Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25185 | −1.59230 | −0.796148 | − | 0.605102i | \(-0.793132\pi\) | ||||
−0.796148 | + | 0.605102i | \(0.793132\pi\) | |||||||
\(3\) | −1.69642 | −0.979428 | −0.489714 | − | 0.871883i | \(-0.662899\pi\) | ||||
−0.489714 | + | 0.871883i | \(0.662899\pi\) | |||||||
\(4\) | 3.07082 | 1.53541 | ||||||||
\(5\) | −1.12007 | −0.500909 | −0.250455 | − | 0.968128i | \(-0.580580\pi\) | ||||
−0.250455 | + | 0.968128i | \(0.580580\pi\) | |||||||
\(6\) | 3.82008 | 1.55954 | ||||||||
\(7\) | −4.02650 | −1.52187 | −0.760937 | − | 0.648826i | \(-0.775260\pi\) | ||||
−0.760937 | + | 0.648826i | \(0.775260\pi\) | |||||||
\(8\) | −2.41131 | −0.852528 | ||||||||
\(9\) | −0.122162 | −0.0407206 | ||||||||
\(10\) | 2.52222 | 0.797596 | ||||||||
\(11\) | −2.48572 | −0.749473 | −0.374736 | − | 0.927131i | \(-0.622267\pi\) | ||||
−0.374736 | + | 0.927131i | \(0.622267\pi\) | |||||||
\(12\) | −5.20939 | −1.50382 | ||||||||
\(13\) | 4.38293 | 1.21561 | 0.607803 | − | 0.794088i | \(-0.292051\pi\) | ||||
0.607803 | + | 0.794088i | \(0.292051\pi\) | |||||||
\(14\) | 9.06706 | 2.42327 | ||||||||
\(15\) | 1.90010 | 0.490604 | ||||||||
\(16\) | −0.711723 | −0.177931 | ||||||||
\(17\) | −3.94588 | −0.957016 | −0.478508 | − | 0.878083i | \(-0.658822\pi\) | ||||
−0.478508 | + | 0.878083i | \(0.658822\pi\) | |||||||
\(18\) | 0.275090 | 0.0648393 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.43952 | −0.769100 | ||||||||
\(21\) | 6.83063 | 1.49057 | ||||||||
\(22\) | 5.59746 | 1.19338 | ||||||||
\(23\) | −3.68526 | −0.768430 | −0.384215 | − | 0.923244i | \(-0.625528\pi\) | ||||
−0.384215 | + | 0.923244i | \(0.625528\pi\) | |||||||
\(24\) | 4.09060 | 0.834990 | ||||||||
\(25\) | −3.74545 | −0.749090 | ||||||||
\(26\) | −9.86969 | −1.93561 | ||||||||
\(27\) | 5.29650 | 1.01931 | ||||||||
\(28\) | −12.3646 | −2.33670 | ||||||||
\(29\) | 3.83383 | 0.711924 | 0.355962 | − | 0.934500i | \(-0.384153\pi\) | ||||
0.355962 | + | 0.934500i | \(0.384153\pi\) | |||||||
\(30\) | −4.27874 | −0.781188 | ||||||||
\(31\) | −4.15303 | −0.745906 | −0.372953 | − | 0.927850i | \(-0.621655\pi\) | ||||
−0.372953 | + | 0.927850i | \(0.621655\pi\) | |||||||
\(32\) | 6.42532 | 1.13585 | ||||||||
\(33\) | 4.21682 | 0.734055 | ||||||||
\(34\) | 8.88552 | 1.52385 | ||||||||
\(35\) | 4.50995 | 0.762320 | ||||||||
\(36\) | −0.375136 | −0.0625227 | ||||||||
\(37\) | 6.52957 | 1.07346 | 0.536728 | − | 0.843756i | \(-0.319660\pi\) | ||||
0.536728 | + | 0.843756i | \(0.319660\pi\) | |||||||
\(38\) | −2.25185 | −0.365298 | ||||||||
\(39\) | −7.43529 | −1.19060 | ||||||||
\(40\) | 2.70083 | 0.427039 | ||||||||
\(41\) | −4.13530 | −0.645825 | −0.322913 | − | 0.946429i | \(-0.604662\pi\) | ||||
−0.322913 | + | 0.946429i | \(0.604662\pi\) | |||||||
\(42\) | −15.3815 | −2.37342 | ||||||||
\(43\) | −4.23897 | −0.646437 | −0.323219 | − | 0.946324i | \(-0.604765\pi\) | ||||
−0.323219 | + | 0.946324i | \(0.604765\pi\) | |||||||
\(44\) | −7.63319 | −1.15075 | ||||||||
\(45\) | 0.136829 | 0.0203973 | ||||||||
\(46\) | 8.29865 | 1.22357 | ||||||||
\(47\) | 7.04135 | 1.02709 | 0.513543 | − | 0.858064i | \(-0.328333\pi\) | ||||
0.513543 | + | 0.858064i | \(0.328333\pi\) | |||||||
\(48\) | 1.20738 | 0.174270 | ||||||||
\(49\) | 9.21269 | 1.31610 | ||||||||
\(50\) | 8.43418 | 1.19277 | ||||||||
\(51\) | 6.69387 | 0.937329 | ||||||||
\(52\) | 13.4592 | 1.86645 | ||||||||
\(53\) | 2.97967 | 0.409289 | 0.204644 | − | 0.978836i | \(-0.434396\pi\) | ||||
0.204644 | + | 0.978836i | \(0.434396\pi\) | |||||||
\(54\) | −11.9269 | −1.62305 | ||||||||
\(55\) | 2.78417 | 0.375418 | ||||||||
\(56\) | 9.70915 | 1.29744 | ||||||||
\(57\) | −1.69642 | −0.224696 | ||||||||
\(58\) | −8.63319 | −1.13359 | ||||||||
\(59\) | −11.9334 | −1.55360 | −0.776801 | − | 0.629746i | \(-0.783159\pi\) | ||||
−0.776801 | + | 0.629746i | \(0.783159\pi\) | |||||||
\(60\) | 5.83487 | 0.753278 | ||||||||
\(61\) | 1.19622 | 0.153160 | 0.0765799 | − | 0.997063i | \(-0.475600\pi\) | ||||
0.0765799 | + | 0.997063i | \(0.475600\pi\) | |||||||
\(62\) | 9.35199 | 1.18770 | ||||||||
\(63\) | 0.491884 | 0.0619716 | ||||||||
\(64\) | −13.0454 | −1.63067 | ||||||||
\(65\) | −4.90918 | −0.608909 | ||||||||
\(66\) | −9.49564 | −1.16883 | ||||||||
\(67\) | 8.71052 | 1.06416 | 0.532080 | − | 0.846694i | \(-0.321411\pi\) | ||||
0.532080 | + | 0.846694i | \(0.321411\pi\) | |||||||
\(68\) | −12.1171 | −1.46941 | ||||||||
\(69\) | 6.25175 | 0.752622 | ||||||||
\(70\) | −10.1557 | −1.21384 | ||||||||
\(71\) | 9.49978 | 1.12742 | 0.563708 | − | 0.825974i | \(-0.309374\pi\) | ||||
0.563708 | + | 0.825974i | \(0.309374\pi\) | |||||||
\(72\) | 0.294570 | 0.0347154 | ||||||||
\(73\) | 11.9836 | 1.40258 | 0.701288 | − | 0.712878i | \(-0.252609\pi\) | ||||
0.701288 | + | 0.712878i | \(0.252609\pi\) | |||||||
\(74\) | −14.7036 | −1.70926 | ||||||||
\(75\) | 6.35385 | 0.733680 | ||||||||
\(76\) | 3.07082 | 0.352247 | ||||||||
\(77\) | 10.0087 | 1.14060 | ||||||||
\(78\) | 16.7431 | 1.89579 | ||||||||
\(79\) | 5.78566 | 0.650938 | 0.325469 | − | 0.945553i | \(-0.394478\pi\) | ||||
0.325469 | + | 0.945553i | \(0.394478\pi\) | |||||||
\(80\) | 0.797177 | 0.0891271 | ||||||||
\(81\) | −8.61859 | −0.957621 | ||||||||
\(82\) | 9.31206 | 1.02835 | ||||||||
\(83\) | −14.2548 | −1.56467 | −0.782334 | − | 0.622859i | \(-0.785971\pi\) | ||||
−0.782334 | + | 0.622859i | \(0.785971\pi\) | |||||||
\(84\) | 20.9756 | 2.28863 | ||||||||
\(85\) | 4.41965 | 0.479378 | ||||||||
\(86\) | 9.54552 | 1.02932 | ||||||||
\(87\) | −6.50378 | −0.697278 | ||||||||
\(88\) | 5.99385 | 0.638947 | ||||||||
\(89\) | 14.2616 | 1.51173 | 0.755865 | − | 0.654727i | \(-0.227217\pi\) | ||||
0.755865 | + | 0.654727i | \(0.227217\pi\) | |||||||
\(90\) | −0.308119 | −0.0324786 | ||||||||
\(91\) | −17.6479 | −1.85000 | ||||||||
\(92\) | −11.3168 | −1.17985 | ||||||||
\(93\) | 7.04528 | 0.730562 | ||||||||
\(94\) | −15.8560 | −1.63542 | ||||||||
\(95\) | −1.12007 | −0.114916 | ||||||||
\(96\) | −10.9000 | −1.11248 | ||||||||
\(97\) | 2.21368 | 0.224765 | 0.112383 | − | 0.993665i | \(-0.464152\pi\) | ||||
0.112383 | + | 0.993665i | \(0.464152\pi\) | |||||||
\(98\) | −20.7456 | −2.09562 | ||||||||
\(99\) | 0.303660 | 0.0305190 | ||||||||
\(100\) | −11.5016 | −1.15016 | ||||||||
\(101\) | −4.48942 | −0.446714 | −0.223357 | − | 0.974737i | \(-0.571702\pi\) | ||||
−0.223357 | + | 0.974737i | \(0.571702\pi\) | |||||||
\(102\) | −15.0736 | −1.49251 | ||||||||
\(103\) | 17.9596 | 1.76961 | 0.884805 | − | 0.465961i | \(-0.154291\pi\) | ||||
0.884805 | + | 0.465961i | \(0.154291\pi\) | |||||||
\(104\) | −10.5686 | −1.03634 | ||||||||
\(105\) | −7.65076 | −0.746638 | ||||||||
\(106\) | −6.70975 | −0.651709 | ||||||||
\(107\) | −5.37537 | −0.519656 | −0.259828 | − | 0.965655i | \(-0.583666\pi\) | ||||
−0.259828 | + | 0.965655i | \(0.583666\pi\) | |||||||
\(108\) | 16.2646 | 1.56506 | ||||||||
\(109\) | −1.59754 | −0.153017 | −0.0765085 | − | 0.997069i | \(-0.524377\pi\) | ||||
−0.0765085 | + | 0.997069i | \(0.524377\pi\) | |||||||
\(110\) | −6.26953 | −0.597776 | ||||||||
\(111\) | −11.0769 | −1.05137 | ||||||||
