Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(97,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.y (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Character | \(\chi\) | \(=\) | 864.97 |
Dual form | 864.2.y.a.481.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.602286 | − | 1.62396i | −0.347730 | − | 0.937595i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.89262 | − | 1.05283i | −1.29362 | − | 0.470839i | −0.398705 | − | 0.917079i | \(-0.630540\pi\) |
−0.894913 | + | 0.446241i | \(0.852763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0578408 | + | 0.328031i | −0.0218618 | + | 0.123984i | −0.993786 | − | 0.111312i | \(-0.964495\pi\) |
0.971924 | + | 0.235296i | \(0.0756059\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.27450 | + | 1.95618i | −0.758168 | + | 0.652060i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0918319 | − | 0.0334241i | 0.0276884 | − | 0.0100777i | −0.328139 | − | 0.944630i | \(-0.606421\pi\) |
0.355827 | + | 0.934552i | \(0.384199\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.709877 | + | 0.595658i | −0.196885 | + | 0.165206i | −0.735900 | − | 0.677090i | \(-0.763241\pi\) |
0.539016 | + | 0.842296i | \(0.318796\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0324330 | + | 5.33160i | 0.00837417 | + | 1.37661i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.04568 | − | 1.81118i | −0.253616 | − | 0.439275i | 0.710903 | − | 0.703290i | \(-0.248287\pi\) |
−0.964519 | + | 0.264015i | \(0.914953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0352132 | + | 0.0609911i | −0.00807847 | + | 0.0139923i | −0.870036 | − | 0.492988i | \(-0.835905\pi\) |
0.861958 | + | 0.506980i | \(0.169238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.567547 | − | 0.103638i | 0.123849 | − | 0.0226156i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.09484 | + | 6.20915i | 0.228290 | + | 1.29470i | 0.856295 | + | 0.516487i | \(0.172761\pi\) |
−0.628005 | + | 0.778209i | \(0.716128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.42857 | + | 2.87691i | 0.685715 | + | 0.575383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.54666 | + | 2.51553i | 0.875005 | + | 0.484113i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.42290 | − | 4.55035i | −1.00701 | − | 0.844979i | −0.0190669 | − | 0.999818i | \(-0.506070\pi\) |
−0.987940 | + | 0.154839i | \(0.950514\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.69111 | + | 9.59077i | 0.303732 | + | 1.72255i | 0.629412 | + | 0.777072i | \(0.283296\pi\) |
−0.325679 | + | 0.945480i | \(0.605593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.109589 | − | 0.129001i | −0.0190769 | − | 0.0224561i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.512672 | − | 0.887973i | 0.0866573 | − | 0.150095i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.24591 | + | 3.89004i | 0.369226 | + | 0.639518i | 0.989445 | − | 0.144911i | \(-0.0462895\pi\) |
−0.620219 | + | 0.784429i | \(0.712956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.39487 | + | 0.794057i | 0.223359 | + | 0.127151i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.632082 | − | 0.530380i | 0.0987147 | − | 0.0828314i | −0.592095 | − | 0.805868i | \(-0.701699\pi\) |
0.690809 | + | 0.723037i | \(0.257254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.73217 | − | 3.17825i | 1.33164 | − | 0.484679i | 0.424473 | − | 0.905441i | \(-0.360459\pi\) |
0.907171 | + | 0.420762i | \(0.138237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.63879 | − | 3.26382i | 1.28779 | − | 0.486542i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.949958 | + | 5.38748i | −0.138566 | + | 0.785844i | 0.833745 | + | 0.552150i | \(0.186193\pi\) |
−0.972310 | + | 0.233694i | \(0.924919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.47359 | + | 2.35619i | 0.924798 | + | 0.336599i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.31148 | + | 2.78900i | −0.323672 | + | 0.390538i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.63841 | −1.18658 | −0.593288 | − | 0.804990i | \(-0.702171\pi\) | ||||
−0.593288 | + | 0.804990i | \(0.702171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.300825 | −0.0405632 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.120256 | + | 0.0204508i | 0.0159282 | + | 0.00270878i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.0152 | + | 4.73715i | 1.69444 | + | 0.616725i | 0.995173 | − | 0.0981376i | \(-0.0312885\pi\) |
0.699265 | + | 0.714863i | \(0.253511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.712093 | + | 4.03848i | −0.0911741 | + | 0.517074i | 0.904679 | + | 0.426095i | \(0.140111\pi\) |
−0.995853 | + | 0.0909796i | \(0.971000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.510129 | − | 0.859255i | −0.0642702 | − | 0.108256i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.68053 | − | 0.975633i | 0.332479 | − | 0.121012i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.50406 | + | 7.97485i | −1.16111 | + | 0.974283i | −0.999920 | − | 0.0126410i | \(-0.995976\pi\) |
−0.161185 | + | 0.986924i | \(0.551532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.42401 | − | 5.51766i | 1.13452 | − | 0.664248i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.92034 | − | 5.05819i | −0.346581 | − | 0.600296i | 0.639059 | − | 0.769158i | \(-0.279324\pi\) |
−0.985640 | + | 0.168862i | \(0.945991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.07395 | + | 3.59218i | −0.242737 | + | 0.420433i | −0.961493 | − | 0.274829i | \(-0.911379\pi\) |
0.718756 | + | 0.695263i | \(0.244712\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.60702 | − | 7.30060i | 0.301032 | − | 0.843000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.00565252 | + | 0.0320570i | 0.000644164 | + | 0.00365324i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.81366 | − | 4.03914i | −0.541579 | − | 0.454438i | 0.330499 | − | 0.943806i | \(-0.392783\pi\) |
−0.872077 | + | 0.489368i | \(0.837227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.34673 | − | 8.89867i | 0.149636 | − | 0.988741i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.4212 | − | 9.58350i | −1.25364 | − | 1.05193i | −0.996330 | − | 0.0855956i | \(-0.972721\pi\) |
−0.257306 | − | 0.966330i | \(-0.582835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11791 | + | 6.33997i | 0.121254 | + | 0.687667i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.12346 | + | 11.5472i | −0.442081 | + | 1.23799i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.08533 | − | 1.87984i | 0.115044 | − | 0.199263i | −0.802753 | − | 0.596312i | \(-0.796632\pi\) |
0.917798 | + | 0.397049i | \(0.129966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.154335 | − | 0.267315i | −0.0161787 | − | 0.0280223i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.5565 | − | 8.52268i | 1.50944 | − | 0.883761i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.166072 | − | 0.139351i | 0.0170386 | − | 0.0142971i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.94990 | + | 1.07368i | −0.299517 | + | 0.109015i | −0.487407 | − | 0.873175i | \(-0.662057\pi\) |
0.187890 | + | 0.982190i | \(0.439835\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.143489 | + | 0.255663i | −0.0144211 | + | 0.0256951i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.78788 | + | 15.8109i | −0.277404 | + | 1.57324i | 0.453815 | + | 0.891096i | \(0.350063\pi\) |
−0.731219 | + | 0.682142i | \(0.761048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.48898 | + | 1.63386i | 0.442313 | + | 0.160989i | 0.553569 | − | 0.832803i | \(-0.313265\pi\) |
−0.111257 | + | 0.993792i | \(0.535488\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.75081 | − | 0.297745i | −0.170862 | − | 0.0290569i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.91001 | −0.571342 | −0.285671 | − | 0.958328i | \(-0.592216\pi\) | ||||
−0.285671 | + | 0.958328i | \(0.592216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7056 | −1.02541 | −0.512706 | − | 0.858564i | \(-0.671357\pi\) | ||||
−0.512706 | + | 0.858564i | \(0.671357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.96459 | − | 5.99019i | 0.471218 | − | 0.568564i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.43312 | − | 1.97749i | −0.511105 | − | 0.186027i | 0.0735773 | − | 0.997290i | \(-0.476558\pi\) |
