Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(17,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.bv (of order \(44\), degree \(20\), 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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(720\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{44})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{44}]$ |
Embedding invariants
Embedding label | 217.27 | ||
Character | \(\chi\) | \(=\) | 920.217 |
Dual form | 920.2.bv.a.513.27 |
$q$-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 \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.45300 | − | 0.316080i | 0.838888 | − | 0.182489i | 0.227458 | − | 0.973788i | \(-0.426958\pi\) |
0.611429 | + | 0.791299i | \(0.290595\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.46408 | − | 1.69011i | −0.654758 | − | 0.755839i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.74304 | − | 2.04386i | 1.41474 | − | 0.772505i | 0.423663 | − | 0.905820i | \(-0.360744\pi\) |
0.991074 | + | 0.133315i | \(0.0425623\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.717605 | + | 0.327719i | −0.239202 | + | 0.109240i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.97107 | + | 3.44095i | 1.19732 | + | 1.03749i | 0.998347 | + | 0.0574805i | \(0.0183067\pi\) |
0.198975 | + | 0.980005i | \(0.436239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.16993 | − | 2.14256i | 0.324479 | − | 0.594239i | −0.663618 | − | 0.748072i | \(-0.730980\pi\) |
0.988097 | + | 0.153833i | \(0.0491617\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.66152 | − | 1.99295i | −0.687200 | − | 0.514578i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.94978 | − | 3.70536i | −1.20050 | − | 0.898681i | −0.203730 | − | 0.979027i | \(-0.565306\pi\) |
−0.996767 | + | 0.0803463i | \(0.974397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.582115 | − | 4.04870i | 0.133546 | − | 0.928835i | −0.807334 | − | 0.590095i | \(-0.799090\pi\) |
0.940880 | − | 0.338740i | \(-0.110001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.79260 | − | 4.15281i | 1.04583 | − | 0.906218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.02482 | + | 4.34742i | 0.422205 | + | 0.906501i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.712923 | + | 4.94891i | −0.142585 | + | 0.989783i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.51025 | + | 3.37633i | −0.867999 | + | 0.649776i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.20765 | − | 0.892526i | 1.15273 | − | 0.165738i | 0.460667 | − | 0.887573i | \(-0.347610\pi\) |
0.692065 | + | 0.721835i | \(0.256701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.73538 | − | 3.04325i | 0.850500 | − | 0.546583i | −0.0412306 | − | 0.999150i | \(-0.513128\pi\) |
0.891731 | + | 0.452566i | \(0.149491\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.85756 | + | 3.74451i | 1.19375 | + | 0.651836i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.93446 | − | 3.33377i | −1.51020 | − | 0.563509i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.55279 | − | 3.56301i | −1.57047 | − | 0.585755i | −0.594583 | − | 0.804034i | \(-0.702683\pi\) |
−0.975886 | + | 0.218280i | \(0.929956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.02268 | − | 3.48292i | 0.163760 | − | 0.557714i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.166757 | − | 0.365147i | 0.0260431 | − | 0.0570264i | −0.896163 | − | 0.443724i | \(-0.853657\pi\) |
0.922207 | + | 0.386698i | \(0.126384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.81424 | − | 8.33991i | −0.276669 | − | 1.27183i | −0.880245 | − | 0.474520i | \(-0.842622\pi\) |
0.603576 | − | 0.797305i | \(-0.293742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.60451 | + | 0.733021i | 0.239187 | + | 0.109272i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.536764 | − | 0.536764i | −0.0782950 | − | 0.0782950i | 0.666875 | − | 0.745170i | \(-0.267632\pi\) |
−0.745170 | + | 0.666875i | \(0.767632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.04853 | − | 9.41169i | 0.864075 | − | 1.34453i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.36319 | − | 3.81934i | −1.17108 | − | 0.534815i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.45425 | + | 2.66327i | 0.199757 | + | 0.365828i | 0.958286 | − | 0.285812i | \(-0.0922633\pi\) |
−0.758529 | + | 0.651640i | \(0.774081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.00160101 | − | 11.7494i | 0.000215880 | − | 1.58428i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.433902 | − | 6.06674i | −0.0574717 | − | 0.803559i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.860416 | − | 2.93031i | −0.112017 | − | 0.381494i | 0.884333 | − | 0.466856i | \(-0.154613\pi\) |
−0.996350 | + | 0.0853625i | \(0.972795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.49955 | + | 7.00143i | 0.576108 | + | 0.896441i | 0.999957 | − | 0.00929148i | \(-0.00295761\pi\) |
−0.423849 | + | 0.905733i | \(0.639321\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.01621 | + | 2.69335i | −0.254019 | + | 0.339330i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.33402 | + | 1.15958i | −0.661604 | + | 0.143829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.51381 | + | 0.537398i | 0.917958 | + | 0.0656537i | 0.522317 | − | 0.852751i | \(-0.325068\pi\) |
0.395641 | + | 0.918405i | \(0.370522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.31619 | + | 5.67678i | 0.519608 | + | 0.683405i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.45881 | + | 1.68355i | 0.173128 | + | 0.199801i | 0.835682 | − | 0.549214i | \(-0.185073\pi\) |
−0.662553 | + | 0.749015i | \(0.730527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.44576 | + | 1.93131i | 0.169214 | + | 0.226043i | 0.877130 | − | 0.480254i | \(-0.159455\pi\) |
−0.707916 | + | 0.706297i | \(0.750364\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.528378 | + | 7.41609i | 0.0610118 | + | 0.856337i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.8967 | + | 4.76333i | 2.49536 | + | 0.542832i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.24346 | + | 2.12687i | −0.814953 | + | 0.239292i | −0.662541 | − | 0.749025i | \(-0.730522\pi\) |
−0.152411 | + | 0.988317i | \(0.548704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.93634 | + | 4.54278i | −0.437371 | + | 0.504753i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.44169 | + | 11.9086i | −0.487539 | + | 1.30714i | 0.427586 | + | 0.903975i | \(0.359364\pi\) |
−0.915126 | + | 0.403169i | \(0.867909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.984434 | + | 13.7906i | 0.106777 | + | 1.49580i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.73759 | − | 3.25895i | 0.936768 | − | 0.349396i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.18949 | − | 0.764437i | −0.126085 | − | 0.0810301i | 0.476078 | − | 0.879403i | \(-0.342058\pi\) |
−0.602163 | + | 0.798373i | \(0.705694\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.4108i | − | 1.09135i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.91859 | − | 5.91859i | 0.613729 | − | 0.613729i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.69500 | + | 4.94379i | −0.789490 | + | 0.507222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.95206 | − | 10.5959i | −0.401270 | − | 1.07585i | −0.967781 | − | 0.251793i | \(-0.918980\pi\) |
0.566511 | − | 0.824054i | \(-0.308293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.97732 | − | 1.16785i | −0.399736 | − | 0.117373i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.18881 | + | 15.7413i | 0.715313 | + | 1.56632i | 0.820358 | + | 0.571851i | \(0.193774\pi\) |
−0.105044 | + | 0.994468i | \(0.533498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.62936 | − | 0.259577i | 0.357611 | − | 0.0255769i | 0.108622 | − | 0.994083i | \(-0.465356\pi\) |
0.248989 | + | 0.968506i | \(0.419902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.0355 | − | 2.01995i | −1.36972 | − | 0.197127i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.615753 | + | 2.83057i | −0.0595271 | + | 0.273642i | −0.997284 | − | 0.0736503i | \(-0.976535\pi\) |
0.937757 | + | 0.347292i | \(0.112899\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.287334 | + | 1.99845i | 0.0275216 | + | 0.191417i | 0.998944 | − | 0.0459396i | \(-0.0146282\pi\) |
