Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(846,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.846");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 846.10 | ||
Root | \(1.17141 - 2.02895i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.846 |
Dual form | 847.2.b.f.846.7 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.502754i | 0.355501i | 0.984076 | + | 0.177750i | \(0.0568820\pi\) | ||||
−0.984076 | + | 0.177750i | \(0.943118\pi\) | |||||||
\(3\) | 2.88003i | 1.66278i | 0.555686 | + | 0.831392i | \(0.312456\pi\) | ||||
−0.555686 | + | 0.831392i | \(0.687544\pi\) | |||||||
\(4\) | 1.74724 | 0.873619 | ||||||||
\(5\) | − | 0.602090i | − | 0.269263i | −0.990896 | − | 0.134631i | \(-0.957015\pi\) | ||
0.990896 | − | 0.134631i | \(-0.0429850\pi\) | |||||||
\(6\) | −1.44795 | −0.591121 | ||||||||
\(7\) | −2.34283 | + | 1.22930i | −0.885505 | + | 0.464630i | ||||
\(8\) | 1.88394i | 0.666073i | ||||||||
\(9\) | −5.29456 | −1.76485 | ||||||||
\(10\) | 0.302703 | 0.0957231 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.03209i | 1.45264i | ||||||||
\(13\) | −2.34283 | −0.649783 | −0.324891 | − | 0.945751i | \(-0.605328\pi\) | ||||
−0.324891 | + | 0.945751i | \(0.605328\pi\) | |||||||
\(14\) | −0.618034 | − | 1.17787i | −0.165177 | − | 0.314798i | ||||
\(15\) | 1.73403 | 0.447726 | ||||||||
\(16\) | 2.54732 | 0.636830 | ||||||||
\(17\) | −1.14524 | −0.277762 | −0.138881 | − | 0.990309i | \(-0.544351\pi\) | ||||
−0.138881 | + | 0.990309i | \(0.544351\pi\) | |||||||
\(18\) | − | 2.66186i | − | 0.627406i | ||||||
\(19\) | −5.07304 | −1.16384 | −0.581918 | − | 0.813248i | \(-0.697697\pi\) | ||||
−0.581918 | + | 0.813248i | \(0.697697\pi\) | |||||||
\(20\) | − | 1.05199i | − | 0.235233i | ||||||
\(21\) | −3.54041 | − | 6.74740i | −0.772580 | − | 1.47240i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.85410 | −0.803636 | −0.401818 | − | 0.915720i | \(-0.631622\pi\) | ||||
−0.401818 | + | 0.915720i | \(0.631622\pi\) | |||||||
\(24\) | −5.42580 | −1.10754 | ||||||||
\(25\) | 4.63749 | 0.927498 | ||||||||
\(26\) | − | 1.17787i | − | 0.230998i | ||||||
\(27\) | − | 6.60838i | − | 1.27178i | ||||||
\(28\) | −4.09347 | + | 2.14787i | −0.773594 | + | 0.405910i | ||||
\(29\) | 2.15911i | 0.400936i | 0.979700 | + | 0.200468i | \(0.0642463\pi\) | ||||
−0.979700 | + | 0.200468i | \(0.935754\pi\) | |||||||
\(30\) | 0.871793i | 0.159167i | ||||||||
\(31\) | 6.23627i | 1.12007i | 0.828470 | + | 0.560034i | \(0.189212\pi\) | ||||
−0.828470 | + | 0.560034i | \(0.810788\pi\) | |||||||
\(32\) | 5.04855i | 0.892467i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.575775i | − | 0.0987447i | ||||||
\(35\) | 0.740147 | + | 1.41059i | 0.125108 | + | 0.238433i | ||||
\(36\) | −9.25085 | −1.54181 | ||||||||
\(37\) | −7.41056 | −1.21829 | −0.609144 | − | 0.793060i | \(-0.708487\pi\) | ||||
−0.609144 | + | 0.793060i | \(0.708487\pi\) | |||||||
\(38\) | − | 2.55049i | − | 0.413745i | ||||||
\(39\) | − | 6.74740i | − | 1.08045i | ||||||
\(40\) | 1.13430 | 0.179349 | ||||||||
\(41\) | 11.7597 | 1.83656 | 0.918279 | − | 0.395935i | \(-0.129579\pi\) | ||||
0.918279 | + | 0.395935i | \(0.129579\pi\) | |||||||
\(42\) | 3.39228 | − | 1.77995i | 0.523441 | − | 0.274653i | ||||
\(43\) | 1.73205i | 0.264135i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) | ||||
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.18780i | 0.475209i | ||||||||
\(46\) | − | 1.93767i | − | 0.285693i | ||||||
\(47\) | 9.92205i | 1.44728i | 0.690178 | + | 0.723640i | \(0.257532\pi\) | ||||
−0.690178 | + | 0.723640i | \(0.742468\pi\) | |||||||
\(48\) | 7.33635i | 1.05891i | ||||||||
\(49\) | 3.97766 | − | 5.76005i | 0.568237 | − | 0.822865i | ||||
\(50\) | 2.33152i | 0.329726i | ||||||||
\(51\) | − | 3.29833i | − | 0.461859i | ||||||
\(52\) | −4.09347 | −0.567663 | ||||||||
\(53\) | 6.12165 | 0.840873 | 0.420436 | − | 0.907322i | \(-0.361877\pi\) | ||||
0.420436 | + | 0.907322i | \(0.361877\pi\) | |||||||
\(54\) | 3.32239 | 0.452120 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.31592 | − | 4.41374i | −0.309478 | − | 0.589811i | ||||
\(57\) | − | 14.6105i | − | 1.93521i | ||||||
\(58\) | −1.08550 | −0.142533 | ||||||||
\(59\) | − | 4.70256i | − | 0.612221i | −0.951996 | − | 0.306111i | \(-0.900972\pi\) | ||
0.951996 | − | 0.306111i | \(-0.0990277\pi\) | |||||||
\(60\) | 3.02977 | 0.391142 | ||||||||
\(61\) | 8.70908 | 1.11508 | 0.557542 | − | 0.830149i | \(-0.311745\pi\) | ||||
0.557542 | + | 0.830149i | \(0.311745\pi\) | |||||||
\(62\) | −3.13531 | −0.398185 | ||||||||
\(63\) | 12.4042 | − | 6.50858i | 1.56278 | − | 0.820004i | ||||
\(64\) | 2.55645 | 0.319557 | ||||||||
\(65\) | 1.41059i | 0.174962i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.46905 | −0.790320 | −0.395160 | − | 0.918612i | \(-0.629311\pi\) | ||||
−0.395160 | + | 0.918612i | \(0.629311\pi\) | |||||||
\(68\) | −2.00101 | −0.242658 | ||||||||
\(69\) | − | 11.0999i | − | 1.33627i | ||||||
\(70\) | −0.709180 | + | 0.372112i | −0.0847633 | + | 0.0444759i | ||||
\(71\) | 5.32603 | 0.632084 | 0.316042 | − | 0.948745i | \(-0.397646\pi\) | ||||
0.316042 | + | 0.948745i | \(0.397646\pi\) | |||||||
\(72\) | − | 9.97462i | − | 1.17552i | ||||||
\(73\) | 2.49756 | 0.292317 | 0.146159 | − | 0.989261i | \(-0.453309\pi\) | ||||
0.146159 | + | 0.989261i | \(0.453309\pi\) | |||||||
\(74\) | − | 3.72569i | − | 0.433102i | ||||||
\(75\) | 13.3561i | 1.54223i | ||||||||
\(76\) | −8.86381 | −1.01675 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.39228 | 0.384100 | ||||||||
\(79\) | − | 1.19060i | − | 0.133953i | −0.997755 | − | 0.0669766i | \(-0.978665\pi\) | ||
0.997755 | − | 0.0669766i | \(-0.0213353\pi\) | |||||||
\(80\) | − | 1.53371i | − | 0.171474i | ||||||
\(81\) | 3.14866 | 0.349851 | ||||||||
\(82\) | 5.91224i | 0.652898i | ||||||||
\(83\) | −7.90565 | −0.867758 | −0.433879 | − | 0.900971i | \(-0.642855\pi\) | ||||
−0.433879 | + | 0.900971i | \(0.642855\pi\) | |||||||
\(84\) | −6.18594 | − | 11.7893i | −0.674941 | − | 1.28632i | ||||
\(85\) | 0.689539i | 0.0747910i | ||||||||
\(86\) | −0.870796 | −0.0939003 | ||||||||
\(87\) | −6.21828 | −0.666670 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9963i | 1.27161i | 0.771850 | + | 0.635804i | \(0.219331\pi\) | ||||
−0.771850 | + | 0.635804i | \(0.780669\pi\) | |||||||
\(90\) | −1.60268 | −0.168937 | ||||||||
\(91\) | 5.48883 | − | 2.88003i | 0.575386 | − | 0.301909i | ||||
\(92\) | −6.73403 | −0.702072 | ||||||||
\(93\) | −17.9606 | −1.86243 | ||||||||
\(94\) | −4.98835 | −0.514509 | ||||||||
\(95\) | 3.05443i | 0.313377i | ||||||||
\(96\) | −14.5400 | −1.48398 | ||||||||
\(97\) | − | 5.82158i | − | 0.591092i | −0.955328 | − | 0.295546i | \(-0.904498\pi\) | ||
0.955328 | − | 0.295546i | \(-0.0955016\pi\) | |||||||
\(98\) | 2.89589 | + | 1.99978i | 0.292529 | + | 0.202009i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.10280 | 0.810280 | ||||||||
\(101\) | 14.4443 | 1.43727 | 0.718633 | − | 0.695390i | \(-0.244768\pi\) | ||||
0.718633 | + | 0.695390i | \(0.244768\pi\) | |||||||
\(102\) | 1.65825 | 0.164191 | ||||||||
\(103\) | − | 5.61792i | − | 0.553550i | −0.960935 | − | 0.276775i | \(-0.910734\pi\) | ||
0.960935 | − | 0.276775i | \(-0.0892657\pi\) | |||||||
\(104\) | − | 4.41374i | − | 0.432803i | ||||||
\(105\) | −4.06254 | + | 2.13164i | −0.396463 | + | 0.208027i | ||||
\(106\) | 3.07768i | 0.298931i | ||||||||
\(107\) | 8.02953i | 0.776244i | 0.921608 | + | 0.388122i | \(0.126876\pi\) | ||||
−0.921608 | + | 0.388122i | \(0.873124\pi\) | |||||||
\(108\) | − | 11.5464i | − | 1.11106i | ||||||
\(109\) | − | 13.2943i | − | 1.27336i | −0.771128 | − | 0.636680i | \(-0.780307\pi\) | ||
