Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (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: | \(6.26704608029\) |
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 | 47.4 | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.3.f.b.93.4 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.36040 | + | 1.36040i | −0.453466 | + | 0.453466i | −0.896503 | − | 0.443038i | \(-0.853901\pi\) |
0.443038 | + | 0.896503i | \(0.353901\pi\) | |||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.17264 | − | 3.86450i | −0.634528 | − | 0.772900i | ||||
\(6\) | −2.72079 | −0.453466 | ||||||||
\(7\) | 7.21891 | + | 7.21891i | 1.03127 | + | 1.03127i | 0.999495 | + | 0.0317775i | \(0.0101168\pi\) |
0.0317775 | + | 0.999495i | \(0.489883\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 5.29864i | 0.588738i | ||||||||
\(10\) | 0.691863 | − | 7.03714i | 0.0691863 | − | 0.703714i | ||||
\(11\) | −14.8137 | −1.34670 | −0.673352 | − | 0.739322i | \(-0.735146\pi\) | ||||
−0.673352 | + | 0.739322i | \(0.735146\pi\) | |||||||
\(12\) | −2.72079 | − | 2.72079i | −0.226733 | − | 0.226733i | ||||
\(13\) | −4.91350 | + | 4.91350i | −0.377962 | + | 0.377962i | −0.870366 | − | 0.492405i | \(-0.836118\pi\) |
0.492405 | + | 0.870366i | \(0.336118\pi\) | |||||||
\(14\) | 14.4378i | 1.03127i | ||||||||
\(15\) | 9.57330 | + | 0.941208i | 0.638220 | + | 0.0627472i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −17.8271 | − | 17.8271i | −1.04865 | − | 1.04865i | −0.998754 | − | 0.0499002i | \(-0.984110\pi\) |
−0.0499002 | − | 0.998754i | \(-0.515890\pi\) | |||||||
\(18\) | −5.29864 | + | 5.29864i | −0.294369 | + | 0.294369i | ||||
\(19\) | 29.6011i | 1.55795i | 0.627054 | + | 0.778976i | \(0.284261\pi\) | ||||
−0.627054 | + | 0.778976i | \(0.715739\pi\) | |||||||
\(20\) | 7.72900 | − | 6.34528i | 0.386450 | − | 0.317264i | ||||
\(21\) | −19.6412 | −0.935293 | ||||||||
\(22\) | −14.8137 | − | 14.8137i | −0.673352 | − | 0.673352i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | − | 5.44159i | − | 0.226733i | ||||||
\(25\) | −4.86874 | + | 24.5213i | −0.194749 | + | 0.980853i | ||||
\(26\) | −9.82700 | −0.377962 | ||||||||
\(27\) | −19.4518 | − | 19.4518i | −0.720438 | − | 0.720438i | ||||
\(28\) | −14.4378 | + | 14.4378i | −0.515636 | + | 0.515636i | ||||
\(29\) | − | 11.0158i | − | 0.379856i | −0.981798 | − | 0.189928i | \(-0.939175\pi\) | ||
0.981798 | − | 0.189928i | \(-0.0608255\pi\) | |||||||
\(30\) | 8.63209 | + | 10.5145i | 0.287736 | + | 0.350484i | ||||
\(31\) | 42.3661 | 1.36665 | 0.683325 | − | 0.730115i | \(-0.260533\pi\) | ||||
0.683325 | + | 0.730115i | \(0.260533\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 20.1526 | − | 20.1526i | 0.610684 | − | 0.610684i | ||||
\(34\) | − | 35.6542i | − | 1.04865i | ||||||
\(35\) | 4.99449 | − | 50.8005i | 0.142700 | − | 1.45144i | ||||
\(36\) | −10.5973 | −0.294369 | ||||||||
\(37\) | 14.7295 | + | 14.7295i | 0.398095 | + | 0.398095i | 0.877561 | − | 0.479466i | \(-0.159169\pi\) |
−0.479466 | + | 0.877561i | \(0.659169\pi\) | |||||||
\(38\) | −29.6011 | + | 29.6011i | −0.778976 | + | 0.778976i | ||||
\(39\) | − | 13.3686i | − | 0.342785i | ||||||
\(40\) | 14.0743 | + | 1.38373i | 0.351857 | + | 0.0345931i | ||||
\(41\) | 23.9580 | 0.584341 | 0.292171 | − | 0.956366i | \(-0.405622\pi\) | ||||
0.292171 | + | 0.956366i | \(0.405622\pi\) | |||||||
\(42\) | −19.6412 | − | 19.6412i | −0.467646 | − | 0.467646i | ||||
\(43\) | 0.419945 | − | 0.419945i | 0.00976615 | − | 0.00976615i | −0.702207 | − | 0.711973i | \(-0.747802\pi\) |
0.711973 | + | 0.702207i | \(0.247802\pi\) | |||||||
\(44\) | − | 29.6275i | − | 0.673352i | ||||||
\(45\) | 20.4766 | − | 16.8107i | 0.455036 | − | 0.373571i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 53.0162 | + | 53.0162i | 1.12800 | + | 1.12800i | 0.990502 | + | 0.137502i | \(0.0439073\pi\) |
0.137502 | + | 0.990502i | \(0.456093\pi\) | |||||||
\(48\) | 5.44159 | − | 5.44159i | 0.113366 | − | 0.113366i | ||||
\(49\) | 55.2252i | 1.12705i | ||||||||
\(50\) | −29.3901 | + | 19.6526i | −0.587801 | + | 0.393052i | ||||
\(51\) | 48.5039 | 0.951057 | ||||||||
\(52\) | −9.82700 | − | 9.82700i | −0.188981 | − | 0.188981i | ||||
\(53\) | −58.3755 | + | 58.3755i | −1.10142 | + | 1.10142i | −0.107186 | + | 0.994239i | \(0.534184\pi\) |
−0.994239 | + | 0.107186i | \(0.965816\pi\) | |||||||
\(54\) | − | 38.9036i | − | 0.720438i | ||||||
\(55\) | 46.9987 | + | 57.2477i | 0.854521 | + | 1.04087i | ||||
\(56\) | −28.8756 | −0.515636 | ||||||||
\(57\) | −40.2692 | − | 40.2692i | −0.706477 | − | 0.706477i | ||||
\(58\) | 11.0158 | − | 11.0158i | 0.189928 | − | 0.189928i | ||||
\(59\) | 13.7747i | 0.233469i | 0.993163 | + | 0.116735i | \(0.0372427\pi\) | ||||
−0.993163 | + | 0.116735i | \(0.962757\pi\) | |||||||
\(60\) | −1.88242 | + | 19.1466i | −0.0313736 | + | 0.319110i | ||||
\(61\) | 39.0198 | 0.639670 | 0.319835 | − | 0.947473i | \(-0.396373\pi\) | ||||
0.319835 | + | 0.947473i | \(0.396373\pi\) | |||||||
\(62\) | 42.3661 | + | 42.3661i | 0.683325 | + | 0.683325i | ||||
\(63\) | −38.2504 | + | 38.2504i | −0.607149 | + | 0.607149i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 34.5770 | + | 3.39947i | 0.531954 | + | 0.0522995i | ||||
\(66\) | 40.3051 | 0.610684 | ||||||||
\(67\) | −16.9106 | − | 16.9106i | −0.252397 | − | 0.252397i | 0.569556 | − | 0.821953i | \(-0.307115\pi\) |
−0.821953 | + | 0.569556i | \(0.807115\pi\) | |||||||
\(68\) | 35.6542 | − | 35.6542i | 0.524327 | − | 0.524327i | ||||
\(69\) | − | 9.22666i | − | 0.133720i | ||||||
\(70\) | 55.7949 | − | 45.8060i | 0.797071 | − | 0.654371i | ||||
\(71\) | 103.112 | 1.45229 | 0.726143 | − | 0.687544i | \(-0.241311\pi\) | ||||
0.726143 | + | 0.687544i | \(0.241311\pi\) | |||||||
\(72\) | −10.5973 | − | 10.5973i | −0.147185 | − | 0.147185i | ||||
\(73\) | 41.5993 | − | 41.5993i | 0.569853 | − | 0.569853i | −0.362234 | − | 0.932087i | \(-0.617986\pi\) |
0.932087 | + | 0.362234i | \(0.117986\pi\) | |||||||
\(74\) | 29.4590i | 0.398095i | ||||||||
\(75\) | −26.7353 | − | 39.9821i | −0.356471 | − | 0.533095i | ||||
\(76\) | −59.2022 | −0.778976 | ||||||||
\(77\) | −106.939 | − | 106.939i | −1.38882 | − | 1.38882i | ||||
\(78\) | 13.3686 | − | 13.3686i | 0.171393 | − | 0.171393i | ||||
\(79\) | − | 155.484i | − | 1.96815i | −0.177757 | − | 0.984074i | \(-0.556884\pi\) | ||
0.177757 | − | 0.984074i | \(-0.443116\pi\) | |||||||
\(80\) | 12.6906 | + | 15.4580i | 0.158632 | + | 0.193225i | ||||
\(81\) | 5.23660 | 0.0646494 | ||||||||
\(82\) | 23.9580 | + | 23.9580i | 0.292171 | + | 0.292171i | ||||
\(83\) | 12.7160 | − | 12.7160i | 0.153205 | − | 0.153205i | −0.626343 | − | 0.779548i | \(-0.715449\pi\) |
0.779548 | + | 0.626343i | \(0.215449\pi\) | |||||||
\(84\) | − | 39.2823i | − | 0.467646i | ||||||
\(85\) | −12.3339 | + | 125.452i | −0.145105 | + | 1.47591i | ||||
\(86\) | 0.839889 | 0.00976615 | ||||||||
\(87\) | 14.9859 | + | 14.9859i | 0.172252 | + | 0.172252i | ||||
\(88\) | 29.6275 | − | 29.6275i | 0.336676 | − | 0.336676i | ||||
\(89\) | 141.715i | 1.59230i | 0.605101 | + | 0.796149i | \(0.293133\pi\) | ||||
−0.605101 | + | 0.796149i | \(0.706867\pi\) | |||||||
\(90\) | 37.2873 | + | 3.66593i | 0.414303 | + | 0.0407326i | ||||
\(91\) | −70.9402 | −0.779563 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | −57.6347 | + | 57.6347i | −0.619728 | + | 0.619728i | ||||
\(94\) | 106.032i | 1.12800i | ||||||||
\(95\) | 114.393 | − | 93.9135i | 1.20414 | − | 0.988563i | ||||
\(96\) | 10.8832 | 0.113366 | ||||||||
\(97\) | −29.4379 | − | 29.4379i | −0.303483 | − | 0.303483i | 0.538892 | − | 0.842375i | \(-0.318843\pi\) |
−0.842375 | + | 0.538892i | \(0.818843\pi\) | |||||||
\(98\) | −55.2252 | + | 55.2252i | −0.563523 | + | 0.563523i | ||||
\(99\) | − | 78.4927i | − | 0.792856i | ||||||
\(100\) | −49.0427 | − | 9.73747i | −0.490427 | − | 0.0973747i | ||||
\(101\) | 105.739 | 1.04692 | 0.523459 | − | 0.852051i | \(-0.324641\pi\) | ||||
0.523459 | + | 0.852051i | \(0.324641\pi\) | |||||||
\(102\) | 48.5039 | + | 48.5039i | 0.475529 | + | 0.475529i | ||||
\(103\) | −15.4223 | + | 15.4223i | −0.149732 | + | 0.149732i | −0.777998 | − | 0.628267i | \(-0.783765\pi\) |
0.628267 | + | 0.777998i | \(0.283765\pi\) | |||||||
\(104\) | − | 19.6540i | − | 0.188981i | ||||||
\(105\) | 62.3143 | + | 75.9033i | 0.593469 | + | 0.722888i | ||||
\(106\) | −116.751 | −1.10142 | ||||||||
\(107\) | −38.0079 | − | 38.0079i | −0.355214 | − | 0.355214i | 0.506831 | − | 0.862045i | \(-0.330817\pi\) |
−0.862045 | + | 0.506831i | \(0.830817\pi\) | |||||||
\(108\) | 38.9036 | − | 38.9036i | 0.360219 | − | 0.360219i | ||||
\(109\) | 146.178i | 1.34108i | 0.741873 | + | 0.670540i | \(0.233938\pi\) | ||||
−0.741873 | + | 0.670540i | \(0.766062\pi\) | |||||||
\(110\) | −10.2491 | + | 104.246i | −0.0931735 | + | 0.947694i | ||||
\(111\) | −40.0760 | −0.361045 | ||||||||
\(112\) | −28.8756 | − | 28.8756i | −0.257818 | − | 0.257818i | ||||
\(113\) | 2.38693 | − | 2.38693i | 0.0211232 | − | 0.0211232i | −0.696466 | − | 0.717590i | \(-0.745245\pi\) |
0.717590 | + | 0.696466i | \(0.245245\pi\) | |||||||
\(114\) | − | 80.5384i | − | 0.706477i | ||||||
\(115\) | 23.8641 | + | 2.34622i | 0.207514 | + | 0.0204019i | ||||
\(116\) | 22.0317 | 0.189928 | ||||||||
