Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(22,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.l (of order \(4\), 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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.3 | ||
Character | \(\chi\) | \(=\) | 105.43 |
Dual form | 105.3.l.a.22.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36784 | + | 1.36784i | −0.683920 | + | 0.683920i | −0.960881 | − | 0.276961i | \(-0.910673\pi\) |
0.276961 | + | 0.960881i | \(0.410673\pi\) | |||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0.258033i | 0.0645082i | ||||||||
\(5\) | 3.39663 | − | 3.66919i | 0.679325 | − | 0.733837i | ||||
\(6\) | 3.35051 | 0.558418 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.267261 | − | 0.267261i | ||||
\(8\) | −5.82430 | − | 5.82430i | −0.728038 | − | 0.728038i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0.372817 | + | 9.66489i | 0.0372817 | + | 0.966489i | ||||
\(11\) | 17.6130 | 1.60118 | 0.800589 | − | 0.599213i | \(-0.204520\pi\) | ||||
0.800589 | + | 0.599213i | \(0.204520\pi\) | |||||||
\(12\) | 0.316024 | − | 0.316024i | 0.0263354 | − | 0.0263354i | ||||
\(13\) | 12.1245 | + | 12.1245i | 0.932651 | + | 0.932651i | 0.997871 | − | 0.0652196i | \(-0.0207748\pi\) |
−0.0652196 | + | 0.997871i | \(0.520775\pi\) | |||||||
\(14\) | 5.11799i | 0.365570i | ||||||||
\(15\) | −8.65382 | + | 0.333816i | −0.576921 | + | 0.0222544i | ||||
\(16\) | 14.9013 | 0.931331 | ||||||||
\(17\) | 13.8772 | − | 13.8772i | 0.816309 | − | 0.816309i | −0.169262 | − | 0.985571i | \(-0.554138\pi\) |
0.985571 | + | 0.169262i | \(0.0541385\pi\) | |||||||
\(18\) | −4.10352 | − | 4.10352i | −0.227973 | − | 0.227973i | ||||
\(19\) | 18.3068i | 0.963516i | 0.876304 | + | 0.481758i | \(0.160002\pi\) | ||||
−0.876304 | + | 0.481758i | \(0.839998\pi\) | |||||||
\(20\) | 0.946770 | + | 0.876441i | 0.0473385 | + | 0.0438220i | ||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | −24.0917 | + | 24.0917i | −1.09508 | + | 1.09508i | ||||
\(23\) | −26.3956 | − | 26.3956i | −1.14763 | − | 1.14763i | −0.987017 | − | 0.160617i | \(-0.948652\pi\) |
−0.160617 | − | 0.987017i | \(-0.551348\pi\) | |||||||
\(24\) | 14.2666i | 0.594440i | ||||||||
\(25\) | −1.92585 | − | 24.9257i | −0.0770341 | − | 0.997028i | ||||
\(26\) | −33.1686 | −1.27572 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0.482735 | + | 0.482735i | 0.0172405 | + | 0.0172405i | ||||
\(29\) | 2.87815i | 0.0992467i | 0.998768 | + | 0.0496234i | \(0.0158021\pi\) | ||||
−0.998768 | + | 0.0496234i | \(0.984198\pi\) | |||||||
\(30\) | 11.3804 | − | 12.2936i | 0.379347 | − | 0.409788i | ||||
\(31\) | 16.1149 | 0.519836 | 0.259918 | − | 0.965631i | \(-0.416304\pi\) | ||||
0.259918 | + | 0.965631i | \(0.416304\pi\) | |||||||
\(32\) | 2.91465 | − | 2.91465i | 0.0910828 | − | 0.0910828i | ||||
\(33\) | −21.5714 | − | 21.5714i | −0.653679 | − | 0.653679i | ||||
\(34\) | 37.9637i | 1.11658i | ||||||||
\(35\) | −0.509912 | − | 13.2189i | −0.0145689 | − | 0.377684i | ||||
\(36\) | −0.774098 | −0.0215027 | ||||||||
\(37\) | 2.52440 | − | 2.52440i | 0.0682270 | − | 0.0682270i | −0.672170 | − | 0.740397i | \(-0.734638\pi\) |
0.740397 | + | 0.672170i | \(0.234638\pi\) | |||||||
\(38\) | −25.0408 | − | 25.0408i | −0.658968 | − | 0.658968i | ||||
\(39\) | − | 29.6988i | − | 0.761507i | ||||||
\(40\) | −41.1534 | + | 1.58747i | −1.02884 | + | 0.0396867i | ||||
\(41\) | −1.89828 | −0.0462996 | −0.0231498 | − | 0.999732i | \(-0.507369\pi\) | ||||
−0.0231498 | + | 0.999732i | \(0.507369\pi\) | |||||||
\(42\) | 6.26823 | − | 6.26823i | 0.149243 | − | 0.149243i | ||||
\(43\) | −42.5974 | − | 42.5974i | −0.990637 | − | 0.990637i | 0.00931954 | − | 0.999957i | \(-0.497033\pi\) |
−0.999957 | + | 0.00931954i | \(0.997033\pi\) | |||||||
\(44\) | 4.54472i | 0.103289i | ||||||||
\(45\) | 11.0076 | + | 10.1899i | 0.244612 | + | 0.226442i | ||||
\(46\) | 72.2098 | 1.56978 | ||||||||
\(47\) | −57.7457 | + | 57.7457i | −1.22863 | + | 1.22863i | −0.264150 | + | 0.964482i | \(0.585091\pi\) |
−0.964482 | + | 0.264150i | \(0.914909\pi\) | |||||||
\(48\) | −18.2503 | − | 18.2503i | −0.380214 | − | 0.380214i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 36.7286 | + | 31.4601i | 0.734572 | + | 0.629202i | ||||
\(51\) | −33.9922 | −0.666513 | ||||||||
\(52\) | −3.12851 | + | 3.12851i | −0.0601636 | + | 0.0601636i | ||||
\(53\) | 66.5567 | + | 66.5567i | 1.25579 | + | 1.25579i | 0.953086 | + | 0.302701i | \(0.0978883\pi\) |
0.302701 | + | 0.953086i | \(0.402112\pi\) | |||||||
\(54\) | 10.0515i | 0.186139i | ||||||||
\(55\) | 59.8247 | − | 64.6253i | 1.08772 | − | 1.17500i | ||||
\(56\) | −21.7925 | −0.389153 | ||||||||
\(57\) | 22.4212 | − | 22.4212i | 0.393354 | − | 0.393354i | ||||
\(58\) | −3.93685 | − | 3.93685i | −0.0678768 | − | 0.0678768i | ||||
\(59\) | − | 16.4673i | − | 0.279107i | −0.990215 | − | 0.139554i | \(-0.955433\pi\) | ||
0.990215 | − | 0.139554i | \(-0.0445668\pi\) | |||||||
\(60\) | −0.0861354 | − | 2.23297i | −0.00143559 | − | 0.0372161i | ||||
\(61\) | −7.37026 | −0.120824 | −0.0604119 | − | 0.998174i | \(-0.519241\pi\) | ||||
−0.0604119 | + | 0.998174i | \(0.519241\pi\) | |||||||
\(62\) | −22.0426 | + | 22.0426i | −0.355526 | + | 0.355526i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.0890871 | + | 0.0890871i | ||||
\(64\) | 67.5787i | 1.05592i | ||||||||
\(65\) | 85.6692 | − | 3.30464i | 1.31799 | − | 0.0508406i | ||||
\(66\) | 59.0124 | 0.894127 | ||||||||
\(67\) | −27.2024 | + | 27.2024i | −0.406006 | + | 0.406006i | −0.880343 | − | 0.474337i | \(-0.842688\pi\) |
0.474337 | + | 0.880343i | \(0.342688\pi\) | |||||||
\(68\) | 3.58078 | + | 3.58078i | 0.0526586 | + | 0.0526586i | ||||
\(69\) | 64.6557i | 0.937039i | ||||||||
\(70\) | 18.7788 | + | 17.3839i | 0.268269 | + | 0.248341i | ||||
\(71\) | −79.5984 | −1.12110 | −0.560552 | − | 0.828119i | \(-0.689411\pi\) | ||||
−0.560552 | + | 0.828119i | \(0.689411\pi\) | |||||||
\(72\) | 17.4729 | − | 17.4729i | 0.242679 | − | 0.242679i | ||||
\(73\) | 63.3051 | + | 63.3051i | 0.867193 | + | 0.867193i | 0.992161 | − | 0.124968i | \(-0.0398827\pi\) |
−0.124968 | + | 0.992161i | \(0.539883\pi\) | |||||||
\(74\) | 6.90594i | 0.0933235i | ||||||||
\(75\) | −28.1690 | + | 32.8863i | −0.375586 | + | 0.438484i | ||||
\(76\) | −4.72376 | −0.0621547 | ||||||||
\(77\) | 32.9508 | − | 32.9508i | 0.427933 | − | 0.427933i | ||||
\(78\) | 40.6231 | + | 40.6231i | 0.520809 | + | 0.520809i | ||||
\(79\) | − | 2.48684i | − | 0.0314790i | −0.999876 | − | 0.0157395i | \(-0.994990\pi\) | ||
0.999876 | − | 0.0157395i | \(-0.00501024\pi\) | |||||||
\(80\) | 50.6141 | − | 54.6756i | 0.632676 | − | 0.683445i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 2.59655 | − | 2.59655i | 0.0316652 | − | 0.0316652i | ||||
\(83\) | −29.0421 | − | 29.0421i | −0.349905 | − | 0.349905i | 0.510169 | − | 0.860074i | \(-0.329583\pi\) |
−0.860074 | + | 0.510169i | \(0.829583\pi\) | |||||||
\(84\) | − | 1.18245i | − | 0.0140768i | ||||||
\(85\) | −3.78237 | − | 98.0540i | −0.0444985 | − | 1.15358i | ||||
\(86\) | 116.533 | 1.35503 | ||||||||
\(87\) | 3.52500 | − | 3.52500i | 0.0405173 | − | 0.0405173i | ||||
\(88\) | −102.583 | − | 102.583i | −1.16572 | − | 1.16572i | ||||
\(89\) | − | 29.3345i | − | 0.329601i | −0.986327 | − | 0.164800i | \(-0.947302\pi\) | ||
0.986327 | − | 0.164800i | \(-0.0526980\pi\) | |||||||
\(90\) | −28.9947 | + | 1.11845i | −0.322163 | + | 0.0124272i | ||||
\(91\) | 45.3656 | 0.498523 | ||||||||
\(92\) | 6.81092 | − | 6.81092i | 0.0740318 | − | 0.0740318i | ||||
\(93\) | −19.7367 | − | 19.7367i | −0.212222 | − | 0.212222i | ||||
\(94\) | − | 157.974i | − | 1.68057i | ||||||
\(95\) | 67.1711 | + | 62.1814i | 0.707064 | + | 0.654541i | ||||
\(96\) | −7.13941 | −0.0743688 | ||||||||
\(97\) | −89.1223 | + | 89.1223i | −0.918786 | + | 0.918786i | −0.996941 | − | 0.0781549i | \(-0.975097\pi\) |
0.0781549 | + | 0.996941i | \(0.475097\pi\) | |||||||
\(98\) | 9.57487 | + | 9.57487i | 0.0977028 | + | 0.0977028i | ||||
\(99\) | 52.8389i | 0.533726i | ||||||||
\(100\) | 6.43165 | − | 0.496933i | 0.0643165 | − | 0.00496933i | ||||
\(101\) | −87.3306 | −0.864660 | −0.432330 | − | 0.901716i | \(-0.642308\pi\) | ||||
−0.432330 | + | 0.901716i | \(0.642308\pi\) | |||||||
\(102\) | 46.4958 | − | 46.4958i | 0.455841 | − | 0.455841i | ||||
\(103\) | 36.7417 | + | 36.7417i | 0.356715 | + | 0.356715i | 0.862601 | − | 0.505885i | \(-0.168834\pi\) |
−0.505885 | + | 0.862601i | \(0.668834\pi\) | |||||||
\(104\) | − | 141.233i | − | 1.35801i | ||||||
\(105\) | −15.5653 | + | 16.8143i | −0.148241 | + | 0.160136i | ||||
\(106\) | −182.078 | −1.71771 | ||||||||
\(107\) | −91.9855 | + | 91.9855i | −0.859677 | + | 0.859677i | −0.991300 | − | 0.131622i | \(-0.957981\pi\) |
0.131622 | + | 0.991300i | \(0.457981\pi\) | |||||||
\(108\) | 0.948073 | + | 0.948073i | 0.00877845 | + | 0.00877845i | ||||
\(109\) | − | 144.628i | − | 1.32686i | −0.748237 | − | 0.663432i | \(-0.769099\pi\) | ||
0.748237 | − | 0.663432i | \(-0.230901\pi\) | |||||||
\(110\) | 6.56642 | + | 170.227i | 0.0596947 | + | 1.54752i | ||||
\(111\) | −6.18349 | −0.0557071 | ||||||||
\(112\) | 27.8778 | − | 27.8778i | 0.248909 | − | 0.248909i | ||||
\(113\) | 28.6801 | + | 28.6801i | 0.253806 | + | 0.253806i | 0.822529 | − | 0.568723i | \(-0.192562\pi\) |
−0.568723 | + | 0.822529i | \(0.692562\pi\) | |||||||
\(114\) | 61.3371i | 0.538045i | ||||||||
