Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(71,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.cu (of order \(12\), degree \(4\), 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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 431.1 | ||
Root | \(-0.115299 - 1.50155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.431 |
Dual form | 1170.2.cu.f.1151.1 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258819 | + | 0.965926i | −0.183013 | + | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03475 | + | 0.277260i | −0.391098 | + | 0.104794i | −0.449009 | − | 0.893527i | \(-0.648223\pi\) |
0.0579107 | + | 0.998322i | \(0.481556\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.866025 | − | 0.500000i | 0.273861 | − | 0.158114i | ||||
\(11\) | −0.105325 | − | 0.0282216i | −0.0317565 | − | 0.00850914i | 0.242906 | − | 0.970050i | \(-0.421899\pi\) |
−0.274662 | + | 0.961541i | \(0.588566\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.19781 | + | 3.40077i | 0.332211 | + | 0.943205i | ||||
\(14\) | − | 1.07125i | − | 0.286304i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 1.09921 | − | 1.90389i | 0.266598 | − | 0.461761i | −0.701383 | − | 0.712785i | \(-0.747434\pi\) |
0.967981 | + | 0.251023i | \(0.0807671\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.578305 | + | 2.15826i | 0.132672 | + | 0.495139i | 0.999997 | − | 0.00260393i | \(-0.000828859\pi\) |
−0.867324 | + | 0.497743i | \(0.834162\pi\) | |||||||
\(20\) | 0.258819 | + | 0.965926i | 0.0578737 | + | 0.215988i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0545200 | − | 0.0944314i | 0.0116237 | − | 0.0201328i | ||||
\(23\) | −1.34004 | − | 2.32102i | −0.279418 | − | 0.483967i | 0.691822 | − | 0.722068i | \(-0.256808\pi\) |
−0.971240 | + | 0.238101i | \(0.923475\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | −3.59491 | + | 0.276806i | −0.705020 | + | 0.0542861i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.03475 | + | 0.277260i | 0.195549 | + | 0.0523972i | ||||
\(29\) | −0.745303 | + | 0.430301i | −0.138399 | + | 0.0799048i | −0.567601 | − | 0.823304i | \(-0.692128\pi\) |
0.429202 | + | 0.903209i | \(0.358795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.123514 | + | 0.123514i | −0.0221837 | + | 0.0221837i | −0.718112 | − | 0.695928i | \(-0.754993\pi\) |
0.695928 | + | 0.718112i | \(0.254993\pi\) | |||||||
\(32\) | −0.965926 | + | 0.258819i | −0.170753 | + | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.55452 | + | 1.55452i | 0.266598 | + | 0.266598i | ||||
\(35\) | 0.927730 | + | 0.535625i | 0.156815 | + | 0.0905372i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.82648 | + | 10.5486i | −0.464671 | + | 1.73418i | 0.193308 | + | 0.981138i | \(0.438078\pi\) |
−0.657978 | + | 0.753037i | \(0.728588\pi\) | |||||||
\(38\) | −2.23440 | −0.362467 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.03528 | + | 3.86370i | −0.161683 | + | 0.603409i | 0.836757 | + | 0.547574i | \(0.184449\pi\) |
−0.998440 | + | 0.0558348i | \(0.982218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5279 | + | 6.07830i | 1.60549 | + | 0.926933i | 0.990361 | + | 0.138510i | \(0.0442313\pi\) |
0.615134 | + | 0.788423i | \(0.289102\pi\) | |||||||
\(44\) | 0.0771029 | + | 0.0771029i | 0.0116237 | + | 0.0116237i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.58877 | − | 0.693658i | 0.381693 | − | 0.102274i | ||||
\(47\) | −8.91173 | + | 8.91173i | −1.29991 | + | 1.29991i | −0.371462 | + | 0.928448i | \(0.621143\pi\) |
−0.928448 | + | 0.371462i | \(0.878857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.06835 | + | 2.92621i | −0.724050 | + | 0.418030i | ||||
\(50\) | −0.965926 | − | 0.258819i | −0.136603 | − | 0.0366025i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.663057 | − | 3.54406i | 0.0919495 | − | 0.491473i | ||||
\(53\) | 3.57666i | 0.491292i | 0.969360 | + | 0.245646i | \(0.0790001\pi\) | ||||
−0.969360 | + | 0.245646i | \(0.921000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0545200 | + | 0.0944314i | 0.00735147 | + | 0.0127331i | ||||
\(56\) | −0.535625 | + | 0.927730i | −0.0715759 | + | 0.123973i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.222740 | − | 0.831277i | −0.0292472 | − | 0.109152i | ||||
\(59\) | −2.10359 | − | 7.85072i | −0.273865 | − | 1.02208i | −0.956598 | − | 0.291409i | \(-0.905876\pi\) |
0.682734 | − | 0.730667i | \(-0.260791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.30104 | + | 7.44963i | −0.550692 | + | 0.953827i | 0.447532 | + | 0.894268i | \(0.352303\pi\) |
−0.998225 | + | 0.0595594i | \(0.981030\pi\) | |||||||
\(62\) | −0.0873374 | − | 0.151273i | −0.0110919 | − | 0.0192117i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.55773 | − | 3.25169i | 0.193213 | − | 0.403322i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.67803 | − | 0.985526i | −0.449343 | − | 0.120401i | 0.0270488 | − | 0.999634i | \(-0.491389\pi\) |
−0.476392 | + | 0.879233i | \(0.658056\pi\) | |||||||
\(68\) | −1.90389 | + | 1.09921i | −0.230881 | + | 0.133299i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.757488 | + | 0.757488i | −0.0905372 | + | 0.0905372i | ||||
\(71\) | −3.12935 | + | 0.838506i | −0.371385 | + | 0.0995123i | −0.439684 | − | 0.898153i | \(-0.644910\pi\) |
0.0682988 | + | 0.997665i | \(0.478243\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.26565 | + | 9.26565i | 1.08446 | + | 1.08446i | 0.996087 | + | 0.0883749i | \(0.0281674\pi\) |
0.0883749 | + | 0.996087i | \(0.471833\pi\) | |||||||
\(74\) | −9.45759 | − | 5.46034i | −1.09942 | − | 0.634752i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.578305 | − | 2.15826i | 0.0663361 | − | 0.247570i | ||||
\(77\) | 0.116809 | 0.0133116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.58347 | 0.403172 | 0.201586 | − | 0.979471i | \(-0.435391\pi\) | ||||
0.201586 | + | 0.979471i | \(0.435391\pi\) | |||||||
\(80\) | 0.258819 | − | 0.965926i | 0.0289368 | − | 0.107994i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.46410 | − | 2.00000i | −0.382546 | − | 0.220863i | ||||
\(83\) | 6.23094 | + | 6.23094i | 0.683934 | + | 0.683934i | 0.960884 | − | 0.276950i | \(-0.0893237\pi\) |
−0.276950 | + | 0.960884i | \(0.589324\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.12351 | + | 0.568994i | −0.230327 | + | 0.0617160i | ||||
\(86\) | −8.59602 | + | 8.59602i | −0.926933 | + | 0.926933i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0944314 | + | 0.0545200i | −0.0100664 | + | 0.00581185i | ||||
\(89\) | −0.486484 | − | 0.130353i | −0.0515672 | − | 0.0138174i | 0.232943 | − | 0.972490i | \(-0.425164\pi\) |
−0.284510 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.18233 | − | 3.18684i | −0.228770 | − | 0.334072i | ||||
\(92\) | 2.68009i | 0.279418i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.30155 | − | 10.9146i | −0.649955 | − | 1.12576i | ||||
\(95\) | 1.11720 | − | 1.93504i | 0.114622 | − | 0.198531i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.35837 | − | 5.06950i | −0.137921 | − | 0.514729i | −0.999969 | − | 0.00790183i | \(-0.997485\pi\) |
0.862047 | − | 0.506828i | \(-0.169182\pi\) | |||||||
\(98\) | −1.51472 | − | 5.65301i | −0.153010 | − | 0.571040i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 4.35338 | + | 7.54028i | 0.433178 | + | 0.750285i | 0.997145 | − | 0.0755116i | \(-0.0240590\pi\) |
−0.563967 | + | 0.825797i | \(0.690726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.66430i | 0.361054i | 0.983570 | + | 0.180527i | \(0.0577803\pi\) | ||||
−0.983570 | + | 0.180527i | \(0.942220\pi\) | |||||||
\(104\) | 3.25169 | + | 1.55773i | 0.318854 | + | 0.152748i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.45479 | − | 0.925708i | −0.335559 | − | 0.0899127i | ||||
\(107\) | −1.44217 | + | 0.832640i | −0.139420 | + | 0.0804944i | −0.568088 | − | 0.822968i | \(-0.692317\pi\) |
0.428667 | + | 0.903462i | \(0.358983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.39561 | − | 3.39561i | 0.325241 | − | 0.325241i | −0.525533 | − | 0.850773i | \(-0.676134\pi\) |
0.850773 | + | 0.525533i | \(0.176134\pi\) | |||||||
\(110\) | −0.105325 | + | 0.0282216i | −0.0100423 | + | 0.00269083i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.757488 | − | 0.757488i | −0.0715759 | − | 0.0715759i | ||||
\(113\) | −8.54251 | − | 4.93202i | −0.803612 | − | 0.463965i | 0.0411207 | − | 0.999154i | \(-0.486907\pi\) |
−0.844733 | + | 0.535189i | \(0.820241\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.693658 | + | 2.58877i | −0.0646839 | + | 0.241404i | ||||
\(116\) | 0.860601 | 0.0799048 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.12766 | 0.748212 | ||||||||
