Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(429,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.c (of order \(3\), degree \(2\), not 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: | \(5.76519902594\) |
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: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 429.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.429 |
Dual form | 722.2.c.d.653.1 |
$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.00000 | − | 3.46410i | 0.894427 | − | 1.54919i | 0.0599153 | − | 0.998203i | \(-0.480917\pi\) |
0.834512 | − | 0.550990i | \(-0.185750\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 2.00000 | + | 3.46410i | 0.632456 | + | 1.09545i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | −1.50000 | + | 2.59808i | −0.400892 | + | 0.694365i | ||||
\(15\) | −2.00000 | − | 3.46410i | −0.516398 | − | 0.894427i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | −2.00000 | −0.471405 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.00000 | −0.894427 | ||||||||
\(21\) | 1.50000 | − | 2.59808i | 0.327327 | − | 0.566947i | ||||
\(22\) | −1.00000 | + | 1.73205i | −0.213201 | + | 0.369274i | ||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −1.50000 | − | 2.59808i | −0.283473 | − | 0.490990i | ||||
\(29\) | 2.50000 | + | 4.33013i | 0.464238 | + | 0.804084i | 0.999167 | − | 0.0408130i | \(-0.0129948\pi\) |
−0.534928 | + | 0.844897i | \(0.679661\pi\) | |||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 6.00000 | − | 10.3923i | 1.01419 | − | 1.75662i | ||||
\(36\) | 1.00000 | − | 1.73205i | 0.166667 | − | 0.288675i | ||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.00000 | − | 3.46410i | 0.316228 | − | 0.547723i | ||||
\(41\) | 4.00000 | − | 6.92820i | 0.624695 | − | 1.08200i | −0.363905 | − | 0.931436i | \(-0.618557\pi\) |
0.988600 | − | 0.150567i | \(-0.0481100\pi\) | |||||||
\(42\) | 1.50000 | + | 2.59808i | 0.231455 | + | 0.400892i | ||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | 8.00000 | 1.19257 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 11.0000 | 1.55563 | ||||||||
\(51\) | 1.50000 | + | 2.59808i | 0.210042 | + | 0.363803i | ||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | 0.500000 | + | 0.866025i | 0.0686803 | + | 0.118958i | 0.898321 | − | 0.439340i | \(-0.144788\pi\) |
−0.829640 | + | 0.558298i | \(0.811454\pi\) | |||||||
\(54\) | −2.50000 | + | 4.33013i | −0.340207 | + | 0.589256i | ||||
\(55\) | 4.00000 | − | 6.92820i | 0.539360 | − | 0.934199i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | −0.656532 | ||||||||
\(59\) | −7.50000 | + | 12.9904i | −0.976417 | + | 1.69120i | −0.301239 | + | 0.953549i | \(0.597400\pi\) |
−0.675178 | + | 0.737655i | \(0.735933\pi\) | |||||||
\(60\) | −2.00000 | + | 3.46410i | −0.258199 | + | 0.447214i | ||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 4.00000 | − | 6.92820i | 0.508001 | − | 0.879883i | ||||
\(63\) | 3.00000 | + | 5.19615i | 0.377964 | + | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 1.00000 | + | 1.73205i | 0.123091 | + | 0.213201i | ||||
\(67\) | −1.50000 | − | 2.59808i | −0.183254 | − | 0.317406i | 0.759733 | − | 0.650236i | \(-0.225330\pi\) |
−0.942987 | + | 0.332830i | \(0.891996\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 6.00000 | + | 10.3923i | 0.717137 | + | 1.24212i | ||||
\(71\) | −1.00000 | + | 1.73205i | −0.118678 | + | 0.205557i | −0.919244 | − | 0.393688i | \(-0.871199\pi\) |
0.800566 | + | 0.599245i | \(0.204532\pi\) | |||||||
\(72\) | 1.00000 | + | 1.73205i | 0.117851 | + | 0.204124i | ||||
\(73\) | −4.50000 | + | 7.79423i | −0.526685 | + | 0.912245i | 0.472831 | + | 0.881153i | \(0.343232\pi\) |
−0.999517 | + | 0.0310925i | \(0.990101\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | −11.0000 | −1.27017 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | −0.500000 | + | 0.866025i | −0.0566139 | + | 0.0980581i | ||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 2.00000 | + | 3.46410i | 0.223607 | + | 0.387298i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.00000 | + | 6.92820i | 0.441726 | + | 0.765092i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | 6.00000 | + | 10.3923i | 0.650791 | + | 1.12720i | ||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | −4.00000 | + | 6.92820i | −0.421637 | + | 0.730297i | ||||
\(91\) | 1.50000 | + | 2.59808i | 0.157243 | + | 0.272352i | ||||
\(92\) | 0.500000 | − | 0.866025i | 0.0521286 | − | 0.0902894i | ||||
\(93\) | −4.00000 | + | 6.92820i | −0.414781 | + | 0.718421i | ||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.00000 | − | 1.73205i | 0.101535 | − | 0.175863i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) |
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | −1.00000 | + | 1.73205i | −0.101015 | + | 0.174964i | ||||
\(99\) | 2.00000 | + | 3.46410i | 0.201008 | + | 0.348155i | ||||
\(100\) | −5.50000 | + | 9.52628i | −0.550000 | + | 0.952628i | ||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | −3.00000 | −0.297044 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 0.500000 | + | 0.866025i | 0.0490290 | + | 0.0849208i | ||||
\(105\) | −6.00000 | − | 10.3923i | −0.585540 | − | 1.01419i | ||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −7.00000 | −0.676716 | −0.338358 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338358 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | 7.50000 | − | 12.9904i | 0.718370 | − | 1.24425i | −0.243276 | − | 0.969957i | \(-0.578222\pi\) |
0.961645 | − | 0.274296i | \(-0.0884447\pi\) | |||||||
\(110\) | 4.00000 | + | 6.92820i | 0.381385 | + | 0.660578i | ||||
\(111\) | −1.00000 | + | 1.73205i | −0.0949158 | + | 0.164399i | ||||
\(112\) | −1.50000 | + | 2.59808i | −0.141737 | + | 0.245495i | ||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 2.50000 | − | 4.33013i | 0.232119 | − | 0.402042i | ||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | −7.50000 | − | 12.9904i | −0.690431 | − | 1.19586i | ||||
\(119\) | −4.50000 | + | 7.79423i | −0.412514 | + | 0.714496i | ||||
\(120\) | −2.00000 | − | 3.46410i | −0.182574 | − | 0.316228i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | −4.00000 | − | 6.92820i | −0.360668 | − | 0.624695i | ||||
\(124\) | 4.00000 | + | 6.92820i | 0.359211 | + | 0.622171i | ||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | −6.00000 | −0.534522 | ||||||||
\(127\) | −9.00000 | − | 15.5885i | −0.798621 | − | 1.38325i | −0.920514 | − | 0.390709i | \(-0.872230\pi\) |
0.121894 | − | 0.992543i | \(-0.461103\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | + | 3.46410i | 0.176090 | + | 0.304997i | ||||
\(130\) | −2.00000 | + | 3.46410i | −0.175412 | + | 0.303822i | ||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | −2.00000 | −0.174078 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.00000 | 0.259161 | ||||||||
\(135\) | 10.0000 | − | 17.3205i | 0.860663 | − | 1.49071i | ||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | 8.50000 | + | 14.7224i | 0.726204 | + | 1.25782i | 0.958477 | + | 0.285171i | \(0.0920506\pi\) |
−0.232273 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(140\) | −12.0000 | −1.01419 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | −1.00000 | − | 1.73205i | −0.0839181 | − | 0.145350i | ||||
\(143\) | 1.00000 | + | 1.73205i | 0.0836242 | + | 0.144841i | ||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 20.0000 | 1.66091 | ||||||||
\(146\) | −4.50000 | − | 7.79423i | −0.372423 | − | 0.645055i | ||||
\(147\) | 1.00000 | − | 1.73205i | 0.0824786 | − | 0.142857i | ||||
\(148\) | 1.00000 | + | 1.73205i | 0.0821995 | + | 0.142374i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 5.50000 | − | 9.52628i | 0.449073 | − | 0.777817i | ||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | −3.00000 | + | 5.19615i | −0.241747 | + | 0.418718i | ||||
