Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), degree \(2\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + 7135 x^{12} - 6640 x^{11} + 20315 x^{10} - 10565 x^{9} + 29358 x^{8} - 9009 x^{7} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.1 | ||
Root | \(1.39981 - 2.42454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.277 |
Dual form | 483.2.i.h.415.1 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39981 | − | 2.42454i | −0.989815 | − | 1.71441i | −0.618196 | − | 0.786024i | \(-0.712136\pi\) |
−0.371618 | − | 0.928386i | \(-0.621197\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.91893 | + | 5.05574i | −1.45947 | + | 2.52787i | ||||
\(5\) | 0.973538 | + | 1.68622i | 0.435379 | + | 0.754099i | 0.997327 | − | 0.0730740i | \(-0.0232809\pi\) |
−0.561947 | + | 0.827173i | \(0.689948\pi\) | |||||||
\(6\) | −2.79962 | −1.14294 | ||||||||
\(7\) | −2.64333 | + | 0.113245i | −0.999084 | + | 0.0428026i | ||||
\(8\) | 10.7446 | 3.79878 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 2.72553 | − | 4.72076i | 0.861890 | − | 1.49284i | ||||
\(11\) | 1.34384 | − | 2.32760i | 0.405184 | − | 0.701799i | −0.589159 | − | 0.808017i | \(-0.700541\pi\) |
0.994343 | + | 0.106218i | \(0.0338742\pi\) | |||||||
\(12\) | 2.91893 | + | 5.05574i | 0.842623 | + | 1.45947i | ||||
\(13\) | 4.19039 | 1.16220 | 0.581102 | − | 0.813831i | \(-0.302622\pi\) | ||||
0.581102 | + | 0.813831i | \(0.302622\pi\) | |||||||
\(14\) | 3.97472 | + | 6.25033i | 1.06229 | + | 1.67047i | ||||
\(15\) | 1.94708 | 0.502733 | ||||||||
\(16\) | −9.20247 | − | 15.9391i | −2.30062 | − | 3.98479i | ||||
\(17\) | 0.316198 | − | 0.547671i | 0.0766893 | − | 0.132830i | −0.825130 | − | 0.564942i | \(-0.808898\pi\) |
0.901820 | + | 0.432113i | \(0.142232\pi\) | |||||||
\(18\) | −1.39981 | + | 2.42454i | −0.329938 | + | 0.571470i | ||||
\(19\) | −2.77713 | − | 4.81013i | −0.637117 | − | 1.10352i | −0.986062 | − | 0.166376i | \(-0.946794\pi\) |
0.348946 | − | 0.937143i | \(-0.386540\pi\) | |||||||
\(20\) | −11.3668 | −2.54169 | ||||||||
\(21\) | −1.22359 | + | 2.34581i | −0.267009 | + | 0.511898i | ||||
\(22\) | −7.52450 | −1.60423 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | 5.37228 | − | 9.30506i | 1.09661 | − | 1.89939i | ||||
\(25\) | 0.604448 | − | 1.04694i | 0.120890 | − | 0.209387i | ||||
\(26\) | −5.86574 | − | 10.1598i | −1.15037 | − | 1.99249i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.14315 | − | 13.6945i | 1.34993 | − | 2.58802i | ||||
\(29\) | 5.57812 | 1.03583 | 0.517915 | − | 0.855432i | \(-0.326708\pi\) | ||||
0.517915 | + | 0.855432i | \(0.326708\pi\) | |||||||
\(30\) | −2.72553 | − | 4.72076i | −0.497612 | − | 0.861890i | ||||
\(31\) | 2.79909 | − | 4.84817i | 0.502732 | − | 0.870757i | −0.497263 | − | 0.867600i | \(-0.665662\pi\) |
0.999995 | − | 0.00315709i | \(-0.00100493\pi\) | |||||||
\(32\) | −15.0188 | + | 26.0134i | −2.65498 | + | 4.59856i | ||||
\(33\) | −1.34384 | − | 2.32760i | −0.233933 | − | 0.405184i | ||||
\(34\) | −1.77047 | −0.303633 | ||||||||
\(35\) | −2.76433 | − | 4.34697i | −0.467258 | − | 0.734773i | ||||
\(36\) | 5.83786 | 0.972977 | ||||||||
\(37\) | −2.05806 | − | 3.56466i | −0.338343 | − | 0.586027i | 0.645778 | − | 0.763525i | \(-0.276533\pi\) |
−0.984121 | + | 0.177498i | \(0.943200\pi\) | |||||||
\(38\) | −7.77490 | + | 13.4665i | −1.26126 | + | 2.18456i | ||||
\(39\) | 2.09519 | − | 3.62898i | 0.335500 | − | 0.581102i | ||||
\(40\) | 10.4602 | + | 18.1177i | 1.65391 | + | 2.86465i | ||||
\(41\) | 5.19481 | 0.811293 | 0.405647 | − | 0.914030i | \(-0.367046\pi\) | ||||
0.405647 | + | 0.914030i | \(0.367046\pi\) | |||||||
\(42\) | 7.40031 | − | 0.317043i | 1.14189 | − | 0.0489208i | ||||
\(43\) | −1.98626 | −0.302902 | −0.151451 | − | 0.988465i | \(-0.548395\pi\) | ||||
−0.151451 | + | 0.988465i | \(0.548395\pi\) | |||||||
\(44\) | 7.84517 | + | 13.5882i | 1.18270 | + | 2.04850i | ||||
\(45\) | 0.973538 | − | 1.68622i | 0.145126 | − | 0.251366i | ||||
\(46\) | −1.39981 | + | 2.42454i | −0.206391 | + | 0.357479i | ||||
\(47\) | 0.146293 | + | 0.253388i | 0.0213391 | + | 0.0369604i | 0.876498 | − | 0.481406i | \(-0.159874\pi\) |
−0.855159 | + | 0.518366i | \(0.826540\pi\) | |||||||
\(48\) | −18.4049 | −2.65652 | ||||||||
\(49\) | 6.97435 | − | 0.598687i | 0.996336 | − | 0.0855268i | ||||
\(50\) | −3.38445 | −0.478633 | ||||||||
\(51\) | −0.316198 | − | 0.547671i | −0.0442766 | − | 0.0766893i | ||||
\(52\) | −12.2315 | + | 21.1855i | −1.69620 | + | 2.93790i | ||||
\(53\) | 5.08608 | − | 8.80935i | 0.698627 | − | 1.21006i | −0.270315 | − | 0.962772i | \(-0.587128\pi\) |
0.968943 | − | 0.247286i | \(-0.0795387\pi\) | |||||||
\(54\) | 1.39981 | + | 2.42454i | 0.190490 | + | 0.329938i | ||||
\(55\) | 5.23313 | 0.705635 | ||||||||
\(56\) | −28.4014 | + | 1.21677i | −3.79529 | + | 0.162597i | ||||
\(57\) | −5.55426 | −0.735679 | ||||||||
\(58\) | −7.80831 | − | 13.5244i | −1.02528 | − | 1.77584i | ||||
\(59\) | −3.65980 | + | 6.33896i | −0.476466 | + | 0.825262i | −0.999636 | − | 0.0269653i | \(-0.991416\pi\) |
0.523171 | + | 0.852228i | \(0.324749\pi\) | |||||||
\(60\) | −5.68338 | + | 9.84391i | −0.733721 | + | 1.27084i | ||||
\(61\) | 3.14346 | + | 5.44464i | 0.402479 | + | 0.697114i | 0.994024 | − | 0.109158i | \(-0.0348153\pi\) |
−0.591545 | + | 0.806272i | \(0.701482\pi\) | |||||||
\(62\) | −15.6728 | −1.99044 | ||||||||
\(63\) | 1.41974 | + | 2.23257i | 0.178870 | + | 0.281277i | ||||
\(64\) | 47.2842 | 5.91053 | ||||||||
\(65\) | 4.07950 | + | 7.06590i | 0.506000 | + | 0.876417i | ||||
\(66\) | −3.76225 | + | 6.51640i | −0.463101 | + | 0.802114i | ||||
\(67\) | −1.57437 | + | 2.72690i | −0.192340 | + | 0.333143i | −0.946025 | − | 0.324092i | \(-0.894941\pi\) |
0.753685 | + | 0.657236i | \(0.228274\pi\) | |||||||
\(68\) | 1.84592 | + | 3.19723i | 0.223851 | + | 0.387721i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −6.66987 | + | 12.7872i | −0.797203 | + | 1.52836i | ||||
\(71\) | 6.00227 | 0.712338 | 0.356169 | − | 0.934422i | \(-0.384083\pi\) | ||||
0.356169 | + | 0.934422i | \(0.384083\pi\) | |||||||
\(72\) | −5.37228 | − | 9.30506i | −0.633129 | − | 1.09661i | ||||
\(73\) | −6.93126 | + | 12.0053i | −0.811243 | + | 1.40511i | 0.100752 | + | 0.994912i | \(0.467875\pi\) |
−0.911994 | + | 0.410202i | \(0.865458\pi\) | |||||||
\(74\) | −5.76178 | + | 9.97970i | −0.669793 | + | 1.16012i | ||||
\(75\) | −0.604448 | − | 1.04694i | −0.0697957 | − | 0.120890i | ||||
\(76\) | 32.4250 | 3.71940 | ||||||||
\(77\) | −3.28863 | + | 6.30480i | −0.374774 | + | 0.718499i | ||||
\(78\) | −11.7315 | −1.32833 | ||||||||
\(79\) | −7.89510 | − | 13.6747i | −0.888268 | − | 1.53852i | −0.841922 | − | 0.539599i | \(-0.818576\pi\) |
−0.0463457 | − | 0.998925i | \(-0.514758\pi\) | |||||||
\(80\) | 17.9179 | − | 31.0347i | 2.00328 | − | 3.46979i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −7.27175 | − | 12.5950i | −0.803030 | − | 1.39089i | ||||
\(83\) | 12.4983 | 1.37186 | 0.685931 | − | 0.727666i | \(-0.259395\pi\) | ||||
0.685931 | + | 0.727666i | \(0.259395\pi\) | |||||||
\(84\) | −8.28823 | − | 13.0334i | −0.904320 | − | 1.42206i | ||||
\(85\) | 1.23132 | 0.133556 | ||||||||
\(86\) | 2.78038 | + | 4.81577i | 0.299816 | + | 0.519297i | ||||
\(87\) | 2.78906 | − | 4.83079i | 0.299019 | − | 0.517915i | ||||
\(88\) | 14.4390 | − | 25.0091i | 1.53920 | − | 2.66598i | ||||
\(89\) | −0.905775 | − | 1.56885i | −0.0960119 | − | 0.166298i | 0.814019 | − | 0.580839i | \(-0.197275\pi\) |
−0.910030 | + | 0.414541i | \(0.863942\pi\) | |||||||
\(90\) | −5.45107 | −0.574593 | ||||||||
\(91\) | −11.0766 | + | 0.474541i | −1.16114 | + | 0.0497454i | ||||
\(92\) | 5.83786 | 0.608639 | ||||||||
\(93\) | −2.79909 | − | 4.84817i | −0.290252 | − | 0.502732i | ||||
\(94\) | 0.409566 | − | 0.709389i | 0.0422435 | − | 0.0731679i | ||||
\(95\) | 5.40728 | − | 9.36568i | 0.554775 | − | 0.960898i | ||||
\(96\) | 15.0188 | + | 26.0134i | 1.53285 | + | 2.65498i | ||||
\(97\) | −2.95190 | −0.299720 | −0.149860 | − | 0.988707i | \(-0.547882\pi\) | ||||
−0.149860 | + | 0.988707i | \(0.547882\pi\) | |||||||
\(98\) | −11.2143 | − | 16.0716i | −1.13282 | − | 1.62347i | ||||
\(99\) | −2.68769 | −0.270123 | ||||||||
\(100\) | 3.52869 | + | 6.11187i | 0.352869 | + | 0.611187i | ||||
\(101\) | 6.40066 | − | 11.0863i | 0.636889 | − | 1.10312i | −0.349222 | − | 0.937040i | \(-0.613554\pi\) |
0.986112 | − | 0.166084i | \(-0.0531124\pi\) | |||||||
\(102\) | −0.885234 | + | 1.53327i | −0.0876512 | + | 0.151816i | ||||
\(103\) | −6.52904 | − | 11.3086i | −0.643325 | − | 1.11427i | −0.984686 | − | 0.174340i | \(-0.944221\pi\) |
0.341360 | − | 0.939933i | \(-0.389112\pi\) | |||||||
\(104\) | 45.0239 | 4.41495 | ||||||||
\(105\) | −5.14676 | + | 0.220497i | −0.502272 | + | 0.0215183i | ||||
\(106\) | −28.4782 | −2.76605 | ||||||||
\(107\) | 6.86084 | + | 11.8833i | 0.663263 | + | 1.14880i | 0.979753 | + | 0.200209i | \(0.0641621\pi\) |
−0.316491 | + | 0.948596i | \(0.602505\pi\) | |||||||
\(108\) | 2.91893 | − | 5.05574i | 0.280874 | − | 0.486489i | ||||
\(109\) | 2.25296 | − | 3.90223i | 0.215794 | − | 0.373766i | −0.737724 | − | 0.675103i | \(-0.764099\pi\) |
0.953518 | + | 0.301336i | \(0.0974327\pi\) | |||||||
\(110\) | −7.32538 | − | 12.6879i | −0.698448 | − | 1.20975i | ||||
\(111\) | −4.11612 | −0.390685 | ||||||||
\(112\) | 26.1302 | + | 41.0902i | 2.46907 | + | 3.88266i | ||||
\(113\) | −16.4013 | −1.54290 | −0.771451 | − | 0.636288i | \(-0.780469\pi\) | ||||
−0.771451 | + | 0.636288i | \(0.780469\pi\) | |||||||
\(114\) | 7.77490 | + | 13.4665i | 0.728186 | + | 1.26126i | ||||