\(112\) | 2.86575 | 0.270788 | ||||||||
\(113\) | −4.95133 | −0.465782 | −0.232891 | − | 0.972503i | \(-0.574818\pi\) | ||||
−0.232891 | + | 0.972503i | \(0.574818\pi\) | |||||||
\(114\) | 3.82008 | 0.357783 | ||||||||
\(115\) | 4.12774 | 0.384914 | ||||||||
\(116\) | 11.7730 | 1.09309 | ||||||||
\(117\) | −0.535427 | −0.0495002 | ||||||||
\(118\) | 26.8723 | 2.47380 | ||||||||
\(119\) | 15.8881 | 1.45646 | ||||||||
\(120\) | −4.58174 | −0.418254 | ||||||||
\(121\) | −4.82119 | −0.438290 | ||||||||
\(122\) | −2.69370 | −0.243876 | ||||||||
\(123\) | 7.01520 | 0.632539 | ||||||||
\(124\) | −12.7532 | −1.14527 | ||||||||
\(125\) | 9.79549 | 0.876135 | ||||||||
\(126\) | −1.10765 | −0.0986771 | ||||||||
\(127\) | 15.9156 | 1.41228 | 0.706142 | − | 0.708071i | \(-0.250434\pi\) | ||||
0.706142 | + | 0.708071i | \(0.250434\pi\) | |||||||
\(128\) | 16.5256 | 1.46067 | ||||||||
\(129\) | 7.19108 | 0.633139 | ||||||||
\(130\) | 11.0547 | 0.969563 | ||||||||
\(131\) | −3.44142 | −0.300678 | −0.150339 | − | 0.988634i | \(-0.548037\pi\) | ||||
−0.150339 | + | 0.988634i | \(0.548037\pi\) | |||||||
\(132\) | 12.9491 | 1.12707 | ||||||||
\(133\) | −4.02650 | −0.349142 | ||||||||
\(134\) | −19.6148 | −1.69446 | ||||||||
\(135\) | −5.93243 | −0.510582 | ||||||||
\(136\) | 9.51475 | 0.815883 | ||||||||
\(137\) | −11.7639 | −1.00505 | −0.502527 | − | 0.864561i | \(-0.667596\pi\) | ||||
−0.502527 | + | 0.864561i | \(0.667596\pi\) | |||||||
\(138\) | −14.0780 | −1.19840 | ||||||||
\(139\) | −4.31817 | −0.366262 | −0.183131 | − | 0.983089i | \(-0.558623\pi\) | ||||
−0.183131 | + | 0.983089i | \(0.558623\pi\) | |||||||
\(140\) | 13.8492 | 1.17047 | ||||||||
\(141\) | −11.9451 | −1.00596 | ||||||||
\(142\) | −21.3921 | −1.79518 | ||||||||
\(143\) | −10.8947 | −0.911064 | ||||||||
\(144\) | 0.0869453 | 0.00724544 | ||||||||
\(145\) | −4.29414 | −0.356609 | ||||||||
\(146\) | −26.9853 | −2.23332 | ||||||||
\(147\) | −15.6286 | −1.28902 | ||||||||
\(148\) | 20.0511 | 1.64819 | ||||||||
\(149\) | 21.3018 | 1.74511 | 0.872557 | − | 0.488512i | \(-0.162460\pi\) | ||||
0.872557 | + | 0.488512i | \(0.162460\pi\) | |||||||
\(150\) | −14.3079 | −1.16824 | ||||||||
\(151\) | −9.06852 | −0.737986 | −0.368993 | − | 0.929432i | \(-0.620297\pi\) | ||||
−0.368993 | + | 0.929432i | \(0.620297\pi\) | |||||||
\(152\) | −2.41131 | −0.195583 | ||||||||
\(153\) | 0.482036 | 0.0389703 | ||||||||
\(154\) | −22.5382 | −1.81618 | ||||||||
\(155\) | 4.65167 | 0.373631 | ||||||||
\(156\) | −22.8324 | −1.82806 | ||||||||
\(157\) | 10.0060 | 0.798564 | 0.399282 | − | 0.916828i | \(-0.369259\pi\) | ||||
0.399282 | + | 0.916828i | \(0.369259\pi\) | |||||||
\(158\) | −13.0284 | −1.03649 | ||||||||
\(159\) | −5.05476 | −0.400869 | ||||||||
\(160\) | −7.19678 | −0.568956 | ||||||||
\(161\) | 14.8387 | 1.16945 | ||||||||
\(162\) | 19.4077 | 1.52482 | ||||||||
\(163\) | −11.4133 | −0.893956 | −0.446978 | − | 0.894545i | \(-0.647500\pi\) | ||||
−0.446978 | + | 0.894545i | \(0.647500\pi\) | |||||||
\(164\) | −12.6987 | −0.991605 | ||||||||
\(165\) | −4.72312 | −0.367695 | ||||||||
\(166\) | 32.0997 | 2.49142 | ||||||||
\(167\) | −8.18730 | −0.633552 | −0.316776 | − | 0.948500i | \(-0.602600\pi\) | ||||
−0.316776 | + | 0.948500i | \(0.602600\pi\) | |||||||
\(168\) | −16.4708 | −1.27075 | ||||||||
\(169\) | 6.21010 | 0.477700 | ||||||||
\(170\) | −9.95237 | −0.763312 | ||||||||
\(171\) | −0.122162 | −0.00934195 | ||||||||
\(172\) | −13.0171 | −0.992545 | ||||||||
\(173\) | 16.8621 | 1.28200 | 0.641002 | − | 0.767539i | \(-0.278519\pi\) | ||||
0.641002 | + | 0.767539i | \(0.278519\pi\) | |||||||
\(174\) | 14.6455 | 1.11027 | ||||||||
\(175\) | 15.0811 | 1.14002 | ||||||||
\(176\) | 1.76914 | 0.133354 | ||||||||
\(177\) | 20.2441 | 1.52164 | ||||||||
\(178\) | −32.1150 | −2.40712 | ||||||||
\(179\) | −9.04301 | −0.675906 | −0.337953 | − | 0.941163i | \(-0.609735\pi\) | ||||
−0.337953 | + | 0.941163i | \(0.609735\pi\) | |||||||
\(180\) | 0.420178 | 0.0313182 | ||||||||
\(181\) | 1.49721 | 0.111287 | 0.0556433 | − | 0.998451i | \(-0.482279\pi\) | ||||
0.0556433 | + | 0.998451i | \(0.482279\pi\) | |||||||
\(182\) | 39.7403 | 2.94575 | ||||||||
\(183\) | −2.02929 | −0.150009 | ||||||||
\(184\) | 8.88632 | 0.655108 | ||||||||
\(185\) | −7.31356 | −0.537703 | ||||||||
\(186\) | −15.8649 | −1.16327 | ||||||||
\(187\) | 9.80835 | 0.717258 | ||||||||
\(188\) | 21.6227 | 1.57700 | ||||||||
\(189\) | −21.3263 | −1.55126 | ||||||||
\(190\) | 2.52222 | 0.182981 | ||||||||
\(191\) | 18.2691 | 1.32191 | 0.660954 | − | 0.750427i | \(-0.270152\pi\) | ||||
0.660954 | + | 0.750427i | \(0.270152\pi\) | |||||||
\(192\) | 22.1304 | 1.59713 | ||||||||
\(193\) | 19.5292 | 1.40574 | 0.702870 | − | 0.711319i | \(-0.251902\pi\) | ||||
0.702870 | + | 0.711319i | \(0.251902\pi\) | |||||||
\(194\) | −4.98487 | −0.357893 | ||||||||
\(195\) | 8.32802 | 0.596382 | ||||||||
\(196\) | 28.2905 | 2.02075 | ||||||||
\(197\) | 6.85772 | 0.488592 | 0.244296 | − | 0.969701i | \(-0.421443\pi\) | ||||
0.244296 | + | 0.969701i | \(0.421443\pi\) | |||||||
\(198\) | −0.683796 | −0.0485953 | ||||||||
\(199\) | 3.97573 | 0.281832 | 0.140916 | − | 0.990022i | \(-0.454995\pi\) | ||||
0.140916 | + | 0.990022i | \(0.454995\pi\) | |||||||
\(200\) | 9.03145 | 0.638620 | ||||||||
\(201\) | −14.7767 | −1.04227 | ||||||||
\(202\) | 10.1095 | 0.711302 | ||||||||
\(203\) | −15.4369 | −1.08346 | ||||||||
\(204\) | 20.5556 | 1.43918 | ||||||||
\(205\) | 4.63181 | 0.323500 | ||||||||
\(206\) | −40.4422 | −2.81774 | ||||||||
\(207\) | 0.450198 | 0.0312909 | ||||||||
\(208\) | −3.11943 | −0.216294 | ||||||||
\(209\) | −2.48572 | −0.171941 | ||||||||
\(210\) | 17.2283 | 1.18887 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 9.15001 | 0.628425 | ||||||||
\(213\) | −16.1156 | −1.10422 | ||||||||
\(214\) | 12.1045 | 0.827447 | ||||||||
\(215\) | 4.74793 | 0.323806 | ||||||||
\(216\) | −12.7715 | −0.868991 | ||||||||
\(217\) | 16.7222 | 1.13517 | ||||||||
\(218\) | 3.59743 | 0.243648 | ||||||||
\(219\) | −20.3292 | −1.37372 | ||||||||
\(220\) | 8.54968 | 0.576419 | ||||||||
\(221\) | −17.2945 | −1.16336 | ||||||||
\(222\) | 24.9435 | 1.67410 | ||||||||
\(223\) | 29.1951 | 1.95505 | 0.977524 | − | 0.210823i | \(-0.0676144\pi\) | ||||
0.977524 | + | 0.210823i | \(0.0676144\pi\) | |||||||
\(224\) | −25.8715 | −1.72861 | ||||||||
\(225\) | 0.457551 | 0.0305034 | ||||||||
\(226\) | 11.1496 | 0.741663 | ||||||||
\(227\) | −9.29434 | −0.616887 | −0.308443 | − | 0.951243i | \(-0.599808\pi\) | ||||
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(228\) | −5.20939 | −0.345000 | ||||||||
\(229\) | −13.4718 | −0.890238 | −0.445119 | − | 0.895471i | \(-0.646839\pi\) | ||||
−0.445119 | + | 0.895471i | \(0.646839\pi\) | |||||||
\(230\) | −9.29504 | −0.612897 | ||||||||
\(231\) | −16.9790 | −1.11714 | ||||||||
\(232\) | −9.24456 | −0.606935 | ||||||||
\(233\) | 4.47067 | 0.292883 | 0.146442 | − | 0.989219i | \(-0.453218\pi\) | ||||
0.146442 | + | 0.989219i | \(0.453218\pi\) | |||||||
\(234\) | 1.20570 | 0.0788191 | ||||||||
\(235\) | −7.88678 | −0.514477 | ||||||||
\(236\) | −36.6454 | −2.38541 | ||||||||
