Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(-0.623490 + 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.991 |
Dual form | 1014.2.e.m.529.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.692021 | −0.309481 | −0.154741 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154741 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −0.178448 | + | 0.309081i | −0.0674470 | + | 0.116822i | −0.897777 | − | 0.440451i | \(-0.854819\pi\) |
0.830330 | + | 0.557272i | \(0.188152\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.346011 | − | 0.599308i | −0.109418 | − | 0.189518i | ||||
\(11\) | −1.46950 | − | 2.54525i | −0.443071 | − | 0.767422i | 0.554845 | − | 0.831954i | \(-0.312778\pi\) |
−0.997916 | + | 0.0645324i | \(0.979444\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.356896 | −0.0953844 | ||||||||
\(15\) | 0.346011 | + | 0.599308i | 0.0893396 | + | 0.154741i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.35690 | + | 5.81431i | −0.814167 | + | 1.41018i | 0.0957578 | + | 0.995405i | \(0.469473\pi\) |
−0.909925 | + | 0.414774i | \(0.863861\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.60388 | − | 6.24210i | 0.826786 | − | 1.43203i | −0.0737611 | − | 0.997276i | \(-0.523500\pi\) |
0.900547 | − | 0.434759i | \(-0.143166\pi\) | |||||||
\(20\) | 0.346011 | − | 0.599308i | 0.0773704 | − | 0.134009i | ||||
\(21\) | 0.356896 | 0.0778811 | ||||||||
\(22\) | 1.46950 | − | 2.54525i | 0.313299 | − | 0.542649i | ||||
\(23\) | −1.19806 | − | 2.07510i | −0.249813 | − | 0.432689i | 0.713661 | − | 0.700492i | \(-0.247036\pi\) |
−0.963474 | + | 0.267802i | \(0.913703\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −4.52111 | −0.904221 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.178448 | − | 0.309081i | −0.0337235 | − | 0.0584108i | ||||
\(29\) | −3.91454 | − | 6.78019i | −0.726912 | − | 1.25905i | −0.958182 | − | 0.286159i | \(-0.907621\pi\) |
0.231270 | − | 0.972890i | \(-0.425712\pi\) | |||||||
\(30\) | −0.346011 | + | 0.599308i | −0.0631726 | + | 0.109418i | ||||
\(31\) | −2.76271 | −0.496197 | −0.248099 | − | 0.968735i | \(-0.579806\pi\) | ||||
−0.248099 | + | 0.968735i | \(0.579806\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.46950 | + | 2.54525i | −0.255807 | + | 0.443071i | ||||
\(34\) | −6.71379 | −1.15141 | ||||||||
\(35\) | 0.123490 | − | 0.213891i | 0.0208736 | − | 0.0361541i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −5.04892 | − | 8.74498i | −0.830037 | − | 1.43767i | −0.898008 | − | 0.439979i | \(-0.854986\pi\) |
0.0679713 | − | 0.997687i | \(-0.478347\pi\) | |||||||
\(38\) | 7.20775 | 1.16925 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.692021 | 0.109418 | ||||||||
\(41\) | −2.44504 | − | 4.23494i | −0.381851 | − | 0.661386i | 0.609476 | − | 0.792805i | \(-0.291380\pi\) |
−0.991327 | + | 0.131419i | \(0.958047\pi\) | |||||||
\(42\) | 0.178448 | + | 0.309081i | 0.0275351 | + | 0.0476922i | ||||
\(43\) | −3.29590 | + | 5.70866i | −0.502620 | + | 0.870563i | 0.497376 | + | 0.867535i | \(0.334297\pi\) |
−0.999995 | + | 0.00302747i | \(0.999036\pi\) | |||||||
\(44\) | 2.93900 | 0.443071 | ||||||||
\(45\) | 0.346011 | − | 0.599308i | 0.0515802 | − | 0.0893396i | ||||
\(46\) | 1.19806 | − | 2.07510i | 0.176645 | − | 0.305957i | ||||
\(47\) | 4.98792 | 0.727563 | 0.363781 | − | 0.931484i | \(-0.381486\pi\) | ||||
0.363781 | + | 0.931484i | \(0.381486\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 3.43631 | + | 5.95187i | 0.490902 | + | 0.850267i | ||||
\(50\) | −2.26055 | − | 3.91539i | −0.319690 | − | 0.553720i | ||||
\(51\) | 6.71379 | 0.940119 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.88769 | −1.22082 | −0.610409 | − | 0.792086i | \(-0.708995\pi\) | ||||
−0.610409 | + | 0.792086i | \(0.708995\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 1.01693 | + | 1.76137i | 0.137122 | + | 0.237503i | ||||
\(56\) | 0.178448 | − | 0.309081i | 0.0238461 | − | 0.0413027i | ||||
\(57\) | −7.20775 | −0.954690 | ||||||||
\(58\) | 3.91454 | − | 6.78019i | 0.514005 | − | 0.890282i | ||||
\(59\) | −0.821552 | + | 1.42297i | −0.106957 | + | 0.185255i | −0.914536 | − | 0.404504i | \(-0.867444\pi\) |
0.807579 | + | 0.589759i | \(0.200777\pi\) | |||||||
\(60\) | −0.692021 | −0.0893396 | ||||||||
\(61\) | 3.24698 | − | 5.62393i | 0.415733 | − | 0.720071i | −0.579772 | − | 0.814779i | \(-0.696858\pi\) |
0.995505 | + | 0.0947079i | \(0.0301917\pi\) | |||||||
\(62\) | −1.38135 | − | 2.39258i | −0.175432 | − | 0.303857i | ||||
\(63\) | −0.178448 | − | 0.309081i | −0.0224823 | − | 0.0389405i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.93900 | −0.361766 | ||||||||
\(67\) | −6.76271 | − | 11.7134i | −0.826196 | − | 1.43101i | −0.901001 | − | 0.433816i | \(-0.857167\pi\) |
0.0748051 | − | 0.997198i | \(-0.476167\pi\) | |||||||
\(68\) | −3.35690 | − | 5.81431i | −0.407083 | − | 0.705089i | ||||
\(69\) | −1.19806 | + | 2.07510i | −0.144230 | + | 0.249813i | ||||
\(70\) | 0.246980 | 0.0295197 | ||||||||
\(71\) | −3.40581 | + | 5.89904i | −0.404196 | + | 0.700087i | −0.994227 | − | 0.107293i | \(-0.965782\pi\) |
0.590032 | + | 0.807380i | \(0.299115\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 3.18598 | 0.372891 | 0.186445 | − | 0.982465i | \(-0.440303\pi\) | ||||
0.186445 | + | 0.982465i | \(0.440303\pi\) | |||||||
\(74\) | 5.04892 | − | 8.74498i | 0.586925 | − | 1.01658i | ||||
\(75\) | 2.26055 | + | 3.91539i | 0.261026 | + | 0.452111i | ||||
\(76\) | 3.60388 | + | 6.24210i | 0.413393 | + | 0.716017i | ||||
\(77\) | 1.04892 | 0.119535 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0465 | 1.69287 | 0.846433 | − | 0.532495i | \(-0.178745\pi\) | ||||
0.846433 | + | 0.532495i | \(0.178745\pi\) | |||||||
\(80\) | 0.346011 | + | 0.599308i | 0.0386852 | + | 0.0670047i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.44504 | − | 4.23494i | 0.270010 | − | 0.467671i | ||||
\(83\) | −14.8267 | −1.62744 | −0.813720 | − | 0.581256i | \(-0.802561\pi\) | ||||
−0.813720 | + | 0.581256i | \(0.802561\pi\) | |||||||
\(84\) | −0.178448 | + | 0.309081i | −0.0194703 | + | 0.0337235i | ||||
\(85\) | 2.32304 | − | 4.02363i | 0.251970 | − | 0.436424i | ||||
\(86\) | −6.59179 | −0.710811 | ||||||||
\(87\) | −3.91454 | + | 6.78019i | −0.419683 | + | 0.726912i | ||||
\(88\) | 1.46950 | + | 2.54525i | 0.156649 | + | 0.271325i | ||||
\(89\) | −0.198062 | − | 0.343054i | −0.0209946 | − | 0.0363636i | 0.855337 | − | 0.518072i | \(-0.173350\pi\) |
−0.876332 | + | 0.481708i | \(0.840017\pi\) | |||||||
\(90\) | 0.692021 | 0.0729455 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.39612 | 0.249813 | ||||||||
\(93\) | 1.38135 | + | 2.39258i | 0.143240 | + | 0.248099i | ||||
\(94\) | 2.49396 | + | 4.31966i | 0.257232 | + | 0.445539i | ||||
\(95\) | −2.49396 | + | 4.31966i | −0.255875 | + | 0.443188i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.208947 | − | 0.361908i | 0.0212154 | − | 0.0367461i | −0.855223 | − | 0.518261i | \(-0.826580\pi\) |
0.876438 | + | 0.481514i | \(0.159913\pi\) | |||||||
\(98\) | −3.43631 | + | 5.95187i | −0.347120 | + | 0.601229i | ||||
\(99\) | 2.93900 | 0.295381 | ||||||||
\(100\) | 2.26055 | − | 3.91539i | 0.226055 | − | 0.391539i | ||||
\(101\) | −5.00753 | − | 8.67330i | −0.498268 | − | 0.863026i | 0.501730 | − | 0.865024i | \(-0.332697\pi\) |
−0.999998 | + | 0.00199864i | \(0.999364\pi\) | |||||||
\(102\) | 3.35690 | + | 5.81431i | 0.332382 | + | 0.575703i | ||||
\(103\) | −9.62565 | −0.948443 | −0.474222 | − | 0.880406i | \(-0.657270\pi\) | ||||
−0.474222 | + | 0.880406i | \(0.657270\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.246980 | −0.0241027 | ||||||||
\(106\) | −4.44385 | − | 7.69697i | −0.431624 | − | 0.747595i | ||||
\(107\) | 3.31551 | + | 5.74263i | 0.320523 | + | 0.555161i | 0.980596 | − | 0.196040i | \(-0.0628082\pi\) |
−0.660073 | + | 0.751201i | \(0.729475\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 12.9879 | 1.24402 | 0.622008 | − | 0.783011i | \(-0.286317\pi\) | ||||
0.622008 | + | 0.783011i | \(0.286317\pi\) | |||||||
\(110\) | −1.01693 | + | 1.76137i | −0.0969601 | + | 0.167940i | ||||
\(111\) | −5.04892 | + | 8.74498i | −0.479222 | + | 0.830037i | ||||
\(112\) | 0.356896 | 0.0337235 | ||||||||
\(113\) | −0.396125 | + | 0.686108i | −0.0372643 | + | 0.0645436i | −0.884056 | − | 0.467381i | \(-0.845198\pi\) |
0.846792 | + | 0.531925i | \(0.178531\pi\) | |||||||
\(114\) | −3.60388 | − | 6.24210i | −0.337534 | − | 0.584626i | ||||
\(115\) | 0.829085 | + | 1.43602i | 0.0773126 | + | 0.133909i | ||||
\(116\) | 7.82908 | 0.726912 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.64310 | −0.151260 | ||||||||
\(119\) | −1.19806 | − | 2.07510i | −0.109826 | − | 0.190225i | ||||
\(120\) | −0.346011 | − | 0.599308i | −0.0315863 | − | 0.0547091i | ||||
\(121\) | 1.18114 | − | 2.04579i | 0.107376 | − | 0.185981i | ||||
\(122\) | 6.49396 | 0.587935 | ||||||||
\(123\) | −2.44504 | + | 4.23494i | −0.220462 | + | 0.381851i | ||||
\(124\) | 1.38135 | − | 2.39258i | 0.124049 | − | 0.214860i | ||||
\(125\) | 6.58881 | 0.589321 | ||||||||
\(126\) | 0.178448 | − | 0.309081i | 0.0158974 | − | 0.0275351i | ||||
\(127\) | 9.10872 | + | 15.7768i | 0.808268 | + | 1.39996i | 0.914062 | + | 0.405574i | \(0.132928\pi\) |
