Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 15 x^{10} + 47 x^{9} + 75 x^{8} - 256 x^{7} - 134 x^{6} + 571 x^{5} + 23 x^{4} - 479 x^{3} + 129 x^{2} + 88 x - 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.27963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27963 | 1.61194 | 0.805972 | − | 0.591954i | \(-0.201643\pi\) | ||||
0.805972 | + | 0.591954i | \(0.201643\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.19672 | 1.59836 | ||||||||
\(5\) | 2.95582 | 1.32188 | 0.660940 | − | 0.750438i | \(-0.270158\pi\) | ||||
0.660940 | + | 0.750438i | \(0.270158\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.183248 | 0.0692611 | 0.0346305 | − | 0.999400i | \(-0.488975\pi\) | ||||
0.0346305 | + | 0.999400i | \(0.488975\pi\) | |||||||
\(8\) | 2.72808 | 0.964523 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.73817 | 2.13080 | ||||||||
\(11\) | 2.01770 | 0.608361 | 0.304180 | − | 0.952614i | \(-0.401617\pi\) | ||||
0.304180 | + | 0.952614i | \(0.401617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.984021 | 0.272918 | 0.136459 | − | 0.990646i | \(-0.456428\pi\) | ||||
0.136459 | + | 0.990646i | \(0.456428\pi\) | |||||||
\(14\) | 0.417737 | 0.111645 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.174418 | −0.0436046 | ||||||||
\(17\) | 6.12205 | 1.48482 | 0.742408 | − | 0.669948i | \(-0.233684\pi\) | ||||
0.742408 | + | 0.669948i | \(0.233684\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.01138 | −0.690859 | −0.345429 | − | 0.938445i | \(-0.612267\pi\) | ||||
−0.345429 | + | 0.938445i | \(0.612267\pi\) | |||||||
\(20\) | 9.44892 | 2.11284 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.59962 | 0.980643 | ||||||||
\(23\) | −3.53879 | −0.737888 | −0.368944 | − | 0.929452i | \(-0.620281\pi\) | ||||
−0.368944 | + | 0.929452i | \(0.620281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.73684 | 0.747369 | ||||||||
\(26\) | 2.24321 | 0.439929 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.585791 | 0.110704 | ||||||||
\(29\) | −1.30450 | −0.242239 | −0.121119 | − | 0.992638i | \(-0.538648\pi\) | ||||
−0.121119 | + | 0.992638i | \(0.538648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.90832 | −1.59998 | −0.799990 | − | 0.600013i | \(-0.795162\pi\) | ||||
−0.799990 | + | 0.600013i | \(0.795162\pi\) | |||||||
\(32\) | −5.85377 | −1.03481 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.9560 | 2.39344 | ||||||||
\(35\) | 0.541646 | 0.0915549 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.94350 | 1.63470 | 0.817350 | − | 0.576141i | \(-0.195442\pi\) | ||||
0.817350 | + | 0.576141i | \(0.195442\pi\) | |||||||
\(38\) | −6.86484 | −1.11362 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.06371 | 1.27498 | ||||||||
\(41\) | 8.60897 | 1.34450 | 0.672248 | − | 0.740326i | \(-0.265329\pi\) | ||||
0.672248 | + | 0.740326i | \(0.265329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.48207 | 0.226013 | 0.113006 | − | 0.993594i | \(-0.463952\pi\) | ||||
0.113006 | + | 0.993594i | \(0.463952\pi\) | |||||||
\(44\) | 6.45004 | 0.972380 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.06713 | −1.18943 | ||||||||
\(47\) | −7.82999 | −1.14212 | −0.571061 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571061 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96642 | −0.995203 | ||||||||
\(50\) | 8.51863 | 1.20472 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.14564 | 0.436222 | ||||||||
\(53\) | −1.11957 | −0.153785 | −0.0768925 | − | 0.997039i | \(-0.524500\pi\) | ||||
−0.0768925 | + | 0.997039i | \(0.524500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.96396 | 0.804181 | ||||||||
\(56\) | 0.499914 | 0.0668039 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.97377 | −0.390475 | ||||||||
\(59\) | −5.43635 | −0.707753 | −0.353876 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353876 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.43259 | 0.951646 | 0.475823 | − | 0.879541i | \(-0.342150\pi\) | ||||
0.475823 | + | 0.879541i | \(0.342150\pi\) | |||||||
\(62\) | −20.3077 | −2.57908 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9956 | −1.62445 | ||||||||
\(65\) | 2.90859 | 0.360766 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.22250 | 1.00454 | 0.502269 | − | 0.864711i | \(-0.332499\pi\) | ||||
0.502269 | + | 0.864711i | \(0.332499\pi\) | |||||||
\(68\) | 19.5705 | 2.37327 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.23475 | 0.147581 | ||||||||
\(71\) | −12.2519 | −1.45404 | −0.727018 | − | 0.686619i | \(-0.759094\pi\) | ||||
−0.727018 | + | 0.686619i | \(0.759094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.79732 | 0.795567 | 0.397783 | − | 0.917479i | \(-0.369780\pi\) | ||||
0.397783 | + | 0.917479i | \(0.369780\pi\) | |||||||
\(74\) | 22.6675 | 2.63504 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.62655 | −1.10424 | ||||||||
\(77\) | 0.369739 | 0.0421357 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19772 | 0.472280 | 0.236140 | − | 0.971719i | \(-0.424118\pi\) | ||||
0.236140 | + | 0.971719i | \(0.424118\pi\) | |||||||
\(80\) | −0.515549 | −0.0576401 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19.6253 | 2.16725 | ||||||||
\(83\) | −3.07677 | −0.337719 | −0.168860 | − | 0.985640i | \(-0.554008\pi\) | ||||
−0.168860 | + | 0.985640i | \(0.554008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0957 | 1.96275 | ||||||||
\(86\) | 3.37856 | 0.364320 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.50446 | 0.586778 | ||||||||
\(89\) | −11.9885 | −1.27077 | −0.635387 | − | 0.772194i | \(-0.719159\pi\) | ||||
−0.635387 | + | 0.772194i | \(0.719159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.180320 | 0.0189026 | ||||||||
\(92\) | −11.3125 | −1.17941 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.8495 | −1.84104 | ||||||||
\(95\) | −8.90109 | −0.913233 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.27936 | 0.942176 | 0.471088 | − | 0.882086i | \(-0.343861\pi\) | ||||
0.471088 | + | 0.882086i | \(0.343861\pi\) | |||||||
\(98\) | −15.8809 | −1.60421 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.9456 | 1.19456 | ||||||||
\(101\) | −1.73615 | −0.172753 | −0.0863765 | − | 0.996263i | \(-0.527529\pi\) | ||||
−0.0863765 | + | 0.996263i | \(0.527529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2715 | −1.20914 | −0.604571 | − | 0.796551i | \(-0.706656\pi\) | ||||
−0.604571 | + | 0.796551i | \(0.706656\pi\) | |||||||
\(104\) | 2.68449 | 0.263236 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.55221 | −0.247893 | ||||||||
\(107\) | 8.45372 | 0.817252 | 0.408626 | − | 0.912702i | \(-0.366008\pi\) | ||||