−0.584682 | + | 0.811263i | \(0.698781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.37020 | − | 19.1134i | 0.314273 | − | 1.78233i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.449405 | − | 2.74347i | 0.0415475 | − | 0.253634i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.654607 | − | 0.238257i | 0.0600077 | − | 0.0218410i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.41917 | + | 7.06452i | −0.765379 | + | 0.642230i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.24201 | − | 0.707037i | −0.111988 | − | 0.0637514i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.806989 | + | 1.39775i | 0.0721793 | + | 0.125018i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.63144 | − | 2.82574i | 0.144767 | − | 0.250744i | −0.784519 | − | 0.620105i | \(-0.787090\pi\) |
0.929286 | + | 0.369361i | \(0.120423\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.4206 | − | 12.2665i | −0.917485 | − | 1.08000i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.51442 | + | 14.2600i | 0.219686 | + | 1.24590i | 0.872588 | + | 0.488457i | \(0.162440\pi\) |
−0.652902 | + | 0.757442i | \(0.726449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0179702 | − | 0.0150788i | −0.00155822 | − | 0.00130750i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.5033 | − | 12.0633i | −0.903984 | − | 1.03824i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6111 | − | 12.2602i | −1.24831 | − | 1.04746i | −0.996827 | − | 0.0795971i | \(-0.974637\pi\) |
−0.251485 | − | 0.967861i | \(-0.580919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.529619 | + | 3.00362i | 0.0449217 | + | 0.254764i | 0.998996 | − | 0.0448077i | \(-0.0142675\pi\) |
−0.954074 | + | 0.299571i | \(0.903156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.32120 | − | 1.70211i | 0.784987 | − | 0.143343i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0452801 | + | 0.0784274i | −0.00378651 | + | 0.00655843i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.8956 | + | 18.8718i | 0.904833 | + | 1.56722i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0725841 | − | 11.9320i | −0.00598664 | − | 0.984132i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7296 | + | 10.6814i | −1.04285 | + | 0.875055i | −0.992324 | − | 0.123667i | \(-0.960534\pi\) |
−0.0505265 | + | 0.998723i | \(0.516090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5710 | + | 4.93945i | −1.10439 | + | 0.401966i | −0.828934 | − | 0.559346i | \(-0.811052\pi\) |
−0.275460 | + | 0.961313i | \(0.588830\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.92140 | + | 2.07399i | 0.478717 | + | 0.167672i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.20568 | − | 29.5229i | 0.418130 | − | 2.37133i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7462 | − | 4.63925i | −1.01726 | − | 0.370253i | −0.221044 | − | 0.975264i | \(-0.570946\pi\) |
−0.796217 | + | 0.605011i | \(0.793169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.20279 | + | 14.0284i | 0.412608 | + | 1.11253i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.10012 | −0.165513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.43138 | 0.738722 | 0.369361 | − | 0.929286i | \(-0.379577\pi\) | ||||
0.369361 | + | 0.929286i | \(0.379577\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.181182 | + | 0.488528i | 0.0141050 | + | 0.0380318i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.59637 | + | 0.945002i | 0.200913 | + | 0.0731264i | 0.440517 | − | 0.897744i | \(-0.354795\pi\) |
−0.239604 | + | 0.970871i | \(0.577017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.10831 | + | 11.9568i | −0.162178 | + | 0.919755i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0392169 | − | 0.207608i | −0.00299899 | − | 0.0158762i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.81604 | − | 3.20878i | 0.670271 | − | 0.243959i | 0.0156064 | − | 0.999878i | \(-0.495032\pi\) |
0.654665 | + | 0.755920i | \(0.272810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.14203 | + | 0.958277i | −0.0863293 | + | 0.0724389i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.145931 | − | 23.9893i | −0.0109689 | − | 1.80315i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.89391 | − | 5.01240i | −0.216301 | − | 0.374644i | 0.737373 | − | 0.675486i | \(-0.236066\pi\) |
−0.953674 | + | 0.300841i | \(0.902733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.75357 | − | 11.6975i | 0.501989 | − | 0.869470i | −0.498009 | − | 0.867172i | \(-0.665935\pi\) |
0.999997 | − | 0.00229800i | \(-0.000731477\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.98722 | − | 1.27591i | 0.516510 | − | 0.0943178i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.40104 | − | 13.6170i | −0.176528 | − | 1.00114i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.156564 | − | 0.131373i | −0.0114491 | − | 0.00960694i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.08815 | + | 1.34595i | −0.0791516 | + | 0.0979033i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3363 | + | 9.51225i | 0.820263 | + | 0.688282i | 0.953034 | − | 0.302865i | \(-0.0979430\pi\) |
−0.132771 | + | 0.991147i | \(0.542387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.85429 | + | 10.5162i | 0.133475 | + | 0.756975i | 0.975909 | + | 0.218176i | \(0.0700106\pi\) |
−0.842434 | + | 0.538799i | \(0.818878\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.19883 | − | 3.76547i | −0.229073 | − | 0.269651i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.17840 | + | 10.7013i | −0.440193 | + | 0.762437i | −0.997703 | − | 0.0677333i | \(-0.978423\pi\) |
0.557511 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.77528 | + | 4.80693i | 0.196734 | + | 0.340754i | 0.947468 | − | 0.319851i | \(-0.103633\pi\) |
−0.750733 | + | 0.660605i | \(0.770300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.6750 | + | 10.6311i | 1.31723 | + | 0.749859i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.80632 | − | 1.51568i | 0.126779 | − | 0.106380i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.38677 | + | 0.868714i | −0.166699 | + | 0.0606736i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.6364 | − | 11.9810i | −1.01730 | − | 0.832738i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.00119513 | + | 0.00677790i | −8.26687e−5 | + | 0.000468837i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4853 | − | 8.54797i | −1.61680 | − | 0.588466i | −0.634029 | − | 0.773309i | \(-0.718600\pi\) |
−0.982768 | + | 0.184843i | \(0.940822\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.45542 | + | 7.78900i | −0.442318 | + | 0.533694i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.6050 | −1.95084 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.24389 | −0.220209 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.08268 | + | 1.20449i | 0.478603 | + | 0.0813919i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.82115 | + | 0.662844i | 0.122504 | + | 0.0445877i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.05241 | − | 17.3111i | 0.204404 | − | 1.15923i | −0.693970 | − | 0.720004i | \(-0.744140\pi\) |
0.898374 | − | 0.439230i | \(-0.144749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.4261 | + | 0.163352i | −0.895071 | + | 0.0108901i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.65362 | − | 0.965838i | 0.176127 | − | 0.0641049i | −0.252452 | − | 0.967610i | \(-0.581237\pi\) |
0.428578 | + | 0.903505i | \(0.359015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0037 | − | 15.1069i | 1.18972 | − | 0.998292i | 0.189854 | − | 0.981812i | \(-0.439199\pi\) |
0.999864 | − | 0.0164797i | \(-0.00524589\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0486550 | − | 0.0284870i | 0.00320126 | − | 0.00187431i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.78503 | − | 15.2161i | −0.575527 | − | 0.996841i | −0.995984 | − | 0.0895291i | \(-0.971464\pi\) |