\(115\) | 0.973538 | − | 1.68622i | 0.0907829 | − | 0.157241i | ||||
\(116\) | −16.2822 | + | 28.2015i | −1.51176 | + | 2.61845i | ||||
\(117\) | −2.09519 | − | 3.62898i | −0.193701 | − | 0.335500i | ||||
\(118\) | 20.4921 | 1.88645 | ||||||||
\(119\) | −0.773794 | + | 1.48348i | −0.0709335 | + | 0.135990i | ||||
\(120\) | 20.9205 | 1.90977 | ||||||||
\(121\) | 1.88817 | + | 3.27041i | 0.171652 | + | 0.297310i | ||||
\(122\) | 8.80049 | − | 15.2429i | 0.796759 | − | 1.38003i | ||||
\(123\) | 2.59741 | − | 4.49884i | 0.234200 | − | 0.405647i | ||||
\(124\) | 16.3407 | + | 28.3030i | 1.46744 | + | 2.54168i | ||||
\(125\) | 12.0892 | 1.08129 | ||||||||
\(126\) | 3.42559 | − | 6.56738i | 0.305175 | − | 0.585068i | ||||
\(127\) | −18.2031 | −1.61527 | −0.807634 | − | 0.589685i | \(-0.799252\pi\) | ||||
−0.807634 | + | 0.589685i | \(0.799252\pi\) | |||||||
\(128\) | −36.1512 | − | 62.6157i | −3.19534 | − | 5.53450i | ||||
\(129\) | −0.993129 | + | 1.72015i | −0.0874402 | + | 0.151451i | ||||
\(130\) | 11.4210 | − | 19.7818i | 1.00169 | − | 1.73498i | ||||
\(131\) | 4.16420 | + | 7.21261i | 0.363828 | + | 0.630169i | 0.988587 | − | 0.150649i | \(-0.0481362\pi\) |
−0.624759 | + | 0.780817i | \(0.714803\pi\) | |||||||
\(132\) | 15.6903 | 1.36567 | ||||||||
\(133\) | 7.88558 | + | 12.4002i | 0.683766 | + | 1.07524i | ||||
\(134\) | 8.81530 | 0.761526 | ||||||||
\(135\) | −0.973538 | − | 1.68622i | −0.0837888 | − | 0.145126i | ||||
\(136\) | 3.39741 | − | 5.88448i | 0.291325 | − | 0.504590i | ||||
\(137\) | 6.65217 | − | 11.5219i | 0.568333 | − | 0.984382i | −0.428398 | − | 0.903590i | \(-0.640922\pi\) |
0.996731 | − | 0.0807919i | \(-0.0257449\pi\) | |||||||
\(138\) | 1.39981 | + | 2.42454i | 0.119160 | + | 0.206391i | ||||
\(139\) | −5.93319 | −0.503247 | −0.251623 | − | 0.967825i | \(-0.580964\pi\) | ||||
−0.251623 | + | 0.967825i | \(0.580964\pi\) | |||||||
\(140\) | 30.0461 | − | 1.28723i | 2.53936 | − | 0.108791i | ||||
\(141\) | 0.292587 | 0.0246403 | ||||||||
\(142\) | −8.40203 | − | 14.5527i | −0.705083 | − | 1.22124i | ||||
\(143\) | 5.63122 | − | 9.75356i | 0.470907 | − | 0.815634i | ||||
\(144\) | −9.20247 | + | 15.9391i | −0.766872 | + | 1.32826i | ||||
\(145\) | 5.43051 | + | 9.40592i | 0.450979 | + | 0.781119i | ||||
\(146\) | 38.8098 | 3.21192 | ||||||||
\(147\) | 2.96870 | − | 6.33931i | 0.244854 | − | 0.522857i | ||||
\(148\) | 24.0293 | 1.97520 | ||||||||
\(149\) | 2.41533 | + | 4.18348i | 0.197872 | + | 0.342724i | 0.947838 | − | 0.318752i | \(-0.103264\pi\) |
−0.749967 | + | 0.661476i | \(0.769930\pi\) | |||||||
\(150\) | −1.69222 | + | 2.93102i | −0.138170 | + | 0.239317i | ||||
\(151\) | −10.4923 | + | 18.1732i | −0.853854 | + | 1.47892i | 0.0238510 | + | 0.999716i | \(0.492407\pi\) |
−0.877705 | + | 0.479202i | \(0.840926\pi\) | |||||||
\(152\) | −29.8390 | − | 51.6827i | −2.42026 | − | 4.19202i | ||||
\(153\) | −0.632396 | −0.0511262 | ||||||||
\(154\) | 19.8897 | − | 0.852112i | 1.60276 | − | 0.0686651i | ||||
\(155\) | 10.9001 | 0.875516 | ||||||||
\(156\) | 12.2315 | + | 21.1855i | 0.979300 | + | 1.69620i | ||||
\(157\) | −0.797219 | + | 1.38082i | −0.0636250 | + | 0.110202i | −0.896083 | − | 0.443886i | \(-0.853599\pi\) |
0.832458 | + | 0.554088i | \(0.186933\pi\) | |||||||
\(158\) | −22.1033 | + | 38.2840i | −1.75844 | + | 3.04571i | ||||
\(159\) | −5.08608 | − | 8.80935i | −0.403353 | − | 0.698627i | ||||
\(160\) | −58.4857 | −4.62370 | ||||||||
\(161\) | 1.41974 | + | 2.23257i | 0.111891 | + | 0.175951i | ||||
\(162\) | 2.79962 | 0.219959 | ||||||||
\(163\) | 5.44883 | + | 9.43766i | 0.426786 | + | 0.739214i | 0.996585 | − | 0.0825692i | \(-0.0263125\pi\) |
−0.569800 | + | 0.821784i | \(0.692979\pi\) | |||||||
\(164\) | −15.1633 | + | 26.2636i | −1.18406 | + | 2.05084i | ||||
\(165\) | 2.61656 | − | 4.53202i | 0.203699 | − | 0.352817i | ||||
\(166\) | −17.4952 | − | 30.3026i | −1.35789 | − | 2.35193i | ||||
\(167\) | −15.5931 | −1.20663 | −0.603313 | − | 0.797504i | \(-0.706153\pi\) | ||||
−0.603313 | + | 0.797504i | \(0.706153\pi\) | |||||||
\(168\) | −13.1469 | + | 25.2047i | −1.01431 | + | 1.94458i | ||||
\(169\) | 4.55935 | 0.350719 | ||||||||
\(170\) | −1.72362 | − | 2.98539i | −0.132195 | − | 0.228969i | ||||
\(171\) | −2.77713 | + | 4.81013i | −0.212372 | + | 0.367840i | ||||
\(172\) | 5.79776 | − | 10.0420i | 0.442075 | − | 0.765696i | ||||
\(173\) | 5.63605 | + | 9.76193i | 0.428501 | + | 0.742186i | 0.996740 | − | 0.0806777i | \(-0.0257084\pi\) |
−0.568239 | + | 0.822864i | \(0.692375\pi\) | |||||||
\(174\) | −15.6166 | −1.18389 | ||||||||
\(175\) | −1.47919 | + | 2.83584i | −0.111817 | + | 0.214370i | ||||
\(176\) | −49.4667 | −3.72869 | ||||||||
\(177\) | 3.65980 | + | 6.33896i | 0.275087 | + | 0.476466i | ||||
\(178\) | −2.53582 | + | 4.39218i | −0.190068 | + | 0.329207i | ||||
\(179\) | −4.08754 | + | 7.07983i | −0.305517 | + | 0.529171i | −0.977376 | − | 0.211508i | \(-0.932163\pi\) |
0.671859 | + | 0.740679i | \(0.265496\pi\) | |||||||
\(180\) | 5.68338 | + | 9.84391i | 0.423614 | + | 0.733721i | ||||
\(181\) | −3.00094 | −0.223058 | −0.111529 | − | 0.993761i | \(-0.535575\pi\) | ||||
−0.111529 | + | 0.993761i | \(0.535575\pi\) | |||||||
\(182\) | 16.6556 | + | 26.1913i | 1.23460 | + | 1.94143i | ||||
\(183\) | 6.28692 | 0.464743 | ||||||||
\(184\) | −5.37228 | − | 9.30506i | −0.396050 | − | 0.685978i | ||||
\(185\) | 4.00720 | − | 6.94067i | 0.294615 | − | 0.510288i | ||||
\(186\) | −7.83639 | + | 13.5730i | −0.574592 | + | 0.995222i | ||||
\(187\) | −0.849841 | − | 1.47197i | −0.0621465 | − | 0.107641i | ||||
\(188\) | −1.70808 | −0.124575 | ||||||||
\(189\) | 2.64333 | − | 0.113245i | 0.192274 | − | 0.00823737i | ||||
\(190\) | −30.2766 | −2.19650 | ||||||||
\(191\) | 5.78941 | + | 10.0276i | 0.418907 | + | 0.725568i | 0.995830 | − | 0.0912304i | \(-0.0290800\pi\) |
−0.576923 | + | 0.816799i | \(0.695747\pi\) | |||||||
\(192\) | 23.6421 | − | 40.9493i | 1.70622 | − | 2.95526i | ||||
\(193\) | −2.84965 | + | 4.93573i | −0.205122 | + | 0.355282i | −0.950172 | − | 0.311727i | \(-0.899092\pi\) |
0.745050 | + | 0.667009i | \(0.232426\pi\) | |||||||
\(194\) | 4.13210 | + | 7.15700i | 0.296667 | + | 0.513843i | ||||
\(195\) | 8.15900 | 0.584278 | ||||||||
\(196\) | −17.3309 | + | 37.0080i | −1.23792 | + | 2.64343i | ||||
\(197\) | −12.9883 | −0.925379 | −0.462689 | − | 0.886521i | \(-0.653115\pi\) | ||||
−0.462689 | + | 0.886521i | \(0.653115\pi\) | |||||||
\(198\) | 3.76225 | + | 6.51640i | 0.267371 | + | 0.463101i | ||||
\(199\) | 10.6628 | − | 18.4685i | 0.755864 | − | 1.30919i | −0.189080 | − | 0.981962i | \(-0.560551\pi\) |
0.944944 | − | 0.327233i | \(-0.106116\pi\) | |||||||
\(200\) | 6.49453 | − | 11.2489i | 0.459233 | − | 0.795414i | ||||
\(201\) | 1.57437 | + | 2.72690i | 0.111048 | + | 0.192340i | ||||
\(202\) | −35.8388 | −2.52161 | ||||||||
\(203\) | −14.7448 | + | 0.631695i | −1.03488 | + | 0.0443363i | ||||
\(204\) | 3.69184 | 0.258481 | ||||||||
\(205\) | 5.05735 | + | 8.75958i | 0.353220 | + | 0.611796i | ||||
\(206\) | −18.2788 | + | 31.6598i | −1.27355 | + | 2.20585i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | −38.5619 | − | 66.7912i | −2.67379 | − | 4.63114i | ||||
\(209\) | −14.9281 | −1.03260 | ||||||||
\(210\) | 7.73908 | + | 12.1699i | 0.534047 | + | 0.839801i | ||||
\(211\) | 7.69191 | 0.529533 | 0.264766 | − | 0.964313i | \(-0.414705\pi\) | ||||
0.264766 | + | 0.964313i | \(0.414705\pi\) | |||||||
\(212\) | 29.6919 | + | 51.4278i | 2.03925 | + | 3.53208i | ||||
\(213\) | 3.00113 | − | 5.19812i | 0.205634 | − | 0.356169i | ||||
\(214\) | 19.2077 | − | 33.2688i | 1.31301 | − | 2.27421i | ||||
\(215\) | −1.93370 | − | 3.34926i | −0.131877 | − | 0.228418i | ||||
\(216\) | −10.7446 | −0.731075 | ||||||||
\(217\) | −6.84988 | + | 13.1323i | −0.465000 | + | 0.891477i | ||||
\(218\) | −12.6148 | −0.854384 | ||||||||
\(219\) | 6.93126 | + | 12.0053i | 0.468371 | + | 0.811243i | ||||
\(220\) | −15.2751 | + | 26.4573i | −1.02985 | + | 1.78375i | ||||
\(221\) | 1.32499 | − | 2.29495i | 0.0891286 | − | 0.154375i | ||||
\(222\) | 5.76178 | + | 9.97970i | 0.386705 | + | 0.669793i | ||||
\(223\) | 20.9689 | 1.40418 | 0.702091 | − | 0.712087i | \(-0.252250\pi\) | ||||
0.702091 | + | 0.712087i | \(0.252250\pi\) | |||||||
\(224\) | 36.7538 | − | 70.4627i | 2.45572 | − | 4.70799i | ||||
\(225\) | −1.20890 | −0.0805931 | ||||||||
\(226\) | 22.9587 | + | 39.7656i | 1.52719 | + | 2.64517i | ||||
\(227\) | 12.0879 | − | 20.9369i | 0.802302 | − | 1.38963i | −0.115795 | − | 0.993273i | \(-0.536941\pi\) |
0.918097 | − | 0.396355i | \(-0.129725\pi\) | |||||||
\(228\) | 16.2125 | − | 28.0809i | 1.07370 | − | 1.85970i | ||||
\(229\) | 4.33927 | + | 7.51584i | 0.286747 | + | 0.496661i | 0.973031 | − | 0.230673i | \(-0.0740927\pi\) |
−0.686284 | + | 0.727334i | \(0.740759\pi\) | |||||||
\(230\) | −5.45107 | −0.359433 | ||||||||
\(231\) | 3.81581 | + | 6.00043i | 0.251062 | + | 0.394800i | ||||
\(232\) | 59.9344 | 3.93489 | ||||||||
\(233\) | −1.34590 | − | 2.33117i | −0.0881729 | − | 0.152720i | 0.818566 | − | 0.574413i | \(-0.194769\pi\) |
−0.906739 | + | 0.421693i | \(0.861436\pi\) | |||||||
\(234\) | −5.86574 | + | 10.1598i | −0.383456 | + | 0.664165i | ||||
\(235\) | −0.284844 | + | 0.493365i | −0.0185812 | + | 0.0321836i | ||||
\(236\) | −21.3654 | − | 37.0060i | −1.39077 | − | 2.40889i | ||||
\(237\) | −15.7902 | −1.02568 | ||||||||
\(238\) | 4.67992 | − | 0.200497i | 0.303354 | − | 0.0129963i | ||||
\(239\) | −0.0523580 | −0.00338675 | −0.00169338 | − | 0.999999i | \(-0.500539\pi\) | ||||
