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 | 415.6 | ||
Root | \(-2.62200 + 1.51381i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.415 |
Dual form | 546.2.bk.c.25.6 |
$q$-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 | ||||
\(5\) | −2.62200 | − | 1.51381i | −1.17259 | − | 0.676998i | −0.218305 | − | 0.975881i | \(-0.570053\pi\) |
−0.954290 | + | 0.298883i | \(0.903386\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −2.43101 | + | 1.04411i | −0.918837 | + | 0.394638i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.51381 | − | 2.62200i | −0.478710 | − | 0.829150i | ||||
\(11\) | −3.75189 | + | 2.16615i | −1.13124 | + | 0.653119i | −0.944245 | − | 0.329242i | \(-0.893207\pi\) |
−0.186991 | + | 0.982362i | \(0.559873\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −0.613563 | + | 3.55296i | −0.170172 | + | 0.985414i | ||||
\(14\) | −2.62738 | − | 0.311278i | −0.702196 | − | 0.0831925i | ||||
\(15\) | − | 3.02763i | − | 0.781730i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.721788 | − | 1.25017i | −0.175059 | − | 0.303211i | 0.765123 | − | 0.643885i | \(-0.222678\pi\) |
−0.940182 | + | 0.340673i | \(0.889345\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 1.12988 | + | 0.652339i | 0.259213 | + | 0.149657i | 0.623976 | − | 0.781444i | \(-0.285516\pi\) |
−0.364762 | + | 0.931101i | \(0.618850\pi\) | |||||||
\(20\) | − | 3.02763i | − | 0.676998i | ||||||
\(21\) | −2.11974 | − | 1.58326i | −0.462564 | − | 0.345496i | ||||
\(22\) | −4.33230 | −0.923650 | ||||||||
\(23\) | −2.36147 | + | 4.09019i | −0.492402 | + | 0.852865i | −0.999962 | − | 0.00875181i | \(-0.997214\pi\) |
0.507560 | + | 0.861616i | \(0.330548\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 2.08326 | + | 3.60832i | 0.416653 | + | 0.721663i | ||||
\(26\) | −2.30784 | + | 2.77017i | −0.452605 | + | 0.543276i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.11974 | − | 1.58326i | −0.400592 | − | 0.299208i | ||||
\(29\) | 3.42053 | 0.635177 | 0.317588 | − | 0.948229i | \(-0.397127\pi\) | ||||
0.317588 | + | 0.948229i | \(0.397127\pi\) | |||||||
\(30\) | 1.51381 | − | 2.62200i | 0.276383 | − | 0.478710i | ||||
\(31\) | 1.46819 | − | 0.847661i | 0.263695 | − | 0.152244i | −0.362324 | − | 0.932052i | \(-0.618017\pi\) |
0.626019 | + | 0.779808i | \(0.284683\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −3.75189 | − | 2.16615i | −0.653119 | − | 0.377079i | ||||
\(34\) | − | 1.44358i | − | 0.247571i | ||||||
\(35\) | 7.95472 | + | 0.942433i | 1.34459 | + | 0.159300i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 9.89112 | + | 5.71064i | 1.62609 | + | 0.938823i | 0.985244 | + | 0.171153i | \(0.0547492\pi\) |
0.640845 | + | 0.767670i | \(0.278584\pi\) | |||||||
\(38\) | 0.652339 | + | 1.12988i | 0.105823 | + | 0.183291i | ||||
\(39\) | −3.38374 | + | 1.24512i | −0.541832 | + | 0.199379i | ||||
\(40\) | 1.51381 | − | 2.62200i | 0.239355 | − | 0.414575i | ||||
\(41\) | − | 8.53413i | − | 1.33281i | −0.745591 | − | 0.666403i | \(-0.767833\pi\) | ||
0.745591 | − | 0.666403i | \(-0.232167\pi\) | |||||||
\(42\) | −1.04411 | − | 2.43101i | −0.161110 | − | 0.375114i | ||||
\(43\) | −5.10592 | −0.778646 | −0.389323 | − | 0.921101i | \(-0.627291\pi\) | ||||
−0.389323 | + | 0.921101i | \(0.627291\pi\) | |||||||
\(44\) | −3.75189 | − | 2.16615i | −0.565618 | − | 0.326560i | ||||
\(45\) | 2.62200 | − | 1.51381i | 0.390865 | − | 0.225666i | ||||
\(46\) | −4.09019 | + | 2.36147i | −0.603066 | + | 0.348180i | ||||
\(47\) | −7.28379 | − | 4.20530i | −1.06245 | − | 0.613406i | −0.136342 | − | 0.990662i | \(-0.543534\pi\) |
−0.926109 | + | 0.377256i | \(0.876868\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.81965 | − | 5.07651i | 0.688522 | − | 0.725216i | ||||
\(50\) | 4.16653i | 0.589236i | ||||||||
\(51\) | 0.721788 | − | 1.25017i | 0.101070 | − | 0.175059i | ||||
\(52\) | −3.38374 | + | 1.24512i | −0.469240 | + | 0.172667i | ||||
\(53\) | 2.05296 | + | 3.55583i | 0.281996 | + | 0.488431i | 0.971876 | − | 0.235492i | \(-0.0756702\pi\) |
−0.689880 | + | 0.723924i | \(0.742337\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 13.1166 | 1.76864 | ||||||||
\(56\) | −1.04411 | − | 2.43101i | −0.139526 | − | 0.324858i | ||||
\(57\) | 1.30468i | 0.172809i | ||||||||
\(58\) | 2.96227 | + | 1.71027i | 0.388965 | + | 0.224569i | ||||
\(59\) | 4.34545 | − | 2.50885i | 0.565730 | − | 0.326624i | −0.189712 | − | 0.981840i | \(-0.560756\pi\) |
0.755442 | + | 0.655215i | \(0.227422\pi\) | |||||||
\(60\) | 2.62200 | − | 1.51381i | 0.338499 | − | 0.195432i | ||||
\(61\) | −0.505338 | + | 0.875271i | −0.0647019 | + | 0.112067i | −0.896562 | − | 0.442919i | \(-0.853943\pi\) |
0.831860 | + | 0.554986i | \(0.187276\pi\) | |||||||
\(62\) | 1.69532 | 0.215306 | ||||||||
\(63\) | 0.311278 | − | 2.62738i | 0.0392173 | − | 0.331018i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.98728 | − | 8.38705i | 0.866666 | − | 1.04029i | ||||
\(66\) | −2.16615 | − | 3.75189i | −0.266635 | − | 0.461825i | ||||
\(67\) | 0.412703 | − | 0.238274i | 0.0504197 | − | 0.0291098i | −0.474578 | − | 0.880213i | \(-0.657399\pi\) |
0.524998 | + | 0.851103i | \(0.324066\pi\) | |||||||
\(68\) | 0.721788 | − | 1.25017i | 0.0875296 | − | 0.151606i | ||||
\(69\) | −4.72295 | −0.568576 | ||||||||
\(70\) | 6.41777 | + | 4.79353i | 0.767070 | + | 0.572936i | ||||
\(71\) | 12.4996i | 1.48343i | 0.670717 | + | 0.741713i | \(0.265986\pi\) | ||||
−0.670717 | + | 0.741713i | \(0.734014\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −3.42087 | + | 1.97504i | −0.400382 | + | 0.231161i | −0.686649 | − | 0.726989i | \(-0.740919\pi\) |
0.286267 | + | 0.958150i | \(0.407586\pi\) | |||||||
\(74\) | 5.71064 | + | 9.89112i | 0.663848 | + | 1.14982i | ||||
\(75\) | −2.08326 | + | 3.60832i | −0.240554 | + | 0.416653i | ||||
\(76\) | 1.30468i | 0.149657i | ||||||||
\(77\) | 6.85917 | − | 9.18334i | 0.781675 | − | 1.04654i | ||||
\(78\) | −3.55296 | − | 0.613563i | −0.402294 | − | 0.0694723i | ||||
\(79\) | −7.34649 | + | 12.7245i | −0.826545 | + | 1.43162i | 0.0741882 | + | 0.997244i | \(0.476363\pi\) |
−0.900733 | + | 0.434373i | \(0.856970\pi\) | |||||||
\(80\) | 2.62200 | − | 1.51381i | 0.293149 | − | 0.169249i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.26706 | − | 7.39077i | 0.471218 | − | 0.816174i | ||||
\(83\) | − | 17.0583i | − | 1.87239i | −0.351485 | − | 0.936194i | \(-0.614323\pi\) | ||
0.351485 | − | 0.936194i | \(-0.385677\pi\) | |||||||
\(84\) | 0.311278 | − | 2.62738i | 0.0339632 | − | 0.286670i | ||||
\(85\) | 4.37061i | 0.474059i | ||||||||
\(86\) | −4.42186 | − | 2.55296i | −0.476821 | − | 0.275293i | ||||
\(87\) | 1.71027 | + | 2.96227i | 0.183360 | + | 0.317588i | ||||
\(88\) | −2.16615 | − | 3.75189i | −0.230913 | − | 0.399952i | ||||
\(89\) | 6.04482 | + | 3.48998i | 0.640750 | + | 0.369937i | 0.784903 | − | 0.619618i | \(-0.212713\pi\) |
−0.144153 | + | 0.989555i | \(0.546046\pi\) | |||||||
\(90\) | 3.02763 | 0.319140 | ||||||||
\(91\) | −2.21812 | − | 9.27793i | −0.232522 | − | 0.972591i | ||||
\(92\) | −4.72295 | −0.492402 | ||||||||
\(93\) | 1.46819 | + | 0.847661i | 0.152244 | + | 0.0878984i | ||||
\(94\) | −4.20530 | − | 7.28379i | −0.433744 | − | 0.751266i | ||||
\(95\) | −1.97504 | − | 3.42087i | −0.202635 | − | 0.350973i | ||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 15.9110i | 1.61552i | 0.589513 | + | 0.807759i | \(0.299320\pi\) | ||||
−0.589513 | + | 0.807759i | \(0.700680\pi\) | |||||||
\(98\) | 6.71220 | − | 1.98656i | 0.678034 | − | 0.200673i | ||||
\(99\) | − | 4.33230i | − | 0.435413i | ||||||
\(100\) | −2.08326 | + | 3.60832i | −0.208326 | + | 0.360832i | ||||
\(101\) | 0.596703 | + | 1.03352i | 0.0593742 | + | 0.102839i | 0.894185 | − | 0.447698i | \(-0.147756\pi\) |
−0.834810 | + | 0.550537i | \(0.814423\pi\) | |||||||
\(102\) | 1.25017 | − | 0.721788i | 0.123786 | − | 0.0714676i | ||||
\(103\) | −7.58706 | + | 13.1412i | −0.747575 | + | 1.29484i | 0.201407 | + | 0.979508i | \(0.435449\pi\) |
−0.948982 | + | 0.315330i | \(0.897885\pi\) | |||||||
\(104\) | −3.55296 | − | 0.613563i | −0.348397 | − | 0.0601648i | ||||
\(105\) | 3.16119 | + | 7.36020i | 0.308500 | + | 0.718282i | ||||
\(106\) | 4.10592i | 0.398803i | ||||||||
\(107\) | −4.00998 | + | 6.94549i | −0.387659 | + | 0.671445i | −0.992134 | − | 0.125179i | \(-0.960050\pi\) |
0.604475 | + | 0.796624i | \(0.293383\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −0.909907 | + | 0.525335i | −0.0871533 | + | 0.0503180i | −0.542943 | − | 0.839769i | \(-0.682690\pi\) |
0.455790 | + | 0.890087i | \(0.349357\pi\) | |||||||
\(110\) | 11.3593 | + | 6.55830i | 1.08307 | + | 0.625309i | ||||
\(111\) | 11.4213i | 1.08406i | ||||||||
\(112\) | 0.311278 | − | 2.62738i | 0.0294130 | − | 0.248264i | ||||
\(113\) | −9.40986 | −0.885205 | −0.442602 | − | 0.896718i | \(-0.645945\pi\) | ||||
−0.442602 | + | 0.896718i | \(0.645945\pi\) | |||||||
\(114\) | −0.652339 | + | 1.12988i | −0.0610971 | + | 0.105823i | ||||
\(115\) | 12.3836 | − | 7.14967i | 1.15478 | − | 0.666710i | ||||
\(116\) | 1.71027 | + | 2.96227i | 0.158794 | + | 0.275040i | ||||
\(117\) | −2.77017 | − | 2.30784i | −0.256103 | − | 0.213360i | ||||
\(118\) | 5.01770 | 0.461916 | ||||||||
\(119\) | 3.06000 | + | 2.28556i | 0.280510 | + | 0.209517i | ||||
\(120\) | 3.02763 | 0.276383 | ||||||||
\(121\) | 3.88443 | − | 6.72803i | 0.353130 | − | 0.611639i | ||||
\(122\) | −0.875271 | + | 0.505338i | −0.0792433 | + | 0.0457512i | ||||
\(123\) | 7.39077 | − | 4.26706i | 0.666403 | − | 0.384748i | ||||
\(124\) | 1.46819 | + | 0.847661i | 0.131848 | + | 0.0761222i | ||||
\(125\) | 2.52345i | 0.225704i | ||||||||
\(126\) | 1.58326 | − | 2.11974i | 0.141048 | − | 0.188841i | ||||
