Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.391 |
Dual form | 585.2.i.b.196.1 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | 0.986869 | − | 0.161521i | \(-0.0516399\pi\) |
−0.633316 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | ||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −1.50000 | − | 0.866025i | −0.433013 | − | 0.250000i | ||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | ||||
\(14\) | 1.00000 | − | 1.73205i | 0.267261 | − | 0.462910i | ||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | −1.50000 | − | 2.59808i | −0.353553 | − | 0.612372i | ||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | −3.00000 | + | 1.73205i | −0.654654 | + | 0.377964i | ||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | − | 5.19615i | − | 1.06066i | ||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | −2.50000 | − | 4.33013i | −0.464238 | − | 0.804084i | 0.534928 | − | 0.844897i | \(-0.320339\pi\) |
−0.999167 | + | 0.0408130i | \(0.987005\pi\) | |||||||
\(30\) | − | 1.73205i | − | 0.316228i | ||||||
\(31\) | 0.500000 | − | 0.866025i | 0.0898027 | − | 0.155543i | −0.817625 | − | 0.575751i | \(-0.804710\pi\) |
0.907428 | + | 0.420208i | \(0.138043\pi\) | |||||||
\(32\) | 2.50000 | − | 4.33013i | 0.441942 | − | 0.765466i | ||||
\(33\) | 1.50000 | − | 0.866025i | 0.261116 | − | 0.150756i | ||||
\(34\) | 1.00000 | + | 1.73205i | 0.171499 | + | 0.297044i | ||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | −1.50000 | − | 2.59808i | −0.243332 | − | 0.421464i | ||||
\(39\) | −1.50000 | − | 0.866025i | −0.240192 | − | 0.138675i | ||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | −3.00000 | − | 1.73205i | −0.462910 | − | 0.267261i | ||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | + | 1.73205i | 0.145865 | + | 0.252646i | 0.929695 | − | 0.368329i | \(-0.120070\pi\) |
−0.783830 | + | 0.620975i | \(0.786737\pi\) | |||||||
\(48\) | 1.50000 | − | 0.866025i | 0.216506 | − | 0.125000i | ||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | − | 3.46410i | − | 0.485071i | ||||||
\(52\) | −0.500000 | − | 0.866025i | −0.0693375 | − | 0.120096i | ||||
\(53\) | 14.0000 | 1.92305 | 0.961524 | − | 0.274721i | \(-0.0885855\pi\) | ||||
0.961524 | + | 0.274721i | \(0.0885855\pi\) | |||||||
\(54\) | −4.50000 | + | 2.59808i | −0.612372 | + | 0.353553i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −3.00000 | − | 5.19615i | −0.400892 | − | 0.694365i | ||||
\(57\) | 5.19615i | 0.688247i | ||||||||
\(58\) | 2.50000 | − | 4.33013i | 0.328266 | − | 0.568574i | ||||
\(59\) | 4.50000 | − | 7.79423i | 0.585850 | − | 1.01472i | −0.408919 | − | 0.912571i | \(-0.634094\pi\) |
0.994769 | − | 0.102151i | \(-0.0325726\pi\) | |||||||
\(60\) | −1.50000 | + | 0.866025i | −0.193649 | + | 0.111803i | ||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 3.00000 | + | 5.19615i | 0.377964 | + | 0.654654i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 1.50000 | + | 0.866025i | 0.184637 | + | 0.106600i | ||||
\(67\) | −7.00000 | + | 12.1244i | −0.855186 | + | 1.48123i | 0.0212861 | + | 0.999773i | \(0.493224\pi\) |
−0.876472 | + | 0.481452i | \(0.840109\pi\) | |||||||
\(68\) | 1.00000 | − | 1.73205i | 0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | − | 1.73205i | −0.119523 | − | 0.207020i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −9.00000 | −1.06066 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | −2.50000 | − | 4.33013i | −0.290619 | − | 0.503367i | ||||
\(75\) | −1.50000 | + | 0.866025i | −0.173205 | + | 0.100000i | ||||
\(76\) | −1.50000 | + | 2.59808i | −0.172062 | + | 0.298020i | ||||
\(77\) | 1.00000 | − | 1.73205i | 0.113961 | − | 0.197386i | ||||
\(78\) | − | 1.73205i | − | 0.196116i | ||||||
\(79\) | 6.00000 | + | 10.3923i | 0.675053 | + | 1.16923i | 0.976453 | + | 0.215728i | \(0.0692125\pi\) |
−0.301401 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00000 | + | 8.66025i | 0.548821 | + | 0.950586i | 0.998356 | + | 0.0573233i | \(0.0182566\pi\) |
−0.449534 | + | 0.893263i | \(0.648410\pi\) | |||||||
\(84\) | 3.46410i | 0.377964i | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | −7.50000 | + | 4.33013i | −0.804084 | + | 0.464238i | ||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | −3.00000 | −0.316228 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 0.866025i | −0.155543 | − | 0.0898027i | ||||
\(94\) | −1.00000 | + | 1.73205i | −0.103142 | + | 0.178647i | ||||
\(95\) | −1.50000 | + | 2.59808i | −0.153897 | + | 0.266557i | ||||
\(96\) | −7.50000 | − | 4.33013i | −0.765466 | − | 0.441942i | ||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | −1.50000 | − | 2.59808i | −0.150756 | − | 0.261116i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 3.00000 | − | 1.73205i | 0.297044 | − | 0.171499i | ||||
\(103\) | 0.500000 | − | 0.866025i | 0.0492665 | − | 0.0853320i | −0.840341 | − | 0.542059i | \(-0.817645\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(104\) | 1.50000 | − | 2.59808i | 0.147087 | − | 0.254762i | ||||
\(105\) | 3.46410i | 0.338062i | ||||||||
\(106\) | 7.00000 | + | 12.1244i | 0.679900 | + | 1.17762i | ||||
\(107\) | 19.0000 | 1.83680 | 0.918400 | − | 0.395654i | \(-0.129482\pi\) | ||||
0.918400 | + | 0.395654i | \(0.129482\pi\) | |||||||
\(108\) | 4.50000 | + | 2.59808i | 0.433013 | + | 0.250000i | ||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0.500000 | + | 0.866025i | 0.0476731 | + | 0.0825723i | ||||
\(111\) | 8.66025i | 0.821995i | ||||||||
\(112\) | 1.00000 | − | 1.73205i | 0.0944911 | − | 0.163663i | ||||
\(113\) | −5.00000 | + | 8.66025i | −0.470360 | + | 0.814688i | −0.999425 | − | 0.0338931i | \(-0.989209\pi\) |
0.529065 | + | 0.848581i | \(0.322543\pi\) | |||||||
\(114\) | −4.50000 | + | 2.59808i | −0.421464 | + | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | −1.50000 | + | 2.59808i | −0.138675 | + | 0.240192i | ||||
\(118\) | 9.00000 | 0.828517 | ||||||||
\(119\) | −2.00000 | − | 3.46410i | −0.183340 | − | 0.317554i | ||||
\(120\) | −4.50000 | − | 2.59808i | −0.410792 | − | 0.237171i | ||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | −0.500000 | + | 0.866025i | −0.0452679 | + | 0.0784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.500000 | − | 0.866025i | −0.0449013 | − | 0.0777714i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.00000 | + | 5.19615i | −0.267261 | + | 0.462910i | ||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | −1.50000 | − | 2.59808i | −0.132583 | − | 0.229640i | ||||
\(129\) | 12.0000 | − | 6.92820i | 1.05654 | − | 0.609994i | ||||
\(130\) | 0.500000 | − | 0.866025i | 0.0438529 | − | 0.0759555i | ||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | − | 1.73205i | − | 0.150756i | ||||||
\(133\) | 3.00000 | + | 5.19615i | 0.260133 | + | 0.450564i | ||||
\(134\) | −14.0000 | −1.20942 | ||||||||
\(135\) | 4.50000 | + | 2.59808i | 0.387298 | + | 0.223607i | ||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 2.50000 | + | 4.33013i | 0.213589 | + | 0.369948i | 0.952835 | − | 0.303488i | \(-0.0981512\pi\) |
−0.739246 | + | 0.673436i | \(0.764818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | + | 10.3923i | −0.508913 | + | 0.881464i | 0.491033 | + | 0.871141i | \(0.336619\pi\) |
−0.999947 | + | 0.0103230i | \(0.996714\pi\) | |||||||
\(140\) | −1.00000 | + | 1.73205i | −0.0845154 | + | 0.146385i | ||||
\(141\) | 3.00000 | − | 1.73205i | 0.252646 | − | 0.145865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | −1.50000 | − | 2.59808i | −0.125000 | − | 0.216506i | ||||
\(145\) | −5.00000 | −0.415227 | ||||||||
\(146\) | 3.00000 | + | 5.19615i | 0.248282 | + | 0.430037i | ||||
\(147\) | −4.50000 | − | 2.59808i | −0.371154 | − | 0.214286i | ||||
\(148\) | −2.50000 | + | 4.33013i | −0.205499 | + | 0.355934i | ||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | −1.50000 | − | 0.866025i | −0.122474 | − | 0.0707107i | ||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | −9.00000 | −0.729996 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | −0.500000 | − | 0.866025i | −0.0401610 | − | 0.0695608i | ||||
