Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Root | \(0.339278 - 0.0446668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.e.1273.3 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.03078 | − | 1.98431i | 0.460979 | − | 0.887411i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −2.13199 | + | 0.674247i | −0.674195 | + | 0.213216i | ||||
\(11\) | 2.62544 | 0.791601 | 0.395800 | − | 0.918337i | \(-0.370467\pi\) | ||||
0.395800 | + | 0.918337i | \(0.370467\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −1.21865 | − | 1.21865i | −0.337993 | − | 0.337993i | 0.517618 | − | 0.855612i | \(-0.326819\pi\) |
−0.855612 | + | 0.517618i | \(0.826819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.13199 | + | 0.674247i | −0.550478 | + | 0.174090i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.35303 | + | 5.35303i | −1.29830 | + | 1.29830i | −0.368788 | + | 0.929514i | \(0.620227\pi\) |
−0.929514 | + | 0.368788i | \(0.879773\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | −4.65232 | −1.06732 | −0.533658 | − | 0.845701i | \(-0.679183\pi\) | ||||
−0.533658 | + | 0.845701i | \(0.679183\pi\) | |||||||
\(20\) | 1.98431 | + | 1.03078i | 0.443705 | + | 0.230490i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.85647 | − | 1.85647i | −0.395800 | − | 0.395800i | ||||
\(23\) | −3.62926 | + | 3.62926i | −0.756753 | + | 0.756753i | −0.975730 | − | 0.218977i | \(-0.929728\pi\) |
0.218977 | + | 0.975730i | \(0.429728\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.87498 | − | 4.09078i | −0.574996 | − | 0.818156i | ||||
\(26\) | 1.72343i | 0.337993i | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.99410i | − | 1.11308i | −0.830822 | − | 0.556538i | \(-0.812129\pi\) | ||
0.830822 | − | 0.556538i | \(-0.187871\pi\) | |||||||
\(30\) | 1.98431 | + | 1.03078i | 0.362284 | + | 0.188194i | ||||
\(31\) | − | 10.0018i | − | 1.79637i | −0.439620 | − | 0.898184i | \(-0.644887\pi\) | ||
0.439620 | − | 0.898184i | \(-0.355113\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1.85647 | − | 1.85647i | −0.323170 | − | 0.323170i | ||||
\(34\) | 7.57033 | 1.29830 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.79841 | + | 2.79841i | 0.460057 | + | 0.460057i | 0.898674 | − | 0.438617i | \(-0.144532\pi\) |
−0.438617 | + | 0.898674i | \(0.644532\pi\) | |||||||
\(38\) | 3.28969 | + | 3.28969i | 0.533658 | + | 0.533658i | ||||
\(39\) | 1.72343i | 0.275970i | ||||||||
\(40\) | −0.674247 | − | 2.13199i | −0.106608 | − | 0.337098i | ||||
\(41\) | − | 5.59423i | − | 0.873671i | −0.899541 | − | 0.436836i | \(-0.856099\pi\) | ||
0.899541 | − | 0.436836i | \(-0.143901\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.545731 | + | 0.545731i | −0.0832233 | + | 0.0832233i | −0.747493 | − | 0.664270i | \(-0.768743\pi\) |
0.664270 | + | 0.747493i | \(0.268743\pi\) | |||||||
\(44\) | 2.62544i | 0.395800i | ||||||||
\(45\) | 1.98431 | + | 1.03078i | 0.295804 | + | 0.153660i | ||||
\(46\) | 5.13255 | 0.756753 | ||||||||
\(47\) | −4.48288 | + | 4.48288i | −0.653895 | + | 0.653895i | −0.953929 | − | 0.300034i | \(-0.903002\pi\) |
0.300034 | + | 0.953929i | \(0.403002\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.859701 | + | 4.92554i | −0.121580 | + | 0.696576i | ||||
\(51\) | 7.57033 | 1.06006 | ||||||||
\(52\) | 1.21865 | − | 1.21865i | 0.168997 | − | 0.168997i | ||||
\(53\) | −6.06671 | + | 6.06671i | −0.833327 | + | 0.833327i | −0.987970 | − | 0.154643i | \(-0.950577\pi\) |
0.154643 | + | 0.987970i | \(0.450577\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.70626 | − | 5.20970i | 0.364912 | − | 0.702475i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.28969 | + | 3.28969i | 0.435730 | + | 0.435730i | ||||
\(58\) | −4.23847 | + | 4.23847i | −0.556538 | + | 0.556538i | ||||
\(59\) | −7.72043 | −1.00511 | −0.502557 | − | 0.864544i | \(-0.667607\pi\) | ||||
−0.502557 | + | 0.864544i | \(0.667607\pi\) | |||||||
\(60\) | −0.674247 | − | 2.13199i | −0.0870450 | − | 0.275239i | ||||
\(61\) | − | 4.80982i | − | 0.615835i | −0.951413 | − | 0.307917i | \(-0.900368\pi\) | ||
0.951413 | − | 0.307917i | \(-0.0996320\pi\) | |||||||
\(62\) | −7.07231 | + | 7.07231i | −0.898184 | + | 0.898184i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −3.67435 | + | 1.16202i | −0.455747 | + | 0.144131i | ||||
\(66\) | 2.62544i | 0.323170i | ||||||||
\(67\) | −1.81260 | − | 1.81260i | −0.221444 | − | 0.221444i | 0.587662 | − | 0.809106i | \(-0.300048\pi\) |
−0.809106 | + | 0.587662i | \(0.800048\pi\) | |||||||
\(68\) | −5.35303 | − | 5.35303i | −0.649151 | − | 0.649151i | ||||
\(69\) | 5.13255 | 0.617886 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.36973 | −0.993304 | −0.496652 | − | 0.867950i | \(-0.665437\pi\) | ||||
−0.496652 | + | 0.867950i | \(0.665437\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −9.65407 | − | 9.65407i | −1.12992 | − | 1.12992i | −0.990189 | − | 0.139734i | \(-0.955375\pi\) |
−0.139734 | − | 0.990189i | \(-0.544625\pi\) | |||||||
\(74\) | − | 3.95756i | − | 0.460057i | ||||||
\(75\) | −0.859701 | + | 4.92554i | −0.0992697 | + | 0.568752i | ||||
\(76\) | − | 4.65232i | − | 0.533658i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.21865 | − | 1.21865i | 0.137985 | − | 0.137985i | ||||
\(79\) | 8.99488i | 1.01200i | 0.862532 | + | 0.506002i | \(0.168877\pi\) | ||||
−0.862532 | + | 0.506002i | \(0.831123\pi\) | |||||||
\(80\) | −1.03078 | + | 1.98431i | −0.115245 | + | 0.221853i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.95571 | + | 3.95571i | −0.436836 | + | 0.436836i | ||||
\(83\) | 7.99504 | + | 7.99504i | 0.877570 | + | 0.877570i | 0.993283 | − | 0.115713i | \(-0.0369152\pi\) |
−0.115713 | + | 0.993283i | \(0.536915\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.10428 | + | 16.1399i | 0.553637 | + | 1.75062i | ||||
\(86\) | 0.771781 | 0.0832233 | ||||||||
\(87\) | −4.23847 | + | 4.23847i | −0.454411 | + | 0.454411i | ||||
\(88\) | 1.85647 | − | 1.85647i | 0.197900 | − | 0.197900i | ||||
\(89\) | −0.162532 | −0.0172284 | −0.00861419 | − | 0.999963i | \(-0.502742\pi\) | ||||
−0.00861419 | + | 0.999963i | \(0.502742\pi\) | |||||||
\(90\) | −0.674247 | − | 2.13199i | −0.0710719 | − | 0.224732i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.62926 | − | 3.62926i | −0.378376 | − | 0.378376i | ||||
\(93\) | −7.07231 | + | 7.07231i | −0.733364 | + | 0.733364i | ||||
\(94\) | 6.33974 | 0.653895 | ||||||||
\(95\) | −4.79552 | + | 9.23165i | −0.492010 | + | 0.947147i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 4.35278 | − | 4.35278i | 0.441958 | − | 0.441958i | −0.450711 | − | 0.892670i | \(-0.648830\pi\) |
0.892670 | + | 0.450711i | \(0.148830\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.62544i | 0.263867i | ||||||||
\(100\) | 4.09078 | − | 2.87498i | 0.409078 | − | 0.287498i | ||||
\(101\) | − | 7.67397i | − | 0.763589i | −0.924247 | − | 0.381795i | \(-0.875306\pi\) | ||
0.924247 | − | 0.381795i | \(-0.124694\pi\) | |||||||
\(102\) | −5.35303 | − | 5.35303i | −0.530029 | − | 0.530029i | ||||
\(103\) | 2.87646 | + | 2.87646i | 0.283426 | + | 0.283426i | 0.834474 | − | 0.551048i | \(-0.185772\pi\) |
−0.551048 | + | 0.834474i | \(0.685772\pi\) | |||||||
\(104\) | −1.72343 | −0.168997 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.57963 | 0.833327 | ||||||||
\(107\) | −1.99197 | − | 1.99197i | −0.192571 | − | 0.192571i | 0.604235 | − | 0.796806i | \(-0.293479\pi\) |
−0.796806 | + | 0.604235i | \(0.793479\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 12.1606i | 1.16478i | 0.812911 | + | 0.582388i | \(0.197881\pi\) | ||||
−0.812911 | + | 0.582388i | \(0.802119\pi\) | |||||||
\(110\) | −5.59742 | + | 1.77020i | −0.533693 | + | 0.168782i | ||||
\(111\) | − | 3.95756i | − | 0.375635i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.63875 | − | 1.63875i | 0.154161 | − | 0.154161i | −0.625813 | − | 0.779973i | \(-0.715233\pi\) |
0.779973 | + | 0.625813i | \(0.215233\pi\) | |||||||
\(114\) | − | 4.65232i | − | 0.435730i | ||||||
\(115\) | 3.46061 | + | 10.9425i | 0.322703 | + | 1.02040i | ||||
\(116\) | 5.99410 | 0.556538 | ||||||||
\(117\) | 1.21865 | − | 1.21865i | 0.112664 | − | 0.112664i | ||||
\(118\) | 5.45917 | + | 5.45917i | 0.502557 | + | 0.502557i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.03078 | + | 1.98431i | −0.0940970 | + | 0.181142i | ||||
\(121\) | −4.10705 | −0.373368 | ||||||||
\(122\) | −3.40106 | + | 3.40106i | −0.307917 | + | 0.307917i | ||||
\(123\) | −3.95571 | + | 3.95571i | −0.356675 | + | 0.356675i | ||||
\(124\) | 10.0018 | 0.898184 | ||||||||
\(125\) | −11.0809 | + | 1.48815i | −0.991102 | + | 0.133105i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.79622 | + | 6.79622i | 0.603067 | + | 0.603067i | 0.941125 | − | 0.338058i | \(-0.109770\pi\) |
