Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(41,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, 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("210.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.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: | \(1.67685844245\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.4 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.41 |
Dual form | 210.2.b.a.41.2 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −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 | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | − | 4.47214i | − | 1.34840i | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||
0.738549 | − | 0.674200i | \(-0.235511\pi\) | |||||||
\(12\) | −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 | ||||
\(15\) | 0.618034 | + | 1.61803i | 0.159576 | + | 0.417775i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | −2.00000 | − | 2.23607i | −0.471405 | − | 0.527046i | ||||
\(19\) | − | 0.472136i | − | 0.108315i | −0.998532 | − | 0.0541577i | \(-0.982753\pi\) | ||
0.998532 | − | 0.0541577i | \(-0.0172474\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −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 | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −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 | \(0.177806\pi\) | ||||
−0.848002 | + | 0.529993i | \(0.822194\pi\) | |||||||
\(30\) | −1.61803 | + | 0.618034i | −0.295411 | + | 0.112837i | ||||
\(31\) | − | 7.23607i | − | 1.29964i | −0.760090 | − | 0.649818i | \(-0.774845\pi\) | ||
0.760090 | − | 0.649818i | \(-0.225155\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 7.23607 | − | 2.76393i | 1.25964 | − | 0.481139i | ||||
\(34\) | 0.763932i | 0.131013i | ||||||||
\(35\) | 0.381966 | + | 2.61803i | 0.0645640 | + | 0.442529i | ||||
\(36\) | 2.23607 | − | 2.00000i | 0.372678 | − | 0.333333i | ||||
\(37\) | 5.23607 | 0.860804 | 0.430402 | − | 0.902637i | \(-0.358372\pi\) | ||||
0.430402 | + | 0.902637i | \(0.358372\pi\) | |||||||
\(38\) | 0.472136 | 0.0765906 | ||||||||
\(39\) | −5.23607 | + | 2.00000i | −0.838442 | + | 0.320256i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 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 | \(-0.0513986\pi\) | ||||
0.986991 | + | 0.160773i | \(0.0513986\pi\) | |||||||
\(44\) | 4.47214i | 0.674200i | ||||||||
\(45\) | −2.23607 | + | 2.00000i | −0.333333 | + | 0.298142i | ||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | 0.618034 | + | 1.61803i | 0.0892055 | + | 0.233543i | ||||
\(49\) | −6.70820 | + | 2.00000i | −0.958315 | + | 0.285714i | ||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 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 | ||||
\(55\) | − | 4.47214i | − | 0.603023i | ||||||
\(56\) | 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 | \(0.594025\pi\) | |||||||
\(60\) | −0.618034 | − | 1.61803i | −0.0797878 | − | 0.208887i | ||||
\(61\) | 2.76393i | 0.353885i | 0.984221 | + | 0.176943i | \(0.0566207\pi\) | ||||
−0.984221 | + | 0.176943i | \(0.943379\pi\) | |||||||
\(62\) | 7.23607 | 0.918982 | ||||||||
\(63\) | −6.09017 | − | 5.09017i | −0.767289 | − | 0.641301i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.23607i | 0.401385i | ||||||||
\(66\) | 2.76393 | + | 7.23607i | 0.340217 | + | 0.890698i | ||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | −0.763932 | −0.0926404 | ||||||||
\(69\) | 6.47214 | − | 2.47214i | 0.779154 | − | 0.297610i | ||||
\(70\) | −2.61803 | + | 0.381966i | −0.312915 | + | 0.0456537i | ||||
\(71\) | − | 2.76393i | − | 0.328018i | −0.986459 | − | 0.164009i | \(-0.947557\pi\) | ||
0.986459 | − | 0.164009i | \(-0.0524427\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 0.618034 | + | 1.61803i | 0.0713644 | + | 0.186834i | ||||
\(76\) | 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 | \(0.332173\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 6.47214i | 0.714728i | ||||||||
\(83\) | −16.6525 | −1.82785 | −0.913923 | − | 0.405887i | \(-0.866963\pi\) | ||||
−0.913923 | + | 0.405887i | \(0.866963\pi\) | |||||||
\(84\) | 4.00000 | − | 2.23607i | 0.436436 | − | 0.243975i | ||||
\(85\) | 0.763932 | 0.0828601 | ||||||||
\(86\) | 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 | \(0.778262\pi\) | |||||||
\(90\) | −2.00000 | − | 2.23607i | −0.210819 | − | 0.235702i | ||||
\(91\) | −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 | ||||||||
\(95\) | − | 0.472136i | − | 0.0484401i | ||||||
\(96\) | −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 | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −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 | ||||||||
\(105\) | −4.00000 | + | 2.23607i | −0.390360 | + | 0.218218i | ||||
\(106\) | 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 | \(0.568707\pi\) | |||||||
\(110\) | 4.47214 | 0.426401 | ||||||||
\(111\) | 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 | ||||
\(115\) | − | 4.00000i | − | 0.373002i | ||||||
\(116\) | − | 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 | ||||
\(120\) | 1.61803 | − | 0.618034i | 0.147706 | − | 0.0564185i | ||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | −2.76393 | −0.250235 | ||||||||
\(123\) | 4.00000 | + | 10.4721i | 0.360668 | + | 0.944241i | ||||
\(124\) | 7.23607i | 0.649818i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 5.09017 | − | 6.09017i | 0.453468 | − | 0.542555i | ||||
