Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, 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("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.07838 | −0.407588 | −0.203794 | − | 0.979014i | \(-0.565327\pi\) | ||||
−0.203794 | + | 0.979014i | \(0.565327\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41855 | 1.03073 | 0.515366 | − | 0.856970i | \(-0.327656\pi\) | ||||
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.921622 | −0.255612 | −0.127806 | − | 0.991799i | \(-0.540793\pi\) | ||||
−0.127806 | + | 0.991799i | \(0.540793\pi\) | |||||||
\(14\) | 1.07838 | 0.288209 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.340173 | 0.0825041 | 0.0412520 | − | 0.999149i | \(-0.486865\pi\) | ||||
0.0412520 | + | 0.999149i | \(0.486865\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.07838 | 0.235321 | ||||||||
\(22\) | −3.41855 | −0.728837 | ||||||||
\(23\) | −0.921622 | −0.192172 | −0.0960858 | − | 0.995373i | \(-0.530632\pi\) | ||||
−0.0960858 | + | 0.995373i | \(0.530632\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.921622 | 0.180745 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.07838 | −0.203794 | ||||||||
\(29\) | −1.41855 | −0.263418 | −0.131709 | − | 0.991288i | \(-0.542046\pi\) | ||||
−0.131709 | + | 0.991288i | \(0.542046\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.26180 | 1.30426 | 0.652128 | − | 0.758108i | \(-0.273876\pi\) | ||||
0.652128 | + | 0.758108i | \(0.273876\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.41855 | −0.595093 | ||||||||
\(34\) | −0.340173 | −0.0583392 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.60197 | 0.920958 | 0.460479 | − | 0.887671i | \(-0.347678\pi\) | ||||
0.460479 | + | 0.887671i | \(0.347678\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0.921622 | 0.147578 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.07838 | −0.168414 | −0.0842072 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842072 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(42\) | −1.07838 | −0.166397 | ||||||||
\(43\) | 0.738205 | 0.112575 | 0.0562876 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562876 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(44\) | 3.41855 | 0.515366 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.921622 | 0.135886 | ||||||||
\(47\) | −7.75872 | −1.13173 | −0.565863 | − | 0.824499i | \(-0.691457\pi\) | ||||
−0.565863 | + | 0.824499i | \(0.691457\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.83710 | −0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.340173 | −0.0476337 | ||||||||
\(52\) | −0.921622 | −0.127806 | ||||||||
\(53\) | 2.68035 | 0.368174 | 0.184087 | − | 0.982910i | \(-0.441067\pi\) | ||||
0.184087 | + | 0.982910i | \(0.441067\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.07838 | 0.144104 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 1.41855 | 0.186265 | ||||||||
\(59\) | 8.34017 | 1.08580 | 0.542899 | − | 0.839798i | \(-0.317327\pi\) | ||||
0.542899 | + | 0.839798i | \(0.317327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −7.26180 | −0.922249 | ||||||||
\(63\) | −1.07838 | −0.135863 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.41855 | 0.420795 | ||||||||
\(67\) | −4.68035 | −0.571795 | −0.285898 | − | 0.958260i | \(-0.592292\pi\) | ||||
−0.285898 | + | 0.958260i | \(0.592292\pi\) | |||||||
\(68\) | 0.340173 | 0.0412520 | ||||||||
\(69\) | 0.921622 | 0.110950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8371 | −1.28613 | −0.643064 | − | 0.765813i | \(-0.722337\pi\) | ||||
−0.643064 | + | 0.765813i | \(0.722337\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.83710 | −0.800222 | −0.400111 | − | 0.916467i | \(-0.631028\pi\) | ||||
−0.400111 | + | 0.916467i | \(0.631028\pi\) | |||||||
\(74\) | −5.60197 | −0.651216 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −3.68649 | −0.420114 | ||||||||
\(78\) | −0.921622 | −0.104353 | ||||||||
\(79\) | 4.73820 | 0.533090 | 0.266545 | − | 0.963823i | \(-0.414118\pi\) | ||||
0.266545 | + | 0.963823i | \(0.414118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.07838 | 0.119087 | ||||||||
\(83\) | 11.0205 | 1.20966 | 0.604830 | − | 0.796355i | \(-0.293241\pi\) | ||||
0.604830 | + | 0.796355i | \(0.293241\pi\) | |||||||
\(84\) | 1.07838 | 0.117661 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.738205 | −0.0796027 | ||||||||
\(87\) | 1.41855 | 0.152085 | ||||||||
\(88\) | −3.41855 | −0.364419 | ||||||||
\(89\) | 9.75872 | 1.03442 | 0.517211 | − | 0.855858i | \(-0.326970\pi\) | ||||
0.517211 | + | 0.855858i | \(0.326970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.993857 | 0.104185 | ||||||||
\(92\) | −0.921622 | −0.0960858 | ||||||||
\(93\) | −7.26180 | −0.753013 | ||||||||
\(94\) | 7.75872 | 0.800251 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 16.2557 | 1.65051 | 0.825256 | − | 0.564759i | \(-0.191031\pi\) | ||||
0.825256 | + | 0.564759i | \(0.191031\pi\) | |||||||
\(98\) | 5.83710 | 0.589636 | ||||||||
\(99\) | 3.41855 | 0.343577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.0205 | −1.29559 | −0.647795 | − | 0.761815i | \(-0.724309\pi\) | ||||
−0.647795 | + | 0.761815i | \(0.724309\pi\) | |||||||
\(102\) | 0.340173 | 0.0336821 | ||||||||
\(103\) | 14.3402 | 1.41298 | 0.706490 | − | 0.707723i | \(-0.250278\pi\) | ||||
0.706490 | + | 0.707723i | \(0.250278\pi\) | |||||||
\(104\) | 0.921622 | 0.0903725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.68035 | −0.260338 | ||||||||
\(107\) | −10.8371 | −1.04766 | −0.523831 | − | 0.851822i | \(-0.675498\pi\) | ||||
−0.523831 | + | 0.851822i | \(0.675498\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 18.6225 | 1.78371 | 0.891855 | − | 0.452321i | \(-0.149404\pi\) | ||||
0.891855 | + | 0.452321i | \(0.149404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.60197 | −0.531715 | ||||||||
\(112\) | −1.07838 | −0.101897 | ||||||||
\(113\) | −13.5174 | −1.27161 | −0.635807 | − | 0.771848i | \(-0.719333\pi\) | ||||
−0.635807 | + | 0.771848i | \(0.719333\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.41855 | −0.131709 | ||||||||
\(117\) | −0.921622 | −0.0852040 | ||||||||
\(118\) | −8.34017 | −0.767775 | ||||||||
\(119\) | −0.366835 | −0.0336277 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.686489 | 0.0624081 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 1.07838 | 0.0972340 | ||||||||
\(124\) | 7.26180 | 0.652128 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.07838 | 0.0960695 | ||||||||
\(127\) | 16.4969 | 1.46387 | 0.731933 | − | 0.681377i | \(-0.238618\pi\) | ||||
