Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), 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: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + 115 x^{11} + 1963 x^{10} + 323 x^{9} + 3007 x^{8} + 1828 x^{7} + 6736 x^{6} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 235.5 | ||
Root | \(2.01466 - 1.46373i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.235 |
Dual form | 429.2.n.b.157.5 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.01466 | + | 1.46373i | 1.42458 | + | 1.03502i | 0.990995 | + | 0.133901i | \(0.0427504\pi\) |
0.433582 | + | 0.901114i | \(0.357250\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | 1.29829 | + | 3.99572i | 0.649144 | + | 1.99786i | ||||
\(5\) | 1.02009 | − | 0.741137i | 0.456197 | − | 0.331446i | −0.335841 | − | 0.941919i | \(-0.609020\pi\) |
0.792038 | + | 0.610472i | \(0.209020\pi\) | |||||||
\(6\) | −2.01466 | + | 1.46373i | −0.822479 | + | 0.597566i | ||||
\(7\) | 0.590393 | + | 1.81704i | 0.223147 | + | 0.686777i | 0.998474 | + | 0.0552171i | \(0.0175851\pi\) |
−0.775327 | + | 0.631560i | \(0.782415\pi\) | |||||||
\(8\) | −1.69400 | + | 5.21361i | −0.598920 | + | 1.84329i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 3.13995 | 0.992939 | ||||||||
\(11\) | −1.53494 | − | 2.94006i | −0.462802 | − | 0.886462i | ||||
\(12\) | −4.20135 | −1.21282 | ||||||||
\(13\) | 0.809017 | + | 0.587785i | 0.224381 | + | 0.163022i | ||||
\(14\) | −1.47023 | + | 4.52489i | −0.392934 | + | 1.20933i | ||||
\(15\) | 0.389639 | + | 1.19918i | 0.100604 | + | 0.309628i | ||||
\(16\) | −4.24623 | + | 3.08507i | −1.06156 | + | 0.771267i | ||||
\(17\) | −1.67827 | + | 1.21934i | −0.407041 | + | 0.295733i | −0.772403 | − | 0.635133i | \(-0.780945\pi\) |
0.365362 | + | 0.930866i | \(0.380945\pi\) | |||||||
\(18\) | −0.769530 | − | 2.36837i | −0.181380 | − | 0.558230i | ||||
\(19\) | 1.50819 | − | 4.64172i | 0.346001 | − | 1.06488i | −0.615044 | − | 0.788493i | \(-0.710862\pi\) |
0.961046 | − | 0.276390i | \(-0.0891382\pi\) | |||||||
\(20\) | 4.28574 | + | 3.11377i | 0.958321 | + | 0.696261i | ||||
\(21\) | −1.91055 | −0.416916 | ||||||||
\(22\) | 1.21109 | − | 8.16995i | 0.258206 | − | 1.74184i | ||||
\(23\) | 0.161641 | 0.0337044 | 0.0168522 | − | 0.999858i | \(-0.494636\pi\) | ||||
0.0168522 | + | 0.999858i | \(0.494636\pi\) | |||||||
\(24\) | −4.43496 | − | 3.22219i | −0.905282 | − | 0.657726i | ||||
\(25\) | −1.05379 | + | 3.24323i | −0.210758 | + | 0.648647i | ||||
\(26\) | 0.769530 | + | 2.36837i | 0.150917 | + | 0.464475i | ||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | −6.49389 | + | 4.71809i | −1.22723 | + | 0.891635i | ||||
\(29\) | −1.72116 | − | 5.29718i | −0.319611 | − | 0.983662i | −0.973815 | − | 0.227343i | \(-0.926996\pi\) |
0.654204 | − | 0.756318i | \(-0.273004\pi\) | |||||||
\(30\) | −0.970298 | + | 2.98627i | −0.177151 | + | 0.545216i | ||||
\(31\) | −1.29968 | − | 0.944270i | −0.233429 | − | 0.169596i | 0.464922 | − | 0.885352i | \(-0.346082\pi\) |
−0.698351 | + | 0.715756i | \(0.746082\pi\) | |||||||
\(32\) | −2.10659 | −0.372396 | ||||||||
\(33\) | 3.27049 | − | 0.551285i | 0.569319 | − | 0.0959664i | ||||
\(34\) | −5.16593 | −0.885949 | ||||||||
\(35\) | 1.94893 | + | 1.41598i | 0.329429 | + | 0.239344i | ||||
\(36\) | 1.29829 | − | 3.99572i | 0.216381 | − | 0.665953i | ||||
\(37\) | −0.577942 | − | 1.77872i | −0.0950131 | − | 0.292420i | 0.892244 | − | 0.451554i | \(-0.149130\pi\) |
−0.987257 | + | 0.159133i | \(0.949130\pi\) | |||||||
\(38\) | 9.83271 | − | 7.14388i | 1.59508 | − | 1.15889i | ||||
\(39\) | −0.809017 | + | 0.587785i | −0.129546 | + | 0.0941210i | ||||
\(40\) | 2.13596 | + | 6.57382i | 0.337725 | + | 1.03941i | ||||
\(41\) | −1.17056 | + | 3.60262i | −0.182811 | + | 0.562635i | −0.999904 | − | 0.0138713i | \(-0.995584\pi\) |
0.817093 | + | 0.576507i | \(0.195584\pi\) | |||||||
\(42\) | −3.84910 | − | 2.79654i | −0.593929 | − | 0.431515i | ||||
\(43\) | 6.60266 | 1.00690 | 0.503448 | − | 0.864025i | \(-0.332064\pi\) | ||||
0.503448 | + | 0.864025i | \(0.332064\pi\) | |||||||
\(44\) | 9.75487 | − | 9.95023i | 1.47060 | − | 1.50005i | ||||
\(45\) | −1.26090 | −0.187963 | ||||||||
\(46\) | 0.325650 | + | 0.236598i | 0.0480145 | + | 0.0348845i | ||||
\(47\) | 0.598370 | − | 1.84159i | 0.0872813 | − | 0.268624i | −0.897884 | − | 0.440232i | \(-0.854896\pi\) |
0.985165 | + | 0.171608i | \(0.0548962\pi\) | |||||||
\(48\) | −1.62192 | − | 4.99174i | −0.234103 | − | 0.720496i | ||||
\(49\) | 2.71004 | − | 1.96896i | 0.387149 | − | 0.281280i | ||||
\(50\) | −6.87025 | + | 4.99153i | −0.971601 | + | 0.705909i | ||||
\(51\) | −0.641043 | − | 1.97293i | −0.0897640 | − | 0.276265i | ||||
\(52\) | −1.29829 | + | 3.99572i | −0.180040 | + | 0.554107i | ||||
\(53\) | 2.08681 | + | 1.51615i | 0.286645 | + | 0.208260i | 0.721811 | − | 0.692091i | \(-0.243310\pi\) |
−0.435166 | + | 0.900350i | \(0.643310\pi\) | |||||||
\(54\) | 2.49025 | 0.338880 | ||||||||
\(55\) | −3.74476 | − | 1.86152i | −0.504943 | − | 0.251007i | ||||
\(56\) | −10.4735 | −1.39958 | ||||||||
\(57\) | 3.94848 | + | 2.86874i | 0.522989 | + | 0.379974i | ||||
\(58\) | 4.28611 | − | 13.1913i | 0.562794 | − | 1.73210i | ||||
\(59\) | −2.07665 | − | 6.39128i | −0.270357 | − | 0.832074i | −0.990411 | − | 0.138155i | \(-0.955883\pi\) |
0.720053 | − | 0.693919i | \(-0.244117\pi\) | |||||||
\(60\) | −4.28574 | + | 3.11377i | −0.553287 | + | 0.401986i | ||||
\(61\) | −11.7076 | + | 8.50611i | −1.49901 | + | 1.08910i | −0.528238 | + | 0.849097i | \(0.677147\pi\) |
−0.970773 | + | 0.239999i | \(0.922853\pi\) | |||||||
\(62\) | −1.23624 | − | 3.80476i | −0.157003 | − | 0.483205i | ||||
\(63\) | 0.590393 | − | 1.81704i | 0.0743825 | − | 0.228926i | ||||
\(64\) | 4.24842 | + | 3.08665i | 0.531052 | + | 0.385832i | ||||
\(65\) | 1.26090 | 0.156395 | ||||||||
\(66\) | 7.39584 | + | 3.67647i | 0.910365 | + | 0.452542i | ||||
\(67\) | −8.27187 | −1.01057 | −0.505285 | − | 0.862953i | \(-0.668612\pi\) | ||||
−0.505285 | + | 0.862953i | \(0.668612\pi\) | |||||||
\(68\) | −7.05101 | − | 5.12286i | −0.855061 | − | 0.621238i | ||||
\(69\) | −0.0499497 | + | 0.153729i | −0.00601323 | + | 0.0185068i | ||||
\(70\) | 1.85380 | + | 5.70542i | 0.221572 | + | 0.681928i | ||||
\(71\) | 11.3711 | − | 8.26161i | 1.34950 | − | 0.980472i | 0.350468 | − | 0.936575i | \(-0.386022\pi\) |
0.999036 | − | 0.0438977i | \(-0.0139776\pi\) | |||||||
\(72\) | 4.43496 | − | 3.22219i | 0.522665 | − | 0.379738i | ||||
\(73\) | 3.42658 | + | 10.5459i | 0.401051 | + | 1.23431i | 0.924148 | + | 0.382035i | \(0.124776\pi\) |
−0.523097 | + | 0.852273i | \(0.675224\pi\) | |||||||
\(74\) | 1.43922 | − | 4.42947i | 0.167306 | − | 0.514915i | ||||
\(75\) | −2.75886 | − | 2.00443i | −0.318566 | − | 0.231452i | ||||
\(76\) | 20.5051 | 2.35209 | ||||||||
\(77\) | 4.43600 | − | 4.52484i | 0.505529 | − | 0.515653i | ||||
\(78\) | −2.49025 | −0.281965 | ||||||||
\(79\) | 5.58324 | + | 4.05646i | 0.628164 | + | 0.456388i | 0.855764 | − | 0.517367i | \(-0.173088\pi\) |
−0.227600 | + | 0.973755i | \(0.573088\pi\) | |||||||
\(80\) | −2.04507 | + | 6.29407i | −0.228646 | + | 0.703699i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −7.63156 | + | 5.54465i | −0.842765 | + | 0.612304i | ||||
\(83\) | 10.8108 | − | 7.85451i | 1.18664 | − | 0.862144i | 0.193734 | − | 0.981054i | \(-0.437940\pi\) |
0.992905 | + | 0.118910i | \(0.0379400\pi\) | |||||||
\(84\) | −2.48045 | − | 7.63402i | −0.270639 | − | 0.832940i | ||||
\(85\) | −0.808290 | + | 2.48766i | −0.0876713 | + | 0.269825i | ||||
\(86\) | 13.3021 | + | 9.66453i | 1.43440 | + | 1.04215i | ||||
\(87\) | 5.56978 | 0.597144 | ||||||||
\(88\) | 17.9285 | − | 3.02209i | 1.91119 | − | 0.322156i | ||||
\(89\) | −6.56886 | −0.696297 | −0.348149 | − | 0.937439i | \(-0.613190\pi\) | ||||
−0.348149 | + | 0.937439i | \(0.613190\pi\) | |||||||
\(90\) | −2.54027 | − | 1.84562i | −0.267768 | − | 0.194545i | ||||
\(91\) | −0.590393 | + | 1.81704i | −0.0618900 | + | 0.190478i | ||||
\(92\) | 0.209856 | + | 0.645870i | 0.0218790 | + | 0.0673366i | ||||
\(93\) | 1.29968 | − | 0.944270i | 0.134770 | − | 0.0979162i | ||||
\(94\) | 3.90111 | − | 2.83432i | 0.402369 | − | 0.292338i | ||||
\(95\) | −1.90167 | − | 5.85273i | −0.195107 | − | 0.600477i | ||||
\(96\) | 0.650971 | − | 2.00348i | 0.0664395 | − | 0.204480i | ||||
\(97\) | −7.51024 | − | 5.45651i | −0.762549 | − | 0.554024i | 0.137142 | − | 0.990551i | \(-0.456208\pi\) |
−0.899691 | + | 0.436527i | \(0.856208\pi\) | |||||||
\(98\) | 8.34183 | 0.842652 | ||||||||
\(99\) | −0.486333 | + | 3.28077i | −0.0488783 | + | 0.329730i | ||||
\(100\) | −14.3272 | −1.43272 | ||||||||
\(101\) | −16.0734 | − | 11.6780i | −1.59936 | − | 1.16200i | −0.888727 | − | 0.458437i | \(-0.848409\pi\) |
−0.710632 | − | 0.703564i | \(-0.751591\pi\) | |||||||
\(102\) | 1.59636 | − | 4.91309i | 0.158063 | − | 0.486468i | ||||
\(103\) | 1.05519 | + | 3.24755i | 0.103971 | + | 0.319990i | 0.989488 | − | 0.144618i | \(-0.0461952\pi\) |
−0.885516 | + | 0.464608i | \(0.846195\pi\) | |||||||
\(104\) | −4.43496 | + | 3.22219i | −0.434883 | + | 0.315961i | ||||
\(105\) | −1.94893 | + | 1.41598i | −0.190196 | + | 0.138185i | ||||
\(106\) | 1.98495 | + | 6.10905i | 0.192796 | + | 0.593364i | ||||
\(107\) | −1.85664 | + | 5.71416i | −0.179488 | + | 0.552409i | −0.999810 | − | 0.0194939i | \(-0.993794\pi\) |
0.820322 | + | 0.571903i | \(0.193794\pi\) | |||||||
\(108\) | 3.39896 | + | 2.46949i | 0.327065 | + | 0.237627i | ||||
\(109\) | −6.09330 | −0.583633 | −0.291816 | − | 0.956474i | \(-0.594260\pi\) | ||||
−0.291816 | + | 0.956474i | \(0.594260\pi\) | |||||||
\(110\) | −4.81963 | − | 9.23164i | −0.459534 | − | 0.880203i | ||||
\(111\) | 1.87026 | 0.177517 | ||||||||
\(112\) | −8.11264 | − | 5.89418i | −0.766572 | − | 0.556947i | ||||
\(113\) | −3.42824 | + | 10.5510i | −0.322501 | + | 0.992557i | 0.650054 | + | 0.759888i | \(0.274746\pi\) |
−0.972556 | + | 0.232670i | \(0.925254\pi\) | |||||||
\(114\) | 3.75576 | + | 11.5590i | 0.351759 | + | 1.08260i | ||||
