Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44055 | −1.72573 | −0.862865 | − | 0.505435i | \(-0.831332\pi\) | ||||
−0.862865 | + | 0.505435i | \(0.831332\pi\) | |||||||
\(3\) | 1.60583 | 0.927126 | 0.463563 | − | 0.886064i | \(-0.346571\pi\) | ||||
0.463563 | + | 0.886064i | \(0.346571\pi\) | |||||||
\(4\) | 3.95629 | 1.97814 | ||||||||
\(5\) | 4.05418 | 1.81309 | 0.906543 | − | 0.422114i | \(-0.138712\pi\) | ||||
0.906543 | + | 0.422114i | \(0.138712\pi\) | |||||||
\(6\) | −3.91911 | −1.59997 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.77442 | −1.68801 | ||||||||
\(9\) | −0.421314 | −0.140438 | ||||||||
\(10\) | −9.89444 | −3.12890 | ||||||||
\(11\) | 5.61936 | 1.69430 | 0.847151 | − | 0.531352i | \(-0.178316\pi\) | ||||
0.847151 | + | 0.531352i | \(0.178316\pi\) | |||||||
\(12\) | 6.35312 | 1.83399 | ||||||||
\(13\) | 3.03148 | 0.840780 | 0.420390 | − | 0.907343i | \(-0.361893\pi\) | ||||
0.420390 | + | 0.907343i | \(0.361893\pi\) | |||||||
\(14\) | −2.44055 | −0.652265 | ||||||||
\(15\) | 6.51032 | 1.68096 | ||||||||
\(16\) | 3.73964 | 0.934909 | ||||||||
\(17\) | −1.73615 | −0.421079 | −0.210539 | − | 0.977585i | \(-0.567522\pi\) | ||||
−0.210539 | + | 0.977585i | \(0.567522\pi\) | |||||||
\(18\) | 1.02824 | 0.242358 | ||||||||
\(19\) | 4.70704 | 1.07987 | 0.539935 | − | 0.841707i | \(-0.318449\pi\) | ||||
0.539935 | + | 0.841707i | \(0.318449\pi\) | |||||||
\(20\) | 16.0395 | 3.58654 | ||||||||
\(21\) | 1.60583 | 0.350421 | ||||||||
\(22\) | −13.7143 | −2.92391 | ||||||||
\(23\) | 1.98175 | 0.413224 | 0.206612 | − | 0.978423i | \(-0.433756\pi\) | ||||
0.206612 | + | 0.978423i | \(0.433756\pi\) | |||||||
\(24\) | −7.66690 | −1.56500 | ||||||||
\(25\) | 11.4364 | 2.28728 | ||||||||
\(26\) | −7.39847 | −1.45096 | ||||||||
\(27\) | −5.49404 | −1.05733 | ||||||||
\(28\) | 3.95629 | 0.747668 | ||||||||
\(29\) | −0.147179 | −0.0273305 | −0.0136652 | − | 0.999907i | \(-0.504350\pi\) | ||||
−0.0136652 | + | 0.999907i | \(0.504350\pi\) | |||||||
\(30\) | −15.8888 | −2.90088 | ||||||||
\(31\) | 8.30517 | 1.49165 | 0.745826 | − | 0.666141i | \(-0.232055\pi\) | ||||
0.745826 | + | 0.666141i | \(0.232055\pi\) | |||||||
\(32\) | 0.422066 | 0.0746114 | ||||||||
\(33\) | 9.02374 | 1.57083 | ||||||||
\(34\) | 4.23717 | 0.726669 | ||||||||
\(35\) | 4.05418 | 0.685282 | ||||||||
\(36\) | −1.66684 | −0.277807 | ||||||||
\(37\) | −5.25613 | −0.864102 | −0.432051 | − | 0.901849i | \(-0.642210\pi\) | ||||
−0.432051 | + | 0.901849i | \(0.642210\pi\) | |||||||
\(38\) | −11.4878 | −1.86356 | ||||||||
\(39\) | 4.86803 | 0.779509 | ||||||||
\(40\) | −19.3564 | −3.06051 | ||||||||
\(41\) | 5.32712 | 0.831956 | 0.415978 | − | 0.909375i | \(-0.363439\pi\) | ||||
0.415978 | + | 0.909375i | \(0.363439\pi\) | |||||||
\(42\) | −3.91911 | −0.604731 | ||||||||
\(43\) | −1.76833 | −0.269668 | −0.134834 | − | 0.990868i | \(-0.543050\pi\) | ||||
−0.134834 | + | 0.990868i | \(0.543050\pi\) | |||||||
\(44\) | 22.2318 | 3.35157 | ||||||||
\(45\) | −1.70808 | −0.254626 | ||||||||
\(46\) | −4.83657 | −0.713114 | ||||||||
\(47\) | 11.9709 | 1.74613 | 0.873067 | − | 0.487600i | \(-0.162127\pi\) | ||||
0.873067 | + | 0.487600i | \(0.162127\pi\) | |||||||
\(48\) | 6.00522 | 0.866778 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −27.9111 | −3.94723 | ||||||||
\(51\) | −2.78796 | −0.390393 | ||||||||
\(52\) | 11.9934 | 1.66318 | ||||||||
\(53\) | −0.255700 | −0.0351231 | −0.0175615 | − | 0.999846i | \(-0.505590\pi\) | ||||
−0.0175615 | + | 0.999846i | \(0.505590\pi\) | |||||||
\(54\) | 13.4085 | 1.82466 | ||||||||
\(55\) | 22.7819 | 3.07191 | ||||||||
\(56\) | −4.77442 | −0.638009 | ||||||||
\(57\) | 7.55871 | 1.00118 | ||||||||
\(58\) | 0.359198 | 0.0471650 | ||||||||
\(59\) | −8.52605 | −1.11000 | −0.554998 | − | 0.831851i | \(-0.687281\pi\) | ||||
−0.554998 | + | 0.831851i | \(0.687281\pi\) | |||||||
\(60\) | 25.7567 | 3.32518 | ||||||||
\(61\) | −12.0498 | −1.54282 | −0.771411 | − | 0.636338i | \(-0.780449\pi\) | ||||
−0.771411 | + | 0.636338i | \(0.780449\pi\) | |||||||
\(62\) | −20.2692 | −2.57419 | ||||||||
\(63\) | −0.421314 | −0.0530806 | ||||||||
\(64\) | −8.50935 | −1.06367 | ||||||||
\(65\) | 12.2902 | 1.52441 | ||||||||
\(66\) | −22.0229 | −2.71083 | ||||||||
\(67\) | 7.20097 | 0.879739 | 0.439869 | − | 0.898062i | \(-0.355025\pi\) | ||||
0.439869 | + | 0.898062i | \(0.355025\pi\) | |||||||
\(68\) | −6.86872 | −0.832955 | ||||||||
\(69\) | 3.18236 | 0.383111 | ||||||||
\(70\) | −9.89444 | −1.18261 | ||||||||
\(71\) | −7.61283 | −0.903477 | −0.451739 | − | 0.892150i | \(-0.649196\pi\) | ||||
−0.451739 | + | 0.892150i | \(0.649196\pi\) | |||||||
\(72\) | 2.01153 | 0.237061 | ||||||||
\(73\) | 2.22604 | 0.260538 | 0.130269 | − | 0.991479i | \(-0.458416\pi\) | ||||
0.130269 | + | 0.991479i | \(0.458416\pi\) | |||||||
\(74\) | 12.8278 | 1.49121 | ||||||||
\(75\) | 18.3649 | 2.12060 | ||||||||
\(76\) | 18.6224 | 2.13614 | ||||||||
\(77\) | 5.61936 | 0.640386 | ||||||||
\(78\) | −11.8807 | −1.34522 | ||||||||
\(79\) | −15.9297 | −1.79223 | −0.896116 | − | 0.443820i | \(-0.853623\pi\) | ||||
−0.896116 | + | 0.443820i | \(0.853623\pi\) | |||||||
\(80\) | 15.1612 | 1.69507 | ||||||||
\(81\) | −7.55855 | −0.839839 | ||||||||
\(82\) | −13.0011 | −1.43573 | ||||||||
\(83\) | −14.6721 | −1.61047 | −0.805237 | − | 0.592953i | \(-0.797962\pi\) | ||||
−0.805237 | + | 0.592953i | \(0.797962\pi\) | |||||||
\(84\) | 6.35312 | 0.693182 | ||||||||
\(85\) | −7.03868 | −0.763452 | ||||||||
\(86\) | 4.31571 | 0.465375 | ||||||||
\(87\) | −0.236345 | −0.0253388 | ||||||||
\(88\) | −26.8292 | −2.86000 | ||||||||
\(89\) | −12.5202 | −1.32714 | −0.663571 | − | 0.748113i | \(-0.730960\pi\) | ||||
−0.663571 | + | 0.748113i | \(0.730960\pi\) | |||||||
\(90\) | 4.16866 | 0.439416 | ||||||||
\(91\) | 3.03148 | 0.317785 | ||||||||
\(92\) | 7.84039 | 0.817417 | ||||||||
\(93\) | 13.3367 | 1.38295 | ||||||||
\(94\) | −29.2156 | −3.01336 | ||||||||
\(95\) | 19.0832 | 1.95790 | ||||||||
\(96\) | 0.677766 | 0.0691742 | ||||||||
\(97\) | −3.70267 | −0.375949 | −0.187975 | − | 0.982174i | \(-0.560192\pi\) | ||||
−0.187975 | + | 0.982174i | \(0.560192\pi\) | |||||||
\(98\) | −2.44055 | −0.246533 | ||||||||
\(99\) | −2.36752 | −0.237944 | ||||||||
\(100\) | 45.2457 | 4.52457 | ||||||||
\(101\) | 3.97789 | 0.395815 | 0.197907 | − | 0.980221i | \(-0.436585\pi\) | ||||
0.197907 | + | 0.980221i | \(0.436585\pi\) | |||||||
\(102\) | 6.80417 | 0.673713 | ||||||||
\(103\) | −7.90372 | −0.778777 | −0.389388 | − | 0.921074i | \(-0.627314\pi\) | ||||
−0.389388 | + | 0.921074i | \(0.627314\pi\) | |||||||
\(104\) | −14.4735 | −1.41925 | ||||||||
\(105\) | 6.51032 | 0.635342 | ||||||||
\(106\) | 0.624048 | 0.0606129 | ||||||||
\(107\) | −13.1151 | −1.26788 | −0.633940 | − | 0.773382i | \(-0.718564\pi\) | ||||
−0.633940 | + | 0.773382i | \(0.718564\pi\) | |||||||
\(108\) | −21.7360 | −2.09155 | ||||||||
\(109\) | 9.17631 | 0.878931 | 0.439465 | − | 0.898260i | \(-0.355168\pi\) | ||||
0.439465 | + | 0.898260i | \(0.355168\pi\) | |||||||
\(110\) | −55.6004 | −5.30129 | ||||||||
\(111\) | −8.44044 | −0.801131 | ||||||||
