0.0373724i | ||||
\(799\) | 1.88854 | 0.0668119 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.3607 | + | 28.9443i | 1.14341 | + | 1.02270i | ||||
\(802\) | 5.52786 | 0.195196 | ||||||||
\(803\) | 30.2492 | 1.06747 | ||||||||
\(804\) | 7.41641 | − | 19.4164i | 0.261557 | − | 0.684764i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 23.4164i | − | 0.824808i | ||||||
\(807\) | 2.76393 | − | 7.23607i | 0.0972950 | − | 0.254722i | ||||
\(808\) | 3.52786i | 0.124110i | ||||||||
\(809\) | 8.36068i | 0.293946i | 0.989141 | + | 0.146973i | \(0.0469530\pi\) | ||||
−0.989141 | + | 0.146973i | \(0.953047\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8328i | 0.591080i | 0.955330 | + | 0.295540i | \(0.0954996\pi\) | ||||
−0.955330 | + | 0.295540i | \(0.904500\pi\) | |||||||
\(812\) | −14.9443 | − | 2.18034i | −0.524441 | − | 0.0765149i | ||||
\(813\) | 29.5967 | + | 11.3050i | 1.03800 | + | 0.396482i | ||||
\(814\) | 23.4164 | 0.820745 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.472136 | − | 1.23607i | 0.0165281 | − | 0.0432710i | ||||
\(817\) | − | 6.11146i | − | 0.213813i | ||||||
\(818\) | −19.4164 | −0.678879 | ||||||||
\(819\) | 16.4721 | + | 19.7082i | 0.575583 | + | 0.688660i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.2918i | 0.638388i | 0.947689 | + | 0.319194i | \(0.103412\pi\) | ||||
−0.947689 | + | 0.319194i | \(0.896588\pi\) | |||||||
\(822\) | 7.70820 | − | 20.1803i | 0.268854 | − | 0.703870i | ||||
\(823\) | −0.180340 | −0.00628625 | −0.00314313 | − | 0.999995i | \(-0.501000\pi\) | ||||
−0.00314313 | + | 0.999995i | \(0.501000\pi\) | |||||||
\(824\) | 16.6525 | 0.580116 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7082 | + | 1.70820i | 0.407381 | + | 0.0594360i | ||||
\(827\) | 14.8328i | 0.515788i | 0.966173 | + | 0.257894i | \(0.0830285\pi\) | ||||
−0.966173 | + | 0.257894i | \(0.916972\pi\) | |||||||
\(828\) | 8.00000 | − | 8.94427i | 0.278019 | − | 0.310835i | ||||
\(829\) | − | 30.1803i | − | 1.04821i | −0.851655 | − | 0.524103i | \(-0.824401\pi\) | ||
0.851655 | − | 0.524103i | \(-0.175599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.2918 | − | 37.4164i | 0.495777 | − | 1.29796i | ||||
\(832\) | − | 3.23607i | − | 0.112190i | ||||||
\(833\) | 5.12461 | + | 1.52786i | 0.177557 | + | 0.0529374i | ||||
\(834\) | 12.6525 | − | 33.1246i | 0.438119 | − | 1.14701i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.11146 | 0.0730262 | ||||||||
\(837\) | 17.2361 | + | 33.4164i | 0.595766 | + | 1.15504i | ||||
\(838\) | − | 16.8328i | − | 0.581480i | ||||||
\(839\) | 14.4721 | 0.499634 | 0.249817 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249817 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.58359 | −0.123572 | ||||||||
\(842\) | − | 12.4721i | − | 0.429818i | ||||||
\(843\) | 32.3607 | + | 12.3607i | 1.11456 | + | 0.425724i | ||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.94427 | + | 5.52786i | −0.169988 | + | 0.190052i | ||||