\(117\) | −26.0349 | − | 26.0349i | −0.222520 | − | 0.222520i | ||||
\(118\) | −13.7747 | + | 13.7747i | −0.116735 | + | 0.116735i | ||||
\(119\) | − | 257.385i | − | 2.16290i | ||||||
\(120\) | −21.0290 | + | 17.2642i | −0.175242 | + | 0.143868i | ||||
\(121\) | 98.4471 | 0.813612 | ||||||||
\(122\) | 39.0198 | + | 39.0198i | 0.319835 | + | 0.319835i | ||||
\(123\) | −32.5924 | + | 32.5924i | −0.264979 | + | 0.264979i | ||||
\(124\) | 84.7322i | 0.683325i | ||||||||
\(125\) | 110.209 | − | 58.9821i | 0.881675 | − | 0.471856i | ||||
\(126\) | −76.5008 | −0.607149 | ||||||||
\(127\) | −134.874 | − | 134.874i | −1.06200 | − | 1.06200i | −0.997946 | − | 0.0640551i | \(-0.979597\pi\) |
−0.0640551 | − | 0.997946i | \(-0.520403\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 1.14258i | 0.00885723i | ||||||||
\(130\) | 31.1775 | + | 37.9765i | 0.239827 | + | 0.292127i | ||||
\(131\) | −48.2924 | −0.368644 | −0.184322 | − | 0.982866i | \(-0.559009\pi\) | ||||
−0.184322 | + | 0.982866i | \(0.559009\pi\) | |||||||
\(132\) | 40.3051 | + | 40.3051i | 0.305342 | + | 0.305342i | ||||
\(133\) | −213.687 | + | 213.687i | −1.60667 | + | 1.60667i | ||||
\(134\) | − | 33.8212i | − | 0.252397i | ||||||
\(135\) | −13.4580 | + | 136.885i | −0.0996889 | + | 1.01396i | ||||
\(136\) | 71.3085 | 0.524327 | ||||||||
\(137\) | −3.29075 | − | 3.29075i | −0.0240200 | − | 0.0240200i | 0.694995 | − | 0.719015i | \(-0.255407\pi\) |
−0.719015 | + | 0.694995i | \(0.755407\pi\) | |||||||
\(138\) | 9.22666 | − | 9.22666i | 0.0668598 | − | 0.0668598i | ||||
\(139\) | − | 108.941i | − | 0.783751i | −0.920018 | − | 0.391876i | \(-0.871826\pi\) | ||
0.920018 | − | 0.391876i | \(-0.128174\pi\) | |||||||
\(140\) | 101.601 | + | 9.98899i | 0.725721 | + | 0.0713499i | ||||
\(141\) | −144.246 | −1.02302 | ||||||||
\(142\) | 103.112 | + | 103.112i | 0.726143 | + | 0.726143i | ||||
\(143\) | 72.7874 | − | 72.7874i | 0.509002 | − | 0.509002i | ||||
\(144\) | − | 21.1946i | − | 0.147185i | ||||||
\(145\) | −42.5707 | + | 34.9492i | −0.293591 | + | 0.241029i | ||||
\(146\) | 83.1985 | 0.569853 | ||||||||
\(147\) | −75.1282 | − | 75.1282i | −0.511076 | − | 0.511076i | ||||
\(148\) | −29.4590 | + | 29.4590i | −0.199048 | + | 0.199048i | ||||
\(149\) | 68.8768i | 0.462260i | 0.972923 | + | 0.231130i | \(0.0742423\pi\) | ||||
−0.972923 | + | 0.231130i | \(0.925758\pi\) | |||||||
\(150\) | 13.2468 | − | 66.7175i | 0.0883121 | − | 0.444783i | ||||
\(151\) | 138.399 | 0.916549 | 0.458275 | − | 0.888811i | \(-0.348468\pi\) | ||||
0.458275 | + | 0.888811i | \(0.348468\pi\) | |||||||
\(152\) | −59.2022 | − | 59.2022i | −0.389488 | − | 0.389488i | ||||
\(153\) | 94.4596 | − | 94.4596i | 0.617383 | − | 0.617383i | ||||
\(154\) | − | 213.878i | − | 1.38882i | ||||||
\(155\) | −134.412 | − | 163.724i | −0.867177 | − | 1.05628i | ||||
\(156\) | 26.7372 | 0.171393 | ||||||||
\(157\) | −135.287 | − | 135.287i | −0.861699 | − | 0.861699i | 0.129836 | − | 0.991535i | \(-0.458555\pi\) |
−0.991535 | + | 0.129836i | \(0.958555\pi\) | |||||||
\(158\) | 155.484 | − | 155.484i | 0.984074 | − | 0.984074i | ||||
\(159\) | − | 158.828i | − | 0.998916i | ||||||
\(160\) | −2.76745 | + | 28.1486i | −0.0172966 | + | 0.175928i | ||||
\(161\) | −48.9610 | −0.304106 | ||||||||
\(162\) | 5.23660 | + | 5.23660i | 0.0323247 | + | 0.0323247i | ||||
\(163\) | −84.3740 | + | 84.3740i | −0.517632 | + | 0.517632i | −0.916854 | − | 0.399222i | \(-0.869280\pi\) |
0.399222 | + | 0.916854i | \(0.369280\pi\) | |||||||
\(164\) | 47.9160i | 0.292171i | ||||||||
\(165\) | −141.816 | − | 13.9428i | −0.859494 | − | 0.0845019i | ||||
\(166\) | 25.4320 | 0.153205 | ||||||||
\(167\) | 217.730 | + | 217.730i | 1.30378 | + | 1.30378i | 0.925826 | + | 0.377949i | \(0.123371\pi\) |
0.377949 | + | 0.925826i | \(0.376629\pi\) | |||||||
\(168\) | 39.2823 | − | 39.2823i | 0.233823 | − | 0.233823i | ||||
\(169\) | 120.715i | 0.714290i | ||||||||
\(170\) | −137.786 | + | 113.118i | −0.810505 | + | 0.665400i | ||||
\(171\) | −156.846 | −0.917225 | ||||||||
\(172\) | 0.839889 | + | 0.839889i | 0.00488308 | + | 0.00488308i | ||||
\(173\) | −222.534 | + | 222.534i | −1.28632 | + | 1.28632i | −0.349321 | + | 0.937003i | \(0.613588\pi\) |
−0.937003 | + | 0.349321i | \(0.886412\pi\) | |||||||
\(174\) | 29.9718i | 0.172252i | ||||||||
\(175\) | −212.164 | + | 141.870i | −1.21237 | + | 0.810687i | ||||
\(176\) | 59.2550 | 0.336676 | ||||||||
\(177\) | −18.7390 | − | 18.7390i | −0.105870 | − | 0.105870i | ||||
\(178\) | −141.715 | + | 141.715i | −0.796149 | + | 0.796149i | ||||
\(179\) | 194.058i | 1.08412i | 0.840339 | + | 0.542061i | \(0.182356\pi\) | ||||
−0.840339 | + | 0.542061i | \(0.817644\pi\) | |||||||
\(180\) | 33.6214 | + | 40.9532i | 0.186785 | + | 0.227518i | ||||
\(181\) | −0.412795 | −0.00228064 | −0.00114032 | − | 0.999999i | \(-0.500363\pi\) | ||||
−0.00114032 | + | 0.999999i | \(0.500363\pi\) | |||||||
\(182\) | −70.9402 | − | 70.9402i | −0.389781 | − | 0.389781i | ||||
\(183\) | −53.0825 | + | 53.0825i | −0.290068 | + | 0.290068i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 10.1908 | − | 103.654i | 0.0550855 | − | 0.560290i | ||||
\(186\) | −115.269 | −0.619728 | ||||||||
\(187\) | 264.086 | + | 264.086i | 1.41223 | + | 1.41223i | ||||
\(188\) | −106.032 | + | 106.032i | −0.564002 | + | 0.564002i | ||||
\(189\) | − | 280.842i | − | 1.48594i | ||||||
\(190\) | 208.307 | + | 20.4799i | 1.09635 | + | 0.107789i | ||||
\(191\) | −313.636 | −1.64207 | −0.821036 | − | 0.570877i | \(-0.806603\pi\) | ||||
−0.821036 | + | 0.570877i | \(0.806603\pi\) | |||||||
\(192\) | 10.8832 | + | 10.8832i | 0.0566832 | + | 0.0566832i | ||||
\(193\) | −11.9642 | + | 11.9642i | −0.0619909 | + | 0.0619909i | −0.737423 | − | 0.675432i | \(-0.763957\pi\) |
0.675432 | + | 0.737423i | \(0.263957\pi\) | |||||||
\(194\) | − | 58.8757i | − | 0.303483i | ||||||
\(195\) | −51.6630 | + | 42.4138i | −0.264939 | + | 0.217507i | ||||
\(196\) | −110.450 | −0.563523 | ||||||||
\(197\) | −57.7317 | − | 57.7317i | −0.293054 | − | 0.293054i | 0.545231 | − | 0.838286i | \(-0.316442\pi\) |
−0.838286 | + | 0.545231i | \(0.816442\pi\) | |||||||
\(198\) | 78.4927 | − | 78.4927i | 0.396428 | − | 0.396428i | ||||
\(199\) | 263.722i | 1.32524i | 0.748957 | + | 0.662619i | \(0.230555\pi\) | ||||
−0.748957 | + | 0.662619i | \(0.769445\pi\) | |||||||
\(200\) | −39.3052 | − | 58.7801i | −0.196526 | − | 0.293901i | ||||
\(201\) | 46.0102 | 0.228907 | ||||||||
\(202\) | 105.739 | + | 105.739i | 0.523459 | + | 0.523459i | ||||
\(203\) | 79.5222 | − | 79.5222i | 0.391735 | − | 0.391735i | ||||
\(204\) | 97.0078i | 0.475529i | ||||||||
\(205\) | −76.0101 | − | 92.5857i | −0.370781 | − | 0.451638i | ||||
\(206\) | −30.8447 | −0.149732 | ||||||||
\(207\) | −17.9686 | − | 17.9686i | −0.0868047 | − | 0.0868047i | ||||
\(208\) | 19.6540 | − | 19.6540i | 0.0944904 | − | 0.0944904i | ||||
\(209\) | − | 438.503i | − | 2.09810i | ||||||
\(210\) | −13.5890 | + | 138.218i | −0.0647095 | + | 0.658179i | ||||
\(211\) | 321.514 | 1.52376 | 0.761881 | − | 0.647717i | \(-0.224276\pi\) | ||||
0.761881 | + | 0.647717i | \(0.224276\pi\) | |||||||
\(212\) | −116.751 | − | 116.751i | −0.550712 | − | 0.550712i | ||||
\(213\) | −140.274 | + | 140.274i | −0.658561 | + | 0.658561i | ||||
\(214\) | − | 76.0158i | − | 0.355214i | ||||||
\(215\) | −2.95521 | − | 0.290544i | −0.0137452 | − | 0.00135137i | ||||
\(216\) | 77.8073 | 0.360219 | ||||||||
\(217\) | 305.837 | + | 305.837i | 1.40939 | + | 1.40939i | ||||
\(218\) | −146.178 | + | 146.178i | −0.670540 | + | 0.670540i | ||||
\(219\) | 113.183i | 0.516817i | ||||||||
\(220\) | −114.495 | + | 93.9973i | −0.520434 | + | 0.427261i | ||||
\(221\) | 175.187 | 0.792702 | ||||||||
\(222\) | −40.0760 | − | 40.0760i | −0.180522 | − | 0.180522i | ||||
\(223\) | −75.9702 | + | 75.9702i | −0.340674 | + | 0.340674i | −0.856621 | − | 0.515947i | \(-0.827440\pi\) |
0.515947 | + | 0.856621i | \(0.327440\pi\) | |||||||
\(224\) | − | 57.7513i | − | 0.257818i | ||||||
\(225\) | −129.930 | − | 25.7977i | −0.577466 | − | 0.114656i | ||||
\(226\) | 4.77385 | 0.0211232 | ||||||||
\(227\) | −63.6613 | − | 63.6613i | −0.280446 | − | 0.280446i | 0.552841 | − | 0.833287i | \(-0.313544\pi\) |
−0.833287 | + | 0.552841i | \(0.813544\pi\) | |||||||
\(228\) | 80.5384 | − | 80.5384i | 0.353239 | − | 0.353239i | ||||
\(229\) | − | 103.156i | − | 0.450462i | −0.974305 | − | 0.225231i | \(-0.927686\pi\) | ||
0.974305 | − | 0.225231i | \(-0.0723137\pi\) | |||||||
\(230\) | 21.5179 | + | 26.2103i | 0.0935560 | + | 0.113958i | ||||
\(231\) | 290.959 | 1.25956 | ||||||||
\(232\) | 22.0317 | + | 22.0317i | 0.0949640 | + | 0.0949640i | ||||
\(233\) | −211.803 | + | 211.803i | −0.909026 | + | 0.909026i | −0.996194 | − | 0.0871679i | \(-0.972218\pi\) |
0.0871679 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(234\) | − | 52.0698i | − | 0.222520i | ||||||
\(235\) | 36.6799 | − | 373.082i | 0.156085 | − | 1.58758i | ||||
\(236\) | −27.5494 | −0.116735 | ||||||||
\(237\) | 211.520 | + | 211.520i | 0.892488 | + | 0.892488i | ||||
\(238\) | 257.385 | − | 257.385i | 1.08145 | − | 1.08145i | ||||
\(239\) | − | 89.5138i | − | 0.374535i | −0.982309 | − | 0.187267i | \(-0.940037\pi\) | ||
0.982309 | − | 0.187267i | \(-0.0599631\pi\) | |||||||
