Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(25,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bk (of order \(6\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 26 x^{18} + 431 x^{16} - 4370 x^{14} + 32381 x^{12} - 160412 x^{10} + 573820 x^{8} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 415.10 | ||
Root | \(2.38129 - 1.37484i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.415 |
Dual form | 546.2.bk.c.25.10 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 2.38129 | + | 1.37484i | 1.06494 | + | 0.614846i | 0.926796 | − | 0.375566i | \(-0.122552\pi\) |
0.138149 | + | 0.990412i | \(0.455885\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0.588218 | − | 2.57953i | 0.222326 | − | 0.974972i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.37484 | + | 2.38129i | 0.434762 | + | 0.753029i | ||||
\(11\) | 0.600231 | − | 0.346544i | 0.180976 | − | 0.104487i | −0.406775 | − | 0.913528i | \(-0.633347\pi\) |
0.587751 | + | 0.809042i | \(0.300013\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 0.924342 | + | 3.48505i | 0.256366 | + | 0.966580i | ||||
\(14\) | 1.79918 | − | 1.93983i | 0.480851 | − | 0.518442i | ||||
\(15\) | 2.74967i | 0.709963i | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.18349 | − | 5.51396i | −0.772109 | − | 1.33733i | −0.936405 | − | 0.350921i | \(-0.885869\pi\) |
0.164296 | − | 0.986411i | \(-0.447465\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 1.78106 | + | 1.02829i | 0.408602 | + | 0.235907i | 0.690189 | − | 0.723629i | \(-0.257527\pi\) |
−0.281587 | + | 0.959536i | \(0.590861\pi\) | |||||||
\(20\) | 2.74967i | 0.614846i | ||||||||
\(21\) | 2.52805 | − | 0.780355i | 0.551666 | − | 0.170287i | ||||
\(22\) | 0.693087 | 0.147767 | ||||||||
\(23\) | 0.903131 | − | 1.56427i | 0.188316 | − | 0.326173i | −0.756373 | − | 0.654141i | \(-0.773030\pi\) |
0.944689 | + | 0.327968i | \(0.106364\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 1.28036 | + | 2.21764i | 0.256071 | + | 0.443528i | ||||
\(26\) | −0.942023 | + | 3.48032i | −0.184746 | + | 0.682546i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.52805 | − | 0.780355i | 0.477757 | − | 0.147473i | ||||
\(29\) | −8.85216 | −1.64380 | −0.821902 | − | 0.569629i | \(-0.807087\pi\) | ||||
−0.821902 | + | 0.569629i | \(0.807087\pi\) | |||||||
\(30\) | −1.37484 | + | 2.38129i | −0.251010 | + | 0.434762i | ||||
\(31\) | 0.817019 | − | 0.471706i | 0.146741 | − | 0.0847209i | −0.424832 | − | 0.905272i | \(-0.639667\pi\) |
0.571573 | + | 0.820551i | \(0.306333\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0.600231 | + | 0.346544i | 0.104487 | + | 0.0603255i | ||||
\(34\) | − | 6.36697i | − | 1.09193i | ||||||
\(35\) | 4.94716 | − | 5.33391i | 0.836222 | − | 0.901595i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.833421 | + | 0.481176i | 0.137014 | + | 0.0791048i | 0.566940 | − | 0.823759i | \(-0.308127\pi\) |
−0.429926 | + | 0.902864i | \(0.641460\pi\) | |||||||
\(38\) | 1.02829 | + | 1.78106i | 0.166811 | + | 0.288926i | ||||
\(39\) | −2.55597 | + | 2.54303i | −0.409283 | + | 0.407211i | ||||
\(40\) | −1.37484 | + | 2.38129i | −0.217381 | + | 0.376515i | ||||
\(41\) | 11.7716i | 1.83841i | 0.393775 | + | 0.919207i | \(0.371169\pi\) | ||||
−0.393775 | + | 0.919207i | \(0.628831\pi\) | |||||||
\(42\) | 2.57953 | + | 0.588218i | 0.398031 | + | 0.0907641i | ||||
\(43\) | −4.97011 | −0.757934 | −0.378967 | − | 0.925410i | \(-0.623721\pi\) | ||||
−0.378967 | + | 0.925410i | \(0.623721\pi\) | |||||||
\(44\) | 0.600231 | + | 0.346544i | 0.0904882 | + | 0.0522434i | ||||
\(45\) | −2.38129 | + | 1.37484i | −0.354981 | + | 0.204949i | ||||
\(46\) | 1.56427 | − | 0.903131i | 0.230639 | − | 0.133159i | ||||
\(47\) | −7.81735 | − | 4.51335i | −1.14028 | − | 0.658339i | −0.193778 | − | 0.981045i | \(-0.562074\pi\) |
−0.946499 | + | 0.322706i | \(0.895407\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.30800 | − | 3.03466i | −0.901143 | − | 0.433523i | ||||
\(50\) | 2.56071i | 0.362139i | ||||||||
\(51\) | 3.18349 | − | 5.51396i | 0.445777 | − | 0.772109i | ||||
\(52\) | −2.55597 | + | 2.54303i | −0.354450 | + | 0.352655i | ||||
\(53\) | 1.98505 | + | 3.43821i | 0.272668 | + | 0.472275i | 0.969544 | − | 0.244917i | \(-0.0787606\pi\) |
−0.696876 | + | 0.717191i | \(0.745427\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 1.90576 | 0.256973 | ||||||||
\(56\) | 2.57953 | + | 0.588218i | 0.344705 | + | 0.0786040i | ||||
\(57\) | 2.05659i | 0.272402i | ||||||||
\(58\) | −7.66619 | − | 4.42608i | −1.00662 | − | 0.581173i | ||||
\(59\) | 10.5042 | − | 6.06459i | 1.36753 | − | 0.789542i | 0.376915 | − | 0.926248i | \(-0.376985\pi\) |
0.990612 | + | 0.136706i | \(0.0436515\pi\) | |||||||
\(60\) | −2.38129 | + | 1.37484i | −0.307423 | + | 0.177491i | ||||
\(61\) | 5.03217 | − | 8.71597i | 0.644303 | − | 1.11597i | −0.340159 | − | 0.940368i | \(-0.610481\pi\) |
0.984462 | − | 0.175598i | \(-0.0561859\pi\) | |||||||
\(62\) | 0.943413 | 0.119814 | ||||||||
\(63\) | 1.93983 | + | 1.79918i | 0.244396 | + | 0.226675i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.59026 | + | 9.56973i | −0.321282 | + | 1.18698i | ||||
\(66\) | 0.346544 | + | 0.600231i | 0.0426566 | + | 0.0738833i | ||||
\(67\) | 8.40673 | − | 4.85363i | 1.02705 | − | 0.592965i | 0.110908 | − | 0.993831i | \(-0.464624\pi\) |
0.916137 | + | 0.400866i | \(0.131291\pi\) | |||||||
\(68\) | 3.18349 | − | 5.51396i | 0.386054 | − | 0.668666i | ||||
\(69\) | 1.80626 | 0.217448 | ||||||||
\(70\) | 6.95132 | − | 2.14572i | 0.830842 | − | 0.256463i | ||||
\(71\) | 7.68213i | 0.911701i | 0.890056 | + | 0.455851i | \(0.150665\pi\) | ||||
−0.890056 | + | 0.455851i | \(0.849335\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 4.89733 | − | 2.82747i | 0.573189 | − | 0.330931i | −0.185233 | − | 0.982695i | \(-0.559304\pi\) |
0.758422 | + | 0.651764i | \(0.225971\pi\) | |||||||
\(74\) | 0.481176 | + | 0.833421i | 0.0559356 | + | 0.0968832i | ||||
\(75\) | −1.28036 | + | 2.21764i | −0.147843 | + | 0.256071i | ||||
\(76\) | 2.05659i | 0.235907i | ||||||||
\(77\) | −0.540854 | − | 1.75216i | −0.0616361 | − | 0.199677i | ||||
\(78\) | −3.48505 | + | 0.924342i | −0.394605 | + | 0.104661i | ||||
\(79\) | −0.339330 | + | 0.587736i | −0.0381776 | + | 0.0661255i | −0.884483 | − | 0.466573i | \(-0.845489\pi\) |
0.846305 | + | 0.532698i | \(0.178822\pi\) | |||||||
\(80\) | −2.38129 | + | 1.37484i | −0.266236 | + | 0.153711i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −5.88580 | + | 10.1945i | −0.649978 | + | 1.12579i | ||||
\(83\) | − | 2.32585i | − | 0.255295i | −0.991820 | − | 0.127648i | \(-0.959257\pi\) | ||
0.991820 | − | 0.127648i | \(-0.0407427\pi\) | |||||||
\(84\) | 1.93983 | + | 1.79918i | 0.211653 | + | 0.196307i | ||||
\(85\) | − | 17.5071i | − | 1.89891i | ||||||
\(86\) | −4.30424 | − | 2.48505i | −0.464138 | − | 0.267970i | ||||
\(87\) | −4.42608 | − | 7.66619i | −0.474525 | − | 0.821902i | ||||
\(88\) | 0.346544 | + | 0.600231i | 0.0369417 | + | 0.0639849i | ||||
\(89\) | −11.5995 | − | 6.69696i | −1.22954 | − | 0.709877i | −0.262608 | − | 0.964903i | \(-0.584583\pi\) |
−0.966934 | + | 0.255026i | \(0.917916\pi\) | |||||||
\(90\) | −2.74967 | −0.289841 | ||||||||
\(91\) | 9.53353 | − | 0.334400i | 0.999385 | − | 0.0350547i | ||||
\(92\) | 1.80626 | 0.188316 | ||||||||
\(93\) | 0.817019 | + | 0.471706i | 0.0847209 | + | 0.0489137i | ||||
\(94\) | −4.51335 | − | 7.81735i | −0.465516 | − | 0.806298i | ||||
\(95\) | 2.82747 | + | 4.89733i | 0.290093 | + | 0.502455i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | − | 9.89969i | − | 1.00516i | −0.864530 | − | 0.502581i | \(-0.832384\pi\) | ||
0.864530 | − | 0.502581i | \(-0.167616\pi\) | |||||||
\(98\) | −3.94556 | − | 5.78209i | −0.398561 | − | 0.584079i | ||||
\(99\) | 0.693087i | 0.0696579i | ||||||||
\(100\) | −1.28036 | + | 2.21764i | −0.128036 | + | 0.221764i | ||||
\(101\) | −4.00174 | − | 6.93121i | −0.398188 | − | 0.689681i | 0.595315 | − | 0.803493i | \(-0.297027\pi\) |
−0.993502 | + | 0.113811i | \(0.963694\pi\) | |||||||
\(102\) | 5.51396 | − | 3.18349i | 0.545963 | − | 0.315212i | ||||
\(103\) | 6.29145 | − | 10.8971i | 0.619915 | − | 1.07372i | −0.369586 | − | 0.929196i | \(-0.620501\pi\) |
0.989501 | − | 0.144527i | \(-0.0461661\pi\) | |||||||
\(104\) | −3.48505 | + | 0.924342i | −0.341738 | + | 0.0906392i | ||||
\(105\) | 7.09288 | + | 1.61741i | 0.692194 | + | 0.157843i | ||||
\(106\) | 3.97011i | 0.385611i | ||||||||
\(107\) | −5.06993 | + | 8.78138i | −0.490129 | + | 0.848928i | −0.999935 | − | 0.0113608i | \(-0.996384\pi\) |
0.509806 | + | 0.860289i | \(0.329717\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −10.7989 | + | 6.23473i | −1.03434 | + | 0.597179i | −0.918226 | − | 0.396057i | \(-0.870378\pi\) |
−0.116118 | + | 0.993235i | \(0.537045\pi\) | |||||||
\(110\) | 1.65044 | + | 0.952882i | 0.157363 | + | 0.0908537i | ||||
\(111\) | 0.962352i | 0.0913424i | ||||||||
\(112\) | 1.93983 | + | 1.79918i | 0.183297 | + | 0.170006i | ||||
\(113\) | −8.21218 | −0.772537 | −0.386269 | − | 0.922386i | \(-0.626236\pi\) | ||||
−0.386269 | + | 0.922386i | \(0.626236\pi\) | |||||||
\(114\) | −1.02829 | + | 1.78106i | −0.0963085 | + | 0.166811i | ||||
\(115\) | 4.30123 | − | 2.48332i | 0.401092 | − | 0.231570i | ||||
\(116\) | −4.42608 | − | 7.66619i | −0.410951 | − | 0.711788i | ||||
\(117\) | −3.48032 | − | 0.942023i | −0.321755 | − | 0.0870900i | ||||
\(118\) | 12.1292 | 1.11658 | ||||||||
\(119\) | −16.0960 | + | 4.96850i | −1.47552 | + | 0.455462i | ||||
\(120\) | −2.74967 | −0.251010 | ||||||||
\(121\) | −5.25982 | + | 9.11027i | −0.478165 | + | 0.828206i | ||||
\(122\) | 8.71597 | − | 5.03217i | 0.789107 | − | 0.455591i | ||||
\(123\) | −10.1945 | + | 5.88580i | −0.919207 | + | 0.530704i | ||||
