Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,2,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, 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("1075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(8.58391821729\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.24217.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 5x^{3} - x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.369680\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.369680 | 0.261404 | 0.130702 | − | 0.991422i | \(-0.458277\pi\) | ||||
0.130702 | + | 0.991422i | \(0.458277\pi\) | |||||||
\(3\) | −1.27684 | −0.737184 | −0.368592 | − | 0.929591i | \(-0.620160\pi\) | ||||
−0.368592 | + | 0.929591i | \(0.620160\pi\) | |||||||
\(4\) | −1.86334 | −0.931668 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.472023 | −0.192702 | ||||||||
\(7\) | 1.49366 | 0.564549 | 0.282274 | − | 0.959334i | \(-0.408911\pi\) | ||||
0.282274 | + | 0.959334i | \(0.408911\pi\) | |||||||
\(8\) | −1.42820 | −0.504945 | ||||||||
\(9\) | −1.36968 | −0.456560 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.68692 | 1.11165 | 0.555824 | − | 0.831300i | \(-0.312403\pi\) | ||||
0.555824 | + | 0.831300i | \(0.312403\pi\) | |||||||
\(12\) | 2.37918 | 0.686811 | ||||||||
\(13\) | 3.61627 | 1.00297 | 0.501486 | − | 0.865166i | \(-0.332787\pi\) | ||||
0.501486 | + | 0.865166i | \(0.332787\pi\) | |||||||
\(14\) | 0.552175 | 0.147575 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.19870 | 0.799674 | ||||||||
\(17\) | −5.00064 | −1.21283 | −0.606417 | − | 0.795147i | \(-0.707394\pi\) | ||||
−0.606417 | + | 0.795147i | \(0.707394\pi\) | |||||||
\(18\) | −0.506344 | −0.119346 | ||||||||
\(19\) | −6.14424 | −1.40959 | −0.704793 | − | 0.709413i | \(-0.748960\pi\) | ||||
−0.704793 | + | 0.709413i | \(0.748960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.90716 | −0.416176 | ||||||||
\(22\) | 1.36298 | 0.290589 | ||||||||
\(23\) | 1.06002 | 0.221030 | 0.110515 | − | 0.993874i | \(-0.464750\pi\) | ||||
0.110515 | + | 0.993874i | \(0.464750\pi\) | |||||||
\(24\) | 1.82358 | 0.372237 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.33686 | 0.262180 | ||||||||
\(27\) | 5.57938 | 1.07375 | ||||||||
\(28\) | −2.78318 | −0.525972 | ||||||||
\(29\) | 0.426517 | 0.0792023 | 0.0396011 | − | 0.999216i | \(-0.487391\pi\) | ||||
0.0396011 | + | 0.999216i | \(0.487391\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0955 | −1.81320 | −0.906602 | − | 0.421987i | \(-0.861333\pi\) | ||||
−0.906602 | + | 0.421987i | \(0.861333\pi\) | |||||||
\(32\) | 4.03889 | 0.713982 | ||||||||
\(33\) | −4.70760 | −0.819489 | ||||||||
\(34\) | −1.84864 | −0.317039 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.55218 | 0.425363 | ||||||||
\(37\) | 8.49430 | 1.39645 | 0.698227 | − | 0.715876i | \(-0.253973\pi\) | ||||
0.698227 | + | 0.715876i | \(0.253973\pi\) | |||||||
\(38\) | −2.27141 | −0.368471 | ||||||||
\(39\) | −4.61739 | −0.739375 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0225 | −1.56525 | −0.782627 | − | 0.622491i | \(-0.786121\pi\) | ||||
−0.782627 | + | 0.622491i | \(0.786121\pi\) | |||||||
\(42\) | −0.705039 | −0.108790 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −6.86997 | −1.03569 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.391870 | 0.0577781 | ||||||||
\(47\) | −12.7077 | −1.85361 | −0.926804 | − | 0.375546i | \(-0.877455\pi\) | ||||
−0.926804 | + | 0.375546i | \(0.877455\pi\) | |||||||
\(48\) | −4.08422 | −0.589507 | ||||||||
\(49\) | −4.76899 | −0.681285 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.38502 | 0.894082 | ||||||||
\(52\) | −6.73832 | −0.934437 | ||||||||
\(53\) | −1.96199 | −0.269500 | −0.134750 | − | 0.990880i | \(-0.543023\pi\) | ||||
−0.134750 | + | 0.990880i | \(0.543023\pi\) | |||||||
\(54\) | 2.06259 | 0.280683 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.13324 | −0.285066 | ||||||||
\(57\) | 7.84522 | 1.03912 | ||||||||
\(58\) | 0.157675 | 0.0207038 | ||||||||
\(59\) | −8.00909 | −1.04269 | −0.521347 | − | 0.853345i | \(-0.674570\pi\) | ||||
−0.521347 | + | 0.853345i | \(0.674570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.9538 | −1.91463 | −0.957317 | − | 0.289039i | \(-0.906664\pi\) | ||||
−0.957317 | + | 0.289039i | \(0.906664\pi\) | |||||||
\(62\) | −3.73211 | −0.473978 | ||||||||
\(63\) | −2.04583 | −0.257751 | ||||||||
\(64\) | −4.90429 | −0.613036 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.74031 | −0.214217 | ||||||||
\(67\) | 3.94582 | 0.482058 | 0.241029 | − | 0.970518i | \(-0.422515\pi\) | ||||
0.241029 | + | 0.970518i | \(0.422515\pi\) | |||||||
\(68\) | 9.31788 | 1.12996 | ||||||||
\(69\) | −1.35348 | −0.162940 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.62426 | 0.192765 | 0.0963824 | − | 0.995344i | \(-0.469273\pi\) | ||||
0.0963824 | + | 0.995344i | \(0.469273\pi\) | |||||||
\(72\) | 1.95618 | 0.230538 | ||||||||
\(73\) | −8.77264 | −1.02676 | −0.513380 | − | 0.858161i | \(-0.671607\pi\) | ||||
−0.513380 | + | 0.858161i | \(0.671607\pi\) | |||||||
\(74\) | 3.14018 | 0.365038 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.4488 | 1.31327 | ||||||||
\(77\) | 5.50699 | 0.627580 | ||||||||
\(78\) | −1.70696 | −0.193275 | ||||||||
\(79\) | 5.75850 | 0.647882 | 0.323941 | − | 0.946077i | \(-0.394992\pi\) | ||||
0.323941 | + | 0.946077i | \(0.394992\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01493 | −0.334993 | ||||||||
\(82\) | −3.70513 | −0.409163 | ||||||||
\(83\) | −1.38813 | −0.152367 | −0.0761834 | − | 0.997094i | \(-0.524273\pi\) | ||||
−0.0761834 | + | 0.997094i | \(0.524273\pi\) | |||||||
\(84\) | 3.55368 | 0.387738 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.369680 | −0.0398637 | ||||||||
\(87\) | −0.544594 | −0.0583866 | ||||||||
\(88\) | −5.26566 | −0.561321 | ||||||||
\(89\) | 10.8191 | 1.14682 | 0.573412 | − | 0.819267i | \(-0.305619\pi\) | ||||
0.573412 | + | 0.819267i | \(0.305619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.40146 | 0.566227 | ||||||||
\(92\) | −1.97518 | −0.205927 | ||||||||
\(93\) | 12.8903 | 1.33666 | ||||||||
\(94\) | −4.69778 | −0.484539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.15702 | −0.526336 | ||||||||
\(97\) | 4.27085 | 0.433639 | 0.216820 | − | 0.976212i | \(-0.430432\pi\) | ||||
0.216820 | + | 0.976212i | \(0.430432\pi\) | |||||||
\(98\) | −1.76300 | −0.178090 | ||||||||
\(99\) | −5.04990 | −0.507534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.92378 | −0.290927 | −0.145463 | − | 0.989364i | \(-0.546467\pi\) | ||||
−0.145463 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(102\) | 2.36042 | 0.233716 | ||||||||
\(103\) | 7.90261 | 0.778667 | 0.389334 | − | 0.921097i | \(-0.372705\pi\) | ||||
0.389334 | + | 0.921097i | \(0.372705\pi\) | |||||||
\(104\) | −5.16475 | −0.506446 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.725308 | −0.0704482 | ||||||||
\(107\) | 4.86805 | 0.470612 | 0.235306 | − | 0.971921i | \(-0.424391\pi\) | ||||
