Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [85,2,Mod(4,85)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(85, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("85.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 85 = 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 85.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.678728417181\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 85.64 |
Dual form | 85.2.j.a.4.1 |
$q$-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 \(\left(\mathbb{Z}/85\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −1.00000 | + | 1.00000i | −0.577350 | + | 0.577350i | −0.934172 | − | 0.356822i | \(-0.883860\pi\) |
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 1.00000 | − | 1.00000i | 0.408248 | − | 0.408248i | ||||
\(7\) | −3.00000 | − | 3.00000i | −1.13389 | − | 1.13389i | −0.989524 | − | 0.144370i | \(-0.953885\pi\) |
−0.144370 | − | 0.989524i | \(-0.546115\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 2.00000 | + | 1.00000i | 0.632456 | + | 0.316228i | ||||
\(11\) | −3.00000 | + | 3.00000i | −0.904534 | + | 0.904534i | −0.995824 | − | 0.0912903i | \(-0.970901\pi\) |
0.0912903 | + | 0.995824i | \(0.470901\pi\) | |||||||
\(12\) | 1.00000 | − | 1.00000i | 0.288675 | − | 0.288675i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 3.00000 | + | 3.00000i | 0.801784 | + | 0.801784i | ||||
\(15\) | 3.00000 | − | 1.00000i | 0.774597 | − | 0.258199i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.00000 | + | 4.00000i | −0.242536 | + | 0.970143i | ||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 2.00000 | + | 1.00000i | 0.447214 | + | 0.223607i | ||||
\(21\) | 6.00000 | 1.30931 | ||||||||
\(22\) | 3.00000 | − | 3.00000i | 0.639602 | − | 0.639602i | ||||
\(23\) | 1.00000 | + | 1.00000i | 0.208514 | + | 0.208514i | 0.803636 | − | 0.595121i | \(-0.202896\pi\) |
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | −3.00000 | + | 3.00000i | −0.612372 | + | 0.612372i | ||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | − | 4.00000i | −0.769800 | − | 0.769800i | ||||
\(28\) | 3.00000 | + | 3.00000i | 0.566947 | + | 0.566947i | ||||
\(29\) | −3.00000 | − | 3.00000i | −0.557086 | − | 0.557086i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | −3.00000 | + | 1.00000i | −0.547723 | + | 0.182574i | ||||
\(31\) | −1.00000 | − | 1.00000i | −0.179605 | − | 0.179605i | 0.611578 | − | 0.791184i | \(-0.290535\pi\) |
−0.791184 | + | 0.611578i | \(0.790535\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | − | 6.00000i | − | 1.04447i | ||||||
\(34\) | 1.00000 | − | 4.00000i | 0.171499 | − | 0.685994i | ||||
\(35\) | 3.00000 | + | 9.00000i | 0.507093 | + | 1.52128i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | − | 3.00000i | −0.948683 | − | 0.474342i | ||||
\(41\) | −3.00000 | + | 3.00000i | −0.468521 | + | 0.468521i | −0.901435 | − | 0.432914i | \(-0.857485\pi\) |
0.432914 | + | 0.901435i | \(0.357485\pi\) | |||||||
\(42\) | −6.00000 | −0.925820 | ||||||||
\(43\) | −12.0000 | −1.82998 | −0.914991 | − | 0.403473i | \(-0.867803\pi\) | ||||
−0.914991 | + | 0.403473i | \(0.867803\pi\) | |||||||
\(44\) | 3.00000 | − | 3.00000i | 0.452267 | − | 0.452267i | ||||
\(45\) | 1.00000 | − | 2.00000i | 0.149071 | − | 0.298142i | ||||
\(46\) | −1.00000 | − | 1.00000i | −0.147442 | − | 0.147442i | ||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | 1.00000 | − | 1.00000i | 0.144338 | − | 0.144338i | ||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | −3.00000 | − | 4.00000i | −0.424264 | − | 0.565685i | ||||
\(51\) | −3.00000 | − | 5.00000i | −0.420084 | − | 0.700140i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 4.00000 | + | 4.00000i | 0.544331 | + | 0.544331i | ||||
\(55\) | 9.00000 | − | 3.00000i | 1.21356 | − | 0.404520i | ||||
\(56\) | −9.00000 | − | 9.00000i | −1.20268 | − | 1.20268i | ||||
\(57\) | 6.00000 | + | 6.00000i | 0.794719 | + | 0.794719i | ||||
\(58\) | 3.00000 | + | 3.00000i | 0.393919 | + | 0.393919i | ||||
\(59\) | − | 6.00000i | − | 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | −3.00000 | + | 1.00000i | −0.387298 | + | 0.129099i | ||||
\(61\) | 1.00000 | − | 1.00000i | 0.128037 | − | 0.128037i | −0.640184 | − | 0.768221i | \(-0.721142\pi\) |
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | 1.00000 | + | 1.00000i | 0.127000 | + | 0.127000i | ||||
\(63\) | 3.00000 | − | 3.00000i | 0.377964 | − | 0.377964i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.00000i | 0.738549i | ||||||||
\(67\) | 6.00000i | 0.733017i | 0.930415 | + | 0.366508i | \(0.119447\pi\) | ||||
−0.930415 | + | 0.366508i | \(0.880553\pi\) | |||||||
\(68\) | 1.00000 | − | 4.00000i | 0.121268 | − | 0.485071i | ||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | −3.00000 | − | 9.00000i | −0.358569 | − | 1.07571i | ||||
\(71\) | 3.00000 | + | 3.00000i | 0.356034 | + | 0.356034i | 0.862349 | − | 0.506314i | \(-0.168992\pi\) |
−0.506314 | + | 0.862349i | \(0.668992\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 3.00000 | − | 3.00000i | 0.351123 | − | 0.351123i | −0.509404 | − | 0.860527i | \(-0.670134\pi\) |
0.860527 | + | 0.509404i | \(0.170134\pi\) | |||||||
\(74\) | −3.00000 | + | 3.00000i | −0.348743 | + | 0.348743i | ||||
\(75\) | −7.00000 | − | 1.00000i | −0.808290 | − | 0.115470i | ||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | 18.0000 | 2.05129 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | + | 7.00000i | −0.787562 | + | 0.787562i | −0.981094 | − | 0.193532i | \(-0.938006\pi\) |
0.193532 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(80\) | 2.00000 | + | 1.00000i | 0.223607 | + | 0.111803i | ||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 3.00000 | − | 3.00000i | 0.331295 | − | 0.331295i | ||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | −6.00000 | −0.654654 | ||||||||
\(85\) | 6.00000 | − | 7.00000i | 0.650791 | − | 0.759257i | ||||
\(86\) | 12.0000 | 1.29399 | ||||||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | −9.00000 | + | 9.00000i | −0.959403 | + | 0.959403i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | −1.00000 | + | 2.00000i | −0.105409 | + | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | − | 1.00000i | −0.104257 | − | 0.104257i | ||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | − | 2.00000i | − | 0.206284i | ||||||
\(95\) | −6.00000 | + | 12.0000i | −0.615587 | + | 1.23117i | ||||
