Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(100,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.7965937851507.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.3 | ||
Root | \(0.333779 + 0.578123i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.100 |
Dual form | 429.2.i.c.133.3 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.333779 | + | 0.578123i | −0.236018 | + | 0.408794i | −0.959568 | − | 0.281477i | \(-0.909176\pi\) |
0.723550 | + | 0.690272i | \(0.242509\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.777183 | + | 1.34612i | 0.388591 | + | 0.673060i | ||||
\(5\) | 0.849177 | 0.379764 | 0.189882 | − | 0.981807i | \(-0.439190\pi\) | ||||
0.189882 | + | 0.981807i | \(0.439190\pi\) | |||||||
\(6\) | −0.333779 | − | 0.578123i | −0.136265 | − | 0.236018i | ||||
\(7\) | 1.61499 | + | 2.79724i | 0.610407 | + | 1.05726i | 0.991172 | + | 0.132584i | \(0.0423276\pi\) |
−0.380764 | + | 0.924672i | \(0.624339\pi\) | |||||||
\(8\) | −2.37275 | −0.838893 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.283438 | + | 0.490929i | −0.0896309 | + | 0.155245i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −1.55437 | −0.448707 | ||||||||
\(13\) | 2.86690 | + | 2.18653i | 0.795134 | + | 0.606433i | ||||
\(14\) | −2.15620 | −0.576267 | ||||||||
\(15\) | −0.424589 | + | 0.735409i | −0.109628 | + | 0.189882i | ||||
\(16\) | −0.762392 | + | 1.32050i | −0.190598 | + | 0.330125i | ||||
\(17\) | 0.394400 | + | 0.683120i | 0.0956560 | + | 0.165681i | 0.909882 | − | 0.414867i | \(-0.136172\pi\) |
−0.814226 | + | 0.580548i | \(0.802838\pi\) | |||||||
\(18\) | 0.667559 | 0.157345 | ||||||||
\(19\) | −1.49508 | − | 2.58956i | −0.342996 | − | 0.594086i | 0.641992 | − | 0.766711i | \(-0.278108\pi\) |
−0.984988 | + | 0.172626i | \(0.944775\pi\) | |||||||
\(20\) | 0.659966 | + | 1.14309i | 0.147573 | + | 0.255604i | ||||
\(21\) | −3.22997 | −0.704838 | ||||||||
\(22\) | 0.333779 | + | 0.578123i | 0.0711620 | + | 0.123256i | ||||
\(23\) | 1.75594 | − | 3.04137i | 0.366138 | − | 0.634169i | −0.622820 | − | 0.782365i | \(-0.714013\pi\) |
0.988958 | + | 0.148196i | \(0.0473465\pi\) | |||||||
\(24\) | 1.18637 | − | 2.05486i | 0.242167 | − | 0.419446i | ||||
\(25\) | −4.27890 | −0.855780 | ||||||||
\(26\) | −2.22099 | + | 0.927601i | −0.435572 | + | 0.181918i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.51028 | + | 4.34793i | −0.474398 | + | 0.821682i | ||||
\(29\) | −0.576749 | + | 0.998959i | −0.107100 | + | 0.185502i | −0.914594 | − | 0.404373i | \(-0.867490\pi\) |
0.807494 | + | 0.589875i | \(0.200823\pi\) | |||||||
\(30\) | −0.283438 | − | 0.490929i | −0.0517484 | − | 0.0896309i | ||||
\(31\) | 0.0322574 | 0.00579360 | 0.00289680 | − | 0.999996i | \(-0.499078\pi\) | ||||
0.00289680 | + | 0.999996i | \(0.499078\pi\) | |||||||
\(32\) | −2.88169 | − | 4.99123i | −0.509415 | − | 0.882333i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | −0.526570 | −0.0903060 | ||||||||
\(35\) | 1.37141 | + | 2.37535i | 0.231810 | + | 0.401508i | ||||
\(36\) | 0.777183 | − | 1.34612i | 0.129530 | − | 0.224353i | ||||
\(37\) | −2.53312 | + | 4.38749i | −0.416442 | + | 0.721299i | −0.995579 | − | 0.0939317i | \(-0.970056\pi\) |
0.579137 | + | 0.815231i | \(0.303390\pi\) | |||||||
\(38\) | 1.99611 | 0.323812 | ||||||||
\(39\) | −3.32704 | + | 1.38954i | −0.532752 | + | 0.222505i | ||||
\(40\) | −2.01488 | −0.318581 | ||||||||
\(41\) | −1.86665 | + | 3.23314i | −0.291522 | + | 0.504932i | −0.974170 | − | 0.225816i | \(-0.927495\pi\) |
0.682648 | + | 0.730748i | \(0.260828\pi\) | |||||||
\(42\) | 1.07810 | − | 1.86732i | 0.166354 | − | 0.288134i | ||||
\(43\) | 1.10048 | + | 1.90609i | 0.167822 | + | 0.290676i | 0.937654 | − | 0.347571i | \(-0.112993\pi\) |
−0.769832 | + | 0.638247i | \(0.779660\pi\) | |||||||
\(44\) | 1.55437 | 0.234329 | ||||||||
\(45\) | −0.424589 | − | 0.735409i | −0.0632939 | − | 0.109628i | ||||
\(46\) | 1.17219 | + | 2.03029i | 0.172830 | + | 0.299350i | ||||
\(47\) | 1.56420 | 0.228162 | 0.114081 | − | 0.993471i | \(-0.463608\pi\) | ||||
0.114081 | + | 0.993471i | \(0.463608\pi\) | |||||||
\(48\) | −0.762392 | − | 1.32050i | −0.110042 | − | 0.190598i | ||||
\(49\) | −1.71636 | + | 2.97282i | −0.245194 | + | 0.424689i | ||||
\(50\) | 1.42821 | − | 2.47373i | 0.201979 | − | 0.349838i | ||||
\(51\) | −0.788800 | −0.110454 | ||||||||
\(52\) | −0.715225 | + | 5.55852i | −0.0991838 | + | 0.770828i | ||||
\(53\) | 0.836264 | 0.114870 | 0.0574348 | − | 0.998349i | \(-0.481708\pi\) | ||||
0.0574348 | + | 0.998349i | \(0.481708\pi\) | |||||||
\(54\) | −0.333779 | + | 0.578123i | −0.0454216 | + | 0.0786725i | ||||
\(55\) | 0.424589 | − | 0.735409i | 0.0572515 | − | 0.0991625i | ||||
\(56\) | −3.83195 | − | 6.63714i | −0.512066 | − | 0.886925i | ||||
\(57\) | 2.99017 | 0.396057 | ||||||||
\(58\) | −0.385014 | − | 0.666864i | −0.0505548 | − | 0.0875635i | ||||
\(59\) | −4.95844 | − | 8.58827i | −0.645534 | − | 1.11810i | −0.984178 | − | 0.177183i | \(-0.943302\pi\) |
0.338644 | − | 0.940914i | \(-0.390032\pi\) | |||||||
\(60\) | −1.31993 | −0.170402 | ||||||||
\(61\) | 3.25237 | + | 5.63326i | 0.416423 | + | 0.721266i | 0.995577 | − | 0.0939527i | \(-0.0299503\pi\) |
−0.579154 | + | 0.815218i | \(0.696617\pi\) | |||||||
\(62\) | −0.0107668 | + | 0.0186487i | −0.00136739 | + | 0.00236839i | ||||
\(63\) | 1.61499 | − | 2.79724i | 0.203469 | − | 0.352419i | ||||
\(64\) | 0.797823 | 0.0997279 | ||||||||
\(65\) | 2.43450 | + | 1.85675i | 0.301963 | + | 0.230301i | ||||
\(66\) | −0.667559 | −0.0821708 | ||||||||
\(67\) | 4.97112 | − | 8.61023i | 0.607319 | − | 1.05191i | −0.384362 | − | 0.923183i | \(-0.625579\pi\) |
0.991680 | − | 0.128724i | \(-0.0410882\pi\) | |||||||
\(68\) | −0.613041 | + | 1.06182i | −0.0743422 | + | 0.128764i | ||||
\(69\) | 1.75594 | + | 3.04137i | 0.211390 | + | 0.366138i | ||||
\(70\) | −1.83099 | −0.218845 | ||||||||
\(71\) | −2.15009 | − | 3.72407i | −0.255169 | − | 0.441966i | 0.709772 | − | 0.704431i | \(-0.248798\pi\) |
−0.964941 | + | 0.262465i | \(0.915464\pi\) | |||||||
\(72\) | 1.18637 | + | 2.05486i | 0.139815 | + | 0.242167i | ||||
\(73\) | 6.19771 | 0.725388 | 0.362694 | − | 0.931908i | \(-0.381857\pi\) | ||||
0.362694 | + | 0.931908i | \(0.381857\pi\) | |||||||
\(74\) | −1.69100 | − | 2.92891i | −0.196575 | − | 0.340478i | ||||
\(75\) | 2.13945 | − | 3.70563i | 0.247042 | − | 0.427890i | ||||
\(76\) | 2.32391 | − | 4.02512i | 0.266570 | − | 0.461713i | ||||
\(77\) | 3.22997 | 0.368090 | ||||||||
\(78\) | 0.307170 | − | 2.38724i | 0.0347801 | − | 0.270301i | ||||
\(79\) | 12.5074 | 1.40719 | 0.703597 | − | 0.710600i | \(-0.251576\pi\) | ||||
0.703597 | + | 0.710600i | \(0.251576\pi\) | |||||||
\(80\) | −0.647406 | + | 1.12134i | −0.0723822 | + | 0.125370i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.24610 | − | 2.15831i | −0.137609 | − | 0.238345i | ||||
\(83\) | 16.6507 | 1.82765 | 0.913824 | − | 0.406110i | \(-0.133115\pi\) | ||||
0.913824 | + | 0.406110i | \(0.133115\pi\) | |||||||
\(84\) | −2.51028 | − | 4.34793i | −0.273894 | − | 0.474398i | ||||
\(85\) | 0.334915 | + | 0.580090i | 0.0363267 | + | 0.0629196i | ||||
\(86\) | −1.46927 | −0.158436 | ||||||||
\(87\) | −0.576749 | − | 0.998959i | −0.0618340 | − | 0.107100i | ||||
\(88\) | −1.18637 | + | 2.05486i | −0.126468 | + | 0.219049i | ||||
\(89\) | 4.75163 | − | 8.23006i | 0.503671 | − | 0.872384i | −0.496320 | − | 0.868140i | \(-0.665316\pi\) |
0.999991 | − | 0.00424439i | \(-0.00135104\pi\) | |||||||
\(90\) | 0.566875 | 0.0597539 | ||||||||
\(91\) | −1.48624 | + | 11.5506i | −0.155800 | + | 1.21083i | ||||
\(92\) | 5.45873 | 0.569112 | ||||||||
\(93\) | −0.0161287 | + | 0.0279357i | −0.00167247 | + | 0.00289680i | ||||
\(94\) | −0.522097 | + | 0.904299i | −0.0538502 | + | 0.0932714i | ||||
\(95\) | −1.26959 | − | 2.19899i | −0.130257 | − | 0.225612i | ||||
\(96\) | 5.76338 | 0.588222 | ||||||||
\(97\) | −5.84903 | − | 10.1308i | −0.593879 | − | 1.02863i | −0.993704 | − | 0.112037i | \(-0.964263\pi\) |
0.399826 | − | 0.916591i | \(-0.369071\pi\) | |||||||
\(98\) | −1.14577 | − | 1.98453i | −0.115740 | − | 0.200468i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −3.32549 | − | 5.75991i | −0.332549 | − | 0.575991i | ||||
\(101\) | −7.10926 | + | 12.3136i | −0.707398 | + | 1.22525i | 0.258421 | + | 0.966032i | \(0.416798\pi\) |
−0.965819 | + | 0.259217i | \(0.916536\pi\) | |||||||
\(102\) | 0.263285 | − | 0.456023i | 0.0260691 | − | 0.0451530i | ||||
\(103\) | 11.7245 | 1.15525 | 0.577623 | − | 0.816304i | \(-0.303980\pi\) | ||||
0.577623 | + | 0.816304i | \(0.303980\pi\) | |||||||
\(104\) | −6.80242 | − | 5.18808i | −0.667032 | − | 0.508733i | ||||
\(105\) | −2.74282 | −0.267672 | ||||||||
\(106\) | −0.279128 | + | 0.483463i | −0.0271113 | + | 0.0469581i | ||||
\(107\) | 5.84391 | − | 10.1219i | 0.564952 | − | 0.978525i | −0.432102 | − | 0.901825i | \(-0.642228\pi\) |
0.997054 | − | 0.0767006i | \(-0.0244386\pi\) | |||||||
\(108\) | 0.777183 | + | 1.34612i | 0.0747845 | + | 0.129530i | ||||
\(109\) | 6.84618 | 0.655745 | 0.327872 | − | 0.944722i | \(-0.393668\pi\) | ||||
0.327872 | + | 0.944722i | \(0.393668\pi\) | |||||||
\(110\) | 0.283438 | + | 0.490929i | 0.0270247 | + | 0.0468082i | ||||
\(111\) | −2.53312 | − | 4.38749i | −0.240433 | − | 0.416442i | ||||
\(112\) | −4.92501 | −0.465370 | ||||||||
\(113\) | 5.17459 | + | 8.96265i | 0.486784 | + | 0.843135i | 0.999885 | − | 0.0151934i | \(-0.00483638\pi\) |
−0.513100 | + | 0.858329i | \(0.671503\pi\) | |||||||
\(114\) | −0.998055 | + | 1.72868i | −0.0934764 | + | 0.161906i | ||||
\(115\) | 1.49110 | − | 2.58266i | 0.139046 | − | 0.240834i | ||||