−0.105794 | + | 0.994388i | \(0.533738\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 6.59179 | 0.580375 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.73556 | 0.239007 | 0.119504 | − | 0.992834i | \(-0.461870\pi\) | ||||
0.119504 | + | 0.992834i | \(0.461870\pi\) | |||||||
\(132\) | −1.46950 | − | 2.54525i | −0.127904 | − | 0.221536i | ||||
\(133\) | 1.28621 | + | 2.22778i | 0.111528 | + | 0.193173i | ||||
\(134\) | 6.76271 | − | 11.7134i | 0.584209 | − | 1.01188i | ||||
\(135\) | −0.692021 | −0.0595597 | ||||||||
\(136\) | 3.35690 | − | 5.81431i | 0.287851 | − | 0.498573i | ||||
\(137\) | 3.82371 | − | 6.62286i | 0.326681 | − | 0.565829i | −0.655170 | − | 0.755482i | \(-0.727403\pi\) |
0.981851 | + | 0.189653i | \(0.0607363\pi\) | |||||||
\(138\) | −2.39612 | −0.203972 | ||||||||
\(139\) | −1.69202 | + | 2.93067i | −0.143515 | + | 0.248576i | −0.928818 | − | 0.370536i | \(-0.879174\pi\) |
0.785303 | + | 0.619112i | \(0.212507\pi\) | |||||||
\(140\) | 0.123490 | + | 0.213891i | 0.0104368 | + | 0.0180771i | ||||
\(141\) | −2.49396 | − | 4.31966i | −0.210029 | − | 0.363781i | ||||
\(142\) | −6.81163 | −0.571619 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.70895 | + | 4.69203i | 0.224966 | + | 0.389652i | ||||
\(146\) | 1.59299 | + | 2.75914i | 0.131837 | + | 0.228348i | ||||
\(147\) | 3.43631 | − | 5.95187i | 0.283422 | − | 0.490902i | ||||
\(148\) | 10.0978 | 0.830037 | ||||||||
\(149\) | −10.4085 | + | 18.0281i | −0.852698 | + | 1.47692i | 0.0260669 | + | 0.999660i | \(0.491702\pi\) |
−0.878765 | + | 0.477255i | \(0.841632\pi\) | |||||||
\(150\) | −2.26055 | + | 3.91539i | −0.184573 | + | 0.319690i | ||||
\(151\) | 0.895461 | 0.0728715 | 0.0364358 | − | 0.999336i | \(-0.488400\pi\) | ||||
0.0364358 | + | 0.999336i | \(0.488400\pi\) | |||||||
\(152\) | −3.60388 | + | 6.24210i | −0.292313 | + | 0.506301i | ||||
\(153\) | −3.35690 | − | 5.81431i | −0.271389 | − | 0.470059i | ||||
\(154\) | 0.524459 | + | 0.908389i | 0.0422621 | + | 0.0732001i | ||||
\(155\) | 1.91185 | 0.153564 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.59179 | 0.685700 | 0.342850 | − | 0.939390i | \(-0.388608\pi\) | ||||
0.342850 | + | 0.939390i | \(0.388608\pi\) | |||||||
\(158\) | 7.52326 | + | 13.0307i | 0.598519 | + | 1.03666i | ||||
\(159\) | 4.44385 | + | 7.69697i | 0.352420 | + | 0.610409i | ||||
\(160\) | −0.346011 | + | 0.599308i | −0.0273546 | + | 0.0473795i | ||||
\(161\) | 0.855167 | 0.0673966 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 0.862937 | − | 1.49465i | 0.0675904 | − | 0.117070i | −0.830250 | − | 0.557392i | \(-0.811802\pi\) |
0.897840 | + | 0.440322i | \(0.145136\pi\) | |||||||
\(164\) | 4.89008 | 0.381851 | ||||||||
\(165\) | 1.01693 | − | 1.76137i | 0.0791676 | − | 0.137122i | ||||
\(166\) | −7.41335 | − | 12.8403i | −0.575387 | − | 0.996600i | ||||
\(167\) | 10.5700 | + | 18.3078i | 0.817933 | + | 1.41670i | 0.907203 | + | 0.420694i | \(0.138213\pi\) |
−0.0892696 | + | 0.996007i | \(0.528453\pi\) | |||||||
\(168\) | −0.356896 | −0.0275351 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.64609 | 0.356339 | ||||||||
\(171\) | 3.60388 | + | 6.24210i | 0.275595 | + | 0.477345i | ||||
\(172\) | −3.29590 | − | 5.70866i | −0.251310 | − | 0.435281i | ||||
\(173\) | −4.67725 | + | 8.10124i | −0.355605 | + | 0.615926i | −0.987221 | − | 0.159355i | \(-0.949058\pi\) |
0.631616 | + | 0.775281i | \(0.282392\pi\) | |||||||
\(174\) | −7.82908 | −0.593521 | ||||||||
\(175\) | 0.806782 | − | 1.39739i | 0.0609870 | − | 0.105633i | ||||
\(176\) | −1.46950 | + | 2.54525i | −0.110768 | + | 0.191855i | ||||
\(177\) | 1.64310 | 0.123503 | ||||||||
\(178\) | 0.198062 | − | 0.343054i | 0.0148454 | − | 0.0257130i | ||||
\(179\) | −1.58761 | − | 2.74983i | −0.118664 | − | 0.205532i | 0.800575 | − | 0.599233i | \(-0.204528\pi\) |
−0.919238 | + | 0.393701i | \(0.871194\pi\) | |||||||
\(180\) | 0.346011 | + | 0.599308i | 0.0257901 | + | 0.0446698i | ||||
\(181\) | −19.7995 | −1.47169 | −0.735844 | − | 0.677151i | \(-0.763214\pi\) | ||||
−0.735844 | + | 0.677151i | \(0.763214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.49396 | −0.480047 | ||||||||
\(184\) | 1.19806 | + | 2.07510i | 0.0883223 | + | 0.152979i | ||||
\(185\) | 3.49396 | + | 6.05171i | 0.256881 | + | 0.444931i | ||||
\(186\) | −1.38135 | + | 2.39258i | −0.101286 | + | 0.175432i | ||||
\(187\) | 19.7318 | 1.44294 | ||||||||
\(188\) | −2.49396 | + | 4.31966i | −0.181891 | + | 0.315044i | ||||
\(189\) | −0.178448 | + | 0.309081i | −0.0129802 | + | 0.0224823i | ||||
\(190\) | −4.98792 | −0.361862 | ||||||||
\(191\) | −7.63102 | + | 13.2173i | −0.552161 | + | 0.956372i | 0.445957 | + | 0.895054i | \(0.352863\pi\) |
−0.998118 | + | 0.0613172i | \(0.980470\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.38404 | + | 4.12928i | 0.171607 | + | 0.297232i | 0.938982 | − | 0.343967i | \(-0.111771\pi\) |
−0.767375 | + | 0.641199i | \(0.778437\pi\) | |||||||
\(194\) | 0.417895 | 0.0300031 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.87263 | −0.490902 | ||||||||
\(197\) | 6.11745 | + | 10.5957i | 0.435850 | + | 0.754915i | 0.997365 | − | 0.0725523i | \(-0.0231144\pi\) |
−0.561514 | + | 0.827467i | \(0.689781\pi\) | |||||||
\(198\) | 1.46950 | + | 2.54525i | 0.104433 | + | 0.180883i | ||||
\(199\) | 5.92423 | − | 10.2611i | 0.419958 | − | 0.727388i | −0.575977 | − | 0.817466i | \(-0.695378\pi\) |
0.995935 | + | 0.0900779i | \(0.0287116\pi\) | |||||||
\(200\) | 4.52111 | 0.319690 | ||||||||
\(201\) | −6.76271 | + | 11.7134i | −0.477005 | + | 0.826196i | ||||
\(202\) | 5.00753 | − | 8.67330i | 0.352329 | − | 0.610251i | ||||
\(203\) | 2.79417 | 0.196112 | ||||||||
\(204\) | −3.35690 | + | 5.81431i | −0.235030 | + | 0.407083i | ||||
\(205\) | 1.69202 | + | 2.93067i | 0.118176 | + | 0.204687i | ||||
\(206\) | −4.81282 | − | 8.33605i | −0.335325 | − | 0.580800i | ||||
\(207\) | 2.39612 | 0.166542 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1836 | −1.46530 | ||||||||
\(210\) | −0.123490 | − | 0.213891i | −0.00852161 | − | 0.0147599i | ||||
\(211\) | 8.63102 | + | 14.9494i | 0.594184 | + | 1.02916i | 0.993661 | + | 0.112414i | \(0.0358583\pi\) |
−0.399477 | + | 0.916743i | \(0.630808\pi\) | |||||||
\(212\) | 4.44385 | − | 7.69697i | 0.305205 | − | 0.528630i | ||||
\(213\) | 6.81163 | 0.466725 | ||||||||
\(214\) | −3.31551 | + | 5.74263i | −0.226644 | + | 0.392558i | ||||
\(215\) | 2.28083 | − | 3.95052i | 0.155551 | − | 0.269423i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.493000 | − | 0.853901i | 0.0334670 | − | 0.0579665i | ||||
\(218\) | 6.49396 | + | 11.2479i | 0.439826 | + | 0.761802i | ||||
\(219\) | −1.59299 | − | 2.75914i | −0.107644 | − | 0.186445i | ||||
\(220\) | −2.03385 | −0.137122 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.0978 | −0.677722 | ||||||||
\(223\) | 3.38404 | + | 5.86133i | 0.226612 | + | 0.392504i | 0.956802 | − | 0.290741i | \(-0.0939016\pi\) |
−0.730190 | + | 0.683245i | \(0.760568\pi\) | |||||||
\(224\) | 0.178448 | + | 0.309081i | 0.0119231 | + | 0.0206513i | ||||
\(225\) | 2.26055 | − | 3.91539i | 0.150704 | − | 0.261026i | ||||
\(226\) | −0.792249 | −0.0526996 | ||||||||
\(227\) | 11.8400 | − | 20.5074i | 0.785846 | − | 1.36113i | −0.142646 | − | 0.989774i | \(-0.545561\pi\) |
0.928492 | − | 0.371352i | \(-0.121106\pi\) | |||||||
\(228\) | 3.60388 | − | 6.24210i | 0.238672 | − | 0.413393i | ||||
\(229\) | 8.29829 | 0.548366 | 0.274183 | − | 0.961677i | \(-0.411593\pi\) | ||||
0.274183 | + | 0.961677i | \(0.411593\pi\) | |||||||
\(230\) | −0.829085 | + | 1.43602i | −0.0546682 | + | 0.0946882i | ||||
\(231\) | −0.524459 | − | 0.908389i | −0.0345068 | − | 0.0597676i | ||||
\(232\) | 3.91454 | + | 6.78019i | 0.257002 | + | 0.445141i | ||||
\(233\) | −23.9651 | −1.57000 | −0.785002 | − | 0.619493i | \(-0.787338\pi\) | ||||
−0.785002 | + | 0.619493i | \(0.787338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.45175 | −0.225167 | ||||||||
\(236\) | −0.821552 | − | 1.42297i | −0.0534785 | − | 0.0926275i | ||||
\(237\) | −7.52326 | − | 13.0307i | −0.488688 | − | 0.846433i | ||||
\(238\) | 1.19806 | − | 2.07510i | 0.0776588 | − | 0.134509i | ||||
\(239\) | −12.6160 | −0.816058 | −0.408029 | − | 0.912969i | \(-0.633784\pi\) | ||||
−0.408029 | + | 0.912969i | \(0.633784\pi\) | |||||||
\(240\) | 0.346011 | − | 0.599308i | 0.0223349 | − | 0.0386852i | ||||
\(241\) | 13.1969 | − | 22.8576i | 0.850085 | − | 1.47239i | −0.0310462 | − | 0.999518i | \(-0.509884\pi\) |
0.881131 | − | 0.472872i | \(-0.156783\pi\) | |||||||
\(242\) | 2.36227 | 0.151853 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.24698 | + | 5.62393i | 0.207867 | + | 0.360035i | ||||
\(245\) | −2.37800 | − | 4.11882i | −0.151925 | − | 0.263142i | ||||
\(246\) | −4.89008 | −0.311780 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.76271 | 0.175432 | ||||||||
\(249\) | 7.41335 | + | 12.8403i | 0.469802 | + | 0.813720i | ||||
\(250\) | 3.29440 | + | 5.70608i | 0.208356 | + | 0.360884i | ||||
\(251\) | 15.0172 | − | 26.0106i | 0.947879 | − | 1.64177i | 0.197996 | − | 0.980203i | \(-0.436557\pi\) |
0.749882 | − | 0.661571i | \(-0.230110\pi\) | |||||||
\(252\) | 0.356896 | 0.0224823 | ||||||||
