Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.11 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.11 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.18497 | − | 2.05570i | −0.728322 | − | 0.685235i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46044 | + | 5.99365i | 0.692087 | + | 1.19873i | 0.971153 | + | 0.238458i | \(0.0766420\pi\) |
−0.279065 | + | 0.960272i | \(0.590025\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.78976 | − | 6.56406i | −0.541395 | − | 0.937723i | −0.998824 | − | 0.0484775i | \(-0.984563\pi\) |
0.457429 | − | 0.889246i | \(-0.348770\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.548164 | + | 8.98329i | 0.0609071 | + | 0.998143i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.11214 | + | 1.92629i | 0.101104 | + | 0.175117i | 0.912140 | − | 0.409879i | \(-0.134429\pi\) |
−0.811036 | + | 0.584996i | \(0.801096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11.6560i | − | 0.896612i | −0.893880 | − | 0.448306i | \(-0.852027\pi\) | ||
0.893880 | − | 0.448306i | \(-0.147973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.76023 | − | 20.2096i | 0.317349 | − | 1.34730i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.1844 | + | 19.3719i | −0.657904 | + | 1.13952i | 0.323253 | + | 0.946312i | \(0.395223\pi\) |
−0.981157 | + | 0.193210i | \(0.938110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.9863 | + | 0.721079i | −0.999280 | + | 0.0379515i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.21326 | + | 22.1329i | −0.248251 | + | 1.05395i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.5116 | 1.45703 | 0.728513 | − | 0.685032i | \(-0.240212\pi\) | ||||
0.728513 | + | 0.685032i | \(0.240212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.4492 | + | 19.8307i | −0.457970 | + | 0.793227i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.2693 | − | 20.7551i | 0.639602 | − | 0.768706i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11.2228 | − | 6.47950i | −0.386994 | − | 0.223431i | 0.293863 | − | 0.955848i | \(-0.405059\pi\) |
−0.680857 | + | 0.732417i | \(0.738392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.6445 | − | 21.7341i | −1.21434 | − | 0.701099i | −0.250637 | − | 0.968081i | \(-0.580640\pi\) |
−0.963701 | + | 0.266983i | \(0.913973\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.52988 | − | 6.49511i | 0.0463600 | − | 0.196821i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 26.2285 | − | 45.4290i | 0.749385 | − | 1.29797i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 65.7083i | − | 1.77590i | −0.459940 | − | 0.887950i | \(-0.652129\pi\) | ||
0.459940 | − | 0.887950i | \(-0.347871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −23.9612 | + | 25.4679i | −0.614390 | + | 0.653023i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −55.5146 | + | 32.0514i | −1.35401 | + | 0.781741i | −0.988809 | − | 0.149186i | \(-0.952335\pi\) |
−0.365206 | + | 0.930927i | \(0.619001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.06038 | −0.0944275 | −0.0472138 | − | 0.998885i | \(-0.515034\pi\) | ||||
−0.0472138 | + | 0.998885i | \(0.515034\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −51.9458 | + | 34.3716i | −1.15435 | + | 0.763814i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.65503 | − | 13.2589i | 0.162873 | − | 0.282104i | −0.773025 | − | 0.634376i | \(-0.781257\pi\) |
0.935898 | + | 0.352271i | \(0.114591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.22462 | + | 7.31726i | −0.0862168 | + | 0.149332i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 64.2603 | − | 19.3352i | 1.26001 | − | 0.379122i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −72.0176 | + | 41.5794i | −1.35882 | + | 0.784517i | −0.989465 | − | 0.144771i | \(-0.953756\pi\) |
−0.369358 | + | 0.929287i | \(0.620422\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.69699 | + | 13.3316i | −0.139945 | + | 0.242392i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 42.9668 | + | 37.4547i | 0.753803 | + | 0.657100i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −83.7382 | + | 48.3463i | −1.41929 | + | 0.819428i | −0.996237 | − | 0.0866761i | \(-0.972375\pi\) |
−0.423055 | + | 0.906104i | \(0.639042\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −45.6758 | + | 79.1128i | −0.748783 | + | 1.29693i | 0.199623 | + | 0.979873i | \(0.436028\pi\) |
−0.948406 | + | 0.317058i | \(0.897305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 56.8895 | − | 37.6427i | 0.903008 | − | 0.597504i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 69.8618 | − | 40.3347i | 1.07480 | − | 0.620534i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 37.2589i | 0.556103i | 0.960566 | + | 0.278052i | \(0.0896887\pi\) | ||||
−0.960566 | + | 0.278052i | \(0.910311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −73.2217 | − | 68.8899i | −1.06118 | − | 0.998405i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69.8995 | − | 40.3565i | −0.984500 | − | 0.568401i | −0.0808744 | − | 0.996724i | \(-0.525771\pi\) |
−0.903626 | + | 0.428323i | \(0.859105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −43.7295 | + | 75.7417i | −0.599034 | + | 1.03756i | 0.393930 | + | 0.919140i | \(0.371115\pi\) |
−0.992964 | + | 0.118417i | \(0.962218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 65.7822 | − | 19.7931i | 0.877096 | − | 0.263908i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.42951 | − | 14.6003i | 0.109474 | − | 0.189615i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 96.2184i | − | 1.21795i | −0.793188 | − | 0.608977i | \(-0.791580\pi\) | ||
0.793188 | − | 0.608977i | \(-0.208420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −80.3990 | + | 9.84863i | −0.992581 | + | 0.121588i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 24.8505 | + | 43.0423i | 0.299404 | + | 0.518582i | 0.976000 | − | 0.217772i | \(-0.0698790\pi\) |
−0.676596 | + | 0.736354i | \(0.736546\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −154.811 | −1.82131 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.2016 | + | 37.2283i | 0.128754 | + | 0.427911i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.8082 | − | 10.8589i | 0.211328 | − | 0.122011i | −0.390600 | − | 0.920560i | \(-0.627732\pi\) |
0.601929 | + | 0.798550i | \(0.294399\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −76.5105 | + | 44.1733i | −0.840774 | + | 0.485421i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 37.5732 | + | 124.874i | 0.404013 | + | 1.34273i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −70.0228 | − | 111.302i | −0.737082 | − | 1.17160i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 154.384i | 1.59158i | 0.605570 | + | 0.795792i | \(0.292945\pi\) | ||||
−0.605570 | + | 0.795792i | \(0.707055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.6948 | + | 11.0466i | −0.168634 | + | 0.111582i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 41.8141 | − | 72.4242i | 0.414001 | − | 0.717071i | −0.581322 | − | 0.813674i | \(-0.697464\pi\) |
0.995323 | + | 0.0966026i | \(0.0307976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −118.486 | − | 68.4077i | −1.15035 | − | 0.664153i | −0.201375 | − | 0.979514i | \(-0.564541\pi\) |
−0.948972 | + | 0.315362i | \(0.897874\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −150.697 | + | 45.3430i | −1.43521 | + | 0.431838i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 37.1337i | − | 0.347044i | −0.984830 | − | 0.173522i | \(-0.944485\pi\) | ||
0.984830 | − | 0.173522i | \(-0.0555148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 63.7561 | + | 36.8096i | 0.584918 | + | 0.337703i | 0.763085 | − | 0.646298i | \(-0.223684\pi\) |
−0.178167 | + | 0.984000i | \(0.557017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −135.077 | + | 143.570i | −1.21691 | + | 1.29343i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −140.095 | − | 80.8841i | −1.23978 | − | 0.715788i | −0.270732 | − | 0.962655i | \(-0.587266\pi\) |
