Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(287,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, 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("624.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.d (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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.287 |
Dual form | 624.2.d.e.287.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | − | 1.41421i | −0.516398 | − | 0.365148i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.24264i | − | 0.973329i | −0.873589 | − | 0.486664i | \(-0.838214\pi\) | ||
0.873589 | − | 0.486664i | \(-0.161786\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.41421i | −0.436436 | − | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.48528i | 1.57568i | 0.615882 | + | 0.787839i | \(0.288800\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.41421i | − | 0.254000i | −0.991903 | − | 0.127000i | \(-0.959465\pi\) | ||
0.991903 | − | 0.127000i | \(-0.0405349\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | + | 5.65685i | −0.696311 | + | 0.984732i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | − | 1.41421i | 0.160128 | − | 0.226455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.07107i | − | 1.10432i | −0.833740 | − | 0.552158i | \(-0.813805\pi\) | ||
0.833740 | − | 0.552158i | \(-0.186195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.48528i | − | 1.29399i | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||
0.762493 | − | 0.646997i | \(-0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | + | 1.41421i | −0.596285 | + | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685i | 0.777029i | 0.921443 | + | 0.388514i | \(0.127012\pi\) | ||||
−0.921443 | + | 0.388514i | \(0.872988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685i | 0.762770i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.00000 | − | 4.24264i | −0.794719 | − | 0.561951i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | + | 1.41421i | −0.503953 | + | 0.178174i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.41421i | − | 0.175412i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.24264i | − | 0.518321i | −0.965834 | − | 0.259161i | \(-0.916554\pi\) | ||
0.965834 | − | 0.259161i | \(-0.0834459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | + | 2.82843i | −0.240772 | + | 0.340503i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | − | 4.24264i | 0.346410 | − | 0.489898i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685i | 0.644658i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.82843i | 0.318223i | 0.987261 | + | 0.159111i | \(0.0508629\pi\) | ||||
−0.987261 | + | 0.159111i | \(0.949137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0000 | + | 8.48528i | 1.28654 | + | 0.909718i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.89949i | − | 1.04934i | −0.851304 | − | 0.524672i | \(-0.824188\pi\) | ||
0.851304 | − | 0.524672i | \(-0.175812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.41421i | − | 0.148250i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 1.41421i | −0.207390 | − | 0.146647i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | −0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | + | 11.3137i | 0.402015 | + | 1.13707i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 19.7990i | − | 1.97007i | −0.172345 | − | 0.985037i | \(-0.555135\pi\) | ||
0.172345 | − | 0.985037i | \(-0.444865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1421i | 1.39347i | 0.717331 | + | 0.696733i | \(0.245364\pi\) | ||||
−0.717331 | + | 0.696733i | \(0.754636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | + | 2.82843i | −0.195180 | + | 0.276026i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | − | 2.82843i | 0.189832 | − | 0.268462i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.82843i | 0.266076i | 0.991111 | + | 0.133038i | \(0.0424732\pi\) | ||||
−0.991111 | + | 0.133038i | \(0.957527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82843i | 0.263752i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 2.82843i | −0.0924500 | − | 0.261488i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0000 | − | 7.07107i | −0.901670 | − | 0.637577i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3137i | 1.00393i | 0.864888 | + | 0.501965i | \(0.167389\pi\) | ||||
−0.864888 | + | 0.501965i | \(0.832611\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | − | 8.48528i | −1.05654 | − | 0.747087i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | −0.520266 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | + | 7.07107i | −0.172133 | + | 0.608581i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.2132i | 1.81237i | 0.422885 | + | 0.906183i | \(0.361017\pi\) | ||||
−0.422885 | + | 0.906183i | \(0.638983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3137i | 0.959616i | 0.877373 | + | 0.479808i | \(0.159294\pi\) | ||||
−0.877373 | + | 0.479808i | \(0.840706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | − | 11.3137i | 0.673722 | − | 0.952786i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | − | 7.07107i | 0.412393 | − | 0.583212i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.41421i | − | 0.115857i | −0.998321 | − | 0.0579284i | \(-0.981550\pi\) | ||
