Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(17,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.n (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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.14 | ||
Character | \(\chi\) | \(=\) | 224.145 |
Dual form | 224.3.n.a.17.14 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 2.78005 | + | 4.81519i | 0.926684 | + | 1.60506i | 0.788830 | + | 0.614611i | \(0.210687\pi\) |
0.137854 | + | 0.990453i | \(0.455980\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.52921 | − | 2.64866i | 0.305841 | − | 0.529732i | −0.671607 | − | 0.740907i | \(-0.734396\pi\) |
0.977448 | + | 0.211175i | \(0.0677290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.608243 | + | 6.97352i | −0.0868918 | + | 0.996218i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −10.9574 | + | 18.9787i | −1.21749 | + | 2.10875i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.106038 | − | 0.0612210i | 0.00963981 | − | 0.00556554i | −0.495172 | − | 0.868795i | \(-0.664895\pi\) |
0.504812 | + | 0.863229i | \(0.331562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.11412 | −0.316471 | −0.158235 | − | 0.987401i | \(-0.550580\pi\) | ||||
−0.158235 | + | 0.987401i | \(0.550580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 17.0051 | 1.13367 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.8551 | − | 10.3087i | 1.05030 | − | 0.606392i | 0.127568 | − | 0.991830i | \(-0.459283\pi\) |
0.922734 | + | 0.385438i | \(0.125950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46893 | − | 7.74042i | 0.235207 | − | 0.407390i | −0.724126 | − | 0.689668i | \(-0.757757\pi\) |
0.959333 | + | 0.282277i | \(0.0910899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −35.2698 | + | 16.4580i | −1.67951 | + | 0.783712i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.51940 | + | 13.0240i | −0.326930 | + | 0.566260i | −0.981901 | − | 0.189394i | \(-0.939348\pi\) |
0.654971 | + | 0.755654i | \(0.272681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.82306 | + | 13.5499i | 0.312922 | + | 0.541998i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −71.8074 | −2.65953 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 31.6239i | − | 1.09048i | −0.838280 | − | 0.545239i | \(-0.816439\pi\) | ||
0.838280 | − | 0.545239i | \(-0.183561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.0318 | + | 13.2974i | −0.742962 | + | 0.428949i | −0.823145 | − | 0.567831i | \(-0.807783\pi\) |
0.0801833 | + | 0.996780i | \(0.474449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.589582 | + | 0.340395i | 0.0178661 | + | 0.0103150i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.5404 | + | 12.2750i | 0.501154 | + | 0.350714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.1405 | + | 14.5149i | 0.679474 | + | 0.392295i | 0.799657 | − | 0.600457i | \(-0.205015\pi\) |
−0.120183 | + | 0.992752i | \(0.538348\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.4375 | − | 19.8103i | −0.293268 | − | 0.507956i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.26915i | − | 0.226077i | −0.993591 | − | 0.113038i | \(-0.963942\pi\) | ||
0.993591 | − | 0.113038i | \(-0.0360583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 45.3391i | − | 1.05440i | −0.849742 | − | 0.527199i | \(-0.823242\pi\) | ||
0.849742 | − | 0.527199i | \(-0.176758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 33.5122 | + | 58.0448i | 0.744715 | + | 1.28988i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 68.6931 | + | 39.6600i | 1.46156 | + | 0.843830i | 0.999083 | − | 0.0428039i | \(-0.0136291\pi\) |
0.462472 | + | 0.886634i | \(0.346962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.2601 | − | 8.48319i | −0.984900 | − | 0.173126i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 99.2764 | + | 57.3172i | 1.94660 | + | 1.12387i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.0507 | − | 31.7835i | 1.03869 | − | 0.599689i | 0.119229 | − | 0.992867i | \(-0.461958\pi\) |
0.919462 | + | 0.393178i | \(0.128624\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.374478i | − | 0.00680869i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 49.6955 | 0.871850 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2561 | − | 24.6923i | −0.241629 | − | 0.418514i | 0.719550 | − | 0.694441i | \(-0.244348\pi\) |
−0.961178 | + | 0.275928i | \(0.911015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6191 | − | 21.8569i | 0.206871 | − | 0.358311i | −0.743856 | − | 0.668339i | \(-0.767005\pi\) |
0.950727 | + | 0.310029i | \(0.100339\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −125.684 | − | 87.9552i | −1.99498 | − | 1.39611i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.29133 | + | 10.8969i | −0.0967897 | + | 0.167645i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65.4798 | − | 37.8048i | 0.977311 | − | 0.564251i | 0.0758537 | − | 0.997119i | \(-0.475832\pi\) |
0.901457 | + | 0.432868i | \(0.142498\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −83.6173 | −1.21184 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.81874 | 0.0397006 | 0.0198503 | − | 0.999803i | \(-0.493681\pi\) | ||||
0.0198503 | + | 0.999803i | \(0.493681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0878 | − | 6.40155i | 0.151888 | − | 0.0876925i | −0.422130 | − | 0.906535i | \(-0.638717\pi\) |
0.574018 | + | 0.818843i | \(0.305384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −43.4970 | + | 75.3391i | −0.579960 | + | 1.00452i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.362429 | + | 0.776695i | 0.00470687 | + | 0.0100869i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.6186 | − | 61.6932i | 0.450868 | − | 0.780926i | −0.547572 | − | 0.836758i | \(-0.684448\pi\) |
0.998440 | + | 0.0558321i | \(0.0177812\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.012 | − | 174.958i | −1.24706 | − | 2.15997i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −30.0525 | −0.362078 | −0.181039 | − | 0.983476i | \(-0.557946\pi\) | ||||
−0.181039 | + | 0.983476i | \(0.557946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 63.0563i | − | 0.741839i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 152.275 | − | 87.9160i | 1.75029 | − | 1.01053i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.3030 | + | 8.83521i | 0.171944 | + | 0.0992720i | 0.583502 | − | 0.812112i | \(-0.301682\pi\) |
−0.411558 | + | 0.911384i | \(0.635015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50238 | − | 28.6899i | 0.0274987 | − | 0.315274i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −128.059 | − | 73.9351i | −1.37698 | − | 0.795001i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.6678 | − | 23.6734i | −0.143872 | − | 0.249193i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 26.1737i | − | 0.269832i | −0.990857 | − | 0.134916i | \(-0.956923\pi\) | ||
0.990857 | − | 0.134916i | \(-0.0430765\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.68329i | 0.0271039i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 67.8445 | + | 117.510i | 0.671727 | + | 1.16347i | 0.977414 | + | 0.211334i | \(0.0677807\pi\) |
−0.305686 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −110.258 | − | 63.6577i | −1.07047 | − | 0.618036i | −0.142160 | − | 0.989844i | \(-0.545405\pi\) |
−0.928310 | + | 0.371807i | \(0.878738\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.3432 | + | 118.585i | −0.0985068 | + | 1.12938i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −69.1003 | − | 39.8951i | −0.645797 | − | 0.372851i | 0.141047 | − | 0.990003i | \(-0.454953\pi\) |
−0.786844 | + | 0.617152i | \(0.788287\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 27.3608 | − | 15.7968i | 0.251017 | − | 0.144925i | −0.369213 | − | 0.929345i | \(-0.620373\pi\) |
0.620230 | + | 0.784420i | \(0.287039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 161.409i | 1.45413i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 57.7985 | 0.511491 | 0.255745 | − | 0.966744i | \(-0.417679\pi\) | ||||
