Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.3 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.g.2881.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.794182 | + | 1.37556i | 0.355169 | + | 0.615171i | 0.987147 | − | 0.159816i | \(-0.0510900\pi\) |
−0.631978 | + | 0.774986i | \(0.717757\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23855 | + | 2.33795i | −0.468128 | + | 0.883661i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.794182 | − | 1.37556i | 0.239455 | − | 0.414748i | −0.721103 | − | 0.692828i | \(-0.756365\pi\) |
0.960558 | + | 0.278080i | \(0.0896979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40545 | − | 4.16635i | 0.667151 | − | 1.15554i | −0.311547 | − | 0.950231i | \(-0.600847\pi\) |
0.978697 | − | 0.205308i | \(-0.0658196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.69963 | + | 4.67589i | 0.654756 | + | 1.13407i | 0.981955 | + | 0.189115i | \(0.0605620\pi\) |
−0.327199 | + | 0.944955i | \(0.606105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.54944 | − | 6.14781i | 0.814298 | − | 1.41041i | −0.0955331 | − | 0.995426i | \(-0.530456\pi\) |
0.909831 | − | 0.414979i | \(-0.136211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.150186 | − | 0.260130i | −0.0313159 | − | 0.0542408i | 0.849943 | − | 0.526875i | \(-0.176636\pi\) |
−0.881259 | + | 0.472634i | \(0.843303\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23855 | − | 2.14523i | 0.247710 | − | 0.429046i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.13781 | − | 7.16689i | −0.768371 | − | 1.33086i | −0.938446 | − | 0.345427i | \(-0.887734\pi\) |
0.170074 | − | 0.985431i | \(-0.445599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.71201 | 0.487091 | 0.243545 | − | 0.969889i | \(-0.421689\pi\) | ||||
0.243545 | + | 0.969889i | \(0.421689\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.19963 | + | 0.153051i | −0.709867 | + | 0.0258703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.93818 | + | 5.08907i | −0.458866 | + | 0.794780i | −0.998901 | − | 0.0468628i | \(-0.985078\pi\) |
0.540035 | + | 0.841643i | \(0.318411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.833104 | + | 1.44298i | 0.127047 | + | 0.220052i | 0.922531 | − | 0.385922i | \(-0.126117\pi\) |
−0.795484 | + | 0.605974i | \(0.792783\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.66621 | 0.388906 | 0.194453 | − | 0.980912i | \(-0.437707\pi\) | ||||
0.194453 | + | 0.980912i | \(0.437707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.93199 | − | 5.79133i | −0.561713 | − | 0.827332i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44437 | − | 4.23377i | −0.335760 | − | 0.581553i | 0.647871 | − | 0.761750i | \(-0.275660\pi\) |
−0.983630 | + | 0.180197i | \(0.942326\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.52290 | 0.340188 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.47710 | 0.843247 | 0.421623 | − | 0.906771i | \(-0.361460\pi\) | ||||
0.421623 | + | 0.906771i | \(0.361460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.47710 | −0.573234 | −0.286617 | − | 0.958045i | \(-0.592531\pi\) | ||||
−0.286617 | + | 0.958045i | \(0.592531\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.64145 | 0.947805 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0531 | 1.22818 | 0.614090 | − | 0.789236i | \(-0.289523\pi\) | ||||
0.614090 | + | 0.789236i | \(0.289523\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7207 | 1.50967 | 0.754833 | − | 0.655917i | \(-0.227718\pi\) | ||||
0.754833 | + | 0.655917i | \(0.227718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.02654 | + | 13.9024i | 0.939436 | + | 1.62715i | 0.766527 | + | 0.642213i | \(0.221983\pi\) |
0.172909 | + | 0.984938i | \(0.444683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23236 | + | 3.56046i | 0.254401 | + | 0.405752i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.38688 | −0.943597 | −0.471799 | − | 0.881706i | \(-0.656395\pi\) | ||||
−0.471799 | + | 0.881706i | \(0.656395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.18292 | + | 2.04887i | 0.129842 | + | 0.224893i | 0.923615 | − | 0.383321i | \(-0.125220\pi\) |
−0.793773 | + | 0.608214i | \(0.791886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28799 | + | 7.42702i | −0.465098 | + | 0.805573i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.60507 | + | 2.78007i | −0.170138 | + | 0.294687i | −0.938468 | − | 0.345367i | \(-0.887755\pi\) |
0.768330 | + | 0.640054i | \(0.221088\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.76145 | + | 10.7840i | 0.708793 | + | 1.13047i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.2756 | 1.15685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.712008 | + | 1.23323i | 0.0722934 | + | 0.125216i | 0.899906 | − | 0.436084i | \(-0.143635\pi\) |
−0.827613 | + | 0.561300i | \(0.810302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.01671 | − | 10.4212i | 0.598685 | − | 1.03695i | −0.394330 | − | 0.918969i | \(-0.629023\pi\) |
0.993015 | − | 0.117984i | \(-0.0376432\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.04944 | − | 5.28179i | −0.300470 | − | 0.520430i | 0.675772 | − | 0.737111i | \(-0.263810\pi\) |
−0.976243 | + | 0.216680i | \(0.930477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.54325 | + | 2.67299i | −0.149192 | + | 0.258408i | −0.930929 | − | 0.365200i | \(-0.881001\pi\) |
0.781737 | + | 0.623608i | \(0.214334\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.14400 | + | 1.98146i | 0.109575 | + | 0.189789i | 0.915598 | − | 0.402095i | \(-0.131718\pi\) |
−0.806023 | + | 0.591884i | \(0.798384\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.73236 | − | 16.8569i | 0.915543 | − | 1.58577i | 0.109440 | − | 0.993993i | \(-0.465094\pi\) |
