Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [71,2,Mod(1,71)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(71, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("71.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 71.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: | \(0.566937854351\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.91223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 71.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.91223 | 1.35215 | 0.676075 | − | 0.736833i | \(-0.263679\pi\) | ||||
0.676075 | + | 0.736833i | \(0.263679\pi\) | |||||||
\(3\) | −1.91223 | −1.10403 | −0.552013 | − | 0.833835i | \(-0.686140\pi\) | ||||
−0.552013 | + | 0.833835i | \(0.686140\pi\) | |||||||
\(4\) | 1.65662 | 0.828310 | ||||||||
\(5\) | 3.25561 | 1.45595 | 0.727976 | − | 0.685602i | \(-0.240461\pi\) | ||||
0.727976 | + | 0.685602i | \(0.240461\pi\) | |||||||
\(6\) | −3.65662 | −1.49281 | ||||||||
\(7\) | −3.82446 | −1.44551 | −0.722755 | − | 0.691105i | \(-0.757124\pi\) | ||||
−0.722755 | + | 0.691105i | \(0.757124\pi\) | |||||||
\(8\) | −0.656620 | −0.232150 | ||||||||
\(9\) | 0.656620 | 0.218873 | ||||||||
\(10\) | 6.22547 | 1.96867 | ||||||||
\(11\) | 1.31324 | 0.395957 | 0.197979 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197979 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(12\) | −3.16784 | −0.914476 | ||||||||
\(13\) | −3.31324 | −0.918928 | −0.459464 | − | 0.888196i | \(-0.651958\pi\) | ||||
−0.459464 | + | 0.888196i | \(0.651958\pi\) | |||||||
\(14\) | −7.31324 | −1.95455 | ||||||||
\(15\) | −6.22547 | −1.60741 | ||||||||
\(16\) | −4.56885 | −1.14221 | ||||||||
\(17\) | 5.13770 | 1.24608 | 0.623038 | − | 0.782192i | \(-0.285898\pi\) | ||||
0.623038 | + | 0.782192i | \(0.285898\pi\) | |||||||
\(18\) | 1.25561 | 0.295950 | ||||||||
\(19\) | 5.48108 | 1.25745 | 0.628723 | − | 0.777629i | \(-0.283578\pi\) | ||||
0.628723 | + | 0.777629i | \(0.283578\pi\) | |||||||
\(20\) | 5.39331 | 1.20598 | ||||||||
\(21\) | 7.31324 | 1.59588 | ||||||||
\(22\) | 2.51122 | 0.535393 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 1.25561 | 0.256300 | ||||||||
\(25\) | 5.59899 | 1.11980 | ||||||||
\(26\) | −6.33568 | −1.24253 | ||||||||
\(27\) | 4.48108 | 0.862384 | ||||||||
\(28\) | −6.33568 | −1.19733 | ||||||||
\(29\) | 4.59899 | 0.854011 | 0.427005 | − | 0.904249i | \(-0.359569\pi\) | ||||
0.427005 | + | 0.904249i | \(0.359569\pi\) | |||||||
\(30\) | −11.9045 | −2.17346 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −7.42345 | −1.31229 | ||||||||
\(33\) | −2.51122 | −0.437147 | ||||||||
\(34\) | 9.82446 | 1.68488 | ||||||||
\(35\) | −12.4509 | −2.10459 | ||||||||
\(36\) | 1.08777 | 0.181295 | ||||||||
\(37\) | −5.65662 | −0.929943 | −0.464971 | − | 0.885326i | \(-0.653935\pi\) | ||||
−0.464971 | + | 0.885326i | \(0.653935\pi\) | |||||||
\(38\) | 10.4811 | 1.70026 | ||||||||
\(39\) | 6.33568 | 1.01452 | ||||||||
\(40\) | −2.13770 | −0.338000 | ||||||||
\(41\) | −9.64892 | −1.50691 | −0.753454 | − | 0.657501i | \(-0.771614\pi\) | ||||
−0.753454 | + | 0.657501i | \(0.771614\pi\) | |||||||
\(42\) | 13.9846 | 2.15787 | ||||||||
\(43\) | 1.43115 | 0.218248 | 0.109124 | − | 0.994028i | \(-0.465195\pi\) | ||||
0.109124 | + | 0.994028i | \(0.465195\pi\) | |||||||
\(44\) | 2.17554 | 0.327975 | ||||||||
\(45\) | 2.13770 | 0.318669 | ||||||||
\(46\) | −7.64892 | −1.12777 | ||||||||
\(47\) | 7.13770 | 1.04114 | 0.520570 | − | 0.853819i | \(-0.325719\pi\) | ||||
0.520570 | + | 0.853819i | \(0.325719\pi\) | |||||||
\(48\) | 8.73669 | 1.26103 | ||||||||
\(49\) | 7.62648 | 1.08950 | ||||||||
\(50\) | 10.7065 | 1.51413 | ||||||||
\(51\) | −9.82446 | −1.37570 | ||||||||
\(52\) | −5.48878 | −0.761157 | ||||||||
\(53\) | −8.62648 | −1.18494 | −0.592469 | − | 0.805593i | \(-0.701847\pi\) | ||||
−0.592469 | + | 0.805593i | \(0.701847\pi\) | |||||||
\(54\) | 8.56885 | 1.16607 | ||||||||
\(55\) | 4.27540 | 0.576495 | ||||||||
\(56\) | 2.51122 | 0.335576 | ||||||||
\(57\) | −10.4811 | −1.38825 | ||||||||
\(58\) | 8.79432 | 1.15475 | ||||||||
\(59\) | −4.51122 | −0.587310 | −0.293655 | − | 0.955911i | \(-0.594872\pi\) | ||||
−0.293655 | + | 0.955911i | \(0.594872\pi\) | |||||||
\(60\) | −10.3132 | −1.33143 | ||||||||
\(61\) | −3.64892 | −0.467196 | −0.233598 | − | 0.972333i | \(-0.575050\pi\) | ||||
−0.233598 | + | 0.972333i | \(0.575050\pi\) | |||||||
\(62\) | 7.64892 | 0.971413 | ||||||||
\(63\) | −2.51122 | −0.316384 | ||||||||
\(64\) | −5.05763 | −0.632204 | ||||||||
\(65\) | −10.7866 | −1.33792 | ||||||||
\(66\) | −4.80202 | −0.591088 | ||||||||
\(67\) | −5.31324 | −0.649116 | −0.324558 | − | 0.945866i | \(-0.605215\pi\) | ||||
−0.324558 | + | 0.945866i | \(0.605215\pi\) | |||||||
\(68\) | 8.51122 | 1.03214 | ||||||||
\(69\) | 7.64892 | 0.920821 | ||||||||
\(70\) | −23.8091 | −2.84573 | ||||||||
\(71\) | 1.00000 | 0.118678 | ||||||||
\(72\) | −0.431150 | −0.0508116 | ||||||||
\(73\) | 16.3933 | 1.91869 | 0.959346 | − | 0.282233i | \(-0.0910752\pi\) | ||||
0.959346 | + | 0.282233i | \(0.0910752\pi\) | |||||||
\(74\) | −10.8168 | −1.25742 | ||||||||
\(75\) | −10.7065 | −1.23629 | ||||||||
\(76\) | 9.08007 | 1.04156 | ||||||||
\(77\) | −5.02243 | −0.572360 | ||||||||
\(78\) | 12.1153 | 1.37178 | ||||||||
\(79\) | 5.08007 | 0.571552 | 0.285776 | − | 0.958296i | \(-0.407749\pi\) | ||||
0.285776 | + | 0.958296i | \(0.407749\pi\) | |||||||
\(80\) | −14.8744 | −1.66301 | ||||||||
\(81\) | −10.5387 | −1.17097 | ||||||||
\(82\) | −18.4509 | −2.03757 | ||||||||
\(83\) | −10.1678 | −1.11607 | −0.558033 | − | 0.829819i | \(-0.688444\pi\) | ||||
−0.558033 | + | 0.829819i | \(0.688444\pi\) | |||||||
\(84\) | 12.1153 | 1.32188 | ||||||||
\(85\) | 16.7263 | 1.81423 | ||||||||
\(86\) | 2.73669 | 0.295105 | ||||||||
\(87\) | −8.79432 | −0.942850 | ||||||||
\(88\) | −0.862301 | −0.0919216 | ||||||||
\(89\) | −3.22547 | −0.341899 | −0.170950 | − | 0.985280i | \(-0.554684\pi\) | ||||
−0.170950 | + | 0.985280i | \(0.554684\pi\) | |||||||
\(90\) | 4.08777 | 0.430889 | ||||||||
\(91\) | 12.6714 | 1.32832 | ||||||||
\(92\) | −6.62648 | −0.690858 | ||||||||
\(93\) | −7.64892 | −0.793156 | ||||||||
\(94\) | 13.6489 | 1.40778 | ||||||||
\(95\) | 17.8442 | 1.83078 | ||||||||
\(96\) | 14.1953 | 1.44880 | ||||||||
\(97\) | 11.8245 | 1.20059 | 0.600296 | − | 0.799778i | \(-0.295049\pi\) | ||||
0.600296 | + | 0.799778i | \(0.295049\pi\) | |||||||
\(98\) | 14.5836 | 1.47316 | ||||||||
\(99\) | 0.862301 | 0.0866645 | ||||||||
\(100\) | 9.27540 | 0.927540 | ||||||||
\(101\) | 2.34338 | 0.233175 | 0.116587 | − | 0.993180i | \(-0.462804\pi\) | ||||
0.116587 | + | 0.993180i | \(0.462804\pi\) | |||||||
\(102\) | −18.7866 | −1.86015 | ||||||||
\(103\) | −16.1876 | −1.59501 | −0.797507 | − | 0.603309i | \(-0.793848\pi\) | ||||
−0.797507 | + | 0.603309i | \(0.793848\pi\) | |||||||
\(104\) | 2.17554 | 0.213329 | ||||||||
\(105\) | 23.8091 | 2.32353 | ||||||||
\(106\) | −16.4958 | −1.60221 | ||||||||
\(107\) | 0.351083 | 0.0339405 | 0.0169703 | − | 0.999856i | \(-0.494598\pi\) | ||||
0.0169703 | + | 0.999856i | \(0.494598\pi\) | |||||||
\(108\) | 7.42345 | 0.714321 | ||||||||
\(109\) | 0.598988 | 0.0573727 | 0.0286863 | − | 0.999588i | \(-0.490868\pi\) | ||||
