Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + 8319228 x^{4} + 2467872 x^{2} + 69312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 21.1 | ||
Root | \(-1.57014i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.21 |
Dual form | 76.3.j.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.27531 | + | 2.71161i | −0.758438 | + | 0.903871i | −0.997748 | − | 0.0670720i | \(-0.978634\pi\) |
0.239310 | + | 0.970943i | \(0.423079\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.68966 | + | 2.07087i | −1.13793 | + | 0.414174i | −0.841166 | − | 0.540777i | \(-0.818130\pi\) |
−0.296766 | + | 0.954950i | \(0.595908\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.17078 | − | 10.6881i | −0.881540 | − | 1.52687i | −0.849629 | − | 0.527381i | \(-0.823174\pi\) |
−0.0319111 | − | 0.999491i | \(-0.510159\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.612961 | − | 3.47627i | −0.0681067 | − | 0.386253i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.21913 | + | 14.2359i | −0.747193 | + | 1.29418i | 0.201970 | + | 0.979392i | \(0.435266\pi\) |
−0.949163 | + | 0.314785i | \(0.898068\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0374 | + | 14.3456i | 0.925953 | + | 1.10351i | 0.994382 | + | 0.105852i | \(0.0337571\pi\) |
−0.0684284 | + | 0.997656i | \(0.521798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.33038 | − | 20.1400i | 0.488692 | − | 1.34267i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.283090 | + | 1.60549i | −0.0166524 | + | 0.0944403i | −0.992001 | − | 0.126228i | \(-0.959713\pi\) |
0.975349 | + | 0.220669i | \(0.0708239\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.9621 | − | 6.19392i | −0.945371 | − | 0.325996i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 43.0225 | + | 7.58602i | 2.04869 | + | 0.361239i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.0092 | + | 7.64671i | 0.913442 | + | 0.332466i | 0.755626 | − | 0.655003i | \(-0.227333\pi\) |
0.157816 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.93266 | − | 7.49539i | 0.357306 | − | 0.299816i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.7687 | − | 9.68142i | −0.621063 | − | 0.358571i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.0677 | − | 2.30418i | 0.450609 | − | 0.0794545i | 0.0562618 | − | 0.998416i | \(-0.482082\pi\) |
0.394347 | + | 0.918962i | \(0.370971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21.3262 | + | 12.3127i | −0.687941 | + | 0.397183i | −0.802840 | − | 0.596194i | \(-0.796679\pi\) |
0.114899 | + | 0.993377i | \(0.463345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −19.9013 | − | 54.6783i | −0.603069 | − | 1.65692i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 57.2433 | + | 48.0328i | 1.63552 | + | 1.37237i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 29.5565i | − | 0.798825i | −0.916771 | − | 0.399412i | \(-0.869214\pi\) | ||
0.916771 | − | 0.399412i | \(-0.130786\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −66.2886 | −1.69971 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7505 | + | 12.8120i | −0.262208 | + | 0.312487i | −0.881045 | − | 0.473032i | \(-0.843160\pi\) |
0.618837 | + | 0.785519i | \(0.287604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.3175 | − | 7.03101i | 0.449245 | − | 0.163512i | −0.107483 | − | 0.994207i | \(-0.534279\pi\) |
0.556728 | + | 0.830695i | \(0.312057\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.6864 | + | 18.5095i | 0.237476 | + | 0.411321i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.01062 | + | 17.0741i | 0.0640558 | + | 0.363278i | 0.999940 | + | 0.0109702i | \(0.00349199\pi\) |
−0.935884 | + | 0.352308i | \(0.885397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −51.6570 | + | 89.4726i | −1.05423 | + | 1.82597i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.70934 | − | 4.42062i | −0.0727321 | − | 0.0866787i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.7549 | + | 37.7914i | −0.259527 | + | 0.713045i | 0.739670 | + | 0.672970i | \(0.234982\pi\) |
−0.999197 | + | 0.0400745i | \(0.987240\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.2833 | − | 98.0185i | 0.314242 | − | 1.78215i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.6648 | − | 34.6130i | 1.01166 | − | 0.607246i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −86.1296 | − | 15.1870i | −1.45982 | − | 0.257406i | −0.613339 | − | 0.789820i | \(-0.710174\pi\) |
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18.8722 | − | 6.86893i | −0.309381 | − | 0.112605i | 0.182664 | − | 0.983175i | \(-0.441528\pi\) |
−0.492045 | + | 0.870570i | \(0.663750\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −33.3723 | + | 28.0027i | −0.529719 | + | 0.444487i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −98.1966 | − | 56.6938i | −1.51072 | − | 0.872213i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42.6487 | − | 7.52012i | 0.636548 | − | 0.112241i | 0.153944 | − | 0.988080i | \(-0.450802\pi\) |
0.482604 | + | 0.875839i | \(0.339691\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −68.5374 | + | 39.5701i | −0.993295 | + | 0.573479i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.32434 | − | 11.8810i | −0.0609062 | − | 0.167338i | 0.905507 | − | 0.424331i | \(-0.139491\pi\) |
−0.966413 | + | 0.256992i | \(0.917268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7881 | + | 10.7305i | 0.175180 | + | 0.146993i | 0.726162 | − | 0.687524i | \(-0.241302\pi\) |
−0.550982 | + | 0.834517i | \(0.685747\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 41.2763i | 0.550351i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 202.874 | 2.63472 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3044 | − | 15.8555i | 0.168410 | − | 0.200703i | −0.675238 | − | 0.737600i | \(-0.735959\pi\) |
0.843648 | + | 0.536897i | \(0.180404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 94.2595 | − | 34.3077i | 1.16370 | − | 0.423551i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 61.6379 | + | 106.760i | 0.742626 | + | 1.28627i | 0.951296 | + | 0.308280i | \(0.0997532\pi\) |
−0.208670 | + | 0.977986i | \(0.566913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.71406 | − | 9.72091i | −0.0201654 | − | 0.114364i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23.4850 | + | 40.6772i | −0.269942 | + | 0.467554i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 58.3959 | + | 69.5935i | 0.656134 | + | 0.781950i | 0.986825 | − | 0.161789i | \(-0.0517264\pi\) |
−0.330692 | + | 0.943739i | \(0.607282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 79.0472 | − | 217.180i | 0.868651 | − | 2.38660i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.1365 | − | 85.8435i | 0.162758 | − | 0.923048i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 115.025 | − | 1.95573i | 1.21079 | − | 0.0205867i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −111.640 | − | 19.6851i | −1.15093 | − | 0.202939i | −0.434547 | − | 0.900649i | \(-0.643091\pi\) |
−0.716380 | + | 0.697710i | \(0.754202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 54.5260 | + | 19.8459i | 0.550768 | + | 0.200463i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −144.471 | + | 121.225i | −1.43040 | + | 1.20025i | −0.484929 | + | 0.874554i | \(0.661154\pi\) |
−0.945474 | + | 0.325697i | \(0.894401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 111.838 | + | 64.5696i | 1.08580 | + | 0.626890i | 0.932456 | − | 0.361283i | \(-0.117661\pi\) |
0.153348 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −260.493 | + | 45.9319i | −2.48089 | + | 0.437447i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.92634 | − | 5.73098i | 0.0927696 | − | 0.0535605i | −0.452898 | − | 0.891563i | \(-0.649610\pi\) |
0.545667 | + | 0.838002i | \(0.316276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −22.5020 | − | 61.8238i | −0.206441 | − | 0.567191i | 0.792657 | − | 0.609668i | \(-0.208697\pi\) |
−0.999097 | + | 0.0424773i | \(0.986475\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 80.1459 | + | 67.2504i | 0.722035 | + | 0.605859i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 140.102i | − | 1.23984i | −0.784665 | − | 0.619920i | \(-0.787165\pi\) | ||