\(96\) | 5.00000 | − | 5.00000i | 0.510310 | − | 0.510310i | ||||
\(97\) | 3.00000 | − | 3.00000i | 0.304604 | − | 0.304604i | −0.538208 | − | 0.842812i | \(-0.680899\pi\) |
0.842812 | + | 0.538208i | \(0.180899\pi\) | |||||||
\(98\) | − | 11.0000i | − | 1.11117i | ||||||
\(99\) | −3.00000 | − | 3.00000i | −0.301511 | − | 0.301511i | ||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 3.00000 | + | 5.00000i | 0.297044 | + | 0.495074i | ||||
\(103\) | − | 6.00000i | − | 0.591198i | −0.955312 | − | 0.295599i | \(-0.904481\pi\) | ||
0.955312 | − | 0.295599i | \(-0.0955191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0000 | − | 6.00000i | −1.17108 | − | 0.585540i | ||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −9.00000 | + | 9.00000i | −0.870063 | + | 0.870063i | −0.992479 | − | 0.122416i | \(-0.960936\pi\) |
0.122416 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(108\) | 4.00000 | + | 4.00000i | 0.384900 | + | 0.384900i | ||||
\(109\) | −7.00000 | + | 7.00000i | −0.670478 | + | 0.670478i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) |
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −9.00000 | + | 3.00000i | −0.858116 | + | 0.286039i | ||||
\(111\) | 6.00000i | 0.569495i | ||||||||
\(112\) | 3.00000 | + | 3.00000i | 0.283473 | + | 0.283473i | ||||
\(113\) | −9.00000 | − | 9.00000i | −0.846649 | − | 0.846649i | 0.143065 | − | 0.989713i | \(-0.454304\pi\) |
−0.989713 | + | 0.143065i | \(0.954304\pi\) | |||||||
\(114\) | −6.00000 | − | 6.00000i | −0.561951 | − | 0.561951i | ||||
\(115\) | −1.00000 | − | 3.00000i | −0.0932505 | − | 0.279751i | ||||
\(116\) | 3.00000 | + | 3.00000i | 0.278543 | + | 0.278543i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 15.0000 | − | 9.00000i | 1.37505 | − | 0.825029i | ||||
\(120\) | 9.00000 | − | 3.00000i | 0.821584 | − | 0.273861i | ||||
\(121\) | − | 7.00000i | − | 0.636364i | ||||||
\(122\) | −1.00000 | + | 1.00000i | −0.0905357 | + | 0.0905357i | ||||
\(123\) | − | 6.00000i | − | 0.541002i | ||||||
\(124\) | 1.00000 | + | 1.00000i | 0.0898027 | + | 0.0898027i | ||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | −3.00000 | + | 3.00000i | −0.267261 | + | 0.267261i | ||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 12.0000 | − | 12.0000i | 1.05654 | − | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 3.00000i | 0.262111 | + | 0.262111i | 0.825911 | − | 0.563800i | \(-0.190661\pi\) |
−0.563800 | + | 0.825911i | \(0.690661\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | −18.0000 | + | 18.0000i | −1.56080 | + | 1.56080i | ||||
\(134\) | − | 6.00000i | − | 0.518321i | ||||||
\(135\) | 4.00000 | + | 12.0000i | 0.344265 | + | 1.03280i | ||||
\(136\) | −3.00000 | + | 12.0000i | −0.257248 | + | 1.02899i | ||||
\(137\) | 4.00000i | 0.341743i | 0.985293 | + | 0.170872i | \(0.0546583\pi\) | ||||
−0.985293 | + | 0.170872i | \(0.945342\pi\) | |||||||
\(138\) | 2.00000 | 0.170251 | ||||||||
\(139\) | 7.00000 | + | 7.00000i | 0.593732 | + | 0.593732i | 0.938638 | − | 0.344905i | \(-0.112089\pi\) |
−0.344905 | + | 0.938638i | \(0.612089\pi\) | |||||||
\(140\) | −3.00000 | − | 9.00000i | −0.253546 | − | 0.760639i | ||||
\(141\) | −2.00000 | − | 2.00000i | −0.168430 | − | 0.168430i | ||||
\(142\) | −3.00000 | − | 3.00000i | −0.251754 | − | 0.251754i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 3.00000 | + | 9.00000i | 0.249136 | + | 0.747409i | ||||
\(146\) | −3.00000 | + | 3.00000i | −0.248282 | + | 0.248282i | ||||
\(147\) | −11.0000 | − | 11.0000i | −0.907265 | − | 0.907265i | ||||
\(148\) | −3.00000 | + | 3.00000i | −0.246598 | + | 0.246598i | ||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 7.00000 | + | 1.00000i | 0.571548 | + | 0.0816497i | ||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | − | 18.0000i | − | 1.45999i | ||||||
\(153\) | −4.00000 | − | 1.00000i | −0.323381 | − | 0.0808452i | ||||
\(154\) | −18.0000 | −1.45048 | ||||||||
\(155\) | 1.00000 | + | 3.00000i | 0.0803219 | + | 0.240966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0000i | 0.957704i | 0.877896 | + | 0.478852i | \(0.158947\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 7.00000 | − | 7.00000i | 0.556890 | − | 0.556890i | ||||
\(159\) | −2.00000 | + | 2.00000i | −0.158610 | + | 0.158610i | ||||
\(160\) | 10.0000 | + | 5.00000i | 0.790569 | + | 0.395285i | ||||
\(161\) | − | 6.00000i | − | 0.472866i | ||||||
\(162\) | −5.00000 | −0.392837 | ||||||||
\(163\) | 9.00000 | + | 9.00000i | 0.704934 | + | 0.704934i | 0.965465 | − | 0.260531i | \(-0.0838976\pi\) |
−0.260531 | + | 0.965465i | \(0.583898\pi\) | |||||||
\(164\) | 3.00000 | − | 3.00000i | 0.234261 | − | 0.234261i | ||||
\(165\) | −6.00000 | + | 12.0000i | −0.467099 | + | 0.934199i | ||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 3.00000 | − | 3.00000i | 0.232147 | − | 0.232147i | −0.581441 | − | 0.813588i | \(-0.697511\pi\) |
0.813588 | + | 0.581441i | \(0.197511\pi\) | |||||||
\(168\) | 18.0000 | 1.38873 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | −6.00000 | + | 7.00000i | −0.460179 | + | 0.536875i | ||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | 12.0000 | 0.914991 | ||||||||
\(173\) | 15.0000 | − | 15.0000i | 1.14043 | − | 1.14043i | 0.152057 | − | 0.988372i | \(-0.451410\pi\) |
0.988372 | − | 0.152057i | \(-0.0485898\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 3.00000 | − | 21.0000i | 0.226779 | − | 1.58745i | ||||
\(176\) | 3.00000 | − | 3.00000i | 0.226134 | − | 0.226134i | ||||
\(177\) | 6.00000 | + | 6.00000i | 0.450988 | + | 0.450988i | ||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | −1.00000 | + | 2.00000i | −0.0745356 | + | 0.149071i | ||||
\(181\) | −11.0000 | + | 11.0000i | −0.817624 | + | 0.817624i | −0.985763 | − | 0.168140i | \(-0.946224\pi\) |
0.168140 | + | 0.985763i | \(0.446224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 3.00000 | + | 3.00000i | 0.221163 | + | 0.221163i | ||||
\(185\) | −9.00000 | + | 3.00000i | −0.661693 | + | 0.220564i | ||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | −9.00000 | − | 15.0000i | −0.658145 | − | 1.09691i | ||||
\(188\) | − | 2.00000i | − | 0.145865i | ||||||
\(189\) | 24.0000i | 1.74574i | ||||||||
\(190\) | 6.00000 | − | 12.0000i | 0.435286 | − | 0.870572i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −7.00000 | + | 7.00000i | −0.505181 | + | 0.505181i | ||||
\(193\) | 3.00000 | + | 3.00000i | 0.215945 | + | 0.215945i | 0.806787 | − | 0.590842i | \(-0.201204\pi\) |
