Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(575,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.3 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.575 |
Dual form | 672.2.h.d.575.4 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70711 | − | 0.292893i | 0.985599 | − | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.585786i | − | 0.261972i | −0.991384 | − | 0.130986i | \(-0.958186\pi\) | ||
0.991384 | − | 0.130986i | \(-0.0418142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | − | 1.00000i | 0.942809 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.171573 | − | 1.00000i | −0.0442999 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.828427i | 0.200923i | 0.994941 | + | 0.100462i | \(0.0320319\pi\) | ||||
−0.994941 | + | 0.100462i | \(0.967968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.24264i | − | 0.514497i | −0.966345 | − | 0.257249i | \(-0.917184\pi\) | ||
0.966345 | − | 0.257249i | \(-0.0828159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.292893 | − | 1.70711i | −0.0639145 | − | 0.372521i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65685 | 0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.53553 | − | 2.53553i | 0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.828427i | 0.153835i | 0.997037 | + | 0.0769175i | \(0.0245078\pi\) | ||||
−0.997037 | + | 0.0769175i | \(0.975492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.82843i | − | 1.22642i | −0.789919 | − | 0.613211i | \(-0.789878\pi\) | ||
0.789919 | − | 0.613211i | \(-0.210122\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.41421 | − | 0.585786i | 0.594338 | − | 0.101972i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.585786 | −0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.82843 | 0.793789 | 0.396894 | − | 0.917864i | \(-0.370088\pi\) | ||||
0.396894 | + | 0.917864i | \(0.370088\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | − | 0.171573i | 0.160128 | − | 0.0274736i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.48528i | − | 0.988996i | −0.869179 | − | 0.494498i | \(-0.835352\pi\) | ||
0.869179 | − | 0.494498i | \(-0.164648\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.585786 | − | 1.65685i | −0.0873239 | − | 0.246989i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.65685 | −1.40860 | −0.704298 | − | 0.709904i | \(-0.748738\pi\) | ||||
−0.704298 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.242641 | + | 1.41421i | 0.0339765 | + | 0.198030i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.31371i | 1.27934i | 0.768651 | + | 0.639668i | \(0.220928\pi\) | ||||
−0.768651 | + | 0.639668i | \(0.779072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.17157i | − | 0.157975i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.656854 | − | 3.82843i | −0.0870025 | − | 0.507088i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.24264 | 0.291967 | 0.145983 | − | 0.989287i | \(-0.453365\pi\) | ||||
0.145983 | + | 0.989287i | \(0.453365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.75736 | 0.737154 | 0.368577 | − | 0.929597i | \(-0.379845\pi\) | ||||
0.368577 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | − | 2.82843i | −0.125988 | − | 0.356348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.343146i | − | 0.0425620i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3137i | 1.62653i | 0.581895 | + | 0.813264i | \(0.302312\pi\) | ||||
−0.581895 | + | 0.813264i | \(0.697688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.82843 | + | 1.17157i | −0.822046 | + | 0.141041i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6569 | −1.38341 | −0.691707 | − | 0.722178i | \(-0.743141\pi\) | ||||
−0.691707 | + | 0.722178i | \(0.743141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.82843 | −1.03329 | −0.516645 | − | 0.856200i | \(-0.672819\pi\) | ||||
−0.516645 | + | 0.856200i | \(0.672819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.94975 | − | 1.36396i | 0.917958 | − | 0.157497i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.58579 | 0.942412 | 0.471206 | − | 0.882023i | \(-0.343819\pi\) | ||||
0.471206 | + | 0.882023i | \(0.343819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.485281 | 0.0526362 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.242641 | + | 1.41421i | 0.0260138 | + | 0.151620i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65685i | 0.387626i | 0.981039 | + | 0.193813i | \(0.0620855\pi\) | ||||
−0.981039 | + | 0.193813i | \(0.937915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.585786i | − | 0.0614071i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 11.6569i | −0.207390 | − | 1.20876i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.31371 | −0.134784 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.3137 | −1.75794 | −0.878970 | − | 0.476876i | \(-0.841769\pi\) | ||||
−0.878970 | + | 0.476876i | \(0.841769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.65685 | − | 2.00000i | 0.568535 | − | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.75736i | 0.970894i | 0.874266 | + | 0.485447i | \(0.161343\pi\) | ||||
−0.874266 | + | 0.485447i | \(0.838657\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9706i | 1.67216i | 0.548608 | + | 0.836080i | \(0.315158\pi\) | ||||
−0.548608 | + | 0.836080i | \(0.684842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | + | 0.171573i | −0.0975900 | + | 0.0167438i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.48528 | −0.240261 | −0.120131 | − | 0.992758i | \(-0.538331\pi\) | ||||
−0.120131 | + | 0.992758i | \(0.538331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4853 | 1.38744 | 0.693719 | − | 0.720246i | \(-0.255971\pi\) | ||||
0.693719 | + | 0.720246i | \(0.255971\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.24264 | − | 1.41421i | 0.782357 | − | 0.134231i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.3137i | − | 1.62874i | −0.580348 | − | 0.814368i | \(-0.697084\pi\) | ||
0.580348 | − | 0.814368i | \(-0.302916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.34315i | 0.218499i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.65685 | − | 0.585786i | 0.153176 | − | 0.0541560i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.828427 | 0.0759418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92893 | + | 17.0711i | 0.264093 | + | 1.53925i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.89949 | − | 11.0711i | −0.167241 | − | 0.974753i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.55635 | −0.834942 | −0.417471 | − | 0.908690i | \(-0.637083\pi\) | ||||
−0.417471 | + | 0.908690i | \(0.637083\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.24264 | −0.194462 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.48528 | − | 2.65685i | −0.127833 | − | 0.228666i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3137i | 0.966595i | 0.875456 | + | 0.483298i | \(0.160561\pi\) | ||||