−0.00169338 | + | 0.999999i | \(0.500539\pi\) | |||||||
\(240\) | −17.9179 | − | 31.0347i | −1.15660 | − | 2.00328i | ||||
\(241\) | 0.149776 | − | 0.259419i | 0.00964789 | − | 0.0167106i | −0.861161 | − | 0.508332i | \(-0.830262\pi\) |
0.870809 | + | 0.491621i | \(0.163596\pi\) | |||||||
\(242\) | 5.28616 | − | 9.15590i | 0.339807 | − | 0.588564i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −36.7022 | −2.34962 | ||||||||
\(245\) | 7.79931 | + | 11.1774i | 0.498280 | + | 0.714099i | ||||
\(246\) | −14.5435 | −0.927259 | ||||||||
\(247\) | −11.6372 | − | 20.1563i | −0.740460 | − | 1.28251i | ||||
\(248\) | 30.0750 | − | 52.0914i | 1.90976 | − | 3.30781i | ||||
\(249\) | 6.24913 | − | 10.8238i | 0.396023 | − | 0.685931i | ||||
\(250\) | −16.9226 | − | 29.3107i | −1.07028 | − | 1.85377i | ||||
\(251\) | −5.72848 | −0.361579 | −0.180789 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180789 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(252\) | −15.4314 | + | 0.661109i | −0.972086 | + | 0.0416460i | ||||
\(253\) | −2.68769 | −0.168973 | ||||||||
\(254\) | 25.4809 | + | 44.1343i | 1.59882 | + | 2.76923i | ||||
\(255\) | 0.615661 | − | 1.06636i | 0.0385542 | − | 0.0667779i | ||||
\(256\) | −53.9253 | + | 93.4014i | −3.37033 | + | 5.83759i | ||||
\(257\) | 8.61484 | + | 14.9213i | 0.537379 | + | 0.930768i | 0.999044 | + | 0.0437133i | \(0.0139188\pi\) |
−0.461665 | + | 0.887054i | \(0.652748\pi\) | |||||||
\(258\) | 5.56077 | 0.346198 | ||||||||
\(259\) | 5.84380 | + | 9.18950i | 0.363116 | + | 0.571008i | ||||
\(260\) | −47.6312 | −2.95396 | ||||||||
\(261\) | −2.78906 | − | 4.83079i | −0.172638 | − | 0.299019i | ||||
\(262\) | 11.6582 | − | 20.1926i | 0.720245 | − | 1.24750i | ||||
\(263\) | −11.7608 | + | 20.3703i | −0.725202 | + | 1.25609i | 0.233689 | + | 0.972311i | \(0.424920\pi\) |
−0.958891 | + | 0.283775i | \(0.908413\pi\) | |||||||
\(264\) | −14.4390 | − | 25.0091i | −0.888659 | − | 1.53920i | ||||
\(265\) | 19.8060 | 1.21667 | ||||||||
\(266\) | 19.0266 | − | 36.4769i | 1.16659 | − | 2.23654i | ||||
\(267\) | −1.81155 | −0.110865 | ||||||||
\(268\) | −9.19098 | − | 15.9193i | −0.561429 | − | 0.972423i | ||||
\(269\) | 6.90462 | − | 11.9592i | 0.420982 | − | 0.729163i | −0.575054 | − | 0.818116i | \(-0.695019\pi\) |
0.996036 | + | 0.0889531i | \(0.0283521\pi\) | |||||||
\(270\) | −2.72553 | + | 4.72076i | −0.165871 | + | 0.287297i | ||||
\(271\) | 11.2211 | + | 19.4355i | 0.681634 | + | 1.18062i | 0.974482 | + | 0.224466i | \(0.0720637\pi\) |
−0.292848 | + | 0.956159i | \(0.594603\pi\) | |||||||
\(272\) | −11.6392 | −0.705731 | ||||||||
\(273\) | −5.12732 | + | 9.82986i | −0.310319 | + | 0.594930i | ||||
\(274\) | −37.2471 | −2.25018 | ||||||||
\(275\) | −1.62457 | − | 2.81383i | −0.0979651 | − | 0.169681i | ||||
\(276\) | 2.91893 | − | 5.05574i | 0.175699 | − | 0.304320i | ||||
\(277\) | −11.1138 | + | 19.2497i | −0.667765 | + | 1.15660i | 0.310763 | + | 0.950487i | \(0.399415\pi\) |
−0.978528 | + | 0.206115i | \(0.933918\pi\) | |||||||
\(278\) | 8.30534 | + | 14.3853i | 0.498121 | + | 0.862771i | ||||
\(279\) | −5.59818 | −0.335154 | ||||||||
\(280\) | −29.7015 | − | 46.7063i | −1.77501 | − | 2.79124i | ||||
\(281\) | 6.99680 | 0.417394 | 0.208697 | − | 0.977980i | \(-0.433078\pi\) | ||||
0.208697 | + | 0.977980i | \(0.433078\pi\) | |||||||
\(282\) | −0.409566 | − | 0.709389i | −0.0243893 | − | 0.0422435i | ||||
\(283\) | −4.03188 | + | 6.98343i | −0.239671 | + | 0.415122i | −0.960620 | − | 0.277866i | \(-0.910373\pi\) |
0.720949 | + | 0.692988i | \(0.243706\pi\) | |||||||
\(284\) | −17.5202 | + | 30.3459i | −1.03963 | + | 1.80070i | ||||
\(285\) | −5.40728 | − | 9.36568i | −0.320299 | − | 0.554775i | ||||
\(286\) | −31.5306 | −1.86444 | ||||||||
\(287\) | −13.7316 | + | 0.588287i | −0.810550 | + | 0.0347255i | ||||
\(288\) | 30.0377 | 1.76999 | ||||||||
\(289\) | 8.30004 | + | 14.3761i | 0.488238 | + | 0.845652i | ||||
\(290\) | 15.2034 | − | 26.3330i | 0.892772 | − | 1.54633i | ||||
\(291\) | −1.47595 | + | 2.55642i | −0.0865217 | + | 0.149860i | ||||
\(292\) | −40.4638 | − | 70.0853i | −2.36796 | − | 4.10143i | ||||
\(293\) | −13.1458 | −0.767986 | −0.383993 | − | 0.923336i | \(-0.625451\pi\) | ||||
−0.383993 | + | 0.923336i | \(0.625451\pi\) | |||||||
\(294\) | −19.5255 | + | 1.67610i | −1.13875 | + | 0.0977519i | ||||
\(295\) | −14.2518 | −0.829773 | ||||||||
\(296\) | −22.1129 | − | 38.3007i | −1.28529 | − | 2.22618i | ||||
\(297\) | −1.34384 | + | 2.32760i | −0.0779777 | + | 0.135061i | ||||
\(298\) | 6.76200 | − | 11.7121i | 0.391712 | − | 0.678466i | ||||
\(299\) | −2.09519 | − | 3.62898i | −0.121168 | − | 0.209869i | ||||
\(300\) | 7.05738 | 0.407458 | ||||||||
\(301\) | 5.25033 | − | 0.224934i | 0.302624 | − | 0.0129650i | ||||
\(302\) | 58.7490 | 3.38063 | ||||||||
\(303\) | −6.40066 | − | 11.0863i | −0.367708 | − | 0.636889i | ||||
\(304\) | −51.1129 | + | 88.5301i | −2.93152 | + | 5.07755i | ||||
\(305\) | −6.12056 | + | 10.6011i | −0.350462 | + | 0.607018i | ||||
\(306\) | 0.885234 | + | 1.53327i | 0.0506054 | + | 0.0876512i | ||||
\(307\) | 15.1086 | 0.862293 | 0.431147 | − | 0.902282i | \(-0.358109\pi\) | ||||
0.431147 | + | 0.902282i | \(0.358109\pi\) | |||||||
\(308\) | −22.2762 | − | 35.0297i | −1.26930 | − | 1.99600i | ||||
\(309\) | −13.0581 | −0.742848 | ||||||||
\(310\) | −15.2580 | − | 26.4277i | −0.866598 | − | 1.50099i | ||||
\(311\) | 10.7414 | − | 18.6047i | 0.609090 | − | 1.05497i | −0.382301 | − | 0.924038i | \(-0.624868\pi\) |
0.991391 | − | 0.130937i | \(-0.0417985\pi\) | |||||||
\(312\) | 22.5119 | − | 38.9918i | 1.27449 | − | 2.20748i | ||||
\(313\) | −7.41912 | − | 12.8503i | −0.419353 | − | 0.726341i | 0.576521 | − | 0.817082i | \(-0.304410\pi\) |
−0.995875 | + | 0.0907410i | \(0.971076\pi\) | |||||||
\(314\) | 4.46382 | 0.251908 | ||||||||
\(315\) | −2.38242 | + | 4.56747i | −0.134234 | + | 0.257348i | ||||
\(316\) | 92.1810 | 5.18559 | ||||||||
\(317\) | 2.35086 | + | 4.07181i | 0.132038 | + | 0.228696i | 0.924462 | − | 0.381274i | \(-0.124515\pi\) |
−0.792424 | + | 0.609970i | \(0.791181\pi\) | |||||||
\(318\) | −14.2391 | + | 24.6628i | −0.798489 | + | 1.38302i | ||||
\(319\) | 7.49612 | − | 12.9837i | 0.419702 | − | 0.726945i | ||||
\(320\) | 46.0330 | + | 79.7314i | 2.57332 | + | 4.45712i | ||||
\(321\) | 13.7217 | 0.765870 | ||||||||
\(322\) | 3.42559 | − | 6.56738i | 0.190900 | − | 0.365986i | ||||
\(323\) | −3.51249 | −0.195440 | ||||||||
\(324\) | −2.91893 | − | 5.05574i | −0.162163 | − | 0.280874i | ||||
\(325\) | 2.53287 | − | 4.38706i | 0.140499 | − | 0.243351i | ||||
\(326\) | 15.2547 | − | 26.4218i | 0.844877 | − | 1.46337i | ||||
\(327\) | −2.25296 | − | 3.90223i | −0.124589 | − | 0.215794i | ||||
\(328\) | 55.8160 | 3.08192 | ||||||||
\(329\) | −0.415396 | − | 0.653219i | −0.0229015 | − | 0.0360132i | ||||
\(330\) | −14.6508 | −0.806498 | ||||||||
\(331\) | 3.93932 | + | 6.82310i | 0.216524 | + | 0.375031i | 0.953743 | − | 0.300623i | \(-0.0971946\pi\) |
−0.737219 | + | 0.675654i | \(0.763861\pi\) | |||||||
\(332\) | −36.4816 | + | 63.1880i | −2.00219 | + | 3.46789i | ||||
\(333\) | −2.05806 | + | 3.56466i | −0.112781 | + | 0.195342i | ||||
\(334\) | 21.8273 | + | 37.8060i | 1.19434 | + | 2.06865i | ||||
\(335\) | −6.13085 | −0.334964 | ||||||||
\(336\) | 48.6503 | − | 2.08427i | 2.65409 | − | 0.113706i | ||||
\(337\) | −18.3857 | −1.00153 | −0.500767 | − | 0.865582i | \(-0.666949\pi\) | ||||
−0.500767 | + | 0.865582i | \(0.666949\pi\) | |||||||
\(338\) | −6.38222 | − | 11.0543i | −0.347147 | − | 0.601276i | ||||
\(339\) | −8.20064 | + | 14.2039i | −0.445398 | + | 0.771451i | ||||
\(340\) | −3.59415 | + | 6.22525i | −0.194920 | + | 0.337611i | ||||
\(341\) | −7.52308 | − | 13.0304i | −0.407398 | − | 0.705633i | ||||
\(342\) | 15.5498 | 0.840837 | ||||||||
\(343\) | −18.3677 | + | 2.37234i | −0.991762 | + | 0.128094i | ||||
\(344\) | −21.3415 | −1.15066 | ||||||||
\(345\) | −0.973538 | − | 1.68622i | −0.0524135 | − | 0.0907829i | ||||
\(346\) | 15.7788 | − | 27.3297i | 0.848274 | − | 1.46925i | ||||
\(347\) | −3.01039 | + | 5.21415i | −0.161606 | + | 0.279910i | −0.935445 | − | 0.353473i | \(-0.885001\pi\) |
0.773839 | + | 0.633383i | \(0.218334\pi\) | |||||||
\(348\) | 16.2822 | + | 28.2015i | 0.872815 | + | 1.51176i | ||||
\(349\) | 13.3378 | 0.713956 | 0.356978 | − | 0.934113i | \(-0.383807\pi\) | ||||
0.356978 | + | 0.934113i | \(0.383807\pi\) | |||||||
\(350\) | 8.94621 | − | 0.383272i | 0.478195 | − | 0.0204868i | ||||
\(351\) | −4.19039 | −0.223666 | ||||||||
\(352\) | 40.3659 | + | 69.9159i | 2.15151 | + | 3.72653i | ||||
\(353\) | −8.74350 | + | 15.1442i | −0.465369 | + | 0.806043i | −0.999218 | − | 0.0395367i | \(-0.987412\pi\) |
0.533849 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(354\) | 10.2460 | − | 17.7467i | 0.544571 | − | 0.943225i | ||||
\(355\) | 5.84343 | + | 10.1211i | 0.310137 | + | 0.537174i | ||||
\(356\) | 10.5756 | 0.560505 | ||||||||
\(357\) | 0.897836 | + | 1.41187i | 0.0475185 | + | 0.0747238i | ||||
\(358\) | 22.8871 | 1.20962 | ||||||||
\(359\) | 4.28362 | + | 7.41944i | 0.226081 | + | 0.391583i | 0.956643 | − | 0.291263i | \(-0.0940754\pi\) |
−0.730562 | + | 0.682846i | \(0.760742\pi\) | |||||||
\(360\) | 10.4602 | − | 18.1177i | 0.551303 | − | 0.954884i | ||||
\(361\) | −5.92488 | + | 10.2622i | −0.311836 | + | 0.540115i | ||||
\(362\) | 4.20075 | + | 7.27591i | 0.220787 | + | 0.382413i | ||||
\(363\) | 3.77634 | 0.198207 | ||||||||
\(364\) | 29.9326 | − | 57.3854i | 1.56889 | − | 3.00781i | ||||
\(365\) | −26.9914 | −1.41279 | ||||||||