0.255745 | + | 0.966744i | \(0.417679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.9974 | + | 39.8327i | 0.199978 | + | 0.346371i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 45.0799 | − | 78.0808i | 0.385299 | − | 0.667357i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 61.0275 | + | 130.783i | 0.512836 | + | 1.09902i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.4925 | + | 104.776i | −0.499938 | + | 0.865918i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 44.6327 | − | 25.7687i | 0.362868 | − | 0.209502i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 124.313 | 0.994500 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −67.8062 | −0.533907 | −0.266954 | − | 0.963709i | \(-0.586017\pi\) | ||||
−0.266954 | + | 0.963709i | \(0.586017\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 218.316 | − | 126.045i | 1.69238 | − | 0.977093i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −56.0784 | + | 97.1307i | −0.428080 | + | 0.741456i | −0.996702 | − | 0.0811427i | \(-0.974143\pi\) |
0.568623 | + | 0.822598i | \(0.307476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 51.2598 | + | 35.8723i | 0.385412 | + | 0.269716i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −109.808 | + | 190.193i | −0.813394 | + | 1.40884i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 29.3413 | + | 50.8207i | 0.214170 | + | 0.370954i | 0.953016 | − | 0.302921i | \(-0.0979619\pi\) |
−0.738845 | + | 0.673875i | \(0.764629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 175.260 | 1.26086 | 0.630430 | − | 0.776246i | \(-0.282879\pi\) | ||||
0.630430 | + | 0.776246i | \(0.282879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 441.027i | 3.12785i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.436252 | + | 0.251870i | −0.00305072 | + | 0.00176133i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −83.7610 | − | 48.3594i | −0.577662 | − | 0.333513i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −93.3174 | − | 255.965i | −0.634812 | − | 1.74126i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −61.6922 | − | 35.6180i | −0.414041 | − | 0.239047i | 0.278483 | − | 0.960441i | \(-0.410168\pi\) |
−0.692525 | + | 0.721394i | \(0.743502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −86.3801 | − | 149.615i | −0.572053 | − | 0.990825i | −0.996355 | − | 0.0853045i | \(-0.972814\pi\) |
0.424302 | − | 0.905521i | \(-0.360520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 451.824i | 2.95310i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 81.3380i | 0.524761i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −134.922 | − | 233.692i | −0.859378 | − | 1.48849i | −0.872524 | − | 0.488572i | \(-0.837518\pi\) |
0.0131460 | − | 0.999914i | \(-0.495815\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 306.087 | + | 176.720i | 1.92508 | + | 1.11144i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −86.2494 | − | 60.3584i | −0.535711 | − | 0.374897i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −236.230 | − | 136.387i | −1.44926 | − | 0.836733i | −0.450826 | − | 0.892612i | \(-0.648871\pi\) |
−0.998438 | + | 0.0558788i | \(0.982204\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.80318 | − | 1.04107i | 0.0109284 | − | 0.00630950i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 82.5676i | 0.494417i | 0.968962 | + | 0.247208i | \(0.0795132\pi\) | ||||
−0.968962 | + | 0.247208i | \(0.920487\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −152.074 | −0.899846 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 97.9355 | + | 169.629i | 0.572722 | + | 0.991984i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −115.129 | + | 199.410i | −0.665488 | + | 1.15266i | 0.313665 | + | 0.949534i | \(0.398443\pi\) |
−0.979153 | + | 0.203125i | \(0.934890\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −99.2491 | + | 46.3127i | −0.567138 | + | 0.264644i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 79.2654 | − | 137.292i | 0.447827 | − | 0.775660i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −228.664 | + | 132.019i | −1.27745 | + | 0.737538i | −0.976379 | − | 0.216063i | \(-0.930678\pi\) |
−0.301074 | + | 0.953601i | \(0.597345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −183.991 | −1.01653 | −0.508263 | − | 0.861202i | \(-0.669712\pi\) | ||||
−0.508263 | + | 0.861202i | \(0.669712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 140.327 | 0.766815 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 76.8901 | − | 44.3925i | 0.415622 | − | 0.239960i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.26221 | − | 2.18622i | 0.00674980 | − | 0.0116910i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 43.6763 | − | 500.751i | 0.231092 | − | 2.64947i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 148.189 | − | 256.671i | 0.775860 | − | 1.34383i | −0.158450 | − | 0.987367i | \(-0.550650\pi\) |
0.934310 | − | 0.356462i | \(-0.116017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −47.8173 | − | 82.8220i | −0.247758 | − | 0.429129i | 0.715145 | − | 0.698976i | \(-0.246360\pi\) |
−0.962903 | + | 0.269846i | \(0.913027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −69.9609 | −0.358774 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 161.104i | − | 0.817786i | −0.912582 | − | 0.408893i | \(-0.865915\pi\) | ||
0.912582 | − | 0.408893i | \(-0.134085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.961074 | + | 0.554877i | −0.00482952 | + | 0.00278832i | −0.502413 | − | 0.864628i | \(-0.667554\pi\) |
0.497583 | + | 0.867416i | \(0.334221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 364.075 | + | 210.199i | 1.81132 | + | 1.04576i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 220.530 | + | 19.2350i | 1.08635 | + | 0.0947536i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.5508 | − | 14.1744i | −0.119760 | − | 0.0691436i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −164.786 | − | 285.417i | −0.796067 | − | 1.37883i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.09437i | − | 0.00523622i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 214.045i | 1.01443i | 0.861819 | + | 0.507216i | \(0.169325\pi\) | ||||
−0.861819 | + | 0.507216i | \(0.830675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.83624 | + | 13.5728i | 0.0367899 | + | 0.0637219i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −120.088 | − | 69.3328i | −0.558549 | − | 0.322478i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −78.7210 | − | 168.701i | −0.362770 | − | 0.777424i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 61.6494 | + | 35.5933i | 0.281504 | + | 0.162526i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −73.4581 | + | 42.4111i | −0.332390 | + | 0.191905i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 290.270i | 1.30166i | 0.759224 | + | 0.650829i | \(0.225579\pi\) | ||||
−0.759224 | + | 0.650829i | \(0.774421\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −342.881 | −1.52392 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −40.7118 | − | 70.5149i | −0.179347 | − | 0.310638i | 0.762310 | − | 0.647212i | \(-0.224065\pi\) |
−0.941657 | + | 0.336574i | \(0.890732\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −117.111 | + | 202.842i | −0.511400 | + | 0.885771i | 0.488512 | + | 0.872557i | \(0.337540\pi\) |
−0.999913 | + | 0.0132145i | \(0.995794\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.73236 | + | 3.90442i | −0.0118284 | + | 0.0169022i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.9903 | − | 53.6768i | 0.133006 | − | 0.230372i | −0.791828 | − | 0.610744i | \(-0.790871\pi\) |
0.924834 | + | 0.380371i | \(0.124204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 210.092 | − | 121.297i | 0.894008 | − | 0.516156i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 396.086 | 1.67125 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −97.0822 | −0.406202 | −0.203101 | − | 0.979158i | \(-0.565102\pi\) | ||||
−0.203101 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −207.622 | + | 119.871i | −0.861502 | + | 0.497388i | −0.864515 | − | 0.502607i | \(-0.832374\pi\) |