\(115\) | −186.506 | + | 7.19436i | −1.62179 | + | 0.0625597i | ||||
\(116\) | −0.742658 | −0.00640222 | ||||||||
\(117\) | −36.3734 | + | 36.3734i | −0.310884 | + | 0.310884i | ||||
\(118\) | 22.5247 | + | 22.5247i | 0.190887 | + | 0.190887i | ||||
\(119\) | − | 51.9239i | − | 0.436335i | ||||||
\(120\) | 52.3467 | + | 48.4582i | 0.436223 | + | 0.403818i | ||||
\(121\) | 189.217 | 1.56377 | ||||||||
\(122\) | 10.0813 | − | 10.0813i | 0.0826338 | − | 0.0826338i | ||||
\(123\) | 2.32491 | + | 2.32491i | 0.0189017 | + | 0.0189017i | ||||
\(124\) | 4.15818i | 0.0335337i | ||||||||
\(125\) | −97.9985 | − | 77.5970i | −0.783988 | − | 0.620776i | ||||
\(126\) | −15.3540 | −0.121857 | ||||||||
\(127\) | 12.2062 | − | 12.2062i | 0.0961116 | − | 0.0961116i | −0.657416 | − | 0.753528i | \(-0.728351\pi\) |
0.753528 | + | 0.657416i | \(0.228351\pi\) | |||||||
\(128\) | −80.7782 | − | 80.7782i | −0.631080 | − | 0.631080i | ||||
\(129\) | 104.342i | 0.808852i | ||||||||
\(130\) | −112.661 | + | 121.702i | −0.866627 | + | 0.936169i | ||||
\(131\) | −23.2249 | −0.177290 | −0.0886448 | − | 0.996063i | \(-0.528254\pi\) | ||||
−0.0886448 | + | 0.996063i | \(0.528254\pi\) | |||||||
\(132\) | 5.56613 | − | 5.56613i | 0.0421676 | − | 0.0421676i | ||||
\(133\) | 34.2489 | + | 34.2489i | 0.257511 | + | 0.257511i | ||||
\(134\) | − | 74.4170i | − | 0.555351i | ||||||
\(135\) | −1.00145 | − | 25.9615i | −0.00741813 | − | 0.192307i | ||||
\(136\) | −161.651 | −1.18861 | ||||||||
\(137\) | −17.2588 | + | 17.2588i | −0.125977 | + | 0.125977i | −0.767284 | − | 0.641307i | \(-0.778392\pi\) |
0.641307 | + | 0.767284i | \(0.278392\pi\) | |||||||
\(138\) | −88.4386 | − | 88.4386i | −0.640859 | − | 0.640859i | ||||
\(139\) | 29.4799i | 0.212085i | 0.994362 | + | 0.106043i | \(0.0338180\pi\) | ||||
−0.994362 | + | 0.106043i | \(0.966182\pi\) | |||||||
\(140\) | 3.41092 | − | 0.131574i | 0.0243637 | − | 0.000939814i | ||||
\(141\) | 141.447 | 1.00317 | ||||||||
\(142\) | 108.878 | − | 108.878i | 0.766745 | − | 0.766745i | ||||
\(143\) | 213.548 | + | 213.548i | 1.49334 | + | 1.49334i | ||||
\(144\) | 44.7039i | 0.310444i | ||||||||
\(145\) | 10.5605 | + | 9.77602i | 0.0728309 | + | 0.0674208i | ||||
\(146\) | −173.182 | −1.18618 | ||||||||
\(147\) | −8.57321 | + | 8.57321i | −0.0583212 | + | 0.0583212i | ||||
\(148\) | 0.651377 | + | 0.651377i | 0.00440120 | + | 0.00440120i | ||||
\(149\) | 14.3848i | 0.0965421i | 0.998834 | + | 0.0482710i | \(0.0153711\pi\) | ||||
−0.998834 | + | 0.0482710i | \(0.984629\pi\) | |||||||
\(150\) | −6.45259 | − | 83.5138i | −0.0430172 | − | 0.556759i | ||||
\(151\) | 15.3569 | 0.101701 | 0.0508506 | − | 0.998706i | \(-0.483807\pi\) | ||||
0.0508506 | + | 0.998706i | \(0.483807\pi\) | |||||||
\(152\) | 106.624 | − | 106.624i | 0.701476 | − | 0.701476i | ||||
\(153\) | 41.6317 | + | 41.6317i | 0.272103 | + | 0.272103i | ||||
\(154\) | 90.1429i | 0.585344i | ||||||||
\(155\) | 54.7364 | − | 59.1286i | 0.353138 | − | 0.381475i | ||||
\(156\) | 7.66325 | 0.0491234 | ||||||||
\(157\) | 63.2769 | − | 63.2769i | 0.403037 | − | 0.403037i | −0.476265 | − | 0.879302i | \(-0.658010\pi\) |
0.879302 | + | 0.476265i | \(0.158010\pi\) | |||||||
\(158\) | 3.40160 | + | 3.40160i | 0.0215291 | + | 0.0215291i | ||||
\(159\) | − | 163.030i | − | 1.02535i | ||||||
\(160\) | −0.794415 | − | 20.5944i | −0.00496509 | − | 0.128715i | ||||
\(161\) | −98.7632 | −0.613436 | ||||||||
\(162\) | 12.3106 | − | 12.3106i | 0.0759911 | − | 0.0759911i | ||||
\(163\) | −121.254 | − | 121.254i | −0.743890 | − | 0.743890i | 0.229434 | − | 0.973324i | \(-0.426312\pi\) |
−0.973324 | + | 0.229434i | \(0.926312\pi\) | |||||||
\(164\) | − | 0.489819i | − | 0.00298670i | ||||||
\(165\) | −152.419 | + | 5.87948i | −0.923754 | + | 0.0356332i | ||||
\(166\) | 79.4498 | 0.478613 | ||||||||
\(167\) | −51.2223 | + | 51.2223i | −0.306720 | + | 0.306720i | −0.843636 | − | 0.536916i | \(-0.819589\pi\) |
0.536916 | + | 0.843636i | \(0.319589\pi\) | |||||||
\(168\) | 26.6903 | + | 26.6903i | 0.158871 | + | 0.158871i | ||||
\(169\) | 125.005i | 0.739677i | ||||||||
\(170\) | 139.296 | + | 128.948i | 0.819387 | + | 0.758520i | ||||
\(171\) | −54.9204 | −0.321172 | ||||||||
\(172\) | 10.9915 | − | 10.9915i | 0.0639042 | − | 0.0639042i | ||||
\(173\) | 78.5418 | + | 78.5418i | 0.453999 | + | 0.453999i | 0.896679 | − | 0.442681i | \(-0.145972\pi\) |
−0.442681 | + | 0.896679i | \(0.645972\pi\) | |||||||
\(174\) | 9.64328i | 0.0554211i | ||||||||
\(175\) | −50.2347 | − | 43.0288i | −0.287055 | − | 0.245879i | ||||
\(176\) | 262.456 | 1.49123 | ||||||||
\(177\) | −20.1683 | + | 20.1683i | −0.113945 | + | 0.113945i | ||||
\(178\) | 40.1248 | + | 40.1248i | 0.225420 | + | 0.225420i | ||||
\(179\) | − | 162.375i | − | 0.907125i | −0.891224 | − | 0.453563i | \(-0.850153\pi\) | ||
0.891224 | − | 0.453563i | \(-0.149847\pi\) | |||||||
\(180\) | −2.62932 | + | 2.84031i | −0.0146073 | + | 0.0157795i | ||||
\(181\) | 257.224 | 1.42113 | 0.710564 | − | 0.703633i | \(-0.248440\pi\) | ||||
0.710564 | + | 0.703633i | \(0.248440\pi\) | |||||||
\(182\) | −62.0528 | + | 62.0528i | −0.340950 | + | 0.340950i | ||||
\(183\) | 9.02668 | + | 9.02668i | 0.0493261 | + | 0.0493261i | ||||
\(184\) | 307.472i | 1.67104i | ||||||||
\(185\) | −0.688048 | − | 17.8369i | −0.00371918 | − | 0.0964158i | ||||
\(186\) | 53.9932 | 0.290286 | ||||||||
\(187\) | 244.420 | − | 244.420i | 1.30706 | − | 1.30706i | ||||
\(188\) | −14.9003 | − | 14.9003i | −0.0792568 | − | 0.0792568i | ||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | −176.933 | + | 6.82510i | −0.931228 | + | 0.0359216i | ||||
\(191\) | −334.101 | −1.74922 | −0.874610 | − | 0.484827i | \(-0.838883\pi\) | ||||
−0.874610 | + | 0.484827i | \(0.838883\pi\) | |||||||
\(192\) | 82.7667 | − | 82.7667i | 0.431076 | − | 0.431076i | ||||
\(193\) | 19.9582 | + | 19.9582i | 0.103410 | + | 0.103410i | 0.756919 | − | 0.653509i | \(-0.226704\pi\) |
−0.653509 | + | 0.756919i | \(0.726704\pi\) | |||||||
\(194\) | − | 243.810i | − | 1.25675i | ||||||
\(195\) | −108.970 | − | 100.876i | −0.558822 | − | 0.517311i | ||||
\(196\) | 1.80623 | 0.00921545 | ||||||||
\(197\) | 36.5252 | − | 36.5252i | 0.185407 | − | 0.185407i | −0.608300 | − | 0.793707i | \(-0.708148\pi\) |
0.793707 | + | 0.608300i | \(0.208148\pi\) | |||||||
\(198\) | −72.2751 | − | 72.2751i | −0.365026 | − | 0.365026i | ||||
\(199\) | 187.619i | 0.942810i | 0.881917 | + | 0.471405i | \(0.156253\pi\) | ||||
−0.881917 | + | 0.471405i | \(0.843747\pi\) | |||||||
\(200\) | −133.958 | + | 156.392i | −0.669791 | + | 0.781958i | ||||
\(201\) | 66.6320 | 0.331502 | ||||||||
\(202\) | 119.454 | − | 119.454i | 0.591358 | − | 0.591358i | ||||
\(203\) | 5.38453 | + | 5.38453i | 0.0265248 | + | 0.0265248i | ||||
\(204\) | − | 8.77110i | − | 0.0429956i | ||||||
\(205\) | −6.44776 | + | 6.96516i | −0.0314525 | + | 0.0339764i | ||||
\(206\) | −100.513 | −0.487929 | ||||||||
\(207\) | 79.1867 | − | 79.1867i | 0.382545 | − | 0.382545i | ||||
\(208\) | 180.670 | + | 180.670i | 0.868607 | + | 0.868607i | ||||
\(209\) | 322.437i | 1.54276i | ||||||||
\(210\) | −1.70846 | − | 44.2901i | −0.00813554 | − | 0.210905i | ||||
\(211\) | −73.6409 | −0.349009 | −0.174505 | − | 0.984656i | \(-0.555832\pi\) | ||||
−0.174505 | + | 0.984656i | \(0.555832\pi\) | |||||||
\(212\) | −17.1738 | + | 17.1738i | −0.0810085 | + | 0.0810085i | ||||
\(213\) | 97.4878 | + | 97.4878i | 0.457689 | + | 0.457689i | ||||
\(214\) | − | 251.643i | − | 1.17590i | ||||||
\(215\) | −300.985 | + | 11.6103i | −1.39993 | + | 0.0540015i | ||||
\(216\) | −42.7997 | −0.198147 | ||||||||
\(217\) | 30.1483 | − | 30.1483i | 0.138932 | − | 0.138932i | ||||
\(218\) | 197.828 | + | 197.828i | 0.907468 | + | 0.907468i | ||||
\(219\) | − | 155.065i | − | 0.708060i | ||||||
\(220\) | 16.6754 | + | 15.4367i | 0.0757974 | + | 0.0701669i | ||||
\(221\) | 336.509 | 1.52266 | ||||||||
\(222\) | 8.45801 | − | 8.45801i | 0.0380992 | − | 0.0380992i | ||||
\(223\) | 258.221 | + | 258.221i | 1.15794 | + | 1.15794i | 0.984917 | + | 0.173025i | \(0.0553542\pi\) |
0.173025 | + | 0.984917i | \(0.444646\pi\) | |||||||
\(224\) | − | 10.9056i | − | 0.0486858i | ||||||
\(225\) | 74.7771 | − | 5.77756i | 0.332343 | − | 0.0256780i | ||||
\(226\) | −78.4596 | −0.347166 | ||||||||
\(227\) | −9.72923 | + | 9.72923i | −0.0428601 | + | 0.0428601i | −0.728212 | − | 0.685352i | \(-0.759648\pi\) |
0.685352 | + | 0.728212i | \(0.259648\pi\) | |||||||
\(228\) | 5.78540 | + | 5.78540i | 0.0253745 | + | 0.0253745i | ||||
\(229\) | 108.047i | 0.471822i | 0.971775 | + | 0.235911i | \(0.0758074\pi\) | ||||
−0.971775 | + | 0.235911i | \(0.924193\pi\) | |||||||
\(230\) | 245.270 | − | 264.951i | 1.06639 | − | 1.15196i | ||||
\(231\) | −80.7128 | −0.349406 | ||||||||
\(232\) | 16.7632 | − | 16.7632i | 0.0722554 | − | 0.0722554i | ||||
\(233\) | −2.47323 | − | 2.47323i | −0.0106147 | − | 0.0106147i | 0.701779 | − | 0.712394i | \(-0.252389\pi\) |
−0.712394 | + | 0.701779i | \(0.752389\pi\) | |||||||
\(234\) | − | 99.5059i | − | 0.425239i | ||||||
\(235\) | 15.7391 | + | 408.020i | 0.0669750 | + | 1.73626i | ||||
\(236\) | 4.24911 | 0.0180047 | ||||||||
\(237\) | −3.04574 | + | 3.04574i | −0.0128512 | + | 0.0128512i | ||||
\(238\) | 71.0236 | + | 71.0236i | 0.298418 | + | 0.298418i | ||||
\(239\) | − | 230.974i | − | 0.966417i | −0.875505 | − | 0.483209i | \(-0.839471\pi\) | ||
