Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.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: | \(18.8926051182\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.69202 | 0.976889 | 0.488445 | − | 0.872595i | \(-0.337564\pi\) | ||||
0.488445 | + | 0.872595i | \(0.337564\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.55496 | −1.14261 | −0.571306 | − | 0.820737i | \(-0.693563\pi\) | ||||
−0.571306 | + | 0.820737i | \(0.693563\pi\) | |||||||
\(6\) | 1.69202 | 0.690765 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.137063 | −0.0456878 | ||||||||
\(10\) | −2.55496 | −0.807949 | ||||||||
\(11\) | −1.64310 | −0.495415 | −0.247707 | − | 0.968835i | \(-0.579677\pi\) | ||||
−0.247707 | + | 0.968835i | \(0.579677\pi\) | |||||||
\(12\) | 1.69202 | 0.488445 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −4.32304 | −1.11621 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.34481 | −1.05377 | −0.526886 | − | 0.849936i | \(-0.676641\pi\) | ||||
−0.526886 | + | 0.849936i | \(0.676641\pi\) | |||||||
\(18\) | −0.137063 | −0.0323061 | ||||||||
\(19\) | −1.08815 | −0.249638 | −0.124819 | − | 0.992180i | \(-0.539835\pi\) | ||||
−0.124819 | + | 0.992180i | \(0.539835\pi\) | |||||||
\(20\) | −2.55496 | −0.571306 | ||||||||
\(21\) | −1.69202 | −0.369229 | ||||||||
\(22\) | −1.64310 | −0.350311 | ||||||||
\(23\) | −2.04892 | −0.427229 | −0.213614 | − | 0.976918i | \(-0.568524\pi\) | ||||
−0.213614 | + | 0.976918i | \(0.568524\pi\) | |||||||
\(24\) | 1.69202 | 0.345382 | ||||||||
\(25\) | 1.52781 | 0.305562 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.30798 | −1.02152 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 10.3666 | 1.92503 | 0.962513 | − | 0.271235i | \(-0.0874320\pi\) | ||||
0.962513 | + | 0.271235i | \(0.0874320\pi\) | |||||||
\(30\) | −4.32304 | −0.789276 | ||||||||
\(31\) | −11.0489 | −1.98444 | −0.992222 | − | 0.124480i | \(-0.960274\pi\) | ||||
−0.992222 | + | 0.124480i | \(0.960274\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.78017 | −0.483965 | ||||||||
\(34\) | −4.34481 | −0.745130 | ||||||||
\(35\) | 2.55496 | 0.431867 | ||||||||
\(36\) | −0.137063 | −0.0228439 | ||||||||
\(37\) | −1.26875 | −0.208581 | −0.104291 | − | 0.994547i | \(-0.533257\pi\) | ||||
−0.104291 | + | 0.994547i | \(0.533257\pi\) | |||||||
\(38\) | −1.08815 | −0.176521 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.55496 | −0.403974 | ||||||||
\(41\) | −4.76271 | −0.743810 | −0.371905 | − | 0.928271i | \(-0.621295\pi\) | ||||
−0.371905 | + | 0.928271i | \(0.621295\pi\) | |||||||
\(42\) | −1.69202 | −0.261085 | ||||||||
\(43\) | −1.30798 | −0.199465 | −0.0997324 | − | 0.995014i | \(-0.531799\pi\) | ||||
−0.0997324 | + | 0.995014i | \(0.531799\pi\) | |||||||
\(44\) | −1.64310 | −0.247707 | ||||||||
\(45\) | 0.350191 | 0.0522034 | ||||||||
\(46\) | −2.04892 | −0.302096 | ||||||||
\(47\) | −7.24698 | −1.05708 | −0.528540 | − | 0.848908i | \(-0.677260\pi\) | ||||
−0.528540 | + | 0.848908i | \(0.677260\pi\) | |||||||
\(48\) | 1.69202 | 0.244222 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.52781 | 0.216065 | ||||||||
\(51\) | −7.35152 | −1.02942 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.29590 | 0.178005 | 0.0890026 | − | 0.996031i | \(-0.471632\pi\) | ||||
0.0890026 | + | 0.996031i | \(0.471632\pi\) | |||||||
\(54\) | −5.30798 | −0.722324 | ||||||||
\(55\) | 4.19806 | 0.566067 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.84117 | −0.243868 | ||||||||
\(58\) | 10.3666 | 1.36120 | ||||||||
\(59\) | 8.45473 | 1.10071 | 0.550356 | − | 0.834930i | \(-0.314492\pi\) | ||||
0.550356 | + | 0.834930i | \(0.314492\pi\) | |||||||
\(60\) | −4.32304 | −0.558103 | ||||||||
\(61\) | 3.52111 | 0.450831 | 0.225416 | − | 0.974263i | \(-0.427626\pi\) | ||||
0.225416 | + | 0.974263i | \(0.427626\pi\) | |||||||
\(62\) | −11.0489 | −1.40321 | ||||||||
\(63\) | 0.137063 | 0.0172684 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.78017 | −0.342215 | ||||||||
\(67\) | −6.57002 | −0.802656 | −0.401328 | − | 0.915934i | \(-0.631451\pi\) | ||||
−0.401328 | + | 0.915934i | \(0.631451\pi\) | |||||||
\(68\) | −4.34481 | −0.526886 | ||||||||
\(69\) | −3.46681 | −0.417355 | ||||||||
\(70\) | 2.55496 | 0.305376 | ||||||||
\(71\) | −15.4547 | −1.83414 | −0.917070 | − | 0.398727i | \(-0.869452\pi\) | ||||
−0.917070 | + | 0.398727i | \(0.869452\pi\) | |||||||
\(72\) | −0.137063 | −0.0161531 | ||||||||
\(73\) | −5.18598 | −0.606973 | −0.303487 | − | 0.952836i | \(-0.598151\pi\) | ||||
−0.303487 | + | 0.952836i | \(0.598151\pi\) | |||||||
\(74\) | −1.26875 | −0.147489 | ||||||||
\(75\) | 2.58509 | 0.298500 | ||||||||
\(76\) | −1.08815 | −0.124819 | ||||||||
\(77\) | 1.64310 | 0.187249 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2295 | 1.15091 | 0.575456 | − | 0.817833i | \(-0.304825\pi\) | ||||
0.575456 | + | 0.817833i | \(0.304825\pi\) | |||||||
\(80\) | −2.55496 | −0.285653 | ||||||||
\(81\) | −8.57002 | −0.952225 | ||||||||
\(82\) | −4.76271 | −0.525953 | ||||||||
\(83\) | 13.9705 | 1.53346 | 0.766729 | − | 0.641971i | \(-0.221883\pi\) | ||||
0.766729 | + | 0.641971i | \(0.221883\pi\) | |||||||
\(84\) | −1.69202 | −0.184615 | ||||||||
\(85\) | 11.1008 | 1.20405 | ||||||||
\(86\) | −1.30798 | −0.141043 | ||||||||
\(87\) | 17.5405 | 1.88054 | ||||||||
\(88\) | −1.64310 | −0.175155 | ||||||||
\(89\) | −3.93900 | −0.417533 | −0.208767 | − | 0.977965i | \(-0.566945\pi\) | ||||
−0.208767 | + | 0.977965i | \(0.566945\pi\) | |||||||
\(90\) | 0.350191 | 0.0369134 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.04892 | −0.213614 | ||||||||
\(93\) | −18.6950 | −1.93858 | ||||||||
\(94\) | −7.24698 | −0.747469 | ||||||||
\(95\) | 2.78017 | 0.285239 | ||||||||
\(96\) | 1.69202 | 0.172691 | ||||||||
\(97\) | 12.0489 | 1.22338 | 0.611691 | − | 0.791097i | \(-0.290490\pi\) | ||||
0.611691 | + | 0.791097i | \(0.290490\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0.225209 | 0.0226344 | ||||||||
\(100\) | 1.52781 | 0.152781 | ||||||||
\(101\) | −1.54288 | −0.153522 | −0.0767610 | − | 0.997050i | \(-0.524458\pi\) | ||||
−0.0767610 | + | 0.997050i | \(0.524458\pi\) | |||||||
\(102\) | −7.35152 | −0.727909 | ||||||||
\(103\) | −2.63773 | −0.259903 | −0.129951 | − | 0.991520i | \(-0.541482\pi\) | ||||
−0.129951 | + | 0.991520i | \(0.541482\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.32304 | 0.421886 | ||||||||
\(106\) | 1.29590 | 0.125869 | ||||||||
\(107\) | 10.1564 | 0.981860 | 0.490930 | − | 0.871199i | \(-0.336657\pi\) | ||||
0.490930 | + | 0.871199i | \(0.336657\pi\) | |||||||
\(108\) | −5.30798 | −0.510760 | ||||||||
\(109\) | −13.2567 | −1.26976 | −0.634879 | − | 0.772611i | \(-0.718950\pi\) | ||||
−0.634879 | + | 0.772611i | \(0.718950\pi\) | |||||||
\(110\) | 4.19806 | 0.400270 | ||||||||
\(111\) | −2.14675 | −0.203761 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −9.86054 | −0.927602 | −0.463801 | − | 0.885939i | \(-0.653515\pi\) | ||||
−0.463801 | + | 0.885939i | \(0.653515\pi\) | |||||||
\(114\) | −1.84117 | −0.172441 | ||||||||
