Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(341,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.f (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 341.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.341 |
Dual form | 570.2.f.a.341.3 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | − | 1.41421i | −0.577350 | − | 0.816497i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000 | + | 1.41421i | 0.408248 | + | 0.577350i | ||||
\(7\) | 3.41421 | 1.29045 | 0.645226 | − | 0.763992i | \(-0.276763\pi\) | ||||
0.645226 | + | 0.763992i | \(0.276763\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 2.58579i | − | 0.779644i | −0.920890 | − | 0.389822i | \(-0.872537\pi\) | ||
0.920890 | − | 0.389822i | \(-0.127463\pi\) | |||||||
\(12\) | −1.00000 | − | 1.41421i | −0.288675 | − | 0.408248i | ||||
\(13\) | 6.24264i | 1.73140i | 0.500566 | + | 0.865699i | \(0.333125\pi\) | ||||
−0.500566 | + | 0.865699i | \(0.666875\pi\) | |||||||
\(14\) | −3.41421 | −0.912487 | ||||||||
\(15\) | 1.41421 | − | 1.00000i | 0.365148 | − | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 1.00000 | − | 2.82843i | 0.235702 | − | 0.666667i | ||||
\(19\) | −4.24264 | − | 1.00000i | −0.973329 | − | 0.229416i | ||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | −3.41421 | − | 4.82843i | −0.745042 | − | 1.05365i | ||||
\(22\) | 2.58579i | 0.551292i | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 1.00000 | + | 1.41421i | 0.204124 | + | 0.288675i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 6.24264i | − | 1.22428i | ||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 3.41421 | 0.645226 | ||||||||
\(29\) | 9.07107 | 1.68446 | 0.842228 | − | 0.539122i | \(-0.181244\pi\) | ||||
0.842228 | + | 0.539122i | \(0.181244\pi\) | |||||||
\(30\) | −1.41421 | + | 1.00000i | −0.258199 | + | 0.182574i | ||||
\(31\) | − | 1.17157i | − | 0.210421i | −0.994450 | − | 0.105210i | \(-0.966448\pi\) | ||
0.994450 | − | 0.105210i | \(-0.0335516\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.65685 | + | 2.58579i | −0.636577 | + | 0.450128i | ||||
\(34\) | − | 2.82843i | − | 0.485071i | ||||||
\(35\) | 3.41421i | 0.577107i | ||||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | 6.24264i | 1.02628i | 0.858304 | + | 0.513142i | \(0.171519\pi\) | ||||
−0.858304 | + | 0.513142i | \(0.828481\pi\) | |||||||
\(38\) | 4.24264 | + | 1.00000i | 0.688247 | + | 0.162221i | ||||
\(39\) | 8.82843 | − | 6.24264i | 1.41368 | − | 0.999623i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | −3.07107 | −0.479620 | −0.239810 | − | 0.970820i | \(-0.577085\pi\) | ||||
−0.239810 | + | 0.970820i | \(0.577085\pi\) | |||||||
\(42\) | 3.41421 | + | 4.82843i | 0.526825 | + | 0.745042i | ||||
\(43\) | 9.41421 | 1.43565 | 0.717827 | − | 0.696221i | \(-0.245137\pi\) | ||||
0.717827 | + | 0.696221i | \(0.245137\pi\) | |||||||
\(44\) | − | 2.58579i | − | 0.389822i | ||||||
\(45\) | −2.82843 | − | 1.00000i | −0.421637 | − | 0.149071i | ||||
\(46\) | − | 6.00000i | − | 0.884652i | ||||||
\(47\) | − | 8.82843i | − | 1.28776i | −0.765127 | − | 0.643879i | \(-0.777324\pi\) | ||
0.765127 | − | 0.643879i | \(-0.222676\pi\) | |||||||
\(48\) | −1.00000 | − | 1.41421i | −0.144338 | − | 0.204124i | ||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.00000 | − | 2.82843i | 0.560112 | − | 0.396059i | ||||
\(52\) | 6.24264i | 0.865699i | ||||||||
\(53\) | 8.82843 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292638\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292638\pi\) | |||||||
\(54\) | −5.00000 | + | 1.41421i | −0.680414 | + | 0.192450i | ||||
\(55\) | 2.58579 | 0.348667 | ||||||||
\(56\) | −3.41421 | −0.456243 | ||||||||
\(57\) | 2.82843 | + | 7.00000i | 0.374634 | + | 0.927173i | ||||
\(58\) | −9.07107 | −1.19109 | ||||||||
\(59\) | 7.17157 | 0.933659 | 0.466830 | − | 0.884347i | \(-0.345396\pi\) | ||||
0.466830 | + | 0.884347i | \(0.345396\pi\) | |||||||
\(60\) | 1.41421 | − | 1.00000i | 0.182574 | − | 0.129099i | ||||
\(61\) | 12.4853 | 1.59858 | 0.799288 | − | 0.600948i | \(-0.205210\pi\) | ||||
0.799288 | + | 0.600948i | \(0.205210\pi\) | |||||||
\(62\) | 1.17157i | 0.148790i | ||||||||
\(63\) | −3.41421 | + | 9.65685i | −0.430150 | + | 1.21665i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | 3.65685 | − | 2.58579i | 0.450128 | − | 0.318288i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 2.82843i | 0.342997i | ||||||||
\(69\) | 8.48528 | − | 6.00000i | 1.02151 | − | 0.722315i | ||||
\(70\) | − | 3.41421i | − | 0.408077i | ||||||
\(71\) | −2.82843 | −0.335673 | −0.167836 | − | 0.985815i | \(-0.553678\pi\) | ||||
−0.167836 | + | 0.985815i | \(0.553678\pi\) | |||||||
\(72\) | 1.00000 | − | 2.82843i | 0.117851 | − | 0.333333i | ||||
\(73\) | −14.4853 | −1.69537 | −0.847687 | − | 0.530497i | \(-0.822005\pi\) | ||||
−0.847687 | + | 0.530497i | \(0.822005\pi\) | |||||||
\(74\) | − | 6.24264i | − | 0.725692i | ||||||
\(75\) | 1.00000 | + | 1.41421i | 0.115470 | + | 0.163299i | ||||
\(76\) | −4.24264 | − | 1.00000i | −0.486664 | − | 0.114708i | ||||
\(77\) | − | 8.82843i | − | 1.00609i | ||||||
\(78\) | −8.82843 | + | 6.24264i | −0.999623 | + | 0.706840i | ||||
\(79\) | 9.31371i | 1.04787i | 0.851757 | + | 0.523937i | \(0.175537\pi\) | ||||
−0.851757 | + | 0.523937i | \(0.824463\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 3.07107 | 0.339143 | ||||||||
\(83\) | 7.17157i | 0.787182i | 0.919286 | + | 0.393591i | \(0.128767\pi\) | ||||
−0.919286 | + | 0.393591i | \(0.871233\pi\) | |||||||
\(84\) | −3.41421 | − | 4.82843i | −0.372521 | − | 0.526825i | ||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | −9.41421 | −1.01516 | ||||||||
\(87\) | −9.07107 | − | 12.8284i | −0.972521 | − | 1.37535i | ||||
\(88\) | 2.58579i | 0.275646i | ||||||||
\(89\) | −13.4142 | −1.42190 | −0.710952 | − | 0.703241i | \(-0.751736\pi\) | ||||
−0.710952 | + | 0.703241i | \(0.751736\pi\) | |||||||
\(90\) | 2.82843 | + | 1.00000i | 0.298142 | + | 0.105409i | ||||
\(91\) | 21.3137i | 2.23428i | ||||||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | −1.65685 | + | 1.17157i | −0.171808 | + | 0.121486i | ||||
\(94\) | 8.82843i | 0.910583i | ||||||||
\(95\) | 1.00000 | − | 4.24264i | 0.102598 | − | 0.435286i | ||||
\(96\) | 1.00000 | + | 1.41421i | 0.102062 | + | 0.144338i | ||||
\(97\) | − | 9.41421i | − | 0.955869i | −0.878396 | − | 0.477934i | \(-0.841386\pi\) | ||
0.878396 | − | 0.477934i | \(-0.158614\pi\) | |||||||
\(98\) | −4.65685 | −0.470413 | ||||||||
\(99\) | 7.31371 | + | 2.58579i | 0.735055 | + | 0.259881i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 3.65685i | 0.363871i | 0.983311 | + | 0.181935i | \(0.0582361\pi\) | ||||
−0.983311 | + | 0.181935i | \(0.941764\pi\) | |||||||
\(102\) | −4.00000 | + | 2.82843i | −0.396059 | + | 0.280056i | ||||
\(103\) | 15.6569i | 1.54272i | 0.636402 | + | 0.771358i | \(0.280422\pi\) | ||||
−0.636402 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(104\) | − | 6.24264i | − | 0.612141i | ||||||
\(105\) | 4.82843 | − | 3.41421i | 0.471206 | − | 0.333193i | ||||
\(106\) | −8.82843 | −0.857493 | ||||||||
\(107\) | 7.65685 | 0.740216 | 0.370108 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370108 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(108\) | 5.00000 | − | 1.41421i | 0.481125 | − | 0.136083i | ||||
\(109\) | − | 13.6569i | − | 1.30809i | −0.756456 | − | 0.654045i | \(-0.773071\pi\) | ||
0.756456 | − | 0.654045i | \(-0.226929\pi\) | |||||||
\(110\) | −2.58579 | −0.246545 | ||||||||
\(111\) | 8.82843 | − | 6.24264i | 0.837957 | − | 0.592525i | ||||
\(112\) | 3.41421 | 0.322613 | ||||||||
\(113\) | −7.17157 | −0.674645 | −0.337322 | − | 0.941389i | \(-0.609521\pi\) | ||||
−0.337322 | + | 0.941389i | \(0.609521\pi\) | |||||||
\(114\) | −2.82843 | − | 7.00000i | −0.264906 | − | 0.655610i | ||||
\(115\) | −6.00000 | −0.559503 | ||||||||
\(116\) | 9.07107 | 0.842228 | ||||||||
\(117\) | −17.6569 | − | 6.24264i | −1.63238 | − | 0.577132i | ||||
\(118\) | −7.17157 | −0.660197 | ||||||||
\(119\) | 9.65685i | 0.885242i | ||||||||
\(120\) | −1.41421 | + | 1.00000i | −0.129099 | + | 0.0912871i | ||||
\(121\) | 4.31371 | 0.392155 | ||||||||
\(122\) | −12.4853 | −1.13036 | ||||||||
\(123\) | 3.07107 | + | 4.34315i | 0.276909 | + | 0.391608i | ||||
\(124\) | − | 1.17157i | − | 0.105210i | ||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.41421 | − | 9.65685i | 0.304162 | − | 0.860301i | ||||
