Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,3,Mod(26,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.26");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.f (of order \(18\), degree \(6\), not 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: | \(6.62127042396\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 107.5 | ||
Character | \(\chi\) | \(=\) | 243.107 |
Dual form | 243.3.f.c.134.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.68916 | − | 2.01307i | 0.844582 | − | 1.00653i | −0.155244 | − | 0.987876i | \(-0.549616\pi\) |
0.999826 | − | 0.0186576i | \(-0.00593925\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.504573 | − | 2.86157i | −0.126143 | − | 0.715393i | ||||
\(5\) | −2.13801 | + | 5.87412i | −0.427601 | + | 1.17482i | 0.519663 | + | 0.854371i | \(0.326057\pi\) |
−0.947264 | + | 0.320453i | \(0.896165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.40961 | + | 7.99430i | −0.201373 | + | 1.14204i | 0.701673 | + | 0.712499i | \(0.252437\pi\) |
−0.903046 | + | 0.429544i | \(0.858674\pi\) | |||||||
\(8\) | 2.49037 | + | 1.43782i | 0.311297 | + | 0.179727i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.21356 | + | 14.2263i | 0.821356 | + | 1.42263i | ||||
\(11\) | 2.77510 | + | 7.62453i | 0.252282 | + | 0.693139i | 0.999589 | + | 0.0286605i | \(0.00912418\pi\) |
−0.747307 | + | 0.664479i | \(0.768654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.43797 | − | 6.24120i | 0.572152 | − | 0.480092i | −0.310207 | − | 0.950669i | \(-0.600399\pi\) |
0.882359 | + | 0.470577i | \(0.155954\pi\) | |||||||
\(14\) | 13.7120 | + | 16.3413i | 0.979429 | + | 1.16724i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.0230 | − | 6.55984i | 1.12644 | − | 0.409990i | ||||
\(17\) | −13.0143 | + | 7.51380i | −0.765546 | + | 0.441988i | −0.831284 | − | 0.555849i | \(-0.812393\pi\) |
0.0657372 | + | 0.997837i | \(0.479060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.93226 | − | 15.4711i | 0.470119 | − | 0.814270i | −0.529297 | − | 0.848437i | \(-0.677544\pi\) |
0.999416 | + | 0.0341664i | \(0.0108776\pi\) | |||||||
\(20\) | 17.8880 | + | 3.15414i | 0.894400 | + | 0.157707i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 20.0363 | + | 7.29262i | 0.910741 | + | 0.331483i | ||||
\(23\) | −25.9334 | + | 4.57276i | −1.12754 | + | 0.198816i | −0.706149 | − | 0.708064i | \(-0.749569\pi\) |
−0.421391 | + | 0.906879i | \(0.638458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.7831 | − | 9.04812i | −0.431325 | − | 0.361925i | ||||
\(26\) | − | 25.5156i | − | 0.981367i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 23.5875 | 0.842411 | ||||||||
\(29\) | 9.75225 | − | 11.6223i | 0.336284 | − | 0.400768i | −0.571229 | − | 0.820791i | \(-0.693533\pi\) |
0.907514 | + | 0.420022i | \(0.137978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.68415 | + | 32.2364i | 0.183360 | + | 1.03988i | 0.928045 | + | 0.372468i | \(0.121488\pi\) |
−0.744685 | + | 0.667416i | \(0.767400\pi\) | |||||||
\(32\) | 13.3043 | − | 36.5533i | 0.415760 | − | 1.14229i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.85748 | + | 38.8907i | −0.201691 | + | 1.14384i | ||||
\(35\) | −43.9457 | − | 25.3721i | −1.25559 | − | 0.724917i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.8096 | − | 27.3831i | −0.427287 | − | 0.740083i | 0.569344 | − | 0.822100i | \(-0.307197\pi\) |
−0.996631 | + | 0.0820163i | \(0.973864\pi\) | |||||||
\(38\) | −16.0564 | − | 44.1145i | −0.422536 | − | 1.16091i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.7704 | + | 11.5547i | −0.344259 | + | 0.288867i | ||||
\(41\) | 10.6189 | + | 12.6551i | 0.258997 | + | 0.308660i | 0.879836 | − | 0.475278i | \(-0.157652\pi\) |
−0.620839 | + | 0.783938i | \(0.713208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 78.7688 | − | 28.6695i | 1.83183 | − | 0.666733i | 0.839466 | − | 0.543412i | \(-0.182868\pi\) |
0.992367 | − | 0.123320i | \(-0.0393542\pi\) | |||||||
\(44\) | 20.4179 | − | 11.7883i | 0.464044 | − | 0.267916i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −34.6005 | + | 59.9298i | −0.752185 | + | 1.30282i | ||||
\(47\) | −12.9701 | − | 2.28698i | −0.275959 | − | 0.0486591i | 0.0339557 | − | 0.999423i | \(-0.489189\pi\) |
−0.309915 | + | 0.950764i | \(0.600301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.8769 | − | 5.77871i | −0.324018 | − | 0.117933i | ||||
\(50\) | −36.4290 | + | 6.42341i | −0.728579 | + | 0.128468i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −21.6126 | − | 18.1352i | −0.415628 | − | 0.348753i | ||||
\(53\) | 25.7140i | 0.485169i | 0.970130 | + | 0.242585i | \(0.0779952\pi\) | ||||
−0.970130 | + | 0.242585i | \(0.922005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.7206 | −0.922193 | ||||||||
\(56\) | −15.0048 | + | 17.8820i | −0.267943 | + | 0.319322i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.92328 | − | 39.2639i | −0.119367 | − | 0.676963i | ||||
\(59\) | 7.76763 | − | 21.3414i | 0.131655 | − | 0.361718i | −0.856296 | − | 0.516485i | \(-0.827240\pi\) |
0.987951 | + | 0.154766i | \(0.0494625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.91937 | − | 33.5704i | 0.0970388 | − | 0.550335i | −0.897065 | − | 0.441899i | \(-0.854305\pi\) |
0.994104 | − | 0.108435i | \(-0.0345840\pi\) | |||||||
\(62\) | 74.4955 | + | 43.0100i | 1.20154 | + | 0.693710i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.7517 | − | 22.0867i | −0.199246 | − | 0.345104i | ||||
\(65\) | 20.7591 | + | 57.0353i | 0.319371 | + | 0.877466i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.20835 | − | 5.20943i | 0.0926620 | − | 0.0777526i | −0.595280 | − | 0.803518i | \(-0.702959\pi\) |
0.687942 | + | 0.725766i | \(0.258514\pi\) | |||||||
\(68\) | 28.0679 | + | 33.4501i | 0.412764 | + | 0.491913i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −125.307 | + | 45.6081i | −1.79010 | + | 0.651545i | ||||
\(71\) | 35.7557 | − | 20.6436i | 0.503601 | − | 0.290754i | −0.226598 | − | 0.973988i | \(-0.572760\pi\) |
0.730199 | + | 0.683234i | \(0.239427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.4046 | − | 69.9827i | 0.553487 | − | 0.958668i | −0.444532 | − | 0.895763i | \(-0.646630\pi\) |
0.998020 | − | 0.0629050i | \(-0.0200365\pi\) | |||||||
\(74\) | −81.8291 | − | 14.4287i | −1.10580 | − | 0.194982i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −48.7787 | − | 17.7540i | −0.641826 | − | 0.233605i | ||||
\(77\) | −64.8646 | + | 11.4374i | −0.842398 | + | 0.148537i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −21.1671 | − | 17.7613i | −0.267937 | − | 0.224826i | 0.498913 | − | 0.866652i | \(-0.333733\pi\) |
−0.766850 | + | 0.641826i | \(0.778177\pi\) | |||||||
\(80\) | 119.894i | 1.49868i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 43.4126 | 0.529421 | ||||||||
\(83\) | −11.3065 | + | 13.4746i | −0.136223 | + | 0.162344i | −0.829843 | − | 0.557997i | \(-0.811570\pi\) |
0.693620 | + | 0.720341i | \(0.256015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.3124 | − | 92.5121i | −0.191910 | − | 1.08838i | ||||
\(86\) | 75.3398 | − | 206.994i | 0.876044 | − | 2.40691i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.05165 | + | 22.9780i | −0.0460414 | + | 0.261114i | ||||
\(89\) | 24.4986 | + | 14.1443i | 0.275265 | + | 0.158924i | 0.631278 | − | 0.775557i | \(-0.282531\pi\) |
−0.356013 | + | 0.934481i | \(0.615864\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 39.4094 | + | 68.2590i | 0.433070 | + | 0.750099i | ||||
\(92\) | 26.1706 | + | 71.9030i | 0.284463 | + | 0.781555i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −26.5124 | + | 22.2466i | −0.282047 | + | 0.236666i | ||||
\(95\) | 71.7821 | + | 85.5466i | 0.755601 | + | 0.900490i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −158.461 | + | 57.6752i | −1.63362 | + | 0.594590i | −0.985907 | − | 0.167294i | \(-0.946497\pi\) |
−0.647714 | + | 0.761883i | \(0.724275\pi\) | |||||||
\(98\) | −38.4516 | + | 22.2000i | −0.392363 | + | 0.226531i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −20.4510 | + | 35.4221i | −0.204510 | + | 0.354221i | ||||
\(101\) | 68.7674 | + | 12.1255i | 0.680865 | + | 0.120055i | 0.503376 | − | 0.864068i | \(-0.332091\pi\) |
0.177490 | + | 0.984123i | \(0.443202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −65.6495 | − | 23.8945i | −0.637374 | − | 0.231985i | 0.00306387 | − | 0.999995i | \(-0.499025\pi\) |
−0.640438 | + | 0.768010i | \(0.721247\pi\) | |||||||
\(104\) | 27.4970 | − | 4.84847i | 0.264395 | − | 0.0466199i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51.7639 | + | 43.4351i | 0.488339 | + | 0.409765i | ||||
\(107\) | − | 121.432i | − | 1.13488i | −0.823416 | − | 0.567438i | \(-0.807935\pi\) | ||
0.823416 | − | 0.567438i | \(-0.192065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −119.633 | −1.09755 | −0.548777 | − | 0.835969i | \(-0.684907\pi\) | ||||
−0.548777 | + | 0.835969i | \(0.684907\pi\) | |||||||
\(110\) | −85.6755 | + | 102.104i | −0.778868 | + | 0.928218i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 27.0359 | + | 153.328i | 0.241392 | + | 1.36900i | ||||
