Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1249,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3120.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.l (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.9133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.1 | ||
Root | \(-1.75233 + 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3120.1249 |
Dual form | 3120.2.l.m.1249.4 |
$q$-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 \(\left(\mathbb{Z}/3120\mathbb{Z}\right)^\times\).
\(n\) | \(1951\) | \(2081\) | \(2341\) | \(2497\) | \(2641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.75233 | − | 1.38900i | −0.783667 | − | 0.621181i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50466 | −0.453673 | −0.226837 | − | 0.973933i | \(-0.572838\pi\) | ||||
−0.226837 | + | 0.973933i | \(0.572838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.38900 | + | 1.75233i | −0.358639 | + | 0.452450i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.72666i | 0.661311i | 0.943751 | + | 0.330656i | \(0.107270\pi\) | ||||
−0.943751 | + | 0.330656i | \(0.892730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.726656 | 0.166706 | 0.0833532 | − | 0.996520i | \(-0.473437\pi\) | ||||
0.0833532 | + | 0.996520i | \(0.473437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.72666i | 0.985576i | 0.870149 | + | 0.492788i | \(0.164022\pi\) | ||||
−0.870149 | + | 0.492788i | \(0.835978\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14134 | + | 4.86799i | 0.228267 | + | 0.973599i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.55602 | 1.40312 | 0.701558 | − | 0.712612i | \(-0.252488\pi\) | ||||
0.701558 | + | 0.712612i | \(0.252488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00933 | 0.540491 | 0.270246 | − | 0.962791i | \(-0.412895\pi\) | ||||
0.270246 | + | 0.962791i | \(0.412895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50466i | 0.261928i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00933i | 0.823529i | 0.911290 | + | 0.411764i | \(0.135087\pi\) | ||||
−0.911290 | + | 0.411764i | \(0.864913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.78734 | 0.903830 | 0.451915 | − | 0.892061i | \(-0.350741\pi\) | ||||
0.451915 | + | 0.892061i | \(0.350741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.72666i | − | 0.415811i | −0.978149 | − | 0.207906i | \(-0.933335\pi\) | ||
0.978149 | − | 0.207906i | \(-0.0666647\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.75233 | + | 1.38900i | 0.261222 | + | 0.207060i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.2313i | − | 1.49239i | −0.665727 | − | 0.746196i | \(-0.731878\pi\) | ||
0.665727 | − | 0.746196i | \(-0.268122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.72666 | 0.381808 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.55602i | − | 1.03790i | −0.854805 | − | 0.518949i | \(-0.826323\pi\) | ||
0.854805 | − | 0.518949i | \(-0.173677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.63667 | + | 2.08998i | 0.355529 | + | 0.281813i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.726656i | − | 0.0962480i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.5140 | −1.62918 | −0.814592 | − | 0.580035i | \(-0.803039\pi\) | ||||
−0.814592 | + | 0.580035i | \(0.803039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.28267 | 0.804414 | 0.402207 | − | 0.915549i | \(-0.368243\pi\) | ||||
0.402207 | + | 0.915549i | \(0.368243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.38900 | − | 1.75233i | 0.172285 | − | 0.217350i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.5653i | − | 1.53510i | −0.640988 | − | 0.767551i | \(-0.721475\pi\) | ||
0.640988 | − | 0.767551i | \(-0.278525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.72666 | 0.569023 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.77801 | −0.567045 | −0.283523 | − | 0.958966i | \(-0.591503\pi\) | ||||
−0.283523 | + | 0.958966i | \(0.591503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0187i | 1.40668i | 0.710855 | + | 0.703339i | \(0.248308\pi\) | ||||
−0.710855 | + | 0.703339i | \(0.751692\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.86799 | − | 1.14134i | 0.562107 | − | 0.131790i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.27334 | 0.593297 | 0.296649 | − | 0.954987i | \(-0.404131\pi\) | ||||
0.296649 | + | 0.954987i | \(0.404131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.78734i | − | 0.854771i | −0.904069 | − | 0.427386i | \(-0.859435\pi\) | ||
0.904069 | − | 0.427386i | \(-0.140565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.78734 | − | 4.77801i | 0.410794 | − | 0.518248i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.55602i | − | 0.810090i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.78734 | −0.189457 | −0.0947286 | − | 0.995503i | \(-0.530198\pi\) | ||||
−0.0947286 | + | 0.995503i | \(0.530198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.00933i | − | 0.312053i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.27334 | − | 1.00933i | −0.130642 | − | 0.103555i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.50466 | 0.151224 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.99067 | −0.297583 | −0.148791 | − | 0.988869i | \(-0.547538\pi\) | ||||
−0.148791 | + | 0.988869i | \(0.547538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.443984i | 0.0437471i | 0.999761 | + | 0.0218735i | \(0.00696312\pi\) | ||||
−0.999761 | + | 0.0218735i | \(0.993037\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.00933i | 0.677617i | 0.940855 | + | 0.338809i | \(0.110024\pi\) | ||||
−0.940855 | + | 0.338809i | \(0.889976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8387 | 1.32551 | 0.662753 | − | 0.748838i | \(-0.269388\pi\) | ||||
0.662753 | + | 0.748838i | \(0.269388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00933 | 0.475464 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.28267i | − | 0.402880i | −0.979501 | − | 0.201440i | \(-0.935438\pi\) | ||