0.408626 | + | 0.912702i | \(0.366008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.16094 | 0.302763 | 0.151382 | − | 0.988475i | \(-0.451628\pi\) | ||||
0.151382 | + | 0.988475i | \(0.451628\pi\) | |||||||
\(110\) | 13.5956 | 1.29629 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0319617 | −0.00302010 | ||||||||
\(113\) | −13.0509 | −1.22772 | −0.613862 | − | 0.789413i | \(-0.710385\pi\) | ||||
−0.613862 | + | 0.789413i | \(0.710385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.4600 | −0.975400 | ||||||||
\(116\) | −4.17011 | −0.387185 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.3929 | −1.14086 | ||||||||
\(119\) | 1.12185 | 0.102840 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.92887 | −0.629897 | ||||||||
\(122\) | 16.9436 | 1.53400 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −28.4774 | −2.55735 | ||||||||
\(125\) | −3.73365 | −0.333948 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.13953 | 0.722267 | 0.361133 | − | 0.932514i | \(-0.382390\pi\) | ||||
0.361133 | + | 0.932514i | \(0.382390\pi\) | |||||||
\(128\) | −17.9177 | −1.58371 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.63050 | 0.581534 | ||||||||
\(131\) | 12.9651 | 1.13276 | 0.566382 | − | 0.824143i | \(-0.308343\pi\) | ||||
0.566382 | + | 0.824143i | \(0.308343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.551829 | −0.0478496 | ||||||||
\(134\) | 18.7443 | 1.61926 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.7015 | 1.43214 | ||||||||
\(137\) | 10.6813 | 0.912565 | 0.456282 | − | 0.889835i | \(-0.349181\pi\) | ||||
0.456282 | + | 0.889835i | \(0.349181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6158 | 1.15488 | 0.577440 | − | 0.816433i | \(-0.304052\pi\) | ||||
0.577440 | + | 0.816433i | \(0.304052\pi\) | |||||||
\(140\) | 1.73149 | 0.146338 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −27.9299 | −2.34382 | ||||||||
\(143\) | 1.98546 | 0.166033 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.85585 | −0.320211 | ||||||||
\(146\) | 15.4954 | 1.28241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 31.7866 | 2.61284 | ||||||||
\(149\) | −1.78257 | −0.146034 | −0.0730169 | − | 0.997331i | \(-0.523263\pi\) | ||||
−0.0730169 | + | 0.997331i | \(0.523263\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.16896 | 0.0951282 | 0.0475641 | − | 0.998868i | \(-0.484854\pi\) | ||||
0.0475641 | + | 0.998868i | \(0.484854\pi\) | |||||||
\(152\) | −8.21530 | −0.666349 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.842870 | 0.0679204 | ||||||||
\(155\) | −26.3313 | −2.11498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.6019 | −1.72402 | −0.862010 | − | 0.506891i | \(-0.830795\pi\) | ||||
−0.862010 | + | 0.506891i | \(0.830795\pi\) | |||||||
\(158\) | 9.56925 | 0.761289 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −17.3027 | −1.36790 | ||||||||
\(161\) | −0.648474 | −0.0511069 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.24197 | 0.645561 | 0.322780 | − | 0.946474i | \(-0.395382\pi\) | ||||
0.322780 | + | 0.946474i | \(0.395382\pi\) | |||||||
\(164\) | 27.5205 | 2.14899 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.01390 | −0.544384 | ||||||||
\(167\) | −3.47700 | −0.269059 | −0.134529 | − | 0.990910i | \(-0.542952\pi\) | ||||
−0.134529 | + | 0.990910i | \(0.542952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0317 | −0.925516 | ||||||||
\(170\) | 41.2514 | 3.16384 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.73775 | 0.361250 | ||||||||
\(173\) | 4.07647 | 0.309929 | 0.154964 | − | 0.987920i | \(-0.450474\pi\) | ||||
0.154964 | + | 0.987920i | \(0.450474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.684768 | 0.0517636 | ||||||||
\(176\) | −0.351925 | −0.0265273 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.3293 | −2.04841 | ||||||||
\(179\) | −10.6107 | −0.793084 | −0.396542 | − | 0.918017i | \(-0.629790\pi\) | ||||
−0.396542 | + | 0.918017i | \(0.629790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.81115 | −0.580598 | −0.290299 | − | 0.956936i | \(-0.593755\pi\) | ||||
−0.290299 | + | 0.956936i | \(0.593755\pi\) | |||||||
\(182\) | 0.411062 | 0.0304700 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.65410 | −0.711710 | ||||||||
\(185\) | 29.3911 | 2.16088 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.3525 | 0.903304 | ||||||||
\(188\) | −25.0303 | −1.82552 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.2912 | −1.47208 | ||||||||
\(191\) | −9.29194 | −0.672341 | −0.336171 | − | 0.941801i | \(-0.609132\pi\) | ||||
−0.336171 | + | 0.941801i | \(0.609132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.49189 | −0.467297 | −0.233648 | − | 0.972321i | \(-0.575066\pi\) | ||||
−0.233648 | + | 0.972321i | \(0.575066\pi\) | |||||||
\(194\) | 21.1535 | 1.51873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.2697 | −1.59069 | ||||||||
\(197\) | −13.1871 | −0.939540 | −0.469770 | − | 0.882789i | \(-0.655663\pi\) | ||||
−0.469770 | + | 0.882789i | \(0.655663\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.2646 | −1.57830 | −0.789148 | − | 0.614203i | \(-0.789477\pi\) | ||||
−0.789148 | + | 0.614203i | \(0.789477\pi\) | |||||||
\(200\) | 10.1944 | 0.720854 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.95777 | −0.278468 | ||||||||
\(203\) | −0.239046 | −0.0167777 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.4465 | 1.77726 | ||||||||
\(206\) | −27.9744 | −1.94907 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.171631 | −0.0119005 | ||||||||
\(209\) | −6.07608 | −0.420291 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5785 | 1.07247 | 0.536234 | − | 0.844069i | \(-0.319846\pi\) | ||||
0.536234 | + | 0.844069i | \(0.319846\pi\) | |||||||
\(212\) | −3.57896 | −0.245804 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.2714 | 1.31736 | ||||||||
\(215\) | 4.38071 | 0.298762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.63243 | −0.110816 | ||||||||
\(218\) | 7.20579 | 0.488037 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.0651 | 1.28537 | ||||||||
\(221\) | 6.02423 | 0.405234 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.78655 | −0.186601 | −0.0933005 | − | 0.995638i | \(-0.529742\pi\) | ||||
−0.0933005 | + | 0.995638i | \(0.529742\pi\) | |||||||
\(224\) | −1.07269 | −0.0716721 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29.7512 | −1.97902 | ||||||||
\(227\) | −8.74781 | −0.580613 | −0.290306 | − | 0.956934i | \(-0.593757\pi\) | ||||
−0.290306 | + | 0.956934i | \(0.593757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.72893 | 0.378578 | 0.189289 | − | 0.981921i | \(-0.439382\pi\) | ||||
0.189289 | + | 0.981921i | \(0.439382\pi\) | |||||||