\(116\) | −1.79296 | −0.166472 | ||||||||
\(117\) | 0.460139 | − | 3.57607i | 0.0425399 | − | 0.330608i | ||||
\(118\) | 6.62009 | 0.609429 | ||||||||
\(119\) | −1.27390 | + | 2.20646i | −0.116778 | + | 0.202266i | ||||
\(120\) | 1.00744 | − | 1.74494i | 0.0919664 | − | 0.159290i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −4.34229 | −0.393132 | ||||||||
\(123\) | −1.86665 | − | 3.23314i | −0.168311 | − | 0.291522i | ||||
\(124\) | 0.0250699 | + | 0.0434223i | 0.00225134 | + | 0.00389944i | ||||
\(125\) | −7.87943 | −0.704757 | ||||||||
\(126\) | 1.07810 | + | 1.86732i | 0.0960446 | + | 0.166354i | ||||
\(127\) | −4.32301 | + | 7.48768i | −0.383605 | + | 0.664424i | −0.991575 | − | 0.129537i | \(-0.958651\pi\) |
0.607969 | + | 0.793961i | \(0.291984\pi\) | |||||||
\(128\) | 5.49708 | − | 9.52122i | 0.485878 | − | 0.841565i | ||||
\(129\) | −2.20096 | −0.193784 | ||||||||
\(130\) | −1.88602 | + | 0.787697i | −0.165414 | + | 0.0690856i | ||||
\(131\) | −10.1086 | −0.883196 | −0.441598 | − | 0.897213i | \(-0.645588\pi\) | ||||
−0.441598 | + | 0.897213i | \(0.645588\pi\) | |||||||
\(132\) | −0.777183 | + | 1.34612i | −0.0676451 | + | 0.117165i | ||||
\(133\) | 4.82908 | − | 8.36421i | 0.418734 | − | 0.725269i | ||||
\(134\) | 3.31851 | + | 5.74783i | 0.286676 | + | 0.496537i | ||||
\(135\) | 0.849177 | 0.0730855 | ||||||||
\(136\) | −0.935811 | − | 1.62087i | −0.0802451 | − | 0.138989i | ||||
\(137\) | −6.91951 | − | 11.9849i | −0.591174 | − | 1.02394i | −0.994075 | − | 0.108699i | \(-0.965331\pi\) |
0.402901 | − | 0.915244i | \(-0.368002\pi\) | |||||||
\(138\) | −2.34438 | −0.199567 | ||||||||
\(139\) | −3.42922 | − | 5.93958i | −0.290863 | − | 0.503789i | 0.683151 | − | 0.730277i | \(-0.260609\pi\) |
−0.974014 | + | 0.226488i | \(0.927276\pi\) | |||||||
\(140\) | −2.13167 | + | 3.69216i | −0.180159 | + | 0.312045i | ||||
\(141\) | −0.782100 | + | 1.35464i | −0.0658647 | + | 0.114081i | ||||
\(142\) | 2.87062 | 0.240897 | ||||||||
\(143\) | 3.32704 | − | 1.38954i | 0.278221 | − | 0.116199i | ||||
\(144\) | 1.52478 | 0.127065 | ||||||||
\(145\) | −0.489762 | + | 0.848293i | −0.0406725 | + | 0.0704469i | ||||
\(146\) | −2.06867 | + | 3.58304i | −0.171204 | + | 0.296534i | ||||
\(147\) | −1.71636 | − | 2.97282i | −0.141563 | − | 0.245194i | ||||
\(148\) | −7.87478 | −0.647303 | ||||||||
\(149\) | 8.21454 | + | 14.2280i | 0.672962 | + | 1.16560i | 0.977060 | + | 0.212963i | \(0.0683114\pi\) |
−0.304099 | + | 0.952641i | \(0.598355\pi\) | |||||||
\(150\) | 1.42821 | + | 2.47373i | 0.116613 | + | 0.201979i | ||||
\(151\) | 7.36374 | 0.599253 | 0.299627 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299627 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(152\) | 3.54745 | + | 6.14437i | 0.287736 | + | 0.498374i | ||||
\(153\) | 0.394400 | − | 0.683120i | 0.0318853 | − | 0.0552270i | ||||
\(154\) | −1.07810 | + | 1.86732i | −0.0868756 | + | 0.150473i | ||||
\(155\) | 0.0273922 | 0.00220020 | ||||||||
\(156\) | −4.45621 | − | 3.39866i | −0.356782 | − | 0.272111i | ||||
\(157\) | 21.5732 | 1.72173 | 0.860865 | − | 0.508833i | \(-0.169923\pi\) | ||||
0.860865 | + | 0.508833i | \(0.169923\pi\) | |||||||
\(158\) | −4.17471 | + | 7.23082i | −0.332122 | + | 0.575253i | ||||
\(159\) | −0.418132 | + | 0.724226i | −0.0331600 | + | 0.0574348i | ||||
\(160\) | −2.44706 | − | 4.23844i | −0.193457 | − | 0.335078i | ||||
\(161\) | 11.3432 | 0.893973 | ||||||||
\(162\) | −0.333779 | − | 0.578123i | −0.0262242 | − | 0.0454216i | ||||
\(163\) | −6.87689 | − | 11.9111i | −0.538640 | − | 0.932951i | −0.998978 | − | 0.0452074i | \(-0.985605\pi\) |
0.460338 | − | 0.887744i | \(-0.347728\pi\) | |||||||
\(164\) | −5.80293 | −0.453132 | ||||||||
\(165\) | 0.424589 | + | 0.735409i | 0.0330542 | + | 0.0572515i | ||||
\(166\) | −5.55765 | + | 9.62613i | −0.431357 | + | 0.747132i | ||||
\(167\) | −5.29848 | + | 9.17724i | −0.410009 | + | 0.710156i | −0.994890 | − | 0.100963i | \(-0.967808\pi\) |
0.584881 | + | 0.811119i | \(0.301141\pi\) | |||||||
\(168\) | 7.66391 | 0.591283 | ||||||||
\(169\) | 3.43820 | + | 12.5371i | 0.264477 | + | 0.964392i | ||||
\(170\) | −0.447151 | −0.0342949 | ||||||||
\(171\) | −1.49508 | + | 2.58956i | −0.114332 | + | 0.198029i | ||||
\(172\) | −1.71055 | + | 2.96276i | −0.130428 | + | 0.225908i | ||||
\(173\) | 2.18012 | + | 3.77608i | 0.165751 | + | 0.287090i | 0.936922 | − | 0.349539i | \(-0.113662\pi\) |
−0.771170 | + | 0.636629i | \(0.780328\pi\) | |||||||
\(174\) | 0.770028 | 0.0583756 | ||||||||
\(175\) | −6.91036 | − | 11.9691i | −0.522374 | − | 0.904779i | ||||
\(176\) | 0.762392 | + | 1.32050i | 0.0574675 | + | 0.0995365i | ||||
\(177\) | 9.91687 | 0.745398 | ||||||||
\(178\) | 3.17199 | + | 5.49404i | 0.237751 | + | 0.411796i | ||||
\(179\) | −6.87137 | + | 11.9016i | −0.513590 | + | 0.889564i | 0.486286 | + | 0.873800i | \(0.338351\pi\) |
−0.999876 | + | 0.0157641i | \(0.994982\pi\) | |||||||
\(180\) | 0.659966 | − | 1.14309i | 0.0491910 | − | 0.0852012i | ||||
\(181\) | −15.1610 | −1.12691 | −0.563453 | − | 0.826148i | \(-0.690527\pi\) | ||||
−0.563453 | + | 0.826148i | \(0.690527\pi\) | |||||||
\(182\) | −6.18159 | − | 4.71458i | −0.458210 | − | 0.349468i | ||||
\(183\) | −6.50473 | −0.480844 | ||||||||
\(184\) | −4.16639 | + | 7.21640i | −0.307150 | + | 0.532000i | ||||
\(185\) | −2.15107 | + | 3.72576i | −0.158150 | + | 0.273923i | ||||
\(186\) | −0.0107668 | − | 0.0186487i | −0.000789464 | − | 0.00136739i | ||||
\(187\) | 0.788800 | 0.0576827 | ||||||||
\(188\) | 1.21567 | + | 2.10560i | 0.0886618 | + | 0.153567i | ||||
\(189\) | 1.61499 | + | 2.79724i | 0.117473 | + | 0.203469i | ||||
\(190\) | 1.69505 | 0.122972 | ||||||||
\(191\) | 1.48435 | + | 2.57097i | 0.107404 | + | 0.186029i | 0.914718 | − | 0.404093i | \(-0.132413\pi\) |
−0.807314 | + | 0.590122i | \(0.799080\pi\) | |||||||
\(192\) | −0.398912 | + | 0.690935i | −0.0287890 | + | 0.0498640i | ||||
\(193\) | 2.90711 | − | 5.03526i | 0.209258 | − | 0.362446i | −0.742223 | − | 0.670153i | \(-0.766228\pi\) |
0.951481 | + | 0.307707i | \(0.0995617\pi\) | |||||||
\(194\) | 7.80913 | 0.560663 | ||||||||
\(195\) | −2.82524 | + | 1.17997i | −0.202320 | + | 0.0844992i | ||||
\(196\) | −5.33570 | −0.381122 | ||||||||
\(197\) | −4.22473 | + | 7.31745i | −0.301000 | + | 0.521346i | −0.976363 | − | 0.216139i | \(-0.930654\pi\) |
0.675363 | + | 0.737485i | \(0.263987\pi\) | |||||||
\(198\) | 0.333779 | − | 0.578123i | 0.0237207 | − | 0.0410854i | ||||
\(199\) | −7.28654 | − | 12.6207i | −0.516529 | − | 0.894654i | −0.999816 | − | 0.0191922i | \(-0.993891\pi\) |
0.483287 | − | 0.875462i | \(-0.339443\pi\) | |||||||
\(200\) | 10.1527 | 0.717907 | ||||||||
\(201\) | 4.97112 | + | 8.61023i | 0.350636 | + | 0.607319i | ||||
\(202\) | −4.74585 | − | 8.22005i | −0.333917 | − | 0.578361i | ||||
\(203\) | −3.72577 | −0.261498 | ||||||||
\(204\) | −0.613041 | − | 1.06182i | −0.0429215 | − | 0.0743422i | ||||
\(205\) | −1.58512 | + | 2.74551i | −0.110710 | + | 0.191755i | ||||
\(206\) | −3.91338 | + | 6.77818i | −0.272658 | + | 0.472258i | ||||
\(207\) | −3.51187 | −0.244092 | ||||||||
\(208\) | −5.07301 | + | 2.11875i | −0.351750 | + | 0.146909i | ||||
\(209\) | −2.99017 | −0.206834 | ||||||||
\(210\) | 0.915496 | − | 1.58569i | 0.0631752 | − | 0.109423i | ||||
\(211\) | −4.79309 | + | 8.30187i | −0.329970 | + | 0.571524i | −0.982506 | − | 0.186234i | \(-0.940372\pi\) |
0.652536 | + | 0.757758i | \(0.273705\pi\) | |||||||
\(212\) | 0.649930 | + | 1.12571i | 0.0446374 | + | 0.0773142i | ||||
\(213\) | 4.30018 | 0.294644 | ||||||||
\(214\) | 3.90115 | + | 6.75699i | 0.266677 | + | 0.461898i | ||||
\(215\) | 0.934504 | + | 1.61861i | 0.0637326 | + | 0.110388i | ||||
\(216\) | −2.37275 | −0.161445 | ||||||||
\(217\) | 0.0520952 | + | 0.0902316i | 0.00353646 | + | 0.00612532i | ||||
\(218\) | −2.28511 | + | 3.95793i | −0.154767 | + | 0.268065i | ||||
\(219\) | −3.09886 | + | 5.36738i | −0.209401 | + | 0.362694i | ||||
\(220\) | 1.31993 | 0.0889898 | ||||||||
\(221\) | −0.362958 | + | 2.82080i | −0.0244152 | + | 0.189748i | ||||
\(222\) | 3.38201 | 0.226986 | ||||||||
\(223\) | 4.60905 | − | 7.98311i | 0.308645 | − | 0.534589i | −0.669421 | − | 0.742883i | \(-0.733458\pi\) |
0.978066 | + | 0.208294i | \(0.0667912\pi\) | |||||||
\(224\) | 9.30777 | − | 16.1215i | 0.621902 | − | 1.07717i | ||||
\(225\) | 2.13945 | + | 3.70563i | 0.142630 | + | 0.247042i | ||||
\(226\) | −6.90868 | −0.459559 | ||||||||
\(227\) | −10.2799 | − | 17.8054i | −0.682304 | − | 1.18179i | −0.974276 | − | 0.225359i | \(-0.927645\pi\) |
0.291972 | − | 0.956427i | \(-0.405689\pi\) | |||||||
\(228\) | 2.32391 | + | 4.02512i | 0.153904 | + | 0.266570i | ||||
\(229\) | −6.92737 | −0.457774 | −0.228887 | − | 0.973453i | \(-0.573509\pi\) | ||||
−0.228887 | + | 0.973453i | \(0.573509\pi\) | |||||||
\(230\) | 0.995397 | + | 1.72408i | 0.0656345 | + | 0.113682i | ||||
\(231\) | −1.61499 | + | 2.79724i | −0.106258 | + | 0.184045i | ||||
\(232\) | 1.36848 | − | 2.37028i | 0.0898451 | − | 0.155616i | ||||
\(233\) | −9.94449 | −0.651485 | −0.325743 | − | 0.945459i | \(-0.605614\pi\) | ||||
−0.325743 | + | 0.945459i | \(0.605614\pi\) | |||||||
\(234\) | 1.91382 | + | 1.45963i | 0.125110 | + | 0.0954193i | ||||
\(235\) | 1.32828 | 0.0866476 | ||||||||
\(236\) | 7.70722 | − | 13.3493i | 0.501698 | − | 0.868966i | ||||
\(237\) | −6.25370 | + | 10.8317i | −0.406222 | + | 0.703597i | ||||
\(238\) | −0.850403 | − | 1.47294i | −0.0551234 | − | 0.0954766i | ||||
\(239\) | −10.7017 | −0.692237 | −0.346118 | − | 0.938191i | \(-0.612500\pi\) | ||||
−0.346118 | + | 0.938191i | \(0.612500\pi\) | |||||||