0.784665 | − | 0.619920i | \(-0.212835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −135.370 | −1.17713 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 42.4908 | − | 50.6386i | 0.363169 | − | 0.432808i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.9065 | − | 6.88140i | 0.158878 | − | 0.0578269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −74.6081 | − | 129.225i | −0.616596 | − | 1.06798i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.2803 | − | 58.3026i | −0.0835798 | − | 0.474005i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 40.3833 | − | 69.9459i | 0.323066 | − | 0.559567i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50.9134 | + | 60.6763i | 0.400893 | + | 0.477766i | 0.928292 | − | 0.371852i | \(-0.121277\pi\) |
−0.527399 | + | 0.849618i | \(0.676833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.8881 | + | 68.3794i | −0.192931 | + | 0.530073i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −33.5765 | + | 190.422i | −0.256309 | + | 1.45360i | 0.536381 | + | 0.843976i | \(0.319791\pi\) |
−0.792690 | + | 0.609625i | \(0.791320\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 44.6386 | + | 230.202i | 0.335629 | + | 1.73084i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 115.457 | + | 20.3582i | 0.855239 | + | 0.150802i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −68.5778 | − | 24.9603i | −0.500568 | − | 0.182192i | 0.0793814 | − | 0.996844i | \(-0.474706\pi\) |
−0.579949 | + | 0.814652i | \(0.696928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −92.5208 | + | 77.6341i | −0.665617 | + | 0.558519i | −0.911764 | − | 0.410713i | \(-0.865280\pi\) |
0.246148 | + | 0.969232i | \(0.420835\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −53.1484 | − | 30.6853i | −0.376939 | − | 0.217626i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −303.160 | + | 53.4553i | −2.12000 | + | 0.373813i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −69.5789 | + | 40.1714i | −0.479855 | + | 0.277044i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −125.079 | − | 343.652i | −0.850879 | − | 2.33777i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 104.661 | + | 87.8213i | 0.702425 | + | 0.589405i | 0.922462 | − | 0.386087i | \(-0.126173\pi\) |
−0.220037 | + | 0.975491i | \(0.570618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 226.087i | 1.49727i | 0.662985 | + | 0.748633i | \(0.269289\pi\) | ||||
−0.662985 | + | 0.748633i | \(0.730711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.75463 | 0.0376120 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 95.8408 | − | 114.219i | 0.618328 | − | 0.736894i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 208.620 | − | 75.9314i | 1.32879 | − | 0.483639i | 0.422524 | − | 0.906352i | \(-0.361144\pi\) |
0.906264 | + | 0.422712i | \(0.138922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −71.1788 | − | 123.285i | −0.447665 | − | 0.775379i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47.9141 | − | 271.734i | −0.297603 | − | 1.68779i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −51.5648 | + | 89.3128i | −0.316348 | + | 0.547931i | −0.979723 | − | 0.200356i | \(-0.935790\pi\) |
0.663375 | + | 0.748287i | \(0.269123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 226.463 | + | 269.888i | 1.37250 | + | 1.63569i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 81.1500 | − | 222.958i | 0.485928 | − | 1.33508i | −0.418409 | − | 0.908259i | \(-0.637412\pi\) |
0.904337 | − | 0.426819i | \(-0.140366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −31.5511 | + | 178.935i | −0.186693 | + | 1.05879i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.5217 | + | 66.2376i | −0.0615305 | + | 0.387355i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −246.700 | − | 43.4998i | −1.42601 | − | 0.251444i | −0.593223 | − | 0.805038i | \(-0.702145\pi\) |
−0.832786 | + | 0.553595i | \(0.813256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −135.233 | − | 49.2208i | −0.772760 | − | 0.281262i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 237.153 | − | 198.995i | 1.33985 | − | 1.12427i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −29.4439 | − | 16.9994i | −0.164491 | − | 0.0949689i | 0.415495 | − | 0.909596i | \(-0.363608\pi\) |
−0.579986 | + | 0.814627i | \(0.696942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 210.383 | − | 37.0962i | 1.16234 | − | 0.204952i | 0.440982 | − | 0.897516i | \(-0.354630\pi\) |
0.721356 | + | 0.692564i | \(0.243519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 61.5661 | − | 35.5452i | 0.336427 | − | 0.194236i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 61.2077 | + | 168.167i | 0.330852 | + | 0.909009i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.5288 | − | 17.2257i | −0.109780 | − | 0.0921163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 238.968i | 1.26438i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28.5507 | −0.149480 | −0.0747399 | − | 0.997203i | \(-0.523813\pi\) | ||||
−0.0747399 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.67587 | + | 1.99723i | −0.00868328 | + | 0.0103483i | −0.770369 | − | 0.637599i | \(-0.779928\pi\) |
0.761685 | + | 0.647947i | \(0.224372\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 377.160 | − | 137.275i | 1.93415 | − | 0.703974i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −39.9438 | − | 69.1846i | −0.202760 | − | 0.351191i | 0.746657 | − | 0.665210i | \(-0.231658\pi\) |
−0.949417 | + | 0.314019i | \(0.898325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28.0487 | + | 159.072i | 0.140948 | + | 0.799356i | 0.970532 | + | 0.240974i | \(0.0774667\pi\) |
−0.829584 | + | 0.558383i | \(0.811422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −76.6475 | + | 132.757i | −0.381331 | + | 0.660485i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −105.265 | − | 125.450i | −0.518547 | − | 0.617980i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.6350 | − | 95.1588i | 0.168951 | − | 0.464189i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.7043 | − | 77.7207i | 0.0662042 | − | 0.375462i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 235.809 | − | 204.798i | 1.12827 | − | 0.979896i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 231.472 | + | 40.8148i | 1.09703 | + | 0.193435i | 0.692733 | − | 0.721194i | \(-0.256406\pi\) |
0.404293 | + | 0.914630i | \(0.367518\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 42.0560 | + | 15.3071i | 0.197446 | + | 0.0718645i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −95.3500 | + | 80.0081i | −0.443488 | + | 0.372131i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 263.198 | + | 151.957i | 1.21289 | + | 0.700265i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −58.1940 | + | 10.2612i | −0.265726 | + | 0.0468547i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.4393 | + | 15.2648i | −0.119635 | + | 0.0690713i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −108.533 | − | 298.193i | −0.486697 | − | 1.33719i | −0.903654 | − | 0.428262i | \(-0.859126\pi\) |
0.416958 | − | 0.908926i | \(-0.363096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.5314 | − | 26.4580i | −0.140140 | − | 0.117591i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 276.181i | 1.21665i | 0.793686 | + | 0.608327i | \(0.208159\pi\) | ||||
−0.793686 | + | 0.608327i | \(0.791841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 85.2800 | 0.372402 | 0.186201 | − | 0.982512i | \(-0.440382\pi\) | ||||
0.186201 | + | 0.982512i | \(0.440382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −461.601 | + | 550.115i | −1.99827 | + | 2.38145i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −156.992 | + | 57.1404i | −0.673785 | + | 0.245238i | −0.656177 | − | 0.754607i | \(-0.727827\pi\) |
−0.0176084 | + | 0.999845i | \(0.505605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −52.4876 | − | 90.9112i | −0.223351 | − | 0.386856i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7225 | + | 72.1527i | 0.0536813 | + | 0.304442i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 83.1245 | − | 143.976i | 0.347801 | − | 0.602409i | −0.638057 | − | 0.769989i | \(-0.720262\pi\) |
