Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 4x^{6} + 22x^{5} + 3x^{4} - 28x^{3} + 7x^{2} + 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.36639\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.36639 | −1.94359 | −0.971794 | − | 0.235833i | \(-0.924218\pi\) | ||||
−0.971794 | + | 0.235833i | \(0.924218\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.659053 | −0.294737 | −0.147369 | − | 0.989082i | \(-0.547080\pi\) | ||||
−0.147369 | + | 0.989082i | \(0.547080\pi\) | |||||||
\(6\) | 3.36639 | 1.37432 | ||||||||
\(7\) | 1.55483 | 0.587669 | 0.293834 | − | 0.955856i | \(-0.405069\pi\) | ||||
0.293834 | + | 0.955856i | \(0.405069\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.33259 | 2.77753 | ||||||||
\(10\) | 0.659053 | 0.208411 | ||||||||
\(11\) | 2.14446 | 0.646579 | 0.323290 | − | 0.946300i | \(-0.395211\pi\) | ||||
0.323290 | + | 0.946300i | \(0.395211\pi\) | |||||||
\(12\) | −3.36639 | −0.971794 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.55483 | −0.415545 | ||||||||
\(15\) | 2.21863 | 0.572848 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.31516 | 0.561508 | 0.280754 | − | 0.959780i | \(-0.409415\pi\) | ||||
0.280754 | + | 0.959780i | \(0.409415\pi\) | |||||||
\(18\) | −8.33259 | −1.96401 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.659053 | −0.147369 | ||||||||
\(21\) | −5.23415 | −1.14219 | ||||||||
\(22\) | −2.14446 | −0.457201 | ||||||||
\(23\) | 0.906597 | 0.189039 | 0.0945193 | − | 0.995523i | \(-0.469869\pi\) | ||||
0.0945193 | + | 0.995523i | \(0.469869\pi\) | |||||||
\(24\) | 3.36639 | 0.687162 | ||||||||
\(25\) | −4.56565 | −0.913130 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.9516 | −3.45479 | ||||||||
\(28\) | 1.55483 | 0.293834 | ||||||||
\(29\) | 6.14787 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(30\) | −2.21863 | −0.405064 | ||||||||
\(31\) | 6.56326 | 1.17880 | 0.589398 | − | 0.807843i | \(-0.299365\pi\) | ||||
0.589398 | + | 0.807843i | \(0.299365\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.21909 | −1.25668 | ||||||||
\(34\) | −2.31516 | −0.397046 | ||||||||
\(35\) | −1.02471 | −0.173208 | ||||||||
\(36\) | 8.33259 | 1.38877 | ||||||||
\(37\) | −1.53099 | −0.251693 | −0.125847 | − | 0.992050i | \(-0.540165\pi\) | ||||
−0.125847 | + | 0.992050i | \(0.540165\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.659053 | 0.104205 | ||||||||
\(41\) | −5.85275 | −0.914046 | −0.457023 | − | 0.889455i | \(-0.651084\pi\) | ||||
−0.457023 | + | 0.889455i | \(0.651084\pi\) | |||||||
\(42\) | 5.23415 | 0.807647 | ||||||||
\(43\) | 0.197219 | 0.0300757 | 0.0150378 | − | 0.999887i | \(-0.495213\pi\) | ||||
0.0150378 | + | 0.999887i | \(0.495213\pi\) | |||||||
\(44\) | 2.14446 | 0.323290 | ||||||||
\(45\) | −5.49162 | −0.818642 | ||||||||
\(46\) | −0.906597 | −0.133670 | ||||||||
\(47\) | 0.0646766 | 0.00943405 | 0.00471703 | − | 0.999989i | \(-0.498499\pi\) | ||||
0.00471703 | + | 0.999989i | \(0.498499\pi\) | |||||||
\(48\) | −3.36639 | −0.485897 | ||||||||
\(49\) | −4.58252 | −0.654646 | ||||||||
\(50\) | 4.56565 | 0.645680 | ||||||||
\(51\) | −7.79373 | −1.09134 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.5347 | −1.72177 | −0.860885 | − | 0.508799i | \(-0.830090\pi\) | ||||
−0.860885 | + | 0.508799i | \(0.830090\pi\) | |||||||
\(54\) | 17.9516 | 2.44290 | ||||||||
\(55\) | −1.41331 | −0.190571 | ||||||||
\(56\) | −1.55483 | −0.207772 | ||||||||
\(57\) | −3.36639 | −0.445889 | ||||||||
\(58\) | −6.14787 | −0.807255 | ||||||||
\(59\) | −14.3903 | −1.87345 | −0.936726 | − | 0.350064i | \(-0.886160\pi\) | ||||
−0.936726 | + | 0.350064i | \(0.886160\pi\) | |||||||
\(60\) | 2.21863 | 0.286424 | ||||||||
\(61\) | −0.404778 | −0.0518265 | −0.0259132 | − | 0.999664i | \(-0.508249\pi\) | ||||
−0.0259132 | + | 0.999664i | \(0.508249\pi\) | |||||||
\(62\) | −6.56326 | −0.833535 | ||||||||
\(63\) | 12.9557 | 1.63227 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.21909 | 0.888609 | ||||||||
\(67\) | −9.25247 | −1.13037 | −0.565185 | − | 0.824964i | \(-0.691195\pi\) | ||||
−0.565185 | + | 0.824964i | \(0.691195\pi\) | |||||||
\(68\) | 2.31516 | 0.280754 | ||||||||
\(69\) | −3.05196 | −0.367413 | ||||||||
\(70\) | 1.02471 | 0.122476 | ||||||||
\(71\) | 5.02728 | 0.596628 | 0.298314 | − | 0.954468i | \(-0.403576\pi\) | ||||
0.298314 | + | 0.954468i | \(0.403576\pi\) | |||||||
\(72\) | −8.33259 | −0.982006 | ||||||||
\(73\) | −6.09824 | −0.713745 | −0.356872 | − | 0.934153i | \(-0.616157\pi\) | ||||
−0.356872 | + | 0.934153i | \(0.616157\pi\) | |||||||
\(74\) | 1.53099 | 0.177974 | ||||||||
\(75\) | 15.3698 | 1.77475 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 3.33426 | 0.379974 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.22818 | −0.475707 | −0.237854 | − | 0.971301i | \(-0.576444\pi\) | ||||
−0.237854 | + | 0.971301i | \(0.576444\pi\) | |||||||
\(80\) | −0.659053 | −0.0736843 | ||||||||
\(81\) | 35.4343 | 3.93715 | ||||||||
\(82\) | 5.85275 | 0.646328 | ||||||||
\(83\) | 4.60991 | 0.506003 | 0.253002 | − | 0.967466i | \(-0.418582\pi\) | ||||
0.253002 | + | 0.967466i | \(0.418582\pi\) | |||||||
\(84\) | −5.23415 | −0.571093 | ||||||||
\(85\) | −1.52581 | −0.165497 | ||||||||
\(86\) | −0.197219 | −0.0212667 | ||||||||
\(87\) | −20.6961 | −2.21886 | ||||||||
\(88\) | −2.14446 | −0.228600 | ||||||||
\(89\) | 14.3869 | 1.52500 | 0.762502 | − | 0.646985i | \(-0.223970\pi\) | ||||
0.762502 | + | 0.646985i | \(0.223970\pi\) | |||||||
\(90\) | 5.49162 | 0.578867 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.906597 | 0.0945193 | ||||||||
\(93\) | −22.0945 | −2.29109 | ||||||||
\(94\) | −0.0646766 | −0.00667088 | ||||||||
\(95\) | −0.659053 | −0.0676174 | ||||||||
\(96\) | 3.36639 | 0.343581 | ||||||||
\(97\) | −15.6508 | −1.58910 | −0.794551 | − | 0.607197i | \(-0.792294\pi\) | ||||
−0.794551 | + | 0.607197i | \(0.792294\pi\) | |||||||
\(98\) | 4.58252 | 0.462904 | ||||||||
\(99\) | 17.8689 | 1.79589 | ||||||||
\(100\) | −4.56565 | −0.456565 | ||||||||
\(101\) | 6.67794 | 0.664479 | 0.332240 | − | 0.943195i | \(-0.392196\pi\) | ||||
0.332240 | + | 0.943195i | \(0.392196\pi\) | |||||||
\(102\) | 7.79373 | 0.771694 | ||||||||
\(103\) | 10.3411 | 1.01893 | 0.509467 | − | 0.860490i | \(-0.329843\pi\) | ||||
0.509467 | + | 0.860490i | \(0.329843\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.44958 | 0.336645 | ||||||||
\(106\) | 12.5347 | 1.21748 | ||||||||
\(107\) | −17.5465 | −1.69628 | −0.848141 | − | 0.529770i | \(-0.822278\pi\) | ||||
−0.848141 | + | 0.529770i | \(0.822278\pi\) | |||||||
\(108\) | −17.9516 | −1.72739 | ||||||||
\(109\) | −10.1078 | −0.968155 | −0.484077 | − | 0.875025i | \(-0.660845\pi\) | ||||
−0.484077 | + | 0.875025i | \(0.660845\pi\) | |||||||
\(110\) | 1.41331 | 0.134754 | ||||||||
\(111\) | 5.15391 | 0.489187 | ||||||||
\(112\) | 1.55483 | 0.146917 | ||||||||
\(113\) | −1.33176 | −0.125282 | −0.0626408 | − | 0.998036i | \(-0.519952\pi\) | ||||
−0.0626408 | + | 0.998036i | \(0.519952\pi\) | |||||||
\(114\) | 3.36639 | 0.315291 | ||||||||
\(115\) | −0.597495 | −0.0557167 | ||||||||
