Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(29,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.29");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bb (of order \(4\), degree \(2\), 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: | \(4.47162251319\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 309.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.309 |
Dual form | 560.2.bb.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | −1.00000 | − | 1.00000i | −0.577350 | − | 0.577350i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 2.00000i | 0.816497i | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 3.00000 | − | 1.00000i | 0.948683 | − | 0.316228i | ||||
\(11\) | 1.00000 | + | 1.00000i | 0.301511 | + | 0.301511i | 0.841605 | − | 0.540094i | \(-0.181611\pi\) |
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | 2.00000 | − | 2.00000i | 0.577350 | − | 0.577350i | ||||
\(13\) | −3.00000 | − | 3.00000i | −0.832050 | − | 0.832050i | 0.155747 | − | 0.987797i | \(-0.450222\pi\) |
−0.987797 | + | 0.155747i | \(0.950222\pi\) | |||||||
\(14\) | −1.00000 | − | 1.00000i | −0.267261 | − | 0.267261i | ||||
\(15\) | 3.00000 | − | 1.00000i | 0.774597 | − | 0.258199i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −1.00000 | + | 1.00000i | −0.235702 | + | 0.235702i | ||||
\(19\) | −3.00000 | + | 3.00000i | −0.688247 | + | 0.688247i | −0.961844 | − | 0.273597i | \(-0.911786\pi\) |
0.273597 | + | 0.961844i | \(0.411786\pi\) | |||||||
\(20\) | −4.00000 | − | 2.00000i | −0.894427 | − | 0.447214i | ||||
\(21\) | −1.00000 | − | 1.00000i | −0.218218 | − | 0.218218i | ||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −4.00000 | −0.816497 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 6.00000i | 1.17670i | ||||||||
\(27\) | −4.00000 | + | 4.00000i | −0.769800 | + | 0.769800i | ||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | −1.00000 | + | 1.00000i | −0.185695 | + | 0.185695i | −0.793832 | − | 0.608137i | \(-0.791917\pi\) |
0.608137 | + | 0.793832i | \(0.291917\pi\) | |||||||
\(30\) | −4.00000 | − | 2.00000i | −0.730297 | − | 0.365148i | ||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | − | 2.00000i | − | 0.348155i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | + | 2.00000i | −0.169031 | + | 0.338062i | ||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | −5.00000 | + | 5.00000i | −0.821995 | + | 0.821995i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 6.00000i | 0.960769i | ||||||||
\(40\) | 2.00000 | + | 6.00000i | 0.316228 | + | 0.948683i | ||||
\(41\) | − | 12.0000i | − | 1.87409i | −0.349215 | − | 0.937043i | \(-0.613552\pi\) | ||
0.349215 | − | 0.937043i | \(-0.386448\pi\) | |||||||
\(42\) | 2.00000i | 0.308607i | ||||||||
\(43\) | −1.00000 | + | 1.00000i | −0.152499 | + | 0.152499i | −0.779233 | − | 0.626734i | \(-0.784391\pi\) |
0.626734 | + | 0.779233i | \(0.284391\pi\) | |||||||
\(44\) | −2.00000 | + | 2.00000i | −0.301511 | + | 0.301511i | ||||
\(45\) | 2.00000 | + | 1.00000i | 0.298142 | + | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0000i | 1.45865i | 0.684167 | + | 0.729325i | \(0.260166\pi\) | ||||
−0.684167 | + | 0.729325i | \(0.739834\pi\) | |||||||
\(48\) | 4.00000 | + | 4.00000i | 0.577350 | + | 0.577350i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | + | 7.00000i | −0.141421 | + | 0.989949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.00000 | − | 6.00000i | 0.832050 | − | 0.832050i | ||||
\(53\) | 3.00000 | − | 3.00000i | 0.412082 | − | 0.412082i | −0.470381 | − | 0.882463i | \(-0.655884\pi\) |
0.882463 | + | 0.470381i | \(0.155884\pi\) | |||||||
\(54\) | 8.00000 | 1.08866 | ||||||||
\(55\) | −3.00000 | + | 1.00000i | −0.404520 | + | 0.134840i | ||||
\(56\) | 2.00000 | − | 2.00000i | 0.267261 | − | 0.267261i | ||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −1.00000 | − | 1.00000i | −0.130189 | − | 0.130189i | 0.639010 | − | 0.769199i | \(-0.279344\pi\) |
−0.769199 | + | 0.639010i | \(0.779344\pi\) | |||||||
\(60\) | 2.00000 | + | 6.00000i | 0.258199 | + | 0.774597i | ||||
\(61\) | −7.00000 | + | 7.00000i | −0.896258 | + | 0.896258i | −0.995103 | − | 0.0988447i | \(-0.968485\pi\) |
0.0988447 | + | 0.995103i | \(0.468485\pi\) | |||||||
\(62\) | 8.00000 | + | 8.00000i | 1.01600 | + | 1.01600i | ||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 9.00000 | − | 3.00000i | 1.11631 | − | 0.372104i | ||||
\(66\) | −2.00000 | + | 2.00000i | −0.246183 | + | 0.246183i | ||||
\(67\) | −3.00000 | − | 3.00000i | −0.366508 | − | 0.366508i | 0.499694 | − | 0.866202i | \(-0.333446\pi\) |
−0.866202 | + | 0.499694i | \(0.833446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00000 | − | 1.00000i | 0.358569 | − | 0.119523i | ||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | −2.00000 | − | 2.00000i | −0.235702 | − | 0.235702i | ||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | −1.00000 | + | 7.00000i | −0.115470 | + | 0.808290i | ||||
\(76\) | −6.00000 | − | 6.00000i | −0.688247 | − | 0.688247i | ||||
\(77\) | 1.00000 | + | 1.00000i | 0.113961 | + | 0.113961i | ||||
\(78\) | 6.00000 | − | 6.00000i | 0.679366 | − | 0.679366i | ||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 4.00000 | − | 8.00000i | 0.447214 | − | 0.894427i | ||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | −12.0000 | + | 12.0000i | −1.32518 | + | 1.32518i | ||||
\(83\) | −5.00000 | − | 5.00000i | −0.548821 | − | 0.548821i | 0.377279 | − | 0.926100i | \(-0.376860\pi\) |
−0.926100 | + | 0.377279i | \(0.876860\pi\) | |||||||
\(84\) | 2.00000 | − | 2.00000i | 0.218218 | − | 0.218218i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −1.00000 | − | 3.00000i | −0.105409 | − | 0.316228i | ||||
\(91\) | −3.00000 | − | 3.00000i | −0.314485 | − | 0.314485i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | + | 8.00000i | 0.829561 | + | 0.829561i | ||||
\(94\) | 10.0000 | − | 10.0000i | 1.03142 | − | 1.03142i | ||||
\(95\) | −3.00000 | − | 9.00000i | −0.307794 | − | 0.923381i | ||||
\(96\) | − | 8.00000i | − | 0.816497i | ||||||
\(97\) | 8.00000i | 0.812277i | 0.913812 | + | 0.406138i | \(0.133125\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | −1.00000 | − | 1.00000i | −0.101015 | − | 0.101015i | ||||
\(99\) | 1.00000 | − | 1.00000i | 0.100504 | − | 0.100504i | ||||
\(100\) | 8.00000 | − | 6.00000i | 0.800000 | − | 0.600000i | ||||
\(101\) | −7.00000 | − | 7.00000i | −0.696526 | − | 0.696526i | 0.267133 | − | 0.963660i | \(-0.413924\pi\) |
−0.963660 | + | 0.267133i | \(0.913924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −12.0000 | −1.17670 | ||||||||
\(105\) | 3.00000 | − | 1.00000i | 0.292770 | − | 0.0975900i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −9.00000 | + | 9.00000i | −0.870063 | + | 0.870063i | −0.992479 | − | 0.122416i | \(-0.960936\pi\) |
0.122416 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(108\) | −8.00000 | − | 8.00000i | −0.769800 | − | 0.769800i | ||||
\(109\) | 3.00000 | − | 3.00000i | 0.287348 | − | 0.287348i | −0.548683 | − | 0.836031i | \(-0.684871\pi\) |
0.836031 | + | 0.548683i | \(0.184871\pi\) | |||||||
\(110\) | 4.00000 | + | 2.00000i | 0.381385 | + | 0.190693i | ||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | − | 16.0000i | − | 1.50515i | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||
0.658505 | − | 0.752577i | \(-0.271189\pi\) | |||||||
\(114\) | −6.00000 | − | 6.00000i | −0.561951 | − | 0.561951i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | − | 2.00000i | −0.185695 | − | 0.185695i | ||||
\(117\) | −3.00000 | + | 3.00000i | −0.277350 | + | 0.277350i | ||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.00000 | − | 8.00000i | 0.365148 | − | 0.730297i | ||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | 14.0000 | 1.26750 | ||||||||
\(123\) | −12.0000 | + | 12.0000i | −1.08200 | + | 1.08200i | ||||
\(124\) | − | 16.0000i | − | 1.43684i | ||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | −1.00000 | + | 1.00000i | −0.0890871 | + | 0.0890871i | ||||
\(127\) | − | 18.0000i | − | 1.59724i | −0.601834 | − | 0.798621i | \(-0.705563\pi\) | ||
0.601834 | − | 0.798621i | \(-0.294437\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | −12.0000 | − | 6.00000i | −1.05247 | − | 0.526235i | ||||