0.998321 | − | 0.0579284i | \(-0.0184495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.0416i | 1.95648i | 0.207476 | + | 0.978240i | \(0.433475\pi\) | ||||
−0.207476 | + | 0.978240i | \(0.566525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | −0.957704 | −0.478852 | − | 0.877896i | \(-0.658947\pi\) | ||||
−0.478852 | + | 0.877896i | \(0.658947\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.00000 | + | 5.65685i | 0.634441 | + | 0.448618i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.82843i | 0.222911i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.5563i | − | 1.21847i | −0.792991 | − | 0.609234i | \(-0.791477\pi\) | ||
0.792991 | − | 0.609234i | \(-0.208523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.00000 | + | 5.65685i | 0.622799 | + | 0.440386i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0000 | + | 4.24264i | −0.917663 | + | 0.324443i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1421i | 1.07521i | 0.843198 | + | 0.537603i | \(0.180670\pi\) | ||||
−0.843198 | + | 0.537603i | \(0.819330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.24264i | − | 0.320713i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | + | 16.9706i | −0.901975 | + | 1.27559i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.82843i | − | 0.207950i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.00000 | + | 7.07107i | −0.145479 | + | 0.514344i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.0000 | 1.88129 | 0.940647 | − | 0.339387i | \(-0.110219\pi\) | ||||
0.940647 | + | 0.339387i | \(0.110219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | − | 1.41421i | −0.143223 | − | 0.101274i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.07107i | 0.503793i | 0.967754 | + | 0.251896i | \(0.0810542\pi\) | ||||
−0.967754 | + | 0.251896i | \(0.918946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.3137i | − | 0.802008i | −0.916076 | − | 0.401004i | \(-0.868661\pi\) | ||
0.916076 | − | 0.401004i | \(-0.131339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | − | 4.24264i | −0.423207 | − | 0.299253i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000 | 0.842235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | −0.698430 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | + | 5.65685i | 0.139010 | + | 0.393179i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.9706i | 1.17388i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.4558i | 1.75245i | 0.481900 | + | 0.876226i | \(0.339947\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | − | 11.3137i | 0.548151 | − | 0.775203i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0000 | −0.818393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.0000 | − | 14.1421i | 0.675737 | − | 0.955637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.8701i | − | 1.79935i | −0.436558 | − | 0.899676i | \(-0.643803\pi\) | ||
0.436558 | − | 0.899676i | \(-0.356197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | − | 8.48528i | −0.200000 | − | 0.565685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | + | 5.65685i | 0.526361 | + | 0.372194i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2.82843i | − | 0.185296i | −0.995699 | − | 0.0926482i | \(-0.970467\pi\) | ||
0.995699 | − | 0.0926482i | \(-0.0295332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 11.3137i | − | 0.738025i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | + | 2.82843i | 0.259828 | + | 0.183726i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 7.07107i | − | 0.451754i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.24264i | − | 0.269953i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.0000 | −1.38863 | −0.694314 | − | 0.719672i | \(-0.744292\pi\) | ||||
−0.694314 | + | 0.719672i | \(0.744292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.82843i | − | 0.176432i | −0.996101 | − | 0.0882162i | \(-0.971883\pi\) | ||
0.996101 | − | 0.0882162i | \(-0.0281166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.82843i | − | 0.175750i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.0000 | − | 8.48528i | 1.48556 | − | 0.525226i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.0000 | − | 9.89949i | −0.856786 | − | 0.605839i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82843i | 0.172452i | 0.996276 | + | 0.0862261i | \(0.0274808\pi\) | ||||
−0.996276 | + | 0.0862261i | \(0.972519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.24264i | − | 0.257722i | −0.991663 | − | 0.128861i | \(-0.958868\pi\) | ||
0.991663 | − | 0.128861i | \(-0.0411321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | − | 1.41421i | −0.121046 | − | 0.0855921i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0000 | −0.723627 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | + | 1.41421i | −0.239474 | + | 0.0846668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.41421i | − | 0.0843649i | −0.999110 | − | 0.0421825i | \(-0.986569\pi\) | ||
0.999110 | − | 0.0421825i | \(-0.0134311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 22.6274i | − | 1.34506i | −0.740070 | − | 0.672530i | \(-0.765208\pi\) | ||
