Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,3,Mod(28,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.28");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.l (of order \(12\), degree \(4\), 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: | \(11.0354507066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 352.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.352 |
Dual form | 405.3.l.h.298.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.814313 | + | 3.03906i | −0.407157 | + | 1.51953i | 0.392887 | + | 0.919587i | \(0.371476\pi\) |
−0.800043 | + | 0.599942i | \(0.795190\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.10867 | − | 2.94949i | −1.27717 | − | 0.737372i | ||||
\(5\) | −4.99585 | + | 0.203583i | −0.999171 | + | 0.0407165i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.530550 | + | 1.98004i | −0.0757929 | + | 0.282863i | −0.993412 | − | 0.114598i | \(-0.963442\pi\) |
0.917619 | + | 0.397461i | \(0.130109\pi\) | |||||||
\(8\) | 4.22474 | − | 4.22474i | 0.528093 | − | 0.528093i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.44949 | − | 15.3485i | 0.344949 | − | 1.53485i | ||||
\(11\) | 1.67423 | + | 2.89986i | 0.152203 | + | 0.263624i | 0.932037 | − | 0.362363i | \(-0.118030\pi\) |
−0.779834 | + | 0.625986i | \(0.784697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.82478 | − | 14.2743i | −0.294214 | − | 1.09802i | −0.941840 | − | 0.336062i | \(-0.890905\pi\) |
0.647626 | − | 0.761958i | \(-0.275762\pi\) | |||||||
\(14\) | −5.58542 | − | 3.22474i | −0.398959 | − | 0.230339i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.39898 | − | 4.15515i | −0.149936 | − | 0.259697i | ||||
\(17\) | −2.65153 | − | 2.65153i | −0.155972 | − | 0.155972i | 0.624807 | − | 0.780779i | \(-0.285178\pi\) |
−0.780779 | + | 0.624807i | \(0.785178\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.6969i | − | 1.08931i | −0.838659 | − | 0.544656i | \(-0.816660\pi\) | ||
0.838659 | − | 0.544656i | \(-0.183340\pi\) | |||||||
\(20\) | 26.1226 | + | 13.6952i | 1.30613 | + | 0.684759i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.1762 | + | 2.72670i | −0.462554 | + | 0.123941i | ||||
\(23\) | 6.02093 | + | 22.4704i | 0.261780 | + | 0.976975i | 0.964192 | + | 0.265205i | \(0.0854395\pi\) |
−0.702413 | + | 0.711770i | \(0.747894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9171 | − | 2.03414i | 0.996684 | − | 0.0813655i | ||||
\(26\) | 46.4949 | 1.78827 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.55051 | − | 8.55051i | 0.305375 | − | 0.305375i | ||||
\(29\) | 0.739215 | − | 0.426786i | 0.0254902 | − | 0.0147168i | −0.487201 | − | 0.873290i | \(-0.661982\pi\) |
0.512691 | + | 0.858573i | \(0.328649\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.34847 | − | 16.1920i | 0.301564 | − | 0.522323i | −0.674927 | − | 0.737885i | \(-0.735825\pi\) |
0.976490 | + | 0.215561i | \(0.0691581\pi\) | |||||||
\(32\) | 37.6657 | − | 10.0925i | 1.17705 | − | 0.315391i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.2173 | − | 5.89898i | 0.300510 | − | 0.173499i | ||||
\(35\) | 2.24745 | − | 10.0000i | 0.0642128 | − | 0.285714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.0454 | + | 38.0454i | 1.02825 | + | 1.02825i | 0.999589 | + | 0.0286652i | \(0.00912566\pi\) |
0.0286652 | + | 0.999589i | \(0.490874\pi\) | |||||||
\(38\) | 62.8992 | + | 16.8538i | 1.65524 | + | 0.443521i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.2461 | + | 21.9663i | −0.506153 | + | 0.549157i | ||||
\(41\) | 14.3485 | − | 24.8523i | 0.349963 | − | 0.606153i | −0.636280 | − | 0.771458i | \(-0.719528\pi\) |
0.986242 | + | 0.165305i | \(0.0528609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.7286 | − | 8.23370i | −0.714619 | − | 0.191481i | −0.116849 | − | 0.993150i | \(-0.537279\pi\) |
−0.597769 | + | 0.801668i | \(0.703946\pi\) | |||||||
\(44\) | − | 19.7526i | − | 0.448922i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −73.1918 | −1.59113 | ||||||||
\(47\) | 7.22994 | − | 26.9825i | 0.153828 | − | 0.574095i | −0.845374 | − | 0.534174i | \(-0.820623\pi\) |
0.999203 | − | 0.0399212i | \(-0.0127107\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 38.7962 | + | 22.3990i | 0.791759 | + | 0.457122i | ||||
\(50\) | −14.1085 | + | 77.3810i | −0.282169 | + | 1.54762i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −22.5623 | + | 84.2036i | −0.433890 | + | 1.61930i | ||||
\(53\) | 28.6969 | − | 28.6969i | 0.541452 | − | 0.541452i | −0.382503 | − | 0.923954i | \(-0.624938\pi\) |
0.923954 | + | 0.382503i | \(0.124938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.95459 | − | 14.1464i | −0.162811 | − | 0.257208i | ||||
\(56\) | 6.12372 | + | 10.6066i | 0.109352 | + | 0.189404i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.695075 | + | 2.59405i | 0.0119840 | + | 0.0447251i | ||||
\(59\) | −96.9378 | − | 55.9671i | −1.64301 | − | 0.948595i | −0.979754 | − | 0.200206i | \(-0.935839\pi\) |
−0.663261 | − | 0.748389i | \(-0.730828\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −47.0454 | − | 81.4850i | −0.771236 | − | 1.33582i | −0.936886 | − | 0.349636i | \(-0.886305\pi\) |
0.165650 | − | 0.986185i | \(-0.447028\pi\) | |||||||
\(62\) | 41.5959 | + | 41.5959i | 0.670902 | + | 0.670902i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 103.495i | 1.61711i | ||||||||
\(65\) | 22.0140 | + | 70.5335i | 0.338677 | + | 1.08513i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 74.9934 | − | 20.0944i | 1.11930 | − | 0.299917i | 0.348703 | − | 0.937233i | \(-0.386622\pi\) |
0.770602 | + | 0.637317i | \(0.219956\pi\) | |||||||
\(68\) | 5.72512 | + | 21.3664i | 0.0841930 | + | 0.314212i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 28.5605 | + | 14.9733i | 0.408006 | + | 0.213904i | ||||
\(71\) | −68.0000 | −0.957746 | −0.478873 | − | 0.877884i | \(-0.658955\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.7878 | + | 39.7878i | −0.545038 | + | 0.545038i | −0.925001 | − | 0.379964i | \(-0.875936\pi\) |
0.379964 | + | 0.925001i | \(0.375936\pi\) | |||||||
\(74\) | −146.603 | + | 84.6413i | −1.98112 | + | 1.14380i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −61.0454 | + | 105.734i | −0.803229 | + | 1.39123i | ||||
\(77\) | −6.63010 | + | 1.77653i | −0.0861052 | + | 0.0230718i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21.2132 | − | 12.2474i | 0.268522 | − | 0.155031i | −0.359694 | − | 0.933070i | \(-0.617119\pi\) |
0.628216 | + | 0.778039i | \(0.283786\pi\) | |||||||
\(80\) | 12.8309 | + | 20.2702i | 0.160386 | + | 0.253377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 63.8434 | + | 63.8434i | 0.778578 | + | 0.778578i | ||||
\(83\) | 28.8866 | + | 7.74013i | 0.348031 | + | 0.0932546i | 0.428600 | − | 0.903494i | \(-0.359007\pi\) |
−0.0805689 | + | 0.996749i | \(0.525674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.7865 | + | 12.7069i | 0.162194 | + | 0.149492i | ||||
\(86\) | 50.0454 | − | 86.6812i | 0.581923 | − | 1.00792i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 19.3244 | + | 5.17795i | 0.219595 | + | 0.0588404i | ||||
\(89\) | − | 94.1816i | − | 1.05822i | −0.848553 | − | 0.529110i | \(-0.822526\pi\) | ||
0.848553 | − | 0.529110i | \(-0.177474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.2929 | 0.332889 | ||||||||
\(92\) | 35.5173 | − | 132.553i | 0.386058 | − | 1.44079i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 76.1139 | + | 43.9444i | 0.809722 | + | 0.467493i | ||||
\(95\) | 4.21354 | + | 103.399i | 0.0443530 | + | 1.08841i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.34248 | − | 19.9384i | 0.0550771 | − | 0.205550i | −0.932904 | − | 0.360125i | \(-0.882734\pi\) |
0.987981 | + | 0.154575i | \(0.0494007\pi\) | |||||||
\(98\) | −99.6640 | + | 99.6640i | −1.01698 | + | 1.01698i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −133.293 | − | 63.1010i | −1.33293 | − | 0.631010i | ||||
\(101\) | −86.8105 | − | 150.360i | −0.859509 | − | 1.48871i | −0.872397 | − | 0.488797i | \(-0.837436\pi\) |
0.0128880 | − | 0.999917i | \(-0.495898\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −23.7011 | − | 88.4536i | −0.230108 | − | 0.858773i | −0.980294 | − | 0.197546i | \(-0.936703\pi\) |
0.750186 | − | 0.661227i | \(-0.229964\pi\) | |||||||
\(104\) | −76.4639 | − | 44.1464i | −0.735229 | − | 0.424485i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 63.8434 | + | 110.580i | 0.602296 | + | 1.04321i | ||||
\(107\) | −4.74235 | − | 4.74235i | −0.0443210 | − | 0.0443210i | 0.684599 | − | 0.728920i | \(-0.259977\pi\) |
−0.728920 | + | 0.684599i | \(0.759977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 39.3031i | 0.360579i | 0.983614 | + | 0.180289i | \(0.0577034\pi\) | ||||
−0.983614 | + | 0.180289i | \(0.942297\pi\) | |||||||
\(110\) | 50.2837 | − | 15.6939i | 0.457124 | − | 0.142672i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.50015 | − | 2.54556i | 0.0848228 | − | 0.0227282i | ||||
\(113\) | 5.25564 | + | 19.6143i | 0.0465101 | + | 0.173578i | 0.985274 | − | 0.170983i | \(-0.0546944\pi\) |