0.875505 | − | 0.483209i | \(-0.160529\pi\) | |||||||
\(240\) | −128.953 | + | 4.97428i | −0.537304 | + | 0.0207262i | ||||
\(241\) | −280.404 | −1.16350 | −0.581752 | − | 0.813366i | \(-0.697633\pi\) | ||||
−0.581752 | + | 0.813366i | \(0.697633\pi\) | |||||||
\(242\) | −258.818 | + | 258.818i | −1.06950 | + | 1.06950i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 1.90177i | − | 0.00779413i | ||||||
\(245\) | −25.6843 | − | 23.7764i | −0.104834 | − | 0.0970465i | ||||
\(246\) | −6.36022 | −0.0258545 | ||||||||
\(247\) | −221.960 | + | 221.960i | −0.898625 | + | 0.898625i | ||||
\(248\) | −93.8582 | − | 93.8582i | −0.378460 | − | 0.378460i | ||||
\(249\) | 71.1383i | 0.285696i | ||||||||
\(250\) | 240.186 | − | 27.9059i | 0.960746 | − | 0.111624i | ||||
\(251\) | 53.4737 | 0.213043 | 0.106521 | − | 0.994310i | \(-0.466029\pi\) | ||||
0.106521 | + | 0.994310i | \(0.466029\pi\) | |||||||
\(252\) | −1.44821 | + | 1.44821i | −0.00574685 | + | 0.00574685i | ||||
\(253\) | −464.904 | − | 464.904i | −1.83757 | − | 1.83757i | ||||
\(254\) | 33.3921i | 0.131465i | ||||||||
\(255\) | −115.459 | + | 124.724i | −0.452779 | + | 0.489112i | ||||
\(256\) | −49.3317 | −0.192702 | ||||||||
\(257\) | 78.9368 | − | 78.9368i | 0.307147 | − | 0.307147i | −0.536655 | − | 0.843802i | \(-0.680312\pi\) |
0.843802 | + | 0.536655i | \(0.180312\pi\) | |||||||
\(258\) | −142.723 | − | 142.723i | −0.553189 | − | 0.553189i | ||||
\(259\) | − | 9.44543i | − | 0.0364688i | ||||||
\(260\) | 0.852705 | + | 22.1055i | 0.00327963 | + | 0.0850210i | ||||
\(261\) | −8.63446 | −0.0330822 | ||||||||
\(262\) | 31.7680 | − | 31.7680i | 0.121252 | − | 0.121252i | ||||
\(263\) | −323.863 | − | 323.863i | −1.23142 | − | 1.23142i | −0.963418 | − | 0.268002i | \(-0.913637\pi\) |
−0.268002 | − | 0.963418i | \(-0.586363\pi\) | |||||||
\(264\) | 251.277i | 0.951806i | ||||||||
\(265\) | 470.277 | − | 18.1406i | 1.77463 | − | 0.0684553i | ||||
\(266\) | −93.6940 | −0.352233 | ||||||||
\(267\) | −35.9272 | + | 35.9272i | −0.134559 | + | 0.134559i | ||||
\(268\) | −7.01911 | − | 7.01911i | −0.0261907 | − | 0.0261907i | ||||
\(269\) | − | 119.052i | − | 0.442573i | −0.975209 | − | 0.221286i | \(-0.928974\pi\) | ||
0.975209 | − | 0.221286i | \(-0.0710256\pi\) | |||||||
\(270\) | 36.8809 | + | 34.1413i | 0.136596 | + | 0.126449i | ||||
\(271\) | 380.174 | 1.40286 | 0.701429 | − | 0.712740i | \(-0.252546\pi\) | ||||
0.701429 | + | 0.712740i | \(0.252546\pi\) | |||||||
\(272\) | 206.789 | − | 206.789i | 0.760253 | − | 0.760253i | ||||
\(273\) | −55.5613 | − | 55.5613i | −0.203521 | − | 0.203521i | ||||
\(274\) | − | 47.2146i | − | 0.172316i | ||||||
\(275\) | −33.9200 | − | 439.016i | −0.123345 | − | 1.59642i | ||||
\(276\) | −16.6833 | −0.0604467 | ||||||||
\(277\) | −374.455 | + | 374.455i | −1.35182 | + | 1.35182i | −0.468198 | + | 0.883624i | \(0.655097\pi\) |
−0.883624 | + | 0.468198i | \(0.844903\pi\) | |||||||
\(278\) | −40.3237 | − | 40.3237i | −0.145049 | − | 0.145049i | ||||
\(279\) | 48.3448i | 0.173279i | ||||||||
\(280\) | −74.0212 | + | 79.9609i | −0.264361 | + | 0.285575i | ||||
\(281\) | −300.844 | −1.07062 | −0.535309 | − | 0.844656i | \(-0.679805\pi\) | ||||
−0.535309 | + | 0.844656i | \(0.679805\pi\) | |||||||
\(282\) | −193.477 | + | 193.477i | −0.686090 | + | 0.686090i | ||||
\(283\) | −137.166 | − | 137.166i | −0.484686 | − | 0.484686i | 0.421938 | − | 0.906624i | \(-0.361350\pi\) |
−0.906624 | + | 0.421938i | \(0.861350\pi\) | |||||||
\(284\) | − | 20.5390i | − | 0.0723204i | ||||||
\(285\) | −6.11110 | − | 158.424i | −0.0214425 | − | 0.555873i | ||||
\(286\) | −584.198 | −2.04265 | ||||||||
\(287\) | −3.55136 | + | 3.55136i | −0.0123741 | + | 0.0123741i | ||||
\(288\) | 8.74395 | + | 8.74395i | 0.0303609 | + | 0.0303609i | ||||
\(289\) | − | 96.1561i | − | 0.332720i | ||||||
\(290\) | −27.8171 | + | 1.07303i | −0.0959209 | + | 0.00370009i | ||||
\(291\) | 218.304 | 0.750186 | ||||||||
\(292\) | −16.3348 | + | 16.3348i | −0.0559411 | + | 0.0559411i | ||||
\(293\) | 193.498 | + | 193.498i | 0.660403 | + | 0.660403i | 0.955475 | − | 0.295072i | \(-0.0953436\pi\) |
−0.295072 | + | 0.955475i | \(0.595344\pi\) | |||||||
\(294\) | − | 23.4536i | − | 0.0797740i | ||||||
\(295\) | −60.4217 | − | 55.9334i | −0.204819 | − | 0.189605i | ||||
\(296\) | −29.4057 | −0.0993436 | ||||||||
\(297\) | 64.7142 | − | 64.7142i | 0.217893 | − | 0.217893i | ||||
\(298\) | −19.6761 | − | 19.6761i | −0.0660270 | − | 0.0660270i | ||||
\(299\) | − | 640.065i | − | 2.14068i | ||||||
\(300\) | −8.48575 | − | 7.26851i | −0.0282858 | − | 0.0242284i | ||||
\(301\) | −159.385 | −0.529518 | ||||||||
\(302\) | −21.0057 | + | 21.0057i | −0.0695554 | + | 0.0695554i | ||||
\(303\) | 106.958 | + | 106.958i | 0.352996 | + | 0.352996i | ||||
\(304\) | 272.795i | 0.897352i | ||||||||
\(305\) | −25.0340 | + | 27.0428i | −0.0820787 | + | 0.0886650i | ||||
\(306\) | −113.891 | −0.372193 | ||||||||
\(307\) | 122.528 | − | 122.528i | 0.399115 | − | 0.399115i | −0.478806 | − | 0.877921i | \(-0.658930\pi\) |
0.877921 | + | 0.478806i | \(0.158930\pi\) | |||||||
\(308\) | 8.50240 | + | 8.50240i | 0.0276052 | + | 0.0276052i | ||||
\(309\) | − | 89.9984i | − | 0.291257i | ||||||
\(310\) | 6.00792 | + | 155.749i | 0.0193804 | + | 0.502416i | ||||
\(311\) | 118.050 | 0.379582 | 0.189791 | − | 0.981825i | \(-0.439219\pi\) | ||||
0.189791 | + | 0.981825i | \(0.439219\pi\) | |||||||
\(312\) | −172.975 | + | 172.975i | −0.554406 | + | 0.554406i | ||||
\(313\) | −289.482 | − | 289.482i | −0.924861 | − | 0.924861i | 0.0725069 | − | 0.997368i | \(-0.476900\pi\) |
−0.997368 | + | 0.0725069i | \(0.976900\pi\) | |||||||
\(314\) | 173.105i | 0.551290i | ||||||||
\(315\) | 39.6568 | − | 1.52974i | 0.125895 | − | 0.00485630i | ||||
\(316\) | 0.641686 | 0.00203065 | ||||||||
\(317\) | −292.255 | + | 292.255i | −0.921942 | + | 0.921942i | −0.997167 | − | 0.0752250i | \(-0.976032\pi\) |
0.0752250 | + | 0.997167i | \(0.476032\pi\) | |||||||
\(318\) | 222.999 | + | 222.999i | 0.701254 | + | 0.701254i | ||||
\(319\) | 50.6928i | 0.158912i | ||||||||
\(320\) | 247.959 | + | 229.540i | 0.774871 | + | 0.717311i | ||||
\(321\) | 225.318 | 0.701924 | ||||||||
\(322\) | 135.092 | − | 135.092i | 0.419541 | − | 0.419541i | ||||
\(323\) | 254.048 | + | 254.048i | 0.786527 | + | 0.786527i | ||||
\(324\) | − | 2.32229i | − | 0.00716758i | ||||||
\(325\) | 278.861 | − | 325.561i | 0.858034 | − | 1.00173i | ||||
\(326\) | 331.712 | 1.01752 | ||||||||
\(327\) | −177.133 | + | 177.133i | −0.541690 | + | 0.541690i | ||||
\(328\) | 11.0562 | + | 11.0562i | 0.0337079 | + | 0.0337079i | ||||
\(329\) | 216.065i | 0.656731i | ||||||||
\(330\) | 200.443 | − | 216.527i | 0.607403 | − | 0.656144i | ||||
\(331\) | 580.718 | 1.75443 | 0.877217 | − | 0.480093i | \(-0.159397\pi\) | ||||
0.877217 | + | 0.480093i | \(0.159397\pi\) | |||||||
\(332\) | 7.49381 | − | 7.49381i | 0.0225717 | − | 0.0225717i | ||||
\(333\) | 7.57319 | + | 7.57319i | 0.0227423 | + | 0.0227423i | ||||
\(334\) | − | 140.128i | − | 0.419544i | ||||||
\(335\) | 7.41427 | + | 192.207i | 0.0221321 | + | 0.573752i | ||||
\(336\) | −68.2863 | −0.203233 | ||||||||
\(337\) | 253.637 | − | 253.637i | 0.752631 | − | 0.752631i | −0.222339 | − | 0.974970i | \(-0.571369\pi\) |
0.974970 | + | 0.222339i | \(0.0713690\pi\) | |||||||
\(338\) | −170.987 | − | 170.987i | −0.505880 | − | 0.505880i | ||||
\(339\) | − | 70.2516i | − | 0.207232i | ||||||
\(340\) | 25.3012 | − | 0.975976i | 0.0744152 | − | 0.00287052i | ||||
\(341\) | 283.832 | 0.832351 | ||||||||
\(342\) | 75.1223 | − | 75.1223i | 0.219656 | − | 0.219656i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 496.200i | 1.44244i | ||||||||
\(345\) | 237.234 | + | 219.611i | 0.687634 | + | 0.636554i | ||||
\(346\) | −214.865 | −0.620997 | ||||||||
\(347\) | 60.2580 | − | 60.2580i | 0.173654 | − | 0.173654i | −0.614929 | − | 0.788583i | \(-0.710815\pi\) |
0.788583 | + | 0.614929i | \(0.210815\pi\) | |||||||
\(348\) | 0.909567 | + | 0.909567i | 0.00261370 | + | 0.00261370i | ||||
\(349\) | − | 348.191i | − | 0.997681i | −0.866694 | − | 0.498841i | \(-0.833759\pi\) | ||
0.866694 | − | 0.498841i | \(-0.166241\pi\) | |||||||
\(350\) | 127.569 | − | 9.85649i | 0.364484 | − | 0.0281614i | ||||
\(351\) | 89.0963 | 0.253836 | ||||||||
\(352\) | 51.3356 | − | 51.3356i | 0.145840 | − | 0.145840i | ||||
\(353\) | 113.128 | + | 113.128i | 0.320476 | + | 0.320476i | 0.848950 | − | 0.528474i | \(-0.177235\pi\) |
−0.528474 | + | 0.848950i | \(0.677235\pi\) | |||||||
\(354\) | − | 55.1740i | − | 0.155859i | ||||||
\(355\) | −270.366 | + | 292.061i | −0.761595 | + | 0.822708i | ||||
\(356\) | 7.56925 | 0.0212619 | ||||||||
\(357\) | −63.5935 | + | 63.5935i | −0.178133 | + | 0.178133i | ||||
\(358\) | 222.103 | + | 222.103i | 0.620401 | + | 0.620401i | ||||
\(359\) | − | 105.651i | − | 0.294293i | −0.989115 | − | 0.147147i | \(-0.952991\pi\) | ||
0.989115 | − | 0.147147i | \(-0.0470089\pi\) | |||||||
\(360\) | −4.76241 | − | 123.460i | −0.0132289 | − | 0.342945i | ||||
\(361\) | 25.8608 | 0.0716365 | ||||||||
\(362\) | −351.841 | + | 351.841i | −0.971937 | + | 0.971937i | ||||
\(363\) | −231.742 | − | 231.742i | −0.638408 | − | 0.638408i | ||||
\(364\) | 11.7058i | 0.0321588i | ||||||||
\(365\) | 447.302 | − | 17.2544i | 1.22548 | − | 0.0472723i | ||||
\(366\) | −24.6941 | −0.0674702 | ||||||||