0.979501 | − | 0.201440i | \(-0.0645621\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.56534 | − | 8.28267i | 0.612222 | − | 0.772363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.73599 | −0.794180 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.78734i | − | 0.521827i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.76166 | − | 10.1157i | 0.425896 | − | 0.904772i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.71733i | − | 0.507331i | −0.967292 | − | 0.253665i | \(-0.918364\pi\) | ||
0.967292 | − | 0.253665i | \(-0.0816362\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.72666 | −0.240069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.55602 | −0.485431 | −0.242716 | − | 0.970097i | \(-0.578038\pi\) | ||||
−0.242716 | + | 0.970097i | \(0.578038\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.38900 | − | 1.75233i | 0.119546 | − | 0.150817i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.67531i | 0.570310i | 0.958481 | + | 0.285155i | \(0.0920450\pi\) | ||||
−0.958481 | + | 0.285155i | \(0.907955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4720 | 1.65159 | 0.825795 | − | 0.563970i | \(-0.190727\pi\) | ||||
0.825795 | + | 0.563970i | \(0.190727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.2313 | −0.861633 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.50466i | − | 0.125826i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.2406 | − | 10.4953i | −1.09958 | − | 0.871590i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5140 | 1.18903 | 0.594516 | − | 0.804084i | \(-0.297344\pi\) | ||||
0.594516 | + | 0.804084i | \(0.297344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.46264 | 0.363165 | 0.181582 | − | 0.983376i | \(-0.441878\pi\) | ||||
0.181582 | + | 0.983376i | \(0.441878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.72666i | − | 0.220437i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.27334 | − | 4.17997i | −0.423565 | − | 0.335743i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.30133i | − | 0.662518i | −0.943540 | − | 0.331259i | \(-0.892527\pi\) | ||
0.943540 | − | 0.331259i | \(-0.107473\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.55602 | −0.599231 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0093i | 0.862317i | 0.902276 | + | 0.431159i | \(0.141895\pi\) | ||||
−0.902276 | + | 0.431159i | \(0.858105\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.08998 | − | 2.63667i | 0.162705 | − | 0.205265i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.76868i | − | 0.446394i | −0.974773 | − | 0.223197i | \(-0.928351\pi\) | ||
0.974773 | − | 0.223197i | \(-0.0716493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.726656 | −0.0555688 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.90663i | 0.373044i | 0.982451 | + | 0.186522i | \(0.0597215\pi\) | ||||
−0.982451 | + | 0.186522i | \(0.940278\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.5140i | 0.940609i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.45331 | 0.706574 | 0.353287 | − | 0.935515i | \(-0.385064\pi\) | ||||
0.353287 | + | 0.935515i | \(0.385064\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4720 | 1.29868 | 0.649341 | − | 0.760498i | \(-0.275045\pi\) | ||||
0.649341 | + | 0.760498i | \(0.275045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.28267i | − | 0.464428i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.95798 | − | 8.77801i | 0.511561 | − | 0.645372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.10270i | − | 0.300019i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1120 | 0.804038 | 0.402019 | − | 0.915631i | \(-0.368309\pi\) | ||||
0.402019 | + | 0.915631i | \(0.368309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.10270i | 0.439282i | 0.975581 | + | 0.219641i | \(0.0704886\pi\) | ||||
−0.975581 | + | 0.219641i | \(0.929511\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.75233 | − | 1.38900i | −0.125487 | − | 0.0994686i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.3620i | − | 1.52198i | −0.648764 | − | 0.760990i | \(-0.724714\pi\) | ||
0.648764 | − | 0.760990i | \(-0.275286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.38538 | 0.594423 | 0.297212 | − | 0.954812i | \(-0.403943\pi\) | ||||
0.297212 | + | 0.954812i | \(0.403943\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.5653 | −0.886291 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1413 | − | 8.03863i | −0.708302 | − | 0.561443i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.72666i | − | 0.328525i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.09337 | −0.0756303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.27334 | 0.0876606 | 0.0438303 | − | 0.999039i | \(-0.486044\pi\) | ||||
0.0438303 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.77801i | 0.327384i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.78734 | + | 4.77801i | −0.258294 | + | 0.325857i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0187 | 0.812146 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.72666 | −0.183415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4626i | 1.10242i | 0.834367 | + | 0.551210i | \(0.185834\pi\) | ||||
−0.834367 | + | 0.551210i | \(0.814166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.14134 | − | 4.86799i | −0.0760891 | − | 0.324533i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 12.2500i | − | 0.813060i | −0.913638 | − | 0.406530i | \(-0.866739\pi\) | ||
0.913638 | − | 0.406530i | \(-0.133261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.27334 | 0.0841449 | 0.0420725 | − | 0.999115i | \(-0.486604\pi\) | ||||
0.0420725 | + | 0.999115i | \(0.486604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.3013i | − | 1.19896i | −0.800390 | − | 0.599480i | \(-0.795374\pi\) | ||
0.800390 | − | 0.599480i | \(-0.204626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.2113 | + | 17.9287i | −0.927046 | + | 1.16954i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.27334i | − | 0.342540i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.23132 | 0.403071 | 0.201535 | − | 0.979481i | \(-0.435407\pi\) | ||||
0.201535 | + | 0.979481i | \(0.435407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5560 | 1.25971 | 0.629857 | − | 0.776711i | \(-0.283114\pi\) | ||||
