Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.b.191.2 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.41421 | + | 1.00000i | −0.816497 | + | 0.577350i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | −0.292893 | + | 1.70711i | −0.119573 | + | 0.696923i | ||||
\(7\) | 4.00000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000 | − | 2.82843i | 0.333333 | − | 0.942809i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | 1.00000 | + | 1.41421i | 0.288675 | + | 0.408248i | ||||
\(13\) | −1.00000 | + | 1.00000i | −0.277350 | + | 0.277350i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) |
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 2.82843 | − | 2.82843i | 0.755929 | − | 0.755929i | ||||
\(15\) | −1.70711 | − | 0.292893i | −0.440773 | − | 0.0756247i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.41421 | − | 1.41421i | −0.342997 | − | 0.342997i | 0.514496 | − | 0.857493i | \(-0.327979\pi\) |
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | −1.29289 | − | 2.70711i | −0.304738 | − | 0.638071i | ||||
\(19\) | −2.00000 | + | 2.00000i | −0.458831 | + | 0.458831i | −0.898272 | − | 0.439440i | \(-0.855177\pi\) |
0.439440 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | −5.65685 | + | 4.00000i | −1.23443 | + | 0.872872i | ||||
\(22\) | 3.00000 | − | 3.00000i | 0.639602 | − | 0.639602i | ||||
\(23\) | −4.24264 | − | 4.24264i | −0.884652 | − | 0.884652i | 0.109351 | − | 0.994003i | \(-0.465123\pi\) |
−0.994003 | + | 0.109351i | \(0.965123\pi\) | |||||||
\(24\) | 1.70711 | + | 0.292893i | 0.348462 | + | 0.0597866i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 1.41421i | 0.277350i | ||||||||
\(27\) | 1.41421 | + | 5.00000i | 0.272166 | + | 0.962250i | ||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(30\) | −1.41421 | + | 1.00000i | −0.258199 | + | 0.182574i | ||||
\(31\) | 5.00000 | + | 5.00000i | 0.898027 | + | 0.898027i | 0.995261 | − | 0.0972349i | \(-0.0309998\pi\) |
−0.0972349 | + | 0.995261i | \(0.531000\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −6.00000 | + | 4.24264i | −1.04447 | + | 0.738549i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 2.82843 | + | 2.82843i | 0.478091 | + | 0.478091i | ||||
\(36\) | −2.82843 | − | 1.00000i | −0.471405 | − | 0.166667i | ||||
\(37\) | 6.00000 | + | 1.00000i | 0.986394 | + | 0.164399i | ||||
\(38\) | 2.82843i | 0.458831i | ||||||||
\(39\) | 0.414214 | − | 2.41421i | 0.0663273 | − | 0.386584i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | −1.17157 | + | 6.82843i | −0.180778 | + | 1.05365i | ||||
\(43\) | 9.00000 | − | 9.00000i | 1.37249 | − | 1.37249i | 0.515745 | − | 0.856742i | \(-0.327515\pi\) |
0.856742 | − | 0.515745i | \(-0.172485\pi\) | |||||||
\(44\) | − | 4.24264i | − | 0.639602i | ||||||
\(45\) | 2.70711 | − | 1.29289i | 0.403552 | − | 0.192733i | ||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | − | 1.41421i | − | 0.206284i | −0.994667 | − | 0.103142i | \(-0.967110\pi\) | ||
0.994667 | − | 0.103142i | \(-0.0328896\pi\) | |||||||
\(48\) | 1.41421 | − | 1.00000i | 0.204124 | − | 0.144338i | ||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0.707107 | + | 0.707107i | 0.100000 | + | 0.100000i | ||||
\(51\) | 3.41421 | + | 0.585786i | 0.478086 | + | 0.0820265i | ||||
\(52\) | 1.00000 | + | 1.00000i | 0.138675 | + | 0.138675i | ||||
\(53\) | − | 2.82843i | − | 0.388514i | −0.980951 | − | 0.194257i | \(-0.937770\pi\) | ||
0.980951 | − | 0.194257i | \(-0.0622296\pi\) | |||||||
\(54\) | 4.53553 | + | 2.53553i | 0.617208 | + | 0.345042i | ||||
\(55\) | 3.00000 | + | 3.00000i | 0.404520 | + | 0.404520i | ||||
\(56\) | −2.82843 | − | 2.82843i | −0.377964 | − | 0.377964i | ||||
\(57\) | 0.828427 | − | 4.82843i | 0.109728 | − | 0.639541i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.82843 | − | 2.82843i | −0.368230 | − | 0.368230i | 0.498601 | − | 0.866831i | \(-0.333847\pi\) |
−0.866831 | + | 0.498601i | \(0.833847\pi\) | |||||||
\(60\) | −0.292893 | + | 1.70711i | −0.0378124 | + | 0.220387i | ||||
\(61\) | 4.00000 | + | 4.00000i | 0.512148 | + | 0.512148i | 0.915184 | − | 0.403036i | \(-0.132045\pi\) |
−0.403036 | + | 0.915184i | \(0.632045\pi\) | |||||||
\(62\) | 7.07107 | 0.898027 | ||||||||
\(63\) | 4.00000 | − | 11.3137i | 0.503953 | − | 1.42539i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −1.41421 | −0.175412 | ||||||||
\(66\) | −1.24264 | + | 7.24264i | −0.152958 | + | 0.891507i | ||||
\(67\) | − | 2.00000i | − | 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | −1.41421 | + | 1.41421i | −0.171499 | + | 0.171499i | ||||
\(69\) | 10.2426 | + | 1.75736i | 1.23307 | + | 0.211561i | ||||
\(70\) | 4.00000 | 0.478091 | ||||||||
\(71\) | 2.82843i | 0.335673i | 0.985815 | + | 0.167836i | \(0.0536780\pi\) | ||||
−0.985815 | + | 0.167836i | \(0.946322\pi\) | |||||||
\(72\) | −2.70711 | + | 1.29289i | −0.319036 | + | 0.152369i | ||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 4.94975 | − | 3.53553i | 0.575396 | − | 0.410997i | ||||
\(75\) | −1.00000 | − | 1.41421i | −0.115470 | − | 0.163299i | ||||
\(76\) | 2.00000 | + | 2.00000i | 0.229416 | + | 0.229416i | ||||
\(77\) | 16.9706 | 1.93398 | ||||||||
\(78\) | −1.41421 | − | 2.00000i | −0.160128 | − | 0.226455i | ||||
\(79\) | −3.00000 | + | 3.00000i | −0.337526 | + | 0.337526i | −0.855436 | − | 0.517909i | \(-0.826710\pi\) |
0.517909 | + | 0.855436i | \(0.326710\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 4.00000 | − | 4.00000i | 0.441726 | − | 0.441726i | ||||
\(83\) | 2.82843i | 0.310460i | 0.987878 | + | 0.155230i | \(0.0496119\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | 4.00000 | + | 5.65685i | 0.436436 | + | 0.617213i | ||||
\(85\) | − | 2.00000i | − | 0.216930i | ||||||
\(86\) | − | 12.7279i | − | 1.37249i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | − | 3.00000i | −0.319801 | − | 0.319801i | ||||
\(89\) | −12.7279 | + | 12.7279i | −1.34916 | + | 1.34916i | −0.462579 | + | 0.886578i | \(0.653076\pi\) |
−0.886578 | + | 0.462579i | \(0.846924\pi\) | |||||||
\(90\) | 1.00000 | − | 2.82843i | 0.105409 | − | 0.298142i | ||||
\(91\) | −4.00000 | + | 4.00000i | −0.419314 | + | 0.419314i | ||||
\(92\) | −4.24264 | + | 4.24264i | −0.442326 | + | 0.442326i | ||||
\(93\) | −12.0711 | − | 2.07107i | −1.25171 | − | 0.214760i | ||||
\(94\) | −1.00000 | − | 1.00000i | −0.103142 | − | 0.103142i | ||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0.292893 | − | 1.70711i | 0.0298933 | − | 0.174231i | ||||
\(97\) | −12.0000 | + | 12.0000i | −1.21842 | + | 1.21842i | −0.250229 | + | 0.968187i | \(0.580506\pi\) |
−0.968187 | + | 0.250229i | \(0.919494\pi\) | |||||||
\(98\) | 6.36396 | − | 6.36396i | 0.642857 | − | 0.642857i | ||||
\(99\) | 4.24264 | − | 12.0000i | 0.426401 | − | 1.20605i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 15.5563 | 1.54791 | 0.773957 | − | 0.633238i | \(-0.218274\pi\) | ||||
0.773957 | + | 0.633238i | \(0.218274\pi\) | |||||||
\(102\) | 2.82843 | − | 2.00000i | 0.280056 | − | 0.198030i | ||||
\(103\) | −10.0000 | − | 10.0000i | −0.985329 | − | 0.985329i | 0.0145647 | − | 0.999894i | \(-0.495364\pi\) |
−0.999894 | + | 0.0145647i | \(0.995364\pi\) | |||||||
\(104\) | 1.41421 | 0.138675 | ||||||||
\(105\) | −6.82843 | − | 1.17157i | −0.666386 | − | 0.114334i | ||||
\(106\) | −2.00000 | − | 2.00000i | −0.194257 | − | 0.194257i | ||||
\(107\) | 14.1421i | 1.36717i | 0.729870 | + | 0.683586i | \(0.239581\pi\) | ||||
−0.729870 | + | 0.683586i | \(0.760419\pi\) | |||||||
\(108\) | 5.00000 | − | 1.41421i | 0.481125 | − | 0.136083i | ||||
\(109\) | 12.0000 | − | 12.0000i | 1.14939 | − | 1.14939i | 0.162719 | − | 0.986672i | \(-0.447974\pi\) |
0.986672 | − | 0.162719i | \(-0.0520264\pi\) | |||||||
\(110\) | 4.24264 | 0.404520 | ||||||||
\(111\) | −9.48528 | + | 4.58579i | −0.900303 | + | 0.435264i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 4.24264 | − | 4.24264i | 0.399114 | − | 0.399114i | −0.478806 | − | 0.877920i | \(-0.658930\pi\) |
0.877920 | + | 0.478806i | \(0.158930\pi\) | |||||||
\(114\) | −2.82843 | − | 4.00000i | −0.264906 | − | 0.374634i | ||||
\(115\) | − | 6.00000i | − | 0.559503i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.82843 | + | 3.82843i | 0.169038 | + | 0.353938i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | −5.65685 | − | 5.65685i | −0.518563 | − | 0.518563i | ||||
\(120\) | 1.00000 | + | 1.41421i | 0.0912871 | + | 0.129099i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 5.65685 | 0.512148 | ||||||||
\(123\) | −8.00000 | + | 5.65685i | −0.721336 | + | 0.510061i | ||||
\(124\) | 5.00000 | − | 5.00000i | 0.449013 | − | 0.449013i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | −5.17157 | − | 10.8284i | −0.460720 | − | 0.964673i | ||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −3.72792 | + | 21.7279i | −0.328225 | + | 1.91304i | ||||
\(130\) | −1.00000 | + | 1.00000i | −0.0877058 | + | 0.0877058i | ||||