0.771128 | − | 0.636680i | \(-0.219693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 21.3426i | − | 2.02575i | ||||||
\(112\) | −5.96792 | + | 3.13141i | −0.563916 | + | 0.295890i | ||||
\(113\) | −1.00658 | −0.0946911 | −0.0473456 | − | 0.998879i | \(-0.515076\pi\) | ||||
−0.0473456 | + | 0.998879i | \(0.515076\pi\) | |||||||
\(114\) | 7.34549 | 0.687968 | ||||||||
\(115\) | 2.32051i | 0.216389i | ||||||||
\(116\) | 3.77247i | 0.350265i | ||||||||
\(117\) | 12.4042 | 1.14677 | ||||||||
\(118\) | 2.36423 | 0.217645 | ||||||||
\(119\) | 2.68310 | − | 1.40784i | 0.245960 | − | 0.129057i | ||||
\(120\) | 3.26682i | 0.298218i | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.37853i | 0.396413i | ||||||||
\(123\) | 33.8683i | 3.05380i | ||||||||
\(124\) | 10.8963i | 0.978513i | ||||||||
\(125\) | − | 5.80263i | − | 0.519003i | ||||||
\(126\) | 3.27222 | + | 6.23627i | 0.291512 | + | 0.555571i | ||||
\(127\) | 9.46758i | 0.840112i | 0.907498 | + | 0.420056i | \(0.137990\pi\) | ||||
−0.907498 | + | 0.420056i | \(0.862010\pi\) | |||||||
\(128\) | 11.3824i | 1.00607i | ||||||||
\(129\) | −4.98835 | −0.439200 | ||||||||
\(130\) | −0.709180 | −0.0621992 | ||||||||
\(131\) | 11.5794 | 1.01170 | 0.505848 | − | 0.862623i | \(-0.331180\pi\) | ||||
0.505848 | + | 0.862623i | \(0.331180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8852 | − | 6.23627i | 1.03058 | − | 0.540753i | ||||
\(134\) | − | 3.25234i | − | 0.280959i | ||||||
\(135\) | −3.97884 | −0.342444 | ||||||||
\(136\) | − | 2.15757i | − | 0.185010i | ||||||
\(137\) | 9.87920 | 0.844037 | 0.422019 | − | 0.906587i | \(-0.361322\pi\) | ||||
0.422019 | + | 0.906587i | \(0.361322\pi\) | |||||||
\(138\) | 5.58053 | 0.475046 | ||||||||
\(139\) | −10.2161 | −0.866521 | −0.433260 | − | 0.901269i | \(-0.642637\pi\) | ||||
−0.433260 | + | 0.901269i | \(0.642637\pi\) | |||||||
\(140\) | 1.29321 | + | 2.46464i | 0.109296 | + | 0.208300i | ||||
\(141\) | −28.5758 | −2.40652 | ||||||||
\(142\) | 2.67769i | 0.224706i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −13.4869 | −1.12391 | ||||||||
\(145\) | 1.29998 | 0.107957 | ||||||||
\(146\) | 1.25566i | 0.103919i | ||||||||
\(147\) | 16.5891 | + | 11.4558i | 1.36825 | + | 0.944856i | ||||
\(148\) | −12.9480 | −1.06432 | ||||||||
\(149\) | 4.58975i | 0.376007i | 0.982168 | + | 0.188003i | \(0.0602016\pi\) | ||||
−0.982168 | + | 0.188003i | \(0.939798\pi\) | |||||||
\(150\) | −6.71483 | −0.548264 | ||||||||
\(151\) | 13.1434i | 1.06960i | 0.844979 | + | 0.534799i | \(0.179613\pi\) | ||||
−0.844979 | + | 0.534799i | \(0.820387\pi\) | |||||||
\(152\) | − | 9.55730i | − | 0.775200i | ||||||
\(153\) | 6.06355 | 0.490209 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.75480 | 0.301592 | ||||||||
\(156\) | − | 11.7893i | − | 0.943901i | ||||||
\(157\) | − | 3.09105i | − | 0.246693i | −0.992364 | − | 0.123346i | \(-0.960637\pi\) | ||
0.992364 | − | 0.123346i | \(-0.0393626\pi\) | |||||||
\(158\) | 0.598580 | 0.0476205 | ||||||||
\(159\) | 17.6305i | 1.39819i | ||||||||
\(160\) | 3.03968 | 0.240308 | ||||||||
\(161\) | 9.02949 | − | 4.73783i | 0.711623 | − | 0.373394i | ||||
\(162\) | 1.58300i | 0.124372i | ||||||||
\(163\) | −2.04431 | −0.160123 | −0.0800613 | − | 0.996790i | \(-0.525512\pi\) | ||||
−0.0800613 | + | 0.996790i | \(0.525512\pi\) | |||||||
\(164\) | 20.5470 | 1.60445 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3.97460i | − | 0.308489i | ||||||
\(167\) | 7.30977 | 0.565647 | 0.282824 | − | 0.959172i | \(-0.408729\pi\) | ||||
0.282824 | + | 0.959172i | \(0.408729\pi\) | |||||||
\(168\) | 12.7117 | − | 6.66991i | 0.980728 | − | 0.514595i | ||||
\(169\) | −7.51117 | −0.577782 | ||||||||
\(170\) | −0.346668 | −0.0265883 | ||||||||
\(171\) | 26.8595 | 2.05400 | ||||||||
\(172\) | 3.02631i | 0.230754i | ||||||||
\(173\) | −8.17601 | −0.621610 | −0.310805 | − | 0.950474i | \(-0.600599\pi\) | ||||
−0.310805 | + | 0.950474i | \(0.600599\pi\) | |||||||
\(174\) | − | 3.12627i | − | 0.237002i | ||||||
\(175\) | −10.8648 | + | 5.70085i | −0.821303 | + | 0.430944i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.5435 | 1.01799 | ||||||||
\(178\) | −6.03120 | −0.452058 | ||||||||
\(179\) | 6.22884 | 0.465565 | 0.232783 | − | 0.972529i | \(-0.425217\pi\) | ||||
0.232783 | + | 0.972529i | \(0.425217\pi\) | |||||||
\(180\) | 5.56984i | 0.415151i | ||||||||
\(181\) | 19.7608i | 1.46881i | 0.678712 | + | 0.734405i | \(0.262539\pi\) | ||||
−0.678712 | + | 0.734405i | \(0.737461\pi\) | |||||||
\(182\) | 1.44795 | + | 2.75953i | 0.107329 | + | 0.204550i | ||||
\(183\) | 25.0824i | 1.85414i | ||||||||
\(184\) | − | 7.26090i | − | 0.535280i | ||||||
\(185\) | 4.46182i | 0.328039i | ||||||||
\(186\) | − | 9.02978i | − | 0.662096i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 17.3362i | 1.26437i | ||||||||
\(189\) | 8.12367 | + | 15.4823i | 0.590910 | + | 1.12617i | ||||
\(190\) | −1.53563 | −0.111406 | ||||||||
\(191\) | 0.619944 | 0.0448576 | 0.0224288 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224288 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(192\) | 7.36266i | 0.531354i | ||||||||
\(193\) | 12.4324i | 0.894905i | 0.894308 | + | 0.447453i | \(0.147669\pi\) | ||||
−0.894308 | + | 0.447453i | \(0.852331\pi\) | |||||||
\(194\) | 2.92683 | 0.210134 | ||||||||
\(195\) | −4.06254 | −0.290925 | ||||||||
\(196\) | 6.94992 | − | 10.0642i | 0.496423 | − | 0.718871i | ||||
\(197\) | 12.4251i | 0.885254i | 0.896706 | + | 0.442627i | \(0.145953\pi\) | ||||
−0.896706 | + | 0.442627i | \(0.854047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.51876i | − | 0.603879i | −0.953327 | − | 0.301939i | \(-0.902366\pi\) | ||
0.953327 | − | 0.301939i | \(-0.0976340\pi\) | |||||||
\(200\) | 8.73675i | 0.617781i | ||||||||
\(201\) | − | 18.6310i | − | 1.31413i | ||||||
\(202\) | 7.26195i | 0.510949i | ||||||||
\(203\) | −2.65418 | − | 5.05841i | −0.186287 | − | 0.355031i | ||||
\(204\) | − | 5.76297i | − | 0.403488i | ||||||
\(205\) | − | 7.08040i | − | 0.494516i | ||||||
\(206\) | 2.82443 | 0.196788 | ||||||||
\(207\) | 20.4058 | 1.41830 | ||||||||
\(208\) | −5.96792 | −0.413801 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.07169 | − | 2.04246i | −0.0739538 | − | 0.140943i | ||||
\(211\) | − | 17.7450i | − | 1.22162i | −0.791777 | − | 0.610810i | \(-0.790844\pi\) | ||
0.791777 | − | 0.610810i | \(-0.209156\pi\) | |||||||
\(212\) | 10.6960 | 0.734603 | ||||||||
\(213\) | 15.3391i | 1.05102i | ||||||||
\(214\) | −4.03688 | −0.275955 | ||||||||
\(215\) | 1.04285 | 0.0711218 | ||||||||
\(216\) | 12.4498 | 0.847101 | ||||||||
\(217\) | −7.66623 | − | 14.6105i | −0.520418 | − | 0.991825i | ||||
\(218\) | 6.68375 | 0.452681 | ||||||||
\(219\) | 7.19303i | 0.486060i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.68310 | 0.180485 | ||||||||
\(222\) | 10.7301 | 0.720156 | ||||||||
\(223\) | − | 1.48564i | − | 0.0994855i | −0.998762 | − | 0.0497428i | \(-0.984160\pi\) | ||
0.998762 | − | 0.0497428i | \(-0.0158401\pi\) | |||||||
\(224\) | −6.20617 | − | 11.8279i | −0.414667 | − | 0.790283i | ||||
\(225\) | −24.5534 | −1.63690 | ||||||||
\(226\) | − | 0.506063i | − | 0.0336628i | ||||||
\(227\) | 23.9850 | 1.59194 | 0.795971 | − | 0.605335i | \(-0.206961\pi\) | ||||
0.795971 | + | 0.605335i | \(0.206961\pi\) | |||||||
\(228\) | − | 25.5280i | − | 1.69063i | ||||||
\(229\) | − | 0.364750i | − | 0.0241033i | −0.999927 | − | 0.0120517i | \(-0.996164\pi\) | ||
0.999927 | − | 0.0120517i | \(-0.00383626\pi\) | |||||||
\(230\) | −1.16665 | −0.0769265 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.06763 | −0.267053 | ||||||||
\(233\) | − | 2.64448i | − | 0.173246i | −0.996241 | − | 0.0866229i | \(-0.972392\pi\) | ||