\(113\) | −42.5349 | + | 116.864i | −0.376415 | + | 1.03419i | 0.596416 | + | 0.802675i | \(0.296591\pi\) |
−0.972831 | + | 0.231516i | \(0.925631\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.5848 | − | 162.113i | 0.248564 | − | 1.40967i | ||||
\(116\) | −38.1787 | − | 22.0425i | −0.329127 | − | 0.190021i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.8408 | − | 51.6859i | −0.252889 | − | 0.438016i | ||||
\(119\) | −41.7225 | − | 114.632i | −0.350609 | − | 0.963291i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 42.2591 | − | 35.4596i | 0.349249 | − | 0.293054i | ||||
\(122\) | −57.5807 | − | 68.6220i | −0.471973 | − | 0.562476i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 89.3787 | − | 32.5312i | 0.720796 | − | 0.262348i | ||||
\(125\) | −59.1363 | + | 34.1424i | −0.473091 | + | 0.273139i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 58.7300 | − | 101.723i | 0.462441 | − | 0.800971i | −0.536641 | − | 0.843811i | \(-0.680307\pi\) |
0.999082 | + | 0.0428396i | \(0.0136404\pi\) | |||||||
\(128\) | 87.2312 | + | 15.3812i | 0.681494 | + | 0.120166i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 149.881 | + | 54.5524i | 1.15293 | + | 0.419634i | ||||
\(131\) | −4.64121 | + | 0.818370i | −0.0354291 | + | 0.00624710i | −0.191335 | − | 0.981525i | \(-0.561282\pi\) |
0.155906 | + | 0.987772i | \(0.450170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 111.090 | + | 93.2155i | 0.835262 | + | 0.700868i | ||||
\(134\) | − | 21.2974i | − | 0.158936i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −43.2139 | −0.317749 | ||||||||
\(137\) | 141.921 | − | 169.135i | 1.03592 | − | 1.23456i | 0.0643220 | − | 0.997929i | \(-0.479512\pi\) |
0.971599 | − | 0.236633i | \(-0.0760440\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.21061 | − | 35.2221i | −0.0446807 | − | 0.253397i | 0.954283 | − | 0.298903i | \(-0.0966209\pi\) |
−0.998964 | + | 0.0455067i | \(0.985510\pi\) | |||||||
\(140\) | −50.4303 | + | 138.556i | −0.360216 | + | 0.989686i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.8404 | − | 106.849i | 0.132679 | − | 0.752457i | ||||
\(143\) | 68.2274 | + | 39.3911i | 0.477114 | + | 0.275462i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 47.4203 | + | 82.1344i | 0.327037 | + | 0.566444i | ||||
\(146\) | −72.6301 | − | 199.549i | −0.497466 | − | 1.36678i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −70.3816 | + | 59.0572i | −0.475551 | + | 0.399035i | ||||
\(149\) | −107.819 | − | 128.493i | −0.723615 | − | 0.862371i | 0.271361 | − | 0.962478i | \(-0.412526\pi\) |
−0.994977 | + | 0.100106i | \(0.968082\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 78.6693 | − | 28.6333i | 0.520989 | − | 0.189624i | −0.0681215 | − | 0.997677i | \(-0.521701\pi\) |
0.589110 | + | 0.808053i | \(0.299478\pi\) | |||||||
\(152\) | 44.4893 | − | 25.6859i | 0.292693 | − | 0.168986i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −86.5428 | + | 149.896i | −0.561966 | + | 0.973354i | ||||
\(155\) | −201.513 | − | 35.5322i | −1.30009 | − | 0.229240i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 69.9547 | + | 25.4614i | 0.445571 | + | 0.162175i | 0.555055 | − | 0.831814i | \(-0.312697\pi\) |
−0.109483 | + | 0.993989i | \(0.534920\pi\) | |||||||
\(158\) | −71.5093 | + | 12.6090i | −0.452590 | + | 0.0798039i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 186.274 | + | 156.302i | 1.16421 | + | 0.976890i | ||||
\(161\) | − | 213.765i | − | 1.32773i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 254.830 | 1.56337 | 0.781687 | − | 0.623670i | \(-0.214359\pi\) | ||||
0.781687 | + | 0.623670i | \(0.214359\pi\) | |||||||
\(164\) | 30.8554 | − | 36.7721i | 0.188143 | − | 0.224220i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.02667 | + | 45.5215i | 0.0483534 | + | 0.274226i | ||||
\(167\) | 54.2442 | − | 149.035i | 0.324816 | − | 0.892424i | −0.664585 | − | 0.747213i | \(-0.731392\pi\) |
0.989401 | − | 0.145211i | \(-0.0463861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9757 | + | 73.5888i | −0.0767792 | + | 0.435437i | ||||
\(170\) | −213.787 | − | 123.430i | −1.25757 | − | 0.726060i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −121.784 | − | 210.937i | −0.708049 | − | 1.22638i | ||||
\(173\) | 101.950 | + | 280.105i | 0.589305 | + | 1.61910i | 0.771778 | + | 0.635892i | \(0.219367\pi\) |
−0.182473 | + | 0.983211i | \(0.558410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 87.5334 | − | 73.4492i | 0.500191 | − | 0.419710i | ||||
\(176\) | 100.031 | + | 119.213i | 0.568360 | + | 0.677345i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 69.8555 | − | 25.4253i | 0.392446 | − | 0.142839i | ||||
\(179\) | 25.3997 | − | 14.6645i | 0.141898 | − | 0.0819248i | −0.427370 | − | 0.904077i | \(-0.640560\pi\) |
0.569268 | + | 0.822152i | \(0.307227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −41.7019 | + | 72.2299i | −0.230397 | + | 0.399060i | −0.957925 | − | 0.287018i | \(-0.907336\pi\) |
0.727528 | + | 0.686078i | \(0.240669\pi\) | |||||||
\(182\) | 203.979 | + | 35.9670i | 1.12076 | + | 0.197621i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −71.1587 | − | 25.8996i | −0.386732 | − | 0.140759i | ||||
\(185\) | 194.653 | − | 34.3225i | 1.05218 | − | 0.185527i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −93.4052 | − | 78.3763i | −0.499493 | − | 0.419124i | ||||
\(188\) | 38.2688i | 0.203557i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 293.463 | 1.54454 | ||||||||
\(191\) | 100.885 | − | 120.230i | 0.528193 | − | 0.629476i | −0.434305 | − | 0.900766i | \(-0.643006\pi\) |
0.962498 | + | 0.271290i | \(0.0874503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.20107 | − | 40.8393i | −0.0373112 | − | 0.211602i | 0.960452 | − | 0.278444i | \(-0.0898188\pi\) |
−0.997764 | + | 0.0668419i | \(0.978708\pi\) | |||||||
\(194\) | −151.563 | + | 416.416i | −0.781253 | + | 2.14648i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.52517 | + | 48.3486i | −0.0434958 | + | 0.246677i | ||||
\(197\) | −182.437 | − | 105.330i | −0.926074 | − | 0.534669i | −0.0405063 | − | 0.999179i | \(-0.512897\pi\) |
−0.885568 | + | 0.464510i | \(0.846230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 87.7654 | + | 152.014i | 0.441032 | + | 0.763890i | 0.997766 | − | 0.0668004i | \(-0.0212791\pi\) |
−0.556734 | + | 0.830691i | \(0.687946\pi\) | |||||||
\(200\) | −13.8445 | − | 38.0374i | −0.0692224 | − | 0.190187i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 140.569 | − | 117.951i | 0.695886 | − | 0.583918i | ||||
\(203\) | 79.1651 | + | 94.3453i | 0.389976 | + | 0.464755i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −97.0407 | + | 35.3199i | −0.473369 | + | 0.172292i | ||||
\(206\) | −158.994 | + | 91.7952i | −0.771815 | + | 0.445608i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 93.1133 | − | 161.277i | 0.447660 | − | 0.775370i | ||||
\(209\) | 142.748 | + | 25.1703i | 0.683005 | + | 0.120432i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 245.123 | + | 89.2173i | 1.16172 | + | 0.422831i | 0.849711 | − | 0.527249i | \(-0.176776\pi\) |
0.312008 | + | 0.950080i | \(0.398999\pi\) | |||||||
\(212\) | 73.5824 | − | 12.9746i | 0.347087 | − | 0.0612007i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −244.450 | − | 205.118i | −1.14229 | − | 0.958495i | ||||
\(215\) | 523.993i | 2.43718i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −265.720 | −1.22452 | ||||||||
\(218\) | −202.081 | + | 240.830i | −0.926975 | + | 1.10473i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.5922 | + | 145.141i | 0.116328 | + | 0.659731i | ||||
\(221\) | −49.9048 | + | 137.112i | −0.225813 | + | 0.620417i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −67.5868 | + | 383.304i | −0.303080 | + | 1.71885i | 0.329328 | + | 0.944216i | \(0.393178\pi\) |
−0.632408 | + | 0.774636i | \(0.717933\pi\) | |||||||
\(224\) | 273.464 | + | 157.885i | 1.22082 | + | 0.704842i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 163.406 | + | 283.027i | 0.723035 | + | 1.25233i | ||||
\(227\) | 119.171 | + | 327.419i | 0.524981 | + | 1.44237i | 0.864912 | + | 0.501924i | \(0.167374\pi\) |
−0.339930 | + | 0.940451i | \(0.610404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −279.242 | + | 234.311i | −1.21940 | + | 1.02319i | −0.220539 | + | 0.975378i | \(0.570782\pi\) |
−0.998856 | + | 0.0478162i | \(0.984774\pi\) | |||||||
\(230\) | −278.059 | − | 331.378i | −1.20895 | − | 1.44077i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 40.9975 | − | 14.9219i | 0.176713 | − | 0.0643184i | ||||
\(233\) | 164.260 | − | 94.8353i | 0.704976 | − | 0.407018i | −0.104222 | − | 0.994554i | \(-0.533235\pi\) |
0.809198 | + | 0.587536i | \(0.199902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.1641 | − | 71.2983i | 0.175166 | − | 0.303397i | ||||
\(236\) | −64.9893 | − | 11.4594i | −0.275378 | − | 0.0485566i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −301.237 | − | 109.641i | −1.26570 | − | 0.460678i | ||||