\(115\) | 5.23490 | 0.488157 | ||||||||
\(116\) | 10.3666 | 0.962513 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.45473 | 0.778321 | ||||||||
\(119\) | 4.34481 | 0.398288 | ||||||||
\(120\) | −4.32304 | −0.394638 | ||||||||
\(121\) | −8.30021 | −0.754564 | ||||||||
\(122\) | 3.52111 | 0.318786 | ||||||||
\(123\) | −8.05861 | −0.726620 | ||||||||
\(124\) | −11.0489 | −0.992222 | ||||||||
\(125\) | 8.87130 | 0.793473 | ||||||||
\(126\) | 0.137063 | 0.0122106 | ||||||||
\(127\) | −16.7114 | −1.48290 | −0.741448 | − | 0.671010i | \(-0.765861\pi\) | ||||
−0.741448 | + | 0.671010i | \(0.765861\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.21313 | −0.194855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.85086 | −0.511192 | −0.255596 | − | 0.966784i | \(-0.582272\pi\) | ||||
−0.255596 | + | 0.966784i | \(0.582272\pi\) | |||||||
\(132\) | −2.78017 | −0.241983 | ||||||||
\(133\) | 1.08815 | 0.0943542 | ||||||||
\(134\) | −6.57002 | −0.567564 | ||||||||
\(135\) | 13.5617 | 1.16720 | ||||||||
\(136\) | −4.34481 | −0.372565 | ||||||||
\(137\) | 20.7995 | 1.77703 | 0.888513 | − | 0.458852i | \(-0.151739\pi\) | ||||
0.888513 | + | 0.458852i | \(0.151739\pi\) | |||||||
\(138\) | −3.46681 | −0.295115 | ||||||||
\(139\) | 4.79225 | 0.406473 | 0.203237 | − | 0.979130i | \(-0.434854\pi\) | ||||
0.203237 | + | 0.979130i | \(0.434854\pi\) | |||||||
\(140\) | 2.55496 | 0.215933 | ||||||||
\(141\) | −12.2620 | −1.03265 | ||||||||
\(142\) | −15.4547 | −1.29693 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.137063 | −0.0114219 | ||||||||
\(145\) | −26.4862 | −2.19956 | ||||||||
\(146\) | −5.18598 | −0.429195 | ||||||||
\(147\) | 1.69202 | 0.139556 | ||||||||
\(148\) | −1.26875 | −0.104291 | ||||||||
\(149\) | 15.3448 | 1.25710 | 0.628548 | − | 0.777771i | \(-0.283650\pi\) | ||||
0.628548 | + | 0.777771i | \(0.283650\pi\) | |||||||
\(150\) | 2.58509 | 0.211072 | ||||||||
\(151\) | 0.521106 | 0.0424070 | 0.0212035 | − | 0.999775i | \(-0.493250\pi\) | ||||
0.0212035 | + | 0.999775i | \(0.493250\pi\) | |||||||
\(152\) | −1.08815 | −0.0882603 | ||||||||
\(153\) | 0.595515 | 0.0481445 | ||||||||
\(154\) | 1.64310 | 0.132405 | ||||||||
\(155\) | 28.2295 | 2.26745 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.0911 | −1.84287 | −0.921436 | − | 0.388529i | \(-0.872983\pi\) | ||||
−0.921436 | + | 0.388529i | \(0.872983\pi\) | |||||||
\(158\) | 10.2295 | 0.813817 | ||||||||
\(159\) | 2.19269 | 0.173891 | ||||||||
\(160\) | −2.55496 | −0.201987 | ||||||||
\(161\) | 2.04892 | 0.161477 | ||||||||
\(162\) | −8.57002 | −0.673325 | ||||||||
\(163\) | 22.9028 | 1.79388 | 0.896941 | − | 0.442150i | \(-0.145784\pi\) | ||||
0.896941 | + | 0.442150i | \(0.145784\pi\) | |||||||
\(164\) | −4.76271 | −0.371905 | ||||||||
\(165\) | 7.10321 | 0.552984 | ||||||||
\(166\) | 13.9705 | 1.08432 | ||||||||
\(167\) | −8.05861 | −0.623594 | −0.311797 | − | 0.950149i | \(-0.600931\pi\) | ||||
−0.311797 | + | 0.950149i | \(0.600931\pi\) | |||||||
\(168\) | −1.69202 | −0.130542 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 11.1008 | 0.851394 | ||||||||
\(171\) | 0.149145 | 0.0114054 | ||||||||
\(172\) | −1.30798 | −0.0997324 | ||||||||
\(173\) | 9.82669 | 0.747110 | 0.373555 | − | 0.927608i | \(-0.378139\pi\) | ||||
0.373555 | + | 0.927608i | \(0.378139\pi\) | |||||||
\(174\) | 17.5405 | 1.32974 | ||||||||
\(175\) | −1.52781 | −0.115492 | ||||||||
\(176\) | −1.64310 | −0.123854 | ||||||||
\(177\) | 14.3056 | 1.07527 | ||||||||
\(178\) | −3.93900 | −0.295241 | ||||||||
\(179\) | −19.2392 | −1.43801 | −0.719003 | − | 0.695007i | \(-0.755401\pi\) | ||||
−0.719003 | + | 0.695007i | \(0.755401\pi\) | |||||||
\(180\) | 0.350191 | 0.0261017 | ||||||||
\(181\) | 9.57971 | 0.712054 | 0.356027 | − | 0.934476i | \(-0.384131\pi\) | ||||
0.356027 | + | 0.934476i | \(0.384131\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.95779 | 0.440412 | ||||||||
\(184\) | −2.04892 | −0.151048 | ||||||||
\(185\) | 3.24160 | 0.238327 | ||||||||
\(186\) | −18.6950 | −1.37078 | ||||||||
\(187\) | 7.13898 | 0.522054 | ||||||||
\(188\) | −7.24698 | −0.528540 | ||||||||
\(189\) | 5.30798 | 0.386099 | ||||||||
\(190\) | 2.78017 | 0.201695 | ||||||||
\(191\) | 1.51142 | 0.109362 | 0.0546812 | − | 0.998504i | \(-0.482586\pi\) | ||||
0.0546812 | + | 0.998504i | \(0.482586\pi\) | |||||||
\(192\) | 1.69202 | 0.122111 | ||||||||
\(193\) | −14.6310 | −1.05316 | −0.526582 | − | 0.850124i | \(-0.676527\pi\) | ||||
−0.526582 | + | 0.850124i | \(0.676527\pi\) | |||||||
\(194\) | 12.0489 | 0.865062 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 22.4480 | 1.59936 | 0.799678 | − | 0.600429i | \(-0.205004\pi\) | ||||
0.799678 | + | 0.600429i | \(0.205004\pi\) | |||||||
\(198\) | 0.225209 | 0.0160049 | ||||||||
\(199\) | −8.32975 | −0.590480 | −0.295240 | − | 0.955423i | \(-0.595400\pi\) | ||||
−0.295240 | + | 0.955423i | \(0.595400\pi\) | |||||||
\(200\) | 1.52781 | 0.108033 | ||||||||
\(201\) | −11.1166 | −0.784106 | ||||||||
\(202\) | −1.54288 | −0.108556 | ||||||||
\(203\) | −10.3666 | −0.727592 | ||||||||
\(204\) | −7.35152 | −0.514709 | ||||||||
\(205\) | 12.1685 | 0.849886 | ||||||||
\(206\) | −2.63773 | −0.183779 | ||||||||
\(207\) | 0.280831 | 0.0195191 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.78794 | 0.123674 | ||||||||
\(210\) | 4.32304 | 0.298318 | ||||||||
\(211\) | 10.4426 | 0.718902 | 0.359451 | − | 0.933164i | \(-0.382964\pi\) | ||||
0.359451 | + | 0.933164i | \(0.382964\pi\) | |||||||
\(212\) | 1.29590 | 0.0890026 | ||||||||
\(213\) | −26.1497 | −1.79175 | ||||||||
\(214\) | 10.1564 | 0.694280 | ||||||||
\(215\) | 3.34183 | 0.227911 | ||||||||
\(216\) | −5.30798 | −0.361162 | ||||||||
\(217\) | 11.0489 | 0.750049 | ||||||||
\(218\) | −13.2567 | −0.897855 | ||||||||
\(219\) | −8.77479 | −0.592945 | ||||||||
\(220\) | 4.19806 | 0.283033 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.14675 | −0.144081 | ||||||||
\(223\) | 15.9312 | 1.06683 | 0.533417 | − | 0.845852i | \(-0.320908\pi\) | ||||
0.533417 | + | 0.845852i | \(0.320908\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −0.209407 | −0.0139605 | ||||||||
\(226\) | −9.86054 | −0.655914 | ||||||||
\(227\) | −5.53079 | −0.367092 | −0.183546 | − | 0.983011i | \(-0.558758\pi\) | ||||
−0.183546 | + | 0.983011i | \(0.558758\pi\) | |||||||
\(228\) | −1.84117 | −0.121934 | ||||||||
\(229\) | −24.1739 | −1.59746 | −0.798728 | − | 0.601692i | \(-0.794493\pi\) | ||||
−0.798728 | + | 0.601692i | \(0.794493\pi\) | |||||||
\(230\) | 5.23490 | 0.345179 | ||||||||
\(231\) | 2.78017 | 0.182922 | ||||||||
\(232\) | 10.3666 | 0.680600 | ||||||||
\(233\) | 24.5284 | 1.60691 | 0.803455 | − | 0.595366i | \(-0.202993\pi\) | ||||
0.803455 | + | 0.595366i | \(0.202993\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.5157 | 1.20783 | ||||||||
\(236\) | 8.45473 | 0.550356 | ||||||||
\(237\) | 17.3086 | 1.12431 | ||||||||
\(238\) | 4.34481 | 0.281632 | ||||||||
\(239\) | 14.0325 | 0.907689 | 0.453844 | − | 0.891081i | \(-0.350052\pi\) | ||||
0.453844 | + | 0.891081i | \(0.350052\pi\) | |||||||