−0.969050 | + | 0.246866i | \(0.920599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.965 | + | 200.857i | 1.00839 | + | 1.74658i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 104.709 | − | 6.38938i | 0.894948 | − | 0.0546101i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 169.544 | 1.42474 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 58.0263 | − | 100.504i | 0.479556 | − | 0.830615i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 187.186 | + | 44.0904i | 1.52184 | + | 0.358458i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.5443 | 0.116355 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −116.814 | + | 67.4425i | −0.919794 | + | 0.531043i | −0.883569 | − | 0.468300i | \(-0.844867\pi\) |
−0.0362248 | + | 0.999344i | \(0.511533\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.87181 | + | 8.34695i | 0.0687737 | + | 0.0647050i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 25.5748 | + | 44.2969i | 0.195228 | + | 0.338144i | 0.946975 | − | 0.321307i | \(-0.104122\pi\) |
−0.751748 | + | 0.659451i | \(0.770789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 76.6869 | + | 121.895i | 0.576593 | + | 0.916501i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 184.158 | + | 31.6844i | 1.36413 | + | 0.234699i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 68.9943 | − | 119.502i | 0.503608 | − | 0.872275i | −0.496383 | − | 0.868104i | \(-0.665339\pi\) |
0.999991 | − | 0.00417145i | \(-0.00132782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 68.8165 | 0.495083 | 0.247541 | − | 0.968877i | \(-0.420377\pi\) | ||||
0.247541 | + | 0.968877i | \(0.420377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −43.9823 | + | 13.2338i | −0.311932 | + | 0.0938566i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.4527 | − | 12.9631i | 0.157012 | − | 0.0906510i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 89.6876i | − | 0.618535i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.2728 | − | 7.30340i | 0.165121 | − | 0.0496830i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −105.104 | − | 182.045i | −0.705395 | − | 1.22178i | −0.966549 | − | 0.256482i | \(-0.917436\pi\) |
0.261154 | − | 0.965297i | \(-0.415897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 94.5876 | − | 54.6102i | 0.626408 | − | 0.361657i | −0.152952 | − | 0.988234i | \(-0.548878\pi\) |
0.779360 | + | 0.626577i | \(0.215545\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −180.154 | − | 89.8534i | −1.17748 | − | 0.587277i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 300.837i | − | 1.94089i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −77.4998 | − | 134.234i | −0.493629 | − | 0.854991i | 0.506344 | − | 0.862332i | \(-0.330997\pi\) |
−0.999973 | + | 0.00734074i | \(0.997663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 242.831 | + | 57.1973i | 1.52724 | + | 0.359731i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −127.001 | − | 219.972i | −0.788826 | − | 1.36629i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −185.560 | −1.13841 | −0.569204 | − | 0.822196i | \(-0.692748\pi\) | ||||
−0.569204 | + | 0.822196i | \(0.692748\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 44.2235 | − | 13.3063i | 0.268021 | − | 0.0806445i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 77.8292i | − | 0.466043i | −0.972472 | − | 0.233021i | \(-0.925139\pi\) | ||
0.972472 | − | 0.233021i | \(-0.0748612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.1385 | 0.196086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.8853 | − | 170.164i | −0.0987443 | − | 0.995113i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 139.414i | 0.805864i | 0.915230 | + | 0.402932i | \(0.132009\pi\) | ||||
−0.915230 | + | 0.402932i | \(0.867991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 173.560 | 0.991770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 282.351 | + | 66.5059i | 1.59520 | + | 0.375740i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 79.8752i | 0.446230i | 0.974792 | + | 0.223115i | \(0.0716225\pi\) | ||||
−0.974792 | + | 0.223115i | \(0.928377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 277.769 | − | 160.370i | 1.53464 | − | 0.886022i | 0.535496 | − | 0.844537i | \(-0.320125\pi\) |
0.999139 | − | 0.0414848i | \(-0.0132088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 262.433 | − | 78.9629i | 1.43406 | − | 0.431492i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 393.833 | − | 227.379i | 2.12882 | − | 1.22908i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −49.7544 | −0.266066 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −201.684 | − | 34.6998i | −1.06711 | − | 0.183597i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9414 | + | 20.6831i | 0.0625204 | + | 0.108289i | 0.895591 | − | 0.444878i | \(-0.146753\pi\) |
−0.833071 | + | 0.553166i | \(0.813419\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 40.9187 | − | 23.6244i | 0.212014 | − | 0.122406i | −0.390233 | − | 0.920716i | \(-0.627606\pi\) |
0.602247 | + | 0.798310i | \(0.294272\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −235.562 | − | 55.4851i | −1.20801 | − | 0.284539i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 323.931 | 1.64432 | 0.822160 | − | 0.569256i | \(-0.192769\pi\) | ||||
0.822160 | + | 0.569256i | \(0.192769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.5516 | − | 39.0605i | −0.113324 | − | 0.196284i | 0.803784 | − | 0.594921i | \(-0.202817\pi\) |
−0.917109 | + | 0.398637i | \(0.869483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 76.5933 | − | 81.4095i | 0.381061 | − | 0.405023i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 98.2231i | 0.483858i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −384.210 | − | 221.824i | −1.87419 | − | 1.08207i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.3698 | + | 301.044i | 0.0887432 | + | 1.45432i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.5045 | − | 35.7711i | −0.107677 | − | 0.171154i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −32.8915 | + | 18.9899i | −0.155884 | + | 0.0899996i | −0.575913 | − | 0.817511i | \(-0.695353\pi\) |
0.420029 | + | 0.907511i | \(0.362020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 69.7671 | + | 231.870i | 0.327545 | + | 1.08859i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0507 | − | 24.3365i | −0.0653521 | − | 0.113193i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 329.468i | 1.51828i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 251.250 | − | 75.5982i | 1.14726 | − | 0.345197i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 225.798 | + | 130.365i | 1.02171 | + | 0.589885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 129.266i | 0.579666i | 0.957077 | + | 0.289833i | \(0.0935998\pi\) | ||||
−0.957077 | + | 0.289833i | \(0.906400\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −184.421 | − | 91.9814i | −0.819648 | − | 0.408806i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 262.063 | − | 151.302i | 1.15446 | − | 0.666529i | 0.204491 | − | 0.978868i | \(-0.434446\pi\) |
0.949971 | + | 0.312340i | \(0.101113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −86.1574 | + | 149.229i | −0.376233 | + | 0.651655i | −0.990511 | − | 0.137435i | \(-0.956114\pi\) |
0.614278 | + | 0.789090i | \(0.289447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −48.4322 | + | 14.5727i | −0.209663 | + | 0.0630852i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −222.274 | + | 384.990i | −0.953965 | + | 1.65232i | −0.217246 | + | 0.976117i | \(0.569707\pi\) |
−0.736719 | + | 0.676199i | \(0.763626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 105.959 | 0.450889 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −197.797 | + | 210.234i | −0.834585 | + | 0.887064i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −131.653 | + | 228.030i | −0.550850 | + | 0.954100i | 0.447364 | + | 0.894352i | \(0.352363\pi\) |
−0.998214 | + | 0.0597478i | \(0.980970\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4042 | + | 6.00684i | 0.0431707 | + | 0.0249246i | 0.521430 | − | 0.853294i | \(-0.325399\pi\) |