\(156\) | −1.50000 | + | 0.866025i | −0.120096 | + | 0.0693375i | ||||
\(157\) | 3.00000 | − | 5.19615i | 0.239426 | − | 0.414698i | −0.721124 | − | 0.692806i | \(-0.756374\pi\) |
0.960550 | + | 0.278108i | \(0.0897074\pi\) | |||||||
\(158\) | −6.00000 | + | 10.3923i | −0.477334 | + | 0.826767i | ||||
\(159\) | − | 24.2487i | − | 1.92305i | ||||||
\(160\) | −2.50000 | − | 4.33013i | −0.197642 | − | 0.342327i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.50000 | + | 7.79423i | 0.353553 | + | 0.612372i | ||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.73205i | − | 0.134840i | ||||||
\(166\) | −5.00000 | + | 8.66025i | −0.388075 | + | 0.672166i | ||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | −9.00000 | + | 5.19615i | −0.694365 | + | 0.400892i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 9.00000 | 0.688247 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −6.00000 | − | 10.3923i | −0.456172 | − | 0.790112i | 0.542583 | − | 0.840002i | \(-0.317446\pi\) |
−0.998755 | + | 0.0498898i | \(0.984113\pi\) | |||||||
\(174\) | −7.50000 | − | 4.33013i | −0.568574 | − | 0.328266i | ||||
\(175\) | −1.00000 | + | 1.73205i | −0.0755929 | + | 0.130931i | ||||
\(176\) | −0.500000 | + | 0.866025i | −0.0376889 | + | 0.0652791i | ||||
\(177\) | −13.5000 | − | 7.79423i | −1.01472 | − | 0.585850i | ||||
\(178\) | 1.00000 | + | 1.73205i | 0.0749532 | + | 0.129823i | ||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 1.50000 | + | 2.59808i | 0.111803 | + | 0.193649i | ||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | −1.00000 | − | 1.73205i | −0.0741249 | − | 0.128388i | ||||
\(183\) | 1.50000 | − | 0.866025i | 0.110883 | − | 0.0640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.50000 | + | 4.33013i | −0.183804 | + | 0.318357i | ||||
\(186\) | − | 1.73205i | − | 0.127000i | ||||||
\(187\) | 1.00000 | + | 1.73205i | 0.0731272 | + | 0.126660i | ||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 9.00000 | − | 5.19615i | 0.654654 | − | 0.377964i | ||||
\(190\) | −3.00000 | −0.217643 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | − | 12.1244i | − | 0.875000i | ||||||
\(193\) | −6.50000 | + | 11.2583i | −0.467880 | + | 0.810392i | −0.999326 | − | 0.0366998i | \(-0.988315\pi\) |
0.531446 | + | 0.847092i | \(0.321649\pi\) | |||||||
\(194\) | 0.500000 | − | 0.866025i | 0.0358979 | − | 0.0621770i | ||||
\(195\) | −1.50000 | + | 0.866025i | −0.107417 | + | 0.0620174i | ||||
\(196\) | −1.50000 | − | 2.59808i | −0.107143 | − | 0.185577i | ||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 1.50000 | − | 2.59808i | 0.106600 | − | 0.184637i | ||||
\(199\) | −22.0000 | −1.55954 | −0.779769 | − | 0.626067i | \(-0.784664\pi\) | ||||
−0.779769 | + | 0.626067i | \(0.784664\pi\) | |||||||
\(200\) | −1.50000 | − | 2.59808i | −0.106066 | − | 0.183712i | ||||
\(201\) | 21.0000 | + | 12.1244i | 1.48123 | + | 0.855186i | ||||
\(202\) | 1.50000 | − | 2.59808i | 0.105540 | − | 0.182800i | ||||
\(203\) | −5.00000 | + | 8.66025i | −0.350931 | + | 0.607831i | ||||
\(204\) | −3.00000 | − | 1.73205i | −0.210042 | − | 0.121268i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −1.50000 | − | 2.59808i | −0.103757 | − | 0.179713i | ||||
\(210\) | −3.00000 | + | 1.73205i | −0.207020 | + | 0.119523i | ||||
\(211\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(212\) | 7.00000 | − | 12.1244i | 0.480762 | − | 0.832704i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.50000 | + | 16.4545i | 0.649407 | + | 1.12481i | ||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 15.5885i | 1.06066i | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | −7.00000 | − | 12.1244i | −0.474100 | − | 0.821165i | ||||
\(219\) | − | 10.3923i | − | 0.702247i | ||||||
\(220\) | 0.500000 | − | 0.866025i | 0.0337100 | − | 0.0583874i | ||||
\(221\) | 1.00000 | − | 1.73205i | 0.0672673 | − | 0.116510i | ||||
\(222\) | −7.50000 | + | 4.33013i | −0.503367 | + | 0.290619i | ||||
\(223\) | 13.0000 | + | 22.5167i | 0.870544 | + | 1.50783i | 0.861435 | + | 0.507869i | \(0.169566\pi\) |
0.00910984 | + | 0.999959i | \(0.497100\pi\) | |||||||
\(224\) | −10.0000 | −0.668153 | ||||||||
\(225\) | 1.50000 | + | 2.59808i | 0.100000 | + | 0.173205i | ||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | 13.0000 | + | 22.5167i | 0.862840 | + | 1.49448i | 0.869176 | + | 0.494503i | \(0.164650\pi\) |
−0.00633544 | + | 0.999980i | \(0.502017\pi\) | |||||||
\(228\) | 4.50000 | + | 2.59808i | 0.298020 | + | 0.172062i | ||||
\(229\) | 8.00000 | − | 13.8564i | 0.528655 | − | 0.915657i | −0.470787 | − | 0.882247i | \(-0.656030\pi\) |
0.999442 | − | 0.0334101i | \(-0.0106368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 1.73205i | −0.197386 | − | 0.113961i | ||||
\(232\) | −7.50000 | − | 12.9904i | −0.492399 | − | 0.852860i | ||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | −3.00000 | −0.196116 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | −4.50000 | − | 7.79423i | −0.292925 | − | 0.507361i | ||||
\(237\) | 18.0000 | − | 10.3923i | 1.16923 | − | 0.675053i | ||||
\(238\) | 2.00000 | − | 3.46410i | 0.129641 | − | 0.224544i | ||||
\(239\) | −7.50000 | + | 12.9904i | −0.485135 | + | 0.840278i | −0.999854 | − | 0.0170808i | \(-0.994563\pi\) |
0.514719 | + | 0.857359i | \(0.327896\pi\) | |||||||
\(240\) | − | 1.73205i | − | 0.111803i | ||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 10.0000 | 0.642824 | ||||||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.50000 | + | 2.59808i | −0.0954427 | + | 0.165312i | ||||
\(248\) | 1.50000 | − | 2.59808i | 0.0952501 | − | 0.164978i | ||||
\(249\) | 15.0000 | − | 8.66025i | 0.950586 | − | 0.548821i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 6.00000 | 0.377964 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.00000 | − | 6.92820i | −0.250982 | − | 0.434714i | ||||
\(255\) | −3.00000 | − | 1.73205i | −0.187867 | − | 0.108465i | ||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 14.0000 | − | 24.2487i | 0.873296 | − | 1.51259i | 0.0147291 | − | 0.999892i | \(-0.495311\pi\) |
0.858567 | − | 0.512702i | \(-0.171355\pi\) | |||||||
\(258\) | 12.0000 | + | 6.92820i | 0.747087 | + | 0.431331i | ||||
\(259\) | 5.00000 | + | 8.66025i | 0.310685 | + | 0.538122i | ||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | 7.50000 | + | 12.9904i | 0.464238 | + | 0.804084i | ||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 4.50000 | − | 2.59808i | 0.276956 | − | 0.159901i | ||||
\(265\) | 7.00000 | − | 12.1244i | 0.430007 | − | 0.744793i | ||||
\(266\) | −3.00000 | + | 5.19615i | −0.183942 | + | 0.318597i | ||||
\(267\) | − | 3.46410i | − | 0.212000i | ||||||
\(268\) | 7.00000 | + | 12.1244i | 0.427593 | + | 0.740613i | ||||
\(269\) | 3.00000 | 0.182913 | 0.0914566 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914566 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(270\) | 5.19615i | 0.316228i | ||||||||
\(271\) | −7.00000 | −0.425220 | −0.212610 | − | 0.977137i | \(-0.568196\pi\) | ||||
−0.212610 | + | 0.977137i | \(0.568196\pi\) | |||||||
\(272\) | 1.00000 | + | 1.73205i | 0.0606339 | + | 0.105021i | ||||
\(273\) | 3.46410i | 0.209657i | ||||||||
\(274\) | −2.50000 | + | 4.33013i | −0.151031 | + | 0.261593i | ||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | −12.0000 | −0.719712 | ||||||||
\(279\) | −1.50000 | + | 2.59808i | −0.0898027 | + | 0.155543i | ||||
\(280\) | −6.00000 | −0.358569 | ||||||||
\(281\) | 6.00000 | + | 10.3923i | 0.357930 | + | 0.619953i | 0.987615 | − | 0.156898i | \(-0.0501493\pi\) |
−0.629685 | + | 0.776851i | \(0.716816\pi\) | |||||||
\(282\) | 3.00000 | + | 1.73205i | 0.178647 | + | 0.103142i | ||||
\(283\) | 12.5000 | − | 21.6506i | 0.743048 | − | 1.28700i | −0.208053 | − | 0.978117i | \(-0.566713\pi\) |
0.951101 | − | 0.308879i | \(-0.0999539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.50000 | + | 2.59808i | 0.266557 | + | 0.153897i | ||||