−0.971423 | + | 0.237356i | \(0.923719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0064 | − | 2.15759i | −1.42434 | − | 0.204789i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.133081 | − | 1.86071i | 0.0125192 | − | 0.175041i | −0.987345 | − | 0.158585i | \(-0.949307\pi\) |
0.999865 | − | 0.0164565i | \(-0.00523851\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.38310 | − | 9.78715i | 0.408727 | − | 0.912657i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.137387 | + | 1.92092i | −0.0127014 | + | 0.177589i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.1004 | − | 3.75267i | −2.39262 | − | 0.344007i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.36378 | + | 16.4404i | 0.214889 | + | 1.49459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.126882 | − | 0.583266i | 0.0114405 | − | 0.0525914i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.40797 | − | 6.04070i | 0.841474 | − | 0.540297i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.02443 | + | 0.144790i | −0.179639 | + | 0.0128480i | −0.160869 | − | 0.986976i | \(-0.551430\pi\) |
−0.0187700 | + | 0.999824i | \(0.505975\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.27216 | − | 11.5444i | −0.464188 | − | 1.01643i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4586 | + | 5.41993i | 1.61274 | + | 0.473542i | 0.959053 | − | 0.283227i | \(-0.0914051\pi\) |
0.653682 | + | 0.756769i | \(0.273223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.09607 | − | 16.3442i | −0.528596 | − | 1.41722i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.3097 | + | 2.67958i | 1.05945 | + | 0.230621i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.50730 | + | 5.50730i | −0.470520 | + | 0.470520i | −0.902083 | − | 0.431563i | \(-0.857962\pi\) |
0.431563 | + | 0.902083i | \(0.357962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.0107i | 1.78210i | 0.453900 | + | 0.891052i | \(0.350032\pi\) | ||||
−0.453900 | + | 0.891052i | \(0.649968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.949576 | − | 0.610255i | −0.0799687 | − | 0.0513928i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0183 | − | 4.48259i | 1.00502 | − | 0.374853i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.5970 | − | 9.18487i | −0.880031 | − | 0.762762i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.81364 | − | 15.5870i | 0.479501 | − | 1.28559i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.792767 | − | 0.914902i | 0.0649460 | − | 0.0749517i | −0.722347 | − | 0.691531i | \(-0.756937\pi\) |
0.787293 | + | 0.616579i | \(0.211482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8935 | + | 3.78588i | −1.04926 | + | 0.308090i | −0.760518 | − | 0.649317i | \(-0.775055\pi\) |
−0.288741 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.76630 | + | 1.03684i | 0.385332 | + | 0.0838239i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0764 | − | 3.54774i | −0.970000 | − | 0.284961i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.82980 | + | 9.12354i | 0.545077 | + | 0.728138i | 0.985504 | − | 0.169651i | \(-0.0542639\pi\) |
−0.440427 | + | 0.897788i | \(0.645173\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.95483 | + | 3.41005i | 0.234333 | + | 0.270435i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.4645 | + | 12.1341i | 1.29758 | + | 0.956305i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.1614 | − | 1.51349i | −1.65749 | − | 0.118546i | −0.789044 | − | 0.614337i | \(-0.789424\pi\) |
−0.868442 | + | 0.495791i | \(0.834878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.71141 | − | 17.0723i | −0.288933 | − | 1.32908i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.30582 | + | 11.0953i | −0.642724 | + | 0.858578i | −0.997067 | − | 0.0765372i | \(-0.975614\pi\) |
0.354343 | + | 0.935115i | \(0.384705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.80650 | + | 5.92302i | 0.292807 | + | 0.455617i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.909107 | + | 3.09613i | 0.0695212 | + | 0.236767i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.621670 | + | 8.69208i | 0.0472647 | + | 0.660847i | 0.964765 | + | 0.263112i | \(0.0847490\pi\) |
−0.917500 | + | 0.397735i | \(0.869796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.44636 | + | 19.9811i | 0.562892 | + | 1.51043i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.17639 | − | 3.98577i | −0.163588 | − | 0.299588i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.25810 | − | 1.03124i | −0.168778 | − | 0.0770785i | 0.329234 | − | 0.944248i | \(-0.393209\pi\) |
−0.498013 | + | 0.867170i | \(0.665937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.90018 | + | 4.51278i | −0.215569 | + | 0.335432i | −0.932150 | − | 0.362072i | \(-0.882070\pi\) |
0.716581 | + | 0.697504i | \(0.245706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.75084 | + | 8.75084i | 0.646880 | + | 0.646880i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.96421 | + | 21.3618i | 0.585541 | + | 1.57055i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.90595 | − | 31.7461i | −0.505013 | − | 2.32151i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.98133 | + | 21.8561i | −0.726035 | + | 1.58979i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.55576 | − | 8.70414i | 0.184929 | − | 0.629809i | −0.813881 | − | 0.581032i | \(-0.802649\pi\) |
0.998810 | − | 0.0487776i | \(-0.0155326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.7563 | − | 8.48766i | −1.63803 | − | 0.610955i | −0.649286 | − | 0.760544i | \(-0.724932\pi\) |
−0.988748 | + | 0.149589i | \(0.952205\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.38379 | + | 3.37085i | −0.528764 | + | 0.241392i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.58998 | − | 3.05236i | −0.398270 | − | 0.217472i | 0.267616 | − | 0.963526i | \(-0.413764\pi\) |
−0.665885 | + | 0.746054i | \(0.731946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.65726 | + | 1.06506i | −0.117480 | + | 0.0754998i | −0.598061 | − | 0.801450i | \(-0.704062\pi\) |
0.480581 | + | 0.876950i | \(0.340426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.0874 | − | 1.59413i | 0.782045 | − | 0.112441i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.4113 | − | 16.0283i | 1.50278 | − | 1.12497i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.861284 | + | 0.252768i | −0.0601547 | + | 0.0176541i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.87776 | − | 2.45616i | −0.200018 | − | 0.170715i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.2430 | − | 14.0746i | 1.12355 | − | 0.973562i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.873331 | − | 6.07415i | 0.0601226 | − | 0.418162i | −0.937426 | − | 0.348185i | \(-0.886798\pi\) |
0.997549 | − | 0.0699773i | \(-0.0222927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.65178 | + | 1.98510i | 0.181697 | + | 0.136017i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.4392 | + | 15.2766i | −0.780144 | + | 1.04185i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5048 | − | 21.0694i | 0.780995 | − | 1.43029i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.71114 | + | 2.34921i | 0.183202 | + | 0.158745i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7298 | + | 6.27020i | −0.923567 | + | 0.421779i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6574 | − | 8.00355i | 0.981533 | − | 0.535957i | 0.0934414 | − | 0.995625i | \(-0.470213\pi\) |
0.888091 | + | 0.459667i | \(0.152031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.11026 | − | 3.78500i | −0.0740171 | − | 0.252333i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.7471 | − | 5.38340i | 1.64252 | − | 0.357309i | 0.706080 | − | 0.708132i | \(-0.250462\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.1054 | 1.65901 | 0.829505 | − | 0.558500i | \(-0.188623\pi\) | ||||
0.829505 | + | 0.558500i | \(0.188623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.3214 | 2.19238 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1278 | + | 3.94347i | −1.18759 | + | 0.258345i | −0.762612 | − | 0.646856i | \(-0.776083\pi\) |
