Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,3,Mod(116,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.116");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.h (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.00545988610\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.39033114624.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 6x^{6} - 30x^{5} + 34x^{4} - 102x^{3} + 486x^{2} - 730x + 373 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 128.1 | ||
Root | \(-0.279898 + 3.02113i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.128 |
Dual form | 147.3.h.c.116.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.03622 | − | 1.75296i | −1.51811 | − | 0.876481i | −0.999773 | − | 0.0213043i | \(-0.993218\pi\) |
−0.518337 | − | 0.855177i | \(-0.673449\pi\) | |||||||
\(3\) | 2.90987 | − | 0.729839i | 0.969956 | − | 0.243280i | ||||
\(4\) | 4.14575 | + | 7.18065i | 1.03644 | + | 1.79516i | ||||
\(5\) | −1.07558 | − | 0.620984i | −0.215115 | − | 0.124197i | 0.388571 | − | 0.921419i | \(-0.372969\pi\) |
−0.603686 | + | 0.797222i | \(0.706302\pi\) | |||||||
\(6\) | −10.1144 | − | 2.88494i | −1.68573 | − | 0.480823i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 15.0457i | − | 1.88071i | ||||||
\(9\) | 7.93467 | − | 4.24747i | 0.881630 | − | 0.471941i | ||||
\(10\) | 2.17712 | + | 3.77089i | 0.217712 | + | 0.377089i | ||||
\(11\) | 6.07244 | − | 3.50592i | 0.552040 | − | 0.318720i | −0.197904 | − | 0.980221i | \(-0.563414\pi\) |
0.749944 | + | 0.661501i | \(0.230080\pi\) | |||||||
\(12\) | 17.3043 | + | 17.8690i | 1.44203 | + | 1.48909i | ||||
\(13\) | 11.6458 | 0.895827 | 0.447914 | − | 0.894077i | \(-0.352167\pi\) | ||||
0.447914 | + | 0.894077i | \(0.352167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.58301 | − | 1.02199i | −0.238867 | − | 0.0681324i | ||||
\(16\) | −9.79150 | + | 16.9594i | −0.611969 | + | 1.05996i | ||||
\(17\) | 3.92129 | − | 2.26395i | 0.230664 | − | 0.133174i | −0.380214 | − | 0.924898i | \(-0.624150\pi\) |
0.610878 | + | 0.791725i | \(0.290816\pi\) | |||||||
\(18\) | −31.5371 | − | 1.01293i | −1.75206 | − | 0.0562740i | ||||
\(19\) | 8.11438 | − | 14.0545i | 0.427073 | − | 0.739711i | −0.569539 | − | 0.821964i | \(-0.692878\pi\) |
0.996611 | + | 0.0822530i | \(0.0262116\pi\) | |||||||
\(20\) | − | 10.2978i | − | 0.514889i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.5830 | −1.11741 | ||||||||
\(23\) | −22.1386 | − | 12.7817i | −0.962548 | − | 0.555727i | −0.0655916 | − | 0.997847i | \(-0.520893\pi\) |
−0.896956 | + | 0.442119i | \(0.854227\pi\) | |||||||
\(24\) | −10.9809 | − | 43.7810i | −0.457538 | − | 1.82421i | ||||
\(25\) | −11.7288 | − | 20.3148i | −0.469150 | − | 0.812592i | ||||
\(26\) | −35.3591 | − | 20.4146i | −1.35996 | − | 0.785175i | ||||
\(27\) | 19.9889 | − | 18.1506i | 0.740329 | − | 0.672245i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.49579i | − | 0.327441i | −0.986507 | − | 0.163720i | \(-0.947650\pi\) | ||
0.986507 | − | 0.163720i | \(-0.0523495\pi\) | |||||||
\(30\) | 9.08729 | + | 9.38385i | 0.302910 | + | 0.312795i | ||||
\(31\) | 14.3542 | + | 24.8623i | 0.463040 | + | 0.802009i | 0.999111 | − | 0.0421640i | \(-0.0134252\pi\) |
−0.536070 | + | 0.844173i | \(0.680092\pi\) | |||||||
\(32\) | 7.33853 | − | 4.23690i | 0.229329 | − | 0.132403i | ||||
\(33\) | 15.1112 | − | 14.6337i | 0.457916 | − | 0.443445i | ||||
\(34\) | −15.8745 | −0.466897 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 63.3948 | + | 39.3672i | 1.76097 | + | 1.09353i | ||||
\(37\) | 16.5203 | − | 28.6139i | 0.446493 | − | 0.773349i | −0.551661 | − | 0.834068i | \(-0.686006\pi\) |
0.998155 | + | 0.0607187i | \(0.0193393\pi\) | |||||||
\(38\) | −49.2741 | + | 28.4484i | −1.29669 | + | 0.748642i | ||||
\(39\) | 33.8876 | − | 8.49952i | 0.868913 | − | 0.217936i | ||||
\(40\) | −9.34313 | + | 16.1828i | −0.233578 | + | 0.404570i | ||||
\(41\) | 67.1946i | 1.63889i | 0.573156 | + | 0.819446i | \(0.305719\pi\) | ||||
−0.573156 | + | 0.819446i | \(0.694281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −24.1255 | −0.561058 | −0.280529 | − | 0.959846i | \(-0.590510\pi\) | ||||
−0.280529 | + | 0.959846i | \(0.590510\pi\) | |||||||
\(44\) | 50.3496 | + | 29.0694i | 1.14431 | + | 0.660668i | ||||
\(45\) | −11.1720 | − | 0.358830i | −0.248266 | − | 0.00797400i | ||||
\(46\) | 44.8118 | + | 77.6162i | 0.974169 | + | 1.68731i | ||||
\(47\) | 28.5921 | + | 16.5076i | 0.608342 | + | 0.351226i | 0.772316 | − | 0.635238i | \(-0.219098\pi\) |
−0.163974 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(48\) | −16.1144 | + | 56.4958i | −0.335716 | + | 1.17700i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 82.2403i | 1.64481i | ||||||||
\(51\) | 9.75810 | − | 9.44972i | 0.191335 | − | 0.185289i | ||||
\(52\) | 48.2804 | + | 83.6241i | 0.928469 | + | 1.60816i | ||||
\(53\) | 13.1530 | − | 7.59387i | 0.248169 | − | 0.143281i | −0.370756 | − | 0.928730i | \(-0.620902\pi\) |
0.618926 | + | 0.785450i | \(0.287568\pi\) | |||||||
\(54\) | −92.5080 | + | 20.0695i | −1.71311 | + | 0.371657i | ||||
\(55\) | −8.70850 | −0.158336 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.3542 | − | 46.8190i | 0.234285 | − | 0.821386i | ||||
\(58\) | −16.6458 | + | 28.8313i | −0.286996 | + | 0.497091i | ||||
\(59\) | 80.0173 | − | 46.1980i | 1.35623 | − | 0.783017i | 0.367112 | − | 0.930177i | \(-0.380346\pi\) |
0.989113 | + | 0.147160i | \(0.0470131\pi\) | |||||||
\(60\) | −7.51572 | − | 29.9652i | −0.125262 | − | 0.499420i | ||||
\(61\) | −28.7601 | + | 49.8140i | −0.471478 | + | 0.816623i | −0.999468 | − | 0.0326275i | \(-0.989612\pi\) |
0.527990 | + | 0.849251i | \(0.322946\pi\) | |||||||
\(62\) | − | 100.650i | − | 1.62338i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 48.6235 | 0.759743 | ||||||||
\(65\) | −12.5259 | − | 7.23183i | −0.192706 | − | 0.111259i | ||||
\(66\) | −71.5333 | + | 17.9416i | −1.08384 | + | 0.271843i | ||||
\(67\) | −7.58301 | − | 13.1342i | −0.113179 | − | 0.196032i | 0.803871 | − | 0.594803i | \(-0.202770\pi\) |
−0.917050 | + | 0.398771i | \(0.869437\pi\) | |||||||
\(68\) | 32.5133 | + | 18.7716i | 0.478137 | + | 0.276053i | ||||
\(69\) | −73.7490 | − | 21.0355i | −1.06883 | − | 0.304863i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70.5584i | 0.993781i | 0.867813 | + | 0.496890i | \(0.165525\pi\) | ||||
−0.867813 | + | 0.496890i | \(0.834475\pi\) | |||||||
\(72\) | −63.9061 | − | 119.383i | −0.887584 | − | 1.65809i | ||||
\(73\) | −38.3948 | − | 66.5017i | −0.525956 | − | 0.910982i | −0.999543 | − | 0.0302350i | \(-0.990374\pi\) |
0.473587 | − | 0.880747i | \(-0.342959\pi\) | |||||||
\(74\) | −100.318 | + | 57.9188i | −1.35565 | + | 0.782686i | ||||
\(75\) | −48.9557 | − | 50.5533i | −0.652742 | − | 0.674044i | ||||
\(76\) | 134.561 | 1.77054 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −117.790 | − | 33.5973i | −1.51012 | − | 0.430734i | ||||
\(79\) | −63.6235 | + | 110.199i | −0.805361 | + | 1.39493i | 0.110686 | + | 0.993855i | \(0.464695\pi\) |
−0.916047 | + | 0.401071i | \(0.868638\pi\) | |||||||
\(80\) | 21.0630 | − | 12.1607i | 0.263288 | − | 0.152009i | ||||
\(81\) | 44.9180 | − | 67.4045i | 0.554544 | − | 0.832155i | ||||
\(82\) | 117.790 | − | 204.017i | 1.43646 | − | 2.48802i | ||||
\(83\) | 74.2844i | 0.894992i | 0.894286 | + | 0.447496i | \(0.147684\pi\) | ||||
−0.894286 | + | 0.447496i | \(0.852316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.62352 | −0.0661591 | ||||||||
\(86\) | 73.2503 | + | 42.2911i | 0.851747 | + | 0.491757i | ||||
\(87\) | −6.93039 | − | 27.6315i | −0.0796597 | − | 0.317603i | ||||
\(88\) | −52.7490 | − | 91.3640i | −0.599421 | − | 1.03823i | ||||
\(89\) | 110.312 | + | 63.6887i | 1.23946 | + | 0.715603i | 0.968984 | − | 0.247124i | \(-0.0794854\pi\) |
0.270477 | + | 0.962727i | \(0.412819\pi\) | |||||||
\(90\) | 33.2915 | + | 20.6735i | 0.369906 | + | 0.229706i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 211.959i | − | 2.30391i | ||||||
\(93\) | 59.9144 | + | 61.8697i | 0.644241 | + | 0.665266i | ||||
\(94\) | −57.8745 | − | 100.242i | −0.615686 | − | 1.06640i | ||||
\(95\) | −17.4553 | + | 10.0778i | −0.183740 | + | 0.106082i | ||||
\(96\) | 18.2619 | − | 17.6848i | 0.190228 | − | 0.184216i | ||||
\(97\) | 23.1660 | 0.238825 | 0.119412 | − | 0.992845i | \(-0.461899\pi\) | ||||
0.119412 | + | 0.992845i | \(0.461899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33.2915 | − | 53.6108i | 0.336278 | − | 0.541524i | ||||
\(100\) | 97.2490 | − | 168.440i | 0.972490 | − | 1.68440i | ||||
\(101\) | −116.833 | + | 67.4535i | −1.15676 | + | 0.667857i | −0.950526 | − | 0.310646i | \(-0.899455\pi\) |
−0.206236 | + | 0.978502i | \(0.566121\pi\) | |||||||
\(102\) | −46.1927 | + | 11.5858i | −0.452870 | + | 0.113587i | ||||
\(103\) | −59.8745 | + | 103.706i | −0.581306 | + | 1.00685i | 0.414019 | + | 0.910268i | \(0.364125\pi\) |
−0.995325 | + | 0.0965831i | \(0.969209\pi\) | |||||||
\(104\) | − | 175.218i | − | 1.68479i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −53.2470 | −0.502331 | ||||||||
\(107\) | −67.4239 | − | 38.9272i | −0.630130 | − | 0.363806i | 0.150673 | − | 0.988584i | \(-0.451856\pi\) |
−0.780802 | + | 0.624778i | \(0.785189\pi\) | |||||||
\(108\) | 213.202 | + | 68.2853i | 1.97409 | + | 0.632272i | ||||
\(109\) | 18.2693 | + | 31.6433i | 0.167608 | + | 0.290306i | 0.937578 | − | 0.347774i | \(-0.113062\pi\) |
−0.769970 | + | 0.638080i | \(0.779729\pi\) | |||||||
\(110\) | 26.4409 | + | 15.2657i | 0.240372 | + | 0.138779i | ||||
\(111\) | 27.1882 | − | 95.3199i | 0.244939 | − | 0.858738i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 21.7596i | − | 0.192563i | −0.995354 | − | 0.0962815i | \(-0.969305\pi\) | ||
