Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(5,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.i (of order \(4\), degree \(2\), 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: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 29.9 | ||
Root | \(1.85381 - 0.750590i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.29 |
Dual form | 48.3.i.b.5.9 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85381 | + | 0.750590i | 0.926906 | + | 0.375295i | ||||
\(3\) | −2.59524 | + | 1.50491i | −0.865079 | + | 0.501636i | ||||
\(4\) | 2.87323 | + | 2.78290i | 0.718308 | + | 0.695726i | ||||
\(5\) | 2.59897 | + | 2.59897i | 0.519793 | + | 0.519793i | 0.917509 | − | 0.397716i | \(-0.130197\pi\) |
−0.397716 | + | 0.917509i | \(0.630197\pi\) | |||||||
\(6\) | −5.94065 | + | 0.841858i | −0.990108 | + | 0.140310i | ||||
\(7\) | − | 7.30027i | − | 1.04290i | −0.853283 | − | 0.521448i | \(-0.825392\pi\) | ||
0.853283 | − | 0.521448i | \(-0.174608\pi\) | |||||||
\(8\) | 3.23761 | + | 7.31559i | 0.404701 | + | 0.914449i | ||||
\(9\) | 4.47050 | − | 7.81118i | 0.496723 | − | 0.867909i | ||||
\(10\) | 2.86723 | + | 6.76875i | 0.286723 | + | 0.676875i | ||||
\(11\) | −11.3161 | − | 11.3161i | −1.02873 | − | 1.02873i | −0.999575 | − | 0.0291601i | \(-0.990717\pi\) |
−0.0291601 | − | 0.999575i | \(-0.509283\pi\) | |||||||
\(12\) | −11.6447 | − | 2.89834i | −0.970394 | − | 0.241528i | ||||
\(13\) | −0.746462 | − | 0.746462i | −0.0574201 | − | 0.0574201i | 0.677814 | − | 0.735234i | \(-0.262928\pi\) |
−0.735234 | + | 0.677814i | \(0.762928\pi\) | |||||||
\(14\) | 5.47951 | − | 13.5333i | 0.391393 | − | 0.966666i | ||||
\(15\) | −10.6561 | − | 2.83373i | −0.710409 | − | 0.188915i | ||||
\(16\) | 0.510910 | + | 15.9918i | 0.0319319 | + | 0.999490i | ||||
\(17\) | − | 6.67452i | − | 0.392619i | −0.980542 | − | 0.196310i | \(-0.937104\pi\) | ||
0.980542 | − | 0.196310i | \(-0.0628957\pi\) | |||||||
\(18\) | 14.1505 | − | 11.1249i | 0.786137 | − | 0.618052i | ||||
\(19\) | 22.1936 | + | 22.1936i | 1.16809 | + | 1.16809i | 0.982658 | + | 0.185428i | \(0.0593670\pi\) |
0.185428 | + | 0.982658i | \(0.440633\pi\) | |||||||
\(20\) | 0.234761 | + | 14.7001i | 0.0117380 | + | 0.735005i | ||||
\(21\) | 10.9862 | + | 18.9459i | 0.523154 | + | 0.902187i | ||||
\(22\) | −12.4841 | − | 29.4716i | −0.567461 | − | 1.33962i | ||||
\(23\) | −21.4389 | −0.932128 | −0.466064 | − | 0.884751i | \(-0.654328\pi\) | ||||
−0.466064 | + | 0.884751i | \(0.654328\pi\) | |||||||
\(24\) | −19.4117 | − | 14.1134i | −0.808819 | − | 0.588058i | ||||
\(25\) | − | 11.4908i | − | 0.459630i | ||||||
\(26\) | −0.823512 | − | 1.94408i | −0.0316736 | − | 0.0747725i | ||||
\(27\) | 0.153096 | + | 26.9996i | 0.00567024 | + | 0.999984i | ||||
\(28\) | 20.3159 | − | 20.9754i | 0.725570 | − | 0.749120i | ||||
\(29\) | −1.54272 | + | 1.54272i | −0.0531973 | + | 0.0531973i | −0.733205 | − | 0.680008i | \(-0.761976\pi\) |
0.680008 | + | 0.733205i | \(0.261976\pi\) | |||||||
\(30\) | −17.6275 | − | 13.2516i | −0.587583 | − | 0.441719i | ||||
\(31\) | −14.6082 | −0.471233 | −0.235616 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235616 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(32\) | −11.0562 | + | 30.0293i | −0.345506 | + | 0.938417i | ||||
\(33\) | 46.3976 | + | 12.3382i | 1.40599 | + | 0.373886i | ||||
\(34\) | 5.00983 | − | 12.3733i | 0.147348 | − | 0.363921i | ||||
\(35\) | 18.9732 | − | 18.9732i | 0.542090 | − | 0.542090i | ||||
\(36\) | 34.5826 | − | 10.0024i | 0.960626 | − | 0.277843i | ||||
\(37\) | −50.1010 | + | 50.1010i | −1.35408 | + | 1.35408i | −0.473039 | + | 0.881041i | \(0.656843\pi\) |
−0.881041 | + | 0.473039i | \(0.843157\pi\) | |||||||
\(38\) | 24.4845 | + | 57.8011i | 0.644329 | + | 1.52108i | ||||
\(39\) | 3.06060 | + | 0.813888i | 0.0784769 | + | 0.0208689i | ||||
\(40\) | −10.5985 | + | 27.4274i | −0.264963 | + | 0.685685i | ||||
\(41\) | 15.0731 | 0.367637 | 0.183819 | − | 0.982960i | \(-0.441154\pi\) | ||||
0.183819 | + | 0.982960i | \(0.441154\pi\) | |||||||
\(42\) | 6.14579 | + | 43.3683i | 0.146328 | + | 1.03258i | ||||
\(43\) | 26.3634 | − | 26.3634i | 0.613102 | − | 0.613102i | −0.330651 | − | 0.943753i | \(-0.607268\pi\) |
0.943753 | + | 0.330651i | \(0.107268\pi\) | |||||||
\(44\) | −1.02217 | − | 64.0053i | −0.0232310 | − | 1.45467i | ||||
\(45\) | 31.9197 | − | 8.68231i | 0.709326 | − | 0.192940i | ||||
\(46\) | −39.7438 | − | 16.0918i | −0.863995 | − | 0.349823i | ||||
\(47\) | 36.6067i | 0.778866i | 0.921055 | + | 0.389433i | \(0.127329\pi\) | ||||
−0.921055 | + | 0.389433i | \(0.872671\pi\) | |||||||
\(48\) | −25.3922 | − | 40.7337i | −0.529004 | − | 0.848619i | ||||
\(49\) | −4.29399 | −0.0876325 | ||||||||
\(50\) | 8.62484 | − | 21.3017i | 0.172497 | − | 0.426034i | ||||
\(51\) | 10.0445 | + | 17.3220i | 0.196952 | + | 0.339646i | ||||
\(52\) | −0.0674268 | − | 4.22209i | −0.00129667 | − | 0.0811940i | ||||
\(53\) | −50.9270 | − | 50.9270i | −0.960887 | − | 0.960887i | 0.0383765 | − | 0.999263i | \(-0.487781\pi\) |
−0.999263 | + | 0.0383765i | \(0.987781\pi\) | |||||||
\(54\) | −19.9818 | + | 50.1670i | −0.370033 | + | 0.929019i | ||||
\(55\) | − | 58.8202i | − | 1.06946i | ||||||
\(56\) | 53.4058 | − | 23.6354i | 0.953675 | − | 0.422061i | ||||
\(57\) | −90.9971 | − | 24.1983i | −1.59644 | − | 0.424532i | ||||
\(58\) | −4.01787 | + | 1.70196i | −0.0692736 | + | 0.0293442i | ||||
\(59\) | 12.1683 | + | 12.1683i | 0.206242 | + | 0.206242i | 0.802668 | − | 0.596426i | \(-0.203413\pi\) |
−0.596426 | + | 0.802668i | \(0.703413\pi\) | |||||||
\(60\) | −22.7315 | − | 37.7969i | −0.378859 | − | 0.629949i | ||||
\(61\) | −27.5789 | − | 27.5789i | −0.452113 | − | 0.452113i | 0.443943 | − | 0.896055i | \(-0.353579\pi\) |
−0.896055 | + | 0.443943i | \(0.853579\pi\) | |||||||
\(62\) | −27.0809 | − | 10.9648i | −0.436788 | − | 0.176851i | ||||
\(63\) | −57.0238 | − | 32.6359i | −0.905139 | − | 0.518030i | ||||
\(64\) | −43.0358 | + | 47.3701i | −0.672434 | + | 0.740157i | ||||
\(65\) | − | 3.88006i | − | 0.0596932i | ||||||
\(66\) | 76.7514 | + | 57.6983i | 1.16290 | + | 0.874217i | ||||
\(67\) | −4.84214 | − | 4.84214i | −0.0722707 | − | 0.0722707i | 0.670047 | − | 0.742318i | \(-0.266274\pi\) |
−0.742318 | + | 0.670047i | \(0.766274\pi\) | |||||||
\(68\) | 18.5745 | − | 19.1774i | 0.273155 | − | 0.282021i | ||||
\(69\) | 55.6391 | − | 32.2636i | 0.806364 | − | 0.467589i | ||||
\(70\) | 49.4137 | − | 20.9316i | 0.705910 | − | 0.299023i | ||||
\(71\) | 74.9072 | 1.05503 | 0.527515 | − | 0.849546i | \(-0.323124\pi\) | ||||
0.527515 | + | 0.849546i | \(0.323124\pi\) | |||||||
\(72\) | 71.6172 | + | 7.41482i | 0.994683 | + | 0.102984i | ||||
\(73\) | 3.47110i | 0.0475494i | 0.999717 | + | 0.0237747i | \(0.00756843\pi\) | ||||
−0.999717 | + | 0.0237747i | \(0.992432\pi\) | |||||||
\(74\) | −130.483 | + | 55.2725i | −1.76328 | + | 0.746925i | ||||
\(75\) | 17.2925 | + | 29.8212i | 0.230567 | + | 0.397616i | ||||
\(76\) | 2.00472 | + | 125.530i | 0.0263779 | + | 1.65171i | ||||
\(77\) | −82.6105 | + | 82.6105i | −1.07286 | + | 1.07286i | ||||
\(78\) | 5.06288 | + | 3.80605i | 0.0649087 | + | 0.0487955i | ||||
\(79\) | 103.463 | 1.30966 | 0.654831 | − | 0.755775i | \(-0.272740\pi\) | ||||
0.654831 | + | 0.755775i | \(0.272740\pi\) | |||||||
\(80\) | −40.2344 | + | 42.8901i | −0.502930 | + | 0.536126i | ||||
\(81\) | −41.0292 | − | 69.8399i | −0.506533 | − | 0.862221i | ||||
\(82\) | 27.9427 | + | 11.3137i | 0.340765 | + | 0.137972i | ||||
\(83\) | 31.7254 | − | 31.7254i | 0.382233 | − | 0.382233i | −0.489673 | − | 0.871906i | \(-0.662884\pi\) |
0.871906 | + | 0.489673i | \(0.162884\pi\) | |||||||
\(84\) | −21.1587 | + | 85.0097i | −0.251889 | + | 1.01202i | ||||
\(85\) | 17.3469 | − | 17.3469i | 0.204081 | − | 0.204081i | ||||
\(86\) | 68.6608 | − | 29.0846i | 0.798381 | − | 0.338194i | ||||
\(87\) | 1.68207 | − | 6.32538i | 0.0193342 | − | 0.0727056i | ||||
\(88\) | 46.1468 | − | 119.421i | 0.524395 | − | 1.35706i | ||||
\(89\) | 78.2605 | 0.879331 | 0.439666 | − | 0.898162i | \(-0.355097\pi\) | ||||
0.439666 | + | 0.898162i | \(0.355097\pi\) | |||||||
\(90\) | 65.6899 | + | 7.86322i | 0.729888 | + | 0.0873691i | ||||
\(91\) | −5.44937 | + | 5.44937i | −0.0598832 | + | 0.0598832i | ||||
\(92\) | −61.5990 | − | 59.6625i | −0.669555 | − | 0.648505i | ||||
\(93\) | 37.9118 | − | 21.9840i | 0.407653 | − | 0.236387i | ||||
\(94\) | −27.4766 | + | 67.8619i | −0.292304 | + | 0.721935i | ||||
\(95\) | 115.361i | 1.21433i | ||||||||
\(96\) | −16.4980 | − | 94.5718i | −0.171854 | − | 0.985122i | ||||
\(97\) | −61.5651 | −0.634692 | −0.317346 | − | 0.948310i | \(-0.602792\pi\) | ||||
−0.317346 | + | 0.948310i | \(0.602792\pi\) | |||||||
\(98\) | −7.96025 | − | 3.22303i | −0.0812271 | − | 0.0328880i | ||||
\(99\) | −138.981 | + | 37.8034i | −1.40384 | + | 0.381853i | ||||
\(100\) | 31.9777 | − | 33.0156i | 0.319777 | − | 0.330156i | ||||
\(101\) | 56.9675 | + | 56.9675i | 0.564034 | + | 0.564034i | 0.930451 | − | 0.366417i | \(-0.119415\pi\) |
−0.366417 | + | 0.930451i | \(0.619415\pi\) | |||||||
\(102\) | 5.61900 | + | 39.6510i | 0.0550882 | + | 0.388735i | ||||
\(103\) | 153.944i | 1.49460i | 0.664485 | + | 0.747301i | \(0.268651\pi\) | ||||
−0.664485 | + | 0.747301i | \(0.731349\pi\) | |||||||
\(104\) | 3.04406 | − | 7.87756i | 0.0292698 | − | 0.0757458i | ||||
\(105\) | −20.6870 | + | 77.7927i | −0.197019 | + | 0.740883i | ||||
\(106\) | −56.1838 | − | 132.634i | −0.530036 | − | 1.25127i | ||||
\(107\) | −76.9344 | − | 76.9344i | −0.719013 | − | 0.719013i | 0.249390 | − | 0.968403i | \(-0.419770\pi\) |
−0.968403 | + | 0.249390i | \(0.919770\pi\) | |||||||
\(108\) | −74.6973 | + | 78.0020i | −0.691641 | + | 0.722241i | ||||
\(109\) | 74.1271 | + | 74.1271i | 0.680065 | + | 0.680065i | 0.960015 | − | 0.279949i | \(-0.0903177\pi\) |
−0.279949 | + | 0.960015i | \(0.590318\pi\) | |||||||
\(110\) | 44.1498 | − | 109.042i | 0.401362 | − | 0.991287i | ||||
\(111\) | 54.6265 | − | 205.421i | 0.492131 | − | 1.85064i | ||||
\(112\) | 116.745 | − | 3.72978i | 1.04236 | − | 0.0333016i | ||||
\(113\) | 38.3909i | 0.339742i | 0.985466 | + | 0.169871i | \(0.0543352\pi\) | ||||
−0.985466 | + | 0.169871i | \(0.945665\pi\) | |||||||