0.731933 | + | 0.681377i | \(0.238618\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.738205 | −0.0649953 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.581449 | 0.0508015 | 0.0254007 | − | 0.999677i | \(-0.491914\pi\) | ||||
0.0254007 | + | 0.999677i | \(0.491914\pi\) | |||||||
\(132\) | −3.41855 | −0.297547 | ||||||||
\(133\) | 1.07838 | 0.0935072 | ||||||||
\(134\) | 4.68035 | 0.404320 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.340173 | −0.0291696 | ||||||||
\(137\) | −5.81658 | −0.496944 | −0.248472 | − | 0.968639i | \(-0.579928\pi\) | ||||
−0.248472 | + | 0.968639i | \(0.579928\pi\) | |||||||
\(138\) | −0.921622 | −0.0784537 | ||||||||
\(139\) | 6.15676 | 0.522209 | 0.261105 | − | 0.965311i | \(-0.415913\pi\) | ||||
0.261105 | + | 0.965311i | \(0.415913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.75872 | 0.653402 | ||||||||
\(142\) | 10.8371 | 0.909429 | ||||||||
\(143\) | −3.15061 | −0.263467 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.83710 | 0.565843 | ||||||||
\(147\) | 5.83710 | 0.481436 | ||||||||
\(148\) | 5.60197 | 0.460479 | ||||||||
\(149\) | 8.34017 | 0.683254 | 0.341627 | − | 0.939836i | \(-0.389022\pi\) | ||||
0.341627 | + | 0.939836i | \(0.389022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2557 | 1.32287 | 0.661433 | − | 0.750004i | \(-0.269949\pi\) | ||||
0.661433 | + | 0.750004i | \(0.269949\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0.340173 | 0.0275014 | ||||||||
\(154\) | 3.68649 | 0.297066 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.921622 | 0.0737888 | ||||||||
\(157\) | 3.65983 | 0.292086 | 0.146043 | − | 0.989278i | \(-0.453346\pi\) | ||||
0.146043 | + | 0.989278i | \(0.453346\pi\) | |||||||
\(158\) | −4.73820 | −0.376951 | ||||||||
\(159\) | −2.68035 | −0.212565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.993857 | 0.0783269 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 6.89496 | 0.540055 | 0.270027 | − | 0.962853i | \(-0.412967\pi\) | ||||
0.270027 | + | 0.962853i | \(0.412967\pi\) | |||||||
\(164\) | −1.07838 | −0.0842072 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.0205 | −0.855358 | ||||||||
\(167\) | −4.68035 | −0.362176 | −0.181088 | − | 0.983467i | \(-0.557962\pi\) | ||||
−0.181088 | + | 0.983467i | \(0.557962\pi\) | |||||||
\(168\) | −1.07838 | −0.0831986 | ||||||||
\(169\) | −12.1506 | −0.934662 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0.738205 | 0.0562876 | ||||||||
\(173\) | −4.52359 | −0.343922 | −0.171961 | − | 0.985104i | \(-0.555010\pi\) | ||||
−0.171961 | + | 0.985104i | \(0.555010\pi\) | |||||||
\(174\) | −1.41855 | −0.107540 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41855 | 0.257683 | ||||||||
\(177\) | −8.34017 | −0.626886 | ||||||||
\(178\) | −9.75872 | −0.731447 | ||||||||
\(179\) | 14.4969 | 1.08355 | 0.541776 | − | 0.840523i | \(-0.317752\pi\) | ||||
0.541776 | + | 0.840523i | \(0.317752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.7792 | −0.949874 | −0.474937 | − | 0.880020i | \(-0.657529\pi\) | ||||
−0.474937 | + | 0.880020i | \(0.657529\pi\) | |||||||
\(182\) | −0.993857 | −0.0736696 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0.921622 | 0.0679429 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.26180 | 0.532461 | ||||||||
\(187\) | 1.16290 | 0.0850396 | ||||||||
\(188\) | −7.75872 | −0.565863 | ||||||||
\(189\) | 1.07838 | 0.0784404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.39803 | −0.318230 | −0.159115 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159115 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 24.6225 | 1.77237 | 0.886183 | − | 0.463336i | \(-0.153348\pi\) | ||||
0.886183 | + | 0.463336i | \(0.153348\pi\) | |||||||
\(194\) | −16.2557 | −1.16709 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.83710 | −0.416936 | ||||||||
\(197\) | −3.91548 | −0.278966 | −0.139483 | − | 0.990224i | \(-0.544544\pi\) | ||||
−0.139483 | + | 0.990224i | \(0.544544\pi\) | |||||||
\(198\) | −3.41855 | −0.242946 | ||||||||
\(199\) | 8.99386 | 0.637558 | 0.318779 | − | 0.947829i | \(-0.396727\pi\) | ||||
0.318779 | + | 0.947829i | \(0.396727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.68035 | 0.330126 | ||||||||
\(202\) | 13.0205 | 0.916121 | ||||||||
\(203\) | 1.52973 | 0.107366 | ||||||||
\(204\) | −0.340173 | −0.0238169 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.3402 | −0.999127 | ||||||||
\(207\) | −0.921622 | −0.0640572 | ||||||||
\(208\) | −0.921622 | −0.0639030 | ||||||||
\(209\) | −3.41855 | −0.236466 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.68035 | −0.322208 | −0.161104 | − | 0.986937i | \(-0.551506\pi\) | ||||
−0.161104 | + | 0.986937i | \(0.551506\pi\) | |||||||
\(212\) | 2.68035 | 0.184087 | ||||||||
\(213\) | 10.8371 | 0.742546 | ||||||||
\(214\) | 10.8371 | 0.740809 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −7.83096 | −0.531600 | ||||||||
\(218\) | −18.6225 | −1.26127 | ||||||||
\(219\) | 6.83710 | 0.462009 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.313511 | −0.0210890 | ||||||||
\(222\) | 5.60197 | 0.375979 | ||||||||
\(223\) | 14.3402 | 0.960289 | 0.480145 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480145 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(224\) | 1.07838 | 0.0720521 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.5174 | 0.899167 | ||||||||
\(227\) | 19.2039 | 1.27461 | 0.637305 | − | 0.770612i | \(-0.280049\pi\) | ||||
0.637305 | + | 0.770612i | \(0.280049\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 2.31351 | 0.152881 | 0.0764406 | − | 0.997074i | \(-0.475644\pi\) | ||||
0.0764406 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.68649 | 0.242553 | ||||||||
\(232\) | 1.41855 | 0.0931324 | ||||||||
\(233\) | 25.6475 | 1.68023 | 0.840113 | − | 0.542411i | \(-0.182489\pi\) | ||||
0.840113 | + | 0.542411i | \(0.182489\pi\) | |||||||
\(234\) | 0.921622 | 0.0602483 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.34017 | 0.542899 | ||||||||
\(237\) | −4.73820 | −0.307779 | ||||||||
\(238\) | 0.366835 | 0.0237784 | ||||||||
\(239\) | 3.60197 | 0.232992 | 0.116496 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116496 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.36683 | −0.152461 | −0.0762306 | − | 0.997090i | \(-0.524289\pi\) | ||||
−0.0762306 | + | 0.997090i | \(0.524289\pi\) | |||||||
\(242\) | −0.686489 | −0.0441292 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.07838 | −0.0687549 | ||||||||
\(247\) | 0.921622 | 0.0586414 | ||||||||
\(248\) | −7.26180 | −0.461124 | ||||||||
\(249\) | −11.0205 | −0.698397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.73820 | 0.425312 | 0.212656 | − | 0.977127i | \(-0.431789\pi\) | ||||
0.212656 | + | 0.977127i | \(0.431789\pi\) | |||||||