−0.424982 | + | 0.905202i | \(0.639720\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.121322 | + | 1.69305i | −0.00791415 | + | 0.110443i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.85246 | + | 5.37985i | −0.639986 | + | 0.349459i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9826 | + | 10.4958i | −1.48662 | + | 0.678918i | −0.982764 | − | 0.184867i | \(-0.940815\pi\) |
−0.503860 | + | 0.863785i | \(0.668087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.874396 | + | 0.757668i | 0.0563248 | + | 0.0488057i | 0.682568 | − | 0.730822i | \(-0.260863\pi\) |
−0.626244 | + | 0.779628i | \(0.715408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.81667 | − | 6.98971i | 0.244839 | − | 0.448390i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.7623 | + | 3.55684i | −1.58201 | + | 0.227238i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.99355 | − | 5.98389i | −0.508617 | − | 0.380746i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.68968 | + | 18.7071i | −0.170452 | + | 1.18552i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.44290 | + | 5.58281i | −0.406672 | + | 0.352384i | −0.834049 | − | 0.551690i | \(-0.813983\pi\) |
0.427377 | + | 0.904074i | \(0.359438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.91856 | + | 24.2312i | −0.434966 | + | 1.52340i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.78931 | + | 19.7265i | 0.362541 | + | 1.23532i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.9526 | + | 14.9363i | −1.24461 | + | 0.931703i | −0.999288 | − | 0.0377381i | \(-0.987985\pi\) |
−0.245322 | + | 0.969442i | \(0.578894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −43.0388 | + | 6.18804i | −2.67430 | + | 0.384506i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.16214 | + | 2.67485i | −0.257630 | + | 0.165569i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5413 | + | 6.30202i | 0.711666 | + | 0.388599i | 0.793928 | − | 0.608012i | \(-0.208033\pi\) |
−0.0822619 | + | 0.996611i | \(0.526214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.37206 | − | 6.35708i | 0.145714 | − | 0.390513i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.96994 | − | 0.734751i | −0.120559 | − | 0.0449660i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.09716 | + | 7.14228i | −0.127866 | + | 0.435473i | −0.998394 | − | 0.0566462i | \(-0.981959\pi\) |
0.870528 | + | 0.492119i | \(0.163777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.668877 | + | 1.46464i | −0.0406314 | + | 0.0889703i | −0.928859 | − | 0.370433i | \(-0.879209\pi\) |
0.888228 | + | 0.459403i | \(0.151937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.29066 | − | 15.1269i | −0.199160 | − | 0.915523i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.8600 | + | 17.1993i | −1.19760 | + | 1.03716i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0946 | + | 14.0946i | 0.846863 | + | 0.846863i | 0.989740 | − | 0.142877i | \(-0.0456354\pi\) |
−0.142877 | + | 0.989740i | \(0.545635\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.40080 | + | 3.73572i | −0.143732 | + | 0.223652i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.1437 | − | 10.5694i | −1.38064 | − | 0.630516i | −0.419797 | − | 0.907618i | \(-0.637899\pi\) |
−0.960841 | + | 0.277102i | \(0.910626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1924 | + | 24.1600i | 0.784204 | + | 1.43616i | 0.896760 | + | 0.442518i | \(0.145915\pi\) |
−0.112555 | + | 0.993645i | \(0.535904\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.61817 | + | 9.61555i | −0.569731 | + | 0.569576i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.122129 | − | 1.70759i | −0.00720906 | − | 0.100796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.98117 | + | 20.3700i | 0.351833 | + | 1.19823i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.09146 | − | 14.1466i | −0.532951 | − | 0.829288i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.77099 | − | 6.37329i | 0.278724 | − | 0.372332i | −0.639232 | − | 0.769014i | \(-0.720748\pi\) |
0.917956 | + | 0.396682i | \(0.129839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.69281 | + | 5.74441i | −0.215004 | + | 0.334452i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.5283 | − | 2.11191i | −1.71341 | − | 0.122545i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.6835 | + | 0.747863i | 0.675675 | + | 0.0432500i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.8363 | − | 27.5086i | −1.37390 | − | 1.58557i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.4208 | + | 20.5998i | 0.885903 | + | 1.18343i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.24546 | − | 17.8554i | 0.300354 | − | 1.02240i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.89536 | − | 1.93507i | −0.507685 | − | 0.110440i | −0.0485749 | − | 0.998820i | \(-0.515468\pi\) |
−0.459110 | + | 0.888379i | \(0.651832\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.19140 | − | 1.52433i | 0.295328 | − | 0.0867162i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.39765 | − | 3.92110i | 0.192663 | − | 0.222345i | −0.651196 | − | 0.758909i | \(-0.725733\pi\) |
0.843860 | + | 0.536564i | \(0.180278\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.65240 | + | 9.79246i | −0.206446 | + | 0.553502i | −0.998367 | − | 0.0571204i | \(-0.981808\pi\) |
0.791922 | + | 0.610623i | \(0.209081\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.50395 | − | 0.535665i | 0.422799 | − | 0.0301813i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.2023 | − | 11.2649i | 1.69633 | − | 0.632699i | 0.699678 | − | 0.714458i | \(-0.253327\pi\) |
0.996652 | + | 0.0817594i | \(0.0260539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.7221 | + | 17.8159i | 1.55214 | + | 0.997501i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.30744i | 0.240418i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8832 | + | 17.8832i | −0.995048 | + | 0.995048i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.76927 | + | 7.31734i | 0.541902 | + | 0.405893i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.04916 | + | 2.81292i | 0.0580190 | + | 0.155555i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.10620 | − | 0.912061i | −0.171250 | − | 0.0502836i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.41892 | + | 20.6246i | 0.517711 | + | 1.13363i | 0.970299 | + | 0.241909i | \(0.0777735\pi\) |
−0.452588 | + | 0.891720i | \(0.649499\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.02279 | − | 0.573801i | 0.439646 | − | 0.0314441i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0926 | − | 13.4859i | −0.551417 | − | 0.736816i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.32691 | − | 33.6813i | 0.399122 | − | 1.83474i | −0.136968 | − | 0.990575i | \(-0.543736\pi\) |
0.536091 | − | 0.844160i | \(-0.319900\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.394768 | − | 2.74567i | −0.0214409 | − | 0.149124i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.2762 | + | 4.20928i | 1.58539 | + | 0.227945i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.27407 | − | 17.8138i | 0.0687932 | − | 0.961854i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.27511 | − | 15.6061i | 0.176326 | − | 0.840205i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.0661572 | − | 0.924999i | 0.00355151 | − | 0.0496566i | −0.995367 | − | 0.0961454i | \(-0.969349\pi\) |
0.998919 | + | 0.0464888i | \(0.0148032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.8023 | − | 3.27847i | −1.22058 | − | 0.175492i | −0.498243 | − | 0.867037i | \(-0.666021\pi\) |
−0.722333 | + | 0.691545i | \(0.756930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.95733 | + | 13.6135i | 0.104475 | + | 0.726637i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.374809 | − | 1.72297i | 0.0199491 | − | 0.0917045i | −0.966096 | − | 0.258183i | \(-0.916876\pi\) |
0.986045 | + | 0.166479i | \(0.0532398\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.709570 | − | 4.93040i | 0.0376601 | − | 0.261678i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −39.1100 | + | 2.79720i | −2.06992 | + | 0.148044i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.76528 | + | 12.6242i | 0.304280 | + | 0.666279i | 0.998572 | − | 0.0534131i | \(-0.0170100\pi\) |