\(115\) | 0.164887 | − | 0.119798i | 0.0153758 | − | 0.0111712i | ||||
\(116\) | 18.9315 | − | 13.7545i | 1.75774 | − | 1.27708i | ||||
\(117\) | −0.309017 | − | 0.951057i | −0.0285686 | − | 0.0879252i | ||||
\(118\) | 5.17139 | − | 15.9159i | 0.476065 | − | 1.46518i | ||||
\(119\) | −3.20643 | − | 2.32961i | −0.293933 | − | 0.213555i | ||||
\(120\) | −6.91212 | −0.630987 | ||||||||
\(121\) | −6.28792 | + | 9.02563i | −0.571629 | + | 0.820512i | ||||
\(122\) | −36.0375 | −3.26269 | ||||||||
\(123\) | −3.06457 | − | 2.22654i | −0.276323 | − | 0.200761i | ||||
\(124\) | 2.08568 | − | 6.41908i | 0.187300 | − | 0.576450i | ||||
\(125\) | 3.27691 | + | 10.0853i | 0.293096 | + | 0.902057i | ||||
\(126\) | 3.84910 | − | 2.79654i | 0.342905 | − | 0.249135i | ||||
\(127\) | 8.67124 | − | 6.30002i | 0.769448 | − | 0.559037i | −0.132346 | − | 0.991204i | \(-0.542251\pi\) |
0.901794 | + | 0.432167i | \(0.142251\pi\) | |||||||
\(128\) | 5.34300 | + | 16.4441i | 0.472259 | + | 1.45346i | ||||
\(129\) | −2.04033 | + | 6.27950i | −0.179641 | + | 0.552879i | ||||
\(130\) | 2.54027 | + | 1.84562i | 0.222797 | + | 0.161871i | ||||
\(131\) | −16.5018 | −1.44177 | −0.720885 | − | 0.693054i | \(-0.756265\pi\) | ||||
−0.720885 | + | 0.693054i | \(0.756265\pi\) | |||||||
\(132\) | 6.44881 | + | 12.3522i | 0.561297 | + | 1.07512i | ||||
\(133\) | 9.32462 | 0.808547 | ||||||||
\(134\) | −16.6650 | − | 12.1078i | −1.43963 | − | 1.04595i | ||||
\(135\) | 0.389639 | − | 1.19918i | 0.0335347 | − | 0.103209i | ||||
\(136\) | −3.51414 | − | 10.8154i | −0.301335 | − | 0.927414i | ||||
\(137\) | −7.21527 | + | 5.24220i | −0.616442 | + | 0.447872i | −0.851677 | − | 0.524067i | \(-0.824414\pi\) |
0.235235 | + | 0.971939i | \(0.424414\pi\) | |||||||
\(138\) | −0.325650 | + | 0.236598i | −0.0277212 | + | 0.0201406i | ||||
\(139\) | 0.943715 | + | 2.90446i | 0.0800449 | + | 0.246353i | 0.983069 | − | 0.183238i | \(-0.0586579\pi\) |
−0.903024 | + | 0.429591i | \(0.858658\pi\) | |||||||
\(140\) | −3.12759 | + | 9.62572i | −0.264329 | + | 0.813522i | ||||
\(141\) | 1.56655 | + | 1.13817i | 0.131928 | + | 0.0958510i | ||||
\(142\) | 35.0017 | 2.93728 | ||||||||
\(143\) | 0.486333 | − | 3.28077i | 0.0406692 | − | 0.274352i | ||||
\(144\) | 5.24863 | 0.437386 | ||||||||
\(145\) | −5.68166 | − | 4.12797i | −0.471837 | − | 0.342809i | ||||
\(146\) | −8.53304 | + | 26.2620i | −0.706200 | + | 2.17346i | ||||
\(147\) | 1.03514 | + | 3.18585i | 0.0853772 | + | 0.262764i | ||||
\(148\) | 6.35694 | − | 4.61859i | 0.522538 | − | 0.379646i | ||||
\(149\) | 2.72614 | − | 1.98065i | 0.223334 | − | 0.162262i | −0.470492 | − | 0.882404i | \(-0.655924\pi\) |
0.693826 | + | 0.720143i | \(0.255924\pi\) | |||||||
\(150\) | −2.62420 | − | 8.07647i | −0.214265 | − | 0.659441i | ||||
\(151\) | −5.66383 | + | 17.4315i | −0.460916 | + | 1.41855i | 0.403132 | + | 0.915142i | \(0.367922\pi\) |
−0.864047 | + | 0.503410i | \(0.832078\pi\) | |||||||
\(152\) | 21.6452 | + | 15.7262i | 1.75566 | + | 1.27556i | ||||
\(153\) | 2.07446 | 0.167710 | ||||||||
\(154\) | 15.5602 | − | 2.62288i | 1.25387 | − | 0.211357i | ||||
\(155\) | −2.02562 | −0.162701 | ||||||||
\(156\) | −3.39896 | − | 2.46949i | −0.272135 | − | 0.197717i | ||||
\(157\) | −0.929535 | + | 2.86081i | −0.0741850 | + | 0.228318i | −0.981273 | − | 0.192624i | \(-0.938300\pi\) |
0.907088 | + | 0.420942i | \(0.138300\pi\) | |||||||
\(158\) | 5.31073 | + | 16.3448i | 0.422499 | + | 1.30032i | ||||
\(159\) | −2.08681 | + | 1.51615i | −0.165495 | + | 0.120239i | ||||
\(160\) | −2.14890 | + | 1.56127i | −0.169886 | + | 0.123429i | ||||
\(161\) | 0.0954314 | + | 0.293708i | 0.00752105 | + | 0.0231474i | ||||
\(162\) | −0.769530 | + | 2.36837i | −0.0604600 | + | 0.186077i | ||||
\(163\) | −14.0565 | − | 10.2126i | −1.10099 | − | 0.799916i | −0.119769 | − | 0.992802i | \(-0.538215\pi\) |
−0.981221 | + | 0.192886i | \(0.938215\pi\) | |||||||
\(164\) | −15.9148 | −1.24274 | ||||||||
\(165\) | 2.92760 | − | 2.98624i | 0.227914 | − | 0.232478i | ||||
\(166\) | 33.2769 | 2.58279 | ||||||||
\(167\) | −19.6954 | − | 14.3095i | −1.52407 | − | 1.10730i | −0.959422 | − | 0.281975i | \(-0.909010\pi\) |
−0.564652 | − | 0.825329i | \(-0.690990\pi\) | |||||||
\(168\) | 3.23648 | − | 9.96086i | 0.249700 | − | 0.768497i | ||||
\(169\) | 0.309017 | + | 0.951057i | 0.0237705 | + | 0.0731582i | ||||
\(170\) | −5.26969 | + | 3.82866i | −0.404167 | + | 0.293645i | ||||
\(171\) | −3.94848 | + | 2.86874i | −0.301948 | + | 0.219378i | ||||
\(172\) | 8.57216 | + | 26.3824i | 0.653621 | + | 2.01164i | ||||
\(173\) | 2.47654 | − | 7.62202i | 0.188288 | − | 0.579491i | −0.811701 | − | 0.584073i | \(-0.801458\pi\) |
0.999990 | + | 0.00458136i | \(0.00145830\pi\) | |||||||
\(174\) | 11.2212 | + | 8.15267i | 0.850677 | + | 0.618053i | ||||
\(175\) | −6.51524 | −0.492506 | ||||||||
\(176\) | 15.5880 | + | 7.74879i | 1.17499 | + | 0.584087i | ||||
\(177\) | 6.72019 | 0.505121 | ||||||||
\(178\) | −13.2340 | − | 9.61505i | −0.991929 | − | 0.720678i | ||||
\(179\) | 4.90264 | − | 15.0888i | 0.366441 | − | 1.12779i | −0.582634 | − | 0.812735i | \(-0.697978\pi\) |
0.949074 | − | 0.315053i | \(-0.102022\pi\) | |||||||
\(180\) | −1.63701 | − | 5.03819i | −0.122015 | − | 0.375525i | ||||
\(181\) | 9.95518 | − | 7.23286i | 0.739963 | − | 0.537614i | −0.152737 | − | 0.988267i | \(-0.548809\pi\) |
0.892699 | + | 0.450652i | \(0.148809\pi\) | |||||||
\(182\) | −3.84910 | + | 2.79654i | −0.285314 | + | 0.207293i | ||||
\(183\) | −4.47192 | − | 13.7632i | −0.330574 | − | 1.01740i | ||||
\(184\) | −0.273820 | + | 0.842730i | −0.0201862 | + | 0.0621269i | ||||
\(185\) | −1.90783 | − | 1.38612i | −0.140266 | − | 0.101909i | ||||
\(186\) | 4.00056 | 0.293335 | ||||||||
\(187\) | 6.16097 | + | 3.06262i | 0.450535 | + | 0.223961i | ||||
\(188\) | 8.13535 | 0.593332 | ||||||||
\(189\) | 1.54567 | + | 1.12299i | 0.112431 | + | 0.0816858i | ||||
\(190\) | 4.73563 | − | 14.5748i | 0.343558 | − | 1.05736i | ||||
\(191\) | 0.859957 | + | 2.64667i | 0.0622243 | + | 0.191507i | 0.977336 | − | 0.211693i | \(-0.0678979\pi\) |
−0.915112 | + | 0.403200i | \(0.867898\pi\) | |||||||
\(192\) | −4.24842 | + | 3.08665i | −0.306603 | + | 0.222760i | ||||
\(193\) | −14.8153 | + | 10.7639i | −1.06643 | + | 0.774804i | −0.975266 | − | 0.221033i | \(-0.929057\pi\) |
−0.0911594 | + | 0.995836i | \(0.529057\pi\) | |||||||
\(194\) | −7.14367 | − | 21.9860i | −0.512886 | − | 1.57850i | ||||
\(195\) | −0.389639 | + | 1.19918i | −0.0279026 | + | 0.0858754i | ||||
\(196\) | 11.3858 | + | 8.27229i | 0.813274 | + | 0.590878i | ||||
\(197\) | 2.73096 | 0.194573 | 0.0972864 | − | 0.995256i | \(-0.468984\pi\) | ||||
0.0972864 | + | 0.995256i | \(0.468984\pi\) | |||||||
\(198\) | −5.78197 | + | 5.89777i | −0.410907 | + | 0.419136i | ||||
\(199\) | −20.8343 | −1.47691 | −0.738454 | − | 0.674304i | \(-0.764444\pi\) | ||||
−0.738454 | + | 0.674304i | \(0.764444\pi\) | |||||||
\(200\) | −15.1238 | − | 10.9881i | −1.06942 | − | 0.776976i | ||||
\(201\) | 2.55615 | − | 7.86701i | 0.180297 | − | 0.554896i | ||||
\(202\) | −15.2888 | − | 47.0542i | −1.07572 | − | 3.31072i | ||||
\(203\) | 8.60904 | − | 6.25483i | 0.604236 | − | 0.439003i | ||||
\(204\) | 7.05101 | − | 5.12286i | 0.493669 | − | 0.358672i | ||||
\(205\) | 1.47596 | + | 4.54254i | 0.103085 | + | 0.317265i | ||||
\(206\) | −2.62769 | + | 8.08721i | −0.183080 | + | 0.563463i | ||||
\(207\) | −0.130770 | − | 0.0950099i | −0.00908914 | − | 0.00660365i | ||||
\(208\) | −5.24863 | −0.363927 | ||||||||
\(209\) | −15.9619 | + | 2.69059i | −1.10411 | + | 0.186112i | ||||
\(210\) | −5.99903 | −0.413973 | ||||||||
\(211\) | 10.4669 | + | 7.60464i | 0.720570 | + | 0.523525i | 0.886566 | − | 0.462602i | \(-0.153084\pi\) |
−0.165996 | + | 0.986126i | \(0.553084\pi\) | |||||||
\(212\) | −3.34885 | + | 10.3067i | −0.230000 | + | 0.707867i | ||||
\(213\) | 4.34338 | + | 13.3676i | 0.297604 | + | 0.915930i | ||||
\(214\) | −12.1045 | + | 8.79443i | −0.827446 | + | 0.601175i | ||||
\(215\) | 6.73529 | − | 4.89347i | 0.459343 | − | 0.333732i | ||||
\(216\) | 1.69400 | + | 5.21361i | 0.115262 | + | 0.354741i | ||||
\(217\) | 0.948459 | − | 2.91906i | 0.0643856 | − | 0.198158i | ||||
\(218\) | −12.2759 | − | 8.91897i | −0.831429 | − | 0.604069i | ||||
\(219\) | −11.0886 | −0.749301 | ||||||||
\(220\) | 2.57633 | − | 17.3798i | 0.173696 | − | 1.17175i | ||||
\(221\) | −2.07446 | −0.139543 | ||||||||
\(222\) | 3.76793 | + | 2.73756i | 0.252887 | + | 0.183733i | ||||
\(223\) | −1.34274 | + | 4.13252i | −0.0899163 | + | 0.276734i | −0.985895 | − | 0.167362i | \(-0.946475\pi\) |
0.895979 | + | 0.444096i | \(0.146475\pi\) | |||||||
\(224\) | −1.24371 | − | 3.82776i | −0.0830991 | − | 0.255753i | ||||
\(225\) | 2.75886 | − | 2.00443i | 0.183924 | − | 0.133629i | ||||
\(226\) | −22.3506 | + | 16.2387i | −1.48674 | + | 1.08018i | ||||
\(227\) | 6.84404 | + | 21.0638i | 0.454255 | + | 1.39805i | 0.872008 | + | 0.489492i | \(0.162818\pi\) |
−0.417753 | + | 0.908561i | \(0.637182\pi\) | |||||||
\(228\) | −6.33641 | + | 19.5015i | −0.419639 | + | 1.29152i | ||||
\(229\) | −16.9314 | − | 12.3013i | −1.11886 | − | 0.812896i | −0.134820 | − | 0.990870i | \(-0.543046\pi\) |
−0.984035 | + | 0.177974i | \(0.943046\pi\) | |||||||
\(230\) | 0.507543 | 0.0334664 | ||||||||
\(231\) | 2.93258 | + | 5.61714i | 0.192950 | + | 0.369580i | ||||
\(232\) | 30.5330 | 2.00459 | ||||||||
\(233\) | 11.1219 | + | 8.08053i | 0.728620 | + | 0.529373i | 0.889126 | − | 0.457662i | \(-0.151313\pi\) |
−0.160507 | + | 0.987035i | \(0.551313\pi\) | |||||||
\(234\) | 0.769530 | − | 2.36837i | 0.0503057 | − | 0.154825i | ||||
\(235\) | −0.754483 | − | 2.32206i | −0.0492171 | − | 0.151475i | ||||
\(236\) | 22.8417 | − | 16.5955i | 1.48687 | − | 1.08027i | ||||
\(237\) | −5.58324 | + | 4.05646i | −0.362671 | + | 0.263496i | ||||
\(238\) | −3.04992 | − | 9.38670i | −0.197697 | − | 0.608449i | ||||
\(239\) | 3.56797 | − | 10.9811i | 0.230793 | − | 0.710307i | −0.766859 | − | 0.641816i | \(-0.778181\pi\) |