−0.875456 | + | 0.483298i | \(0.839439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.2426i | − | 0.868769i | −0.900727 | − | 0.434385i | \(-0.856966\pi\) | ||
0.900727 | − | 0.434385i | \(-0.143034\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.4853 | + | 2.82843i | −1.38831 | + | 0.238197i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.17157 | 0.0979718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.485281 | 0.0403004 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.70711 | + | 0.292893i | −0.140800 | + | 0.0241574i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.65685i | 0.299581i | 0.988718 | + | 0.149791i | \(0.0478599\pi\) | ||||
−0.988718 | + | 0.149791i | \(0.952140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0000i | 1.46482i | 0.680864 | + | 0.732410i | \(0.261604\pi\) | ||||
−0.680864 | + | 0.732410i | \(0.738396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.828427 | + | 2.34315i | 0.0669744 | + | 0.189432i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.24264 | −0.498217 | −0.249108 | − | 0.968476i | \(-0.580138\pi\) | ||||
−0.249108 | + | 0.968476i | \(0.580138\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.72792 | + | 15.8995i | 0.216338 | + | 1.26091i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000i | 0.315244i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.1421i | 1.57765i | 0.614615 | + | 0.788827i | \(0.289311\pi\) | ||||
−0.614615 | + | 0.788827i | \(0.710689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.343146 | − | 2.00000i | −0.0267139 | − | 0.155700i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.17157 | −0.400188 | −0.200094 | − | 0.979777i | \(-0.564125\pi\) | ||||
−0.200094 | + | 0.979777i | \(0.564125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.24264 | − | 6.34315i | −0.171499 | − | 0.485072i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 21.5563i | − | 1.63890i | −0.573151 | − | 0.819449i | \(-0.694279\pi\) | ||
0.573151 | − | 0.819449i | \(-0.305721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.65685i | − | 0.352025i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.82843 | − | 0.656854i | 0.287762 | − | 0.0493722i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.4853 | −0.783707 | −0.391853 | − | 0.920028i | \(-0.628166\pi\) | ||||
−0.391853 | + | 0.920028i | \(0.628166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3848 | −1.21787 | −0.608935 | − | 0.793220i | \(-0.708403\pi\) | ||||
−0.608935 | + | 0.793220i | \(0.708403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.82843 | − | 1.68629i | 0.726538 | − | 0.124654i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.82843i | − | 0.207950i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.65685i | 0.121161i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.53553 | − | 4.53553i | −0.184433 | − | 0.329912i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.65685 | 0.554031 | 0.277015 | − | 0.960866i | \(-0.410655\pi\) | ||||
0.277015 | + | 0.960866i | \(0.410655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.34315 | 0.456590 | 0.228295 | − | 0.973592i | \(-0.426685\pi\) | ||||
0.228295 | + | 0.973592i | \(0.426685\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.100505 | − | 0.585786i | −0.00719732 | − | 0.0419490i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0000i | 1.85242i | 0.377004 | + | 0.926212i | \(0.376954\pi\) | ||||
−0.377004 | + | 0.926212i | \(0.623046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.3137i | − | 1.08556i | −0.839875 | − | 0.542780i | \(-0.817372\pi\) | ||
0.839875 | − | 0.542780i | \(-0.182628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.89949 | + | 22.7279i | 0.275049 | + | 1.60310i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.828427 | 0.0581442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.85786 | 0.409131 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.3137 | + | 4.00000i | −0.786357 | + | 0.278019i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.48528i | − | 0.310253i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.6569i | − | 0.802491i | −0.915971 | − | 0.401245i | \(-0.868577\pi\) | ||
0.915971 | − | 0.401245i | \(-0.131423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.8995 | + | 3.41421i | −1.36349 | + | 0.233938i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.79899 | −0.259089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82843 | −0.463544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0711 | + | 2.58579i | −1.01841 | + | 0.174731i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.485281i | 0.0326436i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.82843i | − | 0.189405i | −0.995506 | − | 0.0947027i | \(-0.969810\pi\) | ||
0.995506 | − | 0.0947027i | \(-0.0301901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.1716 | − | 4.65685i | 0.878105 | − | 0.310457i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.10051 | −0.272160 | −0.136080 | − | 0.990698i | \(-0.543450\pi\) | ||||
−0.136080 | + | 0.990698i | \(0.543450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0711 | 0.863760 | 0.431880 | − | 0.901931i | \(-0.357850\pi\) | ||||
0.431880 | + | 0.901931i | \(0.357850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.585786 | − | 3.41421i | −0.0385419 | − | 0.224639i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.9706i | 1.63588i | 0.575306 | + | 0.817938i | \(0.304883\pi\) | ||||
−0.575306 | + | 0.817938i | \(0.695117\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65685i | 0.369012i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.17157 | − | 6.82843i | −0.0761018 | − | 0.443554i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.65685 | −0.493221 | −0.246611 | − | 0.969115i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969115i | \(0.579317\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.2929 | − | 11.7071i | 0.660289 | − | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.585786i | 0.0374245i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.31371i | − | 0.0835893i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.6569 | − | 2.51472i | 0.928840 | − | 0.159364i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4142 | −1.47789 | −0.738946 | − | 0.673765i | \(-0.764676\pi\) | ||||
−0.738946 | + | 0.673765i | \(0.764676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.828427 | − | 0.142136i | 0.0518781 | − | 0.00890088i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.48528i | − | 0.155028i | −0.996991 | − | 0.0775138i | \(-0.975302\pi\) | ||