\(286\) | 0.500000 | + | 0.866025i | 0.0295656 | + | 0.0512092i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.50000 | + | 12.9904i | −0.441942 | + | 0.765466i | ||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −2.50000 | − | 4.33013i | −0.146805 | − | 0.254274i | ||||
\(291\) | −1.50000 | + | 0.866025i | −0.0879316 | + | 0.0507673i | ||||
\(292\) | 3.00000 | − | 5.19615i | 0.175562 | − | 0.304082i | ||||
\(293\) | −0.500000 | + | 0.866025i | −0.0292103 | + | 0.0505937i | −0.880261 | − | 0.474490i | \(-0.842633\pi\) |
0.851051 | + | 0.525084i | \(0.175966\pi\) | |||||||
\(294\) | − | 5.19615i | − | 0.303046i | ||||||
\(295\) | −4.50000 | − | 7.79423i | −0.262000 | − | 0.453798i | ||||
\(296\) | −15.0000 | −0.871857 | ||||||||
\(297\) | −4.50000 | + | 2.59808i | −0.261116 | + | 0.150756i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.73205i | 0.100000i | ||||||||
\(301\) | 8.00000 | − | 13.8564i | 0.461112 | − | 0.798670i | ||||
\(302\) | −4.00000 | + | 6.92820i | −0.230174 | + | 0.398673i | ||||
\(303\) | −4.50000 | + | 2.59808i | −0.258518 | + | 0.149256i | ||||
\(304\) | −1.50000 | − | 2.59808i | −0.0860309 | − | 0.149010i | ||||
\(305\) | 1.00000 | 0.0572598 | ||||||||
\(306\) | −3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −1.00000 | − | 1.73205i | −0.0569803 | − | 0.0986928i | ||||
\(309\) | −1.50000 | − | 0.866025i | −0.0853320 | − | 0.0492665i | ||||
\(310\) | 0.500000 | − | 0.866025i | 0.0283981 | − | 0.0491869i | ||||
\(311\) | 2.00000 | − | 3.46410i | 0.113410 | − | 0.196431i | −0.803733 | − | 0.594990i | \(-0.797156\pi\) |
0.917143 | + | 0.398559i | \(0.130489\pi\) | |||||||
\(312\) | −4.50000 | − | 2.59808i | −0.254762 | − | 0.147087i | ||||
\(313\) | 14.0000 | + | 24.2487i | 0.791327 | + | 1.37062i | 0.925146 | + | 0.379612i | \(0.123943\pi\) |
−0.133819 | + | 0.991006i | \(0.542724\pi\) | |||||||
\(314\) | 6.00000 | 0.338600 | ||||||||
\(315\) | 6.00000 | 0.338062 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | 13.5000 | + | 23.3827i | 0.758236 | + | 1.31330i | 0.943750 | + | 0.330661i | \(0.107272\pi\) |
−0.185514 | + | 0.982642i | \(0.559395\pi\) | |||||||
\(318\) | 21.0000 | − | 12.1244i | 1.17762 | − | 0.679900i | ||||
\(319\) | 2.50000 | − | 4.33013i | 0.139973 | − | 0.242441i | ||||
\(320\) | 3.50000 | − | 6.06218i | 0.195656 | − | 0.338886i | ||||
\(321\) | − | 32.9090i | − | 1.83680i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 4.50000 | − | 7.79423i | 0.250000 | − | 0.433013i | ||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −6.00000 | − | 10.3923i | −0.332309 | − | 0.575577i | ||||
\(327\) | 24.2487i | 1.34096i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.00000 | − | 3.46410i | 0.110264 | − | 0.190982i | ||||
\(330\) | 1.50000 | − | 0.866025i | 0.0825723 | − | 0.0476731i | ||||
\(331\) | −13.5000 | − | 23.3827i | −0.742027 | − | 1.28523i | −0.951571 | − | 0.307429i | \(-0.900531\pi\) |
0.209544 | − | 0.977799i | \(-0.432802\pi\) | |||||||
\(332\) | 10.0000 | 0.548821 | ||||||||
\(333\) | 15.0000 | 0.821995 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.00000 | + | 12.1244i | 0.382451 | + | 0.662424i | ||||
\(336\) | −3.00000 | − | 1.73205i | −0.163663 | − | 0.0944911i | ||||
\(337\) | 11.0000 | − | 19.0526i | 0.599208 | − | 1.03786i | −0.393730 | − | 0.919226i | \(-0.628816\pi\) |
0.992938 | − | 0.118633i | \(-0.0378512\pi\) | |||||||
\(338\) | 0.500000 | − | 0.866025i | 0.0271964 | − | 0.0471056i | ||||
\(339\) | 15.0000 | + | 8.66025i | 0.814688 | + | 0.470360i | ||||
\(340\) | −1.00000 | − | 1.73205i | −0.0542326 | − | 0.0939336i | ||||
\(341\) | 1.00000 | 0.0541530 | ||||||||
\(342\) | 4.50000 | + | 7.79423i | 0.243332 | + | 0.421464i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 12.0000 | + | 20.7846i | 0.646997 | + | 1.12063i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | − | 10.3923i | 0.322562 | − | 0.558694i | ||||
\(347\) | −8.50000 | + | 14.7224i | −0.456304 | + | 0.790342i | −0.998762 | − | 0.0497412i | \(-0.984160\pi\) |
0.542458 | + | 0.840083i | \(0.317494\pi\) | |||||||
\(348\) | 8.66025i | 0.464238i | ||||||||
\(349\) | −6.00000 | − | 10.3923i | −0.321173 | − | 0.556287i | 0.659558 | − | 0.751654i | \(-0.270744\pi\) |
−0.980730 | + | 0.195367i | \(0.937410\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | 4.50000 | + | 2.59808i | 0.240192 | + | 0.138675i | ||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | 1.50000 | + | 2.59808i | 0.0798369 | + | 0.138282i | 0.903179 | − | 0.429263i | \(-0.141227\pi\) |
−0.823343 | + | 0.567545i | \(0.807893\pi\) | |||||||
\(354\) | − | 15.5885i | − | 0.828517i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00000 | − | 1.73205i | 0.0529999 | − | 0.0917985i | ||||
\(357\) | −6.00000 | + | 3.46410i | −0.317554 | + | 0.183340i | ||||
\(358\) | −9.00000 | − | 15.5885i | −0.475665 | − | 0.823876i | ||||
\(359\) | −31.0000 | −1.63612 | −0.818059 | − | 0.575135i | \(-0.804950\pi\) | ||||
−0.818059 | + | 0.575135i | \(0.804950\pi\) | |||||||
\(360\) | −4.50000 | + | 7.79423i | −0.237171 | + | 0.410792i | ||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 8.50000 | + | 14.7224i | 0.446750 | + | 0.773794i | ||||
\(363\) | −15.0000 | − | 8.66025i | −0.787296 | − | 0.454545i | ||||
\(364\) | −1.00000 | + | 1.73205i | −0.0524142 | + | 0.0907841i | ||||
\(365\) | 3.00000 | − | 5.19615i | 0.157027 | − | 0.271979i | ||||
\(366\) | 1.50000 | + | 0.866025i | 0.0784063 | + | 0.0452679i | ||||
\(367\) | −12.5000 | − | 21.6506i | −0.652495 | − | 1.13015i | −0.982516 | − | 0.186180i | \(-0.940389\pi\) |
0.330021 | − | 0.943974i | \(-0.392944\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.00000 | −0.259938 | ||||||||
\(371\) | −14.0000 | − | 24.2487i | −0.726844 | − | 1.25893i | ||||
\(372\) | −1.50000 | + | 0.866025i | −0.0777714 | + | 0.0449013i | ||||
\(373\) | 10.0000 | − | 17.3205i | 0.517780 | − | 0.896822i | −0.482006 | − | 0.876168i | \(-0.660092\pi\) |
0.999787 | − | 0.0206542i | \(-0.00657489\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | 1.73205i | 0.0894427i | ||||||||
\(376\) | 3.00000 | + | 5.19615i | 0.154713 | + | 0.267971i | ||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 9.00000 | + | 5.19615i | 0.462910 | + | 0.267261i | ||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | 1.50000 | + | 2.59808i | 0.0769484 | + | 0.133278i | ||||
\(381\) | 13.8564i | 0.709885i | ||||||||
\(382\) | 9.00000 | − | 15.5885i | 0.460480 | − | 0.797575i | ||||
\(383\) | 6.00000 | − | 10.3923i | 0.306586 | − | 0.531022i | −0.671027 | − | 0.741433i | \(-0.734147\pi\) |
0.977613 | + | 0.210411i | \(0.0674801\pi\) | |||||||
\(384\) | −4.50000 | + | 2.59808i | −0.229640 | + | 0.132583i | ||||
\(385\) | −1.00000 | − | 1.73205i | −0.0509647 | − | 0.0882735i | ||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | −12.0000 | − | 20.7846i | −0.609994 | − | 1.05654i | ||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 11.0000 | + | 19.0526i | 0.557722 | + | 0.966003i | 0.997686 | + | 0.0679877i | \(0.0216579\pi\) |
−0.439964 | + | 0.898015i | \(0.645009\pi\) | |||||||
\(390\) | −1.50000 | − | 0.866025i | −0.0759555 | − | 0.0438529i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 4.50000 | − | 7.79423i | 0.227284 | − | 0.393668i | ||||
\(393\) | −6.00000 | − | 3.46410i | −0.302660 | − | 0.174741i | ||||
\(394\) | 7.50000 | + | 12.9904i | 0.377845 | + | 0.654446i | ||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | −3.00000 | −0.150756 | ||||||||
\(397\) | −30.0000 | −1.50566 | −0.752828 | − | 0.658217i | \(-0.771311\pi\) | ||||
−0.752828 | + | 0.658217i | \(0.771311\pi\) | |||||||
\(398\) | −11.0000 | − | 19.0526i | −0.551380 | − | 0.955018i | ||||
\(399\) | 9.00000 | − | 5.19615i | 0.450564 | − | 0.260133i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −14.0000 | + | 24.2487i | −0.699127 | + | 1.21092i | 0.269643 | + | 0.962960i | \(0.413094\pi\) |
−0.968770 | + | 0.247962i | \(0.920239\pi\) | |||||||
\(402\) | 24.2487i | 1.20942i | ||||||||
\(403\) | −0.500000 | − | 0.866025i | −0.0249068 | − | 0.0431398i | ||||
