Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (of order \(6\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1849 |
Dual form | 1950.2.z.f.1699.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −3.46410 | − | 2.00000i | −1.30931 | − | 0.755929i | −0.327327 | − | 0.944911i | \(-0.606148\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 0.866025 | − | 3.50000i | 0.240192 | − | 0.970725i | ||||
\(14\) | 4.00000 | 1.06904 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.73205 | + | 1.00000i | 0.420084 | + | 0.242536i | 0.695113 | − | 0.718900i | \(-0.255354\pi\) |
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | −4.33013 | − | 2.50000i | −0.923186 | − | 0.533002i | ||||
\(23\) | 6.06218 | − | 3.50000i | 1.26405 | − | 0.729800i | 0.290196 | − | 0.956967i | \(-0.406280\pi\) |
0.973856 | + | 0.227167i | \(0.0729463\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.46410 | + | 2.00000i | −0.654654 | + | 0.377964i | ||||
\(29\) | 1.00000 | + | 1.73205i | 0.185695 | + | 0.321634i | 0.943811 | − | 0.330487i | \(-0.107213\pi\) |
−0.758115 | + | 0.652121i | \(0.773880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 4.33013 | + | 2.50000i | 0.753778 | + | 0.435194i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −2.59808 | + | 1.50000i | −0.427121 | + | 0.246598i | −0.698119 | − | 0.715981i | \(-0.745980\pi\) |
0.270998 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(38\) | − | 2.00000i | − | 0.324443i | ||||||
\(39\) | −1.00000 | − | 3.46410i | −0.160128 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | − | 8.66025i | −0.780869 | − | 1.35250i | −0.931436 | − | 0.363905i | \(-0.881443\pi\) |
0.150567 | − | 0.988600i | \(-0.451890\pi\) | |||||||
\(42\) | 3.46410 | − | 2.00000i | 0.534522 | − | 0.308607i | ||||
\(43\) | 3.46410 | + | 2.00000i | 0.528271 | + | 0.304997i | 0.740312 | − | 0.672264i | \(-0.234678\pi\) |
−0.212041 | + | 0.977261i | \(0.568011\pi\) | |||||||
\(44\) | 5.00000 | 0.753778 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.50000 | + | 6.06218i | −0.516047 | + | 0.893819i | ||||
\(47\) | − | 12.0000i | − | 1.75038i | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||
0.483779 | − | 0.875190i | \(-0.339264\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 4.50000 | + | 7.79423i | 0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | −2.59808 | − | 2.50000i | −0.360288 | − | 0.346688i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | − | 3.46410i | 0.267261 | − | 0.462910i | ||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | −1.73205 | − | 1.00000i | −0.227429 | − | 0.131306i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50000 | − | 9.52628i | 0.704203 | − | 1.21972i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
0.966978 | − | 0.254858i | \(-0.0820288\pi\) | |||||||
\(62\) | 1.73205 | − | 1.00000i | 0.219971 | − | 0.127000i | ||||
\(63\) | −3.46410 | + | 2.00000i | −0.436436 | + | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | 3.46410 | − | 2.00000i | 0.423207 | − | 0.244339i | −0.273241 | − | 0.961946i | \(-0.588096\pi\) |
0.696449 | + | 0.717607i | \(0.254762\pi\) | |||||||
\(68\) | 1.73205 | − | 1.00000i | 0.210042 | − | 0.121268i | ||||
\(69\) | 3.50000 | − | 6.06218i | 0.421350 | − | 0.729800i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.50000 | + | 2.59808i | −0.178017 | + | 0.308335i | −0.941201 | − | 0.337846i | \(-0.890302\pi\) |
0.763184 | + | 0.646181i | \(0.223635\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | − | 9.00000i | − | 1.05337i | −0.850060 | − | 0.526685i | \(-0.823435\pi\) | ||
0.850060 | − | 0.526685i | \(-0.176565\pi\) | |||||||
\(74\) | 1.50000 | − | 2.59808i | 0.174371 | − | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | + | 1.73205i | 0.114708 | + | 0.198680i | ||||
\(77\) | − | 20.0000i | − | 2.27921i | ||||||
\(78\) | 2.59808 | + | 2.50000i | 0.294174 | + | 0.283069i | ||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 8.66025 | + | 5.00000i | 0.956365 | + | 0.552158i | ||||
\(83\) | − | 3.00000i | − | 0.329293i | −0.986353 | − | 0.164646i | \(-0.947352\pi\) | ||
0.986353 | − | 0.164646i | \(-0.0526483\pi\) | |||||||
\(84\) | −2.00000 | + | 3.46410i | −0.218218 | + | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | −0.431331 | ||||||||
\(87\) | 1.73205 | + | 1.00000i | 0.185695 | + | 0.107211i | ||||
\(88\) | −4.33013 | + | 2.50000i | −0.461593 | + | 0.266501i | ||||
\(89\) | −5.00000 | − | 8.66025i | −0.529999 | − | 0.917985i | −0.999388 | − | 0.0349934i | \(-0.988859\pi\) |
0.469389 | − | 0.882992i | \(-0.344474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | + | 10.3923i | −1.04828 | + | 1.08941i | ||||
\(92\) | − | 7.00000i | − | 0.729800i | ||||||
\(93\) | −1.73205 | + | 1.00000i | −0.179605 | + | 0.103695i | ||||
\(94\) | 6.00000 | + | 10.3923i | 0.618853 | + | 1.07188i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.2583 | − | 6.50000i | −1.14311 | − | 0.659975i | −0.195911 | − | 0.980622i | \(-0.562766\pi\) |
−0.947199 | + | 0.320647i | \(0.896100\pi\) | |||||||
\(98\) | −7.79423 | − | 4.50000i | −0.787336 | − | 0.454569i | ||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00000 | − | 6.92820i | −0.398015 | − | 0.689382i | 0.595466 | − | 0.803380i | \(-0.296967\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(102\) | −1.73205 | + | 1.00000i | −0.171499 | + | 0.0990148i | ||||
\(103\) | − | 16.0000i | − | 1.57653i | −0.615338 | − | 0.788263i | \(-0.710980\pi\) | ||
0.615338 | − | 0.788263i | \(-0.289020\pi\) | |||||||
\(104\) | 3.50000 | + | 0.866025i | 0.343203 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.92820 | + | 4.00000i | −0.669775 | + | 0.386695i | −0.795991 | − | 0.605308i | \(-0.793050\pi\) |
0.126217 | + | 0.992003i | \(0.459717\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 17.0000 | 1.62830 | 0.814152 | − | 0.580651i | \(-0.197202\pi\) | ||||
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.50000 | + | 2.59808i | −0.142374 | + | 0.246598i | ||||
\(112\) | 4.00000i | 0.377964i | ||||||||
\(113\) | −3.46410 | − | 2.00000i | −0.325875 | − | 0.188144i | 0.328133 | − | 0.944632i | \(-0.393581\pi\) |
−0.654008 | + | 0.756487i | \(0.726914\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | −2.59808 | − | 2.50000i | −0.240192 | − | 0.231125i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | − | 6.92820i | −0.366679 | − | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 11.0000i | 0.995893i | ||||||||
\(123\) | −8.66025 | − | 5.00000i | −0.780869 | − | 0.450835i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | − | 3.46410i | 0.178174 | − | 0.308607i | ||||
\(127\) | −19.0526 | + | 11.0000i | −1.69064 | + | 0.976092i | −0.736642 | + | 0.676283i | \(0.763590\pi\) |
−0.953999 | + | 0.299809i | \(0.903077\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0000 | 1.74741 | 0.873704 | − | 0.486458i | \(-0.161711\pi\) | ||||
0.873704 | + | 0.486458i | \(0.161711\pi\) | |||||||
\(132\) | 4.33013 | − | 2.50000i | 0.376889 | − | 0.217597i | ||||
\(133\) | 6.92820 | − | 4.00000i | 0.600751 | − | 0.346844i | ||||
\(134\) | −2.00000 | + | 3.46410i | −0.172774 | + | 0.299253i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | 6.92820 | + | 4.00000i | 0.591916 | + | 0.341743i | 0.765855 | − | 0.643013i | \(-0.222316\pi\) |
−0.173939 | + | 0.984757i | \(0.555649\pi\) | |||||||
\(138\) | 7.00000i | 0.595880i | ||||||||
\(139\) | −2.00000 | + | 3.46410i | −0.169638 | + | 0.293821i | −0.938293 | − | 0.345843i | \(-0.887593\pi\) |
0.768655 | + | 0.639664i | \(0.220926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | − | 10.3923i | −0.505291 | − | 0.875190i | ||||
