Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(289,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bo (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 30 x^{16} - 51 x^{15} + 501 x^{14} - 768 x^{13} + 4499 x^{12} - 2946 x^{11} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 385.2 | ||
Root | \(-0.214696 + 0.371865i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.385 |
Dual form | 912.2.bo.k.289.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.173648 | − | 0.984808i | 0.100256 | − | 0.568579i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.328934 | − | 0.276008i | −0.147104 | − | 0.123435i | 0.566266 | − | 0.824223i | \(-0.308387\pi\) |
−0.713370 | + | 0.700788i | \(0.752832\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95470 | + | 3.38563i | 0.738806 | + | 1.27965i | 0.953033 | + | 0.302865i | \(0.0979431\pi\) |
−0.214228 | + | 0.976784i | \(0.568724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.939693 | − | 0.342020i | −0.313231 | − | 0.114007i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.16709 | + | 3.75351i | −0.653402 | + | 1.13172i | 0.328890 | + | 0.944368i | \(0.393325\pi\) |
−0.982292 | + | 0.187357i | \(0.940008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0235730 | − | 0.133689i | −0.00653797 | − | 0.0370787i | 0.981364 | − | 0.192157i | \(-0.0615482\pi\) |
−0.987902 | + | 0.155078i | \(0.950437\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.328934 | + | 0.276008i | −0.0849304 | + | 0.0712650i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.59735 | + | 2.03727i | −1.35756 | + | 0.494110i | −0.915298 | − | 0.402777i | \(-0.868045\pi\) |
−0.442259 | + | 0.896888i | \(0.645823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.47658 | + | 4.10118i | 0.338751 | + | 0.940876i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.67363 | − | 1.33709i | 0.801651 | − | 0.291777i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.07703 | + | 5.09923i | −1.26715 | + | 1.06326i | −0.272266 | + | 0.962222i | \(0.587773\pi\) |
−0.994882 | + | 0.101041i | \(0.967783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.836224 | − | 4.74246i | −0.167245 | − | 0.948492i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | + | 0.866025i | −0.0962250 | + | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.20815 | + | 2.62355i | 1.33852 | + | 0.487181i | 0.909346 | − | 0.416041i | \(-0.136583\pi\) |
0.429174 | + | 0.903222i | \(0.358805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.60402 | − | 4.51030i | −0.467696 | − | 0.810074i | 0.531622 | − | 0.846982i | \(-0.321583\pi\) |
−0.999319 | + | 0.0369076i | \(0.988249\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.32017 | + | 2.78596i | 0.577968 | + | 0.484973i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.291497 | − | 1.65316i | 0.0492720 | − | 0.279435i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.10285 | −0.838903 | −0.419451 | − | 0.907778i | \(-0.637778\pi\) | ||||
−0.419451 | + | 0.907778i | \(0.637778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.135751 | −0.0217376 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.555615 | + | 3.15105i | −0.0867726 | + | 0.492112i | 0.910187 | + | 0.414197i | \(0.135937\pi\) |
−0.996960 | + | 0.0779151i | \(0.975174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.94070 | + | 6.66304i | 1.21095 | + | 1.01610i | 0.999248 | + | 0.0387688i | \(0.0123436\pi\) |
0.211697 | + | 0.977335i | \(0.432101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.214696 | + | 0.371865i | 0.0320050 | + | 0.0554344i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.56422 | − | 1.29727i | −0.519895 | − | 0.189226i | 0.0687255 | − | 0.997636i | \(-0.478107\pi\) |
−0.588621 | + | 0.808409i | \(0.700329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.14167 | + | 7.17358i | −0.591667 | + | 1.02480i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.03435 | + | 5.86608i | 0.144838 | + | 0.821416i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.49087 | − | 4.60739i | 0.754229 | − | 0.632873i | −0.182389 | − | 0.983226i | \(-0.558383\pi\) |
0.936618 | + | 0.350353i | \(0.113939\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74883 | − | 0.636521i | 0.235812 | − | 0.0858285i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.29528 | − | 0.741988i | 0.568924 | − | 0.0982787i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0603913 | + | 0.0219807i | −0.00786228 | + | 0.00286164i | −0.345948 | − | 0.938254i | \(-0.612443\pi\) |
0.338086 | + | 0.941115i | \(0.390221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.56070 | − | 3.82688i | 0.583937 | − | 0.489982i | −0.302300 | − | 0.953213i | \(-0.597754\pi\) |
0.886238 | + | 0.463231i | \(0.153310\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.678859 | − | 3.85000i | −0.0855282 | − | 0.485054i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0291453 | + | 0.0504812i | −0.00361503 | + | 0.00626142i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.0223 | + | 5.46767i | 1.83527 | + | 0.667983i | 0.991306 | + | 0.131580i | \(0.0420049\pi\) |
0.843962 | + | 0.536403i | \(0.180217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.96650 | + | 6.87018i | 0.477510 | + | 0.827072i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.18052 | + | 4.34697i | 0.614815 | + | 0.515891i | 0.896169 | − | 0.443713i | \(-0.146339\pi\) |
−0.281354 | + | 0.959604i | \(0.590784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.71264 | + | 9.71289i | −0.200450 | + | 1.13681i | 0.703991 | + | 0.710209i | \(0.251399\pi\) |
−0.904441 | + | 0.426599i | \(0.859712\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.81562 | −0.556060 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.9440 | −1.93095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.77304 | − | 10.0554i | 0.199483 | − | 1.13132i | −0.706405 | − | 0.707808i | \(-0.749684\pi\) |
0.905888 | − | 0.423517i | \(-0.139205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.766044 | + | 0.642788i | 0.0851160 | + | 0.0714208i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.33003 | − | 5.76778i | −0.365518 | − | 0.633096i | 0.623341 | − | 0.781950i | \(-0.285775\pi\) |
−0.988859 | + | 0.148854i | \(0.952442\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.40346 | + | 0.874788i | 0.260692 | + | 0.0948841i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.83538 | − | 6.64307i | 0.411196 | − | 0.712212i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.18923 | + | 12.4157i | 0.232057 | + | 1.31606i | 0.848723 | + | 0.528838i | \(0.177372\pi\) |
−0.616665 | + | 0.787225i | \(0.711517\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.406544 | − | 0.341131i | 0.0426174 | − | 0.0357602i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.89396 | + | 1.78126i | −0.507480 | + | 0.184708i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.646262 | − | 1.75657i | 0.0663051 | − | 0.180220i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.87968 | − | 2.86797i | 0.800060 | − | 0.291198i | 0.0905488 | − | 0.995892i | \(-0.471138\pi\) |
0.709511 | + | 0.704694i | \(0.248916\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.32017 | − | 2.78596i | 0.333690 | − | 0.279999i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.211201 | − | 1.19778i | −0.0210153 | − | 0.119184i | 0.972495 | − | 0.232922i | \(-0.0748286\pi\) |
−0.993511 | + | 0.113738i | \(0.963718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.27755 | + | 12.6051i | −0.717078 | + | 1.24202i | 0.245075 | + | 0.969504i | \(0.421188\pi\) |
−0.962153 | + | 0.272511i | \(0.912146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.57743 | − | 0.574137i | −0.153941 | − | 0.0560300i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.67812 | − | 13.2989i | −0.742272 | − | 1.28565i | −0.951458 | − | 0.307777i | \(-0.900415\pi\) |
0.209186 | − | 0.977876i | \(-0.432918\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.41338 | − | 2.86417i | −0.326942 | − | 0.274337i | 0.464510 | − | 0.885568i | \(-0.346230\pi\) |