\(240\) | −4.32304 | −0.279051 | ||||||||
\(241\) | −10.4843 | −0.675351 | −0.337676 | − | 0.941263i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941263i | \(0.609641\pi\) | |||||||
\(242\) | −8.30021 | −0.533558 | ||||||||
\(243\) | 1.42327 | 0.0913029 | ||||||||
\(244\) | 3.52111 | 0.225416 | ||||||||
\(245\) | −2.55496 | −0.163230 | ||||||||
\(246\) | −8.05861 | −0.513798 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.0489 | −0.701607 | ||||||||
\(249\) | 23.6383 | 1.49802 | ||||||||
\(250\) | 8.87130 | 0.561070 | ||||||||
\(251\) | 25.1782 | 1.58923 | 0.794617 | − | 0.607111i | \(-0.207672\pi\) | ||||
0.794617 | + | 0.607111i | \(0.207672\pi\) | |||||||
\(252\) | 0.137063 | 0.00863418 | ||||||||
\(253\) | 3.36658 | 0.211655 | ||||||||
\(254\) | −16.7114 | −1.04857 | ||||||||
\(255\) | 18.7828 | 1.17623 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.9825 | 0.872207 | 0.436103 | − | 0.899897i | \(-0.356358\pi\) | ||||
0.436103 | + | 0.899897i | \(0.356358\pi\) | |||||||
\(258\) | −2.21313 | −0.137783 | ||||||||
\(259\) | 1.26875 | 0.0788363 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.42088 | −0.0879502 | ||||||||
\(262\) | −5.85086 | −0.361467 | ||||||||
\(263\) | −22.6829 | −1.39869 | −0.699345 | − | 0.714785i | \(-0.746525\pi\) | ||||
−0.699345 | + | 0.714785i | \(0.746525\pi\) | |||||||
\(264\) | −2.78017 | −0.171107 | ||||||||
\(265\) | −3.31096 | −0.203391 | ||||||||
\(266\) | 1.08815 | 0.0667185 | ||||||||
\(267\) | −6.66487 | −0.407884 | ||||||||
\(268\) | −6.57002 | −0.401328 | ||||||||
\(269\) | −28.0301 | −1.70903 | −0.854514 | − | 0.519429i | \(-0.826145\pi\) | ||||
−0.854514 | + | 0.519429i | \(0.826145\pi\) | |||||||
\(270\) | 13.5617 | 0.825337 | ||||||||
\(271\) | −0.161227 | −0.00979381 | −0.00489691 | − | 0.999988i | \(-0.501559\pi\) | ||||
−0.00489691 | + | 0.999988i | \(0.501559\pi\) | |||||||
\(272\) | −4.34481 | −0.263443 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.7995 | 1.25655 | ||||||||
\(275\) | −2.51035 | −0.151380 | ||||||||
\(276\) | −3.46681 | −0.208678 | ||||||||
\(277\) | 27.1564 | 1.63167 | 0.815836 | − | 0.578283i | \(-0.196277\pi\) | ||||
0.815836 | + | 0.578283i | \(0.196277\pi\) | |||||||
\(278\) | 4.79225 | 0.287420 | ||||||||
\(279\) | 1.51440 | 0.0906648 | ||||||||
\(280\) | 2.55496 | 0.152688 | ||||||||
\(281\) | 15.4776 | 0.923314 | 0.461657 | − | 0.887058i | \(-0.347255\pi\) | ||||
0.461657 | + | 0.887058i | \(0.347255\pi\) | |||||||
\(282\) | −12.2620 | −0.730194 | ||||||||
\(283\) | −13.7289 | −0.816096 | −0.408048 | − | 0.912961i | \(-0.633790\pi\) | ||||
−0.408048 | + | 0.912961i | \(0.633790\pi\) | |||||||
\(284\) | −15.4547 | −0.917070 | ||||||||
\(285\) | 4.70410 | 0.278647 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.76271 | 0.281134 | ||||||||
\(288\) | −0.137063 | −0.00807653 | ||||||||
\(289\) | 1.87741 | 0.110436 | ||||||||
\(290\) | −26.4862 | −1.55532 | ||||||||
\(291\) | 20.3870 | 1.19511 | ||||||||
\(292\) | −5.18598 | −0.303487 | ||||||||
\(293\) | −21.5948 | −1.26158 | −0.630790 | − | 0.775953i | \(-0.717269\pi\) | ||||
−0.630790 | + | 0.775953i | \(0.717269\pi\) | |||||||
\(294\) | 1.69202 | 0.0986807 | ||||||||
\(295\) | −21.6015 | −1.25769 | ||||||||
\(296\) | −1.26875 | −0.0737446 | ||||||||
\(297\) | 8.72156 | 0.506076 | ||||||||
\(298\) | 15.3448 | 0.888901 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.58509 | 0.149250 | ||||||||
\(301\) | 1.30798 | 0.0753906 | ||||||||
\(302\) | 0.521106 | 0.0299863 | ||||||||
\(303\) | −2.61058 | −0.149974 | ||||||||
\(304\) | −1.08815 | −0.0624095 | ||||||||
\(305\) | −8.99628 | −0.515125 | ||||||||
\(306\) | 0.595515 | 0.0340433 | ||||||||
\(307\) | −3.11231 | −0.177629 | −0.0888144 | − | 0.996048i | \(-0.528308\pi\) | ||||
−0.0888144 | + | 0.996048i | \(0.528308\pi\) | |||||||
\(308\) | 1.64310 | 0.0936245 | ||||||||
\(309\) | −4.46309 | −0.253896 | ||||||||
\(310\) | 28.2295 | 1.60333 | ||||||||
\(311\) | −11.0000 | −0.623753 | −0.311876 | − | 0.950123i | \(-0.600957\pi\) | ||||
−0.311876 | + | 0.950123i | \(0.600957\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.3394 | −1.71489 | −0.857443 | − | 0.514579i | \(-0.827948\pi\) | ||||
−0.857443 | + | 0.514579i | \(0.827948\pi\) | |||||||
\(314\) | −23.0911 | −1.30311 | ||||||||
\(315\) | −0.350191 | −0.0197310 | ||||||||
\(316\) | 10.2295 | 0.575456 | ||||||||
\(317\) | −7.08144 | −0.397733 | −0.198867 | − | 0.980027i | \(-0.563726\pi\) | ||||
−0.198867 | + | 0.980027i | \(0.563726\pi\) | |||||||
\(318\) | 2.19269 | 0.122960 | ||||||||
\(319\) | −17.0334 | −0.953686 | ||||||||
\(320\) | −2.55496 | −0.142827 | ||||||||
\(321\) | 17.1849 | 0.959168 | ||||||||
\(322\) | 2.04892 | 0.114182 | ||||||||
\(323\) | 4.72779 | 0.263061 | ||||||||
\(324\) | −8.57002 | −0.476112 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.9028 | 1.26847 | ||||||||
\(327\) | −22.4306 | −1.24041 | ||||||||
\(328\) | −4.76271 | −0.262977 | ||||||||
\(329\) | 7.24698 | 0.399539 | ||||||||
\(330\) | 7.10321 | 0.391019 | ||||||||
\(331\) | 11.4722 | 0.630569 | 0.315284 | − | 0.948997i | \(-0.397900\pi\) | ||||
0.315284 | + | 0.948997i | \(0.397900\pi\) | |||||||
\(332\) | 13.9705 | 0.766729 | ||||||||
\(333\) | 0.173899 | 0.00952961 | ||||||||
\(334\) | −8.05861 | −0.440947 | ||||||||
\(335\) | 16.7861 | 0.917125 | ||||||||
\(336\) | −1.69202 | −0.0923073 | ||||||||
\(337\) | 3.96077 | 0.215757 | 0.107878 | − | 0.994164i | \(-0.465594\pi\) | ||||
0.107878 | + | 0.994164i | \(0.465594\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.6843 | −0.906164 | ||||||||
\(340\) | 11.1008 | 0.602026 | ||||||||
\(341\) | 18.1545 | 0.983122 | ||||||||
\(342\) | 0.149145 | 0.00806483 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.30798 | −0.0705215 | ||||||||
\(345\) | 8.85756 | 0.476875 | ||||||||
\(346\) | 9.82669 | 0.528286 | ||||||||
\(347\) | 8.24698 | 0.442721 | 0.221361 | − | 0.975192i | \(-0.428950\pi\) | ||||
0.221361 | + | 0.975192i | \(0.428950\pi\) | |||||||
\(348\) | 17.5405 | 0.940269 | ||||||||
\(349\) | −14.5670 | −0.779756 | −0.389878 | − | 0.920867i | \(-0.627483\pi\) | ||||
−0.389878 | + | 0.920867i | \(0.627483\pi\) | |||||||
\(350\) | −1.52781 | −0.0816649 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.64310 | −0.0875777 | ||||||||
\(353\) | 3.04593 | 0.162119 | 0.0810593 | − | 0.996709i | \(-0.474170\pi\) | ||||
0.0810593 | + | 0.996709i | \(0.474170\pi\) | |||||||
\(354\) | 14.3056 | 0.760333 | ||||||||
\(355\) | 39.4862 | 2.09571 | ||||||||
\(356\) | −3.93900 | −0.208767 | ||||||||
\(357\) | 7.35152 | 0.389084 | ||||||||
\(358\) | −19.2392 | −1.01682 | ||||||||
\(359\) | 16.5851 | 0.875328 | 0.437664 | − | 0.899139i | \(-0.355806\pi\) | ||||
0.437664 | + | 0.899139i | \(0.355806\pi\) | |||||||
\(360\) | 0.350191 | 0.0184567 | ||||||||
\(361\) | −17.8159 | −0.937681 | ||||||||
\(362\) | 9.57971 | 0.503499 | ||||||||
\(363\) | −14.0441 | −0.737126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.2500 | 0.693535 | ||||||||
\(366\) | 5.95779 | 0.311419 | ||||||||