\(142\) | − | 3.00000i | − | 0.251754i | ||||||
\(143\) | 17.3205 | − | 5.00000i | 1.44841 | − | 0.418121i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.50000 | + | 7.79423i | 0.372423 | + | 0.645055i | ||||
\(147\) | 7.79423 | + | 4.50000i | 0.642857 | + | 0.371154i | ||||
\(148\) | 3.00000i | 0.246598i | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | −1.73205 | − | 1.00000i | −0.140488 | − | 0.0811107i | ||||
\(153\) | 1.73205 | − | 1.00000i | 0.140028 | − | 0.0808452i | ||||
\(154\) | 10.0000 | + | 17.3205i | 0.805823 | + | 1.39573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.50000 | − | 0.866025i | −0.280224 | − | 0.0693375i | ||||
\(157\) | 17.0000i | 1.35675i | 0.734717 | + | 0.678374i | \(0.237315\pi\) | ||||
−0.734717 | + | 0.678374i | \(0.762685\pi\) | |||||||
\(158\) | −12.1244 | + | 7.00000i | −0.964562 | + | 0.556890i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.0000 | −2.20671 | ||||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 5.19615 | + | 3.00000i | 0.406994 | + | 0.234978i | 0.689497 | − | 0.724288i | \(-0.257831\pi\) |
−0.282503 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(164\) | −10.0000 | −0.780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50000 | + | 2.59808i | 0.116423 | + | 0.201650i | ||||
\(167\) | 12.9904 | − | 7.50000i | 1.00523 | − | 0.580367i | 0.0954356 | − | 0.995436i | \(-0.469576\pi\) |
0.909790 | + | 0.415068i | \(0.136242\pi\) | |||||||
\(168\) | − | 4.00000i | − | 0.308607i | ||||||
\(169\) | −11.5000 | − | 6.06218i | −0.884615 | − | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 3.46410 | − | 2.00000i | 0.264135 | − | 0.152499i | ||||
\(173\) | −13.8564 | − | 8.00000i | −1.05348 | − | 0.608229i | −0.129861 | − | 0.991532i | \(-0.541453\pi\) |
−0.923622 | + | 0.383304i | \(0.874786\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.50000 | − | 4.33013i | 0.188445 | − | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.66025 | + | 5.00000i | 0.649113 | + | 0.374766i | ||||
\(179\) | −0.500000 | − | 0.866025i | −0.0373718 | − | 0.0647298i | 0.846735 | − | 0.532016i | \(-0.178565\pi\) |
−0.884106 | + | 0.467286i | \(0.845232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | 3.46410 | − | 14.0000i | 0.256776 | − | 1.03775i | ||||
\(183\) | − | 11.0000i | − | 0.813143i | ||||||
\(184\) | 3.50000 | + | 6.06218i | 0.258023 | + | 0.446910i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 10.0000i | 0.731272i | ||||||||
\(188\) | −10.3923 | − | 6.00000i | −0.757937 | − | 0.437595i | ||||
\(189\) | −2.00000 | + | 3.46410i | −0.145479 | + | 0.251976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5000 | − | 19.9186i | 0.832111 | − | 1.44126i | −0.0642505 | − | 0.997934i | \(-0.520466\pi\) |
0.896361 | − | 0.443324i | \(-0.146201\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −2.59808 | + | 1.50000i | −0.187014 | + | 0.107972i | −0.590584 | − | 0.806976i | \(-0.701102\pi\) |
0.403570 | + | 0.914949i | \(0.367769\pi\) | |||||||
\(194\) | 13.0000 | 0.933346 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | −1.73205 | + | 1.00000i | −0.123404 | + | 0.0712470i | −0.560431 | − | 0.828201i | \(-0.689365\pi\) |
0.437028 | + | 0.899448i | \(0.356031\pi\) | |||||||
\(198\) | −4.33013 | + | 2.50000i | −0.307729 | + | 0.177667i | ||||
\(199\) | 12.0000 | − | 20.7846i | 0.850657 | − | 1.47338i | −0.0299585 | − | 0.999551i | \(-0.509538\pi\) |
0.880616 | − | 0.473831i | \(-0.157129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | 6.92820 | + | 4.00000i | 0.487467 | + | 0.281439i | ||||
\(203\) | − | 8.00000i | − | 0.561490i | ||||||
\(204\) | 1.00000 | − | 1.73205i | 0.0700140 | − | 0.121268i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | + | 13.8564i | 0.557386 | + | 0.965422i | ||||
\(207\) | − | 7.00000i | − | 0.486534i | ||||||
\(208\) | −3.46410 | + | 1.00000i | −0.240192 | + | 0.0693375i | ||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | + | 13.8564i | 0.550743 | + | 0.953914i | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.00000i | 0.205557i | ||||||||
\(214\) | 4.00000 | − | 6.92820i | 0.273434 | − | 0.473602i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 6.92820 | + | 4.00000i | 0.470317 | + | 0.271538i | ||||
\(218\) | −14.7224 | + | 8.50000i | −0.997129 | + | 0.575693i | ||||
\(219\) | −4.50000 | − | 7.79423i | −0.304082 | − | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.00000 | − | 5.19615i | 0.336336 | − | 0.349531i | ||||
\(222\) | − | 3.00000i | − | 0.201347i | ||||||
\(223\) | 3.46410 | − | 2.00000i | 0.231973 | − | 0.133930i | −0.379509 | − | 0.925188i | \(-0.623907\pi\) |
0.611482 | + | 0.791258i | \(0.290574\pi\) | |||||||
\(224\) | −2.00000 | − | 3.46410i | −0.133631 | − | 0.231455i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | 7.79423 | + | 4.50000i | 0.517321 | + | 0.298675i | 0.735838 | − | 0.677158i | \(-0.236789\pi\) |
−0.218517 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(228\) | 1.73205 | + | 1.00000i | 0.114708 | + | 0.0662266i | ||||
\(229\) | −19.0000 | −1.25556 | −0.627778 | − | 0.778393i | \(-0.716035\pi\) | ||||
−0.627778 | + | 0.778393i | \(0.716035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0000 | − | 17.3205i | −0.657952 | − | 1.13961i | ||||
\(232\) | −1.73205 | + | 1.00000i | −0.113715 | + | 0.0656532i | ||||
\(233\) | 8.00000i | 0.524097i | 0.965055 | + | 0.262049i | \(0.0843981\pi\) | ||||
−0.965055 | + | 0.262049i | \(0.915602\pi\) | |||||||
\(234\) | 3.50000 | + | 0.866025i | 0.228802 | + | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1244 | − | 7.00000i | 0.787562 | − | 0.454699i | ||||
\(238\) | 6.92820 | + | 4.00000i | 0.449089 | + | 0.259281i | ||||
\(239\) | 23.0000 | 1.48775 | 0.743873 | − | 0.668321i | \(-0.232987\pi\) | ||||
0.743873 | + | 0.668321i | \(0.232987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.00000 | + | 12.1244i | −0.450910 | + | 0.780998i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | − | 14.0000i | − | 0.899954i | ||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −5.50000 | − | 9.52628i | −0.352101 | − | 0.609858i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 5.19615 | + | 5.00000i | 0.330623 | + | 0.318142i | ||||
\(248\) | − | 2.00000i | − | 0.127000i | ||||||
\(249\) | −1.50000 | − | 2.59808i | −0.0950586 | − | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.50000 | − | 14.7224i | 0.536515 | − | 0.929272i | −0.462573 | − | 0.886581i | \(-0.653074\pi\) |
0.999088 | − | 0.0426905i | \(-0.0135929\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 30.3109 | + | 17.5000i | 1.90563 | + | 1.10022i | ||||
\(254\) | 11.0000 | − | 19.0526i | 0.690201 | − | 1.19546i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 24.2487 | − | 14.0000i | 1.51259 | − | 0.873296i | 0.512702 | − | 0.858567i | \(-0.328645\pi\) |
0.999892 | − | 0.0147291i | \(-0.00468859\pi\) | |||||||
\(258\) | −3.46410 | + | 2.00000i | −0.215666 | + | 0.124515i | ||||
\(259\) | 12.0000 | 0.745644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −17.3205 | + | 10.0000i | −1.07006 | + | 0.617802i | ||||
\(263\) | 7.79423 | − | 4.50000i | 0.480613 | − | 0.277482i | −0.240059 | − | 0.970758i | \(-0.577167\pi\) |
0.720672 | + | 0.693276i | \(0.243833\pi\) | |||||||
\(264\) | −2.50000 | + | 4.33013i | −0.153864 | + | 0.266501i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | + | 6.92820i | −0.245256 | + | 0.424795i | ||||