\(237\) | −9.81491 | −0.637547 | ||||||||
\(238\) | −35.7775 | −2.31911 | ||||||||
\(239\) | 12.5033 | 0.808774 | 0.404387 | − | 0.914588i | \(-0.367485\pi\) | ||||
0.404387 | + | 0.914588i | \(0.367485\pi\) | |||||||
\(240\) | −1.35235 | −0.0872936 | ||||||||
\(241\) | 13.4302 | 0.865117 | 0.432559 | − | 0.901606i | \(-0.357611\pi\) | ||||
0.432559 | + | 0.901606i | \(0.357611\pi\) | |||||||
\(242\) | 10.8566 | 0.697888 | ||||||||
\(243\) | −1.26874 | −0.0813899 | ||||||||
\(244\) | 3.67336 | 0.235163 | ||||||||
\(245\) | −10.3188 | −0.659246 | ||||||||
\(246\) | −15.7972 | −1.00719 | ||||||||
\(247\) | 4.38293 | 0.278879 | ||||||||
\(248\) | 10.0143 | 0.635906 | ||||||||
\(249\) | 24.1821 | 1.53248 | ||||||||
\(250\) | −22.0579 | −1.39507 | ||||||||
\(251\) | 12.3915 | 0.782145 | 0.391072 | − | 0.920360i | \(-0.372104\pi\) | ||||
0.391072 | + | 0.920360i | \(0.372104\pi\) | |||||||
\(252\) | 1.51049 | 0.0951517 | ||||||||
\(253\) | 9.16053 | 0.575918 | ||||||||
\(254\) | −35.8396 | −2.24877 | ||||||||
\(255\) | −7.49758 | −0.469516 | ||||||||
\(256\) | −11.1223 | −0.695145 | ||||||||
\(257\) | 14.7048 | 0.917258 | 0.458629 | − | 0.888628i | \(-0.348341\pi\) | ||||
0.458629 | + | 0.888628i | \(0.348341\pi\) | |||||||
\(258\) | −16.1932 | −1.00815 | ||||||||
\(259\) | −26.2913 | −1.63366 | ||||||||
\(260\) | −15.0752 | −0.934923 | ||||||||
\(261\) | −0.468347 | −0.0289900 | ||||||||
\(262\) | 7.74955 | 0.478769 | ||||||||
\(263\) | −18.3385 | −1.13080 | −0.565400 | − | 0.824817i | \(-0.691278\pi\) | ||||
−0.565400 | + | 0.824817i | \(0.691278\pi\) | |||||||
\(264\) | −10.1681 | −0.625802 | ||||||||
\(265\) | −3.33743 | −0.205016 | ||||||||
\(266\) | 9.06706 | 0.555937 | ||||||||
\(267\) | −24.1937 | −1.48063 | ||||||||
\(268\) | 26.7484 | 1.63392 | ||||||||
\(269\) | −22.3961 | −1.36551 | −0.682756 | − | 0.730646i | \(-0.739219\pi\) | ||||
−0.682756 | + | 0.730646i | \(0.739219\pi\) | |||||||
\(270\) | 13.3589 | 0.812998 | ||||||||
\(271\) | 4.00112 | 0.243051 | 0.121525 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121525 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(272\) | 2.80837 | 0.170283 | ||||||||
\(273\) | 29.9382 | 1.81194 | ||||||||
\(274\) | 26.4904 | 1.60034 | ||||||||
\(275\) | 9.31014 | 0.561423 | ||||||||
\(276\) | 19.1980 | 1.15558 | ||||||||
\(277\) | 22.0830 | 1.32684 | 0.663420 | − | 0.748248i | \(-0.269104\pi\) | ||||
0.663420 | + | 0.748248i | \(0.269104\pi\) | |||||||
\(278\) | 9.72385 | 0.583198 | ||||||||
\(279\) | 0.507342 | 0.0303738 | ||||||||
\(280\) | −10.8749 | −0.649899 | ||||||||
\(281\) | −21.6769 | −1.29314 | −0.646569 | − | 0.762855i | \(-0.723797\pi\) | ||||
−0.646569 | + | 0.762855i | \(0.723797\pi\) | |||||||
\(282\) | 26.8985 | 1.60178 | ||||||||
\(283\) | 4.33848 | 0.257896 | 0.128948 | − | 0.991651i | \(-0.458840\pi\) | ||||
0.128948 | + | 0.991651i | \(0.458840\pi\) | |||||||
\(284\) | 29.1721 | 1.73104 | ||||||||
\(285\) | 1.90010 | 0.112552 | ||||||||
\(286\) | 24.5333 | 1.45068 | ||||||||
\(287\) | 16.6508 | 0.982864 | ||||||||
\(288\) | −0.784928 | −0.0462523 | ||||||||
\(289\) | −1.43003 | −0.0841196 | ||||||||
\(290\) | 9.66975 | 0.567827 | ||||||||
\(291\) | −3.75533 | −0.220142 | ||||||||
\(292\) | 36.7995 | 2.15353 | ||||||||
\(293\) | −10.6239 | −0.620654 | −0.310327 | − | 0.950630i | \(-0.600439\pi\) | ||||
−0.310327 | + | 0.950630i | \(0.600439\pi\) | |||||||
\(294\) | 35.1932 | 2.05251 | ||||||||
\(295\) | 13.3663 | 0.778214 | ||||||||
\(296\) | −15.7448 | −0.915151 | ||||||||
\(297\) | −13.1656 | −0.763946 | ||||||||
\(298\) | −47.9685 | −2.77874 | ||||||||
\(299\) | −16.1523 | −0.934109 | ||||||||
\(300\) | 19.5115 | 1.12650 | ||||||||
\(301\) | 17.0682 | 0.983796 | ||||||||
\(302\) | 20.4209 | 1.17509 | ||||||||
\(303\) | 7.61595 | 0.437525 | ||||||||
\(304\) | −0.711723 | −0.0408201 | ||||||||
\(305\) | −1.33984 | −0.0767192 | ||||||||
\(306\) | −1.08547 | −0.0620522 | ||||||||
\(307\) | −15.4552 | −0.882074 | −0.441037 | − | 0.897489i | \(-0.645389\pi\) | ||||
−0.441037 | + | 0.897489i | \(0.645389\pi\) | |||||||
\(308\) | 30.7350 | 1.75129 | ||||||||
\(309\) | −30.4670 | −1.73321 | ||||||||
\(310\) | −10.4749 | −0.594932 | ||||||||
\(311\) | −34.1974 | −1.93916 | −0.969578 | − | 0.244784i | \(-0.921283\pi\) | ||||
−0.969578 | + | 0.244784i | \(0.921283\pi\) | |||||||
\(312\) | 17.9288 | 1.01502 | ||||||||
\(313\) | −6.22729 | −0.351987 | −0.175994 | − | 0.984391i | \(-0.556314\pi\) | ||||
−0.175994 | + | 0.984391i | \(0.556314\pi\) | |||||||
\(314\) | −22.5319 | −1.27155 | ||||||||
\(315\) | −0.550943 | −0.0310421 | ||||||||
\(316\) | 17.7667 | 0.999455 | ||||||||
\(317\) | 23.8962 | 1.34215 | 0.671073 | − | 0.741392i | \(-0.265834\pi\) | ||||
0.671073 | + | 0.741392i | \(0.265834\pi\) | |||||||
\(318\) | 11.3826 | 0.638302 | ||||||||
\(319\) | −9.52982 | −0.533567 | ||||||||
\(320\) | 14.6117 | 0.816819 | ||||||||
\(321\) | 9.11887 | 0.508966 | ||||||||
\(322\) | −33.4145 | −1.86212 | ||||||||
\(323\) | −3.94588 | −0.219555 | ||||||||
\(324\) | −26.4661 | −1.47034 | ||||||||
\(325\) | −16.4161 | −0.910599 | ||||||||
\(326\) | 25.7009 | 1.42344 | ||||||||
\(327\) | 2.71010 | 0.149869 | ||||||||
\(328\) | 9.97150 | 0.550584 | ||||||||
\(329\) | −28.3520 | −1.56309 | ||||||||
\(330\) | 10.6358 | 0.585479 | ||||||||
\(331\) | −30.0572 | −1.65209 | −0.826046 | − | 0.563603i | \(-0.809415\pi\) | ||||
−0.826046 | + | 0.563603i | \(0.809415\pi\) | |||||||
\(332\) | −43.7739 | −2.40240 | ||||||||
\(333\) | −0.797664 | −0.0437117 | ||||||||
\(334\) | 18.4365 | 1.00880 | ||||||||
\(335\) | −9.75636 | −0.533047 | ||||||||
\(336\) | −4.86151 | −0.265217 | ||||||||
\(337\) | −25.9760 | −1.41500 | −0.707501 | − | 0.706712i | \(-0.750178\pi\) | ||||
−0.707501 | + | 0.706712i | \(0.750178\pi\) | |||||||
\(338\) | −13.9842 | −0.760640 | ||||||||
\(339\) | 8.39953 | 0.456200 | ||||||||
\(340\) | 13.5719 | 0.736041 | ||||||||
\(341\) | 10.3233 | 0.559037 | ||||||||
\(342\) | 0.275090 | 0.0148751 | ||||||||
\(343\) | −8.90939 | −0.481062 | ||||||||
\(344\) | 10.2215 | 0.551106 | ||||||||
\(345\) | −7.00238 | −0.376995 | ||||||||
\(346\) | −37.9709 | −2.04133 | ||||||||
\(347\) | −2.34371 | −0.125817 | −0.0629084 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629084 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(348\) | −19.9719 | −1.07061 | ||||||||
\(349\) | −0.786662 | −0.0421090 | −0.0210545 | − | 0.999778i | \(-0.506702\pi\) | ||||
−0.0210545 | + | 0.999778i | \(0.506702\pi\) | |||||||
\(350\) | −33.9602 | −1.81525 | ||||||||
\(351\) | 23.2142 | 1.23908 | ||||||||
\(352\) | −15.9715 | −0.851286 | ||||||||
\(353\) | −26.6744 | −1.41974 | −0.709868 | − | 0.704335i | \(-0.751245\pi\) | ||||
−0.709868 | + | 0.704335i | \(0.751245\pi\) | |||||||
\(354\) | −45.5867 | −2.42290 | ||||||||
\(355\) | −10.6404 | −0.564733 | ||||||||
\(356\) | 43.7949 | 2.32112 | ||||||||
\(357\) | −26.9528 | −1.42650 | ||||||||
\(358\) | 20.3635 | 1.07624 | ||||||||
\(359\) | −23.9133 | −1.26209 | −0.631047 | − | 0.775745i | \(-0.717374\pi\) | ||||
−0.631047 | + | 0.775745i | \(0.717374\pi\) | |||||||