\(367\) | 0.966148 | 0.0504325 | 0.0252163 | − | 0.999682i | \(-0.491973\pi\) | ||||
0.0252163 | + | 0.999682i | \(0.491973\pi\) | |||||||
\(368\) | −2.04892 | −0.106807 | ||||||||
\(369\) | 0.652793 | 0.0339830 | ||||||||
\(370\) | 3.24160 | 0.168523 | ||||||||
\(371\) | −1.29590 | −0.0672796 | ||||||||
\(372\) | −18.6950 | −0.969291 | ||||||||
\(373\) | 32.0901 | 1.66156 | 0.830780 | − | 0.556600i | \(-0.187895\pi\) | ||||
0.830780 | + | 0.556600i | \(0.187895\pi\) | |||||||
\(374\) | 7.13898 | 0.369148 | ||||||||
\(375\) | 15.0104 | 0.775135 | ||||||||
\(376\) | −7.24698 | −0.373734 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.30798 | 0.273013 | ||||||||
\(379\) | −0.972853 | −0.0499721 | −0.0249860 | − | 0.999688i | \(-0.507954\pi\) | ||||
−0.0249860 | + | 0.999688i | \(0.507954\pi\) | |||||||
\(380\) | 2.78017 | 0.142620 | ||||||||
\(381\) | −28.2760 | −1.44863 | ||||||||
\(382\) | 1.51142 | 0.0773309 | ||||||||
\(383\) | −5.47650 | −0.279836 | −0.139918 | − | 0.990163i | \(-0.544684\pi\) | ||||
−0.139918 | + | 0.990163i | \(0.544684\pi\) | |||||||
\(384\) | 1.69202 | 0.0863456 | ||||||||
\(385\) | −4.19806 | −0.213953 | ||||||||
\(386\) | −14.6310 | −0.744699 | ||||||||
\(387\) | 0.179276 | 0.00911311 | ||||||||
\(388\) | 12.0489 | 0.611691 | ||||||||
\(389\) | −32.5066 | −1.64815 | −0.824076 | − | 0.566480i | \(-0.808305\pi\) | ||||
−0.824076 | + | 0.566480i | \(0.808305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.90217 | 0.450202 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −9.89977 | −0.499377 | ||||||||
\(394\) | 22.4480 | 1.13092 | ||||||||
\(395\) | −26.1360 | −1.31504 | ||||||||
\(396\) | 0.225209 | 0.0113172 | ||||||||
\(397\) | −34.4674 | −1.72987 | −0.864935 | − | 0.501884i | \(-0.832640\pi\) | ||||
−0.864935 | + | 0.501884i | \(0.832640\pi\) | |||||||
\(398\) | −8.32975 | −0.417533 | ||||||||
\(399\) | 1.84117 | 0.0921736 | ||||||||
\(400\) | 1.52781 | 0.0763906 | ||||||||
\(401\) | 12.9903 | 0.648705 | 0.324353 | − | 0.945936i | \(-0.394854\pi\) | ||||
0.324353 | + | 0.945936i | \(0.394854\pi\) | |||||||
\(402\) | −11.1166 | −0.554447 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.54288 | −0.0767610 | ||||||||
\(405\) | 21.8961 | 1.08802 | ||||||||
\(406\) | −10.3666 | −0.514485 | ||||||||
\(407\) | 2.08469 | 0.103334 | ||||||||
\(408\) | −7.35152 | −0.363954 | ||||||||
\(409\) | 31.4771 | 1.55644 | 0.778221 | − | 0.627990i | \(-0.216122\pi\) | ||||
0.778221 | + | 0.627990i | \(0.216122\pi\) | |||||||
\(410\) | 12.1685 | 0.600960 | ||||||||
\(411\) | 35.1933 | 1.73596 | ||||||||
\(412\) | −2.63773 | −0.129951 | ||||||||
\(413\) | −8.45473 | −0.416030 | ||||||||
\(414\) | 0.280831 | 0.0138021 | ||||||||
\(415\) | −35.6939 | −1.75215 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.10859 | 0.397079 | ||||||||
\(418\) | 1.78794 | 0.0874509 | ||||||||
\(419\) | −22.4101 | −1.09481 | −0.547403 | − | 0.836869i | \(-0.684384\pi\) | ||||
−0.547403 | + | 0.836869i | \(0.684384\pi\) | |||||||
\(420\) | 4.32304 | 0.210943 | ||||||||
\(421\) | −17.2373 | −0.840094 | −0.420047 | − | 0.907502i | \(-0.637986\pi\) | ||||
−0.420047 | + | 0.907502i | \(0.637986\pi\) | |||||||
\(422\) | 10.4426 | 0.508340 | ||||||||
\(423\) | 0.993295 | 0.0482957 | ||||||||
\(424\) | 1.29590 | 0.0629343 | ||||||||
\(425\) | −6.63806 | −0.321993 | ||||||||
\(426\) | −26.1497 | −1.26696 | ||||||||
\(427\) | −3.52111 | −0.170398 | ||||||||
\(428\) | 10.1564 | 0.490930 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.34183 | 0.161157 | ||||||||
\(431\) | 30.4349 | 1.46600 | 0.732998 | − | 0.680230i | \(-0.238120\pi\) | ||||
0.732998 | + | 0.680230i | \(0.238120\pi\) | |||||||
\(432\) | −5.30798 | −0.255380 | ||||||||
\(433\) | 29.1812 | 1.40236 | 0.701179 | − | 0.712985i | \(-0.252657\pi\) | ||||
0.701179 | + | 0.712985i | \(0.252657\pi\) | |||||||
\(434\) | 11.0489 | 0.530365 | ||||||||
\(435\) | −44.8152 | −2.14872 | ||||||||
\(436\) | −13.2567 | −0.634879 | ||||||||
\(437\) | 2.22952 | 0.106652 | ||||||||
\(438\) | −8.77479 | −0.419276 | ||||||||
\(439\) | −23.2349 | −1.10894 | −0.554471 | − | 0.832203i | \(-0.687079\pi\) | ||||
−0.554471 | + | 0.832203i | \(0.687079\pi\) | |||||||
\(440\) | 4.19806 | 0.200135 | ||||||||
\(441\) | −0.137063 | −0.00652683 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.1371 | −1.24181 | −0.620905 | − | 0.783886i | \(-0.713235\pi\) | ||||
−0.620905 | + | 0.783886i | \(0.713235\pi\) | |||||||
\(444\) | −2.14675 | −0.101880 | ||||||||
\(445\) | 10.0640 | 0.477079 | ||||||||
\(446\) | 15.9312 | 0.754366 | ||||||||
\(447\) | 25.9638 | 1.22804 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −4.29350 | −0.202623 | −0.101311 | − | 0.994855i | \(-0.532304\pi\) | ||||
−0.101311 | + | 0.994855i | \(0.532304\pi\) | |||||||
\(450\) | −0.209407 | −0.00987154 | ||||||||
\(451\) | 7.82563 | 0.368494 | ||||||||
\(452\) | −9.86054 | −0.463801 | ||||||||
\(453\) | 0.881723 | 0.0414270 | ||||||||
\(454\) | −5.53079 | −0.259573 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.84117 | −0.0862205 | ||||||||
\(457\) | −0.781495 | −0.0365568 | −0.0182784 | − | 0.999833i | \(-0.505819\pi\) | ||||
−0.0182784 | + | 0.999833i | \(0.505819\pi\) | |||||||
\(458\) | −24.1739 | −1.12957 | ||||||||
\(459\) | 23.0622 | 1.07645 | ||||||||
\(460\) | 5.23490 | 0.244078 | ||||||||
\(461\) | −17.8103 | −0.829508 | −0.414754 | − | 0.909934i | \(-0.636132\pi\) | ||||
−0.414754 | + | 0.909934i | \(0.636132\pi\) | |||||||
\(462\) | 2.78017 | 0.129345 | ||||||||
\(463\) | −36.1226 | −1.67876 | −0.839380 | − | 0.543546i | \(-0.817081\pi\) | ||||
−0.839380 | + | 0.543546i | \(0.817081\pi\) | |||||||
\(464\) | 10.3666 | 0.481257 | ||||||||
\(465\) | 47.7650 | 2.21505 | ||||||||
\(466\) | 24.5284 | 1.13626 | ||||||||
\(467\) | −26.1142 | −1.20842 | −0.604211 | − | 0.796824i | \(-0.706512\pi\) | ||||
−0.604211 | + | 0.796824i | \(0.706512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.57002 | 0.303376 | ||||||||
\(470\) | 18.5157 | 0.854067 | ||||||||
\(471\) | −39.0707 | −1.80028 | ||||||||
\(472\) | 8.45473 | 0.389161 | ||||||||
\(473\) | 2.14914 | 0.0988178 | ||||||||
\(474\) | 17.3086 | 0.795009 | ||||||||
\(475\) | −1.66248 | −0.0762799 | ||||||||
\(476\) | 4.34481 | 0.199144 | ||||||||
\(477\) | −0.177620 | −0.00813266 | ||||||||
\(478\) | 14.0325 | 0.641833 | ||||||||
\(479\) | 7.21983 | 0.329883 | 0.164941 | − | 0.986303i | \(-0.447257\pi\) | ||||
0.164941 | + | 0.986303i | \(0.447257\pi\) | |||||||
\(480\) | −4.32304 | −0.197319 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.4843 | −0.477545 | ||||||||
\(483\) | 3.46681 | 0.157745 | ||||||||
\(484\) | −8.30021 | −0.377282 | ||||||||
\(485\) | −30.7845 | −1.39785 | ||||||||
\(486\) | 1.42327 | 0.0645609 | ||||||||
\(487\) | −26.0858 | −1.18206 | −0.591029 | − | 0.806650i | \(-0.701278\pi\) | ||||
−0.591029 | + | 0.806650i | \(0.701278\pi\) | |||||||
\(488\) | 3.52111 | 0.159393 | ||||||||
\(489\) | 38.7520 | 1.75242 | ||||||||
\(490\) | −2.55496 | −0.115421 | ||||||||