−0.338058 | + | 0.941125i | \(0.609770\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0.771781 | 0.0679515 | ||||||||
\(130\) | 3.41983 | + | 1.77648i | 0.299939 | + | 0.155808i | ||||
\(131\) | 4.23598i | 0.370099i | 0.982729 | + | 0.185050i | \(0.0592446\pi\) | ||||
−0.982729 | + | 0.185050i | \(0.940755\pi\) | |||||||
\(132\) | 1.85647 | − | 1.85647i | 0.161585 | − | 0.161585i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.56340i | 0.221444i | ||||||||
\(135\) | −0.674247 | − | 2.13199i | −0.0580300 | − | 0.183493i | ||||
\(136\) | 7.57033i | 0.649151i | ||||||||
\(137\) | −5.84256 | − | 5.84256i | −0.499163 | − | 0.499163i | 0.412014 | − | 0.911177i | \(-0.364825\pi\) |
−0.911177 | + | 0.412014i | \(0.864825\pi\) | |||||||
\(138\) | −3.62926 | − | 3.62926i | −0.308943 | − | 0.308943i | ||||
\(139\) | −9.35059 | −0.793106 | −0.396553 | − | 0.918012i | \(-0.629794\pi\) | ||||
−0.396553 | + | 0.918012i | \(0.629794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.33974 | 0.533903 | ||||||||
\(142\) | 5.91829 | + | 5.91829i | 0.496652 | + | 0.496652i | ||||
\(143\) | −3.19950 | − | 3.19950i | −0.267556 | − | 0.267556i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −11.8942 | − | 6.17860i | −0.987756 | − | 0.513105i | ||||
\(146\) | 13.6529i | 1.12992i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.79841 | + | 2.79841i | −0.230028 | + | 0.230028i | ||||
\(149\) | − | 4.75815i | − | 0.389803i | −0.980823 | − | 0.194902i | \(-0.937561\pi\) | ||
0.980823 | − | 0.194902i | \(-0.0624387\pi\) | |||||||
\(150\) | 4.09078 | − | 2.87498i | 0.334011 | − | 0.234741i | ||||
\(151\) | 2.15114 | 0.175057 | 0.0875286 | − | 0.996162i | \(-0.472103\pi\) | ||||
0.0875286 | + | 0.996162i | \(0.472103\pi\) | |||||||
\(152\) | −3.28969 | + | 3.28969i | −0.266829 | + | 0.266829i | ||||
\(153\) | −5.35303 | − | 5.35303i | −0.432767 | − | 0.432767i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.8466 | − | 10.3096i | −1.59412 | − | 0.828089i | ||||
\(156\) | −1.72343 | −0.137985 | ||||||||
\(157\) | −2.69007 | + | 2.69007i | −0.214691 | + | 0.214691i | −0.806257 | − | 0.591566i | \(-0.798510\pi\) |
0.591566 | + | 0.806257i | \(0.298510\pi\) | |||||||
\(158\) | 6.36034 | − | 6.36034i | 0.506002 | − | 0.506002i | ||||
\(159\) | 8.57963 | 0.680409 | ||||||||
\(160\) | 2.13199 | − | 0.674247i | 0.168549 | − | 0.0533039i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 3.15459 | − | 3.15459i | 0.247086 | − | 0.247086i | −0.572687 | − | 0.819774i | \(-0.694099\pi\) |
0.819774 | + | 0.572687i | \(0.194099\pi\) | |||||||
\(164\) | 5.59423 | 0.436836 | ||||||||
\(165\) | −5.59742 | + | 1.77020i | −0.435759 | + | 0.137810i | ||||
\(166\) | − | 11.3067i | − | 0.877570i | ||||||
\(167\) | −16.1327 | + | 16.1327i | −1.24839 | + | 1.24839i | −0.291956 | + | 0.956432i | \(0.594306\pi\) |
−0.956432 | + | 0.291956i | \(0.905694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.0298i | − | 0.771521i | ||||||
\(170\) | 7.80336 | − | 15.0219i | 0.598490 | − | 1.15213i | ||||
\(171\) | − | 4.65232i | − | 0.355772i | ||||||
\(172\) | −0.545731 | − | 0.545731i | −0.0416116 | − | 0.0416116i | ||||
\(173\) | 8.75557 | + | 8.75557i | 0.665673 | + | 0.665673i | 0.956711 | − | 0.291038i | \(-0.0940006\pi\) |
−0.291038 | + | 0.956711i | \(0.594001\pi\) | |||||||
\(174\) | 5.99410 | 0.454411 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.62544 | −0.197900 | ||||||||
\(177\) | 5.45917 | + | 5.45917i | 0.410336 | + | 0.410336i | ||||
\(178\) | 0.114928 | + | 0.114928i | 0.00861419 | + | 0.00861419i | ||||
\(179\) | 20.2701i | 1.51506i | 0.652803 | + | 0.757528i | \(0.273593\pi\) | ||||
−0.652803 | + | 0.757528i | \(0.726407\pi\) | |||||||
\(180\) | −1.03078 | + | 1.98431i | −0.0768299 | + | 0.147902i | ||||
\(181\) | 7.52637i | 0.559431i | 0.960083 | + | 0.279715i | \(0.0902401\pi\) | ||||
−0.960083 | + | 0.279715i | \(0.909760\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.40106 | + | 3.40106i | −0.251413 | + | 0.251413i | ||||
\(184\) | 5.13255i | 0.378376i | ||||||||
\(185\) | 8.43748 | − | 2.66837i | 0.620336 | − | 0.196183i | ||||
\(186\) | 10.0018 | 0.733364 | ||||||||
\(187\) | −14.0541 | + | 14.0541i | −1.02774 | + | 1.02774i | ||||
\(188\) | −4.48288 | − | 4.48288i | −0.326947 | − | 0.326947i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.91871 | − | 3.13681i | 0.719579 | − | 0.227568i | ||||
\(191\) | 4.32789 | 0.313155 | 0.156578 | − | 0.987666i | \(-0.449954\pi\) | ||||
0.156578 | + | 0.987666i | \(0.449954\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 15.0388 | − | 15.0388i | 1.08252 | − | 1.08252i | 0.0862422 | − | 0.996274i | \(-0.472514\pi\) |
0.996274 | − | 0.0862422i | \(-0.0274859\pi\) | |||||||
\(194\) | −6.15577 | −0.441958 | ||||||||
\(195\) | 3.41983 | + | 1.77648i | 0.244899 | + | 0.127217i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1314 | − | 14.1314i | −1.00682 | − | 1.00682i | −0.999977 | − | 0.00684089i | \(-0.997822\pi\) |
−0.00684089 | − | 0.999977i | \(-0.502178\pi\) | |||||||
\(198\) | 1.85647 | − | 1.85647i | 0.131933 | − | 0.131933i | ||||
\(199\) | 0.844069 | 0.0598345 | 0.0299172 | − | 0.999552i | \(-0.490476\pi\) | ||||
0.0299172 | + | 0.999552i | \(0.490476\pi\) | |||||||
\(200\) | −4.92554 | − | 0.859701i | −0.348288 | − | 0.0607901i | ||||
\(201\) | 2.56340i | 0.180808i | ||||||||
\(202\) | −5.42632 | + | 5.42632i | −0.381795 | + | 0.381795i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.57033i | 0.530029i | ||||||||
\(205\) | −11.1007 | − | 5.76642i | −0.775305 | − | 0.402744i | ||||
\(206\) | − | 4.06792i | − | 0.283426i | ||||||
\(207\) | −3.62926 | − | 3.62926i | −0.252251 | − | 0.252251i | ||||
\(208\) | 1.21865 | + | 1.21865i | 0.0844983 | + | 0.0844983i | ||||
\(209\) | −12.2144 | −0.844888 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1844 | 1.52724 | 0.763619 | − | 0.645667i | \(-0.223421\pi\) | ||||
0.763619 | + | 0.645667i | \(0.223421\pi\) | |||||||
\(212\) | −6.06671 | − | 6.06671i | −0.416664 | − | 0.416664i | ||||
\(213\) | 5.91829 | + | 5.91829i | 0.405515 | + | 0.405515i | ||||
\(214\) | 2.81707i | 0.192571i | ||||||||
\(215\) | 0.520371 | + | 1.64543i | 0.0354890 | + | 0.112217i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.59885 | − | 8.59885i | 0.582388 | − | 0.582388i | ||||
\(219\) | 13.6529i | 0.922578i | ||||||||
\(220\) | 5.20970 | + | 2.70626i | 0.351238 | + | 0.182456i | ||||
\(221\) | 13.0470 | 0.877634 | ||||||||
\(222\) | −2.79841 | + | 2.79841i | −0.187817 | + | 0.187817i | ||||
\(223\) | −10.7632 | − | 10.7632i | −0.720757 | − | 0.720757i | 0.248002 | − | 0.968759i | \(-0.420226\pi\) |
−0.968759 | + | 0.248002i | \(0.920226\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.09078 | − | 2.87498i | 0.272719 | − | 0.191665i | ||||
\(226\) | −2.31755 | −0.154161 | ||||||||
\(227\) | −2.64357 | + | 2.64357i | −0.175460 | + | 0.175460i | −0.789373 | − | 0.613913i | \(-0.789594\pi\) |
0.613913 | + | 0.789373i | \(0.289594\pi\) | |||||||
\(228\) | −3.28969 | + | 3.28969i | −0.217865 | + | 0.217865i | ||||
\(229\) | 15.1818 | 1.00324 | 0.501619 | − | 0.865089i | \(-0.332738\pi\) | ||||
0.501619 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(230\) | 5.29053 | − | 10.1846i | 0.348847 | − | 0.671551i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.23847 | − | 4.23847i | −0.278269 | − | 0.278269i | ||||
\(233\) | −0.857745 | + | 0.857745i | −0.0561928 | + | 0.0561928i | −0.734645 | − | 0.678452i | \(-0.762651\pi\) |
0.678452 | + | 0.734645i | \(0.262651\pi\) | |||||||
\(234\) | −1.72343 | −0.112664 | ||||||||
\(235\) | 4.27456 | + | 13.5163i | 0.278841 | + | 0.881705i | ||||
\(236\) | − | 7.72043i | − | 0.502557i | ||||||
\(237\) | 6.36034 | − | 6.36034i | 0.413149 | − | 0.413149i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.1593i | 1.04526i | 0.852560 | + | 0.522630i | \(0.175049\pi\) | ||||
−0.852560 | + | 0.522630i | \(0.824951\pi\) | |||||||
\(240\) | 2.13199 | − | 0.674247i | 0.137620 | − | 0.0435225i | ||||
\(241\) | − | 25.2169i | − | 1.62436i | −0.583407 | − | 0.812180i | \(-0.698281\pi\) | ||
0.583407 | − | 0.812180i | \(-0.301719\pi\) | |||||||
\(242\) | 2.90412 | + | 2.90412i | 0.186684 | + | 0.186684i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 4.80982 | 0.307917 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.59423 | 0.356675 | ||||||||
\(247\) | 5.66956 | + | 5.66956i | 0.360745 | + | 0.360745i | ||||
\(248\) | −7.07231 | − | 7.07231i | −0.449092 | − | 0.449092i | ||||
\(249\) | − | 11.3067i | − | 0.716533i | ||||||
\(250\) | 8.88763 | + | 6.78307i | 0.562103 | + | 0.428999i | ||||
\(251\) | − | 2.07559i | − | 0.131010i | −0.997852 | − | 0.0655051i | \(-0.979134\pi\) | ||
0.997852 | − | 0.0655051i | \(-0.0208659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.52841 | + | 9.52841i | −0.599046 | + | 0.599046i | ||||