0.0286863 | + | 0.999588i | \(0.490868\pi\) | |||||||
\(110\) | 8.17554 | 0.779507 | ||||||||
\(111\) | 10.8168 | 1.02668 | ||||||||
\(112\) | 17.4734 | 1.65108 | ||||||||
\(113\) | 3.13770 | 0.295170 | 0.147585 | − | 0.989049i | \(-0.452850\pi\) | ||||
0.147585 | + | 0.989049i | \(0.452850\pi\) | |||||||
\(114\) | −20.0422 | −1.87713 | ||||||||
\(115\) | −13.0224 | −1.21435 | ||||||||
\(116\) | 7.61878 | 0.707386 | ||||||||
\(117\) | −2.17554 | −0.201129 | ||||||||
\(118\) | −8.62648 | −0.794132 | ||||||||
\(119\) | −19.6489 | −1.80121 | ||||||||
\(120\) | 4.08777 | 0.373161 | ||||||||
\(121\) | −9.27540 | −0.843218 | ||||||||
\(122\) | −6.97757 | −0.631719 | ||||||||
\(123\) | 18.4509 | 1.66367 | ||||||||
\(124\) | 6.62648 | 0.595076 | ||||||||
\(125\) | 1.95007 | 0.174420 | ||||||||
\(126\) | −4.80202 | −0.427798 | ||||||||
\(127\) | −4.33568 | −0.384729 | −0.192365 | − | 0.981324i | \(-0.561616\pi\) | ||||
−0.192365 | + | 0.981324i | \(0.561616\pi\) | |||||||
\(128\) | 5.17554 | 0.457458 | ||||||||
\(129\) | −2.73669 | −0.240952 | ||||||||
\(130\) | −20.6265 | −1.80906 | ||||||||
\(131\) | 14.3330 | 1.25228 | 0.626141 | − | 0.779710i | \(-0.284633\pi\) | ||||
0.626141 | + | 0.779710i | \(0.284633\pi\) | |||||||
\(132\) | −4.16013 | −0.362093 | ||||||||
\(133\) | −20.9622 | −1.81765 | ||||||||
\(134\) | −10.1601 | −0.877702 | ||||||||
\(135\) | 14.5886 | 1.25559 | ||||||||
\(136\) | −3.37352 | −0.289277 | ||||||||
\(137\) | 14.2754 | 1.21963 | 0.609815 | − | 0.792544i | \(-0.291244\pi\) | ||||
0.609815 | + | 0.792544i | \(0.291244\pi\) | |||||||
\(138\) | 14.6265 | 1.24509 | ||||||||
\(139\) | −4.45094 | −0.377524 | −0.188762 | − | 0.982023i | \(-0.560447\pi\) | ||||
−0.188762 | + | 0.982023i | \(0.560447\pi\) | |||||||
\(140\) | −20.6265 | −1.74326 | ||||||||
\(141\) | −13.6489 | −1.14945 | ||||||||
\(142\) | 1.91223 | 0.160471 | ||||||||
\(143\) | −4.35108 | −0.363856 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 14.9725 | 1.24340 | ||||||||
\(146\) | 31.3478 | 2.59436 | ||||||||
\(147\) | −14.5836 | −1.20283 | ||||||||
\(148\) | −9.37087 | −0.770281 | ||||||||
\(149\) | −8.45094 | −0.692328 | −0.346164 | − | 0.938174i | \(-0.612516\pi\) | ||||
−0.346164 | + | 0.938174i | \(0.612516\pi\) | |||||||
\(150\) | −20.4734 | −1.67164 | ||||||||
\(151\) | 17.9122 | 1.45768 | 0.728838 | − | 0.684686i | \(-0.240061\pi\) | ||||
0.728838 | + | 0.684686i | \(0.240061\pi\) | |||||||
\(152\) | −3.59899 | −0.291916 | ||||||||
\(153\) | 3.37352 | 0.272733 | ||||||||
\(154\) | −9.60405 | −0.773916 | ||||||||
\(155\) | 13.0224 | 1.04599 | ||||||||
\(156\) | 10.4958 | 0.840337 | ||||||||
\(157\) | −5.97251 | −0.476658 | −0.238329 | − | 0.971184i | \(-0.576600\pi\) | ||||
−0.238329 | + | 0.971184i | \(0.576600\pi\) | |||||||
\(158\) | 9.71425 | 0.772824 | ||||||||
\(159\) | 16.4958 | 1.30820 | ||||||||
\(160\) | −24.1678 | −1.91064 | ||||||||
\(161\) | 15.2978 | 1.20564 | ||||||||
\(162\) | −20.1524 | −1.58332 | ||||||||
\(163\) | −11.3735 | −0.890843 | −0.445421 | − | 0.895321i | \(-0.646946\pi\) | ||||
−0.445421 | + | 0.895321i | \(0.646946\pi\) | |||||||
\(164\) | −15.9846 | −1.24819 | ||||||||
\(165\) | −8.17554 | −0.636465 | ||||||||
\(166\) | −19.4432 | −1.50909 | ||||||||
\(167\) | 9.08007 | 0.702637 | 0.351318 | − | 0.936256i | \(-0.385733\pi\) | ||||
0.351318 | + | 0.936256i | \(0.385733\pi\) | |||||||
\(168\) | −4.80202 | −0.370484 | ||||||||
\(169\) | −2.02243 | −0.155572 | ||||||||
\(170\) | 31.9846 | 2.45311 | ||||||||
\(171\) | 3.59899 | 0.275222 | ||||||||
\(172\) | 2.37087 | 0.180777 | ||||||||
\(173\) | 1.64892 | 0.125365 | 0.0626824 | − | 0.998034i | \(-0.480034\pi\) | ||||
0.0626824 | + | 0.998034i | \(0.480034\pi\) | |||||||
\(174\) | −16.8168 | −1.27487 | ||||||||
\(175\) | −21.4131 | −1.61868 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 8.62648 | 0.648406 | ||||||||
\(178\) | −6.16784 | −0.462299 | ||||||||
\(179\) | 5.19533 | 0.388317 | 0.194159 | − | 0.980970i | \(-0.437802\pi\) | ||||
0.194159 | + | 0.980970i | \(0.437802\pi\) | |||||||
\(180\) | 3.54136 | 0.263957 | ||||||||
\(181\) | 14.0999 | 1.04803 | 0.524017 | − | 0.851708i | \(-0.324433\pi\) | ||||
0.524017 | + | 0.851708i | \(0.324433\pi\) | |||||||
\(182\) | 24.2305 | 1.79609 | ||||||||
\(183\) | 6.97757 | 0.515796 | ||||||||
\(184\) | 2.62648 | 0.193627 | ||||||||
\(185\) | −18.4157 | −1.35395 | ||||||||
\(186\) | −14.6265 | −1.07247 | ||||||||
\(187\) | 6.74704 | 0.493392 | ||||||||
\(188\) | 11.8245 | 0.862387 | ||||||||
\(189\) | −17.1377 | −1.24658 | ||||||||
\(190\) | 34.1223 | 2.47549 | ||||||||
\(191\) | −6.98965 | −0.505753 | −0.252877 | − | 0.967499i | \(-0.581377\pi\) | ||||
−0.252877 | + | 0.967499i | \(0.581377\pi\) | |||||||
\(192\) | 9.67135 | 0.697970 | ||||||||
\(193\) | 7.93972 | 0.571514 | 0.285757 | − | 0.958302i | \(-0.407755\pi\) | ||||
0.285757 | + | 0.958302i | \(0.407755\pi\) | |||||||
\(194\) | 22.6111 | 1.62338 | ||||||||
\(195\) | 20.6265 | 1.47709 | ||||||||
\(196\) | 12.6342 | 0.902442 | ||||||||
\(197\) | −3.48878 | −0.248565 | −0.124283 | − | 0.992247i | \(-0.539663\pi\) | ||||
−0.124283 | + | 0.992247i | \(0.539663\pi\) | |||||||
\(198\) | 1.64892 | 0.117183 | ||||||||
\(199\) | 17.4811 | 1.23920 | 0.619600 | − | 0.784917i | \(-0.287295\pi\) | ||||
0.619600 | + | 0.784917i | \(0.287295\pi\) | |||||||
\(200\) | −3.67641 | −0.259961 | ||||||||
\(201\) | 10.1601 | 0.716641 | ||||||||
\(202\) | 4.48108 | 0.315288 | ||||||||
\(203\) | −17.5886 | −1.23448 | ||||||||
\(204\) | −16.2754 | −1.13951 | ||||||||
\(205\) | −31.4131 | −2.19399 | ||||||||
\(206\) | −30.9545 | −2.15670 | ||||||||
\(207\) | −2.62648 | −0.182553 | ||||||||
\(208\) | 15.1377 | 1.04961 | ||||||||
\(209\) | 7.19798 | 0.497894 | ||||||||
\(210\) | 45.5284 | 3.14176 | ||||||||
\(211\) | −4.23582 | −0.291606 | −0.145803 | − | 0.989314i | \(-0.546577\pi\) | ||||
−0.145803 | + | 0.989314i | \(0.546577\pi\) | |||||||
\(212\) | −14.2908 | −0.981497 | ||||||||
\(213\) | −1.91223 | −0.131024 | ||||||||
\(214\) | 0.671352 | 0.0458927 | ||||||||
\(215\) | 4.65927 | 0.317759 | ||||||||
\(216\) | −2.94237 | −0.200203 | ||||||||
\(217\) | −15.2978 | −1.03848 | ||||||||
\(218\) | 1.14540 | 0.0775765 | ||||||||
\(219\) | −31.3478 | −2.11829 | ||||||||
\(220\) | 7.08271 | 0.477516 | ||||||||
\(221\) | −17.0224 | −1.14505 | ||||||||
\(222\) | 20.6841 | 1.38823 | ||||||||
\(223\) | −19.5259 | −1.30755 | −0.653777 | − | 0.756687i | \(-0.726817\pi\) | ||||
−0.653777 | + | 0.756687i | \(0.726817\pi\) | |||||||
\(224\) | 28.3907 | 1.89693 | ||||||||
\(225\) | 3.67641 | 0.245094 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | −20.0396 | −1.33007 | −0.665037 | − | 0.746811i | \(-0.731584\pi\) | ||||
−0.665037 | + | 0.746811i | \(0.731584\pi\) | |||||||
\(228\) | −17.3632 | −1.14990 | ||||||||
\(229\) | −1.65156 | −0.109138 | −0.0545691 | − | 0.998510i | \(-0.517379\pi\) | ||||
−0.0545691 | + | 0.998510i | \(0.517379\pi\) | |||||||
\(230\) | −24.9019 | −1.64198 | ||||||||
\(231\) | 9.60405 | 0.631900 | ||||||||
\(232\) | −3.01979 | −0.198259 | ||||||||
\(233\) | 23.5809 | 1.54484 | 0.772419 | − | 0.635113i | \(-0.219046\pi\) | ||||
0.772419 | + | 0.635113i | \(0.219046\pi\) | |||||||
