Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.2.b.f.337.4 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.04892i | − 1.44880i | −0.689378 | − | 0.724402i | \(-0.742116\pi\) | ||||
0.689378 | − | 0.724402i | \(-0.257884\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −2.19806 | −1.09903 | ||||||||
\(5\) | 3.35690i | 1.50125i | 0.660729 | + | 0.750625i | \(0.270247\pi\) | ||||
−0.660729 | + | 0.750625i | \(0.729753\pi\) | |||||||
\(6\) | 2.04892i | 0.836467i | ||||||||
\(7\) | − 2.24698i | − 0.849278i | −0.905363 | − | 0.424639i | \(-0.860401\pi\) | ||||
0.905363 | − | 0.424639i | \(-0.139599\pi\) | |||||||
\(8\) | 0.405813i | 0.143477i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.87800 | 2.17502 | ||||||||
\(11\) | − 4.93900i | − 1.48916i | −0.667531 | − | 0.744582i | \(-0.732649\pi\) | ||||
0.667531 | − | 0.744582i | \(-0.267351\pi\) | |||||||
\(12\) | 2.19806 | 0.634526 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.60388 | −1.23044 | ||||||||
\(15\) | − 3.35690i | − 0.866747i | ||||||||
\(16\) | −3.56465 | −0.891162 | ||||||||
\(17\) | −0.911854 | −0.221157 | −0.110579 | − | 0.993867i | \(-0.535270\pi\) | ||||
−0.110579 | + | 0.993867i | \(0.535270\pi\) | |||||||
\(18\) | − 2.04892i | − 0.482934i | ||||||||
\(19\) | − 3.80194i | − 0.872224i | −0.899892 | − | 0.436112i | \(-0.856355\pi\) | ||||
0.899892 | − | 0.436112i | \(-0.143645\pi\) | |||||||
\(20\) | − 7.37867i | − 1.64992i | ||||||||
\(21\) | 2.24698i | 0.490331i | ||||||||
\(22\) | −10.1196 | −2.15751 | ||||||||
\(23\) | −2.02715 | −0.422689 | −0.211345 | − | 0.977412i | \(-0.567784\pi\) | ||||
−0.211345 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(24\) | − 0.405813i | − 0.0828363i | ||||||||
\(25\) | −6.26875 | −1.25375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.93900i | 0.933383i | ||||||||
\(29\) | −3.93900 | −0.731454 | −0.365727 | − | 0.930722i | \(-0.619180\pi\) | ||||
−0.365727 | + | 0.930722i | \(0.619180\pi\) | |||||||
\(30\) | −6.87800 | −1.25575 | ||||||||
\(31\) | − 8.82908i | − 1.58575i | −0.609384 | − | 0.792875i | \(-0.708583\pi\) | ||||
0.609384 | − | 0.792875i | \(-0.291417\pi\) | |||||||
\(32\) | 8.11529i | 1.43459i | ||||||||
\(33\) | 4.93900i | 0.859770i | ||||||||
\(34\) | 1.86831i | 0.320413i | ||||||||
\(35\) | 7.54288 | 1.27498 | ||||||||
\(36\) | −2.19806 | −0.366344 | ||||||||
\(37\) | − 8.80194i | − 1.44703i | −0.690309 | − | 0.723515i | \(-0.742525\pi\) | ||||
0.690309 | − | 0.723515i | \(-0.257475\pi\) | |||||||
\(38\) | −7.78986 | −1.26368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.36227 | −0.215394 | ||||||||
\(41\) | 6.93900i | 1.08369i | 0.840478 | + | 0.541845i | \(0.182274\pi\) | ||||
−0.840478 | + | 0.541845i | \(0.817726\pi\) | |||||||
\(42\) | 4.60388 | 0.710393 | ||||||||
\(43\) | 2.28621 | 0.348643 | 0.174322 | − | 0.984689i | \(-0.444227\pi\) | ||||
0.174322 | + | 0.984689i | \(0.444227\pi\) | |||||||
\(44\) | 10.8562i | 1.63664i | ||||||||
\(45\) | 3.35690i | 0.500416i | ||||||||
\(46\) | 4.15346i | 0.612394i | ||||||||
\(47\) | − 3.80194i | − 0.554570i | −0.960788 | − | 0.277285i | \(-0.910565\pi\) | ||||
0.960788 | − | 0.277285i | \(-0.0894346\pi\) | |||||||
\(48\) | 3.56465 | 0.514512 | ||||||||
\(49\) | 1.95108 | 0.278726 | ||||||||
\(50\) | 12.8442i | 1.81644i | ||||||||
\(51\) | 0.911854 | 0.127685 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.542877 | 0.0745698 | 0.0372849 | − | 0.999305i | \(-0.488129\pi\) | ||||
0.0372849 | + | 0.999305i | \(0.488129\pi\) | |||||||
\(54\) | 2.04892i | 0.278822i | ||||||||
\(55\) | 16.5797 | 2.23561 | ||||||||
\(56\) | 0.911854 | 0.121852 | ||||||||
\(57\) | 3.80194i | 0.503579i | ||||||||
\(58\) | 8.07069i | 1.05973i | ||||||||
\(59\) | 4.71379i | 0.613683i | 0.951761 | + | 0.306842i | \(0.0992722\pi\) | ||||
−0.951761 | + | 0.306842i | \(0.900728\pi\) | |||||||
\(60\) | 7.37867i | 0.952582i | ||||||||
\(61\) | 3.67994 | 0.471168 | 0.235584 | − | 0.971854i | \(-0.424300\pi\) | ||||
0.235584 | + | 0.971854i | \(0.424300\pi\) | |||||||
\(62\) | −18.0901 | −2.29744 | ||||||||
\(63\) | − 2.24698i | − 0.283093i | ||||||||
\(64\) | 9.49827 | 1.18728 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.1196 | 1.24564 | ||||||||
\(67\) | − 1.52111i | − 0.185833i | −0.995674 | − | 0.0929164i | \(-0.970381\pi\) | ||||
0.995674 | − | 0.0929164i | \(-0.0296189\pi\) | |||||||
\(68\) | 2.00431 | 0.243059 | ||||||||
\(69\) | 2.02715 | 0.244040 | ||||||||
\(70\) | − 15.4547i | − 1.84719i | ||||||||
\(71\) | 2.37867i | 0.282296i | 0.989989 | + | 0.141148i | \(0.0450793\pi\) | ||||
−0.989989 | + | 0.141148i | \(0.954921\pi\) | |||||||
\(72\) | 0.405813i | 0.0478255i | ||||||||
\(73\) | − 7.41119i | − 0.867414i | −0.901054 | − | 0.433707i | \(-0.857205\pi\) | ||||
0.901054 | − | 0.433707i | \(-0.142795\pi\) | |||||||
\(74\) | −18.0344 | −2.09646 | ||||||||
\(75\) | 6.26875 | 0.723853 | ||||||||
\(76\) | 8.35690i | 0.958602i | ||||||||
\(77\) | −11.0978 | −1.26472 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.74094 | −0.420888 | −0.210444 | − | 0.977606i | \(-0.567491\pi\) | ||||
−0.210444 | + | 0.977606i | \(0.567491\pi\) | |||||||
\(80\) | − 11.9661i | − 1.33786i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.2174 | 1.57005 | ||||||||
\(83\) | 2.30798i | 0.253334i | 0.991945 | + | 0.126667i | \(0.0404279\pi\) | ||||
−0.991945 | + | 0.126667i | \(0.959572\pi\) | |||||||
\(84\) | − 4.93900i | − 0.538889i | ||||||||
\(85\) | − 3.06100i | − 0.332012i | ||||||||
\(86\) | − 4.68425i | − 0.505116i | ||||||||
\(87\) | 3.93900 | 0.422305 | ||||||||
\(88\) | 2.00431 | 0.213660 | ||||||||
\(89\) | 10.0586i | 1.06621i | 0.846049 | + | 0.533105i | \(0.178975\pi\) | ||||
−0.846049 | + | 0.533105i | \(0.821025\pi\) | |||||||
\(90\) | 6.87800 | 0.725005 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.45580 | 0.464549 | ||||||||
\(93\) | 8.82908i | 0.915533i | ||||||||
\(94\) | −7.78986 | −0.803462 | ||||||||
\(95\) | 12.7627 | 1.30943 | ||||||||
\(96\) | − 8.11529i | − 0.828264i | ||||||||
\(97\) | − 16.1293i | − 1.63768i | −0.574021 | − | 0.818841i | \(-0.694617\pi\) | ||||
0.574021 | − | 0.818841i | \(-0.305383\pi\) | |||||||
\(98\) | − 3.99761i | − 0.403819i | ||||||||
\(99\) | − 4.93900i | − 0.496388i | ||||||||
\(100\) | 13.7791 | 1.37791 | ||||||||
\(101\) | 9.94869 | 0.989932 | 0.494966 | − | 0.868912i | \(-0.335181\pi\) | ||||
0.494966 | + | 0.868912i | \(0.335181\pi\) | |||||||
\(102\) | − 1.86831i | − 0.184991i | ||||||||
\(103\) | 10.9879 | 1.08267 | 0.541336 | − | 0.840806i | \(-0.317919\pi\) | ||||
0.541336 | + | 0.840806i | \(0.317919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.54288 | −0.736109 | ||||||||
\(106\) | − 1.11231i | − 0.108037i | ||||||||
\(107\) | −9.87263 | −0.954423 | −0.477211 | − | 0.878789i | \(-0.658352\pi\) | ||||
−0.477211 | + | 0.878789i | \(0.658352\pi\) | |||||||
\(108\) | 2.19806 | 0.211509 | ||||||||
\(109\) | 20.2446i | 1.93908i | 0.244934 | + | 0.969540i | \(0.421234\pi\) | ||||
−0.244934 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(110\) | − 33.9705i | − 3.23896i | ||||||||
\(111\) | 8.80194i | 0.835443i | ||||||||
\(112\) | 8.00969i | 0.756844i | ||||||||
\(113\) | 9.69202 | 0.911749 | 0.455874 | − | 0.890044i | \(-0.349327\pi\) | ||||
0.455874 | + | 0.890044i | \(0.349327\pi\) | |||||||
\(114\) | 7.78986 | 0.729587 | ||||||||
\(115\) | − 6.80492i | − 0.634562i | ||||||||
