Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, 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("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + 1860 x^{8} - 5877 x^{7} - 2496 x^{6} + 6612 x^{5} + 1842 x^{4} - 3011 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.63671\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63671 | −1.15733 | −0.578663 | − | 0.815567i | \(-0.696425\pi\) | ||||
−0.578663 | + | 0.815567i | \(0.696425\pi\) | |||||||
\(3\) | −0.492566 | −0.284383 | −0.142192 | − | 0.989839i | \(-0.545415\pi\) | ||||
−0.142192 | + | 0.989839i | \(0.545415\pi\) | |||||||
\(4\) | 0.678809 | 0.339404 | ||||||||
\(5\) | −1.90242 | −0.850789 | −0.425395 | − | 0.905008i | \(-0.639865\pi\) | ||||
−0.425395 | + | 0.905008i | \(0.639865\pi\) | |||||||
\(6\) | 0.806186 | 0.329124 | ||||||||
\(7\) | 0.625725 | 0.236502 | 0.118251 | − | 0.992984i | \(-0.462271\pi\) | ||||
0.118251 | + | 0.992984i | \(0.462271\pi\) | |||||||
\(8\) | 2.16240 | 0.764525 | ||||||||
\(9\) | −2.75738 | −0.919126 | ||||||||
\(10\) | 3.11371 | 0.984641 | ||||||||
\(11\) | 1.86394 | 0.561999 | 0.281000 | − | 0.959708i | \(-0.409334\pi\) | ||||
0.281000 | + | 0.959708i | \(0.409334\pi\) | |||||||
\(12\) | −0.334358 | −0.0965208 | ||||||||
\(13\) | −3.61185 | −1.00175 | −0.500873 | − | 0.865521i | \(-0.666988\pi\) | ||||
−0.500873 | + | 0.865521i | \(0.666988\pi\) | |||||||
\(14\) | −1.02413 | −0.273710 | ||||||||
\(15\) | 0.937068 | 0.241950 | ||||||||
\(16\) | −4.89684 | −1.22421 | ||||||||
\(17\) | −0.946611 | −0.229587 | −0.114793 | − | 0.993389i | \(-0.536621\pi\) | ||||
−0.114793 | + | 0.993389i | \(0.536621\pi\) | |||||||
\(18\) | 4.51302 | 1.06373 | ||||||||
\(19\) | −0.390297 | −0.0895402 | −0.0447701 | − | 0.998997i | \(-0.514256\pi\) | ||||
−0.0447701 | + | 0.998997i | \(0.514256\pi\) | |||||||
\(20\) | −1.29138 | −0.288762 | ||||||||
\(21\) | −0.308211 | −0.0672571 | ||||||||
\(22\) | −3.05072 | −0.650417 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.06513 | −0.217418 | ||||||||
\(25\) | −1.38079 | −0.276158 | ||||||||
\(26\) | 5.91154 | 1.15935 | ||||||||
\(27\) | 2.83589 | 0.545767 | ||||||||
\(28\) | 0.424747 | 0.0802697 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.53371 | −0.280015 | ||||||||
\(31\) | 5.69517 | 1.02288 | 0.511442 | − | 0.859318i | \(-0.329112\pi\) | ||||
0.511442 | + | 0.859318i | \(0.329112\pi\) | |||||||
\(32\) | 3.68988 | 0.652285 | ||||||||
\(33\) | −0.918114 | −0.159823 | ||||||||
\(34\) | 1.54932 | 0.265707 | ||||||||
\(35\) | −1.19039 | −0.201213 | ||||||||
\(36\) | −1.87173 | −0.311956 | ||||||||
\(37\) | 5.54547 | 0.911670 | 0.455835 | − | 0.890064i | \(-0.349341\pi\) | ||||
0.455835 | + | 0.890064i | \(0.349341\pi\) | |||||||
\(38\) | 0.638801 | 0.103627 | ||||||||
\(39\) | 1.77907 | 0.284880 | ||||||||
\(40\) | −4.11380 | −0.650449 | ||||||||
\(41\) | 11.6520 | 1.81974 | 0.909871 | − | 0.414892i | \(-0.136181\pi\) | ||||
0.909871 | + | 0.414892i | \(0.136181\pi\) | |||||||
\(42\) | 0.504450 | 0.0778384 | ||||||||
\(43\) | −0.753478 | −0.114904 | −0.0574522 | − | 0.998348i | \(-0.518298\pi\) | ||||
−0.0574522 | + | 0.998348i | \(0.518298\pi\) | |||||||
\(44\) | 1.26526 | 0.190745 | ||||||||
\(45\) | 5.24570 | 0.781983 | ||||||||
\(46\) | −1.63671 | −0.241319 | ||||||||
\(47\) | 8.82078 | 1.28664 | 0.643322 | − | 0.765596i | \(-0.277556\pi\) | ||||
0.643322 | + | 0.765596i | \(0.277556\pi\) | |||||||
\(48\) | 2.41201 | 0.348144 | ||||||||
\(49\) | −6.60847 | −0.944067 | ||||||||
\(50\) | 2.25995 | 0.319605 | ||||||||
\(51\) | 0.466268 | 0.0652906 | ||||||||
\(52\) | −2.45176 | −0.339997 | ||||||||
\(53\) | 3.41241 | 0.468730 | 0.234365 | − | 0.972149i | \(-0.424699\pi\) | ||||
0.234365 | + | 0.972149i | \(0.424699\pi\) | |||||||
\(54\) | −4.64152 | −0.631630 | ||||||||
\(55\) | −3.54600 | −0.478143 | ||||||||
\(56\) | 1.35307 | 0.180811 | ||||||||
\(57\) | 0.192247 | 0.0254637 | ||||||||
\(58\) | 1.63671 | 0.214910 | ||||||||
\(59\) | 10.8373 | 1.41089 | 0.705447 | − | 0.708762i | \(-0.250746\pi\) | ||||
0.705447 | + | 0.708762i | \(0.250746\pi\) | |||||||
\(60\) | 0.636090 | 0.0821189 | ||||||||
\(61\) | −6.58204 | −0.842744 | −0.421372 | − | 0.906888i | \(-0.638451\pi\) | ||||
−0.421372 | + | 0.906888i | \(0.638451\pi\) | |||||||
\(62\) | −9.32133 | −1.18381 | ||||||||
\(63\) | −1.72536 | −0.217375 | ||||||||
\(64\) | 3.75442 | 0.469303 | ||||||||
\(65\) | 6.87126 | 0.852275 | ||||||||
\(66\) | 1.50268 | 0.184967 | ||||||||
\(67\) | 7.92908 | 0.968691 | 0.484345 | − | 0.874877i | \(-0.339058\pi\) | ||||
0.484345 | + | 0.874877i | \(0.339058\pi\) | |||||||
\(68\) | −0.642568 | −0.0779228 | ||||||||
\(69\) | −0.492566 | −0.0592980 | ||||||||
\(70\) | 1.94832 | 0.232869 | ||||||||
\(71\) | −4.28721 | −0.508798 | −0.254399 | − | 0.967099i | \(-0.581878\pi\) | ||||
−0.254399 | + | 0.967099i | \(0.581878\pi\) | |||||||
\(72\) | −5.96256 | −0.702695 | ||||||||
\(73\) | −7.27027 | −0.850921 | −0.425461 | − | 0.904977i | \(-0.639888\pi\) | ||||
−0.425461 | + | 0.904977i | \(0.639888\pi\) | |||||||
\(74\) | −9.07632 | −1.05510 | ||||||||
\(75\) | 0.680129 | 0.0785346 | ||||||||
\(76\) | −0.264937 | −0.0303903 | ||||||||
\(77\) | 1.16631 | 0.132914 | ||||||||
\(78\) | −2.91182 | −0.329699 | ||||||||
\(79\) | 15.1128 | 1.70032 | 0.850161 | − | 0.526523i | \(-0.176505\pi\) | ||||
0.850161 | + | 0.526523i | \(0.176505\pi\) | |||||||
\(80\) | 9.31585 | 1.04154 | ||||||||
\(81\) | 6.87528 | 0.763919 | ||||||||
\(82\) | −19.0710 | −2.10603 | ||||||||
\(83\) | 16.1616 | 1.77396 | 0.886981 | − | 0.461806i | \(-0.152798\pi\) | ||||
0.886981 | + | 0.461806i | \(0.152798\pi\) | |||||||
\(84\) | −0.209216 | −0.0228273 | ||||||||
\(85\) | 1.80085 | 0.195330 | ||||||||
\(86\) | 1.23322 | 0.132982 | ||||||||
\(87\) | 0.492566 | 0.0528086 | ||||||||
\(88\) | 4.03059 | 0.429662 | ||||||||
\(89\) | −16.1681 | −1.71382 | −0.856909 | − | 0.515468i | \(-0.827618\pi\) | ||||
−0.856909 | + | 0.515468i | \(0.827618\pi\) | |||||||
\(90\) | −8.58567 | −0.905009 | ||||||||
\(91\) | −2.26002 | −0.236915 | ||||||||
\(92\) | 0.678809 | 0.0707707 | ||||||||
\(93\) | −2.80525 | −0.290891 | ||||||||
\(94\) | −14.4370 | −1.48907 | ||||||||
\(95\) | 0.742509 | 0.0761799 | ||||||||
\(96\) | −1.81751 | −0.185499 | ||||||||
\(97\) | 12.8667 | 1.30641 | 0.653205 | − | 0.757181i | \(-0.273424\pi\) | ||||
0.653205 | + | 0.757181i | \(0.273424\pi\) | |||||||
\(98\) | 10.8161 | 1.09259 | ||||||||
\(99\) | −5.13959 | −0.516548 | ||||||||
\(100\) | −0.937292 | −0.0937292 | ||||||||
\(101\) | 14.9233 | 1.48493 | 0.742463 | − | 0.669887i | \(-0.233658\pi\) | ||||
0.742463 | + | 0.669887i | \(0.233658\pi\) | |||||||
\(102\) | −0.763144 | −0.0755626 | ||||||||
\(103\) | −18.6970 | −1.84227 | −0.921133 | − | 0.389249i | \(-0.872735\pi\) | ||||
−0.921133 | + | 0.389249i | \(0.872735\pi\) | |||||||
\(104\) | −7.81027 | −0.765860 | ||||||||
\(105\) | 0.586347 | 0.0572216 | ||||||||
\(106\) | −5.58511 | −0.542474 | ||||||||
\(107\) | 19.2587 | 1.86181 | 0.930904 | − | 0.365263i | \(-0.119021\pi\) | ||||
0.930904 | + | 0.365263i | \(0.119021\pi\) | |||||||
\(108\) | 1.92503 | 0.185236 | ||||||||
\(109\) | 7.69095 | 0.736659 | 0.368330 | − | 0.929695i | \(-0.379930\pi\) | ||||