\(240\) | −0.647406 | − | 1.12134i | −0.0417899 | − | 0.0723822i | ||||
\(241\) | −12.2124 | − | 21.1525i | −0.786670 | − | 1.36255i | −0.927997 | − | 0.372589i | \(-0.878470\pi\) |
0.141327 | − | 0.989963i | \(-0.454863\pi\) | |||||||
\(242\) | 0.667559 | 0.0429123 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.05537 | + | 8.75615i | −0.323637 | + | 0.560555i | ||||
\(245\) | −1.45749 | + | 2.52445i | −0.0931159 | + | 0.161281i | ||||
\(246\) | 2.49220 | 0.158897 | ||||||||
\(247\) | 1.37589 | − | 10.6930i | 0.0875459 | − | 0.680382i | ||||
\(248\) | −0.0765386 | −0.00486021 | ||||||||
\(249\) | −8.32533 | + | 14.4199i | −0.527597 | + | 0.913824i | ||||
\(250\) | 2.62999 | − | 4.55528i | 0.166335 | − | 0.288101i | ||||
\(251\) | −2.44258 | − | 4.23068i | −0.154175 | − | 0.267038i | 0.778584 | − | 0.627541i | \(-0.215938\pi\) |
−0.932758 | + | 0.360503i | \(0.882605\pi\) | |||||||
\(252\) | 5.02056 | 0.316265 | ||||||||
\(253\) | −1.75594 | − | 3.04137i | −0.110395 | − | 0.191209i | ||||
\(254\) | −2.88586 | − | 4.99846i | −0.181075 | − | 0.313631i | ||||
\(255\) | −0.669831 | −0.0419464 | ||||||||
\(256\) | 4.46745 | + | 7.73784i | 0.279215 | + | 0.483615i | ||||
\(257\) | −11.6952 | + | 20.2567i | −0.729526 | + | 1.26358i | 0.227557 | + | 0.973765i | \(0.426926\pi\) |
−0.957084 | + | 0.289812i | \(0.906407\pi\) | |||||||
\(258\) | 0.734636 | − | 1.27243i | 0.0457364 | − | 0.0792178i | ||||
\(259\) | −16.3638 | −1.01680 | ||||||||
\(260\) | −0.607352 | + | 4.72017i | −0.0376664 | + | 0.292732i | ||||
\(261\) | 1.15350 | 0.0713998 | ||||||||
\(262\) | 3.37406 | − | 5.84404i | 0.208450 | − | 0.361046i | ||||
\(263\) | 2.67363 | − | 4.63086i | 0.164863 | − | 0.285551i | −0.771744 | − | 0.635934i | \(-0.780615\pi\) |
0.936607 | + | 0.350383i | \(0.113948\pi\) | |||||||
\(264\) | −1.18637 | − | 2.05486i | −0.0730162 | − | 0.126468i | ||||
\(265\) | 0.710136 | 0.0436233 | ||||||||
\(266\) | 3.22369 | + | 5.58360i | 0.197657 | + | 0.342352i | ||||
\(267\) | 4.75163 | + | 8.23006i | 0.290795 | + | 0.503671i | ||||
\(268\) | 15.4539 | 0.943995 | ||||||||
\(269\) | 5.66999 | + | 9.82071i | 0.345705 | + | 0.598779i | 0.985482 | − | 0.169782i | \(-0.0543063\pi\) |
−0.639776 | + | 0.768561i | \(0.720973\pi\) | |||||||
\(270\) | −0.283438 | + | 0.490929i | −0.0172495 | + | 0.0298770i | ||||
\(271\) | −6.23570 | + | 10.8005i | −0.378792 | + | 0.656086i | −0.990887 | − | 0.134698i | \(-0.956994\pi\) |
0.612095 | + | 0.790784i | \(0.290327\pi\) | |||||||
\(272\) | −1.20275 | −0.0729274 | ||||||||
\(273\) | −9.26000 | − | 7.06242i | −0.560441 | − | 0.427437i | ||||
\(274\) | 9.23835 | 0.558109 | ||||||||
\(275\) | −2.13945 | + | 3.70563i | −0.129014 | + | 0.223458i | ||||
\(276\) | −2.72937 | + | 4.72740i | −0.164288 | + | 0.284556i | ||||
\(277\) | 9.94564 | + | 17.2264i | 0.597576 | + | 1.03503i | 0.993178 | + | 0.116609i | \(0.0372026\pi\) |
−0.395602 | + | 0.918422i | \(0.629464\pi\) | |||||||
\(278\) | 4.57841 | 0.274595 | ||||||||
\(279\) | −0.0161287 | − | 0.0279357i | −0.000965600 | − | 0.00167247i | ||||
\(280\) | −3.25401 | − | 5.63611i | −0.194464 | − | 0.336822i | ||||
\(281\) | 19.7804 | 1.18000 | 0.590001 | − | 0.807402i | \(-0.299127\pi\) | ||||
0.590001 | + | 0.807402i | \(0.299127\pi\) | |||||||
\(282\) | −0.522097 | − | 0.904299i | −0.0310905 | − | 0.0538502i | ||||
\(283\) | −2.55376 | + | 4.42324i | −0.151805 | + | 0.262934i | −0.931891 | − | 0.362738i | \(-0.881842\pi\) |
0.780086 | + | 0.625672i | \(0.215175\pi\) | |||||||
\(284\) | 3.34203 | − | 5.78856i | 0.198313 | − | 0.343488i | ||||
\(285\) | 2.53918 | 0.150408 | ||||||||
\(286\) | −0.307170 | + | 2.38724i | −0.0181633 | + | 0.141160i | ||||
\(287\) | −12.0585 | −0.711790 | ||||||||
\(288\) | −2.88169 | + | 4.99123i | −0.169805 | + | 0.294111i | ||||
\(289\) | 8.18890 | − | 14.1836i | 0.481700 | − | 0.834329i | ||||
\(290\) | −0.326945 | − | 0.566285i | −0.0191989 | − | 0.0332534i | ||||
\(291\) | 11.6981 | 0.685752 | ||||||||
\(292\) | 4.81676 | + | 8.34287i | 0.281879 | + | 0.488229i | ||||
\(293\) | −3.49191 | − | 6.04816i | −0.203999 | − | 0.353337i | 0.745814 | − | 0.666154i | \(-0.232061\pi\) |
−0.949813 | + | 0.312817i | \(0.898727\pi\) | |||||||
\(294\) | 2.29154 | 0.133645 | ||||||||
\(295\) | −4.21059 | − | 7.29296i | −0.245150 | − | 0.424612i | ||||
\(296\) | 6.01045 | − | 10.4104i | 0.349350 | − | 0.605092i | ||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | −10.9674 | −0.635323 | ||||||||
\(299\) | 11.6841 | − | 4.87989i | 0.675710 | − | 0.282212i | ||||
\(300\) | 6.65097 | 0.383994 | ||||||||
\(301\) | −3.55452 | + | 6.15662i | −0.204879 | + | 0.354861i | ||||
\(302\) | −2.45787 | + | 4.25715i | −0.141434 | + | 0.244971i | ||||
\(303\) | −7.10926 | − | 12.3136i | −0.408416 | − | 0.707398i | ||||
\(304\) | 4.55936 | 0.261497 | ||||||||
\(305\) | 2.76184 | + | 4.78364i | 0.158142 | + | 0.273910i | ||||
\(306\) | 0.263285 | + | 0.456023i | 0.0150510 | + | 0.0260691i | ||||
\(307\) | −18.8576 | −1.07626 | −0.538129 | − | 0.842862i | \(-0.680869\pi\) | ||||
−0.538129 | + | 0.842862i | \(0.680869\pi\) | |||||||
\(308\) | 2.51028 | + | 4.34793i | 0.143036 | + | 0.247746i | ||||
\(309\) | −5.86223 | + | 10.1537i | −0.333491 | + | 0.577623i | ||||
\(310\) | −0.00914296 | + | 0.0158361i | −0.000519285 | + | 0.000899429i | ||||
\(311\) | −30.2366 | −1.71456 | −0.857281 | − | 0.514849i | \(-0.827848\pi\) | ||||
−0.857281 | + | 0.514849i | \(0.827848\pi\) | |||||||
\(312\) | 7.89422 | − | 3.29703i | 0.446922 | − | 0.186658i | ||||
\(313\) | 28.6369 | 1.61865 | 0.809326 | − | 0.587360i | \(-0.199833\pi\) | ||||
0.809326 | + | 0.587360i | \(0.199833\pi\) | |||||||
\(314\) | −7.20069 | + | 12.4720i | −0.406359 | + | 0.703834i | ||||
\(315\) | 1.37141 | − | 2.37535i | 0.0772702 | − | 0.133836i | ||||
\(316\) | 9.72054 | + | 16.8365i | 0.546823 | + | 0.947126i | ||||
\(317\) | 19.6824 | 1.10547 | 0.552736 | − | 0.833357i | \(-0.313584\pi\) | ||||
0.552736 | + | 0.833357i | \(0.313584\pi\) | |||||||
\(318\) | −0.279128 | − | 0.483463i | −0.0156527 | − | 0.0271113i | ||||
\(319\) | 0.576749 | + | 0.998959i | 0.0322918 | + | 0.0559310i | ||||
\(320\) | 0.677493 | 0.0378730 | ||||||||
\(321\) | 5.84391 | + | 10.1219i | 0.326175 | + | 0.564952i | ||||
\(322\) | −3.78614 | + | 6.55779i | −0.210993 | + | 0.365451i | ||||
\(323\) | 1.17932 | − | 2.04264i | 0.0656192 | − | 0.113656i | ||||
\(324\) | −1.55437 | −0.0863536 | ||||||||
\(325\) | −12.2672 | − | 9.35593i | −0.680460 | − | 0.518973i | ||||
\(326\) | 9.18145 | 0.508514 | ||||||||
\(327\) | −3.42309 | + | 5.92896i | −0.189297 | + | 0.327872i | ||||
\(328\) | 4.42910 | − | 7.67142i | 0.244556 | − | 0.423584i | ||||
\(329\) | 2.52616 | + | 4.37544i | 0.139272 | + | 0.241226i | ||||
\(330\) | −0.566875 | −0.0312055 | ||||||||
\(331\) | −10.7824 | − | 18.6756i | −0.592652 | − | 1.02650i | −0.993874 | − | 0.110522i | \(-0.964748\pi\) |
0.401222 | − | 0.915981i | \(-0.368586\pi\) | |||||||
\(332\) | 12.9406 | + | 22.4138i | 0.710208 | + | 1.23012i | ||||
\(333\) | 5.06624 | 0.277628 | ||||||||
\(334\) | −3.53705 | − | 6.12635i | −0.193539 | − | 0.335219i | ||||
\(335\) | 4.22136 | − | 7.31161i | 0.230637 | − | 0.399476i | ||||
\(336\) | 2.46250 | − | 4.26518i | 0.134341 | − | 0.232685i | ||||
\(337\) | −34.0883 | −1.85691 | −0.928453 | − | 0.371449i | \(-0.878861\pi\) | ||||
−0.928453 | + | 0.371449i | \(0.878861\pi\) | |||||||
\(338\) | −8.39558 | − | 2.19692i | −0.456659 | − | 0.119497i | ||||
\(339\) | −10.3492 | −0.562090 | ||||||||
\(340\) | −0.520581 | + | 0.901672i | −0.0282325 | + | 0.0489000i | ||||
\(341\) | 0.0161287 | − | 0.0279357i | 0.000873418 | − | 0.00151280i | ||||
\(342\) | −0.998055 | − | 1.72868i | −0.0539687 | − | 0.0934764i | ||||
\(343\) | 11.5222 | 0.622141 | ||||||||
\(344\) | −2.61116 | − | 4.52267i | −0.140785 | − | 0.243846i | ||||
\(345\) | 1.49110 | + | 2.58266i | 0.0802781 | + | 0.139046i | ||||
\(346\) | −2.91071 | −0.156481 | ||||||||
\(347\) | 13.1839 | + | 22.8352i | 0.707751 | + | 1.22586i | 0.965690 | + | 0.259699i | \(0.0836234\pi\) |
−0.257939 | + | 0.966161i | \(0.583043\pi\) | |||||||
\(348\) | 0.896479 | − | 1.55275i | 0.0480563 | − | 0.0832360i | ||||
\(349\) | 5.01891 | − | 8.69300i | 0.268656 | − | 0.465326i | −0.699859 | − | 0.714281i | \(-0.746754\pi\) |
0.968515 | + | 0.248955i | \(0.0800872\pi\) | |||||||
\(350\) | 9.22614 | 0.493158 | ||||||||
\(351\) | 2.86690 | + | 2.18653i | 0.153024 | + | 0.116708i | ||||
\(352\) | −5.76338 | −0.307189 | ||||||||
\(353\) | 10.2221 | − | 17.7052i | 0.544069 | − | 0.942355i | −0.454596 | − | 0.890698i | \(-0.650216\pi\) |
0.998665 | − | 0.0516571i | \(-0.0164503\pi\) | |||||||
\(354\) | −3.31005 | + | 5.73317i | −0.175927 | + | 0.304715i | ||||
\(355\) | −1.82581 | − | 3.16239i | −0.0969039 | − | 0.167842i | ||||
\(356\) | 14.7715 | 0.782889 | ||||||||
\(357\) | −1.27390 | − | 2.20646i | −0.0674220 | − | 0.116778i | ||||
\(358\) | −4.58704 | − | 7.94498i | −0.242433 | − | 0.419905i | ||||
\(359\) | 27.9740 | 1.47641 | 0.738206 | − | 0.674575i | \(-0.235673\pi\) | ||||
0.738206 | + | 0.674575i | \(0.235673\pi\) | |||||||
\(360\) | 1.00744 | + | 1.74494i | 0.0530968 | + | 0.0919664i | ||||
\(361\) | 5.02945 | − | 8.71127i | 0.264708 | − | 0.458488i | ||||
\(362\) | 5.06042 | − | 8.76490i | 0.265970 | − | 0.460673i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −16.7036 | + | 6.97628i | −0.875505 | + | 0.365656i | ||||
\(365\) | 5.26296 | 0.275476 | ||||||||
\(366\) | 2.17115 | − | 3.76053i | 0.113488 | − | 0.196566i | ||||