\(114\) | −150.528 | − | 113.161i | −1.32042 | − | 0.992637i | ||||
\(115\) | −55.7191 | − | 55.7191i | −0.484514 | − | 0.484514i | ||||
\(116\) | −8.72584 | + | 0.139352i | −0.0752228 | + | 0.00120131i | ||||
\(117\) | −9.16781 | + | 2.49369i | −0.0783573 | + | 0.0213136i | ||||
\(118\) | 13.4243 | + | 31.6911i | 0.113766 | + | 0.268569i | ||||
\(119\) | −48.7259 | −0.409461 | ||||||||
\(120\) | −13.7700 | − | 87.1304i | −0.114750 | − | 0.726087i | ||||
\(121\) | 135.108i | 1.11659i | ||||||||
\(122\) | −30.4256 | − | 71.8264i | −0.249390 | − | 0.588741i | ||||
\(123\) | −39.1184 | + | 22.6837i | −0.318035 | + | 0.184420i | ||||
\(124\) | −41.9728 | − | 40.6532i | −0.338490 | − | 0.327849i | ||||
\(125\) | 94.8382 | − | 94.8382i | 0.758706 | − | 0.758706i | ||||
\(126\) | −81.2151 | − | 103.302i | −0.644565 | − | 0.819859i | ||||
\(127\) | −43.3417 | −0.341273 | −0.170636 | − | 0.985334i | \(-0.554582\pi\) | ||||
−0.170636 | + | 0.985334i | \(0.554582\pi\) | |||||||
\(128\) | −115.336 | + | 55.5129i | −0.901060 | + | 0.433695i | ||||
\(129\) | −28.7447 | + | 108.094i | −0.222827 | + | 0.837935i | ||||
\(130\) | 2.91233 | − | 7.19289i | 0.0224025 | − | 0.0553299i | ||||
\(131\) | −1.21414 | + | 1.21414i | −0.00926827 | + | 0.00926827i | −0.711726 | − | 0.702457i | \(-0.752086\pi\) |
0.702457 | + | 0.711726i | \(0.252086\pi\) | |||||||
\(132\) | 98.9748 | + | 164.571i | 0.749809 | + | 1.24675i | ||||
\(133\) | 162.020 | − | 162.020i | 1.21819 | − | 1.21819i | ||||
\(134\) | −5.34195 | − | 12.6109i | −0.0398653 | − | 0.0941110i | ||||
\(135\) | −69.7730 | + | 70.5688i | −0.516837 | + | 0.522732i | ||||
\(136\) | 48.8281 | − | 21.6095i | 0.359030 | − | 0.158893i | ||||
\(137\) | 238.227 | 1.73889 | 0.869443 | − | 0.494033i | \(-0.164478\pi\) | ||||
0.869443 | + | 0.494033i | \(0.164478\pi\) | |||||||
\(138\) | 127.361 | − | 18.0485i | 0.922907 | − | 0.130787i | ||||
\(139\) | −26.5704 | + | 26.5704i | −0.191154 | + | 0.191154i | −0.796195 | − | 0.605041i | \(-0.793157\pi\) |
0.605041 | + | 0.796195i | \(0.293157\pi\) | |||||||
\(140\) | 107.315 | − | 1.71382i | 0.766534 | − | 0.0122416i | ||||
\(141\) | −55.0897 | − | 95.0030i | −0.390707 | − | 0.673780i | ||||
\(142\) | 138.864 | + | 56.2245i | 0.977914 | + | 0.395947i | ||||
\(143\) | 16.8940i | 0.118140i | ||||||||
\(144\) | 127.199 | + | 67.5008i | 0.883328 | + | 0.468755i | ||||
\(145\) | −8.01896 | −0.0553032 | ||||||||
\(146\) | −2.60537 | + | 6.43477i | −0.0178450 | + | 0.0440738i | ||||
\(147\) | 11.1439 | − | 6.46207i | 0.0758090 | − | 0.0439596i | ||||
\(148\) | −283.378 | + | 4.52555i | −1.91472 | + | 0.0305780i | ||||
\(149\) | −133.254 | − | 133.254i | −0.894321 | − | 0.894321i | 0.100605 | − | 0.994926i | \(-0.467922\pi\) |
−0.994926 | + | 0.100605i | \(0.967922\pi\) | |||||||
\(150\) | 9.67358 | + | 68.2625i | 0.0644906 | + | 0.455084i | ||||
\(151\) | 23.3716i | 0.154779i | 0.997001 | + | 0.0773895i | \(0.0246585\pi\) | ||||
−0.997001 | + | 0.0773895i | \(0.975342\pi\) | |||||||
\(152\) | −90.5052 | + | 234.214i | −0.595429 | + | 1.54088i | ||||
\(153\) | −52.1359 | − | 29.8385i | −0.340758 | − | 0.195023i | ||||
\(154\) | −215.151 | + | 91.1377i | −1.39708 | + | 0.591803i | ||||
\(155\) | −37.9662 | − | 37.9662i | −0.244943 | − | 0.244943i | ||||
\(156\) | 6.52884 | + | 10.8558i | 0.0418515 | + | 0.0695887i | ||||
\(157\) | −95.8780 | − | 95.8780i | −0.610688 | − | 0.610688i | 0.332438 | − | 0.943125i | \(-0.392129\pi\) |
−0.943125 | + | 0.332438i | \(0.892129\pi\) | |||||||
\(158\) | 191.801 | + | 77.6585i | 1.21393 | + | 0.491509i | ||||
\(159\) | 208.808 | + | 55.5272i | 1.31326 | + | 0.349227i | ||||
\(160\) | −106.780 | + | 49.3106i | −0.667374 | + | 0.308191i | ||||
\(161\) | 156.510i | 0.972113i | ||||||||
\(162\) | −23.6393 | − | 160.266i | −0.145921 | − | 0.989296i | ||||
\(163\) | −103.379 | − | 103.379i | −0.634230 | − | 0.634230i | 0.314896 | − | 0.949126i | \(-0.398030\pi\) |
−0.949126 | + | 0.314896i | \(0.898030\pi\) | |||||||
\(164\) | 43.3086 | + | 41.9471i | 0.264077 | + | 0.255775i | ||||
\(165\) | 88.5190 | + | 152.652i | 0.536479 | + | 0.925166i | ||||
\(166\) | 82.6256 | − | 35.0001i | 0.497744 | − | 0.210844i | ||||
\(167\) | −113.980 | −0.682515 | −0.341258 | − | 0.939970i | \(-0.610853\pi\) | ||||
−0.341258 | + | 0.939970i | \(0.610853\pi\) | |||||||
\(168\) | −103.032 | + | 141.710i | −0.613283 | + | 0.843514i | ||||
\(169\) | − | 167.886i | − | 0.993406i | ||||||
\(170\) | 45.1782 | − | 19.1374i | 0.265754 | − | 0.112573i | ||||
\(171\) | 272.575 | − | 74.1418i | 1.59401 | − | 0.433578i | ||||
\(172\) | 149.115 | − | 2.38136i | 0.866946 | − | 0.0138451i | ||||
\(173\) | −144.265 | + | 144.265i | −0.833901 | + | 0.833901i | −0.988048 | − | 0.154147i | \(-0.950737\pi\) |
0.154147 | + | 0.988048i | \(0.450737\pi\) | |||||||
\(174\) | 7.86601 | − | 10.4635i | 0.0452070 | − | 0.0601352i | ||||
\(175\) | −83.8857 | −0.479347 | ||||||||
\(176\) | 175.184 | − | 186.747i | 0.995361 | − | 1.06106i | ||||
\(177\) | −49.8918 | − | 13.2674i | −0.281875 | − | 0.0749573i | ||||
\(178\) | 145.080 | + | 58.7415i | 0.815057 | + | 0.330008i | ||||
\(179\) | 16.8240 | − | 16.8240i | 0.0939888 | − | 0.0939888i | −0.658549 | − | 0.752538i | \(-0.728829\pi\) |
0.752538 | + | 0.658549i | \(0.228829\pi\) | |||||||
\(180\) | 115.875 | + | 63.8831i | 0.643748 | + | 0.354906i | ||||
\(181\) | 34.2037 | − | 34.2037i | 0.188971 | − | 0.188971i | −0.606280 | − | 0.795251i | \(-0.707339\pi\) |
0.795251 | + | 0.606280i | \(0.207339\pi\) | |||||||
\(182\) | −14.1924 | + | 6.01187i | −0.0779800 | + | 0.0330322i | ||||
\(183\) | 113.077 | + | 30.0700i | 0.617909 | + | 0.164317i | ||||
\(184\) | −69.4109 | − | 156.839i | −0.377233 | − | 0.852384i | ||||
\(185\) | −260.421 | −1.40768 | ||||||||
\(186\) | 86.7822 | − | 12.2980i | 0.466571 | − | 0.0661185i | ||||
\(187\) | −75.5295 | + | 75.5295i | −0.403901 | + | 0.403901i | ||||
\(188\) | −101.873 | + | 105.179i | −0.541877 | + | 0.559465i | ||||
\(189\) | 197.104 | − | 1.11765i | 1.04288 | − | 0.00591347i | ||||
\(190\) | −86.5887 | + | 213.857i | −0.455730 | + | 1.12557i | ||||
\(191\) | − | 150.160i | − | 0.786177i | −0.919501 | − | 0.393088i | \(-0.871407\pi\) | ||
0.919501 | − | 0.393088i | \(-0.128593\pi\) | |||||||
\(192\) | 40.4004 | − | 187.701i | 0.210419 | − | 0.977611i | ||||
\(193\) | 117.637 | 0.609518 | 0.304759 | − | 0.952429i | \(-0.401424\pi\) | ||||
0.304759 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(194\) | −114.130 | − | 46.2102i | −0.588300 | − | 0.238197i | ||||
\(195\) | 5.83913 | + | 10.0697i | 0.0299442 | + | 0.0516393i | ||||
\(196\) | −12.3376 | − | 11.9498i | −0.0629471 | − | 0.0609682i | ||||
\(197\) | −31.8524 | − | 31.8524i | −0.161688 | − | 0.161688i | 0.621626 | − | 0.783314i | \(-0.286472\pi\) |
−0.783314 | + | 0.621626i | \(0.786472\pi\) | |||||||
\(198\) | −286.019 | − | 34.2370i | −1.44454 | − | 0.172914i | ||||
\(199\) | − | 128.347i | − | 0.644959i | −0.946576 | − | 0.322480i | \(-0.895484\pi\) | ||
0.946576 | − | 0.322480i | \(-0.104516\pi\) | |||||||
\(200\) | 84.0617 | − | 37.2026i | 0.420308 | − | 0.186013i | ||||
\(201\) | 19.8535 | + | 5.27952i | 0.0987735 | + | 0.0262663i | ||||
\(202\) | 62.8477 | + | 148.366i | 0.311127 | + | 0.734486i | ||||
\(203\) | 11.2623 | + | 11.2623i | 0.0554793 | + | 0.0554793i | ||||
\(204\) | −19.3451 | + | 77.7230i | −0.0948287 | + | 0.380995i | ||||
\(205\) | 39.1746 | + | 39.1746i | 0.191095 | + | 0.191095i | ||||
\(206\) | −115.549 | + | 285.383i | −0.560916 | + | 1.38536i | ||||
\(207\) | −95.8429 | + | 167.464i | −0.463009 | + | 0.809003i | ||||
\(208\) | 11.5559 | − | 12.3187i | 0.0555573 | − | 0.0592244i | ||||
\(209\) | − | 502.290i | − | 2.40330i | ||||||
\(210\) | −96.7401 | + | 128.686i | −0.460667 | + | 0.612788i | ||||
\(211\) | 78.8045 | + | 78.8045i | 0.373481 | + | 0.373481i | 0.868743 | − | 0.495262i | \(-0.164928\pi\) |
−0.495262 | + | 0.868743i | \(0.664928\pi\) | |||||||
\(212\) | −4.60016 | − | 288.050i | −0.0216989 | − | 1.35873i | ||||
\(213\) | −194.402 | + | 112.728i | −0.912685 | + | 0.529241i | ||||
\(214\) | −84.8757 | − | 200.368i | −0.396616 | − | 0.936299i | ||||
\(215\) | 137.035 | 0.637372 | ||||||||
\(216\) | −197.022 | + | 88.5340i | −0.912140 | + | 0.409880i | ||||
\(217\) | 106.644i | 0.491447i | ||||||||
\(218\) | 81.7786 | + | 193.057i | 0.375131 | + | 0.885581i | ||||
\(219\) | −5.22369 | − | 9.00834i | −0.0238525 | − | 0.0411340i | ||||
\(220\) | 163.691 | − | 169.004i | 0.744050 | − | 0.768200i | ||||
\(221\) | −4.98228 | + | 4.98228i | −0.0225442 | + | 0.0225442i | ||||
\(222\) | 255.454 | − | 339.810i | 1.15070 | − | 1.53068i | ||||
\(223\) | −153.748 | −0.689455 | −0.344727 | − | 0.938703i | \(-0.612029\pi\) | ||||
−0.344727 | + | 0.938703i | \(0.612029\pi\) | |||||||
\(224\) | 219.222 | + | 80.7131i | 0.978671 | + | 0.360326i | ||||
\(225\) | −89.7564 | − | 51.3695i | −0.398917 | − | 0.228309i | ||||
\(226\) | −28.8158 | + | 71.1695i | −0.127504 | + | 0.314909i | ||||
\(227\) | 43.6518 | − | 43.6518i | 0.192299 | − | 0.192299i | −0.604390 | − | 0.796689i | \(-0.706583\pi\) |
0.796689 | + | 0.604390i | \(0.206583\pi\) | |||||||
\(228\) | −194.114 | − | 322.763i | −0.851377 | − | 1.41563i | ||||
\(229\) | −111.882 | + | 111.882i | −0.488566 | + | 0.488566i | −0.907853 | − | 0.419288i | \(-0.862280\pi\) |
0.419288 | + | 0.907853i | \(0.362280\pi\) | |||||||
\(230\) | −61.4705 | − | 145.115i | −0.267263 | − | 0.630934i | ||||
\(231\) | 90.0726 | − | 338.715i | 0.389925 | − | 1.46630i | ||||
\(232\) | −16.2807 | − | 6.29119i | −0.0701753 | − | 0.0271172i | ||||
\(233\) | 32.4793 | 0.139396 | 0.0696980 | − | 0.997568i | \(-0.477796\pi\) | ||||
0.0696980 | + | 0.997568i | \(0.477796\pi\) | |||||||
\(234\) | −18.8671 | − | 2.25843i | −0.0806287 | − | 0.00965142i | ||||
\(235\) | −95.1395 | + | 95.1395i | −0.404849 | + | 0.404849i | ||||
\(236\) | 1.09914 | + | 68.8255i | 0.00465739 | + | 0.291634i | ||||
\(237\) | −268.512 | + | 155.703i | −1.13296 | + | 0.656974i | ||||
\(238\) | −90.3285 | − | 36.5731i | −0.379532 | − | 0.153669i | ||||
\(239\) | 133.305i | 0.557762i | 0.960326 | + | 0.278881i | \(0.0899636\pi\) | ||||
−0.960326 | + | 0.278881i | \(0.910036\pi\) | |||||||
\(240\) | 39.8722 | − | 171.859i | 0.166134 | − | 0.716079i | ||||