\(366\) | −8.80049 | − | 15.2429i | −0.460009 | − | 0.796759i | ||||
\(367\) | 9.85576 | − | 17.0707i | 0.514467 | − | 0.891082i | −0.485392 | − | 0.874296i | \(-0.661323\pi\) |
0.999859 | − | 0.0167860i | \(-0.00534340\pi\) | |||||||
\(368\) | −9.20247 | + | 15.9391i | −0.479712 | + | 0.830885i | ||||
\(369\) | −2.59741 | − | 4.49884i | −0.135216 | − | 0.234200i | ||||
\(370\) | −22.4372 | −1.16646 | ||||||||
\(371\) | −12.4466 | + | 23.8620i | −0.646193 | + | 1.23885i | ||||
\(372\) | 32.6814 | 1.69445 | ||||||||
\(373\) | −10.9629 | − | 18.9883i | −0.567639 | − | 0.983179i | −0.996799 | − | 0.0799507i | \(-0.974524\pi\) |
0.429160 | − | 0.903228i | \(-0.358810\pi\) | |||||||
\(374\) | −2.37923 | + | 4.12095i | −0.123027 | + | 0.213089i | ||||
\(375\) | 6.04460 | − | 10.4695i | 0.312142 | − | 0.540645i | ||||
\(376\) | 1.57186 | + | 2.72254i | 0.0810624 | + | 0.140404i | ||||
\(377\) | 23.3745 | 1.20385 | ||||||||
\(378\) | −3.97472 | − | 6.25033i | −0.204438 | − | 0.321482i | ||||
\(379\) | 9.89943 | 0.508500 | 0.254250 | − | 0.967139i | \(-0.418171\pi\) | ||||
0.254250 | + | 0.967139i | \(0.418171\pi\) | |||||||
\(380\) | 31.5670 | + | 54.6756i | 1.61935 | + | 2.80480i | ||||
\(381\) | −9.10157 | + | 15.7644i | −0.466288 | + | 0.807634i | ||||
\(382\) | 16.2081 | − | 28.0733i | 0.829281 | − | 1.43636i | ||||
\(383\) | 8.76893 | + | 15.1882i | 0.448071 | + | 0.776083i | 0.998260 | − | 0.0589576i | \(-0.0187777\pi\) |
−0.550189 | + | 0.835040i | \(0.685444\pi\) | |||||||
\(384\) | −72.3024 | −3.68966 | ||||||||
\(385\) | −13.8329 | + | 0.592626i | −0.704988 | + | 0.0302030i | ||||
\(386\) | 15.9558 | 0.812131 | ||||||||
\(387\) | 0.993129 | + | 1.72015i | 0.0504836 | + | 0.0874402i | ||||
\(388\) | 8.61639 | − | 14.9240i | 0.437431 | − | 0.757653i | ||||
\(389\) | −9.62382 | + | 16.6689i | −0.487947 | + | 0.845149i | −0.999904 | − | 0.0138623i | \(-0.995587\pi\) |
0.511957 | + | 0.859011i | \(0.328921\pi\) | |||||||
\(390\) | −11.4210 | − | 19.7818i | −0.578327 | − | 1.00169i | ||||
\(391\) | −0.632396 | −0.0319816 | ||||||||
\(392\) | 74.9363 | − | 6.43263i | 3.78486 | − | 0.324897i | ||||
\(393\) | 8.32841 | 0.420113 | ||||||||
\(394\) | 18.1812 | + | 31.4907i | 0.915953 | + | 1.58648i | ||||
\(395\) | 15.3723 | − | 26.6257i | 0.773467 | − | 1.33968i | ||||
\(396\) | 7.84517 | − | 13.5882i | 0.394235 | − | 0.682835i | ||||
\(397\) | 12.2997 | + | 21.3037i | 0.617304 | + | 1.06920i | 0.989976 | + | 0.141239i | \(0.0451086\pi\) |
−0.372671 | + | 0.927963i | \(0.621558\pi\) | |||||||
\(398\) | −59.7034 | −2.99266 | ||||||||
\(399\) | 14.6817 | − | 0.628992i | 0.735005 | − | 0.0314890i | ||||
\(400\) | −22.2497 | −1.11248 | ||||||||
\(401\) | 3.94256 | + | 6.82871i | 0.196882 | + | 0.341010i | 0.947516 | − | 0.319709i | \(-0.103585\pi\) |
−0.750634 | + | 0.660718i | \(0.770252\pi\) | |||||||
\(402\) | 4.40765 | − | 7.63427i | 0.219833 | − | 0.380763i | ||||
\(403\) | 11.7293 | − | 20.3157i | 0.584277 | − | 1.01200i | ||||
\(404\) | 37.3662 | + | 64.7201i | 1.85904 | + | 3.21995i | ||||
\(405\) | −1.94708 | −0.0967510 | ||||||||
\(406\) | 22.1715 | + | 34.8651i | 1.10035 | + | 1.73033i | ||||
\(407\) | −11.0628 | −0.548364 | ||||||||
\(408\) | −3.39741 | − | 5.88448i | −0.168197 | − | 0.291325i | ||||
\(409\) | −2.40339 | + | 4.16279i | −0.118840 | + | 0.205836i | −0.919308 | − | 0.393538i | \(-0.871251\pi\) |
0.800468 | + | 0.599375i | \(0.204584\pi\) | |||||||
\(410\) | 14.1586 | − | 24.5235i | 0.699245 | − | 1.21113i | ||||
\(411\) | −6.65217 | − | 11.5219i | −0.328127 | − | 0.568333i | ||||
\(412\) | 76.2313 | 3.75565 | ||||||||
\(413\) | 8.95619 | − | 17.1704i | 0.440705 | − | 0.844900i | ||||
\(414\) | 2.79962 | 0.137594 | ||||||||
\(415\) | 12.1675 | + | 21.0748i | 0.597281 | + | 1.03452i | ||||
\(416\) | −62.9348 | + | 109.006i | −3.08563 | + | 5.34447i | ||||
\(417\) | −2.96660 | + | 5.13830i | −0.145275 | + | 0.251623i | ||||
\(418\) | 20.8965 | + | 36.1938i | 1.02208 | + | 1.77030i | ||||
\(419\) | 4.37312 | 0.213641 | 0.106820 | − | 0.994278i | \(-0.465933\pi\) | ||||
0.106820 | + | 0.994278i | \(0.465933\pi\) | |||||||
\(420\) | 13.9083 | − | 26.6643i | 0.678654 | − | 1.30108i | ||||
\(421\) | −15.6894 | −0.764655 | −0.382327 | − | 0.924027i | \(-0.624877\pi\) | ||||
−0.382327 | + | 0.924027i | \(0.624877\pi\) | |||||||
\(422\) | −10.7672 | − | 18.6493i | −0.524139 | − | 0.907836i | ||||
\(423\) | 0.146293 | − | 0.253388i | 0.00711303 | − | 0.0123201i | ||||
\(424\) | 54.6477 | − | 94.6526i | 2.65393 | − | 4.59674i | ||||
\(425\) | −0.382251 | − | 0.662078i | −0.0185419 | − | 0.0321155i | ||||
\(426\) | −16.8041 | −0.814159 | ||||||||
\(427\) | −8.92577 | − | 14.0360i | −0.431948 | − | 0.679248i | ||||
\(428\) | −80.1053 | −3.87204 | ||||||||
\(429\) | −5.63122 | − | 9.75356i | −0.271878 | − | 0.470907i | ||||
\(430\) | −5.41362 | + | 9.37666i | −0.261068 | + | 0.452183i | ||||
\(431\) | 1.67317 | − | 2.89801i | 0.0805935 | − | 0.139592i | −0.822912 | − | 0.568170i | \(-0.807652\pi\) |
0.903505 | + | 0.428577i | \(0.140985\pi\) | |||||||
\(432\) | 9.20247 | + | 15.9391i | 0.442754 | + | 0.766872i | ||||
\(433\) | −15.2273 | −0.731779 | −0.365889 | − | 0.930658i | \(-0.619235\pi\) | ||||
−0.365889 | + | 0.930658i | \(0.619235\pi\) | |||||||
\(434\) | 41.4283 | − | 1.77486i | 1.98862 | − | 0.0851962i | ||||
\(435\) | 10.8610 | 0.520746 | ||||||||
\(436\) | 13.1524 | + | 22.7807i | 0.629888 | + | 1.09100i | ||||
\(437\) | −2.77713 | + | 4.81013i | −0.132848 | + | 0.230100i | ||||
\(438\) | 19.4049 | − | 33.6103i | 0.927202 | − | 1.60596i | ||||
\(439\) | −10.7457 | − | 18.6121i | −0.512865 | − | 0.888308i | −0.999889 | − | 0.0149196i | \(-0.995251\pi\) |
0.487024 | − | 0.873389i | \(-0.338083\pi\) | |||||||
\(440\) | 56.2276 | 2.68055 | ||||||||
\(441\) | −4.00565 | − | 5.74062i | −0.190745 | − | 0.273363i | ||||
\(442\) | −7.41895 | −0.352883 | ||||||||
\(443\) | −11.8923 | − | 20.5980i | −0.565019 | − | 0.978642i | −0.997048 | − | 0.0767822i | \(-0.975535\pi\) |
0.432029 | − | 0.901860i | \(-0.357798\pi\) | |||||||
\(444\) | 12.0147 | − | 20.8100i | 0.570191 | − | 0.987600i | ||||
\(445\) | 1.76361 | − | 3.05467i | 0.0836032 | − | 0.144805i | ||||
\(446\) | −29.3525 | − | 50.8400i | −1.38988 | − | 2.40734i | ||||
\(447\) | 4.83066 | 0.228482 | ||||||||
\(448\) | −124.988 | + | 5.35470i | −5.90511 | + | 0.252986i | ||||
\(449\) | −8.36232 | −0.394642 | −0.197321 | − | 0.980339i | \(-0.563224\pi\) | ||||
−0.197321 | + | 0.980339i | \(0.563224\pi\) | |||||||
\(450\) | 1.69222 | + | 2.93102i | 0.0797722 | + | 0.138170i | ||||
\(451\) | 6.98101 | − | 12.0915i | 0.328723 | − | 0.569365i | ||||
\(452\) | 47.8742 | − | 82.9206i | 2.25181 | − | 3.90026i | ||||
\(453\) | 10.4923 | + | 18.1732i | 0.492973 | + | 0.853854i | ||||
\(454\) | −67.6831 | −3.17652 | ||||||||
\(455\) | −11.5836 | − | 18.2155i | −0.543049 | − | 0.853956i | ||||
\(456\) | −59.6780 | −2.79468 | ||||||||
\(457\) | 7.96569 | + | 13.7970i | 0.372619 | + | 0.645395i | 0.989968 | − | 0.141295i | \(-0.0451265\pi\) |
−0.617349 | + | 0.786690i | \(0.711793\pi\) | |||||||
\(458\) | 12.1483 | − | 21.0415i | 0.567653 | − | 0.983204i | ||||
\(459\) | −0.316198 | + | 0.547671i | −0.0147589 | + | 0.0255631i | ||||
\(460\) | 5.68338 | + | 9.84391i | 0.264989 | + | 0.458975i | ||||
\(461\) | −11.6774 | −0.543873 | −0.271936 | − | 0.962315i | \(-0.587664\pi\) | ||||
−0.271936 | + | 0.962315i | \(0.587664\pi\) | |||||||
\(462\) | 9.20690 | − | 17.6510i | 0.428344 | − | 0.821201i | ||||
\(463\) | −6.74188 | −0.313322 | −0.156661 | − | 0.987652i | \(-0.550073\pi\) | ||||
−0.156661 | + | 0.987652i | \(0.550073\pi\) | |||||||
\(464\) | −51.3325 | − | 88.9105i | −2.38305 | − | 4.12756i | ||||
\(465\) | 5.45004 | − | 9.43975i | 0.252740 | − | 0.437758i | ||||
\(466\) | −3.76801 | + | 6.52638i | −0.174550 | + | 0.302329i | ||||
\(467\) | −7.73999 | − | 13.4061i | −0.358164 | − | 0.620358i | 0.629490 | − | 0.777009i | \(-0.283264\pi\) |
−0.987654 | + | 0.156650i | \(0.949931\pi\) | |||||||
\(468\) | 24.4629 | 1.13080 | ||||||||
\(469\) | 3.85278 | − | 7.38637i | 0.177905 | − | 0.341071i | ||||
\(470\) | 1.59491 | 0.0735678 | ||||||||
\(471\) | 0.797219 | + | 1.38082i | 0.0367339 | + | 0.0636250i | ||||
\(472\) | −39.3229 | + | 68.1093i | −1.80999 | + | 3.13499i | ||||
\(473\) | −2.66922 | + | 4.62322i | −0.122731 | + | 0.212576i | ||||
\(474\) | 22.1033 | + | 38.2840i | 1.01524 | + | 1.75844i | ||||
\(475\) | −6.71452 | −0.308083 | ||||||||
\(476\) | −5.24144 | − | 8.24228i | −0.240241 | − | 0.377784i | ||||
\(477\) | −10.1722 | −0.465751 | ||||||||
\(478\) | 0.0732912 | + | 0.126944i | 0.00335226 | + | 0.00580628i | ||||
\(479\) | −9.28598 | + | 16.0838i | −0.424287 | + | 0.734887i | −0.996354 | − | 0.0853204i | \(-0.972809\pi\) |
0.572066 | + | 0.820207i | \(0.306142\pi\) | |||||||
\(480\) | −29.2428 | + | 50.6501i | −1.33475 | + | 2.31185i | ||||
\(481\) | −8.62407 | − | 14.9373i | −0.393224 | − | 0.681083i | ||||
\(482\) | −0.838629 | −0.0381985 | ||||||||
\(483\) | 2.64333 | − | 0.113245i | 0.120276 | − | 0.00515283i | ||||
\(484\) | −22.0458 | −1.00208 | ||||||||
\(485\) | −2.87379 | − | 4.97754i | −0.130492 | − | 0.226019i | ||||
\(486\) | 1.39981 | − | 2.42454i | 0.0634966 | − | 0.109979i | ||||
\(487\) | −9.08084 | + | 15.7285i | −0.411492 | + | 0.712725i | −0.995053 | − | 0.0993441i | \(-0.968326\pi\) |
0.583561 | + | 0.812069i | \(0.301659\pi\) | |||||||
\(488\) | 33.7751 | + | 58.5002i | 1.52893 | + | 2.64818i | ||||
\(489\) | 10.8977 | 0.492810 | ||||||||
\(490\) | 16.1826 | − | 34.5560i | 0.731054 | − | 1.56108i | ||||