\(254\) | − | 9.61130i | − | 0.603067i | ||||||
\(255\) | 7.80336 | − | 15.0219i | 0.488665 | − | 0.940707i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.18355 | − | 3.18355i | 0.198584 | − | 0.198584i | −0.600809 | − | 0.799393i | \(-0.705155\pi\) |
0.799393 | + | 0.600809i | \(0.205155\pi\) | |||||||
\(258\) | −0.545731 | − | 0.545731i | −0.0339757 | − | 0.0339757i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.16202 | − | 3.67435i | −0.0720655 | − | 0.227873i | ||||
\(261\) | 5.99410 | 0.371025 | ||||||||
\(262\) | 2.99529 | − | 2.99529i | 0.185050 | − | 0.185050i | ||||
\(263\) | 15.8389 | − | 15.8389i | 0.976669 | − | 0.976669i | −0.0230649 | − | 0.999734i | \(-0.507342\pi\) |
0.999734 | + | 0.0230649i | \(0.00734243\pi\) | |||||||
\(264\) | −2.62544 | −0.161585 | ||||||||
\(265\) | 5.78479 | + | 18.2917i | 0.355357 | + | 1.12365i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.114928 | + | 0.114928i | 0.00703346 | + | 0.00703346i | ||||
\(268\) | 1.81260 | − | 1.81260i | 0.110722 | − | 0.110722i | ||||
\(269\) | 11.7242 | 0.714838 | 0.357419 | − | 0.933944i | \(-0.383657\pi\) | ||||
0.357419 | + | 0.933944i | \(0.383657\pi\) | |||||||
\(270\) | −1.03078 | + | 1.98431i | −0.0627313 | + | 0.120761i | ||||
\(271\) | − | 24.0471i | − | 1.46075i | −0.683044 | − | 0.730377i | \(-0.739344\pi\) | ||
0.683044 | − | 0.730377i | \(-0.260656\pi\) | |||||||
\(272\) | 5.35303 | − | 5.35303i | 0.324575 | − | 0.324575i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.26262i | 0.499163i | ||||||||
\(275\) | −7.54810 | − | 10.7401i | −0.455167 | − | 0.647653i | ||||
\(276\) | 5.13255i | 0.308943i | ||||||||
\(277\) | −19.2314 | − | 19.2314i | −1.15550 | − | 1.15550i | −0.985432 | − | 0.170068i | \(-0.945601\pi\) |
−0.170068 | − | 0.985432i | \(-0.554399\pi\) | |||||||
\(278\) | 6.61186 | + | 6.61186i | 0.396553 | + | 0.396553i | ||||
\(279\) | 10.0018 | 0.598789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1913 | 1.32382 | 0.661910 | − | 0.749583i | \(-0.269746\pi\) | ||||
0.661910 | + | 0.749583i | \(0.269746\pi\) | |||||||
\(282\) | −4.48288 | − | 4.48288i | −0.266951 | − | 0.266951i | ||||
\(283\) | 7.85084 | + | 7.85084i | 0.466684 | + | 0.466684i | 0.900838 | − | 0.434155i | \(-0.142953\pi\) |
−0.434155 | + | 0.900838i | \(0.642953\pi\) | |||||||
\(284\) | − | 8.36973i | − | 0.496652i | ||||||
\(285\) | 9.91871 | − | 3.13681i | 0.587534 | − | 0.185809i | ||||
\(286\) | 4.52478i | 0.267556i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 40.3099i | − | 2.37117i | ||||||
\(290\) | 4.04150 | + | 12.7794i | 0.237325 | + | 0.750430i | ||||
\(291\) | −6.15577 | −0.360857 | ||||||||
\(292\) | 9.65407 | − | 9.65407i | 0.564961 | − | 0.564961i | ||||
\(293\) | −6.51580 | − | 6.51580i | −0.380657 | − | 0.380657i | 0.490682 | − | 0.871339i | \(-0.336748\pi\) |
−0.871339 | + | 0.490682i | \(0.836748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.95808 | + | 15.3197i | −0.463337 | + | 0.891950i | ||||
\(296\) | 3.95756 | 0.230028 | ||||||||
\(297\) | 1.85647 | − | 1.85647i | 0.107723 | − | 0.107723i | ||||
\(298\) | −3.36452 | + | 3.36452i | −0.194902 | + | 0.194902i | ||||
\(299\) | 8.84561 | 0.511555 | ||||||||
\(300\) | −4.92554 | − | 0.859701i | −0.284376 | − | 0.0496349i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.52108 | − | 1.52108i | −0.0875286 | − | 0.0875286i | ||||
\(303\) | −5.42632 | + | 5.42632i | −0.311734 | + | 0.311734i | ||||
\(304\) | 4.65232 | 0.266829 | ||||||||
\(305\) | −9.54418 | − | 4.95787i | −0.546498 | − | 0.283887i | ||||
\(306\) | 7.57033i | 0.432767i | ||||||||
\(307\) | 20.6010 | − | 20.6010i | 1.17576 | − | 1.17576i | 0.194947 | − | 0.980814i | \(-0.437546\pi\) |
0.980814 | − | 0.194947i | \(-0.0624536\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.06792i | − | 0.231416i | ||||||
\(310\) | 6.74366 | + | 21.3237i | 0.383014 | + | 1.21110i | ||||
\(311\) | 32.8663i | 1.86368i | 0.362870 | + | 0.931840i | \(0.381797\pi\) | ||||
−0.362870 | + | 0.931840i | \(0.618203\pi\) | |||||||
\(312\) | 1.21865 | + | 1.21865i | 0.0689926 | + | 0.0689926i | ||||
\(313\) | 15.6858 | + | 15.6858i | 0.886615 | + | 0.886615i | 0.994196 | − | 0.107582i | \(-0.0343107\pi\) |
−0.107582 | + | 0.994196i | \(0.534311\pi\) | |||||||
\(314\) | 3.80434 | 0.214691 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.99488 | −0.506002 | ||||||||
\(317\) | −10.1572 | − | 10.1572i | −0.570488 | − | 0.570488i | 0.361777 | − | 0.932265i | \(-0.382170\pi\) |
−0.932265 | + | 0.361777i | \(0.882170\pi\) | |||||||
\(318\) | −6.06671 | − | 6.06671i | −0.340204 | − | 0.340204i | ||||
\(319\) | − | 15.7372i | − | 0.881112i | ||||||
\(320\) | −1.98431 | − | 1.03078i | −0.110926 | − | 0.0576224i | ||||
\(321\) | 2.81707i | 0.157234i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.9040 | − | 24.9040i | 1.38570 | − | 1.38570i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −1.48164 | + | 8.48884i | −0.0821865 | + | 0.470876i | ||||
\(326\) | −4.46126 | −0.247086 | ||||||||
\(327\) | 8.59885 | − | 8.59885i | 0.475518 | − | 0.475518i | ||||
\(328\) | −3.95571 | − | 3.95571i | −0.218418 | − | 0.218418i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.20970 | + | 2.70626i | 0.286784 | + | 0.148975i | ||||
\(331\) | −2.89067 | −0.158885 | −0.0794427 | − | 0.996839i | \(-0.525314\pi\) | ||||
−0.0794427 | + | 0.996839i | \(0.525314\pi\) | |||||||
\(332\) | −7.99504 | + | 7.99504i | −0.438785 | + | 0.438785i | ||||
\(333\) | −2.79841 | + | 2.79841i | −0.153352 | + | 0.153352i | ||||
\(334\) | 22.8151 | 1.24839 | ||||||||
\(335\) | −5.46514 | + | 1.72836i | −0.298593 | + | 0.0944306i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4453 | − | 23.4453i | −1.27715 | − | 1.27715i | −0.942257 | − | 0.334891i | \(-0.891301\pi\) |
−0.334891 | − | 0.942257i | \(-0.608699\pi\) | |||||||
\(338\) | −7.09212 | + | 7.09212i | −0.385761 | + | 0.385761i | ||||
\(339\) | −2.31755 | −0.125872 | ||||||||
\(340\) | −16.1399 | + | 5.10428i | −0.875308 | + | 0.276818i | ||||
\(341\) | − | 26.2590i | − | 1.42201i | ||||||
\(342\) | −3.28969 | + | 3.28969i | −0.177886 | + | 0.177886i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.771781i | 0.0416116i | ||||||||
\(345\) | 5.29053 | − | 10.1846i | 0.284833 | − | 0.548319i | ||||
\(346\) | − | 12.3822i | − | 0.665673i | ||||||
\(347\) | −8.01712 | − | 8.01712i | −0.430382 | − | 0.430382i | 0.458376 | − | 0.888758i | \(-0.348431\pi\) |
−0.888758 | + | 0.458376i | \(0.848431\pi\) | |||||||
\(348\) | −4.23847 | − | 4.23847i | −0.227206 | − | 0.227206i | ||||
\(349\) | −6.80786 | −0.364417 | −0.182208 | − | 0.983260i | \(-0.558325\pi\) | ||||
−0.182208 | + | 0.983260i | \(0.558325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.72343 | −0.0919901 | ||||||||
\(352\) | 1.85647 | + | 1.85647i | 0.0989501 | + | 0.0989501i | ||||
\(353\) | −19.6750 | − | 19.6750i | −1.04719 | − | 1.04719i | −0.998830 | − | 0.0483634i | \(-0.984599\pi\) |
−0.0483634 | − | 0.998830i | \(-0.515401\pi\) | |||||||
\(354\) | − | 7.72043i | − | 0.410336i | ||||||
\(355\) | −8.62736 | + | 16.6081i | −0.457893 | + | 0.881469i | ||||
\(356\) | − | 0.162532i | − | 0.00861419i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.3331 | − | 14.3331i | 0.757528 | − | 0.757528i | ||||
\(359\) | − | 13.7385i | − | 0.725092i | −0.931966 | − | 0.362546i | \(-0.881908\pi\) | ||
0.931966 | − | 0.362546i | \(-0.118092\pi\) | |||||||
\(360\) | 2.13199 | − | 0.674247i | 0.112366 | − | 0.0355360i | ||||
\(361\) | 2.64408 | 0.139162 | ||||||||
\(362\) | 5.32195 | − | 5.32195i | 0.279715 | − | 0.279715i | ||||
\(363\) | 2.90412 | + | 2.90412i | 0.152427 | + | 0.152427i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.1079 | + | 9.20544i | −1.52358 | + | 0.481835i | ||||
\(366\) | 4.80982 | 0.251413 | ||||||||
\(367\) | −17.8318 | + | 17.8318i | −0.930812 | + | 0.930812i | −0.997757 | − | 0.0669445i | \(-0.978675\pi\) |
0.0669445 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(368\) | 3.62926 | − | 3.62926i | 0.189188 | − | 0.189188i | ||||
\(369\) | 5.59423 | 0.291224 | ||||||||
\(370\) | −7.85302 | − | 4.07937i | −0.408259 | − | 0.212077i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.07231 | − | 7.07231i | −0.366682 | − | 0.366682i | ||||
\(373\) | 18.9888 | − | 18.9888i | 0.983201 | − | 0.983201i | −0.0166605 | − | 0.999861i | \(-0.505303\pi\) |
0.999861 | + | 0.0166605i | \(0.00530346\pi\) | |||||||
\(374\) | 19.8755 | 1.02774 | ||||||||
\(375\) | 8.88763 | + | 6.78307i | 0.458955 | + | 0.350276i | ||||
\(376\) | 6.33974i | 0.326947i | ||||||||
\(377\) | −7.30472 | + | 7.30472i | −0.376212 | + | 0.376212i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.51982i | − | 0.180801i | −0.995905 | − | 0.0904005i | \(-0.971185\pi\) | ||