\(116\) | 8.65817 | 0.803891 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.65817 | 0.889107 | ||||||||
\(119\) | 2.04892i | 0.187824i | ||||||||
\(120\) | 1.36227 | 0.124358 | ||||||||
\(121\) | −13.3937 | −1.21761 | ||||||||
\(122\) | − 7.53989i | − 0.682630i | ||||||||
\(123\) | − 6.93900i | − 0.625669i | ||||||||
\(124\) | 19.4069i | 1.74279i | ||||||||
\(125\) | − 4.25906i | − 0.380942i | ||||||||
\(126\) | −4.60388 | −0.410146 | ||||||||
\(127\) | −13.8116 | −1.22558 | −0.612792 | − | 0.790244i | \(-0.709954\pi\) | ||||
−0.612792 | + | 0.790244i | \(0.709954\pi\) | |||||||
\(128\) | − 3.23059i | − 0.285546i | ||||||||
\(129\) | −2.28621 | −0.201289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.99462 | 0.261641 | 0.130821 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130821 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(132\) | − 10.8562i | − 0.944914i | ||||||||
\(133\) | −8.54288 | −0.740761 | ||||||||
\(134\) | −3.11662 | −0.269235 | ||||||||
\(135\) | − 3.35690i | − 0.288916i | ||||||||
\(136\) | − 0.370042i | − 0.0317309i | ||||||||
\(137\) | − 23.0194i | − 1.96668i | −0.181781 | − | 0.983339i | \(-0.558186\pi\) | ||||
0.181781 | − | 0.983339i | \(-0.441814\pi\) | |||||||
\(138\) | − 4.15346i | − 0.353566i | ||||||||
\(139\) | 0.982542 | 0.0833381 | 0.0416690 | − | 0.999131i | \(-0.486732\pi\) | ||||
0.0416690 | + | 0.999131i | \(0.486732\pi\) | |||||||
\(140\) | −16.5797 | −1.40124 | ||||||||
\(141\) | 3.80194i | 0.320181i | ||||||||
\(142\) | 4.87369 | 0.408991 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.56465 | −0.297054 | ||||||||
\(145\) | − 13.2228i | − 1.09810i | ||||||||
\(146\) | −15.1849 | −1.25671 | ||||||||
\(147\) | −1.95108 | −0.160923 | ||||||||
\(148\) | 19.3472i | 1.59033i | ||||||||
\(149\) | 10.2591i | 0.840455i | 0.907419 | + | 0.420228i | \(0.138050\pi\) | ||||
−0.907419 | + | 0.420228i | \(0.861950\pi\) | |||||||
\(150\) | − 12.8442i | − 1.04872i | ||||||||
\(151\) | 20.1685i | 1.64129i | 0.571438 | + | 0.820646i | \(0.306386\pi\) | ||||
−0.571438 | + | 0.820646i | \(0.693614\pi\) | |||||||
\(152\) | 1.54288 | 0.125144 | ||||||||
\(153\) | −0.911854 | −0.0737190 | ||||||||
\(154\) | 22.7385i | 1.83232i | ||||||||
\(155\) | 29.6383 | 2.38061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4383 | 0.833070 | 0.416535 | − | 0.909120i | \(-0.363244\pi\) | ||||
0.416535 | + | 0.909120i | \(0.363244\pi\) | |||||||
\(158\) | 7.66487i | 0.609785i | ||||||||
\(159\) | −0.542877 | −0.0430529 | ||||||||
\(160\) | −27.2422 | −2.15368 | ||||||||
\(161\) | 4.55496i | 0.358981i | ||||||||
\(162\) | − 2.04892i | − 0.160978i | ||||||||
\(163\) | 11.0465i | 0.865231i | 0.901579 | + | 0.432615i | \(0.142409\pi\) | ||||
−0.901579 | + | 0.432615i | \(0.857591\pi\) | |||||||
\(164\) | − 15.2524i | − 1.19101i | ||||||||
\(165\) | −16.5797 | −1.29073 | ||||||||
\(166\) | 4.72886 | 0.367031 | ||||||||
\(167\) | − 8.10992i | − 0.627564i | −0.949495 | − | 0.313782i | \(-0.898404\pi\) | ||||
0.949495 | − | 0.313782i | \(-0.101596\pi\) | |||||||
\(168\) | −0.911854 | −0.0703511 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.27173 | −0.481020 | ||||||||
\(171\) | − 3.80194i | − 0.290741i | ||||||||
\(172\) | −5.02523 | −0.383170 | ||||||||
\(173\) | 18.0562 | 1.37279 | 0.686394 | − | 0.727230i | \(-0.259192\pi\) | ||||
0.686394 | + | 0.727230i | \(0.259192\pi\) | |||||||
\(174\) | − 8.07069i | − 0.611837i | ||||||||
\(175\) | 14.0858i | 1.06478i | ||||||||
\(176\) | 17.6058i | 1.32709i | ||||||||
\(177\) | − 4.71379i | − 0.354310i | ||||||||
\(178\) | 20.6093 | 1.54473 | ||||||||
\(179\) | 19.8702 | 1.48517 | 0.742585 | − | 0.669751i | \(-0.233599\pi\) | ||||
0.742585 | + | 0.669751i | \(0.233599\pi\) | |||||||
\(180\) | − 7.37867i | − 0.549973i | ||||||||
\(181\) | 10.0828 | 0.749446 | 0.374723 | − | 0.927137i | \(-0.377738\pi\) | ||||
0.374723 | + | 0.927137i | \(0.377738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.67994 | −0.272029 | ||||||||
\(184\) | − 0.822643i | − 0.0606461i | ||||||||
\(185\) | 29.5472 | 2.17235 | ||||||||
\(186\) | 18.0901 | 1.32643 | ||||||||
\(187\) | 4.50365i | 0.329339i | ||||||||
\(188\) | 8.35690i | 0.609489i | ||||||||
\(189\) | 2.24698i | 0.163444i | ||||||||
\(190\) | − 26.1497i | − 1.89710i | ||||||||
\(191\) | −6.58748 | −0.476653 | −0.238327 | − | 0.971185i | \(-0.576599\pi\) | ||||
−0.238327 | + | 0.971185i | \(0.576599\pi\) | |||||||
\(192\) | −9.49827 | −0.685479 | ||||||||
\(193\) | − 10.8672i | − 0.782242i | −0.920339 | − | 0.391121i | \(-0.872087\pi\) | ||||
0.920339 | − | 0.391121i | \(-0.127913\pi\) | |||||||
\(194\) | −33.0476 | −2.37268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.28860 | −0.306329 | ||||||||
\(197\) | 9.24160i | 0.658437i | 0.944254 | + | 0.329218i | \(0.106785\pi\) | ||||
−0.944254 | + | 0.329218i | \(0.893215\pi\) | |||||||
\(198\) | −10.1196 | −0.719169 | ||||||||
\(199\) | 1.56465 | 0.110915 | 0.0554574 | − | 0.998461i | \(-0.482338\pi\) | ||||
0.0554574 | + | 0.998461i | \(0.482338\pi\) | |||||||
\(200\) | − 2.54394i | − 0.179884i | ||||||||
\(201\) | 1.52111i | 0.107291i | ||||||||
\(202\) | − 20.3840i | − 1.43422i | ||||||||
\(203\) | 8.85086i | 0.621208i | ||||||||
\(204\) | −2.00431 | −0.140330 | ||||||||
\(205\) | −23.2935 | −1.62689 | ||||||||
\(206\) | − 22.5133i | − 1.56858i | ||||||||
\(207\) | −2.02715 | −0.140896 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.7778 | −1.29889 | ||||||||
\(210\) | 15.4547i | 1.06648i | ||||||||
\(211\) | 23.2446 | 1.60022 | 0.800112 | − | 0.599851i | \(-0.204774\pi\) | ||||
0.800112 | + | 0.599851i | \(0.204774\pi\) | |||||||
\(212\) | −1.19328 | −0.0819546 | ||||||||
\(213\) | − 2.37867i | − 0.162984i | ||||||||
\(214\) | 20.2282i | 1.38277i | ||||||||
\(215\) | 7.67456i | 0.523401i | ||||||||
\(216\) | − 0.405813i | − 0.0276121i | ||||||||
\(217\) | −19.8388 | −1.34674 | ||||||||
\(218\) | 41.4795 | 2.80935 | ||||||||
\(219\) | 7.41119i | 0.500802i | ||||||||
\(220\) | −36.4432 | −2.45700 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 18.0344 | 1.21039 | ||||||||
\(223\) | 10.7385i | 0.719106i | 0.933125 | + | 0.359553i | \(0.117071\pi\) | ||||
−0.933125 | + | 0.359553i | \(0.882929\pi\) | |||||||
\(224\) | 18.2349 | 1.21837 | ||||||||
\(225\) | −6.26875 | −0.417917 | ||||||||
\(226\) | − 19.8582i | − 1.32094i | ||||||||
\(227\) | − 6.97584i | − 0.463003i | −0.972835 | − | 0.231501i | \(-0.925636\pi\) | ||||
0.972835 | − | 0.231501i | \(-0.0743637\pi\) | |||||||
\(228\) | − 8.35690i | − 0.553449i | ||||||||
\(229\) | 16.8049i | 1.11050i | 0.831683 | + | 0.555250i | \(0.187378\pi\) | ||||
−0.831683 | + | 0.555250i | \(0.812622\pi\) | |||||||
\(230\) | −13.9427 | −0.919356 | ||||||||
\(231\) | 11.0978 | 0.730184 | ||||||||
\(232\) | − 1.59850i | − 0.104947i | ||||||||
\(233\) | −8.69202 | −0.569433 | −0.284717 | − | 0.958612i | \(-0.591900\pi\) | ||||
−0.284717 | + | 0.958612i | \(0.591900\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7627 | 0.832547 | ||||||||
\(236\) | − 10.3612i | − 0.674457i | ||||||||
\(237\) | 3.74094 | 0.243000 | ||||||||
\(238\) | 4.19806 | 0.272120 | ||||||||
\(239\) | − 22.9191i | − 1.48252i | −0.671220 | − | 0.741258i | \(-0.734229\pi\) | ||||
0.671220 | − | 0.741258i | \(-0.265771\pi\) | |||||||
\(240\) | 11.9661i | 0.772412i | ||||||||
\(241\) | − 21.9801i | − 1.41587i | −0.706280 | − | 0.707933i | \(-0.749628\pi\) | ||||