−0.694293 | + | 0.719693i | \(0.744283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.17727 | + | 0.639304i | 0.114593 | + | 0.0336476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.63105 | + | 23.1407i | 0.453013 | + | 1.21457i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.14741 | − | 5.27109i | 0.0600581 | − | 0.275902i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2472 | − | 11.2472i | 0.587098 | − | 0.587098i | −0.349747 | − | 0.936844i | \(-0.613732\pi\) |
0.936844 | + | 0.349747i | \(0.113732\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.316681i | 0.0164858i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8867 | + | 6.99643i | 0.565207 | + | 0.363237i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1957 | − | 9.39750i | 1.30458 | − | 0.486584i | 0.401424 | − | 0.915892i | \(-0.368515\pi\) |
0.903158 | + | 0.429308i | \(0.141243\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7604 | − | 11.7508i | 0.607304 | − | 0.606808i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.35021 | − | 14.3445i | 0.275550 | − | 0.738777i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.35798 | + | 1.56719i | −0.0697546 | + | 0.0805011i | −0.789554 | − | 0.613681i | \(-0.789688\pi\) |
0.719800 | + | 0.694182i | \(0.244234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.89572 | + | 0.850259i | −0.148352 | + | 0.0435601i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.2127 | − | 2.65670i | −0.624038 | − | 0.135751i | −0.110582 | − | 0.993867i | \(-0.535271\pi\) |
−0.513456 | + | 0.858116i | \(0.671635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0080 | − | 43.9816i | −1.22356 | − | 2.24151i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.03505 | + | 5.39020i | 0.205113 | + | 0.273999i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.03003 | − | 10.4212i | −0.457841 | − | 0.528377i | 0.479149 | − | 0.877734i | \(-0.340945\pi\) |
−0.936990 | + | 0.349357i | \(0.886400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.08634 | − | 29.0215i | 0.307799 | − | 1.46768i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.5334 | + | 2.04075i | 1.43932 | + | 0.102942i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.1997 | + | 9.12830i | 0.714463 | + | 0.459295i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.70180 | − | 3.60919i | 0.135600 | − | 0.181140i | −0.727602 | − | 0.686000i | \(-0.759365\pi\) |
0.863201 | + | 0.504860i | \(0.168456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.0236 | − | 21.8212i | −0.702060 | − | 1.09243i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.66497 | − | 19.2931i | −0.282895 | − | 0.963452i | −0.971247 | − | 0.238075i | \(-0.923484\pi\) |
0.688352 | − | 0.725377i | \(-0.258335\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.980288 | − | 13.7062i | −0.0488316 | − | 0.682755i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.4409 | + | 0.00183150i | 0.667884 | + | 9.10081e-5i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.6746 | − | 47.0196i | −1.27264 | − | 2.33068i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3191 | − | 5.62595i | −0.609141 | − | 0.278185i | 0.0868666 | − | 0.996220i | \(-0.472315\pi\) |
−0.696007 | + | 0.718035i | \(0.745042\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.26134 | + | 9.74283i | −0.308849 | + | 0.480578i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.20970 | − | 9.20970i | −0.453179 | − | 0.453179i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.6299 | − | 9.92830i | 1.30721 | − | 0.487361i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.64106 | + | 30.5285i | 0.325214 | + | 1.49499i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1080 | − | 22.1335i | 0.493809 | − | 1.08129i | −0.484623 | − | 0.874723i | \(-0.661043\pi\) |
0.978432 | − | 0.206568i | \(-0.0662295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.34777 | − | 28.4299i | 0.406845 | − | 1.38559i | −0.460402 | − | 0.887710i | \(-0.652295\pi\) |
0.867247 | − | 0.497877i | \(-0.165887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.561092 | + | 0.209276i | 0.0272812 | + | 0.0101754i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.8663 | − | 21.8544i | 1.06067 | − | 1.06009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.1519 | + | 17.0102i | 1.50755 | + | 0.823182i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.0457 | − | 10.3119i | 0.774692 | − | 0.497865i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.93829 | + | 0.422463i | −0.141533 | + | 0.0203493i | −0.212717 | − | 0.977114i | \(-0.568231\pi\) |
0.0711844 | + | 0.997463i | \(0.477322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.31522 | + | 4.72751i | −0.303490 | + | 0.227190i | −0.740158 | − | 0.672433i | \(-0.765249\pi\) |
0.436668 | + | 0.899623i | \(0.356158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.3005 | − | 9.99608i | −0.877443 | − | 0.479275i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.7801 | − | 5.66719i | 0.898373 | − | 0.271099i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.597120 | − | 0.517408i | 0.0284990 | − | 0.0246945i | −0.640495 | − | 0.767962i | \(-0.721271\pi\) |
0.668994 | + | 0.743268i | \(0.266725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.25606 | + | 8.73609i | −0.0598124 | + | 0.416004i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0231 | − | 7.50322i | −0.476213 | − | 0.356489i | 0.334050 | − | 0.942555i | \(-0.391585\pi\) |
−0.810263 | + | 0.586067i | \(0.800676\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.449527 | + | 3.12956i | 0.0213096 | + | 0.148355i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.862705 | − | 1.57993i | 0.0408045 | − | 0.0747279i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.03870 | + | 1.76655i | 0.0962124 | + | 0.0833685i | 0.701639 | − | 0.712533i | \(-0.252452\pi\) |
−0.605427 | + | 0.795901i | \(0.706997\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.91866 | − | 0.876221i | 0.0903460 | − | 0.0412597i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.5376 | + | 9.57624i | −0.823987 | + | 0.449931i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.5954 | + | 15.2423i | −0.824887 | + | 0.714572i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.7944 | + | 5.17616i | −1.11306 | + | 0.242130i | −0.731248 | − | 0.682111i | \(-0.761062\pi\) |
−0.381808 | + | 0.924242i | \(0.624698\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.8353 | 1.62597 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2517 | −0.570620 | −0.285310 | − | 0.958435i | \(-0.592097\pi\) | ||||
−0.285310 | + | 0.958435i | \(0.592097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1122 | − | 6.76805i | 1.44591 | − | 0.314538i | 0.579949 | − | 0.814653i | \(-0.303073\pi\) |
0.865959 | + | 0.500115i | \(0.166709\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.6683 | − | 1.33774i | −0.865724 | − | 0.0620363i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.08984 | + | 3.87134i | −0.328078 | + | 0.179144i | −0.634843 | − | 0.772641i | \(-0.718935\pi\) |
0.306765 | + | 0.951785i | \(0.400754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.2229 | − | 13.3456i | 1.34939 | − | 0.616244i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8074 | + | 11.0977i | 0.590135 | + | 0.511355i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.4928 | − | 39.3611i | 0.988238 | − | 1.80982i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.6217 | + | 5.76725i | 0.900303 | + | 0.264619i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.91638 | − | 1.43459i | −0.0877451 | − | 0.0656852i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.40277 | − | 9.75651i | 0.0640944 | − | 0.445786i | −0.932352 | − | 0.361553i | \(-0.882247\pi\) |
0.996446 | − | 0.0842335i | \(-0.0268442\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.8100 | + | 16.2990i | −0.857663 | + | 0.743169i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.7582 | + | 12.4268i | 1.26304 | + | 0.565438i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.1220 | + | 22.1926i | −0.550432 | + | 1.00772i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8514 | + | 11.8662i | −0.718298 | + | 0.537711i | −0.894733 | − | 0.446601i | \(-0.852634\pi\) |
