Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 7x^{6} + 40x^{5} - 11x^{4} - 53x^{3} - 2x^{2} + 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.92428\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.92428 | 1.11099 | 0.555493 | − | 0.831521i | \(-0.312530\pi\) | ||||
0.555493 | + | 0.831521i | \(0.312530\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.603023 | 0.269680 | 0.134840 | − | 0.990867i | \(-0.456948\pi\) | ||||
0.134840 | + | 0.990867i | \(0.456948\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00229 | −1.51272 | −0.756362 | − | 0.654153i | \(-0.773025\pi\) | ||||
−0.756362 | + | 0.654153i | \(0.773025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.702869 | 0.234290 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.54052 | 0.765996 | 0.382998 | − | 0.923749i | \(-0.374892\pi\) | ||||
0.382998 | + | 0.923749i | \(0.374892\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.384152 | 0.106545 | 0.0532723 | − | 0.998580i | \(-0.483035\pi\) | ||||
0.0532723 | + | 0.998580i | \(0.483035\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.16039 | 0.299611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.88169 | −1.18398 | −0.591992 | − | 0.805944i | \(-0.701658\pi\) | ||||
−0.591992 | + | 0.805944i | \(0.701658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.138707 | −0.0318217 | −0.0159108 | − | 0.999873i | \(-0.505065\pi\) | ||||
−0.0159108 | + | 0.999873i | \(0.505065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.70154 | −1.68061 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.63393 | 0.966241 | 0.483120 | − | 0.875554i | \(-0.339503\pi\) | ||||
0.483120 | + | 0.875554i | \(0.339503\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.63636 | −0.927273 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.42033 | −0.850693 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.641649 | 0.119151 | 0.0595756 | − | 0.998224i | \(-0.481025\pi\) | ||||
0.0595756 | + | 0.998224i | \(0.481025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.324579 | −0.0582961 | −0.0291481 | − | 0.999575i | \(-0.509279\pi\) | ||||
−0.0291481 | + | 0.999575i | \(0.509279\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.88868 | 0.851010 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.41347 | −0.407951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.71005 | 0.445530 | 0.222765 | − | 0.974872i | \(-0.428492\pi\) | ||||
0.222765 | + | 0.974872i | \(0.428492\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.739217 | 0.118369 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1014 | −1.73374 | −0.866871 | − | 0.498533i | \(-0.833872\pi\) | ||||
−0.866871 | + | 0.498533i | \(0.833872\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.21463 | −0.795223 | −0.397612 | − | 0.917554i | \(-0.630161\pi\) | ||||
−0.397612 | + | 0.917554i | \(0.630161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.423846 | 0.0631833 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.12420 | −0.309847 | −0.154924 | − | 0.987926i | \(-0.549513\pi\) | ||||
−0.154924 | + | 0.987926i | \(0.549513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.01833 | 1.28833 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.39376 | −1.31539 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.74340 | −0.514196 | −0.257098 | − | 0.966385i | \(-0.582766\pi\) | ||||
−0.257098 | + | 0.966385i | \(0.582766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.53199 | 0.206574 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.266912 | −0.0353534 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.32385 | −0.823295 | −0.411647 | − | 0.911343i | \(-0.635046\pi\) | ||||
−0.411647 | + | 0.911343i | \(0.635046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.81794 | −1.00098 | −0.500492 | − | 0.865741i | \(-0.666848\pi\) | ||||
−0.500492 | + | 0.865741i | \(0.666848\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.81309 | −0.354416 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.231652 | 0.0287329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.82671 | −0.467507 | −0.233754 | − | 0.972296i | \(-0.575101\pi\) | ||||
−0.233754 | + | 0.972296i | \(0.575101\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.91699 | 1.07348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.42635 | 1.00002 | 0.500012 | − | 0.866018i | \(-0.333329\pi\) | ||||
0.500012 | + | 0.866018i | \(0.333329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50056 | 0.175627 | 0.0878134 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878134 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.92168 | −1.03019 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.1679 | −1.15874 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50191 | 0.281487 | 0.140743 | − | 0.990046i | \(-0.455051\pi\) | ||||
0.140743 | + | 0.990046i | \(0.455051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6146 | −1.17940 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.03974 | 0.882476 | 0.441238 | − | 0.897390i | \(-0.354539\pi\) | ||||
0.441238 | + | 0.897390i | \(0.354539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.94377 | −0.319297 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.23471 | 0.132375 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.594707 | 0.0630388 | 0.0315194 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315194 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.53749 | −0.161172 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.624582 | −0.0647662 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0836438 | −0.00858167 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.4617 | −1.36683 | −0.683413 | − | 0.730032i | \(-0.739505\pi\) | ||||
−0.683413 | + | 0.730032i | \(0.739505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.78565 | 0.179465 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.55626 | −0.950883 | −0.475442 | − | 0.879747i | \(-0.657712\pi\) | ||||
−0.475442 | + | 0.879747i | \(0.657712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5809 | 1.14110 | 0.570551 | − | 0.821262i | \(-0.306730\pi\) | ||||
0.570551 | + | 0.821262i | \(0.306730\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.64421 | −0.453228 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.97570 | −0.287672 | −0.143836 | − | 0.989602i | \(-0.545944\pi\) | ||||