\(234\) | −4.16013 | −0.271956 | ||||||||
\(235\) | 23.2376 | 1.51585 | ||||||||
\(236\) | −7.47338 | −0.486475 | ||||||||
\(237\) | −9.71425 | −0.631009 | ||||||||
\(238\) | −37.5732 | −2.43551 | ||||||||
\(239\) | 0.571495 | 0.0369669 | 0.0184835 | − | 0.999829i | \(-0.494116\pi\) | ||||
0.0184835 | + | 0.999829i | \(0.494116\pi\) | |||||||
\(240\) | 28.4432 | 1.83600 | ||||||||
\(241\) | 25.4734 | 1.64088 | 0.820442 | − | 0.571730i | \(-0.193727\pi\) | ||||
0.820442 | + | 0.571730i | \(0.193727\pi\) | |||||||
\(242\) | −17.7367 | −1.14016 | ||||||||
\(243\) | 6.70919 | 0.430395 | ||||||||
\(244\) | −6.04487 | −0.386983 | ||||||||
\(245\) | 24.8288 | 1.58626 | ||||||||
\(246\) | 35.2824 | 2.24953 | ||||||||
\(247\) | −18.1601 | −1.15550 | ||||||||
\(248\) | −2.62648 | −0.166782 | ||||||||
\(249\) | 19.4432 | 1.23217 | ||||||||
\(250\) | 3.72898 | 0.235842 | ||||||||
\(251\) | 20.1076 | 1.26918 | 0.634589 | − | 0.772850i | \(-0.281169\pi\) | ||||
0.634589 | + | 0.772850i | \(0.281169\pi\) | |||||||
\(252\) | −4.16013 | −0.262064 | ||||||||
\(253\) | −5.25296 | −0.330251 | ||||||||
\(254\) | −8.29081 | −0.520211 | ||||||||
\(255\) | −31.9846 | −2.00295 | ||||||||
\(256\) | 20.0121 | 1.25076 | ||||||||
\(257\) | −24.2754 | −1.51426 | −0.757129 | − | 0.653266i | \(-0.773399\pi\) | ||||
−0.757129 | + | 0.653266i | \(0.773399\pi\) | |||||||
\(258\) | −5.23317 | −0.325803 | ||||||||
\(259\) | 21.6335 | 1.34424 | ||||||||
\(260\) | −17.8693 | −1.10821 | ||||||||
\(261\) | 3.01979 | 0.186920 | ||||||||
\(262\) | 27.4080 | 1.69327 | ||||||||
\(263\) | 9.54641 | 0.588657 | 0.294329 | − | 0.955704i | \(-0.404904\pi\) | ||||
0.294329 | + | 0.955704i | \(0.404904\pi\) | |||||||
\(264\) | 1.64892 | 0.101484 | ||||||||
\(265\) | −28.0844 | −1.72521 | ||||||||
\(266\) | −40.0844 | −2.45774 | ||||||||
\(267\) | 6.16784 | 0.377466 | ||||||||
\(268\) | −8.80202 | −0.537669 | ||||||||
\(269\) | −11.8847 | −0.724625 | −0.362313 | − | 0.932057i | \(-0.618013\pi\) | ||||
−0.362313 | + | 0.932057i | \(0.618013\pi\) | |||||||
\(270\) | 27.8968 | 1.69775 | ||||||||
\(271\) | −3.51628 | −0.213599 | −0.106799 | − | 0.994281i | \(-0.534060\pi\) | ||||
−0.106799 | + | 0.994281i | \(0.534060\pi\) | |||||||
\(272\) | −23.4734 | −1.42328 | ||||||||
\(273\) | −24.2305 | −1.46650 | ||||||||
\(274\) | 27.2978 | 1.64912 | ||||||||
\(275\) | 7.35282 | 0.443392 | ||||||||
\(276\) | 12.6714 | 0.762726 | ||||||||
\(277\) | 5.99230 | 0.360042 | 0.180021 | − | 0.983663i | \(-0.442383\pi\) | ||||
0.180021 | + | 0.983663i | \(0.442383\pi\) | |||||||
\(278\) | −8.51122 | −0.510469 | ||||||||
\(279\) | 2.62648 | 0.157243 | ||||||||
\(280\) | 8.17554 | 0.488582 | ||||||||
\(281\) | −6.51122 | −0.388427 | −0.194213 | − | 0.980959i | \(-0.562215\pi\) | ||||
−0.194213 | + | 0.980959i | \(0.562215\pi\) | |||||||
\(282\) | −26.0999 | −1.55422 | ||||||||
\(283\) | 11.4734 | 0.682021 | 0.341011 | − | 0.940059i | \(-0.389231\pi\) | ||||
0.341011 | + | 0.940059i | \(0.389231\pi\) | |||||||
\(284\) | 1.65662 | 0.0983023 | ||||||||
\(285\) | −34.1223 | −2.02123 | ||||||||
\(286\) | −8.32027 | −0.491988 | ||||||||
\(287\) | 36.9019 | 2.17825 | ||||||||
\(288\) | −4.87439 | −0.287226 | ||||||||
\(289\) | 9.39595 | 0.552703 | ||||||||
\(290\) | 28.6309 | 1.68126 | ||||||||
\(291\) | −22.6111 | −1.32548 | ||||||||
\(292\) | 27.1575 | 1.58927 | ||||||||
\(293\) | −20.6265 | −1.20501 | −0.602506 | − | 0.798114i | \(-0.705831\pi\) | ||||
−0.602506 | + | 0.798114i | \(0.705831\pi\) | |||||||
\(294\) | −27.8871 | −1.62641 | ||||||||
\(295\) | −14.6868 | −0.855096 | ||||||||
\(296\) | 3.71425 | 0.215887 | ||||||||
\(297\) | 5.88474 | 0.341467 | ||||||||
\(298\) | −16.1601 | −0.936131 | ||||||||
\(299\) | 13.2530 | 0.766439 | ||||||||
\(300\) | −17.7367 | −1.02403 | ||||||||
\(301\) | −5.47338 | −0.315480 | ||||||||
\(302\) | 34.2523 | 1.97100 | ||||||||
\(303\) | −4.48108 | −0.257431 | ||||||||
\(304\) | −25.0422 | −1.43627 | ||||||||
\(305\) | −11.8794 | −0.680215 | ||||||||
\(306\) | 6.45094 | 0.368776 | ||||||||
\(307\) | 11.8245 | 0.674857 | 0.337429 | − | 0.941351i | \(-0.390443\pi\) | ||||
0.337429 | + | 0.941351i | \(0.390443\pi\) | |||||||
\(308\) | −8.32027 | −0.474091 | ||||||||
\(309\) | 30.9545 | 1.76094 | ||||||||
\(310\) | 24.9019 | 1.41433 | ||||||||
\(311\) | −18.3830 | −1.04240 | −0.521201 | − | 0.853434i | \(-0.674516\pi\) | ||||
−0.521201 | + | 0.853434i | \(0.674516\pi\) | |||||||
\(312\) | −4.16013 | −0.235521 | ||||||||
\(313\) | −5.30554 | −0.299887 | −0.149943 | − | 0.988695i | \(-0.547909\pi\) | ||||
−0.149943 | + | 0.988695i | \(0.547909\pi\) | |||||||
\(314\) | −11.4208 | −0.644513 | ||||||||
\(315\) | −8.17554 | −0.460640 | ||||||||
\(316\) | 8.41574 | 0.473423 | ||||||||
\(317\) | −5.88474 | −0.330520 | −0.165260 | − | 0.986250i | \(-0.552846\pi\) | ||||
−0.165260 | + | 0.986250i | \(0.552846\pi\) | |||||||
\(318\) | 31.5438 | 1.76889 | ||||||||
\(319\) | 6.03958 | 0.338152 | ||||||||
\(320\) | −16.4657 | −0.920459 | ||||||||
\(321\) | −0.671352 | −0.0374712 | ||||||||
\(322\) | 29.2530 | 1.63020 | ||||||||
\(323\) | 28.1601 | 1.56687 | ||||||||
\(324\) | −17.4586 | −0.969925 | ||||||||
\(325\) | −18.5508 | −1.02901 | ||||||||
\(326\) | −21.7488 | −1.20455 | ||||||||
\(327\) | −1.14540 | −0.0633409 | ||||||||
\(328\) | 6.33568 | 0.349829 | ||||||||
\(329\) | −27.2978 | −1.50498 | ||||||||
\(330\) | −15.6335 | −0.860596 | ||||||||
\(331\) | 12.7316 | 0.699794 | 0.349897 | − | 0.936788i | \(-0.386217\pi\) | ||||
0.349897 | + | 0.936788i | \(0.386217\pi\) | |||||||
\(332\) | −16.8442 | −0.924448 | ||||||||
\(333\) | −3.71425 | −0.203540 | ||||||||
\(334\) | 17.3632 | 0.950070 | ||||||||
\(335\) | −17.2978 | −0.945082 | ||||||||
\(336\) | −33.4131 | −1.82283 | ||||||||
\(337\) | 28.7712 | 1.56727 | 0.783634 | − | 0.621223i | \(-0.213364\pi\) | ||||
0.783634 | + | 0.621223i | \(0.213364\pi\) | |||||||
\(338\) | −3.86736 | −0.210357 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 27.7092 | 1.50274 | ||||||||
\(341\) | 5.25296 | 0.284464 | ||||||||
\(342\) | 6.88209 | 0.372141 | ||||||||
\(343\) | −2.39595 | −0.129369 | ||||||||
\(344\) | −0.939723 | −0.0506664 | ||||||||
\(345\) | 24.9019 | 1.34067 | ||||||||
\(346\) | 3.15311 | 0.169512 | ||||||||
\(347\) | 1.02243 | 0.0548872 | 0.0274436 | − | 0.999623i | \(-0.491263\pi\) | ||||
0.0274436 | + | 0.999623i | \(0.491263\pi\) | |||||||
\(348\) | −14.5688 | −0.780972 | ||||||||
\(349\) | 2.46635 | 0.132021 | 0.0660103 | − | 0.997819i | \(-0.478973\pi\) | ||||
0.0660103 | + | 0.997819i | \(0.478973\pi\) | |||||||
\(350\) | −40.9468 | −2.18870 | ||||||||
\(351\) | −14.8469 | −0.792469 | ||||||||
\(352\) | −9.74877 | −0.519611 | ||||||||
\(353\) | 8.74175 | 0.465276 | 0.232638 | − | 0.972563i | \(-0.425264\pi\) | ||||
0.232638 | + | 0.972563i | \(0.425264\pi\) | |||||||
\(354\) | 16.4958 | 0.876742 | ||||||||
\(355\) | 3.25561 | 0.172790 | ||||||||
\(356\) | −5.34338 | −0.283199 | ||||||||
\(357\) | 37.5732 | 1.98859 | ||||||||
\(358\) | 9.93466 | 0.525063 | ||||||||
\(359\) | −7.59128 | −0.400653 | −0.200326 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200326 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(360\) | −1.40366 | −0.0739792 | ||||||||