0.176435 | + | 0.984312i | \(0.443543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.2258 | + | 4.48959i | −1.41208 | + | 0.203026i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1221 | + | 14.2170i | −0.998358 | + | 0.641606i | −0.934355 | − | 0.356344i | \(-0.884023\pi\) |
−0.0640030 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.0336 | − | 18.5838i | −1.53280 | − | 0.836971i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.84934 | + | 8.43192i | 0.173015 | + | 0.378987i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.90131 | + | 3.32002i | 0.399278 | + | 0.148923i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.79227 | − | 19.7267i | 0.259298 | − | 0.883087i | −0.722212 | − | 0.691672i | \(-0.756874\pi\) |
0.981509 | − | 0.191414i | \(-0.0613075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.56133 | + | 18.7467i | −0.382492 | + | 0.837541i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.61835 | − | 39.6179i | −0.384273 | − | 1.76647i | −0.610117 | − | 0.792311i | \(-0.708878\pi\) |
0.225844 | − | 0.974163i | \(-0.427486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0795 | − | 35.1964i | 0.715527 | − | 1.56622i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.40297 | + | 7.40297i | 0.328778 | + | 0.328778i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.81281 | + | 5.93285i | −0.169000 | + | 0.262969i | −0.915415 | − | 0.402512i | \(-0.868137\pi\) |
0.746415 | + | 0.665481i | \(0.231774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.35887 | + | 4.27405i | 0.414012 | + | 0.189073i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.0443 | + | 20.2261i | 0.487616 | + | 0.893003i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.75240 | − | 5.75396i | −0.253481 | − | 0.253550i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.284548 | − | 3.97850i | −0.0125144 | − | 0.174974i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.65068 | + | 12.4331i | 0.160247 | + | 0.545751i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.4200 | + | 33.3302i | 0.938427 | + | 1.46022i | 0.887120 | + | 0.461538i | \(0.152702\pi\) |
0.0513070 | + | 0.998683i | \(0.483661\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.4096 | − | 25.9282i | 0.848722 | − | 1.13376i | −0.140894 | − | 0.990025i | \(-0.544998\pi\) |
0.989616 | − | 0.143735i | \(-0.0459113\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.1352 | + | 26.6788i | 0.747840 | + | 1.16436i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.7154 | − | 2.48289i | −1.51223 | − | 0.108157i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8002 | + | 17.6055i | −0.643487 | + | 0.765457i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.57776 | + | 1.82083i | 0.0684688 | + | 0.0790172i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.587256 | − | 0.784483i | −0.0254369 | − | 0.0339797i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.68548 | − | 3.10350i | 0.245805 | − | 0.134176i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.60697 | − | 0.784648i | −0.155652 | − | 0.0338600i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 56.4042 | − | 16.5618i | 2.42950 | − | 0.713366i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.6123 | − | 15.7095i | 0.585240 | − | 0.675403i | −0.383483 | − | 0.923548i | \(-0.625276\pi\) |
0.968723 | + | 0.248145i | \(0.0798210\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.78756 | + | 7.47374i | −0.119626 | + | 0.320729i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.95691 | − | 3.41152i | 0.126660 | − | 0.146134i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0516 | − | 5.61395i | 0.643559 | − | 0.240035i | −0.00642931 | − | 0.999979i | \(-0.502047\pi\) |
0.649988 | + | 0.759944i | \(0.274774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.52340 | − | 3.54967i | −0.235733 | − | 0.151496i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 25.6525i | − | 1.09283i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.7655 | + | 22.7655i | −0.968089 | + | 0.968089i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.3240 | + | 28.5212i | 0.777811 | + | 1.21066i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.49203 | + | 17.4058i | 0.275076 | + | 0.737507i | 0.998872 | + | 0.0474929i | \(0.0151231\pi\) |
−0.723796 | + | 0.690014i | \(0.757604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.9913 | − | 5.86997i | −0.845541 | − | 0.248273i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.0686 | − | 43.9442i | −0.847299 | − | 1.85533i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5000 | + | 1.46619i | −0.863970 | + | 0.0617924i | −0.496287 | − | 0.868159i | \(-0.665304\pi\) |
−0.367683 | + | 0.929951i | \(0.619849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.33964 | + | 2.49932i | −0.140500 | + | 0.105147i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.44910 | + | 25.0491i | −0.228841 | + | 1.05196i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00500 | + | 20.9002i | 0.125976 | + | 0.876183i | 0.950582 | + | 0.310475i | \(0.100488\pi\) |
−0.824605 | + | 0.565708i | \(0.808603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24090 | + | 0.178414i | 0.0519300 | + | 0.00746641i | 0.168231 | − | 0.985748i | \(-0.446195\pi\) |
−0.116301 | + | 0.993214i | \(0.537104\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.962314 | − | 13.4549i | 0.0402012 | − | 0.562087i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.9586 | + | 6.92129i | −0.957438 | + | 0.288638i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.000913547 | 0.0127731i | −3.80315e−5 | 0.000531749i | −0.997471 | − | 0.0710733i | \(-0.977358\pi\) | ||
0.997433 | + | 0.0716051i | \(0.0228121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.7476 | − | 5.13973i | −1.48562 | − | 0.213600i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.71410 | + | 53.6527i | 0.320035 | + | 2.22589i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.38922 | + | 15.5800i | −0.140367 | + | 0.645258i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.44770 | − | 2.58018i | 0.142545 | − | 0.106677i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.768689 | + | 0.0549777i | −0.0317272 | + | 0.00226917i | −0.0871938 | − | 0.996191i | \(-0.527790\pi\) |
0.0554666 | + | 0.998461i | \(0.482335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.56465 | − | 20.9437i | −0.394104 | − | 0.862968i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.08701 | − | 2.66819i | −0.373790 | − | 0.109755i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.06882 | − | 21.6333i | −0.331347 | − | 0.888375i | −0.990641 | − | 0.136490i | \(-0.956418\pi\) |
0.659295 | − | 0.751885i | \(-0.270855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 31.8708 | + | 49.6067i | 1.30657 | + | 2.03368i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.07135 | + | 2.07135i | −0.0847746 | + | 0.0847746i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.2597i | − | 0.582637i | −0.956626 | − | 0.291318i | \(-0.905906\pi\) | ||
0.956626 | − | 0.291318i | \(-0.0940939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0088 | + | 18.6428i | 1.18329 | + | 0.760457i | 0.975989 | − | 0.217819i | \(-0.0698942\pi\) |
0.207305 | + | 0.978276i | \(0.433531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.56806 | + | 2.07678i | −0.226749 | + | 0.0845730i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.3253 | − | 28.0652i | 0.988965 | − | 1.14101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5430 | − | 30.9480i | 0.468516 | − | 1.25614i | −0.461013 | − | 0.887393i | \(-0.652514\pi\) |
0.929530 | − | 0.368748i | \(-0.120213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.0443 | − | 30.0567i | 1.05537 | − | 1.21796i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.77802 | + | 0.522074i | −0.0719311 | + | 0.0211209i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.9030 | + | 8.89790i | 1.65206 | + | 0.359383i | 0.939584 | − | 0.342317i | \(-0.111212\pi\) |
0.712472 | + | 0.701700i | \(0.247575\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.17155 | + | 0.639506i | −0.0472414 | + | 0.0257874i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.14163 | − | 4.19672i | −0.126477 | − | 0.168954i | 0.732833 | − | 0.680409i | \(-0.238198\pi\) |
