Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76342 | −1.95403 | −0.977015 | − | 0.213171i | \(-0.931621\pi\) | ||||
−0.977015 | + | 0.213171i | \(0.931621\pi\) | |||||||
\(3\) | −1.75117 | −1.01104 | −0.505521 | − | 0.862815i | \(-0.668700\pi\) | ||||
−0.505521 | + | 0.862815i | \(0.668700\pi\) | |||||||
\(4\) | 5.63647 | 2.81823 | ||||||||
\(5\) | −3.34867 | −1.49757 | −0.748786 | − | 0.662812i | \(-0.769363\pi\) | ||||
−0.748786 | + | 0.662812i | \(0.769363\pi\) | |||||||
\(6\) | 4.83922 | 1.97560 | ||||||||
\(7\) | −0.176382 | −0.0666663 | −0.0333331 | − | 0.999444i | \(-0.510612\pi\) | ||||
−0.0333331 | + | 0.999444i | \(0.510612\pi\) | |||||||
\(8\) | −10.0491 | −3.55288 | ||||||||
\(9\) | 0.0666133 | 0.0222044 | ||||||||
\(10\) | 9.25378 | 2.92630 | ||||||||
\(11\) | −3.59328 | −1.08342 | −0.541708 | − | 0.840567i | \(-0.682222\pi\) | ||||
−0.541708 | + | 0.840567i | \(0.682222\pi\) | |||||||
\(12\) | −9.87044 | −2.84935 | ||||||||
\(13\) | −2.30488 | −0.639258 | −0.319629 | − | 0.947543i | \(-0.603558\pi\) | ||||
−0.319629 | + | 0.947543i | \(0.603558\pi\) | |||||||
\(14\) | 0.487418 | 0.130268 | ||||||||
\(15\) | 5.86411 | 1.51411 | ||||||||
\(16\) | 16.4968 | 4.12421 | ||||||||
\(17\) | −6.59292 | −1.59902 | −0.799509 | − | 0.600654i | \(-0.794907\pi\) | ||||
−0.799509 | + | 0.600654i | \(0.794907\pi\) | |||||||
\(18\) | −0.184080 | −0.0433881 | ||||||||
\(19\) | −1.28173 | −0.294050 | −0.147025 | − | 0.989133i | \(-0.546970\pi\) | ||||
−0.147025 | + | 0.989133i | \(0.546970\pi\) | |||||||
\(20\) | −18.8747 | −4.22051 | ||||||||
\(21\) | 0.308876 | 0.0674024 | ||||||||
\(22\) | 9.92974 | 2.11703 | ||||||||
\(23\) | −0.795686 | −0.165912 | −0.0829560 | − | 0.996553i | \(-0.526436\pi\) | ||||
−0.0829560 | + | 0.996553i | \(0.526436\pi\) | |||||||
\(24\) | 17.5977 | 3.59211 | ||||||||
\(25\) | 6.21361 | 1.24272 | ||||||||
\(26\) | 6.36934 | 1.24913 | ||||||||
\(27\) | 5.13687 | 0.988592 | ||||||||
\(28\) | −0.994174 | −0.187881 | ||||||||
\(29\) | −1.57744 | −0.292924 | −0.146462 | − | 0.989216i | \(-0.546789\pi\) | ||||
−0.146462 | + | 0.989216i | \(0.546789\pi\) | |||||||
\(30\) | −16.2050 | −2.95861 | ||||||||
\(31\) | 5.46108 | 0.980840 | 0.490420 | − | 0.871486i | \(-0.336843\pi\) | ||||
0.490420 | + | 0.871486i | \(0.336843\pi\) | |||||||
\(32\) | −25.4894 | −4.50594 | ||||||||
\(33\) | 6.29247 | 1.09538 | ||||||||
\(34\) | 18.2190 | 3.12453 | ||||||||
\(35\) | 0.590647 | 0.0998376 | ||||||||
\(36\) | 0.375463 | 0.0625772 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 3.54196 | 0.574582 | ||||||||
\(39\) | 4.03625 | 0.646317 | ||||||||
\(40\) | 33.6510 | 5.32070 | ||||||||
\(41\) | 2.22182 | 0.346990 | 0.173495 | − | 0.984835i | \(-0.444494\pi\) | ||||
0.173495 | + | 0.984835i | \(0.444494\pi\) | |||||||
\(42\) | −0.853554 | −0.131706 | ||||||||
\(43\) | 4.85478 | 0.740348 | 0.370174 | − | 0.928963i | \(-0.379298\pi\) | ||||
0.370174 | + | 0.928963i | \(0.379298\pi\) | |||||||
\(44\) | −20.2534 | −3.05332 | ||||||||
\(45\) | −0.223066 | −0.0332527 | ||||||||
\(46\) | 2.19881 | 0.324197 | ||||||||
\(47\) | 2.23578 | 0.326121 | 0.163061 | − | 0.986616i | \(-0.447863\pi\) | ||||
0.163061 | + | 0.986616i | \(0.447863\pi\) | |||||||
\(48\) | −28.8888 | −4.16974 | ||||||||
\(49\) | −6.96889 | −0.995556 | ||||||||
\(50\) | −17.1708 | −2.42832 | ||||||||
\(51\) | 11.5454 | 1.61667 | ||||||||
\(52\) | −12.9914 | −1.80158 | ||||||||
\(53\) | 1.00587 | 0.138167 | 0.0690837 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690837 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(54\) | −14.1953 | −1.93174 | ||||||||
\(55\) | 12.0327 | 1.62249 | ||||||||
\(56\) | 1.77248 | 0.236857 | ||||||||
\(57\) | 2.24454 | 0.297297 | ||||||||
\(58\) | 4.35914 | 0.572382 | ||||||||
\(59\) | 5.13677 | 0.668750 | 0.334375 | − | 0.942440i | \(-0.391475\pi\) | ||||
0.334375 | + | 0.942440i | \(0.391475\pi\) | |||||||
\(60\) | 33.0529 | 4.26711 | ||||||||
\(61\) | −0.373404 | −0.0478095 | −0.0239047 | − | 0.999714i | \(-0.507610\pi\) | ||||
−0.0239047 | + | 0.999714i | \(0.507610\pi\) | |||||||
\(62\) | −15.0912 | −1.91659 | ||||||||
\(63\) | −0.0117494 | −0.00148029 | ||||||||
\(64\) | 37.4443 | 4.68053 | ||||||||
\(65\) | 7.71829 | 0.957336 | ||||||||
\(66\) | −17.3887 | −2.14040 | ||||||||
\(67\) | 5.08426 | 0.621141 | 0.310570 | − | 0.950550i | \(-0.399480\pi\) | ||||
0.310570 | + | 0.950550i | \(0.399480\pi\) | |||||||
\(68\) | −37.1608 | −4.50641 | ||||||||
\(69\) | 1.39339 | 0.167744 | ||||||||
\(70\) | −1.63220 | −0.195086 | ||||||||
\(71\) | 12.6439 | 1.50055 | 0.750275 | − | 0.661126i | \(-0.229921\pi\) | ||||
0.750275 | + | 0.661126i | \(0.229921\pi\) | |||||||
\(72\) | −0.669401 | −0.0788897 | ||||||||
\(73\) | −10.2930 | −1.20470 | −0.602352 | − | 0.798231i | \(-0.705770\pi\) | ||||
−0.602352 | + | 0.798231i | \(0.705770\pi\) | |||||||