\(124\) | 0.817019 | + | 0.471706i | 0.0733705 | + | 0.0423605i | ||||
\(125\) | − | 6.70725i | − | 0.599915i | ||||||
\(126\) | 0.780355 | + | 2.52805i | 0.0695196 | + | 0.225217i | ||||
\(127\) | 6.39687 | 0.567630 | 0.283815 | − | 0.958879i | \(-0.408400\pi\) | ||||
0.283815 | + | 0.958879i | \(0.408400\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.48505 | − | 4.30424i | −0.218797 | − | 0.378967i | ||||
\(130\) | −7.02809 | + | 6.99251i | −0.616405 | + | 0.613283i | ||||
\(131\) | 0.971460 | − | 1.68262i | 0.0848769 | − | 0.147011i | −0.820462 | − | 0.571701i | \(-0.806284\pi\) |
0.905339 | + | 0.424690i | \(0.139617\pi\) | |||||||
\(132\) | 0.693087i | 0.0603255i | ||||||||
\(133\) | 3.70017 | − | 3.98944i | 0.320845 | − | 0.345928i | ||||
\(134\) | 9.70725 | 0.838579 | ||||||||
\(135\) | −2.38129 | − | 1.37484i | −0.204949 | − | 0.118327i | ||||
\(136\) | 5.51396 | − | 3.18349i | 0.472818 | − | 0.272982i | ||||
\(137\) | 0.0395182 | − | 0.0228159i | 0.00337627 | − | 0.00194929i | −0.498311 | − | 0.866998i | \(-0.666046\pi\) |
0.501687 | + | 0.865049i | \(0.332713\pi\) | |||||||
\(138\) | 1.56427 | + | 0.903131i | 0.133159 | + | 0.0768796i | ||||
\(139\) | 20.8679 | 1.76999 | 0.884996 | − | 0.465599i | \(-0.154161\pi\) | ||||
0.884996 | + | 0.465599i | \(0.154161\pi\) | |||||||
\(140\) | 7.09288 | + | 1.61741i | 0.599458 | + | 0.136696i | ||||
\(141\) | − | 9.02669i | − | 0.760185i | ||||||
\(142\) | −3.84107 | + | 6.65292i | −0.322335 | + | 0.558301i | ||||
\(143\) | 1.76254 | + | 1.77151i | 0.147391 | + | 0.148141i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −21.0795 | − | 12.1703i | −1.75056 | − | 1.01069i | ||||
\(146\) | 5.65495 | 0.468007 | ||||||||
\(147\) | −0.525907 | − | 6.98022i | −0.0433761 | − | 0.575719i | ||||
\(148\) | 0.962352i | 0.0791048i | ||||||||
\(149\) | 3.60487 | + | 2.08127i | 0.295322 | + | 0.170504i | 0.640340 | − | 0.768092i | \(-0.278794\pi\) |
−0.345017 | + | 0.938596i | \(0.612127\pi\) | |||||||
\(150\) | −2.21764 | + | 1.28036i | −0.181070 | + | 0.104541i | ||||
\(151\) | −0.395710 | + | 0.228464i | −0.0322025 | + | 0.0185921i | −0.516015 | − | 0.856580i | \(-0.672585\pi\) |
0.483812 | + | 0.875172i | \(0.339252\pi\) | |||||||
\(152\) | −1.02829 | + | 1.78106i | −0.0834056 | + | 0.144463i | ||||
\(153\) | 6.36697 | 0.514739 | ||||||||
\(154\) | 0.407687 | − | 1.78784i | 0.0328523 | − | 0.144068i | ||||
\(155\) | 2.59408 | 0.208361 | ||||||||
\(156\) | −3.48032 | − | 0.942023i | −0.278648 | − | 0.0754222i | ||||
\(157\) | 0.775828 | + | 1.34377i | 0.0619178 | + | 0.107245i | 0.895323 | − | 0.445418i | \(-0.146945\pi\) |
−0.833405 | + | 0.552663i | \(0.813612\pi\) | |||||||
\(158\) | −0.587736 | + | 0.339330i | −0.0467578 | + | 0.0269956i | ||||
\(159\) | −1.98505 | + | 3.43821i | −0.157425 | + | 0.272668i | ||||
\(160\) | −2.74967 | −0.217381 | ||||||||
\(161\) | −3.50385 | − | 3.24979i | −0.276142 | − | 0.256119i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 5.18296 | + | 2.99238i | 0.405961 | + | 0.234381i | 0.689053 | − | 0.724711i | \(-0.258027\pi\) |
−0.283092 | + | 0.959093i | \(0.591360\pi\) | |||||||
\(164\) | −10.1945 | + | 5.88580i | −0.796057 | + | 0.459604i | ||||
\(165\) | 0.952882 | + | 1.65044i | 0.0741818 | + | 0.128487i | ||||
\(166\) | 1.16293 | − | 2.01425i | 0.0902606 | − | 0.156336i | ||||
\(167\) | 7.21268i | 0.558134i | 0.960272 | + | 0.279067i | \(0.0900251\pi\) | ||||
−0.960272 | + | 0.279067i | \(0.909975\pi\) | |||||||
\(168\) | 0.780355 | + | 2.52805i | 0.0602057 | + | 0.195043i | ||||
\(169\) | −11.2912 | + | 6.44276i | −0.868553 | + | 0.495597i | ||||
\(170\) | 8.75355 | − | 15.1616i | 0.671367 | − | 1.16284i | ||||
\(171\) | −1.78106 | + | 1.02829i | −0.136201 | + | 0.0786356i | ||||
\(172\) | −2.48505 | − | 4.30424i | −0.189483 | − | 0.328195i | ||||
\(173\) | −11.3781 | + | 19.7074i | −0.865058 | + | 1.49832i | 0.00193131 | + | 0.999998i | \(0.499385\pi\) |
−0.866989 | + | 0.498327i | \(0.833948\pi\) | |||||||
\(174\) | − | 8.85216i | − | 0.671080i | ||||||
\(175\) | 6.47361 | − | 1.99826i | 0.489359 | − | 0.151055i | ||||
\(176\) | 0.693087i | 0.0522434i | ||||||||
\(177\) | 10.5042 | + | 6.06459i | 0.789542 | + | 0.455842i | ||||
\(178\) | −6.69696 | − | 11.5995i | −0.501959 | − | 0.869418i | ||||
\(179\) | 7.65842 | + | 13.2648i | 0.572417 | + | 0.991455i | 0.996317 | + | 0.0857464i | \(0.0273275\pi\) |
−0.423900 | + | 0.905709i | \(0.639339\pi\) | |||||||
\(180\) | −2.38129 | − | 1.37484i | −0.177491 | − | 0.102474i | ||||
\(181\) | 20.1559 | 1.49817 | 0.749087 | − | 0.662472i | \(-0.230493\pi\) | ||||
0.749087 | + | 0.662472i | \(0.230493\pi\) | |||||||
\(182\) | 8.42348 | + | 4.47717i | 0.624390 | + | 0.331870i | ||||
\(183\) | 10.0643 | 0.743977 | ||||||||
\(184\) | 1.56427 | + | 0.903131i | 0.115319 | + | 0.0665797i | ||||
\(185\) | 1.32308 | + | 2.29164i | 0.0972746 | + | 0.168484i | ||||
\(186\) | 0.471706 | + | 0.817019i | 0.0345872 | + | 0.0599068i | ||||
\(187\) | −3.82165 | − | 2.20643i | −0.279467 | − | 0.161350i | ||||
\(188\) | − | 9.02669i | − | 0.658339i | ||||||
\(189\) | −0.588218 | + | 2.57953i | −0.0427866 | + | 0.187634i | ||||
\(190\) | 5.65495i | 0.410253i | ||||||||
\(191\) | 9.58276 | − | 16.5978i | 0.693384 | − | 1.20098i | −0.277338 | − | 0.960772i | \(-0.589452\pi\) |
0.970722 | − | 0.240204i | \(-0.0772144\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 3.22142 | − | 1.85989i | 0.231883 | − | 0.133878i | −0.379557 | − | 0.925168i | \(-0.623924\pi\) |
0.611441 | + | 0.791290i | \(0.290590\pi\) | |||||||
\(194\) | 4.94984 | − | 8.57338i | 0.355378 | − | 0.615533i | ||||
\(195\) | −9.58276 | + | 2.54164i | −0.686236 | + | 0.182011i | ||||
\(196\) | −0.525907 | − | 6.98022i | −0.0375648 | − | 0.498587i | ||||
\(197\) | − | 9.45693i | − | 0.673778i | −0.941544 | − | 0.336889i | \(-0.890625\pi\) | ||
0.941544 | − | 0.336889i | \(-0.109375\pi\) | |||||||
\(198\) | −0.346544 | + | 0.600231i | −0.0246278 | + | 0.0426566i | ||||
\(199\) | −1.73497 | − | 3.00506i | −0.122989 | − | 0.213023i | 0.797956 | − | 0.602716i | \(-0.205915\pi\) |
−0.920945 | + | 0.389692i | \(0.872581\pi\) | |||||||
\(200\) | −2.21764 | + | 1.28036i | −0.156811 | + | 0.0905348i | ||||
\(201\) | 8.40673 | + | 4.85363i | 0.592965 | + | 0.342348i | ||||
\(202\) | − | 8.00347i | − | 0.563122i | ||||||
\(203\) | −5.20700 | + | 22.8344i | −0.365460 | + | 1.60266i | ||||
\(204\) | 6.36697 | 0.445777 | ||||||||
\(205\) | −16.1840 | + | 28.0316i | −1.13034 | + | 1.95781i | ||||
\(206\) | 10.8971 | − | 6.29145i | 0.759237 | − | 0.438346i | ||||
\(207\) | 0.903131 | + | 1.56427i | 0.0627719 | + | 0.108724i | ||||
\(208\) | −3.48032 | − | 0.942023i | −0.241316 | − | 0.0653175i | ||||
\(209\) | 1.42539 | 0.0985966 | ||||||||
\(210\) | 5.33391 | + | 4.94716i | 0.368075 | + | 0.341386i | ||||
\(211\) | −28.3961 | −1.95487 | −0.977434 | − | 0.211241i | \(-0.932250\pi\) | ||||
−0.977434 | + | 0.211241i | \(0.932250\pi\) | |||||||
\(212\) | −1.98505 | + | 3.43821i | −0.136334 | + | 0.236137i | ||||
\(213\) | −6.65292 | + | 3.84107i | −0.455851 | + | 0.263185i | ||||
\(214\) | −8.78138 | + | 5.06993i | −0.600283 | + | 0.346574i | ||||
\(215\) | −11.8353 | − | 6.83309i | −0.807158 | − | 0.466013i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −0.736197 | − | 2.38500i | −0.0499763 | − | 0.161904i | ||||
\(218\) | −12.4695 | −0.844538 | ||||||||
\(219\) | 4.89733 | + | 2.82747i | 0.330931 | + | 0.191063i | ||||
\(220\) | 0.952882 | + | 1.65044i | 0.0642433 | + | 0.111273i | ||||
\(221\) | 16.2738 | − | 16.1914i | 1.09469 | − | 1.08915i | ||||
\(222\) | −0.481176 | + | 0.833421i | −0.0322944 | + | 0.0559356i | ||||
\(223\) | 12.2391i | 0.819593i | 0.912177 | + | 0.409797i | \(0.134400\pi\) | ||||
−0.912177 | + | 0.409797i | \(0.865600\pi\) | |||||||
\(224\) | 0.780355 | + | 2.52805i | 0.0521397 | + | 0.168913i | ||||
\(225\) | −2.56071 | −0.170714 | ||||||||
\(226\) | −7.11196 | − | 4.10609i | −0.473081 | − | 0.273133i | ||||
\(227\) | 14.5558 | − | 8.40380i | 0.966103 | − | 0.557780i | 0.0680571 | − | 0.997681i | \(-0.478320\pi\) |
0.898046 | + | 0.439901i | \(0.144987\pi\) | |||||||
\(228\) | −1.78106 | + | 1.02829i | −0.117953 | + | 0.0681004i | ||||
\(229\) | 19.3011 | + | 11.1435i | 1.27545 | + | 0.736381i | 0.976008 | − | 0.217733i | \(-0.0698663\pi\) |
0.299442 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(230\) | 4.96663 | 0.327490 | ||||||||
\(231\) | 1.24699 | − | 1.34447i | 0.0820458 | − | 0.0884599i | ||||
\(232\) | − | 8.85216i | − | 0.581173i | ||||||
\(233\) | −9.06727 | + | 15.7050i | −0.594017 | + | 1.02887i | 0.399668 | + | 0.916660i | \(0.369125\pi\) |
−0.993685 | + | 0.112207i | \(0.964208\pi\) | |||||||
\(234\) | −2.54303 | − | 2.55597i | −0.166243 | − | 0.167089i | ||||
\(235\) | −12.4102 | − | 21.4952i | −0.809554 | − | 1.40219i | ||||
\(236\) | 10.5042 | + | 6.06459i | 0.683763 | + | 0.394771i | ||||
\(237\) | −0.678659 | −0.0440837 | ||||||||
\(238\) | −16.4238 | − | 3.74517i | −1.06460 | − | 0.242763i | ||||
\(239\) | 11.2880i | 0.730158i | 0.930976 | + | 0.365079i | \(0.118958\pi\) | ||||
−0.930976 | + | 0.365079i | \(0.881042\pi\) | |||||||
\(240\) | −2.38129 | − | 1.37484i | −0.153711 | − | 0.0887454i | ||||
\(241\) | −7.51594 | + | 4.33933i | −0.484144 | + | 0.279521i | −0.722142 | − | 0.691745i | \(-0.756842\pi\) |
0.237998 | + | 0.971266i | \(0.423509\pi\) | |||||||
\(242\) | −9.11027 | + | 5.25982i | −0.585630 | + | 0.338114i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 10.0643 | 0.644303 | ||||||||
\(245\) | −10.8490 | − | 15.8989i | −0.693117 | − | 1.01574i | ||||
\(246\) | −11.7716 | −0.750529 | ||||||||
\(247\) | −1.93735 | + | 7.15757i | −0.123271 | + | 0.455425i | ||||
\(248\) | 0.471706 | + | 0.817019i | 0.0299534 | + | 0.0518808i | ||||
