Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(45,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.45 |
Dual form | 418.2.e.d.353.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 1.00000 | − | 1.73205i | 0.408248 | − | 0.707107i | ||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | −1.00000 | − | 1.73205i | −0.267261 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.50000 | + | 2.59808i | −0.802955 | + | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 3.46410i | 0.436436 | + | 0.755929i | ||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 1.00000 | + | 1.73205i | 0.204124 | + | 0.353553i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −1.00000 | + | 1.73205i | −0.188982 | + | 0.327327i | ||||
\(29\) | −4.50000 | + | 7.79423i | −0.835629 | + | 1.44735i | 0.0578882 | + | 0.998323i | \(0.481563\pi\) |
−0.893517 | + | 0.449029i | \(0.851770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.00000 | + | 1.73205i | 0.174078 | + | 0.301511i | ||||
\(34\) | 3.00000 | − | 5.19615i | 0.514496 | − | 0.891133i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −10.0000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 4.00000 | + | 1.73205i | 0.648886 | + | 0.280976i | ||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | 2.00000 | − | 3.46410i | 0.308607 | − | 0.534522i | ||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 1.00000 | − | 1.73205i | 0.144338 | − | 0.250000i | ||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | −6.00000 | + | 10.3923i | −0.840168 | + | 1.45521i | ||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | −2.00000 | − | 3.46410i | −0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | −8.00000 | − | 3.46410i | −1.05963 | − | 0.458831i | ||||
\(58\) | 9.00000 | 1.18176 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | −4.00000 | − | 6.92820i | −0.508001 | − | 0.879883i | ||||
\(63\) | −1.00000 | + | 1.73205i | −0.125988 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | 5.00000 | − | 8.66025i | 0.610847 | − | 1.05802i | −0.380251 | − | 0.924883i | \(-0.624162\pi\) |
0.991098 | − | 0.133135i | \(-0.0425044\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.50000 | − | 7.79423i | −0.534052 | − | 0.925005i | −0.999209 | − | 0.0397765i | \(-0.987335\pi\) |
0.465157 | − | 0.885228i | \(-0.345998\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | + | 3.46410i | 0.234082 | + | 0.405442i | 0.959006 | − | 0.283387i | \(-0.0914581\pi\) |
−0.724923 | + | 0.688830i | \(0.758125\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.581238 | + | 1.00673i | ||||
\(75\) | 10.0000 | 1.15470 | ||||||||
\(76\) | −0.500000 | − | 4.33013i | −0.0573539 | − | 0.496700i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | −1.00000 | − | 1.73205i | −0.113228 | − | 0.196116i | ||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | −9.00000 | −0.987878 | −0.493939 | − | 0.869496i | \(-0.664443\pi\) | ||||
−0.493939 | + | 0.869496i | \(0.664443\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.50000 | + | 4.33013i | −0.269582 | + | 0.466930i | ||||
\(87\) | −18.0000 | −1.92980 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | − | 1.73205i | 0.104828 | − | 0.181568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | + | 13.8564i | 0.829561 | + | 1.43684i | ||||
\(94\) | −3.00000 | −0.309426 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.00000 | −0.204124 | ||||||||
\(97\) | 0.500000 | + | 0.866025i | 0.0507673 | + | 0.0879316i | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | 1.50000 | + | 2.59808i | 0.151523 | + | 0.262445i | ||||
\(99\) | −0.500000 | + | 0.866025i | −0.0502519 | + | 0.0870388i | ||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | 12.0000 | 1.18818 | ||||||||
\(103\) | −19.0000 | −1.87213 | −0.936063 | − | 0.351833i | \(-0.885559\pi\) | ||||
−0.936063 | + | 0.351833i | \(0.885559\pi\) | |||||||
\(104\) | 0.500000 | − | 0.866025i | 0.0490290 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −9.00000 | −0.870063 | −0.435031 | − | 0.900415i | \(-0.643263\pi\) | ||||
−0.435031 | + | 0.900415i | \(0.643263\pi\) | |||||||
\(108\) | −2.00000 | + | 3.46410i | −0.192450 | + | 0.333333i | ||||
\(109\) | −5.50000 | − | 9.52628i | −0.526804 | − | 0.912452i | −0.999512 | − | 0.0312328i | \(-0.990057\pi\) |
0.472708 | − | 0.881219i | \(-0.343277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | − | 17.3205i | −0.949158 | − | 1.64399i | ||||
\(112\) | −1.00000 | − | 1.73205i | −0.0944911 | − | 0.163663i | ||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | 1.00000 | + | 8.66025i | 0.0936586 | + | 0.811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.50000 | − | 7.79423i | −0.417815 | − | 0.723676i | ||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | −3.00000 | + | 5.19615i | −0.276172 | + | 0.478345i | ||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −13.0000 | −1.17696 | ||||||||
\(123\) | −6.00000 | + | 10.3923i | −0.541002 | + | 0.937043i | ||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | −1.00000 | + | 1.73205i | −0.0887357 | + | 0.153695i | −0.906977 | − | 0.421180i | \(-0.861616\pi\) |
0.818241 | + | 0.574875i | \(0.194949\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 5.00000 | − | 8.66025i | 0.440225 | − | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.50000 | + | 2.59808i | 0.131056 | + | 0.226995i | 0.924084 | − | 0.382190i | \(-0.124830\pi\) |
−0.793028 | + | 0.609185i | \(0.791497\pi\) | |||||||
\(132\) | −2.00000 | −0.174078 | ||||||||
\(133\) | −7.00000 | + | 5.19615i | −0.606977 | + | 0.450564i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | + | 5.19615i | 0.257248 | + | 0.445566i | ||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | −4.50000 | + | 7.79423i | −0.377632 | + | 0.654077i | ||||
\(143\) | 0.500000 | − | 0.866025i | 0.0418121 | − | 0.0724207i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | − | 3.46410i | 0.165521 | − | 0.286691i | ||||
\(147\) | −3.00000 | − | 5.19615i | −0.247436 | − | 0.428571i | ||||
\(148\) | 5.00000 | − | 8.66025i | 0.410997 | − | 0.711868i | ||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | −5.00000 | − | 8.66025i | −0.408248 | − | 0.707107i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | −3.50000 | + | 2.59808i | −0.283887 | + | 0.210732i | ||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | −1.00000 | − | 1.73205i | −0.0805823 | − | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | −4.00000 | + | 6.92820i | −0.318223 | + | 0.551178i | ||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.50000 | − | 9.52628i | 0.432121 | − | 0.748455i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | + | 7.79423i | 0.349268 | + | 0.604949i | ||||