0.706280 | − | 0.707933i | \(-0.250372\pi\) | |||||||
\(242\) | 27.4426i | 1.76408i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.08874 | −0.517828 | ||||||||
\(245\) | 6.54958i | 0.418437i | ||||||||
\(246\) | −14.2174 | −0.906471 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.58296 | 0.227518 | ||||||||
\(249\) | − 2.30798i | − 0.146262i | ||||||||
\(250\) | −8.72646 | −0.551910 | ||||||||
\(251\) | −26.6437 | −1.68174 | −0.840868 | − | 0.541241i | \(-0.817955\pi\) | ||||
−0.840868 | + | 0.541241i | \(0.817955\pi\) | |||||||
\(252\) | 4.93900i | 0.311128i | ||||||||
\(253\) | 10.0121i | 0.629454i | ||||||||
\(254\) | 28.2989i | 1.77563i | ||||||||
\(255\) | 3.06100i | 0.191687i | ||||||||
\(256\) | 12.3773 | 0.773584 | ||||||||
\(257\) | −23.1444 | −1.44371 | −0.721853 | − | 0.692047i | \(-0.756709\pi\) | ||||
−0.721853 | + | 0.692047i | \(0.756709\pi\) | |||||||
\(258\) | 4.68425i | 0.291629i | ||||||||
\(259\) | −19.7778 | −1.22893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.93900 | −0.243818 | ||||||||
\(262\) | − 6.13574i | − 0.379067i | ||||||||
\(263\) | −18.5284 | −1.14251 | −0.571255 | − | 0.820773i | \(-0.693543\pi\) | ||||
−0.571255 | + | 0.820773i | \(0.693543\pi\) | |||||||
\(264\) | −2.00431 | −0.123357 | ||||||||
\(265\) | 1.82238i | 0.111948i | ||||||||
\(266\) | 17.5036i | 1.07322i | ||||||||
\(267\) | − 10.0586i | − 0.615577i | ||||||||
\(268\) | 3.34349i | 0.204236i | ||||||||
\(269\) | 9.75840 | 0.594980 | 0.297490 | − | 0.954725i | \(-0.403851\pi\) | ||||
0.297490 | + | 0.954725i | \(0.403851\pi\) | |||||||
\(270\) | −6.87800 | −0.418582 | ||||||||
\(271\) | 22.8019i | 1.38512i | 0.721361 | + | 0.692560i | \(0.243517\pi\) | ||||
−0.721361 | + | 0.692560i | \(0.756483\pi\) | |||||||
\(272\) | 3.25044 | 0.197087 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −47.1648 | −2.84933 | ||||||||
\(275\) | 30.9614i | 1.86704i | ||||||||
\(276\) | −4.45580 | −0.268207 | ||||||||
\(277\) | 23.9705 | 1.44025 | 0.720123 | − | 0.693847i | \(-0.244086\pi\) | ||||
0.720123 | + | 0.693847i | \(0.244086\pi\) | |||||||
\(278\) | − 2.01315i | − 0.120741i | ||||||||
\(279\) | − 8.82908i | − 0.528583i | ||||||||
\(280\) | 3.06100i | 0.182930i | ||||||||
\(281\) | 4.12498i | 0.246076i | 0.992402 | + | 0.123038i | \(0.0392637\pi\) | ||||
−0.992402 | + | 0.123038i | \(0.960736\pi\) | |||||||
\(282\) | 7.78986 | 0.463879 | ||||||||
\(283\) | 15.6558 | 0.930639 | 0.465320 | − | 0.885143i | \(-0.345939\pi\) | ||||
0.465320 | + | 0.885143i | \(0.345939\pi\) | |||||||
\(284\) | − 5.22846i | − 0.310252i | ||||||||
\(285\) | −12.7627 | −0.755998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5918 | 0.920354 | ||||||||
\(288\) | 8.11529i | 0.478198i | ||||||||
\(289\) | −16.1685 | −0.951090 | ||||||||
\(290\) | −27.0925 | −1.59092 | ||||||||
\(291\) | 16.1293i | 0.945516i | ||||||||
\(292\) | 16.2903i | 0.953315i | ||||||||
\(293\) | − 22.5948i | − 1.32000i | −0.751265 | − | 0.660001i | \(-0.770556\pi\) | ||||
0.751265 | − | 0.660001i | \(-0.229444\pi\) | |||||||
\(294\) | 3.99761i | 0.233145i | ||||||||
\(295\) | −15.8237 | −0.921292 | ||||||||
\(296\) | 3.57194 | 0.207615 | ||||||||
\(297\) | 4.93900i | 0.286590i | ||||||||
\(298\) | 21.0200 | 1.21765 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.7791 | −0.795537 | ||||||||
\(301\) | − 5.13706i | − 0.296095i | ||||||||
\(302\) | 41.3236 | 2.37791 | ||||||||
\(303\) | −9.94869 | −0.571537 | ||||||||
\(304\) | 13.5526i | 0.777293i | ||||||||
\(305\) | 12.3532i | 0.707341i | ||||||||
\(306\) | 1.86831i | 0.106804i | ||||||||
\(307\) | 6.55496i | 0.374111i | 0.982349 | + | 0.187056i | \(0.0598945\pi\) | ||||
−0.982349 | + | 0.187056i | \(0.940106\pi\) | |||||||
\(308\) | 24.3937 | 1.38996 | ||||||||
\(309\) | −10.9879 | −0.625081 | ||||||||
\(310\) | − 60.7265i | − 3.44903i | ||||||||
\(311\) | 12.0392 | 0.682682 | 0.341341 | − | 0.939940i | \(-0.389119\pi\) | ||||
0.341341 | + | 0.939940i | \(0.389119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.8950 | −1.91586 | −0.957929 | − | 0.287005i | \(-0.907340\pi\) | ||||
−0.957929 | + | 0.287005i | \(0.907340\pi\) | |||||||
\(314\) | − 21.3873i | − 1.20695i | ||||||||
\(315\) | 7.54288 | 0.424993 | ||||||||
\(316\) | 8.22282 | 0.462570 | ||||||||
\(317\) | − 4.49827i | − 0.252648i | −0.991989 | − | 0.126324i | \(-0.959682\pi\) | ||||
0.991989 | − | 0.126324i | \(-0.0403179\pi\) | |||||||
\(318\) | 1.11231i | 0.0623752i | ||||||||
\(319\) | 19.4547i | 1.08926i | ||||||||
\(320\) | 31.8847i | 1.78241i | ||||||||
\(321\) | 9.87263 | 0.551036 | ||||||||
\(322\) | 9.33273 | 0.520093 | ||||||||
\(323\) | 3.46681i | 0.192899i | ||||||||
\(324\) | −2.19806 | −0.122115 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.6334 | 1.25355 | ||||||||
\(327\) | − 20.2446i | − 1.11953i | ||||||||
\(328\) | −2.81594 | −0.155484 | ||||||||
\(329\) | −8.54288 | −0.470984 | ||||||||
\(330\) | 33.9705i | 1.87001i | ||||||||
\(331\) | − 11.2131i | − 0.616329i | −0.951333 | − | 0.308165i | \(-0.900285\pi\) | ||||
0.951333 | − | 0.308165i | \(-0.0997148\pi\) | |||||||
\(332\) | − 5.07308i | − 0.278421i | ||||||||
\(333\) | − 8.80194i | − 0.482343i | ||||||||
\(334\) | −16.6165 | −0.909217 | ||||||||
\(335\) | 5.10620 | 0.278981 | ||||||||
\(336\) | − 8.00969i | − 0.436964i | ||||||||
\(337\) | −7.04892 | −0.383979 | −0.191989 | − | 0.981397i | \(-0.561494\pi\) | ||||
−0.191989 | + | 0.981397i | \(0.561494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.69202 | −0.526398 | ||||||||
\(340\) | 6.72827i | 0.364891i | ||||||||
\(341\) | −43.6069 | −2.36144 | ||||||||
\(342\) | −7.78986 | −0.421227 | ||||||||
\(343\) | − 20.1129i | − 1.08599i | ||||||||
\(344\) | 0.927774i | 0.0500222i | ||||||||
\(345\) | 6.80492i | 0.366365i | ||||||||
\(346\) | − 36.9957i | − 1.98890i | ||||||||
\(347\) | −2.70410 | −0.145164 | −0.0725819 | − | 0.997362i | \(-0.523124\pi\) | ||||
−0.0725819 | + | 0.997362i | \(0.523124\pi\) | |||||||
\(348\) | −8.65817 | −0.464127 | ||||||||
\(349\) | 0.415502i | 0.0222413i | 0.999938 | + | 0.0111207i | \(0.00353989\pi\) | ||||
−0.999938 | + | 0.0111207i | \(0.996460\pi\) | |||||||
\(350\) | 28.8605 | 1.54266 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.0814 | 2.13635 | ||||||||
\(353\) | − 32.1672i | − 1.71209i | −0.516904 | − | 0.856044i | \(-0.672916\pi\) | ||||
0.516904 | − | 0.856044i | \(-0.327084\pi\) | |||||||
\(354\) | −9.65817 | −0.513326 | ||||||||
\(355\) | −7.98493 | −0.423796 | ||||||||
\(356\) | − 22.1094i | − 1.17180i | ||||||||
\(357\) | − 2.04892i | − 0.108440i | ||||||||
\(358\) | − 40.7125i | − 2.15172i | ||||||||
\(359\) | − 22.3521i | − 1.17970i | −0.807513 | − | 0.589850i | \(-0.799187\pi\) | ||||
0.807513 | − | 0.589850i | \(-0.200813\pi\) | |||||||
\(360\) | −1.36227 | −0.0717981 | ||||||||
\(361\) | 4.54527 | 0.239225 | ||||||||
\(362\) | − 20.6588i | − 1.08580i | ||||||||
\(363\) | 13.3937 | 0.702989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8786 | 1.30221 | ||||||||
\(366\) | 7.53989i | 0.394117i | ||||||||
\(367\) | −2.30260 | −0.120195 | −0.0600974 | − | 0.998193i | \(-0.519141\pi\) | ||||
−0.0600974 | + | 0.998193i | \(0.519141\pi\) | |||||||
\(368\) | 7.22606 | 0.376685 | ||||||||
\(369\) | 6.93900i | 0.361230i | ||||||||
\(370\) | − 60.5397i | − 3.14731i | ||||||||
\(371\) | − 1.21983i | − 0.0633305i | ||||||||