\(239\) | 301.448 | − | 53.1535i | 1.26129 | − | 0.222400i | 0.497272 | − | 0.867594i | \(-0.334335\pi\) |
0.764018 | + | 0.645195i | \(0.223224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −225.911 | − | 189.561i | −0.937388 | − | 0.786562i | 0.0397406 | − | 0.999210i | \(-0.487347\pi\) |
−0.977129 | + | 0.212648i | \(0.931791\pi\) | |||||||
\(242\) | − | 144.967i | − | 0.599039i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −99.0509 | −0.405946 | ||||||||
\(245\) | 67.8897 | − | 80.9078i | 0.277101 | − | 0.330236i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.1205 | − | 170.822i | −0.121945 | − | 0.691587i | ||||
\(248\) | −32.1944 | + | 88.4535i | −0.129816 | + | 0.356667i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −31.1601 | + | 176.718i | −0.124640 | + | 0.706870i | ||||
\(251\) | 158.404 | + | 91.4547i | 0.631092 | + | 0.364361i | 0.781175 | − | 0.624312i | \(-0.214621\pi\) |
−0.150083 | + | 0.988673i | \(0.547954\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −106.833 | − | 185.040i | −0.422265 | − | 0.731384i | ||||
\(254\) | −105.571 | − | 290.055i | −0.415635 | − | 1.14195i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.459 | − | 215.194i | 1.00179 | − | 0.840603i | ||||
\(257\) | −172.501 | − | 205.579i | −0.671210 | − | 0.799918i | 0.317738 | − | 0.948179i | \(-0.397077\pi\) |
−0.988948 | + | 0.148261i | \(0.952632\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 241.194 | − | 87.7874i | 0.931251 | − | 0.338948i | ||||
\(260\) | 152.736 | − | 88.1822i | 0.587447 | − | 0.339162i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.19233 | + | 10.7254i | −0.0236348 | + | 0.0409368i | ||||
\(263\) | −346.629 | − | 61.1200i | −1.31798 | − | 0.232395i | −0.529948 | − | 0.848030i | \(-0.677789\pi\) |
−0.788032 | + | 0.615634i | \(0.788900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −151.047 | − | 54.9766i | −0.569988 | − | 0.207459i | ||||
\(266\) | 375.298 | − | 66.1752i | 1.41089 | − | 0.248779i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.0397 | − | 15.1371i | −0.0673124 | − | 0.0564818i | ||||
\(269\) | − | 164.243i | − | 0.610570i | −0.952261 | − | 0.305285i | \(-0.901248\pi\) | ||
0.952261 | − | 0.305285i | \(-0.0987518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −128.850 | −0.475462 | −0.237731 | − | 0.971331i | \(-0.576404\pi\) | ||||
−0.237731 | + | 0.971331i | \(0.576404\pi\) | |||||||
\(272\) | −185.267 | + | 220.793i | −0.681129 | + | 0.811738i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −100.752 | − | 571.394i | −0.367709 | − | 2.08538i | ||||
\(275\) | 39.0634 | − | 107.326i | 0.142049 | − | 0.390276i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0851 | − | 147.936i | 0.0941700 | − | 0.534064i | −0.900829 | − | 0.434175i | \(-0.857040\pi\) |
0.994999 | − | 0.0998895i | \(-0.0318489\pi\) | |||||||
\(278\) | −81.3953 | − | 46.9936i | −0.292789 | − | 0.169042i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −72.9609 | − | 126.372i | −0.260575 | − | 0.451328i | ||||
\(281\) | −157.671 | − | 433.197i | −0.561106 | − | 1.54163i | −0.818018 | − | 0.575192i | \(-0.804927\pi\) |
0.256912 | − | 0.966435i | \(-0.417295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −52.7479 | + | 44.2607i | −0.186388 | + | 0.156398i | −0.731207 | − | 0.682155i | \(-0.761043\pi\) |
0.544819 | + | 0.838554i | \(0.316598\pi\) | |||||||
\(284\) | −77.1144 | − | 91.9013i | −0.271529 | − | 0.323596i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 194.544 | − | 70.8083i | 0.680224 | − | 0.247581i | ||||
\(287\) | −116.137 | + | 67.0517i | −0.404658 | + | 0.233630i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.5856 | + | 54.7078i | −0.109293 | + | 0.189300i | ||||
\(290\) | 245.443 | + | 43.2782i | 0.846355 | + | 0.149235i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −220.648 | − | 80.3092i | −0.755643 | − | 0.275032i | ||||
\(293\) | −503.007 | + | 88.6936i | −1.71675 | + | 0.302709i | −0.943494 | − | 0.331390i | \(-0.892482\pi\) |
−0.773252 | + | 0.634098i | \(0.781371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 108.755 | + | 91.2560i | 0.368660 | + | 0.309342i | ||||
\(296\) | − | 90.9255i | − | 0.307181i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −440.789 | −1.47916 | ||||||||
\(299\) | −164.352 | + | 195.868i | −0.549674 | + | 0.655076i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 118.159 | + | 670.114i | 0.392556 | + | 2.22629i | ||||
\(302\) | 75.2446 | − | 206.733i | 0.249154 | − | 0.684546i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 59.4981 | − | 337.430i | 0.195717 | − | 1.10997i | ||||
\(305\) | 184.541 | + | 106.545i | 0.605053 | + | 0.349327i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.3017 | − | 45.5559i | −0.0856734 | − | 0.148391i | 0.820005 | − | 0.572357i | \(-0.193971\pi\) |
−0.905678 | + | 0.423966i | \(0.860637\pi\) | |||||||
\(308\) | 65.4578 | + | 179.844i | 0.212525 | + | 0.583909i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −411.918 | + | 345.640i | −1.32877 | + | 1.11497i | ||||
\(311\) | −228.077 | − | 271.812i | −0.733368 | − | 0.873993i | 0.262489 | − | 0.964935i | \(-0.415457\pi\) |
−0.995856 | + | 0.0909416i | \(0.971012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −158.102 | + | 57.5444i | −0.505118 | + | 0.183848i | −0.581995 | − | 0.813193i | \(-0.697728\pi\) |
0.0768764 | + | 0.997041i | \(0.475505\pi\) | |||||||
\(314\) | 169.421 | − | 97.8150i | 0.539556 | − | 0.311513i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −40.1448 | + | 69.5329i | −0.127041 | + | 0.220041i | ||||
\(317\) | −502.240 | − | 88.5585i | −1.58435 | − | 0.279365i | −0.689015 | − | 0.724747i | \(-0.741956\pi\) |
−0.895340 | + | 0.445383i | \(0.853068\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 115.678 | + | 42.1033i | 0.362627 | + | 0.131985i | ||||
\(320\) | 157.003 | − | 27.6839i | 0.490635 | − | 0.0865121i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −430.324 | − | 361.085i | −1.33641 | − | 1.12138i | ||||
\(323\) | 268.461i | 0.831149i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −136.676 | −0.420541 | ||||||||
\(326\) | 430.450 | − | 512.990i | 1.32040 | − | 1.57359i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.24926 | + | 46.7839i | 0.0251502 | + | 0.142634i | ||||
\(329\) | 36.5655 | − | 100.463i | 0.111141 | − | 0.305359i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −58.9261 | + | 334.186i | −0.178024 | + | 1.00963i | 0.756570 | + | 0.653912i | \(0.226874\pi\) |
−0.934595 | + | 0.355714i | \(0.884238\pi\) | |||||||
\(332\) | 44.2634 | + | 25.5555i | 0.133324 | + | 0.0769744i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −208.390 | − | 360.941i | −0.623921 | − | 1.08066i | ||||
\(335\) | 17.3273 | + | 47.6064i | 0.0517233 | + | 0.142109i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −52.2733 | + | 43.8625i | −0.155114 | + | 0.130156i | −0.717042 | − | 0.697030i | \(-0.754504\pi\) |
0.561928 | + | 0.827186i | \(0.310060\pi\) | |||||||
\(338\) | 126.221 | + | 150.424i | 0.373435 | + | 0.445043i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −256.499 | + | 93.3581i | −0.754410 | + | 0.274583i | ||||
\(341\) | −230.013 | + | 132.798i | −0.674526 | + | 0.389438i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −130.305 | + | 225.695i | −0.379897 | + | 0.658002i | ||||
\(344\) | 237.385 | + | 41.8574i | 0.690074 | + | 0.121679i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 736.080 | + | 267.911i | 2.12740 | + | 0.774310i | ||||
\(347\) | 170.468 | − | 30.0581i | 0.491262 | − | 0.0866227i | 0.0774708 | − | 0.996995i | \(-0.475316\pi\) |
0.413791 | + | 0.910372i | \(0.364204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 352.060 | + | 295.414i | 1.00877 | + | 0.846457i | 0.988175 | − | 0.153331i | \(-0.0490000\pi\) |
0.0205933 | + | 0.999788i | \(0.493444\pi\) | |||||||
\(350\) | − | 300.278i | − | 0.857939i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 315.623 | 0.896655 | ||||||||
\(353\) | −258.561 | + | 308.141i | −0.732468 | + | 0.872922i | −0.995778 | − | 0.0917895i | \(-0.970741\pi\) |
0.263310 | + | 0.964711i | \(0.415186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 44.8169 | + | 254.169i | 0.126245 | + | 0.715970i | ||||
\(356\) | 28.1135 | − | 77.2413i | 0.0789706 | − | 0.216970i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.3836 | − | 75.9022i | 0.0373844 | − | 0.212017i | ||||
\(359\) | −197.249 | − | 113.882i | −0.549439 | − | 0.317219i | 0.199457 | − | 0.979907i | \(-0.436082\pi\) |
−0.748896 | + | 0.662688i | \(0.769416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.9294 | + | 36.2507i | 0.0579761 | + | 0.100418i | ||||
\(362\) | 74.9622 | + | 205.957i | 0.207078 | + | 0.568942i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 175.443 | − | 147.214i | 0.481987 | − | 0.404435i | ||||
\(365\) | 324.702 | + | 386.965i | 0.889595 | + | 1.06018i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 221.266 | − | 80.5344i | 0.602906 | − | 0.219440i | −0.0224904 | − | 0.999747i | \(-0.507160\pi\) |
