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 | 1999.3 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.m.1999.2 |
$q$-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 | ||||||||
\(7\) | − | 4.44949i | − | 1.68175i | −0.541230 | − | 0.840875i | \(-0.682041\pi\) | ||
0.541230 | − | 0.840875i | \(-0.317959\pi\) | |||||||
\(8\) | − | 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 | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000i | 1.10940i | 0.832050 | + | 0.554700i | \(0.187167\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 4.44949 | 1.18918 | ||||||||
\(15\) | 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 | ||||||||
\(19\) | −3.55051 | −0.814543 | −0.407271 | − | 0.913307i | \(-0.633520\pi\) | ||||
−0.407271 | + | 0.913307i | \(0.633520\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.89898i | − | 1.04447i | ||||||
\(23\) | 8.89898i | 1.85557i | 0.373121 | + | 0.927783i | \(0.378288\pi\) | ||||
−0.373121 | + | 0.927783i | \(0.621712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.44949i | 0.840875i | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.55051 | −0.278480 | −0.139240 | − | 0.990259i | \(-0.544466\pi\) | ||||
−0.139240 | + | 0.990259i | \(0.544466\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.89898 | 0.840168 | ||||||||
\(35\) | 4.44949 | − | 8.89898i | 0.752101 | − | 1.50420i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.00000i | − | 0.164399i | ||||||
\(38\) | − | 3.55051i | − | 0.575969i | ||||||
\(39\) | 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 | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.89898 | −1.31208 | ||||||||
\(47\) | 4.44949i | 0.649025i | 0.945881 | + | 0.324512i | \(0.105200\pi\) | ||||
−0.945881 | + | 0.324512i | \(0.894800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.7980 | −1.82828 | ||||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.00000i | − | 0.554700i | ||||||
\(53\) | 11.7980i | 1.62057i | 0.586033 | + | 0.810287i | \(0.300689\pi\) | ||||
−0.586033 | + | 0.810287i | \(0.699311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.79796 | − | 4.89898i | −1.32116 | − | 0.660578i | ||||
\(56\) | −4.44949 | −0.594588 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.55051 | −0.462237 | −0.231119 | − | 0.972926i | \(-0.574239\pi\) | ||||
−0.231119 | + | 0.972926i | \(0.574239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000 | 1.53644 | 0.768221 | − | 0.640184i | \(-0.221142\pi\) | ||||
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | − | 1.55051i | − | 0.196915i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | + | 8.00000i | −0.496139 | + | 0.992278i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.55051i | 0.678103i | 0.940768 | + | 0.339051i | \(0.110106\pi\) | ||||
−0.940768 | + | 0.339051i | \(0.889894\pi\) | |||||||
\(68\) | 4.89898i | 0.594089i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.89898 | + | 4.44949i | 1.06363 | + | 0.531816i | ||||
\(71\) | −4.89898 | −0.581402 | −0.290701 | − | 0.956814i | \(-0.593888\pi\) | ||||
−0.290701 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.55051 | 0.407271 | ||||||||
\(77\) | 21.7980i | 2.48411i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.44949 | −0.725624 | −0.362812 | − | 0.931862i | \(-0.618183\pi\) | ||||
−0.362812 | + | 0.931862i | \(0.618183\pi\) | |||||||
\(80\) | 2.00000 | + | 1.00000i | 0.223607 | + | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.00000i | − | 0.220863i | ||||||
\(83\) | 9.55051i | 1.04830i | 0.851625 | + | 0.524152i | \(0.175618\pi\) | ||||
−0.851625 | + | 0.524152i | \(0.824382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.89898 | − | 9.79796i | 0.531369 | − | 1.06274i | ||||
\(86\) | −4.00000 | −0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.89898i | 0.522233i | ||||||||
\(89\) | 15.7980 | 1.67458 | 0.837290 | − | 0.546759i | \(-0.184139\pi\) | ||||
0.837290 | + | 0.546759i | \(0.184139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.7980 | 1.86573 | ||||||||
\(92\) | − | 8.89898i | − | 0.927783i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.44949 | −0.458930 | ||||||||
\(95\) | −7.10102 | − | 3.55051i | −0.728549 | − | 0.364275i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | − | 12.7980i | − | 1.29279i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | −10.6969 | −1.06439 | −0.532193 | − | 0.846623i | \(-0.678632\pi\) | ||||
−0.532193 | + | 0.846623i | \(0.678632\pi\) | |||||||
\(102\) | 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 | ||||||||
\(106\) | −11.7980 | −1.14592 | ||||||||
\(107\) | − | 5.55051i | − | 0.536588i | −0.963337 | − | 0.268294i | \(-0.913540\pi\) | ||
0.963337 | − | 0.268294i | \(-0.0864599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.79796 | 0.555344 | 0.277672 | − | 0.960676i | \(-0.410437\pi\) | ||||