\(127\) | 1.33765 | 0.118697 | 0.0593487 | − | 0.998237i | \(-0.481098\pi\) | ||||
0.0593487 | + | 0.998237i | \(0.481098\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.55296 | − | 4.42186i | −0.224776 | − | 0.389323i | ||||
\(130\) | 10.2447 | − | 3.76976i | 0.898519 | − | 0.330630i | ||||
\(131\) | −6.17186 | + | 10.6900i | −0.539238 | + | 0.933988i | 0.459707 | + | 0.888071i | \(0.347954\pi\) |
−0.998945 | + | 0.0459173i | \(0.985379\pi\) | |||||||
\(132\) | − | 4.33230i | − | 0.377079i | ||||||
\(133\) | −3.42788 | − | 0.406117i | −0.297235 | − | 0.0352148i | ||||
\(134\) | 0.476549 | 0.0411675 | ||||||||
\(135\) | 2.62200 | + | 1.51381i | 0.225666 | + | 0.130288i | ||||
\(136\) | 1.25017 | − | 0.721788i | 0.107201 | − | 0.0618928i | ||||
\(137\) | 7.91249 | − | 4.56828i | 0.676010 | − | 0.390294i | −0.122340 | − | 0.992488i | \(-0.539040\pi\) |
0.798350 | + | 0.602194i | \(0.205707\pi\) | |||||||
\(138\) | −4.09019 | − | 2.36147i | −0.348180 | − | 0.201022i | ||||
\(139\) | 17.8219 | 1.51164 | 0.755819 | − | 0.654781i | \(-0.227239\pi\) | ||||
0.755819 | + | 0.654781i | \(0.227239\pi\) | |||||||
\(140\) | 3.16119 | + | 7.36020i | 0.267169 | + | 0.622051i | ||||
\(141\) | − | 8.41060i | − | 0.708300i | ||||||
\(142\) | −6.24979 | + | 10.8249i | −0.524471 | + | 0.908410i | ||||
\(143\) | −5.39424 | − | 14.6594i | −0.451089 | − | 1.22588i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −8.96864 | − | 5.17805i | −0.744805 | − | 0.430013i | ||||
\(146\) | −3.95008 | −0.326911 | ||||||||
\(147\) | 6.80621 | + | 1.63569i | 0.561367 | + | 0.134909i | ||||
\(148\) | 11.4213i | 0.938823i | ||||||||
\(149\) | −10.6362 | − | 6.14082i | −0.871352 | − | 0.503075i | −0.00355471 | − | 0.999994i | \(-0.501132\pi\) |
−0.867797 | + | 0.496918i | \(0.834465\pi\) | |||||||
\(150\) | −3.60832 | + | 2.08326i | −0.294618 | + | 0.170098i | ||||
\(151\) | 12.6016 | − | 7.27554i | 1.02550 | − | 0.592075i | 0.109811 | − | 0.993953i | \(-0.464976\pi\) |
0.915693 | + | 0.401878i | \(0.131642\pi\) | |||||||
\(152\) | −0.652339 | + | 1.12988i | −0.0529116 | + | 0.0916457i | ||||
\(153\) | 1.44358 | 0.116706 | ||||||||
\(154\) | 10.5319 | − | 4.52342i | 0.848684 | − | 0.364507i | ||||
\(155\) | −5.13281 | −0.412277 | ||||||||
\(156\) | −2.77017 | − | 2.30784i | −0.221791 | − | 0.184775i | ||||
\(157\) | −4.81431 | − | 8.33864i | −0.384224 | − | 0.665496i | 0.607437 | − | 0.794368i | \(-0.292198\pi\) |
−0.991661 | + | 0.128872i | \(0.958864\pi\) | |||||||
\(158\) | −12.7245 | + | 7.34649i | −1.01231 | + | 0.584455i | ||||
\(159\) | −2.05296 | + | 3.55583i | −0.162810 | + | 0.281996i | ||||
\(160\) | 3.02763 | 0.239355 | ||||||||
\(161\) | 1.47015 | − | 12.4090i | 0.115864 | − | 0.977964i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 14.6824 | + | 8.47691i | 1.15002 | + | 0.663963i | 0.948892 | − | 0.315602i | \(-0.102207\pi\) |
0.201126 | + | 0.979565i | \(0.435540\pi\) | |||||||
\(164\) | 7.39077 | − | 4.26706i | 0.577122 | − | 0.333202i | ||||
\(165\) | 6.55830 | + | 11.3593i | 0.510563 | + | 0.884321i | ||||
\(166\) | 8.52913 | − | 14.7729i | 0.661989 | − | 1.14660i | ||||
\(167\) | 23.4489i | 1.81453i | 0.420559 | + | 0.907265i | \(0.361834\pi\) | ||||
−0.420559 | + | 0.907265i | \(0.638166\pi\) | |||||||
\(168\) | 1.58326 | − | 2.11974i | 0.122151 | − | 0.163541i | ||||
\(169\) | −12.2471 | − | 4.35993i | −0.942083 | − | 0.335379i | ||||
\(170\) | −2.18530 | + | 3.78506i | −0.167605 | + | 0.290301i | ||||
\(171\) | −1.12988 | + | 0.652339i | −0.0864044 | + | 0.0498856i | ||||
\(172\) | −2.55296 | − | 4.42186i | −0.194662 | − | 0.337164i | ||||
\(173\) | 8.22674 | − | 14.2491i | 0.625468 | − | 1.08334i | −0.362982 | − | 0.931796i | \(-0.618242\pi\) |
0.988450 | − | 0.151546i | \(-0.0484252\pi\) | |||||||
\(174\) | 3.42053i | 0.259310i | ||||||||
\(175\) | −8.83193 | − | 6.59670i | −0.667631 | − | 0.498664i | ||||
\(176\) | − | 4.33230i | − | 0.326560i | ||||||
\(177\) | 4.34545 | + | 2.50885i | 0.326624 | + | 0.188577i | ||||
\(178\) | 3.48998 | + | 6.04482i | 0.261585 | + | 0.453079i | ||||
\(179\) | −11.1435 | − | 19.3011i | −0.832903 | − | 1.44263i | −0.895726 | − | 0.444606i | \(-0.853344\pi\) |
0.0628236 | − | 0.998025i | \(-0.479989\pi\) | |||||||
\(180\) | 2.62200 | + | 1.51381i | 0.195432 | + | 0.112833i | ||||
\(181\) | 12.4283 | 0.923788 | 0.461894 | − | 0.886935i | \(-0.347170\pi\) | ||||
0.461894 | + | 0.886935i | \(0.347170\pi\) | |||||||
\(182\) | 2.71802 | − | 9.14398i | 0.201473 | − | 0.677797i | ||||
\(183\) | −1.01068 | −0.0747113 | ||||||||
\(184\) | −4.09019 | − | 2.36147i | −0.301533 | − | 0.174090i | ||||
\(185\) | −17.2897 | − | 29.9466i | −1.27116 | − | 2.20172i | ||||
\(186\) | 0.847661 | + | 1.46819i | 0.0621536 | + | 0.107653i | ||||
\(187\) | 5.41613 | + | 3.12700i | 0.396067 | + | 0.228669i | ||||
\(188\) | − | 8.41060i | − | 0.613406i | ||||||
\(189\) | 2.43101 | − | 1.04411i | 0.176830 | − | 0.0759481i | ||||
\(190\) | − | 3.95008i | − | 0.286569i | ||||||
\(191\) | −10.7570 | + | 18.6317i | −0.778352 | + | 1.34815i | 0.154538 | + | 0.987987i | \(0.450611\pi\) |
−0.932891 | + | 0.360159i | \(0.882722\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −1.66424 | + | 0.960851i | −0.119795 | + | 0.0691636i | −0.558700 | − | 0.829370i | \(-0.688700\pi\) |
0.438905 | + | 0.898533i | \(0.355366\pi\) | |||||||
\(194\) | −7.95550 | + | 13.7793i | −0.571172 | + | 0.989299i | ||||
\(195\) | 10.7570 | + | 1.85764i | 0.770328 | + | 0.133028i | ||||
\(196\) | 6.80621 | + | 1.63569i | 0.486158 | + | 0.116835i | ||||
\(197\) | 5.55108i | 0.395498i | 0.980253 | + | 0.197749i | \(0.0633631\pi\) | ||||
−0.980253 | + | 0.197749i | \(0.936637\pi\) | |||||||
\(198\) | 2.16615 | − | 3.75189i | 0.153942 | − | 0.266635i | ||||
\(199\) | −3.54486 | − | 6.13988i | −0.251288 | − | 0.435244i | 0.712592 | − | 0.701578i | \(-0.247521\pi\) |
−0.963881 | + | 0.266334i | \(0.914188\pi\) | |||||||
\(200\) | −3.60832 | + | 2.08326i | −0.255147 | + | 0.147309i | ||||
\(201\) | 0.412703 | + | 0.238274i | 0.0291098 | + | 0.0168066i | ||||
\(202\) | 1.19341i | 0.0839678i | ||||||||
\(203\) | −8.31536 | + | 3.57142i | −0.583624 | + | 0.250665i | ||||
\(204\) | 1.44358 | 0.101070 | ||||||||
\(205\) | −12.9191 | + | 22.3765i | −0.902307 | + | 1.56284i | ||||
\(206\) | −13.1412 | + | 7.58706i | −0.915589 | + | 0.528615i | ||||
\(207\) | −2.36147 | − | 4.09019i | −0.164134 | − | 0.284288i | ||||
\(208\) | −2.77017 | − | 2.30784i | −0.192077 | − | 0.160020i | ||||
\(209\) | −5.65226 | −0.390975 | ||||||||
\(210\) | −0.942433 | + | 7.95472i | −0.0650340 | + | 0.548928i | ||||
\(211\) | 24.2839 | 1.67177 | 0.835885 | − | 0.548904i | \(-0.184955\pi\) | ||||
0.835885 | + | 0.548904i | \(0.184955\pi\) | |||||||
\(212\) | −2.05296 | + | 3.55583i | −0.140998 | + | 0.244216i | ||||
\(213\) | −10.8249 | + | 6.24979i | −0.741713 | + | 0.428228i | ||||
\(214\) | −6.94549 | + | 4.00998i | −0.474784 | + | 0.274116i | ||||
\(215\) | 13.3877 | + | 7.72942i | 0.913037 | + | 0.527142i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −2.68414 | + | 3.59364i | −0.182211 | + | 0.243952i | ||||
\(218\) | −1.05067 | −0.0711604 | ||||||||
\(219\) | −3.42087 | − | 1.97504i | −0.231161 | − | 0.133461i | ||||
\(220\) | 6.55830 | + | 11.3593i | 0.442161 | + | 0.765844i | ||||
\(221\) | 4.88468 | − | 1.79742i | 0.328579 | − | 0.120908i | ||||
\(222\) | −5.71064 | + | 9.89112i | −0.383273 | + | 0.663848i | ||||
\(223\) | − | 2.01368i | − | 0.134846i | −0.997724 | − | 0.0674230i | \(-0.978522\pi\) | ||
0.997724 | − | 0.0674230i | \(-0.0214777\pi\) | |||||||
\(224\) | 1.58326 | − | 2.11974i | 0.105786 | − | 0.141631i | ||||
\(225\) | −4.16653 | −0.277768 | ||||||||
\(226\) | −8.14917 | − | 4.70493i | −0.542075 | − | 0.312967i | ||||
\(227\) | −5.33689 | + | 3.08125i | −0.354222 | + | 0.204510i | −0.666543 | − | 0.745466i | \(-0.732227\pi\) |
0.312321 | + | 0.949977i | \(0.398893\pi\) | |||||||
\(228\) | −1.12988 | + | 0.652339i | −0.0748284 | + | 0.0432022i | ||||
\(229\) | −13.1472 | − | 7.59052i | −0.868789 | − | 0.501596i | −0.00184346 | − | 0.999998i | \(-0.500587\pi\) |
−0.866946 | + | 0.498403i | \(0.833920\pi\) | |||||||
\(230\) | 14.2993 | 0.942870 | ||||||||
\(231\) | 11.3826 | + | 1.34855i | 0.748920 | + | 0.0887280i | ||||
\(232\) | 3.42053i | 0.224569i | ||||||||
\(233\) | 10.4014 | − | 18.0157i | 0.681417 | − | 1.18025i | −0.293132 | − | 0.956072i | \(-0.594698\pi\) |
0.974549 | − | 0.224176i | \(-0.0719691\pi\) | |||||||
\(234\) | −1.24512 | − | 3.38374i | −0.0813960 | − | 0.221202i | ||||
\(235\) | 12.7321 | + | 22.0526i | 0.830549 | + | 1.43855i | ||||
\(236\) | 4.34545 | + | 2.50885i | 0.282865 | + | 0.163312i | ||||
\(237\) | −14.6930 | −0.954412 | ||||||||
\(238\) | 1.50726 | + | 3.50935i | 0.0977009 | + | 0.227477i | ||||
\(239\) | 6.60635i | 0.427329i | 0.976907 | + | 0.213665i | \(0.0685400\pi\) | ||||
−0.976907 | + | 0.213665i | \(0.931460\pi\) | |||||||
\(240\) | 2.62200 | + | 1.51381i | 0.169249 | + | 0.0977162i | ||||
\(241\) | −19.6527 | + | 11.3465i | −1.26594 | + | 0.730892i | −0.974218 | − | 0.225611i | \(-0.927562\pi\) |
−0.291724 | + | 0.956503i | \(0.594229\pi\) | |||||||
\(242\) | 6.72803 | − | 3.88443i | 0.432494 | − | 0.249701i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −1.01068 | −0.0647019 | ||||||||
\(245\) | −20.3220 | + | 6.01456i | −1.29833 | + | 0.384256i | ||||
\(246\) | 8.53413 | 0.544116 | ||||||||
\(247\) | −3.01099 | + | 3.61418i | −0.191585 | + | 0.229965i | ||||
\(248\) | 0.847661 | + | 1.46819i | 0.0538266 | + | 0.0932303i | ||||
\(249\) | 14.7729 | − | 8.52913i | 0.936194 | − | 0.540512i | ||||
\(250\) | −1.26173 | + | 2.18537i | −0.0797985 | + | 0.138215i | ||||