−0.859310 | + | 0.511455i | \(0.829107\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9499 | − | 27.6397i | −0.962630 | − | 1.11093i | −0.993774 | − | 0.111419i | \(-0.964460\pi\) |
0.0311438 | − | 0.999515i | \(-0.490085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.8108 | − | 12.7715i | −0.955495 | − | 0.512503i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.01469 | − | 0.430179i | −0.240974 | − | 0.0172348i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9835 | − | 7.05639i | −0.959339 | − | 0.282255i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.1523 | − | 25.5845i | 0.764868 | − | 1.02174i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.0820 | + | 53.0326i | 1.35894 | + | 2.11455i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6272 | − | 43.0044i | −0.502682 | − | 1.71198i | −0.684826 | − | 0.728707i | \(-0.740122\pi\) |
0.182144 | − | 0.983272i | \(-0.441696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.650971 | − | 9.10176i | −0.0258738 | − | 0.361763i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.20864 | + | 3.20951i | 0.127331 | + | 0.127366i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0888 | − | 23.9703i | −0.518596 | − | 0.949738i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.59858 | − | 0.730046i | −0.0632388 | − | 0.0288802i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6615 | + | 30.5938i | −0.776581 | + | 1.20838i | 0.197081 | + | 0.980387i | \(0.436854\pi\) |
−0.973662 | + | 0.227996i | \(0.926783\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.57170 | + | 4.57170i | 0.180290 | + | 0.180290i | 0.791482 | − | 0.611192i | \(-0.209310\pi\) |
−0.611192 | + | 0.791482i | \(0.709310\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.7924 | + | 25.8125i | −0.464326 | + | 1.01637i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.86552 | − | 13.1726i | −0.112655 | − | 0.517867i | −0.998543 | − | 0.0539672i | \(-0.982813\pi\) |
0.885888 | − | 0.463900i | \(-0.153550\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.66627 | − | 14.5971i | 0.261674 | − | 0.572986i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0568 | − | 34.2502i | 0.394156 | − | 1.34237i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.5955 | + | 12.9034i | 1.35383 | + | 0.504951i | 0.918535 | − | 0.395340i | \(-0.129373\pi\) |
0.435290 | + | 0.900290i | \(0.356646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.8646 | − | 39.1322i | −0.698030 | − | 1.52902i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.67041 | − | 0.912115i | −0.0651690 | − | 0.0355850i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.7076 | + | 14.5933i | −0.884561 | + | 0.568473i | −0.902174 | − | 0.431372i | \(-0.858030\pi\) |
0.0176130 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9130 | − | 2.71928i | 0.735631 | − | 0.105768i | 0.235691 | − | 0.971828i | \(-0.424265\pi\) |
0.499940 | + | 0.866060i | \(0.333355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.9675 | + | 13.4503i | −0.697799 | + | 0.522366i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.6983 | + | 34.2323i | −0.725089 | + | 1.32747i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.4496 | + | 25.1801i | 0.636930 | + | 0.974977i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.7674 | − | 16.2620i | 0.725589 | − | 0.628727i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.22357 | + | 43.2859i | −0.240258 | + | 1.67103i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.92038 | − | 7.42631i | −0.382403 | − | 0.286263i | 0.390733 | − | 0.920504i | \(-0.372222\pi\) |
−0.773135 | + | 0.634241i | \(0.781313\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.4937 | − | 24.7279i | −0.519373 | − | 0.951778i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6135 | + | 23.0999i | −0.484775 | + | 0.887800i | 0.514761 | + | 0.857334i | \(0.327881\pi\) |
−0.999536 | + | 0.0304657i | \(0.990301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.4491 | − | 31.5833i | −1.39879 | − | 1.21206i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.2558 | − | 15.6441i | 1.31269 | − | 0.599484i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.3443 | + | 20.9376i | −1.46720 | + | 0.801154i | −0.996695 | − | 0.0812403i | \(-0.974112\pi\) |
−0.470510 | + | 0.882395i | \(0.655930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3711 | + | 1.24478i | 0.663714 | + | 0.0475607i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.4780 | − | 7.93530i | 1.39172 | − | 0.302751i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.40757 | 0.282206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.4276 | −0.662975 | −0.331488 | − | 0.943460i | \(-0.607551\pi\) | ||||
−0.331488 | + | 0.943460i | \(0.607551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.2742 | + | 3.75777i | −0.656192 | + | 0.142746i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.5103 | − | 30.7614i | 1.34698 | − | 1.16685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.17841 | + | 1.18950i | −0.0825132 | + | 0.0450556i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.0932 | + | 11.4597i | −0.949113 | + | 0.433445i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1061 | − | 22.6211i | −0.986015 | − | 0.854387i | 0.00332702 | − | 0.999994i | \(-0.498941\pi\) |
−0.989342 | + | 0.145607i | \(0.953486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.9864 | + | 36.6023i | −0.753800 | + | 1.38048i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.358861 | + | 2.49835i | 0.0135155 | + | 0.0940933i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 59.0810 | + | 44.2274i | 2.22197 | + | 1.66334i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.54932 | + | 10.7757i | −0.0581859 | + | 0.404692i | 0.939825 | + | 0.341655i | \(0.110988\pi\) |
−0.998011 | + | 0.0630365i | \(0.979922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.50092 | − | 3.90007i | 0.168798 | − | 0.146264i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.8186 | + | 14.4247i | 0.854563 | + | 0.540209i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.1718 | − | 13.7493i | −0.941373 | − | 0.514195i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.0762 | + | 22.5147i | −1.12322 | + | 0.840829i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.1459 | − | 3.47166i | 0.900492 | − | 0.129471i | 0.323507 | − | 0.946226i | \(-0.395138\pi\) |
0.576985 | + | 0.816755i | \(0.304229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0543 | − | 8.38949i | 0.486168 | − | 0.312441i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.50998 | + | 0.824510i | 0.0561567 | + | 0.0306639i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.00854574 | + | 31.3574i | −0.000317381 | + | 1.16459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.53292 | + | 2.43665i | 0.242292 | + | 0.0903704i | 0.467677 | − | 0.883899i | \(-0.345091\pi\) |
−0.225384 | + | 0.974270i | \(0.572364\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.41675 | − | 28.6648i | 0.311731 | − | 1.06166i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.9223 | + | 48.0031i | −0.810825 | + | 1.77546i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.52003 | − | 39.1659i | −0.314694 | − | 1.44663i | −0.814335 | − | 0.580394i | \(-0.802898\pi\) |
0.499641 | − | 0.866233i | \(-0.333465\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −34.8553 | + | 12.9949i | −1.28566 | + | 0.479326i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.9887 | + | 27.9887i | 1.03098 | + | 1.03098i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.7464 | + | 21.3899i | −0.505671 | + | 0.786839i | −0.996427 | − | 0.0844580i | \(-0.973084\pi\) |
0.490756 | + | 0.871297i | \(0.336720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.5060 | − | 6.16797i | −0.496155 | − | 0.226586i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4618 | − | 46.6298i | −0.934103 | − | 1.71068i | −0.663807 | − | 0.747904i | \(-0.731060\pi\) |