−0.143836 | + | 0.989602i | \(0.545944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.18142 | 0.687856 | 0.343928 | − | 0.938996i | \(-0.388242\pi\) | ||||
0.343928 | + | 0.938996i | \(0.388242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.21491 | 0.494978 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.66341 | −0.814985 | −0.407493 | − | 0.913208i | \(-0.633597\pi\) | ||||
−0.407493 | + | 0.913208i | \(0.633597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.79436 | 0.260576 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.270008 | 0.0249623 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.5379 | 1.79104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.54576 | −0.413251 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.3622 | −1.92616 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.81095 | −0.519747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4637 | 1.10597 | 0.552987 | − | 0.833190i | \(-0.313488\pi\) | ||||
0.552987 | + | 0.833190i | \(0.313488\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.0344 | −0.883482 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9630 | −1.30733 | −0.653664 | − | 0.756785i | \(-0.726769\pi\) | ||||
−0.653664 | + | 0.756785i | \(0.726769\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.555147 | 0.0481374 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.66556 | −0.229415 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.02618 | 0.429415 | 0.214708 | − | 0.976678i | \(-0.431120\pi\) | ||||
0.214708 | + | 0.976678i | \(0.431120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.397272 | −0.0336962 | −0.0168481 | − | 0.999858i | \(-0.505363\pi\) | ||||
−0.0168481 | + | 0.999858i | \(0.505363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.08757 | −0.344236 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.975945 | 0.0816126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.386929 | 0.0321327 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.3538 | 1.43132 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.7072 | −1.61448 | −0.807240 | − | 0.590223i | \(-0.799040\pi\) | ||||
−0.807240 | + | 0.590223i | \(0.799040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.35523 | −0.435803 | −0.217901 | − | 0.975971i | \(-0.569921\pi\) | ||||
−0.217901 | + | 0.975971i | \(0.569921\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.43119 | −0.277395 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.195729 | −0.0157213 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6285 | 0.928052 | 0.464026 | − | 0.885822i | \(-0.346404\pi\) | ||||
0.464026 | + | 0.885822i | \(0.346404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.20337 | −0.571264 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.5463 | −1.46166 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.5645 | −1.53241 | −0.766204 | − | 0.642598i | \(-0.777857\pi\) | ||||
−0.766204 | + | 0.642598i | \(0.777857\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.94799 | 0.229501 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.92604 | −0.226424 | −0.113212 | − | 0.993571i | \(-0.536114\pi\) | ||||
−0.113212 | + | 0.993571i | \(0.536114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8524 | −0.988648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0974932 | −0.00745549 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.1084 | −0.768530 | −0.384265 | − | 0.923223i | \(-0.625545\pi\) | ||||
−0.384265 | + | 0.923223i | \(0.625545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.5561 | 1.40271 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1689 | −0.914669 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7844 | 1.40401 | 0.702005 | − | 0.712172i | \(-0.252288\pi\) | ||||
0.702005 | + | 0.712172i | \(0.252288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.52007 | −0.707622 | −0.353811 | − | 0.935317i | \(-0.615114\pi\) | ||||
−0.353811 | + | 0.935317i | \(0.615114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.0439 | −1.11208 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.63422 | 0.120151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4020 | −0.906926 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.6915 | 1.28686 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.24590 | 0.162508 | 0.0812539 | − | 0.996693i | \(-0.474108\pi\) | ||||
0.0812539 | + | 0.996693i | \(0.474108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.34804 | −0.456942 | −0.228471 | − | 0.973551i | \(-0.573373\pi\) | ||||
−0.228471 | + | 0.973551i | \(0.573373\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.445765 | 0.0319219 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.8509 | −1.77055 | −0.885276 | − | 0.465066i | \(-0.846031\pi\) | ||||
−0.885276 | + | 0.465066i | \(0.846031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.89221 | 0.701240 | 0.350620 | − | 0.936518i | \(-0.385971\pi\) | ||||
0.350620 | + | 0.936518i | \(0.385971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.36368 | −0.519394 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.56806 | −0.180243 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.69438 | −0.467555 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.25705 | 0.226380 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.352389 | −0.0243753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.100613 | −0.00692647 | −0.00346324 | − | 0.999994i | \(-0.501102\pi\) | ||||
−0.00346324 | + | 0.999994i | \(0.501102\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.2147 | 1.11101 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.14454 | −0.214456 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.29906 | 0.0881859 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.88750 | 0.195119 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.87531 | −0.126147 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6921 | 1.58654 | 0.793271 | − | 0.608869i | \(-0.208377\pi\) | ||||
0.793271 | + | 0.608869i | \(0.208377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.25876 | −0.217251 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.76432 | 0.117102 | 0.0585510 | − | 0.998284i | \(-0.481352\pi\) | ||||
0.0585510 | + | 0.998284i | \(0.481352\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.79914 | 0.251054 | 0.125527 | − | 0.992090i | \(-0.459938\pi\) | ||||
