Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(43,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.g (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
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 | 43.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.43 |
Dual form | 370.2.g.a.327.1 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.00000 | + | 1.00000i | −0.577350 | + | 0.577350i | −0.934172 | − | 0.356822i | \(-0.883860\pi\) |
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 1.00000 | + | 1.00000i | 0.408248 | + | 0.408248i | ||||
\(7\) | 1.00000 | − | 1.00000i | 0.377964 | − | 0.377964i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) |
0.870367 | + | 0.492403i | \(0.163881\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −1.00000 | − | 2.00000i | −0.316228 | − | 0.632456i | ||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 1.00000 | − | 1.00000i | 0.288675 | − | 0.288675i | ||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −1.00000 | − | 1.00000i | −0.267261 | − | 0.267261i | ||||
\(15\) | −1.00000 | + | 3.00000i | −0.258199 | + | 0.774597i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.00000 | − | 5.00000i | 1.14708 | − | 1.14708i | 0.159954 | − | 0.987124i | \(-0.448865\pi\) |
0.987124 | − | 0.159954i | \(-0.0511347\pi\) | |||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −1.00000 | − | 1.00000i | −0.204124 | − | 0.204124i | ||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −4.00000 | − | 4.00000i | −0.769800 | − | 0.769800i | ||||
\(28\) | −1.00000 | + | 1.00000i | −0.188982 | + | 0.188982i | ||||
\(29\) | 3.00000 | + | 3.00000i | 0.557086 | + | 0.557086i | 0.928477 | − | 0.371391i | \(-0.121119\pi\) |
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 3.00000 | + | 1.00000i | 0.547723 | + | 0.182574i | ||||
\(31\) | 7.00000 | − | 7.00000i | 1.25724 | − | 1.25724i | 0.304830 | − | 0.952407i | \(-0.401400\pi\) |
0.952407 | − | 0.304830i | \(-0.0985998\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.00000 | + | 2.00000i | 0.348155 | + | 0.348155i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | 1.00000 | − | 3.00000i | 0.169031 | − | 0.507093i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −6.00000 | + | 1.00000i | −0.986394 | + | 0.164399i | ||||
\(38\) | −5.00000 | − | 5.00000i | −0.811107 | − | 0.811107i | ||||
\(39\) | −2.00000 | − | 2.00000i | −0.320256 | − | 0.320256i | ||||
\(40\) | 1.00000 | + | 2.00000i | 0.158114 | + | 0.316228i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 2.00000 | 0.308607 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 2.00000i | 0.301511i | ||||||||
\(45\) | 1.00000 | + | 2.00000i | 0.149071 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.00000 | + | 7.00000i | −1.02105 | + | 1.02105i | −0.0212814 | + | 0.999774i | \(0.506775\pi\) |
−0.999774 | + | 0.0212814i | \(0.993225\pi\) | |||||||
\(48\) | −1.00000 | + | 1.00000i | −0.144338 | + | 0.144338i | ||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | −4.00000 | + | 4.00000i | −0.560112 | + | 0.560112i | ||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | 1.00000 | + | 1.00000i | 0.137361 | + | 0.137361i | 0.772444 | − | 0.635083i | \(-0.219034\pi\) |
−0.635083 | + | 0.772444i | \(0.719034\pi\) | |||||||
\(54\) | −4.00000 | + | 4.00000i | −0.544331 | + | 0.544331i | ||||
\(55\) | −2.00000 | − | 4.00000i | −0.269680 | − | 0.539360i | ||||
\(56\) | 1.00000 | + | 1.00000i | 0.133631 | + | 0.133631i | ||||
\(57\) | 10.0000i | 1.32453i | ||||||||
\(58\) | 3.00000 | − | 3.00000i | 0.393919 | − | 0.393919i | ||||
\(59\) | 1.00000 | − | 1.00000i | 0.130189 | − | 0.130189i | −0.639010 | − | 0.769199i | \(-0.720656\pi\) |
0.769199 | + | 0.639010i | \(0.220656\pi\) | |||||||
\(60\) | 1.00000 | − | 3.00000i | 0.129099 | − | 0.387298i | ||||
\(61\) | −3.00000 | + | 3.00000i | −0.384111 | + | 0.384111i | −0.872581 | − | 0.488470i | \(-0.837555\pi\) |
0.488470 | + | 0.872581i | \(0.337555\pi\) | |||||||
\(62\) | −7.00000 | − | 7.00000i | −0.889001 | − | 0.889001i | ||||
\(63\) | 1.00000 | + | 1.00000i | 0.125988 | + | 0.125988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000 | + | 4.00000i | 0.248069 | + | 0.496139i | ||||
\(66\) | 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 | \(0.833446\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | − | 1.00000i | −0.358569 | − | 0.119523i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −9.00000 | + | 9.00000i | −1.05337 | + | 1.05337i | −0.0548772 | + | 0.998493i | \(0.517477\pi\) |
−0.998493 | + | 0.0548772i | \(0.982523\pi\) | |||||||
\(74\) | 1.00000 | + | 6.00000i | 0.116248 | + | 0.697486i | ||||
\(75\) | 1.00000 | + | 7.00000i | 0.115470 | + | 0.808290i | ||||
\(76\) | −5.00000 | + | 5.00000i | −0.573539 | + | 0.573539i | ||||
\(77\) | −2.00000 | − | 2.00000i | −0.227921 | − | 0.227921i | ||||
\(78\) | −2.00000 | + | 2.00000i | −0.226455 | + | 0.226455i | ||||
\(79\) | 1.00000 | − | 1.00000i | 0.112509 | − | 0.112509i | −0.648611 | − | 0.761120i | \(-0.724650\pi\) |
0.761120 | + | 0.648611i | \(0.224650\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | − | 5.00000i | −0.548821 | − | 0.548821i | 0.377279 | − | 0.926100i | \(-0.376860\pi\) |
−0.926100 | + | 0.377279i | \(0.876860\pi\) | |||||||
\(84\) | − | 2.00000i | − | 0.218218i | ||||||
\(85\) | 8.00000 | − | 4.00000i | 0.867722 | − | 0.433861i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | −5.00000 | − | 5.00000i | −0.529999 | − | 0.529999i | 0.390573 | − | 0.920572i | \(-0.372277\pi\) |
−0.920572 | + | 0.390573i | \(0.872277\pi\) | |||||||
\(90\) | 2.00000 | − | 1.00000i | 0.210819 | − | 0.105409i | ||||
\(91\) | 2.00000 | + | 2.00000i | 0.209657 | + | 0.209657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.0000i | 1.45173i | ||||||||
\(94\) | 7.00000 | + | 7.00000i | 0.721995 | + | 0.721995i | ||||
\(95\) | 5.00000 | − | 15.0000i | 0.512989 | − | 1.53897i | ||||
\(96\) | 1.00000 | + | 1.00000i | 0.102062 | + | 0.102062i | ||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 5.00000 | 0.505076 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −3.00000 | + | 4.00000i | −0.300000 | + | 0.400000i | ||||
\(101\) | 8.00000i | 0.796030i | 0.917379 | + | 0.398015i | \(0.130301\pi\) | ||||
−0.917379 | + | 0.398015i | \(0.869699\pi\) | |||||||
\(102\) | 4.00000 | + | 4.00000i | 0.396059 | + | 0.396059i | ||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 2.00000 | + | 4.00000i | 0.195180 | + | 0.390360i | ||||
\(106\) | 1.00000 | − | 1.00000i | 0.0971286 | − | 0.0971286i | ||||
\(107\) | −11.0000 | + | 11.0000i | −1.06341 | + | 1.06341i | −0.0655616 | + | 0.997849i | \(0.520884\pi\) |
−0.997849 | + | 0.0655616i | \(0.979116\pi\) | |||||||
\(108\) | 4.00000 | + | 4.00000i | 0.384900 | + | 0.384900i | ||||
\(109\) | 7.00000 | − | 7.00000i | 0.670478 | − | 0.670478i | −0.287348 | − | 0.957826i | \(-0.592774\pi\) |
0.957826 | + | 0.287348i | \(0.0927736\pi\) | |||||||
\(110\) | −4.00000 | + | 2.00000i | −0.381385 | + | 0.190693i | ||||
\(111\) | 5.00000 | − | 7.00000i | 0.474579 | − | 0.664411i | ||||
\(112\) | 1.00000 | − | 1.00000i | 0.0944911 | − | 0.0944911i | ||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 10.0000 | 0.936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | − | 3.00000i | −0.278543 | − | 0.278543i | ||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | −1.00000 | − | 1.00000i | −0.0920575 | − | 0.0920575i | ||||
\(119\) | 4.00000 | − | 4.00000i | 0.366679 | − | 0.366679i | ||||
\(120\) | −3.00000 | − | 1.00000i | −0.273861 | − | 0.0912871i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 3.00000 | + | 3.00000i | 0.271607 | + | 0.271607i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.00000 | + | 7.00000i | −0.628619 | + | 0.628619i | ||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 1.00000 | − | 1.00000i | 0.0890871 | − | 0.0890871i | ||||
\(127\) | −3.00000 | + | 3.00000i | −0.266207 | + | 0.266207i | −0.827570 | − | 0.561363i | \(-0.810277\pi\) |
0.561363 | + | 0.827570i | \(0.310277\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.00000 | − | 4.00000i | −0.352180 | − | 0.352180i | ||||
\(130\) | 4.00000 | − | 2.00000i | 0.350823 | − | 0.175412i | ||||
\(131\) | −13.0000 | + | 13.0000i | −1.13582 | + | 1.13582i | −0.146623 | + | 0.989192i | \(0.546840\pi\) |
