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 | 341.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.341 |
Dual form | 570.2.f.a.341.4 |
$q$-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 | ||||
\(7\) | 0.585786 | 0.221406 | 0.110703 | − | 0.993854i | \(-0.464690\pi\) | ||||
0.110703 | + | 0.993854i | \(0.464690\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | 5.41421i | 1.63245i | 0.577736 | + | 0.816223i | \(0.303936\pi\) | ||||
−0.577736 | + | 0.816223i | \(0.696064\pi\) | |||||||
\(12\) | −1.00000 | − | 1.41421i | −0.288675 | − | 0.408248i | ||||
\(13\) | 2.24264i | 0.621997i | 0.950410 | + | 0.310998i | \(0.100663\pi\) | ||||
−0.950410 | + | 0.310998i | \(0.899337\pi\) | |||||||
\(14\) | −0.585786 | −0.156558 | ||||||||
\(15\) | −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 | ||||||
\(21\) | −0.585786 | − | 0.828427i | −0.127829 | − | 0.180778i | ||||
\(22\) | − | 5.41421i | − | 1.15431i | ||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 1.00000 | + | 1.41421i | 0.204124 | + | 0.288675i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 2.24264i | − | 0.439818i | ||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 0.585786 | 0.110703 | ||||||||
\(29\) | −5.07107 | −0.941674 | −0.470837 | − | 0.882220i | \(-0.656048\pi\) | ||||
−0.470837 | + | 0.882220i | \(0.656048\pi\) | |||||||
\(30\) | 1.41421 | − | 1.00000i | 0.258199 | − | 0.182574i | ||||
\(31\) | 6.82843i | 1.22642i | 0.789919 | + | 0.613211i | \(0.210122\pi\) | ||||
−0.789919 | + | 0.613211i | \(0.789878\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.65685 | − | 5.41421i | 1.33289 | − | 0.942494i | ||||
\(34\) | − | 2.82843i | − | 0.485071i | ||||||
\(35\) | − | 0.585786i | − | 0.0990160i | ||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | 2.24264i | 0.368688i | 0.982862 | + | 0.184344i | \(0.0590160\pi\) | ||||
−0.982862 | + | 0.184344i | \(0.940984\pi\) | |||||||
\(38\) | −4.24264 | − | 1.00000i | −0.688247 | − | 0.162221i | ||||
\(39\) | 3.17157 | − | 2.24264i | 0.507858 | − | 0.359110i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 11.0711 | 1.72901 | 0.864505 | − | 0.502624i | \(-0.167632\pi\) | ||||
0.864505 | + | 0.502624i | \(0.167632\pi\) | |||||||
\(42\) | 0.585786 | + | 0.828427i | 0.0903888 | + | 0.127829i | ||||
\(43\) | 6.58579 | 1.00432 | 0.502162 | − | 0.864774i | \(-0.332538\pi\) | ||||
0.502162 | + | 0.864774i | \(0.332538\pi\) | |||||||
\(44\) | 5.41421i | 0.816223i | ||||||||
\(45\) | 2.82843 | + | 1.00000i | 0.421637 | + | 0.149071i | ||||
\(46\) | 6.00000i | 0.884652i | ||||||||
\(47\) | 3.17157i | 0.462621i | 0.972880 | + | 0.231311i | \(0.0743014\pi\) | ||||
−0.972880 | + | 0.231311i | \(0.925699\pi\) | |||||||
\(48\) | −1.00000 | − | 1.41421i | −0.144338 | − | 0.204124i | ||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.00000 | − | 2.82843i | 0.560112 | − | 0.396059i | ||||
\(52\) | 2.24264i | 0.310998i | ||||||||
\(53\) | 3.17157 | 0.435649 | 0.217825 | − | 0.975988i | \(-0.430104\pi\) | ||||
0.217825 | + | 0.975988i | \(0.430104\pi\) | |||||||
\(54\) | −5.00000 | + | 1.41421i | −0.680414 | + | 0.192450i | ||||
\(55\) | 5.41421 | 0.730052 | ||||||||
\(56\) | −0.585786 | −0.0782790 | ||||||||
\(57\) | −2.82843 | − | 7.00000i | −0.374634 | − | 0.927173i | ||||
\(58\) | 5.07107 | 0.665864 | ||||||||
\(59\) | 12.8284 | 1.67012 | 0.835059 | − | 0.550160i | \(-0.185433\pi\) | ||||
0.835059 | + | 0.550160i | \(0.185433\pi\) | |||||||
\(60\) | −1.41421 | + | 1.00000i | −0.182574 | + | 0.129099i | ||||
\(61\) | −4.48528 | −0.574281 | −0.287141 | − | 0.957888i | \(-0.592705\pi\) | ||||
−0.287141 | + | 0.957888i | \(0.592705\pi\) | |||||||
\(62\) | − | 6.82843i | − | 0.867211i | ||||||
\(63\) | −0.585786 | + | 1.65685i | −0.0738022 | + | 0.208744i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.24264 | 0.278165 | ||||||||
\(66\) | −7.65685 | + | 5.41421i | −0.942494 | + | 0.666444i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 2.82843i | 0.342997i | ||||||||
\(69\) | −8.48528 | + | 6.00000i | −1.02151 | + | 0.722315i | ||||
\(70\) | 0.585786i | 0.0700149i | ||||||||
\(71\) | 2.82843 | 0.335673 | 0.167836 | − | 0.985815i | \(-0.446322\pi\) | ||||
0.167836 | + | 0.985815i | \(0.446322\pi\) | |||||||
\(72\) | 1.00000 | − | 2.82843i | 0.117851 | − | 0.333333i | ||||
\(73\) | 2.48528 | 0.290880 | 0.145440 | − | 0.989367i | \(-0.453540\pi\) | ||||
0.145440 | + | 0.989367i | \(0.453540\pi\) | |||||||
\(74\) | − | 2.24264i | − | 0.260702i | ||||||
\(75\) | 1.00000 | + | 1.41421i | 0.115470 | + | 0.163299i | ||||
\(76\) | 4.24264 | + | 1.00000i | 0.486664 | + | 0.114708i | ||||
\(77\) | 3.17157i | 0.361434i | ||||||||
\(78\) | −3.17157 | + | 2.24264i | −0.359110 | + | 0.253929i | ||||
\(79\) | 13.3137i | 1.49791i | 0.662621 | + | 0.748955i | \(0.269444\pi\) | ||||
−0.662621 | + | 0.748955i | \(0.730556\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | −11.0711 | −1.22259 | ||||||||
\(83\) | − | 12.8284i | − | 1.40810i | −0.710149 | − | 0.704051i | \(-0.751372\pi\) | ||
0.710149 | − | 0.704051i | \(-0.248628\pi\) | |||||||
\(84\) | −0.585786 | − | 0.828427i | −0.0639145 | − | 0.0903888i | ||||
\(85\) | 2.82843 | 0.306786 | ||||||||
\(86\) | −6.58579 | −0.710164 | ||||||||
\(87\) | 5.07107 | + | 7.17157i | 0.543676 | + | 0.768873i | ||||
\(88\) | − | 5.41421i | − | 0.577157i | ||||||
\(89\) | −10.5858 | −1.12209 | −0.561046 | − | 0.827785i | \(-0.689601\pi\) | ||||
−0.561046 | + | 0.827785i | \(0.689601\pi\) | |||||||
\(90\) | −2.82843 | − | 1.00000i | −0.298142 | − | 0.105409i | ||||
\(91\) | 1.31371i | 0.137714i | ||||||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | 9.65685 | − | 6.82843i | 1.00137 | − | 0.708075i | ||||
\(94\) | − | 3.17157i | − | 0.327123i | ||||||
\(95\) | 1.00000 | − | 4.24264i | 0.102598 | − | 0.435286i | ||||
\(96\) | 1.00000 | + | 1.41421i | 0.102062 | + | 0.144338i | ||||
\(97\) | 6.58579i | 0.668685i | 0.942452 | + | 0.334343i | \(0.108514\pi\) | ||||
−0.942452 | + | 0.334343i | \(0.891486\pi\) | |||||||
\(98\) | 6.65685 | 0.672444 | ||||||||
\(99\) | −15.3137 | − | 5.41421i | −1.53909 | − | 0.544149i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 7.65685i | 0.761885i | 0.924599 | + | 0.380943i | \(0.124401\pi\) | ||||
−0.924599 | + | 0.380943i | \(0.875599\pi\) | |||||||
\(102\) | −4.00000 | + | 2.82843i | −0.396059 | + | 0.280056i | ||||
\(103\) | − | 4.34315i | − | 0.427943i | −0.976840 | − | 0.213971i | \(-0.931360\pi\) | ||
0.976840 | − | 0.213971i | \(-0.0686399\pi\) | |||||||
\(104\) | − | 2.24264i | − | 0.219909i | ||||||
\(105\) | −0.828427 | + | 0.585786i | −0.0808462 | + | 0.0571669i | ||||
\(106\) | −3.17157 | −0.308050 | ||||||||
\(107\) | −3.65685 | −0.353521 | −0.176761 | − | 0.984254i | \(-0.556562\pi\) | ||||
−0.176761 | + | 0.984254i | \(0.556562\pi\) | |||||||
\(108\) | 5.00000 | − | 1.41421i | 0.481125 | − | 0.136083i | ||||
\(109\) | 2.34315i | 0.224433i | 0.993684 | + | 0.112216i | \(0.0357950\pi\) | ||||
−0.993684 | + | 0.112216i | \(0.964205\pi\) | |||||||
\(110\) | −5.41421 | −0.516225 | ||||||||
\(111\) | 3.17157 | − | 2.24264i | 0.301032 | − | 0.212862i | ||||
\(112\) | 0.585786 | 0.0553516 | ||||||||
\(113\) | −12.8284 | −1.20680 | −0.603398 | − | 0.797440i | \(-0.706187\pi\) | ||||
−0.603398 | + | 0.797440i | \(0.706187\pi\) | |||||||
\(114\) | 2.82843 | + | 7.00000i | 0.264906 | + | 0.655610i | ||||
\(115\) | −6.00000 | −0.559503 | ||||||||
\(116\) | −5.07107 | −0.470837 | ||||||||
\(117\) | −6.34315 | − | 2.24264i | −0.586424 | − | 0.207332i | ||||
\(118\) | −12.8284 | −1.18095 | ||||||||
\(119\) | 1.65685i | 0.151884i | ||||||||
\(120\) | 1.41421 | − | 1.00000i | 0.129099 | − | 0.0912871i | ||||
\(121\) | −18.3137 | −1.66488 | ||||||||
\(122\) | 4.48528 | 0.406078 | ||||||||
\(123\) | −11.0711 | − | 15.6569i | −0.998245 | − | 1.41173i | ||||
\(124\) | 6.82843i | 0.613211i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0.585786 | − | 1.65685i | 0.0521860 | − | 0.147604i | ||||
\(127\) | 12.8284i | 1.13834i | 0.822220 | + | 0.569169i | \(0.192735\pi\) | ||||
−0.822220 | + | 0.569169i | \(0.807265\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.58579 | − | 9.31371i | −0.579846 | − | 0.820026i | ||||
\(130\) | −2.24264 | −0.196693 | ||||||||
\(131\) | 4.92893i | 0.430643i | 0.976543 | + | 0.215321i | \(0.0690799\pi\) | ||||