0.995354 | − | 0.0962815i | \(-0.0306949\pi\) | |||||||
\(114\) | −122.618 | + | 118.743i | −1.07560 | + | 1.04161i | ||||
\(115\) | 15.8745 | + | 27.4955i | 0.138039 | + | 0.239091i | ||||
\(116\) | 68.1859 | − | 39.3672i | 0.587810 | − | 0.339372i | ||||
\(117\) | 92.4052 | − | 49.4650i | 0.789788 | − | 0.422777i | ||||
\(118\) | −323.933 | −2.74520 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −15.3765 | + | 53.9088i | −0.128137 | + | 0.449240i | ||||
\(121\) | −35.9170 | + | 62.2101i | −0.296835 | + | 0.514133i | ||||
\(122\) | 174.644 | − | 100.831i | 1.43151 | − | 0.826482i | ||||
\(123\) | 49.0412 | + | 195.527i | 0.398709 | + | 1.58965i | ||||
\(124\) | −119.018 | + | 206.146i | −0.959825 | + | 1.66247i | ||||
\(125\) | 60.1827i | 0.481462i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4170 | −0.121394 | −0.0606968 | − | 0.998156i | \(-0.519332\pi\) | ||||
−0.0606968 | + | 0.998156i | \(0.519332\pi\) | |||||||
\(128\) | −176.986 | − | 102.183i | −1.38270 | − | 0.798303i | ||||
\(129\) | −70.2020 | + | 17.6077i | −0.544202 | + | 0.136494i | ||||
\(130\) | 25.3542 | + | 43.9148i | 0.195033 | + | 0.337807i | ||||
\(131\) | −158.578 | − | 91.5550i | −1.21052 | − | 0.698893i | −0.247646 | − | 0.968850i | \(-0.579657\pi\) |
−0.962872 | + | 0.269957i | \(0.912990\pi\) | |||||||
\(132\) | 167.727 | + | 47.8410i | 1.27066 | + | 0.362432i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 53.1709i | 0.396798i | ||||||||
\(135\) | −32.7708 | + | 7.10958i | −0.242747 | + | 0.0526635i | ||||
\(136\) | −34.0627 | − | 58.9984i | −0.250461 | − | 0.433812i | ||||
\(137\) | −28.5921 | + | 16.5076i | −0.208701 | + | 0.120494i | −0.600708 | − | 0.799469i | \(-0.705114\pi\) |
0.392006 | + | 0.919962i | \(0.371781\pi\) | |||||||
\(138\) | 187.044 | + | 193.148i | 1.35539 | + | 1.39962i | ||||
\(139\) | −64.6418 | −0.465049 | −0.232525 | − | 0.972591i | \(-0.574699\pi\) | ||||
−0.232525 | + | 0.972591i | \(0.574699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 95.2470 | + | 27.1675i | 0.675511 | + | 0.192677i | ||||
\(142\) | 123.686 | − | 214.231i | 0.871030 | − | 1.50867i | ||||
\(143\) | 70.7181 | − | 40.8291i | 0.494532 | − | 0.285518i | ||||
\(144\) | −5.65793 | + | 176.156i | −0.0392912 | + | 1.22331i | ||||
\(145\) | −5.89674 | + | 10.2134i | −0.0406671 | + | 0.0704376i | ||||
\(146\) | 269.218i | 1.84396i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 273.956 | 1.85105 | ||||||||
\(149\) | 169.512 | + | 97.8680i | 1.13767 | + | 0.656832i | 0.945852 | − | 0.324599i | \(-0.105229\pi\) |
0.191815 | + | 0.981431i | \(0.438563\pi\) | |||||||
\(150\) | 60.0221 | + | 239.308i | 0.400147 | + | 1.59539i | ||||
\(151\) | −51.1255 | − | 88.5519i | −0.338579 | − | 0.586437i | 0.645586 | − | 0.763687i | \(-0.276613\pi\) |
−0.984166 | + | 0.177251i | \(0.943280\pi\) | |||||||
\(152\) | −211.460 | − | 122.086i | −1.39118 | − | 0.803200i | ||||
\(153\) | 21.4980 | − | 34.6193i | 0.140510 | − | 0.226270i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 35.6551i | − | 0.230033i | ||||||
\(156\) | 201.522 | + | 208.098i | 1.29181 | + | 1.33396i | ||||
\(157\) | 52.3614 | + | 90.6926i | 0.333512 | + | 0.577660i | 0.983198 | − | 0.182543i | \(-0.0584328\pi\) |
−0.649686 | + | 0.760203i | \(0.725099\pi\) | |||||||
\(158\) | 386.350 | − | 223.059i | 2.44525 | − | 1.41177i | ||||
\(159\) | 32.7311 | − | 31.6967i | 0.205856 | − | 0.199350i | ||||
\(160\) | −10.5242 | −0.0657762 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −254.539 | + | 125.915i | −1.57123 | + | 0.777255i | ||||
\(163\) | 35.4797 | − | 61.4527i | 0.217667 | − | 0.377011i | −0.736427 | − | 0.676517i | \(-0.763489\pi\) |
0.954094 | + | 0.299506i | \(0.0968220\pi\) | |||||||
\(164\) | −482.501 | + | 278.572i | −2.94208 | + | 1.69861i | ||||
\(165\) | −25.3406 | + | 6.35580i | −0.153579 | + | 0.0385200i | ||||
\(166\) | 130.218 | − | 225.544i | 0.784444 | − | 1.35870i | ||||
\(167\) | − | 206.992i | − | 1.23947i | −0.784811 | − | 0.619735i | \(-0.787240\pi\) | ||
0.784811 | − | 0.619735i | \(-0.212760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33.3765 | −0.197494 | ||||||||
\(170\) | 17.0743 | + | 9.85782i | 0.100437 | + | 0.0579872i | ||||
\(171\) | 4.68882 | − | 145.984i | 0.0274200 | − | 0.853705i | ||||
\(172\) | −100.018 | − | 173.237i | −0.581502 | − | 1.00719i | ||||
\(173\) | −93.9323 | − | 54.2318i | −0.542961 | − | 0.313479i | 0.203317 | − | 0.979113i | \(-0.434828\pi\) |
−0.746278 | + | 0.665634i | \(0.768161\pi\) | |||||||
\(174\) | −27.3948 | + | 96.0440i | −0.157441 | + | 0.551977i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 137.313i | 0.780188i | ||||||||
\(177\) | 199.123 | − | 192.830i | 1.12499 | − | 1.08943i | ||||
\(178\) | −223.288 | − | 386.745i | −1.25442 | − | 2.17273i | ||||
\(179\) | −138.007 | + | 79.6784i | −0.770989 | + | 0.445131i | −0.833227 | − | 0.552931i | \(-0.813509\pi\) |
0.0622383 | + | 0.998061i | \(0.480176\pi\) | |||||||
\(180\) | −43.7395 | − | 81.7096i | −0.242997 | − | 0.453942i | ||||
\(181\) | 233.889 | 1.29220 | 0.646102 | − | 0.763251i | \(-0.276398\pi\) | ||||
0.646102 | + | 0.763251i | \(0.276398\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −47.3320 | + | 165.942i | −0.258645 | + | 0.906789i | ||||
\(184\) | −192.310 | + | 333.090i | −1.04516 | + | 1.81027i | ||||
\(185\) | −35.5376 | + | 20.5176i | −0.192095 | + | 0.110906i | ||||
\(186\) | −73.4581 | − | 292.878i | −0.394936 | − | 1.57461i | ||||
\(187\) | 15.8745 | − | 27.4955i | 0.0848904 | − | 0.147035i | ||||
\(188\) | 273.746i | 1.45610i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 70.6640 | 0.371916 | ||||||||
\(191\) | −249.597 | − | 144.105i | −1.30679 | − | 0.754476i | −0.325232 | − | 0.945634i | \(-0.605442\pi\) |
−0.981559 | + | 0.191158i | \(0.938776\pi\) | |||||||
\(192\) | 141.488 | − | 35.4873i | 0.736917 | − | 0.184830i | ||||
\(193\) | −38.5608 | − | 66.7892i | −0.199797 | − | 0.346058i | 0.748666 | − | 0.662948i | \(-0.230695\pi\) |
−0.948462 | + | 0.316890i | \(0.897362\pi\) | |||||||
\(194\) | −70.3371 | − | 40.6091i | −0.362562 | − | 0.209325i | ||||
\(195\) | −41.7268 | − | 11.9018i | −0.213984 | − | 0.0610348i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 136.433i | 0.692554i | 0.938132 | + | 0.346277i | \(0.112554\pi\) | ||||
−0.938132 | + | 0.346277i | \(0.887446\pi\) | |||||||
\(198\) | −195.058 | + | 104.416i | −0.985142 | + | 0.527351i | ||||
\(199\) | 43.2915 | + | 74.9831i | 0.217545 | + | 0.376799i | 0.954057 | − | 0.299625i | \(-0.0968617\pi\) |
−0.736512 | + | 0.676425i | \(0.763528\pi\) | |||||||
\(200\) | −305.650 | + | 176.467i | −1.52825 | + | 0.882336i | ||||
\(201\) | −31.6514 | − | 32.6843i | −0.157469 | − | 0.162608i | ||||
\(202\) | 472.974 | 2.34145 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 108.310 | + | 30.8934i | 0.530930 | + | 0.151438i | ||||
\(205\) | 41.7268 | − | 72.2729i | 0.203545 | − | 0.352551i | ||||
\(206\) | 363.584 | − | 209.915i | 1.76497 | − | 1.01901i | ||||
\(207\) | −229.953 | − | 7.38580i | −1.11088 | − | 0.0356802i | ||||
\(208\) | −114.029 | + | 197.505i | −0.548218 | + | 0.949542i | ||||
\(209\) | − | 113.794i | − | 0.544467i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4170 | 0.0920237 | 0.0460118 | − | 0.998941i | \(-0.485349\pi\) | ||||
0.0460118 | + | 0.998941i | \(0.485349\pi\) | |||||||
\(212\) | 109.058 | + | 62.9646i | 0.514424 | + | 0.297003i | ||||
\(213\) | 51.4963 | + | 205.316i | 0.241767 | + | 0.963924i | ||||
\(214\) | 136.476 | + | 236.383i | 0.637737 | + | 1.10459i | ||||
\(215\) | 25.9488 | + | 14.9816i | 0.120692 | + | 0.0696817i | ||||
\(216\) | −273.088 | − | 300.746i | −1.26430 | − | 1.39234i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 128.101i | − | 0.587621i | ||||||
\(219\) | −160.259 | − | 165.489i | −0.731777 | − | 0.755658i | ||||
\(220\) | −36.1033 | − | 62.5327i | −0.164106 | − | 0.284239i | ||||
\(221\) | 45.6663 | − | 26.3655i | 0.206635 | − | 0.119301i | ||||
\(222\) | −249.642 | + | 241.752i | −1.12451 | + | 1.08897i | ||||
\(223\) | −175.041 | −0.784935 | −0.392468 | − | 0.919766i | \(-0.628378\pi\) | ||||
−0.392468 | + | 0.919766i | \(0.628378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −179.350 | − | 111.374i | −0.797112 | − | 0.494994i | ||||
\(226\) | −38.1438 | + | 66.0670i | −0.168778 | + | 0.292332i | ||||
\(227\) | −153.784 | + | 88.7870i | −0.677461 | + | 0.391132i | −0.798898 | − | 0.601467i | \(-0.794583\pi\) |
0.121437 | + | 0.992599i | \(0.461250\pi\) | |||||||
\(228\) | 391.554 | − | 98.2076i | 1.71734 | − | 0.430735i | ||||
\(229\) | 20.4059 | − | 35.3440i | 0.0891087 | − | 0.154341i | −0.818026 | − | 0.575181i | \(-0.804931\pi\) |
0.907135 | + | 0.420841i | \(0.138265\pi\) | |||||||
\(230\) | − | 111.310i | − | 0.483955i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −142.871 | −0.615821 | ||||||||
\(233\) | 335.754 | + | 193.848i | 1.44101 | + | 0.831965i | 0.997917 | − | 0.0645131i | \(-0.0205494\pi\) |
0.443088 | + | 0.896478i | \(0.353883\pi\) | |||||||
\(234\) | −367.273 | − | 11.7964i | −1.56954 | − | 0.0504118i | ||||
\(235\) | −20.5020 | − | 35.5105i | −0.0872424 | − | 0.151108i | ||||
\(236\) | 663.463 | + | 383.051i | 2.81129 | + | 1.62310i | ||||
\(237\) | −104.708 | + | 367.100i | −0.441808 | + | 1.54895i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 49.5229i | 0.207209i | 0.994619 | + | 0.103604i | \(0.0330376\pi\) | ||||
−0.994619 | + | 0.103604i | \(0.966962\pi\) | |||||||
\(240\) | 52.4153 | − | 50.7588i | 0.218397 | − | 0.211495i | ||||
