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: | \( x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 \) |
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 | 157.1 | ||
Root | \(-2.26411 - 1.64497i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.157 |
Dual form | 429.2.n.b.235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26411 | + | 1.64497i | −1.60097 | + | 1.16317i | −0.715335 | + | 0.698781i | \(0.753726\pi\) |
−0.885631 | + | 0.464389i | \(0.846274\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 1.80222 | − | 5.54667i | 0.901112 | − | 2.77334i | ||||
\(5\) | 2.68510 | + | 1.95084i | 1.20081 | + | 0.872443i | 0.994365 | − | 0.106014i | \(-0.0338088\pi\) |
0.206450 | + | 0.978457i | \(0.433809\pi\) | |||||||
\(6\) | 2.26411 | + | 1.64497i | 0.924319 | + | 0.671557i | ||||
\(7\) | −0.449002 | + | 1.38189i | −0.169707 | + | 0.522304i | −0.999352 | − | 0.0359866i | \(-0.988543\pi\) |
0.829645 | + | 0.558291i | \(0.188543\pi\) | |||||||
\(8\) | 3.31406 | + | 10.1996i | 1.17170 | + | 3.60612i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −9.28845 | −2.93726 | ||||||||
\(11\) | 0.682296 | − | 3.24569i | 0.205720 | − | 0.978611i | ||||
\(12\) | −5.83212 | −1.68359 | ||||||||
\(13\) | 0.809017 | − | 0.587785i | 0.224381 | − | 0.163022i | ||||
\(14\) | −1.25657 | − | 3.86734i | −0.335834 | − | 1.03359i | ||||
\(15\) | 1.02562 | − | 3.15653i | 0.264814 | − | 0.815012i | ||||
\(16\) | −14.8450 | − | 10.7855i | −3.71124 | − | 2.69637i | ||||
\(17\) | 5.09765 | + | 3.70366i | 1.23636 | + | 0.898270i | 0.997350 | − | 0.0727469i | \(-0.0231765\pi\) |
0.239012 | + | 0.971017i | \(0.423177\pi\) | |||||||
\(18\) | 0.864813 | − | 2.66162i | 0.203838 | − | 0.627350i | ||||
\(19\) | 0.174485 | + | 0.537010i | 0.0400297 | + | 0.123199i | 0.969074 | − | 0.246769i | \(-0.0793688\pi\) |
−0.929045 | + | 0.369967i | \(0.879369\pi\) | |||||||
\(20\) | 15.6598 | − | 11.3775i | 3.50165 | − | 2.54410i | ||||
\(21\) | 1.45300 | 0.317071 | ||||||||
\(22\) | 3.79427 | + | 8.47094i | 0.808940 | + | 1.80601i | ||||
\(23\) | −3.52426 | −0.734859 | −0.367430 | − | 0.930051i | \(-0.619762\pi\) | ||||
−0.367430 | + | 0.930051i | \(0.619762\pi\) | |||||||
\(24\) | 8.67633 | − | 6.30373i | 1.77105 | − | 1.28674i | ||||
\(25\) | 1.85891 | + | 5.72114i | 0.371783 | + | 1.14423i | ||||
\(26\) | −0.864813 | + | 2.66162i | −0.169604 | + | 0.521987i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | 6.85567 | + | 4.98094i | 1.29560 | + | 0.941309i | ||||
\(29\) | −0.493471 | + | 1.51875i | −0.0916353 | + | 0.282024i | −0.986362 | − | 0.164589i | \(-0.947370\pi\) |
0.894727 | + | 0.446614i | \(0.147370\pi\) | |||||||
\(30\) | 2.87029 | + | 8.83384i | 0.524040 | + | 1.61283i | ||||
\(31\) | 7.96581 | − | 5.78750i | 1.43070 | − | 1.03947i | 0.440817 | − | 0.897597i | \(-0.354689\pi\) |
0.989885 | − | 0.141869i | \(-0.0453112\pi\) | |||||||
\(32\) | 29.9033 | 5.28621 | ||||||||
\(33\) | −3.29767 | + | 0.354070i | −0.574051 | + | 0.0616356i | ||||
\(34\) | −17.6341 | −3.02422 | ||||||||
\(35\) | −3.90146 | + | 2.83458i | −0.659467 | + | 0.479131i | ||||
\(36\) | 1.80222 | + | 5.54667i | 0.300371 | + | 0.924446i | ||||
\(37\) | −0.422984 | + | 1.30181i | −0.0695382 | + | 0.214016i | −0.979786 | − | 0.200047i | \(-0.935891\pi\) |
0.910248 | + | 0.414063i | \(0.135891\pi\) | |||||||
\(38\) | −1.27842 | − | 0.928827i | −0.207387 | − | 0.150676i | ||||
\(39\) | −0.809017 | − | 0.587785i | −0.129546 | − | 0.0941210i | ||||
\(40\) | −10.9993 | + | 33.8523i | −1.73914 | + | 5.35252i | ||||
\(41\) | 1.12880 | + | 3.47408i | 0.176288 | + | 0.542560i | 0.999690 | − | 0.0248991i | \(-0.00792645\pi\) |
−0.823402 | + | 0.567459i | \(0.807926\pi\) | |||||||
\(42\) | −3.28975 | + | 2.39015i | −0.507620 | + | 0.368808i | ||||
\(43\) | −4.12353 | −0.628832 | −0.314416 | − | 0.949285i | \(-0.601809\pi\) | ||||
−0.314416 | + | 0.949285i | \(0.601809\pi\) | |||||||
\(44\) | −16.7731 | − | 9.63393i | −2.52864 | − | 1.45237i | ||||
\(45\) | −3.31897 | −0.494763 | ||||||||
\(46\) | 7.97931 | − | 5.79731i | 1.17649 | − | 0.854767i | ||||
\(47\) | 1.75847 | + | 5.41201i | 0.256499 | + | 0.789423i | 0.993531 | + | 0.113565i | \(0.0362270\pi\) |
−0.737031 | + | 0.675858i | \(0.763773\pi\) | |||||||
\(48\) | −5.67027 | + | 17.4513i | −0.818433 | + | 2.51888i | ||||
\(49\) | 3.95511 | + | 2.87356i | 0.565016 | + | 0.410508i | ||||
\(50\) | −13.6199 | − | 9.89544i | −1.92614 | − | 1.39943i | ||||
\(51\) | 1.94713 | − | 5.99265i | 0.272653 | − | 0.839139i | ||||
\(52\) | −1.80222 | − | 5.54667i | −0.249923 | − | 0.769185i | ||||
\(53\) | 1.89461 | − | 1.37652i | 0.260245 | − | 0.189079i | −0.450010 | − | 0.893023i | \(-0.648580\pi\) |
0.710255 | + | 0.703945i | \(0.248580\pi\) | |||||||
\(54\) | −2.79859 | −0.380840 | ||||||||
\(55\) | 8.16386 | − | 7.38395i | 1.10081 | − | 0.995652i | ||||
\(56\) | −15.5828 | −2.08234 | ||||||||
\(57\) | 0.456808 | − | 0.331891i | 0.0605057 | − | 0.0439600i | ||||
\(58\) | −1.38102 | − | 4.25036i | −0.181337 | − | 0.558099i | ||||
\(59\) | −2.82208 | + | 8.68548i | −0.367404 | + | 1.13075i | 0.581058 | + | 0.813862i | \(0.302639\pi\) |
−0.948462 | + | 0.316891i | \(0.897361\pi\) | |||||||
\(60\) | −15.6598 | − | 11.3775i | −2.02168 | − | 1.46883i | ||||
\(61\) | 2.21192 | + | 1.60705i | 0.283207 | + | 0.205762i | 0.720315 | − | 0.693647i | \(-0.243997\pi\) |
−0.437108 | + | 0.899409i | \(0.643997\pi\) | |||||||
\(62\) | −8.51519 | + | 26.2071i | −1.08143 | + | 3.32830i | ||||
\(63\) | −0.449002 | − | 1.38189i | −0.0565690 | − | 0.174101i | ||||
\(64\) | −38.0145 | + | 27.6192i | −4.75181 | + | 3.45239i | ||||
\(65\) | 3.31897 | 0.411668 | ||||||||
\(66\) | 6.88385 | − | 6.22623i | 0.847344 | − | 0.766396i | ||||
\(67\) | 6.27162 | 0.766200 | 0.383100 | − | 0.923707i | \(-0.374856\pi\) | ||||
0.383100 | + | 0.923707i | \(0.374856\pi\) | |||||||
\(68\) | 29.7301 | − | 21.6002i | 3.60531 | − | 2.61941i | ||||
\(69\) | 1.08906 | + | 3.35177i | 0.131107 | + | 0.403506i | ||||
\(70\) | 4.17053 | − | 12.8356i | 0.498474 | − | 1.53415i | ||||
\(71\) | −0.143536 | − | 0.104285i | −0.0170345 | − | 0.0123763i | 0.579235 | − | 0.815160i | \(-0.303351\pi\) |
−0.596270 | + | 0.802784i | \(0.703351\pi\) | |||||||
\(72\) | −8.67633 | − | 6.30373i | −1.02252 | − | 0.742901i | ||||
\(73\) | −1.01200 | + | 3.11462i | −0.118446 | + | 0.364538i | −0.992650 | − | 0.121020i | \(-0.961384\pi\) |
0.874204 | + | 0.485558i | \(0.161384\pi\) | |||||||
\(74\) | −1.18376 | − | 3.64324i | −0.137609 | − | 0.423518i | ||||
\(75\) | 4.86670 | − | 3.53586i | 0.561958 | − | 0.408286i | ||||
\(76\) | 3.29308 | 0.377743 | ||||||||
\(77\) | 4.17882 | + | 2.40018i | 0.476220 | + | 0.273525i | ||||
\(78\) | 2.79859 | 0.316878 | ||||||||
\(79\) | 0.0831306 | − | 0.0603979i | 0.00935292 | − | 0.00679530i | −0.583099 | − | 0.812401i | \(-0.698160\pi\) |
0.592452 | + | 0.805606i | \(0.298160\pi\) | |||||||
\(80\) | −18.8195 | − | 57.9203i | −2.10408 | − | 6.47569i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −8.27048 | − | 6.00886i | −0.913322 | − | 0.663567i | ||||
\(83\) | 11.2763 | + | 8.19273i | 1.23774 | + | 0.899269i | 0.997446 | − | 0.0714311i | \(-0.0227566\pi\) |
0.240293 | + | 0.970700i | \(0.422757\pi\) | |||||||
\(84\) | 2.61863 | − | 8.05933i | 0.285716 | − | 0.879345i | ||||
\(85\) | 6.46247 | + | 19.8894i | 0.700953 | + | 2.15731i | ||||
\(86\) | 9.33612 | − | 6.78309i | 1.00674 | − | 0.731439i | ||||
\(87\) | 1.59691 | 0.171206 | ||||||||
\(88\) | 35.3660 | − | 3.79723i | 3.77003 | − | 0.404787i | ||||
\(89\) | −1.06640 | −0.113038 | −0.0565189 | − | 0.998402i | \(-0.518000\pi\) | ||||
−0.0565189 | + | 0.998402i | \(0.518000\pi\) | |||||||
\(90\) | 7.51451 | − | 5.45961i | 0.792099 | − | 0.575494i | ||||
\(91\) | 0.449002 | + | 1.38189i | 0.0470682 | + | 0.144861i | ||||
\(92\) | −6.35151 | + | 19.5479i | −0.662191 | + | 2.03801i | ||||
\(93\) | −7.96581 | − | 5.78750i | −0.826016 | − | 0.600136i | ||||
\(94\) | −12.8840 | − | 9.36075i | −1.32888 | − | 0.965488i | ||||
\(95\) | −0.579112 | + | 1.78232i | −0.0594156 | + | 0.182862i | ||||
\(96\) | −9.24064 | − | 28.4398i | −0.943119 | − | 2.90262i | ||||
\(97\) | 11.8080 | − | 8.57903i | 1.19892 | − | 0.871068i | 0.204744 | − | 0.978815i | \(-0.434364\pi\) |
0.994178 | + | 0.107747i | \(0.0343637\pi\) | |||||||
\(98\) | −13.6817 | −1.38206 | ||||||||
\(99\) | 1.35578 | + | 3.02686i | 0.136261 | + | 0.304211i | ||||
\(100\) | 35.0835 | 3.50835 | ||||||||
\(101\) | −5.64383 | + | 4.10048i | −0.561582 | + | 0.408013i | −0.832038 | − | 0.554719i | \(-0.812826\pi\) |
0.270455 | + | 0.962733i | \(0.412826\pi\) | |||||||
\(102\) | 5.44922 | + | 16.7710i | 0.539553 | + | 1.66057i | ||||
\(103\) | 2.93381 | − | 9.02935i | 0.289077 | − | 0.889689i | −0.696069 | − | 0.717974i | \(-0.745069\pi\) |
0.985147 | − | 0.171714i | \(-0.0549306\pi\) | |||||||
\(104\) | 8.67633 | + | 6.30373i | 0.850785 | + | 0.618131i | ||||
\(105\) | 3.90146 | + | 2.83458i | 0.380744 | + | 0.276626i | ||||
\(106\) | −2.02528 | + | 6.23316i | −0.196712 | + | 0.605418i | ||||
\(107\) | −2.06368 | − | 6.35136i | −0.199504 | − | 0.614009i | −0.999894 | − | 0.0145305i | \(-0.995375\pi\) |
0.800391 | − | 0.599479i | \(-0.204625\pi\) | |||||||
\(108\) | 4.71828 | − | 3.42803i | 0.454017 | − | 0.329863i | ||||
\(109\) | −6.65315 | −0.637256 | −0.318628 | − | 0.947880i | \(-0.603222\pi\) | ||||
−0.318628 | + | 0.947880i | \(0.603222\pi\) | |||||||
\(110\) | −6.33747 | + | 30.1474i | −0.604254 | + | 2.87444i | ||||
\(111\) | 1.36881 | 0.129921 | ||||||||
\(112\) | 21.5697 | − | 15.6713i | 2.03815 | − | 1.48080i | ||||
\(113\) | −3.43813 | − | 10.5815i | −0.323432 | − | 0.995422i | −0.972143 | − | 0.234387i | \(-0.924692\pi\) |
0.648711 | − | 0.761035i | \(-0.275308\pi\) | |||||||
\(114\) | −0.488313 | + | 1.50287i | −0.0457347 | + | 0.140757i | ||||
\(115\) | −9.46301 | − | 6.87528i | −0.882430 | − | 0.641123i | ||||