−0.976543 | + | 0.215321i | \(0.930920\pi\) | |||||||
\(132\) | 7.65685 | − | 5.41421i | 0.666444 | − | 0.471247i | ||||
\(133\) | 2.48528 | + | 0.585786i | 0.215501 | + | 0.0507941i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.41421 | − | 5.00000i | −0.121716 | − | 0.430331i | ||||
\(136\) | − | 2.82843i | − | 0.242536i | ||||||
\(137\) | 14.4853i | 1.23756i | 0.785564 | + | 0.618781i | \(0.212373\pi\) | ||||
−0.785564 | + | 0.618781i | \(0.787627\pi\) | |||||||
\(138\) | 8.48528 | − | 6.00000i | 0.722315 | − | 0.510754i | ||||
\(139\) | 18.1421 | 1.53880 | 0.769398 | − | 0.638770i | \(-0.220556\pi\) | ||||
0.769398 | + | 0.638770i | \(0.220556\pi\) | |||||||
\(140\) | − | 0.585786i | − | 0.0495080i | ||||||
\(141\) | 4.48528 | − | 3.17157i | 0.377729 | − | 0.267095i | ||||
\(142\) | −2.82843 | −0.237356 | ||||||||
\(143\) | −12.1421 | −1.01538 | ||||||||
\(144\) | −1.00000 | + | 2.82843i | −0.0833333 | + | 0.235702i | ||||
\(145\) | 5.07107i | 0.421129i | ||||||||
\(146\) | −2.48528 | −0.205683 | ||||||||
\(147\) | 6.65685 | + | 9.41421i | 0.549048 | + | 0.776471i | ||||
\(148\) | 2.24264i | 0.184344i | ||||||||
\(149\) | − | 14.4853i | − | 1.18668i | −0.804952 | − | 0.593340i | \(-0.797809\pi\) | ||
0.804952 | − | 0.593340i | \(-0.202191\pi\) | |||||||
\(150\) | −1.00000 | − | 1.41421i | −0.0816497 | − | 0.115470i | ||||
\(151\) | − | 20.4853i | − | 1.66707i | −0.552468 | − | 0.833534i | \(-0.686314\pi\) | ||
0.552468 | − | 0.833534i | \(-0.313686\pi\) | |||||||
\(152\) | −4.24264 | − | 1.00000i | −0.344124 | − | 0.0811107i | ||||
\(153\) | −8.00000 | − | 2.82843i | −0.646762 | − | 0.228665i | ||||
\(154\) | − | 3.17157i | − | 0.255573i | ||||||
\(155\) | 6.82843 | 0.548472 | ||||||||
\(156\) | 3.17157 | − | 2.24264i | 0.253929 | − | 0.179555i | ||||
\(157\) | −23.7990 | −1.89937 | −0.949683 | − | 0.313212i | \(-0.898595\pi\) | ||||
−0.949683 | + | 0.313212i | \(0.898595\pi\) | |||||||
\(158\) | − | 13.3137i | − | 1.05918i | ||||||
\(159\) | −3.17157 | − | 4.48528i | −0.251522 | − | 0.355706i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | − | 3.51472i | − | 0.276999i | ||||||
\(162\) | 7.00000 | + | 5.65685i | 0.549972 | + | 0.444444i | ||||
\(163\) | 12.7279 | 0.996928 | 0.498464 | − | 0.866910i | \(-0.333898\pi\) | ||||
0.498464 | + | 0.866910i | \(0.333898\pi\) | |||||||
\(164\) | 11.0711 | 0.864505 | ||||||||
\(165\) | −5.41421 | − | 7.65685i | −0.421496 | − | 0.596085i | ||||
\(166\) | 12.8284i | 0.995679i | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0.585786 | + | 0.828427i | 0.0451944 | + | 0.0639145i | ||||
\(169\) | 7.97056 | 0.613120 | ||||||||
\(170\) | −2.82843 | −0.216930 | ||||||||
\(171\) | −7.07107 | + | 11.0000i | −0.540738 | + | 0.841191i | ||||
\(172\) | 6.58579 | 0.502162 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | −5.07107 | − | 7.17157i | −0.384437 | − | 0.543676i | ||||
\(175\) | −0.585786 | −0.0442813 | ||||||||
\(176\) | 5.41421i | 0.408112i | ||||||||
\(177\) | −12.8284 | − | 18.1421i | −0.964244 | − | 1.36365i | ||||
\(178\) | 10.5858 | 0.793438 | ||||||||
\(179\) | 21.7990 | 1.62933 | 0.814667 | − | 0.579930i | \(-0.196920\pi\) | ||||
0.814667 | + | 0.579930i | \(0.196920\pi\) | |||||||
\(180\) | 2.82843 | + | 1.00000i | 0.210819 | + | 0.0745356i | ||||
\(181\) | − | 10.8284i | − | 0.804871i | −0.915448 | − | 0.402435i | \(-0.868164\pi\) | ||
0.915448 | − | 0.402435i | \(-0.131836\pi\) | |||||||
\(182\) | − | 1.31371i | − | 0.0973786i | ||||||
\(183\) | 4.48528 | + | 6.34315i | 0.331562 | + | 0.468899i | ||||
\(184\) | 6.00000i | 0.442326i | ||||||||
\(185\) | 2.24264 | 0.164882 | ||||||||
\(186\) | −9.65685 | + | 6.82843i | −0.708075 | + | 0.500685i | ||||
\(187\) | −15.3137 | −1.11985 | ||||||||
\(188\) | 3.17157i | 0.231311i | ||||||||
\(189\) | 2.92893 | − | 0.828427i | 0.213048 | − | 0.0602592i | ||||
\(190\) | −1.00000 | + | 4.24264i | −0.0725476 | + | 0.307794i | ||||
\(191\) | 10.2426i | 0.741131i | 0.928806 | + | 0.370566i | \(0.120836\pi\) | ||||
−0.928806 | + | 0.370566i | \(0.879164\pi\) | |||||||
\(192\) | −1.00000 | − | 1.41421i | −0.0721688 | − | 0.102062i | ||||
\(193\) | − | 19.5563i | − | 1.40770i | −0.710350 | − | 0.703848i | \(-0.751463\pi\) | ||
0.710350 | − | 0.703848i | \(-0.248537\pi\) | |||||||
\(194\) | − | 6.58579i | − | 0.472832i | ||||||
\(195\) | −2.24264 | − | 3.17157i | −0.160599 | − | 0.227121i | ||||
\(196\) | −6.65685 | −0.475490 | ||||||||
\(197\) | 18.1421i | 1.29257i | 0.763095 | + | 0.646287i | \(0.223679\pi\) | ||||
−0.763095 | + | 0.646287i | \(0.776321\pi\) | |||||||
\(198\) | 15.3137 | + | 5.41421i | 1.08830 | + | 0.384771i | ||||
\(199\) | −16.9706 | −1.20301 | −0.601506 | − | 0.798869i | \(-0.705432\pi\) | ||||
−0.601506 | + | 0.798869i | \(0.705432\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 7.65685i | − | 0.538734i | ||||||
\(203\) | −2.97056 | −0.208493 | ||||||||
\(204\) | 4.00000 | − | 2.82843i | 0.280056 | − | 0.198030i | ||||
\(205\) | − | 11.0711i | − | 0.773237i | ||||||
\(206\) | 4.34315i | 0.302601i | ||||||||
\(207\) | 16.9706 | + | 6.00000i | 1.17954 | + | 0.417029i | ||||
\(208\) | 2.24264i | 0.155499i | ||||||||
\(209\) | −5.41421 | + | 22.9706i | −0.374509 | + | 1.58891i | ||||
\(210\) | 0.828427 | − | 0.585786i | 0.0571669 | − | 0.0404231i | ||||
\(211\) | 2.00000i | 0.137686i | 0.997628 | + | 0.0688428i | \(0.0219307\pi\) | ||||
−0.997628 | + | 0.0688428i | \(0.978069\pi\) | |||||||
\(212\) | 3.17157 | 0.217825 | ||||||||
\(213\) | −2.82843 | − | 4.00000i | −0.193801 | − | 0.274075i | ||||
\(214\) | 3.65685 | 0.249977 | ||||||||
\(215\) | − | 6.58579i | − | 0.449147i | ||||||
\(216\) | −5.00000 | + | 1.41421i | −0.340207 | + | 0.0962250i | ||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | − | 2.34315i | − | 0.158698i | ||||||
\(219\) | −2.48528 | − | 3.51472i | −0.167940 | − | 0.237503i | ||||
\(220\) | 5.41421 | 0.365026 | ||||||||
\(221\) | −6.34315 | −0.426686 | ||||||||
\(222\) | −3.17157 | + | 2.24264i | −0.212862 | + | 0.150516i | ||||
\(223\) | 18.0000i | 1.20537i | 0.797980 | + | 0.602685i | \(0.205902\pi\) | ||||
−0.797980 | + | 0.602685i | \(0.794098\pi\) | |||||||
\(224\) | −0.585786 | −0.0391395 | ||||||||
\(225\) | 1.00000 | − | 2.82843i | 0.0666667 | − | 0.188562i | ||||
\(226\) | 12.8284 | 0.853334 | ||||||||
\(227\) | 2.34315 | 0.155520 | 0.0777600 | − | 0.996972i | \(-0.475223\pi\) | ||||
0.0777600 | + | 0.996972i | \(0.475223\pi\) | |||||||
\(228\) | −2.82843 | − | 7.00000i | −0.187317 | − | 0.463586i | ||||
\(229\) | 8.48528 | 0.560723 | 0.280362 | − | 0.959894i | \(-0.409546\pi\) | ||||
0.280362 | + | 0.959894i | \(0.409546\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | 4.48528 | − | 3.17157i | 0.295110 | − | 0.208674i | ||||
\(232\) | 5.07107 | 0.332932 | ||||||||
\(233\) | 17.7990i | 1.16605i | 0.812454 | + | 0.583025i | \(0.198131\pi\) | ||||
−0.812454 | + | 0.583025i | \(0.801869\pi\) | |||||||
\(234\) | 6.34315 | + | 2.24264i | 0.414664 | + | 0.146606i | ||||
\(235\) | 3.17157 | 0.206891 | ||||||||
\(236\) | 12.8284 | 0.835059 | ||||||||
\(237\) | 18.8284 | − | 13.3137i | 1.22304 | − | 0.864818i | ||||
\(238\) | − | 1.65685i | − | 0.107398i | ||||||
\(239\) | − | 0.100505i | − | 0.00650113i | −0.999995 | − | 0.00325057i | \(-0.998965\pi\) | ||
0.999995 | − | 0.00325057i | \(-0.00103469\pi\) | |||||||
\(240\) | −1.41421 | + | 1.00000i | −0.0912871 | + | 0.0645497i | ||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | 18.3137 | 1.17725 | ||||||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | −4.48528 | −0.287141 | ||||||||
\(245\) | 6.65685i | 0.425291i | ||||||||
\(246\) | 11.0711 | + | 15.6569i | 0.705866 | + | 0.998245i | ||||
\(247\) | −2.24264 | + | 9.51472i | −0.142696 | + | 0.605407i | ||||
\(248\) | − | 6.82843i | − | 0.433606i | ||||||
\(249\) | −18.1421 | + | 12.8284i | −1.14971 | + | 0.812969i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 4.92893i | 0.311111i | 0.987827 | + | 0.155556i | \(0.0497168\pi\) | ||||
−0.987827 | + | 0.155556i | \(0.950283\pi\) | |||||||
\(252\) | −0.585786 | + | 1.65685i | −0.0369011 | + | 0.104372i | ||||
\(253\) | 32.4853 | 2.04233 | ||||||||
\(254\) | − | 12.8284i | − | 0.804927i | ||||||
