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 | 145.1 | ||
Character | \(\chi\) | \(=\) | 224.145 |
Dual form | 224.3.n.a.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | \(-0.789313\pi\) |
−0.137854 | − | 0.990453i | \(-0.544020\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.52921 | + | 2.64866i | −0.305841 | + | 0.529732i | −0.977448 | − | 0.211175i | \(-0.932271\pi\) |
0.671607 | + | 0.740907i | \(0.265604\pi\) | |||||||
\(6\) | 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 | −0.504812 | − | 0.863229i | \(-0.668438\pi\) |
0.495172 | + | 0.868795i | \(0.335105\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.11412 | 0.316471 | 0.158235 | − | 0.987401i | \(-0.449420\pi\) | ||||
0.158235 | + | 0.987401i | \(0.449420\pi\) | |||||||
\(14\) | 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 | −0.959333 | − | 0.282277i | \(-0.908910\pi\) |
0.724126 | + | 0.689668i | \(0.242243\pi\) | |||||||
\(20\) | 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 | \(0.183561\pi\) | ||||
−0.838280 | + | 0.545239i | \(0.816439\pi\) | |||||||
\(30\) | 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 | 0.120183 | − | 0.992752i | \(-0.461652\pi\) |
−0.799657 | + | 0.600457i | \(0.794985\pi\) | |||||||
\(38\) | 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 | \(0.176758\pi\) | ||||
−0.849742 | + | 0.527199i | \(0.823242\pi\) | |||||||
\(44\) | 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 | −0.919462 | − | 0.393178i | \(-0.871376\pi\) |
−0.119229 | + | 0.992867i | \(0.538042\pi\) | |||||||
\(54\) | 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 | 0.961178 | − | 0.275928i | \(-0.0889850\pi\) |
−0.719550 | + | 0.694441i | \(0.755652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6191 | + | 21.8569i | −0.206871 | + | 0.358311i | −0.950727 | − | 0.310029i | \(-0.899661\pi\) |
0.743856 | + | 0.668339i | \(0.232995\pi\) | |||||||
\(62\) | 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 | −0.901457 | − | 0.432868i | \(-0.857502\pi\) |
−0.0758537 | + | 0.997119i | \(0.524168\pi\) | |||||||
\(68\) | 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 | \(-0.442054\pi\) | ||||
0.181039 | + | 0.983476i | \(0.442054\pi\) | |||||||
\(84\) | 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 | \(-0.932219\pi\) |
0.305686 | − | 0.952132i | \(-0.401114\pi\) | |||||||
\(102\) | 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 | 0.786844 | − | 0.617152i | \(-0.211713\pi\) |
−0.141047 | + | 0.990003i | \(0.545047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.3608 | + | 15.7968i | −0.251017 | + | 0.144925i | −0.620230 | − | 0.784420i | \(-0.712961\pi\) |
0.369213 | + | 0.929345i | \(0.379627\pi\) | |||||||
\(110\) | 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 | −0.568623 | − | 0.822598i | \(-0.692524\pi\) |
0.996702 | + | 0.0811427i | \(0.0258569\pi\) | |||||||
\(132\) | 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 | \(-0.717121\pi\) | ||||
−0.630430 | + | 0.776246i | \(0.717121\pi\) | |||||||
\(140\) | 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 | 0.692525 | − | 0.721394i | \(-0.256498\pi\) |
−0.278483 | + | 0.960441i | \(0.589832\pi\) | |||||||
\(150\) | 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 | \(0.162482\pi\) |
−0.0131460 | + | 0.999914i | \(0.504185\pi\) | |||||||
\(158\) | 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 | 0.998438 | − | 0.0558788i | \(-0.0177960\pi\) |
0.450826 | + | 0.892612i | \(0.351129\pi\) | |||||||
\(164\) | 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 | \(-0.601557\pi\) |
0.979153 | − | 0.203125i | \(-0.0651097\pi\) | |||||||
\(174\) | 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 | 0.301074 | − | 0.953601i | \(-0.402655\pi\) |
0.976379 | + | 0.216063i | \(0.0693216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 183.991 | 1.01653 | 0.508263 | − | 0.861202i | \(-0.330288\pi\) | ||||
0.508263 | + | 0.861202i | \(0.330288\pi\) | |||||||