\(74\) | 2.76342 | 0.321241 | ||||||||
\(75\) | −10.8811 | −1.25644 | ||||||||
\(76\) | −7.22445 | −0.828701 | ||||||||
\(77\) | 0.633792 | 0.0722273 | ||||||||
\(78\) | −11.1538 | −1.26292 | ||||||||
\(79\) | −0.467857 | −0.0526380 | −0.0263190 | − | 0.999654i | \(-0.508379\pi\) | ||||
−0.0263190 | + | 0.999654i | \(0.508379\pi\) | |||||||
\(80\) | −55.2425 | −6.17630 | ||||||||
\(81\) | −9.19540 | −1.02171 | ||||||||
\(82\) | −6.13981 | −0.678029 | ||||||||
\(83\) | −2.93875 | −0.322570 | −0.161285 | − | 0.986908i | \(-0.551564\pi\) | ||||
−0.161285 | + | 0.986908i | \(0.551564\pi\) | |||||||
\(84\) | 1.74097 | 0.189956 | ||||||||
\(85\) | 22.0775 | 2.39464 | ||||||||
\(86\) | −13.4158 | −1.44666 | ||||||||
\(87\) | 2.76238 | 0.296158 | ||||||||
\(88\) | 36.1091 | 3.84925 | ||||||||
\(89\) | 6.61557 | 0.701249 | 0.350624 | − | 0.936516i | \(-0.385969\pi\) | ||||
0.350624 | + | 0.936516i | \(0.385969\pi\) | |||||||
\(90\) | 0.616424 | 0.0649768 | ||||||||
\(91\) | 0.406540 | 0.0426170 | ||||||||
\(92\) | −4.48486 | −0.467579 | ||||||||
\(93\) | −9.56331 | −0.991669 | ||||||||
\(94\) | −6.17838 | −0.637251 | ||||||||
\(95\) | 4.29211 | 0.440361 | ||||||||
\(96\) | 44.6365 | 4.55569 | ||||||||
\(97\) | −3.26485 | −0.331495 | −0.165748 | − | 0.986168i | \(-0.553004\pi\) | ||||
−0.165748 | + | 0.986168i | \(0.553004\pi\) | |||||||
\(98\) | 19.2579 | 1.94535 | ||||||||
\(99\) | −0.239360 | −0.0240566 | ||||||||
\(100\) | 35.0228 | 3.50228 | ||||||||
\(101\) | 3.26979 | 0.325356 | 0.162678 | − | 0.986679i | \(-0.447987\pi\) | ||||
0.162678 | + | 0.986679i | \(0.447987\pi\) | |||||||
\(102\) | −31.9046 | −3.15903 | ||||||||
\(103\) | −19.3110 | −1.90277 | −0.951383 | − | 0.308009i | \(-0.900337\pi\) | ||||
−0.951383 | + | 0.308009i | \(0.900337\pi\) | |||||||
\(104\) | 23.1619 | 2.27121 | ||||||||
\(105\) | −1.03433 | −0.100940 | ||||||||
\(106\) | −2.77965 | −0.269983 | ||||||||
\(107\) | 18.3716 | 1.77605 | 0.888027 | − | 0.459791i | \(-0.152076\pi\) | ||||
0.888027 | + | 0.459791i | \(0.152076\pi\) | |||||||
\(108\) | 28.9538 | 2.78608 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −33.2514 | −3.17040 | ||||||||
\(111\) | 1.75117 | 0.166214 | ||||||||
\(112\) | −2.90975 | −0.274945 | ||||||||
\(113\) | −0.400266 | −0.0376539 | −0.0188269 | − | 0.999823i | \(-0.505993\pi\) | ||||
−0.0188269 | + | 0.999823i | \(0.505993\pi\) | |||||||
\(114\) | −6.20260 | −0.580927 | ||||||||
\(115\) | 2.66449 | 0.248465 | ||||||||
\(116\) | −8.89121 | −0.825528 | ||||||||
\(117\) | −0.153535 | −0.0141944 | ||||||||
\(118\) | −14.1950 | −1.30676 | ||||||||
\(119\) | 1.16288 | 0.106601 | ||||||||
\(120\) | −58.9289 | −5.37944 | ||||||||
\(121\) | 1.91168 | 0.173789 | ||||||||
\(122\) | 1.03187 | 0.0934212 | ||||||||
\(123\) | −3.89079 | −0.350821 | ||||||||
\(124\) | 30.7812 | 2.76423 | ||||||||
\(125\) | −4.06399 | −0.363494 | ||||||||
\(126\) | 0.0324685 | 0.00289252 | ||||||||
\(127\) | −15.5224 | −1.37739 | −0.688694 | − | 0.725052i | \(-0.741816\pi\) | ||||
−0.688694 | + | 0.725052i | \(0.741816\pi\) | |||||||
\(128\) | −52.4952 | −4.63997 | ||||||||
\(129\) | −8.50157 | −0.748522 | ||||||||
\(130\) | −21.3288 | −1.87066 | ||||||||
\(131\) | 6.37464 | 0.556955 | 0.278477 | − | 0.960443i | \(-0.410170\pi\) | ||||
0.278477 | + | 0.960443i | \(0.410170\pi\) | |||||||
\(132\) | 35.4673 | 3.08703 | ||||||||
\(133\) | 0.226075 | 0.0196032 | ||||||||
\(134\) | −14.0499 | −1.21373 | ||||||||
\(135\) | −17.2017 | −1.48049 | ||||||||
\(136\) | 66.2527 | 5.68112 | ||||||||
\(137\) | −11.4555 | −0.978711 | −0.489355 | − | 0.872084i | \(-0.662768\pi\) | ||||
−0.489355 | + | 0.872084i | \(0.662768\pi\) | |||||||
\(138\) | −3.85050 | −0.327777 | ||||||||
\(139\) | 22.6745 | 1.92323 | 0.961613 | − | 0.274409i | \(-0.0884821\pi\) | ||||
0.961613 | + | 0.274409i | \(0.0884821\pi\) | |||||||
\(140\) | 3.32916 | 0.281366 | ||||||||
\(141\) | −3.91523 | −0.329722 | ||||||||
\(142\) | −34.9402 | −2.93212 | ||||||||
\(143\) | 8.28208 | 0.692583 | ||||||||
\(144\) | 1.09891 | 0.0915756 | ||||||||
\(145\) | 5.28235 | 0.438675 | ||||||||
\(146\) | 28.4438 | 2.35403 | ||||||||
\(147\) | 12.2037 | 1.00655 | ||||||||
\(148\) | −5.63647 | −0.463315 | ||||||||
\(149\) | 19.5772 | 1.60383 | 0.801915 | − | 0.597438i | \(-0.203815\pi\) | ||||
0.801915 | + | 0.597438i | \(0.203815\pi\) | |||||||
\(150\) | 30.0691 | 2.45513 | ||||||||
\(151\) | 10.3864 | 0.845236 | 0.422618 | − | 0.906308i | \(-0.361111\pi\) | ||||
0.422618 | + | 0.906308i | \(0.361111\pi\) | |||||||
\(152\) | 12.8802 | 1.04472 | ||||||||
\(153\) | −0.439176 | −0.0355053 | ||||||||
\(154\) | −1.75143 | −0.141134 | ||||||||
\(155\) | −18.2874 | −1.46888 | ||||||||
\(156\) | 22.7502 | 1.82147 | ||||||||
\(157\) | 7.22796 | 0.576854 | 0.288427 | − | 0.957502i | \(-0.406868\pi\) | ||||
0.288427 | + | 0.957502i | \(0.406868\pi\) | |||||||
