Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.92607408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(0.500000 + 0.630453i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.f.673.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.88028 | + | 4.98878i | 0.576055 | + | 0.997757i | 0.995926 | + | 0.0901730i | \(0.0287420\pi\) |
−0.419871 | + | 0.907584i | \(0.637925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.94451 | −0.277787 | −0.138893 | − | 0.990307i | \(-0.544354\pi\) | ||||
−0.138893 | + | 0.990307i | \(0.544354\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.46561 | −0.769601 | −0.384800 | − | 0.923000i | \(-0.625730\pi\) | ||||
−0.384800 | + | 0.923000i | \(0.625730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.7415 | − | 9.66573i | −1.28781 | − | 0.743518i | −0.309547 | − | 0.950884i | \(-0.600178\pi\) |
−0.978263 | + | 0.207366i | \(0.933511\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.64083 | + | 4.98878i | 0.576055 | + | 0.332586i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.5365 | + | 21.7138i | 0.737440 | + | 1.27728i | 0.953644 | + | 0.300936i | \(0.0972990\pi\) |
−0.216204 | + | 0.976348i | \(0.569368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.8181 | + | 6.59651i | −0.937797 | + | 0.347185i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.91676 | + | 1.68399i | −0.138893 | + | 0.0801901i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.6408 | + | 27.0907i | −0.680036 | + | 1.17786i | 0.294933 | + | 0.955518i | \(0.404703\pi\) |
−0.974969 | + | 0.222339i | \(0.928631\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.09198 | + | 7.08751i | −0.163679 | + | 0.283500i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.7071 | + | 7.91383i | 0.472660 | + | 0.272891i | 0.717353 | − | 0.696710i | \(-0.245354\pi\) |
−0.244692 | + | 0.969601i | \(0.578687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.4237i | 0.465280i | 0.972563 | + | 0.232640i | \(0.0747363\pi\) | ||||
−0.972563 | + | 0.232640i | \(0.925264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.6984 | + | 7.33143i | −0.384800 | + | 0.222165i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.60071 | − | 9.70072i | −0.160020 | − | 0.277163i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.6423i | 1.12547i | 0.826638 | + | 0.562734i | \(0.190251\pi\) | ||||
−0.826638 | + | 0.562734i | \(0.809749\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −33.4831 | −0.858541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.53439 | − | 0.885881i | 0.0374242 | − | 0.0216069i | −0.481171 | − | 0.876627i | \(-0.659788\pi\) |
0.518595 | + | 0.855020i | \(0.326455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.4358 | − | 25.0035i | −0.335716 | − | 0.581476i | 0.647906 | − | 0.761720i | \(-0.275645\pi\) |
−0.983622 | + | 0.180243i | \(0.942311\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 17.2817 | 0.384037 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.70506 | + | 2.95325i | −0.0362778 | + | 0.0628350i | −0.883594 | − | 0.468253i | \(-0.844883\pi\) |
0.847316 | + | 0.531088i | \(0.178217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.2189 | −0.922835 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 37.6094 | + | 21.7138i | 0.737440 | + | 0.425761i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −80.0952 | − | 46.2430i | −1.51123 | − | 0.872510i | −0.999914 | − | 0.0131174i | \(-0.995824\pi\) |
−0.511317 | − | 0.859392i | \(-0.670842\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.3833 | − | 42.2331i | −0.443333 | − | 0.767874i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.0145 | + | 25.3257i | −0.368675 | + | 0.444311i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.27292 | + | 2.46697i | −0.0724224 | + | 0.0418131i | −0.535774 | − | 0.844361i | \(-0.679980\pi\) |
0.463352 | + | 0.886175i | \(0.346647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.45989 | − | 12.9209i | 0.122293 | − | 0.211818i | −0.798378 | − | 0.602156i | \(-0.794309\pi\) |
0.920672 | + | 0.390338i | \(0.127642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.91676 | + | 5.05197i | −0.0462978 | + | 0.0801901i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 111.360i | − | 1.71323i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 70.4113 | + | 40.6520i | 1.05091 | + | 0.606746i | 0.922905 | − | 0.385027i | \(-0.125808\pi\) |
0.128009 | + | 0.991773i | \(0.459141\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 54.1814i | 0.785238i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −52.9948 | + | 30.5966i | −0.746406 | + | 0.430938i | −0.824394 | − | 0.566017i | \(-0.808484\pi\) |
0.0779878 | + | 0.996954i | \(0.475150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −38.8299 | − | 67.2553i | −0.531916 | − | 0.921306i | −0.999306 | − | 0.0372545i | \(-0.988139\pi\) |
0.467390 | − | 0.884051i | \(-0.345195\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.1750i | 0.189000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.4614 | 0.213785 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −84.0207 | + | 48.5094i | −1.06355 | + | 0.614043i | −0.926413 | − | 0.376509i | \(-0.877125\pi\) |
−0.137140 | + | 0.990552i | \(0.543791\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 102.323 | 1.23280 | 0.616401 | − | 0.787432i | \(-0.288590\pi\) | ||||
0.616401 | + | 0.787432i | \(0.288590\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72.2171 | + | 125.084i | −0.849612 | + | 1.47157i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 27.4143 | 0.315107 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 103.596 | + | 59.8111i | 1.16400 | + | 0.672034i | 0.952259 | − | 0.305292i | \(-0.0987540\pi\) |
0.211739 | + | 0.977326i | \(0.432087\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.5540 | + | 18.7951i | 0.357737 | + | 0.206539i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4913 | + | 21.6355i | 0.134315 | + | 0.232640i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −84.2297 | − | 69.8911i | −0.886629 | − | 0.735695i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −42.1438 | + | 24.3318i | −0.434473 | + | 0.250843i | −0.701250 | − | 0.712915i | \(-0.747374\pi\) |
0.266778 | + | 0.963758i | \(0.414041\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.6984 | + | 21.9943i | −0.128267 | + | 0.222165i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −81.5540 | + | 141.256i | −0.807465 | + | 1.39857i | 0.107149 | + | 0.994243i | \(0.465828\pi\) |
−0.914614 | + | 0.404327i | \(0.867506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.2732i | 0.177410i | 0.996058 | + | 0.0887050i | \(0.0282728\pi\) | ||||
−0.996058 | + | 0.0887050i | \(0.971727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.8021 | − | 9.70072i | −0.160020 | − | 0.0923878i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 55.4789i | 0.518494i | 0.965811 | + | 0.259247i | \(0.0834744\pi\) | ||||
−0.965811 | + | 0.259247i | \(0.916526\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96.4369 | − | 55.6779i | 0.884743 | − | 0.510806i | 0.0125234 | − | 0.999922i | \(-0.496014\pi\) |
0.872219 | + | 0.489115i | \(0.162680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.0633 | + | 62.4635i | 0.324895 | + | 0.562734i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110.968i | 0.982019i | 0.871154 | + | 0.491010i | \(0.163372\pi\) | ||||