0.368330 | + | 0.929695i | \(0.379930\pi\) | |||||||
\(110\) | 5.80377 | 0.553367 | ||||||||
\(111\) | −2.73151 | −0.259264 | ||||||||
\(112\) | −3.06407 | −0.289527 | ||||||||
\(113\) | 2.99643 | 0.281881 | 0.140940 | − | 0.990018i | \(-0.454987\pi\) | ||||
0.140940 | + | 0.990018i | \(0.454987\pi\) | |||||||
\(114\) | −0.314652 | −0.0294698 | ||||||||
\(115\) | −1.90242 | −0.177402 | ||||||||
\(116\) | −0.678809 | −0.0630258 | ||||||||
\(117\) | 9.95924 | 0.920732 | ||||||||
\(118\) | −17.7375 | −1.63287 | ||||||||
\(119\) | −0.592318 | −0.0542977 | ||||||||
\(120\) | 2.02632 | 0.184977 | ||||||||
\(121\) | −7.52572 | −0.684157 | ||||||||
\(122\) | 10.7729 | 0.975329 | ||||||||
\(123\) | −5.73939 | −0.517504 | ||||||||
\(124\) | 3.86593 | 0.347171 | ||||||||
\(125\) | 12.1390 | 1.08574 | ||||||||
\(126\) | 2.82391 | 0.251574 | ||||||||
\(127\) | −12.9406 | −1.14829 | −0.574147 | − | 0.818752i | \(-0.694666\pi\) | ||||
−0.574147 | + | 0.818752i | \(0.694666\pi\) | |||||||
\(128\) | −13.5246 | −1.19542 | ||||||||
\(129\) | 0.371138 | 0.0326768 | ||||||||
\(130\) | −11.2462 | −0.986361 | ||||||||
\(131\) | −12.3946 | −1.08292 | −0.541461 | − | 0.840726i | \(-0.682129\pi\) | ||||
−0.541461 | + | 0.840726i | \(0.682129\pi\) | |||||||
\(132\) | −0.623224 | −0.0542447 | ||||||||
\(133\) | −0.244218 | −0.0211764 | ||||||||
\(134\) | −12.9776 | −1.12109 | ||||||||
\(135\) | −5.39506 | −0.464333 | ||||||||
\(136\) | −2.04695 | −0.175525 | ||||||||
\(137\) | 1.05173 | 0.0898552 | 0.0449276 | − | 0.998990i | \(-0.485694\pi\) | ||||
0.0449276 | + | 0.998990i | \(0.485694\pi\) | |||||||
\(138\) | 0.806186 | 0.0686271 | ||||||||
\(139\) | −21.9528 | −1.86201 | −0.931005 | − | 0.365007i | \(-0.881067\pi\) | ||||
−0.931005 | + | 0.365007i | \(0.881067\pi\) | |||||||
\(140\) | −0.808049 | −0.0682926 | ||||||||
\(141\) | −4.34482 | −0.365900 | ||||||||
\(142\) | 7.01690 | 0.588845 | ||||||||
\(143\) | −6.73227 | −0.562981 | ||||||||
\(144\) | 13.5024 | 1.12520 | ||||||||
\(145\) | 1.90242 | 0.157988 | ||||||||
\(146\) | 11.8993 | 0.984794 | ||||||||
\(147\) | 3.25511 | 0.268477 | ||||||||
\(148\) | 3.76432 | 0.309425 | ||||||||
\(149\) | −12.7909 | −1.04787 | −0.523934 | − | 0.851759i | \(-0.675536\pi\) | ||||
−0.523934 | + | 0.851759i | \(0.675536\pi\) | |||||||
\(150\) | −1.11317 | −0.0908901 | ||||||||
\(151\) | −1.98814 | −0.161793 | −0.0808963 | − | 0.996723i | \(-0.525778\pi\) | ||||
−0.0808963 | + | 0.996723i | \(0.525778\pi\) | |||||||
\(152\) | −0.843979 | −0.0684557 | ||||||||
\(153\) | 2.61017 | 0.211019 | ||||||||
\(154\) | −1.90891 | −0.153825 | ||||||||
\(155\) | −10.8346 | −0.870258 | ||||||||
\(156\) | 1.20765 | 0.0966895 | ||||||||
\(157\) | 2.97702 | 0.237592 | 0.118796 | − | 0.992919i | \(-0.462097\pi\) | ||||
0.118796 | + | 0.992919i | \(0.462097\pi\) | |||||||
\(158\) | −24.7352 | −1.96783 | ||||||||
\(159\) | −1.68084 | −0.133299 | ||||||||
\(160\) | −7.01971 | −0.554957 | ||||||||
\(161\) | 0.625725 | 0.0493140 | ||||||||
\(162\) | −11.2528 | −0.884104 | ||||||||
\(163\) | 2.96244 | 0.232036 | 0.116018 | − | 0.993247i | \(-0.462987\pi\) | ||||
0.116018 | + | 0.993247i | \(0.462987\pi\) | |||||||
\(164\) | 7.90950 | 0.617628 | ||||||||
\(165\) | 1.74664 | 0.135976 | ||||||||
\(166\) | −26.4517 | −2.05305 | ||||||||
\(167\) | 5.29393 | 0.409657 | 0.204828 | − | 0.978798i | \(-0.434336\pi\) | ||||
0.204828 | + | 0.978798i | \(0.434336\pi\) | |||||||
\(168\) | −0.666475 | −0.0514197 | ||||||||
\(169\) | 0.0454596 | 0.00349689 | ||||||||
\(170\) | −2.94747 | −0.226061 | ||||||||
\(171\) | 1.07620 | 0.0822988 | ||||||||
\(172\) | −0.511468 | −0.0389990 | ||||||||
\(173\) | 12.7744 | 0.971220 | 0.485610 | − | 0.874176i | \(-0.338598\pi\) | ||||
0.485610 | + | 0.874176i | \(0.338598\pi\) | |||||||
\(174\) | −0.806186 | −0.0611168 | ||||||||
\(175\) | −0.863994 | −0.0653118 | ||||||||
\(176\) | −9.12741 | −0.688005 | ||||||||
\(177\) | −5.33808 | −0.401235 | ||||||||
\(178\) | 26.4625 | 1.98345 | ||||||||
\(179\) | −0.984747 | −0.0736034 | −0.0368017 | − | 0.999323i | \(-0.511717\pi\) | ||||
−0.0368017 | + | 0.999323i | \(0.511717\pi\) | |||||||
\(180\) | 3.56083 | 0.265408 | ||||||||
\(181\) | 1.37675 | 0.102333 | 0.0511664 | − | 0.998690i | \(-0.483706\pi\) | ||||
0.0511664 | + | 0.998690i | \(0.483706\pi\) | |||||||
\(182\) | 3.69900 | 0.274188 | ||||||||
\(183\) | 3.24209 | 0.239662 | ||||||||
\(184\) | 2.16240 | 0.159414 | ||||||||
\(185\) | −10.5498 | −0.775639 | ||||||||
\(186\) | 4.59137 | 0.336655 | ||||||||
\(187\) | −1.76443 | −0.129028 | ||||||||
\(188\) | 5.98763 | 0.436693 | ||||||||
\(189\) | 1.77448 | 0.129075 | ||||||||
\(190\) | −1.21527 | −0.0881650 | ||||||||
\(191\) | −18.3610 | −1.32856 | −0.664279 | − | 0.747485i | \(-0.731261\pi\) | ||||
−0.664279 | + | 0.747485i | \(0.731261\pi\) | |||||||
\(192\) | −1.84930 | −0.133462 | ||||||||
\(193\) | 19.1865 | 1.38108 | 0.690539 | − | 0.723296i | \(-0.257374\pi\) | ||||
0.690539 | + | 0.723296i | \(0.257374\pi\) | |||||||
\(194\) | −21.0589 | −1.51194 | ||||||||
\(195\) | −3.38455 | −0.242373 | ||||||||
\(196\) | −4.48589 | −0.320420 | ||||||||
\(197\) | −14.3075 | −1.01937 | −0.509683 | − | 0.860362i | \(-0.670237\pi\) | ||||
−0.509683 | + | 0.860362i | \(0.670237\pi\) | |||||||
\(198\) | 8.41200 | 0.597815 | ||||||||
\(199\) | 12.0238 | 0.852348 | 0.426174 | − | 0.904641i | \(-0.359861\pi\) | ||||
0.426174 | + | 0.904641i | \(0.359861\pi\) | |||||||
\(200\) | −2.98582 | −0.211129 | ||||||||
\(201\) | −3.90559 | −0.275479 | ||||||||
\(202\) | −24.4251 | −1.71854 | ||||||||
\(203\) | −0.625725 | −0.0439173 | ||||||||
\(204\) | 0.316507 | 0.0221599 | ||||||||
\(205\) | −22.1671 | −1.54822 | ||||||||
\(206\) | 30.6014 | 2.13210 | ||||||||
\(207\) | −2.75738 | −0.191651 | ||||||||
\(208\) | 17.6866 | 1.22635 | ||||||||
\(209\) | −0.727490 | −0.0503215 | ||||||||
\(210\) | −0.959678 | −0.0662240 | ||||||||
\(211\) | −10.6373 | −0.732302 | −0.366151 | − | 0.930555i | \(-0.619325\pi\) | ||||
−0.366151 | + | 0.930555i | \(0.619325\pi\) | |||||||
\(212\) | 2.31637 | 0.159089 | ||||||||
\(213\) | 2.11173 | 0.144693 | ||||||||
\(214\) | −31.5208 | −2.15472 | ||||||||
\(215\) | 1.43343 | 0.0977594 | ||||||||
\(216\) | 6.13233 | 0.417252 | ||||||||
\(217\) | 3.56361 | 0.241914 | ||||||||
\(218\) | −12.5878 | −0.852555 | ||||||||
\(219\) | 3.58109 | 0.241988 | ||||||||
\(220\) | −2.40706 | −0.162284 | ||||||||
\(221\) | 3.41902 | 0.229988 | ||||||||
\(222\) | 4.47068 | 0.300053 | ||||||||
\(223\) | 7.75259 | 0.519152 | 0.259576 | − | 0.965723i | \(-0.416417\pi\) | ||||
0.259576 | + | 0.965723i | \(0.416417\pi\) | |||||||
\(224\) | 2.30885 | 0.154266 | ||||||||
\(225\) | 3.80736 | 0.253824 | ||||||||
\(226\) | −4.90428 | −0.326228 | ||||||||
\(227\) | 7.50827 | 0.498341 | 0.249171 | − | 0.968460i | \(-0.419842\pi\) | ||||
0.249171 | + | 0.968460i | \(0.419842\pi\) | |||||||
\(228\) | 0.130499 | 0.00864250 | ||||||||
\(229\) | 10.5239 | 0.695439 | 0.347719 | − | 0.937599i | \(-0.386956\pi\) | ||||
0.347719 | + | 0.937599i | \(0.386956\pi\) | |||||||
\(230\) | 3.11371 | 0.205312 | ||||||||
\(231\) | −0.574486 | −0.0377984 | ||||||||
\(232\) | −2.16240 | −0.141969 | ||||||||
\(233\) | −3.79993 | −0.248942 | −0.124471 | − | 0.992223i | \(-0.539723\pi\) | ||||