\(240\) | −38.2932 | − | 3.76483i | −0.159555 | − | 0.0156868i | ||||
\(241\) | 175.324 | 0.727487 | 0.363744 | − | 0.931499i | \(-0.381498\pi\) | ||||
0.363744 | + | 0.931499i | \(0.381498\pi\) | |||||||
\(242\) | 98.4471 | + | 98.4471i | 0.406806 | + | 0.406806i | ||||
\(243\) | 167.943 | − | 167.943i | 0.691122 | − | 0.691122i | ||||
\(244\) | 78.0397i | 0.319835i | ||||||||
\(245\) | 213.418 | − | 175.210i | 0.871094 | − | 0.715142i | ||||
\(246\) | −65.1848 | −0.264979 | ||||||||
\(247\) | −145.445 | − | 145.445i | −0.588846 | − | 0.588846i | ||||
\(248\) | −84.7322 | + | 84.7322i | −0.341662 | + | 0.341662i | ||||
\(249\) | 34.5976i | 0.138946i | ||||||||
\(250\) | 169.191 | + | 51.2274i | 0.676766 | + | 0.204909i | ||||
\(251\) | 326.776 | 1.30190 | 0.650948 | − | 0.759122i | \(-0.274371\pi\) | ||||
0.650948 | + | 0.759122i | \(0.274371\pi\) | |||||||
\(252\) | −76.5008 | − | 76.5008i | −0.303575 | − | 0.303575i | ||||
\(253\) | 50.2359 | − | 50.2359i | 0.198561 | − | 0.198561i | ||||
\(254\) | − | 269.748i | − | 1.06200i | ||||||
\(255\) | −153.885 | − | 187.443i | −0.603472 | − | 0.735072i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −44.9594 | − | 44.9594i | −0.174939 | − | 0.174939i | 0.614206 | − | 0.789146i | \(-0.289476\pi\) |
−0.789146 | + | 0.614206i | \(0.789476\pi\) | |||||||
\(258\) | −1.14258 | + | 1.14258i | −0.00442861 | + | 0.00442861i | ||||
\(259\) | 212.662i | 0.821089i | ||||||||
\(260\) | −6.79894 | + | 69.1540i | −0.0261498 | + | 0.265977i | ||||
\(261\) | 58.3689 | 0.223636 | ||||||||
\(262\) | −48.2924 | − | 48.2924i | −0.184322 | − | 0.184322i | ||||
\(263\) | 123.550 | − | 123.550i | 0.469771 | − | 0.469771i | −0.432070 | − | 0.901840i | \(-0.642217\pi\) |
0.901840 | + | 0.432070i | \(0.142217\pi\) | |||||||
\(264\) | 80.6103i | 0.305342i | ||||||||
\(265\) | 410.797 | + | 40.3879i | 1.55018 | + | 0.152407i | ||||
\(266\) | −427.375 | −1.60667 | ||||||||
\(267\) | −192.788 | − | 192.788i | −0.722052 | − | 0.722052i | ||||
\(268\) | 33.8212 | − | 33.8212i | 0.126198 | − | 0.126198i | ||||
\(269\) | 237.309i | 0.882189i | 0.897461 | + | 0.441094i | \(0.145410\pi\) | ||||
−0.897461 | + | 0.441094i | \(0.854590\pi\) | |||||||
\(270\) | −150.343 | + | 123.427i | −0.556827 | + | 0.457138i | ||||
\(271\) | 26.2193 | 0.0967502 | 0.0483751 | − | 0.998829i | \(-0.484596\pi\) | ||||
0.0483751 | + | 0.998829i | \(0.484596\pi\) | |||||||
\(272\) | 71.3085 | + | 71.3085i | 0.262164 | + | 0.262164i | ||||
\(273\) | 96.5068 | − | 96.5068i | 0.353505 | − | 0.353505i | ||||
\(274\) | − | 6.58149i | − | 0.0240200i | ||||||
\(275\) | 72.1242 | − | 363.253i | 0.262270 | − | 1.32092i | ||||
\(276\) | 18.4533 | 0.0668598 | ||||||||
\(277\) | −225.480 | − | 225.480i | −0.814007 | − | 0.814007i | 0.171225 | − | 0.985232i | \(-0.445228\pi\) |
−0.985232 | + | 0.171225i | \(0.945228\pi\) | |||||||
\(278\) | 108.941 | − | 108.941i | 0.391876 | − | 0.391876i | ||||
\(279\) | 224.483i | 0.804598i | ||||||||
\(280\) | 91.6119 | + | 111.590i | 0.327185 | + | 0.398535i | ||||
\(281\) | −70.2491 | −0.249997 | −0.124998 | − | 0.992157i | \(-0.539893\pi\) | ||||
−0.124998 | + | 0.992157i | \(0.539893\pi\) | |||||||
\(282\) | −144.246 | − | 144.246i | −0.511511 | − | 0.511511i | ||||
\(283\) | 49.1215 | − | 49.1215i | 0.173574 | − | 0.173574i | −0.614974 | − | 0.788548i | \(-0.710833\pi\) |
0.788548 | + | 0.614974i | \(0.210833\pi\) | |||||||
\(284\) | 206.225i | 0.726143i | ||||||||
\(285\) | −27.8608 | + | 283.380i | −0.0977571 | + | 0.994316i | ||||
\(286\) | 145.575 | 0.509002 | ||||||||
\(287\) | 172.951 | + | 172.951i | 0.602615 | + | 0.602615i | ||||
\(288\) | 21.1946 | − | 21.1946i | 0.0735923 | − | 0.0735923i | ||||
\(289\) | 346.613i | 1.19935i | ||||||||
\(290\) | −77.5199 | − | 7.62144i | −0.267310 | − | 0.0262808i | ||||
\(291\) | 80.0943 | 0.275238 | ||||||||
\(292\) | 83.1985 | + | 83.1985i | 0.284926 | + | 0.284926i | ||||
\(293\) | 369.904 | − | 369.904i | 1.26247 | − | 1.26247i | 0.312580 | − | 0.949891i | \(-0.398807\pi\) |
0.949891 | − | 0.312580i | \(-0.101193\pi\) | |||||||
\(294\) | − | 150.256i | − | 0.511076i | ||||||
\(295\) | 53.2323 | − | 43.7021i | 0.180448 | − | 0.148143i | ||||
\(296\) | −58.9181 | −0.199048 | ||||||||
\(297\) | 288.154 | + | 288.154i | 0.970217 | + | 0.970217i | ||||
\(298\) | −68.8768 | + | 68.8768i | −0.231130 | + | 0.231130i | ||||
\(299\) | − | 33.3250i | − | 0.111455i | ||||||
\(300\) | 79.9643 | − | 53.4706i | 0.266548 | − | 0.178235i | ||||
\(301\) | 6.06308 | 0.0201431 | ||||||||
\(302\) | 138.399 | + | 138.399i | 0.458275 | + | 0.458275i | ||||
\(303\) | −143.847 | + | 143.847i | −0.474741 | + | 0.474741i | ||||
\(304\) | − | 118.404i | − | 0.389488i | ||||||
\(305\) | −123.796 | − | 150.792i | −0.405888 | − | 0.494401i | ||||
\(306\) | 188.919 | 0.617383 | ||||||||
\(307\) | 4.17039 | + | 4.17039i | 0.0135843 | + | 0.0135843i | 0.713866 | − | 0.700282i | \(-0.246942\pi\) |
−0.700282 | + | 0.713866i | \(0.746942\pi\) | |||||||
\(308\) | 213.878 | − | 213.878i | 0.694409 | − | 0.694409i | ||||
\(309\) | − | 41.9610i | − | 0.135796i | ||||||
\(310\) | 29.3115 | − | 298.136i | 0.0945534 | − | 0.961730i | ||||
\(311\) | −385.664 | −1.24008 | −0.620039 | − | 0.784571i | \(-0.712883\pi\) | ||||
−0.620039 | + | 0.784571i | \(0.712883\pi\) | |||||||
\(312\) | 26.7372 | + | 26.7372i | 0.0856963 | + | 0.0856963i | ||||
\(313\) | −156.465 | + | 156.465i | −0.499888 | + | 0.499888i | −0.911403 | − | 0.411515i | \(-0.865000\pi\) |
0.411515 | + | 0.911403i | \(0.365000\pi\) | |||||||
\(314\) | − | 270.574i | − | 0.861699i | ||||||
\(315\) | 269.173 | + | 26.4640i | 0.854519 | + | 0.0840128i | ||||
\(316\) | 310.967 | 0.984074 | ||||||||
\(317\) | −172.672 | − | 172.672i | −0.544708 | − | 0.544708i | 0.380198 | − | 0.924905i | \(-0.375856\pi\) |
−0.924905 | + | 0.380198i | \(0.875856\pi\) | |||||||
\(318\) | 158.828 | − | 158.828i | 0.499458 | − | 0.499458i | ||||
\(319\) | 163.186i | 0.511554i | ||||||||
\(320\) | −30.9160 | + | 25.3811i | −0.0966125 | + | 0.0793160i | ||||
\(321\) | 103.412 | 0.322155 | ||||||||
\(322\) | −48.9610 | − | 48.9610i | −0.152053 | − | 0.152053i | ||||
\(323\) | 527.702 | − | 527.702i | 1.63375 | − | 1.63375i | ||||
\(324\) | 10.4732i | 0.0323247i | ||||||||
\(325\) | −96.5630 | − | 144.408i | −0.297117 | − | 0.444333i | ||||
\(326\) | −168.748 | −0.517632 | ||||||||
\(327\) | −198.860 | − | 198.860i | −0.608134 | − | 0.608134i | ||||
\(328\) | −47.9160 | + | 47.9160i | −0.146085 | + | 0.146085i | ||||
\(329\) | 765.437i | 2.32656i | ||||||||
\(330\) | −127.874 | − | 155.759i | −0.387496 | − | 0.471998i | ||||
\(331\) | 594.585 | 1.79633 | 0.898165 | − | 0.439659i | \(-0.144901\pi\) | ||||
0.898165 | + | 0.439659i | \(0.144901\pi\) | |||||||
\(332\) | 25.4320 | + | 25.4320i | 0.0766024 | + | 0.0766024i | ||||
\(333\) | −78.0465 | + | 78.0465i | −0.234374 | + | 0.234374i | ||||
\(334\) | 435.461i | 1.30378i | ||||||||
\(335\) | −11.6998 | + | 119.002i | −0.0349248 | + | 0.355231i | ||||
\(336\) | 78.5646 | 0.233823 | ||||||||
\(337\) | −318.172 | − | 318.172i | −0.944130 | − | 0.944130i | 0.0543895 | − | 0.998520i | \(-0.482679\pi\) |
−0.998520 | + | 0.0543895i | \(0.982679\pi\) | |||||||
\(338\) | −120.715 | + | 120.715i | −0.357145 | + | 0.357145i | ||||
\(339\) | 6.49433i | 0.0191573i | ||||||||
\(340\) | −250.904 | − | 24.6679i | −0.737953 | − | 0.0725525i | ||||
\(341\) | −627.601 | −1.84047 | ||||||||
\(342\) | −156.846 | − | 156.846i | −0.458613 | − | 0.458613i | ||||
\(343\) | −44.9394 | + | 44.9394i | −0.131019 | + | 0.131019i | ||||
\(344\) | 1.67978i | 0.00488308i | ||||||||
\(345\) | −35.6564 | + | 29.2728i | −0.103352 | + | 0.0848488i | ||||
\(346\) | −445.068 | −1.28632 | ||||||||
\(347\) | 161.848 | + | 161.848i | 0.466422 | + | 0.466422i | 0.900753 | − | 0.434331i | \(-0.143015\pi\) |
−0.434331 | + | 0.900753i | \(0.643015\pi\) | |||||||
\(348\) | −29.9718 | + | 29.9718i | −0.0861258 | + | 0.0861258i | ||||
\(349\) | 66.1242i | 0.189468i | 0.995503 | + | 0.0947339i | \(0.0302000\pi\) | ||||
−0.995503 | + | 0.0947339i | \(0.969800\pi\) | |||||||
\(350\) | −354.034 | − | 70.2939i | −1.01153 | − | 0.200840i | ||||
\(351\) | 191.153 | 0.544596 | ||||||||
\(352\) | 59.2550 | + | 59.2550i | 0.168338 | + | 0.168338i | ||||
\(353\) | 331.118 | − | 331.118i | 0.938012 | − | 0.938012i | −0.0601762 | − | 0.998188i | \(-0.519166\pi\) |
0.998188 | + | 0.0601762i | \(0.0191662\pi\) | |||||||
\(354\) | − | 37.4780i | − | 0.105870i | ||||||
\(355\) | −327.138 | − | 398.478i | −0.921515 | − | 1.12247i | ||||
\(356\) | −283.429 | −0.796149 | ||||||||
\(357\) | 350.145 | + | 350.145i | 0.980799 | + | 0.980799i | ||||
\(358\) | −194.058 | + | 194.058i | −0.542061 | + | 0.542061i | ||||
\(359\) | 134.587i | 0.374893i | 0.982275 | + | 0.187447i | \(0.0600211\pi\) | ||||
−0.982275 | + | 0.187447i | \(0.939979\pi\) | |||||||
\(360\) | −7.33187 | + | 74.5746i | −0.0203663 | + | 0.207152i | ||||
\(361\) | −515.224 | −1.42721 | ||||||||
\(362\) | −0.412795 | − | 0.412795i | −0.00114032 | − | 0.00114032i | ||||
\(363\) | −133.927 | + | 133.927i | −0.368945 | + | 0.368945i | ||||
\(364\) | − | 141.880i | − | 0.389781i | ||||||
\(365\) | −292.740 | − | 28.7810i | −0.802027 | − | 0.0788520i | ||||
\(366\) | −106.165 | −0.290068 | ||||||||