0.996991 | − | 0.0775138i | \(-0.0246982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.82843i | − | 0.300024i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.828427 | + | 2.34315i | 0.0512784 | + | 0.145037i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.3137 | 1.31426 | 0.657130 | − | 0.753777i | \(-0.271770\pi\) | ||||
0.657130 | + | 0.753777i | \(0.271770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.45584 | 0.335150 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.07107 | + | 6.24264i | 0.0655483 | + | 0.382043i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.72792i | 0.410209i | 0.978740 | + | 0.205104i | \(0.0657534\pi\) | ||||
−0.978740 | + | 0.205104i | \(0.934247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.48528i | 0.272461i | 0.990677 | + | 0.136231i | \(0.0434988\pi\) | ||||
−0.990677 | + | 0.136231i | \(0.956501\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.171573 | − | 1.00000i | −0.0103841 | − | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.31371 | 0.561638 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3137 | 1.28062 | 0.640308 | − | 0.768118i | \(-0.278807\pi\) | ||||
0.640308 | + | 0.768118i | \(0.278807\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.82843 | − | 19.3137i | −0.408807 | − | 1.15628i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.9706i | − | 1.48962i | −0.667277 | − | 0.744809i | \(-0.732540\pi\) | ||
0.667277 | − | 0.744809i | \(-0.267460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.75736i | − | 0.104464i | −0.998635 | − | 0.0522321i | \(-0.983366\pi\) | ||
0.998635 | − | 0.0522321i | \(-0.0166336\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.24264 | + | 0.384776i | −0.132843 | + | 0.0227922i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | 0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3137 | 0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.5563 | + | 5.07107i | −1.73262 | + | 0.297271i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26.7279i | − | 1.56146i | −0.624867 | − | 0.780731i | \(-0.714847\pi\) | ||
0.624867 | − | 0.780731i | \(-0.285153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.31371i | − | 0.0764871i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.07107 | − | 5.07107i | 0.526357 | − | 0.294253i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.34315 | −0.135508 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.48528 | −0.373805 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.85786 | + | 16.6569i | 0.164180 | + | 0.956911i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.37258i | − | 0.193114i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.5563i | − | 1.23029i | −0.788416 | − | 0.615143i | \(-0.789098\pi\) | ||
0.788416 | − | 0.615143i | \(-0.210902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.97056 | + | 28.9706i | 0.282765 | + | 1.64808i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.7990 | 1.12270 | 0.561349 | − | 0.827579i | \(-0.310283\pi\) | ||||
0.561349 | + | 0.827579i | \(0.310283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.17157 | −0.179268 | −0.0896339 | − | 0.995975i | \(-0.528570\pi\) | ||||
−0.0896339 | + | 0.995975i | \(0.528570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.65685 | + | 0.585786i | −0.0933532 | + | 0.0330053i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.0000i | − | 0.561656i | −0.959758 | − | 0.280828i | \(-0.909391\pi\) | ||
0.959758 | − | 0.280828i | \(-0.0906090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.65685i | 0.0927660i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.24264 | + | 0.727922i | −0.236801 | + | 0.0406286i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.85786 | 0.103374 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.72792 | 0.151318 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.7279 | − | 4.24264i | 1.36746 | − | 0.234619i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.65685i | 0.532400i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.828427i | 0.0455345i | 0.999741 | + | 0.0227672i | \(0.00724766\pi\) | ||||
−0.999741 | + | 0.0227672i | \(0.992752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.6569 | − | 4.82843i | 0.748391 | − | 0.264596i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.79899 | 0.426104 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.68629 | 0.255279 | 0.127639 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127639 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.07107 | − | 29.5563i | −0.275423 | − | 1.60528i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.6569i | − | 0.739560i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.686292 | + | 4.00000i | 0.0369487 | + | 0.215353i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6569 | 0.625773 | 0.312886 | − | 0.949791i | \(-0.398704\pi\) | ||||
0.312886 | + | 0.949791i | \(0.398704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.0711 | 1.55614 | 0.778069 | − | 0.628178i | \(-0.216199\pi\) | ||||
0.778069 | + | 0.628178i | \(0.216199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.65685 | − | 1.48528i | 0.141812 | − | 0.0792785i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.4558i | − | 1.67423i | −0.547030 | − | 0.837113i | \(-0.684242\pi\) | ||
0.547030 | − | 0.837113i | \(-0.315758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.82843i | 0.362415i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.41421 | − | 0.242641i | 0.0748481 | − | 0.0128419i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6274 | 0.983117 | 0.491559 | − | 0.870844i | \(-0.336427\pi\) | ||||
0.491559 | + | 0.870844i | \(0.336427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.9706 | 0.735293 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.9497 | + | 2.05025i | −0.627199 | + | 0.107610i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.17157i | 0.270692i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.8284i | − | 0.982836i | −0.870924 | − | 0.491418i | \(-0.836479\pi\) | ||
0.870924 | − | 0.491418i | \(-0.163521\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000 | + | 28.2843i | 0.520579 | + | 1.47242i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.31371 | 0.483544 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9706 | 0.568034 | 0.284017 | − | 0.958819i | \(-0.408333\pi\) | ||||
0.284017 | + | 0.958819i | \(0.408333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.65685 | − | 9.65685i | −0.0855596 | − | 0.498678i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.485281i | 0.0249933i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.5147i | − | 0.899671i | −0.893112 | − | 0.449835i | \(-0.851483\pi\) | ||
