Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,3,Mod(134,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.134");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.r (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: | \(15.4496309892\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 512.4 | ||
Root | \(2.10277 + 0.136187i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.512 |
Dual form | 567.3.r.c.134.4 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.03622 | + | 1.75296i | 1.51811 | + | 0.876481i | 0.999773 | + | 0.0213043i | \(0.00678187\pi\) |
0.518337 | + | 0.855177i | \(0.326551\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.14575 | + | 7.18065i | 1.03644 | + | 1.79516i | ||||
\(5\) | 1.07558 | − | 0.620984i | 0.215115 | − | 0.124197i | −0.388571 | − | 0.921419i | \(-0.627031\pi\) |
0.603686 | + | 0.797222i | \(0.293698\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32288 | + | 2.29129i | −0.188982 | + | 0.327327i | ||||
\(8\) | 15.0457i | 1.88071i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.35425 | 0.435425 | ||||||||
\(11\) | 6.07244 | + | 3.50592i | 0.552040 | + | 0.318720i | 0.749944 | − | 0.661501i | \(-0.230080\pi\) |
−0.197904 | + | 0.980221i | \(0.563414\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.82288 | + | 10.0855i | 0.447914 | + | 0.775809i | 0.998250 | − | 0.0591340i | \(-0.0188339\pi\) |
−0.550337 | + | 0.834943i | \(0.685501\pi\) | |||||||
\(14\) | −8.03308 | + | 4.63790i | −0.573791 | + | 0.331279i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.79150 | + | 16.9594i | −0.611969 | + | 1.05996i | ||||
\(17\) | 4.52791i | 0.266348i | 0.991093 | + | 0.133174i | \(0.0425169\pi\) | ||||
−0.991093 | + | 0.133174i | \(0.957483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.2288 | 0.854145 | 0.427073 | − | 0.904217i | \(-0.359545\pi\) | ||||
0.427073 | + | 0.904217i | \(0.359545\pi\) | |||||||
\(20\) | 8.91815 | + | 5.14889i | 0.445907 | + | 0.257445i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.2915 | + | 21.2895i | 0.558705 | + | 0.967705i | ||||
\(23\) | −22.1386 | + | 12.7817i | −0.962548 | + | 0.555727i | −0.896956 | − | 0.442119i | \(-0.854227\pi\) |
−0.0655916 | + | 0.997847i | \(0.520893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.7288 | + | 20.3148i | −0.469150 | + | 0.812592i | ||||
\(26\) | 40.8291i | 1.57035i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −21.9373 | −0.783473 | ||||||||
\(29\) | −8.22359 | − | 4.74789i | −0.283572 | − | 0.163720i | 0.351467 | − | 0.936200i | \(-0.385683\pi\) |
−0.635039 | + | 0.772480i | \(0.719016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.3542 | − | 24.8623i | −0.463040 | − | 0.802009i | 0.536070 | − | 0.844173i | \(-0.319908\pi\) |
−0.999111 | + | 0.0421640i | \(0.986575\pi\) | |||||||
\(32\) | −7.33853 | + | 4.23690i | −0.229329 | + | 0.132403i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.93725 | + | 13.7477i | −0.233449 | + | 0.404345i | ||||
\(35\) | 3.28594i | 0.0938840i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.0405 | −0.892987 | −0.446493 | − | 0.894787i | \(-0.647327\pi\) | ||||
−0.446493 | + | 0.894787i | \(0.647327\pi\) | |||||||
\(38\) | 49.2741 | + | 28.4484i | 1.29669 | + | 0.748642i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.34313 | + | 16.1828i | 0.233578 | + | 0.404570i | ||||
\(41\) | 58.1922 | − | 33.5973i | 1.41932 | − | 0.819446i | 0.423083 | − | 0.906091i | \(-0.360948\pi\) |
0.996239 | + | 0.0866449i | \(0.0276146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.0627 | − | 20.8933i | 0.280529 | − | 0.485890i | −0.690986 | − | 0.722868i | \(-0.742823\pi\) |
0.971515 | + | 0.236978i | \(0.0761568\pi\) | |||||||
\(44\) | 58.1388i | 1.32134i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −89.6235 | −1.94834 | ||||||||
\(47\) | 28.5921 | + | 16.5076i | 0.608342 | + | 0.351226i | 0.772316 | − | 0.635238i | \(-0.219098\pi\) |
−0.163974 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −71.2222 | + | 41.1201i | −1.42444 | + | 0.822403i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −48.2804 | + | 83.6241i | −0.928469 | + | 1.60816i | ||||
\(53\) | − | 15.1877i | − | 0.286561i | −0.989682 | − | 0.143281i | \(-0.954235\pi\) | ||
0.989682 | − | 0.143281i | \(-0.0457651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.70850 | 0.158336 | ||||||||
\(56\) | −34.4740 | − | 19.9036i | −0.615607 | − | 0.355421i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −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 | \(0.0470131\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.7601 | − | 49.8140i | 0.471478 | − | 0.816623i | −0.527990 | − | 0.849251i | \(-0.677054\pi\) |
0.999468 | + | 0.0326275i | \(0.0103875\pi\) | |||||||
\(62\) | − | 100.650i | − | 1.62338i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 48.6235 | 0.759743 | ||||||||
\(65\) | 12.5259 | + | 7.23183i | 0.192706 | + | 0.111259i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.76013 | + | 9.97684i | −0.0822876 | + | 0.142526i | ||||
\(71\) | − | 70.5584i | − | 0.993781i | −0.867813 | − | 0.496890i | \(-0.834475\pi\) | ||
0.867813 | − | 0.496890i | \(-0.165525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.7895 | −1.05191 | −0.525956 | − | 0.850512i | \(-0.676292\pi\) | ||||
−0.525956 | + | 0.850512i | \(0.676292\pi\) | |||||||
\(74\) | −100.318 | − | 57.9188i | −1.35565 | − | 0.782686i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 67.2804 | + | 116.533i | 0.885268 | + | 1.53333i | ||||
\(77\) | −16.0662 | + | 9.27580i | −0.208651 | + | 0.120465i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −63.6235 | + | 110.199i | −0.805361 | + | 1.39493i | 0.110686 | + | 0.993855i | \(0.464695\pi\) |
−0.916047 | + | 0.401071i | \(0.868638\pi\) | |||||||
\(80\) | 24.3215i | 0.304019i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 235.579 | 2.87292 | ||||||||
\(83\) | −64.3321 | − | 37.1422i | −0.775086 | − | 0.447496i | 0.0596000 | − | 0.998222i | \(-0.481017\pi\) |
−0.834686 | + | 0.550726i | \(0.814351\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.81176 | + | 4.87011i | 0.0330796 | + | 0.0572955i | ||||
\(86\) | 73.2503 | − | 42.2911i | 0.851747 | − | 0.491757i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −52.7490 | + | 91.3640i | −0.599421 | + | 1.03823i | ||||
\(89\) | − | 127.377i | − | 1.43121i | −0.698507 | − | 0.715603i | \(-0.746152\pi\) | ||
0.698507 | − | 0.715603i | \(-0.253848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30.8118 | −0.338591 | ||||||||
\(92\) | −183.562 | − | 105.980i | −1.99524 | − | 1.15195i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 57.8745 | + | 100.242i | 0.615686 | + | 1.06640i | ||||
\(95\) | 17.4553 | − | 10.0778i | 0.183740 | − | 0.106082i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5830 | − | 20.0624i | 0.119412 | − | 0.206828i | −0.800123 | − | 0.599837i | \(-0.795232\pi\) |
0.919535 | + | 0.393008i | \(0.128566\pi\) | |||||||
\(98\) | − | 24.5415i | − | 0.250423i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −194.498 | −1.94498 | ||||||||
\(101\) | 116.833 | + | 67.4535i | 1.15676 | + | 0.667857i | 0.950526 | − | 0.310646i | \(-0.100545\pi\) |
0.206236 | + | 0.978502i | \(0.433879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59.8745 | + | 103.706i | 0.581306 | + | 1.00685i | 0.995325 | + | 0.0965831i | \(0.0307914\pi\) |
−0.414019 | + | 0.910268i | \(0.635875\pi\) | |||||||
\(104\) | −151.743 | + | 87.6091i | −1.45907 | + | 0.842396i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.6235 | − | 46.1133i | 0.251165 | − | 0.435031i | ||||
\(107\) | − | 77.8544i | − | 0.727611i | −0.931475 | − | 0.363806i | \(-0.881477\pi\) | ||
0.931475 | − | 0.363806i | \(-0.118523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −36.5385 | −0.335216 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(110\) | 26.4409 | + | 15.2657i | 0.240372 | + | 0.138779i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −25.9059 | − | 44.8703i | −0.231303 | − | 0.400628i | ||||