\(155\) | −16.0000 | + | 27.7128i | −1.28515 | + | 2.22595i | ||||
\(156\) | −0.500000 | − | 0.866025i | −0.0400320 | − | 0.0693375i | ||||
\(157\) | 1.00000 | − | 1.73205i | 0.0798087 | − | 0.138233i | −0.823359 | − | 0.567521i | \(-0.807902\pi\) |
0.903167 | + | 0.429289i | \(0.141236\pi\) | |||||||
\(158\) | 5.00000 | + | 8.66025i | 0.397779 | + | 0.688973i | ||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | −4.00000 | −0.316228 | ||||||||
\(161\) | 1.50000 | + | 2.59808i | 0.118217 | + | 0.204757i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | −8.00000 | −0.624695 | ||||||||
\(165\) | −4.00000 | − | 6.92820i | −0.311400 | − | 0.539360i | ||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | 6.00000 | + | 10.3923i | 0.464294 | + | 0.804181i | 0.999169 | − | 0.0407502i | \(-0.0129748\pi\) |
−0.534875 | + | 0.844931i | \(0.679641\pi\) | |||||||
\(168\) | 1.50000 | − | 2.59808i | 0.115728 | − | 0.200446i | ||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | −12.0000 | −0.920358 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | 0.304997 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | −2.50000 | + | 4.33013i | −0.189525 | + | 0.328266i | ||||
\(175\) | −16.5000 | − | 28.5788i | −1.24728 | − | 2.16036i | ||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 7.50000 | + | 12.9904i | 0.563735 | + | 0.976417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −4.00000 | − | 6.92820i | −0.298142 | − | 0.516398i | ||||
\(181\) | −11.0000 | − | 19.0526i | −0.817624 | − | 1.41617i | −0.907429 | − | 0.420206i | \(-0.861958\pi\) |
0.0898051 | − | 0.995959i | \(-0.471376\pi\) | |||||||
\(182\) | −3.00000 | −0.222375 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | −4.00000 | − | 6.92820i | −0.293294 | − | 0.508001i | ||||
\(187\) | −3.00000 | + | 5.19615i | −0.219382 | + | 0.379980i | ||||
\(188\) | −4.00000 | + | 6.92820i | −0.291730 | + | 0.505291i | ||||
\(189\) | 15.0000 | 1.09109 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.00000 | 0.506502 | 0.253251 | − | 0.967401i | \(-0.418500\pi\) | ||||
0.253251 | + | 0.967401i | \(0.418500\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 3.00000 | − | 5.19615i | 0.215945 | − | 0.374027i | −0.737620 | − | 0.675216i | \(-0.764050\pi\) |
0.953564 | + | 0.301189i | \(0.0973836\pi\) | |||||||
\(194\) | 1.00000 | + | 1.73205i | 0.0717958 | + | 0.124354i | ||||
\(195\) | 2.00000 | − | 3.46410i | 0.143223 | − | 0.248069i | ||||
\(196\) | −1.00000 | − | 1.73205i | −0.0714286 | − | 0.123718i | ||||
\(197\) | 8.00000 | 0.569976 | 0.284988 | − | 0.958531i | \(-0.408010\pi\) | ||||
0.284988 | + | 0.958531i | \(0.408010\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | 12.5000 | + | 21.6506i | 0.886102 | + | 1.53477i | 0.844446 | + | 0.535641i | \(0.179930\pi\) |
0.0416556 | + | 0.999132i | \(0.486737\pi\) | |||||||
\(200\) | −5.50000 | − | 9.52628i | −0.388909 | − | 0.673610i | ||||
\(201\) | −3.00000 | −0.211604 | ||||||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | 7.50000 | + | 12.9904i | 0.526397 | + | 0.911746i | ||||
\(204\) | 1.50000 | − | 2.59808i | 0.105021 | − | 0.181902i | ||||
\(205\) | −16.0000 | − | 27.7128i | −1.11749 | − | 1.93555i | ||||
\(206\) | 3.00000 | − | 5.19615i | 0.209020 | − | 0.362033i | ||||
\(207\) | −1.00000 | + | 1.73205i | −0.0695048 | + | 0.120386i | ||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 12.0000 | 0.828079 | ||||||||
\(211\) | −13.5000 | + | 23.3827i | −0.929378 | + | 1.60973i | −0.145014 | + | 0.989430i | \(0.546323\pi\) |
−0.784364 | + | 0.620301i | \(0.787010\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.0343401 | − | 0.0594789i | ||||
\(213\) | 1.00000 | + | 1.73205i | 0.0685189 | + | 0.118678i | ||||
\(214\) | 3.50000 | − | 6.06218i | 0.239255 | − | 0.414402i | ||||
\(215\) | 8.00000 | + | 13.8564i | 0.545595 | + | 0.944999i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | −24.0000 | −1.62923 | ||||||||
\(218\) | 7.50000 | + | 12.9904i | 0.507964 | + | 0.879820i | ||||
\(219\) | 4.50000 | + | 7.79423i | 0.304082 | + | 0.526685i | ||||
\(220\) | −8.00000 | −0.539360 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | −1.00000 | − | 1.73205i | −0.0671156 | − | 0.116248i | ||||
\(223\) | −7.00000 | + | 12.1244i | −0.468755 | + | 0.811907i | −0.999362 | − | 0.0357107i | \(-0.988630\pi\) |
0.530607 | + | 0.847618i | \(0.321964\pi\) | |||||||
\(224\) | −1.50000 | − | 2.59808i | −0.100223 | − | 0.173591i | ||||
\(225\) | 11.0000 | − | 19.0526i | 0.733333 | − | 1.27017i | ||||
\(226\) | −7.00000 | + | 12.1244i | −0.465633 | + | 0.806500i | ||||
\(227\) | −17.0000 | −1.12833 | −0.564165 | − | 0.825662i | \(-0.690802\pi\) | ||||
−0.564165 | + | 0.825662i | \(0.690802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −2.00000 | + | 3.46410i | −0.131876 | + | 0.228416i | ||||
\(231\) | 3.00000 | − | 5.19615i | 0.197386 | − | 0.341882i | ||||
\(232\) | 2.50000 | + | 4.33013i | 0.164133 | + | 0.284287i | ||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | −1.00000 | − | 1.73205i | −0.0653720 | − | 0.113228i | ||||
\(235\) | −32.0000 | −2.08745 | ||||||||
\(236\) | 15.0000 | 0.976417 | ||||||||
\(237\) | −5.00000 | − | 8.66025i | −0.324785 | − | 0.562544i | ||||
\(238\) | −4.50000 | − | 7.79423i | −0.291692 | − | 0.505225i | ||||
\(239\) | 15.0000 | 0.970269 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(240\) | 4.00000 | 0.258199 | ||||||||
\(241\) | 4.00000 | + | 6.92820i | 0.257663 | + | 0.446285i | 0.965615 | − | 0.259975i | \(-0.0837143\pi\) |
−0.707953 | + | 0.706260i | \(0.750381\pi\) | |||||||
\(242\) | 3.50000 | − | 6.06218i | 0.224989 | − | 0.389692i | ||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | −1.00000 | + | 1.73205i | −0.0640184 | + | 0.110883i | ||||
\(245\) | 4.00000 | − | 6.92820i | 0.255551 | − | 0.442627i | ||||
\(246\) | 8.00000 | 0.510061 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.00000 | −0.508001 | ||||||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 12.0000 | − | 20.7846i | 0.758947 | − | 1.31453i | ||||
\(251\) | −1.00000 | − | 1.73205i | −0.0631194 | − | 0.109326i | 0.832739 | − | 0.553666i | \(-0.186772\pi\) |
−0.895858 | + | 0.444340i | \(0.853438\pi\) | |||||||
\(252\) | 3.00000 | − | 5.19615i | 0.188982 | − | 0.327327i | ||||
\(253\) | 1.00000 | + | 1.73205i | 0.0628695 | + | 0.108893i | ||||
\(254\) | 18.0000 | 1.12942 | ||||||||
\(255\) | 12.0000 | 0.751469 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.00000 | − | 6.92820i | −0.249513 | − | 0.432169i | 0.713878 | − | 0.700270i | \(-0.246937\pi\) |
−0.963391 | + | 0.268101i | \(0.913604\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | −2.00000 | − | 3.46410i | −0.124035 | − | 0.214834i | ||||
\(261\) | −5.00000 | + | 8.66025i | −0.309492 | + | 0.536056i | ||||
\(262\) | −6.00000 | − | 10.3923i | −0.370681 | − | 0.642039i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 1.00000 | − | 1.73205i | 0.0615457 | − | 0.106600i | ||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.50000 | + | 2.59808i | −0.0916271 | + | 0.158703i | ||||
\(269\) | −15.0000 | + | 25.9808i | −0.914566 | + | 1.58408i | −0.107031 | + | 0.994256i | \(0.534134\pi\) |
−0.807535 | + | 0.589819i | \(0.799199\pi\) | |||||||
\(270\) | 10.0000 | + | 17.3205i | 0.608581 | + | 1.05409i | ||||
\(271\) | −3.50000 | + | 6.06218i | −0.212610 | + | 0.368251i | −0.952531 | − | 0.304443i | \(-0.901530\pi\) |
0.739921 | + | 0.672694i | \(0.234863\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | −17.0000 | −1.02701 | ||||||||
\(275\) | −11.0000 | − | 19.0526i | −0.663325 | − | 1.14891i | ||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | 28.0000 | 1.68236 | 0.841178 | − | 0.540758i | \(-0.181862\pi\) | ||||
0.841178 | + | 0.540758i | \(0.181862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.00000 | − | 13.8564i | −0.478947 | − | 0.829561i | ||||
\(280\) | 6.00000 | − | 10.3923i | 0.358569 | − | 0.621059i | ||||