\(491\) | −10.9879 | −0.495878 | −0.247939 | − | 0.968776i | \(-0.579753\pi\) | ||||
−0.247939 | + | 0.968776i | \(0.579753\pi\) | |||||||
\(492\) | −8.05861 | −0.363310 | ||||||||
\(493\) | −45.0409 | −2.02854 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.575400 | −0.0258623 | ||||||||
\(496\) | −11.0489 | −0.496111 | ||||||||
\(497\) | 15.4547 | 0.693239 | ||||||||
\(498\) | 23.6383 | 1.05926 | ||||||||
\(499\) | −6.78150 | −0.303581 | −0.151791 | − | 0.988413i | \(-0.548504\pi\) | ||||
−0.151791 | + | 0.988413i | \(0.548504\pi\) | |||||||
\(500\) | 8.87130 | 0.396736 | ||||||||
\(501\) | −13.6353 | −0.609182 | ||||||||
\(502\) | 25.1782 | 1.12376 | ||||||||
\(503\) | −22.0073 | −0.981257 | −0.490628 | − | 0.871369i | \(-0.663233\pi\) | ||||
−0.490628 | + | 0.871369i | \(0.663233\pi\) | |||||||
\(504\) | 0.137063 | 0.00610529 | ||||||||
\(505\) | 3.94198 | 0.175416 | ||||||||
\(506\) | 3.36658 | 0.149663 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.7114 | −0.741448 | ||||||||
\(509\) | −5.02608 | −0.222777 | −0.111389 | − | 0.993777i | \(-0.535530\pi\) | ||||
−0.111389 | + | 0.993777i | \(0.535530\pi\) | |||||||
\(510\) | 18.7828 | 0.831717 | ||||||||
\(511\) | 5.18598 | 0.229414 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.77586 | 0.255010 | ||||||||
\(514\) | 13.9825 | 0.616743 | ||||||||
\(515\) | 6.73928 | 0.296968 | ||||||||
\(516\) | −2.21313 | −0.0974275 | ||||||||
\(517\) | 11.9075 | 0.523693 | ||||||||
\(518\) | 1.26875 | 0.0557457 | ||||||||
\(519\) | 16.6270 | 0.729843 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.08144 | −0.354054 | −0.177027 | − | 0.984206i | \(-0.556648\pi\) | ||||
−0.177027 | + | 0.984206i | \(0.556648\pi\) | |||||||
\(522\) | −1.42088 | −0.0621902 | ||||||||
\(523\) | −0.530204 | −0.0231842 | −0.0115921 | − | 0.999933i | \(-0.503690\pi\) | ||||
−0.0115921 | + | 0.999933i | \(0.503690\pi\) | |||||||
\(524\) | −5.85086 | −0.255596 | ||||||||
\(525\) | −2.58509 | −0.112823 | ||||||||
\(526\) | −22.6829 | −0.989022 | ||||||||
\(527\) | 48.0055 | 2.09115 | ||||||||
\(528\) | −2.78017 | −0.120991 | ||||||||
\(529\) | −18.8019 | −0.817476 | ||||||||
\(530\) | −3.31096 | −0.143819 | ||||||||
\(531\) | −1.15883 | −0.0502891 | ||||||||
\(532\) | 1.08815 | 0.0471771 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.66487 | −0.288417 | ||||||||
\(535\) | −25.9493 | −1.12189 | ||||||||
\(536\) | −6.57002 | −0.283782 | ||||||||
\(537\) | −32.5532 | −1.40477 | ||||||||
\(538\) | −28.0301 | −1.20846 | ||||||||
\(539\) | −1.64310 | −0.0707735 | ||||||||
\(540\) | 13.5617 | 0.583601 | ||||||||
\(541\) | −14.5550 | −0.625767 | −0.312883 | − | 0.949792i | \(-0.601295\pi\) | ||||
−0.312883 | + | 0.949792i | \(0.601295\pi\) | |||||||
\(542\) | −0.161227 | −0.00692527 | ||||||||
\(543\) | 16.2091 | 0.695598 | ||||||||
\(544\) | −4.34481 | −0.186282 | ||||||||
\(545\) | 33.8702 | 1.45084 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.43727 | −0.146967 | −0.0734836 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734836 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(548\) | 20.7995 | 0.888513 | ||||||||
\(549\) | −0.482615 | −0.0205975 | ||||||||
\(550\) | −2.51035 | −0.107042 | ||||||||
\(551\) | −11.2804 | −0.480559 | ||||||||
\(552\) | −3.46681 | −0.147557 | ||||||||
\(553\) | −10.2295 | −0.435003 | ||||||||
\(554\) | 27.1564 | 1.15377 | ||||||||
\(555\) | 5.48486 | 0.232819 | ||||||||
\(556\) | 4.79225 | 0.203237 | ||||||||
\(557\) | 23.1304 | 0.980065 | 0.490032 | − | 0.871704i | \(-0.336985\pi\) | ||||
0.490032 | + | 0.871704i | \(0.336985\pi\) | |||||||
\(558\) | 1.51440 | 0.0641097 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.55496 | 0.107967 | ||||||||
\(561\) | 12.0793 | 0.509989 | ||||||||
\(562\) | 15.4776 | 0.652882 | ||||||||
\(563\) | 2.02656 | 0.0854092 | 0.0427046 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427046 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(564\) | −12.2620 | −0.516325 | ||||||||
\(565\) | 25.1933 | 1.05989 | ||||||||
\(566\) | −13.7289 | −0.577067 | ||||||||
\(567\) | 8.57002 | 0.359907 | ||||||||
\(568\) | −15.4547 | −0.648466 | ||||||||
\(569\) | 23.5840 | 0.988694 | 0.494347 | − | 0.869265i | \(-0.335407\pi\) | ||||
0.494347 | + | 0.869265i | \(0.335407\pi\) | |||||||
\(570\) | 4.70410 | 0.197033 | ||||||||
\(571\) | −3.99462 | −0.167170 | −0.0835849 | − | 0.996501i | \(-0.526637\pi\) | ||||
−0.0835849 | + | 0.996501i | \(0.526637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.55735 | 0.106835 | ||||||||
\(574\) | 4.76271 | 0.198792 | ||||||||
\(575\) | −3.13036 | −0.130545 | ||||||||
\(576\) | −0.137063 | −0.00571097 | ||||||||
\(577\) | −37.0877 | −1.54398 | −0.771990 | − | 0.635635i | \(-0.780738\pi\) | ||||
−0.771990 | + | 0.635635i | \(0.780738\pi\) | |||||||
\(578\) | 1.87741 | 0.0780900 | ||||||||
\(579\) | −24.7560 | −1.02882 | ||||||||
\(580\) | −26.4862 | −1.09978 | ||||||||
\(581\) | −13.9705 | −0.579592 | ||||||||
\(582\) | 20.3870 | 0.845069 | ||||||||
\(583\) | −2.12929 | −0.0881863 | ||||||||
\(584\) | −5.18598 | −0.214597 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.5948 | −0.892072 | ||||||||
\(587\) | 32.5362 | 1.34291 | 0.671456 | − | 0.741045i | \(-0.265669\pi\) | ||||
0.671456 | + | 0.741045i | \(0.265669\pi\) | |||||||
\(588\) | 1.69202 | 0.0697778 | ||||||||
\(589\) | 12.0228 | 0.495392 | ||||||||
\(590\) | −21.6015 | −0.889319 | ||||||||
\(591\) | 37.9825 | 1.56239 | ||||||||
\(592\) | −1.26875 | −0.0521453 | ||||||||
\(593\) | 17.0871 | 0.701682 | 0.350841 | − | 0.936435i | \(-0.385896\pi\) | ||||
0.350841 | + | 0.936435i | \(0.385896\pi\) | |||||||
\(594\) | 8.72156 | 0.357850 | ||||||||
\(595\) | −11.1008 | −0.455089 | ||||||||
\(596\) | 15.3448 | 0.628548 | ||||||||
\(597\) | −14.0941 | −0.576834 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3521 | 0.872424 | 0.436212 | − | 0.899844i | \(-0.356320\pi\) | ||||
0.436212 | + | 0.899844i | \(0.356320\pi\) | |||||||
\(600\) | 2.58509 | 0.105536 | ||||||||
\(601\) | −9.23251 | −0.376602 | −0.188301 | − | 0.982111i | \(-0.560298\pi\) | ||||
−0.188301 | + | 0.982111i | \(0.560298\pi\) | |||||||
\(602\) | 1.30798 | 0.0533092 | ||||||||
\(603\) | 0.900509 | 0.0366716 | ||||||||
\(604\) | 0.521106 | 0.0212035 | ||||||||
\(605\) | 21.2067 | 0.862174 | ||||||||
\(606\) | −2.61058 | −0.106048 | ||||||||
\(607\) | 7.52303 | 0.305350 | 0.152675 | − | 0.988276i | \(-0.451211\pi\) | ||||
0.152675 | + | 0.988276i | \(0.451211\pi\) | |||||||
\(608\) | −1.08815 | −0.0441301 | ||||||||
\(609\) | −17.5405 | −0.710776 | ||||||||
\(610\) | −8.99628 | −0.364249 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.595515 | 0.0240723 | ||||||||
\(613\) | 19.8465 | 0.801594 | 0.400797 | − | 0.916167i | \(-0.368733\pi\) | ||||
0.400797 | + | 0.916167i | \(0.368733\pi\) | |||||||
\(614\) | −3.11231 | −0.125603 | ||||||||
\(615\) | 20.5894 | 0.830245 | ||||||||
\(616\) | 1.64310 | 0.0662026 | ||||||||
\(617\) | −0.214456 | −0.00863366 | −0.00431683 | − | 0.999991i | \(-0.501374\pi\) | ||||