\(255\) | −2.82843 | − | 4.00000i | −0.177123 | − | 0.250490i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.1421 | −1.75546 | −0.877729 | − | 0.479157i | \(-0.840942\pi\) | ||||
−0.877729 | + | 0.479157i | \(0.840942\pi\) | |||||||
\(258\) | 6.58579 | + | 9.31371i | 0.410013 | + | 0.579846i | ||||
\(259\) | 1.31371i | 0.0816299i | ||||||||
\(260\) | 2.24264 | 0.139083 | ||||||||
\(261\) | 5.07107 | − | 14.3431i | 0.313891 | − | 0.887818i | ||||
\(262\) | − | 4.92893i | − | 0.304510i | ||||||
\(263\) | − | 11.1716i | − | 0.688869i | −0.938810 | − | 0.344434i | \(-0.888071\pi\) | ||
0.938810 | − | 0.344434i | \(-0.111929\pi\) | |||||||
\(264\) | −7.65685 | + | 5.41421i | −0.471247 | + | 0.333222i | ||||
\(265\) | − | 3.17157i | − | 0.194828i | ||||||
\(266\) | −2.48528 | − | 0.585786i | −0.152382 | − | 0.0359169i | ||||
\(267\) | 10.5858 | + | 14.9706i | 0.647840 | + | 0.916184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.3848 | 1.48677 | 0.743383 | − | 0.668866i | \(-0.233220\pi\) | ||||
0.743383 | + | 0.668866i | \(0.233220\pi\) | |||||||
\(270\) | 1.41421 | + | 5.00000i | 0.0860663 | + | 0.304290i | ||||
\(271\) | −28.9706 | −1.75984 | −0.879918 | − | 0.475125i | \(-0.842403\pi\) | ||||
−0.879918 | + | 0.475125i | \(0.842403\pi\) | |||||||
\(272\) | 2.82843i | 0.171499i | ||||||||
\(273\) | 1.85786 | − | 1.31371i | 0.112443 | − | 0.0795093i | ||||
\(274\) | − | 14.4853i | − | 0.875088i | ||||||
\(275\) | − | 5.41421i | − | 0.326489i | ||||||
\(276\) | −8.48528 | + | 6.00000i | −0.510754 | + | 0.361158i | ||||
\(277\) | 24.9706 | 1.50034 | 0.750168 | − | 0.661247i | \(-0.229973\pi\) | ||||
0.750168 | + | 0.661247i | \(0.229973\pi\) | |||||||
\(278\) | −18.1421 | −1.08809 | ||||||||
\(279\) | −19.3137 | − | 6.82843i | −1.15628 | − | 0.408807i | ||||
\(280\) | 0.585786i | 0.0350074i | ||||||||
\(281\) | 0.928932 | 0.0554154 | 0.0277077 | − | 0.999616i | \(-0.491179\pi\) | ||||
0.0277077 | + | 0.999616i | \(0.491179\pi\) | |||||||
\(282\) | −4.48528 | + | 3.17157i | −0.267095 | + | 0.188864i | ||||
\(283\) | 12.7279 | 0.756596 | 0.378298 | − | 0.925684i | \(-0.376509\pi\) | ||||
0.378298 | + | 0.925684i | \(0.376509\pi\) | |||||||
\(284\) | 2.82843 | 0.167836 | ||||||||
\(285\) | −7.00000 | + | 2.82843i | −0.414644 | + | 0.167542i | ||||
\(286\) | 12.1421 | 0.717980 | ||||||||
\(287\) | 6.48528 | 0.382814 | ||||||||
\(288\) | 1.00000 | − | 2.82843i | 0.0589256 | − | 0.166667i | ||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | − | 5.07107i | − | 0.297783i | ||||||
\(291\) | 9.31371 | − | 6.58579i | 0.545979 | − | 0.386066i | ||||
\(292\) | 2.48528 | 0.145440 | ||||||||
\(293\) | −3.17157 | −0.185285 | −0.0926426 | − | 0.995699i | \(-0.529531\pi\) | ||||
−0.0926426 | + | 0.995699i | \(0.529531\pi\) | |||||||
\(294\) | −6.65685 | − | 9.41421i | −0.388236 | − | 0.549048i | ||||
\(295\) | − | 12.8284i | − | 0.746900i | ||||||
\(296\) | − | 2.24264i | − | 0.130351i | ||||||
\(297\) | 7.65685 | + | 27.0711i | 0.444296 | + | 1.57082i | ||||
\(298\) | 14.4853i | 0.839110i | ||||||||
\(299\) | 13.4558 | 0.778172 | ||||||||
\(300\) | 1.00000 | + | 1.41421i | 0.0577350 | + | 0.0816497i | ||||
\(301\) | 3.85786 | 0.222364 | ||||||||
\(302\) | 20.4853i | 1.17880i | ||||||||
\(303\) | 10.8284 | − | 7.65685i | 0.622077 | − | 0.439875i | ||||
\(304\) | 4.24264 | + | 1.00000i | 0.243332 | + | 0.0573539i | ||||
\(305\) | 4.48528i | 0.256826i | ||||||||
\(306\) | 8.00000 | + | 2.82843i | 0.457330 | + | 0.161690i | ||||
\(307\) | 18.1421i | 1.03543i | 0.855554 | + | 0.517713i | \(0.173217\pi\) | ||||
−0.855554 | + | 0.517713i | \(0.826783\pi\) | |||||||
\(308\) | 3.17157i | 0.180717i | ||||||||
\(309\) | −6.14214 | + | 4.34315i | −0.349414 | + | 0.247073i | ||||
\(310\) | −6.82843 | −0.387829 | ||||||||
\(311\) | 5.07107i | 0.287554i | 0.989610 | + | 0.143777i | \(0.0459248\pi\) | ||||
−0.989610 | + | 0.143777i | \(0.954075\pi\) | |||||||
\(312\) | −3.17157 | + | 2.24264i | −0.179555 | + | 0.126965i | ||||
\(313\) | −16.8284 | −0.951199 | −0.475599 | − | 0.879662i | \(-0.657769\pi\) | ||||
−0.475599 | + | 0.879662i | \(0.657769\pi\) | |||||||
\(314\) | 23.7990 | 1.34305 | ||||||||
\(315\) | 1.65685 | + | 0.585786i | 0.0933532 | + | 0.0330053i | ||||
\(316\) | 13.3137i | 0.748955i | ||||||||
\(317\) | 0.343146 | 0.0192730 | 0.00963649 | − | 0.999954i | \(-0.496933\pi\) | ||||
0.00963649 | + | 0.999954i | \(0.496933\pi\) | |||||||
\(318\) | 3.17157 | + | 4.48528i | 0.177853 | + | 0.251522i | ||||
\(319\) | − | 27.4558i | − | 1.53723i | ||||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 3.65685 | + | 5.17157i | 0.204106 | + | 0.288649i | ||||
\(322\) | 3.51472i | 0.195868i | ||||||||
\(323\) | −2.82843 | + | 12.0000i | −0.157378 | + | 0.667698i | ||||
\(324\) | −7.00000 | − | 5.65685i | −0.388889 | − | 0.314270i | ||||
\(325\) | − | 2.24264i | − | 0.124399i | ||||||
\(326\) | −12.7279 | −0.704934 | ||||||||
\(327\) | 3.31371 | − | 2.34315i | 0.183248 | − | 0.129576i | ||||
\(328\) | −11.0711 | −0.611297 | ||||||||
\(329\) | 1.85786i | 0.102427i | ||||||||
\(330\) | 5.41421 | + | 7.65685i | 0.298043 | + | 0.421496i | ||||
\(331\) | − | 16.9706i | − | 0.932786i | −0.884577 | − | 0.466393i | \(-0.845553\pi\) | ||
0.884577 | − | 0.466393i | \(-0.154447\pi\) | |||||||
\(332\) | − | 12.8284i | − | 0.704051i | ||||||
\(333\) | −6.34315 | − | 2.24264i | −0.347602 | − | 0.122896i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.585786 | − | 0.828427i | −0.0319573 | − | 0.0451944i | ||||
\(337\) | − | 29.2132i | − | 1.59134i | −0.605727 | − | 0.795672i | \(-0.707118\pi\) | ||
0.605727 | − | 0.795672i | \(-0.292882\pi\) | |||||||
\(338\) | −7.97056 | −0.433541 | ||||||||
\(339\) | 12.8284 | + | 18.1421i | 0.696745 | + | 0.985346i | ||||
\(340\) | 2.82843 | 0.153393 | ||||||||
\(341\) | −36.9706 | −2.00207 | ||||||||
\(342\) | 7.07107 | − | 11.0000i | 0.382360 | − | 0.594812i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | −6.58579 | −0.355082 | ||||||||
\(345\) | 6.00000 | + | 8.48528i | 0.323029 | + | 0.456832i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | − | 30.2843i | − | 1.62574i | −0.582442 | − | 0.812872i | \(-0.697903\pi\) | ||
0.582442 | − | 0.812872i | \(-0.302097\pi\) | |||||||
\(348\) | 5.07107 | + | 7.17157i | 0.271838 | + | 0.384437i | ||||
\(349\) | −10.9706 | −0.587241 | −0.293620 | − | 0.955922i | \(-0.594860\pi\) | ||||
−0.293620 | + | 0.955922i | \(0.594860\pi\) | |||||||
\(350\) | 0.585786 | 0.0313116 | ||||||||
\(351\) | 3.17157 | + | 11.2132i | 0.169286 | + | 0.598517i | ||||
\(352\) | − | 5.41421i | − | 0.288579i | ||||||
\(353\) | 8.82843i | 0.469890i | 0.972009 | + | 0.234945i | \(0.0754910\pi\) | ||||
−0.972009 | + | 0.234945i | \(0.924509\pi\) | |||||||
\(354\) | 12.8284 | + | 18.1421i | 0.681823 | + | 0.964244i | ||||
\(355\) | − | 2.82843i | − | 0.150117i | ||||||
\(356\) | −10.5858 | −0.561046 | ||||||||
\(357\) | 2.34315 | − | 1.65685i | 0.124012 | − | 0.0876900i | ||||
\(358\) | −21.7990 | −1.15211 | ||||||||
\(359\) | 19.4142i | 1.02464i | 0.858794 | + | 0.512322i | \(0.171214\pi\) | ||||
−0.858794 | + | 0.512322i | \(0.828786\pi\) | |||||||
\(360\) | −2.82843 | − | 1.00000i | −0.149071 | − | 0.0527046i | ||||
\(361\) | 17.0000 | + | 8.48528i | 0.894737 | + | 0.446594i | ||||
\(362\) | 10.8284i | 0.569129i | ||||||||
\(363\) | 18.3137 | + | 25.8995i | 0.961220 | + | 1.35937i | ||||
\(364\) | 1.31371i | 0.0688570i | ||||||||
\(365\) | − | 2.48528i | − | 0.130086i | ||||||
\(366\) | −4.48528 | − | 6.34315i | −0.234449 | − | 0.331562i | ||||
\(367\) | −14.2426 | −0.743460 | −0.371730 | − | 0.928341i | \(-0.621235\pi\) | ||||
−0.371730 | + | 0.928341i | \(0.621235\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | −11.0711 | + | 31.3137i | −0.576337 | + | 1.63013i | ||||
\(370\) | −2.24264 | −0.116589 | ||||||||
\(371\) | 1.85786 | 0.0964555 | ||||||||
\(372\) | 9.65685 | − | 6.82843i | 0.500685 | − | 0.354037i | ||||
\(373\) | − | 14.0416i | − | 0.727048i | −0.931585 | − | 0.363524i | \(-0.881573\pi\) | ||
0.931585 | − | 0.363524i | \(-0.118427\pi\) | |||||||
\(374\) | 15.3137 | 0.791853 | ||||||||
\(375\) | 1.41421 | − | 1.00000i | 0.0730297 | − | 0.0516398i | ||||
\(376\) | − | 3.17157i | − | 0.163561i | ||||||
\(377\) | − | 11.3726i | − | 0.585718i | ||||||