−0.871154 | + | 0.491010i | \(0.836628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −180.200 | −1.56695 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50.2246 | + | 28.9972i | −0.429270 | + | 0.247839i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.3773 | − | 42.2227i | −0.204851 | − | 0.354812i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.3335 | −0.407715 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.53439 | − | 2.65764i | 0.0124747 | − | 0.0216069i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 96.8697 | 0.774958 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 209.627 | + | 121.028i | 1.65061 | + | 0.952979i | 0.976822 | + | 0.214052i | \(0.0686661\pi\) |
0.673785 | + | 0.738927i | \(0.264667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −43.3073 | − | 25.0035i | −0.335716 | − | 0.193825i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −78.7288 | − | 136.362i | −0.600983 | − | 1.04093i | −0.992672 | − | 0.120836i | \(-0.961443\pi\) |
0.391689 | − | 0.920098i | \(-0.371891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.6475 | − | 12.8270i | 0.260507 | − | 0.0964433i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25.9225 | − | 14.9664i | 0.192018 | − | 0.110862i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 121.173 | − | 209.877i | 0.884473 | − | 1.53195i | 0.0381558 | − | 0.999272i | \(-0.487852\pi\) |
0.846317 | − | 0.532680i | \(-0.178815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 65.0431 | − | 112.658i | 0.467936 | − | 0.810489i | −0.531392 | − | 0.847126i | \(-0.678331\pi\) |
0.999329 | + | 0.0366365i | \(0.0116644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.90649i | 0.0418900i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 141.727 | + | 81.8263i | 0.991100 | + | 0.572212i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 91.1760i | 0.628800i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −67.8283 | + | 39.1607i | −0.461417 | + | 0.266399i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −102.368 | − | 177.306i | −0.687030 | − | 1.18997i | −0.972794 | − | 0.231672i | \(-0.925581\pi\) |
0.285764 | − | 0.958300i | \(-0.407753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 234.305i | 1.55169i | 0.630924 | + | 0.775845i | \(0.282676\pi\) | ||||
−0.630924 | + | 0.775845i | \(0.717324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 75.2189 | 0.491627 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −71.9566 | + | 41.5441i | −0.464236 | + | 0.268027i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 44.2955 | + | 76.7220i | 0.282137 | + | 0.488675i | 0.971911 | − | 0.235349i | \(-0.0756234\pi\) |
−0.689774 | + | 0.724025i | \(0.742290\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −160.190 | −1.00749 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.4137 | − | 52.6780i | 0.188905 | − | 0.327193i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −115.918 | −0.711153 | −0.355576 | − | 0.934647i | \(-0.615715\pi\) | ||||
−0.355576 | + | 0.934647i | \(0.615715\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −73.1499 | − | 42.2331i | −0.443333 | − | 0.255958i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −78.0426 | − | 45.0579i | −0.467321 | − | 0.269808i | 0.247797 | − | 0.968812i | \(-0.420293\pi\) |
−0.715118 | + | 0.699004i | \(0.753627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 102.353 | + | 177.280i | 0.605638 | + | 1.04900i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.58896 | + | 56.1876i | −0.0560758 | + | 0.328583i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −38.5739 | + | 22.2707i | −0.222971 | + | 0.128732i | −0.607325 | − | 0.794454i | \(-0.707757\pi\) |
0.384354 | + | 0.923186i | \(0.374424\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.95687 | − | 13.7817i | 0.0454678 | − | 0.0787526i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.27292 | + | 7.40091i | −0.0241408 | + | 0.0418131i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 229.632i | − | 1.28286i | −0.767181 | − | 0.641431i | \(-0.778341\pi\) | ||
0.767181 | − | 0.641431i | \(-0.221659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 157.070 | + | 90.6845i | 0.867791 | + | 0.501019i | 0.866613 | − | 0.498980i | \(-0.166292\pi\) |
0.00117734 | + | 0.999999i | \(0.499625\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 25.8418i | − | 0.141212i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −207.745 | + | 119.941i | −1.12294 | + | 0.648332i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −106.129 | − | 183.821i | −0.567535 | − | 0.982999i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.1039i | 0.0534600i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 278.704 | 1.45918 | 0.729592 | − | 0.683882i | \(-0.239710\pi\) | ||||
0.729592 | + | 0.683882i | \(0.239710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −167.512 | + | 96.7133i | −0.867939 | + | 0.501105i | −0.866663 | − | 0.498894i | \(-0.833740\pi\) |
−0.00127645 | + | 0.999999i | \(0.500406\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −96.4405 | − | 167.040i | −0.494567 | − | 0.856615i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −96.9300 | −0.492030 | −0.246015 | − | 0.969266i | \(-0.579121\pi\) | ||||
−0.246015 | + | 0.969266i | \(0.579121\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −172.893 | + | 299.460i | −0.868811 | + | 1.50482i | −0.00559823 | + | 0.999984i | \(0.501782\pi\) |
−0.863213 | + | 0.504840i | \(0.831551\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 140.823 | 0.700610 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.6536 | − | 15.3885i | −0.131299 | − | 0.0758053i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.83894 | + | 5.10316i | 0.0431168 | + | 0.0248935i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 46.9225 | + | 81.2721i | 0.226679 | + | 0.392619i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 150.841 | − | 55.8435i | 0.721729 | − | 0.267194i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1758 | − | 6.45233i | 0.0529657 | − | 0.0305798i | −0.473283 | − | 0.880910i | \(-0.656931\pi\) |
0.526249 | + | 0.850330i | \(0.323598\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −52.9948 | + | 91.7897i | −0.248802 | + | 0.430938i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 83.1580 | − | 144.034i | 0.386781 | − | 0.669925i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 28.0469i | − | 0.129248i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −116.490 | − | 67.2553i | −0.531916 | − | 0.307102i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 484.697i | − | 2.19320i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 80.3821 | − | 46.4086i | 0.360458 | − | 0.208110i | −0.308824 | − | 0.951119i | \(-0.599935\pi\) |
0.669282 | + | 0.743009i | \(0.266602\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2759 | + | 21.2625i | 0.0545597 | + | 0.0945002i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 280.870i | − | 1.23731i | −0.785662 | − | 0.618656i | \(-0.787677\pi\) | ||
0.785662 | − | 0.618656i | \(-0.212323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 137.541 | 0.600615 | 0.300308 | − | 0.953842i | \(-0.402911\pi\) | ||||
0.300308 | + | 0.953842i | \(0.402911\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.6921 | − | 14.2560i | 0.106892 | − | 0.0617143i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −183.683 | − | 318.148i | −0.788339 | − | 1.36544i | −0.926984 | − | 0.375101i | \(-0.877608\pi\) |
0.138645 | − | 0.990342i | \(-0.455725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.6441 | −0.0835921 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −84.0207 | + | 145.528i | −0.354518 | + | 0.614043i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 196.388 | 0.821707 | 0.410854 | − | 0.911701i | \(-0.365231\pi\) | ||||
0.410854 | + | 0.911701i | \(0.365231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −118.225 | − | 68.2572i | −0.490560 | − | 0.283225i | 0.234247 | − | 0.972177i | \(-0.424738\pi\) |