0.277672 | + | 0.960676i | \(0.410437\pi\) | |||||||
\(110\) | 4.89898 | − | 9.79796i | 0.467099 | − | 0.934199i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 4.44949i | − | 0.420437i | ||||||
\(113\) | 3.10102i | 0.291719i | 0.989305 | + | 0.145860i | \(0.0465948\pi\) | ||||
−0.989305 | + | 0.145860i | \(0.953405\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.89898 | + | 17.7980i | −0.829834 | + | 1.65967i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.55051i | − | 0.326851i | ||||||
\(119\) | −21.7980 | −1.99822 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 12.0000i | 1.08643i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.55051 | 0.139240 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.65153i | 0.235285i | 0.993056 | + | 0.117643i | \(0.0375337\pi\) | ||||
−0.993056 | + | 0.117643i | \(0.962466\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.00000 | − | 4.00000i | −0.701646 | − | 0.350823i | ||||
\(131\) | 10.2474 | 0.895324 | 0.447662 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447662 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.7980i | 1.36986i | ||||||||
\(134\) | −5.55051 | −0.479491 | ||||||||
\(135\) | 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 | ||||||||
\(139\) | 5.79796 | 0.491776 | 0.245888 | − | 0.969298i | \(-0.420920\pi\) | ||||
0.245888 | + | 0.969298i | \(0.420920\pi\) | |||||||
\(140\) | −4.44949 | + | 8.89898i | −0.376051 | + | 0.752101i | ||||
\(141\) | 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 | ||||||||
\(149\) | −18.6969 | −1.53171 | −0.765856 | − | 0.643012i | \(-0.777685\pi\) | ||||
−0.765856 | + | 0.643012i | \(0.777685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 3.55051i | 0.287984i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.7980 | −1.75653 | ||||||||
\(155\) | −3.10102 | − | 1.55051i | −0.249080 | − | 0.124540i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.79796i | 0.622345i | 0.950353 | + | 0.311172i | \(0.100722\pi\) | ||||
−0.950353 | + | 0.311172i | \(0.899278\pi\) | |||||||
\(158\) | − | 6.44949i | − | 0.513094i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | + | 2.00000i | −0.0790569 | + | 0.158114i | ||||
\(161\) | 39.5959 | 3.12060 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.7980i | − | 1.70735i | −0.520808 | − | 0.853674i | \(-0.674369\pi\) | ||
0.520808 | − | 0.853674i | \(-0.325631\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.55051 | −0.741263 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 9.79796 | + | 4.89898i | 0.751469 | + | 0.375735i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 4.00000i | − | 0.304997i | ||||||
\(173\) | − | 19.7980i | − | 1.50521i | −0.658472 | − | 0.752605i | \(-0.728797\pi\) | ||
0.658472 | − | 0.752605i | \(-0.271203\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.7980 | − | 13.3485i | 1.34540 | − | 1.00905i | ||||
\(176\) | −4.89898 | −0.369274 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.7980i | 1.18411i | ||||||||
\(179\) | −9.34847 | −0.698737 | −0.349369 | − | 0.936985i | \(-0.613604\pi\) | ||||
−0.349369 | + | 0.936985i | \(0.613604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6969 | 0.795097 | 0.397549 | − | 0.917581i | \(-0.369861\pi\) | ||||
0.397549 | + | 0.917581i | \(0.369861\pi\) | |||||||
\(182\) | 17.7980i | 1.31927i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.89898 | 0.656041 | ||||||||
\(185\) | 1.00000 | − | 2.00000i | 0.0735215 | − | 0.147043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0000i | 1.75505i | ||||||||
\(188\) | − | 4.44949i | − | 0.324512i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.55051 | − | 7.10102i | 0.257581 | − | 0.515162i | ||||
\(191\) | −11.3485 | −0.821146 | −0.410573 | − | 0.911828i | \(-0.634671\pi\) | ||||
−0.410573 | + | 0.911828i | \(0.634671\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000i | 1.00774i | 0.863779 | + | 0.503871i | \(0.168091\pi\) | ||||
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.7980 | 0.914140 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.44949 | −0.457192 | −0.228596 | − | 0.973521i | \(-0.573414\pi\) | ||||
−0.228596 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(200\) | 4.00000 | − | 3.00000i | 0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 10.6969i | − | 0.752634i | ||||||
\(203\) | 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 | ||||||||
\(209\) | 17.3939 | 1.20316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.69694 | −0.461036 | −0.230518 | − | 0.973068i | \(-0.574042\pi\) | ||||
−0.230518 | + | 0.973068i | \(0.574042\pi\) | |||||||
\(212\) | − | 11.7980i | − | 0.810287i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.55051 | 0.379425 | ||||||||