0.625396 | + | 0.780307i | \(0.284937\pi\) | |||||||
\(368\) | −437.401 | + | 252.534i | −1.18859 | + | 0.686233i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 259.707 | − | 449.825i | 0.701910 | − | 1.21574i | ||||
\(371\) | −205.565 | − | 36.2467i | −0.554084 | − | 0.0976999i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −613.386 | − | 223.254i | −1.64447 | − | 0.598537i | −0.656655 | − | 0.754192i | \(-0.728029\pi\) |
−0.987812 | + | 0.155655i | \(0.950251\pi\) | |||||||
\(374\) | −315.553 | + | 55.6406i | −0.843726 | + | 0.148772i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29.0121 | − | 24.3441i | −0.0771599 | − | 0.0647448i | ||||
\(377\) | − | 147.312i | − | 0.390748i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 625.053 | 1.64922 | 0.824608 | − | 0.565705i | \(-0.191396\pi\) | ||||
0.824608 | + | 0.565705i | \(0.191396\pi\) | |||||||
\(380\) | 208.578 | − | 248.574i | 0.548891 | − | 0.654142i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −71.6198 | − | 406.176i | −0.187486 | − | 1.06329i | ||||
\(383\) | −36.4387 | + | 100.114i | −0.0951401 | + | 0.261395i | −0.978129 | − | 0.207998i | \(-0.933305\pi\) |
0.882989 | + | 0.469393i | \(0.155527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 71.4963 | − | 405.476i | 0.185705 | − | 1.05318i | ||||
\(386\) | −94.3760 | − | 54.4880i | −0.244497 | − | 0.141161i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 244.997 | + | 424.347i | 0.631436 | + | 1.09368i | ||||
\(389\) | 203.034 | + | 557.832i | 0.521939 | + | 1.43401i | 0.868359 | + | 0.495935i | \(0.165175\pi\) |
−0.346421 | + | 0.938079i | \(0.612603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 303.146 | − | 254.370i | 0.775309 | − | 0.650562i | ||||
\(392\) | −31.2306 | − | 37.2192i | −0.0796700 | − | 0.0949470i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −520.201 | + | 189.338i | −1.32031 | + | 0.480553i | ||||
\(395\) | 149.587 | − | 86.3642i | 0.378702 | − | 0.218643i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −187.410 | + | 324.603i | −0.472064 | + | 0.817640i | −0.999489 | − | 0.0319623i | \(-0.989824\pi\) |
0.527425 | + | 0.849602i | \(0.323158\pi\) | |||||||
\(398\) | 454.265 | + | 80.0992i | 1.14137 | + | 0.201254i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −253.699 | − | 92.3387i | −0.634246 | − | 0.230847i | ||||
\(401\) | 270.237 | − | 47.6500i | 0.673907 | − | 0.118828i | 0.173786 | − | 0.984783i | \(-0.444400\pi\) |
0.500121 | + | 0.865955i | \(0.333289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 243.472 | + | 204.298i | 0.604150 | + | 0.506942i | ||||
\(404\) | − | 202.901i | − | 0.502231i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 323.646 | 0.797158 | ||||||||
\(407\) | 164.910 | − | 196.532i | 0.405184 | − | 0.482879i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −95.7625 | − | 543.096i | −0.234138 | − | 1.32786i | −0.844421 | − | 0.535680i | \(-0.820055\pi\) |
0.610283 | − | 0.792183i | \(-0.291056\pi\) | |||||||
\(410\) | −92.8163 | + | 255.011i | −0.226381 | + | 0.621977i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −35.2508 | + | 199.917i | −0.0855602 | + | 0.485236i | ||||
\(413\) | 159.660 | + | 92.1798i | 0.386586 | + | 0.223196i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −54.9779 | − | 95.2245i | −0.132477 | − | 0.229457i | ||||
\(416\) | −129.179 | − | 354.917i | −0.310527 | − | 0.853167i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 291.795 | − | 244.845i | 0.698073 | − | 0.585753i | ||||
\(419\) | −56.3003 | − | 67.0960i | −0.134368 | − | 0.160134i | 0.694665 | − | 0.719334i | \(-0.255553\pi\) |
−0.829033 | + | 0.559200i | \(0.811108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −278.393 | + | 101.327i | −0.661266 | + | 0.240681i | −0.650783 | − | 0.759264i | \(-0.725559\pi\) |
−0.0104830 | + | 0.999945i | \(0.503337\pi\) | |||||||
\(422\) | 593.653 | − | 342.746i | 1.40676 | − | 0.812194i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −36.9720 | + | 64.0374i | −0.0871981 | + | 0.151032i | ||||
\(425\) | 208.321 | + | 36.7325i | 0.490166 | + | 0.0864295i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 260.028 | + | 94.6424i | 0.608965 | + | 0.221645i | ||||
\(428\) | −347.485 | + | 61.2711i | −0.811882 | + | 0.143157i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1054.83 | + | 885.111i | 2.45310 | + | 2.05840i | ||||
\(431\) | 586.175i | 1.36003i | 0.733196 | + | 0.680017i | \(0.238028\pi\) | ||||
−0.733196 | + | 0.680017i | \(0.761972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 415.367 | 0.959277 | 0.479639 | − | 0.877466i | \(-0.340768\pi\) | ||||
0.479639 | + | 0.877466i | \(0.340768\pi\) | |||||||
\(434\) | −448.844 | + | 534.912i | −1.03420 | + | 1.23252i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 60.3638 | + | 342.340i | 0.138449 | + | 0.785183i | ||||
\(437\) | −160.898 | + | 442.064i | −0.368188 | + | 1.01159i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 58.0607 | − | 329.279i | 0.132257 | − | 0.750065i | −0.844474 | − | 0.535596i | \(-0.820087\pi\) |
0.976731 | − | 0.214469i | \(-0.0688021\pi\) | |||||||
\(440\) | −126.313 | − | 72.9270i | −0.287076 | − | 0.165743i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 191.719 | + | 332.067i | 0.433753 | + | 0.751282i | ||||
\(443\) | −154.471 | − | 424.404i | −0.348692 | − | 0.958024i | −0.982783 | − | 0.184765i | \(-0.940848\pi\) |
0.634091 | − | 0.773259i | \(-0.281375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −135.463 | + | 113.667i | −0.304412 | + | 0.255432i | ||||
\(446\) | 657.451 | + | 783.520i | 1.47411 | + | 1.75677i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 194.542 | − | 70.8077i | 0.434247 | − | 0.158053i | ||||
\(449\) | −165.422 | + | 95.5067i | −0.368424 | + | 0.212710i | −0.672770 | − | 0.739852i | \(-0.734896\pi\) |
0.304346 | + | 0.952562i | \(0.401562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −67.0206 | + | 116.083i | −0.148604 | + | 0.257390i | ||||
\(452\) | 355.876 | + | 62.7505i | 0.787336 | + | 0.138829i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 860.416 | + | 313.166i | 1.89519 | + | 0.689792i | ||||
\(455\) | −485.219 | + | 85.5573i | −1.06642 | + | 0.188038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −295.504 | − | 247.957i | −0.646616 | − | 0.542575i | 0.259426 | − | 0.965763i | \(-0.416467\pi\) |
−0.906042 | + | 0.423188i | \(0.860911\pi\) | |||||||
\(458\) | 957.923i | 2.09153i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −478.320 | −1.03983 | ||||||||
\(461\) | 278.361 | − | 331.738i | 0.603821 | − | 0.719606i | −0.374378 | − | 0.927276i | \(-0.622144\pi\) |
0.978199 | + | 0.207670i | \(0.0665882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 96.0025 | + | 544.457i | 0.207349 | + | 1.17593i | 0.893701 | + | 0.448664i | \(0.148100\pi\) |
−0.686352 | + | 0.727270i | \(0.740789\pi\) | |||||||
\(464\) | 99.5246 | − | 273.441i | 0.214493 | − | 0.589314i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 86.5515 | − | 490.858i | 0.185733 | − | 1.05334i | ||||
\(467\) | −186.467 | − | 107.657i | −0.399286 | − | 0.230528i | 0.286890 | − | 0.957964i | \(-0.407379\pi\) |
−0.686176 | + | 0.727436i | \(0.740712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.8943 | + | 56.9747i | 0.0701372 | + | 0.121481i | ||||
\(470\) | −73.9954 | − | 203.301i | −0.157437 | − | 0.432555i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 50.0293 | − | 41.9796i | 0.105994 | − | 0.0889398i | ||||
\(473\) | 437.183 | + | 521.015i | 0.924277 | + | 1.10151i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −236.302 | + | 86.0070i | −0.497479 | + | 0.181067i | ||||
\(476\) | −306.975 | + | 177.232i | −0.644905 | + | 0.372336i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 402.194 | − | 696.621i | 0.841411 | − | 1.45737i | ||||
\(479\) | 223.049 | + | 39.3296i | 0.465656 | + | 0.0821077i | 0.401553 | − | 0.915836i | \(-0.368470\pi\) |
0.0641024 | + | 0.997943i | \(0.479582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −288.495 | − | 105.004i | −0.599781 | − | 0.218303i | ||||
\(482\) | −763.200 | + | 134.573i | −1.58340 | + | 0.279197i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −122.793 | − | 103.036i | −0.253704 | − | 0.212883i | ||||
\(485\) | − | 1054.13i | − | 2.17347i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −443.130 | −0.909919 | −0.454959 | − | 0.890512i | \(-0.650346\pi\) | ||||
−0.454959 | + | 0.890512i | \(0.650346\pi\) | |||||||
\(488\) | 63.0096 | − | 75.0919i | 0.129118 | − | 0.153877i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −48.1960 | − | 273.333i | −0.0983592 | − | 0.557823i | ||||
\(491\) | 228.283 | − | 627.203i | 0.464935 | − | 1.27740i | −0.456796 | − | 0.889571i | \(-0.651003\pi\) |
0.921732 | − | 0.387828i | \(-0.126775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.5911 | + | 224.532i | −0.0803064 | + | 0.455440i | ||||
\(494\) | −394.754 | − | 227.912i | −0.799098 | − | 0.461360i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 313.911 | + | 543.710i | 0.632885 | + | 1.09619i | ||||