−0.478259 | + | 0.878219i | \(0.658732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 195.915 | + | 143.758i | 0.806235 | + | 0.591595i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −58.4761 | −0.238678 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.40487 | + | 221.304i | 0.0340278 | + | 0.895967i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.1848 | − | 145.131i | 0.137288 | − | 0.582857i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −101.728 | − | 176.197i | −0.405289 | − | 0.701981i | 0.589066 | − | 0.808085i | \(-0.299496\pi\) |
−0.994355 | + | 0.106104i | \(0.966162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.2697 | + | 64.5529i | 0.147311 | + | 0.255150i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 338.257 | + | 318.246i | 1.32650 | + | 1.24802i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 152.109i | 0.591863i | 0.955209 | + | 0.295932i | \(0.0956301\pi\) | ||||
−0.955209 | + | 0.295932i | \(0.904370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −431.313 | + | 249.019i | −1.66530 | + | 0.961463i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 52.0553 | − | 104.370i | 0.199446 | − | 0.399884i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 96.2390 | 0.365928 | 0.182964 | − | 0.983120i | \(-0.441431\pi\) | ||||
0.182964 | + | 0.983120i | \(0.441431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −498.425 | − | 287.766i | −1.88085 | − | 1.08591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −63.4181 | − | 14.9377i | −0.237521 | − | 0.0559466i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −209.351 | − | 120.869i | −0.778255 | − | 0.449326i | 0.0575566 | − | 0.998342i | \(-0.481669\pi\) |
−0.835811 | + | 0.549017i | \(0.815002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 87.1064 | − | 150.873i | 0.321426 | − | 0.556726i | −0.659357 | − | 0.751830i | \(-0.729171\pi\) |
0.980783 | + | 0.195104i | \(0.0625045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 257.980 | + | 60.7656i | 0.944982 | + | 0.222585i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −50.9327 | −0.185210 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 190.066 | + | 329.203i | 0.686157 | + | 1.18846i | 0.973072 | + | 0.230503i | \(0.0740371\pi\) |
−0.286914 | + | 0.957956i | \(0.592630\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 174.608 | − | 350.085i | 0.625835 | − | 1.25479i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 113.389 | + | 65.4652i | 0.403520 | + | 0.232972i | 0.688002 | − | 0.725709i | \(-0.258488\pi\) |
−0.284482 | + | 0.958681i | \(0.591822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −53.3848 | − | 92.4652i | −0.188639 | − | 0.326732i | 0.756158 | − | 0.654389i | \(-0.227074\pi\) |
−0.944797 | + | 0.327657i | \(0.893741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −75.8066 | + | 387.138i | −0.265988 | + | 1.35838i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 420.775 | + | 242.934i | 1.46611 | + | 0.846461i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −105.680 | − | 183.043i | −0.365675 | − | 0.633368i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 317.367 | − | 337.323i | 1.09061 | − | 1.15919i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 80.0984 | + | 46.2449i | 0.273374 | + | 0.157832i | 0.630420 | − | 0.776254i | \(-0.282883\pi\) |
−0.357046 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −579.541 | − | 334.598i | −1.96455 | − | 1.13423i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 59.1861 | + | 10.1830i | 0.199280 | + | 0.0342861i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 390.610i | − | 1.30639i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3879 | + | 26.6526i | 0.0511226 | + | 0.0885469i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −240.245 | + | 72.2870i | −0.792888 | + | 0.238571i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −632.233 | −2.07289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 336.092 | + | 194.043i | 1.09476 | + | 0.632062i | 0.934841 | − | 0.355067i | \(-0.115542\pi\) |
0.159923 | + | 0.987130i | \(0.448875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 118.261 | + | 393.040i | 0.382722 | + | 1.27197i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.84097 | − | 6.65275i | 0.0123504 | − | 0.0213915i | −0.859784 | − | 0.510658i | \(-0.829402\pi\) |
0.872135 | + | 0.489266i | \(0.162735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 174.620 | − | 302.450i | 0.557891 | − | 0.966295i | −0.439782 | − | 0.898105i | \(-0.644944\pi\) |
0.997672 | − | 0.0681904i | \(-0.0217225\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 422.480 | + | 210.715i | 1.34121 | + | 0.668938i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 47.7851 | + | 27.5888i | 0.150742 | + | 0.0870308i | 0.573474 | − | 0.819224i | \(-0.305595\pi\) |
−0.422732 | + | 0.906255i | \(0.638929\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.8245i | − | 0.0903589i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −76.3359 | + | 81.1359i | −0.237807 | + | 0.252760i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 198.381 | − | 375.866i | 0.614183 | − | 1.16367i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 231.145 | + | 133.452i | 0.711217 | + | 0.410621i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −63.6353 | − | 211.491i | −0.194603 | − | 0.646763i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −116.043 | −0.352714 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 318.401 | − | 183.829i | 0.961936 | − | 0.555374i | 0.0651679 | − | 0.997874i | \(-0.479242\pi\) |
0.896768 | + | 0.442500i | \(0.145908\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 590.277 | − | 36.0189i | 1.77260 | − | 0.108165i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −223.317 | + | 128.932i | −0.666618 | + | 0.384872i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −154.839 | + | 89.3966i | −0.459464 | + | 0.265272i | −0.711819 | − | 0.702363i | \(-0.752128\pi\) |
0.252355 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 139.830 | + | 464.724i | 0.412478 | + | 1.37087i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 96.6854i | − | 0.283535i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −307.356 | −0.896080 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 159.523 | − | 677.255i | 0.462385 | − | 1.96306i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −146.595 | − | 253.910i | −0.422464 | − | 0.731729i | 0.573716 | − | 0.819054i | \(-0.305501\pi\) |
−0.996180 | + | 0.0873254i | \(0.972168\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −141.578 | − | 245.220i | −0.405667 | − | 0.702637i | 0.588731 | − | 0.808329i | \(-0.299628\pi\) |
−0.994399 | + | 0.105692i | \(0.966294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −241.920 | − | 201.290i | −0.689231 | − | 0.573476i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −163.732 | − | 283.592i | −0.463829 | − | 0.803376i | 0.535319 | − | 0.844650i | \(-0.320192\pi\) |
−0.999148 | + | 0.0412744i | \(0.986858\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 558.604i | − | 1.57353i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −370.449 | − | 348.533i | −1.03767 | − | 0.976283i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −158.090 | + | 273.821i | −0.440363 | + | 0.762732i | −0.997716 | − | 0.0675439i | \(-0.978484\pi\) |
0.557353 | + | 0.830276i | \(0.311817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 359.960 | − | 27.3813i | 0.997119 | − | 0.0758484i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −333.393 | + | 100.314i | −0.918438 | + | 0.276347i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −605.292 | −1.65833 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −186.657 | + | 323.299i | −0.508602 | + | 0.880924i | 0.491349 | + | 0.870963i | \(0.336504\pi\) |