−0.791453 | + | 0.611230i | \(0.790675\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.886100 | + | 5.02532i | −0.0841049 | + | 0.476982i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.89325 | −0.272174 | −0.136087 | − | 0.990697i | \(-0.543453\pi\) | ||||
−0.136087 | + | 0.990697i | \(0.543453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.40637 | 0.317646 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0235730 | + | 0.133689i | −0.00217932 | + | 0.0123596i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.8386 | − | 14.9683i | −1.63526 | − | 1.37214i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.89254 | − | 6.74208i | −0.353868 | − | 0.612917i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00670 | + | 1.09435i | 0.271105 | + | 0.0986741i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.10738 | + | 3.65009i | −0.188490 | + | 0.326474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.85972 | − | 16.2183i | −0.253759 | − | 1.43914i | −0.799237 | − | 0.601016i | \(-0.794763\pi\) |
0.545478 | − | 0.838125i | \(-0.316348\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.94070 | − | 6.66304i | 0.699140 | − | 0.586648i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.92144 | − | 3.24714i | 0.779469 | − | 0.283704i | 0.0785180 | − | 0.996913i | \(-0.474981\pi\) |
0.700951 | + | 0.713209i | \(0.252759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.9988 | + | 13.0157i | −0.953719 | + | 1.12861i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.403497 | − | 0.146861i | 0.0347275 | − | 0.0126398i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.06007 | − | 7.60230i | 0.774054 | − | 0.649508i | −0.167690 | − | 0.985840i | \(-0.553631\pi\) |
0.941744 | + | 0.336332i | \(0.109186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.32623 | + | 7.52142i | 0.112489 | + | 0.637959i | 0.987963 | + | 0.154692i | \(0.0494386\pi\) |
−0.875473 | + | 0.483266i | \(0.839450\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.89648 | + | 3.28481i | −0.159713 | + | 0.276631i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.552888 | + | 0.201235i | 0.0462348 | + | 0.0168281i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.64688 | − | 2.85248i | −0.136766 | − | 0.236886i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.34541 | + | 5.32443i | 0.523360 | + | 0.439152i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.37145 | − | 7.77789i | 0.112354 | − | 0.637190i | −0.875673 | − | 0.482905i | \(-0.839582\pi\) |
0.988026 | − | 0.154285i | \(-0.0493073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.96656 | −0.729689 | −0.364844 | − | 0.931069i | \(-0.618878\pi\) | ||||
−0.364844 | + | 0.931069i | \(0.618878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.95658 | 0.481561 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.388329 | + | 2.20232i | −0.0311913 | + | 0.176895i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.78309 | − | 1.49619i | −0.142306 | − | 0.119409i | 0.568856 | − | 0.822437i | \(-0.307386\pi\) |
−0.711162 | + | 0.703028i | \(0.751831\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.58391 | − | 6.20751i | −0.284223 | − | 0.492288i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −29.1429 | − | 10.6071i | −2.29678 | − | 0.835959i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.06566 | + | 5.30988i | −0.240121 | + | 0.415902i | −0.960749 | − | 0.277421i | \(-0.910520\pi\) |
0.720628 | + | 0.693322i | \(0.243854\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.323170 | − | 1.83279i | −0.0251588 | − | 0.142683i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.83124 | + | 2.37569i | −0.219088 | + | 0.183836i | −0.745725 | − | 0.666253i | \(-0.767897\pi\) |
0.526638 | + | 0.850090i | \(0.323452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1987 | − | 4.43996i | 0.938361 | − | 0.341535i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0151526 | − | 4.35887i | 0.00115875 | − | 0.333331i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.14540 | − | 1.50880i | 0.315169 | − | 0.114712i | −0.179592 | − | 0.983741i | \(-0.557478\pi\) |
0.494761 | + | 0.869029i | \(0.335256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.4217 | − | 12.1012i | 1.09018 | − | 0.914766i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0111599 | + | 0.0632908i | 0.000838827 | + | 0.00475723i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.66948 | + | 16.7480i | −0.722731 | + | 1.25181i | 0.237170 | + | 0.971468i | \(0.423780\pi\) |
−0.959901 | + | 0.280339i | \(0.909553\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3381 | + | 4.12673i | 0.842754 | + | 0.306737i | 0.727082 | − | 0.686550i | \(-0.240876\pi\) |
0.115671 | + | 0.993288i | \(0.463098\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.97678 | − | 5.15594i | −0.220050 | − | 0.381138i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.67850 | + | 1.40843i | 0.123406 | + | 0.103550i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.48305 | − | 25.4246i | 0.327833 | − | 1.85923i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.90939 | −0.284366 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.9344 | −1.44240 | −0.721201 | − | 0.692726i | \(-0.756410\pi\) | ||||
−0.721201 | + | 0.692726i | \(0.756410\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.121315 | + | 0.688010i | −0.00873242 | + | 0.0495240i | −0.988863 | − | 0.148831i | \(-0.952449\pi\) |
0.980130 | + | 0.198355i | \(0.0635600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0446533 | + | 0.0374685i | 0.00319769 | + | 0.00268318i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.21735 | − | 2.10851i | −0.0867326 | − | 0.150225i | 0.819396 | − | 0.573228i | \(-0.194309\pi\) |
−0.906128 | + | 0.423003i | \(0.860976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.704515 | − | 0.256422i | −0.0499417 | − | 0.0181773i | 0.316928 | − | 0.948449i | \(-0.397348\pi\) |
−0.366870 | + | 0.930272i | \(0.619571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.99321 | − | 13.8446i | 0.563797 | − | 0.976525i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.20736 | + | 29.5324i | 0.365485 | + | 2.07277i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.05248 | − | 0.883133i | 0.0735082 | − | 0.0616807i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.45458 | − | 2.71324i | 0.518129 | − | 0.188584i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.5937 | − | 3.34526i | −1.28615 | − | 0.231396i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8375 | + | 5.03644i | −0.952614 | + | 0.346723i | −0.771135 | − | 0.636672i | \(-0.780311\pi\) |
−0.181479 | + | 0.983395i | \(0.558088\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.18052 | − | 4.34697i | 0.354963 | − | 0.297850i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.772912 | − | 4.38340i | −0.0527121 | − | 0.298945i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.1801 | − | 17.6325i | 0.691073 | − | 1.19697i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.26793 | + | 3.37325i | 0.626269 | + | 0.227943i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.404307 | + | 0.700280i | 0.0271966 | + | 0.0471059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9571 | + | 13.3896i | 1.06857 | + | 0.896633i | 0.994922 | − | 0.100652i | \(-0.0320928\pi\) |
0.0736436 | + | 0.997285i | \(0.476537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.836224 | + | 4.74246i | −0.0557483 | + | 0.316164i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7521 | 0.713642 | 0.356821 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356821 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9356 | 0.788727 | 0.394364 | − | 0.918954i | \(-0.370965\pi\) | ||||
0.394364 | + | 0.918954i | \(0.370965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.94229 | + | 16.6866i | −0.193589 | + | 1.09790i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3725 | + | 11.2209i | 0.876061 | + | 0.735103i | 0.965365 | − | 0.260902i | \(-0.0840199\pi\) |