\(281\) | 4.00000 | + | 6.92820i | 0.238620 | + | 0.413302i | 0.960319 | − | 0.278906i | \(-0.0899716\pi\) |
−0.721699 | + | 0.692207i | \(0.756638\pi\) | |||||||
\(282\) | 4.00000 | − | 6.92820i | 0.238197 | − | 0.412568i | ||||
\(283\) | 3.00000 | − | 5.19615i | 0.178331 | − | 0.308879i | −0.762978 | − | 0.646425i | \(-0.776263\pi\) |
0.941309 | + | 0.337546i | \(0.109597\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | −0.118262 | ||||||||
\(287\) | 12.0000 | − | 20.7846i | 0.708338 | − | 1.22688i | ||||
\(288\) | 1.00000 | − | 1.73205i | 0.0589256 | − | 0.102062i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −10.0000 | + | 17.3205i | −0.587220 | + | 1.01710i | ||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | 9.00000 | 0.526685 | ||||||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 1.00000 | + | 1.73205i | 0.0583212 | + | 0.101015i | ||||
\(295\) | 30.0000 | + | 51.9615i | 1.74667 | + | 3.02532i | ||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 10.0000 | 0.580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.500000 | + | 0.866025i | −0.0289157 | + | 0.0500835i | ||||
\(300\) | 5.50000 | + | 9.52628i | 0.317543 | + | 0.550000i | ||||
\(301\) | −6.00000 | + | 10.3923i | −0.345834 | + | 0.599002i | ||||
\(302\) | −1.00000 | + | 1.73205i | −0.0575435 | + | 0.0996683i | ||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.00000 | −0.458079 | ||||||||
\(306\) | 3.00000 | − | 5.19615i | 0.171499 | − | 0.297044i | ||||
\(307\) | 6.00000 | − | 10.3923i | 0.342438 | − | 0.593120i | −0.642447 | − | 0.766330i | \(-0.722081\pi\) |
0.984885 | + | 0.173210i | \(0.0554140\pi\) | |||||||
\(308\) | −3.00000 | − | 5.19615i | −0.170941 | − | 0.296078i | ||||
\(309\) | −3.00000 | + | 5.19615i | −0.170664 | + | 0.295599i | ||||
\(310\) | −16.0000 | − | 27.7128i | −0.908739 | − | 1.57398i | ||||
\(311\) | 7.00000 | 0.396934 | 0.198467 | − | 0.980108i | \(-0.436404\pi\) | ||||
0.198467 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −14.5000 | − | 25.1147i | −0.819588 | − | 1.41957i | −0.905986 | − | 0.423308i | \(-0.860869\pi\) |
0.0863973 | − | 0.996261i | \(-0.472465\pi\) | |||||||
\(314\) | 1.00000 | + | 1.73205i | 0.0564333 | + | 0.0977453i | ||||
\(315\) | 24.0000 | 1.35225 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 13.5000 | + | 23.3827i | 0.758236 | + | 1.31330i | 0.943750 | + | 0.330661i | \(0.107272\pi\) |
−0.185514 | + | 0.982642i | \(0.559395\pi\) | |||||||
\(318\) | −0.500000 | + | 0.866025i | −0.0280386 | + | 0.0485643i | ||||
\(319\) | 5.00000 | + | 8.66025i | 0.279946 | + | 0.484881i | ||||
\(320\) | 2.00000 | − | 3.46410i | 0.111803 | − | 0.193649i | ||||
\(321\) | −3.50000 | + | 6.06218i | −0.195351 | + | 0.338358i | ||||
\(322\) | −3.00000 | −0.167183 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.50000 | − | 9.52628i | 0.305085 | − | 0.528423i | ||||
\(326\) | 8.00000 | − | 13.8564i | 0.443079 | − | 0.767435i | ||||
\(327\) | −7.50000 | − | 12.9904i | −0.414751 | − | 0.718370i | ||||
\(328\) | 4.00000 | − | 6.92820i | 0.220863 | − | 0.382546i | ||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 8.00000 | 0.440386 | ||||||||
\(331\) | 17.0000 | 0.934405 | 0.467202 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(332\) | 3.00000 | + | 5.19615i | 0.164646 | + | 0.285176i | ||||
\(333\) | −2.00000 | − | 3.46410i | −0.109599 | − | 0.189832i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 1.50000 | + | 2.59808i | 0.0818317 | + | 0.141737i | ||||
\(337\) | 16.0000 | − | 27.7128i | 0.871576 | − | 1.50961i | 0.0112091 | − | 0.999937i | \(-0.496432\pi\) |
0.860366 | − | 0.509676i | \(-0.170235\pi\) | |||||||
\(338\) | 6.00000 | + | 10.3923i | 0.326357 | + | 0.565267i | ||||
\(339\) | 7.00000 | − | 12.1244i | 0.380188 | − | 0.658505i | ||||
\(340\) | 6.00000 | − | 10.3923i | 0.325396 | − | 0.563602i | ||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −2.00000 | + | 3.46410i | −0.107833 | + | 0.186772i | ||||
\(345\) | 2.00000 | − | 3.46410i | 0.107676 | − | 0.186501i | ||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | 1.00000 | − | 1.73205i | 0.0536828 | − | 0.0929814i | −0.837935 | − | 0.545770i | \(-0.816237\pi\) |
0.891618 | + | 0.452788i | \(0.149571\pi\) | |||||||
\(348\) | −2.50000 | − | 4.33013i | −0.134014 | − | 0.232119i | ||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 33.0000 | 1.76392 | ||||||||
\(351\) | 2.50000 | + | 4.33013i | 0.133440 | + | 0.231125i | ||||
\(352\) | −1.00000 | − | 1.73205i | −0.0533002 | − | 0.0923186i | ||||
\(353\) | 9.00000 | 0.479022 | 0.239511 | − | 0.970894i | \(-0.423013\pi\) | ||||
0.239511 | + | 0.970894i | \(0.423013\pi\) | |||||||
\(354\) | −15.0000 | −0.797241 | ||||||||
\(355\) | 4.00000 | + | 6.92820i | 0.212298 | + | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.50000 | + | 7.79423i | 0.238165 | + | 0.412514i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.50000 | − | 12.9904i | 0.395835 | − | 0.685606i | −0.597372 | − | 0.801964i | \(-0.703789\pi\) |
0.993207 | + | 0.116358i | \(0.0371219\pi\) | |||||||
\(360\) | 8.00000 | 0.421637 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 22.0000 | 1.15629 | ||||||||
\(363\) | −3.50000 | + | 6.06218i | −0.183702 | + | 0.318182i | ||||
\(364\) | 1.50000 | − | 2.59808i | 0.0786214 | − | 0.136176i | ||||
\(365\) | 18.0000 | + | 31.1769i | 0.942163 | + | 1.63187i | ||||
\(366\) | 1.00000 | − | 1.73205i | 0.0522708 | − | 0.0905357i | ||||
\(367\) | −14.0000 | − | 24.2487i | −0.730794 | − | 1.26577i | −0.956544 | − | 0.291587i | \(-0.905817\pi\) |
0.225750 | − | 0.974185i | \(-0.427517\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 16.0000 | 0.832927 | ||||||||
\(370\) | −4.00000 | − | 6.92820i | −0.207950 | − | 0.360180i | ||||
\(371\) | 1.50000 | + | 2.59808i | 0.0778761 | + | 0.134885i | ||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | 29.0000 | 1.50156 | 0.750782 | − | 0.660551i | \(-0.229677\pi\) | ||||
0.750782 | + | 0.660551i | \(0.229677\pi\) | |||||||
\(374\) | −3.00000 | − | 5.19615i | −0.155126 | − | 0.268687i | ||||
\(375\) | −12.0000 | + | 20.7846i | −0.619677 | + | 1.07331i | ||||
\(376\) | −4.00000 | − | 6.92820i | −0.206284 | − | 0.357295i | ||||
\(377\) | −2.50000 | + | 4.33013i | −0.128757 | + | 0.223013i | ||||
\(378\) | −7.50000 | + | 12.9904i | −0.385758 | + | 0.668153i | ||||
\(379\) | 15.0000 | 0.770498 | 0.385249 | − | 0.922813i | \(-0.374116\pi\) | ||||
0.385249 | + | 0.922813i | \(0.374116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | −0.922168 | ||||||||
\(382\) | −3.50000 | + | 6.06218i | −0.179076 | + | 0.310168i | ||||
\(383\) | 13.0000 | − | 22.5167i | 0.664269 | − | 1.15055i | −0.315214 | − | 0.949021i | \(-0.602076\pi\) |
0.979483 | − | 0.201527i | \(-0.0645904\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 12.0000 | − | 20.7846i | 0.611577 | − | 1.05928i | ||||
\(386\) | 3.00000 | + | 5.19615i | 0.152696 | + | 0.264477i | ||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 15.0000 | + | 25.9808i | 0.760530 | + | 1.31728i | 0.942578 | + | 0.333987i | \(0.108394\pi\) |
−0.182047 | + | 0.983290i | \(0.558272\pi\) | |||||||
\(390\) | 2.00000 | + | 3.46410i | 0.101274 | + | 0.175412i | ||||
\(391\) | −3.00000 | −0.151717 | ||||||||
\(392\) | 2.00000 | 0.101015 | ||||||||
\(393\) | 6.00000 | + | 10.3923i | 0.302660 | + | 0.524222i | ||||
\(394\) | −4.00000 | + | 6.92820i | −0.201517 | + | 0.349038i | ||||
\(395\) | −20.0000 | − | 34.6410i | −1.00631 | − | 1.74298i | ||||
\(396\) | 2.00000 | − | 3.46410i | 0.100504 | − | 0.174078i | ||||
\(397\) | −4.00000 | + | 6.92820i | −0.200754 | + | 0.347717i | −0.948772 | − | 0.315963i | \(-0.897673\pi\) |
0.748017 | + | 0.663679i | \(0.231006\pi\) | |||||||
\(398\) | −25.0000 | −1.25314 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | 4.00000 | − | 6.92820i | 0.199750 | − | 0.345978i | −0.748697 | − | 0.662912i | \(-0.769320\pi\) |