0.985859 | + | 0.167580i | \(0.0535951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −98.2500 | − | 117.090i | −0.407676 | − | 0.485850i | 0.522668 | − | 0.852536i | \(-0.324937\pi\) |
−0.930345 | + | 0.366686i | \(0.880492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −61.8386 | + | 169.900i | −0.254480 | + | 0.699177i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 108.625 | − | 616.044i | 0.443368 | − | 2.51446i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −127.361 | − | 332.235i | −0.515631 | − | 1.34508i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −429.738 | − | 75.7743i | −1.72585 | − | 0.304315i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −35.4203 | − | 12.8919i | −0.141117 | − | 0.0513623i | 0.270496 | − | 0.962721i | \(-0.412812\pi\) |
−0.411613 | + | 0.911359i | \(0.635034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −281.535 | + | 236.236i | −1.11279 | + | 0.933739i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 30.2594 | + | 17.4703i | 0.118664 | + | 0.0685108i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.3796 | + | 4.12245i | −0.0909712 | + | 0.0160407i | −0.218948 | − | 0.975736i | \(-0.570263\pi\) |
0.127977 | + | 0.991777i | \(0.459152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −315.903 | + | 182.387i | −1.21970 | + | 0.704196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.0199 | − | 44.0144i | −0.0613790 | − | 0.168638i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.03448 | + | 6.74173i | 0.0305494 | + | 0.0256339i | 0.657934 | − | 0.753075i | \(-0.271430\pi\) |
−0.627385 | + | 0.778709i | \(0.715875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 243.505i | − | 0.918886i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −321.580 | −1.20442 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 279.542 | − | 333.145i | 1.03919 | − | 1.23846i | 0.0686169 | − | 0.997643i | \(-0.478141\pi\) |
0.970571 | − | 0.240813i | \(-0.0774142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 89.5741 | − | 32.6023i | 0.330532 | − | 0.120304i | −0.171423 | − | 0.985197i | \(-0.554837\pi\) |
0.501955 | + | 0.864894i | \(0.332614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 409.052 | + | 708.499i | 1.49836 | + | 2.59524i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.2853 | + | 188.770i | 0.121038 | + | 0.686438i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −134.671 | + | 233.256i | −0.486175 | + | 0.842080i | −0.999874 | − | 0.0158906i | \(-0.994942\pi\) |
0.513698 | + | 0.857971i | \(0.328275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 55.8743 | + | 66.5884i | 0.200266 | + | 0.238668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −33.9122 | + | 93.1731i | −0.120684 | + | 0.331577i | −0.985294 | − | 0.170867i | \(-0.945343\pi\) |
0.864610 | + | 0.502444i | \(0.167566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7556 | + | 157.410i | −0.0980763 | + | 0.556218i | 0.895685 | + | 0.444689i | \(0.146686\pi\) |
−0.993761 | + | 0.111529i | \(0.964425\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −256.414 | + | 316.353i | −0.899700 | + | 1.11001i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 203.275 | + | 35.8429i | 0.708275 | + | 0.124888i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 269.074 | + | 97.9348i | 0.931051 | + | 0.338875i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 307.394 | − | 257.934i | 1.05634 | − | 0.886373i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −443.330 | − | 255.957i | −1.51307 | − | 0.873573i | −0.999883 | − | 0.0152973i | \(-0.995131\pi\) |
−0.513189 | − | 0.858275i | \(-0.671536\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 521.498 | − | 91.9543i | 1.76779 | − | 0.311709i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 275.648 | − | 159.146i | 0.928109 | − | 0.535844i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 143.199 | + | 393.436i | 0.478926 | + | 1.31584i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −194.352 | − | 163.081i | −0.645689 | − | 0.541797i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 667.574i | − | 2.20322i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 121.601 | 0.398693 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 53.0718 | − | 63.2485i | 0.172872 | − | 0.206021i | −0.672651 | − | 0.739960i | \(-0.734844\pi\) |
0.845523 | + | 0.533939i | \(0.179289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −429.554 | + | 156.345i | −1.39014 | + | 0.505971i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −98.5512 | − | 170.696i | −0.316885 | − | 0.548861i | 0.662951 | − | 0.748662i | \(-0.269304\pi\) |
−0.979836 | + | 0.199802i | \(0.935970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0879 | + | 147.952i | 0.0833479 | + | 0.472689i | 0.997701 | + | 0.0677713i | \(0.0215888\pi\) |
−0.914353 | + | 0.404918i | \(0.867300\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 131.887 | − | 228.436i | 0.418690 | − | 0.725192i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −163.585 | − | 194.953i | −0.516042 | − | 0.614995i | 0.443598 | − | 0.896226i | \(-0.353702\pi\) |
−0.959640 | + | 0.281231i | \(0.909257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −74.6026 | + | 204.969i | −0.233864 | + | 0.642536i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.04535 | + | 39.9562i | −0.0219481 | + | 0.124474i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0291 | − | 27.0844i | 0.0465298 | − | 0.0838526i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 215.052 | + | 37.9195i | 0.661698 | + | 0.116675i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 218.841 | + | 79.6517i | 0.669240 | + | 0.243583i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 163.912 | − | 137.538i | 0.498212 | − | 0.418049i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −324.984 | − | 187.629i | −0.981824 | − | 0.566856i | −0.0790034 | − | 0.996874i | \(-0.525174\pi\) |
−0.902820 | + | 0.430018i | \(0.858507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −102.747 | + | 18.1170i | −0.308548 | + | 0.0544054i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −227.084 | + | 131.107i | −0.677862 | + | 0.391364i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 70.8408 | + | 194.633i | 0.210210 | + | 0.577547i | 0.999326 | − | 0.0366965i | \(-0.0116835\pi\) |
−0.789117 | + | 0.614244i | \(0.789461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 379.902 | + | 318.776i | 1.12066 | + | 0.940342i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 404.797i | − | 1.18709i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 670.320 | 1.95429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 308.010 | − | 367.072i | 0.892783 | − | 1.06398i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −497.854 | + | 181.204i | −1.43474 | + | 0.522201i | −0.938285 | − | 0.345863i | \(-0.887586\pi\) |
−0.496452 | + | 0.868064i | \(0.665364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −88.2775 | − | 152.901i | −0.252944 | − | 0.438112i | 0.711391 | − | 0.702796i | \(-0.248066\pi\) |
−0.964335 | + | 0.264684i | \(0.914732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −62.9657 | − | 357.096i | −0.179390 | − | 1.01737i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −165.850 | + | 287.261i | −0.469831 | + | 0.813771i | −0.999405 | − | 0.0344927i | \(-0.989018\pi\) |
0.529574 | + | 0.848264i | \(0.322352\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.2081 | + | 58.6439i | 0.138614 | + | 0.165194i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.3585 | + | 66.9244i | −0.0682311 | + | 0.187463i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −46.5136 | + | 263.792i | −0.129564 | + | 0.734796i | 0.848927 | + | 0.528509i | \(0.177249\pi\) |
−0.978492 | + | 0.206286i | \(0.933862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 284.271 | + | 222.511i | 0.787454 | + | 0.616374i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 520.165 | + | 91.7191i | 1.43296 | + | 0.252670i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −94.9817 | − | 34.5705i | −0.260224 | − | 0.0947137i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.9988 | + | 26.8502i | −0.0871901 | + | 0.0731612i | −0.685341 | − | 0.728222i | \(-0.740347\pi\) |
