Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(236,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.236");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 236.15 | ||
Character | \(\chi\) | \(=\) | 315.236 |
Dual form | 315.2.be.b.311.15 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36259 | − | 1.36404i | 1.67060 | − | 0.964522i | 0.703300 | − | 0.710893i | \(-0.251709\pi\) |
0.967301 | − | 0.253629i | \(-0.0816244\pi\) | |||||||
\(3\) | −1.43297 | + | 0.972928i | −0.827327 | + | 0.561720i | ||||
\(4\) | 2.72121 | − | 4.71328i | 1.36061 | − | 2.35664i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.05841 | + | 4.25326i | −0.840342 | + | 1.73639i | ||||
\(7\) | 1.49231 | + | 2.18472i | 0.564042 | + | 0.825746i | ||||
\(8\) | − | 9.39122i | − | 3.32030i | ||||||
\(9\) | 1.10682 | − | 2.78836i | 0.368940 | − | 0.929453i | ||||
\(10\) | 2.36259 | − | 1.36404i | 0.747116 | − | 0.431348i | ||||
\(11\) | 0.284157i | 0.0856766i | 0.999082 | + | 0.0428383i | \(0.0136400\pi\) | ||||
−0.999082 | + | 0.0428383i | \(0.986360\pi\) | |||||||
\(12\) | 0.686259 | + | 9.40155i | 0.198106 | + | 2.71399i | ||||
\(13\) | −2.89807 | + | 1.67320i | −0.803781 | + | 0.464063i | −0.844792 | − | 0.535096i | \(-0.820276\pi\) |
0.0410106 | + | 0.999159i | \(0.486942\pi\) | |||||||
\(14\) | 6.50577 | + | 3.12602i | 1.73874 | + | 0.835463i | ||||
\(15\) | −1.43297 | + | 0.972928i | −0.369992 | + | 0.251209i | ||||
\(16\) | −7.36758 | − | 12.7610i | −1.84189 | − | 3.19025i | ||||
\(17\) | −2.65611 | − | 4.60051i | −0.644200 | − | 1.11579i | −0.984486 | − | 0.175466i | \(-0.943857\pi\) |
0.340285 | − | 0.940322i | \(-0.389476\pi\) | |||||||
\(18\) | −1.18847 | − | 8.09749i | −0.280126 | − | 1.90860i | ||||
\(19\) | 0.743281 | + | 0.429133i | 0.170520 | + | 0.0984499i | 0.582831 | − | 0.812593i | \(-0.301945\pi\) |
−0.412311 | + | 0.911043i | \(0.635278\pi\) | |||||||
\(20\) | 2.72121 | − | 4.71328i | 0.608482 | − | 1.05392i | ||||
\(21\) | −4.26402 | − | 1.67873i | −0.930485 | − | 0.366329i | ||||
\(22\) | 0.387602 | + | 0.671346i | 0.0826370 | + | 0.143131i | ||||
\(23\) | 7.91127i | 1.64961i | 0.565415 | + | 0.824807i | \(0.308716\pi\) | ||||
−0.565415 | + | 0.824807i | \(0.691284\pi\) | |||||||
\(24\) | 9.13698 | + | 13.4574i | 1.86508 | + | 2.74697i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.56463 | + | 7.90618i | −0.895198 | + | 1.55053i | ||||
\(27\) | 1.12683 | + | 5.07250i | 0.216858 | + | 0.976203i | ||||
\(28\) | 14.3581 | − | 1.08860i | 2.71343 | − | 0.205727i | ||||
\(29\) | −1.98489 | − | 1.14598i | −0.368585 | − | 0.212803i | 0.304255 | − | 0.952591i | \(-0.401592\pi\) |
−0.672840 | + | 0.739788i | \(0.734926\pi\) | |||||||
\(30\) | −2.05841 | + | 4.25326i | −0.375812 | + | 0.776536i | ||||
\(31\) | 0.992032 | + | 0.572750i | 0.178174 | + | 0.102869i | 0.586435 | − | 0.809997i | \(-0.300531\pi\) |
−0.408260 | + | 0.912866i | \(0.633864\pi\) | |||||||
\(32\) | −18.5470 | − | 10.7081i | −3.27868 | − | 1.89295i | ||||
\(33\) | −0.276464 | − | 0.407189i | −0.0481263 | − | 0.0708825i | ||||
\(34\) | −12.5506 | − | 7.24607i | −2.15240 | − | 1.24269i | ||||
\(35\) | 1.49231 | + | 2.18472i | 0.252247 | + | 0.369285i | ||||
\(36\) | −10.1304 | − | 12.8045i | −1.68840 | − | 2.13408i | ||||
\(37\) | −4.53064 | + | 7.84730i | −0.744832 | + | 1.29009i | 0.205441 | + | 0.978670i | \(0.434137\pi\) |
−0.950273 | + | 0.311418i | \(0.899196\pi\) | |||||||
\(38\) | 2.34142 | 0.379829 | ||||||||
\(39\) | 2.52495 | − | 5.21727i | 0.404316 | − | 0.835432i | ||||
\(40\) | − | 9.39122i | − | 1.48488i | ||||||
\(41\) | 3.15733 | + | 5.46865i | 0.493092 | + | 0.854060i | 0.999968 | − | 0.00795875i | \(-0.00253337\pi\) |
−0.506877 | + | 0.862019i | \(0.669200\pi\) | |||||||
\(42\) | −12.3640 | + | 1.85015i | −1.90780 | + | 0.285485i | ||||
\(43\) | 0.223973 | − | 0.387932i | 0.0341555 | − | 0.0591591i | −0.848442 | − | 0.529288i | \(-0.822459\pi\) |
0.882598 | + | 0.470129i | \(0.155793\pi\) | |||||||
\(44\) | 1.33931 | + | 0.773252i | 0.201909 | + | 0.116572i | ||||
\(45\) | 1.10682 | − | 2.78836i | 0.164995 | − | 0.415664i | ||||
\(46\) | 10.7913 | + | 18.6911i | 1.59109 | + | 2.75585i | ||||
\(47\) | −3.00982 | − | 5.21316i | −0.439027 | − | 0.760418i | 0.558587 | − | 0.829446i | \(-0.311344\pi\) |
−0.997615 | + | 0.0690279i | \(0.978010\pi\) | |||||||
\(48\) | 22.9731 | + | 11.1181i | 3.31588 | + | 1.60475i | ||||
\(49\) | −2.54600 | + | 6.52057i | −0.363714 | + | 0.931511i | ||||
\(50\) | 2.36259 | − | 1.36404i | 0.334120 | − | 0.192904i | ||||
\(51\) | 8.28210 | + | 4.00821i | 1.15973 | + | 0.561261i | ||||
\(52\) | 18.2126i | 2.52563i | ||||||||
\(53\) | 0.483757 | − | 0.279297i | 0.0664491 | − | 0.0383644i | −0.466407 | − | 0.884570i | \(-0.654452\pi\) |
0.532856 | + | 0.846206i | \(0.321119\pi\) | |||||||
\(54\) | 9.58133 | + | 10.4472i | 1.30385 | + | 1.42168i | ||||
\(55\) | 0.284157i | 0.0383157i | ||||||||
\(56\) | 20.5172 | − | 14.0146i | 2.74172 | − | 1.87279i | ||||
\(57\) | −1.48262 | + | 0.108223i | −0.196377 | + | 0.0143344i | ||||
\(58\) | −6.25264 | −0.821011 | ||||||||
\(59\) | 4.59808 | − | 7.96411i | 0.598619 | − | 1.03684i | −0.394406 | − | 0.918936i | \(-0.629050\pi\) |
0.993025 | − | 0.117903i | \(-0.0376171\pi\) | |||||||
\(60\) | 0.686259 | + | 9.40155i | 0.0885957 | + | 1.21373i | ||||
\(61\) | −6.96542 | + | 4.02149i | −0.891831 | + | 0.514899i | −0.874541 | − | 0.484952i | \(-0.838837\pi\) |
−0.0172898 | + | 0.999851i | \(0.505504\pi\) | |||||||
\(62\) | 3.12502 | 0.396877 | ||||||||
\(63\) | 7.74351 | − | 1.74301i | 0.975590 | − | 0.219599i | ||||
\(64\) | −28.9550 | −3.61937 | ||||||||
\(65\) | −2.89807 | + | 1.67320i | −0.359462 | + | 0.207535i | ||||
\(66\) | −1.20859 | − | 0.584912i | −0.148768 | − | 0.0719976i | ||||
\(67\) | −0.802881 | + | 1.39063i | −0.0980875 | + | 0.169893i | −0.910893 | − | 0.412643i | \(-0.864606\pi\) |
0.812805 | + | 0.582535i | \(0.197939\pi\) | |||||||
\(68\) | −28.9113 | −3.50601 | ||||||||
\(69\) | −7.69710 | − | 11.3366i | −0.926622 | − | 1.36477i | ||||
\(70\) | 6.50577 | + | 3.12602i | 0.777588 | + | 0.373630i | ||||
\(71\) | − | 8.30424i | − | 0.985532i | −0.870162 | − | 0.492766i | \(-0.835986\pi\) | ||
0.870162 | − | 0.492766i | \(-0.164014\pi\) | |||||||
\(72\) | −26.1861 | − | 10.3944i | −3.08606 | − | 1.22499i | ||||
\(73\) | 3.55813 | − | 2.05429i | 0.416448 | − | 0.240436i | −0.277109 | − | 0.960839i | \(-0.589376\pi\) |
0.693556 | + | 0.720402i | \(0.256043\pi\) | |||||||
\(74\) | 24.7199i | 2.87363i | ||||||||
\(75\) | −1.43297 | + | 0.972928i | −0.165465 | + | 0.112344i | ||||
\(76\) | 4.04525 | − | 2.33553i | 0.464022 | − | 0.267903i | ||||
\(77\) | −0.620803 | + | 0.424051i | −0.0707471 | + | 0.0483251i | ||||
\(78\) | −1.15115 | − | 15.7704i | −0.130342 | − | 1.78565i | ||||
\(79\) | −2.29456 | − | 3.97429i | −0.258158 | − | 0.447142i | 0.707591 | − | 0.706623i | \(-0.249782\pi\) |
−0.965748 | + | 0.259480i | \(0.916449\pi\) | |||||||
\(80\) | −7.36758 | − | 12.7610i | −0.823720 | − | 1.42673i | ||||
\(81\) | −6.54990 | − | 6.17243i | −0.727766 | − | 0.685825i | ||||
\(82\) | 14.9189 | + | 8.61345i | 1.64752 | + | 0.951196i | ||||
\(83\) | 2.29623 | − | 3.97719i | 0.252044 | − | 0.436553i | −0.712044 | − | 0.702134i | \(-0.752231\pi\) |
0.964088 | + | 0.265581i | \(0.0855639\pi\) | |||||||
\(84\) | −19.5156 | + | 15.5293i | −2.12933 | + | 1.69439i | ||||
\(85\) | −2.65611 | − | 4.60051i | −0.288095 | − | 0.498996i | ||||
\(86\) | − | 1.22203i | − | 0.131775i | ||||||
\(87\) | 3.95925 | − | 0.289002i | 0.424476 | − | 0.0309843i | ||||
\(88\) | 2.66858 | 0.284472 | ||||||||
\(89\) | 5.97567 | − | 10.3502i | 0.633419 | − | 1.09711i | −0.353428 | − | 0.935462i | \(-0.614984\pi\) |
0.986848 | − | 0.161653i | \(-0.0516825\pi\) | |||||||
\(90\) | −1.18847 | − | 8.09749i | −0.125276 | − | 0.853551i | ||||
\(91\) | −7.98031 | − | 3.83453i | −0.836564 | − | 0.401968i | ||||
\(92\) | 37.2880 | + | 21.5282i | 3.88754 | + | 2.24448i | ||||
\(93\) | −1.97880 | + | 0.144441i | −0.205192 | + | 0.0149778i | ||||
\(94\) | −14.2219 | − | 8.21103i | −1.46688 | − | 0.846903i | ||||
\(95\) | 0.743281 | + | 0.429133i | 0.0762590 | + | 0.0440281i | ||||
\(96\) | 36.9956 | − | 2.70047i | 3.77585 | − | 0.275616i | ||||
\(97\) | −3.69117 | − | 2.13110i | −0.374781 | − | 0.216380i | 0.300764 | − | 0.953699i | \(-0.402758\pi\) |
−0.675545 | + | 0.737319i | \(0.736092\pi\) | |||||||
\(98\) | 2.87918 | + | 18.8783i | 0.290841 | + | 1.90699i | ||||
\(99\) | 0.792332 | + | 0.314511i | 0.0796324 | + | 0.0316095i | ||||
\(100\) | 2.72121 | − | 4.71328i | 0.272121 | − | 0.471328i | ||||
\(101\) | −17.4540 | −1.73674 | −0.868369 | − | 0.495919i | \(-0.834831\pi\) | ||||
−0.868369 | + | 0.495919i | \(0.834831\pi\) | |||||||
\(102\) | 25.0345 | − | 1.82738i | 2.47879 | − | 0.180937i | ||||
\(103\) | 6.04027i | 0.595166i | 0.954696 | + | 0.297583i | \(0.0961805\pi\) | ||||
−0.954696 | + | 0.297583i | \(0.903820\pi\) | |||||||
\(104\) | 15.7134 | + | 27.2164i | 1.54083 | + | 2.66879i | ||||
\(105\) | −4.26402 | − | 1.67873i | −0.416126 | − | 0.163827i | ||||
\(106\) | 0.761945 | − | 1.31973i | 0.0740066 | − | 0.128183i | ||||
\(107\) | 16.6602 | + | 9.61880i | 1.61061 | + | 0.929884i | 0.989230 | + | 0.146372i | \(0.0467597\pi\) |
0.621377 | + | 0.783512i | \(0.286574\pi\) | |||||||
\(108\) | 26.9745 | + | 8.49229i | 2.59562 | + | 0.817171i | ||||
\(109\) | −9.81002 | − | 16.9915i | −0.939630 | − | 1.62749i | −0.766163 | − | 0.642647i | \(-0.777836\pi\) |
−0.173467 | − | 0.984840i | \(-0.555497\pi\) | |||||||
\(110\) | 0.387602 | + | 0.671346i | 0.0369564 | + | 0.0640103i | ||||
\(111\) | −1.14258 | − | 15.6529i | −0.108449 | − | 1.48571i | ||||
\(112\) | 16.8845 | − | 35.1395i | 1.59544 | − | 3.32037i | ||||
\(113\) | 15.1511 | − | 8.74750i | 1.42530 | − | 0.822895i | 0.428552 | − | 0.903517i | \(-0.359024\pi\) |
0.996745 | + | 0.0806222i | \(0.0256907\pi\) | |||||||
\(114\) | −3.35519 | + | 2.27803i | −0.314243 | + | 0.213357i | ||||
\(115\) | 7.91127i | 0.737730i | ||||||||