\(112\) | 3.73964 | 0.353362 | ||||||||
\(113\) | 11.5599 | 1.08746 | 0.543732 | − | 0.839259i | \(-0.317011\pi\) | ||||
0.543732 | + | 0.839259i | \(0.317011\pi\) | |||||||
\(114\) | −18.4474 | −1.72776 | ||||||||
\(115\) | 8.03440 | 0.749211 | ||||||||
\(116\) | −0.582283 | −0.0540636 | ||||||||
\(117\) | −1.27720 | −0.118077 | ||||||||
\(118\) | 20.8082 | 1.91555 | ||||||||
\(119\) | −1.73615 | −0.159153 | ||||||||
\(120\) | −31.0830 | −2.83748 | ||||||||
\(121\) | 20.5772 | 1.87066 | ||||||||
\(122\) | 29.4082 | 2.66249 | ||||||||
\(123\) | 8.55444 | 0.771328 | ||||||||
\(124\) | 32.8576 | 2.95070 | ||||||||
\(125\) | 26.0943 | 2.33395 | ||||||||
\(126\) | 1.02824 | 0.0916027 | ||||||||
\(127\) | 9.77573 | 0.867455 | 0.433728 | − | 0.901044i | \(-0.357198\pi\) | ||||
0.433728 | + | 0.901044i | \(0.357198\pi\) | |||||||
\(128\) | 19.9234 | 1.76099 | ||||||||
\(129\) | −2.83964 | −0.250016 | ||||||||
\(130\) | −29.9947 | −2.63071 | ||||||||
\(131\) | −10.8149 | −0.944903 | −0.472451 | − | 0.881357i | \(-0.656631\pi\) | ||||
−0.472451 | + | 0.881357i | \(0.656631\pi\) | |||||||
\(132\) | 35.7005 | 3.10733 | ||||||||
\(133\) | 4.70704 | 0.408152 | ||||||||
\(134\) | −17.5743 | −1.51819 | ||||||||
\(135\) | −22.2739 | −1.91703 | ||||||||
\(136\) | 8.28912 | 0.710786 | ||||||||
\(137\) | −11.8746 | −1.01451 | −0.507256 | − | 0.861795i | \(-0.669340\pi\) | ||||
−0.507256 | + | 0.861795i | \(0.669340\pi\) | |||||||
\(138\) | −7.76671 | −0.661146 | ||||||||
\(139\) | −18.2040 | −1.54405 | −0.772024 | − | 0.635594i | \(-0.780755\pi\) | ||||
−0.772024 | + | 0.635594i | \(0.780755\pi\) | |||||||
\(140\) | 16.0395 | 1.35559 | ||||||||
\(141\) | 19.2232 | 1.61889 | ||||||||
\(142\) | 18.5795 | 1.55916 | ||||||||
\(143\) | 17.0350 | 1.42454 | ||||||||
\(144\) | −1.57556 | −0.131297 | ||||||||
\(145\) | −0.596691 | −0.0495525 | ||||||||
\(146\) | −5.43276 | −0.449618 | ||||||||
\(147\) | 1.60583 | 0.132447 | ||||||||
\(148\) | −20.7947 | −1.70932 | ||||||||
\(149\) | −14.5101 | −1.18872 | −0.594359 | − | 0.804200i | \(-0.702594\pi\) | ||||
−0.594359 | + | 0.804200i | \(0.702594\pi\) | |||||||
\(150\) | −44.8204 | −3.65957 | ||||||||
\(151\) | −1.80705 | −0.147056 | −0.0735278 | − | 0.997293i | \(-0.523426\pi\) | ||||
−0.0735278 | + | 0.997293i | \(0.523426\pi\) | |||||||
\(152\) | −22.4734 | −1.82283 | ||||||||
\(153\) | 0.731465 | 0.0591355 | ||||||||
\(154\) | −13.7143 | −1.10513 | ||||||||
\(155\) | 33.6707 | 2.70449 | ||||||||
\(156\) | 19.2593 | 1.54198 | ||||||||
\(157\) | 6.75914 | 0.539438 | 0.269719 | − | 0.962939i | \(-0.413069\pi\) | ||||
0.269719 | + | 0.962939i | \(0.413069\pi\) | |||||||
\(158\) | 38.8773 | 3.09291 | ||||||||
\(159\) | −0.410610 | −0.0325635 | ||||||||
\(160\) | 1.71113 | 0.135277 | ||||||||
\(161\) | 1.98175 | 0.156184 | ||||||||
\(162\) | 18.4470 | 1.44934 | ||||||||
\(163\) | −9.12240 | −0.714521 | −0.357261 | − | 0.934005i | \(-0.616289\pi\) | ||||
−0.357261 | + | 0.934005i | \(0.616289\pi\) | |||||||
\(164\) | 21.0756 | 1.64573 | ||||||||
\(165\) | 36.5839 | 2.84805 | ||||||||
\(166\) | 35.8080 | 2.77924 | ||||||||
\(167\) | −4.60013 | −0.355969 | −0.177984 | − | 0.984033i | \(-0.556958\pi\) | ||||
−0.177984 | + | 0.984033i | \(0.556958\pi\) | |||||||
\(168\) | −7.66690 | −0.591514 | ||||||||
\(169\) | −3.81015 | −0.293089 | ||||||||
\(170\) | 17.1783 | 1.31751 | ||||||||
\(171\) | −1.98314 | −0.151655 | ||||||||
\(172\) | −6.99604 | −0.533443 | ||||||||
\(173\) | 22.6611 | 1.72289 | 0.861446 | − | 0.507849i | \(-0.169559\pi\) | ||||
0.861446 | + | 0.507849i | \(0.169559\pi\) | |||||||
\(174\) | 0.576811 | 0.0437279 | ||||||||
\(175\) | 11.4364 | 0.864510 | ||||||||
\(176\) | 21.0144 | 1.58402 | ||||||||
\(177\) | −13.6914 | −1.02911 | ||||||||
\(178\) | 30.5563 | 2.29029 | ||||||||
\(179\) | 8.88782 | 0.664307 | 0.332153 | − | 0.943225i | \(-0.392225\pi\) | ||||
0.332153 | + | 0.943225i | \(0.392225\pi\) | |||||||
\(180\) | −6.75767 | −0.503687 | ||||||||
\(181\) | 20.6924 | 1.53805 | 0.769026 | − | 0.639218i | \(-0.220742\pi\) | ||||
0.769026 | + | 0.639218i | \(0.220742\pi\) | |||||||
\(182\) | −7.39847 | −0.548411 | ||||||||
\(183\) | −19.3499 | −1.43039 | ||||||||
\(184\) | −9.46173 | −0.697528 | ||||||||
\(185\) | −21.3093 | −1.56669 | ||||||||
\(186\) | −32.5488 | −2.38660 | ||||||||
\(187\) | −9.75607 | −0.713435 | ||||||||
\(188\) | 47.3603 | 3.45411 | ||||||||
\(189\) | −5.49404 | −0.399633 | ||||||||
\(190\) | −46.5735 | −3.37880 | ||||||||
\(191\) | −4.63599 | −0.335449 | −0.167724 | − | 0.985834i | \(-0.553642\pi\) | ||||
−0.167724 | + | 0.985834i | \(0.553642\pi\) | |||||||
\(192\) | −13.6646 | −0.986154 | ||||||||
\(193\) | −7.66220 | −0.551537 | −0.275769 | − | 0.961224i | \(-0.588932\pi\) | ||||
−0.275769 | + | 0.961224i | \(0.588932\pi\) | |||||||
\(194\) | 9.03655 | 0.648787 | ||||||||
\(195\) | 19.7359 | 1.41332 | ||||||||
\(196\) | 3.95629 | 0.282592 | ||||||||
\(197\) | 0.587802 | 0.0418792 | 0.0209396 | − | 0.999781i | \(-0.493334\pi\) | ||||
0.0209396 | + | 0.999781i | \(0.493334\pi\) | |||||||
\(198\) | 5.77804 | 0.410628 | ||||||||
\(199\) | −1.46974 | −0.104187 | −0.0520936 | − | 0.998642i | \(-0.516589\pi\) | ||||
−0.0520936 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(200\) | −54.6021 | −3.86095 | ||||||||
\(201\) | 11.5635 | 0.815628 | ||||||||
\(202\) | −9.70824 | −0.683070 | ||||||||
\(203\) | −0.147179 | −0.0103300 | ||||||||
\(204\) | −11.0300 | −0.772254 | ||||||||
\(205\) | 21.5971 | 1.50841 | ||||||||
\(206\) | 19.2894 | 1.34396 | ||||||||
\(207\) | −0.834941 | −0.0580324 | ||||||||
\(208\) | 11.3366 | 0.786053 | ||||||||
\(209\) | 26.4506 | 1.82963 | ||||||||
\(210\) | −15.8888 | −1.09643 | ||||||||
\(211\) | −9.30602 | −0.640653 | −0.320326 | − | 0.947307i | \(-0.603793\pi\) | ||||
−0.320326 | + | 0.947307i | \(0.603793\pi\) | |||||||
\(212\) | −1.01162 | −0.0694785 | ||||||||
\(213\) | −12.2249 | −0.837637 | ||||||||
\(214\) | 32.0080 | 2.18802 | ||||||||
\(215\) | −7.16915 | −0.488932 | ||||||||
\(216\) | 26.2309 | 1.78478 | ||||||||
\(217\) | 8.30517 | 0.563792 | ||||||||
\(218\) | −22.3952 | −1.51680 | ||||||||
\(219\) | 3.57464 | 0.241551 | ||||||||
\(220\) | 90.1318 | 6.07669 | ||||||||
\(221\) | −5.26311 | −0.354035 | ||||||||
\(222\) | 20.5993 | 1.38254 | ||||||||
\(223\) | −11.7599 | −0.787503 | −0.393751 | − | 0.919217i | \(-0.628823\pi\) | ||||
−0.393751 | + | 0.919217i | \(0.628823\pi\) | |||||||
\(224\) | 0.422066 | 0.0282005 | ||||||||
\(225\) | −4.81831 | −0.321221 | ||||||||
\(226\) | −28.2125 | −1.87667 | ||||||||
\(227\) | 5.14725 | 0.341635 | 0.170817 | − | 0.985303i | \(-0.445359\pi\) | ||||
0.170817 | + | 0.985303i | \(0.445359\pi\) | |||||||
\(228\) | 29.9044 | 1.98047 | ||||||||
\(229\) | −18.9903 | −1.25492 | −0.627458 | − | 0.778650i | \(-0.715905\pi\) | ||||
−0.627458 | + | 0.778650i | \(0.715905\pi\) | |||||||
\(230\) | −19.6084 | −1.29294 | ||||||||
\(231\) | 9.02374 | 0.593718 | ||||||||
\(232\) | 0.702695 | 0.0461342 | ||||||||
\(233\) | 25.2766 | 1.65593 | 0.827963 | − | 0.560783i | \(-0.189500\pi\) | ||||
0.827963 | + | 0.560783i | \(0.189500\pi\) | |||||||