\(367\) | −230.168 | + | 230.168i | −0.627161 | + | 0.627161i | −0.947353 | − | 0.320191i | \(-0.896253\pi\) |
0.320191 | + | 0.947353i | \(0.396253\pi\) | |||||||
\(368\) | −393.328 | − | 393.328i | −1.06883 | − | 1.06883i | ||||
\(369\) | − | 5.69485i | − | 0.0154332i | ||||||
\(370\) | 25.3392 | + | 23.4569i | 0.0684843 | + | 0.0633970i | ||||
\(371\) | 249.032 | 0.671246 | ||||||||
\(372\) | 5.09271 | − | 5.09271i | 0.0136901 | − | 0.0136901i | ||||
\(373\) | −211.456 | − | 211.456i | −0.566906 | − | 0.566906i | 0.364355 | − | 0.931260i | \(-0.381290\pi\) |
−0.931260 | + | 0.364355i | \(0.881290\pi\) | |||||||
\(374\) | 668.653i | 1.78784i | ||||||||
\(375\) | 24.9866 | + | 215.060i | 0.0666309 | + | 0.573493i | ||||
\(376\) | 672.657 | 1.78898 | ||||||||
\(377\) | −34.8961 | + | 34.8961i | −0.0925626 | + | 0.0925626i | ||||
\(378\) | 18.8047 | + | 18.8047i | 0.0497478 | + | 0.0497478i | ||||
\(379\) | 132.280i | 0.349024i | 0.984655 | + | 0.174512i | \(0.0558347\pi\) | ||||
−0.984655 | + | 0.174512i | \(0.944165\pi\) | |||||||
\(380\) | −16.0448 | + | 17.3323i | −0.0422233 | + | 0.0456114i | ||||
\(381\) | −29.8989 | −0.0784748 | ||||||||
\(382\) | 456.997 | − | 456.997i | 1.19633 | − | 1.19633i | ||||
\(383\) | 149.538 | + | 149.538i | 0.390438 | + | 0.390438i | 0.874844 | − | 0.484406i | \(-0.160964\pi\) |
−0.484406 | + | 0.874844i | \(0.660964\pi\) | |||||||
\(384\) | 197.865i | 0.515274i | ||||||||
\(385\) | −8.98106 | − | 232.825i | −0.0233274 | − | 0.604739i | ||||
\(386\) | −54.5991 | −0.141448 | ||||||||
\(387\) | 127.792 | − | 127.792i | 0.330212 | − | 0.330212i | ||||
\(388\) | −22.9965 | − | 22.9965i | −0.0592692 | − | 0.0592692i | ||||
\(389\) | 289.081i | 0.743140i | 0.928405 | + | 0.371570i | \(0.121180\pi\) | ||||
−0.928405 | + | 0.371570i | \(0.878820\pi\) | |||||||
\(390\) | 287.035 | − | 11.0722i | 0.735988 | − | 0.0283903i | ||||
\(391\) | −732.596 | −1.87365 | ||||||||
\(392\) | −40.7701 | + | 40.7701i | −0.104005 | + | 0.104005i | ||||
\(393\) | 28.4446 | + | 28.4446i | 0.0723781 | + | 0.0723781i | ||||
\(394\) | 99.9213i | 0.253607i | ||||||||
\(395\) | −9.12468 | − | 8.44687i | −0.0231005 | − | 0.0213845i | ||||
\(396\) | −13.6342 | −0.0344297 | ||||||||
\(397\) | −502.891 | + | 502.891i | −1.26673 | + | 1.26673i | −0.318961 | + | 0.947768i | \(0.603334\pi\) |
−0.947768 | + | 0.318961i | \(0.896666\pi\) | |||||||
\(398\) | −256.633 | − | 256.633i | −0.644806 | − | 0.644806i | ||||
\(399\) | − | 83.8923i | − | 0.210256i | ||||||
\(400\) | −28.6977 | − | 371.425i | −0.0717442 | − | 0.928563i | ||||
\(401\) | 405.912 | 1.01225 | 0.506125 | − | 0.862460i | \(-0.331078\pi\) | ||||
0.506125 | + | 0.862460i | \(0.331078\pi\) | |||||||
\(402\) | −91.1418 | + | 91.1418i | −0.226721 | + | 0.226721i | ||||
\(403\) | 195.385 | + | 195.385i | 0.484826 | + | 0.484826i | ||||
\(404\) | − | 22.5342i | − | 0.0557776i | ||||||
\(405\) | −30.5696 | + | 33.0227i | −0.0754806 | + | 0.0815375i | ||||
\(406\) | −14.7304 | −0.0362817 | ||||||||
\(407\) | 44.4621 | − | 44.4621i | 0.109244 | − | 0.109244i | ||||
\(408\) | 197.981 | + | 197.981i | 0.485247 | + | 0.485247i | ||||
\(409\) | − | 505.400i | − | 1.23570i | −0.786297 | − | 0.617849i | \(-0.788004\pi\) | ||
0.786297 | − | 0.617849i | \(-0.211996\pi\) | |||||||
\(410\) | −0.707713 | − | 18.3467i | −0.00172613 | − | 0.0447481i | ||||
\(411\) | 42.2753 | 0.102860 | ||||||||
\(412\) | −9.48056 | + | 9.48056i | −0.0230111 | + | 0.0230111i | ||||
\(413\) | −30.8076 | − | 30.8076i | −0.0745946 | − | 0.0745946i | ||||
\(414\) | 216.629i | 0.523259i | ||||||||
\(415\) | −205.206 | + | 7.91569i | −0.494472 | + | 0.0190740i | ||||
\(416\) | 70.6772 | 0.169897 | ||||||||
\(417\) | 36.1053 | − | 36.1053i | 0.0865834 | − | 0.0865834i | ||||
\(418\) | −441.042 | − | 441.042i | −1.05512 | − | 1.05512i | ||||
\(419\) | 553.591i | 1.32122i | 0.750729 | + | 0.660610i | \(0.229702\pi\) | ||||
−0.750729 | + | 0.660610i | \(0.770298\pi\) | |||||||
\(420\) | −4.33865 | − | 4.01636i | −0.0103301 | − | 0.00956275i | ||||
\(421\) | −320.444 | −0.761150 | −0.380575 | − | 0.924750i | \(-0.624274\pi\) | ||||
−0.380575 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(422\) | 100.729 | − | 100.729i | 0.238694 | − | 0.238694i | ||||
\(423\) | −173.237 | − | 173.237i | −0.409544 | − | 0.409544i | ||||
\(424\) | − | 775.293i | − | 1.82852i | ||||||
\(425\) | −372.626 | − | 319.175i | −0.876767 | − | 0.750999i | ||||
\(426\) | −266.695 | −0.626045 | ||||||||
\(427\) | −13.7885 | + | 13.7885i | −0.0322915 | + | 0.0322915i | ||||
\(428\) | −23.7353 | − | 23.7353i | −0.0554562 | − | 0.0554562i | ||||
\(429\) | − | 523.083i | − | 1.21931i | ||||||
\(430\) | 395.818 | − | 427.580i | 0.920508 | − | 0.994373i | ||||
\(431\) | 221.870 | 0.514780 | 0.257390 | − | 0.966308i | \(-0.417138\pi\) | ||||
0.257390 | + | 0.966308i | \(0.417138\pi\) | |||||||
\(432\) | 54.7508 | − | 54.7508i | 0.126738 | − | 0.126738i | ||||
\(433\) | −162.133 | − | 162.133i | −0.374440 | − | 0.374440i | 0.494651 | − | 0.869091i | \(-0.335296\pi\) |
−0.869091 | + | 0.494651i | \(0.835296\pi\) | |||||||
\(434\) | 82.4759i | 0.190037i | ||||||||
\(435\) | −0.960773 | − | 24.9070i | −0.00220867 | − | 0.0572575i | ||||
\(436\) | 37.3188 | 0.0855936 | ||||||||
\(437\) | 483.219 | − | 483.219i | 1.10576 | − | 1.10576i | ||||
\(438\) | 212.104 | + | 212.104i | 0.484256 | + | 0.484256i | ||||
\(439\) | 606.504i | 1.38156i | 0.723066 | + | 0.690779i | \(0.242732\pi\) | ||||
−0.723066 | + | 0.690779i | \(0.757268\pi\) | |||||||
\(440\) | −724.834 | + | 27.9600i | −1.64735 | + | 0.0635455i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −460.289 | + | 460.289i | −1.04138 | + | 1.04138i | ||||
\(443\) | −9.75385 | − | 9.75385i | −0.0220177 | − | 0.0220177i | 0.696012 | − | 0.718030i | \(-0.254956\pi\) |
−0.718030 | + | 0.696012i | \(0.754956\pi\) | |||||||
\(444\) | − | 1.59554i | − | 0.00359356i | ||||||
\(445\) | −107.634 | − | 99.6382i | −0.241873 | − | 0.223906i | ||||
\(446\) | −706.410 | −1.58388 | ||||||||
\(447\) | 17.6177 | − | 17.6177i | 0.0394131 | − | 0.0394131i | ||||
\(448\) | 126.428 | + | 126.428i | 0.282206 | + | 0.282206i | ||||
\(449\) | 448.959i | 0.999908i | 0.866052 | + | 0.499954i | \(0.166650\pi\) | ||||
−0.866052 | + | 0.499954i | \(0.833350\pi\) | |||||||
\(450\) | −94.3803 | + | 110.186i | −0.209734 | + | 0.244857i | ||||
\(451\) | −33.4344 | −0.0741340 | ||||||||
\(452\) | −7.40041 | + | 7.40041i | −0.0163726 | + | 0.0163726i | ||||
\(453\) | −18.8083 | − | 18.8083i | −0.0415193 | − | 0.0415193i | ||||
\(454\) | − | 26.6161i | − | 0.0586257i | ||||||
\(455\) | 154.090 | − | 166.455i | 0.338659 | − | 0.365835i | ||||
\(456\) | −261.175 | −0.572753 | ||||||||
\(457\) | 368.860 | − | 368.860i | 0.807133 | − | 0.807133i | −0.177066 | − | 0.984199i | \(-0.556661\pi\) |
0.984199 | + | 0.177066i | \(0.0566606\pi\) | |||||||
\(458\) | −147.791 | − | 147.791i | −0.322688 | − | 0.322688i | ||||
\(459\) | − | 101.977i | − | 0.222171i | ||||||
\(460\) | −1.85638 | − | 48.1247i | −0.00403561 | − | 0.104619i | ||||
\(461\) | −507.955 | −1.10186 | −0.550928 | − | 0.834553i | \(-0.685726\pi\) | ||||
−0.550928 | + | 0.834553i | \(0.685726\pi\) | |||||||
\(462\) | 110.402 | − | 110.402i | 0.238966 | − | 0.238966i | ||||
\(463\) | 255.428 | + | 255.428i | 0.551681 | + | 0.551681i | 0.926926 | − | 0.375245i | \(-0.122441\pi\) |
−0.375245 | + | 0.926926i | \(0.622441\pi\) | |||||||
\(464\) | 42.8882i | 0.0924315i | ||||||||
\(465\) | −139.456 | + | 5.37941i | −0.299904 | + | 0.0115686i | ||||
\(466\) | 6.76597 | 0.0145192 | ||||||||
\(467\) | 408.350 | − | 408.350i | 0.874411 | − | 0.874411i | −0.118538 | − | 0.992950i | \(-0.537821\pi\) |
0.992950 | + | 0.118538i | \(0.0378208\pi\) | |||||||
\(468\) | −9.38553 | − | 9.38553i | −0.0200545 | − | 0.0200545i | ||||
\(469\) | 101.782i | 0.217019i | ||||||||
\(470\) | −579.635 | − | 536.577i | −1.23326 | − | 1.14165i | ||||
\(471\) | −154.996 | −0.329079 | ||||||||
\(472\) | −95.9108 | + | 95.9108i | −0.203201 | + | 0.203201i | ||||
\(473\) | −750.267 | − | 750.267i | −1.58619 | − | 1.58619i | ||||
\(474\) | − | 8.33218i | − | 0.0175784i | ||||||
\(475\) | 456.310 | − | 35.2562i | 0.960653 | − | 0.0742236i | ||||
\(476\) | 13.3981 | 0.0281472 | ||||||||
\(477\) | −199.670 | + | 199.670i | −0.418595 | + | 0.418595i | ||||
\(478\) | 315.935 | + | 315.935i | 0.660952 | + | 0.660952i | ||||
\(479\) | 664.740i | 1.38777i | 0.720087 | + | 0.693883i | \(0.244102\pi\) | ||||
−0.720087 | + | 0.693883i | \(0.755898\pi\) | |||||||
\(480\) | −24.2499 | + | 26.1958i | −0.0505206 | + | 0.0545746i | ||||
\(481\) | 61.2140 | 0.127264 | ||||||||
\(482\) | 383.548 | − | 383.548i | 0.795743 | − | 0.795743i | ||||
\(483\) | 120.960 | + | 120.960i | 0.250434 | + | 0.250434i | ||||
\(484\) | 48.8241i | 0.100876i | ||||||||
\(485\) | 24.2911 | + | 629.721i | 0.0500848 | + | 1.29839i | ||||
\(486\) | −30.1546 | −0.0620464 | ||||||||
\(487\) | −334.715 | + | 334.715i | −0.687300 | + | 0.687300i | −0.961634 | − | 0.274334i | \(-0.911543\pi\) |
0.274334 | + | 0.961634i | \(0.411543\pi\) | |||||||
\(488\) | 42.9266 | + | 42.9266i | 0.0879643 | + | 0.0879643i | ||||
\(489\) | 297.010i | 0.607383i | ||||||||
\(490\) | 67.6543 | − | 2.60972i | 0.138070 | − | 0.00532596i | ||||
\(491\) | −312.255 | −0.635958 | −0.317979 | − | 0.948098i | \(-0.603004\pi\) | ||||
−0.317979 | + | 0.948098i | \(0.603004\pi\) | |||||||