\(251\) | 4.82111 | 0.304306 | 0.152153 | − | 0.988357i | \(-0.451379\pi\) | ||||
0.152153 | + | 0.988357i | \(0.451379\pi\) | |||||||
\(252\) | 2.43101 | − | 1.04411i | 0.153139 | − | 0.0657730i | ||||
\(253\) | − | 20.4613i | − | 1.28639i | ||||||
\(254\) | 1.15844 | + | 0.668825i | 0.0726870 | + | 0.0419658i | ||||
\(255\) | −3.78506 | + | 2.18530i | −0.237029 | + | 0.136849i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.91636 | − | 5.05128i | 0.181917 | − | 0.315090i | −0.760616 | − | 0.649202i | \(-0.775103\pi\) |
0.942533 | + | 0.334112i | \(0.108436\pi\) | |||||||
\(258\) | − | 5.10592i | − | 0.317881i | ||||||
\(259\) | −30.0080 | − | 3.55519i | −1.86461 | − | 0.220909i | ||||
\(260\) | 10.7570 | + | 1.85764i | 0.667124 | + | 0.115206i | ||||
\(261\) | −1.71027 | + | 2.96227i | −0.105863 | + | 0.183360i | ||||
\(262\) | −10.6900 | + | 6.17186i | −0.660429 | + | 0.381299i | ||||
\(263\) | 6.68731 | + | 11.5828i | 0.412357 | + | 0.714224i | 0.995147 | − | 0.0983992i | \(-0.0313722\pi\) |
−0.582790 | + | 0.812623i | \(0.698039\pi\) | |||||||
\(264\) | 2.16615 | − | 3.75189i | 0.133317 | − | 0.230913i | ||||
\(265\) | − | 12.4312i | − | 0.763643i | ||||||
\(266\) | −2.76557 | − | 2.06565i | −0.169568 | − | 0.126653i | ||||
\(267\) | 6.97996i | 0.427167i | ||||||||
\(268\) | 0.412703 | + | 0.238274i | 0.0252099 | + | 0.0145549i | ||||
\(269\) | −6.42254 | − | 11.1242i | −0.391589 | − | 0.678252i | 0.601070 | − | 0.799196i | \(-0.294741\pi\) |
−0.992659 | + | 0.120944i | \(0.961408\pi\) | |||||||
\(270\) | 1.51381 | + | 2.62200i | 0.0921278 | + | 0.159570i | ||||
\(271\) | −18.0901 | − | 10.4443i | −1.09890 | − | 0.634447i | −0.162965 | − | 0.986632i | \(-0.552106\pi\) |
−0.935931 | + | 0.352184i | \(0.885439\pi\) | |||||||
\(272\) | 1.44358 | 0.0875296 | ||||||||
\(273\) | 6.92586 | − | 6.55991i | 0.419172 | − | 0.397024i | ||||
\(274\) | 9.13656 | 0.551960 | ||||||||
\(275\) | −15.6323 | − | 9.02533i | −0.942665 | − | 0.544248i | ||||
\(276\) | −2.36147 | − | 4.09019i | −0.142144 | − | 0.246201i | ||||
\(277\) | −13.1983 | − | 22.8602i | −0.793010 | − | 1.37353i | −0.924095 | − | 0.382163i | \(-0.875179\pi\) |
0.131085 | − | 0.991371i | \(-0.458154\pi\) | |||||||
\(278\) | 15.4343 | + | 8.91097i | 0.925685 | + | 0.534445i | ||||
\(279\) | 1.69532i | 0.101496i | ||||||||
\(280\) | −0.942433 | + | 7.95472i | −0.0563211 | + | 0.475385i | ||||
\(281\) | 12.6024i | 0.751798i | 0.926661 | + | 0.375899i | \(0.122666\pi\) | ||||
−0.926661 | + | 0.375899i | \(0.877334\pi\) | |||||||
\(282\) | 4.20530 | − | 7.28379i | 0.250422 | − | 0.433744i | ||||
\(283\) | 0.0878874 | + | 0.152225i | 0.00522437 | + | 0.00904887i | 0.868626 | − | 0.495469i | \(-0.165004\pi\) |
−0.863401 | + | 0.504518i | \(0.831670\pi\) | |||||||
\(284\) | −10.8249 | + | 6.24979i | −0.642343 | + | 0.370857i | ||||
\(285\) | 1.97504 | − | 3.42087i | 0.116991 | − | 0.202635i | ||||
\(286\) | 2.65814 | − | 15.3925i | 0.157179 | − | 0.910178i | ||||
\(287\) | 8.91060 | + | 20.7466i | 0.525976 | + | 1.22463i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 7.45805 | − | 12.9177i | 0.438709 | − | 0.759866i | ||||
\(290\) | −5.17805 | − | 8.96864i | −0.304065 | − | 0.526657i | ||||
\(291\) | −13.7793 | + | 7.95550i | −0.807759 | + | 0.466360i | ||||
\(292\) | −3.42087 | − | 1.97504i | −0.200191 | − | 0.115580i | ||||
\(293\) | − | 0.418273i | − | 0.0244358i | −0.999925 | − | 0.0122179i | \(-0.996111\pi\) | ||
0.999925 | − | 0.0122179i | \(-0.00388917\pi\) | |||||||
\(294\) | 5.07651 | + | 4.81965i | 0.296068 | + | 0.281088i | ||||
\(295\) | −15.1917 | −0.884496 | ||||||||
\(296\) | −5.71064 | + | 9.89112i | −0.331924 | + | 0.574909i | ||||
\(297\) | 3.75189 | − | 2.16615i | 0.217706 | − | 0.125693i | ||||
\(298\) | −6.14082 | − | 10.6362i | −0.355728 | − | 0.616139i | ||||
\(299\) | −13.0834 | − | 10.8998i | −0.756632 | − | 0.630353i | ||||
\(300\) | −4.16653 | −0.240554 | ||||||||
\(301\) | 12.4126 | − | 5.33117i | 0.715449 | − | 0.307283i | ||||
\(302\) | 14.5511 | 0.837320 | ||||||||
\(303\) | −0.596703 | + | 1.03352i | −0.0342797 | + | 0.0593742i | ||||
\(304\) | −1.12988 | + | 0.652339i | −0.0648033 | + | 0.0374142i | ||||
\(305\) | 2.64999 | − | 1.52998i | 0.151738 | − | 0.0876061i | ||||
\(306\) | 1.25017 | + | 0.721788i | 0.0714676 | + | 0.0412618i | ||||
\(307\) | 13.1766i | 0.752025i | 0.926614 | + | 0.376013i | \(0.122705\pi\) | ||||
−0.926614 | + | 0.376013i | \(0.877295\pi\) | |||||||
\(308\) | 11.3826 | + | 1.34855i | 0.648583 | + | 0.0768407i | ||||
\(309\) | −15.1741 | −0.863225 | ||||||||
\(310\) | −4.44514 | − | 2.56640i | −0.252467 | − | 0.145762i | ||||
\(311\) | 8.61548 | + | 14.9225i | 0.488539 | + | 0.846175i | 0.999913 | − | 0.0131837i | \(-0.00419662\pi\) |
−0.511374 | + | 0.859358i | \(0.670863\pi\) | |||||||
\(312\) | −1.24512 | − | 3.38374i | −0.0704910 | − | 0.191566i | ||||
\(313\) | −4.45429 | + | 7.71506i | −0.251772 | + | 0.436081i | −0.964014 | − | 0.265853i | \(-0.914347\pi\) |
0.712242 | + | 0.701934i | \(0.247680\pi\) | |||||||
\(314\) | − | 9.62863i | − | 0.543375i | ||||||
\(315\) | −4.79353 | + | 6.41777i | −0.270085 | + | 0.361600i | ||||
\(316\) | −14.6930 | −0.826545 | ||||||||
\(317\) | 5.12567 | + | 2.95931i | 0.287886 | + | 0.166211i | 0.636988 | − | 0.770874i | \(-0.280180\pi\) |
−0.349102 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(318\) | −3.55583 | + | 2.05296i | −0.199401 | + | 0.115124i | ||||
\(319\) | −12.8334 | + | 7.40939i | −0.718535 | + | 0.414846i | ||||
\(320\) | 2.62200 | + | 1.51381i | 0.146574 | + | 0.0846247i | ||||
\(321\) | −8.01996 | −0.447630 | ||||||||
\(322\) | 7.47767 | − | 10.0114i | 0.416714 | − | 0.557914i | ||||
\(323\) | − | 1.88340i | − | 0.104795i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −14.0984 | + | 5.18782i | −0.782040 | + | 0.287769i | ||||
\(326\) | 8.47691 | + | 14.6824i | 0.469493 | + | 0.813185i | ||||
\(327\) | −0.909907 | − | 0.525335i | −0.0503180 | − | 0.0290511i | ||||
\(328\) | 8.53413 | 0.471218 | ||||||||
\(329\) | 22.0978 | + | 2.61803i | 1.21829 | + | 0.144337i | ||||
\(330\) | 13.1166i | 0.722045i | ||||||||
\(331\) | −10.1165 | − | 5.84078i | −0.556055 | − | 0.321038i | 0.195506 | − | 0.980703i | \(-0.437365\pi\) |
−0.751560 | + | 0.659664i | \(0.770698\pi\) | |||||||
\(332\) | 14.7729 | − | 8.52913i | 0.810767 | − | 0.468097i | ||||
\(333\) | −9.89112 | + | 5.71064i | −0.542030 | + | 0.312941i | ||||
\(334\) | −11.7245 | + | 20.3073i | −0.641533 | + | 1.11117i | ||||
\(335\) | −1.44281 | −0.0788292 | ||||||||
\(336\) | 2.43101 | − | 1.04411i | 0.132623 | − | 0.0569611i | ||||
\(337\) | 6.30335 | 0.343365 | 0.171683 | − | 0.985152i | \(-0.445080\pi\) | ||||
0.171683 | + | 0.985152i | \(0.445080\pi\) | |||||||
\(338\) | −8.42632 | − | 9.89935i | −0.458331 | − | 0.538454i | ||||
\(339\) | −4.70493 | − | 8.14917i | −0.255537 | − | 0.442602i | ||||
\(340\) | −3.78506 | + | 2.18530i | −0.205274 | + | 0.118515i | ||||
\(341\) | −3.67233 | + | 6.36066i | −0.198868 | + | 0.344449i | ||||
\(342\) | −1.30468 | −0.0705489 | ||||||||
\(343\) | −6.41619 | + | 17.3733i | −0.346442 | + | 0.938072i | ||||
\(344\) | − | 5.10592i | − | 0.275293i | ||||||
\(345\) | 12.3836 | + | 7.14967i | 0.666710 | + | 0.384925i | ||||
\(346\) | 14.2491 | − | 8.22674i | 0.766038 | − | 0.442272i | ||||
\(347\) | 4.78819 | + | 8.29339i | 0.257044 | + | 0.445212i | 0.965449 | − | 0.260594i | \(-0.0839183\pi\) |
−0.708405 | + | 0.705806i | \(0.750585\pi\) | |||||||
\(348\) | −1.71027 | + | 2.96227i | −0.0916799 | + | 0.158794i | ||||
\(349\) | − | 18.6506i | − | 0.998346i | −0.866502 | − | 0.499173i | \(-0.833637\pi\) | ||
0.866502 | − | 0.499173i | \(-0.166363\pi\) | |||||||
\(350\) | −4.35033 | − | 10.1289i | −0.232535 | − | 0.541411i | ||||
\(351\) | 0.613563 | − | 3.55296i | 0.0327496 | − | 0.189643i | ||||
\(352\) | 2.16615 | − | 3.75189i | 0.115456 | − | 0.199976i | ||||
\(353\) | −19.5305 | + | 11.2759i | −1.03950 | + | 0.600156i | −0.919692 | − | 0.392641i | \(-0.871562\pi\) |
−0.119809 | + | 0.992797i | \(0.538228\pi\) | |||||||
\(354\) | 2.50885 | + | 4.34545i | 0.133344 | + | 0.230958i | ||||
\(355\) | 18.9220 | − | 32.7739i | 1.00428 | − | 1.73946i | ||||
\(356\) | 6.97996i | 0.369937i | ||||||||
\(357\) | −0.449353 | + | 3.79282i | −0.0237823 | + | 0.200737i | ||||
\(358\) | − | 22.2870i | − | 1.17790i | ||||||
\(359\) | 18.0748 | + | 10.4355i | 0.953953 | + | 0.550765i | 0.894307 | − | 0.447455i | \(-0.147669\pi\) |
0.0596463 | + | 0.998220i | \(0.481003\pi\) | |||||||
\(360\) | 1.51381 | + | 2.62200i | 0.0797850 | + | 0.138192i | ||||
\(361\) | −8.64891 | − | 14.9803i | −0.455206 | − | 0.788439i | ||||
\(362\) | 10.7632 | + | 6.21415i | 0.565702 | + | 0.326608i | ||||
\(363\) | 7.76886 | 0.407759 | ||||||||
\(364\) | 6.92586 | − | 6.55991i | 0.363014 | − | 0.343833i | ||||
\(365\) | 11.9594 | 0.625981 | ||||||||
\(366\) | −0.875271 | − | 0.505338i | −0.0457512 | − | 0.0264144i | ||||
\(367\) | −5.06944 | − | 8.78053i | −0.264623 | − | 0.458340i | 0.702842 | − | 0.711346i | \(-0.251914\pi\) |
−0.967465 | + | 0.253006i | \(0.918581\pi\) | |||||||
\(368\) | −2.36147 | − | 4.09019i | −0.123100 | − | 0.213216i | ||||
\(369\) | 7.39077 | + | 4.26706i | 0.384748 | + | 0.222134i | ||||
\(370\) | − | 34.5794i | − | 1.79770i | ||||||
\(371\) | −8.70348 | − | 6.50076i | −0.451862 | − | 0.337502i | ||||
\(372\) | 1.69532i | 0.0878984i | ||||||||
\(373\) | −13.1811 | + | 22.8303i | −0.682491 | + | 1.18211i | 0.291728 | + | 0.956501i | \(0.405770\pi\) |
−0.974218 | + | 0.225607i | \(0.927563\pi\) | |||||||
\(374\) | 3.12700 | + | 5.41613i | 0.161693 | + | 0.280061i | ||||
\(375\) | −2.18537 | + | 1.26173i | −0.112852 | + | 0.0651552i | ||||
\(376\) | 4.20530 | − | 7.28379i | 0.216872 | − | 0.375633i | ||||