0.995905 | − | 0.0904005i | \(-0.0288147\pi\) | |||||||
\(380\) | −9.23165 | − | 4.79552i | −0.473574 | − | 0.246005i | ||||
\(381\) | − | 9.61130i | − | 0.492402i | ||||||
\(382\) | −3.06028 | − | 3.06028i | −0.156578 | − | 0.156578i | ||||
\(383\) | −6.33781 | − | 6.33781i | −0.323847 | − | 0.323847i | 0.526394 | − | 0.850241i | \(-0.323544\pi\) |
−0.850241 | + | 0.526394i | \(0.823544\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.2681 | −1.08252 | ||||||||
\(387\) | −0.545731 | − | 0.545731i | −0.0277411 | − | 0.0277411i | ||||
\(388\) | 4.35278 | + | 4.35278i | 0.220979 | + | 0.220979i | ||||
\(389\) | 31.5371i | 1.59899i | 0.600670 | + | 0.799497i | \(0.294900\pi\) | ||||
−0.600670 | + | 0.799497i | \(0.705100\pi\) | |||||||
\(390\) | −1.16202 | − | 3.67435i | −0.0588412 | − | 0.186058i | ||||
\(391\) | − | 38.8551i | − | 1.96499i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.99529 | − | 2.99529i | 0.151092 | − | 0.151092i | ||||
\(394\) | 19.9848i | 1.00682i | ||||||||
\(395\) | 17.8486 | + | 9.27176i | 0.898063 | + | 0.466513i | ||||
\(396\) | −2.62544 | −0.131933 | ||||||||
\(397\) | −4.39711 | + | 4.39711i | −0.220685 | + | 0.220685i | −0.808787 | − | 0.588102i | \(-0.799875\pi\) |
0.588102 | + | 0.808787i | \(0.299875\pi\) | |||||||
\(398\) | −0.596847 | − | 0.596847i | −0.0299172 | − | 0.0299172i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.87498 | + | 4.09078i | 0.143749 | + | 0.204539i | ||||
\(401\) | −20.5141 | −1.02442 | −0.512211 | − | 0.858859i | \(-0.671174\pi\) | ||||
−0.512211 | + | 0.858859i | \(0.671174\pi\) | |||||||
\(402\) | 1.81260 | − | 1.81260i | 0.0904041 | − | 0.0904041i | ||||
\(403\) | −12.1887 | + | 12.1887i | −0.607160 | + | 0.607160i | ||||
\(404\) | 7.67397 | 0.381795 | ||||||||
\(405\) | −1.03078 | + | 1.98431i | −0.0512199 | + | 0.0986012i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.34708 | + | 7.34708i | 0.364181 | + | 0.364181i | ||||
\(408\) | 5.35303 | − | 5.35303i | 0.265015 | − | 0.265015i | ||||
\(409\) | 25.6511 | 1.26837 | 0.634184 | − | 0.773182i | \(-0.281336\pi\) | ||||
0.634184 | + | 0.773182i | \(0.281336\pi\) | |||||||
\(410\) | 3.77189 | + | 11.9268i | 0.186280 | + | 0.589025i | ||||
\(411\) | 8.26262i | 0.407565i | ||||||||
\(412\) | −2.87646 | + | 2.87646i | −0.141713 | + | 0.141713i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.13255i | 0.252251i | ||||||||
\(415\) | 24.1058 | − | 7.62351i | 1.18331 | − | 0.374223i | ||||
\(416\) | − | 1.72343i | − | 0.0844983i | ||||||
\(417\) | 6.61186 | + | 6.61186i | 0.323784 | + | 0.323784i | ||||
\(418\) | 8.63688 | + | 8.63688i | 0.422444 | + | 0.422444i | ||||
\(419\) | −1.54146 | −0.0753054 | −0.0376527 | − | 0.999291i | \(-0.511988\pi\) | ||||
−0.0376527 | + | 0.999291i | \(0.511988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0850 | −0.978884 | −0.489442 | − | 0.872036i | \(-0.662800\pi\) | ||||
−0.489442 | + | 0.872036i | \(0.662800\pi\) | |||||||
\(422\) | −15.6867 | − | 15.6867i | −0.763619 | − | 0.763619i | ||||
\(423\) | −4.48288 | − | 4.48288i | −0.217965 | − | 0.217965i | ||||
\(424\) | 8.57963i | 0.416664i | ||||||||
\(425\) | 37.2880 | + | 6.50822i | 1.80873 | + | 0.315695i | ||||
\(426\) | − | 8.36973i | − | 0.405515i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.99197 | − | 1.99197i | 0.0962855 | − | 0.0962855i | ||||
\(429\) | 4.52478i | 0.218458i | ||||||||
\(430\) | 0.795537 | − | 1.53145i | 0.0383642 | − | 0.0738532i | ||||
\(431\) | 21.9006 | 1.05491 | 0.527457 | − | 0.849581i | \(-0.323145\pi\) | ||||
0.527457 | + | 0.849581i | \(0.323145\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 5.51584 | + | 5.51584i | 0.265074 | + | 0.265074i | 0.827112 | − | 0.562038i | \(-0.189982\pi\) |
−0.562038 | + | 0.827112i | \(0.689982\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.04150 | + | 12.7794i | 0.193775 | + | 0.612724i | ||||
\(436\) | −12.1606 | −0.582388 | ||||||||
\(437\) | 16.8845 | − | 16.8845i | 0.807694 | − | 0.807694i | ||||
\(438\) | 9.65407 | − | 9.65407i | 0.461289 | − | 0.461289i | ||||
\(439\) | 5.24407 | 0.250286 | 0.125143 | − | 0.992139i | \(-0.460061\pi\) | ||||
0.125143 | + | 0.992139i | \(0.460061\pi\) | |||||||
\(440\) | −1.77020 | − | 5.59742i | −0.0843909 | − | 0.266847i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.22560 | − | 9.22560i | −0.438817 | − | 0.438817i | ||||
\(443\) | 0.919519 | − | 0.919519i | 0.0436877 | − | 0.0436877i | −0.684925 | − | 0.728613i | \(-0.740165\pi\) |
0.728613 | + | 0.684925i | \(0.240165\pi\) | |||||||
\(444\) | 3.95756 | 0.187817 | ||||||||
\(445\) | −0.167535 | + | 0.322515i | −0.00794193 | + | 0.0152887i | ||||
\(446\) | 15.2215i | 0.720757i | ||||||||
\(447\) | −3.36452 | + | 3.36452i | −0.159136 | + | 0.159136i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.3625i | − | 1.05535i | −0.849445 | − | 0.527676i | \(-0.823063\pi\) | ||
0.849445 | − | 0.527676i | \(-0.176937\pi\) | |||||||
\(450\) | −4.92554 | − | 0.859701i | −0.232192 | − | 0.0405267i | ||||
\(451\) | − | 14.6873i | − | 0.691599i | ||||||
\(452\) | 1.63875 | + | 1.63875i | 0.0770804 | + | 0.0770804i | ||||
\(453\) | −1.52108 | − | 1.52108i | −0.0714668 | − | 0.0714668i | ||||
\(454\) | 3.73858 | 0.175460 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.65232 | 0.217865 | ||||||||
\(457\) | 2.33309 | + | 2.33309i | 0.109137 | + | 0.109137i | 0.759567 | − | 0.650429i | \(-0.225411\pi\) |
−0.650429 | + | 0.759567i | \(0.725411\pi\) | |||||||
\(458\) | −10.7351 | − | 10.7351i | −0.501619 | − | 0.501619i | ||||
\(459\) | 7.57033i | 0.353353i | ||||||||
\(460\) | −10.9425 | + | 3.46061i | −0.510199 | + | 0.161352i | ||||
\(461\) | − | 6.97417i | − | 0.324819i | −0.986723 | − | 0.162410i | \(-0.948073\pi\) | ||
0.986723 | − | 0.162410i | \(-0.0519266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6658 | − | 16.6658i | 0.774527 | − | 0.774527i | −0.204367 | − | 0.978894i | \(-0.565514\pi\) |
0.978894 | + | 0.204367i | \(0.0655136\pi\) | |||||||
\(464\) | 5.99410i | 0.278269i | ||||||||
\(465\) | 6.74366 | + | 21.3237i | 0.312730 | + | 0.988861i | ||||
\(466\) | 1.21304 | 0.0561928 | ||||||||
\(467\) | −8.10351 | + | 8.10351i | −0.374986 | + | 0.374986i | −0.869289 | − | 0.494304i | \(-0.835423\pi\) |
0.494304 | + | 0.869289i | \(0.335423\pi\) | |||||||
\(468\) | 1.21865 | + | 1.21865i | 0.0563322 | + | 0.0563322i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.53489 | − | 12.5800i | 0.301432 | − | 0.580273i | ||||
\(471\) | 3.80434 | 0.175295 | ||||||||
\(472\) | −5.45917 | + | 5.45917i | −0.251279 | + | 0.251279i | ||||
\(473\) | −1.43279 | + | 1.43279i | −0.0658796 | + | 0.0658796i | ||||
\(474\) | −8.99488 | −0.413149 | ||||||||
\(475\) | 13.3753 | + | 19.0316i | 0.613702 | + | 0.873231i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.06671 | − | 6.06671i | −0.277776 | − | 0.277776i | ||||
\(478\) | 11.4264 | − | 11.4264i | 0.522630 | − | 0.522630i | ||||
\(479\) | −10.1172 | −0.462266 | −0.231133 | − | 0.972922i | \(-0.574243\pi\) | ||||
−0.231133 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(480\) | −1.98431 | − | 1.03078i | −0.0905710 | − | 0.0470485i | ||||
\(481\) | − | 6.82059i | − | 0.310992i | ||||||
\(482\) | −17.8310 | + | 17.8310i | −0.812180 | + | 0.812180i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 4.10705i | − | 0.186684i | ||||||
\(485\) | −4.15051 | − | 13.1240i | −0.188465 | − | 0.595932i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −26.1275 | − | 26.1275i | −1.18395 | − | 1.18395i | −0.978713 | − | 0.205235i | \(-0.934204\pi\) |
−0.205235 | − | 0.978713i | \(-0.565796\pi\) | |||||||
\(488\) | −3.40106 | − | 3.40106i | −0.153959 | − | 0.153959i | ||||
\(489\) | −4.46126 | −0.201745 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00737 | −0.361368 | −0.180684 | − | 0.983541i | \(-0.557831\pi\) | ||||
−0.180684 | + | 0.983541i | \(0.557831\pi\) | |||||||
\(492\) | −3.95571 | − | 3.95571i | −0.178337 | − | 0.178337i | ||||
\(493\) | 32.0866 | + | 32.0866i | 1.44511 | + | 1.44511i | ||||
\(494\) | − | 8.01797i | − | 0.360745i | ||||||
\(495\) | 5.20970 | + | 2.70626i | 0.234158 | + | 0.121637i | ||||
\(496\) | 10.0018i | 0.449092i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.99504 | + | 7.99504i | −0.358266 | + | 0.358266i | ||||
\(499\) | − | 11.9668i | − | 0.535708i | −0.963459 | − | 0.267854i | \(-0.913685\pi\) | ||
0.963459 | − | 0.267854i | \(-0.0863146\pi\) | |||||||
\(500\) | −1.48815 | − | 11.0809i | −0.0665523 | − | 0.495551i | ||||
\(501\) | 22.8151 | 1.01930 | ||||||||
\(502\) | −1.46767 | + | 1.46767i | −0.0655051 | + | 0.0655051i | ||||
\(503\) | 20.3121 | + | 20.3121i | 0.905670 | + | 0.905670i | 0.995919 | − | 0.0902493i | \(-0.0287664\pi\) |
−0.0902493 | + | 0.995919i | \(0.528766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2276 | − | 7.91019i | −0.677617 | − | 0.351999i | ||||