−0.938764 | + | 0.344561i | \(0.888028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.6543 | − | 111.033i | −0.301342 | − | 0.965506i | ||||
\(116\) | −5.03520 | −0.0434069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 249.025 | − | 249.025i | 2.11038 | − | 2.11038i | ||||
\(119\) | 6.65691 | − | 3.84337i | 0.0559404 | − | 0.0322972i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 54.8939 | − | 95.0790i | 0.453668 | − | 0.785777i | ||||
\(122\) | 285.947 | − | 76.6194i | 2.34383 | − | 0.628028i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −95.5164 | + | 55.1464i | −0.770294 | + | 0.444729i | ||||
\(125\) | −124.068 | + | 15.2350i | −0.992545 | + | 0.121880i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −114.621 | − | 114.621i | −0.902527 | − | 0.902527i | 0.0931273 | − | 0.995654i | \(-0.470314\pi\) |
−0.995654 | + | 0.0931273i | \(0.970314\pi\) | |||||||
\(128\) | −163.864 | − | 43.9073i | −1.28019 | − | 0.343026i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −232.282 | + | 9.46556i | −1.78678 | + | 0.0728120i | ||||
\(131\) | 13.0681 | − | 22.6346i | 0.0997566 | − | 0.172783i | −0.811827 | − | 0.583898i | \(-0.801527\pi\) |
0.911584 | + | 0.411114i | \(0.134860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40.9808 | + | 10.9808i | 0.308126 | + | 0.0825621i | ||||
\(134\) | 244.272i | 1.82293i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.4041 | −0.164736 | ||||||||
\(137\) | 5.35536 | − | 19.9865i | 0.0390902 | − | 0.145887i | −0.943623 | − | 0.331023i | \(-0.892606\pi\) |
0.982713 | + | 0.185137i | \(0.0592728\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −72.0286 | − | 41.5857i | −0.518191 | − | 0.299178i | 0.218003 | − | 0.975948i | \(-0.430046\pi\) |
−0.736194 | + | 0.676770i | \(0.763379\pi\) | |||||||
\(140\) | −40.9764 | + | 44.4578i | −0.292688 | + | 0.317556i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 55.3733 | − | 206.656i | 0.389953 | − | 1.45532i | ||||
\(143\) | 34.9898 | − | 34.9898i | 0.244684 | − | 0.244684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.60612 | + | 2.28265i | −0.0248698 | + | 0.0157424i | ||||
\(146\) | −88.5176 | − | 153.317i | −0.606285 | − | 1.05012i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −82.1467 | − | 306.576i | −0.555046 | − | 2.07146i | ||||
\(149\) | −103.184 | − | 59.5732i | −0.692509 | − | 0.399820i | 0.112042 | − | 0.993703i | \(-0.464261\pi\) |
−0.804551 | + | 0.593883i | \(0.797594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 72.4847 | + | 125.547i | 0.480031 | + | 0.831438i | 0.999738 | − | 0.0229066i | \(-0.00729205\pi\) |
−0.519707 | + | 0.854345i | \(0.673959\pi\) | |||||||
\(152\) | −87.4393 | − | 87.4393i | −0.575258 | − | 0.575258i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 21.5959i | − | 0.140233i | ||||||
\(155\) | −43.4072 | + | 82.7962i | −0.280046 | + | 0.534169i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −69.8673 | + | 18.7209i | −0.445015 | + | 0.119241i | −0.474366 | − | 0.880328i | \(-0.657323\pi\) |
0.0293510 | + | 0.999569i | \(0.490656\pi\) | |||||||
\(158\) | 19.9465 | + | 74.4414i | 0.126244 | + | 0.471148i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −186.118 | + | 58.0887i | −1.16324 | + | 0.363055i | ||||
\(161\) | −47.6867 | −0.296191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 189.394 | − | 189.394i | 1.16193 | − | 1.16193i | 0.177872 | − | 0.984054i | \(-0.443079\pi\) |
0.984054 | − | 0.177872i | \(-0.0569213\pi\) | |||||||
\(164\) | −146.603 | + | 84.6413i | −0.893921 | + | 0.516106i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −47.0454 | + | 81.4850i | −0.283406 | + | 0.490874i | ||||
\(167\) | −132.553 | + | 35.5173i | −0.793728 | + | 0.212679i | −0.632828 | − | 0.774292i | \(-0.718106\pi\) |
−0.160899 | + | 0.986971i | \(0.551439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42.7675 | + | 24.6918i | −0.253062 | + | 0.146106i | ||||
\(170\) | −49.8434 | + | 31.5505i | −0.293196 | + | 0.185591i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 132.697 | + | 132.697i | 0.771494 | + | 0.771494i | ||||
\(173\) | 47.3070 | + | 12.6759i | 0.273451 | + | 0.0732709i | 0.392938 | − | 0.919565i | \(-0.371459\pi\) |
−0.119488 | + | 0.992836i | \(0.538125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.19210 | + | 50.4161i | −0.0525263 | + | 0.288092i | ||||
\(176\) | 8.03291 | − | 13.9134i | 0.0456415 | − | 0.0790534i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 286.223 | + | 76.6933i | 1.60800 | + | 0.430861i | ||||
\(179\) | − | 183.712i | − | 1.02632i | −0.858292 | − | 0.513161i | \(-0.828474\pi\) | ||
0.858292 | − | 0.513161i | \(-0.171526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7276 | −0.120042 | −0.0600209 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600209 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(182\) | −24.6679 | + | 92.0617i | −0.135538 | + | 0.505834i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 120.369 | + | 69.4949i | 0.654178 | + | 0.377690i | ||||
\(185\) | −197.815 | − | 182.324i | −1.06927 | − | 0.985535i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.24978 | − | 12.1284i | 0.0173785 | − | 0.0648575i | ||||
\(188\) | −116.520 | + | 116.520i | −0.619787 | + | 0.619787i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −317.666 | − | 71.3939i | −1.67193 | − | 0.375757i | ||||
\(191\) | 20.0454 | + | 34.7197i | 0.104950 | + | 0.181778i | 0.913718 | − | 0.406350i | \(-0.133198\pi\) |
−0.808768 | + | 0.588128i | \(0.799865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 28.3909 | + | 105.956i | 0.147103 | + | 0.548996i | 0.999653 | + | 0.0263498i | \(0.00838836\pi\) |
−0.852550 | + | 0.522646i | \(0.824945\pi\) | |||||||
\(194\) | 56.2435 | + | 32.4722i | 0.289915 | + | 0.167382i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −132.131 | − | 228.858i | −0.674138 | − | 1.16764i | ||||
\(197\) | −67.3031 | − | 67.3031i | −0.341640 | − | 0.341640i | 0.515344 | − | 0.856984i | \(-0.327664\pi\) |
−0.856984 | + | 0.515344i | \(0.827664\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 251.394i | 1.26329i | 0.775259 | + | 0.631643i | \(0.217619\pi\) | ||||
−0.775259 | + | 0.631643i | \(0.782381\pi\) | |||||||
\(200\) | 96.6747 | − | 113.862i | 0.483374 | − | 0.569311i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 527.644 | − | 141.382i | 2.61210 | − | 0.699910i | ||||
\(203\) | 0.452863 | + | 1.69011i | 0.00223085 | + | 0.00832565i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −66.6234 | + | 127.079i | −0.324992 | + | 0.619900i | ||||
\(206\) | 288.116 | 1.39862 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −50.1362 | + | 50.1362i | −0.241040 | + | 0.241040i | ||||
\(209\) | 60.0182 | − | 34.6515i | 0.287168 | − | 0.165797i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −132.394 | + | 229.313i | −0.627459 | + | 1.08679i | 0.360601 | + | 0.932720i | \(0.382572\pi\) |
−0.988060 | + | 0.154071i | \(0.950762\pi\) | |||||||
\(212\) | −231.244 | + | 61.9618i | −1.09078 | + | 0.292272i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.2740 | − | 10.5505i | 0.0853926 | − | 0.0493014i | ||||
\(215\) | 155.192 | + | 34.8786i | 0.721822 | + | 0.162226i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.1010 | + | 27.1010i | 0.124889 | + | 0.124889i | ||||
\(218\) | −119.444 | − | 32.0050i | −0.547910 | − | 0.146812i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.02128 | + | 98.6809i | 0.0182785 | + | 0.448549i | ||||
\(221\) | −27.7071 | + | 47.9902i | −0.125372 | + | 0.217150i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 45.6650 | + | 12.2359i | 0.204776 | + | 0.0548695i | 0.359749 | − | 0.933049i | \(-0.382862\pi\) |
−0.154973 | + | 0.987919i | \(0.549529\pi\) | |||||||
\(224\) | 79.9342i | 0.356849i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −63.8888 | −0.282694 | ||||||||
\(227\) | −7.74928 | + | 28.9207i | −0.0341378 | + | 0.127404i | −0.980892 | − | 0.194554i | \(-0.937674\pi\) |
0.946754 | + | 0.321958i | \(0.104341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 211.135 | + | 121.899i | 0.921988 | + | 0.532310i | 0.884269 | − | 0.466978i | \(-0.154657\pi\) |
0.0377192 | + | 0.999288i | \(0.487991\pi\) | |||||||
\(230\) | 365.656 | − | 14.9006i | 1.58981 | − | 0.0647852i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.31993 | − | 4.92606i | 0.00568936 | − | 0.0212330i | ||||
\(233\) | 161.712 | − | 161.712i | 0.694042 | − | 0.694042i | −0.269077 | − | 0.963119i | \(-0.586719\pi\) |
0.963119 | + | 0.269077i | \(0.0867186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.6265 | + | 136.272i | −0.130326 | + | 0.579883i | ||||
\(236\) | 330.149 | + | 571.834i | 1.39894 | + | 2.42303i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.25941 | + | 23.3604i | 0.0263000 | + | 0.0981531i | ||||
\(239\) | 282.499 | + | 163.101i | 1.18201 | + | 0.682431i | 0.956478 | − | 0.291806i | \(-0.0942561\pi\) |
0.225528 | + | 0.974237i | \(0.427589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 66.7878 | + | 115.680i | 0.277128 | + | 0.479999i | 0.970670 | − | 0.240417i | \(-0.0772842\pi\) |