\(131\) | 5.00000 | − | 5.00000i | 0.436852 | − | 0.436852i | −0.454099 | − | 0.890951i | \(-0.650039\pi\) |
0.890951 | + | 0.454099i | \(0.150039\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | −3.00000 | + | 3.00000i | −0.260133 | + | 0.260133i | ||||
\(134\) | 6.00000i | 0.518321i | ||||||||
\(135\) | −4.00000 | − | 12.0000i | −0.344265 | − | 1.03280i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00000 | + | 3.00000i | 0.254457 | + | 0.254457i | 0.822795 | − | 0.568338i | \(-0.192414\pi\) |
−0.568338 | + | 0.822795i | \(0.692414\pi\) | |||||||
\(140\) | −4.00000 | − | 2.00000i | −0.338062 | − | 0.169031i | ||||
\(141\) | 10.0000 | − | 10.0000i | 0.842152 | − | 0.842152i | ||||
\(142\) | 6.00000 | − | 6.00000i | 0.503509 | − | 0.503509i | ||||
\(143\) | − | 6.00000i | − | 0.501745i | ||||||
\(144\) | 4.00000i | 0.333333i | ||||||||
\(145\) | −1.00000 | − | 3.00000i | −0.0830455 | − | 0.249136i | ||||
\(146\) | 10.0000 | + | 10.0000i | 0.827606 | + | 0.827606i | ||||
\(147\) | −1.00000 | − | 1.00000i | −0.0824786 | − | 0.0824786i | ||||
\(148\) | −10.0000 | − | 10.0000i | −0.821995 | − | 0.821995i | ||||
\(149\) | 11.0000 | + | 11.0000i | 0.901155 | + | 0.901155i | 0.995536 | − | 0.0943810i | \(-0.0300872\pi\) |
−0.0943810 | + | 0.995536i | \(0.530087\pi\) | |||||||
\(150\) | 8.00000 | − | 6.00000i | 0.653197 | − | 0.489898i | ||||
\(151\) | 14.0000i | 1.13930i | 0.821886 | + | 0.569652i | \(0.192922\pi\) | ||||
−0.821886 | + | 0.569652i | \(0.807078\pi\) | |||||||
\(152\) | 12.0000i | 0.973329i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 2.00000i | − | 0.161165i | ||||||
\(155\) | 8.00000 | − | 16.0000i | 0.642575 | − | 1.28515i | ||||
\(156\) | −12.0000 | −0.960769 | ||||||||
\(157\) | 17.0000 | + | 17.0000i | 1.35675 | + | 1.35675i | 0.877896 | + | 0.478852i | \(0.158947\pi\) |
0.478852 | + | 0.877896i | \(0.341053\pi\) | |||||||
\(158\) | 8.00000 | + | 8.00000i | 0.636446 | + | 0.636446i | ||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −12.0000 | + | 4.00000i | −0.948683 | + | 0.316228i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.00000 | − | 5.00000i | −0.392837 | − | 0.392837i | ||||
\(163\) | 5.00000 | + | 5.00000i | 0.391630 | + | 0.391630i | 0.875268 | − | 0.483638i | \(-0.160685\pi\) |
−0.483638 | + | 0.875268i | \(0.660685\pi\) | |||||||
\(164\) | 24.0000 | 1.87409 | ||||||||
\(165\) | 4.00000 | + | 2.00000i | 0.311400 | + | 0.155700i | ||||
\(166\) | 10.0000i | 0.776151i | ||||||||
\(167\) | 24.0000 | 1.85718 | 0.928588 | − | 0.371113i | \(-0.121024\pi\) | ||||
0.928588 | + | 0.371113i | \(0.121024\pi\) | |||||||
\(168\) | −4.00000 | −0.308607 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | + | 3.00000i | 0.229416 | + | 0.229416i | ||||
\(172\) | −2.00000 | − | 2.00000i | −0.152499 | − | 0.152499i | ||||
\(173\) | −7.00000 | − | 7.00000i | −0.532200 | − | 0.532200i | 0.389026 | − | 0.921227i | \(-0.372811\pi\) |
−0.921227 | + | 0.389026i | \(0.872811\pi\) | |||||||
\(174\) | −2.00000 | − | 2.00000i | −0.151620 | − | 0.151620i | ||||
\(175\) | −3.00000 | − | 4.00000i | −0.226779 | − | 0.302372i | ||||
\(176\) | −4.00000 | − | 4.00000i | −0.301511 | − | 0.301511i | ||||
\(177\) | 2.00000i | 0.150329i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0000 | + | 13.0000i | −0.971666 | + | 0.971666i | −0.999609 | − | 0.0279439i | \(-0.991104\pi\) |
0.0279439 | + | 0.999609i | \(0.491104\pi\) | |||||||
\(180\) | −2.00000 | + | 4.00000i | −0.149071 | + | 0.298142i | ||||
\(181\) | −15.0000 | − | 15.0000i | −1.11494 | − | 1.11494i | −0.992472 | − | 0.122469i | \(-0.960919\pi\) |
−0.122469 | − | 0.992472i | \(-0.539081\pi\) | |||||||
\(182\) | 6.00000i | 0.444750i | ||||||||
\(183\) | 14.0000 | 1.03491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.00000 | − | 15.0000i | −0.367607 | − | 1.10282i | ||||
\(186\) | − | 16.0000i | − | 1.17318i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −20.0000 | −1.45865 | ||||||||
\(189\) | −4.00000 | + | 4.00000i | −0.290957 | + | 0.290957i | ||||
\(190\) | −6.00000 | + | 12.0000i | −0.435286 | + | 0.870572i | ||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | −8.00000 | + | 8.00000i | −0.577350 | + | 0.577350i | ||||
\(193\) | − | 20.0000i | − | 1.43963i | −0.694165 | − | 0.719816i | \(-0.744226\pi\) | ||
0.694165 | − | 0.719816i | \(-0.255774\pi\) | |||||||
\(194\) | 8.00000 | − | 8.00000i | 0.574367 | − | 0.574367i | ||||
\(195\) | −12.0000 | − | 6.00000i | −0.859338 | − | 0.429669i | ||||
\(196\) | 2.00000i | 0.142857i | ||||||||
\(197\) | −1.00000 | + | 1.00000i | −0.0712470 | + | 0.0712470i | −0.741832 | − | 0.670585i | \(-0.766043\pi\) |
0.670585 | + | 0.741832i | \(0.266043\pi\) | |||||||
\(198\) | −2.00000 | −0.142134 | ||||||||
\(199\) | 10.0000i | 0.708881i | 0.935079 | + | 0.354441i | \(0.115329\pi\) | ||||
−0.935079 | + | 0.354441i | \(0.884671\pi\) | |||||||
\(200\) | −14.0000 | − | 2.00000i | −0.989949 | − | 0.141421i | ||||
\(201\) | 6.00000i | 0.423207i | ||||||||
\(202\) | 14.0000i | 0.985037i | ||||||||
\(203\) | −1.00000 | + | 1.00000i | −0.0701862 | + | 0.0701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.0000 | + | 12.0000i | 1.67623 | + | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.0000 | + | 12.0000i | 0.832050 | + | 0.832050i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | −4.00000 | − | 2.00000i | −0.276026 | − | 0.138013i | ||||
\(211\) | 11.0000 | − | 11.0000i | 0.757271 | − | 0.757271i | −0.218554 | − | 0.975825i | \(-0.570134\pi\) |
0.975825 | + | 0.218554i | \(0.0701339\pi\) | |||||||
\(212\) | 6.00000 | + | 6.00000i | 0.412082 | + | 0.412082i | ||||
\(213\) | 6.00000 | − | 6.00000i | 0.411113 | − | 0.411113i | ||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | −1.00000 | − | 3.00000i | −0.0681994 | − | 0.204598i | ||||
\(216\) | 16.0000i | 1.08866i | ||||||||
\(217\) | −8.00000 | −0.543075 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | 10.0000 | + | 10.0000i | 0.675737 | + | 0.675737i | ||||
\(220\) | −2.00000 | − | 6.00000i | −0.134840 | − | 0.404520i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.0000 | − | 10.0000i | −0.671156 | − | 0.671156i | ||||
\(223\) | 2.00000i | 0.133930i | 0.997755 | + | 0.0669650i | \(0.0213316\pi\) | ||||
−0.997755 | + | 0.0669650i | \(0.978668\pi\) | |||||||
\(224\) | 4.00000 | + | 4.00000i | 0.267261 | + | 0.267261i | ||||
\(225\) | −4.00000 | + | 3.00000i | −0.266667 | + | 0.200000i | ||||
\(226\) | −16.0000 | + | 16.0000i | −1.06430 | + | 1.06430i | ||||
\(227\) | −13.0000 | − | 13.0000i | −0.862840 | − | 0.862840i | 0.128827 | − | 0.991667i | \(-0.458879\pi\) |
−0.991667 | + | 0.128827i | \(0.958879\pi\) | |||||||
\(228\) | 12.0000i | 0.794719i | ||||||||
\(229\) | −7.00000 | − | 7.00000i | −0.462573 | − | 0.462573i | 0.436925 | − | 0.899498i | \(-0.356068\pi\) |
−0.899498 | + | 0.436925i | \(0.856068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.00000i | − | 0.131590i | ||||||
\(232\) | 4.00000i | 0.262613i | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 6.00000 | 0.392232 | ||||||||
\(235\) | −20.0000 | − | 10.0000i | −1.30466 | − | 0.652328i | ||||
\(236\) | 2.00000 | − | 2.00000i | 0.130189 | − | 0.130189i | ||||
\(237\) | 8.00000 | + | 8.00000i | 0.519656 | + | 0.519656i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | −12.0000 | + | 4.00000i | −0.774597 | + | 0.258199i | ||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | −9.00000 | + | 9.00000i | −0.578542 | + | 0.578542i | ||||
\(243\) | 7.00000 | + | 7.00000i | 0.449050 | + | 0.449050i | ||||
\(244\) | −14.0000 | − | 14.0000i | −0.896258 | − | 0.896258i | ||||
\(245\) | −1.00000 | + | 2.00000i | −0.0638877 | + | 0.127775i | ||||
\(246\) | 24.0000 | 1.53018 | ||||||||
\(247\) | 18.0000 | 1.14531 | ||||||||
\(248\) | −16.0000 | + | 16.0000i | −1.01600 | + | 1.01600i | ||||
\(249\) | 10.0000i | 0.633724i | ||||||||
\(250\) | −13.0000 | − | 9.00000i | −0.822192 | − | 0.569210i | ||||
\(251\) | 11.0000 | + | 11.0000i | 0.694314 | + | 0.694314i | 0.963178 | − | 0.268864i | \(-0.0866483\pi\) |