\(127\) | − | 7.17157i | − | 0.636374i | −0.948028 | − | 0.318187i | \(-0.896926\pi\) | ||
0.948028 | − | 0.318187i | \(-0.103074\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.41421 | − | 13.3137i | −0.828875 | − | 1.17221i | ||||
\(130\) | 6.24264 | 0.547516 | ||||||||
\(131\) | − | 19.0711i | − | 1.66625i | −0.553087 | − | 0.833123i | \(-0.686550\pi\) | ||
0.553087 | − | 0.833123i | \(-0.313450\pi\) | |||||||
\(132\) | −3.65685 | + | 2.58579i | −0.318288 | + | 0.225064i | ||||
\(133\) | −14.4853 | − | 3.41421i | −1.25603 | − | 0.296050i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41421 | + | 5.00000i | 0.121716 | + | 0.430331i | ||||
\(136\) | − | 2.82843i | − | 0.242536i | ||||||
\(137\) | 2.48528i | 0.212332i | 0.994348 | + | 0.106166i | \(0.0338575\pi\) | ||||
−0.994348 | + | 0.106166i | \(0.966143\pi\) | |||||||
\(138\) | −8.48528 | + | 6.00000i | −0.722315 | + | 0.510754i | ||||
\(139\) | −10.1421 | −0.860245 | −0.430122 | − | 0.902771i | \(-0.641530\pi\) | ||||
−0.430122 | + | 0.902771i | \(0.641530\pi\) | |||||||
\(140\) | 3.41421i | 0.288554i | ||||||||
\(141\) | −12.4853 | + | 8.82843i | −1.05145 | + | 0.743488i | ||||
\(142\) | 2.82843 | 0.237356 | ||||||||
\(143\) | 16.1421 | 1.34987 | ||||||||
\(144\) | −1.00000 | + | 2.82843i | −0.0833333 | + | 0.235702i | ||||
\(145\) | 9.07107i | 0.753311i | ||||||||
\(146\) | 14.4853 | 1.19881 | ||||||||
\(147\) | −4.65685 | − | 6.58579i | −0.384091 | − | 0.543187i | ||||
\(148\) | 6.24264i | 0.513142i | ||||||||
\(149\) | − | 2.48528i | − | 0.203602i | −0.994805 | − | 0.101801i | \(-0.967539\pi\) | ||
0.994805 | − | 0.101801i | \(-0.0324605\pi\) | |||||||
\(150\) | −1.00000 | − | 1.41421i | −0.0816497 | − | 0.115470i | ||||
\(151\) | 3.51472i | 0.286024i | 0.989721 | + | 0.143012i | \(0.0456787\pi\) | ||||
−0.989721 | + | 0.143012i | \(0.954321\pi\) | |||||||
\(152\) | 4.24264 | + | 1.00000i | 0.344124 | + | 0.0811107i | ||||
\(153\) | −8.00000 | − | 2.82843i | −0.646762 | − | 0.228665i | ||||
\(154\) | 8.82843i | 0.711415i | ||||||||
\(155\) | 1.17157 | 0.0941030 | ||||||||
\(156\) | 8.82843 | − | 6.24264i | 0.706840 | − | 0.499811i | ||||
\(157\) | 15.7990 | 1.26090 | 0.630448 | − | 0.776231i | \(-0.282871\pi\) | ||||
0.630448 | + | 0.776231i | \(0.282871\pi\) | |||||||
\(158\) | − | 9.31371i | − | 0.740959i | ||||||
\(159\) | −8.82843 | − | 12.4853i | −0.700140 | − | 0.990147i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 20.4853i | 1.61447i | ||||||||
\(162\) | 7.00000 | + | 5.65685i | 0.549972 | + | 0.444444i | ||||
\(163\) | −12.7279 | −0.996928 | −0.498464 | − | 0.866910i | \(-0.666102\pi\) | ||||
−0.498464 | + | 0.866910i | \(0.666102\pi\) | |||||||
\(164\) | −3.07107 | −0.239810 | ||||||||
\(165\) | −2.58579 | − | 3.65685i | −0.201303 | − | 0.284686i | ||||
\(166\) | − | 7.17157i | − | 0.556622i | ||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 3.41421 | + | 4.82843i | 0.263412 | + | 0.372521i | ||||
\(169\) | −25.9706 | −1.99774 | ||||||||
\(170\) | 2.82843 | 0.216930 | ||||||||
\(171\) | 7.07107 | − | 11.0000i | 0.540738 | − | 0.841191i | ||||
\(172\) | 9.41421 | 0.717827 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 9.07107 | + | 12.8284i | 0.687676 | + | 0.972521i | ||||
\(175\) | −3.41421 | −0.258090 | ||||||||
\(176\) | − | 2.58579i | − | 0.194911i | ||||||
\(177\) | −7.17157 | − | 10.1421i | −0.539048 | − | 0.762330i | ||||
\(178\) | 13.4142 | 1.00544 | ||||||||
\(179\) | −17.7990 | −1.33036 | −0.665179 | − | 0.746684i | \(-0.731645\pi\) | ||||
−0.665179 | + | 0.746684i | \(0.731645\pi\) | |||||||
\(180\) | −2.82843 | − | 1.00000i | −0.210819 | − | 0.0745356i | ||||
\(181\) | 5.17157i | 0.384400i | 0.981356 | + | 0.192200i | \(0.0615622\pi\) | ||||
−0.981356 | + | 0.192200i | \(0.938438\pi\) | |||||||
\(182\) | − | 21.3137i | − | 1.57988i | ||||||
\(183\) | −12.4853 | − | 17.6569i | −0.922939 | − | 1.30523i | ||||
\(184\) | − | 6.00000i | − | 0.442326i | ||||||
\(185\) | −6.24264 | −0.458968 | ||||||||
\(186\) | 1.65685 | − | 1.17157i | 0.121486 | − | 0.0859039i | ||||
\(187\) | 7.31371 | 0.534831 | ||||||||
\(188\) | − | 8.82843i | − | 0.643879i | ||||||
\(189\) | 17.0711 | − | 4.82843i | 1.24174 | − | 0.351216i | ||||
\(190\) | −1.00000 | + | 4.24264i | −0.0725476 | + | 0.307794i | ||||
\(191\) | − | 1.75736i | − | 0.127158i | −0.997977 | − | 0.0635790i | \(-0.979749\pi\) | ||
0.997977 | − | 0.0635790i | \(-0.0202515\pi\) | |||||||
\(192\) | −1.00000 | − | 1.41421i | −0.0721688 | − | 0.102062i | ||||
\(193\) | − | 11.5563i | − | 0.831844i | −0.909400 | − | 0.415922i | \(-0.863459\pi\) | ||
0.909400 | − | 0.415922i | \(-0.136541\pi\) | |||||||
\(194\) | 9.41421i | 0.675901i | ||||||||
\(195\) | 6.24264 | + | 8.82843i | 0.447045 | + | 0.632217i | ||||
\(196\) | 4.65685 | 0.332632 | ||||||||
\(197\) | 10.1421i | 0.722597i | 0.932450 | + | 0.361299i | \(0.117667\pi\) | ||||
−0.932450 | + | 0.361299i | \(0.882333\pi\) | |||||||
\(198\) | −7.31371 | − | 2.58579i | −0.519763 | − | 0.183764i | ||||
\(199\) | 16.9706 | 1.20301 | 0.601506 | − | 0.798869i | \(-0.294568\pi\) | ||||
0.601506 | + | 0.798869i | \(0.294568\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.65685i | − | 0.257295i | ||||||
\(203\) | 30.9706 | 2.17371 | ||||||||
\(204\) | 4.00000 | − | 2.82843i | 0.280056 | − | 0.198030i | ||||
\(205\) | − | 3.07107i | − | 0.214493i | ||||||
\(206\) | − | 15.6569i | − | 1.09086i | ||||||
\(207\) | −16.9706 | − | 6.00000i | −1.17954 | − | 0.417029i | ||||
\(208\) | 6.24264i | 0.432849i | ||||||||
\(209\) | −2.58579 | + | 10.9706i | −0.178863 | + | 0.758850i | ||||
\(210\) | −4.82843 | + | 3.41421i | −0.333193 | + | 0.235603i | ||||
\(211\) | − | 2.00000i | − | 0.137686i | −0.997628 | − | 0.0688428i | \(-0.978069\pi\) | ||
0.997628 | − | 0.0688428i | \(-0.0219307\pi\) | |||||||
\(212\) | 8.82843 | 0.606339 | ||||||||
\(213\) | 2.82843 | + | 4.00000i | 0.193801 | + | 0.274075i | ||||
\(214\) | −7.65685 | −0.523412 | ||||||||
\(215\) | 9.41421i | 0.642044i | ||||||||
\(216\) | −5.00000 | + | 1.41421i | −0.340207 | + | 0.0962250i | ||||
\(217\) | − | 4.00000i | − | 0.271538i | ||||||
\(218\) | 13.6569i | 0.924959i | ||||||||
\(219\) | 14.4853 | + | 20.4853i | 0.978825 | + | 1.38427i | ||||
\(220\) | 2.58579 | 0.174334 | ||||||||
\(221\) | −17.6569 | −1.18773 | ||||||||
\(222\) | −8.82843 | + | 6.24264i | −0.592525 | + | 0.418979i | ||||
\(223\) | − | 18.0000i | − | 1.20537i | −0.797980 | − | 0.602685i | \(-0.794098\pi\) | ||
0.797980 | − | 0.602685i | \(-0.205902\pi\) | |||||||
\(224\) | −3.41421 | −0.228122 | ||||||||
\(225\) | 1.00000 | − | 2.82843i | 0.0666667 | − | 0.188562i | ||||
\(226\) | 7.17157 | 0.477046 | ||||||||
\(227\) | 13.6569 | 0.906437 | 0.453219 | − | 0.891399i | \(-0.350276\pi\) | ||||
0.453219 | + | 0.891399i | \(0.350276\pi\) | |||||||
\(228\) | 2.82843 | + | 7.00000i | 0.187317 | + | 0.463586i | ||||
\(229\) | −8.48528 | −0.560723 | −0.280362 | − | 0.959894i | \(-0.590454\pi\) | ||||
−0.280362 | + | 0.959894i | \(0.590454\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | −12.4853 | + | 8.82843i | −0.821471 | + | 0.580868i | ||||
\(232\) | −9.07107 | −0.595545 | ||||||||
\(233\) | 21.7990i | 1.42810i | 0.700095 | + | 0.714050i | \(0.253141\pi\) | ||||
−0.700095 | + | 0.714050i | \(0.746859\pi\) | |||||||
\(234\) | 17.6569 | + | 6.24264i | 1.15426 | + | 0.408094i | ||||
\(235\) | 8.82843 | 0.575903 | ||||||||
\(236\) | 7.17157 | 0.466830 | ||||||||
\(237\) | 13.1716 | − | 9.31371i | 0.855586 | − | 0.604990i | ||||
\(238\) | − | 9.65685i | − | 0.625961i | ||||||
\(239\) | 19.8995i | 1.28719i | 0.765366 | + | 0.643596i | \(0.222558\pi\) | ||||
−0.765366 | + | 0.643596i | \(0.777442\pi\) | |||||||
\(240\) | 1.41421 | − | 1.00000i | 0.0912871 | − | 0.0645497i | ||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | −4.31371 | −0.277296 | ||||||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | 12.4853 | 0.799288 | ||||||||
\(245\) | 4.65685i | 0.297516i | ||||||||
\(246\) | −3.07107 | − | 4.34315i | −0.195804 | − | 0.276909i | ||||
\(247\) | 6.24264 | − | 26.4853i | 0.397210 | − | 1.68522i | ||||
\(248\) | 1.17157i | 0.0743950i | ||||||||
\(249\) | 10.1421 | − | 7.17157i | 0.642732 | − | 0.454480i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | − | 19.0711i | − | 1.20376i | −0.798588 | − | 0.601878i | \(-0.794420\pi\) | ||