0.740070 | − | 0.672530i | \(-0.234792\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | + | 8.48528i | −0.355409 | + | 0.502625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | −0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 8.48528i | 0.351726 | − | 0.497416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.0416i | − | 1.40453i | −0.711917 | − | 0.702264i | \(-0.752173\pi\) | ||
0.711917 | − | 0.702264i | \(-0.247827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.9706i | 0.988064i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.0000 | + | 5.65685i | 1.16052 | + | 0.328244i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.0000 | − | 19.7990i | −1.60856 | − | 1.13742i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.5269i | 1.85641i | 0.372071 | + | 0.928204i | \(0.378648\pi\) | ||||
−0.372071 | + | 0.928204i | \(0.621352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.0000 | + | 14.1421i | 1.13776 | + | 0.804518i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000 | 1.02069 | 0.510343 | − | 0.859971i | \(-0.329518\pi\) | ||||
0.510343 | + | 0.859971i | \(0.329518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0000 | −1.46961 | −0.734803 | − | 0.678280i | \(-0.762726\pi\) | ||||
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000 | + | 5.65685i | 0.112687 | + | 0.318728i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.89949i | − | 0.556011i | −0.960579 | − | 0.278006i | \(-0.910327\pi\) | ||
0.960579 | − | 0.278006i | \(-0.0896734\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 33.9411i | − | 1.90034i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | − | 16.9706i | 0.669775 | − | 0.947204i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0000 | − | 14.1421i | 0.553001 | − | 0.782062i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 11.3137i | − | 0.623745i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.2132i | − | 1.16598i | −0.812478 | − | 0.582992i | \(-0.801882\pi\) | ||
0.812478 | − | 0.582992i | \(-0.198118\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | − | 5.65685i | −0.109599 | − | 0.309994i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000 | 0.544735 | 0.272367 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272367 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | + | 2.82843i | 0.217250 | + | 0.153619i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.65685i | 0.306336i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | + | 2.82843i | 0.215353 | + | 0.152277i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.00000 | −0.107366 | −0.0536828 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536828 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 1.41421i | −0.266880 | − | 0.0754851i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.8701i | − | 1.43015i | −0.699048 | − | 0.715074i | \(-0.746393\pi\) | ||
0.699048 | − | 0.715074i | \(-0.253607\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.3137i | − | 0.600469i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | − | 7.07107i | 0.262432 | − | 0.371135i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 14.1421i | − | 0.740233i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.0000 | + | 7.07107i | −1.04116 | + | 0.368105i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.00000 | 0.415339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −38.0000 | −1.96757 | −0.983783 | − | 0.179364i | \(-0.942596\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.0000 | − | 11.3137i | −0.826236 | − | 0.584237i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.48528i | 0.437014i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.24264i | − | 0.217930i | −0.994046 | − | 0.108965i | \(-0.965246\pi\) | ||
0.994046 | − | 0.108965i | \(-0.0347536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0000 | + | 11.3137i | 0.819705 | + | 0.579619i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | 0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.0000 | + | 8.48528i | −1.21999 | + | 0.431331i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.6274i | 1.14726i | 0.819116 | + | 0.573628i | \(0.194464\pi\) | ||||
−0.819116 | + | 0.573628i | \(0.805536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | − | 16.9706i | 0.605320 | − | 0.856052i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | 0.501886 | 0.250943 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250943 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.00000 | + | 8.48528i | −0.300376 | + | 0.424795i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.41421i | − | 0.0704470i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.00000 | + | 9.89949i | 0.397523 | + | 0.491910i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.0000 | + | 21.2132i | 1.47979 | + | 1.04637i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.9706i | 0.835067i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.0000 | + | 11.3137i | 0.783523 | + | 0.554035i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.00000 | − | 22.6274i | −0.388973 | − | 1.10018i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | + | 5.65685i | −0.193122 | + | 0.273115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0000 | −1.73406 | −0.867029 | − | 0.498257i | \(-0.833974\pi\) | ||||