\(367\) | 13.3717 | − | 23.1604i | 0.697995 | − | 1.20896i | −0.271165 | − | 0.962533i | \(-0.587409\pi\) |
0.969161 | − | 0.246430i | \(-0.0792576\pi\) | |||||||
\(368\) | 2.67742 | + | 4.63743i | 0.139570 | + | 0.241743i | ||||
\(369\) | 3.73331 | 0.194348 | ||||||||
\(370\) | −1.43596 | − | 2.48716i | −0.0746521 | − | 0.129301i | ||||
\(371\) | 1.35055 | + | 2.33923i | 0.0701173 | + | 0.121447i | ||||
\(372\) | −0.0501398 | −0.00259963 | ||||||||
\(373\) | −11.8299 | − | 20.4900i | −0.612531 | − | 1.06093i | −0.990812 | − | 0.135244i | \(-0.956818\pi\) |
0.378282 | − | 0.925691i | \(-0.376515\pi\) | |||||||
\(374\) | −0.263285 | + | 0.456023i | −0.0136141 | + | 0.0235804i | ||||
\(375\) | 3.93971 | − | 6.82378i | 0.203446 | − | 0.352379i | ||||
\(376\) | −3.71145 | −0.191403 | ||||||||
\(377\) | −3.83773 | + | 1.60284i | −0.197653 | + | 0.0825502i | ||||
\(378\) | −2.15620 | −0.110903 | ||||||||
\(379\) | 13.3469 | − | 23.1175i | 0.685583 | − | 1.18746i | −0.287670 | − | 0.957730i | \(-0.592881\pi\) |
0.973253 | − | 0.229735i | \(-0.0737859\pi\) | |||||||
\(380\) | 1.97341 | − | 3.41804i | 0.101234 | − | 0.175342i | ||||
\(381\) | −4.32301 | − | 7.48768i | −0.221475 | − | 0.383605i | ||||
\(382\) | −1.98178 | −0.101397 | ||||||||
\(383\) | −14.4494 | − | 25.0271i | −0.738329 | − | 1.27882i | −0.953247 | − | 0.302191i | \(-0.902282\pi\) |
0.214919 | − | 0.976632i | \(-0.431051\pi\) | |||||||
\(384\) | 5.49708 | + | 9.52122i | 0.280522 | + | 0.485878i | ||||
\(385\) | 2.74282 | 0.139787 | ||||||||
\(386\) | 1.94067 | + | 3.36133i | 0.0987773 | + | 0.171087i | ||||
\(387\) | 1.10048 | − | 1.90609i | 0.0559406 | − | 0.0968920i | ||||
\(388\) | 9.09152 | − | 15.7470i | 0.461552 | − | 0.799432i | ||||
\(389\) | −24.7751 | −1.25615 | −0.628073 | − | 0.778154i | \(-0.716156\pi\) | ||||
−0.628073 | + | 0.778154i | \(0.716156\pi\) | |||||||
\(390\) | 0.260842 | − | 2.02719i | 0.0132082 | − | 0.102651i | ||||
\(391\) | 2.77016 | 0.140093 | ||||||||
\(392\) | 4.07249 | − | 7.05376i | 0.205692 | − | 0.356269i | ||||
\(393\) | 5.05432 | − | 8.75434i | 0.254957 | − | 0.441598i | ||||
\(394\) | −2.82025 | − | 4.88482i | −0.142082 | − | 0.246094i | ||||
\(395\) | 10.6210 | 0.534401 | ||||||||
\(396\) | −0.777183 | − | 1.34612i | −0.0390549 | − | 0.0676451i | ||||
\(397\) | −2.56512 | − | 4.44292i | −0.128740 | − | 0.222984i | 0.794449 | − | 0.607331i | \(-0.207760\pi\) |
−0.923189 | + | 0.384347i | \(0.874427\pi\) | |||||||
\(398\) | 9.72838 | 0.487640 | ||||||||
\(399\) | 4.82908 | + | 8.36421i | 0.241756 | + | 0.418734i | ||||
\(400\) | 3.26220 | − | 5.65029i | 0.163110 | − | 0.282515i | ||||
\(401\) | −3.87725 | + | 6.71559i | −0.193621 | + | 0.335361i | −0.946447 | − | 0.322858i | \(-0.895356\pi\) |
0.752827 | + | 0.658219i | \(0.228690\pi\) | |||||||
\(402\) | −6.63702 | −0.331025 | ||||||||
\(403\) | 0.0924786 | + | 0.0705317i | 0.00460669 | + | 0.00351343i | ||||
\(404\) | −22.1008 | −1.09955 | ||||||||
\(405\) | −0.424589 | + | 0.735409i | −0.0210980 | + | 0.0365428i | ||||
\(406\) | 1.24358 | − | 2.15395i | 0.0617180 | − | 0.106899i | ||||
\(407\) | 2.53312 | + | 4.38749i | 0.125562 | + | 0.217480i | ||||
\(408\) | 1.87162 | 0.0926591 | ||||||||
\(409\) | −2.73670 | − | 4.74011i | −0.135321 | − | 0.234383i | 0.790399 | − | 0.612593i | \(-0.209873\pi\) |
−0.925720 | + | 0.378209i | \(0.876540\pi\) | |||||||
\(410\) | −1.05816 | − | 1.83279i | −0.0522588 | − | 0.0905149i | ||||
\(411\) | 13.8390 | 0.682628 | ||||||||
\(412\) | 9.11205 | + | 15.7825i | 0.448919 | + | 0.777550i | ||||
\(413\) | 16.0156 | − | 27.7399i | 0.788077 | − | 1.36499i | ||||
\(414\) | 1.17219 | − | 2.03029i | 0.0576100 | − | 0.0997834i | ||||
\(415\) | 14.1394 | 0.694074 | ||||||||
\(416\) | 2.65196 | − | 20.6102i | 0.130023 | − | 1.01050i | ||||
\(417\) | 6.85844 | 0.335859 | ||||||||
\(418\) | 0.998055 | − | 1.72868i | 0.0488165 | − | 0.0845526i | ||||
\(419\) | −16.8067 | + | 29.1100i | −0.821060 | + | 1.42212i | 0.0838327 | + | 0.996480i | \(0.473284\pi\) |
−0.904893 | + | 0.425639i | \(0.860049\pi\) | |||||||
\(420\) | −2.13167 | − | 3.69216i | −0.104015 | − | 0.180159i | ||||
\(421\) | −31.5135 | −1.53587 | −0.767937 | − | 0.640526i | \(-0.778717\pi\) | ||||
−0.767937 | + | 0.640526i | \(0.778717\pi\) | |||||||
\(422\) | −3.19967 | − | 5.54199i | −0.155757 | − | 0.269780i | ||||
\(423\) | −0.782100 | − | 1.35464i | −0.0380270 | − | 0.0658647i | ||||
\(424\) | −1.98424 | −0.0963633 | ||||||||
\(425\) | −1.68760 | − | 2.92300i | −0.0818605 | − | 0.141786i | ||||
\(426\) | −1.43531 | + | 2.48603i | −0.0695411 | + | 0.120449i | ||||
\(427\) | −10.5051 | + | 18.1953i | −0.508375 | + | 0.880532i | ||||
\(428\) | 18.1671 | 0.878142 | ||||||||
\(429\) | −0.460139 | + | 3.57607i | −0.0222157 | + | 0.172654i | ||||
\(430\) | −1.24767 | −0.0601681 | ||||||||
\(431\) | 14.6349 | − | 25.3483i | 0.704937 | − | 1.22099i | −0.261778 | − | 0.965128i | \(-0.584309\pi\) |
0.966714 | − | 0.255858i | \(-0.0823580\pi\) | |||||||
\(432\) | −0.762392 | + | 1.32050i | −0.0366806 | + | 0.0635327i | ||||
\(433\) | 10.7335 | + | 18.5910i | 0.515820 | + | 0.893426i | 0.999831 | + | 0.0183648i | \(0.00584601\pi\) |
−0.484011 | + | 0.875062i | \(0.660821\pi\) | |||||||
\(434\) | −0.0695533 | −0.00333866 | ||||||||
\(435\) | −0.489762 | − | 0.848293i | −0.0234823 | − | 0.0406725i | ||||
\(436\) | 5.32073 | + | 9.21578i | 0.254817 | + | 0.441356i | ||||
\(437\) | −10.5011 | −0.502335 | ||||||||
\(438\) | −2.06867 | − | 3.58304i | −0.0988448 | − | 0.171204i | ||||
\(439\) | 1.16422 | − | 2.01649i | 0.0555653 | − | 0.0962419i | −0.836905 | − | 0.547348i | \(-0.815637\pi\) |
0.892470 | + | 0.451107i | \(0.148971\pi\) | |||||||
\(440\) | −1.00744 | + | 1.74494i | −0.0480279 | + | 0.0831867i | ||||
\(441\) | 3.43272 | 0.163463 | ||||||||
\(442\) | −1.50962 | − | 1.15136i | −0.0718054 | − | 0.0547646i | ||||
\(443\) | 12.4928 | 0.593550 | 0.296775 | − | 0.954947i | \(-0.404089\pi\) | ||||
0.296775 | + | 0.954947i | \(0.404089\pi\) | |||||||
\(444\) | 3.93739 | − | 6.81976i | 0.186860 | − | 0.323652i | ||||
\(445\) | 4.03497 | − | 6.98878i | 0.191276 | − | 0.331300i | ||||
\(446\) | 3.07681 | + | 5.32919i | 0.145691 | + | 0.252345i | ||||
\(447\) | −16.4291 | −0.777069 | ||||||||
\(448\) | 1.28847 | + | 2.23170i | 0.0608747 | + | 0.105438i | ||||
\(449\) | 13.8002 | + | 23.9027i | 0.651273 | + | 1.12804i | 0.982814 | + | 0.184598i | \(0.0590982\pi\) |
−0.331541 | + | 0.943441i | \(0.607569\pi\) | |||||||
\(450\) | −2.85641 | −0.134653 | ||||||||
\(451\) | 1.86665 | + | 3.23314i | 0.0878973 | + | 0.152243i | ||||
\(452\) | −8.04320 | + | 13.9312i | −0.378321 | + | 0.655270i | ||||
\(453\) | −3.68187 | + | 6.37719i | −0.172989 | + | 0.299627i | ||||
\(454\) | 13.7249 | 0.644143 | ||||||||
\(455\) | −1.26208 | + | 9.80851i | −0.0591671 | + | 0.459830i | ||||
\(456\) | −7.09491 | −0.332249 | ||||||||
\(457\) | −5.36694 | + | 9.29581i | −0.251055 | + | 0.434840i | −0.963816 | − | 0.266567i | \(-0.914111\pi\) |
0.712762 | + | 0.701406i | \(0.247444\pi\) | |||||||
\(458\) | 2.31221 | − | 4.00487i | 0.108043 | − | 0.187135i | ||||
\(459\) | 0.394400 | + | 0.683120i | 0.0184090 | + | 0.0318853i | ||||
\(460\) | 4.63543 | 0.216128 | ||||||||
\(461\) | −17.0750 | − | 29.5747i | −0.795260 | − | 1.37743i | −0.922674 | − | 0.385582i | \(-0.874001\pi\) |
0.127413 | − | 0.991850i | \(-0.459333\pi\) | |||||||
\(462\) | −1.07810 | − | 1.86732i | −0.0501576 | − | 0.0868756i | ||||
\(463\) | 26.5280 | 1.23286 | 0.616431 | − | 0.787409i | \(-0.288578\pi\) | ||||
0.616431 | + | 0.787409i | \(0.288578\pi\) | |||||||
\(464\) | −0.879418 | − | 1.52320i | −0.0408259 | − | 0.0707126i | ||||
\(465\) | −0.0136961 | + | 0.0237224i | −0.000635142 | + | 0.00110010i | ||||
\(466\) | 3.31926 | − | 5.74913i | 0.153762 | − | 0.266323i | ||||
\(467\) | −36.6740 | −1.69707 | −0.848536 | − | 0.529138i | \(-0.822515\pi\) | ||||
−0.848536 | + | 0.529138i | \(0.822515\pi\) | |||||||
\(468\) | 5.17143 | − | 2.15986i | 0.239049 | − | 0.0998394i | ||||
\(469\) | 32.1131 | 1.48285 | ||||||||
\(470\) | −0.443353 | + | 0.767910i | −0.0204504 | + | 0.0354211i | ||||
\(471\) | −10.7866 | + | 18.6830i | −0.497021 | + | 0.860865i | ||||
\(472\) | 11.7651 | + | 20.3778i | 0.541533 | + | 0.937963i | ||||
\(473\) | 2.20096 | 0.101200 | ||||||||
\(474\) | −4.17471 | − | 7.23082i | −0.191751 | − | 0.332122i | ||||
\(475\) | 6.39731 | + | 11.0805i | 0.293529 | + | 0.508406i | ||||
\(476\) | −3.96021 | −0.181516 | ||||||||
\(477\) | −0.418132 | − | 0.724226i | −0.0191449 | − | 0.0331600i | ||||
\(478\) | 3.57201 | − | 6.18691i | 0.163380 | − | 0.282983i | ||||
\(479\) | 2.58285 | − | 4.47362i | 0.118013 | − | 0.204405i | −0.800967 | − | 0.598709i | \(-0.795681\pi\) |
0.918980 | + | 0.394303i | \(0.129014\pi\) | |||||||
\(480\) | 4.89413 | 0.223385 | ||||||||
\(481\) | −16.8556 | + | 7.03975i | −0.768547 | + | 0.320985i | ||||
\(482\) | 16.3050 | 0.742671 | ||||||||
\(483\) | −5.67162 | + | 9.82354i | −0.258068 | + | 0.446986i | ||||
\(484\) | 0.777183 | − | 1.34612i | 0.0353265 | − | 0.0611873i | ||||
\(485\) | −4.96686 | − | 8.60285i | −0.225533 | − | 0.390635i | ||||
\(486\) | 0.667559 | 0.0302811 | ||||||||
\(487\) | 10.1561 | + | 17.5909i | 0.460217 | + | 0.797120i | 0.998971 | − | 0.0453431i | \(-0.0144381\pi\) |
−0.538754 | + | 0.842463i | \(0.681105\pi\) | |||||||
\(488\) | −7.71704 | − | 13.3663i | −0.349334 | − | 0.605064i | ||||
\(489\) | 13.7538 | 0.621967 | ||||||||
\(490\) | −0.972963 | − | 1.68522i | −0.0439540 | − | 0.0761305i | ||||
\(491\) | −15.4868 | + | 26.8240i | −0.698910 | + | 1.21055i | 0.269934 | + | 0.962879i | \(0.412998\pi\) |