0.948447 | + | 0.316934i | \(0.102654\pi\) | |||||||
\(402\) | 1.50000 | − | 2.59808i | 0.0748132 | − | 0.129580i | ||||
\(403\) | −4.00000 | − | 6.92820i | −0.199254 | − | 0.345118i | ||||
\(404\) | −1.00000 | + | 1.73205i | −0.0497519 | + | 0.0861727i | ||||
\(405\) | 2.00000 | + | 3.46410i | 0.0993808 | + | 0.172133i | ||||
\(406\) | −15.0000 | −0.744438 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 1.50000 | + | 2.59808i | 0.0742611 | + | 0.128624i | ||||
\(409\) | 10.0000 | + | 17.3205i | 0.494468 | + | 0.856444i | 0.999980 | − | 0.00637586i | \(-0.00202951\pi\) |
−0.505511 | + | 0.862820i | \(0.668696\pi\) | |||||||
\(410\) | 32.0000 | 1.58037 | ||||||||
\(411\) | 17.0000 | 0.838548 | ||||||||
\(412\) | 3.00000 | + | 5.19615i | 0.147799 | + | 0.255996i | ||||
\(413\) | −22.5000 | + | 38.9711i | −1.10715 | + | 1.91764i | ||||
\(414\) | −1.00000 | − | 1.73205i | −0.0491473 | − | 0.0851257i | ||||
\(415\) | −12.0000 | + | 20.7846i | −0.589057 | + | 1.02028i | ||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −6.00000 | + | 10.3923i | −0.292770 | + | 0.507093i | ||||
\(421\) | 6.50000 | − | 11.2583i | 0.316791 | − | 0.548697i | −0.663026 | − | 0.748596i | \(-0.730728\pi\) |
0.979817 | + | 0.199899i | \(0.0640614\pi\) | |||||||
\(422\) | −13.5000 | − | 23.3827i | −0.657170 | − | 1.13825i | ||||
\(423\) | 8.00000 | − | 13.8564i | 0.388973 | − | 0.673722i | ||||
\(424\) | 0.500000 | + | 0.866025i | 0.0242821 | + | 0.0420579i | ||||
\(425\) | 33.0000 | 1.60074 | ||||||||
\(426\) | −2.00000 | −0.0969003 | ||||||||
\(427\) | −3.00000 | − | 5.19615i | −0.145180 | − | 0.251459i | ||||
\(428\) | 3.50000 | + | 6.06218i | 0.169179 | + | 0.293026i | ||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | −16.0000 | −0.771589 | ||||||||
\(431\) | 9.00000 | + | 15.5885i | 0.433515 | + | 0.750870i | 0.997173 | − | 0.0751385i | \(-0.0239399\pi\) |
−0.563658 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(432\) | −2.50000 | + | 4.33013i | −0.120281 | + | 0.208333i | ||||
\(433\) | −7.00000 | − | 12.1244i | −0.336399 | − | 0.582659i | 0.647354 | − | 0.762190i | \(-0.275876\pi\) |
−0.983752 | + | 0.179530i | \(0.942542\pi\) | |||||||
\(434\) | 12.0000 | − | 20.7846i | 0.576018 | − | 0.997693i | ||||
\(435\) | 10.0000 | − | 17.3205i | 0.479463 | − | 0.830455i | ||||
\(436\) | −15.0000 | −0.718370 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −9.00000 | −0.430037 | ||||||||
\(439\) | −10.0000 | + | 17.3205i | −0.477274 | + | 0.826663i | −0.999661 | − | 0.0260459i | \(-0.991708\pi\) |
0.522387 | + | 0.852709i | \(0.325042\pi\) | |||||||
\(440\) | 4.00000 | − | 6.92820i | 0.190693 | − | 0.330289i | ||||
\(441\) | 2.00000 | + | 3.46410i | 0.0952381 | + | 0.164957i | ||||
\(442\) | 1.50000 | − | 2.59808i | 0.0713477 | − | 0.123578i | ||||
\(443\) | 13.0000 | + | 22.5167i | 0.617649 | + | 1.06980i | 0.989914 | + | 0.141672i | \(0.0452479\pi\) |
−0.372265 | + | 0.928126i | \(0.621419\pi\) | |||||||
\(444\) | 2.00000 | 0.0949158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.00000 | − | 12.1244i | −0.331460 | − | 0.574105i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.00000 | 0.141737 | ||||||||
\(449\) | 10.0000 | 0.471929 | 0.235965 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235965 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(450\) | 11.0000 | + | 19.0526i | 0.518545 | + | 0.898146i | ||||
\(451\) | 8.00000 | − | 13.8564i | 0.376705 | − | 0.652473i | ||||
\(452\) | −7.00000 | − | 12.1244i | −0.329252 | − | 0.570282i | ||||
\(453\) | 1.00000 | − | 1.73205i | 0.0469841 | − | 0.0813788i | ||||
\(454\) | 8.50000 | − | 14.7224i | 0.398925 | − | 0.690958i | ||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00000 | −0.327446 | −0.163723 | − | 0.986506i | \(-0.552350\pi\) | ||||
−0.163723 | + | 0.986506i | \(0.552350\pi\) | |||||||
\(458\) | 5.00000 | − | 8.66025i | 0.233635 | − | 0.404667i | ||||
\(459\) | −7.50000 | + | 12.9904i | −0.350070 | + | 0.606339i | ||||
\(460\) | −2.00000 | − | 3.46410i | −0.0932505 | − | 0.161515i | ||||
\(461\) | 14.0000 | − | 24.2487i | 0.652045 | − | 1.12938i | −0.330581 | − | 0.943778i | \(-0.607245\pi\) |
0.982626 | − | 0.185597i | \(-0.0594220\pi\) | |||||||
\(462\) | 3.00000 | + | 5.19615i | 0.139573 | + | 0.241747i | ||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | −5.00000 | −0.232119 | ||||||||
\(465\) | 16.0000 | + | 27.7128i | 0.741982 | + | 1.28515i | ||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | −2.00000 | −0.0925490 | −0.0462745 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462745 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −4.50000 | − | 7.79423i | −0.207791 | − | 0.359904i | ||||
\(470\) | 16.0000 | − | 27.7128i | 0.738025 | − | 1.27830i | ||||
\(471\) | −1.00000 | − | 1.73205i | −0.0460776 | − | 0.0798087i | ||||
\(472\) | −7.50000 | + | 12.9904i | −0.345215 | + | 0.597931i | ||||
\(473\) | −4.00000 | + | 6.92820i | −0.183920 | + | 0.318559i | ||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.00000 | 0.412514 | ||||||||
\(477\) | −1.00000 | + | 1.73205i | −0.0457869 | + | 0.0793052i | ||||
\(478\) | −7.50000 | + | 12.9904i | −0.343042 | + | 0.594166i | ||||
\(479\) | 10.0000 | + | 17.3205i | 0.456912 | + | 0.791394i | 0.998796 | − | 0.0490589i | \(-0.0156222\pi\) |
−0.541884 | + | 0.840453i | \(0.682289\pi\) | |||||||
\(480\) | −2.00000 | + | 3.46410i | −0.0912871 | + | 0.158114i | ||||
\(481\) | −1.00000 | − | 1.73205i | −0.0455961 | − | 0.0789747i | ||||
\(482\) | −8.00000 | −0.364390 | ||||||||
\(483\) | 3.00000 | 0.136505 | ||||||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | −4.00000 | − | 6.92820i | −0.181631 | − | 0.314594i | ||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | −1.00000 | − | 1.73205i | −0.0452679 | − | 0.0784063i | ||||
\(489\) | −8.00000 | + | 13.8564i | −0.361773 | + | 0.626608i | ||||
\(490\) | 4.00000 | + | 6.92820i | 0.180702 | + | 0.312984i | ||||
\(491\) | 14.0000 | − | 24.2487i | 0.631811 | − | 1.09433i | −0.355370 | − | 0.934726i | \(-0.615645\pi\) |
0.987181 | − | 0.159603i | \(-0.0510215\pi\) | |||||||
\(492\) | −4.00000 | + | 6.92820i | −0.180334 | + | 0.312348i | ||||
\(493\) | −15.0000 | −0.675566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0000 | 0.719147 | ||||||||
\(496\) | 4.00000 | − | 6.92820i | 0.179605 | − | 0.311086i | ||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | −20.0000 | + | 34.6410i | −0.895323 | + | 1.55074i | −0.0619186 | + | 0.998081i | \(0.519722\pi\) |
−0.833404 | + | 0.552664i | \(0.813611\pi\) | |||||||
\(500\) | 12.0000 | + | 20.7846i | 0.536656 | + | 0.929516i | ||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 2.00000 | 0.0892644 | ||||||||
\(503\) | −19.5000 | − | 33.7750i | −0.869462 | − | 1.50595i | −0.862547 | − | 0.505976i | \(-0.831132\pi\) |
−0.00691465 | − | 0.999976i | \(-0.502201\pi\) | |||||||
\(504\) | 3.00000 | + | 5.19615i | 0.133631 | + | 0.231455i | ||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | −2.00000 | −0.0889108 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | −9.00000 | + | 15.5885i | −0.399310 | + | 0.691626i | ||||
\(509\) | 15.0000 | + | 25.9808i | 0.664863 | + | 1.15158i | 0.979322 | + | 0.202306i | \(0.0648436\pi\) |
−0.314459 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(510\) | −6.00000 | + | 10.3923i | −0.265684 | + | 0.460179i | ||||
\(511\) | −13.5000 | + | 23.3827i | −0.597205 | + | 1.03439i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.00000 | 0.352865 | ||||||||
\(515\) | −12.0000 | + | 20.7846i | −0.528783 | + | 0.915879i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | −8.00000 | − | 13.8564i | −0.351840 | − | 0.609404i | ||||
\(518\) | 3.00000 | − | 5.19615i | 0.131812 | − | 0.228306i | ||||
\(519\) | −3.00000 | − | 5.19615i | −0.131685 | − | 0.228086i | ||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | −5.00000 | − | 8.66025i | −0.218844 | − | 0.379049i | ||||