−0.124471 | + | 0.992223i | \(0.539723\pi\) | |||||||
\(234\) | −16.3004 | −1.06559 | ||||||||
\(235\) | −16.7809 | −1.09466 | ||||||||
\(236\) | 7.35645 | 0.478864 | ||||||||
\(237\) | −7.44404 | −0.483543 | ||||||||
\(238\) | 0.969451 | 0.0628402 | ||||||||
\(239\) | −5.77321 | −0.373438 | −0.186719 | − | 0.982413i | \(-0.559785\pi\) | ||||
−0.186719 | + | 0.982413i | \(0.559785\pi\) | |||||||
\(240\) | −4.58867 | −0.296197 | ||||||||
\(241\) | 11.7005 | 0.753694 | 0.376847 | − | 0.926276i | \(-0.377008\pi\) | ||||
0.376847 | + | 0.926276i | \(0.377008\pi\) | |||||||
\(242\) | 12.3174 | 0.791793 | ||||||||
\(243\) | −11.8942 | −0.763013 | ||||||||
\(244\) | −4.46795 | −0.286031 | ||||||||
\(245\) | 12.5721 | 0.803202 | ||||||||
\(246\) | 9.39370 | 0.598921 | ||||||||
\(247\) | 1.40969 | 0.0896966 | ||||||||
\(248\) | 12.3153 | 0.782020 | ||||||||
\(249\) | −7.96063 | −0.504485 | ||||||||
\(250\) | −19.8679 | −1.25656 | ||||||||
\(251\) | −18.4434 | −1.16414 | −0.582068 | − | 0.813140i | \(-0.697756\pi\) | ||||
−0.582068 | + | 0.813140i | \(0.697756\pi\) | |||||||
\(252\) | −1.17119 | −0.0737780 | ||||||||
\(253\) | 1.86394 | 0.117185 | ||||||||
\(254\) | 21.1800 | 1.32895 | ||||||||
\(255\) | −0.887039 | −0.0555486 | ||||||||
\(256\) | 14.6270 | 0.914190 | ||||||||
\(257\) | −1.32683 | −0.0827652 | −0.0413826 | − | 0.999143i | \(-0.513176\pi\) | ||||
−0.0413826 | + | 0.999143i | \(0.513176\pi\) | |||||||
\(258\) | −0.607443 | −0.0378178 | ||||||||
\(259\) | 3.46994 | 0.215612 | ||||||||
\(260\) | 4.66427 | 0.289266 | ||||||||
\(261\) | 2.75738 | 0.170677 | ||||||||
\(262\) | 20.2863 | 1.25329 | ||||||||
\(263\) | 10.6066 | 0.654030 | 0.327015 | − | 0.945019i | \(-0.393957\pi\) | ||||
0.327015 | + | 0.945019i | \(0.393957\pi\) | |||||||
\(264\) | −1.98533 | −0.122189 | ||||||||
\(265\) | −6.49184 | −0.398791 | ||||||||
\(266\) | 0.399714 | 0.0245080 | ||||||||
\(267\) | 7.96387 | 0.487381 | ||||||||
\(268\) | 5.38233 | 0.328778 | ||||||||
\(269\) | 17.9977 | 1.09734 | 0.548670 | − | 0.836039i | \(-0.315134\pi\) | ||||
0.548670 | + | 0.836039i | \(0.315134\pi\) | |||||||
\(270\) | 8.83013 | 0.537384 | ||||||||
\(271\) | 25.3228 | 1.53825 | 0.769127 | − | 0.639097i | \(-0.220692\pi\) | ||||
0.769127 | + | 0.639097i | \(0.220692\pi\) | |||||||
\(272\) | 4.63540 | 0.281062 | ||||||||
\(273\) | 1.11321 | 0.0673745 | ||||||||
\(274\) | −1.72137 | −0.103992 | ||||||||
\(275\) | −2.57371 | −0.155200 | ||||||||
\(276\) | −0.334358 | −0.0201260 | ||||||||
\(277\) | 29.9578 | 1.79999 | 0.899995 | − | 0.435900i | \(-0.143570\pi\) | ||||
0.899995 | + | 0.435900i | \(0.143570\pi\) | |||||||
\(278\) | 35.9302 | 2.15495 | ||||||||
\(279\) | −15.7038 | −0.940159 | ||||||||
\(280\) | −2.57411 | −0.153832 | ||||||||
\(281\) | 13.7978 | 0.823109 | 0.411555 | − | 0.911385i | \(-0.364986\pi\) | ||||
0.411555 | + | 0.911385i | \(0.364986\pi\) | |||||||
\(282\) | 7.11119 | 0.423465 | ||||||||
\(283\) | −5.14314 | −0.305728 | −0.152864 | − | 0.988247i | \(-0.548850\pi\) | ||||
−0.152864 | + | 0.988247i | \(0.548850\pi\) | |||||||
\(284\) | −2.91019 | −0.172688 | ||||||||
\(285\) | −0.365735 | −0.0216643 | ||||||||
\(286\) | 11.0188 | 0.651553 | ||||||||
\(287\) | 7.29096 | 0.430372 | ||||||||
\(288\) | −10.1744 | −0.599532 | ||||||||
\(289\) | −16.1039 | −0.947290 | ||||||||
\(290\) | −3.11371 | −0.182843 | ||||||||
\(291\) | −6.33767 | −0.371521 | ||||||||
\(292\) | −4.93513 | −0.288806 | ||||||||
\(293\) | −2.75536 | −0.160970 | −0.0804848 | − | 0.996756i | \(-0.525647\pi\) | ||||
−0.0804848 | + | 0.996756i | \(0.525647\pi\) | |||||||
\(294\) | −5.32765 | −0.310715 | ||||||||
\(295\) | −20.6171 | −1.20037 | ||||||||
\(296\) | 11.9915 | 0.696995 | ||||||||
\(297\) | 5.28593 | 0.306721 | ||||||||
\(298\) | 20.9349 | 1.21272 | ||||||||
\(299\) | −3.61185 | −0.208879 | ||||||||
\(300\) | 0.461678 | 0.0266550 | ||||||||
\(301\) | −0.471470 | −0.0271751 | ||||||||
\(302\) | 3.25400 | 0.187247 | ||||||||
\(303\) | −7.35071 | −0.422288 | ||||||||
\(304\) | 1.91122 | 0.109616 | ||||||||
\(305\) | 12.5218 | 0.716997 | ||||||||
\(306\) | −4.27208 | −0.244218 | ||||||||
\(307\) | 17.5805 | 1.00337 | 0.501687 | − | 0.865049i | \(-0.332713\pi\) | ||||
0.501687 | + | 0.865049i | \(0.332713\pi\) | |||||||
\(308\) | 0.791704 | 0.0451115 | ||||||||
\(309\) | 9.20948 | 0.523909 | ||||||||
\(310\) | 17.7331 | 1.00717 | ||||||||
\(311\) | 12.4105 | 0.703733 | 0.351867 | − | 0.936050i | \(-0.385547\pi\) | ||||
0.351867 | + | 0.936050i | \(0.385547\pi\) | |||||||
\(312\) | 3.84707 | 0.217798 | ||||||||
\(313\) | 3.10520 | 0.175517 | 0.0877583 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877583 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(314\) | −4.87251 | −0.274972 | ||||||||
\(315\) | 3.28236 | 0.184940 | ||||||||
\(316\) | 10.2587 | 0.577097 | ||||||||
\(317\) | 29.2431 | 1.64246 | 0.821229 | − | 0.570598i | \(-0.193289\pi\) | ||||
0.821229 | + | 0.570598i | \(0.193289\pi\) | |||||||
\(318\) | 2.75104 | 0.154270 | ||||||||
\(319\) | −1.86394 | −0.104361 | ||||||||
\(320\) | −7.14250 | −0.399278 | ||||||||
\(321\) | −9.48618 | −0.529467 | ||||||||
\(322\) | −1.02413 | −0.0570724 | ||||||||
\(323\) | 0.369459 | 0.0205573 | ||||||||
\(324\) | 4.66700 | 0.259278 | ||||||||
\(325\) | 4.98720 | 0.276640 | ||||||||
\(326\) | −4.84865 | −0.268542 | ||||||||
\(327\) | −3.78830 | −0.209493 | ||||||||
\(328\) | 25.1964 | 1.39124 | ||||||||
\(329\) | 5.51938 | 0.304293 | ||||||||
\(330\) | −2.85874 | −0.157368 | ||||||||
\(331\) | −10.2179 | −0.561628 | −0.280814 | − | 0.959762i | \(-0.590604\pi\) | ||||
−0.280814 | + | 0.959762i | \(0.590604\pi\) | |||||||
\(332\) | 10.9706 | 0.602090 | ||||||||
\(333\) | −15.2910 | −0.837940 | ||||||||
\(334\) | −8.66462 | −0.474107 | ||||||||
\(335\) | −15.0845 | −0.824152 | ||||||||
\(336\) | 1.50926 | 0.0823367 | ||||||||
\(337\) | 4.19076 | 0.228285 | 0.114143 | − | 0.993464i | \(-0.463588\pi\) | ||||
0.114143 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(338\) | −0.0744041 | −0.00404705 | ||||||||
\(339\) | −1.47594 | −0.0801621 | ||||||||
\(340\) | 1.22244 | 0.0662959 | ||||||||
\(341\) | 10.6155 | 0.574860 | ||||||||
\(342\) | −1.76142 | −0.0952465 | ||||||||
\(343\) | −8.51515 | −0.459775 | ||||||||
\(344\) | −1.62932 | −0.0878472 | ||||||||
\(345\) | 0.937068 | 0.0504501 | ||||||||
\(346\) | −20.9080 | −1.12402 | ||||||||
\(347\) | −6.16002 | −0.330687 | −0.165344 | − | 0.986236i | \(-0.552873\pi\) | ||||
−0.165344 | + | 0.986236i | \(0.552873\pi\) | |||||||
\(348\) | 0.334358 | 0.0179235 | ||||||||
\(349\) | 7.85979 | 0.420725 | 0.210362 | − | 0.977623i | \(-0.432536\pi\) | ||||
0.210362 | + | 0.977623i | \(0.432536\pi\) | |||||||
\(350\) | 1.41410 | 0.0755870 | ||||||||
\(351\) | −10.2428 | −0.546720 | ||||||||
\(352\) | 6.87772 | 0.366584 | ||||||||
\(353\) | 11.6365 | 0.619351 | 0.309675 | − | 0.950842i | \(-0.399780\pi\) | ||||
0.309675 | + | 0.950842i | \(0.399780\pi\) | |||||||
\(354\) | 8.73687 | 0.464359 | ||||||||
\(355\) | 8.15608 | 0.432880 | ||||||||
\(356\) | −10.9751 | −0.581677 | ||||||||
\(357\) | 0.291756 | 0.0154413 | ||||||||
\(358\) | 1.61174 | 0.0851832 | ||||||||