\(404\) | −3.00000 | −0.149256 | ||||||||
\(405\) | 4.50000 | − | 7.79423i | 0.223607 | − | 0.387298i | ||||
\(406\) | −10.0000 | −0.496292 | ||||||||
\(407\) | −2.50000 | − | 4.33013i | −0.123920 | − | 0.214636i | ||||
\(408\) | − | 10.3923i | − | 0.514496i | ||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50000 | − | 4.33013i | 0.369948 | − | 0.213589i | ||||
\(412\) | −0.500000 | − | 0.866025i | −0.0246332 | − | 0.0426660i | ||||
\(413\) | −18.0000 | −0.885722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0000 | 0.490881 | ||||||||
\(416\) | −2.50000 | − | 4.33013i | −0.122573 | − | 0.212302i | ||||
\(417\) | 18.0000 | + | 10.3923i | 0.881464 | + | 0.508913i | ||||
\(418\) | 1.50000 | − | 2.59808i | 0.0733674 | − | 0.127076i | ||||
\(419\) | −10.0000 | + | 17.3205i | −0.488532 | + | 0.846162i | −0.999913 | − | 0.0131919i | \(-0.995801\pi\) |
0.511381 | + | 0.859354i | \(0.329134\pi\) | |||||||
\(420\) | 3.00000 | + | 1.73205i | 0.146385 | + | 0.0845154i | ||||
\(421\) | −5.00000 | − | 8.66025i | −0.243685 | − | 0.422075i | 0.718076 | − | 0.695965i | \(-0.245023\pi\) |
−0.961761 | + | 0.273890i | \(0.911690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 42.0000 | 2.03970 | ||||||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | − | 1.73205i | 0.0483934 | − | 0.0838198i | ||||
\(428\) | 9.50000 | − | 16.4545i | 0.459200 | − | 0.795357i | ||||
\(429\) | − | 1.73205i | − | 0.0836242i | ||||||
\(430\) | 4.00000 | + | 6.92820i | 0.192897 | + | 0.334108i | ||||
\(431\) | 17.0000 | 0.818861 | 0.409431 | − | 0.912341i | \(-0.365727\pi\) | ||||
0.409431 | + | 0.912341i | \(0.365727\pi\) | |||||||
\(432\) | −4.50000 | + | 2.59808i | −0.216506 | + | 0.125000i | ||||
\(433\) | −38.0000 | −1.82616 | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||||
−0.913082 | + | 0.407777i | \(0.866304\pi\) | |||||||
\(434\) | −1.00000 | − | 1.73205i | −0.0480015 | − | 0.0831411i | ||||
\(435\) | 8.66025i | 0.415227i | ||||||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 9.00000 | − | 5.19615i | 0.430037 | − | 0.248282i | ||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | −4.50000 | + | 7.79423i | −0.214286 | + | 0.371154i | ||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | 3.50000 | + | 6.06218i | 0.166290 | + | 0.288023i | 0.937113 | − | 0.349027i | \(-0.113488\pi\) |
−0.770823 | + | 0.637050i | \(0.780155\pi\) | |||||||
\(444\) | 7.50000 | + | 4.33013i | 0.355934 | + | 0.205499i | ||||
\(445\) | 1.00000 | − | 1.73205i | 0.0474045 | − | 0.0821071i | ||||
\(446\) | −13.0000 | + | 22.5167i | −0.615568 | + | 1.06619i | ||||
\(447\) | 9.00000 | + | 5.19615i | 0.425685 | + | 0.245770i | ||||
\(448\) | −7.00000 | − | 12.1244i | −0.330719 | − | 0.572822i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −1.50000 | + | 2.59808i | −0.0707107 | + | 0.122474i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.00000 | + | 8.66025i | 0.235180 | + | 0.407344i | ||||
\(453\) | 12.0000 | − | 6.92820i | 0.563809 | − | 0.325515i | ||||
\(454\) | −13.0000 | + | 22.5167i | −0.610120 | + | 1.05676i | ||||
\(455\) | −1.00000 | + | 1.73205i | −0.0468807 | + | 0.0811998i | ||||
\(456\) | 15.5885i | 0.729996i | ||||||||
\(457\) | −13.0000 | − | 22.5167i | −0.608114 | − | 1.05328i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
0.383437 | − | 0.923567i | \(-0.374740\pi\) | |||||||
\(458\) | 16.0000 | 0.747631 | ||||||||
\(459\) | 10.3923i | 0.485071i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0000 | + | 22.5167i | 0.605470 | + | 1.04871i | 0.991977 | + | 0.126419i | \(0.0403483\pi\) |
−0.386507 | + | 0.922287i | \(0.626318\pi\) | |||||||
\(462\) | − | 3.46410i | − | 0.161165i | ||||||
\(463\) | 3.00000 | − | 5.19615i | 0.139422 | − | 0.241486i | −0.787856 | − | 0.615859i | \(-0.788809\pi\) |
0.927278 | + | 0.374374i | \(0.122142\pi\) | |||||||
\(464\) | 2.50000 | − | 4.33013i | 0.116060 | − | 0.201021i | ||||
\(465\) | −1.50000 | + | 0.866025i | −0.0695608 | + | 0.0401610i | ||||
\(466\) | −7.00000 | − | 12.1244i | −0.324269 | − | 0.561650i | ||||
\(467\) | −28.0000 | −1.29569 | −0.647843 | − | 0.761774i | \(-0.724329\pi\) | ||||
−0.647843 | + | 0.761774i | \(0.724329\pi\) | |||||||
\(468\) | 1.50000 | + | 2.59808i | 0.0693375 | + | 0.120096i | ||||
\(469\) | 28.0000 | 1.29292 | ||||||||
\(470\) | 1.00000 | + | 1.73205i | 0.0461266 | + | 0.0798935i | ||||
\(471\) | −9.00000 | − | 5.19615i | −0.414698 | − | 0.239426i | ||||
\(472\) | 13.5000 | − | 23.3827i | 0.621388 | − | 1.07628i | ||||
\(473\) | −4.00000 | + | 6.92820i | −0.183920 | + | 0.318559i | ||||
\(474\) | 18.0000 | + | 10.3923i | 0.826767 | + | 0.477334i | ||||
\(475\) | 1.50000 | + | 2.59808i | 0.0688247 | + | 0.119208i | ||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | −42.0000 | −1.92305 | ||||||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | −7.50000 | − | 12.9904i | −0.342684 | − | 0.593546i | 0.642246 | − | 0.766498i | \(-0.278003\pi\) |
−0.984930 | + | 0.172953i | \(0.944669\pi\) | |||||||
\(480\) | −7.50000 | + | 4.33013i | −0.342327 | + | 0.197642i | ||||
\(481\) | −2.50000 | + | 4.33013i | −0.113990 | + | 0.197437i | ||||
\(482\) | 5.00000 | − | 8.66025i | 0.227744 | − | 0.394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | − | 8.66025i | −0.227273 | − | 0.393648i | ||||
\(485\) | −1.00000 | −0.0454077 | ||||||||
\(486\) | 13.5000 | − | 7.79423i | 0.612372 | − | 0.353553i | ||||
\(487\) | −34.0000 | −1.54069 | −0.770344 | − | 0.637629i | \(-0.779915\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(488\) | 1.50000 | + | 2.59808i | 0.0679018 | + | 0.117609i | ||||
\(489\) | 20.7846i | 0.939913i | ||||||||
\(490\) | 1.50000 | − | 2.59808i | 0.0677631 | − | 0.117369i | ||||
\(491\) | 3.00000 | − | 5.19615i | 0.135388 | − | 0.234499i | −0.790358 | − | 0.612646i | \(-0.790105\pi\) |
0.925746 | + | 0.378147i | \(0.123439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.00000 | − | 8.66025i | −0.225189 | − | 0.390038i | ||||
\(494\) | −3.00000 | −0.134976 | ||||||||
\(495\) | −3.00000 | −0.134840 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.0000 | + | 8.66025i | 0.672166 | + | 0.388075i | ||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −9.00000 | −0.401290 | −0.200645 | − | 0.979664i | \(-0.564304\pi\) | ||||
−0.200645 | + | 0.979664i | \(0.564304\pi\) | |||||||
\(504\) | 9.00000 | + | 15.5885i | 0.400892 | + | 0.694365i | ||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.50000 | + | 0.866025i | −0.0666173 | + | 0.0384615i | ||||
\(508\) | −4.00000 | + | 6.92820i | −0.177471 | + | 0.307389i | ||||
\(509\) | 12.0000 | − | 20.7846i | 0.531891 | − | 0.921262i | −0.467416 | − | 0.884037i | \(-0.654815\pi\) |
0.999307 | − | 0.0372243i | \(-0.0118516\pi\) | |||||||
\(510\) | − | 3.46410i | − | 0.153393i | ||||||
\(511\) | −6.00000 | − | 10.3923i | −0.265424 | − | 0.459728i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | − | 15.5885i | − | 0.688247i | ||||||
\(514\) | 28.0000 | 1.23503 | ||||||||
\(515\) | −0.500000 | − | 0.866025i | −0.0220326 | − | 0.0381616i | ||||
\(516\) | − | 13.8564i | − | 0.609994i | ||||||
\(517\) | −1.00000 | + | 1.73205i | −0.0439799 | + | 0.0761755i | ||||
\(518\) | −5.00000 | + | 8.66025i | −0.219687 | + | 0.380510i | ||||
\(519\) | −18.0000 | + | 10.3923i | −0.790112 | + | 0.456172i | ||||
\(520\) | −1.50000 | − | 2.59808i | −0.0657794 | − | 0.113933i | ||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | −7.50000 | + | 12.9904i | −0.328266 | + | 0.568574i | ||||
\(523\) | −15.0000 | −0.655904 | −0.327952 | − | 0.944694i | \(-0.606358\pi\) | ||||
−0.327952 | + | 0.944694i | \(0.606358\pi\) | |||||||
\(524\) | −2.00000 | − | 3.46410i | −0.0873704 | − | 0.151330i | ||||
\(525\) | 3.00000 | + | 1.73205i | 0.130931 | + | 0.0755929i | ||||
\(526\) | −8.00000 | + | 13.8564i | −0.348817 | + | 0.604168i | ||||
\(527\) | 1.00000 | − | 1.73205i | 0.0435607 | − | 0.0754493i | ||||