\(116\) | 6.14787 | 0.570816 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.3903 | 1.32473 | ||||||||
\(119\) | 3.59967 | 0.329981 | ||||||||
\(120\) | −2.21863 | −0.202532 | ||||||||
\(121\) | −6.40129 | −0.581935 | ||||||||
\(122\) | 0.404778 | 0.0366469 | ||||||||
\(123\) | 19.7026 | 1.77653 | ||||||||
\(124\) | 6.56326 | 0.589398 | ||||||||
\(125\) | 6.30427 | 0.563871 | ||||||||
\(126\) | −12.9557 | −1.15419 | ||||||||
\(127\) | −0.0377111 | −0.00334632 | −0.00167316 | − | 0.999999i | \(-0.500533\pi\) | ||||
−0.00167316 | + | 0.999999i | \(0.500533\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.663918 | −0.0584547 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1949 | −0.978102 | −0.489051 | − | 0.872255i | \(-0.662657\pi\) | ||||
−0.489051 | + | 0.872255i | \(0.662657\pi\) | |||||||
\(132\) | −7.21909 | −0.628341 | ||||||||
\(133\) | 1.55483 | 0.134820 | ||||||||
\(134\) | 9.25247 | 0.799292 | ||||||||
\(135\) | 11.8310 | 1.01825 | ||||||||
\(136\) | −2.31516 | −0.198523 | ||||||||
\(137\) | 15.5246 | 1.32636 | 0.663178 | − | 0.748462i | \(-0.269207\pi\) | ||||
0.663178 | + | 0.748462i | \(0.269207\pi\) | |||||||
\(138\) | 3.05196 | 0.259800 | ||||||||
\(139\) | 20.6863 | 1.75459 | 0.877296 | − | 0.479950i | \(-0.159345\pi\) | ||||
0.877296 | + | 0.479950i | \(0.159345\pi\) | |||||||
\(140\) | −1.02471 | −0.0866040 | ||||||||
\(141\) | −0.217727 | −0.0183359 | ||||||||
\(142\) | −5.02728 | −0.421880 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.33259 | 0.694383 | ||||||||
\(145\) | −4.05177 | −0.336481 | ||||||||
\(146\) | 6.09824 | 0.504694 | ||||||||
\(147\) | 15.4266 | 1.27236 | ||||||||
\(148\) | −1.53099 | −0.125847 | ||||||||
\(149\) | −4.50875 | −0.369371 | −0.184686 | − | 0.982798i | \(-0.559127\pi\) | ||||
−0.184686 | + | 0.982798i | \(0.559127\pi\) | |||||||
\(150\) | −15.3698 | −1.25494 | ||||||||
\(151\) | 13.7418 | 1.11829 | 0.559145 | − | 0.829070i | \(-0.311130\pi\) | ||||
0.559145 | + | 0.829070i | \(0.311130\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 19.2913 | 1.55961 | ||||||||
\(154\) | −3.33426 | −0.268682 | ||||||||
\(155\) | −4.32553 | −0.347435 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.5420 | −1.16058 | −0.580289 | − | 0.814410i | \(-0.697061\pi\) | ||||
−0.580289 | + | 0.814410i | \(0.697061\pi\) | |||||||
\(158\) | 4.22818 | 0.336376 | ||||||||
\(159\) | 42.1966 | 3.34641 | ||||||||
\(160\) | 0.659053 | 0.0521027 | ||||||||
\(161\) | 1.40960 | 0.111092 | ||||||||
\(162\) | −35.4343 | −2.78398 | ||||||||
\(163\) | 7.41566 | 0.580839 | 0.290420 | − | 0.956899i | \(-0.406205\pi\) | ||||
0.290420 | + | 0.956899i | \(0.406205\pi\) | |||||||
\(164\) | −5.85275 | −0.457023 | ||||||||
\(165\) | 4.75776 | 0.370391 | ||||||||
\(166\) | −4.60991 | −0.357798 | ||||||||
\(167\) | 5.52469 | 0.427513 | 0.213757 | − | 0.976887i | \(-0.431430\pi\) | ||||
0.213757 | + | 0.976887i | \(0.431430\pi\) | |||||||
\(168\) | 5.23415 | 0.403824 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.52581 | 0.117024 | ||||||||
\(171\) | 8.33259 | 0.637209 | ||||||||
\(172\) | 0.197219 | 0.0150378 | ||||||||
\(173\) | 22.3664 | 1.70049 | 0.850244 | − | 0.526388i | \(-0.176454\pi\) | ||||
0.850244 | + | 0.526388i | \(0.176454\pi\) | |||||||
\(174\) | 20.6961 | 1.56897 | ||||||||
\(175\) | −7.09879 | −0.536618 | ||||||||
\(176\) | 2.14446 | 0.161645 | ||||||||
\(177\) | 48.4432 | 3.64122 | ||||||||
\(178\) | −14.3869 | −1.07834 | ||||||||
\(179\) | −0.851299 | −0.0636291 | −0.0318145 | − | 0.999494i | \(-0.510129\pi\) | ||||
−0.0318145 | + | 0.999494i | \(0.510129\pi\) | |||||||
\(180\) | −5.49162 | −0.409321 | ||||||||
\(181\) | 5.30763 | 0.394513 | 0.197256 | − | 0.980352i | \(-0.436797\pi\) | ||||
0.197256 | + | 0.980352i | \(0.436797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.36264 | 0.100729 | ||||||||
\(184\) | −0.906597 | −0.0668352 | ||||||||
\(185\) | 1.00900 | 0.0741833 | ||||||||
\(186\) | 22.0945 | 1.62005 | ||||||||
\(187\) | 4.96476 | 0.363060 | ||||||||
\(188\) | 0.0646766 | 0.00471703 | ||||||||
\(189\) | −27.9116 | −2.03027 | ||||||||
\(190\) | 0.659053 | 0.0478127 | ||||||||
\(191\) | −20.0068 | −1.44764 | −0.723821 | − | 0.689987i | \(-0.757616\pi\) | ||||
−0.723821 | + | 0.689987i | \(0.757616\pi\) | |||||||
\(192\) | −3.36639 | −0.242948 | ||||||||
\(193\) | −21.3002 | −1.53322 | −0.766611 | − | 0.642111i | \(-0.778059\pi\) | ||||
−0.766611 | + | 0.642111i | \(0.778059\pi\) | |||||||
\(194\) | 15.6508 | 1.12367 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.58252 | −0.327323 | ||||||||
\(197\) | 19.2090 | 1.36858 | 0.684291 | − | 0.729209i | \(-0.260112\pi\) | ||||
0.684291 | + | 0.729209i | \(0.260112\pi\) | |||||||
\(198\) | −17.8689 | −1.26989 | ||||||||
\(199\) | 13.5279 | 0.958964 | 0.479482 | − | 0.877552i | \(-0.340825\pi\) | ||||
0.479482 | + | 0.877552i | \(0.340825\pi\) | |||||||
\(200\) | 4.56565 | 0.322840 | ||||||||
\(201\) | 31.1474 | 2.19697 | ||||||||
\(202\) | −6.67794 | −0.469858 | ||||||||
\(203\) | 9.55887 | 0.670901 | ||||||||
\(204\) | −7.79373 | −0.545670 | ||||||||
\(205\) | 3.85727 | 0.269403 | ||||||||
\(206\) | −10.3411 | −0.720495 | ||||||||
\(207\) | 7.55430 | 0.525060 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.14446 | 0.148335 | ||||||||
\(210\) | −3.44958 | −0.238044 | ||||||||
\(211\) | −22.2608 | −1.53250 | −0.766248 | − | 0.642544i | \(-0.777879\pi\) | ||||
−0.766248 | + | 0.642544i | \(0.777879\pi\) | |||||||
\(212\) | −12.5347 | −0.860885 | ||||||||
\(213\) | −16.9238 | −1.15960 | ||||||||
\(214\) | 17.5465 | 1.19945 | ||||||||
\(215\) | −0.129978 | −0.00886443 | ||||||||
\(216\) | 17.9516 | 1.22145 | ||||||||
\(217\) | 10.2047 | 0.692741 | ||||||||
\(218\) | 10.1078 | 0.684589 | ||||||||
\(219\) | 20.5291 | 1.38723 | ||||||||
\(220\) | −1.41331 | −0.0952855 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.15391 | −0.345908 | ||||||||
\(223\) | 23.7309 | 1.58914 | 0.794568 | − | 0.607175i | \(-0.207697\pi\) | ||||
0.794568 | + | 0.607175i | \(0.207697\pi\) | |||||||
\(224\) | −1.55483 | −0.103886 | ||||||||
\(225\) | −38.0437 | −2.53625 | ||||||||
\(226\) | 1.33176 | 0.0885874 | ||||||||
\(227\) | 13.4937 | 0.895610 | 0.447805 | − | 0.894131i | \(-0.352206\pi\) | ||||
0.447805 | + | 0.894131i | \(0.352206\pi\) | |||||||
\(228\) | −3.36639 | −0.222945 | ||||||||
\(229\) | −17.8510 | −1.17962 | −0.589812 | − | 0.807540i | \(-0.700798\pi\) | ||||
−0.589812 | + | 0.807540i | \(0.700798\pi\) | |||||||
\(230\) | 0.597495 | 0.0393977 | ||||||||
\(231\) | −11.2244 | −0.738513 | ||||||||
\(232\) | −6.14787 | −0.403628 | ||||||||
\(233\) | −28.6359 | −1.87600 | −0.938000 | − | 0.346636i | \(-0.887324\pi\) | ||||
−0.938000 | + | 0.346636i | \(0.887324\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0426253 | −0.00278057 | ||||||||
\(236\) | −14.3903 | −0.936726 | ||||||||
\(237\) | 14.2337 | 0.924579 | ||||||||
\(238\) | −3.59967 | −0.233332 | ||||||||
\(239\) | 7.83970 | 0.507108 | 0.253554 | − | 0.967321i | \(-0.418400\pi\) | ||||
0.253554 | + | 0.967321i | \(0.418400\pi\) | |||||||