\(113\) | 18.8444 | − | 10.8798i | 0.166764 | − | 0.0962815i | −0.414295 | − | 0.910143i | \(-0.635972\pi\) |
0.581059 | + | 0.813861i | \(0.302638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8745 | + | 27.4955i | −0.138039 | + | 0.239091i | ||||
\(116\) | − | 78.7343i | − | 0.678744i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 323.933 | 2.74520 | ||||||||
\(119\) | −10.3747 | − | 5.98986i | −0.0871827 | − | 0.0503350i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.9170 | − | 62.2101i | −0.296835 | − | 0.514133i | ||||
\(122\) | 174.644 | − | 100.831i | 1.43151 | − | 0.826482i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 25.3542 | + | 43.9148i | 0.195033 | + | 0.337807i | ||||
\(131\) | 158.578 | − | 91.5550i | 1.21052 | − | 0.698893i | 0.247646 | − | 0.968850i | \(-0.420343\pi\) |
0.962872 | + | 0.269957i | \(0.0870095\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.4686 | + | 37.1848i | −0.161418 | + | 0.279585i | ||||
\(134\) | − | 53.1709i | − | 0.396798i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −68.1255 | −0.500923 | ||||||||
\(137\) | −28.5921 | − | 16.5076i | −0.208701 | − | 0.120494i | 0.392006 | − | 0.919962i | \(-0.371781\pi\) |
−0.600708 | + | 0.799469i | \(0.705114\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −32.3209 | − | 55.9815i | −0.232525 | − | 0.402744i | 0.726026 | − | 0.687667i | \(-0.241365\pi\) |
−0.958550 | + | 0.284923i | \(0.908032\pi\) | |||||||
\(140\) | −23.5952 | + | 13.6227i | −0.168537 | + | 0.0973050i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 123.686 | − | 214.231i | 0.871030 | − | 1.50867i | ||||
\(143\) | 81.6582i | 0.571037i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.7935 | −0.0813343 | ||||||||
\(146\) | −233.150 | − | 134.609i | −1.59692 | − | 0.921980i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −136.978 | − | 237.252i | −0.925525 | − | 1.60306i | ||||
\(149\) | 169.512 | − | 97.8680i | 1.13767 | − | 0.656832i | 0.191815 | − | 0.981431i | \(-0.438563\pi\) |
0.945852 | + | 0.324599i | \(0.105229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −51.1255 | + | 88.5519i | −0.338579 | + | 0.586437i | −0.984166 | − | 0.177251i | \(-0.943280\pi\) |
0.645586 | + | 0.763687i | \(0.276613\pi\) | |||||||
\(152\) | 244.173i | 1.60640i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −65.0405 | −0.422341 | ||||||||
\(155\) | −30.8782 | − | 17.8275i | −0.199214 | − | 0.115016i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −52.3614 | − | 90.6926i | −0.333512 | − | 0.577660i | 0.649686 | − | 0.760203i | \(-0.274901\pi\) |
−0.983198 | + | 0.182543i | \(0.941567\pi\) | |||||||
\(158\) | −386.350 | + | 223.059i | −2.44525 | + | 1.41177i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.26210 | + | 9.11422i | −0.0328881 | + | 0.0569639i | ||||
\(161\) | − | 67.6345i | − | 0.420090i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −70.9595 | −0.435334 | −0.217667 | − | 0.976023i | \(-0.569845\pi\) | ||||
−0.217667 | + | 0.976023i | \(0.569845\pi\) | |||||||
\(164\) | 482.501 | + | 278.572i | 2.94208 | + | 1.69861i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −130.218 | − | 225.544i | −0.784444 | − | 1.35870i | ||||
\(167\) | −179.260 | + | 103.496i | −1.07341 | + | 0.619735i | −0.929112 | − | 0.369799i | \(-0.879427\pi\) |
−0.144301 | + | 0.989534i | \(0.546093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.6882 | − | 28.9049i | 0.0987470 | − | 0.171035i | ||||
\(170\) | 19.7156i | 0.115974i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 200.037 | 1.16300 | ||||||||
\(173\) | −93.9323 | − | 54.2318i | −0.542961 | − | 0.313479i | 0.203317 | − | 0.979113i | \(-0.434828\pi\) |
−0.746278 | + | 0.665634i | \(0.768161\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −31.0314 | − | 53.7479i | −0.177322 | − | 0.307131i | ||||
\(176\) | −118.917 | + | 68.6565i | −0.675662 | + | 0.390094i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 223.288 | − | 386.745i | 1.25442 | − | 2.17273i | ||||
\(179\) | 159.357i | 0.890261i | 0.895466 | + | 0.445131i | \(0.146843\pi\) | ||||
−0.895466 | + | 0.445131i | \(0.853157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −233.889 | −1.29220 | −0.646102 | − | 0.763251i | \(-0.723602\pi\) | ||||
−0.646102 | + | 0.763251i | \(0.723602\pi\) | |||||||
\(182\) | −93.5513 | − | 54.0118i | −0.514018 | − | 0.296768i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −192.310 | − | 333.090i | −1.04516 | − | 1.81027i | ||||
\(185\) | −35.5376 | + | 20.5176i | −0.192095 | + | 0.110906i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −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 | 0.981559 | − | 0.191158i | \(-0.0612244\pi\) |
0.325232 | + | 0.945634i | \(0.394558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −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 | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 29.0203 | − | 50.2646i | 0.148063 | − | 0.256452i | ||||
\(197\) | − | 136.433i | − | 0.692554i | −0.938132 | − | 0.346277i | \(-0.887446\pi\) | ||
0.938132 | − | 0.346277i | \(-0.112554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 86.5830 | 0.435090 | 0.217545 | − | 0.976050i | \(-0.430195\pi\) | ||||
0.217545 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(200\) | −305.650 | − | 176.467i | −1.52825 | − | 0.882336i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 236.487 | + | 409.607i | 1.17073 | + | 2.02776i | ||||
\(203\) | 21.7576 | − | 12.5617i | 0.107180 | − | 0.0618805i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41.7268 | − | 72.2729i | 0.203545 | − | 0.352551i | ||||
\(206\) | 419.831i | 2.03801i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −228.059 | −1.09644 | ||||||||
\(209\) | 98.5481 | + | 56.8968i | 0.471522 | + | 0.272233i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.70850 | − | 16.8156i | −0.0460118 | − | 0.0796948i | 0.842102 | − | 0.539318i | \(-0.181318\pi\) |
−0.888114 | + | 0.459623i | \(0.847985\pi\) | |||||||
\(212\) | 109.058 | − | 62.9646i | 0.514424 | − | 0.297003i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 136.476 | − | 236.383i | 0.637737 | − | 1.10459i | ||||
\(215\) | − | 29.9631i | − | 0.139363i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 75.9555 | 0.350026 | ||||||||
\(218\) | −110.939 | − | 64.0507i | −0.508895 | − | 0.293810i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 36.1033 | + | 62.5327i | 0.164106 | + | 0.284239i | ||||
\(221\) | −45.6663 | + | 26.3655i | −0.206635 | + | 0.119301i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −87.5203 | + | 151.590i | −0.392468 | + | 0.679774i | −0.992774 | − | 0.119996i | \(-0.961712\pi\) |
0.600307 | + | 0.799770i | \(0.295045\pi\) | |||||||
\(224\) | − | 22.4196i | − | 0.100087i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 76.2876 | 0.337556 | ||||||||
\(227\) | 153.784 | + | 88.7870i | 0.677461 | + | 0.391132i | 0.798898 | − | 0.601467i | \(-0.205417\pi\) |
−0.121437 | + | 0.992599i | \(0.538750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.4059 | − | 35.3440i | −0.0891087 | − | 0.154341i | 0.818026 | − | 0.575181i | \(-0.195069\pi\) |
−0.907135 | + | 0.420841i | \(0.861735\pi\) | |||||||
\(230\) | −96.3970 | + | 55.6548i | −0.419117 | + | 0.241977i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 71.4353 | − | 123.730i | 0.307911 | − | 0.533317i | ||||
\(233\) | 387.696i | 1.66393i | 0.554828 | + | 0.831965i | \(0.312784\pi\) | ||||
−0.554828 | + | 0.831965i | \(0.687216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.0039 | 0.174485 | ||||||||
\(236\) | 663.463 | + | 383.051i | 2.81129 | + | 1.62310i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −21.0000 | − | 36.3731i | −0.0882353 | − | 0.152828i | ||||
\(239\) | −42.8881 | + | 24.7615i | −0.179448 | + | 0.103604i | −0.587033 | − | 0.809563i | \(-0.699704\pi\) |
0.407585 | + | 0.913167i | \(0.366371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −162.624 | + | 281.672i | −0.674786 | + | 1.16876i | 0.301745 | + | 0.953389i | \(0.402431\pi\) |