\(252\) | −1.07838 | −0.0679314 | ||||||||
\(253\) | −3.15061 | −0.198077 | ||||||||
\(254\) | −16.4969 | −1.03511 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.20394 | 0.574126 | 0.287063 | − | 0.957912i | \(-0.407321\pi\) | ||||
0.287063 | + | 0.957912i | \(0.407321\pi\) | |||||||
\(258\) | 0.738205 | 0.0459586 | ||||||||
\(259\) | −6.04104 | −0.375372 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41855 | −0.0878061 | ||||||||
\(262\) | −0.581449 | −0.0359221 | ||||||||
\(263\) | 25.7998 | 1.59088 | 0.795441 | − | 0.606031i | \(-0.207239\pi\) | ||||
0.795441 | + | 0.606031i | \(0.207239\pi\) | |||||||
\(264\) | 3.41855 | 0.210397 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.07838 | −0.0661196 | ||||||||
\(267\) | −9.75872 | −0.597224 | ||||||||
\(268\) | −4.68035 | −0.285898 | ||||||||
\(269\) | 4.73820 | 0.288893 | 0.144447 | − | 0.989513i | \(-0.453860\pi\) | ||||
0.144447 | + | 0.989513i | \(0.453860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3668 | 0.994214 | 0.497107 | − | 0.867689i | \(-0.334396\pi\) | ||||
0.497107 | + | 0.867689i | \(0.334396\pi\) | |||||||
\(272\) | 0.340173 | 0.0206260 | ||||||||
\(273\) | −0.993857 | −0.0601510 | ||||||||
\(274\) | 5.81658 | 0.351393 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.921622 | 0.0554751 | ||||||||
\(277\) | 12.6537 | 0.760286 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(278\) | −6.15676 | −0.369258 | ||||||||
\(279\) | 7.26180 | 0.434752 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.44521 | 0.563454 | 0.281727 | − | 0.959495i | \(-0.409093\pi\) | ||||
0.281727 | + | 0.959495i | \(0.409093\pi\) | |||||||
\(282\) | −7.75872 | −0.462025 | ||||||||
\(283\) | 15.8888 | 0.944492 | 0.472246 | − | 0.881467i | \(-0.343443\pi\) | ||||
0.472246 | + | 0.881467i | \(0.343443\pi\) | |||||||
\(284\) | −10.8371 | −0.643064 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.15061 | 0.186300 | ||||||||
\(287\) | 1.16290 | 0.0686437 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.8843 | −0.993193 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.2557 | −0.952923 | ||||||||
\(292\) | −6.83710 | −0.400111 | ||||||||
\(293\) | 4.47027 | 0.261156 | 0.130578 | − | 0.991438i | \(-0.458317\pi\) | ||||
0.130578 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(294\) | −5.83710 | −0.340427 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.60197 | −0.325608 | ||||||||
\(297\) | −3.41855 | −0.198364 | ||||||||
\(298\) | −8.34017 | −0.483133 | ||||||||
\(299\) | 0.849388 | 0.0491214 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.796064 | −0.0458843 | ||||||||
\(302\) | −16.2557 | −0.935408 | ||||||||
\(303\) | 13.0205 | 0.748009 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.340173 | −0.0194464 | ||||||||
\(307\) | 15.3197 | 0.874339 | 0.437169 | − | 0.899379i | \(-0.355981\pi\) | ||||
0.437169 | + | 0.899379i | \(0.355981\pi\) | |||||||
\(308\) | −3.68649 | −0.210057 | ||||||||
\(309\) | −14.3402 | −0.815784 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.39803 | −0.249390 | −0.124695 | − | 0.992195i | \(-0.539795\pi\) | ||||
−0.124695 | + | 0.992195i | \(0.539795\pi\) | |||||||
\(312\) | −0.921622 | −0.0521766 | ||||||||
\(313\) | 8.31351 | 0.469907 | 0.234954 | − | 0.972007i | \(-0.424506\pi\) | ||||
0.234954 | + | 0.972007i | \(0.424506\pi\) | |||||||
\(314\) | −3.65983 | −0.206536 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.73820 | 0.266545 | ||||||||
\(317\) | 0.470266 | 0.0264128 | 0.0132064 | − | 0.999913i | \(-0.495796\pi\) | ||||
0.0132064 | + | 0.999913i | \(0.495796\pi\) | |||||||
\(318\) | 2.68035 | 0.150306 | ||||||||
\(319\) | −4.84939 | −0.271514 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.8371 | 0.604868 | ||||||||
\(322\) | −0.993857 | −0.0553855 | ||||||||
\(323\) | −0.340173 | −0.0189277 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.89496 | −0.381877 | ||||||||
\(327\) | −18.6225 | −1.02983 | ||||||||
\(328\) | 1.07838 | 0.0595435 | ||||||||
\(329\) | 8.36683 | 0.461279 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5174 | 1.73236 | 0.866178 | − | 0.499736i | \(-0.166570\pi\) | ||||
0.866178 | + | 0.499736i | \(0.166570\pi\) | |||||||
\(332\) | 11.0205 | 0.604830 | ||||||||
\(333\) | 5.60197 | 0.306986 | ||||||||
\(334\) | 4.68035 | 0.256097 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.07838 | 0.0588303 | ||||||||
\(337\) | 0.0578588 | 0.00315177 | 0.00157589 | − | 0.999999i | \(-0.499498\pi\) | ||||
0.00157589 | + | 0.999999i | \(0.499498\pi\) | |||||||
\(338\) | 12.1506 | 0.660906 | ||||||||
\(339\) | 13.5174 | 0.734167 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.8248 | 1.34434 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 13.8432 | 0.747465 | ||||||||
\(344\) | −0.738205 | −0.0398013 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.52359 | 0.243190 | ||||||||
\(347\) | −6.34017 | −0.340358 | −0.170179 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170179 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(348\) | 1.41855 | 0.0760423 | ||||||||
\(349\) | −20.5236 | −1.09860 | −0.549301 | − | 0.835624i | \(-0.685106\pi\) | ||||
−0.549301 | + | 0.835624i | \(0.685106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.921622 | 0.0491926 | ||||||||
\(352\) | −3.41855 | −0.182209 | ||||||||
\(353\) | −22.3812 | −1.19123 | −0.595616 | − | 0.803269i | \(-0.703092\pi\) | ||||
−0.595616 | + | 0.803269i | \(0.703092\pi\) | |||||||
\(354\) | 8.34017 | 0.443275 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.75872 | 0.517211 | ||||||||
\(357\) | 0.366835 | 0.0194150 | ||||||||
\(358\) | −14.4969 | −0.766186 | ||||||||
\(359\) | −0.282314 | −0.0149000 | −0.00744999 | − | 0.999972i | \(-0.502371\pi\) | ||||
−0.00744999 | + | 0.999972i | \(0.502371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 12.7792 | 0.671662 | ||||||||
\(363\) | −0.686489 | −0.0360313 | ||||||||
\(364\) | 0.993857 | 0.0520923 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 27.9155 | 1.45718 | 0.728588 | − | 0.684952i | \(-0.240177\pi\) | ||||
0.728588 | + | 0.684952i | \(0.240177\pi\) | |||||||
\(368\) | −0.921622 | −0.0480429 | ||||||||
\(369\) | −1.07838 | −0.0561381 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.89043 | −0.150063 | ||||||||
\(372\) | −7.26180 | −0.376507 | ||||||||
\(373\) | 3.44521 | 0.178386 | 0.0891932 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891932 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(374\) | −1.16290 | −0.0601321 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.75872 | 0.400126 | ||||||||
\(377\) | 1.30737 | 0.0673329 | ||||||||
\(378\) | −1.07838 | −0.0554658 | ||||||||