\(359\) | −2.33879 | −0.123437 | −0.0617184 | − | 0.998094i | \(-0.519658\pi\) | ||||
−0.0617184 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(360\) | 11.3433 | 0.597845 | ||||||||
\(361\) | −18.8477 | −0.991983 | ||||||||
\(362\) | −2.25333 | −0.118433 | ||||||||
\(363\) | 3.70691 | 0.194563 | ||||||||
\(364\) | −1.53412 | −0.0804099 | ||||||||
\(365\) | 13.8311 | 0.723955 | ||||||||
\(366\) | −5.30635 | −0.277367 | ||||||||
\(367\) | 26.2052 | 1.36790 | 0.683951 | − | 0.729528i | \(-0.260260\pi\) | ||||
0.683951 | + | 0.729528i | \(0.260260\pi\) | |||||||
\(368\) | −4.89684 | −0.255265 | ||||||||
\(369\) | −32.1291 | −1.67257 | ||||||||
\(370\) | 17.2670 | 0.897668 | ||||||||
\(371\) | 2.13523 | 0.110856 | ||||||||
\(372\) | −1.90423 | −0.0987296 | ||||||||
\(373\) | 17.5926 | 0.910909 | 0.455454 | − | 0.890259i | \(-0.349477\pi\) | ||||
0.455454 | + | 0.890259i | \(0.349477\pi\) | |||||||
\(374\) | 2.88785 | 0.149327 | ||||||||
\(375\) | −5.97923 | −0.308766 | ||||||||
\(376\) | 19.0741 | 0.983671 | ||||||||
\(377\) | 3.61185 | 0.186020 | ||||||||
\(378\) | −2.90431 | −0.149382 | ||||||||
\(379\) | −24.9604 | −1.28213 | −0.641064 | − | 0.767488i | \(-0.721507\pi\) | ||||
−0.641064 | + | 0.767488i | \(0.721507\pi\) | |||||||
\(380\) | 0.504022 | 0.0258558 | ||||||||
\(381\) | 6.37411 | 0.326555 | ||||||||
\(382\) | 30.0516 | 1.53757 | ||||||||
\(383\) | −7.00053 | −0.357710 | −0.178855 | − | 0.983875i | \(-0.557239\pi\) | ||||
−0.178855 | + | 0.983875i | \(0.557239\pi\) | |||||||
\(384\) | 6.66178 | 0.339957 | ||||||||
\(385\) | −2.21882 | −0.113082 | ||||||||
\(386\) | −31.4027 | −1.59836 | ||||||||
\(387\) | 2.07762 | 0.105612 | ||||||||
\(388\) | 8.73400 | 0.443402 | ||||||||
\(389\) | −29.5510 | −1.49829 | −0.749147 | − | 0.662404i | \(-0.769536\pi\) | ||||
−0.749147 | + | 0.662404i | \(0.769536\pi\) | |||||||
\(390\) | 5.53952 | 0.280504 | ||||||||
\(391\) | −0.946611 | −0.0478722 | ||||||||
\(392\) | −14.2902 | −0.721763 | ||||||||
\(393\) | 6.10516 | 0.307965 | ||||||||
\(394\) | 23.4172 | 1.17974 | ||||||||
\(395\) | −28.7509 | −1.44662 | ||||||||
\(396\) | −3.48880 | −0.175319 | ||||||||
\(397\) | 10.9239 | 0.548253 | 0.274126 | − | 0.961694i | \(-0.411611\pi\) | ||||
0.274126 | + | 0.961694i | \(0.411611\pi\) | |||||||
\(398\) | −19.6795 | −0.986444 | ||||||||
\(399\) | 0.120294 | 0.00602221 | ||||||||
\(400\) | 6.76150 | 0.338075 | ||||||||
\(401\) | 5.68048 | 0.283669 | 0.141835 | − | 0.989890i | \(-0.454700\pi\) | ||||
0.141835 | + | 0.989890i | \(0.454700\pi\) | |||||||
\(402\) | 6.39231 | 0.318819 | ||||||||
\(403\) | −20.5701 | −1.02467 | ||||||||
\(404\) | 10.1301 | 0.503990 | ||||||||
\(405\) | −13.0797 | −0.649934 | ||||||||
\(406\) | 1.02413 | 0.0508266 | ||||||||
\(407\) | 10.3364 | 0.512358 | ||||||||
\(408\) | 1.00826 | 0.0499163 | ||||||||
\(409\) | −33.6508 | −1.66393 | −0.831963 | − | 0.554832i | \(-0.812783\pi\) | ||||
−0.831963 | + | 0.554832i | \(0.812783\pi\) | |||||||
\(410\) | 36.2810 | 1.79179 | ||||||||
\(411\) | −0.518045 | −0.0255533 | ||||||||
\(412\) | −12.6917 | −0.625273 | ||||||||
\(413\) | 6.78116 | 0.333679 | ||||||||
\(414\) | 4.51302 | 0.221803 | ||||||||
\(415\) | −30.7461 | −1.50927 | ||||||||
\(416\) | −13.3273 | −0.653424 | ||||||||
\(417\) | 10.8132 | 0.529524 | ||||||||
\(418\) | 1.19069 | 0.0582385 | ||||||||
\(419\) | −3.58358 | −0.175070 | −0.0875348 | − | 0.996161i | \(-0.527899\pi\) | ||||
−0.0875348 | + | 0.996161i | \(0.527899\pi\) | |||||||
\(420\) | 0.398017 | 0.0194213 | ||||||||
\(421\) | −31.5947 | −1.53983 | −0.769915 | − | 0.638147i | \(-0.779701\pi\) | ||||
−0.769915 | + | 0.638147i | \(0.779701\pi\) | |||||||
\(422\) | 17.4102 | 0.847513 | ||||||||
\(423\) | −24.3222 | −1.18259 | ||||||||
\(424\) | 7.37900 | 0.358356 | ||||||||
\(425\) | 1.30707 | 0.0634022 | ||||||||
\(426\) | −3.45629 | −0.167458 | ||||||||
\(427\) | −4.11854 | −0.199310 | ||||||||
\(428\) | 13.0730 | 0.631906 | ||||||||
\(429\) | 3.31609 | 0.160102 | ||||||||
\(430\) | −2.34611 | −0.113139 | ||||||||
\(431\) | −9.32434 | −0.449138 | −0.224569 | − | 0.974458i | \(-0.572097\pi\) | ||||
−0.224569 | + | 0.974458i | \(0.572097\pi\) | |||||||
\(432\) | −13.8869 | −0.668133 | ||||||||
\(433\) | −31.0162 | −1.49054 | −0.745272 | − | 0.666761i | \(-0.767680\pi\) | ||||
−0.745272 | + | 0.666761i | \(0.767680\pi\) | |||||||
\(434\) | −5.83258 | −0.279973 | ||||||||
\(435\) | −0.937068 | −0.0449290 | ||||||||
\(436\) | 5.22069 | 0.250025 | ||||||||
\(437\) | −0.390297 | −0.0186704 | ||||||||
\(438\) | −5.86119 | −0.280059 | ||||||||
\(439\) | 23.7687 | 1.13442 | 0.567210 | − | 0.823573i | \(-0.308023\pi\) | ||||
0.567210 | + | 0.823573i | \(0.308023\pi\) | |||||||
\(440\) | −7.66789 | −0.365552 | ||||||||
\(441\) | 18.2221 | 0.867717 | ||||||||
\(442\) | −5.59593 | −0.266171 | ||||||||
\(443\) | 25.0563 | 1.19046 | 0.595230 | − | 0.803555i | \(-0.297061\pi\) | ||||
0.595230 | + | 0.803555i | \(0.297061\pi\) | |||||||
\(444\) | −1.85417 | −0.0879952 | ||||||||
\(445\) | 30.7586 | 1.45810 | ||||||||
\(446\) | −12.6887 | −0.600828 | ||||||||
\(447\) | 6.30034 | 0.297996 | ||||||||
\(448\) | 2.34923 | 0.110991 | ||||||||
\(449\) | 40.3089 | 1.90230 | 0.951148 | − | 0.308734i | \(-0.0999054\pi\) | ||||
0.951148 | + | 0.308734i | \(0.0999054\pi\) | |||||||
\(450\) | −6.23153 | −0.293757 | ||||||||
\(451\) | 21.7187 | 1.02269 | ||||||||
\(452\) | 2.03401 | 0.0956716 | ||||||||
\(453\) | 0.979290 | 0.0460111 | ||||||||
\(454\) | −12.2888 | −0.576744 | ||||||||
\(455\) | 4.29952 | 0.201565 | ||||||||
\(456\) | 0.415715 | 0.0194676 | ||||||||
\(457\) | −1.07682 | −0.0503713 | −0.0251856 | − | 0.999683i | \(-0.508018\pi\) | ||||
−0.0251856 | + | 0.999683i | \(0.508018\pi\) | |||||||
\(458\) | −17.2245 | −0.804849 | ||||||||
\(459\) | −2.68448 | −0.125301 | ||||||||
\(460\) | −1.29138 | −0.0602110 | ||||||||
\(461\) | 36.1413 | 1.68327 | 0.841635 | − | 0.540047i | \(-0.181594\pi\) | ||||
0.841635 | + | 0.540047i | \(0.181594\pi\) | |||||||
\(462\) | 0.940265 | 0.0437451 | ||||||||
\(463\) | −17.3235 | −0.805090 | −0.402545 | − | 0.915400i | \(-0.631874\pi\) | ||||
−0.402545 | + | 0.915400i | \(0.631874\pi\) | |||||||
\(464\) | 4.89684 | 0.227330 | ||||||||
\(465\) | 5.33677 | 0.247487 | ||||||||
\(466\) | 6.21937 | 0.288107 | ||||||||
\(467\) | −11.1144 | −0.514311 | −0.257156 | − | 0.966370i | \(-0.582785\pi\) | ||||
−0.257156 | + | 0.966370i | \(0.582785\pi\) | |||||||
\(468\) | 6.76042 | 0.312500 | ||||||||
\(469\) | 4.96142 | 0.229097 | ||||||||
\(470\) | 27.4653 | 1.26688 | ||||||||
\(471\) | −1.46638 | −0.0675671 | ||||||||
\(472\) | 23.4346 | 1.07866 | ||||||||
\(473\) | −1.40444 | −0.0645762 | ||||||||
\(474\) | 12.1837 | 0.559617 | ||||||||
\(475\) | 0.538917 | 0.0247272 | ||||||||
\(476\) | −0.402071 | −0.0184289 | ||||||||
\(477\) | −9.40930 | −0.430822 | ||||||||
\(478\) | 9.44906 | 0.432190 | ||||||||
\(479\) | −26.5340 | −1.21237 | −0.606184 | − | 0.795324i | \(-0.707301\pi\) | ||||
−0.606184 | + | 0.795324i | \(0.707301\pi\) | |||||||
\(480\) | 3.45767 | 0.157820 | ||||||||
\(481\) | −20.0294 | −0.913263 | ||||||||
\(482\) | −19.1502 | −0.872270 | ||||||||
\(483\) | −0.308211 | −0.0140241 | ||||||||
\(484\) | −5.10853 | −0.232206 | ||||||||