\(361\) | 11.0422 | 0.581170 | ||||||||
\(362\) | 26.9622 | 1.41710 | ||||||||
\(363\) | 17.7367 | 0.930935 | ||||||||
\(364\) | 20.9916 | 1.10026 | ||||||||
\(365\) | 53.3702 | 2.79352 | ||||||||
\(366\) | 13.3427 | 0.697434 | ||||||||
\(367\) | 30.1025 | 1.57134 | 0.785669 | − | 0.618647i | \(-0.212319\pi\) | ||||
0.785669 | + | 0.618647i | \(0.212319\pi\) | |||||||
\(368\) | 18.2754 | 0.952671 | ||||||||
\(369\) | −6.33568 | −0.329822 | ||||||||
\(370\) | −35.2151 | −1.83075 | ||||||||
\(371\) | 32.9916 | 1.71284 | ||||||||
\(372\) | −12.6714 | −0.656979 | ||||||||
\(373\) | 8.39331 | 0.434589 | 0.217295 | − | 0.976106i | \(-0.430277\pi\) | ||||
0.217295 | + | 0.976106i | \(0.430277\pi\) | |||||||
\(374\) | 12.9019 | 0.667140 | ||||||||
\(375\) | −3.72898 | −0.192564 | ||||||||
\(376\) | −4.68676 | −0.241701 | ||||||||
\(377\) | −15.2376 | −0.784774 | ||||||||
\(378\) | −32.7712 | −1.68557 | ||||||||
\(379\) | −10.4389 | −0.536208 | −0.268104 | − | 0.963390i | \(-0.586397\pi\) | ||||
−0.268104 | + | 0.963390i | \(0.586397\pi\) | |||||||
\(380\) | 29.5611 | 1.51645 | ||||||||
\(381\) | 8.29081 | 0.424751 | ||||||||
\(382\) | −13.3658 | −0.683855 | ||||||||
\(383\) | −4.97757 | −0.254342 | −0.127171 | − | 0.991881i | \(-0.540590\pi\) | ||||
−0.127171 | + | 0.991881i | \(0.540590\pi\) | |||||||
\(384\) | −9.89682 | −0.505045 | ||||||||
\(385\) | −16.3511 | −0.833328 | ||||||||
\(386\) | 15.1826 | 0.772772 | ||||||||
\(387\) | 0.939723 | 0.0477688 | ||||||||
\(388\) | 19.5886 | 0.994462 | ||||||||
\(389\) | −15.3528 | −0.778419 | −0.389209 | − | 0.921149i | \(-0.627252\pi\) | ||||
−0.389209 | + | 0.921149i | \(0.627252\pi\) | |||||||
\(390\) | 39.4426 | 1.99725 | ||||||||
\(391\) | −20.5508 | −1.03930 | ||||||||
\(392\) | −5.00770 | −0.252927 | ||||||||
\(393\) | −27.4080 | −1.38255 | ||||||||
\(394\) | −6.67135 | −0.336098 | ||||||||
\(395\) | 16.5387 | 0.832153 | ||||||||
\(396\) | 1.42851 | 0.0717851 | ||||||||
\(397\) | −3.93972 | −0.197729 | −0.0988645 | − | 0.995101i | \(-0.531521\pi\) | ||||
−0.0988645 | + | 0.995101i | \(0.531521\pi\) | |||||||
\(398\) | 33.4278 | 1.67559 | ||||||||
\(399\) | 40.0844 | 2.00673 | ||||||||
\(400\) | −25.5809 | −1.27905 | ||||||||
\(401\) | −11.4734 | −0.572953 | −0.286477 | − | 0.958087i | \(-0.592484\pi\) | ||||
−0.286477 | + | 0.958087i | \(0.592484\pi\) | |||||||
\(402\) | 19.4285 | 0.969006 | ||||||||
\(403\) | −13.2530 | −0.660177 | ||||||||
\(404\) | 3.88209 | 0.193141 | ||||||||
\(405\) | −34.3099 | −1.70487 | ||||||||
\(406\) | −33.6335 | −1.66920 | ||||||||
\(407\) | −7.42851 | −0.368217 | ||||||||
\(408\) | 6.45094 | 0.319369 | ||||||||
\(409\) | −24.6232 | −1.21754 | −0.608768 | − | 0.793348i | \(-0.708336\pi\) | ||||
−0.608768 | + | 0.793348i | \(0.708336\pi\) | |||||||
\(410\) | −60.0690 | −2.96660 | ||||||||
\(411\) | −27.2978 | −1.34650 | ||||||||
\(412\) | −26.8168 | −1.32117 | ||||||||
\(413\) | 17.2530 | 0.848963 | ||||||||
\(414\) | −5.02243 | −0.246839 | ||||||||
\(415\) | −33.1025 | −1.62494 | ||||||||
\(416\) | 24.5957 | 1.20590 | ||||||||
\(417\) | 8.51122 | 0.416796 | ||||||||
\(418\) | 13.7642 | 0.673228 | ||||||||
\(419\) | −5.06534 | −0.247458 | −0.123729 | − | 0.992316i | \(-0.539485\pi\) | ||||
−0.123729 | + | 0.992316i | \(0.539485\pi\) | |||||||
\(420\) | 39.4426 | 1.92460 | ||||||||
\(421\) | −22.0396 | −1.07414 | −0.537072 | − | 0.843537i | \(-0.680470\pi\) | ||||
−0.537072 | + | 0.843537i | \(0.680470\pi\) | |||||||
\(422\) | −8.09986 | −0.394295 | ||||||||
\(423\) | 4.68676 | 0.227878 | ||||||||
\(424\) | 5.66432 | 0.275084 | ||||||||
\(425\) | 28.7659 | 1.39535 | ||||||||
\(426\) | −3.65662 | −0.177164 | ||||||||
\(427\) | 13.9551 | 0.675336 | ||||||||
\(428\) | 0.581612 | 0.0281133 | ||||||||
\(429\) | 8.32027 | 0.401706 | ||||||||
\(430\) | 8.90958 | 0.429658 | ||||||||
\(431\) | −16.4278 | −0.791301 | −0.395650 | − | 0.918401i | \(-0.629481\pi\) | ||||
−0.395650 | + | 0.918401i | \(0.629481\pi\) | |||||||
\(432\) | −20.4734 | −0.985026 | ||||||||
\(433\) | 33.6885 | 1.61897 | 0.809483 | − | 0.587143i | \(-0.199748\pi\) | ||||
0.809483 | + | 0.587143i | \(0.199748\pi\) | |||||||
\(434\) | −29.2530 | −1.40419 | ||||||||
\(435\) | −28.6309 | −1.37274 | ||||||||
\(436\) | 0.992296 | 0.0475224 | ||||||||
\(437\) | −21.9243 | −1.04878 | ||||||||
\(438\) | −59.9441 | −2.86424 | ||||||||
\(439\) | 9.70390 | 0.463142 | 0.231571 | − | 0.972818i | \(-0.425613\pi\) | ||||
0.231571 | + | 0.972818i | \(0.425613\pi\) | |||||||
\(440\) | −2.80731 | −0.133833 | ||||||||
\(441\) | 5.00770 | 0.238462 | ||||||||
\(442\) | −32.5508 | −1.54828 | ||||||||
\(443\) | −22.1601 | −1.05286 | −0.526430 | − | 0.850219i | \(-0.676470\pi\) | ||||
−0.526430 | + | 0.850219i | \(0.676470\pi\) | |||||||
\(444\) | 17.9193 | 0.850410 | ||||||||
\(445\) | −10.5009 | −0.497789 | ||||||||
\(446\) | −37.3381 | −1.76801 | ||||||||
\(447\) | 16.1601 | 0.764348 | ||||||||
\(448\) | 19.3427 | 0.913857 | ||||||||
\(449\) | −29.0224 | −1.36965 | −0.684827 | − | 0.728706i | \(-0.740122\pi\) | ||||
−0.684827 | + | 0.728706i | \(0.740122\pi\) | |||||||
\(450\) | 7.03014 | 0.331404 | ||||||||
\(451\) | −12.6714 | −0.596671 | ||||||||
\(452\) | 5.19798 | 0.244492 | ||||||||
\(453\) | −34.2523 | −1.60931 | ||||||||
\(454\) | −38.3203 | −1.79846 | ||||||||
\(455\) | 41.2530 | 1.93397 | ||||||||
\(456\) | 6.88209 | 0.322283 | ||||||||
\(457\) | 19.5491 | 0.914466 | 0.457233 | − | 0.889347i | \(-0.348840\pi\) | ||||
0.457233 | + | 0.889347i | \(0.348840\pi\) | |||||||
\(458\) | −3.15817 | −0.147571 | ||||||||
\(459\) | 23.0224 | 1.07460 | ||||||||
\(460\) | −21.5732 | −1.00586 | ||||||||
\(461\) | 6.04487 | 0.281538 | 0.140769 | − | 0.990042i | \(-0.455043\pi\) | ||||
0.140769 | + | 0.990042i | \(0.455043\pi\) | |||||||
\(462\) | 18.3651 | 0.854424 | ||||||||
\(463\) | −21.1300 | −0.981994 | −0.490997 | − | 0.871161i | \(-0.663367\pi\) | ||||
−0.490997 | + | 0.871161i | \(0.663367\pi\) | |||||||
\(464\) | −21.0121 | −0.975462 | ||||||||
\(465\) | −24.9019 | −1.15480 | ||||||||
\(466\) | 45.0922 | 2.08885 | ||||||||
\(467\) | 40.8262 | 1.88921 | 0.944606 | − | 0.328208i | \(-0.106445\pi\) | ||||
0.944606 | + | 0.328208i | \(0.106445\pi\) | |||||||
\(468\) | −3.60405 | −0.166597 | ||||||||
\(469\) | 20.3203 | 0.938303 | ||||||||
\(470\) | 44.4355 | 2.04966 | ||||||||
\(471\) | 11.4208 | 0.526243 | ||||||||
\(472\) | 2.96216 | 0.136344 | ||||||||
\(473\) | 1.87945 | 0.0864170 | ||||||||
\(474\) | −18.5759 | −0.853218 | ||||||||
\(475\) | 30.6885 | 1.40808 | ||||||||
\(476\) | −32.5508 | −1.49196 | ||||||||
\(477\) | −5.66432 | −0.259352 | ||||||||
\(478\) | 1.09283 | 0.0499848 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 46.2144 | 2.10939 | ||||||||
\(481\) | 18.7417 | 0.854550 | ||||||||
\(482\) | 48.7109 | 2.21872 | ||||||||
\(483\) | −29.2530 | −1.33106 | ||||||||
\(484\) | −15.3658 | −0.698446 | ||||||||
\(485\) | 38.4958 | 1.74800 | ||||||||
\(486\) | 12.8295 | 0.581959 | ||||||||
\(487\) | 10.9622 | 0.496743 | 0.248371 | − | 0.968665i | \(-0.420105\pi\) | ||||
0.248371 | + | 0.968665i | \(0.420105\pi\) | |||||||
\(488\) | 2.39595 | 0.108460 | ||||||||
\(489\) | 21.7488 | 0.983514 | ||||||||