\(379\) | −28.5113 | −1.46453 | −0.732264 | − | 0.681021i | \(-0.761536\pi\) | ||||
−0.732264 | + | 0.681021i | \(0.761536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.4969 | −0.845163 | ||||||||
\(382\) | 4.39803 | 0.225023 | ||||||||
\(383\) | 2.63931 | 0.134862 | 0.0674312 | − | 0.997724i | \(-0.478520\pi\) | ||||
0.0674312 | + | 0.997724i | \(0.478520\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.6225 | −1.25325 | ||||||||
\(387\) | 0.738205 | 0.0375251 | ||||||||
\(388\) | 16.2557 | 0.825256 | ||||||||
\(389\) | −22.1834 | −1.12474 | −0.562372 | − | 0.826884i | \(-0.690111\pi\) | ||||
−0.562372 | + | 0.826884i | \(0.690111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.313511 | −0.0158549 | ||||||||
\(392\) | 5.83710 | 0.294818 | ||||||||
\(393\) | −0.581449 | −0.0293302 | ||||||||
\(394\) | 3.91548 | 0.197259 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.41855 | 0.171789 | ||||||||
\(397\) | 24.2245 | 1.21579 | 0.607895 | − | 0.794017i | \(-0.292014\pi\) | ||||
0.607895 | + | 0.794017i | \(0.292014\pi\) | |||||||
\(398\) | −8.99386 | −0.450821 | ||||||||
\(399\) | −1.07838 | −0.0539864 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7649 | 0.637447 | 0.318724 | − | 0.947848i | \(-0.396746\pi\) | ||||
0.318724 | + | 0.947848i | \(0.396746\pi\) | |||||||
\(402\) | −4.68035 | −0.233434 | ||||||||
\(403\) | −6.69263 | −0.333384 | ||||||||
\(404\) | −13.0205 | −0.647795 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.52973 | −0.0759194 | ||||||||
\(407\) | 19.1506 | 0.949261 | ||||||||
\(408\) | 0.340173 | 0.0168411 | ||||||||
\(409\) | 22.8781 | 1.13125 | 0.565626 | − | 0.824662i | \(-0.308635\pi\) | ||||
0.565626 | + | 0.824662i | \(0.308635\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.81658 | 0.286911 | ||||||||
\(412\) | 14.3402 | 0.706490 | ||||||||
\(413\) | −8.99386 | −0.442559 | ||||||||
\(414\) | 0.921622 | 0.0452953 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.921622 | 0.0451862 | ||||||||
\(417\) | −6.15676 | −0.301498 | ||||||||
\(418\) | 3.41855 | 0.167207 | ||||||||
\(419\) | 3.47187 | 0.169612 | 0.0848061 | − | 0.996397i | \(-0.472973\pi\) | ||||
0.0848061 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.4657 | −0.997439 | −0.498719 | − | 0.866764i | \(-0.666196\pi\) | ||||
−0.498719 | + | 0.866764i | \(0.666196\pi\) | |||||||
\(422\) | 4.68035 | 0.227836 | ||||||||
\(423\) | −7.75872 | −0.377242 | ||||||||
\(424\) | −2.68035 | −0.130169 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.8371 | −0.525059 | ||||||||
\(427\) | −2.15676 | −0.104373 | ||||||||
\(428\) | −10.8371 | −0.523831 | ||||||||
\(429\) | 3.15061 | 0.152113 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.1917 | −1.59879 | −0.799393 | − | 0.600809i | \(-0.794845\pi\) | ||||
−0.799393 | + | 0.600809i | \(0.794845\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −41.1338 | −1.97676 | −0.988382 | − | 0.151991i | \(-0.951432\pi\) | ||||
−0.988382 | + | 0.151991i | \(0.951432\pi\) | |||||||
\(434\) | 7.83096 | 0.375898 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.6225 | 0.891855 | ||||||||
\(437\) | 0.921622 | 0.0440872 | ||||||||
\(438\) | −6.83710 | −0.326689 | ||||||||
\(439\) | 19.1461 | 0.913792 | 0.456896 | − | 0.889520i | \(-0.348961\pi\) | ||||
0.456896 | + | 0.889520i | \(0.348961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.83710 | −0.277957 | ||||||||
\(442\) | 0.313511 | 0.0149122 | ||||||||
\(443\) | −37.4908 | −1.78124 | −0.890620 | − | 0.454747i | \(-0.849730\pi\) | ||||
−0.890620 | + | 0.454747i | \(0.849730\pi\) | |||||||
\(444\) | −5.60197 | −0.265858 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.3402 | −0.679027 | ||||||||
\(447\) | −8.34017 | −0.394477 | ||||||||
\(448\) | −1.07838 | −0.0509486 | ||||||||
\(449\) | 6.43907 | 0.303878 | 0.151939 | − | 0.988390i | \(-0.451448\pi\) | ||||
0.151939 | + | 0.988390i | \(0.451448\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.68649 | −0.173590 | ||||||||
\(452\) | −13.5174 | −0.635807 | ||||||||
\(453\) | −16.2557 | −0.763757 | ||||||||
\(454\) | −19.2039 | −0.901285 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −13.6742 | −0.639652 | −0.319826 | − | 0.947476i | \(-0.603624\pi\) | ||||
−0.319826 | + | 0.947476i | \(0.603624\pi\) | |||||||
\(458\) | −2.31351 | −0.108103 | ||||||||
\(459\) | −0.340173 | −0.0158779 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5441 | 1.28286 | 0.641429 | − | 0.767183i | \(-0.278342\pi\) | ||||
0.641429 | + | 0.767183i | \(0.278342\pi\) | |||||||
\(462\) | −3.68649 | −0.171511 | ||||||||
\(463\) | 28.5958 | 1.32896 | 0.664480 | − | 0.747306i | \(-0.268653\pi\) | ||||
0.664480 | + | 0.747306i | \(0.268653\pi\) | |||||||
\(464\) | −1.41855 | −0.0658546 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.6475 | −1.18810 | ||||||||
\(467\) | 35.5318 | 1.64422 | 0.822108 | − | 0.569331i | \(-0.192798\pi\) | ||||
0.822108 | + | 0.569331i | \(0.192798\pi\) | |||||||
\(468\) | −0.921622 | −0.0426020 | ||||||||
\(469\) | 5.04718 | 0.233057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.65983 | −0.168636 | ||||||||
\(472\) | −8.34017 | −0.383888 | ||||||||
\(473\) | 2.52359 | 0.116035 | ||||||||
\(474\) | 4.73820 | 0.217633 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.366835 | −0.0168139 | ||||||||
\(477\) | 2.68035 | 0.122725 | ||||||||
\(478\) | −3.60197 | −0.164750 | ||||||||
\(479\) | 24.6491 | 1.12625 | 0.563124 | − | 0.826372i | \(-0.309599\pi\) | ||||
0.563124 | + | 0.826372i | \(0.309599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.16290 | −0.235408 | ||||||||
\(482\) | 2.36683 | 0.107806 | ||||||||
\(483\) | −0.993857 | −0.0452221 | ||||||||
\(484\) | 0.686489 | 0.0312040 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.3340 | −0.694851 | −0.347426 | − | 0.937708i | \(-0.612944\pi\) | ||||
−0.347426 | + | 0.937708i | \(0.612944\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | −6.89496 | −0.311801 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.7792 | −1.47931 | −0.739653 | − | 0.672988i | \(-0.765010\pi\) | ||||
−0.739653 | + | 0.672988i | \(0.765010\pi\) | |||||||
\(492\) | 1.07838 | 0.0486170 | ||||||||
\(493\) | −0.482553 | −0.0217331 | ||||||||
\(494\) | −0.921622 | −0.0414657 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.26180 | 0.326064 | ||||||||
\(497\) | 11.6865 | 0.524211 | ||||||||
\(498\) | 11.0205 | 0.493841 | ||||||||
\(499\) | −25.6742 | −1.14934 | −0.574668 | − | 0.818387i | \(-0.694869\pi\) | ||||
−0.574668 | + | 0.818387i | \(0.694869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.68035 | 0.209102 | ||||||||
\(502\) | −6.73820 | −0.300741 | ||||||||