0.798588 | − | 0.601878i | \(-0.205580\pi\) | |||||||
\(252\) | −3.41421 | + | 9.65685i | −0.215075 | + | 0.608325i | ||||
\(253\) | 15.5147 | 0.975402 | ||||||||
\(254\) | 7.17157i | 0.449985i | ||||||||
\(255\) | 2.82843 | + | 4.00000i | 0.177123 | + | 0.250490i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.142136 | 0.00886618 | 0.00443309 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443309 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(258\) | 9.41421 | + | 13.3137i | 0.586103 | + | 0.828875i | ||||
\(259\) | 21.3137i | 1.32437i | ||||||||
\(260\) | −6.24264 | −0.387152 | ||||||||
\(261\) | −9.07107 | + | 25.6569i | −0.561485 | + | 1.58812i | ||||
\(262\) | 19.0711i | 1.17821i | ||||||||
\(263\) | 16.8284i | 1.03769i | 0.854870 | + | 0.518843i | \(0.173637\pi\) | ||||
−0.854870 | + | 0.518843i | \(0.826363\pi\) | |||||||
\(264\) | 3.65685 | − | 2.58579i | 0.225064 | − | 0.159144i | ||||
\(265\) | 8.82843i | 0.542326i | ||||||||
\(266\) | 14.4853 | + | 3.41421i | 0.888150 | + | 0.209339i | ||||
\(267\) | 13.4142 | + | 18.9706i | 0.820937 | + | 1.16098i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3848 | −0.755113 | −0.377557 | − | 0.925987i | \(-0.623236\pi\) | ||||
−0.377557 | + | 0.925987i | \(0.623236\pi\) | |||||||
\(270\) | −1.41421 | − | 5.00000i | −0.0860663 | − | 0.304290i | ||||
\(271\) | 4.97056 | 0.301940 | 0.150970 | − | 0.988538i | \(-0.451760\pi\) | ||||
0.150970 | + | 0.988538i | \(0.451760\pi\) | |||||||
\(272\) | 2.82843i | 0.171499i | ||||||||
\(273\) | 30.1421 | − | 21.3137i | 1.82429 | − | 1.28996i | ||||
\(274\) | − | 2.48528i | − | 0.150141i | ||||||
\(275\) | 2.58579i | 0.155929i | ||||||||
\(276\) | 8.48528 | − | 6.00000i | 0.510754 | − | 0.361158i | ||||
\(277\) | −8.97056 | −0.538989 | −0.269494 | − | 0.963002i | \(-0.586857\pi\) | ||||
−0.269494 | + | 0.963002i | \(0.586857\pi\) | |||||||
\(278\) | 10.1421 | 0.608285 | ||||||||
\(279\) | 3.31371 | + | 1.17157i | 0.198387 | + | 0.0701402i | ||||
\(280\) | − | 3.41421i | − | 0.204038i | ||||||
\(281\) | 15.0711 | 0.899065 | 0.449532 | − | 0.893264i | \(-0.351591\pi\) | ||||
0.449532 | + | 0.893264i | \(0.351591\pi\) | |||||||
\(282\) | 12.4853 | − | 8.82843i | 0.743488 | − | 0.525725i | ||||
\(283\) | −12.7279 | −0.756596 | −0.378298 | − | 0.925684i | \(-0.623491\pi\) | ||||
−0.378298 | + | 0.925684i | \(0.623491\pi\) | |||||||
\(284\) | −2.82843 | −0.167836 | ||||||||
\(285\) | −7.00000 | + | 2.82843i | −0.414644 | + | 0.167542i | ||||
\(286\) | −16.1421 | −0.954504 | ||||||||
\(287\) | −10.4853 | −0.618927 | ||||||||
\(288\) | 1.00000 | − | 2.82843i | 0.0589256 | − | 0.166667i | ||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | − | 9.07107i | − | 0.532671i | ||||||
\(291\) | −13.3137 | + | 9.41421i | −0.780463 | + | 0.551871i | ||||
\(292\) | −14.4853 | −0.847687 | ||||||||
\(293\) | −8.82843 | −0.515762 | −0.257881 | − | 0.966177i | \(-0.583024\pi\) | ||||
−0.257881 | + | 0.966177i | \(0.583024\pi\) | |||||||
\(294\) | 4.65685 | + | 6.58579i | 0.271593 | + | 0.384091i | ||||
\(295\) | 7.17157i | 0.417545i | ||||||||
\(296\) | − | 6.24264i | − | 0.362846i | ||||||
\(297\) | −3.65685 | − | 12.9289i | −0.212192 | − | 0.750213i | ||||
\(298\) | 2.48528i | 0.143968i | ||||||||
\(299\) | −37.4558 | −2.16613 | ||||||||
\(300\) | 1.00000 | + | 1.41421i | 0.0577350 | + | 0.0816497i | ||||
\(301\) | 32.1421 | 1.85264 | ||||||||
\(302\) | − | 3.51472i | − | 0.202249i | ||||||
\(303\) | 5.17157 | − | 3.65685i | 0.297099 | − | 0.210081i | ||||
\(304\) | −4.24264 | − | 1.00000i | −0.243332 | − | 0.0573539i | ||||
\(305\) | 12.4853i | 0.714905i | ||||||||
\(306\) | 8.00000 | + | 2.82843i | 0.457330 | + | 0.161690i | ||||
\(307\) | 10.1421i | 0.578842i | 0.957202 | + | 0.289421i | \(0.0934628\pi\) | ||||
−0.957202 | + | 0.289421i | \(0.906537\pi\) | |||||||
\(308\) | − | 8.82843i | − | 0.503046i | ||||||
\(309\) | 22.1421 | − | 15.6569i | 1.25962 | − | 0.890687i | ||||
\(310\) | −1.17157 | −0.0665409 | ||||||||
\(311\) | 9.07107i | 0.514373i | 0.966362 | + | 0.257187i | \(0.0827955\pi\) | ||||
−0.966362 | + | 0.257187i | \(0.917205\pi\) | |||||||
\(312\) | −8.82843 | + | 6.24264i | −0.499811 | + | 0.353420i | ||||
\(313\) | −11.1716 | −0.631455 | −0.315727 | − | 0.948850i | \(-0.602248\pi\) | ||||
−0.315727 | + | 0.948850i | \(0.602248\pi\) | |||||||
\(314\) | −15.7990 | −0.891589 | ||||||||
\(315\) | −9.65685 | − | 3.41421i | −0.544102 | − | 0.192369i | ||||
\(316\) | 9.31371i | 0.523937i | ||||||||
\(317\) | 11.6569 | 0.654714 | 0.327357 | − | 0.944901i | \(-0.393842\pi\) | ||||
0.327357 | + | 0.944901i | \(0.393842\pi\) | |||||||
\(318\) | 8.82843 | + | 12.4853i | 0.495074 | + | 0.700140i | ||||
\(319\) | − | 23.4558i | − | 1.31328i | ||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −7.65685 | − | 10.8284i | −0.427364 | − | 0.604384i | ||||
\(322\) | − | 20.4853i | − | 1.14160i | ||||||
\(323\) | 2.82843 | − | 12.0000i | 0.157378 | − | 0.667698i | ||||
\(324\) | −7.00000 | − | 5.65685i | −0.388889 | − | 0.314270i | ||||
\(325\) | − | 6.24264i | − | 0.346279i | ||||||
\(326\) | 12.7279 | 0.704934 | ||||||||
\(327\) | −19.3137 | + | 13.6569i | −1.06805 | + | 0.755226i | ||||
\(328\) | 3.07107 | 0.169571 | ||||||||
\(329\) | − | 30.1421i | − | 1.66179i | ||||||
\(330\) | 2.58579 | + | 3.65685i | 0.142343 | + | 0.201303i | ||||
\(331\) | − | 16.9706i | − | 0.932786i | −0.884577 | − | 0.466393i | \(-0.845553\pi\) | ||
0.884577 | − | 0.466393i | \(-0.154447\pi\) | |||||||
\(332\) | 7.17157i | 0.393591i | ||||||||
\(333\) | −17.6569 | − | 6.24264i | −0.967590 | − | 0.342095i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.41421 | − | 4.82843i | −0.186261 | − | 0.263412i | ||||
\(337\) | − | 13.2132i | − | 0.719769i | −0.932997 | − | 0.359885i | \(-0.882816\pi\) | ||
0.932997 | − | 0.359885i | \(-0.117184\pi\) | |||||||
\(338\) | 25.9706 | 1.41261 | ||||||||
\(339\) | 7.17157 | + | 10.1421i | 0.389506 | + | 0.550845i | ||||
\(340\) | −2.82843 | −0.153393 | ||||||||
\(341\) | −3.02944 | −0.164053 | ||||||||
\(342\) | −7.07107 | + | 11.0000i | −0.382360 | + | 0.594812i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | −9.41421 | −0.507580 | ||||||||
\(345\) | 6.00000 | + | 8.48528i | 0.323029 | + | 0.456832i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | − | 26.2843i | − | 1.41101i | −0.708703 | − | 0.705507i | \(-0.750719\pi\) | ||
0.708703 | − | 0.705507i | \(-0.249281\pi\) | |||||||
\(348\) | −9.07107 | − | 12.8284i | −0.486260 | − | 0.687676i | ||||
\(349\) | 22.9706 | 1.22959 | 0.614793 | − | 0.788688i | \(-0.289240\pi\) | ||||
0.614793 | + | 0.788688i | \(0.289240\pi\) | |||||||
\(350\) | 3.41421 | 0.182497 | ||||||||
\(351\) | 8.82843 | + | 31.2132i | 0.471227 | + | 1.66604i | ||||
\(352\) | 2.58579i | 0.137823i | ||||||||
\(353\) | − | 3.17157i | − | 0.168806i | −0.996432 | − | 0.0844029i | \(-0.973102\pi\) | ||
0.996432 | − | 0.0844029i | \(-0.0268983\pi\) | |||||||
\(354\) | 7.17157 | + | 10.1421i | 0.381165 | + | 0.539048i | ||||
\(355\) | − | 2.82843i | − | 0.150117i | ||||||
\(356\) | −13.4142 | −0.710952 | ||||||||
\(357\) | 13.6569 | − | 9.65685i | 0.722797 | − | 0.511095i | ||||
\(358\) | 17.7990 | 0.940706 | ||||||||
\(359\) | − | 16.5858i | − | 0.875364i | −0.899130 | − | 0.437682i | \(-0.855800\pi\) | ||
0.899130 | − | 0.437682i | \(-0.144200\pi\) | |||||||
\(360\) | 2.82843 | + | 1.00000i | 0.149071 | + | 0.0527046i | ||||
\(361\) | 17.0000 | + | 8.48528i | 0.894737 | + | 0.446594i | ||||
\(362\) | − | 5.17157i | − | 0.271812i | ||||||
\(363\) | −4.31371 | − | 6.10051i | −0.226411 | − | 0.320193i | ||||
\(364\) | 21.3137i | 1.11714i | ||||||||
\(365\) | − | 14.4853i | − | 0.758194i | ||||||
\(366\) | 12.4853 | + | 17.6569i | 0.652616 | + | 0.922939i | ||||
\(367\) | −5.75736 | −0.300532 | −0.150266 | − | 0.988646i | \(-0.548013\pi\) | ||||
−0.150266 | + | 0.988646i | \(0.548013\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 3.07107 | − | 8.68629i | 0.159873 | − | 0.452190i | ||||
\(370\) | 6.24264 | 0.324539 | ||||||||
\(371\) | 30.1421 | 1.56490 | ||||||||
\(372\) | −1.65685 | + | 1.17157i | −0.0859039 | + | 0.0607432i | ||||
\(373\) | − | 34.0416i | − | 1.76261i | −0.472549 | − | 0.881304i | \(-0.656666\pi\) | ||
0.472549 | − | 0.881304i | \(-0.343334\pi\) | |||||||