\(167\) | −3.00000 | + | 5.19615i | −0.232147 | + | 0.402090i | −0.958440 | − | 0.285295i | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | 2.00000 | + | 3.46410i | 0.154303 | + | 0.267261i | ||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 4.33013i | −0.0382360 | − | 0.331133i | ||||
\(172\) | 5.00000 | 0.381246 | ||||||||
\(173\) | 9.00000 | + | 15.5885i | 0.684257 | + | 1.18517i | 0.973670 | + | 0.227964i | \(0.0732068\pi\) |
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(174\) | 9.00000 | + | 15.5885i | 0.682288 | + | 1.18176i | ||||
\(175\) | 5.00000 | − | 8.66025i | 0.377964 | − | 0.654654i | ||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | 6.00000 | − | 10.3923i | 0.450988 | − | 0.781133i | ||||
\(178\) | 15.0000 | 1.12430 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | − | 13.8564i | 0.594635 | − | 1.02994i | −0.398963 | − | 0.916967i | \(-0.630630\pi\) |
0.993598 | − | 0.112972i | \(-0.0360369\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | 26.0000 | 1.92198 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.00000 | − | 13.8564i | 0.586588 | − | 1.01600i | ||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 1.50000 | + | 2.59808i | 0.109399 | + | 0.189484i | ||||
\(189\) | 8.00000 | 0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 0.500000 | − | 0.866025i | 0.0358979 | − | 0.0621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50000 | − | 2.59808i | 0.107143 | − | 0.185577i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 9.50000 | − | 16.4545i | 0.673437 | − | 1.16643i | −0.303486 | − | 0.952836i | \(-0.598151\pi\) |
0.976923 | − | 0.213591i | \(-0.0685161\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | 20.0000 | 1.41069 | ||||||||
\(202\) | −3.00000 | −0.211079 | ||||||||
\(203\) | −9.00000 | + | 15.5885i | −0.631676 | + | 1.09410i | ||||
\(204\) | −6.00000 | − | 10.3923i | −0.420084 | − | 0.727607i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.50000 | + | 16.4545i | 0.661896 | + | 1.14644i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −3.50000 | + | 2.59808i | −0.242100 | + | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | − | 17.3205i | −0.688428 | − | 1.19239i | −0.972346 | − | 0.233544i | \(-0.924968\pi\) |
0.283918 | − | 0.958849i | \(-0.408366\pi\) | |||||||
\(212\) | 3.00000 | + | 5.19615i | 0.206041 | + | 0.356873i | ||||
\(213\) | 9.00000 | − | 15.5885i | 0.616670 | − | 1.06810i | ||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | −5.50000 | + | 9.52628i | −0.372507 | + | 0.645201i | ||||
\(219\) | −4.00000 | + | 6.92820i | −0.270295 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | −10.0000 | + | 17.3205i | −0.671156 | + | 1.16248i | ||||
\(223\) | 3.50000 | + | 6.06218i | 0.234377 | + | 0.405953i | 0.959092 | − | 0.283096i | \(-0.0913615\pi\) |
−0.724714 | + | 0.689050i | \(0.758028\pi\) | |||||||
\(224\) | −1.00000 | + | 1.73205i | −0.0668153 | + | 0.115728i | ||||
\(225\) | 2.50000 | + | 4.33013i | 0.166667 | + | 0.288675i | ||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 7.00000 | − | 5.19615i | 0.463586 | − | 0.344124i | ||||
\(229\) | 20.0000 | 1.32164 | 0.660819 | − | 0.750546i | \(-0.270209\pi\) | ||||
0.660819 | + | 0.750546i | \(0.270209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | + | 3.46410i | 0.131590 | + | 0.227921i | ||||
\(232\) | −4.50000 | + | 7.79423i | −0.295439 | + | 0.511716i | ||||
\(233\) | −6.00000 | − | 10.3923i | −0.393073 | − | 0.680823i | 0.599780 | − | 0.800165i | \(-0.295255\pi\) |
−0.992853 | + | 0.119342i | \(0.961921\pi\) | |||||||
\(234\) | 0.500000 | − | 0.866025i | 0.0326860 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 8.00000 | − | 13.8564i | 0.519656 | − | 0.900070i | ||||
\(238\) | 6.00000 | − | 10.3923i | 0.388922 | − | 0.673633i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | 6.50000 | + | 11.2583i | 0.416120 | + | 0.720741i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | 0.500000 | + | 4.33013i | 0.0318142 | + | 0.275519i | ||||
\(248\) | 8.00000 | 0.508001 | ||||||||
\(249\) | −9.00000 | − | 15.5885i | −0.570352 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000 | − | 15.5885i | 0.568075 | − | 0.983935i | −0.428681 | − | 0.903456i | \(-0.641022\pi\) |
0.996756 | − | 0.0804789i | \(-0.0256450\pi\) | |||||||
\(252\) | −1.00000 | − | 1.73205i | −0.0629941 | − | 0.109109i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.00000 | 0.125491 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.00000 | − | 15.5885i | 0.561405 | − | 0.972381i | −0.435970 | − | 0.899961i | \(-0.643595\pi\) |
0.997374 | − | 0.0724199i | \(-0.0230722\pi\) | |||||||
\(258\) | −10.0000 | −0.622573 | ||||||||
\(259\) | −20.0000 | −1.24274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.50000 | − | 7.79423i | −0.278543 | − | 0.482451i | ||||
\(262\) | 1.50000 | − | 2.59808i | 0.0926703 | − | 0.160510i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 1.00000 | + | 1.73205i | 0.0615457 | + | 0.106600i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 3.46410i | 0.490511 | + | 0.212398i | ||||
\(267\) | −30.0000 | −1.83597 | ||||||||
\(268\) | 5.00000 | + | 8.66025i | 0.305424 | + | 0.529009i | ||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | 3.00000 | − | 5.19615i | 0.181902 | − | 0.315063i | ||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | −9.00000 | −0.543710 | ||||||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.0000 | 1.02143 | 0.510716 | − | 0.859750i | \(-0.329381\pi\) | ||||
0.510716 | + | 0.859750i | \(0.329381\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | −4.00000 | + | 6.92820i | −0.239474 | + | 0.414781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | + | 10.3923i | −0.357930 | + | 0.619953i | −0.987615 | − | 0.156898i | \(-0.949851\pi\) |
0.629685 | + | 0.776851i | \(0.283184\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 9.00000 | 0.534052 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | 6.00000 | + | 10.3923i | 0.354169 | + | 0.613438i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | + | 1.73205i | −0.0586210 | + | 0.101535i | ||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | −3.00000 | + | 5.19615i | −0.174964 | + | 0.303046i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.0000 | −0.581238 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | −3.00000 | + | 5.19615i | −0.173785 | + | 0.301005i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.00000 | + | 8.66025i | −0.288675 | + | 0.500000i | ||||