\(523\) | −14.5000 | − | 25.1147i | −0.634041 | − | 1.09819i | −0.986718 | − | 0.162446i | \(-0.948062\pi\) |
0.352677 | − | 0.935745i | \(-0.385272\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | −33.0000 | −1.44024 | ||||||||
\(526\) | −12.0000 | − | 20.7846i | −0.523225 | − | 0.906252i | ||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | 1.00000 | + | 1.73205i | 0.0435194 | + | 0.0753778i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | −2.00000 | + | 3.46410i | −0.0868744 | + | 0.150471i | ||||
\(531\) | −30.0000 | −1.30189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0000 | + | 24.2487i | −0.605273 | + | 1.04836i | ||||
\(536\) | −1.50000 | − | 2.59808i | −0.0647901 | − | 0.112220i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.0000 | − | 25.9808i | −0.646696 | − | 1.12011i | ||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | −20.0000 | −0.860663 | ||||||||
\(541\) | −1.00000 | − | 1.73205i | −0.0429934 | − | 0.0744667i | 0.843728 | − | 0.536771i | \(-0.180356\pi\) |
−0.886721 | + | 0.462304i | \(0.847023\pi\) | |||||||
\(542\) | −3.50000 | − | 6.06218i | −0.150338 | − | 0.260393i | ||||
\(543\) | −22.0000 | −0.944110 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | −30.0000 | − | 51.9615i | −1.28506 | − | 2.22579i | ||||
\(546\) | −1.50000 | + | 2.59808i | −0.0641941 | + | 0.111187i | ||||
\(547\) | −14.0000 | − | 24.2487i | −0.598597 | − | 1.03680i | −0.993028 | − | 0.117875i | \(-0.962392\pi\) |
0.394432 | − | 0.918925i | \(-0.370941\pi\) | |||||||
\(548\) | 8.50000 | − | 14.7224i | 0.363102 | − | 0.628911i | ||||
\(549\) | 2.00000 | − | 3.46410i | 0.0853579 | − | 0.147844i | ||||
\(550\) | 22.0000 | 0.938083 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 15.0000 | − | 25.9808i | 0.637865 | − | 1.10481i | ||||
\(554\) | −14.0000 | + | 24.2487i | −0.594803 | + | 1.03023i | ||||
\(555\) | 4.00000 | + | 6.92820i | 0.169791 | + | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | − | 24.2487i | −0.593199 | − | 1.02745i | −0.993798 | − | 0.111198i | \(-0.964531\pi\) |
0.400599 | − | 0.916253i | \(-0.368802\pi\) | |||||||
\(558\) | 16.0000 | 0.677334 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 6.00000 | + | 10.3923i | 0.253546 | + | 0.439155i | ||||
\(561\) | 3.00000 | + | 5.19615i | 0.126660 | + | 0.219382i | ||||
\(562\) | −8.00000 | −0.337460 | ||||||||
\(563\) | −36.0000 | −1.51722 | −0.758610 | − | 0.651546i | \(-0.774121\pi\) | ||||
−0.758610 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(564\) | 4.00000 | + | 6.92820i | 0.168430 | + | 0.291730i | ||||
\(565\) | 28.0000 | − | 48.4974i | 1.17797 | − | 2.04030i | ||||
\(566\) | 3.00000 | + | 5.19615i | 0.126099 | + | 0.218411i | ||||
\(567\) | −1.50000 | + | 2.59808i | −0.0629941 | + | 0.109109i | ||||
\(568\) | −1.00000 | + | 1.73205i | −0.0419591 | + | 0.0726752i | ||||
\(569\) | 40.0000 | 1.67689 | 0.838444 | − | 0.544988i | \(-0.183466\pi\) | ||||
0.838444 | + | 0.544988i | \(0.183466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 1.00000 | − | 1.73205i | 0.0418121 | − | 0.0724207i | ||||
\(573\) | 3.50000 | − | 6.06218i | 0.146215 | − | 0.253251i | ||||
\(574\) | 12.0000 | + | 20.7846i | 0.500870 | + | 0.867533i | ||||
\(575\) | 5.50000 | − | 9.52628i | 0.229366 | − | 0.397273i | ||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | −37.0000 | −1.54033 | −0.770165 | − | 0.637845i | \(-0.779826\pi\) | ||||
−0.770165 | + | 0.637845i | \(0.779826\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | −3.00000 | − | 5.19615i | −0.124676 | − | 0.215945i | ||||
\(580\) | −10.0000 | − | 17.3205i | −0.415227 | − | 0.719195i | ||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 1.00000 | + | 1.73205i | 0.0414158 | + | 0.0717342i | ||||
\(584\) | −4.50000 | + | 7.79423i | −0.186211 | + | 0.322527i | ||||
\(585\) | 4.00000 | + | 6.92820i | 0.165380 | + | 0.286446i | ||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | 6.00000 | − | 10.3923i | 0.247647 | − | 0.428936i | −0.715226 | − | 0.698893i | \(-0.753676\pi\) |
0.962872 | + | 0.269957i | \(0.0870095\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −60.0000 | −2.47016 | ||||||||
\(591\) | 4.00000 | − | 6.92820i | 0.164538 | − | 0.284988i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | −17.0000 | − | 29.4449i | −0.698106 | − | 1.20916i | −0.969122 | − | 0.246581i | \(-0.920693\pi\) |
0.271016 | − | 0.962575i | \(-0.412640\pi\) | |||||||
\(594\) | −5.00000 | + | 8.66025i | −0.205152 | + | 0.355335i | ||||
\(595\) | 18.0000 | + | 31.1769i | 0.737928 | + | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.0000 | 1.02318 | ||||||||
\(598\) | −0.500000 | − | 0.866025i | −0.0204465 | − | 0.0354144i | ||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | −11.0000 | −0.449073 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | −6.00000 | − | 10.3923i | −0.244542 | − | 0.423559i | ||||
\(603\) | 3.00000 | − | 5.19615i | 0.122169 | − | 0.211604i | ||||
\(604\) | −1.00000 | − | 1.73205i | −0.0406894 | − | 0.0704761i | ||||
\(605\) | −14.0000 | + | 24.2487i | −0.569181 | + | 0.985850i | ||||
\(606\) | 1.00000 | − | 1.73205i | 0.0406222 | − | 0.0703598i | ||||
\(607\) | −22.0000 | −0.892952 | −0.446476 | − | 0.894795i | \(-0.647321\pi\) | ||||
−0.446476 | + | 0.894795i | \(0.647321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.0000 | 0.607831 | ||||||||
\(610\) | 4.00000 | − | 6.92820i | 0.161955 | − | 0.280515i | ||||
\(611\) | 4.00000 | − | 6.92820i | 0.161823 | − | 0.280285i | ||||
\(612\) | 3.00000 | + | 5.19615i | 0.121268 | + | 0.210042i | ||||
\(613\) | −17.0000 | + | 29.4449i | −0.686624 | + | 1.18927i | 0.286300 | + | 0.958140i | \(0.407575\pi\) |
−0.972924 | + | 0.231127i | \(0.925759\pi\) | |||||||
\(614\) | 6.00000 | + | 10.3923i | 0.242140 | + | 0.419399i | ||||
\(615\) | −32.0000 | −1.29036 | ||||||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | −9.00000 | − | 15.5885i | −0.362326 | − | 0.627568i | 0.626017 | − | 0.779809i | \(-0.284684\pi\) |
−0.988343 | + | 0.152242i | \(0.951351\pi\) | |||||||
\(618\) | −3.00000 | − | 5.19615i | −0.120678 | − | 0.209020i | ||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 32.0000 | 1.28515 | ||||||||
\(621\) | 2.50000 | + | 4.33013i | 0.100322 | + | 0.173762i | ||||
\(622\) | −3.50000 | + | 6.06218i | −0.140337 | + | 0.243071i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.500000 | + | 0.866025i | −0.0200160 | + | 0.0346688i | ||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | 29.0000 | 1.15907 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 3.00000 | − | 5.19615i | 0.119618 | − | 0.207184i | ||||
\(630\) | −12.0000 | + | 20.7846i | −0.478091 | + | 0.828079i | ||||
\(631\) | −16.0000 | − | 27.7128i | −0.636950 | − | 1.10323i | −0.986098 | − | 0.166162i | \(-0.946862\pi\) |
0.349148 | − | 0.937067i | \(-0.386471\pi\) | |||||||
\(632\) | 5.00000 | − | 8.66025i | 0.198889 | − | 0.344486i | ||||
\(633\) | 13.5000 | + | 23.3827i | 0.536577 | + | 0.929378i | ||||
\(634\) | −27.0000 | −1.07231 | ||||||||
\(635\) | −72.0000 | −2.85723 | ||||||||
\(636\) | −0.500000 | − | 0.866025i | −0.0198263 | − | 0.0343401i | ||||
\(637\) | 1.00000 | + | 1.73205i | 0.0396214 | + | 0.0686264i | ||||
\(638\) | −10.0000 | −0.395904 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | 2.00000 | + | 3.46410i | 0.0790569 | + | 0.136931i | ||||
\(641\) | −21.0000 | + | 36.3731i | −0.829450 | + | 1.43665i | 0.0690201 | + | 0.997615i | \(0.478013\pi\) |
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(642\) | −3.50000 | − | 6.06218i | −0.138134 | − | 0.239255i | ||||
\(643\) | 13.0000 | − | 22.5167i | 0.512670 | − | 0.887970i | −0.487222 | − | 0.873278i | \(-0.661990\pi\) |
0.999892 | − | 0.0146923i | \(-0.00467688\pi\) | |||||||
\(644\) | 1.50000 | − | 2.59808i | 0.0591083 | − | 0.102379i | ||||