0.125527 | + | 0.992090i | \(0.459938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.5659 | −1.28734 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.9492 | 0.782818 | 0.391409 | − | 0.920217i | \(-0.371988\pi\) | ||||
0.391409 | + | 0.920217i | \(0.371988\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.28094 | −0.0835596 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.81438 | 0.312728 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6752 | −0.884576 | −0.442288 | − | 0.896873i | \(-0.645833\pi\) | ||||
−0.442288 | + | 0.896873i | \(0.645833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.7093 | 1.59167 | 0.795834 | − | 0.605514i | \(-0.207033\pi\) | ||||
0.795834 | + | 0.605514i | \(0.207033\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.16448 | −0.459601 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.43826 | 0.347438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0532847 | −0.00339042 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4708 | 0.980419 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7726 | 0.740136 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.66465 | −0.354734 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3972 | 0.773315 | 0.386657 | − | 0.922223i | \(-0.373630\pi\) | ||||
0.386657 | + | 0.922223i | \(0.373630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8464 | −0.673964 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.450995 | 0.0279159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.9721 | −0.799894 | −0.399947 | − | 0.916538i | \(-0.630972\pi\) | ||||
−0.399947 | + | 0.916538i | \(0.630972\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.25736 | −0.138668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.14438 | 0.0700352 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.6698 | 1.62609 | 0.813043 | − | 0.582203i | \(-0.197809\pi\) | ||||
0.813043 | + | 0.582203i | \(0.197809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.57074 | −0.0954154 | −0.0477077 | − | 0.998861i | \(-0.515192\pi\) | ||||
−0.0477077 | + | 0.998861i | \(0.515192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.95856 | −0.179060 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.7788 | −0.710287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7004 | 0.883260 | 0.441630 | − | 0.897197i | \(-0.354400\pi\) | ||||
0.441630 | + | 0.897197i | \(0.354400\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.228137 | −0.0136582 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4238 | 0.920106 | 0.460053 | − | 0.887892i | \(-0.347830\pi\) | ||||
0.460053 | + | 0.887892i | \(0.347830\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7896 | 0.760264 | 0.380132 | − | 0.924932i | \(-0.375879\pi\) | ||||
0.380132 | + | 0.924932i | \(0.375879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.160954 | −0.00953411 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 44.4309 | 2.62267 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.83090 | 0.401818 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.9041 | −1.51852 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.5899 | −1.26130 | −0.630649 | − | 0.776068i | \(-0.717211\pi\) | ||||
−0.630649 | + | 0.776068i | \(0.717211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.81343 | −0.222026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.2299 | −0.651627 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.78013 | 0.102948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.8705 | 1.20295 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.3890 | −1.05642 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.71440 | −0.269946 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.4686 | 0.768691 | 0.384346 | − | 0.923189i | \(-0.374427\pi\) | ||||
0.384346 | + | 0.923189i | \(0.374427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.2850 | 1.26775 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.11970 | 0.347017 | 0.173508 | − | 0.984832i | \(-0.444490\pi\) | ||||
0.173508 | + | 0.984832i | \(0.444490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3759 | 0.699530 | 0.349765 | − | 0.936838i | \(-0.386261\pi\) | ||||
0.349765 | + | 0.936838i | \(0.386261\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.69636 | −0.0955789 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.0821 | 1.12792 | 0.563961 | − | 0.825801i | \(-0.309277\pi\) | ||||
0.563961 | + | 0.825801i | \(0.309277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.63012 | 0.0912693 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.72610 | −0.319600 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.677127 | 0.0376763 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.78107 | −0.0987958 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.8191 | 0.764198 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.50168 | 0.468713 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5147 | 0.577939 | 0.288969 | − | 0.957338i | \(-0.406687\pi\) | ||||
0.288969 | + | 0.957338i | \(0.406687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.90481 | 0.104383 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.30760 | −0.126077 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.08384 | −0.385881 | −0.192941 | − | 0.981210i | \(-0.561802\pi\) | ||||
−0.192941 | + | 0.981210i | \(0.561802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.6709 | −0.905437 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.824600 | −0.0446546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.07795 | −0.436168 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.37715 | 0.289496 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3433 | 0.931037 | 0.465519 | − | 0.885038i | \(-0.345868\pi\) | ||||
0.465519 | + | 0.885038i | \(0.345868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.16249 | 0.383399 | 0.191700 | − | 0.981454i | \(-0.438600\pi\) | ||||
0.191700 | + | 0.981454i | \(0.438600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.69808 | −0.0906367 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.5618 | 1.25407 | 0.627035 | − | 0.778991i | \(-0.284268\pi\) | ||||
0.627035 | + | 0.778991i | \(0.284268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08128 | 0.269687 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 37.5966 | 1.98982 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.5104 | −1.66306 | −0.831529 | − | 0.555482i | \(-0.812534\pi\) | ||||