−0.989192 | + | 0.146623i | \(0.953160\pi\) | |||||||
\(132\) | −2.00000 | − | 2.00000i | −0.174078 | − | 0.174078i | ||||
\(133\) | − | 10.0000i | − | 0.867110i | ||||||
\(134\) | −3.00000 | + | 3.00000i | −0.259161 | + | 0.259161i | ||||
\(135\) | −12.0000 | − | 4.00000i | −1.03280 | − | 0.344265i | ||||
\(136\) | 4.00000i | 0.342997i | ||||||||
\(137\) | −7.00000 | + | 7.00000i | −0.598050 | + | 0.598050i | −0.939793 | − | 0.341743i | \(-0.888983\pi\) |
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −1.00000 | + | 3.00000i | −0.0845154 | + | 0.253546i | ||||
\(141\) | − | 14.0000i | − | 1.17901i | ||||||
\(142\) | 8.00000i | 0.671345i | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 9.00000 | + | 3.00000i | 0.747409 | + | 0.249136i | ||||
\(146\) | 9.00000 | + | 9.00000i | 0.744845 | + | 0.744845i | ||||
\(147\) | −5.00000 | − | 5.00000i | −0.412393 | − | 0.412393i | ||||
\(148\) | 6.00000 | − | 1.00000i | 0.493197 | − | 0.0821995i | ||||
\(149\) | − | 24.0000i | − | 1.96616i | −0.183186 | − | 0.983078i | \(-0.558641\pi\) | ||
0.183186 | − | 0.983078i | \(-0.441359\pi\) | |||||||
\(150\) | 7.00000 | − | 1.00000i | 0.571548 | − | 0.0816497i | ||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 5.00000 | + | 5.00000i | 0.405554 | + | 0.405554i | ||||
\(153\) | 4.00000i | 0.323381i | ||||||||
\(154\) | −2.00000 | + | 2.00000i | −0.161165 | + | 0.161165i | ||||
\(155\) | 7.00000 | − | 21.0000i | 0.562254 | − | 1.68676i | ||||
\(156\) | 2.00000 | + | 2.00000i | 0.160128 | + | 0.160128i | ||||
\(157\) | 9.00000 | − | 9.00000i | 0.718278 | − | 0.718278i | −0.249974 | − | 0.968252i | \(-0.580422\pi\) |
0.968252 | + | 0.249974i | \(0.0804222\pi\) | |||||||
\(158\) | −1.00000 | − | 1.00000i | −0.0795557 | − | 0.0795557i | ||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | −1.00000 | − | 2.00000i | −0.0790569 | − | 0.158114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 5.00000i | − | 0.392837i | ||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.00000 | + | 2.00000i | 0.467099 | + | 0.155700i | ||||
\(166\) | −5.00000 | + | 5.00000i | −0.388075 | + | 0.388075i | ||||
\(167\) | −22.0000 | −1.70241 | −0.851206 | − | 0.524832i | \(-0.824128\pi\) | ||||
−0.851206 | + | 0.524832i | \(0.824128\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | −4.00000 | − | 8.00000i | −0.306786 | − | 0.613572i | ||||
\(171\) | 5.00000 | + | 5.00000i | 0.382360 | + | 0.382360i | ||||
\(172\) | − | 4.00000i | − | 0.304997i | ||||||
\(173\) | 3.00000 | − | 3.00000i | 0.228086 | − | 0.228086i | −0.583807 | − | 0.811893i | \(-0.698437\pi\) |
0.811893 | + | 0.583807i | \(0.198437\pi\) | |||||||
\(174\) | 6.00000i | 0.454859i | ||||||||
\(175\) | −1.00000 | − | 7.00000i | −0.0755929 | − | 0.529150i | ||||
\(176\) | − | 2.00000i | − | 0.150756i | ||||||
\(177\) | 2.00000i | 0.150329i | ||||||||
\(178\) | −5.00000 | + | 5.00000i | −0.374766 | + | 0.374766i | ||||
\(179\) | −9.00000 | − | 9.00000i | −0.672692 | − | 0.672692i | 0.285644 | − | 0.958336i | \(-0.407792\pi\) |
−0.958336 | + | 0.285644i | \(0.907792\pi\) | |||||||
\(180\) | −1.00000 | − | 2.00000i | −0.0745356 | − | 0.149071i | ||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 2.00000 | − | 2.00000i | 0.148250 | − | 0.148250i | ||||
\(183\) | − | 6.00000i | − | 0.443533i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.0000 | + | 8.00000i | −0.808736 | + | 0.588172i | ||||
\(186\) | 14.0000 | 1.02653 | ||||||||
\(187\) | − | 8.00000i | − | 0.585018i | ||||||
\(188\) | 7.00000 | − | 7.00000i | 0.510527 | − | 0.510527i | ||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | −15.0000 | − | 5.00000i | −1.08821 | − | 0.362738i | ||||
\(191\) | 1.00000 | + | 1.00000i | 0.0723575 | + | 0.0723575i | 0.742359 | − | 0.670002i | \(-0.233707\pi\) |
−0.670002 | + | 0.742359i | \(0.733707\pi\) | |||||||
\(192\) | 1.00000 | − | 1.00000i | 0.0721688 | − | 0.0721688i | ||||
\(193\) | 18.0000i | 1.29567i | 0.761781 | + | 0.647834i | \(0.224325\pi\) | ||||
−0.761781 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(194\) | − | 8.00000i | − | 0.574367i | ||||||
\(195\) | −6.00000 | − | 2.00000i | −0.429669 | − | 0.143223i | ||||
\(196\) | − | 5.00000i | − | 0.357143i | ||||||
\(197\) | 13.0000 | − | 13.0000i | 0.926212 | − | 0.926212i | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) |
0.997459 | + | 0.0712470i | \(0.0226979\pi\) | |||||||
\(198\) | − | 2.00000i | − | 0.142134i | ||||||
\(199\) | 11.0000 | + | 11.0000i | 0.779769 | + | 0.779769i | 0.979791 | − | 0.200022i | \(-0.0641014\pi\) |
−0.200022 | + | 0.979791i | \(0.564101\pi\) | |||||||
\(200\) | 4.00000 | + | 3.00000i | 0.282843 | + | 0.212132i | ||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 8.00000 | 0.562878 | ||||||||
\(203\) | 6.00000 | 0.421117 | ||||||||
\(204\) | 4.00000 | − | 4.00000i | 0.280056 | − | 0.280056i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 14.0000i | − | 0.975426i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | −10.0000 | − | 10.0000i | −0.691714 | − | 0.691714i | ||||
\(210\) | 4.00000 | − | 2.00000i | 0.276026 | − | 0.138013i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −1.00000 | − | 1.00000i | −0.0686803 | − | 0.0686803i | ||||
\(213\) | 8.00000 | − | 8.00000i | 0.548151 | − | 0.548151i | ||||
\(214\) | 11.0000 | + | 11.0000i | 0.751945 | + | 0.751945i | ||||
\(215\) | 4.00000 | + | 8.00000i | 0.272798 | + | 0.545595i | ||||
\(216\) | 4.00000 | − | 4.00000i | 0.272166 | − | 0.272166i | ||||
\(217\) | − | 14.0000i | − | 0.950382i | ||||||
\(218\) | −7.00000 | − | 7.00000i | −0.474100 | − | 0.474100i | ||||
\(219\) | − | 18.0000i | − | 1.21633i | ||||||
\(220\) | 2.00000 | + | 4.00000i | 0.134840 | + | 0.269680i | ||||
\(221\) | 8.00000i | 0.538138i | ||||||||
\(222\) | −7.00000 | − | 5.00000i | −0.469809 | − | 0.335578i | ||||
\(223\) | 3.00000 | + | 3.00000i | 0.200895 | + | 0.200895i | 0.800383 | − | 0.599489i | \(-0.204629\pi\) |
−0.599489 | + | 0.800383i | \(0.704629\pi\) | |||||||
\(224\) | −1.00000 | − | 1.00000i | −0.0668153 | − | 0.0668153i | ||||
\(225\) | 4.00000 | + | 3.00000i | 0.266667 | + | 0.200000i | ||||
\(226\) | 12.0000i | 0.798228i | ||||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | − | 10.0000i | − | 0.662266i | ||||||
\(229\) | − | 12.0000i | − | 0.792982i | −0.918039 | − | 0.396491i | \(-0.870228\pi\) | ||
0.918039 | − | 0.396491i | \(-0.129772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | −3.00000 | + | 3.00000i | −0.196960 | + | 0.196960i | ||||
\(233\) | 7.00000 | − | 7.00000i | 0.458585 | − | 0.458585i | −0.439606 | − | 0.898191i | \(-0.644882\pi\) |
0.898191 | + | 0.439606i | \(0.144882\pi\) | |||||||
\(234\) | 2.00000i | 0.130744i | ||||||||
\(235\) | −7.00000 | + | 21.0000i | −0.456630 | + | 1.36989i | ||||
\(236\) | −1.00000 | + | 1.00000i | −0.0650945 | + | 0.0650945i | ||||
\(237\) | 2.00000i | 0.129914i | ||||||||
\(238\) | −4.00000 | − | 4.00000i | −0.259281 | − | 0.259281i | ||||
\(239\) | −3.00000 | + | 3.00000i | −0.194054 | + | 0.194054i | −0.797445 | − | 0.603391i | \(-0.793816\pi\) |
0.603391 | + | 0.797445i | \(0.293816\pi\) | |||||||
\(240\) | −1.00000 | + | 3.00000i | −0.0645497 | + | 0.193649i | ||||
\(241\) | 1.00000 | + | 1.00000i | 0.0644157 | + | 0.0644157i | 0.738581 | − | 0.674165i | \(-0.235496\pi\) |
−0.674165 | + | 0.738581i | \(0.735496\pi\) | |||||||
\(242\) | − | 7.00000i | − | 0.449977i | ||||||
\(243\) | 7.00000 | − | 7.00000i | 0.449050 | − | 0.449050i | ||||
\(244\) | 3.00000 | − | 3.00000i | 0.192055 | − | 0.192055i | ||||
\(245\) | 5.00000 | + | 10.0000i | 0.319438 | + | 0.638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | + | 10.0000i | 0.636285 | + | 0.636285i | ||||
\(248\) | 7.00000 | + | 7.00000i | 0.444500 | + | 0.444500i | ||||
\(249\) | 10.0000 | 0.633724 | ||||||||
\(250\) | −11.0000 | − | 2.00000i | −0.695701 | − | 0.126491i | ||||
\(251\) | −5.00000 | + | 5.00000i | −0.315597 | + | 0.315597i | −0.847073 | − | 0.531476i | \(-0.821638\pi\) |
0.531476 | + | 0.847073i | \(0.321638\pi\) | |||||||
\(252\) | −1.00000 | − | 1.00000i | −0.0629941 | − | 0.0629941i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.00000 | + | 3.00000i | 0.188237 | + | 0.188237i | ||||
\(255\) | −4.00000 | + | 12.0000i | −0.250490 | + | 0.751469i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0000 | 0.748539 | 0.374270 | − | 0.927320i | \(-0.377893\pi\) | ||||