0.420458 | − | 0.907312i | \(-0.361870\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.41995 | − | 14.5838i | 0.549257 | − | 0.951340i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.66021 | + | 10.2499i | −0.237756 | + | 0.665803i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.75271 | − | 15.6114i | −0.178058 | − | 1.00982i | −0.934555 | − | 0.355819i | \(-0.884202\pi\) |
0.756497 | − | 0.653997i | \(-0.226909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5895 | + | 11.4030i | 0.875379 | + | 0.734531i | 0.965224 | − | 0.261425i | \(-0.0841925\pi\) |
−0.0898443 | + | 0.995956i | \(0.528637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2622 | + | 3.17251i | −0.979071 | + | 0.203517i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.2450 | − | 13.6311i | −1.03785 | − | 0.870861i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0113328 | − | 0.0642712i | −0.000721086 | − | 0.00408948i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.68442 | + | 24.3195i | −0.550353 | + | 1.54119i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7955 | + | 22.1625i | −0.807647 | + | 1.39889i | 0.106842 | + | 0.994276i | \(0.465926\pi\) |
−0.914489 | + | 0.404610i | \(0.867407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.308076 | + | 0.533604i | 0.0193686 | + | 0.0335474i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.62257 | − | 5.63392i | 0.602589 | − | 0.352810i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.12359 | − | 6.81650i | 0.506735 | − | 0.425201i | −0.353243 | − | 0.935531i | \(-0.614921\pi\) |
0.859979 | + | 0.510330i | \(0.170477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.40596 | + | 0.511728i | −0.0873621 | + | 0.0317972i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.2357 | − | 0.258370i | 1.31446 | − | 0.0159927i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.02163 | − | 22.8078i | 0.247984 | − | 1.40639i | −0.565474 | − | 0.824766i | \(-0.691307\pi\) |
0.813459 | − | 0.581623i | \(-0.197582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.9876 | + | 9.09475i | 1.53498 | + | 0.558686i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.70647 | − | 0.630327i | −0.226832 | − | 0.0385754i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.67441 | 0.345975 | 0.172987 | − | 0.984924i | \(-0.444658\pi\) | ||||
0.172987 | + | 0.984924i | \(0.444658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.2235 | 1.95744 | 0.978718 | − | 0.205207i | \(-0.0657869\pi\) | ||||
0.978718 | + | 0.205207i | \(0.0657869\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.341156 | + | 0.411634i | −0.0206477 | + | 0.0249132i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.411011 | + | 0.149596i | 0.0247849 | + | 0.00902096i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.06996 | − | 17.4106i | 0.184456 | − | 1.04610i | −0.742197 | − | 0.670182i | \(-0.766216\pi\) |
0.926653 | − | 0.375919i | \(-0.122673\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.6077 | − | 18.5061i | −1.35349 | − | 1.10793i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2941 | − | 4.47467i | 0.733402 | − | 0.266936i | 0.0517977 | − | 0.998658i | \(-0.483505\pi\) |
0.681604 | + | 0.731721i | \(0.261283\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2400 | + | 12.7879i | −0.905923 | + | 0.760160i | −0.971339 | − | 0.237698i | \(-0.923607\pi\) |
0.0654159 | + | 0.997858i | \(0.479163\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.326322 | − | 0.185765i | −0.0193297 | − | 0.0110038i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.137421 | + | 0.238020i | 0.00811171 | + | 0.0140499i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31309 | − | 10.9346i | 0.371358 | − | 0.643211i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.52029 | + | 4.14387i | 0.206363 | + | 0.242918i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.558677 | + | 3.16841i | 0.0326382 | + | 0.185101i | 0.996768 | − | 0.0803294i | \(-0.0255972\pi\) |
−0.964130 | + | 0.265430i | \(0.914486\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.6607 | − | 27.4056i | −1.90158 | − | 1.59561i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.501608 | + | 0.0790377i | 0.0291062 | + | 0.00458623i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.47573 | − | 3.75558i | −0.258838 | − | 0.217191i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.537490 | + | 3.04826i | 0.0309804 | + | 0.175699i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.3553 | − | 4.99525i | 1.57152 | − | 0.286969i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.31163 | − | 10.9321i | 0.361403 | − | 0.625968i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3963 | + | 18.0069i | 0.593348 | + | 1.02771i | 0.993778 | + | 0.111381i | \(0.0355275\pi\) |
−0.400430 | + | 0.916327i | \(0.631139\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0503320 | − | 8.27399i | −0.00286329 | − | 0.470691i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.80734 | − | 5.71204i | 0.386009 | − | 0.323900i | −0.429047 | − | 0.903282i | \(-0.641151\pi\) |
0.815056 | + | 0.579382i | \(0.196706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2159 | − | 3.71828i | 0.577436 | − | 0.210169i | −0.0367588 | − | 0.999324i | \(-0.511703\pi\) |
0.614194 | + | 0.789155i | \(0.289481\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.570961 | + | 3.02258i | 0.0321700 | + | 0.170303i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.65746 | + | 26.4138i | −0.261589 | + | 1.48354i | 0.516987 | + | 0.855993i | \(0.327054\pi\) |
−0.778576 | + | 0.627551i | \(0.784057\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.650086 | − | 0.236612i | −0.0363979 | − | 0.0132477i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.55952 | + | 9.59763i | 0.198673 | + | 0.535687i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.147288 | 0.00819531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.14752 | −0.230063 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.44784 | + | 17.3855i | 0.356566 | + | 0.961421i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.71232 | − | 0.623232i | −0.0944030 | − | 0.0343599i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.09405 | + | 23.2185i | −0.225029 | + | 1.27621i | 0.637599 | + | 0.770368i | \(0.279928\pi\) |
−0.862629 | + | 0.505837i | \(0.831184\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.7179 | − | 4.45449i | −0.696939 | − | 0.244105i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 35.8877 | − | 13.0621i | 1.96076 | − | 0.713657i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1354 | + | 9.34371i | −0.606584 | + | 0.508984i | −0.893554 | − | 0.448955i | \(-0.851796\pi\) |
0.286970 | + | 0.957939i | \(0.407352\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0609180 | + | 10.0142i | 0.00330861 | + | 0.543896i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.475861 | + | 0.824215i | 0.0257693 | + | 0.0446337i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.31316 | + | 4.00652i | −0.124899 | + | 0.216332i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −33.0692 | + | 6.03864i | −1.78039 | + | 0.325109i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.04724 | + | 28.6243i | 0.270950 | + | 1.53663i | 0.751540 | + | 0.659688i | \(0.229312\pi\) |
−0.480590 | + | 0.876946i | \(0.659577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5479 | − | 15.5636i | −0.992849 | − | 0.833099i | −0.00687094 | − | 0.999976i | \(-0.502187\pi\) |
−0.985978 | + | 0.166878i | \(0.946632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.72596 | + | 0.922539i | −0.252253 | + | 0.0492415i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.25585 | + | 6.92748i | 0.439414 | + | 0.368712i | 0.835490 | − | 0.549505i | \(-0.185184\pi\) |
−0.396076 | + | 0.918218i | \(0.629628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.12205 | + | 17.7060i | 0.165701 | + | 0.939738i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.781181 | − | 0.919557i | −0.0413445 | − | 0.0486681i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.9754 | + | 27.6703i | −0.843152 | + | 1.46038i | 0.0440654 | + | 0.999029i | \(0.485969\pi\) |