−0.976531 | + | 0.215376i | \(0.930902\pi\) | |||||||
\(242\) | − | 251.845i | − | 1.04068i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 476.929 | 1.95463 | ||||||||
\(245\) | −7.52904 | − | 4.34689i | −0.0307308 | − | 0.0177424i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 94.4980 | + | 163.675i | 0.382583 | + | 0.662653i | ||||
\(248\) | 374.070 | − | 215.969i | 1.50835 | − | 0.870845i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −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 | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 260.998 | + | 452.062i | 1.01952 | + | 1.76587i | ||||
\(257\) | −130.926 | + | 75.5904i | −0.509442 | + | 0.294126i | −0.732604 | − | 0.680655i | \(-0.761695\pi\) |
0.223162 | + | 0.974781i | \(0.428362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 43.7085 | − | 75.7053i | 0.168759 | − | 0.292299i | ||||
\(260\) | 119.925i | 0.461252i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 641.970 | 2.45027 | ||||||||
\(263\) | −99.0641 | − | 57.1947i | −0.376670 | − | 0.217470i | 0.299699 | − | 0.954034i | \(-0.403114\pi\) |
−0.676368 | + | 0.736564i | \(0.736447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.43135 | − | 16.3356i | −0.0355900 | − | 0.0616437i | ||||
\(266\) | −130.367 | + | 75.2674i | −0.490101 | + | 0.282960i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 62.8745 | − | 108.902i | 0.234606 | − | 0.406350i | ||||
\(269\) | 4.76170i | 0.0177015i | 0.999961 | + | 0.00885074i | \(0.00281731\pi\) | ||||
−0.999961 | + | 0.00885074i | \(0.997183\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −518.701 | −1.91402 | −0.957012 | − | 0.290048i | \(-0.906329\pi\) | ||||
−0.957012 | + | 0.290048i | \(0.906329\pi\) | |||||||
\(272\) | −76.7905 | − | 44.3350i | −0.282318 | − | 0.162996i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −57.8745 | − | 100.242i | −0.211221 | − | 0.365845i | ||||
\(275\) | −142.444 | + | 82.2403i | −0.517979 | + | 0.299055i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 60.5425 | − | 104.863i | 0.218565 | − | 0.378566i | −0.735805 | − | 0.677194i | \(-0.763196\pi\) |
0.954369 | + | 0.298628i | \(0.0965291\pi\) | |||||||
\(278\) | − | 226.629i | − | 0.815213i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −49.4392 | −0.176569 | ||||||||
\(281\) | −352.694 | − | 203.628i | −1.25514 | − | 0.724654i | −0.283012 | − | 0.959116i | \(-0.591334\pi\) |
−0.972125 | + | 0.234463i | \(0.924667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 199.317 | + | 345.227i | 0.704300 | + | 1.21988i | 0.966943 | + | 0.254991i | \(0.0820724\pi\) |
−0.262643 | + | 0.964893i | \(0.584594\pi\) | |||||||
\(284\) | 506.656 | − | 292.518i | 1.78400 | − | 1.02999i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −143.144 | + | 247.932i | −0.500503 | + | 0.866896i | ||||
\(287\) | 177.780i | 0.619443i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 268.498 | 0.929059 | ||||||||
\(290\) | −35.8076 | − | 20.6735i | −0.123474 | − | 0.0712880i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −318.350 | − | 551.399i | −1.09024 | − | 1.88835i | ||||
\(293\) | 2.19473 | − | 1.26713i | 0.00749056 | − | 0.00432468i | −0.496250 | − | 0.868180i | \(-0.665290\pi\) |
0.503741 | + | 0.863855i | \(0.331957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 57.3765 | − | 99.3790i | 0.194497 | − | 0.336878i | ||||
\(296\) | − | 497.117i | − | 1.67945i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 686.235 | 2.30280 | ||||||||
\(299\) | −257.821 | − | 148.853i | −0.862276 | − | 0.497835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.9150 | + | 55.2784i | 0.106030 | + | 0.183649i | ||||
\(302\) | −310.456 | + | 179.242i | −1.02800 | + | 0.593517i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −158.904 | + | 275.230i | −0.522710 | + | 0.905361i | ||||
\(305\) | − | 71.4384i | − | 0.234224i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 86.2366 | 0.280901 | 0.140451 | − | 0.990088i | \(-0.455145\pi\) | ||||
0.140451 | + | 0.990088i | \(0.455145\pi\) | |||||||
\(308\) | −133.213 | − | 76.9103i | −0.432509 | − | 0.249709i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −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 | \(0.254869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −159.059 | + | 275.498i | −0.508175 | + | 0.880185i | 0.491780 | + | 0.870719i | \(0.336346\pi\) |
−0.999955 | + | 0.00946567i | \(0.996987\pi\) | |||||||
\(314\) | − | 367.150i | − | 1.16927i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1055.07 | −3.33883 | ||||||||
\(317\) | −315.251 | − | 182.010i | −0.994482 | − | 0.574164i | −0.0878710 | − | 0.996132i | \(-0.528006\pi\) |
−0.906611 | + | 0.421967i | \(0.861340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.2915 | − | 57.6626i | −0.104362 | − | 0.180760i | ||||
\(320\) | 52.2983 | − | 30.1945i | 0.163432 | − | 0.0943577i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 118.561 | − | 205.353i | 0.368201 | − | 0.637743i | ||||
\(323\) | 73.4823i | 0.227500i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −273.180 | −0.840555 | ||||||||
\(326\) | −215.449 | − | 124.389i | −0.660885 | − | 0.381562i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 505.494 | + | 875.541i | 1.54114 | + | 2.66933i | ||||
\(329\) | −75.6475 | + | 43.6751i | −0.229932 | + | 0.132751i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −77.1843 | + | 133.687i | −0.233185 | + | 0.403889i | −0.958744 | − | 0.284272i | \(-0.908248\pi\) |
0.725559 | + | 0.688160i | \(0.241582\pi\) | |||||||
\(332\) | − | 615.929i | − | 1.85521i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −725.697 | −2.17274 | ||||||||
\(335\) | −16.3122 | − | 9.41786i | −0.0486932 | − | 0.0281130i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −201.520 | − | 349.043i | −0.597983 | − | 1.03574i | −0.993118 | − | 0.117114i | \(-0.962636\pi\) |
0.395136 | − | 0.918623i | \(-0.370698\pi\) | |||||||
\(338\) | 101.338 | − | 58.5077i | 0.299817 | − | 0.173100i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −23.3137 | + | 40.3806i | −0.0685698 | + | 0.118766i | ||||
\(341\) | − | 201.300i | − | 0.590321i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | 314.354 | + | 181.492i | 0.913819 | + | 0.527594i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −190.133 | − | 329.319i | −0.549516 | − | 0.951790i | ||||
\(347\) | −408.108 | + | 235.621i | −1.17610 | + | 0.679023i | −0.955110 | − | 0.296252i | \(-0.904263\pi\) |
−0.220993 | + | 0.975275i | \(0.570930\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 182.258 | − | 315.680i | 0.522230 | − | 0.904528i | −0.477436 | − | 0.878667i | \(-0.658434\pi\) |
0.999666 | − | 0.0258617i | \(-0.00823297\pi\) | |||||||
\(350\) | − | 217.587i | − | 0.621678i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −59.4170 | −0.168798 | ||||||||
\(353\) | 74.7744 | + | 43.1710i | 0.211825 | + | 0.122297i | 0.602159 | − | 0.798376i | \(-0.294307\pi\) |
−0.390334 | + | 0.920673i | \(0.627640\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.8157 | − | 75.8910i | −0.123425 | − | 0.213778i | ||||
\(356\) | 914.652 | − | 528.075i | 2.56925 | − | 1.48336i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −279.346 | + | 483.842i | −0.780297 | + | 1.35151i | ||||
\(359\) | 372.068i | 1.03640i | 0.855259 | + | 0.518200i | \(0.173398\pi\) | ||||
−0.855259 | + | 0.518200i | \(0.826602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −97.6275 | −0.270436 | ||||||||
\(362\) | −710.138 | − | 409.998i | −1.96171 | − | 1.13259i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −127.738 | − | 221.249i | −0.350928 | − | 0.607826i | ||||
\(365\) | −82.5930 | + | 47.6851i | −0.226282 | + | 0.130644i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 80.8928 | − | 140.110i | 0.220416 | − | 0.381772i | −0.734518 | − | 0.678589i | \(-0.762592\pi\) |
0.954934 | + | 0.296817i | \(0.0959251\pi\) | |||||||
\(368\) | − | 500.609i | − | 1.36035i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −143.867 | −0.388829 | ||||||||