\(301\) | −5.00000 | − | 8.66025i | −0.288195 | − | 0.499169i | ||||
\(302\) | −4.00000 | − | 6.92820i | −0.230174 | − | 0.398673i | ||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | 4.00000 | + | 1.73205i | 0.229416 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.00000 | + | 5.19615i | 0.171499 | + | 0.297044i | ||||
\(307\) | 3.50000 | + | 6.06218i | 0.199756 | + | 0.345987i | 0.948449 | − | 0.316929i | \(-0.102652\pi\) |
−0.748694 | + | 0.662916i | \(0.769319\pi\) | |||||||
\(308\) | −1.00000 | + | 1.73205i | −0.0569803 | + | 0.0986928i | ||||
\(309\) | −19.0000 | − | 32.9090i | −1.08087 | − | 1.87213i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | 2.00000 | 0.113228 | ||||||||
\(313\) | −8.50000 | + | 14.7224i | −0.480448 | + | 0.832161i | −0.999748 | − | 0.0224310i | \(-0.992859\pi\) |
0.519300 | + | 0.854592i | \(0.326193\pi\) | |||||||
\(314\) | −7.00000 | + | 12.1244i | −0.395033 | + | 0.684217i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −15.0000 | + | 25.9808i | −0.842484 | + | 1.45922i | 0.0453045 | + | 0.998973i | \(0.485574\pi\) |
−0.887788 | + | 0.460252i | \(0.847759\pi\) | |||||||
\(318\) | −6.00000 | − | 10.3923i | −0.336463 | − | 0.582772i | ||||
\(319\) | −4.50000 | + | 7.79423i | −0.251952 | + | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | − | 15.5885i | −0.502331 | − | 0.870063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0000 | − | 10.3923i | −1.33540 | − | 0.578243i | ||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | −2.50000 | − | 4.33013i | −0.138675 | − | 0.240192i | ||||
\(326\) | −1.00000 | − | 1.73205i | −0.0553849 | − | 0.0959294i | ||||
\(327\) | 11.0000 | − | 19.0526i | 0.608301 | − | 1.05361i | ||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | 3.00000 | − | 5.19615i | 0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | 5.00000 | − | 8.66025i | 0.273998 | − | 0.474579i | ||||
\(334\) | 6.00000 | 0.328305 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | − | 3.46410i | 0.109109 | − | 0.188982i | ||||
\(337\) | 17.0000 | + | 29.4449i | 0.926049 | + | 1.60396i | 0.789865 | + | 0.613280i | \(0.210150\pi\) |
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | −3.50000 | + | 2.59808i | −0.189258 | + | 0.140488i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −2.50000 | − | 4.33013i | −0.134791 | − | 0.233465i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.00000 | − | 15.5885i | 0.483843 | − | 0.838041i | ||||
\(347\) | 16.5000 | + | 28.5788i | 0.885766 | + | 1.53419i | 0.844833 | + | 0.535031i | \(0.179700\pi\) |
0.0409337 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(348\) | 9.00000 | − | 15.5885i | 0.482451 | − | 0.835629i | ||||
\(349\) | 5.00000 | 0.267644 | 0.133822 | − | 0.991005i | \(-0.457275\pi\) | ||||
0.133822 | + | 0.991005i | \(0.457275\pi\) | |||||||
\(350\) | −10.0000 | −0.534522 | ||||||||
\(351\) | 2.00000 | − | 3.46410i | 0.106752 | − | 0.184900i | ||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −21.0000 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.50000 | − | 12.9904i | −0.397499 | − | 0.688489i | ||||
\(357\) | −12.0000 | + | 20.7846i | −0.635107 | + | 1.10004i | ||||
\(358\) | 6.00000 | + | 10.3923i | 0.317110 | + | 0.549250i | ||||
\(359\) | 15.0000 | + | 25.9808i | 0.791670 | + | 1.37121i | 0.924932 | + | 0.380131i | \(0.124121\pi\) |
−0.133263 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | −16.0000 | −0.840941 | ||||||||
\(363\) | 1.00000 | + | 1.73205i | 0.0524864 | + | 0.0909091i | ||||
\(364\) | 1.00000 | + | 1.73205i | 0.0524142 | + | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.0000 | − | 22.5167i | −0.679521 | − | 1.17696i | ||||
\(367\) | 3.50000 | − | 6.06218i | 0.182699 | − | 0.316443i | −0.760100 | − | 0.649806i | \(-0.774850\pi\) |
0.942799 | + | 0.333363i | \(0.108183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | −16.0000 | −0.829561 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 3.00000 | − | 5.19615i | 0.155126 | − | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | 4.50000 | + | 7.79423i | 0.231762 | + | 0.401423i | ||||
\(378\) | −4.00000 | − | 6.92820i | −0.205738 | − | 0.356348i | ||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | −1.50000 | − | 2.59808i | −0.0767467 | − | 0.132929i | ||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 1.00000 | − | 1.73205i | 0.0510310 | − | 0.0883883i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | − | 13.8564i | 0.407189 | − | 0.705273i | ||||
\(387\) | 5.00000 | 0.254164 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 12.0000 | − | 20.7846i | 0.608424 | − | 1.05382i | −0.383076 | − | 0.923717i | \(-0.625135\pi\) |
0.991500 | − | 0.130105i | \(-0.0415314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | −3.00000 | + | 5.19615i | −0.151330 | + | 0.262111i | ||||
\(394\) | 7.50000 | + | 12.9904i | 0.377845 | + | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | −19.0000 | −0.952384 | ||||||||
\(399\) | −16.0000 | − | 6.92820i | −0.801002 | − | 0.346844i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | −10.0000 | − | 17.3205i | −0.498755 | − | 0.863868i | ||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0000 | 0.893325 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | −6.00000 | + | 10.3923i | −0.297044 | + | 0.514496i | ||||
\(409\) | 2.00000 | − | 3.46410i | 0.0988936 | − | 0.171289i | −0.812333 | − | 0.583193i | \(-0.801803\pi\) |
0.911227 | + | 0.411905i | \(0.135136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | 9.50000 | − | 16.4545i | 0.468031 | − | 0.810654i | ||||
\(413\) | −6.00000 | − | 10.3923i | −0.295241 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 8.00000 | 0.391762 | ||||||||
\(418\) | 4.00000 | + | 1.73205i | 0.195646 | + | 0.0847174i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | + | 24.2487i | 0.682318 | + | 1.18181i | 0.974272 | + | 0.225377i | \(0.0723615\pi\) |
−0.291953 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(422\) | −10.0000 | + | 17.3205i | −0.486792 | + | 0.843149i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | 30.0000 | 1.45521 | ||||||||
\(426\) | −18.0000 | −0.872103 | ||||||||
\(427\) | 13.0000 | − | 22.5167i | 0.629114 | − | 1.08966i | ||||
\(428\) | 4.50000 | − | 7.79423i | 0.217516 | − | 0.376748i | ||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000 | − | 31.1769i | 0.867029 | − | 1.50174i | 0.00201168 | − | 0.999998i | \(-0.499360\pi\) |
0.865018 | − | 0.501741i | \(-0.167307\pi\) | |||||||
\(432\) | −2.00000 | − | 3.46410i | −0.0962250 | − | 0.166667i | ||||