\(131\) | 8.48528 | − | 8.48528i | 0.741362 | − | 0.741362i | −0.231478 | − | 0.972840i | \(-0.574356\pi\) |
0.972840 | + | 0.231478i | \(0.0743560\pi\) | |||||||
\(132\) | 4.24264 | + | 6.00000i | 0.369274 | + | 0.522233i | ||||
\(133\) | −8.00000 | + | 8.00000i | −0.693688 | + | 0.693688i | ||||
\(134\) | −1.41421 | − | 1.41421i | −0.122169 | − | 0.122169i | ||||
\(135\) | −2.53553 | + | 4.53553i | −0.218224 | + | 0.390357i | ||||
\(136\) | 2.00000i | 0.171499i | ||||||||
\(137\) | − | 9.89949i | − | 0.845771i | −0.906183 | − | 0.422885i | \(-0.861017\pi\) | ||
0.906183 | − | 0.422885i | \(-0.138983\pi\) | |||||||
\(138\) | 8.48528 | − | 6.00000i | 0.722315 | − | 0.510754i | ||||
\(139\) | − | 16.0000i | − | 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 2.82843 | − | 2.82843i | 0.239046 | − | 0.239046i | ||||
\(141\) | 1.41421 | + | 2.00000i | 0.119098 | + | 0.168430i | ||||
\(142\) | 2.00000 | + | 2.00000i | 0.167836 | + | 0.167836i | ||||
\(143\) | −4.24264 | + | 4.24264i | −0.354787 | + | 0.354787i | ||||
\(144\) | −1.00000 | + | 2.82843i | −0.0833333 | + | 0.235702i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.24264 | + | 4.24264i | 0.351123 | + | 0.351123i | ||||
\(147\) | −12.7279 | + | 9.00000i | −1.04978 | + | 0.742307i | ||||
\(148\) | 1.00000 | − | 6.00000i | 0.0821995 | − | 0.493197i | ||||
\(149\) | 9.89949i | 0.810998i | 0.914095 | + | 0.405499i | \(0.132902\pi\) | ||||
−0.914095 | + | 0.405499i | \(0.867098\pi\) | |||||||
\(150\) | −1.70711 | − | 0.292893i | −0.139385 | − | 0.0239146i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 2.82843 | 0.229416 | ||||||||
\(153\) | −5.41421 | + | 2.58579i | −0.437713 | + | 0.209048i | ||||
\(154\) | 12.0000 | − | 12.0000i | 0.966988 | − | 0.966988i | ||||
\(155\) | 7.07107i | 0.567962i | ||||||||
\(156\) | −2.41421 | − | 0.414214i | −0.193292 | − | 0.0331636i | ||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 4.24264i | 0.337526i | ||||||||
\(159\) | 2.82843 | + | 4.00000i | 0.224309 | + | 0.317221i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −16.9706 | − | 16.9706i | −1.33747 | − | 1.33747i | ||||
\(162\) | −8.94975 | + | 0.949747i | −0.703159 | + | 0.0746192i | ||||
\(163\) | −5.00000 | − | 5.00000i | −0.391630 | − | 0.391630i | 0.483638 | − | 0.875268i | \(-0.339315\pi\) |
−0.875268 | + | 0.483638i | \(0.839315\pi\) | |||||||
\(164\) | − | 5.65685i | − | 0.441726i | ||||||
\(165\) | −7.24264 | − | 1.24264i | −0.563839 | − | 0.0967394i | ||||
\(166\) | 2.00000 | + | 2.00000i | 0.155230 | + | 0.155230i | ||||
\(167\) | −12.7279 | − | 12.7279i | −0.984916 | − | 0.984916i | 0.0149717 | − | 0.999888i | \(-0.495234\pi\) |
−0.999888 | + | 0.0149717i | \(0.995234\pi\) | |||||||
\(168\) | 6.82843 | + | 1.17157i | 0.526825 | + | 0.0903888i | ||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | −1.41421 | − | 1.41421i | −0.108465 | − | 0.108465i | ||||
\(171\) | 3.65685 | + | 7.65685i | 0.279647 | + | 0.585534i | ||||
\(172\) | −9.00000 | − | 9.00000i | −0.686244 | − | 0.686244i | ||||
\(173\) | −2.82843 | −0.215041 | −0.107521 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107521 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000i | 0.302372i | ||||||||
\(176\) | −4.24264 | −0.319801 | ||||||||
\(177\) | 6.82843 | + | 1.17157i | 0.513256 | + | 0.0880608i | ||||
\(178\) | 18.0000i | 1.34916i | ||||||||
\(179\) | −12.7279 | + | 12.7279i | −0.951330 | + | 0.951330i | −0.998869 | − | 0.0475398i | \(-0.984862\pi\) |
0.0475398 | + | 0.998869i | \(0.484862\pi\) | |||||||
\(180\) | −1.29289 | − | 2.70711i | −0.0963666 | − | 0.201776i | ||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 5.65685i | 0.419314i | ||||||||
\(183\) | −9.65685 | − | 1.65685i | −0.713855 | − | 0.122478i | ||||
\(184\) | 6.00000i | 0.442326i | ||||||||
\(185\) | 3.53553 | + | 4.94975i | 0.259938 | + | 0.363913i | ||||
\(186\) | −10.0000 | + | 7.07107i | −0.733236 | + | 0.518476i | ||||
\(187\) | −6.00000 | − | 6.00000i | −0.438763 | − | 0.438763i | ||||
\(188\) | −1.41421 | −0.103142 | ||||||||
\(189\) | 5.65685 | + | 20.0000i | 0.411476 | + | 1.45479i | ||||
\(190\) | −2.00000 | + | 2.00000i | −0.145095 | + | 0.145095i | ||||
\(191\) | 2.82843 | + | 2.82843i | 0.204658 | + | 0.204658i | 0.801992 | − | 0.597334i | \(-0.203773\pi\) |
−0.597334 | + | 0.801992i | \(0.703773\pi\) | |||||||
\(192\) | −1.00000 | − | 1.41421i | −0.0721688 | − | 0.102062i | ||||
\(193\) | 18.0000 | − | 18.0000i | 1.29567 | − | 1.29567i | 0.364442 | − | 0.931226i | \(-0.381260\pi\) |
0.931226 | − | 0.364442i | \(-0.118740\pi\) | |||||||
\(194\) | 16.9706i | 1.21842i | ||||||||
\(195\) | 2.00000 | − | 1.41421i | 0.143223 | − | 0.101274i | ||||
\(196\) | − | 9.00000i | − | 0.642857i | ||||||
\(197\) | 19.7990i | 1.41062i | 0.708899 | + | 0.705310i | \(0.249192\pi\) | ||||
−0.708899 | + | 0.705310i | \(0.750808\pi\) | |||||||
\(198\) | −5.48528 | − | 11.4853i | −0.389822 | − | 0.816223i | ||||
\(199\) | −3.00000 | − | 3.00000i | −0.212664 | − | 0.212664i | 0.592734 | − | 0.805398i | \(-0.298049\pi\) |
−0.805398 | + | 0.592734i | \(0.798049\pi\) | |||||||
\(200\) | 0.707107 | − | 0.707107i | 0.0500000 | − | 0.0500000i | ||||
\(201\) | 2.00000 | + | 2.82843i | 0.141069 | + | 0.199502i | ||||
\(202\) | 11.0000 | − | 11.0000i | 0.773957 | − | 0.773957i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.585786 | − | 3.41421i | 0.0410133 | − | 0.239043i | ||||
\(205\) | 4.00000 | + | 4.00000i | 0.279372 | + | 0.279372i | ||||
\(206\) | −14.1421 | −0.985329 | ||||||||
\(207\) | −16.2426 | + | 7.75736i | −1.12894 | + | 0.539174i | ||||
\(208\) | 1.00000 | − | 1.00000i | 0.0693375 | − | 0.0693375i | ||||
\(209\) | −8.48528 | + | 8.48528i | −0.586939 | + | 0.586939i | ||||
\(210\) | −5.65685 | + | 4.00000i | −0.390360 | + | 0.276026i | ||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | −2.82843 | −0.194257 | ||||||||
\(213\) | −2.82843 | − | 4.00000i | −0.193801 | − | 0.274075i | ||||
\(214\) | 10.0000 | + | 10.0000i | 0.683586 | + | 0.683586i | ||||
\(215\) | 12.7279 | 0.868037 | ||||||||
\(216\) | 2.53553 | − | 4.53553i | 0.172521 | − | 0.308604i | ||||
\(217\) | 20.0000 | + | 20.0000i | 1.35769 | + | 1.35769i | ||||
\(218\) | − | 16.9706i | − | 1.14939i | ||||||
\(219\) | −6.00000 | − | 8.48528i | −0.405442 | − | 0.573382i | ||||
\(220\) | 3.00000 | − | 3.00000i | 0.202260 | − | 0.202260i | ||||
\(221\) | 2.82843 | 0.190261 | ||||||||
\(222\) | −3.46447 | + | 9.94975i | −0.232520 | + | 0.667783i | ||||
\(223\) | −12.0000 | −0.803579 | −0.401790 | − | 0.915732i | \(-0.631612\pi\) | ||||
−0.401790 | + | 0.915732i | \(0.631612\pi\) | |||||||
\(224\) | −2.82843 | + | 2.82843i | −0.188982 | + | 0.188982i | ||||
\(225\) | 2.82843 | + | 1.00000i | 0.188562 | + | 0.0666667i | ||||
\(226\) | − | 6.00000i | − | 0.399114i | ||||||
\(227\) | −19.7990 | − | 19.7990i | −1.31411 | − | 1.31411i | −0.918361 | − | 0.395744i | \(-0.870487\pi\) |
−0.395744 | − | 0.918361i | \(-0.629513\pi\) | |||||||
\(228\) | −4.82843 | − | 0.828427i | −0.319770 | − | 0.0548639i | ||||
\(229\) | 26.0000 | 1.71813 | 0.859064 | − | 0.511868i | \(-0.171046\pi\) | ||||
0.859064 | + | 0.511868i | \(0.171046\pi\) | |||||||
\(230\) | −4.24264 | − | 4.24264i | −0.279751 | − | 0.279751i | ||||
\(231\) | −24.0000 | + | 16.9706i | −1.57908 | + | 1.11658i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.07107 | −0.463241 | −0.231621 | − | 0.972806i | \(-0.574403\pi\) | ||||
−0.231621 | + | 0.972806i | \(0.574403\pi\) | |||||||
\(234\) | 4.00000 | + | 1.41421i | 0.261488 | + | 0.0924500i | ||||
\(235\) | 1.00000 | − | 1.00000i | 0.0652328 | − | 0.0652328i | ||||
\(236\) | −2.82843 | + | 2.82843i | −0.184115 | + | 0.184115i | ||||
\(237\) | 1.24264 | − | 7.24264i | 0.0807182 | − | 0.470460i | ||||
\(238\) | −8.00000 | −0.518563 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 1.70711 | + | 0.292893i | 0.110193 | + | 0.0189062i | ||||
\(241\) | 3.00000 | − | 3.00000i | 0.193247 | − | 0.193247i | −0.603851 | − | 0.797098i | \(-0.706368\pi\) |
0.797098 | + | 0.603851i | \(0.206368\pi\) | |||||||
\(242\) | 4.94975 | − | 4.94975i | 0.318182 | − | 0.318182i | ||||
\(243\) | 15.5563 | + | 1.00000i | 0.997940 | + | 0.0641500i | ||||
\(244\) | 4.00000 | − | 4.00000i | 0.256074 | − | 0.256074i | ||||
\(245\) | 6.36396 | + | 6.36396i | 0.406579 | + | 0.406579i | ||||
\(246\) | −1.65685 | + | 9.65685i | −0.105637 | + | 0.615699i | ||||
\(247\) | − | 4.00000i | − | 0.254514i | ||||||
\(248\) | − | 7.07107i | − | 0.449013i | ||||||
\(249\) | −2.82843 | − | 4.00000i | −0.179244 | − | 0.253490i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −2.82843 | + | 2.82843i | −0.178529 | + | 0.178529i | −0.790714 | − | 0.612185i | \(-0.790291\pi\) |
0.612185 | + | 0.790714i | \(0.290291\pi\) | |||||||
\(252\) | −11.3137 | − | 4.00000i | −0.712697 | − | 0.251976i | ||||
\(253\) | −18.0000 | − | 18.0000i | −1.13165 | − | 1.13165i | ||||
\(254\) | −8.48528 | + | 8.48528i | −0.532414 | + | 0.532414i | ||||