\(497\) | 114.629 | + | 314.941i | 0.230642 | + | 0.633684i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −44.0357 | + | 36.9503i | −0.0882478 | + | 0.0740487i | −0.685844 | − | 0.727748i | \(-0.740567\pi\) |
0.597597 | + | 0.801797i | \(0.296122\pi\) | |||||||
\(500\) | 127.540 | + | 151.996i | 0.255079 | + | 0.303991i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 451.675 | − | 164.396i | 0.899751 | − | 0.327483i | ||||
\(503\) | 423.202 | − | 244.336i | 0.841356 | − | 0.485757i | −0.0163686 | − | 0.999866i | \(-0.505211\pi\) |
0.857725 | + | 0.514109i | \(0.171877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −218.252 | + | 378.024i | −0.432182 | + | 0.748562i | ||||
\(506\) | −552.957 | − | 97.5012i | −1.09280 | − | 0.192690i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −320.722 | − | 116.733i | −0.631343 | − | 0.229790i | ||||
\(509\) | −279.933 | + | 49.3598i | −0.549967 | + | 0.0969741i | −0.441725 | − | 0.897150i | \(-0.645633\pi\) |
−0.108242 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 502.508 | + | 421.655i | 0.983382 | + | 0.825156i | ||||
\(512\) | − | 525.459i | − | 1.02629i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −705.227 | −1.37204 | ||||||||
\(515\) | 280.718 | − | 334.547i | 0.545083 | − | 0.649605i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.5562 | − | 105.237i | −0.0358921 | − | 0.203554i | ||||
\(518\) | 230.694 | − | 633.827i | 0.445356 | − | 1.22360i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30.3083 | + | 171.887i | −0.0582852 | + | 0.330552i | ||||
\(521\) | 35.1966 | + | 20.3207i | 0.0675558 | + | 0.0390033i | 0.533397 | − | 0.845865i | \(-0.320915\pi\) |
−0.465842 | + | 0.884868i | \(0.654248\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −174.951 | − | 303.024i | −0.334514 | − | 0.579395i | 0.648877 | − | 0.760893i | \(-0.275239\pi\) |
−0.983391 | + | 0.181498i | \(0.941905\pi\) | |||||||
\(524\) | 4.68365 | + | 12.8682i | 0.00893827 | + | 0.0245577i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −708.552 | + | 594.545i | −1.34706 | + | 1.13031i | ||||
\(527\) | −316.193 | − | 376.824i | −0.599987 | − | 0.715036i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 154.534 | − | 56.2458i | 0.292125 | − | 0.106325i | ||||
\(530\) | −365.815 | + | 211.203i | −0.690216 | + | 0.398497i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 210.690 | − | 364.926i | 0.396034 | − | 0.685951i | ||||
\(533\) | 157.966 | + | 27.8536i | 0.296371 | + | 0.0522582i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 713.304 | + | 259.622i | 1.33328 | + | 0.485274i | ||||
\(536\) | 22.9513 | − | 4.04694i | 0.0428196 | − | 0.00755026i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −330.633 | − | 277.434i | −0.614560 | − | 0.515677i | ||||
\(539\) | − | 137.090i | − | 0.254342i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 145.531 | 0.269003 | 0.134501 | − | 0.990913i | \(-0.457057\pi\) | ||||
0.134501 | + | 0.990913i | \(0.457057\pi\) | |||||||
\(542\) | −217.649 | + | 259.384i | −0.401567 | + | 0.478569i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 101.508 | + | 575.681i | 0.186596 | + | 1.05824i | ||||
\(545\) | 255.777 | − | 702.742i | 0.469316 | − | 1.28943i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 84.3980 | − | 478.645i | 0.154292 | − | 0.875036i | −0.805137 | − | 0.593088i | \(-0.797908\pi\) |
0.959430 | − | 0.281948i | \(-0.0909805\pi\) | |||||||
\(548\) | −555.602 | − | 320.777i | −1.01387 | − | 0.585359i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −150.070 | − | 259.928i | −0.272854 | − | 0.472597i | ||||
\(551\) | −92.7002 | − | 254.692i | −0.168240 | − | 0.462235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 171.826 | − | 144.179i | 0.310716 | − | 0.260722i | ||||
\(554\) | −253.743 | − | 302.399i | −0.458020 | − | 0.545847i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −97.6570 | + | 35.5443i | −0.175642 | + | 0.0639285i | ||||
\(557\) | 2.82805 | − | 1.63278i | 0.00507730 | − | 0.00293138i | −0.497459 | − | 0.867487i | \(-0.665734\pi\) |
0.502537 | + | 0.864556i | \(0.332400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 406.948 | − | 704.855i | 0.727993 | − | 1.26092i | ||||
\(560\) | −958.471 | − | 169.004i | −1.71155 | − | 0.301793i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1138.39 | − | 414.339i | −2.02560 | − | 0.737258i | ||||
\(563\) | 654.650 | − | 115.432i | 1.16279 | − | 0.205031i | 0.441236 | − | 0.897391i | \(-0.354540\pi\) |
0.721552 | + | 0.692360i | \(0.243429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −595.531 | − | 499.710i | −1.05404 | − | 0.884443i | ||||
\(566\) | 180.949i | 0.319697i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 118.727 | 0.209026 | ||||||||
\(569\) | 48.8101 | − | 58.1696i | 0.0857822 | − | 0.102231i | −0.721446 | − | 0.692471i | \(-0.756522\pi\) |
0.807228 | + | 0.590239i | \(0.200967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −51.0684 | − | 289.624i | −0.0894369 | − | 0.507222i | −0.996311 | − | 0.0858194i | \(-0.972649\pi\) |
0.906874 | − | 0.421402i | \(-0.138462\pi\) | |||||||
\(572\) | 78.2948 | − | 215.113i | 0.136879 | − | 0.376072i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −61.1948 | + | 347.053i | −0.106611 | + | 0.604622i | ||||
\(575\) | 321.018 | + | 185.340i | 0.558292 | + | 0.322330i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −529.296 | − | 916.768i | −0.917325 | − | 1.58885i | −0.803461 | − | 0.595357i | \(-0.797011\pi\) |
−0.113864 | − | 0.993496i | \(-0.536323\pi\) | |||||||
\(578\) | 56.7773 | + | 155.994i | 0.0982306 | + | 0.269886i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 211.107 | − | 177.139i | 0.363977 | − | 0.305413i | ||||
\(581\) | −91.7820 | − | 109.381i | −0.157972 | − | 0.188264i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −196.057 | + | 71.3589i | −0.336290 | + | 0.122399i | ||||
\(584\) | 201.245 | − | 116.189i | 0.344597 | − | 0.198953i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −671.115 | + | 1162.40i | −1.14525 | + | 1.98363i | ||||
\(587\) | −136.792 | − | 24.1200i | −0.233035 | − | 0.0410904i | 0.0559110 | − | 0.998436i | \(-0.482194\pi\) |
−0.288946 | + | 0.957345i | \(0.593305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 549.506 | + | 200.004i | 0.932947 | + | 0.339565i | ||||
\(590\) | 367.409 | − | 64.7841i | 0.622727 | − | 0.109804i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −464.565 | − | 389.817i | −0.784739 | − | 0.658474i | ||||
\(593\) | 145.309i | 0.245040i | 0.992466 | + | 0.122520i | \(0.0390975\pi\) | ||||
−0.992466 | + | 0.122520i | \(0.960902\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 762.563 | 1.28162 | ||||||||
\(596\) | −313.291 | + | 373.365i | −0.525656 | + | 0.626452i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 116.676 | + | 661.705i | 0.195111 | + | 1.10653i | ||||
\(599\) | 7.85706 | − | 21.5871i | 0.0131170 | − | 0.0360386i | −0.932961 | − | 0.359977i | \(-0.882785\pi\) |
0.946078 | + | 0.323938i | \(0.105007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −161.036 | + | 913.281i | −0.267947 | + | 1.51960i | 0.492564 | + | 0.870276i | \(0.336060\pi\) |
−0.760511 | + | 0.649325i | \(0.775051\pi\) | |||||||
\(602\) | 1548.58 | + | 894.071i | 2.57238 | + | 1.48517i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −121.631 | − | 210.670i | −0.201375 | − | 0.348792i | ||||
\(605\) | 117.944 | + | 324.048i | 0.194948 | + | 0.535616i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 401.386 | − | 336.803i | 0.661262 | − | 0.554865i | −0.249203 | − | 0.968451i | \(-0.580169\pi\) |
0.910465 | + | 0.413587i | \(0.135724\pi\) | |||||||
\(608\) | −446.683 | − | 532.336i | −0.734677 | − | 0.875553i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 526.202 | − | 191.522i | 0.862626 | − | 0.313970i | ||||
\(611\) | −110.745 | + | 63.9384i | −0.181251 | + | 0.104646i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.0848 | + | 60.7687i | −0.0572346 | + | 0.0991333i | −0.893223 | − | 0.449614i | \(-0.851562\pi\) |
0.835988 | + | 0.548747i | \(0.184895\pi\) | |||||||
\(614\) | −136.135 | − | 24.0043i | −0.221718 | − | 0.0390949i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −177.982 | − | 64.7801i | −0.288932 | − | 0.105163i | ||||
\(617\) | −654.465 | + | 115.400i | −1.06072 | + | 0.187034i | −0.676676 | − | 0.736281i | \(-0.736580\pi\) |
−0.384045 | + | 0.923314i | \(0.625469\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −743.640 | − | 623.988i | −1.20136 | − | 1.00806i | −0.999590 | − | 0.0286254i | \(-0.990887\pi\) |
−0.201768 | − | 0.979433i | \(-0.564669\pi\) | |||||||
\(620\) | 594.574i | 0.958990i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −932.436 | −1.49909 | ||||||||
\(623\) | −147.607 | + | 175.911i | −0.236929 | + | 0.282361i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −135.231 | − | 766.934i | −0.216370 | − | 1.22709i | ||||