\(360\) | −0.329938 | −0.0173893 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −3.37148 | −0.177201 | ||||||||
\(363\) | 8.17877 | 0.429274 | ||||||||
\(364\) | −54.1934 | −2.84050 | ||||||||
\(365\) | −13.4224 | −0.702563 | ||||||||
\(366\) | 4.56964 | 0.238859 | ||||||||
\(367\) | −2.07338 | −0.108230 | −0.0541149 | − | 0.998535i | \(-0.517234\pi\) | ||||
−0.0541149 | + | 0.998535i | \(0.517234\pi\) | |||||||
\(368\) | 2.62288 | 0.136727 | ||||||||
\(369\) | 0.505176 | 0.0262984 | ||||||||
\(370\) | 16.4690 | 0.856183 | ||||||||
\(371\) | −11.9976 | −0.622886 | ||||||||
\(372\) | 21.6348 | 1.12171 | ||||||||
\(373\) | −10.0392 | −0.519809 | −0.259905 | − | 0.965634i | \(-0.583691\pi\) | ||||
−0.259905 | + | 0.965634i | \(0.583691\pi\) | |||||||
\(374\) | −22.0869 | −1.14209 | ||||||||
\(375\) | −16.6173 | −0.858111 | ||||||||
\(376\) | −16.9789 | −0.875619 | ||||||||
\(377\) | 16.8034 | 0.865419 | ||||||||
\(378\) | 48.0236 | 2.47007 | ||||||||
\(379\) | −18.4413 | −0.947267 | −0.473633 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473633 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(380\) | −3.43952 | −0.176444 | ||||||||
\(381\) | −26.9996 | −1.38323 | ||||||||
\(382\) | −41.1393 | −2.10487 | ||||||||
\(383\) | −22.7069 | −1.16027 | −0.580133 | − | 0.814522i | \(-0.697000\pi\) | ||||
−0.580133 | + | 0.814522i | \(0.697000\pi\) | |||||||
\(384\) | −28.0343 | −1.43062 | ||||||||
\(385\) | −11.2105 | −0.571338 | ||||||||
\(386\) | −43.9767 | −2.23835 | ||||||||
\(387\) | 0.517841 | 0.0263233 | ||||||||
\(388\) | 6.79781 | 0.345107 | ||||||||
\(389\) | −31.1974 | −1.58177 | −0.790885 | − | 0.611965i | \(-0.790379\pi\) | ||||
−0.790885 | + | 0.611965i | \(0.790379\pi\) | |||||||
\(390\) | −18.7534 | −0.949617 | ||||||||
\(391\) | 14.5416 | 0.735400 | ||||||||
\(392\) | −22.2147 | −1.12201 | ||||||||
\(393\) | 5.83809 | 0.294493 | ||||||||
\(394\) | −15.4425 | −0.777984 | ||||||||
\(395\) | −6.48033 | −0.326061 | ||||||||
\(396\) | 0.932484 | 0.0468591 | ||||||||
\(397\) | 9.21080 | 0.462277 | 0.231138 | − | 0.972921i | \(-0.425755\pi\) | ||||
0.231138 | + | 0.972921i | \(0.425755\pi\) | |||||||
\(398\) | −8.95274 | −0.448760 | ||||||||
\(399\) | 6.83063 | 0.341959 | ||||||||
\(400\) | 2.66572 | 0.133286 | ||||||||
\(401\) | 25.0044 | 1.24866 | 0.624331 | − | 0.781160i | \(-0.285372\pi\) | ||||
0.624331 | + | 0.781160i | \(0.285372\pi\) | |||||||
\(402\) | 33.2749 | 1.65960 | ||||||||
\(403\) | −18.2025 | −0.906729 | ||||||||
\(404\) | −13.7862 | −0.685889 | ||||||||
\(405\) | 9.65340 | 0.479681 | ||||||||
\(406\) | 34.7615 | 1.72519 | ||||||||
\(407\) | −16.2307 | −0.804526 | ||||||||
\(408\) | −16.1410 | −0.799099 | ||||||||
\(409\) | −22.2158 | −1.09850 | −0.549250 | − | 0.835658i | \(-0.685087\pi\) | ||||
−0.549250 | + | 0.835658i | \(0.685087\pi\) | |||||||
\(410\) | −10.4301 | −0.515107 | ||||||||
\(411\) | 19.9564 | 0.984378 | ||||||||
\(412\) | 55.1506 | 2.71707 | ||||||||
\(413\) | 48.0500 | 2.36439 | ||||||||
\(414\) | −1.01378 | −0.0498244 | ||||||||
\(415\) | 15.9663 | 0.783757 | ||||||||
\(416\) | 28.1617 | 1.38074 | ||||||||
\(417\) | 7.32542 | 0.358727 | ||||||||
\(418\) | 5.59746 | 0.273781 | ||||||||
\(419\) | −27.8399 | −1.36007 | −0.680033 | − | 0.733182i | \(-0.738035\pi\) | ||||
−0.680033 | + | 0.733182i | \(0.738035\pi\) | |||||||
\(420\) | −23.4941 | −1.14639 | ||||||||
\(421\) | −6.78808 | −0.330831 | −0.165415 | − | 0.986224i | \(-0.552896\pi\) | ||||
−0.165415 | + | 0.986224i | \(0.552896\pi\) | |||||||
\(422\) | −2.25185 | −0.109618 | ||||||||
\(423\) | −0.860183 | −0.0418235 | ||||||||
\(424\) | −7.18491 | −0.348930 | ||||||||
\(425\) | 14.7791 | 0.716892 | ||||||||
\(426\) | 36.2899 | 1.75825 | ||||||||
\(427\) | −4.81657 | −0.233090 | ||||||||
\(428\) | −16.5068 | −0.797884 | ||||||||
\(429\) | 18.4821 | 0.892322 | ||||||||
\(430\) | −10.6916 | −0.515596 | ||||||||
\(431\) | −5.23567 | −0.252193 | −0.126097 | − | 0.992018i | \(-0.540245\pi\) | ||||
−0.126097 | + | 0.992018i | \(0.540245\pi\) | |||||||
\(432\) | −3.76964 | −0.181367 | ||||||||
\(433\) | 18.7965 | 0.903303 | 0.451651 | − | 0.892195i | \(-0.350835\pi\) | ||||
0.451651 | + | 0.892195i | \(0.350835\pi\) | |||||||
\(434\) | −37.6558 | −1.80753 | ||||||||
\(435\) | 7.28466 | 0.349273 | ||||||||
\(436\) | −4.90576 | −0.234943 | ||||||||
\(437\) | −3.68526 | −0.176290 | ||||||||
\(438\) | 45.7783 | 2.18737 | ||||||||
\(439\) | −18.1490 | −0.866206 | −0.433103 | − | 0.901345i | \(-0.642581\pi\) | ||||
−0.433103 | + | 0.901345i | \(0.642581\pi\) | |||||||
\(440\) | −6.71351 | −0.320054 | ||||||||
\(441\) | −1.12544 | −0.0535923 | ||||||||
\(442\) | 38.9446 | 1.85241 | ||||||||
\(443\) | −38.4985 | −1.82912 | −0.914560 | − | 0.404451i | \(-0.867463\pi\) | ||||
−0.914560 | + | 0.404451i | \(0.867463\pi\) | |||||||
\(444\) | −34.0151 | −1.61429 | ||||||||
\(445\) | −15.9740 | −0.757240 | ||||||||
\(446\) | −65.7429 | −3.11302 | ||||||||
\(447\) | −36.1368 | −1.70921 | ||||||||
\(448\) | 52.5272 | 2.48168 | ||||||||
\(449\) | −7.60038 | −0.358684 | −0.179342 | − | 0.983787i | \(-0.557397\pi\) | ||||
−0.179342 | + | 0.983787i | \(0.557397\pi\) | |||||||
\(450\) | −1.03033 | −0.0485704 | ||||||||
\(451\) | 10.2792 | 0.484029 | ||||||||
\(452\) | −15.2046 | −0.715165 | ||||||||
\(453\) | 15.3840 | 0.722804 | ||||||||
\(454\) | 20.9294 | 0.982267 | ||||||||
\(455\) | 19.7668 | 0.926682 | ||||||||
\(456\) | 4.09060 | 0.191560 | ||||||||
\(457\) | −3.86933 | −0.181000 | −0.0904999 | − | 0.995896i | \(-0.528846\pi\) | ||||
−0.0904999 | + | 0.995896i | \(0.528846\pi\) | |||||||
\(458\) | 30.3363 | 1.41752 | ||||||||
\(459\) | −20.8993 | −0.975497 | ||||||||
\(460\) | 12.6755 | 0.590999 | ||||||||
\(461\) | −37.6000 | −1.75121 | −0.875604 | − | 0.483030i | \(-0.839536\pi\) | ||||
−0.875604 | + | 0.483030i | \(0.839536\pi\) | |||||||
\(462\) | 38.2342 | 1.77882 | ||||||||
\(463\) | 34.8066 | 1.61760 | 0.808800 | − | 0.588083i | \(-0.200117\pi\) | ||||
0.808800 | + | 0.588083i | \(0.200117\pi\) | |||||||
\(464\) | −2.72862 | −0.126673 | ||||||||
\(465\) | −7.89118 | −0.365945 | ||||||||
\(466\) | −10.0673 | −0.466357 | ||||||||
\(467\) | 20.4310 | 0.945436 | 0.472718 | − | 0.881214i | \(-0.343273\pi\) | ||||
0.472718 | + | 0.881214i | \(0.343273\pi\) | |||||||
\(468\) | −1.64420 | −0.0760031 | ||||||||
\(469\) | −35.0729 | −1.61952 | ||||||||
\(470\) | 17.7598 | 0.819199 | ||||||||
\(471\) | −16.9743 | −0.782136 | ||||||||
\(472\) | 28.7753 | 1.32449 | ||||||||
\(473\) | 10.5369 | 0.484487 | ||||||||
\(474\) | 22.1017 | 1.01516 | ||||||||
\(475\) | −3.74545 | −0.171853 | ||||||||
\(476\) | 48.7894 | 2.23626 | ||||||||
\(477\) | −0.364001 | −0.0166665 | ||||||||
\(478\) | −28.1556 | −1.28781 | ||||||||
\(479\) | −19.2739 | −0.880646 | −0.440323 | − | 0.897840i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897840i | \(0.645136\pi\) | |||||||
\(480\) | 12.2088 | 0.557251 | ||||||||
\(481\) | 28.6187 | 1.30490 | ||||||||
\(482\) | −30.2428 | −1.37752 | ||||||||
\(483\) | −25.1727 | −1.14540 | ||||||||
\(484\) | −14.8050 | −0.672954 | ||||||||
\(485\) | −2.47947 | −0.112587 | ||||||||
\(486\) | 2.85701 | 0.129597 | ||||||||