\(377\) | −2.09871 | + | 12.1530i | −0.108089 | + | 0.625912i | ||||
\(378\) | 2.62738 | + | 0.311278i | 0.135138 | + | 0.0160104i | ||||
\(379\) | − | 34.2225i | − | 1.75789i | −0.476921 | − | 0.878946i | \(-0.658247\pi\) | ||
0.476921 | − | 0.878946i | \(-0.341753\pi\) | |||||||
\(380\) | 1.97504 | − | 3.42087i | 0.101317 | − | 0.175487i | ||||
\(381\) | 0.668825 | + | 1.15844i | 0.0342650 | + | 0.0593487i | ||||
\(382\) | −18.6317 | + | 10.7570i | −0.953283 | + | 0.550378i | ||||
\(383\) | −8.79636 | − | 5.07858i | −0.449473 | − | 0.259503i | 0.258135 | − | 0.966109i | \(-0.416892\pi\) |
−0.707608 | + | 0.706606i | \(0.750226\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −31.8866 | + | 13.6952i | −1.62509 | + | 0.697973i | ||||
\(386\) | −1.92170 | −0.0978121 | ||||||||
\(387\) | 2.55296 | − | 4.42186i | 0.129774 | − | 0.224776i | ||||
\(388\) | −13.7793 | + | 7.95550i | −0.699540 | + | 0.403880i | ||||
\(389\) | 13.1055 | + | 22.6995i | 0.664477 | + | 1.15091i | 0.979427 | + | 0.201800i | \(0.0646791\pi\) |
−0.314949 | + | 0.949108i | \(0.601988\pi\) | |||||||
\(390\) | 8.38705 | + | 6.98728i | 0.424695 | + | 0.353815i | ||||
\(391\) | 6.81793 | 0.344798 | ||||||||
\(392\) | 5.07651 | + | 4.81965i | 0.256402 | + | 0.243429i | ||||
\(393\) | −12.3437 | −0.622659 | ||||||||
\(394\) | −2.77554 | + | 4.80737i | −0.139830 | + | 0.242192i | ||||
\(395\) | 38.5250 | − | 22.2424i | 1.93840 | − | 1.11914i | ||||
\(396\) | 3.75189 | − | 2.16615i | 0.188539 | − | 0.108853i | ||||
\(397\) | 32.3434 | + | 18.6735i | 1.62327 | + | 0.937194i | 0.986038 | + | 0.166520i | \(0.0532529\pi\) |
0.637229 | + | 0.770674i | \(0.280080\pi\) | |||||||
\(398\) | − | 7.08972i | − | 0.355376i | ||||||
\(399\) | −1.36223 | − | 3.17169i | −0.0681969 | − | 0.158783i | ||||
\(400\) | −4.16653 | −0.208326 | ||||||||
\(401\) | 6.62574 | + | 3.82537i | 0.330874 | + | 0.191030i | 0.656229 | − | 0.754562i | \(-0.272151\pi\) |
−0.325355 | + | 0.945592i | \(0.605484\pi\) | |||||||
\(402\) | 0.238274 | + | 0.412703i | 0.0118840 | + | 0.0205838i | ||||
\(403\) | 2.11088 | + | 5.73653i | 0.105150 | + | 0.285757i | ||||
\(404\) | −0.596703 | + | 1.03352i | −0.0296871 | + | 0.0514195i | ||||
\(405\) | 3.02763i | 0.150444i | ||||||||
\(406\) | −8.98702 | − | 1.06474i | −0.446018 | − | 0.0528419i | ||||
\(407\) | −49.4804 | −2.45265 | ||||||||
\(408\) | 1.25017 | + | 0.721788i | 0.0618928 | + | 0.0357338i | ||||
\(409\) | 18.9940 | − | 10.9662i | 0.939192 | − | 0.542243i | 0.0494850 | − | 0.998775i | \(-0.484242\pi\) |
0.889707 | + | 0.456532i | \(0.150909\pi\) | |||||||
\(410\) | −22.3765 | + | 12.9191i | −1.10510 | + | 0.638028i | ||||
\(411\) | 7.91249 | + | 4.56828i | 0.390294 | + | 0.225337i | ||||
\(412\) | −15.1741 | −0.747575 | ||||||||
\(413\) | −7.94433 | + | 10.6362i | −0.390915 | + | 0.523373i | ||||
\(414\) | − | 4.72295i | − | 0.232120i | ||||||
\(415\) | −25.8230 | + | 44.7268i | −1.26760 | + | 2.19555i | ||||
\(416\) | −1.24512 | − | 3.38374i | −0.0610470 | − | 0.165901i | ||||
\(417\) | 8.91097 | + | 15.4343i | 0.436372 | + | 0.755819i | ||||
\(418\) | −4.89500 | − | 2.82613i | −0.239422 | − | 0.138230i | ||||
\(419\) | −3.94624 | −0.192786 | −0.0963932 | − | 0.995343i | \(-0.530731\pi\) | ||||
−0.0963932 | + | 0.995343i | \(0.530731\pi\) | |||||||
\(420\) | −4.79353 | + | 6.41777i | −0.233900 | + | 0.313155i | ||||
\(421\) | − | 13.3130i | − | 0.648836i | −0.945914 | − | 0.324418i | \(-0.894831\pi\) | ||
0.945914 | − | 0.324418i | \(-0.105169\pi\) | |||||||
\(422\) | 21.0305 | + | 12.1419i | 1.02375 | + | 0.591060i | ||||
\(423\) | 7.28379 | − | 4.20530i | 0.354150 | − | 0.204469i | ||||
\(424\) | −3.55583 | + | 2.05296i | −0.172687 | + | 0.0997007i | ||||
\(425\) | 3.00735 | − | 5.20888i | 0.145878 | − | 0.252668i | ||||
\(426\) | −12.4996 | −0.605606 | ||||||||
\(427\) | 0.314601 | − | 2.65543i | 0.0152246 | − | 0.128505i | ||||
\(428\) | −8.01996 | −0.387659 | ||||||||
\(429\) | 9.99827 | − | 12.0012i | 0.482721 | − | 0.579425i | ||||
\(430\) | 7.72942 | + | 13.3877i | 0.372746 | + | 0.645614i | ||||
\(431\) | 32.3134 | − | 18.6562i | 1.55648 | − | 0.898636i | 0.558894 | − | 0.829239i | \(-0.311226\pi\) |
0.997589 | − | 0.0693967i | \(-0.0221074\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −9.35993 | −0.449810 | −0.224905 | − | 0.974381i | \(-0.572207\pi\) | ||||
−0.224905 | + | 0.974381i | \(0.572207\pi\) | |||||||
\(434\) | −4.12135 | + | 1.77011i | −0.197831 | + | 0.0849680i | ||||
\(435\) | − | 10.3561i | − | 0.496537i | ||||||
\(436\) | −0.909907 | − | 0.525335i | −0.0435767 | − | 0.0251590i | ||||
\(437\) | −5.33638 | + | 3.08096i | −0.255274 | + | 0.147382i | ||||
\(438\) | −1.97504 | − | 3.42087i | −0.0943710 | − | 0.163455i | ||||
\(439\) | 11.6412 | − | 20.1631i | 0.555603 | − | 0.962333i | −0.442253 | − | 0.896890i | \(-0.645821\pi\) |
0.997856 | − | 0.0654428i | \(-0.0208460\pi\) | |||||||
\(440\) | 13.1166i | 0.625309i | ||||||||
\(441\) | 1.98656 | + | 6.71220i | 0.0945981 | + | 0.319628i | ||||
\(442\) | 5.12897 | + | 0.885724i | 0.243960 | + | 0.0421296i | ||||
\(443\) | 1.70694 | − | 2.95650i | 0.0810990 | − | 0.140468i | −0.822623 | − | 0.568587i | \(-0.807490\pi\) |
0.903722 | + | 0.428119i | \(0.140824\pi\) | |||||||
\(444\) | −9.89112 | + | 5.71064i | −0.469412 | + | 0.271015i | ||||
\(445\) | −10.5664 | − | 18.3015i | −0.500893 | − | 0.867573i | ||||
\(446\) | 1.00684 | − | 1.74390i | 0.0476753 | − | 0.0825760i | ||||
\(447\) | − | 12.2816i | − | 0.580901i | ||||||
\(448\) | 2.43101 | − | 1.04411i | 0.114855 | − | 0.0493297i | ||||
\(449\) | − | 23.2401i | − | 1.09677i | −0.836227 | − | 0.548383i | \(-0.815244\pi\) | ||
0.836227 | − | 0.548383i | \(-0.184756\pi\) | |||||||
\(450\) | −3.60832 | − | 2.08326i | −0.170098 | − | 0.0982059i | ||||
\(451\) | 18.4862 | + | 32.0191i | 0.870482 | + | 1.50772i | ||||
\(452\) | −4.70493 | − | 8.14917i | −0.221301 | − | 0.383305i | ||||
\(453\) | 12.6016 | + | 7.27554i | 0.592075 | + | 0.341835i | ||||
\(454\) | −6.16251 | −0.289221 | ||||||||
\(455\) | −8.22915 | + | 27.6846i | −0.385788 | + | 1.29787i | ||||
\(456\) | −1.30468 | −0.0610971 | ||||||||
\(457\) | 11.9714 | + | 6.91167i | 0.559997 | + | 0.323314i | 0.753144 | − | 0.657855i | \(-0.228536\pi\) |
−0.193147 | + | 0.981170i | \(0.561870\pi\) | |||||||
\(458\) | −7.59052 | − | 13.1472i | −0.354682 | − | 0.614327i | ||||
\(459\) | 0.721788 | + | 1.25017i | 0.0336902 | + | 0.0583531i | ||||
\(460\) | 12.3836 | + | 7.14967i | 0.577388 | + | 0.333355i | ||||
\(461\) | 22.3943i | 1.04301i | 0.853249 | + | 0.521504i | \(0.174629\pi\) | ||||
−0.853249 | + | 0.521504i | \(0.825371\pi\) | |||||||
\(462\) | 9.18334 | + | 6.85917i | 0.427248 | + | 0.319118i | ||||
\(463\) | 9.18946i | 0.427070i | 0.976935 | + | 0.213535i | \(0.0684978\pi\) | ||||
−0.976935 | + | 0.213535i | \(0.931502\pi\) | |||||||
\(464\) | −1.71027 | + | 2.96227i | −0.0793971 | + | 0.137520i | ||||
\(465\) | −2.56640 | − | 4.44514i | −0.119014 | − | 0.206138i | ||||
\(466\) | 18.0157 | − | 10.4014i | 0.834561 | − | 0.481834i | ||||
\(467\) | −7.09820 | + | 12.2944i | −0.328465 | + | 0.568919i | −0.982208 | − | 0.187799i | \(-0.939865\pi\) |
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(468\) | 0.613563 | − | 3.55296i | 0.0283620 | − | 0.164236i | ||||
\(469\) | −0.754502 | + | 1.01016i | −0.0348397 | + | 0.0466447i | ||||
\(470\) | 25.4642i | 1.17457i | ||||||||
\(471\) | 4.81431 | − | 8.33864i | 0.221832 | − | 0.384224i | ||||
\(472\) | 2.50885 | + | 4.34545i | 0.115479 | + | 0.200016i | ||||
\(473\) | 19.1568 | − | 11.0602i | 0.880833 | − | 0.508549i | ||||
\(474\) | −12.7245 | − | 7.34649i | −0.584455 | − | 0.337435i | ||||
\(475\) | 5.43597i | 0.249419i | ||||||||
\(476\) | −0.449353 | + | 3.79282i | −0.0205960 | + | 0.173843i | ||||
\(477\) | −4.10592 | −0.187997 | ||||||||
\(478\) | −3.30317 | + | 5.72127i | −0.151084 | + | 0.261685i | ||||
\(479\) | 12.2115 | − | 7.05029i | 0.557956 | − | 0.322136i | −0.194369 | − | 0.980929i | \(-0.562266\pi\) |
0.752325 | + | 0.658793i | \(0.228933\pi\) | |||||||
\(480\) | 1.51381 | + | 2.62200i | 0.0690958 | + | 0.119677i | ||||
\(481\) | −26.3585 | + | 31.6389i | −1.20184 | + | 1.44261i | ||||
\(482\) | −22.6930 | −1.03364 | ||||||||
\(483\) | 11.4816 | − | 4.93130i | 0.522429 | − | 0.224382i | ||||
\(484\) | 7.76886 | 0.353130 | ||||||||
\(485\) | 24.0863 | − | 41.7187i | 1.09370 | − | 1.89435i | ||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −11.5866 | + | 6.68951i | −0.525038 | + | 0.303131i | −0.738993 | − | 0.673713i | \(-0.764699\pi\) |
0.213956 | + | 0.976843i | \(0.431365\pi\) | |||||||
\(488\) | −0.875271 | − | 0.505338i | −0.0396217 | − | 0.0228756i | ||||
\(489\) | 16.9538i | 0.766679i | ||||||||
\(490\) | −20.6067 | − | 4.95225i | −0.930915 | − | 0.223720i | ||||
\(491\) | 20.3530 | 0.918518 | 0.459259 | − | 0.888302i | \(-0.348115\pi\) | ||||
0.459259 | + | 0.888302i | \(0.348115\pi\) | |||||||
\(492\) | 7.39077 | + | 4.26706i | 0.333202 | + | 0.192374i | ||||
\(493\) | −2.46890 | − | 4.27626i | −0.111194 | − | 0.192593i | ||||
\(494\) | −4.41468 | + | 1.62448i | −0.198626 | + | 0.0730888i | ||||
\(495\) | −6.55830 | + | 11.3593i | −0.294774 | + | 0.510563i | ||||
\(496\) | 1.69532i | 0.0761222i | ||||||||
\(497\) | −13.0510 | − | 30.3866i | −0.585416 | − | 1.36303i | ||||
\(498\) | 17.0583 | 0.764399 | ||||||||
\(499\) | −25.0796 | − | 14.4797i | −1.12272 | − | 0.648201i | −0.180624 | − | 0.983552i | \(-0.557812\pi\) |
−0.942093 | + | 0.335351i | \(0.891145\pi\) | |||||||
\(500\) | −2.18537 | + | 1.26173i | −0.0977328 | + | 0.0564261i | ||||
\(501\) | −20.3073 | + | 11.7245i | −0.907265 | + | 0.523810i | ||||