\(234\) | 3.11708 | 0.203770 | ||||||||
\(235\) | 48.5322 | 3.16589 | ||||||||
\(236\) | −33.7315 | −2.19573 | ||||||||
\(237\) | −25.5804 | −1.66162 | ||||||||
\(238\) | 4.23717 | 0.274655 | ||||||||
\(239\) | −19.9839 | −1.29265 | −0.646324 | − | 0.763063i | \(-0.723695\pi\) | ||||
−0.646324 | + | 0.763063i | \(0.723695\pi\) | |||||||
\(240\) | 24.3462 | 1.57154 | ||||||||
\(241\) | 11.3576 | 0.731609 | 0.365804 | − | 0.930692i | \(-0.380794\pi\) | ||||
0.365804 | + | 0.930692i | \(0.380794\pi\) | |||||||
\(242\) | −50.2198 | −3.22825 | ||||||||
\(243\) | 4.34439 | 0.278693 | ||||||||
\(244\) | −47.6726 | −3.05192 | ||||||||
\(245\) | 4.05418 | 0.259012 | ||||||||
\(246\) | −20.8775 | −1.33110 | ||||||||
\(247\) | 14.2693 | 0.907933 | ||||||||
\(248\) | −39.6524 | −2.51793 | ||||||||
\(249\) | −23.5609 | −1.49311 | ||||||||
\(250\) | −63.6845 | −4.02776 | ||||||||
\(251\) | −14.4867 | −0.914390 | −0.457195 | − | 0.889367i | \(-0.651146\pi\) | ||||
−0.457195 | + | 0.889367i | \(0.651146\pi\) | |||||||
\(252\) | −1.66684 | −0.105001 | ||||||||
\(253\) | 11.1362 | 0.700127 | ||||||||
\(254\) | −23.8582 | −1.49699 | ||||||||
\(255\) | −11.3029 | −0.707816 | ||||||||
\(256\) | −31.6053 | −1.97533 | ||||||||
\(257\) | 27.0966 | 1.69024 | 0.845119 | − | 0.534578i | \(-0.179529\pi\) | ||||
0.845119 | + | 0.534578i | \(0.179529\pi\) | |||||||
\(258\) | 6.93029 | 0.431461 | ||||||||
\(259\) | −5.25613 | −0.326600 | ||||||||
\(260\) | 48.6234 | 3.01549 | ||||||||
\(261\) | 0.0620086 | 0.00383824 | ||||||||
\(262\) | 26.3943 | 1.63065 | ||||||||
\(263\) | −5.58167 | −0.344180 | −0.172090 | − | 0.985081i | \(-0.555052\pi\) | ||||
−0.172090 | + | 0.985081i | \(0.555052\pi\) | |||||||
\(264\) | −43.0831 | −2.65158 | ||||||||
\(265\) | −1.03665 | −0.0636811 | ||||||||
\(266\) | −11.4878 | −0.704361 | ||||||||
\(267\) | −20.1054 | −1.23043 | ||||||||
\(268\) | 28.4891 | 1.74025 | ||||||||
\(269\) | 8.84328 | 0.539185 | 0.269592 | − | 0.962975i | \(-0.413111\pi\) | ||||
0.269592 | + | 0.962975i | \(0.413111\pi\) | |||||||
\(270\) | 54.3605 | 3.30827 | ||||||||
\(271\) | 0.0306869 | 0.00186410 | 0.000932049 | − | 1.00000i | \(-0.499703\pi\) | ||||
0.000932049 | 1.00000i | \(0.499703\pi\) | ||||||||
\(272\) | −6.49258 | −0.393671 | ||||||||
\(273\) | 4.86803 | 0.294627 | ||||||||
\(274\) | 28.9805 | 1.75077 | ||||||||
\(275\) | 64.2653 | 3.87534 | ||||||||
\(276\) | 12.5903 | 0.757849 | ||||||||
\(277\) | −16.9180 | −1.01650 | −0.508252 | − | 0.861208i | \(-0.669708\pi\) | ||||
−0.508252 | + | 0.861208i | \(0.669708\pi\) | |||||||
\(278\) | 44.4279 | 2.66461 | ||||||||
\(279\) | −3.49908 | −0.209485 | ||||||||
\(280\) | −19.3564 | −1.15676 | ||||||||
\(281\) | −30.8942 | −1.84299 | −0.921497 | − | 0.388386i | \(-0.873033\pi\) | ||||
−0.921497 | + | 0.388386i | \(0.873033\pi\) | |||||||
\(282\) | −46.9152 | −2.79376 | ||||||||
\(283\) | −15.3016 | −0.909586 | −0.454793 | − | 0.890597i | \(-0.650287\pi\) | ||||
−0.454793 | + | 0.890597i | \(0.650287\pi\) | |||||||
\(284\) | −30.1186 | −1.78721 | ||||||||
\(285\) | 30.6444 | 1.81522 | ||||||||
\(286\) | −41.5747 | −2.45836 | ||||||||
\(287\) | 5.32712 | 0.314450 | ||||||||
\(288\) | −0.177822 | −0.0104783 | ||||||||
\(289\) | −13.9858 | −0.822693 | ||||||||
\(290\) | 1.45626 | 0.0855142 | ||||||||
\(291\) | −5.94585 | −0.348552 | ||||||||
\(292\) | 8.80685 | 0.515382 | ||||||||
\(293\) | −19.7498 | −1.15380 | −0.576899 | − | 0.816816i | \(-0.695737\pi\) | ||||
−0.576899 | + | 0.816816i | \(0.695737\pi\) | |||||||
\(294\) | −3.91911 | −0.228567 | ||||||||
\(295\) | −34.5661 | −2.01252 | ||||||||
\(296\) | 25.0949 | 1.45861 | ||||||||
\(297\) | −30.8730 | −1.79143 | ||||||||
\(298\) | 35.4127 | 2.05140 | ||||||||
\(299\) | 6.00764 | 0.347431 | ||||||||
\(300\) | 72.6568 | 4.19484 | ||||||||
\(301\) | −1.76833 | −0.101925 | ||||||||
\(302\) | 4.41020 | 0.253778 | ||||||||
\(303\) | 6.38781 | 0.366970 | ||||||||
\(304\) | 17.6026 | 1.00958 | ||||||||
\(305\) | −48.8522 | −2.79727 | ||||||||
\(306\) | −1.78518 | −0.102052 | ||||||||
\(307\) | 9.43508 | 0.538488 | 0.269244 | − | 0.963072i | \(-0.413226\pi\) | ||||
0.269244 | + | 0.963072i | \(0.413226\pi\) | |||||||
\(308\) | 22.2318 | 1.26678 | ||||||||
\(309\) | −12.6920 | −0.722024 | ||||||||
\(310\) | −82.1750 | −4.66723 | ||||||||
\(311\) | 6.10976 | 0.346453 | 0.173226 | − | 0.984882i | \(-0.444581\pi\) | ||||
0.173226 | + | 0.984882i | \(0.444581\pi\) | |||||||
\(312\) | −23.2420 | −1.31582 | ||||||||
\(313\) | −8.89970 | −0.503041 | −0.251520 | − | 0.967852i | \(-0.580931\pi\) | ||||
−0.251520 | + | 0.967852i | \(0.580931\pi\) | |||||||
\(314\) | −16.4960 | −0.930925 | ||||||||
\(315\) | −1.70808 | −0.0962396 | ||||||||
\(316\) | −63.0225 | −3.54529 | ||||||||
\(317\) | −3.97682 | −0.223360 | −0.111680 | − | 0.993744i | \(-0.535623\pi\) | ||||
−0.111680 | + | 0.993744i | \(0.535623\pi\) | |||||||
\(318\) | 1.00211 | 0.0561958 | ||||||||
\(319\) | −0.827053 | −0.0463061 | ||||||||
\(320\) | −34.4984 | −1.92852 | ||||||||
\(321\) | −21.0605 | −1.17548 | ||||||||
\(322\) | −4.83657 | −0.269532 | ||||||||
\(323\) | −8.17215 | −0.454710 | ||||||||
\(324\) | −29.9038 | −1.66132 | ||||||||
\(325\) | 34.6692 | 1.92310 | ||||||||
\(326\) | 22.2637 | 1.23307 | ||||||||
\(327\) | 14.7356 | 0.814879 | ||||||||
\(328\) | −25.4339 | −1.40435 | ||||||||
\(329\) | 11.9709 | 0.659977 | ||||||||
\(330\) | −89.2848 | −4.91497 | ||||||||
\(331\) | 14.4699 | 0.795336 | 0.397668 | − | 0.917529i | \(-0.369820\pi\) | ||||
0.397668 | + | 0.917529i | \(0.369820\pi\) | |||||||
\(332\) | −58.0471 | −3.18575 | ||||||||
\(333\) | 2.21448 | 0.121353 | ||||||||
\(334\) | 11.2269 | 0.614306 | ||||||||
\(335\) | 29.1940 | 1.59504 | ||||||||
\(336\) | 6.00522 | 0.327611 | ||||||||
\(337\) | 12.5830 | 0.685442 | 0.342721 | − | 0.939437i | \(-0.388652\pi\) | ||||
0.342721 | + | 0.939437i | \(0.388652\pi\) | |||||||
\(338\) | 9.29888 | 0.505792 | ||||||||
\(339\) | 18.5632 | 1.00822 | ||||||||
\(340\) | −27.8470 | −1.51022 | ||||||||
\(341\) | 46.6698 | 2.52731 | ||||||||
\(342\) | 4.83996 | 0.261715 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.44277 | 0.455203 | ||||||||
\(345\) | 12.9019 | 0.694613 | ||||||||
\(346\) | −55.3056 | −2.97325 | ||||||||
\(347\) | 3.30124 | 0.177220 | 0.0886100 | − | 0.996066i | \(-0.471758\pi\) | ||||
0.0886100 | + | 0.996066i | \(0.471758\pi\) | |||||||
\(348\) | −0.935047 | −0.0501238 | ||||||||
\(349\) | −3.61199 | −0.193345 | −0.0966726 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966726 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(350\) | −27.9111 | −1.49191 | ||||||||
\(351\) | −16.6551 | −0.888981 | ||||||||
\(352\) | 2.37174 | 0.126414 | ||||||||
\(353\) | 5.65269 | 0.300862 | 0.150431 | − | 0.988620i | \(-0.451934\pi\) | ||||
0.150431 | + | 0.988620i | \(0.451934\pi\) | |||||||
\(354\) | 33.4145 | 1.77596 | ||||||||
\(355\) | −30.8638 | −1.63808 | ||||||||
\(356\) | −49.5337 | −2.62528 | ||||||||
\(357\) | −2.78796 | −0.147555 | ||||||||
\(358\) | −21.6912 | −1.14641 | ||||||||
\(359\) | 17.4037 | 0.918531 | 0.459265 | − | 0.888299i | \(-0.348113\pi\) | ||||