\(241\) | 159.670 | 0.662532 | 0.331266 | − | 0.943537i | \(-0.392524\pi\) | ||||
0.331266 | + | 0.943537i | \(0.392524\pi\) | |||||||
\(242\) | −101.410 | + | 250.464i | −0.419051 | + | 1.03497i | ||||
\(243\) | 211.583 | + | 119.506i | 0.870712 | + | 0.491793i | ||||
\(244\) | −2.49116 | − | 155.990i | −0.0102097 | − | 0.639302i | ||||
\(245\) | −11.1599 | − | 11.1599i | −0.0455508 | − | 0.0455508i | ||||
\(246\) | −89.5442 | + | 12.6894i | −0.364001 | + | 0.0515831i | ||||
\(247\) | − | 33.1334i | − | 0.134143i | ||||||
\(248\) | −47.2957 | − | 106.868i | −0.190708 | − | 0.430918i | ||||
\(249\) | −34.5911 | + | 130.079i | −0.138920 | + | 0.522404i | ||||
\(250\) | 246.997 | − | 104.628i | 0.987987 | − | 0.418510i | ||||
\(251\) | 106.711 | + | 106.711i | 0.425141 | + | 0.425141i | 0.886969 | − | 0.461828i | \(-0.152806\pi\) |
−0.461828 | + | 0.886969i | \(0.652806\pi\) | |||||||
\(252\) | −73.0199 | − | 252.462i | −0.289762 | − | 1.00183i | ||||
\(253\) | 242.605 | + | 242.605i | 0.958913 | + | 0.958913i | ||||
\(254\) | −80.3473 | − | 32.5318i | −0.316328 | − | 0.128078i | ||||
\(255\) | −18.9138 | + | 71.1246i | −0.0741717 | + | 0.278920i | ||||
\(256\) | −255.478 | + | 16.3408i | −0.997961 | + | 0.0638312i | ||||
\(257\) | 343.816i | 1.33781i | 0.743350 | + | 0.668903i | \(0.233236\pi\) | ||||
−0.743350 | + | 0.668903i | \(0.766764\pi\) | |||||||
\(258\) | −134.421 | + | 178.810i | −0.521013 | + | 0.693061i | ||||
\(259\) | 365.751 | + | 365.751i | 1.41217 | + | 1.41217i | ||||
\(260\) | 10.7978 | − | 11.1483i | 0.0415301 | − | 0.0428781i | ||||
\(261\) | 5.15374 | + | 18.9472i | 0.0197461 | + | 0.0725948i | ||||
\(262\) | −3.16212 | + | 1.33947i | −0.0120691 | + | 0.00511248i | ||||
\(263\) | 266.255 | 1.01238 | 0.506188 | − | 0.862423i | \(-0.331054\pi\) | ||||
0.506188 | + | 0.862423i | \(0.331054\pi\) | |||||||
\(264\) | 59.9557 | + | 379.372i | 0.227105 | + | 1.43702i | ||||
\(265\) | − | 264.715i | − | 0.998925i | ||||||
\(266\) | 421.964 | − | 178.743i | 1.58633 | − | 0.671968i | ||||
\(267\) | −203.104 | + | 117.775i | −0.760691 | + | 0.441104i | ||||
\(268\) | −0.437383 | − | 27.3878i | −0.00163203 | − | 0.102193i | ||||
\(269\) | 102.194 | − | 102.194i | 0.379904 | − | 0.379904i | −0.491164 | − | 0.871067i | \(-0.663428\pi\) |
0.871067 | + | 0.491164i | \(0.163428\pi\) | |||||||
\(270\) | −182.314 | + | 78.4504i | −0.675238 | + | 0.290557i | ||||
\(271\) | −38.5636 | −0.142301 | −0.0711505 | − | 0.997466i | \(-0.522667\pi\) | ||||
−0.0711505 | + | 0.997466i | \(0.522667\pi\) | |||||||
\(272\) | 106.738 | − | 3.41008i | 0.392419 | − | 0.0125371i | ||||
\(273\) | 5.94161 | − | 22.3432i | 0.0217641 | − | 0.0818433i | ||||
\(274\) | 441.629 | + | 178.811i | 1.61178 | + | 0.652595i | ||||
\(275\) | −130.030 | + | 130.030i | −0.472838 | + | 0.472838i | ||||
\(276\) | 249.651 | + | 62.1374i | 0.904531 | + | 0.225135i | ||||
\(277\) | −277.306 | + | 277.306i | −1.00111 | + | 1.00111i | −0.00110593 | + | 0.999999i | \(0.500352\pi\) |
−0.999999 | + | 0.00110593i | \(0.999648\pi\) | |||||||
\(278\) | −69.1999 | + | 29.3130i | −0.248921 | + | 0.105443i | ||||
\(279\) | −65.3061 | + | 114.107i | −0.234072 | + | 0.408987i | ||||
\(280\) | 200.228 | + | 77.3722i | 0.715098 | + | 0.276329i | ||||
\(281\) | −458.765 | −1.63262 | −0.816308 | − | 0.577617i | \(-0.803983\pi\) | ||||
−0.816308 | + | 0.577617i | \(0.803983\pi\) | |||||||
\(282\) | −30.8176 | − | 217.467i | −0.109282 | − | 0.771161i | ||||
\(283\) | 276.746 | − | 276.746i | 0.977900 | − | 0.977900i | −0.0218614 | − | 0.999761i | \(-0.506959\pi\) |
0.999761 | + | 0.0218614i | \(0.00695927\pi\) | |||||||
\(284\) | 215.226 | + | 208.459i | 0.757837 | + | 0.734012i | ||||
\(285\) | −173.608 | − | 299.389i | −0.609149 | − | 1.05049i | ||||
\(286\) | −12.6805 | + | 31.3184i | −0.0443374 | + | 0.109505i | ||||
\(287\) | − | 110.038i | − | 0.383408i | ||||||
\(288\) | 185.138 | + | 220.608i | 0.642840 | + | 0.766000i | ||||
\(289\) | 244.451 | 0.845850 | ||||||||
\(290\) | −14.8656 | − | 6.01895i | −0.0512608 | − | 0.0207550i | ||||
\(291\) | 159.776 | − | 92.6499i | 0.549059 | − | 0.318384i | ||||
\(292\) | −9.65974 | + | 9.97328i | −0.0330813 | + | 0.0341551i | ||||
\(293\) | 306.513 | + | 306.513i | 1.04612 | + | 1.04612i | 0.998884 | + | 0.0472370i | \(0.0150416\pi\) |
0.0472370 | + | 0.998884i | \(0.484958\pi\) | |||||||
\(294\) | 25.5091 | − | 3.61493i | 0.0867656 | − | 0.0122957i | ||||
\(295\) | 63.2500i | 0.214407i | ||||||||
\(296\) | −528.726 | − | 204.311i | −1.78624 | − | 0.690240i | ||||
\(297\) | 303.797 | − | 307.262i | 1.02289 | − | 1.03455i | ||||
\(298\) | −147.009 | − | 347.046i | −0.493317 | − | 1.16459i | ||||
\(299\) | 16.0033 | + | 16.0033i | 0.0535229 | + | 0.0535229i | ||||
\(300\) | −33.3041 | + | 133.807i | −0.111014 | + | 0.446022i | ||||
\(301\) | −192.460 | − | 192.460i | −0.639401 | − | 0.639401i | ||||
\(302\) | −17.5425 | + | 43.3266i | −0.0580877 | + | 0.143466i | ||||
\(303\) | −233.575 | − | 62.1133i | −0.770874 | − | 0.204994i | ||||
\(304\) | −343.578 | + | 366.256i | −1.13019 | + | 1.20479i | ||||
\(305\) | − | 143.353i | − | 0.470010i | ||||||
\(306\) | −74.2537 | − | 94.4476i | −0.242659 | − | 0.308652i | ||||
\(307\) | −359.692 | − | 359.692i | −1.17163 | − | 1.17163i | −0.981820 | − | 0.189814i | \(-0.939211\pi\) |
−0.189814 | − | 0.981820i | \(-0.560789\pi\) | |||||||
\(308\) | −467.256 | + | 7.46209i | −1.51706 | + | 0.0242276i | ||||
\(309\) | −231.672 | − | 399.521i | −0.749746 | − | 1.29295i | ||||
\(310\) | −41.8852 | − | 98.8793i | −0.135113 | − | 0.318965i | ||||
\(311\) | −572.008 | −1.83925 | −0.919626 | − | 0.392794i | \(-0.871508\pi\) | ||||
−0.919626 | + | 0.392794i | \(0.871508\pi\) | |||||||
\(312\) | 3.95495 | + | 25.0252i | 0.0126761 | + | 0.0802088i | ||||
\(313\) | − | 333.314i | − | 1.06490i | −0.846461 | − | 0.532450i | \(-0.821271\pi\) | ||
0.846461 | − | 0.532450i | \(-0.178729\pi\) | |||||||
\(314\) | −105.775 | − | 249.705i | −0.336862 | − | 0.795238i | ||||
\(315\) | −63.3832 | − | 233.022i | −0.201217 | − | 0.739754i | ||||
\(316\) | 297.274 | + | 287.928i | 0.940741 | + | 0.911166i | ||||
\(317\) | 266.382 | − | 266.382i | 0.840322 | − | 0.840322i | −0.148578 | − | 0.988901i | \(-0.547470\pi\) |
0.988901 | + | 0.148578i | \(0.0474697\pi\) | |||||||
\(318\) | 345.413 | + | 259.666i | 1.08620 | + | 0.816560i | ||||
\(319\) | 34.9151 | 0.109452 | ||||||||
\(320\) | −234.962 | + | 11.2647i | −0.734255 | + | 0.0352021i | ||||
\(321\) | 315.442 | + | 83.8838i | 0.982686 | + | 0.261320i | ||||
\(322\) | −117.475 | + | 290.140i | −0.364829 | + | 0.901057i | ||||
\(323\) | 148.132 | − | 148.132i | 0.458613 | − | 0.458613i | ||||
\(324\) | 76.4712 | − | 314.846i | 0.236022 | − | 0.971748i | ||||
\(325\) | −8.57741 | + | 8.57741i | −0.0263920 | + | 0.0263920i | ||||
\(326\) | −114.050 | − | 269.242i | −0.349848 | − | 0.825894i | ||||
\(327\) | −303.932 | − | 80.8229i | −0.929455 | − | 0.247165i | ||||
\(328\) | 48.8009 | + | 110.269i | 0.148783 | + | 0.336186i | ||||
\(329\) | 267.239 | 0.812276 | ||||||||
\(330\) | 49.5183 | + | 349.430i | 0.150055 | + | 1.05888i | ||||
\(331\) | −212.431 | + | 212.431i | −0.641787 | + | 0.641787i | −0.950995 | − | 0.309208i | \(-0.899936\pi\) |
0.309208 | + | 0.950995i | \(0.399936\pi\) | |||||||
\(332\) | 179.443 | − | 2.86571i | 0.540491 | − | 0.00863165i | ||||
\(333\) | 167.371 | + | 615.325i | 0.502617 | + | 1.84782i | ||||
\(334\) | −211.298 | − | 85.5522i | −0.632627 | − | 0.256144i | ||||
\(335\) | − | 25.1691i | − | 0.0751317i | ||||||
\(336\) | −297.367 | + | 185.370i | −0.885022 | + | 0.551696i | ||||
\(337\) | −207.477 | −0.615658 | −0.307829 | − | 0.951442i | \(-0.599602\pi\) | ||||
−0.307829 | + | 0.951442i | \(0.599602\pi\) | |||||||
\(338\) | 126.013 | − | 311.228i | 0.372820 | − | 0.920793i | ||||
\(339\) | −57.7748 | − | 99.6335i | −0.170427 | − | 0.293904i | ||||
\(340\) | 98.1161 | − | 1.56692i | 0.288577 | − | 0.00460858i | ||||
\(341\) | 165.308 | + | 165.308i | 0.484773 | + | 0.484773i | ||||
\(342\) | 560.953 | + | 67.1472i | 1.64021 | + | 0.196337i | ||||
\(343\) | − | 326.366i | − | 0.951505i | ||||||
\(344\) | 278.218 | + | 107.509i | 0.808773 | + | 0.312527i | ||||
\(345\) | 228.456 | + | 60.7521i | 0.662192 | + | 0.176093i | ||||
\(346\) | −375.723 | + | 159.156i | −1.08591 | + | 0.459989i | ||||
\(347\) | 98.4692 | + | 98.4692i | 0.283773 | + | 0.283773i | 0.834612 | − | 0.550839i | \(-0.185692\pi\) |
−0.550839 | + | 0.834612i | \(0.685692\pi\) | |||||||
\(348\) | 22.4359 | − | 13.4932i | 0.0644710 | − | 0.0387737i | ||||
\(349\) | −337.382 | − | 337.382i | −0.966711 | − | 0.966711i | 0.0327527 | − | 0.999463i | \(-0.489573\pi\) |
−0.999463 | + | 0.0327527i | \(0.989573\pi\) | |||||||
\(350\) | −155.508 | − | 62.9637i | −0.444309 | − | 0.179896i | ||||
\(351\) | 20.0399 | − | 20.2684i | 0.0570936 | − | 0.0577448i | ||||
\(352\) | 464.927 | − | 214.702i | 1.32082 | − | 0.609948i | ||||
\(353\) | 293.330i | 0.830964i | 0.909601 | + | 0.415482i | \(0.136387\pi\) | ||||
−0.909601 | + | 0.415482i | \(0.863613\pi\) | |||||||
\(354\) | −82.5316 | − | 62.0436i | −0.233140 | − | 0.175264i | ||||
\(355\) | 194.681 | + | 194.681i | 0.548398 | + | 0.548398i | ||||
\(356\) | 224.860 | + | 217.791i | 0.631630 | + | 0.611773i | ||||
\(357\) | 126.455 | − | 73.3279i | 0.354216 | − | 0.205400i | ||||
\(358\) | 43.8164 | − | 18.5606i | 0.122392 | − | 0.0518452i | ||||
\(359\) | −305.954 | −0.852239 | −0.426119 | − | 0.904667i | \(-0.640120\pi\) | ||||
−0.426119 | + | 0.904667i | \(0.640120\pi\) | |||||||
\(360\) | 166.860 | + | 205.401i | 0.463499 | + | 0.570560i | ||||
\(361\) | 624.114i | 1.72885i | ||||||||
\(362\) | 89.0801 | − | 37.7342i | 0.246078 | − | 0.104238i | ||||
\(363\) | −203.324 | − | 350.636i | −0.560122 | − | 0.965939i | ||||
\(364\) | −30.8224 | + | 0.492234i | −0.0846769 | + | 0.00135229i | ||||
\(365\) | −9.02128 | + | 9.02128i | −0.0247158 | + | 0.0247158i | ||||
\(366\) | 187.054 | + | 140.619i | 0.511076 | + | 0.384205i | ||||
\(367\) | 221.149 | 0.602585 | 0.301292 | − | 0.953532i | \(-0.402582\pi\) | ||||
0.301292 | + | 0.953532i | \(0.402582\pi\) | |||||||
\(368\) | −10.9534 | − | 342.848i | −0.0297646 | − | 0.931653i | ||||