\(249\) | 2.01425 | − | 1.16293i | 0.127648 | − | 0.0736974i | ||||
\(250\) | 3.35363 | − | 5.80865i | 0.212102 | − | 0.367371i | ||||
\(251\) | −21.8442 | −1.37879 | −0.689396 | − | 0.724384i | \(-0.742124\pi\) | ||||
−0.689396 | + | 0.724384i | \(0.742124\pi\) | |||||||
\(252\) | −0.588218 | + | 2.57953i | −0.0370543 | + | 0.162495i | ||||
\(253\) | − | 1.25190i | − | 0.0787061i | ||||||
\(254\) | 5.53985 | + | 3.19843i | 0.347601 | + | 0.200688i | ||||
\(255\) | 15.1616 | − | 8.75355i | 0.949456 | − | 0.548169i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.8097 | + | 22.1871i | −0.799049 | + | 1.38399i | 0.121187 | + | 0.992630i | \(0.461330\pi\) |
−0.920236 | + | 0.391364i | \(0.872003\pi\) | |||||||
\(258\) | − | 4.97011i | − | 0.309425i | ||||||
\(259\) | 1.73144 | − | 1.86680i | 0.107587 | − | 0.115997i | ||||
\(260\) | −9.58276 | + | 2.54164i | −0.594298 | + | 0.157626i | ||||
\(261\) | 4.42608 | − | 7.66619i | 0.273967 | − | 0.474525i | ||||
\(262\) | 1.68262 | − | 0.971460i | 0.103952 | − | 0.0600170i | ||||
\(263\) | 6.43061 | + | 11.1381i | 0.396528 | + | 0.686807i | 0.993295 | − | 0.115608i | \(-0.0368816\pi\) |
−0.596767 | + | 0.802415i | \(0.703548\pi\) | |||||||
\(264\) | −0.346544 | + | 0.600231i | −0.0213283 | + | 0.0369417i | ||||
\(265\) | 10.9165i | 0.670595i | ||||||||
\(266\) | 5.19916 | − | 1.60487i | 0.318781 | − | 0.0984008i | ||||
\(267\) | − | 13.3939i | − | 0.819695i | ||||||
\(268\) | 8.40673 | + | 4.85363i | 0.513523 | + | 0.296482i | ||||
\(269\) | −4.83200 | − | 8.36927i | −0.294612 | − | 0.510283i | 0.680282 | − | 0.732950i | \(-0.261857\pi\) |
−0.974895 | + | 0.222667i | \(0.928524\pi\) | |||||||
\(270\) | −1.37484 | − | 2.38129i | −0.0836699 | − | 0.144921i | ||||
\(271\) | 6.33421 | + | 3.65706i | 0.384776 | + | 0.222151i | 0.679894 | − | 0.733310i | \(-0.262026\pi\) |
−0.295118 | + | 0.955461i | \(0.595359\pi\) | |||||||
\(272\) | 6.36697 | 0.386054 | ||||||||
\(273\) | 5.05636 | + | 8.08908i | 0.306025 | + | 0.489573i | ||||
\(274\) | 0.0456317 | 0.00275671 | ||||||||
\(275\) | 1.53702 | + | 0.887398i | 0.0926857 | + | 0.0535121i | ||||
\(276\) | 0.903131 | + | 1.56427i | 0.0543621 | + | 0.0941579i | ||||
\(277\) | 6.35351 | + | 11.0046i | 0.381745 | + | 0.661203i | 0.991312 | − | 0.131532i | \(-0.0419898\pi\) |
−0.609566 | + | 0.792735i | \(0.708656\pi\) | |||||||
\(278\) | 18.0721 | + | 10.4339i | 1.08389 | + | 0.625787i | ||||
\(279\) | 0.943413i | 0.0564806i | ||||||||
\(280\) | 5.33391 | + | 4.94716i | 0.318762 | + | 0.295649i | ||||
\(281\) | 23.8172i | 1.42082i | 0.703790 | + | 0.710408i | \(0.251490\pi\) | ||||
−0.703790 | + | 0.710408i | \(0.748510\pi\) | |||||||
\(282\) | 4.51335 | − | 7.81735i | 0.268766 | − | 0.465516i | ||||
\(283\) | −14.5614 | − | 25.2211i | −0.865586 | − | 1.49924i | −0.866464 | − | 0.499240i | \(-0.833613\pi\) |
0.000877205 | − | 1.00000i | \(-0.499721\pi\) | |||||||
\(284\) | −6.65292 | + | 3.84107i | −0.394778 | + | 0.227925i | ||||
\(285\) | −2.82747 | + | 4.89733i | −0.167485 | + | 0.290093i | ||||
\(286\) | 0.640650 | + | 2.41545i | 0.0378824 | + | 0.142828i | ||||
\(287\) | 30.3652 | + | 6.92427i | 1.79240 | + | 0.408727i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −11.7692 | + | 20.3848i | −0.692304 | + | 1.19911i | ||||
\(290\) | −12.1703 | − | 21.0795i | −0.714663 | − | 1.23783i | ||||
\(291\) | 8.57338 | − | 4.94984i | 0.502581 | − | 0.290165i | ||||
\(292\) | 4.89733 | + | 2.82747i | 0.286594 | + | 0.165465i | ||||
\(293\) | 6.86285i | 0.400932i | 0.979701 | + | 0.200466i | \(0.0642456\pi\) | ||||
−0.979701 | + | 0.200466i | \(0.935754\pi\) | |||||||
\(294\) | 3.03466 | − | 6.30800i | 0.176985 | − | 0.367890i | ||||
\(295\) | 33.3513 | 1.94179 | ||||||||
\(296\) | −0.481176 | + | 0.833421i | −0.0279678 | + | 0.0484416i | ||||
\(297\) | −0.600231 | + | 0.346544i | −0.0348289 | + | 0.0201085i | ||||
\(298\) | 2.08127 | + | 3.60487i | 0.120565 | + | 0.208824i | ||||
\(299\) | 6.28636 | + | 1.70154i | 0.363550 | + | 0.0984026i | ||||
\(300\) | −2.56071 | −0.147843 | ||||||||
\(301\) | −2.92351 | + | 12.8206i | −0.168508 | + | 0.738965i | ||||
\(302\) | −0.456927 | −0.0262932 | ||||||||
\(303\) | 4.00174 | − | 6.93121i | 0.229894 | − | 0.398188i | ||||
\(304\) | −1.78106 | + | 1.02829i | −0.102151 | + | 0.0589767i | ||||
\(305\) | 23.9661 | − | 13.8368i | 1.37229 | − | 0.792295i | ||||
\(306\) | 5.51396 | + | 3.18349i | 0.315212 | + | 0.181988i | ||||
\(307\) | 26.5794i | 1.51697i | 0.651692 | + | 0.758484i | \(0.274060\pi\) | ||||
−0.651692 | + | 0.758484i | \(0.725940\pi\) | |||||||
\(308\) | 1.24699 | − | 1.34447i | 0.0710537 | − | 0.0766085i | ||||
\(309\) | 12.5829 | 0.715816 | ||||||||
\(310\) | 2.24654 | + | 1.29704i | 0.127595 | + | 0.0736669i | ||||
\(311\) | −5.31600 | − | 9.20758i | −0.301443 | − | 0.522114i | 0.675020 | − | 0.737799i | \(-0.264135\pi\) |
−0.976463 | + | 0.215685i | \(0.930801\pi\) | |||||||
\(312\) | −2.54303 | − | 2.55597i | −0.143971 | − | 0.144703i | ||||
\(313\) | 13.4089 | − | 23.2249i | 0.757915 | − | 1.31275i | −0.185998 | − | 0.982550i | \(-0.559552\pi\) |
0.943912 | − | 0.330196i | \(-0.107115\pi\) | |||||||
\(314\) | 1.55166i | 0.0875650i | ||||||||
\(315\) | 2.14572 | + | 6.95132i | 0.120898 | + | 0.391662i | ||||
\(316\) | −0.678659 | −0.0381776 | ||||||||
\(317\) | −12.8163 | − | 7.39952i | −0.719838 | − | 0.415598i | 0.0948552 | − | 0.995491i | \(-0.469761\pi\) |
−0.814693 | + | 0.579893i | \(0.803095\pi\) | |||||||
\(318\) | −3.43821 | + | 1.98505i | −0.192805 | + | 0.111316i | ||||
\(319\) | −5.31334 | + | 3.06766i | −0.297490 | + | 0.171756i | ||||
\(320\) | −2.38129 | − | 1.37484i | −0.133118 | − | 0.0768557i | ||||
\(321\) | −10.1399 | −0.565952 | ||||||||
\(322\) | −1.40953 | − | 4.56632i | −0.0785498 | − | 0.254471i | ||||
\(323\) | − | 13.0942i | − | 0.728583i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −6.54511 | + | 6.51196i | −0.363057 | + | 0.361219i | ||||
\(326\) | 2.99238 | + | 5.18296i | 0.165733 | + | 0.287057i | ||||
\(327\) | −10.7989 | − | 6.23473i | −0.597179 | − | 0.344781i | ||||
\(328\) | −11.7716 | −0.649978 | ||||||||
\(329\) | −16.2406 | + | 17.5103i | −0.895375 | + | 0.965373i | ||||
\(330\) | 1.90576i | 0.104909i | ||||||||
\(331\) | −6.00025 | − | 3.46425i | −0.329804 | − | 0.190412i | 0.325950 | − | 0.945387i | \(-0.394316\pi\) |
−0.655754 | + | 0.754975i | \(0.727649\pi\) | |||||||
\(332\) | 2.01425 | − | 1.16293i | 0.110546 | − | 0.0638239i | ||||
\(333\) | −0.833421 | + | 0.481176i | −0.0456712 | + | 0.0263683i | ||||
\(334\) | −3.60634 | + | 6.24636i | −0.197330 | + | 0.341786i | ||||
\(335\) | 26.6918 | 1.45833 | ||||||||
\(336\) | −0.588218 | + | 2.57953i | −0.0320899 | + | 0.140725i | ||||
\(337\) | 18.3349 | 0.998768 | 0.499384 | − | 0.866381i | \(-0.333560\pi\) | ||||
0.499384 | + | 0.866381i | \(0.333560\pi\) | |||||||
\(338\) | −12.9998 | − | 0.0659963i | −0.707098 | − | 0.00358972i | ||||
\(339\) | −4.10609 | − | 7.11196i | −0.223012 | − | 0.386269i | ||||
\(340\) | 15.1616 | − | 8.75355i | 0.822253 | − | 0.474728i | ||||
\(341\) | 0.326934 | − | 0.566266i | 0.0177044 | − | 0.0306650i | ||||
\(342\) | −2.05659 | −0.111208 | ||||||||
\(343\) | −11.5385 | + | 14.4867i | −0.623020 | + | 0.782206i | ||||
\(344\) | − | 4.97011i | − | 0.267970i | ||||||
\(345\) | 4.30123 | + | 2.48332i | 0.231570 | + | 0.133697i | ||||
\(346\) | −19.7074 | + | 11.3781i | −1.05948 | + | 0.611688i | ||||
\(347\) | 3.38645 | + | 5.86550i | 0.181794 | + | 0.314876i | 0.942492 | − | 0.334230i | \(-0.108476\pi\) |
−0.760697 | + | 0.649107i | \(0.775143\pi\) | |||||||
\(348\) | 4.42608 | − | 7.66619i | 0.237263 | − | 0.410951i | ||||
\(349\) | 31.1199i | 1.66581i | 0.553416 | + | 0.832905i | \(0.313324\pi\) | ||||
−0.553416 | + | 0.832905i | \(0.686676\pi\) | |||||||
\(350\) | 6.60544 | + | 1.50626i | 0.353076 | + | 0.0805128i | ||||
\(351\) | −0.924342 | − | 3.48505i | −0.0493377 | − | 0.186018i | ||||
\(352\) | −0.346544 | + | 0.600231i | −0.0184708 | + | 0.0319924i | ||||
\(353\) | −8.10390 | + | 4.67879i | −0.431327 | + | 0.249027i | −0.699912 | − | 0.714229i | \(-0.746777\pi\) |
0.268585 | + | 0.963256i | \(0.413444\pi\) | |||||||
\(354\) | 6.06459 | + | 10.5042i | 0.322329 | + | 0.558291i | ||||
\(355\) | −10.5617 | + | 18.2934i | −0.560556 | + | 0.970911i | ||||
\(356\) | − | 13.3939i | − | 0.709877i | ||||||
\(357\) | −12.3509 | − | 11.4553i | −0.653677 | − | 0.606280i | ||||
\(358\) | 15.3168i | 0.809520i | ||||||||
\(359\) | −23.7581 | − | 13.7167i | −1.25390 | − | 0.723942i | −0.282022 | − | 0.959408i | \(-0.591005\pi\) |
−0.971883 | + | 0.235466i | \(0.924338\pi\) | |||||||
\(360\) | −1.37484 | − | 2.38129i | −0.0724603 | − | 0.125505i | ||||
\(361\) | −7.38522 | − | 12.7916i | −0.388696 | − | 0.673241i | ||||
\(362\) | 17.4555 | + | 10.0779i | 0.917440 | + | 0.529684i | ||||
\(363\) | −10.5196 | −0.552137 | ||||||||
\(364\) | 5.05636 | + | 8.08908i | 0.265025 | + | 0.423983i | ||||
\(365\) | 15.5493 | 0.813886 | ||||||||
\(366\) | 8.71597 | + | 5.03217i | 0.455591 | + | 0.263036i | ||||
\(367\) | 8.46693 | + | 14.6652i | 0.441970 | + | 0.765515i | 0.997836 | − | 0.0657574i | \(-0.0209463\pi\) |
−0.555865 | + | 0.831272i | \(0.687613\pi\) | |||||||
\(368\) | 0.903131 | + | 1.56427i | 0.0470790 | + | 0.0815431i | ||||
\(369\) | −10.1945 | − | 5.88580i | −0.530704 | − | 0.306402i | ||||
\(370\) | 2.64615i | 0.137567i | ||||||||
\(371\) | 10.0366 | − | 3.09809i | 0.521076 | − | 0.160845i | ||||
\(372\) | 0.943413i | 0.0489137i | ||||||||
\(373\) | −10.5004 | + | 18.1872i | −0.543689 | + | 0.941697i | 0.454999 | + | 0.890492i | \(0.349640\pi\) |
−0.998688 | + | 0.0512053i | \(0.983694\pi\) | |||||||
\(374\) | −2.20643 | − | 3.82165i | −0.114092 | − | 0.197613i | ||||