\(158\) | 1.29288 | 0.102856 | ||||||||
\(159\) | −1.76146 | −0.139693 | ||||||||
\(160\) | 85.3558 | 6.74797 | ||||||||
\(161\) | 0.140345 | 0.0110607 | ||||||||
\(162\) | 25.4107 | 1.99645 | ||||||||
\(163\) | −12.5252 | −0.981050 | −0.490525 | − | 0.871427i | \(-0.663195\pi\) | ||||
−0.490525 | + | 0.871427i | \(0.663195\pi\) | |||||||
\(164\) | 12.5232 | 0.977898 | ||||||||
\(165\) | −21.0714 | −1.64041 | ||||||||
\(166\) | 8.12099 | 0.630311 | ||||||||
\(167\) | 6.57648 | 0.508903 | 0.254452 | − | 0.967086i | \(-0.418105\pi\) | ||||
0.254452 | + | 0.967086i | \(0.418105\pi\) | |||||||
\(168\) | −3.10392 | −0.239473 | ||||||||
\(169\) | −7.68753 | −0.591349 | ||||||||
\(170\) | −61.0094 | −4.67921 | ||||||||
\(171\) | −0.0853805 | −0.00652921 | ||||||||
\(172\) | 27.3638 | 2.08647 | ||||||||
\(173\) | 12.2550 | 0.931731 | 0.465865 | − | 0.884856i | \(-0.345743\pi\) | ||||
0.465865 | + | 0.884856i | \(0.345743\pi\) | |||||||
\(174\) | −7.63361 | −0.578702 | ||||||||
\(175\) | −1.09597 | −0.0828477 | ||||||||
\(176\) | −59.2778 | −4.46823 | ||||||||
\(177\) | −8.99537 | −0.676134 | ||||||||
\(178\) | −18.2816 | −1.37026 | ||||||||
\(179\) | −21.1699 | −1.58231 | −0.791157 | − | 0.611613i | \(-0.790521\pi\) | ||||
−0.791157 | + | 0.611613i | \(0.790521\pi\) | |||||||
\(180\) | −1.25730 | −0.0937139 | ||||||||
\(181\) | 14.0860 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(182\) | −1.12344 | −0.0832749 | ||||||||
\(183\) | 0.653896 | 0.0483374 | ||||||||
\(184\) | 7.99591 | 0.589466 | ||||||||
\(185\) | 3.34867 | 0.246199 | ||||||||
\(186\) | 26.4274 | 1.93775 | ||||||||
\(187\) | 23.6902 | 1.73240 | ||||||||
\(188\) | 12.6019 | 0.919086 | ||||||||
\(189\) | −0.906054 | −0.0659057 | ||||||||
\(190\) | −11.8609 | −0.860479 | ||||||||
\(191\) | 18.2532 | 1.32075 | 0.660376 | − | 0.750935i | \(-0.270397\pi\) | ||||
0.660376 | + | 0.750935i | \(0.270397\pi\) | |||||||
\(192\) | −65.5715 | −4.73221 | ||||||||
\(193\) | 16.3074 | 1.17383 | 0.586917 | − | 0.809647i | \(-0.300342\pi\) | ||||
0.586917 | + | 0.809647i | \(0.300342\pi\) | |||||||
\(194\) | 9.02214 | 0.647752 | ||||||||
\(195\) | −13.5161 | −0.967906 | ||||||||
\(196\) | −39.2799 | −2.80571 | ||||||||
\(197\) | −8.53385 | −0.608011 | −0.304006 | − | 0.952670i | \(-0.598324\pi\) | ||||
−0.304006 | + | 0.952670i | \(0.598324\pi\) | |||||||
\(198\) | 0.661452 | 0.0470073 | ||||||||
\(199\) | −14.2721 | −1.01172 | −0.505861 | − | 0.862615i | \(-0.668825\pi\) | ||||
−0.505861 | + | 0.862615i | \(0.668825\pi\) | |||||||
\(200\) | −62.4410 | −4.41525 | ||||||||
\(201\) | −8.90342 | −0.627999 | ||||||||
\(202\) | −9.03579 | −0.635756 | ||||||||
\(203\) | 0.278233 | 0.0195282 | ||||||||
\(204\) | 65.0750 | 4.55616 | ||||||||
\(205\) | −7.44015 | −0.519642 | ||||||||
\(206\) | 53.3643 | 3.71806 | ||||||||
\(207\) | −0.0530032 | −0.00368398 | ||||||||
\(208\) | −38.0232 | −2.63643 | ||||||||
\(209\) | 4.60563 | 0.318578 | ||||||||
\(210\) | 2.85827 | 0.197240 | ||||||||
\(211\) | −16.9061 | −1.16386 | −0.581932 | − | 0.813237i | \(-0.697703\pi\) | ||||
−0.581932 | + | 0.813237i | \(0.697703\pi\) | |||||||
\(212\) | 5.66958 | 0.389388 | ||||||||
\(213\) | −22.1416 | −1.51712 | ||||||||
\(214\) | −50.7685 | −3.47046 | ||||||||
\(215\) | −16.2571 | −1.10872 | ||||||||
\(216\) | −51.6208 | −3.51235 | ||||||||
\(217\) | −0.963239 | −0.0653889 | ||||||||
\(218\) | 2.76342 | 0.187162 | ||||||||
\(219\) | 18.0248 | 1.21801 | ||||||||
\(220\) | 67.8221 | 4.57256 | ||||||||
\(221\) | 15.1959 | 1.02219 | ||||||||
\(222\) | −4.83922 | −0.324787 | ||||||||
\(223\) | 17.9583 | 1.20258 | 0.601290 | − | 0.799031i | \(-0.294654\pi\) | ||||
0.601290 | + | 0.799031i | \(0.294654\pi\) | |||||||
\(224\) | 4.49589 | 0.300394 | ||||||||
\(225\) | 0.413909 | 0.0275939 | ||||||||
\(226\) | 1.10610 | 0.0735768 | ||||||||
\(227\) | 13.9871 | 0.928359 | 0.464179 | − | 0.885741i | \(-0.346349\pi\) | ||||
0.464179 | + | 0.885741i | \(0.346349\pi\) | |||||||
\(228\) | 12.6513 | 0.837851 | ||||||||
\(229\) | −2.38396 | −0.157537 | −0.0787684 | − | 0.996893i | \(-0.525099\pi\) | ||||
−0.0787684 | + | 0.996893i | \(0.525099\pi\) | |||||||
\(230\) | −7.36310 | −0.485509 | ||||||||
\(231\) | −1.10988 | −0.0730248 | ||||||||
\(232\) | 15.8518 | 1.04072 | ||||||||
\(233\) | 8.60107 | 0.563475 | 0.281738 | − | 0.959492i | \(-0.409089\pi\) | ||||
0.281738 | + | 0.959492i | \(0.409089\pi\) | |||||||
\(234\) | 0.424282 | 0.0277362 | ||||||||
\(235\) | −7.48688 | −0.488390 | ||||||||
\(236\) | 28.9532 | 1.88469 | ||||||||
\(237\) | 0.819299 | 0.0532192 | ||||||||
\(238\) | −3.21351 | −0.208301 | ||||||||
\(239\) | 27.0519 | 1.74984 | 0.874921 | − | 0.484265i | \(-0.160913\pi\) | ||||
0.874921 | + | 0.484265i | \(0.160913\pi\) | |||||||
\(240\) | 96.7392 | 6.24449 | ||||||||
\(241\) | 10.9254 | 0.703770 | 0.351885 | − | 0.936043i | \(-0.385541\pi\) | ||||