\(267\) | −8.66025 | − | 5.00000i | −0.529999 | − | 0.305995i | ||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | −2.00000 | + | 3.46410i | −0.121942 | + | 0.211210i | −0.920534 | − | 0.390664i | \(-0.872246\pi\) |
0.798591 | + | 0.601874i | \(0.205579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | −3.46410 | + | 14.0000i | −0.209657 | + | 0.847319i | ||||
\(274\) | −8.00000 | −0.483298 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.50000 | − | 6.06218i | −0.210675 | − | 0.364900i | ||||
\(277\) | −26.8468 | − | 15.5000i | −1.61307 | − | 0.931305i | −0.988654 | − | 0.150210i | \(-0.952005\pi\) |
−0.624413 | − | 0.781094i | \(-0.714662\pi\) | |||||||
\(278\) | − | 4.00000i | − | 0.239904i | ||||||
\(279\) | −1.00000 | + | 1.73205i | −0.0598684 | + | 0.103695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 10.3923 | + | 6.00000i | 0.618853 | + | 0.357295i | ||||
\(283\) | −24.2487 | + | 14.0000i | −1.44144 | + | 0.832214i | −0.997946 | − | 0.0640654i | \(-0.979593\pi\) |
−0.443491 | + | 0.896279i | \(0.646260\pi\) | |||||||
\(284\) | 1.50000 | + | 2.59808i | 0.0890086 | + | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.5000 | + | 12.9904i | −0.739140 | + | 0.768137i | ||||
\(287\) | 40.0000i | 2.36113i | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.0000 | −0.762073 | ||||||||
\(292\) | −7.79423 | − | 4.50000i | −0.456123 | − | 0.263343i | ||||
\(293\) | 20.7846 | + | 12.0000i | 1.21425 | + | 0.701047i | 0.963682 | − | 0.267052i | \(-0.0860494\pi\) |
0.250568 | + | 0.968099i | \(0.419383\pi\) | |||||||
\(294\) | −9.00000 | −0.524891 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.50000 | − | 2.59808i | −0.0871857 | − | 0.151010i | ||||
\(297\) | 4.33013 | − | 2.50000i | 0.251259 | − | 0.145065i | ||||
\(298\) | − | 10.0000i | − | 0.579284i | ||||||
\(299\) | −7.00000 | − | 24.2487i | −0.404820 | − | 1.40234i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | − | 13.8564i | −0.461112 | − | 0.798670i | ||||
\(302\) | 8.66025 | − | 5.00000i | 0.498342 | − | 0.287718i | ||||
\(303\) | −6.92820 | − | 4.00000i | −0.398015 | − | 0.229794i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | 24.0000i | 1.36975i | 0.728659 | + | 0.684876i | \(0.240144\pi\) | ||||
−0.728659 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(308\) | −17.3205 | − | 10.0000i | −0.986928 | − | 0.569803i | ||||
\(309\) | −8.00000 | − | 13.8564i | −0.455104 | − | 0.788263i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.00000 | −0.396934 | −0.198467 | − | 0.980108i | \(-0.563596\pi\) | ||||
−0.198467 | + | 0.980108i | \(0.563596\pi\) | |||||||
\(312\) | 3.46410 | − | 1.00000i | 0.196116 | − | 0.0566139i | ||||
\(313\) | 1.00000i | 0.0565233i | 0.999601 | + | 0.0282617i | \(0.00899717\pi\) | ||||
−0.999601 | + | 0.0282617i | \(0.991003\pi\) | |||||||
\(314\) | −8.50000 | − | 14.7224i | −0.479683 | − | 0.830835i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00000 | − | 12.1244i | 0.393781 | − | 0.682048i | ||||
\(317\) | 28.0000i | 1.57264i | 0.617822 | + | 0.786318i | \(0.288015\pi\) | ||||
−0.617822 | + | 0.786318i | \(0.711985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00000 | + | 8.66025i | −0.279946 | + | 0.484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | + | 6.92820i | −0.223258 | + | 0.386695i | ||||
\(322\) | 24.2487 | − | 14.0000i | 1.35133 | − | 0.780189i | ||||
\(323\) | −3.46410 | + | 2.00000i | −0.192748 | + | 0.111283i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | −0.332309 | ||||||||
\(327\) | 14.7224 | − | 8.50000i | 0.814152 | − | 0.470051i | ||||
\(328\) | 8.66025 | − | 5.00000i | 0.478183 | − | 0.276079i | ||||
\(329\) | −24.0000 | + | 41.5692i | −1.32316 | + | 2.29179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | −2.59808 | − | 1.50000i | −0.142588 | − | 0.0823232i | ||||
\(333\) | 3.00000i | 0.164399i | ||||||||
\(334\) | −7.50000 | + | 12.9904i | −0.410382 | + | 0.710802i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | + | 3.46410i | 0.109109 | + | 0.188982i | ||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | 12.9904 | − | 0.500000i | 0.706584 | − | 0.0271964i | ||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.00000 | − | 8.66025i | −0.270765 | − | 0.468979i | ||||
\(342\) | −1.73205 | − | 1.00000i | −0.0936586 | − | 0.0540738i | ||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | −2.00000 | + | 3.46410i | −0.107833 | + | 0.186772i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.0000 | 0.860165 | ||||||||
\(347\) | 9.52628 | + | 5.50000i | 0.511397 | + | 0.295255i | 0.733408 | − | 0.679789i | \(-0.237929\pi\) |
−0.222010 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(348\) | 1.73205 | − | 1.00000i | 0.0928477 | − | 0.0536056i | ||||
\(349\) | 2.50000 | + | 4.33013i | 0.133822 | + | 0.231786i | 0.925147 | − | 0.379610i | \(-0.123942\pi\) |
−0.791325 | + | 0.611396i | \(0.790608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.50000 | − | 0.866025i | −0.186816 | − | 0.0462250i | ||||
\(352\) | 5.00000i | 0.266501i | ||||||||
\(353\) | −5.19615 | + | 3.00000i | −0.276563 | + | 0.159674i | −0.631867 | − | 0.775077i | \(-0.717711\pi\) |
0.355303 | + | 0.934751i | \(0.384378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | −6.92820 | − | 4.00000i | −0.366679 | − | 0.211702i | ||||
\(358\) | 0.866025 | + | 0.500000i | 0.0457709 | + | 0.0264258i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −9.52628 | + | 5.50000i | −0.500690 | + | 0.289074i | ||||
\(363\) | 14.0000i | 0.734809i | ||||||||
\(364\) | 4.00000 | + | 13.8564i | 0.209657 | + | 0.726273i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.50000 | + | 9.52628i | 0.287490 | + | 0.497947i | ||||
\(367\) | −8.66025 | + | 5.00000i | −0.452062 | + | 0.260998i | −0.708700 | − | 0.705509i | \(-0.750718\pi\) |
0.256639 | + | 0.966507i | \(0.417385\pi\) | |||||||
\(368\) | −6.06218 | − | 3.50000i | −0.316013 | − | 0.182450i | ||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | 14.7224 | + | 8.50000i | 0.762299 | + | 0.440113i | 0.830120 | − | 0.557584i | \(-0.188272\pi\) |
−0.0678218 | + | 0.997697i | \(0.521605\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.0000 | 0.618853 | ||||||||
\(377\) | 6.92820 | − | 2.00000i | 0.356821 | − | 0.103005i | ||||
\(378\) | − | 4.00000i | − | 0.205738i | ||||||
\(379\) | 5.00000 | + | 8.66025i | 0.256833 | + | 0.444847i | 0.965392 | − | 0.260804i | \(-0.0839877\pi\) |
−0.708559 | + | 0.705652i | \(0.750654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.0000 | + | 19.0526i | −0.563547 | + | 0.976092i | ||||
\(382\) | 23.0000i | 1.17678i | ||||||||
\(383\) | 32.0429 | + | 18.5000i | 1.63732 | + | 0.945306i | 0.981752 | + | 0.190168i | \(0.0609033\pi\) |
0.655566 | + | 0.755138i | \(0.272430\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.50000 | − | 2.59808i | 0.0763480 | − | 0.132239i | ||||
\(387\) | 3.46410 | − | 2.00000i | 0.176090 | − | 0.101666i | ||||
\(388\) | −11.2583 | + | 6.50000i | −0.571555 | + | 0.329988i | ||||
\(389\) | −26.0000 | −1.31825 | −0.659126 | − | 0.752032i | \(-0.729074\pi\) | ||||
−0.659126 | + | 0.752032i | \(0.729074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | 0.708010 | ||||||||
\(392\) | −7.79423 | + | 4.50000i | −0.393668 | + | 0.227284i | ||||
\(393\) | 17.3205 | − | 10.0000i | 0.873704 | − | 0.504433i | ||||
\(394\) | 1.00000 | − | 1.73205i | 0.0503793 | − | 0.0872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50000 | − | 4.33013i | 0.125630 | − | 0.217597i | ||||
\(397\) | −25.9808 | − | 15.0000i | −1.30394 | − | 0.752828i | −0.322860 | − | 0.946447i | \(-0.604644\pi\) |
−0.981077 | + | 0.193618i | \(0.937978\pi\) | |||||||