−0.724807 | + | 0.688952i | \(0.758071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −130.243 | − | 225.587i | −0.531604 | − | 0.920765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 362.063 | + | 61.7896i | 1.46584 | + | 0.250160i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 153.484 | − | 88.6140i | 0.616401 | − | 0.355879i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.3322 | − | 40.4126i | 0.0929571 | − | 0.161006i | −0.815797 | − | 0.578338i | \(-0.803701\pi\) |
0.908754 | + | 0.417332i | \(0.137035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 132.409 | − | 229.339i | 0.523356 | − | 0.906480i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 250.167i | 0.981048i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.73878 | + | 2.73593i | 0.0184388 | + | 0.0106457i | 0.509191 | − | 0.860653i | \(-0.329945\pi\) |
−0.490752 | + | 0.871299i | \(0.663278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 80.9737i | − | 0.312640i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.1214 | − | 23.7415i | 0.157553 | − | 0.0909635i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −37.1071 | − | 64.2713i | −0.141091 | − | 0.244378i | 0.786816 | − | 0.617187i | \(-0.211728\pi\) |
−0.927908 | + | 0.372809i | \(0.878394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 532.770i | − | 2.01045i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 207.192 | 0.775998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −64.2197 | + | 37.0772i | −0.238735 | + | 0.137834i | −0.614595 | − | 0.788843i | \(-0.710681\pi\) |
0.375860 | + | 0.926676i | \(0.377347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −48.0380 | − | 83.2043i | −0.177262 | − | 0.307027i | 0.763680 | − | 0.645595i | \(-0.223391\pi\) |
−0.940942 | + | 0.338568i | \(0.890057\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 65.1080 | 0.238491 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.6411 | − | 60.0001i | 0.125968 | − | 0.218182i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 123.007 | 0.444068 | 0.222034 | − | 0.975039i | \(-0.428730\pi\) | ||||
0.222034 | + | 0.975039i | \(0.428730\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 37.4738 | + | 21.6355i | 0.134315 | + | 0.0775466i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 352.110 | + | 203.291i | 1.25306 | + | 0.723454i | 0.971716 | − | 0.236153i | \(-0.0758866\pi\) |
0.281344 | + | 0.959607i | \(0.409220\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 92.7689 | + | 160.680i | 0.327805 | + | 0.567776i | 0.982076 | − | 0.188485i | \(-0.0603576\pi\) |
−0.654271 | + | 0.756260i | \(0.727024\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −186.872 | − | 31.8915i | −0.655691 | − | 0.111900i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.98363 | + | 1.72260i | −0.0103959 | + | 0.00600209i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −169.827 | + | 294.149i | −0.587636 | + | 1.01782i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −42.1438 | + | 72.9953i | −0.144824 | + | 0.250843i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 360.407i | 1.23006i | 0.788505 | + | 0.615028i | \(0.210855\pi\) | ||||
−0.788505 | + | 0.615028i | \(0.789145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.6144 | − | 14.2111i | −0.0834385 | − | 0.0481733i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 43.9886i | 0.148110i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 523.703 | − | 302.360i | 1.75152 | − | 1.01124i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.0704 | + | 48.6194i | 0.0932573 | + | 0.161526i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 282.511i | 0.932380i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 85.9461 | 0.281791 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 233.152 | − | 134.610i | 0.759453 | − | 0.438470i | −0.0696463 | − | 0.997572i | \(-0.522187\pi\) |
0.829099 | + | 0.559101i | \(0.188854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.8251 | + | 27.4098i | 0.0512139 | + | 0.0887050i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −53.4530 | −0.171874 | −0.0859372 | − | 0.996301i | \(-0.527388\pi\) | ||||
−0.0859372 | + | 0.996301i | \(0.527388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −119.760 | + | 207.430i | −0.382618 | + | 0.662715i | −0.991436 | − | 0.130596i | \(-0.958311\pi\) |
0.608817 | + | 0.793310i | \(0.291644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −33.6043 | −0.106680 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 391.754 | + | 226.179i | 1.23582 | + | 0.713499i | 0.968236 | − | 0.250036i | \(-0.0804426\pi\) |
0.267580 | + | 0.963536i | \(0.413776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −116.039 | − | 66.9954i | −0.363760 | − | 0.210017i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48.0461 | + | 83.2184i | 0.149676 | + | 0.259247i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −366.612 | − | 304.203i | −1.13502 | − | 0.941805i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 137.012 | − | 79.1039i | 0.421575 | − | 0.243397i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 96.4369 | − | 167.034i | 0.294914 | − | 0.510806i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31549 | − | 5.74260i | 0.0100775 | − | 0.0174547i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 95.4707i | − | 0.288431i | −0.989546 | − | 0.144216i | \(-0.953934\pi\) | ||
0.989546 | − | 0.144216i | \(-0.0460659\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 108.190 | + | 62.4635i | 0.324895 | + | 0.187578i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 468.356i | 1.39808i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −82.2367 | + | 47.4794i | −0.244026 | + | 0.140888i | −0.617026 | − | 0.786943i | \(-0.711663\pi\) |
0.373000 | + | 0.927831i | \(0.378329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 96.1013 | + | 166.452i | 0.283485 | + | 0.491010i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 122.105i | − | 0.358080i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 183.209 | 0.534138 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −270.299 | + | 156.057i | −0.783476 | + | 0.452340i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −115.221 | − | 199.568i | −0.332048 | − | 0.575124i | 0.650865 | − | 0.759193i | \(-0.274406\pi\) |
−0.982913 | + | 0.184069i | \(0.941073\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −209.160 | −0.599312 | −0.299656 | − | 0.954047i | \(-0.596872\pi\) | ||||
−0.299656 | + | 0.954047i | \(0.596872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −50.2246 | + | 86.9916i | −0.143090 | + | 0.247839i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 326.125 | 0.923866 | 0.461933 | − | 0.886915i | \(-0.347156\pi\) | ||||
0.461933 | + | 0.886915i | \(0.347156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −305.279 | − | 176.253i | −0.859942 | − | 0.496488i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −73.1318 | − | 42.2227i | −0.204851 | − | 0.118271i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 268.735 | + | 465.463i | 0.748566 | + | 1.29655i | 0.948510 | + | 0.316747i | \(0.102590\pi\) |
−0.199945 | + | 0.979807i | \(0.564076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 273.972 | − | 235.075i | 0.758925 | − | 0.651178i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −74.0002 | + | 42.7240i | −0.203857 | + | 0.117697i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 223.682 | − | 387.428i | 0.612826 | − | 1.06145i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 181.274 | − | 313.976i | 0.493935 | − | 0.855520i | −0.506041 | − | 0.862509i | \(-0.668892\pi\) |