−0.968845 | + | 0.247669i | \(0.920335\pi\) | |||||||
\(492\) | 2.90146 | − | 5.02548i | 0.130808 | − | 0.226566i | ||||
\(493\) | −0.909879 | −0.0409789 | ||||||||
\(494\) | 5.72264 | + | 4.36455i | 0.257474 | + | 0.196370i | ||||
\(495\) | −0.849177 | −0.0381677 | ||||||||
\(496\) | −0.0245928 | + | 0.0425959i | −0.00110425 | + | 0.00191261i | ||||
\(497\) | 6.94474 | − | 12.0286i | 0.311514 | − | 0.539558i | ||||
\(498\) | −5.55765 | − | 9.62613i | −0.249044 | − | 0.431357i | ||||
\(499\) | −24.8190 | −1.11105 | −0.555525 | − | 0.831500i | \(-0.687483\pi\) | ||||
−0.555525 | + | 0.831500i | \(0.687483\pi\) | |||||||
\(500\) | −6.12376 | − | 10.6067i | −0.273863 | − | 0.474344i | ||||
\(501\) | −5.29848 | − | 9.17724i | −0.236719 | − | 0.410009i | ||||
\(502\) | 3.26114 | 0.145552 | ||||||||
\(503\) | −17.3306 | − | 30.0174i | −0.772732 | − | 1.33841i | −0.936060 | − | 0.351840i | \(-0.885556\pi\) |
0.163328 | − | 0.986572i | \(-0.447777\pi\) | |||||||
\(504\) | −3.83195 | + | 6.63714i | −0.170689 | + | 0.295642i | ||||
\(505\) | −6.03702 | + | 10.4564i | −0.268644 | + | 0.465305i | ||||
\(506\) | 2.34438 | 0.104220 | ||||||||
\(507\) | −12.5765 | − | 3.29098i | −0.558544 | − | 0.146158i | ||||
\(508\) | −13.4391 | −0.596263 | ||||||||
\(509\) | −3.49940 | + | 6.06114i | −0.155108 | + | 0.268655i | −0.933098 | − | 0.359621i | \(-0.882906\pi\) |
0.777990 | + | 0.628276i | \(0.216239\pi\) | |||||||
\(510\) | 0.223576 | − | 0.387244i | 0.00990009 | − | 0.0171475i | ||||
\(511\) | 10.0092 | + | 17.3365i | 0.442782 | + | 0.766921i | ||||
\(512\) | 16.0238 | 0.708157 | ||||||||
\(513\) | −1.49508 | − | 2.58956i | −0.0660095 | − | 0.114332i | ||||
\(514\) | −7.80723 | − | 13.5225i | −0.344362 | − | 0.596453i | ||||
\(515\) | 9.95615 | 0.438720 | ||||||||
\(516\) | −1.71055 | − | 2.96276i | −0.0753028 | − | 0.130428i | ||||
\(517\) | 0.782100 | − | 1.35464i | 0.0343967 | − | 0.0595769i | ||||
\(518\) | 5.46190 | − | 9.46028i | 0.239982 | − | 0.415661i | ||||
\(519\) | −4.36024 | −0.191393 | ||||||||
\(520\) | −5.77646 | − | 4.40559i | −0.253315 | − | 0.193198i | ||||
\(521\) | −25.6505 | −1.12377 | −0.561885 | − | 0.827215i | \(-0.689924\pi\) | ||||
−0.561885 | + | 0.827215i | \(0.689924\pi\) | |||||||
\(522\) | −0.385014 | + | 0.666864i | −0.0168516 | + | 0.0291878i | ||||
\(523\) | 8.57502 | − | 14.8524i | 0.374959 | − | 0.649449i | −0.615362 | − | 0.788245i | \(-0.710990\pi\) |
0.990321 | + | 0.138796i | \(0.0443233\pi\) | |||||||
\(524\) | −7.85627 | − | 13.6075i | −0.343203 | − | 0.594444i | ||||
\(525\) | 13.8207 | 0.603186 | ||||||||
\(526\) | 1.78480 | + | 3.09137i | 0.0778212 | + | 0.134790i | ||||
\(527\) | 0.0127223 | + | 0.0220357i | 0.000554193 | + | 0.000959890i | ||||
\(528\) | −1.52478 | −0.0663577 | ||||||||
\(529\) | 5.33338 | + | 9.23769i | 0.231886 | + | 0.401639i | ||||
\(530\) | −0.237029 | + | 0.410546i | −0.0102959 | + | 0.0178330i | ||||
\(531\) | −4.95844 | + | 8.58827i | −0.215178 | + | 0.372699i | ||||
\(532\) | 15.0123 | 0.650866 | ||||||||
\(533\) | −12.4209 | + | 5.18759i | −0.538007 | + | 0.224700i | ||||
\(534\) | −6.34398 | −0.274531 | ||||||||
\(535\) | 4.96251 | − | 8.59532i | 0.214548 | − | 0.371608i | ||||
\(536\) | −11.7952 | + | 20.4299i | −0.509475 | + | 0.882437i | ||||
\(537\) | −6.87137 | − | 11.9016i | −0.296521 | − | 0.513590i | ||||
\(538\) | −7.57010 | −0.326370 | ||||||||
\(539\) | 1.71636 | + | 2.97282i | 0.0739289 | + | 0.128049i | ||||
\(540\) | 0.659966 | + | 1.14309i | 0.0284004 | + | 0.0491910i | ||||
\(541\) | −39.4496 | −1.69607 | −0.848035 | − | 0.529941i | \(-0.822214\pi\) | ||||
−0.848035 | + | 0.529941i | \(0.822214\pi\) | |||||||
\(542\) | −4.16269 | − | 7.21000i | −0.178803 | − | 0.309696i | ||||
\(543\) | 7.58049 | − | 13.1298i | 0.325310 | − | 0.563453i | ||||
\(544\) | 2.27307 | − | 3.93708i | 0.0974573 | − | 0.168801i | ||||
\(545\) | 5.81362 | 0.249028 | ||||||||
\(546\) | 7.17374 | − | 2.99613i | 0.307008 | − | 0.128222i | ||||
\(547\) | 38.6045 | 1.65061 | 0.825305 | − | 0.564686i | \(-0.191003\pi\) | ||||
0.825305 | + | 0.564686i | \(0.191003\pi\) | |||||||
\(548\) | 10.7554 | − | 18.6290i | 0.459450 | − | 0.795791i | ||||
\(549\) | 3.25237 | − | 5.63326i | 0.138808 | − | 0.240422i | ||||
\(550\) | −1.42821 | − | 2.47373i | −0.0608990 | − | 0.105480i | ||||
\(551\) | 3.44915 | 0.146939 | ||||||||
\(552\) | −4.16639 | − | 7.21640i | −0.177333 | − | 0.307150i | ||||
\(553\) | 20.1993 | + | 34.9862i | 0.858961 | + | 1.48776i | ||||
\(554\) | −13.2786 | −0.564153 | ||||||||
\(555\) | −2.15107 | − | 3.72576i | −0.0913077 | − | 0.158150i | ||||
\(556\) | 5.33026 | − | 9.23228i | 0.226053 | − | 0.391536i | ||||
\(557\) | −23.1516 | + | 40.0998i | −0.980967 | + | 1.69908i | −0.322322 | + | 0.946630i | \(0.604464\pi\) |
−0.658644 | + | 0.752454i | \(0.728870\pi\) | |||||||
\(558\) | 0.0215337 | 0.000911594 | ||||||||
\(559\) | −1.01275 | + | 7.87080i | −0.0428347 | + | 0.332899i | ||||
\(560\) | −4.18221 | −0.176730 | ||||||||
\(561\) | −0.394400 | + | 0.683120i | −0.0166516 | + | 0.0288414i | ||||
\(562\) | −6.60230 | + | 11.4355i | −0.278501 | + | 0.482378i | ||||
\(563\) | −19.5560 | − | 33.8719i | −0.824186 | − | 1.42753i | −0.902540 | − | 0.430606i | \(-0.858300\pi\) |
0.0783546 | − | 0.996926i | \(-0.475033\pi\) | |||||||
\(564\) | −2.43134 | −0.102378 | ||||||||
\(565\) | 4.39414 | + | 7.61088i | 0.184863 | + | 0.320192i | ||||
\(566\) | −1.70478 | − | 2.95277i | −0.0716574 | − | 0.124114i | ||||
\(567\) | −3.22997 | −0.135646 | ||||||||
\(568\) | 5.10162 | + | 8.83627i | 0.214059 | + | 0.370762i | ||||
\(569\) | 14.9816 | − | 25.9489i | 0.628062 | − | 1.08784i | −0.359878 | − | 0.932999i | \(-0.617182\pi\) |
0.987940 | − | 0.154836i | \(-0.0494849\pi\) | |||||||
\(570\) | −0.847526 | + | 1.46796i | −0.0354989 | + | 0.0614860i | ||||
\(571\) | 21.6865 | 0.907552 | 0.453776 | − | 0.891116i | \(-0.350077\pi\) | ||||
0.453776 | + | 0.891116i | \(0.350077\pi\) | |||||||
\(572\) | 4.45621 | + | 3.39866i | 0.186323 | + | 0.142105i | ||||
\(573\) | −2.96870 | −0.124019 | ||||||||
\(574\) | 4.02487 | − | 6.97128i | 0.167995 | − | 0.290976i | ||||
\(575\) | −7.51347 | + | 13.0137i | −0.313333 | + | 0.542709i | ||||
\(576\) | −0.398912 | − | 0.690935i | −0.0166213 | − | 0.0287890i | ||||
\(577\) | −9.43193 | −0.392656 | −0.196328 | − | 0.980538i | \(-0.562902\pi\) | ||||
−0.196328 | + | 0.980538i | \(0.562902\pi\) | |||||||
\(578\) | 5.46657 | + | 9.46837i | 0.227379 | + | 0.393832i | ||||
\(579\) | 2.90711 | + | 5.03526i | 0.120815 | + | 0.209258i | ||||
\(580\) | −1.52254 | −0.0632200 | ||||||||
\(581\) | 26.8906 | + | 46.5759i | 1.11561 | + | 1.93229i | ||||
\(582\) | −3.90457 | + | 6.76291i | −0.161850 | + | 0.280332i | ||||
\(583\) | 0.418132 | − | 0.724226i | 0.0173173 | − | 0.0299944i | ||||
\(584\) | −14.7056 | −0.608522 | ||||||||
\(585\) | 0.390740 | − | 3.03672i | 0.0161551 | − | 0.125553i | ||||
\(586\) | 4.66211 | 0.192590 | ||||||||
\(587\) | −12.7158 | + | 22.0245i | −0.524839 | + | 0.909048i | 0.474743 | + | 0.880125i | \(0.342541\pi\) |
−0.999582 | + | 0.0289230i | \(0.990792\pi\) | |||||||
\(588\) | 2.66785 | − | 4.62085i | 0.110020 | − | 0.190561i | ||||
\(589\) | −0.0482275 | − | 0.0835324i | −0.00198718 | − | 0.00344189i | ||||
\(590\) | 5.62163 | 0.231439 | ||||||||
\(591\) | −4.22473 | − | 7.31745i | −0.173782 | − | 0.301000i | ||||
\(592\) | −3.86246 | − | 6.68997i | −0.158746 | − | 0.274956i | ||||
\(593\) | −2.11145 | −0.0867069 | −0.0433534 | − | 0.999060i | \(-0.513804\pi\) | ||||
−0.0433534 | + | 0.999060i | \(0.513804\pi\) | |||||||
\(594\) | 0.333779 | + | 0.578123i | 0.0136951 | + | 0.0237207i | ||||
\(595\) | −1.08177 | + | 1.87368i | −0.0443481 | + | 0.0768132i | ||||
\(596\) | −12.7684 | + | 22.1155i | −0.523014 | + | 0.905887i | ||||
\(597\) | 14.5731 | 0.596436 | ||||||||
\(598\) | −1.07874 | + | 8.38366i | −0.0441130 | + | 0.342833i | ||||
\(599\) | −30.7915 | −1.25811 | −0.629053 | − | 0.777362i | \(-0.716557\pi\) | ||||
−0.629053 | + | 0.777362i | \(0.716557\pi\) | |||||||
\(600\) | −5.07637 | + | 8.79253i | −0.207242 | + | 0.358954i | ||||
\(601\) | −8.63565 | + | 14.9574i | −0.352255 | + | 0.610124i | −0.986644 | − | 0.162890i | \(-0.947918\pi\) |
0.634389 | + | 0.773014i | \(0.281252\pi\) | |||||||
\(602\) | −2.37285 | − | 4.10990i | −0.0967103 | − | 0.167507i | ||||
\(603\) | −9.94223 | −0.404879 | ||||||||
\(604\) | 5.72298 | + | 9.91248i | 0.232865 | + | 0.403333i | ||||
\(605\) | −0.424589 | − | 0.735409i | −0.0172620 | − | 0.0298986i | ||||
\(606\) | 9.49169 | 0.385574 | ||||||||
\(607\) | −8.44402 | − | 14.6255i | −0.342732 | − | 0.593630i | 0.642207 | − | 0.766531i | \(-0.278019\pi\) |
−0.984939 | + | 0.172902i | \(0.944686\pi\) | |||||||
\(608\) | −8.61673 | + | 14.9246i | −0.349454 | + | 0.605273i | ||||
\(609\) | 1.86288 | − | 3.22661i | 0.0754879 | − | 0.130749i | ||||
\(610\) | −3.68737 | −0.149297 | ||||||||
\(611\) | 4.48440 | + | 3.42017i | 0.181419 | + | 0.138365i | ||||
\(612\) | 1.22608 | 0.0495615 | ||||||||
\(613\) | −11.0967 | + | 19.2201i | −0.448192 | + | 0.776291i | −0.998268 | − | 0.0588232i | \(-0.981265\pi\) |
0.550077 | + | 0.835114i | \(0.314599\pi\) | |||||||
\(614\) | 6.29426 | − | 10.9020i | 0.254016 | − | 0.439968i | ||||
\(615\) | −1.58512 | − | 2.74551i | −0.0639182 | − | 0.110710i | ||||
\(616\) | −7.66391 | −0.308788 | ||||||||
\(617\) | 16.6239 | + | 28.7934i | 0.669253 | + | 1.15918i | 0.978113 | + | 0.208073i | \(0.0667192\pi\) |
−0.308860 | + | 0.951107i | \(0.599948\pi\) | |||||||
\(618\) | −3.91338 | − | 6.77818i | −0.157419 | − | 0.272658i | ||||