\(490\) | 47.4784 | 2.14486 | ||||||||
\(491\) | 23.4734 | 1.05934 | 0.529669 | − | 0.848204i | \(-0.322316\pi\) | ||||
0.529669 | + | 0.848204i | \(0.322316\pi\) | |||||||
\(492\) | 30.5662 | 1.37803 | ||||||||
\(493\) | 23.6282 | 1.06416 | ||||||||
\(494\) | −34.7263 | −1.56241 | ||||||||
\(495\) | 2.80731 | 0.126179 | ||||||||
\(496\) | −18.2754 | −0.820590 | ||||||||
\(497\) | −3.82446 | −0.171550 | ||||||||
\(498\) | 37.1799 | 1.66607 | ||||||||
\(499\) | 7.11021 | 0.318297 | 0.159148 | − | 0.987255i | \(-0.449125\pi\) | ||||
0.159148 | + | 0.987255i | \(0.449125\pi\) | |||||||
\(500\) | 3.23053 | 0.144474 | ||||||||
\(501\) | −17.3632 | −0.775729 | ||||||||
\(502\) | 38.4503 | 1.71612 | ||||||||
\(503\) | −31.8365 | −1.41952 | −0.709761 | − | 0.704443i | \(-0.751197\pi\) | ||||
−0.709761 | + | 0.704443i | \(0.751197\pi\) | |||||||
\(504\) | 1.64892 | 0.0734486 | ||||||||
\(505\) | 7.62913 | 0.339492 | ||||||||
\(506\) | −10.0449 | −0.446549 | ||||||||
\(507\) | 3.86736 | 0.171755 | ||||||||
\(508\) | −7.18257 | −0.318675 | ||||||||
\(509\) | −11.0224 | −0.488561 | −0.244280 | − | 0.969705i | \(-0.578552\pi\) | ||||
−0.244280 | + | 0.969705i | \(0.578552\pi\) | |||||||
\(510\) | −61.1619 | −2.70829 | ||||||||
\(511\) | −62.6955 | −2.77349 | ||||||||
\(512\) | 27.9166 | 1.23375 | ||||||||
\(513\) | 24.5611 | 1.08440 | ||||||||
\(514\) | −46.4201 | −2.04750 | ||||||||
\(515\) | −52.7006 | −2.32227 | ||||||||
\(516\) | −4.53365 | −0.199583 | ||||||||
\(517\) | 9.37352 | 0.412247 | ||||||||
\(518\) | 41.3682 | 1.81762 | ||||||||
\(519\) | −3.15311 | −0.138406 | ||||||||
\(520\) | 7.08271 | 0.310597 | ||||||||
\(521\) | −29.4105 | −1.28850 | −0.644248 | − | 0.764817i | \(-0.722829\pi\) | ||||
−0.644248 | + | 0.764817i | \(0.722829\pi\) | |||||||
\(522\) | 5.77453 | 0.252744 | ||||||||
\(523\) | −20.8623 | −0.912245 | −0.456122 | − | 0.889917i | \(-0.650762\pi\) | ||||
−0.456122 | + | 0.889917i | \(0.650762\pi\) | |||||||
\(524\) | 23.7444 | 1.03728 | ||||||||
\(525\) | 40.9468 | 1.78706 | ||||||||
\(526\) | 18.2549 | 0.795953 | ||||||||
\(527\) | 20.5508 | 0.895207 | ||||||||
\(528\) | 11.4734 | 0.499315 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −53.7039 | −2.33275 | ||||||||
\(531\) | −2.96216 | −0.128547 | ||||||||
\(532\) | −34.7263 | −1.50558 | ||||||||
\(533\) | 31.9692 | 1.38474 | ||||||||
\(534\) | 11.7943 | 0.510390 | ||||||||
\(535\) | 1.14299 | 0.0494158 | ||||||||
\(536\) | 3.48878 | 0.150692 | ||||||||
\(537\) | −9.93466 | −0.428712 | ||||||||
\(538\) | −22.7263 | −0.979802 | ||||||||
\(539\) | 10.0154 | 0.431394 | ||||||||
\(540\) | 24.1678 | 1.04002 | ||||||||
\(541\) | 14.7417 | 0.633797 | 0.316899 | − | 0.948459i | \(-0.397359\pi\) | ||||
0.316899 | + | 0.948459i | \(0.397359\pi\) | |||||||
\(542\) | −6.72393 | −0.288817 | ||||||||
\(543\) | −26.9622 | −1.15706 | ||||||||
\(544\) | −38.1394 | −1.63521 | ||||||||
\(545\) | 1.95007 | 0.0835319 | ||||||||
\(546\) | −46.3343 | −1.98293 | ||||||||
\(547\) | −26.5189 | −1.13387 | −0.566934 | − | 0.823763i | \(-0.691870\pi\) | ||||
−0.566934 | + | 0.823763i | \(0.691870\pi\) | |||||||
\(548\) | 23.6489 | 1.01023 | ||||||||
\(549\) | −2.39595 | −0.102257 | ||||||||
\(550\) | 14.0603 | 0.599532 | ||||||||
\(551\) | 25.2074 | 1.07387 | ||||||||
\(552\) | −5.02243 | −0.213769 | ||||||||
\(553\) | −19.4285 | −0.826184 | ||||||||
\(554\) | 11.4586 | 0.486831 | ||||||||
\(555\) | 35.2151 | 1.49480 | ||||||||
\(556\) | −7.37352 | −0.312707 | ||||||||
\(557\) | 44.1274 | 1.86974 | 0.934868 | − | 0.354996i | \(-0.115518\pi\) | ||||
0.934868 | + | 0.354996i | \(0.115518\pi\) | |||||||
\(558\) | 5.02243 | 0.212617 | ||||||||
\(559\) | −4.74175 | −0.200554 | ||||||||
\(560\) | 56.8865 | 2.40389 | ||||||||
\(561\) | −12.9019 | −0.544718 | ||||||||
\(562\) | −12.4509 | −0.525211 | ||||||||
\(563\) | 4.84689 | 0.204272 | 0.102136 | − | 0.994770i | \(-0.467432\pi\) | ||||
0.102136 | + | 0.994770i | \(0.467432\pi\) | |||||||
\(564\) | −22.6111 | −0.952098 | ||||||||
\(565\) | 10.2151 | 0.429753 | ||||||||
\(566\) | 21.9397 | 0.922195 | ||||||||
\(567\) | 40.3049 | 1.69265 | ||||||||
\(568\) | −0.656620 | −0.0275512 | ||||||||
\(569\) | −37.9665 | −1.59164 | −0.795820 | − | 0.605533i | \(-0.792960\pi\) | ||||
−0.795820 | + | 0.605533i | \(0.792960\pi\) | |||||||
\(570\) | −65.2496 | −2.73301 | ||||||||
\(571\) | −20.7789 | −0.869570 | −0.434785 | − | 0.900534i | \(-0.643176\pi\) | ||||
−0.434785 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(572\) | −7.20809 | −0.301386 | ||||||||
\(573\) | 13.3658 | 0.558365 | ||||||||
\(574\) | 70.5649 | 2.94532 | ||||||||
\(575\) | −22.3960 | −0.933976 | ||||||||
\(576\) | −3.32094 | −0.138373 | ||||||||
\(577\) | 37.9665 | 1.58057 | 0.790284 | − | 0.612741i | \(-0.209933\pi\) | ||||
0.790284 | + | 0.612741i | \(0.209933\pi\) | |||||||
\(578\) | 17.9672 | 0.747338 | ||||||||
\(579\) | −15.1826 | −0.630966 | ||||||||
\(580\) | 24.8038 | 1.02992 | ||||||||
\(581\) | 38.8865 | 1.61328 | ||||||||
\(582\) | −43.2376 | −1.79225 | ||||||||
\(583\) | −11.3286 | −0.469185 | ||||||||
\(584\) | −10.7642 | −0.445425 | ||||||||
\(585\) | −7.08271 | −0.292834 | ||||||||
\(586\) | −39.4426 | −1.62936 | ||||||||
\(587\) | −9.03452 | −0.372895 | −0.186447 | − | 0.982465i | \(-0.559697\pi\) | ||||
−0.186447 | + | 0.982465i | \(0.559697\pi\) | |||||||
\(588\) | −24.1595 | −0.996319 | ||||||||
\(589\) | 21.9243 | 0.903376 | ||||||||
\(590\) | −28.0844 | −1.15622 | ||||||||
\(591\) | 6.67135 | 0.274423 | ||||||||
\(592\) | 25.8442 | 1.06219 | ||||||||
\(593\) | 9.44588 | 0.387896 | 0.193948 | − | 0.981012i | \(-0.437871\pi\) | ||||
0.193948 | + | 0.981012i | \(0.437871\pi\) | |||||||
\(594\) | 11.2530 | 0.461715 | ||||||||
\(595\) | −63.9692 | −2.62248 | ||||||||
\(596\) | −14.0000 | −0.573462 | ||||||||
\(597\) | −33.4278 | −1.36811 | ||||||||
\(598\) | 25.3427 | 1.03634 | ||||||||
\(599\) | 39.9089 | 1.63063 | 0.815317 | − | 0.579015i | \(-0.196563\pi\) | ||||
0.815317 | + | 0.579015i | \(0.196563\pi\) | |||||||
\(600\) | 7.03014 | 0.287004 | ||||||||
\(601\) | 45.5130 | 1.85651 | 0.928256 | − | 0.371942i | \(-0.121308\pi\) | ||||
0.928256 | + | 0.371942i | \(0.121308\pi\) | |||||||
\(602\) | −10.4663 | −0.426576 | ||||||||
\(603\) | −3.48878 | −0.142074 | ||||||||
\(604\) | 29.6738 | 1.20741 | ||||||||
\(605\) | −30.1971 | −1.22769 | ||||||||
\(606\) | −8.56885 | −0.348086 | ||||||||
\(607\) | −40.4509 | −1.64185 | −0.820927 | − | 0.571034i | \(-0.806542\pi\) | ||||
−0.820927 | + | 0.571034i | \(0.806542\pi\) | |||||||
\(608\) | −40.6885 | −1.65014 | ||||||||
\(609\) | 33.6335 | 1.36290 | ||||||||
\(610\) | −22.7162 | −0.919753 | ||||||||
\(611\) | −23.6489 | −0.956733 | ||||||||
\(612\) | 5.58864 | 0.225907 | ||||||||
\(613\) | −22.4683 | −0.907487 | −0.453743 | − | 0.891132i | \(-0.649912\pi\) | ||||
−0.453743 | + | 0.891132i | \(0.649912\pi\) | |||||||
\(614\) | 22.6111 | 0.912509 | ||||||||
\(615\) | 60.0690 | 2.42222 | ||||||||
\(616\) | 3.29783 | 0.132873 | ||||||||
\(617\) | −3.95778 | −0.159334 | −0.0796670 | − | 0.996822i | \(-0.525386\pi\) | ||||
−0.0796670 | + | 0.996822i | \(0.525386\pi\) | |||||||
\(618\) | 59.1920 | 2.38105 | ||||||||