−0.270296 | − | 0.962777i | \(-0.587122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.70696 | 0.000368859i | −0.0991752 | 1.35139e-5i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.715309 | − | 10.0013i | −0.0261718 | − | 0.365929i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.48049 | + | 11.8535i | 0.127174 | + | 0.433116i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.29615 | + | 6.68495i | 0.156769 | + | 0.243937i | 0.910749 | − | 0.412960i | \(-0.135505\pi\) |
−0.753980 | + | 0.656897i | \(0.771869\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.59690 | + | 10.1483i | −0.276846 | + | 0.369823i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.2757 | + | 16.2486i | 0.919877 | + | 0.591346i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.05710 | − | 0.218648i | −0.111112 | − | 0.00794691i | 0.0156723 | − | 0.999877i | \(-0.495011\pi\) |
−0.126785 | + | 0.991930i | \(0.540466\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.39364 | + | 37.3947i | −0.0868836 | + | 1.35734i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.5470 | − | 13.3259i | −0.418577 | − | 0.483063i | 0.506826 | − | 0.862048i | \(-0.330819\pi\) |
−0.925403 | + | 0.378985i | \(0.876273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.16004 | + | 6.89301i | 0.186806 | + | 0.249544i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.22588 | − | 9.57358i | −0.188942 | − | 0.346134i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.28498 | − | 1.58475i | −0.263045 | − | 0.0572220i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.57042 | + | 2.81013i | −0.345118 | + | 0.101336i | −0.449698 | − | 0.893181i | \(-0.648468\pi\) |
0.104580 | + | 0.994516i | \(0.466650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.2700 | + | 28.0091i | −0.874063 | + | 1.00872i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4734 | − | 36.1237i | 0.484606 | − | 1.29928i | −0.432858 | − | 0.901462i | \(-0.642495\pi\) |
0.917464 | − | 0.397818i | \(-0.130232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.6848 | + | 25.6046i | 0.419730 | + | 0.919744i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −60.5792 | + | 22.5949i | −2.17327 | + | 0.810587i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.38130 | − | 0.887707i | −0.0494902 | − | 0.0318054i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7052i | 0.418844i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.9846 | + | 24.9846i | −0.892878 | + | 0.892878i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.42037 | − | 24.9007i | 0.193461 | − | 0.888744i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.8124 | − | 34.3514i | −0.456713 | − | 1.22449i | −0.937601 | − | 0.347712i | \(-0.886959\pi\) |
0.480889 | − | 0.876782i | \(-0.340314\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.7614 | + | 5.50884i | 0.667923 | + | 0.196120i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.30490 | − | 7.23672i | −0.117509 | − | 0.257308i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.2651 | − | 1.44939i | 0.719636 | − | 0.0514693i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.43724 | − | 9.98658i | 0.0509737 | − | 0.354187i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.50463 | + | 29.9013i | −0.230406 | + | 1.05916i | 0.705993 | + | 0.708219i | \(0.250501\pi\) |
−0.936398 | + | 0.350939i | \(0.885863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.667960 | + | 4.64576i | 0.0236307 | + | 0.164355i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.10410 | + | 0.158746i | 0.0390115 | + | 0.00560901i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.904328 | + | 12.6442i | −0.0319131 | + | 0.446203i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.59738 | − | 45.5922i | −0.126791 | − | 1.60691i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.789638 | + | 11.0406i | −0.0277966 | + | 0.388647i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.19238 | − | 1.03411i | −0.252871 | − | 0.0363573i | 0.0147137 | − | 0.999892i | \(-0.495316\pi\) |
−0.267584 | + | 0.963534i | \(0.586225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.75480 | − | 33.0703i | −0.166963 | − | 1.16126i | −0.885116 | − | 0.465371i | \(-0.845921\pi\) |
0.718152 | − | 0.695886i | \(-0.244988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.508934 | + | 2.33953i | −0.0178491 | + | 0.0820509i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.4240 | + | 37.9808i | 0.995650 | + | 1.33041i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.8219 | + | 2.49051i | −1.21826 | + | 0.0871319i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.41183 | + | 7.47087i | 0.119219 | + | 0.261053i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.7861 | + | 8.15874i | 0.969742 | + | 0.284742i | 0.727984 | − | 0.685594i | \(-0.240458\pi\) |
0.241759 | + | 0.970336i | \(0.422276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.17527 | + | 19.2376i | 0.250114 | + | 0.670582i | 0.999960 | + | 0.00896932i | \(0.00285506\pi\) |
−0.749846 | + | 0.661613i | \(0.769872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.4202 | + | 31.2679i | −0.815386 | + | 1.08861i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.0208 | + | 21.0208i | −0.730964 | + | 0.730964i | −0.970811 | − | 0.239847i | \(-0.922903\pi\) |
0.239847 | + | 0.970811i | \(0.422903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 23.8762i | − | 0.829256i | −0.909991 | − | 0.414628i | \(-0.863912\pi\) | ||
0.909991 | − | 0.414628i | \(-0.136088\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9344 | + | 16.0244i | 0.864966 | + | 0.555880i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −64.8125 | + | 24.1738i | −2.24562 | + | 0.837573i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.9126 | − | 2.20668i | 1.06978 | − | 0.0763653i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.0828 | + | 29.7140i | −0.383076 | + | 1.02707i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.46125 | − | 1.68637i | 0.0504480 | − | 0.0582201i | −0.729965 | − | 0.683485i | \(-0.760464\pi\) |
0.780413 | + | 0.625265i | \(0.215009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.91306 | − | 2.91074i | 0.341830 | − | 0.100370i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.9685 | − | 8.04200i | −1.27326 | − | 0.276981i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.43752 | − | 15.1052i | 0.152655 | − | 0.519634i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.4496 | + | 56.7060i | 1.45858 | + | 1.94844i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.8049 | + | 30.9346i | 0.919943 | + | 1.06167i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.85280 | − | 48.7445i | −0.132072 | − | 1.67094i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.7288 | − | 1.98321i | −0.949417 | − | 0.0679037i | −0.411967 | − | 0.911199i | \(-0.635158\pi\) |
−0.537451 | + | 0.843295i | \(0.680613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.90179 | − | 6.06949i | 0.133438 | − | 0.207572i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.5739 | − | 16.7968i | 0.429517 | − | 0.573768i | −0.532613 | − | 0.846359i | \(-0.678790\pi\) |
0.962130 | + | 0.272591i | \(0.0878807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.69163 | − | 10.4124i | −0.228316 | − | 0.355266i | 0.708128 | − | 0.706084i | \(-0.249540\pi\) |
−0.936444 | + | 0.350818i | \(0.885904\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.717188 | − | 2.44252i | −0.0244417 | − | 0.0832408i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.23174 | − | 17.2219i | −0.0419288 | − | 0.586241i | −0.974375 | − | 0.224931i | \(-0.927784\pi\) |
0.932446 | − | 0.361310i | \(-0.117670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7804 | − | 13.7766i | 0.468547 | − | 0.468419i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.1292 | + | 27.7070i | 0.513813 | + | 0.940978i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.0827 | − | 16.4784i | −1.22402 | − | 0.558992i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.94201 | − | 15.4701i | 0.336872 | − | 0.524183i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.30848 | + | 6.30848i | 0.213510 | + | 0.213510i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.8681 | − | 41.8391i | 0.773083 | − | 1.41442i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.8532 | + | 54.4882i | 0.400254 | + | 1.83994i | 0.529482 | + | 0.848321i | \(0.322386\pi\) |