0.806104 | − | 0.591774i | \(-0.201572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.238550 | − | 0.413181i | 0.0222449 | − | 0.0385293i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.2756 | + | 0.520259i | −1.30864 | + | 0.0476921i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.23855 | + | 7.34138i | 0.385323 | + | 0.667399i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8764 | 1.06225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4400 | 1.19260 | 0.596302 | − | 0.802760i | \(-0.296636\pi\) | ||||
0.596302 | + | 0.802760i | \(0.296636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.58836 | + | 2.75113i | 0.138776 | + | 0.240367i | 0.927034 | − | 0.374978i | \(-0.122350\pi\) |
−0.788258 | + | 0.615345i | \(0.789017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.97710 | + | 15.9128i | 0.865124 | + | 1.37981i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.6316 | + | 18.4145i | −0.908320 | + | 1.57326i | −0.0919231 | + | 0.995766i | \(0.529301\pi\) |
−0.816397 | + | 0.577491i | \(0.804032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.52654 | + | 11.3043i | −0.553574 | + | 0.958818i | 0.444439 | + | 0.895809i | \(0.353403\pi\) |
−0.998013 | + | 0.0630092i | \(0.979930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.82072 | − | 6.61769i | −0.319505 | − | 0.553399i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.57234 | − | 11.3836i | 0.545803 | − | 0.945359i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.60439 | + | 4.51093i | 0.213360 | + | 0.369550i | 0.952764 | − | 0.303712i | \(-0.0982261\pi\) |
−0.739404 | + | 0.673262i | \(0.764893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.261450 | + | 0.452845i | −0.0212765 | + | 0.0368520i | −0.876468 | − | 0.481461i | \(-0.840106\pi\) |
0.855191 | + | 0.518313i | \(0.173440\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.15383 | + | 3.73054i | 0.173000 | + | 0.299644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.86398 | 0.707422 | 0.353711 | − | 0.935355i | \(-0.384920\pi\) | ||||
0.353711 | + | 0.935355i | \(0.384920\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.794182 | − | 0.0289431i | 0.0625903 | − | 0.00228104i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9814 | + | 19.0204i | −0.860132 | + | 1.48979i | 0.0116689 | + | 0.999932i | \(0.496286\pi\) |
−0.871801 | + | 0.489860i | \(0.837048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.65019 | − | 2.85821i | 0.127695 | − | 0.221175i | −0.795088 | − | 0.606494i | \(-0.792575\pi\) |
0.922783 | + | 0.385319i | \(0.125909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.07234 | − | 8.78555i | −0.390180 | − | 0.675812i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.1075 | −1.45272 | −0.726360 | − | 0.687315i | \(-0.758789\pi\) | ||||
−0.726360 | + | 0.687315i | \(0.758789\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.48143 | + | 5.55264i | 0.263171 | + | 0.419740i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.03706 | − | 13.9206i | −0.600718 | − | 1.04047i | −0.992712 | − | 0.120507i | \(-0.961548\pi\) |
0.391994 | − | 0.919968i | \(-0.371785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.05308 | 0.598581 | 0.299291 | − | 0.954162i | \(-0.403250\pi\) | ||||
0.299291 | + | 0.954162i | \(0.403250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.58836 | 0.116779 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.57598 | 0.627138 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.9629 | −1.73389 | −0.866946 | − | 0.498402i | \(-0.833920\pi\) | ||||
−0.866946 | + | 0.498402i | \(0.833920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.76509 | 0.702907 | 0.351453 | − | 0.936205i | \(-0.385688\pi\) | ||||
0.351453 | + | 0.936205i | \(0.385688\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2436 | 1.29980 | 0.649900 | − | 0.760020i | \(-0.274811\pi\) | ||||
0.649900 | + | 0.760020i | \(0.274811\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.04944 | − | 15.6741i | −0.641498 | − | 1.11111i | −0.985098 | − | 0.171991i | \(-0.944980\pi\) |
0.343601 | − | 0.939116i | \(-0.388353\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.8807 | − | 0.797418i | 1.53572 | − | 0.0559678i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.33379 | −0.651900 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.63781 | − | 9.76497i | −0.389975 | − | 0.675457i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.166208 | + | 0.287880i | −0.0114422 | + | 0.0198185i | −0.871690 | − | 0.490058i | \(-0.836976\pi\) |
0.860248 | + | 0.509877i | \(0.170309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.32327 | + | 2.29197i | −0.0902464 | + | 0.156311i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.35896 | + | 6.34053i | −0.228021 | + | 0.430423i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.9752 | 1.74728 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.16621 | − | 5.48403i | −0.212025 | − | 0.367238i | 0.740323 | − | 0.672251i | \(-0.234672\pi\) |
−0.952348 | + | 0.305013i | \(0.901339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6545 | − | 20.1862i | 0.773537 | − | 1.33981i | −0.162075 | − | 0.986778i | \(-0.551819\pi\) |
0.935613 | − | 0.353028i | \(-0.114848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.47710 | + | 4.29046i | 0.163691 | + | 0.283522i | 0.936190 | − | 0.351495i | \(-0.114327\pi\) |
−0.772498 | + | 0.635017i | \(0.780993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.13781 | − | 12.3630i | 0.467613 | − | 0.809930i | −0.531702 | − | 0.846932i | \(-0.678447\pi\) |