−0.999950 | + | 0.00996107i | \(0.996829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −318.358 | − | 481.135i | −0.862759 | − | 1.30389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 545.860 | + | 315.152i | 1.47132 | + | 0.849467i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 352.184 | + | 203.333i | 0.944192 | + | 0.545130i | 0.891272 | − | 0.453469i | \(-0.149814\pi\) |
0.0529201 | + | 0.998599i | \(0.483147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.7789 | − | 29.8989i | −0.0847438 | − | 0.0797303i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −75.5248 | + | 130.813i | −0.200331 | + | 0.346984i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 468.372i | − | 1.23581i | −0.786253 | − | 0.617905i | \(-0.787982\pi\) | ||
0.786253 | − | 0.617905i | \(-0.212018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 393.876 | + | 92.7750i | 1.03380 | + | 0.243504i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 200.495 | − | 115.756i | 0.523485 | − | 0.302234i | −0.214874 | − | 0.976642i | \(-0.568934\pi\) |
0.738359 | + | 0.674408i | \(0.235601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 116.679 | 0.303063 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.22576 | − | 36.4756i | −0.00575131 | − | 0.0942522i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.6263 | + | 23.6015i | −0.0350291 | + | 0.0606721i | −0.883008 | − | 0.469357i | \(-0.844486\pi\) |
0.847979 | + | 0.530029i | \(0.177819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −374.806 | + | 649.183i | −0.958583 | + | 1.66031i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.1811 | − | 149.361i | 0.0895194 | − | 0.380055i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 576.700 | − | 332.958i | 1.46000 | − | 0.842931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −65.6998 | + | 113.795i | −0.165491 | + | 0.286638i | −0.936829 | − | 0.349787i | \(-0.886254\pi\) |
0.771339 | + | 0.636425i | \(0.219587\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 83.0210 | − | 423.981i | 0.208073 | − | 1.06261i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.9256 | + | 9.77199i | −0.0422084 | + | 0.0243690i | −0.520956 | − | 0.853584i | \(-0.674424\pi\) |
0.478747 | + | 0.877953i | \(0.341091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −253.331 | + | 438.783i | −0.628614 | + | 1.08879i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −337.245 | − | 447.803i | −0.832704 | − | 1.10569i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 126.573 | − | 73.0770i | 0.310990 | − | 0.179550i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 676.132i | 1.65313i | 0.562838 | + | 0.826567i | \(0.309709\pi\) | ||||
−0.562838 | + | 0.826567i | \(0.690291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −396.410 | + | 119.275i | −0.964502 | + | 0.290208i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 634.696 | + | 366.442i | 1.53679 | + | 0.887268i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −171.987 | + | 297.890i | −0.414427 | + | 0.717808i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −150.362 | − | 141.466i | −0.360580 | − | 0.339248i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4954 | + | 23.3748i | −0.0322087 | + | 0.0557871i | −0.881680 | − | 0.471847i | \(-0.843587\pi\) |
0.849472 | + | 0.527634i | \(0.176921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.8620i | − | 0.0424274i | −0.999775 | − | 0.0212137i | \(-0.993247\pi\) | ||
0.999775 | − | 0.0212137i | \(-0.00675304\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 123.305 | + | 61.4993i | 0.291501 | + | 0.145388i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −256.105 | − | 443.587i | −0.602600 | − | 1.04373i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 692.402 | 1.62155 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −75.7067 | − | 17.8322i | −0.176473 | − | 0.0415670i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −409.592 | + | 236.478i | −0.950330 | + | 0.548673i | −0.893183 | − | 0.449693i | \(-0.851534\pi\) |
−0.0571465 | + | 0.998366i | \(0.518200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −301.419 | + | 174.024i | −0.696117 | + | 0.401903i | −0.805900 | − | 0.592052i | \(-0.798318\pi\) |
0.109782 | + | 0.993956i | \(0.464985\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −184.371 | + | 195.964i | −0.423842 | + | 0.450493i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −636.262 | + | 24.1645i | −1.45598 | + | 0.0552964i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 223.938i | 0.510109i | 0.966927 | + | 0.255055i | \(0.0820934\pi\) | ||||
−0.966927 | + | 0.255055i | \(0.917907\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −68.0488 | − | 33.9399i | −0.154306 | − | 0.0769613i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.6061 | − | 21.8343i | 0.0284561 | − | 0.0492874i | −0.851447 | − | 0.524441i | \(-0.824274\pi\) |
0.879903 | + | 0.475154i | \(0.157608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 130.169 | + | 75.1533i | 0.292515 | + | 0.168884i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −144.582 | + | 613.825i | −0.323451 | + | 1.37321i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 364.578i | 0.811977i | 0.913878 | + | 0.405989i | \(0.133073\pi\) | ||||
−0.913878 | + | 0.405989i | \(0.866927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −123.480 | − | 71.2914i | −0.273792 | − | 0.158074i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −318.933 | − | 75.1227i | −0.704047 | − | 0.165834i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −529.519 | − | 305.718i | −1.16378 | − | 0.671908i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −181.131 | − | 313.729i | −0.396349 | − | 0.686496i | 0.596924 | − | 0.802298i | \(-0.296390\pi\) |
−0.993272 | + | 0.115802i | \(0.963056\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 208.919 | + | 566.670i | 0.455161 | + | 1.23458i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 739.769 | 1.60471 | 0.802353 | − | 0.596850i | \(-0.203581\pi\) | ||||
0.802353 | + | 0.596850i | \(0.203581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 224.968 | − | 389.656i | 0.485893 | − | 0.841591i | −0.513976 | − | 0.857805i | \(-0.671828\pi\) |
0.999869 | + | 0.0162140i | \(0.00516130\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −618.432 | + | 657.320i | −1.32996 | + | 1.41359i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.47232 | −0.0138593 | −0.00692967 | − | 0.999976i | \(-0.502206\pi\) | ||||
−0.00692967 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 244.570 | − | 141.203i | 0.521471 | − | 0.301071i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −106.610 | + | 452.613i | −0.226348 | + | 0.960961i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.51572 | − | 7.82146i | −0.00954699 | − | 0.0165359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 203.079 | − | 384.767i | 0.427536 | − | 0.810036i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −412.997 | − | 624.163i | −0.865822 | − | 1.30852i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −405.295 | + | 701.991i | −0.846126 | + | 1.46553i | 0.0385129 | + | 0.999258i | \(0.487738\pi\) |
−0.884639 | + | 0.466276i | \(0.845595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −765.893 | −1.59229 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −174.705 | + | 741.709i | −0.361707 | + | 1.53563i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −925.322 | + | 534.235i | −1.90788 | + | 1.10152i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 877.229i | − | 1.80129i | −0.434553 | − | 0.900646i | \(-0.643094\pi\) | ||
0.434553 | − | 0.900646i | \(-0.356906\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 405.443 | + | 381.457i | 0.829128 | + | 0.780076i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −442.507 | − | 766.445i | −0.901237 | − | 1.56099i | −0.825890 | − | 0.563831i | \(-0.809327\pi\) |