0.00301303 | + | 0.999995i | \(0.499041\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 238.503 | − | 413.100i | 0.981494 | − | 1.70000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −96.2687 | + | 114.852i | −0.392933 | + | 0.468784i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.3857 | + | 31.8450i | −0.0744361 | + | 0.128927i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −83.5475 | − | 144.709i | −0.335532 | − | 0.581159i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 136.078 | 0.542144 | 0.271072 | − | 0.962559i | \(-0.412622\pi\) | ||||
0.271072 | + | 0.962559i | \(0.412622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.84138i | 0.00727818i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 303.628 | − | 175.300i | 1.19070 | − | 0.687450i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.4497 | − | 9.49721i | −0.0640064 | − | 0.0369541i | 0.467655 | − | 0.883911i | \(-0.345099\pi\) |
−0.531662 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −116.512 | + | 166.490i | −0.449852 | + | 0.642817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 600.181 | + | 346.515i | 2.29954 | + | 1.32764i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 123.286 | + | 213.537i | 0.468767 | + | 0.811928i | 0.999363 | − | 0.0356971i | \(-0.0113652\pi\) |
−0.530596 | + | 0.847625i | \(0.678032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 194.414i | − | 0.733638i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 98.2494i | 0.367975i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 147.121 | + | 254.821i | 0.546918 | + | 0.947290i | 0.998483 | + | 0.0550522i | \(0.0175325\pi\) |
−0.451565 | + | 0.892238i | \(0.649134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −392.032 | − | 226.340i | −1.44661 | − | 0.835202i | −0.448335 | − | 0.893866i | \(-0.647983\pi\) |
−0.998278 | + | 0.0586635i | \(0.981316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 145.104 | − | 67.7100i | 0.531517 | − | 0.248022i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.65908 | + | 0.957871i | 0.00603302 | + | 0.00348317i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 252.424 | − | 145.737i | 0.911277 | − | 0.526126i | 0.0304353 | − | 0.999537i | \(-0.490311\pi\) |
0.880842 | + | 0.473411i | \(0.156977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 582.820i | − | 2.08896i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 495.433 | 1.76311 | 0.881553 | − | 0.472086i | \(-0.156499\pi\) | ||||
0.881553 | + | 0.472086i | \(0.156499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3685 | − | 31.8151i | −0.0649062 | − | 0.112421i | 0.831746 | − | 0.555156i | \(-0.187341\pi\) |
−0.896652 | + | 0.442735i | \(0.854008\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 75.9946 | − | 131.626i | 0.266648 | − | 0.461847i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 64.6386 | + | 5.63789i | 0.225222 | + | 0.0196442i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 68.0371 | − | 117.844i | 0.235423 | − | 0.407764i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 126.032 | − | 72.7644i | 0.433098 | − | 0.250049i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −527.984 | −1.80199 | −0.900996 | − | 0.433828i | \(-0.857163\pi\) | ||||
−0.900996 | + | 0.433828i | \(0.857163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −87.2021 | −0.295600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.61430 | + | 4.39612i | −0.0256374 | + | 0.0148017i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.9357 | − | 53.5822i | 0.103464 | − | 0.179205i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 316.173 | + | 27.5772i | 1.05041 | + | 0.0916185i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −377.222 | + | 653.368i | −1.24496 | + | 2.15633i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −38.5944 | − | 66.8475i | −0.126539 | − | 0.219172i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −174.486 | −0.568359 | −0.284179 | − | 0.958771i | \(-0.591721\pi\) | ||||
−0.284179 | + | 0.958771i | \(0.591721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 707.887i | − | 2.29090i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.9119 | + | 6.87736i | −0.0383020 | + | 0.0221137i | −0.519029 | − | 0.854757i | \(-0.673706\pi\) |
0.480727 | + | 0.876870i | \(0.340373\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −365.368 | − | 210.945i | −1.16731 | − | 0.673947i | −0.214265 | − | 0.976776i | \(-0.568736\pi\) |
−0.953045 | + | 0.302829i | \(0.902069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −425.160 | + | 198.393i | −1.34971 | + | 0.629818i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −408.352 | − | 235.762i | −1.28818 | − | 0.743730i | −0.309848 | − | 0.950786i | \(-0.600278\pi\) |
−0.978329 | + | 0.207056i | \(0.933612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.93605 | − | 3.35333i | −0.00606911 | − | 0.0105120i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 443.642i | − | 1.38206i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 184.275i | − | 0.570510i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.1850 | − | 55.7460i | −0.0990308 | − | 0.171526i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 152.129 | + | 87.8317i | 0.465226 | + | 0.268598i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −318.352 | + | 454.910i | −0.967635 | + | 1.38271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −383.707 | − | 221.533i | −1.15923 | − | 0.669284i | −0.208114 | − | 0.978105i | \(-0.566732\pi\) |
−0.951120 | + | 0.308820i | \(0.900066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −550.949 | + | 318.090i | −1.65450 | + | 0.955227i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 231.245i | − | 0.690284i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 556.978 | 1.65276 | 0.826378 | − | 0.563117i | \(-0.190398\pi\) | ||||
0.826378 | + | 0.563117i | \(0.190398\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 160.683 | + | 278.311i | 0.473990 | + | 0.820975i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.62816 | + | 2.82006i | −0.00477467 | + | 0.00826998i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 88.5116 | − | 331.383i | 0.258051 | − | 0.966131i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −127.868 | + | 221.474i | −0.370632 | + | 0.641953i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 277.806 | − | 160.392i | 0.800595 | − | 0.462223i | −0.0430845 | − | 0.999071i | \(-0.513718\pi\) |
0.843679 | + | 0.536848i | \(0.180385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 222.198 | 0.636670 | 0.318335 | − | 0.947978i | \(-0.396876\pi\) | ||||
0.318335 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 295.424 | 0.841664 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −118.142 | + | 68.2096i | −0.334681 | + | 0.193228i | −0.657918 | − | 0.753090i | \(-0.728562\pi\) |
0.323236 | + | 0.946318i | \(0.395229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.31043 | − | 7.46589i | 0.0121421 | − | 0.0210307i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −460.087 | + | 657.443i | −1.28876 | + | 1.84158i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 124.441 | − | 215.538i | 0.346632 | − | 0.600384i | −0.639017 | − | 0.769193i | \(-0.720659\pi\) |
0.985649 | + | 0.168809i | \(0.0539920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 140.557 | + | 243.452i | 0.389355 | + | 0.674383i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −672.689 | −1.85314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 39.1572i | − | 0.107280i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 225.916 | − | 130.432i | 0.615574 | − | 0.355402i | −0.159570 | − | 0.987187i | \(-0.551011\pi\) |
0.775144 | + | 0.631785i | \(0.217677\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 175.917 | + | 101.566i | 0.476739 | + | 0.275245i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 188.159 | + | 403.229i | 0.507167 | + | 1.08687i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 381.464 | + | 220.239i | 1.02269 | + | 0.590452i | 0.914883 | − | 0.403720i | \(-0.132283\pi\) |