\(626\) | −151.219 | + | 415.472i | −0.241565 | + | 0.663693i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.5625 | − | 213.028i | 0.0598129 | − | 0.339216i | ||||
\(629\) | 411.502 | + | 237.581i | 0.654216 | + | 0.377712i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 94.6588 | + | 163.954i | 0.150014 | + | 0.259832i | 0.931232 | − | 0.364426i | \(-0.118735\pi\) |
−0.781218 | + | 0.624258i | \(0.785401\pi\) | |||||||
\(632\) | −27.1764 | − | 74.6666i | −0.0430006 | − | 0.118143i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1026.64 | + | 861.454i | −1.61931 | + | 1.35876i | ||||
\(635\) | 471.970 | + | 562.472i | 0.743260 | + | 0.885783i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −154.158 | + | 56.1089i | −0.242006 | + | 0.0880830i | ||||
\(638\) | 280.156 | − | 161.748i | 0.439116 | − | 0.253524i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −276.852 | + | 479.522i | −0.432581 | + | 0.749253i | ||||
\(641\) | 682.182 | + | 120.287i | 1.06425 | + | 0.187655i | 0.678240 | − | 0.734841i | \(-0.262743\pi\) |
0.386006 | + | 0.922496i | \(0.373854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1000.40 | − | 364.116i | −1.55583 | − | 0.566277i | −0.586056 | − | 0.810271i | \(-0.699320\pi\) |
−0.969777 | + | 0.243994i | \(0.921542\pi\) | |||||||
\(644\) | −611.705 | + | 107.860i | −0.949852 | + | 0.167485i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 540.430 | + | 453.475i | 0.836579 | + | 0.701973i | ||||
\(647\) | 352.755i | 0.545217i | 0.962125 | + | 0.272608i | \(0.0878863\pi\) | ||||
−0.962125 | + | 0.272608i | \(0.912114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 184.274 | 0.283935 | ||||||||
\(650\) | −230.868 | + | 275.138i | −0.355181 | + | 0.423288i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −128.580 | − | 729.215i | −0.197209 | − | 1.11843i | ||||
\(653\) | −160.213 | + | 440.183i | −0.245350 | + | 0.674093i | 0.754492 | + | 0.656309i | \(0.227883\pi\) |
−0.999842 | + | 0.0177840i | \(0.994339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.11572 | − | 29.0127i | 0.00781026 | − | 0.0442942i | ||||
\(656\) | 274.399 | + | 158.424i | 0.418291 | + | 0.241501i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −140.474 | − | 243.307i | −0.213486 | − | 0.369768i | ||||
\(659\) | 29.3934 | + | 80.7577i | 0.0446030 | + | 0.122546i | 0.959994 | − | 0.280019i | \(-0.0903409\pi\) |
−0.915391 | + | 0.402565i | \(0.868119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 94.3093 | − | 79.1349i | 0.142677 | − | 0.119720i | −0.568656 | − | 0.822575i | \(-0.692536\pi\) |
0.711333 | + | 0.702856i | \(0.248092\pi\) | |||||||
\(662\) | 573.204 | + | 683.118i | 0.865867 | + | 1.03190i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47.5314 | + | 17.3000i | −0.0715834 | + | 0.0260542i | ||||
\(665\) | −785.070 | + | 453.260i | −1.18056 | + | 0.681594i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −199.763 | + | 346.000i | −0.299495 | + | 0.518741i | ||||
\(668\) | −453.844 | − | 80.0249i | −0.679407 | − | 0.119798i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 125.104 | + | 45.5340i | 0.186722 | + | 0.0679612i | ||||
\(671\) | 272.386 | − | 48.0289i | 0.405940 | − | 0.0715781i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −487.674 | − | 409.207i | −0.724627 | − | 0.608035i | 0.204034 | − | 0.978964i | \(-0.434595\pi\) |
−0.928661 | + | 0.370929i | \(0.879039\pi\) | |||||||
\(674\) | 179.321i | 0.266054i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 217.127 | 0.321194 | ||||||||
\(677\) | 106.259 | − | 126.634i | 0.156955 | − | 0.187052i | −0.681836 | − | 0.731505i | \(-0.738818\pi\) |
0.838791 | + | 0.544453i | \(0.183263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −237.704 | − | 1348.09i | −0.350080 | − | 1.98540i | ||||
\(680\) | 92.3916 | − | 253.844i | 0.135870 | − | 0.373300i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −121.198 | + | 687.351i | −0.177710 | + | 1.00785i | ||||
\(683\) | −1129.58 | − | 652.163i | −1.65385 | − | 0.954851i | −0.975468 | − | 0.220142i | \(-0.929348\pi\) |
−0.678383 | − | 0.734709i | \(-0.737319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 690.092 | + | 1195.27i | 1.00743 | + | 1.74493i | ||||
\(686\) | 234.232 | + | 643.548i | 0.341446 | + | 0.938116i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1231.58 | − | 1033.42i | 1.79009 | − | 1.50207i | ||||
\(689\) | 160.486 | + | 191.260i | 0.232926 | + | 0.277590i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 339.997 | − | 123.749i | 0.492035 | − | 0.179086i | −0.0840729 | − | 0.996460i | \(-0.526793\pi\) |
0.576108 | + | 0.817373i | \(0.304571\pi\) | |||||||
\(692\) | 750.099 | − | 433.070i | 1.08396 | − | 0.625824i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 227.439 | − | 393.936i | 0.327722 | − | 0.567632i | ||||
\(695\) | 220.178 | + | 38.8232i | 0.316802 | + | 0.0558608i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −233.285 | − | 84.9087i | −0.334698 | − | 0.121820i | ||||
\(698\) | 1189.37 | − | 209.719i | 1.70398 | − | 0.300457i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −254.347 | − | 213.423i | −0.363353 | − | 0.304890i | ||||
\(701\) | − | 893.344i | − | 1.27438i | −0.770705 | − | 0.637192i | \(-0.780096\pi\) | ||
0.770705 | − | 0.637192i | \(-0.219904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −564.863 | −0.803504 | ||||||||
\(704\) | 133.013 | − | 158.519i | 0.188939 | − | 0.225169i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 183.557 | + | 1041.00i | 0.259996 | + | 1.47451i | ||||
\(707\) | −193.871 | + | 532.655i | −0.274216 | + | 0.753402i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −119.924 | + | 680.121i | −0.169145 | + | 0.959268i | 0.775543 | + | 0.631295i | \(0.217476\pi\) |
−0.944687 | + | 0.327972i | \(0.893635\pi\) | |||||||
\(710\) | 587.363 | + | 339.114i | 0.827272 | + | 0.477626i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 40.6737 | + | 70.4490i | 0.0571260 | + | 0.0989452i | ||||
\(713\) | −294.819 | − | 810.007i | −0.413490 | − | 1.13606i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −377.259 | + | 316.557i | −0.527634 | + | 0.442738i | ||||
\(716\) | −54.7796 | − | 65.2838i | −0.0765079 | − | 0.0911785i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −562.436 | + | 204.710i | −0.783338 | + | 0.285112i | ||||
\(719\) | 417.508 | − | 241.049i | 0.580679 | − | 0.335255i | −0.180724 | − | 0.983534i | \(-0.557844\pi\) |
0.761403 | + | 0.648279i | \(0.224511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 283.560 | − | 491.140i | 0.393287 | − | 0.681192i | ||||
\(722\) | 108.328 | + | 19.1012i | 0.150039 | + | 0.0264560i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 227.733 | + | 82.8879i | 0.314548 | + | 0.114486i | ||||
\(725\) | −210.320 | + | 37.0850i | −0.290096 | + | 0.0511517i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 264.311 | + | 221.783i | 0.363563 | + | 0.305066i | 0.806209 | − | 0.591631i | \(-0.201516\pi\) |
−0.442646 | + | 0.896697i | \(0.645960\pi\) | |||||||
\(728\) | 226.654i | 0.311338i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1327.46 | 1.81844 | ||||||||
\(731\) | −809.703 | + | 964.966i | −1.10766 | + | 1.32006i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 93.6439 | + | 531.081i | 0.127754 | + | 0.724531i | 0.979634 | + | 0.200793i | \(0.0643518\pi\) |
−0.851879 | + | 0.523738i | \(0.824537\pi\) | |||||||
\(734\) | 211.634 | − | 581.460i | 0.288330 | − | 0.792180i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −177.877 | + | 1008.79i | −0.241680 | + | 1.37064i | ||||
\(737\) | 56.9482 | + | 32.8791i | 0.0772704 | + | 0.0446121i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −368.737 | − | 638.671i | −0.498968 | − | 0.864237i | 0.501032 | − | 0.865429i | \(-0.332954\pi\) |
−0.999999 | + | 0.00119161i | \(0.999621\pi\) | |||||||
\(740\) | −196.433 | − | 539.695i | −0.265450 | − | 0.729317i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −420.200 | + | 352.590i | −0.566308 | + | 0.475188i | ||||
\(743\) | −669.302 | − | 797.643i | −0.900810 | − | 1.07354i | −0.996940 | − | 0.0781750i | \(-0.975091\pi\) |
0.0961294 | − | 0.995369i | \(-0.469354\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 985.303 | − | 358.621i | 1.32255 | − | 0.481370i | ||||
\(746\) | −1485.54 | + | 857.674i | −1.99133 | + | 1.14970i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −177.150 | + | 306.832i | −0.236831 | + | 0.410204i | ||||
\(749\) | 970.761 | + | 171.171i | 1.29608 | + | 0.228533i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −226.499 | − | 82.4391i | −0.301597 | − | 0.109772i | 0.186789 | − | 0.982400i | \(-0.440192\pi\) |
−0.488386 | + | 0.872628i | \(0.662414\pi\) | |||||||
\(752\) | −248.762 | + | 43.8635i | −0.330801 | + | 0.0583291i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −296.549 | − | 248.834i | −0.393301 | − | 0.330019i | ||||
\(755\) | 523.331i | 0.693154i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7615 | 0.0432781 | 0.0216391 | − | 0.999766i | \(-0.493112\pi\) | ||||