\(374\) | −7.31371 | −0.378183 | ||||||||
\(375\) | −1.41421 | + | 1.00000i | −0.0730297 | + | 0.0516398i | ||||
\(376\) | 8.82843i | 0.455291i | ||||||||
\(377\) | 56.6274i | 2.91646i | ||||||||
\(378\) | −17.0711 | + | 4.82843i | −0.878041 | + | 0.248347i | ||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 1.00000 | − | 4.24264i | 0.0512989 | − | 0.217643i | ||||
\(381\) | −10.1421 | + | 7.17157i | −0.519597 | + | 0.367411i | ||||
\(382\) | 1.75736i | 0.0899143i | ||||||||
\(383\) | −3.85786 | −0.197128 | −0.0985638 | − | 0.995131i | \(-0.531425\pi\) | ||||
−0.0985638 | + | 0.995131i | \(0.531425\pi\) | |||||||
\(384\) | 1.00000 | + | 1.41421i | 0.0510310 | + | 0.0721688i | ||||
\(385\) | 8.82843 | 0.449938 | ||||||||
\(386\) | 11.5563i | 0.588203i | ||||||||
\(387\) | −9.41421 | + | 26.6274i | −0.478551 | + | 1.35355i | ||||
\(388\) | − | 9.41421i | − | 0.477934i | ||||||
\(389\) | 31.6569i | 1.60507i | 0.596608 | + | 0.802533i | \(0.296515\pi\) | ||||
−0.596608 | + | 0.802533i | \(0.703485\pi\) | |||||||
\(390\) | −6.24264 | − | 8.82843i | −0.316108 | − | 0.447045i | ||||
\(391\) | −16.9706 | −0.858238 | ||||||||
\(392\) | −4.65685 | −0.235207 | ||||||||
\(393\) | −26.9706 | + | 19.0711i | −1.36048 | + | 0.962008i | ||||
\(394\) | − | 10.1421i | − | 0.510953i | ||||||
\(395\) | −9.31371 | −0.468624 | ||||||||
\(396\) | 7.31371 | + | 2.58579i | 0.367528 | + | 0.129941i | ||||
\(397\) | −16.9706 | −0.851728 | −0.425864 | − | 0.904787i | \(-0.640030\pi\) | ||||
−0.425864 | + | 0.904787i | \(0.640030\pi\) | |||||||
\(398\) | −16.9706 | −0.850657 | ||||||||
\(399\) | 9.65685 | + | 23.8995i | 0.483447 | + | 1.19647i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −18.3848 | −0.918092 | −0.459046 | − | 0.888413i | \(-0.651809\pi\) | ||||
−0.459046 | + | 0.888413i | \(0.651809\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.31371 | 0.364322 | ||||||||
\(404\) | 3.65685i | 0.181935i | ||||||||
\(405\) | 5.65685 | − | 7.00000i | 0.281091 | − | 0.347833i | ||||
\(406\) | −30.9706 | −1.53704 | ||||||||
\(407\) | 16.1421 | 0.800136 | ||||||||
\(408\) | −4.00000 | + | 2.82843i | −0.198030 | + | 0.140028i | ||||
\(409\) | − | 12.4853i | − | 0.617357i | −0.951166 | − | 0.308679i | \(-0.900113\pi\) | ||
0.951166 | − | 0.308679i | \(-0.0998868\pi\) | |||||||
\(410\) | 3.07107i | 0.151669i | ||||||||
\(411\) | 3.51472 | − | 2.48528i | 0.173368 | − | 0.122590i | ||||
\(412\) | 15.6569i | 0.771358i | ||||||||
\(413\) | 24.4853 | 1.20484 | ||||||||
\(414\) | 16.9706 | + | 6.00000i | 0.834058 | + | 0.294884i | ||||
\(415\) | −7.17157 | −0.352039 | ||||||||
\(416\) | − | 6.24264i | − | 0.306071i | ||||||
\(417\) | 10.1421 | + | 14.3431i | 0.496663 | + | 0.702387i | ||||
\(418\) | 2.58579 | − | 10.9706i | 0.126475 | − | 0.536588i | ||||
\(419\) | − | 30.3848i | − | 1.48439i | −0.670182 | − | 0.742197i | \(-0.733784\pi\) | ||
0.670182 | − | 0.742197i | \(-0.266216\pi\) | |||||||
\(420\) | 4.82843 | − | 3.41421i | 0.235603 | − | 0.166597i | ||||
\(421\) | − | 32.2843i | − | 1.57344i | −0.617311 | − | 0.786720i | \(-0.711778\pi\) | ||
0.617311 | − | 0.786720i | \(-0.288222\pi\) | |||||||
\(422\) | 2.00000i | 0.0973585i | ||||||||
\(423\) | 24.9706 | + | 8.82843i | 1.21411 | + | 0.429253i | ||||
\(424\) | −8.82843 | −0.428746 | ||||||||
\(425\) | − | 2.82843i | − | 0.137199i | ||||||
\(426\) | −2.82843 | − | 4.00000i | −0.137038 | − | 0.193801i | ||||
\(427\) | 42.6274 | 2.06289 | ||||||||
\(428\) | 7.65685 | 0.370108 | ||||||||
\(429\) | −16.1421 | − | 22.8284i | −0.779350 | − | 1.10217i | ||||
\(430\) | − | 9.41421i | − | 0.453994i | ||||||
\(431\) | −3.31371 | −0.159616 | −0.0798079 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798079 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(432\) | 5.00000 | − | 1.41421i | 0.240563 | − | 0.0680414i | ||||
\(433\) | 22.3848i | 1.07574i | 0.843027 | + | 0.537872i | \(0.180772\pi\) | ||||
−0.843027 | + | 0.537872i | \(0.819228\pi\) | |||||||
\(434\) | 4.00000i | 0.192006i | ||||||||
\(435\) | 12.8284 | − | 9.07107i | 0.615076 | − | 0.434924i | ||||
\(436\) | − | 13.6569i | − | 0.654045i | ||||||
\(437\) | 6.00000 | − | 25.4558i | 0.287019 | − | 1.21772i | ||||
\(438\) | −14.4853 | − | 20.4853i | −0.692134 | − | 0.978825i | ||||
\(439\) | − | 27.9411i | − | 1.33356i | −0.745256 | − | 0.666779i | \(-0.767673\pi\) | ||
0.745256 | − | 0.666779i | \(-0.232327\pi\) | |||||||
\(440\) | −2.58579 | −0.123273 | ||||||||
\(441\) | −4.65685 | + | 13.1716i | −0.221755 | + | 0.627218i | ||||
\(442\) | 17.6569 | 0.839851 | ||||||||
\(443\) | − | 18.0000i | − | 0.855206i | −0.903967 | − | 0.427603i | \(-0.859358\pi\) | ||
0.903967 | − | 0.427603i | \(-0.140642\pi\) | |||||||
\(444\) | 8.82843 | − | 6.24264i | 0.418979 | − | 0.296263i | ||||
\(445\) | − | 13.4142i | − | 0.635895i | ||||||
\(446\) | 18.0000i | 0.852325i | ||||||||
\(447\) | −3.51472 | + | 2.48528i | −0.166240 | + | 0.117550i | ||||
\(448\) | 3.41421 | 0.161306 | ||||||||
\(449\) | 7.75736 | 0.366092 | 0.183046 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183046 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(450\) | −1.00000 | + | 2.82843i | −0.0471405 | + | 0.133333i | ||||
\(451\) | 7.94113i | 0.373933i | ||||||||
\(452\) | −7.17157 | −0.337322 | ||||||||
\(453\) | 4.97056 | − | 3.51472i | 0.233537 | − | 0.165136i | ||||
\(454\) | −13.6569 | −0.640948 | ||||||||
\(455\) | −21.3137 | −0.999202 | ||||||||
\(456\) | −2.82843 | − | 7.00000i | −0.132453 | − | 0.327805i | ||||
\(457\) | 4.82843 | 0.225864 | 0.112932 | − | 0.993603i | \(-0.463976\pi\) | ||||
0.112932 | + | 0.993603i | \(0.463976\pi\) | |||||||
\(458\) | 8.48528 | 0.396491 | ||||||||
\(459\) | 4.00000 | + | 14.1421i | 0.186704 | + | 0.660098i | ||||
\(460\) | −6.00000 | −0.279751 | ||||||||
\(461\) | − | 0.142136i | − | 0.00661992i | −0.999995 | − | 0.00330996i | \(-0.998946\pi\) | ||
0.999995 | − | 0.00330996i | \(-0.00105359\pi\) | |||||||
\(462\) | 12.4853 | − | 8.82843i | 0.580868 | − | 0.410736i | ||||
\(463\) | −23.2132 | −1.07881 | −0.539405 | − | 0.842047i | \(-0.681351\pi\) | ||||
−0.539405 | + | 0.842047i | \(0.681351\pi\) | |||||||
\(464\) | 9.07107 | 0.421114 | ||||||||
\(465\) | −1.17157 | − | 1.65685i | −0.0543304 | − | 0.0768348i | ||||
\(466\) | − | 21.7990i | − | 1.00982i | ||||||
\(467\) | − | 13.7990i | − | 0.638541i | −0.947664 | − | 0.319271i | \(-0.896562\pi\) | ||
0.947664 | − | 0.319271i | \(-0.103438\pi\) | |||||||
\(468\) | −17.6569 | − | 6.24264i | −0.816188 | − | 0.288566i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.82843 | −0.407225 | ||||||||
\(471\) | −15.7990 | − | 22.3431i | −0.727979 | − | 1.02952i | ||||
\(472\) | −7.17157 | −0.330098 | ||||||||
\(473\) | − | 24.3431i | − | 1.11930i | ||||||
\(474\) | −13.1716 | + | 9.31371i | −0.604990 | + | 0.427793i | ||||
\(475\) | 4.24264 | + | 1.00000i | 0.194666 | + | 0.0458831i | ||||
\(476\) | 9.65685i | 0.442621i | ||||||||
\(477\) | −8.82843 | + | 24.9706i | −0.404226 | + | 1.14332i | ||||
\(478\) | − | 19.8995i | − | 0.910182i | ||||||
\(479\) | 0.585786i | 0.0267653i | 0.999910 | + | 0.0133826i | \(0.00425995\pi\) | ||||
−0.999910 | + | 0.0133826i | \(0.995740\pi\) | |||||||
\(480\) | −1.41421 | + | 1.00000i | −0.0645497 | + | 0.0456435i | ||||
\(481\) | −38.9706 | −1.77690 | ||||||||
\(482\) | 8.48528i | 0.386494i | ||||||||
\(483\) | 28.9706 | − | 20.4853i | 1.31821 | − | 0.932113i | ||||
\(484\) | 4.31371 | 0.196078 | ||||||||
\(485\) | 9.41421 | 0.427477 | ||||||||
\(486\) | 1.00000 | − | 15.5563i | 0.0453609 | − | 0.705650i | ||||
\(487\) | 7.85786i | 0.356074i | 0.984024 | + | 0.178037i | \(0.0569746\pi\) | ||||
−0.984024 | + | 0.178037i | \(0.943025\pi\) | |||||||
\(488\) | −12.4853 | −0.565182 | ||||||||
\(489\) | 12.7279 | + | 18.0000i | 0.575577 | + | 0.813988i | ||||
\(490\) | − | 4.65685i | − | 0.210375i | ||||||
\(491\) | 12.4437i | 0.561574i | 0.959770 | + | 0.280787i | \(0.0905955\pi\) | ||||
−0.959770 | + | 0.280787i | \(0.909405\pi\) | |||||||
\(492\) | 3.07107 | + | 4.34315i | 0.138454 | + | 0.195804i | ||||
\(493\) | 25.6569i | 1.15553i | ||||||||
\(494\) | −6.24264 | + | 26.4853i | −0.280870 | + | 1.19163i | ||||
\(495\) | −2.58579 | + | 7.31371i | −0.116222 | + | 0.328727i | ||||
\(496\) | − | 1.17157i | − | 0.0526052i | ||||||
\(497\) | −9.65685 | −0.433169 | ||||||||
\(498\) | −10.1421 | + | 7.17157i | −0.454480 | + | 0.321366i | ||||