0.996241 | − | 0.0866229i | \(-0.0276075\pi\) | |||||||
\(234\) | 6.23627i | 0.407678i | ||||||||
\(235\) | 5.97397 | 0.389699 | ||||||||
\(236\) | − | 8.21649i | − | 0.534848i | ||||||
\(237\) | 3.42897 | 0.222735 | ||||||||
\(238\) | 0.707799 | + | 1.34894i | 0.0458798 | + | 0.0874389i | ||||
\(239\) | 17.6050i | 1.13878i | 0.822069 | + | 0.569388i | \(0.192820\pi\) | ||||
−0.822069 | + | 0.569388i | \(0.807180\pi\) | |||||||
\(240\) | 4.41714 | 0.285125 | ||||||||
\(241\) | −8.56111 | −0.551470 | −0.275735 | − | 0.961234i | \(-0.588921\pi\) | ||||
−0.275735 | + | 0.961234i | \(0.588921\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 10.7569i | − | 0.690058i | ||||||
\(244\) | 15.2168 | 0.974158 | ||||||||
\(245\) | −3.46807 | − | 2.39491i | −0.221567 | − | 0.153005i | ||||
\(246\) | −17.0274 | −1.08563 | ||||||||
\(247\) | 11.8852 | 0.756240 | ||||||||
\(248\) | −11.7488 | −0.746047 | ||||||||
\(249\) | − | 22.7685i | − | 1.44289i | ||||||
\(250\) | 2.91730 | 0.184506 | ||||||||
\(251\) | 3.09714i | 0.195490i | 0.995211 | + | 0.0977449i | \(0.0311629\pi\) | ||||
−0.995211 | + | 0.0977449i | \(0.968837\pi\) | |||||||
\(252\) | 21.6731 | − | 11.3720i | 1.36528 | − | 0.716371i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.75987 | −0.298660 | ||||||||
\(255\) | −1.98589 | −0.124361 | ||||||||
\(256\) | −0.609627 | −0.0381017 | ||||||||
\(257\) | − | 13.6504i | − | 0.851489i | −0.904843 | − | 0.425745i | \(-0.860012\pi\) | ||
0.904843 | − | 0.425745i | \(-0.139988\pi\) | |||||||
\(258\) | − | 2.50792i | − | 0.156136i | ||||||
\(259\) | 17.3616 | − | 9.10977i | 1.07880 | − | 0.566054i | ||||
\(260\) | 2.46464i | 0.152850i | ||||||||
\(261\) | − | 11.4315i | − | 0.707593i | ||||||
\(262\) | 5.82158i | 0.359659i | ||||||||
\(263\) | 21.1997i | 1.30723i | 0.756827 | + | 0.653615i | \(0.226749\pi\) | ||||
−0.756827 | + | 0.653615i | \(0.773251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.68578i | − | 0.226416i | ||||||
\(266\) | 3.13531 | + | 5.97536i | 0.192238 | + | 0.366373i | ||||
\(267\) | −34.5497 | −2.11441 | ||||||||
\(268\) | −11.3030 | −0.690438 | ||||||||
\(269\) | 14.1104i | 0.860324i | 0.902752 | + | 0.430162i | \(0.141544\pi\) | ||||
−0.902752 | + | 0.430162i | \(0.858456\pi\) | |||||||
\(270\) | − | 2.00038i | − | 0.121739i | ||||||
\(271\) | −15.7466 | −0.956538 | −0.478269 | − | 0.878213i | \(-0.658736\pi\) | ||||
−0.478269 | + | 0.878213i | \(0.658736\pi\) | |||||||
\(272\) | −2.91730 | −0.176887 | ||||||||
\(273\) | 8.29456 | + | 15.8080i | 0.502009 | + | 0.956742i | ||||
\(274\) | 4.96681i | 0.300056i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 19.3942i | − | 1.16739i | ||||||
\(277\) | − | 6.68430i | − | 0.401621i | −0.979630 | − | 0.200810i | \(-0.935643\pi\) | ||
0.979630 | − | 0.200810i | \(-0.0643575\pi\) | |||||||
\(278\) | − | 5.13620i | − | 0.308049i | ||||||
\(279\) | − | 33.0183i | − | 1.97675i | ||||||
\(280\) | −2.65747 | + | 1.39439i | −0.158814 | + | 0.0833308i | ||||
\(281\) | − | 22.1229i | − | 1.31974i | −0.751379 | − | 0.659871i | \(-0.770611\pi\) | ||
0.751379 | − | 0.659871i | \(-0.229389\pi\) | |||||||
\(282\) | − | 14.3666i | − | 0.855518i | ||||||
\(283\) | 13.8766 | 0.824880 | 0.412440 | − | 0.910985i | \(-0.364677\pi\) | ||||
0.412440 | + | 0.910985i | \(0.364677\pi\) | |||||||
\(284\) | 9.30585 | 0.552201 | ||||||||
\(285\) | −8.79683 | −0.521079 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.5509 | + | 14.4562i | −1.62628 | + | 0.853320i | ||||
\(288\) | − | 26.7299i | − | 1.57507i | ||||||
\(289\) | −15.6884 | −0.922848 | ||||||||
\(290\) | 0.653568i | 0.0383788i | ||||||||
\(291\) | 16.7663 | 0.982859 | ||||||||
\(292\) | 4.36383 | 0.255374 | ||||||||
\(293\) | 7.11175 | 0.415473 | 0.207736 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207736 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(294\) | −5.75943 | + | 8.34025i | −0.335897 | + | 0.486413i | ||||
\(295\) | −2.83136 | −0.164848 | ||||||||
\(296\) | − | 13.9610i | − | 0.811469i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.30751 | −0.133671 | ||||||||
\(299\) | 9.02949 | 0.522189 | ||||||||
\(300\) | 23.3363i | 1.34732i | ||||||||
\(301\) | −2.12920 | − | 4.05789i | −0.122725 | − | 0.233893i | ||||
\(302\) | −6.60792 | −0.380243 | ||||||||
\(303\) | 41.6001i | 2.38986i | ||||||||
\(304\) | −12.9227 | −0.741165 | ||||||||
\(305\) | − | 5.24365i | − | 0.300250i | ||||||
\(306\) | 3.04848i | 0.174270i | ||||||||
\(307\) | 18.7705 | 1.07129 | 0.535644 | − | 0.844444i | \(-0.320069\pi\) | ||||
0.535644 | + | 0.844444i | \(0.320069\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.1798 | 0.920435 | ||||||||
\(310\) | 1.88774i | 0.107216i | ||||||||
\(311\) | − | 3.58717i | − | 0.203410i | −0.994815 | − | 0.101705i | \(-0.967570\pi\) | ||
0.994815 | − | 0.101705i | \(-0.0324298\pi\) | |||||||
\(312\) | 12.7117 | 0.719658 | ||||||||
\(313\) | − | 26.3802i | − | 1.49110i | −0.666451 | − | 0.745549i | \(-0.732188\pi\) | ||
0.666451 | − | 0.745549i | \(-0.267812\pi\) | |||||||
\(314\) | 1.55404 | 0.0876995 | ||||||||
\(315\) | −3.91875 | − | 7.46845i | −0.220796 | − | 0.420800i | ||||
\(316\) | − | 2.08026i | − | 0.117024i | ||||||
\(317\) | −6.36467 | −0.357475 | −0.178738 | − | 0.983897i | \(-0.557201\pi\) | ||||
−0.178738 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(318\) | −8.86381 | −0.497058 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 1.53921i | − | 0.0860447i | ||||||
\(321\) | −23.1253 | −1.29073 | ||||||||
\(322\) | 2.38197 | + | 4.53961i | 0.132742 | + | 0.252983i | ||||
\(323\) | 5.80986 | 0.323269 | ||||||||
\(324\) | 5.50146 | 0.305636 | ||||||||
\(325\) | −10.8648 | −0.602672 | ||||||||
\(326\) | − | 1.02778i | − | 0.0569237i | ||||||
\(327\) | 38.2879 | 2.11732 | ||||||||
\(328\) | 22.1546i | 1.22328i | ||||||||
\(329\) | −12.1971 | − | 23.2456i | −0.672450 | − | 1.28157i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.41523 | −0.517508 | −0.258754 | − | 0.965943i | \(-0.583312\pi\) | ||||
−0.258754 | + | 0.965943i | \(0.583312\pi\) | |||||||
\(332\) | −13.8131 | −0.758090 | ||||||||
\(333\) | 39.2356 | 2.15010 | ||||||||
\(334\) | 3.67502i | 0.201088i | ||||||||
\(335\) | 3.89495i | 0.212804i | ||||||||
\(336\) | −9.01854 | − | 17.1878i | −0.492002 | − | 0.937670i | ||||
\(337\) | 5.51775i | 0.300571i | 0.988643 | + | 0.150285i | \(0.0480193\pi\) | ||||
−0.988643 | + | 0.150285i | \(0.951981\pi\) | |||||||
\(338\) | − | 3.77627i | − | 0.205402i | ||||||
\(339\) | − | 2.89898i | − | 0.157451i | ||||||
\(340\) | 1.20479i | 0.0653388i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 13.5037i | 0.730198i | ||||||||
\(343\) | −2.23814 | + | 18.3845i | −0.120848 | + | 0.992671i | ||||
\(344\) | −3.26308 | −0.175933 | ||||||||
\(345\) | −6.68315 | −0.359808 | ||||||||
\(346\) | − | 4.11052i | − | 0.220983i | ||||||
\(347\) | − | 32.9752i | − | 1.77020i | −0.465399 | − | 0.885101i | \(-0.654089\pi\) | ||
0.465399 | − | 0.885101i | \(-0.345911\pi\) | |||||||
\(348\) | −10.8648 | −0.582416 | ||||||||
\(349\) | −26.6401 | −1.42601 | −0.713005 | − | 0.701159i | \(-0.752666\pi\) | ||||
−0.713005 | + | 0.701159i | \(0.752666\pi\) | |||||||
\(350\) | −2.86613 | − | 5.46234i | −0.153201 | − | 0.291974i | ||||
\(351\) | 15.4823i | 0.826384i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.7997i | 1.69253i | 0.532764 | + | 0.846264i | \(0.321153\pi\) | ||||
−0.532764 | + | 0.846264i | \(0.678847\pi\) | |||||||
\(354\) | 6.80905i | 0.361897i | ||||||||
\(355\) | − | 3.20675i | − | 0.170197i | ||||||
\(356\) | 20.9604i | 1.11090i | ||||||||
\(357\) | 4.05463 | + | 7.72741i | 0.214594 | + | 0.408978i | ||||