−0.693542 | + | 0.720416i | \(0.743951\pi\) | |||||||
\(242\) | 244.250 | + | 244.250i | 1.00930 | + | 1.00930i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 555.040i | 2.27475i | ||||||||
\(245\) | −198.380 | − | 104.004i | −0.809714 | − | 0.424505i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −295.434 | + | 79.1612i | −1.19609 | + | 0.320491i | ||||
\(248\) | −28.9123 | − | 107.902i | −0.116582 | − | 0.435089i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 54.7304 | − | 389.456i | 0.218922 | − | 1.55782i | ||||
\(251\) | −404.742 | −1.61252 | −0.806260 | − | 0.591562i | \(-0.798512\pi\) | ||||
−0.806260 | + | 0.591562i | \(0.798512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −55.0806 | + | 55.0806i | −0.217710 | + | 0.217710i | ||||
\(254\) | 441.677 | − | 255.002i | 1.73889 | − | 1.00395i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 59.8837 | − | 103.722i | 0.233921 | − | 0.405162i | ||||
\(257\) | 121.900 | − | 32.6631i | 0.474320 | − | 0.127094i | −0.0137364 | − | 0.999906i | \(-0.504373\pi\) |
0.488057 | + | 0.872812i | \(0.337706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −95.5164 | + | 55.1464i | −0.368789 | + | 0.212921i | ||||
\(260\) | 95.5755 | − | 425.262i | 0.367598 | − | 1.63562i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 58.1464 | + | 58.1464i | 0.221933 | + | 0.221933i | ||||
\(263\) | 466.967 | + | 125.123i | 1.77554 | + | 0.475754i | 0.989759 | − | 0.142751i | \(-0.0455950\pi\) |
0.785780 | + | 0.618506i | \(0.212262\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −137.524 | + | 149.208i | −0.518957 | + | 0.563049i | ||||
\(266\) | −66.7423 | + | 115.601i | −0.250911 | + | 0.434591i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −442.385 | − | 118.537i | −1.65069 | − | 0.442301i | ||||
\(269\) | − | 3.50052i | − | 0.0130131i | −0.999979 | − | 0.00650653i | \(-0.997929\pi\) | ||
0.999979 | − | 0.00650653i | \(-0.00207111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −103.576 | −0.382197 | −0.191099 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191099 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(272\) | −4.65655 | + | 17.3785i | −0.0171197 | + | 0.0638915i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 56.3791 | + | 32.5505i | 0.205763 | + | 0.118797i | ||||
\(275\) | 47.6158 | + | 68.8505i | 0.173148 | + | 0.250365i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −104.504 | + | 390.013i | −0.377270 | + | 1.40799i | 0.472730 | + | 0.881208i | \(0.343269\pi\) |
−0.850000 | + | 0.526783i | \(0.823398\pi\) | |||||||
\(278\) | 185.035 | − | 185.035i | 0.665594 | − | 0.665594i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −32.7526 | − | 51.7423i | −0.116973 | − | 0.184794i | ||||
\(281\) | −186.348 | − | 322.765i | −0.663162 | − | 1.14863i | −0.979780 | − | 0.200077i | \(-0.935881\pi\) |
0.316618 | − | 0.948553i | \(-0.397453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.2542 | − | 105.446i | −0.0998381 | − | 0.372601i | 0.897870 | − | 0.440260i | \(-0.145114\pi\) |
−0.997709 | + | 0.0676591i | \(0.978447\pi\) | |||||||
\(284\) | 347.389 | + | 200.565i | 1.22320 | + | 0.706216i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 77.8434 | + | 134.829i | 0.272180 | + | 0.471429i | ||||
\(287\) | 41.5959 | + | 41.5959i | 0.144934 | + | 0.144934i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 274.939i | − | 0.951345i | ||||||
\(290\) | −4.00060 | − | 12.8180i | −0.0137952 | − | 0.0442000i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 320.616 | − | 85.9088i | 1.09800 | − | 0.294208i | ||||
\(293\) | −86.5889 | − | 323.154i | −0.295525 | − | 1.10292i | −0.940799 | − | 0.338964i | \(-0.889923\pi\) |
0.645274 | − | 0.763951i | \(-0.276743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 495.681 | + | 259.869i | 1.68028 | + | 0.880910i | ||||
\(296\) | 321.464 | 1.08603 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 265.070 | − | 265.070i | 0.889498 | − | 0.889498i | ||||
\(299\) | 297.720 | − | 171.889i | 0.995719 | − | 0.574879i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.6061 | − | 56.4755i | 0.108326 | − | 0.187626i | ||||
\(302\) | −440.570 | + | 118.050i | −1.45884 | + | 0.390896i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −85.9990 | + | 49.6515i | −0.282891 | + | 0.163327i | ||||
\(305\) | 251.621 | + | 397.510i | 0.824987 | + | 1.30331i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 168.969 | + | 168.969i | 0.550389 | + | 0.550389i | 0.926553 | − | 0.376164i | \(-0.122757\pi\) |
−0.376164 | + | 0.926553i | \(0.622757\pi\) | |||||||
\(308\) | 39.1108 | + | 10.4797i | 0.126983 | + | 0.0340251i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −216.275 | − | 199.339i | −0.697662 | − | 0.643029i | ||||
\(311\) | −177.151 | + | 306.835i | −0.569617 | + | 0.986606i | 0.426986 | + | 0.904258i | \(0.359575\pi\) |
−0.996604 | + | 0.0823482i | \(0.973758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −208.146 | − | 55.7726i | −0.665003 | − | 0.178187i | −0.0895003 | − | 0.995987i | \(-0.528527\pi\) |
−0.575503 | + | 0.817800i | \(0.695194\pi\) | |||||||
\(314\) | − | 227.576i | − | 0.724763i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −144.495 | −0.457262 | ||||||||
\(317\) | −156.372 | + | 583.589i | −0.493288 | + | 1.84097i | 0.0461283 | + | 0.998936i | \(0.485312\pi\) |
−0.539416 | + | 0.842039i | \(0.681355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.47524 | + | 1.42908i | 0.00775937 | + | 0.00447987i | ||||
\(320\) | −21.0698 | − | 517.045i | −0.0658430 | − | 1.61577i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 38.8319 | − | 144.923i | 0.120596 | − | 0.450071i | ||||
\(323\) | −54.8786 | + | 54.8786i | −0.169903 | + | 0.169903i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −124.338 | − | 347.893i | −0.382579 | − | 1.07044i | ||||
\(326\) | 421.353 | + | 729.805i | 1.29249 | + | 2.23867i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −44.3759 | − | 165.613i | −0.135292 | − | 0.504918i | ||||
\(329\) | 49.5906 | + | 28.6311i | 0.150731 | + | 0.0870247i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −244.712 | − | 423.853i | −0.739310 | − | 1.28052i | −0.952806 | − | 0.303579i | \(-0.901818\pi\) |
0.213496 | − | 0.976944i | \(-0.431515\pi\) | |||||||
\(332\) | −124.742 | − | 124.742i | −0.375730 | − | 0.375730i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 431.757i | − | 1.29269i | ||||||
\(335\) | −370.565 | + | 115.656i | −1.10616 | + | 0.345242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −399.141 | + | 106.950i | −1.18440 | + | 0.317358i | −0.796669 | − | 0.604416i | \(-0.793406\pi\) |
−0.387727 | + | 0.921774i | \(0.626740\pi\) | |||||||
\(338\) | −40.2138 | − | 150.080i | −0.118976 | − | 0.444023i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −32.9517 | − | 105.578i | −0.0969168 | − | 0.310524i | ||||
\(341\) | 62.6061 | 0.183596 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −135.959 | + | 135.959i | −0.396382 | + | 0.396382i | ||||
\(344\) | −164.606 | + | 95.0352i | −0.478505 | + | 0.276265i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −77.0454 | + | 133.447i | −0.222675 | + | 0.385684i | ||||
\(347\) | −437.196 | + | 117.146i | −1.25993 | + | 0.337598i | −0.826166 | − | 0.563428i | \(-0.809482\pi\) |
−0.433767 | + | 0.901025i | \(0.642816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 497.107 | − | 287.005i | 1.42437 | − | 0.822363i | 0.427705 | − | 0.903918i | \(-0.359322\pi\) |
0.996669 | + | 0.0815556i | \(0.0259888\pi\) | |||||||
\(350\) | −145.732 | − | 68.9898i | −0.416378 | − | 0.197114i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 92.3281 | + | 92.3281i | 0.262296 | + | 0.262296i | ||||
\(353\) | −364.073 | − | 97.5531i | −1.03137 | − | 0.276354i | −0.296836 | − | 0.954928i | \(-0.595932\pi\) |
−0.734532 | + | 0.678574i | \(0.762598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 339.718 | − | 13.8436i | 0.956952 | − | 0.0389961i | ||||
\(356\) | −277.788 | + | 481.143i | −0.780303 | + | 1.35152i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 558.311 | + | 149.599i | 1.55953 | + | 0.417874i | ||||
\(359\) | − | 216.272i | − | 0.602430i | −0.953556 | − | 0.301215i | \(-0.902608\pi\) | ||
0.953556 | − | 0.301215i | \(-0.0973922\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −67.3633 | −0.186602 | ||||||||
\(362\) | 17.6930 | − | 66.0313i | 0.0488758 | − | 0.182407i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −154.756 | − | 89.3485i | −0.425154 | − | 0.245463i | ||||
\(365\) | 190.674 | − | 206.874i | 0.522394 | − | 0.566778i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −88.0327 | + | 328.542i | −0.239871 | + | 0.895211i | 0.736021 | + | 0.676958i | \(0.236702\pi\) |
−0.975892 | + | 0.218252i | \(0.929964\pi\) | |||||||
\(368\) | 78.9240 | − | 78.9240i | 0.214467 | − | 0.214467i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 715.176 | − | 452.702i | 1.93291 | − | 1.22352i | ||||
\(371\) | 41.5959 | + | 72.0462i | 0.112118 | + | 0.194195i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −120.864 | − | 451.071i | −0.324032 | − | 1.20930i | −0.915281 | − | 0.402816i | \(-0.868032\pi\) |