−0.0893042 | + | 0.996004i | \(0.528464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.814336 | + | 1.41047i | 0.0531214 | + | 0.0920090i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.59479 | − | 3.49222i | −0.623248 | − | 0.226844i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.01877 | − | 6.96071i | 0.259952 | − | 0.450251i | −0.706277 | − | 0.707936i | \(-0.749626\pi\) |
0.966229 | + | 0.257685i | \(0.0829598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.29513 | − | 7.34503i | −0.0834265 | − | 0.473135i | −0.997685 | − | 0.0680039i | \(-0.978337\pi\) |
0.914259 | − | 0.405131i | \(-0.132774\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.766044 | − | 0.642788i | 0.0491418 | − | 0.0412348i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.34231 | − | 1.21650i | 0.213532 | − | 0.0777193i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.513476 | − | 0.294080i | 0.0326717 | − | 0.0187119i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.25841 | + | 2.27787i | −0.396610 | + | 0.144354i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.93230 | − | 3.29959i | 0.248205 | − | 0.208268i | −0.510194 | − | 0.860059i | \(-0.670426\pi\) |
0.758399 | + | 0.651791i | \(0.225982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.97055 | − | 33.8607i | −0.375365 | − | 2.12880i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.27885 | − | 2.21504i | 0.0800850 | − | 0.138711i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.3124 | − | 6.66517i | −1.14230 | − | 0.415762i | −0.299554 | − | 0.954079i | \(-0.596838\pi\) |
−0.842742 | + | 0.538318i | \(0.819060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.97451 | − | 17.2764i | −0.619786 | − | 1.07350i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.87614 | − | 4.93066i | −0.363724 | − | 0.305200i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.12670 | − | 17.7324i | 0.192801 | − | 1.09343i | −0.722715 | − | 0.691146i | \(-0.757106\pi\) |
0.915516 | − | 0.402282i | \(-0.131783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.07781 | −0.189068 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.6072 | 0.771551 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46795 | − | 19.6677i | 0.211444 | − | 1.19916i | −0.675526 | − | 0.737336i | \(-0.736084\pi\) |
0.886971 | − | 0.461825i | \(-0.152805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.1744 | − | 16.9283i | −1.22551 | − | 1.02832i | −0.998518 | − | 0.0544246i | \(-0.982668\pi\) |
−0.226989 | − | 0.973897i | \(-0.572888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.265353 | − | 0.459604i | −0.0160599 | − | 0.0278165i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.6130 | + | 7.13856i | 1.18271 | + | 0.430471i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.46245 | − | 9.46124i | 0.328207 | − | 0.568471i | −0.653949 | − | 0.756538i | \(-0.726889\pi\) |
0.982156 | + | 0.188068i | \(0.0602224\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.904368 | + | 5.12893i | 0.0541431 | + | 0.307061i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.39555 | + | 7.04470i | −0.500837 | + | 0.420252i | −0.857891 | − | 0.513832i | \(-0.828226\pi\) |
0.357054 | + | 0.934084i | \(0.383781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6993 | + | 7.89791i | −1.28989 | + | 0.469482i | −0.893692 | − | 0.448682i | \(-0.851894\pi\) |
−0.396200 | + | 0.918164i | \(0.629671\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.61766 | − | 0.941469i | −0.0958218 | − | 0.0557678i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.7544 | + | 4.27824i | −0.693838 | + | 0.252536i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1571 | − | 11.8792i | 0.832771 | − | 0.698778i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.45611 | − | 8.25799i | −0.0853584 | − | 0.484092i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.49967 | − | 7.79366i | 0.262874 | − | 0.455310i | −0.704131 | − | 0.710070i | \(-0.748663\pi\) |
0.967004 | + | 0.254760i | \(0.0819965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0259316 | + | 0.00943833i | 0.00150980 | + | 0.000549521i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.16709 | − | 3.75351i | −0.125747 | − | 0.217801i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.824965 | + | 0.692228i | 0.0477090 | + | 0.0400326i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.03695 | + | 39.9085i | −0.405603 | + | 2.30029i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.21626 | −0.0698723 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.55642 | −0.146380 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.55591 | + | 14.4953i | −0.145873 | + | 0.827290i | 0.820788 | + | 0.571233i | \(0.193535\pi\) |
−0.966662 | + | 0.256057i | \(0.917577\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1498 | + | 9.35583i | 0.634293 | + | 0.532235i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.49563 | + | 6.05461i | 0.198219 | + | 0.343325i | 0.947951 | − | 0.318416i | \(-0.103151\pi\) |
−0.749732 | + | 0.661742i | \(0.769818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.2331 | + | 6.63630i | 1.03059 | + | 0.375106i | 0.801307 | − | 0.598253i | \(-0.204138\pi\) |
0.229288 | + | 0.973359i | \(0.426360\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.839332 | + | 1.45377i | −0.0472910 | + | 0.0819104i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.901677 | − | 5.11367i | −0.0506432 | − | 0.287212i | 0.948959 | − | 0.315398i | \(-0.102138\pi\) |
−0.999603 | + | 0.0281860i | \(0.991027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.4682 | + | 21.3704i | −1.42595 | + | 1.19651i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.4302 | + | 5.25215i | −0.805412 | + | 0.293146i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.6202 | − | 19.9476i | −0.924771 | − | 1.10991i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.614303 | + | 0.223588i | −0.0340754 | + | 0.0124024i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.41338 | + | 2.86417i | −0.188760 | + | 0.158389i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.57489 | − | 14.6029i | −0.141958 | − | 0.805085i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.53569 | − | 14.7842i | 0.469164 | − | 0.812616i | −0.530215 | − | 0.847863i | \(-0.677889\pi\) |
0.999379 | + | 0.0352477i | \(0.0112220\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.79511 | + | 1.74528i | 0.262770 | + | 0.0956405i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.43222 | − | 5.94479i | −0.187522 | − | 0.324798i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5345 | + | 13.8741i | 0.900691 | + | 0.755770i | 0.970325 | − | 0.241803i | \(-0.0777387\pi\) |
−0.0696340 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.502407 | + | 2.84929i | −0.0272870 | + | 0.154752i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.5726 | 1.22237 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.01709 | −0.270897 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.591510 | − | 3.35462i | 0.0318458 | − | 0.180607i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6056 | + | 13.0947i | 0.837754 | + | 0.702959i | 0.957057 | − | 0.289899i | \(-0.0936217\pi\) |
−0.119303 | + | 0.992858i | \(0.538066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.6724 | + | 25.4133i | 0.785394 | + | 1.36034i | 0.928764 | + | 0.370673i | \(0.120873\pi\) |
−0.143370 | + | 0.989669i | \(0.545794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.127565 | + | 0.0464297i | 0.00680890 | + | 0.00247824i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.5079 | + | 25.1284i | −0.772178 | + | 1.33745i | 0.164190 | + | 0.986429i | \(0.447499\pi\) |
−0.936367 | + | 0.351022i | \(0.885834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.504248 | − | 2.85973i | −0.0267627 | − | 0.151779i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.8386 | + | 14.9683i | −0.944117 | + | 0.792208i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.3857 | − | 8.51170i | 1.23425 | − | 0.449230i | 0.359199 | − | 0.933261i | \(-0.383050\pi\) |