0.351885 | + | 0.936043i | \(0.385541\pi\) | |||||||
\(242\) | −5.28278 | −0.339590 | ||||||||
\(243\) | 0.692138 | 0.0444007 | ||||||||
\(244\) | −2.10468 | −0.134738 | ||||||||
\(245\) | 23.3365 | 1.49092 | ||||||||
\(246\) | 10.7519 | 0.685515 | ||||||||
\(247\) | 2.95424 | 0.187974 | ||||||||
\(248\) | −54.8788 | −3.48481 | ||||||||
\(249\) | 5.14626 | 0.326131 | ||||||||
\(250\) | 11.2305 | 0.710278 | ||||||||
\(251\) | −2.07463 | −0.130949 | −0.0654747 | − | 0.997854i | \(-0.520856\pi\) | ||||
−0.0654747 | + | 0.997854i | \(0.520856\pi\) | |||||||
\(252\) | −0.0662251 | −0.00417179 | ||||||||
\(253\) | 2.85913 | 0.179752 | ||||||||
\(254\) | 42.8948 | 2.69146 | ||||||||
\(255\) | −38.6616 | −2.42108 | ||||||||
\(256\) | 70.1776 | 4.38610 | ||||||||
\(257\) | 10.1507 | 0.633183 | 0.316591 | − | 0.948562i | \(-0.397462\pi\) | ||||
0.316591 | + | 0.948562i | \(0.397462\pi\) | |||||||
\(258\) | 23.4934 | 1.46263 | ||||||||
\(259\) | 0.176382 | 0.0109599 | ||||||||
\(260\) | 43.5039 | 2.69799 | ||||||||
\(261\) | −0.105079 | −0.00650421 | ||||||||
\(262\) | −17.6158 | −1.08831 | ||||||||
\(263\) | 7.22333 | 0.445410 | 0.222705 | − | 0.974886i | \(-0.428511\pi\) | ||||
0.222705 | + | 0.974886i | \(0.428511\pi\) | |||||||
\(264\) | −63.2334 | −3.89175 | ||||||||
\(265\) | −3.36834 | −0.206916 | ||||||||
\(266\) | −0.624740 | −0.0383053 | ||||||||
\(267\) | −11.5850 | −0.708991 | ||||||||
\(268\) | 28.6572 | 1.75052 | ||||||||
\(269\) | −21.5920 | −1.31649 | −0.658243 | − | 0.752806i | \(-0.728700\pi\) | ||||
−0.658243 | + | 0.752806i | \(0.728700\pi\) | |||||||
\(270\) | 47.5355 | 2.89292 | ||||||||
\(271\) | 9.96214 | 0.605157 | 0.302579 | − | 0.953124i | \(-0.402153\pi\) | ||||
0.302579 | + | 0.953124i | \(0.402153\pi\) | |||||||
\(272\) | −108.762 | −6.59468 | ||||||||
\(273\) | −0.711923 | −0.0430875 | ||||||||
\(274\) | 31.6564 | 1.91243 | ||||||||
\(275\) | −22.3273 | −1.34638 | ||||||||
\(276\) | 7.85377 | 0.472741 | ||||||||
\(277\) | −15.7599 | −0.946921 | −0.473460 | − | 0.880815i | \(-0.656995\pi\) | ||||
−0.473460 | + | 0.880815i | \(0.656995\pi\) | |||||||
\(278\) | −62.6591 | −3.75804 | ||||||||
\(279\) | 0.363781 | 0.0217790 | ||||||||
\(280\) | −5.93545 | −0.354711 | ||||||||
\(281\) | 21.8592 | 1.30401 | 0.652004 | − | 0.758216i | \(-0.273929\pi\) | ||||
0.652004 | + | 0.758216i | \(0.273929\pi\) | |||||||
\(282\) | 10.8194 | 0.644287 | ||||||||
\(283\) | −12.3680 | −0.735199 | −0.367599 | − | 0.929984i | \(-0.619820\pi\) | ||||
−0.367599 | + | 0.929984i | \(0.619820\pi\) | |||||||
\(284\) | 71.2667 | 4.22890 | ||||||||
\(285\) | −7.51623 | −0.445223 | ||||||||
\(286\) | −22.8868 | −1.35333 | ||||||||
\(287\) | −0.391890 | −0.0231325 | ||||||||
\(288\) | −1.69793 | −0.100052 | ||||||||
\(289\) | 26.4666 | 1.55686 | ||||||||
\(290\) | −14.5973 | −0.857184 | ||||||||
\(291\) | 5.71733 | 0.335156 | ||||||||
\(292\) | −58.0161 | −3.39514 | ||||||||
\(293\) | −15.2469 | −0.890731 | −0.445365 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445365 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(294\) | −33.7240 | −1.96682 | ||||||||
\(295\) | −17.2013 | −1.00150 | ||||||||
\(296\) | 10.0491 | 0.584090 | ||||||||
\(297\) | −18.4582 | −1.07106 | ||||||||
\(298\) | −54.1001 | −3.13393 | ||||||||
\(299\) | 1.83396 | 0.106061 | ||||||||
\(300\) | −61.3311 | −3.54095 | ||||||||
\(301\) | −0.856298 | −0.0493562 | ||||||||
\(302\) | −28.7020 | −1.65162 | ||||||||
\(303\) | −5.72598 | −0.328949 | ||||||||
\(304\) | −21.1445 | −1.21272 | ||||||||
\(305\) | 1.25041 | 0.0715981 | ||||||||
\(306\) | 1.21363 | 0.0693783 | ||||||||
\(307\) | 33.4938 | 1.91159 | 0.955796 | − | 0.294030i | \(-0.0949967\pi\) | ||||
0.955796 | + | 0.294030i | \(0.0949967\pi\) | |||||||
\(308\) | 3.57235 | 0.203553 | ||||||||
\(309\) | 33.8169 | 1.92378 | ||||||||
\(310\) | 50.5356 | 2.87023 | ||||||||
\(311\) | −27.8830 | −1.58110 | −0.790549 | − | 0.612399i | \(-0.790205\pi\) | ||||
−0.790549 | + | 0.612399i | \(0.790205\pi\) | |||||||
\(312\) | −40.5605 | −2.29629 | ||||||||
\(313\) | −20.0481 | −1.13318 | −0.566592 | − | 0.823999i | \(-0.691738\pi\) | ||||
−0.566592 | + | 0.823999i | \(0.691738\pi\) | |||||||
\(314\) | −19.9739 | −1.12719 | ||||||||
\(315\) | 0.0393449 | 0.00221684 | ||||||||
\(316\) | −2.63706 | −0.148346 | ||||||||
\(317\) | 6.73344 | 0.378188 | 0.189094 | − | 0.981959i | \(-0.439445\pi\) | ||||
0.189094 | + | 0.981959i | \(0.439445\pi\) | |||||||
\(318\) | 4.86765 | 0.272964 | ||||||||
\(319\) | 5.66820 | 0.317359 | ||||||||
\(320\) | −125.389 | −7.00944 | ||||||||
\(321\) | −32.1720 | −1.79566 | ||||||||
\(322\) | −0.387832 | −0.0216130 | ||||||||
\(323\) | 8.45037 | 0.470191 | ||||||||
\(324\) | −51.8296 | −2.87942 | ||||||||
\(325\) | −14.3216 | −0.794421 | ||||||||
\(326\) | 34.6123 | 1.91700 | ||||||||