0.629857 | + | 0.776711i | \(0.283114\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.2663 | − | 9.72303i | −0.783667 | − | 0.621181i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.726656i | 0.0462360i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.78734 | −0.493502 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.4813 | −1.67148 | −0.835742 | − | 0.549122i | \(-0.814962\pi\) | ||||
−0.835742 | + | 0.549122i | \(0.814962\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.11203i | − | 0.447130i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.77801 | − | 3.78734i | −0.299210 | − | 0.237172i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.8294i | 0.925030i | 0.886611 | + | 0.462515i | \(0.153053\pi\) | ||||
−0.886611 | + | 0.462515i | \(0.846947\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.55602 | −0.467706 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.9507i | 1.41520i | 0.706612 | + | 0.707601i | \(0.250223\pi\) | ||||
−0.706612 | + | 0.707601i | \(0.749777\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4953 | + | 13.2406i | −0.644723 | + | 0.813367i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.78734i | 0.109383i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.9160 | 1.70207 | 0.851033 | − | 0.525112i | \(-0.175977\pi\) | ||||
0.851033 | + | 0.525112i | \(0.175977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.65872 | 0.343743 | 0.171871 | − | 0.985119i | \(-0.445019\pi\) | ||||
0.171871 | + | 0.985119i | \(0.445019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.71733 | − | 7.32469i | −0.103559 | − | 0.441696i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.73599i | 0.464810i | 0.972619 | + | 0.232405i | \(0.0746595\pi\) | ||||
−0.972619 | + | 0.232405i | \(0.925340\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00933 | −0.180164 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.11929 | 0.305391 | 0.152696 | − | 0.988273i | \(-0.451205\pi\) | ||||
0.152696 | + | 0.988273i | \(0.451205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.90663i | 0.410556i | 0.978704 | + | 0.205278i | \(0.0658099\pi\) | ||||
−0.978704 | + | 0.205278i | \(0.934190\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00933 | + | 1.27334i | −0.0597875 | + | 0.0754264i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.56534 | 0.562667 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26.3527i | − | 1.53954i | −0.638321 | − | 0.769770i | \(-0.720371\pi\) | ||
0.638321 | − | 0.769770i | \(-0.279629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.9287 | + | 17.3820i | 1.27674 | + | 1.01202i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.50466i | − | 0.0873095i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.72666 | −0.273350 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.99067i | 0.171810i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.0093 | − | 8.72666i | −0.630392 | − | 0.499687i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.0000i | − | 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.443984 | 0.0252574 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.8973 | 0.674634 | 0.337317 | − | 0.941391i | \(-0.390481\pi\) | ||||
0.337317 | + | 0.941391i | \(0.390481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.7360i | − | 1.00250i | −0.865303 | − | 0.501249i | \(-0.832874\pi\) | ||
0.865303 | − | 0.501249i | \(-0.167126\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.32469i | − | 0.0744023i | −0.999308 | − | 0.0372011i | \(-0.988156\pi\) | ||
0.999308 | − | 0.0372011i | \(-0.0118442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.3693 | −0.636557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.00933 | 0.391223 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98134i | 0.110245i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.86799 | + | 1.14134i | −0.270028 | + | 0.0633099i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 13.8387i | − | 0.765281i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.73599 | 0.205348 | 0.102674 | − | 0.994715i | \(-0.467260\pi\) | ||||
0.102674 | + | 0.994715i | \(0.467260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.00933i | − | 0.274510i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.4533 | + | 22.0187i | −0.953576 | + | 1.20301i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3947i | 1.27439i | 0.770702 | + | 0.637195i | \(0.219906\pi\) | ||||
−0.770702 | + | 0.637195i | \(0.780094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.28267 | −0.232603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.52803 | −0.245207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.28267 | − | 6.56534i | −0.445924 | − | 0.353466i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.5840i | 1.64184i | 0.571047 | + | 0.820918i | \(0.306538\pi\) | ||||
−0.571047 | + | 0.820918i | \(0.693462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.37605 | −0.0736581 | −0.0368290 | − | 0.999322i | \(-0.511726\pi\) | ||||
−0.0368290 | + | 0.999322i | \(0.511726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.9087i | 1.05963i | 0.848112 | + | 0.529817i | \(0.177739\pi\) | ||||
−0.848112 | + | 0.529817i | \(0.822261\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.37266 | + | 6.63667i | 0.444374 | + | 0.352238i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.6940 | 1.40885 | 0.704427 | − | 0.709777i | \(-0.251204\pi\) | ||||
0.704427 | + | 0.709777i | \(0.251204\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4720 | −0.972209 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.73599i | 0.458520i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.6940 | − | 21.0607i | 0.873802 | − | 1.10237i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.12136i | 0.423932i | 0.977277 | + | 0.211966i | \(0.0679865\pi\) | ||||
−0.977277 | + | 0.211966i | \(0.932013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.78734 | −0.301277 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.47197i | 0.490440i | 0.969467 | + | 0.245220i | \(0.0788602\pi\) | ||||