0.999976 | + | 0.00698970i | \(0.00222491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5.31529i | − | 0.0144046i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 155.746 | + | 89.9198i | 0.419800 | + | 0.242371i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 336.486i | − | 0.902108i | −0.892497 | − | 0.451054i | \(-0.851048\pi\) | ||
0.892497 | − | 0.451054i | \(-0.148952\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 145.305 | − | 83.8916i | 0.387479 | − | 0.223711i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −152.986 | − | 264.979i | −0.405798 | − | 0.702863i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 336.744i | 0.888507i | 0.895901 | + | 0.444253i | \(0.146531\pi\) | ||||
−0.895901 | + | 0.444253i | \(0.853469\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 419.254 | 1.10041 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 193.755 | − | 111.865i | 0.505888 | − | 0.292075i | −0.225254 | − | 0.974300i | \(-0.572321\pi\) |
0.731142 | + | 0.682226i | \(0.238988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 47.4134 | + | 82.1225i | 0.123152 | + | 0.213305i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −86.6146 | −0.223810 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 100.458 | − | 173.998i | 0.258246 | − | 0.447295i | −0.707526 | − | 0.706687i | \(-0.750189\pi\) |
0.965772 | + | 0.259392i | \(0.0835221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −784.324 | −2.00594 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −236.186 | − | 136.362i | −0.600983 | − | 0.346978i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −484.006 | − | 279.441i | −1.22533 | − | 0.707445i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −53.1506 | − | 92.0595i | −0.133880 | − | 0.231888i | 0.791289 | − | 0.611443i | \(-0.209410\pi\) |
−0.925169 | + | 0.379555i | \(0.876077\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 40.8627 | − | 49.2460i | 0.102413 | − | 0.123424i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 185.008 | − | 106.815i | 0.461368 | − | 0.266371i | −0.251252 | − | 0.967922i | \(-0.580842\pi\) |
0.712619 | + | 0.701551i | \(0.247509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 139.415 | − | 241.474i | 0.345944 | − | 0.599192i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.9225 | − | 44.8991i | 0.0640061 | − | 0.110862i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 352.528i | − | 0.866161i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −46.6112 | − | 26.9110i | −0.113964 | − | 0.0657970i | 0.441935 | − | 0.897047i | \(-0.354292\pi\) |
−0.555898 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 419.755i | − | 1.02130i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.30872 | − | 4.79704i | 0.0201180 | − | 0.0116151i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 294.717 | + | 510.465i | 0.710162 | + | 1.23004i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 225.316i | − | 0.540326i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 808.890 | 1.93052 | 0.965262 | − | 0.261282i | \(-0.0841454\pi\) | ||||
0.965262 | + | 0.261282i | \(0.0841454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −309.086 | + | 178.451i | −0.734171 | + | 0.423874i | −0.819946 | − | 0.572441i | \(-0.805997\pi\) |
0.0857753 | + | 0.996315i | \(0.472663\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.11517 | + | 8.85974i | 0.0120926 | + | 0.0209450i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −205.196 | −0.482814 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5058 | + | 25.1248i | −0.0339714 | + | 0.0588402i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 283.455 | 0.660733 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.3673 | + | 20.9967i | 0.0843789 | + | 0.0487162i | 0.541596 | − | 0.840639i | \(-0.317820\pi\) |
−0.457217 | + | 0.889355i | \(0.651154\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 533.602 | + | 308.075i | 1.23234 | + | 0.711491i | 0.967517 | − | 0.252807i | \(-0.0813538\pi\) |
0.264821 | + | 0.964298i | \(0.414687\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 78.9607 | + | 136.764i | 0.181519 | + | 0.314400i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 99.9862 | − | 585.881i | 0.228801 | − | 1.34069i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 408.012 | − | 235.566i | 0.929413 | − | 0.536597i | 0.0427870 | − | 0.999084i | \(-0.486376\pi\) |
0.886626 | + | 0.462487i | \(0.153043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −67.8283 | + | 117.482i | −0.153806 | + | 0.266399i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −52.2697 | + | 90.5338i | −0.117990 | + | 0.204365i | −0.918971 | − | 0.394325i | \(-0.870979\pi\) |
0.800981 | + | 0.598690i | \(0.204312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 689.089i | 1.54852i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −307.103 | − | 177.306i | −0.687030 | − | 0.396657i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 713.259i | 1.58855i | 0.607559 | + | 0.794275i | \(0.292149\pi\) | ||||
−0.607559 | + | 0.794275i | \(0.707851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.9896 | + | 7.49952i | −0.0288017 | + | 0.0166287i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 202.914 | + | 351.458i | 0.447934 | + | 0.775845i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 216.540i | 0.475912i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.29457 | −0.0115855 | −0.00579275 | − | 0.999983i | \(-0.501844\pi\) | ||||
−0.00579275 | + | 0.999983i | \(0.501844\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 112.828 | − | 65.1415i | 0.245813 | − | 0.141920i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −93.4120 | − | 161.794i | −0.202629 | − | 0.350964i | 0.746746 | − | 0.665110i | \(-0.231615\pi\) |
−0.949375 | + | 0.314146i | \(0.898282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −718.582 | −1.55201 | −0.776007 | − | 0.630725i | \(-0.782758\pi\) | ||||
−0.776007 | + | 0.630725i | \(0.782758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −71.9566 | + | 124.632i | −0.154745 | + | 0.268027i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −864.548 | −1.85128 | −0.925641 | − | 0.378404i | \(-0.876473\pi\) | ||||
−0.925641 | + | 0.378404i | \(0.876473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −136.915 | − | 79.0480i | −0.291930 | − | 0.168546i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 132.886 | + | 76.7220i | 0.282137 | + | 0.162892i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 122.208 | + | 211.670i | 0.258367 | + | 0.447505i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.1585 | − | 153.279i | 0.0550706 | − | 0.322693i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −240.286 | + | 138.729i | −0.503744 | + | 0.290837i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −63.1395 | + | 109.361i | −0.131815 | + | 0.228311i | −0.924376 | − | 0.381482i | \(-0.875414\pi\) |
0.792561 | + | 0.609793i | \(0.208747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 402.504 | − | 697.157i | 0.836806 | − | 1.44939i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 105.356i | − | 0.218129i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −242.772 | − | 140.164i | −0.500560 | − | 0.288999i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.1199i | − | 0.0248868i | −0.999923 | − | 0.0124434i | \(-0.996039\pi\) | ||
0.999923 | − | 0.0124434i | \(-0.00396097\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −173.877 | + | 100.388i | −0.355576 | + | 0.205292i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −246.271 | − | 426.554i | −0.501570 | − | 0.868745i | −0.999998 | − | 0.00181372i | \(-0.999423\pi\) |