\(327\) | 1.75117 | 0.0968402 | ||||||||
\(328\) | −22.3272 | −1.23281 | ||||||||
\(329\) | −0.394351 | −0.0217413 | ||||||||
\(330\) | 58.2291 | 3.20541 | ||||||||
\(331\) | −1.69861 | −0.0933638 | −0.0466819 | − | 0.998910i | \(-0.514865\pi\) | ||||
−0.0466819 | + | 0.998910i | \(0.514865\pi\) | |||||||
\(332\) | −16.5642 | −0.909077 | ||||||||
\(333\) | −0.0666133 | −0.00365038 | ||||||||
\(334\) | −18.1735 | −0.994412 | ||||||||
\(335\) | −17.0255 | −0.930203 | ||||||||
\(336\) | 5.09548 | 0.277981 | ||||||||
\(337\) | −8.53308 | −0.464827 | −0.232413 | − | 0.972617i | \(-0.574662\pi\) | ||||
−0.232413 | + | 0.972617i | \(0.574662\pi\) | |||||||
\(338\) | 21.2438 | 1.15551 | ||||||||
\(339\) | 0.700936 | 0.0380696 | ||||||||
\(340\) | 124.439 | 6.74867 | ||||||||
\(341\) | −19.6232 | −1.06266 | ||||||||
\(342\) | 0.235942 | 0.0127583 | ||||||||
\(343\) | 2.46387 | 0.133036 | ||||||||
\(344\) | −48.7861 | −2.63037 | ||||||||
\(345\) | −4.66599 | −0.251209 | ||||||||
\(346\) | −33.8657 | −1.82063 | ||||||||
\(347\) | −16.2306 | −0.871303 | −0.435652 | − | 0.900115i | \(-0.643482\pi\) | ||||
−0.435652 | + | 0.900115i | \(0.643482\pi\) | |||||||
\(348\) | 15.5701 | 0.834643 | ||||||||
\(349\) | −5.72432 | −0.306416 | −0.153208 | − | 0.988194i | \(-0.548960\pi\) | ||||
−0.153208 | + | 0.988194i | \(0.548960\pi\) | |||||||
\(350\) | 3.02863 | 0.161887 | ||||||||
\(351\) | −11.8399 | −0.631966 | ||||||||
\(352\) | 91.5908 | 4.88180 | ||||||||
\(353\) | −7.74302 | −0.412119 | −0.206060 | − | 0.978539i | \(-0.566064\pi\) | ||||
−0.206060 | + | 0.978539i | \(0.566064\pi\) | |||||||
\(354\) | 24.8580 | 1.32119 | ||||||||
\(355\) | −42.3402 | −2.24718 | ||||||||
\(356\) | 37.2884 | 1.97628 | ||||||||
\(357\) | −2.03640 | −0.107778 | ||||||||
\(358\) | 58.5013 | 3.09189 | ||||||||
\(359\) | −0.640157 | −0.0337862 | −0.0168931 | − | 0.999857i | \(-0.505377\pi\) | ||||
−0.0168931 | + | 0.999857i | \(0.505377\pi\) | |||||||
\(360\) | 2.24161 | 0.118143 | ||||||||
\(361\) | −17.3572 | −0.913535 | ||||||||
\(362\) | −38.9256 | −2.04588 | ||||||||
\(363\) | −3.34769 | −0.175708 | ||||||||
\(364\) | 2.29145 | 0.120105 | ||||||||
\(365\) | 34.4679 | 1.80413 | ||||||||
\(366\) | −1.80699 | −0.0944526 | ||||||||
\(367\) | −10.9837 | −0.573343 | −0.286672 | − | 0.958029i | \(-0.592549\pi\) | ||||
−0.286672 | + | 0.958029i | \(0.592549\pi\) | |||||||
\(368\) | −13.1263 | −0.684255 | ||||||||
\(369\) | 0.148003 | 0.00770471 | ||||||||
\(370\) | −9.25378 | −0.481081 | ||||||||
\(371\) | −0.177419 | −0.00921111 | ||||||||
\(372\) | −53.9033 | −2.79476 | ||||||||
\(373\) | 34.7953 | 1.80163 | 0.900816 | − | 0.434202i | \(-0.142970\pi\) | ||||
0.900816 | + | 0.434202i | \(0.142970\pi\) | |||||||
\(374\) | −65.4659 | −3.38516 | ||||||||
\(375\) | 7.11675 | 0.367508 | ||||||||
\(376\) | −22.4675 | −1.15867 | ||||||||
\(377\) | 3.63582 | 0.187254 | ||||||||
\(378\) | 2.50380 | 0.128782 | ||||||||
\(379\) | 5.39583 | 0.277165 | 0.138583 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138583 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(380\) | 24.1923 | 1.24104 | ||||||||
\(381\) | 27.1824 | 1.39260 | ||||||||
\(382\) | −50.4411 | −2.58079 | ||||||||
\(383\) | −18.4089 | −0.940650 | −0.470325 | − | 0.882493i | \(-0.655863\pi\) | ||||
−0.470325 | + | 0.882493i | \(0.655863\pi\) | |||||||
\(384\) | 91.9283 | 4.69120 | ||||||||
\(385\) | −2.12236 | −0.108166 | ||||||||
\(386\) | −45.0642 | −2.29371 | ||||||||
\(387\) | 0.323393 | 0.0164390 | ||||||||
\(388\) | −18.4022 | −0.934231 | ||||||||
\(389\) | −19.2042 | −0.973689 | −0.486845 | − | 0.873489i | \(-0.661852\pi\) | ||||
−0.486845 | + | 0.873489i | \(0.661852\pi\) | |||||||
\(390\) | 37.3505 | 1.89132 | ||||||||
\(391\) | 5.24589 | 0.265296 | ||||||||
\(392\) | 70.0308 | 3.53709 | ||||||||
\(393\) | −11.1631 | −0.563104 | ||||||||
\(394\) | 23.5826 | 1.18807 | ||||||||
\(395\) | 1.56670 | 0.0788292 | ||||||||
\(396\) | −1.34915 | −0.0677971 | ||||||||
\(397\) | 10.3905 | 0.521482 | 0.260741 | − | 0.965409i | \(-0.416033\pi\) | ||||
0.260741 | + | 0.965409i | \(0.416033\pi\) | |||||||
\(398\) | 39.4398 | 1.97694 | ||||||||
\(399\) | −0.395897 | −0.0198197 | ||||||||
\(400\) | 102.505 | 5.12524 | ||||||||
\(401\) | −25.8860 | −1.29269 | −0.646343 | − | 0.763047i | \(-0.723702\pi\) | ||||
−0.646343 | + | 0.763047i | \(0.723702\pi\) | |||||||
\(402\) | 24.6039 | 1.22713 | ||||||||
\(403\) | −12.5871 | −0.627010 | ||||||||
\(404\) | 18.4301 | 0.916930 | ||||||||
\(405\) | 30.7924 | 1.53009 | ||||||||
\(406\) | −0.768875 | −0.0381586 | ||||||||
\(407\) | 3.59328 | 0.178112 | ||||||||
\(408\) | −116.020 | −5.74385 | ||||||||
\(409\) | −10.5003 | −0.519208 | −0.259604 | − | 0.965715i | \(-0.583592\pi\) | ||||
−0.259604 | + | 0.965715i | \(0.583592\pi\) | |||||||
\(410\) | 20.5602 | 1.01540 | ||||||||