\(492\) | −0.599904 | + | 0.599904i | −0.00121932 | + | 0.00121932i | ||||
\(493\) | 39.9409 | + | 39.9409i | 0.0810160 | + | 0.0810160i | ||||
\(494\) | − | 607.212i | − | 1.22917i | ||||||
\(495\) | 193.876 | + | 179.474i | 0.391668 | + | 0.362574i | ||||
\(496\) | 240.133 | 0.484139 | ||||||||
\(497\) | −148.915 | + | 148.915i | −0.299628 | + | 0.299628i | ||||
\(498\) | −97.3057 | − | 97.3057i | −0.195393 | − | 0.195393i | ||||
\(499\) | − | 89.3669i | − | 0.179092i | −0.995983 | − | 0.0895460i | \(-0.971458\pi\) | ||
0.995983 | − | 0.0895460i | \(-0.0285416\pi\) | |||||||
\(500\) | 20.0226 | − | 25.2868i | 0.0400451 | − | 0.0505736i | ||||
\(501\) | 125.469 | 0.250436 | ||||||||
\(502\) | −73.1434 | + | 73.1434i | −0.145704 | + | 0.145704i | ||||
\(503\) | 627.521 | + | 627.521i | 1.24756 | + | 1.24756i | 0.956796 | + | 0.290761i | \(0.0939085\pi\) |
0.290761 | + | 0.956796i | \(0.406092\pi\) | |||||||
\(504\) | − | 65.3776i | − | 0.129718i | ||||||
\(505\) | −296.630 | + | 320.432i | −0.587385 | + | 0.634520i | ||||
\(506\) | 1271.83 | 2.51350 | ||||||||
\(507\) | 153.100 | − | 153.100i | 0.301972 | − | 0.301972i | ||||
\(508\) | 3.14959 | + | 3.14959i | 0.00619998 | + | 0.00619998i | ||||
\(509\) | 556.945i | 1.09420i | 0.837069 | + | 0.547098i | \(0.184267\pi\) | ||||
−0.837069 | + | 0.547098i | \(0.815733\pi\) | |||||||
\(510\) | −12.6729 | − | 328.531i | −0.0248488 | − | 0.644178i | ||||
\(511\) | 236.866 | 0.463534 | ||||||||
\(512\) | 390.591 | − | 390.591i | 0.762872 | − | 0.762872i | ||||
\(513\) | 67.2635 | + | 67.2635i | 0.131118 | + | 0.131118i | ||||
\(514\) | 215.946i | 0.420128i | ||||||||
\(515\) | 259.610 | − | 10.0143i | 0.504097 | − | 0.0194452i | ||||
\(516\) | −26.9236 | −0.0521776 | ||||||||
\(517\) | −1017.07 | + | 1017.07i | −1.96726 | + | 1.96726i | ||||
\(518\) | 12.9198 | + | 12.9198i | 0.0249418 | + | 0.0249418i | ||||
\(519\) | − | 192.387i | − | 0.370688i | ||||||
\(520\) | −518.211 | − | 479.716i | −0.996559 | − | 0.922531i | ||||
\(521\) | −64.5705 | −0.123936 | −0.0619679 | − | 0.998078i | \(-0.519738\pi\) | ||||
−0.0619679 | + | 0.998078i | \(0.519738\pi\) | |||||||
\(522\) | 11.8106 | − | 11.8106i | 0.0226256 | − | 0.0226256i | ||||
\(523\) | −431.531 | − | 431.531i | −0.825107 | − | 0.825107i | 0.161728 | − | 0.986835i | \(-0.448293\pi\) |
−0.986835 | + | 0.161728i | \(0.948293\pi\) | |||||||
\(524\) | − | 5.99279i | − | 0.0114366i | ||||||
\(525\) | 8.82537 | + | 114.224i | 0.0168102 | + | 0.217569i | ||||
\(526\) | 885.986 | 1.68438 | ||||||||
\(527\) | 223.631 | − | 223.631i | 0.424347 | − | 0.424347i | ||||
\(528\) | −321.442 | − | 321.442i | −0.608791 | − | 0.608791i | ||||
\(529\) | 864.452i | 1.63413i | ||||||||
\(530\) | −618.450 | + | 668.077i | −1.16689 | + | 1.26052i | ||||
\(531\) | 49.4020 | 0.0930358 | ||||||||
\(532\) | −8.83734 | + | 8.83734i | −0.0166115 | + | 0.0166115i | ||||
\(533\) | −23.0157 | − | 23.0157i | −0.0431814 | − | 0.0431814i | ||||
\(534\) | − | 98.2854i | − | 0.184055i | ||||||
\(535\) | 25.0715 | + | 649.952i | 0.0468626 | + | 1.21486i | ||||
\(536\) | 316.870 | 0.591175 | ||||||||
\(537\) | −198.868 | + | 198.868i | −0.370332 | + | 0.370332i | ||||
\(538\) | 162.844 | + | 162.844i | 0.302684 | + | 0.302684i | ||||
\(539\) | − | 123.291i | − | 0.228740i | ||||||
\(540\) | 6.69891 | − | 0.258406i | 0.0124054 | − | 0.000478530i | ||||
\(541\) | −571.616 | −1.05659 | −0.528295 | − | 0.849061i | \(-0.677169\pi\) | ||||
−0.528295 | + | 0.849061i | \(0.677169\pi\) | |||||||
\(542\) | −520.017 | + | 520.017i | −0.959441 | + | 0.959441i | ||||
\(543\) | −315.034 | − | 315.034i | −0.580173 | − | 0.580173i | ||||
\(544\) | − | 80.8946i | − | 0.148703i | ||||||
\(545\) | −530.667 | − | 491.248i | −0.973702 | − | 0.901372i | ||||
\(546\) | 151.998 | 0.278384 | ||||||||
\(547\) | 259.835 | − | 259.835i | 0.475017 | − | 0.475017i | −0.428516 | − | 0.903534i | \(-0.640964\pi\) |
0.903534 | + | 0.428516i | \(0.140964\pi\) | |||||||
\(548\) | −4.45334 | − | 4.45334i | −0.00812653 | − | 0.00812653i | ||||
\(549\) | − | 22.1108i | − | 0.0402746i | ||||||
\(550\) | 646.900 | + | 554.106i | 1.17618 | + | 1.00747i | ||||
\(551\) | −52.6898 | −0.0956258 | ||||||||
\(552\) | 376.574 | − | 376.574i | 0.682200 | − | 0.682200i | ||||
\(553\) | −4.65245 | − | 4.65245i | −0.00841311 | − | 0.00841311i | ||||
\(554\) | − | 1024.39i | − | 1.84907i | ||||||
\(555\) | −21.0030 | + | 22.6884i | −0.0378432 | + | 0.0408799i | ||||
\(556\) | −7.60677 | −0.0136812 | ||||||||
\(557\) | 503.660 | − | 503.660i | 0.904237 | − | 0.904237i | −0.0915625 | − | 0.995799i | \(-0.529186\pi\) |
0.995799 | + | 0.0915625i | \(0.0291861\pi\) | |||||||
\(558\) | −66.1278 | − | 66.1278i | −0.118509 | − | 0.118509i | ||||
\(559\) | − | 1032.94i | − | 1.84784i | ||||||
\(560\) | −7.59834 | − | 196.979i | −0.0135685 | − | 0.351748i | ||||
\(561\) | −598.703 | −1.06721 | ||||||||
\(562\) | 411.506 | − | 411.506i | 0.732216 | − | 0.732216i | ||||
\(563\) | −405.076 | − | 405.076i | −0.719495 | − | 0.719495i | 0.249007 | − | 0.968502i | \(-0.419896\pi\) |
−0.968502 | + | 0.249007i | \(0.919896\pi\) | |||||||
\(564\) | 36.4981i | 0.0647129i | ||||||||
\(565\) | 202.648 | − | 7.81703i | 0.358670 | − | 0.0138355i | ||||
\(566\) | 375.242 | 0.662972 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | 463.605 | + | 463.605i | 0.816207 | + | 0.816207i | ||||
\(569\) | − | 674.447i | − | 1.18532i | −0.805453 | − | 0.592660i | \(-0.798078\pi\) | ||
0.805453 | − | 0.592660i | \(-0.201922\pi\) | |||||||
\(570\) | 225.057 | + | 208.339i | 0.394837 | + | 0.365507i | ||||
\(571\) | 825.137 | 1.44507 | 0.722537 | − | 0.691333i | \(-0.242976\pi\) | ||||
0.722537 | + | 0.691333i | \(0.242976\pi\) | |||||||
\(572\) | −55.1023 | + | 55.1023i | −0.0963328 | + | 0.0963328i | ||||
\(573\) | 409.189 | + | 409.189i | 0.714116 | + | 0.714116i | ||||
\(574\) | − | 9.71539i | − | 0.0169258i | ||||||
\(575\) | −607.094 | + | 708.762i | −1.05582 | + | 1.23263i | ||||
\(576\) | −202.736 | −0.351972 | ||||||||
\(577\) | 532.596 | − | 532.596i | 0.923043 | − | 0.923043i | −0.0742001 | − | 0.997243i | \(-0.523640\pi\) |
0.997243 | + | 0.0742001i | \(0.0236403\pi\) | |||||||
\(578\) | 131.526 | + | 131.526i | 0.227554 | + | 0.227554i | ||||
\(579\) | − | 48.8873i | − | 0.0844340i | ||||||
\(580\) | −2.52253 | + | 2.72495i | −0.00434919 | + | 0.00469819i | ||||
\(581\) | −108.666 | −0.187032 | ||||||||
\(582\) | −298.605 | + | 298.605i | −0.513067 | + | 0.513067i | ||||
\(583\) | 1172.26 | + | 1172.26i | 2.01074 | + | 2.01074i | ||||
\(584\) | − | 737.416i | − | 1.26270i | ||||||
\(585\) | 9.91391 | + | 257.008i | 0.0169469 | + | 0.439329i | ||||
\(586\) | −529.349 | −0.903325 | ||||||||
\(587\) | 800.352 | − | 800.352i | 1.36346 | − | 1.36346i | 0.493999 | − | 0.869463i | \(-0.335535\pi\) |
0.869463 | − | 0.493999i | \(-0.164465\pi\) | |||||||
\(588\) | −2.21217 | − | 2.21217i | −0.00376219 | − | 0.00376219i | ||||
\(589\) | 295.013i | 0.500871i | ||||||||
\(590\) | 159.155 | − | 6.13931i | 0.269754 | − | 0.0104056i | ||||
\(591\) | −89.4682 | −0.151384 | ||||||||
\(592\) | 37.6168 | − | 37.6168i | 0.0635419 | − | 0.0635419i | ||||
\(593\) | 254.908 | + | 254.908i | 0.429862 | + | 0.429862i | 0.888581 | − | 0.458719i | \(-0.151692\pi\) |
−0.458719 | + | 0.888581i | \(0.651692\pi\) | |||||||
\(594\) | 177.037i | 0.298042i | ||||||||
\(595\) | −190.518 | − | 176.366i | −0.320199 | − | 0.296414i | ||||
\(596\) | −3.71174 | −0.00622775 | ||||||||
\(597\) | 229.786 | − | 229.786i | 0.384900 | − | 0.384900i | ||||
\(598\) | 875.505 | + | 875.505i | 1.46406 | + | 1.46406i | ||||
\(599\) | 661.029i | 1.10355i | 0.833991 | + | 0.551777i | \(0.186050\pi\) | ||||
−0.833991 | + | 0.551777i | \(0.813950\pi\) | |||||||
\(600\) | 355.604 | − | 27.4753i | 0.592674 | − | 0.0457922i | ||||
\(601\) | −410.580 | −0.683162 | −0.341581 | − | 0.939852i | \(-0.610962\pi\) | ||||
−0.341581 | + | 0.939852i | \(0.610962\pi\) | |||||||
\(602\) | 218.013 | − | 218.013i | 0.362148 | − | 0.362148i | ||||
\(603\) | −81.6072 | − | 81.6072i | −0.135335 | − | 0.135335i | ||||
\(604\) | 3.96258i | 0.00656056i | ||||||||
\(605\) | 642.698 | − | 694.271i | 1.06231 | − | 1.14756i | ||||
\(606\) | −292.602 | −0.482842 | ||||||||
\(607\) | −604.297 | + | 604.297i | −0.995548 | + | 0.995548i | −0.999990 | − | 0.00444263i | \(-0.998586\pi\) |
0.00444263 | + | 0.999990i | \(0.498586\pi\) | |||||||
\(608\) | 53.3579 | + | 53.3579i | 0.0877598 | + | 0.0877598i | ||||
\(609\) | − | 13.1894i | − | 0.0216574i | ||||||
\(610\) | −2.74776 | − | 71.2327i | −0.00450452 | − | 0.116775i | ||||
\(611\) | −1400.27 | −2.29177 | ||||||||
\(612\) | −10.7424 | + | 10.7424i | −0.0175529 | + | 0.0175529i | ||||
\(613\) | −61.4626 | − | 61.4626i | −0.100265 | − | 0.100265i | 0.655195 | − | 0.755460i | \(-0.272587\pi\) |
−0.755460 | + | 0.655195i | \(0.772587\pi\) | |||||||
\(614\) | 335.198i | 0.545926i | ||||||||
\(615\) | 16.4274 | − | 0.633677i | 0.0267112 | − | 0.00103037i | ||||
\(616\) | −383.831 | −0.623103 | ||||||||
\(617\) | −509.151 | + | 509.151i | −0.825204 | + | 0.825204i | −0.986849 | − | 0.161645i | \(-0.948320\pi\) |
0.161645 | + | 0.986849i | \(0.448320\pi\) | |||||||
\(618\) | 123.103 | + | 123.103i | 0.199196 | + | 0.199196i | ||||
\(619\) | − | 735.555i | − | 1.18830i | −0.804356 | − | 0.594148i | \(-0.797489\pi\) | ||
0.804356 | − | 0.594148i | \(-0.202511\pi\) | |||||||