−0.831529 | + | 0.555482i | \(0.812534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9808 | −0.998987 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.74733 | −0.459116 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.904870 | 0.0473631 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.1270 | −1.25942 | −0.629709 | − | 0.776832i | \(-0.716826\pi\) | ||||
−0.629709 | + | 0.776832i | \(0.716826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.80281 | −0.406198 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.9822 | 0.777836 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1427 | 0.732279 | 0.366139 | − | 0.930560i | \(-0.380679\pi\) | ||||
0.366139 | + | 0.930560i | \(0.380679\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1819 | −0.577432 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.246490 | 0.0126949 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.30457 | 0.323844 | 0.161922 | − | 0.986804i | \(-0.448231\pi\) | ||||
0.161922 | + | 0.986804i | \(0.448231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.9837 | 1.22872 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.400889 | −0.0204845 | −0.0102422 | − | 0.999948i | \(-0.503260\pi\) | ||||
−0.0102422 | + | 0.999948i | \(0.503260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.13148 | −0.312489 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.66520 | −0.186313 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.00381 | −0.203001 | −0.101501 | − | 0.994835i | \(-0.532364\pi\) | ||||
−0.101501 | + | 0.994835i | \(0.532364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.6214 | −1.14401 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.7931 | −1.45242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.50871 | 0.0759114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.0004 | −1.25473 | −0.627367 | − | 0.778723i | \(-0.715868\pi\) | ||||
−0.627367 | + | 0.778723i | \(0.715868\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.06826 | 0.0534800 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.2154 | −0.909633 | −0.454817 | − | 0.890585i | \(-0.650295\pi\) | ||||
−0.454817 | + | 0.890585i | \(0.650295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.124688 | −0.00621113 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.40084 | −0.318060 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.88495 | 0.341274 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.53089 | −0.125145 | −0.0625723 | − | 0.998040i | \(-0.519930\pi\) | ||||
−0.0625723 | + | 0.998040i | \(0.519930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.67179 | 0.477074 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.3099 | 1.24542 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.84815 | 0.237986 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.764464 | −0.0374360 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.36690 | 0.262190 | 0.131095 | − | 0.991370i | \(-0.458151\pi\) | ||||
0.131095 | + | 0.991370i | \(0.458151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0409 | −1.22042 | −0.610210 | − | 0.792239i | \(-0.708915\pi\) | ||||
−0.610210 | + | 0.792239i | \(0.708915\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.49304 | −0.0725940 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.6333 | 1.09788 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.2897 | 1.51421 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.87800 | 0.0906705 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.67102 | −0.321332 | −0.160666 | − | 0.987009i | \(-0.551364\pi\) | ||||
−0.160666 | + | 0.987009i | \(0.551364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.97305 | −0.383160 | −0.191580 | − | 0.981477i | \(-0.561361\pi\) | ||||
−0.191580 | + | 0.981477i | \(0.561361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.744561 | 0.0356990 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.642760 | −0.0307474 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.8390 | −0.612773 | −0.306386 | − | 0.951907i | \(-0.599120\pi\) | ||||
−0.306386 | + | 0.951907i | \(0.599120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.33871 | 0.301843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.709218 | 0.0336960 | 0.0168480 | − | 0.999858i | \(-0.494637\pi\) | ||||
0.0168480 | + | 0.999858i | \(0.494637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.358622 | 0.0170003 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.9223 | −1.79366 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.5427 | 0.686311 | 0.343155 | − | 0.939279i | \(-0.388504\pi\) | ||||
0.343155 | + | 0.939279i | \(0.388504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.2032 | −1.32804 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.3050 | −0.484171 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.927140 | −0.0434650 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.4798 | 0.864447 | 0.432224 | − | 0.901766i | \(-0.357729\pi\) | ||||
0.432224 | + | 0.901766i | \(0.357729\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.5787 | 1.00721 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.7455 | 1.05936 | 0.529681 | − | 0.848197i | \(-0.322312\pi\) | ||||
0.529681 | + | 0.848197i | \(0.322312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9449 | −0.880442 | −0.440221 | − | 0.897889i | \(-0.645100\pi\) | ||||
−0.440221 | + | 0.897889i | \(0.645100\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.376637 | −0.0174661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.26958 | 0.151298 | 0.0756491 | − | 0.997135i | \(-0.475897\pi\) | ||||
0.0756491 | + | 0.997135i | \(0.475897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.3156 | 0.707209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.3765 | 1.03105 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.2479 | −0.609138 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.643098 | 0.0295074 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.63112 | −0.120471 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.59467 | 0.301318 | 0.150659 | − | 0.988586i | \(-0.451860\pi\) | ||||