0.598151 | + | 0.801384i | \(0.295902\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 51.1276 | + | 29.5185i | 0.138557 | + | 0.0799960i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 488.797 | − | 86.1880i | 1.31751 | − | 0.232313i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 615.732 | − | 355.493i | 1.65076 | − | 0.953064i | 0.673994 | − | 0.738737i | \(-0.264577\pi\) |
0.976762 | − | 0.214327i | \(-0.0687558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 97.7816 | + | 268.653i | 0.260751 | + | 0.716408i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 190.356 | + | 159.727i | 0.504922 | + | 0.423680i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 165.723i | − | 0.437263i | −0.975808 | − | 0.218631i | \(-0.929841\pi\) | ||
0.975808 | − | 0.218631i | \(-0.0701592\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −280.375 | −0.735892 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.68599 | + | 4.39279i | −0.00962399 | + | 0.0114694i | −0.770835 | − | 0.637035i | \(-0.780161\pi\) |
0.761211 | + | 0.648504i | \(0.224605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1154.28 | + | 420.125i | −2.99814 | + | 1.09123i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −36.2826 | − | 62.8433i | −0.0937535 | − | 0.162386i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0073 | − | 73.7682i | −0.0334379 | − | 0.189636i | 0.963514 | − | 0.267659i | \(-0.0862501\pi\) |
−0.996952 | + | 0.0780237i | \(0.975139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.2242 | + | 31.5652i | −0.0466092 | + | 0.0807294i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −439.953 | − | 524.316i | −1.11947 | − | 1.33414i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.8627 | + | 117.764i | −0.108513 | + | 0.298138i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −43.4519 | + | 246.428i | −0.109451 | + | 0.620726i | 0.879898 | + | 0.475162i | \(0.157611\pi\) |
−0.989349 | + | 0.145564i | \(0.953500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −725.785 | − | 402.738i | −1.81901 | − | 1.00937i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 178.013 | + | 31.3885i | 0.443923 | + | 0.0782755i | 0.391141 | − | 0.920331i | \(-0.372080\pi\) |
0.0527811 | + | 0.998606i | \(0.483191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −433.344 | − | 157.724i | −1.07530 | − | 0.391376i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −465.258 | + | 390.398i | −1.14879 | + | 0.963946i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 420.765 | + | 242.929i | 1.03382 | + | 0.596877i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −211.559 | + | 37.3036i | −0.517259 | + | 0.0912068i | −0.426183 | − | 0.904637i | \(-0.640142\pi\) |
−0.0910766 | + | 0.995844i | \(0.529031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 223.719 | − | 129.164i | 0.544328 | − | 0.314268i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 369.167 | + | 1014.28i | 0.893866 | + | 2.45588i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −571.785 | − | 479.785i | −1.37780 | − | 1.15611i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 427.523i | − | 1.02523i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −611.450 | −1.45931 | −0.729654 | − | 0.683816i | \(-0.760319\pi\) | ||||
−0.729654 | + | 0.683816i | \(0.760319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −521.010 | + | 620.916i | −1.23755 | + | 1.47486i | −0.411359 | + | 0.911473i | \(0.634946\pi\) |
−0.826194 | + | 0.563385i | \(0.809499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 57.5088 | − | 20.9315i | 0.135955 | − | 0.0494834i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.50499 | + | 16.4631i | 0.0223647 | + | 0.0387368i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.0405 | + | 244.095i | 0.100798 | + | 0.571651i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 544.834 | − | 943.681i | 1.27001 | − | 2.19972i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 328.866 | + | 391.927i | 0.763030 | + | 0.909344i | 0.998036 | − | 0.0626502i | \(-0.0199552\pi\) |
−0.235005 | + | 0.971994i | \(0.575511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 175.436 | − | 482.008i | 0.405165 | − | 1.11318i | −0.554536 | − | 0.832160i | \(-0.687104\pi\) |
0.959701 | − | 0.281022i | \(-0.0906734\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 49.3846 | − | 280.074i | 0.113528 | − | 0.643848i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −330.005 | − | 267.480i | −0.755159 | − | 0.612082i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.4326 | + | 7.12935i | 0.0921015 | + | 0.0162400i | 0.219509 | − | 0.975610i | \(-0.429554\pi\) |
−0.127407 | + | 0.991850i | \(0.540666\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 342.695 | + | 124.731i | 0.777086 | + | 0.282836i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 643.382 | − | 539.862i | 1.45233 | − | 1.21865i | 0.521472 | − | 0.853268i | \(-0.325383\pi\) |
0.930858 | − | 0.365382i | \(-0.119062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −476.372 | − | 275.034i | −1.07050 | − | 0.618053i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −476.275 | + | 83.9801i | −1.06549 | + | 0.187875i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −417.559 | + | 241.078i | −0.929975 | + | 0.536921i | −0.886804 | − | 0.462146i | \(-0.847080\pi\) |
−0.0431715 | + | 0.999068i | \(0.513746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −94.0307 | − | 258.347i | −0.208494 | − | 0.572832i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −613.061 | − | 514.419i | −1.35334 | − | 1.13558i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1399.38i | 3.07556i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 680.738 | 1.48958 | 0.744790 | − | 0.667299i | \(-0.232550\pi\) | ||||
0.744790 | + | 0.667299i | \(0.232550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.2904 | − | 24.1812i | 0.0442058 | − | 0.0526824i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 415.080 | − | 151.077i | 0.900391 | − | 0.327716i | 0.149982 | − | 0.988689i | \(-0.452079\pi\) |
0.750409 | + | 0.660973i | \(0.229856\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.8258 | + | 58.5880i | 0.0730579 | + | 0.126540i | 0.900240 | − | 0.435394i | \(-0.143391\pi\) |
−0.827182 | + | 0.561934i | \(0.810058\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 91.6488 | + | 519.766i | 0.197094 | + | 1.11778i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −78.4707 | + | 135.915i | −0.168031 | + | 0.291039i | −0.937728 | − | 0.347371i | \(-0.887074\pi\) |
0.769696 | + | 0.638410i | \(0.220408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −343.552 | − | 409.429i | −0.732519 | − | 0.872983i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −268.779 | + | 738.464i | −0.570656 | + | 1.56786i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −58.6802 | + | 332.792i | −0.124060 | + | 0.703577i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −206.875 | + | 79.3045i | −0.435526 | + | 0.166957i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 139.804 | + | 24.6513i | 0.293091 | + | 0.0516798i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 421.235 | + | 153.317i | 0.879405 | + | 0.320077i | 0.741970 | − | 0.670434i | \(-0.233892\pi\) |
0.137435 | + | 0.990511i | \(0.456114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 424.006 | − | 355.784i | 0.881510 | − | 0.739675i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 845.858 | + | 488.356i | 1.75126 | + | 1.01109i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 675.959 | − | 119.190i | 1.39373 | − | 0.245752i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 217.103 | − | 125.345i | 0.445797 | − | 0.257381i | −0.260256 | − | 0.965540i | \(-0.583807\pi\) |
0.706054 | + | 0.708158i | \(0.250474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −124.856 | − | 343.038i | −0.255329 | − | 0.701510i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −413.096 | − | 346.629i | −0.841337 | − | 0.705966i | 0.116527 | − | 0.993188i | \(-0.462824\pi\) |