\(215\) | −4.00000 | + | 8.00000i | −0.272798 | + | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.89898i | 0.468333i | ||||||||
\(218\) | 5.79796i | 0.392687i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.79796 | + | 4.89898i | 0.660578 | + | 0.330289i | ||||
\(221\) | 19.5959 | 1.31816 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.449490i | 0.0301001i | 0.999887 | + | 0.0150500i | \(0.00479075\pi\) | ||||
−0.999887 | + | 0.0150500i | \(0.995209\pi\) | |||||||
\(224\) | 4.44949 | 0.297294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.10102 | −0.206277 | ||||||||
\(227\) | − | 24.8990i | − | 1.65260i | −0.563228 | − | 0.826302i | \(-0.690441\pi\) | ||
0.563228 | − | 0.826302i | \(-0.309559\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −17.7980 | − | 8.89898i | −1.17356 | − | 0.586781i | ||||
\(231\) | 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 | ||||||||
\(235\) | −4.44949 | + | 8.89898i | −0.290253 | + | 0.580505i | ||||
\(236\) | 3.55051 | 0.231119 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 21.7980i | − | 1.41295i | ||||||
\(239\) | −18.0454 | −1.16726 | −0.583630 | − | 0.812020i | \(-0.698368\pi\) | ||||
−0.583630 | + | 0.812020i | \(0.698368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.79796 | 0.502311 | 0.251155 | − | 0.967947i | \(-0.419189\pi\) | ||||
0.251155 | + | 0.967947i | \(0.419189\pi\) | |||||||
\(242\) | 13.0000i | 0.835672i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.0000 | −0.768221 | ||||||||
\(245\) | −25.5959 | − | 12.7980i | −1.63526 | − | 0.817632i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 14.2020i | − | 0.903654i | ||||||
\(248\) | 1.55051i | 0.0984575i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | −21.3485 | −1.34750 | −0.673752 | − | 0.738958i | \(-0.735318\pi\) | ||||
−0.673752 | + | 0.738958i | \(0.735318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 43.5959i | − | 2.74085i | ||||||
\(254\) | −2.65153 | −0.166372 | ||||||||
\(255\) | 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 | ||||||||
\(259\) | −4.44949 | −0.276478 | ||||||||
\(260\) | 4.00000 | − | 8.00000i | 0.248069 | − | 0.496139i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.2474i | 0.633089i | ||||||||
\(263\) | − | 1.75255i | − | 0.108067i | −0.998539 | − | 0.0540335i | \(-0.982792\pi\) | ||
0.998539 | − | 0.0540335i | \(-0.0172078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.7980 | + | 23.5959i | −0.724743 | + | 1.44949i | ||||
\(266\) | −15.7980 | −0.968635 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 5.55051i | − | 0.339051i | ||||||
\(269\) | −18.6969 | −1.13997 | −0.569986 | − | 0.821654i | \(-0.693051\pi\) | ||||
−0.569986 | + | 0.821654i | \(0.693051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.4949 | −1.97392 | −0.986962 | − | 0.160952i | \(-0.948544\pi\) | ||||
−0.986962 | + | 0.160952i | \(0.948544\pi\) | |||||||
\(272\) | − | 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 | \(-0.200361\pi\) | |||||||
\(278\) | 5.79796i | 0.347738i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.89898 | − | 4.44949i | −0.531816 | − | 0.265908i | ||||
\(281\) | −27.7980 | −1.65829 | −0.829144 | − | 0.559036i | \(-0.811171\pi\) | ||||
−0.829144 | + | 0.559036i | \(0.811171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5959i | 0.927081i | 0.886076 | + | 0.463541i | \(0.153421\pi\) | ||||
−0.886076 | + | 0.463541i | \(0.846579\pi\) | |||||||
\(284\) | 4.89898 | 0.290701 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.5959 | 1.15873 | ||||||||
\(287\) | 8.89898i | 0.525290i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 4.00000i | − | 0.234082i | ||||||
\(293\) | − | 25.5959i | − | 1.49533i | −0.664076 | − | 0.747665i | \(-0.731175\pi\) | ||
0.664076 | − | 0.747665i | \(-0.268825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.10102 | − | 3.55051i | −0.413437 | − | 0.206719i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 18.6969i | − | 1.08308i | ||||||
\(299\) | −35.5959 | −2.05857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.7980 | 1.02586 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.55051 | −0.203636 | ||||||||
\(305\) | 24.0000 | + | 12.0000i | 1.37424 | + | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.1464i | − | 0.750306i | −0.926963 | − | 0.375153i | \(-0.877590\pi\) | ||
0.926963 | − | 0.375153i | \(-0.122410\pi\) | |||||||
\(308\) | − | 21.7980i | − | 1.24205i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.55051 | − | 3.10102i | 0.0880631 | − | 0.176126i | ||||
\(311\) | 7.34847 | 0.416693 | 0.208347 | − | 0.978055i | \(-0.433192\pi\) | ||||
0.208347 | + | 0.978055i | \(0.433192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.5959i | − | 0.994580i | −0.867584 | − | 0.497290i | \(-0.834328\pi\) | ||