\(116\) | 7.53465 | + | 5.47425i | 0.699575 | + | 0.508271i | ||||
\(117\) | −0.309017 | + | 0.951057i | −0.0285686 | + | 0.0879252i | ||||
\(118\) | −7.89786 | − | 24.3071i | −0.727057 | − | 2.23765i | ||||
\(119\) | −7.40690 | + | 5.38143i | −0.678989 | + | 0.493314i | ||||
\(120\) | 35.5944 | 3.24931 | ||||||||
\(121\) | −10.0689 | − | 4.42904i | −0.915359 | − | 0.402640i | ||||
\(122\) | −7.65158 | −0.692741 | ||||||||
\(123\) | 2.95523 | − | 2.14710i | 0.266464 | − | 0.193597i | ||||
\(124\) | −17.7452 | − | 54.6142i | −1.59357 | − | 4.90450i | ||||
\(125\) | −1.04158 | + | 3.20567i | −0.0931622 | + | 0.286724i | ||||
\(126\) | 3.28975 | + | 2.39015i | 0.293075 | + | 0.212931i | ||||
\(127\) | −6.14045 | − | 4.46130i | −0.544877 | − | 0.395876i | 0.281016 | − | 0.959703i | \(-0.409329\pi\) |
−0.825893 | + | 0.563827i | \(0.809329\pi\) | |||||||
\(128\) | 22.1550 | − | 68.1860i | 1.95824 | − | 6.02685i | ||||
\(129\) | 1.27424 | + | 3.92171i | 0.112191 | + | 0.345287i | ||||
\(130\) | −7.51451 | + | 5.45961i | −0.659066 | + | 0.478840i | ||||
\(131\) | −16.6057 | −1.45085 | −0.725423 | − | 0.688303i | \(-0.758356\pi\) | ||||
−0.725423 | + | 0.688303i | \(0.758356\pi\) | |||||||
\(132\) | −3.97923 | + | 18.9292i | −0.346348 | + | 1.64758i | ||||
\(133\) | −0.820432 | −0.0711405 | ||||||||
\(134\) | −14.1996 | + | 10.3166i | −1.22666 | + | 0.891222i | ||||
\(135\) | 1.02562 | + | 3.15653i | 0.0882712 | + | 0.271671i | ||||
\(136\) | −20.8821 | + | 64.2684i | −1.79062 | + | 5.51097i | ||||
\(137\) | −0.972861 | − | 0.706825i | −0.0831171 | − | 0.0603881i | 0.545451 | − | 0.838143i | \(-0.316359\pi\) |
−0.628568 | + | 0.777755i | \(0.716359\pi\) | |||||||
\(138\) | −7.97931 | − | 5.79731i | −0.679244 | − | 0.493500i | ||||
\(139\) | 6.35197 | − | 19.5494i | 0.538767 | − | 1.65815i | −0.196599 | − | 0.980484i | \(-0.562990\pi\) |
0.735366 | − | 0.677670i | \(-0.237010\pi\) | |||||||
\(140\) | 8.69117 | + | 26.7487i | 0.734538 | + | 2.26068i | ||||
\(141\) | 4.60373 | − | 3.34481i | 0.387704 | − | 0.281684i | ||||
\(142\) | 0.496525 | 0.0416675 | ||||||||
\(143\) | −1.35578 | − | 3.02686i | −0.113376 | − | 0.253119i | ||||
\(144\) | 18.3494 | 1.52911 | ||||||||
\(145\) | −4.28786 | + | 3.11531i | −0.356087 | + | 0.258712i | ||||
\(146\) | −2.83218 | − | 8.71654i | −0.234393 | − | 0.721386i | ||||
\(147\) | 1.51072 | − | 4.64951i | 0.124602 | − | 0.383485i | ||||
\(148\) | 6.45841 | + | 4.69231i | 0.530878 | + | 0.385706i | ||||
\(149\) | 1.78726 | + | 1.29852i | 0.146418 | + | 0.106379i | 0.658583 | − | 0.752508i | \(-0.271156\pi\) |
−0.512165 | + | 0.858887i | \(0.671156\pi\) | |||||||
\(150\) | −5.20234 | + | 16.0112i | −0.424769 | + | 1.30731i | ||||
\(151\) | −3.68982 | − | 11.3561i | −0.300274 | − | 0.924147i | −0.981399 | − | 0.191980i | \(-0.938509\pi\) |
0.681125 | − | 0.732167i | \(-0.261491\pi\) | |||||||
\(152\) | −4.89906 | + | 3.55938i | −0.397366 | + | 0.288703i | ||||
\(153\) | −6.30104 | −0.509409 | ||||||||
\(154\) | −13.4095 | + | 1.43977i | −1.08057 | + | 0.116020i | ||||
\(155\) | 32.6795 | 2.62488 | ||||||||
\(156\) | −4.71828 | + | 3.42803i | −0.377765 | + | 0.274462i | ||||
\(157\) | 3.97335 | + | 12.2287i | 0.317108 | + | 0.975957i | 0.974878 | + | 0.222739i | \(0.0714996\pi\) |
−0.657771 | + | 0.753218i | \(0.728500\pi\) | |||||||
\(158\) | −0.0888639 | + | 0.273495i | −0.00706963 | + | 0.0217581i | ||||
\(159\) | −1.89461 | − | 1.37652i | −0.150252 | − | 0.109165i | ||||
\(160\) | 80.2936 | + | 58.3367i | 6.34777 | + | 4.61192i | ||||
\(161\) | 1.58240 | − | 4.87013i | 0.124711 | − | 0.383820i | ||||
\(162\) | 0.864813 | + | 2.66162i | 0.0679461 | + | 0.209117i | ||||
\(163\) | −14.6428 | + | 10.6386i | −1.14692 | + | 0.833283i | −0.988068 | − | 0.154020i | \(-0.950778\pi\) |
−0.158848 | + | 0.987303i | \(0.550778\pi\) | |||||||
\(164\) | 21.3039 | 1.66356 | ||||||||
\(165\) | −9.54532 | − | 5.48252i | −0.743102 | − | 0.426814i | ||||
\(166\) | −39.0077 | −3.02758 | ||||||||
\(167\) | −3.41449 | + | 2.48077i | −0.264221 | + | 0.191968i | −0.712006 | − | 0.702173i | \(-0.752213\pi\) |
0.447785 | + | 0.894141i | \(0.352213\pi\) | |||||||
\(168\) | 4.81534 | + | 14.8201i | 0.371512 | + | 1.14340i | ||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | −47.3493 | − | 34.4013i | −3.63152 | − | 2.63846i | ||||
\(171\) | −0.456808 | − | 0.331891i | −0.0349330 | − | 0.0253803i | ||||
\(172\) | −7.43152 | + | 22.8719i | −0.566648 | + | 1.74396i | ||||
\(173\) | 1.58610 | + | 4.88152i | 0.120589 | + | 0.371135i | 0.993072 | − | 0.117510i | \(-0.0374913\pi\) |
−0.872483 | + | 0.488645i | \(0.837491\pi\) | |||||||
\(174\) | −3.61557 | + | 2.62686i | −0.274096 | + | 0.199142i | ||||
\(175\) | −8.74063 | −0.660730 | ||||||||
\(176\) | −45.1350 | + | 40.8232i | −3.40218 | + | 3.07716i | ||||
\(177\) | 9.13245 | 0.686437 | ||||||||
\(178\) | 2.41444 | − | 1.75419i | 0.180970 | − | 0.131482i | ||||
\(179\) | −6.48124 | − | 19.9472i | −0.484431 | − | 1.49092i | −0.832804 | − | 0.553568i | \(-0.813266\pi\) |
0.348373 | − | 0.937356i | \(-0.386734\pi\) | |||||||
\(180\) | −5.98153 | + | 18.4093i | −0.445837 | + | 1.37214i | ||||
\(181\) | 8.10160 | + | 5.88616i | 0.602188 | + | 0.437515i | 0.846655 | − | 0.532143i | \(-0.178613\pi\) |
−0.244467 | + | 0.969658i | \(0.578613\pi\) | |||||||
\(182\) | −3.28975 | − | 2.39015i | −0.243853 | − | 0.177169i | ||||
\(183\) | 0.844877 | − | 2.60026i | 0.0624551 | − | 0.192217i | ||||
\(184\) | −11.6796 | − | 35.9462i | −0.861034 | − | 2.64999i | ||||
\(185\) | −3.67538 | + | 2.67032i | −0.270220 | + | 0.196326i | ||||
\(186\) | 27.5557 | 2.02049 | ||||||||
\(187\) | 15.4990 | − | 14.0184i | 1.13340 | − | 1.02513i | ||||
\(188\) | 33.1878 | 2.42047 | ||||||||
\(189\) | −1.17550 | + | 0.854053i | −0.0855053 | + | 0.0621232i | ||||
\(190\) | −1.62070 | − | 4.98799i | −0.117578 | − | 0.361867i | ||||
\(191\) | 0.261305 | − | 0.804214i | 0.0189074 | − | 0.0581909i | −0.941158 | − | 0.337968i | \(-0.890261\pi\) |
0.960065 | + | 0.279777i | \(0.0902605\pi\) | |||||||
\(192\) | 38.0145 | + | 27.6192i | 2.74346 | + | 1.99324i | ||||
\(193\) | −16.6427 | − | 12.0917i | −1.19797 | − | 0.870376i | −0.203886 | − | 0.978995i | \(-0.565357\pi\) |
−0.994084 | + | 0.108619i | \(0.965357\pi\) | |||||||
\(194\) | −12.6224 | + | 38.8477i | −0.906234 | + | 2.78910i | ||||
\(195\) | −1.02562 | − | 3.15653i | −0.0734461 | − | 0.226044i | ||||
\(196\) | 23.0667 | − | 16.7589i | 1.64762 | − | 1.19707i | ||||
\(197\) | −28.0478 | −1.99832 | −0.999160 | − | 0.0409674i | \(-0.986956\pi\) | ||||
−0.999160 | + | 0.0409674i | \(0.986956\pi\) | |||||||
\(198\) | −8.04872 | − | 4.62292i | −0.571998 | − | 0.328537i | ||||
\(199\) | −8.63345 | −0.612009 | −0.306005 | − | 0.952030i | \(-0.598992\pi\) | ||||
−0.306005 | + | 0.952030i | \(0.598992\pi\) | |||||||
\(200\) | −52.1931 | + | 37.9205i | −3.69061 | + | 2.68138i | ||||
\(201\) | −1.93804 | − | 5.96467i | −0.136699 | − | 0.420715i | ||||
\(202\) | 6.03307 | − | 18.5679i | 0.424485 | − | 1.30643i | ||||
\(203\) | −1.87717 | − | 1.36384i | −0.131751 | − | 0.0957229i | ||||
\(204\) | −29.7301 | − | 21.6002i | −2.08152 | − | 1.51232i | ||||
\(205\) | −3.74644 | + | 11.5304i | −0.261663 | + | 0.805316i | ||||
\(206\) | 8.21055 | + | 25.2695i | 0.572056 | + | 1.76061i | ||||
\(207\) | 2.85119 | − | 2.07151i | 0.198171 | − | 0.143980i | ||||
\(208\) | −18.3494 | −1.27230 | ||||||||
\(209\) | 1.86202 | − | 0.199924i | 0.128798 | − | 0.0138290i | ||||
\(210\) | −13.4961 | −0.931321 | ||||||||
\(211\) | 8.72149 | − | 6.33654i | 0.600412 | − | 0.436225i | −0.245613 | − | 0.969368i | \(-0.578989\pi\) |
0.846025 | + | 0.533143i | \(0.178989\pi\) | |||||||
\(212\) | −4.22057 | − | 12.9896i | −0.289870 | − | 0.892128i | ||||
\(213\) | −0.0548257 | + | 0.168736i | −0.00375659 | + | 0.0115616i | ||||
\(214\) | 15.1202 | + | 10.9855i | 1.03360 | + | 0.750951i | ||||
\(215\) | −11.0721 | − | 8.04436i | −0.755111 | − | 0.548620i | ||||
\(216\) | −3.31406 | + | 10.1996i | −0.225494 | + | 0.693998i | ||||
\(217\) | 4.42100 | + | 13.6065i | 0.300117 | + | 0.923666i | ||||
\(218\) | 15.0635 | − | 10.9442i | 1.02023 | − | 0.741238i | ||||
\(219\) | 3.27490 | 0.221297 | ||||||||
\(220\) | −26.2433 | − | 58.5898i | −1.76932 | − | 3.95012i | ||||
\(221\) | 6.30104 | 0.423854 | ||||||||
\(222\) | −3.09912 | + | 2.25165i | −0.208000 | + | 0.151121i | ||||
\(223\) | 7.89111 | + | 24.2863i | 0.528428 | + | 1.62633i | 0.757437 | + | 0.652908i | \(0.226451\pi\) |
−0.229009 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(224\) | −13.4267 | + | 41.3230i | −0.897107 | + | 2.76101i | ||||
\(225\) | −4.86670 | − | 3.53586i | −0.324446 | − | 0.235724i | ||||
\(226\) | 25.1905 | + | 18.3020i | 1.67565 | + | 1.21743i | ||||
\(227\) | 1.16058 | − | 3.57190i | 0.0770304 | − | 0.237075i | −0.905125 | − | 0.425145i | \(-0.860223\pi\) |
0.982156 | + | 0.188070i | \(0.0602231\pi\) | |||||||
\(228\) | −1.01762 | − | 3.13191i | −0.0673935 | − | 0.207416i | ||||
\(229\) | 6.92165 | − | 5.02887i | 0.457396 | − | 0.332317i | −0.335113 | − | 0.942178i | \(-0.608775\pi\) |
0.792509 | + | 0.609861i | \(0.208775\pi\) | |||||||
\(230\) | 32.7349 | 2.15848 | ||||||||
\(231\) | 0.991377 | − | 4.71599i | 0.0652278 | − | 0.310289i | ||||
\(232\) | −17.1261 | −1.12438 | ||||||||
\(233\) | 0.641360 | − | 0.465975i | 0.0420169 | − | 0.0305271i | −0.566579 | − | 0.824008i | \(-0.691733\pi\) |
0.608595 | + | 0.793481i | \(0.291733\pi\) | |||||||
\(234\) | −0.864813 | − | 2.66162i | −0.0565346 | − | 0.173996i | ||||
\(235\) | −5.83631 | + | 17.9623i | −0.380719 | + | 1.17173i | ||||
\(236\) | 43.0895 | + | 31.3064i | 2.80489 | + | 2.03787i | ||||
\(237\) | −0.0831306 | − | 0.0603979i | −0.00539991 | − | 0.00392327i | ||||
\(238\) | 7.91773 | − | 24.3683i | 0.513230 | − | 1.57956i | ||||
\(239\) | −3.35280 | − | 10.3188i | −0.216874 | − | 0.667471i | −0.999015 | − | 0.0443690i | \(-0.985872\pi\) |
0.782141 | − | 0.623102i | \(-0.214128\pi\) | |||||||