\(230\) | −23.8449 | −1.57229 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.55877 | −0.233645 | ||||||||
\(233\) | 10.2904 | 0.674149 | 0.337074 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337074 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.1440 | −1.50975 | ||||||||
\(236\) | −17.3785 | −1.13124 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.55741 | 0.165772 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.38133 | −0.539889 | −0.269945 | − | 0.962876i | \(-0.587005\pi\) | ||||
−0.269945 | + | 0.962876i | \(0.587005\pi\) | |||||||
\(242\) | −15.7953 | −1.01536 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.7599 | 1.52107 | ||||||||
\(245\) | −20.5915 | −1.31554 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.96327 | −0.188548 | ||||||||
\(248\) | −24.3026 | −1.54322 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.51136 | −0.538306 | ||||||||
\(251\) | −27.6155 | −1.74308 | −0.871538 | − | 0.490328i | \(-0.836877\pi\) | ||||
−0.871538 | + | 0.490328i | \(0.836877\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.14022 | −0.448902 | ||||||||
\(254\) | 18.5551 | 1.16425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.8544 | −0.928403 | ||||||||
\(257\) | 10.4899 | 0.654344 | 0.327172 | − | 0.944965i | \(-0.393904\pi\) | ||||
0.327172 | + | 0.944965i | \(0.393904\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.82212 | 0.113221 | ||||||||
\(260\) | 9.29794 | 0.576634 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 29.5556 | 1.82595 | ||||||||
\(263\) | 8.63295 | 0.532331 | 0.266165 | − | 0.963927i | \(-0.414243\pi\) | ||||
0.266165 | + | 0.963927i | \(0.414243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.30925 | −0.203286 | ||||||||
\(266\) | −1.25797 | −0.0771308 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.2850 | 1.60561 | ||||||||
\(269\) | 15.2172 | 0.927812 | 0.463906 | − | 0.885885i | \(-0.346448\pi\) | ||||
0.463906 | + | 0.885885i | \(0.346448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6574 | 0.768882 | 0.384441 | − | 0.923149i | \(-0.374394\pi\) | ||||
0.384441 | + | 0.923149i | \(0.374394\pi\) | |||||||
\(272\) | −1.06780 | −0.0647448 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.3494 | 1.47100 | ||||||||
\(275\) | 7.53985 | 0.454670 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.31116 | 0.0787798 | 0.0393899 | − | 0.999224i | \(-0.487459\pi\) | ||||
0.0393899 | + | 0.999224i | \(0.487459\pi\) | |||||||
\(278\) | 31.0391 | 1.86160 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.47765 | 0.0883068 | ||||||||
\(281\) | −0.523608 | −0.0312358 | −0.0156179 | − | 0.999878i | \(-0.504972\pi\) | ||||
−0.0156179 | + | 0.999878i | \(0.504972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.6919 | 1.64611 | 0.823057 | − | 0.567959i | \(-0.192267\pi\) | ||||
0.823057 | + | 0.567959i | \(0.192267\pi\) | |||||||
\(284\) | −39.1660 | −2.32407 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.52613 | 0.267636 | ||||||||
\(287\) | 1.57757 | 0.0931212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.4795 | 1.20468 | ||||||||
\(290\) | −8.78992 | −0.516162 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.7291 | 1.27160 | ||||||||
\(293\) | −1.42628 | −0.0833244 | −0.0416622 | − | 0.999132i | \(-0.513265\pi\) | ||||
−0.0416622 | + | 0.999132i | \(0.513265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.0689 | −0.935565 | ||||||||
\(296\) | 27.1267 | 1.57671 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.06360 | −0.235398 | ||||||||
\(299\) | −3.48224 | −0.201383 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.271585 | 0.0156539 | ||||||||
\(302\) | 2.66479 | 0.153341 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.525241 | 0.0301246 | ||||||||
\(305\) | 21.9694 | 1.25796 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.6823 | 1.75113 | 0.875565 | − | 0.483100i | \(-0.160489\pi\) | ||||
0.875565 | + | 0.483100i | \(0.160489\pi\) | |||||||
\(308\) | 1.18195 | 0.0673481 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −60.0257 | −3.40923 | ||||||||
\(311\) | 0.537158 | 0.0304594 | 0.0152297 | − | 0.999884i | \(-0.495152\pi\) | ||||
0.0152297 | + | 0.999884i | \(0.495152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.82980 | −0.272996 | −0.136498 | − | 0.990640i | \(-0.543585\pi\) | ||||
−0.136498 | + | 0.990640i | \(0.543585\pi\) | |||||||
\(314\) | −49.2444 | −2.77902 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4189 | 0.754874 | ||||||||
\(317\) | −32.0675 | −1.80109 | −0.900546 | − | 0.434761i | \(-0.856833\pi\) | ||||
−0.900546 | + | 0.434761i | \(0.856833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.63209 | −0.147369 | ||||||||
\(320\) | −38.4126 | −2.14733 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.47828 | −0.0823814 | ||||||||
\(323\) | −18.4358 | −1.02580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.67713 | 0.203971 | ||||||||
\(326\) | 18.7886 | 1.04061 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.4860 | 1.29680 | ||||||||
\(329\) | −1.43483 | −0.0791046 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.6623 | 1.63038 | 0.815192 | − | 0.579190i | \(-0.196631\pi\) | ||||
0.815192 | + | 0.579190i | \(0.196631\pi\) | |||||||
\(332\) | −9.83556 | −0.539797 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.92629 | −0.433707 | ||||||||
\(335\) | 24.3042 | 1.32788 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.37623 | 0.292862 | 0.146431 | − | 0.989221i | \(-0.453221\pi\) | ||||
0.146431 | + | 0.989221i | \(0.453221\pi\) | |||||||
\(338\) | −27.4278 | −1.49188 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 57.8468 | 3.13718 | ||||||||
\(341\) | −17.9743 | −0.973366 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.55931 | −0.138190 | ||||||||
\(344\) | 4.04320 | 0.217994 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.29286 | 0.499587 | ||||||||
\(347\) | 24.1031 | 1.29392 | 0.646961 | − | 0.762523i | \(-0.276040\pi\) | ||||
0.646961 | + | 0.762523i | \(0.276040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.6810 | −1.16056 | −0.580280 | − | 0.814417i | \(-0.697057\pi\) | ||||
−0.580280 | + | 0.814417i | \(0.697057\pi\) | |||||||
\(350\) | 1.56102 | 0.0834399 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.8112 | −0.629538 | ||||||||
\(353\) | 6.15172 | 0.327423 | 0.163712 | − | 0.986508i | \(-0.447653\pi\) | ||||
0.163712 | + | 0.986508i | \(0.447653\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.2144 | −1.92206 | ||||||||
\(356\) | −38.3237 | −2.03115 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.1886 | −1.27841 | ||||||||