0.867584 | − | 0.497290i | \(-0.165672\pi\) | |||||||
\(314\) | −7.79796 | −0.440064 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.44949 | 0.362812 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.00000 | − | 1.00000i | −0.111803 | − | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 39.5959i | 2.20659i | ||||||||
\(323\) | 17.3939i | 0.967821i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0000 | + | 12.0000i | −0.887520 | + | 0.665640i | ||||
\(326\) | 21.7980 | 1.20728 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000i | 0.110432i | ||||||||
\(329\) | 19.7980 | 1.09150 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.2474 | 0.783111 | 0.391555 | − | 0.920155i | \(-0.371937\pi\) | ||||
0.391555 | + | 0.920155i | \(0.371937\pi\) | |||||||
\(332\) | − | 9.55051i | − | 0.524152i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −5.55051 | + | 11.1010i | −0.303257 | + | 0.606514i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.59592i | 0.195882i | 0.995192 | + | 0.0979411i | \(0.0312257\pi\) | ||||
−0.995192 | + | 0.0979411i | \(0.968774\pi\) | |||||||
\(338\) | − | 3.00000i | − | 0.163178i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.89898 | + | 9.79796i | −0.265684 | + | 0.531369i | ||||
\(341\) | 7.59592 | 0.411342 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 25.7980i | 1.39296i | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.7980 | 1.06434 | ||||||||
\(347\) | 2.20204i | 0.118212i | 0.998252 | + | 0.0591059i | \(0.0188250\pi\) | ||||
−0.998252 | + | 0.0591059i | \(0.981175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.10102 | −0.380109 | −0.190054 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190054 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(350\) | 13.3485 | + | 17.7980i | 0.713506 | + | 0.951341i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.89898i | − | 0.261116i | ||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.79796 | − | 4.89898i | −0.520022 | − | 0.260011i | ||||
\(356\) | −15.7980 | −0.837290 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 9.34847i | − | 0.494082i | ||||||
\(359\) | −12.8990 | −0.680782 | −0.340391 | − | 0.940284i | \(-0.610559\pi\) | ||||
−0.340391 | + | 0.940284i | \(0.610559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.39388 | −0.336520 | ||||||||
\(362\) | 10.6969i | 0.562219i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.7980 | −0.932867 | ||||||||
\(365\) | −4.00000 | + | 8.00000i | −0.209370 | + | 0.418739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.65153i | 0.138409i | 0.997603 | + | 0.0692044i | \(0.0220461\pi\) | ||||
−0.997603 | + | 0.0692044i | \(0.977954\pi\) | |||||||
\(368\) | 8.89898i | 0.463891i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.00000 | + | 1.00000i | 0.103975 | + | 0.0519875i | ||||
\(371\) | 52.4949 | 2.72540 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 11.7980i | − | 0.610875i | −0.952212 | − | 0.305438i | \(-0.901197\pi\) | ||
0.952212 | − | 0.305438i | \(-0.0988027\pi\) | |||||||
\(374\) | −24.0000 | −1.24101 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.44949 | 0.229465 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.5959 | 1.62297 | 0.811487 | − | 0.584371i | \(-0.198659\pi\) | ||||
0.811487 | + | 0.584371i | \(0.198659\pi\) | |||||||
\(380\) | 7.10102 | + | 3.55051i | 0.364275 | + | 0.182137i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 11.3485i | − | 0.580638i | ||||||
\(383\) | 34.6969i | 1.77293i | 0.462795 | + | 0.886465i | \(0.346847\pi\) | ||||
−0.462795 | + | 0.886465i | \(0.653153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.7980 | + | 43.5959i | −1.11093 | + | 2.22185i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | −25.7980 | −1.30801 | −0.654004 | − | 0.756491i | \(-0.726912\pi\) | ||||
−0.654004 | + | 0.756491i | \(0.726912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.5959 | 2.20474 | ||||||||
\(392\) | 12.7980i | 0.646395i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −12.8990 | − | 6.44949i | −0.649018 | − | 0.324509i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2020i | 0.813157i | 0.913616 | + | 0.406579i | \(0.133278\pi\) | ||||
−0.913616 | + | 0.406579i | \(0.866722\pi\) | |||||||
\(398\) | − | 6.44949i | − | 0.323284i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 23.7980 | 1.18841 | 0.594207 | − | 0.804312i | \(-0.297466\pi\) | ||||
0.594207 | + | 0.804312i | \(0.297466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.20204i | − | 0.308946i | ||||||
\(404\) | 10.6969 | 0.532193 | ||||||||
\(405\) | 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 | ||||||
\(413\) | 15.7980i | 0.777367i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.55051 | + | 19.1010i | −0.468816 | + | 0.937632i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.3939i | 0.850762i | ||||||||