\(619\) | −26.2171 | −1.05376 | −0.526878 | − | 0.849941i | \(-0.676637\pi\) | ||||
−0.526878 | + | 0.849941i | \(0.676637\pi\) | |||||||
\(620\) | 0.0212888 | + | 0.0368732i | 0.000854978 | + | 0.00148087i | ||||
\(621\) | 1.75594 | − | 3.04137i | 0.0704633 | − | 0.122046i | ||||
\(622\) | 10.0924 | − | 17.4805i | 0.404667 | − | 0.700903i | ||||
\(623\) | 30.6952 | 1.22978 | ||||||||
\(624\) | 0.701613 | − | 5.45273i | 0.0280870 | − | 0.218284i | ||||
\(625\) | 14.7035 | 0.588138 | ||||||||
\(626\) | −9.55840 | + | 16.5556i | −0.382030 | + | 0.661696i | ||||
\(627\) | 1.49508 | − | 2.58956i | 0.0597079 | − | 0.103417i | ||||
\(628\) | 16.7663 | + | 29.0401i | 0.669050 | + | 1.15883i | ||||
\(629\) | −3.99624 | −0.159341 | ||||||||
\(630\) | 0.915496 | + | 1.58569i | 0.0364742 | + | 0.0631752i | ||||
\(631\) | 4.19122 | + | 7.25940i | 0.166850 | + | 0.288992i | 0.937311 | − | 0.348495i | \(-0.113307\pi\) |
−0.770461 | + | 0.637487i | \(0.779974\pi\) | |||||||
\(632\) | −29.6769 | −1.18048 | ||||||||
\(633\) | −4.79309 | − | 8.30187i | −0.190508 | − | 0.329970i | ||||
\(634\) | −6.56956 | + | 11.3788i | −0.260911 | + | 0.451910i | ||||
\(635\) | −3.67100 | + | 6.35836i | −0.145679 | + | 0.252324i | ||||
\(636\) | −1.29986 | −0.0515428 | ||||||||
\(637\) | −11.4208 | + | 4.76991i | −0.452508 | + | 0.188991i | ||||
\(638\) | −0.770028 | −0.0304857 | ||||||||
\(639\) | −2.15009 | + | 3.72407i | −0.0850563 | + | 0.147322i | ||||
\(640\) | 4.66799 | − | 8.08520i | 0.184519 | − | 0.319596i | ||||
\(641\) | −10.5327 | − | 18.2432i | −0.416017 | − | 0.720563i | 0.579518 | − | 0.814960i | \(-0.303241\pi\) |
−0.995535 | + | 0.0943971i | \(0.969908\pi\) | |||||||
\(642\) | −7.80230 | −0.307932 | ||||||||
\(643\) | 22.2642 | + | 38.5627i | 0.878015 | + | 1.52077i | 0.853516 | + | 0.521066i | \(0.174466\pi\) |
0.0244987 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(644\) | 8.81577 | + | 15.2694i | 0.347390 | + | 0.601697i | ||||
\(645\) | −1.86901 | −0.0735921 | ||||||||
\(646\) | 0.787266 | + | 1.36358i | 0.0309745 | + | 0.0536495i | ||||
\(647\) | 9.16480 | − | 15.8739i | 0.360306 | − | 0.624068i | −0.627705 | − | 0.778451i | \(-0.716006\pi\) |
0.988011 | + | 0.154383i | \(0.0493391\pi\) | |||||||
\(648\) | 1.18637 | − | 2.05486i | 0.0466052 | − | 0.0807225i | ||||
\(649\) | −9.91687 | −0.389271 | ||||||||
\(650\) | 9.50340 | − | 3.96911i | 0.372754 | − | 0.155681i | ||||
\(651\) | −0.104190 | −0.00408355 | ||||||||
\(652\) | 10.6892 | − | 18.5142i | 0.418621 | − | 0.725074i | ||||
\(653\) | 7.09516 | − | 12.2892i | 0.277655 | − | 0.480913i | −0.693147 | − | 0.720797i | \(-0.743776\pi\) |
0.970802 | + | 0.239884i | \(0.0771094\pi\) | |||||||
\(654\) | −2.28511 | − | 3.95793i | −0.0893549 | − | 0.154767i | ||||
\(655\) | −8.58403 | −0.335406 | ||||||||
\(656\) | −2.84624 | − | 4.92984i | −0.111127 | − | 0.192478i | ||||
\(657\) | −3.09886 | − | 5.36738i | −0.120898 | − | 0.209401i | ||||
\(658\) | −3.37272 | −0.131482 | ||||||||
\(659\) | 9.07017 | + | 15.7100i | 0.353324 | + | 0.611974i | 0.986830 | − | 0.161763i | \(-0.0517181\pi\) |
−0.633506 | + | 0.773738i | \(0.718385\pi\) | |||||||
\(660\) | −0.659966 | + | 1.14309i | −0.0256891 | + | 0.0444949i | ||||
\(661\) | 0.628382 | − | 1.08839i | 0.0244412 | − | 0.0423335i | −0.853546 | − | 0.521017i | \(-0.825553\pi\) |
0.877987 | + | 0.478684i | \(0.158886\pi\) | |||||||
\(662\) | 14.3957 | 0.559505 | ||||||||
\(663\) | −2.26141 | − | 1.72473i | −0.0878258 | − | 0.0669830i | ||||
\(664\) | −39.5078 | −1.53320 | ||||||||
\(665\) | 4.10074 | − | 7.10269i | 0.159020 | − | 0.275431i | ||||
\(666\) | −1.69100 | + | 2.92891i | −0.0655251 | + | 0.113493i | ||||
\(667\) | 2.02547 | + | 3.50821i | 0.0784265 | + | 0.135839i | ||||
\(668\) | −16.4716 | −0.637304 | ||||||||
\(669\) | 4.60905 | + | 7.98311i | 0.178196 | + | 0.308645i | ||||
\(670\) | 2.81800 | + | 4.88093i | 0.108869 | + | 0.188567i | ||||
\(671\) | 6.50473 | 0.251112 | ||||||||
\(672\) | 9.30777 | + | 16.1215i | 0.359055 | + | 0.621902i | ||||
\(673\) | −9.68580 | + | 16.7763i | −0.373360 | + | 0.646679i | −0.990080 | − | 0.140504i | \(-0.955128\pi\) |
0.616720 | + | 0.787183i | \(0.288461\pi\) | |||||||
\(674\) | 11.3780 | − | 19.7072i | 0.438263 | − | 0.759093i | ||||
\(675\) | −4.27890 | −0.164695 | ||||||||
\(676\) | −14.2043 | + | 14.3718i | −0.546320 | + | 0.552763i | ||||
\(677\) | 26.3139 | 1.01132 | 0.505662 | − | 0.862732i | \(-0.331248\pi\) | ||||
0.505662 | + | 0.862732i | \(0.331248\pi\) | |||||||
\(678\) | 3.45434 | − | 5.98309i | 0.132663 | − | 0.229779i | ||||
\(679\) | 18.8922 | − | 32.7222i | 0.725016 | − | 1.25576i | ||||
\(680\) | −0.794669 | − | 1.37641i | −0.0304742 | − | 0.0527828i | ||||
\(681\) | 20.5599 | 0.787857 | ||||||||
\(682\) | 0.0107668 | + | 0.0186487i | 0.000412284 | + | 0.000714097i | ||||
\(683\) | −0.939059 | − | 1.62650i | −0.0359321 | − | 0.0622362i | 0.847500 | − | 0.530795i | \(-0.178107\pi\) |
−0.883432 | + | 0.468559i | \(0.844773\pi\) | |||||||
\(684\) | −4.64781 | −0.177713 | ||||||||
\(685\) | −5.87589 | − | 10.1773i | −0.224506 | − | 0.388856i | ||||
\(686\) | −3.84588 | + | 6.66125i | −0.146836 | + | 0.254328i | ||||
\(687\) | 3.46369 | − | 5.99928i | 0.132148 | − | 0.228887i | ||||
\(688\) | −3.35599 | −0.127946 | ||||||||
\(689\) | 2.39748 | + | 1.82851i | 0.0913368 | + | 0.0696608i | ||||
\(690\) | −1.99079 | −0.0757882 | ||||||||
\(691\) | −19.0598 | + | 33.0126i | −0.725070 | + | 1.25586i | 0.233875 | + | 0.972267i | \(0.424859\pi\) |
−0.958945 | + | 0.283592i | \(0.908474\pi\) | |||||||
\(692\) | −3.38870 | + | 5.86940i | −0.128819 | + | 0.223121i | ||||
\(693\) | −1.61499 | − | 2.79724i | −0.0613483 | − | 0.106258i | ||||
\(694\) | −17.6021 | −0.668167 | ||||||||
\(695\) | −2.91201 | − | 5.04376i | −0.110459 | − | 0.191321i | ||||
\(696\) | 1.36848 | + | 2.37028i | 0.0518721 | + | 0.0898451i | ||||
\(697\) | −2.94483 | −0.111543 | ||||||||
\(698\) | 3.35041 | + | 5.80309i | 0.126815 | + | 0.219650i | ||||
\(699\) | 4.97224 | − | 8.61218i | 0.188068 | − | 0.325743i | ||||
\(700\) | 10.7412 | − | 18.6044i | 0.405980 | − | 0.703178i | ||||
\(701\) | 22.4490 | 0.847886 | 0.423943 | − | 0.905689i | \(-0.360646\pi\) | ||||
0.423943 | + | 0.905689i | \(0.360646\pi\) | |||||||
\(702\) | −2.22099 | + | 0.927601i | −0.0838259 | + | 0.0350100i | ||||
\(703\) | 15.1489 | 0.571351 | ||||||||
\(704\) | 0.398912 | − | 0.690935i | 0.0150346 | − | 0.0260406i | ||||
\(705\) | −0.664141 | + | 1.15033i | −0.0250130 | + | 0.0433238i | ||||
\(706\) | 6.82387 | + | 11.8193i | 0.256820 | + | 0.444825i | ||||
\(707\) | −45.9254 | −1.72720 | ||||||||
\(708\) | 7.70722 | + | 13.3493i | 0.289655 | + | 0.501698i | ||||
\(709\) | −10.1426 | − | 17.5675i | −0.380914 | − | 0.659762i | 0.610279 | − | 0.792186i | \(-0.291057\pi\) |
−0.991193 | + | 0.132424i | \(0.957724\pi\) | |||||||
\(710\) | 2.43767 | 0.0914841 | ||||||||
\(711\) | −6.25370 | − | 10.8317i | −0.234532 | − | 0.406222i | ||||
\(712\) | −11.2744 | + | 19.5278i | −0.422526 | + | 0.731837i | ||||
\(713\) | 0.0566419 | − | 0.0981066i | 0.00212126 | − | 0.00367412i | ||||
\(714\) | 1.70081 | 0.0636511 | ||||||||
\(715\) | 2.82524 | − | 1.17997i | 0.105658 | − | 0.0441283i | ||||
\(716\) | −21.3612 | −0.798307 | ||||||||
\(717\) | 5.35086 | − | 9.26796i | 0.199832 | − | 0.346118i | ||||
\(718\) | −9.33715 | + | 16.1724i | −0.348459 | + | 0.603549i | ||||
\(719\) | −16.8621 | − | 29.2060i | −0.628849 | − | 1.08920i | −0.987783 | − | 0.155836i | \(-0.950193\pi\) |
0.358934 | − | 0.933363i | \(-0.383140\pi\) | |||||||
\(720\) | 1.29481 | 0.0482548 | ||||||||
\(721\) | 18.9349 | + | 32.7961i | 0.705171 | + | 1.22139i | ||||
\(722\) | 3.35746 | + | 5.81528i | 0.124952 | + | 0.216422i | ||||
\(723\) | 24.4248 | 0.908368 | ||||||||
\(724\) | −11.7828 | − | 20.4085i | −0.437906 | − | 0.758476i | ||||
\(725\) | 2.46785 | − | 4.27444i | 0.0916537 | − | 0.158749i | ||||
\(726\) | −0.333779 | + | 0.578123i | −0.0123877 | + | 0.0214561i | ||||
\(727\) | 28.7674 | 1.06692 | 0.533461 | − | 0.845825i | \(-0.320891\pi\) | ||||
0.533461 | + | 0.845825i | \(0.320891\pi\) | |||||||
\(728\) | 3.52646 | − | 27.4067i | 0.130699 | − | 1.01576i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.75667 | + | 3.04263i | −0.0650171 | + | 0.112613i | ||||
\(731\) | −0.868059 | + | 1.50352i | −0.0321063 | + | 0.0556098i | ||||
\(732\) | −5.05537 | − | 8.75615i | −0.186852 | − | 0.323637i | ||||
\(733\) | −46.7802 | −1.72787 | −0.863933 | − | 0.503607i | \(-0.832006\pi\) | ||||
−0.863933 | + | 0.503607i | \(0.832006\pi\) | |||||||
\(734\) | 8.92637 | + | 15.4609i | 0.329478 | + | 0.570673i | ||||
\(735\) | −1.45749 | − | 2.52445i | −0.0537605 | − | 0.0931159i | ||||
\(736\) | −20.2402 | −0.746065 | ||||||||
\(737\) | −4.97112 | − | 8.61023i | −0.183113 | − | 0.317162i | ||||
\(738\) | −1.24610 | + | 2.15831i | −0.0458696 | + | 0.0794485i | ||||
\(739\) | 1.24801 | − | 2.16162i | 0.0459089 | − | 0.0795166i | −0.842158 | − | 0.539231i | \(-0.818715\pi\) |
0.888067 | + | 0.459715i | \(0.152048\pi\) | |||||||
\(740\) | −6.68709 | −0.245822 | ||||||||
\(741\) | 8.57250 | + | 6.53808i | 0.314919 | + | 0.240182i | ||||
\(742\) | −1.80315 | −0.0661957 | ||||||||
\(743\) | −8.36060 | + | 14.4810i | −0.306721 | + | 0.531256i | −0.977643 | − | 0.210272i | \(-0.932565\pi\) |
0.670922 | + | 0.741528i | \(0.265898\pi\) | |||||||
\(744\) | 0.0382693 | − | 0.0662844i | 0.00140302 | − | 0.00243010i | ||||
\(745\) | 6.97560 | + | 12.0821i | 0.255566 | + | 0.442654i | ||||
\(746\) | 15.7943 | 0.578272 | ||||||||
\(747\) | −8.32533 | − | 14.4199i | −0.304608 | − | 0.527597i | ||||