0.498428 | − | 0.866931i | \(-0.333911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 396.846i | 0.804962i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −146.300 | −0.295555 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 103.049 | − | 59.4952i | 0.207342 | − | 0.119709i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −173.134 | − | 299.877i | −0.346962 | − | 0.600956i | 0.638746 | − | 0.769417i | \(-0.279453\pi\) |
−0.985708 | + | 0.168462i | \(0.946120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −156.085 | −0.311547 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −166.249 | + | 287.952i | −0.330516 | + | 0.572470i | −0.982613 | − | 0.185665i | \(-0.940556\pi\) |
0.652098 | + | 0.758135i | \(0.273889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −939.592 | −1.86058 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 307.058 | + | 177.280i | 0.605638 | + | 0.349665i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −461.493 | − | 266.443i | −0.906666 | − | 0.523464i | −0.0273090 | − | 0.999627i | \(-0.508694\pi\) |
−0.879357 | + | 0.476163i | \(0.842027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 75.5049 | + | 130.778i | 0.147759 | + | 0.255926i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.2765 | + | 92.5858i | 0.0668158 | + | 0.180479i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −91.1612 | + | 52.6319i | −0.177012 | + | 0.102198i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4343 | − | 25.0010i | 0.0279194 | − | 0.0483579i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −38.5739 | + | 66.8120i | −0.0743235 | + | 0.128732i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 74.3056i | − | 0.142621i | −0.997454 | − | 0.0713106i | \(-0.977282\pi\) | ||
0.997454 | − | 0.0713106i | \(-0.0227181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.3191 | − | 14.6180i | −0.0484113 | − | 0.0279503i | 0.475599 | − | 0.879662i | \(-0.342231\pi\) |
−0.524010 | + | 0.851712i | \(0.675565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 27.5634i | − | 0.0525017i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −313.193 | + | 180.822i | −0.594294 | + | 0.343116i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −224.771 | − | 389.315i | −0.424898 | − | 0.735945i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.8018i | 0.0278754i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.2508 | −0.0642603 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −276.772 | + | 159.795i | −0.517331 | + | 0.298681i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −198.867 | − | 344.448i | −0.370330 | − | 0.641431i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 382.805 | 0.710214 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 109.055 | − | 188.889i | 0.201580 | − | 0.349147i | −0.747458 | − | 0.664310i | \(-0.768726\pi\) |
0.949038 | + | 0.315163i | \(0.102059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 314.140 | 0.578527 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 555.530 | + | 320.735i | 1.01932 | + | 0.588505i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 465.237 | + | 268.605i | 0.850525 | + | 0.491051i | 0.860828 | − | 0.508896i | \(-0.169946\pi\) |
−0.0103027 | + | 0.999947i | \(0.503279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.3797 | − | 38.7627i | −0.0407644 | − | 0.0706060i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −296.440 | − | 50.5903i | −0.538003 | − | 0.0918154i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 163.379 | − | 94.3268i | 0.295441 | − | 0.170573i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −207.745 | + | 359.824i | −0.374315 | + | 0.648332i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −158.164 | + | 273.947i | −0.283956 | + | 0.491826i | −0.972355 | − | 0.233505i | \(-0.924980\pi\) |
0.688399 | + | 0.725332i | \(0.258314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 558.129i | 0.998442i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −318.387 | − | 183.821i | −0.567535 | − | 0.327666i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 595.272i | 1.05732i | 0.848833 | + | 0.528661i | \(0.177306\pi\) | ||||
−0.848833 | + | 0.528661i | \(0.822694\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −553.596 | + | 319.619i | −0.979816 | + | 0.565697i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.75028 | + | 15.1559i | 0.0154326 | + | 0.0267300i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 536.213i | 0.942377i | 0.882032 | + | 0.471189i | \(0.156175\pi\) | ||||
−0.882032 | + | 0.471189i | \(0.843825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 84.5912 | 0.148146 | 0.0740729 | − | 0.997253i | \(-0.476400\pi\) | ||||
0.0740729 | + | 0.997253i | \(0.476400\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 418.056 | − | 241.365i | 0.729592 | − | 0.421230i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −128.004 | − | 221.709i | −0.222615 | − | 0.385581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −850.008 | −1.47315 | −0.736575 | − | 0.676356i | \(-0.763558\pi\) | ||||
−0.736575 | + | 0.676356i | \(0.763558\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −167.512 | + | 290.140i | −0.289313 | + | 0.501105i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −198.967 | −0.342456 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 678.055 | + | 391.475i | 1.16304 | + | 0.671484i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −289.322 | − | 167.040i | −0.494567 | − | 0.285538i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −229.370 | − | 397.281i | −0.390750 | − | 0.676798i | 0.601799 | − | 0.798648i | \(-0.294451\pi\) |
−0.992549 | + | 0.121849i | \(0.961117\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −95.1459 | − | 257.003i | −0.161538 | − | 0.436338i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −145.395 | + | 83.9438i | −0.246015 | + | 0.142037i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −51.3293 | + | 88.9049i | −0.0865586 | + | 0.149924i | −0.906054 | − | 0.423161i | \(-0.860920\pi\) |
0.819496 | + | 0.573085i | \(0.194254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 140.426 | − | 243.226i | 0.236011 | − | 0.408783i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 598.920i | 1.00322i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −322.250 | − | 186.051i | −0.537980 | − | 0.310603i | 0.206280 | − | 0.978493i | \(-0.433864\pi\) |
−0.744260 | + | 0.667890i | \(0.767198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 850.837i | 1.41570i | 0.706362 | + | 0.707851i | \(0.250335\pi\) | ||||
−0.706362 | + | 0.707851i | \(0.749665\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 211.234 | − | 121.956i | 0.350305 | − | 0.202249i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −142.094 | − | 246.114i | −0.234866 | − | 0.406800i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 314.498i | 0.518119i | 0.965861 | + | 0.259060i | \(0.0834126\pi\) | ||||
−0.965861 | + | 0.259060i | \(0.916587\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −53.3073 | −0.0875324 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.0906 | − | 32.9613i | 0.0934379 | − | 0.0539464i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 146.198 | + | 253.222i | 0.238495 | + | 0.413086i | 0.960283 | − | 0.279029i | \(-0.0900125\pi\) |
−0.721787 | + | 0.692115i | \(0.756679\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.6779 | 0.0287445 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −438.183 | + | 758.955i | −0.710183 | + | 1.23007i | 0.254605 | + | 0.967045i | \(0.418055\pi\) |
−0.964788 | + | 0.263028i | \(0.915279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 166.847 | 0.269542 | 0.134771 | − | 0.990877i | \(-0.456970\pi\) | ||||