\(485\) | −24.4778 | −1.11148 | ||||||||
\(486\) | 19.4673 | 0.883055 | ||||||||
\(487\) | −0.676829 | −0.0306701 | −0.0153350 | − | 0.999882i | \(-0.504881\pi\) | ||||
−0.0153350 | + | 0.999882i | \(0.504881\pi\) | |||||||
\(488\) | −14.2330 | −0.644298 | ||||||||
\(489\) | −1.45920 | −0.0659872 | ||||||||
\(490\) | −20.5768 | −0.929567 | ||||||||
\(491\) | 5.74000 | 0.259043 | 0.129521 | − | 0.991577i | \(-0.458656\pi\) | ||||
0.129521 | + | 0.991577i | \(0.458656\pi\) | |||||||
\(492\) | −3.89595 | −0.175643 | ||||||||
\(493\) | 0.946611 | 0.0426332 | ||||||||
\(494\) | −2.30725 | −0.103808 | ||||||||
\(495\) | 9.77767 | 0.439474 | ||||||||
\(496\) | −27.8883 | −1.25222 | ||||||||
\(497\) | −2.68261 | −0.120332 | ||||||||
\(498\) | 13.0292 | 0.583853 | ||||||||
\(499\) | −10.2276 | −0.457851 | −0.228926 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228926 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(500\) | 8.24003 | 0.368505 | ||||||||
\(501\) | −2.60761 | −0.116499 | ||||||||
\(502\) | 30.1864 | 1.34728 | ||||||||
\(503\) | −6.43144 | −0.286764 | −0.143382 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143382 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(504\) | −3.73092 | −0.166188 | ||||||||
\(505\) | −28.3904 | −1.26336 | ||||||||
\(506\) | −3.05072 | −0.135621 | ||||||||
\(507\) | −0.0223919 | −0.000994457 0 | ||||||||
\(508\) | −8.78421 | −0.389736 | ||||||||
\(509\) | −6.86016 | −0.304071 | −0.152036 | − | 0.988375i | \(-0.548583\pi\) | ||||
−0.152036 | + | 0.988375i | \(0.548583\pi\) | |||||||
\(510\) | 1.45182 | 0.0642878 | ||||||||
\(511\) | −4.54919 | −0.201244 | ||||||||
\(512\) | 3.10912 | 0.137405 | ||||||||
\(513\) | −1.10684 | −0.0488681 | ||||||||
\(514\) | 2.17163 | 0.0957864 | ||||||||
\(515\) | 35.5695 | 1.56738 | ||||||||
\(516\) | 0.251931 | 0.0110907 | ||||||||
\(517\) | 16.4414 | 0.723093 | ||||||||
\(518\) | −5.67927 | −0.249533 | ||||||||
\(519\) | −6.29224 | −0.276198 | ||||||||
\(520\) | 14.8584 | 0.651586 | ||||||||
\(521\) | 37.1452 | 1.62736 | 0.813680 | − | 0.581313i | \(-0.197461\pi\) | ||||
0.813680 | + | 0.581313i | \(0.197461\pi\) | |||||||
\(522\) | −4.51302 | −0.197530 | ||||||||
\(523\) | 42.2124 | 1.84582 | 0.922910 | − | 0.385017i | \(-0.125804\pi\) | ||||
0.922910 | + | 0.385017i | \(0.125804\pi\) | |||||||
\(524\) | −8.41357 | −0.367549 | ||||||||
\(525\) | 0.425574 | 0.0185736 | ||||||||
\(526\) | −17.3599 | −0.756926 | ||||||||
\(527\) | −5.39111 | −0.234841 | ||||||||
\(528\) | 4.49585 | 0.195657 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 10.6252 | 0.461531 | ||||||||
\(531\) | −29.8825 | −1.29679 | ||||||||
\(532\) | −0.165778 | −0.00718737 | ||||||||
\(533\) | −42.0854 | −1.82292 | ||||||||
\(534\) | −13.0345 | −0.564059 | ||||||||
\(535\) | −36.6382 | −1.58401 | ||||||||
\(536\) | 17.1459 | 0.740588 | ||||||||
\(537\) | 0.485053 | 0.0209316 | ||||||||
\(538\) | −29.4570 | −1.26998 | ||||||||
\(539\) | −12.3178 | −0.530565 | ||||||||
\(540\) | −3.66221 | −0.157597 | ||||||||
\(541\) | −18.0359 | −0.775423 | −0.387711 | − | 0.921781i | \(-0.626734\pi\) | ||||
−0.387711 | + | 0.921781i | \(0.626734\pi\) | |||||||
\(542\) | −41.4461 | −1.78026 | ||||||||
\(543\) | −0.678139 | −0.0291017 | ||||||||
\(544\) | −3.49288 | −0.149756 | ||||||||
\(545\) | −14.6314 | −0.626742 | ||||||||
\(546\) | −1.82200 | −0.0779743 | ||||||||
\(547\) | 1.10461 | 0.0472299 | 0.0236149 | − | 0.999721i | \(-0.492482\pi\) | ||||
0.0236149 | + | 0.999721i | \(0.492482\pi\) | |||||||
\(548\) | 0.713922 | 0.0304972 | ||||||||
\(549\) | 18.1492 | 0.774588 | ||||||||
\(550\) | 4.21241 | 0.179618 | ||||||||
\(551\) | 0.390297 | 0.0166272 | ||||||||
\(552\) | −1.06513 | −0.0453348 | ||||||||
\(553\) | 9.45644 | 0.402129 | ||||||||
\(554\) | −49.0322 | −2.08318 | ||||||||
\(555\) | 5.19649 | 0.220579 | ||||||||
\(556\) | −14.9017 | −0.631974 | ||||||||
\(557\) | −10.4532 | −0.442917 | −0.221459 | − | 0.975170i | \(-0.571082\pi\) | ||||
−0.221459 | + | 0.975170i | \(0.571082\pi\) | |||||||
\(558\) | 25.7024 | 1.08807 | ||||||||
\(559\) | 2.72145 | 0.115105 | ||||||||
\(560\) | 5.82916 | 0.246327 | ||||||||
\(561\) | 0.869097 | 0.0366933 | ||||||||
\(562\) | −22.5830 | −0.952606 | ||||||||
\(563\) | −19.6296 | −0.827287 | −0.413644 | − | 0.910439i | \(-0.635744\pi\) | ||||
−0.413644 | + | 0.910439i | \(0.635744\pi\) | |||||||
\(564\) | −2.94930 | −0.124188 | ||||||||
\(565\) | −5.70048 | −0.239821 | ||||||||
\(566\) | 8.41781 | 0.353827 | ||||||||
\(567\) | 4.30203 | 0.180668 | ||||||||
\(568\) | −9.27067 | −0.388989 | ||||||||
\(569\) | −5.92670 | −0.248460 | −0.124230 | − | 0.992253i | \(-0.539646\pi\) | ||||
−0.124230 | + | 0.992253i | \(0.539646\pi\) | |||||||
\(570\) | 0.598600 | 0.0250726 | ||||||||
\(571\) | 39.4368 | 1.65038 | 0.825190 | − | 0.564855i | \(-0.191068\pi\) | ||||
0.825190 | + | 0.564855i | \(0.191068\pi\) | |||||||
\(572\) | −4.56993 | −0.191078 | ||||||||
\(573\) | 9.04401 | 0.377819 | ||||||||
\(574\) | −11.9332 | −0.498081 | ||||||||
\(575\) | −1.38079 | −0.0575829 | ||||||||
\(576\) | −10.3524 | −0.431348 | ||||||||
\(577\) | −26.3371 | −1.09643 | −0.548213 | − | 0.836339i | \(-0.684692\pi\) | ||||
−0.548213 | + | 0.836339i | \(0.684692\pi\) | |||||||
\(578\) | 26.3574 | 1.09632 | ||||||||
\(579\) | −9.45063 | −0.392755 | ||||||||
\(580\) | 1.29138 | 0.0536217 | ||||||||
\(581\) | 10.1127 | 0.419545 | ||||||||
\(582\) | 10.3729 | 0.429971 | ||||||||
\(583\) | 6.36053 | 0.263426 | ||||||||
\(584\) | −15.7213 | −0.650550 | ||||||||
\(585\) | −18.9467 | −0.783349 | ||||||||
\(586\) | 4.50971 | 0.186294 | ||||||||
\(587\) | 25.2199 | 1.04094 | 0.520468 | − | 0.853881i | \(-0.325757\pi\) | ||||
0.520468 | + | 0.853881i | \(0.325757\pi\) | |||||||
\(588\) | 2.20959 | 0.0911221 | ||||||||
\(589\) | −2.22281 | −0.0915892 | ||||||||
\(590\) | 33.7442 | 1.38922 | ||||||||
\(591\) | 7.04738 | 0.289890 | ||||||||
\(592\) | −27.1553 | −1.11608 | ||||||||
\(593\) | −16.8992 | −0.693965 | −0.346983 | − | 0.937872i | \(-0.612794\pi\) | ||||
−0.346983 | + | 0.937872i | \(0.612794\pi\) | |||||||
\(594\) | −8.65151 | −0.354976 | ||||||||
\(595\) | 1.12684 | 0.0461959 | ||||||||
\(596\) | −8.68255 | −0.355651 | ||||||||
\(597\) | −5.92253 | −0.242393 | ||||||||
\(598\) | 5.91154 | 0.241741 | ||||||||
\(599\) | −17.5628 | −0.717596 | −0.358798 | − | 0.933415i | \(-0.616813\pi\) | ||||
−0.358798 | + | 0.933415i | \(0.616813\pi\) | |||||||
\(600\) | 1.47071 | 0.0600416 | ||||||||
\(601\) | 23.3210 | 0.951282 | 0.475641 | − | 0.879640i | \(-0.342216\pi\) | ||||
0.475641 | + | 0.879640i | \(0.342216\pi\) | |||||||
\(602\) | 0.771658 | 0.0314504 | ||||||||
\(603\) | −21.8635 | −0.890349 | ||||||||
\(604\) | −1.34957 | −0.0549131 | ||||||||
\(605\) | 14.3171 | 0.582073 | ||||||||
\(606\) | 12.0310 | 0.488725 | ||||||||
\(607\) | 2.37912 | 0.0965657 | 0.0482828 | − | 0.998834i | \(-0.484625\pi\) | ||||
0.0482828 | + | 0.998834i | \(0.484625\pi\) | |||||||
\(608\) | −1.44015 | −0.0584057 | ||||||||
\(609\) | 0.308211 | 0.0124893 | ||||||||
\(610\) | −20.4945 | −0.829800 | ||||||||
\(611\) | −31.8594 | −1.28889 | ||||||||
\(612\) | 1.77180 | 0.0716209 | ||||||||
\(613\) | −2.43882 | −0.0985031 | −0.0492516 | − | 0.998786i | \(-0.515684\pi\) | ||||