\(359\) | −30.5171 | −1.61063 | −0.805315 | − | 0.592847i | \(-0.798004\pi\) | ||||
−0.805315 | + | 0.592847i | \(0.798004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.93157 | −0.522714 | ||||||||
\(362\) | −17.8065 | −0.935891 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.576431 | 0.0302132 | ||||||||
\(365\) | 20.0916 | 1.05164 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.1076 | 1.57160 | 0.785801 | − | 0.618480i | \(-0.212251\pi\) | ||||
0.785801 | + | 0.618480i | \(0.212251\pi\) | |||||||
\(368\) | 0.617229 | 0.0321753 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 67.0010 | 3.48321 | ||||||||
\(371\) | −0.205159 | −0.0106513 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2921 | −0.791796 | −0.395898 | − | 0.918295i | \(-0.629567\pi\) | ||||
−0.395898 | + | 0.918295i | \(0.629567\pi\) | |||||||
\(374\) | 28.1591 | 1.45607 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.3609 | −1.10160 | ||||||||
\(377\) | −1.28365 | −0.0661115 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3522 | −0.583123 | −0.291562 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291562 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(380\) | −28.4543 | −1.45968 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.1822 | −1.08378 | ||||||||
\(383\) | 3.50534 | 0.179114 | 0.0895572 | − | 0.995982i | \(-0.471455\pi\) | ||||
0.0895572 | + | 0.995982i | \(0.471455\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.09288 | 0.0556984 | ||||||||
\(386\) | −14.7991 | −0.753255 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 29.6635 | 1.50594 | ||||||||
\(389\) | 13.2532 | 0.671961 | 0.335981 | − | 0.941869i | \(-0.390932\pi\) | ||||
0.335981 | + | 0.941869i | \(0.390932\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.6646 | −1.09563 | ||||||||
\(392\) | −19.0050 | −0.959896 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −30.0617 | −1.51448 | ||||||||
\(395\) | 12.4077 | 0.624298 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.5340 | 1.23133 | 0.615663 | − | 0.788009i | \(-0.288888\pi\) | ||||
0.615663 | + | 0.788009i | \(0.288888\pi\) | |||||||
\(398\) | −50.7551 | −2.54412 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.651774 | −0.0325887 | ||||||||
\(401\) | 1.35306 | 0.0675688 | 0.0337844 | − | 0.999429i | \(-0.489244\pi\) | ||||
0.0337844 | + | 0.999429i | \(0.489244\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.76597 | −0.436664 | ||||||||
\(404\) | −5.54997 | −0.276122 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.544936 | −0.0270447 | ||||||||
\(407\) | 20.0630 | 0.994488 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4139 | −1.45443 | −0.727213 | − | 0.686412i | \(-0.759185\pi\) | ||||
−0.727213 | + | 0.686412i | \(0.759185\pi\) | |||||||
\(410\) | 58.0087 | 2.86485 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −39.2284 | −1.93265 | ||||||||
\(413\) | −0.996198 | −0.0490197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.09435 | −0.446424 | ||||||||
\(416\) | −5.76024 | −0.282419 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.8512 | −0.677486 | ||||||||
\(419\) | −12.3351 | −0.602608 | −0.301304 | − | 0.953528i | \(-0.597422\pi\) | ||||
−0.301304 | + | 0.953528i | \(0.597422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.2394 | −1.03515 | −0.517573 | − | 0.855639i | \(-0.673164\pi\) | ||||
−0.517573 | + | 0.855639i | \(0.673164\pi\) | |||||||
\(422\) | 35.5132 | 1.72876 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.05429 | −0.148329 | ||||||||
\(425\) | 22.8772 | 1.10971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.36200 | 0.0659120 | ||||||||
\(428\) | 27.0242 | 1.30626 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.98641 | 0.481587 | ||||||||
\(431\) | 30.5427 | 1.47119 | 0.735595 | − | 0.677422i | \(-0.236903\pi\) | ||||
0.735595 | + | 0.677422i | \(0.236903\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6727 | 1.42598 | 0.712989 | − | 0.701175i | \(-0.247341\pi\) | ||||
0.712989 | + | 0.701175i | \(0.247341\pi\) | |||||||
\(434\) | −3.72133 | −0.178630 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1047 | 0.483925 | ||||||||
\(437\) | 10.6566 | 0.509776 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4064 | −0.687579 | −0.343790 | − | 0.939047i | \(-0.611711\pi\) | ||||
−0.343790 | + | 0.939047i | \(0.611711\pi\) | |||||||
\(440\) | 16.2702 | 0.775650 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.7330 | 0.653213 | ||||||||
\(443\) | −24.9621 | −1.18598 | −0.592992 | − | 0.805209i | \(-0.702053\pi\) | ||||
−0.592992 | + | 0.805209i | \(0.702053\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.4357 | −1.67981 | ||||||||
\(446\) | −6.35230 | −0.300790 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.38141 | −0.112511 | ||||||||
\(449\) | −13.0255 | −0.614712 | −0.307356 | − | 0.951595i | \(-0.599444\pi\) | ||||
−0.307356 | + | 0.951595i | \(0.599444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.3704 | 0.817938 | ||||||||
\(452\) | −41.7201 | −1.96235 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.9418 | −0.935915 | ||||||||
\(455\) | 0.532991 | 0.0249870 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.9643 | −0.559668 | −0.279834 | − | 0.960048i | \(-0.590279\pi\) | ||||
−0.279834 | + | 0.960048i | \(0.590279\pi\) | |||||||
\(458\) | 13.0599 | 0.610247 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −33.4377 | −1.55904 | ||||||||
\(461\) | 16.4154 | 0.764542 | 0.382271 | − | 0.924050i | \(-0.375142\pi\) | ||||
0.382271 | + | 0.924050i | \(0.375142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3043 | −1.12952 | −0.564758 | − | 0.825257i | \(-0.691030\pi\) | ||||
−0.564758 | + | 0.825257i | \(0.691030\pi\) | |||||||
\(464\) | 0.227528 | 0.0105627 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.4584 | 1.08669 | ||||||||
\(467\) | −25.6887 | −1.18873 | −0.594366 | − | 0.804195i | \(-0.702597\pi\) | ||||
−0.594366 | + | 0.804195i | \(0.702597\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.50675 | 0.0695754 | ||||||||
\(470\) | −52.7598 | −2.43363 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.8308 | −0.682644 | ||||||||
\(473\) | 2.99037 | 0.137497 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.2531 | −0.516326 | ||||||||
\(476\) | 3.58624 | 0.164375 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.27963 | −0.104268 | ||||||||
\(479\) | 18.5787 | 0.848881 | 0.424441 | − | 0.905456i | \(-0.360471\pi\) | ||||
0.424441 | + | 0.905456i | \(0.360471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.78461 | 0.446140 | ||||||||
\(482\) | −19.1064 | −0.870271 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.1497 | −1.00680 | ||||||||