\(369\) | 67.3845 | − | 117.739i | 0.182614 | − | 0.319076i | ||||
\(370\) | −482.772 | − | 195.470i | −1.30479 | − | 0.528296i | ||||
\(371\) | −371.781 | + | 371.781i | −1.00211 | + | 1.00211i | ||||
\(372\) | 170.109 | + | 42.3396i | 0.457281 | + | 0.113816i | ||||
\(373\) | 147.216 | − | 147.216i | 0.394682 | − | 0.394682i | −0.481671 | − | 0.876352i | \(-0.659970\pi\) |
0.876352 | + | 0.481671i | \(0.159970\pi\) | |||||||
\(374\) | −196.709 | + | 83.3257i | −0.525960 | + | 0.222796i | ||||
\(375\) | −103.405 | + | 388.850i | −0.275746 | + | 1.03693i | ||||
\(376\) | −267.800 | + | 118.518i | −0.712233 | + | 0.315208i | ||||
\(377\) | 2.30317 | 0.00610919 | ||||||||
\(378\) | 366.233 | + | 145.872i | 0.968870 | + | 0.385906i | ||||
\(379\) | 298.572 | − | 298.572i | 0.787790 | − | 0.787790i | −0.193342 | − | 0.981131i | \(-0.561933\pi\) |
0.981131 | + | 0.193342i | \(0.0619326\pi\) | |||||||
\(380\) | −321.038 | + | 331.459i | −0.844837 | + | 0.872259i | ||||
\(381\) | 112.482 | − | 65.2252i | 0.295228 | − | 0.171195i | ||||
\(382\) | 112.708 | − | 278.368i | 0.295048 | − | 0.728712i | ||||
\(383\) | − | 427.326i | − | 1.11573i | −0.829931 | − | 0.557866i | \(-0.811620\pi\) | ||
0.829931 | − | 0.557866i | \(-0.188380\pi\) | |||||||
\(384\) | 215.781 | − | 317.639i | 0.561931 | − | 0.827184i | ||||
\(385\) | −429.404 | −1.11533 | ||||||||
\(386\) | 218.077 | + | 88.2971i | 0.564966 | + | 0.228749i | ||||
\(387\) | −88.0716 | − | 323.787i | −0.227575 | − | 0.836658i | ||||
\(388\) | −176.891 | − | 171.330i | −0.455904 | − | 0.441572i | ||||
\(389\) | 314.075 | + | 314.075i | 0.807391 | + | 0.807391i | 0.984238 | − | 0.176847i | \(-0.0565899\pi\) |
−0.176847 | + | 0.984238i | \(0.556590\pi\) | |||||||
\(390\) | 3.26645 | + | 23.0500i | 0.00837552 | + | 0.0591027i | ||||
\(391\) | 143.095i | 0.365971i | ||||||||
\(392\) | −13.9023 | − | 31.4131i | −0.0354650 | − | 0.0801355i | ||||
\(393\) | 1.32382 | − | 4.97816i | 0.00336849 | − | 0.0126671i | ||||
\(394\) | −35.1403 | − | 82.9565i | −0.0891886 | − | 0.210550i | ||||
\(395\) | 268.898 | + | 268.898i | 0.680753 | + | 0.680753i | ||||
\(396\) | −504.527 | − | 278.152i | −1.27406 | − | 0.702403i | ||||
\(397\) | 189.839 | + | 189.839i | 0.478185 | + | 0.478185i | 0.904551 | − | 0.426366i | \(-0.140206\pi\) |
−0.426366 | + | 0.904551i | \(0.640206\pi\) | |||||||
\(398\) | 96.3358 | − | 237.931i | 0.242050 | − | 0.597816i | ||||
\(399\) | −176.655 | + | 664.304i | −0.442743 | + | 1.66492i | ||||
\(400\) | 183.758 | − | 5.87075i | 0.459396 | − | 0.0146769i | ||||
\(401\) | 268.223i | 0.668886i | 0.942416 | + | 0.334443i | \(0.108548\pi\) | ||||
−0.942416 | + | 0.334443i | \(0.891452\pi\) | |||||||
\(402\) | 32.8418 | + | 24.6890i | 0.0816961 | + | 0.0614155i | ||||
\(403\) | 10.9045 | + | 10.9045i | 0.0270582 | + | 0.0270582i | ||||
\(404\) | 5.14579 | + | 322.216i | 0.0127371 | + | 0.797563i | ||||
\(405\) | 74.8780 | − | 288.145i | 0.184884 | − | 0.711469i | ||||
\(406\) | 12.4248 | + | 29.3315i | 0.0306030 | + | 0.0722451i | ||||
\(407\) | 1133.89 | 2.78598 | ||||||||
\(408\) | −94.2001 | + | 129.564i | −0.230883 | + | 0.317558i | ||||
\(409\) | 25.8478i | 0.0631976i | 0.999501 | + | 0.0315988i | \(0.0100599\pi\) | ||||
−0.999501 | + | 0.0315988i | \(0.989940\pi\) | |||||||
\(410\) | 43.2182 | + | 102.026i | 0.105410 | + | 0.248844i | ||||
\(411\) | −618.257 | + | 358.510i | −1.50427 | + | 0.872288i | ||||
\(412\) | −428.411 | + | 442.317i | −1.03983 | + | 1.07358i | ||||
\(413\) | 88.8319 | − | 88.8319i | 0.215089 | − | 0.215089i | ||||
\(414\) | −303.371 | + | 238.507i | −0.732780 | + | 0.576104i | ||||
\(415\) | 164.906 | 0.397365 | ||||||||
\(416\) | 30.6688 | − | 14.1627i | 0.0737230 | − | 0.0340450i | ||||
\(417\) | 28.9705 | − | 108.942i | 0.0694735 | − | 0.261253i | ||||
\(418\) | 377.014 | − | 931.151i | 0.901946 | − | 2.22763i | ||||
\(419\) | −243.361 | + | 243.361i | −0.580813 | + | 0.580813i | −0.935127 | − | 0.354313i | \(-0.884715\pi\) |
0.354313 | + | 0.935127i | \(0.384715\pi\) | |||||||
\(420\) | −275.928 | + | 165.947i | −0.656971 | + | 0.395111i | ||||
\(421\) | 115.847 | − | 115.847i | 0.275171 | − | 0.275171i | −0.556007 | − | 0.831178i | \(-0.687667\pi\) |
0.831178 | + | 0.556007i | \(0.187667\pi\) | |||||||
\(422\) | 86.9388 | + | 205.238i | 0.206016 | + | 0.486347i | ||||
\(423\) | 285.942 | + | 163.650i | 0.675985 | + | 0.386880i | ||||
\(424\) | 207.679 | − | 537.443i | 0.489810 | − | 1.26755i | ||||
\(425\) | −76.6953 | −0.180460 | ||||||||
\(426\) | −444.997 | + | 63.0612i | −1.04459 | + | 0.148031i | ||||
\(427\) | −201.333 | + | 201.333i | −0.471507 | + | 0.471507i | ||||
\(428\) | −6.94937 | − | 435.151i | −0.0162369 | − | 1.01671i | ||||
\(429\) | −25.4240 | − | 43.8440i | −0.0592634 | − | 0.102201i | ||||
\(430\) | 254.037 | + | 102.857i | 0.590784 | + | 0.239202i | ||||
\(431\) | − | 568.037i | − | 1.31795i | −0.752165 | − | 0.658975i | \(-0.770990\pi\) | ||
0.752165 | − | 0.658975i | \(-0.229010\pi\) | |||||||
\(432\) | −431.695 | + | 16.2426i | −0.999293 | + | 0.0375987i | ||||
\(433\) | −647.222 | −1.49474 | −0.747370 | − | 0.664408i | \(-0.768684\pi\) | ||||
−0.747370 | + | 0.664408i | \(0.768684\pi\) | |||||||
\(434\) | −80.0458 | + | 197.698i | −0.184437 | + | 0.455525i | ||||
\(435\) | 20.8111 | − | 12.0678i | 0.0478416 | − | 0.0277421i | ||||
\(436\) | 6.69579 | + | 419.273i | 0.0153573 | + | 0.961635i | ||||
\(437\) | −475.808 | − | 475.808i | −1.08881 | − | 1.08881i | ||||
\(438\) | −2.92218 | − | 20.6206i | −0.00667163 | − | 0.0470790i | ||||
\(439\) | 486.389i | 1.10795i | 0.832534 | + | 0.553973i | \(0.186889\pi\) | ||||
−0.832534 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(440\) | 430.305 | − | 190.437i | 0.977965 | − | 0.432811i | ||||
\(441\) | −19.1963 | + | 33.5412i | −0.0435291 | + | 0.0760571i | ||||
\(442\) | −12.9758 | + | 5.49655i | −0.0293571 | + | 0.0124356i | ||||
\(443\) | −258.469 | − | 258.469i | −0.583451 | − | 0.583451i | 0.352399 | − | 0.935850i | \(-0.385366\pi\) |
−0.935850 | + | 0.352399i | \(0.885366\pi\) | |||||||
\(444\) | 728.622 | − | 438.202i | 1.64104 | − | 0.986942i | ||||
\(445\) | 203.396 | + | 203.396i | 0.457070 | + | 0.457070i | ||||
\(446\) | −285.020 | − | 115.402i | −0.639059 | − | 0.258749i | ||||
\(447\) | 546.360 | + | 145.290i | 1.22228 | + | 0.325035i | ||||
\(448\) | 345.814 | + | 314.173i | 0.771907 | + | 0.701279i | ||||
\(449\) | − | 498.015i | − | 1.10916i | −0.832129 | − | 0.554582i | \(-0.812878\pi\) | ||
0.832129 | − | 0.554582i | \(-0.187122\pi\) | |||||||
\(450\) | −127.834 | − | 162.600i | −0.284076 | − | 0.361332i | ||||
\(451\) | −170.569 | − | 170.569i | −0.378201 | − | 0.378201i | ||||
\(452\) | −106.838 | + | 110.306i | −0.236368 | + | 0.244040i | ||||
\(453\) | −35.1721 | − | 60.6549i | −0.0776427 | − | 0.133896i | ||||
\(454\) | 113.687 | − | 48.1576i | 0.250411 | − | 0.106074i | ||||
\(455\) | −28.3255 | −0.0622538 | ||||||||
\(456\) | −117.588 | − | 744.042i | −0.257868 | − | 1.63167i | ||||
\(457\) | 466.468i | 1.02072i | 0.859961 | + | 0.510359i | \(0.170487\pi\) | ||||
−0.859961 | + | 0.510359i | \(0.829513\pi\) | |||||||
\(458\) | −291.384 | + | 123.430i | −0.636210 | + | 0.269498i | ||||
\(459\) | 180.209 | − | 1.02185i | 0.392613 | − | 0.00222624i | ||||
\(460\) | −5.03302 | − | 315.155i | −0.0109414 | − | 0.685119i | ||||
\(461\) | −389.251 | + | 389.251i | −0.844362 | + | 0.844362i | −0.989423 | − | 0.145061i | \(-0.953662\pi\) |
0.145061 | + | 0.989423i | \(0.453662\pi\) | |||||||
\(462\) | 421.213 | − | 560.306i | 0.911718 | − | 1.21278i | ||||
\(463\) | 500.857 | 1.08177 | 0.540883 | − | 0.841098i | \(-0.318090\pi\) | ||||
0.540883 | + | 0.841098i | \(0.318090\pi\) | |||||||
\(464\) | −25.4592 | − | 23.8828i | −0.0548689 | − | 0.0514715i | ||||
\(465\) | 155.667 | + | 41.3957i | 0.334768 | + | 0.0890229i | ||||
\(466\) | 60.2104 | + | 24.3786i | 0.129207 | + | 0.0523146i | ||||
\(467\) | 188.836 | − | 188.836i | 0.404359 | − | 0.404359i | −0.475407 | − | 0.879766i | \(-0.657699\pi\) |
0.879766 | + | 0.475407i | \(0.157699\pi\) | |||||||
\(468\) | −33.2809 | − | 18.3482i | −0.0711131 | − | 0.0392055i | ||||
\(469\) | −35.3489 | + | 35.3489i | −0.0753709 | + | 0.0753709i | ||||
\(470\) | −247.781 | + | 104.960i | −0.527195 | + | 0.223319i | ||||
\(471\) | 393.113 | + | 104.538i | 0.834636 | + | 0.221950i | ||||
\(472\) | −49.6221 | + | 128.415i | −0.105132 | + | 0.272065i | ||||
\(473\) | −596.660 | −1.26144 | ||||||||
\(474\) | −614.639 | + | 87.1014i | −1.29671 | + | 0.183758i | ||||
\(475\) | 255.022 | − | 255.022i | 0.536888 | − | 0.536888i | ||||
\(476\) | −140.001 | − | 135.599i | −0.294119 | − | 0.284872i | ||||
\(477\) | −625.470 | + | 170.131i | −1.31126 | + | 0.356668i | ||||
\(478\) | −100.058 | + | 247.123i | −0.209325 | + | 0.516993i | ||||
\(479\) | 326.344i | 0.681303i | 0.940190 | + | 0.340652i | \(0.110648\pi\) | ||||
−0.940190 | + | 0.340652i | \(0.889352\pi\) | |||||||
\(480\) | 202.911 | − | 288.666i | 0.422731 | − | 0.601388i | ||||
\(481\) | 74.7969 | 0.155503 | ||||||||
\(482\) | 295.998 | + | 119.847i | 0.614104 | + | 0.248645i | ||||
\(483\) | −235.533 | − | 406.181i | −0.487647 | − | 0.840954i | ||||
\(484\) | −375.991 | + | 388.195i | −0.776841 | + | 0.802056i | ||||
\(485\) | −160.006 | − | 160.006i | −0.329909 | − | 0.329909i | ||||
\(486\) | 302.535 | + | 380.353i | 0.622500 | + | 0.782620i | ||||
\(487\) | − | 196.238i | − | 0.402952i | −0.979493 | − | 0.201476i | \(-0.935426\pi\) | ||
0.979493 | − | 0.201476i | \(-0.0645739\pi\) | |||||||
\(488\) | 112.466 | − | 291.045i | 0.230463 | − | 0.596405i | ||||
\(489\) | 423.871 | + | 112.718i | 0.866812 | + | 0.230506i | ||||
\(490\) | −12.3119 | − | 29.0650i | −0.0251263 | − | 0.0593162i | ||||
\(491\) | 349.172 | + | 349.172i | 0.711144 | + | 0.711144i | 0.966774 | − | 0.255631i | \(-0.0822831\pi\) |
−0.255631 | + | 0.966774i | \(0.582283\pi\) | |||||||
\(492\) | −175.523 | − | 43.6871i | −0.356753 | − | 0.0887949i | ||||
\(493\) | 10.2969 | + | 10.2969i | 0.0208863 | + | 0.0208863i | ||||
\(494\) | 24.8696 | − | 61.4230i | 0.0503433 | − | 0.124338i | ||||
\(495\) | −459.456 | − | 262.956i | −0.928193 | − | 0.531224i | ||||