−0.957864 | + | 0.287222i | \(0.907268\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.6322i | 0.0438788i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −351.333 | −0.709763 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −100.301 | + | 119.534i | −0.201813 | + | 0.240512i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 569.100 | − | 207.135i | 1.14048 | − | 0.415101i | 0.298393 | − | 0.954443i | \(-0.403549\pi\) |
0.842087 | + | 0.539342i | \(0.181327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 419.934 | + | 727.347i | 0.838191 | + | 1.45179i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −56.2221 | − | 318.851i | −0.111774 | − | 0.633899i | −0.988297 | − | 0.152540i | \(-0.951255\pi\) |
0.876524 | − | 0.481359i | \(-0.159857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 570.948 | − | 988.911i | 1.13059 | − | 1.95824i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −413.414 | − | 492.688i | −0.815412 | − | 0.971770i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −214.210 | + | 588.537i | −0.420845 | + | 1.15626i | 0.530380 | + | 0.847760i | \(0.322049\pi\) |
−0.951224 | + | 0.308501i | \(0.900173\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.7761 | − | 202.897i | 0.0700120 | − | 0.397058i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 241.235 | + | 277.762i | 0.470243 | + | 0.541447i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −770.035 | − | 135.778i | −1.49521 | − | 0.263647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −267.810 | − | 97.4750i | −0.518008 | − | 0.188540i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 679.273 | − | 569.978i | 1.30881 | − | 1.09822i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 809.906 | + | 467.599i | 1.55452 | + | 0.897503i | 0.997765 | + | 0.0668280i | \(0.0212879\pi\) |
0.556757 | + | 0.830675i | \(0.312045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 929.543 | − | 163.904i | 1.77733 | − | 0.313391i | 0.813830 | − | 0.581103i | \(-0.197379\pi\) |
0.963499 | + | 0.267712i | \(0.0862674\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 441.165 | − | 254.707i | 0.840315 | − | 0.485156i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.7306 | − | 37.7244i | −0.0260542 | − | 0.0715834i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3246 | − | 18.7326i | −0.0422015 | − | 0.0354113i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 308.719i | 0.581392i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −313.204 | −0.587625 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.6095 | + | 53.1635i | −0.0833822 | + | 0.0993710i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 113.090 | − | 41.1614i | 0.210596 | − | 0.0766506i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −849.151 | − | 1470.77i | −1.57542 | − | 2.72871i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7223 | + | 145.878i | 0.0475458 | + | 0.269646i | 0.999308 | − | 0.0371903i | \(-0.0118408\pi\) |
−0.951762 | + | 0.306836i | \(0.900730\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −378.097 | + | 654.884i | −0.696312 | + | 1.20605i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 256.058 | + | 305.158i | 0.469831 | + | 0.559922i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −283.423 | + | 778.698i | −0.518141 | + | 1.42358i | 0.354425 | + | 0.935084i | \(0.384676\pi\) |
−0.872566 | + | 0.488496i | \(0.837546\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.3103 | + | 69.8154i | −0.0224232 | + | 0.127168i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −248.994 | − | 39.5522i | −0.451895 | − | 0.0717826i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −251.564 | − | 44.3576i | −0.454908 | − | 0.0802126i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −595.270 | − | 216.660i | −1.07256 | − | 0.390379i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −220.380 | + | 184.921i | −0.395655 | + | 0.331994i | −0.818812 | − | 0.574062i | \(-0.805367\pi\) |
0.423156 | + | 0.906057i | \(0.360922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 333.397 | + | 192.487i | 0.596417 | + | 0.344341i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 93.4191 | − | 16.4723i | 0.166523 | − | 0.0293624i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 477.907 | − | 275.920i | 0.848858 | − | 0.490089i | −0.0114072 | − | 0.999935i | \(-0.503631\pi\) |
0.860265 | + | 0.509846i | \(0.170298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 290.133 | + | 797.133i | 0.513509 | + | 1.41085i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −948.339 | − | 795.751i | −1.67255 | − | 1.40344i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 549.760i | 0.966186i | 0.875569 | + | 0.483093i | \(0.160487\pi\) | ||||
−0.875569 | + | 0.483093i | \(0.839513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −662.672 | −1.16055 | −0.580274 | − | 0.814422i | \(-0.697054\pi\) | ||||
−0.580274 | + | 0.814422i | \(0.697054\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 64.9617 | − | 77.4183i | 0.113371 | − | 0.135111i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 244.983 | − | 89.1665i | 0.426057 | − | 0.155072i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.19265 | + | 5.52984i | 0.00553320 | + | 0.00958378i | 0.868779 | − | 0.495200i | \(-0.164905\pi\) |
−0.863246 | + | 0.504784i | \(0.831572\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.60257 | − | 9.08864i | −0.00276783 | − | 0.0156971i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 760.708 | − | 1317.59i | 1.30931 | − | 2.26779i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −424.942 | − | 506.426i | −0.728889 | − | 0.868656i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −136.893 | + | 376.109i | −0.234004 | + | 0.642922i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −177.108 | + | 1004.43i | −0.301717 | + | 1.71112i | 0.336851 | + | 0.941558i | \(0.390638\pi\) |
−0.638568 | + | 0.769565i | \(0.720473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 459.325 | − | 89.0682i | 0.779839 | − | 0.151219i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 278.486 | + | 49.1047i | 0.471212 | + | 0.0830874i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −729.961 | − | 265.684i | −1.23096 | − | 0.448034i | −0.357036 | − | 0.934091i | \(-0.616213\pi\) |
−0.873927 | + | 0.486057i | \(0.838435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −93.3211 | + | 78.3057i | −0.156842 | + | 0.131606i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −495.161 | − | 285.881i | −0.829415 | − | 0.478863i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 644.567 | − | 113.654i | 1.07607 | − | 0.189740i | 0.392594 | − | 0.919712i | \(-0.371578\pi\) |
0.683477 | + | 0.729972i | \(0.260467\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −353.019 | + | 203.816i | −0.587387 | + | 0.339128i | −0.764063 | − | 0.645141i | \(-0.776799\pi\) |
0.176677 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −52.2840 | − | 143.649i | −0.0867064 | − | 0.238224i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 692.103 | + | 580.743i | 1.14397 | + | 0.959906i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 342.676i | 0.564540i | 0.959335 | + | 0.282270i | \(0.0910874\pi\) | ||||
−0.959335 | + | 0.282270i | \(0.908913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 579.683 | 0.951860 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −208.698 | + | 248.717i | −0.341568 | + | 0.407065i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 119.947 | − | 43.6572i | 0.195672 | − | 0.0712189i | −0.242325 | − | 0.970195i | \(-0.577910\pi\) |
0.437997 | + | 0.898976i | \(0.355688\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 179.228 | + | 310.433i | 0.291428 | + | 0.504769i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 142.570 | + | 808.554i | 0.231070 | + | 1.31046i | 0.850735 | + | 0.525595i | \(0.176157\pi\) |