0.235306 | + | 0.971921i | \(0.424391\pi\) | |||||||
\(108\) | −10.3963 | −1.00038 | ||||||||
\(109\) | 10.1676 | 0.973878 | 0.486939 | − | 0.873436i | \(-0.338113\pi\) | ||||
0.486939 | + | 0.873436i | \(0.338113\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8459 | −1.02944 | ||||||||
\(112\) | 4.77775 | 0.451455 | ||||||||
\(113\) | −7.45085 | −0.700917 | −0.350459 | − | 0.936578i | \(-0.613974\pi\) | ||||
−0.350459 | + | 0.936578i | \(0.613974\pi\) | |||||||
\(114\) | 2.90022 | 0.271631 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.794745 | −0.0737902 | ||||||||
\(117\) | −4.95313 | −0.457917 | ||||||||
\(118\) | −2.96080 | −0.272564 | ||||||||
\(119\) | −7.46924 | −0.684704 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.59337 | 0.235761 | ||||||||
\(122\) | −5.52812 | −0.500492 | ||||||||
\(123\) | 12.7971 | 1.15388 | ||||||||
\(124\) | 18.8113 | 1.68930 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.756304 | −0.0673769 | ||||||||
\(127\) | −7.24053 | −0.642493 | −0.321247 | − | 0.946996i | \(-0.604102\pi\) | ||||
−0.321247 | + | 0.946996i | \(0.604102\pi\) | |||||||
\(128\) | −9.89081 | −0.874232 | ||||||||
\(129\) | 1.27684 | 0.112419 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.60582 | −0.227671 | −0.113836 | − | 0.993500i | \(-0.536314\pi\) | ||||
−0.113836 | + | 0.993500i | \(0.536314\pi\) | |||||||
\(132\) | 8.77185 | 0.763492 | ||||||||
\(133\) | −9.17739 | −0.795780 | ||||||||
\(134\) | 1.45869 | 0.126012 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.14192 | 0.612414 | ||||||||
\(137\) | −20.3626 | −1.73969 | −0.869847 | − | 0.493322i | \(-0.835782\pi\) | ||||
−0.869847 | + | 0.493322i | \(0.835782\pi\) | |||||||
\(138\) | −0.500355 | −0.0425930 | ||||||||
\(139\) | −9.90995 | −0.840551 | −0.420276 | − | 0.907397i | \(-0.638067\pi\) | ||||
−0.420276 | + | 0.907397i | \(0.638067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.2257 | 1.36645 | ||||||||
\(142\) | 0.600459 | 0.0503894 | ||||||||
\(143\) | 13.3329 | 1.11495 | ||||||||
\(144\) | −4.38119 | −0.365099 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.24307 | −0.268399 | ||||||||
\(147\) | 6.08924 | 0.502232 | ||||||||
\(148\) | −15.8277 | −1.30103 | ||||||||
\(149\) | −5.62745 | −0.461019 | −0.230509 | − | 0.973070i | \(-0.574039\pi\) | ||||
−0.230509 | + | 0.973070i | \(0.574039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.99840 | −0.162627 | −0.0813136 | − | 0.996689i | \(-0.525912\pi\) | ||||
−0.0813136 | + | 0.996689i | \(0.525912\pi\) | |||||||
\(152\) | 8.77521 | 0.711763 | ||||||||
\(153\) | 6.84928 | 0.553732 | ||||||||
\(154\) | 2.03583 | 0.164051 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.60376 | 0.688852 | ||||||||
\(157\) | 7.10674 | 0.567179 | 0.283590 | − | 0.958946i | \(-0.408475\pi\) | ||||
0.283590 | + | 0.958946i | \(0.408475\pi\) | |||||||
\(158\) | 2.12881 | 0.169359 | ||||||||
\(159\) | 2.50514 | 0.198671 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.58331 | 0.124782 | ||||||||
\(162\) | −1.11456 | −0.0875683 | ||||||||
\(163\) | −1.80915 | −0.141704 | −0.0708519 | − | 0.997487i | \(-0.522572\pi\) | ||||
−0.0708519 | + | 0.997487i | \(0.522572\pi\) | |||||||
\(164\) | 18.6753 | 1.45830 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.513163 | −0.0398292 | ||||||||
\(167\) | 18.7765 | 1.45297 | 0.726484 | − | 0.687183i | \(-0.241153\pi\) | ||||
0.726484 | + | 0.687183i | \(0.241153\pi\) | |||||||
\(168\) | 2.72380 | 0.210146 | ||||||||
\(169\) | 0.0773888 | 0.00595299 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.41565 | 0.643561 | ||||||||
\(172\) | 1.86334 | 0.142078 | ||||||||
\(173\) | 22.8361 | 1.73620 | 0.868099 | − | 0.496391i | \(-0.165342\pi\) | ||||
0.868099 | + | 0.496391i | \(0.165342\pi\) | |||||||
\(174\) | −0.201326 | −0.0152625 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.7933 | 0.888956 | ||||||||
\(177\) | 10.2263 | 0.768657 | ||||||||
\(178\) | 3.99962 | 0.299784 | ||||||||
\(179\) | 21.0013 | 1.56971 | 0.784856 | − | 0.619678i | \(-0.212737\pi\) | ||||
0.784856 | + | 0.619678i | \(0.212737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8122 | 1.02665 | 0.513326 | − | 0.858194i | \(-0.328413\pi\) | ||||
0.513326 | + | 0.858194i | \(0.328413\pi\) | |||||||
\(182\) | 1.99681 | 0.148014 | ||||||||
\(183\) | 19.0936 | 1.41144 | ||||||||
\(184\) | −1.51393 | −0.111608 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.76530 | 0.349409 | ||||||||
\(187\) | −18.4370 | −1.34824 | ||||||||
\(188\) | 23.6787 | 1.72695 | ||||||||
\(189\) | 8.33368 | 0.606186 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.23502 | −0.668223 | −0.334111 | − | 0.942534i | \(-0.608436\pi\) | ||||
−0.334111 | + | 0.942534i | \(0.608436\pi\) | |||||||
\(192\) | 6.26199 | 0.451920 | ||||||||
\(193\) | −22.2674 | −1.60285 | −0.801423 | − | 0.598098i | \(-0.795923\pi\) | ||||
−0.801423 | + | 0.598098i | \(0.795923\pi\) | |||||||
\(194\) | 1.57885 | 0.113355 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.88624 | 0.634731 | ||||||||
\(197\) | −15.1088 | −1.07646 | −0.538229 | − | 0.842799i | \(-0.680906\pi\) | ||||
−0.538229 | + | 0.842799i | \(0.680906\pi\) | |||||||
\(198\) | −1.86685 | −0.132671 | ||||||||
\(199\) | −3.09122 | −0.219131 | −0.109565 | − | 0.993980i | \(-0.534946\pi\) | ||||
−0.109565 | + | 0.993980i | \(0.534946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.03817 | −0.355365 | ||||||||
\(202\) | −1.08086 | −0.0760492 | ||||||||
\(203\) | 0.637070 | 0.0447136 | ||||||||
\(204\) | −11.8974 | −0.832988 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.92144 | 0.203546 | ||||||||
\(207\) | −1.45189 | −0.100914 | ||||||||
\(208\) | 11.5673 | 0.802051 | ||||||||
\(209\) | −22.6533 | −1.56696 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.82495 | −0.125634 | −0.0628172 | − | 0.998025i | \(-0.520009\pi\) | ||||
−0.0628172 | + | 0.998025i | \(0.520009\pi\) | |||||||
\(212\) | 3.65584 | 0.251084 | ||||||||
\(213\) | −2.07393 | −0.142103 | ||||||||
\(214\) | 1.79962 | 0.123020 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.96847 | −0.542186 | ||||||||
\(217\) | −15.0792 | −1.02364 | ||||||||
\(218\) | 3.75876 | 0.254575 | ||||||||
\(219\) | 11.2013 | 0.756911 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0837 | −1.21644 | ||||||||
\(222\) | −4.00950 | −0.269100 | ||||||||
\(223\) | 25.9914 | 1.74051 | 0.870257 | − | 0.492598i | \(-0.163953\pi\) | ||||
0.870257 | + | 0.492598i | \(0.163953\pi\) | |||||||
\(224\) | 6.03272 | 0.403078 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.75443 | −0.183222 | ||||||||
\(227\) | −21.5629 | −1.43118 | −0.715588 | − | 0.698522i | \(-0.753841\pi\) | ||||
−0.715588 | + | 0.698522i | \(0.753841\pi\) | |||||||
\(228\) | −14.6183 | −0.968119 | ||||||||
\(229\) | −13.9807 | −0.923868 | −0.461934 | − | 0.886914i | \(-0.652844\pi\) | ||||
−0.461934 | + | 0.886914i | \(0.652844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.03154 | −0.462641 | ||||||||