\(496\) | −7.46348 | − | 233.612i | −0.0150473 | − | 0.470992i | ||||
\(497\) | − | 546.843i | − | 1.10029i | ||||||
\(498\) | −161.761 | + | 215.177i | −0.324821 | + | 0.432083i | ||||
\(499\) | −321.326 | − | 321.326i | −0.643940 | − | 0.643940i | 0.307582 | − | 0.951522i | \(-0.400480\pi\) |
−0.951522 | + | 0.307582i | \(0.900480\pi\) | |||||||
\(500\) | 536.418 | − | 8.56660i | 1.07284 | − | 0.0171332i | ||||
\(501\) | 295.805 | − | 171.530i | 0.590430 | − | 0.342374i | ||||
\(502\) | 117.725 | + | 277.917i | 0.234513 | + | 0.553619i | ||||
\(503\) | −623.698 | −1.23996 | −0.619978 | − | 0.784619i | \(-0.712858\pi\) | ||||
−0.619978 | + | 0.784619i | \(0.712858\pi\) | |||||||
\(504\) | 54.1302 | − | 522.825i | 0.107401 | − | 1.03735i | ||||
\(505\) | 296.113i | 0.586362i | ||||||||
\(506\) | 267.647 | + | 631.840i | 0.528947 | + | 1.24870i | ||||
\(507\) | 252.652 | + | 435.703i | 0.498328 | + | 0.859374i | ||||
\(508\) | −124.531 | − | 120.616i | −0.245139 | − | 0.237432i | ||||
\(509\) | 452.448 | − | 452.448i | 0.888897 | − | 0.888897i | −0.105520 | − | 0.994417i | \(-0.533651\pi\) |
0.994417 | + | 0.105520i | \(0.0336508\pi\) | |||||||
\(510\) | −88.4480 | + | 117.655i | −0.173427 | + | 0.230696i | ||||
\(511\) | 25.3400 | 0.0495891 | ||||||||
\(512\) | −485.873 | − | 161.466i | −0.948971 | − | 0.315364i | ||||
\(513\) | −595.821 | + | 602.616i | −1.16144 | + | 1.17469i | ||||
\(514\) | −258.065 | + | 637.370i | −0.502071 | + | 1.24002i | ||||
\(515\) | −400.095 | + | 400.095i | −0.776884 | + | 0.776884i | ||||
\(516\) | −383.404 | + | 230.584i | −0.743032 | + | 0.446869i | ||||
\(517\) | 414.244 | − | 414.244i | 0.801247 | − | 0.801247i | ||||
\(518\) | 403.504 | + | 952.562i | 0.778966 | + | 1.83892i | ||||
\(519\) | 157.296 | − | 591.506i | 0.303075 | − | 1.13970i | ||||
\(520\) | 28.3849 | − | 12.5621i | 0.0545863 | − | 0.0241579i | ||||
\(521\) | −444.986 | −0.854100 | −0.427050 | − | 0.904228i | \(-0.640447\pi\) | ||||
−0.427050 | + | 0.904228i | \(0.640447\pi\) | |||||||
\(522\) | −4.66753 | + | 38.9929i | −0.00894164 | + | 0.0746991i | ||||
\(523\) | 399.942 | − | 399.942i | 0.764707 | − | 0.764707i | −0.212462 | − | 0.977169i | \(-0.568148\pi\) |
0.977169 | + | 0.212462i | \(0.0681483\pi\) | |||||||
\(524\) | −6.86736 | + | 0.109672i | −0.0131056 | + | 0.000209297i | ||||
\(525\) | 217.703 | − | 126.240i | 0.414673 | − | 0.240458i | ||||
\(526\) | 493.586 | + | 199.848i | 0.938377 | + | 0.379939i | ||||
\(527\) | 97.5029i | 0.185015i | ||||||||
\(528\) | −173.606 | + | 748.286i | −0.328800 | + | 1.41721i | ||||
\(529\) | −69.3715 | −0.131137 | ||||||||
\(530\) | 198.692 | − | 490.732i | 0.374891 | − | 0.925909i | ||||
\(531\) | 149.447 | − | 40.6504i | 0.281445 | − | 0.0765544i | ||||
\(532\) | 916.404 | − | 14.6350i | 1.72256 | − | 0.0275094i | ||||
\(533\) | −11.2515 | − | 11.2515i | −0.0211098 | − | 0.0211098i | ||||
\(534\) | −464.918 | + | 65.8842i | −0.870633 | + | 0.123379i | ||||
\(535\) | − | 399.900i | − | 0.747476i | ||||||
\(536\) | 19.7462 | − | 51.1001i | 0.0368399 | − | 0.0953360i | ||||
\(537\) | −18.3437 | + | 68.9808i | −0.0341595 | + | 0.128456i | ||||
\(538\) | 266.154 | − | 112.743i | 0.494711 | − | 0.209559i | ||||
\(539\) | 48.5912 | + | 48.5912i | 0.0901506 | + | 0.0901506i | ||||
\(540\) | −396.860 | + | 8.58897i | −0.734926 | + | 0.0159055i | ||||
\(541\) | −116.940 | − | 116.940i | −0.216155 | − | 0.216155i | 0.590721 | − | 0.806876i | \(-0.298844\pi\) |
−0.806876 | + | 0.590721i | \(0.798844\pi\) | |||||||
\(542\) | −71.4895 | − | 28.9454i | −0.131900 | − | 0.0534048i | ||||
\(543\) | −37.2932 | + | 140.240i | −0.0686800 | + | 0.258269i | ||||
\(544\) | 200.432 | + | 73.7947i | 0.368440 | + | 0.135652i | ||||
\(545\) | 385.308i | 0.706987i | ||||||||
\(546\) | 27.7852 | − | 36.9604i | 0.0508886 | − | 0.0676930i | ||||
\(547\) | 85.6914 | + | 85.6914i | 0.156657 | + | 0.156657i | 0.781084 | − | 0.624427i | \(-0.214667\pi\) |
−0.624427 | + | 0.781084i | \(0.714667\pi\) | |||||||
\(548\) | 684.483 | + | 662.964i | 1.24906 | + | 1.20979i | ||||
\(549\) | −338.715 | + | 92.1322i | −0.616968 | + | 0.167818i | ||||
\(550\) | −338.651 | + | 143.452i | −0.615729 | + | 0.260822i | ||||
\(551\) | −68.4772 | −0.124278 | ||||||||
\(552\) | 416.165 | + | 302.576i | 0.753923 | + | 0.548145i | ||||
\(553\) | − | 755.311i | − | 1.36584i | ||||||
\(554\) | −722.216 | + | 305.930i | −1.30364 | + | 0.552220i | ||||
\(555\) | 675.855 | − | 391.910i | 1.21776 | − | 0.706145i | ||||
\(556\) | −150.286 | + | 2.40006i | −0.270298 | + | 0.00431666i | ||||
\(557\) | 104.194 | − | 104.194i | 0.187062 | − | 0.187062i | −0.607363 | − | 0.794425i | \(-0.707772\pi\) |
0.794425 | + | 0.607363i | \(0.207772\pi\) | |||||||
\(558\) | −206.713 | + | 162.516i | −0.370453 | + | 0.291246i | ||||
\(559\) | −39.3585 | −0.0704087 | ||||||||
\(560\) | 313.109 | + | 293.722i | 0.559124 | + | 0.524504i | ||||
\(561\) | 82.3519 | − | 309.682i | 0.146795 | − | 0.552017i | ||||
\(562\) | −850.464 | − | 344.344i | −1.51328 | − | 0.612712i | ||||
\(563\) | 776.673 | − | 776.673i | 1.37953 | − | 1.37953i | 0.534111 | − | 0.845414i | \(-0.320646\pi\) |
0.845414 | − | 0.534111i | \(-0.179354\pi\) | |||||||
\(564\) | 106.099 | − | 426.275i | 0.188118 | − | 0.755807i | ||||
\(565\) | −99.7766 | + | 99.7766i | −0.176596 | + | 0.176596i | ||||
\(566\) | 720.756 | − | 305.312i | 1.27342 | − | 0.539420i | ||||
\(567\) | −509.850 | + | 299.524i | −0.899207 | + | 0.528261i | ||||
\(568\) | 242.520 | + | 547.990i | 0.426972 | + | 0.964772i | ||||
\(569\) | 456.546 | 0.802366 | 0.401183 | − | 0.915998i | \(-0.368599\pi\) | ||||
0.401183 | + | 0.915998i | \(0.368599\pi\) | |||||||
\(570\) | −97.1175 | − | 685.318i | −0.170382 | − | 1.20231i | ||||
\(571\) | −475.108 | + | 475.108i | −0.832062 | + | 0.832062i | −0.987799 | − | 0.155736i | \(-0.950225\pi\) |
0.155736 | + | 0.987799i | \(0.450225\pi\) | |||||||
\(572\) | −47.0145 | + | 48.5405i | −0.0821931 | + | 0.0848610i | ||||
\(573\) | 225.977 | + | 389.700i | 0.394375 | + | 0.680105i | ||||
\(574\) | 82.5934 | − | 203.990i | 0.143891 | − | 0.355383i | ||||
\(575\) | 246.350i | 0.428434i | ||||||||
\(576\) | 177.625 | + | 547.928i | 0.308376 | + | 0.951264i | ||||
\(577\) | 1127.70 | 1.95443 | 0.977213 | − | 0.212262i | \(-0.0680832\pi\) | ||||
0.977213 | + | 0.212262i | \(0.0680832\pi\) | |||||||
\(578\) | 453.165 | + | 183.482i | 0.784023 | + | 0.317443i | ||||
\(579\) | −305.296 | + | 177.033i | −0.527281 | + | 0.305756i | ||||
\(580\) | −23.0403 | − | 22.3160i | −0.0397247 | − | 0.0384758i | ||||
\(581\) | −231.604 | − | 231.604i | −0.398630 | − | 0.398630i | ||||
\(582\) | 365.737 | − | 51.8291i | 0.628414 | − | 0.0890534i | ||||
\(583\) | 1152.59i | 1.97700i | ||||||||
\(584\) | −25.3932 | + | 11.2381i | −0.0434815 | + | 0.0192433i | ||||
\(585\) | −30.3078 | − | 17.3458i | −0.0518082 | − | 0.0296509i | ||||
\(586\) | 338.152 | + | 798.284i | 0.577051 | + | 1.36226i | ||||
\(587\) | −584.236 | − | 584.236i | −0.995292 | − | 0.995292i | 0.00469688 | − | 0.999989i | \(-0.498505\pi\) |
−0.999989 | + | 0.00469688i | \(0.998505\pi\) | |||||||
\(588\) | 50.0024 | + | 12.4455i | 0.0850381 | + | 0.0211657i | ||||
\(589\) | −324.209 | − | 324.209i | −0.550440 | − | 0.550440i | ||||
\(590\) | −47.4748 | + | 117.254i | −0.0804657 | + | 0.198735i | ||||
\(591\) | 130.600 | + | 34.7296i | 0.220981 | + | 0.0587642i | ||||
\(592\) | −826.804 | − | 775.610i | −1.39663 | − | 1.31015i | ||||
\(593\) | 870.906i | 1.46864i | 0.678801 | + | 0.734322i | \(0.262500\pi\) | ||||
−0.678801 | + | 0.734322i | \(0.737500\pi\) | |||||||
\(594\) | 793.810 | − | 341.579i | 1.33638 | − | 0.575048i | ||||
\(595\) | −126.637 | − | 126.637i | −0.212835 | − | 0.212835i | ||||
\(596\) | −12.0366 | − | 753.702i | −0.0201957 | − | 1.26460i | ||||
\(597\) | 193.150 | + | 333.090i | 0.323535 | + | 0.557940i | ||||
\(598\) | 17.6552 | + | 41.6791i | 0.0295238 | + | 0.0696975i | ||||
\(599\) | 224.305 | 0.374466 | 0.187233 | − | 0.982316i | \(-0.440048\pi\) | ||||
0.187233 | + | 0.982316i | \(0.440048\pi\) | |||||||
\(600\) | −162.174 | + | 223.055i | −0.270289 | + | 0.371758i | ||||
\(601\) | − | 234.358i | − | 0.389946i | −0.980809 | − | 0.194973i | \(-0.937538\pi\) | ||
0.980809 | − | 0.194973i | \(-0.0624620\pi\) | |||||||
\(602\) | −212.326 | − | 501.243i | −0.352701 | − | 0.832629i | ||||
\(603\) | −59.4697 | + | 16.1760i | −0.0986230 | + | 0.0268259i | ||||
\(604\) | −65.0410 | + | 67.1521i | −0.107684 | + | 0.111179i | ||||
\(605\) | −351.140 | + | 351.140i | −0.580396 | + | 0.580396i | ||||
\(606\) | −386.382 | − | 290.465i | −0.637594 | − | 0.479315i | ||||
\(607\) | −620.755 | −1.02266 | −0.511330 | − | 0.859384i | \(-0.670847\pi\) | ||||
−0.511330 | + | 0.859384i | \(0.670847\pi\) | |||||||
\(608\) | −911.837 | + | 421.083i | −1.49973 | + | 0.692571i | ||||
\(609\) | −46.1770 | − | 12.2796i | −0.0758244 | − | 0.0201635i | ||||
\(610\) | 107.599 | − | 265.750i | 0.176392 | − | 0.435655i | ||||
\(611\) | 27.3255 | − | 27.3255i | 0.0447226 | − | 0.0447226i | ||||
\(612\) | −66.7610 | − | 230.822i | −0.109087 | − | 0.377160i | ||||
\(613\) | −645.945 | + | 645.945i | −1.05374 | + | 1.05374i | −0.0552724 | + | 0.998471i | \(0.517603\pi\) |
−0.998471 | + | 0.0552724i | \(0.982397\pi\) | |||||||
\(614\) | −396.820 | − | 936.781i | −0.646286 | − | 1.52570i | ||||
\(615\) | −160.621 | − | 42.7131i | −0.261173 | − | 0.0694523i | ||||
\(616\) | −871.805 | − | 336.884i | −1.41527 | − | 0.546890i | ||||
\(617\) | 169.883 | 0.275337 | 0.137669 | − | 0.990478i | \(-0.456039\pi\) | ||||
0.137669 | + | 0.990478i | \(0.456039\pi\) | |||||||
\(618\) | −129.599 | − | 914.527i | −0.209707 | − | 1.47982i | ||||
\(619\) | −647.603 | + | 647.603i | −1.04621 | + | 1.04621i | −0.0473286 | + | 0.998879i | \(0.515071\pi\) |
−0.998879 | + | 0.0473286i | \(0.984929\pi\) | |||||||
\(620\) | −3.42943 | − | 214.742i | −0.00553134 | − | 0.346358i | ||||
\(621\) | −3.28222 | − | 578.842i | −0.00528539 | − | 0.932113i | ||||
\(622\) | −1060.39 | − | 429.343i | −1.70481 | − | 0.690262i | ||||
\(623\) | − | 571.323i | − | 0.917051i | ||||||
\(624\) | −11.4519 | + | 49.3605i | −0.0183524 | + | 0.0791033i | ||||
\(625\) | 205.694 | 0.329110 | ||||||||
\(626\) | 250.182 | − | 617.901i | 0.399652 | − | 0.987062i | ||||