0.591249 | − | 0.806489i | \(-0.298635\pi\) | |||||||
\(374\) | 34.2124 | + | 19.7526i | 0.0914771 | + | 0.0528143i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −83.4495 | − | 144.539i | −0.221940 | − | 0.384412i | ||||
\(377\) | −8.91939 | − | 8.91939i | −0.0236589 | − | 0.0236589i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 210.000i | − | 0.554090i | −0.960857 | − | 0.277045i | \(-0.910645\pi\) | ||
0.960857 | − | 0.277045i | \(-0.0893551\pi\) | |||||||
\(380\) | 283.448 | − | 540.658i | 0.745917 | − | 1.42278i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −121.838 | + | 32.6465i | −0.318948 | + | 0.0854620i | ||||
\(383\) | 62.4553 | + | 233.086i | 0.163069 | + | 0.608581i | 0.998279 | + | 0.0586495i | \(0.0186794\pi\) |
−0.835210 | + | 0.549931i | \(0.814654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.7614 | − | 10.2251i | 0.0850944 | − | 0.0265586i | ||||
\(386\) | −345.126 | −0.894109 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −86.1010 | + | 86.1010i | −0.221910 | + | 0.221910i | ||||
\(389\) | 474.008 | − | 273.669i | 1.21853 | − | 0.703518i | 0.253926 | − | 0.967224i | \(-0.418278\pi\) |
0.964603 | + | 0.263705i | \(0.0849446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.6163 | − | 75.5457i | 0.111551 | − | 0.193212i | ||||
\(392\) | 258.534 | − | 69.2739i | 0.659525 | − | 0.176719i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 259.344 | − | 149.732i | 0.658233 | − | 0.380031i | ||||
\(395\) | −103.485 | + | 65.5051i | −0.261987 | + | 0.165836i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 45.2577 | + | 45.2577i | 0.113999 | + | 0.113999i | 0.761805 | − | 0.647806i | \(-0.224313\pi\) |
−0.647806 | + | 0.761805i | \(0.724313\pi\) | |||||||
\(398\) | −764.001 | − | 204.713i | −1.91960 | − | 0.514355i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −68.2278 | − | 98.6546i | −0.170569 | − | 0.246636i | ||||
\(401\) | 260.151 | − | 450.595i | 0.648756 | − | 1.12368i | −0.334665 | − | 0.942337i | \(-0.608623\pi\) |
0.983420 | − | 0.181340i | \(-0.0580436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −266.885 | − | 71.5117i | −0.662246 | − | 0.177448i | ||||
\(404\) | 1024.19i | 2.53511i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.50510 | −0.0135594 | ||||||||
\(407\) | −46.6294 | + | 174.023i | −0.114569 | + | 0.427576i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −300.606 | − | 173.555i | −0.734979 | − | 0.424340i | 0.0852621 | − | 0.996359i | \(-0.472827\pi\) |
−0.820241 | + | 0.572018i | \(0.806161\pi\) | |||||||
\(410\) | −331.950 | − | 305.955i | −0.809633 | − | 0.746231i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −139.812 | + | 521.786i | −0.339350 | + | 1.26647i | ||||
\(413\) | 162.247 | − | 162.247i | 0.392851 | − | 0.392851i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −145.889 | − | 32.7878i | −0.351539 | − | 0.0790066i | ||||
\(416\) | −288.126 | − | 499.049i | −0.692611 | − | 1.19964i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 56.4344 | + | 210.616i | 0.135011 | + | 0.503866i | ||||
\(419\) | 505.238 | + | 291.699i | 1.20582 | + | 0.696180i | 0.961843 | − | 0.273602i | \(-0.0882151\pi\) |
0.243975 | + | 0.969781i | \(0.421548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −106.576 | − | 184.594i | −0.253148 | − | 0.438466i | 0.711243 | − | 0.702947i | \(-0.248133\pi\) |
−0.964391 | + | 0.264481i | \(0.914799\pi\) | |||||||
\(422\) | −589.085 | − | 589.085i | −1.39594 | − | 1.39594i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 242.474i | − | 0.571874i | ||||||
\(425\) | −71.4621 | − | 60.6749i | −0.168146 | − | 0.142764i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 186.304 | − | 49.9199i | 0.436308 | − | 0.116908i | ||||
\(428\) | 10.2396 | + | 38.2146i | 0.0239242 | + | 0.0892864i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −232.373 | + | 443.235i | −0.540402 | + | 1.03078i | ||||
\(431\) | 187.364 | 0.434720 | 0.217360 | − | 0.976092i | \(-0.430255\pi\) | ||||
0.217360 | + | 0.976092i | \(0.430255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 154.848 | − | 154.848i | 0.357617 | − | 0.357617i | −0.505317 | − | 0.862934i | \(-0.668624\pi\) |
0.862934 | + | 0.505317i | \(0.168624\pi\) | |||||||
\(434\) | −104.430 | + | 60.2929i | −0.240623 | + | 0.138924i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 115.924 | − | 200.786i | 0.265881 | − | 0.460519i | ||||
\(437\) | 465.069 | − | 124.615i | 1.06423 | − | 0.285160i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −219.043 | + | 126.464i | −0.498958 | + | 0.288074i | −0.728283 | − | 0.685276i | \(-0.759681\pi\) |
0.229325 | + | 0.973350i | \(0.426348\pi\) | |||||||
\(440\) | −97.5959 | − | 21.9342i | −0.221809 | − | 0.0498504i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −123.283 | − | 123.283i | −0.278920 | − | 0.278920i | ||||
\(443\) | 575.275 | + | 154.144i | 1.29859 | + | 0.347956i | 0.840917 | − | 0.541165i | \(-0.182016\pi\) |
0.457673 | + | 0.889121i | \(0.348683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.1737 | + | 470.518i | 0.0430871 | + | 1.05734i | ||||
\(446\) | −74.3712 | + | 128.815i | −0.166752 | + | 0.288822i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −204.924 | − | 54.9092i | −0.457420 | − | 0.122565i | ||||
\(449\) | 297.909i | 0.663495i | 0.943368 | + | 0.331747i | \(0.107638\pi\) | ||||
−0.943368 | + | 0.331747i | \(0.892362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 96.0908 | 0.213062 | ||||||||
\(452\) | 31.0029 | − | 115.704i | 0.0685905 | − | 0.255983i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −81.5814 | − | 47.1010i | −0.179695 | − | 0.103747i | ||||
\(455\) | −151.339 | + | 6.16710i | −0.332612 | + | 0.0135541i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 104.591 | − | 390.338i | 0.228864 | − | 0.854130i | −0.751956 | − | 0.659213i | \(-0.770890\pi\) |
0.980820 | − | 0.194917i | \(-0.0624438\pi\) | |||||||
\(458\) | −542.388 | + | 542.388i | −1.18425 | + | 1.18425i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −150.454 | + | 669.444i | −0.327074 | + | 1.45531i | ||||
\(461\) | −263.310 | − | 456.066i | −0.571171 | − | 0.989298i | −0.996446 | − | 0.0842333i | \(-0.973156\pi\) |
0.425275 | − | 0.905064i | \(-0.360177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 122.875 | + | 458.577i | 0.265389 | + | 0.990447i | 0.962012 | + | 0.273009i | \(0.0880187\pi\) |
−0.696622 | + | 0.717438i | \(0.745315\pi\) | |||||||
\(464\) | −3.54672 | − | 2.04770i | −0.00764380 | − | 0.00441315i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 359.767 | + | 623.135i | 0.772033 | + | 1.33720i | ||||
\(467\) | 488.742 | + | 488.742i | 1.04656 | + | 1.04656i | 0.998862 | + | 0.0476956i | \(0.0151877\pi\) |
0.0476956 | + | 0.998862i | \(0.484812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 159.151i | 0.339341i | ||||||||
\(470\) | −389.200 | − | 204.044i | −0.828086 | − | 0.434137i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −645.984 | + | 173.091i | −1.36861 | + | 0.366718i | ||||
\(473\) | −27.5703 | − | 102.894i | −0.0582882 | − | 0.217534i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −42.1004 | − | 515.708i | −0.0886325 | − | 1.08570i | ||||
\(476\) | −45.3439 | −0.0952603 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −725.716 | + | 725.716i | −1.51823 | + | 1.51823i | ||||
\(479\) | −160.171 | + | 92.4745i | −0.334385 | + | 0.193057i | −0.657786 | − | 0.753205i | \(-0.728507\pi\) |
0.323401 | + | 0.946262i | \(0.395174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 397.555 | − | 688.586i | 0.826518 | − | 1.43157i | ||||
\(482\) | −405.944 | + | 108.772i | −0.842207 | + | 0.225669i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −560.869 | + | 323.818i | −1.15882 | + | 0.669045i | ||||
\(485\) | −22.6311 | + | 100.697i | −0.0466621 | + | 0.207623i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −120.682 | − | 120.682i | −0.247807 | − | 0.247807i | 0.572263 | − | 0.820070i | \(-0.306066\pi\) |
−0.820070 | + | 0.572263i | \(0.806066\pi\) | |||||||
\(488\) | −543.008 | − | 145.499i | −1.11272 | − | 0.298153i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 477.617 | − | 518.197i | 0.974729 | − | 1.05754i | ||||
\(491\) | 52.8411 | − | 91.5234i | 0.107619 | − | 0.186402i | −0.807186 | − | 0.590297i | \(-0.799011\pi\) |
0.914805 | + | 0.403895i | \(0.132344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.09169 | − | 0.828415i | −0.00627117 | − | 0.00168035i | ||||
\(494\) | − | 962.302i | − | 1.94798i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −89.7071 | −0.180861 | ||||||||
\(497\) | 36.0774 | − | 134.643i | 0.0725904 | − | 0.270911i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 640.499 | + | 369.792i | 1.28357 | + | 0.741067i | 0.977498 | − | 0.210943i | \(-0.0676535\pi\) |
0.306067 | + | 0.952010i | \(0.400987\pi\) | |||||||
\(500\) | 678.758 | + | 288.107i | 1.35752 | + | 0.576215i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 329.587 | − | 1230.04i | 0.656548 | − | 2.45027i | ||||
