Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.d (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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.1 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.m.1999.4 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.449490i | − | 0.169891i | −0.996386 | − | 0.0849456i | \(-0.972928\pi\) | ||
0.996386 | − | 0.0849456i | \(-0.0270716\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 2.00000i | −0.316228 | − | 0.632456i | ||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | −0.449490 | −0.120131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.44949 | −1.93845 | −0.969223 | − | 0.246185i | \(-0.920823\pi\) | ||||
−0.969223 | + | 0.246185i | \(0.920823\pi\) | |||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.89898i | − | 1.04447i | ||||||
\(23\) | 0.898979i | 0.187450i | 0.995598 | + | 0.0937251i | \(0.0298775\pi\) | ||||
−0.995598 | + | 0.0937251i | \(0.970123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.449490i | 0.0849456i | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.44949 | −1.15836 | −0.579181 | − | 0.815199i | \(-0.696628\pi\) | ||||
−0.579181 | + | 0.815199i | \(0.696628\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.89898 | −0.840168 | ||||||||
\(35\) | −0.449490 | − | 0.898979i | −0.0759776 | − | 0.151955i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 8.44949i | 1.37069i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | + | 2.00000i | 0.158114 | + | 0.316228i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | −4.89898 | −0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.898979 | 0.132547 | ||||||||
\(47\) | 0.449490i | 0.0655648i | 0.999463 | + | 0.0327824i | \(0.0104368\pi\) | ||||
−0.999463 | + | 0.0327824i | \(0.989563\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.79796 | 0.971137 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000i | 0.554700i | ||||||||
\(53\) | 7.79796i | 1.07113i | 0.844493 | + | 0.535566i | \(0.179902\pi\) | ||||
−0.844493 | + | 0.535566i | \(0.820098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.79796 | − | 4.89898i | 1.32116 | − | 0.660578i | ||||
\(56\) | 0.449490 | 0.0600656 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.44949 | −1.10003 | −0.550015 | − | 0.835155i | \(-0.685378\pi\) | ||||
−0.550015 | + | 0.835155i | \(0.685378\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000 | 1.53644 | 0.768221 | − | 0.640184i | \(-0.221142\pi\) | ||||
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | 6.44949i | 0.819086i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | − | 8.00000i | −0.496139 | − | 0.992278i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.4495i | − | 1.27661i | −0.769784 | − | 0.638304i | \(-0.779636\pi\) | ||
0.769784 | − | 0.638304i | \(-0.220364\pi\) | |||||||
\(68\) | 4.89898i | 0.594089i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.898979 | + | 0.449490i | −0.107449 | + | 0.0537243i | ||||
\(71\) | 4.89898 | 0.581402 | 0.290701 | − | 0.956814i | \(-0.406112\pi\) | ||||
0.290701 | + | 0.956814i | \(0.406112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.44949 | 0.969223 | ||||||||
\(77\) | − | 2.20204i | − | 0.250946i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.55051 | −0.174446 | −0.0872230 | − | 0.996189i | \(-0.527799\pi\) | ||||
−0.0872230 | + | 0.996189i | \(0.527799\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.00000i | 0.220863i | ||||||||
\(83\) | − | 14.4495i | − | 1.58604i | −0.609197 | − | 0.793019i | \(-0.708508\pi\) | ||
0.609197 | − | 0.793019i | \(-0.291492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.89898 | − | 9.79796i | −0.531369 | − | 1.06274i | ||||
\(86\) | −4.00000 | −0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.89898i | 0.522233i | ||||||||
\(89\) | −3.79796 | −0.402583 | −0.201291 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.79796 | −0.188477 | ||||||||
\(92\) | − | 0.898979i | − | 0.0937251i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.449490 | 0.0463613 | ||||||||
\(95\) | −16.8990 | + | 8.44949i | −1.73380 | + | 0.866899i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.00000i | − | 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | − | 6.79796i | − | 0.686698i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 18.6969 | 1.86041 | 0.930207 | − | 0.367034i | \(-0.119627\pi\) | ||||
0.930207 | + | 0.367034i | \(0.119627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.79796i | 0.965422i | 0.875780 | + | 0.482711i | \(0.160348\pi\) | ||||
−0.875780 | + | 0.482711i | \(0.839652\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.79796 | 0.757405 | ||||||||
\(107\) | 10.4495i | 1.01019i | 0.863064 | + | 0.505095i | \(0.168543\pi\) | ||||
−0.863064 | + | 0.505095i | \(0.831457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.7980 | −1.32160 | −0.660802 | − | 0.750560i | \(-0.729784\pi\) | ||||
−0.660802 | + | 0.750560i | \(0.729784\pi\) | |||||||