\(182\) | 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 | \(0.134085\pi\) | ||||
−0.912582 | + | 0.408893i | \(0.865915\pi\) | |||||||
\(198\) | 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 | \(-0.830675\pi\) | ||
0.861819 | − | 0.507216i | \(-0.169325\pi\) | |||||||
\(212\) | 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 | 0.941657 | − | 0.336574i | \(-0.109268\pi\) |
−0.762310 | + | 0.647212i | \(0.775935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 117.111 | − | 202.842i | 0.511400 | − | 0.885771i | −0.488512 | − | 0.872557i | \(-0.662460\pi\) |
0.999913 | − | 0.0132145i | \(-0.00420642\pi\) | |||||||
\(230\) | 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 | \(-0.587378\pi\) | ||||
−0.271072 | + | 0.962559i | \(0.587378\pi\) | |||||||
\(252\) | 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 | \(-0.982467\pi\) |
0.451565 | − | 0.892238i | \(-0.350866\pi\) | |||||||
\(270\) | 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 | −0.880842 | − | 0.473411i | \(-0.843023\pi\) |
−0.0304353 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(278\) | 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 | 0.896652 | − | 0.442735i | \(-0.145992\pi\) |
−0.831746 | + | 0.555156i | \(0.812659\pi\) | |||||||
\(284\) | 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 | \(-0.142837\pi\) | ||||
0.900996 | + | 0.433828i | \(0.142837\pi\) | |||||||
\(294\) | 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 | \(-0.408279\pi\) | ||||
0.284179 | + | 0.958771i | \(0.408279\pi\) | |||||||
\(308\) | 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 | 0.978329 | − | 0.207056i | \(-0.0663883\pi\) |
0.309848 | + | 0.950786i | \(0.399722\pi\) | |||||||
\(318\) | 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 | 0.951120 | − | 0.308820i | \(-0.0999342\pi\) |
0.208114 | + | 0.978105i | \(0.433268\pi\) | |||||||
\(332\) | 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 | −0.843679 | − | 0.536848i | \(-0.819615\pi\) |
0.0430845 | + | 0.999071i | \(0.486282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −222.198 | −0.636670 | −0.318335 | − | 0.947978i | \(-0.603124\pi\) | ||||
−0.318335 | + | 0.947978i | \(0.603124\pi\) | |||||||
\(350\) | 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 | −0.107810 | − | 0.994172i | \(-0.534384\pi\) |
−0.914883 | + | 0.403720i | \(0.867717\pi\) | |||||||
\(374\) | 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 | \(0.122115\pi\) | ||||
−0.927310 | + | 0.374294i | \(0.877885\pi\) | |||||||
\(380\) | 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 | −0.937831 | − | 0.347091i | \(-0.887170\pi\) |
−0.168326 | + | 0.985731i | \(0.553836\pi\) | |||||||
\(390\) | 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 | −0.629502 | − | 0.776999i | \(-0.716741\pi\) |
0.987652 | + | 0.156665i | \(0.0500743\pi\) | |||||||
\(398\) | 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 | \(-0.666607\pi\) | ||||
−0.499838 | + | 0.866119i | \(0.666607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 315.112i | 0.748485i | 0.927331 | + | 0.374243i | \(0.122097\pi\) | ||||
−0.927331 | + | 0.374243i | \(0.877903\pi\) | |||||||
\(422\) | 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 | 0.340339 | − | 0.940303i | \(-0.389458\pi\) |
−0.644157 | + | 0.764894i | \(0.722792\pi\) | |||||||
\(444\) | 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 | \(-0.557476\pi\) | ||||
−0.179586 | + | 0.983742i | \(0.557476\pi\) | |||||||
\(462\) | 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 | \(-0.623475\pi\) |
0.990808 | − | 0.135275i | \(-0.0431916\pi\) | |||||||
\(468\) | 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 | \(0.355097\pi\) | ||||
−0.439667 | + | 0.898161i | \(0.644903\pi\) | |||||||
\(492\) | 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 | 0.774018 | − | 0.633163i | \(-0.218244\pi\) |
−0.161327 | + | 0.986901i | \(0.551577\pi\) | |||||||
\(500\) | 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 | −0.822308 | − | 0.569043i | \(-0.807314\pi\) |