\(372\) | − 19.4069i | − 1.00620i | ||||||||
\(373\) | −19.2760 | −0.998076 | −0.499038 | − | 0.866580i | \(-0.666313\pi\) | ||||
−0.499038 | + | 0.866580i | \(0.666313\pi\) | |||||||
\(374\) | 9.22760 | 0.477148 | ||||||||
\(375\) | 4.25906i | 0.219937i | ||||||||
\(376\) | 1.54288 | 0.0795678 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.60388 | 0.236798 | ||||||||
\(379\) | − 7.33944i | − 0.377002i | −0.982073 | − | 0.188501i | \(-0.939637\pi\) | ||||
0.982073 | − | 0.188501i | \(-0.0603628\pi\) | |||||||
\(380\) | −28.0532 | −1.43910 | ||||||||
\(381\) | 13.8116 | 0.707591 | ||||||||
\(382\) | 13.4972i | 0.690577i | ||||||||
\(383\) | 19.0901i | 0.975457i | 0.872995 | + | 0.487728i | \(0.162174\pi\) | ||||
−0.872995 | + | 0.487728i | \(0.837826\pi\) | |||||||
\(384\) | 3.23059i | 0.164860i | ||||||||
\(385\) | − 37.2543i | − 1.89865i | ||||||||
\(386\) | −22.2661 | −1.13331 | ||||||||
\(387\) | 2.28621 | 0.116214 | ||||||||
\(388\) | 35.4532i | 1.79986i | ||||||||
\(389\) | 23.9879 | 1.21624 | 0.608118 | − | 0.793847i | \(-0.291925\pi\) | ||||
0.608118 | + | 0.793847i | \(0.291925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.84846 | 0.0934807 | ||||||||
\(392\) | 0.791775i | 0.0399907i | ||||||||
\(393\) | −2.99462 | −0.151059 | ||||||||
\(394\) | 18.9353 | 0.953946 | ||||||||
\(395\) | − 12.5579i | − 0.631859i | ||||||||
\(396\) | 10.8562i | 0.545546i | ||||||||
\(397\) | 4.41789i | 0.221728i | 0.993836 | + | 0.110864i | \(0.0353618\pi\) | ||||
−0.993836 | + | 0.110864i | \(0.964638\pi\) | |||||||
\(398\) | − 3.20583i | − 0.160694i | ||||||||
\(399\) | 8.54288 | 0.427679 | ||||||||
\(400\) | 22.3459 | 1.11729 | ||||||||
\(401\) | 20.4088i | 1.01917i | 0.860421 | + | 0.509583i | \(0.170200\pi\) | ||||
−0.860421 | + | 0.509583i | \(0.829800\pi\) | |||||||
\(402\) | 3.11662 | 0.155443 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −21.8678 | −1.08797 | ||||||||
\(405\) | 3.35690i | 0.166805i | ||||||||
\(406\) | 18.1347 | 0.900009 | ||||||||
\(407\) | −43.4728 | −2.15487 | ||||||||
\(408\) | 0.370042i | 0.0183198i | ||||||||
\(409\) | − 22.1491i | − 1.09520i | −0.836739 | − | 0.547602i | \(-0.815541\pi\) | ||||
0.836739 | − | 0.547602i | \(-0.184459\pi\) | |||||||
\(410\) | 47.7265i | 2.35704i | ||||||||
\(411\) | 23.0194i | 1.13546i | ||||||||
\(412\) | −24.1521 | −1.18989 | ||||||||
\(413\) | 10.5918 | 0.521188 | ||||||||
\(414\) | 4.15346i | 0.204131i | ||||||||
\(415\) | −7.74764 | −0.380317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.982542 | −0.0481153 | ||||||||
\(418\) | 38.4741i | 1.88183i | ||||||||
\(419\) | 14.7560 | 0.720878 | 0.360439 | − | 0.932783i | \(-0.382627\pi\) | ||||
0.360439 | + | 0.932783i | \(0.382627\pi\) | |||||||
\(420\) | 16.5797 | 0.809007 | ||||||||
\(421\) | 8.47219i | 0.412909i | 0.978456 | + | 0.206455i | \(0.0661926\pi\) | ||||
−0.978456 | + | 0.206455i | \(0.933807\pi\) | |||||||
\(422\) | − 47.6262i | − 2.31841i | ||||||||
\(423\) | − 3.80194i | − 0.184857i | ||||||||
\(424\) | 0.220306i | 0.0106990i | ||||||||
\(425\) | 5.71618 | 0.277276 | ||||||||
\(426\) | −4.87369 | −0.236131 | ||||||||
\(427\) | − 8.26875i | − 0.400153i | ||||||||
\(428\) | 21.7006 | 1.04894 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.7245 | 0.758305 | ||||||||
\(431\) | 2.39181i | 0.115210i | 0.998339 | + | 0.0576048i | \(0.0183463\pi\) | ||||
−0.998339 | + | 0.0576048i | \(0.981654\pi\) | |||||||
\(432\) | 3.56465 | 0.171504 | ||||||||
\(433\) | 10.4286 | 0.501169 | 0.250584 | − | 0.968095i | \(-0.419377\pi\) | ||||
0.250584 | + | 0.968095i | \(0.419377\pi\) | |||||||
\(434\) | 40.6480i | 1.95117i | ||||||||
\(435\) | 13.2228i | 0.633986i | ||||||||
\(436\) | − 44.4989i | − 2.13111i | ||||||||
\(437\) | 7.70709i | 0.368680i | ||||||||
\(438\) | 15.1849 | 0.725563 | ||||||||
\(439\) | 32.5502 | 1.55353 | 0.776767 | − | 0.629787i | \(-0.216858\pi\) | ||||
0.776767 | + | 0.629787i | \(0.216858\pi\) | |||||||
\(440\) | 6.72827i | 0.320758i | ||||||||
\(441\) | 1.95108 | 0.0929087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.58211 | 0.455260 | 0.227630 | − | 0.973748i | \(-0.426902\pi\) | ||||
0.227630 | + | 0.973748i | \(0.426902\pi\) | |||||||
\(444\) | − 19.3472i | − 0.918178i | ||||||||
\(445\) | −33.7657 | −1.60065 | ||||||||
\(446\) | 22.0024 | 1.04184 | ||||||||
\(447\) | − 10.2591i | − 0.485237i | ||||||||
\(448\) | − 21.3424i | − 1.00833i | ||||||||
\(449\) | 28.3937i | 1.33998i | 0.742369 | + | 0.669992i | \(0.233702\pi\) | ||||
−0.742369 | + | 0.669992i | \(0.766298\pi\) | |||||||
\(450\) | 12.8442i | 0.605479i | ||||||||
\(451\) | 34.2717 | 1.61379 | ||||||||
\(452\) | −21.3037 | −1.00204 | ||||||||
\(453\) | − 20.1685i | − 0.947600i | ||||||||
\(454\) | −14.2929 | −0.670800 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.54288 | −0.0722518 | ||||||||
\(457\) | 4.99569i | 0.233688i | 0.993150 | + | 0.116844i | \(0.0372778\pi\) | ||||
−0.993150 | + | 0.116844i | \(0.962722\pi\) | |||||||
\(458\) | 34.4319 | 1.60890 | ||||||||
\(459\) | 0.911854 | 0.0425617 | ||||||||
\(460\) | 14.9576i | 0.697404i | ||||||||
\(461\) | 1.35258i | 0.0629961i | 0.999504 | + | 0.0314981i | \(0.0100278\pi\) | ||||
−0.999504 | + | 0.0314981i | \(0.989972\pi\) | |||||||
\(462\) | − 22.7385i | − 1.05789i | ||||||||
\(463\) | 3.36467i | 0.156369i | 0.996939 | + | 0.0781846i | \(0.0249124\pi\) | ||||
−0.996939 | + | 0.0781846i | \(0.975088\pi\) | |||||||
\(464\) | 14.0411 | 0.651844 | ||||||||
\(465\) | −29.6383 | −1.37444 | ||||||||
\(466\) | 17.8092i | 0.824997i | ||||||||
\(467\) | −6.91079 | −0.319793 | −0.159897 | − | 0.987134i | \(-0.551116\pi\) | ||||
−0.159897 | + | 0.987134i | \(0.551116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.41789 | −0.157824 | ||||||||
\(470\) | − 26.1497i | − 1.20620i | ||||||||
\(471\) | −10.4383 | −0.480973 | ||||||||
\(472\) | −1.91292 | −0.0880492 | ||||||||
\(473\) | − 11.2916i | − 0.519188i | ||||||||
\(474\) | − 7.66487i | − 0.352059i | ||||||||
\(475\) | 23.8334i | 1.09355i | ||||||||
\(476\) | − 4.50365i | − 0.206424i | ||||||||
\(477\) | 0.542877 | 0.0248566 | ||||||||
\(478\) | −46.9594 | −2.14787 | ||||||||
\(479\) | − 3.51573i | − 0.160638i | −0.996769 | − | 0.0803189i | \(-0.974406\pi\) | ||||
0.996769 | − | 0.0803189i | \(-0.0255939\pi\) | |||||||
\(480\) | 27.2422 | 1.24343 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −45.0355 | −2.05131 | ||||||||
\(483\) | − 4.55496i | − 0.207258i | ||||||||
\(484\) | 29.4403 | 1.33819 | ||||||||
\(485\) | 54.1444 | 2.45857 | ||||||||
\(486\) | 2.04892i | 0.0929408i | ||||||||
\(487\) | − 12.8479i | − 0.582193i | −0.956694 | − | 0.291096i | \(-0.905980\pi\) | ||||
0.956694 | − | 0.291096i | \(-0.0940200\pi\) | |||||||
\(488\) | 1.49337i | 0.0676016i | ||||||||
\(489\) | − 11.0465i | − 0.499541i | ||||||||
\(490\) | 13.4196 | 0.606234 | ||||||||
\(491\) | −28.6708 | −1.29390 | −0.646948 | − | 0.762534i | \(-0.723955\pi\) | ||||
−0.646948 | + | 0.762534i | \(0.723955\pi\) | |||||||
\(492\) | 15.2524i | 0.687629i | ||||||||
\(493\) | 3.59179 | 0.161766 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.5797 | 0.745203 | ||||||||
\(496\) | 31.4726i | 1.41316i | ||||||||
\(497\) | 5.34481 | 0.239748 | ||||||||
\(498\) | −4.72886 | −0.211905 | ||||||||
\(499\) | − 33.5555i | − 1.50215i | −0.660215 | − | 0.751076i | \(-0.729535\pi\) | ||||
0.660215 | − | 0.751076i | \(-0.270465\pi\) | |||||||