\(619\) | −4.80202 | −0.193010 | −0.0965048 | − | 0.995333i | \(-0.530766\pi\) | ||||
−0.0965048 | + | 0.995333i | \(0.530766\pi\) | |||||||
\(620\) | 21.5732 | 0.866402 | ||||||||
\(621\) | −17.9243 | −0.719278 | ||||||||
\(622\) | −35.1524 | −1.40948 | ||||||||
\(623\) | 12.3357 | 0.494218 | ||||||||
\(624\) | −28.9468 | −1.15880 | ||||||||
\(625\) | −21.6463 | −0.865851 | ||||||||
\(626\) | −10.1454 | −0.405492 | ||||||||
\(627\) | −13.7642 | −0.549688 | ||||||||
\(628\) | −9.89418 | −0.394821 | ||||||||
\(629\) | −29.0620 | −1.15878 | ||||||||
\(630\) | −15.6335 | −0.622854 | ||||||||
\(631\) | −32.0449 | −1.27569 | −0.637843 | − | 0.770166i | \(-0.720173\pi\) | ||||
−0.637843 | + | 0.770166i | \(0.720173\pi\) | |||||||
\(632\) | −3.33568 | −0.132686 | ||||||||
\(633\) | 8.09986 | 0.321940 | ||||||||
\(634\) | −11.2530 | −0.446912 | ||||||||
\(635\) | −14.1153 | −0.560147 | ||||||||
\(636\) | 27.3273 | 1.08360 | ||||||||
\(637\) | −25.2684 | −1.00117 | ||||||||
\(638\) | 11.5491 | 0.457232 | ||||||||
\(639\) | 0.656620 | 0.0259755 | ||||||||
\(640\) | 16.8495 | 0.666036 | ||||||||
\(641\) | −40.2677 | −1.59048 | −0.795239 | − | 0.606296i | \(-0.792655\pi\) | ||||
−0.795239 | + | 0.606296i | \(0.792655\pi\) | |||||||
\(642\) | −1.28378 | −0.0506667 | ||||||||
\(643\) | 12.6714 | 0.499709 | 0.249855 | − | 0.968283i | \(-0.419617\pi\) | ||||
0.249855 | + | 0.968283i | \(0.419617\pi\) | |||||||
\(644\) | 25.3427 | 0.998642 | ||||||||
\(645\) | −8.90958 | −0.350815 | ||||||||
\(646\) | 53.8486 | 2.11865 | ||||||||
\(647\) | 32.0000 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(648\) | 6.91993 | 0.271841 | ||||||||
\(649\) | −5.92432 | −0.232550 | ||||||||
\(650\) | −35.4734 | −1.39138 | ||||||||
\(651\) | 29.2530 | 1.14651 | ||||||||
\(652\) | −18.8416 | −0.737894 | ||||||||
\(653\) | 31.6643 | 1.23912 | 0.619560 | − | 0.784949i | \(-0.287311\pi\) | ||||
0.619560 | + | 0.784949i | \(0.287311\pi\) | |||||||
\(654\) | −2.19027 | −0.0856464 | ||||||||
\(655\) | 46.6627 | 1.82326 | ||||||||
\(656\) | 44.0844 | 1.72121 | ||||||||
\(657\) | 10.7642 | 0.419951 | ||||||||
\(658\) | −52.1997 | −2.03496 | ||||||||
\(659\) | −38.0570 | −1.48249 | −0.741244 | − | 0.671235i | \(-0.765764\pi\) | ||||
−0.741244 | + | 0.671235i | \(0.765764\pi\) | |||||||
\(660\) | −13.5438 | −0.527191 | ||||||||
\(661\) | 41.1672 | 1.60122 | 0.800609 | − | 0.599188i | \(-0.204510\pi\) | ||||
0.800609 | + | 0.599188i | \(0.204510\pi\) | |||||||
\(662\) | 24.3458 | 0.946226 | ||||||||
\(663\) | 32.5508 | 1.26417 | ||||||||
\(664\) | 6.67641 | 0.259095 | ||||||||
\(665\) | −68.2446 | −2.64641 | ||||||||
\(666\) | −7.10250 | −0.275216 | ||||||||
\(667\) | −18.3960 | −0.712294 | ||||||||
\(668\) | 15.0422 | 0.582001 | ||||||||
\(669\) | 37.3381 | 1.44357 | ||||||||
\(670\) | −33.0774 | −1.27789 | ||||||||
\(671\) | −4.79191 | −0.184989 | ||||||||
\(672\) | −54.2895 | −2.09426 | ||||||||
\(673\) | 14.9622 | 0.576749 | 0.288374 | − | 0.957518i | \(-0.406885\pi\) | ||||
0.288374 | + | 0.957518i | \(0.406885\pi\) | |||||||
\(674\) | 55.0171 | 2.11918 | ||||||||
\(675\) | 25.0895 | 0.965696 | ||||||||
\(676\) | −3.35041 | −0.128862 | ||||||||
\(677\) | −39.5457 | −1.51987 | −0.759933 | − | 0.650001i | \(-0.774768\pi\) | ||||
−0.759933 | + | 0.650001i | \(0.774768\pi\) | |||||||
\(678\) | −11.4734 | −0.440632 | ||||||||
\(679\) | −45.2221 | −1.73547 | ||||||||
\(680\) | −10.9829 | −0.421173 | ||||||||
\(681\) | 38.3203 | 1.46844 | ||||||||
\(682\) | 10.0449 | 0.384638 | ||||||||
\(683\) | −25.2925 | −0.967792 | −0.483896 | − | 0.875125i | \(-0.660779\pi\) | ||||
−0.483896 | + | 0.875125i | \(0.660779\pi\) | |||||||
\(684\) | 5.96216 | 0.227969 | ||||||||
\(685\) | 46.4751 | 1.77572 | ||||||||
\(686\) | −4.58161 | −0.174927 | ||||||||
\(687\) | 3.15817 | 0.120492 | ||||||||
\(688\) | −6.53871 | −0.249286 | ||||||||
\(689\) | 28.5816 | 1.08887 | ||||||||
\(690\) | 47.6181 | 1.81279 | ||||||||
\(691\) | −12.2600 | −0.466392 | −0.233196 | − | 0.972430i | \(-0.574918\pi\) | ||||
−0.233196 | + | 0.972430i | \(0.574918\pi\) | |||||||
\(692\) | 2.73163 | 0.103841 | ||||||||
\(693\) | −3.29783 | −0.125274 | ||||||||
\(694\) | 1.95513 | 0.0742157 | ||||||||
\(695\) | −14.4905 | −0.549657 | ||||||||
\(696\) | 5.77453 | 0.218883 | ||||||||
\(697\) | −49.5732 | −1.87772 | ||||||||
\(698\) | 4.71622 | 0.178512 | ||||||||
\(699\) | −45.0922 | −1.70554 | ||||||||
\(700\) | −35.4734 | −1.34077 | ||||||||
\(701\) | −7.83987 | −0.296108 | −0.148054 | − | 0.988979i | \(-0.547301\pi\) | ||||
−0.148054 | + | 0.988979i | \(0.547301\pi\) | |||||||
\(702\) | −28.3907 | −1.07154 | ||||||||
\(703\) | −31.0044 | −1.16935 | ||||||||
\(704\) | −6.64189 | −0.250326 | ||||||||
\(705\) | −44.4355 | −1.67354 | ||||||||
\(706\) | 16.7162 | 0.629123 | ||||||||
\(707\) | −8.96216 | −0.337057 | ||||||||
\(708\) | 14.2908 | 0.537081 | ||||||||
\(709\) | −52.6352 | −1.97676 | −0.988379 | − | 0.152009i | \(-0.951426\pi\) | ||||
−0.988379 | + | 0.152009i | \(0.951426\pi\) | |||||||
\(710\) | 6.22547 | 0.233638 | ||||||||
\(711\) | 3.33568 | 0.125098 | ||||||||
\(712\) | 2.11791 | 0.0793720 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 71.8486 | 2.68887 | ||||||||
\(715\) | −14.1654 | −0.529757 | ||||||||
\(716\) | 8.60669 | 0.321647 | ||||||||
\(717\) | −1.09283 | −0.0408125 | ||||||||
\(718\) | −14.5163 | −0.541743 | ||||||||
\(719\) | 1.71161 | 0.0638322 | 0.0319161 | − | 0.999491i | \(-0.489839\pi\) | ||||
0.0319161 | + | 0.999491i | \(0.489839\pi\) | |||||||
\(720\) | −9.76683 | −0.363988 | ||||||||
\(721\) | 61.9089 | 2.30561 | ||||||||
\(722\) | 21.1153 | 0.785829 | ||||||||
\(723\) | −48.7109 | −1.81158 | ||||||||
\(724\) | 23.3581 | 0.868097 | ||||||||
\(725\) | 25.7497 | 0.956319 | ||||||||
\(726\) | 33.9166 | 1.25876 | ||||||||
\(727\) | 15.0378 | 0.557723 | 0.278861 | − | 0.960331i | \(-0.410043\pi\) | ||||
0.278861 | + | 0.960331i | \(0.410043\pi\) | |||||||
\(728\) | −8.32027 | −0.308370 | ||||||||
\(729\) | 18.7866 | 0.695801 | ||||||||
\(730\) | 102.056 | 3.77726 | ||||||||
\(731\) | 7.35282 | 0.271954 | ||||||||
\(732\) | 11.5592 | 0.427239 | ||||||||
\(733\) | 45.7334 | 1.68920 | 0.844600 | − | 0.535398i | \(-0.179838\pi\) | ||||
0.844600 | + | 0.535398i | \(0.179838\pi\) | |||||||
\(734\) | 57.5629 | 2.12468 | ||||||||
\(735\) | −47.4784 | −1.75127 | ||||||||
\(736\) | 29.6938 | 1.09453 | ||||||||
\(737\) | −6.97757 | −0.257022 | ||||||||
\(738\) | −12.1153 | −0.445969 | ||||||||
\(739\) | −31.5284 | −1.15979 | −0.579895 | − | 0.814691i | \(-0.696906\pi\) | ||||
−0.579895 | + | 0.814691i | \(0.696906\pi\) | |||||||
\(740\) | −30.5079 | −1.12149 | ||||||||
\(741\) | 34.7263 | 1.27570 | ||||||||
\(742\) | 63.0875 | 2.31602 | ||||||||
\(743\) | 0.471638 | 0.0173027 | 0.00865136 | − | 0.999963i | \(-0.497246\pi\) | ||||
0.00865136 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(744\) | 5.02243 | 0.184131 | ||||||||
\(745\) | −27.5130 | −1.00800 | ||||||||
\(746\) | 16.0499 | 0.587630 | ||||||||
\(747\) | −6.67641 | −0.244277 | ||||||||
\(748\) | 11.1773 | 0.408682 | ||||||||
\(749\) | −1.34270 | −0.0490613 | ||||||||
\(750\) | −7.13067 | −0.260375 | ||||||||
\(751\) | −16.5059 | −0.602310 | −0.301155 | − | 0.953575i | \(-0.597372\pi\) | ||||