\(119\) | −0.609535 | + | 2.27481i | −0.0558760 | + | 0.208532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.51598 | − | 5.49406i | −0.865089 | − | 0.499460i | ||||
\(122\) | −6.08260 | − | 6.08260i | −0.550692 | − | 0.550692i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.168723 | − | 0.0452092i | 0.0151518 | − | 0.00405990i | ||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.27412 | − | 5.35441i | 0.822945 | − | 0.475127i | −0.0284860 | − | 0.999594i | \(-0.509069\pi\) |
0.851431 | + | 0.524467i | \(0.175735\pi\) | |||||||
\(128\) | 0.965926 | + | 0.258819i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.73772 | + | 2.34625i | 0.240114 | + | 0.205780i | ||||
\(131\) | − | 2.94079i | − | 0.256938i | −0.991714 | − | 0.128469i | \(-0.958994\pi\) | ||
0.991714 | − | 0.128469i | \(-0.0410063\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.19680 | − | 2.07292i | −0.103776 | − | 0.179745i | ||||
\(134\) | 1.90389 | − | 3.29763i | 0.164471 | − | 0.284872i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.568994 | − | 2.12351i | −0.0487908 | − | 0.182090i | ||||
\(137\) | 1.11178 | + | 4.14923i | 0.0949861 | + | 0.354493i | 0.997017 | − | 0.0771778i | \(-0.0245909\pi\) |
−0.902031 | + | 0.431671i | \(0.857924\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.45442 | + | 2.51913i | −0.123363 | + | 0.213670i | −0.921092 | − | 0.389346i | \(-0.872701\pi\) |
0.797729 | + | 0.603016i | \(0.206034\pi\) | |||||||
\(140\) | −0.535625 | − | 0.927730i | −0.0452686 | − | 0.0784075i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 3.23974i | − | 0.271873i | ||||||
\(143\) | −0.0301829 | − | 0.391989i | −0.00252402 | − | 0.0327798i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.831277 | + | 0.222740i | 0.0690338 | + | 0.0184976i | ||||
\(146\) | −11.3481 | + | 6.55180i | −0.939172 | + | 0.542231i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.72209 | − | 7.72209i | 0.634752 | − | 0.634752i | ||||
\(149\) | 14.4305 | − | 3.86664i | 1.18219 | − | 0.316767i | 0.386396 | − | 0.922333i | \(-0.373720\pi\) |
0.795795 | + | 0.605566i | \(0.207053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.78063 | − | 8.78063i | −0.714557 | − | 0.714557i | 0.252928 | − | 0.967485i | \(-0.418606\pi\) |
−0.967485 | + | 0.252928i | \(0.918606\pi\) | |||||||
\(152\) | 1.93504 | + | 1.11720i | 0.156953 | + | 0.0906168i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0302324 | + | 0.112829i | −0.00243620 | + | 0.00909201i | ||||
\(155\) | 0.174675 | 0.0140302 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.19716 | −0.494587 | −0.247294 | − | 0.968941i | \(-0.579541\pi\) | ||||
−0.247294 | + | 0.968941i | \(0.579541\pi\) | |||||||
\(158\) | −0.927470 | + | 3.46136i | −0.0737855 | + | 0.275371i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | + | 0.500000i | 0.0684653 | + | 0.0395285i | ||||
\(161\) | 2.03013 | + | 2.03013i | 0.159997 | + | 0.159997i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6514 | − | 3.65789i | 1.06926 | − | 0.286508i | 0.319073 | − | 0.947730i | \(-0.396628\pi\) |
0.750191 | + | 0.661222i | \(0.229962\pi\) | |||||||
\(164\) | 2.82843 | − | 2.82843i | 0.220863 | − | 0.220863i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.63131 | + | 4.40594i | −0.592304 | + | 0.341967i | ||||
\(167\) | 1.84771 | + | 0.495092i | 0.142980 | + | 0.0383113i | 0.329599 | − | 0.944121i | \(-0.393086\pi\) |
−0.186619 | + | 0.982432i | \(0.559753\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1305 | + | 8.14693i | −0.779271 | + | 0.626687i | ||||
\(170\) | − | 2.19842i | − | 0.168611i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.07830 | − | 10.5279i | −0.463466 | − | 0.802747i | ||||
\(173\) | 5.66735 | − | 9.81614i | 0.430881 | − | 0.746307i | −0.566069 | − | 0.824358i | \(-0.691536\pi\) |
0.996949 | + | 0.0780510i | \(0.0248697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.277260 | − | 1.03475i | −0.0209589 | − | 0.0782196i | ||||
\(176\) | −0.0282216 | − | 0.105325i | −0.00212728 | − | 0.00793913i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.251822 | − | 0.436169i | 0.0188749 | − | 0.0326923i | ||||
\(179\) | −4.03616 | − | 6.99083i | −0.301677 | − | 0.522519i | 0.674839 | − | 0.737965i | \(-0.264213\pi\) |
−0.976516 | + | 0.215446i | \(0.930880\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.34777i | − | 0.397497i | −0.980051 | − | 0.198748i | \(-0.936312\pi\) | ||
0.980051 | − | 0.198748i | \(-0.0636877\pi\) | |||||||
\(182\) | 3.64308 | − | 1.28315i | 0.270043 | − | 0.0951134i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.58877 | − | 0.693658i | −0.190846 | − | 0.0511371i | ||||
\(185\) | 9.45759 | − | 5.46034i | 0.695336 | − | 0.401452i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.169505 | + | 0.169505i | −0.0123954 | + | 0.0123954i | ||||
\(188\) | 12.1737 | − | 3.26192i | 0.887855 | − | 0.237900i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.57996 | + | 1.57996i | 0.114622 | + | 0.114622i | ||||
\(191\) | −0.740223 | − | 0.427368i | −0.0535606 | − | 0.0309232i | 0.472981 | − | 0.881073i | \(-0.343178\pi\) |
−0.526541 | + | 0.850150i | \(0.676511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.33330 | + | 16.1721i | −0.311918 | + | 1.16409i | 0.614908 | + | 0.788599i | \(0.289193\pi\) |
−0.926825 | + | 0.375493i | \(0.877473\pi\) | |||||||
\(194\) | 5.24833 | 0.376808 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.85242 | 0.418030 | ||||||||
\(197\) | −5.60341 | + | 20.9122i | −0.399227 | + | 1.48993i | 0.415233 | + | 0.909715i | \(0.363700\pi\) |
−0.814460 | + | 0.580219i | \(0.802967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12037 | − | 3.53360i | −0.433862 | − | 0.250490i | 0.267129 | − | 0.963661i | \(-0.413925\pi\) |
−0.700990 | + | 0.713171i | \(0.747258\pi\) | |||||||
\(200\) | 0.707107 | + | 0.707107i | 0.0500000 | + | 0.0500000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.41008 | + | 2.25348i | −0.591731 | + | 0.158554i | ||||
\(203\) | 0.651895 | − | 0.651895i | 0.0457541 | − | 0.0457541i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46410 | − | 2.00000i | 0.241943 | − | 0.139686i | ||||
\(206\) | −3.53944 | − | 0.948390i | −0.246604 | − | 0.0660774i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.34625 | + | 2.73772i | −0.162683 | + | 0.189827i | ||||
\(209\) | − | 0.243639i | − | 0.0168528i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3840 | − | 19.7177i | −0.783707 | − | 1.35742i | −0.929769 | − | 0.368145i | \(-0.879993\pi\) |
0.146062 | − | 0.989275i | \(-0.453340\pi\) | |||||||
\(212\) | 1.78833 | − | 3.09748i | 0.122823 | − | 0.212736i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.431006 | − | 1.60854i | −0.0294630 | − | 0.109957i | ||||
\(215\) | −3.14636 | − | 11.7424i | −0.214580 | − | 0.800824i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0935603 | − | 0.162051i | 0.00635128 | − | 0.0110007i | ||||
\(218\) | 2.40106 | + | 4.15876i | 0.162620 | + | 0.281667i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 0.109040i | − | 0.00735147i | ||||||
\(221\) | 7.79134 | + | 1.45768i | 0.524102 | + | 0.0980542i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5443 | + | 3.89713i | 0.973957 | + | 0.260971i | 0.710498 | − | 0.703699i | \(-0.248470\pi\) |
0.263459 | + | 0.964670i | \(0.415136\pi\) | |||||||
\(224\) | 0.927730 | − | 0.535625i | 0.0619866 | − | 0.0357880i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.97493 | − | 6.97493i | 0.463965 | − | 0.463965i | ||||
\(227\) | 4.96291 | − | 1.32981i | 0.329400 | − | 0.0882625i | −0.0903288 | − | 0.995912i | \(-0.528792\pi\) |
0.419729 | + | 0.907649i | \(0.362125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.10674 | − | 9.10674i | −0.601790 | − | 0.601790i | 0.338997 | − | 0.940787i | \(-0.389912\pi\) |
−0.940787 | + | 0.338997i | \(0.889912\pi\) | |||||||
\(230\) | −2.32102 | − | 1.34004i | −0.153044 | − | 0.0883599i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.222740 | + | 0.831277i | −0.0146236 | + | 0.0545760i | ||||
\(233\) | 24.0147 | 1.57325 | 0.786626 | − | 0.617430i | \(-0.211826\pi\) | ||||
0.786626 | + | 0.617430i | \(0.211826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6031 | 0.822135 | ||||||||
\(236\) | −2.10359 | + | 7.85072i | −0.136932 | + | 0.511038i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.03954 | − | 1.17753i | −0.132204 | − | 0.0763280i | ||||
\(239\) | 9.02287 | + | 9.02287i | 0.583641 | + | 0.583641i | 0.935902 | − | 0.352261i | \(-0.114587\pi\) |
−0.352261 | + | 0.935902i | \(0.614587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.76565 | + | 1.54490i | −0.371398 | + | 0.0995158i | −0.439690 | − | 0.898150i | \(-0.644912\pi\) |