\(398\) | 24.0000i | 1.20301i | ||||||||
\(399\) | 4.00000 | − | 6.92820i | 0.200250 | − | 0.346844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | 4.00000i | 0.199502i | ||||||||
\(403\) | −1.73205 | + | 7.00000i | −0.0862796 | + | 0.348695i | ||||
\(404\) | −8.00000 | −0.398015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | + | 6.92820i | 0.198517 | + | 0.343841i | ||||
\(407\) | −12.9904 | − | 7.50000i | −0.643909 | − | 0.371761i | ||||
\(408\) | 2.00000i | 0.0990148i | ||||||||
\(409\) | −15.0000 | + | 25.9808i | −0.741702 | + | 1.28467i | 0.210017 | + | 0.977698i | \(0.432648\pi\) |
−0.951720 | + | 0.306968i | \(0.900685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000 | 0.394611 | ||||||||
\(412\) | −13.8564 | − | 8.00000i | −0.682656 | − | 0.394132i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.50000 | + | 6.06218i | 0.172016 | + | 0.297940i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | − | 2.59808i | 0.122573 | − | 0.127381i | ||||
\(417\) | 4.00000i | 0.195881i | ||||||||
\(418\) | 8.66025 | − | 5.00000i | 0.423587 | − | 0.244558i | ||||
\(419\) | 2.50000 | + | 4.33013i | 0.122133 | + | 0.211541i | 0.920609 | − | 0.390487i | \(-0.127693\pi\) |
−0.798476 | + | 0.602027i | \(0.794360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0000 | 1.12095 | 0.560476 | − | 0.828171i | \(-0.310618\pi\) | ||||
0.560476 | + | 0.828171i | \(0.310618\pi\) | |||||||
\(422\) | −13.8564 | − | 8.00000i | −0.674519 | − | 0.389434i | ||||
\(423\) | −10.3923 | − | 6.00000i | −0.505291 | − | 0.291730i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.50000 | − | 2.59808i | −0.0726752 | − | 0.125877i | ||||
\(427\) | −38.1051 | + | 22.0000i | −1.84404 | + | 1.06465i | ||||
\(428\) | 8.00000i | 0.386695i | ||||||||
\(429\) | 12.5000 | − | 12.9904i | 0.603506 | − | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5000 | + | 25.1147i | 0.698440 | + | 1.20973i | 0.969007 | + | 0.247033i | \(0.0794556\pi\) |
−0.270567 | + | 0.962701i | \(0.587211\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 16.4545 | + | 9.50000i | 0.790752 | + | 0.456541i | 0.840227 | − | 0.542234i | \(-0.182422\pi\) |
−0.0494752 | + | 0.998775i | \(0.515755\pi\) | |||||||
\(434\) | −8.00000 | −0.384012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.50000 | − | 14.7224i | 0.407076 | − | 0.705077i | ||||
\(437\) | 14.0000i | 0.669711i | ||||||||
\(438\) | 7.79423 | + | 4.50000i | 0.372423 | + | 0.215018i | ||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | −1.73205 | + | 7.00000i | −0.0823853 | + | 0.332956i | ||||
\(443\) | 25.0000i | 1.18779i | 0.804544 | + | 0.593893i | \(0.202410\pi\) | ||||
−0.804544 | + | 0.593893i | \(0.797590\pi\) | |||||||
\(444\) | 1.50000 | + | 2.59808i | 0.0711868 | + | 0.123299i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.00000 | + | 3.46410i | −0.0947027 | + | 0.164030i | ||||
\(447\) | 10.0000i | 0.472984i | ||||||||
\(448\) | 3.46410 | + | 2.00000i | 0.163663 | + | 0.0944911i | ||||
\(449\) | −3.00000 | + | 5.19615i | −0.141579 | + | 0.245222i | −0.928091 | − | 0.372353i | \(-0.878551\pi\) |
0.786513 | + | 0.617574i | \(0.211885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.0000 | − | 43.3013i | 1.17720 | − | 2.03898i | ||||
\(452\) | −3.46410 | + | 2.00000i | −0.162938 | + | 0.0940721i | ||||
\(453\) | −8.66025 | + | 5.00000i | −0.406894 | + | 0.234920i | ||||
\(454\) | −9.00000 | −0.422391 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −26.8468 | + | 15.5000i | −1.25584 | + | 0.725059i | −0.972263 | − | 0.233890i | \(-0.924854\pi\) |
−0.283577 | + | 0.958950i | \(0.591521\pi\) | |||||||
\(458\) | 16.4545 | − | 9.50000i | 0.768867 | − | 0.443906i | ||||
\(459\) | 1.00000 | − | 1.73205i | 0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0000 | + | 36.3731i | −0.978068 | + | 1.69406i | −0.308651 | + | 0.951175i | \(0.599877\pi\) |
−0.669417 | + | 0.742887i | \(0.733456\pi\) | |||||||
\(462\) | 17.3205 | + | 10.0000i | 0.805823 | + | 0.465242i | ||||
\(463\) | − | 38.0000i | − | 1.76601i | −0.469364 | − | 0.883005i | \(-0.655517\pi\) | ||
0.469364 | − | 0.883005i | \(-0.344483\pi\) | |||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00000 | − | 6.92820i | −0.185296 | − | 0.320943i | ||||
\(467\) | 9.00000i | 0.416470i | 0.978079 | + | 0.208235i | \(0.0667719\pi\) | ||||
−0.978079 | + | 0.208235i | \(0.933228\pi\) | |||||||
\(468\) | −3.46410 | + | 1.00000i | −0.160128 | + | 0.0462250i | ||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.50000 | + | 14.7224i | 0.391659 | + | 0.678374i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0000i | 0.919601i | ||||||||
\(474\) | −7.00000 | + | 12.1244i | −0.321521 | + | 0.556890i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.9186 | + | 11.5000i | −0.911055 | + | 0.525998i | ||||
\(479\) | −12.0000 | − | 20.7846i | −0.548294 | − | 0.949673i | −0.998392 | − | 0.0566937i | \(-0.981944\pi\) |
0.450098 | − | 0.892979i | \(-0.351389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.00000 | + | 10.3923i | 0.136788 | + | 0.473848i | ||||
\(482\) | − | 14.0000i | − | 0.637683i | ||||||
\(483\) | −24.2487 | + | 14.0000i | −1.10335 | + | 0.637022i | ||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −27.7128 | − | 16.0000i | −1.25579 | − | 0.725029i | −0.283535 | − | 0.958962i | \(-0.591507\pi\) |
−0.972253 | + | 0.233933i | \(0.924840\pi\) | |||||||
\(488\) | 9.52628 | + | 5.50000i | 0.431234 | + | 0.248973i | ||||
\(489\) | 6.00000 | 0.271329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.50000 | − | 4.33013i | −0.112823 | − | 0.195416i | 0.804084 | − | 0.594515i | \(-0.202656\pi\) |
−0.916908 | + | 0.399100i | \(0.869323\pi\) | |||||||
\(492\) | −8.66025 | + | 5.00000i | −0.390434 | + | 0.225417i | ||||
\(493\) | 4.00000i | 0.180151i | ||||||||
\(494\) | −7.00000 | − | 1.73205i | −0.314945 | − | 0.0779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | + | 1.73205i | 0.0449013 | + | 0.0777714i | ||||
\(497\) | 10.3923 | − | 6.00000i | 0.466159 | − | 0.269137i | ||||
\(498\) | 2.59808 | + | 1.50000i | 0.116423 | + | 0.0672166i | ||||
\(499\) | −10.0000 | −0.447661 | −0.223831 | − | 0.974628i | \(-0.571856\pi\) | ||||
−0.223831 | + | 0.974628i | \(0.571856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.50000 | − | 12.9904i | 0.335075 | − | 0.580367i | ||||
\(502\) | 17.0000i | 0.758747i | ||||||||
\(503\) | −18.1865 | − | 10.5000i | −0.810897 | − | 0.468172i | 0.0363700 | − | 0.999338i | \(-0.488421\pi\) |
−0.847267 | + | 0.531167i | \(0.821754\pi\) | |||||||
\(504\) | −2.00000 | − | 3.46410i | −0.0890871 | − | 0.154303i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −35.0000 | −1.55594 | ||||||||
\(507\) | −12.9904 | + | 0.500000i | −0.576923 | + | 0.0222058i | ||||
\(508\) | 22.0000i | 0.976092i | ||||||||
\(509\) | −2.00000 | − | 3.46410i | −0.0886484 | − | 0.153544i | 0.818292 | − | 0.574803i | \(-0.194921\pi\) |
−0.906940 | + | 0.421260i | \(0.861588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0000 | + | 31.1769i | −0.796273 | + | 1.37919i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.73205 | + | 1.00000i | 0.0764719 | + | 0.0441511i | ||||
\(514\) | −14.0000 | + | 24.2487i | −0.617514 | + | 1.06956i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 51.9615 | − | 30.0000i | 2.28527 | − | 1.31940i | ||||
\(518\) | −10.3923 | + | 6.00000i | −0.456612 | + | 0.263625i | ||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | −1.73205 | + | 1.00000i | −0.0758098 | + | 0.0437688i | ||||
\(523\) | −12.1244 | + | 7.00000i | −0.530161 | + | 0.306089i | −0.741082 | − | 0.671414i | \(-0.765687\pi\) |