\(419\) | 5.79796 | 0.283249 | 0.141624 | − | 0.989920i | \(-0.454767\pi\) | ||||
0.141624 | + | 0.989920i | \(0.454767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5959 | −0.955047 | −0.477523 | − | 0.878619i | \(-0.658465\pi\) | ||||
−0.477523 | + | 0.878619i | \(0.658465\pi\) | |||||||
\(422\) | − | 6.69694i | − | 0.326002i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.7980 | 0.572960 | ||||||||
\(425\) | 19.5959 | − | 14.6969i | 0.950542 | − | 0.712906i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 53.3939i | − | 2.58391i | ||||||
\(428\) | 5.55051i | 0.268294i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | − | 4.00000i | −0.385794 | − | 0.192897i | ||||
\(431\) | 15.7526 | 0.758774 | 0.379387 | − | 0.925238i | \(-0.376135\pi\) | ||||
0.379387 | + | 0.925238i | \(0.376135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.3939i | 1.02812i | 0.857753 | + | 0.514062i | \(0.171860\pi\) | ||||
−0.857753 | + | 0.514062i | \(0.828140\pi\) | |||||||
\(434\) | −6.89898 | −0.331162 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.79796 | −0.277672 | ||||||||
\(437\) | − | 31.5959i | − | 1.51144i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.6515 | −0.985644 | −0.492822 | − | 0.870130i | \(-0.664035\pi\) | ||||
−0.492822 | + | 0.870130i | \(0.664035\pi\) | |||||||
\(440\) | −4.89898 | + | 9.79796i | −0.233550 | + | 0.467099i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5959i | 0.932083i | ||||||||
\(443\) | − | 24.6515i | − | 1.17123i | −0.810589 | − | 0.585615i | \(-0.800853\pi\) | ||
0.810589 | − | 0.585615i | \(-0.199147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.5959 | + | 15.7980i | 1.49779 | + | 0.748895i | ||||
\(446\) | −0.449490 | −0.0212840 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.44949i | 0.210219i | ||||||||
\(449\) | −15.7980 | −0.745552 | −0.372776 | − | 0.927921i | \(-0.621594\pi\) | ||||
−0.372776 | + | 0.927921i | \(0.621594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.79796 | 0.461368 | ||||||||
\(452\) | − | 3.10102i | − | 0.145860i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.8990 | 1.16857 | ||||||||
\(455\) | 35.5959 | + | 17.7980i | 1.66876 | + | 0.834381i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000i | 0.0935561i | 0.998905 | + | 0.0467780i | \(0.0148953\pi\) | ||||
−0.998905 | + | 0.0467780i | \(0.985105\pi\) | |||||||
\(458\) | 10.0000i | 0.467269i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.89898 | − | 17.7980i | 0.414917 | − | 0.829834i | ||||
\(461\) | 33.7980 | 1.57413 | 0.787064 | − | 0.616871i | \(-0.211600\pi\) | ||||
0.787064 | + | 0.616871i | \(0.211600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.4949i | − | 0.952479i | −0.879316 | − | 0.476239i | \(-0.842000\pi\) | ||
0.879316 | − | 0.476239i | \(-0.158000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.79796 | 0.453882 | ||||||||
\(467\) | − | 12.0000i | − | 0.555294i | −0.960683 | − | 0.277647i | \(-0.910445\pi\) | ||
0.960683 | − | 0.277647i | \(-0.0895545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.6969 | 1.14040 | ||||||||
\(470\) | −8.89898 | − | 4.44949i | −0.410479 | − | 0.205240i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.55051i | 0.163425i | ||||||||
\(473\) | − | 19.5959i | − | 0.901021i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.6515 | − | 14.2020i | −0.488726 | − | 0.651634i | ||||
\(476\) | 21.7980 | 0.999108 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 18.0454i | − | 0.825378i | ||||||
\(479\) | 5.14643 | 0.235146 | 0.117573 | − | 0.993064i | \(-0.462489\pi\) | ||||
0.117573 | + | 0.993064i | \(0.462489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 7.79796i | 0.355187i | ||||||||
\(483\) | 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 | ||||||||
\(490\) | 12.7980 | − | 25.5959i | 0.578153 | − | 1.15631i | ||||
\(491\) | 9.30306 | 0.419841 | 0.209921 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209921 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 14.2020 | 0.638980 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.55051 | −0.0696200 | ||||||||
\(497\) | 21.7980i | 0.977772i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.6515 | 0.476828 | 0.238414 | − | 0.971164i | \(-0.423372\pi\) | ||||
0.238414 | + | 0.971164i | \(0.423372\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 21.3485i | − | 0.952829i | ||||||
\(503\) | 1.79796i | 0.0801670i | 0.999196 | + | 0.0400835i | \(0.0127624\pi\) | ||||
−0.999196 | + | 0.0400835i | \(0.987238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.3939 | − | 10.6969i | −0.952015 | − | 0.476008i | ||||