\(232\) | −0.609152 | −0.0399928 | ||||||||
\(233\) | 9.27410 | 0.607566 | 0.303783 | − | 0.952741i | \(-0.401750\pi\) | ||||
0.303783 | + | 0.952741i | \(0.401750\pi\) | |||||||
\(234\) | −1.83108 | −0.119701 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 14.9236 | 0.971445 | ||||||||
\(237\) | −7.35269 | −0.477608 | ||||||||
\(238\) | −2.76123 | −0.178984 | ||||||||
\(239\) | 19.8255 | 1.28240 | 0.641202 | − | 0.767372i | \(-0.278436\pi\) | ||||
0.641202 | + | 0.767372i | \(0.278436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.12193 | 0.394348 | 0.197174 | − | 0.980368i | \(-0.436824\pi\) | ||||
0.197174 | + | 0.980368i | \(0.436824\pi\) | |||||||
\(242\) | 0.958717 | 0.0616287 | ||||||||
\(243\) | −12.8886 | −0.826801 | ||||||||
\(244\) | 27.8639 | 1.78380 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.73085 | 0.301628 | ||||||||
\(247\) | −22.2192 | −1.41378 | ||||||||
\(248\) | 14.4184 | 0.915568 | ||||||||
\(249\) | 1.77242 | 0.112322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.80213 | −0.303108 | −0.151554 | − | 0.988449i | \(-0.548428\pi\) | ||||
−0.151554 | + | 0.988449i | \(0.548428\pi\) | |||||||
\(252\) | 3.81207 | 0.240138 | ||||||||
\(253\) | 3.90822 | 0.245708 | ||||||||
\(254\) | −2.67668 | −0.167950 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.15214 | 0.384509 | ||||||||
\(257\) | −26.2603 | −1.63807 | −0.819037 | − | 0.573740i | \(-0.805492\pi\) | ||||
−0.819037 | + | 0.573740i | \(0.805492\pi\) | |||||||
\(258\) | 0.472023 | 0.0293868 | ||||||||
\(259\) | 12.6876 | 0.788367 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.584192 | −0.0361606 | ||||||||
\(262\) | −0.963320 | −0.0595141 | ||||||||
\(263\) | 15.0015 | 0.925032 | 0.462516 | − | 0.886611i | \(-0.346947\pi\) | ||||
0.462516 | + | 0.886611i | \(0.346947\pi\) | |||||||
\(264\) | 6.72340 | 0.413797 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.39270 | −0.208020 | ||||||||
\(267\) | −13.8143 | −0.845420 | ||||||||
\(268\) | −7.35238 | −0.449118 | ||||||||
\(269\) | −14.5177 | −0.885158 | −0.442579 | − | 0.896729i | \(-0.645936\pi\) | ||||
−0.442579 | + | 0.896729i | \(0.645936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.7125 | 0.954465 | 0.477233 | − | 0.878777i | \(-0.341640\pi\) | ||||
0.477233 | + | 0.878777i | \(0.341640\pi\) | |||||||
\(272\) | −15.9955 | −0.969872 | ||||||||
\(273\) | −6.89680 | −0.417413 | ||||||||
\(274\) | −7.52765 | −0.454762 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.52199 | 0.151806 | ||||||||
\(277\) | 1.55966 | 0.0937108 | 0.0468554 | − | 0.998902i | \(-0.485080\pi\) | ||||
0.0468554 | + | 0.998902i | \(0.485080\pi\) | |||||||
\(278\) | −3.66351 | −0.219723 | ||||||||
\(279\) | 13.8276 | 0.827837 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8939 | −0.948153 | −0.474077 | − | 0.880484i | \(-0.657218\pi\) | ||||
−0.474077 | + | 0.880484i | \(0.657218\pi\) | |||||||
\(282\) | 5.99832 | 0.357195 | ||||||||
\(283\) | −2.62323 | −0.155935 | −0.0779675 | − | 0.996956i | \(-0.524843\pi\) | ||||
−0.0779675 | + | 0.996956i | \(0.524843\pi\) | |||||||
\(284\) | −3.02655 | −0.179593 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.92891 | 0.291452 | ||||||||
\(287\) | −14.9702 | −0.883662 | ||||||||
\(288\) | −5.53199 | −0.325976 | ||||||||
\(289\) | 8.00644 | 0.470967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.45319 | −0.319672 | ||||||||
\(292\) | 16.3464 | 0.956600 | ||||||||
\(293\) | −8.11264 | −0.473946 | −0.236973 | − | 0.971516i | \(-0.576155\pi\) | ||||
−0.236973 | + | 0.971516i | \(0.576155\pi\) | |||||||
\(294\) | 2.25107 | 0.131285 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.1316 | −0.705132 | ||||||||
\(297\) | 20.5707 | 1.19363 | ||||||||
\(298\) | −2.08036 | −0.120512 | ||||||||
\(299\) | 3.83333 | 0.221687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49366 | −0.0860929 | ||||||||
\(302\) | −0.738768 | −0.0425113 | ||||||||
\(303\) | 3.73319 | 0.214466 | ||||||||
\(304\) | −19.6536 | −1.12721 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.53205 | 0.144747 | ||||||||
\(307\) | 24.0736 | 1.37395 | 0.686975 | − | 0.726681i | \(-0.258938\pi\) | ||||
0.686975 | + | 0.726681i | \(0.258938\pi\) | |||||||
\(308\) | −10.2614 | −0.584696 | ||||||||
\(309\) | −10.0904 | −0.574021 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.39803 | 0.362799 | 0.181400 | − | 0.983409i | \(-0.441937\pi\) | ||||
0.181400 | + | 0.983409i | \(0.441937\pi\) | |||||||
\(312\) | 6.59456 | 0.373343 | ||||||||
\(313\) | −19.6040 | −1.10808 | −0.554041 | − | 0.832489i | \(-0.686915\pi\) | ||||
−0.554041 | + | 0.832489i | \(0.686915\pi\) | |||||||
\(314\) | 2.62722 | 0.148263 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7300 | −0.603611 | ||||||||
\(317\) | 5.68164 | 0.319113 | 0.159556 | − | 0.987189i | \(-0.448994\pi\) | ||||
0.159556 | + | 0.987189i | \(0.448994\pi\) | |||||||
\(318\) | 0.926103 | 0.0519333 | ||||||||
\(319\) | 1.57253 | 0.0880450 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.21572 | −0.346928 | ||||||||
\(322\) | 0.585319 | 0.0326185 | ||||||||
\(323\) | 30.7252 | 1.70959 | ||||||||
\(324\) | 5.61784 | 0.312102 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.668808 | −0.0370418 | ||||||||
\(327\) | −12.9824 | −0.717927 | ||||||||
\(328\) | 14.3142 | 0.790367 | ||||||||
\(329\) | −18.9809 | −1.04645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2711 | 0.619513 | 0.309756 | − | 0.950816i | \(-0.399752\pi\) | ||||
0.309756 | + | 0.950816i | \(0.399752\pi\) | |||||||
\(332\) | 2.58655 | 0.141955 | ||||||||
\(333\) | −11.6345 | −0.637565 | ||||||||
\(334\) | 6.94130 | 0.379811 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.10042 | −0.332805 | ||||||||
\(337\) | 16.7561 | 0.912765 | 0.456383 | − | 0.889784i | \(-0.349145\pi\) | ||||
0.456383 | + | 0.889784i | \(0.349145\pi\) | |||||||
\(338\) | 0.0286091 | 0.00155613 | ||||||||
\(339\) | 9.51355 | 0.516705 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −37.2213 | −2.01564 | ||||||||
\(342\) | 3.11110 | 0.168229 | ||||||||
\(343\) | −17.5788 | −0.949167 | ||||||||
\(344\) | 1.42820 | 0.0770034 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.44207 | 0.453848 | ||||||||
\(347\) | −34.1337 | −1.83239 | −0.916197 | − | 0.400729i | \(-0.868757\pi\) | ||||
−0.916197 | + | 0.400729i | \(0.868757\pi\) | |||||||
\(348\) | 1.01476 | 0.0543970 | ||||||||
\(349\) | 34.4994 | 1.84671 | 0.923354 | − | 0.383949i | \(-0.125436\pi\) | ||||
0.923354 | + | 0.383949i | \(0.125436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.1765 | 1.07694 | ||||||||
\(352\) | 14.8911 | 0.793697 | ||||||||
\(353\) | −6.40545 | −0.340927 | −0.170464 | − | 0.985364i | \(-0.554527\pi\) | ||||
−0.170464 | + | 0.985364i | \(0.554527\pi\) | |||||||
\(354\) | 3.78047 | 0.200930 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20.1597 | −1.06846 | ||||||||
\(357\) | 9.53702 | 0.504753 | ||||||||
\(358\) | 7.76377 | 0.410328 | ||||||||