−0.590842 | + | 0.806787i | \(0.701204\pi\) | |||||||
\(194\) | −3.00000 | + | 3.00000i | −0.215387 | + | 0.215387i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 11.0000i | − | 0.785714i | ||||||
\(197\) | −13.0000 | − | 13.0000i | −0.926212 | − | 0.926212i | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) |
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 3.00000 | + | 3.00000i | 0.213201 | + | 0.213201i | ||||
\(199\) | −1.00000 | − | 1.00000i | −0.0708881 | − | 0.0708881i | 0.670774 | − | 0.741662i | \(-0.265962\pi\) |
−0.741662 | + | 0.670774i | \(0.765962\pi\) | |||||||
\(200\) | 9.00000 | + | 12.0000i | 0.636396 | + | 0.848528i | ||||
\(201\) | −6.00000 | − | 6.00000i | −0.423207 | − | 0.423207i | ||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 18.0000i | 1.26335i | ||||||||
\(204\) | 3.00000 | + | 5.00000i | 0.210042 | + | 0.350070i | ||||
\(205\) | 9.00000 | − | 3.00000i | 0.628587 | − | 0.209529i | ||||
\(206\) | 6.00000i | 0.418040i | ||||||||
\(207\) | −1.00000 | + | 1.00000i | −0.0695048 | + | 0.0695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.0000 | + | 18.0000i | 1.24509 | + | 1.24509i | ||||
\(210\) | 12.0000 | + | 6.00000i | 0.828079 | + | 0.414039i | ||||
\(211\) | 17.0000 | − | 17.0000i | 1.17033 | − | 1.17033i | 0.188197 | − | 0.982131i | \(-0.439736\pi\) |
0.982131 | − | 0.188197i | \(-0.0602643\pi\) | |||||||
\(212\) | −2.00000 | −0.137361 | ||||||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 9.00000 | − | 9.00000i | 0.615227 | − | 0.615227i | ||||
\(215\) | 24.0000 | + | 12.0000i | 1.63679 | + | 0.818393i | ||||
\(216\) | −12.0000 | − | 12.0000i | −0.816497 | − | 0.816497i | ||||
\(217\) | 6.00000i | 0.407307i | ||||||||
\(218\) | 7.00000 | − | 7.00000i | 0.474100 | − | 0.474100i | ||||
\(219\) | 6.00000i | 0.405442i | ||||||||
\(220\) | −9.00000 | + | 3.00000i | −0.606780 | + | 0.202260i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 6.00000i | − | 0.402694i | ||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 15.0000 | + | 15.0000i | 1.00223 | + | 1.00223i | ||||
\(225\) | −4.00000 | + | 3.00000i | −0.266667 | + | 0.200000i | ||||
\(226\) | 9.00000 | + | 9.00000i | 0.598671 | + | 0.598671i | ||||
\(227\) | −15.0000 | − | 15.0000i | −0.995585 | − | 0.995585i | 0.00440533 | − | 0.999990i | \(-0.498598\pi\) |
−0.999990 | + | 0.00440533i | \(0.998598\pi\) | |||||||
\(228\) | −6.00000 | − | 6.00000i | −0.397360 | − | 0.397360i | ||||
\(229\) | − | 24.0000i | − | 1.58596i | −0.609245 | − | 0.792982i | \(-0.708527\pi\) | ||
0.609245 | − | 0.792982i | \(-0.291473\pi\) | |||||||
\(230\) | 1.00000 | + | 3.00000i | 0.0659380 | + | 0.197814i | ||||
\(231\) | −18.0000 | + | 18.0000i | −1.18431 | + | 1.18431i | ||||
\(232\) | −9.00000 | − | 9.00000i | −0.590879 | − | 0.590879i | ||||
\(233\) | −5.00000 | + | 5.00000i | −0.327561 | + | 0.327561i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) |
0.524097 | + | 0.851658i | \(0.324403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | − | 4.00000i | 0.130466 | − | 0.260931i | ||||
\(236\) | 6.00000i | 0.390567i | ||||||||
\(237\) | − | 14.0000i | − | 0.909398i | ||||||
\(238\) | −15.0000 | + | 9.00000i | −0.972306 | + | 0.583383i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | −3.00000 | + | 1.00000i | −0.193649 | + | 0.0645497i | ||||
\(241\) | −19.0000 | − | 19.0000i | −1.22390 | − | 1.22390i | −0.966235 | − | 0.257663i | \(-0.917048\pi\) |
−0.257663 | − | 0.966235i | \(-0.582952\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 7.00000 | − | 7.00000i | 0.449050 | − | 0.449050i | ||||
\(244\) | −1.00000 | + | 1.00000i | −0.0640184 | + | 0.0640184i | ||||
\(245\) | 11.0000 | − | 22.0000i | 0.702764 | − | 1.40553i | ||||
\(246\) | 6.00000i | 0.382546i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.00000 | − | 3.00000i | −0.190500 | − | 0.190500i | ||||
\(249\) | 4.00000 | − | 4.00000i | 0.253490 | − | 0.253490i | ||||
\(250\) | 2.00000 | + | 11.0000i | 0.126491 | + | 0.695701i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −3.00000 | + | 3.00000i | −0.188982 | + | 0.188982i | ||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.00000 | + | 13.0000i | 0.0626224 | + | 0.814092i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | −12.0000 | + | 12.0000i | −0.747087 | + | 0.747087i | ||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 3.00000i | 0.185695 | − | 0.185695i | ||||
\(262\) | −3.00000 | − | 3.00000i | −0.185341 | − | 0.185341i | ||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | − | 18.0000i | − | 1.10782i | ||||||
\(265\) | −4.00000 | − | 2.00000i | −0.245718 | − | 0.122859i | ||||
\(266\) | 18.0000 | − | 18.0000i | 1.10365 | − | 1.10365i | ||||
\(267\) | −6.00000 | + | 6.00000i | −0.367194 | + | 0.367194i | ||||
\(268\) | − | 6.00000i | − | 0.366508i | ||||||
\(269\) | −3.00000 | − | 3.00000i | −0.182913 | − | 0.182913i | 0.609711 | − | 0.792624i | \(-0.291286\pi\) |
−0.792624 | + | 0.609711i | \(0.791286\pi\) | |||||||
\(270\) | −4.00000 | − | 12.0000i | −0.243432 | − | 0.730297i | ||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 1.00000 | − | 4.00000i | 0.0606339 | − | 0.242536i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.00000i | − | 0.241649i | ||||||
\(275\) | −21.0000 | − | 3.00000i | −1.26635 | − | 0.180907i | ||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | −21.0000 | + | 21.0000i | −1.26177 | + | 1.26177i | −0.311532 | + | 0.950236i | \(0.600842\pi\) |
−0.950236 | + | 0.311532i | \(0.899158\pi\) | |||||||
\(278\) | −7.00000 | − | 7.00000i | −0.419832 | − | 0.419832i | ||||
\(279\) | 1.00000 | − | 1.00000i | 0.0598684 | − | 0.0598684i | ||||
\(280\) | 9.00000 | + | 27.0000i | 0.537853 | + | 1.61356i | ||||
\(281\) | 24.0000i | 1.43172i | 0.698244 | + | 0.715860i | \(0.253965\pi\) | ||||
−0.698244 | + | 0.715860i | \(0.746035\pi\) | |||||||
\(282\) | 2.00000 | + | 2.00000i | 0.119098 | + | 0.119098i | ||||
\(283\) | 9.00000 | + | 9.00000i | 0.534994 | + | 0.534994i | 0.922055 | − | 0.387060i | \(-0.126509\pi\) |
−0.387060 | + | 0.922055i | \(0.626509\pi\) | |||||||
\(284\) | −3.00000 | − | 3.00000i | −0.178017 | − | 0.178017i | ||||
\(285\) | −6.00000 | − | 18.0000i | −0.355409 | − | 1.06623i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.0000 | 1.06251 | ||||||||
\(288\) | − | 5.00000i | − | 0.294628i | ||||||
\(289\) | −15.0000 | − | 8.00000i | −0.882353 | − | 0.470588i | ||||