\(358\) | 3.13158i | 0.165509i | ||||||||
\(359\) | 31.6580i | 1.67085i | 0.549607 | + | 0.835423i | \(0.314777\pi\) | ||||
−0.549607 | + | 0.835423i | \(0.685223\pi\) | |||||||
\(360\) | −6.00562 | −0.316524 | ||||||||
\(361\) | 6.73575 | 0.354513 | ||||||||
\(362\) | −9.93483 | −0.522163 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.59029 | − | 5.03209i | 0.502668 | − | 0.263753i | ||||
\(365\) | − | 1.50375i | − | 0.0787101i | ||||||
\(366\) | −12.6103 | −0.659150 | ||||||||
\(367\) | 10.8963i | 0.568780i | 0.958709 | + | 0.284390i | \(0.0917910\pi\) | ||||
−0.958709 | + | 0.284390i | \(0.908209\pi\) | |||||||
\(368\) | −9.81762 | −0.511779 | ||||||||
\(369\) | −62.2624 | −3.24125 | ||||||||
\(370\) | −2.24320 | −0.116618 | ||||||||
\(371\) | −14.3419 | + | 7.52532i | −0.744597 | + | 0.390695i | ||||
\(372\) | −31.3815 | −1.62706 | ||||||||
\(373\) | − | 5.45840i | − | 0.282625i | −0.989965 | − | 0.141313i | \(-0.954868\pi\) | ||
0.989965 | − | 0.141313i | \(-0.0451322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.7117 | 0.862990 | ||||||||
\(376\) | −18.6925 | −0.963995 | ||||||||
\(377\) | − | 5.05841i | − | 0.260521i | ||||||
\(378\) | −7.78379 | + | 4.08421i | −0.400355 | + | 0.210069i | ||||
\(379\) | 5.95918 | 0.306103 | 0.153051 | − | 0.988218i | \(-0.451090\pi\) | ||||
0.153051 | + | 0.988218i | \(0.451090\pi\) | |||||||
\(380\) | 5.33681i | 0.273773i | ||||||||
\(381\) | −27.2669 | −1.39692 | ||||||||
\(382\) | 0.311679i | 0.0159469i | ||||||||
\(383\) | − | 31.0218i | − | 1.58514i | −0.609780 | − | 0.792570i | \(-0.708742\pi\) | ||
0.609780 | − | 0.792570i | \(-0.291258\pi\) | |||||||
\(384\) | −32.7816 | −1.67288 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.25045 | −0.318140 | ||||||||
\(387\) | − | 9.17044i | − | 0.466160i | ||||||
\(388\) | − | 10.1717i | − | 0.516390i | ||||||
\(389\) | 23.4135 | 1.18711 | 0.593556 | − | 0.804792i | \(-0.297723\pi\) | ||||
0.593556 | + | 0.804792i | \(0.297723\pi\) | |||||||
\(390\) | − | 2.04246i | − | 0.103424i | ||||||
\(391\) | 4.41388 | 0.223220 | ||||||||
\(392\) | 10.8516 | + | 7.49367i | 0.548088 | + | 0.378487i | ||||
\(393\) | 33.3489i | 1.68223i | ||||||||
\(394\) | −6.24678 | −0.314708 | ||||||||
\(395\) | −0.716849 | −0.0360686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.8394i | − | 1.49760i | −0.662798 | − | 0.748798i | \(-0.730631\pi\) | ||
0.662798 | − | 0.748798i | \(-0.269369\pi\) | |||||||
\(398\) | 4.28284 | 0.214679 | ||||||||
\(399\) | 17.9606 | + | 34.2298i | 0.899156 | + | 1.71364i | ||||
\(400\) | 11.8132 | 0.590658 | ||||||||
\(401\) | 20.5447 | 1.02595 | 0.512976 | − | 0.858403i | \(-0.328543\pi\) | ||||
0.512976 | + | 0.858403i | \(0.328543\pi\) | |||||||
\(402\) | 9.36683 | 0.467175 | ||||||||
\(403\) | − | 14.6105i | − | 0.727801i | ||||||
\(404\) | 25.2377 | 1.25562 | ||||||||
\(405\) | − | 1.89577i | − | 0.0942018i | ||||||
\(406\) | 2.54314 | − | 1.33440i | 0.126214 | − | 0.0662252i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.21385 | 0.307632 | ||||||||
\(409\) | 12.4456 | 0.615396 | 0.307698 | − | 0.951484i | \(-0.400441\pi\) | ||||
0.307698 | + | 0.951484i | \(0.400441\pi\) | |||||||
\(410\) | 3.55970 | 0.175801 | ||||||||
\(411\) | 28.4524i | 1.40345i | ||||||||
\(412\) | − | 9.81585i | − | 0.483592i | ||||||
\(413\) | 5.78084 | + | 11.0173i | 0.284457 | + | 0.542125i | ||||
\(414\) | 10.2591i | 0.504206i | ||||||||
\(415\) | 4.75991i | 0.233655i | ||||||||
\(416\) | − | 11.8279i | − | 0.579909i | ||||||
\(417\) | − | 29.4227i | − | 1.44084i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0711i | 0.736272i | 0.929772 | + | 0.368136i | \(0.120004\pi\) | ||||
−0.929772 | + | 0.368136i | \(0.879996\pi\) | |||||||
\(420\) | −7.09822 | + | 3.72449i | −0.346358 | + | 0.181736i | ||||
\(421\) | −6.04842 | −0.294782 | −0.147391 | − | 0.989078i | \(-0.547088\pi\) | ||||
−0.147391 | + | 0.989078i | \(0.547088\pi\) | |||||||
\(422\) | 8.92140 | 0.434287 | ||||||||
\(423\) | − | 52.5329i | − | 2.55424i | ||||||
\(424\) | 11.5328i | 0.560083i | ||||||||
\(425\) | −5.31105 | −0.257624 | ||||||||
\(426\) | −7.71181 | −0.373638 | ||||||||
\(427\) | −20.4039 | + | 10.7060i | −0.987412 | + | 0.518102i | ||||
\(428\) | 14.0295i | 0.678141i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.524297i | 0.0252838i | ||||||||
\(431\) | − | 7.24556i | − | 0.349006i | −0.984657 | − | 0.174503i | \(-0.944168\pi\) | ||
0.984657 | − | 0.174503i | \(-0.0558319\pi\) | |||||||
\(432\) | − | 16.8337i | − | 0.809910i | ||||||
\(433\) | 10.1694i | 0.488712i | 0.969686 | + | 0.244356i | \(0.0785766\pi\) | ||||
−0.969686 | + | 0.244356i | \(0.921423\pi\) | |||||||
\(434\) | 7.34549 | − | 3.85423i | 0.352595 | − | 0.185009i | ||||
\(435\) | 3.74396i | 0.179509i | ||||||||
\(436\) | − | 23.2283i | − | 1.11243i | ||||||
\(437\) | 19.5520 | 0.935300 | ||||||||
\(438\) | −3.61633 | −0.172795 | ||||||||
\(439\) | −8.57434 | −0.409231 | −0.204615 | − | 0.978842i | \(-0.565594\pi\) | ||||
−0.204615 | + | 0.978842i | \(0.565594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0599 | + | 30.4969i | −1.00285 | + | 1.45223i | ||||
\(442\) | 1.34894i | 0.0641626i | ||||||||
\(443\) | −9.81527 | −0.466338 | −0.233169 | − | 0.972436i | \(-0.574909\pi\) | ||||
−0.233169 | + | 0.972436i | \(0.574909\pi\) | |||||||
\(444\) | − | 37.2906i | − | 1.76973i | ||||||
\(445\) | 7.22286 | 0.342397 | ||||||||
\(446\) | 0.746909 | 0.0353672 | ||||||||
\(447\) | −13.2186 | −0.625218 | ||||||||
\(448\) | −5.98933 | + | 3.14264i | −0.282969 | + | 0.148476i | ||||
\(449\) | −15.5194 | −0.732405 | −0.366202 | − | 0.930535i | \(-0.619342\pi\) | ||||
−0.366202 | + | 0.930535i | \(0.619342\pi\) | |||||||
\(450\) | − | 12.3443i | − | 0.581918i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.75874 | −0.0827240 | ||||||||
\(453\) | −37.8535 | −1.77851 | ||||||||
\(454\) | 12.0586i | 0.565937i | ||||||||
\(455\) | −1.73403 | − | 3.30477i | −0.0812928 | − | 0.154930i | ||||
\(456\) | 27.5253 | 1.28899 | ||||||||
\(457\) | − | 27.2910i | − | 1.27662i | −0.769779 | − | 0.638310i | \(-0.779634\pi\) | ||
0.769779 | − | 0.638310i | \(-0.220366\pi\) | |||||||
\(458\) | 0.183379 | 0.00856876 | ||||||||
\(459\) | 7.56820i | 0.353253i | ||||||||
\(460\) | 4.05449i | 0.189042i | ||||||||
\(461\) | 34.0355 | 1.58519 | 0.792595 | − | 0.609748i | \(-0.208730\pi\) | ||||
0.792595 | + | 0.609748i | \(0.208730\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2899 | 0.896477 | 0.448239 | − | 0.893914i | \(-0.352052\pi\) | ||||
0.448239 | + | 0.893914i | \(0.352052\pi\) | |||||||
\(464\) | 5.49993i | 0.255328i | ||||||||
\(465\) | 10.8139i | 0.501483i | ||||||||
\(466\) | 1.32952 | 0.0615890 | ||||||||
\(467\) | − | 24.1293i | − | 1.11657i | −0.829649 | − | 0.558285i | \(-0.811460\pi\) | ||
0.829649 | − | 0.558285i | \(-0.188540\pi\) | |||||||
\(468\) | 21.6731 | 1.00184 | ||||||||
\(469\) | 15.1558 | − | 7.95238i | 0.699832 | − | 0.367207i | ||||
\(470\) | 3.00344i | 0.138538i | ||||||||
\(471\) | 8.90232 | 0.410197 | ||||||||
\(472\) | 8.85934 | 0.407784 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.72393i | 0.0791826i | ||||||||
\(475\) | −23.5262 | −1.07945 | ||||||||
\(476\) | 4.68802 | − | 2.45984i | 0.214875 | − | 0.112746i | ||||
\(477\) | −32.4114 | −1.48402 | ||||||||
\(478\) | −8.85101 | −0.404836 | ||||||||
\(479\) | −38.9852 | −1.78128 | −0.890639 | − | 0.454710i | \(-0.849743\pi\) | ||||
−0.890639 | + | 0.454710i | \(0.849743\pi\) | |||||||
\(480\) | 8.75437i | 0.399580i | ||||||||
\(481\) | 17.3616 | 0.791623 | ||||||||
\(482\) | − | 4.30413i | − | 0.196048i | ||||||