−0.0753463 | − | 0.997157i | \(-0.524006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 251.040 | − | 144.938i | 0.509210 | − | 0.293992i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −123.981 | − | 61.8364i | −0.250466 | − | 0.124922i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 611.766i | 1.23092i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 319.587 | + | 553.540i | 0.640454 | + | 1.10930i | 0.985331 | + | 0.170651i | \(0.0545872\pi\) |
−0.344877 | + | 0.938648i | \(0.612079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −159.994 | + | 170.054i | −0.319349 | + | 0.339429i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.2858 | − | 42.0642i | −0.0482818 | − | 0.0836266i | 0.840874 | − | 0.541230i | \(-0.182041\pi\) |
−0.889156 | + | 0.457604i | \(0.848708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 578.781 | 1.14610 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −72.4066 | − | 68.1230i | −0.142814 | − | 0.134365i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 292.865i | − | 0.575373i | −0.957725 | − | 0.287687i | \(-0.907114\pi\) | ||
0.957725 | − | 0.287687i | \(-0.0928861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 662.897 | 1.29726 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −312.914 | + | 406.515i | −0.609968 | + | 0.792426i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 946.882i | − | 1.83861i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.0539 | 0.0658683 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 286.595 | − | 304.616i | 0.552206 | − | 0.586928i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 228.496i | − | 0.438572i | −0.975661 | − | 0.219286i | \(-0.929627\pi\) | ||
0.975661 | − | 0.219286i | \(-0.0703728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −353.160 | + | 203.897i | −0.675258 | + | 0.389860i | −0.798066 | − | 0.602570i | \(-0.794143\pi\) |
0.122808 | + | 0.992430i | \(0.460810\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −379.222 | − | 356.787i | −0.722328 | − | 0.679595i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 842.059 | − | 486.163i | 1.59784 | − | 0.922511i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 594.027 | 1.12292 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −480.211 | − | 725.743i | −0.904352 | − | 1.36675i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 373.590 | + | 647.076i | 0.700919 | + | 1.21403i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 222.566 | − | 128.499i | 0.416012 | − | 0.240185i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 164.200 | − | 174.525i | 0.305772 | − | 0.324999i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.7935 | −0.0348674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −485.750 | − | 841.344i | −0.897875 | − | 1.55516i | −0.830206 | − | 0.557457i | \(-0.811777\pi\) |
−0.0676689 | − | 0.997708i | \(-0.521556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −936.590 | − | 220.608i | −1.72484 | − | 0.406276i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 509.509i | 0.934879i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 138.605 | + | 80.0238i | 0.253392 | + | 0.146296i | 0.621316 | − | 0.783560i | \(-0.286598\pi\) |
−0.367925 | + | 0.929856i | \(0.619932\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −735.731 | − | 366.952i | −1.34013 | − | 0.668401i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 217.752 | + | 114.929i | 0.395195 | + | 0.208583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −631.584 | + | 364.645i | −1.14210 | + | 0.659394i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1327.94 | − | 312.787i | −2.39268 | − | 0.563580i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 389.437 | + | 674.525i | 0.699169 | + | 1.21100i | 0.968755 | + | 0.248020i | \(0.0797799\pi\) |
−0.269586 | + | 0.962976i | \(0.586887\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.3277i | 0.0846649i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 108.712 | + | 102.280i | 0.193782 | + | 0.182318i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −127.949 | − | 73.8716i | −0.227263 | − | 0.131211i | 0.382046 | − | 0.924143i | \(-0.375220\pi\) |
−0.609309 | + | 0.792933i | \(0.708553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1119.58i | − | 1.98155i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 369.340 | + | 490.420i | 0.651394 | + | 0.864939i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −312.172 | + | 180.232i | −0.548632 | + | 0.316753i | −0.748570 | − | 0.663056i | \(-0.769259\pi\) |
0.199938 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 80.4968 | − | 139.425i | 0.140975 | − | 0.244176i | −0.786889 | − | 0.617095i | \(-0.788310\pi\) |
0.927864 | + | 0.372919i | \(0.121643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.4268 | − | 69.7399i | 0.0286680 | − | 0.121710i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −383.682 | + | 664.557i | −0.667274 | + | 1.15575i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −622.152 | −1.07825 | −0.539126 | − | 0.842225i | \(-0.681245\pi\) | ||||
−0.539126 | + | 0.842225i | \(0.681245\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −137.971 | − | 32.4981i | −0.238291 | − | 0.0561280i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 188.355 | − | 326.241i | 0.324191 | − | 0.561516i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −160.188 | − | 92.4844i | −0.274764 | − | 0.158635i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 400.634 | + | 605.479i | 0.684845 | + | 1.03501i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 649.470 | 1.10642 | 0.553211 | − | 0.833041i | \(-0.313402\pi\) | ||||
0.553211 | + | 0.833041i | \(0.313402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 730.402 | + | 385.505i | 1.24007 | + | 0.654507i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −707.779 | − | 665.906i | −1.19760 | − | 1.12675i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 249.951 | + | 432.928i | 0.421503 | + | 0.730065i | 0.996087 | − | 0.0883811i | \(-0.0281693\pi\) |
−0.574584 | + | 0.818446i | \(0.694836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 586.698 | + | 1016.19i | 0.986046 | + | 1.70788i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.0223 | + | 131.705i | −0.0519636 | + | 0.220612i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 285.505i | 0.476635i | 0.971187 | + | 0.238318i | \(0.0765959\pi\) | ||||
−0.971187 | + | 0.238318i | \(0.923404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 429.579 | − | 248.017i | 0.714773 | − | 0.412675i | −0.0980525 | − | 0.995181i | \(-0.531261\pi\) |
0.812826 | + | 0.582507i | \(0.197928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −334.708 | + | 20.4240i | −0.555071 | + | 0.0338706i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 803.185 | 1.32758 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −751.147 | − | 433.675i | −1.23747 | − | 0.714456i | −0.268897 | − | 0.963169i | \(-0.586659\pi\) |
−0.968577 | + | 0.248713i | \(0.919992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 201.918 | − | 214.614i | 0.331556 | − | 0.352404i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −154.545 | − | 89.2267i | −0.252938 | − | 0.146034i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 329.632 | − | 570.939i | 0.537736 | − | 0.931386i | −0.461290 | − | 0.887249i | \(-0.652613\pi\) |
0.999026 | − | 0.0441360i | \(-0.0140535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 383.482 | + | 1274.50i | 0.623548 | + | 2.07235i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1212.73 | −1.96552 | −0.982761 | − | 0.184883i | \(-0.940809\pi\) | ||||
−0.982761 | + | 0.184883i | \(0.940809\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 199.245 | + | 345.102i | 0.321882 | + | 0.557516i | 0.980876 | − | 0.194632i | \(-0.0623513\pi\) |