\(116\) | −10.8026 | + | 6.23689i | −1.00300 | + | 0.579081i | ||||
\(117\) | 1.45784 | + | 9.93281i | 0.134778 | + | 0.918288i | ||||
\(118\) | − | 25.0879i | − | 2.30953i | ||||||
\(119\) | 6.08708 | − | 12.6683i | 0.558002 | − | 1.16130i | ||||
\(120\) | 9.13698 | + | 13.4574i | 0.834089 | + | 1.22848i | ||||
\(121\) | 10.9193 | 0.992660 | ||||||||
\(122\) | −10.9709 | + | 19.0022i | −0.993263 | + | 1.72038i | ||||
\(123\) | −9.84497 | − | 4.76457i | −0.887691 | − | 0.429607i | ||||
\(124\) | 5.39906 | − | 3.11715i | 0.484850 | − | 0.279928i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 15.9172 | − | 14.6805i | 1.41801 | − | 1.30784i | ||||
\(127\) | −2.11951 | −0.188076 | −0.0940381 | − | 0.995569i | \(-0.529978\pi\) | ||||
−0.0940381 | + | 0.995569i | \(0.529978\pi\) | |||||||
\(128\) | −31.3146 | + | 18.0795i | −2.76785 | + | 1.59802i | ||||
\(129\) | 0.0564834 | + | 0.773806i | 0.00497309 | + | 0.0681298i | ||||
\(130\) | −4.56463 | + | 7.90618i | −0.400345 | + | 0.693418i | ||||
\(131\) | 14.0986 | 1.23180 | 0.615900 | − | 0.787825i | \(-0.288793\pi\) | ||||
0.615900 | + | 0.787825i | \(0.288793\pi\) | |||||||
\(132\) | −2.67152 | + | 0.195005i | −0.232526 | + | 0.0169730i | ||||
\(133\) | 0.171672 | + | 2.26426i | 0.0148858 | + | 0.196336i | ||||
\(134\) | 4.38065i | 0.378430i | ||||||||
\(135\) | 1.12683 | + | 5.07250i | 0.0969821 | + | 0.436571i | ||||
\(136\) | −43.2044 | + | 24.9441i | −3.70475 | + | 2.13894i | ||||
\(137\) | − | 5.70613i | − | 0.487507i | −0.969837 | − | 0.243754i | \(-0.921621\pi\) | ||
0.969837 | − | 0.243754i | \(-0.0783788\pi\) | |||||||
\(138\) | −33.6487 | − | 16.2846i | −2.86437 | − | 1.38624i | ||||
\(139\) | −5.63256 | + | 3.25196i | −0.477747 | + | 0.275828i | −0.719477 | − | 0.694516i | \(-0.755619\pi\) |
0.241730 | + | 0.970344i | \(0.422285\pi\) | |||||||
\(140\) | 14.3581 | − | 1.08860i | 1.21348 | − | 0.0920038i | ||||
\(141\) | 9.38502 | + | 4.54198i | 0.790361 | + | 0.382504i | ||||
\(142\) | −11.3273 | − | 19.6195i | −0.950567 | − | 1.64643i | ||||
\(143\) | −0.475453 | − | 0.823508i | −0.0397593 | − | 0.0688652i | ||||
\(144\) | −43.7369 | + | 6.41929i | −3.64474 | + | 0.534941i | ||||
\(145\) | −1.98489 | − | 1.14598i | −0.164836 | − | 0.0951682i | ||||
\(146\) | 5.60427 | − | 9.70687i | 0.463812 | − | 0.803347i | ||||
\(147\) | −2.69570 | − | 11.8209i | −0.222338 | − | 0.974970i | ||||
\(148\) | 24.6577 | + | 42.7083i | 2.02685 | + | 3.51060i | ||||
\(149\) | − | 9.81189i | − | 0.803821i | −0.915679 | − | 0.401911i | \(-0.868346\pi\) | ||
0.915679 | − | 0.401911i | \(-0.131654\pi\) | |||||||
\(150\) | −2.05841 | + | 4.25326i | −0.168068 | + | 0.347277i | ||||
\(151\) | 9.72438 | 0.791359 | 0.395680 | − | 0.918389i | \(-0.370509\pi\) | ||||
0.395680 | + | 0.918389i | \(0.370509\pi\) | |||||||
\(152\) | 4.03008 | − | 6.98031i | 0.326883 | − | 0.566178i | ||||
\(153\) | −15.7677 | + | 2.31424i | −1.27474 | + | 0.187095i | ||||
\(154\) | −0.888279 | + | 1.84866i | −0.0715796 | + | 0.148969i | ||||
\(155\) | 0.992032 | + | 0.572750i | 0.0796819 | + | 0.0460044i | ||||
\(156\) | −17.7195 | − | 26.0981i | −1.41870 | − | 2.08952i | ||||
\(157\) | 5.43947 | + | 3.14048i | 0.434117 | + | 0.250637i | 0.701099 | − | 0.713064i | \(-0.252693\pi\) |
−0.266982 | + | 0.963701i | \(0.586026\pi\) | |||||||
\(158\) | −10.8422 | − | 6.25974i | −0.862558 | − | 0.497998i | ||||
\(159\) | −0.421474 | + | 0.870886i | −0.0334251 | + | 0.0690657i | ||||
\(160\) | −18.5470 | − | 10.7081i | −1.46627 | − | 0.846552i | ||||
\(161\) | −17.2839 | + | 11.8061i | −1.36216 | + | 0.930450i | ||||
\(162\) | −23.8941 | − | 5.64858i | −1.87730 | − | 0.443794i | ||||
\(163\) | −9.14675 | + | 15.8426i | −0.716429 | + | 1.24089i | 0.245977 | + | 0.969276i | \(0.420891\pi\) |
−0.962406 | + | 0.271615i | \(0.912442\pi\) | |||||||
\(164\) | 34.3670 | 2.68362 | ||||||||
\(165\) | −0.276464 | − | 0.407189i | −0.0215227 | − | 0.0316996i | ||||
\(166\) | − | 12.5286i | − | 0.972409i | ||||||
\(167\) | −3.77161 | − | 6.53262i | −0.291856 | − | 0.505510i | 0.682393 | − | 0.730986i | \(-0.260939\pi\) |
−0.974249 | + | 0.225476i | \(0.927606\pi\) | |||||||
\(168\) | −15.7653 | + | 40.0443i | −1.21632 | + | 3.08949i | ||||
\(169\) | −0.900781 | + | 1.56020i | −0.0692908 | + | 0.120015i | ||||
\(170\) | −12.5506 | − | 7.24607i | −0.962585 | − | 0.555749i | ||||
\(171\) | 2.01926 | − | 1.59756i | 0.154416 | − | 0.122168i | ||||
\(172\) | −1.21896 | − | 2.11129i | −0.0929445 | − | 0.160985i | ||||
\(173\) | −1.23435 | − | 2.13795i | −0.0938458 | − | 0.162546i | 0.815281 | − | 0.579066i | \(-0.196583\pi\) |
−0.909126 | + | 0.416521i | \(0.863249\pi\) | |||||||
\(174\) | 8.95986 | − | 6.08337i | 0.679245 | − | 0.461179i | ||||
\(175\) | 1.49231 | + | 2.18472i | 0.112808 | + | 0.165149i | ||||
\(176\) | 3.62613 | − | 2.09355i | 0.273330 | − | 0.157807i | ||||
\(177\) | 1.15958 | + | 15.8860i | 0.0871597 | + | 1.19406i | ||||
\(178\) | − | 32.6042i | − | 2.44379i | ||||||
\(179\) | −0.894686 | + | 0.516547i | −0.0668720 | + | 0.0386085i | −0.533063 | − | 0.846075i | \(-0.678959\pi\) |
0.466191 | + | 0.884684i | \(0.345626\pi\) | |||||||
\(180\) | −10.1304 | − | 12.8045i | −0.755077 | − | 0.954389i | ||||
\(181\) | 4.90430i | 0.364534i | 0.983249 | + | 0.182267i | \(0.0583435\pi\) | ||||
−0.983249 | + | 0.182267i | \(0.941656\pi\) | |||||||
\(182\) | −24.0847 | + | 1.82605i | −1.78527 | + | 0.135356i | ||||
\(183\) | 6.06864 | − | 12.5395i | 0.448607 | − | 0.926949i | ||||
\(184\) | 74.2965 | 5.47721 | ||||||||
\(185\) | −4.53064 | + | 7.84730i | −0.333099 | + | 0.576945i | ||||
\(186\) | −4.47806 | + | 3.04042i | −0.328348 | + | 0.222934i | ||||
\(187\) | 1.30727 | − | 0.754751i | 0.0955969 | − | 0.0551929i | ||||
\(188\) | −32.7615 | −2.38937 | ||||||||
\(189\) | −9.40041 | + | 10.0316i | −0.683779 | + | 0.729689i | ||||
\(190\) | 2.34142 | 0.169865 | ||||||||
\(191\) | 1.63620 | − | 0.944661i | 0.118391 | − | 0.0683533i | −0.439635 | − | 0.898177i | \(-0.644892\pi\) |
0.558026 | + | 0.829823i | \(0.311559\pi\) | |||||||
\(192\) | 41.4917 | − | 28.1711i | 2.99441 | − | 2.03308i | ||||
\(193\) | −6.19129 | + | 10.7236i | −0.445659 | + | 0.771904i | −0.998098 | − | 0.0616495i | \(-0.980364\pi\) |
0.552439 | + | 0.833553i | \(0.313697\pi\) | |||||||
\(194\) | −11.6276 | −0.834813 | ||||||||
\(195\) | 2.52495 | − | 5.21727i | 0.180816 | − | 0.373617i | ||||
\(196\) | 23.8051 | + | 29.7439i | 1.70036 | + | 2.12456i | ||||
\(197\) | − | 2.13992i | − | 0.152463i | −0.997090 | − | 0.0762316i | \(-0.975711\pi\) | ||
0.997090 | − | 0.0762316i | \(-0.0242888\pi\) | |||||||
\(198\) | 2.30096 | − | 0.337713i | 0.163522 | − | 0.0240002i | ||||
\(199\) | 2.61298 | − | 1.50861i | 0.185230 | − | 0.106942i | −0.404518 | − | 0.914530i | \(-0.632561\pi\) |
0.589747 | + | 0.807588i | \(0.299227\pi\) | |||||||
\(200\) | − | 9.39122i | − | 0.664059i | ||||||
\(201\) | −0.202478 | − | 2.77388i | −0.0142817 | − | 0.195655i | ||||
\(202\) | −41.2366 | + | 23.8080i | −2.90140 | + | 1.67512i | ||||
\(203\) | −0.458440 | − | 6.04659i | −0.0321762 | − | 0.424387i | ||||
\(204\) | 41.4291 | − | 28.1287i | 2.90062 | − | 1.96940i | ||||
\(205\) | 3.15733 | + | 5.46865i | 0.220517 | + | 0.381947i | ||||
\(206\) | 8.23918 | + | 14.2707i | 0.574051 | + | 0.994285i | ||||
\(207\) | 22.0595 | + | 8.75636i | 1.53324 | + | 0.608609i | ||||
\(208\) | 42.7036 | + | 24.6549i | 2.96096 | + | 1.70951i | ||||
\(209\) | −0.121941 | + | 0.211208i | −0.00843485 | + | 0.0146096i | ||||
\(210\) | −12.3640 | + | 1.85015i | −0.853195 | + | 0.127673i | ||||
\(211\) | 2.43826 | + | 4.22319i | 0.167857 | + | 0.290736i | 0.937666 | − | 0.347538i | \(-0.112982\pi\) |
−0.769809 | + | 0.638274i | \(0.779649\pi\) | |||||||
\(212\) | − | 3.04011i | − | 0.208795i | ||||||
\(213\) | 8.07943 | + | 11.8997i | 0.553593 | + | 0.815357i | ||||
\(214\) | 52.4817 | 3.58758 | ||||||||
\(215\) | 0.223973 | − | 0.387932i | 0.0152748 | − | 0.0264568i | ||||
\(216\) | 47.6370 | − | 10.5823i | 3.24128 | − | 0.720035i | ||||
\(217\) | 0.229125 | + | 3.02203i | 0.0155540 | + | 0.205149i | ||||
\(218\) | −46.3541 | − | 26.7625i | −3.13949 | − | 1.81259i | ||||
\(219\) | −3.10003 | + | 6.40555i | −0.209481 | + | 0.432847i | ||||
\(220\) | 1.33931 | + | 0.773252i | 0.0902964 | + | 0.0521326i | ||||
\(221\) | 15.3952 | + | 8.88841i | 1.03559 | + | 0.597899i | ||||
\(222\) | −24.0507 | − | 35.4229i | −1.61418 | − | 2.37743i | ||||
\(223\) | −3.25079 | − | 1.87684i | −0.217689 | − | 0.125683i | 0.387191 | − | 0.922000i | \(-0.373445\pi\) |
−0.604880 | + | 0.796317i | \(0.706779\pi\) | |||||||
\(224\) | −4.28372 | − | 56.4999i | −0.286218 | − | 3.77506i | ||||
\(225\) | 1.10682 | − | 2.78836i | 0.0737881 | − | 0.185891i | ||||
\(226\) | 23.8639 | − | 41.3334i | 1.58740 | − | 2.74946i | ||||
\(227\) | −8.57244 | −0.568973 | −0.284487 | − | 0.958680i | \(-0.591823\pi\) | ||||
−0.284487 | + | 0.958680i | \(0.591823\pi\) | |||||||
\(228\) | −3.52443 | + | 7.28248i | −0.233411 | + | 0.482294i | ||||
\(229\) | − | 1.43175i | − | 0.0946126i | −0.998880 | − | 0.0473063i | \(-0.984936\pi\) | ||
0.998880 | − | 0.0473063i | \(-0.0150637\pi\) | |||||||
\(230\) | 10.7913 | + | 18.6911i | 0.711557 | + | 1.23245i | ||||
\(231\) | 0.477023 | − | 1.21165i | 0.0313858 | − | 0.0797208i | ||||
\(232\) | −10.7621 | + | 18.6405i | −0.706568 | + | 1.22381i | ||||
\(233\) | −2.40835 | − | 1.39046i | −0.157777 | − | 0.0910923i | 0.419033 | − | 0.907971i | \(-0.362369\pi\) |
−0.576809 | + | 0.816879i | \(0.695702\pi\) | |||||||
\(234\) | 16.9930 | + | 21.4786i | 1.11087 | + | 1.40410i | ||||
\(235\) | −3.00982 | − | 5.21316i | −0.196339 | − | 0.340069i | ||||
\(236\) | −25.0247 | − | 43.3441i | −1.62897 | − | 2.82146i | ||||
\(237\) | 7.15474 | + | 3.46261i | 0.464750 | + | 0.224921i | ||||
\(238\) | −2.89874 | − | 38.2329i | −0.187898 | − | 2.47827i | ||||
\(239\) | −6.19653 | + | 3.57757i | −0.400820 | + | 0.231414i | −0.686838 | − | 0.726811i | \(-0.741002\pi\) |
0.286018 | + | 0.958224i | \(0.407668\pi\) | |||||||