0.0682920 | + | 0.997665i | \(0.478245\pi\) | |||||||
\(242\) | 7.76977 | − | 7.76977i | 0.499460 | − | 0.499460i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.44963 | − | 4.30104i | 0.476914 | − | 0.275346i | ||||
\(245\) | 5.65301 | + | 1.51472i | 0.361157 | + | 0.0967718i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.64706 | + | 4.55186i | −0.422943 | + | 0.289628i | ||||
\(248\) | 0.174675i | 0.0110919i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 8.89831 | − | 15.4123i | 0.561656 | − | 0.972817i | −0.435696 | − | 0.900094i | \(-0.643498\pi\) |
0.997352 | − | 0.0727231i | \(-0.0231689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0756364 | + | 0.282279i | 0.00475522 | + | 0.0177467i | ||||
\(254\) | 2.77165 | + | 10.3439i | 0.173909 | + | 0.649036i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.30881 | + | 9.19513i | 0.331155 | + | 0.573576i | 0.982739 | − | 0.185000i | \(-0.0592285\pi\) |
−0.651584 | + | 0.758577i | \(0.725895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.6988i | − | 0.726928i | ||||||
\(260\) | −2.97488 | + | 2.03718i | −0.184494 | + | 0.126340i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.84059 | + | 0.761133i | 0.175492 | + | 0.0470230i | ||||
\(263\) | 7.65056 | − | 4.41706i | 0.471754 | − | 0.272367i | −0.245220 | − | 0.969468i | \(-0.578860\pi\) |
0.716974 | + | 0.697100i | \(0.245527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.52908 | − | 2.52908i | 0.155360 | − | 0.155360i | ||||
\(266\) | 2.31204 | − | 0.619509i | 0.141760 | − | 0.0379845i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.69251 | + | 2.69251i | 0.164471 | + | 0.164471i | ||||
\(269\) | −5.68391 | − | 3.28161i | −0.346554 | − | 0.200083i | 0.316612 | − | 0.948555i | \(-0.397455\pi\) |
−0.663167 | + | 0.748472i | \(0.730788\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.18661 | + | 8.16053i | −0.132827 | + | 0.495717i | −0.999997 | − | 0.00229451i | \(-0.999270\pi\) |
0.867170 | + | 0.498012i | \(0.165936\pi\) | |||||||
\(272\) | 2.19842 | 0.133299 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29560 | −0.259507 | ||||||||
\(275\) | 0.0282216 | − | 0.105325i | 0.00170183 | − | 0.00635131i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3496 | + | 8.28477i | 0.862187 | + | 0.497784i | 0.864744 | − | 0.502213i | \(-0.167481\pi\) |
−0.00255715 | + | 0.999997i | \(0.500814\pi\) | |||||||
\(278\) | −2.05686 | − | 2.05686i | −0.123363 | − | 0.123363i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.03475 | − | 0.277260i | 0.0618380 | − | 0.0165695i | ||||
\(281\) | −13.5794 | + | 13.5794i | −0.810079 | + | 0.810079i | −0.984645 | − | 0.174566i | \(-0.944148\pi\) |
0.174566 | + | 0.984645i | \(0.444148\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.69503 | − | 5.59743i | 0.576310 | − | 0.332733i | −0.183356 | − | 0.983047i | \(-0.558696\pi\) |
0.759666 | + | 0.650314i | \(0.225363\pi\) | |||||||
\(284\) | 3.12935 | + | 0.838506i | 0.185693 | + | 0.0497562i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.386444 | + | 0.0722997i | 0.0228509 | + | 0.00427517i | ||||
\(287\) | − | 4.28500i | − | 0.252936i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.08347 | + | 10.5369i | 0.357851 | + | 0.619816i | ||||
\(290\) | −0.430301 | + | 0.745303i | −0.0252681 | + | 0.0437657i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.39146 | − | 12.6571i | −0.198470 | − | 0.740701i | ||||
\(293\) | −3.44063 | − | 12.8406i | −0.201004 | − | 0.750157i | −0.990631 | − | 0.136569i | \(-0.956392\pi\) |
0.789626 | − | 0.613588i | \(-0.210274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.06383 | + | 7.03876i | −0.236605 | + | 0.409813i | ||||
\(296\) | 5.46034 | + | 9.45759i | 0.317376 | + | 0.549711i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.9395i | 0.865424i | ||||||||
\(299\) | 6.28816 | − | 7.33732i | 0.363654 | − | 0.424328i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5790 | − | 3.37054i | −0.725043 | − | 0.194275i | ||||
\(302\) | 10.7540 | − | 6.20884i | 0.618825 | − | 0.357279i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.57996 | + | 1.57996i | −0.0906168 | + | 0.0906168i | ||||
\(305\) | 8.30898 | − | 2.22638i | 0.475771 | − | 0.127482i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6353 | + | 10.6353i | 0.606991 | + | 0.606991i | 0.942159 | − | 0.335167i | \(-0.108793\pi\) |
−0.335167 | + | 0.942159i | \(0.608793\pi\) | |||||||
\(308\) | −0.101160 | − | 0.0584045i | −0.00576411 | − | 0.00332791i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0452092 | + | 0.168723i | −0.00256771 | + | 0.00958282i | ||||
\(311\) | 14.2635 | 0.808809 | 0.404404 | − | 0.914580i | \(-0.367479\pi\) | ||||
0.404404 | + | 0.914580i | \(0.367479\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1236 | 0.854838 | 0.427419 | − | 0.904054i | \(-0.359423\pi\) | ||||
0.427419 | + | 0.904054i | \(0.359423\pi\) | |||||||
\(314\) | 1.60394 | − | 5.98600i | 0.0905157 | − | 0.337809i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.10337 | − | 1.79173i | −0.174578 | − | 0.100793i | ||||
\(317\) | 5.54215 | + | 5.54215i | 0.311278 | + | 0.311278i | 0.845405 | − | 0.534126i | \(-0.179359\pi\) |
−0.534126 | + | 0.845405i | \(0.679359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0906424 | − | 0.0242876i | 0.00507500 | − | 0.00135984i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.48640 | + | 1.43552i | −0.138562 | + | 0.0799985i | ||||
\(323\) | 4.74477 | + | 1.27136i | 0.264006 | + | 0.0707403i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.40077 | + | 1.19781i | −0.188641 | + | 0.0664423i | ||||
\(326\) | 14.1330i | 0.782755i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000 | + | 3.46410i | 0.110432 | + | 0.191273i | ||||
\(329\) | 6.75053 | − | 11.6923i | 0.372169 | − | 0.644616i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.27247 | − | 30.8733i | −0.454696 | − | 1.69695i | −0.688981 | − | 0.724780i | \(-0.741941\pi\) |
0.234285 | − | 0.972168i | \(-0.424725\pi\) | |||||||
\(332\) | −2.28068 | − | 8.51162i | −0.125169 | − | 0.467136i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.956444 | + | 1.65661i | −0.0523343 | + | 0.0906456i | ||||
\(335\) | 1.90389 | + | 3.29763i | 0.104021 | + | 0.180169i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.3442i | − | 0.563483i | −0.959490 | − | 0.281742i | \(-0.909088\pi\) | ||
0.959490 | − | 0.281742i | \(-0.0909121\pi\) | |||||||
\(338\) | −5.24736 | − | 11.8939i | −0.285419 | − | 0.646944i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.12351 | + | 0.568994i | 0.115164 | + | 0.0308580i | ||||
\(341\) | 0.0164948 | − | 0.00952327i | 0.000893243 | − | 0.000515714i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.73556 | − | 9.73556i | 0.525671 | − | 0.525671i | ||||
\(344\) | 11.7424 | − | 3.14636i | 0.633107 | − | 0.169640i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.01484 | + | 8.01484i | 0.430881 | + | 0.430881i | ||||
\(347\) | −27.4249 | − | 15.8338i | −1.47224 | − | 0.850000i | −0.472731 | − | 0.881207i | \(-0.656732\pi\) |
−0.999513 | + | 0.0312067i | \(0.990065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.22925 | + | 15.7838i | −0.226386 | + | 0.844886i | 0.755458 | + | 0.655197i | \(0.227414\pi\) |
−0.981844 | + | 0.189689i | \(0.939252\pi\) | |||||||
\(350\) | 1.07125 | 0.0572607 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.109040 | 0.00581185 | ||||||||
\(353\) | 0.337999 | − | 1.26143i | 0.0179899 | − | 0.0671392i | −0.956347 | − | 0.292232i | \(-0.905602\pi\) |
0.974337 | + | 0.225093i | \(0.0722686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.80570 | + | 1.61987i | 0.148911 | + | 0.0859737i | ||||
\(356\) | 0.356131 | + | 0.356131i | 0.0188749 | + | 0.0188749i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.79726 | − | 2.08927i | 0.412098 | − | 0.110421i | ||||
\(359\) | −23.5889 | + | 23.5889i | −1.24498 | + | 1.24498i | −0.287064 | + | 0.957911i | \(0.592679\pi\) |
−0.957911 | + | 0.287064i | \(0.907321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1308 | − | 7.00373i | 0.638464 | − | 0.368618i | ||||
\(362\) | 5.16555 | + | 1.38411i | 0.271495 | + | 0.0727470i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.296529 | + | 3.85105i | 0.0155423 | + | 0.201850i | ||||
\(365\) | − | 13.1036i | − | 0.685874i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.3778 | − | 21.4390i | −0.646118 | − | 1.11911i | −0.984042 | − | 0.177935i | \(-0.943058\pi\) |
0.337925 | − | 0.941173i | \(-0.390275\pi\) | |||||||
\(368\) | 1.34004 | − | 2.32102i | 0.0698546 | − | 0.120992i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.82648 | + | 10.5486i | 0.146942 | + | 0.548394i | ||||