\(433\) | −5.50000 | + | 9.52628i | −0.264313 | + | 0.457804i | −0.967383 | − | 0.253317i | \(-0.918479\pi\) |
0.703070 | + | 0.711120i | \(0.251812\pi\) | |||||||
\(434\) | −8.00000 | − | 13.8564i | −0.384012 | − | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0000 | 0.526804 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 8.00000 | 0.382255 | ||||||||
\(439\) | −10.0000 | − | 17.3205i | −0.477274 | − | 0.826663i | 0.522387 | − | 0.852709i | \(-0.325042\pi\) |
−0.999661 | + | 0.0260459i | \(0.991708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | −3.00000 | − | 5.19615i | −0.142695 | − | 0.247156i | ||||
\(443\) | −12.0000 | + | 20.7846i | −0.570137 | + | 0.987507i | 0.426414 | + | 0.904528i | \(0.359777\pi\) |
−0.996551 | + | 0.0829786i | \(0.973557\pi\) | |||||||
\(444\) | 20.0000 | 0.949158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.50000 | − | 6.06218i | 0.165730 | − | 0.287052i | ||||
\(447\) | 6.00000 | − | 10.3923i | 0.283790 | − | 0.491539i | ||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 2.50000 | − | 4.33013i | 0.117851 | − | 0.204124i | ||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | −4.50000 | + | 7.79423i | −0.211662 | + | 0.366610i | ||||
\(453\) | 8.00000 | + | 13.8564i | 0.375873 | + | 0.651031i | ||||
\(454\) | 6.00000 | + | 10.3923i | 0.281594 | + | 0.487735i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.00000 | − | 3.46410i | −0.374634 | − | 0.162221i | ||||
\(457\) | −40.0000 | −1.87112 | −0.935561 | − | 0.353166i | \(-0.885105\pi\) | ||||
−0.935561 | + | 0.353166i | \(0.885105\pi\) | |||||||
\(458\) | −10.0000 | − | 17.3205i | −0.467269 | − | 0.809334i | ||||
\(459\) | 12.0000 | + | 20.7846i | 0.560112 | + | 0.970143i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.50000 | + | 2.59808i | 0.0698620 | + | 0.121004i | 0.898840 | − | 0.438276i | \(-0.144411\pi\) |
−0.828978 | + | 0.559281i | \(0.811077\pi\) | |||||||
\(462\) | 2.00000 | − | 3.46410i | 0.0930484 | − | 0.161165i | ||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | 9.00000 | 0.417815 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | + | 10.3923i | −0.277945 | + | 0.481414i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 10.0000 | − | 17.3205i | 0.461757 | − | 0.799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.0000 | − | 24.2487i | 0.645086 | − | 1.11732i | ||||
\(472\) | −3.00000 | − | 5.19615i | −0.138086 | − | 0.239172i | ||||
\(473\) | −2.50000 | − | 4.33013i | −0.114950 | − | 0.199099i | ||||
\(474\) | −16.0000 | −0.734904 | ||||||||
\(475\) | 2.50000 | + | 21.6506i | 0.114708 | + | 0.993399i | ||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 3.00000 | + | 5.19615i | 0.137361 | + | 0.237915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.0000 | − | 31.1769i | 0.822441 | − | 1.42451i | −0.0814184 | − | 0.996680i | \(-0.525945\pi\) |
0.903859 | − | 0.427830i | \(-0.140722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | + | 8.66025i | −0.227980 | + | 0.394874i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.0000 | 0.453609 | ||||||||
\(487\) | −7.00000 | −0.317200 | −0.158600 | − | 0.987343i | \(-0.550698\pi\) | ||||
−0.158600 | + | 0.987343i | \(0.550698\pi\) | |||||||
\(488\) | 6.50000 | − | 11.2583i | 0.294241 | − | 0.509641i | ||||
\(489\) | 2.00000 | + | 3.46410i | 0.0904431 | + | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | + | 10.3923i | 0.270776 | + | 0.468998i | 0.969061 | − | 0.246822i | \(-0.0793863\pi\) |
−0.698285 | + | 0.715820i | \(0.746053\pi\) | |||||||
\(492\) | −6.00000 | − | 10.3923i | −0.270501 | − | 0.468521i | ||||
\(493\) | −54.0000 | −2.43204 | ||||||||
\(494\) | 3.50000 | − | 2.59808i | 0.157472 | − | 0.116893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | − | 6.92820i | −0.179605 | − | 0.311086i | ||||
\(497\) | −9.00000 | − | 15.5885i | −0.403705 | − | 0.699238i | ||||
\(498\) | −9.00000 | + | 15.5885i | −0.403300 | + | 0.698535i | ||||
\(499\) | −13.0000 | − | 22.5167i | −0.581960 | − | 1.00798i | −0.995247 | − | 0.0973833i | \(-0.968953\pi\) |
0.413287 | − | 0.910601i | \(-0.364381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | −18.0000 | −0.803379 | ||||||||
\(503\) | 15.0000 | − | 25.9808i | 0.668817 | − | 1.15842i | −0.309418 | − | 0.950926i | \(-0.600134\pi\) |
0.978235 | − | 0.207499i | \(-0.0665323\pi\) | |||||||
\(504\) | −1.00000 | + | 1.73205i | −0.0445435 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0000 | + | 20.7846i | −0.532939 | + | 0.923077i | ||||
\(508\) | −1.00000 | − | 1.73205i | −0.0443678 | − | 0.0768473i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −14.0000 | + | 10.3923i | −0.618115 | + | 0.458831i | ||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.00000 | + | 8.66025i | 0.220113 | + | 0.381246i | ||||
\(517\) | 1.50000 | − | 2.59808i | 0.0659699 | − | 0.114263i | ||||
\(518\) | 10.0000 | + | 17.3205i | 0.439375 | + | 0.761019i | ||||
\(519\) | −18.0000 | + | 31.1769i | −0.790112 | + | 1.36851i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0000 | 1.70862 | 0.854311 | − | 0.519763i | \(-0.173980\pi\) | ||||
0.854311 | + | 0.519763i | \(0.173980\pi\) | |||||||
\(522\) | −4.50000 | + | 7.79423i | −0.196960 | + | 0.341144i | ||||
\(523\) | −17.5000 | + | 30.3109i | −0.765222 | + | 1.32540i | 0.174908 | + | 0.984585i | \(0.444037\pi\) |
−0.940129 | + | 0.340818i | \(0.889296\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 20.0000 | 0.872872 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | + | 41.5692i | 1.04546 | + | 1.81078i | ||||
\(528\) | 1.00000 | − | 1.73205i | 0.0435194 | − | 0.0753778i | ||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | −1.00000 | − | 8.66025i | −0.0433555 | − | 0.375470i | ||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | 15.0000 | + | 25.9808i | 0.649113 | + | 1.12430i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.00000 | − | 8.66025i | 0.215967 | − | 0.374066i | ||||
\(537\) | −12.0000 | − | 20.7846i | −0.517838 | − | 0.896922i | ||||
\(538\) | 9.00000 | − | 15.5885i | 0.388018 | − | 0.672066i | ||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0000 | − | 19.0526i | 0.472927 | − | 0.819133i | −0.526593 | − | 0.850118i | \(-0.676531\pi\) |
0.999520 | + | 0.0309841i | \(0.00986412\pi\) | |||||||
\(542\) | −1.00000 | + | 1.73205i | −0.0429537 | + | 0.0743980i | ||||
\(543\) | 32.0000 | 1.37325 | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | − | 3.46410i | −0.0855921 | − | 0.148250i | ||||
\(547\) | −14.5000 | + | 25.1147i | −0.619975 | + | 1.07383i | 0.369514 | + | 0.929225i | \(0.379524\pi\) |