−0.867029 | + | 0.498257i | \(0.833974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000 | − | 16.9706i | 0.575356 | − | 0.813676i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.48528i | 0.405906i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4558i | 1.21494i | 0.794342 | + | 0.607471i | \(0.207816\pi\) | ||||
−0.794342 | + | 0.607471i | \(0.792184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | − | 14.1421i | −0.238095 | − | 0.673435i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0000 | −1.33032 | −0.665160 | − | 0.746701i | \(-0.731637\pi\) | ||||
−0.665160 | + | 0.746701i | \(0.731637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | −0.663664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.00000 | − | 1.41421i | −0.0945968 | − | 0.0668900i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.6985i | − | 1.40156i | −0.713378 | − | 0.700779i | \(-0.752836\pi\) | ||
0.713378 | − | 0.700779i | \(-0.247164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.2843i | 1.33185i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 34.0000 | + | 24.0416i | 1.59746 | + | 1.12957i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.41421i | − | 0.0658665i | −0.999458 | − | 0.0329332i | \(-0.989515\pi\) | ||
0.999458 | − | 0.0329332i | \(-0.0104849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.41421i | − | 0.0657241i | −0.999460 | − | 0.0328620i | \(-0.989538\pi\) | ||
0.999460 | − | 0.0328620i | \(-0.0104622\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | + | 2.82843i | −0.0927478 | + | 0.131165i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.0000 | 1.20314 | 0.601568 | − | 0.798821i | \(-0.294543\pi\) | ||||
0.601568 | + | 0.798821i | \(0.294543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0000 | + | 16.9706i | −0.552931 | + | 0.781962i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.9411i | 1.56061i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 12.7279i | − | 0.583997i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.0000 | − | 5.65685i | 0.732590 | − | 0.259010i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.0000 | −1.27935 | −0.639676 | − | 0.768644i | \(-0.720932\pi\) | ||||
−0.639676 | + | 0.768644i | \(0.720932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | + | 2.82843i | 0.182006 | + | 0.128698i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.48528i | − | 0.385297i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7279i | 0.576757i | 0.957516 | + | 0.288379i | \(0.0931162\pi\) | ||||
−0.957516 | + | 0.288379i | \(0.906884\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.0000 | − | 15.5563i | −0.994874 | − | 0.703482i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0000 | 0.631811 | 0.315906 | − | 0.948791i | \(-0.397692\pi\) | ||||
0.315906 | + | 0.948791i | \(0.397692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0000 | − | 5.65685i | 0.719147 | − | 0.254257i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.3137i | − | 0.507489i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.8701i | 1.20287i | 0.798922 | + | 0.601434i | \(0.205404\pi\) | ||||
−0.798922 | + | 0.601434i | \(0.794596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | − | 11.3137i | 0.357414 | − | 0.505459i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0000 | −1.24598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | − | 1.41421i | 0.0444116 | − | 0.0628074i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.3553i | 1.56710i | 0.621330 | + | 0.783549i | \(0.286593\pi\) | ||||
−0.621330 | + | 0.783549i | \(0.713407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.1421i | − | 0.625611i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.00000 | + | 21.2132i | −0.264906 | + | 0.936586i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.0000 | 0.881305 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.0000 | −1.40736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.0000 | + | 14.1421i | 0.877903 | + | 0.620771i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.7990i | − | 0.867409i | −0.901055 | − | 0.433705i | \(-0.857206\pi\) | ||
0.901055 | − | 0.433705i | \(-0.142794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.2843i | 1.23678i | 0.785869 | + | 0.618392i | \(0.212216\pi\) | ||||
−0.785869 | + | 0.618392i | \(0.787784\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.00000 | − | 4.24264i | −0.261861 | − | 0.185164i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | + | 33.9411i | 0.520756 | + | 1.47292i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7.07107i | − | 0.306282i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.9706i | − | 0.733701i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000 | − | 5.65685i | 0.172613 | − | 0.244111i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.0000 | −0.861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0000 | 1.80572 | 0.902861 | − | 0.429934i | \(-0.141463\pi\) | ||||