−0.887217 | + | 0.461353i | \(0.847364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49752 | + | 16.4502i | 0.499869 | + | 0.865799i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5433 | + | 9.41755i | 0.868296 | + | 0.494293i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.78109 | − | 8.20730i | 0.511965 | − | 0.429590i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.89218 | + | 1.78061i | −0.255370 | + | 0.0929470i | −0.466533 | − | 0.884504i | \(-0.654497\pi\) |
0.211163 | + | 0.977451i | \(0.432275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.400155 | + | 2.44282i | −0.0208312 | + | 0.127168i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.499652 | − | 2.83367i | 0.0259407 | − | 0.147117i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3419 | − | 8.49577i | −1.20860 | − | 0.439894i | −0.342382 | − | 0.939561i | \(-0.611234\pi\) |
−0.866218 | + | 0.499667i | \(0.833456\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.78385 | − | 2.15236i | 0.0921175 | − | 0.111147i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.56004 | 0.337859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.2176 | 1.39808 | 0.699038 | − | 0.715084i | \(-0.253612\pi\) | ||||
0.699038 | + | 0.715084i | \(0.253612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.57149 | − | 0.947495i | −0.285436 | − | 0.0485417i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9645 | + | 3.99075i | 0.560259 | + | 0.203918i | 0.606599 | − | 0.795008i | \(-0.292533\pi\) |
−0.0463398 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0173999 | − | 0.0986799i | 0.000886782 | − | 0.00502919i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.6441 | + | 24.3106i | −0.693570 | + | 1.23578i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.81324 | − | 2.84379i | 0.396147 | − | 0.144186i | −0.136262 | − | 0.990673i | \(-0.543509\pi\) |
0.532409 | + | 0.846487i | \(0.321287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.1010 | − | 8.47576i | 0.510830 | − | 0.428638i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6432 | − | 12.6719i | 1.09176 | − | 0.639213i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.67156 | + | 16.7516i | 0.486629 | + | 0.842866i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.05659 | − | 8.75827i | 0.253783 | − | 0.439565i | −0.710781 | − | 0.703413i | \(-0.751658\pi\) |
0.964564 | + | 0.263848i | \(0.0849918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0136642 | + | 0.0382647i | −0.000684066 | + | 0.00191563i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.67186 | + | 15.1529i | 0.133426 | + | 0.756699i | 0.975943 | + | 0.218028i | \(0.0699624\pi\) |
−0.842516 | + | 0.538671i | \(0.818927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.91330 | − | 5.80094i | −0.344376 | − | 0.288966i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2643 | + | 24.3226i | −0.659110 | + | 1.20860i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.336268 | + | 0.282162i | 0.0166682 | + | 0.0139863i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.56680 | − | 37.2422i | −0.324707 | − | 1.84151i | −0.511724 | − | 0.859150i | \(-0.670993\pi\) |
0.187017 | − | 0.982357i | \(-0.440118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.1100 | + | 31.1120i | −0.548016 | + | 1.53464i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.30675 | + | 3.99540i | −0.113508 | + | 0.196601i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.9473 | + | 39.7459i | 1.12644 | + | 1.95105i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.55878 | − | 2.66912i | 0.223244 | − | 0.130707i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.1838 | + | 17.7753i | −1.03490 | + | 0.868380i | −0.991425 | − | 0.130674i | \(-0.958286\pi\) |
−0.0434699 | + | 0.999055i | \(0.513841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.14169 | − | 1.87142i | 0.250591 | − | 0.0912075i | −0.213671 | − | 0.976906i | \(-0.568542\pi\) |
0.464262 | + | 0.885698i | \(0.346320\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.37819 | − | 14.1121i | −0.407361 | − | 0.686155i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.62540 | − | 9.21810i | 0.0788435 | − | 0.447144i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.28356 | − | 0.467178i | −0.0621158 | − | 0.0226083i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.154635 | + | 0.0262974i | 0.00746583 | + | 0.00126965i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.4164 | −1.07976 | −0.539879 | − | 0.841743i | \(-0.681530\pi\) | ||||
−0.539879 | + | 0.841743i | \(0.681530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.6486 | −1.85733 | −0.928667 | − | 0.370914i | \(-0.879044\pi\) | ||||
−0.928667 | + | 0.370914i | \(0.879044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0848 | − | 29.0603i | 1.15478 | − | 1.39334i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.417256 | − | 0.151869i | −0.0199600 | − | 0.00726486i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.129035 | + | 0.731792i | −0.00615849 | + | 0.0349265i | −0.987732 | − | 0.156158i | \(-0.950089\pi\) |
0.981574 | + | 0.191084i | \(0.0612003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.3333 | + | 7.30433i | −0.920635 | + | 0.347825i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.9081 | − | 6.51802i | 0.850840 | − | 0.309680i | 0.120457 | − | 0.992719i | \(-0.461564\pi\) |
0.730383 | + | 0.683038i | \(0.239342\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.11858 | + | 4.29500i | −0.242644 | + | 0.203603i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.0131 | + | 14.2391i | 1.18308 | + | 0.673488i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7956 | + | 29.0909i | 0.792635 | + | 1.37288i | 0.924330 | + | 0.381594i | \(0.124625\pi\) |
−0.131695 | + | 0.991290i | \(0.542042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0403179 | − | 0.0698326i | 0.00189849 | − | 0.00328829i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.1951 | + | 19.0639i | 0.760912 | + | 0.895698i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.164994 | + | 0.935729i | 0.00773505 | + | 0.0438676i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.9248 | − | 17.5580i | −0.978822 | − | 0.821329i | 0.00508919 | − | 0.999987i | \(-0.498380\pi\) |
−0.983911 | + | 0.178658i | \(0.942824\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.198305 | − | 10.8653i | −0.00925609 | − | 0.507147i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.47834 | + | 5.43597i | 0.301726 | + | 0.253179i | 0.781062 | − | 0.624453i | \(-0.214678\pi\) |
−0.479336 | + | 0.877631i | \(0.659122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.61095 | − | 20.4787i | −0.167815 | − | 0.951726i | −0.946114 | − | 0.323833i | \(-0.895028\pi\) |
0.778299 | − | 0.627893i | \(-0.216083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51.0793 | + | 9.32739i | −2.36875 | + | 0.432547i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.73820 | − | 11.6709i | 0.311807 | − | 0.540065i | −0.666947 | − | 0.745105i | \(-0.732399\pi\) |
0.978754 | + | 0.205040i | \(0.0657325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.06628 | − | 3.57890i | −0.0954119 | − | 0.165258i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.142915 | + | 23.4936i | 0.00658519 | + | 1.08253i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.695662 | − | 0.583730i | 0.0319866 | − | 0.0268399i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.296197 | + | 0.107807i | −0.0135905 | + | 0.00494653i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.6481 | − | 16.8983i | 0.899624 | − | 0.773719i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.31308 | + | 7.44684i | −0.0599961 | + | 0.340255i | −1.00000 | 0.000909967i | \(-0.999710\pi\) | |
0.940003 | + | 0.341165i | \(0.110821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.91145 | − | 1.42365i | −0.178347 | − | 0.0649130i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.26487 | + | 3.41052i | 0.0575538 | + | 0.155184i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.66334 | 0.438790 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.89534 | 0.0858860 | 0.0429430 | − | 0.999078i | \(-0.486327\pi\) | ||||