\(240\) | 2.21863 | 0.143212 | ||||||||
\(241\) | −5.79801 | −0.373483 | −0.186741 | − | 0.982409i | \(-0.559793\pi\) | ||||
−0.186741 | + | 0.982409i | \(0.559793\pi\) | |||||||
\(242\) | 6.40129 | 0.411490 | ||||||||
\(243\) | −65.4310 | −4.19740 | ||||||||
\(244\) | −0.404778 | −0.0259132 | ||||||||
\(245\) | 3.02012 | 0.192948 | ||||||||
\(246\) | −19.7026 | −1.25620 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.56326 | −0.416767 | ||||||||
\(249\) | −15.5188 | −0.983462 | ||||||||
\(250\) | −6.30427 | −0.398717 | ||||||||
\(251\) | −13.5008 | −0.852163 | −0.426082 | − | 0.904685i | \(-0.640106\pi\) | ||||
−0.426082 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(252\) | 12.9557 | 0.816134 | ||||||||
\(253\) | 1.94416 | 0.122228 | ||||||||
\(254\) | 0.0377111 | 0.00236621 | ||||||||
\(255\) | 5.13648 | 0.321659 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.98458 | −0.622821 | −0.311410 | − | 0.950275i | \(-0.600801\pi\) | ||||
−0.311410 | + | 0.950275i | \(0.600801\pi\) | |||||||
\(258\) | 0.663918 | 0.0413337 | ||||||||
\(259\) | −2.38042 | −0.147912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 51.2277 | 3.17092 | ||||||||
\(262\) | 11.1949 | 0.691622 | ||||||||
\(263\) | −5.72498 | −0.353018 | −0.176509 | − | 0.984299i | \(-0.556480\pi\) | ||||
−0.176509 | + | 0.984299i | \(0.556480\pi\) | |||||||
\(264\) | 7.21909 | 0.444305 | ||||||||
\(265\) | 8.26102 | 0.507470 | ||||||||
\(266\) | −1.55483 | −0.0953325 | ||||||||
\(267\) | −48.4318 | −2.96398 | ||||||||
\(268\) | −9.25247 | −0.565185 | ||||||||
\(269\) | −2.30255 | −0.140389 | −0.0701945 | − | 0.997533i | \(-0.522362\pi\) | ||||
−0.0701945 | + | 0.997533i | \(0.522362\pi\) | |||||||
\(270\) | −11.8310 | −0.720015 | ||||||||
\(271\) | 24.5648 | 1.49220 | 0.746102 | − | 0.665832i | \(-0.231923\pi\) | ||||
0.746102 | + | 0.665832i | \(0.231923\pi\) | |||||||
\(272\) | 2.31516 | 0.140377 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.5246 | −0.937875 | ||||||||
\(275\) | −9.79086 | −0.590411 | ||||||||
\(276\) | −3.05196 | −0.183706 | ||||||||
\(277\) | −26.2419 | −1.57672 | −0.788362 | − | 0.615211i | \(-0.789071\pi\) | ||||
−0.788362 | + | 0.615211i | \(0.789071\pi\) | |||||||
\(278\) | −20.6863 | −1.24068 | ||||||||
\(279\) | 54.6890 | 3.27414 | ||||||||
\(280\) | 1.02471 | 0.0612382 | ||||||||
\(281\) | −5.07557 | −0.302783 | −0.151392 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151392 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(282\) | 0.217727 | 0.0129654 | ||||||||
\(283\) | −9.07363 | −0.539371 | −0.269686 | − | 0.962948i | \(-0.586920\pi\) | ||||
−0.269686 | + | 0.962948i | \(0.586920\pi\) | |||||||
\(284\) | 5.02728 | 0.298314 | ||||||||
\(285\) | 2.21863 | 0.131420 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.10000 | −0.537156 | ||||||||
\(288\) | −8.33259 | −0.491003 | ||||||||
\(289\) | −11.6400 | −0.684709 | ||||||||
\(290\) | 4.05177 | 0.237928 | ||||||||
\(291\) | 52.6869 | 3.08856 | ||||||||
\(292\) | −6.09824 | −0.356872 | ||||||||
\(293\) | −15.8216 | −0.924306 | −0.462153 | − | 0.886800i | \(-0.652923\pi\) | ||||
−0.462153 | + | 0.886800i | \(0.652923\pi\) | |||||||
\(294\) | −15.4266 | −0.899695 | ||||||||
\(295\) | 9.48394 | 0.552176 | ||||||||
\(296\) | 1.53099 | 0.0889869 | ||||||||
\(297\) | −38.4965 | −2.23379 | ||||||||
\(298\) | 4.50875 | 0.261185 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 15.3698 | 0.887374 | ||||||||
\(301\) | 0.306642 | 0.0176745 | ||||||||
\(302\) | −13.7418 | −0.790750 | ||||||||
\(303\) | −22.4805 | −1.29147 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0.266770 | 0.0152752 | ||||||||
\(306\) | −19.2913 | −1.10281 | ||||||||
\(307\) | −9.52079 | −0.543380 | −0.271690 | − | 0.962385i | \(-0.587583\pi\) | ||||
−0.271690 | + | 0.962385i | \(0.587583\pi\) | |||||||
\(308\) | 3.33426 | 0.189987 | ||||||||
\(309\) | −34.8120 | −1.98039 | ||||||||
\(310\) | 4.32553 | 0.245674 | ||||||||
\(311\) | 25.2248 | 1.43037 | 0.715183 | − | 0.698938i | \(-0.246343\pi\) | ||||
0.715183 | + | 0.698938i | \(0.246343\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.7340 | −1.73719 | −0.868595 | − | 0.495523i | \(-0.834976\pi\) | ||||
−0.868595 | + | 0.495523i | \(0.834976\pi\) | |||||||
\(314\) | 14.5420 | 0.820653 | ||||||||
\(315\) | −8.53851 | −0.481090 | ||||||||
\(316\) | −4.22818 | −0.237854 | ||||||||
\(317\) | −2.56431 | −0.144026 | −0.0720130 | − | 0.997404i | \(-0.522942\pi\) | ||||
−0.0720130 | + | 0.997404i | \(0.522942\pi\) | |||||||
\(318\) | −42.1966 | −2.36627 | ||||||||
\(319\) | 13.1839 | 0.738155 | ||||||||
\(320\) | −0.659053 | −0.0368422 | ||||||||
\(321\) | 59.0683 | 3.29687 | ||||||||
\(322\) | −1.40960 | −0.0785539 | ||||||||
\(323\) | 2.31516 | 0.128819 | ||||||||
\(324\) | 35.4343 | 1.96857 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.41566 | −0.410716 | ||||||||
\(327\) | 34.0269 | 1.88169 | ||||||||
\(328\) | 5.85275 | 0.323164 | ||||||||
\(329\) | 0.100561 | 0.00554410 | ||||||||
\(330\) | −4.75776 | −0.261906 | ||||||||
\(331\) | 4.57933 | 0.251703 | 0.125851 | − | 0.992049i | \(-0.459834\pi\) | ||||
0.125851 | + | 0.992049i | \(0.459834\pi\) | |||||||
\(332\) | 4.60991 | 0.253002 | ||||||||
\(333\) | −12.7571 | −0.699085 | ||||||||
\(334\) | −5.52469 | −0.302297 | ||||||||
\(335\) | 6.09787 | 0.333162 | ||||||||
\(336\) | −5.23415 | −0.285546 | ||||||||
\(337\) | −23.2052 | −1.26407 | −0.632033 | − | 0.774942i | \(-0.717779\pi\) | ||||
−0.632033 | + | 0.774942i | \(0.717779\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.48323 | 0.243496 | ||||||||
\(340\) | −1.52581 | −0.0827487 | ||||||||
\(341\) | 14.0746 | 0.762185 | ||||||||
\(342\) | −8.33259 | −0.450575 | ||||||||
\(343\) | −18.0088 | −0.972383 | ||||||||
\(344\) | −0.197219 | −0.0106334 | ||||||||
\(345\) | 2.01140 | 0.108290 | ||||||||
\(346\) | −22.3664 | −1.20243 | ||||||||
\(347\) | 20.7095 | 1.11174 | 0.555871 | − | 0.831269i | \(-0.312385\pi\) | ||||
0.555871 | + | 0.831269i | \(0.312385\pi\) | |||||||
\(348\) | −20.6961 | −1.10943 | ||||||||
\(349\) | −18.3764 | −0.983668 | −0.491834 | − | 0.870689i | \(-0.663673\pi\) | ||||
−0.491834 | + | 0.870689i | \(0.663673\pi\) | |||||||
\(350\) | 7.09879 | 0.379446 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.14446 | −0.114300 | ||||||||
\(353\) | 18.3367 | 0.975963 | 0.487982 | − | 0.872854i | \(-0.337733\pi\) | ||||
0.487982 | + | 0.872854i | \(0.337733\pi\) | |||||||
\(354\) | −48.4432 | −2.57473 | ||||||||
\(355\) | −3.31324 | −0.175849 | ||||||||
\(356\) | 14.3869 | 0.762502 | ||||||||
\(357\) | −12.1179 | −0.641346 | ||||||||
\(358\) | 0.851299 | 0.0449925 | ||||||||
\(359\) | −5.11843 | −0.270141 | −0.135070 | − | 0.990836i | \(-0.543126\pi\) | ||||
−0.135070 | + | 0.990836i | \(0.543126\pi\) | |||||||
\(360\) | 5.49162 | 0.289434 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.30763 | −0.278963 | ||||||||
\(363\) | 21.5492 | 1.13104 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.01906 | 0.210367 | ||||||||
\(366\) | −1.36264 | −0.0712264 | ||||||||