\(359\) | 15.4742 | 0.816698 | 0.408349 | − | 0.912826i | \(-0.366105\pi\) | ||||
0.408349 | + | 0.912826i | \(0.366105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7517 | 0.986934 | ||||||||
\(362\) | 5.10609 | 0.268370 | ||||||||
\(363\) | −3.31132 | −0.173799 | ||||||||
\(364\) | −10.0647 | −0.527536 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.05852 | 0.368955 | ||||||||
\(367\) | −13.4623 | −0.702727 | −0.351363 | − | 0.936239i | \(-0.614282\pi\) | ||||
−0.351363 | + | 0.936239i | \(0.614282\pi\) | |||||||
\(368\) | 3.39069 | 0.176752 | ||||||||
\(369\) | 13.7276 | 0.714633 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.93053 | −0.152146 | ||||||||
\(372\) | −24.0190 | −1.24533 | ||||||||
\(373\) | 16.6957 | 0.864471 | 0.432235 | − | 0.901761i | \(-0.357725\pi\) | ||||
0.432235 | + | 0.901761i | \(0.357725\pi\) | |||||||
\(374\) | −6.81579 | −0.352436 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.1491 | 0.935969 | ||||||||
\(377\) | 1.54240 | 0.0794377 | ||||||||
\(378\) | 3.08080 | 0.158459 | ||||||||
\(379\) | 19.2363 | 0.988102 | 0.494051 | − | 0.869433i | \(-0.335516\pi\) | ||||
0.494051 | + | 0.869433i | \(0.335516\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.24500 | 0.473636 | ||||||||
\(382\) | −3.41401 | −0.174676 | ||||||||
\(383\) | −12.3023 | −0.628618 | −0.314309 | − | 0.949321i | \(-0.601773\pi\) | ||||
−0.314309 | + | 0.949321i | \(0.601773\pi\) | |||||||
\(384\) | 12.6290 | 0.644470 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.23184 | −0.418990 | ||||||||
\(387\) | 1.36968 | 0.0696248 | ||||||||
\(388\) | −7.95803 | −0.404008 | ||||||||
\(389\) | −38.1174 | −1.93263 | −0.966315 | − | 0.257363i | \(-0.917146\pi\) | ||||
−0.966315 | + | 0.257363i | \(0.917146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.30080 | −0.268073 | ||||||||
\(392\) | 6.81107 | 0.344011 | ||||||||
\(393\) | 3.32721 | 0.167836 | ||||||||
\(394\) | −5.58543 | −0.281390 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.40966 | 0.472853 | ||||||||
\(397\) | 11.9741 | 0.600963 | 0.300482 | − | 0.953788i | \(-0.402853\pi\) | ||||
0.300482 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(398\) | −1.14276 | −0.0572815 | ||||||||
\(399\) | 11.7181 | 0.586636 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.28174 | 0.263757 | 0.131879 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131879 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(402\) | −1.86251 | −0.0928938 | ||||||||
\(403\) | −36.5080 | −1.81859 | ||||||||
\(404\) | 5.44798 | 0.271047 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.235512 | 0.0116883 | ||||||||
\(407\) | 31.3178 | 1.55237 | ||||||||
\(408\) | −9.11908 | −0.451462 | ||||||||
\(409\) | −13.4050 | −0.662835 | −0.331418 | − | 0.943484i | \(-0.607527\pi\) | ||||
−0.331418 | + | 0.943484i | \(0.607527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.9998 | 1.28247 | ||||||||
\(412\) | −14.7252 | −0.725459 | ||||||||
\(413\) | −11.9628 | −0.588652 | ||||||||
\(414\) | −0.536736 | −0.0263792 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.6057 | 0.716104 | ||||||||
\(417\) | 12.6534 | 0.619641 | ||||||||
\(418\) | −8.37449 | −0.409610 | ||||||||
\(419\) | −24.4193 | −1.19296 | −0.596480 | − | 0.802628i | \(-0.703435\pi\) | ||||
−0.596480 | + | 0.802628i | \(0.703435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.1650 | −0.982782 | −0.491391 | − | 0.870939i | \(-0.663511\pi\) | ||||
−0.491391 | + | 0.870939i | \(0.663511\pi\) | |||||||
\(422\) | −0.674647 | −0.0328413 | ||||||||
\(423\) | 17.4055 | 0.846283 | ||||||||
\(424\) | 2.80211 | 0.136083 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.766690 | −0.0371462 | ||||||||
\(427\) | −22.3358 | −1.08090 | ||||||||
\(428\) | −9.07081 | −0.438454 | ||||||||
\(429\) | −17.0240 | −0.821924 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.3117 | 1.74907 | 0.874536 | − | 0.484961i | \(-0.161166\pi\) | ||||
0.874536 | + | 0.484961i | \(0.161166\pi\) | |||||||
\(432\) | 17.8467 | 0.858652 | ||||||||
\(433\) | 3.88729 | 0.186811 | 0.0934056 | − | 0.995628i | \(-0.470225\pi\) | ||||
0.0934056 | + | 0.995628i | \(0.470225\pi\) | |||||||
\(434\) | −5.57448 | −0.267584 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.9456 | −0.907331 | ||||||||
\(437\) | −6.51304 | −0.311561 | ||||||||
\(438\) | 4.14089 | 0.197859 | ||||||||
\(439\) | −0.0901999 | −0.00430500 | −0.00215250 | − | 0.999998i | \(-0.500685\pi\) | ||||
−0.00215250 | + | 0.999998i | \(0.500685\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.53199 | 0.311047 | ||||||||
\(442\) | −6.68518 | −0.317981 | ||||||||
\(443\) | −34.7294 | −1.65004 | −0.825021 | − | 0.565102i | \(-0.808837\pi\) | ||||
−0.825021 | + | 0.565102i | \(0.808837\pi\) | |||||||
\(444\) | 20.2095 | 0.959100 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.60852 | 0.454976 | ||||||||
\(447\) | 7.18535 | 0.339856 | ||||||||
\(448\) | −7.32532 | −0.346089 | ||||||||
\(449\) | −17.5143 | −0.826549 | −0.413275 | − | 0.910606i | \(-0.635615\pi\) | ||||
−0.413275 | + | 0.910606i | \(0.635615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.9522 | −1.74001 | ||||||||
\(452\) | 13.8834 | 0.653023 | ||||||||
\(453\) | 2.55163 | 0.119886 | ||||||||
\(454\) | −7.97136 | −0.374115 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.2045 | −0.524700 | ||||||||
\(457\) | 16.2351 | 0.759448 | 0.379724 | − | 0.925100i | \(-0.376019\pi\) | ||||
0.379724 | + | 0.925100i | \(0.376019\pi\) | |||||||
\(458\) | −5.16838 | −0.241502 | ||||||||
\(459\) | −27.9005 | −1.30228 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.2284 | −1.82705 | −0.913524 | − | 0.406785i | \(-0.866650\pi\) | ||||
−0.913524 | + | 0.406785i | \(0.866650\pi\) | |||||||
\(462\) | −2.59942 | −0.120936 | ||||||||
\(463\) | 32.1679 | 1.49497 | 0.747486 | − | 0.664278i | \(-0.231261\pi\) | ||||
0.747486 | + | 0.664278i | \(0.231261\pi\) | |||||||
\(464\) | 1.36430 | 0.0633360 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.42845 | 0.158820 | ||||||||
\(467\) | 12.5648 | 0.581429 | 0.290715 | − | 0.956810i | \(-0.406107\pi\) | ||||
0.290715 | + | 0.956810i | \(0.406107\pi\) | |||||||
\(468\) | 9.22935 | 0.426627 | ||||||||
\(469\) | 5.89369 | 0.272145 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.07416 | −0.418115 | ||||||||
\(472\) | 11.4386 | 0.526503 | ||||||||
\(473\) | −3.68692 | −0.169525 | ||||||||
\(474\) | −2.71814 | −0.124848 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.9177 | 0.637917 | ||||||||
\(477\) | 2.68730 | 0.123043 | ||||||||
\(478\) | 7.32909 | 0.335225 | ||||||||
\(479\) | −11.1129 | −0.507763 | −0.253882 | − | 0.967235i | \(-0.581707\pi\) | ||||
−0.253882 | + | 0.967235i | \(0.581707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.7177 | 1.40060 | ||||||||
\(482\) | 2.26316 | 0.103084 | ||||||||
\(483\) | −2.02163 | −0.0919875 | ||||||||
\(484\) | −4.83232 | −0.219651 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.76465 | −0.216129 | ||||||||