\(499\) | −14.3431 | −0.642087 | −0.321044 | − | 0.947064i | \(-0.604034\pi\) | ||||
−0.321044 | + | 0.947064i | \(0.604034\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.0711i | 0.851183i | ||||||||
\(503\) | − | 42.2843i | − | 1.88536i | −0.333695 | − | 0.942681i | \(-0.608295\pi\) | ||
0.333695 | − | 0.942681i | \(-0.391705\pi\) | |||||||
\(504\) | 3.41421 | − | 9.65685i | 0.152081 | − | 0.430150i | ||||
\(505\) | −3.65685 | −0.162728 | ||||||||
\(506\) | −15.5147 | −0.689713 | ||||||||
\(507\) | 25.9706 | + | 36.7279i | 1.15339 | + | 1.63114i | ||||
\(508\) | − | 7.17157i | − | 0.318187i | ||||||
\(509\) | −23.8995 | −1.05933 | −0.529663 | − | 0.848208i | \(-0.677682\pi\) | ||||
−0.529663 | + | 0.848208i | \(0.677682\pi\) | |||||||
\(510\) | −2.82843 | − | 4.00000i | −0.125245 | − | 0.177123i | ||||
\(511\) | −49.4558 | −2.18780 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −22.6274 | + | 1.00000i | −0.999025 | + | 0.0441511i | ||||
\(514\) | −0.142136 | −0.00626933 | ||||||||
\(515\) | −15.6569 | −0.689923 | ||||||||
\(516\) | −9.41421 | − | 13.3137i | −0.414438 | − | 0.586103i | ||||
\(517\) | −22.8284 | −1.00399 | ||||||||
\(518\) | − | 21.3137i | − | 0.936471i | ||||||
\(519\) | 6.00000 | + | 8.48528i | 0.263371 | + | 0.372463i | ||||
\(520\) | 6.24264 | 0.273758 | ||||||||
\(521\) | 22.3848 | 0.980695 | 0.490347 | − | 0.871527i | \(-0.336870\pi\) | ||||
0.490347 | + | 0.871527i | \(0.336870\pi\) | |||||||
\(522\) | 9.07107 | − | 25.6569i | 0.397030 | − | 1.12297i | ||||
\(523\) | 24.9706i | 1.09189i | 0.837822 | + | 0.545943i | \(0.183829\pi\) | ||||
−0.837822 | + | 0.545943i | \(0.816171\pi\) | |||||||
\(524\) | − | 19.0711i | − | 0.833123i | ||||||
\(525\) | 3.41421 | + | 4.82843i | 0.149008 | + | 0.210730i | ||||
\(526\) | − | 16.8284i | − | 0.733754i | ||||||
\(527\) | 3.31371 | 0.144347 | ||||||||
\(528\) | −3.65685 | + | 2.58579i | −0.159144 | + | 0.112532i | ||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | − | 8.82843i | − | 0.383482i | ||||||
\(531\) | −7.17157 | + | 20.2843i | −0.311220 | + | 0.880262i | ||||
\(532\) | −14.4853 | − | 3.41421i | −0.628017 | − | 0.148025i | ||||
\(533\) | − | 19.1716i | − | 0.830413i | ||||||
\(534\) | −13.4142 | − | 18.9706i | −0.580490 | − | 0.820937i | ||||
\(535\) | 7.65685i | 0.331035i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.7990 | + | 25.1716i | 0.768083 | + | 1.08623i | ||||
\(538\) | 12.3848 | 0.533946 | ||||||||
\(539\) | − | 12.0416i | − | 0.518670i | ||||||
\(540\) | 1.41421 | + | 5.00000i | 0.0608581 | + | 0.215166i | ||||
\(541\) | −9.02944 | −0.388206 | −0.194103 | − | 0.980981i | \(-0.562180\pi\) | ||||
−0.194103 | + | 0.980981i | \(0.562180\pi\) | |||||||
\(542\) | −4.97056 | −0.213504 | ||||||||
\(543\) | 7.31371 | − | 5.17157i | 0.313861 | − | 0.221933i | ||||
\(544\) | − | 2.82843i | − | 0.121268i | ||||||
\(545\) | 13.6569 | 0.584995 | ||||||||
\(546\) | −30.1421 | + | 21.3137i | −1.28996 | + | 0.912143i | ||||
\(547\) | − | 18.8284i | − | 0.805045i | −0.915410 | − | 0.402523i | \(-0.868133\pi\) | ||
0.915410 | − | 0.402523i | \(-0.131867\pi\) | |||||||
\(548\) | 2.48528i | 0.106166i | ||||||||
\(549\) | −12.4853 | + | 35.3137i | −0.532859 | + | 1.50715i | ||||
\(550\) | − | 2.58579i | − | 0.110258i | ||||||
\(551\) | −38.4853 | − | 9.07107i | −1.63953 | − | 0.386440i | ||||
\(552\) | −8.48528 | + | 6.00000i | −0.361158 | + | 0.255377i | ||||
\(553\) | 31.7990i | 1.35223i | ||||||||
\(554\) | 8.97056 | 0.381123 | ||||||||
\(555\) | 6.24264 | + | 8.82843i | 0.264985 | + | 0.374746i | ||||
\(556\) | −10.1421 | −0.430122 | ||||||||
\(557\) | 16.6274i | 0.704526i | 0.935901 | + | 0.352263i | \(0.114588\pi\) | ||||
−0.935901 | + | 0.352263i | \(0.885412\pi\) | |||||||
\(558\) | −3.31371 | − | 1.17157i | −0.140280 | − | 0.0495966i | ||||
\(559\) | 58.7696i | 2.48569i | ||||||||
\(560\) | 3.41421i | 0.144277i | ||||||||
\(561\) | −7.31371 | − | 10.3431i | −0.308785 | − | 0.436688i | ||||
\(562\) | −15.0711 | −0.635735 | ||||||||
\(563\) | 2.34315 | 0.0987518 | 0.0493759 | − | 0.998780i | \(-0.484277\pi\) | ||||
0.0493759 | + | 0.998780i | \(0.484277\pi\) | |||||||
\(564\) | −12.4853 | + | 8.82843i | −0.525725 | + | 0.371744i | ||||
\(565\) | − | 7.17157i | − | 0.301710i | ||||||
\(566\) | 12.7279 | 0.534994 | ||||||||
\(567\) | −23.8995 | − | 19.3137i | −1.00368 | − | 0.811100i | ||||
\(568\) | 2.82843 | 0.118678 | ||||||||
\(569\) | 43.0711 | 1.80563 | 0.902817 | − | 0.430026i | \(-0.141496\pi\) | ||||
0.902817 | + | 0.430026i | \(0.141496\pi\) | |||||||
\(570\) | 7.00000 | − | 2.82843i | 0.293198 | − | 0.118470i | ||||
\(571\) | 9.65685 | 0.404127 | 0.202063 | − | 0.979372i | \(-0.435235\pi\) | ||||
0.202063 | + | 0.979372i | \(0.435235\pi\) | |||||||
\(572\) | 16.1421 | 0.674937 | ||||||||
\(573\) | −2.48528 | + | 1.75736i | −0.103824 | + | 0.0734147i | ||||
\(574\) | 10.4853 | 0.437647 | ||||||||
\(575\) | − | 6.00000i | − | 0.250217i | ||||||
\(576\) | −1.00000 | + | 2.82843i | −0.0416667 | + | 0.117851i | ||||
\(577\) | −24.8284 | −1.03362 | −0.516810 | − | 0.856100i | \(-0.672881\pi\) | ||||
−0.516810 | + | 0.856100i | \(0.672881\pi\) | |||||||
\(578\) | −9.00000 | −0.374351 | ||||||||
\(579\) | −16.3431 | + | 11.5563i | −0.679198 | + | 0.480265i | ||||
\(580\) | 9.07107i | 0.376656i | ||||||||
\(581\) | 24.4853i | 1.01582i | ||||||||
\(582\) | 13.3137 | − | 9.41421i | 0.551871 | − | 0.390232i | ||||
\(583\) | − | 22.8284i | − | 0.945457i | ||||||
\(584\) | 14.4853 | 0.599405 | ||||||||
\(585\) | 6.24264 | − | 17.6569i | 0.258101 | − | 0.730021i | ||||
\(586\) | 8.82843 | 0.364699 | ||||||||
\(587\) | 8.82843i | 0.364388i | 0.983263 | + | 0.182194i | \(0.0583199\pi\) | ||||
−0.983263 | + | 0.182194i | \(0.941680\pi\) | |||||||
\(588\) | −4.65685 | − | 6.58579i | −0.192045 | − | 0.271593i | ||||
\(589\) | −1.17157 | + | 4.97056i | −0.0482738 | + | 0.204808i | ||||
\(590\) | − | 7.17157i | − | 0.295249i | ||||||
\(591\) | 14.3431 | − | 10.1421i | 0.589998 | − | 0.417192i | ||||
\(592\) | 6.24264i | 0.256571i | ||||||||
\(593\) | − | 16.1421i | − | 0.662878i | −0.943477 | − | 0.331439i | \(-0.892466\pi\) | ||
0.943477 | − | 0.331439i | \(-0.107534\pi\) | |||||||
\(594\) | 3.65685 | + | 12.9289i | 0.150043 | + | 0.530481i | ||||
\(595\) | −9.65685 | −0.395892 | ||||||||
\(596\) | − | 2.48528i | − | 0.101801i | ||||||
\(597\) | −16.9706 | − | 24.0000i | −0.694559 | − | 0.982255i | ||||
\(598\) | 37.4558 | 1.53168 | ||||||||
\(599\) | −26.8284 | −1.09618 | −0.548090 | − | 0.836419i | \(-0.684645\pi\) | ||||
−0.548090 | + | 0.836419i | \(0.684645\pi\) | |||||||
\(600\) | −1.00000 | − | 1.41421i | −0.0408248 | − | 0.0577350i | ||||
\(601\) | 4.00000i | 0.163163i | 0.996667 | + | 0.0815817i | \(0.0259972\pi\) | ||||
−0.996667 | + | 0.0815817i | \(0.974003\pi\) | |||||||
\(602\) | −32.1421 | −1.31002 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.51472i | 0.143012i | ||||||||
\(605\) | 4.31371i | 0.175377i | ||||||||
\(606\) | −5.17157 | + | 3.65685i | −0.210081 | + | 0.148550i | ||||
\(607\) | − | 18.4853i | − | 0.750294i | −0.926965 | − | 0.375147i | \(-0.877592\pi\) | ||
0.926965 | − | 0.375147i | \(-0.122408\pi\) | |||||||
\(608\) | 4.24264 | + | 1.00000i | 0.172062 | + | 0.0405554i | ||||
\(609\) | −30.9706 | − | 43.7990i | −1.25499 | − | 1.77482i | ||||
\(610\) | − | 12.4853i | − | 0.505514i | ||||||
\(611\) | 55.1127 | 2.22962 | ||||||||
\(612\) | −8.00000 | − | 2.82843i | −0.323381 | − | 0.114332i | ||||
\(613\) | 39.1127 | 1.57975 | 0.789874 | − | 0.613270i | \(-0.210146\pi\) | ||||
0.789874 | + | 0.613270i | \(0.210146\pi\) | |||||||
\(614\) | − | 10.1421i | − | 0.409303i | ||||||
\(615\) | −4.34315 | + | 3.07107i | −0.175133 | + | 0.123837i | ||||
\(616\) | 8.82843i | 0.355707i | ||||||||
\(617\) | 13.1716i | 0.530268i | 0.964212 | + | 0.265134i | \(0.0854161\pi\) | ||||
−0.964212 | + | 0.265134i | \(0.914584\pi\) | |||||||
\(618\) | −22.1421 | + | 15.6569i | −0.890687 | + | 0.629811i | ||||
\(619\) | −9.45584 | −0.380062 | −0.190031 | − | 0.981778i | \(-0.560859\pi\) | ||||
−0.190031 | + | 0.981778i | \(0.560859\pi\) | |||||||
\(620\) | 1.17157 | 0.0470515 | ||||||||
\(621\) | 8.48528 | + | 30.0000i | 0.340503 | + | 1.20386i | ||||
\(622\) | − | 9.07107i | − | 0.363717i | ||||||
\(623\) | −45.7990 | −1.83490 | ||||||||