\(241\) | 162.624 | + | 281.672i | 0.674786 | + | 1.16876i | 0.976531 | + | 0.215376i | \(0.0690976\pi\) |
−0.301745 | + | 0.953389i | \(0.597569\pi\) | |||||||
\(242\) | 218.104 | − | 125.922i | 0.901255 | − | 0.520340i | ||||
\(243\) | 81.5111 | − | 228.921i | 0.335437 | − | 0.942063i | ||||
\(244\) | −476.929 | −1.95463 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 193.852 | − | 679.631i | 0.788017 | − | 2.76273i | ||||
\(247\) | 94.4980 | − | 163.675i | 0.382583 | − | 0.662653i | ||||
\(248\) | 374.070 | − | 215.969i | 1.50835 | − | 0.870845i | ||||
\(249\) | 54.2156 | + | 216.158i | 0.217733 | + | 0.868103i | ||||
\(250\) | 105.498 | − | 182.728i | 0.421992 | − | 0.730912i | ||||
\(251\) | − | 263.732i | − | 1.05073i | −0.850878 | − | 0.525364i | \(-0.823929\pi\) | ||
0.850878 | − | 0.525364i | \(-0.176071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −179.247 | −0.708486 | ||||||||
\(254\) | 46.8094 | + | 27.0254i | 0.184289 | + | 0.106399i | ||||
\(255\) | −16.3637 | + | 4.10426i | −0.0641714 | + | 0.0160952i | ||||
\(256\) | 260.998 | + | 452.062i | 1.01952 | + | 1.76587i | ||||
\(257\) | 130.926 | + | 75.5904i | 0.509442 | + | 0.294126i | 0.732604 | − | 0.680655i | \(-0.238305\pi\) |
−0.223162 | + | 0.974781i | \(0.571638\pi\) | |||||||
\(258\) | 244.014 | + | 69.6006i | 0.945792 | + | 0.269770i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 119.925i | − | 0.461252i | ||||||
\(261\) | −40.3331 | − | 75.3459i | −0.154533 | − | 0.288682i | ||||
\(262\) | 320.985 | + | 555.962i | 1.22513 | + | 2.12199i | ||||
\(263\) | −99.0641 | + | 57.1947i | −0.376670 | + | 0.217470i | −0.676368 | − | 0.736564i | \(-0.736447\pi\) |
0.299699 | + | 0.954034i | \(0.403114\pi\) | |||||||
\(264\) | −220.174 | − | 227.359i | −0.833991 | − | 0.861208i | ||||
\(265\) | −18.8627 | −0.0711800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 367.476 | + | 104.816i | 1.37631 | + | 0.392568i | ||||
\(268\) | 62.8745 | − | 108.902i | 0.234606 | − | 0.406350i | ||||
\(269\) | 4.12375 | − | 2.38085i | 0.0153299 | − | 0.00885074i | −0.492315 | − | 0.870417i | \(-0.663849\pi\) |
0.507645 | + | 0.861566i | \(0.330516\pi\) | |||||||
\(270\) | 111.962 | + | 35.8598i | 0.414675 | + | 0.132814i | ||||
\(271\) | −259.350 | + | 449.208i | −0.957012 | + | 1.65759i | −0.227318 | + | 0.973821i | \(0.572996\pi\) |
−0.729695 | + | 0.683773i | \(0.760338\pi\) | |||||||
\(272\) | 88.6701i | 0.325993i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 115.749 | 0.422442 | ||||||||
\(275\) | −142.444 | − | 82.2403i | −0.517979 | − | 0.299055i | ||||
\(276\) | −154.696 | − | 616.774i | −0.560493 | − | 2.23469i | ||||
\(277\) | 60.5425 | + | 104.863i | 0.218565 | + | 0.378566i | 0.954369 | − | 0.298628i | \(-0.0965291\pi\) |
−0.735805 | + | 0.677194i | \(0.763196\pi\) | |||||||
\(278\) | 196.267 | + | 113.315i | 0.705995 | + | 0.407607i | ||||
\(279\) | 219.498 | + | 136.305i | 0.786731 | + | 0.488548i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 407.255i | − | 1.44931i | −0.689113 | − | 0.724654i | \(-0.742000\pi\) | ||
0.689113 | − | 0.724654i | \(-0.258000\pi\) | |||||||
\(282\) | −241.567 | − | 249.451i | −0.856622 | − | 0.884577i | ||||
\(283\) | −199.317 | − | 345.227i | −0.704300 | − | 1.21988i | −0.966943 | − | 0.254991i | \(-0.917928\pi\) |
0.262643 | − | 0.964893i | \(-0.415406\pi\) | |||||||
\(284\) | −506.656 | + | 292.518i | −1.78400 | + | 1.02999i | ||||
\(285\) | −43.4374 | + | 42.0646i | −0.152412 | + | 0.147595i | ||||
\(286\) | −286.288 | −1.00101 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 40.2327 | − | 64.7886i | 0.139697 | − | 0.224960i | ||||
\(289\) | −134.249 | + | 232.526i | −0.464529 | + | 0.804589i | ||||
\(290\) | 35.8076 | − | 20.6735i | 0.123474 | − | 0.0712880i | ||||
\(291\) | 67.4100 | − | 16.9074i | 0.231650 | − | 0.0581012i | ||||
\(292\) | 318.350 | − | 551.399i | 1.09024 | − | 1.88835i | ||||
\(293\) | 2.53426i | 0.00864935i | 0.999991 | + | 0.00432468i | \(0.00137659\pi\) | ||||
−0.999991 | + | 0.00432468i | \(0.998623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −114.753 | −0.388993 | ||||||||
\(296\) | −430.516 | − | 248.559i | −1.45445 | − | 0.839725i | ||||
\(297\) | 57.7466 | − | 180.298i | 0.194433 | − | 0.607064i | ||||
\(298\) | −343.118 | − | 594.297i | −1.15140 | − | 1.99429i | ||||
\(299\) | −257.821 | − | 148.853i | −0.862276 | − | 0.497835i | ||||
\(300\) | 160.048 | − | 561.115i | 0.533492 | − | 1.87038i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 358.484i | 1.18703i | ||||||||
\(303\) | −290.738 | + | 281.550i | −0.959532 | + | 0.929208i | ||||
\(304\) | 158.904 | + | 275.230i | 0.522710 | + | 0.905361i | ||||
\(305\) | 61.8674 | − | 35.7192i | 0.202844 | − | 0.117112i | ||||
\(306\) | −125.959 | + | 67.4265i | −0.411631 | + | 0.220348i | ||||
\(307\) | −86.2366 | −0.280901 | −0.140451 | − | 0.990088i | \(-0.544855\pi\) | ||||
−0.140451 | + | 0.990088i | \(0.544855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −98.5385 | + | 345.469i | −0.318895 | + | 1.11802i | ||||
\(310\) | −62.5020 | + | 108.257i | −0.201619 | + | 0.349215i | ||||
\(311\) | 131.442 | − | 75.8884i | 0.422645 | − | 0.244014i | −0.273564 | − | 0.961854i | \(-0.588202\pi\) |
0.696208 | + | 0.717840i | \(0.254869\pi\) | |||||||
\(312\) | −127.881 | − | 509.862i | −0.409875 | − | 1.63417i | ||||
\(313\) | 159.059 | − | 275.498i | 0.508175 | − | 0.880185i | −0.491780 | − | 0.870719i | \(-0.663654\pi\) |
0.999955 | − | 0.00946567i | \(-0.00301306\pi\) | |||||||
\(314\) | − | 367.150i | − | 1.16927i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1055.07 | −3.33883 | ||||||||
\(317\) | 315.251 | + | 182.010i | 0.994482 | + | 0.574164i | 0.906611 | − | 0.421967i | \(-0.138660\pi\) |
0.0878710 | + | 0.996132i | \(0.471994\pi\) | |||||||
\(318\) | −154.942 | + | 38.8617i | −0.487239 | + | 0.122207i | ||||
\(319\) | −33.2915 | − | 57.6626i | −0.104362 | − | 0.180760i | ||||
\(320\) | −52.2983 | − | 30.1945i | −0.163432 | − | 0.0943577i | ||||
\(321\) | −224.605 | − | 64.0645i | −0.699705 | − | 0.199578i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 73.4823i | − | 0.227500i | ||||||
\(324\) | 670.227 | + | 43.0983i | 2.06860 | + | 0.133019i | ||||
\(325\) | −136.590 | − | 236.581i | −0.420277 | − | 0.727942i | ||||
\(326\) | −215.449 | + | 124.389i | −0.660885 | + | 0.381562i | ||||
\(327\) | 76.2557 | + | 78.7443i | 0.233198 | + | 0.240808i | ||||
\(328\) | 1010.99 | 3.08228 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 88.0810 | + | 25.1235i | 0.266912 | + | 0.0761318i | ||||
\(331\) | −77.1843 | + | 133.687i | −0.233185 | + | 0.403889i | −0.958744 | − | 0.284272i | \(-0.908248\pi\) |
0.725559 | + | 0.688160i | \(0.241582\pi\) | |||||||
\(332\) | −533.410 | + | 307.964i | −1.60666 | + | 0.927604i | ||||
\(333\) | 9.54607 | − | 297.211i | 0.0286669 | − | 0.892527i | ||||
\(334\) | −362.848 | + | 628.472i | −1.08637 | + | 1.88165i | ||||
\(335\) | 18.8357i | 0.0562260i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 403.041 | 1.19597 | 0.597983 | − | 0.801509i | \(-0.295969\pi\) | ||||
0.597983 | + | 0.801509i | \(0.295969\pi\) | |||||||
\(338\) | 101.338 | + | 58.5077i | 0.299817 | + | 0.173100i | ||||
\(339\) | −15.8810 | − | 63.3176i | −0.0468466 | − | 0.186778i | ||||
\(340\) | −23.3137 | − | 40.3806i | −0.0685698 | − | 0.118766i | ||||
\(341\) | 174.331 | + | 100.650i | 0.511233 | + | 0.295161i | ||||
\(342\) | −270.140 | + | 435.019i | −0.789883 | + | 1.27198i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 362.984i | 1.05519i | ||||||||
\(345\) | 66.2600 | + | 68.4223i | 0.192058 | + | 0.198326i | ||||
\(346\) | 190.133 | + | 329.319i | 0.549516 | + | 0.951790i | ||||
\(347\) | 408.108 | − | 235.621i | 1.17610 | − | 0.679023i | 0.220993 | − | 0.975275i | \(-0.429070\pi\) |
0.955110 | + | 0.296252i | \(0.0957370\pi\) | |||||||
\(348\) | 169.680 | − | 164.318i | 0.487587 | − | 0.472178i | ||||
\(349\) | 364.516 | 1.04446 | 0.522230 | − | 0.852805i | \(-0.325100\pi\) | ||||
0.522230 | + | 0.852805i | \(0.325100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 232.786 | − | 211.377i | 0.663207 | − | 0.602215i | ||||
\(352\) | 29.7085 | − | 51.4566i | 0.0843991 | − | 0.146184i | ||||
\(353\) | −74.7744 | + | 43.1710i | −0.211825 | + | 0.122297i | −0.602159 | − | 0.798376i | \(-0.705693\pi\) |
0.390334 | + | 0.920673i | \(0.372360\pi\) | |||||||
\(354\) | −942.603 | + | 236.419i | −2.66272 | + | 0.667850i | ||||
\(355\) | 43.8157 | − | 75.8910i | 0.123425 | − | 0.213778i | ||||
\(356\) | 1056.15i | 2.96671i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 558.693 | 1.56059 | ||||||||
\(359\) | 322.220 | + | 186.034i | 0.897549 | + | 0.518200i | 0.876404 | − | 0.481576i | \(-0.159935\pi\) |
0.0211451 | + | 0.999776i | \(0.493269\pi\) | |||||||
\(360\) | −5.39884 | + | 168.090i | −0.0149968 | + | 0.466916i | ||||
\(361\) | 48.8137 | + | 84.5479i | 0.135218 | + | 0.234205i | ||||
\(362\) | −710.138 | − | 409.998i | −1.96171 | − | 1.13259i | ||||
\(363\) | −59.1104 | + | 207.237i | −0.162839 | + | 0.570900i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 95.3702i | 0.261288i | ||||||||
\(366\) | 434.601 | − | 420.866i | 1.18744 | − | 1.14991i | ||||
\(367\) | −80.8928 | − | 140.110i | −0.220416 | − | 0.381772i | 0.734518 | − | 0.678589i | \(-0.237408\pi\) |
−0.954934 | + | 0.296817i | \(0.904075\pi\) | |||||||
\(368\) | 433.540 | − | 250.305i | 1.17810 | − | 0.680176i | ||||
\(369\) | 285.407 | + | 533.167i | 0.773460 | + | 1.44490i | ||||
\(370\) | 143.867 | 0.388829 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −195.875 | + | 686.721i | −0.526544 | + | 1.84602i | ||||