\(371\) | 34.7995 | + | 20.0915i | 0.0937991 | + | 0.0541549i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −189.125 | − | 327.575i | −0.507039 | − | 0.878217i | −0.999967 | − | 0.00814693i | \(-0.997407\pi\) |
0.492928 | − | 0.870070i | \(-0.335927\pi\) | |||||||
\(374\) | −96.3970 | + | 55.6548i | −0.257746 | + | 0.148810i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −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 | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 505.221 | + | 875.068i | 1.32257 | + | 2.29075i | ||||
\(383\) | 98.1910 | − | 56.6906i | 0.256373 | − | 0.148017i | −0.366306 | − | 0.930495i | \(-0.619378\pi\) |
0.622679 | + | 0.782477i | \(0.286044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5203 | + | 19.9537i | −0.0299228 | + | 0.0518277i | ||||
\(386\) | − | 270.382i | − | 0.700472i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 192.081 | 0.495054 | ||||||||
\(389\) | 628.374 | + | 362.792i | 1.61536 | + | 0.932628i | 0.988099 | + | 0.153817i | \(0.0491565\pi\) |
0.627259 | + | 0.778811i | \(0.284177\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.8745 | − | 100.242i | −0.148017 | − | 0.256372i | ||||
\(392\) | 91.2096 | − | 52.6599i | 0.232678 | − | 0.134336i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 239.162 | − | 414.241i | 0.607010 | − | 1.05137i | ||||
\(395\) | 158.037i | 0.400093i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −94.3464 | −0.237648 | −0.118824 | − | 0.992915i | \(-0.537912\pi\) | ||||
−0.118824 | + | 0.992915i | \(0.537912\pi\) | |||||||
\(398\) | 262.885 | + | 151.777i | 0.660515 | + | 0.381349i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −229.684 | − | 397.825i | −0.574211 | − | 0.994562i | ||||
\(401\) | −586.875 | + | 338.833i | −1.46353 | + | 0.844969i | −0.999172 | − | 0.0406787i | \(-0.987048\pi\) |
−0.464357 | + | 0.885648i | \(0.653715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 167.166 | − | 289.540i | 0.414804 | − | 0.718462i | ||||
\(404\) | 1118.58i | 2.76877i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 88.0810 | 0.216948 | ||||||||
\(407\) | −200.637 | − | 115.838i | −0.492964 | − | 0.284613i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.68233 | − | 15.0382i | −0.0212282 | − | 0.0367683i | 0.855216 | − | 0.518271i | \(-0.173424\pi\) |
−0.876444 | + | 0.481503i | \(0.840091\pi\) | |||||||
\(410\) | 253.383 | − | 146.291i | 0.618008 | − | 0.356807i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −496.450 | + | 859.876i | −1.20497 | + | 2.08708i | ||||
\(413\) | 244.457i | 0.591905i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −92.2589 | −0.222311 | ||||||||
\(416\) | −85.4626 | − | 49.3419i | −0.205439 | − | 0.118610i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 199.476 | + | 345.502i | 0.477215 | + | 0.826560i | ||||
\(419\) | 117.841 | − | 68.0355i | 0.281243 | − | 0.162376i | −0.352743 | − | 0.935720i | \(-0.614751\pi\) |
0.633986 | + | 0.773344i | \(0.281418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −211.996 | + | 367.188i | −0.503554 | + | 0.872180i | 0.496438 | + | 0.868072i | \(0.334641\pi\) |
−0.999992 | + | 0.00410821i | \(0.998692\pi\) | |||||||
\(422\) | − | 68.0745i | − | 0.161314i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 228.510 | 0.538938 | ||||||||
\(425\) | −91.9836 | − | 53.1068i | −0.216432 | − | 0.124957i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 76.0922 | + | 131.795i | 0.178202 | + | 0.308654i | ||||
\(428\) | 559.045 | − | 322.765i | 1.30618 | − | 0.754124i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 52.5242 | − | 90.9746i | 0.122149 | − | 0.211569i | ||||
\(431\) | 340.244i | 0.789430i | 0.918804 | + | 0.394715i | \(0.129157\pi\) | ||||
−0.918804 | + | 0.394715i | \(0.870843\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 159.166 | 0.367589 | 0.183794 | − | 0.982965i | \(-0.441162\pi\) | ||||
0.183794 | + | 0.982965i | \(0.441162\pi\) | |||||||
\(434\) | 230.618 | + | 133.147i | 0.531377 | + | 0.306791i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −151.480 | − | 262.371i | −0.347431 | − | 0.601767i | ||||
\(437\) | −359.282 | + | 207.432i | −0.822155 | + | 0.474672i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −64.0366 | + | 110.915i | −0.145869 | + | 0.252653i | −0.929697 | − | 0.368326i | \(-0.879931\pi\) |
0.783828 | + | 0.620978i | \(0.213265\pi\) | |||||||
\(440\) | 131.025i | 0.297785i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −184.871 | −0.418259 | ||||||||
\(443\) | 170.901 | + | 98.6700i | 0.385782 | + | 0.222731i | 0.680331 | − | 0.732905i | \(-0.261836\pi\) |
−0.294549 | + | 0.955636i | \(0.595169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −79.0993 | − | 137.004i | −0.177751 | − | 0.307874i | ||||
\(446\) | −531.461 | + | 306.839i | −1.19162 | + | 0.687981i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −64.3229 | + | 111.410i | −0.143578 | + | 0.248684i | ||||
\(449\) | 148.101i | 0.329847i | 0.986306 | + | 0.164923i | \(0.0527377\pi\) | ||||
−0.986306 | + | 0.164923i | \(0.947262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 471.158 | 1.04470 | ||||||||
\(452\) | 156.248 | + | 90.2100i | 0.345682 | + | 0.199580i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 311.280 | + | 539.153i | 0.685640 | + | 1.18756i | ||||
\(455\) | −33.1404 | + | 19.1336i | −0.0728361 | + | 0.0420519i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 61.1072 | − | 105.841i | 0.133714 | − | 0.231599i | −0.791392 | − | 0.611310i | \(-0.790643\pi\) |
0.925105 | + | 0.379710i | \(0.123976\pi\) | |||||||
\(458\) | − | 143.083i | − | 0.312408i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −263.247 | −0.572276 | ||||||||
\(461\) | −521.424 | − | 301.044i | −1.13107 | − | 0.653025i | −0.186868 | − | 0.982385i | \(-0.559834\pi\) |
−0.944204 | + | 0.329361i | \(0.893167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 318.531 | + | 551.711i | 0.687971 | + | 1.19160i | 0.972493 | + | 0.232932i | \(0.0748318\pi\) |
−0.284522 | + | 0.958670i | \(0.591835\pi\) | |||||||
\(464\) | 161.043 | − | 92.9780i | 0.347075 | − | 0.200384i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −679.616 | + | 1177.13i | −1.45840 | + | 2.52603i | ||||
\(467\) | − | 767.706i | − | 1.64391i | −0.569553 | − | 0.821955i | \(-0.692884\pi\) | ||
0.569553 | − | 0.821955i | \(-0.307116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.1255 | 0.0855554 | ||||||||
\(470\) | 124.497 | + | 71.8783i | 0.264887 | + | 0.152933i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 695.080 | + | 1203.91i | 1.47263 | + | 2.55067i | ||||
\(473\) | 146.501 | − | 84.5821i | 0.309726 | − | 0.178821i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −190.343 | + | 329.684i | −0.400722 | + | 0.694072i | ||||
\(476\) | − | 99.3299i | − | 0.208676i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −173.624 | −0.363229 | ||||||||
\(479\) | −341.089 | − | 196.928i | −0.712085 | − | 0.411122i | 0.0997478 | − | 0.995013i | \(-0.468196\pi\) |
−0.811832 | + | 0.583890i | \(0.801530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −192.391 | − | 333.231i | −0.399981 | − | 0.692787i | ||||
\(482\) | −987.521 | + | 570.146i | −2.04880 | + | 1.18287i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 297.806 | − | 515.815i | 0.615301 | − | 1.06573i | ||||
\(485\) | − | 28.7715i | − | 0.0593226i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 573.409 | 1.17743 | 0.588716 | − | 0.808340i | \(-0.299634\pi\) | ||||
0.588716 | + | 0.808340i | \(0.299634\pi\) | |||||||
\(488\) | 749.486 | + | 432.716i | 1.53583 | + | 0.886713i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.2399 | − | 26.3962i | −0.0311018 | − | 0.0538699i | ||||
\(491\) | −147.914 | + | 85.3979i | −0.301250 | + | 0.173927i | −0.643004 | − | 0.765863i | \(-0.722312\pi\) |
0.341754 | + | 0.939789i | \(0.388979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.4980 | − | 37.2357i | 0.0436066 | − | 0.0755288i | ||||
\(494\) | 662.606i | 1.34131i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 562.199 | 1.13347 | ||||||||