\(127\) | −13.7082 | −1.21641 | −0.608203 | − | 0.793781i | \(-0.708109\pi\) | ||||
−0.608203 | + | 0.793781i | \(0.708109\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 8.00000 | + | 20.9443i | 0.704361 | + | 1.84404i | ||||
\(130\) | −3.23607 | −0.283822 | ||||||||
\(131\) | −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 | ||||||
\(135\) | −4.61803 | − | 2.38197i | −0.397457 | − | 0.205007i | ||||
\(136\) | − | 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 | \(-0.665269\pi\) | ||
0.496194 | − | 0.868212i | \(-0.334731\pi\) | |||||||
\(140\) | −0.381966 | − | 2.61803i | −0.0322820 | − | 0.221264i | ||||
\(141\) | 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 | ||||
\(145\) | 5.70820i | 0.474041i | ||||||||
\(146\) | 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 | \(-0.741675\pi\) | ||
0.688374 | − | 0.725356i | \(-0.258325\pi\) | |||||||
\(150\) | −1.61803 | + | 0.618034i | −0.132112 | + | 0.0504623i | ||||
\(151\) | 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 | ||||
\(155\) | − | 7.23607i | − | 0.581215i | ||||||
\(156\) | 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 | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 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 | \(-0.519058\pi\) | ||||
−0.0598358 | + | 0.998208i | \(0.519058\pi\) | |||||||
\(164\) | −6.47214 | −0.505389 | ||||||||
\(165\) | 7.23607 | − | 2.76393i | 0.563327 | − | 0.215172i | ||||
\(166\) | − | 16.6525i | − | 1.29248i | ||||||
\(167\) | 16.9443 | 1.31119 | 0.655594 | − | 0.755114i | \(-0.272418\pi\) | ||||
0.655594 | + | 0.755114i | \(0.272418\pi\) | |||||||
\(168\) | 2.23607 | + | 4.00000i | 0.172516 | + | 0.308607i | ||||
\(169\) | 2.52786 | 0.194451 | ||||||||
\(170\) | 0.763932i | 0.0585909i | ||||||||
\(171\) | 0.944272 | + | 1.05573i | 0.0722103 | + | 0.0807335i | ||||
\(172\) | −12.9443 | −0.986991 | ||||||||
\(173\) | 17.4164 | 1.32414 | 0.662072 | − | 0.749440i | \(-0.269677\pi\) | ||||
0.662072 | + | 0.749440i | \(0.269677\pi\) | |||||||
\(174\) | −3.52786 | − | 9.23607i | −0.267447 | − | 0.700185i | ||||
\(175\) | 0.381966 | + | 2.61803i | 0.0288739 | + | 0.197905i | ||||
\(176\) | − | 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 | \(0.0350955\pi\) | ||||
−0.993928 | + | 0.110033i | \(0.964904\pi\) | |||||||
\(180\) | 2.23607 | − | 2.00000i | 0.166667 | − | 0.149071i | ||||
\(181\) | 6.18034i | 0.459381i | 0.973264 | + | 0.229691i | \(0.0737714\pi\) | ||||
−0.973264 | + | 0.229691i | \(0.926229\pi\) | |||||||
\(182\) | −1.23607 | − | 8.47214i | −0.0916235 | − | 0.627996i | ||||
\(183\) | −4.47214 | + | 1.70820i | −0.330590 | + | 0.126274i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 5.23607 | 0.384963 | ||||||||
\(186\) | 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 | ||||
\(190\) | 0.472136 | 0.0342523 | ||||||||
\(191\) | 2.76393i | 0.199991i | 0.994988 | + | 0.0999956i | \(0.0318829\pi\) | ||||
−0.994988 | + | 0.0999956i | \(0.968117\pi\) | |||||||
\(192\) | −0.618034 | − | 1.61803i | −0.0446028 | − | 0.116772i | ||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | −5.23607 | −0.375928 | ||||||||
\(195\) | −5.23607 | + | 2.00000i | −0.374963 | + | 0.143223i | ||||
\(196\) | 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 | \(0.00203464\pi\) | ||||
−0.999980 | + | 0.00639198i | \(0.997965\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | −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 | ||||
\(205\) | 6.47214 | 0.452034 | ||||||||
\(206\) | −16.6525 | −1.16023 | ||||||||
\(207\) | 8.00000 | + | 8.94427i | 0.556038 | + | 0.621670i | ||||
\(208\) | 3.23607i | 0.224381i | ||||||||
\(209\) | −2.11146 | −0.146052 | ||||||||
\(210\) | −2.23607 | − | 4.00000i | −0.154303 | − | 0.276026i | ||||
\(211\) | −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 | ||||||||
\(215\) | 12.9443 | 0.882792 | ||||||||
\(216\) | −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 | ||||
\(220\) | 4.47214i | 0.301511i | ||||||||
\(221\) | 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 | ||||
\(225\) | −2.23607 | + | 2.00000i | −0.149071 | + | 0.133333i | ||||
\(226\) | −14.9443 | −0.994078 | ||||||||
\(227\) | 5.23607 | 0.347530 | 0.173765 | − | 0.984787i | \(-0.444407\pi\) | ||||
0.173765 | + | 0.984787i | \(0.444407\pi\) | |||||||
\(228\) | −0.763932 | + | 0.291796i | −0.0505926 | + | 0.0193247i | ||||
\(229\) | − | 13.2361i | − | 0.874664i | −0.899300 | − | 0.437332i | \(-0.855923\pi\) | ||
0.899300 | − | 0.437332i | \(-0.144077\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 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 | ||||
\(235\) | 2.47214 | 0.161264 | ||||||||
\(236\) | 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 | \(-0.745349\pi\) | ||
0.696699 | − | 0.717363i | \(-0.254651\pi\) | |||||||
\(240\) | 0.618034 | + | 1.61803i | 0.0398939 | + | 0.104444i | ||||
\(241\) | − | 17.8885i | − | 1.15230i | −0.817343 | − | 0.576151i | \(-0.804554\pi\) | ||
0.817343 | − | 0.576151i | \(-0.195446\pi\) | |||||||
\(242\) | − | 9.00000i | − | 0.578542i | ||||||
\(243\) | 15.0902 | − | 3.90983i | 0.968035 | − | 0.250816i | ||||
\(244\) | − | 2.76393i | − | 0.176943i | ||||||
\(245\) | −6.70820 | + | 2.00000i | −0.428571 | + | 0.127775i | ||||
\(246\) | −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 | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −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 | ||||||