0.0429430 | + | 0.999078i | \(0.486327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.68039 | − | 15.3162i | −0.256876 | − | 0.692622i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.10930 | + | 2.58757i | 0.320838 | + | 0.116776i | 0.497419 | − | 0.867511i | \(-0.334281\pi\) |
−0.176580 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.57086 | + | 14.5801i | −0.115786 | + | 0.656653i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.684226 | − | 0.588467i | 0.0307537 | − | 0.0264496i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.82816 | − | 0.665395i | 0.0820041 | − | 0.0298471i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7824 | + | 18.2776i | −0.975116 | + | 0.818220i | −0.983345 | − | 0.181747i | \(-0.941825\pi\) |
0.00822925 | + | 0.999966i | \(0.497381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0291114 | − | 4.78557i | −0.00130060 | − | 0.213803i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.34878 | − | 7.53231i | −0.193902 | − | 0.335849i | 0.752638 | − | 0.658435i | \(-0.228781\pi\) |
−0.946540 | + | 0.322586i | \(0.895448\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.7104 | − | 42.7996i | 1.09960 | − | 1.90456i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.6872 | − | 3.77761i | 0.918751 | − | 0.167770i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.39133 | + | 24.9045i | 0.194642 | + | 1.10387i | 0.912927 | + | 0.408123i | \(0.133817\pi\) |
−0.718285 | + | 0.695749i | \(0.755072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.05839 | − | 0.888095i | −0.0468204 | − | 0.0392870i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.313527 | + | 0.188726i | −0.0138426 | + | 0.00833246i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.2647 | − | 9.45225i | −0.496384 | − | 0.416516i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0928351 | + | 0.526494i | 0.00408288 | + | 0.0231552i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5207 | − | 12.3843i | −0.461808 | − | 0.543611i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.19117 | + | 2.06317i | −0.0521863 | + | 0.0903892i | −0.890938 | − | 0.454124i | \(-0.849952\pi\) |
0.838752 | + | 0.544513i | \(0.183286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.7971 | − | 27.3615i | −0.690761 | − | 1.19643i | −0.971589 | − | 0.236675i | \(-0.923942\pi\) |
0.280828 | − | 0.959758i | \(-0.409391\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.24403 | + | 1.27746i | 0.0979376 | + | 0.0557527i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.6022 | − | 13.0918i | 0.679643 | − | 0.570289i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7419 | + | 5.72958i | −0.684430 | + | 0.249112i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38.8699 | + | 14.6854i | −1.68681 | + | 0.637294i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.132776 | + | 0.753009i | −0.00575116 | + | 0.0326165i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.0954 | + | 6.22222i | 0.739099 | + | 0.269010i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.39698 | + | 7.71850i | −0.276050 | + | 0.333078i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.673236 | 0.0289983 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.1910 | −1.68495 | −0.842477 | − | 0.538732i | \(-0.818903\pi\) | ||||
−0.842477 | + | 0.538732i | \(0.818903\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.0639 | − | 3.92228i | −0.989767 | − | 0.168321i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.9673 | + | 11.2712i | 1.32649 | + | 0.482803i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.73073 | − | 15.4868i | 0.116758 | − | 0.662166i | −0.869107 | − | 0.494624i | \(-0.835306\pi\) |
0.985865 | − | 0.167542i | \(-0.0535831\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.28033 | − | 10.5785i | −0.268038 | − | 0.451480i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.468489 | − | 0.170516i | 0.0199583 | − | 0.00726422i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.60339 | − | 1.34540i | 0.0681830 | − | 0.0572124i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.6673 | + | 12.1005i | −0.877278 | + | 0.513637i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.08750 | + | 8.81182i | 0.215564 | + | 0.373369i | 0.953447 | − | 0.301561i | \(-0.0975075\pi\) |
−0.737883 | + | 0.674929i | \(0.764174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.30562 | + | 7.45755i | −0.182108 | + | 0.315421i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.119048 | + | 0.333378i | −0.00502622 | + | 0.0140752i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.71490 | + | 15.3970i | 0.114420 | + | 0.648906i | 0.987036 | + | 0.160499i | \(0.0513105\pi\) |
−0.872616 | + | 0.488406i | \(0.837578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.6340 | + | 11.4403i | 0.573585 | + | 0.481295i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.84115 | + | 0.956475i | 0.119317 | + | 0.0401682i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.2876 | + | 27.9316i | 1.39549 | + | 1.17095i | 0.963061 | + | 0.269284i | \(0.0867871\pi\) |
0.432427 | + | 0.901669i | \(0.357657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.41229 | + | 30.6946i | 0.226497 | + | 1.28453i | 0.859802 | + | 0.510627i | \(0.170587\pi\) |
−0.633305 | + | 0.773902i | \(0.718302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.61986 | − | 24.1387i | 0.360100 | − | 1.00841i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.1094 | + | 24.4383i | −0.588405 | + | 1.01915i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.920067 | − | 1.59360i | −0.0383029 | − | 0.0663426i | 0.846238 | − | 0.532804i | \(-0.178862\pi\) |
−0.884541 | + | 0.466462i | \(0.845529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.9611 | − | 9.34508i | 0.663322 | − | 0.388368i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.80430 | − | 3.19218i | 0.157829 | − | 0.132434i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.793282 | + | 0.288731i | −0.0328544 | + | 0.0119580i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.18836 | + | 7.46267i | −0.173167 | + | 0.308544i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.10216 | − | 6.25069i | 0.0454912 | − | 0.257994i | −0.953577 | − | 0.301149i | \(-0.902630\pi\) |
0.999068 | + | 0.0431553i | \(0.0137410\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.644501 | − | 0.234579i | −0.0265562 | − | 0.00966566i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.0997 | + | 3.58824i | 0.867925 | + | 0.147601i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5902 | 0.804472 | 0.402236 | − | 0.915536i | \(-0.368233\pi\) | ||||
0.402236 | + | 0.915536i | \(0.368233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.14437 | −0.0879106 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.13475 | − | 7.40210i | 0.251079 | − | 0.302948i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.9383 | + | 13.4445i | 1.50926 | + | 0.549325i | 0.958439 | − | 0.285299i | \(-0.0920927\pi\) |
0.550820 | + | 0.834624i | \(0.314315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.90024 | − | 27.7907i | 0.199885 | − | 1.13360i | −0.705403 | − | 0.708807i | \(-0.749234\pi\) |
0.905288 | − | 0.424798i | \(-0.139655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.01677 | − | 36.7305i | 0.245022 | − | 1.49578i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.7912 | − | 11.5710i | 1.29250 | − | 0.470430i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.6678 | + | 21.5378i | −1.04182 | + | 0.874194i | −0.992210 | − | 0.124574i | \(-0.960244\pi\) |
−0.0496139 | + | 0.998768i | \(0.515799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.54934 | − | 2.02052i | −0.143826 | − | 0.0818757i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.53474 | − | 4.39030i | −0.102545 | − | 0.177612i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8676 | − | 29.2156i | 0.681278 | − | 1.18001i | −0.293313 | − | 0.956016i | \(-0.594758\pi\) |
0.974591 | − | 0.223992i | \(-0.0719088\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.84828 | + | 3.35281i | 0.114854 | + | 0.135198i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.464372 | − | 2.63359i | −0.0186949 | − | 0.106024i | 0.974032 | − | 0.226408i | \(-0.0726984\pi\) |