\(491\) | 14.1905 | 0.640410 | 0.320205 | − | 0.947348i | \(-0.396248\pi\) | ||||
0.320205 | + | 0.947348i | \(0.396248\pi\) | |||||||
\(492\) | 15.1633 | + | 26.2636i | 0.683615 | + | 1.18406i | ||||
\(493\) | 1.76379 | − | 3.05497i | 0.0794371 | − | 0.137589i | ||||
\(494\) | −32.5798 | + | 56.4299i | −1.46584 | + | 2.53890i | ||||
\(495\) | −2.61656 | − | 4.53202i | −0.117606 | − | 0.203699i | ||||
\(496\) | −103.034 | −4.62637 | ||||||||
\(497\) | −15.8660 | + | 0.679727i | −0.711685 | + | 0.0304899i | ||||
\(498\) | −34.9904 | −1.56796 | ||||||||
\(499\) | −7.16937 | − | 12.4177i | −0.320945 | − | 0.555893i | 0.659738 | − | 0.751495i | \(-0.270667\pi\) |
−0.980683 | + | 0.195603i | \(0.937334\pi\) | |||||||
\(500\) | −35.2875 | + | 61.1198i | −1.57811 | + | 2.73336i | ||||
\(501\) | −7.79653 | + | 13.5040i | −0.348323 | + | 0.603313i | ||||
\(502\) | 8.01878 | + | 13.8889i | 0.357896 | + | 0.619894i | ||||
\(503\) | 10.8254 | 0.482681 | 0.241341 | − | 0.970440i | \(-0.422413\pi\) | ||||
0.241341 | + | 0.970440i | \(0.422413\pi\) | |||||||
\(504\) | 15.2544 | + | 23.9879i | 0.679487 | + | 1.06851i | ||||
\(505\) | 24.9251 | 1.10915 | ||||||||
\(506\) | 3.76225 | + | 6.51640i | 0.167252 | + | 0.289690i | ||||
\(507\) | 2.27968 | − | 3.94851i | 0.101244 | − | 0.175360i | ||||
\(508\) | 53.1337 | − | 92.0303i | 2.35743 | − | 4.08319i | ||||
\(509\) | −13.7751 | − | 23.8592i | −0.610570 | − | 1.05754i | −0.991144 | − | 0.132788i | \(-0.957607\pi\) |
0.380574 | − | 0.924750i | \(-0.375726\pi\) | |||||||
\(510\) | −3.44723 | −0.152646 | ||||||||
\(511\) | 16.9621 | − | 32.5189i | 0.750357 | − | 1.43855i | ||||
\(512\) | 157.336 | 6.95333 | ||||||||
\(513\) | 2.77713 | + | 4.81013i | 0.122613 | + | 0.212372i | ||||
\(514\) | 24.1183 | − | 41.7741i | 1.06381 | − | 1.84257i | ||||
\(515\) | 12.7125 | − | 22.0187i | 0.560181 | − | 0.970262i | ||||
\(516\) | −5.79776 | − | 10.0420i | −0.255232 | − | 0.442075i | ||||
\(517\) | 0.786382 | 0.0345850 | ||||||||
\(518\) | 14.1001 | − | 27.0321i | 0.619524 | − | 1.18772i | ||||
\(519\) | 11.2721 | 0.494791 | ||||||||
\(520\) | 43.8324 | + | 75.9200i | 1.92218 | + | 3.32931i | ||||
\(521\) | 6.81822 | − | 11.8095i | 0.298712 | − | 0.517384i | −0.677130 | − | 0.735864i | \(-0.736776\pi\) |
0.975841 | + | 0.218480i | \(0.0701098\pi\) | |||||||
\(522\) | −7.80831 | + | 13.5244i | −0.341760 | + | 0.591946i | ||||
\(523\) | 5.28178 | + | 9.14831i | 0.230956 | + | 0.400028i | 0.958090 | − | 0.286468i | \(-0.0924813\pi\) |
−0.727134 | + | 0.686496i | \(0.759148\pi\) | |||||||
\(524\) | −48.6201 | −2.12398 | ||||||||
\(525\) | 1.71631 | + | 2.69894i | 0.0749061 | + | 0.117791i | ||||
\(526\) | 65.8515 | 2.87126 | ||||||||
\(527\) | −1.77013 | − | 3.06596i | −0.0771083 | − | 0.133555i | ||||
\(528\) | −24.7333 | + | 42.8394i | −1.07638 | + | 1.86435i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −27.7246 | − | 48.0204i | −1.20428 | − | 2.08587i | ||||
\(531\) | 7.31960 | 0.317644 | ||||||||
\(532\) | −85.7098 | + | 3.67197i | −3.71599 | + | 0.159200i | ||||
\(533\) | 21.7683 | 0.942889 | ||||||||
\(534\) | 2.53582 | + | 4.39218i | 0.109736 | + | 0.190068i | ||||
\(535\) | −13.3586 | + | 23.1377i | −0.577542 | + | 1.00033i | ||||
\(536\) | −16.9160 | + | 29.2993i | −0.730658 | + | 1.26554i | ||||
\(537\) | 4.08754 | + | 7.07983i | 0.176390 | + | 0.305517i | ||||
\(538\) | −38.6606 | −1.66678 | ||||||||
\(539\) | 7.97893 | − | 17.0381i | 0.343677 | − | 0.733882i | ||||
\(540\) | 11.3668 | 0.489148 | ||||||||
\(541\) | −15.8326 | − | 27.4229i | −0.680696 | − | 1.17900i | −0.974769 | − | 0.223218i | \(-0.928344\pi\) |
0.294072 | − | 0.955783i | \(-0.404989\pi\) | |||||||
\(542\) | 31.4148 | − | 54.4121i | 1.34938 | − | 2.33720i | ||||
\(543\) | −1.50047 | + | 2.59889i | −0.0643914 | + | 0.111529i | ||||
\(544\) | 9.49786 | + | 16.4508i | 0.407217 | + | 0.705321i | ||||
\(545\) | 8.77335 | 0.375809 | ||||||||
\(546\) | 31.0102 | − | 1.32853i | 1.32711 | − | 0.0568560i | ||||
\(547\) | −30.4882 | −1.30358 | −0.651792 | − | 0.758398i | \(-0.725982\pi\) | ||||
−0.651792 | + | 0.758398i | \(0.725982\pi\) | |||||||
\(548\) | 38.8345 | + | 67.2633i | 1.65893 | + | 2.87335i | ||||
\(549\) | 3.14346 | − | 5.44464i | 0.134160 | − | 0.232371i | ||||
\(550\) | −4.54817 | + | 7.87766i | −0.193935 | + | 0.335905i | ||||
\(551\) | −15.4912 | − | 26.8315i | −0.659945 | − | 1.14306i | ||||
\(552\) | −10.7446 | −0.457319 | ||||||||
\(553\) | 22.4179 | + | 35.2526i | 0.953307 | + | 1.49909i | ||||
\(554\) | 62.2289 | 2.64385 | ||||||||
\(555\) | −4.00720 | − | 6.94067i | −0.170096 | − | 0.294615i | ||||
\(556\) | 17.3186 | − | 29.9967i | 0.734472 | − | 1.27214i | ||||
\(557\) | −7.06138 | + | 12.2307i | −0.299200 | + | 0.518230i | −0.975953 | − | 0.217980i | \(-0.930053\pi\) |
0.676753 | + | 0.736210i | \(0.263387\pi\) | |||||||
\(558\) | 7.83639 | + | 13.5730i | 0.331741 | + | 0.574592i | ||||
\(559\) | −8.32319 | −0.352034 | ||||||||
\(560\) | −43.8483 | + | 84.0640i | −1.85293 | + | 3.55235i | ||||
\(561\) | −1.69968 | −0.0717606 | ||||||||
\(562\) | −9.79418 | − | 16.9640i | −0.413143 | − | 0.715584i | ||||
\(563\) | 8.64204 | − | 14.9685i | 0.364219 | − | 0.630845i | −0.624432 | − | 0.781079i | \(-0.714669\pi\) |
0.988650 | + | 0.150234i | \(0.0480027\pi\) | |||||||
\(564\) | −0.854041 | + | 1.47924i | −0.0359616 | + | 0.0622874i | ||||
\(565\) | −15.9673 | − | 27.6561i | −0.671748 | − | 1.16350i | ||||
\(566\) | 22.5755 | 0.948918 | ||||||||
\(567\) | 1.22359 | − | 2.34581i | 0.0513860 | − | 0.0985148i | ||||
\(568\) | 64.4917 | 2.70601 | ||||||||
\(569\) | −1.37078 | − | 2.37427i | −0.0574662 | − | 0.0995345i | 0.835861 | − | 0.548941i | \(-0.184969\pi\) |
−0.893327 | + | 0.449406i | \(0.851635\pi\) | |||||||
\(570\) | −15.1383 | + | 26.2203i | −0.634074 | + | 1.09825i | ||||
\(571\) | −15.5954 | + | 27.0120i | −0.652647 | + | 1.13042i | 0.329832 | + | 0.944040i | \(0.393008\pi\) |
−0.982478 | + | 0.186377i | \(0.940325\pi\) | |||||||
\(572\) | 32.8743 | + | 56.9400i | 1.37454 | + | 2.38078i | ||||
\(573\) | 11.5788 | 0.483712 | ||||||||
\(574\) | 20.6479 | + | 32.4693i | 0.861828 | + | 1.35524i | ||||
\(575\) | −1.20890 | −0.0504145 | ||||||||
\(576\) | −23.6421 | − | 40.9493i | −0.985088 | − | 1.70622i | ||||
\(577\) | 2.12410 | − | 3.67904i | 0.0884273 | − | 0.153161i | −0.818419 | − | 0.574622i | \(-0.805149\pi\) |
0.906847 | + | 0.421461i | \(0.138483\pi\) | |||||||
\(578\) | 23.2369 | − | 40.2476i | 0.966529 | − | 1.67408i | ||||
\(579\) | 2.84965 | + | 4.93573i | 0.118427 | + | 0.205122i | ||||
\(580\) | −63.4052 | −2.63276 | ||||||||
\(581\) | −33.0370 | + | 1.41537i | −1.37061 | + | 0.0587193i | ||||
\(582\) | 8.26419 | 0.342562 | ||||||||
\(583\) | −13.6698 | − | 23.6768i | −0.566145 | − | 0.980592i | ||||
\(584\) | −74.4734 | + | 128.992i | −3.08173 | + | 5.33771i | ||||
\(585\) | 4.07950 | − | 7.06590i | 0.168667 | − | 0.292139i | ||||
\(586\) | 18.4016 | + | 31.8725i | 0.760164 | + | 1.31664i | ||||
\(587\) | −27.9648 | −1.15423 | −0.577116 | − | 0.816662i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816662i | \(0.695822\pi\) | |||||||
\(588\) | 23.3845 | + | 33.5130i | 0.964359 | + | 1.38205i | ||||
\(589\) | −31.0937 | −1.28119 | ||||||||
\(590\) | 19.9498 | + | 34.5541i | 0.821321 | + | 1.42257i | ||||
\(591\) | −6.49415 | + | 11.2482i | −0.267134 | + | 0.462689i | ||||
\(592\) | −37.8784 | + | 65.6074i | −1.55679 | + | 2.69645i | ||||
\(593\) | 12.2413 | + | 21.2026i | 0.502690 | + | 0.870685i | 0.999995 | + | 0.00310888i | \(0.000989590\pi\) |
−0.497305 | + | 0.867576i | \(0.665677\pi\) | |||||||
\(594\) | 7.52450 | 0.308734 | ||||||||
\(595\) | −3.25479 | + | 0.139441i | −0.133433 | + | 0.00571653i | ||||
\(596\) | −28.2007 | −1.15515 | ||||||||
\(597\) | −10.6628 | − | 18.4685i | −0.436398 | − | 0.755864i | ||||
\(598\) | −5.86574 | + | 10.1598i | −0.239868 | + | 0.415464i | ||||
\(599\) | 21.9951 | − | 38.0966i | 0.898696 | − | 1.55659i | 0.0695327 | − | 0.997580i | \(-0.477849\pi\) |
0.829163 | − | 0.559007i | \(-0.188817\pi\) | |||||||
\(600\) | −6.49453 | − | 11.2489i | −0.265138 | − | 0.459233i | ||||
\(601\) | 9.57098 | 0.390408 | 0.195204 | − | 0.980763i | \(-0.437463\pi\) | ||||
0.195204 | + | 0.980763i | \(0.437463\pi\) | |||||||
\(602\) | −7.89482 | − | 12.4148i | −0.321769 | − | 0.505989i | ||||
\(603\) | 3.14875 | 0.128227 | ||||||||
\(604\) | −61.2528 | − | 106.093i | −2.49234 | − | 4.31686i | ||||
\(605\) | −3.67641 | + | 6.36774i | −0.149467 | + | 0.258885i | ||||
\(606\) | −17.9194 | + | 31.0373i | −0.727926 | + | 1.26080i | ||||
\(607\) | 0.795419 | + | 1.37771i | 0.0322851 | + | 0.0559194i | 0.881716 | − | 0.471780i | \(-0.156388\pi\) |
−0.849431 | + | 0.527699i | \(0.823055\pi\) | |||||||
\(608\) | 166.837 | 6.76613 | ||||||||
\(609\) | −6.82533 | + | 13.0852i | −0.276576 | + | 0.530240i | ||||
\(610\) | 34.2705 | 1.38757 | ||||||||
\(611\) | 0.613026 | + | 1.06179i | 0.0248004 | + | 0.0429555i | ||||
\(612\) | 1.84592 | − | 3.19723i | 0.0746169 | − | 0.129240i | ||||
\(613\) | −8.61461 | + | 14.9209i | −0.347941 | + | 0.602651i | −0.985883 | − | 0.167433i | \(-0.946452\pi\) |
0.637943 | + | 0.770084i | \(0.279786\pi\) | |||||||
\(614\) | −21.1492 | − | 36.6314i | −0.853511 | − | 1.47832i | ||||
\(615\) | 10.1147 | 0.407864 | ||||||||
\(616\) | −35.3348 | + | 67.7423i | −1.42368 | + | 2.72942i | ||||
\(617\) | −28.9242 | −1.16444 | −0.582222 | − | 0.813030i | \(-0.697817\pi\) | ||||
−0.582222 | + | 0.813030i | \(0.697817\pi\) | |||||||