−0.0492516 | + | 0.998786i | \(0.515684\pi\) | |||||||
\(614\) | −28.7742 | −1.16123 | ||||||||
\(615\) | 10.9187 | 0.440286 | ||||||||
\(616\) | 2.52204 | 0.101616 | ||||||||
\(617\) | 1.46026 | 0.0587877 | 0.0293938 | − | 0.999568i | \(-0.490642\pi\) | ||||
0.0293938 | + | 0.999568i | \(0.490642\pi\) | |||||||
\(618\) | −15.0732 | −0.606334 | ||||||||
\(619\) | 13.7842 | 0.554034 | 0.277017 | − | 0.960865i | \(-0.410654\pi\) | ||||
0.277017 | + | 0.960865i | \(0.410654\pi\) | |||||||
\(620\) | −7.35464 | −0.295369 | ||||||||
\(621\) | 2.83589 | 0.113800 | ||||||||
\(622\) | −20.3123 | −0.814449 | ||||||||
\(623\) | −10.1168 | −0.405321 | ||||||||
\(624\) | −8.71183 | −0.348752 | ||||||||
\(625\) | −16.1895 | −0.647579 | ||||||||
\(626\) | −5.08231 | −0.203130 | ||||||||
\(627\) | 0.358337 | 0.0143106 | ||||||||
\(628\) | 2.02083 | 0.0806398 | ||||||||
\(629\) | −5.24941 | −0.209308 | ||||||||
\(630\) | −5.37227 | −0.214036 | ||||||||
\(631\) | 41.7386 | 1.66159 | 0.830794 | − | 0.556580i | \(-0.187887\pi\) | ||||
0.830794 | + | 0.556580i | \(0.187887\pi\) | |||||||
\(632\) | 32.6799 | 1.29994 | ||||||||
\(633\) | 5.23957 | 0.208254 | ||||||||
\(634\) | −47.8625 | −1.90086 | ||||||||
\(635\) | 24.6185 | 0.976956 | ||||||||
\(636\) | −1.14097 | −0.0452423 | ||||||||
\(637\) | 23.8688 | 0.945716 | ||||||||
\(638\) | 3.05072 | 0.120779 | ||||||||
\(639\) | 11.8215 | 0.467650 | ||||||||
\(640\) | 25.7296 | 1.01705 | ||||||||
\(641\) | −33.0749 | −1.30638 | −0.653190 | − | 0.757194i | \(-0.726570\pi\) | ||||
−0.653190 | + | 0.757194i | \(0.726570\pi\) | |||||||
\(642\) | 15.5261 | 0.612766 | ||||||||
\(643\) | −4.39408 | −0.173285 | −0.0866427 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866427 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(644\) | 0.424747 | 0.0167374 | ||||||||
\(645\) | −0.706060 | −0.0278011 | ||||||||
\(646\) | −0.604696 | −0.0237915 | ||||||||
\(647\) | −23.0920 | −0.907839 | −0.453920 | − | 0.891043i | \(-0.649975\pi\) | ||||
−0.453920 | + | 0.891043i | \(0.649975\pi\) | |||||||
\(648\) | 14.8671 | 0.584035 | ||||||||
\(649\) | 20.2001 | 0.792922 | ||||||||
\(650\) | −8.16259 | −0.320163 | ||||||||
\(651\) | −1.75531 | −0.0687961 | ||||||||
\(652\) | 2.01093 | 0.0787541 | ||||||||
\(653\) | 21.3521 | 0.835573 | 0.417786 | − | 0.908545i | \(-0.362806\pi\) | ||||
0.417786 | + | 0.908545i | \(0.362806\pi\) | |||||||
\(654\) | 6.20033 | 0.242452 | ||||||||
\(655\) | 23.5798 | 0.921338 | ||||||||
\(656\) | −57.0581 | −2.22774 | ||||||||
\(657\) | 20.0469 | 0.782104 | ||||||||
\(658\) | −9.03361 | −0.352167 | ||||||||
\(659\) | −26.4261 | −1.02941 | −0.514707 | − | 0.857366i | \(-0.672099\pi\) | ||||
−0.514707 | + | 0.857366i | \(0.672099\pi\) | |||||||
\(660\) | 1.18563 | 0.0461508 | ||||||||
\(661\) | −20.4354 | −0.794846 | −0.397423 | − | 0.917636i | \(-0.630095\pi\) | ||||
−0.397423 | + | 0.917636i | \(0.630095\pi\) | |||||||
\(662\) | 16.7237 | 0.649987 | ||||||||
\(663\) | −1.68409 | −0.0654047 | ||||||||
\(664\) | 34.9478 | 1.35624 | ||||||||
\(665\) | 0.464606 | 0.0180167 | ||||||||
\(666\) | 25.0268 | 0.969770 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 3.59357 | 0.139039 | ||||||||
\(669\) | −3.81866 | −0.147638 | ||||||||
\(670\) | 24.6888 | 0.953813 | ||||||||
\(671\) | −12.2685 | −0.473621 | ||||||||
\(672\) | −1.13726 | −0.0438708 | ||||||||
\(673\) | −6.31825 | −0.243551 | −0.121775 | − | 0.992558i | \(-0.538859\pi\) | ||||
−0.121775 | + | 0.992558i | \(0.538859\pi\) | |||||||
\(674\) | −6.85905 | −0.264201 | ||||||||
\(675\) | −3.91576 | −0.150718 | ||||||||
\(676\) | 0.0308584 | 0.00118686 | ||||||||
\(677\) | 13.2844 | 0.510561 | 0.255280 | − | 0.966867i | \(-0.417832\pi\) | ||||
0.255280 | + | 0.966867i | \(0.417832\pi\) | |||||||
\(678\) | 2.41568 | 0.0927737 | ||||||||
\(679\) | 8.05098 | 0.308968 | ||||||||
\(680\) | 3.89417 | 0.149335 | ||||||||
\(681\) | −3.69832 | −0.141720 | ||||||||
\(682\) | −17.3744 | −0.665300 | ||||||||
\(683\) | 28.2726 | 1.08182 | 0.540911 | − | 0.841080i | \(-0.318080\pi\) | ||||
0.540911 | + | 0.841080i | \(0.318080\pi\) | |||||||
\(684\) | 0.730531 | 0.0279326 | ||||||||
\(685\) | −2.00083 | −0.0764478 | ||||||||
\(686\) | 13.9368 | 0.532110 | ||||||||
\(687\) | −5.18371 | −0.197771 | ||||||||
\(688\) | 3.68966 | 0.140667 | ||||||||
\(689\) | −12.3251 | −0.469549 | ||||||||
\(690\) | −1.53371 | −0.0583872 | ||||||||
\(691\) | −9.71176 | −0.369453 | −0.184726 | − | 0.982790i | \(-0.559140\pi\) | ||||
−0.184726 | + | 0.982790i | \(0.559140\pi\) | |||||||
\(692\) | 8.67138 | 0.329636 | ||||||||
\(693\) | −3.21597 | −0.122165 | ||||||||
\(694\) | 10.0821 | 0.382713 | ||||||||
\(695\) | 41.7634 | 1.58418 | ||||||||
\(696\) | 1.06513 | 0.0403735 | ||||||||
\(697\) | −11.0299 | −0.417789 | ||||||||
\(698\) | −12.8642 | −0.486916 | ||||||||
\(699\) | 1.87171 | 0.0707947 | ||||||||
\(700\) | −0.586486 | −0.0221671 | ||||||||
\(701\) | −47.1272 | −1.77997 | −0.889984 | − | 0.455991i | \(-0.849285\pi\) | ||||
−0.889984 | + | 0.455991i | \(0.849285\pi\) | |||||||
\(702\) | 16.7645 | 0.632734 | ||||||||
\(703\) | −2.16438 | −0.0816312 | ||||||||
\(704\) | 6.99802 | 0.263748 | ||||||||
\(705\) | 8.26568 | 0.311303 | ||||||||
\(706\) | −19.0456 | −0.716791 | ||||||||
\(707\) | 9.33789 | 0.351187 | ||||||||
\(708\) | −3.62353 | −0.136181 | ||||||||
\(709\) | 24.4222 | 0.917194 | 0.458597 | − | 0.888644i | \(-0.348352\pi\) | ||||
0.458597 | + | 0.888644i | \(0.348352\pi\) | |||||||
\(710\) | −13.3491 | −0.500983 | ||||||||
\(711\) | −41.6717 | −1.56281 | ||||||||
\(712\) | −34.9620 | −1.31026 | ||||||||
\(713\) | 5.69517 | 0.213286 | ||||||||
\(714\) | −0.477518 | −0.0178707 | ||||||||
\(715\) | 12.8076 | 0.478978 | ||||||||
\(716\) | −0.668455 | −0.0249813 | ||||||||
\(717\) | 2.84369 | 0.106199 | ||||||||
\(718\) | 3.82792 | 0.142857 | ||||||||
\(719\) | 15.6219 | 0.582599 | 0.291300 | − | 0.956632i | \(-0.405912\pi\) | ||||
0.291300 | + | 0.956632i | \(0.405912\pi\) | |||||||
\(720\) | −25.6873 | −0.957310 | ||||||||
\(721\) | −11.6991 | −0.435699 | ||||||||
\(722\) | 30.8481 | 1.14805 | ||||||||
\(723\) | −5.76325 | −0.214338 | ||||||||
\(724\) | 0.934549 | 0.0347322 | ||||||||
\(725\) | 1.38079 | 0.0512812 | ||||||||
\(726\) | −6.06713 | −0.225172 | ||||||||
\(727\) | −41.8405 | −1.55178 | −0.775890 | − | 0.630868i | \(-0.782699\pi\) | ||||
−0.775890 | + | 0.630868i | \(0.782699\pi\) | |||||||
\(728\) | −4.88708 | −0.181127 | ||||||||
\(729\) | −14.7672 | −0.546932 | ||||||||
\(730\) | −22.6375 | −0.837852 | ||||||||
\(731\) | 0.713251 | 0.0263805 | ||||||||
\(732\) | 2.20076 | 0.0813423 | ||||||||
\(733\) | 26.7436 | 0.987797 | 0.493899 | − | 0.869519i | \(-0.335571\pi\) | ||||
0.493899 | + | 0.869519i | \(0.335571\pi\) | |||||||
\(734\) | −42.8903 | −1.58311 | ||||||||
\(735\) | −6.19259 | −0.228417 | ||||||||
\(736\) | 3.68988 | 0.136011 | ||||||||
\(737\) | 14.7793 | 0.544404 | ||||||||
\(738\) | 52.5859 | 1.93571 | ||||||||
\(739\) | 8.37011 | 0.307899 | 0.153950 | − | 0.988079i | \(-0.450801\pi\) | ||||
0.153950 | + | 0.988079i | \(0.450801\pi\) | |||||||
\(740\) | −7.16132 | −0.263255 | ||||||||
\(741\) | −0.694367 | −0.0255082 | ||||||||
\(742\) | −3.49474 | −0.128296 | ||||||||