−0.301155 | + | 0.953575i | \(0.597372\pi\) | |||||||
\(752\) | −32.6111 | −1.18920 | ||||||||
\(753\) | −38.4503 | −1.40121 | ||||||||
\(754\) | −29.1377 | −1.06113 | ||||||||
\(755\) | 58.3152 | 2.12231 | ||||||||
\(756\) | −28.3907 | −1.03256 | ||||||||
\(757\) | −32.8918 | −1.19547 | −0.597736 | − | 0.801693i | \(-0.703933\pi\) | ||||
−0.597736 | + | 0.801693i | \(0.703933\pi\) | |||||||
\(758\) | −19.9615 | −0.725034 | ||||||||
\(759\) | 10.0449 | 0.364606 | ||||||||
\(760\) | −11.7169 | −0.425017 | ||||||||
\(761\) | 2.39595 | 0.0868532 | 0.0434266 | − | 0.999057i | \(-0.486173\pi\) | ||||
0.0434266 | + | 0.999057i | \(0.486173\pi\) | |||||||
\(762\) | 15.8539 | 0.574327 | ||||||||
\(763\) | −2.29081 | −0.0829327 | ||||||||
\(764\) | −11.5792 | −0.418921 | ||||||||
\(765\) | 10.9829 | 0.397086 | ||||||||
\(766\) | −9.51825 | −0.343908 | ||||||||
\(767\) | 14.9468 | 0.539696 | ||||||||
\(768\) | −38.2677 | −1.38087 | ||||||||
\(769\) | 53.6335 | 1.93407 | 0.967037 | − | 0.254636i | \(-0.0819557\pi\) | ||||
0.967037 | + | 0.254636i | \(0.0819557\pi\) | |||||||
\(770\) | −31.2670 | −1.12679 | ||||||||
\(771\) | 46.4201 | 1.67178 | ||||||||
\(772\) | 13.1531 | 0.473391 | ||||||||
\(773\) | 30.5059 | 1.09722 | 0.548611 | − | 0.836078i | \(-0.315157\pi\) | ||||
0.548611 | + | 0.836078i | \(0.315157\pi\) | |||||||
\(774\) | 1.79696 | 0.0645906 | ||||||||
\(775\) | 22.3960 | 0.804486 | ||||||||
\(776\) | −7.76418 | −0.278718 | ||||||||
\(777\) | −41.3682 | −1.48408 | ||||||||
\(778\) | −29.3581 | −1.05254 | ||||||||
\(779\) | −52.8865 | −1.89485 | ||||||||
\(780\) | 34.1703 | 1.22349 | ||||||||
\(781\) | 1.31324 | 0.0469915 | ||||||||
\(782\) | −39.2978 | −1.40529 | ||||||||
\(783\) | 20.6084 | 0.736485 | ||||||||
\(784\) | −34.8442 | −1.24444 | ||||||||
\(785\) | −19.4441 | −0.693991 | ||||||||
\(786\) | −52.4105 | −1.86942 | ||||||||
\(787\) | 38.6936 | 1.37928 | 0.689638 | − | 0.724154i | \(-0.257770\pi\) | ||||
0.689638 | + | 0.724154i | \(0.257770\pi\) | |||||||
\(788\) | −5.77959 | −0.205889 | ||||||||
\(789\) | −18.2549 | −0.649893 | ||||||||
\(790\) | 31.6258 | 1.12520 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | −0.566204 | −0.0201192 | ||||||||
\(793\) | 12.0897 | 0.429319 | ||||||||
\(794\) | −7.53365 | −0.267359 | ||||||||
\(795\) | 53.7039 | 1.90468 | ||||||||
\(796\) | 28.9595 | 1.02644 | ||||||||
\(797\) | −35.4450 | −1.25553 | −0.627763 | − | 0.778405i | \(-0.716029\pi\) | ||||
−0.627763 | + | 0.778405i | \(0.716029\pi\) | |||||||
\(798\) | 76.6507 | 2.71340 | ||||||||
\(799\) | 36.6714 | 1.29734 | ||||||||
\(800\) | −41.5638 | −1.46950 | ||||||||
\(801\) | −2.11791 | −0.0748327 | ||||||||
\(802\) | −21.9397 | −0.774719 | ||||||||
\(803\) | 21.5284 | 0.759719 | ||||||||
\(804\) | 16.8315 | 0.593601 | ||||||||
\(805\) | 49.8038 | 1.75535 | ||||||||
\(806\) | −25.3427 | −0.892659 | ||||||||
\(807\) | 22.7263 | 0.800005 | ||||||||
\(808\) | −1.53871 | −0.0541317 | ||||||||
\(809\) | 38.9622 | 1.36984 | 0.684918 | − | 0.728620i | \(-0.259838\pi\) | ||||
0.684918 | + | 0.728620i | \(0.259838\pi\) | |||||||
\(810\) | −65.6084 | −2.30525 | ||||||||
\(811\) | 36.1421 | 1.26912 | 0.634560 | − | 0.772874i | \(-0.281181\pi\) | ||||
0.634560 | + | 0.772874i | \(0.281181\pi\) | |||||||
\(812\) | −29.1377 | −1.02253 | ||||||||
\(813\) | 6.72393 | 0.235818 | ||||||||
\(814\) | −14.2050 | −0.497885 | ||||||||
\(815\) | −37.0277 | −1.29702 | ||||||||
\(816\) | 44.8865 | 1.57134 | ||||||||
\(817\) | 7.84425 | 0.274436 | ||||||||
\(818\) | −47.0851 | −1.64629 | ||||||||
\(819\) | 8.32027 | 0.290734 | ||||||||
\(820\) | −52.0396 | −1.81730 | ||||||||
\(821\) | 14.8788 | 0.519273 | 0.259636 | − | 0.965706i | \(-0.416397\pi\) | ||||
0.259636 | + | 0.965706i | \(0.416397\pi\) | |||||||
\(822\) | −52.1997 | −1.82067 | ||||||||
\(823\) | 24.2151 | 0.844086 | 0.422043 | − | 0.906576i | \(-0.361313\pi\) | ||||
0.422043 | + | 0.906576i | \(0.361313\pi\) | |||||||
\(824\) | 10.6291 | 0.370283 | ||||||||
\(825\) | −14.0603 | −0.489516 | ||||||||
\(826\) | 32.9916 | 1.14793 | ||||||||
\(827\) | 24.4114 | 0.848866 | 0.424433 | − | 0.905459i | \(-0.360473\pi\) | ||||
0.424433 | + | 0.905459i | \(0.360473\pi\) | |||||||
\(828\) | −4.35108 | −0.151211 | ||||||||
\(829\) | −14.2228 | −0.493979 | −0.246990 | − | 0.969018i | \(-0.579441\pi\) | ||||
−0.246990 | + | 0.969018i | \(0.579441\pi\) | |||||||
\(830\) | −63.2996 | −2.19716 | ||||||||
\(831\) | −11.4586 | −0.397496 | ||||||||
\(832\) | 16.7572 | 0.580950 | ||||||||
\(833\) | 39.1826 | 1.35760 | ||||||||
\(834\) | 16.2754 | 0.563571 | ||||||||
\(835\) | 29.5611 | 1.02301 | ||||||||
\(836\) | 11.9243 | 0.412411 | ||||||||
\(837\) | 17.9243 | 0.619555 | ||||||||
\(838\) | −9.68608 | −0.334600 | ||||||||
\(839\) | 10.6241 | 0.366784 | 0.183392 | − | 0.983040i | \(-0.441292\pi\) | ||||
0.183392 | + | 0.983040i | \(0.441292\pi\) | |||||||
\(840\) | −15.6335 | −0.539407 | ||||||||
\(841\) | −7.84931 | −0.270666 | ||||||||
\(842\) | −42.1447 | −1.45240 | ||||||||
\(843\) | 12.4509 | 0.428833 | ||||||||
\(844\) | −7.01714 | −0.241540 | ||||||||
\(845\) | −6.58426 | −0.226505 | ||||||||
\(846\) | 8.96216 | 0.308125 | ||||||||
\(847\) | 35.4734 | 1.21888 | ||||||||
\(848\) | 39.4131 | 1.35345 | ||||||||
\(849\) | −21.9397 | −0.752969 | ||||||||
\(850\) | 55.0070 | 1.88673 | ||||||||
\(851\) | 22.6265 | 0.775626 | ||||||||
\(852\) | −3.16784 | −0.108528 | ||||||||
\(853\) | −56.0415 | −1.91883 | −0.959413 | − | 0.282005i | \(-0.909001\pi\) | ||||
−0.959413 | + | 0.282005i | \(0.909001\pi\) | |||||||
\(854\) | 26.6854 | 0.913156 | ||||||||
\(855\) | 11.7169 | 0.400709 | ||||||||
\(856\) | −0.230528 | −0.00787930 | ||||||||
\(857\) | 11.8968 | 0.406388 | 0.203194 | − | 0.979139i | \(-0.434868\pi\) | ||||
0.203194 | + | 0.979139i | \(0.434868\pi\) | |||||||
\(858\) | 15.9103 | 0.543167 | ||||||||
\(859\) | −53.2221 | −1.81592 | −0.907958 | − | 0.419061i | \(-0.862359\pi\) | ||||
−0.907958 | + | 0.419061i | \(0.862359\pi\) | |||||||
\(860\) | 7.71863 | 0.263203 | ||||||||
\(861\) | −70.5649 | −2.40484 | ||||||||
\(862\) | −31.4138 | −1.06996 | ||||||||
\(863\) | −45.0620 | −1.53393 | −0.766964 | − | 0.641690i | \(-0.778234\pi\) | ||||
−0.766964 | + | 0.641690i | \(0.778234\pi\) | |||||||
\(864\) | −33.2650 | −1.13170 | ||||||||
\(865\) | 5.36823 | 0.182525 | ||||||||
\(866\) | 64.4201 | 2.18908 | ||||||||
\(867\) | −17.9672 | −0.610199 | ||||||||
\(868\) | −25.3427 | −0.860187 | ||||||||
\(869\) | 6.67135 | 0.226310 | ||||||||
\(870\) | −54.7488 | −1.85616 | ||||||||
\(871\) | 17.6040 | 0.596490 | ||||||||
\(872\) | −0.393308 | −0.0133191 | ||||||||
\(873\) | 7.76418 | 0.262778 | ||||||||
\(874\) | −41.9243 | −1.41811 | ||||||||
\(875\) | −7.45797 | −0.252125 | ||||||||
\(876\) | −51.9313 | −1.75460 | ||||||||
\(877\) | −57.0647 | −1.92694 | −0.963468 | − | 0.267822i | \(-0.913696\pi\) | ||||
−0.963468 | + | 0.267822i | \(0.913696\pi\) | |||||||
\(878\) | 18.5561 | 0.626238 | ||||||||
\(879\) | 39.4426 | 1.33036 | ||||||||
\(880\) | −19.5337 | −0.658479 | ||||||||
\(881\) | 22.4329 | 0.755783 | 0.377892 | − | 0.925850i | \(-0.376649\pi\) | ||||
0.377892 | + | 0.925850i | \(0.376649\pi\) | |||||||