0.997652 | − | 0.0684914i | \(-0.0218186\pi\) | |||||||
\(240\) | −5.35406 | − | 3.88995i | −0.345603 | − | 0.251095i | ||||
\(241\) | 19.5720 | 1.26074 | 0.630372 | − | 0.776293i | \(-0.282902\pi\) | ||||
0.630372 | + | 0.776293i | \(0.282902\pi\) | |||||||
\(242\) | −25.8791 | + | 8.97969i | −1.66357 | + | 0.577236i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −49.1879 | − | 35.7371i | −3.14893 | − | 2.28783i | ||||
\(245\) | 1.30521 | − | 4.01702i | 0.0833868 | − | 0.256638i | ||||
\(246\) | −2.91500 | − | 8.97143i | −0.185853 | − | 0.571998i | ||||
\(247\) | 3.94848 | − | 2.86874i | 0.251236 | − | 0.182533i | ||||
\(248\) | 7.12471 | − | 5.17640i | 0.452419 | − | 0.328702i | ||||
\(249\) | 4.12936 | + | 12.7089i | 0.261687 | + | 0.805391i | ||||
\(250\) | −8.16034 | + | 25.1149i | −0.516105 | + | 1.58841i | ||||
\(251\) | −15.1285 | − | 10.9915i | −0.954900 | − | 0.693775i | −0.00293895 | − | 0.999996i | \(-0.500935\pi\) |
−0.951961 | + | 0.306221i | \(0.900935\pi\) | |||||||
\(252\) | 8.02689 | 0.505646 | ||||||||
\(253\) | −0.248108 | − | 0.475233i | −0.0155984 | − | 0.0298776i | ||||
\(254\) | 26.6911 | 1.67475 | ||||||||
\(255\) | −2.11613 | − | 1.53746i | −0.132517 | − | 0.0962794i | ||||
\(256\) | −10.0599 | + | 30.9612i | −0.628744 | + | 1.93507i | ||||
\(257\) | −3.15201 | − | 9.70089i | −0.196617 | − | 0.605125i | −0.999954 | − | 0.00959999i | \(-0.996944\pi\) |
0.803337 | − | 0.595525i | \(-0.203056\pi\) | |||||||
\(258\) | −13.3021 | + | 9.66453i | −0.828152 | + | 0.601687i | ||||
\(259\) | 2.89080 | − | 2.10029i | 0.179626 | − | 0.130506i | ||||
\(260\) | 1.63701 | + | 5.03819i | 0.101523 | + | 0.312455i | ||||
\(261\) | −1.72116 | + | 5.29718i | −0.106537 | + | 0.327887i | ||||
\(262\) | −33.2455 | − | 24.1543i | −2.05391 | − | 1.49225i | ||||
\(263\) | 1.76069 | 0.108569 | 0.0542843 | − | 0.998526i | \(-0.482712\pi\) | ||||
0.0542843 | + | 0.998526i | \(0.482712\pi\) | |||||||
\(264\) | −2.66603 | + | 17.9849i | −0.164083 | + | 1.10689i | ||||
\(265\) | 3.25240 | 0.199793 | ||||||||
\(266\) | 18.7859 | + | 13.6487i | 1.15184 | + | 0.836858i | ||||
\(267\) | 2.02989 | − | 6.24735i | 0.124227 | − | 0.382332i | ||||
\(268\) | −10.7393 | − | 33.0521i | −0.656005 | − | 2.01898i | ||||
\(269\) | 14.5890 | − | 10.5995i | 0.889506 | − | 0.646264i | −0.0462433 | − | 0.998930i | \(-0.514725\pi\) |
0.935749 | + | 0.352666i | \(0.114725\pi\) | |||||||
\(270\) | 2.54027 | − | 1.84562i | 0.154596 | − | 0.112321i | ||||
\(271\) | −0.807860 | − | 2.48634i | −0.0490740 | − | 0.151034i | 0.923517 | − | 0.383558i | \(-0.125302\pi\) |
−0.972591 | + | 0.232524i | \(0.925302\pi\) | |||||||
\(272\) | 3.36460 | − | 10.3552i | 0.204009 | − | 0.627875i | ||||
\(273\) | −1.54567 | − | 1.12299i | −0.0935481 | − | 0.0679667i | ||||
\(274\) | −22.2095 | −1.34172 | ||||||||
\(275\) | 11.1528 | − | 1.87996i | 0.672540 | − | 0.113366i | ||||
\(276\) | −0.679108 | −0.0408775 | ||||||||
\(277\) | 25.9247 | + | 18.8354i | 1.55767 | + | 1.13171i | 0.937890 | + | 0.346932i | \(0.112777\pi\) |
0.619776 | + | 0.784779i | \(0.287223\pi\) | |||||||
\(278\) | −2.35009 | + | 7.23283i | −0.140949 | + | 0.433796i | ||||
\(279\) | 0.496432 | + | 1.52786i | 0.0297206 | + | 0.0914706i | ||||
\(280\) | −10.6838 | + | 7.76227i | −0.638482 | + | 0.463884i | ||||
\(281\) | 19.3116 | − | 14.0307i | 1.15203 | − | 0.837000i | 0.163282 | − | 0.986579i | \(-0.447792\pi\) |
0.988750 | + | 0.149579i | \(0.0477919\pi\) | |||||||
\(282\) | 1.49009 | + | 4.58603i | 0.0887337 | + | 0.273094i | ||||
\(283\) | −6.29039 | + | 19.3598i | −0.373925 | + | 1.15082i | 0.570276 | + | 0.821453i | \(0.306836\pi\) |
−0.944201 | + | 0.329369i | \(0.893164\pi\) | |||||||
\(284\) | 47.7741 | + | 34.7099i | 2.83487 | + | 2.05965i | ||||
\(285\) | 6.15392 | 0.364527 | ||||||||
\(286\) | 5.78197 | − | 5.89777i | 0.341895 | − | 0.348742i | ||||
\(287\) | −7.23721 | −0.427199 | ||||||||
\(288\) | 1.70427 | + | 1.23822i | 0.100425 | + | 0.0729629i | ||||
\(289\) | −3.92347 | + | 12.0752i | −0.230792 | + | 0.710306i | ||||
\(290\) | −5.40435 | − | 16.6329i | −0.317354 | − | 0.976716i | ||||
\(291\) | 7.51024 | − | 5.45651i | 0.440258 | − | 0.319866i | ||||
\(292\) | −37.6899 | + | 27.3833i | −2.20563 | + | 1.60249i | ||||
\(293\) | 9.26129 | + | 28.5033i | 0.541050 | + | 1.66518i | 0.730201 | + | 0.683233i | \(0.239427\pi\) |
−0.189151 | + | 0.981948i | \(0.560573\pi\) | |||||||
\(294\) | −2.57777 | + | 7.93355i | −0.150338 | + | 0.462694i | ||||
\(295\) | −6.85518 | − | 4.98058i | −0.399124 | − | 0.289981i | ||||
\(296\) | 10.2526 | 0.595920 | ||||||||
\(297\) | −2.96992 | − | 1.47635i | −0.172332 | − | 0.0856662i | ||||
\(298\) | 8.39137 | 0.486099 | ||||||||
\(299\) | 0.130770 | + | 0.0950099i | 0.00756262 | + | 0.00549456i | ||||
\(300\) | 4.42734 | − | 13.6260i | 0.255613 | − | 0.786695i | ||||
\(301\) | 3.89816 | + | 11.9973i | 0.224686 | + | 0.691513i | ||||
\(302\) | −36.9257 | + | 26.8281i | −2.12483 | + | 1.54378i | ||||
\(303\) | 16.0734 | − | 11.6780i | 0.923390 | − | 0.670882i | ||||
\(304\) | 7.91591 | + | 24.3627i | 0.454008 | + | 1.39729i | ||||
\(305\) | −5.63864 | + | 17.3539i | −0.322867 | + | 0.993683i | ||||
\(306\) | 4.17932 | + | 3.03645i | 0.238916 | + | 0.173583i | ||||
\(307\) | 10.0204 | 0.571897 | 0.285948 | − | 0.958245i | \(-0.407691\pi\) | ||||
0.285948 | + | 0.958245i | \(0.407691\pi\) | |||||||
\(308\) | 23.8392 | + | 11.8505i | 1.35836 | + | 0.675243i | ||||
\(309\) | −3.41467 | −0.194254 | ||||||||
\(310\) | −4.08092 | − | 2.96496i | −0.231781 | − | 0.168398i | ||||
\(311\) | −4.28808 | + | 13.1973i | −0.243155 | + | 0.748353i | 0.752780 | + | 0.658272i | \(0.228712\pi\) |
−0.995934 | + | 0.0900805i | \(0.971288\pi\) | |||||||
\(312\) | −1.69400 | − | 5.21361i | −0.0959040 | − | 0.295162i | ||||
\(313\) | −16.1603 | + | 11.7412i | −0.913435 | + | 0.663649i | −0.941881 | − | 0.335946i | \(-0.890944\pi\) |
0.0284464 | + | 0.999595i | \(0.490944\pi\) | |||||||
\(314\) | −6.06016 | + | 4.40296i | −0.341995 | + | 0.248474i | ||||
\(315\) | −0.744424 | − | 2.29110i | −0.0419436 | − | 0.129089i | ||||
\(316\) | −8.95984 | + | 27.5755i | −0.504030 | + | 1.55125i | ||||
\(317\) | 12.4786 | + | 9.06621i | 0.700866 | + | 0.509209i | 0.880214 | − | 0.474577i | \(-0.157399\pi\) |
−0.179348 | + | 0.983786i | \(0.557399\pi\) | |||||||
\(318\) | −6.42344 | −0.360209 | ||||||||
\(319\) | −12.9322 | + | 13.1912i | −0.724062 | + | 0.738563i | ||||
\(320\) | 6.62139 | 0.370147 | ||||||||
\(321\) | −4.86075 | − | 3.53154i | −0.271301 | − | 0.197112i | ||||
\(322\) | −0.237648 | + | 0.731405i | −0.0132436 | + | 0.0407596i | ||||
\(323\) | 3.12867 | + | 9.62906i | 0.174084 | + | 0.535775i | ||||
\(324\) | −3.39896 | + | 2.46949i | −0.188831 | + | 0.137194i | ||||
\(325\) | −2.75886 | + | 2.00443i | −0.153034 | + | 0.111186i | ||||
\(326\) | −13.3704 | − | 41.1499i | −0.740519 | − | 2.27908i | ||||
\(327\) | 1.88293 | − | 5.79508i | 0.104127 | − | 0.320468i | ||||
\(328\) | −16.7997 | − | 12.2057i | −0.927609 | − | 0.673948i | ||||
\(329\) | 3.69953 | 0.203962 | ||||||||
\(330\) | 10.2692 | − | 1.73101i | 0.565299 | − | 0.0952888i | ||||
\(331\) | 28.0595 | 1.54229 | 0.771144 | − | 0.636660i | \(-0.219685\pi\) | ||||
0.771144 | + | 0.636660i | \(0.219685\pi\) | |||||||
\(332\) | 45.4199 | + | 32.9995i | 2.49274 | + | 1.81108i | ||||
\(333\) | −0.577942 | + | 1.77872i | −0.0316710 | + | 0.0974734i | ||||
\(334\) | −18.7341 | − | 57.6575i | −1.02508 | − | 3.15488i | ||||
\(335\) | −8.43802 | + | 6.13058i | −0.461018 | + | 0.334950i | ||||
\(336\) | 8.11264 | − | 5.89418i | 0.442581 | − | 0.321554i | ||||
\(337\) | −2.27668 | − | 7.00690i | −0.124019 | − | 0.381690i | 0.869702 | − | 0.493577i | \(-0.164311\pi\) |
−0.993721 | + | 0.111886i | \(0.964311\pi\) | |||||||
\(338\) | −0.769530 | + | 2.36837i | −0.0418569 | + | 0.128822i | ||||
\(339\) | −8.97524 | − | 6.52089i | −0.487468 | − | 0.354166i | ||||
\(340\) | −10.9894 | −0.595983 | ||||||||
\(341\) | −0.781288 | + | 5.27052i | −0.0423091 | + | 0.285415i | ||||
\(342\) | −12.1539 | −0.657207 | ||||||||
\(343\) | 15.9973 | + | 11.6228i | 0.863776 | + | 0.627570i | ||||
\(344\) | −11.1849 | + | 34.4237i | −0.603051 | + | 1.85600i | ||||
\(345\) | 0.0629814 | + | 0.193837i | 0.00339080 | + | 0.0104358i | ||||
\(346\) | 16.1460 | − | 11.7307i | 0.868013 | − | 0.630648i | ||||
\(347\) | 9.27446 | − | 6.73829i | 0.497879 | − | 0.361730i | −0.310327 | − | 0.950630i | \(-0.600439\pi\) |
0.808206 | + | 0.588900i | \(0.200439\pi\) | |||||||
\(348\) | 7.23118 | + | 22.2553i | 0.387632 | + | 1.19301i | ||||
\(349\) | −3.00259 | + | 9.24103i | −0.160725 | + | 0.494661i | −0.998696 | − | 0.0510540i | \(-0.983742\pi\) |
0.837971 | + | 0.545715i | \(0.183742\pi\) | |||||||
\(350\) | −13.1260 | − | 9.53657i | −0.701613 | − | 0.509751i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 3.23348 | + | 6.19350i | 0.172345 | + | 0.330114i | ||||
\(353\) | 14.9952 | 0.798114 | 0.399057 | − | 0.916926i | \(-0.369338\pi\) | ||||
0.399057 | + | 0.916926i | \(0.369338\pi\) | |||||||
\(354\) | 13.5389 | + | 9.83656i | 0.719583 | + | 0.522808i | ||||
\(355\) | 5.47656 | − | 16.8551i | 0.290666 | − | 0.894577i | ||||
\(356\) | −8.52827 | − | 26.2473i | −0.451997 | − | 1.39110i | ||||
\(357\) | 3.20643 | − | 2.32961i | 0.169702 | − | 0.123296i | ||||
\(358\) | 31.9631 | − | 23.2225i | 1.68930 | − | 1.22735i | ||||
\(359\) | 4.75337 | + | 14.6294i | 0.250873 | + | 0.772108i | 0.994615 | + | 0.103641i | \(0.0330493\pi\) |
−0.743742 | + | 0.668467i | \(0.766951\pi\) | |||||||
\(360\) | 2.13596 | − | 6.57382i | 0.112575 | − | 0.346471i | ||||
\(361\) | −3.89959 | − | 2.83322i | −0.205242 | − | 0.149117i | ||||
\(362\) | 30.6432 | 1.61057 | ||||||||
\(363\) | −6.64081 | − | 8.76924i | −0.348552 | − | 0.460266i | ||||
\(364\) | −8.02689 | −0.420723 | ||||||||
\(365\) | 11.3114 | + | 8.21820i | 0.592065 | + | 0.430160i | ||||