0.107810 | + | 0.994172i | \(0.465616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 345.595 | + | 598.589i | 0.921588 | + | 1.59624i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 130.104i | 0.345104i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 283.715i | − | 0.748587i | −0.927310 | − | 0.374294i | \(-0.877885\pi\) | ||
0.927310 | − | 0.374294i | \(-0.122115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −188.505 | − | 326.500i | −0.494763 | − | 0.856955i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −138.511 | − | 79.9691i | −0.361646 | − | 0.208797i | 0.308156 | − | 0.951336i | \(-0.400288\pi\) |
−0.669803 | + | 0.742539i | \(0.733621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.61143 | + | 0.227773i | 0.00678294 | + | 0.000591619i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 860.479 | + | 496.798i | 2.22346 | + | 1.28371i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 430.295 | − | 248.431i | 1.10616 | − | 0.638640i | 0.168326 | − | 0.985731i | \(-0.446164\pi\) |
0.937831 | + | 0.347091i | \(0.112830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 310.060i | 0.792992i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −623.604 | −1.58678 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −108.936 | − | 188.683i | −0.275788 | − | 0.477679i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −142.186 | + | 246.273i | −0.358150 | + | 0.620334i | −0.987652 | − | 0.156665i | \(-0.949926\pi\) |
0.629502 | + | 0.776999i | \(0.283259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.2269 | + | 346.552i | −0.0757566 | + | 0.868552i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −70.8759 | + | 122.761i | −0.176748 | + | 0.306136i | −0.940765 | − | 0.339060i | \(-0.889891\pi\) |
0.764017 | + | 0.645196i | \(0.223224\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 94.7556 | − | 54.7072i | 0.235126 | − | 0.135750i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −617.872 | −1.52561 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.55447 | 0.00873333 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −323.318 | + | 186.668i | −0.790508 | + | 0.456400i | −0.840141 | − | 0.542368i | \(-0.817528\pi\) |
0.0496336 | + | 0.998767i | \(0.484195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −163.141 | + | 282.568i | −0.396937 | + | 0.687514i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 180.864 | − | 84.3964i | 0.437926 | − | 0.204350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.9565 | + | 79.5989i | −0.110738 | + | 0.191805i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 487.231 | + | 843.908i | 1.16842 | + | 2.02376i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 418.864 | 0.999676 | 0.499838 | − | 0.866119i | \(-0.333393\pi\) | ||||
0.499838 | + | 0.866119i | \(0.333393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 315.112i | − | 0.748485i | −0.927331 | − | 0.374243i | \(-0.877903\pi\) | ||
0.927331 | − | 0.374243i | \(-0.122097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1505.39 | + | 869.139i | −3.55885 | + | 2.05470i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 279.364 | + | 161.291i | 0.657326 | + | 0.379507i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 144.744 | + | 101.294i | 0.338980 | + | 0.237222i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.42561 | − | 1.40043i | −0.00565410 | − | 0.00326440i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 111.663 | + | 193.405i | 0.259078 | + | 0.448736i | 0.965995 | − | 0.258560i | \(-0.0832481\pi\) |
−0.706917 | + | 0.707296i | \(0.749915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 591.725i | 1.36657i | 0.730151 | + | 0.683286i | \(0.239450\pi\) | ||||
−0.730151 | + | 0.683286i | \(0.760550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 537.767i | − | 1.23625i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 67.2074 | + | 116.407i | 0.153793 | + | 0.266377i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 443.687 | + | 256.163i | 1.01068 | + | 0.583515i | 0.911390 | − | 0.411544i | \(-0.135010\pi\) |
0.0992873 | + | 0.995059i | \(0.468344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 689.804 | − | 822.962i | 1.56418 | − | 1.86613i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 134.591 | + | 77.7063i | 0.303818 | + | 0.175409i | 0.644157 | − | 0.764894i | \(-0.277208\pi\) |
−0.340339 | + | 0.940303i | \(0.610542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 46.8030 | − | 27.0217i | 0.105175 | − | 0.0607229i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 396.079i | − | 0.886084i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −369.139 | −0.822136 | −0.411068 | − | 0.911605i | \(-0.634844\pi\) | ||||
−0.411068 | + | 0.911605i | \(0.634844\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.567467 | − | 0.982881i | −0.00125824 | − | 0.00217934i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 480.282 | − | 831.873i | 1.06023 | − | 1.83636i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −72.1632 | − | 50.5007i | −0.158600 | − | 0.110991i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 214.079 | − | 370.795i | 0.468444 | − | 0.811369i | −0.530906 | − | 0.847431i | \(-0.678148\pi\) |
0.999350 | + | 0.0360623i | \(0.0114815\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1282.13 | + | 740.238i | −2.79331 | + | 1.61272i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 165.578 | 0.359171 | 0.179586 | − | 0.983742i | \(-0.442524\pi\) | ||||
0.179586 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 605.376 | 1.30751 | 0.653754 | − | 0.756708i | \(-0.273193\pi\) | ||||
0.653754 | + | 0.756708i | \(0.273193\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −391.658 | + | 226.124i | −0.842275 | + | 0.486288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −286.063 | + | 495.476i | −0.612555 | + | 1.06098i | 0.378253 | + | 0.925702i | \(0.376525\pi\) |
−0.990808 | + | 0.135275i | \(0.956808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 223.805 | + | 479.620i | 0.477196 | + | 1.02264i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 750.182 | − | 1299.35i | 1.59274 | − | 2.75871i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.77570 | − | 4.80766i | −0.00586830 | − | 0.0101642i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 139.843 | 0.294406 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1393.06i | 2.92045i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.2540 | + | 18.6218i | −0.0673361 | + | 0.0388765i | −0.533290 | − | 0.845932i | \(-0.679045\pi\) |
0.465954 | + | 0.884809i | \(0.345711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −103.431 | − | 59.7160i | −0.215034 | − | 0.124150i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 50.8596 | − | 583.107i | 0.105299 | − | 1.20726i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −69.3254 | − | 40.0250i | −0.142939 | − | 0.0825259i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 137.172 | + | 237.589i | 0.281668 | + | 0.487863i | 0.971796 | − | 0.235824i | \(-0.0757790\pi\) |
−0.690128 | + | 0.723688i | \(0.742446\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1516.66i | − | 3.10155i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 881.994i | − | 1.79632i | −0.439667 | − | 0.898161i | \(-0.644903\pi\) | ||
0.439667 | − | 0.898161i | \(-0.355097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −326.000 | − | 564.648i | −0.661257 | − | 1.14533i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.10712 | + | 4.10330i | 0.0143578 | + | 0.00828949i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.71448 | + | 19.6566i | −0.00344965 | + | 0.0395504i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −305.733 | − | 176.515i | −0.612692 | − | 0.353738i | 0.161327 | − | 0.986901i | \(-0.448423\pi\) |