0.875051 | + | 0.484030i | \(0.160828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6394 | + | 12.1115i | −0.770495 | + | 0.637446i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.31559 | + | 2.66266i | −0.383969 | + | 0.139753i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.24419 | − | 2.72219i | 0.169808 | − | 0.142486i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.51049 | + | 31.2515i | 0.287645 | + | 1.63132i | 0.695682 | + | 0.718350i | \(0.255103\pi\) |
−0.408036 | + | 0.912966i | \(0.633786\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.59983 | − | 2.77099i | 0.0832839 | − | 0.144252i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.3319 | + | 9.58402i | 1.36708 | + | 0.497578i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.38380 | − | 7.59297i | −0.226985 | − | 0.393149i | 0.729928 | − | 0.683524i | \(-0.239553\pi\) |
−0.956913 | + | 0.290375i | \(0.906220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.22869 | + | 2.70919i | 0.166729 | + | 0.139902i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.180823 | − | 1.02550i | 0.00931284 | − | 0.0528157i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.64917 | 0.290178 | 0.145089 | − | 0.989419i | \(-0.453653\pi\) | ||||
0.145089 | + | 0.989419i | \(0.453653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.4685 | −0.843706 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.874156 | − | 4.95758i | 0.0446673 | − | 0.253321i | −0.954295 | − | 0.298866i | \(-0.903392\pi\) |
0.998962 | + | 0.0455457i | \(0.0145027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.57345 | + | 4.67668i | 0.284050 | + | 0.238346i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.18292 | − | 8.97709i | −0.263463 | − | 0.456331i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.8075 | + | 7.57333i | 1.05498 | + | 0.383983i | 0.810542 | − | 0.585681i | \(-0.199173\pi\) |
0.244443 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.6267 | − | 40.9227i | 1.19486 | − | 2.06955i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.64861 | − | 9.34976i | −0.0831616 | − | 0.471633i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.35860 | + | 2.81820i | −0.168989 | + | 0.141799i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.6035 | + | 11.8667i | −1.63632 | + | 0.595573i | −0.986391 | − | 0.164418i | \(-0.947425\pi\) |
−0.649933 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.9081 | + | 13.0919i | 0.546086 | + | 0.655414i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7032 | − | 8.62724i | 1.18368 | − | 0.430824i | 0.326179 | − | 0.945308i | \(-0.394239\pi\) |
0.857500 | + | 0.514484i | \(0.172017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.541593 | + | 0.454451i | −0.0269787 | + | 0.0226378i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.0745633 | − | 0.422869i | −0.00370508 | − | 0.0210125i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0583 | − | 19.1536i | 0.548140 | − | 0.949407i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2428 | + | 4.81999i | 0.654814 | + | 0.238333i | 0.647996 | − | 0.761644i | \(-0.275607\pi\) |
0.00681846 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.91354 | − | 10.2425i | −0.291693 | − | 0.505228i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.192465 | − | 0.161497i | −0.00947059 | − | 0.00794677i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.496596 | + | 2.81633i | −0.0243769 | + | 0.138248i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.63745 | 0.374008 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0323 | −0.685524 | −0.342762 | − | 0.939422i | \(-0.611362\pi\) | ||||
−0.342762 | + | 0.939422i | \(0.611362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0176863 | − | 0.100304i | 0.000861978 | − | 0.00488852i | −0.984374 | − | 0.176092i | \(-0.943654\pi\) |
0.985236 | + | 0.171203i | \(0.0547655\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.90558 | + | 2.43807i | 0.141274 | + | 0.118543i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.3423 | + | 24.8416i | 0.695704 | + | 1.20499i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.8712 | + | 7.96046i | 1.05842 | + | 0.385234i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.294185 | − | 0.509544i | 0.0142034 | − | 0.0246010i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.60275 | + | 20.4322i | 0.173539 | + | 0.984186i | 0.939817 | + | 0.341678i | \(0.110995\pi\) |
−0.766279 | + | 0.642508i | \(0.777894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7634 | + | 9.87070i | −0.565315 | + | 0.474356i | −0.880088 | − | 0.474812i | \(-0.842516\pi\) |
0.314772 | + | 0.949167i | \(0.398072\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.09513 | + | 1.12653i | −0.148400 | + | 0.0540132i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.8861 | − | 17.3936i | −1.42965 | − | 0.832047i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.8082 | + | 9.02945i | −1.18403 | + | 0.430952i | −0.857624 | − | 0.514277i | \(-0.828060\pi\) |
−0.326407 | + | 0.945229i | \(0.605838\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.34541 | − | 5.32443i | 0.302162 | − | 0.253544i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.05430 | + | 17.3218i | 0.145114 | + | 0.822983i | 0.967275 | + | 0.253729i | \(0.0816570\pi\) |
−0.822161 | + | 0.569255i | \(0.807232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.70673 | − | 4.68819i | 0.128311 | − | 0.222242i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.42158 | − | 2.70123i | −0.351029 | − | 0.127764i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.82244 | + | 15.2809i | 0.416357 | + | 0.721151i | 0.995570 | − | 0.0940252i | \(-0.0299734\pi\) |
−0.579213 | + | 0.815176i | \(0.696640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6234 | − | 8.91411i | −0.500238 | − | 0.419749i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.55703 | + | 8.83034i | −0.0731555 | + | 0.414886i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.227881 | −0.0106832 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7425 | −1.29774 | −0.648869 | − | 0.760900i | \(-0.724758\pi\) | ||||
−0.648869 | + | 0.760900i | \(0.724758\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.03435 | − | 5.86608i | 0.0482792 | − | 0.273805i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7697 | + | 24.9798i | 1.38651 | + | 1.16342i | 0.966730 | + | 0.255800i | \(0.0823389\pi\) |
0.419785 | + | 0.907624i | \(0.362106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.26163 | − | 10.8455i | −0.291003 | − | 0.504031i | 0.683044 | − | 0.730377i | \(-0.260656\pi\) |
−0.974047 | + | 0.226345i | \(0.927322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.10143 | + | 0.764859i | 0.0974516 | + | 0.0354695i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.5781 | + | 23.5180i | −0.628320 | + | 1.08828i | 0.359569 | + | 0.933118i | \(0.382924\pi\) |
−0.987889 | + | 0.155163i | \(0.950410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8525 | + | 61.5477i | 0.501123 | + | 2.84201i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.78309 | + | 1.49619i | −0.0821603 | + | 0.0689407i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.2180 | + | 15.3661i | −1.94118 | + | 0.706533i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.2149 | − | 10.4321i | 0.835759 | − | 0.478660i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.73555 | + | 2.45154i | −0.308399 | + | 0.112248i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.1063 | − | 16.8712i | 0.918682 | − | 0.770866i | −0.0550684 | − | 0.998483i | \(-0.517538\pi\) |
0.973751 | + | 0.227616i | \(0.0730932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.120289 | + | 0.682195i | 0.00548472 | + | 0.0311054i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.5066 | + | 26.8582i | −0.705575 | + | 1.22209i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.38348 | − | 1.23148i | −0.153636 | − | 0.0559188i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.30424 | − | 2.25902i | −0.0591009 | − | 0.102366i | 0.834961 | − | 0.550309i | \(-0.185490\pi\) |