\(255\) | 2.00000 | + | 2.82843i | 0.125245 | + | 0.177123i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.82843 | + | 2.82843i | 0.176432 | + | 0.176432i | 0.789799 | − | 0.613366i | \(-0.210185\pi\) |
−0.613366 | + | 0.789799i | \(0.710185\pi\) | |||||||
\(258\) | 12.7279 | + | 18.0000i | 0.792406 | + | 1.12063i | ||||
\(259\) | 24.0000 | + | 4.00000i | 1.49129 | + | 0.248548i | ||||
\(260\) | 1.41421i | 0.0877058i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 12.0000i | − | 0.741362i | ||||||
\(263\) | −26.8701 | −1.65688 | −0.828439 | − | 0.560079i | \(-0.810771\pi\) | ||||
−0.828439 | + | 0.560079i | \(0.810771\pi\) | |||||||
\(264\) | 7.24264 | + | 1.24264i | 0.445754 | + | 0.0764792i | ||||
\(265\) | 2.00000 | − | 2.00000i | 0.122859 | − | 0.122859i | ||||
\(266\) | 11.3137i | 0.693688i | ||||||||
\(267\) | 5.27208 | − | 30.7279i | 0.322646 | − | 1.88052i | ||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | 21.2132i | 1.29339i | 0.762748 | + | 0.646696i | \(0.223850\pi\) | ||||
−0.762748 | + | 0.646696i | \(0.776150\pi\) | |||||||
\(270\) | 1.41421 | + | 5.00000i | 0.0860663 | + | 0.304290i | ||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 1.41421 | + | 1.41421i | 0.0857493 | + | 0.0857493i | ||||
\(273\) | 1.65685 | − | 9.65685i | 0.100277 | − | 0.584459i | ||||
\(274\) | −7.00000 | − | 7.00000i | −0.422885 | − | 0.422885i | ||||
\(275\) | 4.24264i | 0.255841i | ||||||||
\(276\) | 1.75736 | − | 10.2426i | 0.105781 | − | 0.616535i | ||||
\(277\) | −15.0000 | − | 15.0000i | −0.901263 | − | 0.901263i | 0.0942828 | − | 0.995545i | \(-0.469944\pi\) |
−0.995545 | + | 0.0942828i | \(0.969944\pi\) | |||||||
\(278\) | −11.3137 | − | 11.3137i | −0.678551 | − | 0.678551i | ||||
\(279\) | 19.1421 | − | 9.14214i | 1.14601 | − | 0.547325i | ||||
\(280\) | − | 4.00000i | − | 0.239046i | ||||||
\(281\) | −7.07107 | − | 7.07107i | −0.421825 | − | 0.421825i | 0.464007 | − | 0.885832i | \(-0.346411\pi\) |
−0.885832 | + | 0.464007i | \(0.846411\pi\) | |||||||
\(282\) | 2.41421 | + | 0.414214i | 0.143764 | + | 0.0246661i | ||||
\(283\) | −15.0000 | − | 15.0000i | −0.891657 | − | 0.891657i | 0.103022 | − | 0.994679i | \(-0.467149\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(284\) | 2.82843 | 0.167836 | ||||||||
\(285\) | 4.00000 | − | 2.82843i | 0.236940 | − | 0.167542i | ||||
\(286\) | 6.00000i | 0.354787i | ||||||||
\(287\) | 22.6274 | 1.33565 | ||||||||
\(288\) | 1.29289 | + | 2.70711i | 0.0761845 | + | 0.159518i | ||||
\(289\) | − | 13.0000i | − | 0.764706i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.97056 | − | 28.9706i | 0.291380 | − | 1.69828i | ||||
\(292\) | 6.00000 | 0.351123 | ||||||||
\(293\) | 28.2843i | 1.65238i | 0.563388 | + | 0.826192i | \(0.309498\pi\) | ||||
−0.563388 | + | 0.826192i | \(0.690502\pi\) | |||||||
\(294\) | −2.63604 | + | 15.3640i | −0.153737 | + | 0.896044i | ||||
\(295\) | − | 4.00000i | − | 0.232889i | ||||||
\(296\) | −3.53553 | − | 4.94975i | −0.205499 | − | 0.287698i | ||||
\(297\) | 6.00000 | + | 21.2132i | 0.348155 | + | 1.23091i | ||||
\(298\) | 7.00000 | + | 7.00000i | 0.405499 | + | 0.405499i | ||||
\(299\) | 8.48528 | 0.490716 | ||||||||
\(300\) | −1.41421 | + | 1.00000i | −0.0816497 | + | 0.0577350i | ||||
\(301\) | 36.0000 | − | 36.0000i | 2.07501 | − | 2.07501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.0000 | + | 15.5563i | −1.26387 | + | 0.893689i | ||||
\(304\) | 2.00000 | − | 2.00000i | 0.114708 | − | 0.114708i | ||||
\(305\) | 5.65685i | 0.323911i | ||||||||
\(306\) | −2.00000 | + | 5.65685i | −0.114332 | + | 0.323381i | ||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | − | 16.9706i | − | 0.966988i | ||||||
\(309\) | 24.1421 | + | 4.14214i | 1.37340 | + | 0.235638i | ||||
\(310\) | 5.00000 | + | 5.00000i | 0.283981 | + | 0.283981i | ||||
\(311\) | −8.48528 | + | 8.48528i | −0.481156 | + | 0.481156i | −0.905501 | − | 0.424345i | \(-0.860505\pi\) |
0.424345 | + | 0.905501i | \(0.360505\pi\) | |||||||
\(312\) | −2.00000 | + | 1.41421i | −0.113228 | + | 0.0800641i | ||||
\(313\) | 6.00000 | − | 6.00000i | 0.339140 | − | 0.339140i | −0.516904 | − | 0.856044i | \(-0.672915\pi\) |
0.856044 | + | 0.516904i | \(0.172915\pi\) | |||||||
\(314\) | −12.7279 | + | 12.7279i | −0.718278 | + | 0.718278i | ||||
\(315\) | 10.8284 | − | 5.17157i | 0.610113 | − | 0.291385i | ||||
\(316\) | 3.00000 | + | 3.00000i | 0.168763 | + | 0.168763i | ||||
\(317\) | 8.48528 | 0.476581 | 0.238290 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238290 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(318\) | 4.82843 | + | 0.828427i | 0.270765 | + | 0.0464559i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | −14.1421 | − | 20.0000i | −0.789337 | − | 1.11629i | ||||
\(322\) | −24.0000 | −1.33747 | ||||||||
\(323\) | 5.65685 | 0.314756 | ||||||||
\(324\) | −5.65685 | + | 7.00000i | −0.314270 | + | 0.388889i | ||||
\(325\) | −1.00000 | − | 1.00000i | −0.0554700 | − | 0.0554700i | ||||
\(326\) | −7.07107 | −0.391630 | ||||||||
\(327\) | −4.97056 | + | 28.9706i | −0.274873 | + | 1.60208i | ||||
\(328\) | −4.00000 | − | 4.00000i | −0.220863 | − | 0.220863i | ||||
\(329\) | − | 5.65685i | − | 0.311872i | ||||||
\(330\) | −6.00000 | + | 4.24264i | −0.330289 | + | 0.233550i | ||||
\(331\) | −4.00000 | + | 4.00000i | −0.219860 | + | 0.219860i | −0.808439 | − | 0.588579i | \(-0.799687\pi\) |
0.588579 | + | 0.808439i | \(0.299687\pi\) | |||||||
\(332\) | 2.82843 | 0.155230 | ||||||||
\(333\) | 8.82843 | − | 15.9706i | 0.483795 | − | 0.875181i | ||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 1.41421 | − | 1.41421i | 0.0772667 | − | 0.0772667i | ||||
\(336\) | 5.65685 | − | 4.00000i | 0.308607 | − | 0.218218i | ||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 7.77817 | + | 7.77817i | 0.423077 | + | 0.423077i | ||||
\(339\) | −1.75736 | + | 10.2426i | −0.0954467 | + | 0.556304i | ||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | 21.2132 | + | 21.2132i | 1.14876 | + | 1.14876i | ||||
\(342\) | 8.00000 | + | 2.82843i | 0.432590 | + | 0.152944i | ||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | −12.7279 | −0.686244 | ||||||||
\(345\) | 6.00000 | + | 8.48528i | 0.323029 | + | 0.456832i | ||||
\(346\) | −2.00000 | + | 2.00000i | −0.107521 | + | 0.107521i | ||||
\(347\) | 8.48528 | − | 8.48528i | 0.455514 | − | 0.455514i | −0.441666 | − | 0.897180i | \(-0.645612\pi\) |
0.897180 | + | 0.441666i | \(0.145612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 2.82843 | + | 2.82843i | 0.151186 | + | 0.151186i | ||||
\(351\) | −6.41421 | − | 3.58579i | −0.342365 | − | 0.191395i | ||||
\(352\) | −3.00000 | + | 3.00000i | −0.159901 | + | 0.159901i | ||||
\(353\) | −24.0416 | + | 24.0416i | −1.27961 | + | 1.27961i | −0.338719 | + | 0.940887i | \(0.609994\pi\) |
−0.940887 | + | 0.338719i | \(0.890006\pi\) | |||||||
\(354\) | 5.65685 | − | 4.00000i | 0.300658 | − | 0.212598i | ||||
\(355\) | −2.00000 | + | 2.00000i | −0.106149 | + | 0.106149i | ||||
\(356\) | 12.7279 | + | 12.7279i | 0.674579 | + | 0.674579i | ||||
\(357\) | 13.6569 | + | 2.34315i | 0.722797 | + | 0.124012i | ||||
\(358\) | 18.0000i | 0.951330i | ||||||||
\(359\) | − | 11.3137i | − | 0.597115i | −0.954392 | − | 0.298557i | \(-0.903495\pi\) | ||
0.954392 | − | 0.298557i | \(-0.0965054\pi\) | |||||||
\(360\) | −2.82843 | − | 1.00000i | −0.149071 | − | 0.0527046i | ||||
\(361\) | 11.0000i | 0.578947i | ||||||||
\(362\) | 4.24264 | − | 4.24264i | 0.222988 | − | 0.222988i | ||||
\(363\) | −9.89949 | + | 7.00000i | −0.519589 | + | 0.367405i | ||||
\(364\) | 4.00000 | + | 4.00000i | 0.209657 | + | 0.209657i | ||||
\(365\) | −4.24264 | + | 4.24264i | −0.222070 | + | 0.222070i | ||||
\(366\) | −8.00000 | + | 5.65685i | −0.418167 | + | 0.295689i | ||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 4.24264 | + | 4.24264i | 0.221163 | + | 0.221163i | ||||
\(369\) | 5.65685 | − | 16.0000i | 0.294484 | − | 0.832927i | ||||
\(370\) | 6.00000 | + | 1.00000i | 0.311925 | + | 0.0519875i | ||||
\(371\) | − | 11.3137i | − | 0.587378i | ||||||
\(372\) | −2.07107 | + | 12.0711i | −0.107380 | + | 0.625856i | ||||
\(373\) | 34.0000i | 1.76045i | 0.474554 | + | 0.880227i | \(0.342610\pi\) | ||||
−0.474554 | + | 0.880227i | \(0.657390\pi\) | |||||||
\(374\) | −8.48528 | −0.438763 | ||||||||
\(375\) | 0.292893 | − | 1.70711i | 0.0151249 | − | 0.0881546i | ||||
\(376\) | −1.00000 | + | 1.00000i | −0.0515711 | + | 0.0515711i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 18.1421 | + | 10.1421i | 0.933131 | + | 0.521655i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 2.82843i | 0.145095i | ||||||||
\(381\) | 16.9706 | − | 12.0000i | 0.869428 | − | 0.614779i | ||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | 11.3137 | + | 11.3137i | 0.578103 | + | 0.578103i | 0.934380 | − | 0.356277i | \(-0.115954\pi\) |
−0.356277 | + | 0.934380i | \(0.615954\pi\) | |||||||
\(384\) | −1.70711 | − | 0.292893i | −0.0871154 | − | 0.0149466i | ||||