−0.989490 | + | 0.144604i | \(0.953809\pi\) | |||||||
\(548\) | 4.50000 | + | 7.79423i | 0.192230 | + | 0.332953i | ||||
\(549\) | 6.50000 | + | 11.2583i | 0.277413 | + | 0.480494i | ||||
\(550\) | −5.00000 | −0.213201 | ||||||||
\(551\) | −4.50000 | − | 38.9711i | −0.191706 | − | 1.66023i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | − | 13.8564i | −0.340195 | − | 0.589234i | ||||
\(554\) | −8.50000 | − | 14.7224i | −0.361130 | − | 0.625496i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −10.5000 | + | 18.1865i | −0.444899 | + | 0.770588i | −0.998045 | − | 0.0624962i | \(-0.980094\pi\) |
0.553146 | + | 0.833084i | \(0.313427\pi\) | |||||||
\(558\) | 8.00000 | 0.338667 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | + | 10.3923i | −0.253320 | + | 0.438763i | ||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | −24.0000 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.00000 | − | 3.46410i | 0.0840663 | − | 0.145607i | ||||
\(567\) | 11.0000 | + | 19.0526i | 0.461957 | + | 0.800132i | ||||
\(568\) | −4.50000 | − | 7.79423i | −0.188816 | − | 0.327039i | ||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0000 | 0.962520 | 0.481260 | − | 0.876578i | \(-0.340179\pi\) | ||||
0.481260 | + | 0.876578i | \(0.340179\pi\) | |||||||
\(572\) | 0.500000 | + | 0.866025i | 0.0209061 | + | 0.0362103i | ||||
\(573\) | 3.00000 | + | 5.19615i | 0.125327 | + | 0.217072i | ||||
\(574\) | 6.00000 | − | 10.3923i | 0.250435 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −34.0000 | −1.41544 | −0.707719 | − | 0.706494i | \(-0.750276\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | 19.0000 | 0.790296 | ||||||||
\(579\) | −16.0000 | + | 27.7128i | −0.664937 | + | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 3.00000 | − | 5.19615i | 0.124247 | − | 0.215203i | ||||
\(584\) | 2.00000 | + | 3.46410i | 0.0827606 | + | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | 6.00000 | 0.247436 | ||||||||
\(589\) | −28.0000 | + | 20.7846i | −1.15372 | + | 0.856415i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.0000 | − | 25.9808i | −0.617018 | − | 1.06871i | ||||
\(592\) | 5.00000 | + | 8.66025i | 0.205499 | + | 0.355934i | ||||
\(593\) | 6.00000 | − | 10.3923i | 0.246390 | − | 0.426761i | −0.716131 | − | 0.697966i | \(-0.754089\pi\) |
0.962522 | + | 0.271205i | \(0.0874221\pi\) | |||||||
\(594\) | −2.00000 | − | 3.46410i | −0.0820610 | − | 0.142134i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 38.0000 | 1.55524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.50000 | − | 7.79423i | 0.183865 | − | 0.318464i | −0.759328 | − | 0.650708i | \(-0.774472\pi\) |
0.943193 | + | 0.332244i | \(0.107806\pi\) | |||||||
\(600\) | 10.0000 | 0.408248 | ||||||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | −5.00000 | + | 8.66025i | −0.203785 | + | 0.352966i | ||||
\(603\) | 5.00000 | + | 8.66025i | 0.203616 | + | 0.352673i | ||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | −0.500000 | − | 4.33013i | −0.0202777 | − | 0.175610i | ||||
\(609\) | −36.0000 | −1.45879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.50000 | − | 2.59808i | −0.0606835 | − | 0.105107i | ||||
\(612\) | 3.00000 | − | 5.19615i | 0.121268 | − | 0.210042i | ||||
\(613\) | 12.5000 | + | 21.6506i | 0.504870 | + | 0.874461i | 0.999984 | + | 0.00563283i | \(0.00179300\pi\) |
−0.495114 | + | 0.868828i | \(0.664874\pi\) | |||||||
\(614\) | 3.50000 | − | 6.06218i | 0.141249 | − | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −10.5000 | + | 18.1865i | −0.422714 | + | 0.732162i | −0.996204 | − | 0.0870504i | \(-0.972256\pi\) |
0.573490 | + | 0.819213i | \(0.305589\pi\) | |||||||
\(618\) | −19.0000 | + | 32.9090i | −0.764292 | + | 1.32379i | ||||
\(619\) | 38.0000 | 1.52735 | 0.763674 | − | 0.645601i | \(-0.223393\pi\) | ||||
0.763674 | + | 0.645601i | \(0.223393\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.50000 | + | 12.9904i | 0.300723 | + | 0.520867i | ||||
\(623\) | −15.0000 | + | 25.9808i | −0.600962 | + | 1.04090i | ||||
\(624\) | −1.00000 | − | 1.73205i | −0.0400320 | − | 0.0693375i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 17.0000 | 0.679457 | ||||||||
\(627\) | −8.00000 | − | 3.46410i | −0.319489 | − | 0.138343i | ||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | −30.0000 | − | 51.9615i | −1.19618 | − | 2.07184i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.50000 | − | 11.2583i | 0.258761 | − | 0.448187i | −0.707149 | − | 0.707064i | \(-0.750019\pi\) |
0.965910 | + | 0.258877i | \(0.0833525\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 20.0000 | − | 34.6410i | 0.794929 | − | 1.37686i | ||||
\(634\) | 30.0000 | 1.19145 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | + | 10.3923i | −0.237915 | + | 0.412082i | ||||
\(637\) | −1.50000 | + | 2.59808i | −0.0594322 | + | 0.102940i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | 9.00000 | 0.356034 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | + | 2.59808i | 0.0592464 | + | 0.102618i | 0.894127 | − | 0.447813i | \(-0.147797\pi\) |
−0.834881 | + | 0.550431i | \(0.814464\pi\) | |||||||
\(642\) | −9.00000 | + | 15.5885i | −0.355202 | + | 0.615227i | ||||
\(643\) | −13.0000 | − | 22.5167i | −0.512670 | − | 0.887970i | −0.999892 | − | 0.0146923i | \(-0.995323\pi\) |
0.487222 | − | 0.873278i | \(-0.338010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00000 | + | 25.9808i | 0.118033 | + | 1.02220i | ||||
\(647\) | 21.0000 | 0.825595 | 0.412798 | − | 0.910823i | \(-0.364552\pi\) | ||||
0.412798 | + | 0.910823i | \(0.364552\pi\) | |||||||
\(648\) | 5.50000 | + | 9.52628i | 0.216060 | + | 0.374228i | ||||
\(649\) | −3.00000 | − | 5.19615i | −0.117760 | − | 0.203967i | ||||
\(650\) | −2.50000 | + | 4.33013i | −0.0980581 | + | 0.169842i | ||||
\(651\) | 16.0000 | + | 27.7128i | 0.627089 | + | 1.08615i | ||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | 36.0000 | 1.40879 | 0.704394 | − | 0.709809i | \(-0.251219\pi\) | ||||
0.704394 | + | 0.709809i | \(0.251219\pi\) | |||||||
\(654\) | −22.0000 | −0.860268 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | 19.5000 | − | 33.7750i | 0.759612 | − | 1.31569i | −0.183436 | − | 0.983032i | \(-0.558722\pi\) |
0.943049 | − | 0.332655i | \(-0.107945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 14.0000 | + | 24.2487i | 0.544125 | + | 0.942453i | ||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | −9.00000 | −0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.0000 | −0.387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −3.00000 | − | 5.19615i | −0.116073 | − | 0.201045i | ||||