\(371\) | −0.991665 | − | 3.70095i | −0.0514847 | − | 0.192144i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4375 | + | 19.8104i | −0.592212 | + | 1.02574i | 0.401722 | + | 0.915762i | \(0.368412\pi\) |
−0.993934 | + | 0.109980i | \(0.964921\pi\) | |||||||
\(374\) | −0.119858 | − | 0.207600i | −0.00619771 | − | 0.0107347i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.6031i | 0.649955i | ||||||||
\(377\) | −2.35608 | − | 2.01919i | −0.121344 | − | 0.103994i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.83077 | − | 2.09825i | −0.402240 | − | 0.107780i | 0.0520266 | − | 0.998646i | \(-0.483432\pi\) |
−0.454266 | + | 0.890866i | \(0.650099\pi\) | |||||||
\(380\) | −1.93504 | + | 1.11720i | −0.0992657 | + | 0.0573111i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.604389 | − | 0.604389i | 0.0309232 | − | 0.0309232i | ||||
\(383\) | 9.70618 | − | 2.60076i | 0.495963 | − | 0.132893i | −0.00216304 | − | 0.999998i | \(-0.500689\pi\) |
0.498126 | + | 0.867105i | \(0.334022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0825965 | − | 0.0825965i | −0.00420951 | − | 0.00420951i | ||||
\(386\) | −14.4995 | − | 8.37129i | −0.738005 | − | 0.426087i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.35837 | + | 5.06950i | −0.0689607 | + | 0.257365i | ||||
\(389\) | 0.817452 | 0.0414465 | 0.0207232 | − | 0.999785i | \(-0.493403\pi\) | ||||
0.0207232 | + | 0.999785i | \(0.493403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.89197 | −0.297970 | ||||||||
\(392\) | −1.51472 | + | 5.65301i | −0.0765048 | + | 0.285520i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.7494 | − | 10.8250i | −0.944581 | − | 0.545354i | ||||
\(395\) | −2.53389 | − | 2.53389i | −0.127494 | − | 0.127494i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8506 | + | 2.90742i | −0.544577 | + | 0.145919i | −0.520611 | − | 0.853794i | \(-0.674296\pi\) |
−0.0239659 | + | 0.999713i | \(0.507629\pi\) | |||||||
\(398\) | 4.99726 | − | 4.99726i | 0.250490 | − | 0.250490i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.866025 | + | 0.500000i | −0.0433013 | + | 0.0250000i | ||||
\(401\) | 2.69200 | + | 0.721320i | 0.134432 | + | 0.0360210i | 0.325408 | − | 0.945574i | \(-0.394498\pi\) |
−0.190975 | + | 0.981595i | \(0.561165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.567988 | − | 0.272097i | −0.0282935 | − | 0.0135541i | ||||
\(404\) | − | 8.70676i | − | 0.433178i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.460960 | + | 0.798406i | 0.0228770 | + | 0.0396242i | ||||
\(407\) | 0.595396 | − | 1.03126i | 0.0295127 | − | 0.0511174i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.03354 | − | 15.0534i | −0.199446 | − | 0.744341i | −0.991071 | − | 0.133335i | \(-0.957432\pi\) |
0.791625 | − | 0.611007i | \(-0.209235\pi\) | |||||||
\(410\) | 1.03528 | + | 3.86370i | 0.0511286 | + | 0.190815i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.83215 | − | 3.17337i | 0.0902635 | − | 0.156341i | ||||
\(413\) | 4.35338 | + | 7.54028i | 0.214216 | + | 0.371033i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.81187i | − | 0.432558i | ||||||
\(416\) | −2.03718 | − | 2.97488i | −0.0998808 | − | 0.145856i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.235337 | + | 0.0630583i | 0.0115107 | + | 0.00308428i | ||||
\(419\) | −16.5157 | + | 9.53535i | −0.806845 | + | 0.465832i | −0.845859 | − | 0.533406i | \(-0.820912\pi\) |
0.0390138 | + | 0.999239i | \(0.487578\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.84339 | + | 1.84339i | −0.0898414 | + | 0.0898414i | −0.750599 | − | 0.660758i | \(-0.770235\pi\) |
0.660758 | + | 0.750599i | \(0.270235\pi\) | |||||||
\(422\) | 21.9922 | − | 5.89279i | 1.07056 | − | 0.286857i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.52908 | + | 2.52908i | 0.122823 | + | 0.122823i | ||||
\(425\) | 1.90389 | + | 1.09921i | 0.0923522 | + | 0.0533196i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.38502 | − | 8.90100i | 0.115419 | − | 0.430749i | ||||
\(428\) | 1.66528 | 0.0804944 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.1566 | 0.586244 | ||||||||
\(431\) | −5.92299 | + | 22.1049i | −0.285300 | + | 1.06476i | 0.663319 | + | 0.748337i | \(0.269147\pi\) |
−0.948620 | + | 0.316419i | \(0.897519\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0124 | + | 10.3995i | 0.865623 | + | 0.499768i | 0.865891 | − | 0.500232i | \(-0.166752\pi\) |
−0.000268392 | 1.00000i | \(0.500085\pi\) | ||||||||
\(434\) | 0.132314 | + | 0.132314i | 0.00635128 | + | 0.00635128i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.63849 | + | 1.24288i | −0.222143 | + | 0.0595231i | ||||
\(437\) | 4.23442 | − | 4.23442i | 0.202560 | − | 0.202560i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8169 | − | 15.4827i | 1.27990 | − | 0.738950i | 0.303069 | − | 0.952968i | \(-0.401989\pi\) |
0.976830 | + | 0.214018i | \(0.0686553\pi\) | |||||||
\(440\) | 0.105325 | + | 0.0282216i | 0.00502115 | + | 0.00134541i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.42456 | + | 7.14858i | −0.162890 | + | 0.340023i | ||||
\(443\) | − | 24.8913i | − | 1.18262i | −0.806444 | − | 0.591310i | \(-0.798611\pi\) | ||
0.806444 | − | 0.591310i | \(-0.201389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.251822 | + | 0.436169i | 0.0119375 | + | 0.0206764i | ||||
\(446\) | −7.52867 | + | 13.0400i | −0.356493 | + | 0.617464i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.277260 | + | 1.03475i | 0.0130993 | + | 0.0488873i | ||||
\(449\) | 10.3261 | + | 38.5375i | 0.487318 | + | 1.81870i | 0.569386 | + | 0.822070i | \(0.307181\pi\) |
−0.0820676 | + | 0.996627i | \(0.526152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.218080 | − | 0.377726i | 0.0102690 | − | 0.0177864i | ||||
\(452\) | 4.93202 | + | 8.54251i | 0.231983 | + | 0.401806i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.13799i | 0.241138i | ||||||||
\(455\) | −0.710300 | + | 3.79657i | −0.0332994 | + | 0.177986i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.8773 | + | 4.79022i | 0.836266 | + | 0.224077i | 0.651445 | − | 0.758695i | \(-0.274163\pi\) |
0.184821 | + | 0.982772i | \(0.440830\pi\) | |||||||
\(458\) | 11.1534 | − | 6.43944i | 0.521166 | − | 0.300895i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.89511 | − | 1.89511i | 0.0883599 | − | 0.0883599i | ||||
\(461\) | 12.6049 | − | 3.37748i | 0.587070 | − | 0.157305i | 0.0469562 | − | 0.998897i | \(-0.485048\pi\) |
0.540114 | + | 0.841592i | \(0.318381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8003 | − | 17.8003i | −0.827248 | − | 0.827248i | 0.159887 | − | 0.987135i | \(-0.448887\pi\) |
−0.987135 | + | 0.159887i | \(0.948887\pi\) | |||||||
\(464\) | −0.745303 | − | 0.430301i | −0.0345998 | − | 0.0199762i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.21545 | + | 23.1964i | −0.287925 | + | 1.07455i | ||||
\(467\) | −42.5798 | −1.97036 | −0.985180 | − | 0.171526i | \(-0.945130\pi\) | ||||
−0.985180 | + | 0.171526i | \(0.945130\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.07909 | 0.188355 | ||||||||
\(470\) | −3.26192 | + | 12.1737i | −0.150461 | + | 0.561529i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.03876 | − | 4.06383i | −0.323985 | − | 0.187053i | ||||
\(473\) | −0.937310 | − | 0.937310i | −0.0430976 | − | 0.0430976i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.15826 | + | 0.578305i | −0.0990279 | + | 0.0265344i | ||||
\(476\) | 1.66528 | − | 1.66528i | 0.0763280 | − | 0.0763280i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.0507 | + | 6.38013i | −0.505448 | + | 0.291820i | ||||
\(479\) | −28.3109 | − | 7.58589i | −1.29356 | − | 0.346608i | −0.454548 | − | 0.890722i | \(-0.650199\pi\) |
−0.839011 | + | 0.544114i | \(0.816866\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.2589 | + | 3.02291i | −1.79005 | + | 0.137833i | ||||
\(482\) | − | 5.96904i | − | 0.271882i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.49406 | + | 9.51598i | 0.249730 | + | 0.432545i | ||||
\(485\) | −2.62416 | + | 4.54519i | −0.119157 | + | 0.206386i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.16056 | − | 4.33128i | −0.0525901 | − | 0.196269i | 0.934633 | − | 0.355614i | \(-0.115728\pi\) |
−0.987223 | + | 0.159345i | \(0.949062\pi\) | |||||||
\(488\) | 2.22638 | + | 8.30898i | 0.100784 | + | 0.376130i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.92621 | + | 5.06835i | −0.132193 | + | 0.228965i | ||||
\(491\) | 0.676664 | + | 1.17202i | 0.0305374 | + | 0.0528923i | 0.880890 | − | 0.473321i | \(-0.156945\pi\) |
−0.850353 | + | 0.526213i | \(0.823611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.89197i | 0.0852099i | ||||||||