−0.268864 | + | 0.963178i | \(0.586648\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −18.0000 | + | 18.0000i | −1.12942 | + | 1.12942i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | − | 4.00000i | − | 0.249513i | −0.992187 | − | 0.124757i | \(-0.960185\pi\) | ||
0.992187 | − | 0.124757i | \(-0.0398150\pi\) | |||||||
\(258\) | −2.00000 | − | 2.00000i | −0.124515 | − | 0.124515i | ||||
\(259\) | −5.00000 | + | 5.00000i | −0.310685 | + | 0.310685i | ||||
\(260\) | 6.00000 | + | 18.0000i | 0.372104 | + | 1.11631i | ||||
\(261\) | 1.00000 | + | 1.00000i | 0.0618984 | + | 0.0618984i | ||||
\(262\) | −10.0000 | −0.617802 | ||||||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | −4.00000 | − | 4.00000i | −0.246183 | − | 0.246183i | ||||
\(265\) | 3.00000 | + | 9.00000i | 0.184289 | + | 0.552866i | ||||
\(266\) | 6.00000 | 0.367884 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.00000 | − | 6.00000i | 0.366508 | − | 0.366508i | ||||
\(269\) | −7.00000 | + | 7.00000i | −0.426798 | + | 0.426798i | −0.887536 | − | 0.460738i | \(-0.847585\pi\) |
0.460738 | + | 0.887536i | \(0.347585\pi\) | |||||||
\(270\) | −8.00000 | + | 16.0000i | −0.486864 | + | 0.973729i | ||||
\(271\) | −24.0000 | −1.45790 | −0.728948 | − | 0.684569i | \(-0.759990\pi\) | ||||
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000i | 0.363137i | ||||||||
\(274\) | −10.0000 | − | 10.0000i | −0.604122 | − | 0.604122i | ||||
\(275\) | 1.00000 | − | 7.00000i | 0.0603023 | − | 0.422116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0000 | − | 15.0000i | 0.901263 | − | 0.901263i | −0.0942828 | − | 0.995545i | \(-0.530056\pi\) |
0.995545 | + | 0.0942828i | \(0.0300558\pi\) | |||||||
\(278\) | − | 6.00000i | − | 0.359856i | ||||||
\(279\) | 8.00000i | 0.478947i | ||||||||
\(280\) | 2.00000 | + | 6.00000i | 0.119523 | + | 0.358569i | ||||
\(281\) | 28.0000i | 1.67034i | 0.549992 | + | 0.835170i | \(0.314631\pi\) | ||||
−0.549992 | + | 0.835170i | \(0.685369\pi\) | |||||||
\(282\) | −20.0000 | −1.19098 | ||||||||
\(283\) | 9.00000 | − | 9.00000i | 0.534994 | − | 0.534994i | −0.387060 | − | 0.922055i | \(-0.626509\pi\) |
0.922055 | + | 0.387060i | \(0.126509\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | −6.00000 | + | 12.0000i | −0.355409 | + | 0.710819i | ||||
\(286\) | −6.00000 | + | 6.00000i | −0.354787 | + | 0.354787i | ||||
\(287\) | − | 12.0000i | − | 0.708338i | ||||||
\(288\) | 4.00000 | − | 4.00000i | 0.235702 | − | 0.235702i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | −2.00000 | + | 4.00000i | −0.117444 | + | 0.234888i | ||||
\(291\) | 8.00000 | − | 8.00000i | 0.468968 | − | 0.468968i | ||||
\(292\) | − | 20.0000i | − | 1.17041i | ||||||
\(293\) | −11.0000 | + | 11.0000i | −0.642627 | + | 0.642627i | −0.951200 | − | 0.308574i | \(-0.900148\pi\) |
0.308574 | + | 0.951200i | \(0.400148\pi\) | |||||||
\(294\) | 2.00000i | 0.116642i | ||||||||
\(295\) | 3.00000 | − | 1.00000i | 0.174667 | − | 0.0582223i | ||||
\(296\) | 20.0000i | 1.16248i | ||||||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | − | 22.0000i | − | 1.27443i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −14.0000 | − | 2.00000i | −0.808290 | − | 0.115470i | ||||
\(301\) | −1.00000 | + | 1.00000i | −0.0576390 | + | 0.0576390i | ||||
\(302\) | 14.0000 | − | 14.0000i | 0.805609 | − | 0.805609i | ||||
\(303\) | 14.0000i | 0.804279i | ||||||||
\(304\) | 12.0000 | − | 12.0000i | 0.688247 | − | 0.688247i | ||||
\(305\) | −7.00000 | − | 21.0000i | −0.400819 | − | 1.20246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0000 | + | 15.0000i | 0.856095 | + | 0.856095i | 0.990876 | − | 0.134780i | \(-0.0430329\pi\) |
−0.134780 | + | 0.990876i | \(0.543033\pi\) | |||||||
\(308\) | −2.00000 | + | 2.00000i | −0.113961 | + | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.0000 | + | 8.00000i | −1.36311 | + | 0.454369i | ||||
\(311\) | 26.0000i | 1.47432i | 0.675716 | + | 0.737162i | \(0.263835\pi\) | ||||
−0.675716 | + | 0.737162i | \(0.736165\pi\) | |||||||
\(312\) | 12.0000 | + | 12.0000i | 0.679366 | + | 0.679366i | ||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | − | 34.0000i | − | 1.91873i | ||||||
\(315\) | 2.00000 | + | 1.00000i | 0.112687 | + | 0.0563436i | ||||
\(316\) | − | 16.0000i | − | 0.900070i | ||||||
\(317\) | −13.0000 | − | 13.0000i | −0.730153 | − | 0.730153i | 0.240497 | − | 0.970650i | \(-0.422690\pi\) |
−0.970650 | + | 0.240497i | \(0.922690\pi\) | |||||||
\(318\) | 6.00000 | + | 6.00000i | 0.336463 | + | 0.336463i | ||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 16.0000 | + | 8.00000i | 0.894427 | + | 0.447214i | ||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 10.0000i | 0.555556i | ||||||||
\(325\) | −3.00000 | + | 21.0000i | −0.166410 | + | 1.16487i | ||||
\(326\) | − | 10.0000i | − | 0.553849i | ||||||
\(327\) | −6.00000 | −0.331801 | ||||||||
\(328\) | −24.0000 | − | 24.0000i | −1.32518 | − | 1.32518i | ||||
\(329\) | 10.0000i | 0.551318i | ||||||||
\(330\) | −2.00000 | − | 6.00000i | −0.110096 | − | 0.330289i | ||||
\(331\) | −15.0000 | − | 15.0000i | −0.824475 | − | 0.824475i | 0.162272 | − | 0.986746i | \(-0.448118\pi\) |
−0.986746 | + | 0.162272i | \(0.948118\pi\) | |||||||
\(332\) | 10.0000 | − | 10.0000i | 0.548821 | − | 0.548821i | ||||
\(333\) | 5.00000 | + | 5.00000i | 0.273998 | + | 0.273998i | ||||
\(334\) | −24.0000 | − | 24.0000i | −1.31322 | − | 1.31322i | ||||
\(335\) | 9.00000 | − | 3.00000i | 0.491723 | − | 0.163908i | ||||
\(336\) | 4.00000 | + | 4.00000i | 0.218218 | + | 0.218218i | ||||
\(337\) | 8.00000i | 0.435788i | 0.975972 | + | 0.217894i | \(0.0699187\pi\) | ||||
−0.975972 | + | 0.217894i | \(0.930081\pi\) | |||||||
\(338\) | 5.00000 | − | 5.00000i | 0.271964 | − | 0.271964i | ||||
\(339\) | −16.0000 | + | 16.0000i | −0.869001 | + | 0.869001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | − | 8.00000i | −0.433224 | − | 0.433224i | ||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.00000i | 0.215666i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0000i | 0.752645i | ||||||||
\(347\) | −17.0000 | + | 17.0000i | −0.912608 | + | 0.912608i | −0.996477 | − | 0.0838690i | \(-0.973272\pi\) |
0.0838690 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(348\) | 4.00000i | 0.214423i | ||||||||
\(349\) | −11.0000 | + | 11.0000i | −0.588817 | + | 0.588817i | −0.937311 | − | 0.348494i | \(-0.886693\pi\) |
0.348494 | + | 0.937311i | \(0.386693\pi\) | |||||||
\(350\) | −1.00000 | + | 7.00000i | −0.0534522 | + | 0.374166i | ||||
\(351\) | 24.0000 | 1.28103 | ||||||||
\(352\) | 8.00000i | 0.426401i | ||||||||
\(353\) | − | 36.0000i | − | 1.91609i | −0.286623 | − | 0.958043i | \(-0.592533\pi\) | ||
0.286623 | − | 0.958043i | \(-0.407467\pi\) | |||||||
\(354\) | 2.00000 | − | 2.00000i | 0.106299 | − | 0.106299i | ||||
\(355\) | −12.0000 | − | 6.00000i | −0.636894 | − | 0.318447i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.0000 | 1.37414 | ||||||||
\(359\) | 6.00000i | 0.316668i | 0.987386 | + | 0.158334i | \(0.0506123\pi\) | ||||
−0.987386 | + | 0.158334i | \(0.949388\pi\) | |||||||
\(360\) | 6.00000 | − | 2.00000i | 0.316228 | − | 0.105409i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 30.0000i | 1.57676i | ||||||||
\(363\) | −9.00000 | + | 9.00000i | −0.472377 | + | 0.472377i | ||||
\(364\) | 6.00000 | − | 6.00000i | 0.314485 | − | 0.314485i | ||||
\(365\) | 10.0000 | − | 20.0000i | 0.523424 | − | 1.04685i | ||||
\(366\) | −14.0000 | − | 14.0000i | −0.731792 | − | 0.731792i | ||||
\(367\) | − | 6.00000i | − | 0.313197i | −0.987662 | − | 0.156599i | \(-0.949947\pi\) | ||
0.987662 | − | 0.156599i | \(-0.0500529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0000 | −0.624695 | ||||||||
\(370\) | −10.0000 | + | 20.0000i | −0.519875 | + | 1.03975i | ||||
\(371\) | 3.00000 | − | 3.00000i | 0.155752 | − | 0.155752i | ||||
\(372\) | −16.0000 | + | 16.0000i | −0.829561 | + | 0.829561i | ||||
\(373\) | 15.0000 | − | 15.0000i | 0.776671 | − | 0.776671i | −0.202593 | − | 0.979263i | \(-0.564937\pi\) |
0.979263 | + | 0.202593i | \(0.0649367\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.0000 | − | 9.00000i | −0.671317 | − | 0.464758i | ||||
\(376\) | 20.0000 | + | 20.0000i | 1.03142 | + | 1.03142i | ||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 8.00000 | 0.411476 | ||||||||