\(506\) | 13.4752 | 0.599046 | ||||||||
\(507\) | −7.09212 | + | 7.09212i | −0.314972 | + | 0.314972i | ||||
\(508\) | −6.79622 | + | 6.79622i | −0.301533 | + | 0.301533i | ||||
\(509\) | −29.5594 | −1.31020 | −0.655098 | − | 0.755544i | \(-0.727373\pi\) | ||||
−0.655098 | + | 0.755544i | \(0.727373\pi\) | |||||||
\(510\) | −16.1399 | + | 5.10428i | −0.714686 | + | 0.226021i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −3.28969 | + | 3.28969i | −0.145243 | + | 0.145243i | ||||
\(514\) | −4.50222 | −0.198584 | ||||||||
\(515\) | 8.67278 | − | 2.74279i | 0.382168 | − | 0.120862i | ||||
\(516\) | 0.771781i | 0.0339757i | ||||||||
\(517\) | −11.7695 | + | 11.7695i | −0.517624 | + | 0.517624i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.3822i | − | 0.543520i | ||||||
\(520\) | −1.77648 | + | 3.41983i | −0.0779040 | + | 0.149969i | ||||
\(521\) | − | 8.82958i | − | 0.386831i | −0.981117 | − | 0.193415i | \(-0.938043\pi\) | ||
0.981117 | − | 0.193415i | \(-0.0619565\pi\) | |||||||
\(522\) | −4.23847 | − | 4.23847i | −0.185513 | − | 0.185513i | ||||
\(523\) | −29.1936 | − | 29.1936i | −1.27655 | − | 1.27655i | −0.942587 | − | 0.333960i | \(-0.891615\pi\) |
−0.333960 | − | 0.942587i | \(-0.608385\pi\) | |||||||
\(524\) | −4.23598 | −0.185050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.3996 | −0.976669 | ||||||||
\(527\) | 53.5397 | + | 53.5397i | 2.33223 | + | 2.33223i | ||||
\(528\) | 1.85647 | + | 1.85647i | 0.0807924 | + | 0.0807924i | ||||
\(529\) | − | 3.34303i | − | 0.145349i | ||||||
\(530\) | 8.84372 | − | 17.0247i | 0.384147 | − | 0.739504i | ||||
\(531\) | − | 7.72043i | − | 0.335038i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.81741 | + | 6.81741i | −0.295295 | + | 0.295295i | ||||
\(534\) | − | 0.162532i | − | 0.00703346i | ||||||
\(535\) | −6.00597 | + | 1.89940i | −0.259661 | + | 0.0821183i | ||||
\(536\) | −2.56340 | −0.110722 | ||||||||
\(537\) | 14.3331 | − | 14.3331i | 0.618519 | − | 0.618519i | ||||
\(538\) | −8.29027 | − | 8.29027i | −0.357419 | − | 0.357419i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.13199 | − | 0.674247i | 0.0917463 | − | 0.0290150i | ||||
\(541\) | −25.5347 | −1.09782 | −0.548911 | − | 0.835881i | \(-0.684958\pi\) | ||||
−0.548911 | + | 0.835881i | \(0.684958\pi\) | |||||||
\(542\) | −17.0038 | + | 17.0038i | −0.730377 | + | 0.730377i | ||||
\(543\) | 5.32195 | − | 5.32195i | 0.228387 | − | 0.228387i | ||||
\(544\) | −7.57033 | −0.324575 | ||||||||
\(545\) | 24.1304 | + | 12.5349i | 1.03363 | + | 0.536937i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6183 | + | 22.6183i | 0.967087 | + | 0.967087i | 0.999475 | − | 0.0323883i | \(-0.0103113\pi\) |
−0.0323883 | + | 0.999475i | \(0.510311\pi\) | |||||||
\(548\) | 5.84256 | − | 5.84256i | 0.249582 | − | 0.249582i | ||||
\(549\) | 4.80982 | 0.205278 | ||||||||
\(550\) | −2.25710 | + | 12.9317i | −0.0962429 | + | 0.551410i | ||||
\(551\) | 27.8865i | 1.18800i | ||||||||
\(552\) | 3.62926 | − | 3.62926i | 0.154471 | − | 0.154471i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 27.1973i | 1.15550i | ||||||||
\(555\) | −7.85302 | − | 4.07937i | −0.333342 | − | 0.173160i | ||||
\(556\) | − | 9.35059i | − | 0.396553i | ||||||
\(557\) | −12.4024 | − | 12.4024i | −0.525507 | − | 0.525507i | 0.393722 | − | 0.919229i | \(-0.371187\pi\) |
−0.919229 | + | 0.393722i | \(0.871187\pi\) | |||||||
\(558\) | −7.07231 | − | 7.07231i | −0.299395 | − | 0.299395i | ||||
\(559\) | 1.33011 | 0.0562578 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.8755 | 0.839143 | ||||||||
\(562\) | −15.6916 | − | 15.6916i | −0.661910 | − | 0.661910i | ||||
\(563\) | 11.0433 | + | 11.0433i | 0.465418 | + | 0.465418i | 0.900426 | − | 0.435009i | \(-0.143255\pi\) |
−0.435009 | + | 0.900426i | \(0.643255\pi\) | |||||||
\(564\) | 6.33974i | 0.266951i | ||||||||
\(565\) | −1.56260 | − | 4.94099i | −0.0657390 | − | 0.207869i | ||||
\(566\) | − | 11.1028i | − | 0.466684i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.91829 | + | 5.91829i | −0.248326 | + | 0.248326i | ||||
\(569\) | 17.9102i | 0.750835i | 0.926856 | + | 0.375418i | \(0.122501\pi\) | ||||
−0.926856 | + | 0.375418i | \(0.877499\pi\) | |||||||
\(570\) | −9.23165 | − | 4.79552i | −0.386671 | − | 0.200862i | ||||
\(571\) | −20.4679 | −0.856557 | −0.428278 | − | 0.903647i | \(-0.640880\pi\) | ||||
−0.428278 | + | 0.903647i | \(0.640880\pi\) | |||||||
\(572\) | 3.19950 | − | 3.19950i | 0.133778 | − | 0.133778i | ||||
\(573\) | −3.06028 | − | 3.06028i | −0.127845 | − | 0.127845i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.2805 | + | 4.41246i | 1.05427 | + | 0.184012i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.1035 | + | 18.1035i | −0.753658 | + | 0.753658i | −0.975160 | − | 0.221502i | \(-0.928904\pi\) |
0.221502 | + | 0.975160i | \(0.428904\pi\) | |||||||
\(578\) | −28.5034 | + | 28.5034i | −1.18559 | + | 1.18559i | ||||
\(579\) | −21.2681 | −0.883871 | ||||||||
\(580\) | 6.17860 | − | 11.8942i | 0.256553 | − | 0.493878i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.35278 | + | 4.35278i | 0.180429 | + | 0.180429i | ||||
\(583\) | −15.9278 | + | 15.9278i | −0.659663 | + | 0.659663i | ||||
\(584\) | −13.6529 | −0.564961 | ||||||||
\(585\) | −1.16202 | − | 3.67435i | −0.0480436 | − | 0.151916i | ||||
\(586\) | 9.21473i | 0.380657i | ||||||||
\(587\) | 26.2627 | − | 26.2627i | 1.08398 | − | 1.08398i | 0.0878438 | − | 0.996134i | \(-0.472002\pi\) |
0.996134 | − | 0.0878438i | \(-0.0279977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.5313i | 1.91729i | ||||||||
\(590\) | 16.4599 | − | 5.20548i | 0.677643 | − | 0.214306i | ||||
\(591\) | 19.9848i | 0.822063i | ||||||||
\(592\) | −2.79841 | − | 2.79841i | −0.115014 | − | 0.115014i | ||||
\(593\) | 6.80591 | + | 6.80591i | 0.279485 | + | 0.279485i | 0.832903 | − | 0.553418i | \(-0.186677\pi\) |
−0.553418 | + | 0.832903i | \(0.686677\pi\) | |||||||
\(594\) | −2.62544 | −0.107723 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.75815 | 0.194902 | ||||||||
\(597\) | −0.596847 | − | 0.596847i | −0.0244273 | − | 0.0244273i | ||||
\(598\) | −6.25479 | − | 6.25479i | −0.255777 | − | 0.255777i | ||||
\(599\) | − | 3.88788i | − | 0.158855i | −0.996841 | − | 0.0794273i | \(-0.974691\pi\) | ||
0.996841 | − | 0.0794273i | \(-0.0253091\pi\) | |||||||
\(600\) | 2.87498 | + | 4.09078i | 0.117371 | + | 0.167005i | ||||
\(601\) | 36.4068i | 1.48506i | 0.669811 | + | 0.742531i | \(0.266375\pi\) | ||||
−0.669811 | + | 0.742531i | \(0.733625\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.81260 | − | 1.81260i | 0.0738146 | − | 0.0738146i | ||||
\(604\) | 2.15114i | 0.0875286i | ||||||||
\(605\) | −4.23347 | + | 8.14966i | −0.172115 | + | 0.331331i | ||||
\(606\) | 7.67397 | 0.311734 | ||||||||
\(607\) | 4.89302 | − | 4.89302i | 0.198601 | − | 0.198601i | −0.600799 | − | 0.799400i | \(-0.705151\pi\) |
0.799400 | + | 0.600799i | \(0.205151\pi\) | |||||||
\(608\) | −3.28969 | − | 3.28969i | −0.133414 | − | 0.133414i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.24301 | + | 10.2545i | 0.131306 | + | 0.415193i | ||||
\(611\) | 10.9261 | 0.442024 | ||||||||
\(612\) | 5.35303 | − | 5.35303i | 0.216384 | − | 0.216384i | ||||
\(613\) | 31.5132 | − | 31.5132i | 1.27281 | − | 1.27281i | 0.328198 | − | 0.944609i | \(-0.393559\pi\) |
0.944609 | − | 0.328198i | \(-0.106441\pi\) | |||||||
\(614\) | −29.1342 | −1.17576 | ||||||||
\(615\) | 3.77189 | + | 11.9268i | 0.152097 | + | 0.480937i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.27627 | + | 8.27627i | 0.333190 | + | 0.333190i | 0.853797 | − | 0.520607i | \(-0.174294\pi\) |
−0.520607 | + | 0.853797i | \(0.674294\pi\) | |||||||
\(618\) | −2.87646 | + | 2.87646i | −0.115708 | + | 0.115708i | ||||
\(619\) | −11.5952 | −0.466052 | −0.233026 | − | 0.972471i | \(-0.574863\pi\) | ||||
−0.233026 | + | 0.972471i | \(0.574863\pi\) | |||||||
\(620\) | 10.3096 | − | 19.8466i | 0.414044 | − | 0.797058i | ||||
\(621\) | 5.13255i | 0.205962i | ||||||||
\(622\) | 23.2400 | − | 23.2400i | 0.931840 | − | 0.931840i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 1.72343i | − | 0.0689926i | ||||||
\(625\) | −8.46898 | + | 23.5218i | −0.338759 | + | 0.940873i | ||||
\(626\) | − | 22.1831i | − | 0.886615i | ||||||
\(627\) | 8.63688 | + | 8.63688i | 0.344924 | + | 0.344924i | ||||
\(628\) | −2.69007 | − | 2.69007i | −0.107346 | − | 0.107346i | ||||
\(629\) | −29.9600 | −1.19458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.25813 | 0.0898949 | 0.0449474 | − | 0.998989i | \(-0.485688\pi\) | ||||
0.0449474 | + | 0.998989i | \(0.485688\pi\) | |||||||
\(632\) | 6.36034 | + | 6.36034i | 0.253001 | + | 0.253001i | ||||
\(633\) | −15.6867 | − | 15.6867i | −0.623492 | − | 0.623492i | ||||