\(240\) | 22.9731 | + | 11.1181i | 1.48291 | + | 0.717668i | ||||
\(241\) | − | 26.7513i | − | 1.72320i | −0.507585 | − | 0.861602i | \(-0.669462\pi\) | ||
0.507585 | − | 0.861602i | \(-0.330538\pi\) | |||||||
\(242\) | 25.7977 | − | 14.8943i | 1.65834 | − | 0.957442i | ||||
\(243\) | 15.3912 | + | 2.47234i | 0.987343 | + | 0.158601i | ||||
\(244\) | 43.7733i | 2.80230i | ||||||||
\(245\) | −2.54600 | + | 6.52057i | −0.162658 | + | 0.416584i | ||||
\(246\) | −29.7587 | + | 2.17221i | −1.89734 | + | 0.138495i | ||||
\(247\) | −2.87211 | −0.182748 | ||||||||
\(248\) | 5.37882 | − | 9.31639i | 0.341555 | − | 0.591591i | ||||
\(249\) | 0.579084 | + | 7.93327i | 0.0366979 | + | 0.502751i | ||||
\(250\) | 2.36259 | − | 1.36404i | 0.149423 | − | 0.0862695i | ||||
\(251\) | −9.60803 | −0.606453 | −0.303227 | − | 0.952918i | \(-0.598064\pi\) | ||||
−0.303227 | + | 0.952918i | \(0.598064\pi\) | |||||||
\(252\) | 12.8564 | − | 41.2404i | 0.809879 | − | 2.59790i | ||||
\(253\) | −2.24804 | −0.141333 | ||||||||
\(254\) | −5.00753 | + | 2.89110i | −0.314201 | + | 0.181404i | ||||
\(255\) | 8.28210 | + | 4.00821i | 0.518645 | + | 0.251004i | ||||
\(256\) | −20.3674 | + | 35.2774i | −1.27296 | + | 2.20484i | ||||
\(257\) | 9.96259 | 0.621449 | 0.310725 | − | 0.950500i | \(-0.399428\pi\) | ||||
0.310725 | + | 0.950500i | \(0.399428\pi\) | |||||||
\(258\) | 1.18895 | + | 1.75114i | 0.0740207 | + | 0.109021i | ||||
\(259\) | −23.9053 | + | 1.81245i | −1.48540 | + | 0.112620i | ||||
\(260\) | 18.2126i | 1.12950i | ||||||||
\(261\) | −5.39231 | + | 4.26620i | −0.333776 | + | 0.264071i | ||||
\(262\) | 33.3091 | − | 19.2310i | 2.05785 | − | 1.18810i | ||||
\(263\) | 13.7261i | 0.846387i | 0.906039 | + | 0.423194i | \(0.139091\pi\) | ||||
−0.906039 | + | 0.423194i | \(0.860909\pi\) | |||||||
\(264\) | −3.82400 | + | 2.59634i | −0.235351 | + | 0.159794i | ||||
\(265\) | 0.483757 | − | 0.279297i | 0.0297169 | − | 0.0171571i | ||||
\(266\) | 3.49413 | + | 5.11535i | 0.214239 | + | 0.313642i | ||||
\(267\) | 1.50700 | + | 20.6454i | 0.0922266 | + | 1.26348i | ||||
\(268\) | 4.36962 | + | 7.56841i | 0.266917 | + | 0.462314i | ||||
\(269\) | 4.29238 | + | 7.43463i | 0.261711 | + | 0.453297i | 0.966697 | − | 0.255925i | \(-0.0823799\pi\) |
−0.704986 | + | 0.709222i | \(0.749047\pi\) | |||||||
\(270\) | 9.58133 | + | 10.4472i | 0.583101 | + | 0.635795i | ||||
\(271\) | 25.7871 | + | 14.8882i | 1.56645 | + | 0.904393i | 0.996578 | + | 0.0826626i | \(0.0263424\pi\) |
0.569877 | + | 0.821730i | \(0.306991\pi\) | |||||||
\(272\) | −39.1381 | + | 67.7893i | −2.37310 | + | 4.11033i | ||||
\(273\) | 15.1663 | − | 2.26949i | 0.917906 | − | 0.137356i | ||||
\(274\) | −7.78339 | − | 13.4812i | −0.470212 | − | 0.814431i | ||||
\(275\) | 0.284157i | 0.0171353i | ||||||||
\(276\) | −74.3782 | + | 5.42918i | −4.47704 | + | 0.326798i | ||||
\(277\) | −19.8539 | −1.19291 | −0.596453 | − | 0.802648i | \(-0.703424\pi\) | ||||
−0.596453 | + | 0.802648i | \(0.703424\pi\) | |||||||
\(278\) | −8.87161 | + | 15.3661i | −0.532084 | + | 0.921596i | ||||
\(279\) | 2.69503 | − | 2.13221i | 0.161347 | − | 0.127652i | ||||
\(280\) | 20.5172 | − | 14.0146i | 1.22614 | − | 0.837535i | ||||
\(281\) | 8.54068 | + | 4.93096i | 0.509494 | + | 0.294157i | 0.732626 | − | 0.680632i | \(-0.238295\pi\) |
−0.223132 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(282\) | 28.3684 | − | 2.07073i | 1.68931 | − | 0.123310i | ||||
\(283\) | 9.14106 | + | 5.27759i | 0.543380 | + | 0.313720i | 0.746448 | − | 0.665444i | \(-0.231758\pi\) |
−0.203068 | + | 0.979165i | \(0.565091\pi\) | |||||||
\(284\) | −39.1402 | − | 22.5976i | −2.32254 | − | 1.34092i | ||||
\(285\) | −1.48262 | + | 0.108223i | −0.0878226 | + | 0.00641055i | ||||
\(286\) | −2.24660 | − | 1.29707i | −0.132844 | − | 0.0766975i | ||||
\(287\) | −7.23575 | + | 15.0588i | −0.427113 | + | 0.888894i | ||||
\(288\) | −50.3863 | + | 39.8638i | −2.96904 | + | 2.34900i | ||||
\(289\) | −5.60981 | + | 9.71647i | −0.329989 | + | 0.571557i | ||||
\(290\) | −6.25264 | −0.367167 | ||||||||
\(291\) | 7.36274 | − | 0.537438i | 0.431612 | − | 0.0315052i | ||||
\(292\) | − | 22.3606i | − | 1.30856i | ||||||
\(293\) | −4.31392 | − | 7.47192i | −0.252022 | − | 0.436514i | 0.712061 | − | 0.702118i | \(-0.247762\pi\) |
−0.964082 | + | 0.265604i | \(0.914429\pi\) | |||||||
\(294\) | −22.4930 | − | 24.2508i | −1.31182 | − | 1.41434i | ||||
\(295\) | 4.59808 | − | 7.96411i | 0.267711 | − | 0.463689i | ||||
\(296\) | 73.6957 | + | 42.5482i | 4.28347 | + | 2.47307i | ||||
\(297\) | −1.44139 | + | 0.320197i | −0.0836377 | + | 0.0185797i | ||||
\(298\) | −13.3838 | − | 23.1814i | −0.775303 | − | 1.34286i | ||||
\(299\) | −13.2372 | − | 22.9274i | −0.765525 | − | 1.32593i | ||||
\(300\) | 0.686259 | + | 9.40155i | 0.0396212 | + | 0.542799i | ||||
\(301\) | 1.18176 | − | 0.0895988i | 0.0681155 | − | 0.00516439i | ||||
\(302\) | 22.9747 | − | 13.2645i | 1.32205 | − | 0.763284i | ||||
\(303\) | 25.0111 | − | 16.9815i | 1.43685 | − | 0.975561i | ||||
\(304\) | − | 12.6467i | − | 0.725337i | ||||||
\(305\) | −6.96542 | + | 4.02149i | −0.398839 | + | 0.230270i | ||||
\(306\) | −34.0959 | + | 26.9754i | −1.94913 | + | 1.54208i | ||||
\(307\) | 11.5914i | 0.661558i | 0.943708 | + | 0.330779i | \(0.107311\pi\) | ||||
−0.943708 | + | 0.330779i | \(0.892689\pi\) | |||||||
\(308\) | 0.309334 | + | 4.07995i | 0.0176260 | + | 0.232477i | ||||
\(309\) | −5.87675 | − | 8.65555i | −0.334317 | − | 0.492397i | ||||
\(310\) | 3.12502 | 0.177489 | ||||||||
\(311\) | −2.48593 | + | 4.30576i | −0.140964 | + | 0.244157i | −0.927860 | − | 0.372929i | \(-0.878354\pi\) |
0.786896 | + | 0.617086i | \(0.211687\pi\) | |||||||
\(312\) | −48.9965 | − | 23.7124i | −2.77388 | − | 1.34245i | ||||
\(313\) | 16.9588 | − | 9.79118i | 0.958569 | − | 0.553430i | 0.0628367 | − | 0.998024i | \(-0.479985\pi\) |
0.895732 | + | 0.444594i | \(0.146652\pi\) | |||||||
\(314\) | 17.1350 | 0.966982 | ||||||||
\(315\) | 7.74351 | − | 1.74301i | 0.436297 | − | 0.0982077i | ||||
\(316\) | −24.9759 | −1.40500 | ||||||||
\(317\) | 1.01867 | − | 0.588131i | 0.0572144 | − | 0.0330327i | −0.471120 | − | 0.882069i | \(-0.656150\pi\) |
0.528334 | + | 0.849036i | \(0.322817\pi\) | |||||||
\(318\) | 0.192154 | + | 2.63245i | 0.0107755 | + | 0.147621i | ||||
\(319\) | 0.325637 | − | 0.564020i | 0.0182322 | − | 0.0315791i | ||||
\(320\) | −28.9550 | −1.61863 | ||||||||
\(321\) | −33.2321 | + | 2.42575i | −1.85483 | + | 0.135392i | ||||
\(322\) | −24.7307 | + | 51.4689i | −1.37819 | + | 2.86825i | ||||
\(323\) | − | 4.55930i | − | 0.253686i | ||||||
\(324\) | −46.9160 | + | 14.0750i | −2.60645 | + | 0.781944i | ||||
\(325\) | −2.89807 | + | 1.67320i | −0.160756 | + | 0.0928126i | ||||
\(326\) | 49.9062i | 2.76405i | ||||||||
\(327\) | 30.5890 | + | 14.8038i | 1.69157 | + | 0.818654i | ||||
\(328\) | 51.3573 | − | 29.6512i | 2.83573 | − | 1.63721i | ||||
\(329\) | 6.89770 | − | 14.3553i | 0.380283 | − | 0.791433i | ||||
\(330\) | −1.20859 | − | 0.584912i | −0.0665309 | − | 0.0321983i | ||||
\(331\) | 15.6571 | + | 27.1188i | 0.860590 | + | 1.49059i | 0.871360 | + | 0.490644i | \(0.163239\pi\) |
−0.0107695 | + | 0.999942i | \(0.503428\pi\) | |||||||
\(332\) | −12.4971 | − | 21.6456i | −0.685866 | − | 1.18795i | ||||
\(333\) | 16.8665 | + | 21.3186i | 0.924277 | + | 1.16825i | ||||
\(334\) | −17.8215 | − | 10.2893i | −0.975150 | − | 0.563003i | ||||
\(335\) | −0.802881 | + | 1.39063i | −0.0438661 | + | 0.0759783i | ||||
\(336\) | 9.99320 | + | 66.7814i | 0.545174 | + | 3.64322i | ||||
\(337\) | −12.2086 | − | 21.1459i | −0.665043 | − | 1.15189i | −0.979274 | − | 0.202542i | \(-0.935080\pi\) |
0.314230 | − | 0.949347i | \(-0.398254\pi\) | |||||||
\(338\) | 4.91481i | 0.267330i | ||||||||
\(339\) | −13.2004 | + | 27.2759i | −0.716949 | + | 1.48142i | ||||
\(340\) | −28.9113 | −1.56794 | ||||||||
\(341\) | −0.162751 | + | 0.281893i | −0.00881346 | + | 0.0152654i | ||||
\(342\) | 2.59153 | − | 6.52872i | 0.140134 | − | 0.353033i | ||||
\(343\) | −18.0451 | + | 4.16844i | −0.974341 | + | 0.225075i | ||||
\(344\) | −3.64316 | − | 2.10338i | −0.196426 | − | 0.113406i | ||||
\(345\) | −7.69710 | − | 11.3366i | −0.414398 | − | 0.610344i | ||||
\(346\) | −5.83251 | − | 3.36740i | −0.313558 | − | 0.181033i | ||||
\(347\) | −15.6017 | − | 9.00762i | −0.837540 | − | 0.483554i | 0.0188870 | − | 0.999822i | \(-0.493988\pi\) |
−0.856427 | + | 0.516267i | \(0.827321\pi\) | |||||||
\(348\) | 9.41180 | − | 19.4475i | 0.504526 | − | 1.04249i | ||||
\(349\) | 11.6741 | + | 6.74005i | 0.624901 | + | 0.360787i | 0.778775 | − | 0.627304i | \(-0.215842\pi\) |
−0.153874 | + | 0.988091i | \(0.549175\pi\) | |||||||
\(350\) | 6.50577 | + | 3.12602i | 0.347748 | + | 0.167093i | ||||
\(351\) | −11.7530 | − | 12.8151i | −0.627327 | − | 0.684017i | ||||
\(352\) | 3.04279 | − | 5.27027i | 0.162181 | − | 0.280906i | ||||
\(353\) | 3.23874 | 0.172381 | 0.0861903 | − | 0.996279i | \(-0.472531\pi\) | ||||
0.0861903 | + | 0.996279i | \(0.472531\pi\) | |||||||
\(354\) | 24.4087 | + | 35.9502i | 1.29731 | + | 1.91073i | ||||
\(355\) | − | 8.30424i | − | 0.440743i | ||||||
\(356\) | −32.5221 | − | 56.3300i | −1.72367 | − | 2.98548i | ||||
\(357\) | 3.60268 | + | 24.0756i | 0.190674 | + | 1.27421i | ||||
\(358\) | −1.40918 | + | 2.44078i | −0.0744776 | + | 0.128999i | ||||
\(359\) | −25.9750 | − | 14.9967i | −1.37091 | − | 0.791494i | −0.379865 | − | 0.925042i | \(-0.624030\pi\) |
−0.991042 | + | 0.133548i | \(0.957363\pi\) | |||||||
\(360\) | −26.1861 | − | 10.3944i | −1.38013 | − | 0.547833i | ||||
\(361\) | −9.13169 | − | 15.8165i | −0.480615 | − | 0.832450i | ||||
\(362\) | 6.68967 | + | 11.5868i | 0.351601 | + | 0.608991i | ||||
\(363\) | −15.6470 | + | 10.6237i | −0.821254 | + | 0.557597i | ||||
\(364\) | −39.7894 | + | 27.1789i | −2.08553 | + | 1.42456i | ||||
\(365\) | 3.55813 | − | 2.05429i | 0.186241 | − | 0.107526i | ||||
\(366\) | −2.76675 | − | 37.9036i | −0.144620 | − | 1.98125i | ||||
\(367\) | 1.24882i | 0.0651877i | 0.999469 | + | 0.0325938i | \(0.0103768\pi\) | ||||