\(379\) | −19.0000 | − | 19.0000i | −0.975964 | − | 0.975964i | 0.0237534 | − | 0.999718i | \(-0.492438\pi\) |
−0.999718 | + | 0.0237534i | \(0.992438\pi\) | |||||||
\(380\) | 18.0000 | − | 6.00000i | 0.923381 | − | 0.307794i | ||||
\(381\) | −18.0000 | + | 18.0000i | −0.922168 | + | 0.922168i | ||||
\(382\) | −16.0000 | − | 16.0000i | −0.818631 | − | 0.818631i | ||||
\(383\) | 34.0000i | 1.73732i | 0.495410 | + | 0.868659i | \(0.335018\pi\) | ||||
−0.495410 | + | 0.868659i | \(0.664982\pi\) | |||||||
\(384\) | 16.0000 | 0.816497 | ||||||||
\(385\) | −3.00000 | + | 1.00000i | −0.152894 | + | 0.0509647i | ||||
\(386\) | −20.0000 | + | 20.0000i | −1.01797 | + | 1.01797i | ||||
\(387\) | 1.00000 | + | 1.00000i | 0.0508329 | + | 0.0508329i | ||||
\(388\) | −16.0000 | −0.812277 | ||||||||
\(389\) | 11.0000 | + | 11.0000i | 0.557722 | + | 0.557722i | 0.928658 | − | 0.370936i | \(-0.120963\pi\) |
−0.370936 | + | 0.928658i | \(0.620963\pi\) | |||||||
\(390\) | 6.00000 | + | 18.0000i | 0.303822 | + | 0.911465i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.00000 | − | 2.00000i | 0.101015 | − | 0.101015i | ||||
\(393\) | −10.0000 | −0.504433 | ||||||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | 8.00000 | − | 16.0000i | 0.402524 | − | 0.805047i | ||||
\(396\) | 2.00000 | + | 2.00000i | 0.100504 | + | 0.100504i | ||||
\(397\) | −15.0000 | − | 15.0000i | −0.752828 | − | 0.752828i | 0.222178 | − | 0.975006i | \(-0.428683\pi\) |
−0.975006 | + | 0.222178i | \(0.928683\pi\) | |||||||
\(398\) | 10.0000 | − | 10.0000i | 0.501255 | − | 0.501255i | ||||
\(399\) | 6.00000 | 0.300376 | ||||||||
\(400\) | 12.0000 | + | 16.0000i | 0.600000 | + | 0.800000i | ||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 6.00000 | − | 6.00000i | 0.299253 | − | 0.299253i | ||||
\(403\) | 24.0000 | + | 24.0000i | 1.19553 | + | 1.19553i | ||||
\(404\) | 14.0000 | − | 14.0000i | 0.696526 | − | 0.696526i | ||||
\(405\) | −5.00000 | + | 10.0000i | −0.248452 | + | 0.496904i | ||||
\(406\) | 2.00000 | 0.0992583 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | −12.0000 | − | 36.0000i | −0.592638 | − | 1.77791i | ||||
\(411\) | −10.0000 | − | 10.0000i | −0.493264 | − | 0.493264i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.00000 | − | 1.00000i | −0.0492068 | − | 0.0492068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0000 | − | 5.00000i | 0.736321 | − | 0.245440i | ||||
\(416\) | − | 24.0000i | − | 1.17670i | ||||||
\(417\) | − | 6.00000i | − | 0.293821i | ||||||
\(418\) | 6.00000 | + | 6.00000i | 0.293470 | + | 0.293470i | ||||
\(419\) | 9.00000 | − | 9.00000i | 0.439679 | − | 0.439679i | −0.452225 | − | 0.891904i | \(-0.649370\pi\) |
0.891904 | + | 0.452225i | \(0.149370\pi\) | |||||||
\(420\) | 2.00000 | + | 6.00000i | 0.0975900 | + | 0.292770i | ||||
\(421\) | 19.0000 | + | 19.0000i | 0.926003 | + | 0.926003i | 0.997445 | − | 0.0714415i | \(-0.0227599\pi\) |
−0.0714415 | + | 0.997445i | \(0.522760\pi\) | |||||||
\(422\) | −22.0000 | −1.07094 | ||||||||
\(423\) | 10.0000 | 0.486217 | ||||||||
\(424\) | − | 12.0000i | − | 0.582772i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | −7.00000 | + | 7.00000i | −0.338754 | + | 0.338754i | ||||
\(428\) | −18.0000 | − | 18.0000i | −0.870063 | − | 0.870063i | ||||
\(429\) | −6.00000 | + | 6.00000i | −0.289683 | + | 0.289683i | ||||
\(430\) | −2.00000 | + | 4.00000i | −0.0964486 | + | 0.192897i | ||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 16.0000 | − | 16.0000i | 0.769800 | − | 0.769800i | ||||
\(433\) | 16.0000i | 0.768911i | 0.923144 | + | 0.384455i | \(0.125611\pi\) | ||||
−0.923144 | + | 0.384455i | \(0.874389\pi\) | |||||||
\(434\) | 8.00000 | + | 8.00000i | 0.384012 | + | 0.384012i | ||||
\(435\) | −2.00000 | + | 4.00000i | −0.0958927 | + | 0.191785i | ||||
\(436\) | 6.00000 | + | 6.00000i | 0.287348 | + | 0.287348i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 20.0000i | − | 0.955637i | ||||||
\(439\) | − | 38.0000i | − | 1.81364i | −0.421517 | − | 0.906821i | \(-0.638502\pi\) | ||
0.421517 | − | 0.906821i | \(-0.361498\pi\) | |||||||
\(440\) | −4.00000 | + | 8.00000i | −0.190693 | + | 0.381385i | ||||
\(441\) | − | 1.00000i | − | 0.0476190i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.00000 | + | 1.00000i | −0.0475114 | + | 0.0475114i | −0.730463 | − | 0.682952i | \(-0.760696\pi\) |
0.682952 | + | 0.730463i | \(0.260696\pi\) | |||||||
\(444\) | 20.0000i | 0.949158i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.00000 | − | 2.00000i | 0.0947027 | − | 0.0947027i | ||||
\(447\) | − | 22.0000i | − | 1.04056i | ||||||
\(448\) | − | 8.00000i | − | 0.377964i | ||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | 7.00000 | + | 1.00000i | 0.329983 | + | 0.0471405i | ||||
\(451\) | 12.0000 | − | 12.0000i | 0.565058 | − | 0.565058i | ||||
\(452\) | 32.0000 | 1.50515 | ||||||||
\(453\) | 14.0000 | − | 14.0000i | 0.657777 | − | 0.657777i | ||||
\(454\) | 26.0000i | 1.22024i | ||||||||
\(455\) | 9.00000 | − | 3.00000i | 0.421927 | − | 0.140642i | ||||
\(456\) | 12.0000 | − | 12.0000i | 0.561951 | − | 0.561951i | ||||
\(457\) | −30.0000 | −1.40334 | −0.701670 | − | 0.712502i | \(-0.747562\pi\) | ||||
−0.701670 | + | 0.712502i | \(0.747562\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.00000 | − | 5.00000i | 0.232873 | − | 0.232873i | −0.581018 | − | 0.813891i | \(-0.697345\pi\) |
0.813891 | + | 0.581018i | \(0.197345\pi\) | |||||||
\(462\) | −2.00000 | + | 2.00000i | −0.0930484 | + | 0.0930484i | ||||
\(463\) | 22.0000i | 1.02243i | 0.859454 | + | 0.511213i | \(0.170804\pi\) | ||||
−0.859454 | + | 0.511213i | \(0.829196\pi\) | |||||||
\(464\) | 4.00000 | − | 4.00000i | 0.185695 | − | 0.185695i | ||||
\(465\) | −24.0000 | + | 8.00000i | −1.11297 | + | 0.370991i | ||||
\(466\) | 10.0000 | + | 10.0000i | 0.463241 | + | 0.463241i | ||||
\(467\) | −17.0000 | − | 17.0000i | −0.786666 | − | 0.786666i | 0.194280 | − | 0.980946i | \(-0.437763\pi\) |
−0.980946 | + | 0.194280i | \(0.937763\pi\) | |||||||
\(468\) | −6.00000 | − | 6.00000i | −0.277350 | − | 0.277350i | ||||
\(469\) | −3.00000 | − | 3.00000i | −0.138527 | − | 0.138527i | ||||
\(470\) | 10.0000 | + | 30.0000i | 0.461266 | + | 1.38380i | ||||
\(471\) | − | 34.0000i | − | 1.56664i | ||||||
\(472\) | −4.00000 | −0.184115 | ||||||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | − | 16.0000i | − | 0.734904i | ||||||
\(475\) | 21.0000 | + | 3.00000i | 0.963546 | + | 0.137649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | − | 3.00000i | −0.137361 | − | 0.137361i | ||||
\(478\) | −8.00000 | − | 8.00000i | −0.365911 | − | 0.365911i | ||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 16.0000 | + | 8.00000i | 0.730297 | + | 0.365148i | ||||
\(481\) | 30.0000 | 1.36788 | ||||||||
\(482\) | 10.0000 | + | 10.0000i | 0.455488 | + | 0.455488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0000 | 0.818182 | ||||||||
\(485\) | −16.0000 | − | 8.00000i | −0.726523 | − | 0.363261i | ||||
\(486\) | − | 14.0000i | − | 0.635053i | ||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 28.0000i | 1.26750i | ||||||||
\(489\) | − | 10.0000i | − | 0.452216i | ||||||
\(490\) | 3.00000 | − | 1.00000i | 0.135526 | − | 0.0451754i | ||||
\(491\) | −15.0000 | − | 15.0000i | −0.676941 | − | 0.676941i | 0.282366 | − | 0.959307i | \(-0.408881\pi\) |
−0.959307 | + | 0.282366i | \(0.908881\pi\) | |||||||
\(492\) | −24.0000 | − | 24.0000i | −1.08200 | − | 1.08200i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −18.0000 | − | 18.0000i | −0.809858 | − | 0.809858i | ||||
\(495\) | 1.00000 | + | 3.00000i | 0.0449467 | + | 0.134840i | ||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | 6.00000i | 0.269137i | ||||||||
\(498\) | 10.0000 | − | 10.0000i | 0.448111 | − | 0.448111i | ||||
\(499\) | 19.0000 | − | 19.0000i | 0.850557 | − | 0.850557i | −0.139645 | − | 0.990202i | \(-0.544596\pi\) |
0.990202 | + | 0.139645i | \(0.0445961\pi\) | |||||||
\(500\) | 4.00000 | + | 22.0000i | 0.178885 | + | 0.983870i | ||||
\(501\) | −24.0000 | − | 24.0000i | −1.07224 | − | 1.07224i | ||||
\(502\) | − | 22.0000i | − | 0.981908i | ||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | −2.00000 | − | 2.00000i | −0.0890871 | − | 0.0890871i | ||||