\(240\) | −49.2700 | + | 35.7967i | −3.18036 | + | 2.31067i | ||||
\(241\) | 10.5175 | 0.677495 | 0.338747 | − | 0.940877i | \(-0.389997\pi\) | ||||
0.338747 | + | 0.940877i | \(0.389997\pi\) | |||||||
\(242\) | 30.0828 | − | 6.53530i | 1.93380 | − | 0.420105i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.9002 | − | 9.37252i | 0.825848 | − | 0.600014i | ||||
\(245\) | 5.01403 | + | 15.4316i | 0.320335 | + | 0.985888i | ||||
\(246\) | −3.15904 | + | 9.72253i | −0.201413 | + | 0.619886i | ||||
\(247\) | 0.456808 | + | 0.331891i | 0.0290660 | + | 0.0211177i | ||||
\(248\) | 85.4297 | + | 62.0683i | 5.42479 | + | 3.94134i | ||||
\(249\) | 4.30718 | − | 13.2561i | 0.272956 | − | 0.840073i | ||||
\(250\) | −2.91497 | − | 8.97136i | −0.184359 | − | 0.567399i | ||||
\(251\) | −0.409848 | + | 0.297772i | −0.0258694 | + | 0.0187952i | −0.600645 | − | 0.799516i | \(-0.705089\pi\) |
0.574775 | + | 0.818311i | \(0.305089\pi\) | |||||||
\(252\) | −8.47408 | −0.533817 | ||||||||
\(253\) | −2.40459 | + | 11.4386i | −0.151175 | + | 0.719141i | ||||
\(254\) | 21.2414 | 1.33280 | ||||||||
\(255\) | 16.9190 | − | 12.2923i | 1.05951 | − | 0.769776i | ||||
\(256\) | 32.9623 | + | 101.447i | 2.06014 | + | 6.34046i | ||||
\(257\) | 4.10951 | − | 12.6478i | 0.256344 | − | 0.788947i | −0.737218 | − | 0.675655i | \(-0.763861\pi\) |
0.993562 | − | 0.113291i | \(-0.0361393\pi\) | |||||||
\(258\) | −9.33612 | − | 6.78309i | −0.581241 | − | 0.422297i | ||||
\(259\) | −1.60903 | − | 1.16903i | −0.0999806 | − | 0.0726401i | ||||
\(260\) | 5.98153 | − | 18.4093i | 0.370959 | − | 1.14169i | ||||
\(261\) | −0.493471 | − | 1.51875i | −0.0305451 | − | 0.0940081i | ||||
\(262\) | 37.5971 | − | 27.3159i | 2.32276 | − | 1.68758i | ||||
\(263\) | −25.3323 | −1.56206 | −0.781029 | − | 0.624495i | \(-0.785305\pi\) | ||||
−0.781029 | + | 0.624495i | \(0.785305\pi\) | |||||||
\(264\) | −14.5401 | − | 32.4617i | −0.894880 | − | 1.99788i | ||||
\(265\) | 7.77259 | 0.477466 | ||||||||
\(266\) | 1.85755 | − | 1.34959i | 0.113894 | − | 0.0827485i | ||||
\(267\) | 0.329534 | + | 1.01420i | 0.0201672 | + | 0.0620682i | ||||
\(268\) | 11.3029 | − | 34.7866i | 0.690432 | − | 2.12493i | ||||
\(269\) | −21.1799 | − | 15.3881i | −1.29136 | − | 0.938227i | −0.291526 | − | 0.956563i | \(-0.594163\pi\) |
−0.999832 | + | 0.0183360i | \(0.994163\pi\) | |||||||
\(270\) | −7.51451 | − | 5.45961i | −0.457319 | − | 0.332261i | ||||
\(271\) | 5.64147 | − | 17.3627i | 0.342695 | − | 1.05471i | −0.620111 | − | 0.784514i | \(-0.712913\pi\) |
0.962806 | − | 0.270193i | \(-0.0870874\pi\) | |||||||
\(272\) | −35.7286 | − | 109.961i | −2.16637 | − | 6.66739i | ||||
\(273\) | 1.17550 | − | 0.854053i | 0.0711447 | − | 0.0516896i | ||||
\(274\) | 3.36537 | 0.203309 | ||||||||
\(275\) | 19.8374 | − | 2.12993i | 1.19624 | − | 0.128440i | ||||
\(276\) | 20.5539 | 1.23720 | ||||||||
\(277\) | −11.3139 | + | 8.22000i | −0.679784 | + | 0.493892i | −0.873286 | − | 0.487208i | \(-0.838015\pi\) |
0.193502 | + | 0.981100i | \(0.438015\pi\) | |||||||
\(278\) | 17.7766 | + | 54.7107i | 1.06617 | + | 3.28133i | ||||
\(279\) | −3.04267 | + | 9.36437i | −0.182160 | + | 0.560630i | ||||
\(280\) | −41.8414 | − | 30.3995i | −2.50050 | − | 1.81672i | ||||
\(281\) | −3.86206 | − | 2.80595i | −0.230391 | − | 0.167389i | 0.466601 | − | 0.884468i | \(-0.345479\pi\) |
−0.696992 | + | 0.717079i | \(0.745479\pi\) | |||||||
\(282\) | −4.92124 | + | 15.1460i | −0.293056 | + | 0.901932i | ||||
\(283\) | 6.55905 | + | 20.1867i | 0.389895 | + | 1.19997i | 0.932866 | + | 0.360222i | \(0.117299\pi\) |
−0.542971 | + | 0.839751i | \(0.682701\pi\) | |||||||
\(284\) | −0.837116 | + | 0.608201i | −0.0496737 | + | 0.0360901i | ||||
\(285\) | 1.87404 | 0.111009 | ||||||||
\(286\) | 8.04872 | + | 4.62292i | 0.475931 | + | 0.273359i | ||||
\(287\) | −5.30762 | −0.313299 | ||||||||
\(288\) | −24.1923 | + | 17.5767i | −1.42555 | + | 1.03572i | ||||
\(289\) | 7.01566 | + | 21.5920i | 0.412686 | + | 1.27012i | ||||
\(290\) | 4.58358 | − | 14.1068i | 0.269157 | − | 0.828380i | ||||
\(291\) | −11.8080 | − | 8.57903i | −0.692198 | − | 0.502912i | ||||
\(292\) | 15.4519 | + | 11.2265i | 0.904255 | + | 0.656980i | ||||
\(293\) | 4.93622 | − | 15.1921i | 0.288377 | − | 0.887533i | −0.696989 | − | 0.717082i | \(-0.745477\pi\) |
0.985366 | − | 0.170451i | \(-0.0545226\pi\) | |||||||
\(294\) | 4.22788 | + | 13.0121i | 0.246575 | + | 0.758880i | ||||
\(295\) | −24.5216 | + | 17.8160i | −1.42770 | + | 1.03729i | ||||
\(296\) | −14.6798 | −0.853246 | ||||||||
\(297\) | 2.45976 | − | 2.22477i | 0.142729 | − | 0.129094i | ||||
\(298\) | −6.18259 | −0.358148 | ||||||||
\(299\) | −2.85119 | + | 2.07151i | −0.164888 | + | 0.119798i | ||||
\(300\) | −10.8414 | − | 33.3664i | −0.625929 | − | 1.92641i | ||||
\(301\) | 1.85147 | − | 5.69825i | 0.106717 | − | 0.328442i | ||||
\(302\) | 27.0346 | + | 19.6418i | 1.55567 | + | 1.13026i | ||||
\(303\) | 5.64383 | + | 4.10048i | 0.324230 | + | 0.235567i | ||||
\(304\) | 3.20170 | − | 9.85381i | 0.183630 | − | 0.565155i | ||||
\(305\) | 2.80412 | + | 8.63020i | 0.160564 | + | 0.494164i | ||||
\(306\) | 14.2663 | − | 10.3650i | 0.815547 | − | 0.592530i | ||||
\(307\) | 10.7827 | 0.615399 | 0.307699 | − | 0.951484i | \(-0.400441\pi\) | ||||
0.307699 | + | 0.951484i | \(0.400441\pi\) | |||||||
\(308\) | 20.8442 | − | 18.8529i | 1.18771 | − | 1.07424i | ||||
\(309\) | −9.49402 | −0.540096 | ||||||||
\(310\) | −73.9900 | + | 53.7569i | −4.20235 | + | 3.05319i | ||||
\(311\) | −2.60196 | − | 8.00802i | −0.147544 | − | 0.454093i | 0.849785 | − | 0.527129i | \(-0.176731\pi\) |
−0.997329 | + | 0.0730353i | \(0.976731\pi\) | |||||||
\(312\) | 3.31406 | − | 10.1996i | 0.187622 | − | 0.577441i | ||||
\(313\) | −9.01928 | − | 6.55289i | −0.509800 | − | 0.370391i | 0.302948 | − | 0.953007i | \(-0.402029\pi\) |
−0.812748 | + | 0.582616i | \(0.802029\pi\) | |||||||
\(314\) | −29.1120 | − | 21.1511i | −1.64288 | − | 1.19362i | ||||
\(315\) | 1.49023 | − | 4.58644i | 0.0839647 | − | 0.258417i | ||||
\(316\) | −0.185188 | − | 0.569949i | −0.0104176 | − | 0.0320621i | ||||
\(317\) | −14.9669 | + | 10.8741i | −0.840627 | + | 0.610751i | −0.922546 | − | 0.385888i | \(-0.873895\pi\) |
0.0819187 | + | 0.996639i | \(0.473895\pi\) | |||||||
\(318\) | 6.55393 | 0.367526 | ||||||||
\(319\) | 4.59268 | + | 2.63789i | 0.257141 | + | 0.147693i | ||||
\(320\) | −155.954 | −8.71807 | ||||||||
\(321\) | −5.40279 | + | 3.92536i | −0.301554 | + | 0.219092i | ||||
\(322\) | 4.42850 | + | 13.6295i | 0.246790 | + | 0.759543i | ||||
\(323\) | −1.09944 | + | 3.38373i | −0.0611744 | + | 0.188276i | ||||
\(324\) | −4.71828 | − | 3.42803i | −0.262127 | − | 0.190446i | ||||
\(325\) | 4.86670 | + | 3.53586i | 0.269956 | + | 0.196134i | ||||
\(326\) | 15.6527 | − | 48.1741i | 0.866923 | − | 2.66812i | ||||
\(327\) | 2.05594 | + | 6.32752i | 0.113694 | + | 0.349913i | ||||
\(328\) | −31.6935 | + | 23.0267i | −1.74998 | + | 1.27143i | ||||
\(329\) | −8.26835 | −0.455849 | ||||||||
\(330\) | 30.6302 | − | 3.28876i | 1.68614 | − | 0.181040i | ||||
\(331\) | −16.0478 | −0.882065 | −0.441032 | − | 0.897491i | \(-0.645388\pi\) | ||||
−0.441032 | + | 0.897491i | \(0.645388\pi\) | |||||||
\(332\) | 65.7649 | − | 47.7810i | 3.60932 | − | 2.62232i | ||||
\(333\) | −0.422984 | − | 1.30181i | −0.0231794 | − | 0.0713388i | ||||
\(334\) | 3.64998 | − | 11.2335i | 0.199718 | − | 0.614669i | ||||
\(335\) | 16.8400 | + | 12.2349i | 0.920065 | + | 0.668466i | ||||
\(336\) | −21.5697 | − | 15.6713i | −1.17673 | − | 0.854942i | ||||
\(337\) | 6.27600 | − | 19.3156i | 0.341876 | − | 1.05219i | −0.621360 | − | 0.783526i | \(-0.713419\pi\) |
0.963235 | − | 0.268660i | \(-0.0865806\pi\) | |||||||
\(338\) | 0.864813 | + | 2.66162i | 0.0470396 | + | 0.144773i | ||||
\(339\) | −9.00115 | + | 6.53972i | −0.488875 | + | 0.355189i | ||||
\(340\) | 121.967 | 6.61459 | ||||||||
\(341\) | −13.3494 | − | 29.8033i | −0.722909 | − | 1.61394i | ||||
\(342\) | 1.58021 | 0.0854482 | ||||||||
\(343\) | −13.9753 | + | 10.1537i | −0.754596 | + | 0.548246i | ||||
\(344\) | −13.6656 | − | 42.0585i | −0.736802 | − | 2.26764i | ||||
\(345\) | −3.61455 | + | 11.1244i | −0.194601 | + | 0.598919i | ||||
\(346\) | −11.6211 | − | 8.44320i | −0.624752 | − | 0.453909i | ||||
\(347\) | −12.8189 | − | 9.31344i | −0.688152 | − | 0.499972i | 0.187900 | − | 0.982188i | \(-0.439832\pi\) |
−0.876052 | + | 0.482216i | \(0.839832\pi\) | |||||||
\(348\) | 2.87798 | − | 8.85752i | 0.154276 | − | 0.474813i | ||||
\(349\) | −3.67663 | − | 11.3155i | −0.196805 | − | 0.605705i | −0.999951 | − | 0.00992155i | \(-0.996842\pi\) |
0.803145 | − | 0.595783i | \(-0.203158\pi\) | |||||||
\(350\) | 19.7897 | − | 14.3781i | 1.05781 | − | 0.768541i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 20.4029 | − | 97.0568i | 1.08748 | − | 5.17315i | ||||
\(353\) | 16.1210 | 0.858033 | 0.429016 | − | 0.903297i | \(-0.358860\pi\) | ||||
0.429016 | + | 0.903297i | \(0.358860\pi\) | |||||||
\(354\) | −20.6769 | + | 15.0226i | −1.09896 | + | 0.798443i | ||||
\(355\) | −0.181965 | − | 0.560030i | −0.00965769 | − | 0.0297233i | ||||
\(356\) | −1.92188 | + | 5.91495i | −0.101860 | + | 0.313492i | ||||
\(357\) | 7.40690 | + | 5.38143i | 0.392015 | + | 0.284815i | ||||
\(358\) | 47.4868 | + | 34.5012i | 2.50976 | + | 1.82344i | ||||
\(359\) | −1.66210 | + | 5.11541i | −0.0877222 | + | 0.269981i | −0.985289 | − | 0.170898i | \(-0.945333\pi\) |
0.897567 | + | 0.440879i | \(0.145333\pi\) | |||||||
\(360\) | −10.9993 | − | 33.8523i | −0.579713 | − | 1.78417i | ||||
\(361\) | 15.1134 | − | 10.9805i | 0.795441 | − | 0.577922i | ||||
\(362\) | −28.0255 | −1.47299 | ||||||||
\(363\) | −1.10079 | + | 10.9448i | −0.0577765 | + | 0.574452i | ||||
\(364\) | 8.47408 | 0.444162 | ||||||||
\(365\) | −8.79345 | + | 6.38882i | −0.460270 | + | 0.334406i | ||||
\(366\) | 2.36447 | + | 7.27708i | 0.123593 | + | 0.380379i | ||||