\(627\) | 755.900 | + | 1303.56i | 1.20558 | + | 2.07904i | ||||
\(628\) | −8.66051 | − | 542.298i | −0.0137906 | − | 0.863533i | ||||
\(629\) | 334.400 | + | 334.400i | 0.531638 | + | 0.531638i | ||||
\(630\) | 57.4036 | − | 479.554i | 0.0911169 | − | 0.761197i | ||||
\(631\) | − | 975.374i | − | 1.54576i | −0.634553 | − | 0.772880i | \(-0.718816\pi\) | ||
0.634553 | − | 0.772880i | \(-0.281184\pi\) | |||||||
\(632\) | 334.974 | + | 756.895i | 0.530022 | + | 1.19762i | ||||
\(633\) | −323.110 | − | 85.9228i | −0.510442 | − | 0.135739i | ||||
\(634\) | 693.766 | − | 293.879i | 1.09427 | − | 0.463531i | ||||
\(635\) | −112.643 | − | 112.643i | −0.177391 | − | 0.177391i | ||||
\(636\) | 445.427 | + | 740.635i | 0.700357 | + | 1.16452i | ||||
\(637\) | 3.20530 | + | 3.20530i | 0.00503187 | + | 0.00503187i | ||||
\(638\) | 64.7261 | + | 26.2069i | 0.101452 | + | 0.0410767i | ||||
\(639\) | 334.873 | − | 585.114i | 0.524058 | − | 0.915671i | ||||
\(640\) | −444.030 | − | 155.477i | −0.693796 | − | 0.242933i | ||||
\(641\) | − | 771.555i | − | 1.20367i | −0.798619 | − | 0.601837i | \(-0.794436\pi\) | ||
0.798619 | − | 0.601837i | \(-0.205564\pi\) | |||||||
\(642\) | 521.808 | + | 392.272i | 0.812785 | + | 0.611016i | ||||
\(643\) | 319.214 | + | 319.214i | 0.496445 | + | 0.496445i | 0.910330 | − | 0.413884i | \(-0.135828\pi\) |
−0.413884 | + | 0.910330i | \(0.635828\pi\) | |||||||
\(644\) | −435.553 | + | 449.690i | −0.676324 | + | 0.698276i | ||||
\(645\) | −355.638 | + | 206.225i | −0.551377 | + | 0.319729i | ||||
\(646\) | 385.795 | − | 163.422i | 0.597206 | − | 0.252976i | ||||
\(647\) | −360.720 | −0.557527 | −0.278764 | − | 0.960360i | \(-0.589925\pi\) | ||||
−0.278764 | + | 0.960360i | \(0.589925\pi\) | |||||||
\(648\) | 378.083 | − | 526.267i | 0.583462 | − | 0.812140i | ||||
\(649\) | − | 275.395i | − | 0.424338i | ||||||
\(650\) | −22.3390 | + | 9.46278i | −0.0343677 | + | 0.0145581i | ||||
\(651\) | −160.489 | − | 276.766i | −0.246527 | − | 0.425140i | ||||
\(652\) | −9.33812 | − | 584.728i | −0.0143223 | − | 0.896822i | ||||
\(653\) | 415.043 | − | 415.043i | 0.635595 | − | 0.635595i | −0.313871 | − | 0.949466i | \(-0.601626\pi\) |
0.949466 | + | 0.313871i | \(0.101626\pi\) | |||||||
\(654\) | −502.768 | − | 377.959i | −0.768758 | − | 0.577918i | ||||
\(655\) | −6.31104 | −0.00963517 | ||||||||
\(656\) | 7.70102 | + | 241.047i | 0.0117394 | + | 0.367450i | ||||
\(657\) | 27.1134 | + | 15.5176i | 0.0412685 | + | 0.0236189i | ||||
\(658\) | 495.410 | + | 200.587i | 0.752903 | + | 0.304843i | ||||
\(659\) | −363.535 | + | 363.535i | −0.551646 | + | 0.551646i | −0.926916 | − | 0.375269i | \(-0.877550\pi\) |
0.375269 | + | 0.926916i | \(0.377550\pi\) | |||||||
\(660\) | −170.481 | + | 684.945i | −0.258305 | + | 1.03780i | ||||
\(661\) | −151.997 | + | 151.997i | −0.229951 | + | 0.229951i | −0.812672 | − | 0.582721i | \(-0.801988\pi\) |
0.582721 | + | 0.812672i | \(0.301988\pi\) | |||||||
\(662\) | −553.257 | + | 234.359i | −0.835735 | + | 0.354017i | ||||
\(663\) | 5.43232 | − | 20.4280i | 0.00819354 | − | 0.0308115i | ||||
\(664\) | 334.804 | + | 129.376i | 0.504223 | + | 0.194843i | ||||
\(665\) | 842.166 | 1.26642 | ||||||||
\(666\) | −151.581 | + | 1266.32i | −0.227600 | + | 1.90139i | ||||
\(667\) | 33.0743 | − | 33.0743i | 0.0495867 | − | 0.0495867i | ||||
\(668\) | −327.491 | − | 317.195i | −0.490256 | − | 0.474843i | ||||
\(669\) | 399.013 | − | 231.377i | 0.596433 | − | 0.345855i | ||||
\(670\) | 18.8917 | − | 46.6588i | 0.0281965 | − | 0.0696400i | ||||
\(671\) | 624.170i | 0.930208i | ||||||||
\(672\) | −690.400 | + | 120.440i | −1.02738 | + | 0.179226i | ||||
\(673\) | −271.149 | −0.402896 | −0.201448 | − | 0.979499i | \(-0.564565\pi\) | ||||
−0.201448 | + | 0.979499i | \(0.564565\pi\) | |||||||
\(674\) | −384.622 | − | 155.730i | −0.570656 | − | 0.231053i | ||||
\(675\) | 310.245 | − | 1.75919i | 0.459623 | − | 0.00260621i | ||||
\(676\) | 467.209 | − | 482.374i | 0.691138 | − | 0.713571i | ||||
\(677\) | 639.750 | + | 639.750i | 0.944978 | + | 0.944978i | 0.998563 | − | 0.0535849i | \(-0.0170648\pi\) |
−0.0535849 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(678\) | −32.3197 | − | 228.067i | −0.0476691 | − | 0.336382i | ||||
\(679\) | 449.442i | 0.661918i | ||||||||
\(680\) | 183.065 | + | 70.7402i | 0.269213 | + | 0.104030i | ||||
\(681\) | −47.5948 | + | 178.979i | −0.0698895 | + | 0.262817i | ||||
\(682\) | 182.371 | + | 430.528i | 0.267406 | + | 0.631272i | ||||
\(683\) | −93.1730 | − | 93.1730i | −0.136417 | − | 0.136417i | 0.635601 | − | 0.772018i | \(-0.280752\pi\) |
−0.772018 | + | 0.635601i | \(0.780752\pi\) | |||||||
\(684\) | 989.501 | + | 545.524i | 1.44664 | + | 0.797549i | ||||
\(685\) | 619.145 | + | 619.145i | 0.903861 | + | 0.903861i | ||||
\(686\) | 244.967 | − | 605.021i | 0.357095 | − | 0.881955i | ||||
\(687\) | 121.988 | − | 458.731i | 0.177566 | − | 0.667730i | ||||
\(688\) | 435.068 | + | 408.130i | 0.632367 | + | 0.593212i | ||||
\(689\) | 76.0301i | 0.110348i | ||||||||
\(690\) | 377.915 | + | 284.100i | 0.547703 | + | 0.411739i | ||||
\(691\) | 303.844 | + | 303.844i | 0.439716 | + | 0.439716i | 0.891916 | − | 0.452200i | \(-0.149361\pi\) |
−0.452200 | + | 0.891916i | \(0.649361\pi\) | |||||||
\(692\) | −815.981 | + | 13.0312i | −1.17916 | + | 0.0188313i | ||||
\(693\) | 275.975 | + | 1014.60i | 0.398233 | + | 1.46406i | ||||
\(694\) | 108.633 | + | 256.453i | 0.156532 | + | 0.369529i | ||||
\(695\) | −138.111 | −0.198721 | ||||||||
\(696\) | 51.7198 | − | 8.17376i | 0.0743101 | − | 0.0117439i | ||||
\(697\) | − | 100.606i | − | 0.144341i | ||||||
\(698\) | −372.207 | − | 878.678i | −0.533248 | − | 1.25885i | ||||
\(699\) | −84.2914 | + | 48.8783i | −0.120589 | + | 0.0699261i | ||||
\(700\) | −241.023 | − | 233.446i | −0.344318 | − | 0.333494i | ||||
\(701\) | −797.170 | + | 797.170i | −1.13719 | + | 1.13719i | −0.148238 | + | 0.988952i | \(0.547360\pi\) |
−0.988952 | + | 0.148238i | \(0.952640\pi\) | |||||||
\(702\) | 52.3634 | − | 22.5321i | 0.0745917 | − | 0.0320970i | ||||
\(703\) | −2223.85 | −3.16336 | ||||||||
\(704\) | 1023.04 | − | 49.0472i | 1.45318 | − | 0.0696694i | ||||
\(705\) | 103.733 | − | 390.086i | 0.147140 | − | 0.553313i | ||||
\(706\) | −220.171 | + | 543.779i | −0.311857 | + | 0.770226i | ||||
\(707\) | 415.878 | − | 415.878i | 0.588229 | − | 0.588229i | ||||
\(708\) | −106.429 | − | 176.964i | −0.150323 | − | 0.249950i | ||||
\(709\) | 592.848 | − | 592.848i | 0.836176 | − | 0.836176i | −0.152178 | − | 0.988353i | \(-0.548629\pi\) |
0.988353 | + | 0.152178i | \(0.0486286\pi\) | |||||||
\(710\) | 214.776 | + | 507.028i | 0.302502 | + | 0.714123i | ||||
\(711\) | 462.533 | − | 808.171i | 0.650539 | − | 1.13667i | ||||
\(712\) | 253.377 | + | 572.522i | 0.355866 | + | 0.804104i | ||||
\(713\) | 313.185 | 0.439249 | ||||||||
\(714\) | 289.463 | − | 41.0202i | 0.405410 | − | 0.0574513i | ||||
\(715\) | −43.9070 | + | 43.9070i | −0.0614084 | + | 0.0614084i | ||||
\(716\) | 95.1587 | − | 1.51969i | 0.132903 | − | 0.00212247i | ||||
\(717\) | −200.612 | − | 345.959i | −0.279794 | − | 0.482508i | ||||
\(718\) | −567.180 | − | 229.646i | −0.789945 | − | 0.319841i | ||||
\(719\) | 1252.89i | 1.74255i | 0.490799 | + | 0.871273i | \(0.336705\pi\) | ||||
−0.490799 | + | 0.871273i | \(0.663295\pi\) | |||||||
\(720\) | 155.154 | + | 506.019i | 0.215492 | + | 0.702804i | ||||
\(721\) | 1123.83 | 1.55872 | ||||||||
\(722\) | −468.454 | + | 1156.99i | −0.648828 | + | 1.60248i | ||||
\(723\) | −414.382 | + | 240.289i | −0.573142 | + | 0.332350i | ||||
\(724\) | 193.461 | − | 3.08957i | 0.267211 | − | 0.00426736i | ||||
\(725\) | 17.7270 | + | 17.7270i | 0.0244511 | + | 0.0244511i | ||||
\(726\) | −113.741 | − | 802.626i | −0.156668 | − | 1.10555i | ||||
\(727\) | − | 1182.91i | − | 1.62711i | −0.581490 | − | 0.813553i | \(-0.697530\pi\) | ||
0.581490 | − | 0.813553i | \(-0.302470\pi\) | |||||||
\(728\) | −57.5083 | − | 22.2224i | −0.0789950 | − | 0.0305253i | ||||
\(729\) | −728.953 | + | 8.26707i | −0.999936 | + | 0.0113403i | ||||
\(730\) | −23.4950 | + | 9.95247i | −0.0321850 | + | 0.0136335i | ||||
\(731\) | −175.963 | − | 175.963i | −0.240715 | − | 0.240715i | ||||
\(732\) | 241.215 | + | 401.081i | 0.329529 | + | 0.547925i | ||||
\(733\) | 679.023 | + | 679.023i | 0.926361 | + | 0.926361i | 0.997469 | − | 0.0711072i | \(-0.0226532\pi\) |
−0.0711072 | + | 0.997469i | \(0.522653\pi\) | |||||||
\(734\) | 409.968 | + | 165.992i | 0.558539 | + | 0.226147i | ||||
\(735\) | 45.7574 | + | 12.1680i | 0.0622549 | + | 0.0165551i | ||||
\(736\) | 237.033 | − | 643.797i | 0.322055 | − | 0.874725i | ||||
\(737\) | 109.588i | 0.148695i | ||||||||
\(738\) | 213.292 | − | 167.688i | 0.289013 | − | 0.227219i | ||||
\(739\) | 408.587 | + | 408.587i | 0.552892 | + | 0.552892i | 0.927274 | − | 0.374383i | \(-0.122145\pi\) |
−0.374383 | + | 0.927274i | \(0.622145\pi\) | |||||||
\(740\) | −748.251 | − | 724.727i | −1.01115 | − | 0.979361i | ||||
\(741\) | 49.8627 | + | 85.9889i | 0.0672911 | + | 0.116044i | ||||
\(742\) | −968.267 | + | 410.157i | −1.30494 | + | 0.552772i | ||||
\(743\) | 228.202 | 0.307137 | 0.153568 | − | 0.988138i | \(-0.450923\pi\) | ||||
0.153568 | + | 0.988138i | \(0.450923\pi\) | |||||||
\(744\) | 283.570 | + | 206.171i | 0.381142 | + | 0.277112i | ||||
\(745\) | − | 692.644i | − | 0.929724i | ||||||
\(746\) | 383.410 | − | 162.412i | 0.513955 | − | 0.217711i | ||||
\(747\) | −105.984 | − | 389.641i | −0.141880 | − | 0.521608i | ||||
\(748\) | −427.205 | + | 6.82247i | −0.571129 | + | 0.00912094i | ||||
\(749\) | −561.642 | + | 561.642i | −0.749856 | + | 0.749856i | ||||
\(750\) | −483.560 | + | 643.241i | −0.644747 | + | 0.857654i | ||||
\(751\) | 835.943 | 1.11311 | 0.556553 | − | 0.830812i | \(-0.312124\pi\) | ||||
0.556553 | + | 0.830812i | \(0.312124\pi\) | |||||||
\(752\) | −585.409 | + | 18.7027i | −0.778469 | + | 0.0248707i | ||||
\(753\) | −437.528 | − | 116.350i | −0.581047 | − | 0.154515i | ||||
\(754\) | 4.26963 | + | 1.72873i | 0.00566264 | + | 0.00229275i | ||||
\(755\) | −60.7421 | + | 60.7421i | −0.0804530 | + | 0.0804530i | ||||
\(756\) | 569.436 | + | 545.311i | 0.753222 | + | 0.721310i | ||||