\(487\) | 26.5032 | 1.20097 | 0.600487 | − | 0.799634i | \(-0.294973\pi\) | ||||
0.600487 | + | 0.799634i | \(0.294973\pi\) | |||||||
\(488\) | 21.3570 | 0.966785 | ||||||||
\(489\) | 2.31000 | 0.104462 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.7631 | 1.34319 | 0.671595 | − | 0.740919i | \(-0.265610\pi\) | ||||
0.671595 | + | 0.740919i | \(0.265610\pi\) | |||||||
\(492\) | −23.8454 | −1.07503 | ||||||||
\(493\) | −2.13286 | −0.0960592 | ||||||||
\(494\) | −8.21401 | −0.369566 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −32.2924 | −1.44997 | ||||||||
\(497\) | 2.42609 | 0.108825 | ||||||||
\(498\) | 0.655227 | 0.0293614 | ||||||||
\(499\) | 10.2804 | 0.460215 | 0.230108 | − | 0.973165i | \(-0.426092\pi\) | ||||
0.230108 | + | 0.973165i | \(0.426092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.9746 | −1.07111 | ||||||||
\(502\) | −1.77525 | −0.0792334 | ||||||||
\(503\) | 16.6895 | 0.744149 | 0.372075 | − | 0.928203i | \(-0.378647\pi\) | ||||
0.372075 | + | 0.928203i | \(0.378647\pi\) | |||||||
\(504\) | 2.92186 | 0.130150 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.44479 | 0.0642288 | ||||||||
\(507\) | −0.0988131 | −0.00438845 | ||||||||
\(508\) | 13.4915 | 0.598591 | ||||||||
\(509\) | −29.5802 | −1.31112 | −0.655559 | − | 0.755144i | \(-0.727567\pi\) | ||||
−0.655559 | + | 0.755144i | \(0.727567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.1033 | −0.579656 | ||||||||
\(512\) | 22.0559 | 0.974744 | ||||||||
\(513\) | −34.2811 | −1.51355 | ||||||||
\(514\) | −9.70793 | −0.428198 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.37918 | −0.104738 | ||||||||
\(517\) | −46.8522 | −2.06056 | ||||||||
\(518\) | 4.69034 | 0.206082 | ||||||||
\(519\) | −29.1581 | −1.27990 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.7760 | −1.61119 | −0.805593 | − | 0.592469i | \(-0.798153\pi\) | ||||
−0.805593 | + | 0.592469i | \(0.798153\pi\) | |||||||
\(522\) | −0.215964 | −0.00945251 | ||||||||
\(523\) | 2.28308 | 0.0998322 | 0.0499161 | − | 0.998753i | \(-0.484105\pi\) | ||||
0.0499161 | + | 0.998753i | \(0.484105\pi\) | |||||||
\(524\) | 4.85551 | 0.212114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.54576 | 0.241807 | ||||||||
\(527\) | 50.4840 | 2.19912 | ||||||||
\(528\) | −15.0582 | −0.655324 | ||||||||
\(529\) | −21.8764 | −0.951146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.9699 | 0.476053 | ||||||||
\(532\) | 17.1006 | 0.741403 | ||||||||
\(533\) | −36.2441 | −1.56991 | ||||||||
\(534\) | −5.10687 | −0.220996 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.63541 | −0.243413 | ||||||||
\(537\) | −26.8153 | −1.15717 | ||||||||
\(538\) | −5.36690 | −0.231383 | ||||||||
\(539\) | −17.5829 | −0.757348 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.42128 | −0.319066 | −0.159533 | − | 0.987193i | \(-0.550999\pi\) | ||||
−0.159533 | + | 0.987193i | \(0.550999\pi\) | |||||||
\(542\) | 5.80860 | 0.249501 | ||||||||
\(543\) | −17.6359 | −0.756831 | ||||||||
\(544\) | −20.1971 | −0.865942 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.54961 | −0.109113 | ||||||||
\(547\) | 9.83182 | 0.420378 | 0.210189 | − | 0.977661i | \(-0.432592\pi\) | ||||
0.210189 | + | 0.977661i | \(0.432592\pi\) | |||||||
\(548\) | 37.9424 | 1.62082 | ||||||||
\(549\) | 20.4819 | 0.874146 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.62063 | −0.111642 | ||||||||
\(552\) | 1.93304 | 0.0822756 | ||||||||
\(553\) | 8.60122 | 0.365761 | ||||||||
\(554\) | 0.576575 | 0.0244963 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.4656 | 0.783115 | ||||||||
\(557\) | 15.2177 | 0.644794 | 0.322397 | − | 0.946605i | \(-0.395511\pi\) | ||||
0.322397 | + | 0.946605i | \(0.395511\pi\) | |||||||
\(558\) | 5.11179 | 0.216399 | ||||||||
\(559\) | −3.61627 | −0.152952 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.5411 | 0.993904 | ||||||||
\(562\) | −5.87568 | −0.247851 | ||||||||
\(563\) | 31.8616 | 1.34281 | 0.671404 | − | 0.741092i | \(-0.265692\pi\) | ||||
0.671404 | + | 0.741092i | \(0.265692\pi\) | |||||||
\(564\) | −30.2339 | −1.27308 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.969758 | −0.0407620 | ||||||||
\(567\) | −4.50328 | −0.189120 | ||||||||
\(568\) | −2.31977 | −0.0973356 | ||||||||
\(569\) | −8.07208 | −0.338399 | −0.169200 | − | 0.985582i | \(-0.554118\pi\) | ||||
−0.169200 | + | 0.985582i | \(0.554118\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.1724 | −1.30452 | −0.652262 | − | 0.757993i | \(-0.726180\pi\) | ||||
−0.652262 | + | 0.757993i | \(0.726180\pi\) | |||||||
\(572\) | −24.8436 | −1.03877 | ||||||||
\(573\) | 11.7916 | 0.492603 | ||||||||
\(574\) | −5.53419 | −0.230992 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.71731 | 0.279888 | ||||||||
\(577\) | 39.1328 | 1.62912 | 0.814560 | − | 0.580079i | \(-0.196978\pi\) | ||||
0.814560 | + | 0.580079i | \(0.196978\pi\) | |||||||
\(578\) | 2.95982 | 0.123112 | ||||||||
\(579\) | 28.4320 | 1.18159 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.07338 | −0.0860185 | ||||||||
\(582\) | −2.01594 | −0.0835633 | ||||||||
\(583\) | −7.23369 | −0.299589 | ||||||||
\(584\) | 12.5291 | 0.518457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.99908 | −0.123891 | ||||||||
\(587\) | −15.7507 | −0.650100 | −0.325050 | − | 0.945697i | \(-0.605381\pi\) | ||||
−0.325050 | + | 0.945697i | \(0.605381\pi\) | |||||||
\(588\) | −11.3463 | −0.467913 | ||||||||
\(589\) | 62.0292 | 2.55587 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.2915 | 0.793548 | ||||||||
\(592\) | 27.1707 | 1.11671 | ||||||||
\(593\) | 1.51862 | 0.0623624 | 0.0311812 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311812 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(594\) | 7.60459 | 0.312020 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.4858 | 0.429517 | ||||||||
\(597\) | 3.94699 | 0.161540 | ||||||||
\(598\) | 1.41711 | 0.0579498 | ||||||||
\(599\) | −12.9076 | −0.527390 | −0.263695 | − | 0.964606i | \(-0.584941\pi\) | ||||
−0.263695 | + | 0.964606i | \(0.584941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.34026 | 0.258624 | 0.129312 | − | 0.991604i | \(-0.458723\pi\) | ||||
0.129312 | + | 0.991604i | \(0.458723\pi\) | |||||||
\(602\) | −0.552175 | −0.0225050 | ||||||||
\(603\) | −5.40451 | −0.220089 | ||||||||
\(604\) | 3.72369 | 0.151515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.38009 | 0.0560623 | ||||||||
\(607\) | −22.4914 | −0.912897 | −0.456449 | − | 0.889750i | \(-0.650879\pi\) | ||||
−0.456449 | + | 0.889750i | \(0.650879\pi\) | |||||||
\(608\) | −24.8160 | −1.00642 | ||||||||
\(609\) | −0.813437 | −0.0329621 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.9544 | −1.85912 | ||||||||
\(612\) | −12.7625 | −0.515894 | ||||||||
\(613\) | 12.9445 | 0.522824 | 0.261412 | − | 0.965227i | \(-0.415812\pi\) | ||||
0.261412 | + | 0.965227i | \(0.415812\pi\) | |||||||
\(614\) | 8.89952 | 0.359156 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.86508 | −0.316893 | ||||||||