\(411\) | 20.0606 | 0.989517 | ||||||||
\(412\) | −108.846 | −5.36244 | ||||||||
\(413\) | −0.906035 | −0.0445831 | ||||||||
\(414\) | 0.146470 | 0.00719861 | ||||||||
\(415\) | 9.84091 | 0.483071 | ||||||||
\(416\) | 58.7501 | 2.88046 | ||||||||
\(417\) | −39.7070 | −1.94446 | ||||||||
\(418\) | −12.7273 | −0.622512 | ||||||||
\(419\) | −22.4047 | −1.09454 | −0.547270 | − | 0.836956i | \(-0.684333\pi\) | ||||
−0.547270 | + | 0.836956i | \(0.684333\pi\) | |||||||
\(420\) | −5.82995 | −0.284472 | ||||||||
\(421\) | 11.4152 | 0.556340 | 0.278170 | − | 0.960532i | \(-0.410272\pi\) | ||||
0.278170 | + | 0.960532i | \(0.410272\pi\) | |||||||
\(422\) | 46.7186 | 2.27423 | ||||||||
\(423\) | 0.148932 | 0.00724133 | ||||||||
\(424\) | −10.1081 | −0.490893 | ||||||||
\(425\) | −40.9658 | −1.98714 | ||||||||
\(426\) | 61.1865 | 2.96449 | ||||||||
\(427\) | 0.0658619 | 0.00318728 | ||||||||
\(428\) | 103.551 | 5.00534 | ||||||||
\(429\) | −14.5034 | −0.700230 | ||||||||
\(430\) | 44.9251 | 2.16648 | ||||||||
\(431\) | −28.9744 | −1.39565 | −0.697824 | − | 0.716269i | \(-0.745848\pi\) | ||||
−0.697824 | + | 0.716269i | \(0.745848\pi\) | |||||||
\(432\) | 84.7421 | 4.07716 | ||||||||
\(433\) | −9.18671 | −0.441485 | −0.220742 | − | 0.975332i | \(-0.570848\pi\) | ||||
−0.220742 | + | 0.975332i | \(0.570848\pi\) | |||||||
\(434\) | 2.66183 | 0.127772 | ||||||||
\(435\) | −9.25031 | −0.443518 | ||||||||
\(436\) | −5.63647 | −0.269938 | ||||||||
\(437\) | 1.01986 | 0.0487864 | ||||||||
\(438\) | −49.8101 | −2.38002 | ||||||||
\(439\) | 17.3245 | 0.826853 | 0.413427 | − | 0.910537i | \(-0.364332\pi\) | ||||
0.413427 | + | 0.910537i | \(0.364332\pi\) | |||||||
\(440\) | −120.918 | −5.76453 | ||||||||
\(441\) | −0.464220 | −0.0221057 | ||||||||
\(442\) | −41.9925 | −1.99738 | ||||||||
\(443\) | −28.0561 | −1.33298 | −0.666492 | − | 0.745512i | \(-0.732205\pi\) | ||||
−0.666492 | + | 0.745512i | \(0.732205\pi\) | |||||||
\(444\) | 9.87044 | 0.468430 | ||||||||
\(445\) | −22.1534 | −1.05017 | ||||||||
\(446\) | −49.6264 | −2.34988 | ||||||||
\(447\) | −34.2832 | −1.62154 | ||||||||
\(448\) | −6.60451 | −0.312034 | ||||||||
\(449\) | 7.67474 | 0.362193 | 0.181097 | − | 0.983465i | \(-0.442035\pi\) | ||||
0.181097 | + | 0.983465i | \(0.442035\pi\) | |||||||
\(450\) | −1.14380 | −0.0539194 | ||||||||
\(451\) | −7.98363 | −0.375934 | ||||||||
\(452\) | −2.25609 | −0.106117 | ||||||||
\(453\) | −18.1885 | −0.854569 | ||||||||
\(454\) | −38.6523 | −1.81404 | ||||||||
\(455\) | −1.36137 | −0.0638220 | ||||||||
\(456\) | −22.5555 | −1.05626 | ||||||||
\(457\) | −22.7074 | −1.06221 | −0.531104 | − | 0.847307i | \(-0.678223\pi\) | ||||
−0.531104 | + | 0.847307i | \(0.678223\pi\) | |||||||
\(458\) | 6.58788 | 0.307832 | ||||||||
\(459\) | −33.8670 | −1.58078 | ||||||||
\(460\) | 15.0183 | 0.700233 | ||||||||
\(461\) | −1.98213 | −0.0923169 | −0.0461584 | − | 0.998934i | \(-0.514698\pi\) | ||||
−0.0461584 | + | 0.998934i | \(0.514698\pi\) | |||||||
\(462\) | 3.06706 | 0.142693 | ||||||||
\(463\) | −13.8669 | −0.644451 | −0.322225 | − | 0.946663i | \(-0.604431\pi\) | ||||
−0.322225 | + | 0.946663i | \(0.604431\pi\) | |||||||
\(464\) | −26.0228 | −1.20808 | ||||||||
\(465\) | 32.0244 | 1.48510 | ||||||||
\(466\) | −23.7683 | −1.10105 | ||||||||
\(467\) | −20.6415 | −0.955174 | −0.477587 | − | 0.878585i | \(-0.658488\pi\) | ||||
−0.477587 | + | 0.878585i | \(0.658488\pi\) | |||||||
\(468\) | −0.865398 | −0.0400030 | ||||||||
\(469\) | −0.896773 | −0.0414091 | ||||||||
\(470\) | 20.6894 | 0.954329 | ||||||||
\(471\) | −12.6574 | −0.583223 | ||||||||
\(472\) | −51.6197 | −2.37599 | ||||||||
\(473\) | −17.4446 | −0.802104 | ||||||||
\(474\) | −2.26406 | −0.103992 | ||||||||
\(475\) | −7.96420 | −0.365422 | ||||||||
\(476\) | 6.55451 | 0.300425 | ||||||||
\(477\) | 0.0670045 | 0.00306793 | ||||||||
\(478\) | −74.7557 | −3.41924 | ||||||||
\(479\) | −30.0471 | −1.37289 | −0.686443 | − | 0.727184i | \(-0.740829\pi\) | ||||
−0.686443 | + | 0.727184i | \(0.740829\pi\) | |||||||
\(480\) | −149.473 | −6.82247 | ||||||||
\(481\) | 2.30488 | 0.105093 | ||||||||
\(482\) | −30.1916 | −1.37519 | ||||||||
\(483\) | −0.245769 | −0.0111829 | ||||||||
\(484\) | 10.7751 | 0.489779 | ||||||||
\(485\) | 10.9329 | 0.496438 | ||||||||
\(486\) | −1.91267 | −0.0867603 | ||||||||
\(487\) | −0.485600 | −0.0220046 | −0.0110023 | − | 0.999939i | \(-0.503502\pi\) | ||||
−0.0110023 | + | 0.999939i | \(0.503502\pi\) | |||||||
\(488\) | 3.75236 | 0.169861 | ||||||||
\(489\) | 21.9338 | 0.991882 | ||||||||
\(490\) | −64.4885 | −2.91330 | ||||||||
\(491\) | 42.3091 | 1.90938 | 0.954692 | − | 0.297596i | \(-0.0961848\pi\) | ||||
0.954692 | + | 0.297596i | \(0.0961848\pi\) | |||||||
\(492\) | −21.9303 | −0.988696 | ||||||||
\(493\) | 10.4000 | 0.468391 | ||||||||
\(494\) | −8.16380 | −0.367307 | ||||||||