\(385\) | 12.0000 | + | 12.0000i | 0.611577 | + | 0.611577i | ||||
\(386\) | − | 25.4558i | − | 1.29567i | ||||||
\(387\) | −16.4558 | − | 34.4558i | −0.836498 | − | 1.75149i | ||||
\(388\) | 12.0000 | + | 12.0000i | 0.609208 | + | 0.609208i | ||||
\(389\) | −8.48528 | − | 8.48528i | −0.430221 | − | 0.430221i | 0.458483 | − | 0.888703i | \(-0.348393\pi\) |
−0.888703 | + | 0.458483i | \(0.848393\pi\) | |||||||
\(390\) | 0.414214 | − | 2.41421i | 0.0209745 | − | 0.122248i | ||||
\(391\) | 12.0000i | 0.606866i | ||||||||
\(392\) | −6.36396 | − | 6.36396i | −0.321429 | − | 0.321429i | ||||
\(393\) | −3.51472 | + | 20.4853i | −0.177294 | + | 1.03335i | ||||
\(394\) | 14.0000 | + | 14.0000i | 0.705310 | + | 0.705310i | ||||
\(395\) | −4.24264 | −0.213470 | ||||||||
\(396\) | −12.0000 | − | 4.24264i | −0.603023 | − | 0.213201i | ||||
\(397\) | − | 18.0000i | − | 0.903394i | −0.892171 | − | 0.451697i | \(-0.850819\pi\) | ||
0.892171 | − | 0.451697i | \(-0.149181\pi\) | |||||||
\(398\) | −4.24264 | −0.212664 | ||||||||
\(399\) | 3.31371 | − | 19.3137i | 0.165893 | − | 0.966895i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −15.5563 | + | 15.5563i | −0.776847 | + | 0.776847i | −0.979293 | − | 0.202446i | \(-0.935111\pi\) |
0.202446 | + | 0.979293i | \(0.435111\pi\) | |||||||
\(402\) | 3.41421 | + | 0.585786i | 0.170285 | + | 0.0292164i | ||||
\(403\) | −10.0000 | −0.498135 | ||||||||
\(404\) | − | 15.5563i | − | 0.773957i | ||||||
\(405\) | −0.949747 | − | 8.94975i | −0.0471933 | − | 0.444717i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4558 | + | 4.24264i | 1.26180 | + | 0.210300i | ||||
\(408\) | −2.00000 | − | 2.82843i | −0.0990148 | − | 0.140028i | ||||
\(409\) | 9.00000 | + | 9.00000i | 0.445021 | + | 0.445021i | 0.893695 | − | 0.448674i | \(-0.148104\pi\) |
−0.448674 | + | 0.893695i | \(0.648104\pi\) | |||||||
\(410\) | 5.65685 | 0.279372 | ||||||||
\(411\) | 9.89949 | + | 14.0000i | 0.488306 | + | 0.690569i | ||||
\(412\) | −10.0000 | + | 10.0000i | −0.492665 | + | 0.492665i | ||||
\(413\) | −11.3137 | − | 11.3137i | −0.556711 | − | 0.556711i | ||||
\(414\) | −6.00000 | + | 16.9706i | −0.294884 | + | 0.834058i | ||||
\(415\) | −2.00000 | + | 2.00000i | −0.0981761 | + | 0.0981761i | ||||
\(416\) | − | 1.41421i | − | 0.0693375i | ||||||
\(417\) | 16.0000 | + | 22.6274i | 0.783523 | + | 1.10807i | ||||
\(418\) | 12.0000i | 0.586939i | ||||||||
\(419\) | − | 12.7279i | − | 0.621800i | −0.950443 | − | 0.310900i | \(-0.899370\pi\) | ||
0.950443 | − | 0.310900i | \(-0.100630\pi\) | |||||||
\(420\) | −1.17157 | + | 6.82843i | −0.0571669 | + | 0.333193i | ||||
\(421\) | −14.0000 | − | 14.0000i | −0.682318 | − | 0.682318i | 0.278204 | − | 0.960522i | \(-0.410261\pi\) |
−0.960522 | + | 0.278204i | \(0.910261\pi\) | |||||||
\(422\) | −11.3137 | + | 11.3137i | −0.550743 | + | 0.550743i | ||||
\(423\) | −4.00000 | − | 1.41421i | −0.194487 | − | 0.0687614i | ||||
\(424\) | −2.00000 | + | 2.00000i | −0.0971286 | + | 0.0971286i | ||||
\(425\) | 1.41421 | − | 1.41421i | 0.0685994 | − | 0.0685994i | ||||
\(426\) | −4.82843 | − | 0.828427i | −0.233938 | − | 0.0401374i | ||||
\(427\) | 16.0000 | + | 16.0000i | 0.774294 | + | 0.774294i | ||||
\(428\) | 14.1421 | 0.683586 | ||||||||
\(429\) | 1.75736 | − | 10.2426i | 0.0848461 | − | 0.494519i | ||||
\(430\) | 9.00000 | − | 9.00000i | 0.434019 | − | 0.434019i | ||||
\(431\) | 8.48528 | − | 8.48528i | 0.408722 | − | 0.408722i | −0.472571 | − | 0.881293i | \(-0.656674\pi\) |
0.881293 | + | 0.472571i | \(0.156674\pi\) | |||||||
\(432\) | −1.41421 | − | 5.00000i | −0.0680414 | − | 0.240563i | ||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 28.2843 | 1.35769 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.0000 | − | 12.0000i | −0.574696 | − | 0.574696i | ||||
\(437\) | 16.9706 | 0.811812 | ||||||||
\(438\) | −10.2426 | − | 1.75736i | −0.489412 | − | 0.0839699i | ||||
\(439\) | 5.00000 | + | 5.00000i | 0.238637 | + | 0.238637i | 0.816286 | − | 0.577649i | \(-0.196030\pi\) |
−0.577649 | + | 0.816286i | \(0.696030\pi\) | |||||||
\(440\) | − | 4.24264i | − | 0.202260i | ||||||
\(441\) | 9.00000 | − | 25.4558i | 0.428571 | − | 1.21218i | ||||
\(442\) | 2.00000 | − | 2.00000i | 0.0951303 | − | 0.0951303i | ||||
\(443\) | 2.82843 | 0.134383 | 0.0671913 | − | 0.997740i | \(-0.478596\pi\) | ||||
0.0671913 | + | 0.997740i | \(0.478596\pi\) | |||||||
\(444\) | 4.58579 | + | 9.48528i | 0.217632 | + | 0.450152i | ||||
\(445\) | −18.0000 | −0.853282 | ||||||||
\(446\) | −8.48528 | + | 8.48528i | −0.401790 | + | 0.401790i | ||||
\(447\) | −9.89949 | − | 14.0000i | −0.468230 | − | 0.662177i | ||||
\(448\) | 4.00000i | 0.188982i | ||||||||
\(449\) | −12.7279 | − | 12.7279i | −0.600668 | − | 0.600668i | 0.339822 | − | 0.940490i | \(-0.389633\pi\) |
−0.940490 | + | 0.339822i | \(0.889633\pi\) | |||||||
\(450\) | 2.70711 | − | 1.29289i | 0.127614 | − | 0.0609476i | ||||
\(451\) | 24.0000 | 1.13012 | ||||||||
\(452\) | −4.24264 | − | 4.24264i | −0.199557 | − | 0.199557i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.0000 | −1.31411 | ||||||||
\(455\) | −5.65685 | −0.265197 | ||||||||
\(456\) | −4.00000 | + | 2.82843i | −0.187317 | + | 0.132453i | ||||
\(457\) | −12.0000 | + | 12.0000i | −0.561336 | + | 0.561336i | −0.929687 | − | 0.368351i | \(-0.879923\pi\) |
0.368351 | + | 0.929687i | \(0.379923\pi\) | |||||||
\(458\) | 18.3848 | − | 18.3848i | 0.859064 | − | 0.859064i | ||||
\(459\) | 5.07107 | − | 9.07107i | 0.236697 | − | 0.423401i | ||||
\(460\) | −6.00000 | −0.279751 | ||||||||
\(461\) | −24.0416 | − | 24.0416i | −1.11973 | − | 1.11973i | −0.991781 | − | 0.127950i | \(-0.959160\pi\) |
−0.127950 | − | 0.991781i | \(-0.540840\pi\) | |||||||
\(462\) | −4.97056 | + | 28.9706i | −0.231252 | + | 1.34783i | ||||
\(463\) | −22.0000 | + | 22.0000i | −1.02243 | + | 1.02243i | −0.0226840 | + | 0.999743i | \(0.507221\pi\) |
−0.999743 | + | 0.0226840i | \(0.992779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.07107 | − | 10.0000i | −0.327913 | − | 0.463739i | ||||
\(466\) | −5.00000 | + | 5.00000i | −0.231621 | + | 0.231621i | ||||
\(467\) | 8.48528 | + | 8.48528i | 0.392652 | + | 0.392652i | 0.875632 | − | 0.482980i | \(-0.160445\pi\) |
−0.482980 | + | 0.875632i | \(0.660445\pi\) | |||||||
\(468\) | 3.82843 | − | 1.82843i | 0.176969 | − | 0.0845191i | ||||
\(469\) | − | 8.00000i | − | 0.369406i | ||||||
\(470\) | − | 1.41421i | − | 0.0652328i | ||||||
\(471\) | 25.4558 | − | 18.0000i | 1.17294 | − | 0.829396i | ||||
\(472\) | 4.00000i | 0.184115i | ||||||||
\(473\) | 38.1838 | − | 38.1838i | 1.75569 | − | 1.75569i | ||||
\(474\) | −4.24264 | − | 6.00000i | −0.194871 | − | 0.275589i | ||||
\(475\) | −2.00000 | − | 2.00000i | −0.0917663 | − | 0.0917663i | ||||
\(476\) | −5.65685 | + | 5.65685i | −0.259281 | + | 0.259281i | ||||
\(477\) | −8.00000 | − | 2.82843i | −0.366295 | − | 0.129505i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.4558 | + | 25.4558i | 1.16311 | + | 1.16311i | 0.983792 | + | 0.179316i | \(0.0573883\pi\) |
0.179316 | + | 0.983792i | \(0.442612\pi\) | |||||||
\(480\) | 1.41421 | − | 1.00000i | 0.0645497 | − | 0.0456435i | ||||
\(481\) | −7.00000 | + | 5.00000i | −0.319173 | + | 0.227980i | ||||
\(482\) | − | 4.24264i | − | 0.193247i | ||||||
\(483\) | 40.9706 | + | 7.02944i | 1.86423 | + | 0.319850i | ||||
\(484\) | − | 7.00000i | − | 0.318182i | ||||||
\(485\) | −16.9706 | −0.770594 | ||||||||
\(486\) | 11.7071 | − | 10.2929i | 0.531045 | − | 0.466895i | ||||
\(487\) | 22.0000 | − | 22.0000i | 0.996915 | − | 0.996915i | −0.00308010 | − | 0.999995i | \(-0.500980\pi\) |
0.999995 | + | 0.00308010i | \(0.000980427\pi\) | |||||||
\(488\) | − | 5.65685i | − | 0.256074i | ||||||
\(489\) | 12.0711 | + | 2.07107i | 0.545873 | + | 0.0936569i | ||||
\(490\) | 9.00000 | 0.406579 | ||||||||
\(491\) | − | 21.2132i | − | 0.957338i | −0.877995 | − | 0.478669i | \(-0.841119\pi\) | ||
0.877995 | − | 0.478669i | \(-0.158881\pi\) | |||||||
\(492\) | 5.65685 | + | 8.00000i | 0.255031 | + | 0.360668i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.82843 | − | 2.82843i | −0.127257 | − | 0.127257i | ||||
\(495\) | 11.4853 | − | 5.48528i | 0.516225 | − | 0.246545i | ||||
\(496\) | −5.00000 | − | 5.00000i | −0.224507 | − | 0.224507i | ||||
\(497\) | 11.3137i | 0.507489i | ||||||||
\(498\) | −4.82843 | − | 0.828427i | −0.216367 | − | 0.0371227i | ||||
\(499\) | −12.0000 | − | 12.0000i | −0.537194 | − | 0.537194i | 0.385510 | − | 0.922704i | \(-0.374026\pi\) |
−0.922704 | + | 0.385510i | \(0.874026\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | 30.7279 | + | 5.27208i | 1.37282 | + | 0.235539i | ||||
\(502\) | 4.00000i | 0.178529i | ||||||||
\(503\) | −21.2132 | − | 21.2132i | −0.945850 | − | 0.945850i | 0.0527574 | − | 0.998607i | \(-0.483199\pi\) |
−0.998607 | + | 0.0527574i | \(0.983199\pi\) | |||||||
\(504\) | −10.8284 | + | 5.17157i | −0.482336 | + | 0.230360i | ||||