\(617\) | −4.50654 | −0.181426 | −0.0907132 | − | 0.995877i | \(-0.528915\pi\) | ||||
−0.0907132 | + | 0.995877i | \(0.528915\pi\) | |||||||
\(618\) | −3.73021 | −0.150051 | ||||||||
\(619\) | 22.9420 | 0.922115 | 0.461058 | − | 0.887370i | \(-0.347470\pi\) | ||||
0.461058 | + | 0.887370i | \(0.347470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.91427 | 0.237332 | ||||||||
\(622\) | 2.36523 | 0.0948370 | ||||||||
\(623\) | 16.1600 | 0.647438 | ||||||||
\(624\) | −14.7696 | −0.591259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.24720 | −0.289657 | ||||||||
\(627\) | 28.9247 | 1.15514 | ||||||||
\(628\) | −13.2422 | −0.528423 | ||||||||
\(629\) | −42.4770 | −1.69367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.5001 | 1.01514 | 0.507571 | − | 0.861610i | \(-0.330543\pi\) | ||||
0.507571 | + | 0.861610i | \(0.330543\pi\) | |||||||
\(632\) | −8.22429 | −0.327145 | ||||||||
\(633\) | 2.33016 | 0.0926157 | ||||||||
\(634\) | 2.10039 | 0.0834172 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.66793 | −0.185095 | ||||||||
\(637\) | −17.2459 | −0.683309 | ||||||||
\(638\) | 0.581335 | 0.0230153 | ||||||||
\(639\) | −2.22472 | −0.0880087 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.6768 | −1.64613 | −0.823067 | − | 0.567944i | \(-0.807739\pi\) | ||||
−0.823067 | + | 0.567944i | \(0.807739\pi\) | |||||||
\(642\) | −2.29783 | −0.0906881 | ||||||||
\(643\) | 12.7866 | 0.504253 | 0.252127 | − | 0.967694i | \(-0.418870\pi\) | ||||
0.252127 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(644\) | −2.95024 | −0.116256 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.3585 | 0.446894 | ||||||||
\(647\) | 17.9295 | 0.704881 | 0.352440 | − | 0.935834i | \(-0.385352\pi\) | ||||
0.352440 | + | 0.935834i | \(0.385352\pi\) | |||||||
\(648\) | 4.30593 | 0.169153 | ||||||||
\(649\) | −29.5288 | −1.15911 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.2537 | 0.754613 | ||||||||
\(652\) | 3.37106 | 0.132021 | ||||||||
\(653\) | −19.8948 | −0.778542 | −0.389271 | − | 0.921123i | \(-0.627273\pi\) | ||||
−0.389271 | + | 0.921123i | \(0.627273\pi\) | |||||||
\(654\) | −4.79933 | −0.187669 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −32.0590 | −1.25169 | ||||||||
\(657\) | 12.0157 | 0.468778 | ||||||||
\(658\) | −7.01687 | −0.273546 | ||||||||
\(659\) | 15.5607 | 0.606158 | 0.303079 | − | 0.952965i | \(-0.401985\pi\) | ||||
0.303079 | + | 0.952965i | \(0.401985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.83696 | −0.149240 | −0.0746202 | − | 0.997212i | \(-0.523774\pi\) | ||||
−0.0746202 | + | 0.997212i | \(0.523774\pi\) | |||||||
\(662\) | 4.16669 | 0.161943 | ||||||||
\(663\) | 23.0899 | 0.896739 | ||||||||
\(664\) | 1.98252 | 0.0769368 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.30104 | −0.166662 | ||||||||
\(667\) | 0.452118 | 0.0175061 | ||||||||
\(668\) | −34.9869 | −1.35368 | ||||||||
\(669\) | −33.1869 | −1.28308 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.1333 | −2.12840 | ||||||||
\(672\) | −7.70281 | −0.297143 | ||||||||
\(673\) | 10.5613 | 0.407109 | 0.203555 | − | 0.979064i | \(-0.434751\pi\) | ||||
0.203555 | + | 0.979064i | \(0.434751\pi\) | |||||||
\(674\) | 6.19442 | 0.238600 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.144201 | −0.00554621 | ||||||||
\(677\) | 12.6405 | 0.485814 | 0.242907 | − | 0.970050i | \(-0.421899\pi\) | ||||
0.242907 | + | 0.970050i | \(0.421899\pi\) | |||||||
\(678\) | 3.51697 | 0.135068 | ||||||||
\(679\) | 6.37918 | 0.244811 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.5323 | 1.05504 | ||||||||
\(682\) | −13.7600 | −0.526896 | ||||||||
\(683\) | 19.6198 | 0.750732 | 0.375366 | − | 0.926877i | \(-0.377517\pi\) | ||||
0.375366 | + | 0.926877i | \(0.377517\pi\) | |||||||
\(684\) | −15.6812 | −0.599585 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.49855 | −0.248116 | ||||||||
\(687\) | 17.8511 | 0.681061 | ||||||||
\(688\) | −3.19870 | −0.121949 | ||||||||
\(689\) | −7.09507 | −0.270301 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.6013 | 1.50651 | 0.753253 | − | 0.657731i | \(-0.228484\pi\) | ||||
0.753253 | + | 0.657731i | \(0.228484\pi\) | |||||||
\(692\) | −42.5514 | −1.61756 | ||||||||
\(693\) | −7.54281 | −0.286528 | ||||||||
\(694\) | −12.6186 | −0.478994 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.777789 | 0.0294820 | ||||||||
\(697\) | 50.1190 | 1.89839 | ||||||||
\(698\) | 12.7537 | 0.482736 | ||||||||
\(699\) | −11.8415 | −0.447888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.0682 | 0.946811 | 0.473405 | − | 0.880845i | \(-0.343025\pi\) | ||||
0.473405 | + | 0.880845i | \(0.343025\pi\) | |||||||
\(702\) | 7.45887 | 0.281517 | ||||||||
\(703\) | −52.1911 | −1.96842 | ||||||||
\(704\) | −18.0817 | −0.681480 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.36797 | −0.0891196 | ||||||||
\(707\) | −4.36712 | −0.164242 | ||||||||
\(708\) | −19.0551 | −0.716133 | ||||||||
\(709\) | −18.6983 | −0.702231 | −0.351115 | − | 0.936332i | \(-0.614197\pi\) | ||||
−0.351115 | + | 0.936332i | \(0.614197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.88731 | −0.295797 | ||||||||
\(712\) | −15.4519 | −0.579083 | ||||||||
\(713\) | −10.7015 | −0.400773 | ||||||||
\(714\) | 3.52565 | 0.131944 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −39.1325 | −1.46245 | ||||||||
\(717\) | −25.3140 | −0.945367 | ||||||||
\(718\) | 5.72052 | 0.213488 | ||||||||
\(719\) | 39.5258 | 1.47406 | 0.737031 | − | 0.675859i | \(-0.236227\pi\) | ||||
0.737031 | + | 0.675859i | \(0.236227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8038 | 0.439596 | ||||||||
\(722\) | 6.93215 | 0.257988 | ||||||||
\(723\) | −7.81672 | −0.290707 | ||||||||
\(724\) | −25.7367 | −0.956498 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.22413 | −0.0454317 | ||||||||
\(727\) | 7.56957 | 0.280740 | 0.140370 | − | 0.990099i | \(-0.455171\pi\) | ||||
0.140370 | + | 0.990099i | \(0.455171\pi\) | |||||||
\(728\) | −7.71436 | −0.285913 | ||||||||
\(729\) | 25.5014 | 0.944497 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.00064 | 0.184956 | ||||||||
\(732\) | −35.5777 | −1.31499 | ||||||||
\(733\) | −7.52401 | −0.277906 | −0.138953 | − | 0.990299i | \(-0.544374\pi\) | ||||
−0.138953 | + | 0.990299i | \(0.544374\pi\) | |||||||
\(734\) | −4.97675 | −0.183695 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.28132 | 0.157812 | ||||||||
\(737\) | 14.5479 | 0.535879 | ||||||||
\(738\) | 5.07484 | 0.186807 | ||||||||
\(739\) | −45.8820 | −1.68780 | −0.843898 | − | 0.536504i | \(-0.819744\pi\) | ||||
−0.843898 | + | 0.536504i | \(0.819744\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.3704 | 1.04221 | ||||||||
\(742\) | −1.08336 | −0.0397714 | ||||||||
\(743\) | −10.1826 | −0.373562 | −0.186781 | − | 0.982402i | \(-0.559806\pi\) | ||||
−0.186781 | + | 0.982402i | \(0.559806\pi\) | |||||||
\(744\) | −18.4100 | −0.674942 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.17207 | 0.225976 | ||||||||