−0.00431683 | + | 0.999991i | \(0.501374\pi\) | |||||||
\(618\) | −4.46309 | −0.179532 | ||||||||
\(619\) | 45.6577 | 1.83514 | 0.917569 | − | 0.397577i | \(-0.130149\pi\) | ||||
0.917569 | + | 0.397577i | \(0.130149\pi\) | |||||||
\(620\) | 28.2295 | 1.13372 | ||||||||
\(621\) | 10.8756 | 0.436423 | ||||||||
\(622\) | −11.0000 | −0.441060 | ||||||||
\(623\) | 3.93900 | 0.157813 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3048 | −1.21219 | ||||||||
\(626\) | −30.3394 | −1.21261 | ||||||||
\(627\) | 3.02523 | 0.120816 | ||||||||
\(628\) | −23.0911 | −0.921436 | ||||||||
\(629\) | 5.51248 | 0.219797 | ||||||||
\(630\) | −0.350191 | −0.0139519 | ||||||||
\(631\) | −20.3448 | −0.809914 | −0.404957 | − | 0.914336i | \(-0.632714\pi\) | ||||
−0.404957 | + | 0.914336i | \(0.632714\pi\) | |||||||
\(632\) | 10.2295 | 0.406909 | ||||||||
\(633\) | 17.6692 | 0.702287 | ||||||||
\(634\) | −7.08144 | −0.281240 | ||||||||
\(635\) | 42.6969 | 1.69438 | ||||||||
\(636\) | 2.19269 | 0.0869456 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −17.0334 | −0.674358 | ||||||||
\(639\) | 2.11828 | 0.0837977 | ||||||||
\(640\) | −2.55496 | −0.100994 | ||||||||
\(641\) | −21.3666 | −0.843929 | −0.421965 | − | 0.906612i | \(-0.638659\pi\) | ||||
−0.421965 | + | 0.906612i | \(0.638659\pi\) | |||||||
\(642\) | 17.1849 | 0.678235 | ||||||||
\(643\) | −13.0573 | −0.514929 | −0.257464 | − | 0.966288i | \(-0.582887\pi\) | ||||
−0.257464 | + | 0.966288i | \(0.582887\pi\) | |||||||
\(644\) | 2.04892 | 0.0807387 | ||||||||
\(645\) | 5.65445 | 0.222644 | ||||||||
\(646\) | 4.72779 | 0.186012 | ||||||||
\(647\) | 18.4838 | 0.726673 | 0.363337 | − | 0.931658i | \(-0.381638\pi\) | ||||
0.363337 | + | 0.931658i | \(0.381638\pi\) | |||||||
\(648\) | −8.57002 | −0.336662 | ||||||||
\(649\) | −13.8920 | −0.545309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.6950 | 0.732715 | ||||||||
\(652\) | 22.9028 | 0.896941 | ||||||||
\(653\) | −33.1129 | −1.29581 | −0.647904 | − | 0.761722i | \(-0.724354\pi\) | ||||
−0.647904 | + | 0.761722i | \(0.724354\pi\) | |||||||
\(654\) | −22.4306 | −0.877105 | ||||||||
\(655\) | 14.9487 | 0.584094 | ||||||||
\(656\) | −4.76271 | −0.185953 | ||||||||
\(657\) | 0.710808 | 0.0277313 | ||||||||
\(658\) | 7.24698 | 0.282517 | ||||||||
\(659\) | −26.3545 | −1.02663 | −0.513313 | − | 0.858202i | \(-0.671582\pi\) | ||||
−0.513313 | + | 0.858202i | \(0.671582\pi\) | |||||||
\(660\) | 7.10321 | 0.276492 | ||||||||
\(661\) | 29.9745 | 1.16587 | 0.582937 | − | 0.812518i | \(-0.301904\pi\) | ||||
0.582937 | + | 0.812518i | \(0.301904\pi\) | |||||||
\(662\) | 11.4722 | 0.445879 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.9705 | 0.542159 | ||||||||
\(665\) | −2.78017 | −0.107810 | ||||||||
\(666\) | 0.173899 | 0.00673845 | ||||||||
\(667\) | −21.2403 | −0.822427 | ||||||||
\(668\) | −8.05861 | −0.311797 | ||||||||
\(669\) | 26.9560 | 1.04218 | ||||||||
\(670\) | 16.7861 | 0.648505 | ||||||||
\(671\) | −5.78554 | −0.223348 | ||||||||
\(672\) | −1.69202 | −0.0652711 | ||||||||
\(673\) | 8.85756 | 0.341434 | 0.170717 | − | 0.985320i | \(-0.445392\pi\) | ||||
0.170717 | + | 0.985320i | \(0.445392\pi\) | |||||||
\(674\) | 3.96077 | 0.152563 | ||||||||
\(675\) | −8.10959 | −0.312138 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0575 | −0.694008 | −0.347004 | − | 0.937864i | \(-0.612801\pi\) | ||||
−0.347004 | + | 0.937864i | \(0.612801\pi\) | |||||||
\(678\) | −16.6843 | −0.640755 | ||||||||
\(679\) | −12.0489 | −0.462395 | ||||||||
\(680\) | 11.1008 | 0.425697 | ||||||||
\(681\) | −9.35822 | −0.358608 | ||||||||
\(682\) | 18.1545 | 0.695173 | ||||||||
\(683\) | 35.2137 | 1.34742 | 0.673708 | − | 0.738998i | \(-0.264701\pi\) | ||||
0.673708 | + | 0.738998i | \(0.264701\pi\) | |||||||
\(684\) | 0.149145 | 0.00570270 | ||||||||
\(685\) | −53.1420 | −2.03045 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −40.9028 | −1.56054 | ||||||||
\(688\) | −1.30798 | −0.0498662 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8.85756 | 0.337202 | ||||||||
\(691\) | −10.3120 | −0.392288 | −0.196144 | − | 0.980575i | \(-0.562842\pi\) | ||||
−0.196144 | + | 0.980575i | \(0.562842\pi\) | |||||||
\(692\) | 9.82669 | 0.373555 | ||||||||
\(693\) | −0.225209 | −0.00855500 | ||||||||
\(694\) | 8.24698 | 0.313051 | ||||||||
\(695\) | −12.2440 | −0.464441 | ||||||||
\(696\) | 17.5405 | 0.664870 | ||||||||
\(697\) | 20.6931 | 0.783807 | ||||||||
\(698\) | −14.5670 | −0.551371 | ||||||||
\(699\) | 41.5026 | 1.56977 | ||||||||
\(700\) | −1.52781 | −0.0577458 | ||||||||
\(701\) | 27.6025 | 1.04253 | 0.521267 | − | 0.853394i | \(-0.325460\pi\) | ||||
0.521267 | + | 0.853394i | \(0.325460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.38059 | 0.0520698 | ||||||||
\(704\) | −1.64310 | −0.0619268 | ||||||||
\(705\) | 31.3290 | 1.17992 | ||||||||
\(706\) | 3.04593 | 0.114635 | ||||||||
\(707\) | 1.54288 | 0.0580258 | ||||||||
\(708\) | 14.3056 | 0.537637 | ||||||||
\(709\) | −25.0218 | −0.939712 | −0.469856 | − | 0.882743i | \(-0.655694\pi\) | ||||
−0.469856 | + | 0.882743i | \(0.655694\pi\) | |||||||
\(710\) | 39.4862 | 1.48189 | ||||||||
\(711\) | −1.40209 | −0.0525826 | ||||||||
\(712\) | −3.93900 | −0.147620 | ||||||||
\(713\) | 22.6383 | 0.847812 | ||||||||
\(714\) | 7.35152 | 0.275124 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.2392 | −0.719003 | ||||||||
\(717\) | 23.7433 | 0.886711 | ||||||||
\(718\) | 16.5851 | 0.618950 | ||||||||
\(719\) | −42.3347 | −1.57882 | −0.789408 | − | 0.613869i | \(-0.789612\pi\) | ||||
−0.789408 | + | 0.613869i | \(0.789612\pi\) | |||||||
\(720\) | 0.350191 | 0.0130509 | ||||||||
\(721\) | 2.63773 | 0.0982341 | ||||||||
\(722\) | −17.8159 | −0.663041 | ||||||||
\(723\) | −17.7396 | −0.659743 | ||||||||
\(724\) | 9.57971 | 0.356027 | ||||||||
\(725\) | 15.8382 | 0.588215 | ||||||||
\(726\) | −14.0441 | −0.521227 | ||||||||
\(727\) | −6.22090 | −0.230720 | −0.115360 | − | 0.993324i | \(-0.536802\pi\) | ||||
−0.115360 | + | 0.993324i | \(0.536802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.1183 | 1.04142 | ||||||||
\(730\) | 13.2500 | 0.490403 | ||||||||
\(731\) | 5.68292 | 0.210191 | ||||||||
\(732\) | 5.95779 | 0.220206 | ||||||||
\(733\) | 6.42652 | 0.237369 | 0.118684 | − | 0.992932i | \(-0.462132\pi\) | ||||
0.118684 | + | 0.992932i | \(0.462132\pi\) | |||||||
\(734\) | 0.966148 | 0.0356612 | ||||||||
\(735\) | −4.32304 | −0.159458 | ||||||||
\(736\) | −2.04892 | −0.0755241 | ||||||||
\(737\) | 10.7952 | 0.397648 | ||||||||
\(738\) | 0.652793 | 0.0240296 | ||||||||
\(739\) | 0.244587 | 0.00899727 | 0.00449863 | − | 0.999990i | \(-0.498568\pi\) | ||||
0.00449863 | + | 0.999990i | \(0.498568\pi\) | |||||||
\(740\) | 3.24160 | 0.119164 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.29590 | −0.0475739 | ||||||||
\(743\) | −27.1414 | −0.995720 | −0.497860 | − | 0.867257i | \(-0.665881\pi\) | ||||
−0.497860 | + | 0.867257i | \(0.665881\pi\) | |||||||
\(744\) | −18.6950 | −0.685392 | ||||||||
\(745\) | −39.2054 | −1.43637 | ||||||||
\(746\) | 32.0901 | 1.17490 | ||||||||