−0.992727 | + | 0.120384i | \(0.961587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.4711 | + | 18.8555i | 0.903191 | + | 0.757867i | 0.970811 | − | 0.239844i | \(-0.0770962\pi\) |
−0.0676204 | + | 0.997711i | \(0.521541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.6414 | + | 30.9850i | −0.427025 | + | 1.24338i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.553871 | + | 0.464753i | 0.0221904 | + | 0.0186199i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.74870 | − | 26.9312i | −0.189948 | − | 1.07725i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0117269 | − | 0.00214140i | 0.000468326 | − | 8.55191e-5i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.69704 | − | 8.13550i | 0.187283 | − | 0.324384i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.64926 | + | 11.5168i | 0.264703 | + | 0.458478i | 0.967486 | − | 0.252926i | \(-0.0813929\pi\) |
−0.702783 | + | 0.711404i | \(0.748060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.263326 | + | 43.2876i | 0.0104663 | + | 1.72053i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.69416 | + | 6.45616i | −0.305333 | + | 0.256205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.99894 | + | 2.18344i | −0.237687 | + | 0.0865109i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.5370 | + | 5.79214i | 0.654196 | + | 0.229134i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.52695 | − | 25.6736i | 0.178804 | − | 1.01405i | −0.754857 | − | 0.655889i | \(-0.772294\pi\) |
0.933661 | − | 0.358158i | \(-0.116595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.18214 | + | 1.52217i | 0.164928 | + | 0.0600287i | 0.423164 | − | 0.906053i | \(-0.360919\pi\) |
−0.258237 | + | 0.966082i | \(0.583142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.2284 | + | 46.4534i | 0.678367 | + | 1.82910i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3237 | −0.995578 | −0.497789 | − | 0.867298i | \(-0.665855\pi\) | ||||
−0.497789 | + | 0.867298i | \(0.665855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.35355 | 0.0531314 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.95375 | + | 5.26795i | 0.0765734 | + | 0.206467i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.8225 | + | 4.66701i | 0.501784 | + | 0.182634i | 0.580496 | − | 0.814263i | \(-0.302859\pi\) |
−0.0787124 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.74003 | − | 43.8959i | 0.302428 | − | 1.71515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.30975 | − | 12.2274i | −0.0901120 | − | 0.477038i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.2443 | + | 9.18818i | −0.983379 | + | 0.357921i | −0.783153 | − | 0.621829i | \(-0.786390\pi\) |
−0.200226 | + | 0.979750i | \(0.564168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.2171 | − | 22.8378i | 1.05862 | − | 0.888289i | 0.0646483 | − | 0.997908i | \(-0.479407\pi\) |
0.993974 | + | 0.109619i | \(0.0349630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0204194 | − | 3.35670i | −0.000793022 | − | 0.130363i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0361056 | + | 0.0625368i | 0.00140012 | + | 0.00242507i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.3166 | − | 38.6535i | 0.864102 | − | 1.49667i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.9509 | + | 5.46922i | −1.15797 | + | 0.211452i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0695896 | + | 0.394662i | 0.00268648 | + | 0.0152358i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.75031 | − | 4.82508i | −0.221658 | − | 0.185993i | 0.525196 | − | 0.850981i | \(-0.323992\pi\) |
−0.746854 | + | 0.664988i | \(0.768437\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.35161 | + | 21.7050i | 0.321453 | + | 0.835427i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.47757 | − | 7.11352i | −0.325819 | − | 0.273395i | 0.465175 | − | 0.885219i | \(-0.345992\pi\) |
−0.790994 | + | 0.611824i | \(0.790436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.181575 | − | 1.02976i | −0.00696821 | − | 0.0395187i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.16672 | − | 3.72766i | −0.121349 | − | 0.142844i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9052 | − | 29.2807i | 0.646861 | − | 1.12040i | −0.337008 | − | 0.941502i | \(-0.609415\pi\) |
0.983868 | − | 0.178894i | \(-0.0572519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.3565 | + | 50.8470i | 1.12166 | + | 1.94276i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.3764 | − | 20.1386i | −1.34969 | − | 0.768337i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.13221 | − | 5.14554i | 0.233619 | − | 0.196029i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.63368 | − | 2.77843i | 0.290399 | − | 0.105697i | −0.192713 | − | 0.981255i | \(-0.561729\pi\) |
0.483112 | + | 0.875559i | \(0.339506\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0755660 | − | 0.0618565i | −0.00287051 | − | 0.00234973i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.63030 | − | 9.24592i | 0.0618410 | − | 0.350718i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.62157 | − | 0.590204i | −0.0614214 | − | 0.0223556i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.4193 | + | 23.4310i | −0.734505 | + | 0.886242i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.64774 | 0.100004 | 0.0500019 | − | 0.998749i | \(-0.484077\pi\) | ||||
0.0500019 | + | 0.998749i | \(0.484077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.316344 | −0.0119311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.7547 | − | 4.89007i | −1.08296 | − | 0.184171i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.02520 | − | 1.82902i | −0.188992 | − | 0.0687875i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.65574 | − | 32.0753i | 0.212406 | − | 1.20461i | −0.672946 | − | 0.739692i | \(-0.734971\pi\) |
0.885352 | − | 0.464922i | \(-0.153918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.8499 | − | 0.229343i | 0.706928 | − | 0.00860104i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −57.6990 | + | 21.0007i | −2.16084 | + | 0.786483i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.213548 | − | 0.179188i | 0.00798626 | − | 0.00670127i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.6944 | + | 13.8728i | −0.884882 | + | 0.518089i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00980 | − | 10.4093i | −0.224128 | − | 0.388201i | 0.731930 | − | 0.681380i | \(-0.238620\pi\) |
−0.956057 | + | 0.293179i | \(0.905287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.795603 | + | 1.37802i | −0.0296298 | + | 0.0513203i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.3332 | − | 28.9368i | 0.384296 | − | 1.07617i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.50183 | − | 31.2024i | −0.204333 | − | 1.15883i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3727 | − | 9.54283i | −0.421790 | − | 0.353924i | 0.407054 | − | 0.913404i | \(-0.366556\pi\) |
−0.828844 | + | 0.559480i | \(0.811001\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.3443 | + | 22.8745i | 0.531269 | + | 0.847203i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.8875 | − | 12.4921i | −0.550633 | − | 0.462036i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.45253 | + | 13.9090i | 0.0905861 | + | 0.513740i | 0.996011 | + | 0.0892326i | \(0.0284414\pi\) |
−0.905425 | + | 0.424507i | \(0.860447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.3523 | + | 34.5910i | −0.455623 | + | 1.27591i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.606224 | + | 1.05001i | −0.0223305 | + | 0.0386776i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6568 | − | 32.3145i | −0.686300 | − | 1.18871i | −0.973026 | − | 0.230694i | \(-0.925900\pi\) |
0.286726 | − | 0.958013i | \(-0.407433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0975485 | + | 0.0571136i | −0.00358353 | + | 0.00209812i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.2069 | − | 21.9902i | 0.961437 | − | 0.806742i | −0.0197490 | − | 0.999805i | \(-0.506287\pi\) |