\(110\) | −4.89898 | − | 9.79796i | −0.467099 | − | 0.934199i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 0.449490i | − | 0.0424728i | ||||||
\(113\) | − | 12.8990i | − | 1.21343i | −0.794918 | − | 0.606717i | \(-0.792486\pi\) | ||
0.794918 | − | 0.606717i | \(-0.207514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.898979 | + | 1.79796i | 0.0838303 | + | 0.167661i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.44949i | 0.777839i | ||||||||
\(119\) | −2.20204 | −0.201861 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | − | 12.0000i | − | 1.08643i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.44949 | 0.579181 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.3485i | − | 1.53943i | −0.638389 | − | 0.769714i | \(-0.720399\pi\) | ||
0.638389 | − | 0.769714i | \(-0.279601\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.00000 | + | 4.00000i | −0.701646 | + | 0.350823i | ||||
\(131\) | −14.2474 | −1.24481 | −0.622403 | − | 0.782697i | \(-0.713843\pi\) | ||||
−0.622403 | + | 0.782697i | \(0.713843\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.79796i | 0.329325i | ||||||||
\(134\) | −10.4495 | −0.902698 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.89898 | 0.420084 | ||||||||
\(137\) | 19.5959i | 1.67419i | 0.547056 | + | 0.837096i | \(0.315749\pi\) | ||||
−0.547056 | + | 0.837096i | \(0.684251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7980 | −1.17033 | −0.585164 | − | 0.810915i | \(-0.698970\pi\) | ||||
−0.585164 | + | 0.810915i | \(0.698970\pi\) | |||||||
\(140\) | 0.449490 | + | 0.898979i | 0.0379888 | + | 0.0759776i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 4.89898i | − | 0.411113i | ||||||
\(143\) | − | 19.5959i | − | 1.63869i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 10.6969 | 0.876327 | 0.438164 | − | 0.898895i | \(-0.355629\pi\) | ||||
0.438164 | + | 0.898895i | \(0.355629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | − | 8.44949i | − | 0.685344i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.20204 | −0.177446 | ||||||||
\(155\) | −12.8990 | + | 6.44949i | −1.03607 | + | 0.518035i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7980i | 0.941580i | 0.882245 | + | 0.470790i | \(0.156031\pi\) | ||||
−0.882245 | + | 0.470790i | \(0.843969\pi\) | |||||||
\(158\) | 1.55051i | 0.123352i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | − | 2.00000i | −0.0790569 | − | 0.158114i | ||||
\(161\) | 0.404082 | 0.0318461 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.20204i | 0.172477i | 0.996275 | + | 0.0862386i | \(0.0274847\pi\) | ||||
−0.996275 | + | 0.0862386i | \(0.972515\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4495 | −1.12150 | ||||||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | −9.79796 | + | 4.89898i | −0.751469 | + | 0.375735i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 0.202041i | 0.0153609i | 0.999971 | + | 0.00768045i | \(0.00244479\pi\) | ||||
−0.999971 | + | 0.00768045i | \(0.997555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.79796 | − | 1.34847i | −0.135913 | − | 0.101935i | ||||
\(176\) | 4.89898 | 0.369274 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.79796i | 0.284669i | ||||||||
\(179\) | 5.34847 | 0.399763 | 0.199882 | − | 0.979820i | \(-0.435944\pi\) | ||||
0.199882 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6969 | −1.38973 | −0.694866 | − | 0.719139i | \(-0.744536\pi\) | ||||
−0.694866 | + | 0.719139i | \(0.744536\pi\) | |||||||
\(182\) | 1.79796i | 0.133274i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.898979 | −0.0662736 | ||||||||
\(185\) | 1.00000 | + | 2.00000i | 0.0735215 | + | 0.147043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 24.0000i | − | 1.75505i | ||||||
\(188\) | − | 0.449490i | − | 0.0327824i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.44949 | + | 16.8990i | 0.612990 | + | 1.22598i | ||||
\(191\) | 3.34847 | 0.242287 | 0.121143 | − | 0.992635i | \(-0.461344\pi\) | ||||
0.121143 | + | 0.992635i | \(0.461344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.0000i | − | 1.00774i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) | ||
0.863779 | − | 0.503871i | \(-0.168091\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.79796 | −0.485568 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.55051 | −0.109913 | −0.0549564 | − | 0.998489i | \(-0.517502\pi\) | ||||
−0.0549564 | + | 0.998489i | \(0.517502\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 18.6969i | − | 1.31551i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | + | 2.00000i | −0.279372 | + | 0.139686i | ||||
\(206\) | 9.79796 | 0.682656 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.00000i | − | 0.277350i | ||||||
\(209\) | −41.3939 | −2.86327 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.6969 | 1.56252 | 0.781261 | − | 0.624205i | \(-0.214577\pi\) | ||||
0.781261 | + | 0.624205i | \(0.214577\pi\) | |||||||
\(212\) | − | 7.79796i | − | 0.535566i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.4495 | 0.714312 | ||||||||