0.150659 | + | 0.988586i | \(0.451860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04107 | 0.0474688 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −35.6884 | −1.62388 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.11770 | −0.368606 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.9971 | 1.76713 | 0.883563 | − | 0.468311i | \(-0.155137\pi\) | ||||
0.883563 | + | 0.468311i | \(0.155137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −37.6476 | −1.70248 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2203 | −0.506364 | −0.253182 | − | 0.967419i | \(-0.581477\pi\) | ||||
−0.253182 | + | 0.967419i | \(0.581477\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.13233 | −0.141073 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.07679 | 0.0483981 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −33.7247 | −1.51276 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5343 | −0.829711 | −0.414855 | − | 0.909887i | \(-0.636168\pi\) | ||||
−0.414855 | + | 0.909887i | \(0.636168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.63053 | −0.251554 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.8410 | 0.661729 | 0.330864 | − | 0.943678i | \(-0.392660\pi\) | ||||
0.330864 | + | 0.943678i | \(0.392660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.76264 | −0.256434 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.7317 | −1.09837 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.7025 | 0.518703 | 0.259351 | − | 0.965783i | \(-0.416491\pi\) | ||||
0.259351 | + | 0.965783i | \(0.416491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00566 | −0.265675 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.613133 | 0.0270705 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.98356 | 0.307732 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.39658 | −0.237341 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.4515 | −0.853827 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0091 | 1.05186 | 0.525929 | − | 0.850528i | \(-0.323718\pi\) | ||||
0.525929 | + | 0.850528i | \(0.323718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.0865 | −1.14068 | −0.570341 | − | 0.821408i | \(-0.693189\pi\) | ||||
−0.570341 | + | 0.821408i | \(0.693189\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 35.7072 | 1.55839 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.58449 | 0.0690217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.52672 | −0.0663791 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.44484 | −0.192890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.26461 | −0.184721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.79442 | −0.0775795 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.1465 | 1.55984 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.9112 | 0.986857 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.30995 | 0.314279 | 0.157140 | − | 0.987576i | \(-0.449773\pi\) | ||||
0.157140 | + | 0.987576i | \(0.449773\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.3193 | −0.786158 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.33056 | 0.185501 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.8261 | 1.27527 | 0.637637 | − | 0.770337i | \(-0.279912\pi\) | ||||
0.637637 | + | 0.770337i | \(0.279912\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.49499 | −0.234520 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0890014 | −0.00379159 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0134 | −0.425812 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.14471 | 0.133486 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8225 | −0.543307 | −0.271654 | − | 0.962395i | \(-0.587571\pi\) | ||||
−0.271654 | + | 0.962395i | \(0.587571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00321 | −0.0847267 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.8650 | −1.00758 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.29127 | 0.180856 | 0.0904278 | − | 0.995903i | \(-0.471177\pi\) | ||||
0.0904278 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.22424 | −0.219785 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.4826 | 1.78410 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.3876 | −1.60929 | −0.804646 | − | 0.593754i | \(-0.797645\pi\) | ||||
−0.804646 | + | 0.593754i | \(0.797645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.9056 | −1.58630 | −0.793149 | − | 0.609027i | \(-0.791560\pi\) | ||||
−0.793149 | + | 0.609027i | \(0.791560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.32176 | 0.180544 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.4846 | −0.895968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0575 | −0.710114 | −0.355057 | − | 0.934845i | \(-0.615539\pi\) | ||||
−0.355057 | + | 0.934845i | \(0.615539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.2154 | −0.507656 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.1774 | −1.33494 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.51018 | −0.393871 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.162821 | 0.00673183 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0440 | 0.909853 | 0.454926 | − | 0.890529i | \(-0.349666\pi\) | ||||
0.454926 | + | 0.890529i | \(0.349666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0450215 | 0.00185508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.8202 | −1.96706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4614 | 0.840250 | 0.420125 | − | 0.907466i | \(-0.361986\pi\) | ||||
0.420125 | + | 0.907466i | \(0.361986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.7818 | 0.483008 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.0354 | 0.779068 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.39979 | −0.179771 | −0.0898853 | − | 0.995952i | \(-0.528650\pi\) | ||||
−0.0898853 | + | 0.995952i | \(0.528650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7704 | 0.765660 | 0.382830 | − | 0.923819i | \(-0.374949\pi\) | ||||
0.382830 | + | 0.923819i | \(0.374949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.68968 | −0.109532 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.74120 | −0.111445 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.7247 | 1.00355 | 0.501773 | − | 0.865000i | \(-0.332681\pi\) | ||||
0.501773 | + | 0.865000i | \(0.332681\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.94169 | −0.200247 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.816017 | −0.0330125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2935 | −0.577311 | −0.288655 | − | 0.957433i | \(-0.593208\pi\) | ||||