0.134771 | + | 0.990877i | \(0.456970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 140.767 | + | 81.2721i | 0.226679 | + | 0.130873i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −201.443 | − | 116.303i | −0.323343 | − | 0.186682i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 381.311 | + | 660.450i | 0.610097 | + | 1.05672i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 177.900 | − | 214.398i | 0.283732 | − | 0.341942i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −904.214 | + | 522.048i | −1.43754 | + | 0.829965i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −464.592 | + | 804.698i | −0.736280 | + | 1.27527i | 0.217880 | + | 0.975976i | \(0.430086\pi\) |
−0.954160 | + | 0.299298i | \(0.903248\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1758 | − | 19.3570i | 0.0176552 | − | 0.0305798i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1394.38i | 2.19587i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 757.034 | + | 437.074i | 1.18844 | + | 0.686144i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 183.579i | 0.287292i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 425.692 | − | 245.773i | 0.664106 | − | 0.383422i | −0.129734 | − | 0.991549i | \(-0.541412\pi\) |
0.793840 | + | 0.608127i | \(0.208079\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −175.770 | − | 304.442i | −0.273359 | − | 0.473472i | 0.696361 | − | 0.717692i | \(-0.254801\pi\) |
−0.969720 | + | 0.244220i | \(0.921468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 288.068i | − | 0.446617i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −767.027 | −1.18551 | −0.592757 | − | 0.805381i | \(-0.701961\pi\) | ||||
−0.592757 | + | 0.805381i | \(0.701961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.1729 | − | 20.8844i | 0.0557363 | − | 0.0321794i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.2893 | − | 42.0704i | −0.0373108 | − | 0.0646242i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −254.877 | −0.390317 | −0.195159 | − | 0.980772i | \(-0.562522\pi\) | ||||
−0.195159 | + | 0.980772i | \(0.562522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 453.521 | − | 785.522i | 0.692399 | − | 1.19927i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −232.979 | −0.354611 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 427.502 | + | 246.818i | 0.648713 | + | 0.374535i | 0.787963 | − | 0.615723i | \(-0.211136\pi\) |
−0.139250 | + | 0.990257i | \(0.544469\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1110.75 | − | 641.292i | −1.68041 | − | 0.970185i | −0.961388 | − | 0.275197i | \(-0.911257\pi\) |
−0.719021 | − | 0.694988i | \(-0.755410\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −419.760 | − | 727.046i | −0.633122 | − | 1.09660i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 163.785 | + | 135.904i | 0.246294 | + | 0.204366i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −428.782 | + | 247.558i | −0.642852 | + | 0.371151i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 80.3821 | − | 139.226i | 0.120153 | − | 0.208110i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.1525 | + | 109.383i | −0.0941169 | + | 0.163015i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 337.649i | − | 0.501707i | −0.968025 | − | 0.250853i | \(-0.919289\pi\) | ||
0.968025 | − | 0.250853i | \(-0.0807112\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36.8278 | + | 21.2625i | 0.0545597 | + | 0.0315001i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 394.197i | − | 0.582270i | −0.956682 | − | 0.291135i | \(-0.905967\pi\) | ||
0.956682 | − | 0.291135i | \(-0.0940329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 81.9489 | − | 47.3132i | 0.120691 | − | 0.0696808i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −243.240 | − | 421.305i | −0.357181 | − | 0.618656i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 612.782i | 0.897192i | 0.893735 | + | 0.448596i | \(0.148076\pi\) | ||||
−0.893735 | + | 0.448596i | \(0.851924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1396.04 | 2.03802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 206.311 | − | 119.114i | 0.300308 | − | 0.173383i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 893.945 | + | 1548.36i | 1.29745 | + | 2.24725i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −254.757 | −0.368678 | −0.184339 | − | 0.982863i | \(-0.559014\pi\) | ||||
−0.184339 | + | 0.982863i | \(0.559014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.6921 | − | 42.7680i | 0.0356308 | − | 0.0617143i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 749.369 | 1.07823 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.4717 | + | 22.2117i | 0.0551962 | + | 0.0318675i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −551.049 | − | 318.148i | −0.788339 | − | 0.455148i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.62864 | − | 6.28499i | −0.00517638 | − | 0.00896576i | 0.863426 | − | 0.504476i | \(-0.168314\pi\) |
−0.868602 | + | 0.495510i | \(0.834981\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −274.694 | − | 741.989i | −0.390746 | − | 1.05546i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.4662 | + | 17.0123i | −0.0417960 | + | 0.0241310i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 158.582 | − | 274.672i | 0.224303 | − | 0.388504i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −522.280 | + | 904.615i | −0.736643 | + | 1.27590i | 0.217356 | + | 0.976092i | \(0.430257\pi\) |
−0.953999 | + | 0.299810i | \(0.903077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 291.056i | 0.409362i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −390.747 | − | 225.598i | −0.548033 | − | 0.316407i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 942.729i | 1.31850i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 294.582 | − | 170.077i | 0.410854 | − | 0.237207i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 658.810 | + | 1141.09i | 0.916286 | + | 1.58705i | 0.805007 | + | 0.593265i | \(0.202161\pi\) |
0.111279 | + | 0.993789i | \(0.464505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 35.5324i | − | 0.0492821i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −236.450 | −0.327040 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −112.179 | + | 64.7664i | −0.154729 | + | 0.0893330i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 88.8280 | + | 153.855i | 0.122184 | + | 0.211630i | 0.920629 | − | 0.390439i | \(-0.127677\pi\) |
−0.798444 | + | 0.602068i | \(0.794343\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 361.948 | − | 626.912i | 0.495140 | − | 0.857608i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 321.795 | 0.439011 | 0.219505 | − | 0.975611i | \(-0.429556\pi\) | ||||
0.219505 | + | 0.975611i | \(0.429556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −390.729 | − | 225.587i | −0.531604 | − | 0.306922i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −596.074 | − | 344.144i | −0.808785 | − | 0.466952i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −85.7034 | − | 148.443i | −0.115972 | − | 0.200870i | 0.802196 | − | 0.597061i | \(-0.203665\pi\) |
−0.918168 | + | 0.396191i | \(0.870332\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 596.606 | − | 220.872i | 0.805136 | − | 0.298072i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 257.044 | − | 148.405i | 0.345955 | − | 0.199737i | −0.316947 | − | 0.948443i | \(-0.602658\pi\) |
0.662902 | + | 0.748706i | \(0.269325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 589.693 | − | 1021.38i | 0.791535 | − | 1.37098i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 153.484 | − | 265.842i | 0.205467 | − | 0.355879i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 107.879i | − | 0.144031i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 117.403 | + | 67.7829i | 0.156329 | + | 0.0902568i | 0.576124 | − | 0.817362i | \(-0.304565\pi\) |