\(485\) | 27.4281 | 1.24544 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.99084 | −0.407414 | −0.203707 | − | 0.979032i | \(-0.565299\pi\) | ||||
−0.203707 | + | 0.979032i | \(0.565299\pi\) | |||||||
\(488\) | 20.2767 | 0.917884 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −46.9409 | −2.12057 | ||||||||
\(491\) | 10.3500 | 0.467090 | 0.233545 | − | 0.972346i | \(-0.424967\pi\) | ||||
0.233545 | + | 0.972346i | \(0.424967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.98620 | −0.359680 | ||||||||
\(494\) | −6.75515 | −0.303929 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.55377 | 0.0697665 | ||||||||
\(497\) | −2.24513 | −0.100708 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.9981 | −0.850473 | −0.425236 | − | 0.905082i | \(-0.639809\pi\) | ||||
−0.425236 | + | 0.905082i | \(0.639809\pi\) | |||||||
\(500\) | −11.9355 | −0.533770 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −62.9532 | −2.80974 | ||||||||
\(503\) | −35.2243 | −1.57057 | −0.785286 | − | 0.619133i | \(-0.787484\pi\) | ||||
−0.785286 | + | 0.619133i | \(0.787484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.13173 | −0.228359 | ||||||||
\(506\) | −16.2771 | −0.723605 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.0198 | 1.15444 | ||||||||
\(509\) | 31.4108 | 1.39226 | 0.696130 | − | 0.717915i | \(-0.254904\pi\) | ||||
0.696130 | + | 0.717915i | \(0.254904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.24559 | 0.0551018 | ||||||||
\(512\) | 1.97266 | 0.0871801 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.9132 | 1.05476 | ||||||||
\(515\) | −36.2722 | −1.59834 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.7986 | −0.694822 | ||||||||
\(518\) | 4.15377 | 0.182506 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.93486 | 0.347967 | ||||||||
\(521\) | −40.7369 | −1.78471 | −0.892357 | − | 0.451330i | \(-0.850950\pi\) | ||||
−0.892357 | + | 0.451330i | \(0.850950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.98147 | −0.305278 | −0.152639 | − | 0.988282i | \(-0.548777\pi\) | ||||
−0.152639 | + | 0.988282i | \(0.548777\pi\) | |||||||
\(524\) | 41.4458 | 1.81057 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.6800 | 0.858087 | ||||||||
\(527\) | −54.5372 | −2.37568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.4770 | −0.455522 | ||||||||
\(530\) | −7.54387 | −0.327685 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.76404 | −0.0764809 | ||||||||
\(533\) | 8.47141 | 0.366938 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.9876 | 1.08031 | ||||||||
\(536\) | 22.4316 | 0.968900 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.6897 | 1.49558 | ||||||||
\(539\) | −14.0562 | −0.605442 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.5536 | 1.70054 | 0.850272 | − | 0.526344i | \(-0.176438\pi\) | ||||
0.850272 | + | 0.526344i | \(0.176438\pi\) | |||||||
\(542\) | 28.8542 | 1.23939 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −35.8371 | −1.53650 | ||||||||
\(545\) | 9.34316 | 0.400217 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.1343 | 1.80153 | 0.900766 | − | 0.434305i | \(-0.143006\pi\) | ||||
0.900766 | + | 0.434305i | \(0.143006\pi\) | |||||||
\(548\) | 34.1451 | 1.45861 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.1881 | 0.732902 | ||||||||
\(551\) | 3.92834 | 0.167353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.769222 | 0.0327106 | ||||||||
\(554\) | 2.98896 | 0.126989 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 43.5260 | 1.84591 | ||||||||
\(557\) | −19.3767 | −0.821016 | −0.410508 | − | 0.911857i | \(-0.634649\pi\) | ||||
−0.410508 | + | 0.911857i | \(0.634649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.45838 | 0.0616831 | ||||||||
\(560\) | −0.0944730 | −0.00399221 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.19363 | −0.0503503 | ||||||||
\(563\) | −11.8935 | −0.501252 | −0.250626 | − | 0.968084i | \(-0.580637\pi\) | ||||
−0.250626 | + | 0.968084i | \(0.580637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.5760 | −1.62291 | ||||||||
\(566\) | 63.1274 | 2.65344 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.4242 | −1.40245 | ||||||||
\(569\) | 6.59449 | 0.276455 | 0.138228 | − | 0.990400i | \(-0.455859\pi\) | ||||
0.138228 | + | 0.990400i | \(0.455859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.55651 | −0.190684 | −0.0953420 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953420 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(572\) | 6.34698 | 0.265380 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.59628 | 0.150106 | ||||||||
\(575\) | −13.2239 | −0.551474 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.9337 | 1.82898 | 0.914491 | − | 0.404606i | \(-0.132591\pi\) | ||||
0.914491 | + | 0.404606i | \(0.132591\pi\) | |||||||
\(578\) | 46.6858 | 1.94187 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.3261 | −0.511813 | ||||||||
\(581\) | −0.563810 | −0.0233908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.25897 | −0.0935568 | ||||||||
\(584\) | 18.5437 | 0.767342 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.25140 | −0.134314 | ||||||||
\(587\) | −20.5317 | −0.847435 | −0.423717 | − | 0.905794i | \(-0.639275\pi\) | ||||
−0.423717 | + | 0.905794i | \(0.639275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.8264 | 1.10536 | ||||||||
\(590\) | −36.6311 | −1.50808 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.73433 | −0.0712805 | ||||||||
\(593\) | 43.0656 | 1.76849 | 0.884246 | − | 0.467022i | \(-0.154673\pi\) | ||||
0.884246 | + | 0.467022i | \(0.154673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.31598 | 0.135942 | ||||||||
\(596\) | −5.69838 | −0.233415 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.93823 | −0.324618 | ||||||||
\(599\) | −8.12826 | −0.332112 | −0.166056 | − | 0.986116i | \(-0.553103\pi\) | ||||
−0.166056 | + | 0.986116i | \(0.553103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.2747 | 1.15335 | 0.576674 | − | 0.816975i | \(-0.304350\pi\) | ||||
0.576674 | + | 0.816975i | \(0.304350\pi\) | |||||||
\(602\) | 0.619113 | 0.0252332 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.73682 | 0.152049 | ||||||||
\(605\) | −20.4805 | −0.832649 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1530 | −0.777395 | −0.388697 | − | 0.921365i | \(-0.627075\pi\) | ||||
−0.388697 | + | 0.921365i | \(0.627075\pi\) | |||||||
\(608\) | 17.6280 | 0.714908 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 50.0821 | 2.02776 | ||||||||
\(611\) | −7.70488 | −0.311706 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.8608 | −1.24646 | −0.623229 | − | 0.782040i | \(-0.714179\pi\) | ||||