−0.969467 | + | 0.245220i | \(0.921140\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.1157 | − | 4.76166i | −0.522370 | − | 0.245891i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.55602i | 0.389155i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7267 | 0.859191 | 0.429595 | − | 0.903022i | \(-0.358656\pi\) | ||||
0.429595 | + | 0.903022i | \(0.358656\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.71733 | −0.292908 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 19.6846i | − | 1.00584i | −0.864334 | − | 0.502919i | \(-0.832259\pi\) | ||
0.864334 | − | 0.502919i | \(-0.167741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.72666i | 0.138604i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8880 | −0.651773 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.55602i | 0.280264i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.24065 | − | 7.32469i | −0.464948 | − | 0.368545i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.35061i | 0.168162i | 0.996459 | + | 0.0840812i | \(0.0267955\pi\) | ||||
−0.996459 | + | 0.0840812i | \(0.973205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.3713 | −1.81630 | −0.908149 | − | 0.418647i | \(-0.862504\pi\) | ||||
−0.908149 | + | 0.418647i | \(0.862504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00933i | 0.149905i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.75233 | − | 1.38900i | −0.0870741 | − | 0.0690202i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.53736i | − | 0.373613i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.5933 | −1.75998 | −0.879988 | − | 0.474995i | \(-0.842450\pi\) | ||||
−0.879988 | + | 0.474995i | \(0.842450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.67531 | 0.329269 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8166 | + | 13.6460i | −0.530968 | + | 0.669856i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 19.4720i | − | 0.953546i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.9160 | −0.679839 | −0.339919 | − | 0.940455i | \(-0.610400\pi\) | ||||
−0.339919 | + | 0.940455i | \(0.610400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.70800 | 0.229454 | 0.114727 | − | 0.993397i | \(-0.463401\pi\) | ||||
0.114727 | + | 0.993397i | \(0.463401\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.2313i | 0.497464i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.2733 | + | 3.11203i | −0.643852 | + | 0.150956i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.50466 | −0.0726459 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.89004 | −0.380050 | −0.190025 | − | 0.981779i | \(-0.560857\pi\) | ||||
−0.190025 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.30133i | − | 0.110595i | −0.998470 | − | 0.0552974i | \(-0.982389\pi\) | ||
0.998470 | − | 0.0552974i | \(-0.0176107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4953 | + | 13.2406i | −0.503213 | + | 0.634841i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.43466i | 0.164302i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 41.1307 | 1.96306 | 0.981530 | − | 0.191307i | \(-0.0612725\pi\) | ||||
0.981530 | + | 0.191307i | \(0.0612725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.5933i | 1.40602i | 0.711179 | + | 0.703011i | \(0.248161\pi\) | ||||
−0.711179 | + | 0.703011i | \(0.751839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.13201 | + | 2.48262i | 0.148471 | + | 0.117687i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.5140i | − | 0.686488i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.4461 | 0.540173 | 0.270086 | − | 0.962836i | \(-0.412948\pi\) | ||||
0.270086 | + | 0.962836i | \(0.412948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.70800 | −0.410044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.46264i | − | 0.209673i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5467i | 0.774021i | 0.922075 | + | 0.387011i | \(0.126492\pi\) | ||||
−0.922075 | + | 0.387011i | \(0.873508\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.72666 | −0.127269 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.50466 | 0.163228 | 0.0816142 | − | 0.996664i | \(-0.473992\pi\) | ||||
0.0816142 | + | 0.996664i | \(0.473992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.17997 | + | 5.27334i | −0.193841 | + | 0.244545i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.44398i | − | 0.298192i | −0.988823 | − | 0.149096i | \(-0.952364\pi\) | ||
0.988823 | − | 0.149096i | \(-0.0476363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.30133 | −0.382505 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.10270i | 0.188642i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.829359 | + | 3.53736i | 0.0380536 | + | 0.162305i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.55602i | 0.345966i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.2313 | 1.01577 | 0.507887 | − | 0.861423i | \(-0.330427\pi\) | ||||
0.507887 | + | 0.861423i | \(0.330427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00933 | −0.228406 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.33402 | − | 10.5140i | 0.378429 | − | 0.477416i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9160i | 0.630592i | 0.948993 | + | 0.315296i | \(0.102104\pi\) | ||||
−0.948993 | + | 0.315296i | \(0.897896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.0093 | 0.497859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.1400 | 1.26994 | 0.634971 | − | 0.772536i | \(-0.281012\pi\) | ||||
0.634971 | + | 0.772536i | \(0.281012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.6027i | 0.927897i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.63667 | − | 2.08998i | −0.118510 | − | 0.0939378i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.8480 | 1.73908 | 0.869538 | − | 0.493866i | \(-0.164417\pi\) | ||||
0.869538 | + | 0.493866i | \(0.164417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.76868 | −0.257726 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.19863i | 0.365559i | 0.983154 | + | 0.182779i | \(0.0585094\pi\) | ||||