\(378\) | −2.92893 | + | 0.828427i | −0.150648 | + | 0.0426097i | ||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 1.00000 | − | 4.24264i | 0.0512989 | − | 0.217643i | ||||
\(381\) | 18.1421 | − | 12.8284i | 0.929450 | − | 0.657220i | ||||
\(382\) | − | 10.2426i | − | 0.524059i | ||||||
\(383\) | −32.1421 | −1.64239 | −0.821193 | − | 0.570650i | \(-0.806691\pi\) | ||||
−0.821193 | + | 0.570650i | \(0.806691\pi\) | |||||||
\(384\) | 1.00000 | + | 1.41421i | 0.0510310 | + | 0.0721688i | ||||
\(385\) | 3.17157 | 0.161638 | ||||||||
\(386\) | 19.5563i | 0.995392i | ||||||||
\(387\) | −6.58579 | + | 18.6274i | −0.334774 | + | 0.946885i | ||||
\(388\) | 6.58579i | 0.334343i | ||||||||
\(389\) | − | 20.3431i | − | 1.03144i | −0.856758 | − | 0.515719i | \(-0.827525\pi\) | ||
0.856758 | − | 0.515719i | \(-0.172475\pi\) | |||||||
\(390\) | 2.24264 | + | 3.17157i | 0.113561 | + | 0.160599i | ||||
\(391\) | 16.9706 | 0.858238 | ||||||||
\(392\) | 6.65685 | 0.336222 | ||||||||
\(393\) | 6.97056 | − | 4.92893i | 0.351618 | − | 0.248632i | ||||
\(394\) | − | 18.1421i | − | 0.913988i | ||||||
\(395\) | 13.3137 | 0.669885 | ||||||||
\(396\) | −15.3137 | − | 5.41421i | −0.769543 | − | 0.272074i | ||||
\(397\) | 16.9706 | 0.851728 | 0.425864 | − | 0.904787i | \(-0.359970\pi\) | ||||
0.425864 | + | 0.904787i | \(0.359970\pi\) | |||||||
\(398\) | 16.9706 | 0.850657 | ||||||||
\(399\) | −1.65685 | − | 4.10051i | −0.0829465 | − | 0.205282i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 18.3848 | 0.918092 | 0.459046 | − | 0.888413i | \(-0.348191\pi\) | ||||
0.459046 | + | 0.888413i | \(0.348191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3137 | −0.762830 | ||||||||
\(404\) | 7.65685i | 0.380943i | ||||||||
\(405\) | −5.65685 | + | 7.00000i | −0.281091 | + | 0.347833i | ||||
\(406\) | 2.97056 | 0.147427 | ||||||||
\(407\) | −12.1421 | −0.601863 | ||||||||
\(408\) | −4.00000 | + | 2.82843i | −0.198030 | + | 0.140028i | ||||
\(409\) | − | 4.48528i | − | 0.221783i | −0.993833 | − | 0.110891i | \(-0.964629\pi\) | ||
0.993833 | − | 0.110891i | \(-0.0353706\pi\) | |||||||
\(410\) | 11.0711i | 0.546761i | ||||||||
\(411\) | 20.4853 | − | 14.4853i | 1.01046 | − | 0.714506i | ||||
\(412\) | − | 4.34315i | − | 0.213971i | ||||||
\(413\) | 7.51472 | 0.369775 | ||||||||
\(414\) | −16.9706 | − | 6.00000i | −0.834058 | − | 0.294884i | ||||
\(415\) | −12.8284 | −0.629723 | ||||||||
\(416\) | − | 2.24264i | − | 0.109955i | ||||||
\(417\) | −18.1421 | − | 25.6569i | −0.888424 | − | 1.25642i | ||||
\(418\) | 5.41421 | − | 22.9706i | 0.264818 | − | 1.12353i | ||||
\(419\) | − | 6.38478i | − | 0.311917i | −0.987764 | − | 0.155958i | \(-0.950153\pi\) | ||
0.987764 | − | 0.155958i | \(-0.0498466\pi\) | |||||||
\(420\) | −0.828427 | + | 0.585786i | −0.0404231 | + | 0.0285835i | ||||
\(421\) | − | 24.2843i | − | 1.18354i | −0.806106 | − | 0.591771i | \(-0.798429\pi\) | ||
0.806106 | − | 0.591771i | \(-0.201571\pi\) | |||||||
\(422\) | − | 2.00000i | − | 0.0973585i | ||||||
\(423\) | −8.97056 | − | 3.17157i | −0.436164 | − | 0.154207i | ||||
\(424\) | −3.17157 | −0.154025 | ||||||||
\(425\) | − | 2.82843i | − | 0.137199i | ||||||
\(426\) | 2.82843 | + | 4.00000i | 0.137038 | + | 0.193801i | ||||
\(427\) | −2.62742 | −0.127150 | ||||||||
\(428\) | −3.65685 | −0.176761 | ||||||||
\(429\) | 12.1421 | + | 17.1716i | 0.586228 | + | 0.829051i | ||||
\(430\) | 6.58579i | 0.317595i | ||||||||
\(431\) | 19.3137 | 0.930309 | 0.465154 | − | 0.885230i | \(-0.345999\pi\) | ||||
0.465154 | + | 0.885230i | \(0.345999\pi\) | |||||||
\(432\) | 5.00000 | − | 1.41421i | 0.240563 | − | 0.0680414i | ||||
\(433\) | 14.3848i | 0.691288i | 0.938366 | + | 0.345644i | \(0.112340\pi\) | ||||
−0.938366 | + | 0.345644i | \(0.887660\pi\) | |||||||
\(434\) | − | 4.00000i | − | 0.192006i | ||||||
\(435\) | 7.17157 | − | 5.07107i | 0.343851 | − | 0.243139i | ||||
\(436\) | 2.34315i | 0.112216i | ||||||||
\(437\) | 6.00000 | − | 25.4558i | 0.287019 | − | 1.21772i | ||||
\(438\) | 2.48528 | + | 3.51472i | 0.118751 | + | 0.167940i | ||||
\(439\) | − | 39.9411i | − | 1.90629i | −0.302520 | − | 0.953143i | \(-0.597828\pi\) | ||
0.302520 | − | 0.953143i | \(-0.402172\pi\) | |||||||
\(440\) | −5.41421 | −0.258113 | ||||||||
\(441\) | 6.65685 | − | 18.8284i | 0.316993 | − | 0.896592i | ||||
\(442\) | 6.34315 | 0.301713 | ||||||||
\(443\) | 18.0000i | 0.855206i | 0.903967 | + | 0.427603i | \(0.140642\pi\) | ||||
−0.903967 | + | 0.427603i | \(0.859358\pi\) | |||||||
\(444\) | 3.17157 | − | 2.24264i | 0.150516 | − | 0.106431i | ||||
\(445\) | 10.5858i | 0.501814i | ||||||||
\(446\) | − | 18.0000i | − | 0.852325i | ||||||
\(447\) | −20.4853 | + | 14.4853i | −0.968921 | + | 0.685130i | ||||
\(448\) | 0.585786 | 0.0276758 | ||||||||
\(449\) | 16.2426 | 0.766538 | 0.383269 | − | 0.923637i | \(-0.374798\pi\) | ||||
0.383269 | + | 0.923637i | \(0.374798\pi\) | |||||||
\(450\) | −1.00000 | + | 2.82843i | −0.0471405 | + | 0.133333i | ||||
\(451\) | 59.9411i | 2.82252i | ||||||||
\(452\) | −12.8284 | −0.603398 | ||||||||
\(453\) | −28.9706 | + | 20.4853i | −1.36116 | + | 0.962482i | ||||
\(454\) | −2.34315 | −0.109969 | ||||||||
\(455\) | 1.31371 | 0.0615876 | ||||||||
\(456\) | 2.82843 | + | 7.00000i | 0.132453 | + | 0.327805i | ||||
\(457\) | −0.828427 | −0.0387522 | −0.0193761 | − | 0.999812i | \(-0.506168\pi\) | ||||
−0.0193761 | + | 0.999812i | \(0.506168\pi\) | |||||||
\(458\) | −8.48528 | −0.396491 | ||||||||
\(459\) | 4.00000 | + | 14.1421i | 0.186704 | + | 0.660098i | ||||
\(460\) | −6.00000 | −0.279751 | ||||||||
\(461\) | − | 28.1421i | − | 1.31071i | −0.755321 | − | 0.655355i | \(-0.772519\pi\) | ||
0.755321 | − | 0.655355i | \(-0.227481\pi\) | |||||||
\(462\) | −4.48528 | + | 3.17157i | −0.208674 | + | 0.147555i | ||||
\(463\) | 19.2132 | 0.892913 | 0.446457 | − | 0.894805i | \(-0.352686\pi\) | ||||
0.446457 | + | 0.894805i | \(0.352686\pi\) | |||||||
\(464\) | −5.07107 | −0.235418 | ||||||||
\(465\) | −6.82843 | − | 9.65685i | −0.316661 | − | 0.447826i | ||||
\(466\) | − | 17.7990i | − | 0.824522i | ||||||
\(467\) | − | 25.7990i | − | 1.19383i | −0.802303 | − | 0.596917i | \(-0.796392\pi\) | ||
0.802303 | − | 0.596917i | \(-0.203608\pi\) | |||||||
\(468\) | −6.34315 | − | 2.24264i | −0.293212 | − | 0.103666i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.17157 | −0.146294 | ||||||||
\(471\) | 23.7990 | + | 33.6569i | 1.09660 | + | 1.55083i | ||||
\(472\) | −12.8284 | −0.590476 | ||||||||
\(473\) | 35.6569i | 1.63950i | ||||||||
\(474\) | −18.8284 | + | 13.3137i | −0.864818 | + | 0.611519i | ||||
\(475\) | −4.24264 | − | 1.00000i | −0.194666 | − | 0.0458831i | ||||
\(476\) | 1.65685i | 0.0759418i | ||||||||
\(477\) | −3.17157 | + | 8.97056i | −0.145216 | + | 0.410734i | ||||
\(478\) | 0.100505i | 0.00459699i | ||||||||
\(479\) | − | 3.41421i | − | 0.155999i | −0.996953 | − | 0.0779997i | \(-0.975147\pi\) | ||
0.996953 | − | 0.0779997i | \(-0.0248533\pi\) | |||||||
\(480\) | 1.41421 | − | 1.00000i | 0.0645497 | − | 0.0456435i | ||||
\(481\) | −5.02944 | −0.229323 | ||||||||
\(482\) | 8.48528i | 0.386494i | ||||||||
\(483\) | −4.97056 | + | 3.51472i | −0.226168 | + | 0.159925i | ||||
\(484\) | −18.3137 | −0.832441 | ||||||||
\(485\) | 6.58579 | 0.299045 | ||||||||
\(486\) | 1.00000 | − | 15.5563i | 0.0453609 | − | 0.705650i | ||||
\(487\) | − | 36.1421i | − | 1.63776i | −0.573967 | − | 0.818878i | \(-0.694596\pi\) | ||
0.573967 | − | 0.818878i | \(-0.305404\pi\) | |||||||
\(488\) | 4.48528 | 0.203039 | ||||||||
\(489\) | −12.7279 | − | 18.0000i | −0.575577 | − | 0.813988i | ||||
\(490\) | − | 6.65685i | − | 0.300726i | ||||||
\(491\) | − | 43.5563i | − | 1.96567i | −0.184485 | − | 0.982835i | \(-0.559062\pi\) | ||
0.184485 | − | 0.982835i | \(-0.440938\pi\) | |||||||
\(492\) | −11.0711 | − | 15.6569i | −0.499122 | − | 0.705866i | ||||
\(493\) | − | 14.3431i | − | 0.645983i | ||||||
\(494\) | 2.24264 | − | 9.51472i | 0.100901 | − | 0.428087i | ||||
\(495\) | −5.41421 | + | 15.3137i | −0.243351 | + | 0.688300i | ||||
\(496\) | 6.82843i | 0.306605i | ||||||||
\(497\) | 1.65685 | 0.0743201 | ||||||||
\(498\) | 18.1421 | − | 12.8284i | 0.812969 | − | 0.574856i | ||||
\(499\) | −25.6569 | −1.14856 | −0.574279 | − | 0.818659i | \(-0.694718\pi\) | ||||
−0.574279 | + | 0.818659i | \(0.694718\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 4.92893i | − | 0.219989i | ||||||