−0.288655 | + | 0.957433i | \(0.593208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.8819 | −0.519448 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.8902 | −0.921525 | −0.460763 | − | 0.887523i | \(-0.652424\pi\) | ||||
−0.460763 | + | 0.887523i | \(0.652424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.7725 | −0.794724 | −0.397362 | − | 0.917662i | \(-0.630074\pi\) | ||||
−0.397362 | + | 0.917662i | \(0.630074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.4835 | −0.821974 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.38019 | −0.0953602 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6777 | 0.787107 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.678097 | −0.0270806 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.2296 | −0.527501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9778 | −1.39245 | −0.696223 | − | 0.717826i | \(-0.745138\pi\) | ||||
−0.696223 | + | 0.717826i | \(0.745138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.193608 | −0.00769522 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.51589 | 0.298259 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.46441 | 0.137265 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.92263 | 0.234296 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.1557 | −1.15158 | −0.575790 | − | 0.817597i | \(-0.695306\pi\) | ||||
−0.575790 | + | 0.817597i | \(0.695306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0858 | −0.555491 | −0.277745 | − | 0.960655i | \(-0.589587\pi\) | ||||
−0.277745 | + | 0.960655i | \(0.589587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.05099 | −0.238257 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.6674 | 0.498008 | 0.249004 | − | 0.968502i | \(-0.419897\pi\) | ||||
0.249004 | + | 0.968502i | \(0.419897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0659 | −0.630640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.49976 | 0.0979733 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.42639 | 0.173218 | 0.0866090 | − | 0.996242i | \(-0.472397\pi\) | ||||
0.0866090 | + | 0.996242i | \(0.472397\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.02306 | −0.352560 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.05470 | 0.0411476 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.4817 | 0.486218 | 0.243109 | − | 0.969999i | \(-0.421833\pi\) | ||||
0.243109 | + | 0.969999i | \(0.421833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7710 | 0.807899 | 0.403950 | − | 0.914781i | \(-0.367637\pi\) | ||||
0.403950 | + | 0.914781i | \(0.367637\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.60863 | −0.140148 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.334767 | 0.0129817 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.97335 | 0.115129 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.5904 | 1.76263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.8616 | −0.766750 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.9497 | 1.92542 | 0.962709 | − | 0.270538i | \(-0.0872015\pi\) | ||||
0.962709 | + | 0.270538i | \(0.0872015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.4943 | 0.788825 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.2022 | 1.58353 | 0.791765 | − | 0.610826i | \(-0.209162\pi\) | ||||
0.791765 | + | 0.610826i | \(0.209162\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.8775 | 2.06763 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.39505 | 0.130099 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.2590 | −0.392551 | −0.196275 | − | 0.980549i | \(-0.562885\pi\) | ||||
−0.196275 | + | 0.980549i | \(0.562885\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.03090 | 0.115805 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.31063 | 0.278918 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.43803 | −0.0547847 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.59351 | −0.288871 | −0.144435 | − | 0.989514i | \(-0.546137\pi\) | ||||
−0.144435 | + | 0.989514i | \(0.546137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.14671 | −0.271481 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.239564 | −0.00908718 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.1934 | 2.05272 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.9937 | 0.869700 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.2324 | −1.29294 | −0.646470 | − | 0.762939i | \(-0.723755\pi\) | ||||
−0.646470 | + | 0.762939i | \(0.723755\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.375905 | −0.0141775 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.46490 | −0.0928335 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.2469 | 1.43842 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8905 | 1.42301 | 0.711504 | − | 0.702682i | \(-0.248014\pi\) | ||||
0.711504 | + | 0.702682i | \(0.248014\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.75852 | 0.0659495 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.50408 | −0.0563281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.588517 | 0.0220093 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.3150 | −0.982752 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.35548 | −0.0505510 | −0.0252755 | − | 0.999681i | \(-0.508046\pi\) | ||||
−0.0252755 | + | 0.999681i | \(0.508046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.3502 | −1.72617 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.5478 | 1.76832 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.97492 | −0.110486 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.7958 | 1.73556 | 0.867779 | − | 0.496950i | \(-0.165547\pi\) | ||||
0.867779 | + | 0.496950i | \(0.165547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.0573 | 0.668787 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4562 | 0.941532 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.8275 | −0.584601 | −0.292300 | − | 0.956327i | \(-0.594421\pi\) | ||||
−0.292300 | + | 0.956327i | \(0.594421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.4648 | 0.385998 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.72184 | −0.358109 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.13274 | 0.188811 | 0.0944055 | − | 0.995534i | \(-0.469905\pi\) | ||||