0.459265 | + | 0.888299i | \(0.348113\pi\) | |||||||
\(360\) | 8.15511 | 0.429812 | ||||||||
\(361\) | 3.15626 | 0.166119 | ||||||||
\(362\) | −50.5008 | −2.65426 | ||||||||
\(363\) | 33.0435 | 1.73434 | ||||||||
\(364\) | 11.9934 | 0.628624 | ||||||||
\(365\) | 9.02476 | 0.472378 | ||||||||
\(366\) | 47.2245 | 2.46847 | ||||||||
\(367\) | −15.8799 | −0.828924 | −0.414462 | − | 0.910067i | \(-0.636030\pi\) | ||||
−0.414462 | + | 0.910067i | \(0.636030\pi\) | |||||||
\(368\) | 7.41104 | 0.386327 | ||||||||
\(369\) | −2.24439 | −0.116838 | ||||||||
\(370\) | 52.0064 | 2.70368 | ||||||||
\(371\) | −0.255700 | −0.0132753 | ||||||||
\(372\) | 52.7637 | 2.73567 | ||||||||
\(373\) | −26.8938 | −1.39251 | −0.696254 | − | 0.717795i | \(-0.745151\pi\) | ||||
−0.696254 | + | 0.717795i | \(0.745151\pi\) | |||||||
\(374\) | 23.8102 | 1.23120 | ||||||||
\(375\) | 41.9030 | 2.16386 | ||||||||
\(376\) | −57.1541 | −2.94750 | ||||||||
\(377\) | −0.446170 | −0.0229789 | ||||||||
\(378\) | 13.4085 | 0.689659 | ||||||||
\(379\) | −21.7543 | −1.11744 | −0.558722 | − | 0.829355i | \(-0.688708\pi\) | ||||
−0.558722 | + | 0.829355i | \(0.688708\pi\) | |||||||
\(380\) | 75.4987 | 3.87300 | ||||||||
\(381\) | 15.6981 | 0.804240 | ||||||||
\(382\) | 11.3144 | 0.578894 | ||||||||
\(383\) | 4.06617 | 0.207772 | 0.103886 | − | 0.994589i | \(-0.466872\pi\) | ||||
0.103886 | + | 0.994589i | \(0.466872\pi\) | |||||||
\(384\) | 31.9935 | 1.63266 | ||||||||
\(385\) | 22.7819 | 1.16107 | ||||||||
\(386\) | 18.7000 | 0.951804 | ||||||||
\(387\) | 0.745024 | 0.0378717 | ||||||||
\(388\) | −14.6488 | −0.743682 | ||||||||
\(389\) | −8.17657 | −0.414569 | −0.207284 | − | 0.978281i | \(-0.566463\pi\) | ||||
−0.207284 | + | 0.978281i | \(0.566463\pi\) | |||||||
\(390\) | −48.1664 | −2.43900 | ||||||||
\(391\) | −3.44063 | −0.174000 | ||||||||
\(392\) | −4.77442 | −0.241145 | ||||||||
\(393\) | −17.3669 | −0.876044 | ||||||||
\(394\) | −1.43456 | −0.0722721 | ||||||||
\(395\) | −64.5819 | −3.24947 | ||||||||
\(396\) | −9.36658 | −0.470688 | ||||||||
\(397\) | −34.1595 | −1.71442 | −0.857208 | − | 0.514970i | \(-0.827803\pi\) | ||||
−0.857208 | + | 0.514970i | \(0.827803\pi\) | |||||||
\(398\) | 3.58698 | 0.179799 | ||||||||
\(399\) | 7.55871 | 0.378409 | ||||||||
\(400\) | 42.7680 | 2.13840 | ||||||||
\(401\) | 29.7200 | 1.48415 | 0.742073 | − | 0.670320i | \(-0.233843\pi\) | ||||
0.742073 | + | 0.670320i | \(0.233843\pi\) | |||||||
\(402\) | −28.2214 | −1.40755 | ||||||||
\(403\) | 25.1769 | 1.25415 | ||||||||
\(404\) | 15.7377 | 0.782979 | ||||||||
\(405\) | −30.6438 | −1.52270 | ||||||||
\(406\) | 0.359198 | 0.0178267 | ||||||||
\(407\) | −29.5361 | −1.46405 | ||||||||
\(408\) | 13.3109 | 0.658988 | ||||||||
\(409\) | −17.3535 | −0.858073 | −0.429037 | − | 0.903287i | \(-0.641147\pi\) | ||||
−0.429037 | + | 0.903287i | \(0.641147\pi\) | |||||||
\(410\) | −52.7088 | −2.60310 | ||||||||
\(411\) | −19.0685 | −0.940580 | ||||||||
\(412\) | −31.2694 | −1.54053 | ||||||||
\(413\) | −8.52605 | −0.419539 | ||||||||
\(414\) | 2.03772 | 0.100148 | ||||||||
\(415\) | −59.4834 | −2.91993 | ||||||||
\(416\) | 1.27948 | 0.0627318 | ||||||||
\(417\) | −29.2326 | −1.43153 | ||||||||
\(418\) | −64.5540 | −3.15744 | ||||||||
\(419\) | 8.70836 | 0.425431 | 0.212716 | − | 0.977114i | \(-0.431769\pi\) | ||||
0.212716 | + | 0.977114i | \(0.431769\pi\) | |||||||
\(420\) | 25.7567 | 1.25680 | ||||||||
\(421\) | 13.3328 | 0.649802 | 0.324901 | − | 0.945748i | \(-0.394669\pi\) | ||||
0.324901 | + | 0.945748i | \(0.394669\pi\) | |||||||
\(422\) | 22.7118 | 1.10559 | ||||||||
\(423\) | −5.04351 | −0.245224 | ||||||||
\(424\) | 1.22082 | 0.0592882 | ||||||||
\(425\) | −19.8553 | −0.963125 | ||||||||
\(426\) | 29.8355 | 1.44553 | ||||||||
\(427\) | −12.0498 | −0.583132 | ||||||||
\(428\) | −51.8870 | −2.50805 | ||||||||
\(429\) | 27.3552 | 1.32072 | ||||||||
\(430\) | 17.4967 | 0.843764 | ||||||||
\(431\) | −21.4699 | −1.03417 | −0.517084 | − | 0.855934i | \(-0.672983\pi\) | ||||
−0.517084 | + | 0.855934i | \(0.672983\pi\) | |||||||
\(432\) | −20.5457 | −0.988507 | ||||||||
\(433\) | −29.6160 | −1.42325 | −0.711626 | − | 0.702559i | \(-0.752041\pi\) | ||||
−0.711626 | + | 0.702559i | \(0.752041\pi\) | |||||||
\(434\) | −20.2692 | −0.972952 | ||||||||
\(435\) | −0.958184 | −0.0459414 | ||||||||
\(436\) | 36.3041 | 1.73865 | ||||||||
\(437\) | 9.32821 | 0.446229 | ||||||||
\(438\) | −8.72408 | −0.416853 | ||||||||
\(439\) | 0.394740 | 0.0188399 | 0.00941995 | − | 0.999956i | \(-0.497001\pi\) | ||||
0.00941995 | + | 0.999956i | \(0.497001\pi\) | |||||||
\(440\) | −108.770 | −5.18543 | ||||||||
\(441\) | −0.421314 | −0.0200626 | ||||||||
\(442\) | 12.8449 | 0.610968 | ||||||||
\(443\) | −4.66698 | −0.221735 | −0.110868 | − | 0.993835i | \(-0.535363\pi\) | ||||
−0.110868 | + | 0.993835i | \(0.535363\pi\) | |||||||
\(444\) | −33.3928 | −1.58475 | ||||||||
\(445\) | −50.7593 | −2.40622 | ||||||||
\(446\) | 28.7007 | 1.35902 | ||||||||
\(447\) | −23.3008 | −1.10209 | ||||||||
\(448\) | −8.50935 | −0.402029 | ||||||||
\(449\) | −8.10122 | −0.382320 | −0.191160 | − | 0.981559i | \(-0.561225\pi\) | ||||
−0.191160 | + | 0.981559i | \(0.561225\pi\) | |||||||
\(450\) | 11.7593 | 0.554340 | ||||||||
\(451\) | 29.9350 | 1.40958 | ||||||||
\(452\) | 45.7343 | 2.15116 | ||||||||
\(453\) | −2.90181 | −0.136339 | ||||||||
\(454\) | −12.5621 | −0.589570 | ||||||||
\(455\) | 12.2902 | 0.576171 | ||||||||
\(456\) | −36.0884 | −1.69000 | ||||||||
\(457\) | −1.73849 | −0.0813233 | −0.0406616 | − | 0.999173i | \(-0.512947\pi\) | ||||
−0.0406616 | + | 0.999173i | \(0.512947\pi\) | |||||||
\(458\) | 46.3469 | 2.16565 | ||||||||
\(459\) | 9.53850 | 0.445219 | ||||||||
\(460\) | 31.7864 | 1.48205 | ||||||||
\(461\) | −12.3136 | −0.573503 | −0.286751 | − | 0.958005i | \(-0.592575\pi\) | ||||
−0.286751 | + | 0.958005i | \(0.592575\pi\) | |||||||
\(462\) | −22.0229 | −1.02460 | ||||||||
\(463\) | 18.6885 | 0.868528 | 0.434264 | − | 0.900786i | \(-0.357008\pi\) | ||||
0.434264 | + | 0.900786i | \(0.357008\pi\) | |||||||
\(464\) | −0.550397 | −0.0255515 | ||||||||
\(465\) | 54.0693 | 2.50741 | ||||||||
\(466\) | −61.6888 | −2.85768 | ||||||||
\(467\) | 34.7687 | 1.60890 | 0.804452 | − | 0.594018i | \(-0.202459\pi\) | ||||
0.804452 | + | 0.594018i | \(0.202459\pi\) | |||||||
\(468\) | −5.05298 | −0.233574 | ||||||||
\(469\) | 7.20097 | 0.332510 | ||||||||
\(470\) | −118.445 | −5.46347 | ||||||||
\(471\) | 10.8540 | 0.500127 | ||||||||
\(472\) | 40.7069 | 1.87369 | ||||||||
\(473\) | −9.93691 | −0.456900 | ||||||||
\(474\) | 62.4302 | 2.86751 | ||||||||
\(475\) | 53.8316 | 2.46996 | ||||||||
\(476\) | −6.86872 | −0.314827 | ||||||||
\(477\) | 0.107730 | 0.00493261 | ||||||||
\(478\) | 48.7716 | 2.23076 | ||||||||
\(479\) | 6.58647 | 0.300943 | 0.150472 | − | 0.988614i | \(-0.451921\pi\) | ||||
0.150472 | + | 0.988614i | \(0.451921\pi\) | |||||||
\(480\) | 2.74779 | 0.125419 | ||||||||
\(481\) | −15.9338 | −0.726520 | ||||||||
\(482\) | −27.7189 | −1.26256 | ||||||||
\(483\) | 3.18236 | 0.144802 | ||||||||
\(484\) | 81.4095 | 3.70043 | ||||||||