\(483\) | 13.6451 | + | 26.0052i | 0.620873 | + | 1.18328i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.50512 | −0.159159 | ||||||||
\(486\) | 5.40809 | 0.245316 | ||||||||
\(487\) | −0.834071 | −0.0377954 | −0.0188977 | − | 0.999821i | \(-0.506016\pi\) | ||||
−0.0188977 | + | 0.999821i | \(0.506016\pi\) | |||||||
\(488\) | 16.4074i | 0.742727i | ||||||||
\(489\) | − | 5.88766i | − | 0.266249i | ||||||
\(490\) | 1.20405 | − | 1.74359i | 0.0543934 | − | 0.0787672i | ||||
\(491\) | − | 27.3903i | − | 1.23611i | −0.786136 | − | 0.618053i | \(-0.787922\pi\) | ||
0.786136 | − | 0.618053i | \(-0.212078\pi\) | |||||||
\(492\) | 59.1759i | 2.66786i | ||||||||
\(493\) | − | 2.47270i | − | 0.111365i | ||||||
\(494\) | 5.97536i | 0.268844i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.8858i | 0.713292i | ||||||||
\(497\) | −12.4780 | + | 6.54728i | −0.559713 | + | 0.293685i | ||||
\(498\) | 11.4470 | 0.512950 | ||||||||
\(499\) | 19.9086 | 0.891233 | 0.445617 | − | 0.895224i | \(-0.352984\pi\) | ||||
0.445617 | + | 0.895224i | \(0.352984\pi\) | |||||||
\(500\) | − | 10.1386i | − | 0.453411i | ||||||
\(501\) | 21.0523i | 0.940549i | ||||||||
\(502\) | −1.55710 | −0.0694968 | ||||||||
\(503\) | −1.70877 | −0.0761904 | −0.0380952 | − | 0.999274i | \(-0.512129\pi\) | ||||
−0.0380952 | + | 0.999274i | \(0.512129\pi\) | |||||||
\(504\) | 12.2618 | + | 23.3688i | 0.546183 | + | 1.04093i | ||||
\(505\) | − | 8.69679i | − | 0.387002i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 21.6324i | − | 0.960727i | ||||||
\(508\) | 16.5421i | 0.733938i | ||||||||
\(509\) | − | 12.5195i | − | 0.554916i | −0.960738 | − | 0.277458i | \(-0.910508\pi\) | ||
0.960738 | − | 0.277458i | \(-0.0894919\pi\) | |||||||
\(510\) | − | 0.998414i | − | 0.0442105i | ||||||
\(511\) | −5.85134 | + | 3.07024i | −0.258848 | + | 0.135819i | ||||
\(512\) | 22.4583i | 0.992524i | ||||||||
\(513\) | 33.5246i | 1.48015i | ||||||||
\(514\) | 6.86280 | 0.302705 | ||||||||
\(515\) | −3.38249 | −0.149050 | ||||||||
\(516\) | −8.71584 | −0.383694 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.57998 | + | 8.72864i | 0.201233 | + | 0.383514i | ||||
\(519\) | − | 23.5471i | − | 1.03360i | ||||||
\(520\) | −2.65747 | −0.116538 | ||||||||
\(521\) | 12.8670i | 0.563714i | 0.959456 | + | 0.281857i | \(0.0909504\pi\) | ||||
−0.959456 | + | 0.281857i | \(0.909050\pi\) | |||||||
\(522\) | 5.74724 | 0.251550 | ||||||||
\(523\) | 22.9599 | 1.00397 | 0.501983 | − | 0.864878i | \(-0.332604\pi\) | ||||
0.501983 | + | 0.864878i | \(0.332604\pi\) | |||||||
\(524\) | 20.2319 | 0.883837 | ||||||||
\(525\) | −16.4186 | − | 31.2910i | −0.716566 | − | 1.36565i | ||||
\(526\) | −10.6582 | −0.464722 | ||||||||
\(527\) | − | 7.14204i | − | 0.311112i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.14590 | −0.354169 | ||||||||
\(530\) | 1.85304 | 0.0804910 | ||||||||
\(531\) | 24.8980i | 1.08048i | ||||||||
\(532\) | 20.7664 | − | 10.8963i | 0.900336 | − | 0.472413i | ||||
\(533\) | −27.5509 | −1.19336 | ||||||||
\(534\) | − | 17.3700i | − | 0.751675i | ||||||
\(535\) | 4.83449 | 0.209013 | ||||||||
\(536\) | − | 12.1873i | − | 0.526411i | ||||||
\(537\) | 17.9392i | 0.774135i | ||||||||
\(538\) | −7.09405 | −0.305846 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.95198 | −0.299166 | ||||||||
\(541\) | − | 23.2351i | − | 0.998953i | −0.866327 | − | 0.499477i | \(-0.833526\pi\) | ||
0.866327 | − | 0.499477i | \(-0.166474\pi\) | |||||||
\(542\) | − | 7.91667i | − | 0.340050i | ||||||
\(543\) | −56.9117 | −2.44231 | ||||||||
\(544\) | − | 5.78182i | − | 0.247893i | ||||||
\(545\) | −8.00434 | −0.342868 | ||||||||
\(546\) | −7.94753 | + | 4.17012i | −0.340123 | + | 0.178465i | ||||
\(547\) | − | 32.3259i | − | 1.38216i | −0.722780 | − | 0.691078i | \(-0.757136\pi\) | ||
0.722780 | − | 0.691078i | \(-0.242864\pi\) | |||||||
\(548\) | 17.2613 | 0.737367 | ||||||||
\(549\) | −46.1107 | −1.96796 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.9532i | − | 0.466623i | ||||||
\(552\) | 20.9116 | 0.890056 | ||||||||
\(553\) | 1.46360 | + | 2.78937i | 0.0622387 | + | 0.118616i | ||||
\(554\) | 3.36056 | 0.142776 | ||||||||
\(555\) | −12.8502 | −0.545459 | ||||||||
\(556\) | −17.8500 | −0.757009 | ||||||||
\(557\) | − | 12.4366i | − | 0.526957i | −0.964665 | − | 0.263478i | \(-0.915130\pi\) | ||
0.964665 | − | 0.263478i | \(-0.0848698\pi\) | |||||||
\(558\) | 16.6001 | 0.702738 | ||||||||
\(559\) | − | 4.05789i | − | 0.171631i | ||||||
\(560\) | 1.88539 | + | 3.59322i | 0.0796722 | + | 0.151841i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.1224 | 0.469169 | ||||||||
\(563\) | 2.20132 | 0.0927747 | 0.0463873 | − | 0.998924i | \(-0.485229\pi\) | ||||
0.0463873 | + | 0.998924i | \(0.485229\pi\) | |||||||
\(564\) | −49.9287 | −2.10238 | ||||||||
\(565\) | 0.606052i | 0.0254968i | ||||||||
\(566\) | 6.97653i | 0.293246i | ||||||||
\(567\) | −7.37676 | + | 3.87064i | −0.309795 | + | 0.162551i | ||||
\(568\) | 10.0339i | 0.421014i | ||||||||
\(569\) | − | 45.9285i | − | 1.92542i | −0.270532 | − | 0.962711i | \(-0.587200\pi\) | ||
0.270532 | − | 0.962711i | \(-0.412800\pi\) | |||||||
\(570\) | − | 4.42264i | − | 0.185244i | ||||||
\(571\) | − | 42.4864i | − | 1.77800i | −0.457905 | − | 0.889001i | \(-0.651400\pi\) | ||
0.457905 | − | 0.889001i | \(-0.348600\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.78546i | 0.0745885i | ||||||||
\(574\) | −7.26790 | − | 13.8513i | −0.303356 | − | 0.578144i | ||||
\(575\) | −17.8734 | −0.745370 | ||||||||
\(576\) | −13.5353 | −0.563971 | ||||||||
\(577\) | 30.7067i | 1.27834i | 0.769067 | + | 0.639168i | \(0.220721\pi\) | ||||
−0.769067 | + | 0.639168i | \(0.779279\pi\) | |||||||
\(578\) | − | 7.88742i | − | 0.328073i | ||||||
\(579\) | −35.8057 | −1.48803 | ||||||||
\(580\) | 2.27137 | 0.0943134 | ||||||||
\(581\) | 18.5216 | − | 9.71839i | 0.768404 | − | 0.403187i | ||||
\(582\) | 8.42934i | 0.349407i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.70525i | 0.194705i | ||||||||
\(585\) | − | 7.46845i | − | 0.308782i | ||||||
\(586\) | 3.57546i | 0.147701i | ||||||||
\(587\) | − | 17.4323i | − | 0.719510i | −0.933047 | − | 0.359755i | \(-0.882860\pi\) | ||
0.933047 | − | 0.359755i | \(-0.117140\pi\) | |||||||
\(588\) | 28.9851 | + | 20.0160i | 1.19533 | + | 0.825444i | ||||
\(589\) | − | 31.6369i | − | 1.30357i | ||||||
\(590\) | − | 1.42348i | − | 0.0586037i | ||||||
\(591\) | −35.7847 | −1.47199 | ||||||||
\(592\) | −18.8770 | −0.775842 | ||||||||
\(593\) | −5.06886 | −0.208153 | −0.104077 | − | 0.994569i | \(-0.533189\pi\) | ||||
−0.104077 | + | 0.994569i | \(0.533189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.847648 | − | 1.61547i | −0.0347502 | − | 0.0662278i | ||||
\(596\) | 8.01938i | 0.328487i | ||||||||
\(597\) | 24.5343 | 1.00412 | ||||||||
\(598\) | 4.53961i | 0.185639i | ||||||||
\(599\) | −0.951499 | −0.0388772 | −0.0194386 | − | 0.999811i | \(-0.506188\pi\) | ||||
−0.0194386 | + | 0.999811i | \(0.506188\pi\) | |||||||
\(600\) | −25.1621 | −1.02724 | ||||||||
\(601\) | 19.2998 | 0.787257 | 0.393629 | − | 0.919270i | \(-0.371220\pi\) | ||||
0.393629 | + | 0.919270i | \(0.371220\pi\) | |||||||
\(602\) | 2.04012 | − | 1.07047i | 0.0831492 | − | 0.0436289i | ||||
\(603\) | 34.2507 | 1.39480 | ||||||||
\(604\) | 22.9647i | 0.934422i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.9146 | −0.849598 | ||||||||
\(607\) | 19.2580 | 0.781657 | 0.390828 | − | 0.920464i | \(-0.372189\pi\) | ||||
0.390828 | + | 0.920464i | \(0.372189\pi\) | |||||||
\(608\) | − | 25.6115i | − | 1.03868i | ||||||
\(609\) | 14.5684 | − | 7.64412i | 0.590339 | − | 0.309755i | ||||
\(610\) | 2.63626 | 0.106739 | ||||||||
\(611\) | − | 23.2456i | − | 0.940418i | ||||||