0.210921 | + | 0.977503i | \(0.432354\pi\) | |||||||
\(524\) | 10.0000 | − | 17.3205i | 0.436852 | − | 0.756650i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.50000 | + | 7.79423i | −0.196209 | + | 0.339845i | ||||
\(527\) | −3.46410 | − | 2.00000i | −0.150899 | − | 0.0871214i | ||||
\(528\) | − | 5.00000i | − | 0.217597i | ||||||
\(529\) | 13.0000 | − | 22.5167i | 0.565217 | − | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 8.00000i | − | 0.346844i | ||||||
\(533\) | −34.6410 | + | 10.0000i | −1.50047 | + | 0.433148i | ||||
\(534\) | 10.0000 | 0.432742 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.00000 | + | 3.46410i | 0.0863868 | + | 0.149626i | ||||
\(537\) | −0.866025 | − | 0.500000i | −0.0373718 | − | 0.0215766i | ||||
\(538\) | − | 4.00000i | − | 0.172452i | ||||||
\(539\) | −22.5000 | + | 38.9711i | −0.969144 | + | 1.67861i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | −0.386940 | −0.193470 | − | 0.981106i | \(-0.561974\pi\) | ||||
−0.193470 | + | 0.981106i | \(0.561974\pi\) | |||||||
\(542\) | 1.73205 | + | 1.00000i | 0.0743980 | + | 0.0429537i | ||||
\(543\) | 9.52628 | − | 5.50000i | 0.408812 | − | 0.236028i | ||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.00000 | − | 13.8564i | −0.171184 | − | 0.592999i | ||||
\(547\) | 30.0000i | 1.28271i | 0.767245 | + | 0.641354i | \(0.221627\pi\) | ||||
−0.767245 | + | 0.641354i | \(0.778373\pi\) | |||||||
\(548\) | 6.92820 | − | 4.00000i | 0.295958 | − | 0.170872i | ||||
\(549\) | −5.50000 | − | 9.52628i | −0.234734 | − | 0.406572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.00000 | −0.170406 | ||||||||
\(552\) | 6.06218 | + | 3.50000i | 0.258023 | + | 0.148970i | ||||
\(553\) | −48.4974 | − | 28.0000i | −2.06232 | − | 1.19068i | ||||
\(554\) | 31.0000 | 1.31706 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −13.8564 | + | 8.00000i | −0.587115 | + | 0.338971i | −0.763956 | − | 0.645269i | \(-0.776745\pi\) |
0.176841 | + | 0.984239i | \(0.443412\pi\) | |||||||
\(558\) | − | 2.00000i | − | 0.0846668i | ||||||
\(559\) | 10.0000 | − | 10.3923i | 0.422955 | − | 0.439548i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.00000 | + | 8.66025i | 0.211100 | + | 0.365636i | ||||
\(562\) | −22.5167 | + | 13.0000i | −0.949808 | + | 0.548372i | ||||
\(563\) | −18.1865 | − | 10.5000i | −0.766471 | − | 0.442522i | 0.0651433 | − | 0.997876i | \(-0.479250\pi\) |
−0.831614 | + | 0.555354i | \(0.812583\pi\) | |||||||
\(564\) | −12.0000 | −0.505291 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.0000 | − | 24.2487i | 0.588464 | − | 1.01925i | ||||
\(567\) | 4.00000i | 0.167984i | ||||||||
\(568\) | −2.59808 | − | 1.50000i | −0.109013 | − | 0.0629386i | ||||
\(569\) | −2.00000 | − | 3.46410i | −0.0838444 | − | 0.145223i | 0.821054 | − | 0.570851i | \(-0.193387\pi\) |
−0.904898 | + | 0.425628i | \(0.860053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | −0.418487 | −0.209243 | − | 0.977864i | \(-0.567100\pi\) | ||||
−0.209243 | + | 0.977864i | \(0.567100\pi\) | |||||||
\(572\) | 4.33013 | − | 17.5000i | 0.181052 | − | 0.731712i | ||||
\(573\) | − | 23.0000i | − | 0.960839i | ||||||
\(574\) | −20.0000 | − | 34.6410i | −0.834784 | − | 1.44589i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 37.0000i | − | 1.54033i | −0.637845 | − | 0.770165i | \(-0.720174\pi\) | ||
0.637845 | − | 0.770165i | \(-0.279826\pi\) | |||||||
\(578\) | 11.2583 | + | 6.50000i | 0.468285 | + | 0.270364i | ||||
\(579\) | −1.50000 | + | 2.59808i | −0.0623379 | + | 0.107972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | + | 10.3923i | −0.248922 | + | 0.431145i | ||||
\(582\) | 11.2583 | − | 6.50000i | 0.466673 | − | 0.269434i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.00000 | 0.372423 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | 2.59808 | − | 1.50000i | 0.107234 | − | 0.0619116i | −0.445424 | − | 0.895320i | \(-0.646947\pi\) |
0.552658 | + | 0.833408i | \(0.313614\pi\) | |||||||
\(588\) | 7.79423 | − | 4.50000i | 0.321429 | − | 0.185577i | ||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.00000 | + | 1.73205i | −0.0411345 | + | 0.0712470i | ||||
\(592\) | 2.59808 | + | 1.50000i | 0.106780 | + | 0.0616496i | ||||
\(593\) | − | 4.00000i | − | 0.164260i | −0.996622 | − | 0.0821302i | \(-0.973828\pi\) | ||
0.996622 | − | 0.0821302i | \(-0.0261723\pi\) | |||||||
\(594\) | −2.50000 | + | 4.33013i | −0.102576 | + | 0.177667i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.00000 | + | 8.66025i | 0.204808 | + | 0.354738i | ||||
\(597\) | − | 24.0000i | − | 0.982255i | ||||||
\(598\) | 18.1865 | + | 17.5000i | 0.743703 | + | 0.715628i | ||||
\(599\) | 27.0000 | 1.10319 | 0.551595 | − | 0.834112i | \(-0.314019\pi\) | ||||
0.551595 | + | 0.834112i | \(0.314019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.00000 | + | 15.5885i | 0.367118 | + | 0.635866i | 0.989114 | − | 0.147154i | \(-0.0470113\pi\) |
−0.621996 | + | 0.783020i | \(0.713678\pi\) | |||||||
\(602\) | 13.8564 | + | 8.00000i | 0.564745 | + | 0.326056i | ||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | −5.00000 | + | 8.66025i | −0.203447 | + | 0.352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.00000 | 0.324978 | ||||||||
\(607\) | 25.9808 | + | 15.0000i | 1.05453 | + | 0.608831i | 0.923913 | − | 0.382602i | \(-0.124972\pi\) |
0.130613 | + | 0.991433i | \(0.458305\pi\) | |||||||
\(608\) | −1.73205 | + | 1.00000i | −0.0702439 | + | 0.0405554i | ||||
\(609\) | −4.00000 | − | 6.92820i | −0.162088 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −42.0000 | − | 10.3923i | −1.69914 | − | 0.420428i | ||||
\(612\) | − | 2.00000i | − | 0.0808452i | ||||||
\(613\) | 1.73205 | − | 1.00000i | 0.0699569 | − | 0.0403896i | −0.464614 | − | 0.885514i | \(-0.653807\pi\) |
0.534570 | + | 0.845124i | \(0.320473\pi\) | |||||||
\(614\) | −12.0000 | − | 20.7846i | −0.484281 | − | 0.838799i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.0000 | 0.805823 | ||||||||
\(617\) | −12.1244 | − | 7.00000i | −0.488108 | − | 0.281809i | 0.235681 | − | 0.971830i | \(-0.424268\pi\) |
−0.723789 | + | 0.690021i | \(0.757601\pi\) | |||||||
\(618\) | 13.8564 | + | 8.00000i | 0.557386 | + | 0.321807i | ||||
\(619\) | −44.0000 | −1.76851 | −0.884255 | − | 0.467005i | \(-0.845333\pi\) | ||||
−0.884255 | + | 0.467005i | \(0.845333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.50000 | − | 6.06218i | −0.140450 | − | 0.243267i | ||||
\(622\) | 6.06218 | − | 3.50000i | 0.243071 | − | 0.140337i | ||||
\(623\) | 40.0000i | 1.60257i | ||||||||
\(624\) | −2.50000 | + | 2.59808i | −0.100080 | + | 0.104006i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | −8.66025 | + | 5.00000i | −0.345857 | + | 0.199681i | ||||
\(628\) | 14.7224 | + | 8.50000i | 0.587489 | + | 0.339187i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000 | − | 12.1244i | 0.278666 | − | 0.482663i | −0.692388 | − | 0.721526i | \(-0.743441\pi\) |
0.971053 | + | 0.238863i | \(0.0767746\pi\) | |||||||
\(632\) | 14.0000i | 0.556890i | ||||||||
\(633\) | 13.8564 | + | 8.00000i | 0.550743 | + | 0.317971i | ||||
\(634\) | −14.0000 | − | 24.2487i | −0.556011 | − | 0.963039i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.1769 | − | 9.00000i | 1.23527 | − | 0.356593i | ||||
\(638\) | − | 10.0000i | − | 0.395904i | ||||||
\(639\) | 1.50000 | + | 2.59808i | 0.0593391 | + | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.00000 | − | 10.3923i | 0.236986 | − | 0.410471i | −0.722862 | − | 0.690992i | \(-0.757174\pi\) |
0.959848 | + | 0.280521i | \(0.0905072\pi\) | |||||||