\(743\) | −35.0079 | −1.28432 | −0.642158 | − | 0.766572i | \(-0.721961\pi\) | ||||
−0.642158 | + | 0.766572i | \(0.721961\pi\) | |||||||
\(744\) | −6.06607 | −0.222393 | ||||||||
\(745\) | 24.3336 | 0.891514 | ||||||||
\(746\) | −28.7939 | −1.05422 | ||||||||
\(747\) | −44.5635 | −1.63049 | ||||||||
\(748\) | −1.19771 | −0.0437926 | ||||||||
\(749\) | 12.0506 | 0.440321 | ||||||||
\(750\) | 9.78625 | 0.357343 | ||||||||
\(751\) | 13.3621 | 0.487591 | 0.243796 | − | 0.969827i | \(-0.421607\pi\) | ||||
0.243796 | + | 0.969827i | \(0.421607\pi\) | |||||||
\(752\) | −43.1939 | −1.57512 | ||||||||
\(753\) | 9.08457 | 0.331060 | ||||||||
\(754\) | −5.91154 | −0.215286 | ||||||||
\(755\) | 3.78228 | 0.137651 | ||||||||
\(756\) | 1.20454 | 0.0438086 | ||||||||
\(757\) | 6.34165 | 0.230491 | 0.115246 | − | 0.993337i | \(-0.463234\pi\) | ||||
0.115246 | + | 0.993337i | \(0.463234\pi\) | |||||||
\(758\) | 40.8528 | 1.48384 | ||||||||
\(759\) | −0.918114 | −0.0333254 | ||||||||
\(760\) | 1.60560 | 0.0582414 | ||||||||
\(761\) | −19.1744 | −0.695070 | −0.347535 | − | 0.937667i | \(-0.612981\pi\) | ||||
−0.347535 | + | 0.937667i | \(0.612981\pi\) | |||||||
\(762\) | −10.4325 | −0.377931 | ||||||||
\(763\) | 4.81242 | 0.174221 | ||||||||
\(764\) | −12.4636 | −0.450918 | ||||||||
\(765\) | −4.96564 | −0.179533 | ||||||||
\(766\) | 11.4578 | 0.413988 | ||||||||
\(767\) | −39.1427 | −1.41336 | ||||||||
\(768\) | −7.20478 | −0.259980 | ||||||||
\(769\) | 12.8445 | 0.463183 | 0.231591 | − | 0.972813i | \(-0.425607\pi\) | ||||
0.231591 | + | 0.972813i | \(0.425607\pi\) | |||||||
\(770\) | 3.63156 | 0.130872 | ||||||||
\(771\) | 0.653550 | 0.0235370 | ||||||||
\(772\) | 13.0240 | 0.468744 | ||||||||
\(773\) | 17.6744 | 0.635704 | 0.317852 | − | 0.948140i | \(-0.397038\pi\) | ||||
0.317852 | + | 0.948140i | \(0.397038\pi\) | |||||||
\(774\) | −3.40046 | −0.122227 | ||||||||
\(775\) | −7.86383 | −0.282477 | ||||||||
\(776\) | 27.8229 | 0.998783 | ||||||||
\(777\) | −1.70917 | −0.0613163 | ||||||||
\(778\) | 48.3663 | 1.73401 | ||||||||
\(779\) | −4.54775 | −0.162940 | ||||||||
\(780\) | −2.29746 | −0.0822623 | ||||||||
\(781\) | −7.99110 | −0.285944 | ||||||||
\(782\) | 1.54932 | 0.0554037 | ||||||||
\(783\) | −2.83589 | −0.101346 | ||||||||
\(784\) | 32.3606 | 1.15574 | ||||||||
\(785\) | −5.66355 | −0.202141 | ||||||||
\(786\) | −9.99236 | −0.356416 | ||||||||
\(787\) | −13.0310 | −0.464506 | −0.232253 | − | 0.972655i | \(-0.574610\pi\) | ||||
−0.232253 | + | 0.972655i | \(0.574610\pi\) | |||||||
\(788\) | −9.71205 | −0.345977 | ||||||||
\(789\) | −5.22444 | −0.185995 | ||||||||
\(790\) | 47.0568 | 1.67421 | ||||||||
\(791\) | 1.87494 | 0.0666653 | ||||||||
\(792\) | −11.1139 | −0.394914 | ||||||||
\(793\) | 23.7733 | 0.844216 | ||||||||
\(794\) | −17.8792 | −0.634507 | ||||||||
\(795\) | 3.19766 | 0.113409 | ||||||||
\(796\) | 8.16189 | 0.289291 | ||||||||
\(797\) | 51.3069 | 1.81738 | 0.908691 | − | 0.417469i | \(-0.137083\pi\) | ||||
0.908691 | + | 0.417469i | \(0.137083\pi\) | |||||||
\(798\) | −0.196885 | −0.00696966 | ||||||||
\(799\) | −8.34985 | −0.295397 | ||||||||
\(800\) | −5.09494 | −0.180134 | ||||||||
\(801\) | 44.5817 | 1.57522 | ||||||||
\(802\) | −9.29727 | −0.328298 | ||||||||
\(803\) | −13.5514 | −0.478217 | ||||||||
\(804\) | −2.65115 | −0.0934989 | ||||||||
\(805\) | −1.19039 | −0.0419558 | ||||||||
\(806\) | 33.6672 | 1.18588 | ||||||||
\(807\) | −8.86507 | −0.312065 | ||||||||
\(808\) | 32.2702 | 1.13526 | ||||||||
\(809\) | −39.9620 | −1.40499 | −0.702495 | − | 0.711689i | \(-0.747931\pi\) | ||||
−0.702495 | + | 0.711689i | \(0.747931\pi\) | |||||||
\(810\) | 21.4076 | 0.752186 | ||||||||
\(811\) | 41.7664 | 1.46662 | 0.733308 | − | 0.679897i | \(-0.237976\pi\) | ||||
0.733308 | + | 0.679897i | \(0.237976\pi\) | |||||||
\(812\) | −0.424747 | −0.0149057 | ||||||||
\(813\) | −12.4732 | −0.437453 | ||||||||
\(814\) | −16.9177 | −0.592966 | ||||||||
\(815\) | −5.63581 | −0.197414 | ||||||||
\(816\) | −2.28324 | −0.0799294 | ||||||||
\(817\) | 0.294080 | 0.0102886 | ||||||||
\(818\) | 55.0765 | 1.92570 | ||||||||
\(819\) | 6.23174 | 0.217755 | ||||||||
\(820\) | −15.0472 | −0.525471 | ||||||||
\(821\) | 31.4508 | 1.09764 | 0.548820 | − | 0.835941i | \(-0.315077\pi\) | ||||
0.548820 | + | 0.835941i | \(0.315077\pi\) | |||||||
\(822\) | 0.847888 | 0.0295735 | ||||||||
\(823\) | 3.09308 | 0.107818 | 0.0539090 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539090 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(824\) | −40.4303 | −1.40846 | ||||||||
\(825\) | 1.26772 | 0.0441364 | ||||||||
\(826\) | −11.0988 | −0.386176 | ||||||||
\(827\) | −13.6474 | −0.474566 | −0.237283 | − | 0.971441i | \(-0.576257\pi\) | ||||
−0.237283 | + | 0.971441i | \(0.576257\pi\) | |||||||
\(828\) | −1.87173 | −0.0650472 | ||||||||
\(829\) | 38.3562 | 1.33217 | 0.666083 | − | 0.745877i | \(-0.267970\pi\) | ||||
0.666083 | + | 0.745877i | \(0.267970\pi\) | |||||||
\(830\) | 50.3224 | 1.74672 | ||||||||
\(831\) | −14.7562 | −0.511887 | ||||||||
\(832\) | −13.5604 | −0.470123 | ||||||||
\(833\) | 6.25565 | 0.216745 | ||||||||
\(834\) | −17.6980 | −0.612832 | ||||||||
\(835\) | −10.0713 | −0.348532 | ||||||||
\(836\) | −0.493827 | −0.0170794 | ||||||||
\(837\) | 16.1509 | 0.558256 | ||||||||
\(838\) | 5.86528 | 0.202613 | ||||||||
\(839\) | 25.1781 | 0.869243 | 0.434622 | − | 0.900613i | \(-0.356882\pi\) | ||||
0.434622 | + | 0.900613i | \(0.356882\pi\) | |||||||
\(840\) | 1.26792 | 0.0437473 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 51.7112 | 1.78209 | ||||||||
\(843\) | −6.79634 | −0.234078 | ||||||||
\(844\) | −7.22070 | −0.248547 | ||||||||
\(845\) | −0.0864834 | −0.00297512 | ||||||||
\(846\) | 39.8084 | 1.36864 | ||||||||
\(847\) | −4.70903 | −0.161804 | ||||||||
\(848\) | −16.7100 | −0.573824 | ||||||||
\(849\) | 2.53334 | 0.0869438 | ||||||||
\(850\) | −2.13929 | −0.0733771 | ||||||||
\(851\) | 5.54547 | 0.190096 | ||||||||
\(852\) | 1.43346 | 0.0491096 | ||||||||
\(853\) | 18.3174 | 0.627176 | 0.313588 | − | 0.949559i | \(-0.398469\pi\) | ||||
0.313588 | + | 0.949559i | \(0.398469\pi\) | |||||||
\(854\) | 6.74085 | 0.230667 | ||||||||
\(855\) | −2.04738 | −0.0700189 | ||||||||
\(856\) | 41.6451 | 1.42340 | ||||||||
\(857\) | 6.45885 | 0.220630 | 0.110315 | − | 0.993897i | \(-0.464814\pi\) | ||||
0.110315 | + | 0.993897i | \(0.464814\pi\) | |||||||
\(858\) | −5.42746 | −0.185291 | ||||||||
\(859\) | −26.8098 | −0.914739 | −0.457370 | − | 0.889277i | \(-0.651208\pi\) | ||||
−0.457370 | + | 0.889277i | \(0.651208\pi\) | |||||||
\(860\) | 0.973027 | 0.0331800 | ||||||||
\(861\) | −3.59128 | −0.122390 | ||||||||
\(862\) | 15.2612 | 0.519799 | ||||||||
\(863\) | 36.8892 | 1.25572 | 0.627861 | − | 0.778325i | \(-0.283931\pi\) | ||||
0.627861 | + | 0.778325i | \(0.283931\pi\) | |||||||
\(864\) | 10.4641 | 0.355995 | ||||||||
\(865\) | −24.3023 | −0.826304 | ||||||||
\(866\) | 50.7644 | 1.72504 | ||||||||
\(867\) | 7.93224 | 0.269393 | ||||||||
\(868\) | 2.41901 | 0.0821065 | ||||||||
\(869\) | 28.1693 | 0.955580 | ||||||||
\(870\) | 1.53371 | 0.0519975 | ||||||||
\(871\) | −28.6386 | −0.970383 | ||||||||
\(872\) | 16.6309 | 0.563194 | ||||||||