\(373\) | −189.125 | + | 327.575i | −0.507039 | + | 0.878217i | 0.492928 | + | 0.870070i | \(0.335927\pi\) |
−0.999967 | + | 0.00814693i | \(0.997407\pi\) | |||||||
\(374\) | −96.3970 | + | 55.6548i | −0.257746 | + | 0.148810i | ||||
\(375\) | 43.9237 | + | 175.124i | 0.117130 | + | 0.466997i | ||||
\(376\) | 248.369 | − | 430.187i | 0.660555 | − | 1.14411i | ||||
\(377\) | − | 110.586i | − | 0.293330i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −50.7974 | −0.134030 | −0.0670151 | − | 0.997752i | \(-0.521348\pi\) | ||||
−0.0670151 | + | 0.997752i | \(0.521348\pi\) | |||||||
\(380\) | −144.730 | − | 83.5602i | −0.380870 | − | 0.219895i | ||||
\(381\) | −44.8614 | + | 11.2519i | −0.117747 | + | 0.0295326i | ||||
\(382\) | 505.221 | + | 875.068i | 1.32257 | + | 2.29075i | ||||
\(383\) | −98.1910 | − | 56.6906i | −0.256373 | − | 0.148017i | 0.366306 | − | 0.930495i | \(-0.380622\pi\) |
−0.622679 | + | 0.782477i | \(0.713956\pi\) | |||||||
\(384\) | −589.582 | − | 168.167i | −1.53537 | − | 0.437936i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 270.382i | 0.700472i | ||||||||
\(387\) | −191.428 | + | 102.472i | −0.494646 | + | 0.264786i | ||||
\(388\) | 96.0405 | + | 166.347i | 0.247527 | + | 0.428730i | ||||
\(389\) | 628.374 | − | 362.792i | 1.61536 | − | 0.932628i | 0.627259 | − | 0.778811i | \(-0.284177\pi\) |
0.988099 | − | 0.153817i | \(-0.0491565\pi\) | |||||||
\(390\) | 105.828 | + | 109.282i | 0.271355 | + | 0.280210i | ||||
\(391\) | −115.749 | −0.296033 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −528.261 | − | 150.677i | −1.34418 | − | 0.383402i | ||||
\(394\) | 239.162 | − | 414.241i | 0.607010 | − | 1.05137i | ||||
\(395\) | 136.864 | − | 79.0184i | 0.346491 | − | 0.200047i | ||||
\(396\) | 522.979 | + | 16.7975i | 1.32065 | + | 0.0424178i | ||||
\(397\) | −47.1732 | + | 81.7064i | −0.118824 | + | 0.205809i | −0.919302 | − | 0.393553i | \(-0.871246\pi\) |
0.800478 | + | 0.599362i | \(0.204579\pi\) | |||||||
\(398\) | − | 303.553i | − | 0.762697i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 459.369 | 1.14842 | ||||||||
\(401\) | −586.875 | − | 338.833i | −1.46353 | − | 0.844969i | −0.464357 | − | 0.885648i | \(-0.653715\pi\) |
−0.999172 | + | 0.0406787i | \(0.987048\pi\) | |||||||
\(402\) | 38.8062 | + | 154.720i | 0.0965327 | + | 0.384876i | ||||
\(403\) | 167.166 | + | 289.540i | 0.414804 | + | 0.718462i | ||||
\(404\) | −968.721 | − | 559.291i | −2.39782 | − | 1.38438i | ||||
\(405\) | −90.1699 | + | 44.6053i | −0.222642 | + | 0.110137i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 231.675i | − | 0.569226i | ||||||
\(408\) | −142.177 | − | 146.817i | −0.348474 | − | 0.359846i | ||||
\(409\) | 8.68233 | + | 15.0382i | 0.0212282 | + | 0.0367683i | 0.876444 | − | 0.481503i | \(-0.159909\pi\) |
−0.855216 | + | 0.518271i | \(0.826576\pi\) | |||||||
\(410\) | −253.383 | + | 146.291i | −0.618008 | + | 0.356807i | ||||
\(411\) | −71.1512 | + | 68.9026i | −0.173117 | + | 0.167646i | ||||
\(412\) | −992.899 | −2.40995 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 685.239 | + | 425.523i | 1.65517 | + | 1.02783i | ||||
\(415\) | 46.1294 | − | 79.8985i | 0.111155 | − | 0.192527i | ||||
\(416\) | 85.4626 | − | 49.3419i | 0.205439 | − | 0.118610i | ||||
\(417\) | −188.099 | + | 47.1781i | −0.451077 | + | 0.113137i | ||||
\(418\) | −199.476 | + | 345.502i | −0.477215 | + | 0.826560i | ||||
\(419\) | 136.071i | 0.324752i | 0.986729 | + | 0.162376i | \(0.0519157\pi\) | ||||
−0.986729 | + | 0.162376i | \(0.948084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 423.992 | 1.00711 | 0.503554 | − | 0.863964i | \(-0.332026\pi\) | ||||
0.503554 | + | 0.863964i | \(0.332026\pi\) | |||||||
\(422\) | −58.9543 | − | 34.0373i | −0.139702 | − | 0.0806570i | ||||
\(423\) | 296.984 | + | 9.53878i | 0.702090 | + | 0.0225503i | ||||
\(424\) | −114.255 | − | 197.895i | −0.269469 | − | 0.466734i | ||||
\(425\) | −91.9836 | − | 53.1068i | −0.216432 | − | 0.124957i | ||||
\(426\) | 203.557 | − | 713.655i | 0.477833 | − | 1.67525i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 645.530i | − | 1.50825i | ||||||
\(429\) | 175.982 | − | 170.420i | 0.410214 | − | 0.397250i | ||||
\(430\) | −52.5242 | − | 90.9746i | −0.122149 | − | 0.211569i | ||||
\(431\) | −294.660 | + | 170.122i | −0.683666 | + | 0.394715i | −0.801235 | − | 0.598350i | \(-0.795823\pi\) |
0.117569 | + | 0.993065i | \(0.462490\pi\) | |||||||
\(432\) | 112.102 | + | 516.721i | 0.259495 | + | 1.19611i | ||||
\(433\) | −159.166 | −0.367589 | −0.183794 | − | 0.982965i | \(-0.558838\pi\) | ||||
−0.183794 | + | 0.982965i | \(0.558838\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.70456 | + | 34.0235i | −0.0223093 | + | 0.0782148i | ||||
\(436\) | −151.480 | + | 262.371i | −0.347431 | + | 0.601767i | ||||
\(437\) | −359.282 | + | 207.432i | −0.822155 | + | 0.474672i | ||||
\(438\) | 196.486 | + | 783.390i | 0.448598 | + | 1.78856i | ||||
\(439\) | 64.0366 | − | 110.915i | 0.145869 | − | 0.252653i | −0.783828 | − | 0.620978i | \(-0.786735\pi\) |
0.929697 | + | 0.368326i | \(0.120069\pi\) | |||||||
\(440\) | 131.025i | 0.297785i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −184.871 | −0.418259 | ||||||||
\(443\) | −170.901 | − | 98.6700i | −0.385782 | − | 0.222731i | 0.294549 | − | 0.955636i | \(-0.404831\pi\) |
−0.680331 | + | 0.732905i | \(0.738164\pi\) | |||||||
\(444\) | 797.175 | − | 199.943i | 1.79544 | − | 0.450323i | ||||
\(445\) | −79.0993 | − | 137.004i | −0.177751 | − | 0.307874i | ||||
\(446\) | 531.461 | + | 306.839i | 1.19162 | + | 0.687981i | ||||
\(447\) | 564.686 | + | 161.066i | 1.26328 | + | 0.360327i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 148.101i | − | 0.329847i | −0.986306 | − | 0.164923i | \(-0.947262\pi\) | ||
0.986306 | − | 0.164923i | \(-0.0527377\pi\) | |||||||
\(450\) | 349.313 | + | 652.549i | 0.776251 | + | 1.45011i | ||||
\(451\) | 235.579 | + | 408.035i | 0.522348 | + | 0.904734i | ||||
\(452\) | 156.248 | − | 90.2100i | 0.345682 | − | 0.199580i | ||||
\(453\) | −213.397 | − | 220.361i | −0.471075 | − | 0.486449i | ||||
\(454\) | 622.561 | 1.37128 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −704.423 | − | 200.924i | −1.54479 | − | 0.440622i | ||||
\(457\) | 61.1072 | − | 105.841i | 0.133714 | − | 0.231599i | −0.791392 | − | 0.611310i | \(-0.790643\pi\) |
0.925105 | + | 0.379710i | \(0.123976\pi\) | |||||||
\(458\) | −123.913 | + | 71.5415i | −0.270553 | + | 0.156204i | ||||
\(459\) | 37.2900 | − | 116.428i | 0.0812418 | − | 0.253655i | ||||
\(460\) | −131.624 | + | 227.979i | −0.286138 | + | 0.495606i | ||||
\(461\) | 602.089i | 1.30605i | 0.757337 | + | 0.653025i | \(0.226500\pi\) | ||||
−0.757337 | + | 0.653025i | \(0.773500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −637.061 | −1.37594 | −0.687971 | − | 0.725738i | \(-0.741498\pi\) | ||||
−0.687971 | + | 0.725738i | \(0.741498\pi\) | |||||||
\(464\) | 161.043 | + | 92.9780i | 0.347075 | + | 0.200384i | ||||
\(465\) | −26.0224 | − | 103.752i | −0.0559622 | − | 0.223122i | ||||
\(466\) | −679.616 | − | 1177.13i | −1.45840 | − | 2.52603i | ||||
\(467\) | 664.853 | + | 383.853i | 1.42367 | + | 0.821955i | 0.996610 | − | 0.0822701i | \(-0.0262170\pi\) |
0.427057 | + | 0.904225i | \(0.359550\pi\) | |||||||
\(468\) | 738.280 | + | 458.460i | 1.57752 | + | 0.979616i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 143.757i | 0.305865i | ||||||||
\(471\) | 218.556 | + | 225.688i | 0.464025 | + | 0.479168i | ||||
\(472\) | −695.080 | − | 1203.91i | −1.47263 | − | 2.55067i | ||||
\(473\) | −146.501 | + | 84.5821i | −0.309726 | + | 0.178821i | ||||
\(474\) | 961.430 | − | 931.046i | 2.02833 | − | 1.96423i | ||||
\(475\) | −380.686 | −0.801445 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 72.1097 | − | 116.122i | 0.151173 | − | 0.243442i | ||||
\(478\) | 86.8118 | − | 150.362i | 0.181615 | − | 0.314566i | ||||
\(479\) | 341.089 | − | 196.928i | 0.712085 | − | 0.411122i | −0.0997478 | − | 0.995013i | \(-0.531804\pi\) |
0.811832 | + | 0.583890i | \(0.198470\pi\) | |||||||
\(480\) | −30.6240 | + | 7.68096i | −0.0638001 | + | 0.0160020i | ||||
\(481\) | 192.391 | − | 333.231i | 0.399981 | − | 0.692787i | ||||
\(482\) | − | 1140.29i | − | 2.36575i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −595.612 | −1.23060 | ||||||||
\(485\) | −24.9168 | − | 14.3857i | −0.0513749 | − | 0.0296613i | ||||
\(486\) | −648.776 | + | 552.169i | −1.33493 | + | 1.13615i | ||||
\(487\) | −286.705 | − | 496.587i | −0.588716 | − | 1.01969i | −0.994401 | − | 0.105673i | \(-0.966300\pi\) |
0.405685 | − | 0.914013i | \(-0.367033\pi\) | |||||||
\(488\) | 749.486 | + | 432.716i | 1.53583 | + | 0.886713i | ||||
\(489\) | 58.3908 | − | 204.714i | 0.119409 | − | 0.418638i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 170.796i | 0.347853i | 0.984759 | + | 0.173927i | \(0.0556455\pi\) | ||||
−0.984759 | + | 0.173927i | \(0.944354\pi\) | |||||||
\(492\) | −1200.70 | + | 1162.76i | −2.44045 | + | 2.36332i | ||||
\(493\) | −21.4980 | − | 37.2357i | −0.0436066 | − | 0.0755288i | ||||
\(494\) | −573.833 | + | 331.303i | −1.16161 | + | 0.670654i | ||||
\(495\) | −69.0991 | + | 36.9891i | −0.139594 | + | 0.0747254i | ||||
\(496\) | −562.199 | −1.13347 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 214.306 | − | 751.340i | 0.430333 | − | 1.50871i | ||||
\(499\) | 423.907 | − | 734.229i | 0.849513 | − | 1.47140i | −0.0321299 | − | 0.999484i | \(-0.510229\pi\) |
0.881643 | − | 0.471917i | \(-0.156438\pi\) | |||||||
\(500\) | −432.151 | + | 249.503i | −0.864302 | + | 0.499005i | ||||
\(501\) | −151.070 | − | 602.318i | −0.301538 | − | 1.20223i | ||||