−0.619666 | + | 0.784866i | \(0.712732\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −181.415 | + | 314.220i | −0.293077 | + | 0.507625i | −0.974536 | − | 0.224232i | \(-0.928013\pi\) |
0.681458 | + | 0.731857i | \(0.261346\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −278.266 | − | 331.624i | −0.448093 | − | 0.534016i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 383.475 | − | 1053.59i | 0.615529 | − | 1.69115i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −135.540 | + | 768.687i | −0.216865 | + | 1.22990i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7948 | + | 1105.40i | 0.0299758 | + | 1.76300i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.4526 | + | 8.36717i | 0.0754413 | + | 0.0133023i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −966.329 | − | 351.715i | −1.53142 | − | 0.557393i | −0.567455 | − | 0.823405i | \(-0.692072\pi\) |
−0.963970 | + | 0.266012i | \(0.914294\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −637.347 | + | 534.797i | −1.00687 | + | 0.844861i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −415.333 | − | 239.793i | −0.654068 | − | 0.377626i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1905.35 | + | 335.965i | −2.99114 | + | 0.527418i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.6511 | + | 22.3152i | −0.0604868 | + | 0.0349221i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −152.065 | − | 417.795i | −0.237231 | − | 0.651786i | −0.999987 | − | 0.00510007i | \(-0.998377\pi\) |
0.762756 | − | 0.646686i | \(-0.223846\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 219.708 | + | 184.356i | 0.341691 | + | 0.286713i | 0.797443 | − | 0.603394i | \(-0.206185\pi\) |
−0.455752 | + | 0.890107i | \(0.650630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 440.596i | − | 0.683094i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 116.031 | 0.179337 | 0.0896685 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896685 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 924.111 | − | 1101.31i | 1.42390 | − | 1.69694i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1010.91 | + | 367.940i | −1.55285 | + | 0.565193i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −306.370 | − | 530.649i | −0.469173 | − | 0.812632i | 0.530206 | − | 0.847869i | \(-0.322115\pi\) |
−0.999379 | + | 0.0352370i | \(0.988781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −203.299 | − | 1152.97i | −0.310381 | − | 1.76026i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.4636 | − | 51.0324i | 0.0448456 | − | 0.0776749i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 190.151 | + | 226.613i | 0.288545 | + | 0.343874i | 0.890772 | − | 0.454451i | \(-0.150164\pi\) |
−0.602227 | + | 0.798325i | \(0.705720\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 267.124 | − | 733.918i | 0.404121 | − | 1.11031i | −0.556110 | − | 0.831109i | \(-0.687707\pi\) |
0.960231 | − | 0.279206i | \(-0.0900711\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.7657 | − | 106.425i | 0.0283042 | − | 0.160521i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −730.696 | − | 1217.33i | −1.09879 | − | 1.83057i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 292.160 | + | 51.5157i | 0.438021 | + | 0.0772350i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1055.53 | + | 384.182i | 1.57778 | + | 0.574263i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 252.899 | − | 212.207i | 0.376899 | − | 0.316256i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 636.410 | + | 367.431i | 0.945631 | + | 0.545960i | 0.891721 | − | 0.452586i | \(-0.149498\pi\) |
0.0539099 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −222.355 | + | 39.2072i | −0.329415 | + | 0.0580848i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −588.076 | + | 339.526i | −0.868650 | + | 0.501515i | −0.866899 | − | 0.498483i | \(-0.833891\pi\) |
−0.00175044 | + | 0.999998i | \(0.500557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 478.509 | + | 1314.69i | 0.704726 | + | 1.93622i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −748.895 | − | 628.397i | −1.09970 | − | 0.922757i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 233.214i | 0.341455i | 0.985318 | + | 0.170727i | \(0.0546118\pi\) | ||||
−0.985318 | + | 0.170727i | \(0.945388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 441.874 | 0.645072 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −194.039 | + | 231.247i | −0.282444 | + | 0.336603i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −707.714 | + | 257.587i | −1.02716 | + | 0.373856i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 635.093 | + | 1100.01i | 0.919092 | + | 1.59191i | 0.800797 | + | 0.598936i | \(0.204410\pi\) |
0.118296 | + | 0.992978i | \(0.462257\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −124.354 | − | 705.244i | −0.179442 | − | 1.01767i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 365.642 | − | 633.310i | 0.526103 | − | 0.911238i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.5261 | − | 20.8868i | −0.0251450 | − | 0.0299667i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 202.263 | − | 555.714i | 0.289361 | − | 0.795013i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.0955 | + | 221.722i | −0.0557711 | + | 0.316293i | −0.999912 | − | 0.0132478i | \(-0.995783\pi\) |
0.944141 | + | 0.329541i | \(0.106894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −183.071 | + | 530.896i | −0.260413 | + | 0.755186i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 365.942 | + | 64.5254i | 0.519066 | + | 0.0915254i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2187.17 | + | 796.063i | 3.09359 | + | 1.12597i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −248.832 | + | 208.795i | −0.350962 | + | 0.294492i | −0.801176 | − | 0.598429i | \(-0.795792\pi\) |
0.450214 | + | 0.892921i | \(0.351348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −63.2733 | − | 36.5308i | −0.0889920 | − | 0.0513795i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −542.196 | + | 95.6038i | −0.760444 | + | 0.134087i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1614.18 | − | 931.947i | 2.25759 | − | 1.30342i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 201.272 | + | 552.992i | 0.280715 | + | 0.771257i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 341.999 | + | 286.972i | 0.475660 | + | 0.399126i | 0.848854 | − | 0.528627i | \(-0.177293\pi\) |
−0.373194 | + | 0.927753i | \(0.621737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1593.78i | − | 2.21051i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 541.052 | 0.748343 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 99.4582 | − | 118.530i | 0.137184 | − | 0.163489i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 262.192 | − | 95.4301i | 0.360649 | − | 0.131266i | −0.155339 | − | 0.987861i | \(-0.549647\pi\) |
0.515988 | + | 0.856596i | \(0.327425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 131.389 | + | 227.572i | 0.180232 | + | 0.312171i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.81957 | + | 33.0044i | 0.00796111 | + | 0.0451497i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −610.557 | + | 1057.52i | −0.832956 | + | 1.44272i | 0.0627271 | + | 0.998031i | \(0.480020\pi\) |
−0.895683 | + | 0.444692i | \(0.853313\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1423.32 | + | 1696.24i | 1.93648 | + | 2.30781i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −243.479 | + | 668.954i | −0.330365 | + | 0.907671i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 179.692 | − | 1019.08i | 0.243155 | − | 1.37900i | −0.581583 | − | 0.813487i | \(-0.697566\pi\) |
0.824738 | − | 0.565515i | \(-0.191323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1190.68 | + | 410.586i | 1.60685 | + | 0.554097i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −120.400 | − | 21.2298i | −0.162046 | − | 0.0285731i | 0.0920363 | − | 0.995756i | \(-0.470662\pi\) |
−0.254083 | + | 0.967183i | \(0.581774\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −777.354 | − | 282.934i | −1.04343 | − | 0.379777i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 333.345 | − | 279.710i | 0.446246 | − | 0.374445i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −122.507 | − | 70.7292i | −0.163560 | − | 0.0944315i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −745.826 | + | 131.509i | −0.993111 | + | 0.175112i | −0.646514 | − | 0.762902i | \(-0.723774\pi\) |