\(485\) | −15.0113 | −0.681628 | ||||||||
\(486\) | −10.6027 | −0.480949 | ||||||||
\(487\) | 27.9890 | 1.26830 | 0.634151 | − | 0.773209i | \(-0.281350\pi\) | ||||
0.634151 | + | 0.773209i | \(0.281350\pi\) | |||||||
\(488\) | 57.5309 | 2.60430 | ||||||||
\(489\) | −14.6490 | −0.662451 | ||||||||
\(490\) | −9.89444 | −0.446985 | ||||||||
\(491\) | 20.0508 | 0.904879 | 0.452439 | − | 0.891795i | \(-0.350554\pi\) | ||||
0.452439 | + | 0.891795i | \(0.350554\pi\) | |||||||
\(492\) | 33.8438 | 1.52580 | ||||||||
\(493\) | 0.255526 | 0.0115083 | ||||||||
\(494\) | −34.8249 | −1.56685 | ||||||||
\(495\) | −9.59834 | −0.431413 | ||||||||
\(496\) | 31.0583 | 1.39456 | ||||||||
\(497\) | −7.61283 | −0.341482 | ||||||||
\(498\) | 57.5016 | 2.57671 | ||||||||
\(499\) | 26.2190 | 1.17372 | 0.586862 | − | 0.809687i | \(-0.300363\pi\) | ||||
0.586862 | + | 0.809687i | \(0.300363\pi\) | |||||||
\(500\) | 103.237 | 4.61688 | ||||||||
\(501\) | −7.38702 | −0.330028 | ||||||||
\(502\) | 35.3554 | 1.57799 | ||||||||
\(503\) | 9.09643 | 0.405590 | 0.202795 | − | 0.979221i | \(-0.434998\pi\) | ||||
0.202795 | + | 0.979221i | \(0.434998\pi\) | |||||||
\(504\) | 2.01153 | 0.0896006 | ||||||||
\(505\) | 16.1271 | 0.717646 | ||||||||
\(506\) | −27.1785 | −1.20823 | ||||||||
\(507\) | −6.11846 | −0.271730 | ||||||||
\(508\) | 38.6756 | 1.71595 | ||||||||
\(509\) | 41.2330 | 1.82762 | 0.913811 | − | 0.406140i | \(-0.133126\pi\) | ||||
0.913811 | + | 0.406140i | \(0.133126\pi\) | |||||||
\(510\) | 27.5853 | 1.22150 | ||||||||
\(511\) | 2.22604 | 0.0984741 | ||||||||
\(512\) | 37.2876 | 1.64789 | ||||||||
\(513\) | −25.8607 | −1.14178 | ||||||||
\(514\) | −66.1306 | −2.91690 | ||||||||
\(515\) | −32.0431 | −1.41199 | ||||||||
\(516\) | −11.2344 | −0.494569 | ||||||||
\(517\) | 67.2688 | 2.95848 | ||||||||
\(518\) | 12.8278 | 0.563623 | ||||||||
\(519\) | 36.3899 | 1.59734 | ||||||||
\(520\) | −58.6784 | −2.57322 | ||||||||
\(521\) | 12.1497 | 0.532288 | 0.266144 | − | 0.963933i | \(-0.414250\pi\) | ||||
0.266144 | + | 0.963933i | \(0.414250\pi\) | |||||||
\(522\) | −0.151335 | −0.00662376 | ||||||||
\(523\) | 26.9739 | 1.17948 | 0.589742 | − | 0.807591i | \(-0.299229\pi\) | ||||
0.589742 | + | 0.807591i | \(0.299229\pi\) | |||||||
\(524\) | −42.7869 | −1.86915 | ||||||||
\(525\) | 18.3649 | 0.801510 | ||||||||
\(526\) | 13.6223 | 0.593962 | ||||||||
\(527\) | −14.4190 | −0.628103 | ||||||||
\(528\) | 33.7455 | 1.46858 | ||||||||
\(529\) | −19.0726 | −0.829246 | ||||||||
\(530\) | 2.53001 | 0.109896 | ||||||||
\(531\) | 3.59214 | 0.155886 | ||||||||
\(532\) | 18.6224 | 0.807384 | ||||||||
\(533\) | 16.1490 | 0.699492 | ||||||||
\(534\) | 49.0681 | 2.12339 | ||||||||
\(535\) | −53.1709 | −2.29878 | ||||||||
\(536\) | −34.3805 | −1.48501 | ||||||||
\(537\) | 14.2723 | 0.615896 | ||||||||
\(538\) | −21.5825 | −0.930487 | ||||||||
\(539\) | 5.61936 | 0.242043 | ||||||||
\(540\) | −88.1218 | −3.79216 | ||||||||
\(541\) | −1.52981 | −0.0657715 | −0.0328858 | − | 0.999459i | \(-0.510470\pi\) | ||||
−0.0328858 | + | 0.999459i | \(0.510470\pi\) | |||||||
\(542\) | −0.0748930 | −0.00321693 | ||||||||
\(543\) | 33.2284 | 1.42597 | ||||||||
\(544\) | −0.732771 | −0.0314173 | ||||||||
\(545\) | 37.2024 | 1.59358 | ||||||||
\(546\) | −11.8807 | −0.508446 | ||||||||
\(547\) | 14.3993 | 0.615669 | 0.307835 | − | 0.951440i | \(-0.400396\pi\) | ||||
0.307835 | + | 0.951440i | \(0.400396\pi\) | |||||||
\(548\) | −46.9792 | −2.00685 | ||||||||
\(549\) | 5.07676 | 0.216671 | ||||||||
\(550\) | −156.843 | −6.68779 | ||||||||
\(551\) | −0.692779 | −0.0295134 | ||||||||
\(552\) | −15.1939 | −0.646696 | ||||||||
\(553\) | −15.9297 | −0.677400 | ||||||||
\(554\) | 41.2892 | 1.75421 | ||||||||
\(555\) | −34.2191 | −1.45252 | ||||||||
\(556\) | −72.0205 | −3.05435 | ||||||||
\(557\) | 33.3037 | 1.41112 | 0.705562 | − | 0.708648i | \(-0.250695\pi\) | ||||
0.705562 | + | 0.708648i | \(0.250695\pi\) | |||||||
\(558\) | 8.53969 | 0.361514 | ||||||||
\(559\) | −5.36066 | −0.226732 | ||||||||
\(560\) | 15.1612 | 0.640676 | ||||||||
\(561\) | −15.6666 | −0.661444 | ||||||||
\(562\) | 75.3989 | 3.18051 | ||||||||
\(563\) | 37.7490 | 1.59093 | 0.795464 | − | 0.606000i | \(-0.207227\pi\) | ||||
0.795464 | + | 0.606000i | \(0.207227\pi\) | |||||||
\(564\) | 76.0525 | 3.20239 | ||||||||
\(565\) | 46.8660 | 1.97167 | ||||||||
\(566\) | 37.3444 | 1.56970 | ||||||||
\(567\) | −7.55855 | −0.317429 | ||||||||
\(568\) | 36.3469 | 1.52508 | ||||||||
\(569\) | −18.4976 | −0.775459 | −0.387730 | − | 0.921773i | \(-0.626741\pi\) | ||||
−0.387730 | + | 0.921773i | \(0.626741\pi\) | |||||||
\(570\) | −74.7891 | −3.13257 | ||||||||
\(571\) | −43.4542 | −1.81850 | −0.909251 | − | 0.416249i | \(-0.863344\pi\) | ||||
−0.909251 | + | 0.416249i | \(0.863344\pi\) | |||||||
\(572\) | 67.3952 | 2.81794 | ||||||||
\(573\) | −7.44461 | −0.311003 | ||||||||
\(574\) | −13.0011 | −0.542656 | ||||||||
\(575\) | 22.6641 | 0.945160 | ||||||||
\(576\) | 3.58511 | 0.149379 | ||||||||
\(577\) | −10.6079 | −0.441612 | −0.220806 | − | 0.975318i | \(-0.570869\pi\) | ||||
−0.220806 | + | 0.975318i | \(0.570869\pi\) | |||||||
\(578\) | 34.1330 | 1.41975 | ||||||||
\(579\) | −12.3042 | −0.511344 | ||||||||
\(580\) | −2.36068 | −0.0980220 | ||||||||
\(581\) | −14.6721 | −0.608702 | ||||||||
\(582\) | 14.5112 | 0.601507 | ||||||||
\(583\) | −1.43687 | −0.0595091 | ||||||||
\(584\) | −10.6280 | −0.439791 | ||||||||
\(585\) | −5.17801 | −0.214085 | ||||||||
\(586\) | 48.2005 | 1.99114 | ||||||||
\(587\) | −19.0583 | −0.786620 | −0.393310 | − | 0.919406i | \(-0.628670\pi\) | ||||
−0.393310 | + | 0.919406i | \(0.628670\pi\) | |||||||
\(588\) | 6.35312 | 0.261998 | ||||||||
\(589\) | 39.0928 | 1.61079 | ||||||||
\(590\) | 84.3604 | 3.47306 | ||||||||
\(591\) | 0.943909 | 0.0388272 | ||||||||
\(592\) | −19.6560 | −0.807857 | ||||||||
\(593\) | −5.81928 | −0.238969 | −0.119485 | − | 0.992836i | \(-0.538124\pi\) | ||||
−0.119485 | + | 0.992836i | \(0.538124\pi\) | |||||||
\(594\) | 75.3472 | 3.09153 | ||||||||
\(595\) | −7.03868 | −0.288558 | ||||||||
\(596\) | −57.4063 | −2.35145 | ||||||||
\(597\) | −2.36015 | −0.0965946 | ||||||||
\(598\) | −14.6620 | −0.599572 | ||||||||
\(599\) | −26.4097 | −1.07907 | −0.539535 | − | 0.841963i | \(-0.681400\pi\) | ||||
−0.539535 | + | 0.841963i | \(0.681400\pi\) | |||||||
\(600\) | −87.6817 | −3.57959 | ||||||||
\(601\) | −42.5034 | −1.73375 | −0.866876 | − | 0.498525i | \(-0.833875\pi\) | ||||
−0.866876 | + | 0.498525i | \(0.833875\pi\) | |||||||
\(602\) | 4.31571 | 0.175895 | ||||||||
\(603\) | −3.03387 | −0.123549 | ||||||||
\(604\) | −7.14921 | −0.290897 | ||||||||
\(605\) | 83.4239 | 3.39166 | ||||||||
\(606\) | −15.5898 | −0.633291 | ||||||||
\(607\) | −39.8934 | −1.61923 | −0.809613 | − | 0.586965i | \(-0.800323\pi\) | ||||
−0.809613 | + | 0.586965i | \(0.800323\pi\) | |||||||
\(608\) | 1.98668 | 0.0805706 | ||||||||
\(609\) | −0.236345 | −0.00957716 | ||||||||
\(610\) | 119.226 | 4.82733 | ||||||||
\(611\) | 36.2895 | 1.46812 | ||||||||
\(612\) | 2.89389 | 0.116978 | ||||||||
\(613\) | 11.3211 | 0.457256 | 0.228628 | − | 0.973514i | \(-0.426576\pi\) | ||||