0.0944055 | + | 0.995534i | \(0.469905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.102535 | −0.00376671 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.0053 | 1.21085 | 0.605424 | − | 0.795903i | \(-0.293003\pi\) | ||||
0.605424 | + | 0.795903i | \(0.293003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8839 | −0.435393 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.65089 | 0.206755 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.9096 | 0.435169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.5433 | −1.44296 | −0.721478 | − | 0.692437i | \(-0.756537\pi\) | ||||
−0.721478 | + | 0.692437i | \(0.756537\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.92428 | −0.0701248 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.22933 | −0.117527 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.0059 | −1.45404 | −0.727020 | − | 0.686617i | \(-0.759095\pi\) | ||||
−0.727020 | + | 0.686617i | \(0.759095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.6538 | 0.822281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.2889 | 0.699223 | 0.349611 | − | 0.936895i | \(-0.386314\pi\) | ||||
0.349611 | + | 0.936895i | \(0.386314\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.7421 | −1.04054 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.06909 | −0.0748080 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.42932 | −0.0877175 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.4700 | −0.557863 | −0.278931 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278931 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8557 | 0.859142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.6819 | 0.995648 | 0.497824 | − | 0.867278i | \(-0.334132\pi\) | ||||
0.497824 | + | 0.867278i | \(0.334132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50487 | 0.0540564 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.8716 | −0.748765 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.53984 | 0.0551705 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.4073 | 0.766014 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.83630 | −0.101361 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.01223 | 0.250277 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3519 | 0.582884 | 0.291442 | − | 0.956589i | \(-0.405865\pi\) | ||||
0.291442 | + | 0.956589i | \(0.405865\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.9620 | −0.888671 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.6735 | 1.23285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.00327 | −0.106649 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.34379 | −0.154059 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.4634 | 1.82293 | 0.911464 | − | 0.411380i | \(-0.134953\pi\) | ||||
0.911464 | + | 0.411380i | \(0.134953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.3697 | 0.366854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.418001 | 0.0147693 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.81219 | 0.134529 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1839 | −0.394179 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 51.3203 | 1.80656 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.1922 | −1.23729 | −0.618646 | − | 0.785670i | \(-0.712319\pi\) | ||||
−0.618646 | + | 0.785670i | \(0.712319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.0417 | −1.37094 | −0.685469 | − | 0.728102i | \(-0.740403\pi\) | ||||
−0.685469 | + | 0.728102i | \(0.740403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.02254 | −0.106005 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.7978 | −0.413260 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.723308 | 0.0253053 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.08065 | −0.0377611 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.5854 | −1.03254 | −0.516268 | − | 0.856427i | \(-0.672679\pi\) | ||||
−0.516268 | + | 0.856427i | \(0.672679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.1629 | −1.36513 | −0.682566 | − | 0.730824i | \(-0.739136\pi\) | ||||
−0.682566 | + | 0.730824i | \(0.739136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.6657 | −0.789119 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.0268 | −1.28755 | −0.643774 | − | 0.765216i | \(-0.722632\pi\) | ||||
−0.643774 | + | 0.765216i | \(0.722632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.3337 | 1.43558 | 0.717789 | − | 0.696261i | \(-0.245154\pi\) | ||||
0.717789 | + | 0.696261i | \(0.245154\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.2877 | 0.981290 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.0247 | −1.52537 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.76447 | −0.0610620 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.43475 | 0.0495921 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.8761 | 0.686200 | 0.343100 | − | 0.939299i | \(-0.388523\pi\) | ||||
0.343100 | + | 0.939299i | \(0.388523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5883 | −0.985803 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.6797 | 1.02222 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.75031 | −0.266619 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.1934 | 0.625134 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.6109 | 0.844643 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.5582 | 0.430489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4716 | 0.700933 | 0.350466 | − | 0.936575i | \(-0.386023\pi\) | ||||
0.350466 | + | 0.936575i | \(0.386023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0587906 | −0.00201060 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.0871 | −1.09607 | −0.548037 | − | 0.836454i | \(-0.684625\pi\) | ||||
−0.548037 | + | 0.836454i | \(0.684625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.9196 | −1.22556 | −0.612781 | − | 0.790253i | \(-0.709949\pi\) | ||||
−0.612781 | + | 0.790253i | \(0.709949\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 85.4976 | 2.91375 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.6033 | −1.14387 | −0.571934 | − | 0.820300i | \(-0.693807\pi\) | ||||
−0.571934 | + | 0.820300i | \(0.693807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.09562 | −0.207257 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.1446 | 0.446414 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.35615 | 0.215618 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.47004 | −0.0498103 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.46180 | −0.320233 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.2571 | 0.786234 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.927087 | 0.0313055 | 0.0156528 | − | 0.999877i | \(-0.495017\pi\) | ||||