−0.999469 | + | 0.0325938i | \(0.989623\pi\) | |||||||
\(368\) | 100.956 | − | 58.2869i | 5.26269 | − | 3.03841i | ||||
\(369\) | 18.7432 | − | 2.75095i | 0.975730 | − | 0.143208i | ||||
\(370\) | 24.7199i | 1.28513i | ||||||||
\(371\) | 1.33210 | + | 0.640074i | 0.0691593 | + | 0.0332310i | ||||
\(372\) | −4.70394 | + | 9.71969i | −0.243888 | + | 0.503942i | ||||
\(373\) | 10.1096 | 0.523457 | 0.261728 | − | 0.965142i | \(-0.415708\pi\) | ||||
0.261728 | + | 0.965142i | \(0.415708\pi\) | |||||||
\(374\) | 2.05902 | − | 3.56633i | 0.106470 | − | 0.184411i | ||||
\(375\) | −1.43297 | + | 0.972928i | −0.0739984 | + | 0.0502418i | ||||
\(376\) | −48.9579 | + | 28.2659i | −2.52481 | + | 1.45770i | ||||
\(377\) | 7.66981 | 0.395015 | ||||||||
\(378\) | −8.52582 | + | 36.5230i | −0.438521 | + | 1.87854i | ||||
\(379\) | 15.8027 | 0.811729 | 0.405865 | − | 0.913933i | \(-0.366970\pi\) | ||||
0.405865 | + | 0.913933i | \(0.366970\pi\) | |||||||
\(380\) | 4.04525 | − | 2.33553i | 0.207517 | − | 0.119810i | ||||
\(381\) | 3.03720 | − | 2.06213i | 0.155601 | − | 0.105646i | ||||
\(382\) | 2.57711 | − | 4.46369i | 0.131857 | − | 0.228382i | ||||
\(383\) | 5.90462 | 0.301712 | 0.150856 | − | 0.988556i | \(-0.451797\pi\) | ||||
0.150856 | + | 0.988556i | \(0.451797\pi\) | |||||||
\(384\) | 27.2829 | − | 56.3743i | 1.39228 | − | 2.87684i | ||||
\(385\) | −0.620803 | + | 0.424051i | −0.0316391 | + | 0.0216117i | ||||
\(386\) | 33.7807i | 1.71939i | ||||||||
\(387\) | −0.833797 | − | 1.05389i | −0.0423843 | − | 0.0535721i | ||||
\(388\) | −20.0889 | + | 11.5983i | −1.01986 | + | 0.588816i | ||||
\(389\) | − | 5.61909i | − | 0.284899i | −0.989802 | − | 0.142450i | \(-0.954502\pi\) | ||
0.989802 | − | 0.142450i | \(-0.0454979\pi\) | |||||||
\(390\) | −1.15115 | − | 15.7704i | −0.0582907 | − | 0.798565i | ||||
\(391\) | 36.3959 | − | 21.0132i | 1.84062 | − | 1.06268i | ||||
\(392\) | 61.2361 | + | 23.9100i | 3.09289 | + | 1.20764i | ||||
\(393\) | −20.2029 | + | 13.7169i | −1.01910 | + | 0.691927i | ||||
\(394\) | −2.91894 | − | 5.05576i | −0.147054 | − | 0.254705i | ||||
\(395\) | −2.29456 | − | 3.97429i | −0.115452 | − | 0.199968i | ||||
\(396\) | 3.63848 | − | 2.87863i | 0.182841 | − | 0.144657i | ||||
\(397\) | −16.4935 | − | 9.52254i | −0.827786 | − | 0.477923i | 0.0253078 | − | 0.999680i | \(-0.491943\pi\) |
−0.853094 | + | 0.521757i | \(0.825277\pi\) | |||||||
\(398\) | 4.11560 | − | 7.12843i | 0.206297 | − | 0.357316i | ||||
\(399\) | −2.44897 | − | 3.07760i | −0.122602 | − | 0.154073i | ||||
\(400\) | −7.36758 | − | 12.7610i | −0.368379 | − | 0.638051i | ||||
\(401\) | 21.8989i | 1.09358i | 0.837270 | + | 0.546789i | \(0.184150\pi\) | ||||
−0.837270 | + | 0.546789i | \(0.815850\pi\) | |||||||
\(402\) | −4.26206 | − | 6.27735i | −0.212572 | − | 0.313086i | ||||
\(403\) | −3.83331 | −0.190951 | ||||||||
\(404\) | −47.4961 | + | 82.2656i | −2.36302 | + | 4.09287i | ||||
\(405\) | −6.54990 | − | 6.17243i | −0.325467 | − | 0.306710i | ||||
\(406\) | −9.33089 | − | 13.6603i | −0.463084 | − | 0.677947i | ||||
\(407\) | −2.22986 | − | 1.28741i | −0.110530 | − | 0.0638147i | ||||
\(408\) | 37.6419 | − | 77.7790i | 1.86355 | − | 3.85063i | ||||
\(409\) | 31.7418 | + | 18.3261i | 1.56953 | + | 0.906168i | 0.996223 | + | 0.0868262i | \(0.0276725\pi\) |
0.573305 | + | 0.819342i | \(0.305661\pi\) | |||||||
\(410\) | 14.9189 | + | 8.61345i | 0.736793 | + | 0.425388i | ||||
\(411\) | 5.55165 | + | 8.17672i | 0.273843 | + | 0.403328i | ||||
\(412\) | 28.4695 | + | 16.4369i | 1.40259 | + | 0.809787i | ||||
\(413\) | 24.2611 | − | 1.83943i | 1.19381 | − | 0.0905125i | ||||
\(414\) | 64.0614 | − | 9.40234i | 3.14845 | − | 0.462100i | ||||
\(415\) | 2.29623 | − | 3.97719i | 0.112718 | − | 0.195232i | ||||
\(416\) | 71.6675 | 3.51379 | ||||||||
\(417\) | 4.90738 | − | 10.1400i | 0.240315 | − | 0.496560i | ||||
\(418\) | 0.665331i | 0.0325424i | ||||||||
\(419\) | 6.55229 | + | 11.3489i | 0.320100 | + | 0.554430i | 0.980508 | − | 0.196477i | \(-0.0629500\pi\) |
−0.660408 | + | 0.750907i | \(0.729617\pi\) | |||||||
\(420\) | −19.5156 | + | 15.5293i | −0.952265 | + | 0.757754i | ||||
\(421\) | 1.47281 | − | 2.55098i | 0.0717803 | − | 0.124327i | −0.827901 | − | 0.560874i | \(-0.810465\pi\) |
0.899682 | + | 0.436547i | \(0.143799\pi\) | |||||||
\(422\) | 11.5212 | + | 6.65176i | 0.560843 | + | 0.323803i | ||||
\(423\) | −17.8675 | + | 2.62242i | −0.868748 | + | 0.127507i | ||||
\(424\) | −2.62294 | − | 4.54307i | −0.127381 | − | 0.220631i | ||||
\(425\) | −2.65611 | − | 4.60051i | −0.128840 | − | 0.223158i | ||||
\(426\) | 35.3201 | + | 17.0935i | 1.71126 | + | 0.828184i | ||||
\(427\) | −19.1804 | − | 9.21617i | −0.928205 | − | 0.446002i | ||||
\(428\) | 90.6721 | − | 52.3496i | 4.38280 | − | 2.53041i | ||||
\(429\) | 1.48252 | + | 0.717483i | 0.0715770 | + | 0.0346404i | ||||
\(430\) | − | 1.22203i | − | 0.0589316i | ||||||
\(431\) | −15.9680 | + | 9.21911i | −0.769150 | + | 0.444069i | −0.832571 | − | 0.553918i | \(-0.813132\pi\) |
0.0634211 | + | 0.997987i | \(0.479799\pi\) | |||||||
\(432\) | 56.4283 | − | 51.7515i | 2.71491 | − | 2.48990i | ||||
\(433\) | − | 5.22327i | − | 0.251014i | −0.992093 | − | 0.125507i | \(-0.959944\pi\) | ||
0.992093 | − | 0.125507i | \(-0.0400558\pi\) | |||||||
\(434\) | 4.66350 | + | 6.82729i | 0.223855 | + | 0.327720i | ||||
\(435\) | 3.95925 | − | 0.289002i | 0.189831 | − | 0.0138566i | ||||
\(436\) | −106.781 | −5.11387 | ||||||||
\(437\) | −3.39499 | + | 5.88029i | −0.162404 | + | 0.281293i | ||||
\(438\) | 1.41333 | + | 19.3622i | 0.0675316 | + | 0.925163i | ||||
\(439\) | 13.5381 | − | 7.81621i | 0.646137 | − | 0.373048i | −0.140837 | − | 0.990033i | \(-0.544979\pi\) |
0.786975 | + | 0.616985i | \(0.211646\pi\) | |||||||
\(440\) | 2.66858 | 0.127220 | ||||||||
\(441\) | 15.3637 | + | 14.3163i | 0.731606 | + | 0.681727i | ||||
\(442\) | 48.4966 | 2.30675 | ||||||||
\(443\) | 5.30992 | − | 3.06568i | 0.252282 | − | 0.145655i | −0.368527 | − | 0.929617i | \(-0.620138\pi\) |
0.620809 | + | 0.783962i | \(0.286804\pi\) | |||||||
\(444\) | −76.8859 | − | 37.2097i | −3.64884 | − | 1.76590i | ||||
\(445\) | 5.97567 | − | 10.3502i | 0.283274 | − | 0.490645i | ||||
\(446\) | −10.2404 | −0.484895 | ||||||||
\(447\) | 9.54626 | + | 14.0602i | 0.451523 | + | 0.665023i | ||||
\(448\) | −43.2099 | − | 63.2585i | −2.04148 | − | 2.98868i | ||||
\(449\) | 40.6165i | 1.91681i | 0.285407 | + | 0.958407i | \(0.407871\pi\) | ||||
−0.285407 | + | 0.958407i | \(0.592129\pi\) | |||||||
\(450\) | −1.18847 | − | 8.09749i | −0.0560252 | − | 0.381719i | ||||
\(451\) | −1.55396 | + | 0.897177i | −0.0731729 | + | 0.0422464i | ||||
\(452\) | − | 95.2152i | − | 4.47855i | ||||||
\(453\) | −13.9348 | + | 9.46113i | −0.654713 | + | 0.444523i | ||||
\(454\) | −20.2532 | + | 11.6932i | −0.950528 | + | 0.548787i | ||||
\(455\) | −7.98031 | − | 3.83453i | −0.374123 | − | 0.179766i | ||||
\(456\) | 1.01634 | + | 13.9236i | 0.0475946 | + | 0.652031i | ||||
\(457\) | −10.9639 | − | 18.9901i | −0.512872 | − | 0.888320i | −0.999889 | − | 0.0149271i | \(-0.995248\pi\) |
0.487017 | − | 0.873392i | \(-0.338085\pi\) | |||||||
\(458\) | −1.95296 | − | 3.38263i | −0.0912560 | − | 0.158060i | ||||
\(459\) | 20.3431 | − | 18.6571i | 0.949535 | − | 0.870839i | ||||
\(460\) | 37.2880 | + | 21.5282i | 1.73856 | + | 1.00376i | ||||
\(461\) | −14.8897 | + | 25.7897i | −0.693483 | + | 1.20115i | 0.277206 | + | 0.960810i | \(0.410591\pi\) |
−0.970689 | + | 0.240338i | \(0.922742\pi\) | |||||||
\(462\) | −0.525734 | − | 3.51331i | −0.0244593 | − | 0.163454i | ||||
\(463\) | 1.64857 | + | 2.85540i | 0.0766153 | + | 0.132702i | 0.901788 | − | 0.432180i | \(-0.142255\pi\) |
−0.825172 | + | 0.564881i | \(0.808922\pi\) | |||||||
\(464\) | 33.7723i | 1.56784i | ||||||||
\(465\) | −1.97880 | + | 0.144441i | −0.0917646 | + | 0.00669829i | ||||
\(466\) | −7.58660 | −0.351442 | ||||||||
\(467\) | −16.5766 | + | 28.7116i | −0.767075 | + | 1.32861i | 0.172067 | + | 0.985085i | \(0.444955\pi\) |
−0.939142 | + | 0.343528i | \(0.888378\pi\) | |||||||
\(468\) | 50.7832 | + | 20.1581i | 2.34745 | + | 0.931807i | ||||
\(469\) | −4.23629 | + | 0.321187i | −0.195614 | + | 0.0148310i | ||||
\(470\) | −14.2219 | − | 8.21103i | −0.656009 | − | 0.378747i | ||||
\(471\) | −10.8501 | + | 0.791993i | −0.499945 | + | 0.0364931i | ||||
\(472\) | −74.7927 | − | 43.1816i | −3.44261 | − | 1.98759i | ||||
\(473\) | 0.110234 | + | 0.0636434i | 0.00506855 | + | 0.00292633i | ||||
\(474\) | 21.6268 | − | 1.57864i | 0.993353 | − | 0.0725091i | ||||
\(475\) | 0.743281 | + | 0.429133i | 0.0341041 | + | 0.0196900i | ||||
\(476\) | −43.1448 | − | 63.1632i | −1.97754 | − | 2.89508i | ||||
\(477\) | −0.243349 | − | 1.65802i | −0.0111422 | − | 0.0759155i | ||||
\(478\) | −9.75990 | + | 16.9046i | −0.446407 | + | 0.773200i | ||||
\(479\) | −22.2625 | −1.01720 | −0.508599 | − | 0.861004i | \(-0.669836\pi\) | ||||
−0.508599 | + | 0.861004i | \(0.669836\pi\) | |||||||
\(480\) | 36.9956 | − | 2.70047i | 1.68861 | − | 0.123259i | ||||
\(481\) | − | 30.3227i | − | 1.38260i | ||||||
\(482\) | −36.4899 | − | 63.2023i | −1.66207 | − | 2.87879i | ||||
\(483\) | 13.2809 | − | 33.7338i | 0.604301 | − | 1.53494i | ||||
\(484\) | 29.7136 | − | 51.4655i | 1.35062 | − | 2.33934i | ||||
\(485\) | −3.69117 | − | 2.13110i | −0.167607 | − | 0.0967681i | ||||
\(486\) | 39.7353 | − | 15.1530i | 1.80243 | − | 0.687355i | ||||
\(487\) | −3.44182 | − | 5.96141i | −0.155964 | − | 0.270137i | 0.777446 | − | 0.628950i | \(-0.216515\pi\) |
−0.933410 | + | 0.358813i | \(0.883182\pi\) | |||||||
\(488\) | 37.7667 | + | 65.4138i | 1.70962 | + | 2.96114i | ||||
\(489\) | −2.30671 | − | 31.6012i | −0.104313 | − | 1.42906i | ||||
\(490\) | 2.87918 | + | 18.8783i | 0.130068 | + | 0.852833i | ||||
\(491\) | −10.3634 | + | 5.98332i | −0.467694 | + | 0.270023i | −0.715274 | − | 0.698844i | \(-0.753698\pi\) |
0.247580 | + | 0.968868i | \(0.420365\pi\) | |||||||
\(492\) | −49.2470 | + | 33.4367i | −2.22023 | + | 1.50744i | ||||