\(645\) | 16.0000 | 0.629999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.0000 | 0.904223 | 0.452112 | − | 0.891961i | \(-0.350671\pi\) | ||||
0.452112 | + | 0.891961i | \(0.350671\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −15.0000 | + | 25.9808i | −0.588802 | + | 1.01983i | ||||
\(650\) | 5.50000 | + | 9.52628i | 0.215728 | + | 0.373651i | ||||
\(651\) | −12.0000 | + | 20.7846i | −0.470317 | + | 0.814613i | ||||
\(652\) | 8.00000 | + | 13.8564i | 0.313304 | + | 0.542659i | ||||
\(653\) | −36.0000 | −1.40879 | −0.704394 | − | 0.709809i | \(-0.748781\pi\) | ||||
−0.704394 | + | 0.709809i | \(0.748781\pi\) | |||||||
\(654\) | 15.0000 | 0.586546 | ||||||||
\(655\) | 24.0000 | + | 41.5692i | 0.937758 | + | 1.62424i | ||||
\(656\) | 4.00000 | + | 6.92820i | 0.156174 | + | 0.270501i | ||||
\(657\) | −18.0000 | −0.702247 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | −2.50000 | − | 4.33013i | −0.0973862 | − | 0.168678i | 0.813216 | − | 0.581962i | \(-0.197715\pi\) |
−0.910602 | + | 0.413284i | \(0.864382\pi\) | |||||||
\(660\) | −4.00000 | + | 6.92820i | −0.155700 | + | 0.269680i | ||||
\(661\) | 11.5000 | + | 19.9186i | 0.447298 | + | 0.774743i | 0.998209 | − | 0.0598209i | \(-0.0190530\pi\) |
−0.550911 | + | 0.834564i | \(0.685720\pi\) | |||||||
\(662\) | −8.50000 | + | 14.7224i | −0.330362 | + | 0.572204i | ||||
\(663\) | −1.50000 | + | 2.59808i | −0.0582552 | + | 0.100901i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | −2.50000 | + | 4.33013i | −0.0968004 | + | 0.167663i | ||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 7.00000 | + | 12.1244i | 0.270636 | + | 0.468755i | ||||
\(670\) | 6.00000 | − | 10.3923i | 0.231800 | − | 0.401490i | ||||
\(671\) | −2.00000 | − | 3.46410i | −0.0772091 | − | 0.133730i | ||||
\(672\) | −3.00000 | −0.115728 | ||||||||
\(673\) | 44.0000 | 1.69608 | 0.848038 | − | 0.529936i | \(-0.177784\pi\) | ||||
0.848038 | + | 0.529936i | \(0.177784\pi\) | |||||||
\(674\) | 16.0000 | + | 27.7128i | 0.616297 | + | 1.06746i | ||||
\(675\) | −27.5000 | − | 47.6314i | −1.05848 | − | 1.83333i | ||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 13.0000 | 0.499631 | 0.249815 | − | 0.968294i | \(-0.419630\pi\) | ||||
0.249815 | + | 0.968294i | \(0.419630\pi\) | |||||||
\(678\) | 7.00000 | + | 12.1244i | 0.268833 | + | 0.465633i | ||||
\(679\) | 3.00000 | − | 5.19615i | 0.115129 | − | 0.199410i | ||||
\(680\) | 6.00000 | + | 10.3923i | 0.230089 | + | 0.398527i | ||||
\(681\) | −8.50000 | + | 14.7224i | −0.325721 | + | 0.564165i | ||||
\(682\) | 8.00000 | − | 13.8564i | 0.306336 | − | 0.530589i | ||||
\(683\) | 4.00000 | 0.153056 | 0.0765279 | − | 0.997067i | \(-0.475617\pi\) | ||||
0.0765279 | + | 0.997067i | \(0.475617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 68.0000 | 2.59815 | ||||||||
\(686\) | 7.50000 | − | 12.9904i | 0.286351 | − | 0.495975i | ||||
\(687\) | −5.00000 | + | 8.66025i | −0.190762 | + | 0.330409i | ||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | −0.500000 | + | 0.866025i | −0.0190485 | + | 0.0329929i | ||||
\(690\) | 2.00000 | + | 3.46410i | 0.0761387 | + | 0.131876i | ||||
\(691\) | 42.0000 | 1.59776 | 0.798878 | − | 0.601494i | \(-0.205427\pi\) | ||||
0.798878 | + | 0.601494i | \(0.205427\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 6.00000 | + | 10.3923i | 0.227921 | + | 0.394771i | ||||
\(694\) | 1.00000 | + | 1.73205i | 0.0379595 | + | 0.0657477i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.00000 | 0.189525 | ||||||||
\(697\) | 12.0000 | + | 20.7846i | 0.454532 | + | 0.787273i | ||||
\(698\) | −5.00000 | + | 8.66025i | −0.189253 | + | 0.327795i | ||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | −16.5000 | + | 28.5788i | −0.623641 | + | 1.08018i | ||||
\(701\) | 14.0000 | − | 24.2487i | 0.528773 | − | 0.915861i | −0.470664 | − | 0.882312i | \(-0.655986\pi\) |
0.999437 | − | 0.0335489i | \(-0.0106809\pi\) | |||||||
\(702\) | −5.00000 | −0.188713 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | −16.0000 | + | 27.7128i | −0.602595 | + | 1.04372i | ||||
\(706\) | −4.50000 | + | 7.79423i | −0.169360 | + | 0.293340i | ||||
\(707\) | −3.00000 | − | 5.19615i | −0.112827 | − | 0.195421i | ||||
\(708\) | 7.50000 | − | 12.9904i | 0.281867 | − | 0.488208i | ||||
\(709\) | 15.0000 | + | 25.9808i | 0.563337 | + | 0.975728i | 0.997202 | + | 0.0747503i | \(0.0238160\pi\) |
−0.433865 | + | 0.900978i | \(0.642851\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | 20.0000 | 0.750059 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | − | 6.92820i | −0.149801 | − | 0.259463i | ||||
\(714\) | −9.00000 | −0.336817 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.50000 | − | 12.9904i | 0.280093 | − | 0.485135i | ||||
\(718\) | 7.50000 | + | 12.9904i | 0.279898 | + | 0.484797i | ||||
\(719\) | 2.50000 | − | 4.33013i | 0.0932343 | − | 0.161486i | −0.815636 | − | 0.578565i | \(-0.803613\pi\) |
0.908870 | + | 0.417079i | \(0.136946\pi\) | |||||||
\(720\) | −4.00000 | + | 6.92820i | −0.149071 | + | 0.258199i | ||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.00000 | 0.297523 | ||||||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | 27.5000 | − | 47.6314i | 1.02132 | − | 1.76899i | ||||
\(726\) | −3.50000 | − | 6.06218i | −0.129897 | − | 0.224989i | ||||
\(727\) | 8.50000 | − | 14.7224i | 0.315248 | − | 0.546025i | −0.664243 | − | 0.747517i | \(-0.731246\pi\) |
0.979490 | + | 0.201492i | \(0.0645791\pi\) | |||||||
\(728\) | 1.50000 | + | 2.59808i | 0.0555937 | + | 0.0962911i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −36.0000 | −1.33242 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 1.00000 | + | 1.73205i | 0.0369611 | + | 0.0640184i | ||||
\(733\) | −36.0000 | −1.32969 | −0.664845 | − | 0.746981i | \(-0.731502\pi\) | ||||
−0.664845 | + | 0.746981i | \(0.731502\pi\) | |||||||
\(734\) | 28.0000 | 1.03350 | ||||||||
\(735\) | −4.00000 | − | 6.92820i | −0.147542 | − | 0.255551i | ||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | −3.00000 | − | 5.19615i | −0.110506 | − | 0.191403i | ||||
\(738\) | −8.00000 | + | 13.8564i | −0.294484 | + | 0.510061i | ||||
\(739\) | 20.0000 | − | 34.6410i | 0.735712 | − | 1.27429i | −0.218698 | − | 0.975793i | \(-0.570181\pi\) |
0.954410 | − | 0.298498i | \(-0.0964856\pi\) | |||||||
\(740\) | 8.00000 | 0.294086 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.00000 | −0.110133 | ||||||||
\(743\) | 8.00000 | − | 13.8564i | 0.293492 | − | 0.508342i | −0.681141 | − | 0.732152i | \(-0.738516\pi\) |
0.974633 | + | 0.223810i | \(0.0718494\pi\) | |||||||
\(744\) | −4.00000 | + | 6.92820i | −0.146647 | + | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.5000 | + | 25.1147i | −0.530883 | + | 0.919516i | ||||
\(747\) | −6.00000 | − | 10.3923i | −0.219529 | − | 0.380235i | ||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | −21.0000 | −0.767323 | ||||||||
\(750\) | −12.0000 | − | 20.7846i | −0.438178 | − | 0.758947i | ||||
\(751\) | −16.0000 | − | 27.7128i | −0.583848 | − | 1.01125i | −0.995018 | − | 0.0996961i | \(-0.968213\pi\) |
0.411170 | − | 0.911559i | \(-0.365120\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | −2.00000 | −0.0728841 | ||||||||
\(754\) | −2.50000 | − | 4.33013i | −0.0910446 | − | 0.157694i | ||||
\(755\) | 4.00000 | − | 6.92820i | 0.145575 | − | 0.252143i | ||||
\(756\) | −7.50000 | − | 12.9904i | −0.272772 | − | 0.472456i | ||||
\(757\) | 1.00000 | − | 1.73205i | 0.0363456 | − | 0.0629525i | −0.847280 | − | 0.531146i | \(-0.821762\pi\) |
0.883626 | + | 0.468193i | \(0.155095\pi\) | |||||||
\(758\) | −7.50000 | + | 12.9904i | −0.272412 | + | 0.471832i | ||||
\(759\) | 2.00000 | 0.0725954 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.0000 | 0.978749 | 0.489375 | − | 0.872074i | \(-0.337225\pi\) | ||||
0.489375 | + | 0.872074i | \(0.337225\pi\) | |||||||
\(762\) | 9.00000 | − | 15.5885i | 0.326036 | − | 0.564710i | ||||