\(500\) | 9.36168i | 0.418667i | ||||||||
\(501\) | 8.10992i | 0.362324i | ||||||||
\(502\) | 54.5907i | 2.43650i | ||||||||
\(503\) | 21.5633 | 0.961461 | 0.480730 | − | 0.876868i | \(-0.340372\pi\) | ||||
0.480730 | + | 0.876868i | \(0.340372\pi\) | |||||||
\(504\) | 0.911854 | 0.0406172 | ||||||||
\(505\) | 33.3967i | 1.48613i | ||||||||
\(506\) | 20.5139 | 0.911955 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.3588 | 1.34695 | ||||||||
\(509\) | − 8.89008i | − 0.394046i | −0.980399 | − | 0.197023i | \(-0.936873\pi\) | ||||
0.980399 | − | 0.197023i | \(-0.0631274\pi\) | |||||||
\(510\) | 6.27173 | 0.277717 | ||||||||
\(511\) | −16.6528 | −0.736676 | ||||||||
\(512\) | − 31.8213i | − 1.40632i | ||||||||
\(513\) | 3.80194i | 0.167860i | ||||||||
\(514\) | 47.4209i | 2.09165i | ||||||||
\(515\) | 36.8853i | 1.62536i | ||||||||
\(516\) | 5.02523 | 0.221223 | ||||||||
\(517\) | −18.7778 | −0.825846 | ||||||||
\(518\) | 40.5230i | 1.78048i | ||||||||
\(519\) | −18.0562 | −0.792580 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3478 | 0.847642 | 0.423821 | − | 0.905746i | \(-0.360688\pi\) | ||||
0.423821 | + | 0.905746i | \(0.360688\pi\) | |||||||
\(522\) | 8.07069i | 0.353244i | ||||||||
\(523\) | −12.5948 | −0.550731 | −0.275366 | − | 0.961340i | \(-0.588799\pi\) | ||||
−0.275366 | + | 0.961340i | \(0.588799\pi\) | |||||||
\(524\) | −6.58237 | −0.287552 | ||||||||
\(525\) | − 14.0858i | − 0.614753i | ||||||||
\(526\) | 37.9632i | 1.65527i | ||||||||
\(527\) | 8.05084i | 0.350700i | ||||||||
\(528\) | − 17.6058i | − 0.766194i | ||||||||
\(529\) | −18.8907 | −0.821334 | ||||||||
\(530\) | 3.73391 | 0.162191 | ||||||||
\(531\) | 4.71379i | 0.204561i | ||||||||
\(532\) | 18.7778 | 0.814120 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −20.6093 | −0.891850 | ||||||||
\(535\) | − 33.1414i | − 1.43283i | ||||||||
\(536\) | 0.617285 | 0.0266627 | ||||||||
\(537\) | −19.8702 | −0.857464 | ||||||||
\(538\) | − 19.9941i | − 0.862009i | ||||||||
\(539\) | − 9.63640i | − 0.415069i | ||||||||
\(540\) | 7.37867i | 0.317527i | ||||||||
\(541\) | − 29.0019i | − 1.24689i | −0.781867 | − | 0.623445i | \(-0.785733\pi\) | ||||
0.781867 | − | 0.623445i | \(-0.214267\pi\) | |||||||
\(542\) | 46.7193 | 2.00677 | ||||||||
\(543\) | −10.0828 | −0.432693 | ||||||||
\(544\) | − 7.39996i | − 0.317271i | ||||||||
\(545\) | −67.9590 | −2.91104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7006 | 1.18439 | 0.592197 | − | 0.805793i | \(-0.298261\pi\) | ||||
0.592197 | + | 0.805793i | \(0.298261\pi\) | |||||||
\(548\) | 50.5980i | 2.16144i | ||||||||
\(549\) | 3.67994 | 0.157056 | ||||||||
\(550\) | 63.4373 | 2.70497 | ||||||||
\(551\) | 14.9758i | 0.637992i | ||||||||
\(552\) | 0.822643i | 0.0350140i | ||||||||
\(553\) | 8.40581i | 0.357452i | ||||||||
\(554\) | − 49.1135i | − 2.08663i | ||||||||
\(555\) | −29.5472 | −1.25421 | ||||||||
\(556\) | −2.15969 | −0.0915912 | ||||||||
\(557\) | − 6.80971i | − 0.288537i | −0.989539 | − | 0.144268i | \(-0.953917\pi\) | ||||
0.989539 | − | 0.144268i | \(-0.0460828\pi\) | |||||||
\(558\) | −18.0901 | −0.765814 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −26.8877 | −1.13621 | ||||||||
\(561\) | − 4.50365i | − 0.190144i | ||||||||
\(562\) | 8.45175 | 0.356515 | ||||||||
\(563\) | 19.2524 | 0.811390 | 0.405695 | − | 0.914008i | \(-0.367030\pi\) | ||||
0.405695 | + | 0.914008i | \(0.367030\pi\) | |||||||
\(564\) | − 8.35690i | − 0.351889i | ||||||||
\(565\) | 32.5351i | 1.36876i | ||||||||
\(566\) | − 32.0774i | − 1.34831i | ||||||||
\(567\) | − 2.24698i | − 0.0943643i | ||||||||
\(568\) | −0.965294 | −0.0405028 | ||||||||
\(569\) | −7.84846 | −0.329025 | −0.164512 | − | 0.986375i | \(-0.552605\pi\) | ||||
−0.164512 | + | 0.986375i | \(0.552605\pi\) | |||||||
\(570\) | 26.1497i | 1.09529i | ||||||||
\(571\) | −29.8568 | −1.24947 | −0.624735 | − | 0.780837i | \(-0.714793\pi\) | ||||
−0.624735 | + | 0.780837i | \(0.714793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.58748 | 0.275196 | ||||||||
\(574\) | − 31.9463i | − 1.33341i | ||||||||
\(575\) | 12.7077 | 0.529947 | ||||||||
\(576\) | 9.49827 | 0.395761 | ||||||||
\(577\) | 8.97823i | 0.373769i | 0.982382 | + | 0.186884i | \(0.0598389\pi\) | ||||
−0.982382 | + | 0.186884i | \(0.940161\pi\) | |||||||
\(578\) | 33.1280i | 1.37794i | ||||||||
\(579\) | 10.8672i | 0.451627i | ||||||||
\(580\) | 29.0646i | 1.20684i | ||||||||
\(581\) | 5.18598 | 0.215151 | ||||||||
\(582\) | 33.0476 | 1.36987 | ||||||||
\(583\) | − 2.68127i | − 0.111047i | ||||||||
\(584\) | 3.00756 | 0.124454 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.2948 | −1.91242 | ||||||||
\(587\) | 23.8538i | 0.984553i | 0.870439 | + | 0.492277i | \(0.163835\pi\) | ||||
−0.870439 | + | 0.492277i | \(0.836165\pi\) | |||||||
\(588\) | 4.28860 | 0.176859 | ||||||||
\(589\) | −33.5676 | −1.38313 | ||||||||
\(590\) | 32.4215i | 1.33477i | ||||||||
\(591\) | − 9.24160i | − 0.380149i | ||||||||
\(592\) | 31.3758i | 1.28954i | ||||||||
\(593\) | − 11.9866i | − 0.492230i | −0.969241 | − | 0.246115i | \(-0.920846\pi\) | ||||
0.969241 | − | 0.246115i | \(-0.0791541\pi\) | |||||||
\(594\) | 10.1196 | 0.415212 | ||||||||
\(595\) | −6.87800 | −0.281971 | ||||||||
\(596\) | − 22.5501i | − 0.923686i | ||||||||
\(597\) | −1.56465 | −0.0640367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1142 | 1.18958 | 0.594788 | − | 0.803883i | \(-0.297236\pi\) | ||||
0.594788 | + | 0.803883i | \(0.297236\pi\) | |||||||
\(600\) | 2.54394i | 0.103856i | ||||||||
\(601\) | 37.1366 | 1.51483 | 0.757417 | − | 0.652932i | \(-0.226461\pi\) | ||||
0.757417 | + | 0.652932i | \(0.226461\pi\) | |||||||
\(602\) | −10.5254 | −0.428984 | ||||||||
\(603\) | − 1.52111i | − 0.0619442i | ||||||||
\(604\) | − 44.3317i | − 1.80383i | ||||||||
\(605\) | − 44.9614i | − 1.82794i | ||||||||
\(606\) | 20.3840i | 0.828045i | ||||||||
\(607\) | −14.2325 | −0.577680 | −0.288840 | − | 0.957377i | \(-0.593269\pi\) | ||||
−0.288840 | + | 0.957377i | \(0.593269\pi\) | |||||||
\(608\) | 30.8538 | 1.25129 | ||||||||
\(609\) | − 8.85086i | − 0.358655i | ||||||||
\(610\) | 25.3106 | 1.02480 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00431 | 0.0810195 | ||||||||
\(613\) | 30.3139i | 1.22437i | 0.790715 | + | 0.612184i | \(0.209709\pi\) | ||||
−0.790715 | + | 0.612184i | \(0.790291\pi\) | |||||||
\(614\) | 13.4306 | 0.542014 | ||||||||
\(615\) | 23.2935 | 0.939285 | ||||||||
\(616\) | − 4.50365i | − 0.181457i | ||||||||
\(617\) | − 24.9638i | − 1.00500i | −0.864576 | − | 0.502501i | \(-0.832413\pi\) | ||||
0.864576 | − | 0.502501i | \(-0.167587\pi\) | |||||||
\(618\) | 22.5133i | 0.905619i | ||||||||
\(619\) | − 35.6122i | − 1.43138i | −0.698420 | − | 0.715688i | \(-0.746113\pi\) | ||||
0.698420 | − | 0.715688i | \(-0.253887\pi\) | |||||||
\(620\) | −65.1469 | −2.61636 | ||||||||
\(621\) | 2.02715 | 0.0813466 | ||||||||
\(622\) | − 24.6674i | − 0.989072i | ||||||||
\(623\) | 22.6015 | 0.905509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0465 | −0.681861 | ||||||||
\(626\) | 69.4480i | 2.77570i | ||||||||
\(627\) | 18.7778 | 0.749912 | ||||||||
\(628\) | −22.9441 | −0.915570 | ||||||||
\(629\) | 8.02608i | 0.320021i | ||||||||
\(630\) | − 15.4547i | − 0.615731i | ||||||||
\(631\) | − 23.8829i | − 0.950763i | −0.879780 | − | 0.475382i | \(-0.842310\pi\) | ||||