\(747\) | 1.90129 | 0.0695646 | ||||||||
\(748\) | 34.3543 | 1.25612 | ||||||||
\(749\) | 7.27119 | 0.265684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.2391 | 0.993968 | 0.496984 | − | 0.867760i | \(-0.334441\pi\) | ||||
0.496984 | + | 0.867760i | \(0.334441\pi\) | |||||||
\(752\) | −40.6480 | −1.48228 | ||||||||
\(753\) | 6.13155 | 0.223446 | ||||||||
\(754\) | 0.570195 | 0.0207653 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.5284 | −0.564764 | ||||||||
\(757\) | 46.8819 | 1.70395 | 0.851976 | − | 0.523580i | \(-0.175404\pi\) | ||||
0.851976 | + | 0.523580i | \(0.175404\pi\) | |||||||
\(758\) | 7.11128 | 0.258293 | ||||||||
\(759\) | −4.99017 | −0.181132 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5395 | 0.454556 | 0.227278 | − | 0.973830i | \(-0.427017\pi\) | ||||
0.227278 | + | 0.973830i | \(0.427017\pi\) | |||||||
\(762\) | 3.41769 | 0.123810 | ||||||||
\(763\) | 15.1869 | 0.549802 | ||||||||
\(764\) | 17.2079 | 0.622562 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.54792 | −0.164323 | ||||||||
\(767\) | −28.9630 | −1.04579 | ||||||||
\(768\) | −7.85530 | −0.283454 | ||||||||
\(769\) | 36.2542 | 1.30736 | 0.653680 | − | 0.756771i | \(-0.273224\pi\) | ||||
0.653680 | + | 0.756771i | \(0.273224\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.5302 | 1.20756 | ||||||||
\(772\) | 41.4917 | 1.49332 | ||||||||
\(773\) | −41.4306 | −1.49016 | −0.745078 | − | 0.666977i | \(-0.767588\pi\) | ||||
−0.745078 | + | 0.666977i | \(0.767588\pi\) | |||||||
\(774\) | 0.506344 | 0.0182002 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.09963 | −0.218964 | ||||||||
\(777\) | −16.2000 | −0.581171 | ||||||||
\(778\) | −14.0913 | −0.505196 | ||||||||
\(779\) | 61.5808 | 2.20636 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.98853 | 0.214287 | ||||||||
\(782\) | −1.95960 | −0.0700752 | ||||||||
\(783\) | 2.37970 | 0.0850436 | ||||||||
\(784\) | −15.2546 | −0.544805 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.23000 | 0.0438728 | ||||||||
\(787\) | −42.8889 | −1.52882 | −0.764411 | − | 0.644729i | \(-0.776970\pi\) | ||||
−0.764411 | + | 0.644729i | \(0.776970\pi\) | |||||||
\(788\) | 28.1528 | 1.00290 | ||||||||
\(789\) | −19.1545 | −0.681919 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1290 | −0.395702 | ||||||||
\(792\) | 7.21227 | 0.256277 | ||||||||
\(793\) | −54.0768 | −1.92033 | ||||||||
\(794\) | 4.42659 | 0.157094 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.75998 | 0.204157 | ||||||||
\(797\) | 1.50370 | 0.0532638 | 0.0266319 | − | 0.999645i | \(-0.491522\pi\) | ||||
0.0266319 | + | 0.999645i | \(0.491522\pi\) | |||||||
\(798\) | 4.33193 | 0.153349 | ||||||||
\(799\) | 63.5466 | 2.24812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.8187 | −0.523594 | ||||||||
\(802\) | 1.95256 | 0.0689471 | ||||||||
\(803\) | −32.3440 | −1.14140 | ||||||||
\(804\) | 9.38781 | 0.331083 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.4963 | −0.475387 | ||||||||
\(807\) | 18.5367 | 0.652524 | ||||||||
\(808\) | 4.17574 | 0.146902 | ||||||||
\(809\) | 12.9134 | 0.454012 | 0.227006 | − | 0.973893i | \(-0.427106\pi\) | ||||
0.227006 | + | 0.973893i | \(0.427106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.89382 | −0.171845 | −0.0859227 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859227 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(812\) | −1.18708 | −0.0416582 | ||||||||
\(813\) | −20.0623 | −0.703616 | ||||||||
\(814\) | 11.5776 | 0.405794 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.4237 | 0.714974 | ||||||||
\(817\) | 6.14424 | 0.214960 | ||||||||
\(818\) | −4.95557 | −0.173267 | ||||||||
\(819\) | −7.39827 | −0.258517 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.41317 | −0.154021 | −0.0770104 | − | 0.997030i | \(-0.524537\pi\) | ||||
−0.0770104 | + | 0.997030i | \(0.524537\pi\) | |||||||
\(822\) | 9.61160 | 0.335243 | ||||||||
\(823\) | 17.2753 | 0.602181 | 0.301090 | − | 0.953596i | \(-0.402649\pi\) | ||||
0.301090 | + | 0.953596i | \(0.402649\pi\) | |||||||
\(824\) | −11.2865 | −0.393184 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.42242 | −0.153876 | ||||||||
\(827\) | −30.7326 | −1.06868 | −0.534339 | − | 0.845270i | \(-0.679439\pi\) | ||||
−0.534339 | + | 0.845270i | \(0.679439\pi\) | |||||||
\(828\) | 2.70537 | 0.0940180 | ||||||||
\(829\) | 22.8572 | 0.793864 | 0.396932 | − | 0.917848i | \(-0.370075\pi\) | ||||
0.396932 | + | 0.917848i | \(0.370075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.99143 | −0.0690821 | ||||||||
\(832\) | −17.7352 | −0.614858 | ||||||||
\(833\) | 23.8480 | 0.826285 | ||||||||
\(834\) | 4.67772 | 0.161976 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 42.2108 | 1.45989 | ||||||||
\(837\) | −56.3266 | −1.94693 | ||||||||
\(838\) | −9.02733 | −0.311844 | ||||||||
\(839\) | −4.34672 | −0.150065 | −0.0750327 | − | 0.997181i | \(-0.523906\pi\) | ||||
−0.0750327 | + | 0.997181i | \(0.523906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8181 | −0.993727 | ||||||||
\(842\) | −7.45460 | −0.256903 | ||||||||
\(843\) | 20.2940 | 0.698963 | ||||||||
\(844\) | 3.40049 | 0.117050 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.43446 | 0.221221 | ||||||||
\(847\) | 3.87360 | 0.133098 | ||||||||
\(848\) | −6.27580 | −0.215512 | ||||||||
\(849\) | 3.34945 | 0.114953 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00416 | 0.308659 | ||||||||
\(852\) | 3.86442 | 0.132393 | ||||||||
\(853\) | −15.1263 | −0.517913 | −0.258957 | − | 0.965889i | \(-0.583379\pi\) | ||||
−0.258957 | + | 0.965889i | \(0.583379\pi\) | |||||||
\(854\) | −8.25711 | −0.282552 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.95255 | −0.237633 | ||||||||
\(857\) | 48.5201 | 1.65741 | 0.828707 | − | 0.559683i | \(-0.189077\pi\) | ||||
0.828707 | + | 0.559683i | \(0.189077\pi\) | |||||||
\(858\) | −6.29342 | −0.214854 | ||||||||
\(859\) | 35.1488 | 1.19926 | 0.599631 | − | 0.800277i | \(-0.295314\pi\) | ||||
0.599631 | + | 0.800277i | \(0.295314\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.1145 | 0.651422 | ||||||||
\(862\) | 13.4237 | 0.457213 | ||||||||
\(863\) | −50.2393 | −1.71017 | −0.855083 | − | 0.518492i | \(-0.826494\pi\) | ||||
−0.855083 | + | 0.518492i | \(0.826494\pi\) | |||||||
\(864\) | 22.5345 | 0.766640 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.43705 | 0.0488331 | ||||||||
\(867\) | −10.2229 | −0.347189 | ||||||||
\(868\) | 28.0976 | 0.953695 | ||||||||
\(869\) | 21.2311 | 0.720217 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2691 | 0.483491 | ||||||||
\(872\) | −14.5213 | −0.491755 | ||||||||
\(873\) | −5.84970 | −0.197982 | ||||||||
\(874\) | −2.40774 | −0.0814432 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.8717 | −0.705190 | ||||||||
\(877\) | 19.5625 | 0.660580 | 0.330290 | − | 0.943880i | \(-0.392854\pi\) | ||||
0.330290 | + | 0.943880i | \(0.392854\pi\) | |||||||
\(878\) | −0.0333451 | −0.00112534 | ||||||||