\(290\) | −3.00000 | − | 9.00000i | −0.176166 | − | 0.528498i | ||||
\(291\) | 6.00000i | 0.351726i | ||||||||
\(292\) | −3.00000 | + | 3.00000i | −0.175562 | + | 0.175562i | ||||
\(293\) | − | 4.00000i | − | 0.233682i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) | ||
0.993151 | − | 0.116841i | \(-0.0372769\pi\) | |||||||
\(294\) | 11.0000 | + | 11.0000i | 0.641533 | + | 0.641533i | ||||
\(295\) | −6.00000 | + | 12.0000i | −0.349334 | + | 0.698667i | ||||
\(296\) | 9.00000 | − | 9.00000i | 0.523114 | − | 0.523114i | ||||
\(297\) | 24.0000 | 1.39262 | ||||||||
\(298\) | 18.0000 | 1.04271 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.00000 | + | 1.00000i | 0.404145 | + | 0.0577350i | ||||
\(301\) | 36.0000 | + | 36.0000i | 2.07501 | + | 2.07501i | ||||
\(302\) | 10.0000i | 0.575435i | ||||||||
\(303\) | 6.00000 | − | 6.00000i | 0.344691 | − | 0.344691i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | −3.00000 | + | 1.00000i | −0.171780 | + | 0.0572598i | ||||
\(306\) | 4.00000 | + | 1.00000i | 0.228665 | + | 0.0571662i | ||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | −18.0000 | −1.02565 | ||||||||
\(309\) | 6.00000 | + | 6.00000i | 0.341328 | + | 0.341328i | ||||
\(310\) | −1.00000 | − | 3.00000i | −0.0567962 | − | 0.170389i | ||||
\(311\) | 3.00000 | + | 3.00000i | 0.170114 | + | 0.170114i | 0.787030 | − | 0.616915i | \(-0.211618\pi\) |
−0.616915 | + | 0.787030i | \(0.711618\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | + | 3.00000i | 0.169570 | + | 0.169570i | 0.786790 | − | 0.617220i | \(-0.211741\pi\) |
−0.617220 | + | 0.786790i | \(0.711741\pi\) | |||||||
\(314\) | − | 12.0000i | − | 0.677199i | ||||||
\(315\) | −9.00000 | + | 3.00000i | −0.507093 | + | 0.169031i | ||||
\(316\) | 7.00000 | − | 7.00000i | 0.393781 | − | 0.393781i | ||||
\(317\) | 15.0000 | + | 15.0000i | 0.842484 | + | 0.842484i | 0.989181 | − | 0.146697i | \(-0.0468644\pi\) |
−0.146697 | + | 0.989181i | \(0.546864\pi\) | |||||||
\(318\) | 2.00000 | − | 2.00000i | 0.112154 | − | 0.112154i | ||||
\(319\) | 18.0000 | 1.00781 | ||||||||
\(320\) | −14.0000 | − | 7.00000i | −0.782624 | − | 0.391312i | ||||
\(321\) | − | 18.0000i | − | 1.00466i | ||||||
\(322\) | 6.00000i | 0.334367i | ||||||||
\(323\) | 24.0000 | + | 6.00000i | 1.33540 | + | 0.333849i | ||||
\(324\) | −5.00000 | −0.277778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.00000 | − | 9.00000i | −0.498464 | − | 0.498464i | ||||
\(327\) | − | 14.0000i | − | 0.774202i | ||||||
\(328\) | −9.00000 | + | 9.00000i | −0.496942 | + | 0.496942i | ||||
\(329\) | 6.00000 | − | 6.00000i | 0.330791 | − | 0.330791i | ||||
\(330\) | 6.00000 | − | 12.0000i | 0.330289 | − | 0.660578i | ||||
\(331\) | 18.0000i | 0.989369i | 0.869072 | + | 0.494685i | \(0.164716\pi\) | ||||
−0.869072 | + | 0.494685i | \(0.835284\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | 3.00000 | + | 3.00000i | 0.164399 | + | 0.164399i | ||||
\(334\) | −3.00000 | + | 3.00000i | −0.164153 | + | 0.164153i | ||||
\(335\) | 6.00000 | − | 12.0000i | 0.327815 | − | 0.655630i | ||||
\(336\) | −6.00000 | −0.327327 | ||||||||
\(337\) | 15.0000 | − | 15.0000i | 0.817102 | − | 0.817102i | −0.168585 | − | 0.985687i | \(-0.553920\pi\) |
0.985687 | + | 0.168585i | \(0.0539198\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | 18.0000 | 0.977626 | ||||||||
\(340\) | −6.00000 | + | 7.00000i | −0.325396 | + | 0.379628i | ||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | −36.0000 | −1.94099 | ||||||||
\(345\) | 4.00000 | + | 2.00000i | 0.215353 | + | 0.107676i | ||||
\(346\) | −15.0000 | + | 15.0000i | −0.806405 | + | 0.806405i | ||||
\(347\) | 9.00000 | + | 9.00000i | 0.483145 | + | 0.483145i | 0.906135 | − | 0.422989i | \(-0.139019\pi\) |
−0.422989 | + | 0.906135i | \(0.639019\pi\) | |||||||
\(348\) | −6.00000 | −0.321634 | ||||||||
\(349\) | − | 28.0000i | − | 1.49881i | −0.662114 | − | 0.749403i | \(-0.730341\pi\) | ||
0.662114 | − | 0.749403i | \(-0.269659\pi\) | |||||||
\(350\) | −3.00000 | + | 21.0000i | −0.160357 | + | 1.12250i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0000 | − | 15.0000i | 0.799503 | − | 0.799503i | ||||
\(353\) | 16.0000i | 0.851594i | 0.904819 | + | 0.425797i | \(0.140006\pi\) | ||||
−0.904819 | + | 0.425797i | \(0.859994\pi\) | |||||||
\(354\) | −6.00000 | − | 6.00000i | −0.318896 | − | 0.318896i | ||||
\(355\) | −3.00000 | − | 9.00000i | −0.159223 | − | 0.477670i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | −6.00000 | + | 24.0000i | −0.317554 | + | 1.27021i | ||||
\(358\) | 6.00000i | 0.317110i | ||||||||
\(359\) | 30.0000i | 1.58334i | 0.610949 | + | 0.791670i | \(0.290788\pi\) | ||||
−0.610949 | + | 0.791670i | \(0.709212\pi\) | |||||||
\(360\) | 3.00000 | − | 6.00000i | 0.158114 | − | 0.316228i | ||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 11.0000 | − | 11.0000i | 0.578147 | − | 0.578147i | ||||
\(363\) | 7.00000 | + | 7.00000i | 0.367405 | + | 0.367405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | + | 3.00000i | −0.471082 | + | 0.157027i | ||||
\(366\) | − | 2.00000i | − | 0.104542i | ||||||
\(367\) | −3.00000 | − | 3.00000i | −0.156599 | − | 0.156599i | 0.624459 | − | 0.781058i | \(-0.285320\pi\) |
−0.781058 | + | 0.624459i | \(0.785320\pi\) | |||||||
\(368\) | −1.00000 | − | 1.00000i | −0.0521286 | − | 0.0521286i | ||||
\(369\) | −3.00000 | − | 3.00000i | −0.156174 | − | 0.156174i | ||||
\(370\) | 9.00000 | − | 3.00000i | 0.467888 | − | 0.155963i | ||||
\(371\) | −6.00000 | − | 6.00000i | −0.311504 | − | 0.311504i | ||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | − | 24.0000i | − | 1.24267i | −0.783544 | − | 0.621336i | \(-0.786590\pi\) | ||
0.783544 | − | 0.621336i | \(-0.213410\pi\) | |||||||
\(374\) | 9.00000 | + | 15.0000i | 0.465379 | + | 0.775632i | ||||
\(375\) | 13.0000 | + | 9.00000i | 0.671317 | + | 0.464758i | ||||
\(376\) | 6.00000i | 0.309426i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | − | 24.0000i | − | 1.23443i | ||||||
\(379\) | 11.0000 | + | 11.0000i | 0.565032 | + | 0.565032i | 0.930733 | − | 0.365701i | \(-0.119171\pi\) |
−0.365701 | + | 0.930733i | \(0.619171\pi\) | |||||||
\(380\) | 6.00000 | − | 12.0000i | 0.307794 | − | 0.615587i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0000 | −0.817562 | −0.408781 | − | 0.912633i | \(-0.634046\pi\) | ||||
−0.408781 | + | 0.912633i | \(0.634046\pi\) | |||||||
\(384\) | −3.00000 | + | 3.00000i | −0.153093 | + | 0.153093i | ||||