−0.774018 | + | 0.633163i | \(0.781756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −397.579 | + | 229.542i | −0.793570 | + | 0.458168i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 291.993i | − | 0.580502i | −0.956951 | − | 0.290251i | \(-0.906261\pi\) | ||
0.956951 | − | 0.290251i | \(-0.0937388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 414.993 | 0.821768 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −422.774 | − | 732.266i | −0.833873 | − | 1.44431i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.5606 | + | 71.9851i | −0.0816515 | + | 0.141425i | −0.903959 | − | 0.427618i | \(-0.859353\pi\) |
0.822308 | + | 0.569043i | \(0.192686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.8973 | + | 81.2148i | 0.0741630 | + | 0.158933i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −320.902 | + | 555.819i | −0.625541 | + | 1.08347i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −337.216 | + | 194.692i | −0.654788 | + | 0.378042i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.71210 | 0.0187855 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1280.26 | −2.46679 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 513.150 | − | 296.267i | 0.984933 | − | 0.568651i | 0.0811772 | − | 0.996700i | \(-0.474132\pi\) |
0.903756 | + | 0.428048i | \(0.140799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 151.233 | − | 261.943i | 0.289164 | − | 0.500847i | −0.684446 | − | 0.729063i | \(-0.739956\pi\) |
0.973610 | + | 0.228217i | \(0.0732894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −498.922 | − | 349.152i | −0.950328 | − | 0.665051i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −274.157 | + | 474.855i | −0.520223 | + | 0.901052i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 151.417 | + | 262.262i | 0.286233 | + | 0.495770i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 624.838 | 1.17672 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.1344i | 0.0715467i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −211.337 | + | 122.016i | −0.395023 | + | 0.228067i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1271.40 | − | 734.041i | −2.36759 | − | 1.36693i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.63675 | + | 2.05499i | −0.0104578 | + | 0.00381260i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −630.140 | − | 363.811i | −1.16477 | − | 0.672480i | −0.212327 | − | 0.977199i | \(-0.568104\pi\) |
−0.952442 | + | 0.304719i | \(0.901437\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −511.505 | − | 885.952i | −0.941997 | − | 1.63159i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 96.6260i | − | 0.177296i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1033.51i | 1.88941i | 0.327921 | + | 0.944705i | \(0.393652\pi\) | ||||
−0.327921 | + | 0.944705i | \(0.606348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 276.545 | + | 478.990i | 0.503724 | + | 0.872476i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −244.782 | − | 141.325i | −0.444250 | − | 0.256488i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 408.554 | + | 285.911i | 0.738796 | + | 0.517019i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 427.517 | + | 246.827i | 0.770301 | + | 0.444734i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 625.736 | − | 361.269i | 1.12340 | − | 0.648597i | 0.181136 | − | 0.983458i | \(-0.442023\pi\) |
0.942268 | + | 0.334861i | \(0.108689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 186.530i | 0.333686i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.0361 | 0.0250197 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −206.897 | − | 358.355i | −0.367489 | − | 0.636510i | 0.621683 | − | 0.783269i | \(-0.286449\pi\) |
−0.989172 | + | 0.146759i | \(0.953116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 88.3857 | − | 153.089i | 0.156435 | − | 0.270953i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1281.51 | − | 597.992i | 2.26016 | − | 1.05466i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 258.602 | − | 447.911i | 0.454485 | − | 0.787190i | −0.544174 | − | 0.838972i | \(-0.683157\pi\) |
0.998658 | + | 0.0517822i | \(0.0164901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 615.938 | − | 355.612i | 1.07870 | − | 0.622788i | 0.148155 | − | 0.988964i | \(-0.452667\pi\) |
0.930545 | + | 0.366177i | \(0.119333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1647.89 | 2.87591 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −235.299 | −0.409215 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 527.662 | − | 304.646i | 0.914491 | − | 0.527982i | 0.0326179 | − | 0.999468i | \(-0.489616\pi\) |
0.881874 | + | 0.471486i | \(0.156282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 265.869 | − | 460.499i | 0.459187 | − | 0.795335i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.2792 | − | 209.572i | 0.0314616 | − | 0.360709i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.89164 | − | 6.74051i | 0.00667519 | − | 0.0115618i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −137.873 | − | 238.803i | −0.235680 | − | 0.408210i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 972.801 | 1.65724 | 0.828621 | − | 0.559810i | \(-0.189126\pi\) | ||||
0.828621 | + | 0.559810i | \(0.189126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 237.701i | 0.403567i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 775.745 | − | 447.877i | 1.31260 | − | 0.757829i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −281.520 | − | 162.536i | −0.474739 | − | 0.274091i | 0.243482 | − | 0.969905i | \(-0.421710\pi\) |
−0.718222 | + | 0.695814i | \(0.755044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 439.724 | + | 38.3535i | 0.739033 | + | 0.0644597i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.34367 | − | 3.08517i | −0.00895088 | − | 0.00516779i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 231.570 | + | 401.091i | 0.386595 | + | 0.669602i | 0.991989 | − | 0.126324i | \(-0.0403179\pi\) |
−0.605394 | + | 0.795926i | \(0.706985\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 325.247i | 0.541176i | 0.962695 | + | 0.270588i | \(0.0872182\pi\) | ||||
−0.962695 | + | 0.270588i | \(0.912782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1656.97i | 2.74787i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 185.011 | + | 320.448i | 0.305803 | + | 0.529667i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −346.450 | − | 200.023i | −0.570758 | − | 0.329527i | 0.186694 | − | 0.982418i | \(-0.440223\pi\) |
−0.757452 | + | 0.652891i | \(0.773556\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 520.464 | + | 1115.37i | 0.854621 | + | 1.83147i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −282.612 | − | 163.166i | −0.462540 | − | 0.267047i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −821.365 | + | 474.215i | −1.33991 | + | 0.773597i | −0.986794 | − | 0.161982i | \(-0.948211\pi\) |
−0.353116 | + | 0.935579i | \(0.614878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 157.623i | − | 0.256297i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1066.14 | −1.72793 | −0.863967 | − | 0.503548i | \(-0.832028\pi\) | ||||
−0.863967 | + | 0.503548i | \(0.832028\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 471.501 | + | 816.664i | 0.761715 | + | 1.31933i | 0.941966 | + | 0.335708i | \(0.108976\pi\) |
−0.180251 | + | 0.983621i | \(0.557691\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 539.948 | − | 935.218i | 0.869482 | − | 1.50599i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −70.9205 | + | 101.342i | −0.113837 | + | 0.162668i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.47705 | + | 9.48652i | −0.00876328 | + | 0.0151784i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.26960 | − | 3.04240i | 0.00840446 | − | 0.00485232i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 598.517 | 0.951537 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 575.646 | 0.912276 | 0.456138 | − | 0.889909i | \(-0.349232\pi\) | ||||