\(494\) | −2.67637 | − | 7.59868i | −0.120416 | − | 0.341881i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.168723 | − | 0.0452092i | −0.00757588 | − | 0.00202995i | ||||
\(497\) | 3.00560 | − | 1.73529i | 0.134820 | − | 0.0778382i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0655 | − | 13.0655i | 0.584890 | − | 0.584890i | −0.351353 | − | 0.936243i | \(-0.614278\pi\) |
0.936243 | + | 0.351353i | \(0.114278\pi\) | |||||||
\(500\) | −0.965926 | + | 0.258819i | −0.0431975 | + | 0.0115747i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.5841 | + | 12.5841i | 0.561656 | + | 0.561656i | ||||
\(503\) | −21.6756 | − | 12.5144i | −0.966466 | − | 0.557989i | −0.0683089 | − | 0.997664i | \(-0.521760\pi\) |
−0.898157 | + | 0.439675i | \(0.855094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.25348 | − | 8.41008i | 0.100278 | − | 0.374244i | ||||
\(506\) | −0.292237 | −0.0129915 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.7088 | −0.475127 | ||||||||
\(509\) | −9.53269 | + | 35.5765i | −0.422529 | + | 1.57690i | 0.346731 | + | 0.937965i | \(0.387292\pi\) |
−0.769260 | + | 0.638936i | \(0.779375\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1566 | − | 7.01862i | −0.537777 | − | 0.310486i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2558 | + | 2.74804i | −0.452366 | + | 0.121211i | ||||
\(515\) | 2.59105 | − | 2.59105i | 0.114175 | − | 0.114175i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.19013 | − | 0.687121i | 0.0523418 | − | 0.0302195i | ||||
\(518\) | 11.3002 | + | 3.02787i | 0.496501 | + | 0.133037i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.19781 | − | 3.40077i | −0.0525272 | − | 0.149134i | ||||
\(521\) | − | 20.3941i | − | 0.893480i | −0.894664 | − | 0.446740i | \(-0.852585\pi\) | ||
0.894664 | − | 0.446740i | \(-0.147415\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.63613 | + | 4.56591i | 0.115270 | + | 0.199653i | 0.917888 | − | 0.396840i | \(-0.129893\pi\) |
−0.802618 | + | 0.596494i | \(0.796560\pi\) | |||||||
\(524\) | −1.47040 | + | 2.54680i | −0.0642346 | + | 0.111258i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.28644 | + | 8.53310i | 0.0996933 | + | 0.372061i | ||||
\(527\) | 0.0993889 | + | 0.370924i | 0.00432945 | + | 0.0161577i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.90857 | − | 13.6980i | 0.343851 | − | 0.595567i | ||||
\(530\) | 1.78833 | + | 3.09748i | 0.0776801 | + | 0.134546i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.39360i | 0.103776i | ||||||||
\(533\) | −14.3796 | + | 1.10722i | −0.622851 | + | 0.0479592i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.60854 | + | 0.431006i | 0.0695431 | + | 0.0186340i | ||||
\(536\) | −3.29763 | + | 1.90389i | −0.142436 | + | 0.0822355i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.64090 | − | 4.64090i | 0.200083 | − | 0.200083i | ||||
\(539\) | 0.616404 | − | 0.165165i | 0.0265504 | − | 0.00711415i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3568 | − | 17.3568i | −0.746227 | − | 0.746227i | 0.227541 | − | 0.973768i | \(-0.426931\pi\) |
−0.973768 | + | 0.227541i | \(0.926931\pi\) | |||||||
\(542\) | −7.31653 | − | 4.22420i | −0.314272 | − | 0.181445i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.568994 | + | 2.12351i | −0.0243954 | + | 0.0910449i | ||||
\(545\) | −4.80212 | −0.205700 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.4243 | 1.00155 | 0.500775 | − | 0.865578i | \(-0.333049\pi\) | ||||
0.500775 | + | 0.865578i | \(0.333049\pi\) | |||||||
\(548\) | 1.11178 | − | 4.14923i | 0.0474930 | − | 0.177246i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0944314 | + | 0.0545200i | 0.00402657 | + | 0.00232474i | ||||
\(551\) | −1.35971 | − | 1.35971i | −0.0579257 | − | 0.0579257i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.70799 | + | 0.993552i | −0.157680 | + | 0.0422501i | ||||
\(554\) | −11.7164 | + | 11.7164i | −0.497784 | + | 0.497784i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.51913 | − | 1.45442i | 0.106835 | − | 0.0616813i | ||||
\(557\) | −21.2427 | − | 5.69197i | −0.900083 | − | 0.241177i | −0.221031 | − | 0.975267i | \(-0.570942\pi\) |
−0.679052 | + | 0.734090i | \(0.737609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.06052 | + | 43.0837i | −0.340924 | + | 1.82225i | ||||
\(560\) | 1.07125i | 0.0452686i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.60209 | − | 16.6313i | −0.405040 | − | 0.701549i | ||||
\(563\) | 18.3176 | − | 31.7270i | 0.771994 | − | 1.33713i | −0.164474 | − | 0.986381i | \(-0.552593\pi\) |
0.936468 | − | 0.350752i | \(-0.114074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.55300 | + | 9.52793i | 0.107406 | + | 0.400843i | ||||
\(566\) | 2.89744 | + | 10.8134i | 0.121789 | + | 0.454521i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.61987 | + | 2.80570i | −0.0679682 | + | 0.117724i | ||||
\(569\) | −8.76469 | − | 15.1809i | −0.367435 | − | 0.636416i | 0.621729 | − | 0.783232i | \(-0.286431\pi\) |
−0.989164 | + | 0.146817i | \(0.953097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.1460i | − | 0.675689i | −0.941202 | − | 0.337844i | \(-0.890302\pi\) | ||
0.941202 | − | 0.337844i | \(-0.109698\pi\) | |||||||
\(572\) | −0.169855 | + | 0.354564i | −0.00710200 | + | 0.0148251i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.13899 | + | 1.10904i | 0.172758 | + | 0.0462904i | ||||
\(575\) | 2.32102 | − | 1.34004i | 0.0967934 | − | 0.0558837i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0194 | + | 25.0194i | −1.04157 | + | 1.04157i | −0.0424718 | + | 0.999098i | \(0.513523\pi\) |
−0.999098 | + | 0.0424718i | \(0.986477\pi\) | |||||||
\(578\) | −11.7524 | + | 3.14903i | −0.488834 | + | 0.130983i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.608537 | − | 0.608537i | −0.0252681 | − | 0.0252681i | ||||
\(581\) | −8.17504 | − | 4.71986i | −0.339158 | − | 0.195813i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.100939 | − | 0.376710i | 0.00418047 | − | 0.0156017i | ||||
\(584\) | 13.1036 | 0.542231 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.2936 | 0.549153 | ||||||||
\(587\) | −11.5222 | + | 43.0015i | −0.475573 | + | 1.77486i | 0.143632 | + | 0.989631i | \(0.454122\pi\) |
−0.619205 | + | 0.785230i | \(0.712545\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.338004 | − | 0.195147i | −0.0139272 | − | 0.00804087i | ||||
\(590\) | −5.74712 | − | 5.74712i | −0.236605 | − | 0.236605i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.5486 | + | 2.82648i | −0.433544 | + | 0.116168i | ||||
\(593\) | −31.2099 | + | 31.2099i | −1.28164 | + | 1.28164i | −0.341899 | + | 0.939737i | \(0.611070\pi\) |
−0.939737 | + | 0.341899i | \(0.888930\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.03954 | − | 1.17753i | 0.0836131 | − | 0.0482741i | ||||
\(596\) | −14.4305 | − | 3.86664i | −0.591096 | − | 0.158384i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.45981 | + | 7.97294i | 0.223268 | + | 0.326038i | ||||
\(599\) | 6.90043i | 0.281944i | 0.990014 | + | 0.140972i | \(0.0450227\pi\) | ||||
−0.990014 | + | 0.140972i | \(0.954977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.69946 | + | 11.6038i | 0.273277 | + | 0.473329i | 0.969699 | − | 0.244303i | \(-0.0785592\pi\) |
−0.696422 | + | 0.717632i | \(0.745226\pi\) | |||||||
\(602\) | 6.51139 | − | 11.2781i | 0.265384 | − | 0.459659i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.21393 | + | 11.9946i | 0.130773 | + | 0.488052i | ||||
\(605\) | 2.84393 | + | 10.6137i | 0.115622 | + | 0.431508i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.48852 | + | 9.50640i | −0.222772 | + | 0.385853i | −0.955649 | − | 0.294509i | \(-0.904844\pi\) |
0.732876 | + | 0.680362i | \(0.238177\pi\) | |||||||
\(608\) | −1.11720 | − | 1.93504i | −0.0453084 | − | 0.0784764i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.60209i | 0.348288i | ||||||||
\(611\) | −40.9813 | − | 19.6323i | −1.65793 | − | 0.794237i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5858 | + | 6.31980i | 0.952622 | + | 0.255254i | 0.701475 | − | 0.712694i | \(-0.252525\pi\) |
0.251148 | + | 0.967949i | \(0.419192\pi\) | |||||||
\(614\) | −13.0256 | + | 7.52033i | −0.525670 | + | 0.303496i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0825965 | − | 0.0825965i | 0.00332791 | − | 0.00332791i | ||||
\(617\) | −36.8960 | + | 9.88625i | −1.48538 | + | 0.398006i | −0.908173 | − | 0.418595i | \(-0.862523\pi\) |
−0.577204 | + | 0.816600i | \(0.695856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6963 | + | 19.6963i | 0.791661 | + | 0.791661i | 0.981764 | − | 0.190103i | \(-0.0608823\pi\) |
−0.190103 | + | 0.981764i | \(0.560882\pi\) | |||||||