−0.894062 | + | 0.447943i | \(0.852157\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.69686 | + | 3.94114i | 0.212400 | + | 0.178224i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.68911 | − | 20.9220i | 0.166487 | − | 0.944196i | −0.781030 | − | 0.624493i | \(-0.785306\pi\) |
0.947518 | − | 0.319703i | \(-0.103583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.6914 | −2.05784 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.86106 | −0.0836486 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.59091 | + | 26.0363i | −0.205930 | + | 1.16789i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.6115 | + | 19.8124i | 1.05699 | + | 0.886923i | 0.993812 | − | 0.111078i | \(-0.0354305\pi\) |
0.0631826 | + | 0.998002i | \(0.479875\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.84796 | + | 3.20076i | 0.0825607 | + | 0.142999i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.3001 | − | 7.75260i | −0.949725 | − | 0.345672i | −0.179726 | − | 0.983717i | \(-0.557521\pi\) |
−0.769999 | + | 0.638045i | \(0.779743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.261127 | + | 0.452285i | −0.0116200 | + | 0.0201264i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.25423 | − | 12.7844i | −0.100114 | − | 0.567773i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.51595 | − | 5.46753i | 0.288814 | − | 0.242344i | −0.486856 | − | 0.873482i | \(-0.661856\pi\) |
0.775670 | + | 0.631138i | \(0.217412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.2320 | + | 13.1874i | −1.60281 | + | 0.583374i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.29002 | − | 0.771833i | −0.189409 | − | 0.0340772i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.87294 | − | 2.13757i | 0.258793 | − | 0.0941928i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.5933 | − | 10.5670i | 0.553853 | − | 0.464738i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.766039 | − | 4.34443i | −0.0336254 | − | 0.190699i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.60021 | − | 7.96780i | 0.201539 | − | 0.349076i | −0.747486 | − | 0.664278i | \(-0.768739\pi\) |
0.949024 | + | 0.315202i | \(0.102072\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.2194 | − | 12.4549i | −1.49631 | − | 0.544613i | −0.541209 | − | 0.840888i | \(-0.682033\pi\) |
−0.955103 | + | 0.296275i | \(0.904255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.41308 | − | 16.3039i | −0.410820 | − | 0.711562i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.7643 | + | 19.9406i | 1.03519 | + | 0.868628i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.93419 | − | 39.3258i | 0.301487 | − | 1.70982i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0642671 | 0.00278896 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.434359 | 0.0188142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.14501 | + | 6.49368i | −0.0495032 | + | 0.280746i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.8145 | + | 12.4308i | 0.639293 | + | 0.536431i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.9507 | − | 31.0916i | −0.773193 | − | 1.33921i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.1517 | − | 13.8861i | −1.64027 | − | 0.597009i | −0.653183 | − | 0.757200i | \(-0.726567\pi\) |
−0.987086 | + | 0.160190i | \(0.948789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.03287 | − | 10.4492i | 0.258895 | − | 0.448420i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.332243 | + | 1.88424i | 0.0142317 | + | 0.0807121i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3502 | + | 8.68488i | −0.442544 | + | 0.371339i | −0.836661 | − | 0.547722i | \(-0.815495\pi\) |
0.394116 | + | 0.919061i | \(0.371051\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.59452 | + | 2.03624i | −0.238768 | + | 0.0869046i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.116232 | + | 33.4358i | −0.00495165 | + | 1.42441i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.5098 | − | 13.6524i | 1.59508 | − | 0.580561i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.67850 | − | 1.40843i | 0.0712483 | − | 0.0597844i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.90730 | + | 27.8307i | 0.207929 | + | 1.17922i | 0.892764 | + | 0.450525i | \(0.148763\pi\) |
−0.684835 | + | 0.728698i | \(0.740126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.703590 | − | 1.21865i | 0.0297587 | − | 0.0515435i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.2599 | − | 8.82988i | −1.02425 | − | 0.372798i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.0442 | − | 17.3971i | −0.423314 | − | 0.733201i | 0.572947 | − | 0.819592i | \(-0.305800\pi\) |
−0.996261 | + | 0.0863910i | \(0.972467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.951687 | + | 0.798560i | 0.0400378 | + | 0.0335957i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.678859 | + | 3.85000i | −0.0285094 | + | 0.161685i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.9493 | 1.42323 | 0.711614 | − | 0.702571i | \(-0.247965\pi\) | ||||
0.711614 | + | 0.702571i | \(0.247965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.86417 | 0.412803 | 0.206401 | − | 0.978467i | \(-0.433825\pi\) | ||||
0.206401 | + | 0.978467i | \(0.433825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.46157 | + | 19.6315i | −0.144609 | + | 0.820119i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.2647 | + | 24.5560i | 1.22042 | + | 1.02405i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5868 | − | 28.7292i | −0.690519 | − | 1.19601i | −0.971668 | − | 0.236350i | \(-0.924049\pi\) |
0.281149 | − | 0.959664i | \(-0.409285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.656491 | + | 0.238943i | 0.0272828 | + | 0.00993014i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0184 | − | 22.5485i | 0.540094 | − | 0.935470i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.39466 | + | 30.5946i | 0.223424 | + | 1.26710i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0446533 | − | 0.0374685i | 0.00184618 | − | 0.00154913i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.919917 | + | 0.334822i | −0.0379690 | + | 0.0138196i | −0.360935 | − | 0.932591i | \(-0.617542\pi\) |
0.322966 | + | 0.946411i | \(0.395320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.6525 | − | 17.3394i | 0.603746 | − | 0.714458i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.28787 | + | 0.832717i | −0.0941104 | + | 0.0342534i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.84026 | − | 4.90056i | 0.239831 | − | 0.201242i | −0.514948 | − | 0.857222i | \(-0.672189\pi\) |
0.754779 | + | 0.655980i | \(0.227744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.73632 | + | 9.84718i | 0.0711823 | + | 0.403695i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.374865 | + | 0.649284i | −0.0153422 | + | 0.0265734i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.2157 | + | 12.4535i | 1.39802 | + | 0.508836i | 0.927589 | − | 0.373603i | \(-0.121878\pi\) |
0.470427 | + | 0.882439i | \(0.344100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.5601 | + | 18.2906i | 0.430754 | + | 0.746088i | 0.996938 | − | 0.0781907i | \(-0.0249143\pi\) |
−0.566184 | + | 0.824279i | \(0.691581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.2463 | − | 10.2759i | −0.498708 | − | 0.418466i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.580481 | + | 3.29207i | −0.0235999 | + | 0.133842i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.6970 | 1.89537 | 0.947686 | − | 0.319205i | \(-0.103416\pi\) | ||||
0.947686 | + | 0.319205i | \(0.103416\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.9880 | 1.21517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0894116 | + | 0.507078i | −0.00361721 | + | 0.0205142i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.60940 | + | 1.35044i | 0.0650029 | + | 0.0545439i | 0.674710 | − | 0.738083i | \(-0.264269\pi\) |
−0.609707 | + | 0.792627i | \(0.708713\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.686956 | − | 1.18984i | −0.0277007 | − | 0.0479791i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.04441 | + | 2.92793i | 0.323856 | + | 0.117874i | 0.498832 | − | 0.866699i | \(-0.333763\pi\) |