\(367\) | 451.660 | + | 451.660i | 1.23068 | + | 1.23068i | 0.963702 | + | 0.266979i | \(0.0860254\pi\) |
0.266979 | + | 0.963702i | \(0.413975\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 126.945i | 0.344024i | ||||||||
\(370\) | 113.845 | − | 93.4629i | 0.307688 | − | 0.252602i | ||||
\(371\) | −842.815 | −2.27174 | ||||||||
\(372\) | −115.269 | − | 115.269i | −0.309864 | − | 0.309864i | ||||
\(373\) | 451.866 | − | 451.866i | 1.21144 | − | 1.21144i | 0.240883 | − | 0.970554i | \(-0.422563\pi\) |
0.970554 | − | 0.240883i | \(-0.0774369\pi\) | |||||||
\(374\) | 528.173i | 1.41223i | ||||||||
\(375\) | −69.6895 | + | 230.168i | −0.185839 | + | 0.613780i | ||||
\(376\) | −212.065 | −0.564002 | ||||||||
\(377\) | 54.1263 | + | 54.1263i | 0.143571 | + | 0.143571i | ||||
\(378\) | 280.842 | − | 280.842i | 0.742968 | − | 0.742968i | ||||
\(379\) | 230.954i | 0.609377i | 0.952452 | + | 0.304688i | \(0.0985524\pi\) | ||||
−0.952452 | + | 0.304688i | \(0.901448\pi\) | |||||||
\(380\) | 187.827 | + | 228.787i | 0.494282 | + | 0.602071i | ||||
\(381\) | 366.965 | 0.963162 | ||||||||
\(382\) | −313.636 | − | 313.636i | −0.821036 | − | 0.821036i | ||||
\(383\) | 183.834 | − | 183.834i | 0.479985 | − | 0.479985i | −0.425142 | − | 0.905127i | \(-0.639776\pi\) |
0.905127 | + | 0.425142i | \(0.139776\pi\) | |||||||
\(384\) | 21.7663i | 0.0566832i | ||||||||
\(385\) | −73.9872 | + | 752.545i | −0.192174 | + | 1.95466i | ||||
\(386\) | −23.9285 | −0.0619909 | ||||||||
\(387\) | 2.22514 | + | 2.22514i | 0.00574971 | + | 0.00574971i | ||||
\(388\) | 58.8757 | − | 58.8757i | 0.151742 | − | 0.151742i | ||||
\(389\) | − | 468.206i | − | 1.20362i | −0.798641 | − | 0.601808i | \(-0.794447\pi\) | ||
0.798641 | − | 0.601808i | \(-0.205553\pi\) | |||||||
\(390\) | −94.0768 | − | 9.24925i | −0.241223 | − | 0.0237160i | ||||
\(391\) | 120.909 | 0.309231 | ||||||||
\(392\) | −110.450 | − | 110.450i | −0.281761 | − | 0.281761i | ||||
\(393\) | 65.6968 | − | 65.6968i | 0.167168 | − | 0.167168i | ||||
\(394\) | − | 115.463i | − | 0.293054i | ||||||
\(395\) | −600.867 | + | 493.294i | −1.52118 | + | 1.24884i | ||||
\(396\) | 156.985 | 0.396428 | ||||||||
\(397\) | 53.6961 | + | 53.6961i | 0.135255 | + | 0.135255i | 0.771493 | − | 0.636238i | \(-0.219510\pi\) |
−0.636238 | + | 0.771493i | \(0.719510\pi\) | |||||||
\(398\) | −263.722 | + | 263.722i | −0.662619 | + | 0.662619i | ||||
\(399\) | − | 581.399i | − | 1.45714i | ||||||
\(400\) | 19.4749 | − | 98.0853i | 0.0486874 | − | 0.245213i | ||||
\(401\) | 248.645 | 0.620062 | 0.310031 | − | 0.950727i | \(-0.399661\pi\) | ||||
0.310031 | + | 0.950727i | \(0.399661\pi\) | |||||||
\(402\) | 46.0102 | + | 46.0102i | 0.114453 | + | 0.114453i | ||||
\(403\) | −208.166 | + | 208.166i | −0.516541 | + | 0.516541i | ||||
\(404\) | 211.477i | 0.523459i | ||||||||
\(405\) | −16.6138 | − | 20.2369i | −0.0410218 | − | 0.0499675i | ||||
\(406\) | 159.044 | 0.391735 | ||||||||
\(407\) | −218.199 | − | 218.199i | −0.536117 | − | 0.536117i | ||||
\(408\) | −97.0078 | + | 97.0078i | −0.237764 | + | 0.237764i | ||||
\(409\) | 561.926i | 1.37390i | 0.726703 | + | 0.686952i | \(0.241052\pi\) | ||||
−0.726703 | + | 0.686952i | \(0.758948\pi\) | |||||||
\(410\) | 16.5756 | − | 168.596i | 0.0404284 | − | 0.411209i | ||||
\(411\) | 8.95344 | 0.0217845 | ||||||||
\(412\) | −30.8447 | − | 30.8447i | −0.0748658 | − | 0.0748658i | ||||
\(413\) | −99.4381 | + | 99.4381i | −0.240770 | + | 0.240770i | ||||
\(414\) | − | 35.9371i | − | 0.0868047i | ||||||
\(415\) | −89.4842 | − | 8.79772i | −0.215625 | − | 0.0211993i | ||||
\(416\) | 39.3080 | 0.0944904 | ||||||||
\(417\) | 148.204 | + | 148.204i | 0.355404 | + | 0.355404i | ||||
\(418\) | 438.503 | − | 438.503i | 1.04905 | − | 1.04905i | ||||
\(419\) | − | 453.494i | − | 1.08233i | −0.840918 | − | 0.541163i | \(-0.817984\pi\) | ||
0.840918 | − | 0.541163i | \(-0.182016\pi\) | |||||||
\(420\) | −151.807 | + | 124.629i | −0.361444 | + | 0.296735i | ||||
\(421\) | −62.8563 | −0.149302 | −0.0746512 | − | 0.997210i | \(-0.523784\pi\) | ||||
−0.0746512 | + | 0.997210i | \(0.523784\pi\) | |||||||
\(422\) | 321.514 | + | 321.514i | 0.761881 | + | 0.761881i | ||||
\(423\) | −280.914 | + | 280.914i | −0.664099 | + | 0.664099i | ||||
\(424\) | − | 233.502i | − | 0.550712i | ||||||
\(425\) | 523.940 | − | 350.349i | 1.23280 | − | 0.824351i | ||||
\(426\) | −280.547 | −0.658561 | ||||||||
\(427\) | 281.681 | + | 281.681i | 0.659674 | + | 0.659674i | ||||
\(428\) | 76.0158 | − | 76.0158i | 0.177607 | − | 0.177607i | ||||
\(429\) | 198.039i | 0.461630i | ||||||||
\(430\) | −2.66466 | − | 3.24575i | −0.00619689 | − | 0.00754826i | ||||
\(431\) | −175.877 | −0.408068 | −0.204034 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204034 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(432\) | 77.8073 | + | 77.8073i | 0.180109 | + | 0.180109i | ||||
\(433\) | −342.932 | + | 342.932i | −0.791991 | + | 0.791991i | −0.981818 | − | 0.189827i | \(-0.939207\pi\) |
0.189827 | + | 0.981818i | \(0.439207\pi\) | |||||||
\(434\) | 611.674i | 1.40939i | ||||||||
\(435\) | 10.3682 | − | 105.458i | 0.0238349 | − | 0.242432i | ||||
\(436\) | −292.356 | −0.670540 | ||||||||
\(437\) | −100.382 | − | 100.382i | −0.229707 | − | 0.229707i | ||||
\(438\) | −113.183 | + | 113.183i | −0.258409 | + | 0.258409i | ||||
\(439\) | 55.4496i | 0.126309i | 0.998004 | + | 0.0631544i | \(0.0201161\pi\) | ||||
−0.998004 | + | 0.0631544i | \(0.979884\pi\) | |||||||
\(440\) | −208.493 | − | 20.4982i | −0.473847 | − | 0.0465867i | ||||
\(441\) | −292.619 | −0.663535 | ||||||||
\(442\) | 175.187 | + | 175.187i | 0.396351 | + | 0.396351i | ||||
\(443\) | −154.793 | + | 154.793i | −0.349420 | + | 0.349420i | −0.859894 | − | 0.510473i | \(-0.829470\pi\) |
0.510473 | + | 0.859894i | \(0.329470\pi\) | |||||||
\(444\) | − | 80.1520i | − | 0.180522i | ||||||
\(445\) | 547.656 | − | 449.609i | 1.23069 | − | 1.01036i | ||||
\(446\) | −151.940 | −0.340674 | ||||||||
\(447\) | −93.6997 | − | 93.6997i | −0.209619 | − | 0.209619i | ||||
\(448\) | 57.7513 | − | 57.7513i | 0.128909 | − | 0.128909i | ||||
\(449\) | − | 658.321i | − | 1.46619i | −0.680124 | − | 0.733097i | \(-0.738074\pi\) | ||
0.680124 | − | 0.733097i | \(-0.261926\pi\) | |||||||
\(450\) | −104.132 | − | 155.727i | −0.231405 | − | 0.346061i | ||||
\(451\) | −354.908 | −0.786935 | ||||||||
\(452\) | 4.77385 | + | 4.77385i | 0.0105616 | + | 0.0105616i | ||||
\(453\) | −188.277 | + | 188.277i | −0.415623 | + | 0.415623i | ||||
\(454\) | − | 127.323i | − | 0.280446i | ||||||
\(455\) | 225.068 | + | 274.149i | 0.494654 | + | 0.602524i | ||||
\(456\) | 161.077 | 0.353239 | ||||||||
\(457\) | −630.005 | − | 630.005i | −1.37857 | − | 1.37857i | −0.847045 | − | 0.531522i | \(-0.821620\pi\) |
−0.531522 | − | 0.847045i | \(-0.678380\pi\) | |||||||
\(458\) | 103.156 | − | 103.156i | 0.225231 | − | 0.225231i | ||||
\(459\) | 693.540i | 1.51098i | ||||||||
\(460\) | −4.69244 | + | 47.7282i | −0.0102010 | + | 0.103757i | ||||
\(461\) | −635.738 | −1.37904 | −0.689520 | − | 0.724266i | \(-0.742179\pi\) | ||||
−0.689520 | + | 0.724266i | \(0.742179\pi\) | |||||||
\(462\) | 290.959 | + | 290.959i | 0.629781 | + | 0.629781i | ||||
\(463\) | −30.8108 | + | 30.8108i | −0.0665460 | + | 0.0665460i | −0.739597 | − | 0.673051i | \(-0.764984\pi\) |
0.673051 | + | 0.739597i | \(0.264984\pi\) | |||||||
\(464\) | 44.0633i | 0.0949640i | ||||||||
\(465\) | 405.584 | + | 39.8753i | 0.872223 | + | 0.0857534i | ||||
\(466\) | −423.606 | −0.909026 | ||||||||
\(467\) | 273.937 | + | 273.937i | 0.586588 | + | 0.586588i | 0.936706 | − | 0.350118i | \(-0.113858\pi\) |
−0.350118 | + | 0.936706i | \(0.613858\pi\) | |||||||
\(468\) | 52.0698 | − | 52.0698i | 0.111260 | − | 0.111260i | ||||
\(469\) | − | 244.152i | − | 0.520580i | ||||||
\(470\) | 409.762 | − | 336.402i | 0.871834 | − | 0.715749i | ||||
\(471\) | 368.087 | 0.781502 | ||||||||
\(472\) | −27.5494 | − | 27.5494i | −0.0583673 | − | 0.0583673i | ||||
\(473\) | −6.22095 | + | 6.22095i | −0.0131521 | + | 0.0131521i | ||||
\(474\) | 423.039i | 0.892488i | ||||||||
\(475\) | −725.858 | − | 144.120i | −1.52812 | − | 0.303410i | ||||
\(476\) | 514.769 | 1.08145 | ||||||||
\(477\) | −309.311 | − | 309.311i | −0.648451 | − | 0.648451i | ||||
\(478\) | 89.5138 | − | 89.5138i | 0.187267 | − | 0.187267i | ||||
\(479\) | 617.839i | 1.28985i | 0.764245 | + | 0.644926i | \(0.223112\pi\) | ||||
−0.764245 | + | 0.644926i | \(0.776888\pi\) | |||||||
\(480\) | −34.5284 | − | 42.0580i | −0.0719341 | − | 0.0876209i | ||||
\(481\) | −144.747 | −0.300929 | ||||||||
\(482\) | 175.324 | + | 175.324i | 0.363744 | + | 0.363744i | ||||
\(483\) | 66.6064 | − | 66.6064i | 0.137901 | − | 0.137901i | ||||
\(484\) | 196.894i | 0.406806i | ||||||||
\(485\) | −20.3670 | + | 207.158i | −0.0419937 | + | 0.427130i | ||||
\(486\) | 335.885 | 0.691122 | ||||||||
\(487\) | 182.634 | + | 182.634i | 0.375019 | + | 0.375019i | 0.869301 | − | 0.494283i | \(-0.164569\pi\) |
−0.494283 | + | 0.869301i | \(0.664569\pi\) | |||||||
\(488\) | −78.0397 | + | 78.0397i | −0.159917 | + | 0.159917i | ||||
\(489\) | − | 229.564i | − | 0.469456i | ||||||
\(490\) | 388.628 | + | 38.2083i | 0.793118 | + | 0.0779761i | ||||
\(491\) | −31.9547 | −0.0650808 | −0.0325404 | − | 0.999470i | \(-0.510360\pi\) | ||||