\(620\) | −0.151273 | − | 0.0873374i | −0.00607526 | − | 0.00350756i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.69167 | + | 13.7775i | −0.148022 | + | 0.552427i | ||||
\(623\) | 0.539530 | 0.0216158 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −3.91428 | + | 14.6083i | −0.156446 | + | 0.583865i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.36690 | + | 3.09858i | 0.214162 | + | 0.123647i | ||||
\(629\) | 16.9764 | + | 16.9764i | 0.676895 | + | 0.676895i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.5943 | − | 10.0734i | 1.49661 | − | 0.401015i | 0.584645 | − | 0.811289i | \(-0.301234\pi\) |
0.911962 | + | 0.410274i | \(0.134567\pi\) | |||||||
\(632\) | 2.53389 | − | 2.53389i | 0.100793 | − | 0.100793i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.78772 | + | 3.91889i | −0.269575 | + | 0.155639i | ||||
\(635\) | −10.3439 | − | 2.77165i | −0.410487 | − | 0.109990i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0223 | − | 13.7313i | −0.634826 | − | 0.544053i | ||||
\(638\) | 0.0938399i | 0.00371516i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 16.5081 | − | 28.5928i | 0.652030 | − | 1.12935i | −0.330600 | − | 0.943771i | \(-0.607251\pi\) |
0.982630 | − | 0.185578i | \(-0.0594156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6305 | − | 47.1375i | −0.498097 | − | 1.85892i | −0.511944 | − | 0.859019i | \(-0.671074\pi\) |
0.0138471 | − | 0.999904i | \(-0.495592\pi\) | |||||||
\(644\) | −0.743081 | − | 2.77322i | −0.0292815 | − | 0.109280i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.45608 | + | 4.25405i | −0.0966330 | + | 0.167373i | ||||
\(647\) | 12.2654 | + | 21.2444i | 0.482204 | + | 0.835202i | 0.999791 | − | 0.0204285i | \(-0.00650305\pi\) |
−0.517587 | + | 0.855630i | \(0.673170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.886240i | 0.0347880i | ||||||||
\(650\) | −0.276806 | − | 3.59491i | −0.0108572 | − | 0.141004i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.6514 | − | 3.65789i | −0.534632 | − | 0.143254i | ||||
\(653\) | −18.8702 | + | 10.8947i | −0.738446 | + | 0.426342i | −0.821504 | − | 0.570203i | \(-0.806865\pi\) |
0.0830579 | + | 0.996545i | \(0.473531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.07945 | + | 2.07945i | −0.0812510 | + | 0.0812510i | ||||
\(656\) | −3.86370 | + | 1.03528i | −0.150852 | + | 0.0404207i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.54670 | + | 9.54670i | 0.372169 | + | 0.372169i | ||||
\(659\) | −41.2109 | − | 23.7931i | −1.60535 | − | 0.926848i | −0.990392 | − | 0.138285i | \(-0.955841\pi\) |
−0.614955 | − | 0.788562i | \(-0.710826\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.133840 | + | 0.499497i | −0.00520577 | + | 0.0194282i | −0.968480 | − | 0.249092i | \(-0.919868\pi\) |
0.963274 | + | 0.268520i | \(0.0865346\pi\) | |||||||
\(662\) | 31.9624 | 1.24225 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.81187 | 0.341967 | ||||||||
\(665\) | −0.619509 | + | 2.31204i | −0.0240235 | + | 0.0896570i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.99748 | + | 1.15324i | 0.0773426 | + | 0.0446538i | ||||
\(668\) | −1.35262 | − | 1.35262i | −0.0523343 | − | 0.0523343i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.67803 | + | 0.985526i | −0.142095 | + | 0.0380742i | ||||
\(671\) | 0.663246 | − | 0.663246i | 0.0256043 | − | 0.0256043i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7680 | + | 10.2584i | −0.684906 | + | 0.395431i | −0.801701 | − | 0.597725i | \(-0.796071\pi\) |
0.116795 | + | 0.993156i | \(0.462738\pi\) | |||||||
\(674\) | 9.99171 | + | 2.67727i | 0.384866 | + | 0.103125i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.8468 | − | 1.99019i | 0.494106 | − | 0.0765456i | ||||
\(677\) | 32.3765i | 1.24433i | 0.782886 | + | 0.622165i | \(0.213747\pi\) | ||||
−0.782886 | + | 0.622165i | \(0.786253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.81114 | + | 4.86903i | 0.107882 | + | 0.186856i | ||||
\(680\) | −1.09921 | + | 1.90389i | −0.0421528 | + | 0.0730109i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.00492961 | + | 0.0183975i | 0.000188764 | + | 0.000704478i | ||||
\(683\) | −6.54431 | − | 24.4237i | −0.250411 | − | 0.934547i | −0.970586 | − | 0.240754i | \(-0.922605\pi\) |
0.720175 | − | 0.693793i | \(-0.244062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.14780 | − | 3.72010i | 0.0820633 | − | 0.142138i | ||||
\(686\) | 6.88408 | + | 11.9236i | 0.262835 | + | 0.455244i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.1566i | 0.463466i | ||||||||
\(689\) | −12.1634 | + | 4.28415i | −0.463389 | + | 0.163213i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.8925 | + | 8.27763i | 1.17521 | + | 0.314896i | 0.793024 | − | 0.609191i | \(-0.208506\pi\) |
0.382183 | + | 0.924086i | \(0.375172\pi\) | |||||||
\(692\) | −9.81614 | + | 5.66735i | −0.373154 | + | 0.215440i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.3923 | − | 22.3923i | 0.850000 | − | 0.850000i | ||||
\(695\) | 2.80973 | − | 0.752865i | 0.106579 | − | 0.0285578i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.21808 | + | 6.21808i | 0.235527 | + | 0.235527i | ||||
\(698\) | −14.1513 | − | 8.17028i | −0.535636 | − | 0.309250i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.277260 | + | 1.03475i | −0.0104794 | + | 0.0391098i | ||||
\(701\) | −18.5210 | −0.699528 | −0.349764 | − | 0.936838i | \(-0.613738\pi\) | ||||
−0.349764 | + | 0.936838i | \(0.613738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4012 | −0.920307 | ||||||||
\(704\) | −0.0282216 | + | 0.105325i | −0.00106364 | + | 0.00396957i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.13097 | + | 0.652964i | 0.0425645 | + | 0.0245746i | ||||
\(707\) | −6.59527 | − | 6.59527i | −0.248041 | − | 0.248041i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.77434 | − | 2.35108i | 0.329527 | − | 0.0882966i | −0.0902623 | − | 0.995918i | \(-0.528771\pi\) |
0.419790 | + | 0.907621i | \(0.362104\pi\) | |||||||
\(710\) | −2.29084 | + | 2.29084i | −0.0859737 | + | 0.0859737i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.436169 | + | 0.251822i | −0.0163461 | + | 0.00943744i | ||||
\(713\) | 0.452192 | + | 0.121165i | 0.0169347 | + | 0.00453765i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.255835 | + | 0.298521i | −0.00956770 | + | 0.0111640i | ||||
\(716\) | 8.07231i | 0.301677i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.6799 | − | 28.8904i | −0.622488 | − | 1.07818i | ||||
\(719\) | −17.0038 | + | 29.4515i | −0.634135 | + | 1.09835i | 0.352563 | + | 0.935788i | \(0.385310\pi\) |
−0.986698 | + | 0.162566i | \(0.948023\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.01596 | − | 3.79162i | −0.0378364 | − | 0.141207i | ||||
\(722\) | 3.62540 | + | 13.5302i | 0.134923 | + | 0.503541i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.67389 | + | 4.63131i | −0.0993742 | + | 0.172121i | ||||
\(725\) | −0.430301 | − | 0.745303i | −0.0159810 | − | 0.0276798i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.7524i | 0.806752i | 0.915034 | + | 0.403376i | \(0.132163\pi\) | ||||
−0.915034 | + | 0.403376i | \(0.867837\pi\) | |||||||
\(728\) | −3.79657 | − | 0.710300i | −0.140710 | − | 0.0263255i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.6571 | + | 3.39146i | 0.468461 | + | 0.125524i | ||||
\(731\) | 23.1449 | − | 13.3627i | 0.856043 | − | 0.494237i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.3306 | + | 11.3306i | −0.418506 | + | 0.418506i | −0.884689 | − | 0.466182i | \(-0.845629\pi\) |
0.466182 | + | 0.884689i | \(0.345629\pi\) | |||||||
\(734\) | 23.9121 | − | 6.40724i | 0.882613 | − | 0.236495i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.89511 | + | 1.89511i | 0.0698546 | + | 0.0698546i | ||||
\(737\) | 0.359574 | + | 0.207600i | 0.0132451 | + | 0.00764705i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.06627 | − | 15.1755i | 0.149580 | − | 0.558240i | −0.849929 | − | 0.526898i | \(-0.823355\pi\) |
0.999509 | − | 0.0313424i | \(-0.00997824\pi\) | |||||||
\(740\) | −10.9207 | −0.401452 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.83150 | 0.140659 | ||||||||
\(743\) | −5.97479 | + | 22.2982i | −0.219194 | + | 0.818042i | 0.765454 | + | 0.643490i | \(0.222514\pi\) |
−0.984648 | + | 0.174552i | \(0.944152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.9380 | − | 7.46977i | −0.474012 | − | 0.273671i | ||||
\(746\) | −16.1751 | − | 16.1751i | −0.592212 | − | 0.592212i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.231548 | − | 0.0620431i | 0.00846623 | − | 0.00226852i | ||||
\(749\) | 1.26143 | − | 1.26143i | 0.0460917 | − | 0.0460917i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.5841 | + | 23.4312i | −1.48093 | + | 0.855018i | −0.999766 | − | 0.0216108i | \(-0.993121\pi\) |