−0.174976 | + | 0.984573i | \(0.555985\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.58356 | + | 7.93896i | −0.184229 | + | 0.319094i | −0.943316 | − | 0.331895i | \(-0.892312\pi\) |
0.759087 | + | 0.650989i | \(0.225645\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.37755 | − | 7.81248i | −0.0552792 | − | 0.313504i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.7558 | + | 31.6809i | −1.51265 | + | 1.26927i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.9254 | + | 7.61622i | −0.837015 | + | 0.304649i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.52320 | + | 17.7303i | −0.260512 | + | 0.708081i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.5624 | − | 10.3959i | 1.13886 | − | 0.414510i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4431 | − | 21.3493i | 1.01288 | − | 0.849904i | 0.0241601 | − | 0.999708i | \(-0.492309\pi\) |
0.988716 | + | 0.149804i | \(0.0478644\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.55707 | + | 14.5019i | 0.101634 | + | 0.576397i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.53572 | + | 6.12405i | −0.140311 | + | 0.243026i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.05666 | + | 0.384593i | 0.0418665 | + | 0.0152381i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.38134 | − | 5.85666i | −0.133764 | − | 0.231686i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.2427 | − | 18.6638i | −0.878532 | − | 0.737176i | 0.0873446 | − | 0.996178i | \(-0.472162\pi\) |
−0.965877 | + | 0.259002i | \(0.916606\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.48780 | − | 19.7803i | 0.137545 | − | 0.780058i | −0.835508 | − | 0.549478i | \(-0.814827\pi\) |
0.973053 | − | 0.230580i | \(-0.0740622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.45102 | −0.175259 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.00534 | 0.196780 | 0.0983902 | − | 0.995148i | \(-0.468631\pi\) | ||||
0.0983902 | + | 0.995148i | \(0.468631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0483688 | − | 0.274313i | 0.00189864 | − | 0.0107677i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.5969 | − | 13.0873i | −0.611290 | − | 0.512934i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.89930 | − | 5.02173i | −0.113458 | − | 0.196515i | 0.803704 | − | 0.595029i | \(-0.202859\pi\) |
−0.917162 | + | 0.398514i | \(0.869526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.83080 | − | 1.39430i | −0.149682 | − | 0.0544797i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.93136 | − | 8.54137i | 0.192391 | − | 0.333231i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.65900 | − | 15.0800i | −0.103580 | − | 0.587432i | −0.991778 | − | 0.127971i | \(-0.959154\pi\) |
0.888198 | − | 0.459461i | \(-0.151957\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8445 | − | 17.4907i | 0.810759 | − | 0.680308i | −0.140030 | − | 0.990147i | \(-0.544720\pi\) |
0.950789 | + | 0.309840i | \(0.100275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.759848 | − | 0.276562i | 0.0295101 | − | 0.0107408i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.21034 | − | 1.24555i | 0.279605 | − | 0.0483003i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −57.1822 | + | 20.8126i | −2.21410 | + | 0.805868i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.9571 | − | 13.3896i | 0.616936 | − | 0.517671i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.48079 | + | 25.4118i | 0.172979 | + | 0.981011i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.9591 | + | 24.1779i | −0.538085 | + | 0.931991i | 0.460922 | + | 0.887441i | \(0.347519\pi\) |
−0.999007 | + | 0.0445503i | \(0.985814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.52520 | + | 1.64704i | 0.174175 | + | 0.0633946i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.4697 | + | 26.7943i | 0.594548 | + | 1.02979i | 0.993610 | + | 0.112864i | \(0.0360024\pi\) |
−0.399062 | + | 0.916924i | \(0.630664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.1123 | + | 21.0717i | 0.963720 | + | 0.808657i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.86708 | − | 10.5888i | 0.0715468 | − | 0.405762i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.8497 | 1.63960 | 0.819798 | − | 0.572653i | \(-0.194086\pi\) | ||||
0.819798 | + | 0.572653i | \(0.194086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.07846 | −0.194038 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.07260 | − | 11.7543i | 0.0790745 | − | 0.448454i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.745393 | − | 0.625459i | −0.0283972 | − | 0.0238281i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.60525 | + | 7.97652i | 0.175192 | + | 0.303441i | 0.940228 | − | 0.340547i | \(-0.110612\pi\) |
−0.765036 | + | 0.643988i | \(0.777279\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.9221 | + | 5.79519i | 0.604832 | + | 0.220141i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.63973 | − | 2.84010i | 0.0621986 | − | 0.107731i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.30957 | − | 18.7695i | −0.125359 | − | 0.710945i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.3725 | − | 11.2209i | 0.505794 | − | 0.424412i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.5177 | − | 11.8355i | 1.22818 | − | 0.447020i | 0.355204 | − | 0.934789i | \(-0.384411\pi\) |
0.872973 | + | 0.487769i | \(0.162189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.53478 | − | 20.9277i | −0.284180 | − | 0.789303i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.53045 | − | 0.557039i | 0.0576401 | − | 0.0209793i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.64242 | − | 3.05635i | 0.136987 | − | 0.114946i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.26706 | − | 24.1997i | −0.160253 | − | 0.908839i | −0.953825 | − | 0.300363i | \(-0.902892\pi\) |
0.793572 | − | 0.608476i | \(-0.208219\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.10528 | + | 8.84260i | −0.191463 | + | 0.331623i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.8238 | + | 14.1307i | 1.45396 | + | 0.529199i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.126321 | − | 0.218794i | −0.00472414 | − | 0.00818245i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.15711 | − | 5.16643i | −0.229941 | − | 0.192944i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.52850 | − | 20.0111i | 0.131591 | − | 0.746289i | −0.845582 | − | 0.533845i | \(-0.820747\pi\) |
0.977173 | − | 0.212444i | \(-0.0681423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.9016 | −2.11912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.45834 | −0.277379 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.41447 | − | 36.3783i | 0.238227 | − | 1.35105i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8678 | + | 19.1884i | 0.848121 | + | 0.711658i | 0.959375 | − | 0.282134i | \(-0.0910421\pi\) |
−0.111254 | + | 0.993792i | \(0.535487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | − | 0.866025i | −0.0185185 | − | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.0213 | − | 21.1180i | −2.14599 | − | 0.781078i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.35559 | − | 11.0082i | 0.234749 | − | 0.406597i | −0.724451 | − | 0.689327i | \(-0.757906\pi\) |
0.959200 | + | 0.282729i | \(0.0912398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.617633 | − | 3.50277i | −0.0227817 | − | 0.129202i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53.0776 | + | 44.5374i | −1.95514 | + | 1.64056i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6777 | − | 5.34223i | 0.539926 | − | 0.196517i | −0.0576389 | − | 0.998337i | \(-0.518357\pi\) |
0.597565 | + | 0.801820i | \(0.296135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.200448 | − | 0.556742i | −0.00736365 | − | 0.0204524i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.4945 | − | 4.18366i | 0.421692 | − | 0.153483i | −0.122453 | − | 0.992474i | \(-0.539076\pi\) |
0.544146 | + | 0.838991i | \(0.316854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.59788 | + | 2.17988i | −0.0951790 | + | 0.0798646i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.15651 | + | 6.55888i | 0.0423144 | + | 0.239977i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0168 | − | 51.9906i | 1.09679 | − | 1.89970i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.9015 | + | 5.05974i | 0.507274 | + | 0.184633i | 0.582963 | − | 0.812499i | \(-0.301893\pi\) |