0.879780 | − | 0.475382i | \(-0.157690\pi\) | |||||||
\(632\) | − 1.51812i | − 0.0603877i | ||||||||
\(633\) | −23.2446 | −0.923889 | ||||||||
\(634\) | −9.21659 | −0.366037 | ||||||||
\(635\) | − 46.3642i | − 1.83991i | ||||||||
\(636\) | 1.19328 | 0.0473165 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 39.8611 | 1.57812 | ||||||||
\(639\) | 2.37867i | 0.0940986i | ||||||||
\(640\) | 10.8447 | 0.428676 | ||||||||
\(641\) | 24.6577 | 0.973920 | 0.486960 | − | 0.873424i | \(-0.338106\pi\) | ||||
0.486960 | + | 0.873424i | \(0.338106\pi\) | |||||||
\(642\) | − 20.2282i | − 0.798343i | ||||||||
\(643\) | 47.8165i | 1.88570i | 0.333218 | + | 0.942850i | \(0.391866\pi\) | ||||
−0.333218 | + | 0.942850i | \(0.608134\pi\) | |||||||
\(644\) | − 10.0121i | − 0.394531i | ||||||||
\(645\) | − 7.67456i | − 0.302186i | ||||||||
\(646\) | 7.10321 | 0.279472 | ||||||||
\(647\) | 5.38942 | 0.211880 | 0.105940 | − | 0.994373i | \(-0.466215\pi\) | ||||
0.105940 | + | 0.994373i | \(0.466215\pi\) | |||||||
\(648\) | 0.405813i | 0.0159418i | ||||||||
\(649\) | 23.2814 | 0.913876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8388 | 0.777543 | ||||||||
\(652\) | − 24.2809i | − 0.950915i | ||||||||
\(653\) | −5.03790 | −0.197148 | −0.0985741 | − | 0.995130i | \(-0.531428\pi\) | ||||
−0.0985741 | + | 0.995130i | \(0.531428\pi\) | |||||||
\(654\) | −41.4795 | −1.62198 | ||||||||
\(655\) | 10.0526i | 0.392789i | ||||||||
\(656\) | − 24.7351i | − 0.965743i | ||||||||
\(657\) | − 7.41119i | − 0.289138i | ||||||||
\(658\) | 17.5036i | 0.682363i | ||||||||
\(659\) | −43.9812 | −1.71326 | −0.856632 | − | 0.515927i | \(-0.827447\pi\) | ||||
−0.856632 | + | 0.515927i | \(0.827447\pi\) | |||||||
\(660\) | 36.4432 | 1.41855 | ||||||||
\(661\) | 38.2194i | 1.48656i | 0.668980 | + | 0.743280i | \(0.266731\pi\) | ||||
−0.668980 | + | 0.743280i | \(0.733269\pi\) | |||||||
\(662\) | −22.9748 | −0.892940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.936608 | −0.0363474 | ||||||||
\(665\) | − 28.6775i | − 1.11207i | ||||||||
\(666\) | −18.0344 | −0.698820 | ||||||||
\(667\) | 7.98493 | 0.309178 | ||||||||
\(668\) | 17.8261i | 0.689713i | ||||||||
\(669\) | − 10.7385i | − 0.415176i | ||||||||
\(670\) | − 10.4622i | − 0.404189i | ||||||||
\(671\) | − 18.1752i | − 0.701647i | ||||||||
\(672\) | −18.2349 | −0.703426 | ||||||||
\(673\) | 6.66487 | 0.256912 | 0.128456 | − | 0.991715i | \(-0.458998\pi\) | ||||
0.128456 | + | 0.991715i | \(0.458998\pi\) | |||||||
\(674\) | 14.4426i | 0.556310i | ||||||||
\(675\) | 6.26875 | 0.241284 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.80194 | 0.184553 | 0.0922767 | − | 0.995733i | \(-0.470586\pi\) | ||||
0.0922767 | + | 0.995733i | \(0.470586\pi\) | |||||||
\(678\) | 19.8582i | 0.762648i | ||||||||
\(679\) | −36.2422 | −1.39085 | ||||||||
\(680\) | 1.24219 | 0.0476360 | ||||||||
\(681\) | 6.97584i | 0.267315i | ||||||||
\(682\) | 89.3469i | 3.42127i | ||||||||
\(683\) | − 11.2591i | − 0.430816i | −0.976524 | − | 0.215408i | \(-0.930892\pi\) | ||||
0.976524 | − | 0.215408i | \(-0.0691081\pi\) | |||||||
\(684\) | 8.35690i | 0.319534i | ||||||||
\(685\) | 77.2737 | 2.95247 | ||||||||
\(686\) | −41.2097 | −1.57339 | ||||||||
\(687\) | − 16.8049i | − 0.641148i | ||||||||
\(688\) | −8.14952 | −0.310698 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 13.9427 | 0.530790 | ||||||||
\(691\) | − 24.7144i | − 0.940179i | −0.882619 | − | 0.470090i | \(-0.844222\pi\) | ||||
0.882619 | − | 0.470090i | \(-0.155778\pi\) | |||||||
\(692\) | −39.6887 | −1.50874 | ||||||||
\(693\) | −11.0978 | −0.421572 | ||||||||
\(694\) | 5.54048i | 0.210314i | ||||||||
\(695\) | 3.29829i | 0.125111i | ||||||||
\(696\) | 1.59850i | 0.0605909i | ||||||||
\(697\) | − 6.32736i | − 0.239666i | ||||||||
\(698\) | 0.851329 | 0.0322233 | ||||||||
\(699\) | 8.69202 | 0.328762 | ||||||||
\(700\) | − 30.9614i | − 1.17023i | ||||||||
\(701\) | −25.8920 | −0.977927 | −0.488964 | − | 0.872304i | \(-0.662625\pi\) | ||||
−0.488964 | + | 0.872304i | \(0.662625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.4644 | −1.26213 | ||||||||
\(704\) | − 46.9120i | − 1.76806i | ||||||||
\(705\) | −12.7627 | −0.480671 | ||||||||
\(706\) | −65.9079 | −2.48048 | ||||||||
\(707\) | − 22.3545i | − 0.840728i | ||||||||
\(708\) | 10.3612i | 0.389398i | ||||||||
\(709\) | − 0.0851621i | − 0.00319833i | −0.999999 | − | 0.00159916i | \(-0.999491\pi\) | ||||
0.999999 | − | 0.00159916i | \(-0.000509030\pi\) | |||||||
\(710\) | 16.3605i | 0.613998i | ||||||||
\(711\) | −3.74094 | −0.140296 | ||||||||
\(712\) | −4.08192 | −0.152976 | ||||||||
\(713\) | 17.8979i | 0.670280i | ||||||||
\(714\) | −4.19806 | −0.157109 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43.6760 | −1.63225 | ||||||||
\(717\) | 22.9191i | 0.855931i | ||||||||
\(718\) | −45.7976 | −1.70915 | ||||||||
\(719\) | −27.0508 | −1.00883 | −0.504413 | − | 0.863463i | \(-0.668291\pi\) | ||||
−0.504413 | + | 0.863463i | \(0.668291\pi\) | |||||||
\(720\) | − 11.9661i | − 0.445952i | ||||||||
\(721\) | − 24.6896i | − 0.919490i | ||||||||
\(722\) | − 9.31288i | − 0.346590i | ||||||||
\(723\) | 21.9801i | 0.817451i | ||||||||
\(724\) | −22.1626 | −0.823665 | ||||||||
\(725\) | 24.6926 | 0.917061 | ||||||||
\(726\) | − 27.4426i | − 1.01849i | ||||||||
\(727\) | 47.1584 | 1.74901 | 0.874503 | − | 0.485019i | \(-0.161187\pi\) | ||||
0.874503 | + | 0.485019i | \(0.161187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 50.9742i | − 1.88664i | ||||||||
\(731\) | −2.08469 | −0.0771050 | ||||||||
\(732\) | 8.08874 | 0.298968 | ||||||||
\(733\) | − 9.68186i | − 0.357608i | −0.983885 | − | 0.178804i | \(-0.942777\pi\) | ||||
0.983885 | − | 0.178804i | \(-0.0572227\pi\) | |||||||
\(734\) | 4.71784i | 0.174139i | ||||||||
\(735\) | − 6.54958i | − 0.241585i | ||||||||
\(736\) | − 16.4509i | − 0.606388i | ||||||||
\(737\) | −7.51275 | −0.276736 | ||||||||
\(738\) | 14.2174 | 0.523351 | ||||||||
\(739\) | − 36.3139i | − 1.33583i | −0.744238 | − | 0.667915i | \(-0.767187\pi\) | ||||
0.744238 | − | 0.667915i | \(-0.232813\pi\) | |||||||
\(740\) | −64.9466 | −2.38748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.49934 | −0.0917535 | ||||||||
\(743\) | − 41.7536i | − 1.53179i | −0.642965 | − | 0.765896i | \(-0.722296\pi\) | ||||
0.642965 | − | 0.765896i | \(-0.277704\pi\) | |||||||
\(744\) | −3.58296 | −0.131358 | ||||||||
\(745\) | −34.4386 | −1.26173 | ||||||||
\(746\) | 39.4950i | 1.44602i | ||||||||
\(747\) | 2.30798i | 0.0844445i | ||||||||
\(748\) | − 9.89930i | − 0.361954i | ||||||||
\(749\) | 22.1836i | 0.810571i | ||||||||
\(750\) | 8.72646 | 0.318645 | ||||||||
\(751\) | 22.1927 | 0.809823 | 0.404911 | − | 0.914356i | \(-0.367302\pi\) | ||||
0.404911 | + | 0.914356i | \(0.367302\pi\) | |||||||
\(752\) | 13.5526i | 0.494211i | ||||||||
\(753\) | 26.6437 | 0.970950 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −67.7036 | −2.46399 | ||||||||
\(756\) | − 4.93900i | − 0.179630i | ||||||||
\(757\) | 9.23729 | 0.335735 | 0.167868 | − | 0.985810i | \(-0.446312\pi\) | ||||
0.167868 | + | 0.985810i | \(0.446312\pi\) | |||||||
\(758\) | −15.0379 | −0.546201 | ||||||||
\(759\) | − 10.0121i | − 0.363416i | ||||||||
\(760\) | 5.17928i | 0.187872i | ||||||||
\(761\) | 7.50173i | 0.271937i | 0.990713 | + | 0.135969i | \(0.0434147\pi\) | ||||
−0.990713 | + | 0.135969i | \(0.956585\pi\) | |||||||
\(762\) | − 28.2989i | − 1.02516i | ||||||||