\(873\) | −35.4782 | −1.20076 | ||||||||
\(874\) | 0.638801 | 0.0216078 | ||||||||
\(875\) | 7.59564 | 0.256780 | ||||||||
\(876\) | 2.43087 | 0.0821316 | ||||||||
\(877\) | 5.06724 | 0.171108 | 0.0855542 | − | 0.996334i | \(-0.472734\pi\) | ||||
0.0855542 | + | 0.996334i | \(0.472734\pi\) | |||||||
\(878\) | −38.9025 | −1.31289 | ||||||||
\(879\) | 1.35719 | 0.0457770 | ||||||||
\(880\) | 17.3642 | 0.585347 | ||||||||
\(881\) | 49.1495 | 1.65589 | 0.827945 | − | 0.560809i | \(-0.189510\pi\) | ||||
0.827945 | + | 0.560809i | \(0.189510\pi\) | |||||||
\(882\) | −29.8242 | −1.00423 | ||||||||
\(883\) | 37.3623 | 1.25734 | 0.628671 | − | 0.777671i | \(-0.283599\pi\) | ||||
0.628671 | + | 0.777671i | \(0.283599\pi\) | |||||||
\(884\) | 2.32086 | 0.0780589 | ||||||||
\(885\) | 10.1553 | 0.341366 | ||||||||
\(886\) | −41.0098 | −1.37775 | ||||||||
\(887\) | −28.0049 | −0.940312 | −0.470156 | − | 0.882583i | \(-0.655802\pi\) | ||||
−0.470156 | + | 0.882583i | \(0.655802\pi\) | |||||||
\(888\) | −5.90663 | −0.198213 | ||||||||
\(889\) | −8.09726 | −0.271574 | ||||||||
\(890\) | −50.3428 | −1.68750 | ||||||||
\(891\) | 12.8151 | 0.429322 | ||||||||
\(892\) | 5.26253 | 0.176203 | ||||||||
\(893\) | −3.44272 | −0.115206 | ||||||||
\(894\) | −10.3118 | −0.344878 | ||||||||
\(895\) | 1.87340 | 0.0626210 | ||||||||
\(896\) | −8.46270 | −0.282719 | ||||||||
\(897\) | 1.77907 | 0.0594015 | ||||||||
\(898\) | −65.9739 | −2.20158 | ||||||||
\(899\) | −5.69517 | −0.189945 | ||||||||
\(900\) | 2.58447 | 0.0861489 | ||||||||
\(901\) | −3.23022 | −0.107614 | ||||||||
\(902\) | −35.5471 | −1.18359 | ||||||||
\(903\) | 0.232230 | 0.00772813 | ||||||||
\(904\) | 6.47949 | 0.215505 | ||||||||
\(905\) | −2.61916 | −0.0870637 | ||||||||
\(906\) | −1.60281 | −0.0532498 | ||||||||
\(907\) | 15.4437 | 0.512798 | 0.256399 | − | 0.966571i | \(-0.417464\pi\) | ||||
0.256399 | + | 0.966571i | \(0.417464\pi\) | |||||||
\(908\) | 5.09668 | 0.169139 | ||||||||
\(909\) | −41.1492 | −1.36483 | ||||||||
\(910\) | −7.03705 | −0.233276 | ||||||||
\(911\) | 41.4852 | 1.37447 | 0.687233 | − | 0.726437i | \(-0.258825\pi\) | ||||
0.687233 | + | 0.726437i | \(0.258825\pi\) | |||||||
\(912\) | −0.941401 | −0.0311729 | ||||||||
\(913\) | 30.1242 | 0.996965 | ||||||||
\(914\) | 1.76243 | 0.0582960 | ||||||||
\(915\) | −6.16782 | −0.203902 | ||||||||
\(916\) | 7.14371 | 0.236035 | ||||||||
\(917\) | −7.75561 | −0.256113 | ||||||||
\(918\) | 4.39371 | 0.145014 | ||||||||
\(919\) | −56.7005 | −1.87038 | −0.935188 | − | 0.354152i | \(-0.884770\pi\) | ||||
−0.935188 | + | 0.354152i | \(0.884770\pi\) | |||||||
\(920\) | −4.11380 | −0.135628 | ||||||||
\(921\) | −8.65957 | −0.285343 | ||||||||
\(922\) | −59.1528 | −1.94809 | ||||||||
\(923\) | 15.4848 | 0.509687 | ||||||||
\(924\) | −0.389966 | −0.0128290 | ||||||||
\(925\) | −7.65713 | −0.251765 | ||||||||
\(926\) | 28.3535 | 0.931752 | ||||||||
\(927\) | 51.5546 | 1.69327 | ||||||||
\(928\) | −3.68988 | −0.121126 | ||||||||
\(929\) | −25.5957 | −0.839768 | −0.419884 | − | 0.907578i | \(-0.637929\pi\) | ||||
−0.419884 | + | 0.907578i | \(0.637929\pi\) | |||||||
\(930\) | −8.73472 | −0.286423 | ||||||||
\(931\) | 2.57926 | 0.0845320 | ||||||||
\(932\) | −2.57942 | −0.0844919 | ||||||||
\(933\) | −6.11297 | −0.200130 | ||||||||
\(934\) | 18.1910 | 0.595226 | ||||||||
\(935\) | 3.35669 | 0.109775 | ||||||||
\(936\) | 21.5359 | 0.703922 | ||||||||
\(937\) | −35.6726 | −1.16537 | −0.582687 | − | 0.812697i | \(-0.697999\pi\) | ||||
−0.582687 | + | 0.812697i | \(0.697999\pi\) | |||||||
\(938\) | −8.12039 | −0.265140 | ||||||||
\(939\) | −1.52952 | −0.0499139 | ||||||||
\(940\) | −11.3910 | −0.371533 | ||||||||
\(941\) | 43.2631 | 1.41034 | 0.705169 | − | 0.709039i | \(-0.250871\pi\) | ||||
0.705169 | + | 0.709039i | \(0.250871\pi\) | |||||||
\(942\) | 2.40003 | 0.0781972 | ||||||||
\(943\) | 11.6520 | 0.379442 | ||||||||
\(944\) | −53.0684 | −1.72723 | ||||||||
\(945\) | −3.37582 | −0.109815 | ||||||||
\(946\) | 2.29865 | 0.0747357 | ||||||||
\(947\) | 45.7018 | 1.48511 | 0.742555 | − | 0.669785i | \(-0.233614\pi\) | ||||
0.742555 | + | 0.669785i | \(0.233614\pi\) | |||||||
\(948\) | −5.05308 | −0.164117 | ||||||||
\(949\) | 26.2591 | 0.852408 | ||||||||
\(950\) | −0.882050 | −0.0286175 | ||||||||
\(951\) | −14.4042 | −0.467087 | ||||||||
\(952\) | −1.28083 | −0.0415119 | ||||||||
\(953\) | −53.7722 | −1.74185 | −0.870926 | − | 0.491414i | \(-0.836480\pi\) | ||||
−0.870926 | + | 0.491414i | \(0.836480\pi\) | |||||||
\(954\) | 15.4003 | 0.498602 | ||||||||
\(955\) | 34.9304 | 1.13032 | ||||||||
\(956\) | −3.91891 | −0.126747 | ||||||||
\(957\) | 0.918114 | 0.0296784 | ||||||||
\(958\) | 43.4283 | 1.40311 | ||||||||
\(959\) | 0.658092 | 0.0212509 | ||||||||
\(960\) | 3.51815 | 0.113548 | ||||||||
\(961\) | 1.43500 | 0.0462903 | ||||||||
\(962\) | 32.7823 | 1.05694 | ||||||||
\(963\) | −53.1035 | −1.71124 | ||||||||
\(964\) | 7.94238 | 0.255807 | ||||||||
\(965\) | −36.5009 | −1.17501 | ||||||||
\(966\) | 0.504450 | 0.0162304 | ||||||||
\(967\) | 40.5056 | 1.30257 | 0.651287 | − | 0.758832i | \(-0.274230\pi\) | ||||
0.651287 | + | 0.758832i | \(0.274230\pi\) | |||||||
\(968\) | −16.2736 | −0.523055 | ||||||||
\(969\) | −0.181983 | −0.00584614 | ||||||||
\(970\) | 40.0630 | 1.28635 | ||||||||
\(971\) | 19.0454 | 0.611195 | 0.305597 | − | 0.952161i | \(-0.401144\pi\) | ||||
0.305597 | + | 0.952161i | \(0.401144\pi\) | |||||||
\(972\) | −8.07388 | −0.258970 | ||||||||
\(973\) | −13.7364 | −0.440368 | ||||||||
\(974\) | 1.10777 | 0.0354953 | ||||||||
\(975\) | −2.45653 | −0.0786718 | ||||||||
\(976\) | 32.2312 | 1.03169 | ||||||||
\(977\) | −50.0749 | −1.60204 | −0.801019 | − | 0.598639i | \(-0.795708\pi\) | ||||
−0.801019 | + | 0.598639i | \(0.795708\pi\) | |||||||
\(978\) | 2.38828 | 0.0763687 | ||||||||
\(979\) | −30.1364 | −0.963165 | ||||||||
\(980\) | 8.53405 | 0.272610 | ||||||||
\(981\) | −21.2069 | −0.677083 | ||||||||
\(982\) | −9.39469 | −0.299797 | ||||||||
\(983\) | −22.5598 | −0.719547 | −0.359773 | − | 0.933040i | \(-0.617146\pi\) | ||||
−0.359773 | + | 0.933040i | \(0.617146\pi\) | |||||||
\(984\) | −12.4109 | −0.395644 | ||||||||
\(985\) | 27.2189 | 0.867265 | ||||||||
\(986\) | −1.54932 | −0.0493406 | ||||||||
\(987\) | −2.71866 | −0.0865359 | ||||||||
\(988\) | 0.956912 | 0.0304434 | ||||||||
\(989\) | −0.753478 | −0.0239592 | ||||||||
\(990\) | −16.0032 | −0.508615 | ||||||||
\(991\) | 38.5400 | 1.22426 | 0.612132 | − | 0.790755i | \(-0.290312\pi\) | ||||
0.612132 | + | 0.790755i | \(0.290312\pi\) | |||||||
\(992\) | 21.0145 | 0.667211 | ||||||||
\(993\) | 5.03300 | 0.159717 | ||||||||
\(994\) | 4.39065 | 0.139263 | ||||||||
\(995\) | −22.8744 | −0.725168 | ||||||||
\(996\) | −5.40375 | −0.171224 | ||||||||
\(997\) | −14.3246 | −0.453665 | −0.226833 | − | 0.973934i | \(-0.572837\pi\) | ||||
−0.226833 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(998\) | 16.7396 | 0.529883 | ||||||||
\(999\) | 15.7263 | 0.497560 |
(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 | 667.2.a.d.1.4 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.q.1.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.d.1.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.q.1.13 | 16 | 3.2 | odd | 2 |