0.374270 | + | 0.927320i | \(0.377893\pi\) | |||||||
\(258\) | −4.00000 | + | 4.00000i | −0.249029 | + | 0.249029i | ||||
\(259\) | −5.00000 | + | 7.00000i | −0.310685 | + | 0.434959i | ||||
\(260\) | −2.00000 | − | 4.00000i | −0.124035 | − | 0.248069i | ||||
\(261\) | −3.00000 | + | 3.00000i | −0.185695 | + | 0.185695i | ||||
\(262\) | 13.0000 | + | 13.0000i | 0.803143 | + | 0.803143i | ||||
\(263\) | 11.0000 | − | 11.0000i | 0.678289 | − | 0.678289i | −0.281324 | − | 0.959613i | \(-0.590774\pi\) |
0.959613 | + | 0.281324i | \(0.0907735\pi\) | |||||||
\(264\) | −2.00000 | + | 2.00000i | −0.123091 | + | 0.123091i | ||||
\(265\) | 3.00000 | + | 1.00000i | 0.184289 | + | 0.0614295i | ||||
\(266\) | −10.0000 | −0.613139 | ||||||||
\(267\) | 10.0000 | 0.611990 | ||||||||
\(268\) | 3.00000 | + | 3.00000i | 0.183254 | + | 0.183254i | ||||
\(269\) | 24.0000i | 1.46331i | 0.681677 | + | 0.731653i | \(0.261251\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | −4.00000 | + | 12.0000i | −0.243432 | + | 0.730297i | ||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 7.00000 | + | 7.00000i | 0.422885 | + | 0.422885i | ||||
\(275\) | −8.00000 | − | 6.00000i | −0.482418 | − | 0.361814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.0000i | − | 0.600842i | −0.953807 | − | 0.300421i | \(-0.902873\pi\) | ||
0.953807 | − | 0.300421i | \(-0.0971271\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | 7.00000 | + | 7.00000i | 0.419079 | + | 0.419079i | ||||
\(280\) | 3.00000 | + | 1.00000i | 0.179284 | + | 0.0597614i | ||||
\(281\) | 1.00000 | + | 1.00000i | 0.0596550 | + | 0.0596550i | 0.736305 | − | 0.676650i | \(-0.236569\pi\) |
−0.676650 | + | 0.736305i | \(0.736569\pi\) | |||||||
\(282\) | −14.0000 | −0.833688 | ||||||||
\(283\) | −14.0000 | −0.832214 | −0.416107 | − | 0.909316i | \(-0.636606\pi\) | ||||
−0.416107 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | 10.0000 | + | 20.0000i | 0.592349 | + | 1.18470i | ||||
\(286\) | − | 4.00000i | − | 0.236525i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 3.00000 | − | 9.00000i | 0.176166 | − | 0.528498i | ||||
\(291\) | −8.00000 | + | 8.00000i | −0.468968 | + | 0.468968i | ||||
\(292\) | 9.00000 | − | 9.00000i | 0.526685 | − | 0.526685i | ||||
\(293\) | −19.0000 | − | 19.0000i | −1.10999 | − | 1.10999i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) |
−0.116841 | − | 0.993151i | \(-0.537277\pi\) | |||||||
\(294\) | −5.00000 | + | 5.00000i | −0.291606 | + | 0.291606i | ||||
\(295\) | 1.00000 | − | 3.00000i | 0.0582223 | − | 0.174667i | ||||
\(296\) | −1.00000 | − | 6.00000i | −0.0581238 | − | 0.348743i | ||||
\(297\) | −8.00000 | + | 8.00000i | −0.464207 | + | 0.464207i | ||||
\(298\) | −24.0000 | −1.39028 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | − | 7.00000i | −0.0577350 | − | 0.404145i | ||||
\(301\) | 4.00000 | + | 4.00000i | 0.230556 | + | 0.230556i | ||||
\(302\) | 10.0000 | 0.575435 | ||||||||
\(303\) | −8.00000 | − | 8.00000i | −0.459588 | − | 0.459588i | ||||
\(304\) | 5.00000 | − | 5.00000i | 0.286770 | − | 0.286770i | ||||
\(305\) | −3.00000 | + | 9.00000i | −0.171780 | + | 0.515339i | ||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | −15.0000 | − | 15.0000i | −0.856095 | − | 0.856095i | 0.134780 | − | 0.990876i | \(-0.456967\pi\) |
−0.990876 | + | 0.134780i | \(0.956967\pi\) | |||||||
\(308\) | 2.00000 | + | 2.00000i | 0.113961 | + | 0.113961i | ||||
\(309\) | −14.0000 | + | 14.0000i | −0.796432 | + | 0.796432i | ||||
\(310\) | −21.0000 | − | 7.00000i | −1.19272 | − | 0.397573i | ||||
\(311\) | −17.0000 | + | 17.0000i | −0.963982 | + | 0.963982i | −0.999374 | − | 0.0353919i | \(-0.988732\pi\) |
0.0353919 | + | 0.999374i | \(0.488732\pi\) | |||||||
\(312\) | 2.00000 | − | 2.00000i | 0.113228 | − | 0.113228i | ||||
\(313\) | 34.0000i | 1.92179i | 0.276907 | + | 0.960897i | \(0.410691\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(314\) | −9.00000 | − | 9.00000i | −0.507899 | − | 0.507899i | ||||
\(315\) | 3.00000 | + | 1.00000i | 0.169031 | + | 0.0563436i | ||||
\(316\) | −1.00000 | + | 1.00000i | −0.0562544 | + | 0.0562544i | ||||
\(317\) | 19.0000 | + | 19.0000i | 1.06715 | + | 1.06715i | 0.997577 | + | 0.0695692i | \(0.0221625\pi\) |
0.0695692 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(318\) | 2.00000i | 0.112154i | ||||||||
\(319\) | 6.00000 | − | 6.00000i | 0.335936 | − | 0.335936i | ||||
\(320\) | −2.00000 | + | 1.00000i | −0.111803 | + | 0.0559017i | ||||
\(321\) | − | 22.0000i | − | 1.22792i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.0000 | − | 20.0000i | 1.11283 | − | 1.11283i | ||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 8.00000 | + | 6.00000i | 0.443760 | + | 0.332820i | ||||
\(326\) | − | 2.00000i | − | 0.110770i | ||||||
\(327\) | 14.0000i | 0.774202i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.0000i | 0.771845i | ||||||||
\(330\) | 2.00000 | − | 6.00000i | 0.110096 | − | 0.330289i | ||||
\(331\) | −23.0000 | − | 23.0000i | −1.26419 | − | 1.26419i | −0.949041 | − | 0.315154i | \(-0.897944\pi\) |
−0.315154 | − | 0.949041i | \(-0.602056\pi\) | |||||||
\(332\) | 5.00000 | + | 5.00000i | 0.274411 | + | 0.274411i | ||||
\(333\) | −1.00000 | − | 6.00000i | −0.0547997 | − | 0.328798i | ||||
\(334\) | 22.0000i | 1.20379i | ||||||||
\(335\) | −9.00000 | − | 3.00000i | −0.491723 | − | 0.163908i | ||||
\(336\) | 2.00000i | 0.109109i | ||||||||
\(337\) | −9.00000 | − | 9.00000i | −0.490261 | − | 0.490261i | 0.418127 | − | 0.908388i | \(-0.362687\pi\) |
−0.908388 | + | 0.418127i | \(0.862687\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 12.0000 | − | 12.0000i | 0.651751 | − | 0.651751i | ||||
\(340\) | −8.00000 | + | 4.00000i | −0.433861 | + | 0.216930i | ||||
\(341\) | −14.0000 | − | 14.0000i | −0.758143 | − | 0.758143i | ||||
\(342\) | 5.00000 | − | 5.00000i | 0.270369 | − | 0.270369i | ||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | − | 3.00000i | −0.161281 | − | 0.161281i | ||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | 6.00000 | 0.321634 | ||||||||
\(349\) | 24.0000i | 1.28469i | 0.766415 | + | 0.642345i | \(0.222038\pi\) | ||||
−0.766415 | + | 0.642345i | \(0.777962\pi\) | |||||||
\(350\) | −7.00000 | + | 1.00000i | −0.374166 | + | 0.0534522i | ||||
\(351\) | 8.00000 | − | 8.00000i | 0.427008 | − | 0.427008i | ||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 2.00000 | 0.106299 | ||||||||
\(355\) | −16.0000 | + | 8.00000i | −0.849192 | + | 0.424596i | ||||
\(356\) | 5.00000 | + | 5.00000i | 0.264999 | + | 0.264999i | ||||
\(357\) | 8.00000i | 0.423405i | ||||||||
\(358\) | −9.00000 | + | 9.00000i | −0.475665 | + | 0.475665i | ||||
\(359\) | 22.0000i | 1.16112i | 0.814219 | + | 0.580558i | \(0.197165\pi\) | ||||
−0.814219 | + | 0.580558i | \(0.802835\pi\) | |||||||
\(360\) | −2.00000 | + | 1.00000i | −0.105409 | + | 0.0527046i | ||||
\(361\) | − | 31.0000i | − | 1.63158i | ||||||
\(362\) | 22.0000i | 1.15629i | ||||||||
\(363\) | −7.00000 | + | 7.00000i | −0.367405 | + | 0.367405i | ||||
\(364\) | −2.00000 | − | 2.00000i | −0.104828 | − | 0.104828i | ||||
\(365\) | −9.00000 | + | 27.0000i | −0.471082 | + | 1.41324i | ||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 5.00000 | − | 5.00000i | 0.260998 | − | 0.260998i | −0.564462 | − | 0.825459i | \(-0.690916\pi\) |
0.825459 | + | 0.564462i | \(0.190916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | + | 11.0000i | 0.415900 | + | 0.571863i | ||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | − | 14.0000i | − | 0.725866i | ||||||
\(373\) | 15.0000 | − | 15.0000i | 0.776671 | − | 0.776671i | −0.202593 | − | 0.979263i | \(-0.564937\pi\) |
0.979263 | + | 0.202593i | \(0.0649367\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | 9.00000 | + | 13.0000i | 0.464758 | + | 0.671317i | ||||
\(376\) | −7.00000 | − | 7.00000i | −0.360997 | − | 0.360997i | ||||
\(377\) | −6.00000 | + | 6.00000i | −0.309016 | + | 0.309016i | ||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | − | 30.0000i | − | 1.54100i | −0.637442 | − | 0.770498i | \(-0.720007\pi\) | ||
0.637442 | − | 0.770498i | \(-0.279993\pi\) | |||||||
\(380\) | −5.00000 | + | 15.0000i | −0.256495 | + | 0.769484i | ||||
\(381\) | − | 6.00000i | − | 0.307389i | ||||||