\(367\) | −3.19408 | −0.166730 | −0.0833648 | − | 0.996519i | \(-0.526567\pi\) | ||||
−0.0833648 | + | 0.996519i | \(0.526567\pi\) | |||||||
\(368\) | 0.906597 | 0.0472596 | ||||||||
\(369\) | −48.7686 | −2.53879 | ||||||||
\(370\) | −1.00900 | −0.0524555 | ||||||||
\(371\) | −19.4892 | −1.01183 | ||||||||
\(372\) | −22.0945 | −1.14555 | ||||||||
\(373\) | −21.2217 | −1.09882 | −0.549409 | − | 0.835554i | \(-0.685147\pi\) | ||||
−0.549409 | + | 0.835554i | \(0.685147\pi\) | |||||||
\(374\) | −4.96476 | −0.256722 | ||||||||
\(375\) | −21.2226 | −1.09593 | ||||||||
\(376\) | −0.0646766 | −0.00333544 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 27.9116 | 1.43562 | ||||||||
\(379\) | −11.9023 | −0.611378 | −0.305689 | − | 0.952131i | \(-0.598887\pi\) | ||||
−0.305689 | + | 0.952131i | \(0.598887\pi\) | |||||||
\(380\) | −0.659053 | −0.0338087 | ||||||||
\(381\) | 0.126950 | 0.00650387 | ||||||||
\(382\) | 20.0068 | 1.02364 | ||||||||
\(383\) | 35.6638 | 1.82234 | 0.911169 | − | 0.412034i | \(-0.135181\pi\) | ||||
0.911169 | + | 0.412034i | \(0.135181\pi\) | |||||||
\(384\) | 3.36639 | 0.171790 | ||||||||
\(385\) | −2.19745 | −0.111993 | ||||||||
\(386\) | 21.3002 | 1.08415 | ||||||||
\(387\) | 1.64335 | 0.0835362 | ||||||||
\(388\) | −15.6508 | −0.794551 | ||||||||
\(389\) | −21.3030 | −1.08010 | −0.540052 | − | 0.841632i | \(-0.681595\pi\) | ||||
−0.540052 | + | 0.841632i | \(0.681595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.09891 | 0.106147 | ||||||||
\(392\) | 4.58252 | 0.231452 | ||||||||
\(393\) | 37.6864 | 1.90103 | ||||||||
\(394\) | −19.2090 | −0.967734 | ||||||||
\(395\) | 2.78659 | 0.140209 | ||||||||
\(396\) | 17.8689 | 0.897947 | ||||||||
\(397\) | 32.3064 | 1.62141 | 0.810707 | − | 0.585452i | \(-0.199083\pi\) | ||||
0.810707 | + | 0.585452i | \(0.199083\pi\) | |||||||
\(398\) | −13.5279 | −0.678090 | ||||||||
\(399\) | −5.23415 | −0.262035 | ||||||||
\(400\) | −4.56565 | −0.228282 | ||||||||
\(401\) | −14.9787 | −0.747999 | −0.374000 | − | 0.927429i | \(-0.622014\pi\) | ||||
−0.374000 | + | 0.927429i | \(0.622014\pi\) | |||||||
\(402\) | −31.1474 | −1.55349 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.67794 | 0.332240 | ||||||||
\(405\) | −23.3531 | −1.16042 | ||||||||
\(406\) | −9.55887 | −0.474399 | ||||||||
\(407\) | −3.28315 | −0.162739 | ||||||||
\(408\) | 7.79373 | 0.385847 | ||||||||
\(409\) | 6.43031 | 0.317959 | 0.158979 | − | 0.987282i | \(-0.449180\pi\) | ||||
0.158979 | + | 0.987282i | \(0.449180\pi\) | |||||||
\(410\) | −3.85727 | −0.190497 | ||||||||
\(411\) | −52.2619 | −2.57789 | ||||||||
\(412\) | 10.3411 | 0.509467 | ||||||||
\(413\) | −22.3743 | −1.10097 | ||||||||
\(414\) | −7.55430 | −0.371274 | ||||||||
\(415\) | −3.03817 | −0.149138 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −69.6383 | −3.41020 | ||||||||
\(418\) | −2.14446 | −0.104889 | ||||||||
\(419\) | −0.238887 | −0.0116704 | −0.00583520 | − | 0.999983i | \(-0.501857\pi\) | ||||
−0.00583520 | + | 0.999983i | \(0.501857\pi\) | |||||||
\(420\) | 3.44958 | 0.168322 | ||||||||
\(421\) | 34.4329 | 1.67816 | 0.839079 | − | 0.544010i | \(-0.183095\pi\) | ||||
0.839079 | + | 0.544010i | \(0.183095\pi\) | |||||||
\(422\) | 22.2608 | 1.08364 | ||||||||
\(423\) | 0.538924 | 0.0262034 | ||||||||
\(424\) | 12.5347 | 0.608738 | ||||||||
\(425\) | −10.5702 | −0.512730 | ||||||||
\(426\) | 16.9238 | 0.819960 | ||||||||
\(427\) | −0.629359 | −0.0304568 | ||||||||
\(428\) | −17.5465 | −0.848141 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.129978 | 0.00626810 | ||||||||
\(431\) | −20.1204 | −0.969168 | −0.484584 | − | 0.874745i | \(-0.661029\pi\) | ||||
−0.484584 | + | 0.874745i | \(0.661029\pi\) | |||||||
\(432\) | −17.9516 | −0.863697 | ||||||||
\(433\) | −4.23488 | −0.203515 | −0.101758 | − | 0.994809i | \(-0.532447\pi\) | ||||
−0.101758 | + | 0.994809i | \(0.532447\pi\) | |||||||
\(434\) | −10.2047 | −0.489842 | ||||||||
\(435\) | 13.6399 | 0.653981 | ||||||||
\(436\) | −10.1078 | −0.484077 | ||||||||
\(437\) | 0.906597 | 0.0433684 | ||||||||
\(438\) | −20.5291 | −0.980916 | ||||||||
\(439\) | −18.7969 | −0.897128 | −0.448564 | − | 0.893751i | \(-0.648064\pi\) | ||||
−0.448564 | + | 0.893751i | \(0.648064\pi\) | |||||||
\(440\) | 1.41331 | 0.0673770 | ||||||||
\(441\) | −38.1843 | −1.81830 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3982 | −0.731590 | −0.365795 | − | 0.930695i | \(-0.619203\pi\) | ||||
−0.365795 | + | 0.930695i | \(0.619203\pi\) | |||||||
\(444\) | 5.15391 | 0.244594 | ||||||||
\(445\) | −9.48170 | −0.449476 | ||||||||
\(446\) | −23.7309 | −1.12369 | ||||||||
\(447\) | 15.1782 | 0.717905 | ||||||||
\(448\) | 1.55483 | 0.0734586 | ||||||||
\(449\) | −6.74190 | −0.318170 | −0.159085 | − | 0.987265i | \(-0.550854\pi\) | ||||
−0.159085 | + | 0.987265i | \(0.550854\pi\) | |||||||
\(450\) | 38.0437 | 1.79340 | ||||||||
\(451\) | −12.5510 | −0.591003 | ||||||||
\(452\) | −1.33176 | −0.0626408 | ||||||||
\(453\) | −46.2602 | −2.17349 | ||||||||
\(454\) | −13.4937 | −0.633292 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.36639 | 0.157646 | ||||||||
\(457\) | 28.2888 | 1.32329 | 0.661647 | − | 0.749816i | \(-0.269858\pi\) | ||||
0.661647 | + | 0.749816i | \(0.269858\pi\) | |||||||
\(458\) | 17.8510 | 0.834120 | ||||||||
\(459\) | −41.5608 | −1.93989 | ||||||||
\(460\) | −0.597495 | −0.0278584 | ||||||||
\(461\) | 17.3637 | 0.808709 | 0.404354 | − | 0.914602i | \(-0.367496\pi\) | ||||
0.404354 | + | 0.914602i | \(0.367496\pi\) | |||||||
\(462\) | 11.2244 | 0.522208 | ||||||||
\(463\) | −2.55506 | −0.118744 | −0.0593719 | − | 0.998236i | \(-0.518910\pi\) | ||||
−0.0593719 | + | 0.998236i | \(0.518910\pi\) | |||||||
\(464\) | 6.14787 | 0.285408 | ||||||||
\(465\) | 14.5614 | 0.675270 | ||||||||
\(466\) | 28.6359 | 1.32653 | ||||||||
\(467\) | −13.8566 | −0.641207 | −0.320603 | − | 0.947214i | \(-0.603886\pi\) | ||||
−0.320603 | + | 0.947214i | \(0.603886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3860 | −0.664283 | ||||||||
\(470\) | 0.0426253 | 0.00196616 | ||||||||
\(471\) | 48.9541 | 2.25569 | ||||||||
\(472\) | 14.3903 | 0.662365 | ||||||||
\(473\) | 0.422929 | 0.0194463 | ||||||||
\(474\) | −14.2337 | −0.653776 | ||||||||
\(475\) | −4.56565 | −0.209486 | ||||||||
\(476\) | 3.59967 | 0.164990 | ||||||||
\(477\) | −104.446 | −4.78227 | ||||||||
\(478\) | −7.83970 | −0.358580 | ||||||||
\(479\) | 21.5179 | 0.983176 | 0.491588 | − | 0.870828i | \(-0.336417\pi\) | ||||
0.491588 | + | 0.870828i | \(0.336417\pi\) | |||||||
\(480\) | −2.21863 | −0.101266 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.79801 | 0.264092 | ||||||||
\(483\) | −4.74526 | −0.215917 | ||||||||
\(484\) | −6.40129 | −0.290968 | ||||||||
\(485\) | 10.3147 | 0.468368 | ||||||||
\(486\) | 65.4310 | 2.96801 | ||||||||
\(487\) | −10.7576 | −0.487474 | −0.243737 | − | 0.969841i | \(-0.578373\pi\) | ||||
−0.243737 | + | 0.969841i | \(0.578373\pi\) | |||||||
\(488\) | 0.404778 | 0.0183234 | ||||||||
\(489\) | −24.9640 | −1.12891 | ||||||||
\(490\) | −3.02012 | −0.136435 | ||||||||