\(634\) | 14.3645i | 0.570488i | ||||||||
\(635\) | 20.4912 | − | 6.48040i | 0.813169 | − | 0.257167i | ||||
\(636\) | 8.57963i | 0.340204i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.1279 | + | 11.1279i | −0.440556 | + | 0.440556i | ||||
\(639\) | − | 8.36973i | − | 0.331101i | ||||||
\(640\) | 0.674247 | + | 2.13199i | 0.0266520 | + | 0.0842744i | ||||
\(641\) | 19.2249 | 0.759339 | 0.379669 | − | 0.925122i | \(-0.376038\pi\) | ||||
0.379669 | + | 0.925122i | \(0.376038\pi\) | |||||||
\(642\) | 1.99197 | − | 1.99197i | 0.0786168 | − | 0.0786168i | ||||
\(643\) | −15.5634 | − | 15.5634i | −0.613760 | − | 0.613760i | 0.330163 | − | 0.943924i | \(-0.392896\pi\) |
−0.943924 | + | 0.330163i | \(0.892896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.795537 | − | 1.53145i | 0.0313242 | − | 0.0603009i | ||||
\(646\) | −35.2196 | −1.38570 | ||||||||
\(647\) | 6.98936 | − | 6.98936i | 0.274780 | − | 0.274780i | −0.556241 | − | 0.831021i | \(-0.687757\pi\) |
0.831021 | + | 0.556241i | \(0.187757\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | −20.2696 | −0.795650 | ||||||||
\(650\) | 7.05019 | − | 4.95484i | 0.276531 | − | 0.194345i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.15459 | + | 3.15459i | 0.123543 | + | 0.123543i | ||||
\(653\) | −7.03748 | + | 7.03748i | −0.275398 | + | 0.275398i | −0.831269 | − | 0.555871i | \(-0.812385\pi\) |
0.555871 | + | 0.831269i | \(0.312385\pi\) | |||||||
\(654\) | −12.1606 | −0.475518 | ||||||||
\(655\) | 8.40550 | + | 4.36637i | 0.328430 | + | 0.170608i | ||||
\(656\) | 5.59423i | 0.218418i | ||||||||
\(657\) | 9.65407 | − | 9.65407i | 0.376641 | − | 0.376641i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.2333i | 0.632360i | 0.948699 | + | 0.316180i | \(0.102400\pi\) | ||||
−0.948699 | + | 0.316180i | \(0.897600\pi\) | |||||||
\(660\) | −1.77020 | − | 5.59742i | −0.0689049 | − | 0.217879i | ||||
\(661\) | − | 10.1278i | − | 0.393928i | −0.980411 | − | 0.196964i | \(-0.936892\pi\) | ||
0.980411 | − | 0.196964i | \(-0.0631081\pi\) | |||||||
\(662\) | 2.04401 | + | 2.04401i | 0.0794427 | + | 0.0794427i | ||||
\(663\) | −9.22560 | − | 9.22560i | −0.358293 | − | 0.358293i | ||||
\(664\) | 11.3067 | 0.438785 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.95756 | 0.153352 | ||||||||
\(667\) | 21.7541 | + | 21.7541i | 0.842323 | + | 0.842323i | ||||
\(668\) | −16.1327 | − | 16.1327i | −0.624194 | − | 0.624194i | ||||
\(669\) | 15.2215i | 0.588496i | ||||||||
\(670\) | 5.08658 | + | 2.64230i | 0.196512 | + | 0.102081i | ||||
\(671\) | − | 12.6279i | − | 0.487495i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2038 | − | 15.2038i | 0.586062 | − | 0.586062i | −0.350501 | − | 0.936563i | \(-0.613989\pi\) |
0.936563 | + | 0.350501i | \(0.113989\pi\) | |||||||
\(674\) | 33.1567i | 1.27715i | ||||||||
\(675\) | −4.92554 | − | 0.859701i | −0.189584 | − | 0.0330899i | ||||
\(676\) | 10.0298 | 0.385761 | ||||||||
\(677\) | 8.52782 | − | 8.52782i | 0.327751 | − | 0.327751i | −0.523980 | − | 0.851731i | \(-0.675553\pi\) |
0.851731 | + | 0.523980i | \(0.175553\pi\) | |||||||
\(678\) | 1.63875 | + | 1.63875i | 0.0629359 | + | 0.0629359i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.0219 | + | 7.80336i | 0.576063 | + | 0.299245i | ||||
\(681\) | 3.73858 | 0.143263 | ||||||||
\(682\) | −18.5679 | + | 18.5679i | −0.711003 | + | 0.711003i | ||||
\(683\) | 8.28510 | − | 8.28510i | 0.317020 | − | 0.317020i | −0.530601 | − | 0.847622i | \(-0.678034\pi\) |
0.847622 | + | 0.530601i | \(0.178034\pi\) | |||||||
\(684\) | 4.65232 | 0.177886 | ||||||||
\(685\) | −17.6158 | + | 5.57105i | −0.673067 | + | 0.212859i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7351 | − | 10.7351i | −0.409570 | − | 0.409570i | ||||
\(688\) | 0.545731 | − | 0.545731i | 0.0208058 | − | 0.0208058i | ||||
\(689\) | 14.7864 | 0.563318 | ||||||||
\(690\) | −10.9425 | + | 3.46061i | −0.416576 | + | 0.131743i | ||||
\(691\) | 28.7034i | 1.09193i | 0.837808 | + | 0.545965i | \(0.183837\pi\) | ||||
−0.837808 | + | 0.545965i | \(0.816163\pi\) | |||||||
\(692\) | −8.75557 | + | 8.75557i | −0.332837 | + | 0.332837i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.3379i | 0.430382i | ||||||||
\(695\) | −9.63841 | + | 18.5545i | −0.365606 | + | 0.703811i | ||||
\(696\) | 5.99410i | 0.227206i | ||||||||
\(697\) | 29.9461 | + | 29.9461i | 1.13429 | + | 1.13429i | ||||
\(698\) | 4.81389 | + | 4.81389i | 0.182208 | + | 0.182208i | ||||
\(699\) | 1.21304 | 0.0458812 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.8761 | 1.80825 | 0.904127 | − | 0.427264i | \(-0.140523\pi\) | ||||
0.904127 | + | 0.427264i | \(0.140523\pi\) | |||||||
\(702\) | 1.21865 | + | 1.21865i | 0.0459951 | + | 0.0459951i | ||||
\(703\) | −13.0191 | − | 13.0191i | −0.491025 | − | 0.491025i | ||||
\(704\) | − | 2.62544i | − | 0.0989501i | ||||||
\(705\) | 6.53489 | − | 12.5800i | 0.246118 | − | 0.473791i | ||||
\(706\) | 27.8246i | 1.04719i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.45917 | + | 5.45917i | −0.205168 | + | 0.205168i | ||||
\(709\) | − | 25.4992i | − | 0.957643i | −0.877912 | − | 0.478822i | \(-0.841064\pi\) | ||
0.877912 | − | 0.478822i | \(-0.158936\pi\) | |||||||
\(710\) | 17.8442 | − | 5.64327i | 0.669681 | − | 0.211788i | ||||
\(711\) | −8.99488 | −0.337334 | ||||||||
\(712\) | −0.114928 | + | 0.114928i | −0.00430710 | + | 0.00430710i | ||||
\(713\) | 36.2989 | + | 36.2989i | 1.35941 | + | 1.35941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.64679 | + | 3.05082i | −0.360770 | + | 0.114094i | ||||
\(716\) | −20.2701 | −0.757528 | ||||||||
\(717\) | 11.4264 | − | 11.4264i | 0.426726 | − | 0.426726i | ||||
\(718\) | −9.71461 | + | 9.71461i | −0.362546 | + | 0.362546i | ||||
\(719\) | −32.0876 | −1.19667 | −0.598333 | − | 0.801248i | \(-0.704170\pi\) | ||||
−0.598333 | + | 0.801248i | \(0.704170\pi\) | |||||||
\(720\) | −1.98431 | − | 1.03078i | −0.0739509 | − | 0.0384149i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.86964 | − | 1.86964i | −0.0695809 | − | 0.0695809i | ||||
\(723\) | −17.8310 | + | 17.8310i | −0.663142 | + | 0.663142i | ||||
\(724\) | −7.52637 | −0.279715 | ||||||||
\(725\) | −24.5205 | + | 17.2329i | −0.910670 | + | 0.640014i | ||||
\(726\) | − | 4.10705i | − | 0.152427i | ||||||
\(727\) | −11.3772 | + | 11.3772i | −0.421956 | + | 0.421956i | −0.885877 | − | 0.463921i | \(-0.846442\pi\) |
0.463921 | + | 0.885877i | \(0.346442\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 27.0916 | + | 14.0732i | 1.00271 | + | 0.520871i | ||||
\(731\) | − | 5.84264i | − | 0.216098i | ||||||
\(732\) | −3.40106 | − | 3.40106i | −0.125707 | − | 0.125707i | ||||
\(733\) | −14.8516 | − | 14.8516i | −0.548557 | − | 0.548557i | 0.377466 | − | 0.926023i | \(-0.376795\pi\) |
−0.926023 | + | 0.377466i | \(0.876795\pi\) | |||||||
\(734\) | 25.2180 | 0.930812 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.13255 | −0.189188 | ||||||||
\(737\) | −4.75887 | − | 4.75887i | −0.175295 | − | 0.175295i | ||||
\(738\) | −3.95571 | − | 3.95571i | −0.145612 | − | 0.145612i | ||||
\(739\) | − | 36.7595i | − | 1.35222i | −0.736801 | − | 0.676110i | \(-0.763664\pi\) | ||
0.736801 | − | 0.676110i | \(-0.236336\pi\) | |||||||
\(740\) | 2.66837 | + | 8.43748i | 0.0980913 | + | 0.310168i | ||||
\(741\) | − | 8.01797i | − | 0.294547i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.1637 | + | 17.1637i | −0.629676 | + | 0.629676i | −0.947987 | − | 0.318310i | \(-0.896885\pi\) |
0.318310 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(744\) | 10.0018i | 0.366682i | ||||||||
\(745\) | −9.44166 | − | 4.90462i | −0.345916 | − | 0.179691i | ||||
\(746\) | −26.8542 | −0.983201 | ||||||||
\(747\) | −7.99504 | + | 7.99504i | −0.292523 | + | 0.292523i | ||||
\(748\) | −14.0541 | − | 14.0541i | −0.513868 | − | 0.513868i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.48815 | − | 11.0809i | −0.0543397 | − | 0.404616i | ||||
\(751\) | 30.2637 | 1.10434 | 0.552168 | − | 0.833733i | \(-0.313801\pi\) | ||||
0.552168 | + | 0.833733i | \(0.313801\pi\) | |||||||
\(752\) | 4.48288 | − | 4.48288i | 0.163474 | − | 0.163474i | ||||
\(753\) | −1.46767 | + | 1.46767i | −0.0534847 | + | 0.0534847i | ||||
\(754\) | 10.3304 | 0.376212 | ||||||||
\(755\) | 2.21735 | − | 4.26853i | 0.0806978 | − | 0.155348i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.48321 | − | 1.48321i | −0.0539082 | − | 0.0539082i | 0.679639 | − | 0.733547i | \(-0.262137\pi\) |
−0.733547 | + | 0.679639i | \(0.762137\pi\) | |||||||
\(758\) | −2.48889 | + | 2.48889i | −0.0904005 | + | 0.0904005i | ||||
\(759\) | 13.4752 | 0.489119 | ||||||||
\(760\) | 3.13681 | + | 9.91871i | 0.113784 | + | 0.359789i | ||||
\(761\) | − | 6.91949i | − | 0.250831i | −0.992104 | − | 0.125416i | \(-0.959974\pi\) | ||
0.992104 | − | 0.125416i | \(-0.0400265\pi\) | |||||||