−0.658994 | + | 0.752148i | \(0.729018\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 578.721 | − | 695.535i | 0.931917 | − | 1.12002i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −142.558 | − | 82.3056i | −0.228824 | − | 0.132112i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 336.561 | + | 582.940i | 0.538497 | + | 0.932705i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.3633 | + | 124.421i | −0.0388569 | + | 0.198439i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1272.89 | + | 734.906i | 2.02368 | + | 1.16837i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −185.584 | − | 321.441i | −0.294111 | − | 0.509415i | 0.680667 | − | 0.732593i | \(-0.261690\pi\) |
−0.974778 | + | 0.223178i | \(0.928357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 110.905 | + | 26.1228i | 0.175205 | + | 0.0412683i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −808.454 | − | 466.761i | −1.27316 | − | 0.735057i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 85.2897 | + | 49.2420i | 0.133893 | + | 0.0773030i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 324.218 | − | 650.050i | 0.507383 | − | 1.01729i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 523.079i | 0.816037i | 0.912974 | + | 0.408018i | \(0.133780\pi\) | ||||
−0.912974 | + | 0.408018i | \(0.866220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 452.340 | + | 783.477i | 0.703484 | + | 1.21847i | 0.967236 | + | 0.253880i | \(0.0817068\pi\) |
−0.263751 | + | 0.964591i | \(0.584960\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.3284 | + | 82.0586i | −0.0299665 | + | 0.127223i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.5058 | −0.0517863 | −0.0258932 | − | 0.999665i | \(-0.508243\pi\) | ||||
−0.0258932 | + | 0.999665i | \(0.508243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −186.258 | − | 107.536i | −0.286992 | − | 0.165695i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 677.288 | − | 719.876i | 1.04038 | − | 1.10580i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −210.443 | + | 364.498i | −0.322271 | + | 0.558190i | −0.980956 | − | 0.194229i | \(-0.937780\pi\) |
0.658685 | + | 0.752419i | \(0.271113\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −177.000 | + | 306.573i | −0.270229 | + | 0.468051i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −704.380 | − | 351.316i | −1.07212 | − | 0.534727i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −901.500 | − | 520.481i | −1.36798 | − | 0.789804i | −0.377311 | − | 0.926087i | \(-0.623151\pi\) |
−0.990670 | + | 0.136282i | \(0.956485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 315.285i | − | 0.476982i | −0.971145 | − | 0.238491i | \(-0.923347\pi\) | ||
0.971145 | − | 0.238491i | \(-0.0766527\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −225.370 | − | 749.016i | −0.339925 | − | 1.12974i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −465.224 | + | 881.443i | −0.699585 | + | 1.32548i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −376.095 | − | 217.138i | −0.563860 | − | 0.325545i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 265.732 | − | 282.441i | 0.397207 | − | 0.422184i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −203.192 | −0.302819 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −162.025 | + | 93.5454i | −0.240751 | + | 0.138998i | −0.615522 | − | 0.788120i | \(-0.711055\pi\) |
0.374771 | + | 0.927117i | \(0.377721\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 213.867 | + | 580.091i | 0.316840 | + | 0.859394i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 638.183 | − | 368.455i | 0.942663 | − | 0.544247i | 0.0518690 | − | 0.998654i | \(-0.483482\pi\) |
0.890794 | + | 0.454407i | \(0.150149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1013.38 | − | 585.078i | 1.49247 | − | 0.861675i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −883.631 | − | 208.134i | −1.29755 | − | 0.305629i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 887.445i | 1.29933i | 0.760219 | + | 0.649667i | \(0.225092\pi\) | ||||
−0.760219 | + | 0.649667i | \(0.774908\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 955.002 | 1.39416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 495.022 | − | 148.946i | 0.720555 | − | 0.216807i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 484.648 | + | 839.435i | 0.703408 | + | 1.21834i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −604.385 | − | 1046.83i | −0.874652 | − | 1.51494i | −0.857133 | − | 0.515096i | \(-0.827756\pi\) |
−0.0175197 | − | 0.999847i | \(-0.505577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 135.780 | + | 67.7214i | 0.195931 | + | 0.0977221i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 238.135 | + | 412.462i | 0.342641 | + | 0.593471i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1433.90i | − | 2.05724i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1277.09 | − | 384.260i | 1.82702 | − | 0.549729i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −217.885 | + | 377.388i | −0.310821 | + | 0.538357i | −0.978540 | − | 0.206056i | \(-0.933937\pi\) |
0.667720 | + | 0.744413i | \(0.267270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.3809 | + | 1247.56i | 0.0673981 | + | 1.77462i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −231.517 | − | 217.820i | −0.328393 | − | 0.308965i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −633.863 | −0.896553 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −554.474 | + | 960.378i | −0.782051 | + | 1.35455i | 0.148693 | + | 0.988883i | \(0.452493\pi\) |
−0.930745 | + | 0.365670i | \(0.880840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 864.358 | − | 52.7435i | 1.21569 | − | 0.0741821i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1261.53 | − | 728.343i | −1.76932 | − | 1.02152i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 155.392 | + | 89.7159i | 0.217332 | + | 0.125477i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 756.420 | − | 227.598i | 1.05498 | − | 0.317431i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 108.126 | − | 187.279i | 0.150384 | − | 0.260472i | −0.780985 | − | 0.624550i | \(-0.785282\pi\) |
0.931369 | + | 0.364078i | \(0.118616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1037.00i | 1.43828i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3844 | − | 34.5126i | −0.0143630 | − | 0.0477353i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 256.986 | − | 148.371i | 0.354463 | − | 0.204649i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −852.055 | −1.17201 | −0.586007 | − | 0.810306i | \(-0.699301\pi\) | ||||
−0.586007 | + | 0.810306i | \(0.699301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −132.545 | − | 716.849i | −0.181817 | − | 0.983332i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.4128 | − | 78.6573i | 0.0621242 | − | 0.107602i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 125.080 | − | 216.645i | 0.170641 | − | 0.295559i | −0.768003 | − | 0.640446i | \(-0.778749\pi\) |
0.938644 | + | 0.344887i | \(0.112083\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 127.768 | + | 120.210i | 0.173835 | + | 0.163550i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −71.7714 | + | 41.4372i | −0.0973831 | + | 0.0562242i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −618.939 | + | 1072.03i | −0.837536 | + | 1.45065i | 0.0544130 | + | 0.998519i | \(0.482671\pi\) |
−0.891949 | + | 0.452136i | \(0.850662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 436.571 | − | 500.819i | 0.589164 | − | 0.675870i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 795.437 | − | 459.246i | 1.07057 | − | 0.618096i | 0.142236 | − | 0.989833i | \(-0.454571\pi\) |
0.928338 | + | 0.371736i | \(0.121237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 727.410 | − | 1259.91i | 0.976389 | − | 1.69116i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −373.040 | + | 246.834i | −0.499384 | + | 0.330433i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −243.748 | + | 140.728i | −0.325431 | + | 0.187888i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 91.6457i | − | 0.122032i | −0.998137 | − | 0.0610158i | \(-0.980566\pi\) | ||