\(502\) | −462.313 | + | 800.750i | −0.920942 | + | 1.59512i | ||||
\(503\) | 197.624i | 0.392891i | 0.980515 | + | 0.196445i | \(0.0629398\pi\) | ||||
−0.980515 | + | 0.196445i | \(0.937060\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 167.550 | 0.331783 | ||||||||
\(506\) | 544.233 | + | 314.213i | 1.07556 | + | 0.620975i | ||||
\(507\) | −97.1212 | + | 24.3594i | −0.191560 | + | 0.0480462i | ||||
\(508\) | −63.9150 | − | 110.704i | −0.125817 | − | 0.217921i | ||||
\(509\) | −425.606 | − | 245.724i | −0.836162 | − | 0.482758i | 0.0197959 | − | 0.999804i | \(-0.493698\pi\) |
−0.855958 | + | 0.517046i | \(0.827032\pi\) | |||||||
\(510\) | 56.8784 | + | 16.2235i | 0.111526 | + | 0.0318108i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1012.62i | − | 1.97777i | ||||||
\(513\) | −92.9006 | − | 428.215i | −0.181093 | − | 0.834727i | ||||
\(514\) | −265.014 | − | 459.018i | −0.515592 | − | 0.893032i | ||||
\(515\) | 128.799 | − | 74.3623i | 0.250096 | − | 0.144393i | ||||
\(516\) | −417.475 | − | 431.099i | −0.809060 | − | 0.835463i | ||||
\(517\) | 231.498 | 0.447772 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −312.911 | − | 89.2521i | −0.602912 | − | 0.171969i | ||||
\(520\) | −108.808 | + | 188.461i | −0.209246 | + | 0.362424i | ||||
\(521\) | 753.451 | − | 435.005i | 1.44616 | − | 0.834942i | 0.447912 | − | 0.894078i | \(-0.352168\pi\) |
0.998250 | + | 0.0591353i | \(0.0188343\pi\) | |||||||
\(522\) | −9.61859 | + | 299.469i | −0.0184264 | + | 0.573696i | ||||
\(523\) | 399.354 | − | 691.701i | 0.763582 | − | 1.32256i | −0.177411 | − | 0.984137i | \(-0.556772\pi\) |
0.940993 | − | 0.338426i | \(-0.109895\pi\) | |||||||
\(524\) | − | 1518.26i | − | 2.89744i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 401.041 | 0.762434 | ||||||||
\(527\) | 112.574 | + | 64.9947i | 0.213613 | + | 0.123330i | ||||
\(528\) | 100.216 | + | 399.563i | 0.189804 | + | 0.756748i | ||||
\(529\) | 62.2451 | + | 107.812i | 0.117666 | + | 0.203803i | ||||
\(530\) | 57.2713 | + | 33.0656i | 0.108059 | + | 0.0623879i | ||||
\(531\) | 438.686 | − | 706.437i | 0.826151 | − | 1.33039i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 782.531i | 1.46816i | ||||||||
\(534\) | −931.999 | − | 962.414i | −1.74532 | − | 1.80227i | ||||
\(535\) | 48.3464 | + | 83.7384i | 0.0903671 | + | 0.156520i | ||||
\(536\) | −197.612 | + | 114.091i | −0.368680 | + | 0.212857i | ||||
\(537\) | −343.430 | + | 332.576i | −0.639534 | + | 0.619323i | ||||
\(538\) | −16.6941 | −0.0310300 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −186.911 | − | 205.841i | −0.346132 | − | 0.381188i | ||||
\(541\) | 368.122 | − | 637.605i | 0.680446 | − | 1.17857i | −0.294398 | − | 0.955683i | \(-0.595119\pi\) |
0.974845 | − | 0.222885i | \(-0.0715475\pi\) | |||||||
\(542\) | 1574.89 | − | 909.262i | 2.90570 | − | 1.67761i | ||||
\(543\) | 680.586 | − | 170.701i | 1.25338 | − | 0.314367i | ||||
\(544\) | 19.1843 | − | 33.2282i | 0.0352653 | − | 0.0610812i | ||||
\(545\) | − | 45.3797i | − | 0.0832656i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −228.952 | −0.418559 | −0.209279 | − | 0.977856i | \(-0.567112\pi\) | ||||
−0.209279 | + | 0.977856i | \(0.567112\pi\) | |||||||
\(548\) | −237.071 | − | 136.873i | −0.432612 | − | 0.249768i | ||||
\(549\) | −16.6188 | + | 517.416i | −0.0302710 | + | 0.942469i | ||||
\(550\) | 288.328 | + | 499.399i | 0.524233 | + | 0.907998i | ||||
\(551\) | −133.459 | − | 77.0524i | −0.242212 | − | 0.139841i | ||||
\(552\) | −316.494 | + | 1109.60i | −0.573359 | + | 2.01015i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 424.515i | − | 0.766272i | ||||||
\(555\) | −88.4352 | + | 85.6404i | −0.159343 | + | 0.154307i | ||||
\(556\) | −267.989 | − | 464.170i | −0.481994 | − | 0.834839i | ||||
\(557\) | −784.869 | + | 453.144i | −1.40910 | + | 0.813544i | −0.995301 | − | 0.0968243i | \(-0.969131\pi\) |
−0.413798 | + | 0.910369i | \(0.635798\pi\) | |||||||
\(558\) | −427.507 | − | 798.623i | −0.766141 | − | 1.43122i | ||||
\(559\) | −280.959 | −0.502611 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.1255 | − | 91.5940i | 0.0465695 | − | 0.163269i | ||||
\(562\) | −713.903 | + | 1236.52i | −1.27029 | + | 2.20021i | ||||
\(563\) | −397.173 | + | 229.308i | −0.705459 | + | 0.407297i | −0.809377 | − | 0.587289i | \(-0.800195\pi\) |
0.103919 | + | 0.994586i | \(0.466862\pi\) | |||||||
\(564\) | 199.790 | + | 796.565i | 0.354238 | + | 1.41235i | ||||
\(565\) | −13.5124 | + | 23.4041i | −0.0239157 | + | 0.0414233i | ||||
\(566\) | 1397.58i | 2.46922i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1061.60 | 1.86901 | ||||||||
\(569\) | −500.067 | − | 288.714i | −0.878853 | − | 0.507406i | −0.00857275 | − | 0.999963i | \(-0.502729\pi\) |
−0.870280 | + | 0.492557i | \(0.836062\pi\) | |||||||
\(570\) | 205.623 | − | 51.5733i | 0.360742 | − | 0.0904795i | ||||
\(571\) | 51.5608 | + | 89.3059i | 0.0902991 | + | 0.156403i | 0.907637 | − | 0.419756i | \(-0.137884\pi\) |
−0.817338 | + | 0.576159i | \(0.804551\pi\) | |||||||
\(572\) | 586.359 | + | 338.535i | 1.02510 | + | 0.591844i | ||||
\(573\) | −831.468 | − | 237.161i | −1.45108 | − | 0.413893i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 599.655i | 1.04288i | ||||||||
\(576\) | 385.812 | − | 206.527i | 0.669812 | − | 0.358554i | ||||
\(577\) | −338.292 | − | 585.938i | −0.586294 | − | 1.01549i | −0.994713 | − | 0.102696i | \(-0.967253\pi\) |
0.408419 | − | 0.912795i | \(-0.366080\pi\) | |||||||
\(578\) | 815.219 | − | 470.667i | 1.41041 | − | 0.814302i | ||||
\(579\) | −160.952 | − | 166.205i | −0.277983 | − | 0.287055i | ||||
\(580\) | −97.7856 | −0.168596 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −234.310 | − | 66.8325i | −0.402594 | − | 0.114833i | ||||
\(583\) | 53.2470 | − | 92.2266i | 0.0913328 | − | 0.158193i | ||||
\(584\) | −1000.56 | + | 577.675i | −1.71329 | + | 0.989170i | ||||
\(585\) | −130.106 | − | 4.17884i | −0.222403 | − | 0.00714332i | ||||
\(586\) | 4.44246 | − | 7.69457i | 0.00758099 | − | 0.0131307i | ||||
\(587\) | 158.683i | 0.270329i | 0.990823 | + | 0.135164i | \(0.0431563\pi\) | ||||
−0.990823 | + | 0.135164i | \(0.956844\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 465.903 | 0.791007 | ||||||||
\(590\) | 348.415 | + | 201.158i | 0.590534 | + | 0.340945i | ||||
\(591\) | 99.5741 | + | 397.002i | 0.168484 | + | 0.671747i | ||||
\(592\) | 323.516 | + | 560.347i | 0.546480 | + | 0.946532i | ||||
\(593\) | 810.055 | + | 467.686i | 1.36603 | + | 0.788677i | 0.990418 | − | 0.138100i | \(-0.0440995\pi\) |
0.375611 | + | 0.926777i | \(0.377433\pi\) | |||||||
\(594\) | −491.387 | + | 446.196i | −0.827251 | + | 0.751172i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1622.94i | 2.72306i | ||||||||
\(597\) | 180.698 | + | 186.595i | 0.302677 | + | 0.312555i | ||||
\(598\) | 521.867 | + | 903.900i | 0.872687 | + | 1.51154i | ||||
\(599\) | −63.8836 | + | 36.8832i | −0.106650 | + | 0.0615747i | −0.552376 | − | 0.833595i | \(-0.686279\pi\) |
0.445726 | + | 0.895169i | \(0.352946\pi\) | |||||||
\(600\) | −760.609 | + | 736.571i | −1.26768 | + | 1.22762i | ||||
\(601\) | 934.280 | 1.55454 | 0.777271 | − | 0.629166i | \(-0.216603\pi\) | ||||
0.777271 | + | 0.629166i | \(0.216603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −115.956 | − | 72.0066i | −0.192298 | − | 0.119414i | ||||
\(604\) | 423.907 | − | 734.229i | 0.701833 | − | 1.21561i | ||||
\(605\) | 77.2630 | − | 44.6078i | 0.127707 | − | 0.0737319i | ||||
\(606\) | 1376.29 | − | 345.195i | 2.27111 | − | 0.569628i | ||||
\(607\) | −90.8039 | + | 157.277i | −0.149595 | + | 0.259105i | −0.931078 | − | 0.364821i | \(-0.881130\pi\) |
0.781483 | + | 0.623926i | \(0.214464\pi\) | |||||||
\(608\) | − | 137.519i | − | 0.226183i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −250.458 | −0.410586 | ||||||||
\(611\) | 332.976 | + | 192.244i | 0.544969 | + | 0.314638i | ||||
\(612\) | 337.714 | + | 10.8470i | 0.551821 | + | 0.0177238i | ||||
\(613\) | 448.970 | + | 777.639i | 0.732414 | + | 1.26858i | 0.955849 | + | 0.293860i | \(0.0949398\pi\) |
−0.223434 | + | 0.974719i | \(0.571727\pi\) | |||||||
\(614\) | 261.833 | + | 151.170i | 0.426439 | + | 0.246204i | ||||
\(615\) | 68.6719 | − | 240.759i | 0.111662 | − | 0.391477i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1169.69i | − | 1.89576i | −0.318622 | − | 0.947882i | \(-0.603220\pi\) | ||
0.318622 | − | 0.947882i | \(-0.396780\pi\) | |||||||
\(618\) | 904.778 | − | 876.184i | 1.46404 | − | 1.41777i | ||||
\(619\) | 604.483 | + | 1047.00i | 0.976548 | + | 1.69143i | 0.674730 | + | 0.738064i | \(0.264260\pi\) |
0.301817 | + | 0.953366i | \(0.402407\pi\) | |||||||
\(620\) | 256.027 | − | 147.817i | 0.412946 | − | 0.238415i | ||||
\(621\) | −674.522 | + | 146.336i | −1.08619 | + | 0.235647i | ||||
\(622\) | −532.118 | −0.855495 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −187.664 | + | 657.936i | −0.300744 | + | 1.05438i | ||||
\(625\) | −255.846 | + | 443.139i | −0.409354 | + | 0.709022i | ||||
\(626\) | −965.875 | + | 557.648i | −1.54293 | + | 0.890812i | ||||
\(627\) | −83.0509 | − | 331.124i | −0.132458 | − | 0.528109i | ||||
\(628\) | −434.155 | + | 751.978i | −0.691329 | + | 1.19742i | ||||
\(629\) | − | 149.604i | − | 0.237845i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 901.223 | 1.42825 | 0.714123 | − | 0.700020i | \(-0.246826\pi\) | ||||
0.714123 | + | 0.700020i | \(0.246826\pi\) | |||||||
\(632\) | 1658.02 | + | 957.259i | 2.62345 | + | 1.51465i | ||||
\(633\) | 56.5009 | − | 14.1713i | 0.0892589 | − | 0.0223875i | ||||
\(634\) | −638.114 | − | 1105.25i | −1.00649 | − | 1.74329i | ||||