\(253\) | −3.52111 | + | 6.09873i | −0.221370 | + | 0.383424i | ||||
\(254\) | −9.10872 | + | 15.7768i | −0.571532 | + | 0.989922i | ||||
\(255\) | −4.64609 | −0.290949 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.63102 | − | 9.75322i | −0.351254 | − | 0.608389i | 0.635216 | − | 0.772335i | \(-0.280911\pi\) |
−0.986469 | + | 0.163946i | \(0.947578\pi\) | |||||||
\(258\) | 3.29590 | + | 5.70866i | 0.205194 | + | 0.355406i | ||||
\(259\) | 3.60388 | 0.223934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.82908 | 0.484608 | ||||||||
\(262\) | 1.36778 | + | 2.36907i | 0.0845018 | + | 0.146361i | ||||
\(263\) | 2.77479 | + | 4.80608i | 0.171101 | + | 0.296355i | 0.938805 | − | 0.344449i | \(-0.111934\pi\) |
−0.767704 | + | 0.640804i | \(0.778601\pi\) | |||||||
\(264\) | 1.46950 | − | 2.54525i | 0.0904415 | − | 0.156649i | ||||
\(265\) | 6.15047 | 0.377821 | ||||||||
\(266\) | −1.28621 | + | 2.22778i | −0.0788625 | + | 0.136594i | ||||
\(267\) | −0.198062 | + | 0.343054i | −0.0121212 | + | 0.0209946i | ||||
\(268\) | 13.5254 | 0.826196 | ||||||||
\(269\) | −8.34362 | + | 14.4516i | −0.508719 | + | 0.881128i | 0.491230 | + | 0.871030i | \(0.336548\pi\) |
−0.999949 | + | 0.0100977i | \(0.996786\pi\) | |||||||
\(270\) | −0.346011 | − | 0.599308i | −0.0210575 | − | 0.0364727i | ||||
\(271\) | −3.30678 | − | 5.72751i | −0.200873 | − | 0.347922i | 0.747937 | − | 0.663770i | \(-0.231044\pi\) |
−0.948810 | + | 0.315848i | \(0.897711\pi\) | |||||||
\(272\) | 6.71379 | 0.407083 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.64742 | 0.461997 | ||||||||
\(275\) | 6.64377 | + | 11.5073i | 0.400634 | + | 0.693919i | ||||
\(276\) | −1.19806 | − | 2.07510i | −0.0721149 | − | 0.124907i | ||||
\(277\) | 10.8998 | − | 18.8790i | 0.654904 | − | 1.13433i | −0.327014 | − | 0.945019i | \(-0.606042\pi\) |
0.981918 | − | 0.189307i | \(-0.0606242\pi\) | |||||||
\(278\) | −3.38404 | −0.202961 | ||||||||
\(279\) | 1.38135 | − | 2.39258i | 0.0826995 | − | 0.143240i | ||||
\(280\) | −0.123490 | + | 0.213891i | −0.00737993 | + | 0.0127824i | ||||
\(281\) | −20.5918 | −1.22840 | −0.614202 | − | 0.789149i | \(-0.710522\pi\) | ||||
−0.614202 | + | 0.789149i | \(0.710522\pi\) | |||||||
\(282\) | 2.49396 | − | 4.31966i | 0.148513 | − | 0.257232i | ||||
\(283\) | 6.50604 | + | 11.2688i | 0.386744 | + | 0.669860i | 0.992009 | − | 0.126163i | \(-0.0402664\pi\) |
−0.605265 | + | 0.796024i | \(0.706933\pi\) | |||||||
\(284\) | −3.40581 | − | 5.89904i | −0.202098 | − | 0.350044i | ||||
\(285\) | 4.98792 | 0.295459 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.74525 | 0.103019 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −14.0375 | − | 24.3137i | −0.825735 | − | 1.43022i | ||||
\(290\) | −2.70895 | + | 4.69203i | −0.159075 | + | 0.275526i | ||||
\(291\) | −0.417895 | −0.0244974 | ||||||||
\(292\) | −1.59299 | + | 2.75914i | −0.0932227 | + | 0.161466i | ||||
\(293\) | −7.46950 | + | 12.9376i | −0.436373 | + | 0.755820i | −0.997407 | − | 0.0719730i | \(-0.977070\pi\) |
0.561034 | + | 0.827793i | \(0.310404\pi\) | |||||||
\(294\) | 6.87263 | 0.400820 | ||||||||
\(295\) | 0.568532 | − | 0.984726i | 0.0331012 | − | 0.0573329i | ||||
\(296\) | 5.04892 | + | 8.74498i | 0.293462 | + | 0.508292i | ||||
\(297\) | −1.46950 | − | 2.54525i | −0.0852691 | − | 0.147690i | ||||
\(298\) | −20.8170 | −1.20590 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.52111 | −0.261026 | ||||||||
\(301\) | −1.17629 | − | 2.03740i | −0.0678003 | − | 0.117434i | ||||
\(302\) | 0.447730 | + | 0.775492i | 0.0257640 | + | 0.0446245i | ||||
\(303\) | −5.00753 | + | 8.67330i | −0.287675 | + | 0.498268i | ||||
\(304\) | −7.20775 | −0.413393 | ||||||||
\(305\) | −2.24698 | + | 3.89188i | −0.128662 | + | 0.222849i | ||||
\(306\) | 3.35690 | − | 5.81431i | 0.191901 | − | 0.332382i | ||||
\(307\) | −26.0301 | −1.48562 | −0.742809 | − | 0.669503i | \(-0.766507\pi\) | ||||
−0.742809 | + | 0.669503i | \(0.766507\pi\) | |||||||
\(308\) | −0.524459 | + | 0.908389i | −0.0298838 | + | 0.0517603i | ||||
\(309\) | 4.81282 | + | 8.33605i | 0.273792 | + | 0.474222i | ||||
\(310\) | 0.955927 | + | 1.65571i | 0.0542930 | + | 0.0940382i | ||||
\(311\) | −4.81163 | −0.272842 | −0.136421 | − | 0.990651i | \(-0.543560\pi\) | ||||
−0.136421 | + | 0.990651i | \(0.543560\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0411 | −1.47193 | −0.735966 | − | 0.677018i | \(-0.763272\pi\) | ||||
−0.735966 | + | 0.677018i | \(0.763272\pi\) | |||||||
\(314\) | 4.29590 | + | 7.44071i | 0.242431 | + | 0.419904i | ||||
\(315\) | 0.123490 | + | 0.213891i | 0.00695786 | + | 0.0120514i | ||||
\(316\) | −7.52326 | + | 13.0307i | −0.423217 | + | 0.733033i | ||||
\(317\) | 11.5211 | 0.647090 | 0.323545 | − | 0.946213i | \(-0.395125\pi\) | ||||
0.323545 | + | 0.946213i | \(0.395125\pi\) | |||||||
\(318\) | −4.44385 | + | 7.69697i | −0.249198 | + | 0.431624i | ||||
\(319\) | −11.5048 | + | 19.9270i | −0.644148 | + | 1.11570i | ||||
\(320\) | −0.692021 | −0.0386852 | ||||||||
\(321\) | 3.31551 | − | 5.74263i | 0.185054 | − | 0.320523i | ||||
\(322\) | 0.427583 | + | 0.740596i | 0.0238283 | + | 0.0412718i | ||||
\(323\) | 24.1957 | + | 41.9081i | 1.34628 | + | 2.33183i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.72587 | 0.0955873 | ||||||||
\(327\) | −6.49396 | − | 11.2479i | −0.359117 | − | 0.622008i | ||||
\(328\) | 2.44504 | + | 4.23494i | 0.135005 | + | 0.233835i | ||||
\(329\) | −0.890084 | + | 1.54167i | −0.0490719 | + | 0.0849950i | ||||
\(330\) | 2.03385 | 0.111960 | ||||||||
\(331\) | 1.71917 | − | 2.97769i | 0.0944940 | − | 0.163668i | −0.814903 | − | 0.579597i | \(-0.803210\pi\) |
0.909397 | + | 0.415928i | \(0.136543\pi\) | |||||||
\(332\) | 7.41335 | − | 12.8403i | 0.406860 | − | 0.704703i | ||||
\(333\) | 10.0978 | 0.553358 | ||||||||
\(334\) | −10.5700 | + | 18.3078i | −0.578366 | + | 1.00176i | ||||
\(335\) | 4.67994 | + | 8.10589i | 0.255692 | + | 0.442872i | ||||
\(336\) | −0.178448 | − | 0.309081i | −0.00973513 | − | 0.0168617i | ||||
\(337\) | 8.20105 | 0.446739 | 0.223370 | − | 0.974734i | \(-0.428294\pi\) | ||||
0.223370 | + | 0.974734i | \(0.428294\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.792249 | 0.0430291 | ||||||||
\(340\) | 2.32304 | + | 4.02363i | 0.125985 | + | 0.218212i | ||||
\(341\) | 4.05980 | + | 7.03178i | 0.219851 | + | 0.380792i | ||||
\(342\) | −3.60388 | + | 6.24210i | −0.194875 | + | 0.337534i | ||||
\(343\) | −4.95108 | −0.267333 | ||||||||
\(344\) | 3.29590 | − | 5.70866i | 0.177703 | − | 0.307790i | ||||
\(345\) | 0.829085 | − | 1.43602i | 0.0446364 | − | 0.0773126i | ||||
\(346\) | −9.35450 | −0.502901 | ||||||||
\(347\) | −3.93147 | + | 6.80950i | −0.211052 | + | 0.365553i | −0.952044 | − | 0.305961i | \(-0.901022\pi\) |
0.740992 | + | 0.671514i | \(0.234356\pi\) | |||||||
\(348\) | −3.91454 | − | 6.78019i | −0.209841 | − | 0.363456i | ||||
\(349\) | −9.36227 | − | 16.2159i | −0.501151 | − | 0.868019i | −0.999999 | − | 0.00132953i | \(-0.999577\pi\) |
0.498848 | − | 0.866689i | \(-0.333757\pi\) | |||||||
\(350\) | 1.61356 | 0.0862486 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.93900 | −0.156649 | ||||||||
\(353\) | −15.7724 | − | 27.3186i | −0.839480 | − | 1.45402i | −0.890330 | − | 0.455316i | \(-0.849526\pi\) |
0.0508500 | − | 0.998706i | \(-0.483807\pi\) | |||||||
\(354\) | 0.821552 | + | 1.42297i | 0.0436650 | + | 0.0756300i | ||||
\(355\) | 2.35690 | − | 4.08226i | 0.125091 | − | 0.216664i | ||||
\(356\) | 0.396125 | 0.0209946 | ||||||||
\(357\) | −1.19806 | + | 2.07510i | −0.0634082 | + | 0.109826i | ||||
\(358\) | 1.58761 | − | 2.74983i | 0.0839080 | − | 0.145333i | ||||
\(359\) | −2.39612 | −0.126463 | −0.0632313 | − | 0.997999i | \(-0.520141\pi\) | ||||
−0.0632313 | + | 0.997999i | \(0.520141\pi\) | |||||||
\(360\) | −0.346011 | + | 0.599308i | −0.0182364 | + | 0.0315863i | ||||
\(361\) | −16.4758 | − | 28.5370i | −0.867149 | − | 1.50195i | ||||
\(362\) | −9.89977 | − | 17.1469i | −0.520320 | − | 0.901222i | ||||
\(363\) | −2.36227 | −0.123987 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.20477 | −0.115403 | ||||||||
\(366\) | −3.24698 | − | 5.62393i | −0.169722 | − | 0.293968i | ||||
\(367\) | 0.00215593 | + | 0.00373419i | 0.000112539 | + | 0.000194923i | 0.866082 | − | 0.499903i | \(-0.166631\pi\) |
−0.865969 | + | 0.500097i | \(0.833298\pi\) | |||||||
\(368\) | −1.19806 | + | 2.07510i | −0.0624533 | + | 0.108172i | ||||
\(369\) | 4.89008 | 0.254568 | ||||||||
\(370\) | −3.49396 | + | 6.05171i | −0.181642 | + | 0.314614i | ||||
\(371\) | 1.58599 | − | 2.74702i | 0.0823405 | − | 0.142618i | ||||
\(372\) | −2.76271 | −0.143240 | ||||||||
\(373\) | 16.1564 | − | 27.9838i | 0.836549 | − | 1.44895i | −0.0562144 | − | 0.998419i | \(-0.517903\pi\) |
0.892763 | − | 0.450526i | \(-0.148764\pi\) | |||||||
\(374\) | 9.86592 | + | 17.0883i | 0.510155 | + | 0.883614i | ||||
\(375\) | −3.29440 | − | 5.70608i | −0.170122 | − | 0.294661i | ||||
\(376\) | −4.98792 | −0.257232 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.356896 | −0.0183567 | ||||||||
\(379\) | 9.87800 | + | 17.1092i | 0.507399 | + | 0.878841i | 0.999963 | + | 0.00856468i | \(0.00272625\pi\) |
−0.492564 | + | 0.870276i | \(0.663940\pi\) | |||||||