\(505\) | 21.0000 | − | 7.00000i | 0.934488 | − | 0.311496i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | − | 5.00000i | 0.222058 | − | 0.222058i | ||||
\(508\) | 36.0000 | 1.59724 | ||||||||
\(509\) | −7.00000 | + | 7.00000i | −0.310270 | + | 0.310270i | −0.845014 | − | 0.534744i | \(-0.820408\pi\) |
0.534744 | + | 0.845014i | \(0.320408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | − | 24.0000i | − | 1.05963i | ||||||
\(514\) | −4.00000 | + | 4.00000i | −0.176432 | + | 0.176432i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.00000i | 0.176090i | ||||||||
\(517\) | −10.0000 | + | 10.0000i | −0.439799 | + | 0.439799i | ||||
\(518\) | 10.0000 | 0.439375 | ||||||||
\(519\) | 14.0000i | 0.614532i | ||||||||
\(520\) | 12.0000 | − | 24.0000i | 0.526235 | − | 1.05247i | ||||
\(521\) | 4.00000i | 0.175243i | 0.996154 | + | 0.0876216i | \(0.0279266\pi\) | ||||
−0.996154 | + | 0.0876216i | \(0.972073\pi\) | |||||||
\(522\) | − | 2.00000i | − | 0.0875376i | ||||||
\(523\) | 9.00000 | − | 9.00000i | 0.393543 | − | 0.393543i | −0.482405 | − | 0.875948i | \(-0.660237\pi\) |
0.875948 | + | 0.482405i | \(0.160237\pi\) | |||||||
\(524\) | 10.0000 | + | 10.0000i | 0.436852 | + | 0.436852i | ||||
\(525\) | −1.00000 | + | 7.00000i | −0.0436436 | + | 0.305505i | ||||
\(526\) | −16.0000 | − | 16.0000i | −0.697633 | − | 0.697633i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 8.00000i | 0.348155i | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 6.00000 | − | 12.0000i | 0.260623 | − | 0.521247i | ||||
\(531\) | −1.00000 | + | 1.00000i | −0.0433963 | + | 0.0433963i | ||||
\(532\) | −6.00000 | − | 6.00000i | −0.260133 | − | 0.260133i | ||||
\(533\) | −36.0000 | + | 36.0000i | −1.55933 | + | 1.55933i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | − | 27.0000i | −0.389104 | − | 1.16731i | ||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | 26.0000 | 1.12198 | ||||||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | 1.00000 | + | 1.00000i | 0.0430730 | + | 0.0430730i | ||||
\(540\) | 24.0000 | − | 8.00000i | 1.03280 | − | 0.344265i | ||||
\(541\) | −9.00000 | + | 9.00000i | −0.386940 | + | 0.386940i | −0.873595 | − | 0.486654i | \(-0.838217\pi\) |
0.486654 | + | 0.873595i | \(0.338217\pi\) | |||||||
\(542\) | 24.0000 | + | 24.0000i | 1.03089 | + | 1.03089i | ||||
\(543\) | 30.0000i | 1.28742i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.00000 | + | 9.00000i | 0.128506 | + | 0.385518i | ||||
\(546\) | 6.00000 | − | 6.00000i | 0.256776 | − | 0.256776i | ||||
\(547\) | −15.0000 | − | 15.0000i | −0.641354 | − | 0.641354i | 0.309535 | − | 0.950888i | \(-0.399827\pi\) |
−0.950888 | + | 0.309535i | \(0.899827\pi\) | |||||||
\(548\) | 20.0000i | 0.854358i | ||||||||
\(549\) | 7.00000 | + | 7.00000i | 0.298753 | + | 0.298753i | ||||
\(550\) | −8.00000 | + | 6.00000i | −0.341121 | + | 0.255841i | ||||
\(551\) | − | 6.00000i | − | 0.255609i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | −0.340195 | ||||||||
\(554\) | −30.0000 | −1.27458 | ||||||||
\(555\) | −10.0000 | + | 20.0000i | −0.424476 | + | 0.848953i | ||||
\(556\) | −6.00000 | + | 6.00000i | −0.254457 | + | 0.254457i | ||||
\(557\) | −5.00000 | − | 5.00000i | −0.211857 | − | 0.211857i | 0.593199 | − | 0.805056i | \(-0.297865\pi\) |
−0.805056 | + | 0.593199i | \(0.797865\pi\) | |||||||
\(558\) | 8.00000 | − | 8.00000i | 0.338667 | − | 0.338667i | ||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 4.00000 | − | 8.00000i | 0.169031 | − | 0.338062i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.0000 | − | 28.0000i | 1.18111 | − | 1.18111i | ||||
\(563\) | 3.00000 | + | 3.00000i | 0.126435 | + | 0.126435i | 0.767493 | − | 0.641058i | \(-0.221504\pi\) |
−0.641058 | + | 0.767493i | \(0.721504\pi\) | |||||||
\(564\) | 20.0000 | + | 20.0000i | 0.842152 | + | 0.842152i | ||||
\(565\) | 32.0000 | + | 16.0000i | 1.34625 | + | 0.673125i | ||||
\(566\) | −18.0000 | −0.756596 | ||||||||
\(567\) | 5.00000 | 0.209980 | ||||||||
\(568\) | 12.0000 | + | 12.0000i | 0.503509 | + | 0.503509i | ||||
\(569\) | − | 24.0000i | − | 1.00613i | −0.864248 | − | 0.503066i | \(-0.832205\pi\) | ||
0.864248 | − | 0.503066i | \(-0.167795\pi\) | |||||||
\(570\) | 18.0000 | − | 6.00000i | 0.753937 | − | 0.251312i | ||||
\(571\) | −23.0000 | − | 23.0000i | −0.962520 | − | 0.962520i | 0.0368025 | − | 0.999323i | \(-0.488283\pi\) |
−0.999323 | + | 0.0368025i | \(0.988283\pi\) | |||||||
\(572\) | 12.0000 | 0.501745 | ||||||||
\(573\) | −16.0000 | − | 16.0000i | −0.668410 | − | 0.668410i | ||||
\(574\) | −12.0000 | + | 12.0000i | −0.500870 | + | 0.500870i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 28.0000i | 1.16566i | 0.812596 | + | 0.582828i | \(0.198054\pi\) | ||||
−0.812596 | + | 0.582828i | \(0.801946\pi\) | |||||||
\(578\) | −17.0000 | − | 17.0000i | −0.707107 | − | 0.707107i | ||||
\(579\) | −20.0000 | + | 20.0000i | −0.831172 | + | 0.831172i | ||||
\(580\) | 6.00000 | − | 2.00000i | 0.249136 | − | 0.0830455i | ||||
\(581\) | −5.00000 | − | 5.00000i | −0.207435 | − | 0.207435i | ||||
\(582\) | −16.0000 | −0.663221 | ||||||||
\(583\) | 6.00000 | 0.248495 | ||||||||
\(584\) | −20.0000 | + | 20.0000i | −0.827606 | + | 0.827606i | ||||
\(585\) | −3.00000 | − | 9.00000i | −0.124035 | − | 0.372104i | ||||
\(586\) | 22.0000 | 0.908812 | ||||||||
\(587\) | 21.0000 | − | 21.0000i | 0.866763 | − | 0.866763i | −0.125350 | − | 0.992113i | \(-0.540005\pi\) |
0.992113 | + | 0.125350i | \(0.0400053\pi\) | |||||||
\(588\) | 2.00000 | − | 2.00000i | 0.0824786 | − | 0.0824786i | ||||
\(589\) | 24.0000 | − | 24.0000i | 0.988903 | − | 0.988903i | ||||
\(590\) | −4.00000 | − | 2.00000i | −0.164677 | − | 0.0823387i | ||||
\(591\) | 2.00000 | 0.0822690 | ||||||||
\(592\) | 20.0000 | − | 20.0000i | 0.821995 | − | 0.821995i | ||||
\(593\) | − | 4.00000i | − | 0.164260i | −0.996622 | − | 0.0821302i | \(-0.973828\pi\) | ||
0.996622 | − | 0.0821302i | \(-0.0261723\pi\) | |||||||
\(594\) | 8.00000 | + | 8.00000i | 0.328244 | + | 0.328244i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.0000 | + | 22.0000i | −0.901155 | + | 0.901155i | ||||
\(597\) | 10.0000 | − | 10.0000i | 0.409273 | − | 0.409273i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 18.0000i | − | 0.735460i | −0.929933 | − | 0.367730i | \(-0.880135\pi\) | ||
0.929933 | − | 0.367730i | \(-0.119865\pi\) | |||||||
\(600\) | 12.0000 | + | 16.0000i | 0.489898 | + | 0.653197i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 2.00000 | 0.0815139 | ||||||||
\(603\) | −3.00000 | + | 3.00000i | −0.122169 | + | 0.122169i | ||||
\(604\) | −28.0000 | −1.13930 | ||||||||
\(605\) | 18.0000 | + | 9.00000i | 0.731804 | + | 0.365902i | ||||
\(606\) | 14.0000 | − | 14.0000i | 0.568711 | − | 0.568711i | ||||
\(607\) | − | 14.0000i | − | 0.568242i | −0.958788 | − | 0.284121i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284121i | \(-0.0917018\pi\) | |||||||
\(608\) | −24.0000 | −0.973329 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | −14.0000 | + | 28.0000i | −0.566843 | + | 1.13369i | ||||
\(611\) | 30.0000 | − | 30.0000i | 1.21367 | − | 1.21367i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | − | 3.00000i | 0.121169 | − | 0.121169i | −0.643922 | − | 0.765091i | \(-0.722694\pi\) |
0.765091 | + | 0.643922i | \(0.222694\pi\) | |||||||
\(614\) | − | 30.0000i | − | 1.21070i | ||||||
\(615\) | −12.0000 | − | 36.0000i | −0.483887 | − | 1.45166i | ||||
\(616\) | 4.00000 | 0.161165 | ||||||||
\(617\) | −10.0000 | −0.402585 | −0.201292 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201292 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | − | 13.0000i | −0.522514 | − | 0.522514i | 0.395816 | − | 0.918330i | \(-0.370462\pi\) |
−0.918330 | + | 0.395816i | \(0.870462\pi\) | |||||||
\(620\) | 32.0000 | + | 16.0000i | 1.28515 | + | 0.642575i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.0000 | − | 26.0000i | 1.04251 | − | 1.04251i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 24.0000i | − | 0.960769i | ||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −10.0000 | − | 10.0000i | −0.399680 | − | 0.399680i | ||||
\(627\) | 6.00000 | + | 6.00000i | 0.239617 | + | 0.239617i | ||||