\(503\) | −406.409 | + | 406.409i | −0.807970 | + | 0.807970i | −0.984326 | − | 0.176357i | \(-0.943569\pi\) |
0.176357 | + | 0.984326i | \(0.443569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 464.303 | + | 733.504i | 0.919412 | + | 1.45248i | ||||
\(506\) | −122.540 | − | 212.246i | −0.242175 | − | 0.419459i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 247.487 | + | 923.633i | 0.487179 | + | 1.81818i | ||||
\(509\) | −168.451 | − | 97.2554i | −0.330945 | − | 0.191071i | 0.325315 | − | 0.945606i | \(-0.394530\pi\) |
−0.656261 | + | 0.754534i | \(0.727863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −57.6719 | − | 99.8907i | −0.112861 | − | 0.195481i | ||||
\(512\) | −213.376 | − | 213.376i | −0.416750 | − | 0.416750i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 397.060i | 0.772491i | ||||||||
\(515\) | 136.415 | + | 437.076i | 0.264883 | + | 0.848692i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 90.3500 | − | 24.2092i | 0.174758 | − | 0.0468263i | ||||
\(518\) | −89.8129 | − | 335.186i | −0.173384 | − | 0.647078i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 390.990 | + | 204.982i | 0.751903 | + | 0.394197i | ||||
\(521\) | −589.605 | −1.13168 | −0.565840 | − | 0.824515i | \(-0.691448\pi\) | ||||
−0.565840 | + | 0.824515i | \(0.691448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −141.546 | + | 141.546i | −0.270642 | + | 0.270642i | −0.829359 | − | 0.558716i | \(-0.811294\pi\) |
0.558716 | + | 0.829359i | \(0.311294\pi\) | |||||||
\(524\) | −133.521 | + | 77.0885i | −0.254812 | + | 0.147115i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −760.514 | + | 1317.25i | −1.44584 | + | 2.50428i | ||||
\(527\) | −67.7214 | + | 18.1459i | −0.128504 | + | 0.0344324i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5408 | + | 6.08571i | −0.0199258 | + | 0.0115042i | ||||
\(530\) | −341.464 | − | 539.444i | −0.644272 | − | 1.01782i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −176.969 | − | 176.969i | −0.332649 | − | 0.332649i | ||||
\(533\) | −409.628 | − | 109.759i | −0.768532 | − | 0.205928i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.6575 | + | 22.7266i | 0.0460888 | + | 0.0424796i | ||||
\(536\) | 231.934 | − | 401.722i | 0.432713 | − | 0.749481i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.6383 | + | 2.85052i | 0.0197737 | + | 0.00529836i | ||||
\(539\) | 150.005i | 0.278302i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 431.303 | 0.797233 | 0.398617 | − | 0.917118i | \(-0.369490\pi\) | ||||
0.398617 | + | 0.917118i | \(0.369490\pi\) | |||||||
\(542\) | 84.3429 | − | 314.772i | 0.155614 | − | 0.580760i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −126.632 | − | 73.1112i | −0.232780 | − | 0.134396i | ||||
\(545\) | −8.00142 | − | 196.352i | −0.0146815 | − | 0.360280i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −163.329 | + | 609.551i | −0.298590 | + | 1.11435i | 0.639734 | + | 0.768596i | \(0.279044\pi\) |
−0.938324 | + | 0.345757i | \(0.887622\pi\) | |||||||
\(548\) | −86.3087 | + | 86.3087i | −0.157498 | + | 0.157498i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −248.015 | + | 88.6413i | −0.450936 | + | 0.161166i | ||||
\(551\) | −8.83316 | − | 15.2995i | −0.0160311 | − | 0.0277668i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9958 | + | 48.5009i | 0.0235005 | + | 0.0877050i | ||||
\(554\) | −1100.17 | − | 635.186i | −1.98588 | − | 1.14655i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 245.313 | + | 424.895i | 0.441211 | + | 0.764200i | ||||
\(557\) | 214.091 | + | 214.091i | 0.384364 | + | 0.384364i | 0.872672 | − | 0.488308i | \(-0.162386\pi\) |
−0.488308 | + | 0.872672i | \(0.662386\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 470.120i | 0.841003i | ||||||||
\(560\) | −46.9431 | + | 14.6513i | −0.0838270 | + | 0.0261630i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1132.65 | − | 303.492i | 2.01539 | − | 0.540021i | ||||
\(563\) | 245.972 | + | 917.982i | 0.436896 | + | 1.63052i | 0.736488 | + | 0.676451i | \(0.236483\pi\) |
−0.299592 | + | 0.954067i | \(0.596851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.2495 | − | 96.9203i | −0.0535390 | − | 0.171540i | ||||
\(566\) | 343.464 | 0.606827 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −287.283 | + | 287.283i | −0.505779 | + | 0.505779i | ||||
\(569\) | −841.916 | + | 486.081i | −1.47964 | + | 0.854272i | −0.999734 | − | 0.0230473i | \(-0.992663\pi\) |
−0.479908 | + | 0.877319i | \(0.659330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 462.015 | − | 800.233i | 0.809133 | − | 1.40146i | −0.104333 | − | 0.994542i | \(-0.533271\pi\) |
0.913465 | − | 0.406917i | \(-0.133396\pi\) | |||||||
\(572\) | −281.953 | + | 75.5491i | −0.492925 | + | 0.132079i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −160.285 | + | 92.5403i | −0.279241 | + | 0.161220i | ||||
\(575\) | 195.732 | + | 547.650i | 0.340404 | + | 0.952436i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −497.879 | − | 497.879i | −0.862874 | − | 0.862874i | 0.128797 | − | 0.991671i | \(-0.458889\pi\) |
−0.991671 | + | 0.128797i | \(0.958889\pi\) | |||||||
\(578\) | 835.555 | + | 223.886i | 1.44560 | + | 0.387346i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.1551 | − | 1.02508i | 0.0433709 | − | 0.00176738i | ||||
\(581\) | −30.6515 | + | 53.0900i | −0.0527565 | + | 0.0913770i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 131.262 | + | 35.1717i | 0.225150 | + | 0.0603288i | ||||
\(584\) | 336.186i | 0.575661i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1052.59 | 1.79624 | ||||||||
\(587\) | 107.166 | − | 399.949i | 0.182566 | − | 0.681345i | −0.812573 | − | 0.582860i | \(-0.801934\pi\) |
0.995139 | − | 0.0984849i | \(-0.0313996\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −335.125 | − | 193.485i | −0.568973 | − | 0.328497i | ||||
\(590\) | −1193.40 | + | 1294.79i | −2.02270 | + | 2.19456i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 66.8144 | − | 249.355i | 0.112862 | − | 0.421207i | ||||
\(593\) | 451.258 | − | 451.258i | 0.760974 | − | 0.760974i | −0.215524 | − | 0.976498i | \(-0.569146\pi\) |
0.976498 | + | 0.215524i | \(0.0691461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.4745 | + | 20.5561i | −0.0545790 | + | 0.0345481i | ||||
\(596\) | 351.421 | + | 608.679i | 0.589633 | + | 1.02127i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 279.943 | + | 1044.76i | 0.468131 | + | 1.74709i | ||||
\(599\) | −28.4560 | − | 16.4291i | −0.0475058 | − | 0.0274275i | 0.476059 | − | 0.879413i | \(-0.342065\pi\) |
−0.523565 | + | 0.851986i | \(0.675398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 92.2418 | + | 159.768i | 0.153481 | + | 0.265836i | 0.932505 | − | 0.361158i | \(-0.117618\pi\) |
−0.779024 | + | 0.626994i | \(0.784285\pi\) | |||||||
\(602\) | 145.081 | + | 145.081i | 0.240998 | + | 0.240998i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 855.171i | − | 1.41585i | ||||||
\(605\) | −254.885 | + | 486.176i | −0.421298 | + | 0.803597i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −186.311 | + | 49.9219i | −0.306938 | + | 0.0822437i | −0.409000 | − | 0.912534i | \(-0.634122\pi\) |
0.102062 | + | 0.994778i | \(0.467456\pi\) | |||||||
\(608\) | −208.884 | − | 779.565i | −0.343559 | − | 1.28218i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1412.95 | + | 440.993i | −2.31632 | + | 0.722940i | ||||
\(611\) | −412.808 | −0.675627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7128 | + | 12.7128i | −0.0207386 | + | 0.0207386i | −0.717400 | − | 0.696661i | \(-0.754668\pi\) |
0.696661 | + | 0.717400i | \(0.254668\pi\) | |||||||
\(614\) | −651.102 | + | 375.914i | −1.06043 | + | 0.612237i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.5051 | + | 35.5159i | −0.0332875 | + | 0.0576556i | ||||
\(617\) | 544.705 | − | 145.953i | 0.882828 | − | 0.236553i | 0.211201 | − | 0.977443i | \(-0.432263\pi\) |
0.671627 | + | 0.740890i | \(0.265596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 709.388 | − | 409.565i | 1.14602 | − | 0.661656i | 0.198108 | − | 0.980180i | \(-0.436520\pi\) |
0.947915 | + | 0.318524i | \(0.103187\pi\) | |||||||
\(620\) | 465.959 | − | 294.949i | 0.751547 | − | 0.475724i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −788.232 | − | 788.232i | −1.26725 | − | 1.26725i | ||||
\(623\) | 186.483 | + | 49.9681i | 0.299331 | + | 0.0802056i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 616.725 | − | 101.370i | 0.986759 | − | 0.162192i | ||||
\(626\) | 338.992 | − | 587.152i | 0.541521 | − | 0.937942i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 412.146 | + | 110.434i | 0.656283 | + | 0.175851i | ||||
\(629\) | − | 201.757i | − | 0.320759i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 105.485 | 0.167171 | 0.0835853 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835853 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(632\) | 37.8780 | − | 141.363i | 0.0599336 | − | 0.223675i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1646.23 | − | 950.448i | −2.59657 | − | 1.49913i | ||||