\(635\) | 16.5822 | + | 9.57371i | 0.0261136 | + | 0.0150767i | ||||
\(636\) | 363.298 | + | 103.624i | 0.571223 | + | 0.162931i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 233.435i | 0.365886i | ||||||||
\(639\) | 299.695 | + | 559.858i | 0.469006 | + | 0.876147i | ||||
\(640\) | 126.908 | + | 219.811i | 0.198294 | + | 0.343454i | ||||
\(641\) | −457.806 | + | 264.315i | −0.714206 | + | 0.412347i | −0.812616 | − | 0.582799i | \(-0.801958\pi\) |
0.0984103 | + | 0.995146i | \(0.468624\pi\) | |||||||
\(642\) | 569.648 | + | 588.238i | 0.887302 | + | 0.916259i | ||||
\(643\) | −33.4392 | −0.0520050 | −0.0260025 | − | 0.999662i | \(-0.508278\pi\) | ||||
−0.0260025 | + | 0.999662i | \(0.508278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 86.4418 | + | 24.6559i | 0.134018 | + | 0.0382262i | ||||
\(646\) | −128.812 | + | 223.109i | −0.199399 | + | 0.345369i | ||||
\(647\) | −680.962 | + | 393.154i | −1.05249 | + | 0.607657i | −0.923346 | − | 0.383969i | \(-0.874557\pi\) |
−0.129146 | + | 0.991626i | \(0.541224\pi\) | |||||||
\(648\) | −1014.15 | − | 675.822i | −1.56504 | − | 1.04294i | ||||
\(649\) | 323.933 | − | 561.069i | 0.499127 | − | 0.864513i | ||||
\(650\) | 957.750i | 1.47346i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 588.361 | 0.902394 | ||||||||
\(653\) | −334.119 | − | 192.904i | −0.511668 | − | 0.295412i | 0.221851 | − | 0.975081i | \(-0.428790\pi\) |
−0.733519 | + | 0.679669i | \(0.762123\pi\) | |||||||
\(654\) | −93.4933 | − | 372.758i | −0.142956 | − | 0.569967i | ||||
\(655\) | 113.708 | + | 196.949i | 0.173601 | + | 0.300685i | ||||
\(656\) | −1139.58 | − | 657.936i | −1.73716 | − | 1.00295i | ||||
\(657\) | −587.114 | − | 364.588i | −0.893628 | − | 0.554929i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 97.2583i | 0.147585i | 0.997274 | + | 0.0737924i | \(0.0235102\pi\) | ||||
−0.997274 | + | 0.0737924i | \(0.976490\pi\) | |||||||
\(660\) | −150.695 | − | 155.612i | −0.228325 | − | 0.235776i | ||||
\(661\) | −480.752 | − | 832.687i | −0.727311 | − | 1.25974i | −0.958016 | − | 0.286715i | \(-0.907437\pi\) |
0.230705 | − | 0.973024i | \(-0.425897\pi\) | |||||||
\(662\) | 468.697 | − | 270.602i | 0.708001 | − | 0.408765i | ||||
\(663\) | 113.640 | − | 110.049i | 0.171403 | − | 0.165986i | ||||
\(664\) | 1117.66 | 1.68322 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −549.984 | + | 885.665i | −0.825802 | + | 1.32983i | ||||
\(667\) | −121.373 | + | 210.223i | −0.181968 | + | 0.315178i | ||||
\(668\) | 1486.33 | − | 858.136i | 2.22505 | − | 1.28463i | ||||
\(669\) | −509.345 | + | 127.751i | −0.761353 | + | 0.190959i | ||||
\(670\) | 33.0183 | − | 57.1894i | 0.0492810 | − | 0.0853572i | ||||
\(671\) | 403.323i | 0.601078i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1089.81 | −1.61933 | −0.809663 | − | 0.586895i | \(-0.800350\pi\) | ||||
−0.809663 | + | 0.586895i | \(0.800350\pi\) | |||||||
\(674\) | −1223.72 | − | 706.515i | −1.81561 | − | 1.04824i | ||||
\(675\) | −603.171 | − | 193.186i | −0.893586 | − | 0.286202i | ||||
\(676\) | −138.371 | − | 239.665i | −0.204690 | − | 0.354534i | ||||
\(677\) | −1084.75 | − | 626.279i | −1.60229 | − | 0.925080i | −0.991029 | − | 0.133649i | \(-0.957331\pi\) |
−0.611258 | − | 0.791432i | \(-0.709336\pi\) | |||||||
\(678\) | −62.7752 | + | 220.085i | −0.0925888 | + | 0.324609i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 84.6097i | 0.124426i | ||||||||
\(681\) | −382.690 | + | 370.596i | −0.561953 | + | 0.544193i | ||||
\(682\) | −352.871 | − | 611.190i | −0.517406 | − | 0.896173i | ||||
\(683\) | −295.398 | + | 170.548i | −0.432501 | + | 0.249705i | −0.700412 | − | 0.713739i | \(-0.747000\pi\) |
0.267910 | + | 0.963444i | \(0.413667\pi\) | |||||||
\(684\) | 1067.70 | − | 571.543i | 1.56096 | − | 0.835589i | ||||
\(685\) | 41.0039 | 0.0598598 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.5830 | − | 117.739i | 0.0488836 | − | 0.171382i | ||||
\(688\) | 236.225 | − | 409.153i | 0.343350 | − | 0.594700i | ||||
\(689\) | 153.176 | − | 88.4363i | 0.222317 | − | 0.128355i | ||||
\(690\) | −81.2381 | − | 323.896i | −0.117736 | − | 0.469415i | ||||
\(691\) | −391.833 | + | 678.675i | −0.567053 | + | 0.982164i | 0.429803 | + | 0.902923i | \(0.358583\pi\) |
−0.996855 | + | 0.0792411i | \(0.974750\pi\) | |||||||
\(692\) | − | 899.327i | − | 1.29961i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1652.14 | −2.38060 | ||||||||
\(695\) | 69.5272 | + | 40.1416i | 0.100039 | + | 0.0577576i | ||||
\(696\) | −415.735 | + | 104.272i | −0.597320 | + | 0.149817i | ||||
\(697\) | 152.125 | + | 263.489i | 0.218258 | + | 0.378033i | ||||
\(698\) | −1106.75 | − | 638.983i | −1.58560 | − | 0.915449i | ||||
\(699\) | 1118.48 | + | 319.025i | 1.60011 | + | 0.456402i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1331.76i | 1.89979i | 0.312562 | + | 0.949897i | \(0.398813\pi\) | ||||
−0.312562 | + | 0.949897i | \(0.601187\pi\) | |||||||
\(702\) | −1077.32 | + | 233.724i | −1.53465 | + | 0.332940i | ||||
\(703\) | −268.103 | − | 464.368i | −0.381370 | − | 0.660553i | ||||
\(704\) | 295.263 | − | 170.470i | 0.419408 | − | 0.242145i | ||||
\(705\) | −85.5749 | − | 88.3676i | −0.121383 | − | 0.125344i | ||||
\(706\) | 302.708 | 0.428766 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2210.16 | + | 630.406i | 3.12169 | + | 0.890404i | ||||
\(709\) | −381.982 | + | 661.612i | −0.538761 | + | 0.933162i | 0.460210 | + | 0.887810i | \(0.347774\pi\) |
−0.998971 | + | 0.0453517i | \(0.985559\pi\) | |||||||
\(710\) | −266.068 | + | 153.615i | −0.374744 | + | 0.216358i | ||||
\(711\) | −36.7642 | + | 1144.63i | −0.0517078 | + | 1.60989i | ||||
\(712\) | 958.239 | − | 1659.72i | 1.34584 | − | 2.33107i | ||||
\(713\) | − | 733.888i | − | 1.02930i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −101.417 | −0.141842 | ||||||||
\(716\) | −1144.29 | − | 660.654i | −1.59816 | − | 0.922701i | ||||
\(717\) | 36.1437 | + | 144.105i | 0.0504097 | + | 0.200983i | ||||
\(718\) | −652.221 | − | 1129.68i | −0.908386 | − | 1.57337i | ||||
\(719\) | 540.153 | + | 311.858i | 0.751256 | + | 0.433738i | 0.826148 | − | 0.563454i | \(-0.190528\pi\) |
−0.0748915 | + | 0.997192i | \(0.523861\pi\) | |||||||
\(720\) | 115.476 | − | 185.956i | 0.160383 | − | 0.258272i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 342.274i | − | 0.474064i | ||||||
\(723\) | 678.788 | + | 700.940i | 0.938850 | + | 0.969489i | ||||
\(724\) | 969.645 | + | 1679.47i | 1.33929 | + | 2.31972i | ||||
\(725\) | −192.905 | + | 111.374i | −0.266076 | + | 0.153619i | ||||
\(726\) | 542.750 | − | 525.598i | 0.747590 | − | 0.723964i | ||||
\(727\) | −678.494 | −0.933279 | −0.466640 | − | 0.884448i | \(-0.654536\pi\) | ||||
−0.466640 | + | 0.884448i | \(0.654536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 70.1111 | − | 725.621i | 0.0961744 | − | 0.995364i | ||||
\(730\) | 167.180 | − | 289.565i | 0.229014 | − | 0.396664i | ||||
\(731\) | −94.6029 | + | 54.6190i | −0.129416 | + | 0.0747182i | ||||
\(732\) | −1387.80 | + | 348.081i | −1.89590 | + | 0.475521i | ||||
\(733\) | −197.483 | + | 342.051i | −0.269417 | + | 0.466645i | −0.968712 | − | 0.248189i | \(-0.920164\pi\) |
0.699294 | + | 0.714834i | \(0.253498\pi\) | |||||||
\(734\) | 567.208i | 0.772763i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −216.620 | −0.294320 | ||||||||
\(737\) | −92.0947 | − | 53.1709i | −0.124959 | − | 0.0721450i | ||||
\(738\) | 68.0636 | − | 2119.12i | 0.0922270 | − | 2.87143i | ||||
\(739\) | −146.099 | − | 253.051i | −0.197699 | − | 0.342424i | 0.750083 | − | 0.661344i | \(-0.230013\pi\) |
−0.947782 | + | 0.318919i | \(0.896680\pi\) | |||||||
\(740\) | −294.660 | − | 170.122i | −0.398189 | − | 0.229895i | ||||
\(741\) | 155.520 | − | 545.242i | 0.209879 | − | 0.735819i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 383.452i | − | 0.516086i | −0.966133 | − | 0.258043i | \(-0.916922\pi\) | ||
0.966133 | − | 0.258043i | \(-0.0830776\pi\) | |||||||
\(744\) | 930.872 | − | 901.454i | 1.25117 | − | 1.21163i | ||||
\(745\) | −121.549 | − | 210.529i | −0.163153 | − | 0.282589i | ||||
\(746\) | 1148.45 | − | 663.060i | 1.53948 | − | 0.888820i | ||||
\(747\) | 315.520 | + | 589.422i | 0.422383 | + | 0.789052i | ||||
\(748\) | 263.247 | 0.351935 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 173.624 | − | 608.711i | 0.231498 | − | 0.811614i | ||||
\(751\) | 348.166 | − | 603.041i | 0.463603 | − | 0.802984i | −0.535534 | − | 0.844514i | \(-0.679890\pi\) |
0.999137 | + | 0.0415293i | \(0.0132230\pi\) | |||||||
\(752\) | −559.918 | + | 323.269i | −0.744572 | + | 0.429879i | ||||
\(753\) | −192.482 | − | 767.427i | −0.255620 | − | 1.01916i | ||||
\(754\) | −193.852 | + | 335.762i | −0.257099 | + | 0.445308i | ||||
\(755\) | 126.993i | 0.168202i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 967.357 | 1.27788 | 0.638941 | − | 0.769256i | \(-0.279373\pi\) | ||||
0.638941 | + | 0.769256i | \(0.279373\pi\) | |||||||
\(758\) | 154.232 | + | 89.0459i | 0.203472 | + | 0.117475i | ||||
\(759\) | −521.585 | + | 130.821i | −0.687201 | + | 0.172360i | ||||
\(760\) | 151.627 | + | 262.626i | 0.199510 | + | 0.345561i | ||||
\(761\) | −77.6876 | − | 44.8529i | −0.102086 | − | 0.0589395i | 0.448088 | − | 0.893990i | \(-0.352105\pi\) |
−0.550174 | + | 0.835050i | \(0.685439\pi\) | |||||||
\(762\) | 155.933 | + | 44.4771i | 0.204637 | + | 0.0583689i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 2389.69i | − | 3.12787i | ||||||
\(765\) | −44.6208 | + | 23.8857i | −0.0583279 | + | 0.0312232i | ||||
\(766\) | 198.753 | + | 344.250i | 0.259469 | + | 0.449413i | ||||
\(767\) | 931.861 | − | 538.010i | 1.21494 | − | 0.701448i | ||||