\(847\) | 3.43769 | − | 23.5623i | 0.118121 | − | 0.809610i | ||||
\(848\) | − | 8.47214i | − | 0.290934i | ||||||
\(849\) | −14.1803 | − | 5.41641i | −0.486668 | − | 0.185891i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.9443i | 0.717960i | ||||||||
\(852\) | 4.47214 | + | 1.70820i | 0.153213 | + | 0.0585221i | ||||
\(853\) | − | 5.70820i | − | 0.195445i | −0.995214 | − | 0.0977226i | \(-0.968844\pi\) | ||
0.995214 | − | 0.0977226i | \(-0.0311558\pi\) | |||||||
\(854\) | −1.05573 | + | 7.23607i | −0.0361263 | + | 0.247613i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4164 | −0.526922 | ||||||||
\(857\) | 42.6525 | 1.45698 | 0.728490 | − | 0.685056i | \(-0.240222\pi\) | ||||
0.728490 | + | 0.685056i | \(0.240222\pi\) | |||||||
\(858\) | 23.4164 | + | 8.94427i | 0.799423 | + | 0.305352i | ||||
\(859\) | 34.9443i | 1.19228i | 0.802879 | + | 0.596142i | \(0.203300\pi\) | ||||
−0.802879 | + | 0.596142i | \(0.796700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.8885 | − | 14.4721i | −0.882279 | − | 0.493209i | ||||
\(862\) | 9.59675 | 0.326867 | ||||||||
\(863\) | 21.5279i | 0.732817i | 0.930454 | + | 0.366409i | \(0.119413\pi\) | ||||
−0.930454 | + | 0.366409i | \(0.880587\pi\) | |||||||
\(864\) | 2.38197 | + | 4.61803i | 0.0810361 | + | 0.157109i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.65248 | 0.158098 | ||||||||
\(867\) | 10.1459 | − | 26.5623i | 0.344573 | − | 0.902103i | ||||
\(868\) | 18.9443 | + | 2.76393i | 0.643010 | + | 0.0938140i | ||||
\(869\) | 40.0000i | 1.35691i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.8328i | 1.31580i | ||||||||
\(872\) | 4.47214i | 0.151446i | ||||||||
\(873\) | 10.4721 | − | 11.7082i | 0.354428 | − | 0.396263i | ||||
\(874\) | 1.88854i | 0.0638809i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.9443 | − | 4.18034i | −0.369773 | − | 0.141241i | ||||
\(877\) | −7.34752 | −0.248108 | −0.124054 | − | 0.992275i | \(-0.539590\pi\) | ||||
−0.124054 | + | 0.992275i | \(0.539590\pi\) | |||||||
\(878\) | −12.1803 | −0.411067 | ||||||||
\(879\) | −18.1803 | + | 47.5967i | −0.613208 | + | 1.60540i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.4164 | −0.384629 | −0.192314 | − | 0.981333i | \(-0.561599\pi\) | ||||
−0.192314 | + | 0.981333i | \(0.561599\pi\) | |||||||
\(882\) | −17.8885 | + | 11.0000i | −0.602339 | + | 0.370389i | ||||
\(883\) | −21.8885 | −0.736608 | −0.368304 | − | 0.929705i | \(-0.620061\pi\) | ||||
−0.368304 | + | 0.929705i | \(0.620061\pi\) | |||||||
\(884\) | 2.47214i | 0.0831469i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.52786 | 0.320095 | ||||||||
\(887\) | 26.4721 | 0.888847 | 0.444424 | − | 0.895817i | \(-0.353408\pi\) | ||||
0.444424 | + | 0.895817i | \(0.353408\pi\) | |||||||
\(888\) | −8.47214 | − | 3.23607i | −0.284306 | − | 0.108595i | ||||