0.228628 | + | 0.973514i | \(0.426576\pi\) | |||||||
\(614\) | −23.0268 | −0.929285 | ||||||||
\(615\) | 34.6813 | 1.39848 | ||||||||
\(616\) | −26.8292 | −1.08098 | ||||||||
\(617\) | 33.5516 | 1.35074 | 0.675369 | − | 0.737480i | \(-0.263984\pi\) | ||||
0.675369 | + | 0.737480i | \(0.263984\pi\) | |||||||
\(618\) | 30.9755 | 1.24602 | ||||||||
\(619\) | −6.65515 | −0.267493 | −0.133747 | − | 0.991016i | \(-0.542701\pi\) | ||||
−0.133747 | + | 0.991016i | \(0.542701\pi\) | |||||||
\(620\) | 133.211 | 5.34988 | ||||||||
\(621\) | −10.8878 | −0.436914 | ||||||||
\(622\) | −14.9112 | −0.597884 | ||||||||
\(623\) | −12.5202 | −0.501613 | ||||||||
\(624\) | 18.2047 | 0.728770 | ||||||||
\(625\) | 48.6092 | 1.94437 | ||||||||
\(626\) | 21.7202 | 0.868112 | ||||||||
\(627\) | 42.4751 | 1.69629 | ||||||||
\(628\) | 26.7411 | 1.06709 | ||||||||
\(629\) | 9.12544 | 0.363855 | ||||||||
\(630\) | 4.16866 | 0.166084 | ||||||||
\(631\) | 21.3981 | 0.851846 | 0.425923 | − | 0.904759i | \(-0.359949\pi\) | ||||
0.425923 | + | 0.904759i | \(0.359949\pi\) | |||||||
\(632\) | 76.0551 | 3.02531 | ||||||||
\(633\) | −14.9439 | −0.593966 | ||||||||
\(634\) | 9.70562 | 0.385460 | ||||||||
\(635\) | 39.6326 | 1.57277 | ||||||||
\(636\) | −1.62449 | −0.0644153 | ||||||||
\(637\) | 3.03148 | 0.120111 | ||||||||
\(638\) | 2.01847 | 0.0799118 | ||||||||
\(639\) | 3.20739 | 0.126883 | ||||||||
\(640\) | 80.7729 | 3.19283 | ||||||||
\(641\) | 38.6480 | 1.52650 | 0.763251 | − | 0.646102i | \(-0.223602\pi\) | ||||
0.763251 | + | 0.646102i | \(0.223602\pi\) | |||||||
\(642\) | 51.3993 | 2.02857 | ||||||||
\(643\) | 9.46299 | 0.373184 | 0.186592 | − | 0.982438i | \(-0.440256\pi\) | ||||
0.186592 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(644\) | 7.84039 | 0.308955 | ||||||||
\(645\) | −11.5124 | −0.453301 | ||||||||
\(646\) | 19.9445 | 0.784707 | ||||||||
\(647\) | 34.8896 | 1.37165 | 0.685825 | − | 0.727766i | \(-0.259441\pi\) | ||||
0.685825 | + | 0.727766i | \(0.259441\pi\) | |||||||
\(648\) | 36.0877 | 1.41766 | ||||||||
\(649\) | −47.9109 | −1.88067 | ||||||||
\(650\) | −84.6118 | −3.31875 | ||||||||
\(651\) | 13.3367 | 0.522706 | ||||||||
\(652\) | −36.0908 | −1.41343 | ||||||||
\(653\) | −11.0205 | −0.431264 | −0.215632 | − | 0.976475i | \(-0.569181\pi\) | ||||
−0.215632 | + | 0.976475i | \(0.569181\pi\) | |||||||
\(654\) | −35.9629 | −1.40626 | ||||||||
\(655\) | −43.8456 | −1.71319 | ||||||||
\(656\) | 19.9215 | 0.777803 | ||||||||
\(657\) | −0.937861 | −0.0365894 | ||||||||
\(658\) | −29.2156 | −1.13894 | ||||||||
\(659\) | 25.0437 | 0.975562 | 0.487781 | − | 0.872966i | \(-0.337806\pi\) | ||||
0.487781 | + | 0.872966i | \(0.337806\pi\) | |||||||
\(660\) | 144.736 | 5.63385 | ||||||||
\(661\) | 46.6718 | 1.81532 | 0.907662 | − | 0.419701i | \(-0.137865\pi\) | ||||
0.907662 | + | 0.419701i | \(0.137865\pi\) | |||||||
\(662\) | −35.3145 | −1.37254 | ||||||||
\(663\) | −8.45165 | −0.328235 | ||||||||
\(664\) | 70.0508 | 2.71850 | ||||||||
\(665\) | 19.0832 | 0.740015 | ||||||||
\(666\) | −5.40455 | −0.209422 | ||||||||
\(667\) | −0.291673 | −0.0112936 | ||||||||
\(668\) | −18.1994 | −0.704158 | ||||||||
\(669\) | −18.8844 | −0.730114 | ||||||||
\(670\) | −71.2496 | −2.75261 | ||||||||
\(671\) | −67.7123 | −2.61400 | ||||||||
\(672\) | 0.677766 | 0.0261454 | ||||||||
\(673\) | −37.9417 | −1.46255 | −0.731273 | − | 0.682085i | \(-0.761073\pi\) | ||||
−0.731273 | + | 0.682085i | \(0.761073\pi\) | |||||||
\(674\) | −30.7095 | −1.18289 | ||||||||
\(675\) | −62.8321 | −2.41841 | ||||||||
\(676\) | −15.0741 | −0.579772 | ||||||||
\(677\) | −4.47977 | −0.172171 | −0.0860857 | − | 0.996288i | \(-0.527436\pi\) | ||||
−0.0860857 | + | 0.996288i | \(0.527436\pi\) | |||||||
\(678\) | −45.3045 | −1.73991 | ||||||||
\(679\) | −3.70267 | −0.142095 | ||||||||
\(680\) | 33.6056 | 1.28872 | ||||||||
\(681\) | 8.26560 | 0.316738 | ||||||||
\(682\) | −113.900 | −4.36145 | ||||||||
\(683\) | 15.3383 | 0.586905 | 0.293452 | − | 0.955974i | \(-0.405196\pi\) | ||||
0.293452 | + | 0.955974i | \(0.405196\pi\) | |||||||
\(684\) | −7.84588 | −0.299995 | ||||||||
\(685\) | −48.1416 | −1.83940 | ||||||||
\(686\) | −2.44055 | −0.0931807 | ||||||||
\(687\) | −30.4952 | −1.16347 | ||||||||
\(688\) | −6.61292 | −0.252115 | ||||||||
\(689\) | −0.775148 | −0.0295308 | ||||||||
\(690\) | −31.4877 | −1.19871 | ||||||||
\(691\) | 30.9027 | 1.17560 | 0.587798 | − | 0.809008i | \(-0.299995\pi\) | ||||
0.587798 | + | 0.809008i | \(0.299995\pi\) | |||||||
\(692\) | 89.6539 | 3.40813 | ||||||||
\(693\) | −2.36752 | −0.0899345 | ||||||||
\(694\) | −8.05685 | −0.305834 | ||||||||
\(695\) | −73.8025 | −2.79949 | ||||||||
\(696\) | 1.12841 | 0.0427722 | ||||||||
\(697\) | −9.24869 | −0.350319 | ||||||||
\(698\) | 8.81524 | 0.333662 | ||||||||
\(699\) | 40.5899 | 1.53525 | ||||||||
\(700\) | 45.2457 | 1.71013 | ||||||||
\(701\) | 27.2746 | 1.03015 | 0.515074 | − | 0.857146i | \(-0.327764\pi\) | ||||
0.515074 | + | 0.857146i | \(0.327764\pi\) | |||||||
\(702\) | 40.6475 | 1.53414 | ||||||||
\(703\) | −24.7408 | −0.933118 | ||||||||
\(704\) | −47.8171 | −1.80218 | ||||||||
\(705\) | 77.9344 | 2.93518 | ||||||||
\(706\) | −13.7957 | −0.519207 | ||||||||
\(707\) | 3.97789 | 0.149604 | ||||||||
\(708\) | −54.1670 | −2.03572 | ||||||||
\(709\) | −7.72825 | −0.290240 | −0.145120 | − | 0.989414i | \(-0.546357\pi\) | ||||
−0.145120 | + | 0.989414i | \(0.546357\pi\) | |||||||
\(710\) | 75.3247 | 2.82689 | ||||||||
\(711\) | 6.71141 | 0.251697 | ||||||||
\(712\) | 59.7769 | 2.24023 | ||||||||
\(713\) | 16.4588 | 0.616387 | ||||||||
\(714\) | 6.80417 | 0.254640 | ||||||||
\(715\) | 69.0628 | 2.58280 | ||||||||
\(716\) | 35.1628 | 1.31409 | ||||||||
\(717\) | −32.0907 | −1.19845 | ||||||||
\(718\) | −42.4746 | −1.58514 | ||||||||
\(719\) | 1.76981 | 0.0660027 | 0.0330013 | − | 0.999455i | \(-0.489493\pi\) | ||||
0.0330013 | + | 0.999455i | \(0.489493\pi\) | |||||||
\(720\) | −6.38761 | −0.238052 | ||||||||
\(721\) | −7.90372 | −0.294350 | ||||||||
\(722\) | −7.70301 | −0.286676 | ||||||||
\(723\) | 18.2384 | 0.678293 | ||||||||
\(724\) | 81.8650 | 3.04249 | ||||||||
\(725\) | −1.68320 | −0.0625124 | ||||||||
\(726\) | −80.6444 | −2.99299 | ||||||||
\(727\) | −12.2925 | −0.455903 | −0.227951 | − | 0.973673i | \(-0.573203\pi\) | ||||
−0.227951 | + | 0.973673i | \(0.573203\pi\) | |||||||
\(728\) | −14.4735 | −0.536425 | ||||||||
\(729\) | 29.6520 | 1.09822 | ||||||||
\(730\) | −22.0254 | −0.815196 | ||||||||
\(731\) | 3.07010 | 0.113552 | ||||||||
\(732\) | −76.5540 | −2.82952 | ||||||||
\(733\) | −44.0270 | −1.62618 | −0.813088 | − | 0.582141i | \(-0.802215\pi\) | ||||
−0.813088 | + | 0.582141i | \(0.802215\pi\) | |||||||
\(734\) | 38.7557 | 1.43050 | ||||||||
\(735\) | 6.51032 | 0.240137 | ||||||||
\(736\) | 0.836431 | 0.0308313 | ||||||||
\(737\) | 40.4649 | 1.49054 | ||||||||
\(738\) | 5.47755 | 0.201631 | ||||||||
\(739\) | −7.22370 | −0.265728 | −0.132864 | − | 0.991134i | \(-0.542417\pi\) | ||||
−0.132864 | + | 0.991134i | \(0.542417\pi\) | |||||||
\(740\) | −84.3057 | −3.09914 | ||||||||
\(741\) | 22.9140 | 0.841768 | ||||||||