0.902861 | + | 0.429934i | \(0.141463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.00000 | − | 11.3137i | 0.343313 | − | 0.485518i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 14.1421i | − | 0.605783i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9706i | 0.725609i | 0.931865 | + | 0.362804i | \(0.118181\pi\) | ||||
−0.931865 | + | 0.362804i | \(0.881819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.0000 | 1.53365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | − | 2.82843i | −0.169791 | − | 0.120060i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3848i | 0.778988i | 0.921029 | + | 0.389494i | \(0.127350\pi\) | ||||
−0.921029 | + | 0.389494i | \(0.872650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.48528i | − | 0.358889i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | 0.168281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.00000 | + | 9.89949i | 0.335968 | + | 0.415740i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.1421i | 0.592869i | 0.955053 | + | 0.296435i | \(0.0957977\pi\) | ||||
−0.955053 | + | 0.296435i | \(0.904202\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3137i | 0.473464i | 0.971575 | + | 0.236732i | \(0.0760763\pi\) | ||||
−0.971575 | + | 0.236732i | \(0.923924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.0000 | − | 36.7696i | 1.08617 | − | 1.53607i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0000 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0000 | + | 14.1421i | −0.415586 | + | 0.587727i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.6274i | − | 0.937132i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.00000 | + | 1.41421i | −0.165380 | + | 0.0584705i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.0000 | 1.32078 | 0.660391 | − | 0.750922i | \(-0.270391\pi\) | ||||
0.660391 | + | 0.750922i | \(0.270391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | + | 7.07107i | 0.411345 | + | 0.290865i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.7279i | 0.522673i | 0.965248 | + | 0.261337i | \(0.0841632\pi\) | ||||
−0.965248 | + | 0.261337i | \(0.915837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.0000 | − | 11.3137i | −0.654836 | − | 0.463039i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0000 | + | 4.24264i | −0.488678 | + | 0.172774i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7.07107i | − | 0.287480i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.9411i | 1.37763i | 0.724938 | + | 0.688814i | \(0.241868\pi\) | ||||
−0.724938 | + | 0.688814i | \(0.758132\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | − | 16.9706i | 0.486265 | − | 0.687682i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.0000 | + | 14.1421i | −0.403239 | + | 0.570266i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.07107i | − | 0.284670i | −0.989819 | − | 0.142335i | \(-0.954539\pi\) | ||
0.989819 | − | 0.142335i | \(-0.0454611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.6985i | 1.19368i | 0.802359 | + | 0.596841i | \(0.203578\pi\) | ||||
−0.802359 | + | 0.596841i | \(0.796422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0000 | + | 2.82843i | 0.401286 | + | 0.113501i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.0000 | −0.560898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0000 | + | 16.9706i | 0.958468 | + | 0.677739i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5563i | 0.619288i | 0.950852 | + | 0.309644i | \(0.100210\pi\) | ||||
−0.950852 | + | 0.309644i | \(0.899790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.0000 | + | 25.4558i | 1.43087 | + | 1.01178i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | 0.634941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | 0.198107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | − | 22.6274i | −0.316475 | − | 0.895127i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.6274i | − | 0.893729i | −0.894602 | − | 0.446865i | \(-0.852541\pi\) | ||
0.894602 | − | 0.446865i | \(-0.147459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.0416i | − | 0.948109i | −0.880495 | − | 0.474055i | \(-0.842790\pi\) | ||
0.880495 | − | 0.474055i | \(-0.157210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | + | 16.9706i | −0.472500 | + | 0.668215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.0000 | 1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.00000 | + | 2.82843i | −0.0783862 | + | 0.110855i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 42.4264i | − | 1.66027i | −0.557560 | − | 0.830137i | \(-0.688262\pi\) | ||
0.557560 | − | 0.830137i | \(-0.311738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 16.9706i | − | 0.663095i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0000 | − | 28.2843i | −0.390137 | − | 1.10347i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0000 | 1.63609 | 0.818044 | − | 0.575156i | \(-0.195059\pi\) | ||||
0.818044 | + | 0.575156i | \(0.195059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.0000 | −1.63361 | −0.816805 | − | 0.576913i | \(-0.804257\pi\) | ||||