−0.129228 | + | 0.991615i | \(0.541250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.91776 | − | 10.7684i | 0.165872 | − | 0.363209i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.85817 | + | 19.9511i | −0.197367 | + | 0.672169i | 0.800024 | + | 0.599969i | \(0.204820\pi\) |
−0.997390 | + | 0.0722003i | \(0.976998\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.9903 | − | 7.82897i | −0.706379 | − | 0.263466i | −0.0295049 | − | 0.999565i | \(-0.509393\pi\) |
−0.676874 | + | 0.736099i | \(0.736666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.54995 | + | 9.51383i | −0.119330 | + | 0.319804i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.3296 | − | 9.46266i | −0.581870 | − | 0.317725i | 0.161218 | − | 0.986919i | \(-0.448458\pi\) |
−0.743088 | + | 0.669194i | \(0.766640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.28158 | + | 4.67959i | −0.244216 | + | 0.156948i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.2629 | + | 4.49493i | −1.04735 | + | 0.150586i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.48565 | + | 1.86074i | −0.0831792 | + | 0.0622672i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.56314 | + | 5.32625i | 0.0522500 | + | 0.178037i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.2125 | − | 2.60628i | 0.574708 | − | 0.0870212i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.6794 | − | 23.1179i | 0.889809 | − | 0.771024i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.67012 | − | 18.5711i | 0.0889546 | − | 0.618693i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −43.3290 | − | 32.4357i | −1.44190 | − | 1.07939i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.8732 | − | 1.70545i | 0.394678 | − | 0.0566912i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.8017 | + | 23.4445i | −0.425073 | + | 0.778463i | −0.999187 | − | 0.0403122i | \(-0.987165\pi\) |
0.574114 | + | 0.818775i | \(0.305347\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.3174 | − | 8.94012i | −0.342208 | − | 0.296525i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4398 | − | 9.79124i | 0.710333 | − | 0.324398i | −0.0272743 | − | 0.999628i | \(-0.508683\pi\) |
0.737608 | + | 0.675230i | \(0.235955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.6153 | + | 32.0064i | −1.93988 | + | 1.05926i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.97790 | − | 27.6018i | 0.0653874 | − | 0.912487i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.1688 | − | 17.4397i | 2.64741 | − | 0.575908i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.33631 | −0.143042 | −0.0715208 | − | 0.997439i | \(-0.522785\pi\) | ||||
−0.0715208 | + | 0.997439i | \(0.522785\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5366 | −0.446045 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.31381 | − | 1.15595i | 0.174906 | − | 0.0380485i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.4434 | − | 44.7358i | 0.803695 | − | 1.47090i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.51938 | + | 1.37568i | −0.0827472 | + | 0.0451834i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.8991 | − | 20.9614i | 1.50590 | − | 0.687722i | 0.519864 | − | 0.854249i | \(-0.325983\pi\) |
0.986037 | + | 0.166527i | \(0.0532553\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.5842 | − | 29.9673i | −1.13345 | − | 0.982140i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.69740 | − | 6.77128i | 0.121047 | − | 0.221682i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.5435 | + | 58.1508i | −1.42402 | + | 1.90173i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.7827 | + | 19.3007i | 0.842285 | + | 0.630526i | 0.930792 | − | 0.365549i | \(-0.119119\pi\) |
−0.0885074 | + | 0.996076i | \(0.528210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.21172 | + | 15.3829i | −0.0721768 | + | 0.502000i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.14588 | + | 3.59242i | −0.135152 | + | 0.117110i | −0.719813 | − | 0.694168i | \(-0.755773\pi\) |
0.584662 | + | 0.811277i | \(0.301227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.92510 | − | 0.0143940i | 0.0626900 | − | 0.000468734i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 51.5526 | − | 15.1296i | 1.67701 | − | 0.492165i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.2655 | + | 30.8910i | −1.34095 | + | 1.00382i | −0.343032 | + | 0.939324i | \(0.611454\pi\) |
−0.997918 | + | 0.0644983i | \(0.979455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.82939 | − | 0.838139i | 0.189230 | − | 0.0272071i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.3232 | − | 25.9142i | 1.30757 | − | 0.840324i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.8110 | − | 5.90326i | −0.350203 | − | 0.191225i | 0.294513 | − | 0.955647i | \(-0.404843\pi\) |
−0.644716 | + | 0.764422i | \(0.723024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.4528 | + | 8.42406i | −0.597118 | + | 0.272596i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 45.9114 | + | 17.1241i | 1.48411 | + | 0.553543i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.35792 | + | 31.8702i | −0.302183 | + | 1.02914i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.284645 | − | 0.623287i | 0.00918211 | − | 0.0201060i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.485765 | − | 2.23303i | −0.0156536 | − | 0.0719583i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.9721 | + | 50.8872i | 0.610732 | + | 1.63812i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.8904 | + | 15.8904i | 0.511000 | + | 0.511000i | 0.914833 | − | 0.403833i | \(-0.132322\pi\) |
−0.403833 | + | 0.914833i | \(0.632322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.3317 | + | 31.6368i | −0.653149 | + | 1.01632i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.51859 | + | 3.89031i | 0.273375 | + | 0.124846i | 0.547386 | − | 0.836881i | \(-0.315623\pi\) |
−0.274011 | + | 0.961727i | \(0.588350\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.9428 | + | 78.6439i | 1.37668 | + | 2.52121i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.5076 | + | 7.54420i | 0.528666 | + | 0.241608i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.72135 | + | 24.0676i | 0.0550709 | + | 0.769991i | 0.947692 | + | 0.319185i | \(0.103409\pi\) |
−0.892622 | + | 0.450807i | \(0.851136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.09314 | − | 7.12859i | −0.0668971 | − | 0.227831i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.861122 | − | 1.33993i | −0.0274935 | − | 0.0427808i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.6437 | + | 20.8976i | −0.498958 | + | 0.666529i | −0.977353 | − | 0.211615i | \(-0.932128\pi\) |
0.478395 | + | 0.878145i | \(0.341219\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.02538 | + | 13.9166i | 0.0963966 | + | 0.443419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.80158 | − | 0.343415i | −0.152836 | − | 0.0109310i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.5836 | − | 24.7741i | 1.03610 | − | 0.787771i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2266 | − | 23.3428i | −0.642521 | − | 0.741508i | 0.337298 | − | 0.941398i | \(-0.390487\pi\) |
−0.979818 | + | 0.199890i | \(0.935942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.2047 | + | 26.9903i | 0.641176 | + | 0.856510i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.22642 | + | 1.24162i | 0.133987 | + | 0.0393619i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.2891 | − | 2.67334i | −0.389201 | − | 0.0846655i | 0.0137068 | − | 0.999906i | \(-0.495637\pi\) |
−0.402908 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 55.1154 | − | 16.1833i | 1.74377 | − | 0.512018i |
(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 | 920.2.bv.a.217.27 | yes | 720 | |
5.3 | odd | 4 | inner | 920.2.bv.a.33.27 | ✓ | 720 | |
23.7 | odd | 22 | inner | 920.2.bv.a.697.27 | yes | 720 | |
115.53 | even | 44 | inner | 920.2.bv.a.513.27 | yes | 720 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.bv.a.33.27 | ✓ | 720 | 5.3 | odd | 4 | inner | |
920.2.bv.a.217.27 | yes | 720 | 1.1 | even | 1 | trivial | |
920.2.bv.a.513.27 | yes | 720 | 115.53 | even | 44 | inner | |
920.2.bv.a.697.27 | yes | 720 | 23.7 | odd | 22 | inner |