0.998137 | − | 0.0610158i | \(-0.0194340\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −139.938 | + | 594.107i | −0.185841 | + | 0.788987i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 654.629 | + | 377.950i | 0.867058 | + | 0.500596i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 337.641 | − | 584.812i | 0.446026 | − | 0.772539i | −0.552097 | − | 0.833780i | \(-0.686172\pi\) |
0.998123 | + | 0.0612407i | \(0.0195057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 51.2687 | − | 217.661i | 0.0675478 | − | 0.286774i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −446.414 | + | 773.212i | −0.586615 | + | 1.01605i | 0.408056 | + | 0.912957i | \(0.366207\pi\) |
−0.994672 | + | 0.103091i | \(0.967127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 557.999i | − | 0.731322i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −84.8619 | − | 1390.71i | −0.110931 | − | 1.81793i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 563.522 | + | 976.049i | 0.734709 | + | 1.27255i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 453.086 | 0.589188 | 0.294594 | − | 0.955622i | \(-0.404816\pi\) | ||||
0.294594 | + | 0.955622i | \(0.404816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 312.691 | − | 332.353i | 0.405565 | − | 0.431067i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.5624 | − | 27.4601i | 0.0615296 | − | 0.0355241i | −0.468920 | − | 0.883241i | \(-0.655357\pi\) |
0.530449 | + | 0.847717i | \(0.322023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 862.002 | − | 497.677i | 1.11226 | − | 0.642164i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1454.31 | + | 342.554i | 1.87170 | + | 0.440868i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1030.91 | − | 648.568i | 1.32337 | − | 0.832565i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 179.529i | − | 0.229870i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −328.292 | + | 121.034i | −0.419275 | + | 0.154577i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 536.366 | − | 929.014i | 0.683269 | − | 1.18346i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 190.023 | + | 109.710i | 0.241452 | + | 0.139402i | 0.615844 | − | 0.787868i | \(-0.288815\pi\) |
−0.374392 | + | 0.927271i | \(0.622149\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −210.279 | − | 197.839i | −0.266513 | − | 0.250746i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1226.13i | 1.55010i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 922.136 | + | 532.395i | 1.16284 | + | 0.671369i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 497.481 | + | 1653.37i | 0.625762 | + | 2.07971i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 907.132 | + | 523.733i | 1.13818 | + | 0.657130i | 0.945980 | − | 0.324225i | \(-0.105103\pi\) |
0.192203 | + | 0.981355i | \(0.438437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 171.233 | + | 296.585i | 0.214309 | + | 0.371195i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 107.859 | + | 163.007i | 0.134655 | + | 0.203505i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −194.534 | −0.242258 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 878.958 | − | 1522.40i | 1.09187 | − | 1.89118i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 208.954 | + | 694.457i | 0.258927 | + | 0.860541i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −62.3044 | −0.0770141 | −0.0385071 | − | 0.999258i | \(-0.512260\pi\) | ||||
−0.0385071 | + | 0.999258i | \(0.512260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −746.263 | + | 430.855i | −0.920176 | + | 0.531264i | −0.883691 | − | 0.468070i | \(-0.844949\pi\) |
−0.0364847 | + | 0.999334i | \(0.511616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −500.474 | + | 150.587i | −0.615590 | + | 0.185224i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −642.120 | − | 1112.18i | −0.787877 | − | 1.36464i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 77.0917 | − | 2.92786i | 0.0943595 | − | 0.00358367i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −438.762 | − | 663.102i | −0.535729 | − | 0.809648i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.03640 | − | 8.72330i | 0.00613447 | − | 0.0106252i | −0.862942 | − | 0.505303i | \(-0.831381\pi\) |
0.869076 | + | 0.494678i | \(0.164714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.00510 | 0.00851167 | 0.00425583 | − | 0.999991i | \(-0.498645\pi\) | ||||
0.00425583 | + | 0.999991i | \(0.498645\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 111.286 | + | 104.703i | 0.134893 | + | 0.126912i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −447.780 | + | 258.526i | −0.541451 | + | 0.312607i | −0.745667 | − | 0.666319i | \(-0.767869\pi\) |
0.204216 | + | 0.978926i | \(0.434536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.6185i | 0.0477907i | 0.999714 | + | 0.0238954i | \(0.00760685\pi\) | ||||
−0.999714 | + | 0.0238954i | \(0.992393\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 261.457 | − | 1110.02i | 0.314630 | − | 1.33576i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −94.4994 | − | 163.678i | −0.113445 | − | 0.196492i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 466.481 | − | 269.323i | 0.558660 | − | 0.322542i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1101.18 | + | 405.982i | −1.31563 | + | 0.485045i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 550.781i | 0.656473i | 0.944596 | + | 0.328237i | \(0.106454\pi\) | ||||
−0.944596 | + | 0.328237i | \(0.893546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −336.532 | − | 582.891i | −0.400157 | − | 0.693092i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −113.174 | − | 376.134i | −0.134252 | − | 0.446185i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 114.674 | + | 198.621i | 0.135709 | + | 0.235054i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −879.624 | −1.03852 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −73.4370 | + | 311.777i | −0.0864982 | + | 0.367228i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2201.99i | − | 2.58753i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1615.11 | 1.89344 | 0.946721 | − | 0.322054i | \(-0.104373\pi\) | ||||
0.946721 | + | 0.322054i | \(0.104373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 961.475 | − | 690.047i | 1.12453 | − | 0.807073i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 221.522i | − | 0.258485i | −0.991613 | − | 0.129242i | \(-0.958745\pi\) | ||
0.991613 | − | 0.129242i | \(-0.0412545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −249.578 | −0.290545 | −0.145272 | − | 0.989392i | \(-0.546406\pi\) | ||||
−0.145272 | + | 0.989392i | \(0.546406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −419.978 | − | 1395.79i | −0.487779 | − | 1.62113i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 769.113i | − | 0.891208i | −0.895230 | − | 0.445604i | \(-0.852989\pi\) | ||
0.895230 | − | 0.445604i | \(-0.147011\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −835.601 | + | 482.435i | −0.966013 | + | 0.557728i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −145.375 | + | 617.190i | −0.167676 | + | 0.711869i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 185.344 | − | 107.009i | 0.213285 | − | 0.123140i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 434.289 | 0.498609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1386.87 | + | 84.6275i | −1.58863 | + | 0.0969387i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −55.1196 | − | 95.4700i | −0.0629939 | − | 0.109109i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1173.21 | − | 677.351i | 1.33775 | − | 0.772351i | 0.351277 | − | 0.936272i | \(-0.385748\pi\) |
0.986473 | + | 0.163921i | \(0.0524142\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −79.9467 | − | 265.702i | −0.0909519 | − | 0.302278i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 415.081 | 0.471148 | 0.235574 | − | 0.971856i | \(-0.424303\pi\) | ||||
0.235574 | + | 0.971856i | \(0.424303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −264.348 | − | 457.865i | −0.299375 | − | 0.518533i | 0.676618 | − | 0.736334i | \(-0.263445\pi\) |