−0.623229 | + | 0.782040i | \(0.714179\pi\) | |||||||
\(614\) | 69.9443 | 2.82272 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00868 | 0.0406409 | ||||||||
\(617\) | 41.4736 | 1.66966 | 0.834832 | − | 0.550504i | \(-0.185565\pi\) | ||||
0.834832 | + | 0.550504i | \(0.185565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 48.0533 | 1.93143 | 0.965713 | − | 0.259612i | \(-0.0835946\pi\) | ||||
0.965713 | + | 0.259612i | \(0.0835946\pi\) | |||||||
\(620\) | −84.1739 | −3.38051 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.22452 | 0.0490989 | ||||||||
\(623\) | −2.19685 | −0.0880151 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.7202 | −1.18881 | ||||||||
\(626\) | −11.0102 | −0.440055 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −69.0553 | −2.75561 | ||||||||
\(629\) | 60.8746 | 2.42723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.36423 | 0.0941183 | 0.0470592 | − | 0.998892i | \(-0.485015\pi\) | ||||
0.0470592 | + | 0.998892i | \(0.485015\pi\) | |||||||
\(632\) | 11.4517 | 0.455525 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −73.1021 | −2.90326 | ||||||||
\(635\) | 24.0590 | 0.954750 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.85511 | −0.271609 | ||||||||
\(638\) | −6.00019 | −0.237550 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −52.9613 | −2.09348 | ||||||||
\(641\) | 18.2702 | 0.721628 | 0.360814 | − | 0.932638i | \(-0.382499\pi\) | ||||
0.360814 | + | 0.932638i | \(0.382499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.0250 | −1.81505 | −0.907524 | − | 0.420001i | \(-0.862030\pi\) | ||||
−0.907524 | + | 0.420001i | \(0.862030\pi\) | |||||||
\(644\) | −2.07299 | −0.0816872 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −42.0269 | −1.65353 | ||||||||
\(647\) | 5.66198 | 0.222595 | 0.111298 | − | 0.993787i | \(-0.464499\pi\) | ||||
0.111298 | + | 0.993787i | \(0.464499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9690 | −0.430569 | ||||||||
\(650\) | 8.38251 | 0.328789 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26.3473 | 1.03184 | ||||||||
\(653\) | 20.6692 | 0.808849 | 0.404424 | − | 0.914571i | \(-0.367472\pi\) | ||||
0.404424 | + | 0.914571i | \(0.367472\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.3224 | 1.49738 | ||||||||
\(656\) | −1.50156 | −0.0586262 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.27088 | −0.127512 | ||||||||
\(659\) | 33.1249 | 1.29036 | 0.645182 | − | 0.764029i | \(-0.276781\pi\) | ||||
0.645182 | + | 0.764029i | \(0.276781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.5473 | 1.57711 | 0.788553 | − | 0.614967i | \(-0.210831\pi\) | ||||
0.788553 | + | 0.614967i | \(0.210831\pi\) | |||||||
\(662\) | 67.6190 | 2.62809 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.39367 | −0.325738 | ||||||||
\(665\) | −1.63110 | −0.0632515 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.61633 | 0.178745 | ||||||||
\(668\) | −11.1150 | −0.430053 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 55.4046 | 2.14047 | ||||||||
\(671\) | 14.9968 | 0.578944 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.1681 | 0.970158 | 0.485079 | − | 0.874470i | \(-0.338791\pi\) | ||||
0.485079 | + | 0.874470i | \(0.338791\pi\) | |||||||
\(674\) | 12.2558 | 0.472076 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −38.4620 | −1.47931 | ||||||||
\(677\) | 33.7809 | 1.29831 | 0.649153 | − | 0.760658i | \(-0.275123\pi\) | ||||
0.649153 | + | 0.760658i | \(0.275123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.70042 | 0.0652561 | ||||||||
\(680\) | 49.3664 | 1.89312 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −40.9749 | −1.56901 | ||||||||
\(683\) | −9.09130 | −0.347869 | −0.173934 | − | 0.984757i | \(-0.555648\pi\) | ||||
−0.173934 | + | 0.984757i | \(0.555648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.5719 | 1.20630 | ||||||||
\(686\) | −5.83429 | −0.222754 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.258499 | −0.00985520 | ||||||||
\(689\) | −1.10168 | −0.0419708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0041 | 0.722951 | 0.361476 | − | 0.932382i | \(-0.382273\pi\) | ||||
0.361476 | + | 0.932382i | \(0.382273\pi\) | |||||||
\(692\) | 13.0313 | 0.495378 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 54.9462 | 2.08573 | ||||||||
\(695\) | 40.2459 | 1.52661 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.7046 | 1.99633 | ||||||||
\(698\) | −49.4248 | −1.87076 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.18901 | 0.0827368 | ||||||||
\(701\) | −5.72366 | −0.216179 | −0.108090 | − | 0.994141i | \(-0.534473\pi\) | ||||
−0.108090 | + | 0.994141i | \(0.534473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.9437 | −1.12935 | ||||||||
\(704\) | −26.2213 | −0.988253 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.0237 | 0.527788 | ||||||||
\(707\) | −0.318145 | −0.0119651 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.9353 | 1.01158 | 0.505788 | − | 0.862658i | \(-0.331202\pi\) | ||||
0.505788 | + | 0.862658i | \(0.331202\pi\) | |||||||
\(710\) | −82.5555 | −3.09825 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −32.7055 | −1.22569 | ||||||||
\(713\) | 31.5246 | 1.18061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.86867 | 0.219476 | ||||||||
\(716\) | −33.9196 | −1.26763 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −69.5677 | −2.59624 | ||||||||
\(719\) | 43.7251 | 1.63067 | 0.815335 | − | 0.578989i | \(-0.196553\pi\) | ||||
0.815335 | + | 0.578989i | \(0.196553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.24871 | −0.0837465 | ||||||||
\(722\) | −22.6403 | −0.842586 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.9701 | −0.928005 | ||||||||
\(725\) | −4.87470 | −0.181042 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.0927 | 1.78366 | 0.891829 | − | 0.452373i | \(-0.149422\pi\) | ||||
0.891829 | + | 0.452373i | \(0.149422\pi\) | |||||||
\(728\) | 0.491927 | 0.0182320 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 45.8015 | 1.69519 | ||||||||
\(731\) | 9.07328 | 0.335587 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.9464 | −1.69707 | −0.848535 | − | 0.529139i | \(-0.822515\pi\) | ||||
−0.848535 | + | 0.529139i | \(0.822515\pi\) | |||||||
\(734\) | 68.6341 | 2.53333 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.7153 | 0.763574 | ||||||||
\(737\) | 16.5906 | 0.611121 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.2656 | −1.29727 | −0.648633 | − | 0.761101i | \(-0.724659\pi\) | ||||
−0.648633 | + | 0.761101i | \(0.724659\pi\) | |||||||
\(740\) | 93.9553 | 3.45386 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.467687 | −0.0171693 | ||||||||