\(380\) | −2.49396 | − | 4.31966i | −0.127937 | − | 0.221594i | ||||
\(381\) | 9.10872 | − | 15.7768i | 0.466654 | − | 0.808268i | ||||
\(382\) | −15.2620 | −0.780874 | ||||||||
\(383\) | 14.4058 | − | 24.9516i | 0.736103 | − | 1.27497i | −0.218135 | − | 0.975919i | \(-0.569997\pi\) |
0.954238 | − | 0.299049i | \(-0.0966693\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −0.725873 | −0.0369939 | ||||||||
\(386\) | −2.38404 | + | 4.12928i | −0.121345 | + | 0.210175i | ||||
\(387\) | −3.29590 | − | 5.70866i | −0.167540 | − | 0.290188i | ||||
\(388\) | 0.208947 | + | 0.361908i | 0.0106077 | + | 0.0183731i | ||||
\(389\) | 34.7821 | 1.76352 | 0.881761 | − | 0.471697i | \(-0.156358\pi\) | ||||
0.881761 | + | 0.471697i | \(0.156358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0871 | 0.813559 | ||||||||
\(392\) | −3.43631 | − | 5.95187i | −0.173560 | − | 0.300615i | ||||
\(393\) | −1.36778 | − | 2.36907i | −0.0689954 | − | 0.119504i | ||||
\(394\) | −6.11745 | + | 10.5957i | −0.308193 | + | 0.533805i | ||||
\(395\) | −10.4125 | −0.523911 | ||||||||
\(396\) | −1.46950 | + | 2.54525i | −0.0738452 | + | 0.127904i | ||||
\(397\) | −2.57673 | + | 4.46302i | −0.129322 | + | 0.223993i | −0.923414 | − | 0.383805i | \(-0.874614\pi\) |
0.794092 | + | 0.607798i | \(0.207947\pi\) | |||||||
\(398\) | 11.8485 | 0.593910 | ||||||||
\(399\) | 1.28621 | − | 2.22778i | 0.0643910 | − | 0.111528i | ||||
\(400\) | 2.26055 | + | 3.91539i | 0.113028 | + | 0.195770i | ||||
\(401\) | 6.66248 | + | 11.5398i | 0.332708 | + | 0.576268i | 0.983042 | − | 0.183381i | \(-0.0587042\pi\) |
−0.650333 | + | 0.759649i | \(0.725371\pi\) | |||||||
\(402\) | −13.5254 | −0.674587 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.0151 | 0.498268 | ||||||||
\(405\) | 0.346011 | + | 0.599308i | 0.0171934 | + | 0.0297799i | ||||
\(406\) | 1.39708 | + | 2.41982i | 0.0693361 | + | 0.120094i | ||||
\(407\) | −14.8388 | + | 25.7015i | −0.735531 | + | 1.27398i | ||||
\(408\) | −6.71379 | −0.332382 | ||||||||
\(409\) | −12.0118 | + | 20.8051i | −0.593947 | + | 1.02875i | 0.399747 | + | 0.916626i | \(0.369098\pi\) |
−0.993694 | + | 0.112122i | \(0.964235\pi\) | |||||||
\(410\) | −1.69202 | + | 2.93067i | −0.0835630 | + | 0.144735i | ||||
\(411\) | −7.64742 | −0.377219 | ||||||||
\(412\) | 4.81282 | − | 8.33605i | 0.237111 | − | 0.410688i | ||||
\(413\) | −0.293209 | − | 0.507852i | −0.0144278 | − | 0.0249898i | ||||
\(414\) | 1.19806 | + | 2.07510i | 0.0588815 | + | 0.101986i | ||||
\(415\) | 10.2604 | 0.503663 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.38404 | 0.165717 | ||||||||
\(418\) | −10.5918 | − | 18.3455i | −0.518062 | − | 0.897309i | ||||
\(419\) | −6.90246 | − | 11.9554i | −0.337207 | − | 0.584060i | 0.646699 | − | 0.762745i | \(-0.276149\pi\) |
−0.983906 | + | 0.178685i | \(0.942816\pi\) | |||||||
\(420\) | 0.123490 | − | 0.213891i | 0.00602569 | − | 0.0104368i | ||||
\(421\) | −7.72587 | −0.376536 | −0.188268 | − | 0.982118i | \(-0.560287\pi\) | ||||
−0.188268 | + | 0.982118i | \(0.560287\pi\) | |||||||
\(422\) | −8.63102 | + | 14.9494i | −0.420152 | + | 0.727724i | ||||
\(423\) | −2.49396 | + | 4.31966i | −0.121260 | + | 0.210029i | ||||
\(424\) | 8.88769 | 0.431624 | ||||||||
\(425\) | 15.1769 | − | 26.2871i | 0.736187 | − | 1.27511i | ||||
\(426\) | 3.40581 | + | 5.89904i | 0.165012 | + | 0.285809i | ||||
\(427\) | 1.15883 | + | 2.00716i | 0.0560799 | + | 0.0971332i | ||||
\(428\) | −6.63102 | −0.320523 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.56166 | 0.219983 | ||||||||
\(431\) | 0.320060 | + | 0.554360i | 0.0154168 | + | 0.0267026i | 0.873631 | − | 0.486589i | \(-0.161759\pi\) |
−0.858214 | + | 0.513292i | \(0.828426\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −10.6380 | + | 18.4256i | −0.511231 | + | 0.885478i | 0.488685 | + | 0.872461i | \(0.337477\pi\) |
−0.999915 | + | 0.0130171i | \(0.995856\pi\) | |||||||
\(434\) | 0.985999 | 0.0473295 | ||||||||
\(435\) | 2.70895 | − | 4.69203i | 0.129884 | − | 0.224966i | ||||
\(436\) | −6.49396 | + | 11.2479i | −0.311004 | + | 0.538675i | ||||
\(437\) | −17.2707 | −0.826168 | ||||||||
\(438\) | 1.59299 | − | 2.75914i | 0.0761160 | − | 0.131837i | ||||
\(439\) | −6.35905 | − | 11.0142i | −0.303501 | − | 0.525679i | 0.673425 | − | 0.739255i | \(-0.264822\pi\) |
−0.976926 | + | 0.213576i | \(0.931489\pi\) | |||||||
\(440\) | −1.01693 | − | 1.76137i | −0.0484800 | − | 0.0839699i | ||||
\(441\) | −6.87263 | −0.327268 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.5972 | 1.07362 | 0.536812 | − | 0.843702i | \(-0.319628\pi\) | ||||
0.536812 | + | 0.843702i | \(0.319628\pi\) | |||||||
\(444\) | −5.04892 | − | 8.74498i | −0.239611 | − | 0.415018i | ||||
\(445\) | 0.137063 | + | 0.237401i | 0.00649743 | + | 0.0112539i | ||||
\(446\) | −3.38404 | + | 5.86133i | −0.160239 | + | 0.277542i | ||||
\(447\) | 20.8170 | 0.984610 | ||||||||
\(448\) | −0.178448 | + | 0.309081i | −0.00843087 | + | 0.0146027i | ||||
\(449\) | 5.82371 | − | 10.0870i | 0.274838 | − | 0.476033i | −0.695256 | − | 0.718762i | \(-0.744709\pi\) |
0.970094 | + | 0.242729i | \(0.0780425\pi\) | |||||||
\(450\) | 4.52111 | 0.213127 | ||||||||
\(451\) | −7.18598 | + | 12.4465i | −0.338375 | + | 0.586082i | ||||
\(452\) | −0.396125 | − | 0.686108i | −0.0186321 | − | 0.0322718i | ||||
\(453\) | −0.447730 | − | 0.775492i | −0.0210362 | − | 0.0364358i | ||||
\(454\) | 23.6799 | 1.11135 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.20775 | 0.337534 | ||||||||
\(457\) | −10.5945 | − | 18.3502i | −0.495589 | − | 0.858385i | 0.504398 | − | 0.863471i | \(-0.331714\pi\) |
−0.999987 | + | 0.00508594i | \(0.998381\pi\) | |||||||
\(458\) | 4.14914 | + | 7.18653i | 0.193877 | + | 0.335804i | ||||
\(459\) | −3.35690 | + | 5.81431i | −0.156686 | + | 0.271389i | ||||
\(460\) | −1.65817 | −0.0773126 | ||||||||
\(461\) | 12.0347 | − | 20.8447i | 0.560511 | − | 0.970833i | −0.436941 | − | 0.899490i | \(-0.643938\pi\) |
0.997452 | − | 0.0713432i | \(-0.0227285\pi\) | |||||||
\(462\) | 0.524459 | − | 0.908389i | 0.0244000 | − | 0.0422621i | ||||
\(463\) | 18.1715 | 0.844502 | 0.422251 | − | 0.906479i | \(-0.361240\pi\) | ||||
0.422251 | + | 0.906479i | \(0.361240\pi\) | |||||||
\(464\) | −3.91454 | + | 6.78019i | −0.181728 | + | 0.314762i | ||||
\(465\) | −0.955927 | − | 1.65571i | −0.0443301 | − | 0.0767819i | ||||
\(466\) | −11.9825 | − | 20.7544i | −0.555081 | − | 0.961428i | ||||
\(467\) | −2.93123 | −0.135641 | −0.0678206 | − | 0.997698i | \(-0.521605\pi\) | ||||
−0.0678206 | + | 0.997698i | \(0.521605\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82717 | 0.222898 | ||||||||
\(470\) | −1.72587 | − | 2.98930i | −0.0796086 | − | 0.137886i | ||||
\(471\) | −4.29590 | − | 7.44071i | −0.197944 | − | 0.342850i | ||||
\(472\) | 0.821552 | − | 1.42297i | 0.0378150 | − | 0.0654975i | ||||
\(473\) | 19.3733 | 0.890785 | ||||||||
\(474\) | 7.52326 | − | 13.0307i | 0.345555 | − | 0.598519i | ||||
\(475\) | −16.2935 | + | 28.2212i | −0.747597 | + | 1.29488i | ||||
\(476\) | 2.39612 | 0.109826 | ||||||||
\(477\) | 4.44385 | − | 7.69697i | 0.203470 | − | 0.352420i | ||||
\(478\) | −6.30798 | − | 10.9257i | −0.288520 | − | 0.499732i | ||||
\(479\) | −15.3545 | − | 26.5948i | −0.701565 | − | 1.21515i | −0.967917 | − | 0.251271i | \(-0.919152\pi\) |
0.266352 | − | 0.963876i | \(-0.414182\pi\) | |||||||
\(480\) | 0.692021 | 0.0315863 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 26.3937 | 1.20220 | ||||||||
\(483\) | −0.427583 | − | 0.740596i | −0.0194557 | − | 0.0336983i | ||||
\(484\) | 1.18114 | + | 2.04579i | 0.0536880 | + | 0.0929904i | ||||
\(485\) | −0.144596 | + | 0.250448i | −0.00656577 | + | 0.0113722i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 12.0749 | − | 20.9143i | 0.547164 | − | 0.947717i | −0.451303 | − | 0.892371i | \(-0.649041\pi\) |
0.998467 | − | 0.0553458i | \(-0.0176261\pi\) | |||||||
\(488\) | −3.24698 | + | 5.62393i | −0.146984 | + | 0.254584i | ||||
\(489\) | −1.72587 | −0.0780467 | ||||||||
\(490\) | 2.37800 | − | 4.11882i | 0.107427 | − | 0.186069i | ||||
\(491\) | −7.29859 | − | 12.6415i | −0.329381 | − | 0.570504i | 0.653009 | − | 0.757351i | \(-0.273507\pi\) |
−0.982389 | + | 0.186847i | \(0.940173\pi\) | |||||||
\(492\) | −2.44504 | − | 4.23494i | −0.110231 | − | 0.190926i | ||||
\(493\) | 52.5628 | 2.36731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.03385 | −0.0914148 | ||||||||
\(496\) | 1.38135 | + | 2.39258i | 0.0620246 | + | 0.107430i | ||||
\(497\) | −1.21552 | − | 2.10534i | −0.0545236 | − | 0.0944376i | ||||
\(498\) | −7.41335 | + | 12.8403i | −0.332200 | + | 0.575387i | ||||
\(499\) | −6.85517 | −0.306879 | −0.153440 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153440 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(500\) | −3.29440 | + | 5.70608i | −0.147330 | + | 0.255184i | ||||
\(501\) | 10.5700 | − | 18.3078i | 0.472234 | − | 0.817933i | ||||
\(502\) | 30.0344 | 1.34050 | ||||||||
\(503\) | 13.3666 | − | 23.1516i | 0.595987 | − | 1.03228i | −0.397420 | − | 0.917637i | \(-0.630094\pi\) |
0.993407 | − | 0.114642i | \(-0.0365722\pi\) | |||||||
\(504\) | 0.178448 | + | 0.309081i | 0.00794870 | + | 0.0137676i | ||||