−0.0325404 | + | 0.999470i | \(0.510360\pi\) | |||||||
\(492\) | −65.1848 | − | 65.1848i | −0.132489 | − | 0.132489i | ||||
\(493\) | −196.381 | + | 196.381i | −0.398338 | + | 0.398338i | ||||
\(494\) | − | 290.890i | − | 0.588846i | ||||||
\(495\) | −303.335 | + | 249.029i | −0.612799 | + | 0.503089i | ||||
\(496\) | −169.464 | −0.341662 | ||||||||
\(497\) | 744.358 | + | 744.358i | 1.49770 | + | 1.49770i | ||||
\(498\) | −34.5976 | + | 34.5976i | −0.0694731 | + | 0.0694731i | ||||
\(499\) | − | 138.737i | − | 0.278030i | −0.990290 | − | 0.139015i | \(-0.955606\pi\) | ||
0.990290 | − | 0.139015i | \(-0.0443936\pi\) | |||||||
\(500\) | 117.964 | + | 220.419i | 0.235928 | + | 0.440838i | ||||
\(501\) | −592.400 | −1.18243 | ||||||||
\(502\) | 326.776 | + | 326.776i | 0.650948 | + | 0.650948i | ||||
\(503\) | 159.071 | − | 159.071i | 0.316245 | − | 0.316245i | −0.531078 | − | 0.847323i | \(-0.678213\pi\) |
0.847323 | + | 0.531078i | \(0.178213\pi\) | |||||||
\(504\) | − | 153.002i | − | 0.303575i | ||||||
\(505\) | −335.471 | − | 408.627i | −0.664298 | − | 0.809163i | ||||
\(506\) | 100.472 | 0.198561 | ||||||||
\(507\) | −164.220 | − | 164.220i | −0.323906 | − | 0.323906i | ||||
\(508\) | 269.748 | − | 269.748i | 0.531001 | − | 0.531001i | ||||
\(509\) | − | 128.670i | − | 0.252790i | −0.991980 | − | 0.126395i | \(-0.959659\pi\) | ||
0.991980 | − | 0.126395i | \(-0.0403406\pi\) | |||||||
\(510\) | 33.5581 | − | 341.329i | 0.0658001 | − | 0.669272i | ||||
\(511\) | 600.602 | 1.17535 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 575.795 | − | 575.795i | 1.12241 | − | 1.12241i | ||||
\(514\) | − | 89.9188i | − | 0.174939i | ||||||
\(515\) | 108.529 | + | 10.6701i | 0.210736 | + | 0.0207187i | ||||
\(516\) | −2.28516 | −0.00442861 | ||||||||
\(517\) | −785.368 | − | 785.368i | −1.51909 | − | 1.51909i | ||||
\(518\) | −212.662 | + | 212.662i | −0.410545 | + | 0.410545i | ||||
\(519\) | − | 605.469i | − | 1.16661i | ||||||
\(520\) | −75.9529 | + | 62.3550i | −0.146063 | + | 0.119914i | ||||
\(521\) | 452.310 | 0.868157 | 0.434078 | − | 0.900875i | \(-0.357074\pi\) | ||||
0.434078 | + | 0.900875i | \(0.357074\pi\) | |||||||
\(522\) | 58.3689 | + | 58.3689i | 0.111818 | + | 0.111818i | ||||
\(523\) | 66.3514 | − | 66.3514i | 0.126867 | − | 0.126867i | −0.640822 | − | 0.767689i | \(-0.721406\pi\) |
0.767689 | + | 0.640822i | \(0.221406\pi\) | |||||||
\(524\) | − | 96.5848i | − | 0.184322i | ||||||
\(525\) | 95.6276 | − | 481.627i | 0.182148 | − | 0.917385i | ||||
\(526\) | 247.099 | 0.469771 | ||||||||
\(527\) | −755.266 | − | 755.266i | −1.43314 | − | 1.43314i | ||||
\(528\) | −80.6103 | + | 80.6103i | −0.152671 | + | 0.152671i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 370.409 | + | 451.184i | 0.698884 | + | 0.851291i | ||||
\(531\) | −72.9871 | −0.137452 | ||||||||
\(532\) | −427.375 | − | 427.375i | −0.803336 | − | 0.803336i | ||||
\(533\) | −117.718 | + | 117.718i | −0.220859 | + | 0.220859i | ||||
\(534\) | − | 385.576i | − | 0.722052i | ||||||
\(535\) | −26.2962 | + | 267.467i | −0.0491519 | + | 0.499938i | ||||
\(536\) | 67.6424 | 0.126198 | ||||||||
\(537\) | −263.996 | − | 263.996i | −0.491612 | − | 0.491612i | ||||
\(538\) | −237.309 | + | 237.309i | −0.441094 | + | 0.441094i | ||||
\(539\) | − | 818.093i | − | 1.51780i | ||||||
\(540\) | −273.770 | − | 26.9160i | −0.506982 | − | 0.0498444i | ||||
\(541\) | −598.507 | −1.10630 | −0.553148 | − | 0.833083i | \(-0.686574\pi\) | ||||
−0.553148 | + | 0.833083i | \(0.686574\pi\) | |||||||
\(542\) | 26.2193 | + | 26.2193i | 0.0483751 | + | 0.0483751i | ||||
\(543\) | 0.561565 | − | 0.561565i | 0.00103419 | − | 0.00103419i | ||||
\(544\) | 142.617i | 0.262164i | ||||||||
\(545\) | 564.904 | − | 463.769i | 1.03652 | − | 0.850953i | ||||
\(546\) | 193.014 | 0.353505 | ||||||||
\(547\) | 87.9130 | + | 87.9130i | 0.160718 | + | 0.160718i | 0.782885 | − | 0.622166i | \(-0.213747\pi\) |
−0.622166 | + | 0.782885i | \(0.713747\pi\) | |||||||
\(548\) | 6.58149 | − | 6.58149i | 0.0120100 | − | 0.0120100i | ||||
\(549\) | 206.752i | 0.376598i | ||||||||
\(550\) | 435.377 | − | 291.128i | 0.791594 | − | 0.529325i | ||||
\(551\) | 326.080 | 0.591797 | ||||||||
\(552\) | 18.4533 | + | 18.4533i | 0.0334299 | + | 0.0334299i | ||||
\(553\) | 1122.42 | − | 1122.42i | 2.02970 | − | 2.02970i | ||||
\(554\) | − | 450.960i | − | 0.814007i | ||||||
\(555\) | 127.147 | + | 154.874i | 0.229093 | + | 0.279052i | ||||
\(556\) | 217.883 | 0.391876 | ||||||||
\(557\) | 688.697 | + | 688.697i | 1.23644 | + | 1.23644i | 0.961446 | + | 0.274995i | \(0.0886762\pi\) |
0.274995 | + | 0.961446i | \(0.411324\pi\) | |||||||
\(558\) | −224.483 | + | 224.483i | −0.402299 | + | 0.402299i | ||||
\(559\) | 4.12680i | 0.00738246i | ||||||||
\(560\) | −19.9780 | + | 203.202i | −0.0356750 | + | 0.362860i | ||||
\(561\) | −718.525 | −1.28079 | ||||||||
\(562\) | −70.2491 | − | 70.2491i | −0.124998 | − | 0.124998i | ||||
\(563\) | 51.4275 | − | 51.4275i | 0.0913454 | − | 0.0913454i | −0.659958 | − | 0.751303i | \(-0.729426\pi\) |
0.751303 | + | 0.659958i | \(0.229426\pi\) | |||||||
\(564\) | − | 288.492i | − | 0.511511i | ||||||
\(565\) | −16.7971 | − | 1.65143i | −0.0297294 | − | 0.00292288i | ||||
\(566\) | 98.2430 | 0.173574 | ||||||||
\(567\) | 37.8025 | + | 37.8025i | 0.0666712 | + | 0.0666712i | ||||
\(568\) | −206.225 | + | 206.225i | −0.363071 | + | 0.363071i | ||||
\(569\) | 632.828i | 1.11218i | 0.831124 | + | 0.556088i | \(0.187698\pi\) | ||||
−0.831124 | + | 0.556088i | \(0.812302\pi\) | |||||||
\(570\) | −311.241 | + | 255.519i | −0.546036 | + | 0.448279i | ||||
\(571\) | 696.211 | 1.21928 | 0.609642 | − | 0.792677i | \(-0.291313\pi\) | ||||
0.609642 | + | 0.792677i | \(0.291313\pi\) | |||||||
\(572\) | 145.575 | + | 145.575i | 0.254501 | + | 0.254501i | ||||
\(573\) | 426.669 | − | 426.669i | 0.744623 | − | 0.744623i | ||||
\(574\) | 345.901i | 0.602615i | ||||||||
\(575\) | −66.6452 | − | 99.6665i | −0.115905 | − | 0.173333i | ||||
\(576\) | 42.3891 | 0.0735923 | ||||||||
\(577\) | −75.3419 | − | 75.3419i | −0.130575 | − | 0.130575i | 0.638799 | − | 0.769374i | \(-0.279432\pi\) |
−0.769374 | + | 0.638799i | \(0.779432\pi\) | |||||||
\(578\) | −346.613 | + | 346.613i | −0.599676 | + | 0.599676i | ||||
\(579\) | − | 32.5522i | − | 0.0562215i | ||||||
\(580\) | −69.8985 | − | 85.1413i | −0.120515 | − | 0.146795i | ||||
\(581\) | 183.591 | 0.315992 | ||||||||
\(582\) | 80.0943 | + | 80.0943i | 0.137619 | + | 0.137619i | ||||
\(583\) | 864.760 | − | 864.760i | 1.48329 | − | 1.48329i | ||||
\(584\) | 166.397i | 0.284926i | ||||||||
\(585\) | −18.0126 | + | 183.211i | −0.0307907 | + | 0.313181i | ||||
\(586\) | 739.808 | 1.26247 | ||||||||
\(587\) | 537.340 | + | 537.340i | 0.915401 | + | 0.915401i | 0.996691 | − | 0.0812898i | \(-0.0259039\pi\) |
−0.0812898 | + | 0.996691i | \(0.525904\pi\) | |||||||
\(588\) | 150.256 | − | 150.256i | 0.255538 | − | 0.255538i | ||||
\(589\) | 1254.08i | 2.12917i | ||||||||
\(590\) | 96.9343 | + | 9.53019i | 0.164295 | + | 0.0161529i | ||||
\(591\) | 157.076 | 0.265780 | ||||||||
\(592\) | −58.9181 | − | 58.9181i | −0.0995238 | − | 0.0995238i | ||||
\(593\) | −100.376 | + | 100.376i | −0.169268 | + | 0.169268i | −0.786657 | − | 0.617390i | \(-0.788190\pi\) |
0.617390 | + | 0.786657i | \(0.288190\pi\) | |||||||
\(594\) | 576.309i | 0.970217i | ||||||||
\(595\) | −994.663 | + | 816.589i | −1.67170 | + | 1.37242i | ||||
\(596\) | −137.754 | −0.231130 | ||||||||
\(597\) | −358.767 | − | 358.767i | −0.600949 | − | 0.600949i | ||||
\(598\) | 33.3250 | − | 33.3250i | 0.0557274 | − | 0.0557274i | ||||
\(599\) | − | 57.7918i | − | 0.0964805i | −0.998836 | − | 0.0482403i | \(-0.984639\pi\) | ||
0.998836 | − | 0.0482403i | \(-0.0153613\pi\) | |||||||
\(600\) | 133.435 | + | 26.4936i | 0.222392 | + | 0.0441561i | ||||
\(601\) | 855.388 | 1.42327 | 0.711637 | − | 0.702547i | \(-0.247954\pi\) | ||||
0.711637 | + | 0.702547i | \(0.247954\pi\) | |||||||
\(602\) | 6.06308 | + | 6.06308i | 0.0100716 | + | 0.0100716i | ||||
\(603\) | 89.6032 | − | 89.6032i | 0.148596 | − | 0.148596i | ||||
\(604\) | 276.798i | 0.458275i | ||||||||
\(605\) | −312.337 | − | 380.449i | −0.516259 | − | 0.628841i | ||||
\(606\) | −287.693 | −0.474741 | ||||||||
\(607\) | 171.294 | + | 171.294i | 0.282198 | + | 0.282198i | 0.833985 | − | 0.551787i | \(-0.186054\pi\) |
−0.551787 | + | 0.833985i | \(0.686054\pi\) | |||||||
\(608\) | 118.404 | − | 118.404i | 0.194744 | − | 0.194744i | ||||
\(609\) | 216.364i | 0.355277i | ||||||||
\(610\) | 26.9964 | − | 274.588i | 0.0442564 | − | 0.450144i | ||||
\(611\) | −520.990 | −0.852684 | ||||||||
\(612\) | 188.919 | + | 188.919i | 0.308691 | + | 0.308691i | ||||
\(613\) | −107.859 | + | 107.859i | −0.175952 | + | 0.175952i | −0.789589 | − | 0.613636i | \(-0.789706\pi\) |
0.613636 | + | 0.789589i | \(0.289706\pi\) | |||||||
\(614\) | 8.34078i | 0.0135843i | ||||||||
\(615\) | 229.357 | + | 22.5495i | 0.372938 | + | 0.0366658i | ||||
\(616\) | 427.756 | 0.694409 | ||||||||
\(617\) | 234.765 | + | 234.765i | 0.380495 | + | 0.380495i | 0.871280 | − | 0.490786i | \(-0.163290\pi\) |
−0.490786 | + | 0.871280i | \(0.663290\pi\) | |||||||
\(618\) | 41.9610 | − | 41.9610i | 0.0678981 | − | 0.0678981i | ||||