\(506\) | 43.5959 | 1.93807 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 2.65153i | − | 0.117643i | ||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7980 | 0.787335 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.89898 | 0.216085 | ||||||||
\(515\) | −9.79796 | + | 19.5959i | −0.431750 | + | 0.863499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 21.7980i | − | 0.958673i | ||||||
\(518\) | − | 4.44949i | − | 0.195499i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.00000 | + | 4.00000i | 0.350823 | + | 0.175412i | ||||
\(521\) | −17.7980 | −0.779743 | −0.389871 | − | 0.920869i | \(-0.627481\pi\) | ||||
−0.389871 | + | 0.920869i | \(0.627481\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.89898i | − | 0.389125i | −0.980890 | − | 0.194563i | \(-0.937671\pi\) | ||
0.980890 | − | 0.194563i | \(-0.0623287\pi\) | |||||||
\(524\) | −10.2474 | −0.447662 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.75255 | 0.0764149 | ||||||||
\(527\) | 7.59592i | 0.330883i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −56.1918 | −2.44312 | ||||||||
\(530\) | −23.5959 | − | 11.7980i | −1.02494 | − | 0.512471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 15.7980i | − | 0.684928i | ||||||
\(533\) | − | 8.00000i | − | 0.346518i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.55051 | − | 11.1010i | 0.239969 | − | 0.479939i | ||||
\(536\) | 5.55051 | 0.239746 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 18.6969i | − | 0.806082i | ||||||
\(539\) | 62.6969 | 2.70055 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.404082 | 0.0173728 | 0.00868642 | − | 0.999962i | \(-0.497235\pi\) | ||||
0.00868642 | + | 0.999962i | \(0.497235\pi\) | |||||||
\(542\) | − | 32.4949i | − | 1.39578i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.89898 | 0.210042 | ||||||||
\(545\) | 11.5959 | + | 5.79796i | 0.496715 | + | 0.248357i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6969i | 0.457368i | 0.973501 | + | 0.228684i | \(0.0734423\pi\) | ||||
−0.973501 | + | 0.228684i | \(0.926558\pi\) | |||||||
\(548\) | − | 19.5959i | − | 0.837096i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19.5959 | − | 14.6969i | 0.835573 | − | 0.626680i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.6969i | 1.22032i | ||||||||
\(554\) | 19.5959 | 0.832551 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.79796 | −0.245888 | ||||||||
\(557\) | − | 12.0000i | − | 0.508456i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 4.44949 | − | 8.89898i | 0.188025 | − | 0.376051i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 27.7980i | − | 1.17259i | ||||||
\(563\) | 34.6969i | 1.46230i | 0.682216 | + | 0.731151i | \(0.261016\pi\) | ||||
−0.682216 | + | 0.731151i | \(0.738984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.10102 | + | 6.20204i | −0.130461 | + | 0.260922i | ||||
\(566\) | −15.5959 | −0.655545 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.89898i | 0.205557i | ||||||||
\(569\) | 21.5959 | 0.905348 | 0.452674 | − | 0.891676i | \(-0.350470\pi\) | ||||
0.452674 | + | 0.891676i | \(0.350470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.3939 | −1.06270 | −0.531350 | − | 0.847152i | \(-0.678315\pi\) | ||||
−0.531350 | + | 0.847152i | \(0.678315\pi\) | |||||||
\(572\) | 19.5959i | 0.819346i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.89898 | −0.371436 | ||||||||
\(575\) | −35.5959 | + | 26.6969i | −1.48445 | + | 1.11334i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.6969i | 1.27793i | 0.769236 | + | 0.638965i | \(0.220637\pi\) | ||||
−0.769236 | + | 0.638965i | \(0.779363\pi\) | |||||||
\(578\) | − | 7.00000i | − | 0.291162i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.4949 | 1.76299 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 57.7980i | − | 2.39375i | ||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.5959 | 1.05736 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.50510 | 0.226834 | ||||||||
\(590\) | 3.55051 | − | 7.10102i | 0.146172 | − | 0.292344i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.00000i | − | 0.0410997i | ||||||
\(593\) | − | 24.0000i | − | 0.985562i | −0.870153 | − | 0.492781i | \(-0.835980\pi\) | ||
0.870153 | − | 0.492781i | \(-0.164020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −43.5959 | − | 21.7980i | −1.78726 | − | 0.893629i | ||||
\(596\) | 18.6969 | 0.765856 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 35.5959i | − | 1.45563i | ||||||
\(599\) | 11.5959 | 0.473796 | 0.236898 | − | 0.971534i | \(-0.423869\pi\) | ||||
0.236898 | + | 0.971534i | \(0.423869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 17.7980i | 0.725391i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 26.0000 | + | 13.0000i | 1.05705 | + | 0.528525i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.6969i | − | 1.08360i | −0.840509 | − | 0.541798i | \(-0.817744\pi\) | ||