\(669\) | −7.00000 | + | 12.1244i | −0.270636 | + | 0.468755i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.50000 | − | 11.2583i | 0.250930 | − | 0.434623i | ||||
\(672\) | −4.00000 | −0.154303 | ||||||||
\(673\) | 38.0000 | 1.46479 | 0.732396 | − | 0.680879i | \(-0.238402\pi\) | ||||
0.732396 | + | 0.680879i | \(0.238402\pi\) | |||||||
\(674\) | 17.0000 | − | 29.4449i | 0.654816 | − | 1.13417i | ||||
\(675\) | 10.0000 | − | 17.3205i | 0.384900 | − | 0.666667i | ||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | 15.0000 | 0.576497 | 0.288248 | − | 0.957556i | \(-0.406927\pi\) | ||||
0.288248 | + | 0.957556i | \(0.406927\pi\) | |||||||
\(678\) | 9.00000 | − | 15.5885i | 0.345643 | − | 0.598671i | ||||
\(679\) | 1.00000 | + | 1.73205i | 0.0383765 | + | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | − | 20.7846i | −0.459841 | − | 0.796468i | ||||
\(682\) | −4.00000 | − | 6.92820i | −0.153168 | − | 0.265295i | ||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 4.00000 | + | 1.73205i | 0.152944 | + | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0000 | + | 17.3205i | 0.381802 | + | 0.661300i | ||||
\(687\) | 20.0000 | + | 34.6410i | 0.763048 | + | 1.32164i | ||||
\(688\) | −2.50000 | + | 4.33013i | −0.0953116 | + | 0.165085i | ||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | −1.00000 | + | 1.73205i | −0.0379869 | + | 0.0657952i | ||||
\(694\) | 16.5000 | − | 28.5788i | 0.626331 | − | 1.08484i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.0000 | −0.682288 | ||||||||
\(697\) | −18.0000 | + | 31.1769i | −0.681799 | + | 1.18091i | ||||
\(698\) | −2.50000 | − | 4.33013i | −0.0946264 | − | 0.163898i | ||||
\(699\) | 12.0000 | − | 20.7846i | 0.453882 | − | 0.786146i | ||||
\(700\) | 5.00000 | + | 8.66025i | 0.188982 | + | 0.327327i | ||||
\(701\) | −7.50000 | − | 12.9904i | −0.283271 | − | 0.490640i | 0.688917 | − | 0.724840i | \(-0.258086\pi\) |
−0.972188 | + | 0.234200i | \(0.924753\pi\) | |||||||
\(702\) | −4.00000 | −0.150970 | ||||||||
\(703\) | 35.0000 | − | 25.9808i | 1.32005 | − | 0.979883i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.5000 | + | 18.1865i | 0.395173 | + | 0.684459i | ||||
\(707\) | 3.00000 | − | 5.19615i | 0.112827 | − | 0.195421i | ||||
\(708\) | 6.00000 | + | 10.3923i | 0.225494 | + | 0.390567i | ||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | −7.50000 | + | 12.9904i | −0.281074 | + | 0.486835i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 24.0000 | 0.898177 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00000 | − | 10.3923i | 0.224231 | − | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.0000 | − | 25.9808i | 0.559795 | − | 0.969593i | ||||
\(719\) | 7.50000 | + | 12.9904i | 0.279703 | + | 0.484459i | 0.971311 | − | 0.237814i | \(-0.0764307\pi\) |
−0.691608 | + | 0.722273i | \(0.743097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.0000 | −1.41519 | ||||||||
\(722\) | −18.5000 | + | 4.33013i | −0.688499 | + | 0.161151i | ||||
\(723\) | −52.0000 | −1.93390 | ||||||||
\(724\) | 8.00000 | + | 13.8564i | 0.297318 | + | 0.514969i | ||||
\(725\) | 22.5000 | + | 38.9711i | 0.835629 | + | 1.44735i | ||||
\(726\) | 1.00000 | − | 1.73205i | 0.0371135 | − | 0.0642824i | ||||
\(727\) | 6.50000 | + | 11.2583i | 0.241072 | + | 0.417548i | 0.961020 | − | 0.276479i | \(-0.0891678\pi\) |
−0.719948 | + | 0.694028i | \(0.755834\pi\) | |||||||
\(728\) | 1.00000 | − | 1.73205i | 0.0370625 | − | 0.0641941i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | − | 25.9808i | 0.554795 | − | 0.960933i | ||||
\(732\) | −13.0000 | + | 22.5167i | −0.480494 | + | 0.832240i | ||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | −7.00000 | −0.258375 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.00000 | − | 8.66025i | 0.184177 | − | 0.319005i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | −11.5000 | − | 19.9186i | −0.423034 | − | 0.732717i | 0.573200 | − | 0.819415i | \(-0.305702\pi\) |
−0.996235 | + | 0.0866983i | \(0.972368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00000 | + | 5.19615i | −0.257151 | + | 0.190885i | ||||
\(742\) | −12.0000 | −0.440534 | ||||||||
\(743\) | −9.00000 | − | 15.5885i | −0.330178 | − | 0.571885i | 0.652369 | − | 0.757902i | \(-0.273775\pi\) |
−0.982547 | + | 0.186017i | \(0.940442\pi\) | |||||||
\(744\) | 8.00000 | + | 13.8564i | 0.293294 | + | 0.508001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.0000 | + | 19.0526i | 0.402739 | + | 0.697564i | ||||
\(747\) | 4.50000 | − | 7.79423i | 0.164646 | − | 0.285176i | ||||
\(748\) | −6.00000 | −0.219382 | ||||||||
\(749\) | −18.0000 | −0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5000 | + | 19.9186i | −0.419641 | + | 0.726839i | −0.995903 | − | 0.0904254i | \(-0.971177\pi\) |
0.576262 | + | 0.817265i | \(0.304511\pi\) | |||||||
\(752\) | −3.00000 | −0.109399 | ||||||||
\(753\) | 36.0000 | 1.31191 | ||||||||
\(754\) | 4.50000 | − | 7.79423i | 0.163880 | − | 0.283849i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | + | 6.92820i | −0.145479 | + | 0.251976i | ||||
\(757\) | −19.0000 | − | 32.9090i | −0.690567 | − | 1.19610i | −0.971652 | − | 0.236414i | \(-0.924028\pi\) |
0.281086 | − | 0.959683i | \(-0.409305\pi\) | |||||||
\(758\) | −1.00000 | − | 1.73205i | −0.0363216 | − | 0.0629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(762\) | 2.00000 | + | 3.46410i | 0.0724524 | + | 0.125491i | ||||
\(763\) | −11.0000 | − | 19.0526i | −0.398227 | − | 0.689749i | ||||
\(764\) | −1.50000 | + | 2.59808i | −0.0542681 | + | 0.0939951i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | −2.00000 | −0.0721688 | ||||||||
\(769\) | 11.0000 | − | 19.0526i | 0.396670 | − | 0.687053i | −0.596643 | − | 0.802507i | \(-0.703499\pi\) |
0.993313 | + | 0.115454i | \(0.0368323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | 1.29651 | ||||||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | 27.0000 | − | 46.7654i | 0.971123 | − | 1.68203i | 0.278944 | − | 0.960307i | \(-0.410016\pi\) |
0.692179 | − | 0.721726i | \(-0.256651\pi\) | |||||||
\(774\) | −2.50000 | − | 4.33013i | −0.0898606 | − | 0.155643i | ||||
\(775\) | 20.0000 | − | 34.6410i | 0.718421 | − | 1.24434i | ||||
\(776\) | 0.500000 | + | 0.866025i | 0.0179490 | + | 0.0310885i | ||||
\(777\) | −20.0000 | − | 34.6410i | −0.717496 | − | 1.24274i | ||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | −24.0000 | − | 10.3923i | −0.859889 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.50000 | − | 7.79423i | −0.161023 | − | 0.278899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.0000 | + | 31.1769i | −0.643268 | + | 1.11417i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.00000 | 0.214013 | ||||||||