\(619\) | 35.0950i | 0.0566964i | 0.999598 | + | 0.0283482i | \(0.00902472\pi\) | ||||
−0.999598 | + | 0.0283482i | \(0.990975\pi\) | |||||||
\(620\) | 327.448 | − | 268.825i | 0.528142 | − | 0.433588i | ||||
\(621\) | 131.929 | 0.212446 | ||||||||
\(622\) | −385.664 | − | 385.664i | −0.620039 | − | 0.620039i | ||||
\(623\) | −1023.02 | + | 1023.02i | −1.64209 | + | 1.64209i | ||||
\(624\) | 53.4745i | 0.0856963i | ||||||||
\(625\) | −577.591 | − | 238.776i | −0.924145 | − | 0.382041i | ||||
\(626\) | −312.930 | −0.499888 | ||||||||
\(627\) | 596.538 | + | 596.538i | 0.951416 | + | 0.951416i | ||||
\(628\) | 270.574 | − | 270.574i | 0.430850 | − | 0.430850i | ||||
\(629\) | − | 525.170i | − | 0.834929i | ||||||
\(630\) | 242.709 | + | 295.637i | 0.385253 | + | 0.469266i | ||||
\(631\) | −826.767 | −1.31025 | −0.655124 | − | 0.755521i | \(-0.727384\pi\) | ||||
−0.655124 | + | 0.755521i | \(0.727384\pi\) | |||||||
\(632\) | 310.967 | + | 310.967i | 0.492037 | + | 0.492037i | ||||
\(633\) | −437.386 | + | 437.386i | −0.690974 | + | 0.690974i | ||||
\(634\) | − | 345.345i | − | 0.544708i | ||||||
\(635\) | −93.3144 | + | 949.128i | −0.146952 | + | 1.49469i | ||||
\(636\) | 317.655 | 0.499458 | ||||||||
\(637\) | −271.349 | − | 271.349i | −0.425980 | − | 0.425980i | ||||
\(638\) | −163.186 | + | 163.186i | −0.255777 | + | 0.255777i | ||||
\(639\) | 546.355i | 0.855016i | ||||||||
\(640\) | −56.2971 | − | 5.53490i | −0.0879642 | − | 0.00864829i | ||||
\(641\) | 52.1713 | 0.0813904 | 0.0406952 | − | 0.999172i | \(-0.487043\pi\) | ||||
0.0406952 | + | 0.999172i | \(0.487043\pi\) | |||||||
\(642\) | 103.412 | + | 103.412i | 0.161077 | + | 0.161077i | ||||
\(643\) | 241.431 | − | 241.431i | 0.375476 | − | 0.375476i | −0.493991 | − | 0.869467i | \(-0.664463\pi\) |
0.869467 | + | 0.493991i | \(0.164463\pi\) | |||||||
\(644\) | − | 97.9220i | − | 0.152053i | ||||||
\(645\) | 4.41551 | − | 3.62500i | 0.00684575 | − | 0.00562016i | ||||
\(646\) | 1055.40 | 1.63375 | ||||||||
\(647\) | −320.910 | − | 320.910i | −0.495998 | − | 0.495998i | 0.414192 | − | 0.910190i | \(-0.364064\pi\) |
−0.910190 | + | 0.414192i | \(0.864064\pi\) | |||||||
\(648\) | −10.4732 | + | 10.4732i | −0.0161624 | + | 0.0161624i | ||||
\(649\) | − | 204.055i | − | 0.314414i | ||||||
\(650\) | 47.8451 | − | 240.971i | 0.0736078 | − | 0.370725i | ||||
\(651\) | −832.119 | −1.27822 | ||||||||
\(652\) | −168.748 | − | 168.748i | −0.258816 | − | 0.258816i | ||||
\(653\) | 358.411 | − | 358.411i | 0.548869 | − | 0.548869i | −0.377245 | − | 0.926114i | \(-0.623128\pi\) |
0.926114 | + | 0.377245i | \(0.123128\pi\) | |||||||
\(654\) | − | 397.720i | − | 0.608134i | ||||||
\(655\) | 153.214 | + | 186.626i | 0.233915 | + | 0.284925i | ||||
\(656\) | −95.8320 | −0.146085 | ||||||||
\(657\) | 220.420 | + | 220.420i | 0.335494 | + | 0.335494i | ||||
\(658\) | −765.437 | + | 765.437i | −1.16328 | + | 1.16328i | ||||
\(659\) | − | 654.343i | − | 0.992934i | −0.868056 | − | 0.496467i | \(-0.834630\pi\) | ||
0.868056 | − | 0.496467i | \(-0.165370\pi\) | |||||||
\(660\) | 27.8856 | − | 283.633i | 0.0422510 | − | 0.429747i | ||||
\(661\) | 205.380 | 0.310711 | 0.155355 | − | 0.987859i | \(-0.450348\pi\) | ||||
0.155355 | + | 0.987859i | \(0.450348\pi\) | |||||||
\(662\) | 594.585 | + | 594.585i | 0.898165 | + | 0.898165i | ||||
\(663\) | −238.324 | + | 238.324i | −0.359463 | + | 0.359463i | ||||
\(664\) | 50.8640i | 0.0766024i | ||||||||
\(665\) | 1503.75 | + | 147.842i | 2.26128 | + | 0.222319i | ||||
\(666\) | −156.093 | −0.234374 | ||||||||
\(667\) | 37.3565 | + | 37.3565i | 0.0560067 | + | 0.0560067i | ||||
\(668\) | −435.461 | + | 435.461i | −0.651888 | + | 0.651888i | ||||
\(669\) | − | 206.699i | − | 0.308967i | ||||||
\(670\) | −130.702 | + | 107.302i | −0.195078 | + | 0.160153i | ||||
\(671\) | −578.030 | −0.861446 | ||||||||
\(672\) | 78.5646 | + | 78.5646i | 0.116912 | + | 0.116912i | ||||
\(673\) | −181.364 | + | 181.364i | −0.269486 | + | 0.269486i | −0.828893 | − | 0.559407i | \(-0.811029\pi\) |
0.559407 | + | 0.828893i | \(0.311029\pi\) | |||||||
\(674\) | − | 636.344i | − | 0.944130i | ||||||
\(675\) | 571.690 | − | 382.279i | 0.846949 | − | 0.566339i | ||||
\(676\) | −241.430 | −0.357145 | ||||||||
\(677\) | 49.6207 | + | 49.6207i | 0.0732950 | + | 0.0732950i | 0.742804 | − | 0.669509i | \(-0.233495\pi\) |
−0.669509 | + | 0.742804i | \(0.733495\pi\) | |||||||
\(678\) | −6.49433 | + | 6.49433i | −0.00957866 | + | 0.00957866i | ||||
\(679\) | − | 425.018i | − | 0.625947i | ||||||
\(680\) | −226.236 | − | 275.572i | −0.332700 | − | 0.405253i | ||||
\(681\) | 173.209 | 0.254345 | ||||||||
\(682\) | −627.601 | − | 627.601i | −0.920236 | − | 0.920236i | ||||
\(683\) | −665.906 | + | 665.906i | −0.974972 | + | 0.974972i | −0.999694 | − | 0.0247224i | \(-0.992130\pi\) |
0.0247224 | + | 0.999694i | \(0.492130\pi\) | |||||||
\(684\) | − | 313.691i | − | 0.458613i | ||||||
\(685\) | −2.27675 | + | 23.1574i | −0.00332372 | + | 0.0338065i | ||||
\(686\) | −89.8789 | −0.131019 | ||||||||
\(687\) | 140.333 | + | 140.333i | 0.204269 | + | 0.204269i | ||||
\(688\) | −1.67978 | + | 1.67978i | −0.00244154 | + | 0.00244154i | ||||
\(689\) | − | 573.656i | − | 0.832593i | ||||||
\(690\) | −64.9293 | − | 6.38358i | −0.0941004 | − | 0.00925157i | ||||
\(691\) | 868.900 | 1.25745 | 0.628727 | − | 0.777626i | \(-0.283576\pi\) | ||||
0.628727 | + | 0.777626i | \(0.283576\pi\) | |||||||
\(692\) | −445.068 | − | 445.068i | −0.643162 | − | 0.643162i | ||||
\(693\) | 566.632 | − | 566.632i | 0.817651 | − | 0.817651i | ||||
\(694\) | 323.697i | 0.466422i | ||||||||
\(695\) | −421.004 | + | 345.632i | −0.605761 | + | 0.497312i | ||||
\(696\) | −59.9436 | −0.0861258 | ||||||||
\(697\) | −427.102 | − | 427.102i | −0.612772 | − | 0.612772i | ||||
\(698\) | −66.1242 | + | 66.1242i | −0.0947339 | + | 0.0947339i | ||||
\(699\) | − | 576.272i | − | 0.824424i | ||||||
\(700\) | −283.740 | − | 424.328i | −0.405344 | − | 0.606183i | ||||
\(701\) | 769.630 | 1.09790 | 0.548952 | − | 0.835854i | \(-0.315027\pi\) | ||||
0.548952 | + | 0.835854i | \(0.315027\pi\) | |||||||
\(702\) | 191.153 | + | 191.153i | 0.272298 | + | 0.272298i | ||||
\(703\) | −436.010 | + | 436.010i | −0.620213 | + | 0.620213i | ||||
\(704\) | 118.510i | 0.168338i | ||||||||
\(705\) | 457.640 | + | 557.439i | 0.649135 | + | 0.790693i | ||||
\(706\) | 662.236 | 0.938012 | ||||||||
\(707\) | 763.318 | + | 763.318i | 1.07966 | + | 1.07966i | ||||
\(708\) | 37.4780 | − | 37.4780i | 0.0529351 | − | 0.0529351i | ||||
\(709\) | − | 1193.36i | − | 1.68316i | −0.540133 | − | 0.841580i | \(-0.681626\pi\) | ||
0.540133 | − | 0.841580i | \(-0.318374\pi\) | |||||||
\(710\) | 71.3396 | − | 725.615i | 0.100478 | − | 1.02199i | ||||
\(711\) | 823.853 | 1.15872 | ||||||||
\(712\) | −283.429 | − | 283.429i | −0.398075 | − | 0.398075i | ||||
\(713\) | −143.671 | + | 143.671i | −0.201501 | + | 0.201501i | ||||
\(714\) | 700.291i | 0.980799i | ||||||||
\(715\) | −512.215 | − | 50.3589i | −0.716384 | − | 0.0704320i | ||||
\(716\) | −388.116 | −0.542061 | ||||||||
\(717\) | 121.774 | + | 121.774i | 0.169839 | + | 0.169839i | ||||
\(718\) | −134.587 | + | 134.587i | −0.187447 | + | 0.187447i | ||||
\(719\) | − | 1266.00i | − | 1.76078i | −0.474252 | − | 0.880389i | \(-0.657281\pi\) | ||
0.474252 | − | 0.880389i | \(-0.342719\pi\) | |||||||
\(720\) | −81.9064 | + | 67.2427i | −0.113759 | + | 0.0933926i | ||||
\(721\) | −222.665 | −0.308828 | ||||||||
\(722\) | −515.224 | − | 515.224i | −0.713607 | − | 0.713607i | ||||
\(723\) | −238.511 | + | 238.511i | −0.329890 | + | 0.329890i | ||||
\(724\) | − | 0.825590i | − | 0.00114032i | ||||||
\(725\) | 270.123 | + | 53.6331i | 0.372583 | + | 0.0739768i | ||||
\(726\) | −267.854 | −0.368945 | ||||||||
\(727\) | −712.318 | − | 712.318i | −0.979805 | − | 0.979805i | 0.0199952 | − | 0.999800i | \(-0.493635\pi\) |
−0.999800 | + | 0.0199952i | \(0.993635\pi\) | |||||||
\(728\) | 141.880 | − | 141.880i | 0.194891 | − | 0.194891i | ||||
\(729\) | 504.066i | 0.691449i | ||||||||
\(730\) | −263.959 | − | 321.521i | −0.361587 | − | 0.440439i | ||||
\(731\) | −14.9728 | −0.0204826 | ||||||||
\(732\) | −106.165 | − | 106.165i | −0.145034 | − | 0.145034i | ||||
\(733\) | −785.498 | + | 785.498i | −1.07162 | + | 1.07162i | −0.0743915 | + | 0.997229i | \(0.523701\pi\) |
−0.997229 | + | 0.0743915i | \(0.976299\pi\) | |||||||
\(734\) | 903.320i | 1.23068i | ||||||||
\(735\) | −51.9784 | + | 528.688i | −0.0707190 | + | 0.719303i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 250.509 | + | 250.509i | 0.339904 | + | 0.339904i | ||||
\(738\) | −126.945 | + | 126.945i | −0.172012 | + | 0.172012i | ||||
\(739\) | 176.725i | 0.239141i | 0.992826 | + | 0.119570i | \(0.0381517\pi\) | ||||
−0.992826 | + | 0.119570i | \(0.961848\pi\) | |||||||
\(740\) | 207.307 | + | 20.3816i | 0.280145 | + | 0.0275427i | ||||
\(741\) | 395.726 | 0.534043 | ||||||||
\(742\) | −842.815 | − | 842.815i | −1.13587 | − | 1.13587i | ||||
\(743\) | −433.606 | + | 433.606i | −0.583588 | + | 0.583588i | −0.935887 | − | 0.352300i | \(-0.885400\pi\) |
0.352300 | + | 0.935887i | \(0.385400\pi\) | |||||||
\(744\) | − | 230.539i | − | 0.309864i | ||||||
\(745\) | 266.174 | − | 218.521i | 0.357281 | − | 0.293317i | ||||