\(642\) | − | 8.00000i | − | 0.315735i | ||||||
\(643\) | 22.5167 | + | 13.0000i | 0.887970 | + | 0.512670i | 0.873278 | − | 0.487222i | \(-0.161990\pi\) |
0.0146923 | + | 0.999892i | \(0.495323\pi\) | |||||||
\(644\) | −14.0000 | + | 24.2487i | −0.551677 | + | 0.955533i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00000 | − | 3.46410i | 0.0786889 | − | 0.136293i | ||||
\(647\) | 38.9711 | − | 22.5000i | 1.53211 | − | 0.884566i | 0.532850 | − | 0.846210i | \(-0.321121\pi\) |
0.999264 | − | 0.0383563i | \(-0.0122122\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | 0.313545 | ||||||||
\(652\) | 5.19615 | − | 3.00000i | 0.203497 | − | 0.117489i | ||||
\(653\) | 6.92820 | − | 4.00000i | 0.271122 | − | 0.156532i | −0.358276 | − | 0.933616i | \(-0.616635\pi\) |
0.629397 | + | 0.777084i | \(0.283302\pi\) | |||||||
\(654\) | −8.50000 | + | 14.7224i | −0.332376 | + | 0.575693i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.00000 | + | 8.66025i | −0.195217 | + | 0.338126i | ||||
\(657\) | −7.79423 | − | 4.50000i | −0.304082 | − | 0.175562i | ||||
\(658\) | − | 48.0000i | − | 1.87123i | ||||||
\(659\) | −13.5000 | + | 23.3827i | −0.525885 | + | 0.910860i | 0.473660 | + | 0.880708i | \(0.342933\pi\) |
−0.999545 | + | 0.0301523i | \(0.990401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | 1.73205 | − | 7.00000i | 0.0672673 | − | 0.271857i | ||||
\(664\) | 3.00000 | 0.116423 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.50000 | − | 2.59808i | −0.0581238 | − | 0.100673i | ||||
\(667\) | 12.1244 | + | 7.00000i | 0.469457 | + | 0.271041i | ||||
\(668\) | − | 15.0000i | − | 0.580367i | ||||||
\(669\) | 2.00000 | − | 3.46410i | 0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55.0000 | 2.12325 | ||||||||
\(672\) | −3.46410 | − | 2.00000i | −0.133631 | − | 0.0771517i | ||||
\(673\) | 0.866025 | − | 0.500000i | 0.0333828 | − | 0.0192736i | −0.483216 | − | 0.875501i | \(-0.660531\pi\) |
0.516599 | + | 0.856228i | \(0.327198\pi\) | |||||||
\(674\) | 7.00000 | + | 12.1244i | 0.269630 | + | 0.467013i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | − | 4.00000i | − | 0.153732i | −0.997041 | − | 0.0768662i | \(-0.975509\pi\) | ||
0.997041 | − | 0.0768662i | \(-0.0244914\pi\) | |||||||
\(678\) | 3.46410 | − | 2.00000i | 0.133038 | − | 0.0768095i | ||||
\(679\) | 26.0000 | + | 45.0333i | 0.997788 | + | 1.72822i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | 0.344881 | ||||||||
\(682\) | 8.66025 | + | 5.00000i | 0.331618 | + | 0.191460i | ||||
\(683\) | 12.9904 | + | 7.50000i | 0.497063 | + | 0.286980i | 0.727500 | − | 0.686108i | \(-0.240682\pi\) |
−0.230437 | + | 0.973087i | \(0.574015\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.00000 | + | 6.92820i | 0.152721 | + | 0.264520i | ||||
\(687\) | −16.4545 | + | 9.50000i | −0.627778 | + | 0.362448i | ||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | + | 15.5885i | 0.342376 | + | 0.593013i | 0.984873 | − | 0.173275i | \(-0.0554350\pi\) |
−0.642497 | + | 0.766288i | \(0.722102\pi\) | |||||||
\(692\) | −13.8564 | + | 8.00000i | −0.526742 | + | 0.304114i | ||||
\(693\) | −17.3205 | − | 10.0000i | −0.657952 | − | 0.379869i | ||||
\(694\) | −11.0000 | −0.417554 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00000 | + | 1.73205i | −0.0379049 | + | 0.0656532i | ||||
\(697\) | − | 20.0000i | − | 0.757554i | ||||||
\(698\) | −4.33013 | − | 2.50000i | −0.163898 | − | 0.0946264i | ||||
\(699\) | 4.00000 | + | 6.92820i | 0.151294 | + | 0.262049i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 3.46410 | − | 1.00000i | 0.130744 | − | 0.0377426i | ||||
\(703\) | − | 6.00000i | − | 0.226294i | ||||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.00000 | − | 5.19615i | 0.112906 | − | 0.195560i | ||||
\(707\) | 32.0000i | 1.20348i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50000 | + | 4.33013i | −0.0938895 | + | 0.162621i | −0.909145 | − | 0.416481i | \(-0.863263\pi\) |
0.815255 | + | 0.579102i | \(0.196597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.00000 | − | 12.1244i | 0.262521 | − | 0.454699i | ||||
\(712\) | 8.66025 | − | 5.00000i | 0.324557 | − | 0.187383i | ||||
\(713\) | −12.1244 | + | 7.00000i | −0.454061 | + | 0.262152i | ||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.00000 | −0.0373718 | ||||||||
\(717\) | 19.9186 | − | 11.5000i | 0.743873 | − | 0.429475i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50000 | + | 12.9904i | −0.279703 | + | 0.484459i | −0.971311 | − | 0.237814i | \(-0.923569\pi\) |
0.691608 | + | 0.722273i | \(0.256903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | + | 55.4256i | −1.19174 | + | 2.06416i | ||||
\(722\) | −12.9904 | − | 7.50000i | −0.483452 | − | 0.279121i | ||||
\(723\) | 14.0000i | 0.520666i | ||||||||
\(724\) | 5.50000 | − | 9.52628i | 0.204406 | − | 0.354041i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.00000 | − | 12.1244i | −0.259794 | − | 0.449977i | ||||
\(727\) | 14.0000i | 0.519231i | 0.965712 | + | 0.259616i | \(0.0835959\pi\) | ||||
−0.965712 | + | 0.259616i | \(0.916404\pi\) | |||||||
\(728\) | −10.3923 | − | 10.0000i | −0.385164 | − | 0.370625i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | −9.52628 | − | 5.50000i | −0.352101 | − | 0.203286i | ||||
\(733\) | 33.0000i | 1.21888i | 0.792831 | + | 0.609441i | \(0.208606\pi\) | ||||
−0.792831 | + | 0.609441i | \(0.791394\pi\) | |||||||
\(734\) | 5.00000 | − | 8.66025i | 0.184553 | − | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.00000 | 0.258023 | ||||||||
\(737\) | 17.3205 | + | 10.0000i | 0.638009 | + | 0.368355i | ||||
\(738\) | 8.66025 | − | 5.00000i | 0.318788 | − | 0.184053i | ||||
\(739\) | 19.0000 | + | 32.9090i | 0.698926 | + | 1.21058i | 0.968839 | + | 0.247691i | \(0.0796718\pi\) |
−0.269913 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.00000 | + | 1.73205i | 0.257151 | + | 0.0636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.0000 | −0.622414 | ||||||||
\(747\) | −2.59808 | − | 1.50000i | −0.0950586 | − | 0.0548821i | ||||
\(748\) | 8.66025 | + | 5.00000i | 0.316650 | + | 0.182818i | ||||
\(749\) | 32.0000 | 1.16925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | + | 27.7128i | 0.583848 | + | 1.01125i | 0.995018 | + | 0.0996961i | \(0.0317870\pi\) |
−0.411170 | + | 0.911559i | \(0.634880\pi\) | |||||||
\(752\) | −10.3923 | + | 6.00000i | −0.378968 | + | 0.218797i | ||||
\(753\) | − | 17.0000i | − | 0.619514i | ||||||
\(754\) | −5.00000 | + | 5.19615i | −0.182089 | + | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | + | 3.46410i | 0.0727393 | + | 0.125988i | ||||
\(757\) | 19.0526 | − | 11.0000i | 0.692477 | − | 0.399802i | −0.112062 | − | 0.993701i | \(-0.535746\pi\) |
0.804539 | + | 0.593899i | \(0.202412\pi\) | |||||||
\(758\) | −8.66025 | − | 5.00000i | −0.314555 | − | 0.181608i | ||||
\(759\) | 35.0000 | 1.27042 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.00000 | − | 13.8564i | 0.290000 | − | 0.502294i | −0.683810 | − | 0.729661i | \(-0.739678\pi\) |
0.973809 | + | 0.227366i | \(0.0730114\pi\) | |||||||
\(762\) | − | 22.0000i | − | 0.796976i | ||||||
\(763\) | −58.8897 | − | 34.0000i | −2.13195 | − | 1.23088i | ||||
\(764\) | −11.5000 | − | 19.9186i | −0.416055 | − | 0.720629i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.0000 | −1.33686 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −13.0000 | − | 22.5167i | −0.468792 | − | 0.811972i | 0.530572 | − | 0.847640i | \(-0.321977\pi\) |
−0.999364 | + | 0.0356685i | \(0.988644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | − | 24.2487i | 0.504198 | − | 0.873296i | ||||