\(889\) | −5.23607 | + | 35.8885i | −0.175612 | + | 1.20366i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.0000 | + | 4.47214i | −1.34005 | + | 0.149822i | ||||
\(892\) | − | 4.29180i | − | 0.143700i | ||||||
\(893\) | − | 1.16718i | − | 0.0390583i | ||||||
\(894\) | 10.9443 | − | 28.6525i | 0.366031 | − | 0.958282i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.61803 | + | 0.381966i | 0.0874624 | + | 0.0127606i | ||||
\(897\) | −8.00000 | + | 20.9443i | −0.267112 | + | 0.699309i | ||||
\(898\) | −1.52786 | −0.0509855 | ||||||||
\(899\) | 41.3050 | 1.37760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.47214i | 0.215618i | ||||||||
\(902\) | −28.9443 | −0.963739 | ||||||||
\(903\) | 51.7771 | + | 28.9443i | 1.72303 | + | 0.963205i | ||||
\(904\) | 14.9443 | 0.497039 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.94427 | − | 1.88854i | −0.164262 | − | 0.0627427i | ||||
\(907\) | 26.4721 | 0.878993 | 0.439496 | − | 0.898244i | \(-0.355157\pi\) | ||||
0.439496 | + | 0.898244i | \(0.355157\pi\) | |||||||
\(908\) | 5.23607 | 0.173765 | ||||||||
\(909\) | 7.88854 | + | 7.05573i | 0.261646 | + | 0.234024i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19.3475i | − | 0.641012i | −0.947246 | − | 0.320506i | \(-0.896147\pi\) | ||
0.947246 | − | 0.320506i | \(-0.103853\pi\) | |||||||
\(912\) | −0.763932 | − | 0.291796i | −0.0252963 | − | 0.00966233i | ||||
\(913\) | 74.4721i | 2.46467i | ||||||||
\(914\) | − | 9.05573i | − | 0.299537i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.2361i | − | 0.437332i | ||||||
\(917\) | 8.18034 | − | 56.0689i | 0.270139 | − | 1.85156i | ||||
\(918\) | −1.81966 | − | 3.52786i | −0.0600577 | − | 0.116437i | ||||
\(919\) | 44.7214 | 1.47522 | 0.737611 | − | 0.675226i | \(-0.235954\pi\) | ||||
0.737611 | + | 0.675226i | \(0.235954\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.76393 | − | 2.58359i | −0.222879 | − | 0.0851323i | ||||
\(922\) | 10.9443i | 0.360430i | ||||||||
\(923\) | −8.94427 | −0.294404 | ||||||||
\(924\) | −10.0000 | + | 17.8885i | −0.328976 | + | 0.588490i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 0.180340i | − | 0.00592634i | ||||||
\(927\) | 33.3050 | − | 37.2361i | 1.09388 | − | 1.22299i | ||||
\(928\) | 5.70820 | 0.187381 | ||||||||
\(929\) | 2.11146 | 0.0692746 | 0.0346373 | − | 0.999400i | \(-0.488972\pi\) | ||||
0.0346373 | + | 0.999400i | \(0.488972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.944272 | − | 3.16718i | 0.0309473 | − | 0.103800i | ||||
\(932\) | − | 20.4721i | − | 0.670587i | ||||||
\(933\) | −16.3607 | + | 42.8328i | −0.535625 | + | 1.40228i | ||||
\(934\) | 20.2918i | 0.663968i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.23607 | − | 6.47214i | −0.236518 | − | 0.211548i | ||||
\(937\) | − | 16.0689i | − | 0.524948i | −0.964939 | − | 0.262474i | \(-0.915462\pi\) | ||
0.964939 | − | 0.262474i | \(-0.0845383\pi\) | |||||||
\(938\) | −31.4164 | − | 4.58359i | −1.02578 | − | 0.149660i | ||||