\(762\) | −6.79622 | + | 6.79622i | −0.246201 | + | 0.246201i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.32789i | 0.156578i | ||||||||
\(765\) | −16.1399 | + | 5.10428i | −0.583539 | + | 0.184546i | ||||
\(766\) | 8.96302i | 0.323847i | ||||||||
\(767\) | 9.40852 | + | 9.40852i | 0.339722 | + | 0.339722i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | −16.5757 | −0.597736 | −0.298868 | − | 0.954294i | \(-0.596609\pi\) | ||||
−0.298868 | + | 0.954294i | \(0.596609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50222 | −0.162143 | ||||||||
\(772\) | 15.0388 | + | 15.0388i | 0.541258 | + | 0.541258i | ||||
\(773\) | −4.74612 | − | 4.74612i | −0.170706 | − | 0.170706i | 0.616584 | − | 0.787289i | \(-0.288516\pi\) |
−0.787289 | + | 0.616584i | \(0.788516\pi\) | |||||||
\(774\) | 0.771781i | 0.0277411i | ||||||||
\(775\) | −40.9150 | + | 28.7548i | −1.46971 | + | 1.03290i | ||||
\(776\) | − | 6.15577i | − | 0.220979i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.3001 | − | 22.3001i | 0.799497 | − | 0.799497i | ||||
\(779\) | 26.0261i | 0.932483i | ||||||||
\(780\) | −1.77648 | + | 3.41983i | −0.0636083 | + | 0.122450i | ||||
\(781\) | −21.9742 | −0.786300 | ||||||||
\(782\) | −27.4747 | + | 27.4747i | −0.982493 | + | 0.982493i | ||||
\(783\) | −4.23847 | − | 4.23847i | −0.151470 | − | 0.151470i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.56506 | + | 8.11082i | 0.0915511 | + | 0.289488i | ||||
\(786\) | −4.23598 | −0.151092 | ||||||||
\(787\) | −10.6060 | + | 10.6060i | −0.378063 | + | 0.378063i | −0.870403 | − | 0.492340i | \(-0.836142\pi\) |
0.492340 | + | 0.870403i | \(0.336142\pi\) | |||||||
\(788\) | 14.1314 | − | 14.1314i | 0.503409 | − | 0.503409i | ||||
\(789\) | −22.3996 | −0.797447 | ||||||||
\(790\) | −6.06478 | − | 19.1770i | −0.215775 | − | 0.682288i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.85647 | + | 1.85647i | 0.0659667 | + | 0.0659667i | ||||
\(793\) | −5.86150 | + | 5.86150i | −0.208148 | + | 0.208148i | ||||
\(794\) | 6.21845 | 0.220685 | ||||||||
\(795\) | 8.84372 | − | 17.0247i | 0.313654 | − | 0.603802i | ||||
\(796\) | 0.844069i | 0.0299172i | ||||||||
\(797\) | 29.9616 | − | 29.9616i | 1.06130 | − | 1.06130i | 0.0633012 | − | 0.997994i | \(-0.479837\pi\) |
0.997994 | − | 0.0633012i | \(-0.0201629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 47.9940i | − | 1.69790i | ||||||
\(800\) | 0.859701 | − | 4.92554i | 0.0303950 | − | 0.174144i | ||||
\(801\) | − | 0.162532i | − | 0.00574280i | ||||||
\(802\) | 14.5056 | + | 14.5056i | 0.512211 | + | 0.512211i | ||||
\(803\) | −25.3462 | − | 25.3462i | −0.894448 | − | 0.894448i | ||||
\(804\) | −2.56340 | −0.0904041 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.2374 | 0.607160 | ||||||||
\(807\) | −8.29027 | − | 8.29027i | −0.291831 | − | 0.291831i | ||||
\(808\) | −5.42632 | − | 5.42632i | −0.190897 | − | 0.190897i | ||||
\(809\) | − | 8.67329i | − | 0.304937i | −0.988308 | − | 0.152468i | \(-0.951278\pi\) | ||
0.988308 | − | 0.152468i | \(-0.0487222\pi\) | |||||||
\(810\) | 2.13199 | − | 0.674247i | 0.0749106 | − | 0.0236906i | ||||
\(811\) | 21.4366i | 0.752741i | 0.926469 | + | 0.376370i | \(0.122828\pi\) | ||||
−0.926469 | + | 0.376370i | \(0.877172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.0038 | + | 17.0038i | −0.596351 | + | 0.596351i | ||||
\(814\) | − | 10.3903i | − | 0.364181i | ||||||
\(815\) | −3.00799 | − | 9.51137i | −0.105365 | − | 0.333169i | ||||
\(816\) | −7.57033 | −0.265015 | ||||||||
\(817\) | 2.53892 | − | 2.53892i | 0.0888254 | − | 0.0888254i | ||||
\(818\) | −18.1381 | − | 18.1381i | −0.634184 | − | 0.634184i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.76642 | − | 11.1007i | 0.201372 | − | 0.387653i | ||||
\(821\) | 19.1999 | 0.670082 | 0.335041 | − | 0.942204i | \(-0.391250\pi\) | ||||
0.335041 | + | 0.942204i | \(0.391250\pi\) | |||||||
\(822\) | 5.84256 | − | 5.84256i | 0.203783 | − | 0.203783i | ||||
\(823\) | 7.13593 | − | 7.13593i | 0.248743 | − | 0.248743i | −0.571712 | − | 0.820455i | \(-0.693720\pi\) |
0.820455 | + | 0.571712i | \(0.193720\pi\) | |||||||
\(824\) | 4.06792 | 0.141713 | ||||||||
\(825\) | −2.25710 | + | 12.9317i | −0.0785820 | + | 0.450225i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.93550 | − | 2.93550i | −0.102077 | − | 0.102077i | 0.654224 | − | 0.756301i | \(-0.272995\pi\) |
−0.756301 | + | 0.654224i | \(0.772995\pi\) | |||||||
\(828\) | 3.62926 | − | 3.62926i | 0.126125 | − | 0.126125i | ||||
\(829\) | 0.632225 | 0.0219581 | 0.0109790 | − | 0.999940i | \(-0.496505\pi\) | ||||
0.0109790 | + | 0.999940i | \(0.496505\pi\) | |||||||
\(830\) | −22.4360 | − | 11.6547i | −0.778765 | − | 0.404542i | ||||
\(831\) | 27.1973i | 0.943462i | ||||||||
\(832\) | −1.21865 | + | 1.21865i | −0.0422492 | + | 0.0422492i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 9.35059i | − | 0.323784i | ||||||
\(835\) | 15.3830 | + | 48.6417i | 0.532352 | + | 1.68331i | ||||
\(836\) | − | 12.2144i | − | 0.422444i | ||||||
\(837\) | −7.07231 | − | 7.07231i | −0.244455 | − | 0.244455i | ||||
\(838\) | 1.08998 | + | 1.08998i | 0.0376527 | + | 0.0376527i | ||||
\(839\) | 7.93406 | 0.273914 | 0.136957 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136957 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.92921 | −0.238938 | ||||||||
\(842\) | 14.2023 | + | 14.2023i | 0.489442 | + | 0.489442i | ||||
\(843\) | −15.6916 | − | 15.6916i | −0.540447 | − | 0.540447i | ||||
\(844\) | 22.1844i | 0.763619i | ||||||||
\(845\) | −19.9022 | − | 10.3385i | −0.684656 | − | 0.355655i | ||||
\(846\) | 6.33974i | 0.217965i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.06671 | − | 6.06671i | 0.208332 | − | 0.208332i | ||||
\(849\) | − | 11.1028i | − | 0.381046i | ||||||
\(850\) | −21.7646 | − | 30.9686i | −0.746518 | − | 1.06221i | ||||
\(851\) | −20.3123 | −0.696298 | ||||||||
\(852\) | −5.91829 | + | 5.91829i | −0.202757 | + | 0.202757i | ||||
\(853\) | 13.0203 | + | 13.0203i | 0.445806 | + | 0.445806i | 0.893957 | − | 0.448152i | \(-0.147918\pi\) |
−0.448152 | + | 0.893957i | \(0.647918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.23165 | − | 4.79552i | −0.315716 | − | 0.164003i | ||||
\(856\) | −2.81707 | −0.0962855 | ||||||||
\(857\) | 8.06970 | − | 8.06970i | 0.275656 | − | 0.275656i | −0.555716 | − | 0.831372i | \(-0.687556\pi\) |
0.831372 | + | 0.555716i | \(0.187556\pi\) | |||||||
\(858\) | 3.19950 | − | 3.19950i | 0.109229 | − | 0.109229i | ||||
\(859\) | −12.8977 | −0.440063 | −0.220031 | − | 0.975493i | \(-0.570616\pi\) | ||||
−0.220031 | + | 0.975493i | \(0.570616\pi\) | |||||||
\(860\) | −1.64543 | + | 0.520371i | −0.0561087 | + | 0.0177445i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.4861 | − | 15.4861i | −0.527457 | − | 0.527457i | ||||
\(863\) | −8.97306 | + | 8.97306i | −0.305447 | + | 0.305447i | −0.843140 | − | 0.537694i | \(-0.819296\pi\) |
0.537694 | + | 0.843140i | \(0.319296\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 26.3988 | − | 8.34869i | 0.897588 | − | 0.283864i | ||||
\(866\) | − | 7.80057i | − | 0.265074i | ||||||
\(867\) | −28.5034 | + | 28.5034i | −0.968027 | + | 0.968027i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.6156i | 0.801103i | ||||||||
\(870\) | 6.17860 | − | 11.8942i | 0.209474 | − | 0.403250i | ||||
\(871\) | 4.41785i | 0.149693i | ||||||||
\(872\) | 8.59885 | + | 8.59885i | 0.291194 | + | 0.291194i | ||||
\(873\) | 4.35278 | + | 4.35278i | 0.147319 | + | 0.147319i | ||||
\(874\) | −23.8782 | −0.807694 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.6529 | −0.461289 | ||||||||
\(877\) | −18.4582 | − | 18.4582i | −0.623289 | − | 0.623289i | 0.323082 | − | 0.946371i | \(-0.395281\pi\) |
−0.946371 | + | 0.323082i | \(0.895281\pi\) | |||||||
\(878\) | −3.70812 | − | 3.70812i | −0.125143 | − | 0.125143i | ||||
\(879\) | 9.21473i | 0.310805i | ||||||||
\(880\) | −2.70626 | + | 5.20970i | −0.0912279 | + | 0.175619i | ||||
\(881\) | − | 34.2689i | − | 1.15455i | −0.816551 | − | 0.577274i | \(-0.804116\pi\) | ||
0.816551 | − | 0.577274i | \(-0.195884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.0880 | + | 33.0880i | −1.11350 | + | 1.11350i | −0.120827 | + | 0.992674i | \(0.538555\pi\) |
−0.992674 | + | 0.120827i | \(0.961445\pi\) | |||||||
\(884\) | 13.0470i | 0.438817i | ||||||||
\(885\) | 16.4599 | − | 5.20548i | 0.553293 | − | 0.174980i | ||||
\(886\) | −1.30040 | −0.0436877 | ||||||||
\(887\) | −13.4304 | + | 13.4304i | −0.450949 | + | 0.450949i | −0.895670 | − | 0.444720i | \(-0.853303\pi\) |
0.444720 | + | 0.895670i | \(0.353303\pi\) | |||||||
\(888\) | −2.79841 | − | 2.79841i | −0.0939087 | − | 0.0939087i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.346518 | − | 0.109587i | 0.0116153 | − | 0.00367336i | ||||