0.893112 | − | 0.449835i | \(-0.148517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.585786 | + | 3.41421i | 0.0300107 | + | 0.174915i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.65685 | −0.289052 | −0.144526 | − | 0.989501i | \(-0.546166\pi\) | ||||
−0.144526 | + | 0.989501i | \(0.546166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.17157 | −0.0597089 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.48528 | − | 18.3431i | −0.329665 | − | 0.932435i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.4853i | 0.531625i | 0.964025 | + | 0.265812i | \(0.0856402\pi\) | ||||
−0.964025 | + | 0.265812i | \(0.914360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.31371i | − | 0.167581i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.3137 | + | 2.79899i | −0.822918 | + | 0.141190i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.34315 | −0.117896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.75736 | 0.489708 | 0.244854 | − | 0.969560i | \(-0.421260\pi\) | ||||
0.244854 | + | 0.969560i | \(0.421260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.82843 | + | 0.656854i | −0.191661 | + | 0.0328838i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.3431i | 1.01589i | 0.861390 | + | 0.507944i | \(0.169594\pi\) | ||||
−0.861390 | + | 0.507944i | \(0.830406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.31371 | − | 4.10051i | −0.164659 | − | 0.203756i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.65685 | 0.478672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.51472 | 0.470473 | 0.235236 | − | 0.971938i | \(-0.424414\pi\) | ||||
0.235236 | + | 0.971938i | \(0.424414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.31371 | + | 19.3137i | 0.163453 | + | 0.952675i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.24264i | − | 0.110353i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.02944i | − | 0.246885i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.00000 | − | 17.4853i | −0.146911 | − | 0.856258i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.72792 | 0.328681 | 0.164340 | − | 0.986404i | \(-0.447450\pi\) | ||||
0.164340 | + | 0.986404i | \(0.447450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.34315 | −0.211672 | −0.105836 | − | 0.994384i | \(-0.533752\pi\) | ||||
−0.105836 | + | 0.994384i | \(0.533752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.3137 | + | 9.65685i | −1.32804 | + | 0.469532i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.85786i | 0.187134i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.75736i | − | 0.278618i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.00000 | − | 0.343146i | 0.0965609 | − | 0.0165672i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.9706 | −0.911667 | −0.455834 | − | 0.890065i | \(-0.650659\pi\) | ||||
−0.455834 | + | 0.890065i | \(0.650659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.828427 | − | 0.142136i | 0.0397200 | − | 0.00681488i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.97056i | 0.429120i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.2843i | − | 0.777206i | −0.921405 | − | 0.388603i | \(-0.872958\pi\) | ||
0.921405 | − | 0.388603i | \(-0.127042\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.82843 | + | 1.00000i | −0.134687 | + | 0.0476190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8284 | 1.36968 | 0.684840 | − | 0.728694i | \(-0.259872\pi\) | ||||
0.684840 | + | 0.728694i | \(0.259872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.14214 | 0.101547 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.07107 | + | 6.24264i | 0.0506598 | + | 0.295267i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.6569i | − | 1.39959i | −0.714342 | − | 0.699797i | \(-0.753274\pi\) | ||
0.714342 | − | 0.699797i | \(-0.246726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.0000i | 0.941763i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.27208 | + | 30.7279i | 0.247704 | + | 1.44372i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.343146 | −0.0160869 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0000 | −1.12267 | −0.561336 | − | 0.827588i | \(-0.689713\pi\) | ||||
−0.561336 | + | 0.827588i | \(0.689713\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.10051 | + | 3.75736i | 0.0980432 | + | 0.175379i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 26.0416i | − | 1.21288i | −0.795129 | − | 0.606440i | \(-0.792597\pi\) | ||
0.795129 | − | 0.606440i | \(-0.207403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.65685i | 0.448792i | 0.974498 | + | 0.224396i | \(0.0720409\pi\) | ||||
−0.974498 | + | 0.224396i | \(0.927959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.82843 | + | 1.17157i | −0.316661 | + | 0.0543304i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.0416 | −1.39016 | −0.695080 | − | 0.718932i | \(-0.744631\pi\) | ||||
−0.695080 | + | 0.718932i | \(0.744631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3137 | 0.614770 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6569 | + | 1.82843i | −0.491042 | + | 0.0842495i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.9706i | − | 0.596387i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10.4437i | − | 0.479188i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.31371 | + | 26.3431i | 0.426445 | + | 1.20617i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3137 | 0.516937 | 0.258468 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258468 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.82843 | 0.128965 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.17157 | + | 6.82843i | 0.0533084 | + | 0.310704i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.1421i | 0.460531i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000i | 0.996915i | 0.866914 | + | 0.498458i | \(0.166100\pi\) | ||||
−0.866914 | + | 0.498458i | \(0.833900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.89949 | + | 34.3848i | 0.266784 | + | 1.55493i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8284 | −0.578939 | −0.289469 | − | 0.957187i | \(-0.593479\pi\) | ||||
−0.289469 | + | 0.957187i | \(0.593479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.686292 | −0.0309090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.17157 | − | 3.31371i | −0.0526583 | − | 0.148940i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.6569i | 0.522881i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.62742i | − | 0.386216i | −0.981177 | − | 0.193108i | \(-0.938143\pi\) | ||
0.981177 | − | 0.193108i | \(-0.0618568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.82843 | + | 1.51472i | −0.394425 | + | 0.0676726i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | −1.13502 | −0.567510 | − | 0.823367i | \(-0.692093\pi\) | ||||