\(366\) | 11.1362 | − | 34.2737i | 0.582099 | − | 1.79152i | ||||
\(367\) | −6.44465 | − | 19.8346i | −0.336408 | − | 1.03536i | −0.966024 | − | 0.258451i | \(-0.916788\pi\) |
0.629617 | − | 0.776906i | \(-0.283212\pi\) | |||||||
\(368\) | −0.686363 | + | 0.498672i | −0.0357791 | + | 0.0259951i | ||||
\(369\) | 3.06457 | − | 2.22654i | 0.159535 | − | 0.115909i | ||||
\(370\) | −1.81471 | − | 5.58510i | −0.0943422 | − | 0.290356i | ||||
\(371\) | −1.52288 | + | 4.68694i | −0.0790640 | + | 0.243334i | ||||
\(372\) | 5.46039 | + | 3.96721i | 0.283108 | + | 0.205690i | ||||
\(373\) | −27.8062 | −1.43975 | −0.719876 | − | 0.694103i | \(-0.755801\pi\) | ||||
−0.719876 | + | 0.694103i | \(0.755801\pi\) | |||||||
\(374\) | 7.92938 | + | 15.1881i | 0.410018 | + | 0.785360i | ||||
\(375\) | −10.6043 | −0.547605 | ||||||||
\(376\) | 8.58771 | + | 6.23933i | 0.442877 | + | 0.321769i | ||||
\(377\) | 1.72116 | − | 5.29718i | 0.0886441 | − | 0.272819i | ||||
\(378\) | 1.47023 | + | 4.52489i | 0.0756202 | + | 0.232735i | ||||
\(379\) | 11.5980 | − | 8.42642i | 0.595748 | − | 0.432836i | −0.248619 | − | 0.968601i | \(-0.579977\pi\) |
0.844367 | + | 0.535765i | \(0.179977\pi\) | |||||||
\(380\) | 20.9169 | − | 15.1970i | 1.07302 | − | 0.779592i | ||||
\(381\) | 3.31212 | + | 10.1936i | 0.169685 | + | 0.522236i | ||||
\(382\) | −2.14151 | + | 6.59088i | −0.109569 | + | 0.337219i | ||||
\(383\) | −0.0800400 | − | 0.0581524i | −0.00408985 | − | 0.00297145i | 0.585738 | − | 0.810500i | \(-0.300805\pi\) |
−0.589828 | + | 0.807529i | \(0.700805\pi\) | |||||||
\(384\) | −17.2903 | −0.882342 | ||||||||
\(385\) | 1.17158 | − | 7.90341i | 0.0597093 | − | 0.402795i | ||||
\(386\) | −45.6031 | −2.32114 | ||||||||
\(387\) | −5.34166 | − | 3.88095i | −0.271532 | − | 0.197280i | ||||
\(388\) | 12.0522 | − | 37.0929i | 0.611859 | − | 1.88311i | ||||
\(389\) | 2.90510 | + | 8.94097i | 0.147294 | + | 0.453325i | 0.997299 | − | 0.0734500i | \(-0.0234009\pi\) |
−0.850005 | + | 0.526775i | \(0.823401\pi\) | |||||||
\(390\) | −2.54027 | + | 1.84562i | −0.128632 | + | 0.0934564i | ||||
\(391\) | −0.271277 | + | 0.197094i | −0.0137191 | + | 0.00996748i | ||||
\(392\) | 5.67456 | + | 17.4645i | 0.286609 | + | 0.882091i | ||||
\(393\) | 5.09934 | − | 15.6942i | 0.257228 | − | 0.791666i | ||||
\(394\) | 5.50194 | + | 3.99740i | 0.277184 | + | 0.201386i | ||||
\(395\) | 8.70179 | 0.437835 | ||||||||
\(396\) | −13.7405 | + | 2.31614i | −0.690484 | + | 0.116390i | ||||
\(397\) | 6.12632 | 0.307471 | 0.153736 | − | 0.988112i | \(-0.450870\pi\) | ||||
0.153736 | + | 0.988112i | \(0.450870\pi\) | |||||||
\(398\) | −41.9740 | − | 30.4959i | −2.10397 | − | 1.52862i | ||||
\(399\) | −2.88146 | + | 8.86824i | −0.144254 | + | 0.443967i | ||||
\(400\) | −5.53096 | − | 17.0225i | −0.276548 | − | 0.851127i | ||||
\(401\) | 24.5645 | − | 17.8472i | 1.22669 | − | 0.891245i | 0.230055 | − | 0.973178i | \(-0.426109\pi\) |
0.996638 | + | 0.0819329i | \(0.0261093\pi\) | |||||||
\(402\) | 16.6650 | − | 12.1078i | 0.831172 | − | 0.603882i | ||||
\(403\) | −0.496432 | − | 1.52786i | −0.0247290 | − | 0.0761082i | ||||
\(404\) | 25.7941 | − | 79.3860i | 1.28330 | − | 3.94960i | ||||
\(405\) | 1.02009 | + | 0.741137i | 0.0506885 | + | 0.0368274i | ||||
\(406\) | 26.4996 | 1.31516 | ||||||||
\(407\) | −4.34245 | + | 4.42942i | −0.215247 | + | 0.219558i | ||||
\(408\) | 11.3720 | 0.562998 | ||||||||
\(409\) | 14.6140 | + | 10.6177i | 0.722615 | + | 0.525010i | 0.887219 | − | 0.461349i | \(-0.152635\pi\) |
−0.164604 | + | 0.986360i | \(0.552635\pi\) | |||||||
\(410\) | −3.67551 | + | 11.3121i | −0.181520 | + | 0.558663i | ||||
\(411\) | −2.75599 | − | 8.48206i | −0.135943 | − | 0.418389i | ||||
\(412\) | −11.6063 | + | 8.43251i | −0.571804 | + | 0.415440i | ||||
\(413\) | 10.3872 | − | 7.54673i | 0.511120 | − | 0.371350i | ||||
\(414\) | −0.124387 | − | 0.382824i | −0.00611330 | − | 0.0188148i | ||||
\(415\) | 5.20669 | − | 16.0246i | 0.255587 | − | 0.786615i | ||||
\(416\) | −1.70427 | − | 1.23822i | −0.0835585 | − | 0.0607088i | ||||
\(417\) | −3.05393 | −0.149551 | ||||||||
\(418\) | −36.0960 | − | 17.9433i | −1.76552 | − | 0.877638i | ||||
\(419\) | −26.3754 | −1.28852 | −0.644262 | − | 0.764805i | \(-0.722835\pi\) | ||||
−0.644262 | + | 0.764805i | \(0.722835\pi\) | |||||||
\(420\) | −8.18813 | − | 5.94902i | −0.399540 | − | 0.290283i | ||||
\(421\) | −7.27845 | + | 22.4008i | −0.354730 | + | 1.09175i | 0.601436 | + | 0.798921i | \(0.294596\pi\) |
−0.956166 | + | 0.292826i | \(0.905404\pi\) | |||||||
\(422\) | 9.95601 | + | 30.6414i | 0.484651 | + | 1.49160i | ||||
\(423\) | −1.56655 | + | 1.13817i | −0.0761685 | + | 0.0553396i | ||||
\(424\) | −11.4397 | + | 8.31142i | −0.555560 | + | 0.403638i | ||||
\(425\) | −2.18605 | − | 6.72796i | −0.106039 | − | 0.326354i | ||||
\(426\) | −10.8161 | + | 33.2886i | −0.524042 | + | 1.61284i | ||||
\(427\) | −22.3681 | − | 16.2513i | −1.08247 | − | 0.786458i | ||||
\(428\) | −25.2426 | −1.22015 | ||||||||
\(429\) | 2.96992 | + | 1.47635i | 0.143389 | + | 0.0712786i | ||||
\(430\) | 20.7320 | 0.999787 | ||||||||
\(431\) | 7.67426 | + | 5.57568i | 0.369656 | + | 0.268571i | 0.757068 | − | 0.653336i | \(-0.226631\pi\) |
−0.387412 | + | 0.921907i | \(0.626631\pi\) | |||||||
\(432\) | −1.62192 | + | 4.99174i | −0.0780345 | + | 0.240165i | ||||
\(433\) | −7.91492 | − | 24.3596i | −0.380367 | − | 1.17065i | −0.939786 | − | 0.341764i | \(-0.888976\pi\) |
0.559419 | − | 0.828885i | \(-0.311024\pi\) | |||||||
\(434\) | 6.18353 | − | 4.49260i | 0.296819 | − | 0.215652i | ||||
\(435\) | 5.68166 | − | 4.12797i | 0.272415 | − | 0.197921i | ||||
\(436\) | −7.91086 | − | 24.3471i | −0.378862 | − | 1.16602i | ||||
\(437\) | 0.243784 | − | 0.750290i | 0.0116618 | − | 0.0358912i | ||||
\(438\) | −22.3398 | − | 16.2308i | −1.06744 | − | 0.775538i | ||||
\(439\) | −4.50447 | −0.214987 | −0.107493 | − | 0.994206i | \(-0.534282\pi\) | ||||
−0.107493 | + | 0.994206i | \(0.534282\pi\) | |||||||
\(440\) | 16.0489 | − | 16.3703i | 0.765099 | − | 0.780422i | ||||
\(441\) | −3.34980 | −0.159514 | ||||||||
\(442\) | −4.17932 | − | 3.03645i | −0.198790 | − | 0.144429i | ||||
\(443\) | 6.95166 | − | 21.3950i | 0.330284 | − | 1.01651i | −0.638715 | − | 0.769443i | \(-0.720534\pi\) |
0.968999 | − | 0.247065i | \(-0.0794662\pi\) | |||||||
\(444\) | 2.42814 | + | 7.47304i | 0.115234 | + | 0.354655i | ||||
\(445\) | −6.70080 | + | 4.86842i | −0.317649 | + | 0.230785i | ||||
\(446\) | −8.75405 | + | 6.36019i | −0.414516 | + | 0.301164i | ||||
\(447\) | 1.04129 | + | 3.20477i | 0.0492514 | + | 0.151580i | ||||
\(448\) | −3.10035 | + | 9.54189i | −0.146478 | + | 0.450812i | ||||
\(449\) | −2.99271 | − | 2.17433i | −0.141235 | − | 0.102613i | 0.514924 | − | 0.857236i | \(-0.327820\pi\) |
−0.656159 | + | 0.754622i | \(0.727820\pi\) | |||||||
\(450\) | 8.49210 | 0.400321 | ||||||||
\(451\) | 12.3887 | − | 2.08828i | 0.583360 | − | 0.0983332i | ||||
\(452\) | −46.6098 | −2.19234 | ||||||||
\(453\) | −14.8281 | − | 10.7732i | −0.696684 | − | 0.506171i | ||||
\(454\) | −17.0434 | + | 52.4541i | −0.799885 | + | 2.46179i | ||||
\(455\) | 0.744424 | + | 2.29110i | 0.0348991 | + | 0.107409i | ||||
\(456\) | −21.6452 | + | 15.7262i | −1.01363 | + | 0.736445i | ||||
\(457\) | 26.3345 | − | 19.1332i | 1.23188 | − | 0.895012i | 0.234848 | − | 0.972032i | \(-0.424541\pi\) |
0.997030 | + | 0.0770205i | \(0.0245407\pi\) | |||||||
\(458\) | −16.1050 | − | 49.5659i | −0.752535 | − | 2.31606i | ||||
\(459\) | −0.641043 | + | 1.97293i | −0.0299213 | + | 0.0920884i | ||||
\(460\) | 0.692749 | + | 0.503312i | 0.0322996 | + | 0.0234670i | ||||
\(461\) | 12.2504 | 0.570558 | 0.285279 | − | 0.958445i | \(-0.407914\pi\) | ||||
0.285279 | + | 0.958445i | \(0.407914\pi\) | |||||||
\(462\) | −2.31385 | + | 15.6091i | −0.107650 | + | 0.726201i | ||||
\(463\) | 25.9828 | 1.20752 | 0.603761 | − | 0.797166i | \(-0.293668\pi\) | ||||
0.603761 | + | 0.797166i | \(0.293668\pi\) | |||||||
\(464\) | 23.6506 | + | 17.1832i | 1.09795 | + | 0.797708i | ||||
\(465\) | 0.625950 | − | 1.92648i | 0.0290277 | − | 0.0893381i | ||||
\(466\) | 10.5790 | + | 32.5590i | 0.490065 | + | 1.50826i | ||||
\(467\) | 10.3350 | − | 7.50884i | 0.478248 | − | 0.347467i | −0.322399 | − | 0.946604i | \(-0.604489\pi\) |
0.800647 | + | 0.599136i | \(0.204489\pi\) | |||||||
\(468\) | 3.39896 | − | 2.46949i | 0.157117 | − | 0.114152i | ||||
\(469\) | −4.88365 | − | 15.0303i | −0.225506 | − | 0.694036i | ||||
\(470\) | 1.87885 | − | 5.78251i | 0.0866650 | − | 0.266727i | ||||
\(471\) | −2.43355 | − | 1.76808i | −0.112132 | − | 0.0814689i | ||||
\(472\) | 36.8395 | 1.69567 | ||||||||
\(473\) | −10.1347 | − | 19.4122i | −0.465993 | − | 0.892575i | ||||
\(474\) | −17.1859 | −0.789374 | ||||||||
\(475\) | 13.4649 | + | 9.78280i | 0.617810 | + | 0.448866i | ||||
\(476\) | 5.14558 | − | 15.8365i | 0.235847 | − | 0.725864i | ||||
\(477\) | −0.797089 | − | 2.45319i | −0.0364962 | − | 0.112324i | ||||
\(478\) | 23.2616 | − | 16.9005i | 1.06396 | − | 0.773012i | ||||
\(479\) | 2.63863 | − | 1.91708i | 0.120562 | − | 0.0875934i | −0.525870 | − | 0.850565i | \(-0.676260\pi\) |
0.646432 | + | 0.762971i | \(0.276260\pi\) | |||||||
\(480\) | −0.820808 | − | 2.52619i | −0.0374646 | − | 0.115304i | ||||
\(481\) | 0.577942 | − | 1.77872i | 0.0263519 | − | 0.0811028i | ||||
\(482\) | 39.4309 | + | 28.6482i | 1.79603 | + | 1.30489i | ||||
\(483\) | −0.308822 | −0.0140519 | ||||||||
\(484\) | −44.2274 | − | 13.4069i | −2.01034 | − | 0.609405i | ||||
\(485\) | −11.7051 | −0.531502 | ||||||||
\(486\) | −2.01466 | − | 1.46373i | −0.0913866 | − | 0.0663963i | ||||
\(487\) | 8.63548 | − | 26.5773i | 0.391311 | − | 1.20433i | −0.540487 | − | 0.841353i | \(-0.681760\pi\) |
0.931798 | − | 0.362978i | \(-0.118240\pi\) | |||||||
\(488\) | −24.5147 | − | 75.4484i | −1.10973 | − | 3.41539i | ||||
\(489\) | 14.0565 | − | 10.2126i | 0.635657 | − | 0.461832i | ||||
\(490\) | 8.50939 | − | 6.18244i | 0.384415 | − | 0.279294i | ||||