\(505\) | 3.46532 | + | 6.00211i | 0.154205 | + | 0.267090i | ||||
\(506\) | −7.04221 | −0.313065 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.2174 | −0.808268 | ||||||||
\(509\) | −10.3297 | − | 17.8916i | −0.457858 | − | 0.793033i | 0.540989 | − | 0.841029i | \(-0.318050\pi\) |
−0.998848 | + | 0.0479959i | \(0.984717\pi\) | |||||||
\(510\) | −2.32304 | − | 4.02363i | −0.102866 | − | 0.178169i | ||||
\(511\) | −0.568532 | + | 0.984726i | −0.0251504 | + | 0.0435617i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.60388 | − | 6.24210i | 0.159115 | − | 0.275595i | ||||
\(514\) | 5.63102 | − | 9.75322i | 0.248374 | − | 0.430196i | ||||
\(515\) | 6.66115 | 0.293525 | ||||||||
\(516\) | −3.29590 | + | 5.70866i | −0.145094 | + | 0.251310i | ||||
\(517\) | −7.32975 | − | 12.6955i | −0.322362 | − | 0.558347i | ||||
\(518\) | 1.80194 | + | 3.12105i | 0.0791726 | + | 0.137131i | ||||
\(519\) | 9.35450 | 0.410617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0965 | −0.661390 | −0.330695 | − | 0.943738i | \(-0.607283\pi\) | ||||
−0.330695 | + | 0.943738i | \(0.607283\pi\) | |||||||
\(522\) | 3.91454 | + | 6.78019i | 0.171335 | + | 0.296761i | ||||
\(523\) | −0.0174584 | − | 0.0302388i | −0.000763402 | − | 0.00132225i | 0.865643 | − | 0.500661i | \(-0.166910\pi\) |
−0.866407 | + | 0.499339i | \(0.833576\pi\) | |||||||
\(524\) | −1.36778 | + | 2.36907i | −0.0597518 | + | 0.103493i | ||||
\(525\) | −1.61356 | −0.0704217 | ||||||||
\(526\) | −2.77479 | + | 4.80608i | −0.120987 | + | 0.209555i | ||||
\(527\) | 9.27413 | − | 16.0633i | 0.403987 | − | 0.699727i | ||||
\(528\) | 2.93900 | 0.127904 | ||||||||
\(529\) | 8.62929 | − | 14.9464i | 0.375187 | − | 0.649842i | ||||
\(530\) | 3.07524 | + | 5.32647i | 0.133580 | + | 0.231367i | ||||
\(531\) | −0.821552 | − | 1.42297i | −0.0356523 | − | 0.0617516i | ||||
\(532\) | −2.57242 | −0.111528 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.396125 | −0.0171420 | ||||||||
\(535\) | −2.29440 | − | 3.97403i | −0.0991958 | − | 0.171812i | ||||
\(536\) | 6.76271 | + | 11.7134i | 0.292105 | + | 0.505940i | ||||
\(537\) | −1.58761 | + | 2.74983i | −0.0685106 | + | 0.118664i | ||||
\(538\) | −16.6872 | −0.719438 | ||||||||
\(539\) | 10.0993 | − | 17.4925i | 0.435009 | − | 0.753457i | ||||
\(540\) | 0.346011 | − | 0.599308i | 0.0148899 | − | 0.0257901i | ||||
\(541\) | −13.0858 | −0.562600 | −0.281300 | − | 0.959620i | \(-0.590766\pi\) | ||||
−0.281300 | + | 0.959620i | \(0.590766\pi\) | |||||||
\(542\) | 3.30678 | − | 5.72751i | 0.142038 | − | 0.246018i | ||||
\(543\) | 9.89977 | + | 17.1469i | 0.424840 | + | 0.735844i | ||||
\(544\) | 3.35690 | + | 5.81431i | 0.143926 | + | 0.249287i | ||||
\(545\) | −8.98792 | −0.385000 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.97584 | −0.255508 | −0.127754 | − | 0.991806i | \(-0.540777\pi\) | ||||
−0.127754 | + | 0.991806i | \(0.540777\pi\) | |||||||
\(548\) | 3.82371 | + | 6.62286i | 0.163341 | + | 0.282914i | ||||
\(549\) | 3.24698 | + | 5.62393i | 0.138578 | + | 0.240024i | ||||
\(550\) | −6.64377 | + | 11.5073i | −0.283291 | + | 0.490675i | ||||
\(551\) | −56.4301 | −2.40400 | ||||||||
\(552\) | 1.19806 | − | 2.07510i | 0.0509929 | − | 0.0883223i | ||||
\(553\) | −2.68502 | + | 4.65059i | −0.114179 | + | 0.197763i | ||||
\(554\) | 21.7995 | 0.926174 | ||||||||
\(555\) | 3.49396 | − | 6.05171i | 0.148310 | − | 0.256881i | ||||
\(556\) | −1.69202 | − | 2.93067i | −0.0717577 | − | 0.124288i | ||||
\(557\) | −5.21983 | − | 9.04102i | −0.221171 | − | 0.383080i | 0.733993 | − | 0.679158i | \(-0.237655\pi\) |
−0.955164 | + | 0.296077i | \(0.904321\pi\) | |||||||
\(558\) | 2.76271 | 0.116955 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.246980 | −0.0104368 | ||||||||
\(561\) | −9.86592 | − | 17.0883i | −0.416539 | − | 0.721468i | ||||
\(562\) | −10.2959 | − | 17.8330i | −0.434306 | − | 0.752240i | ||||
\(563\) | 2.83028 | − | 4.90219i | 0.119282 | − | 0.206603i | −0.800201 | − | 0.599732i | \(-0.795274\pi\) |
0.919483 | + | 0.393129i | \(0.128607\pi\) | |||||||
\(564\) | 4.98792 | 0.210029 | ||||||||
\(565\) | 0.274127 | − | 0.474801i | 0.0115326 | − | 0.0199750i | ||||
\(566\) | −6.50604 | + | 11.2688i | −0.273469 | + | 0.473663i | ||||
\(567\) | 0.356896 | 0.0149882 | ||||||||
\(568\) | 3.40581 | − | 5.89904i | 0.142905 | − | 0.247518i | ||||
\(569\) | −10.3284 | − | 17.8893i | −0.432990 | − | 0.749961i | 0.564139 | − | 0.825680i | \(-0.309208\pi\) |
−0.997129 | + | 0.0757191i | \(0.975875\pi\) | |||||||
\(570\) | 2.49396 | + | 4.31966i | 0.104460 | + | 0.180931i | ||||
\(571\) | 44.3672 | 1.85671 | 0.928354 | − | 0.371697i | \(-0.121224\pi\) | ||||
0.928354 | + | 0.371697i | \(0.121224\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2620 | 0.637581 | ||||||||
\(574\) | 0.872625 | + | 1.51143i | 0.0364227 | + | 0.0630859i | ||||
\(575\) | 5.41657 | + | 9.38177i | 0.225886 | + | 0.391247i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −29.4426 | −1.22571 | −0.612857 | − | 0.790194i | \(-0.709980\pi\) | ||||
−0.612857 | + | 0.790194i | \(0.709980\pi\) | |||||||
\(578\) | 14.0375 | − | 24.3137i | 0.583883 | − | 1.01132i | ||||
\(579\) | 2.38404 | − | 4.12928i | 0.0990774 | − | 0.171607i | ||||
\(580\) | −5.41789 | −0.224966 | ||||||||
\(581\) | 2.64579 | − | 4.58265i | 0.109766 | − | 0.190120i | ||||
\(582\) | −0.208947 | − | 0.361908i | −0.00866115 | − | 0.0150015i | ||||
\(583\) | 13.0605 | + | 22.6214i | 0.540909 | + | 0.936882i | ||||
\(584\) | −3.18598 | −0.131837 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.9390 | −0.617124 | ||||||||
\(587\) | −9.78179 | − | 16.9426i | −0.403738 | − | 0.699294i | 0.590436 | − | 0.807085i | \(-0.298956\pi\) |
−0.994174 | + | 0.107790i | \(0.965623\pi\) | |||||||
\(588\) | 3.43631 | + | 5.95187i | 0.141711 | + | 0.245451i | ||||
\(589\) | −9.95646 | + | 17.2451i | −0.410249 | + | 0.710572i | ||||
\(590\) | 1.13706 | 0.0468122 | ||||||||
\(591\) | 6.11745 | − | 10.5957i | 0.251638 | − | 0.435850i | ||||
\(592\) | −5.04892 | + | 8.74498i | −0.207509 | + | 0.359417i | ||||
\(593\) | 10.8793 | 0.446761 | 0.223380 | − | 0.974731i | \(-0.428291\pi\) | ||||
0.223380 | + | 0.974731i | \(0.428291\pi\) | |||||||
\(594\) | 1.46950 | − | 2.54525i | 0.0602943 | − | 0.104433i | ||||
\(595\) | 0.829085 | + | 1.43602i | 0.0339892 | + | 0.0588710i | ||||
\(596\) | −10.4085 | − | 18.0281i | −0.426349 | − | 0.738458i | ||||
\(597\) | −11.8485 | −0.484925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0543 | 0.655961 | 0.327980 | − | 0.944685i | \(-0.393632\pi\) | ||||
0.327980 | + | 0.944685i | \(0.393632\pi\) | |||||||
\(600\) | −2.26055 | − | 3.91539i | −0.0922867 | − | 0.159845i | ||||
\(601\) | −6.44773 | − | 11.1678i | −0.263008 | − | 0.455544i | 0.704032 | − | 0.710169i | \(-0.251381\pi\) |
−0.967040 | + | 0.254625i | \(0.918048\pi\) | |||||||
\(602\) | 1.17629 | − | 2.03740i | 0.0479421 | − | 0.0830381i | ||||
\(603\) | 13.5254 | 0.550798 | ||||||||
\(604\) | −0.447730 | + | 0.775492i | −0.0182179 | + | 0.0315543i | ||||
\(605\) | −0.817372 | + | 1.41573i | −0.0332309 | + | 0.0575576i | ||||
\(606\) | −10.0151 | −0.406834 | ||||||||
\(607\) | −22.2371 | + | 38.5157i | −0.902574 | + | 1.56330i | −0.0784334 | + | 0.996919i | \(0.524992\pi\) |
−0.824141 | + | 0.566385i | \(0.808342\pi\) | |||||||
\(608\) | −3.60388 | − | 6.24210i | −0.146156 | − | 0.253150i | ||||
\(609\) | −1.39708 | − | 2.41982i | −0.0566127 | − | 0.0980561i | ||||
\(610\) | −4.49396 | −0.181955 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.71379 | 0.271389 | ||||||||
\(613\) | 21.0127 | + | 36.3950i | 0.848694 | + | 1.46998i | 0.882374 | + | 0.470548i | \(0.155944\pi\) |
−0.0336804 | + | 0.999433i | \(0.510723\pi\) | |||||||
\(614\) | −13.0151 | − | 22.5428i | −0.525245 | − | 0.909752i | ||||
\(615\) | 1.69202 | − | 2.93067i | 0.0682289 | − | 0.118176i | ||||
\(616\) | −1.04892 | −0.0422621 | ||||||||
\(617\) | −8.33273 | + | 14.4327i | −0.335463 | + | 0.581039i | −0.983574 | − | 0.180507i | \(-0.942226\pi\) |
0.648111 | + | 0.761546i | \(0.275559\pi\) | |||||||
\(618\) | −4.81282 | + | 8.33605i | −0.193600 | + | 0.335325i | ||||
\(619\) | −39.7512 | −1.59774 | −0.798868 | − | 0.601506i | \(-0.794568\pi\) | ||||
−0.798868 | + | 0.601506i | \(0.794568\pi\) | |||||||
\(620\) | −0.955927 | + | 1.65571i | −0.0383910 | + | 0.0664951i | ||||
\(621\) | −1.19806 | − | 2.07510i | −0.0480766 | − | 0.0832711i | ||||
\(622\) | −2.40581 | − | 4.16699i | −0.0964643 | − | 0.167081i | ||||
\(623\) | 0.141375 | 0.00566408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0459 | 0.721837 | ||||||||
\(626\) | −13.0206 | − | 22.5523i | −0.520407 | − | 0.901371i | ||||
\(627\) | 10.5918 | + | 18.3455i | 0.422996 | + | 0.732650i | ||||
\(628\) | −4.29590 | + | 7.44071i | −0.171425 | + | 0.296917i | ||||
\(629\) | 67.7948 | 2.70315 | ||||||||
\(630\) | −0.123490 | + | 0.213891i | −0.00491995 | + | 0.00852161i | ||||
\(631\) | 7.28836 | − | 12.6238i | 0.290145 | − | 0.502546i | −0.683699 | − | 0.729764i | \(-0.739630\pi\) |
0.973844 | + | 0.227218i | \(0.0729631\pi\) | |||||||
\(632\) | −15.0465 | −0.598519 | ||||||||
\(633\) | 8.63102 | − | 14.9494i | 0.343052 | − | 0.594184i | ||||