\(882\) | 9.57588 | 0.322437 | ||||||||
\(883\) | −10.3805 | −0.349333 | −0.174667 | − | 0.984628i | \(-0.555885\pi\) | ||||
−0.174667 | + | 0.984628i | \(0.555885\pi\) | |||||||
\(884\) | −28.1997 | −0.948459 | ||||||||
\(885\) | 28.0844 | 0.944048 | ||||||||
\(886\) | −42.3753 | −1.42362 | ||||||||
\(887\) | −29.4734 | −0.989619 | −0.494810 | − | 0.869001i | \(-0.664762\pi\) | ||||
−0.494810 | + | 0.869001i | \(0.664762\pi\) | |||||||
\(888\) | −7.10250 | −0.238344 | ||||||||
\(889\) | 16.5816 | 0.556129 | ||||||||
\(890\) | −20.0801 | −0.673085 | ||||||||
\(891\) | −13.8399 | −0.463653 | ||||||||
\(892\) | −32.3471 | −1.08306 | ||||||||
\(893\) | 39.1223 | 1.30918 | ||||||||
\(894\) | 30.9019 | 1.03351 | ||||||||
\(895\) | 16.9140 | 0.565372 | ||||||||
\(896\) | −19.7936 | −0.661259 | ||||||||
\(897\) | −25.3427 | −0.846168 | ||||||||
\(898\) | −55.4975 | −1.85198 | ||||||||
\(899\) | 18.3960 | 0.613539 | ||||||||
\(900\) | 6.09042 | 0.203014 | ||||||||
\(901\) | −44.3203 | −1.47652 | ||||||||
\(902\) | −24.2305 | −0.806788 | ||||||||
\(903\) | 10.4663 | 0.348298 | ||||||||
\(904\) | −2.06028 | −0.0685238 | ||||||||
\(905\) | 45.9036 | 1.52589 | ||||||||
\(906\) | −65.4982 | −2.17603 | ||||||||
\(907\) | 13.5939 | 0.451379 | 0.225690 | − | 0.974199i | \(-0.427537\pi\) | ||||
0.225690 | + | 0.974199i | \(0.427537\pi\) | |||||||
\(908\) | −33.1980 | −1.10171 | ||||||||
\(909\) | 1.53871 | 0.0510358 | ||||||||
\(910\) | 78.8851 | 2.61502 | ||||||||
\(911\) | −20.3203 | −0.673241 | −0.336620 | − | 0.941640i | \(-0.609284\pi\) | ||||
−0.336620 | + | 0.941640i | \(0.609284\pi\) | |||||||
\(912\) | 47.8865 | 1.58568 | ||||||||
\(913\) | −13.3528 | −0.441914 | ||||||||
\(914\) | 37.3823 | 1.23650 | ||||||||
\(915\) | 22.7162 | 0.750975 | ||||||||
\(916\) | −2.73601 | −0.0904004 | ||||||||
\(917\) | −54.8161 | −1.81019 | ||||||||
\(918\) | 44.0242 | 1.45301 | ||||||||
\(919\) | 17.4734 | 0.576393 | 0.288197 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288197 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(920\) | 8.55080 | 0.281911 | ||||||||
\(921\) | −22.6111 | −0.745060 | ||||||||
\(922\) | 11.5592 | 0.380681 | ||||||||
\(923\) | −3.31324 | −0.109057 | ||||||||
\(924\) | 15.9103 | 0.523409 | ||||||||
\(925\) | −31.6714 | −1.04135 | ||||||||
\(926\) | −40.4054 | −1.32780 | ||||||||
\(927\) | −10.6291 | −0.349106 | ||||||||
\(928\) | −34.1403 | −1.12071 | ||||||||
\(929\) | 7.36581 | 0.241665 | 0.120832 | − | 0.992673i | \(-0.461444\pi\) | ||||
0.120832 | + | 0.992673i | \(0.461444\pi\) | |||||||
\(930\) | −47.6181 | −1.56146 | ||||||||
\(931\) | 41.8013 | 1.36998 | ||||||||
\(932\) | 39.0647 | 1.27961 | ||||||||
\(933\) | 35.1524 | 1.15084 | ||||||||
\(934\) | 78.0690 | 2.55450 | ||||||||
\(935\) | 21.9657 | 0.718356 | ||||||||
\(936\) | 1.42851 | 0.0466921 | ||||||||
\(937\) | 8.96745 | 0.292954 | 0.146477 | − | 0.989214i | \(-0.453207\pi\) | ||||
0.146477 | + | 0.989214i | \(0.453207\pi\) | |||||||
\(938\) | 38.8570 | 1.26873 | ||||||||
\(939\) | 10.1454 | 0.331083 | ||||||||
\(940\) | 38.4958 | 1.25559 | ||||||||
\(941\) | 11.0455 | 0.360075 | 0.180037 | − | 0.983660i | \(-0.442378\pi\) | ||||
0.180037 | + | 0.983660i | \(0.442378\pi\) | |||||||
\(942\) | 21.8392 | 0.711559 | ||||||||
\(943\) | 38.5957 | 1.25685 | ||||||||
\(944\) | 20.6111 | 0.670833 | ||||||||
\(945\) | −55.7936 | −1.81497 | ||||||||
\(946\) | 3.59393 | 0.116849 | ||||||||
\(947\) | −36.1729 | −1.17546 | −0.587731 | − | 0.809057i | \(-0.699978\pi\) | ||||
−0.587731 | + | 0.809057i | \(0.699978\pi\) | |||||||
\(948\) | −16.0928 | −0.522671 | ||||||||
\(949\) | −54.3150 | −1.76314 | ||||||||
\(950\) | 58.6834 | 1.90394 | ||||||||
\(951\) | 11.2530 | 0.364902 | ||||||||
\(952\) | 12.9019 | 0.418152 | ||||||||
\(953\) | −25.7307 | −0.833500 | −0.416750 | − | 0.909021i | \(-0.636831\pi\) | ||||
−0.416750 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(954\) | −10.8315 | −0.350682 | ||||||||
\(955\) | −22.7556 | −0.736353 | ||||||||
\(956\) | 0.946750 | 0.0306201 | ||||||||
\(957\) | −11.5491 | −0.373328 | ||||||||
\(958\) | −45.8935 | −1.48275 | ||||||||
\(959\) | −54.5957 | −1.76299 | ||||||||
\(960\) | 31.4861 | 1.01621 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 35.8385 | 1.15548 | ||||||||
\(963\) | 0.230528 | 0.00742868 | ||||||||
\(964\) | 42.1997 | 1.35916 | ||||||||
\(965\) | 25.8486 | 0.832097 | ||||||||
\(966\) | −55.9384 | −1.79979 | ||||||||
\(967\) | 0.862301 | 0.0277297 | 0.0138649 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138649 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(968\) | 6.09042 | 0.195753 | ||||||||
\(969\) | −53.8486 | −1.72987 | ||||||||
\(970\) | 73.6128 | 2.36356 | ||||||||
\(971\) | 52.7505 | 1.69284 | 0.846422 | − | 0.532512i | \(-0.178752\pi\) | ||||
0.846422 | + | 0.532512i | \(0.178752\pi\) | |||||||
\(972\) | 11.1146 | 0.356501 | ||||||||
\(973\) | 17.0224 | 0.545714 | ||||||||
\(974\) | 20.9622 | 0.671671 | ||||||||
\(975\) | 35.4734 | 1.13606 | ||||||||
\(976\) | 16.6714 | 0.533637 | ||||||||
\(977\) | 25.8761 | 0.827851 | 0.413925 | − | 0.910311i | \(-0.364157\pi\) | ||||
0.413925 | + | 0.910311i | \(0.364157\pi\) | |||||||
\(978\) | 41.5886 | 1.32986 | ||||||||
\(979\) | −4.23582 | −0.135377 | ||||||||
\(980\) | 41.1320 | 1.31391 | ||||||||
\(981\) | 0.393308 | 0.0125574 | ||||||||
\(982\) | 44.8865 | 1.43238 | ||||||||
\(983\) | 50.4881 | 1.61032 | 0.805160 | − | 0.593057i | \(-0.202079\pi\) | ||||
0.805160 | + | 0.593057i | \(0.202079\pi\) | |||||||
\(984\) | −12.1153 | −0.386221 | ||||||||
\(985\) | −11.3581 | −0.361900 | ||||||||
\(986\) | 45.1826 | 1.43891 | ||||||||
\(987\) | 52.1997 | 1.66154 | ||||||||
\(988\) | −30.0844 | −0.957114 | ||||||||
\(989\) | −5.72460 | −0.182032 | ||||||||
\(990\) | 5.36823 | 0.170613 | ||||||||
\(991\) | −6.74175 | −0.214159 | −0.107079 | − | 0.994250i | \(-0.534150\pi\) | ||||
−0.107079 | + | 0.994250i | \(0.534150\pi\) | |||||||
\(992\) | −29.6938 | −0.942779 | ||||||||
\(993\) | −24.3458 | −0.772590 | ||||||||
\(994\) | −7.31324 | −0.231962 | ||||||||
\(995\) | 56.9116 | 1.80422 | ||||||||
\(996\) | 32.2101 | 1.02061 | ||||||||
\(997\) | 55.5706 | 1.75994 | 0.879969 | − | 0.475031i | \(-0.157563\pi\) | ||||
0.879969 | + | 0.475031i | \(0.157563\pi\) | |||||||
\(998\) | 13.5963 | 0.430385 | ||||||||
\(999\) | −25.3478 | −0.801968 |
(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 | 71.2.a.a.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 639.2.a.h.1.1 | 3 | |||
4.3 | odd | 2 | 1136.2.a.h.1.3 | 3 | |||
5.4 | even | 2 | 1775.2.a.f.1.1 | 3 | |||
7.6 | odd | 2 | 3479.2.a.k.1.3 | 3 | |||
8.3 | odd | 2 | 4544.2.a.u.1.1 | 3 | |||
8.5 | even | 2 | 4544.2.a.r.1.3 | 3 | |||
11.10 | odd | 2 | 8591.2.a.g.1.1 | 3 | |||
71.70 | odd | 2 | 5041.2.a.a.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
71.2.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
639.2.a.h.1.1 | 3 | 3.2 | odd | 2 | |||
1136.2.a.h.1.3 | 3 | 4.3 | odd | 2 | |||
1775.2.a.f.1.1 | 3 | 5.4 | even | 2 | |||
3479.2.a.k.1.3 | 3 | 7.6 | odd | 2 | |||
4544.2.a.r.1.3 | 3 | 8.5 | even | 2 | |||
4544.2.a.u.1.1 | 3 | 8.3 | odd | 2 | |||
5041.2.a.a.1.3 | 3 | 71.70 | odd | 2 | |||
8591.2.a.g.1.1 | 3 | 11.10 | odd | 2 |