\(747\) | −1.91484 | −0.0700603 | ||||||||
\(748\) | 7.13898 | 0.261027 | ||||||||
\(749\) | −10.1564 | −0.371108 | ||||||||
\(750\) | 15.0104 | 0.548103 | ||||||||
\(751\) | 17.1903 | 0.627283 | 0.313641 | − | 0.949542i | \(-0.398451\pi\) | ||||
0.313641 | + | 0.949542i | \(0.398451\pi\) | |||||||
\(752\) | −7.24698 | −0.264270 | ||||||||
\(753\) | 42.6021 | 1.55251 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.33140 | −0.0484548 | ||||||||
\(756\) | 5.30798 | 0.193049 | ||||||||
\(757\) | 34.7778 | 1.26402 | 0.632010 | − | 0.774960i | \(-0.282230\pi\) | ||||
0.632010 | + | 0.774960i | \(0.282230\pi\) | |||||||
\(758\) | −0.972853 | −0.0353356 | ||||||||
\(759\) | 5.69633 | 0.206764 | ||||||||
\(760\) | 2.78017 | 0.100847 | ||||||||
\(761\) | 15.0441 | 0.545349 | 0.272675 | − | 0.962106i | \(-0.412092\pi\) | ||||
0.272675 | + | 0.962106i | \(0.412092\pi\) | |||||||
\(762\) | −28.2760 | −1.02433 | ||||||||
\(763\) | 13.2567 | 0.479924 | ||||||||
\(764\) | 1.51142 | 0.0546812 | ||||||||
\(765\) | −1.52152 | −0.0550105 | ||||||||
\(766\) | −5.47650 | −0.197874 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.69202 | 0.0610556 | ||||||||
\(769\) | 28.8170 | 1.03917 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(770\) | −4.19806 | −0.151288 | ||||||||
\(771\) | 23.6588 | 0.852049 | ||||||||
\(772\) | −14.6310 | −0.526582 | ||||||||
\(773\) | 30.0428 | 1.08056 | 0.540282 | − | 0.841484i | \(-0.318317\pi\) | ||||
0.540282 | + | 0.841484i | \(0.318317\pi\) | |||||||
\(774\) | 0.179276 | 0.00644394 | ||||||||
\(775\) | −16.8807 | −0.606371 | ||||||||
\(776\) | 12.0489 | 0.432531 | ||||||||
\(777\) | 2.14675 | 0.0770143 | ||||||||
\(778\) | −32.5066 | −1.16542 | ||||||||
\(779\) | 5.18252 | 0.185683 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.3937 | 0.908659 | ||||||||
\(782\) | 8.90217 | 0.318341 | ||||||||
\(783\) | −55.0256 | −1.96645 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 58.9969 | 2.10569 | ||||||||
\(786\) | −9.89977 | −0.353113 | ||||||||
\(787\) | −11.1946 | −0.399045 | −0.199522 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199522 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(788\) | 22.4480 | 0.799678 | ||||||||
\(789\) | −38.3800 | −1.36636 | ||||||||
\(790\) | −26.1360 | −0.929877 | ||||||||
\(791\) | 9.86054 | 0.350601 | ||||||||
\(792\) | 0.225209 | 0.00800247 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −34.4674 | −1.22320 | ||||||||
\(795\) | −5.60222 | −0.198690 | ||||||||
\(796\) | −8.32975 | −0.295240 | ||||||||
\(797\) | −3.46788 | −0.122839 | −0.0614193 | − | 0.998112i | \(-0.519563\pi\) | ||||
−0.0614193 | + | 0.998112i | \(0.519563\pi\) | |||||||
\(798\) | 1.84117 | 0.0651766 | ||||||||
\(799\) | 31.4868 | 1.11392 | ||||||||
\(800\) | 1.52781 | 0.0540163 | ||||||||
\(801\) | 0.539893 | 0.0190762 | ||||||||
\(802\) | 12.9903 | 0.458704 | ||||||||
\(803\) | 8.52111 | 0.300703 | ||||||||
\(804\) | −11.1166 | −0.392053 | ||||||||
\(805\) | −5.23490 | −0.184506 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.4276 | −1.66953 | ||||||||
\(808\) | −1.54288 | −0.0542782 | ||||||||
\(809\) | 42.5303 | 1.49529 | 0.747643 | − | 0.664101i | \(-0.231185\pi\) | ||||
0.747643 | + | 0.664101i | \(0.231185\pi\) | |||||||
\(810\) | 21.8961 | 0.769349 | ||||||||
\(811\) | −21.2519 | −0.746255 | −0.373127 | − | 0.927780i | \(-0.621715\pi\) | ||||
−0.373127 | + | 0.927780i | \(0.621715\pi\) | |||||||
\(812\) | −10.3666 | −0.363796 | ||||||||
\(813\) | −0.272799 | −0.00956747 | ||||||||
\(814\) | 2.08469 | 0.0730683 | ||||||||
\(815\) | −58.5156 | −2.04971 | ||||||||
\(816\) | −7.35152 | −0.257355 | ||||||||
\(817\) | 1.42327 | 0.0497940 | ||||||||
\(818\) | 31.4771 | 1.10057 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.1685 | 0.424943 | ||||||||
\(821\) | 2.81295 | 0.0981728 | 0.0490864 | − | 0.998795i | \(-0.484369\pi\) | ||||
0.0490864 | + | 0.998795i | \(0.484369\pi\) | |||||||
\(822\) | 35.1933 | 1.22751 | ||||||||
\(823\) | 34.5244 | 1.20344 | 0.601722 | − | 0.798706i | \(-0.294482\pi\) | ||||
0.601722 | + | 0.798706i | \(0.294482\pi\) | |||||||
\(824\) | −2.63773 | −0.0918896 | ||||||||
\(825\) | −4.24757 | −0.147881 | ||||||||
\(826\) | −8.45473 | −0.294178 | ||||||||
\(827\) | −14.8877 | −0.517696 | −0.258848 | − | 0.965918i | \(-0.583343\pi\) | ||||
−0.258848 | + | 0.965918i | \(0.583343\pi\) | |||||||
\(828\) | 0.280831 | 0.00975957 | ||||||||
\(829\) | −27.6606 | −0.960691 | −0.480346 | − | 0.877079i | \(-0.659489\pi\) | ||||
−0.480346 | + | 0.877079i | \(0.659489\pi\) | |||||||
\(830\) | −35.6939 | −1.23895 | ||||||||
\(831\) | 45.9493 | 1.59396 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.34481 | −0.150539 | ||||||||
\(834\) | 8.10859 | 0.280777 | ||||||||
\(835\) | 20.5894 | 0.712526 | ||||||||
\(836\) | 1.78794 | 0.0618371 | ||||||||
\(837\) | 58.6474 | 2.02715 | ||||||||
\(838\) | −22.4101 | −0.774145 | ||||||||
\(839\) | 9.57673 | 0.330625 | 0.165313 | − | 0.986241i | \(-0.447137\pi\) | ||||
0.165313 | + | 0.986241i | \(0.447137\pi\) | |||||||
\(840\) | 4.32304 | 0.149159 | ||||||||
\(841\) | 78.4661 | 2.70573 | ||||||||
\(842\) | −17.2373 | −0.594036 | ||||||||
\(843\) | 26.1884 | 0.901975 | ||||||||
\(844\) | 10.4426 | 0.359451 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.993295 | 0.0341502 | ||||||||
\(847\) | 8.30021 | 0.285199 | ||||||||
\(848\) | 1.29590 | 0.0445013 | ||||||||
\(849\) | −23.2295 | −0.797235 | ||||||||
\(850\) | −6.63806 | −0.227683 | ||||||||
\(851\) | 2.59956 | 0.0891119 | ||||||||
\(852\) | −26.1497 | −0.895875 | ||||||||
\(853\) | −39.5816 | −1.35525 | −0.677625 | − | 0.735408i | \(-0.736991\pi\) | ||||
−0.677625 | + | 0.735408i | \(0.736991\pi\) | |||||||
\(854\) | −3.52111 | −0.120490 | ||||||||
\(855\) | −0.381059 | −0.0130319 | ||||||||
\(856\) | 10.1564 | 0.347140 | ||||||||
\(857\) | −17.6547 | −0.603073 | −0.301537 | − | 0.953455i | \(-0.597500\pi\) | ||||
−0.301537 | + | 0.953455i | \(0.597500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.6862 | 1.28584 | 0.642918 | − | 0.765935i | \(-0.277724\pi\) | ||||
0.642918 | + | 0.765935i | \(0.277724\pi\) | |||||||
\(860\) | 3.34183 | 0.113955 | ||||||||
\(861\) | 8.05861 | 0.274637 | ||||||||
\(862\) | 30.4349 | 1.03662 | ||||||||
\(863\) | −25.9758 | −0.884228 | −0.442114 | − | 0.896959i | \(-0.645771\pi\) | ||||
−0.442114 | + | 0.896959i | \(0.645771\pi\) | |||||||
\(864\) | −5.30798 | −0.180581 | ||||||||
\(865\) | −25.1068 | −0.853656 | ||||||||
\(866\) | 29.1812 | 0.991617 | ||||||||
\(867\) | 3.17662 | 0.107884 | ||||||||
\(868\) | 11.0489 | 0.375025 | ||||||||
\(869\) | −16.8082 | −0.570178 | ||||||||
\(870\) | −44.8152 | −1.51938 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.2567 | −0.448927 | ||||||||
\(873\) | −1.65146 | −0.0558936 | ||||||||
\(874\) | 2.22952 | 0.0754147 | ||||||||
\(875\) | −8.87130 | −0.299905 | ||||||||
\(876\) | −8.77479 | −0.296473 | ||||||||
\(877\) | −29.8133 | −1.00672 | −0.503362 | − | 0.864076i | \(-0.667904\pi\) | ||||