\(255\) | 0.472136 | + | 1.23607i | 0.0295663 | + | 0.0774056i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.18034 | −0.510276 | −0.255138 | − | 0.966905i | \(-0.582121\pi\) | ||||
−0.255138 | + | 0.966905i | \(0.582121\pi\) | |||||||
\(258\) | −20.9443 | + | 8.00000i | −1.30393 | + | 0.498058i | ||||
\(259\) | 2.00000 | + | 13.7082i | 0.124274 | + | 0.851786i | ||||
\(260\) | − | 3.23607i | − | 0.200692i | ||||||
\(261\) | −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 | ||||
\(265\) | − | 8.47214i | − | 0.520439i | ||||||
\(266\) | 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 | \(0.543533\pi\) | |||||||
\(270\) | 2.38197 | − | 4.61803i | 0.144962 | − | 0.281045i | ||||
\(271\) | 18.2918i | 1.11115i | 0.831467 | + | 0.555574i | \(0.187501\pi\) | ||||
−0.831467 | + | 0.555574i | \(0.812499\pi\) | |||||||
\(272\) | 0.763932 | 0.0463202 | ||||||||
\(273\) | −7.23607 | − | 12.9443i | −0.437947 | − | 0.783423i | ||||
\(274\) | −12.4721 | −0.753469 | ||||||||
\(275\) | − | 4.47214i | − | 0.269680i | ||||||
\(276\) | −6.47214 | + | 2.47214i | −0.389577 | + | 0.148805i | ||||
\(277\) | 23.1246 | 1.38942 | 0.694712 | − | 0.719288i | \(-0.255532\pi\) | ||||
0.694712 | + | 0.719288i | \(0.255532\pi\) | |||||||
\(278\) | 20.4721 | 1.22784 | ||||||||
\(279\) | 14.4721 | + | 16.1803i | 0.866424 | + | 0.968692i | ||||
\(280\) | 2.61803 | − | 0.381966i | 0.156457 | − | 0.0228268i | ||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | −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 | ||||||||
\(285\) | 0.763932 | − | 0.291796i | 0.0452514 | − | 0.0172845i | ||||
\(286\) | 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 | ||||||||
\(290\) | −5.70820 | −0.335197 | ||||||||
\(291\) | −8.47214 | + | 3.23607i | −0.496645 | + | 0.189702i | ||||
\(292\) | 6.76393i | 0.395829i | ||||||||
\(293\) | −29.4164 | −1.71852 | −0.859262 | − | 0.511535i | \(-0.829077\pi\) | ||||
−0.859262 | + | 0.511535i | \(0.829077\pi\) | |||||||
\(294\) | 9.61803 | − | 7.38197i | 0.560935 | − | 0.430525i | ||||
\(295\) | −4.47214 | −0.260378 | ||||||||
\(296\) | − | 5.23607i | − | 0.304340i | ||||||
\(297\) | −10.6525 | + | 20.6525i | −0.618119 | + | 1.19838i | ||||
\(298\) | 17.7082 | 1.02581 | ||||||||
\(299\) | 12.9443 | 0.748587 | ||||||||
\(300\) | −0.618034 | − | 1.61803i | −0.0356822 | − | 0.0934172i | ||||
\(301\) | 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 | ||||||
\(305\) | 2.76393i | 0.158262i | ||||||||
\(306\) | −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 | ||||
\(310\) | 7.23607 | 0.410981 | ||||||||
\(311\) | 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 | ||||||||
\(315\) | −6.09017 | − | 5.09017i | −0.343142 | − | 0.286799i | ||||
\(316\) | −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 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 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 | ||||
\(325\) | 3.23607i | 0.179505i | ||||||||
\(326\) | − | 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 | ||||
\(330\) | 2.76393 | + | 7.23607i | 0.152149 | + | 0.398332i | ||||
\(331\) | 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 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | −4.00000 | + | 2.23607i | −0.218218 | + | 0.121988i | ||||
\(337\) | −5.41641 | −0.295051 | −0.147525 | − | 0.989058i | \(-0.547131\pi\) | ||||
−0.147525 | + | 0.989058i | \(0.547131\pi\) | |||||||
\(338\) | 2.52786i | 0.137498i | ||||||||
\(339\) | −24.1803 | + | 9.23607i | −1.31330 | + | 0.501634i | ||||
\(340\) | −0.763932 | −0.0414300 | ||||||||
\(341\) | −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 | ||||||
\(345\) | 6.47214 | − | 2.47214i | 0.348448 | − | 0.133095i | ||||
\(346\) | 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 | \(-0.981414\pi\) | ||
0.998296 | − | 0.0583555i | \(-0.0185857\pi\) | |||||||
\(350\) | −2.61803 | + | 0.381966i | −0.139940 | + | 0.0204169i | ||||
\(351\) | 7.70820 | − | 14.9443i | 0.411433 | − | 0.797666i | ||||
\(352\) | 4.47214 | 0.238366 | ||||||||
\(353\) | −14.2918 | −0.760676 | −0.380338 | − | 0.924848i | \(-0.624192\pi\) | ||||
−0.380338 | + | 0.924848i | \(0.624192\pi\) | |||||||
\(354\) | 7.23607 | − | 2.76393i | 0.384593 | − | 0.146901i | ||||
\(355\) | − | 2.76393i | − | 0.146694i | ||||||
\(356\) | 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 | \(0.0865771\pi\) | ||||
−0.963238 | + | 0.268649i | \(0.913423\pi\) | |||||||
\(360\) | 2.00000 | + | 2.23607i | 0.105409 | + | 0.117851i | ||||
\(361\) | 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 | ||||
\(365\) | − | 6.76393i | − | 0.354040i | ||||||
\(366\) | −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 | ||||
\(370\) | 5.23607i | 0.272210i | ||||||||
\(371\) | 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 | \(-0.581819\pi\) | ||||
−0.254221 | + | 0.967146i | \(0.581819\pi\) | |||||||
\(374\) | 3.41641 | 0.176658 | ||||||||
\(375\) | 0.618034 | + | 1.61803i | 0.0319151 | + | 0.0835549i | ||||
\(376\) | − | 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 | \(0.348051\pi\) | |||||||
\(380\) | 0.472136i | 0.0242201i | ||||||||
\(381\) | −8.47214 | − | 22.1803i | −0.434041 | − | 1.13633i | ||||
\(382\) | −2.76393 | −0.141415 | ||||||||
\(383\) | 21.8885 | 1.11845 | 0.559226 | − | 0.829015i | \(-0.311098\pi\) | ||||
0.559226 | + | 0.829015i | \(0.311098\pi\) | |||||||
\(384\) | 1.61803 | − | 0.618034i | 0.0825700 | − | 0.0315389i | ||||
\(385\) | 11.7082 | − | 1.70820i | 0.596705 | − | 0.0870581i | ||||