\(763\) | 22.5000 | − | 38.9711i | 0.814555 | − | 1.41085i | ||||
\(764\) | −3.50000 | − | 6.06218i | −0.126626 | − | 0.219322i | ||||
\(765\) | −12.0000 | + | 20.7846i | −0.433861 | + | 0.751469i | ||||
\(766\) | 13.0000 | + | 22.5167i | 0.469709 | + | 0.813560i | ||||
\(767\) | −15.0000 | −0.541619 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 17.5000 | + | 30.3109i | 0.631066 | + | 1.09304i | 0.987334 | + | 0.158655i | \(0.0507157\pi\) |
−0.356268 | + | 0.934384i | \(0.615951\pi\) | |||||||
\(770\) | 12.0000 | + | 20.7846i | 0.432450 | + | 0.749025i | ||||
\(771\) | −8.00000 | −0.288113 | ||||||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | −4.50000 | − | 7.79423i | −0.161854 | − | 0.280339i | 0.773680 | − | 0.633577i | \(-0.218414\pi\) |
−0.935534 | + | 0.353238i | \(0.885081\pi\) | |||||||
\(774\) | 4.00000 | − | 6.92820i | 0.143777 | − | 0.249029i | ||||
\(775\) | 44.0000 | + | 76.2102i | 1.58053 | + | 2.73755i | ||||
\(776\) | 1.00000 | − | 1.73205i | 0.0358979 | − | 0.0621770i | ||||
\(777\) | −3.00000 | + | 5.19615i | −0.107624 | + | 0.186411i | ||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −4.00000 | −0.143223 | ||||||||
\(781\) | −2.00000 | + | 3.46410i | −0.0715656 | + | 0.123955i | ||||
\(782\) | 1.50000 | − | 2.59808i | 0.0536399 | − | 0.0929070i | ||||
\(783\) | 12.5000 | + | 21.6506i | 0.446714 | + | 0.773731i | ||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | −4.00000 | − | 6.92820i | −0.142766 | − | 0.247278i | ||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | −17.0000 | −0.605985 | −0.302992 | − | 0.952993i | \(-0.597986\pi\) | ||||
−0.302992 | + | 0.952993i | \(0.597986\pi\) | |||||||
\(788\) | −4.00000 | − | 6.92820i | −0.142494 | − | 0.246807i | ||||
\(789\) | 12.0000 | + | 20.7846i | 0.427211 | + | 0.739952i | ||||
\(790\) | 40.0000 | 1.42314 | ||||||||
\(791\) | 42.0000 | 1.49335 | ||||||||
\(792\) | 2.00000 | + | 3.46410i | 0.0710669 | + | 0.123091i | ||||
\(793\) | 1.00000 | − | 1.73205i | 0.0355110 | − | 0.0615069i | ||||
\(794\) | −4.00000 | − | 6.92820i | −0.141955 | − | 0.245873i | ||||
\(795\) | 2.00000 | − | 3.46410i | 0.0709327 | − | 0.122859i | ||||
\(796\) | 12.5000 | − | 21.6506i | 0.443051 | − | 0.767386i | ||||
\(797\) | 3.00000 | 0.106265 | 0.0531327 | − | 0.998587i | \(-0.483079\pi\) | ||||
0.0531327 | + | 0.998587i | \(0.483079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | −5.50000 | + | 9.52628i | −0.194454 | + | 0.336805i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.00000 | + | 6.92820i | 0.141245 | + | 0.244643i | ||||
\(803\) | −9.00000 | + | 15.5885i | −0.317603 | + | 0.550105i | ||||
\(804\) | 1.50000 | + | 2.59808i | 0.0529009 | + | 0.0916271i | ||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 15.0000 | + | 25.9808i | 0.528025 | + | 0.914566i | ||||
\(808\) | −1.00000 | − | 1.73205i | −0.0351799 | − | 0.0609333i | ||||
\(809\) | −15.0000 | −0.527372 | −0.263686 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263686 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(810\) | −4.00000 | −0.140546 | ||||||||
\(811\) | 1.50000 | + | 2.59808i | 0.0526721 | + | 0.0912308i | 0.891159 | − | 0.453691i | \(-0.149893\pi\) |
−0.838487 | + | 0.544921i | \(0.816560\pi\) | |||||||
\(812\) | 7.50000 | − | 12.9904i | 0.263198 | − | 0.455873i | ||||
\(813\) | 3.50000 | + | 6.06218i | 0.122750 | + | 0.212610i | ||||
\(814\) | 2.00000 | − | 3.46410i | 0.0701000 | − | 0.121417i | ||||
\(815\) | −32.0000 | + | 55.4256i | −1.12091 | + | 1.94147i | ||||
\(816\) | −3.00000 | −0.105021 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −20.0000 | −0.699284 | ||||||||
\(819\) | −3.00000 | + | 5.19615i | −0.104828 | + | 0.181568i | ||||
\(820\) | −16.0000 | + | 27.7128i | −0.558744 | + | 0.967773i | ||||
\(821\) | −6.00000 | − | 10.3923i | −0.209401 | − | 0.362694i | 0.742125 | − | 0.670262i | \(-0.233818\pi\) |
−0.951526 | + | 0.307568i | \(0.900485\pi\) | |||||||
\(822\) | −8.50000 | + | 14.7224i | −0.296472 | + | 0.513504i | ||||
\(823\) | −14.5000 | − | 25.1147i | −0.505438 | − | 0.875445i | −0.999980 | − | 0.00629095i | \(-0.997998\pi\) |
0.494542 | − | 0.869154i | \(-0.335336\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | −22.0000 | −0.765942 | ||||||||
\(826\) | −22.5000 | − | 38.9711i | −0.782875 | − | 1.35598i | ||||
\(827\) | −11.5000 | − | 19.9186i | −0.399894 | − | 0.692637i | 0.593818 | − | 0.804599i | \(-0.297620\pi\) |
−0.993712 | + | 0.111962i | \(0.964286\pi\) | |||||||
\(828\) | 2.00000 | 0.0695048 | ||||||||
\(829\) | −15.0000 | −0.520972 | −0.260486 | − | 0.965478i | \(-0.583883\pi\) | ||||
−0.260486 | + | 0.965478i | \(0.583883\pi\) | |||||||
\(830\) | −12.0000 | − | 20.7846i | −0.416526 | − | 0.721444i | ||||
\(831\) | 14.0000 | − | 24.2487i | 0.485655 | − | 0.841178i | ||||
\(832\) | 0.500000 | + | 0.866025i | 0.0173344 | + | 0.0300240i | ||||
\(833\) | −3.00000 | + | 5.19615i | −0.103944 | + | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.0000 | 1.66111 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.0000 | −1.38260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0000 | + | 17.3205i | −0.345238 | + | 0.597970i | −0.985397 | − | 0.170272i | \(-0.945535\pi\) |
0.640159 | + | 0.768243i | \(0.278869\pi\) | |||||||
\(840\) | −6.00000 | − | 10.3923i | −0.207020 | − | 0.358569i | ||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 6.50000 | + | 11.2583i | 0.224005 | + | 0.387988i | ||||
\(843\) | 8.00000 | 0.275535 | ||||||||
\(844\) | 27.0000 | 0.929378 | ||||||||
\(845\) | −24.0000 | − | 41.5692i | −0.825625 | − | 1.43002i | ||||
\(846\) | 8.00000 | + | 13.8564i | 0.275046 | + | 0.476393i | ||||
\(847\) | −21.0000 | −0.721569 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | −3.00000 | − | 5.19615i | −0.102960 | − | 0.178331i | ||||
\(850\) | −16.5000 | + | 28.5788i | −0.565945 | + | 0.980246i | ||||
\(851\) | −1.00000 | − | 1.73205i | −0.0342796 | − | 0.0593739i | ||||
\(852\) | 1.00000 | − | 1.73205i | 0.0342594 | − | 0.0593391i | ||||
\(853\) | 3.00000 | − | 5.19615i | 0.102718 | − | 0.177913i | −0.810086 | − | 0.586312i | \(-0.800579\pi\) |
0.912804 | + | 0.408399i | \(0.133913\pi\) | |||||||
\(854\) | 6.00000 | 0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.00000 | −0.239255 | ||||||||
\(857\) | 6.00000 | − | 10.3923i | 0.204956 | − | 0.354994i | −0.745163 | − | 0.666883i | \(-0.767628\pi\) |
0.950119 | + | 0.311888i | \(0.100962\pi\) | |||||||
\(858\) | −1.00000 | + | 1.73205i | −0.0341394 | + | 0.0591312i | ||||
\(859\) | 25.0000 | + | 43.3013i | 0.852989 | + | 1.47742i | 0.878498 | + | 0.477746i | \(0.158546\pi\) |
−0.0255092 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(860\) | 8.00000 | − | 13.8564i | 0.272798 | − | 0.472500i | ||||
\(861\) | −12.0000 | − | 20.7846i | −0.408959 | − | 0.708338i | ||||
\(862\) | −18.0000 | −0.613082 | ||||||||
\(863\) | 54.0000 | 1.83818 | 0.919091 | − | 0.394046i | \(-0.128925\pi\) | ||||
0.919091 | + | 0.394046i | \(0.128925\pi\) | |||||||
\(864\) | −2.50000 | − | 4.33013i | −0.0850517 | − | 0.147314i | ||||
\(865\) | −12.0000 | − | 20.7846i | −0.408012 | − | 0.706698i | ||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 12.0000 | + | 20.7846i | 0.407307 | + | 0.705476i | ||||
\(869\) | 10.0000 | − | 17.3205i | 0.339227 | − | 0.587558i | ||||
\(870\) | 10.0000 | + | 17.3205i | 0.339032 | + | 0.587220i | ||||
\(871\) | 1.50000 | − | 2.59808i | 0.0508256 | − | 0.0880325i | ||||
\(872\) | 7.50000 | − | 12.9904i | 0.253982 | − | 0.439910i | ||||
\(873\) | 4.00000 | 0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −72.0000 | −2.43404 | ||||||||
\(876\) | 4.50000 | − | 7.79423i | 0.152041 | − | 0.263343i | ||||
\(877\) | −6.50000 | + | 11.2583i | −0.219489 | + | 0.380167i | −0.954652 | − | 0.297724i | \(-0.903772\pi\) |
0.735163 | + | 0.677891i | \(0.237106\pi\) | |||||||