\(612\) | 10.5945 | 0.428256 | ||||||||
\(613\) | 4.95657i | 0.200194i | 0.994978 | + | 0.100097i | \(0.0319153\pi\) | ||||
−0.994978 | + | 0.100097i | \(0.968085\pi\) | |||||||
\(614\) | 9.43693i | 0.380844i | ||||||||
\(615\) | 20.3917 | 0.822274 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.6246 | −1.67574 | −0.837871 | − | 0.545869i | \(-0.816200\pi\) | ||||
−0.837871 | + | 0.545869i | \(0.816200\pi\) | |||||||
\(618\) | 8.13444i | 0.327215i | ||||||||
\(619\) | 6.13121i | 0.246434i | 0.992380 | + | 0.123217i | \(0.0393212\pi\) | ||||
−0.992380 | + | 0.123217i | \(0.960679\pi\) | |||||||
\(620\) | 6.56052 | 0.263477 | ||||||||
\(621\) | 25.4694i | 1.02205i | ||||||||
\(622\) | 1.80347 | 0.0723124 | ||||||||
\(623\) | −14.7470 | − | 28.1053i | −0.590828 | − | 1.12601i | ||||
\(624\) | − | 17.1878i | − | 0.688062i | ||||||
\(625\) | 19.6937 | 0.787749 | ||||||||
\(626\) | 13.2628 | 0.530086 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 5.40081i | − | 0.215516i | ||||||
\(629\) | 8.48688 | 0.338394 | ||||||||
\(630\) | 3.75480 | − | 1.97017i | 0.149595 | − | 0.0784933i | ||||
\(631\) | −7.86270 | −0.313009 | −0.156505 | − | 0.987677i | \(-0.550023\pi\) | ||||
−0.156505 | + | 0.987677i | \(0.550023\pi\) | |||||||
\(632\) | 2.24302 | 0.0892226 | ||||||||
\(633\) | 51.1062 | 2.03129 | ||||||||
\(634\) | − | 3.19986i | − | 0.127083i | ||||||
\(635\) | 5.70033 | 0.226211 | ||||||||
\(636\) | 30.8047i | 1.22149i | ||||||||
\(637\) | −9.31896 | + | 13.4948i | −0.369231 | + | 0.534683i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.1990 | −1.11553 | ||||||||
\(640\) | 6.85321 | 0.270897 | ||||||||
\(641\) | 12.8203 | 0.506370 | 0.253185 | − | 0.967418i | \(-0.418522\pi\) | ||||
0.253185 | + | 0.967418i | \(0.418522\pi\) | |||||||
\(642\) | − | 11.6263i | − | 0.458854i | ||||||
\(643\) | − | 3.76638i | − | 0.148532i | −0.997238 | − | 0.0742659i | \(-0.976339\pi\) | ||
0.997238 | − | 0.0742659i | \(-0.0236613\pi\) | |||||||
\(644\) | 15.7767 | − | 8.27813i | 0.621688 | − | 0.326204i | ||||
\(645\) | 3.00344i | 0.118260i | ||||||||
\(646\) | 2.92093i | 0.114923i | ||||||||
\(647\) | 32.2695i | 1.26865i | 0.773068 | + | 0.634323i | \(0.218721\pi\) | ||||
−0.773068 | + | 0.634323i | \(0.781279\pi\) | |||||||
\(648\) | 5.93188i | 0.233026i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 5.46234i | − | 0.214250i | ||||||
\(651\) | 42.0786 | − | 22.0789i | 1.64919 | − | 0.865342i | ||||
\(652\) | −3.57189 | −0.139886 | ||||||||
\(653\) | 18.6427 | 0.729547 | 0.364773 | − | 0.931096i | \(-0.381146\pi\) | ||||
0.364773 | + | 0.931096i | \(0.381146\pi\) | |||||||
\(654\) | 19.2494i | 0.752710i | ||||||||
\(655\) | − | 6.97183i | − | 0.272412i | ||||||
\(656\) | 29.9557 | 1.16957 | ||||||||
\(657\) | −13.2235 | −0.515896 | ||||||||
\(658\) | 11.6868 | − | 6.13217i | 0.455600 | − | 0.239057i | ||||
\(659\) | − | 29.3896i | − | 1.14486i | −0.819954 | − | 0.572429i | \(-0.806001\pi\) | ||
0.819954 | − | 0.572429i | \(-0.193999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6779i | 0.415321i | 0.978201 | + | 0.207660i | \(0.0665849\pi\) | ||||
−0.978201 | + | 0.207660i | \(0.933415\pi\) | |||||||
\(662\) | − | 4.73354i | − | 0.183974i | ||||||
\(663\) | 7.72741i | 0.300108i | ||||||||
\(664\) | − | 14.8938i | − | 0.577990i | ||||||
\(665\) | −3.75480 | − | 7.15599i | −0.145605 | − | 0.277497i | ||||
\(666\) | 19.7259i | 0.764362i | ||||||||
\(667\) | − | 8.32141i | − | 0.322206i | ||||||
\(668\) | 12.7719 | 0.494160 | ||||||||
\(669\) | 4.27867 | 0.165423 | ||||||||
\(670\) | −1.95820 | −0.0756519 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 34.0646 | − | 17.8739i | 1.31407 | − | 0.689502i | ||||
\(673\) | 3.94666i | 0.152133i | 0.997103 | + | 0.0760663i | \(0.0242361\pi\) | ||||
−0.997103 | + | 0.0760663i | \(0.975764\pi\) | |||||||
\(674\) | −2.77407 | −0.106853 | ||||||||
\(675\) | − | 30.6463i | − | 1.17958i | ||||||
\(676\) | −13.1238 | −0.504762 | ||||||||
\(677\) | 22.7416 | 0.874029 | 0.437015 | − | 0.899454i | \(-0.356036\pi\) | ||||
0.437015 | + | 0.899454i | \(0.356036\pi\) | |||||||
\(678\) | 1.45747 | 0.0559739 | ||||||||
\(679\) | 7.15645 | + | 13.6390i | 0.274639 | + | 0.523415i | ||||
\(680\) | −1.29905 | −0.0498163 | ||||||||
\(681\) | 69.0775i | 2.64706i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.2074 | 0.926271 | 0.463136 | − | 0.886287i | \(-0.346724\pi\) | ||||
0.463136 | + | 0.886287i | \(0.346724\pi\) | |||||||
\(684\) | 46.9300 | 1.79441 | ||||||||
\(685\) | − | 5.94817i | − | 0.227268i | ||||||
\(686\) | −9.24290 | − | 1.12524i | −0.352895 | − | 0.0429617i | ||||
\(687\) | 1.05049 | 0.0400787 | ||||||||
\(688\) | 4.41208i | 0.168209i | ||||||||
\(689\) | −14.3419 | −0.546385 | ||||||||
\(690\) | − | 3.35998i | − | 0.127912i | ||||||
\(691\) | − | 42.7569i | − | 1.62655i | −0.581880 | − | 0.813275i | \(-0.697683\pi\) | ||
0.581880 | − | 0.813275i | \(-0.302317\pi\) | |||||||
\(692\) | −14.2854 | −0.543051 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.5784 | 0.629308 | ||||||||
\(695\) | 6.15102i | 0.233322i | ||||||||
\(696\) | − | 11.7149i | − | 0.444051i | ||||||
\(697\) | −13.4677 | −0.510126 | ||||||||
\(698\) | − | 13.3934i | − | 0.506948i | ||||||
\(699\) | 7.61618 | 0.288070 | ||||||||
\(700\) | −18.9834 | + | 9.96074i | −0.717506 | + | 0.376481i | ||||
\(701\) | − | 0.417984i | − | 0.0157870i | −0.999969 | − | 0.00789352i | \(-0.997487\pi\) | ||
0.999969 | − | 0.00789352i | \(-0.00251261\pi\) | |||||||
\(702\) | −7.78379 | −0.293780 | ||||||||
\(703\) | 37.5941 | 1.41789 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.2052i | 0.647985i | ||||||||
\(706\) | −15.9874 | −0.601695 | ||||||||
\(707\) | −33.8406 | + | 17.7564i | −1.27271 | + | 0.667797i | ||||
\(708\) | 23.6637 | 0.889337 | ||||||||
\(709\) | −38.7298 | −1.45453 | −0.727264 | − | 0.686357i | \(-0.759209\pi\) | ||||
−0.727264 | + | 0.686357i | \(0.759209\pi\) | |||||||
\(710\) | 1.61221 | 0.0605050 | ||||||||
\(711\) | 6.30371i | 0.236407i | ||||||||
\(712\) | −22.6004 | −0.846984 | ||||||||
\(713\) | − | 24.0352i | − | 0.900127i | ||||||
\(714\) | −3.88499 | + | 2.03848i | −0.145392 | + | 0.0762882i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.8833 | 0.406727 | ||||||||
\(717\) | −50.7030 | −1.89354 | ||||||||
\(718\) | −15.9162 | −0.593987 | ||||||||
\(719\) | − | 27.7446i | − | 1.03470i | −0.855774 | − | 0.517350i | \(-0.826918\pi\) | ||
0.855774 | − | 0.517350i | \(-0.173082\pi\) | |||||||
\(720\) | 8.12033i | 0.302627i | ||||||||
\(721\) | 6.90609 | + | 13.1618i | 0.257196 | + | 0.490171i | ||||
\(722\) | 3.38643i | 0.126030i | ||||||||
\(723\) | − | 24.6562i | − | 0.916975i | ||||||
\(724\) | 34.5268i | 1.28318i | ||||||||
\(725\) | 10.0128i | 0.371867i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.575775i | − | 0.0213543i | −0.999943 | − | 0.0106772i | \(-0.996601\pi\) | ||
0.999943 | − | 0.0106772i | \(-0.00339871\pi\) | |||||||
\(728\) | 5.42580 | + | 10.3406i | 0.201093 | + | 0.383249i | ||||
\(729\) | 40.4262 | 1.49727 | ||||||||
\(730\) | 0.756018 | 0.0279815 | ||||||||
\(731\) | − | 1.98362i | − | 0.0733668i | ||||||
\(732\) | 43.8249i | 1.61982i | ||||||||
\(733\) | 20.4997 | 0.757174 | 0.378587 | − | 0.925566i | \(-0.376410\pi\) | ||||
0.378587 | + | 0.925566i | \(0.376410\pi\) | |||||||
\(734\) | −5.47814 | −0.202202 | ||||||||
\(735\) | 6.89740 | − | 9.98813i | 0.254414 | − | 0.368418i | ||||
\(736\) | − | 19.4576i | − | 0.717218i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 31.3027i | − | 1.15227i | ||||||
\(739\) | 30.6943i | 1.12911i | 0.825396 | + | 0.564554i | \(0.190952\pi\) | ||||
−0.825396 | + | 0.564554i | \(0.809048\pi\) | |||||||