\(503\) | − | 14.2843i | − | 0.636904i | −0.947939 | − | 0.318452i | \(-0.896837\pi\) | ||
0.947939 | − | 0.318452i | \(-0.103163\pi\) | |||||||
\(504\) | 0.585786 | − | 1.65685i | 0.0260930 | − | 0.0738022i | ||||
\(505\) | 7.65685 | 0.340726 | ||||||||
\(506\) | −32.4853 | −1.44415 | ||||||||
\(507\) | −7.97056 | − | 11.2721i | −0.353985 | − | 0.500611i | ||||
\(508\) | 12.8284i | 0.569169i | ||||||||
\(509\) | −4.10051 | −0.181752 | −0.0908758 | − | 0.995862i | \(-0.528967\pi\) | ||||
−0.0908758 | + | 0.995862i | \(0.528967\pi\) | |||||||
\(510\) | 2.82843 | + | 4.00000i | 0.125245 | + | 0.177123i | ||||
\(511\) | 1.45584 | 0.0644028 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 22.6274 | − | 1.00000i | 0.999025 | − | 0.0441511i | ||||
\(514\) | 28.1421 | 1.24130 | ||||||||
\(515\) | −4.34315 | −0.191382 | ||||||||
\(516\) | −6.58579 | − | 9.31371i | −0.289923 | − | 0.410013i | ||||
\(517\) | −17.1716 | −0.755205 | ||||||||
\(518\) | − | 1.31371i | − | 0.0577210i | ||||||
\(519\) | 6.00000 | + | 8.48528i | 0.263371 | + | 0.372463i | ||||
\(520\) | −2.24264 | −0.0983463 | ||||||||
\(521\) | −14.3848 | −0.630208 | −0.315104 | − | 0.949057i | \(-0.602039\pi\) | ||||
−0.315104 | + | 0.949057i | \(0.602039\pi\) | |||||||
\(522\) | −5.07107 | + | 14.3431i | −0.221955 | + | 0.627782i | ||||
\(523\) | 8.97056i | 0.392255i | 0.980578 | + | 0.196128i | \(0.0628367\pi\) | ||||
−0.980578 | + | 0.196128i | \(0.937163\pi\) | |||||||
\(524\) | 4.92893i | 0.215321i | ||||||||
\(525\) | 0.585786 | + | 0.828427i | 0.0255658 | + | 0.0361555i | ||||
\(526\) | 11.1716i | 0.487104i | ||||||||
\(527\) | −19.3137 | −0.841318 | ||||||||
\(528\) | 7.65685 | − | 5.41421i | 0.333222 | − | 0.235623i | ||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 3.17157i | 0.137764i | ||||||||
\(531\) | −12.8284 | + | 36.2843i | −0.556706 | + | 1.57460i | ||||
\(532\) | 2.48528 | + | 0.585786i | 0.107751 | + | 0.0253971i | ||||
\(533\) | 24.8284i | 1.07544i | ||||||||
\(534\) | −10.5858 | − | 14.9706i | −0.458092 | − | 0.647840i | ||||
\(535\) | 3.65685i | 0.158100i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.7990 | − | 30.8284i | −0.940696 | − | 1.33034i | ||||
\(538\) | −24.3848 | −1.05130 | ||||||||
\(539\) | − | 36.0416i | − | 1.55242i | ||||||
\(540\) | −1.41421 | − | 5.00000i | −0.0608581 | − | 0.215166i | ||||
\(541\) | −42.9706 | −1.84745 | −0.923724 | − | 0.383058i | \(-0.874871\pi\) | ||||
−0.923724 | + | 0.383058i | \(0.874871\pi\) | |||||||
\(542\) | 28.9706 | 1.24439 | ||||||||
\(543\) | −15.3137 | + | 10.8284i | −0.657174 | + | 0.464692i | ||||
\(544\) | − | 2.82843i | − | 0.121268i | ||||||
\(545\) | 2.34315 | 0.100369 | ||||||||
\(546\) | −1.85786 | + | 1.31371i | −0.0795093 | + | 0.0562215i | ||||
\(547\) | 13.1716i | 0.563176i | 0.959535 | + | 0.281588i | \(0.0908611\pi\) | ||||
−0.959535 | + | 0.281588i | \(0.909139\pi\) | |||||||
\(548\) | 14.4853i | 0.618781i | ||||||||
\(549\) | 4.48528 | − | 12.6863i | 0.191427 | − | 0.541438i | ||||
\(550\) | 5.41421i | 0.230863i | ||||||||
\(551\) | −21.5147 | − | 5.07107i | −0.916558 | − | 0.216035i | ||||
\(552\) | 8.48528 | − | 6.00000i | 0.361158 | − | 0.255377i | ||||
\(553\) | 7.79899i | 0.331647i | ||||||||
\(554\) | −24.9706 | −1.06090 | ||||||||
\(555\) | −2.24264 | − | 3.17157i | −0.0951948 | − | 0.134626i | ||||
\(556\) | 18.1421 | 0.769398 | ||||||||
\(557\) | 28.6274i | 1.21298i | 0.795090 | + | 0.606491i | \(0.207424\pi\) | ||||
−0.795090 | + | 0.606491i | \(0.792576\pi\) | |||||||
\(558\) | 19.3137 | + | 6.82843i | 0.817614 | + | 0.289070i | ||||
\(559\) | 14.7696i | 0.624686i | ||||||||
\(560\) | − | 0.585786i | − | 0.0247540i | ||||||
\(561\) | 15.3137 | + | 21.6569i | 0.646545 | + | 0.914353i | ||||
\(562\) | −0.928932 | −0.0391846 | ||||||||
\(563\) | 13.6569 | 0.575568 | 0.287784 | − | 0.957695i | \(-0.407082\pi\) | ||||
0.287784 | + | 0.957695i | \(0.407082\pi\) | |||||||
\(564\) | 4.48528 | − | 3.17157i | 0.188864 | − | 0.133547i | ||||
\(565\) | 12.8284i | 0.539696i | ||||||||
\(566\) | −12.7279 | −0.534994 | ||||||||
\(567\) | −4.10051 | − | 3.31371i | −0.172205 | − | 0.139163i | ||||
\(568\) | −2.82843 | −0.118678 | ||||||||
\(569\) | 28.9289 | 1.21276 | 0.606382 | − | 0.795174i | \(-0.292620\pi\) | ||||
0.606382 | + | 0.795174i | \(0.292620\pi\) | |||||||
\(570\) | 7.00000 | − | 2.82843i | 0.293198 | − | 0.118470i | ||||
\(571\) | −1.65685 | −0.0693372 | −0.0346686 | − | 0.999399i | \(-0.511038\pi\) | ||||
−0.0346686 | + | 0.999399i | \(0.511038\pi\) | |||||||
\(572\) | −12.1421 | −0.507688 | ||||||||
\(573\) | 14.4853 | − | 10.2426i | 0.605131 | − | 0.427892i | ||||
\(574\) | −6.48528 | −0.270690 | ||||||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | −1.00000 | + | 2.82843i | −0.0416667 | + | 0.117851i | ||||
\(577\) | −19.1716 | −0.798123 | −0.399062 | − | 0.916924i | \(-0.630664\pi\) | ||||
−0.399062 | + | 0.916924i | \(0.630664\pi\) | |||||||
\(578\) | −9.00000 | −0.374351 | ||||||||
\(579\) | −27.6569 | + | 19.5563i | −1.14938 | + | 0.812734i | ||||
\(580\) | 5.07107i | 0.210565i | ||||||||
\(581\) | − | 7.51472i | − | 0.311763i | ||||||
\(582\) | −9.31371 | + | 6.58579i | −0.386066 | + | 0.272990i | ||||
\(583\) | 17.1716i | 0.711174i | ||||||||
\(584\) | −2.48528 | −0.102842 | ||||||||
\(585\) | −2.24264 | + | 6.34315i | −0.0927218 | + | 0.262257i | ||||
\(586\) | 3.17157 | 0.131016 | ||||||||
\(587\) | − | 3.17157i | − | 0.130905i | −0.997856 | − | 0.0654524i | \(-0.979151\pi\) | ||
0.997856 | − | 0.0654524i | \(-0.0208491\pi\) | |||||||
\(588\) | 6.65685 | + | 9.41421i | 0.274524 | + | 0.388236i | ||||
\(589\) | −6.82843 | + | 28.9706i | −0.281360 | + | 1.19371i | ||||
\(590\) | 12.8284i | 0.528138i | ||||||||
\(591\) | 25.6569 | − | 18.1421i | 1.05538 | − | 0.746268i | ||||
\(592\) | 2.24264i | 0.0921720i | ||||||||
\(593\) | − | 12.1421i | − | 0.498618i | −0.968424 | − | 0.249309i | \(-0.919797\pi\) | ||
0.968424 | − | 0.249309i | \(-0.0802034\pi\) | |||||||
\(594\) | −7.65685 | − | 27.0711i | −0.314165 | − | 1.11074i | ||||
\(595\) | 1.65685 | 0.0679244 | ||||||||
\(596\) | − | 14.4853i | − | 0.593340i | ||||||
\(597\) | 16.9706 | + | 24.0000i | 0.694559 | + | 0.982255i | ||||
\(598\) | −13.4558 | −0.550250 | ||||||||
\(599\) | −21.1716 | −0.865047 | −0.432524 | − | 0.901623i | \(-0.642377\pi\) | ||||
−0.432524 | + | 0.901623i | \(0.642377\pi\) | |||||||
\(600\) | −1.00000 | − | 1.41421i | −0.0408248 | − | 0.0577350i | ||||
\(601\) | − | 4.00000i | − | 0.163163i | −0.996667 | − | 0.0815817i | \(-0.974003\pi\) | ||
0.996667 | − | 0.0815817i | \(-0.0259972\pi\) | |||||||
\(602\) | −3.85786 | −0.157235 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 20.4853i | − | 0.833534i | ||||||
\(605\) | 18.3137i | 0.744558i | ||||||||
\(606\) | −10.8284 | + | 7.65685i | −0.439875 | + | 0.311038i | ||||
\(607\) | 1.51472i | 0.0614805i | 0.999527 | + | 0.0307403i | \(0.00978647\pi\) | ||||
−0.999527 | + | 0.0307403i | \(0.990214\pi\) | |||||||
\(608\) | −4.24264 | − | 1.00000i | −0.172062 | − | 0.0405554i | ||||
\(609\) | 2.97056 | + | 4.20101i | 0.120373 | + | 0.170234i | ||||
\(610\) | − | 4.48528i | − | 0.181604i | ||||||
\(611\) | −7.11270 | −0.287749 | ||||||||
\(612\) | −8.00000 | − | 2.82843i | −0.323381 | − | 0.114332i | ||||
\(613\) | −23.1127 | −0.933513 | −0.466757 | − | 0.884386i | \(-0.654578\pi\) | ||||
−0.466757 | + | 0.884386i | \(0.654578\pi\) | |||||||
\(614\) | − | 18.1421i | − | 0.732157i | ||||||
\(615\) | −15.6569 | + | 11.0711i | −0.631345 | + | 0.446429i | ||||
\(616\) | − | 3.17157i | − | 0.127786i | ||||||
\(617\) | − | 18.8284i | − | 0.758004i | −0.925396 | − | 0.379002i | \(-0.876267\pi\) | ||
0.925396 | − | 0.379002i | \(-0.123733\pi\) | |||||||
\(618\) | 6.14214 | − | 4.34315i | 0.247073 | − | 0.174707i | ||||
\(619\) | 41.4558 | 1.66625 | 0.833126 | − | 0.553084i | \(-0.186549\pi\) | ||||
0.833126 | + | 0.553084i | \(0.186549\pi\) | |||||||
\(620\) | 6.82843 | 0.274236 | ||||||||
\(621\) | −8.48528 | − | 30.0000i | −0.340503 | − | 1.20386i | ||||
\(622\) | − | 5.07107i | − | 0.203331i | ||||||
\(623\) | −6.20101 | −0.248438 | ||||||||
\(624\) | 3.17157 | − | 2.24264i | 0.126965 | − | 0.0897775i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.8284 | 0.672599 | ||||||||
\(627\) | 37.8995 | − | 15.3137i | 1.51356 | − | 0.611571i | ||||