−0.567510 | + | 0.823367i | \(0.692093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.71573 | 0.254347 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.6066 | + | 3.70711i | −0.959583 | + | 0.164638i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 32.8701i | − | 1.45694i | −0.685078 | − | 0.728470i | \(-0.740232\pi\) | ||
0.685078 | − | 0.728470i | \(-0.259768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.82843i | 0.390547i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.68629 | − | 10.1716i | −0.251056 | − | 0.449086i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.94113 | 0.438058 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3137 | −0.849416 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.31371 | − | 36.7990i | −0.277141 | − | 1.61530i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.6569i | 1.03643i | 0.855252 | + | 0.518213i | \(0.173402\pi\) | ||||
−0.855252 | + | 0.518213i | \(0.826598\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.1005i | 0.878934i | 0.898259 | + | 0.439467i | \(0.144833\pi\) | ||||
−0.898259 | + | 0.439467i | \(0.855167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.36396 | − | 7.94975i | −0.0595281 | − | 0.346955i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.65685 | 0.246416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.34315 | − | 2.24264i | 0.275269 | − | 0.0973223i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.85786i | 0.253732i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.45584i | 0.0629416i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.8995 | + | 3.07107i | −0.772420 | + | 0.132526i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6274 | −1.40276 | −0.701381 | − | 0.712786i | \(-0.747433\pi\) | ||||
−0.701381 | + | 0.712786i | \(0.747433\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.9706 | + | 4.79899i | −1.20033 | + | 0.205944i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.48528i | − | 0.363470i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.1421i | 0.861216i | 0.902539 | + | 0.430608i | \(0.141701\pi\) | ||||
−0.902539 | + | 0.430608i | \(0.858299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.2843 | − | 5.75736i | 0.694996 | − | 0.245718i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.85786 | 0.0791477 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.828427 | − | 4.82843i | −0.0351648 | − | 0.204955i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3137i | 1.24206i | 0.783786 | + | 0.621031i | \(0.213286\pi\) | ||||
−0.783786 | + | 0.621031i | \(0.786714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.79899i | − | 0.160680i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.485281 | + | 2.82843i | 0.0204886 | + | 0.119416i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.2132 | 1.48406 | 0.742030 | − | 0.670367i | \(-0.233863\pi\) | ||||
0.742030 | + | 0.670367i | \(0.233863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1421 | −0.426683 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.65685 | − | 7.00000i | −0.237566 | − | 0.293972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21.3137i | − | 0.893517i | −0.894655 | − | 0.446759i | \(-0.852578\pi\) | ||
0.894655 | − | 0.446759i | \(-0.147422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.1421i | − | 0.842922i | −0.906846 | − | 0.421461i | \(-0.861517\pi\) | ||
0.906846 | − | 0.421461i | \(-0.138483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.0711 | − | 2.24264i | 0.546052 | − | 0.0936877i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.6274 | −0.776817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.68629 | 0.278354 | 0.139177 | − | 0.990268i | \(-0.455554\pi\) | ||||
0.139177 | + | 0.990268i | \(0.455554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8284 | − | 1.85786i | 0.450014 | − | 0.0772102i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8.58579i | − | 0.356198i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.6274i | 0.771469i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.343146 | − | 0.970563i | −0.0141873 | − | 0.0401278i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.27208 | 0.217602 | 0.108801 | − | 0.994064i | \(-0.465299\pi\) | ||||
0.108801 | + | 0.994064i | \(0.465299\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3137 | −0.630990 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.61522 | + | 44.3848i | 0.313248 | + | 1.82575i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.51472i | 0.226462i | 0.993569 | + | 0.113231i | \(0.0361201\pi\) | ||||
−0.993569 | + | 0.113231i | \(0.963880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.485281i | − | 0.0198946i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.48528 | − | 26.1421i | −0.183570 | − | 1.06993i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.6274 | 1.16968 | 0.584842 | − | 0.811147i | \(-0.301156\pi\) | ||||
0.584842 | + | 0.811147i | \(0.301156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1421 | 0.495288 | 0.247644 | − | 0.968851i | \(-0.420344\pi\) | ||||
0.247644 | + | 0.968851i | \(0.420344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3137 | + | 37.6569i | 0.542176 | + | 1.53351i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.10051i | 0.166709i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.1421i | − | 1.06108i | −0.847661 | − | 0.530538i | \(-0.821990\pi\) | ||
0.847661 | − | 0.530538i | \(-0.178010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.41421 | − | 0.242641i | 0.0573068 | − | 0.00983230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.65685 | −0.228852 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.7696 | −1.88900 | −0.944502 | − | 0.328505i | \(-0.893455\pi\) | ||||
−0.944502 | + | 0.328505i | \(0.893455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0000 | − | 1.71573i | 0.403239 | − | 0.0691849i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16.6274i | − | 0.669395i | −0.942326 | − | 0.334697i | \(-0.891366\pi\) | ||
0.942326 | − | 0.334697i | \(-0.108634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.75736i | 0.392181i | 0.980586 | + | 0.196091i | \(0.0628247\pi\) | ||||
−0.980586 | + | 0.196091i | \(0.937175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.1421 | + | 10.1421i | −0.728019 | + | 0.406990i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.65685 | 0.146509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.31371 | − | 7.65685i | −0.0524645 | − | 0.305785i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00000i | 0.159490i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.9706i | 0.994062i | 0.867733 | + | 0.497031i | \(0.165577\pi\) | ||||