\(503\) | 24.7526 | 1.10366 | 0.551832 | − | 0.833956i | \(-0.313929\pi\) | ||||
0.551832 | + | 0.833956i | \(0.313929\pi\) | |||||||
\(504\) | 1.07838 | 0.0480348 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.15061 | 0.140062 | ||||||||
\(507\) | 12.1506 | 0.539628 | ||||||||
\(508\) | 16.4969 | 0.731933 | ||||||||
\(509\) | −20.9360 | −0.927972 | −0.463986 | − | 0.885843i | \(-0.653581\pi\) | ||||
−0.463986 | + | 0.885843i | \(0.653581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.37298 | 0.326161 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −9.20394 | −0.405968 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.738205 | −0.0324977 | ||||||||
\(517\) | −26.5236 | −1.16651 | ||||||||
\(518\) | 6.04104 | 0.265428 | ||||||||
\(519\) | 4.52359 | 0.198564 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.5486 | 1.03168 | 0.515842 | − | 0.856683i | \(-0.327479\pi\) | ||||
0.515842 | + | 0.856683i | \(0.327479\pi\) | |||||||
\(522\) | 1.41855 | 0.0620883 | ||||||||
\(523\) | −14.7838 | −0.646449 | −0.323225 | − | 0.946322i | \(-0.604767\pi\) | ||||
−0.323225 | + | 0.946322i | \(0.604767\pi\) | |||||||
\(524\) | 0.581449 | 0.0254007 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.7998 | −1.12492 | ||||||||
\(527\) | 2.47027 | 0.107606 | ||||||||
\(528\) | −3.41855 | −0.148773 | ||||||||
\(529\) | −22.1506 | −0.963070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.34017 | 0.361933 | ||||||||
\(532\) | 1.07838 | 0.0467536 | ||||||||
\(533\) | 0.993857 | 0.0430487 | ||||||||
\(534\) | 9.75872 | 0.422301 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.68035 | 0.202160 | ||||||||
\(537\) | −14.4969 | −0.625589 | ||||||||
\(538\) | −4.73820 | −0.204279 | ||||||||
\(539\) | −19.9544 | −0.859498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.8371 | −1.75572 | −0.877862 | − | 0.478914i | \(-0.841031\pi\) | ||||
−0.877862 | + | 0.478914i | \(0.841031\pi\) | |||||||
\(542\) | −16.3668 | −0.703016 | ||||||||
\(543\) | 12.7792 | 0.548410 | ||||||||
\(544\) | −0.340173 | −0.0145848 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.993857 | 0.0425332 | ||||||||
\(547\) | 42.0410 | 1.79754 | 0.898772 | − | 0.438415i | \(-0.144460\pi\) | ||||
0.898772 | + | 0.438415i | \(0.144460\pi\) | |||||||
\(548\) | −5.81658 | −0.248472 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41855 | 0.0604323 | ||||||||
\(552\) | −0.921622 | −0.0392268 | ||||||||
\(553\) | −5.10957 | −0.217281 | ||||||||
\(554\) | −12.6537 | −0.537604 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.15676 | 0.261105 | ||||||||
\(557\) | −26.7526 | −1.13354 | −0.566772 | − | 0.823875i | \(-0.691808\pi\) | ||||
−0.566772 | + | 0.823875i | \(0.691808\pi\) | |||||||
\(558\) | −7.26180 | −0.307416 | ||||||||
\(559\) | −0.680346 | −0.0287756 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.16290 | −0.0490976 | ||||||||
\(562\) | −9.44521 | −0.398422 | ||||||||
\(563\) | −21.9877 | −0.926672 | −0.463336 | − | 0.886183i | \(-0.653348\pi\) | ||||
−0.463336 | + | 0.886183i | \(0.653348\pi\) | |||||||
\(564\) | 7.75872 | 0.326701 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.8888 | −0.667857 | ||||||||
\(567\) | −1.07838 | −0.0452876 | ||||||||
\(568\) | 10.8371 | 0.454715 | ||||||||
\(569\) | −32.5958 | −1.36649 | −0.683244 | − | 0.730190i | \(-0.739431\pi\) | ||||
−0.683244 | + | 0.730190i | \(0.739431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.1445 | −1.34520 | −0.672602 | − | 0.740004i | \(-0.734823\pi\) | ||||
−0.672602 | + | 0.740004i | \(0.734823\pi\) | |||||||
\(572\) | −3.15061 | −0.131734 | ||||||||
\(573\) | 4.39803 | 0.183730 | ||||||||
\(574\) | −1.16290 | −0.0485384 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −13.6742 | −0.569265 | −0.284632 | − | 0.958637i | \(-0.591871\pi\) | ||||
−0.284632 | + | 0.958637i | \(0.591871\pi\) | |||||||
\(578\) | 16.8843 | 0.702294 | ||||||||
\(579\) | −24.6225 | −1.02328 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.8843 | −0.493043 | ||||||||
\(582\) | 16.2557 | 0.673818 | ||||||||
\(583\) | 9.16290 | 0.379488 | ||||||||
\(584\) | 6.83710 | 0.282921 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.47027 | −0.184665 | ||||||||
\(587\) | −30.9672 | −1.27815 | −0.639076 | − | 0.769143i | \(-0.720683\pi\) | ||||
−0.639076 | + | 0.769143i | \(0.720683\pi\) | |||||||
\(588\) | 5.83710 | 0.240718 | ||||||||
\(589\) | −7.26180 | −0.299217 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.91548 | 0.161061 | ||||||||
\(592\) | 5.60197 | 0.230239 | ||||||||
\(593\) | −42.3812 | −1.74039 | −0.870194 | − | 0.492709i | \(-0.836007\pi\) | ||||
−0.870194 | + | 0.492709i | \(0.836007\pi\) | |||||||
\(594\) | 3.41855 | 0.140265 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.34017 | 0.341627 | ||||||||
\(597\) | −8.99386 | −0.368094 | ||||||||
\(598\) | −0.849388 | −0.0347340 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4764 | 0.468133 | 0.234066 | − | 0.972221i | \(-0.424797\pi\) | ||||
0.234066 | + | 0.972221i | \(0.424797\pi\) | |||||||
\(602\) | 0.796064 | 0.0324451 | ||||||||
\(603\) | −4.68035 | −0.190598 | ||||||||
\(604\) | 16.2557 | 0.661433 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.0205 | −0.528922 | ||||||||
\(607\) | −15.3340 | −0.622389 | −0.311195 | − | 0.950346i | \(-0.600729\pi\) | ||||
−0.311195 | + | 0.950346i | \(0.600729\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −1.52973 | −0.0619879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.15061 | 0.289283 | ||||||||
\(612\) | 0.340173 | 0.0137507 | ||||||||
\(613\) | 4.34017 | 0.175298 | 0.0876490 | − | 0.996151i | \(-0.472065\pi\) | ||||
0.0876490 | + | 0.996151i | \(0.472065\pi\) | |||||||
\(614\) | −15.3197 | −0.618251 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.68649 | 0.148533 | ||||||||
\(617\) | −30.1834 | −1.21514 | −0.607569 | − | 0.794267i | \(-0.707855\pi\) | ||||
−0.607569 | + | 0.794267i | \(0.707855\pi\) | |||||||
\(618\) | 14.3402 | 0.576846 | ||||||||
\(619\) | −7.94668 | −0.319404 | −0.159702 | − | 0.987165i | \(-0.551053\pi\) | ||||
−0.159702 | + | 0.987165i | \(0.551053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.921622 | 0.0369834 | ||||||||
\(622\) | 4.39803 | 0.176345 | ||||||||
\(623\) | −10.5236 | −0.421619 | ||||||||
\(624\) | 0.921622 | 0.0368944 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.31351 | −0.332275 | ||||||||
\(627\) | 3.41855 | 0.136524 | ||||||||
\(628\) | 3.65983 | 0.146043 | ||||||||
\(629\) | 1.90564 | 0.0759828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.68035 | 0.345559 | 0.172780 | − | 0.984961i | \(-0.444725\pi\) | ||||
0.172780 | + | 0.984961i | \(0.444725\pi\) | |||||||