\(628\) | −23.7990 | −0.949683 | ||||||||
\(629\) | −6.34315 | −0.252918 | ||||||||
\(630\) | −1.65685 | − | 0.585786i | −0.0660107 | − | 0.0233383i | ||||
\(631\) | 23.5147 | 0.936106 | 0.468053 | − | 0.883700i | \(-0.344956\pi\) | ||||
0.468053 | + | 0.883700i | \(0.344956\pi\) | |||||||
\(632\) | − | 13.3137i | − | 0.529591i | ||||||
\(633\) | 2.82843 | − | 2.00000i | 0.112420 | − | 0.0794929i | ||||
\(634\) | −0.343146 | −0.0136281 | ||||||||
\(635\) | 12.8284 | 0.509081 | ||||||||
\(636\) | −3.17157 | − | 4.48528i | −0.125761 | − | 0.177853i | ||||
\(637\) | − | 14.9289i | − | 0.591506i | ||||||
\(638\) | 27.4558i | 1.08699i | ||||||||
\(639\) | −2.82843 | + | 8.00000i | −0.111891 | + | 0.316475i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 11.2721 | 0.445220 | 0.222610 | − | 0.974908i | \(-0.428542\pi\) | ||||
0.222610 | + | 0.974908i | \(0.428542\pi\) | |||||||
\(642\) | −3.65685 | − | 5.17157i | −0.144325 | − | 0.204106i | ||||
\(643\) | −20.7279 | −0.817429 | −0.408715 | − | 0.912662i | \(-0.634023\pi\) | ||||
−0.408715 | + | 0.912662i | \(0.634023\pi\) | |||||||
\(644\) | − | 3.51472i | − | 0.138499i | ||||||
\(645\) | −9.31371 | + | 6.58579i | −0.366727 | + | 0.259315i | ||||
\(646\) | 2.82843 | − | 12.0000i | 0.111283 | − | 0.472134i | ||||
\(647\) | 2.68629i | 0.105609i | 0.998605 | + | 0.0528045i | \(0.0168160\pi\) | ||||
−0.998605 | + | 0.0528045i | \(0.983184\pi\) | |||||||
\(648\) | 7.00000 | + | 5.65685i | 0.274986 | + | 0.222222i | ||||
\(649\) | 69.4558i | 2.72638i | ||||||||
\(650\) | 2.24264i | 0.0879636i | ||||||||
\(651\) | 5.65685 | − | 4.00000i | 0.221710 | − | 0.156772i | ||||
\(652\) | 12.7279 | 0.498464 | ||||||||
\(653\) | − | 15.1127i | − | 0.591406i | −0.955280 | − | 0.295703i | \(-0.904446\pi\) | ||
0.955280 | − | 0.295703i | \(-0.0955538\pi\) | |||||||
\(654\) | −3.31371 | + | 2.34315i | −0.129576 | + | 0.0916242i | ||||
\(655\) | 4.92893 | 0.192589 | ||||||||
\(656\) | 11.0711 | 0.432253 | ||||||||
\(657\) | −2.48528 | + | 7.02944i | −0.0969601 | + | 0.274244i | ||||
\(658\) | − | 1.85786i | − | 0.0724271i | ||||||
\(659\) | 8.82843 | 0.343907 | 0.171953 | − | 0.985105i | \(-0.444992\pi\) | ||||
0.171953 | + | 0.985105i | \(0.444992\pi\) | |||||||
\(660\) | −5.41421 | − | 7.65685i | −0.210748 | − | 0.298043i | ||||
\(661\) | − | 3.51472i | − | 0.136707i | −0.997661 | − | 0.0683534i | \(-0.978225\pi\) | ||
0.997661 | − | 0.0683534i | \(-0.0217745\pi\) | |||||||
\(662\) | 16.9706i | 0.659580i | ||||||||
\(663\) | 6.34315 | + | 8.97056i | 0.246347 | + | 0.348388i | ||||
\(664\) | 12.8284i | 0.497840i | ||||||||
\(665\) | 0.585786 | − | 2.48528i | 0.0227158 | − | 0.0963751i | ||||
\(666\) | 6.34315 | + | 2.24264i | 0.245792 | + | 0.0869006i | ||||
\(667\) | 30.4264i | 1.17812i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.4558 | − | 18.0000i | 0.984180 | − | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 24.2843i | − | 0.937484i | ||||||
\(672\) | 0.585786 | + | 0.828427i | 0.0225972 | + | 0.0319573i | ||||
\(673\) | − | 37.6985i | − | 1.45317i | −0.687077 | − | 0.726585i | \(-0.741106\pi\) | ||
0.687077 | − | 0.726585i | \(-0.258894\pi\) | |||||||
\(674\) | 29.2132i | 1.12525i | ||||||||
\(675\) | −5.00000 | + | 1.41421i | −0.192450 | + | 0.0544331i | ||||
\(676\) | 7.97056 | 0.306560 | ||||||||
\(677\) | 37.5980 | 1.44501 | 0.722504 | − | 0.691367i | \(-0.242991\pi\) | ||||
0.722504 | + | 0.691367i | \(0.242991\pi\) | |||||||
\(678\) | −12.8284 | − | 18.1421i | −0.492673 | − | 0.696745i | ||||
\(679\) | 3.85786i | 0.148051i | ||||||||
\(680\) | −2.82843 | −0.108465 | ||||||||
\(681\) | −2.34315 | − | 3.31371i | −0.0897895 | − | 0.126982i | ||||
\(682\) | 36.9706 | 1.41568 | ||||||||
\(683\) | −39.2548 | −1.50204 | −0.751022 | − | 0.660277i | \(-0.770439\pi\) | ||||
−0.751022 | + | 0.660277i | \(0.770439\pi\) | |||||||
\(684\) | −7.07107 | + | 11.0000i | −0.270369 | + | 0.420596i | ||||
\(685\) | 14.4853 | 0.553454 | ||||||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | −8.48528 | − | 12.0000i | −0.323734 | − | 0.457829i | ||||
\(688\) | 6.58579 | 0.251081 | ||||||||
\(689\) | 7.11270i | 0.270972i | ||||||||
\(690\) | −6.00000 | − | 8.48528i | −0.228416 | − | 0.323029i | ||||
\(691\) | 36.9706 | 1.40643 | 0.703213 | − | 0.710979i | \(-0.251748\pi\) | ||||
0.703213 | + | 0.710979i | \(0.251748\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −8.97056 | − | 3.17157i | −0.340764 | − | 0.120478i | ||||
\(694\) | 30.2843i | 1.14958i | ||||||||
\(695\) | − | 18.1421i | − | 0.688170i | ||||||
\(696\) | −5.07107 | − | 7.17157i | −0.192218 | − | 0.271838i | ||||
\(697\) | 31.3137i | 1.18609i | ||||||||
\(698\) | 10.9706 | 0.415242 | ||||||||
\(699\) | 25.1716 | − | 17.7990i | 0.952076 | − | 0.673220i | ||||
\(700\) | −0.585786 | −0.0221406 | ||||||||
\(701\) | 2.48528i | 0.0938678i | 0.998898 | + | 0.0469339i | \(0.0149450\pi\) | ||||
−0.998898 | + | 0.0469339i | \(0.985055\pi\) | |||||||
\(702\) | −3.17157 | − | 11.2132i | −0.119703 | − | 0.423215i | ||||
\(703\) | −2.24264 | + | 9.51472i | −0.0845828 | + | 0.358854i | ||||
\(704\) | 5.41421i | 0.204056i | ||||||||
\(705\) | −3.17157 | − | 4.48528i | −0.119448 | − | 0.168925i | ||||
\(706\) | − | 8.82843i | − | 0.332262i | ||||||
\(707\) | 4.48528i | 0.168686i | ||||||||
\(708\) | −12.8284 | − | 18.1421i | −0.482122 | − | 0.681823i | ||||
\(709\) | 19.5147 | 0.732891 | 0.366445 | − | 0.930440i | \(-0.380575\pi\) | ||||
0.366445 | + | 0.930440i | \(0.380575\pi\) | |||||||
\(710\) | 2.82843i | 0.106149i | ||||||||
\(711\) | −37.6569 | − | 13.3137i | −1.41224 | − | 0.499303i | ||||
\(712\) | 10.5858 | 0.396719 | ||||||||
\(713\) | 40.9706 | 1.53436 | ||||||||
\(714\) | −2.34315 | + | 1.65685i | −0.0876900 | + | 0.0620062i | ||||
\(715\) | 12.1421i | 0.454090i | ||||||||
\(716\) | 21.7990 | 0.814667 | ||||||||
\(717\) | −0.142136 | + | 0.100505i | −0.00530815 | + | 0.00375343i | ||||
\(718\) | − | 19.4142i | − | 0.724532i | ||||||
\(719\) | − | 30.7279i | − | 1.14596i | −0.819570 | − | 0.572979i | \(-0.805788\pi\) | ||
0.819570 | − | 0.572979i | \(-0.194212\pi\) | |||||||
\(720\) | 2.82843 | + | 1.00000i | 0.105409 | + | 0.0372678i | ||||
\(721\) | − | 2.54416i | − | 0.0947493i | ||||||
\(722\) | −17.0000 | − | 8.48528i | −0.632674 | − | 0.315789i | ||||
\(723\) | −12.0000 | + | 8.48528i | −0.446285 | + | 0.315571i | ||||
\(724\) | − | 10.8284i | − | 0.402435i | ||||||
\(725\) | 5.07107 | 0.188335 | ||||||||
\(726\) | −18.3137 | − | 25.8995i | −0.679685 | − | 0.961220i | ||||
\(727\) | 25.5563 | 0.947833 | 0.473916 | − | 0.880570i | \(-0.342840\pi\) | ||||
0.473916 | + | 0.880570i | \(0.342840\pi\) | |||||||
\(728\) | − | 1.31371i | − | 0.0486893i | ||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 2.48528i | 0.0919844i | ||||||||
\(731\) | 18.6274i | 0.688960i | ||||||||
\(732\) | 4.48528 | + | 6.34315i | 0.165781 | + | 0.234449i | ||||
\(733\) | −15.5147 | −0.573049 | −0.286525 | − | 0.958073i | \(-0.592500\pi\) | ||||
−0.286525 | + | 0.958073i | \(0.592500\pi\) | |||||||
\(734\) | 14.2426 | 0.525705 | ||||||||
\(735\) | 9.41421 | − | 6.65685i | 0.347248 | − | 0.245542i | ||||
\(736\) | 6.00000i | 0.221163i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.0711 | − | 31.3137i | 0.407532 | − | 1.15267i | ||||
\(739\) | −20.4853 | −0.753563 | −0.376782 | − | 0.926302i | \(-0.622969\pi\) | ||||
−0.376782 | + | 0.926302i | \(0.622969\pi\) | |||||||
\(740\) | 2.24264 | 0.0824411 | ||||||||
\(741\) | 15.6985 | − | 6.34315i | 0.576698 | − | 0.233021i | ||||
\(742\) | −1.85786 | −0.0682043 | ||||||||
\(743\) | 43.1716 | 1.58381 | 0.791906 | − | 0.610643i | \(-0.209089\pi\) | ||||
0.791906 | + | 0.610643i | \(0.209089\pi\) | |||||||
\(744\) | −9.65685 | + | 6.82843i | −0.354037 | + | 0.250342i | ||||
\(745\) | −14.4853 | −0.530700 | ||||||||
\(746\) | 14.0416i | 0.514101i | ||||||||
\(747\) | 36.2843 | + | 12.8284i | 1.32757 | + | 0.469368i | ||||
\(748\) | −15.3137 | −0.559925 | ||||||||
\(749\) | −2.14214 | −0.0782719 | ||||||||
\(750\) | −1.41421 | + | 1.00000i | −0.0516398 | + | 0.0365148i | ||||
\(751\) | − | 48.4853i | − | 1.76925i | −0.466300 | − | 0.884627i | \(-0.654413\pi\) | ||
0.466300 | − | 0.884627i | \(-0.345587\pi\) | |||||||
\(752\) | 3.17157i | 0.115655i | ||||||||