\(386\) | − | 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 | \(0.0635213\pi\) | ||||
−0.980154 | + | 0.198236i | \(0.936479\pi\) | |||||||
\(390\) | −2.00000 | − | 5.23607i | −0.101274 | − | 0.265139i | ||||
\(391\) | − | 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 | ||||||||
\(395\) | 8.94427 | 0.450035 | ||||||||
\(396\) | −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 | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 5.52786i | 0.276048i | 0.990429 | + | 0.138024i | \(0.0440752\pi\) | ||||
−0.990429 | + | 0.138024i | \(0.955925\pi\) | |||||||
\(402\) | 19.4164 | − | 7.41641i | 0.968402 | − | 0.369897i | ||||
\(403\) | 23.4164 | 1.16645 | ||||||||
\(404\) | 3.52786 | 0.175518 | ||||||||
\(405\) | 1.00000 | − | 8.94427i | 0.0496904 | − | 0.444444i | ||||
\(406\) | −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 | \(-0.840622\pi\) | ||
0.877247 | − | 0.480040i | \(-0.159378\pi\) | |||||||
\(410\) | 6.47214i | 0.319636i | ||||||||
\(411\) | −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 | ||||
\(415\) | −16.6525 | −0.817438 | ||||||||
\(416\) | −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 | \(0.634879\pi\) | |||||||
\(420\) | 4.00000 | − | 2.23607i | 0.195180 | − | 0.109109i | ||||
\(421\) | −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 | ||||||||
\(425\) | 0.763932 | 0.0370561 | ||||||||
\(426\) | 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 | ||||
\(430\) | 12.9443i | 0.624228i | ||||||||
\(431\) | 9.59675i | 0.462259i | 0.972923 | + | 0.231130i | \(0.0742421\pi\) | ||||
−0.972923 | + | 0.231130i | \(0.925758\pi\) | |||||||
\(432\) | −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 | ||||
\(435\) | −9.23607 | + | 3.52786i | −0.442836 | + | 0.169148i | ||||
\(436\) | 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 | \(-0.906123\pi\) | ||
0.956824 | − | 0.290668i | \(-0.0938775\pi\) | |||||||
\(440\) | −4.47214 | −0.213201 | ||||||||
\(441\) | 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 | ||||
\(445\) | −14.4721 | −0.686045 | ||||||||
\(446\) | −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 | \(-0.988522\pi\) | ||
0.999350 | − | 0.0360522i | \(-0.0114783\pi\) | |||||||
\(450\) | −2.00000 | − | 2.23607i | −0.0942809 | − | 0.105409i | ||||
\(451\) | − | 28.9443i | − | 1.36293i | ||||||
\(452\) | − | 14.9443i | − | 0.702919i | ||||||
\(453\) | 1.88854 | + | 4.94427i | 0.0887315 | + | 0.232302i | ||||
\(454\) | 5.23607i | 0.245741i | ||||||||
\(455\) | −8.47214 | + | 1.23607i | −0.397180 | + | 0.0579478i | ||||
\(456\) | −0.291796 | − | 0.763932i | −0.0136646 | − | 0.0357744i | ||||
\(457\) | 9.05573 | 0.423609 | 0.211805 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211805 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(458\) | 13.2361 | 0.618481 | ||||||||
\(459\) | −3.52786 | − | 1.81966i | −0.164667 | − | 0.0849345i | ||||
\(460\) | 4.00000i | 0.186501i | ||||||||
\(461\) | 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 | \(-0.498666\pi\) | ||||
0.00419055 | + | 0.999991i | \(0.498666\pi\) | |||||||
\(464\) | 5.70820i | 0.264997i | ||||||||
\(465\) | 11.7082 | − | 4.47214i | 0.542955 | − | 0.207390i | ||||
\(466\) | −20.4721 | −0.948353 | ||||||||
\(467\) | −20.2918 | −0.938992 | −0.469496 | − | 0.882935i | \(-0.655564\pi\) | ||||
−0.469496 | + | 0.882935i | \(0.655564\pi\) | |||||||
\(468\) | 6.47214 | + | 7.23607i | 0.299175 | + | 0.334487i | ||||
\(469\) | −4.58359 | − | 31.4164i | −0.211651 | − | 1.45067i | ||||
\(470\) | 2.47214i | 0.114031i | ||||||||
\(471\) | 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 | ||||
\(475\) | − | 0.472136i | − | 0.0216631i | ||||||
\(476\) | −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 | \(0.484640\pi\) | |||||||
\(480\) | −1.61803 | + | 0.618034i | −0.0738528 | + | 0.0282093i | ||||
\(481\) | 16.9443i | 0.772592i | ||||||||
\(482\) | 17.8885 | 0.814801 | ||||||||
\(483\) | 8.94427 | + | 16.0000i | 0.406978 | + | 0.728025i | ||||
\(484\) | 9.00000 | 0.409091 | ||||||||
\(485\) | 5.23607i | 0.237758i | ||||||||
\(486\) | 3.90983 | + | 15.0902i | 0.177353 | + | 0.684504i | ||||
\(487\) | −31.5967 | −1.43179 | −0.715893 | − | 0.698210i | \(-0.753980\pi\) | ||||
−0.715893 | + | 0.698210i | \(0.753980\pi\) | |||||||
\(488\) | 2.76393 | 0.125117 | ||||||||
\(489\) | −0.944272 | − | 2.47214i | −0.0427015 | − | 0.111794i | ||||
\(490\) | −2.00000 | − | 6.70820i | −0.0903508 | − | 0.303046i | ||||
\(491\) | − | 13.4164i | − | 0.605474i | −0.953074 | − | 0.302737i | \(-0.902100\pi\) | ||
0.953074 | − | 0.302737i | \(-0.0979004\pi\) | |||||||
\(492\) | −4.00000 | − | 10.4721i | −0.180334 | − | 0.472120i | ||||
\(493\) | 4.36068i | 0.196395i | ||||||||
\(494\) | 1.52786i | 0.0687419i | ||||||||
\(495\) | 8.94427 | + | 10.0000i | 0.402015 | + | 0.449467i | ||||
\(496\) | − | 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 | \(0.631129\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 10.4721 | + | 27.4164i | 0.467861 | + | 1.22487i | ||||
\(502\) | − | 3.52786i | − | 0.157456i | ||||||
\(503\) | 16.3607 | 0.729487 | 0.364743 | − | 0.931108i | \(-0.381157\pi\) | ||||
0.364743 | + | 0.931108i | \(0.381157\pi\) | |||||||
\(504\) | −5.09017 | + | 6.09017i | −0.226734 | + | 0.271278i | ||||
\(505\) | −3.52786 | −0.156988 | ||||||||
\(506\) | − | 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 | \(0.317533\pi\) | |||||||
\(510\) | −1.23607 | + | 0.472136i | −0.0547340 | + | 0.0209065i | ||||