\(215\) | −4.00000 | − | 8.00000i | −0.272798 | − | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.89898i | 0.196796i | ||||||||
\(218\) | 13.7980i | 0.934516i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.79796 | + | 4.89898i | −0.660578 | + | 0.330289i | ||||
\(221\) | −19.5959 | −1.31816 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.44949i | 0.297960i | 0.988840 | + | 0.148980i | \(0.0475990\pi\) | ||||
−0.988840 | + | 0.148980i | \(0.952401\pi\) | |||||||
\(224\) | −0.449490 | −0.0300328 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.8990 | −0.858027 | ||||||||
\(227\) | 15.1010i | 1.00229i | 0.865363 | + | 0.501145i | \(0.167088\pi\) | ||||
−0.865363 | + | 0.501145i | \(0.832912\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 1.79796 | − | 0.898979i | 0.118554 | − | 0.0592770i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.79796i | − | 0.641886i | −0.947099 | − | 0.320943i | \(-0.896000\pi\) | ||
0.947099 | − | 0.320943i | \(-0.104000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.449490 | + | 0.898979i | 0.0293215 | + | 0.0586430i | ||||
\(236\) | 8.44949 | 0.550015 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.20204i | 0.142737i | ||||||||
\(239\) | 26.0454 | 1.68474 | 0.842369 | − | 0.538902i | \(-0.181161\pi\) | ||||
0.842369 | + | 0.538902i | \(0.181161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7980 | −0.759973 | −0.379987 | − | 0.924992i | \(-0.624071\pi\) | ||||
−0.379987 | + | 0.924992i | \(0.624071\pi\) | |||||||
\(242\) | − | 13.0000i | − | 0.835672i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.0000 | −0.768221 | ||||||||
\(245\) | 13.5959 | − | 6.79796i | 0.868611 | − | 0.434306i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.7980i | 2.15051i | ||||||||
\(248\) | − | 6.44949i | − | 0.409543i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | −6.65153 | −0.419841 | −0.209920 | − | 0.977718i | \(-0.567321\pi\) | ||||
−0.209920 | + | 0.977718i | \(0.567321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.40408i | 0.276882i | ||||||||
\(254\) | −17.3485 | −1.08854 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.89898i | − | 0.305590i | −0.988258 | − | 0.152795i | \(-0.951173\pi\) | ||
0.988258 | − | 0.152795i | \(-0.0488274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.449490 | 0.0279299 | ||||||||
\(260\) | 4.00000 | + | 8.00000i | 0.248069 | + | 0.496139i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.2474i | 0.880210i | ||||||||
\(263\) | 26.2474i | 1.61849i | 0.587473 | + | 0.809244i | \(0.300123\pi\) | ||||
−0.587473 | + | 0.809244i | \(0.699877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.79796 | + | 15.5959i | 0.479025 | + | 0.958050i | ||||
\(266\) | 3.79796 | 0.232868 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.4495i | 0.638304i | ||||||||
\(269\) | 10.6969 | 0.652204 | 0.326102 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326102 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4949 | 1.00199 | 0.500997 | − | 0.865449i | \(-0.332967\pi\) | ||||
0.500997 | + | 0.865449i | \(0.332967\pi\) | |||||||
\(272\) | − | 4.89898i | − | 0.297044i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.5959 | 1.18383 | ||||||||
\(275\) | 14.6969 | − | 19.5959i | 0.886259 | − | 1.18168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 19.5959i | − | 1.17740i | −0.808350 | − | 0.588702i | \(-0.799639\pi\) | ||
0.808350 | − | 0.588702i | \(-0.200361\pi\) | |||||||
\(278\) | 13.7980i | 0.827547i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.898979 | − | 0.449490i | 0.0537243 | − | 0.0268622i | ||||
\(281\) | −8.20204 | −0.489293 | −0.244646 | − | 0.969612i | \(-0.578672\pi\) | ||||
−0.244646 | + | 0.969612i | \(0.578672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.5959i | 1.40263i | 0.712851 | + | 0.701316i | \(0.247404\pi\) | ||||
−0.712851 | + | 0.701316i | \(0.752596\pi\) | |||||||
\(284\) | −4.89898 | −0.290701 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.5959 | −1.15873 | ||||||||
\(287\) | 0.898979i | 0.0530651i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00000i | 0.234082i | ||||||||
\(293\) | − | 13.5959i | − | 0.794282i | −0.917758 | − | 0.397141i | \(-0.870002\pi\) | ||
0.917758 | − | 0.397141i | \(-0.129998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.8990 | + | 8.44949i | −0.983897 | + | 0.491948i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 10.6969i | − | 0.619657i | ||||||
\(299\) | 3.59592 | 0.207957 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.79796 | −0.103633 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.44949 | −0.484611 | ||||||||
\(305\) | 24.0000 | − | 12.0000i | 1.37424 | − | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.1464i | − | 1.20689i | −0.797404 | − | 0.603445i | \(-0.793794\pi\) | ||
0.797404 | − | 0.603445i | \(-0.206206\pi\) | |||||||
\(308\) | 2.20204i | 0.125473i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.44949 | + | 12.8990i | 0.366306 | + | 0.732613i | ||||