\(375\) | 5.80865 | − | 3.35363i | 0.299957 | − | 0.173181i | ||||
\(376\) | 4.51335 | − | 7.81735i | 0.232758 | − | 0.403149i | ||||
\(377\) | −8.18242 | − | 30.8502i | −0.421416 | − | 1.58887i | ||||
\(378\) | −1.79918 | + | 1.93983i | −0.0925398 | + | 0.0997743i | ||||
\(379\) | 8.36838i | 0.429855i | 0.976630 | + | 0.214927i | \(0.0689515\pi\) | ||||
−0.976630 | + | 0.214927i | \(0.931049\pi\) | |||||||
\(380\) | −2.82747 | + | 4.89733i | −0.145046 | + | 0.251228i | ||||
\(381\) | 3.19843 | + | 5.53985i | 0.163861 | + | 0.283815i | ||||
\(382\) | 16.5978 | − | 9.58276i | 0.849219 | − | 0.490297i | ||||
\(383\) | 19.8299 | + | 11.4488i | 1.01326 | + | 0.585005i | 0.912144 | − | 0.409869i | \(-0.134426\pi\) |
0.101115 | + | 0.994875i | \(0.467759\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 1.12101 | − | 4.91598i | 0.0571317 | − | 0.250542i | ||||
\(386\) | 3.71978 | 0.189332 | ||||||||
\(387\) | 2.48505 | − | 4.30424i | 0.126322 | − | 0.218797i | ||||
\(388\) | 8.57338 | − | 4.94984i | 0.435248 | − | 0.251290i | ||||
\(389\) | −3.55927 | − | 6.16484i | −0.180462 | − | 0.312570i | 0.761576 | − | 0.648076i | \(-0.224426\pi\) |
−0.942038 | + | 0.335506i | \(0.891093\pi\) | |||||||
\(390\) | −9.56973 | − | 2.59026i | −0.484582 | − | 0.131163i | ||||
\(391\) | −11.5004 | −0.581601 | ||||||||
\(392\) | 3.03466 | − | 6.30800i | 0.153273 | − | 0.318602i | ||||
\(393\) | 1.94292 | 0.0980074 | ||||||||
\(394\) | 4.72846 | − | 8.18994i | 0.238217 | − | 0.412603i | ||||
\(395\) | −1.61608 | + | 0.933046i | −0.0813140 | + | 0.0469466i | ||||
\(396\) | −0.600231 | + | 0.346544i | −0.0301627 | + | 0.0174145i | ||||
\(397\) | 21.0936 | + | 12.1784i | 1.05866 | + | 0.611217i | 0.925061 | − | 0.379819i | \(-0.124014\pi\) |
0.133598 | + | 0.991036i | \(0.457347\pi\) | |||||||
\(398\) | − | 3.46995i | − | 0.173933i | ||||||
\(399\) | 5.30504 | + | 1.20972i | 0.265584 | + | 0.0605619i | ||||
\(400\) | −2.56071 | −0.128036 | ||||||||
\(401\) | 6.38990 | + | 3.68921i | 0.319096 | + | 0.184230i | 0.650990 | − | 0.759087i | \(-0.274354\pi\) |
−0.331893 | + | 0.943317i | \(0.607687\pi\) | |||||||
\(402\) | 4.85363 | + | 8.40673i | 0.242077 | + | 0.419289i | ||||
\(403\) | 2.39913 | + | 2.41134i | 0.119509 | + | 0.120117i | ||||
\(404\) | 4.00174 | − | 6.93121i | 0.199094 | − | 0.344841i | ||||
\(405\) | − | 2.74967i | − | 0.136632i | ||||||
\(406\) | −15.9266 | + | 17.1717i | −0.790425 | + | 0.852218i | ||||
\(407\) | 0.666994 | 0.0330616 | ||||||||
\(408\) | 5.51396 | + | 3.18349i | 0.272982 | + | 0.157606i | ||||
\(409\) | −22.5412 | + | 13.0142i | −1.11459 | + | 0.643510i | −0.940015 | − | 0.341133i | \(-0.889189\pi\) |
−0.174577 | + | 0.984643i | \(0.555856\pi\) | |||||||
\(410\) | −28.0316 | + | 16.1840i | −1.38438 | + | 0.799272i | ||||
\(411\) | 0.0395182 | + | 0.0228159i | 0.00194929 | + | 0.00112542i | ||||
\(412\) | 12.5829 | 0.619915 | ||||||||
\(413\) | −9.46506 | − | 30.6632i | −0.465745 | − | 1.50884i | ||||
\(414\) | 1.80626i | 0.0887729i | ||||||||
\(415\) | 3.19767 | − | 5.53852i | 0.156967 | − | 0.271875i | ||||
\(416\) | −2.54303 | − | 2.55597i | −0.124682 | − | 0.125317i | ||||
\(417\) | 10.4339 | + | 18.0721i | 0.510953 | + | 0.884996i | ||||
\(418\) | 1.23443 | + | 0.712697i | 0.0603778 | + | 0.0348592i | ||||
\(419\) | −19.1284 | −0.934482 | −0.467241 | − | 0.884130i | \(-0.654752\pi\) | ||||
−0.467241 | + | 0.884130i | \(0.654752\pi\) | |||||||
\(420\) | 2.14572 | + | 6.95132i | 0.104701 | + | 0.339190i | ||||
\(421\) | 10.2725i | 0.500651i | 0.968162 | + | 0.250326i | \(0.0805377\pi\) | ||||
−0.968162 | + | 0.250326i | \(0.919462\pi\) | |||||||
\(422\) | −24.5917 | − | 14.1980i | −1.19711 | − | 0.691150i | ||||
\(423\) | 7.81735 | − | 4.51335i | 0.380092 | − | 0.219446i | ||||
\(424\) | −3.43821 | + | 1.98505i | −0.166974 | + | 0.0964027i | ||||
\(425\) | 8.15199 | − | 14.1197i | 0.395429 | − | 0.684904i | ||||
\(426\) | −7.68213 | −0.372200 | ||||||||
\(427\) | −19.5231 | − | 18.1076i | −0.944791 | − | 0.876286i | ||||
\(428\) | −10.1399 | −0.490129 | ||||||||
\(429\) | −0.652904 | + | 2.41216i | −0.0315225 | + | 0.116460i | ||||
\(430\) | −6.83309 | − | 11.8353i | −0.329521 | − | 0.570747i | ||||
\(431\) | −0.932887 | + | 0.538602i | −0.0449356 | + | 0.0259436i | −0.522299 | − | 0.852762i | \(-0.674926\pi\) |
0.477364 | + | 0.878706i | \(0.341592\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 1.44276 | 0.0693347 | 0.0346674 | − | 0.999399i | \(-0.488963\pi\) | ||||
0.0346674 | + | 0.999399i | \(0.488963\pi\) | |||||||
\(434\) | 0.554933 | − | 2.43357i | 0.0266376 | − | 0.116815i | ||||
\(435\) | − | 24.3406i | − | 1.16704i | ||||||
\(436\) | −10.7989 | − | 6.23473i | −0.517172 | − | 0.298589i | ||||
\(437\) | 3.21706 | − | 1.85737i | 0.153893 | − | 0.0888500i | ||||
\(438\) | 2.82747 | + | 4.89733i | 0.135102 | + | 0.234003i | ||||
\(439\) | −11.2961 | + | 19.5655i | −0.539135 | + | 0.933810i | 0.459815 | + | 0.888015i | \(0.347916\pi\) |
−0.998951 | + | 0.0457954i | \(0.985418\pi\) | |||||||
\(440\) | 1.90576i | 0.0908537i | ||||||||
\(441\) | 5.78209 | − | 3.94556i | 0.275338 | − | 0.187884i | ||||
\(442\) | 22.1892 | − | 5.88526i | 1.05543 | − | 0.279933i | ||||
\(443\) | 11.7902 | − | 20.4213i | 0.560172 | − | 0.970246i | −0.437309 | − | 0.899311i | \(-0.644069\pi\) |
0.997481 | − | 0.0709346i | \(-0.0225982\pi\) | |||||||
\(444\) | −0.833421 | + | 0.481176i | −0.0395524 | + | 0.0228356i | ||||
\(445\) | −18.4145 | − | 31.8948i | −0.872930 | − | 1.51196i | ||||
\(446\) | −6.11957 | + | 10.5994i | −0.289770 | + | 0.501896i | ||||
\(447\) | 4.16254i | 0.196881i | ||||||||
\(448\) | −0.588218 | + | 2.57953i | −0.0277907 | + | 0.121872i | ||||
\(449\) | − | 4.09767i | − | 0.193381i | −0.995315 | − | 0.0966904i | \(-0.969174\pi\) | ||
0.995315 | − | 0.0966904i | \(-0.0308257\pi\) | |||||||
\(450\) | −2.21764 | − | 1.28036i | −0.104541 | − | 0.0603565i | ||||
\(451\) | 4.07937 | + | 7.06568i | 0.192090 | + | 0.332710i | ||||
\(452\) | −4.10609 | − | 7.11196i | −0.193134 | − | 0.334518i | ||||
\(453\) | −0.395710 | − | 0.228464i | −0.0185921 | − | 0.0107342i | ||||
\(454\) | 16.8076 | 0.788820 | ||||||||
\(455\) | 23.1618 | + | 12.3107i | 1.08584 | + | 0.577137i | ||||
\(456\) | −2.05659 | −0.0963085 | ||||||||
\(457\) | −6.40916 | − | 3.70033i | −0.299808 | − | 0.173094i | 0.342549 | − | 0.939500i | \(-0.388710\pi\) |
−0.642356 | + | 0.766406i | \(0.722043\pi\) | |||||||
\(458\) | 11.1435 | + | 19.3011i | 0.520700 | + | 0.901879i | ||||
\(459\) | 3.18349 | + | 5.51396i | 0.148592 | + | 0.257370i | ||||
\(460\) | 4.30123 | + | 2.48332i | 0.200546 | + | 0.115785i | ||||
\(461\) | 1.27247i | 0.0592650i | 0.999561 | + | 0.0296325i | \(0.00943370\pi\) | ||||
−0.999561 | + | 0.0296325i | \(0.990566\pi\) | |||||||
\(462\) | 1.75216 | − | 0.540854i | 0.0815179 | − | 0.0251628i | ||||
\(463\) | − | 34.3620i | − | 1.59694i | −0.602037 | − | 0.798468i | \(-0.705644\pi\) | ||
0.602037 | − | 0.798468i | \(-0.294356\pi\) | |||||||
\(464\) | 4.42608 | − | 7.66619i | 0.205476 | − | 0.355894i | ||||
\(465\) | 1.29704 | + | 2.24654i | 0.0601487 | + | 0.104181i | ||||
\(466\) | −15.7050 | + | 9.06727i | −0.727519 | + | 0.420033i | ||||
\(467\) | 14.7113 | − | 25.4807i | 0.680756 | − | 1.17910i | −0.293995 | − | 0.955807i | \(-0.594985\pi\) |
0.974751 | − | 0.223297i | \(-0.0716819\pi\) | |||||||
\(468\) | −0.924342 | − | 3.48505i | −0.0427277 | − | 0.161097i | ||||
\(469\) | −7.57511 | − | 24.5404i | −0.349786 | − | 1.13317i | ||||
\(470\) | − | 24.8205i | − | 1.14488i | ||||||
\(471\) | −0.775828 | + | 1.34377i | −0.0357483 | + | 0.0619178i | ||||
\(472\) | 6.06459 | + | 10.5042i | 0.279145 | + | 0.483494i | ||||
\(473\) | −2.98321 | + | 1.72236i | −0.137168 | + | 0.0791941i | ||||
\(474\) | −0.587736 | − | 0.339330i | −0.0269956 | − | 0.0155859i | ||||
\(475\) | 5.26633i | 0.241636i | ||||||||
\(476\) | −12.3509 | − | 11.4553i | −0.566101 | − | 0.525054i | ||||
\(477\) | −3.97011 | −0.181779 | ||||||||
\(478\) | −5.64399 | + | 9.77567i | −0.258150 | + | 0.447129i | ||||
\(479\) | 3.36031 | − | 1.94008i | 0.153536 | − | 0.0886443i | −0.421263 | − | 0.906938i | \(-0.638413\pi\) |
0.574800 | + | 0.818294i | \(0.305080\pi\) | |||||||
\(480\) | −1.37484 | − | 2.38129i | −0.0627525 | − | 0.108690i | ||||
\(481\) | −0.906557 | + | 3.34929i | −0.0413354 | + | 0.152714i | ||||
\(482\) | −8.67866 | −0.395302 | ||||||||
\(483\) | 1.06248 | − | 4.65932i | 0.0483444 | − | 0.212006i | ||||
\(484\) | −10.5196 | −0.478165 | ||||||||
\(485\) | 13.6105 | − | 23.5740i | 0.618019 | − | 1.07044i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 12.6285 | − | 7.29107i | 0.572252 | − | 0.330390i | −0.185796 | − | 0.982588i | \(-0.559486\pi\) |
0.758048 | + | 0.652198i | \(0.226153\pi\) | |||||||
\(488\) | 8.71597 | + | 5.03217i | 0.394554 | + | 0.227796i | ||||
\(489\) | 5.98476i | 0.270640i | ||||||||
\(490\) | −1.44607 | − | 19.1933i | −0.0653269 | − | 0.867066i | ||||
\(491\) | 19.2613 | 0.869250 | 0.434625 | − | 0.900612i | \(-0.356881\pi\) | ||||
0.434625 | + | 0.900612i | \(0.356881\pi\) | |||||||
\(492\) | −10.1945 | − | 5.88580i | −0.459604 | − | 0.265352i | ||||
\(493\) | 28.1807 | + | 48.8104i | 1.26920 | + | 2.19831i | ||||
\(494\) | −5.25658 | + | 5.22996i | −0.236505 | + | 0.235307i | ||||
\(495\) | −0.952882 | + | 1.65044i | −0.0428289 | + | 0.0741818i | ||||
\(496\) | 0.943413i | 0.0423605i | ||||||||
\(497\) | 19.8163 | + | 4.51877i | 0.888884 | + | 0.202695i | ||||
\(498\) | 2.32585 | 0.104224 | ||||||||
\(499\) | −16.9387 | − | 9.77954i | −0.758278 | − | 0.437792i | 0.0703990 | − | 0.997519i | \(-0.477573\pi\) |
−0.828677 | + | 0.559727i | \(0.810906\pi\) | |||||||
\(500\) | 5.80865 | − | 3.35363i | 0.259771 | − | 0.149979i | ||||