0.456138 | + | 0.889909i | \(0.349232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1030.67 | + | 595.056i | −1.62823 | + | 0.940057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −103.690 | + | 179.596i | −0.163291 | + | 0.282828i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 198.548 | + | 34.9008i | 0.311692 | + | 0.0547894i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.8860 | + | 53.4961i | −0.0483349 | + | 0.0837185i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −396.899 | − | 687.449i | −0.619187 | − | 1.07246i | −0.989634 | − | 0.143610i | \(-0.954129\pi\) |
0.370447 | − | 0.928854i | \(-0.379204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −841.343 | −1.30847 | −0.654233 | − | 0.756293i | \(-0.727008\pi\) | ||||
−0.654233 | + | 0.756293i | \(0.727008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 770.995i | − | 1.19534i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −476.604 | + | 275.167i | −0.736637 | + | 0.425297i | −0.820845 | − | 0.571151i | \(-0.806497\pi\) |
0.0842084 | + | 0.996448i | \(0.473164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.02337 | − | 1.74555i | −0.00465851 | − | 0.00268959i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 593.479 | − | 848.054i | 0.911642 | − | 1.30269i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −713.506 | − | 411.943i | −1.09266 | − | 0.630847i | −0.158375 | − | 0.987379i | \(-0.550626\pi\) |
−0.934283 | + | 0.356532i | \(0.883959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 171.511 | + | 297.066i | 0.261849 | + | 0.453535i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 280.577i | 0.427058i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 354.257i | − | 0.537567i | −0.963201 | − | 0.268784i | \(-0.913378\pi\) | ||
0.963201 | − | 0.268784i | \(-0.0866217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −84.3031 | − | 146.017i | −0.127539 | − | 0.220904i | 0.795184 | − | 0.606369i | \(-0.207374\pi\) |
−0.922722 | + | 0.385465i | \(0.874041\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −408.435 | − | 235.810i | −0.616040 | − | 0.355671i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 173.400 | − | 80.9138i | 0.260752 | − | 0.121675i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 411.869 | + | 237.793i | 0.617494 | + | 0.356511i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1397.70 | + | 806.965i | −2.08924 | + | 1.20623i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.09022i | − | 0.00460539i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 514.054 | 0.763824 | 0.381912 | − | 0.924199i | \(-0.375266\pi\) | ||||
0.381912 | + | 0.924199i | \(0.375266\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −561.753 | − | 972.986i | −0.832227 | − | 1.44146i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −260.650 | + | 451.460i | −0.385008 | + | 0.666853i | −0.991770 | − | 0.128030i | \(-0.959135\pi\) |
0.606762 | + | 0.794883i | \(0.292468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 182.523 | + | 15.9200i | 0.268812 | + | 0.0234462i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 226.362 | − | 392.070i | 0.332396 | − | 0.575727i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −441.591 | + | 254.953i | −0.646547 | + | 0.373284i | −0.787132 | − | 0.616785i | \(-0.788435\pi\) |
0.140585 | + | 0.990069i | \(0.455102\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 179.476 | 0.262009 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1302.30 | −1.89563 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −226.485 | + | 130.761i | −0.328715 | + | 0.189784i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −467.402 | + | 809.565i | −0.676415 | + | 1.17158i | 0.299639 | + | 0.954053i | \(0.403134\pi\) |
−0.976053 | + | 0.217532i | \(0.930199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.7120 | − | 1.63209i | −0.0270014 | − | 0.00235511i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 268.008 | − | 464.203i | 0.385623 | − | 0.667919i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −95.5526 | − | 165.502i | −0.137091 | − | 0.237449i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 344.619 | 0.493017 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 364.276i | 0.519651i | 0.965656 | + | 0.259826i | \(0.0836651\pi\) | ||||
−0.965656 | + | 0.259826i | \(0.916335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 224.703 | − | 129.732i | 0.319634 | − | 0.184541i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1168.13 | + | 674.422i | 1.65693 | + | 0.956626i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −860.725 | + | 401.640i | −1.21743 | + | 0.568091i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −429.168 | − | 247.780i | −0.605315 | − | 0.349479i | 0.165815 | − | 0.986157i | \(-0.446975\pi\) |
−0.771130 | + | 0.636678i | \(0.780308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 780.572 | + | 1351.99i | 1.09785 | + | 1.90153i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 399.955i | − | 0.560946i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.54065i | 0.00215475i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −269.894 | − | 467.470i | −0.376421 | − | 0.651980i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 582.836 | + | 336.500i | 0.810620 | + | 0.468012i | 0.847171 | − | 0.531320i | \(-0.178304\pi\) |
−0.0365511 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 510.983 | − | 730.171i | 0.708714 | − | 1.01272i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1154.40 | − | 666.493i | −1.59668 | − | 0.921844i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 428.502 | − | 247.395i | 0.591037 | − | 0.341235i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 165.434i | − | 0.227557i | −0.993506 | − | 0.113778i | \(-0.963705\pi\) | ||
0.993506 | − | 0.113778i | \(-0.0362954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 833.991 | 1.14402 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −467.386 | − | 809.536i | −0.639378 | − | 1.10744i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −474.614 | + | 822.055i | −0.647495 | + | 1.12149i | 0.336225 | + | 0.941782i | \(0.390850\pi\) |
−0.983719 | + | 0.179712i | \(0.942483\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −820.667 | − | 144.257i | −1.11655 | − | 0.196268i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.62889 | − | 8.01748i | 0.00628073 | − | 0.0108785i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 62.4587 | − | 36.0605i | 0.0845178 | − | 0.0487964i | −0.457145 | − | 0.889392i | \(-0.651128\pi\) |
0.541663 | + | 0.840596i | \(0.317795\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −204.453 | −0.275915 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −159.310 | −0.214415 | −0.107208 | − | 0.994237i | \(-0.534191\pi\) | ||||
−0.107208 | + | 0.994237i | \(0.534191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −188.680 | + | 108.934i | −0.253262 | + | 0.146221i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 329.297 | − | 570.358i | 0.440825 | − | 0.763532i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 320.239 | − | 457.607i | 0.427556 | − | 0.610957i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 382.562 | − | 662.616i | 0.509403 | − | 0.882312i | −0.490538 | − | 0.871420i | \(-0.663200\pi\) |
0.999941 | − | 0.0108919i | \(-0.00346706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 378.305 | + | 655.243i | 0.502397 | + | 0.870176i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −528.371 | −0.699830 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 950.822i | 1.25604i | 0.778197 | + | 0.628020i | \(0.216134\pi\) | ||||
−0.778197 | + | 0.628020i | \(0.783866\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.86660 | + | 5.11913i | −0.0116819 | + | 0.00674457i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 529.627 | + | 305.781i | 0.695962 | + | 0.401814i | 0.805842 | − | 0.592131i | \(-0.201713\pi\) |