\(502\) | 4.17520 | + | 2.41055i | 0.186348 | + | 0.107588i | ||||
\(503\) | −7.66467 | −0.341751 | −0.170875 | − | 0.985293i | \(-0.554660\pi\) | ||||
−0.170875 | + | 0.985293i | \(0.554660\pi\) | |||||||
\(504\) | 2.62738 | + | 0.311278i | 0.117033 | + | 0.0138654i | ||||
\(505\) | − | 3.61319i | − | 0.160785i | ||||||
\(506\) | 10.2306 | − | 17.7200i | 0.454807 | − | 0.787749i | ||||
\(507\) | −2.34773 | − | 12.7862i | −0.104266 | − | 0.567857i | ||||
\(508\) | 0.668825 | + | 1.15844i | 0.0296743 | + | 0.0513974i | ||||
\(509\) | −17.5811 | − | 10.1505i | −0.779269 | − | 0.449911i | 0.0569024 | − | 0.998380i | \(-0.481878\pi\) |
−0.836171 | + | 0.548469i | \(0.815211\pi\) | |||||||
\(510\) | −4.37061 | −0.193534 | ||||||||
\(511\) | 6.25401 | − | 8.37312i | 0.276661 | − | 0.370405i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.12988 | − | 0.652339i | −0.0498856 | − | 0.0288015i | ||||
\(514\) | 5.05128 | − | 2.91636i | 0.222802 | − | 0.128635i | ||||
\(515\) | 39.7866 | − | 22.9708i | 1.75321 | − | 1.01221i | ||||
\(516\) | 2.55296 | − | 4.42186i | 0.112388 | − | 0.194662i | ||||
\(517\) | 36.4373 | 1.60251 | ||||||||
\(518\) | −24.2101 | − | 18.0829i | −1.06373 | − | 0.794516i | ||||
\(519\) | 16.4535 | 0.722228 | ||||||||
\(520\) | 8.38705 | + | 6.98728i | 0.367797 | + | 0.306413i | ||||
\(521\) | 21.6166 | + | 37.4410i | 0.947038 | + | 1.64032i | 0.751618 | + | 0.659599i | \(0.229274\pi\) |
0.195420 | + | 0.980720i | \(0.437393\pi\) | |||||||
\(522\) | −2.96227 | + | 1.71027i | −0.129655 | + | 0.0748563i | ||||
\(523\) | 15.0038 | − | 25.9873i | 0.656068 | − | 1.13634i | −0.325557 | − | 0.945523i | \(-0.605552\pi\) |
0.981625 | − | 0.190821i | \(-0.0611150\pi\) | |||||||
\(524\) | −12.3437 | −0.539238 | ||||||||
\(525\) | 1.29695 | − | 10.9470i | 0.0566034 | − | 0.477768i | ||||
\(526\) | 13.3746i | 0.583161i | ||||||||
\(527\) | −2.11945 | − | 1.22366i | −0.0923245 | − | 0.0533036i | ||||
\(528\) | 3.75189 | − | 2.16615i | 0.163280 | − | 0.0942697i | ||||
\(529\) | 0.346872 | + | 0.600800i | 0.0150814 | + | 0.0261217i | ||||
\(530\) | 6.21560 | − | 10.7657i | 0.269989 | − | 0.467634i | ||||
\(531\) | 5.01770i | 0.217749i | ||||||||
\(532\) | −1.36223 | − | 3.17169i | −0.0590602 | − | 0.137510i | ||||
\(533\) | 30.3214 | + | 5.23622i | 1.31337 | + | 0.226806i | ||||
\(534\) | −3.48998 | + | 6.04482i | −0.151026 | + | 0.261585i | ||||
\(535\) | 21.0283 | − | 12.1407i | 0.909134 | − | 0.524889i | ||||
\(536\) | 0.238274 | + | 0.412703i | 0.0102919 | + | 0.0178261i | ||||
\(537\) | 11.1435 | − | 19.3011i | 0.480877 | − | 0.832903i | ||||
\(538\) | − | 12.8451i | − | 0.553791i | ||||||
\(539\) | −7.08629 | + | 29.4866i | −0.305228 | + | 1.27008i | ||||
\(540\) | 3.02763i | 0.130288i | ||||||||
\(541\) | 33.6447 | + | 19.4248i | 1.44650 | + | 0.835136i | 0.998271 | − | 0.0587827i | \(-0.0187219\pi\) |
0.448228 | + | 0.893919i | \(0.352055\pi\) | |||||||
\(542\) | −10.4443 | − | 18.0901i | −0.448622 | − | 0.777036i | ||||
\(543\) | 6.21415 | + | 10.7632i | 0.266675 | + | 0.461894i | ||||
\(544\) | 1.25017 | + | 0.721788i | 0.0536007 | + | 0.0309464i | ||||
\(545\) | 3.18104 | 0.136261 | ||||||||
\(546\) | 9.27793 | − | 2.21812i | 0.397059 | − | 0.0949267i | ||||
\(547\) | 40.6208 | 1.73682 | 0.868411 | − | 0.495846i | \(-0.165142\pi\) | ||||
0.868411 | + | 0.495846i | \(0.165142\pi\) | |||||||
\(548\) | 7.91249 | + | 4.56828i | 0.338005 | + | 0.195147i | ||||
\(549\) | −0.505338 | − | 0.875271i | −0.0215673 | − | 0.0373557i | ||||
\(550\) | −9.02533 | − | 15.6323i | −0.384841 | − | 0.666565i | ||||
\(551\) | 3.86480 | + | 2.23134i | 0.164646 | + | 0.0950585i | ||||
\(552\) | − | 4.72295i | − | 0.201022i | ||||||
\(553\) | 4.57360 | − | 38.6040i | 0.194489 | − | 1.64161i | ||||
\(554\) | − | 26.3966i | − | 1.12149i | ||||||
\(555\) | 17.2897 | − | 29.9466i | 0.733906 | − | 1.27116i | ||||
\(556\) | 8.91097 | + | 15.4343i | 0.377909 | + | 0.654558i | ||||
\(557\) | 37.8923 | − | 21.8772i | 1.60555 | − | 0.926965i | 0.615201 | − | 0.788370i | \(-0.289075\pi\) |
0.990349 | − | 0.138594i | \(-0.0442585\pi\) | |||||||
\(558\) | −0.847661 | + | 1.46819i | −0.0358844 | + | 0.0621536i | ||||
\(559\) | 3.13281 | − | 18.1412i | 0.132504 | − | 0.767289i | ||||
\(560\) | −4.79353 | + | 6.41777i | −0.202564 | + | 0.271200i | ||||
\(561\) | 6.25401i | 0.264044i | ||||||||
\(562\) | −6.30121 | + | 10.9140i | −0.265801 | + | 0.460380i | ||||
\(563\) | 14.3953 | + | 24.9334i | 0.606689 | + | 1.05082i | 0.991782 | + | 0.127938i | \(0.0408358\pi\) |
−0.385094 | + | 0.922878i | \(0.625831\pi\) | |||||||
\(564\) | 7.28379 | − | 4.20530i | 0.306703 | − | 0.177075i | ||||
\(565\) | 24.6727 | + | 14.2448i | 1.03799 | + | 0.599282i | ||||
\(566\) | 0.175775i | 0.00738837i | ||||||||
\(567\) | 2.11974 | + | 1.58326i | 0.0890205 | + | 0.0664908i | ||||
\(568\) | −12.4996 | −0.524471 | ||||||||
\(569\) | 2.53148 | − | 4.38465i | 0.106125 | − | 0.183814i | −0.808072 | − | 0.589083i | \(-0.799489\pi\) |
0.914197 | + | 0.405269i | \(0.132822\pi\) | |||||||
\(570\) | 3.42087 | − | 1.97504i | 0.143284 | − | 0.0827252i | ||||
\(571\) | −9.83001 | − | 17.0261i | −0.411373 | − | 0.712519i | 0.583667 | − | 0.811993i | \(-0.301617\pi\) |
−0.995040 | + | 0.0994738i | \(0.968284\pi\) | |||||||
\(572\) | 9.99827 | − | 12.0012i | 0.418049 | − | 0.501797i | ||||
\(573\) | −21.5141 | −0.898764 | ||||||||
\(574\) | −2.65648 | + | 22.4224i | −0.110879 | + | 0.935891i | ||||
\(575\) | −19.6783 | −0.820641 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −11.1308 | + | 6.42637i | −0.463381 | + | 0.267533i | −0.713465 | − | 0.700691i | \(-0.752875\pi\) |
0.250084 | + | 0.968224i | \(0.419542\pi\) | |||||||
\(578\) | 12.9177 | − | 7.45805i | 0.537306 | − | 0.310214i | ||||
\(579\) | −1.66424 | − | 0.960851i | −0.0691636 | − | 0.0399316i | ||||
\(580\) | − | 10.3561i | − | 0.430013i | ||||||
\(581\) | 17.8108 | + | 41.4689i | 0.738915 | + | 1.72042i | ||||
\(582\) | −15.9110 | −0.659533 | ||||||||
\(583\) | −15.4050 | − | 8.89406i | −0.638008 | − | 0.368354i | ||||
\(584\) | −1.97504 | − | 3.42087i | −0.0817276 | − | 0.141556i | ||||
\(585\) | 3.76976 | + | 10.2447i | 0.155860 | + | 0.423566i | ||||
\(586\) | 0.209136 | − | 0.362235i | 0.00863935 | − | 0.0149638i | ||||
\(587\) | 24.3430i | 1.00474i | 0.864652 | + | 0.502371i | \(0.167539\pi\) | ||||
−0.864652 | + | 0.502371i | \(0.832461\pi\) | |||||||
\(588\) | 1.98656 | + | 6.71220i | 0.0819243 | + | 0.276806i | ||||
\(589\) | 2.21185 | 0.0911376 | ||||||||
\(590\) | −13.1564 | − | 7.59586i | −0.541641 | − | 0.312716i | ||||
\(591\) | −4.80737 | + | 2.77554i | −0.197749 | + | 0.114170i | ||||
\(592\) | −9.89112 | + | 5.71064i | −0.406522 | + | 0.234706i | ||||
\(593\) | −20.4283 | − | 11.7943i | −0.838890 | − | 0.484333i | 0.0179970 | − | 0.999838i | \(-0.494271\pi\) |
−0.856887 | + | 0.515505i | \(0.827604\pi\) | |||||||
\(594\) | 4.33230 | 0.177757 | ||||||||
\(595\) | −4.56341 | − | 10.6250i | −0.187082 | − | 0.435583i | ||||
\(596\) | − | 12.2816i | − | 0.503075i | ||||||
\(597\) | 3.54486 | − | 6.13988i | 0.145081 | − | 0.251288i | ||||
\(598\) | −5.88064 | − | 15.9812i | −0.240477 | − | 0.653521i | ||||
\(599\) | −7.77854 | − | 13.4728i | −0.317823 | − | 0.550485i | 0.662211 | − | 0.749318i | \(-0.269618\pi\) |
−0.980033 | + | 0.198833i | \(0.936285\pi\) | |||||||
\(600\) | −3.60832 | − | 2.08326i | −0.147309 | − | 0.0850488i | ||||
\(601\) | 30.6284 | 1.24936 | 0.624679 | − | 0.780882i | \(-0.285230\pi\) | ||||
0.624679 | + | 0.780882i | \(0.285230\pi\) | |||||||
\(602\) | 13.4152 | + | 1.58936i | 0.546762 | + | 0.0647775i | ||||
\(603\) | 0.476549i | 0.0194066i | ||||||||
\(604\) | 12.6016 | + | 7.27554i | 0.512752 | + | 0.296037i | ||||
\(605\) | −20.3700 | + | 11.7606i | −0.828157 | + | 0.478136i | ||||
\(606\) | −1.03352 | + | 0.596703i | −0.0419839 | + | 0.0242394i | ||||
\(607\) | 7.88760 | − | 13.6617i | 0.320148 | − | 0.554512i | −0.660371 | − | 0.750940i | \(-0.729601\pi\) |
0.980518 | + | 0.196428i | \(0.0629341\pi\) | |||||||
\(608\) | −1.30468 | −0.0529116 | ||||||||
\(609\) | −7.25062 | − | 5.41560i | −0.293810 | − | 0.219451i | ||||
\(610\) | 3.05995 | 0.123894 | ||||||||
\(611\) | 19.4103 | − | 23.2988i | 0.785258 | − | 0.942570i | ||||
\(612\) | 0.721788 | + | 1.25017i | 0.0291765 | + | 0.0505352i | ||||
\(613\) | 18.5248 | − | 10.6953i | 0.748211 | − | 0.431980i | −0.0768359 | − | 0.997044i | \(-0.524482\pi\) |
0.825047 | + | 0.565064i | \(0.191148\pi\) | |||||||
\(614\) | −6.58828 | + | 11.4112i | −0.265881 | + | 0.460520i | ||||
\(615\) | −25.8382 | −1.04189 | ||||||||
\(616\) | 9.18334 | + | 6.85917i | 0.370007 | + | 0.276364i | ||||
\(617\) | 34.4919i | 1.38859i | 0.719690 | + | 0.694296i | \(0.244284\pi\) | ||||
−0.719690 | + | 0.694296i | \(0.755716\pi\) | |||||||
\(618\) | −13.1412 | − | 7.58706i | −0.528615 | − | 0.305196i | ||||
\(619\) | −34.7726 | + | 20.0760i | −1.39763 | + | 0.806921i | −0.994144 | − | 0.108066i | \(-0.965534\pi\) |
−0.403484 | + | 0.914987i | \(0.632201\pi\) | |||||||
\(620\) | −2.56640 | − | 4.44514i | −0.103069 | − | 0.178521i | ||||
\(621\) | 2.36147 | − | 4.09019i | 0.0947627 | − | 0.164134i | ||||
\(622\) | 17.2310i | 0.690899i | ||||||||
\(623\) | −18.3390 | − | 2.17271i | −0.734736 | − | 0.0870476i | ||||
\(624\) | 0.613563 | − | 3.55296i | 0.0245622 | − | 0.142232i | ||||
\(625\) | 14.2363 | − | 24.6581i | 0.569454 | − | 0.986323i | ||||
\(626\) | −7.71506 | + | 4.45429i | −0.308356 | + | 0.178029i | ||||
\(627\) | −2.82613 | − | 4.89500i | −0.112865 | − | 0.195487i | ||||
\(628\) | 4.81431 | − | 8.33864i | 0.192112 | − | 0.332748i | ||||
\(629\) | − | 16.4875i | − | 0.657399i | ||||||
\(630\) | −7.36020 | + | 3.16119i | −0.293237 | + | 0.125945i | ||||