\(505\) | 11.0000 | + | 11.0000i | 0.489494 | + | 0.489494i | ||||
\(506\) | −25.4558 | −1.13165 | ||||||||
\(507\) | −11.0000 | − | 15.5563i | −0.488527 | − | 0.690882i | ||||
\(508\) | 12.0000i | 0.532414i | ||||||||
\(509\) | −24.0416 | −1.06563 | −0.532813 | − | 0.846233i | \(-0.678865\pi\) | ||||
−0.532813 | + | 0.846233i | \(0.678865\pi\) | |||||||
\(510\) | 3.41421 | + | 0.585786i | 0.151184 | + | 0.0259391i | ||||
\(511\) | 24.0000i | 1.06170i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −12.8284 | − | 7.17157i | −0.566389 | − | 0.316633i | ||||
\(514\) | 4.00000 | 0.176432 | ||||||||
\(515\) | − | 14.1421i | − | 0.623177i | ||||||
\(516\) | 21.7279 | + | 3.72792i | 0.956518 | + | 0.164113i | ||||
\(517\) | − | 6.00000i | − | 0.263880i | ||||||
\(518\) | 19.7990 | − | 14.1421i | 0.869918 | − | 0.621370i | ||||
\(519\) | 4.00000 | − | 2.82843i | 0.175581 | − | 0.124154i | ||||
\(520\) | 1.00000 | + | 1.00000i | 0.0438529 | + | 0.0438529i | ||||
\(521\) | 8.48528 | 0.371747 | 0.185873 | − | 0.982574i | \(-0.440489\pi\) | ||||
0.185873 | + | 0.982574i | \(0.440489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.00000 | + | 9.00000i | −0.393543 | + | 0.393543i | −0.875948 | − | 0.482405i | \(-0.839763\pi\) |
0.482405 | + | 0.875948i | \(0.339763\pi\) | |||||||
\(524\) | −8.48528 | − | 8.48528i | −0.370681 | − | 0.370681i | ||||
\(525\) | −4.00000 | − | 5.65685i | −0.174574 | − | 0.246885i | ||||
\(526\) | −19.0000 | + | 19.0000i | −0.828439 | + | 0.828439i | ||||
\(527\) | − | 14.1421i | − | 0.616041i | ||||||
\(528\) | 6.00000 | − | 4.24264i | 0.261116 | − | 0.184637i | ||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | − | 2.82843i | − | 0.122859i | ||||||
\(531\) | −10.8284 | + | 5.17157i | −0.469914 | + | 0.224427i | ||||
\(532\) | 8.00000 | + | 8.00000i | 0.346844 | + | 0.346844i | ||||
\(533\) | −5.65685 | + | 5.65685i | −0.245026 | + | 0.245026i | ||||
\(534\) | −18.0000 | − | 25.4558i | −0.778936 | − | 1.10158i | ||||
\(535\) | −10.0000 | + | 10.0000i | −0.432338 | + | 0.432338i | ||||
\(536\) | −1.41421 | + | 1.41421i | −0.0610847 | + | 0.0610847i | ||||
\(537\) | 5.27208 | − | 30.7279i | 0.227507 | − | 1.32601i | ||||
\(538\) | 15.0000 | + | 15.0000i | 0.646696 | + | 0.646696i | ||||
\(539\) | 38.1838 | 1.64469 | ||||||||
\(540\) | 4.53553 | + | 2.53553i | 0.195178 | + | 0.109112i | ||||
\(541\) | 2.00000 | − | 2.00000i | 0.0859867 | − | 0.0859867i | −0.662805 | − | 0.748792i | \(-0.730634\pi\) |
0.748792 | + | 0.662805i | \(0.230634\pi\) | |||||||
\(542\) | −5.65685 | + | 5.65685i | −0.242983 | + | 0.242983i | ||||
\(543\) | −8.48528 | + | 6.00000i | −0.364138 | + | 0.257485i | ||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 16.9706 | 0.726939 | ||||||||
\(546\) | −5.65685 | − | 8.00000i | −0.242091 | − | 0.342368i | ||||
\(547\) | −21.0000 | − | 21.0000i | −0.897895 | − | 0.897895i | 0.0973546 | − | 0.995250i | \(-0.468962\pi\) |
−0.995250 | + | 0.0973546i | \(0.968962\pi\) | |||||||
\(548\) | −9.89949 | −0.422885 | ||||||||
\(549\) | 15.3137 | − | 7.31371i | 0.653573 | − | 0.312141i | ||||
\(550\) | 3.00000 | + | 3.00000i | 0.127920 | + | 0.127920i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −6.00000 | − | 8.48528i | −0.255377 | − | 0.361158i | ||||
\(553\) | −12.0000 | + | 12.0000i | −0.510292 | + | 0.510292i | ||||
\(554\) | −21.2132 | −0.901263 | ||||||||
\(555\) | −9.94975 | − | 3.46447i | −0.422343 | − | 0.147058i | ||||
\(556\) | −16.0000 | −0.678551 | ||||||||
\(557\) | −24.0416 | + | 24.0416i | −1.01868 | + | 1.01868i | −0.0188543 | + | 0.999822i | \(0.506002\pi\) |
−0.999822 | + | 0.0188543i | \(0.993998\pi\) | |||||||
\(558\) | 7.07107 | − | 20.0000i | 0.299342 | − | 0.846668i | ||||
\(559\) | 18.0000i | 0.761319i | ||||||||
\(560\) | −2.82843 | − | 2.82843i | −0.119523 | − | 0.119523i | ||||
\(561\) | 14.4853 | + | 2.48528i | 0.611569 | + | 0.104929i | ||||
\(562\) | −10.0000 | −0.421825 | ||||||||
\(563\) | 5.65685 | + | 5.65685i | 0.238408 | + | 0.238408i | 0.816191 | − | 0.577783i | \(-0.196082\pi\) |
−0.577783 | + | 0.816191i | \(0.696082\pi\) | |||||||
\(564\) | 2.00000 | − | 1.41421i | 0.0842152 | − | 0.0595491i | ||||
\(565\) | 6.00000 | 0.252422 | ||||||||
\(566\) | −21.2132 | −0.891657 | ||||||||
\(567\) | −28.0000 | − | 22.6274i | −1.17589 | − | 0.950262i | ||||
\(568\) | 2.00000 | − | 2.00000i | 0.0839181 | − | 0.0839181i | ||||
\(569\) | 18.3848 | − | 18.3848i | 0.770730 | − | 0.770730i | −0.207504 | − | 0.978234i | \(-0.566534\pi\) |
0.978234 | + | 0.207504i | \(0.0665341\pi\) | |||||||
\(570\) | 0.828427 | − | 4.82843i | 0.0346990 | − | 0.202241i | ||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 4.24264 | + | 4.24264i | 0.177394 | + | 0.177394i | ||||
\(573\) | −6.82843 | − | 1.17157i | −0.285262 | − | 0.0489432i | ||||
\(574\) | 16.0000 | − | 16.0000i | 0.667827 | − | 0.667827i | ||||
\(575\) | 4.24264 | − | 4.24264i | 0.176930 | − | 0.176930i | ||||
\(576\) | 2.82843 | + | 1.00000i | 0.117851 | + | 0.0416667i | ||||
\(577\) | 20.0000 | − | 20.0000i | 0.832611 | − | 0.832611i | −0.155262 | − | 0.987873i | \(-0.549622\pi\) |
0.987873 | + | 0.155262i | \(0.0496223\pi\) | |||||||
\(578\) | −9.19239 | − | 9.19239i | −0.382353 | − | 0.382353i | ||||
\(579\) | −7.45584 | + | 43.4558i | −0.309854 | + | 1.80596i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.3137i | 0.469372i | ||||||||
\(582\) | −16.9706 | − | 24.0000i | −0.703452 | − | 0.994832i | ||||
\(583\) | − | 12.0000i | − | 0.496989i | ||||||
\(584\) | 4.24264 | − | 4.24264i | 0.175562 | − | 0.175562i | ||||
\(585\) | −1.41421 | + | 4.00000i | −0.0584705 | + | 0.165380i | ||||
\(586\) | 20.0000 | + | 20.0000i | 0.826192 | + | 0.826192i | ||||
\(587\) | 16.9706 | − | 16.9706i | 0.700450 | − | 0.700450i | −0.264057 | − | 0.964507i | \(-0.585061\pi\) |
0.964507 | + | 0.264057i | \(0.0850607\pi\) | |||||||
\(588\) | 9.00000 | + | 12.7279i | 0.371154 | + | 0.524891i | ||||
\(589\) | −20.0000 | −0.824086 | ||||||||
\(590\) | −2.82843 | − | 2.82843i | −0.116445 | − | 0.116445i | ||||
\(591\) | −19.7990 | − | 28.0000i | −0.814422 | − | 1.15177i | ||||
\(592\) | −6.00000 | − | 1.00000i | −0.246598 | − | 0.0410997i | ||||
\(593\) | 15.5563i | 0.638823i | 0.947616 | + | 0.319411i | \(0.103485\pi\) | ||||
−0.947616 | + | 0.319411i | \(0.896515\pi\) | |||||||
\(594\) | 19.2426 | + | 10.7574i | 0.789535 | + | 0.441380i | ||||
\(595\) | − | 8.00000i | − | 0.327968i | ||||||
\(596\) | 9.89949 | 0.405499 | ||||||||
\(597\) | 7.24264 | + | 1.24264i | 0.296422 | + | 0.0508579i | ||||
\(598\) | 6.00000 | − | 6.00000i | 0.245358 | − | 0.245358i | ||||
\(599\) | 16.9706i | 0.693398i | 0.937976 | + | 0.346699i | \(0.112698\pi\) | ||||
−0.937976 | + | 0.346699i | \(0.887302\pi\) | |||||||
\(600\) | −0.292893 | + | 1.70711i | −0.0119573 | + | 0.0696923i | ||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | − | 50.9117i | − | 2.07501i | ||||||
\(603\) | −5.65685 | − | 2.00000i | −0.230365 | − | 0.0814463i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.94975 | + | 4.94975i | 0.201236 | + | 0.201236i | ||||
\(606\) | −4.55635 | + | 26.5563i | −0.185089 | + | 1.07878i | ||||
\(607\) | −22.0000 | − | 22.0000i | −0.892952 | − | 0.892952i | 0.101848 | − | 0.994800i | \(-0.467525\pi\) |
−0.994800 | + | 0.101848i | \(0.967525\pi\) | |||||||
\(608\) | − | 2.82843i | − | 0.114708i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000 | + | 4.00000i | 0.161955 | + | 0.161955i | ||||
\(611\) | 1.41421 | + | 1.41421i | 0.0572130 | + | 0.0572130i | ||||
\(612\) | 2.58579 | + | 5.41421i | 0.104524 | + | 0.218857i | ||||
\(613\) | − | 16.0000i | − | 0.646234i | −0.946359 | − | 0.323117i | \(-0.895269\pi\) | ||
0.946359 | − | 0.323117i | \(-0.104731\pi\) | |||||||
\(614\) | 2.82843 | + | 2.82843i | 0.114146 | + | 0.114146i | ||||
\(615\) | −9.65685 | − | 1.65685i | −0.389402 | − | 0.0668108i | ||||
\(616\) | −12.0000 | − | 12.0000i | −0.483494 | − | 0.483494i | ||||
\(617\) | −21.2132 | −0.854011 | −0.427006 | − | 0.904249i | \(-0.640432\pi\) | ||||
−0.427006 | + | 0.904249i | \(0.640432\pi\) | |||||||
\(618\) | 20.0000 | − | 14.1421i | 0.804518 | − | 0.568880i | ||||
\(619\) | 16.0000i | 0.643094i | 0.946894 | + | 0.321547i | \(0.104203\pi\) | ||||
−0.946894 | + | 0.321547i | \(0.895797\pi\) | |||||||
\(620\) | 7.07107 | 0.283981 | ||||||||
\(621\) | 15.2132 | − | 27.2132i | 0.610485 | − | 1.09203i | ||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | −50.9117 | + | 50.9117i | −2.03973 | + | 2.03973i | ||||
\(624\) | −0.414214 | + | 2.41421i | −0.0165818 | + | 0.0966459i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | − | 8.48528i | − | 0.339140i | ||||||
\(627\) | 3.51472 | − | 20.4853i | 0.140364 | − | 0.818103i | ||||
\(628\) | 18.0000i | 0.718278i | ||||||||
\(629\) | −7.07107 | − | 9.89949i | −0.281942 | − | 0.394719i | ||||
\(630\) | 4.00000 | − | 11.3137i | 0.159364 | − | 0.450749i | ||||