0.999315 | + | 0.0370017i | \(0.0117807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.11745 | + | 3.66754i | 0.138127 | + | 0.239244i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.48762 | − | 4.30868i | 0.160911 | − | 0.278706i | −0.774285 | − | 0.632837i | \(-0.781890\pi\) |
0.935196 | + | 0.354132i | \(0.115224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | − | 11.2583i | 0.418702 | − | 0.725213i | −0.577107 | − | 0.816668i | \(-0.695819\pi\) |
0.995809 | + | 0.0914555i | \(0.0291519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.84362 | − | 10.0081i | 0.309448 | − | 0.639392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.0760 | − | 29.5765i | −1.08652 | − | 1.88191i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.43268 | 0.153549 | 0.0767746 | − | 0.997048i | \(-0.475538\pi\) | ||||
0.0767746 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.477100 | −0.0299950 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.493810 | − | 0.855304i | −0.0308030 | − | 0.0533524i | 0.850213 | − | 0.526439i | \(-0.176473\pi\) |
−0.881016 | + | 0.473087i | \(0.843140\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.40545 | + | 2.24159i | 0.0873302 | + | 0.139286i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.59269 | + | 14.8830i | −0.529848 | + | 0.917724i | 0.469545 | + | 0.882908i | \(0.344418\pi\) |
−0.999394 | + | 0.0348158i | \(0.988916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.88255 | − | 6.72477i | 0.238503 | − | 0.413099i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4523 | − | 19.8360i | −0.698262 | − | 1.20942i | −0.969069 | − | 0.246791i | \(-0.920624\pi\) |
0.270807 | − | 0.962634i | \(-0.412709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00364 | + | 12.1307i | −0.425441 | + | 0.736885i | −0.996462 | − | 0.0840504i | \(-0.973214\pi\) |
0.571021 | + | 0.820936i | \(0.306548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.96727 | − | 3.40741i | −0.118631 | − | 0.205474i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1476 | + | 24.5044i | −0.850049 | + | 1.47233i | 0.0311139 | + | 0.999516i | \(0.490095\pi\) |
−0.881163 | + | 0.472813i | \(0.843239\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.79782 | + | 15.2383i | 0.524834 | + | 0.909039i | 0.999582 | + | 0.0289175i | \(0.00920600\pi\) |
−0.474748 | + | 0.880122i | \(0.657461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.5229 | 1.10107 | 0.550536 | − | 0.834811i | \(-0.314423\pi\) | ||||
0.550536 | + | 0.834811i | \(0.314423\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.25890 | − | 13.1724i | −0.487508 | − | 0.777541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.07598 | + | 10.5239i | −0.357411 | + | 0.619054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.04256 | − | 12.1981i | 0.411431 | − | 0.712619i | −0.583616 | − | 0.812030i | \(-0.698362\pi\) |
0.995046 | + | 0.0994108i | \(0.0316958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.14400 | + | 8.90966i | 0.299495 | + | 0.518741i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.44506 | −0.0835698 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.40545 | + | 0.160552i | −0.253926 | + | 0.00925405i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.55563 | − | 6.15854i | −0.203595 | − | 0.352637i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.85532 | 0.334180 | 0.167090 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167090 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.810892 | 0.0459815 | 0.0229907 | − | 0.999736i | \(-0.492681\pi\) | ||||
0.0229907 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5760 | 0.597790 | 0.298895 | − | 0.954286i | \(-0.403382\pi\) | ||||
0.298895 | + | 0.954286i | \(0.403382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1964 | −0.685018 | −0.342509 | − | 0.939515i | \(-0.611277\pi\) | ||||
−0.342509 | + | 0.939515i | \(0.611277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.1447 | −0.735961 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.3287 | 2.13267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.95853 | − | 10.3205i | −0.330520 | − | 0.572477i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.30223 | + | 6.23345i | −0.182058 | + | 0.343661i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6662 | 0.861093 | 0.430546 | − | 0.902568i | \(-0.358321\pi\) | ||||
0.430546 | + | 0.902568i | \(0.358321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.98398 | + | 13.8287i | 0.436211 | + | 0.755540i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.21201 | + | 7.29541i | −0.229443 | + | 0.397406i | −0.957643 | − | 0.287958i | \(-0.907024\pi\) |
0.728200 | + | 0.685364i | \(0.240357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.15383 | − | 3.73054i | 0.116636 | − | 0.202020i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4098 | − | 2.01993i | 0.994035 | − | 0.109066i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.567323 | 0.0304555 | 0.0152277 | − | 0.999884i | \(-0.495153\pi\) | ||||
0.0152277 | + | 0.999884i | \(0.495153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.00364189 | − | 0.00630794i | −0.000194946 | − | 0.000337656i | 0.865928 | − | 0.500169i | \(-0.166729\pi\) |
−0.866123 | + | 0.499831i | \(0.833395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.32691 | − | 5.76238i | 0.177074 | − | 0.306701i | −0.763803 | − | 0.645449i | \(-0.776670\pi\) |
0.940877 | + | 0.338748i | \(0.110004\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1025 | + | 17.4981i | 0.536186 | + | 0.928702i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.398568 | + | 0.690339i | −0.0210356 | + | 0.0364347i | −0.876352 | − | 0.481672i | \(-0.840030\pi\) |