0.840509 | − | 0.541798i | \(-0.182256\pi\) | |||||||
\(608\) | − | 3.55051i | − | 0.143992i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | + | 24.0000i | −0.485866 | + | 0.971732i | ||||
\(611\) | −17.7980 | −0.720028 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.7980i | 1.60742i | 0.595018 | + | 0.803712i | \(0.297145\pi\) | ||||
−0.595018 | + | 0.803712i | \(0.702855\pi\) | |||||||
\(614\) | 13.1464 | 0.530547 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.7980 | 0.878265 | ||||||||
\(617\) | 19.5959i | 0.788902i | 0.918917 | + | 0.394451i | \(0.129065\pi\) | ||||
−0.918917 | + | 0.394451i | \(0.870935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.8990 | 0.518454 | 0.259227 | − | 0.965816i | \(-0.416532\pi\) | ||||
0.259227 | + | 0.965816i | \(0.416532\pi\) | |||||||
\(620\) | 3.10102 | + | 1.55051i | 0.124540 | + | 0.0622700i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.34847i | 0.294647i | ||||||||
\(623\) | − | 70.2929i | − | 2.81622i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 17.5959 | 0.703274 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 7.79796i | − | 0.311172i | ||||||
\(629\) | −4.89898 | −0.195335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2474 | −0.806038 | −0.403019 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403019 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(632\) | 6.44949i | 0.256547i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −2.65153 | + | 5.30306i | −0.105223 | + | 0.210446i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 51.1918i | − | 2.02829i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 2.00000i | 0.0395285 | − | 0.0790569i | ||||
\(641\) | −17.7980 | −0.702977 | −0.351489 | − | 0.936192i | \(-0.614324\pi\) | ||||
−0.351489 | + | 0.936192i | \(0.614324\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23.1010i | − | 0.911015i | −0.890232 | − | 0.455508i | \(-0.849458\pi\) | ||
0.890232 | − | 0.455508i | \(-0.150542\pi\) | |||||||
\(644\) | −39.5959 | −1.56030 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.3939 | −0.684353 | ||||||||
\(647\) | − | 32.0000i | − | 1.25805i | −0.777385 | − | 0.629025i | \(-0.783454\pi\) | ||
0.777385 | − | 0.629025i | \(-0.216546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3939 | 0.682769 | ||||||||
\(650\) | −12.0000 | − | 16.0000i | −0.470679 | − | 0.627572i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.7980i | 0.853674i | ||||||||
\(653\) | − | 34.0000i | − | 1.33052i | −0.746611 | − | 0.665261i | \(-0.768320\pi\) | ||
0.746611 | − | 0.665261i | \(-0.231680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4949 | + | 10.2474i | 0.800802 | + | 0.400401i | ||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.7980i | 0.771805i | ||||||||
\(659\) | 31.5959 | 1.23080 | 0.615401 | − | 0.788214i | \(-0.288994\pi\) | ||||
0.615401 | + | 0.788214i | \(0.288994\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1918 | −1.21322 | −0.606611 | − | 0.794999i | \(-0.707471\pi\) | ||||
−0.606611 | + | 0.794999i | \(0.707471\pi\) | |||||||
\(662\) | 14.2474i | 0.553743i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.55051 | 0.370632 | ||||||||
\(665\) | −15.7980 | + | 31.5959i | −0.612619 | + | 1.22524i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 8.00000i | − | 0.309529i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.1010 | − | 5.55051i | −0.428870 | − | 0.214435i | ||||
\(671\) | −58.7878 | −2.26948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000i | 0.925132i | 0.886585 | + | 0.462566i | \(0.153071\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | −3.59592 | −0.138510 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 18.0000i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.89898 | 0.341511 | ||||||||
\(680\) | −9.79796 | − | 4.89898i | −0.375735 | − | 0.187867i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.59592i | 0.290863i | ||||||||
\(683\) | − | 15.5959i | − | 0.596761i | −0.954447 | − | 0.298381i | \(-0.903554\pi\) | ||
0.954447 | − | 0.298381i | \(-0.0964465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5959 | + | 39.1918i | −0.748722 | + | 1.49744i | ||||
\(686\) | −25.7980 | −0.984971 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | −47.1918 | −1.79787 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.7980 | 1.43790 | 0.718951 | − | 0.695061i | \(-0.244623\pi\) | ||||
0.718951 | + | 0.695061i | \(0.244623\pi\) | |||||||
\(692\) | 19.7980i | 0.752605i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.20204 | −0.0835883 | ||||||||
\(695\) | 11.5959 | + | 5.79796i | 0.439858 | + | 0.219929i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.79796i | 0.371124i | ||||||||
\(698\) | − | 7.10102i | − | 0.268778i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.7980 | + | 13.3485i | −0.672700 | + | 0.504525i | ||||