\(631\) | 1.00000 | + | 1.00000i | 0.0398094 | + | 0.0398094i | 0.726731 | − | 0.686922i | \(-0.241039\pi\) |
−0.686922 | + | 0.726731i | \(0.741039\pi\) | |||||||
\(632\) | 4.24264 | 0.168763 | ||||||||
\(633\) | 22.6274 | − | 16.0000i | 0.899359 | − | 0.635943i | ||||
\(634\) | 6.00000 | − | 6.00000i | 0.238290 | − | 0.238290i | ||||
\(635\) | −8.48528 | − | 8.48528i | −0.336728 | − | 0.336728i | ||||
\(636\) | 4.00000 | − | 2.82843i | 0.158610 | − | 0.112154i | ||||
\(637\) | −9.00000 | + | 9.00000i | −0.356593 | + | 0.356593i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | + | 2.82843i | 0.316475 | + | 0.111891i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 22.6274i | 0.893729i | 0.894602 | + | 0.446865i | \(0.147459\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(642\) | −24.1421 | − | 4.14214i | −0.952814 | − | 0.163477i | ||||
\(643\) | 17.0000 | + | 17.0000i | 0.670415 | + | 0.670415i | 0.957812 | − | 0.287397i | \(-0.0927899\pi\) |
−0.287397 | + | 0.957812i | \(0.592790\pi\) | |||||||
\(644\) | −16.9706 | + | 16.9706i | −0.668734 | + | 0.668734i | ||||
\(645\) | −18.0000 | + | 12.7279i | −0.708749 | + | 0.501161i | ||||
\(646\) | 4.00000 | − | 4.00000i | 0.157378 | − | 0.157378i | ||||
\(647\) | 22.6274 | − | 22.6274i | 0.889576 | − | 0.889576i | −0.104907 | − | 0.994482i | \(-0.533454\pi\) |
0.994482 | + | 0.104907i | \(0.0334543\pi\) | |||||||
\(648\) | 0.949747 | + | 8.94975i | 0.0373096 | + | 0.351579i | ||||
\(649\) | −12.0000 | − | 12.0000i | −0.471041 | − | 0.471041i | ||||
\(650\) | −1.41421 | −0.0554700 | ||||||||
\(651\) | −48.2843 | − | 8.28427i | −1.89241 | − | 0.324686i | ||||
\(652\) | −5.00000 | + | 5.00000i | −0.195815 | + | 0.195815i | ||||
\(653\) | −4.24264 | + | 4.24264i | −0.166027 | + | 0.166027i | −0.785231 | − | 0.619203i | \(-0.787456\pi\) |
0.619203 | + | 0.785231i | \(0.287456\pi\) | |||||||
\(654\) | 16.9706 | + | 24.0000i | 0.663602 | + | 0.938474i | ||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | −5.65685 | −0.220863 | ||||||||
\(657\) | 16.9706 | + | 6.00000i | 0.662085 | + | 0.234082i | ||||
\(658\) | −4.00000 | − | 4.00000i | −0.155936 | − | 0.155936i | ||||
\(659\) | 9.89949 | 0.385630 | 0.192815 | − | 0.981235i | \(-0.438238\pi\) | ||||
0.192815 | + | 0.981235i | \(0.438238\pi\) | |||||||
\(660\) | −1.24264 | + | 7.24264i | −0.0483697 | + | 0.281919i | ||||
\(661\) | 10.0000 | + | 10.0000i | 0.388955 | + | 0.388955i | 0.874315 | − | 0.485360i | \(-0.161311\pi\) |
−0.485360 | + | 0.874315i | \(0.661311\pi\) | |||||||
\(662\) | 5.65685i | 0.219860i | ||||||||
\(663\) | −4.00000 | + | 2.82843i | −0.155347 | + | 0.109847i | ||||
\(664\) | 2.00000 | − | 2.00000i | 0.0776151 | − | 0.0776151i | ||||
\(665\) | −11.3137 | −0.438727 | ||||||||
\(666\) | −5.05025 | − | 17.5355i | −0.195693 | − | 0.679488i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −12.7279 | + | 12.7279i | −0.492458 | + | 0.492458i | ||||
\(669\) | 16.9706 | − | 12.0000i | 0.656120 | − | 0.463947i | ||||
\(670\) | − | 2.00000i | − | 0.0772667i | ||||||
\(671\) | 16.9706 | + | 16.9706i | 0.655141 | + | 0.655141i | ||||
\(672\) | 1.17157 | − | 6.82843i | 0.0451944 | − | 0.263412i | ||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 1.41421 | + | 1.41421i | 0.0544735 | + | 0.0544735i | ||||
\(675\) | −5.00000 | + | 1.41421i | −0.192450 | + | 0.0544331i | ||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | 28.2843 | 1.08705 | 0.543526 | − | 0.839392i | \(-0.317089\pi\) | ||||
0.543526 | + | 0.839392i | \(0.317089\pi\) | |||||||
\(678\) | 6.00000 | + | 8.48528i | 0.230429 | + | 0.325875i | ||||
\(679\) | −48.0000 | + | 48.0000i | −1.84207 | + | 1.84207i | ||||
\(680\) | −1.41421 | + | 1.41421i | −0.0542326 | + | 0.0542326i | ||||
\(681\) | 47.7990 | + | 8.20101i | 1.83166 | + | 0.314263i | ||||
\(682\) | 30.0000 | 1.14876 | ||||||||
\(683\) | 22.6274 | + | 22.6274i | 0.865814 | + | 0.865814i | 0.992006 | − | 0.126192i | \(-0.0402755\pi\) |
−0.126192 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(684\) | 7.65685 | − | 3.65685i | 0.292767 | − | 0.139823i | ||||
\(685\) | 7.00000 | − | 7.00000i | 0.267456 | − | 0.267456i | ||||
\(686\) | 5.65685 | − | 5.65685i | 0.215980 | − | 0.215980i | ||||
\(687\) | −36.7696 | + | 26.0000i | −1.40285 | + | 0.991962i | ||||
\(688\) | −9.00000 | + | 9.00000i | −0.343122 | + | 0.343122i | ||||
\(689\) | 2.82843 | + | 2.82843i | 0.107754 | + | 0.107754i | ||||
\(690\) | 10.2426 | + | 1.75736i | 0.389931 | + | 0.0669015i | ||||
\(691\) | 28.0000i | 1.06517i | 0.846376 | + | 0.532585i | \(0.178779\pi\) | ||||
−0.846376 | + | 0.532585i | \(0.821221\pi\) | |||||||
\(692\) | 2.82843i | 0.107521i | ||||||||
\(693\) | 16.9706 | − | 48.0000i | 0.644658 | − | 1.82337i | ||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | 11.3137 | − | 11.3137i | 0.429153 | − | 0.429153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | − | 8.00000i | −0.303022 | − | 0.303022i | ||||
\(698\) | −9.89949 | + | 9.89949i | −0.374701 | + | 0.374701i | ||||
\(699\) | 10.0000 | − | 7.07107i | 0.378235 | − | 0.267452i | ||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | −35.3553 | − | 35.3553i | −1.33535 | − | 1.33535i | −0.900503 | − | 0.434850i | \(-0.856802\pi\) |
−0.434850 | − | 0.900503i | \(-0.643198\pi\) | |||||||
\(702\) | −7.07107 | + | 2.00000i | −0.266880 | + | 0.0754851i | ||||
\(703\) | −14.0000 | + | 10.0000i | −0.528020 | + | 0.377157i | ||||
\(704\) | 4.24264i | 0.159901i | ||||||||
\(705\) | −0.414214 | + | 2.41421i | −0.0156002 | + | 0.0909245i | ||||
\(706\) | 34.0000i | 1.27961i | ||||||||
\(707\) | 62.2254 | 2.34023 | ||||||||
\(708\) | 1.17157 | − | 6.82843i | 0.0440304 | − | 0.256628i | ||||
\(709\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(710\) | 2.82843i | 0.106149i | ||||||||
\(711\) | 5.48528 | + | 11.4853i | 0.205714 | + | 0.430732i | ||||
\(712\) | 18.0000 | 0.674579 | ||||||||
\(713\) | − | 42.4264i | − | 1.58888i | ||||||
\(714\) | 11.3137 | − | 8.00000i | 0.423405 | − | 0.299392i | ||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | 12.7279 | + | 12.7279i | 0.475665 | + | 0.475665i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.00000 | − | 8.00000i | −0.298557 | − | 0.298557i | ||||
\(719\) | − | 19.7990i | − | 0.738378i | −0.929354 | − | 0.369189i | \(-0.879636\pi\) | ||
0.929354 | − | 0.369189i | \(-0.120364\pi\) | |||||||
\(720\) | −2.70711 | + | 1.29289i | −0.100888 | + | 0.0481833i | ||||
\(721\) | −40.0000 | − | 40.0000i | −1.48968 | − | 1.48968i | ||||
\(722\) | 7.77817 | + | 7.77817i | 0.289474 | + | 0.289474i | ||||
\(723\) | −1.24264 | + | 7.24264i | −0.0462143 | + | 0.269357i | ||||
\(724\) | − | 6.00000i | − | 0.222988i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.05025 | + | 11.9497i | −0.0760920 | + | 0.443497i | ||||
\(727\) | 8.00000 | + | 8.00000i | 0.296704 | + | 0.296704i | 0.839721 | − | 0.543018i | \(-0.182718\pi\) |
−0.543018 | + | 0.839721i | \(0.682718\pi\) | |||||||
\(728\) | 5.65685 | 0.209657 | ||||||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 6.00000i | 0.222070i | ||||||||
\(731\) | −25.4558 | −0.941518 | ||||||||
\(732\) | −1.65685 | + | 9.65685i | −0.0612391 | + | 0.356928i | ||||
\(733\) | − | 24.0000i | − | 0.886460i | −0.896408 | − | 0.443230i | \(-0.853832\pi\) | ||
0.896408 | − | 0.443230i | \(-0.146168\pi\) | |||||||
\(734\) | 5.65685 | − | 5.65685i | 0.208798 | − | 0.208798i | ||||
\(735\) | −15.3640 | − | 2.63604i | −0.566708 | − | 0.0972318i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | − | 8.48528i | − | 0.312559i | ||||||
\(738\) | −7.31371 | − | 15.3137i | −0.269221 | − | 0.563705i | ||||
\(739\) | − | 40.0000i | − | 1.47142i | −0.677295 | − | 0.735712i | \(-0.736848\pi\) | ||
0.677295 | − | 0.735712i | \(-0.263152\pi\) | |||||||
\(740\) | 4.94975 | − | 3.53553i | 0.181956 | − | 0.129969i | ||||
\(741\) | 4.00000 | + | 5.65685i | 0.146944 | + | 0.207810i | ||||
\(742\) | −8.00000 | − | 8.00000i | −0.293689 | − | 0.293689i | ||||
\(743\) | 49.4975 | 1.81589 | 0.907943 | − | 0.419093i | \(-0.137652\pi\) | ||||
0.907943 | + | 0.419093i | \(0.137652\pi\) | |||||||
\(744\) | 7.07107 | + | 10.0000i | 0.259238 | + | 0.366618i | ||||
\(745\) | −7.00000 | + | 7.00000i | −0.256460 | + | 0.256460i | ||||
\(746\) | 24.0416 | + | 24.0416i | 0.880227 | + | 0.880227i | ||||
\(747\) | 8.00000 | + | 2.82843i | 0.292705 | + | 0.103487i | ||||
\(748\) | −6.00000 | + | 6.00000i | −0.219382 | + | 0.219382i | ||||
\(749\) | 56.5685i | 2.06697i | ||||||||
\(750\) | −1.00000 | − | 1.41421i | −0.0365148 | − | 0.0516398i | ||||
\(751\) | 2.00000i | 0.0729810i | 0.999334 | + | 0.0364905i | \(0.0116179\pi\) | ||||
−0.999334 | + | 0.0364905i | \(0.988382\pi\) | |||||||
\(752\) | 1.41421i | 0.0515711i | ||||||||
\(753\) | 1.17157 | − | 6.82843i | 0.0426945 | − | 0.248842i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.0000 | − | 5.65685i | 0.727393 | − | 0.205738i | ||||