−0.346597 | + | 0.938014i | \(0.612663\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 115.550 | − | 66.7130i | 0.153453 | − | 0.0885963i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −468.197 | − | 1286.36i | −0.620128 | − | 1.70379i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 830.988 | + | 697.282i | 1.09774 | + | 0.921112i | 0.997271 | − | 0.0738286i | \(-0.0235218\pi\) |
0.100467 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1300.93i | − | 1.71400i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 125.987 | 0.165555 | 0.0827774 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827774 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −521.924 | + | 622.005i | −0.684042 | + | 0.815209i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.7419 | + | 11.9171i | −0.0427999 | + | 0.0155779i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −818.909 | − | 1418.39i | −1.06768 | − | 1.84927i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5819 | − | 82.6982i | −0.0189622 | − | 0.107540i | 0.973858 | − | 0.227159i | \(-0.0729437\pi\) |
−0.992820 | + | 0.119619i | \(0.961833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.0174 | − | 72.7763i | 0.0544973 | − | 0.0943921i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −101.121 | − | 120.511i | −0.130816 | − | 0.155900i | 0.696660 | − | 0.717401i | \(-0.254669\pi\) |
−0.827476 | + | 0.561501i | \(0.810224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −98.2111 | + | 269.833i | −0.126724 | + | 0.348171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 224.216 | − | 1271.59i | 0.288567 | − | 1.63654i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 272.458 | − | 163.542i | 0.349753 | − | 0.209938i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 204.680 | + | 36.0906i | 0.262074 | + | 0.0462108i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −241.436 | − | 87.8754i | −0.308347 | − | 0.112229i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1029.73 | + | 864.048i | −1.31176 | + | 1.10070i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1094.56 | − | 631.944i | −1.39080 | − | 0.802978i | −0.397395 | − | 0.917648i | \(-0.630086\pi\) |
−0.993404 | + | 0.114670i | \(0.963419\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.5619 | + | 6.44685i | −0.0463396 | + | 0.00817092i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1497.42 | + | 864.538i | −1.89308 | + | 1.09297i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −128.634 | − | 353.418i | −0.162211 | − | 0.445672i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 660.291 | + | 554.050i | 0.830555 | + | 0.696918i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 477.946i | − | 0.599682i | −0.953989 | − | 0.299841i | \(-0.903066\pi\) | ||
0.953989 | − | 0.299841i | \(-0.0969335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.2645 | −0.0353748 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 206.132 | − | 245.658i | 0.257343 | − | 0.306689i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −257.866 | + | 93.8557i | −0.321129 | + | 0.116881i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 835.341 | + | 1446.85i | 1.03769 | + | 1.79733i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 267.315 | + | 1516.02i | 0.331245 | + | 1.87858i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −232.123 | + | 402.050i | −0.286926 | + | 0.496971i | −0.973075 | − | 0.230491i | \(-0.925967\pi\) |
0.686148 | + | 0.727462i | \(0.259300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 67.3090 | + | 80.2157i | 0.0829951 | + | 0.0989097i | 0.805944 | − | 0.591992i | \(-0.201658\pi\) |
−0.722949 | + | 0.690902i | \(0.757214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −115.404 | + | 317.071i | −0.141949 | + | 0.390001i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 108.431 | − | 614.943i | 0.133044 | − | 0.754532i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −390.532 | + | 6.64010i | −0.478007 | + | 0.00812742i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −803.431 | − | 141.667i | −0.980991 | − | 0.172975i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 195.635 | + | 71.2054i | 0.238289 | + | 0.0867300i | 0.458404 | − | 0.888744i | \(-0.348421\pi\) |
−0.220115 | + | 0.975474i | \(0.570643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 523.589 | − | 439.343i | 0.636195 | − | 0.533831i | −0.266652 | − | 0.963793i | \(-0.585917\pi\) |
0.902847 | + | 0.429962i | \(0.141473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −587.607 | − | 339.255i | −0.712251 | − | 0.411218i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 831.241 | − | 146.570i | 1.00513 | − | 0.177231i | 0.353229 | − | 0.935537i | \(-0.385084\pi\) |
0.651899 | + | 0.758306i | \(0.273973\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −77.9552 | + | 45.0075i | −0.0940353 | + | 0.0542913i | −0.546280 | − | 0.837602i | \(-0.683957\pi\) |
0.452245 | + | 0.891894i | \(0.350623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −326.083 | − | 895.906i | −0.392398 | − | 1.07811i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −129.023 | − | 108.263i | −0.154890 | − | 0.129968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1436.61i | 1.72049i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 476.816 | 0.569673 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 495.740 | − | 590.800i | 0.590870 | − | 0.704171i | −0.384903 | − | 0.922957i | \(-0.625765\pi\) |
0.975773 | + | 0.218786i | \(0.0702096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −624.827 | + | 227.418i | −0.742957 | + | 0.270414i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −175.489 | − | 303.955i | −0.208171 | − | 0.360563i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −191.036 | − | 1083.42i | −0.226078 | − | 1.28215i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −920.780 | + | 1594.84i | −1.08711 | + | 1.88293i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −363.682 | − | 433.419i | −0.428365 | − | 0.510505i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 226.010 | − | 620.958i | 0.265582 | − | 0.729680i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 110.511 | − | 626.742i | 0.129556 | − | 0.734750i | −0.848941 | − | 0.528488i | \(-0.822759\pi\) |
0.978497 | − | 0.206262i | \(-0.0661298\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −77.3044 | − | 398.659i | −0.0904145 | − | 0.466268i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −861.767 | − | 151.953i | −1.00556 | − | 0.177308i | −0.353469 | − | 0.935446i | \(-0.614998\pi\) |
−0.652094 | + | 0.758138i | \(0.726109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 328.931 | + | 119.721i | 0.382923 | + | 0.139373i | 0.526307 | − | 0.850294i | \(-0.323576\pi\) |
−0.143384 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −559.706 | + | 469.649i | −0.650065 | + | 0.545470i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −573.859 | − | 331.317i | −0.664958 | − | 0.383914i | 0.129206 | − | 0.991618i | \(-0.458757\pi\) |
−0.794163 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1493.72 | − | 263.383i | 1.72684 | − | 0.304489i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −877.789 | + | 506.791i | −1.01244 | + | 0.584535i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 116.368 | + | 319.719i | 0.133911 | + | 0.367916i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 621.260 | + | 521.299i | 0.713272 | + | 0.598506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 400.157i | 0.458370i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −996.786 | −1.13918 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −361.550 | + | 430.879i | −0.412258 | + | 0.491310i | −0.931717 | − | 0.363186i | \(-0.881689\pi\) |
0.519459 | + | 0.854495i | \(0.326134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1702.77 | − | 619.758i | 1.93717 | − | 0.705072i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 638.016 | + | 1105.08i | 0.724195 | + | 1.25434i | 0.959305 | + | 0.282373i | \(0.0911217\pi\) |