\(487\) | 8.21480 | 0.372248 | 0.186124 | − | 0.982526i | \(-0.440407\pi\) | ||||
0.186124 | + | 0.982526i | \(0.440407\pi\) | |||||||
\(488\) | −2.88445 | −0.130573 | ||||||||
\(489\) | 19.3617 | 0.875566 | ||||||||
\(490\) | 23.2364 | 1.04971 | ||||||||
\(491\) | 38.6937 | 1.74622 | 0.873112 | − | 0.487520i | \(-0.162098\pi\) | ||||
0.873112 | + | 0.487520i | \(0.162098\pi\) | |||||||
\(492\) | 21.5424 | 0.971206 | ||||||||
\(493\) | −15.1278 | −0.681323 | ||||||||
\(494\) | −9.86969 | −0.444059 | ||||||||
\(495\) | −0.340120 | −0.0152872 | ||||||||
\(496\) | 2.95581 | 0.132720 | ||||||||
\(497\) | −38.2509 | −1.71579 | ||||||||
\(498\) | −54.4545 | −2.44016 | ||||||||
\(499\) | −30.7776 | −1.37779 | −0.688897 | − | 0.724859i | \(-0.741905\pi\) | ||||
−0.688897 | + | 0.724859i | \(0.741905\pi\) | |||||||
\(500\) | 30.0801 | 1.34522 | ||||||||
\(501\) | 13.8891 | 0.620519 | ||||||||
\(502\) | −27.9038 | −1.24541 | ||||||||
\(503\) | −7.64072 | −0.340683 | −0.170341 | − | 0.985385i | \(-0.554487\pi\) | ||||
−0.170341 | + | 0.985385i | \(0.554487\pi\) | |||||||
\(504\) | −1.18609 | −0.0528325 | ||||||||
\(505\) | 5.02846 | 0.223763 | ||||||||
\(506\) | −20.6281 | −0.917031 | ||||||||
\(507\) | −10.5349 | −0.467873 | ||||||||
\(508\) | 48.8740 | 2.16843 | ||||||||
\(509\) | 32.5693 | 1.44361 | 0.721805 | − | 0.692097i | \(-0.243313\pi\) | ||||
0.721805 | + | 0.692097i | \(0.243313\pi\) | |||||||
\(510\) | 16.8834 | 0.747609 | ||||||||
\(511\) | −48.2520 | −2.13454 | ||||||||
\(512\) | −8.00541 | −0.353793 | ||||||||
\(513\) | 5.29650 | 0.233846 | ||||||||
\(514\) | −33.1129 | −1.46055 | ||||||||
\(515\) | −20.1159 | −0.886414 | ||||||||
\(516\) | 22.0825 | 0.972127 | ||||||||
\(517\) | −17.5028 | −0.769773 | ||||||||
\(518\) | 59.2040 | 2.60128 | ||||||||
\(519\) | −28.6052 | −1.25563 | ||||||||
\(520\) | 11.8376 | 0.519112 | ||||||||
\(521\) | 1.36055 | 0.0596066 | 0.0298033 | − | 0.999556i | \(-0.490512\pi\) | ||||
0.0298033 | + | 0.999556i | \(0.490512\pi\) | |||||||
\(522\) | 1.05465 | 0.0461606 | ||||||||
\(523\) | −14.7344 | −0.644290 | −0.322145 | − | 0.946690i | \(-0.604404\pi\) | ||||
−0.322145 | + | 0.946690i | \(0.604404\pi\) | |||||||
\(524\) | −10.5680 | −0.461664 | ||||||||
\(525\) | −25.5838 | −1.11657 | ||||||||
\(526\) | 41.2955 | 1.80057 | ||||||||
\(527\) | 16.3874 | 0.713845 | ||||||||
\(528\) | −3.00121 | −0.130611 | ||||||||
\(529\) | −9.41885 | −0.409515 | ||||||||
\(530\) | 7.51537 | 0.326447 | ||||||||
\(531\) | 1.45781 | 0.0632636 | ||||||||
\(532\) | −12.3646 | −0.536075 | ||||||||
\(533\) | −18.1247 | −0.785070 | ||||||||
\(534\) | 54.4805 | 2.35760 | ||||||||
\(535\) | 6.02077 | 0.260301 | ||||||||
\(536\) | −21.0038 | −0.907226 | ||||||||
\(537\) | 15.3407 | 0.662001 | ||||||||
\(538\) | 50.4325 | 2.17430 | ||||||||
\(539\) | −22.9002 | −0.986380 | ||||||||
\(540\) | −18.2174 | −0.783952 | ||||||||
\(541\) | −16.8589 | −0.724820 | −0.362410 | − | 0.932019i | \(-0.618046\pi\) | ||||
−0.362410 | + | 0.932019i | \(0.618046\pi\) | |||||||
\(542\) | −9.00990 | −0.387008 | ||||||||
\(543\) | −2.53989 | −0.108997 | ||||||||
\(544\) | −25.3535 | −1.08702 | ||||||||
\(545\) | 1.78936 | 0.0766476 | ||||||||
\(546\) | −67.4162 | −2.88515 | ||||||||
\(547\) | 45.3508 | 1.93906 | 0.969529 | − | 0.244976i | \(-0.0787800\pi\) | ||||
0.969529 | + | 0.244976i | \(0.0787800\pi\) | |||||||
\(548\) | −36.1246 | −1.54317 | ||||||||
\(549\) | −0.146132 | −0.00623676 | ||||||||
\(550\) | −20.9650 | −0.893951 | ||||||||
\(551\) | 3.83383 | 0.163326 | ||||||||
\(552\) | −15.0749 | −0.641631 | ||||||||
\(553\) | −23.2960 | −0.990645 | ||||||||
\(554\) | −49.7276 | −2.11272 | ||||||||
\(555\) | 12.4069 | 0.526642 | ||||||||
\(556\) | −13.2603 | −0.562362 | ||||||||
\(557\) | 4.93287 | 0.209013 | 0.104506 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104506 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(558\) | −1.14246 | −0.0483640 | ||||||||
\(559\) | −18.5791 | −0.785814 | ||||||||
\(560\) | −3.20983 | −0.135640 | ||||||||
\(561\) | −16.6391 | −0.702503 | ||||||||
\(562\) | 48.8132 | 2.05906 | ||||||||
\(563\) | 29.9198 | 1.26097 | 0.630484 | − | 0.776202i | \(-0.282856\pi\) | ||||
0.630484 | + | 0.776202i | \(0.282856\pi\) | |||||||
\(564\) | −36.6811 | −1.54455 | ||||||||
\(565\) | 5.54582 | 0.233314 | ||||||||
\(566\) | −9.76960 | −0.410647 | ||||||||
\(567\) | 34.7027 | 1.45738 | ||||||||
\(568\) | −22.9069 | −0.961154 | ||||||||
\(569\) | −1.35117 | −0.0566440 | −0.0283220 | − | 0.999599i | \(-0.509016\pi\) | ||||
−0.0283220 | + | 0.999599i | \(0.509016\pi\) | |||||||
\(570\) | −4.27874 | −0.179217 | ||||||||
\(571\) | 15.7296 | 0.658265 | 0.329132 | − | 0.944284i | \(-0.393244\pi\) | ||||
0.329132 | + | 0.944284i | \(0.393244\pi\) | |||||||
\(572\) | −33.4558 | −1.39886 | ||||||||
\(573\) | −30.9921 | −1.29471 | ||||||||
\(574\) | −37.4950 | −1.56501 | ||||||||
\(575\) | 13.8030 | 0.575623 | ||||||||
\(576\) | 1.59365 | 0.0664020 | ||||||||
\(577\) | 4.21519 | 0.175481 | 0.0877404 | − | 0.996143i | \(-0.472035\pi\) | ||||
0.0877404 | + | 0.996143i | \(0.472035\pi\) | |||||||
\(578\) | 3.22022 | 0.133943 | ||||||||
\(579\) | −33.1296 | −1.37682 | ||||||||
\(580\) | −13.1865 | −0.547540 | ||||||||
\(581\) | 57.3970 | 2.38123 | ||||||||
\(582\) | 8.45644 | 0.350531 | ||||||||
\(583\) | −7.40662 | −0.306751 | ||||||||
\(584\) | −28.8962 | −1.19573 | ||||||||
\(585\) | 0.599714 | 0.0247951 | ||||||||
\(586\) | 23.9234 | 0.988266 | ||||||||
\(587\) | −42.4642 | −1.75269 | −0.876343 | − | 0.481687i | \(-0.840024\pi\) | ||||
−0.876343 | + | 0.481687i | \(0.840024\pi\) | |||||||
\(588\) | −47.9925 | −1.97918 | ||||||||
\(589\) | −4.15303 | −0.171123 | ||||||||
\(590\) | −30.0988 | −1.23915 | ||||||||
\(591\) | −11.6336 | −0.478541 | ||||||||
\(592\) | −4.64724 | −0.191001 | ||||||||
\(593\) | −8.01253 | −0.329035 | −0.164518 | − | 0.986374i | \(-0.552607\pi\) | ||||
−0.164518 | + | 0.986374i | \(0.552607\pi\) | |||||||
\(594\) | 29.6469 | 1.21643 | ||||||||
\(595\) | −17.7957 | −0.729553 | ||||||||
\(596\) | 65.4140 | 2.67946 | ||||||||
\(597\) | −6.74451 | −0.276034 | ||||||||
\(598\) | 36.3724 | 1.48738 | ||||||||
\(599\) | 13.1507 | 0.537323 | 0.268661 | − | 0.963235i | \(-0.413419\pi\) | ||||
0.268661 | + | 0.963235i | \(0.413419\pi\) | |||||||
\(600\) | −15.3211 | −0.625483 | ||||||||
\(601\) | 21.4682 | 0.875705 | 0.437852 | − | 0.899047i | \(-0.355739\pi\) | ||||
0.437852 | + | 0.899047i | \(0.355739\pi\) | |||||||
\(602\) | −38.4350 | −1.56649 | ||||||||
\(603\) | −1.06409 | −0.0433332 | ||||||||
\(604\) | −27.8478 | −1.13311 | ||||||||
\(605\) | 5.40006 | 0.219544 | ||||||||
\(606\) | −17.1499 | −0.696669 | ||||||||
\(607\) | −0.756094 | −0.0306889 | −0.0153445 | − | 0.999882i | \(-0.504884\pi\) | ||||
−0.0153445 | + | 0.999882i | \(0.504884\pi\) | |||||||
\(608\) | 6.42532 | 0.260581 | ||||||||
\(609\) | 26.1874 | 1.06117 | ||||||||
\(610\) | 3.01712 | 0.122160 | ||||||||
\(611\) | 30.8617 | 1.24853 | ||||||||
\(612\) | 1.48024 | 0.0598353 | ||||||||
\(613\) | 16.2818 | 0.657614 | 0.328807 | − | 0.944397i | \(-0.393353\pi\) | ||||