\(757\) | −5.00000 | + | 5.00000i | −0.181728 | + | 0.181728i | −0.792108 | − | 0.610380i | \(-0.791017\pi\) |
0.610380 | + | 0.792108i | \(0.291017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 43.4558 | + | 7.45584i | 1.57735 | + | 0.270630i | ||||
\(760\) | 2.00000 | + | 2.00000i | 0.0725476 | + | 0.0725476i | ||||
\(761\) | 22.6274 | 0.820243 | 0.410122 | − | 0.912031i | \(-0.365486\pi\) | ||||
0.410122 | + | 0.912031i | \(0.365486\pi\) | |||||||
\(762\) | 3.51472 | − | 20.4853i | 0.127325 | − | 0.742103i | ||||
\(763\) | 48.0000 | − | 48.0000i | 1.73772 | − | 1.73772i | ||||
\(764\) | 2.82843 | − | 2.82843i | 0.102329 | − | 0.102329i | ||||
\(765\) | −5.65685 | − | 2.00000i | −0.204524 | − | 0.0723102i | ||||
\(766\) | 16.0000 | 0.578103 | ||||||||
\(767\) | 5.65685 | 0.204257 | ||||||||
\(768\) | −1.41421 | + | 1.00000i | −0.0510310 | + | 0.0360844i | ||||
\(769\) | 19.0000 | + | 19.0000i | 0.685158 | + | 0.685158i | 0.961158 | − | 0.276000i | \(-0.0890090\pi\) |
−0.276000 | + | 0.961158i | \(0.589009\pi\) | |||||||
\(770\) | 16.9706 | 0.611577 | ||||||||
\(771\) | −6.82843 | − | 1.17157i | −0.245920 | − | 0.0421932i | ||||
\(772\) | −18.0000 | − | 18.0000i | −0.647834 | − | 0.647834i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | −36.0000 | − | 12.7279i | −1.29399 | − | 0.457496i | ||||
\(775\) | −5.00000 | + | 5.00000i | −0.179605 | + | 0.179605i | ||||
\(776\) | 16.9706 | 0.609208 | ||||||||
\(777\) | −37.9411 | + | 18.3431i | −1.36113 | + | 0.658057i | ||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | −11.3137 | + | 11.3137i | −0.405356 | + | 0.405356i | ||||
\(780\) | −1.41421 | − | 2.00000i | −0.0506370 | − | 0.0716115i | ||||
\(781\) | 12.0000i | 0.429394i | ||||||||
\(782\) | 8.48528 | + | 8.48528i | 0.303433 | + | 0.303433i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | −12.7279 | − | 12.7279i | −0.454279 | − | 0.454279i | ||||
\(786\) | 12.0000 | + | 16.9706i | 0.428026 | + | 0.605320i | ||||
\(787\) | 14.0000 | 0.499046 | 0.249523 | − | 0.968369i | \(-0.419726\pi\) | ||||
0.249523 | + | 0.968369i | \(0.419726\pi\) | |||||||
\(788\) | 19.7990 | 0.705310 | ||||||||
\(789\) | 38.0000 | − | 26.8701i | 1.35284 | − | 0.956599i | ||||
\(790\) | −3.00000 | + | 3.00000i | −0.106735 | + | 0.106735i | ||||
\(791\) | 16.9706 | − | 16.9706i | 0.603404 | − | 0.603404i | ||||
\(792\) | −11.4853 | + | 5.48528i | −0.408112 | + | 0.194911i | ||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | −12.7279 | − | 12.7279i | −0.451697 | − | 0.451697i | ||||
\(795\) | −0.828427 | + | 4.82843i | −0.0293813 | + | 0.171247i | ||||
\(796\) | −3.00000 | + | 3.00000i | −0.106332 | + | 0.106332i | ||||
\(797\) | 18.3848 | − | 18.3848i | 0.651222 | − | 0.651222i | −0.302065 | − | 0.953287i | \(-0.597676\pi\) |
0.953287 | + | 0.302065i | \(0.0976760\pi\) | |||||||
\(798\) | −11.3137 | − | 16.0000i | −0.400501 | − | 0.566394i | ||||
\(799\) | −2.00000 | + | 2.00000i | −0.0707549 | + | 0.0707549i | ||||
\(800\) | −0.707107 | − | 0.707107i | −0.0250000 | − | 0.0250000i | ||||
\(801\) | 23.2721 | + | 48.7279i | 0.822278 | + | 1.72172i | ||||
\(802\) | 22.0000i | 0.776847i | ||||||||
\(803\) | 25.4558i | 0.898317i | ||||||||
\(804\) | 2.82843 | − | 2.00000i | 0.0997509 | − | 0.0705346i | ||||
\(805\) | − | 24.0000i | − | 0.845889i | ||||||
\(806\) | −7.07107 | + | 7.07107i | −0.249068 | + | 0.249068i | ||||
\(807\) | −21.2132 | − | 30.0000i | −0.746740 | − | 1.05605i | ||||
\(808\) | −11.0000 | − | 11.0000i | −0.386979 | − | 0.386979i | ||||
\(809\) | −7.07107 | + | 7.07107i | −0.248606 | + | 0.248606i | −0.820398 | − | 0.571793i | \(-0.806248\pi\) |
0.571793 | + | 0.820398i | \(0.306248\pi\) | |||||||
\(810\) | −7.00000 | − | 5.65685i | −0.245955 | − | 0.198762i | ||||
\(811\) | 48.0000 | 1.68551 | 0.842754 | − | 0.538299i | \(-0.180933\pi\) | ||||
0.842754 | + | 0.538299i | \(0.180933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.3137 | − | 8.00000i | 0.396789 | − | 0.280572i | ||||
\(814\) | 21.0000 | − | 15.0000i | 0.736050 | − | 0.525750i | ||||
\(815\) | − | 7.07107i | − | 0.247689i | ||||||
\(816\) | −3.41421 | − | 0.585786i | −0.119521 | − | 0.0205066i | ||||
\(817\) | 36.0000i | 1.25948i | ||||||||
\(818\) | 12.7279 | 0.445021 | ||||||||
\(819\) | 7.31371 | + | 15.3137i | 0.255562 | + | 0.535104i | ||||
\(820\) | 4.00000 | − | 4.00000i | 0.139686 | − | 0.139686i | ||||
\(821\) | 26.8701i | 0.937771i | 0.883259 | + | 0.468886i | \(0.155344\pi\) | ||||
−0.883259 | + | 0.468886i | \(0.844656\pi\) | |||||||
\(822\) | 16.8995 | + | 2.89949i | 0.589438 | + | 0.101131i | ||||
\(823\) | −36.0000 | −1.25488 | −0.627441 | − | 0.778664i | \(-0.715897\pi\) | ||||
−0.627441 | + | 0.778664i | \(0.715897\pi\) | |||||||
\(824\) | 14.1421i | 0.492665i | ||||||||
\(825\) | −4.24264 | − | 6.00000i | −0.147710 | − | 0.208893i | ||||
\(826\) | −16.0000 | −0.556711 | ||||||||
\(827\) | 16.9706 | + | 16.9706i | 0.590124 | + | 0.590124i | 0.937665 | − | 0.347541i | \(-0.112983\pi\) |
−0.347541 | + | 0.937665i | \(0.612983\pi\) | |||||||
\(828\) | 7.75736 | + | 16.2426i | 0.269587 | + | 0.564471i | ||||
\(829\) | 12.0000 | + | 12.0000i | 0.416777 | + | 0.416777i | 0.884091 | − | 0.467314i | \(-0.154778\pi\) |
−0.467314 | + | 0.884091i | \(0.654778\pi\) | |||||||
\(830\) | 2.82843i | 0.0981761i | ||||||||
\(831\) | 36.2132 | + | 6.21320i | 1.25622 | + | 0.215534i | ||||
\(832\) | −1.00000 | − | 1.00000i | −0.0346688 | − | 0.0346688i | ||||
\(833\) | −12.7279 | − | 12.7279i | −0.440996 | − | 0.440996i | ||||
\(834\) | 27.3137 | + | 4.68629i | 0.945796 | + | 0.162273i | ||||
\(835\) | − | 18.0000i | − | 0.622916i | ||||||
\(836\) | 8.48528 | + | 8.48528i | 0.293470 | + | 0.293470i | ||||
\(837\) | −17.9289 | + | 32.0711i | −0.619715 | + | 1.10854i | ||||
\(838\) | −9.00000 | − | 9.00000i | −0.310900 | − | 0.310900i | ||||
\(839\) | 19.7990 | 0.683537 | 0.341769 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341769 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(840\) | 4.00000 | + | 5.65685i | 0.138013 | + | 0.195180i | ||||
\(841\) | 29.0000i | 1.00000i | ||||||||
\(842\) | −19.7990 | −0.682318 | ||||||||
\(843\) | 17.0711 | + | 2.92893i | 0.587959 | + | 0.100878i | ||||
\(844\) | 16.0000i | 0.550743i | ||||||||
\(845\) | −7.77817 | + | 7.77817i | −0.267577 | + | 0.267577i | ||||
\(846\) | −3.82843 | + | 1.82843i | −0.131624 | + | 0.0628626i | ||||
\(847\) | 28.0000 | 0.962091 | ||||||||
\(848\) | 2.82843i | 0.0971286i | ||||||||
\(849\) | 36.2132 | + | 6.21320i | 1.24283 | + | 0.213237i | ||||
\(850\) | − | 2.00000i | − | 0.0685994i | ||||||
\(851\) | −21.2132 | − | 29.6985i | −0.727179 | − | 1.01805i | ||||
\(852\) | −4.00000 | + | 2.82843i | −0.137038 | + | 0.0969003i | ||||
\(853\) | 37.0000 | + | 37.0000i | 1.26686 | + | 1.26686i | 0.947703 | + | 0.319152i | \(0.103398\pi\) |
0.319152 | + | 0.947703i | \(0.396602\pi\) | |||||||
\(854\) | 22.6274 | 0.774294 | ||||||||
\(855\) | −2.82843 | + | 8.00000i | −0.0967302 | + | 0.273594i | ||||
\(856\) | 10.0000 | − | 10.0000i | 0.341793 | − | 0.341793i | ||||
\(857\) | 12.7279 | + | 12.7279i | 0.434778 | + | 0.434778i | 0.890250 | − | 0.455472i | \(-0.150530\pi\) |
−0.455472 | + | 0.890250i | \(0.650530\pi\) | |||||||
\(858\) | −6.00000 | − | 8.48528i | −0.204837 | − | 0.289683i | ||||
\(859\) | −34.0000 | + | 34.0000i | −1.16007 | + | 1.16007i | −0.175604 | + | 0.984461i | \(0.556188\pi\) |
−0.984461 | + | 0.175604i | \(0.943812\pi\) | |||||||
\(860\) | − | 12.7279i | − | 0.434019i | ||||||
\(861\) | −32.0000 | + | 22.6274i | −1.09056 | + | 0.771140i | ||||
\(862\) | − | 12.0000i | − | 0.408722i | ||||||
\(863\) | − | 7.07107i | − | 0.240702i | −0.992731 | − | 0.120351i | \(-0.961598\pi\) | ||
0.992731 | − | 0.120351i | \(-0.0384020\pi\) | |||||||
\(864\) | −4.53553 | − | 2.53553i | −0.154302 | − | 0.0862606i | ||||
\(865\) | −2.00000 | − | 2.00000i | −0.0680020 | − | 0.0680020i | ||||
\(866\) | −4.24264 | + | 4.24264i | −0.144171 | + | 0.144171i | ||||
\(867\) | 13.0000 | + | 18.3848i | 0.441503 | + | 0.624380i | ||||
\(868\) | 20.0000 | − | 20.0000i | 0.678844 | − | 0.678844i | ||||
\(869\) | −12.7279 | + | 12.7279i | −0.431765 | + | 0.431765i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | + | 2.00000i | 0.0677674 | + | 0.0677674i | ||||
\(872\) | −16.9706 | −0.574696 | ||||||||
\(873\) | 21.9411 | + | 45.9411i | 0.742595 | + | 1.55487i | ||||
\(874\) | 12.0000 | − | 12.0000i | 0.405906 | − | 0.405906i | ||||
\(875\) | −2.82843 | + | 2.82843i | −0.0956183 | + | 0.0956183i | ||||
\(876\) | −8.48528 | + | 6.00000i | −0.286691 | + | 0.202721i | ||||
\(877\) | 20.0000 | 0.675352 | 0.337676 | − | 0.941262i | \(-0.390359\pi\) | ||||
0.337676 | + | 0.941262i | \(0.390359\pi\) | |||||||
\(878\) | 7.07107 | 0.238637 | ||||||||
\(879\) | −28.2843 | − | 40.0000i | −0.954005 | − | 1.34917i | ||||
\(880\) | −3.00000 | − | 3.00000i | −0.101130 | − | 0.101130i | ||||
\(881\) | −11.3137 | −0.381169 | −0.190584 | − | 0.981671i | \(-0.561038\pi\) | ||||