\(624\) | 8.82843 | − | 6.24264i | 0.353420 | − | 0.249906i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.1716 | 0.446506 | ||||||||
\(627\) | 18.1005 | − | 7.31371i | 0.722865 | − | 0.292081i | ||||
\(628\) | 15.7990 | 0.630448 | ||||||||
\(629\) | −17.6569 | −0.704025 | ||||||||
\(630\) | 9.65685 | + | 3.41421i | 0.384738 | + | 0.136026i | ||||
\(631\) | 40.4853 | 1.61169 | 0.805847 | − | 0.592124i | \(-0.201710\pi\) | ||||
0.805847 | + | 0.592124i | \(0.201710\pi\) | |||||||
\(632\) | − | 9.31371i | − | 0.370479i | ||||||
\(633\) | −2.82843 | + | 2.00000i | −0.112420 | + | 0.0794929i | ||||
\(634\) | −11.6569 | −0.462953 | ||||||||
\(635\) | 7.17157 | 0.284595 | ||||||||
\(636\) | −8.82843 | − | 12.4853i | −0.350070 | − | 0.495074i | ||||
\(637\) | 29.0711i | 1.15184i | ||||||||
\(638\) | 23.4558i | 0.928626i | ||||||||
\(639\) | 2.82843 | − | 8.00000i | 0.111891 | − | 0.316475i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 36.7279 | 1.45067 | 0.725333 | − | 0.688398i | \(-0.241686\pi\) | ||||
0.725333 | + | 0.688398i | \(0.241686\pi\) | |||||||
\(642\) | 7.65685 | + | 10.8284i | 0.302192 | + | 0.427364i | ||||
\(643\) | 4.72792 | 0.186451 | 0.0932255 | − | 0.995645i | \(-0.470282\pi\) | ||||
0.0932255 | + | 0.995645i | \(0.470282\pi\) | |||||||
\(644\) | 20.4853i | 0.807233i | ||||||||
\(645\) | 13.3137 | − | 9.41421i | 0.524227 | − | 0.370684i | ||||
\(646\) | −2.82843 | + | 12.0000i | −0.111283 | + | 0.472134i | ||||
\(647\) | − | 25.3137i | − | 0.995185i | −0.867411 | − | 0.497592i | \(-0.834218\pi\) | ||
0.867411 | − | 0.497592i | \(-0.165782\pi\) | |||||||
\(648\) | 7.00000 | + | 5.65685i | 0.274986 | + | 0.222222i | ||||
\(649\) | − | 18.5442i | − | 0.727922i | ||||||
\(650\) | 6.24264i | 0.244857i | ||||||||
\(651\) | −5.65685 | + | 4.00000i | −0.221710 | + | 0.156772i | ||||
\(652\) | −12.7279 | −0.498464 | ||||||||
\(653\) | − | 47.1127i | − | 1.84366i | −0.387592 | − | 0.921831i | \(-0.626693\pi\) | ||
0.387592 | − | 0.921831i | \(-0.373307\pi\) | |||||||
\(654\) | 19.3137 | − | 13.6569i | 0.755226 | − | 0.534025i | ||||
\(655\) | 19.0711 | 0.745168 | ||||||||
\(656\) | −3.07107 | −0.119905 | ||||||||
\(657\) | 14.4853 | − | 40.9706i | 0.565125 | − | 1.59841i | ||||
\(658\) | 30.1421i | 1.17506i | ||||||||
\(659\) | 3.17157 | 0.123547 | 0.0617735 | − | 0.998090i | \(-0.480324\pi\) | ||||
0.0617735 | + | 0.998090i | \(0.480324\pi\) | |||||||
\(660\) | −2.58579 | − | 3.65685i | −0.100652 | − | 0.142343i | ||||
\(661\) | 20.4853i | 0.796785i | 0.917215 | + | 0.398393i | \(0.130432\pi\) | ||||
−0.917215 | + | 0.398393i | \(0.869568\pi\) | |||||||
\(662\) | 16.9706i | 0.659580i | ||||||||
\(663\) | 17.6569 | + | 24.9706i | 0.685735 | + | 0.969776i | ||||
\(664\) | − | 7.17157i | − | 0.278311i | ||||||
\(665\) | 3.41421 | − | 14.4853i | 0.132398 | − | 0.561715i | ||||
\(666\) | 17.6569 | + | 6.24264i | 0.684189 | + | 0.241897i | ||||
\(667\) | 54.4264i | 2.10740i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.4558 | + | 18.0000i | −0.984180 | + | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 32.2843i | − | 1.24632i | ||||||
\(672\) | 3.41421 | + | 4.82843i | 0.131706 | + | 0.186261i | ||||
\(673\) | − | 21.6985i | − | 0.836415i | −0.908351 | − | 0.418208i | \(-0.862658\pi\) | ||
0.908351 | − | 0.418208i | \(-0.137342\pi\) | |||||||
\(674\) | 13.2132i | 0.508954i | ||||||||
\(675\) | −5.00000 | + | 1.41421i | −0.192450 | + | 0.0544331i | ||||
\(676\) | −25.9706 | −0.998868 | ||||||||
\(677\) | −41.5980 | −1.59874 | −0.799370 | − | 0.600839i | \(-0.794833\pi\) | ||||
−0.799370 | + | 0.600839i | \(0.794833\pi\) | |||||||
\(678\) | −7.17157 | − | 10.1421i | −0.275423 | − | 0.389506i | ||||
\(679\) | − | 32.1421i | − | 1.23350i | ||||||
\(680\) | 2.82843 | 0.108465 | ||||||||
\(681\) | −13.6569 | − | 19.3137i | −0.523332 | − | 0.740103i | ||||
\(682\) | 3.02944 | 0.116003 | ||||||||
\(683\) | 51.2548 | 1.96121 | 0.980606 | − | 0.195990i | \(-0.0627921\pi\) | ||||
0.980606 | + | 0.195990i | \(0.0627921\pi\) | |||||||
\(684\) | 7.07107 | − | 11.0000i | 0.270369 | − | 0.420596i | ||||
\(685\) | −2.48528 | −0.0949577 | ||||||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | 8.48528 | + | 12.0000i | 0.323734 | + | 0.457829i | ||||
\(688\) | 9.41421 | 0.358914 | ||||||||
\(689\) | 55.1127i | 2.09963i | ||||||||
\(690\) | −6.00000 | − | 8.48528i | −0.228416 | − | 0.323029i | ||||
\(691\) | 3.02944 | 0.115245 | 0.0576226 | − | 0.998338i | \(-0.481648\pi\) | ||||
0.0576226 | + | 0.998338i | \(0.481648\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 24.9706 | + | 8.82843i | 0.948553 | + | 0.335364i | ||||
\(694\) | 26.2843i | 0.997737i | ||||||||
\(695\) | − | 10.1421i | − | 0.384713i | ||||||
\(696\) | 9.07107 | + | 12.8284i | 0.343838 | + | 0.486260i | ||||
\(697\) | − | 8.68629i | − | 0.329017i | ||||||
\(698\) | −22.9706 | −0.869449 | ||||||||
\(699\) | 30.8284 | − | 21.7990i | 1.16604 | − | 0.824514i | ||||
\(700\) | −3.41421 | −0.129045 | ||||||||
\(701\) | 14.4853i | 0.547102i | 0.961858 | + | 0.273551i | \(0.0881982\pi\) | ||||
−0.961858 | + | 0.273551i | \(0.911802\pi\) | |||||||
\(702\) | −8.82843 | − | 31.2132i | −0.333208 | − | 1.17807i | ||||
\(703\) | 6.24264 | − | 26.4853i | 0.235446 | − | 0.998911i | ||||
\(704\) | − | 2.58579i | − | 0.0974555i | ||||||
\(705\) | −8.82843 | − | 12.4853i | −0.332498 | − | 0.470223i | ||||
\(706\) | 3.17157i | 0.119364i | ||||||||
\(707\) | 12.4853i | 0.469557i | ||||||||
\(708\) | −7.17157 | − | 10.1421i | −0.269524 | − | 0.381165i | ||||
\(709\) | 36.4853 | 1.37023 | 0.685117 | − | 0.728433i | \(-0.259751\pi\) | ||||
0.685117 | + | 0.728433i | \(0.259751\pi\) | |||||||
\(710\) | 2.82843i | 0.106149i | ||||||||
\(711\) | −26.3431 | − | 9.31371i | −0.987945 | − | 0.349291i | ||||
\(712\) | 13.4142 | 0.502719 | ||||||||
\(713\) | 7.02944 | 0.263254 | ||||||||
\(714\) | −13.6569 | + | 9.65685i | −0.511095 | + | 0.361399i | ||||
\(715\) | 16.1421i | 0.603682i | ||||||||
\(716\) | −17.7990 | −0.665179 | ||||||||
\(717\) | 28.1421 | − | 19.8995i | 1.05099 | − | 0.743160i | ||||
\(718\) | 16.5858i | 0.618976i | ||||||||
\(719\) | 5.27208i | 0.196615i | 0.995156 | + | 0.0983077i | \(0.0313429\pi\) | ||||
−0.995156 | + | 0.0983077i | \(0.968657\pi\) | |||||||
\(720\) | −2.82843 | − | 1.00000i | −0.105409 | − | 0.0372678i | ||||
\(721\) | 53.4558i | 1.99080i | ||||||||
\(722\) | −17.0000 | − | 8.48528i | −0.632674 | − | 0.315789i | ||||
\(723\) | −12.0000 | + | 8.48528i | −0.446285 | + | 0.315571i | ||||
\(724\) | 5.17157i | 0.192200i | ||||||||
\(725\) | −9.07107 | −0.336891 | ||||||||
\(726\) | 4.31371 | + | 6.10051i | 0.160097 | + | 0.226411i | ||||
\(727\) | −5.55635 | −0.206074 | −0.103037 | − | 0.994678i | \(-0.532856\pi\) | ||||
−0.103037 | + | 0.994678i | \(0.532856\pi\) | |||||||
\(728\) | − | 21.3137i | − | 0.789939i | ||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 14.4853i | 0.536124i | ||||||||
\(731\) | 26.6274i | 0.984851i | ||||||||
\(732\) | −12.4853 | − | 17.6569i | −0.461469 | − | 0.652616i | ||||
\(733\) | −32.4853 | −1.19987 | −0.599936 | − | 0.800048i | \(-0.704807\pi\) | ||||
−0.599936 | + | 0.800048i | \(0.704807\pi\) | |||||||
\(734\) | 5.75736 | 0.212508 | ||||||||
\(735\) | 6.58579 | − | 4.65685i | 0.242920 | − | 0.171771i | ||||
\(736\) | − | 6.00000i | − | 0.221163i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.07107 | + | 8.68629i | −0.113048 | + | 0.319747i | ||||
\(739\) | −3.51472 | −0.129291 | −0.0646455 | − | 0.997908i | \(-0.520592\pi\) | ||||
−0.0646455 | + | 0.997908i | \(0.520592\pi\) | |||||||
\(740\) | −6.24264 | −0.229484 | ||||||||
\(741\) | −43.6985 | + | 17.6569i | −1.60530 | + | 0.648641i | ||||
\(742\) | −30.1421 | −1.10655 | ||||||||
\(743\) | 48.8284 | 1.79134 | 0.895671 | − | 0.444718i | \(-0.146696\pi\) | ||||
0.895671 | + | 0.444718i | \(0.146696\pi\) | |||||||
\(744\) | 1.65685 | − | 1.17157i | 0.0607432 | − | 0.0429519i | ||||
\(745\) | 2.48528 | 0.0910537 | ||||||||
\(746\) | 34.0416i | 1.24635i | ||||||||
\(747\) | −20.2843 | − | 7.17157i | −0.742163 | − | 0.262394i | ||||
\(748\) | 7.31371 | 0.267416 | ||||||||
\(749\) | 26.1421 | 0.955213 | ||||||||
\(750\) | 1.41421 | − | 1.00000i | 0.0516398 | − | 0.0365148i | ||||
\(751\) | 31.5147i | 1.14999i | 0.818157 | + | 0.574994i | \(0.194996\pi\) | ||||
−0.818157 | + | 0.574994i | \(0.805004\pi\) | |||||||