0.328807 | + | 0.944397i | \(0.393353\pi\) | |||||||
\(614\) | 34.8027 | 1.40452 | ||||||||
\(615\) | −7.85749 | −0.316845 | ||||||||
\(616\) | −24.1342 | −0.972396 | ||||||||
\(617\) | −12.8861 | −0.518776 | −0.259388 | − | 0.965773i | \(-0.583521\pi\) | ||||
−0.259388 | + | 0.965773i | \(0.583521\pi\) | |||||||
\(618\) | 68.6070 | 2.75978 | ||||||||
\(619\) | 45.7103 | 1.83725 | 0.918627 | − | 0.395126i | \(-0.129299\pi\) | ||||
0.918627 | + | 0.395126i | \(0.129299\pi\) | |||||||
\(620\) | 14.2844 | 0.573676 | ||||||||
\(621\) | −19.5190 | −0.783269 | ||||||||
\(622\) | 77.0073 | 3.08771 | ||||||||
\(623\) | −57.4245 | −2.30066 | ||||||||
\(624\) | 5.29186 | 0.211844 | ||||||||
\(625\) | 7.75565 | 0.310226 | ||||||||
\(626\) | 14.0229 | 0.560468 | ||||||||
\(627\) | 4.21682 | 0.168404 | ||||||||
\(628\) | 30.7265 | 1.22612 | ||||||||
\(629\) | −25.7649 | −1.02731 | ||||||||
\(630\) | 1.24064 | 0.0494283 | ||||||||
\(631\) | 24.8898 | 0.990847 | 0.495423 | − | 0.868652i | \(-0.335013\pi\) | ||||
0.495423 | + | 0.868652i | \(0.335013\pi\) | |||||||
\(632\) | −13.9510 | −0.554943 | ||||||||
\(633\) | −1.69642 | −0.0674266 | ||||||||
\(634\) | −53.8106 | −2.13709 | ||||||||
\(635\) | −17.8266 | −0.707426 | ||||||||
\(636\) | −15.5222 | −0.615497 | ||||||||
\(637\) | 40.3786 | 1.59986 | ||||||||
\(638\) | 21.4597 | 0.849598 | ||||||||
\(639\) | −1.16051 | −0.0459091 | ||||||||
\(640\) | −18.5098 | −0.731662 | ||||||||
\(641\) | −23.4241 | −0.925197 | −0.462598 | − | 0.886568i | \(-0.653083\pi\) | ||||
−0.462598 | + | 0.886568i | \(0.653083\pi\) | |||||||
\(642\) | −20.5343 | −0.810425 | ||||||||
\(643\) | −22.3000 | −0.879427 | −0.439714 | − | 0.898138i | \(-0.644920\pi\) | ||||
−0.439714 | + | 0.898138i | \(0.644920\pi\) | |||||||
\(644\) | 45.5669 | 1.79559 | ||||||||
\(645\) | −8.05449 | −0.317145 | ||||||||
\(646\) | 8.88552 | 0.349596 | ||||||||
\(647\) | −47.3142 | −1.86011 | −0.930056 | − | 0.367418i | \(-0.880242\pi\) | ||||
−0.930056 | + | 0.367418i | \(0.880242\pi\) | |||||||
\(648\) | 20.7821 | 0.816399 | ||||||||
\(649\) | 29.6632 | 1.16438 | ||||||||
\(650\) | 36.9665 | 1.44994 | ||||||||
\(651\) | −28.3678 | −1.11182 | ||||||||
\(652\) | −35.0481 | −1.37259 | ||||||||
\(653\) | −18.8337 | −0.737019 | −0.368510 | − | 0.929624i | \(-0.620132\pi\) | ||||
−0.368510 | + | 0.929624i | \(0.620132\pi\) | |||||||
\(654\) | −6.10274 | −0.238636 | ||||||||
\(655\) | 3.85462 | 0.150613 | ||||||||
\(656\) | 2.94319 | 0.114912 | ||||||||
\(657\) | −1.46394 | −0.0571137 | ||||||||
\(658\) | 63.8443 | 2.48891 | ||||||||
\(659\) | 6.66147 | 0.259494 | 0.129747 | − | 0.991547i | \(-0.458583\pi\) | ||||
0.129747 | + | 0.991547i | \(0.458583\pi\) | |||||||
\(660\) | −14.5038 | −0.564561 | ||||||||
\(661\) | 6.19938 | 0.241128 | 0.120564 | − | 0.992706i | \(-0.461530\pi\) | ||||
0.120564 | + | 0.992706i | \(0.461530\pi\) | |||||||
\(662\) | 67.6842 | 2.63062 | ||||||||
\(663\) | 29.3388 | 1.13942 | ||||||||
\(664\) | 34.3728 | 1.33392 | ||||||||
\(665\) | 4.50995 | 0.174888 | ||||||||
\(666\) | 1.79622 | 0.0696020 | ||||||||
\(667\) | −14.1287 | −0.547064 | ||||||||
\(668\) | −25.1417 | −0.972761 | ||||||||
\(669\) | −49.5271 | −1.91483 | ||||||||
\(670\) | 21.9698 | 0.848769 | ||||||||
\(671\) | −2.97346 | −0.114789 | ||||||||
\(672\) | 43.8890 | 1.69305 | ||||||||
\(673\) | 22.8410 | 0.880458 | 0.440229 | − | 0.897886i | \(-0.354897\pi\) | ||||
0.440229 | + | 0.897886i | \(0.354897\pi\) | |||||||
\(674\) | 58.4940 | 2.25310 | ||||||||
\(675\) | −19.8378 | −0.763556 | ||||||||
\(676\) | 19.0701 | 0.733464 | ||||||||
\(677\) | 48.8853 | 1.87881 | 0.939407 | − | 0.342804i | \(-0.111377\pi\) | ||||
0.939407 | + | 0.342804i | \(0.111377\pi\) | |||||||
\(678\) | −18.9145 | −0.726405 | ||||||||
\(679\) | −8.91339 | −0.342064 | ||||||||
\(680\) | −10.6572 | −0.408683 | ||||||||
\(681\) | 15.7671 | 0.604196 | ||||||||
\(682\) | −23.2464 | −0.890152 | ||||||||
\(683\) | 13.3277 | 0.509968 | 0.254984 | − | 0.966945i | \(-0.417930\pi\) | ||||
0.254984 | + | 0.966945i | \(0.417930\pi\) | |||||||
\(684\) | −0.375136 | −0.0143437 | ||||||||
\(685\) | 13.1763 | 0.503441 | ||||||||
\(686\) | 20.0626 | 0.765993 | ||||||||
\(687\) | 22.8537 | 0.871925 | ||||||||
\(688\) | 3.01697 | 0.115021 | ||||||||
\(689\) | 13.0597 | 0.497534 | ||||||||
\(690\) | 15.7683 | 0.600288 | ||||||||
\(691\) | −3.26772 | −0.124310 | −0.0621550 | − | 0.998067i | \(-0.519797\pi\) | ||||
−0.0621550 | + | 0.998067i | \(0.519797\pi\) | |||||||
\(692\) | 51.7805 | 1.96840 | ||||||||
\(693\) | −1.22269 | −0.0464460 | ||||||||
\(694\) | 5.27767 | 0.200338 | ||||||||
\(695\) | 4.83664 | 0.183464 | ||||||||
\(696\) | 15.6826 | 0.594449 | ||||||||
\(697\) | 16.3174 | 0.618065 | ||||||||
\(698\) | 1.77144 | 0.0670501 | ||||||||
\(699\) | −7.58412 | −0.286858 | ||||||||
\(700\) | 46.3111 | 1.75040 | ||||||||
\(701\) | 44.7460 | 1.69003 | 0.845017 | − | 0.534739i | \(-0.179590\pi\) | ||||
0.845017 | + | 0.534739i | \(0.179590\pi\) | |||||||
\(702\) | −52.2748 | −1.97298 | ||||||||
\(703\) | 6.52957 | 0.246268 | ||||||||
\(704\) | 32.4272 | 1.22215 | ||||||||
\(705\) | 13.3793 | 0.503893 | ||||||||
\(706\) | 60.0667 | 2.26064 | ||||||||
\(707\) | 18.0767 | 0.679843 | ||||||||
\(708\) | 62.1660 | 2.33634 | ||||||||
\(709\) | 5.55058 | 0.208456 | 0.104228 | − | 0.994553i | \(-0.466763\pi\) | ||||
0.104228 | + | 0.994553i | \(0.466763\pi\) | |||||||
\(710\) | 23.9605 | 0.899223 | ||||||||
\(711\) | −0.706787 | −0.0265066 | ||||||||
\(712\) | −34.3893 | −1.28879 | ||||||||
\(713\) | 15.3050 | 0.573177 | ||||||||
\(714\) | 60.6937 | 2.27140 | ||||||||
\(715\) | 12.2028 | 0.456360 | ||||||||
\(716\) | −27.7694 | −1.03779 | ||||||||
\(717\) | −21.2109 | −0.792136 | ||||||||
\(718\) | 53.8490 | 2.00963 | ||||||||
\(719\) | −12.7436 | −0.475255 | −0.237628 | − | 0.971356i | \(-0.576370\pi\) | ||||
−0.237628 | + | 0.971356i | \(0.576370\pi\) | |||||||
\(720\) | −0.0973845 | −0.00362931 | ||||||||
\(721\) | −72.3142 | −2.69312 | ||||||||
\(722\) | −2.25185 | −0.0838051 | ||||||||
\(723\) | −22.7833 | −0.847320 | ||||||||
\(724\) | 4.59765 | 0.170870 | ||||||||
\(725\) | −14.3594 | −0.533295 | ||||||||
\(726\) | −18.4173 | −0.683531 | ||||||||
\(727\) | −2.71026 | −0.100518 | −0.0502589 | − | 0.998736i | \(-0.516005\pi\) | ||||
−0.0502589 | + | 0.998736i | \(0.516005\pi\) | |||||||
\(728\) | 42.5545 | 1.57718 | ||||||||
\(729\) | 28.0081 | 1.03734 | ||||||||
\(730\) | 30.2253 | 1.11869 | ||||||||
\(731\) | 16.7265 | 0.618651 | ||||||||
\(732\) | −6.23156 | −0.230325 | ||||||||
\(733\) | 20.5859 | 0.760357 | 0.380179 | − | 0.924913i | \(-0.375863\pi\) | ||||
0.380179 | + | 0.924913i | \(0.375863\pi\) | |||||||
\(734\) | 4.66894 | 0.172334 | ||||||||
\(735\) | 17.5051 | 0.645684 | ||||||||
\(736\) | −23.6790 | −0.872818 | ||||||||
\(737\) | −21.6519 | −0.797559 | ||||||||
\(738\) | −1.13758 | −0.0418748 | ||||||||
\(739\) | 15.1848 | 0.558584 | 0.279292 | − | 0.960206i | \(-0.409900\pi\) | ||||
0.279292 | + | 0.960206i | \(0.409900\pi\) | |||||||
\(740\) | −22.4586 | −0.825594 | ||||||||
\(741\) | −7.43529 | −0.273142 | ||||||||
\(742\) | 27.0168 | 0.991819 | ||||||||