−0.867733 | + | 0.497031i | \(0.834423\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.41421 | − | 19.8995i | −0.135703 | − | 0.790934i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.17157 | 0.0464925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.585786 | −0.0232097 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.9706 | + | 11.6569i | −1.30430 | + | 0.461138i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 15.6569i | − | 0.618409i | −0.950996 | − | 0.309204i | \(-0.899937\pi\) | ||
0.950996 | − | 0.309204i | \(-0.100063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.2426i | 1.82363i | 0.410599 | + | 0.911816i | \(0.365319\pi\) | ||||
−0.410599 | + | 0.911816i | \(0.634681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.48528 | + | 1.11270i | −0.255358 | + | 0.0438125i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.4558 | −1.15803 | −0.579014 | − | 0.815317i | \(-0.696562\pi\) | ||||
−0.579014 | + | 0.815317i | \(0.696562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.48528 | 0.176063 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.6569 | + | 2.00000i | −0.456868 | + | 0.0783862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.4853i | − | 0.566853i | −0.958994 | − | 0.283426i | \(-0.908529\pi\) | ||
0.958994 | − | 0.283426i | \(-0.0914712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.59798i | 0.218731i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.9706 | + | 8.82843i | −0.974194 | + | 0.344430i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.9706 | 0.738988 | 0.369494 | − | 0.929233i | \(-0.379531\pi\) | ||||
0.369494 | + | 0.929233i | \(0.379531\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.1838 | −1.40739 | −0.703693 | − | 0.710504i | \(-0.748467\pi\) | ||||
−0.703693 | + | 0.710504i | \(0.748467\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.142136 | + | 0.828427i | 0.00552009 | + | 0.0321734i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.31371i | 0.0509434i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.31371i | − | 0.128307i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.828427 | − | 4.82843i | −0.0320288 | − | 0.186678i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.5147 | 0.444521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.1213 | − | 11.8076i | 0.812960 | − | 0.454475i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 48.8701i | − | 1.87823i | −0.343605 | − | 0.939114i | \(-0.611648\pi\) | ||
0.343605 | − | 0.939114i | \(-0.388352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3137i | 0.664439i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00000 | + | 1.20101i | −0.268241 | + | 0.0460228i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.4853 | 1.77871 | 0.889355 | − | 0.457217i | \(-0.151154\pi\) | ||||
0.889355 | + | 0.457217i | \(0.151154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.62742 | 0.253221 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.3137 | − | 3.82843i | 0.851321 | − | 0.146064i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.45584i | 0.207851i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0416i | 0.990670i | 0.868702 | + | 0.495335i | \(0.164955\pi\) | ||||
−0.868702 | + | 0.495335i | \(0.835045\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | − | 5.65685i | −0.0759737 | − | 0.214886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | −0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.28427 | −0.313789 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.31371 | + | 42.6274i | 0.276630 | + | 1.61232i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.142136i | 0.00536839i | 0.999996 | + | 0.00268419i | \(0.000854407\pi\) | ||||
−0.999996 | + | 0.00268419i | \(0.999146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 10.8284i | − | 0.408402i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.65685 | + | 9.65685i | 0.0624007 | + | 0.363698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.75736 | 0.366963 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.4853 | 0.844452 | 0.422226 | − | 0.906490i | \(-0.361249\pi\) | ||||
0.422226 | + | 0.906490i | \(0.361249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 11.3137i | −0.150012 | − | 0.424297i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.3137i | 1.02291i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.686292i | − | 0.0256658i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.3137 | − | 3.31371i | 0.721284 | − | 0.123753i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.3137 | −1.61533 | −0.807664 | − | 0.589642i | \(-0.799269\pi\) | ||||
−0.807664 | + | 0.589642i | \(0.799269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.9706 | 0.632017 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.0711 | + | 2.24264i | −0.486118 | + | 0.0834047i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.85786i | 0.143277i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.6274i | 1.28426i | 0.766596 | + | 0.642130i | \(0.221949\pi\) | ||||
−0.766596 | + | 0.642130i | \(0.778051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | − | 23.0000i | 0.523783 | − | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.37258 | 0.198712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.3848 | −1.34390 | −0.671951 | − | 0.740595i | \(-0.734544\pi\) | ||||
−0.671951 | + | 0.740595i | \(0.734544\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.171573 | + | 1.00000i | 0.00632856 | + | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.6274i | 0.980834i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 40.1421i | − | 1.47665i | −0.674444 | − | 0.738326i | \(-0.735617\pi\) | ||
0.674444 | − | 0.738326i | \(-0.264383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.384776 | − | 2.24264i | −0.0141351 | − | 0.0823855i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.9411 | −1.68542 | −0.842708 | − | 0.538371i | \(-0.819040\pi\) | ||||
−0.842708 | + | 0.538371i | \(0.819040\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.14214 | 0.0784818 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.2843 | − | 8.58579i | 0.888515 | − | 0.314137i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.48528i | 0.0908102i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26.2843i | − | 0.959127i | −0.877507 | − | 0.479563i | \(-0.840795\pi\) | ||
0.877507 | − | 0.479563i | \(-0.159205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −39.9706 | + | 6.85786i | −1.45661 | + | 0.249914i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.5442 | 0.383741 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.1127 | 0.476589 | 0.238295 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238295 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.6569 | + | 2.34315i | −0.495712 | + | 0.0850508i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34.9706i | − | 1.26768i | −0.773463 | − | 0.633841i | \(-0.781477\pi\) | ||