\(634\) | 5.76055 | + | 9.97757i | 0.228781 | + | 0.396260i | ||||
\(635\) | −6.30343 | − | 10.9179i | −0.250144 | − | 0.433262i | ||||
\(636\) | −8.88769 | −0.352420 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −23.0097 | −0.910962 | ||||||||
\(639\) | −3.40581 | − | 5.89904i | −0.134732 | − | 0.233362i | ||||
\(640\) | −0.346011 | − | 0.599308i | −0.0136773 | − | 0.0236897i | ||||
\(641\) | −19.2174 | + | 33.2856i | −0.759043 | + | 1.31470i | 0.184296 | + | 0.982871i | \(0.441000\pi\) |
−0.943339 | + | 0.331831i | \(0.892334\pi\) | |||||||
\(642\) | 6.63102 | 0.261706 | ||||||||
\(643\) | −0.521106 | + | 0.902583i | −0.0205504 | + | 0.0355944i | −0.876118 | − | 0.482097i | \(-0.839875\pi\) |
0.855567 | + | 0.517692i | \(0.173209\pi\) | |||||||
\(644\) | −0.427583 | + | 0.740596i | −0.0168491 | + | 0.0291836i | ||||
\(645\) | −4.56166 | −0.179615 | ||||||||
\(646\) | −24.1957 | + | 41.9081i | −0.951966 | + | 1.64885i | ||||
\(647\) | 14.0804 | + | 24.3879i | 0.553557 | + | 0.958788i | 0.998014 | + | 0.0629884i | \(0.0200631\pi\) |
−0.444458 | + | 0.895800i | \(0.646604\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 4.82908 | 0.189558 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.985999 | −0.0386444 | ||||||||
\(652\) | 0.862937 | + | 1.49465i | 0.0337952 | + | 0.0585350i | ||||
\(653\) | −5.31013 | − | 9.19742i | −0.207802 | − | 0.359923i | 0.743220 | − | 0.669047i | \(-0.233298\pi\) |
−0.951022 | + | 0.309124i | \(0.899964\pi\) | |||||||
\(654\) | 6.49396 | − | 11.2479i | 0.253934 | − | 0.439826i | ||||
\(655\) | −1.89307 | −0.0739683 | ||||||||
\(656\) | −2.44504 | + | 4.23494i | −0.0954628 | + | 0.165347i | ||||
\(657\) | −1.59299 | + | 2.75914i | −0.0621485 | + | 0.107644i | ||||
\(658\) | −1.78017 | −0.0693982 | ||||||||
\(659\) | 20.1814 | − | 34.9553i | 0.786157 | − | 1.36166i | −0.142148 | − | 0.989845i | \(-0.545401\pi\) |
0.928305 | − | 0.371818i | \(-0.121266\pi\) | |||||||
\(660\) | 1.01693 | + | 1.76137i | 0.0395838 | + | 0.0685611i | ||||
\(661\) | −15.9584 | − | 27.6407i | −0.620709 | − | 1.07510i | −0.989354 | − | 0.145529i | \(-0.953512\pi\) |
0.368645 | − | 0.929570i | \(-0.379822\pi\) | |||||||
\(662\) | 3.43834 | 0.133635 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.8267 | 0.575387 | ||||||||
\(665\) | −0.890084 | − | 1.54167i | −0.0345160 | − | 0.0597834i | ||||
\(666\) | 5.04892 | + | 8.74498i | 0.195642 | + | 0.338861i | ||||
\(667\) | −9.37973 | + | 16.2462i | −0.363185 | + | 0.629054i | ||||
\(668\) | −21.1400 | −0.817933 | ||||||||
\(669\) | 3.38404 | − | 5.86133i | 0.130835 | − | 0.226612i | ||||
\(670\) | −4.67994 | + | 8.10589i | −0.180802 | + | 0.313158i | ||||
\(671\) | −19.0858 | −0.736797 | ||||||||
\(672\) | 0.178448 | − | 0.309081i | 0.00688378 | − | 0.0119231i | ||||
\(673\) | −1.91401 | − | 3.31516i | −0.0737797 | − | 0.127790i | 0.826775 | − | 0.562532i | \(-0.190173\pi\) |
−0.900555 | + | 0.434742i | \(0.856839\pi\) | |||||||
\(674\) | 4.10052 | + | 7.10231i | 0.157946 | + | 0.273571i | ||||
\(675\) | −4.52111 | −0.174017 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.78927 | 0.0687670 | 0.0343835 | − | 0.999409i | \(-0.489053\pi\) | ||||
0.0343835 | + | 0.999409i | \(0.489053\pi\) | |||||||
\(678\) | 0.396125 | + | 0.686108i | 0.0152131 | + | 0.0263498i | ||||
\(679\) | 0.0745725 | + | 0.129163i | 0.00286183 | + | 0.00495683i | ||||
\(680\) | −2.32304 | + | 4.02363i | −0.0890847 | + | 0.154299i | ||||
\(681\) | −23.6799 | −0.907417 | ||||||||
\(682\) | −4.05980 | + | 7.03178i | −0.155458 | + | 0.269261i | ||||
\(683\) | 0.379863 | − | 0.657941i | 0.0145350 | − | 0.0251754i | −0.858666 | − | 0.512535i | \(-0.828707\pi\) |
0.873201 | + | 0.487359i | \(0.162040\pi\) | |||||||
\(684\) | −7.20775 | −0.275595 | ||||||||
\(685\) | −2.64609 | + | 4.58316i | −0.101102 | + | 0.175114i | ||||
\(686\) | −2.47554 | − | 4.28776i | −0.0945166 | − | 0.163708i | ||||
\(687\) | −4.14914 | − | 7.18653i | −0.158300 | − | 0.274183i | ||||
\(688\) | 6.59179 | 0.251310 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.65817 | 0.0631254 | ||||||||
\(691\) | 2.32975 | + | 4.03524i | 0.0886278 | + | 0.153508i | 0.906931 | − | 0.421278i | \(-0.138418\pi\) |
−0.818304 | + | 0.574786i | \(0.805085\pi\) | |||||||
\(692\) | −4.67725 | − | 8.10124i | −0.177802 | − | 0.307963i | ||||
\(693\) | −0.524459 | + | 0.908389i | −0.0199225 | + | 0.0345068i | ||||
\(694\) | −7.86294 | −0.298473 | ||||||||
\(695\) | 1.17092 | − | 2.02808i | 0.0444153 | − | 0.0769296i | ||||
\(696\) | 3.91454 | − | 6.78019i | 0.148380 | − | 0.257002i | ||||
\(697\) | 32.8310 | 1.24356 | ||||||||
\(698\) | 9.36227 | − | 16.2159i | 0.354367 | − | 0.613782i | ||||
\(699\) | 11.9825 | + | 20.7544i | 0.453221 | + | 0.785002i | ||||
\(700\) | 0.806782 | + | 1.39739i | 0.0304935 | + | 0.0528163i | ||||
\(701\) | −24.3284 | −0.918872 | −0.459436 | − | 0.888211i | \(-0.651948\pi\) | ||||
−0.459436 | + | 0.888211i | \(0.651948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −72.7827 | −2.74505 | ||||||||
\(704\) | −1.46950 | − | 2.54525i | −0.0553839 | − | 0.0959277i | ||||
\(705\) | 1.72587 | + | 2.98930i | 0.0650001 | + | 0.112584i | ||||
\(706\) | 15.7724 | − | 27.3186i | 0.593602 | − | 1.02815i | ||||
\(707\) | 3.57434 | 0.134427 | ||||||||
\(708\) | −0.821552 | + | 1.42297i | −0.0308758 | + | 0.0534785i | ||||
\(709\) | −14.6963 | + | 25.4548i | −0.551932 | + | 0.955975i | 0.446203 | + | 0.894932i | \(0.352776\pi\) |
−0.998135 | + | 0.0610430i | \(0.980557\pi\) | |||||||
\(710\) | 4.71379 | 0.176905 | ||||||||
\(711\) | −7.52326 | + | 13.0307i | −0.282144 | + | 0.488688i | ||||
\(712\) | 0.198062 | + | 0.343054i | 0.00742270 | + | 0.0128565i | ||||
\(713\) | 3.30990 | + | 5.73291i | 0.123957 | + | 0.214699i | ||||
\(714\) | −2.39612 | −0.0896727 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.17523 | 0.118664 | ||||||||
\(717\) | 6.30798 | + | 10.9257i | 0.235576 | + | 0.408029i | ||||
\(718\) | −1.19806 | − | 2.07510i | −0.0447113 | − | 0.0774422i | ||||
\(719\) | 25.7439 | − | 44.5898i | 0.960086 | − | 1.66292i | 0.237812 | − | 0.971311i | \(-0.423570\pi\) |
0.722274 | − | 0.691607i | \(-0.243097\pi\) | |||||||
\(720\) | −0.692021 | −0.0257901 | ||||||||
\(721\) | 1.71768 | − | 2.97510i | 0.0639696 | − | 0.110799i | ||||
\(722\) | 16.4758 | − | 28.5370i | 0.613167 | − | 1.06204i | ||||
\(723\) | −26.3937 | −0.981593 | ||||||||
\(724\) | 9.89977 | − | 17.1469i | 0.367922 | − | 0.637260i | ||||
\(725\) | 17.6981 | + | 30.6539i | 0.657290 | + | 1.13846i | ||||
\(726\) | −1.18114 | − | 2.04579i | −0.0438361 | − | 0.0759263i | ||||
\(727\) | −3.67324 | −0.136233 | −0.0681164 | − | 0.997677i | \(-0.521699\pi\) | ||||
−0.0681164 | + | 0.997677i | \(0.521699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.10238 | − | 1.90938i | −0.0408010 | − | 0.0706695i | ||||
\(731\) | −22.1280 | − | 38.3268i | −0.818432 | − | 1.41757i | ||||
\(732\) | 3.24698 | − | 5.62393i | 0.120012 | − | 0.207867i | ||||
\(733\) | −18.3612 | −0.678187 | −0.339093 | − | 0.940753i | \(-0.610120\pi\) | ||||
−0.339093 | + | 0.940753i | \(0.610120\pi\) | |||||||
\(734\) | −0.00215593 | + | 0.00373419i | −7.95770e−5 | + | 0.000137831i | ||||
\(735\) | −2.37800 | + | 4.11882i | −0.0877139 | + | 0.151925i | ||||
\(736\) | −2.39612 | −0.0883223 | ||||||||
\(737\) | −19.8756 | + | 34.4256i | −0.732127 | + | 1.26808i | ||||
\(738\) | 2.44504 | + | 4.23494i | 0.0900032 | + | 0.155890i | ||||
\(739\) | 0.841166 | + | 1.45694i | 0.0309428 | + | 0.0535945i | 0.881082 | − | 0.472963i | \(-0.156816\pi\) |
−0.850139 | + | 0.526558i | \(0.823482\pi\) | |||||||
\(740\) | −6.98792 | −0.256881 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.17198 | 0.116447 | ||||||||
\(743\) | 24.1468 | + | 41.8234i | 0.885858 | + | 1.53435i | 0.844727 | + | 0.535198i | \(0.179763\pi\) |
0.0411318 | + | 0.999154i | \(0.486904\pi\) | |||||||
\(744\) | −1.38135 | − | 2.39258i | −0.0506429 | − | 0.0877161i | ||||
\(745\) | 7.20291 | − | 12.4758i | 0.263894 | − | 0.457078i | ||||
\(746\) | 32.3129 | 1.18306 | ||||||||
\(747\) | 7.41335 | − | 12.8403i | 0.271240 | − | 0.469802i | ||||
\(748\) | −9.86592 | + | 17.0883i | −0.360734 | + | 0.624809i | ||||
\(749\) | −2.36658 | −0.0864731 | ||||||||
\(750\) | 3.29440 | − | 5.70608i | 0.120295 | − | 0.208356i | ||||
\(751\) | −5.85056 | − | 10.1335i | −0.213490 | − | 0.369775i | 0.739314 | − | 0.673360i | \(-0.235150\pi\) |
−0.952804 | + | 0.303585i | \(0.901816\pi\) | |||||||
\(752\) | −2.49396 | − | 4.31966i | −0.0909453 | − | 0.157522i | ||||
\(753\) | −30.0344 | −1.09452 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.619678 | −0.0225524 | ||||||||
\(756\) | −0.178448 | − | 0.309081i | −0.00649009 | − | 0.0112412i | ||||
\(757\) | −12.5918 | − | 21.8096i | −0.457657 | − | 0.792684i | 0.541180 | − | 0.840907i | \(-0.317978\pi\) |
−0.998837 | + | 0.0482223i | \(0.984644\pi\) | |||||||
\(758\) | −9.87800 | + | 17.1092i | −0.358785 | + | 0.621434i | ||||
\(759\) | 7.04221 | 0.255616 | ||||||||
\(760\) | 2.49396 | − | 4.31966i | 0.0904654 | − | 0.156691i | ||||
\(761\) | 11.2078 | − | 19.4124i | 0.406281 | − | 0.703699i | −0.588189 | − | 0.808724i | \(-0.700159\pi\) |
0.994470 | + | 0.105025i | \(0.0334922\pi\) | |||||||