\(491\) | 3.58734 | + | 11.0407i | 0.161894 | + | 0.498260i | 0.998794 | − | 0.0490965i | \(-0.0156342\pi\) |
−0.836900 | + | 0.547356i | \(0.815634\pi\) | |||||||
\(492\) | 4.91794 | − | 15.1359i | 0.221718 | − | 0.682378i | ||||
\(493\) | 9.34762 | + | 6.79144i | 0.420996 | + | 0.305871i | ||||
\(494\) | 12.1539 | 0.546829 | ||||||||
\(495\) | 1.93540 | + | 3.70711i | 0.0869898 | + | 0.166622i | ||||
\(496\) | 8.43186 | 0.378602 | ||||||||
\(497\) | 21.7251 | + | 15.7842i | 0.974504 | + | 0.708019i | ||||
\(498\) | −10.2831 | + | 31.6482i | −0.460798 | + | 1.41819i | ||||
\(499\) | 1.63506 | + | 5.03219i | 0.0731953 | + | 0.225272i | 0.980961 | − | 0.194206i | \(-0.0622131\pi\) |
−0.907765 | + | 0.419478i | \(0.862213\pi\) | |||||||
\(500\) | −36.0437 | + | 26.1873i | −1.61192 | + | 1.17113i | ||||
\(501\) | 19.6954 | − | 14.3095i | 0.879924 | − | 0.639302i | ||||
\(502\) | −14.3901 | − | 44.2880i | −0.642259 | − | 1.97667i | ||||
\(503\) | −9.26606 | + | 28.5180i | −0.413153 | + | 1.27156i | 0.500739 | + | 0.865598i | \(0.333062\pi\) |
−0.913892 | + | 0.405957i | \(0.866938\pi\) | |||||||
\(504\) | 8.47321 | + | 6.15615i | 0.377427 | + | 0.274217i | ||||
\(505\) | −25.0512 | −1.11476 | ||||||||
\(506\) | 0.195761 | − | 1.32059i | 0.00870266 | − | 0.0587076i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 36.4309 | + | 26.4686i | 1.61636 | + | 1.17435i | ||||
\(509\) | 4.66586 | − | 14.3600i | 0.206811 | − | 0.636497i | −0.792824 | − | 0.609451i | \(-0.791390\pi\) |
0.999634 | − | 0.0270463i | \(-0.00861016\pi\) | |||||||
\(510\) | −2.01284 | − | 6.19490i | −0.0891302 | − | 0.274315i | ||||
\(511\) | −17.1394 | + | 12.4525i | −0.758201 | + | 0.550865i | ||||
\(512\) | −37.6098 | + | 27.3252i | −1.66214 | + | 1.20761i | ||||
\(513\) | −1.50819 | − | 4.64172i | −0.0665880 | − | 0.204937i | ||||
\(514\) | 7.84929 | − | 24.1576i | 0.346217 | − | 1.06555i | ||||
\(515\) | 3.48327 | + | 2.53074i | 0.153491 | + | 0.111518i | ||||
\(516\) | −27.7401 | −1.22119 | ||||||||
\(517\) | −6.33286 | + | 1.06749i | −0.278519 | + | 0.0469481i | ||||
\(518\) | 8.89823 | 0.390966 | ||||||||
\(519\) | 6.48368 | + | 4.71067i | 0.284602 | + | 0.206775i | ||||
\(520\) | −2.13596 | + | 6.57382i | −0.0936682 | + | 0.288281i | ||||
\(521\) | 0.680615 | + | 2.09472i | 0.0298183 | + | 0.0917712i | 0.964858 | − | 0.262772i | \(-0.0846365\pi\) |
−0.935040 | + | 0.354543i | \(0.884637\pi\) | |||||||
\(522\) | −11.2212 | + | 8.15267i | −0.491138 | + | 0.356833i | ||||
\(523\) | 30.2212 | − | 21.9570i | 1.32148 | − | 0.960112i | 0.321568 | − | 0.946887i | \(-0.395790\pi\) |
0.999913 | − | 0.0132251i | \(-0.00420981\pi\) | |||||||
\(524\) | −21.4241 | − | 65.9366i | −0.935917 | − | 2.88046i | ||||
\(525\) | 2.01332 | − | 6.19636i | 0.0878685 | − | 0.270432i | ||||
\(526\) | 3.54718 | + | 2.57718i | 0.154664 | + | 0.112370i | ||||
\(527\) | 3.33260 | 0.145170 | ||||||||
\(528\) | −12.1865 | + | 12.4306i | −0.530349 | + | 0.540970i | ||||
\(529\) | −22.9739 | −0.998864 | ||||||||
\(530\) | 6.55247 | + | 4.76065i | 0.284621 | + | 0.206789i | ||||
\(531\) | −2.07665 | + | 6.39128i | −0.0901191 | + | 0.277358i | ||||
\(532\) | 12.1060 | + | 37.2585i | 0.524863 | + | 1.61536i | ||||
\(533\) | −3.06457 | + | 2.22654i | −0.132741 | + | 0.0964423i | ||||
\(534\) | 13.2340 | − | 9.61505i | 0.572690 | − | 0.416084i | ||||
\(535\) | 2.34104 | + | 7.20497i | 0.101212 | + | 0.311498i | ||||
\(536\) | 14.0126 | − | 43.1262i | 0.605251 | − | 1.86277i | ||||
\(537\) | 12.8353 | + | 9.32538i | 0.553883 | + | 0.402420i | ||||
\(538\) | 44.9066 | 1.93606 | ||||||||
\(539\) | −9.94861 | − | 4.94546i | −0.428517 | − | 0.213016i | ||||
\(540\) | 5.29747 | 0.227967 | ||||||||
\(541\) | 36.4346 | + | 26.4713i | 1.56645 | + | 1.13809i | 0.930462 | + | 0.366388i | \(0.119406\pi\) |
0.635985 | + | 0.771702i | \(0.280594\pi\) | |||||||
\(542\) | 2.01177 | − | 6.19160i | 0.0864131 | − | 0.265952i | ||||
\(543\) | 3.80254 | + | 11.7030i | 0.163183 | + | 0.502225i | ||||
\(544\) | 3.53543 | − | 2.56864i | 0.151580 | − | 0.110130i | ||||
\(545\) | −6.21570 | + | 4.51597i | −0.266251 | + | 0.193443i | ||||
\(546\) | −1.47023 | − | 4.52489i | −0.0629198 | − | 0.193647i | ||||
\(547\) | 8.51328 | − | 26.2012i | 0.364001 | − | 1.12028i | −0.586602 | − | 0.809875i | \(-0.699535\pi\) |
0.950604 | − | 0.310406i | \(-0.100465\pi\) | |||||||
\(548\) | −30.3139 | − | 22.0243i | −1.29494 | − | 0.940832i | ||||
\(549\) | 14.4715 | 0.617626 | ||||||||
\(550\) | 25.2208 | + | 12.5373i | 1.07542 | + | 0.534591i | ||||
\(551\) | −27.1838 | −1.15807 | ||||||||
\(552\) | −0.716869 | − | 0.520836i | −0.0305120 | − | 0.0221682i | ||||
\(553\) | −4.07446 | + | 12.5399i | −0.173264 | + | 0.533251i | ||||
\(554\) | 24.6594 | + | 75.8938i | 1.04768 | + | 3.22442i | ||||
\(555\) | 1.90783 | − | 1.38612i | 0.0809828 | − | 0.0588374i | ||||
\(556\) | −10.3802 | + | 7.54164i | −0.440218 | + | 0.319837i | ||||
\(557\) | −6.81240 | − | 20.9664i | −0.288651 | − | 0.888375i | −0.985281 | − | 0.170945i | \(-0.945318\pi\) |
0.696630 | − | 0.717431i | \(-0.254682\pi\) | |||||||
\(558\) | −1.23624 | + | 3.80476i | −0.0523342 | + | 0.161068i | ||||
\(559\) | 5.34166 | + | 3.88095i | 0.225928 | + | 0.164147i | ||||
\(560\) | −12.6440 | −0.534306 | ||||||||
\(561\) | −4.81657 | + | 4.91303i | −0.203356 | + | 0.207428i | ||||
\(562\) | 59.4433 | 2.50747 | ||||||||
\(563\) | 17.0046 | + | 12.3546i | 0.716658 | + | 0.520683i | 0.885315 | − | 0.464992i | \(-0.153943\pi\) |
−0.168657 | + | 0.985675i | \(0.553943\pi\) | |||||||
\(564\) | −2.51396 | + | 7.73718i | −0.105857 | + | 0.325794i | ||||
\(565\) | 4.32265 | + | 13.3038i | 0.181855 | + | 0.559693i | ||||
\(566\) | −41.0106 | + | 29.7959i | −1.72380 | + | 1.25242i | ||||
\(567\) | −1.54567 | + | 1.12299i | −0.0649120 | + | 0.0471613i | ||||
\(568\) | 23.8100 | + | 73.2797i | 0.999047 | + | 3.07475i | ||||
\(569\) | −9.49743 | + | 29.2301i | −0.398153 | + | 1.22539i | 0.528326 | + | 0.849042i | \(0.322820\pi\) |
−0.926479 | + | 0.376347i | \(0.877180\pi\) | |||||||
\(570\) | 12.3980 | + | 9.00769i | 0.519296 | + | 0.377291i | ||||
\(571\) | 10.2972 | 0.430926 | 0.215463 | − | 0.976512i | \(-0.430874\pi\) | ||||
0.215463 | + | 0.976512i | \(0.430874\pi\) | |||||||
\(572\) | 13.7405 | − | 2.31614i | 0.574517 | − | 0.0968426i | ||||
\(573\) | −2.78288 | −0.116256 | ||||||||
\(574\) | −14.5805 | − | 10.5933i | −0.608577 | − | 0.442157i | ||||
\(575\) | −0.170335 | + | 0.524238i | −0.00710347 | + | 0.0218622i | ||||
\(576\) | −1.62275 | − | 4.99431i | −0.0676146 | − | 0.208096i | ||||
\(577\) | 33.7966 | − | 24.5547i | 1.40697 | − | 1.02222i | 0.413218 | − | 0.910632i | \(-0.364405\pi\) |
0.993754 | − | 0.111592i | \(-0.0355951\pi\) | |||||||
\(578\) | −25.5793 | + | 18.5845i | −1.06396 | + | 0.773011i | ||||
\(579\) | −5.65893 | − | 17.4164i | −0.235177 | − | 0.723800i | ||||
\(580\) | 9.11778 | − | 28.0616i | 0.378595 | − | 1.16520i | ||||
\(581\) | 20.6546 | + | 15.0064i | 0.856896 | + | 0.622572i | ||||
\(582\) | 23.1174 | 0.958248 | ||||||||
\(583\) | 1.25446 | − | 8.46254i | 0.0519546 | − | 0.350483i | ||||
\(584\) | −60.7869 | −2.51538 | ||||||||
\(585\) | −1.02009 | − | 0.741137i | −0.0421754 | − | 0.0306422i | ||||
\(586\) | −23.0629 | + | 70.9804i | −0.952721 | + | 2.93217i | ||||
\(587\) | −0.371585 | − | 1.14362i | −0.0153370 | − | 0.0472023i | 0.943095 | − | 0.332523i | \(-0.107900\pi\) |
−0.958432 | + | 0.285321i | \(0.907900\pi\) | |||||||
\(588\) | −11.3858 | + | 8.27229i | −0.469544 | + | 0.341143i | ||||
\(589\) | −6.34319 | + | 4.60859i | −0.261366 | + | 0.189894i | ||||
\(590\) | −6.52059 | − | 20.0683i | −0.268448 | − | 0.826199i | ||||
\(591\) | −0.843913 | + | 2.59730i | −0.0347139 | + | 0.106839i | ||||
\(592\) | 7.94156 | + | 5.76988i | 0.326396 | + | 0.237141i | ||||
\(593\) | −27.6102 | −1.13381 | −0.566907 | − | 0.823782i | \(-0.691860\pi\) | ||||
−0.566907 | + | 0.823782i | \(0.691860\pi\) | |||||||
\(594\) | −3.82238 | − | 7.32149i | −0.156834 | − | 0.300404i | ||||
\(595\) | −4.99739 | −0.204873 | ||||||||
\(596\) | 11.4534 | + | 8.32142i | 0.469152 | + | 0.340859i | ||||
\(597\) | 6.43817 | − | 19.8146i | 0.263497 | − | 0.810959i | ||||
\(598\) | 0.124387 | + | 0.382824i | 0.00508657 | + | 0.0156549i | ||||
\(599\) | −31.4893 | + | 22.8783i | −1.28662 | + | 0.934782i | −0.999731 | − | 0.0231829i | \(-0.992620\pi\) |
−0.286886 | + | 0.957965i | \(0.592620\pi\) | |||||||
\(600\) | 15.1238 | − | 10.9881i | 0.617427 | − | 0.448587i | ||||
\(601\) | −11.7616 | − | 36.1985i | −0.479765 | − | 1.47657i | −0.839422 | − | 0.543481i | \(-0.817106\pi\) |
0.359656 | − | 0.933085i | \(-0.382894\pi\) | |||||||
\(602\) | −9.70740 | + | 29.8763i | −0.395644 | + | 1.21767i | ||||
\(603\) | 6.69208 | + | 4.86208i | 0.272523 | + | 0.197999i | ||||
\(604\) | −77.0045 | −3.13327 | ||||||||
\(605\) | 0.274995 | + | 13.8671i | 0.0111801 | + | 0.563779i | ||||
\(606\) | 49.4757 | 2.00981 | ||||||||
\(607\) | 19.3361 | + | 14.0485i | 0.784830 | + | 0.570212i | 0.906425 | − | 0.422368i | \(-0.138801\pi\) |
−0.121595 | + | 0.992580i | \(0.538801\pi\) | |||||||
\(608\) | −3.17712 | + | 9.77818i | −0.128849 | + | 0.396558i | ||||
\(609\) | 3.28836 | + | 10.1205i | 0.133251 | + | 0.410105i | ||||
\(610\) | −36.7614 | + | 26.7087i | −1.48843 | + | 1.08141i | ||||
\(611\) | 1.56655 | − | 1.13817i | 0.0633760 | − | 0.0460454i | ||||
\(612\) | 2.69325 | + | 8.28896i | 0.108868 | + | 0.335061i | ||||
\(613\) | −0.232089 | + | 0.714295i | −0.00937397 | + | 0.0288501i | −0.955634 | − | 0.294556i | \(-0.904828\pi\) |
0.946260 | + | 0.323407i | \(0.104828\pi\) | |||||||
\(614\) | 20.1877 | + | 14.6672i | 0.814710 | + | 0.591922i | ||||
\(615\) | −4.77631 | −0.192599 | ||||||||
\(616\) | 16.0761 | + | 30.7926i | 0.647726 | + | 1.24067i | ||||
\(617\) | −0.717569 | −0.0288882 | −0.0144441 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144441 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(618\) | −6.87939 | − | 4.99817i | −0.276730 | − | 0.201056i | ||||