\(311\) | −7.34847 | −0.416693 | −0.208347 | − | 0.978055i | \(-0.566808\pi\) | ||||
−0.208347 | + | 0.978055i | \(0.566808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.5959i | − | 1.22067i | −0.792142 | − | 0.610337i | \(-0.791034\pi\) | ||
0.792142 | − | 0.610337i | \(-0.208966\pi\) | |||||||
\(314\) | 11.7980 | 0.665797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.55051 | 0.0872230 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.00000 | + | 1.00000i | −0.111803 | + | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 0.404082i | − | 0.0225186i | ||||||
\(323\) | 41.3939i | 2.30322i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0000 | − | 12.0000i | −0.887520 | − | 0.665640i | ||||
\(326\) | 2.20204 | 0.121960 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.00000i | − | 0.110432i | ||||||
\(329\) | 0.202041 | 0.0111389 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2474 | −0.563251 | −0.281625 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281625 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(332\) | 14.4495i | 0.793019i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −10.4495 | − | 20.8990i | −0.570917 | − | 1.14183i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.5959i | 1.93903i | 0.245026 | + | 0.969517i | \(0.421204\pi\) | ||||
−0.245026 | + | 0.969517i | \(0.578796\pi\) | |||||||
\(338\) | 3.00000i | 0.163178i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.89898 | + | 9.79796i | 0.265684 | + | 0.531369i | ||||
\(341\) | −31.5959 | −1.71101 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.20204i | − | 0.334879i | ||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.202041 | 0.0108618 | ||||||||
\(347\) | − | 21.7980i | − | 1.17018i | −0.810970 | − | 0.585088i | \(-0.801060\pi\) | ||
0.810970 | − | 0.585088i | \(-0.198940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8990 | −0.904582 | −0.452291 | − | 0.891871i | \(-0.649393\pi\) | ||||
−0.452291 | + | 0.891871i | \(0.649393\pi\) | |||||||
\(350\) | −1.34847 | + | 1.79796i | −0.0720787 | + | 0.0961049i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.89898i | − | 0.261116i | ||||||
\(353\) | − | 6.00000i | − | 0.319348i | −0.987170 | − | 0.159674i | \(-0.948956\pi\) | ||
0.987170 | − | 0.159674i | \(-0.0510443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.79796 | − | 4.89898i | 0.520022 | − | 0.260011i | ||||
\(356\) | 3.79796 | 0.201291 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 5.34847i | − | 0.282675i | ||||||
\(359\) | −3.10102 | −0.163666 | −0.0818328 | − | 0.996646i | \(-0.526077\pi\) | ||||
−0.0818328 | + | 0.996646i | \(0.526077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.3939 | 2.75757 | ||||||||
\(362\) | 18.6969i | 0.982689i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.79796 | 0.0942387 | ||||||||
\(365\) | −4.00000 | − | 8.00000i | −0.209370 | − | 0.418739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 17.3485i | − | 0.905583i | −0.891617 | − | 0.452791i | \(-0.850428\pi\) | ||
0.891617 | − | 0.452791i | \(-0.149572\pi\) | |||||||
\(368\) | 0.898979i | 0.0468625i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.00000 | − | 1.00000i | 0.103975 | − | 0.0519875i | ||||
\(371\) | 3.50510 | 0.181976 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.79796i | − | 0.403763i | −0.979410 | − | 0.201882i | \(-0.935294\pi\) | ||
0.979410 | − | 0.201882i | \(-0.0647056\pi\) | |||||||
\(374\) | −24.0000 | −1.24101 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.449490 | −0.0231807 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.59592 | −0.390176 | −0.195088 | − | 0.980786i | \(-0.562499\pi\) | ||||
−0.195088 | + | 0.980786i | \(0.562499\pi\) | |||||||
\(380\) | 16.8990 | − | 8.44949i | 0.866899 | − | 0.433450i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3.34847i | − | 0.171323i | ||||||
\(383\) | − | 5.30306i | − | 0.270974i | −0.990779 | − | 0.135487i | \(-0.956740\pi\) | ||
0.990779 | − | 0.135487i | \(-0.0432599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.20204 | − | 4.40408i | −0.112226 | − | 0.224453i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.00000i | 0.101535i | ||||||||
\(389\) | −6.20204 | −0.314456 | −0.157228 | − | 0.987562i | \(-0.550256\pi\) | ||||
−0.157228 | + | 0.987562i | \(0.550256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40408 | 0.222724 | ||||||||
\(392\) | 6.79796i | 0.343349i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −3.10102 | + | 1.55051i | −0.156029 | + | 0.0780146i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 35.7980i | − | 1.79665i | −0.439334 | − | 0.898324i | \(-0.644785\pi\) | ||
0.439334 | − | 0.898324i | \(-0.355215\pi\) | |||||||
\(398\) | 1.55051i | 0.0777201i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 4.20204 | 0.209840 | 0.104920 | − | 0.994481i | \(-0.466541\pi\) | ||||
0.104920 | + | 0.994481i | \(0.466541\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.7980i | 1.28509i | ||||||||