\(501\) | −6.24636 | + | 3.60634i | −0.279067 | + | 0.161119i | ||||
\(502\) | −18.9176 | − | 10.9221i | −0.844334 | − | 0.487477i | ||||
\(503\) | 15.3764 | 0.685598 | 0.342799 | − | 0.939409i | \(-0.388625\pi\) | ||||
0.342799 | + | 0.939409i | \(0.388625\pi\) | |||||||
\(504\) | −1.79918 | + | 1.93983i | −0.0801418 | + | 0.0864070i | ||||
\(505\) | − | 22.0069i | − | 0.979296i | ||||||
\(506\) | 0.625949 | − | 1.08417i | 0.0278268 | − | 0.0481974i | ||||
\(507\) | −11.2252 | − | 6.55707i | −0.498528 | − | 0.291210i | ||||
\(508\) | 3.19843 | + | 5.53985i | 0.141908 | + | 0.245791i | ||||
\(509\) | 7.64473 | + | 4.41369i | 0.338847 | + | 0.195633i | 0.659762 | − | 0.751475i | \(-0.270657\pi\) |
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(510\) | 17.5071 | 0.775228 | ||||||||
\(511\) | −4.41287 | − | 14.2960i | −0.195214 | − | 0.632418i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.78106 | − | 1.02829i | −0.0786356 | − | 0.0454003i | ||||
\(514\) | −22.1871 | + | 12.8097i | −0.978632 | + | 0.565013i | ||||
\(515\) | 29.9635 | − | 17.2994i | 1.32035 | − | 0.762304i | ||||
\(516\) | 2.48505 | − | 4.30424i | 0.109398 | − | 0.189483i | ||||
\(517\) | −6.25628 | −0.275151 | ||||||||
\(518\) | 2.43287 | − | 0.750976i | 0.106894 | − | 0.0329960i | ||||
\(519\) | −22.7561 | −0.998883 | ||||||||
\(520\) | −9.56973 | − | 2.59026i | −0.419661 | − | 0.113590i | ||||
\(521\) | −14.3434 | − | 24.8435i | −0.628395 | − | 1.08841i | −0.987874 | − | 0.155259i | \(-0.950379\pi\) |
0.359478 | − | 0.933153i | \(-0.382955\pi\) | |||||||
\(522\) | 7.66619 | − | 4.42608i | 0.335540 | − | 0.193724i | ||||
\(523\) | 13.6397 | − | 23.6247i | 0.596423 | − | 1.03303i | −0.396922 | − | 0.917853i | \(-0.629921\pi\) |
0.993344 | − | 0.115182i | \(-0.0367452\pi\) | |||||||
\(524\) | 1.94292 | 0.0848769 | ||||||||
\(525\) | 4.96735 | + | 4.60718i | 0.216793 | + | 0.201074i | ||||
\(526\) | 12.8612i | 0.560775i | ||||||||
\(527\) | −5.20194 | − | 3.00334i | −0.226600 | − | 0.130828i | ||||
\(528\) | −0.600231 | + | 0.346544i | −0.0261217 | + | 0.0150814i | ||||
\(529\) | 9.86871 | + | 17.0931i | 0.429074 | + | 0.743178i | ||||
\(530\) | −5.45825 | + | 9.45396i | −0.237091 | + | 0.410654i | ||||
\(531\) | 12.1292i | 0.526361i | ||||||||
\(532\) | 5.30504 | + | 1.20972i | 0.230003 | + | 0.0524481i | ||||
\(533\) | −41.0246 | + | 10.8810i | −1.77697 | + | 0.471308i | ||||
\(534\) | 6.69696 | − | 11.5995i | 0.289806 | − | 0.501959i | ||||
\(535\) | −24.1459 | + | 13.9407i | −1.04392 | + | 0.602708i | ||||
\(536\) | 4.85363 | + | 8.40673i | 0.209645 | + | 0.363115i | ||||
\(537\) | −7.65842 | + | 13.2648i | −0.330485 | + | 0.572417i | ||||
\(538\) | − | 9.66400i | − | 0.416645i | ||||||
\(539\) | −4.83790 | + | 0.364499i | −0.208383 | + | 0.0157001i | ||||
\(540\) | − | 2.74967i | − | 0.118327i | ||||||
\(541\) | 4.22098 | + | 2.43698i | 0.181474 | + | 0.104774i | 0.587985 | − | 0.808872i | \(-0.299921\pi\) |
−0.406511 | + | 0.913646i | \(0.633255\pi\) | |||||||
\(542\) | 3.65706 | + | 6.33421i | 0.157084 | + | 0.272078i | ||||
\(543\) | 10.0779 | + | 17.4555i | 0.432486 | + | 0.749087i | ||||
\(544\) | 5.51396 | + | 3.18349i | 0.236409 | + | 0.136491i | ||||
\(545\) | −34.2869 | −1.46869 | ||||||||
\(546\) | 0.334400 | + | 9.53353i | 0.0143110 | + | 0.407997i | ||||
\(547\) | −11.3711 | −0.486193 | −0.243097 | − | 0.970002i | \(-0.578163\pi\) | ||||
−0.243097 | + | 0.970002i | \(0.578163\pi\) | |||||||
\(548\) | 0.0395182 | + | 0.0228159i | 0.00168814 | + | 0.000974646i | ||||
\(549\) | 5.03217 | + | 8.71597i | 0.214768 | + | 0.371989i | ||||
\(550\) | 0.887398 | + | 1.53702i | 0.0378388 | + | 0.0655387i | ||||
\(551\) | −15.7662 | − | 9.10262i | −0.671662 | − | 0.387785i | ||||
\(552\) | 1.80626i | 0.0768796i | ||||||||
\(553\) | 1.31649 | + | 1.22103i | 0.0559827 | + | 0.0519235i | ||||
\(554\) | 12.7070i | 0.539870i | ||||||||
\(555\) | −1.32308 | + | 2.29164i | −0.0561615 | + | 0.0972746i | ||||
\(556\) | 10.4339 | + | 18.0721i | 0.442498 | + | 0.766429i | ||||
\(557\) | −1.00500 | + | 0.580239i | −0.0425833 | + | 0.0245855i | −0.521141 | − | 0.853471i | \(-0.674493\pi\) |
0.478557 | + | 0.878056i | \(0.341160\pi\) | |||||||
\(558\) | −0.471706 | + | 0.817019i | −0.0199689 | + | 0.0345872i | ||||
\(559\) | −4.59408 | − | 17.3211i | −0.194309 | − | 0.732604i | ||||
\(560\) | 2.14572 | + | 6.95132i | 0.0906733 | + | 0.293747i | ||||
\(561\) | − | 4.41287i | − | 0.186311i | ||||||
\(562\) | −11.9086 | + | 20.6263i | −0.502335 | + | 0.870069i | ||||
\(563\) | 3.86680 | + | 6.69750i | 0.162966 | + | 0.282266i | 0.935931 | − | 0.352183i | \(-0.114560\pi\) |
−0.772965 | + | 0.634449i | \(0.781227\pi\) | |||||||
\(564\) | 7.81735 | − | 4.51335i | 0.329170 | − | 0.190046i | ||||
\(565\) | −19.5556 | − | 11.2904i | −0.822709 | − | 0.474991i | ||||
\(566\) | − | 29.1228i | − | 1.22412i | ||||||
\(567\) | −2.52805 | + | 0.780355i | −0.106168 | + | 0.0327718i | ||||
\(568\) | −7.68213 | −0.322335 | ||||||||
\(569\) | 13.2494 | − | 22.9487i | 0.555445 | − | 0.962059i | −0.442424 | − | 0.896806i | \(-0.645881\pi\) |
0.997869 | − | 0.0652529i | \(-0.0207854\pi\) | |||||||
\(570\) | −4.89733 | + | 2.82747i | −0.205126 | + | 0.118430i | ||||
\(571\) | −16.2913 | − | 28.2174i | −0.681770 | − | 1.18086i | −0.974440 | − | 0.224647i | \(-0.927877\pi\) |
0.292670 | − | 0.956214i | \(-0.405456\pi\) | |||||||
\(572\) | −0.652904 | + | 2.41216i | −0.0272993 | + | 0.100858i | ||||
\(573\) | 19.1655 | 0.800651 | ||||||||
\(574\) | 22.8349 | + | 21.1792i | 0.953112 | + | 0.884003i | ||||
\(575\) | 4.62531 | 0.192889 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 25.5216 | − | 14.7349i | 1.06248 | − | 0.613422i | 0.136361 | − | 0.990659i | \(-0.456459\pi\) |
0.926117 | + | 0.377237i | \(0.123126\pi\) | |||||||
\(578\) | −20.3848 | + | 11.7692i | −0.847896 | + | 0.489533i | ||||
\(579\) | 3.22142 | + | 1.85989i | 0.133878 | + | 0.0772944i | ||||
\(580\) | − | 24.3406i | − | 1.01069i | ||||||
\(581\) | −5.99962 | − | 1.36811i | −0.248906 | − | 0.0567587i | ||||
\(582\) | 9.89969 | 0.410355 | ||||||||
\(583\) | 2.38298 | + | 1.37581i | 0.0986930 | + | 0.0569804i | ||||
\(584\) | 2.82747 | + | 4.89733i | 0.117002 | + | 0.202653i | ||||
\(585\) | −6.99251 | − | 7.02809i | −0.289105 | − | 0.290576i | ||||
\(586\) | −3.43142 | + | 5.94340i | −0.141751 | + | 0.245520i | ||||
\(587\) | − | 23.0017i | − | 0.949381i | −0.880153 | − | 0.474690i | \(-0.842560\pi\) | ||
0.880153 | − | 0.474690i | \(-0.157440\pi\) | |||||||
\(588\) | 5.78209 | − | 3.94556i | 0.238449 | − | 0.162712i | ||||
\(589\) | 1.94021 | 0.0799450 | ||||||||
\(590\) | 28.8831 | + | 16.6756i | 1.18910 | + | 0.686525i | ||||
\(591\) | 8.18994 | − | 4.72846i | 0.336889 | − | 0.194503i | ||||
\(592\) | −0.833421 | + | 0.481176i | −0.0342534 | + | 0.0197762i | ||||
\(593\) | −38.6090 | − | 22.2909i | −1.58548 | − | 0.915378i | −0.994038 | − | 0.109031i | \(-0.965225\pi\) |
−0.591443 | − | 0.806347i | \(-0.701441\pi\) | |||||||
\(594\) | −0.693087 | −0.0284377 | ||||||||
\(595\) | −45.1602 | − | 10.2980i | −1.85139 | − | 0.422177i | ||||
\(596\) | 4.16254i | 0.170504i | ||||||||
\(597\) | 1.73497 | − | 3.00506i | 0.0710077 | − | 0.122989i | ||||
\(598\) | 4.59338 | + | 4.61676i | 0.187837 | + | 0.188793i | ||||
\(599\) | 2.90326 | + | 5.02860i | 0.118624 | + | 0.205463i | 0.919223 | − | 0.393738i | \(-0.128818\pi\) |
−0.800599 | + | 0.599201i | \(0.795485\pi\) | |||||||
\(600\) | −2.21764 | − | 1.28036i | −0.0905348 | − | 0.0522703i | ||||
\(601\) | −3.28026 | −0.133805 | −0.0669023 | − | 0.997760i | \(-0.521312\pi\) | ||||
−0.0669023 | + | 0.997760i | \(0.521312\pi\) | |||||||
\(602\) | −8.94211 | + | 9.64118i | −0.364453 | + | 0.392945i | ||||
\(603\) | 9.70725i | 0.395310i | ||||||||
\(604\) | −0.395710 | − | 0.228464i | −0.0161012 | − | 0.00929605i | ||||
\(605\) | −25.0503 | + | 14.4628i | −1.01844 | + | 0.587996i | ||||
\(606\) | 6.93121 | − | 4.00174i | 0.281561 | − | 0.162559i | ||||
\(607\) | 0.434594 | − | 0.752739i | 0.0176396 | − | 0.0305527i | −0.857071 | − | 0.515199i | \(-0.827718\pi\) |
0.874710 | + | 0.484646i | \(0.161052\pi\) | |||||||
\(608\) | −2.05659 | −0.0834056 | ||||||||
\(609\) | −22.3787 | + | 6.90783i | −0.906831 | + | 0.279919i | ||||
\(610\) | 27.6737 | 1.12047 | ||||||||
\(611\) | 8.50335 | − | 31.4157i | 0.344009 | − | 1.27094i | ||||
\(612\) | 3.18349 | + | 5.51396i | 0.128685 | + | 0.222889i | ||||
\(613\) | 17.2225 | − | 9.94341i | 0.695610 | − | 0.401611i | −0.110100 | − | 0.993920i | \(-0.535117\pi\) |
0.805710 | + | 0.592310i | \(0.201784\pi\) | |||||||
\(614\) | −13.2897 | + | 23.0185i | −0.536329 | + | 0.928949i | ||||
\(615\) | −32.3681 | −1.30521 | ||||||||
\(616\) | 1.75216 | − | 0.540854i | 0.0705965 | − | 0.0217916i | ||||
\(617\) | 6.32742i | 0.254732i | 0.991856 | + | 0.127366i | \(0.0406524\pi\) | ||||
−0.991856 | + | 0.127366i | \(0.959348\pi\) | |||||||
\(618\) | 10.8971 | + | 6.29145i | 0.438346 | + | 0.253079i | ||||
\(619\) | 22.8722 | − | 13.2053i | 0.919311 | − | 0.530764i | 0.0358959 | − | 0.999356i | \(-0.488572\pi\) |
0.883415 | + | 0.468591i | \(0.155238\pi\) | |||||||
\(620\) | 1.29704 | + | 2.24654i | 0.0520903 | + | 0.0902231i | ||||
\(621\) | −0.903131 | + | 1.56427i | −0.0362414 | + | 0.0627719i | ||||
\(622\) | − | 10.6320i | − | 0.426304i | ||||||
\(623\) | −24.0981 | + | 25.9820i | −0.965469 | + | 1.04095i | ||||
\(624\) | −0.924342 | − | 3.48505i | −0.0370033 | − | 0.139514i | ||||
\(625\) | 15.6232 | − | 27.0601i | 0.624926 | − | 1.08240i | ||||
\(626\) | 23.2249 | − | 13.4089i | 0.928252 | − | 0.535927i | ||||
\(627\) | 0.712697 | + | 1.23443i | 0.0284624 | + | 0.0492983i | ||||
\(628\) | −0.775828 | + | 1.34377i | −0.0309589 | + | 0.0536224i | ||||
\(629\) | − | 6.12727i | − | 0.244310i | ||||||