\(382\) | 1.00000 | − | 1.00000i | 0.0511645 | − | 0.0511645i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | −1.00000 | − | 1.00000i | −0.0510310 | − | 0.0510310i | ||||
\(385\) | −6.00000 | − | 2.00000i | −0.305788 | − | 0.101929i | ||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | −8.00000 | −0.406138 | ||||||||
\(389\) | −25.0000 | + | 25.0000i | −1.26755 | + | 1.26755i | −0.320201 | + | 0.947350i | \(0.603750\pi\) |
−0.947350 | + | 0.320201i | \(0.896250\pi\) | |||||||
\(390\) | −2.00000 | + | 6.00000i | −0.101274 | + | 0.303822i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.00000 | −0.252538 | ||||||||
\(393\) | − | 26.0000i | − | 1.31153i | ||||||
\(394\) | −13.0000 | − | 13.0000i | −0.654931 | − | 0.654931i | ||||
\(395\) | 1.00000 | − | 3.00000i | 0.0503155 | − | 0.150946i | ||||
\(396\) | −2.00000 | −0.100504 | ||||||||
\(397\) | 15.0000 | + | 15.0000i | 0.752828 | + | 0.752828i | 0.975006 | − | 0.222178i | \(-0.0713165\pi\) |
−0.222178 | + | 0.975006i | \(0.571317\pi\) | |||||||
\(398\) | 11.0000 | − | 11.0000i | 0.551380 | − | 0.551380i | ||||
\(399\) | 10.0000 | + | 10.0000i | 0.500626 | + | 0.500626i | ||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | −7.00000 | + | 7.00000i | −0.349563 | + | 0.349563i | −0.859947 | − | 0.510384i | \(-0.829503\pi\) |
0.510384 | + | 0.859947i | \(0.329503\pi\) | |||||||
\(402\) | − | 6.00000i | − | 0.299253i | ||||||
\(403\) | 14.0000 | + | 14.0000i | 0.697390 | + | 0.697390i | ||||
\(404\) | − | 8.00000i | − | 0.398015i | ||||||
\(405\) | 10.0000 | − | 5.00000i | 0.496904 | − | 0.248452i | ||||
\(406\) | − | 6.00000i | − | 0.297775i | ||||||
\(407\) | 2.00000 | + | 12.0000i | 0.0991363 | + | 0.594818i | ||||
\(408\) | −4.00000 | − | 4.00000i | −0.198030 | − | 0.198030i | ||||
\(409\) | −13.0000 | − | 13.0000i | −0.642809 | − | 0.642809i | 0.308436 | − | 0.951245i | \(-0.400194\pi\) |
−0.951245 | + | 0.308436i | \(0.900194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 14.0000i | − | 0.690569i | ||||||
\(412\) | −14.0000 | −0.689730 | ||||||||
\(413\) | − | 2.00000i | − | 0.0984136i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | − | 5.00000i | −0.736321 | − | 0.245440i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 4.00000 | − | 4.00000i | 0.195881 | − | 0.195881i | ||||
\(418\) | −10.0000 | + | 10.0000i | −0.489116 | + | 0.489116i | ||||
\(419\) | 26.0000i | 1.27018i | 0.772437 | + | 0.635092i | \(0.219038\pi\) | ||||
−0.772437 | + | 0.635092i | \(0.780962\pi\) | |||||||
\(420\) | −2.00000 | − | 4.00000i | −0.0975900 | − | 0.195180i | ||||
\(421\) | 9.00000 | − | 9.00000i | 0.438633 | − | 0.438633i | −0.452919 | − | 0.891552i | \(-0.649617\pi\) |
0.891552 | + | 0.452919i | \(0.149617\pi\) | |||||||
\(422\) | − | 4.00000i | − | 0.194717i | ||||||
\(423\) | −7.00000 | − | 7.00000i | −0.340352 | − | 0.340352i | ||||
\(424\) | −1.00000 | + | 1.00000i | −0.0485643 | + | 0.0485643i | ||||
\(425\) | 12.0000 | − | 16.0000i | 0.582086 | − | 0.776114i | ||||
\(426\) | −8.00000 | − | 8.00000i | −0.387601 | − | 0.387601i | ||||
\(427\) | 6.00000i | 0.290360i | ||||||||
\(428\) | 11.0000 | − | 11.0000i | 0.531705 | − | 0.531705i | ||||
\(429\) | −4.00000 | + | 4.00000i | −0.193122 | + | 0.193122i | ||||
\(430\) | 8.00000 | − | 4.00000i | 0.385794 | − | 0.192897i | ||||
\(431\) | −1.00000 | + | 1.00000i | −0.0481683 | + | 0.0481683i | −0.730781 | − | 0.682612i | \(-0.760844\pi\) |
0.682612 | + | 0.730781i | \(0.260844\pi\) | |||||||
\(432\) | −4.00000 | − | 4.00000i | −0.192450 | − | 0.192450i | ||||
\(433\) | −11.0000 | − | 11.0000i | −0.528626 | − | 0.528626i | 0.391536 | − | 0.920163i | \(-0.371944\pi\) |
−0.920163 | + | 0.391536i | \(0.871944\pi\) | |||||||
\(434\) | −14.0000 | −0.672022 | ||||||||
\(435\) | −12.0000 | + | 6.00000i | −0.575356 | + | 0.287678i | ||||
\(436\) | −7.00000 | + | 7.00000i | −0.335239 | + | 0.335239i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −18.0000 | −0.860073 | ||||||||
\(439\) | 27.0000 | + | 27.0000i | 1.28864 | + | 1.28864i | 0.935613 | + | 0.353026i | \(0.114847\pi\) |
0.353026 | + | 0.935613i | \(0.385153\pi\) | |||||||
\(440\) | 4.00000 | − | 2.00000i | 0.190693 | − | 0.0953463i | ||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 8.00000 | 0.380521 | ||||||||
\(443\) | −21.0000 | + | 21.0000i | −0.997740 | + | 0.997740i | −0.999997 | − | 0.00225734i | \(-0.999281\pi\) |
0.00225734 | + | 0.999997i | \(0.499281\pi\) | |||||||
\(444\) | −5.00000 | + | 7.00000i | −0.237289 | + | 0.332205i | ||||
\(445\) | −15.0000 | − | 5.00000i | −0.711068 | − | 0.237023i | ||||
\(446\) | 3.00000 | − | 3.00000i | 0.142054 | − | 0.142054i | ||||
\(447\) | 24.0000 | + | 24.0000i | 1.13516 | + | 1.13516i | ||||
\(448\) | −1.00000 | + | 1.00000i | −0.0472456 | + | 0.0472456i | ||||
\(449\) | 11.0000 | − | 11.0000i | 0.519122 | − | 0.519122i | −0.398184 | − | 0.917306i | \(-0.630359\pi\) |
0.917306 | + | 0.398184i | \(0.130359\pi\) | |||||||
\(450\) | 3.00000 | − | 4.00000i | 0.141421 | − | 0.188562i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.0000 | 0.564433 | ||||||||
\(453\) | −10.0000 | − | 10.0000i | −0.469841 | − | 0.469841i | ||||
\(454\) | − | 6.00000i | − | 0.281594i | ||||||
\(455\) | 6.00000 | + | 2.00000i | 0.281284 | + | 0.0937614i | ||||
\(456\) | −10.0000 | −0.468293 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | −16.0000 | − | 16.0000i | −0.746816 | − | 0.746816i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.00000 | + | 1.00000i | 0.0465746 | + | 0.0465746i | 0.730011 | − | 0.683436i | \(-0.239515\pi\) |
−0.683436 | + | 0.730011i | \(0.739515\pi\) | |||||||
\(462\) | − | 4.00000i | − | 0.186097i | ||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 3.00000 | + | 3.00000i | 0.139272 | + | 0.139272i | ||||
\(465\) | 14.0000 | + | 28.0000i | 0.649234 | + | 1.29847i | ||||
\(466\) | −7.00000 | − | 7.00000i | −0.324269 | − | 0.324269i | ||||
\(467\) | 14.0000 | 0.647843 | 0.323921 | − | 0.946084i | \(-0.394999\pi\) | ||||
0.323921 | + | 0.946084i | \(0.394999\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | 21.0000 | + | 7.00000i | 0.968658 | + | 0.322886i | ||||
\(471\) | 18.0000i | 0.829396i | ||||||||
\(472\) | 1.00000 | + | 1.00000i | 0.0460287 | + | 0.0460287i | ||||
\(473\) | 8.00000 | 0.367840 | ||||||||
\(474\) | 2.00000 | 0.0918630 | ||||||||
\(475\) | −5.00000 | − | 35.0000i | −0.229416 | − | 1.60591i | ||||
\(476\) | −4.00000 | + | 4.00000i | −0.183340 | + | 0.183340i | ||||
\(477\) | −1.00000 | + | 1.00000i | −0.0457869 | + | 0.0457869i | ||||
\(478\) | 3.00000 | + | 3.00000i | 0.137217 | + | 0.137217i | ||||
\(479\) | 13.0000 | − | 13.0000i | 0.593985 | − | 0.593985i | −0.344720 | − | 0.938705i | \(-0.612026\pi\) |
0.938705 | + | 0.344720i | \(0.112026\pi\) | |||||||
\(480\) | 3.00000 | + | 1.00000i | 0.136931 | + | 0.0456435i | ||||
\(481\) | −2.00000 | − | 12.0000i | −0.0911922 | − | 0.547153i | ||||
\(482\) | 1.00000 | − | 1.00000i | 0.0455488 | − | 0.0455488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 16.0000 | − | 8.00000i | 0.726523 | − | 0.363261i | ||||
\(486\) | −7.00000 | − | 7.00000i | −0.317526 | − | 0.317526i | ||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | −3.00000 | − | 3.00000i | −0.135804 | − | 0.135804i | ||||
\(489\) | −2.00000 | + | 2.00000i | −0.0904431 | + | 0.0904431i | ||||
\(490\) | 10.0000 | − | 5.00000i | 0.451754 | − | 0.225877i | ||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | + | 12.0000i | 0.540453 | + | 0.540453i | ||||
\(494\) | 10.0000 | − | 10.0000i | 0.449921 | − | 0.449921i | ||||
\(495\) | 4.00000 | − | 2.00000i | 0.179787 | − | 0.0898933i | ||||
\(496\) | 7.00000 | − | 7.00000i | 0.314309 | − | 0.314309i | ||||
\(497\) | −8.00000 | + | 8.00000i | −0.358849 | + | 0.358849i | ||||
\(498\) | − | 10.0000i | − | 0.448111i | ||||||
\(499\) | −13.0000 | − | 13.0000i | −0.581960 | − | 0.581960i | 0.353482 | − | 0.935441i | \(-0.384998\pi\) |
−0.935441 | + | 0.353482i | \(0.884998\pi\) | |||||||
\(500\) | −2.00000 | + | 11.0000i | −0.0894427 | + | 0.491935i | ||||
\(501\) | 22.0000 | − | 22.0000i | 0.982888 | − | 0.982888i | ||||
\(502\) | 5.00000 | + | 5.00000i | 0.223161 | + | 0.223161i | ||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | −1.00000 | + | 1.00000i | −0.0445435 | + | 0.0445435i | ||||