\(743\) | −27.5772 | −1.01171 | −0.505855 | − | 0.862619i | \(-0.668823\pi\) | ||||
−0.505855 | + | 0.862619i | \(0.668823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.26895 | −0.193039 | ||||||||
\(746\) | −34.8604 | −1.27633 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 39.4875 | 1.44380 | ||||||||
\(749\) | 1.54912 | 0.0566038 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.38797 | −0.0506479 | −0.0253239 | − | 0.999679i | \(-0.508062\pi\) | ||||
−0.0253239 | + | 0.999679i | \(0.508062\pi\) | |||||||
\(752\) | 1.36569 | 0.0498018 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.92626 | −0.106568 | ||||||||
\(755\) | 3.45522 | 0.125748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.69778 | −0.352472 | −0.176236 | − | 0.984348i | \(-0.556392\pi\) | ||||
−0.176236 | + | 0.984348i | \(0.556392\pi\) | |||||||
\(758\) | −25.8788 | −0.939961 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.2829 | −0.880834 | ||||||||
\(761\) | −47.9029 | −1.73648 | −0.868240 | − | 0.496144i | \(-0.834749\pi\) | ||||
−0.868240 | + | 0.496144i | \(0.834749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.579235 | 0.0209697 | ||||||||
\(764\) | −29.7037 | −1.07464 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.99088 | 0.288722 | ||||||||
\(767\) | −5.34949 | −0.193159 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.1787 | 1.26858 | 0.634288 | − | 0.773097i | \(-0.281293\pi\) | ||||
0.634288 | + | 0.773097i | \(0.281293\pi\) | |||||||
\(770\) | 2.49137 | 0.0897826 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.7528 | −0.746908 | ||||||||
\(773\) | 49.0826 | 1.76538 | 0.882689 | − | 0.469958i | \(-0.155731\pi\) | ||||
0.882689 | + | 0.469958i | \(0.155731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.2890 | −1.19578 | ||||||||
\(776\) | 25.3149 | 0.908750 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.2123 | 1.08316 | ||||||||
\(779\) | −25.9249 | −0.928856 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7208 | −0.884578 | ||||||||
\(782\) | −49.3874 | −1.76609 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.21507 | 0.0433954 | ||||||||
\(785\) | −63.8513 | −2.27895 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.4029 | 0.834222 | 0.417111 | − | 0.908856i | \(-0.363043\pi\) | ||||
0.417111 | + | 0.908856i | \(0.363043\pi\) | |||||||
\(788\) | −42.1554 | −1.50172 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 28.2849 | 1.00633 | ||||||||
\(791\) | −2.39154 | −0.0850335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.31383 | 0.259722 | ||||||||
\(794\) | 55.9285 | 1.98483 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −71.1737 | −2.52268 | ||||||||
\(797\) | 40.7729 | 1.44425 | 0.722126 | − | 0.691762i | \(-0.243165\pi\) | ||||
0.722126 | + | 0.691762i | \(0.243165\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.9356 | −1.69584 | ||||||||
\(800\) | −21.8746 | −0.773385 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.08449 | 0.108917 | ||||||||
\(803\) | 13.7150 | 0.483992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.91677 | −0.0675572 | ||||||||
\(806\) | −19.9832 | −0.703878 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.73635 | −0.166624 | ||||||||
\(809\) | −5.76489 | −0.202683 | −0.101341 | − | 0.994852i | \(-0.532313\pi\) | ||||
−0.101341 | + | 0.994852i | \(0.532313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.4033 | 0.927146 | 0.463573 | − | 0.886059i | \(-0.346567\pi\) | ||||
0.463573 | + | 0.886059i | \(0.346567\pi\) | |||||||
\(812\) | −0.764163 | −0.0268169 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 45.7363 | 1.60306 | ||||||||
\(815\) | 24.3617 | 0.853354 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.46307 | −0.156143 | ||||||||
\(818\) | −67.0529 | −2.34445 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 81.3454 | 2.84071 | ||||||||
\(821\) | 17.6703 | 0.616697 | 0.308348 | − | 0.951273i | \(-0.400224\pi\) | ||||
0.308348 | + | 0.951273i | \(0.400224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.687817 | −0.0239758 | −0.0119879 | − | 0.999928i | \(-0.503816\pi\) | ||||
−0.0119879 | + | 0.999928i | \(0.503816\pi\) | |||||||
\(824\) | −33.4776 | −1.16625 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.27096 | −0.0790170 | ||||||||
\(827\) | 30.2380 | 1.05148 | 0.525739 | − | 0.850646i | \(-0.323789\pi\) | ||||
0.525739 | + | 0.850646i | \(0.323789\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 55.7717 | 1.93703 | 0.968516 | − | 0.248953i | \(-0.0800864\pi\) | ||||
0.968516 | + | 0.248953i | \(0.0800864\pi\) | |||||||
\(830\) | −20.7318 | −0.719611 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.7880 | −0.443343 | ||||||||
\(833\) | −42.6488 | −1.47769 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.2774 | −0.355663 | ||||||||
\(836\) | −19.4235 | −0.671777 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.1195 | −0.971370 | ||||||||
\(839\) | 43.3319 | 1.49598 | 0.747991 | − | 0.663709i | \(-0.231019\pi\) | ||||
0.747991 | + | 0.663709i | \(0.231019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2983 | −0.941320 | ||||||||
\(842\) | −48.4180 | −1.66860 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 49.8001 | 1.71419 | ||||||||
\(845\) | −35.5635 | −1.22342 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.26970 | −0.0436273 | ||||||||
\(848\) | 0.195274 | 0.00670574 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 52.1515 | 1.78878 | ||||||||
\(851\) | −35.1879 | −1.20623 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.6565 | 1.76869 | 0.884343 | − | 0.466837i | \(-0.154607\pi\) | ||||
0.884343 | + | 0.466837i | \(0.154607\pi\) | |||||||
\(854\) | 3.10487 | 0.106246 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.0625 | 0.788258 | ||||||||
\(857\) | 3.12227 | 0.106655 | 0.0533274 | − | 0.998577i | \(-0.483017\pi\) | ||||
0.0533274 | + | 0.998577i | \(0.483017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.7795 | 0.845466 | 0.422733 | − | 0.906254i | \(-0.361071\pi\) | ||||
0.422733 | + | 0.906254i | \(0.361071\pi\) | |||||||
\(860\) | 14.0039 | 0.477529 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 69.6261 | 2.37147 | ||||||||
\(863\) | 34.0270 | 1.15829 | 0.579146 | − | 0.815224i | \(-0.303386\pi\) | ||||
0.579146 | + | 0.815224i | \(0.303386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0493 | 0.409689 | ||||||||
\(866\) | 67.6428 | 2.29860 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.21841 | −0.177124 | ||||||||
\(869\) | 8.46976 | 0.287317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.09111 | 0.274157 | ||||||||