\(497\) | 161.670 | + | 93.3400i | 0.325291 | + | 0.187807i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 423.907 | + | 734.229i | 0.849513 | + | 1.47140i | 0.881643 | + | 0.471917i | \(0.156438\pi\) |
−0.0321299 | + | 0.999484i | \(0.510229\pi\) | |||||||
\(500\) | −432.151 | + | 249.503i | −0.864302 | + | 0.499005i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −63.9150 | − | 110.704i | −0.125817 | − | 0.217921i | ||||
\(509\) | 425.606 | − | 245.724i | 0.836162 | − | 0.482758i | −0.0197959 | − | 0.999804i | \(-0.506302\pi\) |
0.855958 | + | 0.517046i | \(0.172968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 101.583 | − | 175.947i | 0.198793 | − | 0.344319i | ||||
\(512\) | 1012.62i | 1.97777i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −530.029 | −1.03118 | ||||||||
\(515\) | 128.799 | + | 74.3623i | 0.250096 | + | 0.144393i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 115.749 | + | 200.483i | 0.223886 | + | 0.387782i | ||||
\(518\) | 265.417 | − | 153.239i | 0.512388 | − | 0.295828i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −108.808 | + | 188.461i | −0.209246 | + | 0.362424i | ||||
\(521\) | 870.010i | 1.66988i | 0.550338 | + | 0.834942i | \(0.314499\pi\) | ||||
−0.550338 | + | 0.834942i | \(0.685501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 798.707 | 1.52716 | 0.763582 | − | 0.645710i | \(-0.223439\pi\) | ||||
0.763582 | + | 0.645710i | \(0.223439\pi\) | |||||||
\(524\) | 1314.85 | + | 759.129i | 2.50925 | + | 1.44872i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −200.520 | − | 347.311i | −0.381217 | − | 0.660288i | ||||
\(527\) | 112.574 | − | 64.9947i | 0.213613 | − | 0.123330i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.2451 | − | 107.812i | 0.117666 | − | 0.203803i | ||||
\(530\) | − | 66.1312i | − | 0.124776i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −356.014 | −0.669200 | ||||||||
\(533\) | 677.692 | + | 391.266i | 1.27147 | + | 0.734082i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −48.3464 | − | 83.7384i | −0.0903671 | − | 0.156520i | ||||
\(536\) | 197.612 | − | 114.091i | 0.368680 | − | 0.212857i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.34707 | + | 14.4576i | −0.0155150 | + | 0.0268728i | ||||
\(539\) | − | 49.0829i | − | 0.0910630i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −736.243 | −1.36089 | −0.680446 | − | 0.732798i | \(-0.738214\pi\) | ||||
−0.680446 | + | 0.732798i | \(0.738214\pi\) | |||||||
\(542\) | −1574.89 | − | 909.262i | −2.90570 | − | 1.67761i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.1843 | − | 33.2282i | −0.0352653 | − | 0.0610812i | ||||
\(545\) | −39.3000 | + | 22.6899i | −0.0721101 | + | 0.0416328i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 114.476 | − | 198.278i | 0.209279 | − | 0.362482i | −0.742208 | − | 0.670169i | \(-0.766222\pi\) |
0.951488 | + | 0.307687i | \(0.0995549\pi\) | |||||||
\(548\) | − | 273.746i | − | 0.499537i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −576.656 | −1.04847 | ||||||||
\(551\) | −133.459 | − | 77.0524i | −0.242212 | − | 0.139841i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −168.332 | − | 291.560i | −0.304398 | − | 0.527233i | ||||
\(554\) | 367.641 | − | 212.257i | 0.663611 | − | 0.383136i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 267.989 | − | 464.170i | 0.481994 | − | 0.834839i | ||||
\(557\) | 906.288i | 1.62709i | 0.581503 | + | 0.813544i | \(0.302465\pi\) | ||||
−0.581503 | + | 0.813544i | \(0.697535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 280.959 | 0.502611 | ||||||||
\(560\) | −55.7275 | − | 32.1743i | −0.0995134 | − | 0.0574541i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −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 | \(0.466862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 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 | 0.870280 | − | 0.492557i | \(-0.163938\pi\) |
0.00857275 | + | 0.999963i | \(0.497271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −311.642 | + | 539.779i | −0.542930 | + | 0.940382i | ||||
\(575\) | − | 599.655i | − | 1.04288i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −676.583 | −1.17259 | −0.586294 | − | 0.810099i | \(-0.699414\pi\) | ||||
−0.586294 | + | 0.810099i | \(0.699414\pi\) | |||||||
\(578\) | 815.219 | + | 470.667i | 1.41041 | + | 0.814302i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −48.8928 | − | 84.6848i | −0.0842979 | − | 0.146008i | ||||
\(581\) | 170.207 | − | 98.2690i | 0.292955 | − | 0.169138i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53.2470 | − | 92.2266i | 0.0913328 | − | 0.158193i | ||||
\(584\) | − | 1155.35i | − | 1.97834i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.88492 | 0.0151620 | ||||||||
\(587\) | −137.424 | − | 79.3415i | −0.234112 | − | 0.135164i | 0.378356 | − | 0.925660i | \(-0.376490\pi\) |
−0.612467 | + | 0.790496i | \(0.709823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −232.952 | − | 403.484i | −0.395504 | − | 0.685032i | ||||
\(590\) | 348.415 | − | 201.158i | 0.590534 | − | 0.340945i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 323.516 | − | 560.347i | 0.546480 | − | 0.946532i | ||||
\(593\) | − | 935.371i | − | 1.57735i | −0.614807 | − | 0.788677i | \(-0.710766\pi\) | ||
0.614807 | − | 0.788677i | \(-0.289234\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.8784 | −0.0250058 | ||||||||
\(596\) | 1405.51 | + | 811.472i | 2.35824 | + | 1.36153i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −521.867 | − | 903.900i | −0.872687 | − | 1.51154i | ||||
\(599\) | 63.8836 | − | 36.8832i | 0.106650 | − | 0.0615747i | −0.445726 | − | 0.895169i | \(-0.647054\pi\) |
0.552376 | + | 0.833595i | \(0.313721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 467.140 | − | 809.110i | 0.777271 | − | 1.34627i | −0.156238 | − | 0.987719i | \(-0.549937\pi\) |
0.933509 | − | 0.358553i | \(-0.116730\pi\) | |||||||
\(602\) | 223.783i | 0.371733i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −847.814 | −1.40367 | ||||||||
\(605\) | −77.2630 | − | 44.6078i | −0.127707 | − | 0.0737319i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 90.8039 | + | 157.277i | 0.149595 | + | 0.259105i | 0.931078 | − | 0.364821i | \(-0.118870\pi\) |
−0.781483 | + | 0.623926i | \(0.785536\pi\) | |||||||
\(608\) | −119.095 | + | 68.7596i | −0.195880 | + | 0.113091i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 125.229 | − | 216.903i | 0.205293 | − | 0.355578i | ||||
\(611\) | 384.488i | 0.629276i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −897.940 | −1.46483 | −0.732414 | − | 0.680859i | \(-0.761606\pi\) | ||||
−0.732414 | + | 0.680859i | \(0.761606\pi\) | |||||||
\(614\) | 261.833 | + | 151.170i | 0.426439 | + | 0.246204i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −139.561 | − | 241.726i | −0.226560 | − | 0.392413i | ||||
\(617\) | 1012.98 | − | 584.843i | 1.64178 | − | 0.947882i | 0.661579 | − | 0.749876i | \(-0.269887\pi\) |
0.980201 | − | 0.198006i | \(-0.0634467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −604.483 | + | 1047.00i | −0.976548 | + | 1.69143i | −0.301817 | + | 0.953366i | \(0.597593\pi\) |
−0.674730 | + | 0.738064i | \(0.735740\pi\) | |||||||
\(620\) | − | 295.634i | − | 0.476829i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 532.118 | 0.855495 | ||||||||
\(623\) | 291.858 | + | 168.504i | 0.468472 | + | 0.270472i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −255.846 | − | 443.139i | −0.409354 | − | 0.709022i | ||||
\(626\) | −965.875 | + | 557.648i | −1.54293 | + | 0.890812i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −638.114 | − | 1105.25i | −1.00649 | − | 1.74329i | ||||
\(635\) | −16.5822 | + | 9.57371i | −0.0261136 | + | 0.0150767i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.7601 | − | 70.5986i | 0.0639876 | − | 0.110830i | ||||
\(638\) | − | 233.435i | − | 0.365886i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 253.816 | 0.396587 | ||||||||