\(757\) | 144.017 | − | 144.017i | 0.190247 | − | 0.190247i | −0.605556 | − | 0.795803i | \(-0.707049\pi\) |
0.795803 | + | 0.605556i | \(0.207049\pi\) | |||||||
\(758\) | 777.602 | − | 329.391i | 1.02586 | − | 0.434553i | ||||
\(759\) | −994.715 | − | 264.519i | −1.31056 | − | 0.348510i | ||||
\(760\) | −843.933 | + | 373.494i | −1.11044 | + | 0.491439i | ||||
\(761\) | 1238.49 | 1.62745 | 0.813727 | − | 0.581247i | \(-0.197435\pi\) | ||||
0.813727 | + | 0.581247i | \(0.197435\pi\) | |||||||
\(762\) | 257.477 | − | 36.4875i | 0.337897 | − | 0.0478839i | ||||
\(763\) | 541.148 | − | 541.148i | 0.709238 | − | 0.709238i | ||||
\(764\) | 417.880 | − | 431.444i | 0.546963 | − | 0.564717i | ||||
\(765\) | −57.9503 | − | 213.049i | −0.0757520 | − | 0.278495i | ||||
\(766\) | 320.746 | − | 792.181i | 0.418729 | − | 1.03418i | ||||
\(767\) | − | 18.1663i | − | 0.0236849i | ||||||
\(768\) | 638.434 | − | 426.879i | 0.831295 | − | 0.555832i | ||||
\(769\) | −906.729 | −1.17910 | −0.589551 | − | 0.807732i | \(-0.700695\pi\) | ||||
−0.589551 | + | 0.807732i | \(0.700695\pi\) | |||||||
\(770\) | −796.033 | − | 322.306i | −1.03381 | − | 0.418579i | ||||
\(771\) | −517.411 | − | 892.284i | −0.671091 | − | 1.15731i | ||||
\(772\) | 337.998 | + | 327.372i | 0.437822 | + | 0.424057i | ||||
\(773\) | −989.152 | − | 989.152i | −1.27963 | − | 1.27963i | −0.940876 | − | 0.338752i | \(-0.889995\pi\) |
−0.338752 | − | 0.940876i | \(-0.610005\pi\) | |||||||
\(774\) | 79.7629 | − | 666.345i | 0.103053 | − | 0.860911i | ||||
\(775\) | 167.859i | 0.216593i | ||||||||
\(776\) | −199.324 | − | 450.385i | −0.256861 | − | 0.580394i | ||||
\(777\) | −1499.63 | − | 398.789i | −1.93003 | − | 0.513241i | ||||
\(778\) | 346.494 | + | 817.977i | 0.445366 | + | 1.05138i | ||||
\(779\) | 334.528 | + | 334.528i | 0.429432 | + | 0.429432i | ||||
\(780\) | −11.2457 | + | 45.1822i | −0.0144176 | + | 0.0579259i | ||||
\(781\) | −847.656 | − | 847.656i | −1.08535 | − | 1.08535i | ||||
\(782\) | −107.405 | + | 265.271i | −0.137347 | + | 0.339221i | ||||
\(783\) | −41.8890 | − | 41.4166i | −0.0534981 | − | 0.0528948i | ||||
\(784\) | −2.19385 | − | 68.6689i | −0.00279827 | − | 0.0875878i | ||||
\(785\) | − | 498.367i | − | 0.634862i | ||||||
\(786\) | 6.19066 | − | 8.23494i | 0.00787616 | − | 0.0104770i | ||||
\(787\) | 100.012 | + | 100.012i | 0.127080 | + | 0.127080i | 0.767786 | − | 0.640706i | \(-0.221358\pi\) |
−0.640706 | + | 0.767786i | \(0.721358\pi\) | |||||||
\(788\) | −2.87718 | − | 180.162i | −0.00365125 | − | 0.228632i | ||||
\(789\) | −690.994 | + | 400.689i | −0.875785 | + | 0.507844i | ||||
\(790\) | 296.654 | + | 700.317i | 0.375511 | + | 0.886477i | ||||
\(791\) | 280.264 | 0.354316 | ||||||||
\(792\) | −726.519 | − | 894.333i | −0.917322 | − | 1.12921i | ||||
\(793\) | 41.1731i | 0.0519207i | ||||||||
\(794\) | 209.435 | + | 494.418i | 0.263772 | + | 0.622692i | ||||
\(795\) | 398.372 | + | 686.998i | 0.501097 | + | 0.864149i | ||||
\(796\) | 357.177 | − | 368.770i | 0.448714 | − | 0.463279i | ||||
\(797\) | 264.491 | − | 264.491i | 0.331858 | − | 0.331858i | −0.521433 | − | 0.853292i | \(-0.674603\pi\) |
0.853292 | + | 0.521433i | \(0.174603\pi\) | |||||||
\(798\) | −826.103 | + | 1098.90i | −1.03522 | + | 1.37707i | ||||
\(799\) | 244.332 | 0.305798 | ||||||||
\(800\) | 345.060 | + | 127.044i | 0.431325 | + | 0.158805i | ||||
\(801\) | 349.864 | − | 611.307i | 0.436784 | − | 0.763180i | ||||
\(802\) | −201.326 | + | 497.235i | −0.251029 | + | 0.619994i | ||||
\(803\) | 39.2793 | − | 39.2793i | 0.0489157 | − | 0.0489157i | ||||
\(804\) | 42.3512 | + | 70.4196i | 0.0526756 | + | 0.0875865i | ||||
\(805\) | −406.765 | + | 406.765i | −0.505298 | + | 0.505298i | ||||
\(806\) | 12.0300 | + | 28.3996i | 0.0149256 | + | 0.0352352i | ||||
\(807\) | −111.425 | + | 419.011i | −0.138073 | + | 0.519220i | ||||
\(808\) | −232.312 | + | 601.189i | −0.287515 | + | 0.744046i | ||||
\(809\) | −1041.53 | −1.28743 | −0.643717 | − | 0.765264i | \(-0.722609\pi\) | ||||
−0.643717 | + | 0.765264i | \(0.722609\pi\) | |||||||
\(810\) | 355.088 | − | 477.963i | 0.438380 | − | 0.590078i | ||||
\(811\) | −442.482 | + | 442.482i | −0.545600 | + | 0.545600i | −0.925165 | − | 0.379565i | \(-0.876074\pi\) |
0.379565 | + | 0.925165i | \(0.376074\pi\) | |||||||
\(812\) | 1.01731 | + | 63.7010i | 0.00125284 | + | 0.0784495i | ||||
\(813\) | 100.082 | − | 58.0346i | 0.123102 | − | 0.0713833i | ||||
\(814\) | 2102.03 | + | 851.089i | 2.58234 | + | 1.04556i | ||||
\(815\) | − | 537.359i | − | 0.659337i | ||||||
\(816\) | −271.878 | + | 169.481i | −0.333184 | + | 0.207697i | ||||
\(817\) | 1170.20 | 1.43231 | ||||||||
\(818\) | −19.4011 | + | 47.9169i | −0.0237177 | + | 0.0585782i | ||||
\(819\) | 18.2046 | + | 66.9275i | 0.0222279 | + | 0.0817186i | ||||
\(820\) | 3.53858 | + | 221.577i | 0.00431534 | + | 0.270215i | ||||
\(821\) | 104.027 | + | 104.027i | 0.126708 | + | 0.126708i | 0.767617 | − | 0.640909i | \(-0.221442\pi\) |
−0.640909 | + | 0.767617i | \(0.721442\pi\) | |||||||
\(822\) | −1415.23 | + | 200.554i | −1.72169 | + | 0.243983i | ||||
\(823\) | 349.420i | 0.424568i | 0.977208 | + | 0.212284i | \(0.0680902\pi\) | ||||
−0.977208 | + | 0.212284i | \(0.931910\pi\) | |||||||
\(824\) | −1126.19 | + | 498.411i | −1.36674 | + | 0.604867i | ||||
\(825\) | 141.776 | − | 533.143i | 0.171850 | − | 0.646234i | ||||
\(826\) | 231.354 | − | 98.0013i | 0.280090 | − | 0.118646i | ||||
\(827\) | 554.122 | + | 554.122i | 0.670038 | + | 0.670038i | 0.957725 | − | 0.287686i | \(-0.0928861\pi\) |
−0.287686 | + | 0.957725i | \(0.592886\pi\) | |||||||
\(828\) | −741.413 | + | 214.440i | −0.895427 | + | 0.258986i | ||||
\(829\) | −583.639 | − | 583.639i | −0.704027 | − | 0.704027i | 0.261245 | − | 0.965272i | \(-0.415867\pi\) |
−0.965272 | + | 0.261245i | \(0.915867\pi\) | |||||||
\(830\) | 305.705 | + | 123.777i | 0.368319 | + | 0.149129i | ||||
\(831\) | 302.355 | − | 1137.00i | 0.363845 | − | 1.36823i | ||||
\(832\) | 67.4845 | − | 3.23538i | 0.0811111 | − | 0.00388868i | ||||
\(833\) | 28.6604i | 0.0344062i | ||||||||
\(834\) | 135.477 | − | 180.214i | 0.162442 | − | 0.216084i | ||||
\(835\) | −296.230 | − | 296.230i | −0.354767 | − | 0.354767i | ||||
\(836\) | 1397.82 | − | 1443.19i | 1.67204 | − | 1.72631i | ||||
\(837\) | −2.23646 | − | 394.415i | −0.00267200 | − | 0.471225i | ||||
\(838\) | −633.809 | + | 268.481i | −0.756335 | + | 0.320383i | ||||
\(839\) | 1235.55 | 1.47264 | 0.736322 | − | 0.676632i | \(-0.236561\pi\) | ||||
0.736322 | + | 0.676632i | \(0.236561\pi\) | |||||||
\(840\) | −636.076 | + | 100.525i | −0.757233 | + | 0.119672i | ||||
\(841\) | 836.240i | 0.994340i | ||||||||
\(842\) | 301.712 | − | 127.805i | 0.358327 | − | 0.151787i | ||||
\(843\) | 1190.60 | − | 690.399i | 1.41234 | − | 0.818979i | ||||
\(844\) | 7.11829 | + | 445.729i | 0.00843400 | + | 0.528114i | ||||
\(845\) | 436.329 | − | 436.329i | 0.516365 | − | 0.516365i | ||||
\(846\) | 407.248 | + | 518.002i | 0.481380 | + | 0.612295i | ||||
\(847\) | 986.322 | 1.16449 | ||||||||
\(848\) | 788.397 | − | 840.436i | 0.929714 | − | 0.991080i | ||||
\(849\) | −301.744 | + | 1134.70i | −0.355411 | + | 1.33651i | ||||
\(850\) | −142.179 | − | 57.5667i | −0.167269 | − | 0.0677256i | ||||
\(851\) | 1074.11 | − | 1074.11i | 1.26218 | − | 1.26218i | ||||
\(852\) | −872.273 | − | 217.107i | −1.02380 | − | 0.254820i | ||||
\(853\) | 535.104 | − | 535.104i | 0.627320 | − | 0.627320i | −0.320073 | − | 0.947393i | \(-0.603707\pi\) |
0.947393 | + | 0.320073i | \(0.103707\pi\) | |||||||
\(854\) | −524.353 | + | 222.115i | −0.613996 | + | 0.260088i | ||||
\(855\) | 901.105 | + | 515.722i | 1.05392 | + | 0.603183i | ||||
\(856\) | 313.737 | − | 811.905i | 0.366515 | − | 0.948487i | ||||
\(857\) | −261.325 | −0.304929 | −0.152465 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152465 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(858\) | −14.2224 | − | 100.362i | −0.0165762 | − | 0.116971i | ||||
\(859\) | −81.4524 | + | 81.4524i | −0.0948224 | + | 0.0948224i | −0.752927 | − | 0.658104i | \(-0.771359\pi\) |
0.658104 | + | 0.752927i | \(0.271359\pi\) | |||||||
\(860\) | 393.733 | + | 381.355i | 0.457829 | + | 0.443436i | ||||
\(861\) | 165.597 | + | 285.575i | 0.192331 | + | 0.331678i | ||||
\(862\) | 426.362 | − | 1053.03i | 0.494620 | − | 1.22162i | ||||
\(863\) | 1250.31i | 1.44879i | 0.689383 | + | 0.724397i | \(0.257882\pi\) | ||||
−0.689383 | + | 0.724397i | \(0.742118\pi\) | |||||||
\(864\) | −812.472 | − | 293.915i | −0.940361 | − | 0.340179i | ||||
\(865\) | −749.878 | −0.866911 | ||||||||
\(866\) | −1199.83 | − | 485.798i | −1.38548 | − | 0.560968i | ||||
\(867\) | −634.407 | + | 367.876i | −0.731727 | + | 0.424309i | ||||
\(868\) | −296.780 | + | 306.413i | −0.341912 | + | 0.353010i | ||||
\(869\) | −1170.80 | − | 1170.80i | −1.34730 | − | 1.34730i | ||||
\(870\) | 47.6378 | − | 6.75083i | 0.0547561 | − | 0.00775957i | ||||
\(871\) | 7.22894i | 0.00829959i | ||||||||
\(872\) | −302.289 | + | 782.279i | −0.346662 | + | 0.897108i | ||||
\(873\) | −275.227 | + | 480.897i | −0.315266 | + | 0.550855i | ||||
\(874\) | −524.922 | − | 1239.19i | −0.600597 | − | 1.41784i | ||||
\(875\) | −692.345 | − | 692.345i | −0.791251 | − | 0.791251i | ||||
\(876\) | 10.0604 | − | 40.4201i | 0.0114845 | − | 0.0461416i | ||||
\(877\) | 288.263 | + | 288.263i | 0.328692 | + | 0.328692i | 0.852089 | − | 0.523397i | \(-0.175336\pi\) |
−0.523397 | + | 0.852089i | \(0.675336\pi\) | |||||||
\(878\) | −365.078 | + | 901.672i | −0.415807 | + | 1.02696i | ||||
\(879\) | −1256.75 | − | 334.200i | −1.42975 | − | 0.380205i | ||||
\(880\) | 940.644 | − | 30.0518i | 1.06891 | − | 0.0341498i | ||||
\(881\) | 1682.63i | 1.90991i | 0.296744 | + | 0.954957i | \(0.404099\pi\) | ||||
−0.296744 | + | 0.954957i | \(0.595901\pi\) | |||||||
\(882\) | −60.7620 | + | 47.7704i | −0.0688912 | + | 0.0541615i | ||||
\(883\) | −477.885 | − | 477.885i | −0.541206 | − | 0.541206i | 0.382676 | − | 0.923882i | \(-0.375002\pi\) |
−0.923882 | + | 0.382676i | \(0.875002\pi\) | |||||||
\(884\) | −28.1804 | + | 0.450042i | −0.0318783 | + | 0.000509097i | ||||
\(885\) | −95.1854 | − | 164.149i | −0.107554 | − | 0.185479i | ||||
\(886\) | −285.148 | − | 673.156i | −0.321838 | − | 0.759770i | ||||