\(872\) | 8.62331 | 0.292022 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.2932 | 0.821730 | ||||||||
\(875\) | −0.684183 | −0.0231296 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.41045 | 0.0476275 | 0.0238138 | − | 0.999716i | \(-0.492419\pi\) | ||||
0.0238138 | + | 0.999716i | \(0.492419\pi\) | |||||||
\(878\) | −32.8412 | −1.10834 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.04022 | −0.0350660 | ||||||||
\(881\) | −3.11367 | −0.104902 | −0.0524511 | − | 0.998623i | \(-0.516703\pi\) | ||||
−0.0524511 | + | 0.998623i | \(0.516703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.280218 | −0.00943009 | −0.00471505 | − | 0.999989i | \(-0.501501\pi\) | ||||
−0.00471505 | + | 0.999989i | \(0.501501\pi\) | |||||||
\(884\) | 19.2578 | 0.647709 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.9043 | −1.91174 | ||||||||
\(887\) | −51.2584 | −1.72109 | −0.860545 | − | 0.509375i | \(-0.829877\pi\) | ||||
−0.860545 | + | 0.509375i | \(0.829877\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.49155 | 0.0500250 | ||||||||
\(890\) | −80.7802 | −2.70776 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.90781 | −0.298255 | ||||||||
\(893\) | 23.5791 | 0.789045 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3634 | −1.04836 | ||||||||
\(896\) | −3.28337 | −0.109690 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.6934 | −0.990881 | ||||||||
\(899\) | 11.6209 | 0.387578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.85408 | −0.228343 | ||||||||
\(902\) | 39.5980 | 1.31847 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −35.6039 | −1.18417 | ||||||||
\(905\) | −23.0883 | −0.767482 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.2941 | 1.00590 | 0.502949 | − | 0.864316i | \(-0.332248\pi\) | ||||
0.502949 | + | 0.864316i | \(0.332248\pi\) | |||||||
\(908\) | −27.9643 | −0.928029 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.21502 | 0.0402776 | ||||||||
\(911\) | −16.8868 | −0.559485 | −0.279742 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279742 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.20801 | −0.205455 | ||||||||
\(914\) | −27.2743 | −0.902153 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.3138 | 0.605105 | ||||||||
\(917\) | 2.37582 | 0.0784565 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.94560 | −0.163140 | −0.0815701 | − | 0.996668i | \(-0.525993\pi\) | ||||
−0.0815701 | + | 0.996668i | \(0.525993\pi\) | |||||||
\(920\) | −28.5357 | −0.940795 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 37.4211 | 1.23240 | ||||||||
\(923\) | −12.0562 | −0.396833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.1573 | 1.22172 | ||||||||
\(926\) | −55.4048 | −1.82071 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.63623 | 0.250672 | ||||||||
\(929\) | 30.1457 | 0.989048 | 0.494524 | − | 0.869164i | \(-0.335342\pi\) | ||||
0.494524 | + | 0.869164i | \(0.335342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.9786 | 0.687545 | ||||||||
\(932\) | 32.8956 | 1.07753 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −58.5608 | −1.91617 | ||||||||
\(935\) | 36.5117 | 1.19406 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.7140 | −1.55875 | −0.779374 | − | 0.626559i | \(-0.784463\pi\) | ||||
−0.779374 | + | 0.626559i | \(0.784463\pi\) | |||||||
\(938\) | 3.43484 | 0.112152 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −73.9849 | −2.41312 | ||||||||
\(941\) | −29.1888 | −0.951527 | −0.475763 | − | 0.879573i | \(-0.657828\pi\) | ||||
−0.475763 | + | 0.879573i | \(0.657828\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.4653 | −0.992087 | ||||||||
\(944\) | 0.948200 | 0.0308613 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.81694 | 0.221638 | ||||||||
\(947\) | −52.9404 | −1.72033 | −0.860166 | − | 0.510013i | \(-0.829640\pi\) | ||||
−0.860166 | + | 0.510013i | \(0.829640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.68871 | 0.217125 | ||||||||
\(950\) | −25.6529 | −0.832289 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.06050 | 0.0991914 | ||||||||
\(953\) | 53.2278 | 1.72422 | 0.862109 | − | 0.506722i | \(-0.169143\pi\) | ||||
0.862109 | + | 0.506722i | \(0.169143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.4653 | −0.888755 | ||||||||
\(956\) | −3.19672 | −0.103389 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42.3525 | 1.36835 | ||||||||
\(959\) | 1.95732 | 0.0632052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.3581 | 1.55994 | ||||||||
\(962\) | 22.3053 | 0.719152 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.7928 | −0.862937 | ||||||||
\(965\) | −19.1888 | −0.617710 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.6823 | 1.40473 | 0.702365 | − | 0.711817i | \(-0.252128\pi\) | ||||
0.702365 | + | 0.711817i | \(0.252128\pi\) | |||||||
\(968\) | −18.9025 | −0.607550 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 62.5259 | 2.00759 | ||||||||
\(971\) | 19.1283 | 0.613857 | 0.306928 | − | 0.951733i | \(-0.400699\pi\) | ||||
0.306928 | + | 0.951733i | \(0.400699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.49507 | 0.0799882 | ||||||||
\(974\) | −20.4958 | −0.656728 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.29638 | −0.0414961 | ||||||||
\(977\) | −35.6262 | −1.13978 | −0.569892 | − | 0.821720i | \(-0.693015\pi\) | ||||
−0.569892 | + | 0.821720i | \(0.693015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.1892 | −0.773089 | ||||||||
\(980\) | −65.8251 | −2.10271 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.5942 | 0.752922 | ||||||||
\(983\) | 39.5475 | 1.26137 | 0.630684 | − | 0.776039i | \(-0.282774\pi\) | ||||
0.630684 | + | 0.776039i | \(0.282774\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.9785 | −1.24196 | ||||||||
\(986\) | −18.2056 | −0.579784 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.47273 | −0.301368 | ||||||||
\(989\) | −5.24471 | −0.166772 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.2695 | 1.97806 | 0.989028 | − | 0.147728i | \(-0.0471960\pi\) | ||||
0.989028 | + | 0.147728i | \(0.0471960\pi\) | |||||||
\(992\) | 52.1473 | 1.65568 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.11808 | −0.162336 | ||||||||
\(995\) | −65.8100 | −2.08632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.16335 | 0.195195 | 0.0975976 | − | 0.995226i | \(-0.468884\pi\) | ||||
0.0975976 | + | 0.995226i | \(0.468884\pi\) | |||||||
\(998\) | −43.3087 | −1.37091 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.2.a.h.1.11 | 12 | ||
3.2 | odd | 2 | 717.2.a.g.1.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.2.a.g.1.2 | ✓ | 12 | 3.2 | odd | 2 | ||
2151.2.a.h.1.11 | 12 | 1.1 | even | 1 | trivial |