\(752\) | − | 8.82843i | − | 0.321940i | ||||||
\(753\) | −26.9706 | + | 19.0711i | −0.982862 | + | 0.694988i | ||||
\(754\) | − | 56.6274i | − | 2.06225i | ||||||
\(755\) | −3.51472 | −0.127914 | ||||||||
\(756\) | 17.0711 | − | 4.82843i | 0.620869 | − | 0.175608i | ||||
\(757\) | 38.3431 | 1.39361 | 0.696803 | − | 0.717263i | \(-0.254605\pi\) | ||||
0.696803 | + | 0.717263i | \(0.254605\pi\) | |||||||
\(758\) | − | 8.00000i | − | 0.290573i | ||||||
\(759\) | −15.5147 | − | 21.9411i | −0.563149 | − | 0.796412i | ||||
\(760\) | −1.00000 | + | 4.24264i | −0.0362738 | + | 0.153897i | ||||
\(761\) | 6.82843i | 0.247530i | 0.992312 | + | 0.123765i | \(0.0394969\pi\) | ||||
−0.992312 | + | 0.123765i | \(0.960503\pi\) | |||||||
\(762\) | 10.1421 | − | 7.17157i | 0.367411 | − | 0.259799i | ||||
\(763\) | − | 46.6274i | − | 1.68803i | ||||||
\(764\) | − | 1.75736i | − | 0.0635790i | ||||||
\(765\) | 2.82843 | − | 8.00000i | 0.102262 | − | 0.289241i | ||||
\(766\) | 3.85786 | 0.139390 | ||||||||
\(767\) | 44.7696i | 1.61653i | ||||||||
\(768\) | −1.00000 | − | 1.41421i | −0.0360844 | − | 0.0510310i | ||||
\(769\) | 9.31371 | 0.335861 | 0.167930 | − | 0.985799i | \(-0.446292\pi\) | ||||
0.167930 | + | 0.985799i | \(0.446292\pi\) | |||||||
\(770\) | −8.82843 | −0.318154 | ||||||||
\(771\) | −0.142136 | − | 0.201010i | −0.00511889 | − | 0.00723920i | ||||
\(772\) | − | 11.5563i | − | 0.415922i | ||||||
\(773\) | −11.6569 | −0.419268 | −0.209634 | − | 0.977780i | \(-0.567227\pi\) | ||||
−0.209634 | + | 0.977780i | \(0.567227\pi\) | |||||||
\(774\) | 9.41421 | − | 26.6274i | 0.338387 | − | 0.957103i | ||||
\(775\) | 1.17157i | 0.0420841i | ||||||||
\(776\) | 9.41421i | 0.337951i | ||||||||
\(777\) | 30.1421 | − | 21.3137i | 1.08134 | − | 0.764625i | ||||
\(778\) | − | 31.6569i | − | 1.13495i | ||||||
\(779\) | 13.0294 | + | 3.07107i | 0.466828 | + | 0.110032i | ||||
\(780\) | 6.24264 | + | 8.82843i | 0.223522 | + | 0.316108i | ||||
\(781\) | 7.31371i | 0.261705i | ||||||||
\(782\) | 16.9706 | 0.606866 | ||||||||
\(783\) | 45.3553 | − | 12.8284i | 1.62087 | − | 0.458451i | ||||
\(784\) | 4.65685 | 0.166316 | ||||||||
\(785\) | 15.7990i | 0.563890i | ||||||||
\(786\) | 26.9706 | − | 19.0711i | 0.962008 | − | 0.680242i | ||||
\(787\) | 11.0294i | 0.393157i | 0.980488 | + | 0.196578i | \(0.0629831\pi\) | ||||
−0.980488 | + | 0.196578i | \(0.937017\pi\) | |||||||
\(788\) | 10.1421i | 0.361299i | ||||||||
\(789\) | 23.7990 | − | 16.8284i | 0.847266 | − | 0.599108i | ||||
\(790\) | 9.31371 | 0.331367 | ||||||||
\(791\) | −24.4853 | −0.870596 | ||||||||
\(792\) | −7.31371 | − | 2.58579i | −0.259881 | − | 0.0918819i | ||||
\(793\) | 77.9411i | 2.76777i | ||||||||
\(794\) | 16.9706 | 0.602263 | ||||||||
\(795\) | 12.4853 | − | 8.82843i | 0.442807 | − | 0.313112i | ||||
\(796\) | 16.9706 | 0.601506 | ||||||||
\(797\) | 35.6569 | 1.26303 | 0.631515 | − | 0.775363i | \(-0.282433\pi\) | ||||
0.631515 | + | 0.775363i | \(0.282433\pi\) | |||||||
\(798\) | −9.65685 | − | 23.8995i | −0.341849 | − | 0.846033i | ||||
\(799\) | 24.9706 | 0.883395 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 13.4142 | − | 37.9411i | 0.473968 | − | 1.34058i | ||||
\(802\) | 18.3848 | 0.649189 | ||||||||
\(803\) | 37.4558i | 1.32179i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.4853 | −0.722011 | ||||||||
\(806\) | −7.31371 | −0.257614 | ||||||||
\(807\) | 12.3848 | + | 17.5147i | 0.435965 | + | 0.616547i | ||||
\(808\) | − | 3.65685i | − | 0.128648i | ||||||
\(809\) | − | 12.6863i | − | 0.446026i | −0.974815 | − | 0.223013i | \(-0.928411\pi\) | ||
0.974815 | − | 0.223013i | \(-0.0715893\pi\) | |||||||
\(810\) | −5.65685 | + | 7.00000i | −0.198762 | + | 0.245955i | ||||
\(811\) | − | 46.9706i | − | 1.64936i | −0.565600 | − | 0.824680i | \(-0.691355\pi\) | ||
0.565600 | − | 0.824680i | \(-0.308645\pi\) | |||||||
\(812\) | 30.9706 | 1.08685 | ||||||||
\(813\) | −4.97056 | − | 7.02944i | −0.174325 | − | 0.246533i | ||||
\(814\) | −16.1421 | −0.565782 | ||||||||
\(815\) | − | 12.7279i | − | 0.445840i | ||||||
\(816\) | 4.00000 | − | 2.82843i | 0.140028 | − | 0.0990148i | ||||
\(817\) | −39.9411 | − | 9.41421i | −1.39736 | − | 0.329362i | ||||
\(818\) | 12.4853i | 0.436538i | ||||||||
\(819\) | −60.2843 | − | 21.3137i | −2.10650 | − | 0.744761i | ||||
\(820\) | − | 3.07107i | − | 0.107246i | ||||||
\(821\) | − | 0.343146i | − | 0.0119759i | −0.999982 | − | 0.00598793i | \(-0.998094\pi\) | ||
0.999982 | − | 0.00598793i | \(-0.00190603\pi\) | |||||||
\(822\) | −3.51472 | + | 2.48528i | −0.122590 | + | 0.0866841i | ||||
\(823\) | 9.75736 | 0.340120 | 0.170060 | − | 0.985434i | \(-0.445604\pi\) | ||||
0.170060 | + | 0.985434i | \(0.445604\pi\) | |||||||
\(824\) | − | 15.6569i | − | 0.545432i | ||||||
\(825\) | 3.65685 | − | 2.58579i | 0.127315 | − | 0.0900255i | ||||
\(826\) | −24.4853 | −0.851952 | ||||||||
\(827\) | −20.2843 | −0.705353 | −0.352677 | − | 0.935745i | \(-0.614728\pi\) | ||||
−0.352677 | + | 0.935745i | \(0.614728\pi\) | |||||||
\(828\) | −16.9706 | − | 6.00000i | −0.589768 | − | 0.208514i | ||||
\(829\) | 43.5980i | 1.51422i | 0.653287 | + | 0.757110i | \(0.273389\pi\) | ||||
−0.653287 | + | 0.757110i | \(0.726611\pi\) | |||||||
\(830\) | 7.17157 | 0.248929 | ||||||||
\(831\) | 8.97056 | + | 12.6863i | 0.311185 | + | 0.440083i | ||||
\(832\) | 6.24264i | 0.216425i | ||||||||
\(833\) | 13.1716i | 0.456368i | ||||||||
\(834\) | −10.1421 | − | 14.3431i | −0.351193 | − | 0.496663i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.58579 | + | 10.9706i | −0.0894313 | + | 0.379425i | ||||
\(837\) | −1.65685 | − | 5.85786i | −0.0572693 | − | 0.202477i | ||||
\(838\) | 30.3848i | 1.04962i | ||||||||
\(839\) | 2.82843 | 0.0976481 | 0.0488241 | − | 0.998807i | \(-0.484453\pi\) | ||||
0.0488241 | + | 0.998807i | \(0.484453\pi\) | |||||||
\(840\) | −4.82843 | + | 3.41421i | −0.166597 | + | 0.117802i | ||||
\(841\) | 53.2843 | 1.83739 | ||||||||
\(842\) | 32.2843i | 1.11259i | ||||||||
\(843\) | −15.0711 | − | 21.3137i | −0.519075 | − | 0.734083i | ||||
\(844\) | − | 2.00000i | − | 0.0688428i | ||||||
\(845\) | − | 25.9706i | − | 0.893415i | ||||||
\(846\) | −24.9706 | − | 8.82843i | −0.858506 | − | 0.303528i | ||||
\(847\) | 14.7279 | 0.506057 | ||||||||
\(848\) | 8.82843 | 0.303169 | ||||||||
\(849\) | 12.7279 | + | 18.0000i | 0.436821 | + | 0.617758i | ||||
\(850\) | 2.82843i | 0.0970143i | ||||||||
\(851\) | −37.4558 | −1.28397 | ||||||||
\(852\) | 2.82843 | + | 4.00000i | 0.0969003 | + | 0.137038i | ||||
\(853\) | −12.0000 | −0.410872 | −0.205436 | − | 0.978671i | \(-0.565861\pi\) | ||||
−0.205436 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(854\) | −42.6274 | −1.45868 | ||||||||
\(855\) | 11.0000 | + | 7.07107i | 0.376192 | + | 0.241825i | ||||
\(856\) | −7.65685 | −0.261706 | ||||||||
\(857\) | 0.828427 | 0.0282985 | 0.0141493 | − | 0.999900i | \(-0.495496\pi\) | ||||
0.0141493 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(858\) | 16.1421 | + | 22.8284i | 0.551083 | + | 0.779350i | ||||
\(859\) | 44.9706 | 1.53438 | 0.767188 | − | 0.641422i | \(-0.221655\pi\) | ||||
0.767188 | + | 0.641422i | \(0.221655\pi\) | |||||||
\(860\) | 9.41421i | 0.321022i | ||||||||
\(861\) | 10.4853 | + | 14.8284i | 0.357337 | + | 0.505351i | ||||
\(862\) | 3.31371 | 0.112865 | ||||||||
\(863\) | −51.1716 | −1.74190 | −0.870950 | − | 0.491371i | \(-0.836496\pi\) | ||||
−0.870950 | + | 0.491371i | \(0.836496\pi\) | |||||||
\(864\) | −5.00000 | + | 1.41421i | −0.170103 | + | 0.0481125i | ||||
\(865\) | − | 6.00000i | − | 0.204006i | ||||||
\(866\) | − | 22.3848i | − | 0.760666i | ||||||
\(867\) | −9.00000 | − | 12.7279i | −0.305656 | − | 0.432263i | ||||
\(868\) | − | 4.00000i | − | 0.135769i | ||||||
\(869\) | 24.0833 | 0.816969 | ||||||||
\(870\) | −12.8284 | + | 9.07107i | −0.434924 | + | 0.307538i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 13.6569i | 0.462479i | ||||||||
\(873\) | 26.6274 | + | 9.41421i | 0.901202 | + | 0.318623i | ||||
\(874\) | −6.00000 | + | 25.4558i | −0.202953 | + | 0.861057i | ||||
\(875\) | − | 3.41421i | − | 0.115421i | ||||||
\(876\) | 14.4853 | + | 20.4853i | 0.489412 | + | 0.692134i | ||||
\(877\) | 12.8701i | 0.434591i | 0.976106 | + | 0.217295i | \(0.0697235\pi\) | ||||
−0.976106 | + | 0.217295i | \(0.930276\pi\) | |||||||
\(878\) | 27.9411i | 0.942967i | ||||||||