−0.816805 | + | 0.576913i | \(0.804257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.48528i | 0.329045i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.9706i | − | 0.657103i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.0000 | − | 26.8701i | −1.46916 | − | 1.03886i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.0000 | − | 4.24264i | −0.577350 | − | 0.163299i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 22.6274i | − | 0.869642i | −0.900517 | − | 0.434821i | \(-0.856812\pi\) | ||
0.900517 | − | 0.434821i | \(-0.143188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.48528i | − | 0.325635i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0000 | + | 33.9411i | −0.919682 | + | 1.30063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.0000 | 1.14624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.00000 | + | 2.82843i | −0.0763048 | + | 0.107911i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.65685i | 0.215509i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.8406i | 1.66778i | 0.551934 | + | 0.833888i | \(0.313890\pi\) | ||||
−0.551934 | + | 0.833888i | \(0.686110\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.0000 | − | 5.65685i | 0.607790 | − | 0.214886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000 | 0.606915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.00000 | − | 2.82843i | −0.151294 | − | 0.106981i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.2843i | − | 1.06828i | −0.845395 | − | 0.534141i | \(-0.820635\pi\) | ||
0.845395 | − | 0.534141i | \(-0.179365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.48528i | − | 0.320028i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.0000 | − | 11.3137i | −0.602595 | − | 0.426099i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.0000 | −1.05305 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | 0.525781 | 0.262891 | − | 0.964826i | \(-0.415324\pi\) | ||||
0.262891 | + | 0.964826i | \(0.415324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | − | 2.82843i | 0.300023 | − | 0.106074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.82843i | 0.105925i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685i | 0.211554i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.00000 | + | 11.3137i | −0.298765 | + | 0.422518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0000 | 1.11881 | 0.559406 | − | 0.828894i | \(-0.311029\pi\) | ||||
0.559406 | + | 0.828894i | \(0.311029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | 0.744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.00000 | + | 8.48528i | −0.223142 | + | 0.315571i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.4558i | 0.945406i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6274i | 0.839204i | 0.907708 | + | 0.419602i | \(0.137830\pi\) | ||||
−0.907708 | + | 0.419602i | \(0.862170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.0000 | − | 7.07107i | −0.368856 | − | 0.260820i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.9706i | 0.625119i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.24264i | 0.156068i | 0.996951 | + | 0.0780340i | \(0.0248643\pi\) | ||||
−0.996951 | + | 0.0780340i | \(0.975136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | − | 4.24264i | −0.220416 | − | 0.155857i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0000 | −1.32071 | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||||
−0.660356 | + | 0.750953i | \(0.729595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | −0.0732743 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 16.9706i | − | 0.620091i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.48528i | 0.309632i | 0.987943 | + | 0.154816i | \(0.0494785\pi\) | ||||
−0.987943 | + | 0.154816i | \(0.950521\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0000 | + | 31.1127i | −0.801725 | + | 1.13381i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.0000 | 1.23739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0000 | 0.872295 | 0.436147 | − | 0.899875i | \(-0.356343\pi\) | ||||
0.436147 | + | 0.899875i | \(0.356343\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | − | 11.3137i | 0.290382 | − | 0.410662i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0416i | 0.871508i | 0.900066 | + | 0.435754i | \(0.143518\pi\) | ||||
−0.900066 | + | 0.435754i | \(0.856482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 14.1421i | − | 0.511980i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.0000 | 1.37032 | 0.685158 | − | 0.728395i | \(-0.259733\pi\) | ||||
0.685158 | + | 0.728395i | \(0.259733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.00000 | − | 2.82843i | −0.144056 | − | 0.101863i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3553i | 1.27164i | 0.771836 | + | 0.635822i | \(0.219339\pi\) | ||||
−0.771836 | + | 0.635822i | \(0.780661\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.24264i | − | 0.152400i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | − | 2.82843i | −0.143499 | − | 0.101469i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.0000 | −1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.0000 | − | 42.4264i | 0.428845 | − | 1.51620i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9706i | 0.605705i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.41421i | − | 0.0504113i | −0.999682 | − | 0.0252056i | \(-0.991976\pi\) | ||