\(768\) | 1089.40 | + | 1124.95i | 1.41849 | + | 1.46478i | ||||
\(769\) | −926.219 | −1.20445 | −0.602223 | − | 0.798328i | \(-0.705718\pi\) | ||||
−0.602223 | + | 0.798328i | \(0.705718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 436.148 | + | 124.403i | 0.565691 | + | 0.161353i | ||||
\(772\) | 319.727 | − | 553.783i | 0.414154 | − | 0.717336i | ||||
\(773\) | −367.303 | + | 212.063i | −0.475166 | + | 0.274337i | −0.718400 | − | 0.695631i | \(-0.755125\pi\) |
0.243234 | + | 0.969968i | \(0.421792\pi\) | |||||||
\(774\) | 760.847 | + | 24.4375i | 0.983006 | + | 0.0315730i | ||||
\(775\) | 336.715 | − | 583.207i | 0.434471 | − | 0.752526i | ||||
\(776\) | − | 348.548i | − | 0.449160i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2543.84 | −3.26972 | ||||||||
\(779\) | 944.387 | + | 545.242i | 1.21231 | + | 0.699926i | ||||
\(780\) | −87.5262 | − | 348.967i | −0.112213 | − | 0.447394i | ||||
\(781\) | 247.373 | + | 428.462i | 0.316738 | + | 0.548607i | ||||
\(782\) | 351.439 | + | 202.904i | 0.449411 | + | 0.259468i | ||||
\(783\) | −172.354 | − | 189.810i | −0.220120 | − | 0.242414i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 130.063i | − | 0.165685i | ||||||
\(786\) | 1339.79 | + | 1383.51i | 1.70456 | + | 1.76019i | ||||
\(787\) | −77.9444 | − | 135.004i | −0.0990399 | − | 0.171542i | 0.812248 | − | 0.583313i | \(-0.198244\pi\) |
−0.911288 | + | 0.411771i | \(0.864910\pi\) | |||||||
\(788\) | −979.679 | + | 565.618i | −1.24325 | + | 0.717789i | ||||
\(789\) | −246.521 | + | 238.730i | −0.312447 | + | 0.302573i | ||||
\(790\) | −554.065 | −0.701348 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −806.612 | − | 500.893i | −1.01845 | − | 0.632441i | ||||
\(793\) | −334.933 | + | 580.122i | −0.422362 | + | 0.731553i | ||||
\(794\) | 286.456 | − | 165.386i | 0.360776 | − | 0.208294i | ||||
\(795\) | −54.8880 | + | 13.7667i | −0.0690415 | + | 0.0173166i | ||||
\(796\) | −358.952 | + | 621.722i | −0.450944 | + | 0.781058i | ||||
\(797\) | 719.191i | 0.902373i | 0.892430 | + | 0.451186i | \(0.148999\pi\) | ||||
−0.892430 | + | 0.451186i | \(0.851001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 149.490 | 0.187097 | ||||||||
\(800\) | −172.144 | − | 99.3871i | −0.215179 | − | 0.124234i | ||||
\(801\) | 1145.80 | + | 36.8019i | 1.43047 | + | 0.0459449i | ||||
\(802\) | 1187.92 | + | 2057.54i | 1.48120 | + | 2.56551i | ||||
\(803\) | −466.300 | − | 269.218i | −0.580697 | − | 0.335266i | ||||
\(804\) | 103.476 | − | 362.778i | 0.128701 | − | 0.451217i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1172.14i | − | 1.45427i | ||||||
\(807\) | 10.2619 | − | 9.93763i | 0.0127162 | − | 0.0123143i | ||||
\(808\) | 1014.88 | + | 1757.83i | 1.25604 | + | 2.17553i | ||||
\(809\) | −183.808 | + | 106.122i | −0.227204 | + | 0.131176i | −0.609282 | − | 0.792954i | \(-0.708542\pi\) |
0.382077 | + | 0.924130i | \(0.375209\pi\) | |||||||
\(810\) | 351.967 | + | 22.6329i | 0.434527 | + | 0.0279418i | ||||
\(811\) | −1058.66 | −1.30538 | −0.652690 | − | 0.757625i | \(-0.726359\pi\) | ||||
−0.652690 | + | 0.757625i | \(0.726359\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −426.826 | + | 1496.42i | −0.525001 | + | 1.84061i | ||||
\(814\) | −406.118 | + | 703.416i | −0.498916 | + | 0.864148i | ||||
\(815\) | −76.3224 | + | 44.0647i | −0.0936471 | + | 0.0540672i | ||||
\(816\) | 64.7148 | + | 258.018i | 0.0793074 | + | 0.316199i | ||||
\(817\) | −195.763 | + | 339.072i | −0.239612 | + | 0.415021i | ||||
\(818\) | − | 60.8792i | − | 0.0744244i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 691.956 | 0.843848 | ||||||||
\(821\) | −708.903 | − | 409.286i | −0.863463 | − | 0.498521i | 0.00170721 | − | 0.999999i | \(-0.499457\pi\) |
−0.865171 | + | 0.501478i | \(0.832790\pi\) | |||||||
\(822\) | 336.814 | − | 84.4781i | 0.409750 | − | 0.102771i | ||||
\(823\) | −103.425 | − | 179.137i | −0.125668 | − | 0.217664i | 0.796326 | − | 0.604868i | \(-0.206774\pi\) |
−0.921994 | + | 0.387204i | \(0.873441\pi\) | |||||||
\(824\) | 1560.32 | + | 900.853i | 1.89360 | + | 1.09327i | ||||
\(825\) | −474.516 | − | 135.347i | −0.575171 | − | 0.164057i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 438.639i | − | 0.530398i | −0.964194 | − | 0.265199i | \(-0.914562\pi\) | ||
0.964194 | − | 0.265199i | \(-0.0854376\pi\) | |||||||
\(828\) | −900.291 | − | 1681.83i | −1.08731 | − | 2.03119i | ||||
\(829\) | 327.402 | + | 567.077i | 0.394936 | + | 0.684049i | 0.993093 | − | 0.117330i | \(-0.0374334\pi\) |
−0.598157 | + | 0.801379i | \(0.704100\pi\) | |||||||
\(830\) | −280.118 | + | 161.726i | −0.337492 | + | 0.194851i | ||||
\(831\) | 252.703 | + | 260.950i | 0.304096 | + | 0.314020i | ||||
\(832\) | 566.257 | 0.680598 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 653.812 | + | 186.488i | 0.783947 | + | 0.223606i | ||||
\(835\) | −128.539 | + | 222.635i | −0.153938 | + | 0.266629i | ||||
\(836\) | 817.112 | − | 471.760i | 0.977407 | − | 0.564306i | ||||
\(837\) | 738.191 | + | 236.431i | 0.881949 | + | 0.282475i | ||||
\(838\) | 238.527 | − | 413.142i | 0.284639 | − | 0.493009i | ||||
\(839\) | − | 50.9710i | − | 0.0607521i | −0.999539 | − | 0.0303761i | \(-0.990330\pi\) | ||
0.999539 | − | 0.0303761i | \(-0.00967049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 750.830 | 0.892782 | ||||||||
\(842\) | −1287.33 | − | 743.242i | −1.52890 | − | 0.882710i | ||||
\(843\) | −297.231 | − | 1185.06i | −0.352587 | − | 1.40576i | ||||
\(844\) | 80.4980 | + | 139.427i | 0.0953768 | + | 0.165197i | ||||
\(845\) | 35.8990 | + | 20.7263i | 0.0424840 | + | 0.0245281i | ||||
\(846\) | −884.988 | − | 549.564i | −1.04609 | − | 0.649603i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 297.422i | 0.350733i | ||||||||
\(849\) | −831.946 | − | 859.096i | −0.979913 | − | 1.01189i | ||||
\(850\) | 186.188 | + | 322.487i | 0.219045 | + | 0.379397i | ||||
\(851\) | −731.471 | + | 422.315i | −0.859543 | + | 0.496257i | ||||
\(852\) | −1260.81 | + | 1220.97i | −1.47982 | + | 1.43306i | ||||
\(853\) | 883.941 | 1.03627 | 0.518137 | − | 0.855298i | \(-0.326626\pi\) | ||||
0.518137 | + | 0.855298i | \(0.326626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −95.6967 | + | 154.105i | −0.111926 | + | 0.180240i | ||||
\(856\) | −585.686 | + | 1014.44i | −0.684213 | + | 1.18509i | ||||
\(857\) | 481.961 | − | 278.260i | 0.562382 | − | 0.324691i | −0.191719 | − | 0.981450i | \(-0.561406\pi\) |
0.754101 | + | 0.656759i | \(0.228073\pi\) | |||||||
\(858\) | −833.059 | + | 208.944i | −0.970931 | + | 0.243524i | ||||
\(859\) | −321.539 | + | 556.922i | −0.374318 | + | 0.648338i | −0.990225 | − | 0.139481i | \(-0.955457\pi\) |
0.615907 | + | 0.787819i | \(0.288790\pi\) | |||||||
\(860\) | 248.439i | 0.288883i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1192.87 | 1.38384 | ||||||||
\(863\) | 177.442 | + | 102.446i | 0.205611 | + | 0.118709i | 0.599270 | − | 0.800547i | \(-0.295458\pi\) |
−0.393659 | + | 0.919256i | \(0.628791\pi\) | |||||||
\(864\) | 69.7867 | − | 217.890i | 0.0807716 | − | 0.252187i | ||||
\(865\) | 67.3542 | + | 116.661i | 0.0778662 | + | 0.134868i | ||||
\(866\) | 483.263 | + | 279.012i | 0.558040 | + | 0.322185i | ||||
\(867\) | −220.940 | + | 774.601i | −0.254833 | + | 0.893426i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 892.237i | 1.02674i | ||||||||
\(870\) | 89.1070 | − | 86.2909i | 0.102422 | − | 0.0991850i | ||||
\(871\) | −88.3098 | − | 152.957i | −0.101389 | − | 0.175611i | ||||
\(872\) | 476.095 | − | 274.874i | 0.545981 | − | 0.315222i | ||||
\(873\) | 183.815 | − | 98.3969i | 0.210555 | − | 0.112711i | ||||
\(874\) | 1454.48 | 1.66416 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 523.925 | − | 1836.84i | 0.598088 | − | 2.09685i | ||||
\(877\) | 103.605 | − | 179.450i | 0.118136 | − | 0.204617i | −0.800893 | − | 0.598807i | \(-0.795641\pi\) |
0.919029 | + | 0.394190i | \(0.128975\pi\) | |||||||
\(878\) | −388.858 | + | 224.507i | −0.442891 | + | 0.255703i | ||||
\(879\) | 1.84960 | + | 7.37437i | 0.00210421 | + | 0.00838949i | ||||
\(880\) | 85.2693 | − | 147.691i | 0.0968969 | − | 0.167830i | ||||
\(881\) | − | 1391.37i | − | 1.57931i | −0.613552 | − | 0.789654i | \(-0.710260\pi\) | ||
0.613552 | − | 0.789654i | \(-0.289740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1091.99 | −1.23668 | −0.618342 | − | 0.785909i | \(-0.712195\pi\) | ||||
−0.618342 | + | 0.785909i | \(0.712195\pi\) | |||||||
\(884\) | 378.642 | + | 218.609i | 0.428328 | + | 0.247296i | ||||
\(885\) | −333.916 | + | 83.7511i | −0.377306 | + | 0.0946340i | ||||
\(886\) | 345.929 | + | 599.167i | 0.390439 | + | 0.676261i | ||||
\(887\) | −129.426 | − | 74.7243i | −0.145915 | − | 0.0842439i | 0.425265 | − | 0.905069i | \(-0.360181\pi\) |
−0.571180 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(888\) | −1434.15 | − | 409.066i | −1.61504 | − | 0.460659i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 554.632i | 0.623183i | ||||||||
\(891\) | 36.4468 | − | 566.789i | 0.0409055 | − | 0.636127i | ||||
\(892\) | −725.674 | − | 1256.91i | −0.813536 | − | 1.40909i | ||||
\(893\) | 464.014 | − | 267.898i | 0.519612 | − | 0.299998i | ||||
\(894\) | −1432.17 | − | 1478.91i | −1.60198 | − | 1.65426i | ||||
\(895\) | 197.916 | 0.221135 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −858.863 | − | 244.975i | −0.957483 | − | 0.273104i | ||||
\(898\) | −259.616 | + | 449.667i | −0.289104 | + | 0.500743i | ||||
\(899\) | 236.087 | − | 136.305i | 0.262611 | − | 0.151618i | ||||
\(900\) | 56.1944 | − | 1749.58i | 0.0624382 | − | 1.94398i | ||||
\(901\) | 34.3844 | − | 59.5554i | 0.0381624 | − | 0.0660993i | ||||