\(493\) | 12.1753i | 0.548350i | ||||||||
\(494\) | −6.78561 | + | 3.91767i | −0.305299 | + | 0.176264i | ||||
\(495\) | 0.792332 | + | 0.314511i | 0.0356127 | + | 0.0141362i | ||||
\(496\) | − | 16.8791i | − | 0.757895i | ||||||
\(497\) | 18.1424 | − | 12.3925i | 0.813799 | − | 0.555881i | ||||
\(498\) | 12.1894 | + | 17.9532i | 0.546222 | + | 0.804500i | ||||
\(499\) | −21.2056 | −0.949291 | −0.474645 | − | 0.880177i | \(-0.657424\pi\) | ||||
−0.474645 | + | 0.880177i | \(0.657424\pi\) | |||||||
\(500\) | 2.72121 | − | 4.71328i | 0.121696 | − | 0.210784i | ||||
\(501\) | 11.7604 | + | 5.69156i | 0.525415 | + | 0.254280i | ||||
\(502\) | −22.6998 | + | 13.1057i | −1.01314 | + | 0.584938i | ||||
\(503\) | −10.5680 | −0.471203 | −0.235601 | − | 0.971850i | \(-0.575706\pi\) | ||||
−0.235601 | + | 0.971850i | \(0.575706\pi\) | |||||||
\(504\) | −16.3690 | − | 72.7210i | −0.729134 | − | 3.23925i | ||||
\(505\) | −17.4540 | −0.776693 | ||||||||
\(506\) | −5.31120 | + | 3.06642i | −0.236112 | + | 0.136319i | ||||
\(507\) | −0.227167 | − | 3.11212i | −0.0100888 | − | 0.138214i | ||||
\(508\) | −5.76764 | + | 9.98985i | −0.255898 | + | 0.443228i | ||||
\(509\) | 21.5549 | 0.955403 | 0.477702 | − | 0.878522i | \(-0.341470\pi\) | ||||
0.477702 | + | 0.878522i | \(0.341470\pi\) | |||||||
\(510\) | 25.0345 | − | 1.82738i | 1.10855 | − | 0.0809177i | ||||
\(511\) | 9.79789 | + | 4.70788i | 0.433433 | + | 0.208264i | ||||
\(512\) | 38.8098i | 1.71517i | ||||||||
\(513\) | −1.33923 | + | 4.25385i | −0.0591283 | + | 0.187812i | ||||
\(514\) | 23.5375 | − | 13.5894i | 1.03819 | − | 0.599401i | ||||
\(515\) | 6.04027i | 0.266166i | ||||||||
\(516\) | 3.80087 | + | 1.83947i | 0.167324 | + | 0.0809781i | ||||
\(517\) | 1.48136 | − | 0.855262i | 0.0651500 | − | 0.0376144i | ||||
\(518\) | −54.0061 | + | 36.8898i | −2.37289 | + | 1.62085i | ||||
\(519\) | 3.84886 | + | 1.86270i | 0.168946 | + | 0.0817633i | ||||
\(520\) | 15.7134 | + | 27.2164i | 0.689079 | + | 1.19352i | ||||
\(521\) | −17.9132 | − | 31.0265i | −0.784791 | − | 1.35930i | −0.929124 | − | 0.369768i | \(-0.879437\pi\) |
0.144333 | − | 0.989529i | \(-0.453896\pi\) | |||||||
\(522\) | −6.92055 | + | 17.4346i | −0.302904 | + | 0.763091i | ||||
\(523\) | 5.63357 | + | 3.25254i | 0.246339 | + | 0.142224i | 0.618087 | − | 0.786110i | \(-0.287908\pi\) |
−0.371748 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(524\) | 38.3653 | − | 66.4506i | 1.67599 | − | 2.90291i | ||||
\(525\) | −4.26402 | − | 1.67873i | −0.186097 | − | 0.0732658i | ||||
\(526\) | 18.7230 | + | 32.4291i | 0.816359 | + | 1.41398i | ||||
\(527\) | − | 6.08514i | − | 0.265073i | ||||||
\(528\) | −3.15928 | + | 6.52797i | −0.137490 | + | 0.284093i | ||||
\(529\) | −39.5882 | −1.72122 | ||||||||
\(530\) | 0.761945 | − | 1.31973i | 0.0330968 | − | 0.0573253i | ||||
\(531\) | −17.1176 | − | 21.6360i | −0.742838 | − | 0.938920i | ||||
\(532\) | 11.1393 | + | 5.35240i | 0.482948 | + | 0.232056i | ||||
\(533\) | −18.3003 | − | 10.5657i | −0.792675 | − | 0.457651i | ||||
\(534\) | 31.7216 | + | 46.7209i | 1.37273 | + | 2.02181i | ||||
\(535\) | 16.6602 | + | 9.61880i | 0.720285 | + | 0.415857i | ||||
\(536\) | 13.0597 | + | 7.54003i | 0.564094 | + | 0.325680i | ||||
\(537\) | 0.779497 | − | 1.61066i | 0.0336378 | − | 0.0695052i | ||||
\(538\) | 20.2823 | + | 11.7100i | 0.874430 | + | 0.504853i | ||||
\(539\) | −1.85287 | − | 0.723464i | −0.0798086 | − | 0.0311618i | ||||
\(540\) | 26.9745 | + | 8.49229i | 1.16080 | + | 0.365450i | ||||
\(541\) | −17.8864 | + | 30.9801i | −0.768994 | + | 1.33194i | 0.169114 | + | 0.985596i | \(0.445909\pi\) |
−0.938109 | + | 0.346341i | \(0.887424\pi\) | |||||||
\(542\) | 81.2324 | 3.48923 | ||||||||
\(543\) | −4.77154 | − | 7.02773i | −0.204766 | − | 0.301589i | ||||
\(544\) | 113.768i | 4.87775i | ||||||||
\(545\) | −9.81002 | − | 16.9915i | −0.420215 | − | 0.727834i | ||||
\(546\) | 32.7360 | − | 26.0493i | 1.40097 | − | 1.11481i | ||||
\(547\) | 5.55863 | − | 9.62783i | 0.237670 | − | 0.411656i | −0.722375 | − | 0.691501i | \(-0.756950\pi\) |
0.960045 | + | 0.279845i | \(0.0902831\pi\) | |||||||
\(548\) | −26.8946 | − | 15.5276i | −1.14888 | − | 0.663306i | ||||
\(549\) | 3.50388 | + | 23.8732i | 0.149542 | + | 1.01888i | ||||
\(550\) | 0.387602 | + | 0.671346i | 0.0165274 | + | 0.0286263i | ||||
\(551\) | −0.983554 | − | 1.70356i | −0.0419008 | − | 0.0725743i | ||||
\(552\) | −106.465 | + | 72.2851i | −4.53144 | + | 3.07666i | ||||
\(553\) | 5.25851 | − | 10.9438i | 0.223615 | − | 0.465380i | ||||
\(554\) | −46.9066 | + | 27.0816i | −1.99287 | + | 1.15058i | ||||
\(555\) | −1.14258 | − | 15.6529i | −0.0484996 | − | 0.664431i | ||||
\(556\) | 35.3971i | 1.50117i | ||||||||
\(557\) | −26.1440 | + | 15.0942i | −1.10776 | + | 0.639564i | −0.938247 | − | 0.345965i | \(-0.887552\pi\) |
−0.169509 | + | 0.985529i | \(0.554218\pi\) | |||||||
\(558\) | 3.45883 | − | 8.71367i | 0.146424 | − | 0.368879i | ||||
\(559\) | 1.49901i | 0.0634013i | ||||||||
\(560\) | 16.8845 | − | 35.1395i | 0.713501 | − | 1.48492i | ||||
\(561\) | −1.13896 | + | 2.35342i | −0.0480869 | + | 0.0993613i | ||||
\(562\) | 26.9041 | 1.13488 | ||||||||
\(563\) | −10.8494 | + | 18.7917i | −0.457248 | + | 0.791978i | −0.998814 | − | 0.0486807i | \(-0.984498\pi\) |
0.541566 | + | 0.840658i | \(0.317832\pi\) | |||||||
\(564\) | 46.9463 | − | 31.8745i | 1.97679 | − | 1.34216i | ||||
\(565\) | 15.1511 | − | 8.74750i | 0.637412 | − | 0.368010i | ||||
\(566\) | 28.7954 | 1.21036 | ||||||||
\(567\) | 3.71053 | − | 23.5209i | 0.155828 | − | 0.987784i | ||||
\(568\) | −77.9869 | −3.27226 | ||||||||
\(569\) | 18.7418 | − | 10.8206i | 0.785699 | − | 0.453624i | −0.0527472 | − | 0.998608i | \(-0.516798\pi\) |
0.838446 | + | 0.544984i | \(0.183464\pi\) | |||||||
\(570\) | −3.35519 | + | 2.27803i | −0.140534 | + | 0.0954164i | ||||
\(571\) | 8.70565 | − | 15.0786i | 0.364320 | − | 0.631021i | −0.624347 | − | 0.781147i | \(-0.714635\pi\) |
0.988667 | + | 0.150126i | \(0.0479681\pi\) | |||||||
\(572\) | −5.17523 | −0.216387 | ||||||||
\(573\) | −1.42554 | + | 2.94558i | −0.0595529 | + | 0.123053i | ||||
\(574\) | 3.44575 | + | 45.4476i | 0.143823 | + | 1.89695i | ||||
\(575\) | 7.91127i | 0.329923i | ||||||||
\(576\) | −32.0480 | + | 80.7369i | −1.33533 | + | 3.36404i | ||||
\(577\) | 31.1294 | − | 17.9726i | 1.29593 | − | 0.748207i | 0.316234 | − | 0.948681i | \(-0.397582\pi\) |
0.979699 | + | 0.200474i | \(0.0642482\pi\) | |||||||
\(578\) | 30.6080i | 1.27313i | ||||||||
\(579\) | −1.56137 | − | 21.3904i | −0.0648885 | − | 0.888953i | ||||
\(580\) | −10.8026 | + | 6.23689i | −0.448554 | + | 0.258973i | ||||
\(581\) | 12.1157 | − | 0.918592i | 0.502646 | − | 0.0381096i | ||||
\(582\) | 16.6620 | − | 11.3128i | 0.690664 | − | 0.468932i | ||||
\(583\) | 0.0793642 | + | 0.137463i | 0.00328693 | + | 0.00569313i | ||||
\(584\) | −19.2923 | − | 33.4152i | −0.798320 | − | 1.38273i | ||||
\(585\) | 1.45784 | + | 9.93281i | 0.0602744 | + | 0.410671i | ||||
\(586\) | −20.3840 | − | 11.7687i | −0.842055 | − | 0.486161i | ||||
\(587\) | 21.2857 | − | 36.8680i | 0.878556 | − | 1.52170i | 0.0256305 | − | 0.999671i | \(-0.491841\pi\) |
0.852926 | − | 0.522032i | \(-0.174826\pi\) | |||||||
\(588\) | −63.0507 | − | 19.4615i | −2.60017 | − | 0.802580i | ||||
\(589\) | 0.491572 | + | 0.851428i | 0.0202549 | + | 0.0350825i | ||||
\(590\) | − | 25.0879i | − | 1.03285i | ||||||
\(591\) | 2.08199 | + | 3.06645i | 0.0856417 | + | 0.126137i | ||||
\(592\) | 133.519 | 5.48761 | ||||||||
\(593\) | −12.0906 | + | 20.9416i | −0.496503 | + | 0.859968i | −0.999992 | − | 0.00403339i | \(-0.998716\pi\) |
0.503489 | + | 0.864002i | \(0.332049\pi\) | |||||||
\(594\) | −2.96864 | + | 2.72260i | −0.121805 | + | 0.111710i | ||||
\(595\) | 6.08708 | − | 12.6683i | 0.249546 | − | 0.519348i | ||||
\(596\) | −46.2462 | − | 26.7002i | −1.89432 | − | 1.09368i | ||||
\(597\) | −2.27657 | + | 4.70404i | −0.0931737 | + | 0.192524i | ||||
\(598\) | −62.5479 | − | 36.1120i | −2.55777 | − | 1.47673i | ||||
\(599\) | −17.4661 | − | 10.0840i | −0.713644 | − | 0.412023i | 0.0987646 | − | 0.995111i | \(-0.468511\pi\) |
−0.812409 | + | 0.583088i | \(0.801844\pi\) | |||||||
\(600\) | 9.13698 | + | 13.4574i | 0.373016 | + | 0.549394i | ||||
\(601\) | 5.59991 | + | 3.23311i | 0.228425 | + | 0.131881i | 0.609845 | − | 0.792520i | \(-0.291232\pi\) |
−0.381420 | + | 0.924402i | \(0.624565\pi\) | |||||||
\(602\) | 2.66980 | − | 1.82365i | 0.108813 | − | 0.0743266i | ||||
\(603\) | 2.98893 | + | 3.77790i | 0.121719 | + | 0.153848i | ||||
\(604\) | 26.4621 | − | 45.8337i | 1.07673 | − | 1.86495i | ||||
\(605\) | 10.9193 | 0.443931 | ||||||||
\(606\) | 35.9275 | − | 74.2364i | 1.45945 | − | 3.01565i | ||||
\(607\) | 30.8419i | 1.25184i | 0.779889 | + | 0.625918i | \(0.215276\pi\) | ||||
−0.779889 | + | 0.625918i | \(0.784724\pi\) | |||||||
\(608\) | −9.19043 | − | 15.9183i | −0.372721 | − | 0.645572i | ||||
\(609\) | 6.53983 | + | 8.21856i | 0.265007 | + | 0.333033i | ||||
\(610\) | −10.9709 | + | 19.0022i | −0.444201 | + | 0.769378i | ||||
\(611\) | 17.4454 | + | 10.0721i | 0.705764 | + | 0.407473i | ||||
\(612\) | −31.9997 | + | 80.6152i | −1.29351 | + | 3.25868i | ||||
\(613\) | −19.4865 | − | 33.7516i | −0.787052 | − | 1.36321i | −0.927765 | − | 0.373164i | \(-0.878273\pi\) |
0.140713 | − | 0.990050i | \(-0.455061\pi\) | |||||||
\(614\) | 15.8112 | + | 27.3858i | 0.638087 | + | 1.10520i | ||||
\(615\) | −9.84497 | − | 4.76457i | −0.396987 | − | 0.192126i | ||||
\(616\) | 3.98236 | + | 5.83010i | 0.160454 | + | 0.234901i | ||||
\(617\) | −6.83491 | + | 3.94614i | −0.275163 | + | 0.158866i | −0.631232 | − | 0.775594i | \(-0.717450\pi\) |
0.356068 | + | 0.934460i | \(0.384117\pi\) | |||||||
\(618\) | −25.6909 | − | 12.4334i | −1.03344 | − | 0.500143i | ||||
\(619\) | − | 30.7413i | − | 1.23560i | −0.786336 | − | 0.617799i | \(-0.788024\pi\) | ||
0.786336 | − | 0.617799i | \(-0.211976\pi\) | |||||||
\(620\) | 5.39906 | − | 3.11715i | 0.216832 | − | 0.125188i | ||||