−0.975993 | + | 0.217801i | \(0.930112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 578.444 | + | 1922.45i | 0.653609 | + | 2.17226i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 97.2678i | 0.109659i | 0.998496 | + | 0.0548296i | \(0.0174616\pi\) | ||||
−0.998496 | + | 0.0548296i | \(0.982538\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 885.394 | + | 511.182i | 0.995944 | + | 0.575008i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −108.386 | − | 143.919i | −0.121646 | − | 0.161525i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −135.780 | + | 257.257i | −0.152049 | + | 0.288082i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −478.744 | + | 276.403i | −0.534909 | + | 0.308830i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −802.978 | + | 853.470i | −0.895182 | + | 0.951471i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 281.652 | + | 487.835i | 0.313294 | + | 0.542642i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1860.16i | − | 2.06455i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.1678 | − | 89.8681i | 0.0234417 | − | 0.0995217i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1922.40 | + | 1109.90i | 2.12420 | + | 1.22641i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 311.781i | 0.343750i | 0.985119 | + | 0.171875i | \(0.0549825\pi\) | ||||
−0.985119 | + | 0.171875i | \(0.945018\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 673.529 | + | 335.928i | 0.740956 | + | 0.369558i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1130.78 | + | 652.854i | −1.24125 | + | 0.716634i | −0.969348 | − | 0.245692i | \(-0.920985\pi\) |
−0.271899 | + | 0.962326i | \(0.587652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.2746 | + | 95.7384i | −0.0605417 | + | 0.104861i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1381.41 | + | 1299.68i | 1.50973 | + | 1.42042i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 193.845 | − | 335.749i | 0.211390 | − | 0.366139i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −246.269 | −0.267975 | −0.133987 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133987 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −335.456 | − | 1114.88i | −0.364230 | − | 1.21051i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −470.394 | + | 814.746i | −0.509636 | + | 0.882715i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1303.04 | + | 752.310i | 1.40869 | + | 0.813308i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 549.577 | − | 1101.89i | 0.592855 | − | 1.18866i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 828.515 | 0.891835 | 0.445918 | − | 0.895074i | \(-0.352877\pi\) | ||||
0.445918 | + | 0.895074i | \(0.352877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 74.9336 | − | 141.974i | 0.0804873 | − | 0.152496i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.0685 | + | 6.64015i | −0.0236532 | + | 0.00711699i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −172.172 | − | 298.211i | −0.184141 | − | 0.318942i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 193.550 | + | 335.238i | 0.206564 | + | 0.357778i | 0.950630 | − | 0.310327i | \(-0.100439\pi\) |
−0.744066 | + | 0.668106i | \(0.767105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1003.29 | + | 301.878i | −1.06846 | + | 0.321488i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1159.48i | 1.23218i | 0.787677 | + | 0.616088i | \(0.211283\pi\) | ||||
−0.787677 | + | 0.616088i | \(0.788717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1860.38 | + | 1074.09i | −1.97283 | + | 1.13902i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −489.936 | − | 1328.90i | −0.518451 | − | 1.40624i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 583.759 | 0.616429 | 0.308215 | − | 0.951317i | \(-0.400268\pi\) | ||||
0.308215 | + | 0.951317i | \(0.400268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 882.842 | + | 509.709i | 0.930286 | + | 0.537101i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.6946 | − | 158.513i | −0.0501521 | − | 0.166680i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.42367 | − | 1.97666i | −0.00359252 | − | 0.00207414i | 0.498203 | − | 0.867061i | \(-0.333994\pi\) |
−0.501795 | + | 0.864986i | \(0.667327\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −82.6449 | + | 143.145i | −0.0865392 | + | 0.149890i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −59.2546 | + | 62.9806i | −0.0619171 | + | 0.0658104i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1045.89 | −1.09060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 464.238 | + | 804.084i | 0.483078 | + | 0.836716i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 333.583 | − | 20.3553i | 0.346400 | − | 0.0211374i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 283.193 | + | 163.501i | 0.293464 | + | 0.169432i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −142.706 | − | 247.174i | −0.147576 | − | 0.255609i | 0.782755 | − | 0.622330i | \(-0.213814\pi\) |
−0.930331 | + | 0.366721i | \(0.880480\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1206.12 | + | 413.441i | −1.24471 | + | 0.426668i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −708.039 | − | 408.787i | −0.729186 | − | 0.420996i | 0.0889384 | − | 0.996037i | \(-0.471653\pi\) |
−0.818124 | + | 0.575041i | \(0.804986\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −260.798 | − | 451.716i | −0.268035 | − | 0.464251i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −230.708 | − | 766.755i | −0.236623 | − | 0.786415i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 508.019 | + | 293.305i | 0.519979 | + | 0.300210i | 0.736926 | − | 0.675974i | \(-0.236277\pi\) |
−0.216947 | + | 0.976183i | \(0.569610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.8349 | + | 24.1534i | 0.0427322 | + | 0.0246715i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −295.722 | + | 592.917i | −0.301450 | + | 0.604401i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1248.92i | 1.27051i | 0.772300 | + | 0.635257i | \(0.219106\pi\) | ||||
−0.772300 | + | 0.635257i | \(0.780894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1120.94 | + | 1941.53i | 1.13801 | + | 1.97110i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 253.550 | + | 238.550i | 0.256890 | + | 0.241692i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −136.070 | −0.137583 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.4153 | − | 31.4167i | −0.0549095 | − | 0.0317020i | 0.472294 | − | 0.881441i | \(-0.343426\pi\) |
−0.527203 | + | 0.849739i | \(0.676759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1073.59 | − | 252.878i | −1.08116 | − | 0.254661i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 156.076 | − | 270.332i | 0.156861 | − | 0.271691i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0885 | − | 26.1341i | 0.0151339 | − | 0.0262127i | −0.858359 | − | 0.513049i | \(-0.828516\pi\) |
0.873493 | + | 0.486836i | \(0.161849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1363.78 | − | 1134.73i | −1.36514 | − | 1.13587i |
(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 | 684.3.s.a.445.11 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.7 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.34 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.3 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.3 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.34 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.11 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.7 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.11 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.11 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.3 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.3 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.7 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.7 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.34 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.34 | 80 | 9.2 | odd | 6 |