\(511\) | 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 | ||||||
\(515\) | 16.6525i | 0.733796i | ||||||||
\(516\) | −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 | ||||
\(520\) | 3.23607 | 0.141911 | ||||||||
\(521\) | −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 | ||||||||
\(525\) | −4.00000 | + | 2.23607i | −0.174574 | + | 0.0975900i | ||||
\(526\) | −4.94427 | −0.215580 | ||||||||
\(527\) | − | 5.52786i | − | 0.240798i | ||||||
\(528\) | 7.23607 | − | 2.76393i | 0.314909 | − | 0.120285i | ||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 8.47214 | 0.368006 | ||||||||
\(531\) | 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 | ||||
\(535\) | − | 15.4164i | − | 0.666509i | ||||||
\(536\) | 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 | ||||
\(540\) | 4.61803 | + | 2.38197i | 0.198729 | + | 0.102503i | ||||
\(541\) | 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 | ||||||||
\(545\) | −4.47214 | −0.191565 | ||||||||
\(546\) | 12.9443 | − | 7.23607i | 0.553964 | − | 0.309675i | ||||
\(547\) | −8.58359 | −0.367008 | −0.183504 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183504 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(548\) | − | 12.4721i | − | 0.532783i | ||||||
\(549\) | −5.52786 | − | 6.18034i | −0.235923 | − | 0.263770i | ||||
\(550\) | 4.47214 | 0.190693 | ||||||||
\(551\) | 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 | ||||||||
\(555\) | 3.23607 | + | 8.47214i | 0.137363 | + | 0.359622i | ||||
\(556\) | 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 | ||||||||
\(560\) | 0.381966 | + | 2.61803i | 0.0161410 | + | 0.110632i | ||||
\(561\) | 5.52786 | − | 2.11146i | 0.233387 | − | 0.0891457i | ||||
\(562\) | −20.0000 | −0.843649 | ||||||||
\(563\) | 17.8197 | 0.751009 | 0.375505 | − | 0.926821i | \(-0.377469\pi\) | ||||
0.375505 | + | 0.926821i | \(0.377469\pi\) | |||||||
\(564\) | −1.52786 | − | 4.00000i | −0.0643347 | − | 0.168430i | ||||
\(565\) | 14.9443i | 0.628710i | ||||||||
\(566\) | −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 | \(0.126556\pi\) | ||||
−0.921997 | + | 0.387196i | \(0.873444\pi\) | |||||||
\(570\) | 0.291796 | + | 0.763932i | 0.0122220 | + | 0.0319976i | ||||
\(571\) | −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 | ||||
\(575\) | − | 4.00000i | − | 0.166812i | ||||||
\(576\) | 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 | ||||
\(580\) | − | 5.70820i | − | 0.237020i | ||||||
\(581\) | −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 | ||||||||
\(585\) | −6.47214 | − | 7.23607i | −0.267590 | − | 0.299175i | ||||
\(586\) | − | 29.4164i | − | 1.21518i | ||||||
\(587\) | −23.7082 | −0.978542 | −0.489271 | − | 0.872132i | \(-0.662737\pi\) | ||||
−0.489271 | + | 0.872132i | \(0.662737\pi\) | |||||||
\(588\) | 7.38197 | + | 9.61803i | 0.304427 | + | 0.396641i | ||||
\(589\) | −3.41641 | −0.140771 | ||||||||
\(590\) | − | 4.47214i | − | 0.184115i | ||||||
\(591\) | −20.1803 | + | 7.70820i | −0.830108 | + | 0.317073i | ||||
\(592\) | 5.23607 | 0.215201 | ||||||||
\(593\) | 47.0132 | 1.93060 | 0.965299 | − | 0.261145i | \(-0.0841002\pi\) | ||||
0.965299 | + | 0.261145i | \(0.0841002\pi\) | |||||||
\(594\) | −20.6525 | − | 10.6525i | −0.847381 | − | 0.437076i | ||||
\(595\) | 0.291796 | + | 2.00000i | 0.0119625 | + | 0.0819920i | ||||
\(596\) | 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 | \(0.318876\pi\) | ||||
−0.538806 | + | 0.842430i | \(0.681124\pi\) | |||||||
\(600\) | 1.61803 | − | 0.618034i | 0.0660560 | − | 0.0252311i | ||||
\(601\) | 14.4721i | 0.590331i | 0.955446 | + | 0.295165i | \(0.0953747\pi\) | ||||
−0.955446 | + | 0.295165i | \(0.904625\pi\) | |||||||
\(602\) | −33.8885 | + | 4.94427i | −1.38119 | + | 0.201513i | ||||
\(603\) | 26.8328 | − | 24.0000i | 1.09272 | − | 0.977356i | ||||
\(604\) | −3.05573 | −0.124336 | ||||||||
\(605\) | −9.00000 | −0.365902 | ||||||||
\(606\) | 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 | ||||
\(610\) | −2.76393 | −0.111908 | ||||||||
\(611\) | 8.00000i | 0.323645i | ||||||||
\(612\) | 1.70820 | − | 1.52786i | 0.0690501 | − | 0.0617602i | ||||
\(613\) | −20.0689 | −0.810575 | −0.405287 | − | 0.914189i | \(-0.632829\pi\) | ||||
−0.405287 | + | 0.914189i | \(0.632829\pi\) | |||||||
\(614\) | −4.18034 | −0.168705 | ||||||||
\(615\) | 4.00000 | + | 10.4721i | 0.161296 | + | 0.422277i | ||||
\(616\) | −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 | \(0.0907834\pi\) | ||||
−0.959604 | + | 0.281354i | \(0.909217\pi\) | |||||||
\(620\) | 7.23607i | 0.290607i | ||||||||
\(621\) | −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 | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.70820 | −0.308082 | ||||||||
\(627\) | −1.30495 | − | 3.41641i | −0.0521148 | − | 0.136438i | ||||
\(628\) | 4.76393i | 0.190102i | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 5.09017 | − | 6.09017i | 0.202797 | − | 0.242638i | ||||
\(631\) | 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 | ||||||||
\(635\) | −13.7082 | −0.543993 | ||||||||
\(636\) | −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 | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 3.41641i | − | 0.134940i | −0.997721 | − | 0.0674700i | \(-0.978507\pi\) | ||
0.997721 | − | 0.0674700i | \(-0.0214927\pi\) | |||||||
\(642\) | 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 | ||||
\(645\) | 8.00000 | + | 20.9443i | 0.315000 | + | 0.824680i | ||||