0.0216391 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(758\) | 1055.82 | − | 1258.27i | 1.39290 | − | 1.65999i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 55.7639 | + | 316.253i | 0.0733735 | + | 0.416122i | ||||
\(761\) | −109.225 | + | 300.094i | −0.143529 | + | 0.394342i | −0.990538 | − | 0.137236i | \(-0.956178\pi\) |
0.847010 | + | 0.531577i | \(0.178400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 168.637 | − | 956.386i | 0.221018 | − | 1.25345i | ||||
\(764\) | −394.950 | − | 228.025i | −0.516951 | − | 0.298462i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 139.986 | + | 242.463i | 0.182750 | + | 0.316531i | ||||
\(767\) | −75.4204 | − | 207.216i | −0.0983317 | − | 0.270164i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −364.796 | + | 306.100i | −0.474377 | + | 0.398050i | −0.848388 | − | 0.529375i | \(-0.822427\pi\) |
0.374011 | + | 0.927424i | \(0.377982\pi\) | |||||||
\(770\) | −695.481 | − | 828.842i | −0.903222 | − | 1.07642i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −113.231 | + | 41.2128i | −0.146672 | + | 0.0533844i | ||||
\(773\) | 1122.62 | − | 648.147i | 1.45229 | − | 0.838482i | 0.453682 | − | 0.891164i | \(-0.350110\pi\) |
0.998611 | + | 0.0526817i | \(0.0167769\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 230.386 | − | 399.040i | 0.297272 | − | 0.514890i | ||||
\(776\) | −477.554 | − | 84.2057i | −0.615405 | − | 0.108513i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1465.91 | + | 533.548i | 1.88420 | + | 0.685794i | ||||
\(779\) | 290.639 | − | 51.2475i | 0.373092 | − | 0.0657863i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 256.623 | + | 215.332i | 0.328583 | + | 0.275714i | ||||
\(782\) | − | 1039.93i | − | 1.32983i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −324.056 | −0.413337 | ||||||||
\(785\) | −299.127 | + | 356.486i | −0.381054 | + | 0.454122i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 149.503 | + | 847.873i | 0.189966 | + | 1.07735i | 0.919408 | + | 0.393306i | \(0.128669\pi\) |
−0.729442 | + | 0.684043i | \(0.760220\pi\) | |||||||
\(788\) | −209.356 | + | 575.202i | −0.265681 | + | 0.729952i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 78.8203 | − | 447.012i | 0.0997725 | − | 0.565838i | ||||
\(791\) | −874.285 | − | 504.769i | −1.10529 | − | 0.638140i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −165.492 | − | 286.640i | −0.208690 | − | 0.361462i | ||||
\(794\) | 336.882 | + | 925.576i | 0.424285 | + | 1.16571i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 390.716 | − | 327.849i | 0.490849 | − | 0.411871i | ||||
\(797\) | −372.897 | − | 444.402i | −0.467876 | − | 0.557593i | 0.479572 | − | 0.877503i | \(-0.340792\pi\) |
−0.947448 | + | 0.319909i | \(0.896348\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 185.980 | − | 67.6913i | 0.232766 | − | 0.0847200i | ||||
\(800\) | −474.201 | + | 273.780i | −0.592751 | + | 0.342225i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 360.552 | − | 624.494i | 0.449566 | − | 0.778671i | ||||
\(803\) | 645.713 | + | 113.857i | 0.804125 | + | 0.141789i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1255.68 | + | 457.031i | 1.55985 | + | 0.567741i | ||||
\(806\) | 822.529 | − | 145.034i | 1.02051 | − | 0.179943i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 153.822 | + | 129.072i | 0.190374 | + | 0.159743i | ||||
\(809\) | 661.323i | 0.817457i | 0.912656 | + | 0.408729i | \(0.134028\pi\) | ||||
−0.912656 | + | 0.408729i | \(0.865972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −168.725 | −0.208045 | −0.104023 | − | 0.994575i | \(-0.533171\pi\) | ||||
−0.104023 | + | 0.994575i | \(0.533171\pi\) | |||||||
\(812\) | 230.031 | − | 274.141i | 0.283290 | − | 0.337612i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −117.072 | − | 663.949i | −0.143823 | − | 0.815663i | ||||
\(815\) | −544.828 | + | 1496.90i | −0.668501 | + | 1.83669i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 260.034 | − | 1474.73i | 0.318279 | − | 1.80505i | ||||
\(818\) | −1255.05 | − | 724.602i | −1.53429 | − | 0.885822i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 150.035 | + | 259.868i | 0.182969 | + | 0.316912i | ||||
\(821\) | −51.8428 | − | 142.437i | −0.0631460 | − | 0.173492i | 0.904107 | − | 0.427306i | \(-0.140537\pi\) |
−0.967253 | + | 0.253814i | \(0.918315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 172.223 | − | 144.512i | 0.209263 | − | 0.175592i | −0.532132 | − | 0.846661i | \(-0.678609\pi\) |
0.741395 | + | 0.671069i | \(0.234165\pi\) | |||||||
\(824\) | −129.136 | − | 153.898i | −0.156718 | − | 0.186770i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 455.256 | − | 165.700i | 0.551158 | − | 0.200605i | ||||
\(827\) | 292.855 | − | 169.080i | 0.354117 | − | 0.204449i | −0.312380 | − | 0.949957i | \(-0.601126\pi\) |
0.666497 | + | 0.745508i | \(0.267793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 401.806 | − | 695.949i | 0.484688 | − | 0.839504i | −0.515157 | − | 0.857096i | \(-0.672267\pi\) |
0.999845 | + | 0.0175917i | \(0.00559990\pi\) | |||||||
\(830\) | −284.560 | − | 50.1756i | −0.342843 | − | 0.0604525i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −232.694 | − | 84.6938i | −0.279681 | − | 0.101795i | ||||
\(833\) | 250.046 | − | 44.0899i | 0.300176 | − | 0.0529291i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 759.474 | + | 637.274i | 0.909550 | + | 0.763203i | ||||
\(836\) | − | 421.184i | − | 0.503809i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −230.169 | −0.274665 | ||||||||
\(839\) | 548.904 | − | 654.158i | 0.654236 | − | 0.779688i | −0.332311 | − | 0.943170i | \(-0.607828\pi\) |
0.986546 | + | 0.163482i | \(0.0522727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 106.067 | + | 601.537i | 0.126120 | + | 0.715263i | ||||
\(842\) | −266.274 | + | 731.581i | −0.316240 | + | 0.868861i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 131.620 | − | 746.453i | 0.155948 | − | 0.884423i | ||||
\(845\) | −404.527 | − | 233.554i | −0.478731 | − | 0.276395i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 223.906 | + | 387.816i | 0.264351 | + | 0.457870i | ||||
\(848\) | 168.679 | + | 463.443i | 0.198914 | + | 0.546513i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 425.833 | − | 357.316i | 0.500980 | − | 0.420372i | ||||
\(851\) | 535.214 | + | 637.843i | 0.628923 | + | 0.749522i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 750.923 | − | 273.313i | 0.880331 | − | 0.320414i | 0.137988 | − | 0.990434i | \(-0.455937\pi\) |
0.742343 | + | 0.670020i | \(0.233714\pi\) | |||||||
\(854\) | 629.751 | − | 363.587i | 0.737414 | − | 0.425746i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 174.597 | − | 302.410i | 0.203968 | − | 0.353283i | ||||
\(857\) | −1529.66 | − | 269.721i | −1.78490 | − | 0.314726i | −0.819031 | − | 0.573749i | \(-0.805489\pi\) |
−0.965871 | + | 0.259022i | \(0.916600\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.5482 | + | 9.66277i | 0.0309060 | + | 0.0112489i | 0.357427 | − | 0.933941i | \(-0.383654\pi\) |
−0.326521 | + | 0.945190i | \(0.605876\pi\) | |||||||
\(860\) | 1499.44 | − | 264.393i | 1.74354 | − | 0.307433i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1180.01 | + | 990.146i | 1.36892 | + | 1.14866i | ||||
\(863\) | − | 951.550i | − | 1.10261i | −0.834305 | − | 0.551304i | \(-0.814131\pi\) | ||
0.834305 | − | 0.551304i | \(-0.185869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1863.34 | −2.15415 | ||||||||
\(866\) | 701.623 | − | 836.162i | 0.810189 | − | 0.965545i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 134.075 | + | 760.377i | 0.154464 | + | 0.876010i | ||||
\(869\) | 76.6806 | − | 210.678i | 0.0882400 | − | 0.242438i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6645 | − | 77.4951i | 0.0156883 | − | 0.0889726i | ||||
\(872\) | −297.932 | − | 172.011i | −0.341665 | − | 0.197260i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 618.122 | + | 1070.62i | 0.707233 | + | 1.22496i | ||||
\(875\) | −189.585 | − | 520.881i | −0.216669 | − | 0.595293i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −174.806 | + | 146.679i | −0.199322 | + | 0.167251i | −0.736986 | − | 0.675908i | \(-0.763752\pi\) |
0.537663 | + | 0.843160i | \(0.319307\pi\) | |||||||
\(878\) | −564.786 | − | 673.086i | −0.643264 | − | 0.766613i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −914.138 | + | 332.719i | −1.03879 | + | 0.378090i | ||||
\(881\) | −1343.36 | + | 775.592i | −1.52482 | + | 0.880354i | −0.525250 | + | 0.850948i | \(0.676028\pi\) |
−0.999568 | + | 0.0294054i | \(0.990639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −781.794 | + | 1354.11i | −0.885384 | + | 1.53353i | −0.0401121 | + | 0.999195i | \(0.512772\pi\) |
−0.845272 | + | 0.534336i | \(0.820562\pi\) | |||||||
\(884\) | 417.537 | + | 73.6231i | 0.472327 | + | 0.0832840i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1115.28 | − | 405.929i | −1.25878 | − | 0.458159i | ||||
\(887\) | −691.493 | + | 121.929i | −0.779587 | + | 0.137462i | −0.549260 | − | 0.835651i | \(-0.685090\pi\) |