\(528\) | 1.50000 | + | 0.866025i | 0.0652791 | + | 0.0376889i | ||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 14.0000 | 0.608121 | ||||||||
\(531\) | −13.5000 | + | 23.3827i | −0.585850 | + | 1.01472i | ||||
\(532\) | 6.00000 | 0.260133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.00000 | − | 1.73205i | 0.129823 | − | 0.0749532i | ||||
\(535\) | 9.50000 | − | 16.4545i | 0.410721 | − | 0.711389i | ||||
\(536\) | −21.0000 | + | 36.3731i | −0.907062 | + | 1.57108i | ||||
\(537\) | 31.1769i | 1.34538i | ||||||||
\(538\) | 1.50000 | + | 2.59808i | 0.0646696 | + | 0.112011i | ||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 4.50000 | − | 2.59808i | 0.193649 | − | 0.111803i | ||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | −3.50000 | − | 6.06218i | −0.150338 | − | 0.260393i | ||||
\(543\) | − | 29.4449i | − | 1.26360i | ||||||
\(544\) | 5.00000 | − | 8.66025i | 0.214373 | − | 0.371305i | ||||
\(545\) | −7.00000 | + | 12.1244i | −0.299847 | + | 0.519350i | ||||
\(546\) | −3.00000 | + | 1.73205i | −0.128388 | + | 0.0741249i | ||||
\(547\) | 7.50000 | + | 12.9904i | 0.320677 | + | 0.555429i | 0.980628 | − | 0.195880i | \(-0.0627563\pi\) |
−0.659951 | + | 0.751309i | \(0.729423\pi\) | |||||||
\(548\) | 5.00000 | 0.213589 | ||||||||
\(549\) | −1.50000 | − | 2.59808i | −0.0640184 | − | 0.110883i | ||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 7.50000 | + | 12.9904i | 0.319511 | + | 0.553409i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | − | 20.7846i | 0.510292 | − | 0.883852i | ||||
\(554\) | 5.00000 | − | 8.66025i | 0.212430 | − | 0.367939i | ||||
\(555\) | 7.50000 | + | 4.33013i | 0.318357 | + | 0.183804i | ||||
\(556\) | 6.00000 | + | 10.3923i | 0.254457 | + | 0.440732i | ||||
\(557\) | −5.00000 | −0.211857 | −0.105928 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105928 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(558\) | −3.00000 | −0.127000 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | −1.00000 | − | 1.73205i | −0.0422577 | − | 0.0731925i | ||||
\(561\) | 3.00000 | − | 1.73205i | 0.126660 | − | 0.0731272i | ||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | 9.50000 | − | 16.4545i | 0.400377 | − | 0.693474i | −0.593394 | − | 0.804912i | \(-0.702212\pi\) |
0.993771 | + | 0.111438i | \(0.0355457\pi\) | |||||||
\(564\) | − | 3.46410i | − | 0.145865i | ||||||
\(565\) | 5.00000 | + | 8.66025i | 0.210352 | + | 0.364340i | ||||
\(566\) | 25.0000 | 1.05083 | ||||||||
\(567\) | −9.00000 | − | 15.5885i | −0.377964 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.50000 | + | 9.52628i | 0.230572 | + | 0.399362i | 0.957977 | − | 0.286846i | \(-0.0926069\pi\) |
−0.727405 | + | 0.686209i | \(0.759274\pi\) | |||||||
\(570\) | 5.19615i | 0.217643i | ||||||||
\(571\) | −6.00000 | + | 10.3923i | −0.251092 | + | 0.434904i | −0.963827 | − | 0.266529i | \(-0.914123\pi\) |
0.712735 | + | 0.701434i | \(0.247456\pi\) | |||||||
\(572\) | 0.500000 | − | 0.866025i | 0.0209061 | − | 0.0362103i | ||||
\(573\) | −27.0000 | + | 15.5885i | −1.12794 | + | 0.651217i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −21.0000 | −0.875000 | ||||||||
\(577\) | 11.0000 | 0.457936 | 0.228968 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(578\) | −6.50000 | − | 11.2583i | −0.270364 | − | 0.468285i | ||||
\(579\) | 19.5000 | + | 11.2583i | 0.810392 | + | 0.467880i | ||||
\(580\) | −2.50000 | + | 4.33013i | −0.103807 | + | 0.179799i | ||||
\(581\) | 10.0000 | − | 17.3205i | 0.414870 | − | 0.718576i | ||||
\(582\) | −1.50000 | − | 0.866025i | −0.0621770 | − | 0.0358979i | ||||
\(583\) | 7.00000 | + | 12.1244i | 0.289910 | + | 0.502140i | ||||
\(584\) | 18.0000 | 0.744845 | ||||||||
\(585\) | 1.50000 | + | 2.59808i | 0.0620174 | + | 0.107417i | ||||
\(586\) | −1.00000 | −0.0413096 | ||||||||
\(587\) | 7.00000 | + | 12.1244i | 0.288921 | + | 0.500426i | 0.973552 | − | 0.228464i | \(-0.0733702\pi\) |
−0.684632 | + | 0.728889i | \(0.740037\pi\) | |||||||
\(588\) | −4.50000 | + | 2.59808i | −0.185577 | + | 0.107143i | ||||
\(589\) | −1.50000 | + | 2.59808i | −0.0618064 | + | 0.107052i | ||||
\(590\) | 4.50000 | − | 7.79423i | 0.185262 | − | 0.320883i | ||||
\(591\) | − | 25.9808i | − | 1.06871i | ||||||
\(592\) | −2.50000 | − | 4.33013i | −0.102749 | − | 0.177967i | ||||
\(593\) | −31.0000 | −1.27302 | −0.636509 | − | 0.771270i | \(-0.719622\pi\) | ||||
−0.636509 | + | 0.771270i | \(0.719622\pi\) | |||||||
\(594\) | −4.50000 | − | 2.59808i | −0.184637 | − | 0.106600i | ||||
\(595\) | −4.00000 | −0.163984 | ||||||||
\(596\) | 3.00000 | + | 5.19615i | 0.122885 | + | 0.212843i | ||||
\(597\) | 38.1051i | 1.55954i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.00000 | + | 12.1244i | −0.286012 | + | 0.495388i | −0.972854 | − | 0.231419i | \(-0.925663\pi\) |
0.686842 | + | 0.726807i | \(0.258996\pi\) | |||||||
\(600\) | −4.50000 | + | 2.59808i | −0.183712 | + | 0.106066i | ||||
\(601\) | 8.50000 | + | 14.7224i | 0.346722 | + | 0.600541i | 0.985665 | − | 0.168714i | \(-0.0539613\pi\) |
−0.638943 | + | 0.769254i | \(0.720628\pi\) | |||||||
\(602\) | 16.0000 | 0.652111 | ||||||||
\(603\) | 21.0000 | − | 36.3731i | 0.855186 | − | 1.48123i | ||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | −4.50000 | − | 2.59808i | −0.182800 | − | 0.105540i | ||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | −7.50000 | + | 12.9904i | −0.304165 | + | 0.526830i | ||||
\(609\) | 15.0000 | + | 8.66025i | 0.607831 | + | 0.350931i | ||||
\(610\) | 0.500000 | + | 0.866025i | 0.0202444 | + | 0.0350643i | ||||
\(611\) | 2.00000 | 0.0809113 | ||||||||
\(612\) | −3.00000 | + | 5.19615i | −0.121268 | + | 0.210042i | ||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | −4.50000 | + | 7.79423i | −0.181163 | + | 0.313784i | −0.942277 | − | 0.334835i | \(-0.891320\pi\) |
0.761114 | + | 0.648618i | \(0.224653\pi\) | |||||||
\(618\) | − | 1.73205i | − | 0.0696733i | ||||||
\(619\) | 5.50000 | + | 9.52628i | 0.221064 | + | 0.382893i | 0.955131 | − | 0.296183i | \(-0.0957138\pi\) |
−0.734068 | + | 0.679076i | \(0.762380\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.00000 | 0.160385 | ||||||||
\(623\) | −2.00000 | − | 3.46410i | −0.0801283 | − | 0.138786i | ||||
\(624\) | − | 1.73205i | − | 0.0693375i | ||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −14.0000 | + | 24.2487i | −0.559553 | + | 0.969173i | ||||
\(627\) | −4.50000 | + | 2.59808i | −0.179713 | + | 0.103757i | ||||
\(628\) | −3.00000 | − | 5.19615i | −0.119713 | − | 0.207349i | ||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 3.00000 | + | 5.19615i | 0.119523 | + | 0.207020i | ||||
\(631\) | −5.00000 | −0.199047 | −0.0995234 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995234 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(632\) | 18.0000 | + | 31.1769i | 0.716002 | + | 1.24015i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.5000 | + | 23.3827i | −0.536153 | + | 0.928645i | ||||
\(635\) | −4.00000 | + | 6.92820i | −0.158735 | + | 0.274937i | ||||
\(636\) | −21.0000 | − | 12.1244i | −0.832704 | − | 0.480762i | ||||
\(637\) | −1.50000 | − | 2.59808i | −0.0594322 | − | 0.102940i | ||||
\(638\) | 5.00000 | 0.197952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | −8.50000 | − | 14.7224i | −0.335730 | − | 0.581501i | 0.647895 | − | 0.761730i | \(-0.275650\pi\) |
−0.983625 | + | 0.180229i | \(0.942316\pi\) | |||||||
\(642\) | 28.5000 | − | 16.4545i | 1.12481 | − | 0.649407i | ||||
\(643\) | −16.0000 | + | 27.7128i | −0.630978 | + | 1.09289i | 0.356374 | + | 0.934344i | \(0.384013\pi\) |
−0.987352 | + | 0.158543i | \(0.949320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 13.8564i | − | 0.545595i | ||||||
\(646\) | −3.00000 | − | 5.19615i | −0.118033 | − | 0.204440i | ||||
\(647\) | 41.0000 | 1.61188 | 0.805938 | − | 0.592000i | \(-0.201661\pi\) | ||||
0.805938 | + | 0.592000i | \(0.201661\pi\) | |||||||
\(648\) | 27.0000 | 1.06066 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | −0.500000 | − | 0.866025i | −0.0196116 | − | 0.0339683i | ||||
\(651\) | 3.46410i | 0.135769i | ||||||||