\(646\) | 0.360680 | 0.0141908 | ||||||||
\(647\) | −18.8328 | −0.740394 | −0.370197 | − | 0.928953i | \(-0.620710\pi\) | ||||
−0.370197 | + | 0.928953i | \(0.620710\pi\) | |||||||
\(648\) | −8.94427 | − | 1.00000i | −0.351364 | − | 0.0392837i | ||||
\(649\) | 20.0000i | 0.785069i | ||||||||
\(650\) | −3.23607 | −0.126929 | ||||||||
\(651\) | 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 | ||||
\(655\) | −21.4164 | −0.836808 | ||||||||
\(656\) | 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 | \(-0.710969\pi\) | ||
0.615310 | − | 0.788285i | \(-0.289031\pi\) | |||||||
\(660\) | −7.23607 | + | 2.76393i | −0.281664 | + | 0.107586i | ||||
\(661\) | 31.7082i | 1.23331i | 0.787235 | + | 0.616653i | \(0.211512\pi\) | ||||
−0.787235 | + | 0.616653i | \(0.788488\pi\) | |||||||
\(662\) | 20.9443i | 0.814022i | ||||||||
\(663\) | −4.00000 | + | 1.52786i | −0.155347 | + | 0.0593373i | ||||
\(664\) | 16.6525i | 0.646241i | ||||||||
\(665\) | 1.23607 | − | 0.180340i | 0.0479327 | − | 0.00699328i | ||||
\(666\) | −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 | ||||
\(670\) | − | 12.0000i | − | 0.463600i | ||||||
\(671\) | 12.3607 | 0.477179 | ||||||||
\(672\) | −2.23607 | − | 4.00000i | −0.0862582 | − | 0.154303i | ||||
\(673\) | 28.4721 | 1.09752 | 0.548760 | − | 0.835980i | \(-0.315100\pi\) | ||||
0.548760 | + | 0.835980i | \(0.315100\pi\) | |||||||
\(674\) | − | 5.41641i | − | 0.208632i | ||||||
\(675\) | −4.61803 | − | 2.38197i | −0.177748 | − | 0.0916819i | ||||
\(676\) | −2.52786 | −0.0972255 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | −9.23607 | − | 24.1803i | −0.354709 | − | 0.928640i | ||||
\(679\) | −13.7082 | + | 2.00000i | −0.526073 | + | 0.0767530i | ||||
\(680\) | − | 0.763932i | − | 0.0292955i | ||||||
\(681\) | 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 | ||||
\(685\) | 12.4721i | 0.476536i | ||||||||
\(686\) | 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 | ||||||||
\(690\) | 2.47214 | + | 6.47214i | 0.0941126 | + | 0.246390i | ||||
\(691\) | − | 38.9443i | − | 1.48151i | −0.671775 | − | 0.740755i | \(-0.734468\pi\) | ||
0.671775 | − | 0.740755i | \(-0.265532\pi\) | |||||||
\(692\) | −17.4164 | −0.662072 | ||||||||
\(693\) | −22.7639 | + | 27.2361i | −0.864730 | + | 1.03461i | ||||
\(694\) | 6.47214 | 0.245679 | ||||||||
\(695\) | − | 20.4721i | − | 0.776552i | ||||||
\(696\) | 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 | ||||
\(700\) | −0.381966 | − | 2.61803i | −0.0144370 | − | 0.0989524i | ||||
\(701\) | 14.0689i | 0.531374i | 0.964059 | + | 0.265687i | \(0.0855988\pi\) | ||||
−0.964059 | + | 0.265687i | \(0.914401\pi\) | |||||||
\(702\) | 14.9443 | + | 7.70820i | 0.564035 | + | 0.290927i | ||||
\(703\) | − | 2.47214i | − | 0.0932384i | ||||||
\(704\) | 4.47214i | 0.168550i | ||||||||
\(705\) | 1.52786 | + | 4.00000i | 0.0575427 | + | 0.150649i | ||||
\(706\) | − | 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 | \(0.651984\pi\) | |||||||
\(710\) | 2.76393 | 0.103729 | ||||||||
\(711\) | −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 | ||||
\(715\) | 14.4721 | 0.541227 | ||||||||
\(716\) | − | 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 | \(0.657919\pi\) | |||||||
\(720\) | −2.23607 | + | 2.00000i | −0.0833333 | + | 0.0745356i | ||||
\(721\) | −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 | ||||||
\(725\) | 5.70820i | 0.211997i | ||||||||
\(726\) | 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 | ||||
\(730\) | 6.76393 | 0.250344 | ||||||||
\(731\) | 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 | ||||||||
\(735\) | −7.38197 | − | 9.61803i | −0.272288 | − | 0.354767i | ||||
\(736\) | 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 | \(0.552604\pi\) | |||||||
\(740\) | −5.23607 | −0.192482 | ||||||||
\(741\) | 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 | ||||
\(745\) | − | 17.7082i | − | 0.648778i | ||||||
\(746\) | − | 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 | ||||
\(750\) | −1.61803 | + | 0.618034i | −0.0590822 | + | 0.0225674i | ||||
\(751\) | 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 | ||||||
\(755\) | 3.05573 | 0.111209 | ||||||||
\(756\) | −4.47214 | + | 13.0000i | −0.162650 | + | 0.472805i | ||||
\(757\) | 28.6525 | 1.04139 | 0.520696 | − | 0.853742i | \(-0.325673\pi\) | ||||
0.520696 | + | 0.853742i | \(0.325673\pi\) | |||||||
\(758\) | 17.8885i | 0.649741i | ||||||||
\(759\) | −11.0557 | − | 28.9443i | −0.401298 | − | 1.05061i | ||||
\(760\) | −0.472136 | −0.0171262 | ||||||||
\(761\) | 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 | ||||||
\(765\) | −1.70820 | + | 1.52786i | −0.0617602 | + | 0.0552400i | ||||
\(766\) | 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 | \(-0.775147\pi\) | ||
0.760706 | − | 0.649097i | \(-0.224853\pi\) | |||||||
\(770\) | 1.70820 | + | 11.7082i | 0.0615594 | + | 0.421934i | ||||
\(771\) | −5.05573 | − | 13.2361i | −0.182078 | − | 0.476685i | ||||
\(772\) | 6.00000 | 0.215945 | ||||||||
\(773\) | 37.4164 | 1.34577 | 0.672887 | − | 0.739745i | \(-0.265054\pi\) | ||||
0.672887 | + | 0.739745i | \(0.265054\pi\) | |||||||
\(774\) | −25.8885 | − | 28.9443i | −0.930544 | − | 1.04038i | ||||
\(775\) | − | 7.23607i | − | 0.259927i | ||||||
\(776\) | 5.23607 | 0.187964 | ||||||||
\(777\) | −20.9443 | + | 11.7082i | −0.751372 | + | 0.420029i | ||||
\(778\) | −7.81966 | −0.280348 | ||||||||
\(779\) | − | 3.05573i | − | 0.109483i | ||||||