\(748\) | 0.613041 | + | 1.06182i | 0.0224150 | + | 0.0388239i | ||||
\(749\) | 37.7513 | 1.37940 | ||||||||
\(750\) | 2.62999 | + | 4.55528i | 0.0960336 | + | 0.166335i | ||||
\(751\) | 13.7170 | − | 23.7585i | 0.500539 | − | 0.866959i | −0.499461 | − | 0.866337i | \(-0.666468\pi\) |
1.00000 | 0.000622786i | \(-0.000198239\pi\) | ||||||||
\(752\) | −1.19253 | + | 2.06553i | −0.0434872 | + | 0.0753221i | ||||
\(753\) | 4.88517 | 0.178025 | ||||||||
\(754\) | 0.354320 | − | 2.75367i | 0.0129036 | − | 0.100283i | ||||
\(755\) | 6.25312 | 0.227574 | ||||||||
\(756\) | −2.51028 | + | 4.34793i | −0.0912980 | + | 0.158133i | ||||
\(757\) | −15.5355 | + | 26.9083i | −0.564648 | + | 0.977999i | 0.432434 | + | 0.901666i | \(0.357655\pi\) |
−0.997082 | + | 0.0763338i | \(0.975679\pi\) | |||||||
\(758\) | 8.90982 | + | 15.4323i | 0.323619 | + | 0.560525i | ||||
\(759\) | 3.51187 | 0.127473 | ||||||||
\(760\) | 3.01242 | + | 5.21766i | 0.109272 | + | 0.189264i | ||||
\(761\) | −7.72426 | − | 13.3788i | −0.280004 | − | 0.484982i | 0.691381 | − | 0.722490i | \(-0.257003\pi\) |
−0.971385 | + | 0.237509i | \(0.923669\pi\) | |||||||
\(762\) | 5.77173 | 0.209088 | ||||||||
\(763\) | 11.0565 | + | 19.1504i | 0.400271 | + | 0.693291i | ||||
\(764\) | −2.30722 | + | 3.99622i | −0.0834723 | + | 0.144578i | ||||
\(765\) | 0.334915 | − | 0.580090i | 0.0121089 | − | 0.0209732i | ||||
\(766\) | 19.2916 | 0.697034 | ||||||||
\(767\) | 4.56314 | − | 35.4634i | 0.164766 | − | 1.28051i | ||||
\(768\) | −8.93489 | −0.322410 | ||||||||
\(769\) | 8.45407 | − | 14.6429i | 0.304861 | − | 0.528035i | −0.672369 | − | 0.740216i | \(-0.734723\pi\) |
0.977230 | + | 0.212181i | \(0.0680565\pi\) | |||||||
\(770\) | −0.915496 | + | 1.58569i | −0.0329922 | + | 0.0571441i | ||||
\(771\) | −11.6952 | − | 20.2567i | −0.421192 | − | 0.729526i | ||||
\(772\) | 9.03743 | 0.325264 | ||||||||
\(773\) | −26.3558 | − | 45.6496i | −0.947952 | − | 1.64190i | −0.749729 | − | 0.661745i | \(-0.769816\pi\) |
−0.198223 | − | 0.980157i | \(-0.563517\pi\) | |||||||
\(774\) | 0.734636 | + | 1.27243i | 0.0264059 | + | 0.0457364i | ||||
\(775\) | −0.138026 | −0.00495804 | ||||||||
\(776\) | 13.8783 | + | 24.0378i | 0.498200 | + | 0.862908i | ||||
\(777\) | 8.18190 | − | 14.1715i | 0.293524 | − | 0.508399i | ||||
\(778\) | 8.26941 | − | 14.3230i | 0.296473 | − | 0.513506i | ||||
\(779\) | 11.1632 | 0.399964 | ||||||||
\(780\) | −3.78411 | − | 2.88607i | −0.135493 | − | 0.103338i | ||||
\(781\) | −4.30018 | −0.153873 | ||||||||
\(782\) | −0.924623 | + | 1.60149i | −0.0330644 | + | 0.0572693i | ||||
\(783\) | −0.576749 | + | 0.998959i | −0.0206113 | + | 0.0356999i | ||||
\(784\) | −2.61708 | − | 4.53291i | −0.0934671 | − | 0.161890i | ||||
\(785\) | 18.3195 | 0.653850 | ||||||||
\(786\) | 3.37406 | + | 5.84404i | 0.120349 | + | 0.208450i | ||||
\(787\) | −3.38669 | − | 5.86591i | −0.120722 | − | 0.209097i | 0.799330 | − | 0.600892i | \(-0.205188\pi\) |
−0.920053 | + | 0.391795i | \(0.871854\pi\) | |||||||
\(788\) | −13.1335 | −0.467863 | ||||||||
\(789\) | 2.67363 | + | 4.63086i | 0.0951837 | + | 0.164863i | ||||
\(790\) | −3.54507 | + | 6.14024i | −0.126128 | + | 0.218460i | ||||
\(791\) | −16.7138 | + | 28.9491i | −0.594274 | + | 1.02931i | ||||
\(792\) | 2.37275 | 0.0843119 | ||||||||
\(793\) | −2.99308 | + | 23.2614i | −0.106287 | + | 0.826036i | ||||
\(794\) | 3.42474 | 0.121539 | ||||||||
\(795\) | −0.355068 | + | 0.614996i | −0.0125930 | + | 0.0218117i | ||||
\(796\) | 11.3259 | − | 19.6171i | 0.401437 | − | 0.695310i | ||||
\(797\) | 14.3568 | + | 24.8667i | 0.508543 | + | 0.880823i | 0.999951 | + | 0.00989301i | \(0.00314909\pi\) |
−0.491408 | + | 0.870930i | \(0.663518\pi\) | |||||||
\(798\) | −6.44738 | −0.228235 | ||||||||
\(799\) | 0.616920 | + | 1.06854i | 0.0218251 | + | 0.0378021i | ||||
\(800\) | 12.3305 | + | 21.3570i | 0.435947 | + | 0.755083i | ||||
\(801\) | −9.50325 | −0.335781 | ||||||||
\(802\) | −2.58829 | − | 4.48305i | −0.0913957 | − | 0.158302i | ||||
\(803\) | 3.09886 | − | 5.36738i | 0.109356 | − | 0.189411i | ||||
\(804\) | −7.72693 | + | 13.3834i | −0.272508 | + | 0.471998i | ||||
\(805\) | 9.63242 | 0.339498 | ||||||||
\(806\) | −0.0716434 | + | 0.0299220i | −0.00252353 | + | 0.00105396i | ||||
\(807\) | −11.3400 | −0.399186 | ||||||||
\(808\) | 16.8685 | − | 29.2171i | 0.593431 | − | 1.02785i | ||||
\(809\) | 21.5142 | − | 37.2637i | 0.756400 | − | 1.31012i | −0.188276 | − | 0.982116i | \(-0.560290\pi\) |
0.944676 | − | 0.328006i | \(-0.106377\pi\) | |||||||
\(810\) | −0.283438 | − | 0.490929i | −0.00995899 | − | 0.0172495i | ||||
\(811\) | 8.68276 | 0.304893 | 0.152446 | − | 0.988312i | \(-0.451285\pi\) | ||||
0.152446 | + | 0.988312i | \(0.451285\pi\) | |||||||
\(812\) | −2.89560 | − | 5.01533i | −0.101616 | − | 0.176004i | ||||
\(813\) | −6.23570 | − | 10.8005i | −0.218695 | − | 0.378792i | ||||
\(814\) | −3.38201 | −0.118539 | ||||||||
\(815\) | −5.83970 | − | 10.1147i | −0.204556 | − | 0.354301i | ||||
\(816\) | 0.601374 | − | 1.04161i | 0.0210523 | − | 0.0364637i | ||||
\(817\) | 3.29062 | − | 5.69952i | 0.115124 | − | 0.199401i | ||||
\(818\) | 3.65382 | 0.127753 | ||||||||
\(819\) | 10.7462 | − | 4.48818i | 0.375504 | − | 0.156830i | ||||
\(820\) | −4.92771 | −0.172083 | ||||||||
\(821\) | −5.92189 | + | 10.2570i | −0.206675 | + | 0.357972i | −0.950665 | − | 0.310219i | \(-0.899598\pi\) |
0.743990 | + | 0.668191i | \(0.232931\pi\) | |||||||
\(822\) | −4.61918 | + | 8.00065i | −0.161112 | + | 0.279055i | ||||
\(823\) | 8.34044 | + | 14.4461i | 0.290730 | + | 0.503558i | 0.973982 | − | 0.226623i | \(-0.0727687\pi\) |
−0.683253 | + | 0.730182i | \(0.739435\pi\) | |||||||
\(824\) | −27.8192 | −0.969128 | ||||||||
\(825\) | −2.13945 | − | 3.70563i | −0.0744861 | − | 0.129014i | ||||
\(826\) | 10.6914 | + | 18.5180i | 0.372000 | + | 0.644323i | ||||
\(827\) | −43.0588 | −1.49730 | −0.748651 | − | 0.662965i | \(-0.769298\pi\) | ||||
−0.748651 | + | 0.662965i | \(0.769298\pi\) | |||||||
\(828\) | −2.72937 | − | 4.72740i | −0.0948520 | − | 0.164288i | ||||
\(829\) | 1.74789 | − | 3.02743i | 0.0607066 | − | 0.105147i | −0.834075 | − | 0.551651i | \(-0.813998\pi\) |
0.894781 | + | 0.446504i | \(0.147331\pi\) | |||||||
\(830\) | −4.71943 | + | 8.17429i | −0.163814 | + | 0.283734i | ||||
\(831\) | −19.8913 | −0.690021 | ||||||||
\(832\) | 2.28728 | + | 1.74446i | 0.0792971 | + | 0.0604784i | ||||
\(833\) | −2.70773 | −0.0938172 | ||||||||
\(834\) | −2.28920 | + | 3.96502i | −0.0792687 | + | 0.137297i | ||||
\(835\) | −4.49935 | + | 7.79310i | −0.155706 | + | 0.269691i | ||||
\(836\) | −2.32391 | − | 4.02512i | −0.0803740 | − | 0.139212i | ||||
\(837\) | 0.0322574 | 0.00111498 | ||||||||
\(838\) | −11.2194 | − | 19.4327i | −0.387569 | − | 0.671290i | ||||
\(839\) | 0.538989 | + | 0.933557i | 0.0186080 | + | 0.0322300i | 0.875179 | − | 0.483798i | \(-0.160743\pi\) |
−0.856571 | + | 0.516028i | \(0.827410\pi\) | |||||||
\(840\) | 6.50801 | 0.224548 | ||||||||
\(841\) | 13.8347 | + | 23.9624i | 0.477059 | + | 0.826291i | ||||
\(842\) | 10.5186 | − | 18.2187i | 0.362493 | − | 0.627857i | ||||
\(843\) | −9.89022 | + | 17.1304i | −0.340637 | + | 0.590001i | ||||
\(844\) | −14.9004 | −0.512894 | ||||||||
\(845\) | 2.91964 | + | 10.6462i | 0.100439 | + | 0.366241i | ||||
\(846\) | 1.04419 | 0.0359002 | ||||||||
\(847\) | 1.61499 | − | 2.79724i | 0.0554916 | − | 0.0961142i | ||||
\(848\) | −0.637561 | + | 1.10429i | −0.0218939 | + | 0.0379214i | ||||
\(849\) | −2.55376 | − | 4.42324i | −0.0876448 | − | 0.151805i | ||||
\(850\) | 2.25314 | 0.0772820 | ||||||||
\(851\) | 8.89598 | + | 15.4083i | 0.304950 | + | 0.528190i | ||||
\(852\) | 3.34203 | + | 5.78856i | 0.114496 | + | 0.198313i | ||||
\(853\) | −2.87104 | −0.0983025 | −0.0491513 | − | 0.998791i | \(-0.515652\pi\) | ||||
−0.0491513 | + | 0.998791i | \(0.515652\pi\) | |||||||
\(854\) | −7.01274 | − | 12.1464i | −0.239971 | − | 0.415642i | ||||
\(855\) | −1.26959 | + | 2.19899i | −0.0434191 | + | 0.0752040i | ||||
\(856\) | −13.8661 | + | 24.0168i | −0.473934 | + | 0.820878i | ||||
\(857\) | 12.4441 | 0.425082 | 0.212541 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212541 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(858\) | −1.91382 | − | 1.45963i | −0.0653368 | − | 0.0498311i | ||||
\(859\) | −20.3537 | −0.694460 | −0.347230 | − | 0.937780i | \(-0.612878\pi\) | ||||
−0.347230 | + | 0.937780i | \(0.612878\pi\) | |||||||
\(860\) | −1.45256 | + | 2.51591i | −0.0495319 | + | 0.0857918i | ||||
\(861\) | 6.02924 | − | 10.4430i | 0.205476 | − | 0.355895i | ||||
\(862\) | 9.76963 | + | 16.9215i | 0.332755 | + | 0.576348i | ||||
\(863\) | −2.44402 | −0.0831953 | −0.0415977 | − | 0.999134i | \(-0.513245\pi\) | ||||
−0.0415977 | + | 0.999134i | \(0.513245\pi\) | |||||||
\(864\) | −2.88169 | − | 4.99123i | −0.0980370 | − | 0.169805i | ||||
\(865\) | 1.85131 | + | 3.20656i | 0.0629463 | + | 0.109026i | ||||
\(866\) | −14.3305 | −0.486970 | ||||||||
\(867\) | 8.18890 | + | 14.1836i | 0.278110 | + | 0.481700i | ||||
\(868\) | −0.0809751 | + | 0.140253i | −0.00274847 | + | 0.00476049i | ||||
\(869\) | 6.25370 | − | 10.8317i | 0.212142 | − | 0.367441i | ||||
\(870\) | 0.653890 | 0.0221689 | ||||||||
\(871\) | 33.0782 | − | 13.8152i | 1.12081 | − | 0.468109i | ||||
\(872\) | −16.2442 | −0.550100 | ||||||||
\(873\) | −5.84903 | + | 10.1308i | −0.197960 | + | 0.342876i | ||||
\(874\) | 3.50504 | − | 6.07091i | 0.118560 | − | 0.205352i | ||||
\(875\) | −12.7252 | − | 22.0406i | −0.430189 | − | 0.745109i | ||||
\(876\) | −9.63352 | −0.325486 | ||||||||