\(628\) | −34.0000 | + | 34.0000i | −1.35675 | + | 1.35675i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.00000 | − | 3.00000i | −0.0398410 | − | 0.119523i | ||||
\(631\) | 46.0000i | 1.83123i | 0.402055 | + | 0.915616i | \(0.368296\pi\) | ||||
−0.402055 | + | 0.915616i | \(0.631704\pi\) | |||||||
\(632\) | −16.0000 | + | 16.0000i | −0.636446 | + | 0.636446i | ||||
\(633\) | −22.0000 | −0.874421 | ||||||||
\(634\) | 26.0000i | 1.03259i | ||||||||
\(635\) | 36.0000 | + | 18.0000i | 1.42862 | + | 0.714308i | ||||
\(636\) | − | 12.0000i | − | 0.475831i | ||||||
\(637\) | −3.00000 | − | 3.00000i | −0.118864 | − | 0.118864i | ||||
\(638\) | 2.00000 | + | 2.00000i | 0.0791808 | + | 0.0791808i | ||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | −8.00000 | − | 24.0000i | −0.316228 | − | 0.948683i | ||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | −18.0000 | − | 18.0000i | −0.710403 | − | 0.710403i | ||||
\(643\) | 19.0000 | + | 19.0000i | 0.749287 | + | 0.749287i | 0.974345 | − | 0.225058i | \(-0.0722573\pi\) |
−0.225058 | + | 0.974345i | \(0.572257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.00000 | + | 4.00000i | −0.0787499 | + | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.00000 | −0.314512 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(648\) | 10.0000 | − | 10.0000i | 0.392837 | − | 0.392837i | ||||
\(649\) | − | 2.00000i | − | 0.0785069i | ||||||
\(650\) | 24.0000 | − | 18.0000i | 0.941357 | − | 0.706018i | ||||
\(651\) | 8.00000 | + | 8.00000i | 0.313545 | + | 0.313545i | ||||
\(652\) | −10.0000 | + | 10.0000i | −0.391630 | + | 0.391630i | ||||
\(653\) | −9.00000 | − | 9.00000i | −0.352197 | − | 0.352197i | 0.508729 | − | 0.860927i | \(-0.330115\pi\) |
−0.860927 | + | 0.508729i | \(0.830115\pi\) | |||||||
\(654\) | 6.00000 | + | 6.00000i | 0.234619 | + | 0.234619i | ||||
\(655\) | 5.00000 | + | 15.0000i | 0.195366 | + | 0.586098i | ||||
\(656\) | 48.0000i | 1.87409i | ||||||||
\(657\) | 10.0000i | 0.390137i | ||||||||
\(658\) | 10.0000 | − | 10.0000i | 0.389841 | − | 0.389841i | ||||
\(659\) | 23.0000 | − | 23.0000i | 0.895953 | − | 0.895953i | −0.0991224 | − | 0.995075i | \(-0.531604\pi\) |
0.995075 | + | 0.0991224i | \(0.0316036\pi\) | |||||||
\(660\) | −4.00000 | + | 8.00000i | −0.155700 | + | 0.311400i | ||||
\(661\) | 1.00000 | + | 1.00000i | 0.0388955 | + | 0.0388955i | 0.726287 | − | 0.687392i | \(-0.241244\pi\) |
−0.687392 | + | 0.726287i | \(0.741244\pi\) | |||||||
\(662\) | 30.0000i | 1.16598i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.0000 | −0.776151 | ||||||||
\(665\) | −3.00000 | − | 9.00000i | −0.116335 | − | 0.349005i | ||||
\(666\) | − | 10.0000i | − | 0.387492i | ||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 48.0000i | 1.85718i | ||||||||
\(669\) | 2.00000 | − | 2.00000i | 0.0773245 | − | 0.0773245i | ||||
\(670\) | −12.0000 | − | 6.00000i | −0.463600 | − | 0.231800i | ||||
\(671\) | −14.0000 | −0.540464 | ||||||||
\(672\) | − | 8.00000i | − | 0.308607i | ||||||
\(673\) | 44.0000i | 1.69608i | 0.529936 | + | 0.848038i | \(0.322216\pi\) | ||||
−0.529936 | + | 0.848038i | \(0.677784\pi\) | |||||||
\(674\) | 8.00000 | − | 8.00000i | 0.308148 | − | 0.308148i | ||||
\(675\) | 28.0000 | + | 4.00000i | 1.07772 | + | 0.153960i | ||||
\(676\) | −10.0000 | −0.384615 | ||||||||
\(677\) | −7.00000 | + | 7.00000i | −0.269032 | + | 0.269032i | −0.828710 | − | 0.559678i | \(-0.810925\pi\) |
0.559678 | + | 0.828710i | \(0.310925\pi\) | |||||||
\(678\) | 32.0000 | 1.22895 | ||||||||
\(679\) | 8.00000i | 0.307012i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.0000i | 0.996322i | ||||||||
\(682\) | 16.0000i | 0.612672i | ||||||||
\(683\) | −29.0000 | + | 29.0000i | −1.10965 | + | 1.10965i | −0.116459 | + | 0.993196i | \(0.537154\pi\) |
−0.993196 | + | 0.116459i | \(0.962846\pi\) | |||||||
\(684\) | −6.00000 | + | 6.00000i | −0.229416 | + | 0.229416i | ||||
\(685\) | −10.0000 | + | 20.0000i | −0.382080 | + | 0.764161i | ||||
\(686\) | −1.00000 | − | 1.00000i | −0.0381802 | − | 0.0381802i | ||||
\(687\) | 14.0000i | 0.534133i | ||||||||
\(688\) | 4.00000 | − | 4.00000i | 0.152499 | − | 0.152499i | ||||
\(689\) | −18.0000 | −0.685745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.00000 | − | 1.00000i | 0.0380418 | − | 0.0380418i | −0.687830 | − | 0.725872i | \(-0.741437\pi\) |
0.725872 | + | 0.687830i | \(0.241437\pi\) | |||||||
\(692\) | 14.0000 | − | 14.0000i | 0.532200 | − | 0.532200i | ||||
\(693\) | 1.00000 | − | 1.00000i | 0.0379869 | − | 0.0379869i | ||||
\(694\) | 34.0000 | 1.29062 | ||||||||
\(695\) | −9.00000 | + | 3.00000i | −0.341389 | + | 0.113796i | ||||
\(696\) | 4.00000 | − | 4.00000i | 0.151620 | − | 0.151620i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 22.0000 | 0.832712 | ||||||||
\(699\) | 10.0000 | + | 10.0000i | 0.378235 | + | 0.378235i | ||||
\(700\) | 8.00000 | − | 6.00000i | 0.302372 | − | 0.226779i | ||||
\(701\) | −9.00000 | + | 9.00000i | −0.339925 | + | 0.339925i | −0.856339 | − | 0.516414i | \(-0.827267\pi\) |
0.516414 | + | 0.856339i | \(0.327267\pi\) | |||||||
\(702\) | −24.0000 | − | 24.0000i | −0.905822 | − | 0.905822i | ||||
\(703\) | − | 30.0000i | − | 1.13147i | ||||||
\(704\) | 8.00000 | − | 8.00000i | 0.301511 | − | 0.301511i | ||||
\(705\) | 10.0000 | + | 30.0000i | 0.376622 | + | 1.12987i | ||||
\(706\) | −36.0000 | + | 36.0000i | −1.35488 | + | 1.35488i | ||||
\(707\) | −7.00000 | − | 7.00000i | −0.263262 | − | 0.263262i | ||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | 31.0000 | + | 31.0000i | 1.16423 | + | 1.16423i | 0.983540 | + | 0.180689i | \(0.0578328\pi\) |
0.180689 | + | 0.983540i | \(0.442167\pi\) | |||||||
\(710\) | 6.00000 | + | 18.0000i | 0.225176 | + | 0.675528i | ||||
\(711\) | 8.00000i | 0.300023i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | + | 6.00000i | 0.448775 | + | 0.224387i | ||||
\(716\) | −26.0000 | − | 26.0000i | −0.971666 | − | 0.971666i | ||||
\(717\) | −8.00000 | − | 8.00000i | −0.298765 | − | 0.298765i | ||||
\(718\) | 6.00000 | − | 6.00000i | 0.223918 | − | 0.223918i | ||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | −8.00000 | − | 4.00000i | −0.298142 | − | 0.149071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | − | 1.00000i | 0.0372161 | − | 0.0372161i | ||||
\(723\) | 10.0000 | + | 10.0000i | 0.371904 | + | 0.371904i | ||||
\(724\) | 30.0000 | − | 30.0000i | 1.11494 | − | 1.11494i | ||||
\(725\) | 7.00000 | + | 1.00000i | 0.259973 | + | 0.0371391i | ||||
\(726\) | 18.0000 | 0.668043 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | −12.0000 | −0.444750 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | −30.0000 | + | 10.0000i | −1.11035 | + | 0.370117i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 28.0000i | 1.03491i | ||||||||
\(733\) | −31.0000 | − | 31.0000i | −1.14501 | − | 1.14501i | −0.987520 | − | 0.157491i | \(-0.949660\pi\) |
−0.157491 | − | 0.987520i | \(-0.550340\pi\) | |||||||
\(734\) | −6.00000 | + | 6.00000i | −0.221464 | + | 0.221464i | ||||
\(735\) | 3.00000 | − | 1.00000i | 0.110657 | − | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.00000i | − | 0.221013i | ||||||
\(738\) | 12.0000 | + | 12.0000i | 0.441726 | + | 0.441726i | ||||
\(739\) | −9.00000 | + | 9.00000i | −0.331070 | + | 0.331070i | −0.852993 | − | 0.521923i | \(-0.825215\pi\) |
0.521923 | + | 0.852993i | \(0.325215\pi\) | |||||||
\(740\) | 30.0000 | − | 10.0000i | 1.10282 | − | 0.367607i | ||||
\(741\) | −18.0000 | − | 18.0000i | −0.661247 | − | 0.661247i | ||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 32.0000 | 1.17318 | ||||||||
\(745\) | −33.0000 | + | 11.0000i | −1.20903 | + | 0.403009i | ||||
\(746\) | −30.0000 | −1.09838 | ||||||||
\(747\) | −5.00000 | + | 5.00000i | −0.182940 | + | 0.182940i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00000 | + | 9.00000i | −0.328853 | + | 0.328853i | ||||
\(750\) | 4.00000 | + | 22.0000i | 0.146059 | + | 0.803326i | ||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | − | 40.0000i | − | 1.45865i | ||||||
\(753\) | − | 22.0000i | − | 0.801725i | ||||||
\(754\) | −6.00000 | − | 6.00000i | −0.218507 | − | 0.218507i | ||||
\(755\) | −28.0000 | − | 14.0000i | −1.01902 | − | 0.509512i | ||||