\(630\) | −1.61741 | + | 7.09288i | −0.0644391 | + | 0.282587i | ||||
\(631\) | − | 25.5607i | − | 1.01756i | −0.860898 | − | 0.508778i | \(-0.830097\pi\) | ||
0.860898 | − | 0.508778i | \(-0.169903\pi\) | |||||||
\(632\) | −0.587736 | − | 0.339330i | −0.0233789 | − | 0.0134978i | ||||
\(633\) | −14.1980 | − | 24.5917i | −0.564322 | − | 0.977434i | ||||
\(634\) | −7.39952 | − | 12.8163i | −0.293873 | − | 0.509002i | ||||
\(635\) | 15.2328 | + | 8.79465i | 0.604495 | + | 0.349005i | ||||
\(636\) | −3.97011 | −0.157425 | ||||||||
\(637\) | 4.74520 | − | 24.7888i | 0.188012 | − | 0.982167i | ||||
\(638\) | −6.13532 | −0.242899 | ||||||||
\(639\) | −6.65292 | − | 3.84107i | −0.263185 | − | 0.151950i | ||||
\(640\) | −1.37484 | − | 2.38129i | −0.0543452 | − | 0.0941287i | ||||
\(641\) | 3.40779 | + | 5.90247i | 0.134600 | + | 0.233133i | 0.925444 | − | 0.378883i | \(-0.123692\pi\) |
−0.790845 | + | 0.612017i | \(0.790359\pi\) | |||||||
\(642\) | −8.78138 | − | 5.06993i | −0.346574 | − | 0.200094i | ||||
\(643\) | 29.4326i | 1.16071i | 0.814364 | + | 0.580355i | \(0.197086\pi\) | ||||
−0.814364 | + | 0.580355i | \(0.802914\pi\) | |||||||
\(644\) | 1.06248 | − | 4.65932i | 0.0418674 | − | 0.183603i | ||||
\(645\) | − | 13.6662i | − | 0.538105i | ||||||
\(646\) | 6.54712 | − | 11.3399i | 0.257593 | − | 0.446164i | ||||
\(647\) | 18.4312 | + | 31.9237i | 0.724605 | + | 1.25505i | 0.959137 | + | 0.282943i | \(0.0913109\pi\) |
−0.234532 | + | 0.972108i | \(0.575356\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 4.20329 | − | 7.28031i | 0.164993 | − | 0.285777i | ||||
\(650\) | −8.92421 | + | 2.36697i | −0.350036 | + | 0.0928403i | ||||
\(651\) | 1.69737 | − | 1.83006i | 0.0665251 | − | 0.0717258i | ||||
\(652\) | 5.98476i | 0.234381i | ||||||||
\(653\) | 10.0181 | − | 17.3518i | 0.392037 | − | 0.679028i | −0.600681 | − | 0.799489i | \(-0.705104\pi\) |
0.992718 | + | 0.120461i | \(0.0384372\pi\) | |||||||
\(654\) | −6.23473 | − | 10.7989i | −0.243797 | − | 0.422269i | ||||
\(655\) | 4.62665 | − | 2.67120i | 0.180778 | − | 0.104372i | ||||
\(656\) | −10.1945 | − | 5.88580i | −0.398028 | − | 0.229802i | ||||
\(657\) | 5.65495i | 0.220620i | ||||||||
\(658\) | −22.8199 | + | 7.04403i | −0.889614 | + | 0.274605i | ||||
\(659\) | −30.1565 | −1.17473 | −0.587365 | − | 0.809322i | \(-0.699835\pi\) | ||||
−0.587365 | + | 0.809322i | \(0.699835\pi\) | |||||||
\(660\) | −0.952882 | + | 1.65044i | −0.0370909 | + | 0.0642433i | ||||
\(661\) | −26.5850 | + | 15.3488i | −1.03404 | + | 0.597001i | −0.918138 | − | 0.396261i | \(-0.870308\pi\) |
−0.115897 | + | 0.993261i | \(0.536974\pi\) | |||||||
\(662\) | −3.46425 | − | 6.00025i | −0.134642 | − | 0.233206i | ||||
\(663\) | 22.1591 | + | 5.99783i | 0.860587 | + | 0.232936i | ||||
\(664\) | 2.32585 | 0.0902606 | ||||||||
\(665\) | 14.2960 | − | 4.41287i | 0.554375 | − | 0.171124i | ||||
\(666\) | −0.962352 | −0.0372904 | ||||||||
\(667\) | −7.99466 | + | 13.8472i | −0.309554 | + | 0.536164i | ||||
\(668\) | −6.24636 | + | 3.60634i | −0.241679 | + | 0.139533i | ||||
\(669\) | −10.5994 | + | 6.11957i | −0.409797 | + | 0.236596i | ||||
\(670\) | 23.1158 | + | 13.3459i | 0.893040 | + | 0.515597i | ||||
\(671\) | − | 6.97547i | − | 0.269285i | ||||||
\(672\) | −1.79918 | + | 1.93983i | −0.0694049 | + | 0.0748307i | ||||
\(673\) | 37.5864 | 1.44885 | 0.724425 | − | 0.689353i | \(-0.242105\pi\) | ||||
0.724425 | + | 0.689353i | \(0.242105\pi\) | |||||||
\(674\) | 15.8785 | + | 9.16747i | 0.611618 | + | 0.353118i | ||||
\(675\) | −1.28036 | − | 2.21764i | −0.0492809 | − | 0.0853570i | ||||
\(676\) | −11.2252 | − | 6.55707i | −0.431738 | − | 0.252195i | ||||
\(677\) | 14.8873 | − | 25.7855i | 0.572165 | − | 0.991019i | −0.424178 | − | 0.905579i | \(-0.639437\pi\) |
0.996343 | − | 0.0854400i | \(-0.0272296\pi\) | |||||||
\(678\) | − | 8.21218i | − | 0.315387i | ||||||
\(679\) | −25.5366 | − | 5.82318i | −0.980004 | − | 0.223473i | ||||
\(680\) | 17.5071 | 0.671367 | ||||||||
\(681\) | 14.5558 | + | 8.40380i | 0.557780 | + | 0.322034i | ||||
\(682\) | 0.566266 | − | 0.326934i | 0.0216834 | − | 0.0125189i | ||||
\(683\) | −44.6289 | + | 25.7665i | −1.70768 | + | 0.985927i | −0.770251 | + | 0.637740i | \(0.779869\pi\) |
−0.937425 | + | 0.348187i | \(0.886797\pi\) | |||||||
\(684\) | −1.78106 | − | 1.02829i | −0.0681004 | − | 0.0393178i | ||||
\(685\) | 0.125472 | 0.00479406 | ||||||||
\(686\) | −17.2360 | + | 6.77657i | −0.658072 | + | 0.258731i | ||||
\(687\) | 22.2869i | 0.850300i | ||||||||
\(688\) | 2.48505 | − | 4.30424i | 0.0947417 | − | 0.164098i | ||||
\(689\) | −10.1475 | + | 10.0961i | −0.386588 | + | 0.384631i | ||||
\(690\) | 2.48332 | + | 4.30123i | 0.0945382 | + | 0.163745i | ||||
\(691\) | −36.8206 | − | 21.2584i | −1.40072 | − | 0.808707i | −0.406255 | − | 0.913760i | \(-0.633165\pi\) |
−0.994467 | + | 0.105053i | \(0.966499\pi\) | |||||||
\(692\) | −22.7561 | −0.865058 | ||||||||
\(693\) | 1.78784 | + | 0.407687i | 0.0679145 | + | 0.0154867i | ||||
\(694\) | 6.77289i | 0.257096i | ||||||||
\(695\) | 49.6925 | + | 28.6900i | 1.88494 | + | 1.08827i | ||||
\(696\) | 7.66619 | − | 4.42608i | 0.290586 | − | 0.167770i | ||||
\(697\) | 64.9081 | − | 37.4747i | 2.45857 | − | 1.41946i | ||||
\(698\) | −15.5599 | + | 26.9506i | −0.588953 | + | 1.02010i | ||||
\(699\) | −18.1345 | −0.685912 | ||||||||
\(700\) | 4.96735 | + | 4.60718i | 0.187748 | + | 0.174135i | ||||
\(701\) | 21.9298 | 0.828278 | 0.414139 | − | 0.910214i | \(-0.364083\pi\) | ||||
0.414139 | + | 0.910214i | \(0.364083\pi\) | |||||||
\(702\) | 0.942023 | − | 3.48032i | 0.0355543 | − | 0.131356i | ||||
\(703\) | 0.989580 | + | 1.71400i | 0.0373227 | + | 0.0646449i | ||||
\(704\) | −0.600231 | + | 0.346544i | −0.0226221 | + | 0.0130609i | ||||
\(705\) | 12.4102 | − | 21.4952i | 0.467396 | − | 0.809554i | ||||
\(706\) | −9.35758 | −0.352177 | ||||||||
\(707\) | −20.2332 | + | 6.24555i | −0.760948 | + | 0.234888i | ||||
\(708\) | 12.1292i | 0.455842i | ||||||||
\(709\) | 13.2657 | + | 7.65895i | 0.498204 | + | 0.287638i | 0.727971 | − | 0.685607i | \(-0.240463\pi\) |
−0.229768 | + | 0.973245i | \(0.573797\pi\) | |||||||
\(710\) | −18.2934 | + | 10.5617i | −0.686538 | + | 0.396373i | ||||
\(711\) | −0.339330 | − | 0.587736i | −0.0127259 | − | 0.0220418i | ||||
\(712\) | 6.69696 | − | 11.5995i | 0.250979 | − | 0.434709i | ||||
\(713\) | − | 1.70405i | − | 0.0638172i | ||||||
\(714\) | −4.96850 | − | 16.0960i | −0.185941 | − | 0.602379i | ||||
\(715\) | 1.76158 | + | 6.64169i | 0.0658793 | + | 0.248385i | ||||
\(716\) | −7.65842 | + | 13.2648i | −0.286209 | + | 0.495728i | ||||
\(717\) | −9.77567 | + | 5.64399i | −0.365079 | + | 0.210779i | ||||
\(718\) | −13.7167 | − | 23.7581i | −0.511904 | − | 0.886644i | ||||
\(719\) | −6.26926 | + | 10.8587i | −0.233804 | + | 0.404961i | −0.958924 | − | 0.283662i | \(-0.908451\pi\) |
0.725120 | + | 0.688622i | \(0.241784\pi\) | |||||||
\(720\) | − | 2.74967i | − | 0.102474i | ||||||
\(721\) | −24.4087 | − | 22.6389i | −0.909028 | − | 0.843116i | ||||
\(722\) | − | 14.7704i | − | 0.549699i | ||||||
\(723\) | −7.51594 | − | 4.33933i | −0.279521 | − | 0.161381i | ||||
\(724\) | 10.0779 | + | 17.4555i | 0.374543 | + | 0.648728i | ||||
\(725\) | −11.3339 | − | 19.6309i | −0.420931 | − | 0.729073i | ||||
\(726\) | −9.11027 | − | 5.25982i | −0.338114 | − | 0.195210i | ||||
\(727\) | 42.7300 | 1.58477 | 0.792383 | − | 0.610023i | \(-0.208840\pi\) | ||||
0.792383 | + | 0.610023i | \(0.208840\pi\) | |||||||
\(728\) | 0.334400 | + | 9.53353i | 0.0123937 | + | 0.353336i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.4661 | + | 7.77463i | 0.498401 | + | 0.287752i | ||||
\(731\) | 15.8223 | + | 27.4050i | 0.585207 | + | 1.01361i | ||||
\(732\) | 5.03217 | + | 8.71597i | 0.185994 | + | 0.322152i | ||||
\(733\) | 23.9996 | + | 13.8562i | 0.886445 | + | 0.511789i | 0.872778 | − | 0.488117i | \(-0.162316\pi\) |
0.0136668 | + | 0.999907i | \(0.495650\pi\) | |||||||
\(734\) | 16.9339i | 0.625040i | ||||||||
\(735\) | 8.34433 | − | 17.3449i | 0.307785 | − | 0.639778i | ||||
\(736\) | 1.80626i | 0.0665797i | ||||||||
\(737\) | 3.36399 | − | 5.82659i | 0.123914 | − | 0.214625i | ||||
\(738\) | −5.88580 | − | 10.1945i | −0.216659 | − | 0.375265i | ||||
\(739\) | −24.5022 | + | 14.1464i | −0.901330 | + | 0.520383i | −0.877631 | − | 0.479336i | \(-0.840877\pi\) |
−0.0236983 | + | 0.999719i | \(0.507544\pi\) | |||||||
\(740\) | −1.32308 | + | 2.29164i | −0.0486373 | + | 0.0842422i | ||||
\(741\) | −7.16732 | + | 1.90099i | −0.263298 | + | 0.0698346i | ||||
\(742\) | 10.2410 | + | 2.33529i | 0.375960 | + | 0.0857312i | ||||
\(743\) | 37.4869i | 1.37526i | 0.726061 | + | 0.687630i | \(0.241349\pi\) | ||||
−0.726061 | + | 0.687630i | \(0.758651\pi\) | |||||||
\(744\) | −0.471706 | + | 0.817019i | −0.0172936 | + | 0.0299534i | ||||
\(745\) | 5.72282 | + | 9.91221i | 0.209668 | + | 0.363155i | ||||
\(746\) | −18.1872 | + | 10.5004i | −0.665880 | + | 0.384446i | ||||
\(747\) | 2.01425 | + | 1.16293i | 0.0736974 | + | 0.0425492i | ||||
\(748\) | − | 4.41287i | − | 0.161350i | ||||||
\(749\) | 19.6697 | + | 18.2434i | 0.718713 | + | 0.666601i | ||||
\(750\) | 6.70725 | 0.244914 | ||||||||
\(751\) | 1.04017 | − | 1.80163i | 0.0379564 | − | 0.0657423i | −0.846423 | − | 0.532511i | \(-0.821249\pi\) |
0.884380 | + | 0.466769i | \(0.154582\pi\) | |||||||
\(752\) | 7.81735 | − | 4.51335i | 0.285069 | − | 0.164585i | ||||
\(753\) | −10.9221 | − | 18.9176i | −0.398023 | − | 0.689396i | ||||
\(754\) | 8.33893 | − | 30.8083i | 0.303686 | − | 1.12197i | ||||
\(755\) | −1.25640 | −0.0457251 | ||||||||
\(756\) | −2.52805 | + | 0.780355i | −0.0919444 | + | 0.0283812i | ||||
\(757\) | −18.0167 | −0.654826 | −0.327413 | − | 0.944881i | \(-0.606177\pi\) | ||||