\(619\) | −1.18056 | + | 3.63338i | −0.0474505 | + | 0.146038i | −0.971975 | − | 0.235086i | \(-0.924463\pi\) |
0.924524 | + | 0.381124i | \(0.124463\pi\) | |||||||
\(620\) | −2.62983 | − | 8.09379i | −0.105617 | − | 0.325055i | ||||
\(621\) | 0.130770 | − | 0.0950099i | 0.00524762 | − | 0.00381262i | ||||
\(622\) | −27.9564 | + | 20.3115i | −1.12095 | + | 0.814417i | ||||
\(623\) | −3.87820 | − | 11.9359i | −0.155377 | − | 0.478201i | ||||
\(624\) | 1.62192 | − | 4.99174i | 0.0649286 | − | 0.199830i | ||||
\(625\) | −2.97697 | − | 2.16290i | −0.119079 | − | 0.0865160i | ||||
\(626\) | −49.7434 | −1.98814 | ||||||||
\(627\) | 2.37359 | − | 16.0121i | 0.0947922 | − | 0.639462i | ||||
\(628\) | −12.6378 | −0.504304 | ||||||||
\(629\) | 3.13881 | + | 2.28048i | 0.125152 | + | 0.0909286i | ||||
\(630\) | 1.85380 | − | 5.70542i | 0.0738573 | − | 0.227309i | ||||
\(631\) | −4.68725 | − | 14.4259i | −0.186596 | − | 0.574285i | 0.813376 | − | 0.581739i | \(-0.197627\pi\) |
−0.999972 | + | 0.00745397i | \(0.997627\pi\) | |||||||
\(632\) | −30.6068 | + | 22.2372i | −1.21747 | + | 0.884547i | ||||
\(633\) | −10.4669 | + | 7.60464i | −0.416021 | + | 0.302257i | ||||
\(634\) | 11.8695 | + | 36.5306i | 0.471398 | + | 1.45081i | ||||
\(635\) | 4.17624 | − | 12.8531i | 0.165729 | − | 0.510061i | ||||
\(636\) | −8.76740 | − | 6.36989i | −0.347650 | − | 0.252583i | ||||
\(637\) | 3.34980 | 0.132724 | ||||||||
\(638\) | −45.3622 | + | 7.64641i | −1.79591 | + | 0.302724i | ||||
\(639\) | −14.0555 | −0.556026 | ||||||||
\(640\) | 17.6376 | + | 12.8145i | 0.697188 | + | 0.506537i | ||||
\(641\) | −14.6229 | + | 45.0046i | −0.577568 | + | 1.77757i | 0.0496933 | + | 0.998765i | \(0.484176\pi\) |
−0.627262 | + | 0.778808i | \(0.715824\pi\) | |||||||
\(642\) | −4.62351 | − | 14.2297i | −0.182475 | − | 0.561601i | ||||
\(643\) | −1.05779 | + | 0.768531i | −0.0417152 | + | 0.0303079i | −0.608447 | − | 0.793594i | \(-0.708207\pi\) |
0.566732 | + | 0.823902i | \(0.308207\pi\) | |||||||
\(644\) | −1.04968 | + | 0.762634i | −0.0413630 | + | 0.0300520i | ||||
\(645\) | 2.57265 | + | 7.91781i | 0.101298 | + | 0.311763i | ||||
\(646\) | −7.79117 | + | 23.9788i | −0.306540 | + | 0.943432i | ||||
\(647\) | −33.7737 | − | 24.5380i | −1.32778 | − | 0.964689i | −0.999800 | − | 0.0200041i | \(-0.993632\pi\) |
−0.327980 | − | 0.944685i | \(-0.606368\pi\) | |||||||
\(648\) | −5.48191 | −0.215350 | ||||||||
\(649\) | −15.6032 | + | 15.9157i | −0.612480 | + | 0.624747i | ||||
\(650\) | −8.49210 | −0.333088 | ||||||||
\(651\) | 2.48310 | + | 1.80408i | 0.0973203 | + | 0.0707073i | ||||
\(652\) | 22.5575 | − | 69.4248i | 0.883419 | − | 2.71888i | ||||
\(653\) | −8.09531 | − | 24.9148i | −0.316794 | − | 0.974991i | −0.975010 | − | 0.222162i | \(-0.928689\pi\) |
0.658216 | − | 0.752829i | \(-0.271311\pi\) | |||||||
\(654\) | 12.2759 | − | 8.91897i | 0.480026 | − | 0.348759i | ||||
\(655\) | −16.8333 | + | 12.2301i | −0.657731 | + | 0.477870i | ||||
\(656\) | −6.14385 | − | 18.9088i | −0.239877 | − | 0.738266i | ||||
\(657\) | 3.42658 | − | 10.5459i | 0.133684 | − | 0.411436i | ||||
\(658\) | 7.45327 | + | 5.41512i | 0.290559 | + | 0.211103i | ||||
\(659\) | 2.89025 | 0.112588 | 0.0562942 | − | 0.998414i | \(-0.482072\pi\) | ||||
0.0562942 | + | 0.998414i | \(0.482072\pi\) | |||||||
\(660\) | 15.7330 | + | 7.82089i | 0.612408 | + | 0.304428i | ||||
\(661\) | −37.1700 | −1.44575 | −0.722874 | − | 0.690980i | \(-0.757179\pi\) | ||||
−0.722874 | + | 0.690980i | \(0.757179\pi\) | |||||||
\(662\) | 56.5302 | + | 41.0716i | 2.19711 | + | 1.59629i | ||||
\(663\) | 0.641043 | − | 1.97293i | 0.0248961 | − | 0.0766222i | ||||
\(664\) | 22.6368 | + | 69.6688i | 0.878477 | + | 2.70367i | ||||
\(665\) | 9.51192 | − | 6.91081i | 0.368856 | − | 0.267990i | ||||
\(666\) | −3.76793 | + | 2.73756i | −0.146004 | + | 0.106078i | ||||
\(667\) | −0.278209 | − | 0.856239i | −0.0107723 | − | 0.0331537i | ||||
\(668\) | 31.6066 | − | 97.2751i | 1.22290 | − | 3.76369i | ||||
\(669\) | −3.51533 | − | 2.55404i | −0.135911 | − | 0.0987448i | ||||
\(670\) | −25.9732 | −1.00343 | ||||||||
\(671\) | 42.9790 | + | 21.3649i | 1.65919 | + | 0.824781i | ||||
\(672\) | 4.02474 | 0.155258 | ||||||||
\(673\) | −38.0215 | − | 27.6242i | −1.46562 | − | 1.06484i | −0.981854 | − | 0.189638i | \(-0.939268\pi\) |
−0.483766 | − | 0.875197i | \(-0.660732\pi\) | |||||||
\(674\) | 5.66950 | − | 17.4489i | 0.218381 | − | 0.672108i | ||||
\(675\) | 1.05379 | + | 3.24323i | 0.0405604 | + | 0.124832i | ||||
\(676\) | −3.39896 | + | 2.46949i | −0.130729 | + | 0.0949804i | ||||
\(677\) | −28.1649 | + | 20.4630i | −1.08246 | + | 0.786456i | −0.978111 | − | 0.208084i | \(-0.933277\pi\) |
−0.104353 | + | 0.994540i | \(0.533277\pi\) | |||||||
\(678\) | −8.53717 | − | 26.2747i | −0.327868 | − | 1.00907i | ||||
\(679\) | 5.48071 | − | 16.8679i | 0.210330 | − | 0.647331i | ||||
\(680\) | −11.6004 | − | 8.42821i | −0.444856 | − | 0.323207i | ||||
\(681\) | −22.1478 | −0.848705 | ||||||||
\(682\) | −9.28867 | + | 9.47469i | −0.355681 | + | 0.362805i | ||||
\(683\) | −24.2852 | −0.929248 | −0.464624 | − | 0.885508i | \(-0.653811\pi\) | ||||
−0.464624 | + | 0.885508i | \(0.653811\pi\) | |||||||
\(684\) | −16.5889 | − | 12.0526i | −0.634294 | − | 0.460842i | ||||
\(685\) | −3.47502 | + | 10.6950i | −0.132774 | + | 0.408635i | ||||
\(686\) | 15.2165 | + | 46.8317i | 0.580970 | + | 1.78804i | ||||
\(687\) | 16.9314 | − | 12.3013i | 0.645971 | − | 0.469326i | ||||
\(688\) | −28.0364 | + | 20.3697i | −1.06888 | + | 0.776586i | ||||
\(689\) | 0.797089 | + | 2.45319i | 0.0303667 | + | 0.0934590i | ||||
\(690\) | −0.156839 | + | 0.482702i | −0.00597077 | + | 0.0183762i | ||||
\(691\) | 35.9438 | + | 26.1147i | 1.36737 | + | 0.993449i | 0.997938 | + | 0.0641895i | \(0.0204462\pi\) |
0.369428 | + | 0.929260i | \(0.379554\pi\) | |||||||
\(692\) | 33.6707 | 1.27997 | ||||||||
\(693\) | −6.24843 | + | 1.05326i | −0.237358 | + | 0.0400099i | ||||
\(694\) | 28.5479 | 1.08366 | ||||||||
\(695\) | 3.11527 | + | 2.26338i | 0.118169 | + | 0.0858548i | ||||
\(696\) | −9.43523 | + | 29.0387i | −0.357642 | + | 1.10071i | ||||
\(697\) | −2.42829 | − | 7.47350i | −0.0919779 | − | 0.283079i | ||||
\(698\) | −19.5756 | + | 14.2225i | −0.740947 | + | 0.538330i | ||||
\(699\) | −11.1219 | + | 8.08053i | −0.420669 | + | 0.305634i | ||||
\(700\) | −8.45866 | − | 26.0331i | −0.319707 | − | 0.983958i | ||||
\(701\) | −6.00995 | + | 18.4967i | −0.226993 | + | 0.698612i | 0.771091 | + | 0.636726i | \(0.219712\pi\) |
−0.998083 | + | 0.0618861i | \(0.980288\pi\) | |||||||
\(702\) | 2.01466 | + | 1.46373i | 0.0760383 | + | 0.0552450i | ||||
\(703\) | −9.12797 | −0.344268 | ||||||||
\(704\) | 2.55390 | − | 17.2284i | 0.0962536 | − | 0.649321i | ||||
\(705\) | 2.44156 | 0.0919544 | ||||||||
\(706\) | 30.2102 | + | 21.9490i | 1.13697 | + | 0.826060i | ||||
\(707\) | 11.7298 | − | 36.1005i | 0.441144 | − | 1.35770i | ||||
\(708\) | 8.72475 | + | 26.8520i | 0.327896 | + | 1.00916i | ||||
\(709\) | −3.18721 | + | 2.31565i | −0.119698 | + | 0.0869659i | −0.646024 | − | 0.763317i | \(-0.723569\pi\) |
0.526326 | + | 0.850283i | \(0.323569\pi\) | |||||||
\(710\) | 35.7048 | − | 25.9410i | 1.33998 | − | 0.973549i | ||||
\(711\) | −2.13261 | − | 6.56350i | −0.0799791 | − | 0.246150i | ||||
\(712\) | 11.1277 | − | 34.2474i | 0.417027 | − | 1.28348i | ||||
\(713\) | −0.210080 | − | 0.152632i | −0.00786757 | − | 0.00571612i | ||||
\(714\) | 9.86976 | 0.369367 | ||||||||
\(715\) | −1.93540 | − | 3.70711i | −0.0723798 | − | 0.138638i | ||||
\(716\) | 66.6555 | 2.49103 | ||||||||
\(717\) | 9.34106 | + | 6.78668i | 0.348848 | + | 0.253453i | ||||
\(718\) | −11.8371 | + | 36.4308i | −0.441756 | + | 1.35958i | ||||
\(719\) | −10.2069 | − | 31.4135i | −0.380652 | − | 1.17153i | −0.939586 | − | 0.342314i | \(-0.888789\pi\) |
0.558934 | − | 0.829212i | \(-0.311211\pi\) | |||||||
\(720\) | 5.35406 | − | 3.88995i | 0.199534 | − | 0.144970i | ||||
\(721\) | −5.27795 | + | 3.83466i | −0.196561 | + | 0.142810i | ||||
\(722\) | −3.70926 | − | 11.4159i | −0.138044 | − | 0.424857i | ||||
\(723\) | −6.04809 | + | 18.6141i | −0.224931 | + | 0.692266i | ||||
\(724\) | 41.8252 | + | 30.3878i | 1.55442 | + | 1.12935i | ||||
\(725\) | 18.9937 | 0.705410 | ||||||||
\(726\) | −0.543111 | − | 27.3874i | −0.0201567 | − | 1.01644i | ||||
\(727\) | −19.8138 | −0.734853 | −0.367427 | − | 0.930052i | \(-0.619761\pi\) | ||||
−0.367427 | + | 0.930052i | \(0.619761\pi\) | |||||||
\(728\) | −8.47321 | − | 6.15615i | −0.314038 | − | 0.228162i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 10.7593 | + | 33.1137i | 0.398219 | + | 1.22559i | ||||
\(731\) | −11.0811 | + | 8.05087i | −0.409848 | + | 0.297772i | ||||
\(732\) | 49.1879 | − | 35.7371i | 1.81804 | − | 1.32088i | ||||
\(733\) | 9.82460 | + | 30.2370i | 0.362880 | + | 1.11683i | 0.951298 | + | 0.308273i | \(0.0997509\pi\) |
−0.588418 | + | 0.808557i | \(0.700249\pi\) | |||||||
\(734\) | 16.0488 | − | 49.3931i | 0.592371 | − | 1.82313i | ||||
\(735\) | 3.41708 | + | 2.48266i | 0.126041 | + | 0.0915742i | ||||
\(736\) | −0.340510 | −0.0125514 | ||||||||
\(737\) | 12.6968 | + | 24.3198i | 0.467693 | + | 0.895831i | ||||
\(738\) | 9.43312 | 0.347238 | ||||||||
\(739\) | −3.56988 | − | 2.59367i | −0.131320 | − | 0.0954096i | 0.520186 | − | 0.854053i | \(-0.325863\pi\) |
−0.651506 | + | 0.758643i | \(0.725863\pi\) | |||||||
\(740\) | 3.06163 | − | 9.42273i | 0.112548 | − | 0.346386i | ||||
\(741\) | 1.50819 | + | 4.64172i | 0.0554046 | + | 0.170518i | ||||
\(742\) | −9.92850 | + | 7.21348i | −0.364487 | + | 0.264815i | ||||
\(743\) | −41.7830 | + | 30.3572i | −1.53287 | + | 1.11370i | −0.578255 | + | 0.815856i | \(0.696266\pi\) |
−0.954616 | + | 0.297840i | \(0.903734\pi\) | |||||||
\(744\) | 2.72140 | + | 8.37559i | 0.0997712 | + | 0.307064i | ||||
\(745\) | 1.31296 | − | 4.04088i | 0.0481032 | − | 0.148046i | ||||
\(746\) | −56.0199 | − | 40.7009i | −2.05104 | − | 1.49016i | ||||