\(404\) | −18.6969 | −0.930207 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.89898i | 0.242833i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 2.00000 | + | 4.00000i | 0.0987730 | + | 0.197546i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 9.79796i | − | 0.482711i | ||||||
\(413\) | 3.79796i | 0.186885i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.4495 | − | 28.8990i | −0.709298 | − | 1.41860i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 41.3939i | 2.02464i | ||||||||
\(419\) | −13.7980 | −0.674074 | −0.337037 | − | 0.941491i | \(-0.609425\pi\) | ||||
−0.337037 | + | 0.941491i | \(0.609425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5959 | 0.955047 | 0.477523 | − | 0.878619i | \(-0.341535\pi\) | ||||
0.477523 | + | 0.878619i | \(0.341535\pi\) | |||||||
\(422\) | − | 22.6969i | − | 1.10487i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.79796 | −0.378702 | ||||||||
\(425\) | −19.5959 | − | 14.6969i | −0.950542 | − | 0.712906i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.39388i | − | 0.261028i | ||||||
\(428\) | − | 10.4495i | − | 0.505095i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | + | 4.00000i | −0.385794 | + | 0.192897i | ||||
\(431\) | 40.2474 | 1.93865 | 0.969326 | − | 0.245780i | \(-0.0790440\pi\) | ||||
0.969326 | + | 0.245780i | \(0.0790440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.3939i | 1.79704i | 0.438938 | + | 0.898518i | \(0.355355\pi\) | ||||
−0.438938 | + | 0.898518i | \(0.644645\pi\) | |||||||
\(434\) | 2.89898 | 0.139155 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.7980 | 0.660802 | ||||||||
\(437\) | − | 7.59592i | − | 0.363362i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.3485 | −1.68709 | −0.843545 | − | 0.537058i | \(-0.819536\pi\) | ||||
−0.843545 | + | 0.537058i | \(0.819536\pi\) | |||||||
\(440\) | 4.89898 | + | 9.79796i | 0.233550 | + | 0.467099i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5959i | 0.932083i | ||||||||
\(443\) | 39.3485i | 1.86950i | 0.355303 | + | 0.934751i | \(0.384378\pi\) | ||||
−0.355303 | + | 0.934751i | \(0.615622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.59592 | + | 3.79796i | −0.360081 | + | 0.180041i | ||||
\(446\) | 4.44949 | 0.210689 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.449490i | 0.0212364i | ||||||||
\(449\) | 3.79796 | 0.179237 | 0.0896184 | − | 0.995976i | \(-0.471435\pi\) | ||||
0.0896184 | + | 0.995976i | \(0.471435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.79796 | −0.461368 | ||||||||
\(452\) | 12.8990i | 0.606717i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.1010 | 0.708726 | ||||||||
\(455\) | −3.59592 | + | 1.79796i | −0.168579 | + | 0.0842896i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.00000i | − | 0.0935561i | −0.998905 | − | 0.0467780i | \(-0.985105\pi\) | ||
0.998905 | − | 0.0467780i | \(-0.0148953\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.898979 | − | 1.79796i | −0.0419151 | − | 0.0838303i | ||||
\(461\) | 14.2020 | 0.661455 | 0.330727 | − | 0.943726i | \(-0.392706\pi\) | ||||
0.330727 | + | 0.943726i | \(0.392706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.4949i | − | 1.32427i | −0.749384 | − | 0.662135i | \(-0.769650\pi\) | ||
0.749384 | − | 0.662135i | \(-0.230350\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.79796 | −0.453882 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.69694 | −0.216884 | ||||||||
\(470\) | 0.898979 | − | 0.449490i | 0.0414668 | − | 0.0207334i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 8.44949i | − | 0.388919i | ||||||
\(473\) | − | 19.5959i | − | 0.901021i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.3485 | + | 33.7980i | −1.16307 | + | 1.55076i | ||||
\(476\) | 2.20204 | 0.100930 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 26.0454i | − | 1.19129i | ||||||
\(479\) | −29.1464 | −1.33173 | −0.665867 | − | 0.746070i | \(-0.731938\pi\) | ||||
−0.665867 | + | 0.746070i | \(0.731938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 11.7980i | 0.537382i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.0000 | −0.590909 | ||||||||
\(485\) | −2.00000 | − | 4.00000i | −0.0908153 | − | 0.181631i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.3939i | 1.33196i | 0.745968 | + | 0.665982i | \(0.231987\pi\) | ||||
−0.745968 | + | 0.665982i | \(0.768013\pi\) | |||||||
\(488\) | 12.0000i | 0.543214i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.79796 | − | 13.5959i | −0.307100 | − | 0.614201i | ||||
\(491\) | 38.6969 | 1.74637 | 0.873184 | − | 0.487390i | \(-0.162051\pi\) | ||||
0.873184 | + | 0.487390i | \(0.162051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 33.7980 | 1.52064 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.44949 | −0.289591 | ||||||||
\(497\) | − | 2.20204i | − | 0.0987750i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3485 | 1.13475 | 0.567377 | − | 0.823458i | \(-0.307958\pi\) | ||||
0.567377 | + | 0.823458i | \(0.307958\pi\) | |||||||