−0.327413 | + | 0.944881i | \(0.606177\pi\) | |||||||
\(758\) | −4.18419 | + | 7.24723i | −0.151977 | + | 0.263231i | ||||
\(759\) | 1.08417 | − | 0.625949i | 0.0393530 | − | 0.0227205i | ||||
\(760\) | −4.89733 | + | 2.82747i | −0.177645 | + | 0.102563i | ||||
\(761\) | 26.7066 | + | 15.4190i | 0.968113 | + | 0.558940i | 0.898660 | − | 0.438645i | \(-0.144542\pi\) |
0.0694523 | + | 0.997585i | \(0.477875\pi\) | |||||||
\(762\) | 6.39687i | 0.231734i | ||||||||
\(763\) | 9.73060 | + | 31.5234i | 0.352272 | + | 1.14122i | ||||
\(764\) | 19.1655 | 0.693384 | ||||||||
\(765\) | 15.1616 | + | 8.75355i | 0.548169 | + | 0.316485i | ||||
\(766\) | 11.4488 | + | 19.8299i | 0.413661 | + | 0.716482i | ||||
\(767\) | 30.8449 | + | 31.0018i | 1.11374 | + | 1.11941i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | − | 28.1580i | − | 1.01540i | −0.861533 | − | 0.507702i | \(-0.830495\pi\) | ||
0.861533 | − | 0.507702i | \(-0.169505\pi\) | |||||||
\(770\) | 3.42881 | − | 3.69686i | 0.123566 | − | 0.133226i | ||||
\(771\) | −25.6195 | −0.922663 | ||||||||
\(772\) | 3.22142 | + | 1.85989i | 0.115942 | + | 0.0669389i | ||||
\(773\) | −6.87642 | + | 3.97011i | −0.247328 | + | 0.142795i | −0.618540 | − | 0.785753i | \(-0.712276\pi\) |
0.371212 | + | 0.928548i | \(0.378942\pi\) | |||||||
\(774\) | 4.30424 | − | 2.48505i | 0.154713 | − | 0.0893234i | ||||
\(775\) | 2.09215 | + | 1.20790i | 0.0751522 | + | 0.0433892i | ||||
\(776\) | 9.89969 | 0.355378 | ||||||||
\(777\) | 2.48242 | + | 0.566073i | 0.0890563 | + | 0.0203078i | ||||
\(778\) | − | 7.11855i | − | 0.255212i | ||||||
\(779\) | −12.1047 | + | 20.9659i | −0.433694 | + | 0.751181i | ||||
\(780\) | −6.99251 | − | 7.02809i | −0.250372 | − | 0.251646i | ||||
\(781\) | 2.66219 | + | 4.61105i | 0.0952608 | + | 0.164996i | ||||
\(782\) | −9.95966 | − | 5.75021i | −0.356157 | − | 0.205627i | ||||
\(783\) | 8.85216 | 0.316350 | ||||||||
\(784\) | 5.78209 | − | 3.94556i | 0.206503 | − | 0.140913i | ||||
\(785\) | 4.26655i | 0.152280i | ||||||||
\(786\) | 1.68262 | + | 0.971460i | 0.0600170 | + | 0.0346508i | ||||
\(787\) | 38.5395 | − | 22.2508i | 1.37378 | − | 0.793154i | 0.382381 | − | 0.924005i | \(-0.375104\pi\) |
0.991402 | + | 0.130851i | \(0.0417708\pi\) | |||||||
\(788\) | 8.18994 | − | 4.72846i | 0.291754 | − | 0.168445i | ||||
\(789\) | −6.43061 | + | 11.1381i | −0.228936 | + | 0.396528i | ||||
\(790\) | −1.86609 | −0.0663926 | ||||||||
\(791\) | −4.83056 | + | 21.1836i | −0.171755 | + | 0.753203i | ||||
\(792\) | −0.693087 | −0.0246278 | ||||||||
\(793\) | 35.0271 | + | 9.48084i | 1.24385 | + | 0.336674i | ||||
\(794\) | 12.1784 | + | 21.0936i | 0.432196 | + | 0.748585i | ||||
\(795\) | −9.45396 | + | 5.45825i | −0.335298 | + | 0.193584i | ||||
\(796\) | 1.73497 | − | 3.00506i | 0.0614945 | − | 0.106512i | ||||
\(797\) | 30.4829 | 1.07976 | 0.539879 | − | 0.841742i | \(-0.318470\pi\) | ||||
0.539879 | + | 0.841742i | \(0.318470\pi\) | |||||||
\(798\) | 3.98944 | + | 3.70017i | 0.141225 | + | 0.130985i | ||||
\(799\) | 57.4727i | 2.03324i | ||||||||
\(800\) | −2.21764 | − | 1.28036i | −0.0784054 | − | 0.0452674i | ||||
\(801\) | 11.5995 | − | 6.69696i | 0.409848 | − | 0.236626i | ||||
\(802\) | 3.68921 | + | 6.38990i | 0.130271 | + | 0.225635i | ||||
\(803\) | 1.95969 | − | 3.39427i | 0.0691558 | − | 0.119781i | ||||
\(804\) | 9.70725i | 0.342348i | ||||||||
\(805\) | −3.87574 | − | 12.5559i | −0.136602 | − | 0.442538i | ||||
\(806\) | 0.872036 | + | 3.28784i | 0.0307162 | + | 0.115809i | ||||
\(807\) | 4.83200 | − | 8.36927i | 0.170094 | − | 0.294612i | ||||
\(808\) | 6.93121 | − | 4.00174i | 0.243839 | − | 0.140781i | ||||
\(809\) | 3.12627 | + | 5.41487i | 0.109914 | + | 0.190377i | 0.915735 | − | 0.401782i | \(-0.131609\pi\) |
−0.805821 | + | 0.592159i | \(0.798276\pi\) | |||||||
\(810\) | 1.37484 | − | 2.38129i | 0.0483069 | − | 0.0836699i | ||||
\(811\) | − | 28.5397i | − | 1.00216i | −0.865400 | − | 0.501082i | \(-0.832936\pi\) | ||
0.865400 | − | 0.501082i | \(-0.167064\pi\) | |||||||
\(812\) | −22.3787 | + | 6.90783i | −0.785339 | + | 0.242417i | ||||
\(813\) | 7.31412i | 0.256517i | ||||||||
\(814\) | 0.577633 | + | 0.333497i | 0.0202460 | + | 0.0116891i | ||||
\(815\) | 8.22808 | + | 14.2514i | 0.288217 | + | 0.499206i | ||||
\(816\) | 3.18349 | + | 5.51396i | 0.111444 | + | 0.193027i | ||||
\(817\) | −8.85204 | − | 5.11073i | −0.309694 | − | 0.178802i | ||||
\(818\) | −26.0284 | −0.910061 | ||||||||
\(819\) | −4.47717 | + | 8.42348i | −0.156445 | + | 0.294340i | ||||
\(820\) | −32.3681 | −1.13034 | ||||||||
\(821\) | 15.1241 | + | 8.73193i | 0.527836 | + | 0.304746i | 0.740135 | − | 0.672459i | \(-0.234762\pi\) |
−0.212299 | + | 0.977205i | \(0.568095\pi\) | |||||||
\(822\) | 0.0228159 | + | 0.0395182i | 0.000795795 | + | 0.00137836i | ||||
\(823\) | 7.13184 | + | 12.3527i | 0.248600 | + | 0.430588i | 0.963138 | − | 0.269009i | \(-0.0866961\pi\) |
−0.714537 | + | 0.699597i | \(0.753363\pi\) | |||||||
\(824\) | 10.8971 | + | 6.29145i | 0.379619 | + | 0.219173i | ||||
\(825\) | 1.77480i | 0.0617905i | ||||||||
\(826\) | 7.13460 | − | 31.2876i | 0.248245 | − | 1.08864i | ||||
\(827\) | − | 12.5853i | − | 0.437635i | −0.975766 | − | 0.218818i | \(-0.929780\pi\) | ||
0.975766 | − | 0.218818i | \(-0.0702200\pi\) | |||||||
\(828\) | −0.903131 | + | 1.56427i | −0.0313860 | + | 0.0543621i | ||||
\(829\) | 5.13167 | + | 8.88832i | 0.178230 | + | 0.308704i | 0.941274 | − | 0.337642i | \(-0.109629\pi\) |
−0.763044 | + | 0.646346i | \(0.776296\pi\) | |||||||
\(830\) | 5.53852 | − | 3.19767i | 0.192245 | − | 0.110993i | ||||
\(831\) | −6.35351 | + | 11.0046i | −0.220401 | + | 0.381745i | ||||
\(832\) | −0.924342 | − | 3.48505i | −0.0320458 | − | 0.120822i | ||||
\(833\) | 3.34843 | + | 44.4428i | 0.116016 | + | 1.53985i | ||||
\(834\) | 20.8679i | 0.722596i | ||||||||
\(835\) | −9.91626 | + | 17.1755i | −0.343166 | + | 0.594381i | ||||
\(836\) | 0.712697 | + | 1.23443i | 0.0246491 | + | 0.0426936i | ||||
\(837\) | −0.817019 | + | 0.471706i | −0.0282403 | + | 0.0163046i | ||||
\(838\) | −16.5657 | − | 9.56418i | −0.572251 | − | 0.330389i | ||||
\(839\) | 32.1258i | 1.10911i | 0.832148 | + | 0.554553i | \(0.187111\pi\) | ||||
−0.832148 | + | 0.554553i | \(0.812889\pi\) | |||||||
\(840\) | −1.61741 | + | 7.09288i | −0.0558059 | + | 0.244728i | ||||
\(841\) | 49.3607 | 1.70209 | ||||||||
\(842\) | −5.13625 | + | 8.89625i | −0.177007 | + | 0.306585i | ||||
\(843\) | −20.6263 | + | 11.9086i | −0.710408 | + | 0.410154i | ||||
\(844\) | −14.1980 | − | 24.5917i | −0.488717 | − | 0.846483i | ||||
\(845\) | −35.7453 | − | 0.181468i | −1.22968 | − | 0.00624270i | ||||
\(846\) | 9.02669 | 0.310344 | ||||||||
\(847\) | 20.4063 | + | 18.9267i | 0.701170 | + | 0.650329i | ||||
\(848\) | −3.97011 | −0.136334 | ||||||||
\(849\) | 14.5614 | − | 25.2211i | 0.499747 | − | 0.865586i | ||||
\(850\) | 14.1197 | − | 8.15199i | 0.484300 | − | 0.279611i | ||||
\(851\) | 1.50538 | − | 0.869130i | 0.0516036 | − | 0.0297934i | ||||
\(852\) | −6.65292 | − | 3.84107i | −0.227925 | − | 0.131593i | ||||
\(853\) | − | 6.55511i | − | 0.224443i | −0.993683 | − | 0.112221i | \(-0.964203\pi\) | ||
0.993683 | − | 0.112221i | \(-0.0357966\pi\) | |||||||
\(854\) | −7.85376 | − | 25.4432i | −0.268750 | − | 0.870648i | ||||
\(855\) | −5.65495 | −0.193395 | ||||||||
\(856\) | −8.78138 | − | 5.06993i | −0.300141 | − | 0.173287i | ||||
\(857\) | −8.45109 | − | 14.6377i | −0.288684 | − | 0.500015i | 0.684812 | − | 0.728720i | \(-0.259884\pi\) |
−0.973496 | + | 0.228705i | \(0.926551\pi\) | |||||||
\(858\) | −1.77151 | + | 1.76254i | −0.0604784 | + | 0.0601722i | ||||
\(859\) | −25.6471 | + | 44.4221i | −0.875068 | + | 1.51566i | −0.0183773 | + | 0.999831i | \(0.505850\pi\) |
−0.856690 | + | 0.515831i | \(0.827483\pi\) | |||||||
\(860\) | − | 13.6662i | − | 0.466013i | ||||||
\(861\) | 9.18602 | + | 29.7592i | 0.313059 | + | 1.01419i | ||||
\(862\) | −1.07720 | −0.0366897 | ||||||||
\(863\) | −36.2199 | − | 20.9116i | −1.23294 | − | 0.711839i | −0.265299 | − | 0.964166i | \(-0.585471\pi\) |
−0.967642 | + | 0.252327i | \(0.918804\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | −54.1889 | + | 31.2860i | −1.84248 | + | 1.06375i | ||||
\(866\) | 1.24947 | + | 0.721381i | 0.0424587 | + | 0.0245135i | ||||
\(867\) | −23.5383 | −0.799404 | ||||||||
\(868\) | 1.69737 | − | 1.83006i | 0.0576124 | − | 0.0621164i | ||||
\(869\) | 0.470370i | 0.0159562i | ||||||||
\(870\) | 12.1703 | − | 21.0795i | 0.412611 | − | 0.714663i | ||||
\(871\) | 24.6858 | + | 24.8115i | 0.836448 | + | 0.840705i | ||||
\(872\) | −6.23473 | − | 10.7989i | −0.211135 | − | 0.365696i | ||||
\(873\) | 8.57338 | + | 4.94984i | 0.290165 | + | 0.167527i | ||||
\(874\) | 3.71474 | 0.125653 | ||||||||
\(875\) | −17.3016 | − | 3.94533i | −0.584901 | − | 0.133376i | ||||
\(876\) | 5.65495i | 0.191063i | ||||||||
\(877\) | 32.7437 | + | 18.9046i | 1.10568 | + | 0.638363i | 0.937706 | − | 0.347429i | \(-0.112945\pi\) |
0.167971 | + | 0.985792i | \(0.446278\pi\) | |||||||
\(878\) | −19.5655 | + | 11.2961i | −0.660303 | + | 0.381226i | ||||
\(879\) | −5.94340 | + | 3.43142i | −0.200466 | + | 0.115739i | ||||
\(880\) | −0.952882 | + | 1.65044i | −0.0321216 | + | 0.0556363i | ||||
\(881\) | 20.8312 | 0.701819 | 0.350910 | − | 0.936409i | \(-0.385872\pi\) | ||||
0.350910 | + | 0.936409i | \(0.385872\pi\) | |||||||
\(882\) | 6.98022 | − | 0.525907i | 0.235036 | − | 0.0177082i | ||||
\(883\) | −28.4623 | −0.957833 | −0.478916 | − | 0.877860i | \(-0.658970\pi\) | ||||
−0.478916 | + | 0.877860i | \(0.658970\pi\) | |||||||
\(884\) | 22.1591 | + | 5.99783i | 0.745290 | + | 0.201729i | ||||
\(885\) | 16.6756 | + | 28.8831i | 0.560546 | + | 0.970893i | ||||
\(886\) | 20.4213 | − | 11.7902i | 0.686067 | − | 0.396101i | ||||