−0.109879 | + | 0.993945i | \(0.535046\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 93.5172 | + | 200.410i | 0.122565 | + | 0.262660i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1196.73 | + | 690.931i | 1.56435 | + | 0.903178i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.6513 | + | 101.587i | 0.0764685 | + | 0.132447i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 979.152i | 1.27328i | 0.771161 | + | 0.636640i | \(0.219676\pi\) | ||||
−0.771161 | + | 0.636640i | \(0.780324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 105.611i | − | 0.136979i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −228.660 | − | 396.051i | −0.295809 | − | 0.512356i | 0.679364 | − | 0.733802i | \(-0.262256\pi\) |
−0.975173 | + | 0.221445i | \(0.928923\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −360.359 | − | 208.053i | −0.464979 | − | 0.268456i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1125.59 | − | 98.1756i | −1.44863 | − | 0.126352i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −71.7471 | − | 41.4232i | −0.0921015 | − | 0.0531748i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.298893 | − | 0.172566i | 0.000382706 | − | 0.000220955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2270.83i | 2.90016i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −825.296 | −1.05133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −91.5206 | − | 158.518i | −0.116290 | − | 0.201421i | 0.802004 | − | 0.597318i | \(-0.203767\pi\) |
−0.918295 | + | 0.395897i | \(0.870434\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −685.481 | + | 1187.29i | −0.868797 | + | 1.50480i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.1555 | + | 403.059i | −0.0444444 | + | 0.509556i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.9165 | + | 89.9220i | −0.0654685 | + | 0.113395i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 936.141 | − | 540.481i | 1.17754 | − | 0.679851i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −619.727 | −0.777575 | −0.388787 | − | 0.921328i | \(-0.627106\pi\) | ||||
−0.388787 | + | 0.921328i | \(0.627106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1635.37 | 2.04677 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −335.362 | + | 193.621i | −0.418679 | + | 0.241725i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.783819 | − | 1.35761i | 0.000976113 | − | 0.00169068i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −291.762 | + | 136.145i | −0.362438 | + | 0.169124i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −818.008 | + | 1416.83i | −1.01364 | + | 1.75568i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 335.874 | + | 581.750i | 0.415171 | + | 0.719098i | 0.995446 | − | 0.0953227i | \(-0.0303883\pi\) |
−0.580275 | + | 0.814421i | \(0.697055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1133.22 | −1.39732 | −0.698658 | − | 0.715456i | \(-0.746219\pi\) | ||||
−0.698658 | + | 0.715456i | \(0.746219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2516.95i | − | 3.09587i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −722.489 | + | 417.129i | −0.886489 | + | 0.511815i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −350.944 | − | 202.617i | −0.429551 | − | 0.248002i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 517.079 | + | 361.858i | 0.631354 | + | 0.441829i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 620.954 | + | 358.508i | 0.756338 | + | 0.436672i | 0.827979 | − | 0.560758i | \(-0.189490\pi\) |
−0.0716414 | + | 0.997430i | \(0.522824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −362.895 | − | 628.553i | −0.440942 | − | 0.763734i | 0.556818 | − | 0.830635i | \(-0.312022\pi\) |
−0.997760 | + | 0.0669009i | \(0.978689\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.6517i | 0.0129112i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 436.858i | 0.528244i | 0.964489 | + | 0.264122i | \(0.0850822\pi\) | ||||
−0.964489 | + | 0.264122i | \(0.914918\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 588.361 | + | 1019.07i | 0.709724 | + | 1.22928i | 0.964959 | + | 0.262399i | \(0.0845137\pi\) |
−0.255235 | + | 0.966879i | \(0.582153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1403.50 | + | 810.313i | 1.68893 | + | 0.975105i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −949.140 | + | 346.029i | −1.13942 | + | 0.415400i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 218.694 | + | 126.263i | 0.261909 | + | 0.151213i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1653.85 | − | 954.853i | 1.97593 | − | 1.14080i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1551.16i | − | 1.84881i | −0.381407 | − | 0.924407i | \(-0.624560\pi\) | ||
0.381407 | − | 0.924407i | \(-0.375440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −159.070 | −0.189143 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1377.33 | + | 2385.60i | 1.63384 | + | 2.82990i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −232.552 | + | 402.793i | −0.275210 | + | 0.476678i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −693.864 | − | 485.575i | −0.819202 | − | 0.573288i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 102.131 | − | 176.895i | 0.120295 | − | 0.208357i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −378.084 | + | 218.287i | −0.444282 | + | 0.256506i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −138.736 | −0.162645 | −0.0813225 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813225 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 599.054 | 0.700648 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1475.23 | − | 851.725i | 1.72139 | − | 0.993844i | 0.805302 | − | 0.592865i | \(-0.202003\pi\) |
0.916087 | − | 0.400980i | \(-0.131330\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 256.796 | − | 444.784i | 0.298948 | − | 0.517793i | −0.676948 | − | 0.736031i | \(-0.736698\pi\) |
0.975896 | + | 0.218238i | \(0.0700310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 152.551 | + | 326.921i | 0.177179 | + | 0.379699i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 117.938 | − | 204.275i | 0.136661 | − | 0.236703i | −0.789570 | − | 0.613660i | \(-0.789696\pi\) |
0.926231 | + | 0.376958i | \(0.123030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 352.113 | + | 609.878i | 0.407067 | + | 0.705061i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 756.587 | 0.872649 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.72242i | − | 0.0100373i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −269.392 | + | 155.533i | −0.309290 | + | 0.178569i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 496.745 | + | 286.796i | 0.569009 | + | 0.328517i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −75.6122 | + | 866.897i | −0.0864139 | + | 0.990739i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 384.546 | + | 222.017i | 0.438478 | + | 0.253156i | 0.702952 | − | 0.711237i | \(-0.251865\pi\) |
−0.264474 | + | 0.964393i | \(0.585198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1467.82 | − | 2542.34i | −1.66988 | − | 2.89231i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 71.7252i | 0.0814134i | 0.999171 | + | 0.0407067i | \(0.0129609\pi\) | ||||
−0.999171 | + | 0.0407067i | \(0.987039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 973.840i | − | 1.10288i | −0.834216 | − | 0.551438i | \(-0.814079\pi\) | ||
0.834216 | − | 0.551438i | \(-0.185921\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −242.426 | − | 419.895i | −0.273928 | − | 0.474457i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −715.042 | − | 412.830i | −0.806135 | − | 0.465422i | 0.0394767 | − | 0.999220i | \(-0.487431\pi\) |
−0.845612 | + | 0.533798i | \(0.820764\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.2426 | − | 472.848i | 0.0463922 | − | 0.531888i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.4222 | − | 12.3681i | −0.0240428 | − | 0.0138811i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 613.970 | − | 354.476i | 0.687536 | − | 0.396949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 807.539i | 0.902278i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 344.011 | 0.383513 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 420.516 | + | 728.355i | 0.467760 | + | 0.810184i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 655.291 | − | 1135.00i | 0.727293 | − | 1.25971i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 746.189 | + | 1599.10i | 0.826344 | + | 1.77088i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −281.360 | + | 487.330i | −0.310895 | + | 0.538486i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −637.046 | + | 367.799i | −0.702366 | + | 0.405511i | −0.808228 | − | 0.588870i | \(-0.799573\pi\) |