0.855316 | + | 0.518107i | \(0.173363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6971 | − | 27.1881i | −0.826162 | − | 1.43095i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7491 | + | 22.0820i | −0.667317 | + | 1.15583i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.71634 | + | 13.3651i | −0.402790 | + | 0.697652i | −0.994061 | − | 0.108820i | \(-0.965293\pi\) |
0.591272 | + | 0.806472i | \(0.298626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.9258 | − | 0.471067i | 0.671074 | − | 0.0244566i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.12110 | − | 8.87000i | −0.265160 | − | 0.459271i | 0.702445 | − | 0.711738i | \(-0.252092\pi\) |
−0.967606 | + | 0.252467i | \(0.918758\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.8131 | −2.05048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0087 | −1.28461 | −0.642304 | − | 0.766450i | \(-0.722021\pi\) | ||||
−0.642304 | + | 0.766450i | \(0.722021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.13348 | + | 5.42734i | 0.160113 | + | 0.277324i | 0.934909 | − | 0.354887i | \(-0.115481\pi\) |
−0.774796 | + | 0.632211i | \(0.782147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.12474 | + | 5.89841i | −0.159251 | + | 0.300611i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8171 | + | 18.7357i | −0.548448 | + | 0.949940i | 0.449933 | + | 0.893062i | \(0.351448\pi\) |
−0.998381 | + | 0.0568774i | \(0.981886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.810892 | − | 1.40451i | 0.0410086 | − | 0.0710290i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.66071 | − | 11.5367i | −0.335137 | − | 0.580473i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.05308 | − | 3.55605i | 0.103041 | − | 0.178473i | −0.809895 | − | 0.586575i | \(-0.800476\pi\) |
0.912936 | + | 0.408102i | \(0.133809\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.37085 | + | 14.4987i | 0.418021 | + | 0.724033i | 0.995740 | − | 0.0922024i | \(-0.0293907\pi\) |
−0.577720 | + | 0.816235i | \(0.696057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.52359 | − | 11.2992i | 0.324963 | − | 0.562853i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.794182 | − | 1.37556i | −0.0393661 | − | 0.0681842i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.76509 | −0.433406 | −0.216703 | − | 0.976238i | \(-0.569530\pi\) | ||||
−0.216703 | + | 0.976238i | \(0.569530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.02221 | + | 15.1431i | −0.394747 | + | 0.745144i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.87890 | + | 3.25436i | −0.0922318 | + | 0.159750i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.210149 | + | 0.363988i | −0.0102664 | + | 0.0177820i | −0.871113 | − | 0.491083i | \(-0.836601\pi\) |
0.860847 | + | 0.508865i | \(0.169935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.28799 | + | 5.69497i | 0.160247 | + | 0.277556i | 0.934957 | − | 0.354761i | \(-0.115438\pi\) |
−0.774710 | + | 0.632316i | \(0.782104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.3745 | 0.648758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.54511 | − | 10.4672i | 0.268347 | − | 0.506544i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0439 | + | 19.1287i | 0.531968 | + | 0.921395i | 0.999304 | + | 0.0373155i | \(0.0118806\pi\) |
−0.467336 | + | 0.884080i | \(0.654786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.43268 | −0.453306 | −0.226653 | − | 0.973976i | \(-0.572778\pi\) | ||||
−0.226653 | + | 0.973976i | \(0.572778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.13231 | −0.102002 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.2064 | 1.48940 | 0.744701 | − | 0.667398i | \(-0.232592\pi\) | ||||
0.744701 | + | 0.667398i | \(0.232592\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0545 | 0.620236 | 0.310118 | − | 0.950698i | \(-0.399631\pi\) | ||||
0.310118 | + | 0.950698i | \(0.399631\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.09888 | −0.241710 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.91706 | 0.468015 | 0.234008 | − | 0.972235i | \(-0.424816\pi\) | ||||
0.234008 | + | 0.972235i | \(0.424816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.66690 | + | 8.08330i | 0.219756 | + | 0.380628i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.46431 | + | 17.8653i | −0.443694 | + | 0.837538i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.5229 | −1.14713 | −0.573566 | − | 0.819159i | \(-0.694441\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694441\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.75526 | − | 3.04020i | −0.0817506 | − | 0.141596i | 0.822251 | − | 0.569125i | \(-0.192718\pi\) |
−0.904002 | + | 0.427528i | \(0.859384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.69413 | + | 15.0587i | −0.404050 | + | 0.699836i | −0.994210 | − | 0.107451i | \(-0.965731\pi\) |
0.590160 | + | 0.807286i | \(0.299065\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.69894 | − | 11.6029i | 0.309990 | − | 0.536918i | −0.668370 | − | 0.743829i | \(-0.733008\pi\) |
0.978360 | + | 0.206911i | \(0.0663410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4512 | + | 23.5036i | −0.574945 | + | 1.08529i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.64654 | 0.121688 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.79232 | − | 15.2287i | −0.403419 | − | 0.698743i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.4029 | + | 18.0183i | −0.475321 | + | 0.823279i | −0.999600 | − | 0.0282667i | \(-0.991001\pi\) |