\(740\) | 7.79586i | 0.286582i | ||||||||
\(741\) | 34.2298i | 1.25746i | ||||||||
\(742\) | −3.78339 | − | 7.21047i | −0.138892 | − | 0.264705i | ||||
\(743\) | 23.7676i | 0.871950i | 0.899959 | + | 0.435975i | \(0.143596\pi\) | ||||
−0.899959 | + | 0.435975i | \(0.856404\pi\) | |||||||
\(744\) | − | 33.8368i | − | 1.24052i | ||||||
\(745\) | 2.76344 | 0.101245 | ||||||||
\(746\) | 2.74423 | 0.100473 | ||||||||
\(747\) | 41.8569 | 1.53146 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.87067 | − | 18.8118i | −0.360666 | − | 0.687367i | ||||
\(750\) | 8.40189i | 0.306794i | ||||||||
\(751\) | 12.7514 | 0.465304 | 0.232652 | − | 0.972560i | \(-0.425260\pi\) | ||||
0.232652 | + | 0.972560i | \(0.425260\pi\) | |||||||
\(752\) | 25.2746i | 0.921671i | ||||||||
\(753\) | −8.91985 | −0.325057 | ||||||||
\(754\) | 2.54314 | 0.0926155 | ||||||||
\(755\) | 7.91353 | 0.288003 | ||||||||
\(756\) | 14.1940 | + | 27.0512i | 0.516230 | + | 0.983844i | ||||
\(757\) | 25.0044 | 0.908800 | 0.454400 | − | 0.890798i | \(-0.349854\pi\) | ||||
0.454400 | + | 0.890798i | \(0.349854\pi\) | |||||||
\(758\) | 2.99600i | 0.108820i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.75435 | −0.208732 | ||||||||
\(761\) | −3.28328 | −0.119019 | −0.0595094 | − | 0.998228i | \(-0.518954\pi\) | ||||
−0.0595094 | + | 0.998228i | \(0.518954\pi\) | |||||||
\(762\) | − | 13.7085i | − | 0.496608i | ||||||
\(763\) | 16.3426 | + | 31.1461i | 0.591642 | + | 1.12757i | ||||
\(764\) | 1.08319 | 0.0391884 | ||||||||
\(765\) | − | 3.65080i | − | 0.131995i | ||||||
\(766\) | 15.5963 | 0.563519 | ||||||||
\(767\) | 11.0173i | 0.397811i | ||||||||
\(768\) | − | 1.75574i | − | 0.0633549i | ||||||
\(769\) | −16.9051 | −0.609613 | −0.304806 | − | 0.952414i | \(-0.598592\pi\) | ||||
−0.304806 | + | 0.952414i | \(0.598592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.3136 | 1.41584 | ||||||||
\(772\) | 21.7224i | 0.781806i | ||||||||
\(773\) | 2.95877i | 0.106420i | 0.998583 | + | 0.0532098i | \(0.0169452\pi\) | ||||
−0.998583 | + | 0.0532098i | \(0.983055\pi\) | |||||||
\(774\) | 4.61048 | 0.165720 | ||||||||
\(775\) | 28.9206i | 1.03886i | ||||||||
\(776\) | 10.9675 | 0.393711 | ||||||||
\(777\) | 26.2364 | + | 50.0020i | 0.941225 | + | 1.79381i | ||||
\(778\) | 11.7712i | 0.422020i | ||||||||
\(779\) | −59.6575 | −2.13745 | ||||||||
\(780\) | −7.09822 | −0.254157 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.21910i | 0.0793548i | ||||||||
\(783\) | 14.2682 | 0.509904 | ||||||||
\(784\) | 10.1324 | − | 14.6727i | 0.361870 | − | 0.524025i | ||||
\(785\) | −1.86109 | −0.0664252 | ||||||||
\(786\) | −16.7663 | −0.598035 | ||||||||
\(787\) | −17.2483 | −0.614836 | −0.307418 | − | 0.951575i | \(-0.599465\pi\) | ||||
−0.307418 | + | 0.951575i | \(0.599465\pi\) | |||||||
\(788\) | 21.7097i | 0.773375i | ||||||||
\(789\) | −61.0558 | −2.17364 | ||||||||
\(790\) | − | 0.360399i | − | 0.0128224i | ||||||
\(791\) | 2.35824 | − | 1.23739i | 0.0838494 | − | 0.0439964i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.4039 | −0.724562 | ||||||||
\(794\) | 15.0019 | 0.532397 | ||||||||
\(795\) | 10.6151 | 0.376480 | ||||||||
\(796\) | − | 14.8843i | − | 0.527560i | ||||||
\(797\) | 22.2363i | 0.787651i | 0.919185 | + | 0.393826i | \(0.128849\pi\) | ||||
−0.919185 | + | 0.393826i | \(0.871151\pi\) | |||||||
\(798\) | −17.2092 | + | 9.02978i | −0.609199 | + | 0.319651i | ||||
\(799\) | − | 11.3632i | − | 0.402000i | ||||||
\(800\) | 23.4126i | 0.827761i | ||||||||
\(801\) | − | 63.5152i | − | 2.24420i | ||||||
\(802\) | 10.3289i | 0.364727i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 32.5528i | − | 1.14805i | ||||||
\(805\) | −2.85260 | − | 5.43656i | −0.100541 | − | 0.191614i | ||||
\(806\) | 7.34549 | 0.258734 | ||||||||
\(807\) | −40.6382 | −1.43053 | ||||||||
\(808\) | 27.2123i | 0.957324i | ||||||||
\(809\) | − | 9.44132i | − | 0.331939i | −0.986131 | − | 0.165970i | \(-0.946925\pi\) | ||
0.986131 | − | 0.165970i | \(-0.0530753\pi\) | |||||||
\(810\) | 0.953109 | 0.0334888 | ||||||||
\(811\) | 29.6025 | 1.03948 | 0.519742 | − | 0.854323i | \(-0.326028\pi\) | ||||
0.519742 | + | 0.854323i | \(0.326028\pi\) | |||||||
\(812\) | −4.63749 | − | 8.83824i | −0.162744 | − | 0.310162i | ||||
\(813\) | − | 45.3506i | − | 1.59052i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.23086i | 0.0431150i | ||||||||
\(816\) | − | 8.40189i | − | 0.294125i | ||||||
\(817\) | − | 8.78677i | − | 0.307410i | ||||||
\(818\) | 6.25709i | 0.218774i | ||||||||
\(819\) | −29.0609 | + | 15.2485i | −1.01547 | + | 0.532825i | ||||
\(820\) | − | 12.3711i | − | 0.432019i | ||||||
\(821\) | 40.3174i | 1.40709i | 0.710653 | + | 0.703543i | \(0.248400\pi\) | ||||
−0.710653 | + | 0.703543i | \(0.751600\pi\) | |||||||
\(822\) | −14.3045 | −0.498928 | ||||||||
\(823\) | −41.4204 | −1.44382 | −0.721912 | − | 0.691984i | \(-0.756737\pi\) | ||||
−0.721912 | + | 0.691984i | \(0.756737\pi\) | |||||||
\(824\) | 10.5838 | 0.368705 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.53898 | + | 2.90634i | −0.192726 | + | 0.101125i | ||||
\(827\) | 30.7178i | 1.06816i | 0.845433 | + | 0.534081i | \(0.179342\pi\) | ||||
−0.845433 | + | 0.534081i | \(0.820658\pi\) | |||||||
\(828\) | 35.6537 | 1.23905 | ||||||||
\(829\) | 44.6514i | 1.55081i | 0.631466 | + | 0.775404i | \(0.282454\pi\) | ||||
−0.631466 | + | 0.775404i | \(0.717546\pi\) | |||||||
\(830\) | −2.39306 | −0.0830645 | ||||||||
\(831\) | 19.2510 | 0.667809 | ||||||||
\(832\) | −5.98933 | −0.207643 | ||||||||
\(833\) | −4.55538 | + | 6.59666i | −0.157835 | + | 0.228561i | ||||
\(834\) | 14.7924 | 0.512219 | ||||||||
\(835\) | − | 4.40114i | − | 0.152308i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.2117 | 1.42448 | ||||||||
\(838\) | −7.57707 | −0.261745 | ||||||||
\(839\) | 1.76555i | 0.0609536i | 0.999535 | + | 0.0304768i | \(0.00970258\pi\) | ||||
−0.999535 | + | 0.0304768i | \(0.990297\pi\) | |||||||
\(840\) | −4.01589 | − | 7.65358i | −0.138561 | − | 0.264074i | ||||
\(841\) | 24.3383 | 0.839250 | ||||||||
\(842\) | − | 3.04087i | − | 0.104795i | ||||||
\(843\) | 63.7145 | 2.19445 | ||||||||
\(844\) | − | 31.0048i | − | 1.06723i | ||||||
\(845\) | 4.52240i | 0.155575i | ||||||||
\(846\) | 26.4111 | 0.908033 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.5938 | 0.535493 | ||||||||
\(849\) | 39.9651i | 1.37160i | ||||||||
\(850\) | − | 2.67015i | − | 0.0915854i | ||||||
\(851\) | 28.5610 | 0.979060 | ||||||||
\(852\) | 26.8011i | 0.918191i | ||||||||
\(853\) | −32.1461 | −1.10066 | −0.550331 | − | 0.834947i | \(-0.685498\pi\) | ||||
−0.550331 | + | 0.834947i | \(0.685498\pi\) | |||||||
\(854\) | −5.38251 | − | 10.2581i | −0.184186 | − | 0.351026i | ||||
\(855\) | − | 16.1718i | − | 0.553065i | ||||||
\(856\) | −15.1271 | −0.517035 | ||||||||
\(857\) | 16.6829 | 0.569876 | 0.284938 | − | 0.958546i | \(-0.408027\pi\) | ||||
0.284938 | + | 0.958546i | \(0.408027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.8229i | 1.15402i | 0.816736 | + | 0.577011i | \(0.195781\pi\) | ||||
−0.816736 | + | 0.577011i | \(0.804219\pi\) | |||||||
\(860\) | 1.82211 | 0.0621333 | ||||||||
\(861\) | −41.6341 | − | 79.3474i | −1.41889 | − | 2.70415i | ||||
\(862\) | 3.64274 | 0.124072 | ||||||||
\(863\) | 45.3184 | 1.54266 | 0.771329 | − | 0.636437i | \(-0.219593\pi\) | ||||
0.771329 | + | 0.636437i | \(0.219593\pi\) | |||||||
\(864\) | 33.3628 | 1.13503 | ||||||||
\(865\) | 4.92269i | 0.167376i | ||||||||
\(866\) | −5.11273 | −0.173738 | ||||||||
\(867\) | − | 45.1831i | − | 1.53450i | ||||||
\(868\) | −13.3947 | − | 25.5280i | −0.454647 | − | 0.866477i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.88229 | −0.0638157 | ||||||||