0.981186 | + | 0.193063i | \(0.0618423\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.0676 | − | 17.4952i | 1.76106 | − | 0.640973i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 44.7245 | − | 0.544153i | 1.63638 | − | 0.0199095i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.341840 | − | 1.93867i | 0.0124905 | − | 0.0708374i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.3393 | − | 9.95070i | −0.997626 | − | 0.363106i | −0.208958 | − | 0.977925i | \(-0.567007\pi\) |
−0.788669 | + | 0.614818i | \(0.789229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43.6977 | + | 7.43129i | 1.59243 | + | 0.270811i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.4562 | 1.61793 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.3705 | −0.813070 | −0.406535 | − | 0.913635i | \(-0.633263\pi\) | ||||
−0.406535 | + | 0.913635i | \(0.633263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.681002 | − | 0.821686i | 0.0247188 | − | 0.0298253i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.32069 | − | 1.20863i | −0.120375 | − | 0.0438129i | 0.281130 | − | 0.959670i | \(-0.409291\pi\) |
−0.401505 | + | 0.915857i | \(0.631513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.619221 | − | 3.51178i | 0.0224173 | − | 0.127135i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.9448 | − | 12.2335i | −0.540331 | − | 0.442302i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0609 | + | 4.38982i | −0.435495 | + | 0.158507i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.8620 | + | 11.6316i | −0.499876 | + | 0.419445i | −0.857550 | − | 0.514401i | \(-0.828014\pi\) |
0.357674 | + | 0.933846i | \(0.383570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.9625 | − | 9.08691i | −0.574874 | − | 0.327257i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.6595 | − | 21.9269i | −0.455330 | − | 0.788654i | 0.543377 | − | 0.839489i | \(-0.317145\pi\) |
−0.998707 | + | 0.0508344i | \(0.983812\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.7937 | + | 37.7478i | −0.782854 | + | 1.35594i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.67782 | + | 1.97502i | 0.0601913 | + | 0.0708534i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0100908 | + | 0.0572278i | 0.000361541 | + | 0.00205040i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.437246 | − | 0.366893i | −0.0156459 | − | 0.0131285i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.2095 | − | 34.3303i | −0.472071 | − | 1.22687i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.9857 | + | 26.8392i | 1.14162 | + | 0.957931i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.54013 | + | 14.4058i | 0.0905459 | + | 0.513511i | 0.996022 | + | 0.0891131i | \(0.0284032\pi\) |
−0.905476 | + | 0.424398i | \(0.860486\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39.4612 | + | 7.20584i | −1.40485 | + | 0.256535i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.962935 | − | 1.66785i | 0.0342380 | − | 0.0593020i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.90005 | − | 3.29099i | −0.0674728 | − | 0.116866i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.280170 | − | 46.0566i | −0.00993660 | − | 1.63346i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.74716 | + | 4.82244i | −0.203575 | + | 0.170820i | −0.738875 | − | 0.673842i | \(-0.764643\pi\) |
0.535300 | + | 0.844662i | \(0.320198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.7510 | − | 3.91306i | 0.380344 | − | 0.138434i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.20873 | + | 6.39880i | 0.0427083 | + | 0.226090i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.0703892 | + | 0.399197i | −0.00248398 | + | 0.0140874i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.07485 | + | 2.21106i | 0.214110 | + | 0.0779298i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.41762 | − | 9.21503i | −0.120306 | − | 0.324384i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.1354 | −1.02435 | −0.512173 | − | 0.858882i | \(-0.671159\pi\) | ||||
−0.512173 | + | 0.858882i | \(0.671159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.0684 | −1.30165 | −0.650823 | − | 0.759229i | \(-0.725576\pi\) | ||||
−0.650823 | + | 0.759229i | \(0.725576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.4078 | − | 52.3297i | −0.680660 | − | 1.83528i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.2814 | − | 9.92961i | −0.955625 | − | 0.347819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.113643 | + | 0.644501i | −0.00397586 | + | 0.0225482i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.873951 | + | 0.306103i | 0.0305383 | + | 0.0106961i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.72069 | + | 3.53804i | −0.339254 | + | 0.123478i | −0.506029 | − | 0.862517i | \(-0.668887\pi\) |
0.166774 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.1697 | − | 21.1199i | 0.877360 | − | 0.736192i | −0.0882747 | − | 0.996096i | \(-0.528135\pi\) |
0.965634 | + | 0.259904i | \(0.0836909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.00460839 | − | 0.757565i | −0.000160444 | − | 0.0263750i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4009 | − | 31.8712i | −0.639861 | − | 1.10827i | −0.985463 | − | 0.169890i | \(-0.945659\pi\) |
0.345602 | − | 0.938381i | \(-0.387675\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9054 | − | 31.0130i | 0.621880 | − | 1.07713i | −0.367255 | − | 0.930120i | \(-0.619702\pi\) |
0.989135 | − | 0.147008i | \(-0.0469642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.1231 | + | 5.50066i | −1.04496 | + | 0.190816i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.50184 | − | 14.1887i | −0.0866837 | − | 0.491608i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.51539 | − | 5.46706i | −0.225474 | − | 0.189195i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.4369 | + | 47.8600i | −0.568143 | + | 1.65428i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.9870 | − | 16.7711i | −0.690027 | − | 0.579001i | 0.228890 | − | 0.973452i | \(-0.426490\pi\) |
−0.918917 | + | 0.394451i | \(0.870935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.66632 | + | 20.7927i | 0.126425 | + | 0.716991i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.6712 | − | 17.2700i | −0.505304 | − | 0.594812i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.6870 | − | 32.3668i | 0.642852 | − | 1.11345i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.83041 | − | 3.17037i | −0.0628938 | − | 0.108935i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.9458 | + | 17.0472i | 1.02774 | + | 0.585058i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.6949 | + | 18.2042i | −0.743692 | + | 0.624031i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.0619 | + | 7.30193i | −0.686906 | + | 0.250013i | −0.661810 | − | 0.749672i | \(-0.730211\pi\) |
−0.0250961 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.105136 | + | 0.641819i | −0.00359556 | + | 0.0219497i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.46145 | − | 25.3022i | 0.152400 | − | 0.864306i | −0.808724 | − | 0.588189i | \(-0.799841\pi\) |
0.961124 | − | 0.276117i | \(-0.0890477\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.92252 | − | 2.51959i | −0.236193 | − | 0.0859673i | 0.221212 | − | 0.975226i | \(-0.428999\pi\) |
−0.457405 | + | 0.889259i | \(0.651221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.303769 | − | 0.366523i | 0.0103524 | − | 0.0124911i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.4586 | −0.492176 | −0.246088 | − | 0.969247i | \(-0.579145\pi\) | ||||
−0.246088 | + | 0.969247i | \(0.579145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.8797 | −0.981940 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.5596 | − | 3.66646i | −0.732204 | − | 0.124520i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.577052 | − | 0.210030i | −0.0195751 | − | 0.00712477i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.99643 | − | 11.3223i | 0.0676465 | − | 0.383643i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.60926 | − | 8.21262i | 0.156000 | − | 0.277955i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.505181 | + | 0.183871i | −0.0170782 | + | 0.00621597i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.35388 | − | 2.81424i | 0.113252 | − | 0.0950301i | −0.584403 | − | 0.811464i | \(-0.698671\pi\) |