\(746\) | 903.732 | 1.21144 | ||||||||
\(747\) | 67.3775 | + | 67.3775i | 0.0901975 | + | 0.0901975i | ||||
\(748\) | −528.173 | + | 528.173i | −0.706114 | + | 0.706114i | ||||
\(749\) | − | 548.751i | − | 0.732645i | ||||||
\(750\) | −299.857 | + | 160.478i | −0.399809 | + | 0.213971i | ||||
\(751\) | 197.940 | 0.263569 | 0.131785 | − | 0.991278i | \(-0.457929\pi\) | ||||
0.131785 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(752\) | −212.065 | − | 212.065i | −0.282001 | − | 0.282001i | ||||
\(753\) | −444.545 | + | 444.545i | −0.590365 | + | 0.590365i | ||||
\(754\) | 108.253i | 0.143571i | ||||||||
\(755\) | −439.090 | − | 534.843i | −0.581576 | − | 0.708401i | ||||
\(756\) | 561.684 | 0.742968 | ||||||||
\(757\) | −660.110 | − | 660.110i | −0.872008 | − | 0.872008i | 0.120683 | − | 0.992691i | \(-0.461491\pi\) |
−0.992691 | + | 0.120683i | \(0.961491\pi\) | |||||||
\(758\) | −230.954 | + | 230.954i | −0.304688 | + | 0.304688i | ||||
\(759\) | 136.681i | 0.180081i | ||||||||
\(760\) | −40.9598 | + | 416.614i | −0.0538944 | + | 0.548176i | ||||
\(761\) | 886.095 | 1.16438 | 0.582191 | − | 0.813052i | \(-0.302196\pi\) | ||||
0.582191 | + | 0.813052i | \(0.302196\pi\) | |||||||
\(762\) | 366.965 | + | 366.965i | 0.481581 | + | 0.481581i | ||||
\(763\) | −1055.24 | + | 1055.24i | −1.38302 | + | 1.38302i | ||||
\(764\) | − | 627.271i | − | 0.821036i | ||||||
\(765\) | −664.725 | − | 65.3531i | −0.868922 | − | 0.0854288i | ||||
\(766\) | 367.668 | 0.479985 | ||||||||
\(767\) | −67.6819 | − | 67.6819i | −0.0882424 | − | 0.0882424i | ||||
\(768\) | −21.7663 | + | 21.7663i | −0.0283416 | + | 0.0283416i | ||||
\(769\) | − | 666.097i | − | 0.866185i | −0.901349 | − | 0.433093i | \(-0.857422\pi\) | ||
0.901349 | − | 0.433093i | \(-0.142578\pi\) | |||||||
\(770\) | −826.532 | + | 678.558i | −1.07342 | + | 0.881244i | ||||
\(771\) | 122.325 | 0.158658 | ||||||||
\(772\) | −23.9285 | − | 23.9285i | −0.0309955 | − | 0.0309955i | ||||
\(773\) | 686.942 | − | 686.942i | 0.888670 | − | 0.888670i | −0.105725 | − | 0.994395i | \(-0.533716\pi\) |
0.994395 | + | 0.105725i | \(0.0337165\pi\) | |||||||
\(774\) | 4.45027i | 0.00574971i | ||||||||
\(775\) | −206.269 | + | 1038.87i | −0.266154 | + | 1.34048i | ||||
\(776\) | 117.751 | 0.151742 | ||||||||
\(777\) | −289.305 | − | 289.305i | −0.372336 | − | 0.372336i | ||||
\(778\) | 468.206 | − | 468.206i | 0.601808 | − | 0.601808i | ||||
\(779\) | 709.183i | 0.910376i | ||||||||
\(780\) | −84.8276 | − | 103.326i | −0.108753 | − | 0.132469i | ||||
\(781\) | −1527.48 | −1.95580 | ||||||||
\(782\) | 120.909 | + | 120.909i | 0.154616 | + | 0.154616i | ||||
\(783\) | −214.278 | + | 214.278i | −0.273663 | + | 0.273663i | ||||
\(784\) | − | 220.901i | − | 0.281761i | ||||||
\(785\) | −93.5999 | + | 952.032i | −0.119236 | + | 1.21278i | ||||
\(786\) | 131.394 | 0.167168 | ||||||||
\(787\) | −202.388 | − | 202.388i | −0.257164 | − | 0.257164i | 0.566736 | − | 0.823900i | \(-0.308206\pi\) |
−0.823900 | + | 0.566736i | \(0.808206\pi\) | |||||||
\(788\) | 115.463 | − | 115.463i | 0.146527 | − | 0.146527i | ||||
\(789\) | 336.153i | 0.426050i | ||||||||
\(790\) | −1094.16 | − | 107.573i | −1.38501 | − | 0.136169i | ||||
\(791\) | 34.4620 | 0.0435676 | ||||||||
\(792\) | 156.985 | + | 156.985i | 0.198214 | + | 0.198214i | ||||
\(793\) | −191.724 | + | 191.724i | −0.241771 | + | 0.241771i | ||||
\(794\) | 107.392i | 0.135255i | ||||||||
\(795\) | −613.790 | + | 503.903i | −0.772063 | + | 0.633840i | ||||
\(796\) | −527.445 | −0.662619 | ||||||||
\(797\) | 374.756 | + | 374.756i | 0.470208 | + | 0.470208i | 0.901982 | − | 0.431774i | \(-0.142112\pi\) |
−0.431774 | + | 0.901982i | \(0.642112\pi\) | |||||||
\(798\) | 581.399 | − | 581.399i | 0.728571 | − | 0.728571i | ||||
\(799\) | − | 1890.25i | − | 2.36577i | ||||||
\(800\) | 117.560 | − | 78.6104i | 0.146950 | − | 0.0982630i | ||||
\(801\) | −750.895 | −0.937447 | ||||||||
\(802\) | 248.645 | + | 248.645i | 0.310031 | + | 0.310031i | ||||
\(803\) | −616.241 | + | 616.241i | −0.767423 | + | 0.767423i | ||||
\(804\) | 92.0205i | 0.114453i | ||||||||
\(805\) | 155.336 | + | 189.210i | 0.192963 | + | 0.235043i | ||||
\(806\) | −416.332 | −0.516541 | ||||||||
\(807\) | −322.834 | − | 322.834i | −0.400042 | − | 0.400042i | ||||
\(808\) | −211.477 | + | 211.477i | −0.261729 | + | 0.261729i | ||||
\(809\) | 928.234i | 1.14738i | 0.819071 | + | 0.573692i | \(0.194490\pi\) | ||||
−0.819071 | + | 0.573692i | \(0.805510\pi\) | |||||||
\(810\) | 3.62301 | − | 36.8507i | 0.00447285 | − | 0.0454947i | ||||
\(811\) | −111.016 | −0.136888 | −0.0684440 | − | 0.997655i | \(-0.521803\pi\) | ||||
−0.0684440 | + | 0.997655i | \(0.521803\pi\) | |||||||
\(812\) | 159.044 | + | 159.044i | 0.195868 | + | 0.195868i | ||||
\(813\) | −35.6686 | + | 35.6686i | −0.0438729 | + | 0.0438729i | ||||
\(814\) | − | 436.399i | − | 0.536117i | ||||||
\(815\) | 593.751 | + | 58.3752i | 0.728529 | + | 0.0716261i | ||||
\(816\) | −194.016 | −0.237764 | ||||||||
\(817\) | 12.4308 | + | 12.4308i | 0.0152152 | + | 0.0152152i | ||||
\(818\) | −561.926 | + | 561.926i | −0.686952 | + | 0.686952i | ||||
\(819\) | − | 375.887i | − | 0.458958i | ||||||
\(820\) | 185.171 | − | 152.020i | 0.225819 | − | 0.185390i | ||||
\(821\) | −151.544 | −0.184585 | −0.0922923 | − | 0.995732i | \(-0.529419\pi\) | ||||
−0.0922923 | + | 0.995732i | \(0.529419\pi\) | |||||||
\(822\) | 8.95344 | + | 8.95344i | 0.0108923 | + | 0.0108923i | ||||
\(823\) | 720.489 | − | 720.489i | 0.875442 | − | 0.875442i | −0.117617 | − | 0.993059i | \(-0.537525\pi\) |
0.993059 | + | 0.117617i | \(0.0375255\pi\) | |||||||
\(824\) | − | 61.6894i | − | 0.0748658i | ||||||
\(825\) | 396.050 | + | 592.285i | 0.480061 | + | 0.717922i | ||||
\(826\) | −198.876 | −0.240770 | ||||||||
\(827\) | 449.514 | + | 449.514i | 0.543548 | + | 0.543548i | 0.924567 | − | 0.381019i | \(-0.124427\pi\) |
−0.381019 | + | 0.924567i | \(0.624427\pi\) | |||||||
\(828\) | 35.9371 | − | 35.9371i | 0.0434023 | − | 0.0434023i | ||||
\(829\) | − | 321.318i | − | 0.387598i | −0.981041 | − | 0.193799i | \(-0.937919\pi\) | ||
0.981041 | − | 0.193799i | \(-0.0620809\pi\) | |||||||
\(830\) | −80.6865 | − | 98.2819i | −0.0972126 | − | 0.118412i | ||||
\(831\) | 613.485 | 0.738249 | ||||||||
\(832\) | 39.3080 | + | 39.3080i | 0.0472452 | + | 0.0472452i | ||||
\(833\) | 984.507 | − | 984.507i | 1.18188 | − | 1.18188i | ||||
\(834\) | 296.407i | 0.355404i | ||||||||
\(835\) | 150.640 | − | 1532.20i | 0.180407 | − | 1.83497i | ||||
\(836\) | 877.006 | 1.04905 | ||||||||
\(837\) | −824.098 | − | 824.098i | −0.984586 | − | 0.984586i | ||||
\(838\) | 453.494 | − | 453.494i | 0.541163 | − | 0.541163i | ||||
\(839\) | − | 439.686i | − | 0.524060i | −0.965060 | − | 0.262030i | \(-0.915608\pi\) | ||
0.965060 | − | 0.262030i | \(-0.0843919\pi\) | |||||||
\(840\) | −276.435 | − | 27.1780i | −0.329089 | − | 0.0323547i | ||||
\(841\) | 719.652 | 0.855709 | ||||||||
\(842\) | −62.8563 | − | 62.8563i | −0.0746512 | − | 0.0746512i | ||||
\(843\) | 95.5667 | − | 95.5667i | 0.113365 | − | 0.113365i | ||||
\(844\) | 643.028i | 0.761881i | ||||||||
\(845\) | 466.503 | − | 382.985i | 0.552075 | − | 0.453237i | ||||
\(846\) | −561.827 | −0.664099 | ||||||||
\(847\) | 710.680 | + | 710.680i | 0.839056 | + | 0.839056i | ||||
\(848\) | 233.502 | − | 233.502i | 0.275356 | − | 0.275356i | ||||
\(849\) | 133.649i | 0.157420i | ||||||||
\(850\) | 874.289 | + | 173.591i | 1.02858 | + | 0.204225i | ||||
\(851\) | −99.9005 | −0.117392 | ||||||||
\(852\) | −280.547 | − | 280.547i | −0.329281 | − | 0.329281i | ||||
\(853\) | 649.971 | − | 649.971i | 0.761983 | − | 0.761983i | −0.214698 | − | 0.976681i | \(-0.568877\pi\) |
0.976681 | + | 0.214698i | \(0.0688767\pi\) | |||||||
\(854\) | 563.361i | 0.659674i | ||||||||
\(855\) | 497.614 | + | 606.130i | 0.582005 | + | 0.708924i | ||||
\(856\) | 152.032 | 0.177607 | ||||||||
\(857\) | −451.584 | − | 451.584i | −0.526935 | − | 0.526935i | 0.392722 | − | 0.919657i | \(-0.371533\pi\) |
−0.919657 | + | 0.392722i | \(0.871533\pi\) | |||||||
\(858\) | −198.039 | + | 198.039i | −0.230815 | + | 0.230815i | ||||
\(859\) | 1259.30i | 1.46601i | 0.680225 | + | 0.733003i | \(0.261882\pi\) | ||||
−0.680225 | + | 0.733003i | \(0.738118\pi\) | |||||||
\(860\) | 0.581088 | − | 5.91042i | 0.000675684 | − | 0.00687258i | ||||
\(861\) | −470.563 | −0.546530 | ||||||||
\(862\) | −175.877 | − | 175.877i | −0.204034 | − | 0.204034i | ||||
\(863\) | 267.447 | − | 267.447i | 0.309904 | − | 0.309904i | −0.534968 | − | 0.844872i | \(-0.679676\pi\) |
0.844872 | + | 0.534968i | \(0.179676\pi\) | |||||||
\(864\) | 155.615i | 0.180109i | ||||||||
\(865\) | 1566.00 | + | 153.963i | 1.81041 | + | 0.177992i | ||||
\(866\) | −685.864 | −0.791991 | ||||||||
\(867\) | −471.531 | − | 471.531i | −0.543865 | − | 0.543865i | ||||
\(868\) | −611.674 | + | 611.674i | −0.704694 | + | 0.704694i | ||||
\(869\) | 2303.30i | 2.65051i | ||||||||
\(870\) | 115.826 | − | 95.0896i | 0.133133 | − | 0.109298i | ||||
\(871\) | 166.180 | 0.190793 | ||||||||
\(872\) | −292.356 | − | 292.356i | −0.335270 | − | 0.335270i | ||||
\(873\) | 155.981 | − | 155.981i | 0.178672 | − | 0.178672i | ||||
\(874\) | − | 200.764i | − | 0.229707i | ||||||