\(491\) | 38.1963 | 1.72378 | 0.861888 | − | 0.507099i | \(-0.169282\pi\) | ||||
0.861888 | + | 0.507099i | \(0.169282\pi\) | |||||||
\(492\) | 19.7026 | 0.888264 | ||||||||
\(493\) | 14.2333 | 0.641035 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.7766 | −0.529317 | ||||||||
\(496\) | 6.56326 | 0.294699 | ||||||||
\(497\) | 7.81654 | 0.350620 | ||||||||
\(498\) | 15.5188 | 0.695412 | ||||||||
\(499\) | −20.3365 | −0.910386 | −0.455193 | − | 0.890393i | \(-0.650430\pi\) | ||||
−0.455193 | + | 0.890393i | \(0.650430\pi\) | |||||||
\(500\) | 6.30427 | 0.281935 | ||||||||
\(501\) | −18.5983 | −0.830909 | ||||||||
\(502\) | 13.5008 | 0.602570 | ||||||||
\(503\) | 15.9668 | 0.711923 | 0.355962 | − | 0.934501i | \(-0.384153\pi\) | ||||
0.355962 | + | 0.934501i | \(0.384153\pi\) | |||||||
\(504\) | −12.9557 | −0.577094 | ||||||||
\(505\) | −4.40111 | −0.195847 | ||||||||
\(506\) | −1.94416 | −0.0864285 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.0377111 | −0.00167316 | ||||||||
\(509\) | 2.43816 | 0.108070 | 0.0540348 | − | 0.998539i | \(-0.482792\pi\) | ||||
0.0540348 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(510\) | −5.13648 | −0.227447 | ||||||||
\(511\) | −9.48169 | −0.419445 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −17.9516 | −0.792582 | ||||||||
\(514\) | 9.98458 | 0.440401 | ||||||||
\(515\) | −6.81530 | −0.300318 | ||||||||
\(516\) | −0.663918 | −0.0292274 | ||||||||
\(517\) | 0.138696 | 0.00609986 | ||||||||
\(518\) | 2.38042 | 0.104590 | ||||||||
\(519\) | −75.2942 | −3.30505 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.1880 | −1.27875 | −0.639375 | − | 0.768895i | \(-0.720807\pi\) | ||||
−0.639375 | + | 0.768895i | \(0.720807\pi\) | |||||||
\(522\) | −51.2277 | −2.24218 | ||||||||
\(523\) | −14.4899 | −0.633598 | −0.316799 | − | 0.948493i | \(-0.602608\pi\) | ||||
−0.316799 | + | 0.948493i | \(0.602608\pi\) | |||||||
\(524\) | −11.1949 | −0.489051 | ||||||||
\(525\) | 23.8973 | 1.04296 | ||||||||
\(526\) | 5.72498 | 0.249621 | ||||||||
\(527\) | 15.1950 | 0.661904 | ||||||||
\(528\) | −7.21909 | −0.314171 | ||||||||
\(529\) | −22.1781 | −0.964264 | ||||||||
\(530\) | −8.26102 | −0.358836 | ||||||||
\(531\) | −119.908 | −5.20357 | ||||||||
\(532\) | 1.55483 | 0.0674102 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 48.4318 | 2.09585 | ||||||||
\(535\) | 11.5641 | 0.499958 | ||||||||
\(536\) | 9.25247 | 0.399646 | ||||||||
\(537\) | 2.86580 | 0.123669 | ||||||||
\(538\) | 2.30255 | 0.0992700 | ||||||||
\(539\) | −9.82703 | −0.423280 | ||||||||
\(540\) | 11.8310 | 0.509127 | ||||||||
\(541\) | −1.93121 | −0.0830293 | −0.0415147 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415147 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(542\) | −24.5648 | −1.05515 | ||||||||
\(543\) | −17.8675 | −0.766770 | ||||||||
\(544\) | −2.31516 | −0.0992616 | ||||||||
\(545\) | 6.66159 | 0.285351 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.5237 | −0.749261 | −0.374630 | − | 0.927174i | \(-0.622230\pi\) | ||||
−0.374630 | + | 0.927174i | \(0.622230\pi\) | |||||||
\(548\) | 15.5246 | 0.663178 | ||||||||
\(549\) | −3.37285 | −0.143950 | ||||||||
\(550\) | 9.79086 | 0.417483 | ||||||||
\(551\) | 6.14787 | 0.261908 | ||||||||
\(552\) | 3.05196 | 0.129900 | ||||||||
\(553\) | −6.57408 | −0.279558 | ||||||||
\(554\) | 26.2419 | 1.11491 | ||||||||
\(555\) | −3.39670 | −0.144182 | ||||||||
\(556\) | 20.6863 | 0.877296 | ||||||||
\(557\) | 17.4101 | 0.737689 | 0.368844 | − | 0.929491i | \(-0.379754\pi\) | ||||
0.368844 | + | 0.929491i | \(0.379754\pi\) | |||||||
\(558\) | −54.6890 | −2.31517 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.02471 | −0.0433020 | ||||||||
\(561\) | −16.7133 | −0.705638 | ||||||||
\(562\) | 5.07557 | 0.214100 | ||||||||
\(563\) | 10.3029 | 0.434214 | 0.217107 | − | 0.976148i | \(-0.430338\pi\) | ||||
0.217107 | + | 0.976148i | \(0.430338\pi\) | |||||||
\(564\) | −0.217727 | −0.00916795 | ||||||||
\(565\) | 0.877701 | 0.0369252 | ||||||||
\(566\) | 9.07363 | 0.381393 | ||||||||
\(567\) | 55.0942 | 2.31374 | ||||||||
\(568\) | −5.02728 | −0.210940 | ||||||||
\(569\) | −16.5450 | −0.693602 | −0.346801 | − | 0.937939i | \(-0.612732\pi\) | ||||
−0.346801 | + | 0.937939i | \(0.612732\pi\) | |||||||
\(570\) | −2.21863 | −0.0929282 | ||||||||
\(571\) | 0.221196 | 0.00925678 | 0.00462839 | − | 0.999989i | \(-0.498527\pi\) | ||||
0.00462839 | + | 0.999989i | \(0.498527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 67.3508 | 2.81362 | ||||||||
\(574\) | 9.10000 | 0.379827 | ||||||||
\(575\) | −4.13920 | −0.172617 | ||||||||
\(576\) | 8.33259 | 0.347191 | ||||||||
\(577\) | 10.2652 | 0.427344 | 0.213672 | − | 0.976905i | \(-0.431458\pi\) | ||||
0.213672 | + | 0.976905i | \(0.431458\pi\) | |||||||
\(578\) | 11.6400 | 0.484162 | ||||||||
\(579\) | 71.7049 | 2.97995 | ||||||||
\(580\) | −4.05177 | −0.168241 | ||||||||
\(581\) | 7.16760 | 0.297362 | ||||||||
\(582\) | −52.6869 | −2.18394 | ||||||||
\(583\) | −26.8801 | −1.11326 | ||||||||
\(584\) | 6.09824 | 0.252347 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8216 | 0.653583 | ||||||||
\(587\) | −7.79489 | −0.321730 | −0.160865 | − | 0.986976i | \(-0.551428\pi\) | ||||
−0.160865 | + | 0.986976i | \(0.551428\pi\) | |||||||
\(588\) | 15.4266 | 0.636180 | ||||||||
\(589\) | 6.56326 | 0.270434 | ||||||||
\(590\) | −9.48394 | −0.390447 | ||||||||
\(591\) | −64.6649 | −2.65996 | ||||||||
\(592\) | −1.53099 | −0.0629233 | ||||||||
\(593\) | 8.18825 | 0.336251 | 0.168126 | − | 0.985766i | \(-0.446229\pi\) | ||||
0.168126 | + | 0.985766i | \(0.446229\pi\) | |||||||
\(594\) | 38.4965 | 1.57953 | ||||||||
\(595\) | −2.37237 | −0.0972577 | ||||||||
\(596\) | −4.50875 | −0.184686 | ||||||||
\(597\) | −45.5400 | −1.86383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.5390 | 0.757484 | 0.378742 | − | 0.925502i | \(-0.376357\pi\) | ||||
0.378742 | + | 0.925502i | \(0.376357\pi\) | |||||||
\(600\) | −15.3698 | −0.627468 | ||||||||
\(601\) | 7.26286 | 0.296258 | 0.148129 | − | 0.988968i | \(-0.452675\pi\) | ||||
0.148129 | + | 0.988968i | \(0.452675\pi\) | |||||||
\(602\) | −0.306642 | −0.0124978 | ||||||||
\(603\) | −77.0971 | −3.13964 | ||||||||
\(604\) | 13.7418 | 0.559145 | ||||||||
\(605\) | 4.21879 | 0.171518 | ||||||||
\(606\) | 22.4805 | 0.913210 | ||||||||
\(607\) | −20.9815 | −0.851611 | −0.425806 | − | 0.904815i | \(-0.640009\pi\) | ||||
−0.425806 | + | 0.904815i | \(0.640009\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −32.1789 | −1.30395 | ||||||||
\(610\) | −0.266770 | −0.0108012 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 19.2913 | 0.779803 | ||||||||
\(613\) | −43.8165 | −1.76973 | −0.884866 | − | 0.465845i | \(-0.845750\pi\) | ||||
−0.884866 | + | 0.465845i | \(0.845750\pi\) | |||||||
\(614\) | 9.52079 | 0.384228 | ||||||||
\(615\) | −12.9851 | −0.523609 | ||||||||
\(616\) | −3.33426 | −0.134341 | ||||||||
\(617\) | 2.29861 | 0.0925385 | 0.0462693 | − | 0.998929i | \(-0.485267\pi\) | ||||
0.0462693 | + | 0.998929i | \(0.485267\pi\) | |||||||