\(367\) | −8.32910 | + | 25.6343i | −0.434775 | + | 1.33810i | 0.458541 | + | 0.888673i | \(0.348372\pi\) |
−0.893317 | + | 0.449428i | \(0.851628\pi\) | |||||||
\(368\) | 52.3175 | + | 38.0109i | 2.72724 | + | 1.98146i | ||||
\(369\) | −2.95523 | − | 2.14710i | −0.153843 | − | 0.111774i | ||||
\(370\) | 3.92887 | − | 12.0918i | 0.204252 | − | 0.628623i | ||||
\(371\) | 1.05150 | + | 3.23620i | 0.0545913 | + | 0.168015i | ||||
\(372\) | −46.4576 | + | 33.7534i | −2.40871 | + | 1.75003i | ||||
\(373\) | −26.4683 | −1.37048 | −0.685239 | − | 0.728318i | \(-0.740302\pi\) | ||||
−0.685239 | + | 0.728318i | \(0.740302\pi\) | |||||||
\(374\) | −12.0316 | + | 57.2346i | −0.622142 | + | 2.95953i | ||||
\(375\) | 3.37064 | 0.174059 | ||||||||
\(376\) | −49.3729 | + | 35.8715i | −2.54621 | + | 1.84993i | ||||
\(377\) | 0.493471 | + | 1.51875i | 0.0254151 | + | 0.0782195i | ||||
\(378\) | 1.25657 | − | 3.86734i | 0.0646312 | − | 0.198914i | ||||
\(379\) | −1.38630 | − | 1.00721i | −0.0712094 | − | 0.0517367i | 0.551611 | − | 0.834101i | \(-0.314013\pi\) |
−0.622820 | + | 0.782365i | \(0.714013\pi\) | |||||||
\(380\) | 8.84227 | + | 6.42429i | 0.453599 | + | 0.329559i | ||||
\(381\) | −2.34544 | + | 7.21854i | −0.120161 | + | 0.369817i | ||||
\(382\) | 0.731286 | + | 2.25067i | 0.0374158 | + | 0.115154i | ||||
\(383\) | 10.0660 | − | 7.31335i | 0.514347 | − | 0.373695i | −0.300123 | − | 0.953900i | \(-0.597028\pi\) |
0.814470 | + | 0.580206i | \(0.197028\pi\) | |||||||
\(384\) | −71.6950 | −3.65867 | ||||||||
\(385\) | 6.53819 | + | 14.5969i | 0.333217 | + | 0.743929i | ||||
\(386\) | 57.5714 | 2.93031 | ||||||||
\(387\) | 3.33601 | − | 2.42375i | 0.169579 | − | 0.123206i | ||||
\(388\) | −26.3044 | − | 80.9566i | −1.33540 | − | 4.10995i | ||||
\(389\) | −2.29869 | + | 7.07463i | −0.116548 | + | 0.358698i | −0.992267 | − | 0.124124i | \(-0.960388\pi\) |
0.875719 | + | 0.482822i | \(0.160388\pi\) | |||||||
\(390\) | 7.51451 | + | 5.45961i | 0.380512 | + | 0.276458i | ||||
\(391\) | −17.9655 | − | 13.0527i | −0.908552 | − | 0.660102i | ||||
\(392\) | −16.2018 | + | 49.8639i | −0.818312 | + | 2.51851i | ||||
\(393\) | 5.13144 | + | 15.7930i | 0.258847 | + | 0.796650i | ||||
\(394\) | 63.5032 | − | 46.1378i | 3.19925 | − | 2.32439i | ||||
\(395\) | 0.341041 | 0.0171596 | ||||||||
\(396\) | 19.2324 | − | 2.06498i | 0.966465 | − | 0.103769i | ||||
\(397\) | −9.60558 | −0.482090 | −0.241045 | − | 0.970514i | \(-0.577490\pi\) | ||||
−0.241045 | + | 0.970514i | \(0.577490\pi\) | |||||||
\(398\) | 19.5471 | − | 14.2018i | 0.979806 | − | 0.711871i | ||||
\(399\) | 0.253527 | + | 0.780277i | 0.0126922 | + | 0.0390627i | ||||
\(400\) | 34.1099 | − | 104.979i | 1.70549 | − | 5.24897i | ||||
\(401\) | 12.8427 | + | 9.33075i | 0.641333 | + | 0.465956i | 0.860308 | − | 0.509775i | \(-0.170271\pi\) |
−0.218975 | + | 0.975730i | \(0.570271\pi\) | |||||||
\(402\) | 14.1996 | + | 10.3166i | 0.708213 | + | 0.514547i | ||||
\(403\) | 3.04267 | − | 9.36437i | 0.151566 | − | 0.466473i | ||||
\(404\) | 12.5726 | + | 38.6945i | 0.625510 | + | 1.92512i | ||||
\(405\) | 2.68510 | − | 1.95084i | 0.133424 | − | 0.0969381i | ||||
\(406\) | 6.49359 | 0.322272 | ||||||||
\(407\) | 3.93667 | + | 2.26109i | 0.195133 | + | 0.112078i | ||||
\(408\) | 67.5758 | 3.34550 | ||||||||
\(409\) | 1.80031 | − | 1.30800i | 0.0890196 | − | 0.0646766i | −0.542385 | − | 0.840130i | \(-0.682479\pi\) |
0.631405 | + | 0.775453i | \(0.282479\pi\) | |||||||
\(410\) | −10.4848 | − | 32.2688i | −0.517806 | − | 1.59364i | ||||
\(411\) | −0.371600 | + | 1.14367i | −0.0183297 | + | 0.0564129i | ||||
\(412\) | −44.7955 | − | 32.5458i | −2.20692 | − | 1.60342i | ||||
\(413\) | −10.7352 | − | 7.79960i | −0.528246 | − | 0.383793i | ||||
\(414\) | −3.04783 | + | 9.38024i | −0.149792 | + | 0.461014i | ||||
\(415\) | 14.2954 | + | 43.9967i | 0.701733 | + | 2.15971i | ||||
\(416\) | 24.1923 | − | 17.5767i | 1.18613 | − | 0.861771i | ||||
\(417\) | −20.5554 | −1.00660 | ||||||||
\(418\) | −3.88694 | + | 3.51562i | −0.190116 | + | 0.171954i | ||||
\(419\) | 31.9645 | 1.56157 | 0.780784 | − | 0.624801i | \(-0.214820\pi\) | ||||
0.780784 | + | 0.624801i | \(0.214820\pi\) | |||||||
\(420\) | 22.7538 | − | 16.5316i | 1.11027 | − | 0.806659i | ||||
\(421\) | 4.77937 | + | 14.7094i | 0.232932 | + | 0.716891i | 0.997389 | + | 0.0722165i | \(0.0230073\pi\) |
−0.764457 | + | 0.644675i | \(0.776993\pi\) | |||||||
\(422\) | −9.32299 | + | 28.6932i | −0.453836 | + | 1.39676i | ||||
\(423\) | −4.60373 | − | 3.34481i | −0.223841 | − | 0.162630i | ||||
\(424\) | 20.3188 | + | 14.7625i | 0.986769 | + | 0.716930i | ||||
\(425\) | −11.7131 | + | 36.0492i | −0.568168 | + | 1.74864i | ||||
\(426\) | −0.153435 | − | 0.472224i | −0.00743394 | − | 0.0228793i | ||||
\(427\) | −3.21392 | + | 2.33505i | −0.155532 | + | 0.113001i | ||||
\(428\) | −38.9481 | −1.88263 | ||||||||
\(429\) | −2.45976 | + | 2.22477i | −0.118758 | + | 0.107413i | ||||
\(430\) | 38.3012 | 1.84705 | ||||||||
\(431\) | −2.09262 | + | 1.52038i | −0.100798 | + | 0.0732341i | −0.637043 | − | 0.770829i | \(-0.719842\pi\) |
0.536245 | + | 0.844063i | \(0.319842\pi\) | |||||||
\(432\) | −5.67027 | − | 17.4513i | −0.272811 | − | 0.839626i | ||||
\(433\) | 0.0334366 | − | 0.102907i | 0.00160686 | − | 0.00494540i | −0.950250 | − | 0.311489i | \(-0.899172\pi\) |
0.951857 | + | 0.306543i | \(0.0991724\pi\) | |||||||
\(434\) | −32.3919 | − | 23.5341i | −1.55486 | − | 1.12967i | ||||
\(435\) | 4.28786 | + | 3.11531i | 0.205587 | + | 0.149368i | ||||
\(436\) | −11.9905 | + | 36.9029i | −0.574239 | + | 1.76733i | ||||
\(437\) | −0.614932 | − | 1.89257i | −0.0294162 | − | 0.0905337i | ||||
\(438\) | −7.41473 | + | 5.38712i | −0.354290 | + | 0.257406i | ||||
\(439\) | 5.45264 | 0.260240 | 0.130120 | − | 0.991498i | \(-0.458464\pi\) | ||||
0.130120 | + | 0.991498i | \(0.458464\pi\) | |||||||
\(440\) | 102.369 | + | 58.7975i | 4.88026 | + | 2.80306i | ||||
\(441\) | −4.88879 | −0.232799 | ||||||||
\(442\) | −14.2663 | + | 10.3650i | −0.678576 | + | 0.493015i | ||||
\(443\) | −9.45640 | − | 29.1038i | −0.449287 | − | 1.38276i | −0.877713 | − | 0.479186i | \(-0.840932\pi\) |
0.428426 | − | 0.903577i | \(-0.359068\pi\) | |||||||
\(444\) | 2.46689 | − | 7.59232i | 0.117074 | − | 0.360315i | ||||
\(445\) | −2.86338 | − | 2.08037i | −0.135737 | − | 0.0986190i | ||||
\(446\) | −57.8166 | − | 42.0062i | −2.73770 | − | 1.98905i | ||||
\(447\) | 0.682674 | − | 2.10105i | 0.0322894 | − | 0.0993765i | ||||
\(448\) | −21.0979 | − | 64.9328i | −0.996784 | − | 3.06779i | ||||
\(449\) | 16.7174 | − | 12.1459i | 0.788945 | − | 0.573202i | −0.118705 | − | 0.992930i | \(-0.537874\pi\) |
0.907650 | + | 0.419728i | \(0.137874\pi\) | |||||||
\(450\) | 16.8351 | 0.793615 | ||||||||
\(451\) | 12.0459 | − | 1.29337i | 0.567221 | − | 0.0609023i | ||||
\(452\) | −64.8883 | −3.05209 | ||||||||
\(453\) | −9.66008 | + | 7.01846i | −0.453870 | + | 0.329756i | ||||
\(454\) | 3.24799 | + | 9.99629i | 0.152436 | + | 0.469149i | ||||
\(455\) | −1.49023 | + | 4.58644i | −0.0698628 | + | 0.215016i | ||||
\(456\) | 4.89906 | + | 3.55938i | 0.229419 | + | 0.166683i | ||||
\(457\) | −18.0279 | − | 13.0981i | −0.843311 | − | 0.612701i | 0.0799824 | − | 0.996796i | \(-0.474514\pi\) |
−0.923294 | + | 0.384095i | \(0.874514\pi\) | |||||||
\(458\) | −7.39902 | + | 22.7718i | −0.345733 | + | 1.06406i | ||||
\(459\) | 1.94713 | + | 5.99265i | 0.0908842 | + | 0.279713i | ||||
\(460\) | −55.1894 | + | 40.0974i | −2.57322 | + | 1.86955i | ||||
\(461\) | 26.8924 | 1.25251 | 0.626253 | − | 0.779620i | \(-0.284588\pi\) | ||||
0.626253 | + | 0.779620i | \(0.284588\pi\) | |||||||
\(462\) | 5.51308 | + | 12.3083i | 0.256491 | + | 0.572634i | ||||
\(463\) | 23.9466 | 1.11289 | 0.556447 | − | 0.830883i | \(-0.312164\pi\) | ||||
0.556447 | + | 0.830883i | \(0.312164\pi\) | |||||||
\(464\) | 23.7060 | − | 17.2234i | 1.10052 | − | 0.799577i | ||||
\(465\) | −10.0985 | − | 31.0801i | −0.468308 | − | 1.44130i | ||||
\(466\) | −0.685593 | + | 2.11004i | −0.0317595 | + | 0.0977456i | ||||
\(467\) | 4.89609 | + | 3.55722i | 0.226564 | + | 0.164608i | 0.695276 | − | 0.718742i | \(-0.255282\pi\) |
−0.468712 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(468\) | 4.71828 | + | 3.42803i | 0.218103 | + | 0.158461i | ||||
\(469\) | −2.81597 | + | 8.66667i | −0.130029 | + | 0.400190i | ||||
\(470\) | −16.3335 | − | 50.2692i | −0.753406 | − | 2.31875i | ||||
\(471\) | 10.4024 | − | 7.55776i | 0.479315 | − | 0.348243i | ||||
\(472\) | −97.9413 | −4.50812 | ||||||||
\(473\) | −2.81347 | + | 13.3837i | −0.129363 | + | 0.615382i | ||||
\(474\) | 0.287570 | 0.0132085 | ||||||||
\(475\) | −2.74796 | + | 1.99651i | −0.126085 | + | 0.0916062i | ||||
\(476\) | 16.5001 | + | 50.7822i | 0.756282 | + | 2.32760i | ||||
\(477\) | −0.723677 | + | 2.22725i | −0.0331349 | + | 0.101979i | ||||
\(478\) | 24.5653 | + | 17.8477i | 1.12359 | + | 0.816336i | ||||
\(479\) | 3.24047 | + | 2.35434i | 0.148061 | + | 0.107573i | 0.659350 | − | 0.751836i | \(-0.270832\pi\) |
−0.511289 | + | 0.859409i | \(0.670832\pi\) | |||||||
\(480\) | 30.6694 | − | 94.3908i | 1.39986 | − | 4.30833i | ||||
\(481\) | 0.422984 | + | 1.30181i | 0.0192864 | + | 0.0593575i | ||||
\(482\) | −23.8129 | + | 17.3011i | −1.08465 | + | 0.788042i | ||||
\(483\) | −5.12076 | −0.233003 | ||||||||
\(484\) | −42.7129 | + | 47.8670i | −1.94150 | + | 2.17577i | ||||
\(485\) | 48.4421 | 2.19964 | ||||||||
\(486\) | 2.26411 | − | 1.64497i | 0.102702 | − | 0.0746174i | ||||
\(487\) | −4.85268 | − | 14.9350i | −0.219896 | − | 0.676770i | −0.998770 | − | 0.0495895i | \(-0.984209\pi\) |
0.778874 | − | 0.627181i | \(-0.215791\pi\) | |||||||
\(488\) | −9.06092 | + | 27.8866i | −0.410169 | + | 1.26237i | ||||
\(489\) | 14.6428 | + | 10.6386i | 0.662172 | + | 0.481096i | ||||
\(490\) | −36.7368 | − | 26.6909i | −1.65960 | − | 1.20577i | ||||
\(491\) | 2.67084 | − | 8.21999i | 0.120533 | − | 0.370963i | −0.872528 | − | 0.488565i | \(-0.837521\pi\) |