\(879\) | 8.82843 | + | 12.4853i | 0.297775 | + | 0.421118i | ||||
\(880\) | 2.58579 | 0.0871668 | ||||||||
\(881\) | 28.2843i | 0.952921i | 0.879196 | + | 0.476461i | \(0.158081\pi\) | ||||
−0.879196 | + | 0.476461i | \(0.841919\pi\) | |||||||
\(882\) | 4.65685 | − | 13.1716i | 0.156804 | − | 0.443510i | ||||
\(883\) | 18.5858 | 0.625462 | 0.312731 | − | 0.949842i | \(-0.398756\pi\) | ||||
0.312731 | + | 0.949842i | \(0.398756\pi\) | |||||||
\(884\) | −17.6569 | −0.593864 | ||||||||
\(885\) | 10.1421 | − | 7.17157i | 0.340924 | − | 0.241070i | ||||
\(886\) | 18.0000i | 0.604722i | ||||||||
\(887\) | −43.1716 | −1.44956 | −0.724780 | − | 0.688981i | \(-0.758059\pi\) | ||||
−0.724780 | + | 0.688981i | \(0.758059\pi\) | |||||||
\(888\) | −8.82843 | + | 6.24264i | −0.296263 | + | 0.209489i | ||||
\(889\) | − | 24.4853i | − | 0.821210i | ||||||
\(890\) | 13.4142i | 0.449645i | ||||||||
\(891\) | −14.6274 | + | 18.1005i | −0.490037 | + | 0.606390i | ||||
\(892\) | − | 18.0000i | − | 0.602685i | ||||||
\(893\) | −8.82843 | + | 37.4558i | −0.295432 | + | 1.25341i | ||||
\(894\) | 3.51472 | − | 2.48528i | 0.117550 | − | 0.0831202i | ||||
\(895\) | − | 17.7990i | − | 0.594955i | ||||||
\(896\) | −3.41421 | −0.114061 | ||||||||
\(897\) | 37.4558 | + | 52.9706i | 1.25061 | + | 1.76864i | ||||
\(898\) | −7.75736 | −0.258866 | ||||||||
\(899\) | − | 10.6274i | − | 0.354444i | ||||||
\(900\) | 1.00000 | − | 2.82843i | 0.0333333 | − | 0.0942809i | ||||
\(901\) | 24.9706i | 0.831890i | ||||||||
\(902\) | − | 7.94113i | − | 0.264411i | ||||||
\(903\) | −32.1421 | − | 45.4558i | −1.06962 | − | 1.51268i | ||||
\(904\) | 7.17157 | 0.238523 | ||||||||
\(905\) | −5.17157 | −0.171909 | ||||||||
\(906\) | −4.97056 | + | 3.51472i | −0.165136 | + | 0.116769i | ||||
\(907\) | − | 20.9706i | − | 0.696316i | −0.937436 | − | 0.348158i | \(-0.886807\pi\) | ||
0.937436 | − | 0.348158i | \(-0.113193\pi\) | |||||||
\(908\) | 13.6569 | 0.453219 | ||||||||
\(909\) | −10.3431 | − | 3.65685i | −0.343060 | − | 0.121290i | ||||
\(910\) | 21.3137 | 0.706543 | ||||||||
\(911\) | −0.686292 | −0.0227379 | −0.0113689 | − | 0.999935i | \(-0.503619\pi\) | ||||
−0.0113689 | + | 0.999935i | \(0.503619\pi\) | |||||||
\(912\) | 2.82843 | + | 7.00000i | 0.0936586 | + | 0.231793i | ||||
\(913\) | 18.5442 | 0.613722 | ||||||||
\(914\) | −4.82843 | −0.159710 | ||||||||
\(915\) | 17.6569 | − | 12.4853i | 0.583718 | − | 0.412751i | ||||
\(916\) | −8.48528 | −0.280362 | ||||||||
\(917\) | − | 65.1127i | − | 2.15021i | ||||||
\(918\) | −4.00000 | − | 14.1421i | −0.132020 | − | 0.466760i | ||||
\(919\) | −13.4558 | −0.443867 | −0.221934 | − | 0.975062i | \(-0.571237\pi\) | ||||
−0.221934 | + | 0.975062i | \(0.571237\pi\) | |||||||
\(920\) | 6.00000 | 0.197814 | ||||||||
\(921\) | 14.3431 | − | 10.1421i | 0.472623 | − | 0.334195i | ||||
\(922\) | 0.142136i | 0.00468099i | ||||||||
\(923\) | − | 17.6569i | − | 0.581182i | ||||||
\(924\) | −12.4853 | + | 8.82843i | −0.410736 | + | 0.290434i | ||||
\(925\) | − | 6.24264i | − | 0.205257i | ||||||
\(926\) | 23.2132 | 0.762833 | ||||||||
\(927\) | −44.2843 | − | 15.6569i | −1.45449 | − | 0.514239i | ||||
\(928\) | −9.07107 | −0.297772 | ||||||||
\(929\) | − | 38.8284i | − | 1.27392i | −0.770897 | − | 0.636960i | \(-0.780192\pi\) | ||
0.770897 | − | 0.636960i | \(-0.219808\pi\) | |||||||
\(930\) | 1.17157 | + | 1.65685i | 0.0384174 | + | 0.0543304i | ||||
\(931\) | −19.7574 | − | 4.65685i | −0.647521 | − | 0.152622i | ||||
\(932\) | 21.7990i | 0.714050i | ||||||||
\(933\) | 12.8284 | − | 9.07107i | 0.419984 | − | 0.296973i | ||||
\(934\) | 13.7990i | 0.451517i | ||||||||
\(935\) | 7.31371i | 0.239184i | ||||||||
\(936\) | 17.6569 | + | 6.24264i | 0.577132 | + | 0.204047i | ||||
\(937\) | −38.9706 | −1.27311 | −0.636556 | − | 0.771230i | \(-0.719642\pi\) | ||||
−0.636556 | + | 0.771230i | \(0.719642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.1716 | + | 15.7990i | 0.364571 | + | 0.515581i | ||||
\(940\) | 8.82843 | 0.287952 | ||||||||
\(941\) | −32.8701 | −1.07153 | −0.535767 | − | 0.844366i | \(-0.679977\pi\) | ||||
−0.535767 | + | 0.844366i | \(0.679977\pi\) | |||||||
\(942\) | 15.7990 | + | 22.3431i | 0.514759 | + | 0.727979i | ||||
\(943\) | − | 18.4264i | − | 0.600046i | ||||||
\(944\) | 7.17157 | 0.233415 | ||||||||
\(945\) | 4.82843 | + | 17.0711i | 0.157069 | + | 0.555322i | ||||
\(946\) | 24.3431i | 0.791464i | ||||||||
\(947\) | − | 25.3137i | − | 0.822585i | −0.911503 | − | 0.411292i | \(-0.865077\pi\) | ||
0.911503 | − | 0.411292i | \(-0.134923\pi\) | |||||||
\(948\) | 13.1716 | − | 9.31371i | 0.427793 | − | 0.302495i | ||||
\(949\) | − | 90.4264i | − | 2.93537i | ||||||
\(950\) | −4.24264 | − | 1.00000i | −0.137649 | − | 0.0324443i | ||||
\(951\) | −11.6569 | − | 16.4853i | −0.377999 | − | 0.534572i | ||||
\(952\) | − | 9.65685i | − | 0.312980i | ||||||
\(953\) | −51.9411 | −1.68254 | −0.841269 | − | 0.540617i | \(-0.818191\pi\) | ||||
−0.841269 | + | 0.540617i | \(0.818191\pi\) | |||||||
\(954\) | 8.82843 | − | 24.9706i | 0.285831 | − | 0.808452i | ||||
\(955\) | 1.75736 | 0.0568668 | ||||||||
\(956\) | 19.8995i | 0.643596i | ||||||||
\(957\) | −33.1716 | + | 23.4558i | −1.07228 | + | 0.758220i | ||||
\(958\) | − | 0.585786i | − | 0.0189259i | ||||||
\(959\) | 8.48528i | 0.274004i | ||||||||
\(960\) | 1.41421 | − | 1.00000i | 0.0456435 | − | 0.0322749i | ||||
\(961\) | 29.6274 | 0.955723 | ||||||||
\(962\) | 38.9706 | 1.25646 | ||||||||
\(963\) | −7.65685 | + | 21.6569i | −0.246739 | + | 0.697882i | ||||
\(964\) | − | 8.48528i | − | 0.273293i | ||||||
\(965\) | 11.5563 | 0.372012 | ||||||||
\(966\) | −28.9706 | + | 20.4853i | −0.932113 | + | 0.659103i | ||||
\(967\) | 41.7574 | 1.34283 | 0.671413 | − | 0.741083i | \(-0.265688\pi\) | ||||
0.671413 | + | 0.741083i | \(0.265688\pi\) | |||||||
\(968\) | −4.31371 | −0.138648 | ||||||||
\(969\) | −19.7990 | + | 8.00000i | −0.636035 | + | 0.256997i | ||||
\(970\) | −9.41421 | −0.302272 | ||||||||
\(971\) | 1.11270 | 0.0357082 | 0.0178541 | − | 0.999841i | \(-0.494317\pi\) | ||||
0.0178541 | + | 0.999841i | \(0.494317\pi\) | |||||||
\(972\) | −1.00000 | + | 15.5563i | −0.0320750 | + | 0.498970i | ||||
\(973\) | −34.6274 | −1.11010 | ||||||||
\(974\) | − | 7.85786i | − | 0.251782i | ||||||
\(975\) | −8.82843 | + | 6.24264i | −0.282736 | + | 0.199925i | ||||
\(976\) | 12.4853 | 0.399644 | ||||||||
\(977\) | 46.2843 | 1.48077 | 0.740383 | − | 0.672186i | \(-0.234644\pi\) | ||||
0.740383 | + | 0.672186i | \(0.234644\pi\) | |||||||
\(978\) | −12.7279 | − | 18.0000i | −0.406994 | − | 0.575577i | ||||
\(979\) | 34.6863i | 1.10858i | ||||||||
\(980\) | 4.65685i | 0.148758i | ||||||||
\(981\) | 38.6274 | + | 13.6569i | 1.23328 | + | 0.436030i | ||||
\(982\) | − | 12.4437i | − | 0.397093i | ||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −3.07107 | − | 4.34315i | −0.0979021 | − | 0.138454i | ||||
\(985\) | −10.1421 | −0.323155 | ||||||||
\(986\) | − | 25.6569i | − | 0.817081i | ||||||
\(987\) | −42.6274 | + | 30.1421i | −1.35685 | + | 0.959435i | ||||
\(988\) | 6.24264 | − | 26.4853i | 0.198605 | − | 0.842609i | ||||
\(989\) | 56.4853i | 1.79613i | ||||||||
\(990\) | 2.58579 | − | 7.31371i | 0.0821817 | − | 0.232445i | ||||
\(991\) | − | 30.9706i | − | 0.983812i | −0.870648 | − | 0.491906i | \(-0.836300\pi\) | ||
0.870648 | − | 0.491906i | \(-0.163700\pi\) | |||||||
\(992\) | 1.17157i | 0.0371975i | ||||||||
\(993\) | −24.0000 | + | 16.9706i | −0.761617 | + | 0.538545i | ||||
\(994\) | 9.65685 | 0.306297 | ||||||||
\(995\) | 16.9706i | 0.538003i | ||||||||
\(996\) | 10.1421 | − | 7.17157i | 0.321366 | − | 0.227240i | ||||
\(997\) | −16.4853 | −0.522094 | −0.261047 | − | 0.965326i | \(-0.584068\pi\) | ||||
−0.261047 | + | 0.965326i | \(0.584068\pi\) | |||||||
\(998\) | 14.3431 | 0.454024 | ||||||||
\(999\) | 8.82843 | + | 31.2132i | 0.279319 | + | 0.987542i |
(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 | 570.2.f.a.341.2 | ✓ | 4 | |
3.2 | odd | 2 | 570.2.f.b.341.1 | yes | 4 | ||
19.18 | odd | 2 | 570.2.f.b.341.4 | yes | 4 | ||
57.56 | even | 2 | inner | 570.2.f.a.341.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.f.a.341.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
570.2.f.a.341.3 | yes | 4 | 57.56 | even | 2 | inner | |
570.2.f.b.341.1 | yes | 4 | 3.2 | odd | 2 | ||
570.2.f.b.341.4 | yes | 4 | 19.18 | odd | 2 |