0.524280 | + | 0.851546i | \(0.324335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.40545 | − | 4.16635i | −0.109679 | − | 0.189969i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.13093 | + | 1.95882i | −0.0513528 | + | 0.0889456i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.2472 | − | 28.1410i | −0.736231 | − | 1.27519i | −0.954181 | − | 0.299230i | \(-0.903270\pi\) |
0.217950 | − | 0.975960i | \(-0.430063\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.66071 | + | 16.7328i | −0.435982 | + | 0.755142i | −0.997375 | − | 0.0724067i | \(-0.976932\pi\) |
0.561394 | + | 0.827549i | \(0.310265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3411 | − | 38.6959i | 1.00619 | − | 1.74277i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.7552 | + | 29.7402i | −0.706717 | + | 1.33403i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.57530 | − | 9.65670i | −0.249585 | − | 0.432293i | 0.713826 | − | 0.700323i | \(-0.246961\pi\) |
−0.963411 | + | 0.268030i | \(0.913627\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7651 | −1.81763 | −0.908813 | − | 0.417204i | \(-0.863010\pi\) | ||||
−0.908813 | + | 0.417204i | \(0.863010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1135 | 0.850537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.722528 | + | 1.25146i | 0.0320255 | + | 0.0554698i | 0.881594 | − | 0.472009i | \(-0.156471\pi\) |
−0.849568 | + | 0.527478i | \(0.823138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.4443 | + | 1.54684i | −1.87762 | + | 0.0684280i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.84362 | − | 8.38940i | 0.213436 | − | 0.369681i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.11745 | − | 3.66754i | 0.0931255 | − | 0.161298i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.64214 | − | 16.7007i | −0.422430 | − | 0.731670i | 0.573747 | − | 0.819033i | \(-0.305489\pi\) |
−0.996177 | + | 0.0873630i | \(0.972156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.3454 | − | 31.7752i | 0.802189 | − | 1.38943i | −0.115984 | − | 0.993251i | \(-0.537002\pi\) |
0.918173 | − | 0.396180i | \(-0.129665\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.32141 | + | 12.6811i | 0.318926 | + | 0.552396i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4549 | − | 19.8404i | 0.498039 | − | 0.862628i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.1353 | + | 24.4830i | 0.612266 | + | 1.06048i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.90249 | −0.211953 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.0891 | + | 0.809332i | −0.477639 | + | 0.0348604i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.62543 | + | 2.81532i | −0.0698825 | + | 0.121040i | −0.898849 | − | 0.438258i | \(-0.855596\pi\) |
0.828967 | + | 0.559298i | \(0.188929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.81708 | + | 3.14728i | −0.0778352 | + | 0.134815i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.95853 | + | 5.12432i | 0.126498 | + | 0.219100i | 0.922317 | − | 0.386433i | \(-0.126293\pi\) |
−0.795820 | + | 0.605534i | \(0.792960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58.7476 | −2.50273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.3876 | − | 19.6081i | 0.441724 | − | 0.833820i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8040 | − | 22.1772i | −0.542523 | − | 0.939678i | −0.998758 | − | 0.0498188i | \(-0.984136\pi\) |
0.456235 | − | 0.889859i | \(-0.349198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.01594 | 0.339038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −46.6377 | −1.96555 | −0.982773 | − | 0.184817i | \(-0.940831\pi\) | ||||
−0.982773 | + | 0.184817i | \(0.940831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.9171 | 1.30069 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.1978 | −1.30788 | −0.653939 | − | 0.756547i | \(-0.726885\pi\) | ||||
−0.653939 | + | 0.756547i | \(0.726885\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6762 | 0.656030 | 0.328015 | − | 0.944672i | \(-0.393620\pi\) | ||||
0.328015 | + | 0.944672i | \(0.393620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.744051 | −0.0310291 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.99567 | + | 12.1169i | 0.291234 | + | 0.504431i | 0.974102 | − | 0.226110i | \(-0.0726010\pi\) |
−0.682868 | + | 0.730542i | \(0.739268\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.25526 | + | 0.227966i | −0.259512 | + | 0.00945763i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.76509 | −0.321597 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.44801 | + | 2.50803i | 0.0597658 | + | 0.103517i | 0.894360 | − | 0.447348i | \(-0.147631\pi\) |
−0.834594 | + | 0.550865i | \(0.814298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.62612 | − | 16.6729i | 0.396637 | − | 0.686996i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.04394 | − | 3.54021i | 0.0839346 | − | 0.145379i | −0.821002 | − | 0.570925i | \(-0.806585\pi\) |
0.904937 | + | 0.425546i | \(0.139918\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0531 | − | 19.2238i | −0.494128 | − | 0.788100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.7651 | −0.807580 | −0.403790 | − | 0.914852i | \(-0.632307\pi\) | ||||
−0.403790 | + | 0.914852i | \(0.632307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4320 | − | 23.2649i | −0.547902 | − | 0.948994i | −0.998418 | − | 0.0562261i | \(-0.982093\pi\) |
0.450516 | − | 0.892768i | \(-0.351240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.73236 | + | 11.6608i | −0.273709 | + | 0.474079i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.62110 | − | 13.2001i | −0.309331 | − | 0.535777i | 0.668885 | − | 0.743366i | \(-0.266772\pi\) |