0.993061 | + | 0.117602i | \(0.0375206\pi\) | |||||||
\(492\) | −6.58328 | − | 20.2612i | −0.296797 | − | 0.913448i | ||||
\(493\) | −8.14047 | + | 5.91440i | −0.366628 | + | 0.266371i | ||||
\(494\) | −1.58021 | −0.0710972 | ||||||||
\(495\) | −2.26452 | + | 10.7723i | −0.101783 | + | 0.484180i | ||||
\(496\) | −180.673 | −8.11247 | ||||||||
\(497\) | 0.208557 | − | 0.151526i | 0.00935508 | − | 0.00679686i | ||||
\(498\) | 12.0540 | + | 37.0985i | 0.540154 | + | 1.66242i | ||||
\(499\) | 4.25665 | − | 13.1006i | 0.190554 | − | 0.586464i | −0.809446 | − | 0.587194i | \(-0.800232\pi\) |
1.00000 | 0.000730306i | \(0.000232464\pi\) | ||||||||
\(500\) | 15.9036 | + | 11.5547i | 0.711232 | + | 0.516740i | ||||
\(501\) | 3.41449 | + | 2.48077i | 0.152548 | + | 0.110833i | ||||
\(502\) | 0.438114 | − | 1.34838i | 0.0195540 | − | 0.0601810i | ||||
\(503\) | 4.24711 | + | 13.0713i | 0.189369 | + | 0.582819i | 0.999996 | − | 0.00274417i | \(-0.000873499\pi\) |
−0.810627 | + | 0.585563i | \(0.800873\pi\) | |||||||
\(504\) | 12.6067 | − | 9.15932i | 0.561548 | − | 0.407989i | ||||
\(505\) | −23.1537 | −1.03033 | ||||||||
\(506\) | −13.3720 | − | 29.8538i | −0.594457 | − | 1.32716i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −35.8119 | + | 26.0188i | −1.58889 | + | 1.15440i | ||||
\(509\) | −2.03872 | − | 6.27454i | −0.0903648 | − | 0.278114i | 0.895653 | − | 0.444753i | \(-0.146709\pi\) |
−0.986018 | + | 0.166639i | \(0.946709\pi\) | |||||||
\(510\) | −18.0858 | + | 55.6624i | −0.800853 | + | 2.46477i | ||||
\(511\) | −3.84966 | − | 2.79694i | −0.170299 | − | 0.123729i | ||||
\(512\) | −125.503 | − | 91.1834i | −5.54651 | − | 4.02978i | ||||
\(513\) | −0.174485 | + | 0.537010i | −0.00770371 | + | 0.0237096i | ||||
\(514\) | 11.5008 | + | 35.3960i | 0.507281 | + | 1.56125i | ||||
\(515\) | 25.4924 | − | 18.5213i | 1.12333 | − | 0.816148i | ||||
\(516\) | 24.0489 | 1.05869 | ||||||||
\(517\) | 18.7655 | − | 2.01484i | 0.825305 | − | 0.0886127i | ||||
\(518\) | 5.56605 | 0.244558 | ||||||||
\(519\) | 4.15247 | − | 3.01694i | 0.182273 | − | 0.132429i | ||||
\(520\) | 10.9993 | + | 33.8523i | 0.482351 | + | 1.48452i | ||||
\(521\) | −11.4727 | + | 35.3094i | −0.502629 | + | 1.54693i | 0.302092 | + | 0.953279i | \(0.402315\pi\) |
−0.804721 | + | 0.593653i | \(0.797685\pi\) | |||||||
\(522\) | 3.61557 | + | 2.62686i | 0.158249 | + | 0.114975i | ||||
\(523\) | 12.4815 | + | 9.06835i | 0.545778 | + | 0.396531i | 0.826227 | − | 0.563338i | \(-0.190483\pi\) |
−0.280448 | + | 0.959869i | \(0.590483\pi\) | |||||||
\(524\) | −29.9272 | + | 92.1064i | −1.30738 | + | 4.02369i | ||||
\(525\) | 2.70100 | + | 8.31283i | 0.117881 | + | 0.362802i | ||||
\(526\) | 57.3551 | − | 41.6709i | 2.50080 | − | 1.81694i | ||||
\(527\) | 62.0419 | 2.70259 | ||||||||
\(528\) | 52.7726 | + | 30.3109i | 2.29663 | + | 1.31911i | ||||
\(529\) | −10.5796 | −0.459982 | ||||||||
\(530\) | −17.5980 | + | 12.7857i | −0.764408 | + | 0.555375i | ||||
\(531\) | −2.82208 | − | 8.68548i | −0.122468 | − | 0.376918i | ||||
\(532\) | −1.47860 | + | 4.55067i | −0.0641055 | + | 0.197297i | ||||
\(533\) | 2.95523 | + | 2.14710i | 0.128005 | + | 0.0930012i | ||||
\(534\) | −2.41444 | − | 1.75419i | −0.104483 | − | 0.0759112i | ||||
\(535\) | 6.84930 | − | 21.0800i | 0.296121 | − | 0.911367i | ||||
\(536\) | 20.7846 | + | 63.9683i | 0.897756 | + | 2.76301i | ||||
\(537\) | −16.9681 | + | 12.3281i | −0.732228 | + | 0.531995i | ||||
\(538\) | 73.2664 | 3.15874 | ||||||||
\(539\) | 12.0252 | − | 10.8764i | 0.517963 | − | 0.468481i | ||||
\(540\) | 19.3566 | 0.832977 | ||||||||
\(541\) | −4.14803 | + | 3.01372i | −0.178338 | + | 0.129570i | −0.673373 | − | 0.739303i | \(-0.735155\pi\) |
0.495035 | + | 0.868873i | \(0.335155\pi\) | |||||||
\(542\) | 15.7882 | + | 48.5910i | 0.678160 | + | 2.08716i | ||||
\(543\) | 3.09454 | − | 9.52401i | 0.132799 | − | 0.408714i | ||||
\(544\) | 152.437 | + | 110.752i | 6.53568 | + | 4.74845i | ||||
\(545\) | −17.8644 | − | 12.9792i | −0.765227 | − | 0.555970i | ||||
\(546\) | −1.25657 | + | 3.86734i | −0.0537764 | + | 0.165507i | ||||
\(547\) | −6.54167 | − | 20.1332i | −0.279702 | − | 0.860834i | −0.987937 | − | 0.154857i | \(-0.950508\pi\) |
0.708235 | − | 0.705977i | \(-0.249492\pi\) | |||||||
\(548\) | −5.67384 | + | 4.12229i | −0.242374 | + | 0.176095i | ||||
\(549\) | −2.73408 | −0.116688 | ||||||||
\(550\) | −41.4103 | + | 37.4543i | −1.76574 | + | 1.59706i | ||||
\(551\) | −0.901687 | −0.0384131 | ||||||||
\(552\) | −30.5777 | + | 22.2160i | −1.30147 | + | 0.945575i | ||||
\(553\) | 0.0461373 | + | 0.141996i | 0.00196196 | + | 0.00603828i | ||||
\(554\) | 12.0941 | − | 37.2219i | 0.513831 | − | 1.58141i | ||||
\(555\) | 3.67538 | + | 2.67032i | 0.156011 | + | 0.113349i | ||||
\(556\) | −96.9862 | − | 70.4646i | −4.11313 | − | 2.98837i | ||||
\(557\) | −1.21493 | + | 3.73918i | −0.0514784 | + | 0.158434i | −0.973491 | − | 0.228726i | \(-0.926544\pi\) |
0.922012 | + | 0.387160i | \(0.126544\pi\) | |||||||
\(558\) | −8.51519 | − | 26.2071i | −0.360477 | − | 1.10943i | ||||
\(559\) | −3.33601 | + | 2.42375i | −0.141098 | + | 0.102514i | ||||
\(560\) | 88.4893 | 3.73936 | ||||||||
\(561\) | −18.1217 | − | 10.4085i | −0.765100 | − | 0.439449i | ||||
\(562\) | 13.3598 | 0.563550 | ||||||||
\(563\) | 3.47682 | − | 2.52605i | 0.146530 | − | 0.106460i | −0.512105 | − | 0.858923i | \(-0.671134\pi\) |
0.658635 | + | 0.752462i | \(0.271134\pi\) | |||||||
\(564\) | −10.2556 | − | 31.5635i | −0.431839 | − | 1.32906i | ||||
\(565\) | 11.4111 | − | 35.1196i | 0.480067 | − | 1.47749i | ||||
\(566\) | −48.0569 | − | 34.9154i | −2.01998 | − | 1.46760i | ||||
\(567\) | 1.17550 | + | 0.854053i | 0.0493665 | + | 0.0358669i | ||||
\(568\) | 0.587980 | − | 1.80962i | 0.0246711 | − | 0.0759299i | ||||
\(569\) | 10.4358 | + | 32.1181i | 0.437491 | + | 1.34646i | 0.890512 | + | 0.454959i | \(0.150346\pi\) |
−0.453021 | + | 0.891500i | \(0.649654\pi\) | |||||||
\(570\) | −4.24304 | + | 3.08275i | −0.177721 | + | 0.129122i | ||||
\(571\) | 46.5604 | 1.94849 | 0.974245 | − | 0.225491i | \(-0.0723985\pi\) | ||||
0.974245 | + | 0.225491i | \(0.0723985\pi\) | |||||||
\(572\) | −19.2324 | + | 2.06498i | −0.804147 | + | 0.0863410i | ||||
\(573\) | −0.845601 | −0.0353255 | ||||||||
\(574\) | 12.0170 | − | 8.73088i | 0.501581 | − | 0.364420i | ||||
\(575\) | −6.55129 | − | 20.1628i | −0.273208 | − | 0.840847i | ||||
\(576\) | 14.5203 | − | 44.6887i | 0.605010 | − | 1.86203i | ||||
\(577\) | 22.6409 | + | 16.4496i | 0.942552 | + | 0.684804i | 0.949033 | − | 0.315175i | \(-0.102063\pi\) |
−0.00648198 | + | 0.999979i | \(0.502063\pi\) | |||||||
\(578\) | −51.4024 | − | 37.3461i | −2.13806 | − | 1.55339i | ||||
\(579\) | −6.35696 | + | 19.5647i | −0.264186 | + | 0.813081i | ||||
\(580\) | 9.55194 | + | 29.3978i | 0.396623 | + | 1.22068i | ||||
\(581\) | −16.3845 | + | 11.9041i | −0.679745 | + | 0.493863i | ||||
\(582\) | 40.8469 | 1.69316 | ||||||||
\(583\) | −3.17505 | − | 7.08850i | −0.131497 | − | 0.293576i | ||||
\(584\) | −35.1218 | −1.45335 | ||||||||
\(585\) | −2.68510 | + | 1.95084i | −0.111015 | + | 0.0806574i | ||||
\(586\) | 13.8145 | + | 42.5165i | 0.570670 | + | 1.75634i | ||||
\(587\) | −12.4171 | + | 38.2158i | −0.512507 | + | 1.57733i | 0.275265 | + | 0.961368i | \(0.411234\pi\) |
−0.787773 | + | 0.615966i | \(0.788766\pi\) | |||||||
\(588\) | −23.0667 | − | 16.7589i | −0.951254 | − | 0.691126i | ||||
\(589\) | 4.49787 | + | 3.26789i | 0.185331 | + | 0.134651i | ||||
\(590\) | 26.2128 | − | 80.6746i | 1.07916 | − | 3.32132i | ||||
\(591\) | 8.66724 | + | 26.6750i | 0.356523 | + | 1.09726i | ||||
\(592\) | 20.3199 | − | 14.7632i | 0.835141 | − | 0.606765i | ||||
\(593\) | 13.8199 | 0.567514 | 0.283757 | − | 0.958896i | \(-0.408419\pi\) | ||||
0.283757 | + | 0.958896i | \(0.408419\pi\) | |||||||
\(594\) | −1.90947 | + | 9.08335i | −0.0783464 | + | 0.372694i | ||||
\(595\) | −30.3866 | −1.24573 | ||||||||
\(596\) | 10.4235 | − | 7.57314i | 0.426965 | − | 0.310208i | ||||
\(597\) | 2.66788 | + | 8.21090i | 0.109189 | + | 0.336050i | ||||
\(598\) | 3.04783 | − | 9.38024i | 0.124635 | − | 0.383587i | ||||
\(599\) | −12.7630 | − | 9.27283i | −0.521480 | − | 0.378878i | 0.295681 | − | 0.955287i | \(-0.404453\pi\) |
−0.817161 | + | 0.576409i | \(0.804453\pi\) | |||||||
\(600\) | 52.1931 | + | 37.9205i | 2.13077 | + | 1.54810i | ||||
\(601\) | 7.82421 | − | 24.0804i | 0.319156 | − | 0.982262i | −0.654854 | − | 0.755756i | \(-0.727270\pi\) |
0.974010 | − | 0.226506i | \(-0.0727303\pi\) | |||||||
\(602\) | 5.18152 | + | 15.9471i | 0.211183 | + | 0.649955i | ||||
\(603\) | −5.07385 | + | 3.68637i | −0.206623 | + | 0.150120i | ||||
\(604\) | −69.6385 | −2.83355 | ||||||||
\(605\) | −18.3958 | − | 31.5353i | −0.747896 | − | 1.28209i | ||||
\(606\) | −19.5234 | −0.793085 | ||||||||
\(607\) | −19.9390 | + | 14.4865i | −0.809298 | + | 0.587989i | −0.913627 | − | 0.406554i | \(-0.866730\pi\) |
0.104329 | + | 0.994543i | \(0.466730\pi\) | |||||||
\(608\) | 5.21769 | + | 16.0584i | 0.211605 | + | 0.651254i | ||||
\(609\) | −0.717014 | + | 2.20674i | −0.0290549 | + | 0.0894217i | ||||
\(610\) | −20.5453 | − | 14.9270i | −0.831854 | − | 0.604377i | ||||
\(611\) | 4.60373 | + | 3.34481i | 0.186247 | + | 0.135316i | ||||
\(612\) | −11.3559 | + | 34.9498i | −0.459035 | + | 1.41276i | ||||
\(613\) | 8.08207 | + | 24.8740i | 0.326432 | + | 1.00465i | 0.970790 | + | 0.239930i | \(0.0771244\pi\) |
−0.644359 | + | 0.764723i | \(0.722876\pi\) | |||||||
\(614\) | −24.4131 | + | 17.7372i | −0.985233 | + | 0.715814i | ||||
\(615\) | 12.1237 | 0.488877 | ||||||||
\(616\) | −10.6321 | + | 50.5768i | −0.428378 | + | 2.03780i | ||||
\(617\) | −34.0203 | −1.36960 | −0.684802 | − | 0.728729i | \(-0.740111\pi\) | ||||
−0.684802 | + | 0.728729i | \(0.740111\pi\) | |||||||
\(618\) | 21.4955 | − | 15.6174i | 0.864676 | − | 0.628224i | ||||
\(619\) | −6.57446 | − | 20.2341i | −0.264250 | − | 0.813277i | −0.991865 | − | 0.127292i | \(-0.959371\pi\) |