\(635\) | 595.964 | + | 549.294i | 0.938526 | + | 0.865031i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 171.342 | − | 639.458i | 0.268983 | − | 1.00386i | ||||
\(638\) | −6.35867 | + | 6.35867i | −0.00996657 | + | 0.00996657i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 827.580 | + | 185.994i | 1.29309 | + | 0.290616i | ||||
\(641\) | −82.3939 | − | 142.710i | −0.128540 | − | 0.222637i | 0.794571 | − | 0.607171i | \(-0.207696\pi\) |
−0.923111 | + | 0.384534i | \(0.874362\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −279.780 | − | 1044.15i | −0.435116 | − | 1.62388i | −0.740788 | − | 0.671739i | \(-0.765548\pi\) |
0.305672 | − | 0.952137i | \(-0.401119\pi\) | |||||||
\(644\) | 243.616 | + | 140.652i | 0.378285 | + | 0.218403i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −122.091 | − | 211.467i | −0.188995 | − | 0.327349i | ||||
\(647\) | 321.287 | + | 321.287i | 0.496580 | + | 0.496580i | 0.910372 | − | 0.413792i | \(-0.135796\pi\) |
−0.413792 | + | 0.910372i | \(0.635796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 374.808i | − | 0.577516i | ||||||
\(650\) | 1158.52 | − | 94.5771i | 1.78234 | − | 0.145503i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1526.17 | + | 408.935i | −2.34074 | + | 0.627201i | ||||
\(653\) | −62.1595 | − | 231.982i | −0.0951907 | − | 0.355256i | 0.901858 | − | 0.432033i | \(-0.142204\pi\) |
−0.997048 | + | 0.0767769i | \(0.975537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.6784 | + | 115.740i | −0.0926387 | + | 0.176702i | ||||
\(656\) | −137.687 | −0.209888 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −127.394 | + | 127.394i | −0.193608 | + | 0.193608i | ||||
\(659\) | 830.313 | − | 479.381i | 1.25996 | − | 0.727438i | 0.286893 | − | 0.957963i | \(-0.407378\pi\) |
0.973066 | + | 0.230525i | \(0.0740444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −198.196 | + | 343.286i | −0.299843 | + | 0.519344i | −0.976100 | − | 0.217322i | \(-0.930268\pi\) |
0.676257 | + | 0.736666i | \(0.263601\pi\) | |||||||
\(662\) | 1487.39 | − | 398.544i | 2.24681 | − | 0.602030i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 154.738 | − | 89.3383i | 0.233040 | − | 0.134546i | ||||
\(665\) | −206.969 | − | 46.5153i | −0.311232 | − | 0.0699478i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0408 | + | 14.0408i | 0.0210507 | + | 0.0210507i | ||||
\(668\) | 781.925 | + | 209.516i | 1.17055 | + | 0.313647i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −49.7296 | − | 1220.35i | −0.0742233 | − | 1.82142i | ||||
\(671\) | 157.530 | − | 272.850i | 0.234769 | − | 0.406632i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −224.994 | − | 60.2870i | −0.334315 | − | 0.0895795i | 0.0877564 | − | 0.996142i | \(-0.472030\pi\) |
−0.422072 | + | 0.906562i | \(0.638697\pi\) | |||||||
\(674\) | − | 1300.10i | − | 1.92894i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 291.313 | 0.430937 | ||||||||
\(677\) | 199.260 | − | 743.648i | 0.294328 | − | 1.09845i | −0.647422 | − | 0.762132i | \(-0.724153\pi\) |
0.941750 | − | 0.336315i | \(-0.109181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.6444 | + | 21.1566i | 0.0539681 | + | 0.0311585i | ||||
\(680\) | 111.928 | − | 4.56108i | 0.164599 | − | 0.00670747i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −50.9810 | + | 190.264i | −0.0747522 | + | 0.278979i | ||||
\(683\) | 786.590 | − | 786.590i | 1.15167 | − | 1.15167i | 0.165452 | − | 0.986218i | \(-0.447092\pi\) |
0.986218 | − | 0.165452i | \(-0.0529082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.6857 | + | 100.940i | −0.0331178 | + | 0.147357i | ||||
\(686\) | −302.474 | − | 523.901i | −0.440925 | − | 0.763704i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 39.5050 | + | 147.435i | 0.0574200 | + | 0.214294i | ||||
\(689\) | −519.387 | − | 299.868i | −0.753828 | − | 0.435223i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −178.439 | − | 309.066i | −0.258233 | − | 0.447273i | 0.707535 | − | 0.706678i | \(-0.249807\pi\) |
−0.965769 | + | 0.259405i | \(0.916474\pi\) | |||||||
\(692\) | −204.288 | − | 204.288i | −0.295214 | − | 0.295214i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1424.06i | − | 2.05196i | ||||||
\(695\) | 368.310 | + | 193.092i | 0.529943 | + | 0.277831i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −103.942 | + | 27.8512i | −0.149128 | + | 0.0399586i | ||||
\(698\) | 467.423 | + | 1744.45i | 0.669661 | + | 2.49921i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 195.661 | − | 230.447i | 0.279516 | − | 0.329210i | ||||
\(701\) | 885.680 | 1.26345 | 0.631726 | − | 0.775192i | \(-0.282347\pi\) | ||||
0.631726 | + | 0.775192i | \(0.282347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 787.423 | − | 787.423i | 1.12009 | − | 1.12009i | ||||
\(704\) | −300.121 | + | 173.275i | −0.426308 | + | 0.246129i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 592.939 | − | 1027.00i | 0.839857 | − | 1.45467i | ||||
\(707\) | 343.776 | − | 92.1146i | 0.486247 | − | 0.130289i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −633.107 | + | 365.524i | −0.892958 | + | 0.515549i | −0.874909 | − | 0.484288i | \(-0.839079\pi\) |
−0.0180489 | + | 0.999837i | \(0.505745\pi\) | |||||||
\(710\) | −234.565 | + | 1043.70i | −0.330374 | + | 1.46999i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −397.893 | − | 397.893i | −0.558839 | − | 0.558839i | ||||
\(713\) | 420.128 | + | 112.573i | 0.589240 | + | 0.157886i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −167.681 | + | 181.927i | −0.234518 | + | 0.254444i | ||||
\(716\) | −541.856 | + | 938.522i | −0.756782 | + | 1.31078i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 657.265 | + | 176.113i | 0.915410 | + | 0.245283i | ||||
\(719\) | 629.271i | 0.875204i | 0.899169 | + | 0.437602i | \(0.144172\pi\) | ||||
−0.899169 | + | 0.437602i | \(0.855828\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 187.716 | 0.260356 | ||||||||
\(722\) | 54.8548 | − | 204.721i | 0.0759762 | − | 0.283547i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 110.999 | + | 64.0852i | 0.153313 | + | 0.0885155i | ||||
\(725\) | 17.5510 | − | 12.1379i | 0.0242082 | − | 0.0167420i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.81028 | + | 21.6843i | −0.00799213 | + | 0.0298270i | −0.969807 | − | 0.243875i | \(-0.921581\pi\) |
0.961815 | + | 0.273702i | \(0.0882481\pi\) | |||||||
\(728\) | 127.980 | − | 127.980i | 0.175796 | − | 0.175796i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 473.434 | + | 747.929i | 0.648539 | + | 1.02456i | ||||
\(731\) | 59.6459 | + | 103.310i | 0.0815950 | + | 0.141327i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −143.935 | − | 537.172i | −0.196364 | − | 0.732840i | −0.991910 | − | 0.126947i | \(-0.959482\pi\) |
0.795546 | − | 0.605894i | \(-0.207184\pi\) | |||||||
\(734\) | −926.773 | − | 535.073i | −1.26263 | − | 0.728982i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 453.565 | + | 785.598i | 0.616257 | + | 1.06739i | ||||
\(737\) | 183.828 | + | 183.828i | 0.249427 | + | 0.249427i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 192.334i | − | 0.260262i | −0.991497 | − | 0.130131i | \(-0.958460\pi\) | ||
0.991497 | − | 0.130131i | \(-0.0415398\pi\) | |||||||
\(740\) | 472.807 | + | 1514.88i | 0.638928 | + | 2.04714i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −252.825 | + | 67.7442i | −0.340734 | + | 0.0912995i | ||||
\(743\) | −16.3619 | − | 61.0634i | −0.0220214 | − | 0.0821850i | 0.954041 | − | 0.299677i | \(-0.0968790\pi\) |
−0.976062 | + | 0.217492i | \(0.930212\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 527.619 | + | 276.613i | 0.708214 | + | 0.371292i | ||||
\(746\) | 1469.25 | 1.96951 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −52.3745 | + | 52.3745i | −0.0700194 | + | 0.0700194i | ||||
\(749\) | 11.9061 | − | 6.87398i | 0.0158960 | − | 0.00917755i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −113.893 | + | 197.269i | −0.151656 | + | 0.262675i | −0.931836 | − | 0.362879i | \(-0.881794\pi\) |
0.780181 | + | 0.625554i | \(0.215127\pi\) | |||||||
\(752\) | −129.461 | + | 34.6889i | −0.172155 | + | 0.0461289i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.3697 | − | 19.8434i | 0.0455832 | − | 0.0263175i | ||||
\(755\) | −387.682 | − | 612.459i | −0.513486 | − | 0.811204i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −235.925 | − | 235.925i | −0.311658 | − | 0.311658i | 0.533894 | − | 0.845552i | \(-0.320728\pi\) |
−0.845552 | + | 0.533894i | \(0.820728\pi\) | |||||||
\(758\) | 638.202 | + | 171.006i | 0.841955 | + | 0.225601i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 454.635 | + | 419.033i | 0.598204 | + | 0.551359i | ||||
\(761\) | 440.621 | − | 763.178i | 0.579003 | − | 1.00286i | −0.416592 | − | 0.909094i | \(-0.636775\pi\) |
0.995594 | − | 0.0937680i | \(-0.0298912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −77.8216 | − | 20.8522i | −0.101994 | − | 0.0273293i | ||||
\(764\) | − | 236.495i | − | 0.309548i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −759.221 | −0.991151 | ||||||||