−0.0756887 | + | 0.997131i | \(0.524116\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.56663 | − | 4.44553i | −0.0935331 | − | 0.162004i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.94941 | + | 2.47485i | 0.107340 | + | 0.0900689i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.14819 | − | 40.5394i | 0.259805 | − | 1.47343i | −0.523624 | − | 0.851949i | \(-0.675420\pi\) |
0.783430 | − | 0.621480i | \(-0.213468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.3830 | −1.24802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.5028 | −0.525726 | −0.262863 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262863 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.02489 | − | 17.1550i | 0.109508 | − | 0.621053i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.95932 | − | 1.64406i | −0.0708393 | − | 0.0594413i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.00436218 | + | 0.00755551i | 0.000157509 | + | 0.000272814i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.8302 | − | 12.3132i | −1.21995 | − | 0.444025i | −0.349804 | − | 0.936823i | \(-0.613752\pi\) |
−0.870144 | + | 0.492798i | \(0.835974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.74382 | + | 16.8768i | −0.350915 | + | 0.607803i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.70404 | − | 9.66407i | −0.0612900 | − | 0.347593i | −0.999996 | − | 0.00287358i | \(-0.999085\pi\) |
0.938706 | − | 0.344719i | \(-0.112026\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.2124 | + | 16.1211i | −0.690129 | + | 0.579087i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.7459 | + | 6.82297i | −0.672507 | + | 0.244773i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.7435 | + | 2.37411i | −0.492410 | + | 0.0850613i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.5430 | + | 10.0248i | −0.985567 | + | 0.358717i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.87614 | + | 4.93066i | −0.209996 | + | 0.176208i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.173558 | + | 0.984294i | 0.00619453 | + | 0.0351309i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.60527 | − | 6.24451i | 0.128514 | − | 0.222593i | −0.794587 | − | 0.607150i | \(-0.792313\pi\) |
0.923101 | + | 0.384558i | \(0.125646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9201 | − | 6.15841i | −0.602371 | − | 0.219245i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.65542 | − | 9.79547i | −0.201083 | − | 0.348287i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.619121 | − | 0.519504i | −0.0219856 | − | 0.0184481i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.534456 | + | 3.03105i | −0.0189552 | + | 0.107500i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.8912 | −1.37760 | −0.688798 | − | 0.724953i | \(-0.741861\pi\) | ||||
−0.688798 | + | 0.724953i | \(0.741861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5931 | 0.799286 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.18923 | − | 12.4157i | 0.0773525 | − | 0.438688i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.7459 | − | 27.4771i | −1.15558 | − | 0.969646i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.65842 | + | 11.5327i | 0.234678 | + | 0.406475i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.7667 | − | 6.83052i | −0.660619 | − | 0.240446i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.6692 | − | 21.9436i | 0.445424 | − | 0.771497i | −0.552658 | − | 0.833408i | \(-0.686386\pi\) |
0.998082 | + | 0.0619116i | \(0.0197197\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.87067 | + | 16.2804i | 0.100803 | + | 0.571682i | 0.992814 | + | 0.119668i | \(0.0381830\pi\) |
−0.892011 | + | 0.452014i | \(0.850706\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.1744 | + | 16.9283i | −0.707546 | + | 0.593702i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.47397 | − | 0.900452i | 0.0866594 | − | 0.0315414i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.6012 | + | 42.4048i | −0.545818 | + | 1.48356i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.498700 | + | 0.181512i | −0.0174260 | + | 0.00634254i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5824 | − | 21.4662i | 0.892832 | − | 0.749175i | −0.0759445 | − | 0.997112i | \(-0.524197\pi\) |
0.968776 | + | 0.247937i | \(0.0797527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.36134 | + | 13.3918i | 0.0823112 | + | 0.466810i | 0.997904 | + | 0.0647043i | \(0.0206104\pi\) |
−0.915593 | + | 0.402106i | \(0.868278\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.4359 | − | 18.0755i | 0.363331 | − | 0.629307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4874 | + | 10.0046i | 0.955831 | + | 0.347894i | 0.772398 | − | 0.635138i | \(-0.219057\pi\) |
0.183433 | + | 0.983032i | \(0.441279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.4167 | − | 40.5589i | −0.813295 | − | 1.40867i | −0.910546 | − | 0.413408i | \(-0.864338\pi\) |
0.0972508 | − | 0.995260i | \(-0.468995\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.36895 | − | 7.02239i | −0.290316 | − | 0.243604i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.56786 | − | 48.5908i | 0.296859 | − | 1.68357i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.58700 | 0.0549204 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.20805 | 0.180016 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.07186 | − | 17.4214i | 0.106052 | − | 0.601453i | −0.884742 | − | 0.466080i | \(-0.845666\pi\) |
0.990795 | − | 0.135373i | \(-0.0432232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8591 | + | 19.1811i | 0.788245 | + | 0.661416i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.47981 | + | 9.49130i | 0.188735 | + | 0.326898i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.23803 | − | 1.90649i | −0.180194 | − | 0.0655851i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.2175 | − | 26.3574i | 0.522879 | − | 0.905652i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.00988 | + | 22.7411i | 0.137619 | + | 0.780474i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.0101 | − | 26.0206i | 1.06301 | − | 0.891974i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9217 | − | 3.97519i | 0.373953 | − | 0.136108i | −0.148205 | − | 0.988957i | \(-0.547349\pi\) |
0.522158 | + | 0.852849i | \(0.325127\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.20807 | + | 1.42960i | −0.0413151 | + | 0.0488912i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.8227 | + | 16.6781i | −1.56527 | + | 0.569713i | −0.971937 | − | 0.235241i | \(-0.924412\pi\) |
−0.593337 | + | 0.804954i | \(0.702190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.1582 | − | 23.6276i | 0.960747 | − | 0.806162i | −0.0203276 | − | 0.999793i | \(-0.506471\pi\) |
0.981074 | + | 0.193631i | \(0.0620265\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.17212 | + | 12.3187i | 0.0740256 | + | 0.419820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.63689 | + | 2.83518i | −0.0557205 | + | 0.0965107i | −0.892540 | − | 0.450968i | \(-0.851079\pi\) |
0.836820 | + | 0.547479i | \(0.184412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.78001 | − | 0.647869i | −0.0605220 | − | 0.0220282i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.24039 | − | 16.0048i | −0.313820 | − | 0.543553i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.9008 | + | 28.4462i | 1.15001 | + | 0.964970i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.376848 | − | 2.13721i | 0.0127690 | − | 0.0724165i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.38538 | −0.283802 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.4771 | −0.557029 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.17156 | + | 29.3294i | −0.174631 | + | 0.990384i | 0.763937 | + | 0.645291i | \(0.223264\pi\) |