\(652\) | −6.00000 | + | 10.3923i | −0.234978 | + | 0.406994i | ||||
\(653\) | −24.0000 | + | 41.5692i | −0.939193 | + | 1.62673i | −0.172211 | + | 0.985060i | \(0.555091\pi\) |
−0.766982 | + | 0.641669i | \(0.778242\pi\) | |||||||
\(654\) | −21.0000 | + | 12.1244i | −0.821165 | + | 0.474100i | ||||
\(655\) | −2.00000 | − | 3.46410i | −0.0781465 | − | 0.135354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.0000 | −0.702247 | ||||||||
\(658\) | 4.00000 | 0.155936 | ||||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | −1.50000 | − | 0.866025i | −0.0583874 | − | 0.0337100i | ||||
\(661\) | −19.0000 | + | 32.9090i | −0.739014 | + | 1.28001i | 0.213925 | + | 0.976850i | \(0.431375\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 13.5000 | − | 23.3827i | 0.524692 | − | 0.908794i | ||||
\(663\) | −3.00000 | − | 1.73205i | −0.116510 | − | 0.0672673i | ||||
\(664\) | 15.0000 | + | 25.9808i | 0.582113 | + | 1.00825i | ||||
\(665\) | 6.00000 | 0.232670 | ||||||||
\(666\) | 7.50000 | + | 12.9904i | 0.290619 | + | 0.503367i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.0000 | − | 22.5167i | 1.50783 | − | 0.870544i | ||||
\(670\) | −7.00000 | + | 12.1244i | −0.270434 | + | 0.468405i | ||||
\(671\) | −0.500000 | + | 0.866025i | −0.0193023 | + | 0.0334325i | ||||
\(672\) | 17.3205i | 0.668153i | ||||||||
\(673\) | −12.0000 | − | 20.7846i | −0.462566 | − | 0.801188i | 0.536522 | − | 0.843886i | \(-0.319738\pi\) |
−0.999088 | + | 0.0426985i | \(0.986405\pi\) | |||||||
\(674\) | 22.0000 | 0.847408 | ||||||||
\(675\) | 4.50000 | − | 2.59808i | 0.173205 | − | 0.100000i | ||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | −3.00000 | − | 5.19615i | −0.115299 | − | 0.199704i | 0.802600 | − | 0.596518i | \(-0.203449\pi\) |
−0.917899 | + | 0.396813i | \(0.870116\pi\) | |||||||
\(678\) | 17.3205i | 0.665190i | ||||||||
\(679\) | −1.00000 | + | 1.73205i | −0.0383765 | + | 0.0664700i | ||||
\(680\) | 3.00000 | − | 5.19615i | 0.115045 | − | 0.199263i | ||||
\(681\) | 39.0000 | − | 22.5167i | 1.49448 | − | 0.862840i | ||||
\(682\) | 0.500000 | + | 0.866025i | 0.0191460 | + | 0.0331618i | ||||
\(683\) | −20.0000 | −0.765279 | −0.382639 | − | 0.923898i | \(-0.624985\pi\) | ||||
−0.382639 | + | 0.923898i | \(0.624985\pi\) | |||||||
\(684\) | 4.50000 | − | 7.79423i | 0.172062 | − | 0.298020i | ||||
\(685\) | 5.00000 | 0.191040 | ||||||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | −24.0000 | − | 13.8564i | −0.915657 | − | 0.528655i | ||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 7.00000 | − | 12.1244i | 0.266679 | − | 0.461901i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.500000 | − | 0.866025i | −0.0190209 | − | 0.0329452i | 0.856358 | − | 0.516382i | \(-0.172722\pi\) |
−0.875379 | + | 0.483437i | \(0.839388\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | −3.00000 | + | 5.19615i | −0.113961 | + | 0.197386i | ||||
\(694\) | −17.0000 | −0.645311 | ||||||||
\(695\) | 6.00000 | + | 10.3923i | 0.227593 | + | 0.394203i | ||||
\(696\) | −22.5000 | + | 12.9904i | −0.852860 | + | 0.492399i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.00000 | − | 10.3923i | 0.227103 | − | 0.393355i | ||||
\(699\) | 24.2487i | 0.917170i | ||||||||
\(700\) | 1.00000 | + | 1.73205i | 0.0377964 | + | 0.0654654i | ||||
\(701\) | −5.00000 | −0.188847 | −0.0944237 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944237 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(702\) | 5.19615i | 0.196116i | ||||||||
\(703\) | 15.0000 | 0.565736 | ||||||||
\(704\) | 3.50000 | + | 6.06218i | 0.131911 | + | 0.228477i | ||||
\(705\) | − | 3.46410i | − | 0.130466i | ||||||
\(706\) | −1.50000 | + | 2.59808i | −0.0564532 | + | 0.0977799i | ||||
\(707\) | −3.00000 | + | 5.19615i | −0.112827 | + | 0.195421i | ||||
\(708\) | −13.5000 | + | 7.79423i | −0.507361 | + | 0.292925i | ||||
\(709\) | −2.00000 | − | 3.46410i | −0.0751116 | − | 0.130097i | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.0000 | − | 31.1769i | −0.675053 | − | 1.16923i | ||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −6.00000 | − | 3.46410i | −0.224544 | − | 0.129641i | ||||
\(715\) | 0.500000 | − | 0.866025i | 0.0186989 | − | 0.0323875i | ||||
\(716\) | −9.00000 | + | 15.5885i | −0.336346 | + | 0.582568i | ||||
\(717\) | 22.5000 | + | 12.9904i | 0.840278 | + | 0.485135i | ||||
\(718\) | −15.5000 | − | 26.8468i | −0.578455 | − | 1.00191i | ||||
\(719\) | −2.00000 | −0.0745874 | −0.0372937 | − | 0.999304i | \(-0.511874\pi\) | ||||
−0.0372937 | + | 0.999304i | \(0.511874\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | −5.00000 | − | 8.66025i | −0.186081 | − | 0.322301i | ||||
\(723\) | −15.0000 | + | 8.66025i | −0.557856 | + | 0.322078i | ||||
\(724\) | 8.50000 | − | 14.7224i | 0.315900 | − | 0.547155i | ||||
\(725\) | −2.50000 | + | 4.33013i | −0.0928477 | + | 0.160817i | ||||
\(726\) | − | 17.3205i | − | 0.642824i | ||||||
\(727\) | −24.0000 | − | 41.5692i | −0.890111 | − | 1.54172i | −0.839742 | − | 0.542986i | \(-0.817294\pi\) |
−0.0503692 | − | 0.998731i | \(-0.516040\pi\) | |||||||
\(728\) | −6.00000 | −0.222375 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | 8.00000 | + | 13.8564i | 0.295891 | + | 0.512498i | ||||
\(732\) | − | 1.73205i | − | 0.0640184i | ||||||
\(733\) | −6.50000 | + | 11.2583i | −0.240083 | + | 0.415836i | −0.960738 | − | 0.277458i | \(-0.910508\pi\) |
0.720655 | + | 0.693294i | \(0.243841\pi\) | |||||||
\(734\) | 12.5000 | − | 21.6506i | 0.461383 | − | 0.799140i | ||||
\(735\) | −4.50000 | + | 2.59808i | −0.165985 | + | 0.0958315i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.0000 | −0.515697 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.00000 | 0.331070 | 0.165535 | − | 0.986204i | \(-0.447065\pi\) | ||||
0.165535 | + | 0.986204i | \(0.447065\pi\) | |||||||
\(740\) | 2.50000 | + | 4.33013i | 0.0919018 | + | 0.159179i | ||||
\(741\) | 4.50000 | + | 2.59808i | 0.165312 | + | 0.0954427i | ||||
\(742\) | 14.0000 | − | 24.2487i | 0.513956 | − | 0.890198i | ||||
\(743\) | 24.0000 | − | 41.5692i | 0.880475 | − | 1.52503i | 0.0296605 | − | 0.999560i | \(-0.490557\pi\) |
0.850814 | − | 0.525467i | \(-0.176109\pi\) | |||||||
\(744\) | −4.50000 | − | 2.59808i | −0.164978 | − | 0.0952501i | ||||
\(745\) | 3.00000 | + | 5.19615i | 0.109911 | + | 0.190372i | ||||
\(746\) | 20.0000 | 0.732252 | ||||||||
\(747\) | −15.0000 | − | 25.9808i | −0.548821 | − | 0.950586i | ||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | −19.0000 | − | 32.9090i | −0.694245 | − | 1.20247i | ||||
\(750\) | −1.50000 | + | 0.866025i | −0.0547723 | + | 0.0316228i | ||||
\(751\) | −1.00000 | + | 1.73205i | −0.0364905 | + | 0.0632034i | −0.883694 | − | 0.468065i | \(-0.844951\pi\) |
0.847203 | + | 0.531269i | \(0.178285\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | − | 20.7846i | − | 0.757433i | ||||||
\(754\) | −2.50000 | − | 4.33013i | −0.0910446 | − | 0.157694i | ||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | − | 10.3923i | − | 0.377964i | ||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | −11.5000 | − | 19.9186i | −0.417699 | − | 0.723476i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.50000 | + | 7.79423i | −0.163232 | + | 0.282726i | ||||
\(761\) | 18.0000 | − | 31.1769i | 0.652499 | − | 1.13016i | −0.330015 | − | 0.943976i | \(-0.607054\pi\) |
0.982514 | − | 0.186187i | \(-0.0596129\pi\) | |||||||
\(762\) | −12.0000 | + | 6.92820i | −0.434714 | + | 0.250982i | ||||
\(763\) | 14.0000 | + | 24.2487i | 0.506834 | + | 0.877862i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | −3.00000 | + | 5.19615i | −0.108465 | + | 0.187867i | ||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | −4.50000 | − | 7.79423i | −0.162486 | − | 0.281433i | ||||
\(768\) | −25.5000 | − | 14.7224i | −0.920152 | − | 0.531250i | ||||
\(769\) | 20.0000 | − | 34.6410i | 0.721218 | − | 1.24919i | −0.239293 | − | 0.970947i | \(-0.576916\pi\) |
0.960512 | − | 0.278240i | \(-0.0897509\pi\) | |||||||