\(618\) | 34.8120 | 1.40035 | ||||||||
\(619\) | −40.0864 | −1.61121 | −0.805604 | − | 0.592455i | \(-0.798159\pi\) | ||||
−0.805604 | + | 0.592455i | \(0.798159\pi\) | |||||||
\(620\) | −4.32553 | −0.173718 | ||||||||
\(621\) | −16.2749 | −0.653088 | ||||||||
\(622\) | −25.2248 | −1.01142 | ||||||||
\(623\) | 22.3691 | 0.896198 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6734 | 0.746936 | ||||||||
\(626\) | 30.7340 | 1.22838 | ||||||||
\(627\) | −7.21909 | −0.288303 | ||||||||
\(628\) | −14.5420 | −0.580289 | ||||||||
\(629\) | −3.54448 | −0.141328 | ||||||||
\(630\) | 8.53851 | 0.340182 | ||||||||
\(631\) | 9.22321 | 0.367170 | 0.183585 | − | 0.983004i | \(-0.441230\pi\) | ||||
0.183585 | + | 0.983004i | \(0.441230\pi\) | |||||||
\(632\) | 4.22818 | 0.168188 | ||||||||
\(633\) | 74.9386 | 2.97854 | ||||||||
\(634\) | 2.56431 | 0.101842 | ||||||||
\(635\) | 0.0248536 | 0.000986286 0 | ||||||||
\(636\) | 42.1966 | 1.67321 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.1839 | −0.521954 | ||||||||
\(639\) | 41.8903 | 1.65715 | ||||||||
\(640\) | 0.659053 | 0.0260513 | ||||||||
\(641\) | 38.7348 | 1.52993 | 0.764967 | − | 0.644070i | \(-0.222755\pi\) | ||||
0.764967 | + | 0.644070i | \(0.222755\pi\) | |||||||
\(642\) | −59.0683 | −2.33124 | ||||||||
\(643\) | 6.83413 | 0.269512 | 0.134756 | − | 0.990879i | \(-0.456975\pi\) | ||||
0.134756 | + | 0.990879i | \(0.456975\pi\) | |||||||
\(644\) | 1.40960 | 0.0555460 | ||||||||
\(645\) | 0.437557 | 0.0172288 | ||||||||
\(646\) | −2.31516 | −0.0910887 | ||||||||
\(647\) | 31.7010 | 1.24630 | 0.623148 | − | 0.782104i | \(-0.285854\pi\) | ||||
0.623148 | + | 0.782104i | \(0.285854\pi\) | |||||||
\(648\) | −35.4343 | −1.39199 | ||||||||
\(649\) | −30.8593 | −1.21133 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.3531 | −1.34640 | ||||||||
\(652\) | 7.41566 | 0.290420 | ||||||||
\(653\) | −46.1273 | −1.80510 | −0.902551 | − | 0.430582i | \(-0.858308\pi\) | ||||
−0.902551 | + | 0.430582i | \(0.858308\pi\) | |||||||
\(654\) | −34.0269 | −1.33056 | ||||||||
\(655\) | 7.37802 | 0.288283 | ||||||||
\(656\) | −5.85275 | −0.228511 | ||||||||
\(657\) | −50.8141 | −1.98245 | ||||||||
\(658\) | −0.100561 | −0.00392027 | ||||||||
\(659\) | 11.3580 | 0.442445 | 0.221222 | − | 0.975223i | \(-0.428995\pi\) | ||||
0.221222 | + | 0.975223i | \(0.428995\pi\) | |||||||
\(660\) | 4.75776 | 0.185196 | ||||||||
\(661\) | −47.2706 | −1.83861 | −0.919307 | − | 0.393541i | \(-0.871250\pi\) | ||||
−0.919307 | + | 0.393541i | \(0.871250\pi\) | |||||||
\(662\) | −4.57933 | −0.177981 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.60991 | −0.178899 | ||||||||
\(665\) | −1.02471 | −0.0397366 | ||||||||
\(666\) | 12.7571 | 0.494328 | ||||||||
\(667\) | 5.57364 | 0.215812 | ||||||||
\(668\) | 5.52469 | 0.213757 | ||||||||
\(669\) | −79.8874 | −3.08862 | ||||||||
\(670\) | −6.09787 | −0.235581 | ||||||||
\(671\) | −0.868030 | −0.0335099 | ||||||||
\(672\) | 5.23415 | 0.201912 | ||||||||
\(673\) | −19.8580 | −0.765470 | −0.382735 | − | 0.923858i | \(-0.625018\pi\) | ||||
−0.382735 | + | 0.923858i | \(0.625018\pi\) | |||||||
\(674\) | 23.2052 | 0.893830 | ||||||||
\(675\) | 81.9607 | 3.15467 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3639 | 1.12855 | 0.564273 | − | 0.825588i | \(-0.309156\pi\) | ||||
0.564273 | + | 0.825588i | \(0.309156\pi\) | |||||||
\(678\) | −4.48323 | −0.172177 | ||||||||
\(679\) | −24.3343 | −0.933866 | ||||||||
\(680\) | 1.52581 | 0.0585122 | ||||||||
\(681\) | −45.4252 | −1.74070 | ||||||||
\(682\) | −14.0746 | −0.538946 | ||||||||
\(683\) | −12.1806 | −0.466078 | −0.233039 | − | 0.972467i | \(-0.574867\pi\) | ||||
−0.233039 | + | 0.972467i | \(0.574867\pi\) | |||||||
\(684\) | 8.33259 | 0.318605 | ||||||||
\(685\) | −10.2315 | −0.390926 | ||||||||
\(686\) | 18.0088 | 0.687579 | ||||||||
\(687\) | 60.0933 | 2.29270 | ||||||||
\(688\) | 0.197219 | 0.00751892 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.01140 | −0.0765728 | ||||||||
\(691\) | −12.5640 | −0.477958 | −0.238979 | − | 0.971025i | \(-0.576813\pi\) | ||||
−0.238979 | + | 0.971025i | \(0.576813\pi\) | |||||||
\(692\) | 22.3664 | 0.850244 | ||||||||
\(693\) | 27.7830 | 1.05539 | ||||||||
\(694\) | −20.7095 | −0.786120 | ||||||||
\(695\) | −13.6334 | −0.517144 | ||||||||
\(696\) | 20.6961 | 0.784485 | ||||||||
\(697\) | −13.5500 | −0.513244 | ||||||||
\(698\) | 18.3764 | 0.695558 | ||||||||
\(699\) | 96.3996 | 3.64617 | ||||||||
\(700\) | −7.09879 | −0.268309 | ||||||||
\(701\) | 46.7967 | 1.76749 | 0.883743 | − | 0.467973i | \(-0.155016\pi\) | ||||
0.883743 | + | 0.467973i | \(0.155016\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.53099 | −0.0577423 | ||||||||
\(704\) | 2.14446 | 0.0808224 | ||||||||
\(705\) | 0.143493 | 0.00540427 | ||||||||
\(706\) | −18.3367 | −0.690110 | ||||||||
\(707\) | 10.3830 | 0.390494 | ||||||||
\(708\) | 48.4432 | 1.82061 | ||||||||
\(709\) | 32.9155 | 1.23617 | 0.618084 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618084 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(710\) | 3.31324 | 0.124344 | ||||||||
\(711\) | −35.2317 | −1.32129 | ||||||||
\(712\) | −14.3869 | −0.539171 | ||||||||
\(713\) | 5.95023 | 0.222838 | ||||||||
\(714\) | 12.1179 | 0.453500 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.851299 | −0.0318145 | ||||||||
\(717\) | −26.3915 | −0.985609 | ||||||||
\(718\) | 5.11843 | 0.191018 | ||||||||
\(719\) | 22.7335 | 0.847816 | 0.423908 | − | 0.905705i | \(-0.360658\pi\) | ||||
0.423908 | + | 0.905705i | \(0.360658\pi\) | |||||||
\(720\) | −5.49162 | −0.204661 | ||||||||
\(721\) | 16.0785 | 0.598796 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 19.5184 | 0.725896 | ||||||||
\(724\) | 5.30763 | 0.197256 | ||||||||
\(725\) | −28.0690 | −1.04246 | ||||||||
\(726\) | −21.5492 | −0.799768 | ||||||||
\(727\) | −49.8150 | −1.84753 | −0.923767 | − | 0.382954i | \(-0.874907\pi\) | ||||
−0.923767 | + | 0.382954i | \(0.874907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 113.964 | 4.22087 | ||||||||
\(730\) | −4.01906 | −0.148752 | ||||||||
\(731\) | 0.456594 | 0.0168877 | ||||||||
\(732\) | 1.36264 | 0.0503647 | ||||||||
\(733\) | −5.01600 | −0.185270 | −0.0926351 | − | 0.995700i | \(-0.529529\pi\) | ||||
−0.0926351 | + | 0.995700i | \(0.529529\pi\) | |||||||
\(734\) | 3.19408 | 0.117896 | ||||||||
\(735\) | −10.1669 | −0.375012 | ||||||||
\(736\) | −0.906597 | −0.0334176 | ||||||||
\(737\) | −19.8416 | −0.730873 | ||||||||
\(738\) | 48.7686 | 1.79520 | ||||||||
\(739\) | 11.1272 | 0.409321 | 0.204661 | − | 0.978833i | \(-0.434391\pi\) | ||||
0.204661 | + | 0.978833i | \(0.434391\pi\) | |||||||
\(740\) | 1.00900 | 0.0370917 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.4892 | 0.715472 | ||||||||
\(743\) | 35.9871 | 1.32024 | 0.660118 | − | 0.751161i | \(-0.270506\pi\) | ||||
0.660118 | + | 0.751161i | \(0.270506\pi\) | |||||||
\(744\) | 22.0945 | 0.810023 | ||||||||
\(745\) | 2.97151 | 0.108868 | ||||||||
\(746\) | 21.2217 | 0.776982 | ||||||||
\(747\) | 38.4125 | 1.40544 | ||||||||