\(641\) | −457.806 | − | 264.315i | −0.714206 | − | 0.412347i | 0.0984103 | − | 0.995146i | \(-0.468624\pi\) |
−0.812616 | + | 0.582799i | \(0.801958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.7196 | − | 28.9592i | −0.0260025 | − | 0.0450377i | 0.852731 | − | 0.522350i | \(-0.174944\pi\) |
−0.878734 | + | 0.477312i | \(0.841611\pi\) | |||||||
\(644\) | 485.660 | − | 280.396i | 0.754131 | − | 0.435397i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −128.812 | + | 223.109i | −0.199399 | + | 0.345369i | ||||
\(647\) | − | 786.308i | − | 1.21531i | −0.794200 | − | 0.607657i | \(-0.792110\pi\) | ||
0.794200 | − | 0.607657i | \(-0.207890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 647.867 | 0.998254 | ||||||||
\(650\) | −829.435 | − | 478.875i | −1.27605 | − | 0.736730i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −294.180 | − | 509.535i | −0.451197 | − | 0.781496i | ||||
\(653\) | −334.119 | + | 192.904i | −0.511668 | + | 0.295412i | −0.733519 | − | 0.679669i | \(-0.762123\pi\) |
0.221851 | + | 0.975081i | \(0.428790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 113.708 | − | 196.949i | 0.173601 | − | 0.300685i | ||||
\(656\) | 1315.87i | 2.00590i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −306.243 | −0.465415 | ||||||||
\(659\) | 84.2282 | + | 48.6292i | 0.127812 | + | 0.0737924i | 0.562543 | − | 0.826768i | \(-0.309823\pi\) |
−0.434731 | + | 0.900560i | \(0.643156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 480.752 | + | 832.687i | 0.727311 | + | 1.25974i | 0.958016 | + | 0.286715i | \(0.0925633\pi\) |
−0.230705 | + | 0.973024i | \(0.574103\pi\) | |||||||
\(662\) | −468.697 | + | 270.602i | −0.708001 | + | 0.408765i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 558.829 | − | 967.921i | 0.841610 | − | 1.45771i | ||||
\(665\) | 53.3267i | 0.0801906i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 242.745 | 0.363936 | ||||||||
\(668\) | −1486.33 | − | 858.136i | −2.22505 | − | 1.28463i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −33.0183 | − | 57.1894i | −0.0492810 | − | 0.0853572i | ||||
\(671\) | 349.288 | − | 201.662i | 0.520549 | − | 0.300539i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 544.903 | − | 943.800i | 0.809663 | − | 1.40238i | −0.103435 | − | 0.994636i | \(-0.532983\pi\) |
0.913098 | − | 0.407741i | \(-0.133683\pi\) | |||||||
\(674\) | − | 1413.03i | − | 2.09648i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 276.741 | 0.409380 | ||||||||
\(677\) | −1084.75 | − | 626.279i | −1.60229 | − | 0.925080i | −0.991029 | − | 0.133649i | \(-0.957331\pi\) |
−0.611258 | − | 0.791432i | \(-0.709336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.6458 | + | 53.0800i | 0.0451337 | + | 0.0781738i | ||||
\(680\) | −73.2742 | + | 42.3049i | −0.107756 | + | 0.0622130i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 352.871 | − | 611.190i | 0.517406 | − | 0.896173i | ||||
\(683\) | 341.097i | 0.499409i | 0.968322 | + | 0.249705i | \(0.0803335\pi\) | ||||
−0.968322 | + | 0.249705i | \(0.919666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.0039 | −0.0598598 | ||||||||
\(686\) | 56.2316 | + | 32.4653i | 0.0819702 | + | 0.0473255i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 236.225 | + | 409.153i | 0.343350 | + | 0.594700i | ||||
\(689\) | 153.176 | − | 88.4363i | 0.222317 | − | 0.128355i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 391.833 | − | 678.675i | 0.567053 | − | 0.982164i | −0.429803 | − | 0.902923i | \(-0.641417\pi\) |
0.996855 | − | 0.0792411i | \(-0.0252497\pi\) | |||||||
\(692\) | − | 899.327i | − | 1.29961i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1652.14 | −2.38060 | ||||||||
\(695\) | −69.5272 | − | 40.1416i | −0.100039 | − | 0.0577576i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 152.125 | + | 263.489i | 0.218258 | + | 0.378033i | ||||
\(698\) | 1106.75 | − | 638.983i | 1.58560 | − | 0.915449i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 257.297 | − | 445.651i | 0.367567 | − | 0.636644i | ||||
\(701\) | − | 1331.76i | − | 1.89979i | −0.312562 | − | 0.949897i | \(-0.601187\pi\) | ||
0.312562 | − | 0.949897i | \(-0.398813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −536.207 | −0.762740 | ||||||||
\(704\) | 295.263 | + | 170.470i | 0.419408 | + | 0.242145i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 151.354 | + | 262.153i | 0.214383 | + | 0.371322i | ||||
\(707\) | −309.111 | + | 178.465i | −0.437215 | + | 0.252426i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −381.982 | + | 661.612i | −0.538761 | + | 0.933162i | 0.460210 | + | 0.887810i | \(0.347774\pi\) |
−0.998971 | + | 0.0453517i | \(0.985559\pi\) | |||||||
\(710\) | − | 307.229i | − | 0.432717i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1916.48 | 2.69168 | ||||||||
\(713\) | 635.566 | + | 366.944i | 0.891397 | + | 0.514648i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 50.7085 | + | 87.8297i | 0.0709210 | + | 0.122839i | ||||
\(716\) | −1144.29 | + | 660.654i | −1.59816 | + | 0.922701i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −652.221 | + | 1129.68i | −0.908386 | + | 1.57337i | ||||
\(719\) | − | 623.715i | − | 0.867476i | −0.901039 | − | 0.433738i | \(-0.857194\pi\) | ||
0.901039 | − | 0.433738i | \(-0.142806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −316.826 | −0.439426 | ||||||||
\(722\) | −296.418 | − | 171.137i | −0.410552 | − | 0.237032i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −969.645 | − | 1679.47i | −1.33929 | − | 2.31972i | ||||
\(725\) | 192.905 | − | 111.374i | 0.266076 | − | 0.153619i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −339.247 | + | 587.593i | −0.466640 | + | 0.808244i | −0.999274 | − | 0.0381019i | \(-0.987869\pi\) |
0.532634 | + | 0.846346i | \(0.321202\pi\) | |||||||
\(728\) | − | 463.584i | − | 0.636791i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −334.361 | −0.458028 | ||||||||
\(731\) | 94.6029 | + | 54.6190i | 0.129416 | + | 0.0747182i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 197.483 | + | 342.051i | 0.269417 | + | 0.466645i | 0.968712 | − | 0.248189i | \(-0.0798355\pi\) |
−0.699294 | + | 0.714834i | \(0.746502\pi\) | |||||||
\(734\) | 491.217 | − | 283.604i | 0.669232 | − | 0.386381i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 108.310 | − | 187.598i | 0.147160 | − | 0.254889i | ||||
\(737\) | − | 106.342i | − | 0.144290i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 292.199 | 0.395397 | 0.197699 | − | 0.980263i | \(-0.436653\pi\) | ||||
0.197699 | + | 0.980263i | \(0.436653\pi\) | |||||||
\(740\) | −294.660 | − | 170.122i | −0.398189 | − | 0.229895i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 70.4392 | + | 122.004i | 0.0949316 | + | 0.164426i | ||||
\(743\) | 332.079 | − | 191.726i | 0.446943 | − | 0.258043i | −0.259595 | − | 0.965718i | \(-0.583589\pi\) |
0.706538 | + | 0.707675i | \(0.250256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 121.549 | − | 210.529i | 0.163153 | − | 0.282589i | ||||
\(746\) | − | 1326.12i | − | 1.77764i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −263.247 | −0.351935 | ||||||||
\(749\) | 178.387 | + | 102.992i | 0.238167 | + | 0.137506i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 348.166 | + | 603.041i | 0.463603 | + | 0.802984i | 0.999137 | − | 0.0415293i | \(-0.0132230\pi\) |
−0.535534 | + | 0.844514i | \(0.679890\pi\) | |||||||
\(752\) | −559.918 | + | 323.269i | −0.744572 | + | 0.429879i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 151.627 | + | 262.626i | 0.199510 | + | 0.345561i | ||||
\(761\) | 77.6876 | − | 44.8529i | 0.102086 | − | 0.0589395i | −0.448088 | − | 0.893990i | \(-0.647895\pi\) |
0.550174 | + | 0.835050i | \(0.314561\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.3360 | − | 83.7203i | 0.0633499 | − | 0.109725i | ||||
\(764\) | 2389.69i | 3.12787i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 397.506 | 0.518937 | ||||||||
\(767\) | 931.861 | + | 538.010i | 1.21494 | + | 0.701448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −463.110 | − | 802.130i | −0.602223 | − | 1.04308i | −0.992484 | − | 0.122377i | \(-0.960948\pi\) |