\(747\) | −13.3629 | −0.488922 | ||||||||
\(748\) | −4.23865 | + | 28.5937i | −0.154980 | + | 1.04549i | ||||
\(749\) | −11.4790 | −0.419434 | ||||||||
\(750\) | −21.3640 | − | 15.5219i | −0.780105 | − | 0.566779i | ||||
\(751\) | −14.2945 | + | 43.9941i | −0.521616 | + | 1.60537i | 0.249297 | + | 0.968427i | \(0.419800\pi\) |
−0.770913 | + | 0.636940i | \(0.780200\pi\) | |||||||
\(752\) | 3.14062 | + | 9.66585i | 0.114527 | + | 0.352477i | ||||
\(753\) | 15.1285 | − | 10.9915i | 0.551312 | − | 0.400551i | ||||
\(754\) | 11.2212 | − | 8.15267i | 0.408652 | − | 0.296903i | ||||
\(755\) | 7.14150 | + | 21.9793i | 0.259906 | + | 0.799908i | ||||
\(756\) | −2.48045 | + | 7.63402i | −0.0902129 | + | 0.277647i | ||||
\(757\) | −7.53673 | − | 5.47576i | −0.273927 | − | 0.199020i | 0.442337 | − | 0.896849i | \(-0.354149\pi\) |
−0.716264 | + | 0.697829i | \(0.754149\pi\) | |||||||
\(758\) | 35.6999 | 1.29668 | ||||||||
\(759\) | 0.528643 | − | 0.0891099i | 0.0191885 | − | 0.00323449i | ||||
\(760\) | 33.7352 | 1.22371 | ||||||||
\(761\) | 25.3709 | + | 18.4330i | 0.919694 | + | 0.668196i | 0.943448 | − | 0.331521i | \(-0.107562\pi\) |
−0.0237542 | + | 0.999718i | \(0.507562\pi\) | |||||||
\(762\) | −8.24800 | + | 25.3847i | −0.298794 | + | 0.919592i | ||||
\(763\) | −3.59744 | − | 11.0718i | −0.130236 | − | 0.400826i | ||||
\(764\) | −9.45890 | + | 6.87229i | −0.342211 | + | 0.248631i | ||||
\(765\) | 2.11613 | − | 1.53746i | 0.0765088 | − | 0.0555869i | ||||
\(766\) | −0.0761333 | − | 0.234314i | −0.00275081 | − | 0.00846612i | ||||
\(767\) | 2.07665 | − | 6.39128i | 0.0749836 | − | 0.230776i | ||||
\(768\) | −26.3372 | − | 19.1351i | −0.950361 | − | 0.690477i | ||||
\(769\) | 11.2536 | 0.405816 | 0.202908 | − | 0.979198i | \(-0.434961\pi\) | ||||
0.202908 | + | 0.979198i | \(0.434961\pi\) | |||||||
\(770\) | 13.9288 | − | 14.2078i | 0.501959 | − | 0.512012i | ||||
\(771\) | 10.2001 | 0.367348 | ||||||||
\(772\) | −62.2441 | − | 45.2230i | −2.24021 | − | 1.62761i | ||||
\(773\) | −5.73080 | + | 17.6376i | −0.206122 | + | 0.634380i | 0.793543 | + | 0.608514i | \(0.208234\pi\) |
−0.999665 | + | 0.0258655i | \(0.991766\pi\) | |||||||
\(774\) | −5.08094 | − | 15.6375i | −0.182631 | − | 0.562080i | ||||
\(775\) | 4.43208 | − | 3.22009i | 0.159205 | − | 0.115669i | ||||
\(776\) | 41.1704 | − | 29.9121i | 1.47793 | − | 1.07378i | ||||
\(777\) | 1.10419 | + | 3.39834i | 0.0396125 | + | 0.121915i | ||||
\(778\) | −7.23442 | + | 22.2653i | −0.259367 | + | 0.798248i | ||||
\(779\) | 14.9569 | + | 10.8668i | 0.535888 | + | 0.389345i | ||||
\(780\) | −5.29747 | −0.189680 | ||||||||
\(781\) | −41.7436 | − | 20.7507i | −1.49370 | − | 0.742520i | ||||
\(782\) | −0.835023 | −0.0298604 | ||||||||
\(783\) | −4.50605 | − | 3.27384i | −0.161033 | − | 0.116997i | ||||
\(784\) | −5.43309 | + | 16.7213i | −0.194039 | + | 0.597190i | ||||
\(785\) | 1.17205 | + | 3.60719i | 0.0418322 | + | 0.128746i | ||||
\(786\) | 33.2455 | − | 24.1543i | 1.18583 | − | 0.861554i | ||||
\(787\) | 36.7753 | − | 26.7188i | 1.31090 | − | 0.952424i | 0.310901 | − | 0.950442i | \(-0.399369\pi\) |
0.999998 | − | 0.00198155i | \(-0.000630748\pi\) | |||||||
\(788\) | 3.54557 | + | 10.9122i | 0.126306 | + | 0.388729i | ||||
\(789\) | −0.544083 | + | 1.67451i | −0.0193699 | + | 0.0596143i | ||||
\(790\) | 17.5311 | + | 12.7371i | 0.623729 | + | 0.453165i | ||||
\(791\) | −21.1957 | −0.753631 | ||||||||
\(792\) | −16.2808 | − | 8.09319i | −0.578513 | − | 0.287579i | ||||
\(793\) | −14.4715 | −0.513896 | ||||||||
\(794\) | 12.3424 | + | 8.96729i | 0.438016 | + | 0.318237i | ||||
\(795\) | −1.00505 | + | 3.09322i | −0.0356454 | + | 0.109705i | ||||
\(796\) | −27.0490 | − | 83.2482i | −0.958726 | − | 2.95065i | ||||
\(797\) | 9.50516 | − | 6.90591i | 0.336690 | − | 0.244620i | −0.406574 | − | 0.913618i | \(-0.633277\pi\) |
0.743264 | + | 0.668998i | \(0.233277\pi\) | |||||||
\(798\) | −18.7859 | + | 13.6487i | −0.665013 | + | 0.483160i | ||||
\(799\) | 1.24130 | + | 3.82031i | 0.0439139 | + | 0.135153i | ||||
\(800\) | 2.21990 | − | 6.83216i | 0.0784854 | − | 0.241553i | ||||
\(801\) | 5.31432 | + | 3.86108i | 0.187772 | + | 0.136424i | ||||
\(802\) | 75.6125 | 2.66997 | ||||||||
\(803\) | 25.7461 | − | 26.2617i | 0.908560 | − | 0.926756i | ||||
\(804\) | 34.7530 | 1.22564 | ||||||||
\(805\) | 0.315026 | + | 0.228880i | 0.0111032 | + | 0.00806695i | ||||
\(806\) | 1.23624 | − | 3.80476i | 0.0435447 | − | 0.134017i | ||||
\(807\) | 5.57249 | + | 17.1504i | 0.196161 | + | 0.603722i | ||||
\(808\) | 88.1126 | − | 64.0176i | 3.09979 | − | 2.25213i | ||||
\(809\) | 15.3353 | − | 11.1417i | 0.539160 | − | 0.391723i | −0.284613 | − | 0.958643i | \(-0.591865\pi\) |
0.823773 | + | 0.566920i | \(0.191865\pi\) | |||||||
\(810\) | 0.970298 | + | 2.98627i | 0.0340928 | + | 0.104927i | ||||
\(811\) | −4.46416 | + | 13.7393i | −0.156758 | + | 0.482451i | −0.998335 | − | 0.0576864i | \(-0.981628\pi\) |
0.841577 | + | 0.540137i | \(0.181628\pi\) | |||||||
\(812\) | 36.1696 | + | 26.2787i | 1.26930 | + | 0.922203i | ||||
\(813\) | 2.61429 | 0.0916871 | ||||||||
\(814\) | −15.2320 | + | 2.56756i | −0.533882 | + | 0.0899930i | ||||
\(815\) | −21.9078 | −0.767397 | ||||||||
\(816\) | 8.80864 | + | 6.39985i | 0.308364 | + | 0.224040i | ||||
\(817\) | 9.95804 | − | 30.6477i | 0.348388 | − | 1.07223i | ||||
\(818\) | 13.9007 | + | 42.7819i | 0.486026 | + | 1.49583i | ||||
\(819\) | 1.54567 | − | 1.12299i | 0.0540100 | − | 0.0392406i | ||||
\(820\) | −16.2345 | + | 11.7950i | −0.566933 | + | 0.411901i | ||||
\(821\) | 3.26399 | + | 10.0455i | 0.113914 | + | 0.350591i | 0.991719 | − | 0.128427i | \(-0.0409928\pi\) |
−0.877805 | + | 0.479018i | \(0.840993\pi\) | |||||||
\(822\) | 6.86310 | − | 21.1225i | 0.239378 | − | 0.736730i | ||||
\(823\) | −7.97204 | − | 5.79203i | −0.277888 | − | 0.201897i | 0.440108 | − | 0.897945i | \(-0.354940\pi\) |
−0.717996 | + | 0.696048i | \(0.754940\pi\) | |||||||
\(824\) | −18.7189 | −0.652105 | ||||||||
\(825\) | −1.65846 | + | 11.1879i | −0.0577403 | + | 0.389513i | ||||
\(826\) | 31.9730 | 1.11248 | ||||||||
\(827\) | 2.99180 | + | 2.17367i | 0.104035 | + | 0.0755859i | 0.638587 | − | 0.769550i | \(-0.279519\pi\) |
−0.534551 | + | 0.845136i | \(0.679519\pi\) | |||||||
\(828\) | 0.209856 | − | 0.645870i | 0.00729300 | − | 0.0224455i | ||||
\(829\) | −8.15935 | − | 25.1119i | −0.283386 | − | 0.872172i | −0.986878 | − | 0.161469i | \(-0.948377\pi\) |
0.703492 | − | 0.710703i | \(-0.251623\pi\) | |||||||
\(830\) | 33.9454 | − | 24.6627i | 1.17826 | − | 0.856056i | ||||
\(831\) | −25.9247 | + | 18.8354i | −0.899319 | + | 0.653394i | ||||
\(832\) | 1.62275 | + | 4.99431i | 0.0562587 | + | 0.173147i | ||||
\(833\) | −2.14736 | + | 6.60891i | −0.0744018 | + | 0.228985i | ||||
\(834\) | −6.15261 | − | 4.47013i | −0.213047 | − | 0.154788i | ||||
\(835\) | −30.6963 | −1.06229 | ||||||||
\(836\) | −31.4740 | − | 60.2861i | −1.08855 | − | 2.08504i | ||||
\(837\) | −1.60649 | −0.0555284 | ||||||||
\(838\) | −53.1374 | − | 38.6066i | −1.83560 | − | 1.33364i | ||||
\(839\) | −13.0433 | + | 40.1433i | −0.450306 | + | 1.38590i | 0.426253 | + | 0.904604i | \(0.359833\pi\) |
−0.876559 | + | 0.481295i | \(0.840167\pi\) | |||||||
\(840\) | −4.08087 | − | 12.5596i | −0.140803 | − | 0.433348i | ||||
\(841\) | −1.63623 | + | 1.18879i | −0.0564219 | + | 0.0409929i | ||||
\(842\) | −47.4523 | + | 34.4761i | −1.63531 | + | 1.18813i | ||||
\(843\) | 7.37637 | + | 22.7021i | 0.254056 | + | 0.781903i | ||||
\(844\) | −16.7970 | + | 51.6958i | −0.578176 | + | 1.77944i | ||||
\(845\) | 1.02009 | + | 0.741137i | 0.0350921 | + | 0.0254959i | ||||
\(846\) | −4.82204 | −0.165785 | ||||||||
\(847\) | −20.1123 | − | 6.09676i | −0.691067 | − | 0.209487i | ||||
\(848\) | −13.5385 | −0.464914 | ||||||||
\(849\) | −16.4685 | − | 11.9650i | −0.565196 | − | 0.410639i | ||||
\(850\) | 5.44380 | − | 16.7543i | 0.186721 | − | 0.574668i | ||||
\(851\) | −0.0934189 | − | 0.287514i | −0.00320236 | − | 0.00985584i | ||||
\(852\) | −47.7741 | + | 34.7099i | −1.63671 | + | 1.18914i | ||||
\(853\) | −31.2896 | + | 22.7332i | −1.07134 | + | 0.778371i | −0.976152 | − | 0.217088i | \(-0.930344\pi\) |
−0.0951844 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(854\) | −21.2763 | − | 65.4817i | −0.728060 | − | 2.24074i | ||||
\(855\) | −1.90167 | + | 5.85273i | −0.0650356 | + | 0.200159i | ||||
\(856\) | −26.6462 | − | 19.3596i | −0.910749 | − | 0.661698i | ||||
\(857\) | −22.2215 | −0.759072 | −0.379536 | − | 0.925177i | \(-0.623916\pi\) | ||||
−0.379536 | + | 0.925177i | \(0.623916\pi\) | |||||||
\(858\) | 3.82238 | + | 7.32149i | 0.130494 | + | 0.249952i | ||||
\(859\) | 23.8601 | 0.814097 | 0.407049 | − | 0.913406i | \(-0.366558\pi\) | ||||
0.407049 | + | 0.913406i | \(0.366558\pi\) | |||||||
\(860\) | 28.2973 | + | 20.5592i | 0.964930 | + | 0.701062i | ||||
\(861\) | 2.23642 | − | 6.88299i | 0.0762170 | − | 0.234572i | ||||
\(862\) | 7.29969 | + | 22.4661i | 0.248628 | + | 0.765200i | ||||
\(863\) | 32.8199 | − | 23.8450i | 1.11720 | − | 0.811694i | 0.133418 | − | 0.991060i | \(-0.457405\pi\) |
0.983782 | + | 0.179366i | \(0.0574046\pi\) | |||||||
\(864\) | −1.70427 | + | 1.23822i | −0.0579803 | + | 0.0421251i | ||||
\(865\) | −3.12267 | − | 9.61058i | −0.106174 | − | 0.326769i | ||||
\(866\) | 19.7101 | − | 60.6616i | 0.669778 | − | 2.06136i | ||||
\(867\) | −10.2718 | − | 7.46288i | −0.348848 | − | 0.253453i | ||||
\(868\) | 12.8951 | 0.437688 | ||||||||
\(869\) | 3.35632 | − | 22.6415i | 0.113855 | − | 0.768061i | ||||
\(870\) | 17.4888 | 0.592927 | ||||||||
\(871\) | −6.69208 | − | 4.86208i | −0.226752 | − | 0.164745i | ||||
\(872\) | 10.3221 | − | 31.7681i | 0.349550 | − | 1.07580i | ||||
\(873\) | 2.86866 | + | 8.82882i | 0.0970893 | + | 0.298810i | ||||
\(874\) | 1.58936 | − | 1.15474i | 0.0537610 | − | 0.0390597i | ||||
\(875\) | −16.3908 | + | 11.9086i | −0.554109 | + | 0.402584i | ||||
\(876\) | −14.3963 | − | 44.3071i | −0.486404 | − | 1.49700i | ||||