0.697655 | + | 0.716434i | \(0.254227\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.80890 | − | 2.81556i | 0.162200 | − | 0.0949665i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.66740 | − | 4.62007i | −0.0898669 | − | 0.155654i | 0.817588 | − | 0.575804i | \(-0.195311\pi\) |
−0.907455 | + | 0.420150i | \(0.861977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.5393 | − | 23.4508i | 0.455635 | − | 0.789184i | −0.543089 | − | 0.839675i | \(-0.682745\pi\) |
0.998724 | + | 0.0504914i | \(0.0160788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.8345 | + | 69.5457i | −0.834803 | + | 2.33775i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.99487 | + | 33.9986i | 0.201288 | + | 1.14156i | 0.903175 | + | 0.429273i | \(0.141230\pi\) |
−0.701887 | + | 0.712289i | \(0.747659\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.832568 | + | 0.698607i | 0.0279234 | + | 0.0234305i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.173757 | − | 0.862195i | −0.00582109 | − | 0.0288846i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.295137 | − | 0.247649i | −0.00987639 | − | 0.00828727i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.09379 | + | 17.5457i | 0.103414 | + | 0.586490i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.40325 | + | 9.53035i | −0.113631 | + | 0.318209i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.4706 | − | 59.7049i | 1.14966 | − | 1.99127i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.03305 | + | 15.6457i | 0.300935 | + | 0.521234i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.62653 | − | 2.70879i | 0.153961 | − | 0.0901428i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.8510 | + | 26.7261i | −1.05876 | + | 0.888407i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.9575 | − | 5.08010i | 0.463450 | − | 0.168682i | −0.0997331 | − | 0.995014i | \(-0.531799\pi\) |
0.563183 | + | 0.826332i | \(0.309577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.5878 | − | 41.4154i | −0.815526 | − | 1.37366i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.28045 | + | 12.9331i | −0.0755548 | + | 0.428492i | 0.923443 | + | 0.383735i | \(0.125363\pi\) |
−0.998998 | + | 0.0447571i | \(0.985749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.36915 | − | 0.498329i | −0.0453122 | − | 0.0164923i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.5547 | − | 3.66562i | −0.712575 | − | 0.121182i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.82315 | −0.159275 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.3820 | −0.903250 | −0.451625 | − | 0.892208i | \(-0.649156\pi\) | ||||
−0.451625 | + | 0.892208i | \(0.649156\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.9810 | − | 27.7285i | 0.757250 | − | 0.913685i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.08603 | + | 1.85116i | 0.167409 | + | 0.0609318i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.49103 | + | 19.7986i | −0.114784 | + | 0.650974i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.4063 | + | 5.06504i | −0.440321 | + | 0.166358i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7384 | + | 8.64007i | −0.778832 | + | 0.283472i | −0.700685 | − | 0.713470i | \(-0.747122\pi\) |
−0.0781462 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.371663 | + | 0.311862i | −0.0121808 | + | 0.0102209i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.3761 | − | 7.61458i | −0.437914 | − | 0.249290i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.314567 | + | 0.544847i | 0.0102875 | + | 0.0178184i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.0584 | − | 27.8140i | 0.524605 | − | 0.908643i | −0.474984 | − | 0.879994i | \(-0.657546\pi\) |
0.999590 | − | 0.0286488i | \(-0.00912046\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1912 | − | 14.3507i | −0.397845 | − | 0.468318i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.719414 | − | 4.08000i | −0.0234522 | − | 0.133004i | 0.970834 | − | 0.239754i | \(-0.0770668\pi\) |
−0.994286 | + | 0.106750i | \(0.965956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.98524 | + | 3.34401i | 0.129777 | + | 0.108896i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.56466 | − | 2.74767i | 0.148489 | − | 0.0893819i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.15127 | + | 0.966033i | 0.0374113 | + | 0.0313918i | 0.661302 | − | 0.750120i | \(-0.270004\pi\) |
−0.623890 | + | 0.781512i | \(0.714449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.667463 | − | 3.78537i | −0.0216668 | − | 0.122878i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.7000 | − | 8.34510i | 1.48193 | − | 0.270609i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.8407 | + | 23.9729i | −0.448346 | + | 0.776558i | −0.998279 | − | 0.0586513i | \(-0.981320\pi\) |
0.549933 | + | 0.835209i | \(0.314653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.7767 | − | 39.4504i | −0.737037 | − | 1.27659i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.00728899 | + | 1.19822i | 0.000235620 | + | 0.0387331i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.86684 | − | 4.08377i | 0.157159 | − | 0.131872i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −59.9925 | + | 21.8355i | −1.93524 | + | 0.704370i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.4423 | − | 11.5610i | 0.433173 | − | 0.372549i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.70800 | − | 32.3717i | 0.183747 | − | 1.04208i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.2872 | + | 9.20379i | 0.813182 | + | 0.295974i | 0.714937 | − | 0.699188i | \(-0.246455\pi\) |
0.0982442 | + | 0.995162i | \(0.468677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0887093 | − | 0.239190i | −0.00284975 | − | 0.00768388i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.449240 | 0.0144168 | 0.00720839 | − | 0.999974i | \(-0.497705\pi\) | ||||
0.00720839 | + | 0.999974i | \(0.497705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.01591 | −0.0325687 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.49800 | + | 6.73542i | 0.0799999 | + | 0.215706i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.8034 | − | 5.75198i | −0.505597 | − | 0.184022i | 0.0766127 | − | 0.997061i | \(-0.475590\pi\) |
−0.582210 | + | 0.813039i | \(0.697812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0368357 | − | 0.208906i | 0.00117727 | − | 0.00667665i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.3500 | − | 20.9421i | 0.777434 | − | 0.668630i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.7692 | + | 10.4711i | −0.917596 | + | 0.333978i | −0.757282 | − | 0.653089i | \(-0.773473\pi\) |
−0.160314 | + | 0.987066i | \(0.551251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.1384 | − | 24.4500i | 0.928426 | − | 0.779042i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0191991 | + | 3.15610i | 0.000611113 | + | 0.100460i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.2946 | + | 50.7397i | 0.931513 | + | 1.61343i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.39924 | + | 14.5479i | −0.266811 | + | 0.462129i | −0.968036 | − | 0.250810i | \(-0.919303\pi\) |
0.701226 | + | 0.712939i | \(0.252636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.1718 | − | 7.33561i | 1.27481 | − | 0.232789i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.96697 | − | 16.8265i | −0.0940591 | − | 0.533436i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7023 | + | 15.6931i | 0.592309 | + | 0.497006i | 0.888963 | − | 0.457979i | \(-0.151426\pi\) |
−0.296654 | + | 0.954985i | \(0.595871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.425918 | + | 23.3363i | 0.0134755 | + | 0.738329i |
(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 | 864.2.y.a.97.3 | ✓ | 48 | |
4.3 | odd | 2 | inner | 864.2.y.a.97.6 | yes | 48 | |
27.22 | even | 9 | inner | 864.2.y.a.481.3 | yes | 48 | |
108.103 | odd | 18 | inner | 864.2.y.a.481.6 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.y.a.97.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
864.2.y.a.97.6 | yes | 48 | 4.3 | odd | 2 | inner | |
864.2.y.a.481.3 | yes | 48 | 27.22 | even | 9 | inner | |
864.2.y.a.481.6 | yes | 48 | 108.103 | odd | 18 | inner |