\(767\) | −428.123 | + | 1597.78i | −0.558179 | + | 2.08315i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1046.51 | + | 604.201i | 1.36087 | + | 0.785697i | 0.989739 | − | 0.142885i | \(-0.0456378\pi\) |
0.371128 | + | 0.928582i | \(0.378971\pi\) | |||||||
\(770\) | 4.39655 | + | 107.890i | 0.00570981 | + | 0.140117i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 167.477 | − | 625.033i | 0.216939 | − | 0.809629i | ||||
\(773\) | −815.226 | + | 815.226i | −1.05463 | + | 1.05463i | −0.0562070 | + | 0.998419i | \(0.517901\pi\) |
−0.998419 | + | 0.0562070i | \(0.982099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 200.000 | − | 422.474i | 0.258065 | − | 0.545128i | ||||
\(776\) | −61.6640 | − | 106.805i | −0.0794640 | − | 0.137636i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 445.704 | + | 1663.39i | 0.572884 | + | 2.13803i | ||||
\(779\) | −514.366 | − | 296.969i | −0.660290 | − | 0.381219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −113.848 | − | 197.190i | −0.145772 | − | 0.252485i | ||||
\(782\) | 194.070 | + | 194.070i | 0.248172 | + | 0.248172i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 214.939i | − | 0.274157i | ||||||
\(785\) | 345.236 | − | 107.751i | 0.439791 | − | 0.137262i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1110.59 | + | 297.582i | −1.41117 | + | 0.378122i | −0.882343 | − | 0.470606i | \(-0.844035\pi\) |
−0.528829 | + | 0.848728i | \(0.677369\pi\) | |||||||
\(788\) | 145.319 | + | 542.339i | 0.184415 | + | 0.688247i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −114.805 | − | 367.838i | −0.145323 | − | 0.465617i | ||||
\(791\) | −41.6255 | −0.0526239 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −983.201 | + | 983.201i | −1.23985 | + | 1.23985i | ||||
\(794\) | −174.395 | + | 100.687i | −0.219640 | + | 0.126809i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 741.484 | − | 1284.29i | 0.931512 | − | 1.61343i | ||||
\(797\) | −425.130 | + | 113.913i | −0.533413 | + | 0.142928i | −0.515464 | − | 0.856911i | \(-0.672380\pi\) |
−0.0179491 | + | 0.999839i | \(0.505714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −90.7153 | + | 52.3745i | −0.113536 | + | 0.0655501i | ||||
\(800\) | 917.991 | − | 328.093i | 1.14749 | − | 0.410116i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1157.54 | + | 1157.54i | 1.44332 | + | 1.44332i | ||||
\(803\) | −181.993 | − | 48.7649i | −0.226641 | − | 0.0607283i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 238.236 | − | 9.70819i | 0.295945 | − | 0.0120599i | ||||
\(806\) | 434.656 | − | 752.846i | 0.539276 | − | 0.934053i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1001.99 | − | 268.481i | −1.24008 | − | 0.332279i | ||||
\(809\) | − | 150.000i | − | 0.185414i | −0.995693 | − | 0.0927070i | \(-0.970448\pi\) | ||
0.995693 | − | 0.0927070i | \(-0.0295520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −132.847 | −0.163806 | −0.0819032 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819032 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(812\) | 2.67143 | − | 9.96990i | 0.00328993 | − | 0.0122782i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −490.896 | − | 283.419i | −0.603066 | − | 0.348180i | ||||
\(815\) | −907.627 | + | 984.741i | −1.11365 | + | 1.20827i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −170.412 | + | 635.988i | −0.208583 | + | 0.778443i | ||||
\(818\) | 772.232 | − | 772.232i | 0.944048 | − | 0.944048i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 715.176 | − | 452.702i | 0.872166 | − | 0.552075i | ||||
\(821\) | −254.947 | − | 441.581i | −0.310532 | − | 0.537857i | 0.667946 | − | 0.744210i | \(-0.267174\pi\) |
−0.978478 | + | 0.206353i | \(0.933840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 109.943 | + | 410.312i | 0.133588 | + | 0.498556i | 1.00000 | 0.000773801i | \(-0.000246309\pi\) | |
−0.866412 | + | 0.499330i | \(0.833580\pi\) | |||||||
\(824\) | −473.825 | − | 273.563i | −0.575030 | − | 0.331994i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 360.959 | + | 625.200i | 0.436997 | + | 0.756900i | ||||
\(827\) | −1030.76 | − | 1030.76i | −1.24638 | − | 1.24638i | −0.957307 | − | 0.289073i | \(-0.906653\pi\) |
−0.289073 | − | 0.957307i | \(-0.593347\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4235i | 0.0451429i | 0.999745 | + | 0.0225714i | \(0.00718533\pi\) | ||||
−0.999745 | + | 0.0225714i | \(0.992815\pi\) | |||||||
\(830\) | 218.443 | − | 416.665i | 0.263184 | − | 0.502006i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1477.31 | − | 395.845i | 1.77562 | − | 0.475775i | ||||
\(833\) | −43.4777 | − | 162.261i | −0.0521941 | − | 0.194791i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 654.982 | − | 204.425i | 0.784410 | − | 0.244820i | ||||
\(836\) | −408.817 | −0.489016 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1297.91 | + | 1297.91i | −1.54882 | + | 1.54882i | ||||
\(839\) | −997.984 | + | 576.186i | −1.18949 | + | 0.686754i | −0.958191 | − | 0.286129i | \(-0.907631\pi\) |
−0.231301 | + | 0.972882i | \(0.574298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.136 | + | 727.696i | −0.499567 | + | 0.865275i | ||||
\(842\) | 647.778 | − | 173.572i | 0.769333 | − | 0.206142i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1352.71 | − | 780.989i | 1.60274 | − | 0.925342i | ||||
\(845\) | 208.633 | − | 132.064i | 0.246903 | − | 0.156288i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 159.136 | + | 159.136i | 0.187882 | + | 0.187882i | ||||
\(848\) | −188.084 | − | 50.3968i | −0.221797 | − | 0.0594302i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 242.587 | − | 167.769i | 0.285397 | − | 0.197375i | ||||
\(851\) | −625.828 | + | 1083.97i | −0.735403 | + | 1.27375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −948.800 | − | 254.230i | −1.11231 | − | 0.298042i | −0.344542 | − | 0.938771i | \(-0.611966\pi\) |
−0.767768 | + | 0.640728i | \(0.778632\pi\) | |||||||
\(854\) | 606.838i | 0.710583i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.0704 | −0.0468112 | ||||||||
\(857\) | 152.697 | − | 569.873i | 0.178176 | − | 0.664963i | −0.817813 | − | 0.575485i | \(-0.804813\pi\) |
0.995989 | − | 0.0894780i | \(-0.0285199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −421.639 | − | 243.434i | −0.490849 | − | 0.283392i | 0.234077 | − | 0.972218i | \(-0.424793\pi\) |
−0.724927 | + | 0.688826i | \(0.758126\pi\) | |||||||
\(860\) | −689.949 | − | 635.920i | −0.802267 | − | 0.739442i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −152.573 | + | 569.411i | −0.176999 | + | 0.660570i | ||||
\(863\) | −411.319 | + | 411.319i | −0.476615 | + | 0.476615i | −0.904047 | − | 0.427432i | \(-0.859418\pi\) |
0.427432 | + | 0.904047i | \(0.359418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −238.919 | − | 53.6959i | −0.276207 | − | 0.0620762i | ||||
\(866\) | 344.497 | + | 596.687i | 0.397803 | + | 0.689015i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −58.5159 | − | 218.384i | −0.0674146 | − | 0.251595i | ||||
\(869\) | 71.0318 | + | 41.0102i | 0.0817397 | + | 0.0471924i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −573.666 | − | 993.619i | −0.658630 | − | 1.14078i | ||||
\(872\) | 166.045 | + | 166.045i | 0.190419 | + | 0.190419i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1514.85i | 1.73323i | ||||||||
\(875\) | 35.6585 | − | 253.743i | 0.0407526 | − | 0.289992i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −454.259 | + | 121.718i | −0.517969 | + | 0.138789i | −0.508327 | − | 0.861164i | \(-0.669736\pi\) |
−0.00964182 | + | 0.999954i | \(0.503069\pi\) | |||||||
\(878\) | −205.963 | − | 768.665i | −0.234582 | − | 0.875472i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −37.2987 | + | 71.1447i | −0.0423849 | + | 0.0808463i | ||||
\(881\) | 533.151 | 0.605166 | 0.302583 | − | 0.953123i | \(-0.402151\pi\) | ||||
0.302583 | + | 0.953123i | \(0.402151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −745.939 | + | 745.939i | −0.844778 | + | 0.844778i | −0.989476 | − | 0.144698i | \(-0.953779\pi\) |
0.144698 | + | 0.989476i | \(0.453779\pi\) | |||||||
\(884\) | 283.093 | − | 163.444i | 0.320241 | − | 0.184891i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −936.908 | + | 1622.77i | −1.05746 | + | 1.83157i | ||||
\(887\) | 527.568 | − | 141.361i | 0.594778 | − | 0.159370i | 0.0511420 | − | 0.998691i | \(-0.483714\pi\) |
0.543636 | + | 0.839321i | \(0.317047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 287.766 | − | 166.142i | 0.323696 | − | 0.186886i | ||||
\(890\) | −1445.54 | − | 324.879i | −1.62421 | − | 0.365032i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −197.197 | − | 197.197i | −0.221073 | − | 0.221073i | ||||
\(893\) | −558.455 | − | 149.638i | −0.625369 | − | 0.167567i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.4005 | + | 917.797i | 0.0417883 | + | 1.02547i | ||||
\(896\) | 173.876 | − | 301.163i | 0.194058 | − | 0.336119i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −905.363 | − | 242.591i | −1.00820 | − | 0.270146i | ||||