−0.419795 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 80.8252i | − | 0.107338i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1168.90 | + | 674.864i | −1.54821 | + | 0.893859i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.71078 | + | 8.15931i | 0.00622296 | + | 0.0107785i | 0.869120 | − | 0.494601i | \(-0.164686\pi\) |
−0.862897 | + | 0.505380i | \(0.831352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 458.679i | − | 0.604320i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −501.946 | −0.659587 | −0.329794 | − | 0.944053i | \(-0.606979\pi\) | ||||
−0.329794 | + | 0.944053i | \(0.606979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −187.522 | + | 108.266i | −0.245770 | + | 0.141895i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 216.651 | + | 375.251i | 0.283204 | + | 0.490524i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 95.3803 | 0.124355 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 722.257 | − | 1250.99i | 0.939216 | − | 1.62677i | 0.172279 | − | 0.985048i | \(-0.444887\pi\) |
0.766937 | − | 0.641722i | \(-0.221780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.47756 | 0.0122926 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −572.771 | − | 330.690i | −0.740972 | − | 0.427800i | 0.0814506 | − | 0.996677i | \(-0.474045\pi\) |
−0.822423 | + | 0.568877i | \(0.807378\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −102.228 | − | 59.0213i | −0.131907 | − | 0.0761565i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −70.1253 | − | 121.461i | −0.0902514 | − | 0.156320i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.4963 | + | 25.9064i | −0.0275947 | + | 0.0332559i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 448.633 | − | 259.019i | 0.574435 | − | 0.331650i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 41.1214 | − | 71.2244i | 0.0525178 | − | 0.0909635i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −255.166 | + | 441.961i | −0.325053 | + | 0.563008i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1319.00i | − | 1.67598i | −0.545686 | − | 0.837990i | \(-0.683731\pi\) | ||
0.545686 | − | 0.837990i | \(-0.316269\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −111.321 | − | 64.2713i | −0.141091 | − | 0.0814592i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 215.778i | − | 0.272792i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −249.780 | + | 144.211i | −0.314981 | + | 0.181854i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −461.393 | − | 799.156i | −0.580368 | − | 1.00523i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 512.600i | 0.643162i | 0.946882 | + | 0.321581i | \(0.104214\pi\) | ||||
−0.946882 | + | 0.321581i | \(0.895786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −85.5017 | −0.107011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 310.787 | − | 179.433i | 0.387999 | − | 0.224011i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 328.719 | + | 569.357i | 0.409363 | + | 0.709038i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 350.399 | 0.435278 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −64.2197 | + | 111.232i | −0.0795783 | + | 0.137834i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 368.489 | 0.455487 | 0.227743 | − | 0.973721i | \(-0.426865\pi\) | ||||
0.227743 | + | 0.973721i | \(0.426865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.72688 | + | 3.30642i | 0.00706150 | + | 0.00407696i | 0.503527 | − | 0.863980i | \(-0.332036\pi\) |
−0.496465 | + | 0.868057i | \(0.665369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −144.114 | − | 83.2043i | −0.177262 | − | 0.102342i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −333.876 | − | 578.290i | −0.409663 | − | 0.709558i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 422.154 | + | 350.290i | 0.516713 | + | 0.428751i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 97.6621 | − | 56.3852i | 0.119246 | − | 0.0688464i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −541.742 | + | 938.324i | −0.659856 | + | 1.14290i | 0.320796 | + | 0.947148i | \(0.396049\pi\) |
−0.980653 | + | 0.195756i | \(0.937284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 160.542 | − | 278.067i | 0.195069 | − | 0.337869i | −0.751854 | − | 0.659329i | \(-0.770840\pi\) |
0.946923 | + | 0.321460i | \(0.104174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 120.000i | − | 0.145455i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 710.535 | + | 410.228i | 0.859172 | + | 0.496043i | 0.863735 | − | 0.503946i | \(-0.168119\pi\) |
−0.00456293 | + | 0.999990i | \(0.501452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1041.55i | 1.25640i | 0.778053 | + | 0.628199i | \(0.216208\pi\) | ||||
−0.778053 | + | 0.628199i | \(0.783792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 184.510 | − | 106.527i | 0.222034 | − | 0.128191i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −566.886 | − | 981.875i | −0.680535 | − | 1.17872i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 519.117i | − | 0.621697i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 74.9476 | 0.0895431 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −791.650 | + | 457.059i | −0.943564 | + | 0.544767i | −0.891076 | − | 0.453855i | \(-0.850048\pi\) |
−0.0524880 | + | 0.998622i | \(0.516715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −295.243 | − | 511.375i | −0.351061 | − | 0.608056i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 704.219 | 0.835373 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −589.608 | + | 1021.23i | −0.697761 | + | 1.20856i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 95.9292 | 0.113258 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 278.307 | + | 160.680i | 0.327805 | + | 0.189259i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1128.12 | − | 651.320i | −1.32564 | − | 0.765359i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.45117 | − | 5.97759i | −0.00404592 | − | 0.00700773i | 0.863995 | − | 0.503500i | \(-0.167955\pi\) |
−0.868041 | + | 0.496492i | \(0.834621\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −307.927 | + | 113.999i | −0.360148 | + | 0.133332i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 543.649 | − | 313.876i | 0.634363 | − | 0.366250i | −0.148077 | − | 0.988976i | \(-0.547308\pi\) |
0.782440 | + | 0.622726i | \(0.213975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −347.688 | + | 602.214i | −0.404759 | + | 0.701064i | −0.994293 | − | 0.106680i | \(-0.965978\pi\) |
0.589534 | + | 0.807743i | \(0.299311\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.98363 | + | 5.16780i | −0.00346531 | + | 0.00600209i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 636.029i | − | 0.736998i | −0.929628 | − | 0.368499i | \(-0.879872\pi\) | ||
0.929628 | − | 0.368499i | \(-0.120128\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −222.207 | − | 128.291i | −0.256887 | − | 0.148314i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 588.297i | 0.678544i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 711.287 | − | 410.662i | 0.818512 | − | 0.472568i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −785.862 | − | 1361.15i | −0.902253 | − | 1.56275i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 145.991i | 0.167229i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −188.364 | −0.215273 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −710.586 | + | 410.257i | −0.810246 | + | 0.467796i | −0.847041 | − | 0.531527i | \(-0.821618\pi\) |
0.0367954 | + | 0.999323i | \(0.488285\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 312.121 | + | 540.610i | 0.355087 | + | 0.615028i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1473.56 | 1.67260 | 0.836301 | − | 0.548271i | \(-0.184714\pi\) | ||||