\(748\) | 4.96476 | 0.181530 | ||||||||
\(749\) | −27.2817 | −0.996852 | ||||||||
\(750\) | 21.2226 | 0.774941 | ||||||||
\(751\) | 18.2229 | 0.664962 | 0.332481 | − | 0.943110i | \(-0.392114\pi\) | ||||
0.332481 | + | 0.943110i | \(0.392114\pi\) | |||||||
\(752\) | 0.0646766 | 0.00235851 | ||||||||
\(753\) | 45.4490 | 1.65625 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.05655 | −0.329602 | ||||||||
\(756\) | −27.9116 | −1.01514 | ||||||||
\(757\) | −24.9727 | −0.907649 | −0.453824 | − | 0.891091i | \(-0.649941\pi\) | ||||
−0.453824 | + | 0.891091i | \(0.649941\pi\) | |||||||
\(758\) | 11.9023 | 0.432310 | ||||||||
\(759\) | −6.54481 | −0.237561 | ||||||||
\(760\) | 0.659053 | 0.0239064 | ||||||||
\(761\) | −16.5240 | −0.598994 | −0.299497 | − | 0.954097i | \(-0.596819\pi\) | ||||
−0.299497 | + | 0.954097i | \(0.596819\pi\) | |||||||
\(762\) | −0.126950 | −0.00459893 | ||||||||
\(763\) | −15.7159 | −0.568954 | ||||||||
\(764\) | −20.0068 | −0.723821 | ||||||||
\(765\) | −12.7140 | −0.459674 | ||||||||
\(766\) | −35.6638 | −1.28859 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.36639 | −0.121474 | ||||||||
\(769\) | −3.79823 | −0.136968 | −0.0684839 | − | 0.997652i | \(-0.521816\pi\) | ||||
−0.0684839 | + | 0.997652i | \(0.521816\pi\) | |||||||
\(770\) | 2.19745 | 0.0791907 | ||||||||
\(771\) | 33.6120 | 1.21051 | ||||||||
\(772\) | −21.3002 | −0.766611 | ||||||||
\(773\) | −34.8182 | −1.25232 | −0.626162 | − | 0.779693i | \(-0.715375\pi\) | ||||
−0.626162 | + | 0.779693i | \(0.715375\pi\) | |||||||
\(774\) | −1.64335 | −0.0590690 | ||||||||
\(775\) | −29.9655 | −1.07639 | ||||||||
\(776\) | 15.6508 | 0.561833 | ||||||||
\(777\) | 8.01343 | 0.287480 | ||||||||
\(778\) | 21.3030 | 0.763749 | ||||||||
\(779\) | −5.85275 | −0.209697 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7808 | 0.385767 | ||||||||
\(782\) | −2.09891 | −0.0750570 | ||||||||
\(783\) | −110.364 | −3.94409 | ||||||||
\(784\) | −4.58252 | −0.163661 | ||||||||
\(785\) | 9.58395 | 0.342066 | ||||||||
\(786\) | −37.6864 | −1.34423 | ||||||||
\(787\) | −13.1410 | −0.468426 | −0.234213 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234213 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(788\) | 19.2090 | 0.684291 | ||||||||
\(789\) | 19.2725 | 0.686121 | ||||||||
\(790\) | −2.78659 | −0.0991426 | ||||||||
\(791\) | −2.07066 | −0.0736241 | ||||||||
\(792\) | −17.8689 | −0.634944 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −32.3064 | −1.14651 | ||||||||
\(795\) | −27.8098 | −0.986312 | ||||||||
\(796\) | 13.5279 | 0.479482 | ||||||||
\(797\) | 38.4927 | 1.36348 | 0.681741 | − | 0.731594i | \(-0.261223\pi\) | ||||
0.681741 | + | 0.731594i | \(0.261223\pi\) | |||||||
\(798\) | 5.23415 | 0.185287 | ||||||||
\(799\) | 0.149737 | 0.00529730 | ||||||||
\(800\) | 4.56565 | 0.161420 | ||||||||
\(801\) | 119.880 | 4.23575 | ||||||||
\(802\) | 14.9787 | 0.528915 | ||||||||
\(803\) | −13.0774 | −0.461492 | ||||||||
\(804\) | 31.1474 | 1.09849 | ||||||||
\(805\) | −0.929000 | −0.0327430 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.75129 | 0.272858 | ||||||||
\(808\) | −6.67794 | −0.234929 | ||||||||
\(809\) | −0.282721 | −0.00993995 | −0.00496998 | − | 0.999988i | \(-0.501582\pi\) | ||||
−0.00496998 | + | 0.999988i | \(0.501582\pi\) | |||||||
\(810\) | 23.3531 | 0.820544 | ||||||||
\(811\) | 51.1669 | 1.79671 | 0.898356 | − | 0.439268i | \(-0.144762\pi\) | ||||
0.898356 | + | 0.439268i | \(0.144762\pi\) | |||||||
\(812\) | 9.55887 | 0.335450 | ||||||||
\(813\) | −82.6947 | −2.90023 | ||||||||
\(814\) | 3.28315 | 0.115074 | ||||||||
\(815\) | −4.88731 | −0.171195 | ||||||||
\(816\) | −7.79373 | −0.272835 | ||||||||
\(817\) | 0.197219 | 0.00689984 | ||||||||
\(818\) | −6.43031 | −0.224831 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.85727 | 0.134702 | ||||||||
\(821\) | −4.43545 | −0.154798 | −0.0773991 | − | 0.997000i | \(-0.524662\pi\) | ||||
−0.0773991 | + | 0.997000i | \(0.524662\pi\) | |||||||
\(822\) | 52.2619 | 1.82284 | ||||||||
\(823\) | −45.5433 | −1.58754 | −0.793770 | − | 0.608218i | \(-0.791885\pi\) | ||||
−0.793770 | + | 0.608218i | \(0.791885\pi\) | |||||||
\(824\) | −10.3411 | −0.360248 | ||||||||
\(825\) | 32.9599 | 1.14751 | ||||||||
\(826\) | 22.3743 | 0.778503 | ||||||||
\(827\) | −40.8431 | −1.42025 | −0.710127 | − | 0.704073i | \(-0.751363\pi\) | ||||
−0.710127 | + | 0.704073i | \(0.751363\pi\) | |||||||
\(828\) | 7.55430 | 0.262530 | ||||||||
\(829\) | −3.65715 | −0.127018 | −0.0635090 | − | 0.997981i | \(-0.520229\pi\) | ||||
−0.0635090 | + | 0.997981i | \(0.520229\pi\) | |||||||
\(830\) | 3.03817 | 0.105457 | ||||||||
\(831\) | 88.3406 | 3.06450 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.6093 | −0.367589 | ||||||||
\(834\) | 69.6383 | 2.41138 | ||||||||
\(835\) | −3.64106 | −0.126004 | ||||||||
\(836\) | 2.14446 | 0.0741677 | ||||||||
\(837\) | −117.821 | −4.07249 | ||||||||
\(838\) | 0.238887 | 0.00825222 | ||||||||
\(839\) | −23.6861 | −0.817735 | −0.408868 | − | 0.912594i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912594i | \(0.634076\pi\) | |||||||
\(840\) | −3.44958 | −0.119022 | ||||||||
\(841\) | 8.79634 | 0.303322 | ||||||||
\(842\) | −34.4329 | −1.18664 | ||||||||
\(843\) | 17.0864 | 0.588486 | ||||||||
\(844\) | −22.2608 | −0.766248 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.538924 | −0.0185286 | ||||||||
\(847\) | −9.95289 | −0.341985 | ||||||||
\(848\) | −12.5347 | −0.430443 | ||||||||
\(849\) | 30.5454 | 1.04832 | ||||||||
\(850\) | 10.5702 | 0.362555 | ||||||||
\(851\) | −1.38799 | −0.0475797 | ||||||||
\(852\) | −16.9238 | −0.579799 | ||||||||
\(853\) | −17.2391 | −0.590254 | −0.295127 | − | 0.955458i | \(-0.595362\pi\) | ||||
−0.295127 | + | 0.955458i | \(0.595362\pi\) | |||||||
\(854\) | 0.629359 | 0.0215362 | ||||||||
\(855\) | −5.49162 | −0.187809 | ||||||||
\(856\) | 17.5465 | 0.599726 | ||||||||
\(857\) | −12.5765 | −0.429604 | −0.214802 | − | 0.976658i | \(-0.568911\pi\) | ||||
−0.214802 | + | 0.976658i | \(0.568911\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.90850 | −0.269835 | −0.134917 | − | 0.990857i | \(-0.543077\pi\) | ||||
−0.134917 | + | 0.990857i | \(0.543077\pi\) | |||||||
\(860\) | −0.129978 | −0.00443221 | ||||||||
\(861\) | 30.6342 | 1.04401 | ||||||||
\(862\) | 20.1204 | 0.685305 | ||||||||
\(863\) | −45.0795 | −1.53453 | −0.767263 | − | 0.641333i | \(-0.778382\pi\) | ||||
−0.767263 | + | 0.641333i | \(0.778382\pi\) | |||||||
\(864\) | 17.9516 | 0.610726 | ||||||||
\(865\) | −14.7407 | −0.501198 | ||||||||
\(866\) | 4.23488 | 0.143907 | ||||||||
\(867\) | 39.1850 | 1.33079 | ||||||||
\(868\) | 10.2047 | 0.346371 | ||||||||
\(869\) | −9.06717 | −0.307583 | ||||||||
\(870\) | −13.6399 | −0.462434 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.1078 | 0.342294 | ||||||||
\(873\) | −130.412 | −4.41378 | ||||||||
\(874\) | −0.906597 | −0.0306661 | ||||||||
\(875\) | 9.80203 | 0.331369 | ||||||||
\(876\) | 20.5291 | 0.693613 | ||||||||
\(877\) | 3.09592 | 0.104542 | 0.0522710 | − | 0.998633i | \(-0.483354\pi\) | ||||