\(620\) | 15.2571 | + | 14.1238i | 0.0246083 | + | 0.0227803i | ||||
\(621\) | −193.967 | −0.312346 | ||||||||
\(622\) | −161.473 | + | 161.473i | −0.259603 | + | 0.259603i | ||||
\(623\) | −54.8798 | − | 54.8798i | −0.0880895 | − | 0.0880895i | ||||
\(624\) | − | 442.550i | − | 0.709214i | ||||||
\(625\) | −617.582 | + | 96.0065i | −0.988131 | + | 0.153610i | ||||
\(626\) | 791.928 | 1.26506 | ||||||||
\(627\) | 394.903 | − | 394.903i | 0.629830 | − | 0.629830i | ||||
\(628\) | 16.3275 | + | 16.3275i | 0.0259992 | + | 0.0259992i | ||||
\(629\) | − | 70.0634i | − | 0.111389i | ||||||
\(630\) | −52.1517 | + | 56.3365i | −0.0827804 | + | 0.0894230i | ||||
\(631\) | 649.002 | 1.02853 | 0.514265 | − | 0.857631i | \(-0.328065\pi\) | ||||
0.514265 | + | 0.857631i | \(0.328065\pi\) | |||||||
\(632\) | −14.4841 | + | 14.4841i | −0.0229179 | + | 0.0229179i | ||||
\(633\) | 90.1914 | + | 90.1914i | 0.142482 | + | 0.142482i | ||||
\(634\) | − | 799.517i | − | 1.26107i | ||||||
\(635\) | −3.32691 | − | 86.2465i | −0.00523922 | − | 0.135821i | ||||
\(636\) | 42.0671 | 0.0661432 | ||||||||
\(637\) | 84.8713 | − | 84.8713i | 0.133236 | − | 0.133236i | ||||
\(638\) | −69.3396 | − | 69.3396i | −0.108683 | − | 0.108683i | ||||
\(639\) | − | 238.795i | − | 0.373702i | ||||||
\(640\) | −570.763 | + | 22.0168i | −0.891818 | + | 0.0344013i | ||||
\(641\) | −103.576 | −0.161585 | −0.0807925 | − | 0.996731i | \(-0.525745\pi\) | ||||
−0.0807925 | + | 0.996731i | \(0.525745\pi\) | |||||||
\(642\) | −308.198 | + | 308.198i | −0.480059 | + | 0.480059i | ||||
\(643\) | 504.926 | + | 504.926i | 0.785266 | + | 0.785266i | 0.980714 | − | 0.195448i | \(-0.0626160\pi\) |
−0.195448 | + | 0.980714i | \(0.562616\pi\) | |||||||
\(644\) | − | 25.4841i | − | 0.0395716i | ||||||
\(645\) | 382.850 | + | 354.410i | 0.593566 | + | 0.549473i | ||||
\(646\) | −694.994 | −1.07584 | ||||||||
\(647\) | 134.888 | − | 134.888i | 0.208482 | − | 0.208482i | −0.595140 | − | 0.803622i | \(-0.702903\pi\) |
0.803622 | + | 0.595140i | \(0.202903\pi\) | |||||||
\(648\) | 52.4187 | + | 52.4187i | 0.0808931 | + | 0.0808931i | ||||
\(649\) | − | 290.039i | − | 0.446901i | ||||||
\(650\) | 63.8779 | + | 826.752i | 0.0982738 | + | 1.27193i | ||||
\(651\) | −73.8478 | −0.113438 | ||||||||
\(652\) | 31.2875 | − | 31.2875i | 0.0479870 | − | 0.0479870i | ||||
\(653\) | −123.054 | − | 123.054i | −0.188444 | − | 0.188444i | 0.606579 | − | 0.795023i | \(-0.292541\pi\) |
−0.795023 | + | 0.606579i | \(0.792541\pi\) | |||||||
\(654\) | − | 484.578i | − | 0.740944i | ||||||
\(655\) | −78.8864 | + | 85.2166i | −0.120437 | + | 0.130102i | ||||
\(656\) | −28.2869 | −0.0431202 | ||||||||
\(657\) | −189.915 | + | 189.915i | −0.289064 | + | 0.289064i | ||||
\(658\) | −295.542 | − | 295.542i | −0.449151 | − | 0.449151i | ||||
\(659\) | − | 811.814i | − | 1.23189i | −0.787790 | − | 0.615944i | \(-0.788775\pi\) | ||
0.787790 | − | 0.615944i | \(-0.211225\pi\) | |||||||
\(660\) | −1.51710 | − | 39.3292i | −0.00229864 | − | 0.0595897i | ||||
\(661\) | 979.510 | 1.48186 | 0.740930 | − | 0.671582i | \(-0.234385\pi\) | ||||
0.740930 | + | 0.671582i | \(0.234385\pi\) | |||||||
\(662\) | −794.329 | + | 794.329i | −1.19989 | + | 1.19989i | ||||
\(663\) | −412.137 | − | 412.137i | −0.621625 | − | 0.621625i | ||||
\(664\) | 338.300i | 0.509488i | ||||||||
\(665\) | 241.996 | − | 9.33486i | 0.363904 | − | 0.0140374i | ||||
\(666\) | −20.7178 | −0.0311078 | ||||||||
\(667\) | 75.9705 | − | 75.9705i | 0.113899 | − | 0.113899i | ||||
\(668\) | −13.2170 | − | 13.2170i | −0.0197860 | − | 0.0197860i | ||||
\(669\) | − | 632.510i | − | 0.945456i | ||||||
\(670\) | −273.050 | − | 252.767i | −0.407537 | − | 0.377264i | ||||
\(671\) | −129.812 | −0.193461 | ||||||||
\(672\) | −13.3566 | + | 13.3566i | −0.0198759 | + | 0.0198759i | ||||
\(673\) | −327.449 | − | 327.449i | −0.486552 | − | 0.486552i | 0.420664 | − | 0.907216i | \(-0.361797\pi\) |
−0.907216 | + | 0.420664i | \(0.861797\pi\) | |||||||
\(674\) | 693.868i | 1.02948i | ||||||||
\(675\) | −98.6589 | − | 84.5069i | −0.146161 | − | 0.125195i | ||||
\(676\) | −32.2555 | −0.0477152 | ||||||||
\(677\) | 463.677 | − | 463.677i | 0.684900 | − | 0.684900i | −0.276200 | − | 0.961100i | \(-0.589075\pi\) |
0.961100 | + | 0.276200i | \(0.0890754\pi\) | |||||||
\(678\) | 96.0929 | + | 96.0929i | 0.141730 | + | 0.141730i | ||||
\(679\) | 333.465i | 0.491112i | ||||||||
\(680\) | −549.067 | + | 593.126i | −0.807451 | + | 0.872244i | ||||
\(681\) | 23.8317 | 0.0349951 | ||||||||
\(682\) | −388.236 | + | 388.236i | −0.569261 | + | 0.569261i | ||||
\(683\) | 667.534 | + | 667.534i | 0.977356 | + | 0.977356i | 0.999749 | − | 0.0223933i | \(-0.00712859\pi\) |
−0.0223933 | + | 0.999749i | \(0.507129\pi\) | |||||||
\(684\) | − | 14.1713i | − | 0.0207182i | ||||||
\(685\) | 4.70405 | + | 121.948i | 0.00686723 | + | 0.178026i | ||||
\(686\) | 35.8259 | 0.0522243 | ||||||||
\(687\) | 132.330 | − | 132.330i | 0.192621 | − | 0.192621i | ||||
\(688\) | −634.756 | − | 634.756i | −0.922610 | − | 0.922610i | ||||
\(689\) | 1613.93i | 2.34242i | ||||||||
\(690\) | −624.890 | + | 24.1048i | −0.905638 | + | 0.0349344i | ||||
\(691\) | −622.518 | −0.900895 | −0.450447 | − | 0.892803i | \(-0.648736\pi\) | ||||
−0.450447 | + | 0.892803i | \(0.648736\pi\) | |||||||
\(692\) | −20.2663 | + | 20.2663i | −0.0292866 | + | 0.0292866i | ||||
\(693\) | 98.8525 | + | 98.8525i | 0.142644 | + | 0.142644i | ||||
\(694\) | 164.846i | 0.237531i | ||||||||
\(695\) | 108.167 | + | 100.132i | 0.155636 | + | 0.144075i | ||||
\(696\) | −41.0614 | −0.0589963 | ||||||||
\(697\) | −26.3430 | + | 26.3430i | −0.0377948 | + | 0.0377948i | ||||
\(698\) | 476.269 | + | 476.269i | 0.682334 | + | 0.682334i | ||||
\(699\) | 6.05816i | 0.00866689i | ||||||||
\(700\) | 11.1028 | − | 12.9622i | 0.0158612 | − | 0.0185174i | ||||
\(701\) | −821.585 | −1.17202 | −0.586009 | − | 0.810304i | \(-0.699302\pi\) | ||||
−0.586009 | + | 0.810304i | \(0.699302\pi\) | |||||||
\(702\) | −121.869 | + | 121.869i | −0.173603 | + | 0.173603i | ||||
\(703\) | 46.2137 | + | 46.2137i | 0.0657378 | + | 0.0657378i | ||||
\(704\) | 1190.26i | 1.69071i | ||||||||
\(705\) | 480.444 | − | 518.997i | 0.681481 | − | 0.736166i | ||||
\(706\) | −309.482 | −0.438359 | ||||||||
\(707\) | −163.381 | + | 163.381i | −0.231090 | + | 0.231090i | ||||
\(708\) | −5.20408 | − | 5.20408i | −0.00735039 | − | 0.00735039i | ||||
\(709\) | − | 1124.01i | − | 1.58535i | −0.609647 | − | 0.792673i | \(-0.708689\pi\) | ||
0.609647 | − | 0.792673i | \(-0.291311\pi\) | |||||||
\(710\) | −29.6757 | − | 769.310i | −0.0417967 | − | 1.08354i | ||||
\(711\) | 7.46052 | 0.0104930 | ||||||||
\(712\) | −170.853 | + | 170.853i | −0.239962 | + | 0.239962i | ||||
\(713\) | −425.363 | − | 425.363i | −0.596581 | − | 0.596581i | ||||
\(714\) | − | 173.971i | − | 0.243658i | ||||||
\(715\) | 1508.89 | − | 58.2045i | 2.11033 | − | 0.0814048i | ||||
\(716\) | 41.8982 | 0.0585170 | ||||||||
\(717\) | −282.884 | + | 282.884i | −0.394538 | + | 0.394538i | ||||
\(718\) | 144.514 | + | 144.514i | 0.201273 | + | 0.201273i | ||||
\(719\) | − | 826.757i | − | 1.14987i | −0.818199 | − | 0.574936i | \(-0.805027\pi\) | ||
0.818199 | − | 0.574936i | \(-0.194973\pi\) | |||||||
\(720\) | 164.027 | + | 151.842i | 0.227815 | + | 0.210892i | ||||
\(721\) | 137.475 | 0.190672 | ||||||||
\(722\) | −35.3734 | + | 35.3734i | −0.0489936 | + | 0.0489936i | ||||
\(723\) | 343.424 | + | 343.424i | 0.474998 | + | 0.474998i | ||||
\(724\) | 66.3722i | 0.0916744i | ||||||||
\(725\) | 71.7400 | − | 5.54290i | 0.0989518 | − | 0.00764538i | ||||
\(726\) | 633.972 | 0.873239 | ||||||||
\(727\) | 829.278 | − | 829.278i | 1.14069 | − | 1.14069i | 0.152360 | − | 0.988325i | \(-0.451313\pi\) |
0.988325 | − | 0.152360i | \(-0.0486874\pi\) | |||||||
\(728\) | −264.223 | − | 264.223i | −0.362944 | − | 0.362944i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −588.236 | + | 635.438i | −0.805803 | + | 0.870463i | ||||
\(731\) | −1182.27 | −1.61733 | ||||||||
\(732\) | −2.32918 | + | 2.32918i | −0.00318194 | + | 0.00318194i | ||||
\(733\) | −306.100 | − | 306.100i | −0.417599 | − | 0.417599i | 0.466776 | − | 0.884375i | \(-0.345415\pi\) |
−0.884375 | + | 0.466776i | \(0.845415\pi\) | |||||||
\(734\) | − | 629.666i | − | 0.857856i | ||||||
\(735\) | 2.33671 | + | 60.5767i | 0.00317920 | + | 0.0824173i | ||||
\(736\) | −153.868 | −0.209059 | ||||||||
\(737\) | −479.115 | + | 479.115i | −0.650088 | + | 0.650088i | ||||
\(738\) | 7.78964 | + | 7.78964i | 0.0105551 | + | 0.0105551i | ||||
\(739\) | − | 1152.24i | − | 1.55919i | −0.626283 | − | 0.779596i | \(-0.715425\pi\) | ||
0.626283 | − | 0.779596i | \(-0.284575\pi\) | |||||||
\(740\) | 4.60251 | − | 0.177539i | 0.00621961 | − | 0.000239918i | ||||
\(741\) | 543.689 | 0.733724 | ||||||||
\(742\) | −340.636 | + | 340.636i | −0.459078 | + | 0.459078i | ||||
\(743\) | −87.8428 | − | 87.8428i | −0.118227 | − | 0.118227i | 0.645518 | − | 0.763745i | \(-0.276642\pi\) |
−0.763745 | + | 0.645518i | \(0.776642\pi\) | |||||||
\(744\) | 229.905i | 0.309012i | ||||||||
\(745\) | 52.7804 | + | 48.8597i | 0.0708462 | + | 0.0655835i | ||||
\(746\) | 578.475 | 0.775436 | ||||||||
\(747\) | 87.1263 | − | 87.1263i | 0.116635 | − | 0.116635i | ||||
\(748\) | 63.0682 | + | 63.0682i | 0.0843158 | + | 0.0843158i | ||||
\(749\) | 344.178i | 0.459517i | ||||||||