−0.481168 | + | 0.876629i | \(0.659787\pi\) | |||||||
\(752\) | −12.1737 | − | 3.26192i | −0.443928 | − | 0.118950i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.56019 | − | 1.75320i | 0.0932365 | − | 0.0638476i | ||||
\(755\) | 12.4177i | 0.451926i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.79868 | + | 4.84746i | 0.101720 | + | 0.176184i | 0.912393 | − | 0.409315i | \(-0.134232\pi\) |
−0.810673 | + | 0.585499i | \(0.800899\pi\) | |||||||
\(758\) | 4.05351 | − | 7.02088i | 0.147230 | − | 0.255010i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.578305 | − | 2.15826i | −0.0209773 | − | 0.0782884i | ||||
\(761\) | −0.436236 | − | 1.62806i | −0.0158136 | − | 0.0590170i | 0.957568 | − | 0.288207i | \(-0.0930590\pi\) |
−0.973382 | + | 0.229190i | \(0.926392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.57214 | + | 4.45507i | −0.0931176 | + | 0.161284i | ||||
\(764\) | 0.427368 | + | 0.740223i | 0.0154616 | + | 0.0267803i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.0486i | 0.363070i | ||||||||
\(767\) | 24.1788 | − | 16.5575i | 0.873047 | − | 0.597856i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.70684 | + | 2.33299i | 0.313977 | + | 0.0841298i | 0.412366 | − | 0.911018i | \(-0.364702\pi\) |
−0.0983896 | + | 0.995148i | \(0.531369\pi\) | |||||||
\(770\) | 0.101160 | − | 0.0584045i | 0.00364554 | − | 0.00210475i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.8388 | − | 11.8388i | 0.426087 | − | 0.426087i | ||||
\(773\) | 11.2273 | − | 3.00836i | 0.403819 | − | 0.108203i | −0.0511917 | − | 0.998689i | \(-0.516302\pi\) |
0.455011 | + | 0.890486i | \(0.349635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.123514 | − | 0.123514i | −0.00443675 | − | 0.00443675i | ||||
\(776\) | −4.54519 | − | 2.62416i | −0.163163 | − | 0.0942020i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.211572 | + | 0.789598i | −0.00758523 | + | 0.0283085i | ||||
\(779\) | −8.93759 | −0.320222 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.353261 | 0.0126407 | ||||||||
\(782\) | 1.52495 | − | 5.69120i | 0.0545322 | − | 0.203517i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.06835 | − | 2.92621i | −0.181012 | − | 0.104508i | ||||
\(785\) | 4.38205 | + | 4.38205i | 0.156402 | + | 0.156402i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.36173 | − | 2.24052i | 0.298064 | − | 0.0798659i | −0.106688 | − | 0.994293i | \(-0.534025\pi\) |
0.404752 | + | 0.914427i | \(0.367358\pi\) | |||||||
\(788\) | 15.3088 | − | 15.3088i | 0.545354 | − | 0.545354i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.10337 | − | 1.79173i | 0.110413 | − | 0.0637470i | ||||
\(791\) | 10.2068 | + | 2.73490i | 0.362912 | + | 0.0972420i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.4863 | − | 5.70368i | −1.08260 | − | 0.202543i | ||||
\(794\) | − | 11.2334i | − | 0.398658i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.53360 | + | 6.12037i | 0.125245 | + | 0.216931i | ||||
\(797\) | 20.2024 | − | 34.9917i | 0.715607 | − | 1.23947i | −0.247118 | − | 0.968986i | \(-0.579483\pi\) |
0.962725 | − | 0.270483i | \(-0.0871833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.17108 | + | 26.7628i | 0.253695 | + | 0.946801i | ||||
\(800\) | −0.258819 | − | 0.965926i | −0.00915064 | − | 0.0341506i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.39348 | + | 2.41359i | −0.0492056 | + | 0.0852267i | ||||
\(803\) | −0.714408 | − | 1.23739i | −0.0252109 | − | 0.0436666i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 2.87104i | − | 0.101191i | ||||||
\(806\) | 0.409832 | − | 0.478210i | 0.0144357 | − | 0.0168442i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.41008 | + | 2.25348i | 0.295866 | + | 0.0792770i | ||||
\(809\) | 40.9883 | − | 23.6646i | 1.44107 | − | 0.832003i | 0.443150 | − | 0.896448i | \(-0.353861\pi\) |
0.997921 | + | 0.0644447i | \(0.0205276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.7947 | − | 21.7947i | 0.765317 | − | 0.765317i | −0.211961 | − | 0.977278i | \(-0.567985\pi\) |
0.977278 | + | 0.211961i | \(0.0679851\pi\) | |||||||
\(812\) | −0.890506 | + | 0.238610i | −0.0312506 | + | 0.00837358i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.842017 | + | 0.842017i | 0.0295127 | + | 0.0295127i | ||||
\(815\) | −12.2396 | − | 7.06651i | −0.428733 | − | 0.247529i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.03022 | + | 26.2371i | −0.245956 | + | 0.917922i | ||||
\(818\) | 15.5844 | 0.544896 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | 11.6235 | − | 43.3794i | 0.405662 | − | 1.51395i | −0.397169 | − | 0.917746i | \(-0.630007\pi\) |
0.802831 | − | 0.596207i | \(-0.203326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.74668 | − | 2.16315i | −0.130601 | − | 0.0754025i | 0.433276 | − | 0.901261i | \(-0.357358\pi\) |
−0.563877 | + | 0.825859i | \(0.690691\pi\) | |||||||
\(824\) | 2.59105 | + | 2.59105i | 0.0902635 | + | 0.0902635i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.41008 | + | 2.25348i | −0.292624 | + | 0.0784084i | ||||
\(827\) | −6.56307 | + | 6.56307i | −0.228220 | + | 0.228220i | −0.811949 | − | 0.583729i | \(-0.801593\pi\) |
0.583729 | + | 0.811949i | \(0.301593\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.4626 | − | 17.5876i | 1.05801 | − | 0.610843i | 0.133130 | − | 0.991099i | \(-0.457497\pi\) |
0.924881 | + | 0.380255i | \(0.124164\pi\) | |||||||
\(830\) | 8.51162 | + | 2.28068i | 0.295443 | + | 0.0791636i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.40077 | − | 1.19781i | 0.117901 | − | 0.0415264i | ||||
\(833\) | 12.8661i | 0.445784i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.956444 | − | 1.65661i | −0.0330991 | − | 0.0573293i | ||||
\(836\) | −0.121819 | + | 0.210997i | −0.00421321 | + | 0.00729749i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.93586 | − | 18.4209i | −0.170506 | − | 0.636339i | ||||
\(839\) | −2.40907 | − | 8.99078i | −0.0831704 | − | 0.310396i | 0.911791 | − | 0.410654i | \(-0.134700\pi\) |
−0.994961 | + | 0.100258i | \(0.968033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1297 | + | 24.4733i | −0.487230 | + | 0.843908i | ||||
\(842\) | −1.30347 | − | 2.25768i | −0.0449207 | − | 0.0778049i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.7680i | 0.783707i | ||||||||
\(845\) | 12.9241 | + | 1.40261i | 0.444603 | + | 0.0482514i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3699 | + | 3.04656i | 0.390675 | + | 0.104681i | ||||
\(848\) | −3.09748 | + | 1.78833i | −0.106368 | + | 0.0614115i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.55452 | + | 1.55452i | −0.0533196 | + | 0.0533196i | ||||
\(851\) | 28.2711 | − | 7.57522i | 0.969121 | − | 0.259675i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.6039 | + | 23.6039i | 0.808183 | + | 0.808183i | 0.984359 | − | 0.176175i | \(-0.0563726\pi\) |
−0.176175 | + | 0.984359i | \(0.556373\pi\) | |||||||
\(854\) | 7.98042 | + | 4.60750i | 0.273084 | + | 0.157665i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.431006 | + | 1.60854i | −0.0147315 | + | 0.0549787i | ||||
\(857\) | −4.43651 | −0.151548 | −0.0757742 | − | 0.997125i | \(-0.524143\pi\) | ||||
−0.0757742 | + | 0.997125i | \(0.524143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.6789 | 0.569078 | 0.284539 | − | 0.958664i | \(-0.408159\pi\) | ||||
0.284539 | + | 0.958664i | \(0.408159\pi\) | |||||||
\(860\) | −3.14636 | + | 11.7424i | −0.107290 | + | 0.400412i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.8187 | − | 11.4423i | −0.675028 | − | 0.389728i | ||||
\(863\) | 35.0616 | + | 35.0616i | 1.19351 | + | 1.19351i | 0.976075 | + | 0.217436i | \(0.0697693\pi\) |
0.217436 | + | 0.976075i | \(0.430231\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.9485 | + | 2.93364i | −0.372259 | + | 0.0997466i | ||||
\(866\) | −14.7071 | + | 14.7071i | −0.499768 | + | 0.499768i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.162051 | + | 0.0935603i | −0.00550037 | + | 0.00317564i | ||||
\(869\) | −0.377427 | − | 0.101131i | −0.0128033 | − | 0.00343064i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.05402 | − | 13.6886i | −0.0357140 | − | 0.463822i | ||||
\(872\) | − | 4.80212i | − | 0.162620i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.99419 | + | 5.18609i | 0.101280 | + | 0.175422i | ||||
\(875\) | −0.535625 | + | 0.927730i | −0.0181074 | + | 0.0313630i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.14801 | − | 22.9447i | −0.207603 | − | 0.774786i | −0.988640 | − | 0.150301i | \(-0.951976\pi\) |
0.781037 | − | 0.624485i | \(-0.214691\pi\) | |||||||