−0.235110 | + | 0.971969i | \(0.575545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 129.225 | + | 732.873i | 0.146348 | + | 0.829981i | 0.966275 | + | 0.257513i | \(0.0829030\pi\) |
−0.819927 | + | 0.572468i | \(0.805986\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −937.228 | + | 1623.33i | −1.05902 | + | 1.83427i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −630.328 | − | 751.196i | −0.710629 | − | 0.846895i | 0.283055 | − | 0.959104i | \(-0.408652\pi\) |
−0.993685 | + | 0.112208i | \(0.964208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 334.339 | − | 918.588i | 0.376084 | − | 1.03328i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −286.329 | + | 1623.85i | −0.321357 | + | 1.82251i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.6785 | − | 325.333i | 0.0578707 | − | 0.364315i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 202.729 | + | 35.7466i | 0.226513 | + | 0.0399404i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1392.67 | − | 506.890i | −1.55258 | − | 0.565094i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −250.312 | + | 210.037i | −0.278434 | + | 0.233634i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −56.7796 | − | 32.7817i | −0.0630184 | − | 0.0363837i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 884.425 | − | 155.948i | 0.979430 | − | 0.172700i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1120.19 | + | 646.741i | −1.23778 | + | 0.714631i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −342.939 | − | 942.216i | −0.378102 | − | 1.03883i | −0.972142 | − | 0.234392i | \(-0.924690\pi\) |
0.594040 | − | 0.804435i | \(-0.297532\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 509.967 | + | 427.913i | 0.561020 | + | 0.470752i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 420.233i | − | 0.461287i | −0.973038 | − | 0.230644i | \(-0.925917\pi\) | ||
0.973038 | − | 0.230644i | \(-0.0740832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2026.44 | −2.21954 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −276.681 | + | 329.736i | −0.302384 | + | 0.360367i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2242.44 | − | 816.181i | 2.44541 | − | 0.890056i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 143.066 | + | 247.798i | 0.155676 | + | 0.269639i | 0.933305 | − | 0.359085i | \(-0.116911\pi\) |
−0.777629 | + | 0.628724i | \(0.783578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 50.7505 | + | 287.820i | 0.0551036 | + | 0.312508i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 118.387 | − | 205.052i | 0.128263 | − | 0.222158i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −221.538 | − | 264.018i | −0.239500 | − | 0.285425i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 155.909 | − | 428.358i | 0.168187 | − | 0.462090i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 133.744 | − | 758.499i | 0.143965 | − | 0.816468i | −0.824227 | − | 0.566260i | \(-0.808390\pi\) |
0.968192 | − | 0.250208i | \(-0.0804991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1482.05 | − | 1287.15i | 1.59189 | − | 1.38255i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 687.096 | + | 121.153i | 0.736437 | + | 0.129854i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 152.474 | + | 55.4962i | 0.163074 | + | 0.0593542i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 73.1662 | − | 61.3938i | 0.0780856 | − | 0.0655216i | −0.602909 | − | 0.797810i | \(-0.705992\pi\) |
0.680995 | + | 0.732288i | \(0.261548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −460.546 | − | 265.896i | −0.490464 | − | 0.283170i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 980.482 | − | 172.885i | 1.04196 | − | 0.183725i | 0.373619 | − | 0.927582i | \(-0.378117\pi\) |
0.668339 | + | 0.743857i | \(0.267006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −323.829 | + | 186.963i | −0.343403 | + | 0.198264i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −494.870 | − | 1359.65i | −0.523672 | − | 1.43878i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 537.232 | + | 450.791i | 0.567299 | + | 0.476021i | 0.880748 | − | 0.473584i | \(-0.157040\pi\) |
−0.313449 | + | 0.949605i | \(0.601485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 312.621i | 0.329422i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 900.846 | 0.947262 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 441.334 | − | 525.961i | 0.463099 | − | 0.551900i | −0.483066 | − | 0.875584i | \(-0.660477\pi\) |
0.946165 | + | 0.323683i | \(0.104921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 162.444 | − | 59.1246i | 0.170098 | − | 0.0619106i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −386.052 | − | 668.662i | −0.403398 | − | 0.698706i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 156.401 | + | 886.991i | 0.163087 | + | 0.924913i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −177.297 | + | 307.087i | −0.184492 | + | 0.319549i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.0069 | − | 30.9938i | −0.0270061 | − | 0.0321846i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.39916 | − | 14.8341i | 0.00559498 | − | 0.0153721i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 140.913 | − | 799.159i | 0.145722 | − | 0.826431i | −0.821062 | − | 0.570838i | \(-0.806618\pi\) |
0.966785 | − | 0.255593i | \(-0.0822706\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 39.2464 | + | 102.379i | 0.0405019 | + | 0.105654i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −130.384 | − | 22.9902i | −0.134278 | − | 0.0236769i | 0.106105 | − | 0.994355i | \(-0.466162\pi\) |
−0.240383 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1400.69 | + | 509.808i | 1.43955 | + | 0.523955i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −592.133 | + | 496.859i | −0.607316 | + | 0.509599i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 233.290 | + | 134.690i | 0.238782 | + | 0.137861i | 0.614617 | − | 0.788826i | \(-0.289311\pi\) |
−0.375835 | + | 0.926687i | \(0.622644\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1470.69 | + | 259.323i | −1.50224 | + | 0.264885i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −201.123 | + | 116.119i | −0.205019 | + | 0.118368i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −228.444 | − | 627.646i | −0.232395 | − | 0.638501i | 0.767602 | − | 0.640927i | \(-0.221450\pi\) |
−0.999997 | + | 0.00242643i | \(0.999228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 370.539 | + | 310.919i | 0.376181 | + | 0.315654i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 757.408i | 0.767384i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 459.609 | 0.464721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −678.867 | + | 809.043i | −0.685033 | + | 0.816390i | −0.990745 | − | 0.135734i | \(-0.956661\pi\) |
0.305713 | + | 0.952124i | \(0.401105\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1248.22 | − | 454.314i | 1.25702 | − | 0.457517i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −489.004 | − | 846.980i | −0.491462 | − | 0.851237i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −252.072 | − | 1429.57i | −0.252830 | − | 1.43387i | −0.801581 | − | 0.597886i | \(-0.796008\pi\) |
0.548751 | − | 0.835986i | \(-0.315104\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −286.149 | + | 495.625i | −0.286436 | + | 0.496121i |
(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 | 76.3.j.a.21.1 | ✓ | 18 | |
4.3 | odd | 2 | 304.3.z.b.97.3 | 18 | |||
19.3 | odd | 18 | 1444.3.c.c.721.3 | 18 | |||
19.10 | odd | 18 | inner | 76.3.j.a.29.1 | yes | 18 | |
19.16 | even | 9 | 1444.3.c.c.721.16 | 18 | |||
76.67 | even | 18 | 304.3.z.b.257.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.j.a.21.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
76.3.j.a.29.1 | yes | 18 | 19.10 | odd | 18 | inner | |
304.3.z.b.97.3 | 18 | 4.3 | odd | 2 | |||
304.3.z.b.257.3 | 18 | 76.67 | even | 18 | |||
1444.3.c.c.721.3 | 18 | 19.3 | odd | 18 | |||
1444.3.c.c.721.16 | 18 | 19.16 | even | 9 |