\(500\) | −2.00000 | + | 11.0000i | −0.0894427 | + | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.65153i | 0.296872i | ||||||||
\(503\) | 17.7980i | 0.793572i | 0.917911 | + | 0.396786i | \(0.129874\pi\) | ||||
−0.917911 | + | 0.396786i | \(0.870126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.3939 | − | 18.6969i | 1.66401 | − | 0.832003i | ||||
\(506\) | 4.40408 | 0.195785 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.3485i | 0.769714i | ||||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.79796 | −0.0795370 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.89898 | −0.216085 | ||||||||
\(515\) | 9.79796 | + | 19.5959i | 0.431750 | + | 0.863499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.20204i | 0.0968457i | ||||||||
\(518\) | − | 0.449490i | − | 0.0197494i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.00000 | − | 4.00000i | 0.350823 | − | 0.175412i | ||||
\(521\) | 1.79796 | 0.0787700 | 0.0393850 | − | 0.999224i | \(-0.487460\pi\) | ||||
0.0393850 | + | 0.999224i | \(0.487460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.898979i | − | 0.0393096i | −0.999807 | − | 0.0196548i | \(-0.993743\pi\) | ||
0.999807 | − | 0.0196548i | \(-0.00625672\pi\) | |||||||
\(524\) | 14.2474 | 0.622403 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.2474 | 1.14444 | ||||||||
\(527\) | 31.5959i | 1.37634i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1918 | 0.964862 | ||||||||
\(530\) | 15.5959 | − | 7.79796i | 0.677443 | − | 0.338722i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 3.79796i | − | 0.164662i | ||||||
\(533\) | 8.00000i | 0.346518i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4495 | + | 20.8990i | 0.451771 | + | 0.903542i | ||||
\(536\) | 10.4495 | 0.451349 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.6969i | − | 0.461178i | ||||||
\(539\) | 33.3031 | 1.43446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.5959 | 1.70236 | 0.851181 | − | 0.524873i | \(-0.175887\pi\) | ||||
0.851181 | + | 0.524873i | \(0.175887\pi\) | |||||||
\(542\) | − | 16.4949i | − | 0.708517i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.89898 | −0.210042 | ||||||||
\(545\) | −27.5959 | + | 13.7980i | −1.18208 | + | 0.591040i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6969i | 0.799423i | 0.916641 | + | 0.399712i | \(0.130890\pi\) | ||||
−0.916641 | + | 0.399712i | \(0.869110\pi\) | |||||||
\(548\) | − | 19.5959i | − | 0.837096i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −19.5959 | − | 14.6969i | −0.835573 | − | 0.626680i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.696938i | 0.0296368i | ||||||||
\(554\) | −19.5959 | −0.832551 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.7980 | 0.585164 | ||||||||
\(557\) | 12.0000i | 0.508456i | 0.967144 | + | 0.254228i | \(0.0818214\pi\) | ||||
−0.967144 | + | 0.254228i | \(0.918179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | −0.449490 | − | 0.898979i | −0.0189944 | − | 0.0379888i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.20204i | 0.345982i | ||||||||
\(563\) | − | 5.30306i | − | 0.223497i | −0.993736 | − | 0.111749i | \(-0.964355\pi\) | ||
0.993736 | − | 0.111749i | \(-0.0356452\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.8990 | − | 25.7980i | −0.542664 | − | 1.08533i | ||||
\(566\) | 23.5959 | 0.991810 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.89898i | 0.205557i | ||||||||
\(569\) | −17.5959 | −0.737659 | −0.368830 | − | 0.929497i | \(-0.620241\pi\) | ||||
−0.368830 | + | 0.929497i | \(0.620241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.3939 | 1.39749 | 0.698745 | − | 0.715371i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715371i | \(0.253742\pi\) | |||||||
\(572\) | 19.5959i | 0.819346i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.898979 | 0.0375227 | ||||||||
\(575\) | 3.59592 | + | 2.69694i | 0.149960 | + | 0.112470i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.30306i | − | 0.0542472i | −0.999632 | − | 0.0271236i | \(-0.991365\pi\) | ||
0.999632 | − | 0.0271236i | \(-0.00863476\pi\) | |||||||
\(578\) | 7.00000i | 0.291162i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.49490 | −0.269454 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.2020i | 1.58217i | ||||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5959 | −0.561642 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.4949 | 2.24542 | ||||||||
\(590\) | 8.44949 | + | 16.8990i | 0.347860 | + | 0.695720i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 24.0000i | 0.985562i | 0.870153 | + | 0.492781i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492781i | \(0.835980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.40408 | + | 2.20204i | −0.180550 | + | 0.0902749i | ||||
\(596\) | −10.6969 | −0.438164 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 3.59592i | − | 0.147048i | ||||||
\(599\) | −27.5959 | −1.12754 | −0.563769 | − | 0.825932i | \(-0.690649\pi\) | ||||