\(878\) | 8.01445 | + | 29.9103i | 0.270474 | + | 1.00942i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0545200 | + | 0.0944314i | −0.00183787 | + | 0.00318328i | ||||
\(881\) | 8.12877 | + | 14.0795i | 0.273865 | + | 0.474349i | 0.969848 | − | 0.243710i | \(-0.0783644\pi\) |
−0.695983 | + | 0.718058i | \(0.745031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 23.3980i | − | 0.787406i | −0.919238 | − | 0.393703i | \(-0.871194\pi\) | ||
0.919238 | − | 0.393703i | \(-0.128806\pi\) | |||||||
\(884\) | −6.01866 | − | 5.15806i | −0.202429 | − | 0.173484i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.0431 | + | 6.44234i | 0.807745 | + | 0.216435i | ||||
\(887\) | 35.3067 | − | 20.3844i | 1.18548 | − | 0.684440i | 0.228207 | − | 0.973613i | \(-0.426714\pi\) |
0.957277 | + | 0.289173i | \(0.0933803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.11181 | + | 8.11181i | −0.272061 | + | 0.272061i | ||||
\(890\) | −0.486484 | + | 0.130353i | −0.0163070 | + | 0.00436944i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.6472 | − | 10.6472i | −0.356493 | − | 0.356493i | ||||
\(893\) | −24.3876 | − | 14.0802i | −0.816098 | − | 0.471175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.08927 | + | 7.79726i | −0.0698365 | + | 0.260634i | ||||
\(896\) | −1.07125 | −0.0357880 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.8970 | −1.33138 | ||||||||
\(899\) | 0.0389071 | − | 0.145203i | 0.00129762 | − | 0.00484280i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.80957 | + | 3.93151i | 0.226860 | + | 0.130978i | ||||
\(902\) | 0.308412 | + | 0.308412i | 0.0102690 | + | 0.0102690i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.52793 | + | 2.55300i | −0.316894 | + | 0.0849116i | ||||
\(905\) | −3.78145 | + | 3.78145i | −0.125700 | + | 0.125700i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3499 | − | 27.3375i | 1.57223 | − | 0.907727i | 0.576334 | − | 0.817214i | \(-0.304483\pi\) |
0.995895 | − | 0.0905127i | \(-0.0288506\pi\) | |||||||
\(908\) | −4.96291 | − | 1.32981i | −0.164700 | − | 0.0441313i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.48337 | − | 1.66872i | −0.115473 | − | 0.0553176i | ||||
\(911\) | − | 19.4958i | − | 0.645925i | −0.946412 | − | 0.322962i | \(-0.895321\pi\) | ||
0.946412 | − | 0.322962i | \(-0.104679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.480423 | − | 0.832117i | −0.0158997 | − | 0.0275391i | ||||
\(914\) | −9.25399 | + | 16.0284i | −0.306095 | + | 0.530171i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.33330 | + | 12.4400i | 0.110135 | + | 0.411030i | ||||
\(917\) | 0.815364 | + | 3.04298i | 0.0269257 | + | 0.100488i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.0266 | + | 26.0269i | −0.495683 | + | 0.858549i | −0.999988 | − | 0.00497727i | \(-0.998416\pi\) |
0.504304 | + | 0.863526i | \(0.331749\pi\) | |||||||
\(920\) | 1.34004 | + | 2.32102i | 0.0441799 | + | 0.0765219i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.0496i | 0.429765i | ||||||||
\(923\) | −6.59992 | − | 9.63783i | −0.217239 | − | 0.317233i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5486 | − | 2.82648i | −0.346835 | − | 0.0929342i | ||||
\(926\) | 21.8008 | − | 12.5867i | 0.716418 | − | 0.413624i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.608537 | − | 0.608537i | 0.0199762 | − | 0.0199762i | ||||
\(929\) | 34.5256 | − | 9.25111i | 1.13275 | − | 0.303519i | 0.356717 | − | 0.934213i | \(-0.383896\pi\) |
0.776032 | + | 0.630693i | \(0.217229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.24658 | − | 9.24658i | −0.303044 | − | 0.303044i | ||||
\(932\) | −20.7973 | − | 12.0073i | −0.681238 | − | 0.393313i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.0205 | − | 41.1290i | 0.360601 | − | 1.34578i | ||||
\(935\) | 0.239716 | 0.00783955 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.51941 | 0.310986 | 0.155493 | − | 0.987837i | \(-0.450303\pi\) | ||||
0.155493 | + | 0.987837i | \(0.450303\pi\) | |||||||
\(938\) | −1.05575 | + | 3.94009i | −0.0344713 | + | 0.128649i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.9146 | − | 6.30155i | −0.355995 | − | 0.205534i | ||||
\(941\) | 23.7474 | + | 23.7474i | 0.774144 | + | 0.774144i | 0.978828 | − | 0.204684i | \(-0.0656168\pi\) |
−0.204684 | + | 0.978828i | \(0.565617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3551 | − | 2.77463i | 0.337207 | − | 0.0903544i | ||||
\(944\) | 5.74712 | − | 5.74712i | 0.187053 | − | 0.187053i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.14797 | − | 0.662778i | 0.0373236 | − | 0.0215488i | ||||
\(947\) | 15.7557 | + | 4.22174i | 0.511993 | + | 0.137188i | 0.505560 | − | 0.862791i | \(-0.331286\pi\) |
0.00643231 | + | 0.999979i | \(0.497953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.4119 | + | 42.6088i | −0.662599 | + | 1.38314i | ||||
\(950\) | − | 2.23440i | − | 0.0724934i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.17753 | + | 2.03954i | 0.0381640 | + | 0.0661020i | ||||
\(953\) | −0.0598968 | + | 0.103744i | −0.00194025 | + | 0.00336061i | −0.866994 | − | 0.498319i | \(-0.833951\pi\) |
0.865054 | + | 0.501679i | \(0.167284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.221222 | + | 0.825611i | 0.00715857 | + | 0.0267161i | ||||
\(956\) | −3.30260 | − | 12.3255i | −0.106814 | − | 0.398634i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.6548 | − | 25.3829i | 0.473475 | − | 0.820084i | ||||
\(959\) | −2.30083 | − | 3.98516i | −0.0742978 | − | 0.128688i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9695i | 0.999016i | ||||||||
\(962\) | 7.24104 | − | 38.7036i | 0.233460 | − | 1.24785i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.76565 | + | 1.54490i | 0.185699 | + | 0.0497579i | ||||
\(965\) | 14.4995 | − | 8.37129i | 0.466755 | − | 0.269481i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1095 | + | 12.1095i | −0.389416 | + | 0.389416i | −0.874479 | − | 0.485063i | \(-0.838797\pi\) |
0.485063 | + | 0.874479i | \(0.338797\pi\) | |||||||
\(968\) | −10.6137 | + | 2.84393i | −0.341137 | + | 0.0914074i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.71113 | − | 3.71113i | −0.119157 | − | 0.119157i | ||||
\(971\) | 46.2626 | + | 26.7097i | 1.48464 | + | 0.857156i | 0.999847 | − | 0.0174747i | \(-0.00556267\pi\) |
0.484790 | + | 0.874631i | \(0.338896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.806506 | − | 3.00992i | 0.0258554 | − | 0.0964937i | ||||
\(974\) | 4.48407 | 0.143679 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.60209 | −0.275346 | ||||||||
\(977\) | −4.45733 | + | 16.6350i | −0.142603 | + | 0.532200i | 0.857248 | + | 0.514904i | \(0.172172\pi\) |
−0.999850 | + | 0.0172960i | \(0.994494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0475599 | + | 0.0274587i | 0.00152002 | + | 0.000877584i | ||||
\(980\) | −4.13829 | − | 4.13829i | −0.132193 | − | 0.132193i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.30721 | + | 0.350267i | −0.0417149 | + | 0.0111775i | ||||
\(983\) | 7.63036 | − | 7.63036i | 0.243371 | − | 0.243371i | −0.574872 | − | 0.818243i | \(-0.694948\pi\) |
0.818243 | + | 0.574872i | \(0.194948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.7494 | − | 10.8250i | 0.597405 | − | 0.344912i | ||||
\(986\) | −1.82750 | − | 0.489677i | −0.0581994 | − | 0.0155945i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.03246 | − | 0.618495i | 0.255547 | − | 0.0196769i | ||||
\(989\) | − | 32.5808i | − | 1.03601i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.66822 | + | 9.81765i | 0.180057 | + | 0.311868i | 0.941900 | − | 0.335894i | \(-0.109038\pi\) |
−0.761843 | + | 0.647762i | \(0.775705\pi\) | |||||||
\(992\) | 0.0873374 | − | 0.151273i | 0.00277297 | − | 0.00480292i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.898250 | + | 3.35231i | 0.0284908 | + | 0.106329i | ||||
\(995\) | 1.82913 | + | 6.82639i | 0.0579872 | + | 0.216411i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.23856 | + | 5.60935i | −0.102566 | + | 0.177650i | −0.912741 | − | 0.408538i | \(-0.866039\pi\) |
0.810175 | + | 0.586188i | \(0.199372\pi\) | |||||||
\(998\) | 9.23867 | + | 16.0018i | 0.292445 | + | 0.506530i | ||||
\(999\) | 0 | 0 |
(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 | 1170.2.cu.f.431.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1170.2.cu.f.431.3 | yes | 16 | |
13.7 | odd | 12 | inner | 1170.2.cu.f.1151.3 | yes | 16 | |
39.20 | even | 12 | inner | 1170.2.cu.f.1151.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.cu.f.431.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1170.2.cu.f.431.3 | yes | 16 | 3.2 | odd | 2 | inner | |
1170.2.cu.f.1151.1 | yes | 16 | 39.20 | even | 12 | inner | |
1170.2.cu.f.1151.3 | yes | 16 | 13.7 | odd | 12 | inner |