0.999682 | − | 0.0252056i | \(-0.00802405\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.00000 | + | 11.3137i | −0.284808 | + | 0.402779i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.00000 | − | 11.3137i | 0.283731 | − | 0.401256i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.3137i | 0.400752i | 0.979719 | + | 0.200376i | \(0.0642164\pi\) | ||||
−0.979719 | + | 0.200376i | \(0.935784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.0000 | + | 9.89949i | −0.989331 | + | 0.349781i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.0000 | −1.41157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.00000 | + | 2.82843i | 0.140807 | + | 0.0995654i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 8.48528i | − | 0.298327i | −0.988813 | − | 0.149163i | \(-0.952342\pi\) | ||
0.988813 | − | 0.149163i | \(-0.0476580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.5563i | 0.546257i | 0.961978 | + | 0.273129i | \(0.0880585\pi\) | ||||
−0.961978 | + | 0.273129i | \(0.911942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00000 | − | 4.24264i | −0.210429 | − | 0.148796i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0000 | −0.770626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00000 | + | 1.41421i | −0.139771 | + | 0.0494166i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.3553i | 1.23391i | 0.786998 | + | 0.616955i | \(0.211634\pi\) | ||||
−0.786998 | + | 0.616955i | \(0.788366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 31.1127i | − | 1.08452i | −0.840211 | − | 0.542260i | \(-0.817569\pi\) | ||
0.840211 | − | 0.542260i | \(-0.182431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | + | 16.9706i | −0.417786 | + | 0.590839i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0000 | 0.972480 | 0.486240 | − | 0.873825i | \(-0.338368\pi\) | ||||
0.486240 | + | 0.873825i | \(0.338368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.0000 | + | 31.1127i | −0.763172 | + | 1.07929i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 11.3137i | − | 0.391527i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | + | 7.07107i | −0.0691301 | + | 0.244412i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0000 | −1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.00000 | − | 1.41421i | −0.0688837 | − | 0.0487081i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.41421i | − | 0.0486504i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.07107i | − | 0.242965i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.0000 | − | 22.6274i | −1.09824 | − | 0.776571i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0000 | 0.890223 | 0.445112 | − | 0.895475i | \(-0.353164\pi\) | ||||
0.445112 | + | 0.895475i | \(0.353164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | + | 16.9706i | 0.205196 | + | 0.580381i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.7990i | − | 0.676321i | −0.941089 | − | 0.338160i | \(-0.890195\pi\) | ||
0.941089 | − | 0.338160i | \(-0.109805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.48528i | − | 0.289514i | −0.989467 | − | 0.144757i | \(-0.953760\pi\) | ||
0.989467 | − | 0.144757i | \(-0.0462401\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.0000 | + | 14.1421i | −0.340799 | + | 0.481963i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.0000 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0000 | 0.680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.0000 | − | 24.0416i | 0.577350 | − | 0.816497i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.3137i | − | 0.383791i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.24264i | − | 0.143756i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | − | 16.9706i | −0.203069 | − | 0.574367i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.0000 | −0.540899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.0000 | 1.41824 | 0.709120 | − | 0.705088i | \(-0.249093\pi\) | ||||
0.709120 | + | 0.705088i | \(0.249093\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −34.0000 | − | 24.0416i | −1.14679 | − | 0.810904i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.82843i | − | 0.0952921i | −0.998864 | − | 0.0476461i | \(-0.984828\pi\) | ||
0.998864 | − | 0.0476461i | \(-0.0151720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.9411i | − | 1.14221i | −0.820877 | − | 0.571105i | \(-0.806515\pi\) | ||
0.820877 | − | 0.571105i | \(-0.193485\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0000 | + | 16.9706i | 0.806751 | + | 0.570459i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | 0.201460 | 0.100730 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100730 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.0000 | − | 22.6274i | 0.938035 | − | 0.758047i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 33.9411i | − | 1.13580i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.65685i | − | 0.189088i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | + | 2.82843i | −0.0667781 | + | 0.0944384i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0000 | + | 16.9706i | −0.399335 | + | 0.564745i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.3137i | − | 0.376080i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45.2548i | − | 1.50266i | −0.659925 | − | 0.751331i | \(-0.729412\pi\) | ||