0.773463 | − | 0.633841i | \(-0.218523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 14.4853i | − | 0.524402i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.37258 | − | 0.485281i | 0.0496258 | − | 0.0175454i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.31371 | 0.0474353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.6569 | 0.708844 | 0.354422 | − | 0.935086i | \(-0.384678\pi\) | ||||
0.354422 | + | 0.935086i | \(0.384678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.727922 | − | 4.24264i | −0.0262155 | − | 0.152795i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.7279i | 0.961337i | 0.876903 | + | 0.480668i | \(0.159606\pi\) | ||||
−0.876903 | + | 0.480668i | \(0.840394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 31.7990i | − | 1.14225i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.41421 | − | 8.24264i | −0.0507346 | − | 0.295703i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.4264 | 0.803509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.3137 | −0.834230 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.10051 | + | 3.75736i | 0.0750659 | + | 0.134277i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.65685i | 0.130519i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.2426i | 1.50579i | 0.658142 | + | 0.752894i | \(0.271343\pi\) | ||||
−0.658142 | + | 0.752894i | \(0.728657\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.3848 | − | 6.24264i | 1.29533 | − | 0.222244i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.3137 | −0.615605 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.37258 | 0.119764 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.31371 | − | 1.59798i | 0.330323 | − | 0.0566745i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.8995i | 1.12994i | 0.825112 | + | 0.564969i | \(0.191112\pi\) | ||||
−0.825112 | + | 0.564969i | \(0.808888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.00000i | − | 0.283020i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.65685 | + | 10.3431i | 0.129209 | + | 0.365457i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.6569 | −0.623097 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.34315 | 0.0825850 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.97056 | + | 11.4853i | 0.0693671 | + | 0.404301i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.3137i | 1.17125i | 0.810583 | + | 0.585624i | \(0.199150\pi\) | ||||
−0.810583 | + | 0.585624i | \(0.800850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.55635i | 0.0546508i | 0.999627 | + | 0.0273254i | \(0.00869903\pi\) | ||||
−0.999627 | + | 0.0273254i | \(0.991301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.31371 | + | 7.65685i | 0.0460738 | + | 0.268538i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7990 | 0.413301 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5442 | −0.508836 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.585786 | − | 1.65685i | −0.0204690 | − | 0.0578952i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.97056i | − | 0.243274i | −0.992575 | − | 0.121637i | \(-0.961186\pi\) | ||
0.992575 | − | 0.121637i | \(-0.0388144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.970563i | − | 0.0338317i | −0.999857 | − | 0.0169158i | \(-0.994615\pi\) | ||
0.999857 | − | 0.0169158i | \(-0.00538474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.8995 | − | 2.72792i | 0.553549 | − | 0.0949741i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.4558 | −1.65020 | −0.825101 | − | 0.564986i | \(-0.808882\pi\) | ||||
−0.825101 | + | 0.564986i | \(0.808882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.3848 | 0.430141 | 0.215071 | − | 0.976599i | \(-0.431002\pi\) | ||||
0.215071 | + | 0.976599i | \(0.431002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.3848 | − | 6.24264i | 1.26217 | − | 0.216555i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.828427i | − | 0.0287033i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.02944i | 0.104838i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.3137 | − | 30.9706i | −0.598449 | − | 1.07050i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.82843 | 0.235743 | 0.117872 | − | 0.993029i | \(-0.462393\pi\) | ||||
0.117872 | + | 0.993029i | \(0.462393\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.3137 | 0.976335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.31371 | − | 42.6274i | −0.251898 | − | 1.46817i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.41421i | 0.255057i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000i | 0.240523i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.514719 | − | 3.00000i | −0.0176651 | − | 0.102960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.3137 | −0.662065 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.41421 | 0.253858 | 0.126929 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126929 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.71573 | + | 1.31371i | −0.127075 | + | 0.0449279i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 38.0000i | − | 1.29806i | −0.760765 | − | 0.649028i | \(-0.775176\pi\) | ||
0.760765 | − | 0.649028i | \(-0.224824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 27.4142i | − | 0.935361i | −0.883898 | − | 0.467680i | \(-0.845090\pi\) | ||
0.883898 | − | 0.467680i | \(-0.154910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.0711 | − | 2.92893i | 0.581780 | − | 0.0998177i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.6274 | −1.92762 | −0.963810 | − | 0.266591i | \(-0.914103\pi\) | ||||
−0.963810 | + | 0.266591i | \(0.914103\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.6274 | −0.429345 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.8492 | − | 4.77817i | 0.945810 | − | 0.162275i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.00000i | − | 0.271381i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.79899i | 0.264259i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.9706 | + | 17.3137i | −1.65740 | + | 0.585980i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.65685 | −0.191237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.2010 | −0.614604 | −0.307302 | − | 0.951612i | \(-0.599426\pi\) | ||||
−0.307302 | + | 0.951612i | \(0.599426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.82843 | − | 45.6274i | −0.264046 | − | 1.53897i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.1421i | 1.21766i | 0.793301 | + | 0.608830i | \(0.208361\pi\) | ||||
−0.793301 | + | 0.608830i | \(0.791639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.3137i | 0.448042i | 0.974584 | + | 0.224021i | \(0.0719184\pi\) | ||||