\(742\) | 0.624048 | 0.0229095 | ||||||||
\(743\) | 12.2947 | 0.451048 | 0.225524 | − | 0.974238i | \(-0.427591\pi\) | ||||
0.225524 | + | 0.974238i | \(0.427591\pi\) | |||||||
\(744\) | −63.6749 | −2.33443 | ||||||||
\(745\) | −58.8268 | −2.15525 | ||||||||
\(746\) | 65.6357 | 2.40309 | ||||||||
\(747\) | 6.18157 | 0.226172 | ||||||||
\(748\) | −38.5978 | −1.41128 | ||||||||
\(749\) | −13.1151 | −0.479214 | ||||||||
\(750\) | −102.266 | −3.73424 | ||||||||
\(751\) | 29.7606 | 1.08598 | 0.542990 | − | 0.839739i | \(-0.317292\pi\) | ||||
0.542990 | + | 0.839739i | \(0.317292\pi\) | |||||||
\(752\) | 44.7668 | 1.63248 | ||||||||
\(753\) | −23.2631 | −0.847754 | ||||||||
\(754\) | 1.08890 | 0.0396554 | ||||||||
\(755\) | −7.32611 | −0.266624 | ||||||||
\(756\) | −21.7360 | −0.790531 | ||||||||
\(757\) | 48.9921 | 1.78065 | 0.890324 | − | 0.455327i | \(-0.150478\pi\) | ||||
0.890324 | + | 0.455327i | \(0.150478\pi\) | |||||||
\(758\) | 53.0925 | 1.92841 | ||||||||
\(759\) | 17.8828 | 0.649106 | ||||||||
\(760\) | −91.1113 | −3.30495 | ||||||||
\(761\) | 17.4016 | 0.630806 | 0.315403 | − | 0.948958i | \(-0.397860\pi\) | ||||
0.315403 | + | 0.948958i | \(0.397860\pi\) | |||||||
\(762\) | −38.3121 | −1.38790 | ||||||||
\(763\) | 9.17631 | 0.332205 | ||||||||
\(764\) | −18.3413 | −0.663566 | ||||||||
\(765\) | 2.96549 | 0.107218 | ||||||||
\(766\) | −9.92370 | −0.358558 | ||||||||
\(767\) | −25.8465 | −0.933263 | ||||||||
\(768\) | −50.7527 | −1.83138 | ||||||||
\(769\) | −47.1929 | −1.70182 | −0.850909 | − | 0.525312i | \(-0.823948\pi\) | ||||
−0.850909 | + | 0.525312i | \(0.823948\pi\) | |||||||
\(770\) | −55.6004 | −2.00370 | ||||||||
\(771\) | 43.5125 | 1.56706 | ||||||||
\(772\) | −30.3139 | −1.09102 | ||||||||
\(773\) | −49.9860 | −1.79787 | −0.898936 | − | 0.438080i | \(-0.855659\pi\) | ||||
−0.898936 | + | 0.438080i | \(0.855659\pi\) | |||||||
\(774\) | −1.81827 | −0.0653563 | ||||||||
\(775\) | 94.9812 | 3.41183 | ||||||||
\(776\) | 17.6781 | 0.634607 | ||||||||
\(777\) | −8.44044 | −0.302799 | ||||||||
\(778\) | 19.9553 | 0.715434 | ||||||||
\(779\) | 25.0750 | 0.898404 | ||||||||
\(780\) | 78.0808 | 2.79574 | ||||||||
\(781\) | −42.7793 | −1.53076 | ||||||||
\(782\) | 8.39703 | 0.300277 | ||||||||
\(783\) | 0.808609 | 0.0288973 | ||||||||
\(784\) | 3.73964 | 0.133558 | ||||||||
\(785\) | 27.4028 | 0.978048 | ||||||||
\(786\) | 42.3848 | 1.51181 | ||||||||
\(787\) | −46.4030 | −1.65409 | −0.827044 | − | 0.562136i | \(-0.809980\pi\) | ||||
−0.827044 | + | 0.562136i | \(0.809980\pi\) | |||||||
\(788\) | 2.32551 | 0.0828430 | ||||||||
\(789\) | −8.96320 | −0.319099 | ||||||||
\(790\) | 157.615 | 5.60771 | ||||||||
\(791\) | 11.5599 | 0.411023 | ||||||||
\(792\) | 11.3035 | 0.401653 | ||||||||
\(793\) | −36.5287 | −1.29717 | ||||||||
\(794\) | 83.3680 | 2.95862 | ||||||||
\(795\) | −1.66469 | −0.0590404 | ||||||||
\(796\) | −5.81472 | −0.206097 | ||||||||
\(797\) | 54.7396 | 1.93898 | 0.969488 | − | 0.245140i | \(-0.0788338\pi\) | ||||
0.969488 | + | 0.245140i | \(0.0788338\pi\) | |||||||
\(798\) | −18.4474 | −0.653031 | ||||||||
\(799\) | −20.7833 | −0.735261 | ||||||||
\(800\) | 4.82691 | 0.170657 | ||||||||
\(801\) | 5.27495 | 0.186381 | ||||||||
\(802\) | −72.5331 | −2.56123 | ||||||||
\(803\) | 12.5089 | 0.441430 | ||||||||
\(804\) | 45.7486 | 1.61343 | ||||||||
\(805\) | 8.03440 | 0.283175 | ||||||||
\(806\) | −61.4455 | −2.16433 | ||||||||
\(807\) | 14.2008 | 0.499892 | ||||||||
\(808\) | −18.9921 | −0.668140 | ||||||||
\(809\) | −18.8141 | −0.661469 | −0.330735 | − | 0.943724i | \(-0.607296\pi\) | ||||
−0.330735 | + | 0.943724i | \(0.607296\pi\) | |||||||
\(810\) | 74.7876 | 2.62777 | ||||||||
\(811\) | −13.1392 | −0.461379 | −0.230689 | − | 0.973027i | \(-0.574098\pi\) | ||||
−0.230689 | + | 0.973027i | \(0.574098\pi\) | |||||||
\(812\) | −0.582283 | −0.0204341 | ||||||||
\(813\) | 0.0492779 | 0.00172825 | ||||||||
\(814\) | 72.0843 | 2.52655 | ||||||||
\(815\) | −36.9839 | −1.29549 | ||||||||
\(816\) | −10.4260 | −0.364982 | ||||||||
\(817\) | −8.32362 | −0.291207 | ||||||||
\(818\) | 42.3520 | 1.48080 | ||||||||
\(819\) | −1.27720 | −0.0446291 | ||||||||
\(820\) | 85.4444 | 2.98385 | ||||||||
\(821\) | −17.6974 | −0.617644 | −0.308822 | − | 0.951120i | \(-0.599935\pi\) | ||||
−0.308822 | + | 0.951120i | \(0.599935\pi\) | |||||||
\(822\) | 46.5377 | 1.62319 | ||||||||
\(823\) | −13.8177 | −0.481655 | −0.240827 | − | 0.970568i | \(-0.577419\pi\) | ||||
−0.240827 | + | 0.970568i | \(0.577419\pi\) | |||||||
\(824\) | 37.7357 | 1.31458 | ||||||||
\(825\) | 103.199 | 3.59293 | ||||||||
\(826\) | 20.8082 | 0.724012 | ||||||||
\(827\) | −2.30044 | −0.0799943 | −0.0399971 | − | 0.999200i | \(-0.512735\pi\) | ||||
−0.0399971 | + | 0.999200i | \(0.512735\pi\) | |||||||
\(828\) | −3.30327 | −0.114796 | ||||||||
\(829\) | 14.8132 | 0.514482 | 0.257241 | − | 0.966347i | \(-0.417187\pi\) | ||||
0.257241 | + | 0.966347i | \(0.417187\pi\) | |||||||
\(830\) | 145.172 | 5.03900 | ||||||||
\(831\) | −27.1674 | −0.942427 | ||||||||
\(832\) | −25.7959 | −0.894311 | ||||||||
\(833\) | −1.73615 | −0.0601541 | ||||||||
\(834\) | 71.3436 | 2.47043 | ||||||||
\(835\) | −18.6498 | −0.645402 | ||||||||
\(836\) | 104.646 | 3.61926 | ||||||||
\(837\) | −45.6290 | −1.57717 | ||||||||
\(838\) | −21.2532 | −0.734179 | ||||||||
\(839\) | 2.15298 | 0.0743292 | 0.0371646 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371646 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(840\) | −31.0830 | −1.07247 | ||||||||
\(841\) | −28.9783 | −0.999253 | ||||||||
\(842\) | −32.5394 | −1.12138 | ||||||||
\(843\) | −49.6108 | −1.70869 | ||||||||
\(844\) | −36.8173 | −1.26730 | ||||||||
\(845\) | −15.4471 | −0.531395 | ||||||||
\(846\) | 12.3089 | 0.423190 | ||||||||
\(847\) | 20.5772 | 0.707042 | ||||||||
\(848\) | −0.956224 | −0.0328369 | ||||||||
\(849\) | −24.5718 | −0.843301 | ||||||||
\(850\) | 48.4579 | 1.66209 | ||||||||
\(851\) | −10.4164 | −0.357068 | ||||||||
\(852\) | −48.3652 | −1.65697 | ||||||||
\(853\) | 32.7125 | 1.12006 | 0.560028 | − | 0.828474i | \(-0.310791\pi\) | ||||
0.560028 | + | 0.828474i | \(0.310791\pi\) | |||||||
\(854\) | 29.4082 | 1.00633 | ||||||||
\(855\) | −8.04002 | −0.274963 | ||||||||
\(856\) | 62.6168 | 2.14020 | ||||||||
\(857\) | −28.9878 | −0.990204 | −0.495102 | − | 0.868835i | \(-0.664869\pi\) | ||||
−0.495102 | + | 0.868835i | \(0.664869\pi\) | |||||||
\(858\) | −66.7618 | −2.27921 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | −28.3632 | −0.967177 | ||||||||
\(861\) | 8.55444 | 0.291535 | ||||||||
\(862\) | 52.3984 | 1.78470 | ||||||||
\(863\) | 46.8259 | 1.59397 | 0.796985 | − | 0.603999i | \(-0.206427\pi\) | ||||
0.796985 | + | 0.603999i | \(0.206427\pi\) | |||||||
\(864\) | −2.31885 | −0.0788889 | ||||||||
\(865\) | 91.8723 | 3.12375 | ||||||||
\(866\) | 72.2792 | 2.45615 | ||||||||
\(867\) | −22.4588 | −0.762739 | ||||||||
\(868\) | 32.8576 | 1.11526 | ||||||||
\(869\) | −89.5148 | −3.03658 | ||||||||
\(870\) | 2.33850 | 0.0792824 | ||||||||
\(871\) | 21.8296 | 0.739667 | ||||||||
\(872\) | −43.8115 | −1.48365 | ||||||||