\(787\) | 35.0000 | 1.24762 | 0.623808 | − | 0.781578i | \(-0.285585\pi\) | ||||
0.623808 | + | 0.781578i | \(0.285585\pi\) | |||||||
\(788\) | 7.50000 | − | 12.9904i | 0.267176 | − | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | −0.500000 | + | 0.866025i | −0.0177667 | + | 0.0307729i | ||||
\(793\) | −6.50000 | − | 11.2583i | −0.230822 | − | 0.399795i | ||||
\(794\) | −1.00000 | + | 1.73205i | −0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.50000 | + | 16.4545i | 0.336719 | + | 0.583214i | ||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | 2.00000 | + | 17.3205i | 0.0707992 | + | 0.613139i | ||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 2.50000 | + | 4.33013i | 0.0883883 | + | 0.153093i | ||||
\(801\) | −7.50000 | − | 12.9904i | −0.264999 | − | 0.458993i | ||||
\(802\) | 9.00000 | − | 15.5885i | 0.317801 | − | 0.550448i | ||||
\(803\) | 2.00000 | + | 3.46410i | 0.0705785 | + | 0.122245i | ||||
\(804\) | −10.0000 | + | 17.3205i | −0.352673 | + | 0.610847i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.00000 | −0.281788 | ||||||||
\(807\) | −18.0000 | + | 31.1769i | −0.633630 | + | 1.09748i | ||||
\(808\) | 1.50000 | − | 2.59808i | 0.0527698 | − | 0.0914000i | ||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.50000 | − | 6.06218i | 0.122902 | − | 0.212872i | −0.798009 | − | 0.602645i | \(-0.794113\pi\) |
0.920911 | + | 0.389774i | \(0.127447\pi\) | |||||||
\(812\) | −9.00000 | − | 15.5885i | −0.315838 | − | 0.547048i | ||||
\(813\) | 2.00000 | − | 3.46410i | 0.0701431 | − | 0.121491i | ||||
\(814\) | 5.00000 | + | 8.66025i | 0.175250 | + | 0.303542i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.0000 | 0.420084 | ||||||||
\(817\) | 20.0000 | + | 8.66025i | 0.699711 | + | 0.302984i | ||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 1.00000 | + | 1.73205i | 0.0349428 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | + | 5.19615i | −0.104701 | + | 0.181347i | −0.913616 | − | 0.406578i | \(-0.866722\pi\) |
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(822\) | −9.00000 | − | 15.5885i | −0.313911 | − | 0.543710i | ||||
\(823\) | 6.50000 | − | 11.2583i | 0.226576 | − | 0.392441i | −0.730215 | − | 0.683217i | \(-0.760580\pi\) |
0.956791 | + | 0.290776i | \(0.0939136\pi\) | |||||||
\(824\) | −19.0000 | −0.661896 | ||||||||
\(825\) | 10.0000 | 0.348155 | ||||||||
\(826\) | −6.00000 | + | 10.3923i | −0.208767 | + | 0.361595i | ||||
\(827\) | −22.5000 | + | 38.9711i | −0.782402 | + | 1.35516i | 0.148137 | + | 0.988967i | \(0.452672\pi\) |
−0.930539 | + | 0.366193i | \(0.880661\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.0000 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.0000 | + | 29.4449i | 0.589723 | + | 1.02143i | ||||
\(832\) | 0.500000 | − | 0.866025i | 0.0173344 | − | 0.0300240i | ||||
\(833\) | −9.00000 | − | 15.5885i | −0.311832 | − | 0.540108i | ||||
\(834\) | −4.00000 | − | 6.92820i | −0.138509 | − | 0.239904i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.500000 | − | 4.33013i | −0.0172929 | − | 0.149761i | ||||
\(837\) | 32.0000 | 1.10608 | ||||||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | −4.50000 | − | 7.79423i | −0.155357 | − | 0.269087i | 0.777832 | − | 0.628473i | \(-0.216320\pi\) |
−0.933189 | + | 0.359386i | \(0.882986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 14.0000 | − | 24.2487i | 0.482472 | − | 0.835666i | ||||
\(843\) | −24.0000 | −0.826604 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.50000 | − | 2.59808i | 0.0515711 | − | 0.0893237i | ||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −4.00000 | + | 6.92820i | −0.137280 | + | 0.237775i | ||||
\(850\) | −15.0000 | − | 25.9808i | −0.514496 | − | 0.891133i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 9.00000 | + | 15.5885i | 0.308335 | + | 0.534052i | ||||
\(853\) | −1.00000 | − | 1.73205i | −0.0342393 | − | 0.0593043i | 0.848398 | − | 0.529359i | \(-0.177568\pi\) |
−0.882637 | + | 0.470055i | \(0.844234\pi\) | |||||||
\(854\) | −26.0000 | −0.889702 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | −0.307614 | ||||||||
\(857\) | 15.0000 | + | 25.9808i | 0.512390 | + | 0.887486i | 0.999897 | + | 0.0143666i | \(0.00457319\pi\) |
−0.487507 | + | 0.873119i | \(0.662093\pi\) | |||||||
\(858\) | −1.00000 | − | 1.73205i | −0.0341394 | − | 0.0591312i | ||||
\(859\) | 17.0000 | − | 29.4449i | 0.580033 | − | 1.00465i | −0.415442 | − | 0.909620i | \(-0.636373\pi\) |
0.995475 | − | 0.0950262i | \(-0.0302935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | + | 20.7846i | −0.408959 | + | 0.708338i | ||||
\(862\) | −36.0000 | −1.22616 | ||||||||
\(863\) | −33.0000 | −1.12333 | −0.561667 | − | 0.827364i | \(-0.689840\pi\) | ||||
−0.561667 | + | 0.827364i | \(0.689840\pi\) | |||||||
\(864\) | −2.00000 | + | 3.46410i | −0.0680414 | + | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.0000 | 0.373795 | ||||||||
\(867\) | −38.0000 | −1.29055 | ||||||||
\(868\) | −8.00000 | + | 13.8564i | −0.271538 | + | 0.470317i | ||||
\(869\) | −4.00000 | − | 6.92820i | −0.135691 | − | 0.235023i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | − | 8.66025i | −0.169419 | − | 0.293442i | ||||
\(872\) | −5.50000 | − | 9.52628i | −0.186254 | − | 0.322601i | ||||
\(873\) | −1.00000 | −0.0338449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | − | 6.92820i | −0.135147 | − | 0.234082i | ||||
\(877\) | −19.0000 | − | 32.9090i | −0.641584 | − | 1.11126i | −0.985079 | − | 0.172102i | \(-0.944944\pi\) |
0.343495 | − | 0.939155i | \(-0.388389\pi\) | |||||||
\(878\) | −10.0000 | + | 17.3205i | −0.337484 | + | 0.584539i | ||||
\(879\) | −9.00000 | − | 15.5885i | −0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | −3.00000 | −0.101015 | ||||||||
\(883\) | −10.0000 | + | 17.3205i | −0.336527 | + | 0.582882i | −0.983777 | − | 0.179396i | \(-0.942586\pi\) |
0.647250 | + | 0.762278i | \(0.275919\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | 6.00000 | − | 10.3923i | 0.201460 | − | 0.348939i | −0.747539 | − | 0.664218i | \(-0.768765\pi\) |
0.948999 | + | 0.315279i | \(0.102098\pi\) | |||||||
\(888\) | −10.0000 | − | 17.3205i | −0.335578 | − | 0.581238i | ||||
\(889\) | −2.00000 | + | 3.46410i | −0.0670778 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.50000 | + | 9.52628i | 0.184257 | + | 0.319142i | ||||
\(892\) | −7.00000 | −0.234377 | ||||||||
\(893\) | 1.50000 | + | 12.9904i | 0.0501956 | + | 0.434707i | ||||