0.836301 | + | 0.548271i | \(0.184714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −204.732 | + | 354.606i | −0.231859 | + | 0.401592i | −0.958355 | − | 0.285578i | \(-0.907814\pi\) |
0.726496 | + | 0.687171i | \(0.241148\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.2287 | −0.0556257 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1177.32 | + | 679.728i | 1.32731 | + | 0.766322i | 0.984883 | − | 0.173223i | \(-0.0554181\pi\) |
0.342426 | + | 0.939545i | \(0.388751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −407.621 | − | 235.340i | −0.458517 | − | 0.264725i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.0952 | + | 65.9829i | 0.0427556 | + | 0.0740549i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.8998 | − | 63.8688i | 0.0122058 | − | 0.0715216i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1145.59 | − | 661.404i | 1.27998 | − | 0.738999i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 523.703 | − | 907.080i | 0.583838 | − | 1.01124i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −114.146 | + | 197.707i | −0.126970 | + | 0.219919i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2318.90i | − | 2.57369i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 84.2113 | + | 48.6194i | 0.0932573 | + | 0.0538421i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1044.79i | 1.15446i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1396.68 | + | 806.372i | −1.53989 | + | 0.889054i | −0.541042 | + | 0.840996i | \(0.681970\pi\) |
−0.998845 | + | 0.0480579i | \(0.984697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 244.662 | + | 423.767i | 0.269155 | + | 0.466190i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.81037i | − | 0.00637801i | −0.999995 | − | 0.00318901i | \(-0.998985\pi\) | ||
0.999995 | − | 0.00318901i | \(-0.00101509\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −866.223 | −0.948766 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 128.919 | − | 74.4315i | 0.140895 | − | 0.0813459i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 153.089 | + | 265.157i | 0.166945 | + | 0.289157i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 223.733 | 0.243452 | 0.121726 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121726 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 233.152 | − | 403.831i | 0.253151 | − | 0.438470i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1182.95 | 1.28164 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −295.140 | − | 170.399i | −0.319071 | − | 0.184216i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.4752 | + | 27.4098i | 0.0512139 | + | 0.0295683i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −87.0368 | − | 150.752i | −0.0936887 | − | 0.162274i | 0.815372 | − | 0.578938i | \(-0.196533\pi\) |
−0.909061 | + | 0.416664i | \(0.863199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 805.717 | − | 298.287i | 0.865431 | − | 0.320394i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −80.1794 | + | 46.2916i | −0.0859372 | + | 0.0496159i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 611.361 | − | 1058.91i | 0.653862 | − | 1.13252i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 71.6605 | − | 124.120i | 0.0764786 | − | 0.132465i | −0.825250 | − | 0.564768i | \(-0.808966\pi\) |
0.901728 | + | 0.432303i | \(0.142299\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 414.859i | 0.441810i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −133.495 | − | 77.0732i | −0.141865 | − | 0.0819057i | 0.427388 | − | 0.904068i | \(-0.359434\pi\) |
−0.569252 | + | 0.822163i | \(0.692767\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.4237i | 0.0587738i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50.4064 | + | 29.1022i | −0.0533401 | + | 0.0307959i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 79.3787 | + | 137.488i | 0.0838213 | + | 0.145183i | 0.904888 | − | 0.425649i | \(-0.139954\pi\) |
−0.821067 | + | 0.570832i | \(0.806621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1501.28i | 1.58196i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 783.508 | 0.823878 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 191.938 | − | 110.815i | 0.201404 | − | 0.116280i | −0.395906 | − | 0.918291i | \(-0.629570\pi\) |
0.597310 | + | 0.802010i | \(0.296236\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 802.745 | + | 1390.40i | 0.840571 | + | 1.45591i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −232.079 | −0.242507 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −235.621 | + | 408.108i | −0.245695 | + | 0.425556i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 752.958 | 0.783515 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 144.138 | + | 83.2184i | 0.149676 | + | 0.0864157i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −964.963 | − | 557.122i | −0.999962 | − | 0.577328i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 252.311 | + | 437.015i | 0.260921 | + | 0.451929i | 0.966487 | − | 0.256716i | \(-0.0826404\pi\) |
−0.705566 | + | 0.708645i | \(0.749307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −813.366 | − | 138.809i | −0.839387 | − | 0.143249i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1145.39 | − | 661.292i | 1.17960 | − | 0.681042i | 0.223678 | − | 0.974663i | \(-0.428194\pi\) |
0.955922 | + | 0.293621i | \(0.0948603\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −126.477 | + | 219.064i | −0.129986 | + | 0.225143i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 137.012 | − | 237.312i | 0.140525 | − | 0.243397i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1211.93i | 1.24046i | 0.784419 | + | 0.620231i | \(0.212961\pi\) | ||||
−0.784419 | + | 0.620231i | \(0.787039\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −877.001 | − | 506.337i | −0.895814 | − | 0.517198i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 334.067i | − | 0.340538i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −924.023 | + | 533.485i | −0.940003 | + | 0.542711i | −0.889961 | − | 0.456036i | \(-0.849269\pi\) |
−0.0500419 | + | 0.998747i | \(0.515935\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −279.185 | − | 483.563i | −0.283437 | − | 0.490927i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 11.4852i | − | 0.0116365i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 903.150 | 0.913195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 225.943 | − | 130.448i | 0.227995 | − | 0.131633i | −0.381652 | − | 0.924306i | \(-0.624645\pi\) |
0.609647 | + | 0.792673i | \(0.291311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −82.6800 | − | 143.206i | −0.0832629 | − | 0.144216i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1991.92 | −2.00193 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 361.653 | − | 626.401i | 0.362741 | − | 0.628286i | −0.625670 | − | 0.780088i | \(-0.715174\pi\) |
0.988411 | + | 0.151802i | \(0.0485076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 216.380 | 0.216596 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 912.3.be.f.145.3 | 6 | ||
4.3 | odd | 2 | 57.3.g.b.31.2 | ✓ | 6 | ||
12.11 | even | 2 | 171.3.p.c.145.2 | 6 | |||
19.8 | odd | 6 | inner | 912.3.be.f.673.3 | 6 | ||
76.27 | even | 6 | 57.3.g.b.46.2 | yes | 6 | ||
228.179 | odd | 6 | 171.3.p.c.46.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.g.b.31.2 | ✓ | 6 | 4.3 | odd | 2 | ||
57.3.g.b.46.2 | yes | 6 | 76.27 | even | 6 | ||
171.3.p.c.46.2 | 6 | 228.179 | odd | 6 | |||
171.3.p.c.145.2 | 6 | 12.11 | even | 2 | |||
912.3.be.f.145.3 | 6 | 1.1 | even | 1 | trivial | ||
912.3.be.f.673.3 | 6 | 19.8 | odd | 6 | inner |