\(887\) | −1366.70 | −1.54081 | −0.770405 | − | 0.637555i | \(-0.779946\pi\) | ||||
−0.770405 | + | 0.637555i | \(0.779946\pi\) | |||||||
\(888\) | 1679.64 | − | 265.448i | 1.89148 | − | 0.298928i | ||||
\(889\) | 316.406i | 0.355912i | ||||||||
\(890\) | 224.391 | + | 529.725i | 0.252125 | + | 0.595197i | ||||
\(891\) | −326.024 | + | 1254.60i | −0.365908 | + | 1.40808i | ||||
\(892\) | −441.755 | − | 427.867i | −0.495240 | − | 0.479671i | ||||
\(893\) | −812.435 | + | 812.435i | −0.909782 | + | 0.909782i | ||||
\(894\) | 903.795 | + | 679.433i | 1.01096 | + | 0.759992i | ||||
\(895\) | 87.4499 | 0.0977094 | ||||||||
\(896\) | 405.260 | + | 841.982i | 0.452299 | + | 0.939712i | ||||
\(897\) | −65.6160 | − | 17.4489i | −0.0731506 | − | 0.0194525i | ||||
\(898\) | 373.805 | − | 923.225i | 0.416263 | − | 1.02809i | ||||
\(899\) | 22.5364 | − | 22.5364i | 0.0250683 | − | 0.0250683i | ||||
\(900\) | −114.935 | − | 397.380i | −0.127705 | − | 0.441533i | ||||
\(901\) | −339.914 | + | 339.914i | −0.377263 | + | 0.377263i | ||||
\(902\) | −188.175 | − | 444.230i | −0.208620 | − | 0.492494i | ||||
\(903\) | 789.113 | + | 209.844i | 0.873879 | + | 0.232386i | ||||
\(904\) | −280.852 | + | 124.295i | −0.310677 | + | 0.137494i | ||||
\(905\) | 177.788 | 0.196451 | ||||||||
\(906\) | −19.6756 | − | 138.843i | −0.0217170 | − | 0.153248i | ||||
\(907\) | 330.495 | − | 330.495i | 0.364383 | − | 0.364383i | −0.501041 | − | 0.865424i | \(-0.667049\pi\) |
0.865424 | + | 0.501041i | \(0.167049\pi\) | |||||||
\(908\) | 246.900 | − | 3.94300i | 0.271917 | − | 0.00434251i | ||||
\(909\) | 699.657 | − | 190.310i | 0.769699 | − | 0.209362i | ||||
\(910\) | −52.5101 | − | 21.2608i | −0.0577034 | − | 0.0233635i | ||||
\(911\) | 1633.72i | 1.79332i | 0.442715 | + | 0.896662i | \(0.354015\pi\) | ||||
−0.442715 | + | 0.896662i | \(0.645985\pi\) | |||||||
\(912\) | 340.485 | − | 1467.57i | 0.373339 | − | 1.60918i | ||||
\(913\) | −718.014 | −0.786434 | ||||||||
\(914\) | −350.126 | + | 864.744i | −0.383070 | + | 0.946109i | ||||
\(915\) | 215.733 | + | 372.035i | 0.235774 | + | 0.406596i | ||||
\(916\) | −632.817 | + | 10.1061i | −0.690848 | + | 0.0110329i | ||||
\(917\) | 8.86358 | + | 8.86358i | 0.00966585 | + | 0.00966585i | ||||
\(918\) | 334.841 | + | 133.369i | 0.364750 | + | 0.145282i | ||||
\(919\) | 765.918i | 0.833426i | 0.909038 | + | 0.416713i | \(0.136818\pi\) | ||||
−0.909038 | + | 0.416713i | \(0.863182\pi\) | |||||||
\(920\) | 227.221 | − | 588.015i | 0.246980 | − | 0.639146i | ||||
\(921\) | 1474.79 | + | 392.182i | 1.60129 | + | 0.425822i | ||||
\(922\) | −1013.76 | + | 429.430i | −1.09953 | + | 0.465759i | ||||
\(923\) | −55.9153 | − | 55.9153i | −0.0605800 | − | 0.0605800i | ||||
\(924\) | 1201.41 | − | 722.543i | 1.30023 | − | 0.781973i | ||||
\(925\) | 575.698 | + | 575.698i | 0.622377 | + | 0.622377i | ||||
\(926\) | 928.495 | + | 375.938i | 1.00269 | + | 0.405981i | ||||
\(927\) | 1202.49 | + | 688.208i | 1.29718 | + | 0.742403i | ||||
\(928\) | −29.2703 | − | 63.3835i | −0.0315413 | − | 0.0683012i | ||||
\(929\) | − | 1283.88i | − | 1.38200i | −0.722855 | − | 0.691000i | \(-0.757170\pi\) | ||
0.722855 | − | 0.691000i | \(-0.242830\pi\) | |||||||
\(930\) | 257.506 | + | 193.582i | 0.276888 | + | 0.208152i | ||||
\(931\) | −95.2993 | − | 95.2993i | −0.102362 | − | 0.102362i | ||||
\(932\) | 93.3205 | + | 90.3867i | 0.100129 | + | 0.0969814i | ||||
\(933\) | 1484.50 | − | 860.819i | 1.59110 | − | 0.922635i | ||||
\(934\) | 491.804 | − | 208.328i | 0.526557 | − | 0.223049i | ||||
\(935\) | −392.597 | −0.419890 | ||||||||
\(936\) | −47.9246 | − | 58.9943i | −0.0512015 | − | 0.0630282i | ||||
\(937\) | 1617.33i | 1.72607i | 0.505141 | + | 0.863037i | \(0.331440\pi\) | ||||
−0.505141 | + | 0.863037i | \(0.668560\pi\) | |||||||
\(938\) | −92.0628 | + | 38.9977i | −0.0981480 | + | 0.0415754i | ||||
\(939\) | 501.607 | + | 865.029i | 0.534193 | + | 0.921223i | ||||
\(940\) | −538.122 | + | 8.59381i | −0.572470 | + | 0.00914236i | ||||
\(941\) | 721.542 | − | 721.542i | 0.766782 | − | 0.766782i | −0.210757 | − | 0.977539i | \(-0.567593\pi\) |
0.977539 | + | 0.210757i | \(0.0675928\pi\) | |||||||
\(942\) | 650.293 | + | 488.861i | 0.690332 | + | 0.518961i | ||||
\(943\) | −323.152 | −0.342685 | ||||||||
\(944\) | −188.377 | + | 200.810i | −0.199552 | + | 0.212723i | ||||
\(945\) | 515.172 | + | 509.362i | 0.545155 | + | 0.539008i | ||||
\(946\) | −1106.10 | − | 447.847i | −1.16923 | − | 0.473411i | ||||
\(947\) | −442.411 | + | 442.411i | −0.467171 | + | 0.467171i | −0.900997 | − | 0.433826i | \(-0.857163\pi\) |
0.433826 | + | 0.900997i | \(0.357163\pi\) | |||||||
\(948\) | −1204.80 | − | 299.872i | −1.27089 | − | 0.316321i | ||||
\(949\) | 2.59105 | − | 2.59105i | 0.00273029 | − | 0.00273029i | ||||
\(950\) | 664.178 | − | 281.345i | 0.699135 | − | 0.296153i | ||||
\(951\) | −290.444 | + | 1092.21i | −0.305409 | + | 1.14848i | ||||
\(952\) | −157.755 | − | 356.458i | −0.165709 | − | 0.374431i | ||||
\(953\) | 66.7031 | 0.0699928 | 0.0349964 | − | 0.999387i | \(-0.488858\pi\) | ||||
0.0349964 | + | 0.999387i | \(0.488858\pi\) | |||||||
\(954\) | −1287.20 | − | 154.081i | −1.34927 | − | 0.161510i | ||||
\(955\) | 390.260 | − | 390.260i | 0.408649 | − | 0.408649i | ||||
\(956\) | −370.975 | + | 383.017i | −0.388050 | + | 0.400645i | ||||
\(957\) | −90.6131 | + | 52.5441i | −0.0946845 | + | 0.0549050i | ||||
\(958\) | −244.951 | + | 604.981i | −0.255690 | + | 0.631504i | ||||
\(959\) | − | 1739.13i | − | 1.81348i | ||||||
\(960\) | 592.829 | − | 382.830i | 0.617530 | − | 0.398781i | ||||
\(961\) | −747.600 | −0.777940 | ||||||||
\(962\) | 138.659 | + | 56.1418i | 0.144137 | + | 0.0583594i | ||||
\(963\) | −944.885 | + | 257.013i | −0.981189 | + | 0.266888i | ||||
\(964\) | 458.769 | + | 444.347i | 0.475902 | + | 0.460940i | ||||
\(965\) | 305.735 | + | 305.735i | 0.316823 | + | 0.316823i | ||||
\(966\) | −131.759 | − | 929.772i | −0.136397 | − | 0.962496i | ||||
\(967\) | − | 81.7617i | − | 0.0845519i | −0.999106 | − | 0.0422759i | \(-0.986539\pi\) | ||
0.999106 | − | 0.0422759i | \(-0.0134609\pi\) | |||||||
\(968\) | −988.391 | + | 437.425i | −1.02107 | + | 0.451886i | ||||
\(969\) | −161.512 | + | 607.362i | −0.166679 | + | 0.626793i | ||||
\(970\) | −176.522 | − | 416.719i | −0.181981 | − | 0.429607i | ||||
\(971\) | −558.759 | − | 558.759i | −0.575447 | − | 0.575447i | 0.358198 | − | 0.933646i | \(-0.383391\pi\) |
−0.933646 | + | 0.358198i | \(0.883391\pi\) | |||||||
\(972\) | 275.354 | + | 932.183i | 0.283286 | + | 0.959036i | ||||
\(973\) | 193.971 | + | 193.971i | 0.199354 | + | 0.199354i | ||||
\(974\) | 147.294 | − | 363.788i | 0.151226 | − | 0.373499i | ||||
\(975\) | 9.35219 | − | 35.1686i | 0.00959199 | − | 0.0360704i | ||||
\(976\) | 426.947 | − | 455.127i | 0.437445 | − | 0.466319i | ||||
\(977\) | − | 250.154i | − | 0.256043i | −0.991771 | − | 0.128021i | \(-0.959137\pi\) | ||
0.991771 | − | 0.128021i | \(-0.0408626\pi\) | |||||||
\(978\) | 701.172 | + | 527.110i | 0.716945 | + | 0.538967i | ||||
\(979\) | −885.602 | − | 885.602i | −0.904599 | − | 0.904599i | ||||
\(980\) | −1.00806 | − | 63.1221i | −0.00102863 | − | 0.0644103i | ||||
\(981\) | 910.406 | − | 247.635i | 0.928039 | − | 0.252431i | ||||
\(982\) | 385.214 | + | 909.383i | 0.392275 | + | 0.926052i | ||||
\(983\) | 1147.26 | 1.16710 | 0.583551 | − | 0.812077i | \(-0.301663\pi\) | ||||
0.583551 | + | 0.812077i | \(0.301663\pi\) | |||||||
\(984\) | −292.595 | − | 212.733i | −0.297352 | − | 0.216192i | ||||
\(985\) | − | 165.567i | − | 0.168088i | ||||||
\(986\) | 11.3598 | + | 26.8173i | 0.0115211 | + | 0.0271981i | ||||
\(987\) | −693.548 | + | 402.170i | −0.702683 | + | 0.407467i | ||||
\(988\) | 92.2070 | − | 95.1998i | 0.0933269 | − | 0.0963561i | ||||
\(989\) | −565.203 | + | 565.203i | −0.571489 | + | 0.571489i | ||||
\(990\) | −654.372 | − | 832.333i | −0.660982 | − | 0.840741i | ||||
\(991\) | 1364.34 | 1.37673 | 0.688364 | − | 0.725365i | \(-0.258329\pi\) | ||||
0.688364 | + | 0.725365i | \(0.258329\pi\) | |||||||
\(992\) | 161.511 | − | 438.675i | 0.162813 | − | 0.442213i | ||||
\(993\) | 231.620 | − | 871.000i | 0.233253 | − | 0.877140i | ||||
\(994\) | 410.454 | − | 1013.74i | 0.412932 | − | 1.01986i | ||||
\(995\) | 333.569 | − | 333.569i | 0.335245 | − | 0.335245i | ||||
\(996\) | −461.384 | + | 277.482i | −0.463237 | + | 0.278597i | ||||
\(997\) | −328.128 | + | 328.128i | −0.329115 | + | 0.329115i | −0.852250 | − | 0.523135i | \(-0.824762\pi\) |
0.523135 | + | 0.852250i | \(0.324762\pi\) | |||||||
\(998\) | −354.494 | − | 836.861i | −0.355204 | − | 0.838539i | ||||
\(999\) | −1360.38 | − | 1345.03i | −1.36174 | − | 1.34638i |
(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 | 48.3.i.b.29.9 | yes | 20 | |
3.2 | odd | 2 | inner | 48.3.i.b.29.2 | yes | 20 | |
4.3 | odd | 2 | 192.3.i.b.17.9 | 20 | |||
8.3 | odd | 2 | 384.3.i.c.161.2 | 20 | |||
8.5 | even | 2 | 384.3.i.d.161.9 | 20 | |||
12.11 | even | 2 | 192.3.i.b.17.3 | 20 | |||
16.3 | odd | 4 | 384.3.i.c.353.8 | 20 | |||
16.5 | even | 4 | inner | 48.3.i.b.5.2 | ✓ | 20 | |
16.11 | odd | 4 | 192.3.i.b.113.3 | 20 | |||
16.13 | even | 4 | 384.3.i.d.353.3 | 20 | |||
24.5 | odd | 2 | 384.3.i.d.161.3 | 20 | |||
24.11 | even | 2 | 384.3.i.c.161.8 | 20 | |||
48.5 | odd | 4 | inner | 48.3.i.b.5.9 | yes | 20 | |
48.11 | even | 4 | 192.3.i.b.113.9 | 20 | |||
48.29 | odd | 4 | 384.3.i.d.353.9 | 20 | |||
48.35 | even | 4 | 384.3.i.c.353.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.2 | ✓ | 20 | 16.5 | even | 4 | inner | |
48.3.i.b.5.9 | yes | 20 | 48.5 | odd | 4 | inner | |
48.3.i.b.29.2 | yes | 20 | 3.2 | odd | 2 | inner | |
48.3.i.b.29.9 | yes | 20 | 1.1 | even | 1 | trivial | |
192.3.i.b.17.3 | 20 | 12.11 | even | 2 | |||
192.3.i.b.17.9 | 20 | 4.3 | odd | 2 | |||
192.3.i.b.113.3 | 20 | 16.11 | odd | 4 | |||
192.3.i.b.113.9 | 20 | 48.11 | even | 4 | |||
384.3.i.c.161.2 | 20 | 8.3 | odd | 2 | |||
384.3.i.c.161.8 | 20 | 24.11 | even | 2 | |||
384.3.i.c.353.2 | 20 | 48.35 | even | 4 | |||
384.3.i.c.353.8 | 20 | 16.3 | odd | 4 | |||
384.3.i.d.161.3 | 20 | 24.5 | odd | 2 | |||
384.3.i.d.161.9 | 20 | 8.5 | even | 2 | |||
384.3.i.d.353.3 | 20 | 16.13 | even | 4 | |||
384.3.i.d.353.9 | 20 | 48.29 | odd | 4 |