−0.983154 | + | 0.182779i | \(0.941491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.24065 | + | 4.15405i | 0.233206 | + | 0.184853i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.0700 | −0.712291 | −0.356145 | − | 0.934431i | \(-0.615909\pi\) | ||||
−0.356145 | + | 0.934431i | \(0.615909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.726656i | 0.0320827i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.616696 | − | 0.778008i | 0.0271749 | − | 0.0342831i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3947i | 0.677058i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.90663 | 0.215377 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0280 | −1.00887 | −0.504437 | − | 0.863448i | \(-0.668300\pi\) | ||||
−0.504437 | + | 0.863448i | \(0.668300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.47875i | 0.239569i | 0.992800 | + | 0.119784i | \(0.0382204\pi\) | ||||
−0.992800 | + | 0.119784i | \(0.961780\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.20541i | 0.357433i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.658719 | 0.0286399 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5140 | 0.543061 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.78734i | 0.250677i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.73599 | − | 12.2827i | 0.420923 | − | 0.531026i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.45331i | − | 0.407941i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.5327 | −0.453673 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8387 | 0.766945 | 0.383473 | − | 0.923552i | \(-0.374728\pi\) | ||||
0.383473 | + | 0.923552i | \(0.374728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 17.4720i | − | 0.749794i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.2500 | − | 19.2220i | −1.03875 | − | 0.823380i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.1053i | − | 1.24445i | −0.782838 | − | 0.622225i | \(-0.786229\pi\) | ||
0.782838 | − | 0.622225i | \(-0.213771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.28267 | −0.268138 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.49063 | 0.233909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.77801 | − | 6.95798i | −0.372606 | − | 0.295350i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 44.0114i | 1.86482i | 0.361399 | + | 0.932411i | \(0.382299\pi\) | ||||
−0.361399 | + | 0.932411i | \(0.617701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.72666 | 0.115325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.10270 | −0.173216 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.43466i | 0.313333i | 0.987652 | + | 0.156667i | \(0.0500748\pi\) | ||||
−0.987652 | + | 0.156667i | \(0.949925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.94865 | + | 7.50466i | −0.250262 | + | 0.315724i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.48130 | −0.355555 | −0.177777 | − | 0.984071i | \(-0.556891\pi\) | ||||
−0.177777 | + | 0.984071i | \(0.556891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.7826 | −1.70670 | −0.853350 | − | 0.521339i | \(-0.825433\pi\) | ||||
−0.853350 | + | 0.521339i | \(0.825433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 11.1120i | − | 0.464212i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.0093 | + | 5.39470i | −0.959555 | + | 0.224975i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.57467i | 0.0655545i | 0.999463 | + | 0.0327773i | \(0.0104352\pi\) | ||||
−0.999463 | + | 0.0327773i | \(0.989565\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.10270 | 0.253620 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3693i | 0.470867i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.38900 | + | 1.75233i | −0.0574282 | + | 0.0724500i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 27.8247i | − | 1.14845i | −0.818699 | − | 0.574223i | \(-0.805304\pi\) | ||
0.818699 | − | 0.574223i | \(-0.194696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.18675 | 0.0901034 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.3620 | −0.878716 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 32.6940i | − | 1.34258i | −0.741195 | − | 0.671290i | \(-0.765740\pi\) | ||
0.741195 | − | 0.671290i | \(-0.234260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8.38538i | − | 0.343191i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.1400 | −1.31321 | −0.656603 | − | 0.754237i | \(-0.728007\pi\) | ||||
−0.656603 | + | 0.754237i | \(0.728007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.8667 | 1.66699 | 0.833493 | − | 0.552530i | \(-0.186337\pi\) | ||||
0.833493 | + | 0.552530i | \(0.186337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.5653i | 0.511700i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.3083 | + | 12.1343i | 0.622373 | + | 0.493330i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.9907i | − | 0.608453i | −0.952600 | − | 0.304226i | \(-0.901602\pi\) | ||
0.952600 | − | 0.304226i | \(-0.0983979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2313 | 0.413915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.5747i | − | 0.548276i | −0.961690 | − | 0.274138i | \(-0.911608\pi\) | ||
0.961690 | − | 0.274138i | \(-0.0883925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.03863 | + | 10.1413i | −0.324149 | + | 0.408938i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.69396i | − | 0.188972i | −0.995526 | − | 0.0944859i | \(-0.969879\pi\) | ||
0.995526 | − | 0.0944859i | \(-0.0301207\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.8667 | −0.838702 | −0.419351 | − | 0.907824i | \(-0.637742\pi\) | ||||
−0.419351 | + | 0.907824i | \(0.637742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.72666 | −0.189674 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.3947 | + | 11.1120i | −0.895788 | + | 0.444481i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.09337i | 0.0436652i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.6587 | −0.544609 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.9533 | −1.82937 | −0.914685 | − | 0.404167i | \(-0.867562\pi\) | ||||