\(894\) | −12.0000 | −0.401340 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | − | 1.73205i | −0.0334077 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.00000 | + | 15.5885i | 0.300334 | + | 0.520194i | ||||
\(899\) | −36.0000 | + | 62.3538i | −1.20067 | + | 2.07962i | ||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 3.00000 | − | 5.19615i | 0.0998891 | − | 0.173013i | ||||
\(903\) | 10.0000 | − | 17.3205i | 0.332779 | − | 0.576390i | ||||
\(904\) | 9.00000 | 0.299336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.00000 | − | 13.8564i | 0.265782 | − | 0.460348i | ||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 6.00000 | − | 10.3923i | 0.199117 | − | 0.344881i | ||||
\(909\) | 1.50000 | + | 2.59808i | 0.0497519 | + | 0.0861727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | 1.00000 | + | 8.66025i | 0.0331133 | + | 0.286770i | ||||
\(913\) | −9.00000 | −0.297857 | ||||||||
\(914\) | 20.0000 | + | 34.6410i | 0.661541 | + | 1.14582i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | + | 17.3205i | −0.330409 | + | 0.572286i | ||||
\(917\) | 3.00000 | + | 5.19615i | 0.0990687 | + | 0.171592i | ||||
\(918\) | 12.0000 | − | 20.7846i | 0.396059 | − | 0.685994i | ||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.00000 | + | 12.1244i | −0.230658 | + | 0.399511i | ||||
\(922\) | 1.50000 | − | 2.59808i | 0.0493999 | − | 0.0855631i | ||||
\(923\) | −9.00000 | −0.296239 | ||||||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | −25.0000 | + | 43.3013i | −0.821995 | + | 1.42374i | ||||
\(926\) | −8.50000 | − | 14.7224i | −0.279327 | − | 0.483809i | ||||
\(927\) | 9.50000 | − | 16.4545i | 0.312021 | − | 0.540436i | ||||
\(928\) | −4.50000 | − | 7.79423i | −0.147720 | − | 0.255858i | ||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5000 | − | 7.79423i | 0.344124 | − | 0.255446i | ||||
\(932\) | 12.0000 | 0.393073 | ||||||||
\(933\) | −15.0000 | − | 25.9808i | −0.491078 | − | 0.850572i | ||||
\(934\) | 6.00000 | + | 10.3923i | 0.196326 | + | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 0.866025i | 0.0163430 | + | 0.0283069i | ||||
\(937\) | −10.0000 | + | 17.3205i | −0.326686 | + | 0.565836i | −0.981852 | − | 0.189648i | \(-0.939265\pi\) |
0.655166 | + | 0.755485i | \(0.272599\pi\) | |||||||
\(938\) | −20.0000 | −0.653023 | ||||||||
\(939\) | −34.0000 | −1.10955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.00000 | + | 15.5885i | −0.293392 | + | 0.508169i | −0.974609 | − | 0.223912i | \(-0.928117\pi\) |
0.681218 | + | 0.732081i | \(0.261451\pi\) | |||||||
\(942\) | −28.0000 | −0.912289 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.00000 | + | 5.19615i | −0.0976417 | + | 0.169120i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.50000 | + | 4.33013i | −0.0812820 | + | 0.140785i | ||||
\(947\) | 9.00000 | + | 15.5885i | 0.292461 | + | 0.506557i | 0.974391 | − | 0.224860i | \(-0.0721926\pi\) |
−0.681930 | + | 0.731417i | \(0.738859\pi\) | |||||||
\(948\) | 8.00000 | + | 13.8564i | 0.259828 | + | 0.450035i | ||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 17.5000 | − | 12.9904i | 0.567775 | − | 0.421464i | ||||
\(951\) | −60.0000 | −1.94563 | ||||||||
\(952\) | 6.00000 | + | 10.3923i | 0.194461 | + | 0.336817i | ||||
\(953\) | −24.0000 | − | 41.5692i | −0.777436 | − | 1.34656i | −0.933415 | − | 0.358799i | \(-0.883186\pi\) |
0.155979 | − | 0.987760i | \(-0.450147\pi\) | |||||||
\(954\) | 3.00000 | − | 5.19615i | 0.0971286 | − | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.0000 | −0.581857 | ||||||||
\(958\) | −36.0000 | −1.16311 | ||||||||
\(959\) | 9.00000 | − | 15.5885i | 0.290625 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 10.0000 | 0.322413 | ||||||||
\(963\) | 4.50000 | − | 7.79423i | 0.145010 | − | 0.251166i | ||||
\(964\) | −13.0000 | − | 22.5167i | −0.418702 | − | 0.725213i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | + | 13.8564i | 0.257263 | + | 0.445592i | 0.965508 | − | 0.260375i | \(-0.0838461\pi\) |
−0.708245 | + | 0.705967i | \(0.750513\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −6.00000 | − | 51.9615i | −0.192748 | − | 1.66924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0000 | − | 36.3731i | −0.673922 | − | 1.16727i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.302861 | − | 0.953035i | \(-0.402058\pi\) | |||||||
\(972\) | −5.00000 | − | 8.66025i | −0.160375 | − | 0.277778i | ||||
\(973\) | 4.00000 | − | 6.92820i | 0.128234 | − | 0.222108i | ||||
\(974\) | 3.50000 | + | 6.06218i | 0.112147 | + | 0.194245i | ||||
\(975\) | 5.00000 | − | 8.66025i | 0.160128 | − | 0.277350i | ||||
\(976\) | −13.0000 | −0.416120 | ||||||||
\(977\) | −9.00000 | −0.287936 | −0.143968 | − | 0.989582i | \(-0.545986\pi\) | ||||
−0.143968 | + | 0.989582i | \(0.545986\pi\) | |||||||
\(978\) | 2.00000 | − | 3.46410i | 0.0639529 | − | 0.110770i | ||||
\(979\) | −7.50000 | + | 12.9904i | −0.239701 | + | 0.415174i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0000 | 0.351203 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | −16.5000 | − | 28.5788i | −0.526268 | − | 0.911523i | −0.999532 | − | 0.0306024i | \(-0.990257\pi\) |
0.473263 | − | 0.880921i | \(-0.343076\pi\) | |||||||
\(984\) | −6.00000 | + | 10.3923i | −0.191273 | + | 0.331295i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.0000 | + | 46.7654i | 0.859855 | + | 1.48931i | ||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | −4.00000 | − | 1.73205i | −0.127257 | − | 0.0551039i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.50000 | − | 4.33013i | −0.0794151 | − | 0.137551i | 0.823583 | − | 0.567196i | \(-0.191972\pi\) |
−0.902998 | + | 0.429645i | \(0.858639\pi\) | |||||||
\(992\) | −4.00000 | + | 6.92820i | −0.127000 | + | 0.219971i | ||||
\(993\) | −28.0000 | − | 48.4974i | −0.888553 | − | 1.53902i | ||||
\(994\) | −9.00000 | + | 15.5885i | −0.285463 | + | 0.494436i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18.0000 | 0.570352 | ||||||||
\(997\) | −19.0000 | + | 32.9090i | −0.601736 | + | 1.04224i | 0.390822 | + | 0.920466i | \(0.372191\pi\) |
−0.992558 | + | 0.121771i | \(0.961143\pi\) | |||||||
\(998\) | −13.0000 | + | 22.5167i | −0.411508 | + | 0.712752i | ||||
\(999\) | −40.0000 | −1.26554 |
(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 | 418.2.e.d.45.1 | ✓ | 2 | |
19.7 | even | 3 | 7942.2.a.l.1.1 | 1 | |||
19.11 | even | 3 | inner | 418.2.e.d.353.1 | yes | 2 | |
19.12 | odd | 6 | 7942.2.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.e.d.45.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
418.2.e.d.353.1 | yes | 2 | 19.11 | even | 3 | inner | |
7942.2.a.j.1.1 | 1 | 19.12 | odd | 6 | |||
7942.2.a.l.1.1 | 1 | 19.7 | even | 3 |