0.903959 | + | 0.427618i | \(0.140647\pi\) | |||||||
\(510\) | 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 | −0.973610 | − | 0.228217i | \(-0.926711\pi\) |
0.684446 | + | 0.729063i | \(0.260044\pi\) | |||||||
\(524\) | 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 | 0.952442 | − | 0.304719i | \(-0.0985626\pi\) |
0.212327 | + | 0.977199i | \(0.431896\pi\) | |||||||
\(542\) | 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 | \(-0.606348\pi\) | ||
0.327921 | − | 0.944705i | \(-0.393652\pi\) | |||||||
\(548\) | 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 | −0.942268 | − | 0.334861i | \(-0.891311\pi\) |
−0.181136 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(558\) | 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 | 0.989172 | − | 0.146759i | \(-0.0468841\pi\) |
−0.621683 | + | 0.783269i | \(0.713551\pi\) | |||||||
\(564\) | 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 | −0.930545 | − | 0.366177i | \(-0.880667\pi\) |
−0.148155 | + | 0.988964i | \(0.547333\pi\) | |||||||
\(572\) | 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 | \(-0.810874\pi\) | ||||
−0.828621 | + | 0.559810i | \(0.810874\pi\) | |||||||
\(588\) | 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 | 0.353116 | − | 0.935579i | \(-0.385122\pi\) |
0.986794 | + | 0.161982i | \(0.0517886\pi\) | |||||||
\(614\) | 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 | \(-0.891024\pi\) |
0.180251 | − | 0.983621i | \(-0.442309\pi\) | |||||||
\(620\) | 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 | \(-0.272992\pi\) | ||||
0.654233 | + | 0.756293i | \(0.272992\pi\) | |||||||
\(644\) | 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 | 0.934283 | − | 0.356532i | \(-0.116041\pi\) |
0.158375 | + | 0.987379i | \(0.449374\pi\) | |||||||
\(654\) | 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 | \(0.0866217\pi\) | ||||
−0.963201 | + | 0.268784i | \(0.913378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 84.3031 | + | 146.017i | 0.127539 | + | 0.220904i | 0.922722 | − | 0.385465i | \(-0.125959\pi\) |
−0.795184 | + | 0.606369i | \(0.792626\pi\) | |||||||
\(662\) | 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 | −0.606762 | − | 0.794883i | \(-0.707532\pi\) |
0.991770 | + | 0.128030i | \(0.0408654\pi\) | |||||||
\(678\) | 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 | −0.140585 | − | 0.990069i | \(-0.544898\pi\) |
0.787132 | + | 0.616785i | \(0.211565\pi\) | |||||||
\(684\) | 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 | \(-0.596866\pi\) |
0.976053 | − | 0.217532i | \(-0.0698005\pi\) | |||||||
\(692\) | 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 | \(-0.916335\pi\) | ||
0.965656 | − | 0.259826i | \(-0.0836651\pi\) | |||||||
\(702\) | 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 | 0.771130 | − | 0.636678i | \(-0.219692\pi\) |
−0.165815 | + | 0.986157i | \(0.553025\pi\) | |||||||
\(710\) | 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 | \(-0.609150\pi\) |
0.983719 | − | 0.179712i | \(-0.0575165\pi\) | |||||||
\(734\) | 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 | −0.541663 | − | 0.840596i | \(-0.682205\pi\) |
0.457145 | + | 0.889392i | \(0.348872\pi\) | |||||||
\(740\) | 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 | \(-0.783866\pi\) | ||
0.778197 | − | 0.628020i | \(-0.216134\pi\) | |||||||
\(758\) | 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 | 0.975173 | − | 0.221445i | \(-0.0710774\pi\) |
−0.679364 | + | 0.733802i | \(0.737744\pi\) | |||||||
\(774\) | 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 | 0.918295 | − | 0.395897i | \(-0.129566\pi\) |
−0.802004 | + | 0.597318i | \(0.796233\pi\) | |||||||
\(788\) | 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 | \(-0.372894\pi\) | ||||
0.388787 | + | 0.921328i | \(0.372894\pi\) | |||||||
\(798\) | 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 | \(-0.253781\pi\) | ||||
0.698658 | + | 0.715456i | \(0.253781\pi\) | |||||||