\(877\) | 5.58578 | − | 17.1913i | 0.188618 | − | 0.580508i | −0.811373 | − | 0.584528i | \(-0.801280\pi\) |
0.999992 | + | 0.00402011i | \(0.00127965\pi\) | |||||||
\(878\) | −9.07495 | − | 6.59334i | −0.306265 | − | 0.222514i | ||||
\(879\) | −29.9701 | −1.01087 | ||||||||
\(880\) | 21.6440 | − | 3.64839i | 0.729620 | − | 0.122987i | ||||
\(881\) | 20.4421 | 0.688713 | 0.344356 | − | 0.938839i | \(-0.388097\pi\) | ||||
0.344356 | + | 0.938839i | \(0.388097\pi\) | |||||||
\(882\) | −6.74868 | − | 4.90321i | −0.227240 | − | 0.165100i | ||||
\(883\) | 5.71729 | − | 17.5960i | 0.192402 | − | 0.592152i | −0.807595 | − | 0.589737i | \(-0.799231\pi\) |
0.999997 | − | 0.00241506i | \(-0.000768737\pi\) | |||||||
\(884\) | −2.69325 | − | 8.28896i | −0.0905837 | − | 0.278788i | ||||
\(885\) | 6.85518 | − | 4.98058i | 0.230434 | − | 0.167420i | ||||
\(886\) | 45.3218 | − | 32.9282i | 1.52262 | − | 1.10625i | ||||
\(887\) | −6.59708 | − | 20.3037i | −0.221508 | − | 0.681733i | −0.998627 | − | 0.0523790i | \(-0.983320\pi\) |
0.777119 | − | 0.629354i | \(-0.216680\pi\) | |||||||
\(888\) | −3.16823 | + | 9.75080i | −0.106319 | + | 0.327215i | ||||
\(889\) | 16.5668 | + | 12.0365i | 0.555634 | + | 0.403692i | ||||
\(890\) | −20.6259 | −0.691381 | ||||||||
\(891\) | 2.32184 | − | 2.36834i | 0.0777847 | − | 0.0793425i | ||||
\(892\) | −18.2556 | −0.611244 | ||||||||
\(893\) | −7.64571 | − | 5.55493i | −0.255854 | − | 0.185889i | ||||
\(894\) | −2.59308 | + | 7.98067i | −0.0867255 | + | 0.266914i | ||||
\(895\) | −6.18172 | − | 19.0254i | −0.206632 | − | 0.635949i | ||||
\(896\) | −26.7251 | + | 19.4169i | −0.892822 | + | 0.648673i | ||||
\(897\) | −0.130770 | + | 0.0950099i | −0.00436628 | + | 0.00317229i | ||||
\(898\) | −2.84664 | − | 8.76107i | −0.0949937 | − | 0.292361i | ||||
\(899\) | −2.76502 | + | 8.50986i | −0.0922186 | + | 0.283820i | ||||
\(900\) | 11.5909 | + | 8.42131i | 0.386364 | + | 0.280710i | ||||
\(901\) | −5.35093 | −0.178265 | ||||||||
\(902\) | 28.0156 | + | 13.9265i | 0.932817 | + | 0.463703i | ||||
\(903\) | −12.6147 | −0.419792 | ||||||||
\(904\) | −49.2014 | − | 35.7469i | −1.63642 | − | 1.18893i | ||||
\(905\) | 4.79461 | − | 14.7563i | 0.159378 | − | 0.490516i | ||||
\(906\) | −14.1043 | − | 43.4087i | −0.468586 | − | 1.44216i | ||||
\(907\) | −32.1360 | + | 23.3482i | −1.06706 | + | 0.775263i | −0.975381 | − | 0.220526i | \(-0.929223\pi\) |
−0.0916766 | + | 0.995789i | \(0.529223\pi\) | |||||||
\(908\) | −75.2795 | + | 54.6937i | −2.49824 | + | 1.81508i | ||||
\(909\) | 6.13947 | + | 18.8954i | 0.203633 | + | 0.626719i | ||||
\(910\) | −1.85380 | + | 5.70542i | −0.0614530 | + | 0.189133i | ||||
\(911\) | −44.7247 | − | 32.4944i | −1.48180 | − | 1.07659i | −0.976973 | − | 0.213365i | \(-0.931558\pi\) |
−0.504824 | − | 0.863223i | \(-0.668442\pi\) | |||||||
\(912\) | −25.6164 | −0.848244 | ||||||||
\(913\) | −39.6866 | − | 19.7282i | −1.31344 | − | 0.652909i | ||||
\(914\) | 81.0608 | 2.68125 | ||||||||
\(915\) | −14.7621 | − | 10.7253i | −0.488021 | − | 0.354568i | ||||
\(916\) | 27.1710 | − | 83.6236i | 0.897754 | − | 2.76300i | ||||
\(917\) | −9.74255 | − | 29.9845i | −0.321727 | − | 0.990175i | ||||
\(918\) | −4.17932 | + | 3.03645i | −0.137938 | + | 0.100218i | ||||
\(919\) | 17.0582 | − | 12.3935i | 0.562697 | − | 0.408824i | −0.269748 | − | 0.962931i | \(-0.586940\pi\) |
0.832445 | + | 0.554107i | \(0.186940\pi\) | |||||||
\(920\) | 0.345258 | + | 1.06260i | 0.0113828 | + | 0.0350327i | ||||
\(921\) | −3.09649 | + | 9.53000i | −0.102033 | + | 0.314024i | ||||
\(922\) | 24.6803 | + | 17.9313i | 0.812804 | + | 0.590536i | ||||
\(923\) | 14.0555 | 0.462642 | ||||||||
\(924\) | −18.6372 | + | 19.0104i | −0.613118 | + | 0.625397i | ||||
\(925\) | 6.37785 | 0.209702 | ||||||||
\(926\) | 52.3463 | + | 38.0318i | 1.72021 | + | 1.24980i | ||||
\(927\) | 1.05519 | − | 3.24755i | 0.0346571 | − | 0.106663i | ||||
\(928\) | 3.62577 | + | 11.1590i | 0.119022 | + | 0.366311i | ||||
\(929\) | 6.60183 | − | 4.79651i | 0.216599 | − | 0.157368i | −0.474195 | − | 0.880420i | \(-0.657261\pi\) |
0.690794 | + | 0.723051i | \(0.257261\pi\) | |||||||
\(930\) | 4.08092 | − | 2.96496i | 0.133819 | − | 0.0972249i | ||||
\(931\) | −5.05211 | − | 15.5488i | −0.165576 | − | 0.509592i | ||||
\(932\) | −17.8481 | + | 54.9308i | −0.584634 | + | 1.79932i | ||||
\(933\) | −11.2263 | − | 8.15641i | −0.367534 | − | 0.267029i | ||||
\(934\) | 31.8124 | 1.04093 | ||||||||
\(935\) | 8.55455 | − | 1.44198i | 0.279764 | − | 0.0471579i | ||||
\(936\) | 5.48191 | 0.179182 | ||||||||
\(937\) | 22.0908 | + | 16.0499i | 0.721676 | + | 0.524328i | 0.886919 | − | 0.461925i | \(-0.152841\pi\) |
−0.165243 | + | 0.986253i | \(0.552841\pi\) | |||||||
\(938\) | 12.1615 | − | 37.4293i | 0.397087 | − | 1.22211i | ||||
\(939\) | −6.17269 | − | 18.9976i | −0.201438 | − | 0.619963i | ||||
\(940\) | 8.29877 | − | 6.02941i | 0.270676 | − | 0.196658i | ||||
\(941\) | −32.9114 | + | 23.9115i | −1.07288 | + | 0.779493i | −0.976428 | − | 0.215844i | \(-0.930750\pi\) |
−0.0964527 | + | 0.995338i | \(0.530750\pi\) | |||||||
\(942\) | −2.31478 | − | 7.12415i | −0.0754195 | − | 0.232117i | ||||
\(943\) | −0.189210 | + | 0.582330i | −0.00616154 | + | 0.0189633i | ||||
\(944\) | 28.5355 | + | 20.7322i | 0.928751 | + | 0.674777i | ||||
\(945\) | 2.40901 | 0.0783650 | ||||||||
\(946\) | 7.99643 | − | 53.9434i | 0.259986 | − | 1.75385i | ||||
\(947\) | −42.2692 | −1.37356 | −0.686782 | − | 0.726864i | \(-0.740977\pi\) | ||||
−0.686782 | + | 0.726864i | \(0.740977\pi\) | |||||||
\(948\) | −23.4572 | − | 17.0426i | −0.761853 | − | 0.553519i | ||||
\(949\) | −3.42658 | + | 10.5459i | −0.111231 | + | 0.342335i | ||||
\(950\) | 12.8077 | + | 39.4179i | 0.415535 | + | 1.27889i | ||||
\(951\) | −12.4786 | + | 9.06621i | −0.404645 | + | 0.293992i | ||||
\(952\) | 17.5773 | − | 12.7707i | 0.569685 | − | 0.413900i | ||||
\(953\) | 13.1569 | + | 40.4928i | 0.426194 | + | 1.31169i | 0.901847 | + | 0.432056i | \(0.142212\pi\) |
−0.475653 | + | 0.879633i | \(0.657788\pi\) | |||||||
\(954\) | 1.98495 | − | 6.10905i | 0.0642652 | − | 0.197788i | ||||
\(955\) | 2.83878 | + | 2.06249i | 0.0918607 | + | 0.0667407i | ||||
\(956\) | 48.5096 | 1.56891 | ||||||||
\(957\) | −8.54928 | − | 16.3755i | −0.276359 | − | 0.529345i | ||||
\(958\) | 8.12201 | 0.262410 | ||||||||
\(959\) | −13.7851 | − | 10.0155i | −0.445145 | − | 0.323417i | ||||
\(960\) | −2.04612 | + | 6.29731i | −0.0660383 | + | 0.203245i | ||||
\(961\) | −8.78201 | − | 27.0283i | −0.283291 | − | 0.871879i | ||||
\(962\) | 3.76793 | − | 2.73756i | 0.121483 | − | 0.0882625i | ||||
\(963\) | 4.86075 | − | 3.53154i | 0.156636 | − | 0.113802i | ||||
\(964\) | 25.4101 | + | 78.2043i | 0.818405 | + | 2.51879i | ||||
\(965\) | −7.13532 | + | 21.9603i | −0.229694 | + | 0.706926i | ||||
\(966\) | −0.622171 | − | 0.452033i | −0.0200180 | − | 0.0145439i | ||||
\(967\) | 33.9106 | 1.09049 | 0.545246 | − | 0.838276i | \(-0.316436\pi\) | ||||
0.545246 | + | 0.838276i | \(0.316436\pi\) | |||||||
\(968\) | −36.4043 | − | 48.0722i | −1.17008 | − | 1.54510i | ||||
\(969\) | −10.1246 | −0.325249 | ||||||||
\(970\) | −23.5818 | − | 17.1332i | −0.757165 | − | 0.550113i | ||||
\(971\) | 5.94329 | − | 18.2916i | 0.190729 | − | 0.587004i | −0.809271 | − | 0.587436i | \(-0.800137\pi\) |
1.00000 | 0.000431941i | \(0.000137491\pi\) | ||||||||
\(972\) | −1.29829 | − | 3.99572i | −0.0416426 | − | 0.128163i | ||||
\(973\) | −4.72036 | + | 3.42954i | −0.151328 | + | 0.109946i | ||||
\(974\) | 56.2995 | − | 40.9040i | 1.80395 | − | 1.31065i | ||||
\(975\) | −1.05379 | − | 3.24323i | −0.0337483 | − | 0.103867i | ||||
\(976\) | 23.4715 | − | 72.2378i | 0.751304 | − | 2.31227i | ||||
\(977\) | −7.51874 | − | 5.46268i | −0.240546 | − | 0.174767i | 0.460981 | − | 0.887410i | \(-0.347498\pi\) |
−0.701526 | + | 0.712643i | \(0.747498\pi\) | |||||||
\(978\) | 43.2676 | 1.38354 | ||||||||
\(979\) | 10.0828 | + | 19.3128i | 0.322247 | + | 0.617241i | ||||
\(980\) | 17.7454 | 0.566857 | ||||||||
\(981\) | 4.92959 | + | 3.58155i | 0.157390 | + | 0.114350i | ||||
\(982\) | −8.93338 | + | 27.4941i | −0.285076 | + | 0.877373i | ||||
\(983\) | 0.0166207 | + | 0.0511532i | 0.000530118 | + | 0.00163153i | 0.951321 | − | 0.308201i | \(-0.0997270\pi\) |
−0.950791 | + | 0.309833i | \(0.899727\pi\) | |||||||
\(984\) | 16.7997 | − | 12.2057i | 0.535555 | − | 0.389104i | ||||
\(985\) | 2.78582 | − | 2.02401i | 0.0887635 | − | 0.0644905i | ||||
\(986\) | 8.89137 | + | 27.3648i | 0.283159 | + | 0.871474i | ||||
\(987\) | −1.14322 | + | 3.51846i | −0.0363890 | + | 0.111994i | ||||
\(988\) | 16.5889 | + | 12.0526i | 0.527765 | + | 0.383443i | ||||
\(989\) | 1.06726 | 0.0339368 | ||||||||
\(990\) | −1.52706 | + | 10.3015i | −0.0485332 | + | 0.327402i | ||||
\(991\) | 26.5066 | 0.842011 | 0.421005 | − | 0.907058i | \(-0.361677\pi\) | ||||
0.421005 | + | 0.907058i | \(0.361677\pi\) | |||||||
\(992\) | 2.73788 | + | 1.98919i | 0.0869278 | + | 0.0631568i | ||||
\(993\) | −8.67086 | + | 26.6862i | −0.275161 | + | 0.846860i | ||||
\(994\) | 20.6647 | + | 63.5995i | 0.655446 | + | 2.01725i | ||||
\(995\) | −21.2528 | + | 15.4411i | −0.673760 | + | 0.489516i | ||||
\(996\) | −45.4199 | + | 32.9995i | −1.43919 | + | 1.04563i | ||||
\(997\) | 4.89437 | + | 15.0633i | 0.155006 | + | 0.477060i | 0.998162 | − | 0.0606100i | \(-0.0193046\pi\) |
−0.843155 | + | 0.537670i | \(0.819305\pi\) | |||||||
\(998\) | −4.07171 | + | 12.5314i | −0.128888 | + | 0.396675i | ||||
\(999\) | −1.51307 | − | 1.09931i | −0.0478715 | − | 0.0347807i |
(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.n.b.235.5 | yes | 20 | |
11.3 | even | 5 | inner | 429.2.n.b.157.5 | ✓ | 20 | |
11.5 | even | 5 | 4719.2.a.bn.1.1 | 10 | |||
11.6 | odd | 10 | 4719.2.a.bi.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.b.157.5 | ✓ | 20 | 11.3 | even | 5 | inner | |
429.2.n.b.235.5 | yes | 20 | 1.1 | even | 1 | trivial | |
4719.2.a.bi.1.10 | 10 | 11.6 | odd | 10 | |||
4719.2.a.bn.1.1 | 10 | 11.5 | even | 5 |