\(871\) | 15.1558 | 0.513536 | ||||||||
\(872\) | 25.0456 | 0.848151 | ||||||||
\(873\) | 30.8227i | 1.04319i | ||||||||
\(874\) | 9.82986i | 0.332500i | ||||||||
\(875\) | 7.13316 | + | 13.5946i | 0.241145 | + | 0.459580i | ||||
\(876\) | 12.5679i | 0.424632i | ||||||||
\(877\) | 42.6831i | 1.44130i | 0.693297 | + | 0.720652i | \(0.256158\pi\) | ||||
−0.693297 | + | 0.720652i | \(0.743842\pi\) | |||||||
\(878\) | − | 4.31078i | − | 0.145482i | ||||||
\(879\) | 20.4820i | 0.690842i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 21.4936i | − | 0.724139i | −0.932151 | − | 0.362070i | \(-0.882070\pi\) | ||
0.932151 | − | 0.362070i | \(-0.117930\pi\) | |||||||
\(882\) | −15.3325 | − | 10.5880i | −0.516271 | − | 0.356516i | ||||
\(883\) | 14.8074 | 0.498310 | 0.249155 | − | 0.968464i | \(-0.419847\pi\) | ||||
0.249155 | + | 0.968464i | \(0.419847\pi\) | |||||||
\(884\) | 4.68802 | 0.157675 | ||||||||
\(885\) | − | 8.15440i | − | 0.274107i | ||||||
\(886\) | − | 4.93467i | − | 0.165783i | ||||||
\(887\) | −9.23398 | −0.310047 | −0.155023 | − | 0.987911i | \(-0.549545\pi\) | ||||
−0.155023 | + | 0.987911i | \(0.549545\pi\) | |||||||
\(888\) | 40.2082 | 1.34930 | ||||||||
\(889\) | −11.6385 | − | 22.1809i | −0.390342 | − | 0.743923i | ||||
\(890\) | 3.63132i | 0.121722i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 2.59576i | − | 0.0869124i | ||||||
\(893\) | − | 50.3350i | − | 1.68440i | ||||||
\(894\) | − | 6.64570i | − | 0.222266i | ||||||
\(895\) | − | 3.75032i | − | 0.125359i | ||||||
\(896\) | −13.9923 | − | 26.6669i | −0.467450 | − | 0.890879i | ||||
\(897\) | 26.0052i | 0.868287i | ||||||||
\(898\) | − | 7.80243i | − | 0.260370i | ||||||
\(899\) | −13.4648 | −0.449075 | ||||||||
\(900\) | −42.9007 | −1.43002 | ||||||||
\(901\) | −7.01077 | −0.233563 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.6868 | − | 6.13217i | 0.388914 | − | 0.204066i | ||||
\(904\) | − | 1.89634i | − | 0.0630712i | ||||||
\(905\) | 11.8978 | 0.395496 | ||||||||
\(906\) | − | 19.0310i | − | 0.632262i | ||||||
\(907\) | 1.00834 | 0.0334813 | 0.0167407 | − | 0.999860i | \(-0.494671\pi\) | ||||
0.0167407 | + | 0.999860i | \(0.494671\pi\) | |||||||
\(908\) | 41.9075 | 1.39075 | ||||||||
\(909\) | −76.4764 | −2.53656 | ||||||||
\(910\) | 1.66149 | − | 0.871793i | 0.0550777 | − | 0.0288997i | ||||
\(911\) | 26.1008 | 0.864759 | 0.432379 | − | 0.901692i | \(-0.357674\pi\) | ||||
0.432379 | + | 0.901692i | \(0.357674\pi\) | |||||||
\(912\) | − | 37.2176i | − | 1.23240i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.7207 | 0.453840 | ||||||||
\(915\) | 15.1018 | 0.499252 | ||||||||
\(916\) | − | 0.637305i | − | 0.0210571i | ||||||
\(917\) | −27.1285 | + | 14.2345i | −0.895861 | + | 0.470065i | ||||
\(918\) | −3.80495 | −0.125582 | ||||||||
\(919\) | 47.3762i | 1.56280i | 0.624034 | + | 0.781398i | \(0.285493\pi\) | ||||
−0.624034 | + | 0.781398i | \(0.714507\pi\) | |||||||
\(920\) | −4.37171 | −0.144131 | ||||||||
\(921\) | 54.0595i | 1.78132i | ||||||||
\(922\) | 17.1115i | 0.563536i | ||||||||
\(923\) | −12.4780 | −0.410717 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.3664 | −1.12996 | ||||||||
\(926\) | 9.69807i | 0.318698i | ||||||||
\(927\) | 29.7444i | 0.976934i | ||||||||
\(928\) | −10.9004 | −0.357822 | ||||||||
\(929\) | 21.8535i | 0.716988i | 0.933532 | + | 0.358494i | \(0.116710\pi\) | ||||
−0.933532 | + | 0.358494i | \(0.883290\pi\) | |||||||
\(930\) | −5.43674 | −0.178278 | ||||||||
\(931\) | −20.1788 | + | 29.2210i | −0.661334 | + | 0.957679i | ||||
\(932\) | − | 4.62054i | − | 0.151351i | ||||||
\(933\) | 10.3312 | 0.338227 | ||||||||
\(934\) | 12.1311 | 0.396942 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 23.3688i | 0.763833i | ||||||||
\(937\) | 21.2841 | 0.695321 | 0.347660 | − | 0.937621i | \(-0.386976\pi\) | ||||
0.347660 | + | 0.937621i | \(0.386976\pi\) | |||||||
\(938\) | 3.99809 | + | 7.61966i | 0.130542 | + | 0.248791i | ||||
\(939\) | 75.9757 | 2.47937 | ||||||||
\(940\) | 10.4379 | 0.340448 | ||||||||
\(941\) | 2.43028 | 0.0792248 | 0.0396124 | − | 0.999215i | \(-0.487388\pi\) | ||||
0.0396124 | + | 0.999215i | \(0.487388\pi\) | |||||||
\(942\) | 4.47568i | 0.145825i | ||||||||
\(943\) | −45.3231 | −1.47592 | ||||||||
\(944\) | − | 11.9789i | − | 0.389880i | ||||||
\(945\) | 9.32173 | − | 4.89117i | 0.303236 | − | 0.159110i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.50040 | 0.0812520 | 0.0406260 | − | 0.999174i | \(-0.487065\pi\) | ||||
0.0406260 | + | 0.999174i | \(0.487065\pi\) | |||||||
\(948\) | 5.99122 | 0.194586 | ||||||||
\(949\) | −5.85134 | −0.189943 | ||||||||
\(950\) | − | 11.8279i | − | 0.383747i | ||||||
\(951\) | − | 18.3304i | − | 0.594405i | ||||||
\(952\) | 2.65229 | + | 5.05480i | 0.0859612 | + | 0.163827i | ||||
\(953\) | − | 23.0007i | − | 0.745065i | −0.928019 | − | 0.372532i | \(-0.878490\pi\) | ||
0.928019 | − | 0.372532i | \(-0.121510\pi\) | |||||||
\(954\) | − | 16.2950i | − | 0.527569i | ||||||
\(955\) | − | 0.373262i | − | 0.0120785i | ||||||
\(956\) | 30.7602i | 0.994856i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 19.6000i | − | 0.633246i | ||||||
\(959\) | −23.1452 | + | 12.1445i | −0.747399 | + | 0.392165i | ||||
\(960\) | 4.43298 | 0.143074 | ||||||||
\(961\) | −7.89110 | −0.254552 | ||||||||
\(962\) | 8.72864i | 0.281423i | ||||||||
\(963\) | − | 42.5128i | − | 1.36996i | ||||||
\(964\) | −14.9583 | −0.481774 | ||||||||
\(965\) | 7.48543 | 0.240965 | ||||||||
\(966\) | −13.0742 | + | 6.86013i | −0.420656 | + | 0.220721i | ||||
\(967\) | 38.6426i | 1.24266i | 0.783548 | + | 0.621331i | \(0.213408\pi\) | ||||
−0.783548 | + | 0.621331i | \(0.786592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.7326i | 0.537527i | ||||||||
\(970\) | − | 1.76221i | − | 0.0565812i | ||||||
\(971\) | 55.2628i | 1.77347i | 0.462280 | + | 0.886734i | \(0.347032\pi\) | ||||
−0.462280 | + | 0.886734i | \(0.652968\pi\) | |||||||
\(972\) | − | 18.7949i | − | 0.602847i | ||||||
\(973\) | 23.9346 | − | 12.5587i | 0.767308 | − | 0.402612i | ||||
\(974\) | − | 0.419333i | − | 0.0134363i | ||||||
\(975\) | − | 31.2910i | − | 1.00211i | ||||||
\(976\) | 22.1848 | 0.710118 | ||||||||
\(977\) | 53.9445 | 1.72584 | 0.862919 | − | 0.505343i | \(-0.168634\pi\) | ||||
0.862919 | + | 0.505343i | \(0.168634\pi\) | |||||||
\(978\) | 2.96005 | 0.0946519 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.05954 | − | 4.18447i | −0.193565 | − | 0.133668i | ||||
\(981\) | 70.3873i | 2.24729i | ||||||||
\(982\) | 13.7706 | 0.439437 | ||||||||
\(983\) | − | 31.9443i | − | 1.01887i | −0.860510 | − | 0.509433i | \(-0.829855\pi\) | ||
0.860510 | − | 0.509433i | \(-0.170145\pi\) | |||||||
\(984\) | −63.8058 | −2.03405 | ||||||||
\(985\) | 7.48104 | 0.238366 | ||||||||
\(986\) | 1.24316 | 0.0395903 | ||||||||
\(987\) | 66.9481 | − | 35.1281i | 2.13098 | − | 1.11814i | ||||
\(988\) | 20.7664 | 0.660666 | ||||||||
\(989\) | − | 6.67550i | − | 0.212269i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.5004 | 1.47713 | 0.738567 | − | 0.674180i | \(-0.235503\pi\) | ||||
0.738567 | + | 0.674180i | \(0.235503\pi\) | |||||||
\(992\) | −31.4842 | −0.999623 | ||||||||
\(993\) | − | 27.1161i | − | 0.860504i | ||||||
\(994\) | −3.29167 | − | 6.27335i | −0.104405 | − | 0.198979i | ||||
\(995\) | −5.12906 | −0.162602 | ||||||||
\(996\) | − | 39.7820i | − | 1.26054i | ||||||
\(997\) | −54.9489 | −1.74025 | −0.870125 | − | 0.492831i | \(-0.835962\pi\) | ||||
−0.870125 | + | 0.492831i | \(0.835962\pi\) | |||||||
\(998\) | 10.0092i | 0.316834i | ||||||||
\(999\) | 48.9718i | 1.54940i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))