\(879\) | 10.3585 | 0.349385 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8014 | 0.700815 | 0.350408 | − | 0.936597i | \(-0.386043\pi\) | ||||
0.350408 | + | 0.936597i | \(0.386043\pi\) | |||||||
\(882\) | 2.41475 | 0.0813089 | ||||||||
\(883\) | 23.2400 | 0.782089 | 0.391045 | − | 0.920372i | \(-0.372114\pi\) | ||||
0.391045 | + | 0.920372i | \(0.372114\pi\) | |||||||
\(884\) | 33.6960 | 1.13332 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.8388 | −0.431327 | ||||||||
\(887\) | 10.7445 | 0.360764 | 0.180382 | − | 0.983597i | \(-0.442267\pi\) | ||||
0.180382 | + | 0.983597i | \(0.442267\pi\) | |||||||
\(888\) | 15.4901 | 0.519812 | ||||||||
\(889\) | −10.8149 | −0.362719 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.1158 | −0.372394 | ||||||||
\(892\) | −48.4308 | −1.62158 | ||||||||
\(893\) | 78.0792 | 2.61282 | ||||||||
\(894\) | 2.65628 | 0.0888394 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14.7735 | −0.493547 | ||||||||
\(897\) | −4.89455 | −0.163424 | ||||||||
\(898\) | −6.47468 | −0.216063 | ||||||||
\(899\) | −4.30590 | −0.143610 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.81120 | 0.326859 | ||||||||
\(902\) | −13.6605 | −0.454845 | ||||||||
\(903\) | 1.90716 | 0.0634663 | ||||||||
\(904\) | 10.6413 | 0.353925 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.943289 | 0.0313387 | ||||||||
\(907\) | 2.28878 | 0.0759976 | 0.0379988 | − | 0.999278i | \(-0.487902\pi\) | ||||
0.0379988 | + | 0.999278i | \(0.487902\pi\) | |||||||
\(908\) | 40.1788 | 1.33338 | ||||||||
\(909\) | 4.00464 | 0.132825 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.4981 | −0.612871 | −0.306435 | − | 0.951891i | \(-0.599136\pi\) | ||||
−0.306435 | + | 0.951891i | \(0.599136\pi\) | |||||||
\(912\) | 25.0945 | 0.830960 | ||||||||
\(913\) | −5.11791 | −0.169378 | ||||||||
\(914\) | 6.00181 | 0.198522 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0507 | 0.860739 | ||||||||
\(917\) | −3.89220 | −0.128532 | ||||||||
\(918\) | −10.3143 | −0.340422 | ||||||||
\(919\) | −17.9354 | −0.591635 | −0.295817 | − | 0.955245i | \(-0.595592\pi\) | ||||
−0.295817 | + | 0.955245i | \(0.595592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.7381 | −1.01285 | ||||||||
\(922\) | −14.5020 | −0.477597 | ||||||||
\(923\) | 5.87378 | 0.193338 | ||||||||
\(924\) | 13.1021 | 0.431028 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.8919 | 0.390791 | ||||||||
\(927\) | −10.8240 | −0.355508 | ||||||||
\(928\) | 1.72266 | 0.0565490 | ||||||||
\(929\) | 26.5507 | 0.871100 | 0.435550 | − | 0.900164i | \(-0.356554\pi\) | ||||
0.435550 | + | 0.900164i | \(0.356554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.3019 | 0.960329 | ||||||||
\(932\) | −17.2808 | −0.566050 | ||||||||
\(933\) | −8.16926 | −0.267450 | ||||||||
\(934\) | 4.64496 | 0.151988 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.07406 | 0.231223 | ||||||||
\(937\) | 4.50444 | 0.147154 | 0.0735768 | − | 0.997290i | \(-0.476559\pi\) | ||||
0.0735768 | + | 0.997290i | \(0.476559\pi\) | |||||||
\(938\) | 2.17878 | 0.0711398 | ||||||||
\(939\) | 25.0311 | 0.816860 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.4544 | 0.764592 | 0.382296 | − | 0.924040i | \(-0.375133\pi\) | ||||
0.382296 | + | 0.924040i | \(0.375133\pi\) | |||||||
\(942\) | −3.35454 | −0.109297 | ||||||||
\(943\) | −10.6241 | −0.345968 | ||||||||
\(944\) | −25.6186 | −0.833815 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.36298 | −0.0443143 | ||||||||
\(947\) | −43.5192 | −1.41418 | −0.707092 | − | 0.707121i | \(-0.749993\pi\) | ||||
−0.707092 | + | 0.707121i | \(0.749993\pi\) | |||||||
\(948\) | 13.7005 | 0.444972 | ||||||||
\(949\) | −31.7242 | −1.02981 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.25455 | −0.235245 | ||||||||
\(952\) | 10.6676 | 0.345738 | ||||||||
\(953\) | −16.4190 | −0.531863 | −0.265931 | − | 0.963992i | \(-0.585679\pi\) | ||||
−0.265931 | + | 0.963992i | \(0.585679\pi\) | |||||||
\(954\) | 0.993441 | 0.0321638 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −36.9415 | −1.19478 | ||||||||
\(957\) | −2.00787 | −0.0649054 | ||||||||
\(958\) | −4.10824 | −0.132731 | ||||||||
\(959\) | −30.4147 | −0.982142 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.9190 | 2.28771 | ||||||||
\(962\) | 11.3557 | 0.366123 | ||||||||
\(963\) | −6.66767 | −0.214863 | ||||||||
\(964\) | −11.4072 | −0.367402 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.747358 | −0.0240459 | ||||||||
\(967\) | −24.3957 | −0.784513 | −0.392257 | − | 0.919856i | \(-0.628306\pi\) | ||||
−0.392257 | + | 0.919856i | \(0.628306\pi\) | |||||||
\(968\) | −3.70385 | −0.119046 | ||||||||
\(969\) | −39.2311 | −1.26029 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.7521 | 1.88545 | 0.942723 | − | 0.333577i | \(-0.108256\pi\) | ||||
0.942723 | + | 0.333577i | \(0.108256\pi\) | |||||||
\(972\) | 24.0157 | 0.770304 | ||||||||
\(973\) | −14.8021 | −0.474532 | ||||||||
\(974\) | 9.79771 | 0.313939 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47.8326 | −1.53108 | ||||||||
\(977\) | 16.7134 | 0.534708 | 0.267354 | − | 0.963598i | \(-0.413851\pi\) | ||||
0.267354 | + | 0.963598i | \(0.413851\pi\) | |||||||
\(978\) | 0.853961 | 0.0273066 | ||||||||
\(979\) | 39.8892 | 1.27486 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.9263 | −0.444634 | ||||||||
\(982\) | 11.0028 | 0.351114 | ||||||||
\(983\) | 40.7041 | 1.29826 | 0.649130 | − | 0.760677i | \(-0.275133\pi\) | ||||
0.649130 | + | 0.760677i | \(0.275133\pi\) | |||||||
\(984\) | −18.2769 | −0.582646 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.788477 | −0.0251102 | ||||||||
\(987\) | 24.2356 | 0.771427 | ||||||||
\(988\) | 41.4019 | 1.31717 | ||||||||
\(989\) | −1.06002 | −0.0337068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.2848 | −0.962029 | −0.481015 | − | 0.876713i | \(-0.659732\pi\) | ||||
−0.481015 | + | 0.876713i | \(0.659732\pi\) | |||||||
\(992\) | −40.7746 | −1.29460 | ||||||||
\(993\) | −14.3913 | −0.456695 | ||||||||
\(994\) | 0.896879 | 0.0284473 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.30261 | −0.104647 | ||||||||
\(997\) | −10.3490 | −0.327756 | −0.163878 | − | 0.986481i | \(-0.552400\pi\) | ||||
−0.163878 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(998\) | 3.80047 | 0.120302 | ||||||||
\(999\) | 47.3929 | 1.49945 |
(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 | 1075.2.a.n.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 9675.2.a.cc.1.3 | 5 | |||
5.2 | odd | 4 | 1075.2.b.i.474.6 | 10 | |||
5.3 | odd | 4 | 1075.2.b.i.474.5 | 10 | |||
5.4 | even | 2 | 1075.2.a.o.1.3 | yes | 5 | ||
15.14 | odd | 2 | 9675.2.a.cb.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1075.2.a.n.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1075.2.a.o.1.3 | yes | 5 | 5.4 | even | 2 | ||
1075.2.b.i.474.5 | 10 | 5.3 | odd | 4 | |||
1075.2.b.i.474.6 | 10 | 5.2 | odd | 4 | |||
9675.2.a.cb.1.3 | 5 | 15.14 | odd | 2 | |||
9675.2.a.cc.1.3 | 5 | 3.2 | odd | 2 |