\(875\) | 1221.38 | + | 369.806i | 1.39586 | + | 0.422635i | ||||
\(876\) | −226.366 | −0.258409 | ||||||||
\(877\) | −278.861 | − | 278.861i | −0.317972 | − | 0.317972i | 0.530016 | − | 0.847988i | \(-0.322186\pi\) |
−0.847988 | + | 0.530016i | \(0.822186\pi\) | |||||||
\(878\) | −55.4496 | + | 55.4496i | −0.0631544 | + | 0.0631544i | ||||
\(879\) | 1006.43i | 1.14497i | ||||||||
\(880\) | −187.995 | − | 228.991i | −0.213630 | − | 0.260217i | ||||
\(881\) | −1222.79 | −1.38796 | −0.693979 | − | 0.719995i | \(-0.744144\pi\) | ||||
−0.693979 | + | 0.719995i | \(0.744144\pi\) | |||||||
\(882\) | −292.619 | − | 292.619i | −0.331767 | − | 0.331767i | ||||
\(883\) | −160.195 | + | 160.195i | −0.181421 | + | 0.181421i | −0.791975 | − | 0.610554i | \(-0.790947\pi\) |
0.610554 | + | 0.791975i | \(0.290947\pi\) | |||||||
\(884\) | 350.374i | 0.396351i | ||||||||
\(885\) | −12.9648 | + | 131.869i | −0.0146495 | + | 0.149005i | ||||
\(886\) | −309.587 | −0.349420 | ||||||||
\(887\) | 982.564 | + | 982.564i | 1.10774 | + | 1.10774i | 0.993447 | + | 0.114291i | \(0.0364597\pi\) |
0.114291 | + | 0.993447i | \(0.463540\pi\) | |||||||
\(888\) | 80.1520 | − | 80.1520i | 0.0902612 | − | 0.0902612i | ||||
\(889\) | − | 1947.29i | − | 2.19043i | ||||||
\(890\) | 997.265 | + | 98.0470i | 1.12052 | + | 0.110165i | ||||
\(891\) | −77.5737 | −0.0870636 | ||||||||
\(892\) | −151.940 | − | 151.940i | −0.170337 | − | 0.170337i | ||||
\(893\) | −1569.34 | + | 1569.34i | −1.75737 | + | 1.75737i | ||||
\(894\) | − | 187.399i | − | 0.209619i | ||||||
\(895\) | 749.937 | − | 615.675i | 0.837918 | − | 0.687905i | ||||
\(896\) | 115.503 | 0.128909 | ||||||||
\(897\) | 45.3352 | + | 45.3352i | 0.0505409 | + | 0.0505409i | ||||
\(898\) | 658.321 | − | 658.321i | 0.733097 | − | 0.733097i | ||||
\(899\) | − | 466.698i | − | 0.519130i | ||||||
\(900\) | 51.5954 | − | 259.859i | 0.0573282 | − | 0.288733i | ||||
\(901\) | 2081.34 | 2.31003 | ||||||||
\(902\) | −354.908 | − | 354.908i | −0.393468 | − | 0.393468i | ||||
\(903\) | −8.24820 | + | 8.24820i | −0.00913421 | + | 0.00913421i | ||||
\(904\) | 9.54770i | 0.0105616i | ||||||||
\(905\) | 1.30965 | + | 1.59525i | 0.00144713 | + | 0.00176270i | ||||
\(906\) | −376.555 | −0.415623 | ||||||||
\(907\) | 290.205 | + | 290.205i | 0.319961 | + | 0.319961i | 0.848752 | − | 0.528791i | \(-0.177354\pi\) |
−0.528791 | + | 0.848752i | \(0.677354\pi\) | |||||||
\(908\) | 127.323 | − | 127.323i | 0.140223 | − | 0.140223i | ||||
\(909\) | 560.272i | 0.616360i | ||||||||
\(910\) | −49.0809 | + | 499.216i | −0.0539351 | + | 0.548589i | ||||
\(911\) | −1529.66 | −1.67910 | −0.839551 | − | 0.543280i | \(-0.817182\pi\) | ||||
−0.839551 | + | 0.543280i | \(0.817182\pi\) | |||||||
\(912\) | 161.077 | + | 161.077i | 0.176619 | + | 0.176619i | ||||
\(913\) | −188.372 | + | 188.372i | −0.206321 | + | 0.206321i | ||||
\(914\) | − | 1260.01i | − | 1.37857i | ||||||
\(915\) | 373.549 | + | 36.7258i | 0.408250 | + | 0.0401375i | ||||
\(916\) | 206.312 | 0.225231 | ||||||||
\(917\) | −348.618 | − | 348.618i | −0.380173 | − | 0.380173i | ||||
\(918\) | −693.540 | + | 693.540i | −0.755490 | + | 0.755490i | ||||
\(919\) | − | 44.0845i | − | 0.0479701i | −0.999712 | − | 0.0239850i | \(-0.992365\pi\) | ||
0.999712 | − | 0.0239850i | \(-0.00763540\pi\) | |||||||
\(920\) | −52.4206 | + | 43.0358i | −0.0569790 | + | 0.0467780i | ||||
\(921\) | −11.3468 | −0.0123201 | ||||||||
\(922\) | −635.738 | − | 635.738i | −0.689520 | − | 0.689520i | ||||
\(923\) | −506.642 | + | 506.642i | −0.548908 | + | 0.548908i | ||||
\(924\) | 581.918i | 0.629781i | ||||||||
\(925\) | −432.902 | + | 289.473i | −0.468002 | + | 0.312944i | ||||
\(926\) | −61.6216 | −0.0665460 | ||||||||
\(927\) | −81.7175 | − | 81.7175i | −0.0881526 | − | 0.0881526i | ||||
\(928\) | −44.0633 | + | 44.0633i | −0.0474820 | + | 0.0474820i | ||||
\(929\) | − | 973.596i | − | 1.04800i | −0.851717 | − | 0.524002i | \(-0.824438\pi\) | ||
0.851717 | − | 0.524002i | \(-0.175562\pi\) | |||||||
\(930\) | 365.708 | + | 445.459i | 0.393235 | + | 0.478988i | ||||
\(931\) | −1634.73 | −1.75588 | ||||||||
\(932\) | −423.606 | − | 423.606i | −0.454513 | − | 0.454513i | ||||
\(933\) | 524.657 | − | 524.657i | 0.562333 | − | 0.562333i | ||||
\(934\) | 547.873i | 0.586588i | ||||||||
\(935\) | 182.712 | − | 1858.41i | 0.195414 | − | 1.98761i | ||||
\(936\) | 104.140 | 0.111260 | ||||||||
\(937\) | 423.335 | + | 423.335i | 0.451798 | + | 0.451798i | 0.895951 | − | 0.444153i | \(-0.146495\pi\) |
−0.444153 | + | 0.895951i | \(0.646495\pi\) | |||||||
\(938\) | 244.152 | − | 244.152i | 0.260290 | − | 0.260290i | ||||
\(939\) | − | 425.708i | − | 0.453364i | ||||||
\(940\) | 746.164 | + | 73.3598i | 0.793792 | + | 0.0780424i | ||||
\(941\) | −1808.69 | −1.92210 | −0.961049 | − | 0.276377i | \(-0.910866\pi\) | ||||
−0.961049 | + | 0.276377i | \(0.910866\pi\) | |||||||
\(942\) | 368.087 | + | 368.087i | 0.390751 | + | 0.390751i | ||||
\(943\) | −81.2455 | + | 81.2455i | −0.0861564 | + | 0.0861564i | ||||
\(944\) | − | 55.0987i | − | 0.0583673i | ||||||
\(945\) | −1085.31 | + | 891.009i | −1.14848 | + | 0.942867i | ||||
\(946\) | −12.4419 | −0.0131521 | ||||||||
\(947\) | 964.707 | + | 964.707i | 1.01870 | + | 1.01870i | 0.999822 | + | 0.0188762i | \(0.00600883\pi\) |
0.0188762 | + | 0.999822i | \(0.493991\pi\) | |||||||
\(948\) | −423.039 | + | 423.039i | −0.446244 | + | 0.446244i | ||||
\(949\) | 408.796i | 0.430765i | ||||||||
\(950\) | −581.738 | − | 869.978i | −0.612356 | − | 0.915766i | ||||
\(951\) | 469.806 | 0.494012 | ||||||||
\(952\) | 514.769 | + | 514.769i | 0.540724 | + | 0.540724i | ||||
\(953\) | 713.688 | − | 713.688i | 0.748886 | − | 0.748886i | −0.225384 | − | 0.974270i | \(-0.572364\pi\) |
0.974270 | + | 0.225384i | \(0.0723638\pi\) | |||||||
\(954\) | − | 618.622i | − | 0.648451i | ||||||
\(955\) | 995.052 | + | 1212.05i | 1.04194 | + | 1.26916i | ||||
\(956\) | 179.028 | 0.187267 | ||||||||
\(957\) | −221.997 | − | 221.997i | −0.231972 | − | 0.231972i | ||||
\(958\) | −617.839 | + | 617.839i | −0.644926 | + | 0.644926i | ||||
\(959\) | − | 47.5112i | − | 0.0495424i | ||||||
\(960\) | 7.52966 | − | 76.5864i | 0.00784340 | − | 0.0797775i | ||||
\(961\) | 833.888 | 0.867730 | ||||||||
\(962\) | −144.747 | − | 144.747i | −0.150465 | − | 0.150465i | ||||
\(963\) | 201.390 | − | 201.390i | 0.209128 | − | 0.209128i | ||||
\(964\) | 350.649i | 0.363744i | ||||||||
\(965\) | 84.1941 | + | 8.27762i | 0.0872478 | + | 0.00857784i | ||||
\(966\) | 133.213 | 0.137901 | ||||||||
\(967\) | 448.530 | + | 448.530i | 0.463836 | + | 0.463836i | 0.899911 | − | 0.436074i | \(-0.143631\pi\) |
−0.436074 | + | 0.899911i | \(0.643631\pi\) | |||||||
\(968\) | −196.894 | + | 196.894i | −0.203403 | + | 0.203403i | ||||
\(969\) | 1435.77i | 1.48170i | ||||||||
\(970\) | −227.525 | + | 186.791i | −0.234562 | + | 0.192568i | ||||
\(971\) | 1066.76 | 1.09862 | 0.549311 | − | 0.835618i | \(-0.314890\pi\) | ||||
0.549311 | + | 0.835618i | \(0.314890\pi\) | |||||||
\(972\) | 335.885 | + | 335.885i | 0.345561 | + | 0.345561i | ||||
\(973\) | 786.438 | − | 786.438i | 0.808261 | − | 0.808261i | ||||
\(974\) | 365.268i | 0.375019i | ||||||||
\(975\) | 327.816 | + | 65.0883i | 0.336222 | + | 0.0667572i | ||||
\(976\) | −156.079 | −0.159917 | ||||||||
\(977\) | 526.975 | + | 526.975i | 0.539381 | + | 0.539381i | 0.923347 | − | 0.383966i | \(-0.125442\pi\) |
−0.383966 | + | 0.923347i | \(0.625442\pi\) | |||||||
\(978\) | 229.564 | − | 229.564i | 0.234728 | − | 0.234728i | ||||
\(979\) | − | 2099.32i | − | 2.14435i | ||||||
\(980\) | 350.419 | + | 426.836i | 0.357571 | + | 0.435547i | ||||
\(981\) | −774.544 | −0.789545 | ||||||||
\(982\) | −31.9547 | − | 31.9547i | −0.0325404 | − | 0.0325404i | ||||
\(983\) | −566.331 | + | 566.331i | −0.576125 | + | 0.576125i | −0.933833 | − | 0.357708i | \(-0.883558\pi\) |
0.357708 | + | 0.933833i | \(0.383558\pi\) | |||||||
\(984\) | − | 130.370i | − | 0.132489i | ||||||
\(985\) | −39.9424 | + | 406.266i | −0.0405507 | + | 0.412453i | ||||
\(986\) | −392.761 | −0.398338 | ||||||||
\(987\) | −1041.30 | − | 1041.30i | −1.05501 | − | 1.05501i | ||||
\(988\) | 290.890 | − | 290.890i | 0.294423 | − | 0.294423i | ||||
\(989\) | 2.84820i | 0.00287988i | ||||||||
\(990\) | −552.364 | − | 54.3062i | −0.557944 | − | 0.0548548i | ||||
\(991\) | 71.4593 | 0.0721083 | 0.0360541 | − | 0.999350i | \(-0.488521\pi\) | ||||
0.0360541 | + | 0.999350i | \(0.488521\pi\) | |||||||
\(992\) | −169.464 | − | 169.464i | −0.170831 | − | 0.170831i | ||||
\(993\) | −808.871 | + | 808.871i | −0.814573 | + | 0.814573i | ||||
\(994\) | 1488.72i | 1.49770i | ||||||||
\(995\) | 1019.15 | − | 836.695i | 1.02428 | − | 0.840900i | ||||
\(996\) | −69.1952 | −0.0694731 | ||||||||
\(997\) | 694.965 | + | 694.965i | 0.697056 | + | 0.697056i | 0.963775 | − | 0.266718i | \(-0.0859393\pi\) |
−0.266718 | + | 0.963775i | \(0.585939\pi\) | |||||||
\(998\) | 138.737 | − | 138.737i | 0.139015 | − | 0.139015i | ||||
\(999\) | − | 573.032i | − | 0.573606i |
(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 | 230.3.f.b.47.4 | ✓ | 24 | |
5.3 | odd | 4 | inner | 230.3.f.b.93.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.b.47.4 | ✓ | 24 | 1.1 | even | 1 | trivial | |
230.3.f.b.93.4 | yes | 24 | 5.3 | odd | 4 | inner |