\(618\) | 18.2788 | + | 31.6598i | 0.735282 | + | 1.27355i | ||||
\(619\) | 10.9323 | − | 18.9352i | 0.439404 | − | 0.761071i | −0.558239 | − | 0.829680i | \(-0.688523\pi\) |
0.997644 | + | 0.0686093i | \(0.0218562\pi\) | |||||||
\(620\) | −31.8166 | + | 55.1080i | −1.27779 | + | 2.21319i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | −60.1438 | −2.41154 | ||||||||
\(623\) | 2.57192 | + | 4.04440i | 0.103042 | + | 0.162036i | ||||
\(624\) | −77.1238 | −3.08742 | ||||||||
\(625\) | 8.74704 | + | 15.1503i | 0.349882 | + | 0.606013i | ||||
\(626\) | −20.7707 | + | 35.9759i | −0.830164 | + | 1.43789i | ||||
\(627\) | −7.46405 | + | 12.9281i | −0.298085 | + | 0.516299i | ||||
\(628\) | −4.65406 | − | 8.06107i | −0.185717 | − | 0.321672i | ||||
\(629\) | −2.60302 | −0.103789 | ||||||||
\(630\) | 14.4090 | − | 0.617307i | 0.574067 | − | 0.0245941i | ||||
\(631\) | −11.5152 | −0.458412 | −0.229206 | − | 0.973378i | \(-0.573613\pi\) | ||||
−0.229206 | + | 0.973378i | \(0.573613\pi\) | |||||||
\(632\) | −84.8293 | − | 146.929i | −3.37433 | − | 5.84451i | ||||
\(633\) | 3.84595 | − | 6.66139i | 0.152863 | − | 0.264766i | ||||
\(634\) | 6.58152 | − | 11.3995i | 0.261386 | − | 0.452733i | ||||
\(635\) | −17.7214 | − | 30.6944i | −0.703254 | − | 1.21807i | ||||
\(636\) | 59.3837 | 2.35472 | ||||||||
\(637\) | 29.2252 | − | 2.50873i | 1.15795 | − | 0.0993996i | ||||
\(638\) | −41.9725 | −1.66171 | ||||||||
\(639\) | −3.00113 | − | 5.19812i | −0.118723 | − | 0.205634i | ||||
\(640\) | 70.3891 | − | 121.917i | 2.78237 | − | 4.81921i | ||||
\(641\) | −4.63400 | + | 8.02633i | −0.183032 | + | 0.317021i | −0.942912 | − | 0.333043i | \(-0.891925\pi\) |
0.759879 | + | 0.650064i | \(0.225258\pi\) | |||||||
\(642\) | −19.2077 | − | 33.2688i | −0.758069 | − | 1.31301i | ||||
\(643\) | 13.8712 | 0.547025 | 0.273513 | − | 0.961868i | \(-0.411814\pi\) | ||||
0.273513 | + | 0.961868i | \(0.411814\pi\) | |||||||
\(644\) | −15.4314 | + | 0.661109i | −0.608082 | + | 0.0260514i | ||||
\(645\) | −3.86740 | −0.152279 | ||||||||
\(646\) | 4.91681 | + | 8.51617i | 0.193449 | + | 0.335064i | ||||
\(647\) | 3.65031 | − | 6.32253i | 0.143509 | − | 0.248564i | −0.785307 | − | 0.619107i | \(-0.787495\pi\) |
0.928816 | + | 0.370542i | \(0.120828\pi\) | |||||||
\(648\) | −5.37228 | + | 9.30506i | −0.211043 | + | 0.365537i | ||||
\(649\) | 9.83640 | + | 17.0371i | 0.386112 | + | 0.668766i | ||||
\(650\) | −14.1822 | −0.556270 | ||||||||
\(651\) | 7.94794 | + | 12.4983i | 0.311504 | + | 0.489847i | ||||
\(652\) | −63.6191 | −2.49152 | ||||||||
\(653\) | 14.1389 | + | 24.4892i | 0.553296 | + | 0.958337i | 0.998034 | + | 0.0626765i | \(0.0199636\pi\) |
−0.444737 | + | 0.895661i | \(0.646703\pi\) | |||||||
\(654\) | −6.30742 | + | 10.9248i | −0.246639 | + | 0.427192i | ||||
\(655\) | −8.10802 | + | 14.0435i | −0.316806 | + | 0.548725i | ||||
\(656\) | −47.8051 | − | 82.8008i | −1.86648 | − | 3.23283i | ||||
\(657\) | 13.8625 | 0.540829 | ||||||||
\(658\) | −1.00228 | + | 1.92153i | −0.0390730 | + | 0.0749090i | ||||
\(659\) | 26.3606 | 1.02686 | 0.513431 | − | 0.858131i | \(-0.328374\pi\) | ||||
0.513431 | + | 0.858131i | \(0.328374\pi\) | |||||||
\(660\) | 15.2751 | + | 26.4573i | 0.594584 | + | 1.02985i | ||||
\(661\) | 8.46466 | − | 14.6612i | 0.329237 | − | 0.570255i | −0.653124 | − | 0.757251i | \(-0.726542\pi\) |
0.982361 | + | 0.186996i | \(0.0598751\pi\) | |||||||
\(662\) | 11.0286 | − | 19.1021i | 0.428638 | − | 0.742423i | ||||
\(663\) | −1.32499 | − | 2.29495i | −0.0514584 | − | 0.0891286i | ||||
\(664\) | 134.288 | 5.21140 | ||||||||
\(665\) | −13.2326 | + | 25.3689i | −0.513138 | + | 0.983764i | ||||
\(666\) | 11.5236 | 0.446529 | ||||||||
\(667\) | −2.78906 | − | 4.83079i | −0.107993 | − | 0.187049i | ||||
\(668\) | 45.5151 | − | 78.8344i | 1.76103 | − | 3.05020i | ||||
\(669\) | 10.4845 | − | 18.1596i | 0.405353 | − | 0.702091i | ||||
\(670\) | 8.58202 | + | 14.8645i | 0.331552 | + | 0.574266i | ||||
\(671\) | 16.8973 | 0.652312 | ||||||||
\(672\) | −42.6456 | − | 67.0611i | −1.64509 | − | 2.58694i | ||||
\(673\) | −23.7746 | −0.916444 | −0.458222 | − | 0.888838i | \(-0.651513\pi\) | ||||
−0.458222 | + | 0.888838i | \(0.651513\pi\) | |||||||
\(674\) | 25.7365 | + | 44.5770i | 0.991334 | + | 1.71704i | ||||
\(675\) | −0.604448 | + | 1.04694i | −0.0232652 | + | 0.0402966i | ||||
\(676\) | −13.3084 | + | 23.0509i | −0.511863 | + | 0.886573i | ||||
\(677\) | −11.3542 | − | 19.6661i | −0.436377 | − | 0.755828i | 0.561030 | − | 0.827796i | \(-0.310405\pi\) |
−0.997407 | + | 0.0719679i | \(0.977072\pi\) | |||||||
\(678\) | 45.9173 | 1.76344 | ||||||||
\(679\) | 7.80283 | − | 0.334288i | 0.299445 | − | 0.0128288i | ||||
\(680\) | 13.2300 | 0.507348 | ||||||||
\(681\) | −12.0879 | − | 20.9369i | −0.463210 | − | 0.802302i | ||||
\(682\) | −21.0618 | + | 36.4800i | −0.806496 | + | 1.39689i | ||||
\(683\) | −5.42079 | + | 9.38908i | −0.207421 | + | 0.359263i | −0.950901 | − | 0.309494i | \(-0.899840\pi\) |
0.743481 | + | 0.668757i | \(0.233174\pi\) | |||||||
\(684\) | −16.2125 | − | 28.0809i | −0.619900 | − | 1.07370i | ||||
\(685\) | 25.9046 | 0.989762 | ||||||||
\(686\) | 31.4631 | + | 41.2124i | 1.20127 | + | 1.57350i | ||||
\(687\) | 8.67855 | 0.331107 | ||||||||
\(688\) | 18.2785 | + | 31.6593i | 0.696861 | + | 1.20700i | ||||
\(689\) | 21.3127 | − | 36.9146i | 0.811948 | − | 1.40633i | ||||
\(690\) | −2.72553 | + | 4.72076i | −0.103759 | + | 0.179716i | ||||
\(691\) | −7.50102 | − | 12.9921i | −0.285352 | − | 0.494245i | 0.687342 | − | 0.726334i | \(-0.258777\pi\) |
−0.972695 | + | 0.232089i | \(0.925444\pi\) | |||||||
\(692\) | −65.8050 | −2.50153 | ||||||||
\(693\) | 7.10443 | − | 0.304367i | 0.269875 | − | 0.0115620i | ||||
\(694\) | 16.8559 | 0.639841 | ||||||||
\(695\) | −5.77619 | − | 10.0047i | −0.219103 | − | 0.379498i | ||||
\(696\) | 29.9672 | − | 51.9047i | 1.13590 | − | 1.96744i | ||||
\(697\) | 1.64259 | − | 2.84505i | 0.0622175 | − | 0.107764i | ||||
\(698\) | −18.6704 | − | 32.3380i | −0.706684 | − | 1.22401i | ||||
\(699\) | −2.69180 | −0.101813 | ||||||||
\(700\) | −10.0196 | − | 15.7561i | −0.378706 | − | 0.595523i | ||||
\(701\) | −8.60412 | −0.324973 | −0.162486 | − | 0.986711i | \(-0.551951\pi\) | ||||
−0.162486 | + | 0.986711i | \(0.551951\pi\) | |||||||
\(702\) | 5.86574 | + | 10.1598i | 0.221388 | + | 0.383456i | ||||
\(703\) | −11.4310 | + | 19.7990i | −0.431128 | + | 0.746735i | ||||
\(704\) | 63.5425 | − | 110.059i | 2.39485 | − | 4.14800i | ||||
\(705\) | 0.284844 | + | 0.493365i | 0.0107279 | + | 0.0185812i | ||||
\(706\) | 48.9569 | 1.84252 | ||||||||
\(707\) | −15.6636 | + | 30.0295i | −0.589089 | + | 1.12937i | ||||
\(708\) | −42.7308 | −1.60592 | ||||||||
\(709\) | 14.5604 | + | 25.2194i | 0.546829 | + | 0.947135i | 0.998489 | + | 0.0549454i | \(0.0174985\pi\) |
−0.451661 | + | 0.892190i | \(0.649168\pi\) | |||||||
\(710\) | 16.3594 | − | 28.3353i | 0.613957 | − | 1.06340i | ||||
\(711\) | −7.89510 | + | 13.6747i | −0.296089 | + | 0.512842i | ||||
\(712\) | −9.73215 | − | 16.8566i | −0.364728 | − | 0.631727i | ||||
\(713\) | −5.59818 | −0.209654 | ||||||||
\(714\) | 2.16633 | − | 4.15318i | 0.0810727 | − | 0.155429i | ||||
\(715\) | 21.9288 | 0.820092 | ||||||||
\(716\) | −23.8625 | − | 41.3311i | −0.891784 | − | 1.54462i | ||||
\(717\) | −0.0261790 | + | 0.0453433i | −0.000977672 | + | 0.00169338i | ||||
\(718\) | 11.9925 | − | 20.7716i | 0.447556 | − | 0.775189i | ||||
\(719\) | 7.65789 | + | 13.2639i | 0.285591 | + | 0.494658i | 0.972752 | − | 0.231847i | \(-0.0744767\pi\) |
−0.687161 | + | 0.726505i | \(0.741143\pi\) | |||||||
\(720\) | −35.8358 | −1.33552 | ||||||||
\(721\) | 18.5390 | + | 29.1530i | 0.690429 | + | 1.08571i | ||||
\(722\) | 33.1748 | 1.23464 | ||||||||
\(723\) | −0.149776 | − | 0.259419i | −0.00557021 | − | 0.00964789i | ||||
\(724\) | 8.75955 | − | 15.1720i | 0.325546 | − | 0.563863i | ||||
\(725\) | 3.37169 | − | 5.83993i | 0.125221 | − | 0.216890i | ||||
\(726\) | −5.28616 | − | 9.15590i | −0.196188 | − | 0.339807i | ||||
\(727\) | 32.6484 | 1.21086 | 0.605432 | − | 0.795897i | \(-0.293000\pi\) | ||||
0.605432 | + | 0.795897i | \(0.293000\pi\) | |||||||
\(728\) | −119.013 | + | 5.09873i | −4.41091 | + | 0.188972i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 37.7828 | + | 65.4417i | 1.39840 | + | 2.42211i | ||||
\(731\) | −0.628051 | + | 1.08782i | −0.0232293 | + | 0.0402343i | ||||
\(732\) | −18.3511 | + | 31.7850i | −0.678276 | + | 1.17481i | ||||
\(733\) | 21.7266 | + | 37.6316i | 0.802490 | + | 1.38995i | 0.917972 | + | 0.396644i | \(0.129825\pi\) |
−0.115482 | + | 0.993310i | \(0.536841\pi\) | |||||||
\(734\) | −55.1848 | −2.03691 | ||||||||
\(735\) | 13.5796 | − | 1.16569i | 0.500891 | − | 0.0429971i | ||||
\(736\) | 30.0377 | 1.10720 | ||||||||
\(737\) | 4.23142 | + | 7.32904i | 0.155867 | + | 0.269969i | ||||
\(738\) | −7.27175 | + | 12.5950i | −0.267677 | + | 0.463630i | ||||
\(739\) | −1.74434 | + | 3.02129i | −0.0641667 | + | 0.111140i | −0.896324 | − | 0.443400i | \(-0.853772\pi\) |
0.832157 | + | 0.554540i | \(0.187106\pi\) | |||||||
\(740\) | 23.3935 | + | 40.5187i | 0.859961 | + | 1.48950i | ||||
\(741\) | −23.2745 | −0.855010 | ||||||||
\(742\) | 75.2771 | − | 3.22501i | 2.76351 | − | 0.118394i | ||||
\(743\) | 22.0130 | 0.807577 | 0.403789 | − | 0.914852i | \(-0.367693\pi\) | ||||
0.403789 | + | 0.914852i | \(0.367693\pi\) | |||||||
\(744\) | −30.0750 | − | 52.0914i | −1.10260 | − | 1.90976i | ||||
\(745\) | −4.70283 | + | 8.14554i | −0.172298 | + | 0.298430i | ||||
\(746\) | −30.6920 | + | 53.1601i | −1.12371 | + | 1.94633i | ||||