\(495\) | 0.801539 | 0.0360265 | ||||||||
\(496\) | 90.0905 | 4.04518 | ||||||||
\(497\) | −2.23016 | −0.100036 | ||||||||
\(498\) | −14.2213 | −0.637270 | ||||||||
\(499\) | 23.9997 | 1.07437 | 0.537186 | − | 0.843464i | \(-0.319487\pi\) | ||||
0.537186 | + | 0.843464i | \(0.319487\pi\) | |||||||
\(500\) | −22.9065 | −1.02441 | ||||||||
\(501\) | −11.5166 | −0.514522 | ||||||||
\(502\) | 5.73306 | 0.255879 | ||||||||
\(503\) | 1.63735 | 0.0730057 | 0.0365029 | − | 0.999334i | \(-0.488378\pi\) | ||||
0.0365029 | + | 0.999334i | \(0.488378\pi\) | |||||||
\(504\) | 0.118071 | 0.00525928 | ||||||||
\(505\) | −10.9495 | −0.487245 | ||||||||
\(506\) | −7.90095 | −0.351240 | ||||||||
\(507\) | 13.4622 | 0.597878 | ||||||||
\(508\) | −87.4913 | −3.88180 | ||||||||
\(509\) | −9.84015 | −0.436157 | −0.218078 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218078 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(510\) | 106.838 | 4.73087 | ||||||||
\(511\) | 1.81550 | 0.0803131 | ||||||||
\(512\) | −88.9393 | −3.93060 | ||||||||
\(513\) | −6.58410 | −0.290695 | ||||||||
\(514\) | −28.0506 | −1.23726 | ||||||||
\(515\) | 64.6661 | 2.84953 | ||||||||
\(516\) | −47.9188 | −2.10951 | ||||||||
\(517\) | −8.03377 | −0.353325 | ||||||||
\(518\) | −0.487418 | −0.0214159 | ||||||||
\(519\) | −21.4607 | −0.942018 | ||||||||
\(520\) | −77.5616 | −3.40130 | ||||||||
\(521\) | −41.3914 | −1.81339 | −0.906694 | − | 0.421788i | \(-0.861403\pi\) | ||||
−0.906694 | + | 0.421788i | \(0.861403\pi\) | |||||||
\(522\) | 0.290376 | 0.0127094 | ||||||||
\(523\) | 3.91017 | 0.170980 | 0.0854899 | − | 0.996339i | \(-0.472754\pi\) | ||||
0.0854899 | + | 0.996339i | \(0.472754\pi\) | |||||||
\(524\) | 35.9304 | 1.56963 | ||||||||
\(525\) | 1.91924 | 0.0837624 | ||||||||
\(526\) | −19.9611 | −0.870344 | ||||||||
\(527\) | −36.0045 | −1.56838 | ||||||||
\(528\) | 103.806 | 4.51756 | ||||||||
\(529\) | −22.3669 | −0.972473 | ||||||||
\(530\) | 9.30813 | 0.404320 | ||||||||
\(531\) | 0.342177 | 0.0148492 | ||||||||
\(532\) | 1.27427 | 0.0552464 | ||||||||
\(533\) | −5.12102 | −0.221816 | ||||||||
\(534\) | 32.0142 | 1.38539 | ||||||||
\(535\) | −61.5206 | −2.65977 | ||||||||
\(536\) | −51.0920 | −2.20684 | ||||||||
\(537\) | 37.0722 | 1.59979 | ||||||||
\(538\) | 59.6676 | 2.57245 | ||||||||
\(539\) | 25.0412 | 1.07860 | ||||||||
\(540\) | −96.9569 | −4.17236 | ||||||||
\(541\) | 17.1081 | 0.735535 | 0.367767 | − | 0.929918i | \(-0.380122\pi\) | ||||
0.367767 | + | 0.929918i | \(0.380122\pi\) | |||||||
\(542\) | −27.5295 | −1.18249 | ||||||||
\(543\) | −24.6671 | −1.05857 | ||||||||
\(544\) | 168.050 | 7.20508 | ||||||||
\(545\) | 3.34867 | 0.143441 | ||||||||
\(546\) | 1.96734 | 0.0841943 | ||||||||
\(547\) | 34.8810 | 1.49140 | 0.745701 | − | 0.666281i | \(-0.232115\pi\) | ||||
0.745701 | + | 0.666281i | \(0.232115\pi\) | |||||||
\(548\) | −64.5686 | −2.75824 | ||||||||
\(549\) | −0.0248737 | −0.00106158 | ||||||||
\(550\) | 61.6995 | 2.63088 | ||||||||
\(551\) | 2.02186 | 0.0861343 | ||||||||
\(552\) | −14.0022 | −0.595974 | ||||||||
\(553\) | 0.0825217 | 0.00350918 | ||||||||
\(554\) | 43.5512 | 1.85031 | ||||||||
\(555\) | −5.86411 | −0.248918 | ||||||||
\(556\) | 127.804 | 5.42010 | ||||||||
\(557\) | 11.8897 | 0.503783 | 0.251891 | − | 0.967756i | \(-0.418947\pi\) | ||||
0.251891 | + | 0.967756i | \(0.418947\pi\) | |||||||
\(558\) | −1.00528 | −0.0425568 | ||||||||
\(559\) | −11.1897 | −0.473273 | ||||||||
\(560\) | 9.74380 | 0.411751 | ||||||||
\(561\) | −41.4857 | −1.75153 | ||||||||
\(562\) | −60.4059 | −2.54807 | ||||||||
\(563\) | −19.7699 | −0.833201 | −0.416600 | − | 0.909090i | \(-0.636779\pi\) | ||||
−0.416600 | + | 0.909090i | \(0.636779\pi\) | |||||||
\(564\) | −22.0681 | −0.929234 | ||||||||
\(565\) | 1.34036 | 0.0563894 | ||||||||
\(566\) | 34.1778 | 1.43660 | ||||||||
\(567\) | 1.62191 | 0.0681137 | ||||||||
\(568\) | −127.059 | −5.33128 | ||||||||
\(569\) | −8.95719 | −0.375505 | −0.187752 | − | 0.982216i | \(-0.560120\pi\) | ||||
−0.187752 | + | 0.982216i | \(0.560120\pi\) | |||||||
\(570\) | 20.7705 | 0.869979 | ||||||||
\(571\) | 32.0748 | 1.34229 | 0.671145 | − | 0.741327i | \(-0.265803\pi\) | ||||
0.671145 | + | 0.741327i | \(0.265803\pi\) | |||||||
\(572\) | 46.6817 | 1.95186 | ||||||||
\(573\) | −31.9645 | −1.33534 | ||||||||
\(574\) | 1.08295 | 0.0452017 | ||||||||
\(575\) | −4.94408 | −0.206183 | ||||||||
\(576\) | 2.49428 | 0.103929 | ||||||||
\(577\) | 27.7462 | 1.15509 | 0.577544 | − | 0.816360i | \(-0.304011\pi\) | ||||
0.577544 | + | 0.816360i | \(0.304011\pi\) | |||||||
\(578\) | −73.1382 | −3.04215 | ||||||||
\(579\) | −28.5571 | −1.18679 | ||||||||
\(580\) | 29.7738 | 1.23629 | ||||||||
\(581\) | 0.518344 | 0.0215045 | ||||||||
\(582\) | −15.7993 | −0.654904 | ||||||||
\(583\) | −3.61439 | −0.149693 | ||||||||
\(584\) | 103.435 | 4.28017 | ||||||||