\(385\) | −36.0000 | − | 18.0000i | −1.83473 | − | 0.917365i | ||||
\(386\) | −3.00000 | − | 3.00000i | −0.152696 | − | 0.152696i | ||||
\(387\) | − | 12.0000i | − | 0.609994i | ||||||
\(388\) | −3.00000 | + | 3.00000i | −0.152302 | + | 0.152302i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.00000 | + | 3.00000i | −0.252861 | + | 0.151717i | ||||
\(392\) | 33.0000i | 1.66675i | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 13.0000 | + | 13.0000i | 0.654931 | + | 0.654931i | ||||
\(395\) | 21.0000 | − | 7.00000i | 1.05662 | − | 0.352208i | ||||
\(396\) | 3.00000 | + | 3.00000i | 0.150756 | + | 0.150756i | ||||
\(397\) | 27.0000 | + | 27.0000i | 1.35509 | + | 1.35509i | 0.879862 | + | 0.475229i | \(0.157635\pi\) |
0.475229 | + | 0.879862i | \(0.342365\pi\) | |||||||
\(398\) | 1.00000 | + | 1.00000i | 0.0501255 | + | 0.0501255i | ||||
\(399\) | − | 36.0000i | − | 1.80225i | ||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | 9.00000 | − | 9.00000i | 0.449439 | − | 0.449439i | −0.445729 | − | 0.895168i | \(-0.647056\pi\) |
0.895168 | + | 0.445729i | \(0.147056\pi\) | |||||||
\(402\) | 6.00000 | + | 6.00000i | 0.299253 | + | 0.299253i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | −10.0000 | − | 5.00000i | −0.496904 | − | 0.248452i | ||||
\(406\) | − | 18.0000i | − | 0.893325i | ||||||
\(407\) | 18.0000i | 0.892227i | ||||||||
\(408\) | −9.00000 | − | 15.0000i | −0.445566 | − | 0.742611i | ||||
\(409\) | −30.0000 | −1.48340 | −0.741702 | − | 0.670729i | \(-0.765981\pi\) | ||||
−0.741702 | + | 0.670729i | \(0.765981\pi\) | |||||||
\(410\) | −9.00000 | + | 3.00000i | −0.444478 | + | 0.148159i | ||||
\(411\) | −4.00000 | − | 4.00000i | −0.197305 | − | 0.197305i | ||||
\(412\) | 6.00000i | 0.295599i | ||||||||
\(413\) | −18.0000 | + | 18.0000i | −0.885722 | + | 0.885722i | ||||
\(414\) | 1.00000 | − | 1.00000i | 0.0491473 | − | 0.0491473i | ||||
\(415\) | 8.00000 | + | 4.00000i | 0.392705 | + | 0.196352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.0000 | −0.685583 | ||||||||
\(418\) | −18.0000 | − | 18.0000i | −0.880409 | − | 0.880409i | ||||
\(419\) | −15.0000 | + | 15.0000i | −0.732798 | + | 0.732798i | −0.971173 | − | 0.238375i | \(-0.923385\pi\) |
0.238375 | + | 0.971173i | \(0.423385\pi\) | |||||||
\(420\) | 12.0000 | + | 6.00000i | 0.585540 | + | 0.292770i | ||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −17.0000 | + | 17.0000i | −0.827547 | + | 0.827547i | ||||
\(423\) | −2.00000 | −0.0972433 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −19.0000 | + | 8.00000i | −0.921635 | + | 0.388057i | ||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | 9.00000 | − | 9.00000i | 0.435031 | − | 0.435031i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.0000 | − | 12.0000i | −1.15738 | − | 0.578691i | ||||
\(431\) | 9.00000 | − | 9.00000i | 0.433515 | − | 0.433515i | −0.456307 | − | 0.889822i | \(-0.650828\pi\) |
0.889822 | + | 0.456307i | \(0.150828\pi\) | |||||||
\(432\) | 4.00000 | + | 4.00000i | 0.192450 | + | 0.192450i | ||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | − | 6.00000i | − | 0.288009i | ||||||
\(435\) | −12.0000 | − | 6.00000i | −0.575356 | − | 0.287678i | ||||
\(436\) | 7.00000 | − | 7.00000i | 0.335239 | − | 0.335239i | ||||
\(437\) | 6.00000 | − | 6.00000i | 0.287019 | − | 0.287019i | ||||
\(438\) | − | 6.00000i | − | 0.286691i | ||||||
\(439\) | 19.0000 | + | 19.0000i | 0.906821 | + | 0.906821i | 0.996014 | − | 0.0891938i | \(-0.0284290\pi\) |
−0.0891938 | + | 0.996014i | \(0.528429\pi\) | |||||||
\(440\) | 27.0000 | − | 9.00000i | 1.28717 | − | 0.429058i | ||||
\(441\) | −11.0000 | −0.523810 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.0000i | 1.04525i | 0.852562 | + | 0.522626i | \(0.175047\pi\) | ||||
−0.852562 | + | 0.522626i | \(0.824953\pi\) | |||||||
\(444\) | − | 6.00000i | − | 0.284747i | ||||||
\(445\) | −12.0000 | − | 6.00000i | −0.568855 | − | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | − | 18.0000i | 0.851371 | − | 0.851371i | ||||
\(448\) | −21.0000 | − | 21.0000i | −0.992157 | − | 0.992157i | ||||
\(449\) | −15.0000 | + | 15.0000i | −0.707894 | + | 0.707894i | −0.966092 | − | 0.258198i | \(-0.916871\pi\) |
0.258198 | + | 0.966092i | \(0.416871\pi\) | |||||||
\(450\) | 4.00000 | − | 3.00000i | 0.188562 | − | 0.141421i | ||||
\(451\) | − | 18.0000i | − | 0.847587i | ||||||
\(452\) | 9.00000 | + | 9.00000i | 0.423324 | + | 0.423324i | ||||
\(453\) | 10.0000 | + | 10.0000i | 0.469841 | + | 0.469841i | ||||
\(454\) | 15.0000 | + | 15.0000i | 0.703985 | + | 0.703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.0000 | + | 18.0000i | 0.842927 | + | 0.842927i | ||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | 24.0000i | 1.12145i | ||||||||
\(459\) | 20.0000 | − | 12.0000i | 0.933520 | − | 0.560112i | ||||
\(460\) | 1.00000 | + | 3.00000i | 0.0466252 | + | 0.139876i | ||||
\(461\) | − | 12.0000i | − | 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||
0.960161 | − | 0.279448i | \(-0.0901514\pi\) | |||||||
\(462\) | 18.0000 | − | 18.0000i | 0.837436 | − | 0.837436i | ||||
\(463\) | 18.0000i | 0.836531i | 0.908325 | + | 0.418265i | \(0.137362\pi\) | ||||
−0.908325 | + | 0.418265i | \(0.862638\pi\) | |||||||
\(464\) | 3.00000 | + | 3.00000i | 0.139272 | + | 0.139272i | ||||
\(465\) | −4.00000 | − | 2.00000i | −0.185496 | − | 0.0927478i | ||||
\(466\) | 5.00000 | − | 5.00000i | 0.231621 | − | 0.231621i | ||||
\(467\) | −28.0000 | −1.29569 | −0.647843 | − | 0.761774i | \(-0.724329\pi\) | ||||
−0.647843 | + | 0.761774i | \(0.724329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000 | − | 18.0000i | 0.831163 | − | 0.831163i | ||||
\(470\) | −2.00000 | + | 4.00000i | −0.0922531 | + | 0.184506i | ||||
\(471\) | −12.0000 | − | 12.0000i | −0.552931 | − | 0.552931i | ||||
\(472\) | − | 18.0000i | − | 0.828517i | ||||||
\(473\) | 36.0000 | − | 36.0000i | 1.65528 | − | 1.65528i | ||||
\(474\) | 14.0000i | 0.643041i | ||||||||
\(475\) | 24.0000 | − | 18.0000i | 1.10120 | − | 0.825897i | ||||
\(476\) | −15.0000 | + | 9.00000i | −0.687524 | + | 0.412514i | ||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 24.0000 | 1.09773 | ||||||||
\(479\) | −9.00000 | − | 9.00000i | −0.411220 | − | 0.411220i | 0.470943 | − | 0.882164i | \(-0.343914\pi\) |
−0.882164 | + | 0.470943i | \(0.843914\pi\) | |||||||
\(480\) | −15.0000 | + | 5.00000i | −0.684653 | + | 0.228218i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 19.0000 | + | 19.0000i | 0.865426 | + | 0.865426i | ||||