−0.230326 | + | 0.973113i | \(0.573979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 730.420 | + | 612.895i | 0.821620 | + | 0.689421i | ||||
\(890\) | 464.699i | 0.522134i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1130.95 | 1.26789 | ||||||||
\(893\) | −151.234 | + | 180.234i | −0.169355 | + | 0.201830i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.8365 | + | 180.554i | 0.0355715 | + | 0.201736i | ||||
\(896\) | −245.924 | + | 675.671i | −0.274469 | + | 0.754097i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −87.1642 | + | 494.333i | −0.0970649 | + | 0.550482i | ||||
\(899\) | 430.094 | + | 248.315i | 0.478413 | + | 0.276212i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −193.210 | − | 334.649i | −0.214439 | − | 0.371419i | ||||
\(902\) | 120.474 | + | 331.000i | 0.133564 | + | 0.366963i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −273.956 | + | 229.877i | −0.303049 | + | 0.254288i | ||||
\(905\) | −335.128 | − | 399.390i | −0.370307 | − | 0.441315i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1517.15 | + | 552.196i | −1.67271 | + | 0.608816i | −0.992282 | − | 0.124000i | \(-0.960428\pi\) |
−0.680426 | + | 0.732816i | \(0.738205\pi\) | |||||||
\(908\) | 876.803 | − | 506.222i | 0.965642 | − | 0.557514i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −647.383 | + | 1121.30i | −0.711410 | + | 1.23220i | ||||
\(911\) | 603.650 | + | 106.440i | 0.662623 | + | 0.116838i | 0.494838 | − | 0.868985i | \(-0.335227\pi\) |
0.167785 | + | 0.985824i | \(0.446338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −134.114 | − | 48.8135i | −0.146894 | − | 0.0534650i | ||||
\(914\) | −998.308 | + | 176.029i | −1.09224 | + | 0.192592i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 811.397 | + | 680.843i | 0.885805 | + | 0.743278i | ||||
\(917\) | − | 38.2568i | − | 0.0417195i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 628.091 | 0.683451 | 0.341725 | − | 0.939800i | \(-0.388989\pi\) | ||||
0.341725 | + | 0.939800i | \(0.388989\pi\) | |||||||
\(920\) | 304.275 | − | 362.621i | 0.330734 | − | 0.394153i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −197.613 | − | 1120.72i | −0.214331 | − | 1.21553i | ||||
\(923\) | 137.109 | − | 376.704i | 0.148547 | − | 0.408131i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −77.2881 | + | 438.323i | −0.0835547 | + | 0.473862i | ||||
\(926\) | 1258.19 | + | 726.418i | 1.35874 | + | 0.784469i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −295.086 | − | 511.103i | −0.317980 | − | 0.550758i | ||||
\(929\) | −428.742 | − | 1177.96i | −0.461509 | − | 1.26799i | −0.924350 | − | 0.381545i | \(-0.875392\pi\) |
0.462841 | − | 0.886441i | \(-0.346830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −231.220 | + | 194.016i | −0.248356 | + | 0.208396i | ||||
\(932\) | −354.259 | − | 422.189i | −0.380106 | − | 0.452993i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −531.693 | + | 193.520i | −0.569265 | + | 0.207195i | ||||
\(935\) | 660.093 | − | 381.105i | 0.705981 | − | 0.407599i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 460.132 | − | 796.972i | 0.491070 | − | 0.850557i | −0.508878 | − | 0.860839i | \(-0.669939\pi\) |
0.999947 | + | 0.0102815i | \(0.00327275\pi\) | |||||||
\(938\) | 170.258 | + | 30.0211i | 0.181512 | + | 0.0320054i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −224.796 | − | 81.8189i | −0.239144 | − | 0.0870414i | ||||
\(941\) | 673.068 | − | 118.680i | 0.715269 | − | 0.126121i | 0.195841 | − | 0.980636i | \(-0.437256\pi\) |
0.519428 | + | 0.854514i | \(0.326145\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −333.252 | − | 279.632i | −0.353396 | − | 0.296534i | ||||
\(944\) | − | 435.590i | − | 0.461430i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1787.31 | 1.88934 | ||||||||
\(947\) | −541.088 | + | 644.844i | −0.571371 | + | 0.680933i | −0.971912 | − | 0.235346i | \(-0.924378\pi\) |
0.400541 | + | 0.916279i | \(0.368822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −136.248 | − | 772.703i | −0.143570 | − | 0.814228i | ||||
\(950\) | −226.016 | + | 620.973i | −0.237911 | + | 0.653656i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 60.9148 | − | 345.465i | 0.0639861 | − | 0.362883i | ||||
\(953\) | 1277.52 | + | 737.576i | 1.34052 | + | 0.773952i | 0.986884 | − | 0.161430i | \(-0.0516105\pi\) |
0.353640 | + | 0.935382i | \(0.384944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 490.553 | + | 849.662i | 0.513668 | + | 0.889698i | ||||
\(956\) | −304.205 | − | 835.797i | −0.318206 | − | 0.874265i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 455.940 | − | 382.579i | 0.475929 | − | 0.399352i | ||||
\(959\) | 1152.06 | + | 1372.98i | 1.20132 | + | 1.43167i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −103.831 | + | 37.7915i | −0.108045 | + | 0.0393252i | ||||
\(962\) | −698.694 | + | 403.391i | −0.726294 | + | 0.419326i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −428.456 | + | 742.107i | −0.444456 | + | 0.769821i | ||||
\(965\) | 255.291 | + | 45.0147i | 0.264550 | + | 0.0466473i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −305.163 | − | 111.070i | −0.315577 | − | 0.114861i | 0.179375 | − | 0.983781i | \(-0.442592\pi\) |
−0.494953 | + | 0.868920i | \(0.664815\pi\) | |||||||
\(968\) | 156.225 | − | 27.5467i | 0.161390 | − | 0.0284574i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2122.04 | − | 1780.60i | −2.18767 | − | 1.83567i | ||||
\(971\) | 1203.37i | 1.23931i | 0.784873 | + | 0.619657i | \(0.212728\pi\) | ||||
−0.784873 | + | 0.619657i | \(0.787272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 290.331 | 0.298387 | ||||||||
\(974\) | −748.520 | + | 892.051i | −0.768501 | + | 0.915864i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −113.532 | − | 643.870i | −0.116323 | − | 0.659702i | ||||
\(977\) | −64.7541 | + | 177.910i | −0.0662785 | + | 0.182099i | −0.968410 | − | 0.249362i | \(-0.919779\pi\) |
0.902132 | + | 0.431460i | \(0.142001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.8573 | + | 226.042i | −0.0407123 | + | 0.230891i | ||||
\(980\) | −265.779 | − | 153.448i | −0.271203 | − | 0.156579i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −876.994 | − | 1519.00i | −0.893070 | − | 1.54684i | ||||
\(983\) | 432.552 | + | 1188.43i | 0.440033 | + | 1.20898i | 0.939470 | + | 0.342630i | \(0.111318\pi\) |
−0.499437 | + | 0.866350i | \(0.666460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1008.77 | − | 846.459i | 1.02413 | − | 0.859349i | ||||
\(986\) | 385.123 | + | 458.971i | 0.390591 | + | 0.465488i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −473.621 | + | 172.384i | −0.479374 | + | 0.174478i | ||||
\(989\) | −1911.64 | + | 1103.69i | −1.93291 | + | 1.11596i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 697.271 | − | 1207.71i | 0.703604 | − | 1.21868i | −0.263589 | − | 0.964635i | \(-0.584906\pi\) |
0.967193 | − | 0.254043i | \(-0.0817603\pi\) | |||||||
\(992\) | 1253.97 | + | 221.109i | 1.26408 | + | 0.222892i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 827.625 | + | 301.231i | 0.832621 | + | 0.303049i | ||||
\(995\) | −1080.59 | + | 190.538i | −1.08602 | + | 0.191495i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 772.720 | + | 648.389i | 0.775045 | + | 0.650340i | 0.941996 | − | 0.335625i | \(-0.108947\pi\) |
−0.166950 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(998\) | 151.062i | 0.151365i | ||||||||
\(999\) | 0 | 0 |
(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 | 243.3.f.c.107.5 | 30 | ||
3.2 | odd | 2 | 243.3.f.b.107.1 | 30 | |||
9.2 | odd | 6 | 243.3.f.a.26.5 | 30 | |||
9.4 | even | 3 | 27.3.f.a.20.5 | ✓ | 30 | ||
9.5 | odd | 6 | 81.3.f.a.62.1 | 30 | |||
9.7 | even | 3 | 243.3.f.d.26.1 | 30 | |||
27.4 | even | 9 | 243.3.f.a.215.5 | 30 | |||
27.5 | odd | 18 | inner | 243.3.f.c.134.5 | 30 | ||
27.7 | even | 9 | 729.3.b.a.728.5 | 30 | |||
27.13 | even | 9 | 81.3.f.a.17.1 | 30 | |||
27.14 | odd | 18 | 27.3.f.a.23.5 | yes | 30 | ||
27.20 | odd | 18 | 729.3.b.a.728.26 | 30 | |||
27.22 | even | 9 | 243.3.f.b.134.1 | 30 | |||
27.23 | odd | 18 | 243.3.f.d.215.1 | 30 | |||
36.31 | odd | 6 | 432.3.bc.a.209.5 | 30 | |||
108.95 | even | 18 | 432.3.bc.a.401.5 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.20.5 | ✓ | 30 | 9.4 | even | 3 | ||
27.3.f.a.23.5 | yes | 30 | 27.14 | odd | 18 | ||
81.3.f.a.17.1 | 30 | 27.13 | even | 9 | |||
81.3.f.a.62.1 | 30 | 9.5 | odd | 6 | |||
243.3.f.a.26.5 | 30 | 9.2 | odd | 6 | |||
243.3.f.a.215.5 | 30 | 27.4 | even | 9 | |||
243.3.f.b.107.1 | 30 | 3.2 | odd | 2 | |||
243.3.f.b.134.1 | 30 | 27.22 | even | 9 | |||
243.3.f.c.107.5 | 30 | 1.1 | even | 1 | trivial | ||
243.3.f.c.134.5 | 30 | 27.5 | odd | 18 | inner | ||
243.3.f.d.26.1 | 30 | 9.7 | even | 3 | |||
243.3.f.d.215.1 | 30 | 27.23 | odd | 18 | |||
432.3.bc.a.209.5 | 30 | 36.31 | odd | 6 | |||
432.3.bc.a.401.5 | 30 | 108.95 | even | 18 | |||
729.3.b.a.728.5 | 30 | 27.7 | even | 9 | |||
729.3.b.a.728.26 | 30 | 27.20 | odd | 18 |