\(762\) | 18.2174 | 0.659948 | ||||||||
\(763\) | −2.31767 | + | 4.01432i | −0.0839052 | + | 0.145328i | ||||
\(764\) | −7.63102 | − | 13.2173i | −0.276081 | − | 0.478186i | ||||
\(765\) | 2.32304 | + | 4.02363i | 0.0839898 | + | 0.145475i | ||||
\(766\) | 28.8116 | 1.04101 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −0.0663757 | − | 0.114966i | −0.00239357 | − | 0.00414579i | 0.864826 | − | 0.502071i | \(-0.167429\pi\) |
−0.867220 | + | 0.497926i | \(0.834095\pi\) | |||||||
\(770\) | −0.362937 | − | 0.628625i | −0.0130793 | − | 0.0226541i | ||||
\(771\) | −5.63102 | + | 9.75322i | −0.202796 | + | 0.351254i | ||||
\(772\) | −4.76809 | −0.171607 | ||||||||
\(773\) | −24.0347 | + | 41.6293i | −0.864467 | + | 1.49730i | 0.00310775 | + | 0.999995i | \(0.499011\pi\) |
−0.867575 | + | 0.497306i | \(0.834323\pi\) | |||||||
\(774\) | 3.29590 | − | 5.70866i | 0.118469 | − | 0.205194i | ||||
\(775\) | 12.4905 | 0.448672 | ||||||||
\(776\) | −0.208947 | + | 0.361908i | −0.00750077 | + | 0.0129917i | ||||
\(777\) | −1.80194 | − | 3.12105i | −0.0646442 | − | 0.111967i | ||||
\(778\) | 17.3910 | + | 30.1222i | 0.623499 | + | 1.07993i | ||||
\(779\) | −35.2465 | −1.26284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0194 | 0.716350 | ||||||||
\(782\) | 8.04354 | + | 13.9318i | 0.287636 | + | 0.498201i | ||||
\(783\) | −3.91454 | − | 6.78019i | −0.139894 | − | 0.242304i | ||||
\(784\) | 3.43631 | − | 5.95187i | 0.122725 | − | 0.212567i | ||||
\(785\) | −5.94571 | −0.212211 | ||||||||
\(786\) | 1.36778 | − | 2.36907i | 0.0487871 | − | 0.0845018i | ||||
\(787\) | 3.10454 | − | 5.37722i | 0.110665 | − | 0.191677i | −0.805374 | − | 0.592767i | \(-0.798035\pi\) |
0.916039 | + | 0.401090i | \(0.131369\pi\) | |||||||
\(788\) | −12.2349 | −0.435850 | ||||||||
\(789\) | 2.77479 | − | 4.80608i | 0.0987852 | − | 0.171101i | ||||
\(790\) | −5.20626 | − | 9.01751i | −0.185230 | − | 0.320828i | ||||
\(791\) | −0.141375 | − | 0.244869i | −0.00502672 | − | 0.00870654i | ||||
\(792\) | −2.93900 | −0.104433 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.15346 | −0.182889 | ||||||||
\(795\) | −3.07524 | − | 5.32647i | −0.109067 | − | 0.188910i | ||||
\(796\) | 5.92423 | + | 10.2611i | 0.209979 | + | 0.363694i | ||||
\(797\) | −0.163915 | + | 0.283909i | −0.00580616 | + | 0.0100566i | −0.868914 | − | 0.494963i | \(-0.835182\pi\) |
0.863108 | + | 0.505020i | \(0.168515\pi\) | |||||||
\(798\) | 2.57242 | 0.0910626 | ||||||||
\(799\) | −16.7439 | + | 29.0013i | −0.592357 | + | 1.02599i | ||||
\(800\) | −2.26055 | + | 3.91539i | −0.0799226 | + | 0.138430i | ||||
\(801\) | 0.396125 | 0.0139964 | ||||||||
\(802\) | −6.66248 | + | 11.5398i | −0.235260 | + | 0.407483i | ||||
\(803\) | −4.68180 | − | 8.10912i | −0.165217 | − | 0.286164i | ||||
\(804\) | −6.76271 | − | 11.7134i | −0.238502 | − | 0.413098i | ||||
\(805\) | −0.591794 | −0.0208580 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.6872 | 0.587419 | ||||||||
\(808\) | 5.00753 | + | 8.67330i | 0.176164 | + | 0.305126i | ||||
\(809\) | 18.7192 | + | 32.4226i | 0.658131 | + | 1.13992i | 0.981099 | + | 0.193506i | \(0.0619860\pi\) |
−0.322968 | + | 0.946410i | \(0.604681\pi\) | |||||||
\(810\) | −0.346011 | + | 0.599308i | −0.0121576 | + | 0.0210575i | ||||
\(811\) | −17.1448 | −0.602037 | −0.301018 | − | 0.953618i | \(-0.597327\pi\) | ||||
−0.301018 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(812\) | −1.39708 | + | 2.41982i | −0.0490280 | + | 0.0849191i | ||||
\(813\) | −3.30678 | + | 5.72751i | −0.115974 | + | 0.200873i | ||||
\(814\) | −29.6775 | −1.04020 | ||||||||
\(815\) | −0.597171 | + | 1.03433i | −0.0209180 | + | 0.0362310i | ||||
\(816\) | −3.35690 | − | 5.81431i | −0.117515 | − | 0.203542i | ||||
\(817\) | 23.7560 | + | 41.1466i | 0.831117 | + | 1.43954i | ||||
\(818\) | −24.0237 | −0.839969 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.38404 | −0.118176 | ||||||||
\(821\) | −8.89426 | − | 15.4053i | −0.310412 | − | 0.537649i | 0.668040 | − | 0.744126i | \(-0.267134\pi\) |
−0.978452 | + | 0.206476i | \(0.933800\pi\) | |||||||
\(822\) | −3.82371 | − | 6.62286i | −0.133367 | − | 0.230999i | ||||
\(823\) | −6.11506 | + | 10.5916i | −0.213157 | + | 0.369200i | −0.952701 | − | 0.303909i | \(-0.901708\pi\) |
0.739544 | + | 0.673109i | \(0.235041\pi\) | |||||||
\(824\) | 9.62565 | 0.335325 | ||||||||
\(825\) | 6.64377 | − | 11.5073i | 0.231306 | − | 0.400634i | ||||
\(826\) | 0.293209 | − | 0.507852i | 0.0102020 | − | 0.0176704i | ||||
\(827\) | −20.5623 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(828\) | −1.19806 | + | 2.07510i | −0.0416355 | + | 0.0721149i | ||||
\(829\) | 12.7235 | + | 22.0377i | 0.441905 | + | 0.765401i | 0.997831 | − | 0.0658303i | \(-0.0209696\pi\) |
−0.555926 | + | 0.831232i | \(0.687636\pi\) | |||||||
\(830\) | 5.13019 | + | 8.88576i | 0.178072 | + | 0.308429i | ||||
\(831\) | −21.7995 | −0.756218 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.1414 | −1.59870 | ||||||||
\(834\) | 1.69202 | + | 2.93067i | 0.0585899 | + | 0.101481i | ||||
\(835\) | −7.31468 | − | 12.6694i | −0.253135 | − | 0.438443i | ||||
\(836\) | 10.5918 | − | 18.3455i | 0.366325 | − | 0.634493i | ||||
\(837\) | −2.76271 | −0.0954932 | ||||||||
\(838\) | 6.90246 | − | 11.9554i | 0.238442 | − | 0.412993i | ||||
\(839\) | 2.88338 | − | 4.99416i | 0.0995453 | − | 0.172418i | −0.811951 | − | 0.583725i | \(-0.801595\pi\) |
0.911497 | + | 0.411308i | \(0.134928\pi\) | |||||||
\(840\) | 0.246980 | 0.00852161 | ||||||||
\(841\) | −16.1473 | + | 27.9679i | −0.556803 | + | 0.964411i | ||||
\(842\) | −3.86294 | − | 6.69080i | −0.133126 | − | 0.230580i | ||||
\(843\) | 10.2959 | + | 17.8330i | 0.354610 | + | 0.614202i | ||||
\(844\) | −17.2620 | −0.594184 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.98792 | −0.171488 | ||||||||
\(847\) | 0.421543 | + | 0.730133i | 0.0144844 | + | 0.0250877i | ||||
\(848\) | 4.44385 | + | 7.69697i | 0.152602 | + | 0.264315i | ||||
\(849\) | 6.50604 | − | 11.2688i | 0.223287 | − | 0.386744i | ||||
\(850\) | 30.3538 | 1.04113 | ||||||||
\(851\) | −12.0978 | + | 20.9541i | −0.414708 | + | 0.718296i | ||||
\(852\) | −3.40581 | + | 5.89904i | −0.116681 | + | 0.202098i | ||||
\(853\) | 21.1728 | 0.724944 | 0.362472 | − | 0.931995i | \(-0.381933\pi\) | ||||
0.362472 | + | 0.931995i | \(0.381933\pi\) | |||||||
\(854\) | −1.15883 | + | 2.00716i | −0.0396545 | + | 0.0686836i | ||||
\(855\) | −2.49396 | − | 4.31966i | −0.0852916 | − | 0.147729i | ||||
\(856\) | −3.31551 | − | 5.74263i | −0.113322 | − | 0.196279i | ||||
\(857\) | 12.0086 | 0.410207 | 0.205103 | − | 0.978740i | \(-0.434247\pi\) | ||||
0.205103 | + | 0.978740i | \(0.434247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.66296 | −0.0567393 | −0.0283697 | − | 0.999598i | \(-0.509032\pi\) | ||||
−0.0283697 | + | 0.999598i | \(0.509032\pi\) | |||||||
\(860\) | 2.28083 | + | 3.95052i | 0.0777757 | + | 0.134711i | ||||
\(861\) | −0.872625 | − | 1.51143i | −0.0297390 | − | 0.0515094i | ||||
\(862\) | −0.320060 | + | 0.554360i | −0.0109013 | + | 0.0188816i | ||||
\(863\) | 23.8323 | 0.811262 | 0.405631 | − | 0.914037i | \(-0.367052\pi\) | ||||
0.405631 | + | 0.914037i | \(0.367052\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 3.23676 | − | 5.60623i | 0.110053 | − | 0.190618i | ||||
\(866\) | −21.2760 | −0.722989 | ||||||||
\(867\) | −14.0375 | + | 24.3137i | −0.476738 | + | 0.825735i | ||||
\(868\) | 0.493000 | + | 0.853901i | 0.0167335 | + | 0.0289833i | ||||
\(869\) | −22.1109 | − | 38.2972i | −0.750060 | − | 1.29914i | ||||
\(870\) | 5.41789 | 0.183684 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −12.9879 | −0.439826 | ||||||||
\(873\) | 0.208947 | + | 0.361908i | 0.00707180 | + | 0.0122487i | ||||
\(874\) | −8.63533 | − | 14.9568i | −0.292095 | − | 0.505923i | ||||
\(875\) | −1.17576 | + | 2.03648i | −0.0397479 | + | 0.0688454i | ||||
\(876\) | 3.18598 | 0.107644 | ||||||||
\(877\) | −21.1588 | + | 36.6482i | −0.714483 | + | 1.23752i | 0.248676 | + | 0.968587i | \(0.420005\pi\) |
−0.963159 | + | 0.268934i | \(0.913329\pi\) | |||||||
\(878\) | 6.35905 | − | 11.0142i | 0.214608 | − | 0.371711i | ||||
\(879\) | 14.9390 | 0.503880 | ||||||||
\(880\) | 1.01693 | − | 1.76137i | 0.0342806 | − | 0.0593757i | ||||
\(881\) | −11.1371 | − | 19.2900i | −0.375217 | − | 0.649895i | 0.615142 | − | 0.788416i | \(-0.289099\pi\) |
−0.990360 | + | 0.138521i | \(0.955765\pi\) | |||||||
\(882\) | −3.43631 | − | 5.95187i | −0.115707 | − | 0.200410i | ||||
\(883\) | −8.54229 | −0.287471 | −0.143735 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143735 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.13706 | −0.0382220 | ||||||||
\(886\) | 11.2986 | + | 19.5697i | 0.379583 | + | 0.657458i | ||||
\(887\) | 9.45712 | + | 16.3802i | 0.317539 | + | 0.549994i | 0.979974 | − | 0.199126i | \(-0.0638102\pi\) |
−0.662435 | + | 0.749120i | \(0.730477\pi\) | |||||||
\(888\) | 5.04892 | − | 8.74498i | 0.169431 | − | 0.293462i | ||||
\(889\) | −6.50173 | −0.218061 | ||||||||
\(890\) | −0.137063 | + | 0.237401i | −0.00459437 | + | 0.00795769i | ||||
\(891\) | −1.46950 | + | 2.54525i | −0.0492301 | + | 0.0852691i | ||||
\(892\) | −6.76809 | −0.226612 | ||||||||