\(743\) | −12.0796 | −0.443159 | −0.221580 | − | 0.975142i | \(-0.571121\pi\) | ||||
−0.221580 | + | 0.975142i | \(0.571121\pi\) | |||||||
\(744\) | −16.9884 | −0.622824 | ||||||||
\(745\) | −23.8595 | −0.874144 | ||||||||
\(746\) | 22.6067 | 0.827690 | ||||||||
\(747\) | 1.74139 | 0.0637142 | ||||||||
\(748\) | 30.1196 | 1.10128 | ||||||||
\(749\) | 21.6439 | 0.790851 | ||||||||
\(750\) | 37.4195 | 1.36637 | ||||||||
\(751\) | −12.9709 | −0.473314 | −0.236657 | − | 0.971593i | \(-0.576052\pi\) | ||||
−0.236657 | + | 0.971593i | \(0.576052\pi\) | |||||||
\(752\) | −5.01148 | −0.182750 | ||||||||
\(753\) | −21.0212 | −0.766054 | ||||||||
\(754\) | −37.8387 | −1.37800 | ||||||||
\(755\) | 10.1574 | 0.369664 | ||||||||
\(756\) | −65.4892 | −2.38182 | ||||||||
\(757\) | 37.8880 | 1.37706 | 0.688532 | − | 0.725206i | \(-0.258256\pi\) | ||||
0.688532 | + | 0.725206i | \(0.258256\pi\) | |||||||
\(758\) | 41.5270 | 1.50833 | ||||||||
\(759\) | −15.5401 | −0.564070 | ||||||||
\(760\) | 2.70083 | 0.0979695 | ||||||||
\(761\) | 30.8382 | 1.11788 | 0.558942 | − | 0.829206i | \(-0.311207\pi\) | ||||
0.558942 | + | 0.829206i | \(0.311207\pi\) | |||||||
\(762\) | 60.7989 | 2.20251 | ||||||||
\(763\) | 6.43251 | 0.232872 | ||||||||
\(764\) | 56.1011 | 2.02967 | ||||||||
\(765\) | −0.539912 | −0.0195206 | ||||||||
\(766\) | 51.1324 | 1.84749 | ||||||||
\(767\) | −52.3035 | −1.88857 | ||||||||
\(768\) | 18.8681 | 0.680844 | ||||||||
\(769\) | 8.31375 | 0.299801 | 0.149901 | − | 0.988701i | \(-0.452105\pi\) | ||||
0.149901 | + | 0.988701i | \(0.452105\pi\) | |||||||
\(770\) | 25.2443 | 0.909740 | ||||||||
\(771\) | −24.9454 | −0.898388 | ||||||||
\(772\) | 59.9704 | 2.15838 | ||||||||
\(773\) | −43.7621 | −1.57401 | −0.787007 | − | 0.616944i | \(-0.788371\pi\) | ||||
−0.787007 | + | 0.616944i | \(0.788371\pi\) | |||||||
\(774\) | −1.16610 | −0.0419145 | ||||||||
\(775\) | 15.5550 | 0.558751 | ||||||||
\(776\) | −5.33788 | −0.191619 | ||||||||
\(777\) | 44.6011 | 1.60006 | ||||||||
\(778\) | 70.2517 | 2.51865 | ||||||||
\(779\) | −4.13530 | −0.148162 | ||||||||
\(780\) | 25.5738 | 0.915690 | ||||||||
\(781\) | −23.6138 | −0.844968 | ||||||||
\(782\) | −32.7455 | −1.17098 | ||||||||
\(783\) | 20.3058 | 0.725672 | ||||||||
\(784\) | −6.55688 | −0.234174 | ||||||||
\(785\) | −11.2074 | −0.400008 | ||||||||
\(786\) | −13.1465 | −0.468920 | ||||||||
\(787\) | −13.4709 | −0.480185 | −0.240092 | − | 0.970750i | \(-0.577178\pi\) | ||||
−0.240092 | + | 0.970750i | \(0.577178\pi\) | |||||||
\(788\) | 21.0588 | 0.750189 | ||||||||
\(789\) | 31.1098 | 1.10754 | ||||||||
\(790\) | 14.5927 | 0.519185 | ||||||||
\(791\) | 19.9365 | 0.708861 | ||||||||
\(792\) | −0.732220 | −0.0260183 | ||||||||
\(793\) | 5.24294 | 0.186182 | ||||||||
\(794\) | −20.7413 | −0.736081 | ||||||||
\(795\) | 5.66167 | 0.200799 | ||||||||
\(796\) | 12.2087 | 0.432727 | ||||||||
\(797\) | −18.9963 | −0.672884 | −0.336442 | − | 0.941704i | \(-0.609224\pi\) | ||||
−0.336442 | + | 0.941704i | \(0.609224\pi\) | |||||||
\(798\) | −15.3815 | −0.544500 | ||||||||
\(799\) | −27.7843 | −0.982938 | ||||||||
\(800\) | −24.0657 | −0.850851 | ||||||||
\(801\) | −1.74223 | −0.0615586 | ||||||||
\(802\) | −56.3062 | −1.98824 | ||||||||
\(803\) | −29.7879 | −1.05119 | ||||||||
\(804\) | −45.3765 | −1.60031 | ||||||||
\(805\) | −16.6203 | −0.585790 | ||||||||
\(806\) | 40.9891 | 1.44378 | ||||||||
\(807\) | 37.9931 | 1.33742 | ||||||||
\(808\) | 10.8254 | 0.380837 | ||||||||
\(809\) | 53.5150 | 1.88149 | 0.940744 | − | 0.339118i | \(-0.110128\pi\) | ||||
0.940744 | + | 0.339118i | \(0.110128\pi\) | |||||||
\(810\) | −21.7380 | −0.763795 | ||||||||
\(811\) | 27.9357 | 0.980955 | 0.490477 | − | 0.871454i | \(-0.336822\pi\) | ||||
0.490477 | + | 0.871454i | \(0.336822\pi\) | |||||||
\(812\) | −47.4039 | −1.66355 | ||||||||
\(813\) | −6.78757 | −0.238051 | ||||||||
\(814\) | 36.5490 | 1.28104 | ||||||||
\(815\) | 12.7836 | 0.447791 | ||||||||
\(816\) | −4.76418 | −0.166779 | ||||||||
\(817\) | −4.23897 | −0.148303 | ||||||||
\(818\) | 50.0266 | 1.74914 | ||||||||
\(819\) | 2.15590 | 0.0753331 | ||||||||
\(820\) | 14.2234 | 0.496704 | ||||||||
\(821\) | −21.3327 | −0.744515 | −0.372258 | − | 0.928129i | \(-0.621416\pi\) | ||||
−0.372258 | + | 0.928129i | \(0.621416\pi\) | |||||||
\(822\) | −44.9388 | −1.56742 | ||||||||
\(823\) | −20.0414 | −0.698599 | −0.349300 | − | 0.937011i | \(-0.613580\pi\) | ||||
−0.349300 | + | 0.937011i | \(0.613580\pi\) | |||||||
\(824\) | −43.3062 | −1.50864 | ||||||||
\(825\) | −15.7939 | −0.549873 | ||||||||
\(826\) | −108.201 | −3.76480 | ||||||||
\(827\) | 3.61644 | 0.125756 | 0.0628780 | − | 0.998021i | \(-0.479972\pi\) | ||||
0.0628780 | + | 0.998021i | \(0.479972\pi\) | |||||||
\(828\) | 1.38248 | 0.0480443 | ||||||||
\(829\) | 27.5824 | 0.957978 | 0.478989 | − | 0.877821i | \(-0.341003\pi\) | ||||
0.478989 | + | 0.877821i | \(0.341003\pi\) | |||||||
\(830\) | −35.9538 | −1.24797 | ||||||||
\(831\) | −37.4620 | −1.29954 | ||||||||
\(832\) | −57.1771 | −1.98226 | ||||||||
\(833\) | −36.3522 | −1.25953 | ||||||||
\(834\) | −16.4957 | −0.571200 | ||||||||
\(835\) | 9.17032 | 0.317352 | ||||||||
\(836\) | −7.63319 | −0.263999 | ||||||||
\(837\) | −21.9965 | −0.760310 | ||||||||
\(838\) | 62.6911 | 2.16563 | ||||||||
\(839\) | −23.0648 | −0.796285 | −0.398142 | − | 0.917324i | \(-0.630345\pi\) | ||||
−0.398142 | + | 0.917324i | \(0.630345\pi\) | |||||||
\(840\) | 18.4484 | 0.636530 | ||||||||
\(841\) | −14.3018 | −0.493165 | ||||||||
\(842\) | 15.2857 | 0.526781 | ||||||||
\(843\) | 36.7732 | 1.26654 | ||||||||
\(844\) | 3.07082 | 0.105702 | ||||||||
\(845\) | −6.95573 | −0.239284 | ||||||||
\(846\) | 1.93700 | 0.0665955 | ||||||||
\(847\) | 19.4125 | 0.667022 | ||||||||
\(848\) | −2.12070 | −0.0728250 | ||||||||
\(849\) | −7.35988 | −0.252591 | ||||||||
\(850\) | −33.2803 | −1.14150 | ||||||||
\(851\) | −24.0632 | −0.824875 | ||||||||
\(852\) | −49.4881 | −1.69543 | ||||||||
\(853\) | −37.9284 | −1.29864 | −0.649322 | − | 0.760514i | \(-0.724947\pi\) | ||||
−0.649322 | + | 0.760514i | \(0.724947\pi\) | |||||||
\(854\) | 10.8462 | 0.371148 | ||||||||
\(855\) | 0.136829 | 0.00467947 | ||||||||
\(856\) | 12.9617 | 0.443022 | ||||||||
\(857\) | −17.8439 | −0.609537 | −0.304769 | − | 0.952426i | \(-0.598579\pi\) | ||||
−0.304769 | + | 0.952426i | \(0.598579\pi\) | |||||||
\(858\) | −41.6188 | −1.42084 | ||||||||
\(859\) | 18.5329 | 0.632334 | 0.316167 | − | 0.948704i | \(-0.397604\pi\) | ||||
0.316167 | + | 0.948704i | \(0.397604\pi\) | |||||||
\(860\) | 14.5800 | 0.497175 | ||||||||
\(861\) | −28.2467 | −0.962645 | ||||||||
\(862\) | 11.7899 | 0.401566 | ||||||||
\(863\) | 38.7756 | 1.31994 | 0.659968 | − | 0.751294i | \(-0.270570\pi\) | ||||
0.659968 | + | 0.751294i | \(0.270570\pi\) | |||||||
\(864\) | 34.0317 | 1.15778 | ||||||||
\(865\) | −18.8867 | −0.642167 | ||||||||
\(866\) | −42.3269 | −1.43833 | ||||||||
\(867\) | 2.42594 | 0.0823891 | ||||||||
\(868\) | 51.3507 | 1.74296 | ||||||||
\(869\) | −14.3815 | −0.487860 | ||||||||
\(870\) | −16.4039 | −0.556146 | ||||||||
\(871\) | 38.1776 | 1.29360 | ||||||||