\(631\) | − | 27.1665i | − | 1.08148i | −0.841189 | − | 0.540741i | \(-0.818144\pi\) | ||
0.841189 | − | 0.540741i | \(-0.181856\pi\) | |||||||
\(632\) | −12.7245 | − | 7.34649i | −0.506153 | − | 0.292228i | ||||
\(633\) | 12.1419 | + | 21.0305i | 0.482599 | + | 0.835885i | ||||
\(634\) | 2.95931 | + | 5.12567i | 0.117529 | + | 0.203566i | ||||
\(635\) | −3.50732 | − | 2.02495i | −0.139184 | − | 0.0803578i | ||||
\(636\) | −4.10592 | −0.162810 | ||||||||
\(637\) | 15.0795 | + | 20.2388i | 0.597471 | + | 0.801891i | ||||
\(638\) | −14.8188 | −0.586681 | ||||||||
\(639\) | −10.8249 | − | 6.24979i | −0.428228 | − | 0.247238i | ||||
\(640\) | 1.51381 | + | 2.62200i | 0.0598387 | + | 0.103644i | ||||
\(641\) | −0.880967 | − | 1.52588i | −0.0347961 | − | 0.0602686i | 0.848103 | − | 0.529832i | \(-0.177745\pi\) |
−0.882899 | + | 0.469563i | \(0.844412\pi\) | |||||||
\(642\) | −6.94549 | − | 4.00998i | −0.274116 | − | 0.158261i | ||||
\(643\) | 41.7007i | 1.64451i | 0.569117 | + | 0.822257i | \(0.307285\pi\) | ||||
−0.569117 | + | 0.822257i | \(0.692715\pi\) | |||||||
\(644\) | 11.4816 | − | 4.93130i | 0.452437 | − | 0.194320i | ||||
\(645\) | 15.4588i | 0.608691i | ||||||||
\(646\) | 0.941700 | − | 1.63107i | 0.0370507 | − | 0.0641737i | ||||
\(647\) | 9.84997 | + | 17.0606i | 0.387242 | + | 0.670723i | 0.992077 | − | 0.125627i | \(-0.0400944\pi\) |
−0.604835 | + | 0.796351i | \(0.706761\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −10.8691 | + | 18.8258i | −0.426649 | + | 0.738978i | ||||
\(650\) | −14.8035 | − | 2.55642i | −0.580641 | − | 0.100271i | ||||
\(651\) | −4.45425 | − | 0.527716i | −0.174576 | − | 0.0206828i | ||||
\(652\) | 16.9538i | 0.663963i | ||||||||
\(653\) | −19.1239 | + | 33.1235i | −0.748374 | + | 1.29622i | 0.200227 | + | 0.979749i | \(0.435832\pi\) |
−0.948602 | + | 0.316473i | \(0.897501\pi\) | |||||||
\(654\) | −0.525335 | − | 0.909907i | −0.0205422 | − | 0.0355802i | ||||
\(655\) | 32.3653 | − | 18.6861i | 1.26462 | − | 0.730126i | ||||
\(656\) | 7.39077 | + | 4.26706i | 0.288561 | + | 0.166601i | ||||
\(657\) | − | 3.95008i | − | 0.154107i | ||||||
\(658\) | 17.8283 | + | 13.3162i | 0.695018 | + | 0.519119i | ||||
\(659\) | 23.3092 | 0.907999 | 0.454000 | − | 0.891002i | \(-0.349997\pi\) | ||||
0.454000 | + | 0.891002i | \(0.349997\pi\) | |||||||
\(660\) | −6.55830 | + | 11.3593i | −0.255281 | + | 0.442161i | ||||
\(661\) | 21.3745 | − | 12.3406i | 0.831373 | − | 0.479994i | −0.0229493 | − | 0.999737i | \(-0.507306\pi\) |
0.854323 | + | 0.519743i | \(0.173972\pi\) | |||||||
\(662\) | −5.84078 | − | 10.1165i | −0.227008 | − | 0.393190i | ||||
\(663\) | 3.99895 | + | 3.33154i | 0.155307 | + | 0.129386i | ||||
\(664\) | 17.0583 | 0.661989 | ||||||||
\(665\) | 8.37312 | + | 6.25401i | 0.324696 | + | 0.242520i | ||||
\(666\) | −11.4213 | −0.442566 | ||||||||
\(667\) | −8.07750 | + | 13.9906i | −0.312762 | + | 0.541720i | ||||
\(668\) | −20.3073 | + | 11.7245i | −0.785715 | + | 0.453633i | ||||
\(669\) | 1.74390 | − | 1.00684i | 0.0674230 | − | 0.0389267i | ||||
\(670\) | −1.24951 | − | 0.721406i | −0.0482729 | − | 0.0278703i | ||||
\(671\) | − | 4.37856i | − | 0.169032i | ||||||
\(672\) | 2.62738 | + | 0.311278i | 0.101353 | + | 0.0120078i | ||||
\(673\) | −15.4368 | −0.595044 | −0.297522 | − | 0.954715i | \(-0.596160\pi\) | ||||
−0.297522 | + | 0.954715i | \(0.596160\pi\) | |||||||
\(674\) | 5.45886 | + | 3.15167i | 0.210267 | + | 0.121398i | ||||
\(675\) | −2.08326 | − | 3.60832i | −0.0801848 | − | 0.138884i | ||||
\(676\) | −2.34773 | − | 12.7862i | −0.0902973 | − | 0.491779i | ||||
\(677\) | −7.38329 | + | 12.7882i | −0.283763 | + | 0.491492i | −0.972308 | − | 0.233701i | \(-0.924916\pi\) |
0.688546 | + | 0.725193i | \(0.258250\pi\) | |||||||
\(678\) | − | 9.40986i | − | 0.361383i | ||||||
\(679\) | −16.6129 | − | 38.6799i | −0.637545 | − | 1.48440i | ||||
\(680\) | −4.37061 | −0.167605 | ||||||||
\(681\) | −5.33689 | − | 3.08125i | −0.204510 | − | 0.118074i | ||||
\(682\) | −6.36066 | + | 3.67233i | −0.243562 | + | 0.140621i | ||||
\(683\) | −18.1593 | + | 10.4843i | −0.694846 | + | 0.401169i | −0.805425 | − | 0.592698i | \(-0.798063\pi\) |
0.110579 | + | 0.993867i | \(0.464729\pi\) | |||||||
\(684\) | −1.12988 | − | 0.652339i | −0.0432022 | − | 0.0249428i | ||||
\(685\) | −27.6621 | −1.05691 | ||||||||
\(686\) | −14.2432 | + | 11.8376i | −0.543810 | + | 0.451964i | ||||
\(687\) | − | 15.1810i | − | 0.579193i | ||||||
\(688\) | 2.55296 | − | 4.42186i | 0.0973308 | − | 0.168582i | ||||
\(689\) | −13.8934 | + | 5.11237i | −0.529295 | + | 0.194766i | ||||
\(690\) | 7.14967 | + | 12.3836i | 0.272183 | + | 0.471435i | ||||
\(691\) | 10.6634 | + | 6.15650i | 0.405654 | + | 0.234204i | 0.688920 | − | 0.724837i | \(-0.258085\pi\) |
−0.283267 | + | 0.959041i | \(0.591418\pi\) | |||||||
\(692\) | 16.4535 | 0.625468 | ||||||||
\(693\) | 4.52342 | + | 10.5319i | 0.171830 | + | 0.400073i | ||||
\(694\) | 9.57638i | 0.363514i | ||||||||
\(695\) | −46.7292 | − | 26.9791i | −1.77254 | − | 1.02338i | ||||
\(696\) | −2.96227 | + | 1.71027i | −0.112284 | + | 0.0648275i | ||||
\(697\) | −10.6691 | + | 6.15983i | −0.404122 | + | 0.233320i | ||||
\(698\) | 9.32532 | − | 16.1519i | 0.352969 | − | 0.611360i | ||||
\(699\) | 20.8027 | 0.786832 | ||||||||
\(700\) | 1.29695 | − | 10.9470i | 0.0490200 | − | 0.413759i | ||||
\(701\) | 25.8563 | 0.976577 | 0.488289 | − | 0.872682i | \(-0.337621\pi\) | ||||
0.488289 | + | 0.872682i | \(0.337621\pi\) | |||||||
\(702\) | 2.30784 | − | 2.77017i | 0.0871039 | − | 0.104553i | ||||
\(703\) | 7.45054 | + | 12.9047i | 0.281002 | + | 0.486710i | ||||
\(704\) | 3.75189 | − | 2.16615i | 0.141405 | − | 0.0816399i | ||||
\(705\) | −12.7321 | + | 22.0526i | −0.479518 | + | 0.830549i | ||||
\(706\) | −22.5518 | −0.848749 | ||||||||
\(707\) | −2.52971 | − | 1.88947i | −0.0951394 | − | 0.0710610i | ||||
\(708\) | 5.01770i | 0.188577i | ||||||||
\(709\) | −25.1577 | − | 14.5248i | −0.944818 | − | 0.545491i | −0.0533509 | − | 0.998576i | \(-0.516990\pi\) |
−0.891467 | + | 0.453085i | \(0.850324\pi\) | |||||||
\(710\) | 32.7739 | − | 18.9220i | 1.22998 | − | 0.710131i | ||||
\(711\) | −7.34649 | − | 12.7245i | −0.275515 | − | 0.477206i | ||||
\(712\) | −3.48998 | + | 6.04482i | −0.130793 | + | 0.226539i | ||||
\(713\) | 8.00693i | 0.299862i | ||||||||
\(714\) | −2.28556 | + | 3.06000i | −0.0855349 | + | 0.114518i | ||||
\(715\) | −8.04786 | + | 46.6028i | −0.300973 | + | 1.74285i | ||||
\(716\) | 11.1435 | − | 19.3011i | 0.416451 | − | 0.721315i | ||||
\(717\) | −5.72127 | + | 3.30317i | −0.213665 | + | 0.123359i | ||||
\(718\) | 10.4355 | + | 18.0748i | 0.389450 | + | 0.674547i | ||||
\(719\) | −21.7536 | + | 37.6783i | −0.811272 | + | 1.40516i | 0.100703 | + | 0.994917i | \(0.467891\pi\) |
−0.911974 | + | 0.410247i | \(0.865442\pi\) | |||||||
\(720\) | 3.02763i | 0.112833i | ||||||||
\(721\) | 4.72336 | − | 39.8681i | 0.175907 | − | 1.48477i | ||||
\(722\) | − | 17.2978i | − | 0.643758i | ||||||
\(723\) | −19.6527 | − | 11.3465i | −0.730892 | − | 0.421981i | ||||
\(724\) | 6.21415 | + | 10.7632i | 0.230947 | + | 0.400012i | ||||
\(725\) | 7.12587 | + | 12.3424i | 0.264648 | + | 0.458384i | ||||
\(726\) | 6.72803 | + | 3.88443i | 0.249701 | + | 0.144165i | ||||
\(727\) | −20.3751 | −0.755671 | −0.377835 | − | 0.925873i | \(-0.623331\pi\) | ||||
−0.377835 | + | 0.925873i | \(0.623331\pi\) | |||||||
\(728\) | 9.27793 | − | 2.21812i | 0.343863 | − | 0.0822089i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.3571 | + | 5.97968i | 0.383334 | + | 0.221318i | ||||
\(731\) | 3.68539 | + | 6.38329i | 0.136309 | + | 0.236094i | ||||
\(732\) | −0.505338 | − | 0.875271i | −0.0186778 | − | 0.0323510i | ||||
\(733\) | −19.0444 | − | 10.9953i | −0.703420 | − | 0.406120i | 0.105200 | − | 0.994451i | \(-0.466452\pi\) |
−0.808620 | + | 0.588331i | \(0.799785\pi\) | |||||||
\(734\) | − | 10.1389i | − | 0.374233i | ||||||
\(735\) | −15.3698 | − | 14.5921i | −0.566923 | − | 0.538238i | ||||
\(736\) | − | 4.72295i | − | 0.174090i | ||||||
\(737\) | −1.03228 | + | 1.78796i | −0.0380244 | + | 0.0658602i | ||||
\(738\) | 4.26706 | + | 7.39077i | 0.157073 | + | 0.272058i | ||||
\(739\) | −36.9626 | + | 21.3404i | −1.35969 | + | 0.785018i | −0.989582 | − | 0.143971i | \(-0.954013\pi\) |
−0.370109 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(740\) | 17.2897 | − | 29.9466i | 0.635581 | − | 1.10086i | ||||
\(741\) | −4.63547 | − | 0.800501i | −0.170288 | − | 0.0294072i | ||||
\(742\) | −4.28705 | − | 9.98156i | −0.157383 | − | 0.366435i | ||||
\(743\) | − | 17.2071i | − | 0.631266i | −0.948881 | − | 0.315633i | \(-0.897783\pi\) | ||
0.948881 | − | 0.315633i | \(-0.102217\pi\) | |||||||
\(744\) | −0.847661 | + | 1.46819i | −0.0310768 | + | 0.0538266i | ||||
\(745\) | 18.5921 | + | 32.2025i | 0.681162 | + | 1.17981i | ||||
\(746\) | −22.8303 | + | 13.1811i | −0.835877 | + | 0.482594i | ||||
\(747\) | 14.7729 | + | 8.52913i | 0.540512 | + | 0.312065i | ||||
\(748\) | 6.25401i | 0.228669i | ||||||||
\(749\) | 2.49643 | − | 21.0714i | 0.0912177 | − | 0.769934i | ||||
\(750\) | −2.52345 | −0.0921434 | ||||||||
\(751\) | −7.30117 | + | 12.6460i | −0.266423 | + | 0.461459i | −0.967936 | − | 0.251199i | \(-0.919175\pi\) |
0.701512 | + | 0.712657i | \(0.252509\pi\) | |||||||
\(752\) | 7.28379 | − | 4.20530i | 0.265613 | − | 0.153352i | ||||
\(753\) | 2.41055 | + | 4.17520i | 0.0878455 | + | 0.152153i | ||||
\(754\) | −7.89405 | + | 9.47547i | −0.287484 | + | 0.345076i | ||||
\(755\) | −44.0552 | −1.60333 | ||||||||
\(756\) | 2.11974 | + | 1.58326i | 0.0770940 | + | 0.0575827i | ||||
\(757\) | 25.4627 | 0.925456 | 0.462728 | − | 0.886500i | \(-0.346871\pi\) | ||||
0.462728 | + | 0.886500i | \(0.346871\pi\) | |||||||