−0.914685 | + | 0.404167i | \(0.867562\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.27334i | − | 0.0506109i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.94139 | + | 10.0187i | −0.315144 | + | 0.397578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000i | 0.277350i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.77801 | 0.189015 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0187 | 0.790689 | 0.395345 | − | 0.918533i | \(-0.370625\pi\) | ||||
0.395345 | + | 0.918533i | \(0.370625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.5840i | − | 1.04837i | −0.851604 | − | 0.524185i | \(-0.824370\pi\) | ||
0.851604 | − | 0.524185i | \(-0.175630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.77801 | + | 3.78734i | 0.188134 | + | 0.149126i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9.39470i | − | 0.369344i | −0.982800 | − | 0.184672i | \(-0.940878\pi\) | ||
0.982800 | − | 0.184672i | \(-0.0591223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.8294 | 0.739117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.00000i | − | 0.0782660i | −0.999234 | − | 0.0391330i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391330i | \(-0.0124596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.73599 | + | 7.71733i | 0.380416 | + | 0.301541i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.0187i | − | 0.468892i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.6774 | 1.85725 | 0.928623 | − | 0.371024i | \(-0.120993\pi\) | ||||
0.928623 | + | 0.371024i | \(0.120993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0959 | −0.859432 | −0.429716 | − | 0.902964i | \(-0.641386\pi\) | ||||
−0.429716 | + | 0.902964i | \(0.641386\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.72666i | 0.105895i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.7147i | 1.38288i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.4626 | 0.636482 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.45331 | −0.364941 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.6027i | 1.87349i | 0.350006 | + | 0.936747i | \(0.386180\pi\) | ||||
−0.350006 | + | 0.936747i | \(0.613820\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.86799 | + | 1.14134i | −0.187369 | + | 0.0439300i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4253i | 0.400678i | 0.979727 | + | 0.200339i | \(0.0642043\pi\) | ||||
−0.979727 | + | 0.200339i | \(0.935796\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2500 | −0.469420 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 9.13795i | − | 0.349654i | −0.984599 | − | 0.174827i | \(-0.944063\pi\) | ||
0.984599 | − | 0.174827i | \(-0.0559366\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.27203 | − | 11.6974i | 0.354266 | − | 0.446933i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.27334i | − | 0.0485811i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.55602 | 0.287861 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7173 | −1.28267 | −0.641334 | − | 0.767262i | \(-0.721619\pi\) | ||||
−0.641334 | + | 0.767262i | \(0.721619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.1214 | − | 27.0466i | −1.29430 | − | 1.02594i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7801i | 0.597713i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.3013 | −0.692220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9813 | −0.754685 | −0.377342 | − | 0.926074i | \(-0.623162\pi\) | ||||
−0.377342 | + | 0.926074i | \(0.623162\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.64006i | 0.137288i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.9287 | + | 14.2113i | 0.675233 | + | 0.535230i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.3293 | 1.62727 | 0.813633 | − | 0.581378i | \(-0.197486\pi\) | ||||
0.813633 | + | 0.581378i | \(0.197486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.27334 | −0.197766 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.2241i | 0.532695i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.08998 | + | 2.63667i | −0.0781610 | + | 0.0986059i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.23132i | − | 0.232713i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.6867 | −1.29360 | −0.646798 | − | 0.762661i | \(-0.723892\pi\) | ||||
−0.646798 | + | 0.762661i | \(0.723892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 19.5560i | − | 0.727296i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.62395 | + | 36.7826i | 0.320286 | + | 1.36607i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.39470i | 0.200078i | 0.994983 | + | 0.100039i | \(0.0318968\pi\) | ||||
−0.994983 | + | 0.100039i | \(0.968103\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.43466 | 0.274981 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.11203i | 0.336561i | 0.985739 | + | 0.168280i | \(0.0538214\pi\) | ||||
−0.985739 | + | 0.168280i | \(0.946179\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.72303 | + | 12.2663i | −0.358639 | + | 0.452450i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.9066i | 0.696435i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.82936 | −0.177651 | −0.0888254 | − | 0.996047i | \(-0.528311\pi\) | ||||
−0.0888254 | + | 0.996047i | \(0.528311\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.726656 | 0.0266944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 50.4087i | − | 1.84931i | −0.380801 | − | 0.924657i | \(-0.624352\pi\) | ||
0.380801 | − | 0.924657i | \(-0.375648\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.4333 | − | 20.1600i | −0.931805 | − | 0.738605i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.78734i | 0.284924i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.88797 | −0.178365 | −0.0891823 | − | 0.996015i | \(-0.528425\pi\) | ||||
−0.0891823 | + | 0.996015i | \(0.528425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.4813i | 0.965032i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.82003 | − | 6.19863i | −0.284600 | − | 0.225591i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 32.2241i | − | 1.17120i | −0.810599 | − | 0.585602i | \(-0.800858\pi\) | ||