0.727616 | − | 0.685985i | \(-0.240629\pi\) | |||||||
\(620\) | 58.8958 | − | 181.263i | 2.36531 | − | 7.27969i | ||||
\(621\) | −2.85119 | − | 2.07151i | −0.114414 | − | 0.0831268i | ||||
\(622\) | 19.0641 | + | 13.8509i | 0.764401 | + | 0.555370i | ||||
\(623\) | 0.478814 | − | 1.47364i | 0.0191833 | − | 0.0590401i | ||||
\(624\) | 5.67027 | + | 17.4513i | 0.226992 | + | 0.698611i | ||||
\(625\) | 15.2830 | − | 11.1037i | 0.611319 | − | 0.444149i | ||||
\(626\) | 31.1999 | 1.24700 | ||||||||
\(627\) | −0.765534 | − | 1.70910i | −0.0305725 | − | 0.0682550i | ||||
\(628\) | 74.9895 | 2.99241 | ||||||||
\(629\) | −6.97769 | + | 5.06959i | −0.278219 | + | 0.202138i | ||||
\(630\) | 4.17053 | + | 12.8356i | 0.166158 | + | 0.511382i | ||||
\(631\) | −0.786766 | + | 2.42142i | −0.0313207 | + | 0.0963951i | −0.965495 | − | 0.260422i | \(-0.916138\pi\) |
0.934174 | + | 0.356817i | \(0.116138\pi\) | |||||||
\(632\) | 0.891537 | + | 0.647740i | 0.0354635 | + | 0.0257657i | ||||
\(633\) | −8.72149 | − | 6.33654i | −0.346648 | − | 0.251855i | ||||
\(634\) | 15.9992 | − | 49.2404i | 0.635408 | − | 1.95559i | ||||
\(635\) | −7.78446 | − | 23.9581i | −0.308917 | − | 0.950749i | ||||
\(636\) | −11.0496 | + | 8.02800i | −0.438145 | + | 0.318331i | ||||
\(637\) | 4.88879 | 0.193701 | ||||||||
\(638\) | −14.7376 | + | 1.58237i | −0.583467 | + | 0.0626466i | ||||
\(639\) | 0.177420 | 0.00701861 | ||||||||
\(640\) | 192.509 | − | 139.866i | 7.60957 | − | 5.52868i | ||||
\(641\) | −14.4758 | − | 44.5520i | −0.571760 | − | 1.75970i | −0.646955 | − | 0.762528i | \(-0.723958\pi\) |
0.0751953 | − | 0.997169i | \(-0.476042\pi\) | |||||||
\(642\) | 5.77540 | − | 17.7749i | 0.227937 | − | 0.701518i | ||||
\(643\) | −32.5566 | − | 23.6538i | −1.28391 | − | 0.932814i | −0.284245 | − | 0.958752i | \(-0.591743\pi\) |
−0.999664 | + | 0.0259373i | \(0.991743\pi\) | |||||||
\(644\) | −24.1612 | − | 17.5541i | −0.952084 | − | 0.691730i | ||||
\(645\) | −4.22917 | + | 13.0160i | −0.166523 | + | 0.512506i | ||||
\(646\) | −3.07688 | − | 9.46967i | −0.121058 | − | 0.372579i | ||||
\(647\) | 19.0509 | − | 13.8413i | 0.748969 | − | 0.544158i | −0.146538 | − | 0.989205i | \(-0.546813\pi\) |
0.895507 | + | 0.445047i | \(0.146813\pi\) | |||||||
\(648\) | 10.7245 | 0.421300 | ||||||||
\(649\) | 26.2648 | + | 15.0857i | 1.03098 | + | 0.592164i | ||||
\(650\) | −16.8351 | −0.660328 | ||||||||
\(651\) | 11.5743 | − | 8.40925i | 0.453634 | − | 0.329584i | ||||
\(652\) | 32.6194 | + | 100.392i | 1.27748 | + | 3.93166i | ||||
\(653\) | 13.1703 | − | 40.5341i | 0.515395 | − | 1.58622i | −0.267167 | − | 0.963650i | \(-0.586088\pi\) |
0.782562 | − | 0.622573i | \(-0.213912\pi\) | |||||||
\(654\) | −15.0635 | − | 10.9442i | −0.589028 | − | 0.427954i | ||||
\(655\) | −44.5880 | − | 32.3951i | −1.74220 | − | 1.26578i | ||||
\(656\) | 20.7127 | − | 63.7472i | 0.808696 | − | 2.48891i | ||||
\(657\) | −1.01200 | − | 3.11462i | −0.0394819 | − | 0.121513i | ||||
\(658\) | 18.7204 | − | 13.6012i | 0.729799 | − | 0.530230i | ||||
\(659\) | −25.4615 | −0.991841 | −0.495920 | − | 0.868368i | \(-0.665169\pi\) | ||||
−0.495920 | + | 0.868368i | \(0.665169\pi\) | |||||||
\(660\) | −47.6126 | + | 43.0641i | −1.85332 | + | 1.67627i | ||||
\(661\) | −14.6713 | −0.570648 | −0.285324 | − | 0.958431i | \(-0.592101\pi\) | ||||
−0.285324 | + | 0.958431i | \(0.592101\pi\) | |||||||
\(662\) | 36.3339 | − | 26.3981i | 1.41216 | − | 1.02599i | ||||
\(663\) | −1.94713 | − | 5.99265i | −0.0756203 | − | 0.232735i | ||||
\(664\) | −46.1925 | + | 142.166i | −1.79262 | + | 5.51710i | ||||
\(665\) | −2.20294 | − | 1.60053i | −0.0854265 | − | 0.0620660i | ||||
\(666\) | 3.09912 | + | 2.25165i | 0.120089 | + | 0.0872495i | ||||
\(667\) | 1.73912 | − | 5.35246i | 0.0673390 | − | 0.207248i | ||||
\(668\) | 7.60637 | + | 23.4100i | 0.294299 | + | 0.905760i | ||||
\(669\) | 20.6592 | − | 15.0098i | 0.798730 | − | 0.580311i | ||||
\(670\) | −58.2536 | −2.25053 | ||||||||
\(671\) | 6.72517 | − | 6.08270i | 0.259622 | − | 0.234820i | ||||
\(672\) | 43.4496 | 1.67611 | ||||||||
\(673\) | 27.0932 | − | 19.6843i | 1.04437 | − | 0.758776i | 0.0732322 | − | 0.997315i | \(-0.476669\pi\) |
0.971133 | + | 0.238539i | \(0.0766686\pi\) | |||||||
\(674\) | 17.5640 | + | 54.0564i | 0.676539 | + | 2.08217i | ||||
\(675\) | −1.85891 | + | 5.72114i | −0.0715496 | + | 0.220207i | ||||
\(676\) | −4.71828 | − | 3.42803i | −0.181472 | − | 0.131847i | ||||
\(677\) | −12.3527 | − | 8.97475i | −0.474752 | − | 0.344928i | 0.324538 | − | 0.945873i | \(-0.394791\pi\) |
−0.799290 | + | 0.600945i | \(0.794791\pi\) | |||||||
\(678\) | 9.62193 | − | 29.6133i | 0.369528 | − | 1.13729i | ||||
\(679\) | 6.55342 | + | 20.1693i | 0.251497 | + | 0.774029i | ||||
\(680\) | −181.448 | + | 131.830i | −6.95821 | + | 5.05544i | ||||
\(681\) | −3.75572 | −0.143919 | ||||||||
\(682\) | 79.2500 | + | 45.5186i | 3.03464 | + | 1.74300i | ||||
\(683\) | −37.3798 | −1.43030 | −0.715149 | − | 0.698972i | \(-0.753641\pi\) | ||||
−0.715149 | + | 0.698972i | \(0.753641\pi\) | |||||||
\(684\) | −2.66416 | + | 1.93563i | −0.101867 | + | 0.0740105i | ||||
\(685\) | −1.23333 | − | 3.79580i | −0.0471231 | − | 0.145030i | ||||
\(686\) | 14.9391 | − | 45.9779i | 0.570379 | − | 1.75545i | ||||
\(687\) | −6.92165 | − | 5.02887i | −0.264078 | − | 0.191864i | ||||
\(688\) | 61.2136 | + | 44.4743i | 2.33375 | + | 1.69557i | ||||
\(689\) | 0.723677 | − | 2.22725i | 0.0275699 | − | 0.0848514i | ||||
\(690\) | −10.1156 | − | 31.1328i | −0.385096 | − | 1.18520i | ||||
\(691\) | −29.1368 | + | 21.1691i | −1.10841 | + | 0.805310i | −0.982413 | − | 0.186720i | \(-0.940214\pi\) |
−0.126001 | + | 0.992030i | \(0.540214\pi\) | |||||||
\(692\) | 29.9347 | 1.13795 | ||||||||
\(693\) | −4.79152 | + | 0.514464i | −0.182015 | + | 0.0195429i | ||||
\(694\) | 44.3436 | 1.68326 | ||||||||
\(695\) | 55.1934 | − | 40.1003i | 2.09360 | − | 1.52109i | ||||
\(696\) | 5.29225 | + | 16.2879i | 0.200602 | + | 0.617390i | ||||
\(697\) | −7.11260 | + | 21.8903i | −0.269409 | + | 0.829155i | ||||
\(698\) | 26.9379 | + | 19.5716i | 1.01962 | + | 0.740795i | ||||
\(699\) | −0.641360 | − | 0.465975i | −0.0242585 | − | 0.0176248i | ||||
\(700\) | −15.7526 | + | 48.4814i | −0.595391 | + | 1.83243i | ||||
\(701\) | 1.99272 | + | 6.13297i | 0.0752641 | + | 0.231639i | 0.981610 | − | 0.190897i | \(-0.0611398\pi\) |
−0.906346 | + | 0.422537i | \(0.861140\pi\) | |||||||
\(702\) | −2.26411 | + | 1.64497i | −0.0854533 | + | 0.0620854i | ||||
\(703\) | −0.772891 | −0.0291501 | ||||||||
\(704\) | 63.7059 | + | 142.228i | 2.40101 | + | 5.36040i | ||||
\(705\) | 18.8867 | 0.711314 | ||||||||
\(706\) | −36.4996 | + | 26.5185i | −1.37368 | + | 0.998038i | ||||
\(707\) | −3.13231 | − | 9.64026i | −0.117803 | − | 0.362559i | ||||
\(708\) | 16.4587 | − | 50.6547i | 0.618557 | − | 1.90372i | ||||
\(709\) | 38.2892 | + | 27.8187i | 1.43798 | + | 1.04475i | 0.988460 | + | 0.151483i | \(0.0484049\pi\) |
0.449520 | + | 0.893270i | \(0.351595\pi\) | |||||||
\(710\) | 1.33322 | + | 0.968642i | 0.0500349 | + | 0.0363525i | ||||
\(711\) | −0.0317531 | + | 0.0977259i | −0.00119083 | + | 0.00366501i | ||||
\(712\) | −3.53410 | − | 10.8769i | −0.132446 | − | 0.407627i | ||||
\(713\) | −28.0736 | + | 20.3967i | −1.05136 | + | 0.763861i | ||||
\(714\) | −25.6223 | −0.958891 | ||||||||
\(715\) | 2.26452 | − | 10.7723i | 0.0846883 | − | 0.402862i | ||||
\(716\) | −122.321 | −4.57136 | ||||||||
\(717\) | −8.77773 | + | 6.37740i | −0.327810 | + | 0.238168i | ||||
\(718\) | −4.65153 | − | 14.3160i | −0.173594 | − | 0.534267i | ||||
\(719\) | −3.91576 | + | 12.0515i | −0.146033 | + | 0.449444i | −0.997142 | − | 0.0755446i | \(-0.975930\pi\) |
0.851109 | + | 0.524989i | \(0.175930\pi\) | |||||||
\(720\) | 49.2700 | + | 35.7967i | 1.83618 | + | 1.33407i | ||||
\(721\) | 11.1603 | + | 8.10840i | 0.415630 | + | 0.301973i | ||||
\(722\) | −16.1557 | + | 49.7222i | −0.601253 | + | 1.85047i | ||||
\(723\) | −3.25010 | − | 10.0028i | −0.120873 | − | 0.372007i | ||||
\(724\) | 47.2495 | − | 34.3288i | 1.75601 | − | 1.27582i | ||||
\(725\) | −9.60629 | −0.356769 | ||||||||
\(726\) | −15.5115 | − | 26.5909i | −0.575687 | − | 0.986883i | ||||
\(727\) | −3.68862 | −0.136803 | −0.0684017 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684017 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(728\) | −12.6067 | + | 9.15932i | −0.467236 | + | 0.339467i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 9.39991 | − | 28.9299i | 0.347906 | − | 1.07075i | ||||
\(731\) | −21.0203 | − | 15.2722i | −0.777465 | − | 0.564861i | ||||
\(732\) | −12.9002 | − | 9.37252i | −0.476804 | − | 0.346418i | ||||
\(733\) | −5.41476 | + | 16.6649i | −0.199999 | + | 0.615532i | 0.799883 | + | 0.600156i | \(0.204895\pi\) |
−0.999882 | + | 0.0153766i | \(0.995105\pi\) | |||||||
\(734\) | −23.3098 | − | 71.7400i | −0.860379 | − | 2.64797i | ||||
\(735\) | 13.1269 | − | 9.53725i | 0.484193 | − | 0.351787i | ||||
\(736\) | −105.387 | −3.88462 | ||||||||
\(737\) | 4.27910 | − | 20.3557i | 0.157623 | − | 0.749812i | ||||
\(738\) | 10.2229 | 0.376309 | ||||||||
\(739\) | −28.1312 | + | 20.4385i | −1.03482 | + | 0.751844i | −0.969269 | − | 0.246005i | \(-0.920882\pi\) |
−0.0655559 | + | 0.997849i | \(0.520882\pi\) | |||||||
\(740\) | 8.18755 | + | 25.1987i | 0.300980 | + | 0.926322i | ||||
\(741\) | 0.174485 | − | 0.537010i | 0.00640988 | − | 0.0197276i | ||||
\(742\) | −7.70417 | − | 5.59740i | −0.282829 | − | 0.205487i | ||||
\(743\) | 32.6343 | + | 23.7102i | 1.19724 | + | 0.869843i | 0.994010 | − | 0.109289i | \(-0.0348574\pi\) |
0.203226 | + | 0.979132i | \(0.434857\pi\) | |||||||
\(744\) | 32.6312 | − | 100.429i | 1.19632 | − | 3.68189i | ||||
\(745\) | 2.26578 | + | 6.97334i | 0.0830116 | + | 0.255483i | ||||
\(746\) | 59.9272 | − | 43.5397i | 2.19409 | − | 1.59410i | ||||
\(747\) | −13.9383 | −0.509976 | ||||||||