\(632\) | −4.73820 | −0.188476 | ||||||||
\(633\) | 4.68035 | 0.186027 | ||||||||
\(634\) | −0.470266 | −0.0186767 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.68035 | −0.106283 | ||||||||
\(637\) | 5.37960 | 0.213148 | ||||||||
\(638\) | 4.84939 | 0.191989 | ||||||||
\(639\) | −10.8371 | −0.428709 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.6430 | −1.64480 | −0.822400 | − | 0.568910i | \(-0.807365\pi\) | ||||
−0.822400 | + | 0.568910i | \(0.807365\pi\) | |||||||
\(642\) | −10.8371 | −0.427706 | ||||||||
\(643\) | −29.7854 | −1.17462 | −0.587310 | − | 0.809362i | \(-0.699813\pi\) | ||||
−0.587310 | + | 0.809362i | \(0.699813\pi\) | |||||||
\(644\) | 0.993857 | 0.0391634 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.340173 | 0.0133839 | ||||||||
\(647\) | 28.9216 | 1.13703 | 0.568513 | − | 0.822674i | \(-0.307519\pi\) | ||||
0.568513 | + | 0.822674i | \(0.307519\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 28.5113 | 1.11917 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.83096 | 0.306919 | ||||||||
\(652\) | 6.89496 | 0.270027 | ||||||||
\(653\) | 41.9565 | 1.64189 | 0.820943 | − | 0.571011i | \(-0.193448\pi\) | ||||
0.820943 | + | 0.571011i | \(0.193448\pi\) | |||||||
\(654\) | 18.6225 | 0.728197 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.07838 | −0.0421036 | ||||||||
\(657\) | −6.83710 | −0.266741 | ||||||||
\(658\) | −8.36683 | −0.326173 | ||||||||
\(659\) | 43.0082 | 1.67536 | 0.837681 | − | 0.546159i | \(-0.183911\pi\) | ||||
0.837681 | + | 0.546159i | \(0.183911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.3090 | −1.33446 | −0.667232 | − | 0.744850i | \(-0.732521\pi\) | ||||
−0.667232 | + | 0.744850i | \(0.732521\pi\) | |||||||
\(662\) | −31.5174 | −1.22496 | ||||||||
\(663\) | 0.313511 | 0.0121758 | ||||||||
\(664\) | −11.0205 | −0.427679 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.60197 | −0.217072 | ||||||||
\(667\) | 1.30737 | 0.0506215 | ||||||||
\(668\) | −4.68035 | −0.181088 | ||||||||
\(669\) | −14.3402 | −0.554423 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.83710 | 0.263943 | ||||||||
\(672\) | −1.07838 | −0.0415993 | ||||||||
\(673\) | −31.0928 | −1.19854 | −0.599269 | − | 0.800548i | \(-0.704542\pi\) | ||||
−0.599269 | + | 0.800548i | \(0.704542\pi\) | |||||||
\(674\) | −0.0578588 | −0.00222864 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1506 | −0.467331 | ||||||||
\(677\) | −35.9877 | −1.38312 | −0.691560 | − | 0.722319i | \(-0.743076\pi\) | ||||
−0.691560 | + | 0.722319i | \(0.743076\pi\) | |||||||
\(678\) | −13.5174 | −0.519134 | ||||||||
\(679\) | −17.5297 | −0.672729 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.2039 | −0.735896 | ||||||||
\(682\) | −24.8248 | −0.950591 | ||||||||
\(683\) | −27.4017 | −1.04850 | −0.524249 | − | 0.851565i | \(-0.675654\pi\) | ||||
−0.524249 | + | 0.851565i | \(0.675654\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.8432 | −0.528538 | ||||||||
\(687\) | −2.31351 | −0.0882659 | ||||||||
\(688\) | 0.738205 | 0.0281438 | ||||||||
\(689\) | −2.47027 | −0.0941097 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.83096 | 0.145737 | 0.0728683 | − | 0.997342i | \(-0.476785\pi\) | ||||
0.0728683 | + | 0.997342i | \(0.476785\pi\) | |||||||
\(692\) | −4.52359 | −0.171961 | ||||||||
\(693\) | −3.68649 | −0.140038 | ||||||||
\(694\) | 6.34017 | 0.240670 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.41855 | −0.0537700 | ||||||||
\(697\) | −0.366835 | −0.0138949 | ||||||||
\(698\) | 20.5236 | 0.776829 | ||||||||
\(699\) | −25.6475 | −0.970079 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.5790 | 1.75926 | 0.879632 | − | 0.475654i | \(-0.157789\pi\) | ||||
0.879632 | + | 0.475654i | \(0.157789\pi\) | |||||||
\(702\) | −0.921622 | −0.0347844 | ||||||||
\(703\) | −5.60197 | −0.211282 | ||||||||
\(704\) | 3.41855 | 0.128841 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.3812 | 0.842328 | ||||||||
\(707\) | 14.0410 | 0.528068 | ||||||||
\(708\) | −8.34017 | −0.313443 | ||||||||
\(709\) | 15.1917 | 0.570534 | 0.285267 | − | 0.958448i | \(-0.407918\pi\) | ||||
0.285267 | + | 0.958448i | \(0.407918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.73820 | 0.177697 | ||||||||
\(712\) | −9.75872 | −0.365724 | ||||||||
\(713\) | −6.69263 | −0.250641 | ||||||||
\(714\) | −0.366835 | −0.0137285 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.4969 | 0.541776 | ||||||||
\(717\) | −3.60197 | −0.134518 | ||||||||
\(718\) | 0.282314 | 0.0105359 | ||||||||
\(719\) | −8.45136 | −0.315182 | −0.157591 | − | 0.987504i | \(-0.550373\pi\) | ||||
−0.157591 | + | 0.987504i | \(0.550373\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4641 | −0.575914 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 2.36683 | 0.0880235 | ||||||||
\(724\) | −12.7792 | −0.474937 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.686489 | 0.0254780 | ||||||||
\(727\) | 39.9688 | 1.48236 | 0.741180 | − | 0.671306i | \(-0.234266\pi\) | ||||
0.741180 | + | 0.671306i | \(0.234266\pi\) | |||||||
\(728\) | −0.993857 | −0.0368348 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.251117 | 0.00928791 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | 38.7480 | 1.43119 | 0.715596 | − | 0.698515i | \(-0.246155\pi\) | ||||
0.715596 | + | 0.698515i | \(0.246155\pi\) | |||||||
\(734\) | −27.9155 | −1.03038 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.921622 | 0.0339714 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 1.07838 | 0.0396956 | ||||||||
\(739\) | −15.1506 | −0.557324 | −0.278662 | − | 0.960389i | \(-0.589891\pi\) | ||||
−0.278662 | + | 0.960389i | \(0.589891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.921622 | −0.0338566 | ||||||||
\(742\) | 2.89043 | 0.106111 | ||||||||
\(743\) | 28.8781 | 1.05944 | 0.529718 | − | 0.848174i | \(-0.322298\pi\) | ||||
0.529718 | + | 0.848174i | \(0.322298\pi\) | |||||||
\(744\) | 7.26180 | 0.266230 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.44521 | −0.126138 | ||||||||
\(747\) | 11.0205 | 0.403220 | ||||||||
\(748\) | 1.16290 | 0.0425198 | ||||||||
\(749\) | 11.6865 | 0.427015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.2679 | −0.520644 | −0.260322 | − | 0.965522i | \(-0.583829\pi\) | ||||
−0.260322 | + | 0.965522i | \(0.583829\pi\) | |||||||
\(752\) | −7.75872 | −0.282932 | ||||||||
\(753\) | −6.73820 | −0.245554 | ||||||||
\(754\) | −1.30737 | −0.0476115 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.07838 | 0.0392202 | ||||||||
\(757\) | 22.2122 | 0.807315 | 0.403658 | − | 0.914910i | \(-0.367739\pi\) | ||||
0.403658 | + | 0.914910i | \(0.367739\pi\) | |||||||
\(758\) | 28.5113 | 1.03558 | ||||||||