\(756\) | −8.00000 | − | 8.00000i | −0.290957 | − | 0.290957i | ||||
\(757\) | −9.00000 | + | 9.00000i | −0.327111 | + | 0.327111i | −0.851487 | − | 0.524376i | \(-0.824299\pi\) |
0.524376 | + | 0.851487i | \(0.324299\pi\) | |||||||
\(758\) | 38.0000i | 1.38022i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.0000 | − | 12.0000i | −0.870572 | − | 0.435286i | ||||
\(761\) | 12.0000i | 0.435000i | 0.976060 | + | 0.217500i | \(0.0697902\pi\) | ||||
−0.976060 | + | 0.217500i | \(0.930210\pi\) | |||||||
\(762\) | 36.0000 | 1.30414 | ||||||||
\(763\) | 3.00000 | − | 3.00000i | 0.108607 | − | 0.108607i | ||||
\(764\) | 32.0000i | 1.15772i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.0000 | − | 34.0000i | 1.22847 | − | 1.22847i | ||||
\(767\) | 6.00000i | 0.216647i | ||||||||
\(768\) | −16.0000 | − | 16.0000i | −0.577350 | − | 0.577350i | ||||
\(769\) | 46.0000 | 1.65880 | 0.829401 | − | 0.558653i | \(-0.188682\pi\) | ||||
0.829401 | + | 0.558653i | \(0.188682\pi\) | |||||||
\(770\) | 4.00000 | + | 2.00000i | 0.144150 | + | 0.0720750i | ||||
\(771\) | −4.00000 | + | 4.00000i | −0.144056 | + | 0.144056i | ||||
\(772\) | 40.0000 | 1.43963 | ||||||||
\(773\) | −3.00000 | + | 3.00000i | −0.107903 | + | 0.107903i | −0.758997 | − | 0.651094i | \(-0.774310\pi\) |
0.651094 | + | 0.758997i | \(0.274310\pi\) | |||||||
\(774\) | − | 2.00000i | − | 0.0718885i | ||||||
\(775\) | 24.0000 | + | 32.0000i | 0.862105 | + | 1.14947i | ||||
\(776\) | 16.0000 | + | 16.0000i | 0.574367 | + | 0.574367i | ||||
\(777\) | 10.0000 | 0.358748 | ||||||||
\(778\) | − | 22.0000i | − | 0.788738i | ||||||
\(779\) | 36.0000 | + | 36.0000i | 1.28983 | + | 1.28983i | ||||
\(780\) | 12.0000 | − | 24.0000i | 0.429669 | − | 0.859338i | ||||
\(781\) | −6.00000 | + | 6.00000i | −0.214697 | + | 0.214697i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.00000i | − | 0.285897i | ||||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | −51.0000 | + | 17.0000i | −1.82027 | + | 0.606756i | ||||
\(786\) | 10.0000 | + | 10.0000i | 0.356688 | + | 0.356688i | ||||
\(787\) | −13.0000 | − | 13.0000i | −0.463400 | − | 0.463400i | 0.436368 | − | 0.899768i | \(-0.356265\pi\) |
−0.899768 | + | 0.436368i | \(0.856265\pi\) | |||||||
\(788\) | −2.00000 | − | 2.00000i | −0.0712470 | − | 0.0712470i | ||||
\(789\) | −16.0000 | − | 16.0000i | −0.569615 | − | 0.569615i | ||||
\(790\) | −24.0000 | + | 8.00000i | −0.853882 | + | 0.284627i | ||||
\(791\) | − | 16.0000i | − | 0.568895i | ||||||
\(792\) | − | 4.00000i | − | 0.142134i | ||||||
\(793\) | 42.0000 | 1.49146 | ||||||||
\(794\) | 30.0000i | 1.06466i | ||||||||
\(795\) | 6.00000 | − | 12.0000i | 0.212798 | − | 0.425596i | ||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | −11.0000 | − | 11.0000i | −0.389640 | − | 0.389640i | 0.484919 | − | 0.874559i | \(-0.338849\pi\) |
−0.874559 | + | 0.484919i | \(0.838849\pi\) | |||||||
\(798\) | −6.00000 | − | 6.00000i | −0.212398 | − | 0.212398i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | − | 28.0000i | 0.141421 | − | 0.989949i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.0000 | − | 30.0000i | −1.05934 | − | 1.05934i | ||||
\(803\) | −10.0000 | − | 10.0000i | −0.352892 | − | 0.352892i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 48.0000i | − | 1.69073i | ||||||
\(807\) | 14.0000 | 0.492823 | ||||||||
\(808\) | −28.0000 | −0.985037 | ||||||||
\(809\) | 56.0000i | 1.96886i | 0.175791 | + | 0.984428i | \(0.443752\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | 15.0000 | − | 5.00000i | 0.527046 | − | 0.175682i | ||||
\(811\) | 11.0000 | + | 11.0000i | 0.386262 | + | 0.386262i | 0.873352 | − | 0.487090i | \(-0.161942\pi\) |
−0.487090 | + | 0.873352i | \(0.661942\pi\) | |||||||
\(812\) | −2.00000 | − | 2.00000i | −0.0701862 | − | 0.0701862i | ||||
\(813\) | 24.0000 | + | 24.0000i | 0.841717 | + | 0.841717i | ||||
\(814\) | 10.0000 | + | 10.0000i | 0.350500 | + | 0.350500i | ||||
\(815\) | −15.0000 | + | 5.00000i | −0.525427 | + | 0.175142i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.00000i | − | 0.209913i | ||||||
\(818\) | 12.0000 | − | 12.0000i | 0.419570 | − | 0.419570i | ||||
\(819\) | −3.00000 | + | 3.00000i | −0.104828 | + | 0.104828i | ||||
\(820\) | −24.0000 | + | 48.0000i | −0.838116 | + | 1.67623i | ||||
\(821\) | −25.0000 | − | 25.0000i | −0.872506 | − | 0.872506i | 0.120239 | − | 0.992745i | \(-0.461634\pi\) |
−0.992745 | + | 0.120239i | \(0.961634\pi\) | |||||||
\(822\) | 20.0000i | 0.697580i | ||||||||
\(823\) | −56.0000 | −1.95204 | −0.976019 | − | 0.217687i | \(-0.930149\pi\) | ||||
−0.976019 | + | 0.217687i | \(0.930149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.00000 | + | 6.00000i | −0.278524 | + | 0.208893i | ||||
\(826\) | 2.00000i | 0.0695889i | ||||||||
\(827\) | 31.0000 | − | 31.0000i | 1.07798 | − | 1.07798i | 0.0812847 | − | 0.996691i | \(-0.474098\pi\) |
0.996691 | − | 0.0812847i | \(-0.0259023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.00000 | − | 9.00000i | 0.312583 | − | 0.312583i | −0.533327 | − | 0.845909i | \(-0.679058\pi\) |
0.845909 | + | 0.533327i | \(0.179058\pi\) | |||||||
\(830\) | −20.0000 | − | 10.0000i | −0.694210 | − | 0.347105i | ||||
\(831\) | −30.0000 | −1.04069 | ||||||||
\(832\) | −24.0000 | + | 24.0000i | −0.832050 | + | 0.832050i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.00000 | + | 6.00000i | −0.207763 | + | 0.207763i | ||||
\(835\) | −24.0000 | + | 48.0000i | −0.830554 | + | 1.66111i | ||||
\(836\) | − | 12.0000i | − | 0.415029i | ||||||
\(837\) | 32.0000 | − | 32.0000i | 1.10608 | − | 1.10608i | ||||
\(838\) | −18.0000 | −0.621800 | ||||||||
\(839\) | − | 46.0000i | − | 1.58810i | −0.607855 | − | 0.794048i | \(-0.707970\pi\) | ||
0.607855 | − | 0.794048i | \(-0.292030\pi\) | |||||||
\(840\) | 4.00000 | − | 8.00000i | 0.138013 | − | 0.276026i | ||||
\(841\) | 27.0000i | 0.931034i | ||||||||
\(842\) | − | 38.0000i | − | 1.30957i | ||||||
\(843\) | 28.0000 | − | 28.0000i | 0.964371 | − | 0.964371i | ||||
\(844\) | 22.0000 | + | 22.0000i | 0.757271 | + | 0.757271i | ||||
\(845\) | −10.0000 | − | 5.00000i | −0.344010 | − | 0.172005i | ||||
\(846\) | −10.0000 | − | 10.0000i | −0.343807 | − | 0.343807i | ||||
\(847\) | − | 9.00000i | − | 0.309244i | ||||||
\(848\) | −12.0000 | + | 12.0000i | −0.412082 | + | 0.412082i | ||||
\(849\) | −18.0000 | −0.617758 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 12.0000 | + | 12.0000i | 0.411113 | + | 0.411113i | ||||
\(853\) | −7.00000 | + | 7.00000i | −0.239675 | + | 0.239675i | −0.816716 | − | 0.577040i | \(-0.804208\pi\) |
0.577040 | + | 0.816716i | \(0.304208\pi\) | |||||||
\(854\) | 14.0000 | 0.479070 | ||||||||
\(855\) | −9.00000 | + | 3.00000i | −0.307794 | + | 0.102598i | ||||
\(856\) | 36.0000i | 1.23045i | ||||||||
\(857\) | 42.0000 | 1.43469 | 0.717346 | − | 0.696717i | \(-0.245357\pi\) | ||||
0.717346 | + | 0.696717i | \(0.245357\pi\) | |||||||
\(858\) | 12.0000 | 0.409673 | ||||||||
\(859\) | 11.0000 | + | 11.0000i | 0.375315 | + | 0.375315i | 0.869409 | − | 0.494094i | \(-0.164500\pi\) |
−0.494094 | + | 0.869409i | \(0.664500\pi\) | |||||||
\(860\) | 6.00000 | − | 2.00000i | 0.204598 | − | 0.0681994i | ||||
\(861\) | −12.0000 | + | 12.0000i | −0.408959 | + | 0.408959i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 26.0000i | − | 0.885050i | −0.896756 | − | 0.442525i | \(-0.854083\pi\) | ||
0.896756 | − | 0.442525i | \(-0.145917\pi\) | |||||||
\(864\) | −32.0000 | −1.08866 | ||||||||
\(865\) | 21.0000 | − | 7.00000i | 0.714021 | − | 0.238007i | ||||
\(866\) | 16.0000 | − | 16.0000i | 0.543702 | − | 0.543702i | ||||
\(867\) | −17.0000 | − | 17.0000i | −0.577350 | − | 0.577350i | ||||
\(868\) | − | 16.0000i | − | 0.543075i | ||||||
\(869\) | −8.00000 | − | 8.00000i | −0.271381 | − | 0.271381i | ||||
\(870\) | 6.00000 | − | 2.00000i | 0.203419 | − | 0.0678064i | ||||
\(871\) | 18.0000i | 0.609907i | ||||||||
\(872\) | − | 12.0000i | − | 0.406371i | ||||||
\(873\) | 8.00000 | 0.270759 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.0000 | − | 2.00000i | 0.371868 | − | 0.0676123i | ||||
\(876\) | −20.0000 | + | 20.0000i | −0.675737 | + | 0.675737i | ||||