\(505\) | 8.00000 | + | 16.0000i | 0.355995 | + | 0.711991i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | + | 9.00000i | −0.399704 | + | 0.399704i | ||||
\(508\) | 3.00000 | − | 3.00000i | 0.133103 | − | 0.133103i | ||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 12.0000 | + | 4.00000i | 0.531369 | + | 0.177123i | ||||
\(511\) | 18.0000i | 0.796273i | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −40.0000 | −1.76604 | ||||||||
\(514\) | − | 12.0000i | − | 0.529297i | ||||||
\(515\) | 28.0000 | − | 14.0000i | 1.23383 | − | 0.616914i | ||||
\(516\) | 4.00000 | + | 4.00000i | 0.176090 | + | 0.176090i | ||||
\(517\) | 14.0000 | + | 14.0000i | 0.615719 | + | 0.615719i | ||||
\(518\) | 7.00000 | + | 5.00000i | 0.307562 | + | 0.219687i | ||||
\(519\) | 6.00000i | 0.263371i | ||||||||
\(520\) | −4.00000 | + | 2.00000i | −0.175412 | + | 0.0877058i | ||||
\(521\) | − | 12.0000i | − | 0.525730i | −0.964833 | − | 0.262865i | \(-0.915333\pi\) | ||
0.964833 | − | 0.262865i | \(-0.0846673\pi\) | |||||||
\(522\) | 3.00000 | + | 3.00000i | 0.131306 | + | 0.131306i | ||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | 13.0000 | − | 13.0000i | 0.567908 | − | 0.567908i | ||||
\(525\) | 8.00000 | + | 6.00000i | 0.349149 | + | 0.261861i | ||||
\(526\) | −11.0000 | − | 11.0000i | −0.479623 | − | 0.479623i | ||||
\(527\) | 28.0000 | − | 28.0000i | 1.21970 | − | 1.21970i | ||||
\(528\) | 2.00000 | + | 2.00000i | 0.0870388 | + | 0.0870388i | ||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 1.00000 | − | 3.00000i | 0.0434372 | − | 0.130312i | ||||
\(531\) | 1.00000 | + | 1.00000i | 0.0433963 | + | 0.0433963i | ||||
\(532\) | 10.0000i | 0.433555i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 10.0000i | − | 0.432742i | ||||||
\(535\) | −11.0000 | + | 33.0000i | −0.475571 | + | 1.42671i | ||||
\(536\) | 3.00000 | − | 3.00000i | 0.129580 | − | 0.129580i | ||||
\(537\) | 18.0000 | 0.776757 | ||||||||
\(538\) | 24.0000 | 1.03471 | ||||||||
\(539\) | 10.0000 | 0.430730 | ||||||||
\(540\) | 12.0000 | + | 4.00000i | 0.516398 | + | 0.172133i | ||||
\(541\) | −3.00000 | − | 3.00000i | −0.128980 | − | 0.128980i | 0.639670 | − | 0.768650i | \(-0.279071\pi\) |
−0.768650 | + | 0.639670i | \(0.779071\pi\) | |||||||
\(542\) | − | 8.00000i | − | 0.343629i | ||||||
\(543\) | 22.0000 | − | 22.0000i | 0.944110 | − | 0.944110i | ||||
\(544\) | − | 4.00000i | − | 0.171499i | ||||||
\(545\) | 7.00000 | − | 21.0000i | 0.299847 | − | 0.899541i | ||||
\(546\) | 4.00000i | 0.171184i | ||||||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | 7.00000 | − | 7.00000i | 0.299025 | − | 0.299025i | ||||
\(549\) | −3.00000 | − | 3.00000i | −0.128037 | − | 0.128037i | ||||
\(550\) | −6.00000 | + | 8.00000i | −0.255841 | + | 0.341121i | ||||
\(551\) | 30.0000 | 1.27804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | 3.00000 | − | 19.0000i | 0.127343 | − | 0.806505i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | 7.00000 | − | 7.00000i | 0.296334 | − | 0.296334i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 1.00000 | − | 3.00000i | 0.0422577 | − | 0.126773i | ||||
\(561\) | 8.00000 | + | 8.00000i | 0.337760 | + | 0.337760i | ||||
\(562\) | 1.00000 | − | 1.00000i | 0.0421825 | − | 0.0421825i | ||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | 14.0000i | 0.589506i | ||||||||
\(565\) | −24.0000 | + | 12.0000i | −1.00969 | + | 0.504844i | ||||
\(566\) | 14.0000i | 0.588464i | ||||||||
\(567\) | 5.00000 | − | 5.00000i | 0.209980 | − | 0.209980i | ||||
\(568\) | − | 8.00000i | − | 0.335673i | ||||||
\(569\) | 7.00000 | + | 7.00000i | 0.293455 | + | 0.293455i | 0.838444 | − | 0.544988i | \(-0.183466\pi\) |
−0.544988 | + | 0.838444i | \(0.683466\pi\) | |||||||
\(570\) | 20.0000 | − | 10.0000i | 0.837708 | − | 0.418854i | ||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | −2.00000 | −0.0835512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 12.0000 | 0.499567 | 0.249783 | − | 0.968302i | \(-0.419641\pi\) | ||||
0.249783 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(578\) | 1.00000i | 0.0415945i | ||||||||
\(579\) | −18.0000 | − | 18.0000i | −0.748054 | − | 0.748054i | ||||
\(580\) | −9.00000 | − | 3.00000i | −0.373705 | − | 0.124568i | ||||
\(581\) | −10.0000 | −0.414870 | ||||||||
\(582\) | 8.00000 | + | 8.00000i | 0.331611 | + | 0.331611i | ||||
\(583\) | 2.00000 | − | 2.00000i | 0.0828315 | − | 0.0828315i | ||||
\(584\) | −9.00000 | − | 9.00000i | −0.372423 | − | 0.372423i | ||||
\(585\) | −4.00000 | + | 2.00000i | −0.165380 | + | 0.0826898i | ||||
\(586\) | −19.0000 | + | 19.0000i | −0.784883 | + | 0.784883i | ||||
\(587\) | − | 36.0000i | − | 1.48588i | −0.669359 | − | 0.742940i | \(-0.733431\pi\) | ||
0.669359 | − | 0.742940i | \(-0.266569\pi\) | |||||||
\(588\) | 5.00000 | + | 5.00000i | 0.206197 | + | 0.206197i | ||||
\(589\) | − | 70.0000i | − | 2.88430i | ||||||
\(590\) | −3.00000 | − | 1.00000i | −0.123508 | − | 0.0411693i | ||||
\(591\) | 26.0000i | 1.06950i | ||||||||
\(592\) | −6.00000 | + | 1.00000i | −0.246598 | + | 0.0410997i | ||||
\(593\) | 29.0000 | + | 29.0000i | 1.19089 | + | 1.19089i | 0.976819 | + | 0.214069i | \(0.0686716\pi\) |
0.214069 | + | 0.976819i | \(0.431328\pi\) | |||||||
\(594\) | 8.00000 | + | 8.00000i | 0.328244 | + | 0.328244i | ||||
\(595\) | 4.00000 | − | 12.0000i | 0.163984 | − | 0.491952i | ||||
\(596\) | 24.0000i | 0.983078i | ||||||||
\(597\) | −22.0000 | −0.900400 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0000i | 0.572024i | 0.958226 | + | 0.286012i | \(0.0923298\pi\) | ||||
−0.958226 | + | 0.286012i | \(0.907670\pi\) | |||||||
\(600\) | −7.00000 | + | 1.00000i | −0.285774 | + | 0.0408248i | ||||
\(601\) | −42.0000 | −1.71322 | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(602\) | 4.00000 | − | 4.00000i | 0.163028 | − | 0.163028i | ||||
\(603\) | 3.00000 | − | 3.00000i | 0.122169 | − | 0.122169i | ||||
\(604\) | − | 10.0000i | − | 0.406894i | ||||||
\(605\) | 14.0000 | − | 7.00000i | 0.569181 | − | 0.284590i | ||||
\(606\) | −8.00000 | + | 8.00000i | −0.324978 | + | 0.324978i | ||||
\(607\) | − | 40.0000i | − | 1.62355i | −0.583970 | − | 0.811775i | \(-0.698502\pi\) | ||
0.583970 | − | 0.811775i | \(-0.301498\pi\) | |||||||
\(608\) | −5.00000 | − | 5.00000i | −0.202777 | − | 0.202777i | ||||
\(609\) | −6.00000 | + | 6.00000i | −0.243132 | + | 0.243132i | ||||
\(610\) | 9.00000 | + | 3.00000i | 0.364399 | + | 0.121466i | ||||
\(611\) | −14.0000 | − | 14.0000i | −0.566379 | − | 0.566379i | ||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | −17.0000 | + | 17.0000i | −0.686624 | + | 0.686624i | −0.961484 | − | 0.274861i | \(-0.911368\pi\) |
0.274861 | + | 0.961484i | \(0.411368\pi\) | |||||||
\(614\) | −15.0000 | + | 15.0000i | −0.605351 | + | 0.605351i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 2.00000i | 0.0805823 | − | 0.0805823i | ||||
\(617\) | 15.0000 | + | 15.0000i | 0.603877 | + | 0.603877i | 0.941339 | − | 0.337462i | \(-0.109568\pi\) |
−0.337462 | + | 0.941339i | \(0.609568\pi\) | |||||||
\(618\) | 14.0000 | + | 14.0000i | 0.563163 | + | 0.563163i | ||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | −7.00000 | + | 21.0000i | −0.281127 | + | 0.843380i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.0000 | + | 17.0000i | 0.681638 | + | 0.681638i | ||||
\(623\) | −10.0000 | −0.400642 | ||||||||
\(624\) | −2.00000 | − | 2.00000i | −0.0800641 | − | 0.0800641i | ||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 34.0000 | 1.35891 | ||||||||
\(627\) | 20.0000 | 0.798723 | ||||||||
\(628\) | −9.00000 | + | 9.00000i | −0.359139 | + | 0.359139i | ||||
\(629\) | −24.0000 | + | 4.00000i | −0.956943 | + | 0.159490i | ||||
\(630\) | 1.00000 | − | 3.00000i | 0.0398410 | − | 0.119523i | ||||
\(631\) | 19.0000 | − | 19.0000i | 0.756378 | − | 0.756378i | −0.219283 | − | 0.975661i | \(-0.570372\pi\) |
0.975661 | + | 0.219283i | \(0.0703719\pi\) | |||||||
\(632\) | 1.00000 | + | 1.00000i | 0.0397779 | + | 0.0397779i | ||||
\(633\) | −4.00000 | + | 4.00000i | −0.158986 | + | 0.158986i | ||||
\(634\) | 19.0000 | − | 19.0000i | 0.754586 | − | 0.754586i | ||||
\(635\) | −3.00000 | + | 9.00000i | −0.119051 | + | 0.357154i | ||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | −10.0000 | −0.396214 | ||||||||
\(638\) | −6.00000 | − | 6.00000i | −0.237542 | − | 0.237542i | ||||