\(483\) | 6.00000 | + | 6.00000i | 0.273009 | + | 0.273009i | ||||
\(484\) | 7.00000i | 0.318182i | ||||||||
\(485\) | −9.00000 | + | 3.00000i | −0.408669 | + | 0.136223i | ||||
\(486\) | −7.00000 | + | 7.00000i | −0.317526 | + | 0.317526i | ||||
\(487\) | −3.00000 | − | 3.00000i | −0.135943 | − | 0.135943i | 0.635861 | − | 0.771804i | \(-0.280645\pi\) |
−0.771804 | + | 0.635861i | \(0.780645\pi\) | |||||||
\(488\) | 3.00000 | − | 3.00000i | 0.135804 | − | 0.135804i | ||||
\(489\) | −18.0000 | −0.813988 | ||||||||
\(490\) | −11.0000 | + | 22.0000i | −0.496929 | + | 0.993859i | ||||
\(491\) | − | 6.00000i | − | 0.270776i | −0.990793 | − | 0.135388i | \(-0.956772\pi\) | ||
0.990793 | − | 0.135388i | \(-0.0432281\pi\) | |||||||
\(492\) | 6.00000i | 0.270501i | ||||||||
\(493\) | 15.0000 | − | 9.00000i | 0.675566 | − | 0.405340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | + | 9.00000i | 0.134840 | + | 0.404520i | ||||
\(496\) | 1.00000 | + | 1.00000i | 0.0449013 | + | 0.0449013i | ||||
\(497\) | − | 18.0000i | − | 0.807410i | ||||||
\(498\) | −4.00000 | + | 4.00000i | −0.179244 | + | 0.179244i | ||||
\(499\) | −23.0000 | + | 23.0000i | −1.02962 | + | 1.02962i | −0.0300737 | + | 0.999548i | \(0.509574\pi\) |
−0.999548 | + | 0.0300737i | \(0.990426\pi\) | |||||||
\(500\) | 2.00000 | + | 11.0000i | 0.0894427 | + | 0.491935i | ||||
\(501\) | 6.00000i | 0.268060i | ||||||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | −3.00000 | − | 3.00000i | −0.133763 | − | 0.133763i | 0.637055 | − | 0.770818i | \(-0.280152\pi\) |
−0.770818 | + | 0.637055i | \(0.780152\pi\) | |||||||
\(504\) | 9.00000 | − | 9.00000i | 0.400892 | − | 0.400892i | ||||
\(505\) | 12.0000 | + | 6.00000i | 0.533993 | + | 0.266996i | ||||
\(506\) | 6.00000 | 0.266733 | ||||||||
\(507\) | −13.0000 | + | 13.0000i | −0.577350 | + | 0.577350i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | −1.00000 | − | 13.0000i | −0.0442807 | − | 0.575650i | ||||
\(511\) | −18.0000 | −0.796273 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | −24.0000 | + | 24.0000i | −1.05963 | + | 1.05963i | ||||
\(514\) | 14.0000 | 0.617514 | ||||||||
\(515\) | −6.00000 | + | 12.0000i | −0.264392 | + | 0.528783i | ||||
\(516\) | −12.0000 | + | 12.0000i | −0.528271 | + | 0.528271i | ||||
\(517\) | −6.00000 | − | 6.00000i | −0.263880 | − | 0.263880i | ||||
\(518\) | 18.0000 | 0.790875 | ||||||||
\(519\) | 30.0000i | 1.31685i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | − | 9.00000i | 0.394297 | − | 0.394297i | −0.481919 | − | 0.876216i | \(-0.660060\pi\) |
0.876216 | + | 0.481919i | \(0.160060\pi\) | |||||||
\(522\) | −3.00000 | + | 3.00000i | −0.131306 | + | 0.131306i | ||||
\(523\) | 6.00000i | 0.262362i | 0.991358 | + | 0.131181i | \(0.0418769\pi\) | ||||
−0.991358 | + | 0.131181i | \(0.958123\pi\) | |||||||
\(524\) | −3.00000 | − | 3.00000i | −0.131056 | − | 0.131056i | ||||
\(525\) | 18.0000 | + | 24.0000i | 0.785584 | + | 1.04745i | ||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | 5.00000 | − | 3.00000i | 0.217803 | − | 0.130682i | ||||
\(528\) | 6.00000i | 0.261116i | ||||||||
\(529\) | − | 21.0000i | − | 0.913043i | ||||||
\(530\) | 4.00000 | + | 2.00000i | 0.173749 | + | 0.0868744i | ||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 18.0000 | − | 18.0000i | 0.780399 | − | 0.780399i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.00000 | − | 6.00000i | 0.259645 | − | 0.259645i | ||||
\(535\) | 27.0000 | − | 9.00000i | 1.16731 | − | 0.389104i | ||||
\(536\) | 18.0000i | 0.777482i | ||||||||
\(537\) | 6.00000 | + | 6.00000i | 0.258919 | + | 0.258919i | ||||
\(538\) | 3.00000 | + | 3.00000i | 0.129339 | + | 0.129339i | ||||
\(539\) | −33.0000 | − | 33.0000i | −1.42141 | − | 1.42141i | ||||
\(540\) | −4.00000 | − | 12.0000i | −0.172133 | − | 0.516398i | ||||
\(541\) | 1.00000 | + | 1.00000i | 0.0429934 | + | 0.0429934i | 0.728277 | − | 0.685283i | \(-0.240322\pi\) |
−0.685283 | + | 0.728277i | \(0.740322\pi\) | |||||||
\(542\) | −24.0000 | −1.03089 | ||||||||
\(543\) | − | 22.0000i | − | 0.944110i | ||||||
\(544\) | 5.00000 | − | 20.0000i | 0.214373 | − | 0.857493i | ||||
\(545\) | 21.0000 | − | 7.00000i | 0.899541 | − | 0.299847i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.00000 | + | 9.00000i | −0.384812 | + | 0.384812i | −0.872832 | − | 0.488020i | \(-0.837719\pi\) |
0.488020 | + | 0.872832i | \(0.337719\pi\) | |||||||
\(548\) | − | 4.00000i | − | 0.170872i | ||||||
\(549\) | 1.00000 | + | 1.00000i | 0.0426790 | + | 0.0426790i | ||||
\(550\) | 21.0000 | + | 3.00000i | 0.895443 | + | 0.127920i | ||||
\(551\) | −18.0000 | + | 18.0000i | −0.766826 | + | 0.766826i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 42.0000 | 1.78602 | ||||||||
\(554\) | 21.0000 | − | 21.0000i | 0.892205 | − | 0.892205i | ||||
\(555\) | 6.00000 | − | 12.0000i | 0.254686 | − | 0.509372i | ||||
\(556\) | −7.00000 | − | 7.00000i | −0.296866 | − | 0.296866i | ||||
\(557\) | − | 32.0000i | − | 1.35588i | −0.735116 | − | 0.677942i | \(-0.762872\pi\) | ||
0.735116 | − | 0.677942i | \(-0.237128\pi\) | |||||||
\(558\) | −1.00000 | + | 1.00000i | −0.0423334 | + | 0.0423334i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.00000 | − | 9.00000i | −0.126773 | − | 0.380319i | ||||
\(561\) | 24.0000 | + | 6.00000i | 1.01328 | + | 0.253320i | ||||
\(562\) | − | 24.0000i | − | 1.01238i | ||||||
\(563\) | −28.0000 | −1.18006 | −0.590030 | − | 0.807382i | \(-0.700884\pi\) | ||||
−0.590030 | + | 0.807382i | \(0.700884\pi\) | |||||||
\(564\) | 2.00000 | + | 2.00000i | 0.0842152 | + | 0.0842152i | ||||
\(565\) | 9.00000 | + | 27.0000i | 0.378633 | + | 1.13590i | ||||
\(566\) | −9.00000 | − | 9.00000i | −0.378298 | − | 0.378298i | ||||
\(567\) | −15.0000 | − | 15.0000i | −0.629941 | − | 0.629941i | ||||
\(568\) | 9.00000 | + | 9.00000i | 0.377632 | + | 0.377632i | ||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 6.00000 | + | 18.0000i | 0.251312 | + | 0.753937i | ||||
\(571\) | −23.0000 | + | 23.0000i | −0.962520 | + | 0.962520i | −0.999323 | − | 0.0368025i | \(-0.988283\pi\) |
0.0368025 | + | 0.999323i | \(0.488283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.0000 | −0.751305 | ||||||||
\(575\) | −1.00000 | + | 7.00000i | −0.0417029 | + | 0.291920i | ||||
\(576\) | 7.00000i | 0.291667i | ||||||||
\(577\) | 36.0000i | 1.49870i | 0.662174 | + | 0.749350i | \(0.269634\pi\) | ||||