\(877\) | −11.6174 | − | 20.1219i | −0.392292 | − | 0.679469i | 0.600460 | − | 0.799655i | \(-0.294984\pi\) |
−0.992751 | + | 0.120186i | \(0.961651\pi\) | |||||||
\(878\) | 0.777186 | + | 1.34613i | 0.0262288 | + | 0.0454296i | ||||
\(879\) | 6.98382 | 0.235558 | ||||||||
\(880\) | 0.647406 | + | 1.12134i | 0.0218240 | + | 0.0378004i | ||||
\(881\) | 23.8079 | − | 41.2365i | 0.802109 | − | 1.38929i | −0.116117 | − | 0.993236i | \(-0.537045\pi\) |
0.918226 | − | 0.396057i | \(-0.129622\pi\) | |||||||
\(882\) | −1.14577 | + | 1.98453i | −0.0385801 | + | 0.0668227i | ||||
\(883\) | 14.6456 | 0.492864 | 0.246432 | − | 0.969160i | \(-0.420742\pi\) | ||||
0.246432 | + | 0.969160i | \(0.420742\pi\) | |||||||
\(884\) | −4.07922 | + | 1.70369i | −0.137199 | + | 0.0573014i | ||||
\(885\) | 8.42118 | 0.283075 | ||||||||
\(886\) | −4.16983 | + | 7.22236i | −0.140088 | + | 0.242640i | ||||
\(887\) | −20.9277 | + | 36.2479i | −0.702684 | + | 1.21708i | 0.264837 | + | 0.964293i | \(0.414682\pi\) |
−0.967521 | + | 0.252791i | \(0.918651\pi\) | |||||||
\(888\) | 6.01045 | + | 10.4104i | 0.201697 | + | 0.349350i | ||||
\(889\) | −27.9264 | −0.936622 | ||||||||
\(890\) | 2.69358 | + | 4.66542i | 0.0902890 | + | 0.156385i | ||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 14.3283 | 0.479747 | ||||||||
\(893\) | −2.33861 | − | 4.05059i | −0.0782585 | − | 0.135548i | ||||
\(894\) | 5.48369 | − | 9.49803i | 0.183402 | − | 0.317661i | ||||
\(895\) | −5.83501 | + | 10.1065i | −0.195043 | + | 0.337824i | ||||
\(896\) | 35.5108 | 1.18633 | ||||||||
\(897\) | −1.61595 | + | 12.5587i | −0.0539550 | + | 0.419323i | ||||
\(898\) | −18.4249 | −0.614848 | ||||||||
\(899\) | −0.0186044 | + | 0.0322238i | −0.000620492 | + | 0.00107472i | ||||
\(900\) | −3.32549 | + | 5.75991i | −0.110850 | + | 0.191997i | ||||
\(901\) | 0.329822 | + | 0.571269i | 0.0109880 | + | 0.0190317i | ||||
\(902\) | −2.49220 | −0.0829812 | ||||||||
\(903\) | −3.55452 | − | 6.15662i | −0.118287 | − | 0.204879i | ||||
\(904\) | −12.2780 | − | 21.2661i | −0.408360 | − | 0.707300i | ||||
\(905\) | −12.8744 | −0.427958 | ||||||||
\(906\) | −2.45787 | − | 4.25715i | −0.0816571 | − | 0.141434i | ||||
\(907\) | −1.63040 | + | 2.82394i | −0.0541367 | + | 0.0937674i | −0.891824 | − | 0.452383i | \(-0.850574\pi\) |
0.837687 | + | 0.546150i | \(0.183907\pi\) | |||||||
\(908\) | 15.9788 | − | 27.6761i | 0.530275 | − | 0.918463i | ||||
\(909\) | 14.2185 | 0.471599 | ||||||||
\(910\) | −5.24927 | − | 4.00351i | −0.174011 | − | 0.132715i | ||||
\(911\) | 34.8710 | 1.15533 | 0.577664 | − | 0.816275i | \(-0.303965\pi\) | ||||
0.577664 | + | 0.816275i | \(0.303965\pi\) | |||||||
\(912\) | −2.27968 | + | 3.94852i | −0.0754877 | + | 0.130749i | ||||
\(913\) | 8.32533 | − | 14.4199i | 0.275528 | − | 0.477229i | ||||
\(914\) | −3.58274 | − | 6.20550i | −0.118507 | − | 0.205260i | ||||
\(915\) | −5.52367 | −0.182607 | ||||||||
\(916\) | −5.38383 | − | 9.32508i | −0.177887 | − | 0.308109i | ||||
\(917\) | −16.3253 | − | 28.2763i | −0.539110 | − | 0.933765i | ||||
\(918\) | −0.526570 | −0.0173794 | ||||||||
\(919\) | −15.4941 | − | 26.8366i | −0.511103 | − | 0.885257i | −0.999917 | − | 0.0128686i | \(-0.995904\pi\) |
0.488814 | − | 0.872388i | \(-0.337430\pi\) | |||||||
\(920\) | −3.53800 | + | 6.12800i | −0.116645 | + | 0.202034i | ||||
\(921\) | 9.42878 | − | 16.3311i | 0.310689 | − | 0.538129i | ||||
\(922\) | 22.7971 | 0.750782 | ||||||||
\(923\) | 1.97868 | − | 15.3778i | 0.0651292 | − | 0.506165i | ||||
\(924\) | −5.02056 | −0.165164 | ||||||||
\(925\) | 10.8390 | − | 18.7736i | 0.356383 | − | 0.617273i | ||||
\(926\) | −8.85451 | + | 15.3365i | −0.290977 | + | 0.503987i | ||||
\(927\) | −5.86223 | − | 10.1537i | −0.192541 | − | 0.333491i | ||||
\(928\) | 6.64805 | 0.218233 | ||||||||
\(929\) | 9.76291 | + | 16.9099i | 0.320311 | + | 0.554794i | 0.980552 | − | 0.196259i | \(-0.0628794\pi\) |
−0.660241 | + | 0.751053i | \(0.729546\pi\) | |||||||
\(930\) | −0.00914296 | − | 0.0158361i | −0.000299810 | − | 0.000519285i | ||||
\(931\) | 10.2644 | 0.336402 | ||||||||
\(932\) | −7.72868 | − | 13.3865i | −0.253161 | − | 0.438489i | ||||
\(933\) | 15.1183 | − | 26.1857i | 0.494951 | − | 0.857281i | ||||
\(934\) | 12.2410 | − | 21.2021i | 0.400539 | − | 0.693753i | ||||
\(935\) | 0.669831 | 0.0219058 | ||||||||
\(936\) | −1.09179 | + | 8.48511i | −0.0356864 | + | 0.277344i | ||||
\(937\) | 28.0493 | 0.916329 | 0.458165 | − | 0.888867i | \(-0.348507\pi\) | ||||
0.458165 | + | 0.888867i | \(0.348507\pi\) | |||||||
\(938\) | −10.7187 | + | 18.5653i | −0.349978 | + | 0.606180i | ||||
\(939\) | −14.3184 | + | 24.8003i | −0.467265 | + | 0.809326i | ||||
\(940\) | 1.03232 | + | 1.78803i | 0.0336705 | + | 0.0583190i | ||||
\(941\) | −18.6286 | −0.607274 | −0.303637 | − | 0.952788i | \(-0.598201\pi\) | ||||
−0.303637 | + | 0.952788i | \(0.598201\pi\) | |||||||
\(942\) | −7.20069 | − | 12.4720i | −0.234611 | − | 0.406359i | ||||
\(943\) | 6.55545 | + | 11.3544i | 0.213475 | + | 0.369749i | ||||
\(944\) | 15.1211 | 0.492150 | ||||||||
\(945\) | 1.37141 | + | 2.37535i | 0.0446119 | + | 0.0772702i | ||||
\(946\) | −0.734636 | + | 1.27243i | −0.0238851 | + | 0.0413701i | ||||
\(947\) | −6.92545 | + | 11.9952i | −0.225047 | + | 0.389793i | −0.956333 | − | 0.292278i | \(-0.905587\pi\) |
0.731287 | + | 0.682070i | \(0.238920\pi\) | |||||||
\(948\) | −19.4411 | −0.631417 | ||||||||
\(949\) | 17.7682 | + | 13.5515i | 0.576781 | + | 0.439899i | ||||
\(950\) | −8.54115 | −0.277112 | ||||||||
\(951\) | −9.84118 | + | 17.0454i | −0.319122 | + | 0.552736i | ||||
\(952\) | 3.02264 | − | 5.23537i | 0.0979644 | − | 0.169679i | ||||
\(953\) | 4.05889 | + | 7.03020i | 0.131480 | + | 0.227731i | 0.924247 | − | 0.381794i | \(-0.124694\pi\) |
−0.792767 | + | 0.609525i | \(0.791360\pi\) | |||||||
\(954\) | 0.558255 | 0.0180742 | ||||||||
\(955\) | 1.26047 | + | 2.18321i | 0.0407880 | + | 0.0706469i | ||||
\(956\) | −8.31719 | − | 14.4058i | −0.268997 | − | 0.465917i | ||||
\(957\) | −1.15350 | −0.0372873 | ||||||||
\(958\) | 1.72420 | + | 2.98641i | 0.0557064 | + | 0.0964864i | ||||
\(959\) | 22.3498 | − | 38.7110i | 0.721713 | − | 1.25004i | ||||
\(960\) | −0.338747 | + | 0.586727i | −0.0109330 | + | 0.0189365i | ||||
\(961\) | −30.9990 | −0.999966 | ||||||||
\(962\) | 1.55619 | − | 12.0943i | 0.0501737 | − | 0.389936i | ||||
\(963\) | −11.6878 | −0.376635 | ||||||||
\(964\) | 18.9825 | − | 32.8787i | 0.611386 | − | 1.05895i | ||||
\(965\) | 2.46865 | − | 4.27583i | 0.0794687 | − | 0.137644i | ||||
\(966\) | −3.78614 | − | 6.55779i | −0.121817 | − | 0.210993i | ||||
\(967\) | 19.8745 | 0.639122 | 0.319561 | − | 0.947566i | \(-0.396465\pi\) | ||||
0.319561 | + | 0.947566i | \(0.396465\pi\) | |||||||
\(968\) | 1.18637 | + | 2.05486i | 0.0381315 | + | 0.0660457i | ||||
\(969\) | 1.17932 | + | 2.04264i | 0.0378852 | + | 0.0656192i | ||||
\(970\) | 6.63134 | 0.212919 | ||||||||
\(971\) | −18.3152 | − | 31.7229i | −0.587764 | − | 1.01804i | −0.994525 | − | 0.104502i | \(-0.966675\pi\) |
0.406761 | − | 0.913535i | \(-0.366658\pi\) | |||||||
\(972\) | 0.777183 | − | 1.34612i | 0.0249282 | − | 0.0431768i | ||||
\(973\) | 11.0763 | − | 19.1847i | 0.355089 | − | 0.615033i | ||||
\(974\) | −13.5596 | −0.434478 | ||||||||
\(975\) | 14.2361 | − | 5.94571i | 0.455918 | − | 0.190415i | ||||
\(976\) | −9.91831 | −0.317477 | ||||||||
\(977\) | 0.562945 | − | 0.975049i | 0.0180102 | − | 0.0311946i | −0.856880 | − | 0.515516i | \(-0.827600\pi\) |
0.874890 | + | 0.484322i | \(0.160934\pi\) | |||||||
\(978\) | −4.59073 | + | 7.95137i | −0.146795 | + | 0.254257i | ||||
\(979\) | −4.75163 | − | 8.23006i | −0.151863 | − | 0.263034i | ||||
\(980\) | −4.53096 | −0.144736 | ||||||||
\(981\) | −3.42309 | − | 5.92896i | −0.109291 | − | 0.189297i | ||||
\(982\) | −10.3384 | − | 17.9066i | −0.329910 | − | 0.571421i | ||||
\(983\) | 53.9539 | 1.72086 | 0.860432 | − | 0.509566i | \(-0.170194\pi\) | ||||
0.860432 | + | 0.509566i | \(0.170194\pi\) | |||||||
\(984\) | 4.42910 | + | 7.67142i | 0.141195 | + | 0.244556i | ||||
\(985\) | −3.58754 | + | 6.21381i | −0.114309 | + | 0.197988i | ||||
\(986\) | 0.303699 | − | 0.526022i | 0.00967174 | − | 0.0167519i | ||||
\(987\) | −5.05232 | −0.160817 | ||||||||
\(988\) | 15.4634 | − | 6.45833i | 0.491957 | − | 0.205467i | ||||
\(989\) | 7.72950 | 0.245784 | ||||||||
\(990\) | 0.283438 | − | 0.490929i | 0.00900824 | − | 0.0156027i | ||||
\(991\) | 15.5233 | − | 26.8872i | 0.493114 | − | 0.854098i | −0.506855 | − | 0.862032i | \(-0.669192\pi\) |
0.999969 | + | 0.00793312i | \(0.00252522\pi\) | |||||||
\(992\) | −0.0929558 | − | 0.161004i | −0.00295135 | − | 0.00511189i | ||||
\(993\) | 21.5647 | 0.684335 | ||||||||
\(994\) | 4.63602 | + | 8.02982i | 0.147046 | + | 0.254690i | ||||
\(995\) | −6.18756 | − | 10.7172i | −0.196159 | − | 0.339757i | ||||
\(996\) | −25.8812 | −0.820078 | ||||||||
\(997\) | −23.2190 | − | 40.2165i | −0.735352 | − | 1.27367i | −0.954569 | − | 0.297992i | \(-0.903683\pi\) |
0.219216 | − | 0.975676i | \(-0.429650\pi\) | |||||||
\(998\) | 8.28406 | − | 14.3484i | 0.262227 | − | 0.454191i | ||||
\(999\) | −2.53312 | + | 4.38749i | −0.0801443 | + | 0.138814i |
(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 | 429.2.i.c.100.3 | ✓ | 10 | |
13.3 | even | 3 | inner | 429.2.i.c.133.3 | yes | 10 | |
13.4 | even | 6 | 5577.2.a.p.1.3 | 5 | |||
13.9 | even | 3 | 5577.2.a.v.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.c.100.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
429.2.i.c.133.3 | yes | 10 | 13.3 | even | 3 | inner | |
5577.2.a.p.1.3 | 5 | 13.4 | even | 6 | |||
5577.2.a.v.1.3 | 5 | 13.9 | even | 3 |