\(939\) | −12.4721 | − | 4.76393i | −0.407013 | − | 0.155465i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.0000 | 0.717180 | 0.358590 | − | 0.933495i | \(-0.383258\pi\) | ||||
0.358590 | + | 0.933495i | \(0.383258\pi\) | |||||||
\(942\) | −2.94427 | + | 7.70820i | −0.0959296 | + | 0.251147i | ||||
\(943\) | − | 25.8885i | − | 0.843047i | ||||||
\(944\) | −4.47214 | −0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.8885 | 1.88212 | ||||||||
\(947\) | 15.6393i | 0.508210i | 0.967177 | + | 0.254105i | \(0.0817808\pi\) | ||||
−0.967177 | + | 0.254105i | \(0.918219\pi\) | |||||||
\(948\) | 5.52786 | − | 14.4721i | 0.179537 | − | 0.470033i | ||||
\(949\) | 21.8885 | 0.710532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.2361 | − | 4.29180i | −0.364354 | − | 0.139171i | ||||
\(952\) | −2.00000 | − | 0.291796i | −0.0648204 | − | 0.00945716i | ||||
\(953\) | 49.4164i | 1.60075i | 0.599497 | + | 0.800377i | \(0.295367\pi\) | ||||
−0.599497 | + | 0.800377i | \(0.704633\pi\) | |||||||
\(954\) | −18.9443 | − | 16.9443i | −0.613343 | − | 0.548591i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 22.1803i | − | 0.717363i | ||||||
\(957\) | −15.7771 | + | 41.3050i | −0.510001 | + | 1.33520i | ||||
\(958\) | 2.11146i | 0.0682181i | ||||||||
\(959\) | −32.6525 | − | 4.76393i | −1.05440 | − | 0.153835i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3607 | −0.689054 | ||||||||
\(962\) | 16.9443 | 0.546305 | ||||||||
\(963\) | −30.8328 | + | 34.4721i | −0.993574 | + | 1.11085i | ||||
\(964\) | − | 17.8885i | − | 0.576151i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.0000 | − | 8.94427i | −0.514792 | − | 0.287777i | ||||
\(967\) | −45.4853 | −1.46271 | −0.731354 | − | 0.681998i | \(-0.761111\pi\) | ||||
−0.731354 | + | 0.681998i | \(0.761111\pi\) | |||||||
\(968\) | 9.00000i | 0.289271i | ||||||||
\(969\) | 0.583592 | + | 0.222912i | 0.0187477 | + | 0.00716098i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.0000 | −1.86131 | −0.930654 | − | 0.365900i | \(-0.880761\pi\) | ||||
−0.930654 | + | 0.365900i | \(0.880761\pi\) | |||||||
\(972\) | 15.0902 | + | 3.90983i | 0.484017 | + | 0.125408i | ||||
\(973\) | −53.5967 | − | 7.81966i | −1.71823 | − | 0.250687i | ||||
\(974\) | 31.5967i | 1.01243i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 2.76393i | − | 0.0884713i | ||||||
\(977\) | − | 25.4164i | − | 0.813143i | −0.913619 | − | 0.406571i | \(-0.866724\pi\) | ||
0.913619 | − | 0.406571i | \(-0.133276\pi\) | |||||||
\(978\) | −2.47214 | − | 0.944272i | −0.0790502 | − | 0.0301945i | ||||
\(979\) | − | 64.7214i | − | 2.06850i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | + | 8.94427i | 0.319275 | + | 0.285569i | ||||
\(982\) | −13.4164 | −0.428135 | ||||||||
\(983\) | 39.4164 | 1.25719 | 0.628594 | − | 0.777734i | \(-0.283631\pi\) | ||||
0.628594 | + | 0.777734i | \(0.283631\pi\) | |||||||