0.390260 | − | 0.920705i | \(-0.372385\pi\) | |||||||
\(770\) | −69.9561 | + | 40.3892i | −0.0908520 | + | 0.0524534i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 319.727 | − | 553.783i | 0.414154 | − | 0.717336i | ||||
\(773\) | − | 424.125i | − | 0.548674i | −0.961634 | − | 0.274337i | \(-0.911542\pi\) | ||
0.961634 | − | 0.274337i | \(-0.0884584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 673.430 | 0.868942 | ||||||||
\(776\) | 301.852 | + | 174.274i | 0.388984 | + | 0.224580i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1271.92 | + | 2203.03i | 1.63486 | + | 2.83166i | ||||
\(779\) | 944.387 | − | 545.242i | 1.21231 | − | 0.699926i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 247.373 | − | 428.462i | 0.316738 | − | 0.548607i | ||||
\(782\) | − | 405.807i | − | 0.518935i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 137.081 | 0.174848 | ||||||||
\(785\) | −112.637 | − | 65.0313i | −0.143487 | − | 0.0828424i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 77.9444 | + | 135.004i | 0.0990399 | + | 0.171542i | 0.911288 | − | 0.411771i | \(-0.135090\pi\) |
−0.812248 | + | 0.583313i | \(0.801756\pi\) | |||||||
\(788\) | 979.679 | − | 565.618i | 1.24325 | − | 0.717789i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −277.033 | + | 479.835i | −0.350674 | + | 0.607386i | ||||
\(791\) | 57.5705i | 0.0727820i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 669.867 | 0.844725 | ||||||||
\(794\) | −286.456 | − | 165.386i | −0.360776 | − | 0.208294i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 358.952 | + | 621.722i | 0.450944 | + | 0.781058i | ||||
\(797\) | 622.838 | − | 359.595i | 0.781478 | − | 0.451186i | −0.0554761 | − | 0.998460i | \(-0.517668\pi\) |
0.836954 | + | 0.547274i | \(0.184334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −74.7451 | + | 129.462i | −0.0935483 | + | 0.162030i | ||||
\(800\) | − | 198.774i | − | 0.248468i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2375.84 | −2.96240 | ||||||||
\(803\) | −466.300 | − | 269.218i | −0.580697 | − | 0.335266i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.0000 | − | 72.7461i | −0.0521739 | − | 0.0903679i | ||||
\(806\) | 1015.11 | − | 586.071i | 1.25944 | − | 0.727136i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1014.88 | + | 1757.83i | −1.25604 | + | 2.17553i | ||||
\(809\) | 212.244i | 0.262353i | 0.991359 | + | 0.131176i | \(0.0418755\pi\) | ||||
−0.991359 | + | 0.131176i | \(0.958125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1058.66 | 1.30538 | 0.652690 | − | 0.757625i | \(-0.273641\pi\) | ||||
0.652690 | + | 0.757625i | \(0.273641\pi\) | |||||||
\(812\) | 180.403 | + | 104.156i | 0.222171 | + | 0.128271i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −406.118 | − | 703.416i | −0.498916 | − | 0.864148i | ||||
\(815\) | −76.3224 | + | 44.0647i | −0.0936471 | + | 0.0540672i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 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 | 0.865171 | − | 0.501478i | \(-0.167210\pi\) |
−0.00170721 | + | 0.999999i | \(0.500543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −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 | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −428.523 | + | 742.224i | −0.518794 | + | 0.898577i | ||||
\(827\) | 438.639i | 0.530398i | 0.964194 | + | 0.265199i | \(0.0854376\pi\) | ||||
−0.964194 | + | 0.265199i | \(0.914562\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 654.804 | 0.789872 | 0.394936 | − | 0.918709i | \(-0.370767\pi\) | ||||
0.394936 | + | 0.918709i | \(0.370767\pi\) | |||||||
\(830\) | −280.118 | − | 161.726i | −0.337492 | − | 0.194851i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 283.129 | + | 490.393i | 0.340299 | + | 0.589415i | ||||
\(833\) | 27.4490 | − | 15.8477i | 0.0329520 | − | 0.0190248i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −128.539 | + | 222.635i | −0.153938 | + | 0.266629i | ||||
\(836\) | 943.520i | 1.12861i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 477.055 | 0.569278 | ||||||||
\(839\) | 44.1422 | + | 25.4855i | 0.0526129 | + | 0.0303761i | 0.526076 | − | 0.850438i | \(-0.323663\pi\) |
−0.473463 | + | 0.880814i | \(0.656996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −375.415 | − | 650.238i | −0.446391 | − | 0.773172i | ||||
\(842\) | −1287.33 | + | 743.242i | −1.52890 | + | 0.882710i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 80.4980 | − | 139.427i | 0.0953768 | − | 0.165197i | ||||
\(845\) | − | 41.4525i | − | 0.0490563i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 190.055 | 0.224386 | ||||||||
\(848\) | 257.575 | + | 148.711i | 0.303744 | + | 0.175366i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −186.188 | − | 322.487i | −0.219045 | − | 0.379397i | ||||
\(851\) | 731.471 | − | 422.315i | 0.859543 | − | 0.496257i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 441.971 | − | 765.516i | 0.518137 | − | 0.897439i | −0.481641 | − | 0.876368i | \(-0.659959\pi\) |
0.999778 | − | 0.0210706i | \(-0.00670748\pi\) | |||||||
\(854\) | 533.547i | 0.624762i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1171.37 | 1.36843 | ||||||||
\(857\) | −481.961 | − | 278.260i | −0.562382 | − | 0.324691i | 0.191719 | − | 0.981450i | \(-0.438594\pi\) |
−0.754101 | + | 0.656759i | \(0.771927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 321.539 | + | 556.922i | 0.374318 | + | 0.648338i | 0.990225 | − | 0.139481i | \(-0.0445435\pi\) |
−0.615907 | + | 0.787819i | \(0.711210\pi\) | |||||||
\(860\) | 215.155 | − | 124.220i | 0.250180 | − | 0.144441i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −596.435 | + | 1033.06i | −0.691920 | + | 1.19844i | ||||
\(863\) | 204.892i | 0.237419i | 0.992929 | + | 0.118709i | \(0.0378757\pi\) | ||||
−0.992929 | + | 0.118709i | \(0.962124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −134.708 | −0.155732 | ||||||||
\(866\) | 483.263 | + | 279.012i | 0.558040 | + | 0.322185i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 314.893 | + | 545.410i | 0.362780 | + | 0.628353i | ||||
\(869\) | −772.700 | + | 446.118i | −0.889183 | + | 0.513370i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 88.3098 | − | 152.957i | 0.101389 | − | 0.175611i | ||||
\(872\) | − | 549.747i | − | 0.630444i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1454.48 | −1.66416 | ||||||||
\(875\) | −137.896 | − | 79.6143i | −0.157595 | − | 0.0909877i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 103.605 | + | 179.450i | 0.118136 | + | 0.204617i | 0.919029 | − | 0.394190i | \(-0.128975\pi\) |
−0.800893 | + | 0.598807i | \(0.795641\pi\) | |||||||
\(878\) | −388.858 | + | 224.507i | −0.442891 | + | 0.255703i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 345.929 | + | 599.167i | 0.390439 | + | 0.676261i | ||||
\(887\) | 129.426 | − | 74.7243i | 0.145915 | − | 0.0842439i | −0.425265 | − | 0.905069i | \(-0.639819\pi\) |
0.571180 | + | 0.820825i | \(0.306486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.3948 | − | 35.3248i | 0.0229412 | − | 0.0397354i | ||||
\(890\) | − | 554.632i | − | 0.623183i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1451.35 | −1.62707 | ||||||||
\(893\) | 464.014 | + | 267.898i | 0.519612 | + | 0.299998i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 98.9581 | + | 171.400i | 0.110568 | + | 0.191509i | ||||
\(896\) | −468.260 | + | 270.350i | −0.522612 | + | 0.301730i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −259.616 | + | 449.667i | −0.289104 | + | 0.500743i | ||||
\(899\) | 272.610i | 0.303237i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68.7687 | 0.0763249 | ||||||||
\(902\) | 1430.54 | + | 825.922i | 1.58596 | + | 0.915657i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 163.694 | + | 283.527i | 0.181078 | + | 0.313636i | ||||
\(905\) | −251.565 | + | 145.241i | −0.277973 | + | 0.160488i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −296.859 | + | 514.174i | −0.327297 | + | 0.566896i | −0.981975 | − | 0.189013i | \(-0.939471\pi\) |