−0.978216 | + | 0.207589i | \(0.933438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.41342 | − | 11.1084i | 0.259459 | − | 0.449396i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.36033 | − | 2.35617i | −0.0549434 | − | 0.0951648i | 0.837246 | − | 0.546827i | \(-0.184165\pi\) |
−0.892189 | + | 0.451662i | \(0.850831\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.21812 | − | 15.9663i | 0.371108 | − | 0.642777i | −0.618629 | − | 0.785684i | \(-0.712311\pi\) |
0.989736 | + | 0.142906i | \(0.0456448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0537728 | − | 0.0931373i | 0.00216131 | − | 0.00374350i | −0.864943 | − | 0.501871i | \(-0.832645\pi\) |
0.867104 | + | 0.498127i | \(0.165979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.51169 | − | 7.19583i | −0.180757 | − | 0.288295i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.23924 | + | 5.61053i | 0.129570 | + | 0.224421i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.39926 | 0.215282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7266 | −1.42225 | −0.711126 | − | 0.703064i | \(-0.751815\pi\) | ||||
−0.711126 | + | 0.703064i | \(0.751815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.6738 | + | 18.4875i | 0.423576 | + | 0.733655i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.5869 | + | 2.45133i | −1.33076 | + | 0.0971254i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.65638 | − | 14.9933i | 0.341906 | − | 0.592199i | −0.642880 | − | 0.765967i | \(-0.722261\pi\) |
0.984787 | + | 0.173767i | \(0.0555941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.4821 | + | 25.0838i | −0.571119 | + | 0.989207i | 0.425332 | + | 0.905037i | \(0.360157\pi\) |
−0.996451 | + | 0.0841700i | \(0.973176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.27816 | + | 2.21384i | 0.0502497 | + | 0.0870350i | 0.890056 | − | 0.455851i | \(-0.150665\pi\) |
−0.839807 | + | 0.542886i | \(0.817332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.14400 | − | 8.90966i | 0.201920 | − | 0.349735i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.9883 | + | 25.9605i | 0.586538 | + | 1.01591i | 0.994682 | + | 0.102996i | \(0.0328428\pi\) |
−0.408144 | + | 0.912918i | \(0.633824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.52290 | + | 4.36979i | −0.0985779 | + | 0.170742i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.63162 | − | 13.2183i | −0.297286 | − | 0.514914i | 0.678228 | − | 0.734851i | \(-0.262748\pi\) |
−0.975514 | + | 0.219937i | \(0.929415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.2522 | −1.05999 | −0.529994 | − | 0.848001i | \(-0.677806\pi\) | ||||
−0.529994 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.9654 | + | 26.3618i | −0.541555 | + | 1.02227i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.24288 | + | 2.15273i | −0.0481245 | + | 0.0833541i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.55563 | + | 6.15854i | −0.137264 | + | 0.237748i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2280 | + | 40.2320i | 0.895372 | + | 1.55083i | 0.833344 | + | 0.552755i | \(0.186423\pi\) |
0.0620280 | + | 0.998074i | \(0.480243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.09888 | −0.195966 | −0.0979830 | − | 0.995188i | \(-0.531239\pi\) | ||||
−0.0979830 | + | 0.995188i | \(0.531239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.76509 | + | 0.137215i | −0.144491 | + | 0.00526582i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.77197 | − | 13.4614i | −0.297386 | − | 0.515088i | 0.678151 | − | 0.734923i | \(-0.262782\pi\) |
−0.975537 | + | 0.219835i | \(0.929448\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.7738 | −1.29043 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.5192 | −0.896009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.2967 | −0.886246 | −0.443123 | − | 0.896461i | \(-0.646130\pi\) | ||||
−0.443123 | + | 0.896461i | \(0.646130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.7330 | −0.786449 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.7280 | −1.20178 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.6464 | 1.72404 | 0.862020 | − | 0.506874i | \(-0.169199\pi\) | ||||
0.862020 | + | 0.506874i | \(0.169199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.54944 | − | 6.14781i | −0.133870 | − | 0.231869i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.9123 | + | 26.9740i | 0.636053 | + | 1.01446i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0014 | 0.676056 | 0.338028 | − | 0.941136i | \(-0.390240\pi\) | ||||
0.338028 | + | 0.941136i | \(0.390240\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.407305 | − | 0.705474i | −0.0152537 | − | 0.0264202i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.06870 | − | 10.5113i | 0.226957 | − | 0.393100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4389 | − | 31.9371i | 0.687654 | − | 1.19105i | −0.284941 | − | 0.958545i | \(-0.591974\pi\) |
0.972595 | − | 0.232506i | \(-0.0746926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.1254 | − | 0.587674i | 0.600542 | − | 0.0218861i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.4995 | −0.761333 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2429 | − | 26.4014i | −0.565327 | − | 0.979175i | −0.997019 | − | 0.0771543i | \(-0.975417\pi\) |
0.431692 | − | 0.902021i | \(-0.357917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.49814 | + | 7.79101i | −0.166370 | + | 0.288161i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.07530 | − | 5.32657i | −0.113589 | − | 0.196741i | 0.803626 | − | 0.595135i | \(-0.202901\pi\) |
−0.917215 | + | 0.398393i | \(0.869568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.98398 | − | 13.8287i | 0.294094 | − | 0.509385i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3912 | + | 35.3186i | 0.750103 | + | 1.29922i | 0.947772 | + | 0.318947i | \(0.103329\pi\) |