−0.563769 | + | 0.825932i | \(0.690649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 1.79796i | 0.0732793i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 26.0000 | − | 13.0000i | 1.05705 | − | 0.528525i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.69694i | − | 0.109465i | −0.998501 | − | 0.0547327i | \(-0.982569\pi\) | ||
0.998501 | − | 0.0547327i | \(-0.0174307\pi\) | |||||||
\(608\) | 8.44949i | 0.342672i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | − | 24.0000i | −0.485866 | − | 0.971732i | ||||
\(611\) | 1.79796 | 0.0727376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.2020i | − | 0.815953i | −0.912992 | − | 0.407976i | \(-0.866235\pi\) | ||
0.912992 | − | 0.407976i | \(-0.133765\pi\) | |||||||
\(614\) | −21.1464 | −0.853400 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.20204 | 0.0887228 | ||||||||
\(617\) | 19.5959i | 0.788902i | 0.918917 | + | 0.394451i | \(0.129065\pi\) | ||||
−0.918917 | + | 0.394451i | \(0.870935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.10102 | 0.124641 | 0.0623203 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623203 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(620\) | 12.8990 | − | 6.44949i | 0.518035 | − | 0.259018i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.34847i | 0.294647i | ||||||||
\(623\) | 1.70714i | 0.0683953i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | −21.5959 | −0.863146 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 11.7980i | − | 0.470790i | ||||||
\(629\) | 4.89898 | 0.195335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.24745 | 0.169088 | 0.0845441 | − | 0.996420i | \(-0.473057\pi\) | ||||
0.0845441 | + | 0.996420i | \(0.473057\pi\) | |||||||
\(632\) | − | 1.55051i | − | 0.0616760i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −17.3485 | − | 34.6969i | −0.688453 | − | 1.37691i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 27.1918i | − | 1.07738i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | + | 2.00000i | 0.0395285 | + | 0.0790569i | ||||
\(641\) | 1.79796 | 0.0710151 | 0.0355076 | − | 0.999369i | \(-0.488695\pi\) | ||||
0.0355076 | + | 0.999369i | \(0.488695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8990i | 1.29741i | 0.761040 | + | 0.648705i | \(0.224689\pi\) | ||||
−0.761040 | + | 0.648705i | \(0.775311\pi\) | |||||||
\(644\) | −0.404082 | −0.0159231 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 41.3939 | 1.62862 | ||||||||
\(647\) | 32.0000i | 1.25805i | 0.777385 | + | 0.629025i | \(0.216546\pi\) | ||||
−0.777385 | + | 0.629025i | \(0.783454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.3939 | −1.62485 | ||||||||
\(650\) | −12.0000 | + | 16.0000i | −0.470679 | + | 0.627572i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 2.20204i | − | 0.0862386i | ||||||
\(653\) | 34.0000i | 1.33052i | 0.746611 | + | 0.665261i | \(0.231680\pi\) | ||||
−0.746611 | + | 0.665261i | \(0.768320\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.4949 | + | 14.2474i | −1.11339 | + | 0.556694i | ||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 0.202041i | − | 0.00787638i | ||||||
\(659\) | −7.59592 | −0.295895 | −0.147947 | − | 0.988995i | \(-0.547267\pi\) | ||||
−0.147947 | + | 0.988995i | \(0.547267\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.1918 | 1.83555 | 0.917775 | − | 0.397101i | \(-0.129984\pi\) | ||||
0.917775 | + | 0.397101i | \(0.129984\pi\) | |||||||
\(662\) | 10.2474i | 0.398278i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.4495 | 0.560749 | ||||||||
\(665\) | 3.79796 | + | 7.59592i | 0.147279 | + | 0.294557i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.8990 | + | 10.4495i | −0.807398 | + | 0.403699i | ||||
\(671\) | 58.7878 | 2.26948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.0000i | − | 0.925132i | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||
0.886585 | − | 0.462566i | \(-0.153071\pi\) | |||||||
\(674\) | 35.5959 | 1.37110 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | − | 18.0000i | − | 0.691796i | −0.938272 | − | 0.345898i | \(-0.887574\pi\) | ||
0.938272 | − | 0.345898i | \(-0.112426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.898979 | −0.0344997 | ||||||||
\(680\) | 9.79796 | − | 4.89898i | 0.375735 | − | 0.187867i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.5959i | 1.20987i | ||||||||
\(683\) | − | 23.5959i | − | 0.902873i | −0.892303 | − | 0.451436i | \(-0.850912\pi\) | ||
0.892303 | − | 0.451436i | \(-0.149088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.5959 | + | 39.1918i | 0.748722 | + | 1.49744i | ||||
\(686\) | −6.20204 | −0.236795 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | 31.1918 | 1.18831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2020 | 0.692438 | 0.346219 | − | 0.938154i | \(-0.387465\pi\) | ||||
0.346219 | + | 0.938154i | \(0.387465\pi\) | |||||||
\(692\) | − | 0.202041i | − | 0.00768045i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7980 | −0.827439 | ||||||||
\(695\) | −27.5959 | + | 13.7980i | −1.04677 | + | 0.523386i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.79796i | 0.371124i | ||||||||