−0.662174 | + | 0.749350i | \(0.730366\pi\) | |||||||
\(578\) | 15.0000 | + | 8.00000i | 0.623918 | + | 0.332756i | ||||
\(579\) | −6.00000 | −0.249351 | ||||||||
\(580\) | −3.00000 | − | 9.00000i | −0.124568 | − | 0.373705i | ||||
\(581\) | 12.0000 | + | 12.0000i | 0.497844 | + | 0.497844i | ||||
\(582\) | − | 6.00000i | − | 0.248708i | ||||||
\(583\) | −6.00000 | + | 6.00000i | −0.248495 | + | 0.248495i | ||||
\(584\) | 9.00000 | − | 9.00000i | 0.372423 | − | 0.372423i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.00000i | 0.165238i | ||||||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | 11.0000 | + | 11.0000i | 0.453632 | + | 0.453632i | ||||
\(589\) | −6.00000 | + | 6.00000i | −0.247226 | + | 0.247226i | ||||
\(590\) | 6.00000 | − | 12.0000i | 0.247016 | − | 0.494032i | ||||
\(591\) | 26.0000 | 1.06950 | ||||||||
\(592\) | −3.00000 | + | 3.00000i | −0.123299 | + | 0.123299i | ||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | −24.0000 | −0.984732 | ||||||||
\(595\) | −39.0000 | + | 3.00000i | −1.59884 | + | 0.122988i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 2.00000 | 0.0818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | −21.0000 | − | 3.00000i | −0.857321 | − | 0.122474i | ||||
\(601\) | 29.0000 | − | 29.0000i | 1.18293 | − | 1.18293i | 0.203954 | − | 0.978980i | \(-0.434621\pi\) |
0.978980 | − | 0.203954i | \(-0.0653794\pi\) | |||||||
\(602\) | −36.0000 | − | 36.0000i | −1.46725 | − | 1.46725i | ||||
\(603\) | −6.00000 | −0.244339 | ||||||||
\(604\) | 10.0000i | 0.406894i | ||||||||
\(605\) | −7.00000 | + | 14.0000i | −0.284590 | + | 0.569181i | ||||
\(606\) | −6.00000 | + | 6.00000i | −0.243733 | + | 0.243733i | ||||
\(607\) | −33.0000 | + | 33.0000i | −1.33943 | + | 1.33943i | −0.442816 | + | 0.896612i | \(0.646021\pi\) |
−0.896612 | + | 0.442816i | \(0.853979\pi\) | |||||||
\(608\) | 30.0000i | 1.21666i | ||||||||
\(609\) | −18.0000 | − | 18.0000i | −0.729397 | − | 0.729397i | ||||
\(610\) | 3.00000 | − | 1.00000i | 0.121466 | − | 0.0404888i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | + | 1.00000i | 0.161690 | + | 0.0404226i | ||||
\(613\) | − | 36.0000i | − | 1.45403i | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||
0.686624 | − | 0.727013i | \(-0.259092\pi\) | |||||||
\(614\) | 18.0000i | 0.726421i | ||||||||
\(615\) | −6.00000 | + | 12.0000i | −0.241943 | + | 0.483887i | ||||
\(616\) | 54.0000 | 2.17572 | ||||||||
\(617\) | 15.0000 | − | 15.0000i | 0.603877 | − | 0.603877i | −0.337462 | − | 0.941339i | \(-0.609568\pi\) |
0.941339 | + | 0.337462i | \(0.109568\pi\) | |||||||
\(618\) | −6.00000 | − | 6.00000i | −0.241355 | − | 0.241355i | ||||
\(619\) | 13.0000 | − | 13.0000i | 0.522514 | − | 0.522514i | −0.395816 | − | 0.918330i | \(-0.629538\pi\) |
0.918330 | + | 0.395816i | \(0.129538\pi\) | |||||||
\(620\) | −1.00000 | − | 3.00000i | −0.0401610 | − | 0.120483i | ||||
\(621\) | − | 8.00000i | − | 0.321029i | ||||||
\(622\) | −3.00000 | − | 3.00000i | −0.120289 | − | 0.120289i | ||||
\(623\) | −18.0000 | − | 18.0000i | −0.721155 | − | 0.721155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −3.00000 | − | 3.00000i | −0.119904 | − | 0.119904i | ||||
\(627\) | −36.0000 | −1.43770 | ||||||||
\(628\) | − | 12.0000i | − | 0.478852i | ||||||
\(629\) | 9.00000 | + | 15.0000i | 0.358854 | + | 0.598089i | ||||
\(630\) | 9.00000 | − | 3.00000i | 0.358569 | − | 0.119523i | ||||
\(631\) | − | 34.0000i | − | 1.35352i | −0.736204 | − | 0.676759i | \(-0.763384\pi\) | ||
0.736204 | − | 0.676759i | \(-0.236616\pi\) | |||||||
\(632\) | −21.0000 | + | 21.0000i | −0.835335 | + | 0.835335i | ||||
\(633\) | 34.0000i | 1.35138i | ||||||||
\(634\) | −15.0000 | − | 15.0000i | −0.595726 | − | 0.595726i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000 | − | 2.00000i | 0.0793052 | − | 0.0793052i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.0000 | −0.712627 | ||||||||
\(639\) | −3.00000 | + | 3.00000i | −0.118678 | + | 0.118678i | ||||
\(640\) | −6.00000 | − | 3.00000i | −0.237171 | − | 0.118585i | ||||
\(641\) | 9.00000 | + | 9.00000i | 0.355479 | + | 0.355479i | 0.862143 | − | 0.506665i | \(-0.169122\pi\) |
−0.506665 | + | 0.862143i | \(0.669122\pi\) | |||||||
\(642\) | 18.0000i | 0.710403i | ||||||||
\(643\) | −9.00000 | + | 9.00000i | −0.354925 | + | 0.354925i | −0.861938 | − | 0.507013i | \(-0.830750\pi\) |
0.507013 | + | 0.861938i | \(0.330750\pi\) | |||||||
\(644\) | 6.00000i | 0.236433i | ||||||||
\(645\) | −36.0000 | + | 12.0000i | −1.41750 | + | 0.472500i | ||||
\(646\) | −24.0000 | − | 6.00000i | −0.944267 | − | 0.236067i | ||||
\(647\) | − | 46.0000i | − | 1.80845i | −0.427060 | − | 0.904223i | \(-0.640451\pi\) | ||
0.427060 | − | 0.904223i | \(-0.359549\pi\) | |||||||
\(648\) | 15.0000 | 0.589256 | ||||||||
\(649\) | 18.0000 | + | 18.0000i | 0.706562 | + | 0.706562i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | − | 6.00000i | −0.235159 | − | 0.235159i | ||||
\(652\) | −9.00000 | − | 9.00000i | −0.352467 | − | 0.352467i | ||||
\(653\) | −21.0000 | − | 21.0000i | −0.821794 | − | 0.821794i | 0.164572 | − | 0.986365i | \(-0.447376\pi\) |
−0.986365 | + | 0.164572i | \(0.947376\pi\) | |||||||
\(654\) | 14.0000i | 0.547443i | ||||||||
\(655\) | −3.00000 | − | 9.00000i | −0.117220 | − | 0.351659i | ||||
\(656\) | 3.00000 | − | 3.00000i | 0.117130 | − | 0.117130i | ||||
\(657\) | 3.00000 | + | 3.00000i | 0.117041 | + | 0.117041i | ||||
\(658\) | −6.00000 | + | 6.00000i | −0.233904 | + | 0.233904i | ||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 6.00000 | − | 12.0000i | 0.233550 | − | 0.467099i | ||||
\(661\) | 36.0000i | 1.40024i | 0.714026 | + | 0.700119i | \(0.246870\pi\) | ||||
−0.714026 | + | 0.700119i | \(0.753130\pi\) | |||||||
\(662\) | − | 18.0000i | − | 0.699590i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 54.0000 | − | 18.0000i | 2.09403 | − | 0.698010i | ||||
\(666\) | −3.00000 | − | 3.00000i | −0.116248 | − | 0.116248i | ||||
\(667\) | − | 6.00000i | − | 0.232321i | ||||||
\(668\) | −3.00000 | + | 3.00000i | −0.116073 | + | 0.116073i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | + | 12.0000i | −0.231800 | + | 0.463600i | ||||
\(671\) | 6.00000i | 0.231627i | ||||||||
\(672\) | −30.0000 | −1.15728 | ||||||||
\(673\) | 15.0000 | + | 15.0000i | 0.578208 | + | 0.578208i | 0.934409 | − | 0.356202i | \(-0.115928\pi\) |
−0.356202 | + | 0.934409i | \(0.615928\pi\) | |||||||