−0.197670 | + | 0.980269i | \(0.563337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.25271 | − | 12.5621i | 0.266076 | − | 0.460858i | −0.701769 | − | 0.712405i | \(-0.747606\pi\) |
0.967845 | + | 0.251547i | \(0.0809394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.13671 | + | 7.16500i | −0.151557 | + | 0.262505i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.33792 | − | 6.91867i | −0.158504 | − | 0.252803i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.09455 | + | 3.62787i | 0.0764314 | + | 0.132383i | 0.901708 | − | 0.432346i | \(-0.142314\pi\) |
−0.825276 | + | 0.564729i | \(0.808981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.830556 | −0.0302270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.38688 | 0.0867525 | 0.0433763 | − | 0.999059i | \(-0.486189\pi\) | ||||
0.0433763 | + | 0.999059i | \(0.486189\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.81708 | + | 3.14728i | 0.0658692 | + | 0.114089i | 0.897079 | − | 0.441870i | \(-0.145685\pi\) |
−0.831210 | + | 0.555959i | \(0.812351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.04944 | + | 0.220465i | −0.219005 | + | 0.00798138i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5803 | − | 26.9859i | 0.562573 | − | 0.974404i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.9672 | + | 34.5842i | −0.720035 | + | 1.24714i | 0.240950 | + | 0.970538i | \(0.422541\pi\) |
−0.960985 | + | 0.276600i | \(0.910792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0698 | − | 31.2978i | −0.649925 | − | 1.12570i | −0.983140 | − | 0.182853i | \(-0.941467\pi\) |
0.333215 | − | 0.942851i | \(-0.391867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.35896 | − | 5.81788i | 0.120657 | − | 0.208985i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.8578 | + | 36.1267i | 0.747308 | + | 1.29438i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1025 | − | 17.4981i | 0.361497 | − | 0.626131i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.03961 | + | 12.1930i | 0.251254 | + | 0.435186i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.6377 | 1.59116 | 0.795582 | − | 0.605846i | \(-0.207165\pi\) | ||||
0.795582 | + | 0.605846i | \(0.207165\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.3566 | + | 43.6319i | 0.972689 | + | 1.55137i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7694 | + | 18.6532i | −0.382433 | + | 0.662394i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.2836 | + | 45.5245i | −0.931012 | + | 1.61256i | −0.149418 | + | 0.988774i | \(0.547740\pi\) |
−0.781595 | + | 0.623786i | \(0.785593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.19777 | + | 12.4669i | 0.254639 | + | 0.441047i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.4981 | 0.899810 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.670538 | + | 1.06946i | 0.0236334 | + | 0.0376936i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.40290 | − | 12.8222i | −0.260272 | − | 0.450804i | 0.706042 | − | 0.708170i | \(-0.250479\pi\) |
−0.966314 | + | 0.257365i | \(0.917146\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0704 | −0.950571 | −0.475285 | − | 0.879832i | \(-0.657655\pi\) | ||||
−0.475285 | + | 0.879832i | \(0.657655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.8850 | −1.22197 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.8282 | 0.413817 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.8182 | −1.52926 | −0.764632 | − | 0.644467i | \(-0.777079\pi\) | ||||
−0.764632 | + | 0.644467i | \(0.777079\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.3425 | −1.09253 | −0.546265 | − | 0.837613i | \(-0.683951\pi\) | ||||
−0.546265 | + | 0.837613i | \(0.683951\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7665 | −0.513480 | −0.256740 | − | 0.966480i | \(-0.582648\pi\) | ||||
−0.256740 | + | 0.966480i | \(0.582648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0036 | − | 25.9871i | −0.521098 | − | 0.902568i | −0.999699 | − | 0.0245357i | \(-0.992189\pi\) |
0.478601 | − | 0.878033i | \(-0.341144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.4647 | − | 34.0200i | 0.570469 | − | 1.17872i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.24219 | 0.181414 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.0167 | + | 31.2059i | 0.622006 | + | 1.07735i | 0.989112 | + | 0.147167i | \(0.0470154\pi\) |
−0.367106 | + | 0.930179i | \(0.619651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7429 | + | 34.1957i | −0.680789 | + | 1.17916i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.05673 | − | 13.9547i | 0.277160 | − | 0.480055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.4134 | + | 0.816833i | −0.770134 | + | 0.0280667i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.300372 | −0.0102966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2658 | − | 21.2450i | −0.419972 | − | 0.727413i | 0.575964 | − | 0.817475i | \(-0.304627\pi\) |
−0.995936 | + | 0.0900617i | \(0.971294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.5240 | − | 25.1563i | 0.496130 | − | 0.859323i | −0.503860 | − | 0.863785i | \(-0.668087\pi\) |
0.999990 | + | 0.00446273i | \(0.00142053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6476 | + | 21.9064i | 0.431532 | + | 0.747435i | 0.997005 | − | 0.0773313i | \(-0.0246399\pi\) |
−0.565474 | + | 0.824766i | \(0.691307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.34981 | + | 2.33795i | −0.0459482 | + | 0.0795846i | −0.888085 | − | 0.459680i | \(-0.847964\pi\) |