\(639\) | − | 8.00000i | − | 0.316475i | ||||||
\(640\) | 1.00000 | + | 2.00000i | 0.0395285 | + | 0.0790569i | ||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | −22.0000 | −0.868271 | ||||||||
\(643\) | −14.0000 | −0.552106 | −0.276053 | − | 0.961142i | \(-0.589027\pi\) | ||||
−0.276053 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | − | 4.00000i | −0.472500 | − | 0.157500i | ||||
\(646\) | −20.0000 | − | 20.0000i | −0.786889 | − | 0.786889i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 5.00000i | 0.196419i | ||||||||
\(649\) | −2.00000 | − | 2.00000i | −0.0785069 | − | 0.0785069i | ||||
\(650\) | 6.00000 | − | 8.00000i | 0.235339 | − | 0.313786i | ||||
\(651\) | 14.0000 | + | 14.0000i | 0.548703 | + | 0.548703i | ||||
\(652\) | −2.00000 | −0.0783260 | ||||||||
\(653\) | −12.0000 | −0.469596 | −0.234798 | − | 0.972044i | \(-0.575443\pi\) | ||||
−0.234798 | + | 0.972044i | \(0.575443\pi\) | |||||||
\(654\) | 14.0000 | 0.547443 | ||||||||
\(655\) | −13.0000 | + | 39.0000i | −0.507952 | + | 1.52386i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.00000 | − | 9.00000i | −0.351123 | − | 0.351123i | ||||
\(658\) | 14.0000 | 0.545777 | ||||||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | −6.00000 | − | 2.00000i | −0.233550 | − | 0.0778499i | ||||
\(661\) | 21.0000 | − | 21.0000i | 0.816805 | − | 0.816805i | −0.168838 | − | 0.985644i | \(-0.554002\pi\) |
0.985644 | + | 0.168838i | \(0.0540016\pi\) | |||||||
\(662\) | −23.0000 | + | 23.0000i | −0.893920 | + | 0.893920i | ||||
\(663\) | −8.00000 | − | 8.00000i | −0.310694 | − | 0.310694i | ||||
\(664\) | 5.00000 | − | 5.00000i | 0.194038 | − | 0.194038i | ||||
\(665\) | −10.0000 | − | 20.0000i | −0.387783 | − | 0.775567i | ||||
\(666\) | −6.00000 | + | 1.00000i | −0.232495 | + | 0.0387492i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 22.0000 | 0.851206 | ||||||||
\(669\) | −6.00000 | −0.231973 | ||||||||
\(670\) | −3.00000 | + | 9.00000i | −0.115900 | + | 0.347700i | ||||
\(671\) | 6.00000 | + | 6.00000i | 0.231627 | + | 0.231627i | ||||
\(672\) | 2.00000 | 0.0771517 | ||||||||
\(673\) | −23.0000 | − | 23.0000i | −0.886585 | − | 0.886585i | 0.107609 | − | 0.994193i | \(-0.465681\pi\) |
−0.994193 | + | 0.107609i | \(0.965681\pi\) | |||||||
\(674\) | −9.00000 | + | 9.00000i | −0.346667 | + | 0.346667i | ||||
\(675\) | −28.0000 | + | 4.00000i | −1.07772 | + | 0.153960i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −13.0000 | − | 13.0000i | −0.499631 | − | 0.499631i | 0.411692 | − | 0.911323i | \(-0.364938\pi\) |
−0.911323 | + | 0.411692i | \(0.864938\pi\) | |||||||
\(678\) | −12.0000 | − | 12.0000i | −0.460857 | − | 0.460857i | ||||
\(679\) | 8.00000 | − | 8.00000i | 0.307012 | − | 0.307012i | ||||
\(680\) | 4.00000 | + | 8.00000i | 0.153393 | + | 0.306786i | ||||
\(681\) | −6.00000 | + | 6.00000i | −0.229920 | + | 0.229920i | ||||
\(682\) | −14.0000 | + | 14.0000i | −0.536088 | + | 0.536088i | ||||
\(683\) | − | 36.0000i | − | 1.37750i | −0.724998 | − | 0.688751i | \(-0.758159\pi\) | ||
0.724998 | − | 0.688751i | \(-0.241841\pi\) | |||||||
\(684\) | −5.00000 | − | 5.00000i | −0.191180 | − | 0.191180i | ||||
\(685\) | −7.00000 | + | 21.0000i | −0.267456 | + | 0.802369i | ||||
\(686\) | 12.0000 | − | 12.0000i | 0.458162 | − | 0.458162i | ||||
\(687\) | 12.0000 | + | 12.0000i | 0.457829 | + | 0.457829i | ||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | −2.00000 | + | 2.00000i | −0.0761939 | + | 0.0761939i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.0000i | 1.74992i | 0.484193 | + | 0.874961i | \(0.339113\pi\) | ||||
−0.484193 | + | 0.874961i | \(0.660887\pi\) | |||||||
\(692\) | −3.00000 | + | 3.00000i | −0.114043 | + | 0.114043i | ||||
\(693\) | 2.00000 | − | 2.00000i | 0.0759737 | − | 0.0759737i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −8.00000 | + | 4.00000i | −0.303457 | + | 0.151729i | ||||
\(696\) | − | 6.00000i | − | 0.227429i | ||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 24.0000 | 0.908413 | ||||||||
\(699\) | 14.0000i | 0.529529i | ||||||||
\(700\) | 1.00000 | + | 7.00000i | 0.0377964 | + | 0.264575i | ||||
\(701\) | −19.0000 | − | 19.0000i | −0.717620 | − | 0.717620i | 0.250497 | − | 0.968117i | \(-0.419406\pi\) |
−0.968117 | + | 0.250497i | \(0.919406\pi\) | |||||||
\(702\) | −8.00000 | − | 8.00000i | −0.301941 | − | 0.301941i | ||||
\(703\) | −25.0000 | + | 35.0000i | −0.942893 | + | 1.32005i | ||||
\(704\) | 2.00000i | 0.0753778i | ||||||||
\(705\) | −14.0000 | − | 28.0000i | −0.527271 | − | 1.05454i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.00000 | + | 8.00000i | 0.300871 | + | 0.300871i | ||||
\(708\) | − | 2.00000i | − | 0.0751646i | ||||||
\(709\) | 27.0000 | − | 27.0000i | 1.01401 | − | 1.01401i | 0.0141058 | − | 0.999901i | \(-0.495510\pi\) |
0.999901 | − | 0.0141058i | \(-0.00449016\pi\) | |||||||
\(710\) | 8.00000 | + | 16.0000i | 0.300235 | + | 0.600469i | ||||
\(711\) | 1.00000 | + | 1.00000i | 0.0375029 | + | 0.0375029i | ||||
\(712\) | 5.00000 | − | 5.00000i | 0.187383 | − | 0.187383i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | 8.00000 | − | 4.00000i | 0.299183 | − | 0.149592i | ||||
\(716\) | 9.00000 | + | 9.00000i | 0.336346 | + | 0.336346i | ||||
\(717\) | − | 6.00000i | − | 0.224074i | ||||||
\(718\) | 22.0000 | 0.821033 | ||||||||
\(719\) | 46.0000i | 1.71551i | 0.514058 | + | 0.857755i | \(0.328142\pi\) | ||||
−0.514058 | + | 0.857755i | \(0.671858\pi\) | |||||||
\(720\) | 1.00000 | + | 2.00000i | 0.0372678 | + | 0.0745356i | ||||
\(721\) | 14.0000 | − | 14.0000i | 0.521387 | − | 0.521387i | ||||
\(722\) | −31.0000 | −1.15370 | ||||||||
\(723\) | −2.00000 | −0.0743808 | ||||||||
\(724\) | 22.0000 | 0.817624 | ||||||||
\(725\) | 21.0000 | − | 3.00000i | 0.779920 | − | 0.111417i | ||||
\(726\) | 7.00000 | + | 7.00000i | 0.259794 | + | 0.259794i | ||||
\(727\) | 24.0000i | 0.890111i | 0.895503 | + | 0.445055i | \(0.146816\pi\) | ||||
−0.895503 | + | 0.445055i | \(0.853184\pi\) | |||||||
\(728\) | −2.00000 | + | 2.00000i | −0.0741249 | + | 0.0741249i | ||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 27.0000 | + | 9.00000i | 0.999315 | + | 0.333105i | ||||
\(731\) | 16.0000i | 0.591781i | ||||||||
\(732\) | 6.00000i | 0.221766i | ||||||||
\(733\) | 23.0000 | − | 23.0000i | 0.849524 | − | 0.849524i | −0.140549 | − | 0.990074i | \(-0.544887\pi\) |
0.990074 | + | 0.140549i | \(0.0448868\pi\) | |||||||
\(734\) | −5.00000 | − | 5.00000i | −0.184553 | − | 0.184553i | ||||
\(735\) | −15.0000 | − | 5.00000i | −0.553283 | − | 0.184428i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.00000 | + | 6.00000i | −0.221013 | + | 0.221013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 11.0000 | − | 8.00000i | 0.404368 | − | 0.294086i | ||||
\(741\) | −20.0000 | −0.734718 | ||||||||
\(742\) | − | 2.00000i | − | 0.0734223i | ||||||
\(743\) | 23.0000 | − | 23.0000i | 0.843788 | − | 0.843788i | −0.145561 | − | 0.989349i | \(-0.546499\pi\) |
0.989349 | + | 0.145561i | \(0.0464987\pi\) | |||||||
\(744\) | −14.0000 | −0.513265 | ||||||||
\(745\) | −24.0000 | − | 48.0000i | −0.879292 | − | 1.75858i | ||||
\(746\) | −15.0000 | − | 15.0000i | −0.549189 | − | 0.549189i | ||||
\(747\) | 5.00000 | − | 5.00000i | 0.182940 | − | 0.182940i | ||||
\(748\) | 8.00000i | 0.292509i | ||||||||
\(749\) | 22.0000i | 0.803863i | ||||||||
\(750\) | 13.0000 | − | 9.00000i | 0.474693 | − | 0.328634i | ||||
\(751\) | 2.00000i | 0.0729810i | 0.999334 | + | 0.0364905i | \(0.0116179\pi\) | ||||
−0.999334 | + | 0.0364905i | \(0.988382\pi\) | |||||||
\(752\) | −7.00000 | + | 7.00000i | −0.255264 | + | 0.255264i | ||||
\(753\) | − | 10.0000i | − | 0.364420i | ||||||
\(754\) | 6.00000 | + | 6.00000i | 0.218507 | + | 0.218507i | ||||
\(755\) | 10.0000 | + | 20.0000i | 0.363937 | + | 0.727875i | ||||
\(756\) | 8.00000 | 0.290957 | ||||||||
\(757\) | −28.0000 | −1.01768 | −0.508839 | − | 0.860862i | \(-0.669925\pi\) | ||||
−0.508839 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(758\) | −30.0000 | −1.08965 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.0000 | + | 5.00000i | 0.544107 | + | 0.181369i | ||||
\(761\) | − | 8.00000i | − | 0.290000i | −0.989432 | − | 0.145000i | \(-0.953682\pi\) | ||
0.989432 | − | 0.145000i | \(-0.0463182\pi\) | |||||||
\(762\) | −6.00000 | −0.217357 | ||||||||