\(772\) | 3.00000i | 0.107972i | ||||||||
\(773\) | 12.1244 | + | 7.00000i | 0.436083 | + | 0.251773i | 0.701935 | − | 0.712241i | \(-0.252320\pi\) |
−0.265852 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(774\) | −2.00000 | + | 3.46410i | −0.0718885 | + | 0.124515i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.50000 | − | 11.2583i | 0.233336 | − | 0.404151i | ||||
\(777\) | 10.3923 | − | 6.00000i | 0.372822 | − | 0.215249i | ||||
\(778\) | 22.5167 | − | 13.0000i | 0.807261 | − | 0.466073i | ||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0000 | −0.536742 | ||||||||
\(782\) | −12.1244 | + | 7.00000i | −0.433566 | + | 0.250319i | ||||
\(783\) | 1.73205 | − | 1.00000i | 0.0618984 | − | 0.0357371i | ||||
\(784\) | 4.50000 | − | 7.79423i | 0.160714 | − | 0.278365i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.0000 | + | 17.3205i | −0.356688 | + | 0.617802i | ||||
\(787\) | −32.9090 | − | 19.0000i | −1.17308 | − | 0.677277i | −0.218675 | − | 0.975798i | \(-0.570173\pi\) |
−0.954403 | + | 0.298521i | \(0.903507\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | 4.50000 | − | 7.79423i | 0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.00000 | + | 13.8564i | 0.284447 | + | 0.492677i | ||||
\(792\) | 5.00000i | 0.177667i | ||||||||
\(793\) | −28.5788 | − | 27.5000i | −1.01486 | − | 0.976554i | ||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0000 | − | 20.7846i | −0.425329 | − | 0.736691i | ||||
\(797\) | −10.3923 | − | 6.00000i | −0.368114 | − | 0.212531i | 0.304520 | − | 0.952506i | \(-0.401504\pi\) |
−0.672634 | + | 0.739975i | \(0.734837\pi\) | |||||||
\(798\) | 8.00000i | 0.283197i | ||||||||
\(799\) | 12.0000 | − | 20.7846i | 0.424529 | − | 0.735307i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | 15.5885 | + | 9.00000i | 0.550448 | + | 0.317801i | ||||
\(803\) | 38.9711 | − | 22.5000i | 1.37526 | − | 0.794008i | ||||
\(804\) | −2.00000 | − | 3.46410i | −0.0705346 | − | 0.122169i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | − | 6.92820i | −0.0704470 | − | 0.244036i | ||||
\(807\) | 4.00000i | 0.140807i | ||||||||
\(808\) | 6.92820 | − | 4.00000i | 0.243733 | − | 0.140720i | ||||
\(809\) | −3.00000 | − | 5.19615i | −0.105474 | − | 0.182687i | 0.808458 | − | 0.588555i | \(-0.200303\pi\) |
−0.913932 | + | 0.405868i | \(0.866969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0000 | 1.33436 | 0.667180 | − | 0.744896i | \(-0.267501\pi\) | ||||
0.667180 | + | 0.744896i | \(0.267501\pi\) | |||||||
\(812\) | −6.92820 | − | 4.00000i | −0.243132 | − | 0.140372i | ||||
\(813\) | −1.73205 | − | 1.00000i | −0.0607457 | − | 0.0350715i | ||||
\(814\) | 15.0000 | 0.525750 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.00000 | − | 1.73205i | −0.0350070 | − | 0.0606339i | ||||
\(817\) | −6.92820 | + | 4.00000i | −0.242387 | + | 0.139942i | ||||
\(818\) | − | 30.0000i | − | 1.04893i | ||||||
\(819\) | 4.00000 | + | 13.8564i | 0.139771 | + | 0.484182i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | − | 25.9808i | −0.523504 | − | 0.906735i | −0.999626 | − | 0.0273557i | \(-0.991291\pi\) |
0.476122 | − | 0.879379i | \(-0.342042\pi\) | |||||||
\(822\) | −6.92820 | + | 4.00000i | −0.241649 | + | 0.139516i | ||||
\(823\) | 24.2487 | + | 14.0000i | 0.845257 | + | 0.488009i | 0.859048 | − | 0.511896i | \(-0.171057\pi\) |
−0.0137907 | + | 0.999905i | \(0.504390\pi\) | |||||||
\(824\) | 16.0000 | 0.557386 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.0000i | 1.49526i | 0.664117 | + | 0.747628i | \(0.268807\pi\) | ||||
−0.664117 | + | 0.747628i | \(0.731193\pi\) | |||||||
\(828\) | −6.06218 | − | 3.50000i | −0.210675 | − | 0.121633i | ||||
\(829\) | −23.0000 | − | 39.8372i | −0.798823 | − | 1.38360i | −0.920383 | − | 0.391018i | \(-0.872123\pi\) |
0.121560 | − | 0.992584i | \(-0.461210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.0000 | −1.07538 | ||||||||
\(832\) | −0.866025 | + | 3.50000i | −0.0300240 | + | 0.121341i | ||||
\(833\) | 18.0000i | 0.623663i | ||||||||
\(834\) | −2.00000 | − | 3.46410i | −0.0692543 | − | 0.119952i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.00000 | + | 8.66025i | −0.172929 | + | 0.299521i | ||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | −4.33013 | − | 2.50000i | −0.149582 | − | 0.0863611i | ||||
\(839\) | 4.50000 | − | 7.79423i | 0.155357 | − | 0.269087i | −0.777832 | − | 0.628473i | \(-0.783680\pi\) |
0.933189 | + | 0.359386i | \(0.117014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | −19.9186 | + | 11.5000i | −0.686440 | + | 0.396316i | ||||
\(843\) | 22.5167 | − | 13.0000i | 0.775515 | − | 0.447744i | ||||
\(844\) | 16.0000 | 0.550743 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 48.4974 | − | 28.0000i | 1.66639 | − | 0.962091i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | + | 24.2487i | −0.480479 | + | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5000 | + | 18.1865i | −0.359935 | + | 0.623426i | ||||
\(852\) | 2.59808 | + | 1.50000i | 0.0890086 | + | 0.0513892i | ||||
\(853\) | 22.0000i | 0.753266i | 0.926363 | + | 0.376633i | \(0.122918\pi\) | ||||
−0.926363 | + | 0.376633i | \(0.877082\pi\) | |||||||
\(854\) | 22.0000 | − | 38.1051i | 0.752825 | − | 1.30393i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | − | 6.92820i | −0.136717 | − | 0.236801i | ||||
\(857\) | − | 22.0000i | − | 0.751506i | −0.926720 | − | 0.375753i | \(-0.877384\pi\) | ||
0.926720 | − | 0.375753i | \(-0.122616\pi\) | |||||||
\(858\) | −4.33013 | + | 17.5000i | −0.147828 | + | 0.597440i | ||||
\(859\) | 26.0000 | 0.887109 | 0.443554 | − | 0.896248i | \(-0.353717\pi\) | ||||
0.443554 | + | 0.896248i | \(0.353717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | + | 34.6410i | 0.681598 | + | 1.18056i | ||||
\(862\) | −25.1147 | − | 14.5000i | −0.855411 | − | 0.493872i | ||||
\(863\) | − | 45.0000i | − | 1.53182i | −0.642949 | − | 0.765909i | \(-0.722289\pi\) | ||
0.642949 | − | 0.765909i | \(-0.277711\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.0000 | −0.645646 | ||||||||
\(867\) | −11.2583 | − | 6.50000i | −0.382353 | − | 0.220752i | ||||
\(868\) | 6.92820 | − | 4.00000i | 0.235159 | − | 0.135769i | ||||
\(869\) | 35.0000 | + | 60.6218i | 1.18729 | + | 2.05645i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | − | 13.8564i | −0.135535 | − | 0.469506i | ||||
\(872\) | 17.0000i | 0.575693i | ||||||||
\(873\) | −11.2583 | + | 6.50000i | −0.381037 | + | 0.219992i | ||||
\(874\) | −7.00000 | − | 12.1244i | −0.236779 | − | 0.410112i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.00000 | −0.304082 | ||||||||
\(877\) | 26.8468 | + | 15.5000i | 0.906552 | + | 0.523398i | 0.879320 | − | 0.476231i | \(-0.157998\pi\) |
0.0272316 | + | 0.999629i | \(0.491331\pi\) | |||||||
\(878\) | −6.92820 | − | 4.00000i | −0.233816 | − | 0.134993i | ||||
\(879\) | 24.0000 | 0.809500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | − | 31.1769i | −0.606435 | − | 1.05038i | −0.991823 | − | 0.127622i | \(-0.959266\pi\) |
0.385387 | − | 0.922755i | \(-0.374068\pi\) | |||||||
\(882\) | −7.79423 | + | 4.50000i | −0.262445 | + | 0.151523i | ||||
\(883\) | 40.0000i | 1.34611i | 0.739594 | + | 0.673054i | \(0.235018\pi\) | ||||
−0.739594 | + | 0.673054i | \(0.764982\pi\) | |||||||
\(884\) | −2.00000 | − | 6.92820i | −0.0672673 | − | 0.233021i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.5000 | − | 21.6506i | −0.419946 | − | 0.727367i | ||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | −2.59808 | − | 1.50000i | −0.0871857 | − | 0.0503367i | ||||