\(893\) | 17.9758 | − | 31.1351i | 0.601538 | − | 1.04190i | ||||
\(894\) | 10.4085 | + | 18.0281i | 0.348112 | + | 0.602948i | ||||
\(895\) | 1.09866 | + | 1.90294i | 0.0367242 | + | 0.0636083i | ||||
\(896\) | −0.356896 | −0.0119231 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.6474 | 0.388679 | ||||||||
\(899\) | 10.8147 | + | 18.7317i | 0.360692 | + | 0.624737i | ||||
\(900\) | 2.26055 | + | 3.91539i | 0.0753518 | + | 0.130513i | ||||
\(901\) | 29.8351 | − | 51.6758i | 0.993950 | − | 1.72157i | ||||
\(902\) | −14.3720 | −0.478534 | ||||||||
\(903\) | −1.17629 | + | 2.03740i | −0.0391445 | + | 0.0678003i | ||||
\(904\) | 0.396125 | − | 0.686108i | 0.0131749 | − | 0.0228196i | ||||
\(905\) | 13.7017 | 0.455460 | ||||||||
\(906\) | 0.447730 | − | 0.775492i | 0.0148748 | − | 0.0257640i | ||||
\(907\) | −6.97584 | − | 12.0825i | −0.231629 | − | 0.401193i | 0.726659 | − | 0.686999i | \(-0.241072\pi\) |
−0.958288 | + | 0.285806i | \(0.907739\pi\) | |||||||
\(908\) | 11.8400 | + | 20.5074i | 0.392923 | + | 0.680563i | ||||
\(909\) | 10.0151 | 0.332179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.0422 | 1.49232 | 0.746158 | − | 0.665769i | \(-0.231897\pi\) | ||||
0.746158 | + | 0.665769i | \(0.231897\pi\) | |||||||
\(912\) | 3.60388 | + | 6.24210i | 0.119336 | + | 0.206696i | ||||
\(913\) | 21.7878 | + | 37.7376i | 0.721072 | + | 1.24893i | ||||
\(914\) | 10.5945 | − | 18.3502i | 0.350434 | − | 0.606970i | ||||
\(915\) | 4.49396 | 0.148566 | ||||||||
\(916\) | −4.14914 | + | 7.18653i | −0.137092 | + | 0.237450i | ||||
\(917\) | −0.488155 | + | 0.845510i | −0.0161203 | + | 0.0279212i | ||||
\(918\) | −6.71379 | −0.221588 | ||||||||
\(919\) | −19.9988 | + | 34.6389i | −0.659700 | + | 1.14263i | 0.320994 | + | 0.947081i | \(0.395983\pi\) |
−0.980693 | + | 0.195552i | \(0.937350\pi\) | |||||||
\(920\) | −0.829085 | − | 1.43602i | −0.0273341 | − | 0.0473441i | ||||
\(921\) | 13.0151 | + | 22.5428i | 0.428861 | + | 0.742809i | ||||
\(922\) | 24.0694 | 0.792682 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.04892 | 0.0345068 | ||||||||
\(925\) | 22.8267 | + | 39.5370i | 0.750537 | + | 1.29997i | ||||
\(926\) | 9.08575 | + | 15.7370i | 0.298576 | + | 0.517149i | ||||
\(927\) | 4.81282 | − | 8.33605i | 0.158074 | − | 0.273792i | ||||
\(928\) | −7.82908 | −0.257002 | ||||||||
\(929\) | 17.3424 | − | 30.0380i | 0.568986 | − | 0.985513i | −0.427680 | − | 0.903930i | \(-0.640669\pi\) |
0.996667 | − | 0.0815832i | \(-0.0259976\pi\) | |||||||
\(930\) | 0.955927 | − | 1.65571i | 0.0313461 | − | 0.0542930i | ||||
\(931\) | 49.5362 | 1.62348 | ||||||||
\(932\) | 11.9825 | − | 20.7544i | 0.392501 | − | 0.679832i | ||||
\(933\) | 2.40581 | + | 4.16699i | 0.0787628 | + | 0.136421i | ||||
\(934\) | −1.46562 | − | 2.53852i | −0.0479564 | − | 0.0830629i | ||||
\(935\) | −13.6549 | −0.446562 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1260 | −0.624821 | −0.312410 | − | 0.949947i | \(-0.601136\pi\) | ||||
−0.312410 | + | 0.949947i | \(0.601136\pi\) | |||||||
\(938\) | 2.41358 | + | 4.18045i | 0.0788063 | + | 0.136496i | ||||
\(939\) | 13.0206 | + | 22.5523i | 0.424910 | + | 0.735966i | ||||
\(940\) | 1.72587 | − | 2.98930i | 0.0562918 | − | 0.0975002i | ||||
\(941\) | 22.5972 | 0.736647 | 0.368323 | − | 0.929698i | \(-0.379932\pi\) | ||||
0.368323 | + | 0.929698i | \(0.379932\pi\) | |||||||
\(942\) | 4.29590 | − | 7.44071i | 0.139968 | − | 0.242431i | ||||
\(943\) | −5.85862 | + | 10.1474i | −0.190783 | + | 0.330446i | ||||
\(944\) | 1.64310 | 0.0534785 | ||||||||
\(945\) | 0.123490 | − | 0.213891i | 0.00401712 | − | 0.00695786i | ||||
\(946\) | 9.68664 | + | 16.7778i | 0.314940 | + | 0.545492i | ||||
\(947\) | −13.7180 | − | 23.7602i | −0.445774 | − | 0.772104i | 0.552332 | − | 0.833625i | \(-0.313738\pi\) |
−0.998106 | + | 0.0615209i | \(0.980405\pi\) | |||||||
\(948\) | 15.0465 | 0.488688 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −32.5870 | −1.05726 | ||||||||
\(951\) | −5.76055 | − | 9.97757i | −0.186799 | − | 0.323545i | ||||
\(952\) | 1.19806 | + | 2.07510i | 0.0388294 | + | 0.0672545i | ||||
\(953\) | 0.923936 | − | 1.60030i | 0.0299292 | − | 0.0518389i | −0.850673 | − | 0.525695i | \(-0.823805\pi\) |
0.880602 | + | 0.473857i | \(0.157138\pi\) | |||||||
\(954\) | 8.88769 | 0.287750 | ||||||||
\(955\) | 5.28083 | − | 9.14667i | 0.170884 | − | 0.295979i | ||||
\(956\) | 6.30798 | − | 10.9257i | 0.204015 | − | 0.353364i | ||||
\(957\) | 23.0097 | 0.743798 | ||||||||
\(958\) | 15.3545 | − | 26.5948i | 0.496081 | − | 0.859238i | ||||
\(959\) | 1.36467 | + | 2.36367i | 0.0440674 | + | 0.0763269i | ||||
\(960\) | 0.346011 | + | 0.599308i | 0.0111674 | + | 0.0193426i | ||||
\(961\) | −23.3674 | −0.753788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.63102 | −0.213682 | ||||||||
\(964\) | 13.1969 | + | 22.8576i | 0.425042 | + | 0.736195i | ||||
\(965\) | −1.64981 | − | 2.85755i | −0.0531092 | − | 0.0919879i | ||||
\(966\) | 0.427583 | − | 0.740596i | 0.0137573 | − | 0.0238283i | ||||
\(967\) | 8.88471 | 0.285713 | 0.142856 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142856 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(968\) | −1.18114 | + | 2.04579i | −0.0379632 | + | 0.0657541i | ||||
\(969\) | 24.1957 | − | 41.9081i | 0.777277 | − | 1.34628i | ||||
\(970\) | −0.289192 | −0.00928540 | ||||||||
\(971\) | −17.5432 | + | 30.3857i | −0.562987 | + | 0.975122i | 0.434247 | + | 0.900794i | \(0.357015\pi\) |
−0.997234 | + | 0.0743284i | \(0.976319\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −0.603875 | − | 1.04594i | −0.0193594 | − | 0.0335314i | ||||
\(974\) | 24.1497 | 0.773807 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.49396 | −0.207867 | ||||||||
\(977\) | −4.16852 | − | 7.22009i | −0.133363 | − | 0.230991i | 0.791608 | − | 0.611029i | \(-0.209244\pi\) |
−0.924971 | + | 0.380038i | \(0.875911\pi\) | |||||||
\(978\) | −0.862937 | − | 1.49465i | −0.0275937 | − | 0.0477936i | ||||
\(979\) | −0.582105 | + | 1.00824i | −0.0186042 | + | 0.0322234i | ||||
\(980\) | 4.75600 | 0.151925 | ||||||||
\(981\) | −6.49396 | + | 11.2479i | −0.207336 | + | 0.359117i | ||||
\(982\) | 7.29859 | − | 12.6415i | 0.232907 | − | 0.403407i | ||||
\(983\) | 55.6051 | 1.77353 | 0.886763 | − | 0.462224i | \(-0.152949\pi\) | ||||
0.886763 | + | 0.462224i | \(0.152949\pi\) | |||||||
\(984\) | 2.44504 | − | 4.23494i | 0.0779451 | − | 0.135005i | ||||
\(985\) | −4.23341 | − | 7.33247i | −0.134888 | − | 0.233632i | ||||
\(986\) | 26.2814 | + | 45.5208i | 0.836971 | + | 1.44968i | ||||
\(987\) | 1.78017 | 0.0566634 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7948 | 0.502244 | ||||||||
\(990\) | −1.01693 | − | 1.76137i | −0.0323200 | − | 0.0559799i | ||||
\(991\) | 21.7983 | + | 37.7558i | 0.692447 | + | 1.19935i | 0.971034 | + | 0.238943i | \(0.0768008\pi\) |
−0.278586 | + | 0.960411i | \(0.589866\pi\) | |||||||
\(992\) | −1.38135 | + | 2.39258i | −0.0438581 | + | 0.0759644i | ||||
\(993\) | −3.43834 | −0.109112 | ||||||||
\(994\) | 1.21552 | − | 2.10534i | 0.0385540 | − | 0.0667774i | ||||
\(995\) | −4.09970 | + | 7.10088i | −0.129969 | + | 0.225113i | ||||
\(996\) | −14.8267 | −0.469802 | ||||||||
\(997\) | −11.2295 | + | 19.4501i | −0.355643 | + | 0.615991i | −0.987228 | − | 0.159316i | \(-0.949071\pi\) |
0.631585 | + | 0.775306i | \(0.282405\pi\) | |||||||
\(998\) | −3.42758 | − | 5.93675i | −0.108498 | − | 0.187924i | ||||
\(999\) | −5.04892 | − | 8.74498i | −0.159741 | − | 0.276679i |
(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 | 1014.2.e.m.991.1 | 6 | ||
13.2 | odd | 12 | 1014.2.b.g.337.6 | 6 | |||
13.3 | even | 3 | 1014.2.a.m.1.1 | ✓ | 3 | ||
13.4 | even | 6 | 1014.2.e.k.529.3 | 6 | |||
13.5 | odd | 4 | 1014.2.i.g.361.6 | 12 | |||
13.6 | odd | 12 | 1014.2.i.g.823.3 | 12 | |||
13.7 | odd | 12 | 1014.2.i.g.823.4 | 12 | |||
13.8 | odd | 4 | 1014.2.i.g.361.1 | 12 | |||
13.9 | even | 3 | inner | 1014.2.e.m.529.1 | 6 | ||
13.10 | even | 6 | 1014.2.a.o.1.3 | yes | 3 | ||
13.11 | odd | 12 | 1014.2.b.g.337.1 | 6 | |||
13.12 | even | 2 | 1014.2.e.k.991.3 | 6 | |||
39.2 | even | 12 | 3042.2.b.r.1351.1 | 6 | |||
39.11 | even | 12 | 3042.2.b.r.1351.6 | 6 | |||
39.23 | odd | 6 | 3042.2.a.bd.1.1 | 3 | |||
39.29 | odd | 6 | 3042.2.a.be.1.3 | 3 | |||
52.3 | odd | 6 | 8112.2.a.ce.1.1 | 3 | |||
52.23 | odd | 6 | 8112.2.a.bz.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.1 | ✓ | 3 | 13.3 | even | 3 | ||
1014.2.a.o.1.3 | yes | 3 | 13.10 | even | 6 | ||
1014.2.b.g.337.1 | 6 | 13.11 | odd | 12 | |||
1014.2.b.g.337.6 | 6 | 13.2 | odd | 12 | |||
1014.2.e.k.529.3 | 6 | 13.4 | even | 6 | |||
1014.2.e.k.991.3 | 6 | 13.12 | even | 2 | |||
1014.2.e.m.529.1 | 6 | 13.9 | even | 3 | inner | ||
1014.2.e.m.991.1 | 6 | 1.1 | even | 1 | trivial | ||
1014.2.i.g.361.1 | 12 | 13.8 | odd | 4 | |||
1014.2.i.g.361.6 | 12 | 13.5 | odd | 4 | |||
1014.2.i.g.823.3 | 12 | 13.6 | odd | 12 | |||
1014.2.i.g.823.4 | 12 | 13.7 | odd | 12 | |||
3042.2.a.bd.1.1 | 3 | 39.23 | odd | 6 | |||
3042.2.a.be.1.3 | 3 | 39.29 | odd | 6 | |||
3042.2.b.r.1351.1 | 6 | 39.2 | even | 12 | |||
3042.2.b.r.1351.6 | 6 | 39.11 | even | 12 | |||
8112.2.a.bz.1.3 | 3 | 52.23 | odd | 6 | |||
8112.2.a.ce.1.1 | 3 | 52.3 | odd | 6 |