\(891\) | −2.62544 | −0.0879557 | ||||||||
\(892\) | 10.7632 | − | 10.7632i | 0.360378 | − | 0.360378i | ||||
\(893\) | 20.8558 | − | 20.8558i | 0.697912 | − | 0.697912i | ||||
\(894\) | 4.75815 | 0.159136 | ||||||||
\(895\) | 40.2221 | + | 20.8940i | 1.34448 | + | 0.698410i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.25479 | − | 6.25479i | −0.208841 | − | 0.208841i | ||||
\(898\) | −15.8127 | + | 15.8127i | −0.527676 | + | 0.527676i | ||||
\(899\) | −59.9515 | −1.99949 | ||||||||
\(900\) | 2.87498 | + | 4.09078i | 0.0958327 | + | 0.136359i | ||||
\(901\) | − | 64.9506i | − | 2.16382i | ||||||
\(902\) | −10.3855 | + | 10.3855i | −0.345799 | + | 0.345799i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.31755i | − | 0.0770804i | ||||||
\(905\) | 14.9347 | + | 7.75804i | 0.496445 | + | 0.257886i | ||||
\(906\) | 2.15114i | 0.0714668i | ||||||||
\(907\) | 39.9835 | + | 39.9835i | 1.32763 | + | 1.32763i | 0.907432 | + | 0.420200i | \(0.138040\pi\) |
0.420200 | + | 0.907432i | \(0.361960\pi\) | |||||||
\(908\) | −2.64357 | − | 2.64357i | −0.0877301 | − | 0.0877301i | ||||
\(909\) | 7.67397 | 0.254530 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6286 | −0.617193 | −0.308596 | − | 0.951193i | \(-0.599859\pi\) | ||||
−0.308596 | + | 0.951193i | \(0.599859\pi\) | |||||||
\(912\) | −3.28969 | − | 3.28969i | −0.108932 | − | 0.108932i | ||||
\(913\) | 20.9905 | + | 20.9905i | 0.694685 | + | 0.694685i | ||||
\(914\) | − | 3.29949i | − | 0.109137i | ||||||
\(915\) | 3.24301 | + | 10.2545i | 0.107211 | + | 0.339003i | ||||
\(916\) | 15.1818i | 0.501619i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.35303 | − | 5.35303i | 0.176676 | − | 0.176676i | ||||
\(919\) | − | 44.3232i | − | 1.46209i | −0.682331 | − | 0.731043i | \(-0.739034\pi\) | ||
0.682331 | − | 0.731043i | \(-0.260966\pi\) | |||||||
\(920\) | 10.1846 | + | 5.29053i | 0.335775 | + | 0.174424i | ||||
\(921\) | −29.1342 | −0.960005 | ||||||||
\(922\) | −4.93148 | + | 4.93148i | −0.162410 | + | 0.162410i | ||||
\(923\) | 10.1998 | + | 10.1998i | 0.335730 | + | 0.335730i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.40232 | − | 19.4931i | 0.111867 | − | 0.640929i | ||||
\(926\) | −23.5691 | −0.774527 | ||||||||
\(927\) | −2.87646 | + | 2.87646i | −0.0944752 | + | 0.0944752i | ||||
\(928\) | 4.23847 | − | 4.23847i | 0.139135 | − | 0.139135i | ||||
\(929\) | 14.0476 | 0.460886 | 0.230443 | − | 0.973086i | \(-0.425982\pi\) | ||||
0.230443 | + | 0.973086i | \(0.425982\pi\) | |||||||
\(930\) | 10.3096 | − | 19.8466i | 0.338066 | − | 0.650795i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.857745 | − | 0.857745i | −0.0280964 | − | 0.0280964i | ||||
\(933\) | 23.2400 | − | 23.2400i | 0.760844 | − | 0.760844i | ||||
\(934\) | 11.4601 | 0.374986 | ||||||||
\(935\) | 13.4010 | + | 42.3744i | 0.438259 | + | 1.38579i | ||||
\(936\) | − | 1.72343i | − | 0.0563322i | ||||||
\(937\) | −24.1561 | + | 24.1561i | −0.789145 | + | 0.789145i | −0.981354 | − | 0.192209i | \(-0.938435\pi\) |
0.192209 | + | 0.981354i | \(0.438435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 22.1831i | − | 0.723918i | ||||||
\(940\) | −13.5163 | + | 4.27456i | −0.440853 | + | 0.139421i | ||||
\(941\) | 52.3393i | 1.70621i | 0.521738 | + | 0.853106i | \(0.325284\pi\) | ||||
−0.521738 | + | 0.853106i | \(0.674716\pi\) | |||||||
\(942\) | −2.69007 | − | 2.69007i | −0.0876473 | − | 0.0876473i | ||||
\(943\) | 20.3029 | + | 20.3029i | 0.661153 | + | 0.661153i | ||||
\(944\) | 7.72043 | 0.251279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.02627 | 0.0658796 | ||||||||
\(947\) | −27.5701 | − | 27.5701i | −0.895908 | − | 0.895908i | 0.0991635 | − | 0.995071i | \(-0.468383\pi\) |
−0.995071 | + | 0.0991635i | \(0.968383\pi\) | |||||||
\(948\) | 6.36034 | + | 6.36034i | 0.206574 | + | 0.206574i | ||||
\(949\) | 23.5299i | 0.763813i | ||||||||
\(950\) | 3.99960 | − | 22.9152i | 0.129764 | − | 0.743466i | ||||
\(951\) | 14.3645i | 0.465801i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45944 | − | 1.45944i | 0.0472759 | − | 0.0472759i | −0.683074 | − | 0.730350i | \(-0.739357\pi\) |
0.730350 | + | 0.683074i | \(0.239357\pi\) | |||||||
\(954\) | 8.57963i | 0.277776i | ||||||||
\(955\) | 4.46111 | − | 8.58789i | 0.144358 | − | 0.277898i | ||||
\(956\) | −16.1593 | −0.522630 | ||||||||
\(957\) | −11.1279 | + | 11.1279i | −0.359712 | + | 0.359712i | ||||
\(958\) | 7.15393 | + | 7.15393i | 0.231133 | + | 0.231133i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.674247 | + | 2.13199i | 0.0217612 | + | 0.0688098i | ||||
\(961\) | −69.0351 | −2.22694 | ||||||||
\(962\) | −4.82288 | + | 4.82288i | −0.155496 | + | 0.155496i | ||||
\(963\) | 1.99197 | − | 1.99197i | 0.0641903 | − | 0.0641903i | ||||
\(964\) | 25.2169 | 0.812180 | ||||||||
\(965\) | −14.3399 | − | 45.3434i | −0.461619 | − | 1.45965i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.2656 | + | 11.2656i | 0.362279 | + | 0.362279i | 0.864651 | − | 0.502373i | \(-0.167539\pi\) |
−0.502373 | + | 0.864651i | \(0.667539\pi\) | |||||||
\(968\) | −2.90412 | + | 2.90412i | −0.0933420 | + | 0.0933420i | ||||
\(969\) | −35.2196 | −1.13142 | ||||||||
\(970\) | −6.34525 | + | 12.2150i | −0.203734 | + | 0.392199i | ||||
\(971\) | 9.80195i | 0.314559i | 0.987554 | + | 0.157280i | \(0.0502724\pi\) | ||||
−0.987554 | + | 0.157280i | \(0.949728\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.9498i | 1.18395i | ||||||||
\(975\) | 7.05019 | − | 4.95484i | 0.225787 | − | 0.158682i | ||||
\(976\) | 4.80982i | 0.153959i | ||||||||
\(977\) | −34.8727 | − | 34.8727i | −1.11568 | − | 1.11568i | −0.992368 | − | 0.123309i | \(-0.960649\pi\) |
−0.123309 | − | 0.992368i | \(-0.539351\pi\) | |||||||
\(978\) | 3.15459 | + | 3.15459i | 0.100873 | + | 0.100873i | ||||
\(979\) | −0.426719 | −0.0136380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1606 | −0.388258 | ||||||||
\(982\) | 5.66207 | + | 5.66207i | 0.180684 | + | 0.180684i | ||||
\(983\) | −4.22505 | − | 4.22505i | −0.134758 | − | 0.134758i | 0.636510 | − | 0.771268i | \(-0.280377\pi\) |
−0.771268 | + | 0.636510i | \(0.780377\pi\) | |||||||
\(984\) | 5.59423i | 0.178337i | ||||||||
\(985\) | −42.6073 | + | 13.4747i | −1.35758 | + | 0.429339i | ||||
\(986\) | − | 45.3773i | − | 1.44511i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.66956 | + | 5.66956i | −0.180373 | + | 0.180373i | ||||
\(989\) | − | 3.96120i | − | 0.125959i | ||||||
\(990\) | −1.77020 | − | 5.59742i | −0.0562606 | − | 0.177898i | ||||
\(991\) | 13.0417 | 0.414284 | 0.207142 | − | 0.978311i | \(-0.433584\pi\) | ||||
0.207142 | + | 0.978311i | \(0.433584\pi\) | |||||||
\(992\) | 7.07231 | − | 7.07231i | 0.224546 | − | 0.224546i | ||||
\(993\) | 2.04401 | + | 2.04401i | 0.0648647 | + | 0.0648647i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.870050 | − | 1.67490i | 0.0275824 | − | 0.0530977i | ||||
\(996\) | 11.3067 | 0.358266 | ||||||||
\(997\) | −15.0223 | + | 15.0223i | −0.475761 | + | 0.475761i | −0.903773 | − | 0.428012i | \(-0.859214\pi\) |
0.428012 | + | 0.903773i | \(0.359214\pi\) | |||||||
\(998\) | −8.46182 | + | 8.46182i | −0.267854 | + | 0.267854i | ||||
\(999\) | 3.95756 | 0.125212 |
(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 | 1470.2.m.e.97.3 | 16 | ||
5.3 | odd | 4 | 1470.2.m.d.1273.2 | 16 | |||
7.4 | even | 3 | 210.2.u.b.187.3 | yes | 16 | ||
7.5 | odd | 6 | 210.2.u.a.157.2 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.d.97.2 | 16 | |||
21.5 | even | 6 | 630.2.bv.a.577.3 | 16 | |||
21.11 | odd | 6 | 630.2.bv.b.397.2 | 16 | |||
35.4 | even | 6 | 1050.2.bc.g.607.1 | 16 | |||
35.12 | even | 12 | 1050.2.bc.g.493.1 | 16 | |||
35.13 | even | 4 | inner | 1470.2.m.e.1273.3 | 16 | ||
35.18 | odd | 12 | 210.2.u.a.103.2 | ✓ | 16 | ||
35.19 | odd | 6 | 1050.2.bc.h.157.3 | 16 | |||
35.32 | odd | 12 | 1050.2.bc.h.943.3 | 16 | |||
35.33 | even | 12 | 210.2.u.b.73.3 | yes | 16 | ||
105.53 | even | 12 | 630.2.bv.a.523.3 | 16 | |||
105.68 | odd | 12 | 630.2.bv.b.73.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.103.2 | ✓ | 16 | 35.18 | odd | 12 | ||
210.2.u.a.157.2 | yes | 16 | 7.5 | odd | 6 | ||
210.2.u.b.73.3 | yes | 16 | 35.33 | even | 12 | ||
210.2.u.b.187.3 | yes | 16 | 7.4 | even | 3 | ||
630.2.bv.a.523.3 | 16 | 105.53 | even | 12 | |||
630.2.bv.a.577.3 | 16 | 21.5 | even | 6 | |||
630.2.bv.b.73.2 | 16 | 105.68 | odd | 12 | |||
630.2.bv.b.397.2 | 16 | 21.11 | odd | 6 | |||
1050.2.bc.g.493.1 | 16 | 35.12 | even | 12 | |||
1050.2.bc.g.607.1 | 16 | 35.4 | even | 6 | |||
1050.2.bc.h.157.3 | 16 | 35.19 | odd | 6 | |||
1050.2.bc.h.943.3 | 16 | 35.32 | odd | 12 | |||
1470.2.m.d.97.2 | 16 | 7.6 | odd | 2 | |||
1470.2.m.d.1273.2 | 16 | 5.3 | odd | 4 | |||
1470.2.m.e.97.3 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.e.1273.3 | 16 | 35.13 | even | 4 | inner |