\(780\) | 5.23607 | − | 2.00000i | 0.187481 | − | 0.0716115i | ||||
\(781\) | −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 | ||||
\(785\) | − | 4.76393i | − | 0.170032i | ||||||
\(786\) | 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 | ||||
\(790\) | 8.94427i | 0.318223i | ||||||||
\(791\) | −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 | ||||||||
\(795\) | 13.7082 | − | 5.23607i | 0.486180 | − | 0.185704i | ||||
\(796\) | − | 0.180340i | − | 0.00639198i | ||||||
\(797\) | −5.41641 | −0.191859 | −0.0959295 | − | 0.995388i | \(-0.530582\pi\) | ||||
−0.0959295 | + | 0.995388i | \(0.530582\pi\) | |||||||
\(798\) | −1.88854 | + | 1.05573i | −0.0668537 | + | 0.0373724i | ||||
\(799\) | 1.88854 | 0.0668119 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 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 | ||||
\(805\) | 10.4721 | − | 1.52786i | 0.369094 | − | 0.0538501i | ||||
\(806\) | 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 | \(-0.953047\pi\) | ||
0.989141 | − | 0.146973i | \(-0.0469530\pi\) | |||||||
\(810\) | 8.94427 | + | 1.00000i | 0.314270 | + | 0.0351364i | ||||
\(811\) | − | 16.8328i | − | 0.591080i | −0.955330 | − | 0.295540i | \(-0.904500\pi\) | ||
0.955330 | − | 0.295540i | \(-0.0954996\pi\) | |||||||
\(812\) | 14.9443 | − | 2.18034i | 0.524441 | − | 0.0765149i | ||||
\(813\) | −29.5967 | + | 11.3050i | −1.03800 | + | 0.396482i | ||||
\(814\) | 23.4164 | 0.820745 | ||||||||
\(815\) | −1.52786 | −0.0535187 | ||||||||
\(816\) | 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 | ||||
\(820\) | −6.47214 | −0.226017 | ||||||||
\(821\) | − | 18.2918i | − | 0.638388i | −0.947689 | − | 0.319194i | \(-0.896588\pi\) | ||
0.947689 | − | 0.319194i | \(-0.103412\pi\) | |||||||
\(822\) | −7.70820 | − | 20.1803i | −0.268854 | − | 0.703870i | ||||
\(823\) | 0.180340 | 0.00628625 | 0.00314313 | − | 0.999995i | \(-0.499000\pi\) | ||||
0.00314313 | + | 0.999995i | \(0.499000\pi\) | |||||||
\(824\) | 16.6525 | 0.580116 | ||||||||
\(825\) | 7.23607 | − | 2.76393i | 0.251928 | − | 0.0962278i | ||||
\(826\) | 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 | \(0.175599\pi\) | ||||
−0.851655 | + | 0.524103i | \(0.824401\pi\) | |||||||
\(830\) | − | 16.6525i | − | 0.578016i | ||||||
\(831\) | 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 | ||||
\(835\) | 16.9443 | 0.586381 | ||||||||
\(836\) | 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 | \(0.419630\pi\) | |||||||
\(840\) | 2.23607 | + | 4.00000i | 0.0771517 | + | 0.138013i | ||||
\(841\) | −3.58359 | −0.123572 | ||||||||
\(842\) | − | 12.4721i | − | 0.429818i | ||||||
\(843\) | −32.3607 | + | 12.3607i | −1.11456 | + | 0.425724i | ||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 2.52786 | 0.0869612 | ||||||||
\(846\) | −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 | ||||
\(850\) | 0.763932i | 0.0262027i | ||||||||
\(851\) | − | 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 | ||||
\(855\) | 0.944272 | + | 1.05573i | 0.0322934 | + | 0.0361051i | ||||
\(856\) | −15.4164 | −0.526922 | ||||||||
\(857\) | −42.6525 | −1.45698 | −0.728490 | − | 0.685056i | \(-0.759778\pi\) | ||||
−0.728490 | + | 0.685056i | \(0.759778\pi\) | |||||||
\(858\) | −23.4164 | + | 8.94427i | −0.799423 | + | 0.305352i | ||||
\(859\) | − | 34.9443i | − | 1.19228i | −0.802879 | − | 0.596142i | \(-0.796700\pi\) | ||
0.802879 | − | 0.596142i | \(-0.203300\pi\) | |||||||
\(860\) | −12.9443 | −0.441396 | ||||||||
\(861\) | −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 | ||||
\(865\) | 17.4164 | 0.592176 | ||||||||
\(866\) | 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 | ||||||
\(870\) | −3.52786 | − | 9.23607i | −0.119606 | − | 0.313132i | ||||
\(871\) | − | 38.8328i | − | 1.31580i | ||||||
\(872\) | 4.47214i | 0.151446i | ||||||||
\(873\) | −10.4721 | − | 11.7082i | −0.354428 | − | 0.396263i | ||||
\(874\) | − | 1.88854i | − | 0.0638809i | ||||||
\(875\) | 0.381966 | + | 2.61803i | 0.0129128 | + | 0.0885057i | ||||
\(876\) | −10.9443 | + | 4.18034i | −0.369773 | + | 0.141241i | ||||
\(877\) | 7.34752 | 0.248108 | 0.124054 | − | 0.992275i | \(-0.460410\pi\) | ||||
0.124054 | + | 0.992275i | \(0.460410\pi\) | |||||||
\(878\) | 12.1803 | 0.411067 | ||||||||
\(879\) | −18.1803 | − | 47.5967i | −0.613208 | − | 1.60540i | ||||
\(880\) | − | 4.47214i | − | 0.150756i | ||||||
\(881\) | −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 | \(-0.379939\pi\) | ||||
0.368304 | + | 0.929705i | \(0.379939\pi\) | |||||||
\(884\) | − | 2.47214i | − | 0.0831469i | ||||||
\(885\) | −2.76393 | − | 7.23607i | −0.0929086 | − | 0.243238i | ||||
\(886\) | 9.52786 | 0.320095 | ||||||||
\(887\) | −26.4721 | −0.888847 | −0.444424 | − | 0.895817i | \(-0.646592\pi\) | ||||
−0.444424 | + | 0.895817i | \(0.646592\pi\) | |||||||
\(888\) | 8.47214 | − | 3.23607i | 0.284306 | − | 0.108595i | ||||
\(889\) | −5.23607 | − | 35.8885i | −0.175612 | − | 1.20366i | ||||
\(890\) | − | 14.4721i | − | 0.485107i | ||||||
\(891\) | −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 | ||||
\(895\) | 2.94427i | 0.0984162i | ||||||||
\(896\) | 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 | ||||||||
\(900\) | 2.23607 | − | 2.00000i | 0.0745356 | − | 0.0666667i | ||||
\(901\) | − | 6.47214i | − | 0.215618i | ||||||
\(902\) | 28.9443 | 0.963739 | ||||||||
\(903\) | −51.7771 | + | 28.9443i | −1.72303 | + | 0.963205i | ||||
\(904\) | 14.9443 | 0.497039 | ||||||||