−0.503362 | + | 0.864076i | \(0.667904\pi\) | |||||||
\(878\) | −23.2349 | −0.784140 | ||||||||
\(879\) | −36.5388 | −1.23242 | ||||||||
\(880\) | 4.19806 | 0.141517 | ||||||||
\(881\) | 56.3769 | 1.89938 | 0.949692 | − | 0.313184i | \(-0.101396\pi\) | ||||
0.949692 | + | 0.313184i | \(0.101396\pi\) | |||||||
\(882\) | −0.137063 | −0.00461516 | ||||||||
\(883\) | −33.0726 | −1.11298 | −0.556491 | − | 0.830854i | \(-0.687853\pi\) | ||||
−0.556491 | + | 0.830854i | \(0.687853\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.5502 | −1.22862 | ||||||||
\(886\) | −26.1371 | −0.878092 | ||||||||
\(887\) | −42.7469 | −1.43530 | −0.717650 | − | 0.696404i | \(-0.754782\pi\) | ||||
−0.717650 | + | 0.696404i | \(0.754782\pi\) | |||||||
\(888\) | −2.14675 | −0.0720403 | ||||||||
\(889\) | 16.7114 | 0.560482 | ||||||||
\(890\) | 10.0640 | 0.337345 | ||||||||
\(891\) | 14.0814 | 0.471746 | ||||||||
\(892\) | 15.9312 | 0.533417 | ||||||||
\(893\) | 7.88577 | 0.263887 | ||||||||
\(894\) | 25.9638 | 0.868358 | ||||||||
\(895\) | 49.1554 | 1.64308 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.29350 | −0.143276 | ||||||||
\(899\) | −114.540 | −3.82011 | ||||||||
\(900\) | −0.209407 | −0.00698023 | ||||||||
\(901\) | −5.63043 | −0.187577 | ||||||||
\(902\) | 7.82563 | 0.260565 | ||||||||
\(903\) | 2.21313 | 0.0736483 | ||||||||
\(904\) | −9.86054 | −0.327957 | ||||||||
\(905\) | −24.4758 | −0.813602 | ||||||||
\(906\) | 0.881723 | 0.0292933 | ||||||||
\(907\) | −30.7881 | −1.02230 | −0.511150 | − | 0.859491i | \(-0.670780\pi\) | ||||
−0.511150 | + | 0.859491i | \(0.670780\pi\) | |||||||
\(908\) | −5.53079 | −0.183546 | ||||||||
\(909\) | 0.211472 | 0.00701408 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8901 | −0.393936 | −0.196968 | − | 0.980410i | \(-0.563110\pi\) | ||||
−0.196968 | + | 0.980410i | \(0.563110\pi\) | |||||||
\(912\) | −1.84117 | −0.0609671 | ||||||||
\(913\) | −22.9549 | −0.759697 | ||||||||
\(914\) | −0.781495 | −0.0258496 | ||||||||
\(915\) | −15.2219 | −0.503220 | ||||||||
\(916\) | −24.1739 | −0.798728 | ||||||||
\(917\) | 5.85086 | 0.193212 | ||||||||
\(918\) | 23.0622 | 0.761165 | ||||||||
\(919\) | −42.9705 | −1.41746 | −0.708732 | − | 0.705477i | \(-0.750733\pi\) | ||||
−0.708732 | + | 0.705477i | \(0.750733\pi\) | |||||||
\(920\) | 5.23490 | 0.172589 | ||||||||
\(921\) | −5.26609 | −0.173524 | ||||||||
\(922\) | −17.8103 | −0.586551 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.78017 | 0.0914608 | ||||||||
\(925\) | −1.93841 | −0.0637345 | ||||||||
\(926\) | −36.1226 | −1.18706 | ||||||||
\(927\) | 0.361536 | 0.0118744 | ||||||||
\(928\) | 10.3666 | 0.340300 | ||||||||
\(929\) | −15.0519 | −0.493837 | −0.246918 | − | 0.969036i | \(-0.579418\pi\) | ||||
−0.246918 | + | 0.969036i | \(0.579418\pi\) | |||||||
\(930\) | 47.7650 | 1.56627 | ||||||||
\(931\) | −1.08815 | −0.0356625 | ||||||||
\(932\) | 24.5284 | 0.803455 | ||||||||
\(933\) | −18.6122 | −0.609337 | ||||||||
\(934\) | −26.1142 | −0.854484 | ||||||||
\(935\) | −18.2398 | −0.596505 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.25965 | 0.237162 | 0.118581 | − | 0.992944i | \(-0.462165\pi\) | ||||
0.118581 | + | 0.992944i | \(0.462165\pi\) | |||||||
\(938\) | 6.57002 | 0.214519 | ||||||||
\(939\) | −51.3350 | −1.67525 | ||||||||
\(940\) | 18.5157 | 0.603917 | ||||||||
\(941\) | −25.4588 | −0.829932 | −0.414966 | − | 0.909837i | \(-0.636207\pi\) | ||||
−0.414966 | + | 0.909837i | \(0.636207\pi\) | |||||||
\(942\) | −39.0707 | −1.27299 | ||||||||
\(943\) | 9.75840 | 0.317777 | ||||||||
\(944\) | 8.45473 | 0.275178 | ||||||||
\(945\) | −13.5617 | −0.441161 | ||||||||
\(946\) | 2.14914 | 0.0698747 | ||||||||
\(947\) | −30.9831 | −1.00682 | −0.503408 | − | 0.864049i | \(-0.667921\pi\) | ||||
−0.503408 | + | 0.864049i | \(0.667921\pi\) | |||||||
\(948\) | 17.3086 | 0.562156 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.66248 | −0.0539380 | ||||||||
\(951\) | −11.9820 | −0.388541 | ||||||||
\(952\) | 4.34481 | 0.140816 | ||||||||
\(953\) | 12.4179 | 0.402255 | 0.201128 | − | 0.979565i | \(-0.435539\pi\) | ||||
0.201128 | + | 0.979565i | \(0.435539\pi\) | |||||||
\(954\) | −0.177620 | −0.00575066 | ||||||||
\(955\) | −3.86161 | −0.124959 | ||||||||
\(956\) | 14.0325 | 0.453844 | ||||||||
\(957\) | −28.8208 | −0.931645 | ||||||||
\(958\) | 7.21983 | 0.233262 | ||||||||
\(959\) | −20.7995 | −0.671652 | ||||||||
\(960\) | −4.32304 | −0.139526 | ||||||||
\(961\) | 91.0786 | 2.93802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.39208 | −0.0448590 | ||||||||
\(964\) | −10.4843 | −0.337676 | ||||||||
\(965\) | 37.3817 | 1.20336 | ||||||||
\(966\) | 3.46681 | 0.111543 | ||||||||
\(967\) | 54.8426 | 1.76362 | 0.881810 | − | 0.471605i | \(-0.156325\pi\) | ||||
0.881810 | + | 0.471605i | \(0.156325\pi\) | |||||||
\(968\) | −8.30021 | −0.266779 | ||||||||
\(969\) | 7.99953 | 0.256982 | ||||||||
\(970\) | −30.7845 | −0.988430 | ||||||||
\(971\) | 14.5338 | 0.466411 | 0.233206 | − | 0.972427i | \(-0.425078\pi\) | ||||
0.233206 | + | 0.972427i | \(0.425078\pi\) | |||||||
\(972\) | 1.42327 | 0.0456515 | ||||||||
\(973\) | −4.79225 | −0.153632 | ||||||||
\(974\) | −26.0858 | −0.835841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.52111 | 0.112708 | ||||||||
\(977\) | 42.8866 | 1.37206 | 0.686032 | − | 0.727571i | \(-0.259351\pi\) | ||||
0.686032 | + | 0.727571i | \(0.259351\pi\) | |||||||
\(978\) | 38.7520 | 1.23915 | ||||||||
\(979\) | 6.47219 | 0.206852 | ||||||||
\(980\) | −2.55496 | −0.0816151 | ||||||||
\(981\) | 1.81700 | 0.0580124 | ||||||||
\(982\) | −10.9879 | −0.350639 | ||||||||
\(983\) | 10.7918 | 0.344204 | 0.172102 | − | 0.985079i | \(-0.444944\pi\) | ||||
0.172102 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(984\) | −8.05861 | −0.256899 | ||||||||
\(985\) | −57.3538 | −1.82744 | ||||||||
\(986\) | −45.0409 | −1.43439 | ||||||||
\(987\) | 12.2620 | 0.390305 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.67994 | 0.0852171 | ||||||||
\(990\) | −0.575400 | −0.0182874 | ||||||||
\(991\) | −44.6045 | −1.41691 | −0.708454 | − | 0.705757i | \(-0.750607\pi\) | ||||
−0.708454 | + | 0.705757i | \(0.750607\pi\) | |||||||
\(992\) | −11.0489 | −0.350803 | ||||||||
\(993\) | 19.4112 | 0.615995 | ||||||||
\(994\) | 15.4547 | 0.490194 | ||||||||
\(995\) | 21.2822 | 0.674690 | ||||||||
\(996\) | 23.6383 | 0.749009 | ||||||||
\(997\) | 41.8751 | 1.32620 | 0.663099 | − | 0.748531i | \(-0.269241\pi\) | ||||
0.663099 | + | 0.748531i | \(0.269241\pi\) | |||||||
\(998\) | −6.78150 | −0.214664 | ||||||||
\(999\) | 6.73450 | 0.213070 |
(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 | 2366.2.a.bb.1.3 | yes | 3 | |
13.5 | odd | 4 | 2366.2.d.o.337.3 | 6 | |||
13.8 | odd | 4 | 2366.2.d.o.337.6 | 6 | |||
13.12 | even | 2 | 2366.2.a.w.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2366.2.a.w.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
2366.2.a.bb.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
2366.2.d.o.337.3 | 6 | 13.5 | odd | 4 | |||
2366.2.d.o.337.6 | 6 | 13.8 | odd | 4 |