\(877\) | −5.00000 | − | 5.00000i | −0.168838 | − | 0.168838i | 0.617630 | − | 0.786468i | \(-0.288093\pi\) |
−0.786468 | + | 0.617630i | \(0.788093\pi\) | |||||||
\(878\) | −38.0000 | + | 38.0000i | −1.28244 | + | 1.28244i | ||||
\(879\) | 22.0000 | 0.742042 | ||||||||
\(880\) | 12.0000 | − | 4.00000i | 0.404520 | − | 0.134840i | ||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | −1.00000 | + | 1.00000i | −0.0336718 | + | 0.0336718i | ||||
\(883\) | 21.0000 | + | 21.0000i | 0.706706 | + | 0.706706i | 0.965841 | − | 0.259135i | \(-0.0834374\pi\) |
−0.259135 | + | 0.965841i | \(0.583437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | − | 2.00000i | −0.134459 | − | 0.0672293i | ||||
\(886\) | 2.00000 | 0.0671913 | ||||||||
\(887\) | −48.0000 | −1.61168 | −0.805841 | − | 0.592132i | \(-0.798286\pi\) | ||||
−0.805841 | + | 0.592132i | \(0.798286\pi\) | |||||||
\(888\) | 20.0000 | − | 20.0000i | 0.671156 | − | 0.671156i | ||||
\(889\) | − | 18.0000i | − | 0.603701i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | + | 5.00000i | 0.167506 | + | 0.167506i | ||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | −30.0000 | − | 30.0000i | −1.00391 | − | 1.00391i | ||||
\(894\) | −22.0000 | + | 22.0000i | −0.735790 | + | 0.735790i | ||||
\(895\) | −13.0000 | − | 39.0000i | −0.434542 | − | 1.30363i | ||||
\(896\) | −8.00000 | + | 8.00000i | −0.267261 | + | 0.267261i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.0000 | + | 34.0000i | 1.13459 | + | 1.13459i | ||||
\(899\) | 8.00000 | − | 8.00000i | 0.266815 | − | 0.266815i | ||||
\(900\) | −6.00000 | − | 8.00000i | −0.200000 | − | 0.266667i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −24.0000 | −0.799113 | ||||||||
\(903\) | 2.00000 | 0.0665558 | ||||||||
\(904\) | −32.0000 | − | 32.0000i | −1.06430 | − | 1.06430i | ||||
\(905\) | 45.0000 | − | 15.0000i | 1.49585 | − | 0.498617i | ||||
\(906\) | −28.0000 | −0.930238 | ||||||||
\(907\) | −13.0000 | + | 13.0000i | −0.431658 | + | 0.431658i | −0.889192 | − | 0.457534i | \(-0.848733\pi\) |
0.457534 | + | 0.889192i | \(0.348733\pi\) | |||||||
\(908\) | 26.0000 | − | 26.0000i | 0.862840 | − | 0.862840i | ||||
\(909\) | −7.00000 | + | 7.00000i | −0.232175 | + | 0.232175i | ||||
\(910\) | −12.0000 | − | 6.00000i | −0.397796 | − | 0.198898i | ||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | −24.0000 | −0.794719 | ||||||||
\(913\) | − | 10.0000i | − | 0.330952i | ||||||
\(914\) | 30.0000 | + | 30.0000i | 0.992312 | + | 0.992312i | ||||
\(915\) | −14.0000 | + | 28.0000i | −0.462826 | + | 0.925651i | ||||
\(916\) | 14.0000 | − | 14.0000i | 0.462573 | − | 0.462573i | ||||
\(917\) | 5.00000 | − | 5.00000i | 0.165115 | − | 0.165115i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.0000i | − | 0.329870i | −0.986304 | − | 0.164935i | \(-0.947259\pi\) | ||
0.986304 | − | 0.164935i | \(-0.0527414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 30.0000i | − | 0.988534i | ||||||
\(922\) | −10.0000 | −0.329332 | ||||||||
\(923\) | 18.0000 | − | 18.0000i | 0.592477 | − | 0.592477i | ||||
\(924\) | 4.00000 | 0.131590 | ||||||||
\(925\) | 35.0000 | + | 5.00000i | 1.15079 | + | 0.164399i | ||||
\(926\) | 22.0000 | − | 22.0000i | 0.722965 | − | 0.722965i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.00000 | −0.262613 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 32.0000 | + | 16.0000i | 1.04932 | + | 0.524661i | ||||
\(931\) | −3.00000 | + | 3.00000i | −0.0983210 | + | 0.0983210i | ||||
\(932\) | − | 20.0000i | − | 0.655122i | ||||||
\(933\) | 26.0000 | − | 26.0000i | 0.851202 | − | 0.851202i | ||||
\(934\) | 34.0000i | 1.11251i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.0000i | 0.392232i | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 6.00000i | 0.195907i | ||||||||
\(939\) | −10.0000 | − | 10.0000i | −0.326338 | − | 0.326338i | ||||
\(940\) | 20.0000 | − | 40.0000i | 0.652328 | − | 1.30466i | ||||
\(941\) | 41.0000 | − | 41.0000i | 1.33656 | − | 1.33656i | 0.437195 | − | 0.899367i | \(-0.355972\pi\) |
0.899367 | − | 0.437195i | \(-0.144028\pi\) | |||||||
\(942\) | −34.0000 | + | 34.0000i | −1.10778 | + | 1.10778i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 4.00000 | + | 4.00000i | 0.130189 | + | 0.130189i | ||||
\(945\) | −4.00000 | − | 12.0000i | −0.130120 | − | 0.390360i | ||||
\(946\) | 2.00000 | + | 2.00000i | 0.0650256 | + | 0.0650256i | ||||
\(947\) | 1.00000 | + | 1.00000i | 0.0324956 | + | 0.0324956i | 0.723168 | − | 0.690672i | \(-0.242685\pi\) |
−0.690672 | + | 0.723168i | \(0.742685\pi\) | |||||||
\(948\) | −16.0000 | + | 16.0000i | −0.519656 | + | 0.519656i | ||||
\(949\) | 30.0000 | + | 30.0000i | 0.973841 | + | 0.973841i | ||||
\(950\) | −18.0000 | − | 24.0000i | −0.583997 | − | 0.778663i | ||||
\(951\) | 26.0000i | 0.843108i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0000 | −0.453504 | −0.226752 | − | 0.973952i | \(-0.572811\pi\) | ||||
−0.226752 | + | 0.973952i | \(0.572811\pi\) | |||||||
\(954\) | 6.00000i | 0.194257i | ||||||||
\(955\) | −16.0000 | + | 32.0000i | −0.517748 | + | 1.03550i | ||||
\(956\) | 16.0000i | 0.517477i | ||||||||
\(957\) | 2.00000 | + | 2.00000i | 0.0646508 | + | 0.0646508i | ||||
\(958\) | −16.0000 | − | 16.0000i | −0.516937 | − | 0.516937i | ||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | −8.00000 | − | 24.0000i | −0.258199 | − | 0.774597i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | −30.0000 | − | 30.0000i | −0.967239 | − | 0.967239i | ||||
\(963\) | 9.00000 | + | 9.00000i | 0.290021 | + | 0.290021i | ||||
\(964\) | − | 20.0000i | − | 0.644157i | ||||||
\(965\) | 40.0000 | + | 20.0000i | 1.28765 | + | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | −18.0000 | − | 18.0000i | −0.578542 | − | 0.578542i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.00000 | + | 24.0000i | 0.256865 | + | 0.770594i | ||||
\(971\) | 31.0000 | + | 31.0000i | 0.994837 | + | 0.994837i | 0.999987 | − | 0.00514940i | \(-0.00163911\pi\) |
−0.00514940 | + | 0.999987i | \(0.501639\pi\) | |||||||
\(972\) | −14.0000 | + | 14.0000i | −0.449050 | + | 0.449050i | ||||
\(973\) | 3.00000 | + | 3.00000i | 0.0961756 | + | 0.0961756i | ||||
\(974\) | 8.00000 | + | 8.00000i | 0.256337 | + | 0.256337i | ||||
\(975\) | 24.0000 | − | 18.0000i | 0.768615 | − | 0.576461i | ||||
\(976\) | 28.0000 | − | 28.0000i | 0.896258 | − | 0.896258i | ||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | −10.0000 | + | 10.0000i | −0.319765 | + | 0.319765i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −4.00000 | − | 2.00000i | −0.127775 | − | 0.0638877i | ||||
\(981\) | −3.00000 | − | 3.00000i | −0.0957826 | − | 0.0957826i | ||||
\(982\) | 30.0000i | 0.957338i | ||||||||
\(983\) | 24.0000 | 0.765481 | 0.382741 | − | 0.923856i | \(-0.374980\pi\) | ||||
0.382741 | + | 0.923856i | \(0.374980\pi\) | |||||||
\(984\) | 48.0000i | 1.53018i | ||||||||
\(985\) | −1.00000 | − | 3.00000i | −0.0318626 | − | 0.0955879i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.0000 | − | 10.0000i | 0.318304 | − | 0.318304i | ||||
\(988\) | 36.0000i | 1.14531i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.00000 | − | 4.00000i | 0.0635642 | − | 0.127128i | ||||
\(991\) | −24.0000 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | −32.0000 | − | 32.0000i | −1.01600 | − | 1.01600i | ||||
\(993\) | 30.0000i | 0.952021i | ||||||||
\(994\) | 6.00000 | − | 6.00000i | 0.190308 | − | 0.190308i | ||||
\(995\) | −20.0000 | − | 10.0000i | −0.634043 | − | 0.317021i | ||||
\(996\) | −20.0000 | −0.633724 | ||||||||
\(997\) | −27.0000 | + | 27.0000i | −0.855099 | + | 0.855099i | −0.990756 | − | 0.135657i | \(-0.956685\pi\) |
0.135657 | + | 0.990756i | \(0.456685\pi\) | |||||||
\(998\) | −38.0000 | −1.20287 | ||||||||
\(999\) | − | 40.0000i | − | 1.26554i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 560.2.bb.a.309.1 | yes | 2 | |
5.4 | even | 2 | 560.2.bb.b.309.1 | yes | 2 | ||
16.13 | even | 4 | 560.2.bb.b.29.1 | yes | 2 | ||
80.29 | even | 4 | inner | 560.2.bb.a.29.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bb.a.29.1 | ✓ | 2 | 80.29 | even | 4 | inner | |
560.2.bb.a.309.1 | yes | 2 | 1.1 | even | 1 | trivial | |
560.2.bb.b.29.1 | yes | 2 | 16.13 | even | 4 | ||
560.2.bb.b.309.1 | yes | 2 | 5.4 | even | 2 |