0.0156528 | + | 0.999877i | \(0.495017\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.5452 | −1.40128 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.3087 | 1.49280 | 0.746400 | − | 0.665498i | \(-0.231781\pi\) | ||||
0.746400 | + | 0.665498i | \(0.231781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0593 | 0.809661 | 0.404831 | − | 0.914392i | \(-0.367330\pi\) | ||||
0.404831 | + | 0.914392i | \(0.367330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.33811 | −0.246668 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.3116 | −0.681997 | −0.340998 | − | 0.940064i | \(-0.610765\pi\) | ||||
−0.340998 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49.8833 | −1.67303 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9666 | −0.903414 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.294643 | 0.00985985 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3274 | 0.378634 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.42548 | 0.114373 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.208266 | −0.00694605 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.2741 | 0.608799 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.1607 | 1.33646 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.74082 | −0.190831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.0040 | 1.26190 | 0.630951 | − | 0.775822i | \(-0.282665\pi\) | ||||
0.630951 | + | 0.775822i | \(0.282665\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.71680 | −0.222782 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.9105 | 0.725929 | 0.362964 | − | 0.931803i | \(-0.381765\pi\) | ||||
0.362964 | + | 0.931803i | \(0.381765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.4251 | 0.675973 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.07184 | −0.299906 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.8865 | 1.97762 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.3579 | −0.374661 | −0.187330 | − | 0.982297i | \(-0.559984\pi\) | ||||
−0.187330 | + | 0.982297i | \(0.559984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.9173 | 0.854005 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.23700 | 0.106547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.5648 | −0.413128 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.13987 | 0.267348 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.3826 | 1.25929 | 0.629646 | − | 0.776882i | \(-0.283200\pi\) | ||||
0.629646 | + | 0.776882i | \(0.283200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.25091 | −0.0409969 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.7760 | 0.385531 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.47871 | −0.244580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.5093 | −1.29071 | −0.645356 | − | 0.763882i | \(-0.723291\pi\) | ||||
−0.645356 | + | 0.763882i | \(0.723291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.8148 | 0.777168 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6166 | 0.932874 | 0.466437 | − | 0.884554i | \(-0.345537\pi\) | ||||
0.466437 | + | 0.884554i | \(0.345537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51.4429 | −1.67521 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.6684 | 0.347041 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.6198 | 0.540071 | 0.270035 | − | 0.962850i | \(-0.412965\pi\) | ||||
0.270035 | + | 0.962850i | \(0.412965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.576441 | 0.0187121 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.6436 | 1.25311 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.9975 | 1.78154 | 0.890772 | − | 0.454450i | \(-0.150164\pi\) | ||||
0.890772 | + | 0.454450i | \(0.150164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.35433 | 0.0438251 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.13682 | 0.101399 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.1162 | −0.649587 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8946 | −0.996602 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.09153 | −0.0673987 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.82801 | −0.123228 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.3308 | −0.493005 | −0.246503 | − | 0.969142i | \(-0.579281\pi\) | ||||
−0.246503 | + | 0.969142i | \(0.579281\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.30298 | 0.0418579 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5706 | −0.628049 | −0.314024 | − | 0.949415i | \(-0.601677\pi\) | ||||
−0.314024 | + | 0.949415i | \(0.601677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.59000 | 0.0509730 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.42728 | −0.109761 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.5920 | −1.39463 | −0.697316 | − | 0.716764i | \(-0.745622\pi\) | ||||
−0.697316 | + | 0.716764i | \(0.745622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.51086 | 0.0482874 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.04760 | 0.161158 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.4342 | 0.683644 | 0.341822 | − | 0.939765i | \(-0.388956\pi\) | ||||
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.9857 | −0.477483 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.3597 | 0.520733 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.1642 | −0.768377 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.8476 | 1.58346 | 0.791730 | − | 0.610871i | \(-0.209181\pi\) | ||||
0.791730 | + | 0.610871i | \(0.209181\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.2332 | 0.642082 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.96523 | 0.189111 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.58701 | 0.145272 | 0.0726361 | − | 0.997359i | \(-0.476859\pi\) | ||||
0.0726361 | + | 0.997359i | \(0.476859\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.9793 | −0.379010 |
(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 | 4016.2.a.h.1.8 | 9 | ||
4.3 | odd | 2 | 2008.2.a.a.1.2 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.a.1.2 | ✓ | 9 | 4.3 | odd | 2 | ||
4016.2.a.h.1.8 | 9 | 1.1 | even | 1 | trivial |