\(763\) | − | 14.0000i | − | 0.506834i | ||||||
\(764\) | −1.00000 | − | 1.00000i | −0.0361787 | − | 0.0361787i | ||||
\(765\) | 4.00000 | + | 8.00000i | 0.144620 | + | 0.289241i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00000 | + | 2.00000i | 0.0722158 | + | 0.0722158i | ||||
\(768\) | −1.00000 | + | 1.00000i | −0.0360844 | + | 0.0360844i | ||||
\(769\) | 39.0000 | + | 39.0000i | 1.40638 | + | 1.40638i | 0.777529 | + | 0.628846i | \(0.216473\pi\) |
0.628846 | + | 0.777529i | \(0.283527\pi\) | |||||||
\(770\) | −2.00000 | + | 6.00000i | −0.0720750 | + | 0.216225i | ||||
\(771\) | −12.0000 | + | 12.0000i | −0.432169 | + | 0.432169i | ||||
\(772\) | − | 18.0000i | − | 0.647834i | ||||||
\(773\) | 25.0000 | + | 25.0000i | 0.899188 | + | 0.899188i | 0.995364 | − | 0.0961768i | \(-0.0306614\pi\) |
−0.0961768 | + | 0.995364i | \(0.530661\pi\) | |||||||
\(774\) | 4.00000i | 0.143777i | ||||||||
\(775\) | −7.00000 | − | 49.0000i | −0.251447 | − | 1.76013i | ||||
\(776\) | 8.00000i | 0.287183i | ||||||||
\(777\) | −2.00000 | − | 12.0000i | −0.0717496 | − | 0.430498i | ||||
\(778\) | 25.0000 | + | 25.0000i | 0.896293 | + | 0.896293i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 6.00000 | + | 2.00000i | 0.214834 | + | 0.0716115i | ||||
\(781\) | 16.0000i | 0.572525i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 24.0000i | − | 0.857690i | ||||||
\(784\) | 5.00000i | 0.178571i | ||||||||
\(785\) | 9.00000 | − | 27.0000i | 0.321224 | − | 0.963671i | ||||
\(786\) | −26.0000 | −0.927389 | ||||||||
\(787\) | 13.0000 | − | 13.0000i | 0.463400 | − | 0.463400i | −0.436368 | − | 0.899768i | \(-0.643735\pi\) |
0.899768 | + | 0.436368i | \(0.143735\pi\) | |||||||
\(788\) | −13.0000 | + | 13.0000i | −0.463106 | + | 0.463106i | ||||
\(789\) | 22.0000i | 0.783221i | ||||||||
\(790\) | −3.00000 | − | 1.00000i | −0.106735 | − | 0.0355784i | ||||
\(791\) | −12.0000 | + | 12.0000i | −0.426671 | + | 0.426671i | ||||
\(792\) | 2.00000i | 0.0710669i | ||||||||
\(793\) | −6.00000 | − | 6.00000i | −0.213066 | − | 0.213066i | ||||
\(794\) | 15.0000 | − | 15.0000i | 0.532330 | − | 0.532330i | ||||
\(795\) | −4.00000 | + | 2.00000i | −0.141865 | + | 0.0709327i | ||||
\(796\) | −11.0000 | − | 11.0000i | −0.389885 | − | 0.389885i | ||||
\(797\) | − | 2.00000i | − | 0.0708436i | −0.999372 | − | 0.0354218i | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | 10.0000 | − | 10.0000i | 0.353996 | − | 0.353996i | ||||
\(799\) | −28.0000 | + | 28.0000i | −0.990569 | + | 0.990569i | ||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | 5.00000 | − | 5.00000i | 0.176666 | − | 0.176666i | ||||
\(802\) | 7.00000 | + | 7.00000i | 0.247179 | + | 0.247179i | ||||
\(803\) | 18.0000 | + | 18.0000i | 0.635206 | + | 0.635206i | ||||
\(804\) | −6.00000 | −0.211604 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.0000 | − | 14.0000i | 0.493129 | − | 0.493129i | ||||
\(807\) | −24.0000 | − | 24.0000i | −0.844840 | − | 0.844840i | ||||
\(808\) | −8.00000 | −0.281439 | ||||||||
\(809\) | −33.0000 | − | 33.0000i | −1.16022 | − | 1.16022i | −0.984428 | − | 0.175791i | \(-0.943752\pi\) |
−0.175791 | − | 0.984428i | \(-0.556248\pi\) | |||||||
\(810\) | −5.00000 | − | 10.0000i | −0.175682 | − | 0.351364i | ||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | −6.00000 | −0.210559 | ||||||||
\(813\) | −8.00000 | + | 8.00000i | −0.280572 | + | 0.280572i | ||||
\(814\) | 12.0000 | − | 2.00000i | 0.420600 | − | 0.0701000i | ||||
\(815\) | 4.00000 | − | 2.00000i | 0.140114 | − | 0.0700569i | ||||
\(816\) | −4.00000 | + | 4.00000i | −0.140028 | + | 0.140028i | ||||
\(817\) | 20.0000 | + | 20.0000i | 0.699711 | + | 0.699711i | ||||
\(818\) | −13.0000 | + | 13.0000i | −0.454534 | + | 0.454534i | ||||
\(819\) | −2.00000 | + | 2.00000i | −0.0698857 | + | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | −14.0000 | −0.488306 | ||||||||
\(823\) | 31.0000 | + | 31.0000i | 1.08059 | + | 1.08059i | 0.996454 | + | 0.0841380i | \(0.0268136\pi\) |
0.0841380 | + | 0.996454i | \(0.473186\pi\) | |||||||
\(824\) | 14.0000i | 0.487713i | ||||||||
\(825\) | 14.0000 | − | 2.00000i | 0.487417 | − | 0.0696311i | ||||
\(826\) | −2.00000 | −0.0695889 | ||||||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.0000 | + | 15.0000i | 0.520972 | + | 0.520972i | 0.917865 | − | 0.396893i | \(-0.129912\pi\) |
−0.396893 | + | 0.917865i | \(0.629912\pi\) | |||||||
\(830\) | −5.00000 | + | 15.0000i | −0.173553 | + | 0.520658i | ||||
\(831\) | 10.0000 | + | 10.0000i | 0.346896 | + | 0.346896i | ||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | 20.0000i | 0.692959i | ||||||||
\(834\) | −4.00000 | − | 4.00000i | −0.138509 | − | 0.138509i | ||||
\(835\) | −44.0000 | + | 22.0000i | −1.52268 | + | 0.761341i | ||||
\(836\) | 10.0000 | + | 10.0000i | 0.345857 | + | 0.345857i | ||||
\(837\) | −56.0000 | −1.93564 | ||||||||
\(838\) | 26.0000 | 0.898155 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | −4.00000 | + | 2.00000i | −0.138013 | + | 0.0690066i | ||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | −9.00000 | − | 9.00000i | −0.310160 | − | 0.310160i | ||||
\(843\) | −2.00000 | −0.0688837 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 18.0000 | − | 9.00000i | 0.619219 | − | 0.309609i | ||||
\(846\) | −7.00000 | + | 7.00000i | −0.240665 | + | 0.240665i | ||||
\(847\) | 7.00000 | − | 7.00000i | 0.240523 | − | 0.240523i | ||||
\(848\) | 1.00000 | + | 1.00000i | 0.0343401 | + | 0.0343401i | ||||
\(849\) | 14.0000 | − | 14.0000i | 0.480479 | − | 0.480479i | ||||
\(850\) | −16.0000 | − | 12.0000i | −0.548795 | − | 0.411597i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −8.00000 | + | 8.00000i | −0.274075 | + | 0.274075i | ||||
\(853\) | −44.0000 | −1.50653 | −0.753266 | − | 0.657716i | \(-0.771523\pi\) | ||||
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(854\) | 6.00000 | 0.205316 | ||||||||
\(855\) | 15.0000 | + | 5.00000i | 0.512989 | + | 0.170996i | ||||
\(856\) | −11.0000 | − | 11.0000i | −0.375972 | − | 0.375972i | ||||
\(857\) | −48.0000 | −1.63965 | −0.819824 | − | 0.572615i | \(-0.805929\pi\) | ||||
−0.819824 | + | 0.572615i | \(0.805929\pi\) | |||||||
\(858\) | 4.00000 | + | 4.00000i | 0.136558 | + | 0.136558i | ||||
\(859\) | 33.0000 | − | 33.0000i | 1.12595 | − | 1.12595i | 0.135116 | − | 0.990830i | \(-0.456859\pi\) |
0.990830 | − | 0.135116i | \(-0.0431406\pi\) | |||||||
\(860\) | −4.00000 | − | 8.00000i | −0.136399 | − | 0.272798i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.00000 | + | 1.00000i | 0.0340601 | + | 0.0340601i | ||||
\(863\) | −5.00000 | − | 5.00000i | −0.170202 | − | 0.170202i | 0.616866 | − | 0.787068i | \(-0.288402\pi\) |
−0.787068 | + | 0.616866i | \(0.788402\pi\) | |||||||
\(864\) | −4.00000 | + | 4.00000i | −0.136083 | + | 0.136083i | ||||
\(865\) | 3.00000 | − | 9.00000i | 0.102003 | − | 0.306009i | ||||
\(866\) | −11.0000 | + | 11.0000i | −0.373795 | + | 0.373795i | ||||
\(867\) | 1.00000 | − | 1.00000i | 0.0339618 | − | 0.0339618i | ||||
\(868\) | 14.0000i | 0.475191i | ||||||||
\(869\) | −2.00000 | − | 2.00000i | −0.0678454 | − | 0.0678454i | ||||
\(870\) | 6.00000 | + | 12.0000i | 0.203419 | + | 0.406838i | ||||
\(871\) | 6.00000 | − | 6.00000i | 0.203302 | − | 0.203302i | ||||
\(872\) | 7.00000 | + | 7.00000i | 0.237050 | + | 0.237050i | ||||
\(873\) | 8.00000i | 0.270759i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.00000 | − | 13.0000i | −0.304256 | − | 0.439480i | ||||
\(876\) | 18.0000i | 0.608164i | ||||||||
\(877\) | 33.0000 | − | 33.0000i | 1.11433 | − | 1.11433i | 0.121773 | − | 0.992558i | \(-0.461142\pi\) |
0.992558 | − | 0.121773i | \(-0.0388579\pi\) | |||||||
\(878\) | 27.0000 | − | 27.0000i | 0.911206 | − | 0.911206i | ||||
\(879\) | 38.0000 | 1.28171 | ||||||||
\(880\) | −2.00000 | − | 4.00000i | −0.0674200 | − | 0.134840i | ||||
\(881\) | 44.0000i | 1.48240i | 0.671286 | + | 0.741199i | \(0.265742\pi\) | ||||
−0.671286 | + | 0.741199i | \(0.734258\pi\) | |||||||
\(882\) | 5.00000i | 0.168359i | ||||||||
\(883\) | −38.0000 | −1.27880 | −0.639401 | − | 0.768874i | \(-0.720818\pi\) | ||||
−0.639401 | + | 0.768874i | \(0.720818\pi\) | |||||||
\(884\) | − | 8.00000i | − | 0.269069i | ||||||
\(885\) | 2.00000 | + | 4.00000i | 0.0672293 | + | 0.134459i | ||||
\(886\) | 21.0000 | + | 21.0000i | 0.705509 | + | 0.705509i | ||||