0.105862 | + | 0.994381i | \(0.466240\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2973.59 | −3.27128 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −235.528 | −0.258538 | −0.129269 | − | 0.991610i | \(-0.541263\pi\) | ||||
−0.129269 | + | 0.991610i | \(0.541263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.18670 | + | 1.83984i | −0.00349036 | + | 0.00201516i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 214.589 | − | 371.679i | 0.234524 | − | 0.406207i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −643.234 | − | 450.143i | −0.701455 | − | 0.490887i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −717.115 | + | 1242.08i | −0.780321 | + | 1.35156i | 0.151434 | + | 0.988467i | \(0.451611\pi\) |
−0.931755 | + | 0.363088i | \(0.881722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −485.080 | − | 840.184i | −0.526689 | − | 0.912252i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.5966 | −0.0125641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 454.204i | 0.491031i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2416.29 | − | 1395.04i | 2.60657 | − | 1.50490i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1194.57 | − | 689.687i | −1.28587 | − | 0.742397i | −0.307955 | − | 0.951401i | \(-0.599645\pi\) |
−0.977915 | + | 0.209003i | \(0.932978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −281.334 | + | 335.642i | −0.302185 | + | 0.360518i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −66.2316 | − | 38.2388i | −0.0709878 | − | 0.0409848i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.86037 | − | 6.68635i | −0.00412874 | − | 0.00715118i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 541.545i | 0.577956i | 0.957336 | + | 0.288978i | \(0.0933154\pi\) | ||||
−0.957336 | + | 0.288978i | \(0.906685\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2345.76i | − | 2.49814i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.9285 | − | 84.7467i | −0.0519963 | − | 0.0900603i | 0.838856 | − | 0.544354i | \(-0.183225\pi\) |
−0.890852 | + | 0.454294i | \(0.849892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 120.721 | + | 69.6984i | 0.128018 | + | 0.0739114i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1259.53 | − | 881.434i | −1.33283 | − | 0.932735i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 674.176 | + | 389.236i | 0.711907 | + | 0.411020i | 0.811767 | − | 0.583982i | \(-0.198506\pi\) |
−0.0998594 | + | 0.995002i | \(0.531839\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.6166 | + | 26.3367i | −0.0480680 | + | 0.0277521i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2621.73i | − | 2.75681i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 348.435 | 0.365620 | 0.182810 | − | 0.983148i | \(-0.441481\pi\) | ||||
0.182810 | + | 0.983148i | \(0.441481\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −453.224 | − | 785.006i | −0.474580 | − | 0.821996i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7646 | − | 18.6449i | 0.0112483 | − | 0.0194826i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −372.246 | + | 173.701i | −0.388161 | + | 0.181128i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −126.857 | + | 219.722i | −0.132005 | + | 0.228639i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1514.32 | − | 874.291i | 1.57250 | − | 0.907883i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −292.490 | −0.303098 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1055.75 | 1.09177 | 0.545887 | − | 0.837859i | \(-0.316193\pi\) | ||||
0.545887 | + | 0.837859i | \(0.316193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 887.319 | − | 512.294i | 0.915706 | − | 0.528683i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 426.302 | − | 738.377i | 0.439034 | − | 0.760429i | −0.558581 | − | 0.829450i | \(-0.688654\pi\) |
0.997615 | + | 0.0690206i | \(0.0219874\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −106.600 | + | 1222.18i | −0.109558 | + | 1.25609i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 178.952 | − | 309.954i | 0.183540 | − | 0.317901i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −169.835 | − | 294.163i | −0.173834 | − | 0.301089i | 0.765923 | − | 0.642932i | \(-0.222282\pi\) |
−0.939757 | + | 0.341843i | \(0.888949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.16360 | 0.00221001 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 692.365i | 0.705774i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 905.444 | − | 522.759i | 0.921103 | − | 0.531799i | 0.0371164 | − | 0.999311i | \(-0.488183\pi\) |
0.883987 | + | 0.467512i | \(0.154849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −426.709 | − | 246.361i | −0.433208 | − | 0.250112i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3075.52 | − | 268.252i | −3.11602 | − | 0.271785i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 590.496 | + | 340.923i | 0.597063 | + | 0.344715i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −409.911 | − | 709.987i | −0.413634 | − | 0.716435i | 0.581650 | − | 0.813439i | \(-0.302407\pi\) |
−0.995284 | + | 0.0970040i | \(0.969074\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2463.49i | − | 2.48086i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.39408i | 0.00341114i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −380.211 | − | 658.545i | −0.381355 | − | 0.660526i | 0.609901 | − | 0.792478i | \(-0.291209\pi\) |
−0.991256 | + | 0.131951i | \(0.957876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1805.28 | − | 1042.28i | −1.80708 | − | 1.04332i |
(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 | 224.3.n.a.145.14 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.5.8 | yes | 28 | ||
7.2 | even | 3 | 1568.3.h.a.881.1 | 28 | |||
7.3 | odd | 6 | inner | 224.3.n.a.17.1 | 28 | ||
7.5 | odd | 6 | 1568.3.h.a.881.27 | 28 | |||
8.3 | odd | 2 | 56.3.j.a.5.3 | ✓ | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.145.1 | 28 | ||
28.3 | even | 6 | 56.3.j.a.45.3 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.325.3 | 28 | |||
28.19 | even | 6 | 392.3.h.a.293.21 | 28 | |||
28.23 | odd | 6 | 392.3.h.a.293.22 | 28 | |||
28.27 | even | 2 | 392.3.j.e.117.8 | 28 | |||
56.3 | even | 6 | 56.3.j.a.45.8 | yes | 28 | ||
56.5 | odd | 6 | 1568.3.h.a.881.2 | 28 | |||
56.11 | odd | 6 | 392.3.j.e.325.8 | 28 | |||
56.19 | even | 6 | 392.3.h.a.293.24 | 28 | |||
56.27 | even | 2 | 392.3.j.e.117.3 | 28 | |||
56.37 | even | 6 | 1568.3.h.a.881.28 | 28 | |||
56.45 | odd | 6 | inner | 224.3.n.a.17.14 | 28 | ||
56.51 | odd | 6 | 392.3.h.a.293.23 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.3 | ✓ | 28 | 8.3 | odd | 2 | ||
56.3.j.a.5.8 | yes | 28 | 4.3 | odd | 2 | ||
56.3.j.a.45.3 | yes | 28 | 28.3 | even | 6 | ||
56.3.j.a.45.8 | yes | 28 | 56.3 | even | 6 | ||
224.3.n.a.17.1 | 28 | 7.3 | odd | 6 | inner | ||
224.3.n.a.17.14 | 28 | 56.45 | odd | 6 | inner | ||
224.3.n.a.145.1 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.14 | 28 | 1.1 | even | 1 | trivial | ||
392.3.h.a.293.21 | 28 | 28.19 | even | 6 | |||
392.3.h.a.293.22 | 28 | 28.23 | odd | 6 | |||
392.3.h.a.293.23 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.24 | 28 | 56.19 | even | 6 | |||
392.3.j.e.117.3 | 28 | 56.27 | even | 2 | |||
392.3.j.e.117.8 | 28 | 28.27 | even | 2 | |||
392.3.j.e.325.3 | 28 | 28.11 | odd | 6 | |||
392.3.j.e.325.8 | 28 | 56.11 | odd | 6 | |||
1568.3.h.a.881.1 | 28 | 7.2 | even | 3 | |||
1568.3.h.a.881.2 | 28 | 56.5 | odd | 6 | |||
1568.3.h.a.881.27 | 28 | 7.5 | odd | 6 | |||
1568.3.h.a.881.28 | 28 | 56.37 | even | 6 |