\(763\) | 45.4892 | 1.64682 | ||||||||
\(764\) | 14.4797 | 0.523857 | ||||||||
\(765\) | − 3.06100i | − 0.110671i | ||||||||
\(766\) | 39.1140 | 1.41325 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.3773 | −0.446629 | ||||||||
\(769\) | 5.14005i | 0.185355i | 0.995696 | + | 0.0926774i | \(0.0295425\pi\) | ||||
−0.995696 | + | 0.0926774i | \(0.970457\pi\) | |||||||
\(770\) | −76.3309 | −2.75078 | ||||||||
\(771\) | 23.1444 | 0.833524 | ||||||||
\(772\) | 23.8869i | 0.859708i | ||||||||
\(773\) | − 8.50173i | − 0.305786i | −0.988243 | − | 0.152893i | \(-0.951141\pi\) | ||||
0.988243 | − | 0.152893i | \(-0.0488590\pi\) | |||||||
\(774\) | − 4.68425i | − 0.168372i | ||||||||
\(775\) | 55.3473i | 1.98813i | ||||||||
\(776\) | 6.54548 | 0.234969 | ||||||||
\(777\) | 19.7778 | 0.709524 | ||||||||
\(778\) | − 49.1493i | − 1.76209i | ||||||||
\(779\) | 26.3817 | 0.945221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7482 | 0.420385 | ||||||||
\(782\) | − 3.78735i | − 0.135435i | ||||||||
\(783\) | 3.93900 | 0.140768 | ||||||||
\(784\) | −6.95492 | −0.248390 | ||||||||
\(785\) | 35.0404i | 1.25065i | ||||||||
\(786\) | 6.13574i | 0.218854i | ||||||||
\(787\) | 7.78554i | 0.277525i | 0.990326 | + | 0.138762i | \(0.0443124\pi\) | ||||
−0.990326 | + | 0.138762i | \(0.955688\pi\) | |||||||
\(788\) | − 20.3136i | − 0.723643i | ||||||||
\(789\) | 18.5284 | 0.659629 | ||||||||
\(790\) | −25.7302 | −0.915439 | ||||||||
\(791\) | − 21.7778i | − 0.774329i | ||||||||
\(792\) | 2.00431 | 0.0712201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.05190 | 0.321240 | ||||||||
\(795\) | − 1.82238i | − 0.0646332i | ||||||||
\(796\) | −3.43919 | −0.121899 | ||||||||
\(797\) | −21.3840 | −0.757462 | −0.378731 | − | 0.925507i | \(-0.623639\pi\) | ||||
−0.378731 | + | 0.925507i | \(0.623639\pi\) | |||||||
\(798\) | − 17.5036i | − 0.619622i | ||||||||
\(799\) | 3.46681i | 0.122647i | ||||||||
\(800\) | − 50.8727i | − 1.79862i | ||||||||
\(801\) | 10.0586i | 0.355403i | ||||||||
\(802\) | 41.8159 | 1.47657 | ||||||||
\(803\) | −36.6039 | −1.29172 | ||||||||
\(804\) | − 3.34349i | − 0.117916i | ||||||||
\(805\) | −15.2905 | −0.538920 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.75840 | −0.343512 | ||||||||
\(808\) | 4.03731i | 0.142032i | ||||||||
\(809\) | 2.28621 | 0.0803788 | 0.0401894 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401894 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(810\) | 6.87800 | 0.241668 | ||||||||
\(811\) | 17.8079i | 0.625320i | 0.949865 | + | 0.312660i | \(0.101220\pi\) | ||||
−0.949865 | + | 0.312660i | \(0.898780\pi\) | |||||||
\(812\) | − 19.4547i | − 0.682727i | ||||||||
\(813\) | − 22.8019i | − 0.799699i | ||||||||
\(814\) | 89.0721i | 3.12198i | ||||||||
\(815\) | −37.0820 | −1.29893 | ||||||||
\(816\) | −3.25044 | −0.113788 | ||||||||
\(817\) | − 8.69202i | − 0.304095i | ||||||||
\(818\) | −45.3818 | −1.58674 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51.2006 | 1.78800 | ||||||||
\(821\) | 13.9054i | 0.485302i | 0.970114 | + | 0.242651i | \(0.0780170\pi\) | ||||
−0.970114 | + | 0.242651i | \(0.921983\pi\) | |||||||
\(822\) | 47.1648 | 1.64506 | ||||||||
\(823\) | 7.24831 | 0.252660 | 0.126330 | − | 0.991988i | \(-0.459680\pi\) | ||||
0.126330 | + | 0.991988i | \(0.459680\pi\) | |||||||
\(824\) | 4.45904i | 0.155338i | ||||||||
\(825\) | − 30.9614i | − 1.07794i | ||||||||
\(826\) | − 21.7017i | − 0.755099i | ||||||||
\(827\) | − 54.1191i | − 1.88191i | −0.338536 | − | 0.940953i | \(-0.609932\pi\) | ||||
0.338536 | − | 0.940953i | \(-0.390068\pi\) | |||||||
\(828\) | 4.45580 | 0.154850 | ||||||||
\(829\) | 5.79178 | 0.201157 | 0.100578 | − | 0.994929i | \(-0.467931\pi\) | ||||
0.100578 | + | 0.994929i | \(0.467931\pi\) | |||||||
\(830\) | 15.8743i | 0.551004i | ||||||||
\(831\) | −23.9705 | −0.831526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77910 | −0.0616422 | ||||||||
\(834\) | 2.01315i | 0.0697096i | ||||||||
\(835\) | 27.2241 | 0.942130 | ||||||||
\(836\) | 41.2747 | 1.42752 | ||||||||
\(837\) | 8.82908i | 0.305178i | ||||||||
\(838\) | − 30.2338i | − 1.04441i | ||||||||
\(839\) | 5.29350i | 0.182752i | 0.995816 | + | 0.0913760i | \(0.0291265\pi\) | ||||
−0.995816 | + | 0.0913760i | \(0.970873\pi\) | |||||||
\(840\) | − 3.06100i | − 0.105614i | ||||||||
\(841\) | −13.4843 | −0.464975 | ||||||||
\(842\) | 17.3588 | 0.598224 | ||||||||
\(843\) | − 4.12498i | − 0.142072i | ||||||||
\(844\) | −51.0930 | −1.75870 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.78986 | −0.267821 | ||||||||
\(847\) | 30.0954i | 1.03409i | ||||||||
\(848\) | −1.93516 | −0.0664538 | ||||||||
\(849\) | −15.6558 | −0.537305 | ||||||||
\(850\) | − 11.7120i | − 0.401718i | ||||||||
\(851\) | 17.8428i | 0.611644i | ||||||||
\(852\) | 5.22846i | 0.179124i | ||||||||
\(853\) | 13.5961i | 0.465522i | 0.972534 | + | 0.232761i | \(0.0747760\pi\) | ||||
−0.972534 | + | 0.232761i | \(0.925224\pi\) | |||||||
\(854\) | −16.9420 | −0.579743 | ||||||||
\(855\) | 12.7627 | 0.436475 | ||||||||
\(856\) | − 4.00644i | − 0.136937i | ||||||||
\(857\) | 23.8323 | 0.814097 | 0.407048 | − | 0.913407i | \(-0.366558\pi\) | ||||
0.407048 | + | 0.913407i | \(0.366558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.9861 | −0.920754 | −0.460377 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460377 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(860\) | − 16.8692i | − 0.575234i | ||||||||
\(861\) | −15.5918 | −0.531367 | ||||||||
\(862\) | 4.90063 | 0.166916 | ||||||||
\(863\) | − 27.0291i | − 0.920080i | −0.887898 | − | 0.460040i | \(-0.847835\pi\) | ||||
0.887898 | − | 0.460040i | \(-0.152165\pi\) | |||||||
\(864\) | − 8.11529i | − 0.276088i | ||||||||
\(865\) | 60.6128i | 2.06090i | ||||||||
\(866\) | − 21.3674i | − 0.726095i | ||||||||
\(867\) | 16.1685 | 0.549112 | ||||||||
\(868\) | 43.6069 | 1.48011 | ||||||||
\(869\) | 18.4765i | 0.626772i | ||||||||
\(870\) | 27.0925 | 0.918520 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.21552 | −0.278213 | ||||||||
\(873\) | − 16.1293i | − 0.545894i | ||||||||
\(874\) | 15.7912 | 0.534145 | ||||||||
\(875\) | −9.57002 | −0.323526 | ||||||||
\(876\) | − 16.2903i | − 0.550397i | ||||||||
\(877\) | 40.8780i | 1.38035i | 0.723642 | + | 0.690176i | \(0.242467\pi\) | ||||
−0.723642 | + | 0.690176i | \(0.757533\pi\) | |||||||
\(878\) | − 66.6926i | − 2.25077i | ||||||||
\(879\) | 22.5948i | 0.762103i | ||||||||
\(880\) | −59.1008 | −1.99229 | ||||||||
\(881\) | 22.4964 | 0.757921 | 0.378961 | − | 0.925413i | \(-0.376282\pi\) | ||||
0.378961 | + | 0.925413i | \(0.376282\pi\) | |||||||
\(882\) | − 3.99761i | − 0.134606i | ||||||||
\(883\) | 4.16315 | 0.140101 | 0.0700505 | − | 0.997543i | \(-0.477684\pi\) | ||||
0.0700505 | + | 0.997543i | \(0.477684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.8237 | 0.531908 | ||||||||
\(886\) | − 19.6329i | − 0.659582i | ||||||||
\(887\) | −26.3002 | −0.883075 | −0.441537 | − | 0.897243i | \(-0.645567\pi\) | ||||
−0.441537 | + | 0.897243i | \(0.645567\pi\) | |||||||
\(888\) | −3.57194 | −0.119867 | ||||||||
\(889\) | 31.0344i | 1.04086i | ||||||||
\(890\) | 69.1831i | 2.31902i | ||||||||
\(891\) | − 4.93900i | − 0.165463i | ||||||||
\(892\) | − 23.6040i | − 0.790320i | ||||||||
\(893\) | −14.4547 | −0.483709 | ||||||||
\(894\) | −21.0200 | −0.703013 | ||||||||
\(895\) | 66.7023i | 2.22961i | ||||||||