\(621\) | −40.1299 | + | 8.91465i | −1.61036 | + | 0.357733i | ||||
\(622\) | 13.5637i | 0.543853i | ||||||||
\(623\) | 31.5298 | − | 2.39053i | 1.26321 | − | 0.0957744i | ||||
\(624\) | −85.1805 | + | 6.21769i | −3.40995 | + | 0.248907i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.7111 | − | 46.2650i | 1.06759 | − | 1.84912i | ||||
\(627\) | −0.0307522 | − | 0.421296i | −0.00122812 | − | 0.0168249i | ||||
\(628\) | 29.6039 | − | 17.0918i | 1.18132 | − | 0.682038i | ||||
\(629\) | 48.1354 | 1.91929 | ||||||||
\(630\) | 15.9172 | − | 14.6805i | 0.634155 | − | 0.584884i | ||||
\(631\) | 23.5241 | 0.936478 | 0.468239 | − | 0.883602i | \(-0.344889\pi\) | ||||
0.468239 | + | 0.883602i | \(0.344889\pi\) | |||||||
\(632\) | −37.3234 | + | 21.5487i | −1.48465 | + | 0.857161i | ||||
\(633\) | −7.60281 | − | 3.67946i | −0.302185 | − | 0.146245i | ||||
\(634\) | 1.60447 | − | 2.77902i | 0.0637216 | − | 0.110369i | ||||
\(635\) | −2.11951 | −0.0841103 | ||||||||
\(636\) | 2.95781 | + | 4.35639i | 0.117285 | + | 0.172742i | ||||
\(637\) | −3.53175 | − | 23.1571i | −0.139933 | − | 0.917517i | ||||
\(638\) | − | 1.77673i | − | 0.0703414i | ||||||
\(639\) | −23.1552 | − | 9.19130i | −0.916005 | − | 0.363602i | ||||
\(640\) | −31.3146 | + | 18.0795i | −1.23782 | + | 0.714656i | ||||
\(641\) | 30.7331i | 1.21389i | 0.794745 | + | 0.606943i | \(0.207604\pi\) | ||||
−0.794745 | + | 0.606943i | \(0.792396\pi\) | |||||||
\(642\) | −75.2048 | + | 51.0609i | −2.96810 | + | 2.01521i | ||||
\(643\) | −17.2128 | + | 9.93780i | −0.678806 | + | 0.391909i | −0.799405 | − | 0.600793i | \(-0.794852\pi\) |
0.120599 | + | 0.992701i | \(0.461518\pi\) | |||||||
\(644\) | 8.61223 | + | 113.591i | 0.339369 | + | 4.47610i | ||||
\(645\) | 0.0564834 | + | 0.773806i | 0.00222403 | + | 0.0304686i | ||||
\(646\) | −6.21906 | − | 10.7717i | −0.244686 | − | 0.423808i | ||||
\(647\) | −11.7226 | − | 20.3041i | −0.460861 | − | 0.798235i | 0.538143 | − | 0.842854i | \(-0.319126\pi\) |
−0.999004 | + | 0.0446187i | \(0.985793\pi\) | |||||||
\(648\) | −57.9666 | + | 61.5115i | −2.27714 | + | 2.41640i | ||||
\(649\) | 2.26306 | + | 1.30658i | 0.0888328 | + | 0.0512876i | ||||
\(650\) | −4.56463 | + | 7.90618i | −0.179040 | + | 0.310106i | ||||
\(651\) | −3.26855 | − | 4.10757i | −0.128105 | − | 0.160988i | ||||
\(652\) | 49.7805 | + | 86.2224i | 1.94956 | + | 3.37673i | ||||
\(653\) | 16.1529i | 0.632113i | 0.948740 | + | 0.316057i | \(0.102359\pi\) | ||||
−0.948740 | + | 0.316057i | \(0.897641\pi\) | |||||||
\(654\) | 92.4621 | − | 6.74921i | 3.61556 | − | 0.263915i | ||||
\(655\) | 14.0986 | 0.550877 | ||||||||
\(656\) | 46.5237 | − | 80.5814i | 1.81645 | − | 3.14618i | ||||
\(657\) | −1.78988 | − | 12.1951i | −0.0698299 | − | 0.475775i | ||||
\(658\) | −3.28477 | − | 43.3244i | −0.128054 | − | 1.68896i | ||||
\(659\) | −4.06154 | − | 2.34493i | −0.158215 | − | 0.0913455i | 0.418802 | − | 0.908078i | \(-0.362450\pi\) |
−0.577017 | + | 0.816732i | \(0.695783\pi\) | |||||||
\(660\) | −2.67152 | + | 0.195005i | −0.103989 | + | 0.00759058i | ||||
\(661\) | 16.3751 | + | 9.45416i | 0.636917 | + | 0.367724i | 0.783426 | − | 0.621485i | \(-0.213470\pi\) |
−0.146509 | + | 0.989209i | \(0.546804\pi\) | |||||||
\(662\) | 73.9824 | + | 42.7138i | 2.87541 | + | 1.66012i | ||||
\(663\) | −30.7087 | + | 2.24156i | −1.19263 | + | 0.0870549i | ||||
\(664\) | −37.3506 | − | 21.5644i | −1.44949 | − | 0.836861i | ||||
\(665\) | 0.171672 | + | 2.26426i | 0.00665715 | + | 0.0878043i | ||||
\(666\) | 68.9280 | + | 27.3605i | 2.67090 | + | 1.06020i | ||||
\(667\) | 9.06613 | − | 15.7030i | 0.351042 | − | 0.608022i | ||||
\(668\) | −41.0534 | −1.58841 | ||||||||
\(669\) | 6.48433 | − | 0.473319i | 0.250699 | − | 0.0182996i | ||||
\(670\) | 4.38065i | 0.169239i | ||||||||
\(671\) | −1.14273 | − | 1.97927i | −0.0441148 | − | 0.0764090i | ||||
\(672\) | 61.1088 | + | 76.7951i | 2.35732 | + | 2.96244i | ||||
\(673\) | 13.1728 | − | 22.8160i | 0.507775 | − | 0.879492i | −0.492185 | − | 0.870491i | \(-0.663802\pi\) |
0.999959 | − | 0.00900082i | \(-0.00286509\pi\) | |||||||
\(674\) | −57.6876 | − | 33.3060i | −2.22204 | − | 1.28290i | ||||
\(675\) | 1.12683 | + | 5.07250i | 0.0433717 | + | 0.195241i | ||||
\(676\) | 4.90243 | + | 8.49126i | 0.188555 | + | 0.326587i | ||||
\(677\) | −22.0887 | − | 38.2587i | −0.848936 | − | 1.47040i | −0.882159 | − | 0.470952i | \(-0.843910\pi\) |
0.0332229 | − | 0.999448i | \(-0.489423\pi\) | |||||||
\(678\) | 6.01820 | + | 82.4475i | 0.231128 | + | 3.16638i | ||||
\(679\) | −0.852530 | − | 11.2444i | −0.0327171 | − | 0.431521i | ||||
\(680\) | −43.2044 | + | 24.9441i | −1.65681 | + | 0.956562i | ||||
\(681\) | 12.2841 | − | 8.34037i | 0.470727 | − | 0.319604i | ||||
\(682\) | 0.887995i | 0.0340031i | ||||||||
\(683\) | 10.2520 | − | 5.91898i | 0.392281 | − | 0.226484i | −0.290867 | − | 0.956764i | \(-0.593944\pi\) |
0.683148 | + | 0.730280i | \(0.260610\pi\) | |||||||
\(684\) | −2.03492 | − | 13.8646i | −0.0778071 | − | 0.530127i | ||||
\(685\) | − | 5.70613i | − | 0.218020i | ||||||
\(686\) | −36.9471 | + | 34.4625i | −1.41065 | + | 1.31578i | ||||
\(687\) | 1.39299 | + | 2.05166i | 0.0531458 | + | 0.0782756i | ||||
\(688\) | −6.60055 | −0.251643 | ||||||||
\(689\) | −0.934642 | + | 1.61885i | −0.0356070 | + | 0.0616732i | ||||
\(690\) | −33.6487 | − | 16.2846i | −1.28098 | − | 0.619945i | ||||
\(691\) | −34.9953 | + | 20.2045i | −1.33128 | + | 0.768616i | −0.985496 | − | 0.169697i | \(-0.945721\pi\) |
−0.345786 | + | 0.938313i | \(0.612388\pi\) | |||||||
\(692\) | −13.4357 | −0.510749 | ||||||||
\(693\) | 0.495289 | + | 2.20037i | 0.0188145 | + | 0.0835852i | ||||
\(694\) | −49.1470 | −1.86560 | ||||||||
\(695\) | −5.63256 | + | 3.25196i | −0.213655 | + | 0.123354i | ||||
\(696\) | −2.71409 | − | 37.1822i | −0.102877 | − | 1.40939i | ||||
\(697\) | 16.7724 | − | 29.0506i | 0.635300 | − | 1.10037i | ||||
\(698\) | 36.7748 | 1.39195 | ||||||||
\(699\) | 4.80393 | − | 0.350659i | 0.181701 | − | 0.0132632i | ||||
\(700\) | 14.3581 | − | 1.08860i | 0.542685 | − | 0.0411453i | ||||
\(701\) | − | 30.0434i | − | 1.13472i | −0.823468 | − | 0.567362i | \(-0.807964\pi\) | ||
0.823468 | − | 0.567362i | \(-0.192036\pi\) | |||||||
\(702\) | −45.2477 | − | 14.2452i | −1.70776 | − | 0.537650i | ||||
\(703\) | −6.73507 | + | 3.88850i | −0.254018 | + | 0.146657i | ||||
\(704\) | − | 8.22776i | − | 0.310095i | ||||||
\(705\) | 9.38502 | + | 4.54198i | 0.353460 | + | 0.171061i | ||||
\(706\) | 7.65180 | − | 4.41777i | 0.287979 | − | 0.166265i | ||||
\(707\) | −26.0468 | − | 38.1321i | −0.979592 | − | 1.43411i | ||||
\(708\) | 78.0304 | + | 37.7636i | 2.93256 | + | 1.41924i | ||||
\(709\) | −0.901305 | − | 1.56111i | −0.0338492 | − | 0.0586286i | 0.848605 | − | 0.529028i | \(-0.177443\pi\) |
−0.882454 | + | 0.470399i | \(0.844110\pi\) | |||||||
\(710\) | −11.3273 | − | 19.6195i | −0.425107 | − | 0.736306i | ||||
\(711\) | −13.6214 | + | 1.99922i | −0.510843 | + | 0.0749767i | ||||
\(712\) | −97.2006 | − | 56.1188i | −3.64275 | − | 2.10314i | ||||
\(713\) | −4.53118 | + | 7.84823i | −0.169694 | + | 0.293919i | ||||
\(714\) | 41.3517 | + | 51.9664i | 1.54755 | + | 1.94479i | ||||
\(715\) | −0.475453 | − | 0.823508i | −0.0177809 | − | 0.0307974i | ||||
\(716\) | 5.62254i | 0.210124i | ||||||||
\(717\) | 5.39874 | − | 11.1553i | 0.201620 | − | 0.416604i | ||||
\(718\) | −81.8242 | −3.05365 | ||||||||
\(719\) | 13.5692 | − | 23.5026i | 0.506047 | − | 0.876499i | −0.493929 | − | 0.869502i | \(-0.664440\pi\) |
0.999976 | − | 0.00699644i | \(-0.00222705\pi\) | |||||||
\(720\) | −43.7369 | + | 6.41929i | −1.62998 | + | 0.239233i | ||||
\(721\) | −13.1963 | + | 9.01398i | −0.491456 | + | 0.335698i | ||||
\(722\) | −43.1488 | − | 24.9120i | −1.60583 | − | 0.927128i | ||||
\(723\) | 26.0271 | + | 38.3339i | 0.967959 | + | 1.42565i | ||||
\(724\) | 23.1154 | + | 13.3457i | 0.859075 | + | 0.495987i | ||||
\(725\) | −1.98489 | − | 1.14598i | −0.0737170 | − | 0.0425605i | ||||
\(726\) | −22.4763 | + | 46.4424i | −0.834174 | + | 1.72364i | ||||
\(727\) | 9.18421 | + | 5.30251i | 0.340624 | + | 0.196659i | 0.660548 | − | 0.750784i | \(-0.270324\pi\) |
−0.319924 | + | 0.947443i | \(0.603657\pi\) | |||||||
\(728\) | −36.0109 | + | 74.9449i | −1.33465 | + | 2.77764i | ||||
\(729\) | −24.4605 | + | 11.4317i | −0.905945 | + | 0.423396i | ||||
\(730\) | 5.60427 | − | 9.70687i | 0.207423 | − | 0.359268i | ||||
\(731\) | −2.37958 | −0.0880120 | ||||||||
\(732\) | −42.5883 | − | 62.7259i | −1.57411 | − | 2.31842i | ||||
\(733\) | 44.3831i | 1.63933i | 0.572845 | + | 0.819663i | \(0.305839\pi\) | ||||
−0.572845 | + | 0.819663i | \(0.694161\pi\) | |||||||
\(734\) | 1.70344 | + | 2.95044i | 0.0628750 | + | 0.108903i | ||||
\(735\) | −2.69570 | − | 11.8209i | −0.0994325 | − | 0.436020i | ||||
\(736\) | 84.7149 | − | 146.730i | 3.12263 | − | 5.40856i | ||||
\(737\) | −0.395158 | − | 0.228144i | −0.0145558 | − | 0.00840380i | ||||
\(738\) | 40.5300 | − | 32.0658i | 1.49193 | − | 1.18036i | ||||
\(739\) | 21.2312 | + | 36.7736i | 0.781004 | + | 1.35274i | 0.931358 | + | 0.364106i | \(0.118625\pi\) |
−0.150354 | + | 0.988632i | \(0.548041\pi\) | |||||||
\(740\) | 24.6577 | + | 42.7083i | 0.906434 | + | 1.56999i | ||||
\(741\) | 4.11565 | − | 2.79436i | 0.151192 | − | 0.102653i | ||||
\(742\) | 4.02030 | − | 0.304811i | 0.147590 | − | 0.0111900i | ||||
\(743\) | −8.84967 | + | 5.10936i | −0.324663 | + | 0.187444i | −0.653469 | − | 0.756953i | \(-0.726687\pi\) |
0.328806 | + | 0.944397i | \(0.393354\pi\) | |||||||
\(744\) | 1.35648 | + | 18.5833i | 0.0497309 | + | 0.681298i | ||||
\(745\) | − | 9.81189i | − | 0.359480i | ||||||
\(746\) | 23.8849 | − | 13.7899i | 0.874488 | − | 0.504886i | ||||
\(747\) | −8.54831 | − | 10.8048i | −0.312766 | − | 0.395325i | ||||
\(748\) | − | 8.21536i | − | 0.300383i | ||||||
\(749\) | 3.84793 | + | 50.7522i | 0.140600 | + | 1.85445i | ||||
\(750\) | −2.05841 | + | 4.25326i | −0.0751625 | + | 0.155307i | ||||
\(751\) | 29.9846 | 1.09415 | 0.547076 | − | 0.837083i | \(-0.315741\pi\) | ||||