\(878\) | −10.0000 | − | 17.3205i | −0.337484 | − | 0.584539i | ||||
\(879\) | 4.50000 | − | 7.79423i | 0.151781 | − | 0.262893i | ||||
\(880\) | 4.00000 | + | 6.92820i | 0.134840 | + | 0.233550i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | −4.00000 | −0.134687 | ||||||||
\(883\) | −17.0000 | − | 29.4449i | −0.572096 | − | 0.990899i | −0.996351 | − | 0.0853558i | \(-0.972797\pi\) |
0.424255 | − | 0.905543i | \(-0.360536\pi\) | |||||||
\(884\) | 1.50000 | + | 2.59808i | 0.0504505 | + | 0.0873828i | ||||
\(885\) | 60.0000 | 2.01688 | ||||||||
\(886\) | −26.0000 | −0.873487 | ||||||||
\(887\) | 1.00000 | + | 1.73205i | 0.0335767 | + | 0.0581566i | 0.882325 | − | 0.470640i | \(-0.155977\pi\) |
−0.848749 | + | 0.528796i | \(0.822644\pi\) | |||||||
\(888\) | −1.00000 | + | 1.73205i | −0.0335578 | + | 0.0581238i | ||||
\(889\) | −27.0000 | − | 46.7654i | −0.905551 | − | 1.56846i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 14.0000 | 0.468755 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.50000 | + | 2.59808i | −0.0501115 | + | 0.0867956i | ||||
\(897\) | 0.500000 | + | 0.866025i | 0.0166945 | + | 0.0289157i | ||||
\(898\) | −5.00000 | + | 8.66025i | −0.166852 | + | 0.288996i | ||||
\(899\) | −20.0000 | − | 34.6410i | −0.667037 | − | 1.15534i | ||||
\(900\) | −22.0000 | −0.733333 | ||||||||
\(901\) | −3.00000 | −0.0999445 | ||||||||
\(902\) | 8.00000 | + | 13.8564i | 0.266371 | + | 0.461368i | ||||
\(903\) | 6.00000 | + | 10.3923i | 0.199667 | + | 0.345834i | ||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | −88.0000 | −2.92522 | ||||||||
\(906\) | 1.00000 | + | 1.73205i | 0.0332228 | + | 0.0575435i | ||||
\(907\) | −26.5000 | + | 45.8993i | −0.879918 | + | 1.52406i | −0.0284883 | + | 0.999594i | \(0.509069\pi\) |
−0.851430 | + | 0.524469i | \(0.824264\pi\) | |||||||
\(908\) | 8.50000 | + | 14.7224i | 0.282082 | + | 0.488581i | ||||
\(909\) | 2.00000 | − | 3.46410i | 0.0663358 | − | 0.114897i | ||||
\(910\) | −6.00000 | + | 10.3923i | −0.198898 | + | 0.344502i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 3.50000 | − | 6.06218i | 0.115770 | − | 0.200519i | ||||
\(915\) | −4.00000 | + | 6.92820i | −0.132236 | + | 0.229039i | ||||
\(916\) | 5.00000 | + | 8.66025i | 0.165205 | + | 0.286143i | ||||
\(917\) | −18.0000 | + | 31.1769i | −0.594412 | + | 1.02955i | ||||
\(918\) | −7.50000 | − | 12.9904i | −0.247537 | − | 0.428746i | ||||
\(919\) | 5.00000 | 0.164935 | 0.0824674 | − | 0.996594i | \(-0.473720\pi\) | ||||
0.0824674 | + | 0.996594i | \(0.473720\pi\) | |||||||
\(920\) | 4.00000 | 0.131876 | ||||||||
\(921\) | −6.00000 | − | 10.3923i | −0.197707 | − | 0.342438i | ||||
\(922\) | 14.0000 | + | 24.2487i | 0.461065 | + | 0.798589i | ||||
\(923\) | −2.00000 | −0.0658308 | ||||||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | 11.0000 | + | 19.0526i | 0.361678 | + | 0.626444i | ||||
\(926\) | −2.00000 | + | 3.46410i | −0.0657241 | + | 0.113837i | ||||
\(927\) | −6.00000 | − | 10.3923i | −0.197066 | − | 0.341328i | ||||
\(928\) | 2.50000 | − | 4.33013i | 0.0820665 | − | 0.142143i | ||||
\(929\) | 27.5000 | − | 47.6314i | 0.902246 | − | 1.56274i | 0.0776734 | − | 0.996979i | \(-0.475251\pi\) |
0.824572 | − | 0.565757i | \(-0.191416\pi\) | |||||||
\(930\) | −32.0000 | −1.04932 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 3.50000 | − | 6.06218i | 0.114585 | − | 0.198467i | ||||
\(934\) | 1.00000 | − | 1.73205i | 0.0327210 | − | 0.0566744i | ||||
\(935\) | 12.0000 | + | 20.7846i | 0.392442 | + | 0.679729i | ||||
\(936\) | −1.00000 | + | 1.73205i | −0.0326860 | + | 0.0566139i | ||||
\(937\) | 3.50000 | + | 6.06218i | 0.114340 | + | 0.198043i | 0.917516 | − | 0.397699i | \(-0.130191\pi\) |
−0.803176 | + | 0.595742i | \(0.796858\pi\) | |||||||
\(938\) | 9.00000 | 0.293860 | ||||||||
\(939\) | −29.0000 | −0.946379 | ||||||||
\(940\) | 16.0000 | + | 27.7128i | 0.521862 | + | 0.903892i | ||||
\(941\) | −3.50000 | − | 6.06218i | −0.114097 | − | 0.197621i | 0.803322 | − | 0.595545i | \(-0.203064\pi\) |
−0.917418 | + | 0.397924i | \(0.869731\pi\) | |||||||
\(942\) | 2.00000 | 0.0651635 | ||||||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | −7.50000 | − | 12.9904i | −0.244104 | − | 0.422801i | ||||
\(945\) | 30.0000 | − | 51.9615i | 0.975900 | − | 1.69031i | ||||
\(946\) | −4.00000 | − | 6.92820i | −0.130051 | − | 0.225255i | ||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | −5.00000 | + | 8.66025i | −0.162392 | + | 0.281272i | ||||
\(949\) | −9.00000 | −0.292152 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.0000 | 0.875535 | ||||||||
\(952\) | −4.50000 | + | 7.79423i | −0.145846 | + | 0.252612i | ||||
\(953\) | 23.0000 | − | 39.8372i | 0.745043 | − | 1.29045i | −0.205132 | − | 0.978734i | \(-0.565762\pi\) |
0.950175 | − | 0.311718i | \(-0.100904\pi\) | |||||||
\(954\) | −1.00000 | − | 1.73205i | −0.0323762 | − | 0.0560772i | ||||
\(955\) | 14.0000 | − | 24.2487i | 0.453029 | − | 0.784670i | ||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 10.0000 | 0.323254 | ||||||||
\(958\) | −20.0000 | −0.646171 | ||||||||
\(959\) | 25.5000 | + | 44.1673i | 0.823438 | + | 1.42624i | ||||
\(960\) | −2.00000 | − | 3.46410i | −0.0645497 | − | 0.111803i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 2.00000 | 0.0644826 | ||||||||
\(963\) | −7.00000 | − | 12.1244i | −0.225572 | − | 0.390702i | ||||
\(964\) | 4.00000 | − | 6.92820i | 0.128831 | − | 0.223142i | ||||
\(965\) | −12.0000 | − | 20.7846i | −0.386294 | − | 0.669080i | ||||
\(966\) | −1.50000 | + | 2.59808i | −0.0482617 | + | 0.0835917i | ||||
\(967\) | −24.0000 | + | 41.5692i | −0.771788 | + | 1.33678i | 0.164794 | + | 0.986328i | \(0.447304\pi\) |
−0.936582 | + | 0.350448i | \(0.886029\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.00000 | 0.256865 | ||||||||
\(971\) | 14.0000 | − | 24.2487i | 0.449281 | − | 0.778178i | −0.549058 | − | 0.835784i | \(-0.685013\pi\) |
0.998339 | + | 0.0576061i | \(0.0183467\pi\) | |||||||
\(972\) | 8.00000 | − | 13.8564i | 0.256600 | − | 0.444444i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.00000 | − | 1.73205i | 0.0320421 | − | 0.0554985i | ||||
\(975\) | −5.50000 | − | 9.52628i | −0.176141 | − | 0.305085i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 8.00000 | 0.255943 | 0.127971 | − | 0.991778i | \(-0.459153\pi\) | ||||
0.127971 | + | 0.991778i | \(0.459153\pi\) | |||||||
\(978\) | −8.00000 | − | 13.8564i | −0.255812 | − | 0.443079i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.00000 | −0.255551 | ||||||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | 14.0000 | + | 24.2487i | 0.446758 | + | 0.773807i | ||||
\(983\) | 3.00000 | − | 5.19615i | 0.0956851 | − | 0.165732i | −0.814209 | − | 0.580572i | \(-0.802829\pi\) |
0.909894 | + | 0.414840i | \(0.136162\pi\) | |||||||
\(984\) | −4.00000 | − | 6.92820i | −0.127515 | − | 0.220863i | ||||
\(985\) | 16.0000 | − | 27.7128i | 0.509802 | − | 0.883004i | ||||
\(986\) | 7.50000 | − | 12.9904i | 0.238849 | − | 0.413698i | ||||
\(987\) | −24.0000 | −0.763928 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | −8.00000 | + | 13.8564i | −0.254257 | + | 0.440386i | ||||
\(991\) | 4.00000 | − | 6.92820i | 0.127064 | − | 0.220082i | −0.795474 | − | 0.605988i | \(-0.792778\pi\) |
0.922538 | + | 0.385906i | \(0.126111\pi\) | |||||||
\(992\) | 4.00000 | + | 6.92820i | 0.127000 | + | 0.219971i | ||||
\(993\) | 8.50000 | − | 14.7224i | 0.269739 | − | 0.467202i | ||||
\(994\) | −3.00000 | − | 5.19615i | −0.0951542 | − | 0.164812i | ||||
\(995\) | 100.000 | 3.17021 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | −14.0000 | − | 24.2487i | −0.443384 | − | 0.767964i | 0.554554 | − | 0.832148i | \(-0.312889\pi\) |
−0.997938 | + | 0.0641836i | \(0.979556\pi\) | |||||||
\(998\) | −20.0000 | − | 34.6410i | −0.633089 | − | 1.09654i | ||||
\(999\) | −10.0000 | −0.316386 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))