\(984\) | 10.4721 | + | 4.00000i | 0.333840 | + | 0.127515i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.36068 | −0.138872 | ||||||||
\(987\) | 9.88854 | + | 5.52786i | 0.314756 | + | 0.175954i | ||||
\(988\) | 1.52786 | 0.0486078 | ||||||||
\(989\) | 51.7771i | 1.64642i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4721 | 0.840915 | 0.420458 | − | 0.907312i | \(-0.361870\pi\) | ||||
0.420458 | + | 0.907312i | \(0.361870\pi\) | |||||||
\(992\) | −7.23607 | −0.229745 | ||||||||
\(993\) | −12.9443 | + | 33.8885i | −0.410774 | + | 1.07542i | ||||
\(994\) | 1.05573 | − | 7.23607i | 0.0334857 | − | 0.229514i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.2918 | − | 26.9443i | 0.326108 | − | 0.853762i | ||||
\(997\) | 20.7639i | 0.657600i | 0.944400 | + | 0.328800i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328800i | \(0.893356\pi\) | |||||||
\(998\) | − | 17.8885i | − | 0.566252i | ||||||
\(999\) | −24.1803 | + | 12.4721i | −0.765032 | + | 0.394601i |
(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.251.3 | 4 | ||
3.2 | odd | 2 | 1050.2.b.a.251.2 | 4 | |||
5.2 | odd | 4 | 1050.2.d.c.1049.4 | 4 | |||
5.3 | odd | 4 | 1050.2.d.d.1049.1 | 4 | |||
5.4 | even | 2 | 210.2.b.a.41.2 | ✓ | 4 | ||
7.6 | odd | 2 | 1050.2.b.a.251.4 | 4 | |||
15.2 | even | 4 | 1050.2.d.f.1049.3 | 4 | |||
15.8 | even | 4 | 1050.2.d.a.1049.2 | 4 | |||
15.14 | odd | 2 | 210.2.b.b.41.3 | yes | 4 | ||
20.19 | odd | 2 | 1680.2.f.i.881.2 | 4 | |||
21.20 | even | 2 | inner | 1050.2.b.c.251.1 | 4 | ||
35.13 | even | 4 | 1050.2.d.f.1049.4 | 4 | |||
35.27 | even | 4 | 1050.2.d.a.1049.1 | 4 | |||
35.34 | odd | 2 | 210.2.b.b.41.1 | yes | 4 | ||
60.59 | even | 2 | 1680.2.f.e.881.4 | 4 | |||
105.62 | odd | 4 | 1050.2.d.d.1049.2 | 4 | |||
105.83 | odd | 4 | 1050.2.d.c.1049.3 | 4 | |||
105.104 | even | 2 | 210.2.b.a.41.4 | yes | 4 | ||
140.139 | even | 2 | 1680.2.f.e.881.3 | 4 | |||
420.419 | odd | 2 | 1680.2.f.i.881.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.b.a.41.2 | ✓ | 4 | 5.4 | even | 2 | ||
210.2.b.a.41.4 | yes | 4 | 105.104 | even | 2 | ||
210.2.b.b.41.1 | yes | 4 | 35.34 | odd | 2 | ||
210.2.b.b.41.3 | yes | 4 | 15.14 | odd | 2 | ||
1050.2.b.a.251.2 | 4 | 3.2 | odd | 2 | |||
1050.2.b.a.251.4 | 4 | 7.6 | odd | 2 | |||
1050.2.b.c.251.1 | 4 | 21.20 | even | 2 | inner | ||
1050.2.b.c.251.3 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.d.a.1049.1 | 4 | 35.27 | even | 4 | |||
1050.2.d.a.1049.2 | 4 | 15.8 | even | 4 | |||
1050.2.d.c.1049.3 | 4 | 105.83 | odd | 4 | |||
1050.2.d.c.1049.4 | 4 | 5.2 | odd | 4 | |||
1050.2.d.d.1049.1 | 4 | 5.3 | odd | 4 | |||
1050.2.d.d.1049.2 | 4 | 105.62 | odd | 4 | |||
1050.2.d.f.1049.3 | 4 | 15.2 | even | 4 | |||
1050.2.d.f.1049.4 | 4 | 35.13 | even | 4 | |||
1680.2.f.e.881.3 | 4 | 140.139 | even | 2 | |||
1680.2.f.e.881.4 | 4 | 60.59 | even | 2 | |||
1680.2.f.i.881.1 | 4 | 420.419 | odd | 2 | |||
1680.2.f.i.881.2 | 4 | 20.19 | odd | 2 |