\(750\) | −328.345 | − | 259.989i | −0.437793 | − | 0.346653i | ||||
\(751\) | −601.083 | −0.800377 | −0.400189 | − | 0.916433i | \(-0.631055\pi\) | ||||
−0.400189 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(752\) | −860.485 | + | 860.485i | −1.14426 | + | 1.14426i | ||||
\(753\) | −65.4916 | − | 65.4916i | −0.0869743 | − | 0.0869743i | ||||
\(754\) | − | 95.4645i | − | 0.126611i | ||||||
\(755\) | 52.1616 | − | 56.3472i | 0.0690882 | − | 0.0746321i | ||||
\(756\) | 3.54736 | 0.00469228 | ||||||||
\(757\) | 650.454 | − | 650.454i | 0.859252 | − | 0.859252i | −0.131998 | − | 0.991250i | \(-0.542139\pi\) |
0.991250 | + | 0.131998i | \(0.0421393\pi\) | |||||||
\(758\) | −180.938 | − | 180.938i | −0.238704 | − | 0.238704i | ||||
\(759\) | 1138.78i | 1.50037i | ||||||||
\(760\) | −29.0615 | − | 753.388i | −0.0382388 | − | 0.991300i | ||||
\(761\) | 344.833 | 0.453131 | 0.226566 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226566 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(762\) | 40.8969 | − | 40.8969i | 0.0536704 | − | 0.0536704i | ||||
\(763\) | −270.574 | − | 270.574i | −0.354619 | − | 0.354619i | ||||
\(764\) | − | 86.2090i | − | 0.112839i | ||||||
\(765\) | 294.162 | − | 11.3471i | 0.384526 | − | 0.0148328i | ||||
\(766\) | −409.087 | −0.534056 | ||||||||
\(767\) | 199.658 | − | 199.658i | 0.260310 | − | 0.260310i | ||||
\(768\) | 60.4187 | + | 60.4187i | 0.0786702 | + | 0.0786702i | ||||
\(769\) | − | 953.105i | − | 1.23941i | −0.784836 | − | 0.619704i | \(-0.787253\pi\) | ||
0.784836 | − | 0.619704i | \(-0.212747\pi\) | |||||||
\(770\) | 330.751 | + | 306.182i | 0.429547 | + | 0.397639i | ||||
\(771\) | −193.355 | −0.250785 | ||||||||
\(772\) | −5.14986 | + | 5.14986i | −0.00667080 | + | 0.00667080i | ||||
\(773\) | −716.434 | − | 716.434i | −0.926823 | − | 0.926823i | 0.0706765 | − | 0.997499i | \(-0.477484\pi\) |
−0.997499 | + | 0.0706765i | \(0.977484\pi\) | |||||||
\(774\) | 349.598i | 0.451677i | ||||||||
\(775\) | −31.0350 | − | 401.676i | −0.0400451 | − | 0.518291i | ||||
\(776\) | 1038.15 | 1.33782 | ||||||||
\(777\) | −11.5682 | + | 11.5682i | −0.0148883 | + | 0.0148883i | ||||
\(778\) | −395.417 | − | 395.417i | −0.508248 | − | 0.508248i | ||||
\(779\) | − | 34.7515i | − | 0.0446104i | ||||||
\(780\) | 26.0292 | − | 28.1179i | 0.0333708 | − | 0.0360486i | ||||
\(781\) | −1401.96 | −1.79509 | ||||||||
\(782\) | 1002.07 | − | 1002.07i | 1.28142 | − | 1.28142i | ||||
\(783\) | 10.5750 | + | 10.5750i | 0.0135058 | + | 0.0135058i | ||||
\(784\) | − | 104.309i | − | 0.133047i | ||||||
\(785\) | −17.2467 | − | 447.103i | −0.0219703 | − | 0.569557i | ||||
\(786\) | −77.8153 | −0.0990017 | ||||||||
\(787\) | 475.797 | − | 475.797i | 0.604570 | − | 0.604570i | −0.336952 | − | 0.941522i | \(-0.609396\pi\) |
0.941522 | + | 0.336952i | \(0.109396\pi\) | |||||||
\(788\) | 9.42471 | + | 9.42471i | 0.0119603 | + | 0.0119603i | ||||
\(789\) | 793.300i | 1.00545i | ||||||||
\(790\) | 24.0350 | − | 0.927137i | 0.0304241 | − | 0.00117359i | ||||
\(791\) | 107.311 | 0.135665 | ||||||||
\(792\) | 307.750 | − | 307.750i | 0.388573 | − | 0.388573i | ||||
\(793\) | −89.3604 | − | 89.3604i | −0.112687 | − | 0.112687i | ||||
\(794\) | − | 1375.75i | − | 1.73268i | ||||||
\(795\) | −598.187 | − | 553.752i | −0.752437 | − | 0.696543i | ||||
\(796\) | −48.4119 | −0.0608189 | ||||||||
\(797\) | −523.540 | + | 523.540i | −0.656889 | + | 0.656889i | −0.954643 | − | 0.297754i | \(-0.903762\pi\) |
0.297754 | + | 0.954643i | \(0.403762\pi\) | |||||||
\(798\) | 114.751 | + | 114.751i | 0.143799 | + | 0.143799i | ||||
\(799\) | 1602.70i | 2.00589i | ||||||||
\(800\) | −78.2629 | − | 67.0365i | −0.0978286 | − | 0.0837957i | ||||
\(801\) | 88.0034 | 0.109867 | ||||||||
\(802\) | −555.222 | + | 555.222i | −0.692297 | + | 0.692297i | ||||
\(803\) | 1114.99 | + | 1114.99i | 1.38853 | + | 1.38853i | ||||
\(804\) | 17.1932i | 0.0213846i | ||||||||
\(805\) | −335.462 | + | 362.381i | −0.416723 | + | 0.450162i | ||||
\(806\) | −534.510 | −0.663164 | ||||||||
\(807\) | −145.808 | + | 145.808i | −0.180680 | + | 0.180680i | ||||
\(808\) | 508.640 | + | 508.640i | 0.629505 | + | 0.629505i | ||||
\(809\) | 801.958i | 0.991295i | 0.868524 | + | 0.495648i | \(0.165069\pi\) | ||||
−0.868524 | + | 0.495648i | \(0.834931\pi\) | |||||||
\(810\) | −3.35536 | − | 86.9841i | −0.00414241 | − | 0.107388i | ||||
\(811\) | 56.4562 | 0.0696130 | 0.0348065 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348065 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(812\) | −1.38939 | + | 1.38939i | −0.00171107 | + | 0.00171107i | ||||
\(813\) | −465.616 | − | 465.616i | −0.572714 | − | 0.572714i | ||||
\(814\) | 121.634i | 0.149428i | ||||||||
\(815\) | −856.758 | + | 33.0489i | −1.05124 | + | 0.0405508i | ||||
\(816\) | −506.527 | −0.620744 | ||||||||
\(817\) | 779.822 | − | 779.822i | 0.954495 | − | 0.954495i | ||||
\(818\) | 691.306 | + | 691.306i | 0.845118 | + | 0.845118i | ||||
\(819\) | 136.097i | 0.166174i | ||||||||
\(820\) | −1.79724 | − | 1.66373i | −0.00219175 | − | 0.00202894i | ||||
\(821\) | 983.386 | 1.19779 | 0.598896 | − | 0.800827i | \(-0.295606\pi\) | ||||
0.598896 | + | 0.800827i | \(0.295606\pi\) | |||||||
\(822\) | −57.8258 | + | 57.8258i | −0.0703477 | + | 0.0703477i | ||||
\(823\) | 8.06828 | + | 8.06828i | 0.00980350 | + | 0.00980350i | 0.711992 | − | 0.702188i | \(-0.247793\pi\) |
−0.702188 | + | 0.711992i | \(0.747793\pi\) | |||||||
\(824\) | − | 427.989i | − | 0.519405i | ||||||
\(825\) | −496.139 | + | 579.226i | −0.601381 | + | 0.702092i | ||||
\(826\) | 84.2796 | 0.102033 | ||||||||
\(827\) | 917.498 | − | 917.498i | 1.10943 | − | 1.10943i | 0.116204 | − | 0.993225i | \(-0.462927\pi\) |
0.993225 | − | 0.116204i | \(-0.0370725\pi\) | |||||||
\(828\) | 20.4328 | + | 20.4328i | 0.0246773 | + | 0.0246773i | ||||
\(829\) | 589.450i | 0.711037i | 0.934669 | + | 0.355518i | \(0.115696\pi\) | ||||
−0.934669 | + | 0.355518i | \(0.884304\pi\) | |||||||
\(830\) | 269.861 | − | 291.516i | 0.325134 | − | 0.351224i | ||||
\(831\) | 917.223 | 1.10376 | ||||||||
\(832\) | −819.356 | + | 819.356i | −0.984803 | + | 0.984803i | ||||
\(833\) | −97.1407 | − | 97.1407i | −0.116616 | − | 0.116616i | ||||
\(834\) | 98.7725i | 0.118432i | ||||||||
\(835\) | 13.9611 | + | 361.927i | 0.0167199 | + | 0.433446i | ||||
\(836\) | −83.1994 | −0.0995208 | ||||||||
\(837\) | 59.2100 | − | 59.2100i | 0.0707407 | − | 0.0707407i | ||||
\(838\) | −757.224 | − | 757.224i | −0.903609 | − | 0.903609i | ||||
\(839\) | − | 230.274i | − | 0.274463i | −0.990539 | − | 0.137231i | \(-0.956180\pi\) | ||
0.990539 | − | 0.137231i | \(-0.0438204\pi\) | |||||||
\(840\) | 188.589 | − | 7.27469i | 0.224510 | − | 0.00866035i | ||||
\(841\) | 832.716 | 0.990150 | ||||||||
\(842\) | 438.316 | − | 438.316i | 0.520566 | − | 0.520566i | ||||
\(843\) | 368.457 | + | 368.457i | 0.437078 | + | 0.437078i | ||||
\(844\) | − | 19.0018i | − | 0.0225140i | ||||||
\(845\) | 458.668 | + | 424.597i | 0.542803 | + | 0.502481i | ||||
\(846\) | 473.921 | 0.560190 | ||||||||
\(847\) | 353.992 | − | 353.992i | 0.417936 | − | 0.417936i | ||||
\(848\) | 991.780 | + | 991.780i | 1.16955 | + | 1.16955i | ||||
\(849\) | 335.987i | 0.395744i | ||||||||
\(850\) | 946.272 | − | 73.1125i | 1.11326 | − | 0.0860147i | ||||
\(851\) | −133.266 | −0.156599 | ||||||||
\(852\) | −25.1550 | + | 25.1550i | −0.0295247 | + | 0.0295247i | ||||
\(853\) | −843.744 | − | 843.744i | −0.989148 | − | 0.989148i | 0.0107933 | − | 0.999942i | \(-0.496564\pi\) |
−0.999942 | + | 0.0107933i | \(0.996564\pi\) | |||||||
\(854\) | − | 37.7209i | − | 0.0441696i | ||||||
\(855\) | −186.544 | + | 201.513i | −0.218180 | + | 0.235688i | ||||
\(856\) | 1071.50 | 1.25176 | ||||||||
\(857\) | 437.772 | − | 437.772i | 0.510819 | − | 0.510819i | −0.403959 | − | 0.914777i | \(-0.632366\pi\) |
0.914777 | + | 0.403959i | \(0.132366\pi\) | |||||||
\(858\) | 715.494 | + | 715.494i | 0.833909 | + | 0.833909i | ||||
\(859\) | 1402.95i | 1.63324i | 0.577175 | + | 0.816621i | \(0.304155\pi\) | ||||
−0.577175 | + | 0.816621i | \(0.695845\pi\) | |||||||
\(860\) | −2.99584 | − | 77.6640i | −0.00348354 | − | 0.0903070i | ||||
\(861\) | 8.69903 | 0.0101034 | ||||||||
\(862\) | −303.482 | + | 303.482i | −0.352068 | + | 0.352068i | ||||
\(863\) | 1049.60 | + | 1049.60i | 1.21622 | + | 1.21622i | 0.968944 | + | 0.247281i | \(0.0795369\pi\) |
0.247281 | + | 0.968944i | \(0.420463\pi\) | |||||||
\(864\) | − | 21.4182i | − | 0.0247896i | ||||||
\(865\) | 554.961 | − | 21.4073i | 0.641574 | − | 0.0247483i | ||||
\(866\) | 443.543 | 0.512174 | ||||||||
\(867\) | −117.767 | + | 117.767i | −0.135832 | + | 0.135832i | ||||
\(868\) | 7.77924 | + | 7.77924i | 0.00896225 | + | 0.00896225i | ||||
\(869\) | − | 43.8006i | − | 0.0504035i | ||||||
\(870\) | 35.3830 | + | 32.7546i | 0.0406701 | + | 0.0376490i | ||||
\(871\) | −659.629 | −0.757324 | ||||||||
\(872\) | −842.358 | + | 842.358i | −0.966007 | + | 0.966007i | ||||
\(873\) | −267.367 | − | 267.367i | −0.306262 | − | 0.306262i | ||||
\(874\) | 1321.93i | 1.51251i | ||||||||
\(875\) | −328.509 | + | 38.1676i | −0.375439 | + | 0.0436201i | ||||
\(876\) | 40.0119 | 0.0456757 | ||||||||
\(877\) | −236.787 | + | 236.787i | −0.269996 | + | 0.269996i | −0.829099 | − | 0.559102i | \(-0.811146\pi\) |
0.559102 | + | 0.829099i | \(0.311146\pi\) | |||||||
\(878\) | −829.599 | − | 829.599i | −0.944874 | − | 0.944874i | ||||