\(872\) | 3.85218 | 0.130451 | ||||||||
\(873\) | −0.270427 | −0.00915258 | ||||||||
\(874\) | 8.29865 | 0.280706 | ||||||||
\(875\) | −39.4415 | −1.33337 | ||||||||
\(876\) | −62.4273 | −2.10922 | ||||||||
\(877\) | 1.77452 | 0.0599211 | 0.0299606 | − | 0.999551i | \(-0.490462\pi\) | ||||
0.0299606 | + | 0.999551i | \(0.490462\pi\) | |||||||
\(878\) | 40.8688 | 1.37926 | ||||||||
\(879\) | 18.0226 | 0.607886 | ||||||||
\(880\) | −1.98156 | −0.0667983 | ||||||||
\(881\) | −2.26884 | −0.0764392 | −0.0382196 | − | 0.999269i | \(-0.512169\pi\) | ||||
−0.0382196 | + | 0.999269i | \(0.512169\pi\) | |||||||
\(882\) | 2.53432 | 0.0853349 | ||||||||
\(883\) | −44.5844 | −1.50039 | −0.750193 | − | 0.661219i | \(-0.770039\pi\) | ||||
−0.750193 | + | 0.661219i | \(0.770039\pi\) | |||||||
\(884\) | −53.1083 | −1.78623 | ||||||||
\(885\) | −22.6748 | −0.762204 | ||||||||
\(886\) | 86.6928 | 2.91250 | ||||||||
\(887\) | 8.29649 | 0.278569 | 0.139284 | − | 0.990252i | \(-0.455520\pi\) | ||||
0.139284 | + | 0.990252i | \(0.455520\pi\) | |||||||
\(888\) | 26.7099 | 0.896324 | ||||||||
\(889\) | −64.0842 | −2.14932 | ||||||||
\(890\) | 35.9710 | 1.20575 | ||||||||
\(891\) | 21.4234 | 0.717711 | ||||||||
\(892\) | 89.6528 | 3.00180 | ||||||||
\(893\) | 7.04135 | 0.235630 | ||||||||
\(894\) | 81.3746 | 2.72158 | ||||||||
\(895\) | 10.1288 | 0.338568 | ||||||||
\(896\) | −66.5402 | −2.22295 | ||||||||
\(897\) | 27.4010 | 0.914893 | ||||||||
\(898\) | 17.1149 | 0.571131 | ||||||||
\(899\) | −15.9220 | −0.531028 | ||||||||
\(900\) | 1.40505 | 0.0468352 | ||||||||
\(901\) | −11.7574 | −0.391696 | ||||||||
\(902\) | −23.1472 | −0.770717 | ||||||||
\(903\) | −28.9549 | −0.963557 | ||||||||
\(904\) | 11.9392 | 0.397092 | ||||||||
\(905\) | −1.67697 | −0.0557444 | ||||||||
\(906\) | −34.6425 | −1.15092 | ||||||||
\(907\) | −5.64883 | −0.187566 | −0.0937832 | − | 0.995593i | \(-0.529896\pi\) | ||||
−0.0937832 | + | 0.995593i | \(0.529896\pi\) | |||||||
\(908\) | −28.5412 | −0.947173 | ||||||||
\(909\) | 0.548436 | 0.0181905 | ||||||||
\(910\) | −44.5118 | −1.47555 | ||||||||
\(911\) | −25.9750 | −0.860589 | −0.430294 | − | 0.902689i | \(-0.641590\pi\) | ||||
−0.430294 | + | 0.902689i | \(0.641590\pi\) | |||||||
\(912\) | 1.20738 | 0.0399803 | ||||||||
\(913\) | 35.4335 | 1.17268 | ||||||||
\(914\) | 8.71315 | 0.288205 | ||||||||
\(915\) | 2.27294 | 0.0751409 | ||||||||
\(916\) | −41.3693 | −1.36688 | ||||||||
\(917\) | 13.8569 | 0.457594 | ||||||||
\(918\) | 47.0621 | 1.55328 | ||||||||
\(919\) | 7.83511 | 0.258456 | 0.129228 | − | 0.991615i | \(-0.458750\pi\) | ||||
0.129228 | + | 0.991615i | \(0.458750\pi\) | |||||||
\(920\) | −9.95327 | −0.328150 | ||||||||
\(921\) | 26.2185 | 0.863928 | ||||||||
\(922\) | 84.6695 | 2.78844 | ||||||||
\(923\) | 41.6369 | 1.37050 | ||||||||
\(924\) | −52.1395 | −1.71526 | ||||||||
\(925\) | −24.4562 | −0.804115 | ||||||||
\(926\) | −78.3792 | −2.57570 | ||||||||
\(927\) | −2.19397 | −0.0720596 | ||||||||
\(928\) | 24.6335 | 0.808636 | ||||||||
\(929\) | 19.8932 | 0.652675 | 0.326338 | − | 0.945253i | \(-0.394185\pi\) | ||||
0.326338 | + | 0.945253i | \(0.394185\pi\) | |||||||
\(930\) | 17.7697 | 0.582693 | ||||||||
\(931\) | 9.21269 | 0.301934 | ||||||||
\(932\) | 13.7286 | 0.449695 | ||||||||
\(933\) | 58.0131 | 1.89926 | ||||||||
\(934\) | −46.0076 | −1.50541 | ||||||||
\(935\) | −10.9860 | −0.359281 | ||||||||
\(936\) | 1.29108 | 0.0422003 | ||||||||
\(937\) | 7.08249 | 0.231375 | 0.115687 | − | 0.993286i | \(-0.463093\pi\) | ||||
0.115687 | + | 0.993286i | \(0.463093\pi\) | |||||||
\(938\) | 78.9788 | 2.57875 | ||||||||
\(939\) | 10.5641 | 0.344746 | ||||||||
\(940\) | −24.2188 | −0.789931 | ||||||||
\(941\) | −22.4772 | −0.732736 | −0.366368 | − | 0.930470i | \(-0.619399\pi\) | ||||
−0.366368 | + | 0.930470i | \(0.619399\pi\) | |||||||
\(942\) | 38.2236 | 1.24539 | ||||||||
\(943\) | 15.2397 | 0.496272 | ||||||||
\(944\) | 8.49330 | 0.276433 | ||||||||
\(945\) | 23.8869 | 0.777041 | ||||||||
\(946\) | −23.7275 | −0.771448 | ||||||||
\(947\) | −43.3377 | −1.40829 | −0.704143 | − | 0.710058i | \(-0.748669\pi\) | ||||
−0.704143 | + | 0.710058i | \(0.748669\pi\) | |||||||
\(948\) | −30.1398 | −0.978895 | ||||||||
\(949\) | 52.5234 | 1.70498 | ||||||||
\(950\) | 8.43418 | 0.273641 | ||||||||
\(951\) | −40.5380 | −1.31453 | ||||||||
\(952\) | −38.3111 | −1.24167 | ||||||||
\(953\) | 19.1723 | 0.621052 | 0.310526 | − | 0.950565i | \(-0.399495\pi\) | ||||
0.310526 | + | 0.950565i | \(0.399495\pi\) | |||||||
\(954\) | 0.819676 | 0.0265380 | ||||||||
\(955\) | −20.4626 | −0.662155 | ||||||||
\(956\) | 38.3955 | 1.24180 | ||||||||
\(957\) | 16.1666 | 0.522591 | ||||||||
\(958\) | 43.4018 | 1.40225 | ||||||||
\(959\) | 47.3672 | 1.52957 | ||||||||
\(960\) | −24.7876 | −0.800016 | ||||||||
\(961\) | −13.7523 | −0.443624 | ||||||||
\(962\) | −64.4449 | −2.07779 | ||||||||
\(963\) | 0.656664 | 0.0211607 | ||||||||
\(964\) | 41.2418 | 1.32831 | ||||||||
\(965\) | −21.8740 | −0.704148 | ||||||||
\(966\) | 56.6850 | 1.82381 | ||||||||
\(967\) | 37.2765 | 1.19873 | 0.599366 | − | 0.800475i | \(-0.295419\pi\) | ||||
0.599366 | + | 0.800475i | \(0.295419\pi\) | |||||||
\(968\) | 11.6254 | 0.373655 | ||||||||
\(969\) | 6.69387 | 0.215038 | ||||||||
\(970\) | 5.58339 | 0.179272 | ||||||||
\(971\) | 48.7357 | 1.56400 | 0.782002 | − | 0.623276i | \(-0.214199\pi\) | ||||
0.782002 | + | 0.623276i | \(0.214199\pi\) | |||||||
\(972\) | −3.89607 | −0.124967 | ||||||||
\(973\) | 17.3871 | 0.557405 | ||||||||
\(974\) | −18.4985 | −0.592729 | ||||||||
\(975\) | 27.8485 | 0.891866 | ||||||||
\(976\) | −0.851375 | −0.0272518 | ||||||||
\(977\) | −0.607532 | −0.0194367 | −0.00971833 | − | 0.999953i | \(-0.503093\pi\) | ||||
−0.00971833 | + | 0.999953i | \(0.503093\pi\) | |||||||
\(978\) | −43.5996 | −1.39416 | ||||||||
\(979\) | −35.4504 | −1.13300 | ||||||||
\(980\) | −31.6872 | −1.01221 | ||||||||
\(981\) | 0.195159 | 0.00623094 | ||||||||
\(982\) | −87.1324 | −2.78051 | ||||||||
\(983\) | −18.7593 | −0.598330 | −0.299165 | − | 0.954201i | \(-0.596708\pi\) | ||||
−0.299165 | + | 0.954201i | \(0.596708\pi\) | |||||||
\(984\) | −16.9158 | −0.539257 | ||||||||
\(985\) | −7.68111 | −0.244740 | ||||||||
\(986\) | 34.0655 | 1.08487 | ||||||||
\(987\) | 48.0968 | 1.53094 | ||||||||
\(988\) | 13.4592 | 0.428194 | ||||||||
\(989\) | 15.6217 | 0.496742 | ||||||||
\(990\) | 0.765897 | 0.0243418 | ||||||||
\(991\) | −28.4052 | −0.902321 | −0.451161 | − | 0.892443i | \(-0.648990\pi\) | ||||
−0.451161 | + | 0.892443i | \(0.648990\pi\) | |||||||
\(992\) | −26.6845 | −0.847235 | ||||||||
\(993\) | 50.9896 | 1.61811 | ||||||||
\(994\) | 86.1351 | 2.73204 | ||||||||
\(995\) | −4.45309 | −0.141172 | ||||||||
\(996\) | 74.2589 | 2.35298 | ||||||||
\(997\) | −34.1448 | −1.08138 | −0.540689 | − | 0.841223i | \(-0.681836\pi\) | ||||
−0.540689 | + | 0.841223i | \(0.681836\pi\) | |||||||
\(998\) | 69.3064 | 2.19386 | ||||||||
\(999\) | 34.5839 | 1.09418 |
(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 | 4009.2.a.c.1.12 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.12 | ✓ | 71 | 1.1 | even | 1 | trivial |