\(674\) | −15.0000 | + | 15.0000i | −0.577778 | + | 0.577778i | ||||
\(675\) | 4.00000 | − | 28.0000i | 0.153960 | − | 1.07772i | ||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 11.0000 | − | 11.0000i | 0.422764 | − | 0.422764i | −0.463390 | − | 0.886154i | \(-0.653367\pi\) |
0.886154 | + | 0.463390i | \(0.153367\pi\) | |||||||
\(678\) | −18.0000 | −0.691286 | ||||||||
\(679\) | −18.0000 | −0.690777 | ||||||||
\(680\) | 18.0000 | − | 21.0000i | 0.690268 | − | 0.805313i | ||||
\(681\) | 30.0000 | 1.14960 | ||||||||
\(682\) | −6.00000 | −0.229752 | ||||||||
\(683\) | 15.0000 | − | 15.0000i | 0.573959 | − | 0.573959i | −0.359273 | − | 0.933232i | \(-0.616975\pi\) |
0.933232 | + | 0.359273i | \(0.116975\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | 4.00000 | − | 8.00000i | 0.152832 | − | 0.305664i | ||||
\(686\) | −12.0000 | + | 12.0000i | −0.458162 | + | 0.458162i | ||||
\(687\) | 24.0000 | + | 24.0000i | 0.915657 | + | 0.915657i | ||||
\(688\) | 12.0000 | 0.457496 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.00000 | − | 2.00000i | −0.152277 | − | 0.0761387i | ||||
\(691\) | −19.0000 | + | 19.0000i | −0.722794 | + | 0.722794i | −0.969173 | − | 0.246379i | \(-0.920759\pi\) |
0.246379 | + | 0.969173i | \(0.420759\pi\) | |||||||
\(692\) | −15.0000 | + | 15.0000i | −0.570214 | + | 0.570214i | ||||
\(693\) | 18.0000i | 0.683763i | ||||||||
\(694\) | −9.00000 | − | 9.00000i | −0.341635 | − | 0.341635i | ||||
\(695\) | −7.00000 | − | 21.0000i | −0.265525 | − | 0.796575i | ||||
\(696\) | 18.0000 | 0.682288 | ||||||||
\(697\) | −9.00000 | − | 15.0000i | −0.340899 | − | 0.568166i | ||||
\(698\) | 28.0000i | 1.05982i | ||||||||
\(699\) | − | 10.0000i | − | 0.378235i | ||||||
\(700\) | −3.00000 | + | 21.0000i | −0.113389 | + | 0.793725i | ||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | − | 18.0000i | −0.678883 | − | 0.678883i | ||||
\(704\) | −21.0000 | + | 21.0000i | −0.791467 | + | 0.791467i | ||||
\(705\) | 2.00000 | + | 6.00000i | 0.0753244 | + | 0.225973i | ||||
\(706\) | − | 16.0000i | − | 0.602168i | ||||||
\(707\) | 18.0000 | + | 18.0000i | 0.676960 | + | 0.676960i | ||||
\(708\) | −6.00000 | − | 6.00000i | −0.225494 | − | 0.225494i | ||||
\(709\) | 5.00000 | + | 5.00000i | 0.187779 | + | 0.187779i | 0.794735 | − | 0.606956i | \(-0.207610\pi\) |
−0.606956 | + | 0.794735i | \(0.707610\pi\) | |||||||
\(710\) | 3.00000 | + | 9.00000i | 0.112588 | + | 0.337764i | ||||
\(711\) | −7.00000 | − | 7.00000i | −0.262521 | − | 0.262521i | ||||
\(712\) | 18.0000 | 0.674579 | ||||||||
\(713\) | − | 2.00000i | − | 0.0749006i | ||||||
\(714\) | 6.00000 | − | 24.0000i | 0.224544 | − | 0.898177i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00000i | 0.224231i | ||||||||
\(717\) | 24.0000 | − | 24.0000i | 0.896296 | − | 0.896296i | ||||
\(718\) | − | 30.0000i | − | 1.11959i | ||||||
\(719\) | −21.0000 | − | 21.0000i | −0.783168 | − | 0.783168i | 0.197196 | − | 0.980364i | \(-0.436816\pi\) |
−0.980364 | + | 0.197196i | \(0.936816\pi\) | |||||||
\(720\) | −1.00000 | + | 2.00000i | −0.0372678 | + | 0.0745356i | ||||
\(721\) | −18.0000 | + | 18.0000i | −0.670355 | + | 0.670355i | ||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 38.0000 | 1.41324 | ||||||||
\(724\) | 11.0000 | − | 11.0000i | 0.408812 | − | 0.408812i | ||||
\(725\) | 3.00000 | − | 21.0000i | 0.111417 | − | 0.779920i | ||||
\(726\) | −7.00000 | − | 7.00000i | −0.259794 | − | 0.259794i | ||||
\(727\) | 18.0000i | 0.667583i | 0.942647 | + | 0.333792i | \(0.108328\pi\) | ||||
−0.942647 | + | 0.333792i | \(0.891672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 9.00000 | − | 3.00000i | 0.333105 | − | 0.111035i | ||||
\(731\) | 12.0000 | − | 48.0000i | 0.443836 | − | 1.77534i | ||||
\(732\) | − | 2.00000i | − | 0.0739221i | ||||||
\(733\) | 42.0000 | 1.55131 | 0.775653 | − | 0.631160i | \(-0.217421\pi\) | ||||
0.775653 | + | 0.631160i | \(0.217421\pi\) | |||||||
\(734\) | 3.00000 | + | 3.00000i | 0.110732 | + | 0.110732i | ||||
\(735\) | 11.0000 | + | 33.0000i | 0.405741 | + | 1.21722i | ||||
\(736\) | −5.00000 | − | 5.00000i | −0.184302 | − | 0.184302i | ||||
\(737\) | −18.0000 | − | 18.0000i | −0.663039 | − | 0.663039i | ||||
\(738\) | 3.00000 | + | 3.00000i | 0.110432 | + | 0.110432i | ||||
\(739\) | 34.0000i | 1.25071i | 0.780340 | + | 0.625355i | \(0.215046\pi\) | ||||
−0.780340 | + | 0.625355i | \(0.784954\pi\) | |||||||
\(740\) | 9.00000 | − | 3.00000i | 0.330847 | − | 0.110282i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | + | 6.00000i | 0.220267 | + | 0.220267i | ||||
\(743\) | −9.00000 | + | 9.00000i | −0.330178 | + | 0.330178i | −0.852654 | − | 0.522476i | \(-0.825008\pi\) |
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 36.0000 | + | 18.0000i | 1.31894 | + | 0.659469i | ||||
\(746\) | 24.0000i | 0.878702i | ||||||||
\(747\) | − | 4.00000i | − | 0.146352i | ||||||
\(748\) | 9.00000 | + | 15.0000i | 0.329073 | + | 0.548454i | ||||
\(749\) | 54.0000 | 1.97312 | ||||||||
\(750\) | −13.0000 | − | 9.00000i | −0.474693 | − | 0.328634i | ||||
\(751\) | 19.0000 | + | 19.0000i | 0.693320 | + | 0.693320i | 0.962961 | − | 0.269641i | \(-0.0869050\pi\) |
−0.269641 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(752\) | − | 2.00000i | − | 0.0729325i | ||||||
\(753\) | 12.0000 | − | 12.0000i | 0.437304 | − | 0.437304i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | + | 20.0000i | −0.363937 | + | 0.727875i | ||||
\(756\) | − | 24.0000i | − | 0.872872i | ||||||
\(757\) | −42.0000 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(758\) | −11.0000 | − | 11.0000i | −0.399538 | − | 0.399538i | ||||
\(759\) | 6.00000 | − | 6.00000i | 0.217786 | − | 0.217786i | ||||
\(760\) | −18.0000 | + | 36.0000i | −0.652929 | + | 1.30586i | ||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.0000 | 1.52050 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.00000 | + | 6.00000i | 0.253086 | + | 0.216930i | ||||
\(766\) | 16.0000 | 0.578103 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 17.0000 | − | 17.0000i | 0.613435 | − | 0.613435i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 36.0000 | + | 18.0000i | 1.29735 | + | 0.648675i | ||||
\(771\) | 14.0000 | − | 14.0000i | 0.504198 | − | 0.504198i | ||||
\(772\) | −3.00000 | − | 3.00000i | −0.107972 | − | 0.107972i | ||||
\(773\) | −26.0000 | −0.935155 | −0.467578 | − | 0.883952i | \(-0.654873\pi\) | ||||
−0.467578 | + | 0.883952i | \(0.654873\pi\) | |||||||
\(774\) |