\(701\) | 13.7980 | 0.521142 | 0.260571 | − | 0.965455i | \(-0.416089\pi\) | ||||
0.260571 | + | 0.965455i | \(0.416089\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.55051i | 0.133910i | ||||||||
\(704\) | 4.89898 | 0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | −0.225813 | ||||||||
\(707\) | 47.5959i | 1.79003i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.79796 | −0.217747 | −0.108873 | − | 0.994056i | \(-0.534724\pi\) | ||||
−0.108873 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(710\) | 4.89898 | − | 9.79796i | 0.183855 | − | 0.367711i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 15.7980i | − | 0.592054i | ||||||
\(713\) | − | 13.7980i | − | 0.516738i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.5959 | − | 39.1918i | 0.732846 | − | 1.46569i | ||||
\(716\) | 9.34847 | 0.349369 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 12.8990i | − | 0.481386i | ||||||
\(719\) | 51.5959 | 1.92420 | 0.962102 | − | 0.272692i | \(-0.0879138\pi\) | ||||
0.962102 | + | 0.272692i | \(0.0879138\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.5959 | 1.62360 | ||||||||
\(722\) | − | 6.39388i | − | 0.237955i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.6969 | −0.397549 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.898979i | − | 0.0333413i | −0.999861 | − | 0.0166707i | \(-0.994693\pi\) | ||
0.999861 | − | 0.0166707i | \(-0.00530668\pi\) | |||||||
\(728\) | − | 17.7980i | − | 0.659636i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | − | 4.00000i | −0.296093 | − | 0.148047i | ||||
\(731\) | 19.5959 | 0.724781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17.5959i | − | 0.649920i | −0.945728 | − | 0.324960i | \(-0.894649\pi\) | ||
0.945728 | − | 0.324960i | \(-0.105351\pi\) | |||||||
\(734\) | −2.65153 | −0.0978698 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.89898 | −0.328021 | ||||||||
\(737\) | − | 27.1918i | − | 1.00162i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.7980 | 1.68471 | 0.842353 | − | 0.538927i | \(-0.181170\pi\) | ||||
0.842353 | + | 0.538927i | \(0.181170\pi\) | |||||||
\(740\) | −1.00000 | + | 2.00000i | −0.0367607 | + | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.4949i | 1.92715i | ||||||||
\(743\) | 13.7526i | 0.504532i | 0.967658 | + | 0.252266i | \(0.0811758\pi\) | ||||
−0.967658 | + | 0.252266i | \(0.918824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.3939 | − | 18.6969i | −1.37001 | − | 0.685003i | ||||
\(746\) | 11.7980 | 0.431954 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | −24.6969 | −0.902406 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.6969 | 1.12015 | 0.560074 | − | 0.828443i | \(-0.310773\pi\) | ||||
0.560074 | + | 0.828443i | \(0.310773\pi\) | |||||||
\(752\) | 4.44949i | 0.162256i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | − | 8.00000i | −0.582300 | − | 0.291150i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5959i | 1.22106i | 0.791991 | + | 0.610532i | \(0.209044\pi\) | ||||
−0.791991 | + | 0.610532i | \(0.790956\pi\) | |||||||
\(758\) | 31.5959i | 1.14762i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.55051 | + | 7.10102i | −0.128791 | + | 0.257581i | ||||
\(761\) | −25.1918 | −0.913203 | −0.456602 | − | 0.889671i | \(-0.650934\pi\) | ||||
−0.456602 | + | 0.889671i | \(0.650934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 25.7980i | − | 0.933949i | ||||||
\(764\) | 11.3485 | 0.410573 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.6969 | −1.25365 | ||||||||
\(767\) | − | 14.2020i | − | 0.512806i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7980 | 1.29091 | 0.645454 | − | 0.763799i | \(-0.276668\pi\) | ||||
0.645454 | + | 0.763799i | \(0.276668\pi\) | |||||||
\(770\) | −43.5959 | − | 21.7980i | −1.57109 | − | 0.785544i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 14.0000i | − | 0.503871i | ||||||
\(773\) | 6.00000i | 0.215805i | 0.994161 | + | 0.107903i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107903i | \(0.965587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.65153 | − | 6.20204i | −0.167088 | − | 0.222784i | ||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 25.7980i | − | 0.924902i | ||||||
\(779\) | 7.10102 | 0.254420 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 43.5959i | 1.55899i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.7980 | −0.457070 | ||||||||
\(785\) | −7.79796 | + | 15.5959i | −0.278321 | + | 0.556642i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.7423i | 1.02455i | 0.858820 | + | 0.512277i | \(0.171198\pi\) | ||||
−0.858820 | + | 0.512277i | \(0.828802\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.44949 | − | 12.8990i | 0.229463 | − | 0.458925i | ||||
\(791\) | 13.7980 |