\(759\) | 3.15061 | 0.114360 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.48255 | 0.0899925 | 0.0449962 | − | 0.998987i | \(-0.485672\pi\) | ||||
0.0449962 | + | 0.998987i | \(0.485672\pi\) | |||||||
\(762\) | 16.4969 | 0.597621 | ||||||||
\(763\) | −20.0821 | −0.727020 | ||||||||
\(764\) | −4.39803 | −0.159115 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.63931 | −0.0953621 | ||||||||
\(767\) | −7.68649 | −0.277543 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −22.3135 | −0.804646 | −0.402323 | − | 0.915498i | \(-0.631797\pi\) | ||||
−0.402323 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.20394 | −0.331472 | ||||||||
\(772\) | 24.6225 | 0.886183 | ||||||||
\(773\) | 24.2101 | 0.870776 | 0.435388 | − | 0.900243i | \(-0.356611\pi\) | ||||
0.435388 | + | 0.900243i | \(0.356611\pi\) | |||||||
\(774\) | −0.738205 | −0.0265342 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.2557 | −0.583544 | ||||||||
\(777\) | 6.04104 | 0.216721 | ||||||||
\(778\) | 22.1834 | 0.795314 | ||||||||
\(779\) | 1.07838 | 0.0386369 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.0472 | −1.32565 | ||||||||
\(782\) | 0.313511 | 0.0112111 | ||||||||
\(783\) | 1.41855 | 0.0506949 | ||||||||
\(784\) | −5.83710 | −0.208468 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.581449 | 0.0207396 | ||||||||
\(787\) | 31.0349 | 1.10627 | 0.553137 | − | 0.833090i | \(-0.313431\pi\) | ||||
0.553137 | + | 0.833090i | \(0.313431\pi\) | |||||||
\(788\) | −3.91548 | −0.139483 | ||||||||
\(789\) | −25.7998 | −0.918496 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.5769 | 0.518295 | ||||||||
\(792\) | −3.41855 | −0.121473 | ||||||||
\(793\) | −1.84324 | −0.0654555 | ||||||||
\(794\) | −24.2245 | −0.859694 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.99386 | 0.318779 | ||||||||
\(797\) | −25.2039 | −0.892769 | −0.446385 | − | 0.894841i | \(-0.647289\pi\) | ||||
−0.446385 | + | 0.894841i | \(0.647289\pi\) | |||||||
\(798\) | 1.07838 | 0.0381742 | ||||||||
\(799\) | −2.63931 | −0.0933720 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.75872 | 0.344808 | ||||||||
\(802\) | −12.7649 | −0.450743 | ||||||||
\(803\) | −23.3730 | −0.824814 | ||||||||
\(804\) | 4.68035 | 0.165063 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.69263 | 0.235738 | ||||||||
\(807\) | −4.73820 | −0.166793 | ||||||||
\(808\) | 13.0205 | 0.458060 | ||||||||
\(809\) | 17.9467 | 0.630972 | 0.315486 | − | 0.948930i | \(-0.397833\pi\) | ||||
0.315486 | + | 0.948930i | \(0.397833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.5113 | 1.42254 | 0.711272 | − | 0.702917i | \(-0.248119\pi\) | ||||
0.711272 | + | 0.702917i | \(0.248119\pi\) | |||||||
\(812\) | 1.52973 | 0.0536831 | ||||||||
\(813\) | −16.3668 | −0.574010 | ||||||||
\(814\) | −19.1506 | −0.671229 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.340173 | −0.0119084 | ||||||||
\(817\) | −0.738205 | −0.0258265 | ||||||||
\(818\) | −22.8781 | −0.799915 | ||||||||
\(819\) | 0.993857 | 0.0347282 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.3340 | 1.72177 | 0.860885 | − | 0.508800i | \(-0.169911\pi\) | ||||
0.860885 | + | 0.508800i | \(0.169911\pi\) | |||||||
\(822\) | −5.81658 | −0.202877 | ||||||||
\(823\) | −5.24742 | −0.182914 | −0.0914568 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914568 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(824\) | −14.3402 | −0.499564 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.99386 | 0.312936 | ||||||||
\(827\) | 22.5236 | 0.783222 | 0.391611 | − | 0.920131i | \(-0.371918\pi\) | ||||
0.391611 | + | 0.920131i | \(0.371918\pi\) | |||||||
\(828\) | −0.921622 | −0.0320286 | ||||||||
\(829\) | 43.2495 | 1.50212 | 0.751059 | − | 0.660235i | \(-0.229543\pi\) | ||||
0.751059 | + | 0.660235i | \(0.229543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.6537 | −0.438951 | ||||||||
\(832\) | −0.921622 | −0.0319515 | ||||||||
\(833\) | −1.98562 | −0.0687978 | ||||||||
\(834\) | 6.15676 | 0.213191 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.41855 | −0.118233 | ||||||||
\(837\) | −7.26180 | −0.251004 | ||||||||
\(838\) | −3.47187 | −0.119934 | ||||||||
\(839\) | −34.6681 | −1.19687 | −0.598437 | − | 0.801170i | \(-0.704211\pi\) | ||||
−0.598437 | + | 0.801170i | \(0.704211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9877 | −0.930611 | ||||||||
\(842\) | 20.4657 | 0.705296 | ||||||||
\(843\) | −9.44521 | −0.325310 | ||||||||
\(844\) | −4.68035 | −0.161104 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.75872 | 0.266750 | ||||||||
\(847\) | −0.740294 | −0.0254368 | ||||||||
\(848\) | 2.68035 | 0.0920435 | ||||||||
\(849\) | −15.8888 | −0.545303 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.16290 | −0.176982 | ||||||||
\(852\) | 10.8371 | 0.371273 | ||||||||
\(853\) | −28.0554 | −0.960599 | −0.480300 | − | 0.877105i | \(-0.659472\pi\) | ||||
−0.480300 | + | 0.877105i | \(0.659472\pi\) | |||||||
\(854\) | 2.15676 | 0.0738027 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.8371 | 0.370405 | ||||||||
\(857\) | −49.0882 | −1.67682 | −0.838411 | − | 0.545039i | \(-0.816515\pi\) | ||||
−0.838411 | + | 0.545039i | \(0.816515\pi\) | |||||||
\(858\) | −3.15061 | −0.107560 | ||||||||
\(859\) | −37.7275 | −1.28725 | −0.643623 | − | 0.765342i | \(-0.722570\pi\) | ||||
−0.643623 | + | 0.765342i | \(0.722570\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.16290 | −0.0396315 | ||||||||
\(862\) | 33.1917 | 1.13051 | ||||||||
\(863\) | 44.9939 | 1.53161 | 0.765804 | − | 0.643074i | \(-0.222341\pi\) | ||||
0.765804 | + | 0.643074i | \(0.222341\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 41.1338 | 1.39778 | ||||||||
\(867\) | 16.8843 | 0.573420 | ||||||||
\(868\) | −7.83096 | −0.265800 | ||||||||
\(869\) | 16.1978 | 0.549473 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.31351 | 0.146158 | ||||||||
\(872\) | −18.6225 | −0.630637 | ||||||||
\(873\) | 16.2557 | 0.550170 | ||||||||
\(874\) | −0.921622 | −0.0311743 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.83710 | 0.231004 | ||||||||
\(877\) | −2.64915 | −0.0894554 | −0.0447277 | − | 0.998999i | \(-0.514242\pi\) | ||||
−0.0447277 | + | 0.998999i | \(0.514242\pi\) | |||||||
\(878\) | −19.1461 | −0.646149 | ||||||||
\(879\) | −4.47027 | −0.150778 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.2511 | 1.01919 | 0.509593 | − | 0.860416i | \(-0.329796\pi\) | ||||
0.509593 | + | 0.860416i | \(0.329796\pi\) | |||||||
\(882\) | 5.83710 | 0.196545 | ||||||||
\(883\) | 19.9955 | 0.672901 | 0.336450 | − | 0.941701i | \(-0.390774\pi\) | ||||
0.336450 | + | 0.941701i | \(0.390774\pi\) | |||||||