\(758\) | 17.1113 | − | 29.6376i | 0.621509 | − | 1.07648i | ||||
\(759\) | 17.7200 | − | 10.2306i | 0.643194 | − | 0.371348i | ||||
\(760\) | 3.42087 | − | 1.97504i | 0.124088 | − | 0.0716421i | ||||
\(761\) | −32.9141 | − | 19.0030i | −1.19314 | − | 0.688858i | −0.234120 | − | 0.972208i | \(-0.575221\pi\) |
−0.959017 | + | 0.283350i | \(0.908554\pi\) | |||||||
\(762\) | 1.33765i | 0.0484580i | ||||||||
\(763\) | 1.66349 | − | 2.22714i | 0.0602223 | − | 0.0806280i | ||||
\(764\) | −21.5141 | −0.778352 | ||||||||
\(765\) | −3.78506 | − | 2.18530i | −0.136849 | − | 0.0790098i | ||||
\(766\) | −5.07858 | − | 8.79636i | −0.183497 | − | 0.317825i | ||||
\(767\) | 6.24764 | + | 16.9786i | 0.225589 | + | 0.613061i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 11.8756i | 0.428246i | 0.976807 | + | 0.214123i | \(0.0686893\pi\) | ||||
−0.976807 | + | 0.214123i | \(0.931311\pi\) | |||||||
\(770\) | −34.4622 | − | 4.08290i | −1.24193 | − | 0.147138i | ||||
\(771\) | 5.83271 | 0.210060 | ||||||||
\(772\) | −1.66424 | − | 0.960851i | −0.0598974 | − | 0.0345818i | ||||
\(773\) | −7.11167 | + | 4.10592i | −0.255789 | + | 0.147680i | −0.622412 | − | 0.782690i | \(-0.713847\pi\) |
0.366623 | + | 0.930370i | \(0.380514\pi\) | |||||||
\(774\) | 4.42186 | − | 2.55296i | 0.158940 | − | 0.0917643i | ||||
\(775\) | 6.11726 | + | 3.53180i | 0.219739 | + | 0.126866i | ||||
\(776\) | −15.9110 | −0.571172 | ||||||||
\(777\) | −11.9251 | − | 27.7653i | −0.427811 | − | 0.996074i | ||||
\(778\) | 26.2111i | 0.939713i | ||||||||
\(779\) | 5.56714 | − | 9.64257i | 0.199463 | − | 0.345481i | ||||
\(780\) | 3.76976 | + | 10.2447i | 0.134979 | + | 0.366819i | ||||
\(781\) | −27.0760 | − | 46.8970i | −0.968855 | − | 1.67811i | ||||
\(782\) | 5.90450 | + | 3.40897i | 0.211145 | + | 0.121904i | ||||
\(783\) | −3.42053 | −0.122240 | ||||||||
\(784\) | 1.98656 | + | 6.71220i | 0.0709486 | + | 0.239721i | ||||
\(785\) | 29.1519i | 1.04048i | ||||||||
\(786\) | −10.6900 | − | 6.17186i | −0.381299 | − | 0.220143i | ||||
\(787\) | 5.02129 | − | 2.89905i | 0.178990 | − | 0.103340i | −0.407828 | − | 0.913059i | \(-0.633714\pi\) |
0.586818 | + | 0.809719i | \(0.300380\pi\) | |||||||
\(788\) | −4.80737 | + | 2.77554i | −0.171256 | + | 0.0988745i | ||||
\(789\) | −6.68731 | + | 11.5828i | −0.238075 | + | 0.412357i | ||||
\(790\) | 44.4849 | 1.58270 | ||||||||
\(791\) | 22.8755 | − | 9.82496i | 0.813359 | − | 0.349335i | ||||
\(792\) | 4.33230 | 0.153942 | ||||||||
\(793\) | −2.79975 | − | 2.33248i | −0.0994220 | − | 0.0828288i | ||||
\(794\) | 18.6735 | + | 32.3434i | 0.662696 | + | 1.14782i | ||||
\(795\) | 10.7657 | − | 6.21560i | 0.381822 | − | 0.220445i | ||||
\(796\) | 3.54486 | − | 6.13988i | 0.125644 | − | 0.217622i | ||||
\(797\) | 14.6546 | 0.519093 | 0.259546 | − | 0.965731i | \(-0.416427\pi\) | ||||
0.259546 | + | 0.965731i | \(0.416427\pi\) | |||||||
\(798\) | 0.406117 | − | 3.42788i | 0.0143764 | − | 0.121346i | ||||
\(799\) | 12.1413i | 0.429530i | ||||||||
\(800\) | −3.60832 | − | 2.08326i | −0.127573 | − | 0.0736545i | ||||
\(801\) | −6.04482 | + | 3.48998i | −0.213583 | + | 0.123312i | ||||
\(802\) | 3.82537 | + | 6.62574i | 0.135079 | + | 0.233963i | ||||
\(803\) | 8.55646 | − | 14.8202i | 0.301951 | − | 0.522995i | ||||
\(804\) | 0.476549i | 0.0168066i | ||||||||
\(805\) | −22.6396 | + | 30.3108i | −0.797941 | + | 1.06832i | ||||
\(806\) | −1.04019 | + | 6.02342i | −0.0366390 | + | 0.212166i | ||||
\(807\) | 6.42254 | − | 11.1242i | 0.226084 | − | 0.391589i | ||||
\(808\) | −1.03352 | + | 0.596703i | −0.0363591 | + | 0.0209919i | ||||
\(809\) | −6.20487 | − | 10.7471i | −0.218152 | − | 0.377850i | 0.736091 | − | 0.676882i | \(-0.236669\pi\) |
−0.954243 | + | 0.299033i | \(0.903336\pi\) | |||||||
\(810\) | −1.51381 | + | 2.62200i | −0.0531900 | + | 0.0921278i | ||||
\(811\) | 10.7414i | 0.377181i | 0.982056 | + | 0.188591i | \(0.0603920\pi\) | ||||
−0.982056 | + | 0.188591i | \(0.939608\pi\) | |||||||
\(812\) | −7.25062 | − | 5.41560i | −0.254447 | − | 0.190050i | ||||
\(813\) | − | 20.8886i | − | 0.732597i | ||||||
\(814\) | −42.8513 | − | 24.7402i | −1.50194 | − | 0.867144i | ||||
\(815\) | −25.6649 | − | 44.4530i | −0.899003 | − | 1.55712i | ||||
\(816\) | 0.721788 | + | 1.25017i | 0.0252676 | + | 0.0437648i | ||||
\(817\) | −5.76910 | − | 3.33079i | −0.201835 | − | 0.116530i | ||||
\(818\) | 21.9324 | 0.766847 | ||||||||
\(819\) | 9.14398 | + | 2.71802i | 0.319517 | + | 0.0949752i | ||||
\(820\) | −25.8382 | −0.902307 | ||||||||
\(821\) | 6.92640 | + | 3.99896i | 0.241733 | + | 0.139565i | 0.615973 | − | 0.787767i | \(-0.288763\pi\) |
−0.374240 | + | 0.927332i | \(0.622096\pi\) | |||||||
\(822\) | 4.56828 | + | 7.91249i | 0.159337 | + | 0.275980i | ||||
\(823\) | 3.88251 | + | 6.72471i | 0.135336 | + | 0.234408i | 0.925726 | − | 0.378196i | \(-0.123455\pi\) |
−0.790390 | + | 0.612604i | \(0.790122\pi\) | |||||||
\(824\) | −13.1412 | − | 7.58706i | −0.457794 | − | 0.264308i | ||||
\(825\) | − | 18.0507i | − | 0.628443i | ||||||
\(826\) | −12.1981 | + | 5.23905i | −0.424426 | + | 0.182290i | ||||
\(827\) | 9.73829i | 0.338634i | 0.985562 | + | 0.169317i | \(0.0541561\pi\) | ||||
−0.985562 | + | 0.169317i | \(0.945844\pi\) | |||||||
\(828\) | 2.36147 | − | 4.09019i | 0.0820669 | − | 0.142144i | ||||
\(829\) | 17.3342 | + | 30.0237i | 0.602042 | + | 1.04277i | 0.992511 | + | 0.122152i | \(0.0389794\pi\) |
−0.390469 | + | 0.920616i | \(0.627687\pi\) | |||||||
\(830\) | −44.7268 | + | 25.8230i | −1.55249 | + | 0.896330i | ||||
\(831\) | 13.1983 | − | 22.8602i | 0.457845 | − | 0.793010i | ||||
\(832\) | 0.613563 | − | 3.55296i | 0.0212715 | − | 0.123177i | ||||
\(833\) | −9.82528 | − | 2.36124i | −0.340426 | − | 0.0818120i | ||||
\(834\) | 17.8219i | 0.617124i | ||||||||
\(835\) | 35.4973 | − | 61.4831i | 1.22843 | − | 2.12771i | ||||
\(836\) | −2.82613 | − | 4.89500i | −0.0977437 | − | 0.169297i | ||||
\(837\) | −1.46819 | + | 0.847661i | −0.0507482 | + | 0.0292995i | ||||
\(838\) | −3.41754 | − | 1.97312i | −0.118057 | − | 0.0681603i | ||||
\(839\) | − | 26.5655i | − | 0.917142i | −0.888658 | − | 0.458571i | \(-0.848361\pi\) | ||
0.888658 | − | 0.458571i | \(-0.151639\pi\) | |||||||
\(840\) | −7.36020 | + | 3.16119i | −0.253951 | + | 0.109071i | ||||
\(841\) | −17.3000 | −0.596550 | ||||||||
\(842\) | 6.65651 | − | 11.5294i | 0.229398 | − | 0.397330i | ||||
\(843\) | −10.9140 | + | 6.30121i | −0.375899 | + | 0.217025i | ||||
\(844\) | 12.1419 | + | 21.0305i | 0.417943 | + | 0.723898i | ||||
\(845\) | 25.5117 | + | 29.9715i | 0.877631 | + | 1.03105i | ||||
\(846\) | 8.41060 | 0.289162 | ||||||||
\(847\) | −2.41827 | + | 20.4117i | −0.0830928 | + | 0.701355i | ||||
\(848\) | −4.10592 | −0.140998 | ||||||||
\(849\) | −0.0878874 | + | 0.152225i | −0.00301629 | + | 0.00522437i | ||||
\(850\) | 5.20888 | − | 3.00735i | 0.178663 | − | 0.103151i | ||||
\(851\) | −46.7152 | + | 26.9711i | −1.60138 | + | 0.924556i | ||||
\(852\) | −10.8249 | − | 6.24979i | −0.370857 | − | 0.214114i | ||||
\(853\) | − | 10.1138i | − | 0.346289i | −0.984896 | − | 0.173145i | \(-0.944607\pi\) | ||
0.984896 | − | 0.173145i | \(-0.0553928\pi\) | |||||||
\(854\) | 1.60017 | − | 2.14237i | 0.0547565 | − | 0.0733103i | ||||
\(855\) | 3.95008 | 0.135090 | ||||||||
\(856\) | −6.94549 | − | 4.00998i | −0.237392 | − | 0.137058i | ||||
\(857\) | 24.0913 | + | 41.7273i | 0.822942 | + | 1.42538i | 0.903482 | + | 0.428625i | \(0.141002\pi\) |
−0.0805406 | + | 0.996751i | \(0.525665\pi\) | |||||||
\(858\) | 14.6594 | − | 5.39424i | 0.500463 | − | 0.184156i | ||||
\(859\) | 5.76772 | − | 9.98998i | 0.196792 | − | 0.340854i | −0.750694 | − | 0.660650i | \(-0.770281\pi\) |
0.947487 | + | 0.319796i | \(0.103614\pi\) | |||||||
\(860\) | 15.4588i | 0.527142i | ||||||||
\(861\) | −13.5118 | + | 18.0901i | −0.460480 | + | 0.616509i | ||||
\(862\) | 37.3123 | 1.27086 | ||||||||
\(863\) | 15.4694 | + | 8.93124i | 0.526583 | + | 0.304023i | 0.739624 | − | 0.673020i | \(-0.235003\pi\) |
−0.213041 | + | 0.977043i | \(0.568337\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | −43.1411 | + | 24.9075i | −1.46684 | + | 0.846881i | ||||
\(866\) | −8.10594 | − | 4.67997i | −0.275451 | − | 0.159032i | ||||
\(867\) | 14.9161 | 0.506577 | ||||||||
\(868\) | −4.45425 | − | 0.527716i | −0.151187 | − | 0.0179119i | ||||
\(869\) | − | 63.6545i | − | 2.15933i | ||||||
\(870\) | 5.17805 | − | 8.96864i | 0.175552 | − | 0.304065i | ||||
\(871\) | 0.593360 | + | 1.61252i | 0.0201053 | + | 0.0546380i | ||||
\(872\) | −0.525335 | − | 0.909907i | −0.0177901 | − | 0.0308134i | ||||
\(873\) | −13.7793 | − | 7.95550i | −0.466360 | − | 0.269253i | ||||
\(874\) | −6.16192 | −0.208430 | ||||||||
\(875\) | −2.63477 | − | 6.13454i | −0.0890715 | − | 0.207385i | ||||
\(876\) | − | 3.95008i | − | 0.133461i | ||||||
\(877\) | 44.8185 | + | 25.8760i | 1.51341 | + | 0.873769i | 0.999877 | + | 0.0157009i | \(0.00499795\pi\) |
0.513536 | + | 0.858068i | \(0.328335\pi\) | |||||||
\(878\) | 20.1631 | − | 11.6412i | 0.680472 | − | 0.392871i | ||||
\(879\) | 0.362235 | − | 0.209136i | 0.0122179 | − | 0.00705400i | ||||
\(880\) | −6.55830 | + | 11.3593i | −0.221080 | + | 0.382922i | ||||
\(881\) | −29.6192 | −0.997895 | −0.498947 | − | 0.866632i | \(-0.666280\pi\) | ||||
−0.498947 | + | 0.866632i | \(0.666280\pi\) | |||||||
\(882\) | −1.63569 | + | 6.80621i | −0.0550765 | + | 0.229177i | ||||
\(883\) | 13.2143 | 0.444695 | 0.222348 | − | 0.974967i | \(-0.428628\pi\) | ||||
0.222348 | + | 0.974967i | \(0.428628\pi\) | |||||||
\(884\) | 3.99895 | + | 3.33154i | 0.134499 | + | 0.112052i | ||||
\(885\) | −7.59586 | − | 13.1564i | −0.255332 | − | 0.442248i | ||||
\(886\) | 2.95650 | − | 1.70694i | 0.0993255 | − | 0.0573456i | ||||