\(770\) | 1.00000 | − | 1.73205i | 0.0360375 | − | 0.0624188i | ||||
\(771\) | −42.0000 | − | 24.2487i | −1.51259 | − | 0.873296i | ||||
\(772\) | 6.50000 | + | 11.2583i | 0.233940 | + | 0.405196i | ||||
\(773\) | 31.0000 | 1.11499 | 0.557496 | − | 0.830179i | \(-0.311762\pi\) | ||||
0.557496 | + | 0.830179i | \(0.311762\pi\) | |||||||
\(774\) | 12.0000 | − | 20.7846i | 0.431331 | − | 0.747087i | ||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | −1.50000 | − | 2.59808i | −0.0538469 | − | 0.0932655i | ||||
\(777\) | 15.0000 | − | 8.66025i | 0.538122 | − | 0.310685i | ||||
\(778\) | −11.0000 | + | 19.0526i | −0.394369 | + | 0.683067i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.73205i | 0.0620174i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.5000 | − | 12.9904i | 0.804084 | − | 0.464238i | ||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | −3.00000 | − | 5.19615i | −0.107075 | − | 0.185459i | ||||
\(786\) | − | 6.92820i | − | 0.247121i | ||||||
\(787\) | −19.0000 | + | 32.9090i | −0.677277 | + | 1.17308i | 0.298521 | + | 0.954403i | \(0.403507\pi\) |
−0.975798 | + | 0.218675i | \(0.929827\pi\) | |||||||
\(788\) | 7.50000 | − | 12.9904i | 0.267176 | − | 0.462763i | ||||
\(789\) | 24.0000 | − | 13.8564i | 0.854423 | − | 0.493301i | ||||
\(790\) | 6.00000 | + | 10.3923i | 0.213470 | + | 0.369742i | ||||
\(791\) | 20.0000 | 0.711118 | ||||||||
\(792\) | −4.50000 | − | 7.79423i | −0.159901 | − | 0.276956i | ||||
\(793\) | 1.00000 | 0.0355110 | ||||||||
\(794\) | −15.0000 | − | 25.9808i | −0.532330 | − | 0.922023i | ||||
\(795\) | −21.0000 | − | 12.1244i | −0.744793 | − | 0.430007i | ||||
\(796\) | −11.0000 | + | 19.0526i | −0.389885 | + | 0.675300i | ||||
\(797\) | 21.0000 | − | 36.3731i | 0.743858 | − | 1.28840i | −0.206868 | − | 0.978369i | \(-0.566327\pi\) |
0.950726 | − | 0.310031i | \(-0.100340\pi\) | |||||||
\(798\) | 9.00000 | + | 5.19615i | 0.318597 | + | 0.183942i | ||||
\(799\) | 2.00000 | + | 3.46410i | 0.0707549 | + | 0.122551i | ||||
\(800\) | −5.00000 | −0.176777 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | −28.0000 | −0.988714 | ||||||||
\(803\) | 3.00000 | + | 5.19615i | 0.105868 | + | 0.183368i | ||||
\(804\) | 21.0000 | − | 12.1244i | 0.740613 | − | 0.427593i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.500000 | − | 0.866025i | 0.0176117 | − | 0.0305044i | ||||
\(807\) | − | 5.19615i | − | 0.182913i | ||||||
\(808\) | −4.50000 | − | 7.79423i | −0.158309 | − | 0.274200i | ||||
\(809\) | −5.00000 | −0.175791 | −0.0878953 | − | 0.996130i | \(-0.528014\pi\) | ||||
−0.0878953 | + | 0.996130i | \(0.528014\pi\) | |||||||
\(810\) | 9.00000 | 0.316228 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | 5.00000 | + | 8.66025i | 0.175466 | + | 0.303915i | ||||
\(813\) | 12.1244i | 0.425220i | ||||||||
\(814\) | 2.50000 | − | 4.33013i | 0.0876250 | − | 0.151771i | ||||
\(815\) | −6.00000 | + | 10.3923i | −0.210171 | + | 0.364027i | ||||
\(816\) | 3.00000 | − | 1.73205i | 0.105021 | − | 0.0606339i | ||||
\(817\) | −12.0000 | − | 20.7846i | −0.419827 | − | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | 0.209657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0000 | − | 27.7128i | −0.558404 | − | 0.967184i | −0.997630 | − | 0.0688073i | \(-0.978081\pi\) |
0.439226 | − | 0.898377i | \(-0.355253\pi\) | |||||||
\(822\) | 7.50000 | + | 4.33013i | 0.261593 | + | 0.151031i | ||||
\(823\) | −5.50000 | + | 9.52628i | −0.191718 | + | 0.332065i | −0.945820 | − | 0.324692i | \(-0.894739\pi\) |
0.754102 | + | 0.656758i | \(0.228073\pi\) | |||||||
\(824\) | 1.50000 | − | 2.59808i | 0.0522550 | − | 0.0905083i | ||||
\(825\) | −1.50000 | − | 0.866025i | −0.0522233 | − | 0.0301511i | ||||
\(826\) | −9.00000 | − | 15.5885i | −0.313150 | − | 0.542392i | ||||
\(827\) | −44.0000 | −1.53003 | −0.765015 | − | 0.644013i | \(-0.777268\pi\) | ||||
−0.765015 | + | 0.644013i | \(0.777268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 5.00000 | + | 8.66025i | 0.173553 | + | 0.300602i | ||||
\(831\) | −15.0000 | + | 8.66025i | −0.520344 | + | 0.300421i | ||||
\(832\) | 3.50000 | − | 6.06218i | 0.121341 | − | 0.210168i | ||||
\(833\) | 3.00000 | − | 5.19615i | 0.103944 | − | 0.180036i | ||||
\(834\) | 20.7846i | 0.719712i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.00000 | −0.103757 | ||||||||
\(837\) | 4.50000 | + | 2.59808i | 0.155543 | + | 0.0898027i | ||||
\(838\) | −20.0000 | −0.690889 | ||||||||
\(839\) | −2.50000 | − | 4.33013i | −0.0863096 | − | 0.149493i | 0.819639 | − | 0.572880i | \(-0.194174\pi\) |
−0.905949 | + | 0.423388i | \(0.860841\pi\) | |||||||
\(840\) | 10.3923i | 0.358569i | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 5.00000 | − | 8.66025i | 0.172311 | − | 0.298452i | ||||
\(843\) | 18.0000 | − | 10.3923i | 0.619953 | − | 0.357930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 3.00000 | − | 5.19615i | 0.103142 | − | 0.178647i | ||||
\(847\) | −20.0000 | −0.687208 | ||||||||
\(848\) | 7.00000 | + | 12.1244i | 0.240381 | + | 0.416352i | ||||
\(849\) | −37.5000 | − | 21.6506i | −1.28700 | − | 0.743048i | ||||
\(850\) | 1.00000 | − | 1.73205i | 0.0342997 | − | 0.0594089i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0000 | + | 46.7654i | 0.924462 | + | 1.60122i | 0.792424 | + | 0.609971i | \(0.208819\pi\) |
0.132039 | + | 0.991245i | \(0.457848\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 4.50000 | − | 7.79423i | 0.153897 | − | 0.266557i | ||||
\(856\) | 57.0000 | 1.94822 | ||||||||
\(857\) | −12.0000 | − | 20.7846i | −0.409912 | − | 0.709989i | 0.584967 | − | 0.811057i | \(-0.301107\pi\) |
−0.994880 | + | 0.101068i | \(0.967774\pi\) | |||||||
\(858\) | 1.50000 | − | 0.866025i | 0.0512092 | − | 0.0295656i | ||||
\(859\) | −14.0000 | + | 24.2487i | −0.477674 | + | 0.827355i | −0.999672 | − | 0.0255910i | \(-0.991853\pi\) |
0.521999 | + | 0.852946i | \(0.325187\pi\) | |||||||
\(860\) | 4.00000 | − | 6.92820i | 0.136399 | − | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.50000 | + | 14.7224i | 0.289511 | + | 0.501448i | ||||
\(863\) | −30.0000 | −1.02121 | −0.510606 | − | 0.859815i | \(-0.670579\pi\) | ||||
−0.510606 | + | 0.859815i | \(0.670579\pi\) | |||||||
\(864\) | 22.5000 | + | 12.9904i | 0.765466 | + | 0.441942i | ||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | −19.0000 | − | 32.9090i | −0.645646 | − | 1.11829i | ||||
\(867\) | 22.5167i | 0.764706i | ||||||||
\(868\) | −1.00000 | + | 1.73205i | −0.0339422 | + | 0.0587896i | ||||
\(869\) | −6.00000 | + | 10.3923i | −0.203536 | + | 0.352535i | ||||
\(870\) | −7.50000 | + | 4.33013i | −0.254274 | + | 0.146805i | ||||
\(871\) | 7.00000 | + | 12.1244i | 0.237186 | + | 0.410818i | ||||
\(872\) | −42.0000 | −1.42230 | ||||||||
\(873\) | 1.50000 | + | 2.59808i | 0.0507673 | + | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | + | 1.73205i | 0.0338062 | + | 0.0585540i | ||||
\(876\) | −9.00000 | − | 5.19615i | −0.304082 | − | 0.175562i | ||||
\(877\) | −7.50000 | + | 12.9904i | −0.253257 | + | 0.438654i | −0.964421 | − | 0.264373i | \(-0.914835\pi\) |
0.711164 | + | 0.703027i | \(0.248168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.50000 | + | 0.866025i | 0.0505937 | + | 0.0292103i | ||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | 23.0000 | 0.774890 | 0.387445 | − | 0.921893i | \(-0.373358\pi\) | ||||
0.387445 | + | 0.921893i | \(0.373358\pi\) | |||||||
\(882\) | −9.00000 | −0.303046 | ||||||||
\(883\) | 47.0000 | 1.58168 | 0.790838 | − | 0.612026i | \(-0.209645\pi\) | ||||
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(884\) | −1.00000 | − | 1.73205i | −0.0336336 | − | 0.0582552i | ||||
\(885\) | −13.5000 | + | 7.79423i | −0.453798 | + | 0.262000i | ||||
\(886\) | −3.50000 | + | 6.06218i | −0.117585 | + | 0.203663i | ||||
\(887\) | 11.5000 | − | 19.9186i | 0.386132 | − | 0.668801i | −0.605793 | − | 0.795622i | \(-0.707144\pi\) |
0.991926 | + | 0.126821i | \(0.0404775\pi\) | |||||||
\(888\) | 25.9808i | 0.871857i | ||||||||
\(889\) | 8.00000 | + | 13.8564i | 0.268311 | + | 0.464729i | ||||