0.659925 | − | 0.751331i | \(-0.270588\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56.0000 | + | 19.7990i | −1.85740 | + | 0.656691i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0000 | 1.39152 | 0.695761 | − | 0.718273i | \(-0.255067\pi\) | ||||
0.695761 | + | 0.718273i | \(0.255067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 16.9706i | − | 0.560417i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 31.1127i | − | 1.02631i | −0.858295 | − | 0.513157i | \(-0.828476\pi\) | ||
0.858295 | − | 0.513157i | \(-0.171524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.0000 | + | 32.5269i | 1.51575 | + | 1.07180i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.00000 | 0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.0000 | − | 14.1421i | 1.31377 | − | 0.464489i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 24.0416i | − | 0.788780i | −0.918943 | − | 0.394390i | \(-0.870956\pi\) | ||
0.918943 | − | 0.394390i | \(-0.129044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 21.2132i | − | 0.695235i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.0000 | − | 25.4558i | 0.589294 | − | 0.833387i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.0000 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.0000 | + | 36.7696i | −0.848478 | + | 1.19993i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 35.3553i | − | 1.15255i | −0.817255 | − | 0.576276i | \(-0.804506\pi\) | ||
0.817255 | − | 0.576276i | \(-0.195494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1421i | 0.460531i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0000 | + | 2.82843i | 0.325300 | + | 0.0920087i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000 | 0.324614 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.0000 | − | 9.89949i | −0.453981 | − | 0.321013i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.0833i | 1.55757i | 0.627291 | + | 0.778785i | \(0.284164\pi\) | ||||
−0.627291 | + | 0.778785i | \(0.715836\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 36.7696i | − | 1.18983i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.0000 | − | 33.9411i | −1.55162 | − | 1.09716i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.0000 | 0.968751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.0000 | 0.935484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | − | 33.9411i | −0.386695 | − | 1.09374i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.1421i | 0.455251i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6985i | 0.955039i | 0.878621 | + | 0.477519i | \(0.158464\pi\) | ||||
−0.878621 | + | 0.477519i | \(0.841536\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.0000 | −0.706014 | −0.353007 | − | 0.935621i | \(-0.614841\pi\) | ||||
−0.353007 | + | 0.935621i | \(0.614841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000 | 0.512936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00000 | − | 4.24264i | 0.0960769 | − | 0.135873i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 24.0416i | − | 0.769160i | −0.923092 | − | 0.384580i | \(-0.874346\pi\) | ||
0.923092 | − | 0.384580i | \(-0.125654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39.5980i | 1.26556i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | − | 28.2843i | −0.319275 | − | 0.903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.0000 | −1.02064 | −0.510321 | − | 0.859984i | \(-0.670473\pi\) | ||||
−0.510321 | + | 0.859984i | \(0.670473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000 | 0.318626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0000 | − | 11.3137i | −0.509286 | − | 0.360119i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706i | 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 33.9411i | − | 1.07818i | −0.842250 | − | 0.539088i | \(-0.818769\pi\) | ||
0.842250 | − | 0.539088i | \(-0.181231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.0000 | − | 21.2132i | −0.952021 | − | 0.673181i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.0000 | −0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | − | 2.82843i | −0.316386 | − | 0.0894875i |
(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 | 624.2.d.e.287.1 | yes | 2 | |
3.2 | odd | 2 | 624.2.d.b.287.1 | ✓ | 2 | ||
4.3 | odd | 2 | 624.2.d.b.287.2 | yes | 2 | ||
8.3 | odd | 2 | 2496.2.d.f.1535.1 | 2 | |||
8.5 | even | 2 | 2496.2.d.c.1535.2 | 2 | |||
12.11 | even | 2 | inner | 624.2.d.e.287.2 | yes | 2 | |
24.5 | odd | 2 | 2496.2.d.f.1535.2 | 2 | |||
24.11 | even | 2 | 2496.2.d.c.1535.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.d.b.287.1 | ✓ | 2 | 3.2 | odd | 2 | ||
624.2.d.b.287.2 | yes | 2 | 4.3 | odd | 2 | ||
624.2.d.e.287.1 | yes | 2 | 1.1 | even | 1 | trivial | |
624.2.d.e.287.2 | yes | 2 | 12.11 | even | 2 | inner | |
2496.2.d.c.1535.1 | 2 | 24.11 | even | 2 | |||
2496.2.d.c.1535.2 | 2 | 8.5 | even | 2 | |||
2496.2.d.f.1535.1 | 2 | 8.3 | odd | 2 | |||
2496.2.d.f.1535.2 | 2 | 24.5 | odd | 2 |