\(887\) | −23.0000 | − | 23.0000i | −0.772264 | − | 0.772264i | 0.206238 | − | 0.978502i | \(-0.433878\pi\) |
−0.978502 | + | 0.206238i | \(0.933878\pi\) | |||||||
\(888\) | 7.00000 | + | 5.00000i | 0.234905 | + | 0.167789i | ||||
\(889\) | 6.00000i | 0.201234i | ||||||||
\(890\) | −5.00000 | + | 15.0000i | −0.167600 | + | 0.502801i | ||||
\(891\) | − | 10.0000i | − | 0.335013i | ||||||
\(892\) | −3.00000 | − | 3.00000i | −0.100447 | − | 0.100447i | ||||
\(893\) | 70.0000i | 2.34246i | ||||||||
\(894\) | 24.0000 | − | 24.0000i | 0.802680 | − | 0.802680i | ||||
\(895\) | −27.0000 | − | 9.00000i | −0.902510 | − | 0.300837i | ||||
\(896\) | 1.00000 | + | 1.00000i | 0.0334077 | + | 0.0334077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.0000 | − | 11.0000i | −0.367075 | − | 0.367075i | ||||
\(899\) | 42.0000 | 1.40078 | ||||||||
\(900\) | −4.00000 | − | 3.00000i | −0.133333 | − | 0.100000i | ||||
\(901\) | 4.00000 | + | 4.00000i | 0.133259 | + | 0.133259i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | − | 12.0000i | − | 0.399114i | ||||||
\(905\) | −44.0000 | + | 22.0000i | −1.46261 | + | 0.731305i | ||||
\(906\) | −10.0000 | + | 10.0000i | −0.332228 | + | 0.332228i | ||||
\(907\) | −42.0000 | −1.39459 | −0.697294 | − | 0.716786i | \(-0.745613\pi\) | ||||
−0.697294 | + | 0.716786i | \(0.745613\pi\) | |||||||
\(908\) | −6.00000 | −0.199117 | ||||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 2.00000 | − | 6.00000i | 0.0662994 | − | 0.198898i | ||||
\(911\) | 41.0000 | + | 41.0000i | 1.35839 | + | 1.35839i | 0.875903 | + | 0.482488i | \(0.160267\pi\) |
0.482488 | + | 0.875903i | \(0.339733\pi\) | |||||||
\(912\) | 10.0000i | 0.331133i | ||||||||
\(913\) | −10.0000 | + | 10.0000i | −0.330952 | + | 0.330952i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.00000 | − | 12.0000i | −0.198354 | − | 0.396708i | ||||
\(916\) | 12.0000i | 0.396491i | ||||||||
\(917\) | 26.0000i | 0.858596i | ||||||||
\(918\) | −16.0000 | + | 16.0000i | −0.528079 | + | 0.528079i | ||||
\(919\) | 7.00000 | + | 7.00000i | 0.230909 | + | 0.230909i | 0.813072 | − | 0.582163i | \(-0.197794\pi\) |
−0.582163 | + | 0.813072i | \(0.697794\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0000 | 0.988534 | ||||||||
\(922\) | 1.00000 | − | 1.00000i | 0.0329332 | − | 0.0329332i | ||||
\(923\) | − | 16.0000i | − | 0.526646i | ||||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | −14.0000 | + | 27.0000i | −0.460317 | + | 0.887755i | ||||
\(926\) | −16.0000 | −0.525793 | ||||||||
\(927\) | 14.0000i | 0.459820i | ||||||||
\(928\) | 3.00000 | − | 3.00000i | 0.0984798 | − | 0.0984798i | ||||
\(929\) | −34.0000 | −1.11550 | −0.557752 | − | 0.830008i | \(-0.688336\pi\) | ||||
−0.557752 | + | 0.830008i | \(0.688336\pi\) | |||||||
\(930\) | 28.0000 | − | 14.0000i | 0.918156 | − | 0.459078i | ||||
\(931\) | 25.0000 | + | 25.0000i | 0.819342 | + | 0.819342i | ||||
\(932\) | −7.00000 | + | 7.00000i | −0.229293 | + | 0.229293i | ||||
\(933\) | − | 34.0000i | − | 1.11311i | ||||||
\(934\) | − | 14.0000i | − | 0.458094i | ||||||
\(935\) | −8.00000 | − | 16.0000i | −0.261628 | − | 0.523256i | ||||
\(936\) | − | 2.00000i | − | 0.0653720i | ||||||
\(937\) | −11.0000 | + | 11.0000i | −0.359354 | + | 0.359354i | −0.863575 | − | 0.504221i | \(-0.831780\pi\) |
0.504221 | + | 0.863575i | \(0.331780\pi\) | |||||||
\(938\) | 6.00000i | 0.195907i | ||||||||
\(939\) | −34.0000 | − | 34.0000i | −1.10955 | − | 1.10955i | ||||
\(940\) | 7.00000 | − | 21.0000i | 0.228315 | − | 0.684944i | ||||
\(941\) | 50.0000 | 1.62995 | 0.814977 | − | 0.579494i | \(-0.196750\pi\) | ||||
0.814977 | + | 0.579494i | \(0.196750\pi\) | |||||||
\(942\) | 18.0000 | 0.586472 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.00000 | − | 1.00000i | 0.0325472 | − | 0.0325472i | ||||
\(945\) | −16.0000 | + | 8.00000i | −0.520480 | + | 0.260240i | ||||
\(946\) | − | 8.00000i | − | 0.260102i | ||||||
\(947\) | −10.0000 | −0.324956 | −0.162478 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162478 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(948\) | − | 2.00000i | − | 0.0649570i | ||||||
\(949\) | −18.0000 | − | 18.0000i | −0.584305 | − | 0.584305i | ||||
\(950\) | −35.0000 | + | 5.00000i | −1.13555 | + | 0.162221i | ||||
\(951\) | −38.0000 | −1.23223 | ||||||||
\(952\) | 4.00000 | + | 4.00000i | 0.129641 | + | 0.129641i | ||||
\(953\) | −1.00000 | + | 1.00000i | −0.0323932 | + | 0.0323932i | −0.723118 | − | 0.690725i | \(-0.757292\pi\) |
0.690725 | + | 0.723118i | \(0.257292\pi\) | |||||||
\(954\) | 1.00000 | + | 1.00000i | 0.0323762 | + | 0.0323762i | ||||
\(955\) | 3.00000 | + | 1.00000i | 0.0970777 | + | 0.0323592i | ||||
\(956\) | 3.00000 | − | 3.00000i | 0.0970269 | − | 0.0970269i | ||||
\(957\) | 12.0000i | 0.387905i | ||||||||
\(958\) | −13.0000 | − | 13.0000i | −0.420011 | − | 0.420011i | ||||
\(959\) | 14.0000i | 0.452084i | ||||||||
\(960\) | 1.00000 | − | 3.00000i | 0.0322749 | − | 0.0968246i | ||||
\(961\) | − | 67.0000i | − | 2.16129i | ||||||
\(962\) | −12.0000 | + | 2.00000i | −0.386896 | + | 0.0644826i | ||||
\(963\) | −11.0000 | − | 11.0000i | −0.354470 | − | 0.354470i | ||||
\(964\) | −1.00000 | − | 1.00000i | −0.0322078 | − | 0.0322078i | ||||
\(965\) | 18.0000 | + | 36.0000i | 0.579441 | + | 1.15888i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0000 | 1.09337 | 0.546683 | − | 0.837340i | \(-0.315890\pi\) | ||||
0.546683 | + | 0.837340i | \(0.315890\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | 40.0000i | 1.28499i | ||||||||
\(970\) | −8.00000 | − | 16.0000i | −0.256865 | − | 0.513729i | ||||
\(971\) | 52.0000 | 1.66876 | 0.834380 | − | 0.551190i | \(-0.185826\pi\) | ||||
0.834380 | + | 0.551190i | \(0.185826\pi\) | |||||||
\(972\) | −7.00000 | + | 7.00000i | −0.224525 | + | 0.224525i | ||||
\(973\) | −4.00000 | + | 4.00000i | −0.128234 | + | 0.128234i | ||||
\(974\) | − | 2.00000i | − | 0.0640841i | ||||||
\(975\) | −14.0000 | + | 2.00000i | −0.448359 | + | 0.0640513i | ||||
\(976\) | −3.00000 | + | 3.00000i | −0.0960277 | + | 0.0960277i | ||||
\(977\) | − | 2.00000i | − | 0.0639857i | −0.999488 | − | 0.0319928i | \(-0.989815\pi\) | ||
0.999488 | − | 0.0319928i | \(-0.0101854\pi\) | |||||||
\(978\) | 2.00000 | + | 2.00000i | 0.0639529 | + | 0.0639529i | ||||
\(979\) | −10.0000 | + | 10.0000i | −0.319601 | + | 0.319601i | ||||
\(980\) | −5.00000 | − | 10.0000i | −0.159719 | − | 0.319438i | ||||
\(981\) | 7.00000 | + | 7.00000i | 0.223493 | + | 0.223493i | ||||
\(982\) | − | 12.0000i | − | 0.382935i | ||||||
\(983\) | −21.0000 | + | 21.0000i | −0.669796 | + | 0.669796i | −0.957669 | − | 0.287873i | \(-0.907052\pi\) |
0.287873 | + | 0.957669i | \(0.407052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0000 | − | 39.0000i | 0.414214 | − | 1.24264i | ||||
\(986\) | 12.0000 | − | 12.0000i | 0.382158 | − | 0.382158i | ||||
\(987\) | −14.0000 | − | 14.0000i | −0.445625 | − | 0.445625i | ||||
\(988\) | −10.0000 | − | 10.0000i | −0.318142 | − | 0.318142i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −2.00000 | − | 4.00000i | −0.0635642 | − | 0.127128i | ||||
\(991\) | 3.00000 | − | 3.00000i | 0.0952981 | − | 0.0952981i | −0.657850 | − | 0.753149i | \(-0.728534\pi\) |
0.753149 | + | 0.657850i | \(0.228534\pi\) | |||||||
\(992\) | −7.00000 | − | 7.00000i | −0.222250 | − | 0.222250i | ||||
\(993\) | 46.0000 | 1.45977 | ||||||||
\(994\) | 8.00000 | + | 8.00000i | 0.253745 | + | 0.253745i | ||||
\(995\) | 33.0000 | + | 11.0000i | 1.04617 | + | 0.348723i | ||||
\(996\) | −10.0000 | −0.316862 | ||||||||
\(997\) | 20.0000 | 0.633406 | 0.316703 | − | 0.948525i | \(-0.397424\pi\) | ||||
0.316703 | + | 0.948525i | \(0.397424\pi\) | |||||||
\(998\) | −13.0000 | + | 13.0000i | −0.411508 | + | 0.411508i | ||||
\(999\) | 28.0000 | + | 20.0000i | 0.885881 | + | 0.632772i |
(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 | 370.2.g.a.43.1 | ✓ | 2 | |
5.2 | odd | 4 | 370.2.h.b.117.1 | yes | 2 | ||
37.31 | odd | 4 | 370.2.h.b.253.1 | yes | 2 | ||
185.142 | even | 4 | inner | 370.2.g.a.327.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.a.43.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
370.2.g.a.327.1 | yes | 2 | 185.142 | even | 4 | inner | |
370.2.h.b.117.1 | yes | 2 | 5.2 | odd | 4 | ||
370.2.h.b.253.1 | yes | 2 | 37.31 | odd | 4 |