\(747\) | −6.24913 | − | 10.8238i | −0.228644 | − | 0.396023i | ||||
\(748\) | 9.92251 | 0.362803 | ||||||||
\(749\) | −19.4812 | − | 30.6346i | −0.711827 | − | 1.11936i | ||||
\(750\) | −33.8451 | −1.23585 | ||||||||
\(751\) | −7.71696 | − | 13.3662i | −0.281596 | − | 0.487739i | 0.690182 | − | 0.723636i | \(-0.257530\pi\) |
−0.971778 | + | 0.235897i | \(0.924197\pi\) | |||||||
\(752\) | 2.69252 | − | 4.66358i | 0.0981862 | − | 0.170063i | ||||
\(753\) | −2.86424 | + | 4.96101i | −0.104379 | + | 0.180789i | ||||
\(754\) | −32.7198 | − | 56.6724i | −1.19159 | − | 2.06389i | ||||
\(755\) | −40.8587 | −1.48700 | ||||||||
\(756\) | −7.14315 | + | 13.6945i | −0.259794 | + | 0.498065i | ||||
\(757\) | −13.1778 | −0.478955 | −0.239478 | − | 0.970902i | \(-0.576976\pi\) | ||||
−0.239478 | + | 0.970902i | \(0.576976\pi\) | |||||||
\(758\) | −13.8573 | − | 24.0016i | −0.503321 | − | 0.871777i | ||||
\(759\) | −1.34384 | + | 2.32760i | −0.0487784 | + | 0.0844867i | ||||
\(760\) | 58.0988 | − | 100.630i | 2.10747 | − | 3.65024i | ||||
\(761\) | −5.35343 | − | 9.27241i | −0.194062 | − | 0.336125i | 0.752531 | − | 0.658557i | \(-0.228833\pi\) |
−0.946592 | + | 0.322432i | \(0.895499\pi\) | |||||||
\(762\) | 50.9618 | 1.84615 | ||||||||
\(763\) | −5.51339 | + | 10.5700i | −0.199598 | + | 0.382660i | ||||
\(764\) | −67.5956 | −2.44552 | ||||||||
\(765\) | −0.615661 | − | 1.06636i | −0.0222593 | − | 0.0385542i | ||||
\(766\) | 24.5497 | − | 42.5213i | 0.887015 | − | 1.53636i | ||||
\(767\) | −15.3360 | + | 26.5627i | −0.553750 | + | 0.959124i | ||||
\(768\) | 53.9253 | + | 93.4014i | 1.94586 | + | 3.37033i | ||||
\(769\) | 30.1544 | 1.08739 | 0.543697 | − | 0.839282i | \(-0.317024\pi\) | ||||
0.543697 | + | 0.839282i | \(0.317024\pi\) | |||||||
\(770\) | 20.8002 | + | 32.7088i | 0.749588 | + | 1.17874i | ||||
\(771\) | 17.2297 | 0.620512 | ||||||||
\(772\) | −16.6358 | − | 28.8141i | −0.598737 | − | 1.03704i | ||||
\(773\) | −23.1191 | + | 40.0435i | −0.831537 | + | 1.44026i | 0.0652818 | + | 0.997867i | \(0.479205\pi\) |
−0.896819 | + | 0.442398i | \(0.854128\pi\) | |||||||
\(774\) | 2.78038 | − | 4.81577i | 0.0999388 | − | 0.173099i | ||||
\(775\) | −3.38381 | − | 5.86093i | −0.121550 | − | 0.210531i | ||||
\(776\) | −31.7169 | −1.13857 | ||||||||
\(777\) | 10.8802 | − | 0.466130i | 0.390327 | − | 0.0167223i | ||||
\(778\) | 53.8860 | 1.93191 | ||||||||
\(779\) | −14.4267 | − | 24.9877i | −0.516889 | − | 0.895277i | ||||
\(780\) | −23.8156 | + | 41.2498i | −0.852734 | + | 1.47698i | ||||
\(781\) | 8.06611 | − | 13.9709i | 0.288628 | − | 0.499918i | ||||
\(782\) | 0.885234 | + | 1.53327i | 0.0316559 | + | 0.0548296i | ||||
\(783\) | −5.57812 | −0.199346 | ||||||||
\(784\) | −73.7238 | − | 105.656i | −2.63299 | − | 3.77342i | ||||
\(785\) | −3.10449 | −0.110804 | ||||||||
\(786\) | −11.6582 | − | 20.1926i | −0.415834 | − | 0.720245i | ||||
\(787\) | −18.3653 | + | 31.8096i | −0.654651 | + | 1.13389i | 0.327330 | + | 0.944910i | \(0.393851\pi\) |
−0.981981 | + | 0.188978i | \(0.939482\pi\) | |||||||
\(788\) | 37.9120 | − | 65.6655i | 1.35056 | − | 2.33924i | ||||
\(789\) | 11.7608 | + | 20.3703i | 0.418695 | + | 0.725202i | ||||
\(790\) | −86.0734 | −3.06236 | ||||||||
\(791\) | 43.3539 | − | 1.85736i | 1.54149 | − | 0.0660403i | ||||
\(792\) | −28.8780 | −1.02614 | ||||||||
\(793\) | 13.1723 | + | 22.8151i | 0.467763 | + | 0.810189i | ||||
\(794\) | 34.4345 | − | 59.6423i | 1.22203 | − | 2.11662i | ||||
\(795\) | 9.90299 | − | 17.1525i | 0.351223 | − | 0.608336i | ||||
\(796\) | 62.2478 | + | 107.816i | 2.20631 | + | 3.82145i | ||||
\(797\) | −32.2468 | −1.14224 | −0.571120 | − | 0.820867i | \(-0.693491\pi\) | ||||
−0.571120 | + | 0.820867i | \(0.693491\pi\) | |||||||
\(798\) | −22.0766 | − | 34.7159i | −0.781504 | − | 1.22893i | ||||
\(799\) | 0.185031 | 0.00654592 | ||||||||
\(800\) | 18.1562 | + | 31.4475i | 0.641920 | + | 1.11184i | ||||
\(801\) | −0.905775 | + | 1.56885i | −0.0320040 | + | 0.0554325i | ||||
\(802\) | 11.0377 | − | 19.1178i | 0.389753 | − | 0.675073i | ||||
\(803\) | 18.6291 | + | 32.2665i | 0.657405 | + | 1.13866i | ||||
\(804\) | −18.3820 | −0.648282 | ||||||||
\(805\) | −2.38242 | + | 4.56747i | −0.0839694 | + | 0.160982i | ||||
\(806\) | −65.6750 | −2.31330 | ||||||||
\(807\) | −6.90462 | − | 11.9592i | −0.243054 | − | 0.420982i | ||||
\(808\) | 68.7722 | − | 119.117i | 2.41940 | − | 4.19052i | ||||
\(809\) | −3.40031 | + | 5.88951i | −0.119548 | + | 0.207064i | −0.919589 | − | 0.392882i | \(-0.871478\pi\) |
0.800040 | + | 0.599946i | \(0.204811\pi\) | |||||||
\(810\) | 2.72553 | + | 4.72076i | 0.0957655 | + | 0.165871i | ||||
\(811\) | −32.1358 | −1.12844 | −0.564220 | − | 0.825625i | \(-0.690823\pi\) | ||||
−0.564220 | + | 0.825625i | \(0.690823\pi\) | |||||||
\(812\) | 39.8454 | − | 76.3897i | 1.39830 | − | 2.68075i | ||||
\(813\) | 22.4422 | 0.787083 | ||||||||
\(814\) | 15.4859 | + | 26.8223i | 0.542779 | + | 0.940121i | ||||
\(815\) | −10.6093 | + | 18.3758i | −0.371627 | + | 0.643677i | ||||
\(816\) | −5.81960 | + | 10.0799i | −0.203727 | + | 0.352865i | ||||
\(817\) | 5.51609 | + | 9.55416i | 0.192984 | + | 0.334258i | ||||
\(818\) | 13.4571 | 0.470517 | ||||||||
\(819\) | 5.94925 | + | 9.35532i | 0.207883 | + | 0.326901i | ||||
\(820\) | −59.0482 | −2.06205 | ||||||||
\(821\) | 15.3962 | + | 26.6670i | 0.537331 | + | 0.930684i | 0.999047 | + | 0.0436564i | \(0.0139007\pi\) |
−0.461716 | + | 0.887028i | \(0.652766\pi\) | |||||||
\(822\) | −18.6235 | + | 32.2569i | −0.649571 | + | 1.12509i | ||||
\(823\) | 27.6175 | − | 47.8350i | 0.962687 | − | 1.66742i | 0.246981 | − | 0.969020i | \(-0.420561\pi\) |
0.715705 | − | 0.698402i | \(-0.246105\pi\) | |||||||
\(824\) | −70.1516 | − | 121.506i | −2.44385 | − | 4.23287i | ||||
\(825\) | −3.24913 | −0.113120 | ||||||||
\(826\) | −54.1673 | + | 2.32063i | −1.88472 | + | 0.0807450i | ||||
\(827\) | 25.1429 | 0.874303 | 0.437152 | − | 0.899388i | \(-0.355987\pi\) | ||||
0.437152 | + | 0.899388i | \(0.355987\pi\) | |||||||
\(828\) | −2.91893 | − | 5.05574i | −0.101440 | − | 0.175699i | ||||
\(829\) | −9.89887 | + | 17.1453i | −0.343802 | + | 0.595482i | −0.985135 | − | 0.171780i | \(-0.945048\pi\) |
0.641333 | + | 0.767262i | \(0.278382\pi\) | |||||||
\(830\) | 34.0645 | − | 59.0014i | 1.18239 | − | 2.04797i | ||||
\(831\) | 11.1138 | + | 19.2497i | 0.385534 | + | 0.667765i | ||||
\(832\) | 198.139 | 6.86924 | ||||||||
\(833\) | 1.87739 | − | 4.00895i | 0.0650478 | − | 0.138902i | ||||
\(834\) | 16.6107 | 0.575181 | ||||||||
\(835\) | −15.1804 | − | 26.2933i | −0.525340 | − | 0.909916i | ||||
\(836\) | 43.5741 | − | 75.4726i | 1.50704 | − | 2.61027i | ||||
\(837\) | −2.79909 | + | 4.84817i | −0.0967507 | + | 0.167577i | ||||
\(838\) | −6.12153 | − | 10.6028i | −0.211465 | − | 0.366268i | ||||
\(839\) | 32.6430 | 1.12696 | 0.563480 | − | 0.826130i | \(-0.309462\pi\) | ||||
0.563480 | + | 0.826130i | \(0.309462\pi\) | |||||||
\(840\) | −55.2996 | + | 2.36914i | −1.90802 | + | 0.0817431i | ||||
\(841\) | 2.11543 | 0.0729458 | ||||||||
\(842\) | 21.9622 | + | 38.0396i | 0.756866 | + | 1.31093i | ||||
\(843\) | 3.49840 | − | 6.05940i | 0.120491 | − | 0.208697i | ||||
\(844\) | −22.4522 | + | 38.8883i | −0.772835 | + | 1.33859i | ||||
\(845\) | 4.43870 | + | 7.68805i | 0.152696 | + | 0.264477i | ||||
\(846\) | −0.819132 | −0.0281623 | ||||||||
\(847\) | −5.36141 | − | 8.43094i | −0.184220 | − | 0.289690i | ||||
\(848\) | −187.218 | −6.42909 | ||||||||
\(849\) | 4.03188 | + | 6.98343i | 0.138374 | + | 0.239671i | ||||
\(850\) | −1.07016 | + | 1.85356i | −0.0367061 | + | 0.0635768i | ||||
\(851\) | −2.05806 | + | 3.56466i | −0.0705494 | + | 0.122195i | ||||
\(852\) | 17.5202 | + | 30.3459i | 0.600233 | + | 1.03963i | ||||
\(853\) | 50.0984 | 1.71534 | 0.857668 | − | 0.514204i | \(-0.171913\pi\) | ||||
0.857668 | + | 0.514204i | \(0.171913\pi\) | |||||||
\(854\) | −21.5364 | + | 41.2886i | −0.736960 | + | 1.41287i | ||||
\(855\) | −10.8146 | −0.369850 | ||||||||
\(856\) | 73.7167 | + | 127.681i | 2.51959 | + | 4.36405i | ||||
\(857\) | −1.80216 | + | 3.12143i | −0.0615605 | + | 0.106626i | −0.895163 | − | 0.445739i | \(-0.852941\pi\) |
0.833603 | + | 0.552365i | \(0.186274\pi\) | |||||||
\(858\) | −15.7653 | + | 27.3063i | −0.538218 | + | 0.932220i | ||||
\(859\) | −2.20328 | − | 3.81619i | −0.0751749 | − | 0.130207i | 0.825987 | − | 0.563689i | \(-0.190618\pi\) |
−0.901162 | + | 0.433482i | \(0.857285\pi\) | |||||||
\(860\) | 22.5773 | 0.769881 | ||||||||
\(861\) | −6.35632 | + | 12.1860i | −0.216623 | + | 0.415299i | ||||
\(862\) | −9.36845 | −0.319091 | ||||||||
\(863\) | −23.5854 | − | 40.8511i | −0.802857 | − | 1.39059i | −0.917728 | − | 0.397209i | \(-0.869979\pi\) |
0.114871 | − | 0.993380i | \(-0.463354\pi\) | |||||||
\(864\) | 15.0188 | − | 26.0134i | 0.510951 | − | 0.884994i | ||||
\(865\) | −10.9738 | + | 19.0072i | −0.373121 | + | 0.646265i | ||||
\(866\) | 21.3154 | + | 36.9193i | 0.724325 | + | 1.25457i | ||||
\(867\) | 16.6001 | 0.563768 | ||||||||
\(868\) | −46.3990 | − | 72.9634i | −1.57489 | − | 2.47654i | ||||
\(869\) | −42.4391 | −1.43965 | ||||||||
\(870\) | −15.2034 | − | 26.3330i | −0.515442 | − | 0.892772i | ||||
\(871\) | −6.59724 | + | 11.4268i | −0.223539 | + | 0.387181i | ||||
\(872\) | 24.2070 | − | 41.9278i | 0.819753 | − | 1.41985i | ||||
\(873\) | 1.47595 | + | 2.55642i | 0.0499533 | + | 0.0865217i | ||||
\(874\) | 15.5498 | 0.525980 | ||||||||
\(875\) | −31.9557 | + | 1.36904i | −1.08030 | + | 0.0462820i | ||||
\(876\) | −80.9276 | −2.73429 | ||||||||