\(748\) | −49.8227 | − | 111.232i | −1.82170 | − | 4.06706i | ||||
\(749\) | 9.70346 | 0.354557 | ||||||||
\(750\) | −7.63149 | + | 5.54461i | −0.278663 | + | 0.202460i | ||||
\(751\) | 8.04575 | + | 24.7623i | 0.293594 | + | 0.903588i | 0.983690 | + | 0.179871i | \(0.0575680\pi\) |
−0.690097 | + | 0.723717i | \(0.742432\pi\) | |||||||
\(752\) | 32.2668 | − | 99.3071i | 1.17665 | − | 3.62136i | ||||
\(753\) | 0.409848 | + | 0.297772i | 0.0149357 | + | 0.0108514i | ||||
\(754\) | −3.61557 | − | 2.62686i | −0.131671 | − | 0.0956648i | ||||
\(755\) | 12.2464 | − | 37.6906i | 0.445693 | − | 1.37170i | ||||
\(756\) | 2.61863 | + | 8.05933i | 0.0952388 | + | 0.293115i | ||||
\(757\) | 5.97447 | − | 4.34071i | 0.217146 | − | 0.157766i | −0.473895 | − | 0.880581i | \(-0.657152\pi\) |
0.691041 | + | 0.722816i | \(0.257152\pi\) | |||||||
\(758\) | 4.79556 | 0.174182 | ||||||||
\(759\) | 11.6219 | − | 1.24783i | 0.421847 | − | 0.0452935i | ||||
\(760\) | −20.0983 | −0.729041 | ||||||||
\(761\) | 12.1032 | − | 8.79351i | 0.438741 | − | 0.318764i | −0.346393 | − | 0.938089i | \(-0.612594\pi\) |
0.785135 | + | 0.619325i | \(0.212594\pi\) | |||||||
\(762\) | −6.56394 | − | 20.2017i | −0.237787 | − | 0.731832i | ||||
\(763\) | 2.98728 | − | 9.19390i | 0.108147 | − | 0.332842i | ||||
\(764\) | −3.98978 | − | 2.89875i | −0.144345 | − | 0.104873i | ||||
\(765\) | −16.9190 | − | 12.2923i | −0.611706 | − | 0.444431i | ||||
\(766\) | −10.7602 | + | 33.1164i | −0.388781 | + | 1.19655i | ||||
\(767\) | 2.82208 | + | 8.68548i | 0.101900 | + | 0.313614i | ||||
\(768\) | 86.2963 | − | 62.6979i | 3.11395 | − | 2.26242i | ||||
\(769\) | −43.2060 | −1.55805 | −0.779024 | − | 0.626994i | \(-0.784285\pi\) | ||||
−0.779024 | + | 0.626994i | \(0.784285\pi\) | |||||||
\(770\) | −38.8147 | − | 22.2939i | −1.39879 | − | 0.803417i | ||||
\(771\) | −13.2987 | −0.478939 | ||||||||
\(772\) | −97.0624 | + | 70.5199i | −3.49335 | + | 2.53807i | ||||
\(773\) | 5.86015 | + | 18.0357i | 0.210775 | + | 0.648699i | 0.999427 | + | 0.0338586i | \(0.0107796\pi\) |
−0.788652 | + | 0.614840i | \(0.789220\pi\) | |||||||
\(774\) | −3.56608 | + | 10.9753i | −0.128180 | + | 0.394498i | ||||
\(775\) | 47.9189 | + | 34.8151i | 1.72130 | + | 1.25060i | ||||
\(776\) | 126.636 | + | 92.0061i | 4.54595 | + | 3.30283i | ||||
\(777\) | −0.614597 | + | 1.89153i | −0.0220485 | + | 0.0678584i | ||||
\(778\) | −6.43308 | − | 19.7990i | −0.230637 | − | 0.709828i | ||||
\(779\) | −1.66866 | + | 1.21235i | −0.0597859 | + | 0.0434370i | ||||
\(780\) | −19.3566 | −0.693079 | ||||||||
\(781\) | −0.436409 | + | 0.394718i | −0.0156159 | + | 0.0141241i | ||||
\(782\) | 62.1470 | 2.22237 | ||||||||
\(783\) | −1.29192 | + | 0.938638i | −0.0461696 | + | 0.0335442i | ||||
\(784\) | −27.7207 | − | 85.3156i | −0.990026 | − | 3.04699i | ||||
\(785\) | −13.1874 | + | 40.5867i | −0.470679 | + | 1.44860i | ||||
\(786\) | −37.5971 | − | 27.3159i | −1.34104 | − | 0.974326i | ||||
\(787\) | −14.2971 | − | 10.3874i | −0.509636 | − | 0.370272i | 0.303049 | − | 0.952975i | \(-0.401995\pi\) |
−0.812686 | + | 0.582702i | \(0.801995\pi\) | |||||||
\(788\) | −50.5484 | + | 155.572i | −1.80071 | + | 5.54202i | ||||
\(789\) | 7.82812 | + | 24.0925i | 0.278688 | + | 0.857715i | ||||
\(790\) | −0.772154 | + | 0.561003i | −0.0274720 | + | 0.0199596i | ||||
\(791\) | 16.1661 | 0.574802 | ||||||||
\(792\) | −26.3797 | + | 23.8596i | −0.937363 | + | 0.847815i | ||||
\(793\) | 2.73408 | 0.0970900 | ||||||||
\(794\) | 21.7481 | − | 15.8009i | 0.771810 | − | 0.560753i | ||||
\(795\) | −2.40186 | − | 7.39217i | −0.0851853 | − | 0.262173i | ||||
\(796\) | −15.5594 | + | 47.8869i | −0.551489 | + | 1.69731i | ||||
\(797\) | −41.6958 | − | 30.2937i | −1.47694 | − | 1.07306i | −0.978527 | − | 0.206120i | \(-0.933916\pi\) |
−0.498413 | − | 0.866940i | \(-0.666084\pi\) | |||||||
\(798\) | −1.85755 | − | 1.34959i | −0.0657565 | − | 0.0477749i | ||||
\(799\) | −11.0802 | + | 34.1013i | −0.391989 | + | 1.20642i | ||||
\(800\) | 55.5877 | + | 171.081i | 1.96532 | + | 6.04864i | ||||
\(801\) | 0.862732 | − | 0.626812i | 0.0304831 | − | 0.0221473i | ||||
\(802\) | −44.4260 | −1.56874 | ||||||||
\(803\) | 9.41858 | + | 5.40972i | 0.332374 | + | 0.190905i | ||||
\(804\) | −36.5768 | −1.28997 | ||||||||
\(805\) | 13.7498 | − | 9.98979i | 0.484616 | − | 0.352094i | ||||
\(806\) | 8.51519 | + | 26.2071i | 0.299935 | + | 0.923105i | ||||
\(807\) | −8.08998 | + | 24.8984i | −0.284781 | + | 0.876466i | ||||
\(808\) | −60.5275 | − | 43.9758i | −2.12935 | − | 1.54706i | ||||
\(809\) | 37.4295 | + | 27.1941i | 1.31595 | + | 0.956093i | 0.999973 | + | 0.00732641i | \(0.00233209\pi\) |
0.315977 | + | 0.948767i | \(0.397668\pi\) | |||||||
\(810\) | −2.87029 | + | 8.83384i | −0.100852 | + | 0.310389i | ||||
\(811\) | −15.1093 | − | 46.5016i | −0.530559 | − | 1.63289i | −0.753055 | − | 0.657958i | \(-0.771420\pi\) |
0.222496 | − | 0.974934i | \(-0.428580\pi\) | |||||||
\(812\) | −10.9479 | + | 7.95409i | −0.384195 | + | 0.279134i | ||||
\(813\) | −18.2562 | −0.640272 | ||||||||
\(814\) | −12.6325 | + | 1.35634i | −0.442768 | + | 0.0475399i | ||||
\(815\) | −60.0718 | −2.10422 | ||||||||
\(816\) | −93.5387 | + | 67.9599i | −3.27451 | + | 2.37907i | ||||
\(817\) | −0.719495 | − | 2.21438i | −0.0251720 | − | 0.0774713i | ||||
\(818\) | −1.92447 | + | 5.92292i | −0.0672876 | + | 0.207090i | ||||
\(819\) | −1.17550 | − | 0.854053i | −0.0410754 | − | 0.0298430i | ||||
\(820\) | 57.2033 | + | 41.5606i | 1.99763 | + | 1.45136i | ||||
\(821\) | 8.57194 | − | 26.3817i | 0.299163 | − | 0.920729i | −0.682628 | − | 0.730766i | \(-0.739163\pi\) |
0.981791 | − | 0.189963i | \(-0.0608368\pi\) | |||||||
\(822\) | −1.03996 | − | 3.20066i | −0.0362726 | − | 0.111636i | ||||
\(823\) | 9.26950 | − | 6.73468i | 0.323114 | − | 0.234756i | −0.414389 | − | 0.910100i | \(-0.636005\pi\) |
0.737503 | + | 0.675344i | \(0.236005\pi\) | |||||||
\(824\) | 101.819 | 3.54703 | ||||||||
\(825\) | −8.15577 | − | 18.2083i | −0.283947 | − | 0.633931i | ||||
\(826\) | 37.1358 | 1.29212 | ||||||||
\(827\) | −40.3450 | + | 29.3124i | −1.40293 | + | 1.01929i | −0.408631 | + | 0.912700i | \(0.633994\pi\) |
−0.994303 | + | 0.106592i | \(0.966006\pi\) | |||||||
\(828\) | −6.35151 | − | 19.5479i | −0.220730 | − | 0.679338i | ||||
\(829\) | −4.11804 | + | 12.6740i | −0.143025 | + | 0.440187i | −0.996752 | − | 0.0805350i | \(-0.974337\pi\) |
0.853726 | + | 0.520722i | \(0.174337\pi\) | |||||||
\(830\) | −104.740 | − | 76.0978i | −3.63556 | − | 2.64139i | ||||
\(831\) | 11.3139 | + | 8.22000i | 0.392473 | + | 0.285149i | ||||
\(832\) | −14.5203 | + | 44.6887i | −0.503399 | + | 1.54930i | ||||
\(833\) | 9.51910 | + | 29.2968i | 0.329817 | + | 1.01507i | ||||
\(834\) | 46.5397 | − | 33.8130i | 1.61154 | − | 1.17085i | ||||
\(835\) | −14.0079 | −0.484762 | ||||||||
\(836\) | 2.24686 | − | 10.6883i | 0.0777092 | − | 0.369663i | ||||
\(837\) | 9.84629 | 0.340337 | ||||||||
\(838\) | −72.3711 | + | 52.5807i | −2.50002 | + | 1.81637i | ||||
\(839\) | 1.91070 | + | 5.88051i | 0.0659645 | + | 0.203018i | 0.978606 | − | 0.205743i | \(-0.0659610\pi\) |
−0.912642 | + | 0.408761i | \(0.865961\pi\) | |||||||
\(840\) | −15.9820 | + | 49.1875i | −0.551431 | + | 1.69713i | ||||
\(841\) | 21.3984 | + | 15.5469i | 0.737876 | + | 0.536098i | ||||
\(842\) | −35.0175 | − | 25.4417i | −1.20678 | − | 0.876780i | ||||
\(843\) | −1.47518 | + | 4.54012i | −0.0508077 | + | 0.156370i | ||||
\(844\) | −19.4286 | − | 59.7951i | −0.668761 | − | 2.05823i | ||||
\(845\) | 2.68510 | − | 1.95084i | 0.0923704 | − | 0.0671110i | ||||
\(846\) | 15.9255 | 0.547529 | ||||||||
\(847\) | 10.6414 | − | 11.9255i | 0.365643 | − | 0.409765i | ||||
\(848\) | −42.9718 | −1.47566 | ||||||||
\(849\) | 17.1718 | − | 12.4761i | 0.589335 | − | 0.428177i | ||||
\(850\) | −32.7802 | − | 100.887i | −1.12435 | − | 3.46040i | ||||
\(851\) | 1.49071 | − | 4.58792i | 0.0511008 | − | 0.157272i | ||||
\(852\) | 0.837116 | + | 0.608201i | 0.0286791 | + | 0.0208366i | ||||
\(853\) | −14.1104 | − | 10.2518i | −0.483132 | − | 0.351016i | 0.319405 | − | 0.947618i | \(-0.396517\pi\) |
−0.802537 | + | 0.596602i | \(0.796517\pi\) | |||||||
\(854\) | 3.43557 | − | 10.5736i | 0.117563 | − | 0.361822i | ||||
\(855\) | −0.579112 | − | 1.78232i | −0.0198052 | − | 0.0609541i | ||||
\(856\) | 57.9424 | − | 42.0976i | 1.98043 | − | 1.43887i | ||||
\(857\) | −48.0265 | −1.64055 | −0.820276 | − | 0.571967i | \(-0.806180\pi\) | ||||
−0.820276 | + | 0.571967i | \(0.806180\pi\) | |||||||
\(858\) | 1.90947 | − | 9.08335i | 0.0651882 | − | 0.310100i | ||||
\(859\) | −51.2114 | −1.74731 | −0.873655 | − | 0.486546i | \(-0.838257\pi\) | ||||
−0.873655 | + | 0.486546i | \(0.838257\pi\) | |||||||
\(860\) | −64.5738 | + | 46.9156i | −2.20195 | + | 1.59981i | ||||
\(861\) | 1.64014 | + | 5.04784i | 0.0558960 | + | 0.172030i | ||||
\(862\) | 2.23694 | − | 6.88461i | 0.0761906 | − | 0.234491i | ||||
\(863\) | 29.2239 | + | 21.2324i | 0.994791 | + | 0.722758i | 0.960965 | − | 0.276669i | \(-0.0892307\pi\) |
0.0338263 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(864\) | 24.1923 | + | 17.5767i | 0.823039 | + | 0.597973i | ||||
\(865\) | −5.26423 | + | 16.2016i | −0.178989 | + | 0.550872i | ||||
\(866\) | 0.0935753 | + | 0.287995i | 0.00317982 | + | 0.00978648i | ||||
\(867\) | 18.3672 | − | 13.3446i | 0.623784 | − | 0.453206i | ||||
\(868\) | 83.4382 | 2.83208 | ||||||||
\(869\) | −0.139313 | − | 0.311025i | −0.00472587 | − | 0.0105508i | ||||
\(870\) | −14.8328 | −0.502878 | ||||||||
\(871\) | 5.07385 | − | 3.68637i | 0.171921 | − | 0.124908i | ||||
\(872\) | −22.0490 | − | 67.8598i | −0.746673 | − | 2.29802i | ||||
\(873\) | −4.51026 | + | 13.8812i | −0.152649 | + | 0.469806i | ||||
\(874\) | 4.50549 | + | 3.27343i | 0.152400 | + | 0.110725i | ||||
\(875\) | −3.96220 | − | 2.87870i | −0.133947 | − | 0.0973180i | ||||
\(876\) | 5.90211 | − | 18.1648i | 0.199414 | − | 0.613732i | ||||