0.842137 | + | 0.539264i | \(0.181298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1749 | − | 26.2836i | −0.515961 | − | 0.893671i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.66071 | + | 11.5367i | −0.225949 | + | 0.391355i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.1822 | − | 41.8847i | 0.819381 | − | 1.41921i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.7095 | + | 27.7663i | −0.497271 | + | 0.938672i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.54580 | + | 9.60561i | 0.187268 | + | 0.324358i | 0.944339 | − | 0.328975i | \(-0.106703\pi\) |
−0.757070 | + | 0.653334i | \(0.773370\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3942 | 1.36091 | 0.680457 | − | 0.732788i | \(-0.261781\pi\) | ||||
0.680457 | + | 0.732788i | \(0.261781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2581 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2836 | − | 35.1322i | −0.681056 | − | 1.17962i | −0.974659 | − | 0.223696i | \(-0.928188\pi\) |
0.293603 | − | 0.955928i | \(-0.405146\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6461 | + | 31.4219i | −0.558291 | + | 1.05386i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.46355 | − | 16.3913i | 0.316686 | − | 0.548516i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7658 | − | 22.1110i | 0.426713 | − | 0.739089i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.2218 | − | 19.4367i | −0.374267 | − | 0.648249i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1978 | − | 22.8592i | 0.439681 | − | 0.761551i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.39561 | + | 11.0775i | 0.212597 | + | 0.368230i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0567 | − | 26.0790i | 0.499950 | − | 0.865939i | −0.500050 | − | 0.865997i | \(-0.666685\pi\) |
1.00000 | 5.72941e-5i | \(1.82373e-5\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6113 | + | 25.3075i | 0.484093 | + | 0.838473i | 0.999833 | − | 0.0182717i | \(-0.00581638\pi\) |
−0.515740 | + | 0.856745i | \(0.672483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.75781 | 0.124365 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.39926 | + | 0.306102i | −0.277368 | + | 0.0101084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.52359 | − | 9.56714i | 0.182206 | − | 0.315591i | −0.760425 | − | 0.649426i | \(-0.775009\pi\) |
0.942632 | + | 0.333835i | \(0.108343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.5989 | − | 52.9988i | 1.00717 | − | 1.74448i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.23855 | − | 2.14523i | −0.0407233 | − | 0.0705348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.3338 | 1.38893 | 0.694463 | − | 0.719528i | \(-0.255642\pi\) | ||||
0.694463 | + | 0.719528i | \(0.255642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.5604 | + | 3.61715i | −1.62428 | + | 0.118547i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.81089 | + | 11.7968i | 0.222740 | + | 0.385797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7651 | −0.384349 | −0.192174 | − | 0.981361i | \(-0.561554\pi\) | ||||
−0.192174 | + | 0.981361i | \(0.561554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.5760 | −0.475164 | −0.237582 | − | 0.971368i | \(-0.576355\pi\) | ||||
−0.237582 | + | 0.971368i | \(0.576355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.76509 | 0.0574793 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.24357 | 0.202889 | 0.101444 | − | 0.994841i | \(-0.467654\pi\) | ||||
0.101444 | + | 0.994841i | \(0.467654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 77.2297 | 2.50698 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.0173 | −0.907570 | −0.453785 | − | 0.891111i | \(-0.649927\pi\) | ||||
−0.453785 | + | 0.891111i | \(0.649927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.0309 | − | 32.9624i | −0.615825 | − | 1.06664i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.8843 | − | 47.6634i | −0.965015 | − | 1.53913i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.6450 | −0.762742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.75526 | + | 13.4325i | 0.249651 | + | 0.432408i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.7837 | + | 27.3381i | −0.507568 | + | 0.879134i | 0.492393 | + | 0.870373i | \(0.336122\pi\) |
−0.999962 | + | 0.00876132i | \(0.997211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.82141 | − | 4.88683i | 0.0905434 | − | 0.156826i | −0.817196 | − | 0.576359i | \(-0.804473\pi\) |
0.907740 | + | 0.419533i | \(0.137806\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3454 | − | 29.2596i | −0.588127 | − | 0.938021i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.49304 | −0.207731 | −0.103865 | − | 0.994591i | \(-0.533121\pi\) | ||||
−0.103865 | + | 0.994591i | \(0.533121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.54944 | + | 4.41576i | 0.0814805 | + | 0.141128i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.1531 | − | 26.2460i | 0.483310 | − | 0.837118i | −0.516506 | − | 0.856283i | \(-0.672768\pi\) |
0.999816 | + | 0.0191658i | \(0.00610104\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4887 | + | 25.0952i | 0.461649 | + | 0.799599i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.250241 | − | 0.433430i | 0.00795720 | − | 0.0137823i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1669 | − | 19.3416i | −0.354728 | − | 0.614407i | 0.632343 | − | 0.774688i | \(-0.282093\pi\) |
−0.987071 | + | 0.160281i | \(0.948760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3738 | − | 24.8962i | 0.455680 | − | 0.789262i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.38255 | − | 7.59079i | 0.138797 | − | 0.240403i | −0.788245 | − | 0.615362i | \(-0.789010\pi\) |
0.927041 | + | 0.374959i | \(0.122343\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))