0.547076 | + | 0.837083i | \(0.315741\pi\) | |||||||
\(752\) | −44.3502 | + | 76.8167i | −1.61728 | + | 2.80122i | ||||
\(753\) | 13.7680 | − | 9.34792i | 0.501735 | − | 0.340657i | ||||
\(754\) | 18.1206 | − | 10.4619i | 0.659913 | − | 0.381001i | ||||
\(755\) | 9.72438 | 0.353907 | ||||||||
\(756\) | 21.7011 | + | 71.6048i | 0.789260 | + | 2.60424i | ||||
\(757\) | −39.0362 | −1.41879 | −0.709397 | − | 0.704809i | \(-0.751033\pi\) | ||||
−0.709397 | + | 0.704809i | \(0.751033\pi\) | |||||||
\(758\) | 37.3352 | − | 21.5555i | 1.35608 | − | 0.782931i | ||||
\(759\) | 3.22138 | − | 2.18718i | 0.116929 | − | 0.0793898i | ||||
\(760\) | 4.03008 | − | 6.98031i | 0.146187 | − | 0.253203i | ||||
\(761\) | 9.67729 | 0.350801 | 0.175401 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175401 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(762\) | 4.36282 | − | 9.01484i | 0.158048 | − | 0.326573i | ||||
\(763\) | 22.4819 | − | 46.7887i | 0.813901 | − | 1.69387i | ||||
\(764\) | − | 10.2825i | − | 0.372008i | ||||||
\(765\) | −15.7677 | + | 2.31424i | −0.570083 | + | 0.0836714i | ||||
\(766\) | 13.9502 | − | 8.05414i | 0.504040 | − | 0.291008i | ||||
\(767\) | 30.7741i | 1.11119i | ||||||||
\(768\) | −5.13643 | − | 70.3675i | −0.185345 | − | 2.53917i | ||||
\(769\) | 4.16188 | − | 2.40286i | 0.150081 | − | 0.0866494i | −0.423079 | − | 0.906093i | \(-0.639051\pi\) |
0.573160 | + | 0.819443i | \(0.305717\pi\) | |||||||
\(770\) | −0.888279 | + | 1.84866i | −0.0320114 | + | 0.0666211i | ||||
\(771\) | −14.2761 | + | 9.69288i | −0.514142 | + | 0.349081i | ||||
\(772\) | 33.6957 | + | 58.3626i | 1.21273 | + | 2.10052i | ||||
\(773\) | −7.44040 | − | 12.8872i | −0.267613 | − | 0.463519i | 0.700632 | − | 0.713523i | \(-0.252901\pi\) |
−0.968245 | + | 0.250004i | \(0.919568\pi\) | |||||||
\(774\) | −3.40746 | − | 1.35257i | −0.122479 | − | 0.0486171i | ||||
\(775\) | 0.992032 | + | 0.572750i | 0.0356348 | + | 0.0205738i | ||||
\(776\) | −20.0136 | + | 34.6645i | −0.718446 | + | 1.24438i | ||||
\(777\) | 32.4922 | − | 25.8553i | 1.16565 | − | 0.927554i | ||||
\(778\) | −7.66467 | − | 13.2756i | −0.274792 | − | 0.475953i | ||||
\(779\) | 5.41966i | 0.194179i | ||||||||
\(780\) | −17.7195 | − | 26.0981i | −0.634461 | − | 0.934463i | ||||
\(781\) | 2.35971 | 0.0844370 | ||||||||
\(782\) | 57.3256 | − | 99.2909i | 2.04996 | − | 3.55064i | ||||
\(783\) | 3.57633 | − | 11.3597i | 0.127808 | − | 0.405962i | ||||
\(784\) | 101.967 | − | 15.5513i | 3.64168 | − | 0.555403i | ||||
\(785\) | 5.43947 | + | 3.14048i | 0.194143 | + | 0.112088i | ||||
\(786\) | −29.0207 | + | 59.9650i | −1.03513 | + | 2.13888i | ||||
\(787\) | −40.9130 | − | 23.6211i | −1.45839 | − | 0.842002i | −0.459458 | − | 0.888199i | \(-0.651956\pi\) |
−0.998932 | + | 0.0461971i | \(0.985290\pi\) | |||||||
\(788\) | −10.0861 | − | 5.82319i | −0.359301 | − | 0.207442i | ||||
\(789\) | −13.3545 | − | 19.6691i | −0.475433 | − | 0.700239i | ||||
\(790\) | −10.8422 | − | 6.25974i | −0.385748 | − | 0.222711i | ||||
\(791\) | 41.7210 | + | 20.0469i | 1.48343 | + | 0.712786i | ||||
\(792\) | 2.95364 | − | 7.44096i | 0.104953 | − | 0.264403i | ||||
\(793\) | 13.4575 | − | 23.3091i | 0.477891 | − | 0.827731i | ||||
\(794\) | −51.9565 | −1.84387 | ||||||||
\(795\) | −0.421474 | + | 0.870886i | −0.0149481 | + | 0.0308871i | ||||
\(796\) | − | 16.4210i | − | 0.582026i | ||||||
\(797\) | −1.11087 | − | 1.92408i | −0.0393489 | − | 0.0681543i | 0.845680 | − | 0.533690i | \(-0.179195\pi\) |
−0.885029 | + | 0.465536i | \(0.845862\pi\) | |||||||
\(798\) | −9.98387 | − | 3.93061i | −0.353425 | − | 0.139142i | ||||
\(799\) | −15.9888 | + | 27.6934i | −0.565643 | + | 0.979723i | ||||
\(800\) | −18.5470 | − | 10.7081i | −0.655736 | − | 0.378590i | ||||
\(801\) | −22.2460 | − | 28.1181i | −0.786023 | − | 0.993503i | ||||
\(802\) | 29.8710 | + | 51.7380i | 1.05478 | + | 1.82693i | ||||
\(803\) | 0.583741 | + | 1.01107i | 0.0205998 | + | 0.0356798i | ||||
\(804\) | −13.6251 | − | 6.59399i | −0.480519 | − | 0.232552i | ||||
\(805\) | −17.2839 | + | 11.8061i | −0.609178 | + | 0.416110i | ||||
\(806\) | −9.05653 | + | 5.22879i | −0.319003 | + | 0.184176i | ||||
\(807\) | −13.3842 | − | 6.47743i | −0.471147 | − | 0.228016i | ||||
\(808\) | 163.914i | 5.76649i | ||||||||
\(809\) | 33.7187 | − | 19.4675i | 1.18549 | − | 0.684442i | 0.228210 | − | 0.973612i | \(-0.426713\pi\) |
0.957278 | + | 0.289170i | \(0.0933793\pi\) | |||||||
\(810\) | −23.8941 | − | 5.64858i | −0.839555 | − | 0.198471i | ||||
\(811\) | 36.6692i | 1.28763i | 0.765181 | + | 0.643815i | \(0.222649\pi\) | ||||
−0.765181 | + | 0.643815i | \(0.777351\pi\) | |||||||
\(812\) | −29.7468 | − | 14.2933i | −1.04391 | − | 0.501596i | ||||
\(813\) | −51.4373 | + | 3.75463i | −1.80399 | + | 0.131681i | ||||
\(814\) | −7.02433 | −0.246203 | ||||||||
\(815\) | −9.14675 | + | 15.8426i | −0.320397 | + | 0.554943i | ||||
\(816\) | −9.87020 | − | 135.219i | −0.345526 | − | 4.73360i | ||||
\(817\) | 0.332949 | − | 0.192228i | 0.0116484 | − | 0.00672522i | ||||
\(818\) | 99.9902 | 3.49608 | ||||||||
\(819\) | −19.5248 | + | 18.0078i | −0.682253 | + | 0.629245i | ||||
\(820\) | 34.3670 | 1.20015 | ||||||||
\(821\) | 4.31256 | − | 2.48986i | 0.150509 | − | 0.0868966i | −0.422854 | − | 0.906198i | \(-0.638972\pi\) |
0.573363 | + | 0.819301i | \(0.305638\pi\) | |||||||
\(822\) | 24.2696 | + | 11.7455i | 0.846501 | + | 0.409673i | ||||
\(823\) | −23.6293 | + | 40.9272i | −0.823666 | + | 1.42663i | 0.0792685 | + | 0.996853i | \(0.474742\pi\) |
−0.902935 | + | 0.429778i | \(0.858592\pi\) | |||||||
\(824\) | 56.7255 | 1.97613 | ||||||||
\(825\) | −0.276464 | − | 0.407189i | −0.00962526 | − | 0.0141765i | ||||
\(826\) | 54.8100 | − | 37.4390i | 1.90708 | − | 1.30267i | ||||
\(827\) | 11.6675i | 0.405720i | 0.979208 | + | 0.202860i | \(0.0650236\pi\) | ||||
−0.979208 | + | 0.202860i | \(0.934976\pi\) | |||||||
\(828\) | 101.300 | − | 80.1445i | 3.52041 | − | 2.78521i | ||||
\(829\) | −32.9245 | + | 19.0090i | −1.14352 | + | 0.660209i | −0.947299 | − | 0.320351i | \(-0.896199\pi\) |
−0.196217 | + | 0.980560i | \(0.562866\pi\) | |||||||
\(830\) | − | 12.5286i | − | 0.434874i | ||||||
\(831\) | 28.4501 | − | 19.3164i | 0.986924 | − | 0.670080i | ||||
\(832\) | 83.9137 | − | 48.4476i | 2.90918 | − | 1.67962i | ||||
\(833\) | 36.7604 | − | 5.60644i | 1.27367 | − | 0.194251i | ||||
\(834\) | −2.23732 | − | 30.6506i | −0.0774720 | − | 1.06134i | ||||
\(835\) | −3.77161 | − | 6.53262i | −0.130522 | − | 0.226071i | ||||
\(836\) | 0.663656 | + | 1.14949i | 0.0229530 | + | 0.0397558i | ||||
\(837\) | −1.78742 | + | 5.67747i | −0.0617824 | + | 0.196242i | ||||
\(838\) | 30.9607 | + | 17.8752i | 1.06952 | + | 0.617488i | ||||
\(839\) | 0.674120 | − | 1.16761i | 0.0232732 | − | 0.0403104i | −0.854154 | − | 0.520020i | \(-0.825925\pi\) |
0.877427 | + | 0.479709i | \(0.159258\pi\) | |||||||
\(840\) | −15.7653 | + | 40.0443i | −0.543955 | + | 1.38166i | ||||
\(841\) | −11.8735 | − | 20.5655i | −0.409430 | − | 0.709154i | ||||
\(842\) | − | 8.03588i | − | 0.276935i | ||||||
\(843\) | −17.0360 | + | 1.24353i | −0.586752 | + | 0.0428296i | ||||
\(844\) | 26.5401 | 0.913547 | ||||||||
\(845\) | −0.900781 | + | 1.56020i | −0.0309878 | + | 0.0536725i | ||||
\(846\) | −38.6364 | + | 30.5677i | −1.32835 | + | 1.05094i | ||||
\(847\) | 16.2950 | + | 23.8555i | 0.559901 | + | 0.819685i | ||||
\(848\) | −7.12823 | − | 4.11549i | −0.244784 | − | 0.141326i | ||||
\(849\) | −18.2336 | + | 1.33095i | −0.625776 | + | 0.0456781i | ||||
\(850\) | −12.5506 | − | 7.24607i | −0.430481 | − | 0.248538i | ||||
\(851\) | −62.0821 | − | 35.8431i | −2.12815 | − | 1.22869i | ||||
\(852\) | 78.0727 | − | 5.69886i | 2.67473 | − | 0.195240i | ||||
\(853\) | 40.1559 | + | 23.1840i | 1.37491 | + | 0.793805i | 0.991541 | − | 0.129790i | \(-0.0414304\pi\) |
0.383369 | + | 0.923595i | \(0.374764\pi\) | |||||||
\(854\) | −57.8866 | + | 4.38885i | −1.98084 | + | 0.150183i | ||||
\(855\) | 2.01926 | − | 1.59756i | 0.0690571 | − | 0.0546354i | ||||
\(856\) | 90.3322 | − | 156.460i | 3.08749 | − | 5.34769i | ||||
\(857\) | 28.7173 | 0.980966 | 0.490483 | − | 0.871451i | \(-0.336820\pi\) | ||||
0.490483 | + | 0.871451i | \(0.336820\pi\) | |||||||
\(858\) | 4.48127 | − | 0.327107i | 0.152988 | − | 0.0111673i | ||||
\(859\) | 45.4624i | 1.55116i | 0.631250 | + | 0.775579i | \(0.282542\pi\) | ||||
−0.631250 | + | 0.775579i | \(0.717458\pi\) | |||||||
\(860\) | −1.21896 | − | 2.11129i | −0.0415660 | − | 0.0719945i | ||||
\(861\) | −4.28252 | − | 28.6187i | −0.145948 | − | 0.975324i | ||||
\(862\) | −25.1505 | + | 43.5619i | −0.856629 | + | 1.48373i | ||||
\(863\) | −9.01372 | − | 5.20407i | −0.306831 | − | 0.177149i | 0.338677 | − | 0.940903i | \(-0.390021\pi\) |
−0.645507 | + | 0.763754i | \(0.723354\pi\) | |||||||
\(864\) | 33.4176 | − | 106.146i | 1.13689 | − | 3.61116i | ||||
\(865\) | −1.23435 | − | 2.13795i | −0.0419691 | − | 0.0726926i | ||||
\(866\) | −7.12475 | − | 12.3404i | −0.242109 | − | 0.419345i | ||||
\(867\) | −1.41473 | − | 19.3814i | −0.0480467 | − | 0.658226i | ||||
\(868\) | 14.8672 | + | 7.14367i | 0.504625 | + | 0.242472i | ||||
\(869\) | 1.12932 | − | 0.652014i | 0.0383096 | − | 0.0221181i | ||||
\(870\) | 8.95986 | − | 6.08337i | 0.303768 | − | 0.206245i | ||||
\(871\) | − | 5.37353i | − | 0.182075i | ||||||
\(872\) | −159.571 | + | 92.1281i | −5.40374 | + | 3.11985i | ||||
\(873\) | −10.0277 | + | 7.93356i | −0.339387 | + | 0.268510i | ||||
\(874\) | 18.5236i | 0.626570i | ||||||||
\(875\) | 1.49231 | + | 2.18472i | 0.0504494 | + | 0.0738570i | ||||
\(876\) | 21.7553 | + | 32.0422i | 0.735043 | + | 1.08260i | ||||
\(877\) | 42.6874 | 1.44145 | 0.720726 | − | 0.693220i | \(-0.243809\pi\) | ||||
0.720726 | + | 0.693220i | \(0.243809\pi\) | |||||||
\(878\) | 21.3233 | − | 36.9330i | 0.719625 | − | 1.24643i | ||||
\(879\) | 13.4514 | + | 6.50993i | 0.453703 | + | 0.219574i | ||||
\(880\) | 3.62613 | − | 2.09355i | 0.122237 | − | 0.0705735i | ||||