\(877\) | 10.3355 | + | 31.8094i | 0.349005 | + | 1.07413i | 0.959404 | + | 0.282034i | \(0.0910091\pi\) |
−0.610399 | + | 0.792094i | \(0.708991\pi\) | |||||||
\(878\) | −12.3454 | + | 8.96944i | −0.416636 | + | 0.302704i | ||||
\(879\) | −15.9739 | −0.538788 | ||||||||
\(880\) | −200.832 | + | 21.5632i | −6.77003 | + | 0.726896i | ||||
\(881\) | −41.7535 | −1.40671 | −0.703355 | − | 0.710839i | \(-0.748316\pi\) | ||||
−0.703355 | + | 0.710839i | \(0.748316\pi\) | |||||||
\(882\) | 11.0687 | − | 8.04191i | 0.372704 | − | 0.270785i | ||||
\(883\) | −6.08964 | − | 18.7420i | −0.204933 | − | 0.630717i | −0.999716 | − | 0.0238246i | \(-0.992416\pi\) |
0.794784 | − | 0.606893i | \(-0.207584\pi\) | |||||||
\(884\) | 11.3559 | − | 34.9498i | 0.381940 | − | 1.17549i | ||||
\(885\) | 24.5216 | + | 17.8160i | 0.824284 | + | 0.598877i | ||||
\(886\) | 69.2852 | + | 50.3387i | 2.32768 | + | 1.69116i | ||||
\(887\) | 2.57577 | − | 7.92740i | 0.0864858 | − | 0.266176i | −0.898456 | − | 0.439064i | \(-0.855310\pi\) |
0.984941 | + | 0.172888i | \(0.0553100\pi\) | |||||||
\(888\) | 4.53631 | + | 13.9613i | 0.152229 | + | 0.468511i | ||||
\(889\) | 8.92209 | − | 6.48228i | 0.299237 | − | 0.217409i | ||||
\(890\) | 9.90516 | 0.332022 | ||||||||
\(891\) | −2.87599 | − | 1.65187i | −0.0963493 | − | 0.0553399i | ||||
\(892\) | 148.930 | 4.98654 | ||||||||
\(893\) | −2.59948 | + | 1.88863i | −0.0869883 | + | 0.0632007i | ||||
\(894\) | 1.91053 | + | 5.88000i | 0.0638976 | + | 0.196656i | ||||
\(895\) | 21.5111 | − | 66.2042i | 0.719035 | − | 2.21296i | ||||
\(896\) | 84.2777 | + | 61.2313i | 2.81552 | + | 2.04560i | ||||
\(897\) | 2.85119 | + | 2.07151i | 0.0951984 | + | 0.0691657i | ||||
\(898\) | −17.8704 | + | 54.9994i | −0.596343 | + | 1.83535i | ||||
\(899\) | 4.85886 | + | 14.9540i | 0.162052 | + | 0.498745i | ||||
\(900\) | −28.3832 | + | 20.6216i | −0.946105 | + | 0.687386i | ||||
\(901\) | 14.7562 | 0.491601 | ||||||||
\(902\) | −25.1458 | + | 22.7436i | −0.837263 | + | 0.757278i | ||||
\(903\) | −5.99150 | −0.199384 | ||||||||
\(904\) | 96.5331 | − | 70.1354i | 3.21064 | − | 2.33267i | ||||
\(905\) | 10.2707 | + | 31.6099i | 0.341409 | + | 1.05075i | ||||
\(906\) | 10.3263 | − | 31.7811i | 0.343069 | − | 1.05586i | ||||
\(907\) | −1.71490 | − | 1.24595i | −0.0569422 | − | 0.0413709i | 0.558950 | − | 0.829201i | \(-0.311204\pi\) |
−0.615892 | + | 0.787830i | \(0.711204\pi\) | |||||||
\(908\) | −17.7205 | − | 12.8747i | −0.588077 | − | 0.427263i | ||||
\(909\) | 2.15575 | − | 6.63472i | 0.0715018 | − | 0.220060i | ||||
\(910\) | −4.17053 | − | 12.8356i | −0.138252 | − | 0.425495i | ||||
\(911\) | 1.69530 | − | 1.23171i | 0.0561678 | − | 0.0408083i | −0.559347 | − | 0.828934i | \(-0.688948\pi\) |
0.615515 | + | 0.788125i | \(0.288948\pi\) | |||||||
\(912\) | −10.3609 | −0.343084 | ||||||||
\(913\) | 34.2848 | − | 31.0096i | 1.13466 | − | 1.02627i | ||||
\(914\) | 62.3631 | 2.06279 | ||||||||
\(915\) | 7.34129 | − | 5.33376i | 0.242696 | − | 0.176329i | ||||
\(916\) | −15.4192 | − | 47.4553i | −0.509464 | − | 1.56797i | ||||
\(917\) | 7.45600 | − | 22.9472i | 0.246219 | − | 0.757783i | ||||
\(918\) | −14.2663 | − | 10.3650i | −0.470856 | − | 0.342097i | ||||
\(919\) | 17.8228 | + | 12.9490i | 0.587919 | + | 0.427148i | 0.841570 | − | 0.540147i | \(-0.181632\pi\) |
−0.253651 | + | 0.967296i | \(0.581632\pi\) | |||||||
\(920\) | 38.7644 | − | 119.304i | 1.27802 | − | 3.93335i | ||||
\(921\) | −3.33202 | − | 10.2549i | −0.109794 | − | 0.337911i | ||||
\(922\) | −60.8874 | + | 44.2373i | −2.00522 | + | 1.45688i | ||||
\(923\) | −0.177420 | −0.00583984 | ||||||||
\(924\) | −24.3714 | − | 13.9981i | −0.801759 | − | 0.460504i | ||||
\(925\) | −8.23414 | −0.270737 | ||||||||
\(926\) | −54.2178 | + | 39.3915i | −1.78171 | + | 1.29449i | ||||
\(927\) | 2.93381 | + | 9.02935i | 0.0963591 | + | 0.296563i | ||||
\(928\) | −14.7564 | + | 45.4156i | −0.484404 | + | 1.49084i | ||||
\(929\) | 26.3112 | + | 19.1162i | 0.863243 | + | 0.627183i | 0.928765 | − | 0.370668i | \(-0.120871\pi\) |
−0.0655221 | + | 0.997851i | \(0.520871\pi\) | |||||||
\(930\) | 73.9900 | + | 53.7569i | 2.42623 | + | 1.76276i | ||||
\(931\) | −0.853021 | + | 2.62533i | −0.0279566 | + | 0.0860417i | ||||
\(932\) | −1.42874 | − | 4.39721i | −0.0467999 | − | 0.144035i | ||||
\(933\) | −6.81203 | + | 4.94923i | −0.223016 | + | 0.162031i | ||||
\(934\) | −16.9368 | −0.554189 | ||||||||
\(935\) | 68.9641 | − | 7.40465i | 2.25537 | − | 0.242158i | ||||
\(936\) | −10.7245 | −0.350543 | ||||||||
\(937\) | 19.1828 | − | 13.9371i | 0.626675 | − | 0.455306i | −0.228572 | − | 0.973527i | \(-0.573406\pi\) |
0.855247 | + | 0.518221i | \(0.173406\pi\) | |||||||
\(938\) | −7.88076 | − | 24.2545i | −0.257316 | − | 0.791937i | ||||
\(939\) | −3.44506 | + | 10.6028i | −0.112425 | + | 0.346009i | ||||
\(940\) | 89.1128 | + | 64.7442i | 2.90654 | + | 2.11172i | ||||
\(941\) | 33.9072 | + | 24.6350i | 1.10534 | + | 0.803078i | 0.981924 | − | 0.189277i | \(-0.0606143\pi\) |
0.123418 | + | 0.992355i | \(0.460614\pi\) | |||||||
\(942\) | −11.1198 | + | 34.2232i | −0.362302 | + | 1.11505i | ||||
\(943\) | −3.97818 | − | 12.2436i | −0.129547 | − | 0.398705i | ||||
\(944\) | 135.571 | − | 98.4980i | 4.41246 | − | 3.20584i | ||||
\(945\) | −4.82247 | −0.156875 | ||||||||
\(946\) | −15.6458 | − | 34.9302i | −0.508688 | − | 1.13568i | ||||
\(947\) | −0.286780 | −0.00931909 | −0.00465954 | − | 0.999989i | \(-0.501483\pi\) | ||||
−0.00465954 | + | 0.999989i | \(0.501483\pi\) | |||||||
\(948\) | −0.484828 | + | 0.352248i | −0.0157465 | + | 0.0114405i | ||||
\(949\) | 1.01200 | + | 3.11462i | 0.0328509 | + | 0.101105i | ||||
\(950\) | 2.93748 | − | 9.04064i | 0.0953045 | − | 0.293317i | ||||
\(951\) | 14.9669 | + | 10.8741i | 0.485336 | + | 0.352617i | ||||
\(952\) | −79.4356 | − | 57.7133i | −2.57452 | − | 1.87050i | ||||
\(953\) | 6.30094 | − | 19.3923i | 0.204107 | − | 0.628178i | −0.795642 | − | 0.605768i | \(-0.792866\pi\) |
0.999749 | − | 0.0224100i | \(-0.00713392\pi\) | |||||||
\(954\) | −2.02528 | − | 6.23316i | −0.0655707 | − | 0.201806i | ||||
\(955\) | 2.27053 | − | 1.64963i | 0.0734725 | − | 0.0533809i | ||||
\(956\) | −63.2778 | −2.04655 | ||||||||
\(957\) | 1.08956 | − | 5.18305i | 0.0352206 | − | 0.167544i | ||||
\(958\) | −11.2096 | −0.362166 | ||||||||
\(959\) | 1.41357 | − | 1.02702i | 0.0456465 | − | 0.0331641i | ||||
\(960\) | 48.1923 | + | 148.321i | 1.55540 | + | 4.78703i | ||||
\(961\) | 20.3795 | − | 62.7216i | 0.657402 | − | 2.02328i | ||||
\(962\) | −3.09912 | − | 2.25165i | −0.0999198 | − | 0.0725960i | ||||
\(963\) | 5.40279 | + | 3.92536i | 0.174102 | + | 0.126493i | ||||
\(964\) | 18.9550 | − | 58.3374i | 0.610499 | − | 1.87892i | ||||
\(965\) | −21.0986 | − | 64.9347i | −0.679186 | − | 2.09032i | ||||
\(966\) | 11.5940 | − | 8.42350i | 0.373029 | − | 0.271022i | ||||
\(967\) | −16.4422 | −0.528746 | −0.264373 | − | 0.964421i | \(-0.585165\pi\) | ||||
−0.264373 | + | 0.964421i | \(0.585165\pi\) | |||||||
\(968\) | 11.8055 | − | 117.378i | 0.379442 | − | 3.77266i | ||||
\(969\) | 3.55786 | 0.114295 | ||||||||
\(970\) | −109.678 | + | 79.6858i | −3.52155 | + | 2.55856i | ||||
\(971\) | −1.93945 | − | 5.96903i | −0.0622401 | − | 0.191555i | 0.915101 | − | 0.403224i | \(-0.132110\pi\) |
−0.977342 | + | 0.211668i | \(0.932110\pi\) | |||||||
\(972\) | −1.80222 | + | 5.54667i | −0.0578064 | + | 0.177910i | ||||
\(973\) | 24.1629 | + | 17.5554i | 0.774628 | + | 0.562800i | ||||
\(974\) | 35.5547 | + | 25.8320i | 1.13925 | + | 0.827710i | ||||
\(975\) | 1.85891 | − | 5.72114i | 0.0595328 | − | 0.183223i | ||||
\(976\) | −15.5030 | − | 47.7132i | −0.496238 | − | 1.52726i | ||||
\(977\) | 28.2617 | − | 20.5333i | 0.904173 | − | 0.656920i | −0.0353618 | − | 0.999375i | \(-0.511258\pi\) |
0.939534 | + | 0.342455i | \(0.111258\pi\) | |||||||
\(978\) | −50.6532 | −1.61971 | ||||||||
\(979\) | −0.727598 | + | 3.46118i | −0.0232541 | + | 0.110620i | ||||
\(980\) | 94.6304 | 3.02286 | ||||||||
\(981\) | 5.38251 | − | 3.91062i | 0.171850 | − | 0.124857i | ||||
\(982\) | 7.47459 | + | 23.0044i | 0.238524 | + | 0.734100i | ||||
\(983\) | −13.6864 | + | 42.1223i | −0.436527 | + | 1.34349i | 0.454986 | + | 0.890498i | \(0.349644\pi\) |
−0.891514 | + | 0.452994i | \(0.850356\pi\) | |||||||
\(984\) | 31.6935 | + | 23.0267i | 1.01035 | + | 0.734063i | ||||
\(985\) | −75.3112 | − | 54.7168i | −2.39961 | − | 1.74342i | ||||
\(986\) | 8.70190 | − | 26.7817i | 0.277125 | − | 0.852902i | ||||
\(987\) | 2.55506 | + | 7.86366i | 0.0813284 | + | 0.250303i | ||||
\(988\) | 2.66416 | − | 1.93563i | 0.0847582 | − | 0.0615805i | ||||
\(989\) | 14.5324 | 0.462103 | ||||||||
\(990\) | −12.5931 | − | 28.1148i | −0.400234 | − | 0.893547i | ||||
\(991\) | 23.8078 | 0.756279 | 0.378139 | − | 0.925749i | \(-0.376564\pi\) | ||||
0.378139 | + | 0.925749i | \(0.376564\pi\) | |||||||
\(992\) | 238.204 | − | 173.066i | 7.56300 | − | 5.49484i | ||||
\(993\) | 4.95903 | + | 15.2623i | 0.157370 | + | 0.484335i | ||||
\(994\) | −0.222941 | + | 0.686142i | −0.00707126 | + | 0.0217631i | ||||
\(995\) | −23.1817 | − | 16.8425i | −0.734910 | − | 0.533943i | ||||
\(996\) | −65.7649 | − | 47.7810i | −2.08384 | − | 1.51400i | ||||
\(997\) | −14.1070 | + | 43.4168i | −0.446772 | + | 1.37502i | 0.433757 | + | 0.901030i | \(0.357188\pi\) |
−0.880529 | + | 0.473993i | \(0.842812\pi\) | |||||||
\(998\) | 11.9126 | + | 36.6633i | 0.377087 | + | 1.16056i | ||||
\(999\) | −1.10739 | + | 0.804564i | −0.0350362 | + | 0.0254553i |
(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.157.1 | ✓ | 20 | |
11.2 | odd | 10 | 4719.2.a.bi.1.1 | 10 | |||
11.4 | even | 5 | inner | 429.2.n.b.235.1 | yes | 20 | |
11.9 | even | 5 | 4719.2.a.bn.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.b.157.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
429.2.n.b.235.1 | yes | 20 | 11.4 | even | 5 | inner | |
4719.2.a.bi.1.1 | 10 | 11.2 | odd | 10 | |||
4719.2.a.bn.1.10 | 10 | 11.9 | even | 5 |