\(896\) | −7.25906 | −0.242508 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 58.1764 | 1.94137 | ||||||||
\(899\) | 34.7778i | 1.15990i | ||||||||
\(900\) | 13.7791 | 0.459303 | ||||||||
\(901\) | −0.495024 | −0.0164916 | ||||||||
\(902\) | − 70.2199i | − 2.33807i | ||||||||
\(903\) | 5.13706i | 0.170951i | ||||||||
\(904\) | 3.93315i | 0.130815i | ||||||||
\(905\) | 33.8468i | 1.12511i | ||||||||
\(906\) | −41.3236 | −1.37289 | ||||||||
\(907\) | 57.9114 | 1.92292 | 0.961458 | − | 0.274952i | \(-0.0886620\pi\) | ||||
0.961458 | + | 0.274952i | \(0.0886620\pi\) | |||||||
\(908\) | 15.3333i | 0.508854i | ||||||||
\(909\) | 9.94869 | 0.329977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.286799 | −0.00950208 | −0.00475104 | − | 0.999989i | \(-0.501512\pi\) | ||||
−0.00475104 | + | 0.999989i | \(0.501512\pi\) | |||||||
\(912\) | − 13.5526i | − 0.448770i | ||||||||
\(913\) | 11.3991 | 0.377255 | ||||||||
\(914\) | 10.2358 | 0.338569 | ||||||||
\(915\) | − 12.3532i | − 0.408383i | ||||||||
\(916\) | − 36.9383i | − 1.22047i | ||||||||
\(917\) | − 6.72886i | − 0.222206i | ||||||||
\(918\) | − 1.86831i | − 0.0616635i | ||||||||
\(919\) | −31.1239 | −1.02668 | −0.513342 | − | 0.858184i | \(-0.671593\pi\) | ||||
−0.513342 | + | 0.858184i | \(0.671593\pi\) | |||||||
\(920\) | 2.76153 | 0.0910449 | ||||||||
\(921\) | − 6.55496i | − 0.215993i | ||||||||
\(922\) | 2.77133 | 0.0912690 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −24.3937 | −0.802495 | ||||||||
\(925\) | 55.1771i | 1.81421i | ||||||||
\(926\) | 6.89392 | 0.226548 | ||||||||
\(927\) | 10.9879 | 0.360891 | ||||||||
\(928\) | − 31.9661i | − 1.04934i | ||||||||
\(929\) | 7.62671i | 0.250224i | 0.992143 | + | 0.125112i | \(0.0399291\pi\) | ||||
−0.992143 | + | 0.125112i | \(0.960071\pi\) | |||||||
\(930\) | 60.7265i | 1.99130i | ||||||||
\(931\) | − 7.41789i | − 0.243112i | ||||||||
\(932\) | 19.1056 | 0.625825 | ||||||||
\(933\) | −12.0392 | −0.394147 | ||||||||
\(934\) | 14.1596i | 0.463317i | ||||||||
\(935\) | −15.1183 | −0.494421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.67324 | −0.185337 | −0.0926683 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926683 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(938\) | 7.00298i | 0.228656i | ||||||||
\(939\) | 33.8950 | 1.10612 | ||||||||
\(940\) | −28.0532 | −0.914995 | ||||||||
\(941\) | 41.5394i | 1.35415i | 0.735916 | + | 0.677073i | \(0.236752\pi\) | ||||
−0.735916 | + | 0.677073i | \(0.763248\pi\) | |||||||
\(942\) | 21.3873i | 0.696836i | ||||||||
\(943\) | − 14.0664i | − 0.458064i | ||||||||
\(944\) | − 16.8030i | − 0.546891i | ||||||||
\(945\) | −7.54288 | −0.245370 | ||||||||
\(946\) | −23.1355 | −0.752201 | ||||||||
\(947\) | 47.3110i | 1.53740i | 0.639610 | + | 0.768700i | \(0.279096\pi\) | ||||
−0.639610 | + | 0.768700i | \(0.720904\pi\) | |||||||
\(948\) | −8.22282 | −0.267065 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 48.8327 | 1.58434 | ||||||||
\(951\) | 4.49827i | 0.145866i | ||||||||
\(952\) | −0.831478 | −0.0269483 | ||||||||
\(953\) | 34.3435 | 1.11249 | 0.556247 | − | 0.831017i | \(-0.312241\pi\) | ||||
0.556247 | + | 0.831017i | \(0.312241\pi\) | |||||||
\(954\) | − 1.11231i | − 0.0360123i | ||||||||
\(955\) | − 22.1135i | − 0.715576i | ||||||||
\(956\) | 50.3777i | 1.62933i | ||||||||
\(957\) | − 19.4547i | − 0.628882i | ||||||||
\(958\) | −7.20344 | −0.232733 | ||||||||
\(959\) | −51.7241 | −1.67026 | ||||||||
\(960\) | − 31.8847i | − 1.02907i | ||||||||
\(961\) | −46.9527 | −1.51460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.87263 | −0.318141 | ||||||||
\(964\) | 48.3137i | 1.55608i | ||||||||
\(965\) | 36.4802 | 1.17434 | ||||||||
\(966\) | −9.33273 | −0.300276 | ||||||||
\(967\) | 48.5096i | 1.55996i | 0.625802 | + | 0.779982i | \(0.284772\pi\) | ||||
−0.625802 | + | 0.779982i | \(0.715228\pi\) | |||||||
\(968\) | − 5.43535i | − 0.174699i | ||||||||
\(969\) | − 3.46681i | − 0.111370i | ||||||||
\(970\) | − 110.937i | − 3.56198i | ||||||||
\(971\) | 41.4650 | 1.33068 | 0.665338 | − | 0.746542i | \(-0.268288\pi\) | ||||
0.665338 | + | 0.746542i | \(0.268288\pi\) | |||||||
\(972\) | 2.19806 | 0.0705029 | ||||||||
\(973\) | − 2.20775i | − 0.0707772i | ||||||||
\(974\) | −26.3242 | −0.843483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.1177 | −0.419887 | ||||||||
\(977\) | − 2.09677i | − 0.0670816i | −0.999437 | − | 0.0335408i | \(-0.989322\pi\) | ||||
0.999437 | − | 0.0335408i | \(-0.0106784\pi\) | |||||||
\(978\) | −22.6334 | −0.723737 | ||||||||
\(979\) | 49.6795 | 1.58776 | ||||||||
\(980\) | − 14.3964i | − 0.459876i | ||||||||
\(981\) | 20.2446i | 0.646360i | ||||||||
\(982\) | 58.7442i | 1.87460i | ||||||||
\(983\) | − 25.2336i | − 0.804826i | −0.915458 | − | 0.402413i | \(-0.868172\pi\) | ||||
0.915458 | − | 0.402413i | \(-0.131828\pi\) | |||||||
\(984\) | 2.81594 | 0.0897688 | ||||||||
\(985\) | −31.0231 | −0.988478 | ||||||||
\(986\) | − 7.35929i | − 0.234367i | ||||||||
\(987\) | 8.54288 | 0.271923 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.63448 | −0.147368 | ||||||||
\(990\) | − 33.9705i | − 1.07965i | ||||||||
\(991\) | 12.0489 | 0.382746 | 0.191373 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191373 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(992\) | 71.6506 | 2.27491 | ||||||||
\(993\) | 11.2131i | 0.355838i | ||||||||
\(994\) | − 10.9511i | − 0.347347i | ||||||||
\(995\) | 5.25236i | 0.166511i | ||||||||
\(996\) | 5.07308i | 0.160747i | ||||||||
\(997\) | −1.43403 | −0.0454160 | −0.0227080 | − | 0.999742i | \(-0.507229\pi\) | ||||
−0.0227080 | + | 0.999742i | \(0.507229\pi\) | |||||||
\(998\) | −68.7525 | −2.17632 | ||||||||
\(999\) | 8.80194i | 0.278481i |
(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 | 507.2.b.f.337.3 | 6 | ||
3.2 | odd | 2 | 1521.2.b.k.1351.4 | 6 | |||
13.2 | odd | 12 | 507.2.e.i.22.3 | 6 | |||
13.3 | even | 3 | 507.2.j.i.316.4 | 12 | |||
13.4 | even | 6 | 507.2.j.i.361.4 | 12 | |||
13.5 | odd | 4 | 507.2.a.l.1.1 | yes | 3 | ||
13.6 | odd | 12 | 507.2.e.i.484.3 | 6 | |||
13.7 | odd | 12 | 507.2.e.l.484.1 | 6 | |||
13.8 | odd | 4 | 507.2.a.i.1.3 | ✓ | 3 | ||
13.9 | even | 3 | 507.2.j.i.361.3 | 12 | |||
13.10 | even | 6 | 507.2.j.i.316.3 | 12 | |||
13.11 | odd | 12 | 507.2.e.l.22.1 | 6 | |||
13.12 | even | 2 | inner | 507.2.b.f.337.4 | 6 | ||
39.5 | even | 4 | 1521.2.a.n.1.3 | 3 | |||
39.8 | even | 4 | 1521.2.a.s.1.1 | 3 | |||
39.38 | odd | 2 | 1521.2.b.k.1351.3 | 6 | |||
52.31 | even | 4 | 8112.2.a.cp.1.2 | 3 | |||
52.47 | even | 4 | 8112.2.a.cg.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
507.2.a.l.1.1 | yes | 3 | 13.5 | odd | 4 | ||
507.2.b.f.337.3 | 6 | 1.1 | even | 1 | trivial | ||
507.2.b.f.337.4 | 6 | 13.12 | even | 2 | inner | ||
507.2.e.i.22.3 | 6 | 13.2 | odd | 12 | |||
507.2.e.i.484.3 | 6 | 13.6 | odd | 12 | |||
507.2.e.l.22.1 | 6 | 13.11 | odd | 12 | |||
507.2.e.l.484.1 | 6 | 13.7 | odd | 12 | |||
507.2.j.i.316.3 | 12 | 13.10 | even | 6 | |||
507.2.j.i.316.4 | 12 | 13.3 | even | 3 | |||
507.2.j.i.361.3 | 12 | 13.9 | even | 3 | |||
507.2.j.i.361.4 | 12 | 13.4 | even | 6 | |||
1521.2.a.n.1.3 | 3 | 39.5 | even | 4 | |||
1521.2.a.s.1.1 | 3 | 39.8 | even | 4 | |||
1521.2.b.k.1351.3 | 6 | 39.38 | odd | 2 | |||
1521.2.b.k.1351.4 | 6 | 3.2 | odd | 2 | |||
8112.2.a.cg.1.2 | 3 | 52.47 | even | 4 | |||
8112.2.a.cp.1.2 | 3 | 52.31 | even | 4 |