\(698\) | 16.8990i | 0.639636i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.79796 | + | 1.34847i | 0.0679565 | + | 0.0509673i | ||||
\(701\) | −5.79796 | −0.218986 | −0.109493 | − | 0.993988i | \(-0.534923\pi\) | ||||
−0.109493 | + | 0.993988i | \(0.534923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.44949i | − | 0.318679i | ||||||
\(704\) | −4.89898 | −0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | − | 8.40408i | − | 0.316068i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7980 | 0.518193 | 0.259097 | − | 0.965851i | \(-0.416575\pi\) | ||||
0.259097 | + | 0.965851i | \(0.416575\pi\) | |||||||
\(710\) | −4.89898 | − | 9.79796i | −0.183855 | − | 0.367711i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 3.79796i | − | 0.142335i | ||||||
\(713\) | − | 5.79796i | − | 0.217135i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.5959 | − | 39.1918i | −0.732846 | − | 1.46569i | ||||
\(716\) | −5.34847 | −0.199882 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.10102i | 0.115729i | ||||||||
\(719\) | 12.4041 | 0.462594 | 0.231297 | − | 0.972883i | \(-0.425703\pi\) | ||||
0.231297 | + | 0.972883i | \(0.425703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.40408 | 0.164017 | ||||||||
\(722\) | − | 52.3939i | − | 1.94990i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.6969 | 0.694866 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.89898i | − | 0.330045i | −0.986290 | − | 0.165022i | \(-0.947230\pi\) | ||
0.986290 | − | 0.165022i | \(-0.0527697\pi\) | |||||||
\(728\) | − | 1.79796i | − | 0.0666368i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | + | 4.00000i | −0.296093 | + | 0.148047i | ||||
\(731\) | −19.5959 | −0.724781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.5959i | − | 0.797663i | −0.917024 | − | 0.398832i | \(-0.869416\pi\) | ||
0.917024 | − | 0.398832i | \(-0.130584\pi\) | |||||||
\(734\) | −17.3485 | −0.640344 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.898979 | 0.0331368 | ||||||||
\(737\) | − | 51.1918i | − | 1.88568i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2020 | 0.963858 | 0.481929 | − | 0.876210i | \(-0.339936\pi\) | ||||
0.481929 | + | 0.876210i | \(0.339936\pi\) | |||||||
\(740\) | −1.00000 | − | 2.00000i | −0.0367607 | − | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 3.50510i | − | 0.128676i | ||||||
\(743\) | − | 38.2474i | − | 1.40316i | −0.712589 | − | 0.701581i | \(-0.752478\pi\) | ||
0.712589 | − | 0.701581i | \(-0.247522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.3939 | − | 10.6969i | 0.783811 | − | 0.391906i | ||||
\(746\) | −7.79796 | −0.285504 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.0000i | 0.877527i | ||||||||
\(749\) | 4.69694 | 0.171622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.30306 | 0.0475494 | 0.0237747 | − | 0.999717i | \(-0.492432\pi\) | ||||
0.0237747 | + | 0.999717i | \(0.492432\pi\) | |||||||
\(752\) | 0.449490i | 0.0163912i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | + | 8.00000i | −0.582300 | + | 0.291150i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.59592i | 0.203387i | 0.994816 | + | 0.101694i | \(0.0324261\pi\) | ||||
−0.994816 | + | 0.101694i | \(0.967574\pi\) | |||||||
\(758\) | 7.59592i | 0.275896i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.44949 | − | 16.8990i | −0.306495 | − | 0.612990i | ||||
\(761\) | 53.1918 | 1.92820 | 0.964101 | − | 0.265535i | \(-0.0855485\pi\) | ||||
0.964101 | + | 0.265535i | \(0.0855485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.20204i | 0.224529i | ||||||||
\(764\) | −3.34847 | −0.121143 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.30306 | −0.191607 | ||||||||
\(767\) | 33.7980i | 1.22037i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2020 | 0.584261 | 0.292130 | − | 0.956379i | \(-0.405636\pi\) | ||||
0.292130 | + | 0.956379i | \(0.405636\pi\) | |||||||
\(770\) | −4.40408 | + | 2.20204i | −0.158712 | + | 0.0793561i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0000i | 0.503871i | ||||||||
\(773\) | − | 6.00000i | − | 0.215805i | −0.994161 | − | 0.107903i | \(-0.965587\pi\) | ||
0.994161 | − | 0.107903i | \(-0.0344134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.3485 | + | 25.7980i | −0.695018 | + | 0.926690i | ||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.20204i | 0.222354i | ||||||||
\(779\) | 16.8990 | 0.605469 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | − | 4.40408i | − | 0.157490i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.79796 | 0.242784 | ||||||||
\(785\) | 11.7980 | + | 23.5959i | 0.421087 | + | 0.842174i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.7423i | 1.59489i | 0.603390 | + | 0.797446i | \(0.293816\pi\) | ||||
−0.603390 | + | 0.797446i | \(0.706184\pi\) | |||||||
\(788\) | − | 2.00000i | − | 0.0712470i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.55051 | + | 3.10102i | 0.0551647 | + | 0.110329i | ||||
\(791\) |