\(753\) | 6.97056 | − | 4.92893i | 0.254021 | − | 0.179620i | ||||
\(754\) | 11.3726i | 0.414165i | ||||||||
\(755\) | −20.4853 | −0.745536 | ||||||||
\(756\) | 2.92893 | − | 0.828427i | 0.106524 | − | 0.0301296i | ||||
\(757\) | 49.6569 | 1.80481 | 0.902405 | − | 0.430890i | \(-0.141800\pi\) | ||||
0.902405 | + | 0.430890i | \(0.141800\pi\) | |||||||
\(758\) | 8.00000i | 0.290573i | ||||||||
\(759\) | −32.4853 | − | 45.9411i | −1.17914 | − | 1.66756i | ||||
\(760\) | −1.00000 | + | 4.24264i | −0.0362738 | + | 0.153897i | ||||
\(761\) | − | 1.17157i | − | 0.0424695i | −0.999775 | − | 0.0212347i | \(-0.993240\pi\) | ||
0.999775 | − | 0.0212347i | \(-0.00675974\pi\) | |||||||
\(762\) | −18.1421 | + | 12.8284i | −0.657220 | + | 0.464725i | ||||
\(763\) | 1.37258i | 0.0496908i | ||||||||
\(764\) | 10.2426i | 0.370566i | ||||||||
\(765\) | −2.82843 | + | 8.00000i | −0.102262 | + | 0.289241i | ||||
\(766\) | 32.1421 | 1.16134 | ||||||||
\(767\) | 28.7696i | 1.03881i | ||||||||
\(768\) | −1.00000 | − | 1.41421i | −0.0360844 | − | 0.0510310i | ||||
\(769\) | −13.3137 | −0.480105 | −0.240052 | − | 0.970760i | \(-0.577165\pi\) | ||||
−0.240052 | + | 0.970760i | \(0.577165\pi\) | |||||||
\(770\) | −3.17157 | −0.114296 | ||||||||
\(771\) | 28.1421 | + | 39.7990i | 1.01351 | + | 1.43333i | ||||
\(772\) | − | 19.5563i | − | 0.703848i | ||||||
\(773\) | −0.343146 | −0.0123421 | −0.00617105 | − | 0.999981i | \(-0.501964\pi\) | ||||
−0.00617105 | + | 0.999981i | \(0.501964\pi\) | |||||||
\(774\) | 6.58579 | − | 18.6274i | 0.236721 | − | 0.669549i | ||||
\(775\) | − | 6.82843i | − | 0.245284i | ||||||
\(776\) | − | 6.58579i | − | 0.236416i | ||||||
\(777\) | 1.85786 | − | 1.31371i | 0.0666505 | − | 0.0471290i | ||||
\(778\) | 20.3431i | 0.729337i | ||||||||
\(779\) | 46.9706 | + | 11.0711i | 1.68290 | + | 0.396662i | ||||
\(780\) | −2.24264 | − | 3.17157i | −0.0802994 | − | 0.113561i | ||||
\(781\) | 15.3137i | 0.547968i | ||||||||
\(782\) | −16.9706 | −0.606866 | ||||||||
\(783\) | −25.3553 | + | 7.17157i | −0.906126 | + | 0.256291i | ||||
\(784\) | −6.65685 | −0.237745 | ||||||||
\(785\) | 23.7990i | 0.849422i | ||||||||
\(786\) | −6.97056 | + | 4.92893i | −0.248632 | + | 0.175809i | ||||
\(787\) | − | 44.9706i | − | 1.60303i | −0.597976 | − | 0.801514i | \(-0.704028\pi\) | ||
0.597976 | − | 0.801514i | \(-0.295972\pi\) | |||||||
\(788\) | 18.1421i | 0.646287i | ||||||||
\(789\) | −15.7990 | + | 11.1716i | −0.562459 | + | 0.397719i | ||||
\(790\) | −13.3137 | −0.473680 | ||||||||
\(791\) | −7.51472 | −0.267193 | ||||||||
\(792\) | 15.3137 | + | 5.41421i | 0.544149 | + | 0.192386i | ||||
\(793\) | − | 10.0589i | − | 0.357201i | ||||||
\(794\) | −16.9706 | −0.602263 | ||||||||
\(795\) | −4.48528 | + | 3.17157i | −0.159077 | + | 0.112484i | ||||
\(796\) | −16.9706 | −0.601506 | ||||||||
\(797\) | 24.3431 | 0.862278 | 0.431139 | − | 0.902285i | \(-0.358112\pi\) | ||||
0.431139 | + | 0.902285i | \(0.358112\pi\) | |||||||
\(798\) | 1.65685 | + | 4.10051i | 0.0586520 | + | 0.145156i | ||||
\(799\) | −8.97056 | −0.317356 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 10.5858 | − | 29.9411i | 0.374030 | − | 1.05792i | ||||
\(802\) | −18.3848 | −0.649189 | ||||||||
\(803\) | 13.4558i | 0.474846i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.51472 | −0.123878 | ||||||||
\(806\) | 15.3137 | 0.539402 | ||||||||
\(807\) | −24.3848 | − | 34.4853i | −0.858385 | − | 1.21394i | ||||
\(808\) | − | 7.65685i | − | 0.269367i | ||||||
\(809\) | 35.3137i | 1.24156i | 0.783983 | + | 0.620782i | \(0.213185\pi\) | ||||
−0.783983 | + | 0.620782i | \(0.786815\pi\) | |||||||
\(810\) | 5.65685 | − | 7.00000i | 0.198762 | − | 0.245955i | ||||
\(811\) | 13.0294i | 0.457525i | 0.973482 | + | 0.228763i | \(0.0734680\pi\) | ||||
−0.973482 | + | 0.228763i | \(0.926532\pi\) | |||||||
\(812\) | −2.97056 | −0.104246 | ||||||||
\(813\) | 28.9706 | + | 40.9706i | 1.01604 | + | 1.43690i | ||||
\(814\) | 12.1421 | 0.425582 | ||||||||
\(815\) | − | 12.7279i | − | 0.445840i | ||||||
\(816\) | 4.00000 | − | 2.82843i | 0.140028 | − | 0.0990148i | ||||
\(817\) | 27.9411 | + | 6.58579i | 0.977536 | + | 0.230408i | ||||
\(818\) | 4.48528i | 0.156824i | ||||||||
\(819\) | −3.71573 | − | 1.31371i | −0.129838 | − | 0.0459047i | ||||
\(820\) | − | 11.0711i | − | 0.386618i | ||||||
\(821\) | 11.6569i | 0.406827i | 0.979093 | + | 0.203414i | \(0.0652036\pi\) | ||||
−0.979093 | + | 0.203414i | \(0.934796\pi\) | |||||||
\(822\) | −20.4853 | + | 14.4853i | −0.714506 | + | 0.505232i | ||||
\(823\) | 18.2426 | 0.635898 | 0.317949 | − | 0.948108i | \(-0.397006\pi\) | ||||
0.317949 | + | 0.948108i | \(0.397006\pi\) | |||||||
\(824\) | 4.34315i | 0.151301i | ||||||||
\(825\) | −7.65685 | + | 5.41421i | −0.266577 | + | 0.188499i | ||||
\(826\) | −7.51472 | −0.261471 | ||||||||
\(827\) | 36.2843 | 1.26173 | 0.630864 | − | 0.775894i | \(-0.282701\pi\) | ||||
0.630864 | + | 0.775894i | \(0.282701\pi\) | |||||||
\(828\) | 16.9706 | + | 6.00000i | 0.589768 | + | 0.208514i | ||||
\(829\) | 35.5980i | 1.23637i | 0.786033 | + | 0.618184i | \(0.212132\pi\) | ||||
−0.786033 | + | 0.618184i | \(0.787868\pi\) | |||||||
\(830\) | 12.8284 | 0.445281 | ||||||||
\(831\) | −24.9706 | − | 35.3137i | −0.866219 | − | 1.22502i | ||||
\(832\) | 2.24264i | 0.0777496i | ||||||||
\(833\) | − | 18.8284i | − | 0.652366i | ||||||
\(834\) | 18.1421 | + | 25.6569i | 0.628211 | + | 0.888424i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.41421 | + | 22.9706i | −0.187254 | + | 0.794454i | ||||
\(837\) | 9.65685 | + | 34.1421i | 0.333790 | + | 1.18012i | ||||
\(838\) | 6.38478i | 0.220558i | ||||||||
\(839\) | −2.82843 | −0.0976481 | −0.0488241 | − | 0.998807i | \(-0.515547\pi\) | ||||
−0.0488241 | + | 0.998807i | \(0.515547\pi\) | |||||||
\(840\) | 0.828427 | − | 0.585786i | 0.0285835 | − | 0.0202116i | ||||
\(841\) | −3.28427 | −0.113251 | ||||||||
\(842\) | 24.2843i | 0.836891i | ||||||||
\(843\) | −0.928932 | − | 1.31371i | −0.0319941 | − | 0.0452465i | ||||
\(844\) | 2.00000i | 0.0688428i | ||||||||
\(845\) | − | 7.97056i | − | 0.274196i | ||||||
\(846\) | 8.97056 | + | 3.17157i | 0.308414 | + | 0.109041i | ||||
\(847\) | −10.7279 | −0.368616 | ||||||||
\(848\) | 3.17157 | 0.108912 | ||||||||
\(849\) | −12.7279 | − | 18.0000i | −0.436821 | − | 0.617758i | ||||
\(850\) | 2.82843i | 0.0970143i | ||||||||
\(851\) | 13.4558 | 0.461260 | ||||||||
\(852\) | −2.82843 | − | 4.00000i | −0.0969003 | − | 0.137038i | ||||
\(853\) | −12.0000 | −0.410872 | −0.205436 | − | 0.978671i | \(-0.565861\pi\) | ||||
−0.205436 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(854\) | 2.62742 | 0.0899084 | ||||||||
\(855\) | 11.0000 | + | 7.07107i | 0.376192 | + | 0.241825i | ||||
\(856\) | 3.65685 | 0.124989 | ||||||||
\(857\) | −4.82843 | −0.164936 | −0.0824680 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824680 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(858\) | −12.1421 | − | 17.1716i | −0.414526 | − | 0.586228i | ||||
\(859\) | 11.0294 | 0.376320 | 0.188160 | − | 0.982138i | \(-0.439748\pi\) | ||||
0.188160 | + | 0.982138i | \(0.439748\pi\) | |||||||
\(860\) | − | 6.58579i | − | 0.224573i | ||||||
\(861\) | −6.48528 | − | 9.17157i | −0.221018 | − | 0.312566i | ||||
\(862\) | −19.3137 | −0.657828 | ||||||||
\(863\) | −56.8284 | −1.93446 | −0.967231 | − | 0.253898i | \(-0.918287\pi\) | ||||
−0.967231 | + | 0.253898i | \(0.918287\pi\) | |||||||
\(864\) | −5.00000 | + | 1.41421i | −0.170103 | + | 0.0481125i | ||||
\(865\) | 6.00000i | 0.204006i | ||||||||
\(866\) | − | 14.3848i | − | 0.488815i | ||||||
\(867\) | −9.00000 | − | 12.7279i | −0.305656 | − | 0.432263i | ||||
\(868\) | 4.00000i | 0.135769i | ||||||||
\(869\) | −72.0833 | −2.44526 | ||||||||
\(870\) | −7.17157 | + | 5.07107i | −0.243139 | + | 0.171925i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 2.34315i | − | 0.0793489i | ||||||
\(873\) | −18.6274 | − | 6.58579i | −0.630443 | − | 0.222895i | ||||
\(874\) | −6.00000 | + | 25.4558i | −0.202953 | + | 0.861057i | ||||
\(875\) | 0.585786i | 0.0198032i | ||||||||
\(876\) | −2.48528 | − | 3.51472i | −0.0839699 | − | 0.118751i | ||||
\(877\) | 40.8701i | 1.38008i | 0.723769 | + | 0.690042i | \(0.242408\pi\) | ||||
−0.723769 | + | 0.690042i | \(0.757592\pi\) | |||||||
\(878\) | 39.9411i | 1.34795i | ||||||||