\(887\) | 22.3022 | − | 38.6285i | 0.748834 | − | 1.29702i | −0.199548 | − | 0.979888i | \(-0.563947\pi\) |
0.948382 | − | 0.317130i | \(-0.102719\pi\) | |||||||
\(888\) | −0.962352 | −0.0322944 | ||||||||
\(889\) | 3.76276 | − | 16.5009i | 0.126199 | − | 0.553424i | ||||
\(890\) | − | 36.8289i | − | 1.23451i | ||||||
\(891\) | −0.600231 | − | 0.346544i | −0.0201085 | − | 0.0116096i | ||||
\(892\) | −10.5994 | + | 6.11957i | −0.354894 | + | 0.204898i | ||||
\(893\) | −9.28209 | − | 16.0771i | −0.310613 | − | 0.537998i | ||||
\(894\) | −2.08127 | + | 3.60487i | −0.0696081 | + | 0.120565i | ||||
\(895\) | 42.1163i | 1.40779i | ||||||||
\(896\) | −1.79918 | + | 1.93983i | −0.0601064 | + | 0.0648053i | ||||
\(897\) | 1.66960 | + | 6.29492i | 0.0557465 | + | 0.210181i | ||||
\(898\) | 2.04883 | − | 3.54868i | 0.0683705 | − | 0.118421i | ||||
\(899\) | −7.23238 | + | 4.17562i | −0.241213 | + | 0.139265i | ||||
\(900\) | −1.28036 | − | 2.21764i | −0.0426785 | − | 0.0739213i | ||||
\(901\) | 12.6388 | − | 21.8910i | 0.421059 | − | 0.729295i | ||||
\(902\) | 8.15874i | 0.271656i | ||||||||
\(903\) | −12.5647 | + | 3.87845i | −0.418126 | + | 0.129067i | ||||
\(904\) | − | 8.21218i | − | 0.273133i | ||||||
\(905\) | 47.9969 | + | 27.7110i | 1.59547 | + | 0.921146i | ||||
\(906\) | −0.228464 | − | 0.395710i | −0.00759019 | − | 0.0131466i | ||||
\(907\) | −25.3044 | − | 43.8285i | −0.840219 | − | 1.45530i | −0.889709 | − | 0.456528i | \(-0.849093\pi\) |
0.0494896 | − | 0.998775i | \(-0.484241\pi\) | |||||||
\(908\) | 14.5558 | + | 8.40380i | 0.483052 | + | 0.278890i | ||||
\(909\) | 8.00347 | 0.265458 | ||||||||
\(910\) | 13.9034 | + | 22.2423i | 0.460892 | + | 0.737326i | ||||
\(911\) | 34.6935 | 1.14945 | 0.574723 | − | 0.818348i | \(-0.305110\pi\) | ||||
0.574723 | + | 0.818348i | \(0.305110\pi\) | |||||||
\(912\) | −1.78106 | − | 1.02829i | −0.0589767 | − | 0.0340502i | ||||
\(913\) | −0.806009 | − | 1.39605i | −0.0266750 | − | 0.0462025i | ||||
\(914\) | −3.70033 | − | 6.40916i | −0.122396 | − | 0.211996i | ||||
\(915\) | 23.9661 | + | 13.8368i | 0.792295 | + | 0.457432i | ||||
\(916\) | 22.2869i | 0.736381i | ||||||||
\(917\) | −3.76894 | − | 3.49566i | −0.124461 | − | 0.115437i | ||||
\(918\) | 6.36697i | 0.210141i | ||||||||
\(919\) | 7.62505 | − | 13.2070i | 0.251527 | − | 0.435658i | −0.712419 | − | 0.701754i | \(-0.752401\pi\) |
0.963946 | + | 0.266096i | \(0.0857339\pi\) | |||||||
\(920\) | 2.48332 | + | 4.30123i | 0.0818725 | + | 0.141807i | ||||
\(921\) | −23.0185 | + | 13.2897i | −0.758484 | + | 0.437911i | ||||
\(922\) | −0.636237 | + | 1.10199i | −0.0209534 | + | 0.0362923i | ||||
\(923\) | −26.7726 | + | 7.10092i | −0.881232 | + | 0.233730i | ||||
\(924\) | 1.78784 | + | 0.407687i | 0.0588157 | + | 0.0134119i | ||||
\(925\) | 2.46430i | 0.0810258i | ||||||||
\(926\) | 17.1810 | − | 29.7583i | 0.564602 | − | 0.977920i | ||||
\(927\) | 6.29145 | + | 10.8971i | 0.206638 | + | 0.357908i | ||||
\(928\) | 7.66619 | − | 4.42608i | 0.251655 | − | 0.145293i | ||||
\(929\) | 31.1416 | + | 17.9796i | 1.02172 | + | 0.589892i | 0.914603 | − | 0.404354i | \(-0.132503\pi\) |
0.107121 | + | 0.994246i | \(0.465837\pi\) | |||||||
\(930\) | 2.59408i | 0.0850632i | ||||||||
\(931\) | −8.11438 | − | 11.8914i | −0.265938 | − | 0.389724i | ||||
\(932\) | −18.1345 | −0.594017 | ||||||||
\(933\) | 5.31600 | − | 9.20758i | 0.174038 | − | 0.301443i | ||||
\(934\) | 25.4807 | − | 14.7113i | 0.833752 | − | 0.481367i | ||||
\(935\) | −6.06697 | − | 10.5083i | −0.198411 | − | 0.343658i | ||||
\(936\) | 0.942023 | − | 3.48032i | 0.0307910 | − | 0.113758i | ||||
\(937\) | −55.4856 | −1.81263 | −0.906317 | − | 0.422598i | \(-0.861118\pi\) | ||||
−0.906317 | + | 0.422598i | \(0.861118\pi\) | |||||||
\(938\) | 5.70998 | − | 25.0402i | 0.186438 | − | 0.817591i | ||||
\(939\) | 26.8178 | 0.875164 | ||||||||
\(940\) | 12.4102 | − | 21.4952i | 0.404777 | − | 0.701095i | ||||
\(941\) | −21.1317 | + | 12.2004i | −0.688875 | + | 0.397722i | −0.803190 | − | 0.595722i | \(-0.796866\pi\) |
0.114316 | + | 0.993444i | \(0.463532\pi\) | |||||||
\(942\) | −1.34377 | + | 0.775828i | −0.0437825 | + | 0.0252778i | ||||
\(943\) | 18.4139 | + | 10.6313i | 0.599640 | + | 0.346202i | ||||
\(944\) | 12.1292i | 0.394771i | ||||||||
\(945\) | −4.94716 | + | 5.33391i | −0.160931 | + | 0.173512i | ||||
\(946\) | −3.44472 | −0.111997 | ||||||||
\(947\) | 5.98798 | + | 3.45716i | 0.194583 | + | 0.112343i | 0.594126 | − | 0.804372i | \(-0.297498\pi\) |
−0.399543 | + | 0.916714i | \(0.630831\pi\) | |||||||
\(948\) | −0.339330 | − | 0.587736i | −0.0110209 | − | 0.0190888i | ||||
\(949\) | 14.3807 | + | 14.4539i | 0.466817 | + | 0.469193i | ||||
\(950\) | −2.63316 | + | 4.56077i | −0.0854311 | + | 0.147971i | ||||
\(951\) | − | 14.7990i | − | 0.479892i | ||||||
\(952\) | −4.96850 | − | 16.0960i | −0.161030 | − | 0.521676i | ||||
\(953\) | 11.5990 | 0.375727 | 0.187864 | − | 0.982195i | \(-0.439844\pi\) | ||||
0.187864 | + | 0.982195i | \(0.439844\pi\) | |||||||
\(954\) | −3.43821 | − | 1.98505i | −0.111316 | − | 0.0642685i | ||||
\(955\) | 45.6386 | − | 26.3495i | 1.47683 | − | 0.852649i | ||||
\(956\) | −9.77567 | + | 5.64399i | −0.316168 | + | 0.182540i | ||||
\(957\) | −5.31334 | − | 3.06766i | −0.171756 | − | 0.0991633i | ||||
\(958\) | 3.88015 | 0.125362 | ||||||||
\(959\) | −0.0356090 | − | 0.115359i | −0.00114987 | − | 0.00372515i | ||||
\(960\) | − | 2.74967i | − | 0.0887454i | ||||||
\(961\) | −15.0550 | + | 26.0760i | −0.485645 | + | 0.841161i | ||||
\(962\) | −2.45974 | + | 2.44729i | −0.0793054 | + | 0.0789038i | ||||
\(963\) | −5.06993 | − | 8.78138i | −0.163376 | − | 0.282976i | ||||
\(964\) | −7.51594 | − | 4.33933i | −0.242072 | − | 0.139760i | ||||
\(965\) | 10.2282 | 0.329257 | ||||||||
\(966\) | 3.24979 | − | 3.50385i | 0.104560 | − | 0.112734i | ||||
\(967\) | − | 55.2168i | − | 1.77565i | −0.460179 | − | 0.887826i | \(-0.652215\pi\) | ||
0.460179 | − | 0.887826i | \(-0.347785\pi\) | |||||||
\(968\) | −9.11027 | − | 5.25982i | −0.292815 | − | 0.169057i | ||||
\(969\) | 11.3399 | − | 6.54712i | 0.364291 | − | 0.210324i | ||||
\(970\) | 23.5740 | − | 13.6105i | 0.756916 | − | 0.437006i | ||||
\(971\) | −14.6904 | + | 25.4446i | −0.471438 | + | 0.816555i | −0.999466 | − | 0.0326719i | \(-0.989598\pi\) |
0.528028 | + | 0.849227i | \(0.322932\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 12.2749 | − | 53.8295i | 0.393515 | − | 1.72569i | ||||
\(974\) | 14.5821 | 0.467242 | ||||||||
\(975\) | −8.91208 | − | 2.41225i | −0.285415 | − | 0.0772537i | ||||
\(976\) | 5.03217 | + | 8.71597i | 0.161076 | + | 0.278992i | ||||
\(977\) | 24.0268 | − | 13.8719i | 0.768687 | − | 0.443802i | −0.0637191 | − | 0.997968i | \(-0.520296\pi\) |
0.832406 | + | 0.554166i | \(0.186963\pi\) | |||||||
\(978\) | −2.99238 | + | 5.18296i | −0.0956858 | + | 0.165733i | ||||
\(979\) | −9.28316 | −0.296691 | ||||||||
\(980\) | 8.34433 | − | 17.3449i | 0.266550 | − | 0.554064i | ||||
\(981\) | − | 12.4695i | − | 0.398119i | ||||||
\(982\) | 16.6808 | + | 9.63064i | 0.532305 | + | 0.307326i | ||||
\(983\) | 42.1491 | − | 24.3348i | 1.34435 | − | 0.776160i | 0.356906 | − | 0.934140i | \(-0.383832\pi\) |
0.987442 | + | 0.157981i | \(0.0504984\pi\) | |||||||
\(984\) | −5.88580 | − | 10.1945i | −0.187632 | − | 0.324989i | ||||
\(985\) | 13.0017 | − | 22.5197i | 0.414270 | − | 0.717536i | ||||
\(986\) | 56.3614i | 1.79491i | ||||||||
\(987\) | −23.2847 | − | 5.30967i | −0.741159 | − | 0.169009i | ||||
\(988\) | −7.16732 | + | 1.90099i | −0.228023 | + | 0.0604786i | ||||
\(989\) | −4.48866 | + | 7.77458i | −0.142731 | + | 0.247217i | ||||
\(990\) | −1.65044 | + | 0.952882i | −0.0524544 | + | 0.0302846i | ||||
\(991\) | −18.9014 | − | 32.7382i | −0.600422 | − | 1.03996i | −0.992757 | − | 0.120139i | \(-0.961666\pi\) |
0.392335 | − | 0.919822i | \(-0.371667\pi\) | |||||||
\(992\) | −0.471706 | + | 0.817019i | −0.0149767 | + | 0.0259404i | ||||
\(993\) | − | 6.92849i | − | 0.219869i | ||||||
\(994\) | 14.9021 | + | 13.8215i | 0.472664 | + | 0.438392i | ||||
\(995\) | − | 9.54123i | − | 0.302477i | ||||||
\(996\) | 2.01425 | + | 1.16293i | 0.0638239 | + | 0.0368487i | ||||
\(997\) | −9.99148 | − | 17.3058i | −0.316433 | − | 0.548079i | 0.663308 | − | 0.748347i | \(-0.269152\pi\) |
−0.979741 | + | 0.200268i | \(0.935819\pi\) | |||||||
\(998\) | −9.77954 | − | 16.9387i | −0.309566 | − | 0.536184i | ||||
\(999\) | −0.833421 | − | 0.481176i | −0.0263683 | − | 0.0152237i |
(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 | 546.2.bk.c.415.10 | yes | 20 | |
3.2 | odd | 2 | 1638.2.dm.e.415.1 | 20 | |||
7.2 | even | 3 | 3822.2.c.m.883.1 | 10 | |||
7.4 | even | 3 | inner | 546.2.bk.c.25.1 | ✓ | 20 | |
7.5 | odd | 6 | 3822.2.c.n.883.5 | 10 | |||
13.12 | even | 2 | inner | 546.2.bk.c.415.1 | yes | 20 | |
21.11 | odd | 6 | 1638.2.dm.e.1117.10 | 20 | |||
39.38 | odd | 2 | 1638.2.dm.e.415.10 | 20 | |||
91.12 | odd | 6 | 3822.2.c.n.883.6 | 10 | |||
91.25 | even | 6 | inner | 546.2.bk.c.25.10 | yes | 20 | |
91.51 | even | 6 | 3822.2.c.m.883.10 | 10 | |||
273.116 | odd | 6 | 1638.2.dm.e.1117.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bk.c.25.1 | ✓ | 20 | 7.4 | even | 3 | inner | |
546.2.bk.c.25.10 | yes | 20 | 91.25 | even | 6 | inner | |
546.2.bk.c.415.1 | yes | 20 | 13.12 | even | 2 | inner | |
546.2.bk.c.415.10 | yes | 20 | 1.1 | even | 1 | trivial | |
1638.2.dm.e.415.1 | 20 | 3.2 | odd | 2 | |||
1638.2.dm.e.415.10 | 20 | 39.38 | odd | 2 | |||
1638.2.dm.e.1117.1 | 20 | 273.116 | odd | 6 | |||
1638.2.dm.e.1117.10 | 20 | 21.11 | odd | 6 | |||
3822.2.c.m.883.1 | 10 | 7.2 | even | 3 | |||
3822.2.c.m.883.10 | 10 | 91.51 | even | 6 | |||
3822.2.c.n.883.5 | 10 | 7.5 | odd | 6 | |||
3822.2.c.n.883.6 | 10 | 91.12 | odd | 6 |