\(899\) | − | 15.9592i | − | 0.0177521i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −152.182 | −0.168903 | ||||||||
\(902\) | −78.2480 | + | 292.026i | −0.0867495 | + | 0.323753i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 105.069 | + | 60.6617i | 0.116227 | + | 0.0671037i | ||||
\(905\) | 108.548 | − | 4.42335i | 0.119942 | − | 0.00488768i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −346.751 | + | 1294.09i | −0.382306 | + | 1.42678i | 0.460065 | + | 0.887885i | \(0.347826\pi\) |
−0.842371 | + | 0.538899i | \(0.818841\pi\) | |||||||
\(908\) | 124.890 | − | 124.890i | 0.137544 | − | 0.137544i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 104.495 | − | 464.949i | 0.114830 | − | 0.510933i | ||||
\(911\) | 574.681 | + | 995.377i | 0.630824 | + | 1.09262i | 0.987383 | + | 0.158347i | \(0.0506165\pi\) |
−0.356559 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.9176 | + | 96.7258i | 0.0283873 | + | 0.105943i | ||||
\(914\) | 1101.09 | + | 635.714i | 1.20469 | + | 0.695530i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −719.080 | − | 1245.48i | −0.785021 | − | 1.35970i | ||||
\(917\) | 37.8842 | + | 37.8842i | 0.0413132 | + | 0.0413132i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 412.577i | 0.448941i | 0.974481 | + | 0.224470i | \(0.0720652\pi\) | ||||
−0.974481 | + | 0.224470i | \(0.927935\pi\) | |||||||
\(920\) | −615.492 | − | 322.681i | −0.669013 | − | 0.350741i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1600.43 | − | 428.833i | 1.73582 | − | 0.465112i | ||||
\(923\) | 260.085 | + | 970.650i | 0.281782 | + | 1.05163i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1025.37 | + | 870.592i | 1.10851 | + | 0.941180i | ||||
\(926\) | −1493.70 | −1.61307 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.5357 | − | 23.5357i | 0.0253618 | − | 0.0253618i | ||||
\(929\) | −131.382 | + | 75.8536i | −0.141423 | + | 0.0816508i | −0.569042 | − | 0.822308i | \(-0.692686\pi\) |
0.427619 | + | 0.903959i | \(0.359353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 463.590 | − | 802.962i | 0.497949 | − | 0.862473i | ||||
\(932\) | −1303.10 | + | 349.164i | −1.39817 | + | 0.374640i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1883.31 | + | 1087.33i | −2.01639 | + | 1.16416i | ||||
\(935\) | −13.7663 | + | 61.2531i | −0.0147233 | + | 0.0655113i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 662.090 | + | 662.090i | 0.706606 | + | 0.706606i | 0.965820 | − | 0.259214i | \(-0.0834635\pi\) |
−0.259214 | + | 0.965820i | \(0.583463\pi\) | |||||||
\(938\) | −483.669 | − | 129.599i | −0.515639 | − | 0.138165i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 558.395 | − | 605.838i | 0.594037 | − | 0.644508i | ||||
\(941\) | 766.885 | − | 1328.28i | 0.814969 | − | 1.41157i | −0.0943819 | − | 0.995536i | \(-0.530087\pi\) |
0.909350 | − | 0.416031i | \(-0.136579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 644.832 | + | 172.782i | 0.683809 | + | 0.183226i | ||||
\(944\) | 537.056i | 0.568915i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 335.151 | 0.354282 | ||||||||
\(947\) | 429.417 | − | 1602.61i | 0.453450 | − | 1.69230i | −0.239155 | − | 0.970982i | \(-0.576870\pi\) |
0.692605 | − | 0.721317i | \(-0.256463\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 720.120 | + | 415.762i | 0.758820 | + | 0.438105i | ||||
\(950\) | 1601.55 | + | 292.002i | 1.68584 | + | 0.307371i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.8865 | − | 44.3610i | 0.0124858 | − | 0.0465977i | ||||
\(953\) | −145.501 | + | 145.501i | −0.152676 | + | 0.152676i | −0.779312 | − | 0.626636i | \(-0.784431\pi\) |
0.626636 | + | 0.779312i | \(0.284431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −107.212 | − | 169.373i | −0.112264 | − | 0.177354i | ||||
\(956\) | −962.130 | − | 1666.46i | −1.00641 | − | 1.74316i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −150.606 | − | 562.071i | −0.157209 | − | 0.586713i | ||||
\(959\) | 36.7327 | + | 21.2077i | 0.0383032 | + | 0.0221143i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 305.712 | + | 529.509i | 0.318119 | + | 0.550998i | ||||
\(962\) | 1768.92 | + | 1768.92i | 1.83879 | + | 1.83879i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 787.959i | − | 0.817385i | ||||||
\(965\) | −163.407 | − | 523.562i | −0.169334 | − | 0.542551i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1573.24 | + | 421.548i | −1.62693 | + | 0.435934i | −0.953026 | − | 0.302888i | \(-0.902049\pi\) |
−0.673901 | + | 0.738822i | \(0.735382\pi\) | |||||||
\(968\) | −169.772 | − | 633.597i | −0.175384 | − | 0.654542i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −287.595 | − | 150.776i | −0.296490 | − | 0.155439i | ||||
\(971\) | 72.4383 | 0.0746017 | 0.0373009 | − | 0.999304i | \(-0.488124\pi\) | ||||
0.0373009 | + | 0.999304i | \(0.488124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 120.556 | − | 120.556i | 0.123901 | − | 0.123901i | ||||
\(974\) | 465.033 | − | 268.487i | 0.477447 | − | 0.275654i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −225.722 | + | 390.962i | −0.231272 | + | 0.400576i | ||||
\(977\) | −964.876 | + | 258.538i | −0.987591 | + | 0.264624i | −0.716238 | − | 0.697856i | \(-0.754138\pi\) |
−0.271352 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 273.113 | − | 157.682i | 0.278972 | − | 0.161065i | ||||
\(980\) | 706.699 | + | 1116.44i | 0.721122 | + | 1.13923i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 235.116 | + | 235.116i | 0.239425 | + | 0.239425i | ||||
\(983\) | 183.953 | + | 49.2900i | 0.187134 | + | 0.0501424i | 0.351169 | − | 0.936312i | \(-0.385784\pi\) |
−0.164035 | + | 0.986455i | \(0.552451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 349.938 | + | 322.535i | 0.355267 | + | 0.327446i | ||||
\(986\) | 5.03520 | − | 8.72123i | 0.00510670 | − | 0.00884506i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1742.76 | + | 466.970i | 1.76392 | + | 0.472642i | ||||
\(989\) | − | 740.059i | − | 0.748290i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1131.94 | −1.14222 | −0.571109 | − | 0.820874i | \(-0.693487\pi\) | ||||
−0.571109 | + | 0.820874i | \(0.693487\pi\) | |||||||
\(992\) | 188.699 | − | 704.233i | 0.190221 | − | 0.709913i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 379.809 | + | 219.283i | 0.382101 | + | 0.220606i | ||||
\(995\) | −51.1794 | − | 1255.93i | −0.0514366 | − | 1.26224i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −408.216 | + | 1523.48i | −0.409444 | + | 1.52807i | 0.386265 | + | 0.922388i | \(0.373765\pi\) |
−0.795709 | + | 0.605679i | \(0.792902\pi\) | |||||||
\(998\) | −1645.39 | + | 1645.39i | −1.64868 | + | 1.64868i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.3.l.h.352.1 | 8 | ||
3.2 | odd | 2 | 405.3.l.f.352.2 | 8 | |||
5.3 | odd | 4 | inner | 405.3.l.h.28.2 | 8 | ||
9.2 | odd | 6 | 405.3.l.f.217.1 | 8 | |||
9.4 | even | 3 | 15.3.f.a.7.1 | ✓ | 4 | ||
9.5 | odd | 6 | 45.3.g.b.37.2 | 4 | |||
9.7 | even | 3 | inner | 405.3.l.h.217.2 | 8 | ||
15.8 | even | 4 | 405.3.l.f.28.1 | 8 | |||
36.23 | even | 6 | 720.3.bh.k.577.1 | 4 | |||
36.31 | odd | 6 | 240.3.bg.a.97.1 | 4 | |||
45.4 | even | 6 | 75.3.f.c.7.2 | 4 | |||
45.13 | odd | 12 | 15.3.f.a.13.1 | yes | 4 | ||
45.14 | odd | 6 | 225.3.g.a.82.1 | 4 | |||
45.22 | odd | 12 | 75.3.f.c.43.2 | 4 | |||
45.23 | even | 12 | 45.3.g.b.28.2 | 4 | |||
45.32 | even | 12 | 225.3.g.a.118.1 | 4 | |||
45.38 | even | 12 | 405.3.l.f.298.2 | 8 | |||
45.43 | odd | 12 | inner | 405.3.l.h.298.1 | 8 | ||
72.13 | even | 6 | 960.3.bg.i.577.1 | 4 | |||
72.67 | odd | 6 | 960.3.bg.h.577.2 | 4 | |||
180.23 | odd | 12 | 720.3.bh.k.433.1 | 4 | |||
180.67 | even | 12 | 1200.3.bg.k.193.2 | 4 | |||
180.103 | even | 12 | 240.3.bg.a.193.1 | 4 | |||
180.139 | odd | 6 | 1200.3.bg.k.1057.2 | 4 | |||
360.13 | odd | 12 | 960.3.bg.i.193.1 | 4 | |||
360.283 | even | 12 | 960.3.bg.h.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.1 | ✓ | 4 | 9.4 | even | 3 | ||
15.3.f.a.13.1 | yes | 4 | 45.13 | odd | 12 | ||
45.3.g.b.28.2 | 4 | 45.23 | even | 12 | |||
45.3.g.b.37.2 | 4 | 9.5 | odd | 6 | |||
75.3.f.c.7.2 | 4 | 45.4 | even | 6 | |||
75.3.f.c.43.2 | 4 | 45.22 | odd | 12 | |||
225.3.g.a.82.1 | 4 | 45.14 | odd | 6 | |||
225.3.g.a.118.1 | 4 | 45.32 | even | 12 | |||
240.3.bg.a.97.1 | 4 | 36.31 | odd | 6 | |||
240.3.bg.a.193.1 | 4 | 180.103 | even | 12 | |||
405.3.l.f.28.1 | 8 | 15.8 | even | 4 | |||
405.3.l.f.217.1 | 8 | 9.2 | odd | 6 | |||
405.3.l.f.298.2 | 8 | 45.38 | even | 12 | |||
405.3.l.f.352.2 | 8 | 3.2 | odd | 2 | |||
405.3.l.h.28.2 | 8 | 5.3 | odd | 4 | inner | ||
405.3.l.h.217.2 | 8 | 9.7 | even | 3 | inner | ||
405.3.l.h.298.1 | 8 | 45.43 | odd | 12 | inner | ||
405.3.l.h.352.1 | 8 | 1.1 | even | 1 | trivial | ||
720.3.bh.k.433.1 | 4 | 180.23 | odd | 12 | |||
720.3.bh.k.577.1 | 4 | 36.23 | even | 6 | |||
960.3.bg.h.193.2 | 4 | 360.283 | even | 12 | |||
960.3.bg.h.577.2 | 4 | 72.67 | odd | 6 | |||
960.3.bg.i.193.1 | 4 | 360.13 | odd | 12 | |||
960.3.bg.i.577.1 | 4 | 72.13 | even | 6 | |||
1200.3.bg.k.193.2 | 4 | 180.67 | even | 12 | |||
1200.3.bg.k.1057.2 | 4 | 180.139 | odd | 6 |