0.654677 | + | 0.755909i | \(0.272805\pi\) | |||||||
\(908\) | 1472.35i | 1.62154i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −134.162 | −0.147431 | ||||||||
\(911\) | −981.854 | − | 566.874i | −1.07778 | − | 0.622254i | −0.147480 | − | 0.989065i | \(-0.547116\pi\) |
−0.930296 | + | 0.366811i | \(0.880450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −260.435 | − | 451.087i | −0.285252 | − | 0.494071i | ||||
\(914\) | 371.070 | − | 214.237i | 0.405984 | − | 0.234395i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 169.195 | − | 293.055i | 0.184711 | − | 0.319929i | ||||
\(917\) | 484.464i | 0.528314i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −684.988 | −0.745363 | −0.372681 | − | 0.927959i | \(-0.621562\pi\) | ||||
−0.372681 | + | 0.927959i | \(0.621562\pi\) | |||||||
\(920\) | −413.688 | − | 238.843i | −0.449661 | − | 0.259612i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1055.44 | − | 1828.07i | −1.14473 | − | 1.98273i | ||||
\(923\) | 711.618 | − | 410.853i | 0.770984 | − | 0.445128i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 387.524 | − | 671.212i | 0.418945 | − | 0.725634i | ||||
\(926\) | 2233.49i | 2.41197i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 80.4654 | 0.0867084 | ||||||||
\(929\) | 166.551 | + | 96.1584i | 0.179280 | + | 0.103507i | 0.586954 | − | 0.809620i | \(-0.300327\pi\) |
−0.407674 | + | 0.913127i | \(0.633660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −56.8006 | − | 98.3816i | −0.0610104 | − | 0.105673i | ||||
\(932\) | −2783.91 | + | 1607.29i | −2.98702 | + | 1.72456i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1345.76 | − | 2330.92i | 1.44086 | − | 2.49563i | ||||
\(935\) | 39.4313i | 0.0421725i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1270.28 | −1.35569 | −0.677844 | − | 0.735206i | \(-0.737086\pi\) | ||||
−0.677844 | + | 0.735206i | \(0.737086\pi\) | |||||||
\(938\) | 121.830 | + | 70.3385i | 0.129883 | + | 0.0749877i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | \(0.306757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | 0.0404090 | − | 0.999183i | \(-0.487134\pi\) |
−0.845114 | + | 0.534587i | \(0.820467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −447.136 | − | 774.462i | −0.471165 | − | 0.816082i | ||||
\(950\) | −1155.85 | + | 667.329i | −1.21668 | + | 0.702451i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 90.1216 | − | 156.095i | 0.0946655 | − | 0.163965i | ||||
\(953\) | 563.276i | 0.591056i | 0.955334 | + | 0.295528i | \(0.0954955\pi\) | ||||
−0.955334 | + | 0.295528i | \(0.904505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 357.948 | 0.374814 | ||||||||
\(956\) | −355.607 | − | 205.310i | −0.371974 | − | 0.214759i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −690.413 | − | 1195.83i | −0.720682 | − | 1.24826i | ||||
\(959\) | 75.6475 | − | 43.6751i | 0.0788816 | − | 0.0455423i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.4111 | − | 118.491i | 0.0711874 | − | 0.123300i | ||||
\(962\) | − | 1349.02i | − | 1.40230i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2696.79 | −2.79750 | ||||||||
\(965\) | −82.9501 | − | 47.8913i | −0.0859587 | − | 0.0496283i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −118.838 | − | 205.833i | −0.122893 | − | 0.212858i | 0.798014 | − | 0.602639i | \(-0.205884\pi\) |
−0.920908 | + | 0.389781i | \(0.872551\pi\) | |||||||
\(968\) | 935.993 | − | 540.396i | 0.966935 | − | 0.558260i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 50.4353 | − | 87.3565i | 0.0519951 | − | 0.0900582i | ||||
\(971\) | − | 1355.00i | − | 1.39546i | −0.716359 | − | 0.697732i | \(-0.754192\pi\) | ||
0.716359 | − | 0.697732i | \(-0.245808\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 171.026 | 0.175772 | ||||||||
\(974\) | 1741.00 | + | 1005.16i | 1.78747 | + | 1.03200i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 563.210 | + | 975.508i | 0.577059 | + | 0.999496i | ||||
\(977\) | −427.579 | + | 246.863i | −0.437645 | + | 0.252674i | −0.702598 | − | 0.711587i | \(-0.747977\pi\) |
0.264953 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 446.575 | − | 773.491i | 0.456154 | − | 0.790083i | ||||
\(980\) | − | 72.0845i | − | 0.0735556i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −598.797 | −0.609773 | ||||||||
\(983\) | 1331.99 | + | 769.026i | 1.35503 | + | 0.782325i | 0.988949 | − | 0.148259i | \(-0.0473670\pi\) |
0.366078 | + | 0.930584i | \(0.380700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −84.7229 | − | 146.744i | −0.0860130 | − | 0.148979i | ||||
\(986\) | 130.545 | − | 75.3705i | 0.132399 | − | 0.0764406i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −783.531 | + | 1357.11i | −0.793047 | + | 1.37360i | ||||
\(989\) | 616.731i | 0.623590i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1514.73 | 1.52849 | 0.764243 | − | 0.644929i | \(-0.223113\pi\) | ||||
0.764243 | + | 0.644929i | \(0.223113\pi\) | |||||||
\(992\) | 210.678 | + | 121.635i | 0.212377 | + | 0.122616i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 327.243 | + | 566.802i | 0.329218 | + | 0.570223i | ||||
\(995\) | 93.1267 | − | 53.7667i | 0.0935946 | − | 0.0540369i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −913.216 | + | 1581.74i | −0.915964 | + | 1.58650i | −0.110481 | + | 0.993878i | \(0.535239\pi\) |
−0.805484 | + | 0.592618i | \(0.798094\pi\) | |||||||
\(998\) | 2972.37i | 2.97833i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 567.3.r.c.512.4 | 8 | ||
3.2 | odd | 2 | inner | 567.3.r.c.512.1 | 8 | ||
9.2 | odd | 6 | 21.3.b.a.8.4 | yes | 4 | ||
9.4 | even | 3 | inner | 567.3.r.c.134.1 | 8 | ||
9.5 | odd | 6 | inner | 567.3.r.c.134.4 | 8 | ||
9.7 | even | 3 | 21.3.b.a.8.1 | ✓ | 4 | ||
36.7 | odd | 6 | 336.3.d.c.113.1 | 4 | |||
36.11 | even | 6 | 336.3.d.c.113.2 | 4 | |||
45.2 | even | 12 | 525.3.f.a.449.1 | 8 | |||
45.7 | odd | 12 | 525.3.f.a.449.7 | 8 | |||
45.29 | odd | 6 | 525.3.c.a.176.1 | 4 | |||
45.34 | even | 6 | 525.3.c.a.176.4 | 4 | |||
45.38 | even | 12 | 525.3.f.a.449.8 | 8 | |||
45.43 | odd | 12 | 525.3.f.a.449.2 | 8 | |||
63.2 | odd | 6 | 147.3.h.e.116.4 | 8 | |||
63.11 | odd | 6 | 147.3.h.e.128.1 | 8 | |||
63.16 | even | 3 | 147.3.h.e.116.1 | 8 | |||
63.20 | even | 6 | 147.3.b.f.50.4 | 4 | |||
63.25 | even | 3 | 147.3.h.e.128.4 | 8 | |||
63.34 | odd | 6 | 147.3.b.f.50.1 | 4 | |||
63.38 | even | 6 | 147.3.h.c.128.1 | 8 | |||
63.47 | even | 6 | 147.3.h.c.116.4 | 8 | |||
63.52 | odd | 6 | 147.3.h.c.128.4 | 8 | |||
63.61 | odd | 6 | 147.3.h.c.116.1 | 8 | |||
72.11 | even | 6 | 1344.3.d.b.449.3 | 4 | |||
72.29 | odd | 6 | 1344.3.d.f.449.2 | 4 | |||
72.43 | odd | 6 | 1344.3.d.b.449.4 | 4 | |||
72.61 | even | 6 | 1344.3.d.f.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.b.a.8.1 | ✓ | 4 | 9.7 | even | 3 | ||
21.3.b.a.8.4 | yes | 4 | 9.2 | odd | 6 | ||
147.3.b.f.50.1 | 4 | 63.34 | odd | 6 | |||
147.3.b.f.50.4 | 4 | 63.20 | even | 6 | |||
147.3.h.c.116.1 | 8 | 63.61 | odd | 6 | |||
147.3.h.c.116.4 | 8 | 63.47 | even | 6 | |||
147.3.h.c.128.1 | 8 | 63.38 | even | 6 | |||
147.3.h.c.128.4 | 8 | 63.52 | odd | 6 | |||
147.3.h.e.116.1 | 8 | 63.16 | even | 3 | |||
147.3.h.e.116.4 | 8 | 63.2 | odd | 6 | |||
147.3.h.e.128.1 | 8 | 63.11 | odd | 6 | |||
147.3.h.e.128.4 | 8 | 63.25 | even | 3 | |||
336.3.d.c.113.1 | 4 | 36.7 | odd | 6 | |||
336.3.d.c.113.2 | 4 | 36.11 | even | 6 | |||
525.3.c.a.176.1 | 4 | 45.29 | odd | 6 | |||
525.3.c.a.176.4 | 4 | 45.34 | even | 6 | |||
525.3.f.a.449.1 | 8 | 45.2 | even | 12 | |||
525.3.f.a.449.2 | 8 | 45.43 | odd | 12 | |||
525.3.f.a.449.7 | 8 | 45.7 | odd | 12 | |||
525.3.f.a.449.8 | 8 | 45.38 | even | 12 | |||
567.3.r.c.134.1 | 8 | 9.4 | even | 3 | inner | ||
567.3.r.c.134.4 | 8 | 9.5 | odd | 6 | inner | ||
567.3.r.c.512.1 | 8 | 3.2 | odd | 2 | inner | ||
567.3.r.c.512.4 | 8 | 1.1 | even | 1 | trivial | ||
1344.3.d.b.449.3 | 4 | 72.11 | even | 6 | |||
1344.3.d.b.449.4 | 4 | 72.43 | odd | 6 | |||
1344.3.d.f.449.1 | 4 | 72.61 | even | 6 | |||
1344.3.d.f.449.2 | 4 | 72.29 | odd | 6 |