\(890\) | 2.00000 | 0.0670402 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 26.0000 | 0.870544 | ||||||||
\(893\) | −3.00000 | − | 5.19615i | −0.100391 | − | 0.173883i | ||||
\(894\) | 10.3923i | 0.347571i | ||||||||
\(895\) | −9.00000 | + | 15.5885i | −0.300837 | + | 0.521065i | ||||
\(896\) | −3.00000 | + | 5.19615i | −0.100223 | + | 0.173591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | −5.00000 | −0.166759 | ||||||||
\(900\) | 3.00000 | 0.100000 | ||||||||
\(901\) | 28.0000 | 0.932815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | − | 13.8564i | −0.798670 | − | 0.461112i | ||||
\(904\) | −15.0000 | + | 25.9808i | −0.498893 | + | 0.864107i | ||||
\(905\) | 8.50000 | − | 14.7224i | 0.282550 | − | 0.489390i | ||||
\(906\) | 12.0000 | + | 6.92820i | 0.398673 | + | 0.230174i | ||||
\(907\) | 0.500000 | + | 0.866025i | 0.0166022 | + | 0.0287559i | 0.874207 | − | 0.485553i | \(-0.161382\pi\) |
−0.857605 | + | 0.514309i | \(0.828048\pi\) | |||||||
\(908\) | 26.0000 | 0.862840 | ||||||||
\(909\) | 4.50000 | + | 7.79423i | 0.149256 | + | 0.258518i | ||||
\(910\) | −2.00000 | −0.0662994 | ||||||||
\(911\) | −21.0000 | − | 36.3731i | −0.695761 | − | 1.20509i | −0.969923 | − | 0.243410i | \(-0.921734\pi\) |
0.274162 | − | 0.961683i | \(-0.411599\pi\) | |||||||
\(912\) | −4.50000 | + | 2.59808i | −0.149010 | + | 0.0860309i | ||||
\(913\) | −5.00000 | + | 8.66025i | −0.165476 | + | 0.286613i | ||||
\(914\) | 13.0000 | − | 22.5167i | 0.430002 | − | 0.744785i | ||||
\(915\) | − | 1.73205i | − | 0.0572598i | ||||||
\(916\) | −8.00000 | − | 13.8564i | −0.264327 | − | 0.457829i | ||||
\(917\) | −8.00000 | −0.264183 | ||||||||
\(918\) | −9.00000 | + | 5.19615i | −0.297044 | + | 0.171499i | ||||
\(919\) | 38.0000 | 1.25350 | 0.626752 | − | 0.779219i | \(-0.284384\pi\) | ||||
0.626752 | + | 0.779219i | \(0.284384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 3.46410i | − | 0.114146i | ||||||
\(922\) | −13.0000 | + | 22.5167i | −0.428132 | + | 0.741547i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.00000 | + | 1.73205i | −0.0986928 | + | 0.0569803i | ||||
\(925\) | 2.50000 | + | 4.33013i | 0.0821995 | + | 0.142374i | ||||
\(926\) | 6.00000 | 0.197172 | ||||||||
\(927\) | −1.50000 | + | 2.59808i | −0.0492665 | + | 0.0853320i | ||||
\(928\) | −25.0000 | −0.820665 | ||||||||
\(929\) | 28.0000 | + | 48.4974i | 0.918650 | + | 1.59115i | 0.801467 | + | 0.598038i | \(0.204053\pi\) |
0.117183 | + | 0.993110i | \(0.462614\pi\) | |||||||
\(930\) | −1.50000 | − | 0.866025i | −0.0491869 | − | 0.0283981i | ||||
\(931\) | −4.50000 | + | 7.79423i | −0.147482 | + | 0.255446i | ||||
\(932\) | −7.00000 | + | 12.1244i | −0.229293 | + | 0.397146i | ||||
\(933\) | −6.00000 | − | 3.46410i | −0.196431 | − | 0.113410i | ||||
\(934\) | −14.0000 | − | 24.2487i | −0.458094 | − | 0.793442i | ||||
\(935\) | 2.00000 | 0.0654070 | ||||||||
\(936\) | −4.50000 | + | 7.79423i | −0.147087 | + | 0.254762i | ||||
\(937\) | 60.0000 | 1.96011 | 0.980057 | − | 0.198715i | \(-0.0636769\pi\) | ||||
0.980057 | + | 0.198715i | \(0.0636769\pi\) | |||||||
\(938\) | 14.0000 | + | 24.2487i | 0.457116 | + | 0.791748i | ||||
\(939\) | 42.0000 | − | 24.2487i | 1.37062 | − | 0.791327i | ||||
\(940\) | 1.00000 | − | 1.73205i | 0.0326164 | − | 0.0564933i | ||||
\(941\) | 18.0000 | − | 31.1769i | 0.586783 | − | 1.01634i | −0.407867 | − | 0.913041i | \(-0.633727\pi\) |
0.994651 | − | 0.103297i | \(-0.0329393\pi\) | |||||||
\(942\) | − | 10.3923i | − | 0.338600i | ||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 9.00000 | 0.292925 | ||||||||
\(945\) | − | 10.3923i | − | 0.338062i | ||||||
\(946\) | −8.00000 | −0.260102 | ||||||||
\(947\) | −12.0000 | − | 20.7846i | −0.389948 | − | 0.675409i | 0.602494 | − | 0.798123i | \(-0.294174\pi\) |
−0.992442 | + | 0.122714i | \(0.960840\pi\) | |||||||
\(948\) | − | 20.7846i | − | 0.675053i | ||||||
\(949\) | 3.00000 | − | 5.19615i | 0.0973841 | − | 0.168674i | ||||
\(950\) | −1.50000 | + | 2.59808i | −0.0486664 | + | 0.0842927i | ||||
\(951\) | 40.5000 | − | 23.3827i | 1.31330 | − | 0.758236i | ||||
\(952\) | −6.00000 | − | 10.3923i | −0.194461 | − | 0.336817i | ||||
\(953\) | −48.0000 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(954\) | −21.0000 | − | 36.3731i | −0.679900 | − | 1.17762i | ||||
\(955\) | −18.0000 | −0.582466 | ||||||||
\(956\) | 7.50000 | + | 12.9904i | 0.242567 | + | 0.420139i | ||||
\(957\) | −7.50000 | − | 4.33013i | −0.242441 | − | 0.139973i | ||||
\(958\) | 7.50000 | − | 12.9904i | 0.242314 | − | 0.419700i | ||||
\(959\) | 5.00000 | − | 8.66025i | 0.161458 | − | 0.279654i | ||||
\(960\) | −10.5000 | − | 6.06218i | −0.338886 | − | 0.195656i | ||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | −5.00000 | −0.161206 | ||||||||
\(963\) | −57.0000 | −1.83680 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 6.50000 | + | 11.2583i | 0.209242 | + | 0.362418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0000 | − | 43.3013i | 0.803946 | − | 1.39247i | −0.113055 | − | 0.993589i | \(-0.536064\pi\) |
0.917000 | − | 0.398886i | \(-0.130603\pi\) | |||||||
\(968\) | 15.0000 | − | 25.9808i | 0.482118 | − | 0.835053i | ||||
\(969\) | 10.3923i | 0.333849i | ||||||||
\(970\) | −0.500000 | − | 0.866025i | −0.0160540 | − | 0.0278064i | ||||
\(971\) | 50.0000 | 1.60458 | 0.802288 | − | 0.596937i | \(-0.203616\pi\) | ||||
0.802288 | + | 0.596937i | \(0.203616\pi\) | |||||||
\(972\) | −13.5000 | − | 7.79423i | −0.433013 | − | 0.250000i | ||||
\(973\) | 24.0000 | 0.769405 | ||||||||
\(974\) | −17.0000 | − | 29.4449i | −0.544715 | − | 0.943474i | ||||
\(975\) | 1.73205i | 0.0554700i | ||||||||
\(976\) | −0.500000 | + | 0.866025i | −0.0160046 | + | 0.0277208i | ||||
\(977\) | 4.50000 | − | 7.79423i | 0.143968 | − | 0.249359i | −0.785020 | − | 0.619471i | \(-0.787347\pi\) |
0.928987 | + | 0.370111i | \(0.120681\pi\) | |||||||
\(978\) | −18.0000 | + | 10.3923i | −0.575577 | + | 0.332309i | ||||
\(979\) | 1.00000 | + | 1.73205i | 0.0319601 | + | 0.0553566i | ||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | 42.0000 | 1.34096 | ||||||||
\(982\) | 6.00000 | 0.191468 | ||||||||
\(983\) | 2.00000 | + | 3.46410i | 0.0637901 | + | 0.110488i | 0.896157 | − | 0.443738i | \(-0.146348\pi\) |
−0.832367 | + | 0.554226i | \(0.813015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.50000 | − | 12.9904i | 0.238970 | − | 0.413908i | ||||
\(986\) | 5.00000 | − | 8.66025i | 0.159232 | − | 0.275799i | ||||
\(987\) | −6.00000 | − | 3.46410i | −0.190982 | − | 0.110264i | ||||
\(988\) | 1.50000 | + | 2.59808i | 0.0477214 | + | 0.0826558i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −1.50000 | − | 2.59808i | −0.0476731 | − | 0.0825723i | ||||
\(991\) | −18.0000 | −0.571789 | −0.285894 | − | 0.958261i | \(-0.592291\pi\) | ||||
−0.285894 | + | 0.958261i | \(0.592291\pi\) | |||||||
\(992\) | −2.50000 | − | 4.33013i | −0.0793751 | − | 0.137482i | ||||
\(993\) | −40.5000 | + | 23.3827i | −1.28523 | + | 0.742027i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.0000 | + | 19.0526i | −0.348723 | + | 0.604007i | ||||
\(996\) | − | 17.3205i | − | 0.548821i | ||||||
\(997\) | 20.0000 | + | 34.6410i | 0.633406 | + | 1.09709i | 0.986850 | + | 0.161636i | \(0.0516771\pi\) |
−0.353444 | + | 0.935456i | \(0.614990\pi\) | |||||||
\(998\) | −28.0000 | −0.886325 | ||||||||
\(999\) | − | 25.9808i | − | 0.821995i |
(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 | 585.2.i.b.391.1 | yes | 2 | |
3.2 | odd | 2 | 1755.2.i.b.1171.1 | 2 | |||
9.2 | odd | 6 | 1755.2.i.b.586.1 | 2 | |||
9.4 | even | 3 | 5265.2.a.e.1.1 | 1 | |||
9.5 | odd | 6 | 5265.2.a.m.1.1 | 1 | |||
9.7 | even | 3 | inner | 585.2.i.b.196.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.b.196.1 | ✓ | 2 | 9.7 | even | 3 | inner | |
585.2.i.b.391.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1755.2.i.b.586.1 | 2 | 9.2 | odd | 6 | |||
1755.2.i.b.1171.1 | 2 | 3.2 | odd | 2 | |||
5265.2.a.e.1.1 | 1 | 9.4 | even | 3 | |||
5265.2.a.m.1.1 | 1 | 9.5 | odd | 6 |