\(902\) | − | 1651.84i | − | 1.83131i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −327.388 | −0.362155 | ||||||||
\(905\) | −251.565 | − | 145.241i | −0.277973 | − | 0.160488i | ||||
\(906\) | 261.636 | + | 1043.14i | 0.288781 | + | 1.15137i | ||||
\(907\) | −296.859 | − | 514.174i | −0.327297 | − | 0.566896i | 0.654677 | − | 0.755909i | \(-0.272805\pi\) |
−0.981975 | + | 0.189013i | \(0.939471\pi\) | |||||||
\(908\) | −1275.10 | − | 736.177i | −1.40429 | − | 0.810768i | ||||
\(909\) | −640.524 | + | 1031.47i | −0.704647 | + | 1.13473i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1133.75i | − | 1.24451i | −0.782815 | − | 0.622254i | \(-0.786217\pi\) | ||
0.782815 | − | 0.622254i | \(-0.213783\pi\) | |||||||
\(912\) | 663.263 | + | 684.908i | 0.727262 | + | 0.750996i | ||||
\(913\) | 260.435 | + | 451.087i | 0.285252 | + | 0.494071i | ||||
\(914\) | −371.070 | + | 214.237i | −0.405984 | + | 0.234395i | ||||
\(915\) | 153.957 | − | 149.091i | 0.168259 | − | 0.162941i | ||||
\(916\) | 338.391 | 0.369422 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −317.314 | + | 288.132i | −0.345658 | + | 0.313869i | ||||
\(919\) | 342.494 | − | 593.217i | 0.372681 | − | 0.645503i | −0.617296 | − | 0.786731i | \(-0.711772\pi\) |
0.989977 | + | 0.141228i | \(0.0451051\pi\) | |||||||
\(920\) | 413.688 | − | 238.843i | 0.449661 | − | 0.259612i | ||||
\(921\) | −250.937 | + | 62.9388i | −0.272462 | + | 0.0683375i | ||||
\(922\) | 1055.44 | − | 1828.07i | 1.14473 | − | 1.98273i | ||||
\(923\) | 821.706i | 0.890256i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −775.048 | −0.837890 | ||||||||
\(926\) | 1934.26 | + | 1116.74i | 2.08883 | + | 1.20599i | ||||
\(927\) | −34.5979 | + | 1077.19i | −0.0373224 | + | 1.16201i | ||||
\(928\) | −40.2327 | − | 69.6851i | −0.0433542 | − | 0.0750917i | ||||
\(929\) | 166.551 | + | 96.1584i | 0.179280 | + | 0.103507i | 0.586954 | − | 0.809620i | \(-0.300327\pi\) |
−0.407674 | + | 0.913127i | \(0.633660\pi\) | |||||||
\(930\) | −102.863 | + | 360.629i | −0.110605 | + | 0.387773i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3214.58i | 3.44912i | ||||||||
\(933\) | 327.094 | − | 316.757i | 0.350583 | − | 0.339504i | ||||
\(934\) | −1345.76 | − | 2330.92i | −1.44086 | − | 2.49563i | ||||
\(935\) | −34.1485 | + | 19.7156i | −0.0365225 | + | 0.0210863i | ||||
\(936\) | −744.234 | − | 1390.30i | −0.795122 | − | 1.48536i | ||||
\(937\) | 1270.28 | 1.35569 | 0.677844 | − | 0.735206i | \(-0.262914\pi\) | ||||
0.677844 | + | 0.735206i | \(0.262914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 261.771 | − | 917.750i | 0.278777 | − | 0.977370i | ||||
\(940\) | 169.992 | − | 294.435i | 0.180843 | − | 0.313229i | ||||
\(941\) | 135.923 | − | 78.4754i | 0.144446 | − | 0.0833957i | −0.426035 | − | 0.904706i | \(-0.640090\pi\) |
0.570481 | + | 0.821311i | \(0.306757\pi\) | |||||||
\(942\) | −267.960 | − | 1068.36i | −0.284459 | − | 1.13414i | ||||
\(943\) | 858.863 | − | 1487.59i | 0.910777 | − | 1.57751i | ||||
\(944\) | 1809.39i | 1.91673i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 593.077 | 0.626931 | ||||||||
\(947\) | 762.055 | + | 439.973i | 0.804704 | + | 0.464596i | 0.845114 | − | 0.534587i | \(-0.179533\pi\) |
−0.0404090 | + | 0.999183i | \(0.512866\pi\) | |||||||
\(948\) | −3070.11 | + | 770.030i | −3.23852 | + | 0.812268i | ||||
\(949\) | −447.136 | − | 774.462i | −0.471165 | − | 0.816082i | ||||
\(950\) | 1155.85 | + | 667.329i | 1.21668 | + | 0.702451i | ||||
\(951\) | 1050.18 | + | 299.543i | 1.10429 | + | 0.314977i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 563.276i | − | 0.591056i | −0.955334 | − | 0.295528i | \(-0.904505\pi\) | ||
0.955334 | − | 0.295528i | \(-0.0954955\pi\) | |||||||
\(954\) | −422.498 | + | 226.165i | −0.442870 | + | 0.237070i | ||||
\(955\) | 178.974 | + | 309.992i | 0.187407 | + | 0.324599i | ||||
\(956\) | −355.607 | + | 205.310i | −0.371974 | + | 0.214759i | ||||
\(957\) | −138.958 | − | 143.493i | −0.145202 | − | 0.149941i | ||||
\(958\) | −1380.83 | −1.44136 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −174.218 | − | 49.6926i | −0.181477 | − | 0.0517631i | ||||
\(961\) | 68.4111 | − | 118.491i | 0.0711874 | − | 0.123300i | ||||
\(962\) | −1168.28 | + | 674.508i | −1.21443 | + | 0.701151i | ||||
\(963\) | −700.328 | − | 22.4937i | −0.727236 | − | 0.0233580i | ||||
\(964\) | −1348.39 | + | 2335.49i | −1.39875 | + | 2.42270i | ||||
\(965\) | 95.7826i | 0.0992566i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 237.676 | 0.245787 | 0.122893 | − | 0.992420i | \(-0.460783\pi\) | ||||
0.122893 | + | 0.992420i | \(0.460783\pi\) | |||||||
\(968\) | 935.993 | + | 540.396i | 0.966935 | + | 0.558260i | ||||
\(969\) | −53.6302 | − | 213.824i | −0.0553460 | − | 0.220665i | ||||
\(970\) | 50.4353 | + | 87.3565i | 0.0519951 | + | 0.0900582i | ||||
\(971\) | 1173.46 | + | 677.498i | 1.20851 | + | 0.697732i | 0.962433 | − | 0.271519i | \(-0.0875258\pi\) |
0.246075 | + | 0.969251i | \(0.420859\pi\) | |||||||
\(972\) | 1981.73 | − | 363.748i | 2.03882 | − | 0.374226i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2010.33i | 2.06399i | ||||||||
\(975\) | −570.126 | − | 588.731i | −0.584744 | − | 0.603827i | ||||
\(976\) | −563.210 | − | 975.508i | −0.577059 | − | 0.999496i | ||||
\(977\) | 427.579 | − | 246.863i | 0.437645 | − | 0.252674i | −0.264953 | − | 0.964261i | \(-0.585357\pi\) |
0.702598 | + | 0.711587i | \(0.252023\pi\) | |||||||
\(978\) | −536.143 | + | 519.199i | −0.548203 | + | 0.530878i | ||||
\(979\) | 893.150 | 0.912309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 279.365 | + | 173.481i | 0.284775 | + | 0.176841i | ||||
\(982\) | 299.399 | − | 518.574i | 0.304887 | − | 0.528079i | ||||
\(983\) | −1331.99 | + | 769.026i | −1.35503 | + | 0.782325i | −0.988949 | − | 0.148259i | \(-0.952633\pi\) |
−0.366078 | + | 0.930584i | \(0.619300\pi\) | |||||||
\(984\) | 2941.84 | − | 737.858i | 2.98968 | − | 0.749856i | ||||
\(985\) | 84.7229 | − | 146.744i | 0.0860130 | − | 0.148979i | ||||
\(986\) | 150.741i | 0.152881i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1567.06 | 1.58609 | ||||||||
\(989\) | 534.105 | + | 308.365i | 0.540045 | + | 0.311795i | ||||
\(990\) | 274.640 | + | 8.82112i | 0.277414 | + | 0.00891022i | ||||
\(991\) | −757.365 | − | 1311.79i | −0.764243 | − | 1.32371i | −0.940646 | − | 0.339389i | \(-0.889780\pi\) |
0.176403 | − | 0.984318i | \(-0.443554\pi\) | |||||||
\(992\) | 210.678 | + | 121.635i | 0.212377 | + | 0.122616i | ||||
\(993\) | −127.026 | + | 445.344i | −0.127922 | + | 0.448483i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 107.533i | − | 0.108074i | ||||||
\(996\) | −1327.39 | + | 1285.44i | −1.33272 | + | 1.29060i | ||||
\(997\) | 913.216 | + | 1581.74i | 0.915964 | + | 1.58650i | 0.805484 | + | 0.592618i | \(0.201906\pi\) |
0.110481 | + | 0.993878i | \(0.464761\pi\) | |||||||
\(998\) | −2574.15 | + | 1486.19i | −2.57931 | + | 1.48916i | ||||
\(999\) | −189.139 | − | 871.813i | −0.189328 | − | 0.872686i |
(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 | 147.3.h.c.128.1 | 8 | ||
3.2 | odd | 2 | inner | 147.3.h.c.128.4 | 8 | ||
7.2 | even | 3 | 147.3.b.f.50.4 | 4 | |||
7.3 | odd | 6 | 147.3.h.e.116.4 | 8 | |||
7.4 | even | 3 | inner | 147.3.h.c.116.4 | 8 | ||
7.5 | odd | 6 | 21.3.b.a.8.4 | yes | 4 | ||
7.6 | odd | 2 | 147.3.h.e.128.1 | 8 | |||
21.2 | odd | 6 | 147.3.b.f.50.1 | 4 | |||
21.5 | even | 6 | 21.3.b.a.8.1 | ✓ | 4 | ||
21.11 | odd | 6 | inner | 147.3.h.c.116.1 | 8 | ||
21.17 | even | 6 | 147.3.h.e.116.1 | 8 | |||
21.20 | even | 2 | 147.3.h.e.128.4 | 8 | |||
28.19 | even | 6 | 336.3.d.c.113.2 | 4 | |||
35.12 | even | 12 | 525.3.f.a.449.1 | 8 | |||
35.19 | odd | 6 | 525.3.c.a.176.1 | 4 | |||
35.33 | even | 12 | 525.3.f.a.449.8 | 8 | |||
56.5 | odd | 6 | 1344.3.d.f.449.2 | 4 | |||
56.19 | even | 6 | 1344.3.d.b.449.3 | 4 | |||
63.5 | even | 6 | 567.3.r.c.512.4 | 8 | |||
63.40 | odd | 6 | 567.3.r.c.512.1 | 8 | |||
63.47 | even | 6 | 567.3.r.c.134.1 | 8 | |||
63.61 | odd | 6 | 567.3.r.c.134.4 | 8 | |||
84.47 | odd | 6 | 336.3.d.c.113.1 | 4 | |||
105.47 | odd | 12 | 525.3.f.a.449.7 | 8 | |||
105.68 | odd | 12 | 525.3.f.a.449.2 | 8 | |||
105.89 | even | 6 | 525.3.c.a.176.4 | 4 | |||
168.5 | even | 6 | 1344.3.d.f.449.1 | 4 | |||
168.131 | odd | 6 | 1344.3.d.b.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.b.a.8.1 | ✓ | 4 | 21.5 | even | 6 | ||
21.3.b.a.8.4 | yes | 4 | 7.5 | odd | 6 | ||
147.3.b.f.50.1 | 4 | 21.2 | odd | 6 | |||
147.3.b.f.50.4 | 4 | 7.2 | even | 3 | |||
147.3.h.c.116.1 | 8 | 21.11 | odd | 6 | inner | ||
147.3.h.c.116.4 | 8 | 7.4 | even | 3 | inner | ||
147.3.h.c.128.1 | 8 | 1.1 | even | 1 | trivial | ||
147.3.h.c.128.4 | 8 | 3.2 | odd | 2 | inner | ||
147.3.h.e.116.1 | 8 | 21.17 | even | 6 | |||
147.3.h.e.116.4 | 8 | 7.3 | odd | 6 | |||
147.3.h.e.128.1 | 8 | 7.6 | odd | 2 | |||
147.3.h.e.128.4 | 8 | 21.20 | even | 2 | |||
336.3.d.c.113.1 | 4 | 84.47 | odd | 6 | |||
336.3.d.c.113.2 | 4 | 28.19 | even | 6 | |||
525.3.c.a.176.1 | 4 | 35.19 | odd | 6 | |||
525.3.c.a.176.4 | 4 | 105.89 | even | 6 | |||
525.3.f.a.449.1 | 8 | 35.12 | even | 12 | |||
525.3.f.a.449.2 | 8 | 105.68 | odd | 12 | |||
525.3.f.a.449.7 | 8 | 105.47 | odd | 12 | |||
525.3.f.a.449.8 | 8 | 35.33 | even | 12 | |||
567.3.r.c.134.1 | 8 | 63.47 | even | 6 | |||
567.3.r.c.134.4 | 8 | 63.61 | odd | 6 | |||
567.3.r.c.512.1 | 8 | 63.40 | odd | 6 | |||
567.3.r.c.512.4 | 8 | 63.5 | even | 6 | |||
1344.3.d.b.449.3 | 4 | 56.19 | even | 6 | |||
1344.3.d.b.449.4 | 4 | 168.131 | odd | 6 | |||
1344.3.d.f.449.1 | 4 | 168.5 | even | 6 | |||
1344.3.d.f.449.2 | 4 | 56.5 | odd | 6 |