−0.190584 | + | 0.981671i | \(0.561038\pi\) | |||||||
\(882\) | −11.6360 | − | 24.3640i | −0.391806 | − | 0.820377i | ||||
\(883\) | 3.00000 | + | 3.00000i | 0.100958 | + | 0.100958i | 0.755782 | − | 0.654824i | \(-0.227257\pi\) |
−0.654824 | + | 0.755782i | \(0.727257\pi\) | |||||||
\(884\) | − | 2.82843i | − | 0.0951303i | ||||||
\(885\) | 4.00000 | + | 5.65685i | 0.134459 | + | 0.190153i | ||||
\(886\) | 2.00000 | − | 2.00000i | 0.0671913 | − | 0.0671913i | ||||
\(887\) | −26.8701 | −0.902208 | −0.451104 | − | 0.892471i | \(-0.648970\pi\) | ||||
−0.451104 | + | 0.892471i | \(0.648970\pi\) | |||||||
\(888\) | 9.94975 | + | 3.46447i | 0.333892 | + | 0.116260i | ||||
\(889\) | −48.0000 | −1.60987 | ||||||||
\(890\) | −12.7279 | + | 12.7279i | −0.426641 | + | 0.426641i | ||||
\(891\) | −29.6985 | − | 24.0000i | −0.994937 | − | 0.804030i | ||||
\(892\) | 12.0000i | 0.401790i | ||||||||
\(893\) | 2.82843 | + | 2.82843i | 0.0946497 | + | 0.0946497i | ||||
\(894\) | −16.8995 | − | 2.89949i | −0.565204 | − | 0.0969736i | ||||
\(895\) | −18.0000 | −0.601674 | ||||||||
\(896\) | 2.82843 | + | 2.82843i | 0.0944911 | + | 0.0944911i | ||||
\(897\) | −12.0000 | + | 8.48528i | −0.400668 | + | 0.283315i | ||||
\(898\) | −18.0000 | −0.600668 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | − | 2.82843i | 0.0333333 | − | 0.0942809i | ||||
\(901\) | −4.00000 | + | 4.00000i | −0.133259 | + | 0.133259i | ||||
\(902\) | 16.9706 | − | 16.9706i | 0.565058 | − | 0.565058i | ||||
\(903\) | −14.9117 | + | 86.9117i | −0.496230 | + | 2.89224i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 4.24264 | + | 4.24264i | 0.141030 | + | 0.141030i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.0000 | + | 19.0000i | −0.630885 | + | 0.630885i | −0.948290 | − | 0.317405i | \(-0.897188\pi\) |
0.317405 | + | 0.948290i | \(0.397188\pi\) | |||||||
\(908\) | −19.7990 | + | 19.7990i | −0.657053 | + | 0.657053i | ||||
\(909\) | 15.5563 | − | 44.0000i | 0.515972 | − | 1.45939i | ||||
\(910\) | −4.00000 | + | 4.00000i | −0.132599 | + | 0.132599i | ||||
\(911\) | 5.65685 | + | 5.65685i | 0.187420 | + | 0.187420i | 0.794580 | − | 0.607160i | \(-0.207691\pi\) |
−0.607160 | + | 0.794580i | \(0.707691\pi\) | |||||||
\(912\) | −0.828427 | + | 4.82843i | −0.0274320 | + | 0.159885i | ||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 16.9706i | 0.561336i | ||||||||
\(915\) | −5.65685 | − | 8.00000i | −0.187010 | − | 0.264472i | ||||
\(916\) | − | 26.0000i | − | 0.859064i | ||||||
\(917\) | 33.9411 | − | 33.9411i | 1.12083 | − | 1.12083i | ||||
\(918\) | −2.82843 | − | 10.0000i | −0.0933520 | − | 0.330049i | ||||
\(919\) | −5.00000 | − | 5.00000i | −0.164935 | − | 0.164935i | 0.619814 | − | 0.784749i | \(-0.287208\pi\) |
−0.784749 | + | 0.619814i | \(0.787208\pi\) | |||||||
\(920\) | −4.24264 | + | 4.24264i | −0.139876 | + | 0.139876i | ||||
\(921\) | −4.00000 | − | 5.65685i | −0.131804 | − | 0.186400i | ||||
\(922\) | −34.0000 | −1.11973 | ||||||||
\(923\) | −2.82843 | − | 2.82843i | −0.0930988 | − | 0.0930988i | ||||
\(924\) | 16.9706 | + | 24.0000i | 0.558291 | + | 0.789542i | ||||
\(925\) | −1.00000 | + | 6.00000i | −0.0328798 | + | 0.197279i | ||||
\(926\) | 31.1127i | 1.02243i | ||||||||
\(927\) | −38.2843 | + | 18.2843i | −1.25742 | + | 0.600534i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.7401 | −1.76316 | −0.881578 | − | 0.472038i | \(-0.843518\pi\) | ||||
−0.881578 | + | 0.472038i | \(0.843518\pi\) | |||||||
\(930\) | −12.0711 | − | 2.07107i | −0.395826 | − | 0.0679130i | ||||
\(931\) | −18.0000 | + | 18.0000i | −0.589926 | + | 0.589926i | ||||
\(932\) | 7.07107i | 0.231621i | ||||||||
\(933\) | 3.51472 | − | 20.4853i | 0.115067 | − | 0.670658i | ||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | − | 8.48528i | − | 0.277498i | ||||||
\(936\) | 1.41421 | − | 4.00000i | 0.0462250 | − | 0.130744i | ||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | −5.65685 | − | 5.65685i | −0.184703 | − | 0.184703i | ||||
\(939\) | −2.48528 | + | 14.4853i | −0.0811041 | + | 0.472709i | ||||
\(940\) | −1.00000 | − | 1.00000i | −0.0326164 | − | 0.0326164i | ||||
\(941\) | − | 24.0416i | − | 0.783735i | −0.920022 | − | 0.391867i | \(-0.871829\pi\) | ||
0.920022 | − | 0.391867i | \(-0.128171\pi\) | |||||||
\(942\) | 5.27208 | − | 30.7279i | 0.171774 | − | 1.00117i | ||||
\(943\) | −24.0000 | − | 24.0000i | −0.781548 | − | 0.781548i | ||||
\(944\) | 2.82843 | + | 2.82843i | 0.0920575 | + | 0.0920575i | ||||
\(945\) | −10.1421 | + | 18.1421i | −0.329924 | + | 0.590164i | ||||
\(946\) | − | 54.0000i | − | 1.75569i | ||||||
\(947\) | −2.82843 | − | 2.82843i | −0.0919115 | − | 0.0919115i | 0.659656 | − | 0.751568i | \(-0.270702\pi\) |
−0.751568 | + | 0.659656i | \(0.770702\pi\) | |||||||
\(948\) | −7.24264 | − | 1.24264i | −0.235230 | − | 0.0403591i | ||||
\(949\) | −6.00000 | − | 6.00000i | −0.194768 | − | 0.194768i | ||||
\(950\) | −2.82843 | −0.0917663 | ||||||||
\(951\) | −12.0000 | + | 8.48528i | −0.389127 | + | 0.275154i | ||||
\(952\) | 8.00000i | 0.259281i | ||||||||
\(953\) | −57.9828 | −1.87825 | −0.939123 | − | 0.343582i | \(-0.888360\pi\) | ||||
−0.939123 | + | 0.343582i | \(0.888360\pi\) | |||||||
\(954\) | −7.65685 | + | 3.65685i | −0.247900 | + | 0.118395i | ||||
\(955\) | 4.00000i | 0.129437i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.0000 | 1.16311 | ||||||||
\(959\) | − | 39.5980i | − | 1.27869i | ||||||
\(960\) | 0.292893 | − | 1.70711i | 0.00945309 | − | 0.0550966i | ||||
\(961\) | 19.0000i | 0.612903i | ||||||||
\(962\) | −1.41421 | + | 8.48528i | −0.0455961 | + | 0.273576i | ||||
\(963\) | 40.0000 | + | 14.1421i | 1.28898 | + | 0.455724i | ||||
\(964\) | −3.00000 | − | 3.00000i | −0.0966235 | − | 0.0966235i | ||||
\(965\) | 25.4558 | 0.819453 | ||||||||
\(966\) | 33.9411 | − | 24.0000i | 1.09204 | − | 0.772187i | ||||
\(967\) | −12.0000 | + | 12.0000i | −0.385894 | + | 0.385894i | −0.873220 | − | 0.487326i | \(-0.837972\pi\) |
0.487326 | + | 0.873220i | \(0.337972\pi\) | |||||||
\(968\) | −4.94975 | − | 4.94975i | −0.159091 | − | 0.159091i | ||||
\(969\) | −8.00000 | + | 5.65685i | −0.256997 | + | 0.181724i | ||||
\(970\) | −12.0000 | + | 12.0000i | −0.385297 | + | 0.385297i | ||||
\(971\) | 7.07107i | 0.226921i | 0.993542 | + | 0.113461i | \(0.0361936\pi\) | ||||
−0.993542 | + | 0.113461i | \(0.963806\pi\) | |||||||
\(972\) | 1.00000 | − | 15.5563i | 0.0320750 | − | 0.498970i | ||||
\(973\) | − | 64.0000i | − | 2.05175i | ||||||
\(974\) | − | 31.1127i | − | 0.996915i | ||||||
\(975\) | 2.41421 | + | 0.414214i | 0.0773167 | + | 0.0132655i | ||||
\(976\) | −4.00000 | − | 4.00000i | −0.128037 | − | 0.128037i | ||||
\(977\) | 22.6274 | − | 22.6274i | 0.723915 | − | 0.723915i | −0.245485 | − | 0.969400i | \(-0.578947\pi\) |
0.969400 | + | 0.245485i | \(0.0789473\pi\) | |||||||
\(978\) | 10.0000 | − | 7.07107i | 0.319765 | − | 0.226108i | ||||
\(979\) | −54.0000 | + | 54.0000i | −1.72585 | + | 1.72585i | ||||
\(980\) | 6.36396 | − | 6.36396i | 0.203289 | − | 0.203289i | ||||
\(981\) | −21.9411 | − | 45.9411i | −0.700526 | − | 1.46679i | ||||
\(982\) | −15.0000 | − | 15.0000i | −0.478669 | − | 0.478669i | ||||
\(983\) | −1.41421 | −0.0451064 | −0.0225532 | − | 0.999746i | \(-0.507180\pi\) | ||||
−0.0225532 | + | 0.999746i | \(0.507180\pi\) | |||||||
\(984\) | 9.65685 | + | 1.65685i | 0.307849 | + | 0.0528186i | ||||
\(985\) | −14.0000 | + | 14.0000i | −0.446077 | + | 0.446077i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.65685 | + | 8.00000i | 0.180060 | + | 0.254643i | ||||
\(988\) | −4.00000 | −0.127257 | ||||||||
\(989\) | −76.3675 | −2.42835 | ||||||||
\(990\) | 4.24264 | − | 12.0000i | 0.134840 | − | 0.381385i | ||||
\(991\) | 3.00000 | + | 3.00000i | 0.0952981 | + | 0.0952981i | 0.753149 | − | 0.657850i | \(-0.228534\pi\) |
−0.657850 | + | 0.753149i | \(0.728534\pi\) | |||||||
\(992\) | −7.07107 | −0.224507 | ||||||||
\(993\) | 1.65685 | − | 9.65685i | 0.0525787 | − | 0.306451i | ||||
\(994\) | 8.00000 | + | 8.00000i | 0.253745 | + | 0.253745i | ||||
\(995\) | − | 4.24264i | − | 0.134501i | ||||||
\(996\) | −4.00000 | + | 2.82843i | −0.126745 | + | 0.0896221i | ||||
\(997\) | 43.0000 | − | 43.0000i | 1.36182 | − | 1.36182i | 0.490231 | − | 0.871592i | \(-0.336912\pi\) |
0.871592 | − | 0.490231i | \(-0.163088\pi\) | |||||||
\(998\) | −16.9706 | −0.537194 | ||||||||
\(999\) | 3.48528 | + | 31.4142i | 0.110269 | + | 0.993902i |
(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 | 1110.2.u.b.401.2 | yes | 4 | |
3.2 | odd | 2 | inner | 1110.2.u.b.401.1 | yes | 4 | |
37.6 | odd | 4 | inner | 1110.2.u.b.191.1 | ✓ | 4 | |
111.80 | even | 4 | inner | 1110.2.u.b.191.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.b.191.1 | ✓ | 4 | 37.6 | odd | 4 | inner | |
1110.2.u.b.191.2 | yes | 4 | 111.80 | even | 4 | inner | |
1110.2.u.b.401.1 | yes | 4 | 3.2 | odd | 2 | inner | |
1110.2.u.b.401.2 | yes | 4 | 1.1 | even | 1 | trivial |