\(887\) | −26.1349 | + | 45.2669i | −0.877523 | + | 1.51991i | −0.0234721 | + | 0.999724i | \(0.507472\pi\) |
−0.854051 | + | 0.520190i | \(0.825861\pi\) | |||||||
\(888\) | −11.4213 | −0.383273 | ||||||||
\(889\) | −3.25185 | + | 1.39666i | −0.109063 | + | 0.0468425i | ||||
\(890\) | − | 21.1327i | − | 0.708370i | ||||||
\(891\) | 3.75189 | + | 2.16615i | 0.125693 | + | 0.0725688i | ||||
\(892\) | 1.74390 | − | 1.00684i | 0.0583901 | − | 0.0337115i | ||||
\(893\) | −5.48656 | − | 9.50300i | −0.183601 | − | 0.318006i | ||||
\(894\) | 6.14082 | − | 10.6362i | 0.205380 | − | 0.355728i | ||||
\(895\) | 67.4766i | 2.25549i | ||||||||
\(896\) | 2.62738 | + | 0.311278i | 0.0877745 | + | 0.0103991i | ||||
\(897\) | 2.89783 | − | 16.7805i | 0.0967556 | − | 0.560283i | ||||
\(898\) | 11.6200 | − | 20.1265i | 0.387765 | − | 0.671629i | ||||
\(899\) | 5.02200 | − | 2.89945i | 0.167493 | − | 0.0967022i | ||||
\(900\) | −2.08326 | − | 3.60832i | −0.0694421 | − | 0.120277i | ||||
\(901\) | 2.96361 | − | 5.13311i | 0.0987320 | − | 0.171009i | ||||
\(902\) | 36.9724i | 1.23105i | ||||||||
\(903\) | 10.8232 | + | 8.08402i | 0.360174 | + | 0.269019i | ||||
\(904\) | − | 9.40986i | − | 0.312967i | ||||||
\(905\) | −32.5870 | − | 18.8141i | −1.08323 | − | 0.625403i | ||||
\(906\) | 7.27554 | + | 12.6016i | 0.241714 | + | 0.418660i | ||||
\(907\) | −13.5944 | − | 23.5462i | −0.451395 | − | 0.781839i | 0.547078 | − | 0.837082i | \(-0.315740\pi\) |
−0.998473 | + | 0.0552423i | \(0.982407\pi\) | |||||||
\(908\) | −5.33689 | − | 3.08125i | −0.177111 | − | 0.102255i | ||||
\(909\) | −1.19341 | −0.0395828 | ||||||||
\(910\) | −20.9689 | + | 19.8610i | −0.695113 | + | 0.658384i | ||||
\(911\) | −40.7858 | −1.35129 | −0.675647 | − | 0.737226i | \(-0.736135\pi\) | ||||
−0.675647 | + | 0.737226i | \(0.736135\pi\) | |||||||
\(912\) | −1.12988 | − | 0.652339i | −0.0374142 | − | 0.0216011i | ||||
\(913\) | 36.9508 | + | 64.0006i | 1.22289 | + | 2.11811i | ||||
\(914\) | 6.91167 | + | 11.9714i | 0.228618 | + | 0.395978i | ||||
\(915\) | 2.64999 | + | 1.52998i | 0.0876061 | + | 0.0505794i | ||||
\(916\) | − | 15.1810i | − | 0.501596i | ||||||
\(917\) | 3.84233 | − | 32.4316i | 0.126885 | − | 1.07099i | ||||
\(918\) | 1.44358i | 0.0476451i | ||||||||
\(919\) | −1.84415 | + | 3.19416i | −0.0608329 | + | 0.105366i | −0.894838 | − | 0.446391i | \(-0.852709\pi\) |
0.834005 | + | 0.551757i | \(0.186042\pi\) | |||||||
\(920\) | 7.14967 | + | 12.3836i | 0.235717 | + | 0.408275i | ||||
\(921\) | −11.4112 | + | 6.58828i | −0.376013 | + | 0.217091i | ||||
\(922\) | −11.1972 | + | 19.3940i | −0.368759 | + | 0.638709i | ||||
\(923\) | −44.4105 | − | 7.66927i | −1.46179 | − | 0.252437i | ||||
\(924\) | 4.52342 | + | 10.5319i | 0.148810 | + | 0.346474i | ||||
\(925\) | 47.5870i | 1.56465i | ||||||||
\(926\) | −4.59473 | + | 7.95830i | −0.150992 | + | 0.261526i | ||||
\(927\) | −7.58706 | − | 13.1412i | −0.249192 | − | 0.431613i | ||||
\(928\) | −2.96227 | + | 1.71027i | −0.0972412 | + | 0.0561422i | ||||
\(929\) | −12.8508 | − | 7.41939i | −0.421620 | − | 0.243422i | 0.274150 | − | 0.961687i | \(-0.411603\pi\) |
−0.695770 | + | 0.718264i | \(0.744937\pi\) | |||||||
\(930\) | − | 5.13281i | − | 0.168311i | ||||||
\(931\) | 8.75725 | − | 2.59182i | 0.287007 | − | 0.0849434i | ||||
\(932\) | 20.8027 | 0.681417 | ||||||||
\(933\) | −8.61548 | + | 14.9225i | −0.282058 | + | 0.488539i | ||||
\(934\) | −12.2944 | + | 7.09820i | −0.402286 | + | 0.232260i | ||||
\(935\) | −9.46740 | − | 16.3980i | −0.309617 | − | 0.536272i | ||||
\(936\) | 2.30784 | − | 2.77017i | 0.0754342 | − | 0.0905460i | ||||
\(937\) | 17.1603 | 0.560603 | 0.280302 | − | 0.959912i | \(-0.409566\pi\) | ||||
0.280302 | + | 0.959912i | \(0.409566\pi\) | |||||||
\(938\) | −1.15850 | + | 0.497571i | −0.0378263 | + | 0.0162463i | ||||
\(939\) | −8.90859 | −0.290721 | ||||||||
\(940\) | −12.7321 | + | 22.0526i | −0.415275 | + | 0.719277i | ||||
\(941\) | −47.0047 | + | 27.1382i | −1.53231 | + | 0.884679i | −0.533055 | + | 0.846081i | \(0.678956\pi\) |
−0.999255 | + | 0.0385989i | \(0.987711\pi\) | |||||||
\(942\) | 8.33864 | − | 4.81431i | 0.271688 | − | 0.156859i | ||||
\(943\) | 34.9062 | + | 20.1531i | 1.13670 | + | 0.656276i | ||||
\(944\) | 5.01770i | 0.163312i | ||||||||
\(945\) | −7.95472 | − | 0.942433i | −0.258767 | − | 0.0306573i | ||||
\(946\) | 22.1204 | 0.719197 | ||||||||
\(947\) | 13.7462 | + | 7.93635i | 0.446690 | + | 0.257897i | 0.706431 | − | 0.707781i | \(-0.250304\pi\) |
−0.259741 | + | 0.965678i | \(0.583637\pi\) | |||||||
\(948\) | −7.34649 | − | 12.7245i | −0.238603 | − | 0.413272i | ||||
\(949\) | −4.91832 | − | 13.3660i | −0.159655 | − | 0.433879i | ||||
\(950\) | −2.71798 | + | 4.70769i | −0.0881831 | + | 0.152738i | ||||
\(951\) | 5.91861i | 0.191924i | ||||||||
\(952\) | −2.28556 | + | 3.06000i | −0.0740754 | + | 0.0991751i | ||||
\(953\) | −37.8350 | −1.22560 | −0.612799 | − | 0.790239i | \(-0.709956\pi\) | ||||
−0.612799 | + | 0.790239i | \(0.709956\pi\) | |||||||
\(954\) | −3.55583 | − | 2.05296i | −0.115124 | − | 0.0664671i | ||||
\(955\) | 56.4100 | − | 32.5683i | 1.82538 | − | 1.05389i | ||||
\(956\) | −5.72127 | + | 3.30317i | −0.185039 | + | 0.106832i | ||||
\(957\) | −12.8334 | − | 7.40939i | −0.414846 | − | 0.239512i | ||||
\(958\) | 14.1006 | 0.455569 | ||||||||
\(959\) | −14.4656 | + | 19.3671i | −0.467118 | + | 0.625396i | ||||
\(960\) | 3.02763i | 0.0977162i | ||||||||
\(961\) | −14.0629 | + | 24.3577i | −0.453643 | + | 0.785733i | ||||
\(962\) | −38.6466 | + | 14.2209i | −1.24602 | + | 0.458499i | ||||
\(963\) | −4.00998 | − | 6.94549i | −0.129220 | − | 0.223815i | ||||
\(964\) | −19.6527 | − | 11.3465i | −0.632971 | − | 0.365446i | ||||
\(965\) | 5.81820 | 0.187294 | ||||||||
\(966\) | 12.4090 | + | 1.47015i | 0.399252 | + | 0.0473013i | ||||
\(967\) | 17.8749i | 0.574816i | 0.957808 | + | 0.287408i | \(0.0927936\pi\) | ||||
−0.957808 | + | 0.287408i | \(0.907206\pi\) | |||||||
\(968\) | 6.72803 | + | 3.88443i | 0.216247 | + | 0.124850i | ||||
\(969\) | 1.63107 | − | 0.941700i | 0.0523976 | − | 0.0302518i | ||||
\(970\) | 41.7187 | − | 24.0863i | 1.33951 | − | 0.773364i | ||||
\(971\) | 6.16502 | − | 10.6781i | 0.197845 | − | 0.342678i | −0.749984 | − | 0.661455i | \(-0.769939\pi\) |
0.947829 | + | 0.318778i | \(0.103272\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −43.3254 | + | 18.6081i | −1.38895 | + | 0.596550i | ||||
\(974\) | −13.3790 | −0.428692 | ||||||||
\(975\) | −11.5420 | − | 9.61568i | −0.369640 | − | 0.307948i | ||||
\(976\) | −0.505338 | − | 0.875271i | −0.0161755 | − | 0.0280167i | ||||
\(977\) | 33.5617 | − | 19.3769i | 1.07374 | − | 0.619921i | 0.144536 | − | 0.989500i | \(-0.453831\pi\) |
0.929200 | + | 0.369578i | \(0.120498\pi\) | |||||||
\(978\) | −8.47691 | + | 14.6824i | −0.271062 | + | 0.469493i | ||||
\(979\) | −30.2393 | −0.966453 | ||||||||
\(980\) | −15.3698 | − | 14.5921i | −0.490969 | − | 0.466128i | ||||
\(981\) | − | 1.05067i | − | 0.0335453i | ||||||
\(982\) | 17.6262 | + | 10.1765i | 0.562475 | + | 0.324745i | ||||
\(983\) | 6.61511 | − | 3.81923i | 0.210989 | − | 0.121815i | −0.390782 | − | 0.920483i | \(-0.627795\pi\) |
0.601771 | + | 0.798669i | \(0.294462\pi\) | |||||||
\(984\) | 4.26706 | + | 7.39077i | 0.136029 | + | 0.235609i | ||||
\(985\) | 8.40330 | − | 14.5549i | 0.267751 | − | 0.463759i | ||||
\(986\) | − | 4.93779i | − | 0.157251i | ||||||
\(987\) | 8.78162 | + | 20.4463i | 0.279522 | + | 0.650812i | ||||
\(988\) | −4.63547 | − | 0.800501i | −0.147474 | − | 0.0254673i | ||||
\(989\) | 12.0575 | − | 20.8842i | 0.383407 | − | 0.664080i | ||||
\(990\) | −11.3593 | + | 6.55830i | −0.361023 | + | 0.208436i | ||||
\(991\) | −11.0735 | − | 19.1798i | −0.351760 | − | 0.609266i | 0.634798 | − | 0.772678i | \(-0.281083\pi\) |
−0.986558 | + | 0.163412i | \(0.947750\pi\) | |||||||
\(992\) | −0.847661 | + | 1.46819i | −0.0269133 | + | 0.0466152i | ||||
\(993\) | − | 11.6816i | − | 0.370703i | ||||||
\(994\) | 3.89084 | − | 32.8411i | 0.123410 | − | 1.04166i | ||||
\(995\) | 21.4650i | 0.680487i | ||||||||
\(996\) | 14.7729 | + | 8.52913i | 0.468097 | + | 0.270256i | ||||
\(997\) | 3.59787 | + | 6.23169i | 0.113946 | + | 0.197359i | 0.917358 | − | 0.398064i | \(-0.130318\pi\) |
−0.803412 | + | 0.595423i | \(0.796984\pi\) | |||||||
\(998\) | −14.4797 | − | 25.0796i | −0.458347 | − | 0.793881i | ||||
\(999\) | −9.89112 | − | 5.71064i | −0.312941 | − | 0.180677i |
(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.415.6 | yes | 20 | |
3.2 | odd | 2 | 1638.2.dm.e.415.5 | 20 | |||
7.2 | even | 3 | 3822.2.c.m.883.5 | 10 | |||
7.4 | even | 3 | inner | 546.2.bk.c.25.5 | ✓ | 20 | |
7.5 | odd | 6 | 3822.2.c.n.883.1 | 10 | |||
13.12 | even | 2 | inner | 546.2.bk.c.415.5 | yes | 20 | |
21.11 | odd | 6 | 1638.2.dm.e.1117.6 | 20 | |||
39.38 | odd | 2 | 1638.2.dm.e.415.6 | 20 | |||
91.12 | odd | 6 | 3822.2.c.n.883.10 | 10 | |||
91.25 | even | 6 | inner | 546.2.bk.c.25.6 | yes | 20 | |
91.51 | even | 6 | 3822.2.c.m.883.6 | 10 | |||
273.116 | odd | 6 | 1638.2.dm.e.1117.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bk.c.25.5 | ✓ | 20 | 7.4 | even | 3 | inner | |
546.2.bk.c.25.6 | yes | 20 | 91.25 | even | 6 | inner | |
546.2.bk.c.415.5 | yes | 20 | 13.12 | even | 2 | inner | |
546.2.bk.c.415.6 | yes | 20 | 1.1 | even | 1 | trivial | |
1638.2.dm.e.415.5 | 20 | 3.2 | odd | 2 | |||
1638.2.dm.e.415.6 | 20 | 39.38 | odd | 2 | |||
1638.2.dm.e.1117.5 | 20 | 273.116 | odd | 6 | |||
1638.2.dm.e.1117.6 | 20 | 21.11 | odd | 6 | |||
3822.2.c.m.883.5 | 10 | 7.2 | even | 3 | |||
3822.2.c.m.883.6 | 10 | 91.51 | even | 6 | |||
3822.2.c.n.883.1 | 10 | 7.5 | odd | 6 | |||
3822.2.c.n.883.10 | 10 | 91.12 | odd | 6 |