0.0522710 | + | 0.998633i | \(0.483354\pi\) | |||||||
\(878\) | 18.7969 | 0.634365 | ||||||||
\(879\) | 53.2616 | 1.79647 | ||||||||
\(880\) | −1.41331 | −0.0476428 | ||||||||
\(881\) | −33.6727 | −1.13446 | −0.567232 | − | 0.823558i | \(-0.691986\pi\) | ||||
−0.567232 | + | 0.823558i | \(0.691986\pi\) | |||||||
\(882\) | 38.1843 | 1.28573 | ||||||||
\(883\) | −12.9000 | −0.434119 | −0.217060 | − | 0.976158i | \(-0.569647\pi\) | ||||
−0.217060 | + | 0.976158i | \(0.569647\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.9266 | −1.07320 | ||||||||
\(886\) | 15.3982 | 0.517312 | ||||||||
\(887\) | −28.4001 | −0.953582 | −0.476791 | − | 0.879017i | \(-0.658200\pi\) | ||||
−0.476791 | + | 0.879017i | \(0.658200\pi\) | |||||||
\(888\) | −5.15391 | −0.172954 | ||||||||
\(889\) | −0.0586342 | −0.00196653 | ||||||||
\(890\) | 9.48170 | 0.317827 | ||||||||
\(891\) | 75.9875 | 2.54568 | ||||||||
\(892\) | 23.7309 | 0.794568 | ||||||||
\(893\) | 0.0646766 | 0.00216432 | ||||||||
\(894\) | −15.1782 | −0.507636 | ||||||||
\(895\) | 0.561051 | 0.0187539 | ||||||||
\(896\) | −1.55483 | −0.0519431 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.74190 | 0.224980 | ||||||||
\(899\) | 40.3501 | 1.34575 | ||||||||
\(900\) | −38.0437 | −1.26812 | ||||||||
\(901\) | −29.0198 | −0.966788 | ||||||||
\(902\) | 12.5510 | 0.417902 | ||||||||
\(903\) | −1.03228 | −0.0343520 | ||||||||
\(904\) | 1.33176 | 0.0442937 | ||||||||
\(905\) | −3.49800 | −0.116278 | ||||||||
\(906\) | 46.2602 | 1.53689 | ||||||||
\(907\) | 31.6558 | 1.05111 | 0.525557 | − | 0.850759i | \(-0.323857\pi\) | ||||
0.525557 | + | 0.850759i | \(0.323857\pi\) | |||||||
\(908\) | 13.4937 | 0.447805 | ||||||||
\(909\) | 55.6445 | 1.84561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6057 | −0.616434 | −0.308217 | − | 0.951316i | \(-0.599732\pi\) | ||||
−0.308217 | + | 0.951316i | \(0.599732\pi\) | |||||||
\(912\) | −3.36639 | −0.111472 | ||||||||
\(913\) | 9.88577 | 0.327171 | ||||||||
\(914\) | −28.2888 | −0.935710 | ||||||||
\(915\) | −0.898052 | −0.0296887 | ||||||||
\(916\) | −17.8510 | −0.589812 | ||||||||
\(917\) | −17.4061 | −0.574800 | ||||||||
\(918\) | 41.5608 | 1.37171 | ||||||||
\(919\) | 41.0076 | 1.35272 | 0.676358 | − | 0.736573i | \(-0.263557\pi\) | ||||
0.676358 | + | 0.736573i | \(0.263557\pi\) | |||||||
\(920\) | 0.597495 | 0.0196988 | ||||||||
\(921\) | 32.0507 | 1.05611 | ||||||||
\(922\) | −17.3637 | −0.571844 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −11.2244 | −0.369257 | ||||||||
\(925\) | 6.98996 | 0.229828 | ||||||||
\(926\) | 2.55506 | 0.0839646 | ||||||||
\(927\) | 86.1678 | 2.83012 | ||||||||
\(928\) | −6.14787 | −0.201814 | ||||||||
\(929\) | 2.65194 | 0.0870072 | 0.0435036 | − | 0.999053i | \(-0.486148\pi\) | ||||
0.0435036 | + | 0.999053i | \(0.486148\pi\) | |||||||
\(930\) | −14.5614 | −0.477488 | ||||||||
\(931\) | −4.58252 | −0.150186 | ||||||||
\(932\) | −28.6359 | −0.938000 | ||||||||
\(933\) | −84.9165 | −2.78004 | ||||||||
\(934\) | 13.8566 | 0.453402 | ||||||||
\(935\) | −3.27204 | −0.107007 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6898 | 0.479894 | 0.239947 | − | 0.970786i | \(-0.422870\pi\) | ||||
0.239947 | + | 0.970786i | \(0.422870\pi\) | |||||||
\(938\) | 14.3860 | 0.469719 | ||||||||
\(939\) | 103.463 | 3.37638 | ||||||||
\(940\) | −0.0426253 | −0.00139028 | ||||||||
\(941\) | 29.2022 | 0.951965 | 0.475982 | − | 0.879455i | \(-0.342093\pi\) | ||||
0.475982 | + | 0.879455i | \(0.342093\pi\) | |||||||
\(942\) | −48.9541 | −1.59501 | ||||||||
\(943\) | −5.30608 | −0.172790 | ||||||||
\(944\) | −14.3903 | −0.468363 | ||||||||
\(945\) | 18.3952 | 0.598396 | ||||||||
\(946\) | −0.422929 | −0.0137506 | ||||||||
\(947\) | 48.7605 | 1.58450 | 0.792251 | − | 0.610195i | \(-0.208909\pi\) | ||||
0.792251 | + | 0.610195i | \(0.208909\pi\) | |||||||
\(948\) | 14.2337 | 0.462289 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.56565 | 0.148129 | ||||||||
\(951\) | 8.63248 | 0.279927 | ||||||||
\(952\) | −3.59967 | −0.116666 | ||||||||
\(953\) | −23.7242 | −0.768502 | −0.384251 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384251 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(954\) | 104.446 | 3.38158 | ||||||||
\(955\) | 13.1855 | 0.426674 | ||||||||
\(956\) | 7.83970 | 0.253554 | ||||||||
\(957\) | −44.3821 | −1.43467 | ||||||||
\(958\) | −21.5179 | −0.695210 | ||||||||
\(959\) | 24.1380 | 0.779458 | ||||||||
\(960\) | 2.21863 | 0.0716060 | ||||||||
\(961\) | 12.0763 | 0.389560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −146.208 | −4.71148 | ||||||||
\(964\) | −5.79801 | −0.186741 | ||||||||
\(965\) | 14.0380 | 0.451898 | ||||||||
\(966\) | 4.74526 | 0.152676 | ||||||||
\(967\) | 21.4717 | 0.690484 | 0.345242 | − | 0.938514i | \(-0.387797\pi\) | ||||
0.345242 | + | 0.938514i | \(0.387797\pi\) | |||||||
\(968\) | 6.40129 | 0.205745 | ||||||||
\(969\) | −7.79373 | −0.250371 | ||||||||
\(970\) | −10.3147 | −0.331186 | ||||||||
\(971\) | −45.8967 | −1.47289 | −0.736447 | − | 0.676495i | \(-0.763498\pi\) | ||||
−0.736447 | + | 0.676495i | \(0.763498\pi\) | |||||||
\(972\) | −65.4310 | −2.09870 | ||||||||
\(973\) | 32.1636 | 1.03112 | ||||||||
\(974\) | 10.7576 | 0.344696 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.404778 | −0.0129566 | ||||||||
\(977\) | 29.3098 | 0.937704 | 0.468852 | − | 0.883277i | \(-0.344668\pi\) | ||||
0.468852 | + | 0.883277i | \(0.344668\pi\) | |||||||
\(978\) | 24.9640 | 0.798261 | ||||||||
\(979\) | 30.8521 | 0.986036 | ||||||||
\(980\) | 3.02012 | 0.0964742 | ||||||||
\(981\) | −84.2245 | −2.68908 | ||||||||
\(982\) | −38.1963 | −1.21889 | ||||||||
\(983\) | −3.36484 | −0.107322 | −0.0536609 | − | 0.998559i | \(-0.517089\pi\) | ||||
−0.0536609 | + | 0.998559i | \(0.517089\pi\) | |||||||
\(984\) | −19.7026 | −0.628098 | ||||||||
\(985\) | −12.6597 | −0.403372 | ||||||||
\(986\) | −14.2333 | −0.453280 | ||||||||
\(987\) | −0.338527 | −0.0107754 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.178799 | 0.00568546 | ||||||||
\(990\) | 11.7766 | 0.374284 | ||||||||
\(991\) | 39.4061 | 1.25177 | 0.625887 | − | 0.779913i | \(-0.284737\pi\) | ||||
0.625887 | + | 0.779913i | \(0.284737\pi\) | |||||||
\(992\) | −6.56326 | −0.208384 | ||||||||
\(993\) | −15.4158 | −0.489206 | ||||||||
\(994\) | −7.81654 | −0.247926 | ||||||||
\(995\) | −8.91557 | −0.282642 | ||||||||
\(996\) | −15.5188 | −0.491731 | ||||||||
\(997\) | 18.4286 | 0.583638 | 0.291819 | − | 0.956474i | \(-0.405739\pi\) | ||||
0.291819 | + | 0.956474i | \(0.405739\pi\) | |||||||
\(998\) | 20.3365 | 0.643740 | ||||||||
\(999\) | 27.4837 | 0.869546 |
(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 | 6422.2.a.bg.1.1 | 8 | ||
13.6 | odd | 12 | 494.2.m.a.153.8 | ✓ | 16 | ||
13.11 | odd | 12 | 494.2.m.a.381.8 | yes | 16 | ||
13.12 | even | 2 | 6422.2.a.bh.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.a.153.8 | ✓ | 16 | 13.6 | odd | 12 | ||
494.2.m.a.381.8 | yes | 16 | 13.11 | odd | 12 | ||
6422.2.a.bg.1.1 | 8 | 1.1 | even | 1 | trivial | ||
6422.2.a.bh.1.1 | 8 | 13.12 | even | 2 |