\(879\) | − | 473.972i | − | 0.539217i | ||||||
\(880\) | 891.465 | − | 963.000i | 1.01303 | − | 1.09432i | ||||
\(881\) | 311.627 | 0.353720 | 0.176860 | − | 0.984236i | \(-0.443406\pi\) | ||||
0.176860 | + | 0.984236i | \(0.443406\pi\) | |||||||
\(882\) | −28.7246 | + | 28.7246i | −0.0325676 | + | 0.0325676i | ||||
\(883\) | −54.4472 | − | 54.4472i | −0.0616616 | − | 0.0616616i | 0.675604 | − | 0.737265i | \(-0.263883\pi\) |
−0.737265 | + | 0.675604i | \(0.763883\pi\) | |||||||
\(884\) | 86.8302i | 0.0982242i | ||||||||
\(885\) | 5.49706 | + | 142.505i | 0.00621136 | + | 0.161023i | ||||
\(886\) | 26.6834 | 0.0301167 | ||||||||
\(887\) | −485.748 | + | 485.748i | −0.547631 | + | 0.547631i | −0.925755 | − | 0.378124i | \(-0.876569\pi\) |
0.378124 | + | 0.925755i | \(0.376569\pi\) | |||||||
\(888\) | 36.0145 | + | 36.0145i | 0.0405569 | + | 0.0405569i | ||||
\(889\) | − | 45.6713i | − | 0.0513738i | ||||||
\(890\) | 283.515 | − | 10.9364i | 0.318556 | − | 0.0122881i | ||||
\(891\) | −158.517 | −0.177909 | ||||||||
\(892\) | −66.6295 | + | 66.6295i | −0.0746968 | + | 0.0746968i | ||||
\(893\) | −1057.14 | − | 1057.14i | −1.18381 | − | 1.18381i | ||||
\(894\) | 48.1963i | 0.0539108i | ||||||||
\(895\) | −595.786 | − | 551.529i | −0.665682 | − | 0.616233i | ||||
\(896\) | −302.244 | −0.337326 | ||||||||
\(897\) | −783.916 | + | 783.916i | −0.873931 | + | 0.873931i | ||||
\(898\) | −614.103 | − | 614.103i | −0.683856 | − | 0.683856i | ||||
\(899\) | 46.3812i | 0.0515920i | ||||||||
\(900\) | 1.49080 | + | 19.2949i | 0.00165644 | + | 0.0214388i | ||||
\(901\) | 1847.25 | 2.05022 | ||||||||
\(902\) | 45.7329 | − | 45.7329i | 0.0507017 | − | 0.0507017i | ||||
\(903\) | 195.206 | + | 195.206i | 0.216175 | + | 0.216175i | ||||
\(904\) | − | 334.083i | − | 0.369561i | ||||||
\(905\) | 873.694 | − | 943.803i | 0.965408 | − | 1.04288i | ||||
\(906\) | 51.4533 | 0.0567918 | ||||||||
\(907\) | 355.846 | − | 355.846i | 0.392334 | − | 0.392334i | −0.483185 | − | 0.875518i | \(-0.660520\pi\) |
0.875518 | + | 0.483185i | \(0.160520\pi\) | |||||||
\(908\) | −2.51046 | − | 2.51046i | −0.00276482 | − | 0.00276482i | ||||
\(909\) | − | 261.992i | − | 0.288220i | ||||||
\(910\) | 16.9131 | + | 438.454i | 0.0185858 | + | 0.481817i | ||||
\(911\) | 440.542 | 0.483581 | 0.241790 | − | 0.970329i | \(-0.422265\pi\) | ||||
0.241790 | + | 0.970329i | \(0.422265\pi\) | |||||||
\(912\) | 334.104 | − | 334.104i | 0.366342 | − | 0.366342i | ||||
\(913\) | −511.517 | − | 511.517i | −0.560260 | − | 0.560260i | ||||
\(914\) | 1009.08i | 1.10403i | ||||||||
\(915\) | 63.7808 | − | 2.46031i | 0.0697058 | − | 0.00268886i | ||||
\(916\) | −27.8797 | −0.0304364 | ||||||||
\(917\) | −43.4499 | + | 43.4499i | −0.0473826 | + | 0.0473826i | ||||
\(918\) | 139.487 | + | 139.487i | 0.151947 | + | 0.151947i | ||||
\(919\) | 576.067i | 0.626841i | 0.949614 | + | 0.313420i | \(0.101475\pi\) | ||||
−0.949614 | + | 0.313420i | \(0.898525\pi\) | |||||||
\(920\) | 1128.17 | + | 1044.37i | 1.22627 | + | 1.13518i | ||||
\(921\) | −300.132 | −0.325876 | ||||||||
\(922\) | 694.801 | − | 694.801i | 0.753580 | − | 0.753580i | ||||
\(923\) | −965.089 | − | 965.089i | −1.04560 | − | 1.04560i | ||||
\(924\) | − | 20.8265i | − | 0.0225395i | ||||||
\(925\) | −67.7840 | − | 58.0608i | −0.0732800 | − | 0.0627684i | ||||
\(926\) | −698.769 | −0.754611 | ||||||||
\(927\) | −110.225 | + | 110.225i | −0.118905 | + | 0.118905i | ||||
\(928\) | 8.38881 | + | 8.38881i | 0.00903967 | + | 0.00903967i | ||||
\(929\) | − | 513.292i | − | 0.552521i | −0.961083 | − | 0.276260i | \(-0.910905\pi\) | ||
0.961083 | − | 0.276260i | \(-0.0890952\pi\) | |||||||
\(930\) | 183.395 | − | 198.111i | 0.197199 | − | 0.213023i | ||||
\(931\) | 128.148 | 0.137645 | ||||||||
\(932\) | 0.638175 | − | 0.638175i | 0.000684737 | − | 0.000684737i | ||||
\(933\) | −144.581 | − | 144.581i | −0.154964 | − | 0.154964i | ||||
\(934\) | 1117.11i | 1.19605i | ||||||||
\(935\) | −66.6188 | − | 1727.02i | −0.0712501 | − | 1.84708i | ||||
\(936\) | 423.699 | 0.452670 | ||||||||
\(937\) | −224.557 | + | 224.557i | −0.239655 | + | 0.239655i | −0.816707 | − | 0.577052i | \(-0.804203\pi\) |
0.577052 | + | 0.816707i | \(0.304203\pi\) | |||||||
\(938\) | −139.221 | − | 139.221i | −0.148424 | − | 0.148424i | ||||
\(939\) | 709.082i | 0.755146i | ||||||||
\(940\) | −105.283 | + | 4.06121i | −0.112003 | + | 0.00432044i | ||||
\(941\) | 595.500 | 0.632838 | 0.316419 | − | 0.948620i | \(-0.397519\pi\) | ||||
0.316419 | + | 0.948620i | \(0.397519\pi\) | |||||||
\(942\) | 212.010 | − | 212.010i | 0.225063 | − | 0.225063i | ||||
\(943\) | 50.1063 | + | 50.1063i | 0.0531350 | + | 0.0531350i | ||||
\(944\) | − | 245.385i | − | 0.259941i | ||||||
\(945\) | −50.4430 | − | 46.6959i | −0.0533788 | − | 0.0494136i | ||||
\(946\) | 2052.49 | 2.16965 | ||||||||
\(947\) | −890.942 | + | 890.942i | −0.940805 | + | 0.940805i | −0.998343 | − | 0.0575384i | \(-0.981675\pi\) |
0.0575384 | + | 0.998343i | \(0.481675\pi\) | |||||||
\(948\) | −0.785902 | − | 0.785902i | −0.000829010 | − | 0.000829010i | ||||
\(949\) | 1535.08i | 1.61758i | ||||||||
\(950\) | −575.934 | + | 672.384i | −0.606246 | + | 0.707772i | ||||
\(951\) | 715.877 | 0.752762 | ||||||||
\(952\) | −302.421 | + | 302.421i | −0.317669 | + | 0.317669i | ||||
\(953\) | 270.103 | + | 270.103i | 0.283424 | + | 0.283424i | 0.834473 | − | 0.551049i | \(-0.185772\pi\) |
−0.551049 | + | 0.834473i | \(0.685772\pi\) | |||||||
\(954\) | − | 546.233i | − | 0.572571i | ||||||
\(955\) | −1134.82 | + | 1225.88i | −1.18829 | + | 1.28364i | ||||
\(956\) | 59.5988 | 0.0623418 | ||||||||
\(957\) | 62.0858 | − | 62.0858i | 0.0648754 | − | 0.0648754i | ||||
\(958\) | −909.258 | − | 909.258i | −0.949121 | − | 0.949121i | ||||
\(959\) | 64.5766i | 0.0673374i | ||||||||
\(960\) | −22.5588 | − | 584.814i | −0.0234988 | − | 0.609181i | ||||
\(961\) | −701.309 | −0.729770 | ||||||||
\(962\) | −83.7308 | + | 83.7308i | −0.0870383 | + | 0.0870383i | ||||
\(963\) | −275.956 | − | 275.956i | −0.286559 | − | 0.286559i | ||||
\(964\) | − | 72.3535i | − | 0.0750555i | ||||||
\(965\) | 141.021 | − | 5.43978i | 0.146135 | − | 0.00563708i | ||||
\(966\) | −330.907 | −0.342554 | ||||||||
\(967\) | 1139.02 | − | 1139.02i | 1.17789 | − | 1.17789i | 0.197611 | − | 0.980281i | \(-0.436682\pi\) |
0.980281 | − | 0.197611i | \(-0.0633182\pi\) | |||||||
\(968\) | −1102.06 | − | 1102.06i | −1.13849 | − | 1.13849i | ||||
\(969\) | − | 622.288i | − | 0.642196i | ||||||
\(970\) | −894.584 | − | 828.131i | −0.922251 | − | 0.853743i | ||||
\(971\) | −736.722 | −0.758725 | −0.379363 | − | 0.925248i | \(-0.623857\pi\) | ||||
−0.379363 | + | 0.925248i | \(0.623857\pi\) | |||||||
\(972\) | −2.84422 | + | 2.84422i | −0.00292615 | + | 0.00292615i | ||||
\(973\) | 55.1518 | + | 55.1518i | 0.0566822 | + | 0.0566822i | ||||
\(974\) | − | 915.673i | − | 0.940116i | ||||||
\(975\) | −740.263 | + | 57.1955i | −0.759244 | + | 0.0586620i | ||||
\(976\) | −109.826 | −0.112527 | ||||||||
\(977\) | −993.980 | + | 993.980i | −1.01738 | + | 1.01738i | −0.0175332 | + | 0.999846i | \(0.505581\pi\) |
−0.999846 | + | 0.0175332i | \(0.994419\pi\) | |||||||
\(978\) | −406.263 | − | 406.263i | −0.415401 | − | 0.415401i | ||||
\(979\) | − | 516.667i | − | 0.527750i | ||||||
\(980\) | 6.13509 | − | 6.62739i | 0.00626029 | − | 0.00676264i | ||||
\(981\) | 433.884 | 0.442288 | ||||||||
\(982\) | 427.115 | − | 427.115i | 0.434944 | − | 0.434944i | ||||
\(983\) | −546.928 | − | 546.928i | −0.556387 | − | 0.556387i | 0.371890 | − | 0.928277i | \(-0.378710\pi\) |
−0.928277 | + | 0.371890i | \(0.878710\pi\) | |||||||
\(984\) | − | 27.0820i | − | 0.0275224i | ||||||
\(985\) | −9.95530 | − | 258.081i | −0.0101069 | − | 0.262011i | ||||
\(986\) | −109.265 | −0.110817 | ||||||||
\(987\) | 264.624 | − | 264.624i | 0.268109 | − | 0.268109i | ||||
\(988\) | −57.2730 | − | 57.2730i | −0.0579686 | − | 0.0579686i | ||||
\(989\) | 2248.77i | 2.27378i | ||||||||
\(990\) | −510.682 | + | 19.6993i | −0.515841 | + | 0.0198982i | ||||
\(991\) | −1132.40 | −1.14269 | −0.571343 | − | 0.820711i | \(-0.693577\pi\) | ||||
−0.571343 | + | 0.820711i | \(0.693577\pi\) | |||||||
\(992\) | 46.9694 | − | 46.9694i | 0.0473481 | − | 0.0473481i | ||||
\(993\) | −711.231 | − | 711.231i | −0.716245 | − | 0.716245i | ||||
\(994\) | − | 407.384i | − | 0.409843i | ||||||
\(995\) | 688.409 | + | 637.272i | 0.691869 | + | 0.640474i | ||||
\(996\) | −18.3560 | −0.0184297 | ||||||||
\(997\) | −44.1992 | + | 44.1992i | −0.0443322 | + | 0.0443322i | −0.728925 | − | 0.684593i | \(-0.759980\pi\) |
0.684593 | + | 0.728925i | \(0.259980\pi\) | |||||||
\(998\) | 122.239 | + | 122.239i | 0.122484 | + | 0.122484i | ||||
\(999\) | − | 18.5505i | − | 0.0185690i |
(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 | 105.3.l.a.43.3 | yes | 24 | |
3.2 | odd | 2 | 315.3.o.b.253.10 | 24 | |||
5.2 | odd | 4 | inner | 105.3.l.a.22.3 | ✓ | 24 | |
5.3 | odd | 4 | 525.3.l.e.232.10 | 24 | |||
5.4 | even | 2 | 525.3.l.e.43.10 | 24 | |||
15.2 | even | 4 | 315.3.o.b.127.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.3 | ✓ | 24 | 5.2 | odd | 4 | inner | |
105.3.l.a.43.3 | yes | 24 | 1.1 | even | 1 | trivial | |
315.3.o.b.127.10 | 24 | 15.2 | even | 4 | |||
315.3.o.b.253.10 | 24 | 3.2 | odd | 2 | |||
525.3.l.e.43.10 | 24 | 5.4 | even | 2 | |||
525.3.l.e.232.10 | 24 | 5.3 | odd | 4 |