\(879\) | 3.17157 | + | 4.48528i | 0.106974 | + | 0.151285i | ||||
\(880\) | 5.41421 | 0.182513 | ||||||||
\(881\) | 28.2843i | 0.952921i | 0.879196 | + | 0.476461i | \(0.158081\pi\) | ||||
−0.879196 | + | 0.476461i | \(0.841919\pi\) | |||||||
\(882\) | −6.65685 | + | 18.8284i | −0.224148 | + | 0.633986i | ||||
\(883\) | 21.4142 | 0.720646 | 0.360323 | − | 0.932828i | \(-0.382667\pi\) | ||||
0.360323 | + | 0.932828i | \(0.382667\pi\) | |||||||
\(884\) | −6.34315 | −0.213343 | ||||||||
\(885\) | −18.1421 | + | 12.8284i | −0.609841 | + | 0.431223i | ||||
\(886\) | − | 18.0000i | − | 0.604722i | ||||||
\(887\) | −48.8284 | −1.63950 | −0.819749 | − | 0.572723i | \(-0.805887\pi\) | ||||
−0.819749 | + | 0.572723i | \(0.805887\pi\) | |||||||
\(888\) | −3.17157 | + | 2.24264i | −0.106431 | + | 0.0752581i | ||||
\(889\) | 7.51472i | 0.252036i | ||||||||
\(890\) | − | 10.5858i | − | 0.354836i | ||||||
\(891\) | 30.6274 | − | 37.8995i | 1.02606 | − | 1.26968i | ||||
\(892\) | 18.0000i | 0.602685i | ||||||||
\(893\) | −3.17157 | + | 13.4558i | −0.106133 | + | 0.450283i | ||||
\(894\) | 20.4853 | − | 14.4853i | 0.685130 | − | 0.484460i | ||||
\(895\) | − | 21.7990i | − | 0.728660i | ||||||
\(896\) | −0.585786 | −0.0195698 | ||||||||
\(897\) | −13.4558 | − | 19.0294i | −0.449278 | − | 0.635374i | ||||
\(898\) | −16.2426 | −0.542024 | ||||||||
\(899\) | − | 34.6274i | − | 1.15489i | ||||||
\(900\) | 1.00000 | − | 2.82843i | 0.0333333 | − | 0.0942809i | ||||
\(901\) | 8.97056i | 0.298853i | ||||||||
\(902\) | − | 59.9411i | − | 1.99582i | ||||||
\(903\) | −3.85786 | − | 5.45584i | −0.128382 | − | 0.181559i | ||||
\(904\) | 12.8284 | 0.426667 | ||||||||
\(905\) | −10.8284 | −0.359949 | ||||||||
\(906\) | 28.9706 | − | 20.4853i | 0.962482 | − | 0.680578i | ||||
\(907\) | − | 12.9706i | − | 0.430680i | −0.976539 | − | 0.215340i | \(-0.930914\pi\) | ||
0.976539 | − | 0.215340i | \(-0.0690860\pi\) | |||||||
\(908\) | 2.34315 | 0.0777600 | ||||||||
\(909\) | −21.6569 | − | 7.65685i | −0.718313 | − | 0.253962i | ||||
\(910\) | −1.31371 | −0.0435490 | ||||||||
\(911\) | −23.3137 | −0.772418 | −0.386209 | − | 0.922411i | \(-0.626216\pi\) | ||||
−0.386209 | + | 0.922411i | \(0.626216\pi\) | |||||||
\(912\) | −2.82843 | − | 7.00000i | −0.0936586 | − | 0.231793i | ||||
\(913\) | 69.4558 | 2.29865 | ||||||||
\(914\) | 0.828427 | 0.0274019 | ||||||||
\(915\) | 6.34315 | − | 4.48528i | 0.209698 | − | 0.148279i | ||||
\(916\) | 8.48528 | 0.280362 | ||||||||
\(917\) | 2.88730i | 0.0953471i | ||||||||
\(918\) | −4.00000 | − | 14.1421i | −0.132020 | − | 0.466760i | ||||
\(919\) | 37.4558 | 1.23555 | 0.617777 | − | 0.786353i | \(-0.288033\pi\) | ||||
0.617777 | + | 0.786353i | \(0.288033\pi\) | |||||||
\(920\) | 6.00000 | 0.197814 | ||||||||
\(921\) | 25.6569 | − | 18.1421i | 0.845422 | − | 0.597804i | ||||
\(922\) | 28.1421i | 0.926812i | ||||||||
\(923\) | 6.34315i | 0.208787i | ||||||||
\(924\) | 4.48528 | − | 3.17157i | 0.147555 | − | 0.104337i | ||||
\(925\) | − | 2.24264i | − | 0.0737376i | ||||||
\(926\) | −19.2132 | −0.631385 | ||||||||
\(927\) | 12.2843 | + | 4.34315i | 0.403468 | + | 0.142648i | ||||
\(928\) | 5.07107 | 0.166466 | ||||||||
\(929\) | 33.1716i | 1.08832i | 0.838980 | + | 0.544162i | \(0.183152\pi\) | ||||
−0.838980 | + | 0.544162i | \(0.816848\pi\) | |||||||
\(930\) | 6.82843 | + | 9.65685i | 0.223913 | + | 0.316661i | ||||
\(931\) | −28.2426 | − | 6.65685i | −0.925615 | − | 0.218170i | ||||
\(932\) | 17.7990i | 0.583025i | ||||||||
\(933\) | 7.17157 | − | 5.07107i | 0.234787 | − | 0.166019i | ||||
\(934\) | 25.7990i | 0.844169i | ||||||||
\(935\) | 15.3137i | 0.500812i | ||||||||
\(936\) | 6.34315 | + | 2.24264i | 0.207332 | + | 0.0733030i | ||||
\(937\) | −5.02944 | −0.164305 | −0.0821523 | − | 0.996620i | \(-0.526179\pi\) | ||||
−0.0821523 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.8284 | + | 23.7990i | 0.549175 | + | 0.776651i | ||||
\(940\) | 3.17157 | 0.103445 | ||||||||
\(941\) | 20.8701 | 0.680344 | 0.340172 | − | 0.940363i | \(-0.389515\pi\) | ||||
0.340172 | + | 0.940363i | \(0.389515\pi\) | |||||||
\(942\) | −23.7990 | − | 33.6569i | −0.775413 | − | 1.09660i | ||||
\(943\) | − | 66.4264i | − | 2.16314i | ||||||
\(944\) | 12.8284 | 0.417530 | ||||||||
\(945\) | −0.828427 | − | 2.92893i | −0.0269487 | − | 0.0952782i | ||||
\(946\) | − | 35.6569i | − | 1.15930i | ||||||
\(947\) | 2.68629i | 0.0872927i | 0.999047 | + | 0.0436464i | \(0.0138975\pi\) | ||||
−0.999047 | + | 0.0436464i | \(0.986103\pi\) | |||||||
\(948\) | 18.8284 | − | 13.3137i | 0.611519 | − | 0.432409i | ||||
\(949\) | 5.57359i | 0.180926i | ||||||||
\(950\) | 4.24264 | + | 1.00000i | 0.137649 | + | 0.0324443i | ||||
\(951\) | −0.343146 | − | 0.485281i | −0.0111273 | − | 0.0157363i | ||||
\(952\) | − | 1.65685i | − | 0.0536990i | ||||||
\(953\) | 15.9411 | 0.516384 | 0.258192 | − | 0.966094i | \(-0.416873\pi\) | ||||
0.258192 | + | 0.966094i | \(0.416873\pi\) | |||||||
\(954\) | 3.17157 | − | 8.97056i | 0.102683 | − | 0.290433i | ||||
\(955\) | 10.2426 | 0.331444 | ||||||||
\(956\) | − | 0.100505i | − | 0.00325057i | ||||||
\(957\) | −38.8284 | + | 27.4558i | −1.25514 | + | 0.887521i | ||||
\(958\) | 3.41421i | 0.110308i | ||||||||
\(959\) | 8.48528i | 0.274004i | ||||||||
\(960\) | −1.41421 | + | 1.00000i | −0.0456435 | + | 0.0322749i | ||||
\(961\) | −15.6274 | −0.504110 | ||||||||
\(962\) | 5.02944 | 0.162156 | ||||||||
\(963\) | 3.65685 | − | 10.3431i | 0.117840 | − | 0.333303i | ||||
\(964\) | − | 8.48528i | − | 0.273293i | ||||||
\(965\) | −19.5563 | −0.629541 | ||||||||
\(966\) | 4.97056 | − | 3.51472i | 0.159925 | − | 0.113084i | ||||
\(967\) | 50.2426 | 1.61569 | 0.807847 | − | 0.589392i | \(-0.200633\pi\) | ||||
0.807847 | + | 0.589392i | \(0.200633\pi\) | |||||||
\(968\) | 18.3137 | 0.588625 | ||||||||
\(969\) | 19.7990 | − | 8.00000i | 0.636035 | − | 0.256997i | ||||
\(970\) | −6.58579 | −0.211457 | ||||||||
\(971\) | −61.1127 | −1.96120 | −0.980600 | − | 0.196020i | \(-0.937198\pi\) | ||||
−0.980600 | + | 0.196020i | \(0.937198\pi\) | |||||||
\(972\) | −1.00000 | + | 15.5563i | −0.0320750 | + | 0.498970i | ||||
\(973\) | 10.6274 | 0.340699 | ||||||||
\(974\) | 36.1421i | 1.15807i | ||||||||
\(975\) | −3.17157 | + | 2.24264i | −0.101572 | + | 0.0718220i | ||||
\(976\) | −4.48528 | −0.143570 | ||||||||
\(977\) | −10.2843 | −0.329023 | −0.164511 | − | 0.986375i | \(-0.552605\pi\) | ||||
−0.164511 | + | 0.986375i | \(0.552605\pi\) | |||||||
\(978\) | 12.7279 | + | 18.0000i | 0.406994 | + | 0.575577i | ||||
\(979\) | − | 57.3137i | − | 1.83175i | ||||||
\(980\) | 6.65685i | 0.212645i | ||||||||
\(981\) | −6.62742 | − | 2.34315i | −0.211597 | − | 0.0748109i | ||||
\(982\) | 43.5563i | 1.38994i | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 11.0711 | + | 15.6569i | 0.352933 | + | 0.499122i | ||||
\(985\) | 18.1421 | 0.578057 | ||||||||
\(986\) | 14.3431i | 0.456779i | ||||||||
\(987\) | 2.62742 | − | 1.85786i | 0.0836316 | − | 0.0591365i | ||||
\(988\) | −2.24264 | + | 9.51472i | −0.0713479 | + | 0.302704i | ||||
\(989\) | − | 39.5147i | − | 1.25649i | ||||||
\(990\) | 5.41421 | − | 15.3137i | 0.172075 | − | 0.486702i | ||||
\(991\) | − | 2.97056i | − | 0.0943630i | −0.998886 | − | 0.0471815i | \(-0.984976\pi\) | ||
0.998886 | − | 0.0471815i | \(-0.0150239\pi\) | |||||||
\(992\) | − | 6.82843i | − | 0.216803i | ||||||
\(993\) | −24.0000 | + | 16.9706i | −0.761617 | + | 0.538545i | ||||
\(994\) | −1.65685 | −0.0525522 | ||||||||
\(995\) | 16.9706i | 0.538003i | ||||||||
\(996\) | −18.1421 | + | 12.8284i | −0.574856 | + | 0.406484i | ||||
\(997\) | 0.485281 | 0.0153690 | 0.00768451 | − | 0.999970i | \(-0.497554\pi\) | ||||
0.00768451 | + | 0.999970i | \(0.497554\pi\) | |||||||
\(998\) | 25.6569 | 0.812154 | ||||||||
\(999\) | 3.17157 | + | 11.2132i | 0.100344 | + | 0.354770i |
(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.341.1 | ✓ | 4 | |
3.2 | odd | 2 | 570.2.f.b.341.2 | yes | 4 | ||
19.18 | odd | 2 | 570.2.f.b.341.3 | yes | 4 | ||
57.56 | even | 2 | inner | 570.2.f.a.341.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.f.a.341.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
570.2.f.a.341.4 | yes | 4 | 57.56 | even | 2 | inner | |
570.2.f.b.341.2 | yes | 4 | 3.2 | odd | 2 | ||
570.2.f.b.341.3 | yes | 4 | 19.18 | odd | 2 |