0.810599 | − | 0.585602i | \(-0.199142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.11203 | −0.258150 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.4740 | 1.32218 | 0.661091 | − | 0.750305i | \(-0.270094\pi\) | ||||
0.661091 | + | 0.750305i | \(0.270094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.78734 | + | 4.77801i | −0.136931 | + | 0.172749i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.5140i | − | 0.451854i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.1120 | −0.472832 | −0.236416 | − | 0.971652i | \(-0.575973\pi\) | ||||
−0.236416 | + | 0.971652i | \(0.575973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8294 | 0.534066 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 12.5913i | − | 0.452876i | −0.974026 | − | 0.226438i | \(-0.927292\pi\) | ||
0.974026 | − | 0.226438i | \(-0.0727081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.43466 | + | 14.6494i | 0.123376 | + | 0.526222i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.20541 | 0.150674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.18930 | 0.257253 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.55602i | 0.270030i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.5306 | + | 14.5467i | −0.411544 | + | 0.519194i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.9253i | 1.31624i | 0.752911 | + | 0.658122i | \(0.228649\pi\) | ||||
−0.752911 | + | 0.658122i | \(0.771351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.9507 | 0.817067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.28267i | 0.223104i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.2406 | + | 10.4953i | 0.469597 | + | 0.372231i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0466i | 0.887198i | 0.896225 | + | 0.443599i | \(0.146298\pi\) | ||||
−0.896225 | + | 0.443599i | \(0.853702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.8973 | 0.986935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.78734 | 0.0631524 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 18.0840i | − | 0.638172i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 27.9160i | − | 0.982688i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.2334 | −0.394945 | −0.197473 | − | 0.980308i | \(-0.563273\pi\) | ||||
−0.197473 | + | 0.980308i | \(0.563273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.8387 | −1.11801 | −0.559004 | − | 0.829165i | \(-0.688816\pi\) | ||||
−0.559004 | + | 0.829165i | \(0.688816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.65872i | − | 0.198460i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.2920 | − | 19.2920i | 0.535655 | − | 0.675769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.98134i | − | 0.0693184i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.1073 | −1.12055 | −0.560277 | − | 0.828306i | \(-0.689305\pi\) | ||||
−0.560277 | + | 0.828306i | \(0.689305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.7054i | 1.62805i | 0.580832 | + | 0.814023i | \(0.302727\pi\) | ||||
−0.580832 | + | 0.814023i | \(0.697273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.32469 | + | 1.71733i | −0.255013 | + | 0.0597897i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.6940i | 0.928240i | 0.885772 | + | 0.464120i | \(0.153629\pi\) | ||||
−0.885772 | + | 0.464120i | \(0.846371\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8294 | 1.00129 | 0.500643 | − | 0.865654i | \(-0.333097\pi\) | ||||
0.500643 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.73599 | 0.268358 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.0866i | 0.661311i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.01272 | + | 10.1086i | −0.277292 | + | 0.349824i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.00933i | 0.104018i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.68463 | 0.265303 | 0.132652 | − | 0.991163i | \(-0.457651\pi\) | ||||
0.132652 | + | 0.991163i | \(0.457651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0934 | 0.968737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.11929i | − | 0.176318i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.75233 | + | 1.38900i | 0.0602821 | + | 0.0477832i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.90663 | 0.237035 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.6774 | −0.811650 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.4626i | 0.632149i | 0.948734 | + | 0.316074i | \(0.102365\pi\) | ||||
−0.948734 | + | 0.316074i | \(0.897635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.27334 | + | 1.00933i | 0.0435474 | + | 0.0345183i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2827i | 1.10276i | 0.834256 | + | 0.551378i | \(0.185898\pi\) | ||||
−0.834256 | + | 0.551378i | \(0.814102\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9694 | −0.647227 | −0.323613 | − | 0.946189i | \(-0.604898\pi\) | ||||
−0.323613 | + | 0.946189i | \(0.604898\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16.8807i | − | 0.574626i | −0.957837 | − | 0.287313i | \(-0.907238\pi\) | ||
0.957837 | − | 0.287313i | \(-0.0927620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.81532 | − | 8.59804i | 0.231728 | − | 0.292342i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 9.56534i | − | 0.324856i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.93461 | −0.269163 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5653 | 0.425760 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.00000i | − | 0.203069i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 28.1214i | − | 0.949591i | −0.880096 | − | 0.474795i | \(-0.842522\pi\) | ||
0.880096 | − | 0.474795i | \(-0.157478\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.3527 | −0.888854 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.4066 | −1.66455 | −0.832275 | − | 0.554363i | \(-0.812962\pi\) | ||||
−0.832275 | + | 0.554363i | \(0.812962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.65872i | 0.190431i | 0.995457 | + | 0.0952155i | \(0.0303540\pi\) | ||||
−0.995457 | + | 0.0952155i | \(0.969646\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.3820 | − | 21.9287i | 0.584289 | − | 0.737124i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.2640i | 0.949013i | 0.880252 | + | 0.474506i | \(0.157373\pi\) | ||||