−0.938569 | + | 0.345093i | \(0.887847\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.89390 | − | 5.78466i | −0.232525 | − | 0.195112i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.54296 | + | 4.40453i | 0.0856744 | + | 0.148392i | 0.905678 | − | 0.423965i | \(-0.139362\pi\) |
−0.820004 | + | 0.572358i | \(0.806029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.5651 | − | 9.66890i | −0.893986 | − | 0.325384i | −0.146146 | − | 0.989263i | \(-0.546687\pi\) |
−0.747840 | + | 0.663879i | \(0.768909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0137979 | − | 0.0238987i | 0.000463812 | − | 0.000803346i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00988 | − | 17.0699i | −0.101062 | − | 0.573150i | −0.992720 | − | 0.120442i | \(-0.961569\pi\) |
0.891659 | − | 0.452709i | \(-0.149542\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.3193 | − | 41.3838i | 1.65412 | − | 1.38797i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.07279 | + | 1.48238i | −0.136444 | + | 0.0496615i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0574734 | − | 16.5331i | 0.00192328 | − | 0.553258i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.80322 | − | 2.84014i | 0.260833 | − | 0.0949354i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.824965 | − | 0.692228i | 0.0275448 | − | 0.0231128i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.93718 | − | 39.3427i | −0.231368 | − | 1.31215i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.3478 | + | 36.9755i | −0.711199 | + | 1.23183i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.0803 | + | 13.8601i | 1.26723 | + | 0.461235i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.59047 | − | 4.48683i | −0.0861102 | − | 0.149147i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.4639 | − | 19.6885i | −0.779106 | − | 0.653747i | 0.163917 | − | 0.986474i | \(-0.447587\pi\) |
−0.943023 | + | 0.332727i | \(0.892031\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.211201 | + | 1.19778i | −0.00700511 | + | 0.0397279i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.9437 | −1.35652 | −0.678262 | − | 0.734820i | \(-0.737266\pi\) | ||||
−0.678262 | + | 0.734820i | \(0.737266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.8659 | 0.955321 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.443917 | + | 2.51758i | −0.0146755 | + | 0.0832287i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.4323 | + | 23.8575i | 0.938917 | + | 0.787845i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.628356 | + | 1.08835i | 0.0207276 | + | 0.0359012i | 0.876203 | − | 0.481942i | \(-0.160068\pi\) |
−0.855476 | + | 0.517843i | \(0.826735\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8312 | + | 5.03416i | 0.455755 | + | 0.165881i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.459022 | − | 0.795050i | 0.0151089 | − | 0.0261694i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.26712 | + | 24.2001i | 0.140302 | + | 0.795693i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.1498 | − | 9.35583i | 0.366209 | − | 0.307286i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.6540 | − | 7.51744i | 0.677635 | − | 0.246639i | 0.0198035 | − | 0.999804i | \(-0.493696\pi\) |
0.657832 | + | 0.753165i | \(0.271474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.5357 | − | 6.39335i | −1.16464 | − | 0.209534i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.56964 | − | 2.39115i | 0.215080 | − | 0.0782828i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.49204 | + | 7.12566i | −0.277719 | + | 0.233034i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.28843 | − | 47.0060i | −0.270771 | − | 1.53562i | −0.752082 | − | 0.659070i | \(-0.770950\pi\) |
0.481310 | − | 0.876550i | \(-0.340161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.70162 | − | 16.8037i | 0.316600 | − | 0.548368i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.92400 | − | 0.700280i | −0.0627208 | − | 0.0228285i | 0.310469 | − | 0.950583i | \(-0.399514\pi\) |
−0.373190 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.6915 | − | 21.9822i | −0.413291 | − | 0.715840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.28593 | + | 1.07902i | 0.0418314 | + | 0.0351007i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.91185 | − | 50.5416i | 0.289596 | − | 1.64238i | −0.398793 | − | 0.917041i | \(-0.630571\pi\) |
0.688390 | − | 0.725341i | \(-0.258318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.33888 | 0.0434619 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.19255 | −0.168380 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.270252 | + | 1.53267i | −0.00875432 | + | 0.0496482i | −0.988872 | − | 0.148769i | \(-0.952469\pi\) |
0.980118 | + | 0.198417i | \(0.0635801\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.55710 | + | 5.50206i | 0.212183 | + | 0.178042i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.6232 | + | 28.7922i | 0.537352 | + | 0.930720i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.4483 | + | 15.8139i | 1.40302 | + | 0.510657i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.93812 | − | 3.35692i | 0.0625200 | − | 0.108288i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.66658 | + | 15.1229i | 0.0859295 | + | 0.487330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.229801 | − | 0.192826i | 0.00739755 | − | 0.00620728i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.8643 | + | 5.41015i | −0.478002 | + | 0.173979i | −0.569774 | − | 0.821801i | \(-0.692969\pi\) |
0.0917716 | + | 0.995780i | \(0.470747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.5306 | + | 12.9038i | −0.723786 | + | 0.414530i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.8360 | + | 6.49179i | −0.572386 | + | 0.208331i | −0.611965 | − | 0.790885i | \(-0.709621\pi\) |
0.0395789 | + | 0.999216i | \(0.487398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8724 | + | 19.1922i | −0.733255 | + | 0.615274i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.113519 | + | 0.643796i | 0.00363551 | + | 0.0206180i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.12329 | − | 1.94559i | 0.0359372 | − | 0.0622451i | −0.847497 | − | 0.530800i | \(-0.821892\pi\) |
0.883435 | + | 0.468554i | \(0.155225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.3467 | − | 18.6887i | −1.64105 | − | 0.597293i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.22793 | + | 3.85888i | 0.0711322 | + | 0.123205i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.1151 | + | 10.1658i | 0.386412 | + | 0.324238i | 0.815214 | − | 0.579160i | \(-0.196619\pi\) |
−0.428801 | + | 0.903399i | \(0.641064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.181539 | + | 1.02956i | −0.00578432 | + | 0.0328045i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.8282 | −0.471987 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −82.2323 | −2.61483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.20236 | + | 23.8328i | −0.133492 | + | 0.757072i | 0.842405 | + | 0.538844i | \(0.181139\pi\) |
−0.975898 | + | 0.218228i | \(0.929972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.0774 | − | 10.9733i | −0.415000 | − | 0.348226i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.160964 | + | 0.278798i | 0.00510291 | + | 0.00883849i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.3811 | − | 15.4255i | −1.34222 | − | 0.488529i | −0.431711 | − | 0.902012i | \(-0.642090\pi\) |
−0.910512 | + | 0.413483i | \(0.864312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.55142 | − | 4.41919i | 0.0807234 | − | 0.139817i |
(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 | 912.2.bo.k.385.2 | 18 | ||
4.3 | odd | 2 | 456.2.bg.c.385.2 | yes | 18 | ||
19.4 | even | 9 | inner | 912.2.bo.k.289.2 | 18 | ||
76.23 | odd | 18 | 456.2.bg.c.289.2 | ✓ | 18 | ||
76.55 | odd | 18 | 8664.2.a.bo.1.4 | 9 | |||
76.59 | even | 18 | 8664.2.a.bq.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.bg.c.289.2 | ✓ | 18 | 76.23 | odd | 18 | ||
456.2.bg.c.385.2 | yes | 18 | 4.3 | odd | 2 | ||
912.2.bo.k.289.2 | 18 | 19.4 | even | 9 | inner | ||
912.2.bo.k.385.2 | 18 | 1.1 | even | 1 | trivial | ||
8664.2.a.bo.1.4 | 9 | 76.55 | odd | 18 | |||
8664.2.a.bq.1.4 | 9 | 76.59 | even | 18 |