\(884\) | −0.313511 | −0.0105445 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37.4908 | 1.25953 | ||||||||
\(887\) | −57.0759 | −1.91642 | −0.958211 | − | 0.286062i | \(-0.907654\pi\) | ||||
−0.958211 | + | 0.286062i | \(0.907654\pi\) | |||||||
\(888\) | 5.60197 | 0.187990 | ||||||||
\(889\) | −17.7899 | −0.596655 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.41855 | 0.114526 | ||||||||
\(892\) | 14.3402 | 0.480145 | ||||||||
\(893\) | 7.75872 | 0.259636 | ||||||||
\(894\) | 8.34017 | 0.278937 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.07838 | 0.0360261 | ||||||||
\(897\) | −0.849388 | −0.0283602 | ||||||||
\(898\) | −6.43907 | −0.214875 | ||||||||
\(899\) | −10.3012 | −0.343565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.911781 | 0.0303758 | ||||||||
\(902\) | 3.68649 | 0.122747 | ||||||||
\(903\) | 0.796064 | 0.0264913 | ||||||||
\(904\) | 13.5174 | 0.449584 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16.2557 | 0.540058 | ||||||||
\(907\) | 15.4017 | 0.511406 | 0.255703 | − | 0.966755i | \(-0.417693\pi\) | ||||
0.255703 | + | 0.966755i | \(0.417693\pi\) | |||||||
\(908\) | 19.2039 | 0.637305 | ||||||||
\(909\) | −13.0205 | −0.431863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5585 | −1.24437 | −0.622184 | − | 0.782871i | \(-0.713754\pi\) | ||||
−0.622184 | + | 0.782871i | \(0.713754\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 37.6742 | 1.24683 | ||||||||
\(914\) | 13.6742 | 0.452302 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.31351 | 0.0764406 | ||||||||
\(917\) | −0.627022 | −0.0207061 | ||||||||
\(918\) | 0.340173 | 0.0112274 | ||||||||
\(919\) | −10.0410 | −0.331223 | −0.165612 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165612 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3197 | −0.504800 | ||||||||
\(922\) | −27.5441 | −0.907117 | ||||||||
\(923\) | 9.98771 | 0.328750 | ||||||||
\(924\) | 3.68649 | 0.121277 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28.5958 | −0.939717 | ||||||||
\(927\) | 14.3402 | 0.470993 | ||||||||
\(928\) | 1.41855 | 0.0465662 | ||||||||
\(929\) | 1.26633 | 0.0415469 | 0.0207735 | − | 0.999784i | \(-0.493387\pi\) | ||||
0.0207735 | + | 0.999784i | \(0.493387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.83710 | 0.191303 | ||||||||
\(932\) | 25.6475 | 0.840113 | ||||||||
\(933\) | 4.39803 | 0.143985 | ||||||||
\(934\) | −35.5318 | −1.16264 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.921622 | 0.0301242 | ||||||||
\(937\) | −14.1568 | −0.462481 | −0.231241 | − | 0.972897i | \(-0.574278\pi\) | ||||
−0.231241 | + | 0.972897i | \(0.574278\pi\) | |||||||
\(938\) | −5.04718 | −0.164796 | ||||||||
\(939\) | −8.31351 | −0.271301 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.2085 | 0.495782 | 0.247891 | − | 0.968788i | \(-0.420263\pi\) | ||||
0.247891 | + | 0.968788i | \(0.420263\pi\) | |||||||
\(942\) | 3.65983 | 0.119244 | ||||||||
\(943\) | 0.993857 | 0.0323644 | ||||||||
\(944\) | 8.34017 | 0.271450 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.52359 | −0.0820490 | ||||||||
\(947\) | −2.53797 | −0.0824728 | −0.0412364 | − | 0.999149i | \(-0.513130\pi\) | ||||
−0.0412364 | + | 0.999149i | \(0.513130\pi\) | |||||||
\(948\) | −4.73820 | −0.153890 | ||||||||
\(949\) | 6.30122 | 0.204546 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.470266 | −0.0152494 | ||||||||
\(952\) | 0.366835 | 0.0118892 | ||||||||
\(953\) | 55.0759 | 1.78408 | 0.892042 | − | 0.451952i | \(-0.149272\pi\) | ||||
0.892042 | + | 0.451952i | \(0.149272\pi\) | |||||||
\(954\) | −2.68035 | −0.0867794 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.60197 | 0.116496 | ||||||||
\(957\) | 4.84939 | 0.156758 | ||||||||
\(958\) | −24.6491 | −0.796378 | ||||||||
\(959\) | 6.27247 | 0.202549 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.7337 | 0.701086 | ||||||||
\(962\) | 5.16290 | 0.166459 | ||||||||
\(963\) | −10.8371 | −0.349221 | ||||||||
\(964\) | −2.36683 | −0.0762306 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.993857 | 0.0319768 | ||||||||
\(967\) | −12.6491 | −0.406769 | −0.203385 | − | 0.979099i | \(-0.565194\pi\) | ||||
−0.203385 | + | 0.979099i | \(0.565194\pi\) | |||||||
\(968\) | −0.686489 | −0.0220646 | ||||||||
\(969\) | 0.340173 | 0.0109279 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.0677 | 1.22165 | 0.610825 | − | 0.791765i | \(-0.290838\pi\) | ||||
0.610825 | + | 0.791765i | \(0.290838\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −6.63931 | −0.212846 | ||||||||
\(974\) | 15.3340 | 0.491334 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −6.16904 | −0.197365 | −0.0986826 | − | 0.995119i | \(-0.531463\pi\) | ||||
−0.0986826 | + | 0.995119i | \(0.531463\pi\) | |||||||
\(978\) | 6.89496 | 0.220477 | ||||||||
\(979\) | 33.3607 | 1.06621 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6225 | 0.594570 | ||||||||
\(982\) | 32.7792 | 1.04603 | ||||||||
\(983\) | −1.98771 | −0.0633982 | −0.0316991 | − | 0.999497i | \(-0.510092\pi\) | ||||
−0.0316991 | + | 0.999497i | \(0.510092\pi\) | |||||||
\(984\) | −1.07838 | −0.0343774 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.482553 | 0.0153676 | ||||||||
\(987\) | −8.36683 | −0.266319 | ||||||||
\(988\) | 0.921622 | 0.0293207 | ||||||||
\(989\) | −0.680346 | −0.0216337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.907246 | −0.0288196 | −0.0144098 | − | 0.999896i | \(-0.504587\pi\) | ||||
−0.0144098 | + | 0.999896i | \(0.504587\pi\) | |||||||
\(992\) | −7.26180 | −0.230562 | ||||||||
\(993\) | −31.5174 | −1.00018 | ||||||||
\(994\) | −11.6865 | −0.370673 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.0205 | −0.349199 | ||||||||
\(997\) | −17.3874 | −0.550663 | −0.275332 | − | 0.961349i | \(-0.588788\pi\) | ||||
−0.275332 | + | 0.961349i | \(0.588788\pi\) | |||||||
\(998\) | 25.6742 | 0.812703 | ||||||||
\(999\) | −5.60197 | −0.177238 |
(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 | 2850.2.a.bk.1.2 | 3 | ||
3.2 | odd | 2 | 8550.2.a.cr.1.2 | 3 | |||
5.2 | odd | 4 | 570.2.d.d.229.3 | ✓ | 6 | ||
5.3 | odd | 4 | 570.2.d.d.229.6 | yes | 6 | ||
5.4 | even | 2 | 2850.2.a.bn.1.2 | 3 | |||
15.2 | even | 4 | 1710.2.d.e.1369.4 | 6 | |||
15.8 | even | 4 | 1710.2.d.e.1369.1 | 6 | |||
15.14 | odd | 2 | 8550.2.a.cf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.d.229.3 | ✓ | 6 | 5.2 | odd | 4 | ||
570.2.d.d.229.6 | yes | 6 | 5.3 | odd | 4 | ||
1710.2.d.e.1369.1 | 6 | 15.8 | even | 4 | |||
1710.2.d.e.1369.4 | 6 | 15.2 | even | 4 | |||
2850.2.a.bk.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2850.2.a.bn.1.2 | 3 | 5.4 | even | 2 | |||
8550.2.a.cf.1.2 | 3 | 15.14 | odd | 2 | |||
8550.2.a.cr.1.2 | 3 | 3.2 | odd | 2 |