−0.880252 | + | 0.474506i | \(0.842627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50466 | −0.0504082 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.43466i | − | 0.248791i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.5653 | − | 13.1307i | −0.553718 | − | 0.438911i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.72666i | 0.157818i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7385 | 0.758373 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6027 | 0.686374 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.6167 | − | 24.2686i | −1.01773 | − | 0.806717i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 14.5840i | − | 0.484254i | −0.970245 | − | 0.242127i | \(-0.922155\pi\) | ||
0.970245 | − | 0.242127i | \(-0.0778450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.99067 | 0.0991943 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1680 | −0.966379 | −0.483190 | − | 0.875516i | \(-0.660522\pi\) | ||||
−0.483190 | + | 0.875516i | \(0.660522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7173i | 0.387787i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.72666 | + | 11.0093i | −0.288494 | + | 0.363957i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.36672 | 0.0780708 | 0.0390354 | − | 0.999238i | \(-0.487571\pi\) | ||||
0.0390354 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | −0.659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.77801i | − | 0.157270i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.3854 | + | 5.71733i | −0.801786 | + | 0.187985i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.443984i | − | 0.0145824i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.1753 | −1.02283 | −0.511414 | − | 0.859335i | \(-0.670878\pi\) | ||||
−0.511414 | + | 0.859335i | \(0.670878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.08660 | 0.166706 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 11.8973i | − | 0.389500i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.69867 | + | 7.18930i | −0.186366 | + | 0.235115i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.46942i | − | 0.211347i | −0.994401 | − | 0.105673i | \(-0.966300\pi\) | ||
0.994401 | − | 0.105673i | \(-0.0336998\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.7360 | −0.578792 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.4020 | −0.632486 | −0.316243 | − | 0.948678i | \(-0.602421\pi\) | ||||
−0.316243 | + | 0.948678i | \(0.602421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.3548i | 0.890793i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.0632i | 1.62684i | 0.581679 | + | 0.813418i | \(0.302396\pi\) | ||||
−0.581679 | + | 0.813418i | \(0.697604\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0187 | −0.390142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.32469 | −0.0429562 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.30133i | 0.204120i | 0.994778 | + | 0.102060i | \(0.0325434\pi\) | ||||
−0.994778 | + | 0.102060i | \(0.967457\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.4720 | − | 15.4347i | −0.630098 | − | 0.499454i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.3693i | 0.367516i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9439 | −0.707869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 7.00933i | − | 0.225872i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.47668 | − | 10.6940i | 0.272874 | − | 0.344251i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 37.2334i | − | 1.19735i | −0.800994 | − | 0.598673i | \(-0.795695\pi\) | ||
0.800994 | − | 0.598673i | \(-0.204305\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.98134 | 0.0636499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.4533 | −0.431737 | −0.215869 | − | 0.976422i | \(-0.569258\pi\) | ||||
−0.215869 | + | 0.976422i | \(0.569258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.14134 | + | 4.86799i | 0.0365520 | + | 0.155901i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.4647i | 1.19860i | 0.800524 | + | 0.599301i | \(0.204555\pi\) | ||||
−0.800524 | + | 0.599301i | \(0.795445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.68934 | 0.0859517 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.8387 | −0.441835 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 29.2406i | − | 0.932632i | −0.884618 | − | 0.466316i | \(-0.845581\pi\) | ||
0.884618 | − | 0.466316i | \(-0.154419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.6719 | + | 37.4333i | −0.945426 | + | 1.19273i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.8880 | 0.409814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.11203 | −0.0988569 | −0.0494285 | − | 0.998778i | \(-0.515740\pi\) | ||||
−0.0494285 | + | 0.998778i | \(0.515740\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.73599i | − | 0.118558i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6940 | − | 11.6473i | −0.465830 | − | 0.369245i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.3200i | 1.34029i | 0.742231 | + | 0.670144i | \(0.233768\pi\) | ||||
−0.742231 | + | 0.670144i | \(0.766232\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.00933 | −0.158488 |
(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 | 3120.2.l.m.1249.1 | 6 | ||
4.3 | odd | 2 | 1560.2.l.c.1249.4 | yes | 6 | ||
5.4 | even | 2 | inner | 3120.2.l.m.1249.4 | 6 | ||
12.11 | even | 2 | 4680.2.l.e.2809.6 | 6 | |||
20.3 | even | 4 | 7800.2.a.bj.1.3 | 3 | |||
20.7 | even | 4 | 7800.2.a.bp.1.3 | 3 | |||
20.19 | odd | 2 | 1560.2.l.c.1249.1 | ✓ | 6 | ||
60.59 | even | 2 | 4680.2.l.e.2809.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.c.1249.1 | ✓ | 6 | 20.19 | odd | 2 | ||
1560.2.l.c.1249.4 | yes | 6 | 4.3 | odd | 2 | ||
3120.2.l.m.1249.1 | 6 | 1.1 | even | 1 | trivial | ||
3120.2.l.m.1249.4 | 6 | 5.4 | even | 2 | inner | ||
4680.2.l.e.2809.5 | 6 | 60.59 | even | 2 | |||
4680.2.l.e.2809.6 | 6 | 12.11 | even | 2 | |||
7800.2.a.bj.1.3 | 3 | 20.3 | even | 4 | |||
7800.2.a.bp.1.3 | 3 | 20.7 | even | 4 |