\(905\) | 6.18034i | 0.205441i | ||||||||
\(906\) | −4.94427 | + | 1.88854i | −0.164262 | + | 0.0627427i | ||||
\(907\) | −26.4721 | −0.878993 | −0.439496 | − | 0.898244i | \(-0.644843\pi\) | ||||
−0.439496 | + | 0.898244i | \(0.644843\pi\) | |||||||
\(908\) | −5.23607 | −0.173765 | ||||||||
\(909\) | 7.88854 | − | 7.05573i | 0.261646 | − | 0.234024i | ||||
\(910\) | −1.23607 | − | 8.47214i | −0.0409753 | − | 0.280849i | ||||
\(911\) | 19.3475i | 0.641012i | 0.947246 | + | 0.320506i | \(0.103853\pi\) | ||||
−0.947246 | + | 0.320506i | \(0.896147\pi\) | |||||||
\(912\) | 0.763932 | − | 0.291796i | 0.0252963 | − | 0.00966233i | ||||
\(913\) | 74.4721i | 2.46467i | ||||||||
\(914\) | 9.05573i | 0.299537i | ||||||||
\(915\) | −4.47214 | + | 1.70820i | −0.147844 | + | 0.0564715i | ||||
\(916\) | 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 | \(0.235954\pi\) | |||||||
\(920\) | −4.00000 | −0.131876 | ||||||||
\(921\) | −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 | ||||
\(925\) | 5.23607 | 0.172161 | ||||||||
\(926\) | 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 | \(0.488972\pi\) | |||||||
\(930\) | 4.47214 | + | 11.7082i | 0.146647 | + | 0.383927i | ||||
\(931\) | 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 | ||||||
\(935\) | − | 3.41641i | − | 0.111728i | ||||||
\(936\) | −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 | ||||
\(940\) | −2.47214 | −0.0806322 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | 4.47214 | − | 13.0000i | 0.145479 | − | 0.422890i | ||||
\(946\) | 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 | ||||||||
\(950\) | 0.472136 | 0.0153181 | ||||||||
\(951\) | −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 | ||||
\(955\) | 2.76393i | 0.0894387i | ||||||||
\(956\) | 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 | ||||
\(960\) | −0.618034 | − | 1.61803i | −0.0199470 | − | 0.0522218i | ||||
\(961\) | −21.3607 | −0.689054 | ||||||||
\(962\) | −16.9443 | −0.546305 | ||||||||
\(963\) | 30.8328 | + | 34.4721i | 0.993574 | + | 1.11085i | ||||
\(964\) | 17.8885i | 0.576151i | ||||||||
\(965\) | −6.00000 | −0.193147 | ||||||||
\(966\) | −16.0000 | + | 8.94427i | −0.514792 | + | 0.287777i | ||||
\(967\) | 45.4853 | 1.46271 | 0.731354 | − | 0.681998i | \(-0.238889\pi\) | ||||
0.731354 | + | 0.681998i | \(0.238889\pi\) | |||||||
\(968\) | 9.00000i | 0.289271i | ||||||||
\(969\) | 0.583592 | − | 0.222912i | 0.0187477 | − | 0.00716098i | ||||
\(970\) | −5.23607 | −0.168120 | ||||||||
\(971\) | −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 | ||||||
\(975\) | −5.23607 | + | 2.00000i | −0.167688 | + | 0.0640513i | ||||
\(976\) | 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 | ||||||||
\(980\) | 6.70820 | − | 2.00000i | 0.214286 | − | 0.0638877i | ||||
\(981\) | 10.0000 | − | 8.94427i | 0.319275 | − | 0.285569i | ||||
\(982\) | 13.4164 | 0.428135 | ||||||||
\(983\) | −39.4164 | −1.25719 | −0.628594 | − | 0.777734i | \(-0.716369\pi\) | ||||
−0.628594 | + | 0.777734i | \(0.716369\pi\) | |||||||
\(984\) | 10.4721 | − | 4.00000i | 0.333840 | − | 0.127515i | ||||
\(985\) | 12.4721i | 0.397395i | ||||||||
\(986\) | −4.36068 | −0.138872 | ||||||||
\(987\) | −9.88854 | + | 5.52786i | −0.314756 | + | 0.175954i | ||||
\(988\) | −1.52786 | −0.0486078 | ||||||||
\(989\) | − | 51.7771i | − | 1.64642i | ||||||
\(990\) | −10.0000 | + | 8.94427i | −0.317821 | + | 0.284268i | ||||
\(991\) | 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 | ||||
\(995\) | 0.180340i | 0.00571716i | ||||||||
\(996\) | 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 | 210.2.b.a.41.4 | yes | 4 | |
3.2 | odd | 2 | 210.2.b.b.41.1 | yes | 4 | ||
4.3 | odd | 2 | 1680.2.f.i.881.1 | 4 | |||
5.2 | odd | 4 | 1050.2.d.c.1049.3 | 4 | |||
5.3 | odd | 4 | 1050.2.d.d.1049.2 | 4 | |||
5.4 | even | 2 | 1050.2.b.c.251.1 | 4 | |||
7.6 | odd | 2 | 210.2.b.b.41.3 | yes | 4 | ||
12.11 | even | 2 | 1680.2.f.e.881.3 | 4 | |||
15.2 | even | 4 | 1050.2.d.f.1049.4 | 4 | |||
15.8 | even | 4 | 1050.2.d.a.1049.1 | 4 | |||
15.14 | odd | 2 | 1050.2.b.a.251.4 | 4 | |||
21.20 | even | 2 | inner | 210.2.b.a.41.2 | ✓ | 4 | |
28.27 | even | 2 | 1680.2.f.e.881.4 | 4 | |||
35.13 | even | 4 | 1050.2.d.f.1049.3 | 4 | |||
35.27 | even | 4 | 1050.2.d.a.1049.2 | 4 | |||
35.34 | odd | 2 | 1050.2.b.a.251.2 | 4 | |||
84.83 | odd | 2 | 1680.2.f.i.881.2 | 4 | |||
105.62 | odd | 4 | 1050.2.d.d.1049.1 | 4 | |||
105.83 | odd | 4 | 1050.2.d.c.1049.4 | 4 | |||
105.104 | even | 2 | 1050.2.b.c.251.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.b.a.41.2 | ✓ | 4 | 21.20 | even | 2 | inner | |
210.2.b.a.41.4 | yes | 4 | 1.1 | even | 1 | trivial | |
210.2.b.b.41.1 | yes | 4 | 3.2 | odd | 2 | ||
210.2.b.b.41.3 | yes | 4 | 7.6 | odd | 2 | ||
1050.2.b.a.251.2 | 4 | 35.34 | odd | 2 | |||
1050.2.b.a.251.4 | 4 | 15.14 | odd | 2 | |||
1050.2.b.c.251.1 | 4 | 5.4 | even | 2 | |||
1050.2.b.c.251.3 | 4 | 105.104 | even | 2 | |||
1050.2.d.a.1049.1 | 4 | 15.8 | even | 4 | |||
1050.2.d.a.1049.2 | 4 | 35.27 | even | 4 | |||
1050.2.d.c.1049.3 | 4 | 5.2 | odd | 4 | |||
1050.2.d.c.1049.4 | 4 | 105.83 | odd | 4 | |||
1050.2.d.d.1049.1 | 4 | 105.62 | odd | 4 | |||
1050.2.d.d.1049.2 | 4 | 5.3 | odd | 4 | |||
1050.2.d.f.1049.3 | 4 | 35.13 | even | 4 | |||
1050.2.d.f.1049.4 | 4 | 15.2 | even | 4 | |||
1680.2.f.e.881.3 | 4 | 12.11 | even | 2 | |||
1680.2.f.e.881.4 | 4 | 28.27 | even | 2 | |||
1680.2.f.i.881.1 | 4 | 4.3 | odd | 2 | |||
1680.2.f.i.881.2 | 4 | 84.83 | odd | 2 |