\(812\) | 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 | 0.0716414 | − | 0.997430i | \(-0.477176\pi\) |
−0.827979 | + | 0.560758i | \(0.810510\pi\) | |||||||
\(822\) | 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 | \(-0.914918\pi\) | ||
0.964489 | − | 0.264122i | \(-0.0850822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −588.361 | − | 1019.07i | −0.709724 | − | 1.22928i | −0.964959 | − | 0.262399i | \(-0.915486\pi\) |
0.255235 | − | 0.966879i | \(-0.417847\pi\) | |||||||
\(830\) | 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 | \(-0.474086\pi\) | ||||
0.0813225 | + | 0.996688i | \(0.474086\pi\) | |||||||
\(854\) | 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 | −0.975896 | − | 0.218238i | \(-0.929969\pi\) |
0.676948 | + | 0.736031i | \(0.263302\pi\) | |||||||
\(860\) | 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 | 0.264474 | − | 0.964393i | \(-0.414802\pi\) |
−0.702952 | + | 0.711237i | \(0.748135\pi\) | |||||||
\(878\) | 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 | \(0.185921\pi\) | ||||
−0.834216 | + | 0.551438i | \(0.814079\pi\) | |||||||
\(884\) | 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 | −0.105862 | − | 0.994381i | \(-0.533760\pi\) |
0.808228 | + | 0.588870i | \(0.200427\pi\) | |||||||
\(908\) | 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 | 0.890852 | − | 0.454294i | \(-0.150108\pi\) |
−0.838856 | + | 0.544354i | \(0.816775\pi\) | |||||||
\(942\) | 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 | 0.0998594 | − | 0.995002i | \(-0.468161\pi\) |
−0.811767 | + | 0.583982i | \(0.801494\pi\) | |||||||
\(948\) | 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 | −0.997615 | − | 0.0690206i | \(-0.978013\pi\) |
0.558581 | + | 0.829450i | \(0.311346\pi\) | |||||||
\(972\) | 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 | 0.991256 | − | 0.131951i | \(-0.0421242\pi\) |
−0.609901 | + | 0.792478i | \(0.708791\pi\) | |||||||
\(998\) | 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.145.1 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.5.3 | ✓ | 28 | ||
7.2 | even | 3 | 1568.3.h.a.881.28 | 28 | |||
7.3 | odd | 6 | inner | 224.3.n.a.17.14 | 28 | ||
7.5 | odd | 6 | 1568.3.h.a.881.2 | 28 | |||
8.3 | odd | 2 | 56.3.j.a.5.8 | yes | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.145.14 | 28 | ||
28.3 | even | 6 | 56.3.j.a.45.8 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.325.8 | 28 | |||
28.19 | even | 6 | 392.3.h.a.293.24 | 28 | |||
28.23 | odd | 6 | 392.3.h.a.293.23 | 28 | |||
28.27 | even | 2 | 392.3.j.e.117.3 | 28 | |||
56.3 | even | 6 | 56.3.j.a.45.3 | yes | 28 | ||
56.5 | odd | 6 | 1568.3.h.a.881.27 | 28 | |||
56.11 | odd | 6 | 392.3.j.e.325.3 | 28 | |||
56.19 | even | 6 | 392.3.h.a.293.21 | 28 | |||
56.27 | even | 2 | 392.3.j.e.117.8 | 28 | |||
56.37 | even | 6 | 1568.3.h.a.881.1 | 28 | |||
56.45 | odd | 6 | inner | 224.3.n.a.17.1 | 28 | ||
56.51 | odd | 6 | 392.3.h.a.293.22 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.3 | ✓ | 28 | 4.3 | odd | 2 | ||
56.3.j.a.5.8 | yes | 28 | 8.3 | odd | 2 | ||
56.3.j.a.45.3 | yes | 28 | 56.3 | even | 6 | ||
56.3.j.a.45.8 | yes | 28 | 28.3 | even | 6 | ||
224.3.n.a.17.1 | 28 | 56.45 | odd | 6 | inner | ||
224.3.n.a.17.14 | 28 | 7.3 | odd | 6 | inner | ||
224.3.n.a.145.1 | 28 | 1.1 | even | 1 | trivial | ||
224.3.n.a.145.14 | 28 | 8.5 | even | 2 | inner | ||
392.3.h.a.293.21 | 28 | 56.19 | even | 6 | |||
392.3.h.a.293.22 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.23 | 28 | 28.23 | odd | 6 | |||
392.3.h.a.293.24 | 28 | 28.19 | even | 6 | |||
392.3.j.e.117.3 | 28 | 28.27 | even | 2 | |||
392.3.j.e.117.8 | 28 | 56.27 | even | 2 | |||
392.3.j.e.325.3 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.325.8 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.1 | 28 | 56.37 | even | 6 | |||
1568.3.h.a.881.2 | 28 | 7.5 | odd | 6 | |||
1568.3.h.a.881.27 | 28 | 56.5 | odd | 6 | |||
1568.3.h.a.881.28 | 28 | 7.2 | even | 3 |