\(881\) | −5.57362 | −0.187780 | −0.0938900 | − | 0.995583i | \(-0.529930\pi\) | ||||
−0.0938900 | + | 0.995583i | \(0.529930\pi\) | |||||||
\(882\) | 55.8261 | + | 12.8667i | 1.87976 | + | 0.433244i | ||||
\(883\) | 41.3715 | 1.39226 | 0.696131 | − | 0.717915i | \(-0.254903\pi\) | ||||
0.696131 | + | 0.717915i | \(0.254903\pi\) | |||||||
\(884\) | 83.7872 | − | 48.3745i | 2.81807 | − | 1.62701i | ||||
\(885\) | 1.15958 | + | 15.8860i | 0.0389790 | + | 0.534001i | ||||
\(886\) | 8.36344 | − | 14.4859i | 0.280975 | − | 0.486663i | ||||
\(887\) | 11.9236 | 0.400354 | 0.200177 | − | 0.979760i | \(-0.435848\pi\) | ||||
0.200177 | + | 0.979760i | \(0.435848\pi\) | |||||||
\(888\) | −147.000 | + | 10.7302i | −4.93301 | + | 0.360081i | ||||
\(889\) | −3.16298 | − | 4.63054i | −0.106083 | − | 0.155303i | ||||
\(890\) | − | 32.6042i | − | 1.09290i | ||||||
\(891\) | 1.75394 | − | 1.86120i | 0.0587592 | − | 0.0623525i | ||||
\(892\) | −17.6922 | + | 10.2146i | −0.592378 | + | 0.342010i | ||||
\(893\) | − | 5.16646i | − | 0.172889i | ||||||
\(894\) | 41.7325 | + | 20.1969i | 1.39574 | + | 0.675485i | ||||
\(895\) | −0.894686 | + | 0.516547i | −0.0299060 | + | 0.0172663i | ||||
\(896\) | −86.2299 | − | 41.4334i | −2.88074 | − | 1.38419i | ||||
\(897\) | 41.2752 | + | 19.9756i | 1.37814 | + | 0.666965i | ||||
\(898\) | 55.4026 | + | 95.9601i | 1.84881 | + | 3.20223i | ||||
\(899\) | −1.31272 | − | 2.27369i | −0.0437815 | − | 0.0758319i | ||||
\(900\) | −10.1304 | − | 12.8045i | −0.337681 | − | 0.426816i | ||||
\(901\) | −2.56982 | − | 1.48369i | −0.0856131 | − | 0.0494287i | ||||
\(902\) | −2.44757 | + | 4.23932i | −0.0814952 | + | 0.141154i | ||||
\(903\) | −1.60626 | + | 1.27816i | −0.0534529 | + | 0.0425345i | ||||
\(904\) | −82.1497 | − | 142.287i | −2.73226 | − | 4.73241i | ||||
\(905\) | 4.90430i | 0.163025i | ||||||||
\(906\) | −20.0168 | + | 41.3603i | −0.665012 | + | 1.37411i | ||||
\(907\) | −43.4138 | −1.44153 | −0.720766 | − | 0.693179i | \(-0.756210\pi\) | ||||
−0.720766 | + | 0.693179i | \(0.756210\pi\) | |||||||
\(908\) | −23.3275 | + | 40.4043i | −0.774149 | + | 1.34086i | ||||
\(909\) | −19.3185 | + | 48.6680i | −0.640753 | + | 1.61422i | ||||
\(910\) | −24.0847 | + | 1.82605i | −0.798398 | + | 0.0605330i | ||||
\(911\) | 44.9154 | + | 25.9319i | 1.48811 | + | 0.859163i | 0.999908 | − | 0.0135658i | \(-0.00431825\pi\) |
0.488206 | + | 0.872729i | \(0.337652\pi\) | |||||||
\(912\) | 12.3043 | + | 18.1224i | 0.407437 | + | 0.600091i | ||||
\(913\) | 1.13015 | + | 0.652490i | 0.0374024 | + | 0.0215943i | ||||
\(914\) | −51.8065 | − | 29.9105i | −1.71361 | − | 0.989352i | ||||
\(915\) | 6.06864 | − | 12.5395i | 0.200623 | − | 0.414544i | ||||
\(916\) | −6.74823 | − | 3.89609i | −0.222968 | − | 0.128731i | ||||
\(917\) | 21.0395 | + | 30.8015i | 0.694786 | + | 1.01715i | ||||
\(918\) | 22.6134 | − | 71.8279i | 0.746352 | − | 2.37067i | ||||
\(919\) | −20.6435 | + | 35.7555i | −0.680965 | + | 1.17947i | 0.293721 | + | 0.955891i | \(0.405106\pi\) |
−0.974687 | + | 0.223575i | \(0.928227\pi\) | |||||||
\(920\) | 74.2965 | 2.44948 | ||||||||
\(921\) | −11.2776 | − | 16.6102i | −0.371610 | − | 0.547325i | ||||
\(922\) | 81.2407i | 2.67552i | ||||||||
\(923\) | 13.8947 | + | 24.0663i | 0.457349 | + | 0.792152i | ||||
\(924\) | −4.41277 | − | 5.54550i | −0.145170 | − | 0.182434i | ||||
\(925\) | −4.53064 | + | 7.84730i | −0.148966 | + | 0.258018i | ||||
\(926\) | 7.78976 | + | 4.49742i | 0.255987 | + | 0.147794i | ||||
\(927\) | 16.8425 | + | 6.68550i | 0.553179 | + | 0.219581i | ||||
\(928\) | 24.5425 | + | 42.5089i | 0.805648 | + | 1.39542i | ||||
\(929\) | −18.7874 | − | 32.5407i | −0.616395 | − | 1.06763i | −0.990138 | − | 0.140095i | \(-0.955259\pi\) |
0.373743 | − | 0.927532i | \(-0.378074\pi\) | |||||||
\(930\) | −4.47806 | + | 3.04042i | −0.146841 | + | 0.0996992i | ||||
\(931\) | −4.69059 | + | 3.75404i | −0.153728 | + | 0.123034i | ||||
\(932\) | −13.1073 | + | 7.56750i | −0.429344 | + | 0.247882i | ||||
\(933\) | −0.626924 | − | 8.58868i | −0.0205246 | − | 0.281181i | ||||
\(934\) | 90.4448i | 2.95944i | ||||||||
\(935\) | 1.30727 | − | 0.754751i | 0.0427522 | − | 0.0246830i | ||||
\(936\) | 93.2812 | − | 13.6909i | 3.04899 | − | 0.447502i | ||||
\(937\) | 27.8462i | 0.909695i | 0.890569 | + | 0.454848i | \(0.150306\pi\) | ||||
−0.890569 | + | 0.454848i | \(0.849694\pi\) | |||||||
\(938\) | −9.57049 | + | 6.53730i | −0.312488 | + | 0.213451i | ||||
\(939\) | −14.7754 | + | 30.5302i | −0.482177 | + | 0.996316i | ||||
\(940\) | −32.7615 | −1.06856 | ||||||||
\(941\) | −18.9891 | + | 32.8900i | −0.619026 | + | 1.07218i | 0.370638 | + | 0.928778i | \(0.379139\pi\) |
−0.989664 | + | 0.143407i | \(0.954194\pi\) | |||||||
\(942\) | −24.5539 | + | 16.6711i | −0.800010 | + | 0.543173i | ||||
\(943\) | −43.2640 | + | 24.9785i | −1.40887 | + | 0.813411i | ||||
\(944\) | −135.507 | −4.41037 | ||||||||
\(945\) | −9.40041 | + | 10.0316i | −0.305795 | + | 0.326327i | ||||
\(946\) | 0.347249 | 0.0112900 | ||||||||
\(947\) | −2.62274 | + | 1.51424i | −0.0852278 | + | 0.0492063i | −0.542008 | − | 0.840373i | \(-0.682336\pi\) |
0.456780 | + | 0.889579i | \(0.349003\pi\) | |||||||
\(948\) | 35.7898 | − | 24.2998i | 1.16240 | − | 0.789220i | ||||
\(949\) | −6.87449 | + | 11.9070i | −0.223155 | + | 0.386516i | ||||
\(950\) | 2.34142 | 0.0759657 | ||||||||
\(951\) | −0.887521 | + | 1.83387i | −0.0287799 | + | 0.0594674i | ||||
\(952\) | −118.970 | − | 57.1651i | −3.85585 | − | 1.85273i | ||||
\(953\) | − | 7.98502i | − | 0.258660i | −0.991602 | − | 0.129330i | \(-0.958717\pi\) | ||
0.991602 | − | 0.129330i | \(-0.0412827\pi\) | |||||||
\(954\) | −2.83654 | − | 3.58528i | −0.0918363 | − | 0.116078i | ||||
\(955\) | 1.63620 | − | 0.944661i | 0.0529462 | − | 0.0305685i | ||||
\(956\) | 38.9413i | 1.25945i | ||||||||
\(957\) | 0.0821221 | + | 1.12505i | 0.00265463 | + | 0.0363676i | ||||
\(958\) | −52.5970 | + | 30.3669i | −1.69933 | + | 0.981110i | ||||
\(959\) | 12.4663 | − | 8.51533i | 0.402557 | − | 0.274974i | ||||
\(960\) | 41.4917 | − | 28.1711i | 1.33914 | − | 0.909219i | ||||
\(961\) | −14.8439 | − | 25.7104i | −0.478836 | − | 0.829368i | ||||
\(962\) | −41.3614 | − | 71.6401i | −1.33355 | − | 2.30977i | ||||
\(963\) | 45.2606 | − | 35.8085i | 1.45850 | − | 1.15391i | ||||
\(964\) | −126.086 | − | 72.7960i | −4.06097 | − | 2.34460i | ||||
\(965\) | −6.19129 | + | 10.7236i | −0.199305 | + | 0.345206i | ||||
\(966\) | −14.6370 | − | 97.8147i | −0.470939 | − | 3.14714i | ||||
\(967\) | −12.9808 | − | 22.4834i | −0.417435 | − | 0.723018i | 0.578246 | − | 0.815863i | \(-0.303737\pi\) |
−0.995681 | + | 0.0928442i | \(0.970404\pi\) | |||||||
\(968\) | − | 102.545i | − | 3.29592i | ||||||
\(969\) | 4.43587 | + | 6.53334i | 0.142501 | + | 0.209881i | ||||
\(970\) | −11.6276 | −0.373340 | ||||||||
\(971\) | −2.20423 | + | 3.81784i | −0.0707372 | + | 0.122520i | −0.899225 | − | 0.437487i | \(-0.855868\pi\) |
0.828487 | + | 0.560008i | \(0.189202\pi\) | |||||||
\(972\) | 53.5354 | − | 65.8150i | 1.71715 | − | 2.11102i | ||||
\(973\) | −15.5102 | − | 7.45262i | −0.497233 | − | 0.238920i | ||||
\(974\) | −16.2632 | − | 9.38957i | −0.521107 | − | 0.300861i | ||||
\(975\) | 2.52495 | − | 5.21727i | 0.0808632 | − | 0.167086i | ||||
\(976\) | 102.637 | + | 59.2572i | 3.28532 | + | 1.89678i | ||||
\(977\) | 26.6864 | + | 15.4074i | 0.853772 | + | 0.492925i | 0.861922 | − | 0.507041i | \(-0.169261\pi\) |
−0.00814977 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(978\) | −48.5551 | − | 71.5142i | −1.55262 | − | 2.28677i | ||||
\(979\) | 2.94107 | + | 1.69803i | 0.0939970 | + | 0.0542692i | ||||
\(980\) | 23.8051 | + | 29.7439i | 0.760425 | + | 0.950134i | ||||
\(981\) | −58.2362 | + | 8.54737i | −1.85934 | + | 0.272896i | ||||
\(982\) | −16.3230 | + | 28.2722i | −0.520887 | + | 0.902203i | ||||
\(983\) | −49.8598 | −1.59028 | −0.795140 | − | 0.606425i | \(-0.792603\pi\) | ||||
−0.795140 | + | 0.606425i | \(0.792603\pi\) | |||||||
\(984\) | −44.7452 | + | 92.4563i | −1.42642 | + | 2.94740i | ||||
\(985\) | − | 2.13992i | − | 0.0681836i | ||||||
\(986\) | 16.6077 | + | 28.7653i | 0.528896 | + | 0.916075i | ||||
\(987\) | 4.08245 | + | 27.2817i | 0.129946 | + | 0.868386i | ||||
\(988\) | −7.81562 | + | 13.5371i | −0.248648 | + | 0.430671i | ||||
\(989\) | 3.06904 | + | 1.77191i | 0.0975896 | + | 0.0563434i | ||||
\(990\) | 2.30096 | − | 0.337713i | 0.0731293 | − | 0.0107332i | ||||
\(991\) | 14.3732 | + | 24.8951i | 0.456579 | + | 0.790818i | 0.998777 | − | 0.0494322i | \(-0.0157412\pi\) |
−0.542198 | + | 0.840251i | \(0.682408\pi\) | |||||||
\(992\) | −12.2662 | − | 21.2456i | −0.389451 | − | 0.674549i | ||||
\(993\) | −48.8208 | − | 23.6273i | −1.54928 | − | 0.749791i | ||||
\(994\) | 25.9592 | − | 54.0254i | 0.823375 | − | 1.71358i | ||||
\(995\) | 2.61298 | − | 1.50861i | 0.0828372 | − | 0.0478261i | ||||
\(996\) | 38.9675 | + | 18.8587i | 1.23473 | + | 0.597562i | ||||
\(997\) | − | 42.4777i | − | 1.34528i | −0.739968 | − | 0.672642i | \(-0.765160\pi\) | ||
0.739968 | − | 0.672642i | \(-0.234840\pi\) | |||||||
\(998\) | −50.1000 | + | 28.9252i | −1.58589 | + | 0.915612i | ||||
\(999\) | −44.9107 | − | 14.1391i | −1.42091 | − | 0.447341i |
(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 | 315.2.be.b.236.15 | yes | 30 | |
3.2 | odd | 2 | 945.2.be.b.656.1 | 30 | |||
7.3 | odd | 6 | 315.2.t.b.101.15 | ✓ | 30 | ||
9.4 | even | 3 | 945.2.t.b.341.15 | 30 | |||
9.5 | odd | 6 | 315.2.t.b.131.1 | yes | 30 | ||
21.17 | even | 6 | 945.2.t.b.521.1 | 30 | |||
63.31 | odd | 6 | 945.2.be.b.206.1 | 30 | |||
63.59 | even | 6 | inner | 315.2.be.b.311.15 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.t.b.101.15 | ✓ | 30 | 7.3 | odd | 6 | ||
315.2.t.b.131.1 | yes | 30 | 9.5 | odd | 6 | ||
315.2.be.b.236.15 | yes | 30 | 1.1 | even | 1 | trivial | |
315.2.be.b.311.15 | yes | 30 | 63.59 | even | 6 | inner | |
945.2.t.b.341.15 | 30 | 9.4 | even | 3 | |||
945.2.t.b.521.1 | 30 | 21.17 | even | 6 | |||
945.2.be.b.206.1 | 30 | 63.31 | odd | 6 | |||
945.2.be.b.656.1 | 30 | 3.2 | odd | 2 |