\(877\) | −20.5203 | − | 35.5421i | −0.692920 | − | 1.20017i | −0.970877 | − | 0.239579i | \(-0.922991\pi\) |
0.277957 | − | 0.960594i | \(-0.410343\pi\) | |||||||
\(878\) | −30.0839 | + | 52.1069i | −1.01528 | + | 1.75852i | ||||
\(879\) | −6.57290 | + | 11.3846i | −0.221699 | + | 0.383993i | ||||
\(880\) | −48.1577 | − | 83.4116i | −1.62340 | − | 2.81180i | ||||
\(881\) | 50.3825 | 1.69743 | 0.848715 | − | 0.528851i | \(-0.177377\pi\) | ||||
0.848715 | + | 0.528851i | \(0.177377\pi\) | |||||||
\(882\) | −8.31122 | + | 17.7476i | −0.279853 | + | 0.597594i | ||||
\(883\) | 7.65081 | 0.257470 | 0.128735 | − | 0.991679i | \(-0.458908\pi\) | ||||
0.128735 | + | 0.991679i | \(0.458908\pi\) | |||||||
\(884\) | 7.73513 | + | 13.3976i | 0.260160 | + | 0.450611i | ||||
\(885\) | −7.12591 | + | 12.3424i | −0.239535 | + | 0.414886i | ||||
\(886\) | −33.2938 | + | 57.6666i | −1.11853 | + | 1.93735i | ||||
\(887\) | 18.6564 | + | 32.3138i | 0.626421 | + | 1.08499i | 0.988264 | + | 0.152754i | \(0.0488142\pi\) |
−0.361843 | + | 0.932239i | \(0.617852\pi\) | |||||||
\(888\) | −44.2259 | −1.48412 | ||||||||
\(889\) | 48.1168 | − | 2.06142i | 1.61379 | − | 0.0691377i | ||||
\(890\) | −9.87488 | −0.331007 | ||||||||
\(891\) | 1.34384 | + | 2.32760i | 0.0450204 | + | 0.0779777i | ||||
\(892\) | −61.2068 | + | 106.013i | −2.04936 | + | 3.54959i | ||||
\(893\) | 0.812551 | − | 1.40738i | 0.0271910 | − | 0.0470962i | ||||
\(894\) | −6.76200 | − | 11.7121i | −0.226155 | − | 0.391712i | ||||
\(895\) | −15.9175 | −0.532064 | ||||||||
\(896\) | 102.650 | + | 161.420i | 3.42931 | + | 5.39266i | ||||
\(897\) | −4.19039 | −0.139913 | ||||||||
\(898\) | 11.7057 | + | 20.2748i | 0.390623 | + | 0.676578i | ||||
\(899\) | 15.6137 | − | 27.0437i | 0.520745 | − | 0.901957i | ||||
\(900\) | 3.52869 | − | 6.11187i | 0.117623 | − | 0.203729i | ||||
\(901\) | −3.21642 | − | 5.57100i | −0.107154 | − | 0.185597i | ||||
\(902\) | −39.0883 | −1.30150 | ||||||||
\(903\) | 2.43037 | − | 4.65939i | 0.0808775 | − | 0.155055i | ||||
\(904\) | −176.225 | −5.86114 | ||||||||
\(905\) | −2.92153 | − | 5.06024i | −0.0971150 | − | 0.168208i | ||||
\(906\) | 29.3745 | − | 50.8782i | 0.975903 | − | 1.69031i | ||||
\(907\) | −25.0612 | + | 43.4073i | −0.832144 | + | 1.44132i | 0.0641906 | + | 0.997938i | \(0.479553\pi\) |
−0.896335 | + | 0.443378i | \(0.853780\pi\) | |||||||
\(908\) | 70.5676 | + | 122.227i | 2.34187 | + | 4.05623i | ||||
\(909\) | −12.8013 | −0.424593 | ||||||||
\(910\) | −27.9494 | + | 53.5832i | −0.926512 | + | 1.77627i | ||||
\(911\) | 33.1001 | 1.09666 | 0.548328 | − | 0.836264i | \(-0.315265\pi\) | ||||
0.548328 | + | 0.836264i | \(0.315265\pi\) | |||||||
\(912\) | 51.1129 | + | 88.5301i | 1.69252 | + | 2.93152i | ||||
\(913\) | 16.7957 | − | 29.0910i | 0.555857 | − | 0.962772i | ||||
\(914\) | 22.3009 | − | 38.6263i | 0.737648 | − | 1.27764i | ||||
\(915\) | 6.12056 | + | 10.6011i | 0.202339 | + | 0.350462i | ||||
\(916\) | −50.6642 | −1.67399 | ||||||||
\(917\) | −11.8241 | − | 18.5937i | −0.390468 | − | 0.614018i | ||||
\(918\) | 1.77047 | 0.0584341 | ||||||||
\(919\) | 22.9767 | + | 39.7968i | 0.757931 | + | 1.31278i | 0.943904 | + | 0.330221i | \(0.107123\pi\) |
−0.185972 | + | 0.982555i | \(0.559543\pi\) | |||||||
\(920\) | 10.4602 | − | 18.1177i | 0.344864 | − | 0.597321i | ||||
\(921\) | 7.55430 | − | 13.0844i | 0.248923 | − | 0.431147i | ||||
\(922\) | 16.3462 | + | 28.3124i | 0.538333 | + | 0.932420i | ||||
\(923\) | 25.1518 | 0.827883 | ||||||||
\(924\) | −41.4747 | + | 1.77685i | −1.36442 | + | 0.0584542i | ||||
\(925\) | −4.97596 | −0.163609 | ||||||||
\(926\) | 9.43735 | + | 16.3460i | 0.310131 | + | 0.537162i | ||||
\(927\) | −6.52904 | + | 11.3086i | −0.214442 | + | 0.371424i | ||||
\(928\) | −83.7769 | + | 145.106i | −2.75011 | + | 4.76333i | ||||
\(929\) | 11.2680 | + | 19.5168i | 0.369692 | + | 0.640325i | 0.989517 | − | 0.144415i | \(-0.0461300\pi\) |
−0.619826 | + | 0.784740i | \(0.712797\pi\) | |||||||
\(930\) | −30.5161 | −1.00066 | ||||||||
\(931\) | −22.2484 | − | 31.8849i | −0.729163 | − | 1.04498i | ||||
\(932\) | 15.7144 | 0.514741 | ||||||||
\(933\) | −10.7414 | − | 18.6047i | −0.351658 | − | 0.609090i | ||||
\(934\) | −21.6690 | + | 37.5319i | −0.709032 | + | 1.22808i | ||||
\(935\) | 1.65470 | − | 2.86603i | 0.0541146 | − | 0.0937293i | ||||
\(936\) | −22.5119 | − | 38.9918i | −0.735826 | − | 1.27449i | ||||
\(937\) | −20.5555 | −0.671520 | −0.335760 | − | 0.941948i | \(-0.608993\pi\) | ||||
−0.335760 | + | 0.941948i | \(0.608993\pi\) | |||||||
\(938\) | −23.3017 | + | 0.998289i | −0.760828 | + | 0.0325953i | ||||
\(939\) | −14.8382 | −0.484227 | ||||||||
\(940\) | −1.66288 | − | 2.88020i | −0.0542373 | − | 0.0939417i | ||||
\(941\) | 19.9421 | − | 34.5407i | 0.650093 | − | 1.12599i | −0.333007 | − | 0.942924i | \(-0.608063\pi\) |
0.983100 | − | 0.183070i | \(-0.0586034\pi\) | |||||||
\(942\) | 2.23191 | − | 3.86578i | 0.0727196 | − | 0.125954i | ||||
\(943\) | −2.59741 | − | 4.49884i | −0.0845832 | − | 0.146502i | ||||
\(944\) | 134.717 | 4.38466 | ||||||||
\(945\) | 2.76433 | + | 4.34697i | 0.0899238 | + | 0.141407i | ||||
\(946\) | 14.9456 | 0.485923 | ||||||||
\(947\) | −1.36901 | − | 2.37120i | −0.0444869 | − | 0.0770536i | 0.842925 | − | 0.538032i | \(-0.180832\pi\) |
−0.887411 | + | 0.460978i | \(0.847499\pi\) | |||||||
\(948\) | 46.0905 | − | 79.8311i | 1.49695 | − | 2.59279i | ||||
\(949\) | −29.0447 | + | 50.3069i | −0.942830 | + | 1.63303i | ||||
\(950\) | 9.39905 | + | 16.2796i | 0.304945 | + | 0.528181i | ||||
\(951\) | 4.70173 | 0.152464 | ||||||||
\(952\) | −8.31407 | + | 15.9394i | −0.269461 | + | 0.516597i | ||||
\(953\) | 20.6225 | 0.668027 | 0.334014 | − | 0.942568i | \(-0.391597\pi\) | ||||
0.334014 | + | 0.942568i | \(0.391597\pi\) | |||||||
\(954\) | 14.2391 | + | 24.6628i | 0.461008 | + | 0.798489i | ||||
\(955\) | −11.2724 | + | 19.5244i | −0.364767 | + | 0.631795i | ||||
\(956\) | 0.152829 | − | 0.264708i | 0.00494285 | − | 0.00856127i | ||||
\(957\) | −7.49612 | − | 12.9837i | −0.242315 | − | 0.419702i | ||||
\(958\) | 51.9944 | 1.67986 | ||||||||
\(959\) | −16.2791 | + | 31.2095i | −0.525678 | + | 1.00781i | ||||
\(960\) | 92.0659 | 2.97141 | ||||||||
\(961\) | −0.169823 | − | 0.294143i | −0.00547817 | − | 0.00948847i | ||||
\(962\) | −24.1441 | + | 41.8188i | −0.778437 | + | 1.34829i | ||||
\(963\) | 6.86084 | − | 11.8833i | 0.221088 | − | 0.382935i | ||||
\(964\) | 0.874370 | + | 1.51445i | 0.0281615 | + | 0.0487772i | ||||
\(965\) | −11.0969 | −0.357223 | ||||||||
\(966\) | −3.97472 | − | 6.25033i | −0.127885 | − | 0.201101i | ||||
\(967\) | 46.6896 | 1.50144 | 0.750719 | − | 0.660622i | \(-0.229707\pi\) | ||||
0.750719 | + | 0.660622i | \(0.229707\pi\) | |||||||
\(968\) | 20.2876 | + | 35.1391i | 0.652067 | + | 1.12941i | ||||
\(969\) | −1.75624 | + | 3.04190i | −0.0564187 | + | 0.0977201i | ||||
\(970\) | −8.04550 | + | 13.9352i | −0.258326 | + | 0.447433i | ||||
\(971\) | 19.9032 | + | 34.4733i | 0.638723 | + | 1.10630i | 0.985713 | + | 0.168432i | \(0.0538702\pi\) |
−0.346991 | + | 0.937869i | \(0.612796\pi\) | |||||||
\(972\) | −5.83786 | −0.187250 | ||||||||
\(973\) | 15.6834 | − | 0.671905i | 0.502786 | − | 0.0215403i | ||||
\(974\) | 50.8458 | 1.62920 | ||||||||
\(975\) | −2.53287 | − | 4.38706i | −0.0811169 | − | 0.140499i | ||||
\(976\) | 57.8552 | − | 100.208i | 1.85190 | − | 3.20759i | ||||
\(977\) | 16.1499 | − | 27.9725i | 0.516683 | − | 0.894921i | −0.483130 | − | 0.875549i | \(-0.660500\pi\) |
0.999812 | − | 0.0193718i | \(-0.00616661\pi\) | |||||||
\(978\) | −15.2547 | − | 26.4218i | −0.487790 | − | 0.844877i | ||||
\(979\) | −4.86888 | −0.155610 | ||||||||
\(980\) | −79.2758 | + | 6.80514i | −2.53237 | + | 0.217382i | ||||
\(981\) | −4.50591 | −0.143863 | ||||||||
\(982\) | −19.8641 | − | 34.4056i | −0.633887 | − | 1.09793i | ||||
\(983\) | −28.5393 | + | 49.4314i | −0.910261 | + | 1.57662i | −0.0965653 | + | 0.995327i | \(0.530786\pi\) |
−0.813696 | + | 0.581291i | \(0.802548\pi\) | |||||||
\(984\) | 27.9080 | − | 48.3380i | 0.889674 | − | 1.54096i | ||||
\(985\) | −12.6446 | − | 21.9011i | −0.402891 | − | 0.697827i | ||||
\(986\) | −9.87588 | −0.314512 | ||||||||
\(987\) | −0.773403 | + | 0.0331340i | −0.0246177 | + | 0.00105467i | ||||
\(988\) | 135.873 | 4.32271 | ||||||||
\(989\) | 0.993129 | + | 1.72015i | 0.0315797 | + | 0.0546976i | ||||
\(990\) | −7.32538 | + | 12.6879i | −0.232816 | + | 0.403249i | ||||
\(991\) | 18.5164 | − | 32.0714i | 0.588193 | − | 1.01878i | −0.406276 | − | 0.913750i | \(-0.633173\pi\) |
0.994469 | − | 0.105030i | \(-0.0334938\pi\) | |||||||
\(992\) | 84.0782 | + | 145.628i | 2.66949 | + | 4.62369i | ||||
\(993\) | 7.87864 | 0.250021 | ||||||||
\(994\) | 23.8573 | + | 37.5162i | 0.756709 | + | 1.18994i | ||||
\(995\) | 41.5224 | 1.31635 | ||||||||
\(996\) | 36.4816 | + | 63.1880i | 1.15596 | + | 2.00219i | ||||
\(997\) | 23.5094 | − | 40.7195i | 0.744550 | − | 1.28960i | −0.205855 | − | 0.978583i | \(-0.565997\pi\) |
0.950405 | − | 0.311016i | \(-0.100669\pi\) | |||||||
\(998\) | −20.0715 | + | 34.7648i | −0.635352 | + | 1.10046i | ||||
\(999\) | 2.05806 | + | 3.56466i | 0.0651141 | + | 0.112781i |
(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 | 483.2.i.h.277.1 | ✓ | 20 | |
7.2 | even | 3 | inner | 483.2.i.h.415.1 | yes | 20 | |
7.3 | odd | 6 | 3381.2.a.bj.1.10 | 10 | |||
7.4 | even | 3 | 3381.2.a.bi.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
483.2.i.h.415.1 | yes | 20 | 7.2 | even | 3 | inner | |
3381.2.a.bi.1.10 | 10 | 7.4 | even | 3 | |||
3381.2.a.bj.1.10 | 10 | 7.3 | odd | 6 |