\(889\) | 88.0000 | 2.95143 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | 20.7846 | + | 12.0000i | 0.695530 | + | 0.401565i | ||||
\(894\) | −5.00000 | − | 8.66025i | −0.167225 | − | 0.289642i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.00000 | −0.133631 | ||||||||
\(897\) | −18.1865 | − | 17.5000i | −0.607231 | − | 0.584308i | ||||
\(898\) | − | 6.00000i | − | 0.200223i | ||||||
\(899\) | −2.00000 | − | 3.46410i | −0.0667037 | − | 0.115534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 50.0000i | 1.66482i | ||||||||
\(903\) | −13.8564 | − | 8.00000i | −0.461112 | − | 0.266223i | ||||
\(904\) | 2.00000 | − | 3.46410i | 0.0665190 | − | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.00000 | − | 8.66025i | 0.166114 | − | 0.287718i | ||||
\(907\) | 34.6410 | − | 20.0000i | 1.15024 | − | 0.664089i | 0.201291 | − | 0.979531i | \(-0.435486\pi\) |
0.948945 | + | 0.315442i | \(0.102153\pi\) | |||||||
\(908\) | 7.79423 | − | 4.50000i | 0.258661 | − | 0.149338i | ||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.0000 | 0.894550 | 0.447275 | − | 0.894397i | \(-0.352395\pi\) | ||||
0.447275 | + | 0.894397i | \(0.352395\pi\) | |||||||
\(912\) | 1.73205 | − | 1.00000i | 0.0573539 | − | 0.0331133i | ||||
\(913\) | 12.9904 | − | 7.50000i | 0.429919 | − | 0.248214i | ||||
\(914\) | 15.5000 | − | 26.8468i | 0.512694 | − | 0.888013i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.50000 | + | 16.4545i | −0.313889 | + | 0.543671i | ||||
\(917\) | −69.2820 | − | 40.0000i | −2.28789 | − | 1.32092i | ||||
\(918\) | 2.00000i | 0.0660098i | ||||||||
\(919\) | −5.00000 | + | 8.66025i | −0.164935 | + | 0.285675i | −0.936632 | − | 0.350315i | \(-0.886075\pi\) |
0.771697 | + | 0.635990i | \(0.219408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0000 | + | 20.7846i | 0.395413 | + | 0.684876i | ||||
\(922\) | − | 42.0000i | − | 1.38320i | ||||||
\(923\) | 7.79423 | + | 7.50000i | 0.256550 | + | 0.246866i | ||||
\(924\) | −20.0000 | −0.657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19.0000 | + | 32.9090i | 0.624379 | + | 1.08146i | ||||
\(927\) | −13.8564 | − | 8.00000i | −0.455104 | − | 0.262754i | ||||
\(928\) | 2.00000i | 0.0656532i | ||||||||
\(929\) | −8.00000 | + | 13.8564i | −0.262471 | + | 0.454614i | −0.966898 | − | 0.255163i | \(-0.917871\pi\) |
0.704427 | + | 0.709777i | \(0.251204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 6.92820 | + | 4.00000i | 0.226941 | + | 0.131024i | ||||
\(933\) | −6.06218 | + | 3.50000i | −0.198467 | + | 0.114585i | ||||
\(934\) | −4.50000 | − | 7.79423i | −0.147244 | − | 0.255035i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | 43.0000i | 1.40475i | 0.711808 | + | 0.702374i | \(0.247877\pi\) | ||||
−0.711808 | + | 0.702374i | \(0.752123\pi\) | |||||||
\(938\) | 13.8564 | − | 8.00000i | 0.452428 | − | 0.261209i | ||||
\(939\) | 0.500000 | + | 0.866025i | 0.0163169 | + | 0.0282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.0000 | 1.30396 | 0.651981 | − | 0.758235i | \(-0.273938\pi\) | ||||
0.651981 | + | 0.758235i | \(0.273938\pi\) | |||||||
\(942\) | −14.7224 | − | 8.50000i | −0.479683 | − | 0.276945i | ||||
\(943\) | −60.6218 | − | 35.0000i | −1.97412 | − | 1.13976i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | − | 17.3205i | −0.325128 | − | 0.563138i | ||||
\(947\) | 9.52628 | − | 5.50000i | 0.309562 | − | 0.178726i | −0.337168 | − | 0.941444i | \(-0.609469\pi\) |
0.646731 | + | 0.762718i | \(0.276136\pi\) | |||||||
\(948\) | − | 14.0000i | − | 0.454699i | ||||||
\(949\) | −31.5000 | − | 7.79423i | −1.02253 | − | 0.253011i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.0000 | + | 24.2487i | 0.453981 | + | 0.786318i | ||||
\(952\) | 6.92820 | − | 4.00000i | 0.224544 | − | 0.129641i | ||||
\(953\) | −51.9615 | − | 30.0000i | −1.68320 | − | 0.971795i | −0.959512 | − | 0.281666i | \(-0.909113\pi\) |
−0.723686 | − | 0.690129i | \(-0.757554\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.5000 | − | 19.9186i | 0.371937 | − | 0.644213i | ||||
\(957\) | 10.0000i | 0.323254i | ||||||||
\(958\) | 20.7846 | + | 12.0000i | 0.671520 | + | 0.387702i | ||||
\(959\) | −16.0000 | − | 27.7128i | −0.516667 | − | 0.894893i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −7.79423 | − | 7.50000i | −0.251296 | − | 0.241810i | ||||
\(963\) | 8.00000i | 0.257796i | ||||||||
\(964\) | 7.00000 | + | 12.1244i | 0.225455 | + | 0.390499i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.0000 | − | 24.2487i | 0.450443 | − | 0.780189i | ||||
\(967\) | 14.0000i | 0.450210i | 0.974335 | + | 0.225105i | \(0.0722725\pi\) | ||||
−0.974335 | + | 0.225105i | \(0.927728\pi\) | |||||||
\(968\) | −12.1244 | − | 7.00000i | −0.389692 | − | 0.224989i | ||||
\(969\) | −2.00000 | + | 3.46410i | −0.0642493 | + | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | + | 10.3923i | −0.192549 | + | 0.333505i | −0.946094 | − | 0.323891i | \(-0.895009\pi\) |
0.753545 | + | 0.657396i | \(0.228342\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 13.8564 | − | 8.00000i | 0.444216 | − | 0.256468i | ||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0000 | −0.352101 | ||||||||
\(977\) | 31.1769 | − | 18.0000i | 0.997438 | − | 0.575871i | 0.0899487 | − | 0.995946i | \(-0.471330\pi\) |
0.907489 | + | 0.420075i | \(0.137996\pi\) | |||||||
\(978\) | −5.19615 | + | 3.00000i | −0.166155 | + | 0.0959294i | ||||
\(979\) | 25.0000 | − | 43.3013i | 0.799003 | − | 1.38391i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.50000 | − | 14.7224i | 0.271384 | − | 0.470051i | ||||
\(982\) | 4.33013 | + | 2.50000i | 0.138180 | + | 0.0797782i | ||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 5.00000 | − | 8.66025i | 0.159394 | − | 0.276079i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.00000 | − | 3.46410i | −0.0636930 | − | 0.110319i | ||||
\(987\) | 48.0000i | 1.52786i | ||||||||
\(988\) | 6.92820 | − | 2.00000i | 0.220416 | − | 0.0636285i | ||||
\(989\) | 28.0000 | 0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.0000 | + | 38.1051i | 0.698853 | + | 1.21045i | 0.968864 | + | 0.247592i | \(0.0796392\pi\) |
−0.270011 | + | 0.962857i | \(0.587027\pi\) | |||||||
\(992\) | −1.73205 | − | 1.00000i | −0.0549927 | − | 0.0317500i | ||||
\(993\) | − | 10.0000i | − | 0.317340i | ||||||
\(994\) | −6.00000 | + | 10.3923i | −0.190308 | + | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.00000 | −0.0950586 | ||||||||
\(997\) | 1.73205 | + | 1.00000i | 0.0548546 | + | 0.0316703i | 0.527176 | − | 0.849756i | \(-0.323251\pi\) |
−0.472322 | + | 0.881426i | \(0.656584\pi\) | |||||||
\(998\) | 8.66025 | − | 5.00000i | 0.274136 | − | 0.158272i | ||||
\(999\) | 1.50000 | + | 2.59808i | 0.0474579 | + | 0.0821995i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1950.2.z.f.1849.1 | 4 | ||
5.2 | odd | 4 | 1950.2.i.h.601.1 | yes | 2 | ||
5.3 | odd | 4 | 1950.2.i.u.601.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1950.2.z.f.1849.2 | 4 | ||
13.9 | even | 3 | inner | 1950.2.z.f.1699.2 | 4 | ||
65.9 | even | 6 | inner | 1950.2.z.f.1699.1 | 4 | ||
65.22 | odd | 12 | 1950.2.i.h.451.1 | ✓ | 2 | ||
65.48 | odd | 12 | 1950.2.i.u.451.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.h.451.1 | ✓ | 2 | 65.22 | odd | 12 | ||
1950.2.i.h.601.1 | yes | 2 | 5.2 | odd | 4 | ||
1950.2.i.u.451.1 | yes | 2 | 65.48 | odd | 12 | ||
1950.2.i.u.601.1 | yes | 2 | 5.3 | odd | 4 | ||
1950.2.z.f.1699.1 | 4 | 65.9 | even | 6 | inner | ||
1950.2.z.f.1699.2 | 4 | 13.9 | even | 3 | inner | ||
1950.2.z.f.1849.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.z.f.1849.2 | 4 | 5.4 | even | 2 | inner |