−0.974584 | + | 0.224021i | \(0.928082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.384776 | − | 2.24264i | −0.0129341 | − | 0.0753855i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.82843 | 0.0949693 | 0.0474846 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474846 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.0000 | − | 11.3137i | 0.469018 | − | 0.379023i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.6569i | 0.724719i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.14214i | 0.205309i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.00000 | + | 0.686292i | −0.133556 | + | 0.0229146i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.65685 | 0.188667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.71573 | −0.257048 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.0711 | + | 1.89949i | −0.368422 | + | 0.0632112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.59798i | 0.319048i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 41.5980i | − | 1.38124i | −0.723219 | − | 0.690619i | \(-0.757338\pi\) | ||
0.723219 | − | 0.690619i | \(-0.242662\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.75736 | + | 27.5980i | 0.323631 | + | 0.915367i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9706 | 0.562260 | 0.281130 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281130 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.1716 | 0.568296 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.987807 | − | 5.75736i | −0.0326559 | − | 0.190332i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.55635i | 0.315578i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.3431i | − | 0.605085i | −0.953136 | − | 0.302542i | \(-0.902165\pi\) | ||
0.953136 | − | 0.302542i | \(-0.0978353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.31371 | − | 36.7990i | −0.208044 | − | 1.21257i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.82843 | −0.224760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4853 | 0.739311 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.9706 | + | 48.0000i | 0.557386 | + | 1.57653i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 5.79899i | − | 0.190259i | −0.995465 | − | 0.0951293i | \(-0.969674\pi\) | ||
0.995465 | − | 0.0951293i | \(-0.0303265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.24264i | 0.0734996i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.7990 | − | 5.79899i | 1.10653 | − | 0.189850i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.970563 | 0.0317408 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.4853 | 1.25726 | 0.628630 | − | 0.777705i | \(-0.283616\pi\) | ||||
0.628630 | + | 0.777705i | \(0.283616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.41421 | + | 0.928932i | −0.176686 | + | 0.0303146i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.6985i | 1.42453i | 0.701911 | + | 0.712265i | \(0.252331\pi\) | ||||
−0.701911 | + | 0.712265i | \(0.747669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 40.0000i | − | 1.30258i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.65685 | + | 1.48528i | −0.0864275 | + | 0.0483162i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.6863 | −1.12715 | −0.563577 | − | 0.826064i | \(-0.690575\pi\) | ||||
−0.563577 | + | 0.826064i | \(0.690575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.17157 | −0.167876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.92893 | − | 17.0711i | −0.0949771 | − | 0.553567i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.3137i | − | 0.755205i | −0.925968 | − | 0.377603i | \(-0.876749\pi\) | ||
0.925968 | − | 0.377603i | \(-0.123251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.48528i | − | 0.145140i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.485281 | + | 2.82843i | 0.0156869 | + | 0.0914301i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3137 | 0.365339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.6274 | −0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.02944 | + | 2.48528i | −0.226520 | + | 0.0800871i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3.71573i | − | 0.119614i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3431i | 0.525560i | 0.964856 | + | 0.262780i | \(0.0846394\pi\) | ||||
−0.964856 | + | 0.262780i | \(0.915361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.17157 | − | 0.544156i | 0.101886 | − | 0.0174808i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.6985 | −0.503788 | −0.251894 | − | 0.967755i | \(-0.581053\pi\) | ||||
−0.251894 | + | 0.967755i | \(0.581053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2426 | −0.328364 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.65685 | − | 0.798990i | 0.149139 | − | 0.0255882i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.0000i | 1.40768i | 0.710356 | + | 0.703842i | \(0.248534\pi\) | ||||
−0.710356 | + | 0.703842i | \(0.751466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.31371i | 0.233747i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 40.9706 | − | 14.4853i | 1.30809 | − | 0.462479i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.4558 | −1.06708 | −0.533538 | − | 0.845776i | \(-0.679138\pi\) | ||||
−0.533538 | + | 0.845776i | \(0.679138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.2304 | 0.485282 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.82843 | + | 16.4853i | 0.0900298 | + | 0.524732i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.9411i | 0.824880i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 21.9411i | − | 0.696983i | −0.937312 | − | 0.348491i | \(-0.886694\pi\) | ||
0.937312 | − | 0.348491i | \(-0.113306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.242641 | + | 1.41421i | 0.00769997 | + | 0.0448787i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.97056 | −0.284386 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.0416 | 1.83820 | 0.919098 | − | 0.394028i | \(-0.128919\pi\) | ||||
0.919098 | + | 0.394028i | \(0.128919\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.8995 | − | 12.2426i | 0.692869 | − | 0.387340i |
(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 | 672.2.h.d.575.3 | yes | 4 | |
3.2 | odd | 2 | 672.2.h.a.575.1 | ✓ | 4 | ||
4.3 | odd | 2 | 672.2.h.a.575.2 | yes | 4 | ||
8.3 | odd | 2 | 1344.2.h.e.575.3 | 4 | |||
8.5 | even | 2 | 1344.2.h.a.575.2 | 4 | |||
12.11 | even | 2 | inner | 672.2.h.d.575.4 | yes | 4 | |
24.5 | odd | 2 | 1344.2.h.e.575.4 | 4 | |||
24.11 | even | 2 | 1344.2.h.a.575.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.h.a.575.1 | ✓ | 4 | 3.2 | odd | 2 | ||
672.2.h.a.575.2 | yes | 4 | 4.3 | odd | 2 | ||
672.2.h.d.575.3 | yes | 4 | 1.1 | even | 1 | trivial | |
672.2.h.d.575.4 | yes | 4 | 12.11 | even | 2 | inner | |
1344.2.h.a.575.1 | 4 | 24.11 | even | 2 | |||
1344.2.h.a.575.2 | 4 | 8.5 | even | 2 | |||
1344.2.h.e.575.3 | 4 | 8.3 | odd | 2 | |||
1344.2.h.e.575.4 | 4 | 24.5 | odd | 2 |