\(873\) | 1.55999 | 0.0527975 | ||||||||
\(874\) | −22.7660 | −0.770070 | ||||||||
\(875\) | 26.0943 | 0.882149 | ||||||||
\(876\) | 14.1423 | 0.477824 | ||||||||
\(877\) | 39.4096 | 1.33077 | 0.665384 | − | 0.746501i | \(-0.268268\pi\) | ||||
0.665384 | + | 0.746501i | \(0.268268\pi\) | |||||||
\(878\) | −0.963382 | −0.0325126 | ||||||||
\(879\) | −31.7149 | −1.06972 | ||||||||
\(880\) | 85.1961 | 2.87196 | ||||||||
\(881\) | 57.8516 | 1.94907 | 0.974536 | − | 0.224232i | \(-0.0719873\pi\) | ||||
0.974536 | + | 0.224232i | \(0.0719873\pi\) | |||||||
\(882\) | 1.02824 | 0.0346226 | ||||||||
\(883\) | 36.5295 | 1.22932 | 0.614659 | − | 0.788793i | \(-0.289294\pi\) | ||||
0.614659 | + | 0.788793i | \(0.289294\pi\) | |||||||
\(884\) | −20.8224 | −0.700332 | ||||||||
\(885\) | −55.5073 | −1.86586 | ||||||||
\(886\) | 11.3900 | 0.382655 | ||||||||
\(887\) | 16.4771 | 0.553247 | 0.276623 | − | 0.960978i | \(-0.410785\pi\) | ||||
0.276623 | + | 0.960978i | \(0.410785\pi\) | |||||||
\(888\) | 40.2982 | 1.35232 | ||||||||
\(889\) | 9.77573 | 0.327867 | ||||||||
\(890\) | 123.881 | 4.15249 | ||||||||
\(891\) | −42.4743 | −1.42294 | ||||||||
\(892\) | −46.5257 | −1.55779 | ||||||||
\(893\) | 56.3475 | 1.88560 | ||||||||
\(894\) | 56.8668 | 1.90191 | ||||||||
\(895\) | 36.0329 | 1.20445 | ||||||||
\(896\) | 19.9234 | 0.665593 | ||||||||
\(897\) | 9.64724 | 0.322112 | ||||||||
\(898\) | 19.7714 | 0.659782 | ||||||||
\(899\) | −1.22235 | −0.0407676 | ||||||||
\(900\) | −19.0626 | −0.635421 | ||||||||
\(901\) | 0.443934 | 0.0147896 | ||||||||
\(902\) | −73.0579 | −2.43256 | ||||||||
\(903\) | −2.83964 | −0.0944973 | ||||||||
\(904\) | −55.1918 | −1.83565 | ||||||||
\(905\) | 83.8906 | 2.78862 | ||||||||
\(906\) | 7.08202 | 0.235284 | ||||||||
\(907\) | −44.2731 | −1.47006 | −0.735031 | − | 0.678033i | \(-0.762833\pi\) | ||||
−0.735031 | + | 0.678033i | \(0.762833\pi\) | |||||||
\(908\) | 20.3640 | 0.675803 | ||||||||
\(909\) | −1.67594 | −0.0555874 | ||||||||
\(910\) | −29.9947 | −0.994316 | ||||||||
\(911\) | −33.7779 | −1.11911 | −0.559555 | − | 0.828793i | \(-0.689028\pi\) | ||||
−0.559555 | + | 0.828793i | \(0.689028\pi\) | |||||||
\(912\) | 28.2668 | 0.936008 | ||||||||
\(913\) | −82.4479 | −2.72863 | ||||||||
\(914\) | 4.24288 | 0.140342 | ||||||||
\(915\) | −78.4482 | −2.59342 | ||||||||
\(916\) | −75.1312 | −2.48241 | ||||||||
\(917\) | −10.8149 | −0.357140 | ||||||||
\(918\) | −23.2792 | −0.768328 | ||||||||
\(919\) | 58.3753 | 1.92562 | 0.962811 | − | 0.270175i | \(-0.0870816\pi\) | ||||
0.962811 | + | 0.270175i | \(0.0870816\pi\) | |||||||
\(920\) | −38.3596 | −1.26468 | ||||||||
\(921\) | 15.1511 | 0.499246 | ||||||||
\(922\) | 30.0520 | 0.989711 | ||||||||
\(923\) | −23.0781 | −0.759626 | ||||||||
\(924\) | 35.7005 | 1.17446 | ||||||||
\(925\) | −60.1111 | −1.97644 | ||||||||
\(926\) | −45.6102 | −1.49885 | ||||||||
\(927\) | 3.32995 | 0.109370 | ||||||||
\(928\) | −0.0621193 | −0.00203917 | ||||||||
\(929\) | −25.5947 | −0.839735 | −0.419868 | − | 0.907585i | \(-0.637923\pi\) | ||||
−0.419868 | + | 0.907585i | \(0.637923\pi\) | |||||||
\(930\) | −131.959 | −4.32710 | ||||||||
\(931\) | 4.70704 | 0.154267 | ||||||||
\(932\) | 100.002 | 3.27566 | ||||||||
\(933\) | 9.81123 | 0.321205 | ||||||||
\(934\) | −84.8548 | −2.77653 | ||||||||
\(935\) | −39.5529 | −1.29352 | ||||||||
\(936\) | 6.09790 | 0.199316 | ||||||||
\(937\) | 41.0242 | 1.34020 | 0.670101 | − | 0.742270i | \(-0.266251\pi\) | ||||
0.670101 | + | 0.742270i | \(0.266251\pi\) | |||||||
\(938\) | −17.5743 | −0.573822 | ||||||||
\(939\) | −14.2914 | −0.466382 | ||||||||
\(940\) | 192.007 | 6.26259 | ||||||||
\(941\) | −3.27021 | −0.106606 | −0.0533028 | − | 0.998578i | \(-0.516975\pi\) | ||||
−0.0533028 | + | 0.998578i | \(0.516975\pi\) | |||||||
\(942\) | −26.4898 | −0.863085 | ||||||||
\(943\) | 10.5570 | 0.343785 | ||||||||
\(944\) | −31.8843 | −1.03775 | ||||||||
\(945\) | −22.2739 | −0.724569 | ||||||||
\(946\) | 24.2515 | 0.788485 | ||||||||
\(947\) | 7.62585 | 0.247807 | 0.123903 | − | 0.992294i | \(-0.460459\pi\) | ||||
0.123903 | + | 0.992294i | \(0.460459\pi\) | |||||||
\(948\) | −101.203 | −3.28693 | ||||||||
\(949\) | 6.74818 | 0.219055 | ||||||||
\(950\) | −131.379 | −4.26249 | ||||||||
\(951\) | −6.38609 | −0.207083 | ||||||||
\(952\) | 8.28912 | 0.268652 | ||||||||
\(953\) | −15.5860 | −0.504880 | −0.252440 | − | 0.967613i | \(-0.581233\pi\) | ||||
−0.252440 | + | 0.967613i | \(0.581233\pi\) | |||||||
\(954\) | −0.262920 | −0.00851236 | ||||||||
\(955\) | −18.7952 | −0.608197 | ||||||||
\(956\) | −79.0619 | −2.55704 | ||||||||
\(957\) | −1.32811 | −0.0429316 | ||||||||
\(958\) | −16.0746 | −0.519347 | ||||||||
\(959\) | −11.8746 | −0.383449 | ||||||||
\(960\) | −55.3986 | −1.78798 | ||||||||
\(961\) | 37.9758 | 1.22503 | ||||||||
\(962\) | 38.8873 | 1.25378 | ||||||||
\(963\) | 5.52556 | 0.178059 | ||||||||
\(964\) | 44.9340 | 1.44723 | ||||||||
\(965\) | −31.0639 | −0.999984 | ||||||||
\(966\) | −7.76671 | −0.249890 | ||||||||
\(967\) | −8.39129 | −0.269846 | −0.134923 | − | 0.990856i | \(-0.543079\pi\) | ||||
−0.134923 | + | 0.990856i | \(0.543079\pi\) | |||||||
\(968\) | −98.2444 | −3.15769 | ||||||||
\(969\) | −13.1231 | −0.421574 | ||||||||
\(970\) | 36.6358 | 1.17631 | ||||||||
\(971\) | 19.2995 | 0.619351 | 0.309675 | − | 0.950842i | \(-0.399780\pi\) | ||||
0.309675 | + | 0.950842i | \(0.399780\pi\) | |||||||
\(972\) | 17.1877 | 0.551295 | ||||||||
\(973\) | −18.2040 | −0.583595 | ||||||||
\(974\) | −68.3086 | −2.18875 | ||||||||
\(975\) | 55.6727 | 1.78295 | ||||||||
\(976\) | −45.0619 | −1.44240 | ||||||||
\(977\) | 40.3448 | 1.29075 | 0.645373 | − | 0.763868i | \(-0.276702\pi\) | ||||
0.645373 | + | 0.763868i | \(0.276702\pi\) | |||||||
\(978\) | 35.7516 | 1.14321 | ||||||||
\(979\) | −70.3558 | −2.24858 | ||||||||
\(980\) | 16.0395 | 0.512363 | ||||||||
\(981\) | −3.86611 | −0.123435 | ||||||||
\(982\) | −48.9349 | −1.56158 | ||||||||
\(983\) | −10.1453 | −0.323585 | −0.161792 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161792 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(984\) | −40.8425 | −1.30201 | ||||||||
\(985\) | 2.38306 | 0.0759305 | ||||||||
\(986\) | −0.623623 | −0.0198602 | ||||||||
\(987\) | 19.2232 | 0.611881 | ||||||||
\(988\) | 56.4534 | 1.79602 | ||||||||
\(989\) | −3.50440 | −0.111434 | ||||||||
\(990\) | 23.4252 | 0.744503 | ||||||||
\(991\) | 45.5718 | 1.44764 | 0.723818 | − | 0.689991i | \(-0.242386\pi\) | ||||
0.723818 | + | 0.689991i | \(0.242386\pi\) | |||||||
\(992\) | 3.50533 | 0.111294 | ||||||||
\(993\) | 23.2361 | 0.737377 | ||||||||
\(994\) | 18.5795 | 0.589306 | ||||||||
\(995\) | −5.95860 | −0.188900 | ||||||||
\(996\) | −93.2137 | −2.95359 | ||||||||
\(997\) | −30.8439 | −0.976837 | −0.488419 | − | 0.872609i | \(-0.662426\pi\) | ||||
−0.488419 | + | 0.872609i | \(0.662426\pi\) | |||||||
\(998\) | −63.9888 | −2.02553 | ||||||||
\(999\) | 28.8774 | 0.913640 |
(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 | 6013.2.a.e.1.7 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.7 | ✓ | 109 | 1.1 | even | 1 | trivial |