\(585\) | 0.514140 | 0.0212571 | ||||||||
\(586\) | 42.1334 | 1.74051 | ||||||||
\(587\) | −12.5540 | −0.518160 | −0.259080 | − | 0.965856i | \(-0.583419\pi\) | ||||
−0.259080 | + | 0.965856i | \(0.583419\pi\) | |||||||
\(588\) | 68.7860 | 2.83669 | ||||||||
\(589\) | −6.99966 | −0.288416 | ||||||||
\(590\) | 47.5345 | 1.95696 | ||||||||
\(591\) | 14.9443 | 0.614725 | ||||||||
\(592\) | −16.4968 | −0.678015 | ||||||||
\(593\) | 19.6325 | 0.806209 | 0.403105 | − | 0.915154i | \(-0.367931\pi\) | ||||
0.403105 | + | 0.915154i | \(0.367931\pi\) | |||||||
\(594\) | 51.0078 | 2.09287 | ||||||||
\(595\) | −3.89409 | −0.159642 | ||||||||
\(596\) | 110.346 | 4.51997 | ||||||||
\(597\) | 24.9930 | 1.02289 | ||||||||
\(598\) | −5.06799 | −0.207246 | ||||||||
\(599\) | 30.0019 | 1.22584 | 0.612922 | − | 0.790143i | \(-0.289994\pi\) | ||||
0.612922 | + | 0.790143i | \(0.289994\pi\) | |||||||
\(600\) | 109.345 | 4.46400 | ||||||||
\(601\) | −34.7296 | −1.41665 | −0.708324 | − | 0.705887i | \(-0.750549\pi\) | ||||
−0.708324 | + | 0.705887i | \(0.750549\pi\) | |||||||
\(602\) | 2.36631 | 0.0964435 | ||||||||
\(603\) | 0.338679 | 0.0137921 | ||||||||
\(604\) | 58.5428 | 2.38207 | ||||||||
\(605\) | −6.40160 | −0.260262 | ||||||||
\(606\) | 15.8233 | 0.642776 | ||||||||
\(607\) | −9.33742 | −0.378994 | −0.189497 | − | 0.981881i | \(-0.560686\pi\) | ||||
−0.189497 | + | 0.981881i | \(0.560686\pi\) | |||||||
\(608\) | 32.6707 | 1.32497 | ||||||||
\(609\) | −0.487235 | −0.0197438 | ||||||||
\(610\) | −3.45540 | −0.139905 | ||||||||
\(611\) | −5.15319 | −0.208476 | ||||||||
\(612\) | −2.47540 | −0.100062 | ||||||||
\(613\) | −0.353579 | −0.0142809 | −0.00714046 | − | 0.999975i | \(-0.502273\pi\) | ||||
−0.00714046 | + | 0.999975i | \(0.502273\pi\) | |||||||
\(614\) | −92.5573 | −3.73531 | ||||||||
\(615\) | 13.0290 | 0.525380 | ||||||||
\(616\) | −6.36902 | −0.256615 | ||||||||
\(617\) | −38.8012 | −1.56208 | −0.781040 | − | 0.624481i | \(-0.785310\pi\) | ||||
−0.781040 | + | 0.624481i | \(0.785310\pi\) | |||||||
\(618\) | −93.4501 | −3.75912 | ||||||||
\(619\) | 28.1691 | 1.13221 | 0.566107 | − | 0.824332i | \(-0.308449\pi\) | ||||
0.566107 | + | 0.824332i | \(0.308449\pi\) | |||||||
\(620\) | −103.076 | −4.13964 | ||||||||
\(621\) | −4.08734 | −0.164019 | ||||||||
\(622\) | 77.0522 | 3.08951 | ||||||||
\(623\) | −1.16687 | −0.0467496 | ||||||||
\(624\) | 66.5852 | 2.66554 | ||||||||
\(625\) | −17.4591 | −0.698364 | ||||||||
\(626\) | 55.4011 | 2.21427 | ||||||||
\(627\) | −8.06527 | −0.322096 | ||||||||
\(628\) | 40.7402 | 1.62571 | ||||||||
\(629\) | 6.59292 | 0.262877 | ||||||||
\(630\) | −0.108726 | −0.00433176 | ||||||||
\(631\) | 25.3595 | 1.00954 | 0.504772 | − | 0.863253i | \(-0.331577\pi\) | ||||
0.504772 | + | 0.863253i | \(0.331577\pi\) | |||||||
\(632\) | 4.70153 | 0.187017 | ||||||||
\(633\) | 29.6056 | 1.17672 | ||||||||
\(634\) | −18.6073 | −0.738990 | ||||||||
\(635\) | 51.9794 | 2.06274 | ||||||||
\(636\) | −9.92842 | −0.393687 | ||||||||
\(637\) | 16.0624 | 0.636417 | ||||||||
\(638\) | −15.6636 | −0.620128 | ||||||||
\(639\) | 0.842249 | 0.0333188 | ||||||||
\(640\) | 175.789 | 6.94868 | ||||||||
\(641\) | 28.8401 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(642\) | 88.9045 | 3.50878 | ||||||||
\(643\) | −21.6175 | −0.852509 | −0.426255 | − | 0.904603i | \(-0.640167\pi\) | ||||
−0.426255 | + | 0.904603i | \(0.640167\pi\) | |||||||
\(644\) | 0.791050 | 0.0311717 | ||||||||
\(645\) | 28.4690 | 1.12097 | ||||||||
\(646\) | −23.3519 | −0.918768 | ||||||||
\(647\) | −8.17114 | −0.321241 | −0.160620 | − | 0.987016i | \(-0.551349\pi\) | ||||
−0.160620 | + | 0.987016i | \(0.551349\pi\) | |||||||
\(648\) | 92.4052 | 3.63002 | ||||||||
\(649\) | −18.4579 | −0.724534 | ||||||||
\(650\) | 39.5766 | 1.55232 | ||||||||
\(651\) | 1.68680 | 0.0661109 | ||||||||
\(652\) | −70.5979 | −2.76483 | ||||||||
\(653\) | 40.3451 | 1.57882 | 0.789412 | − | 0.613863i | \(-0.210385\pi\) | ||||
0.789412 | + | 0.613863i | \(0.210385\pi\) | |||||||
\(654\) | −4.83922 | −0.189229 | ||||||||
\(655\) | −21.3466 | −0.834080 | ||||||||
\(656\) | 36.6530 | 1.43106 | ||||||||
\(657\) | −0.685650 | −0.0267497 | ||||||||
\(658\) | 1.08976 | 0.0424831 | ||||||||
\(659\) | 47.8631 | 1.86448 | 0.932240 | − | 0.361841i | \(-0.117852\pi\) | ||||
0.932240 | + | 0.361841i | \(0.117852\pi\) | |||||||
\(660\) | −118.768 | −4.62305 | ||||||||
\(661\) | 3.88147 | 0.150972 | 0.0754859 | − | 0.997147i | \(-0.475949\pi\) | ||||
0.0754859 | + | 0.997147i | \(0.475949\pi\) | |||||||
\(662\) | 4.69395 | 0.182436 | ||||||||
\(663\) | −26.6106 | −1.03347 | ||||||||
\(664\) | 29.5317 | 1.14605 | ||||||||
\(665\) | −0.757052 | −0.0293572 | ||||||||
\(666\) | 0.184080 | 0.00713296 | ||||||||
\(667\) | 1.25515 | 0.0485996 | ||||||||
\(668\) | 37.0681 | 1.43421 | ||||||||
\(669\) | −31.4482 | −1.21586 | ||||||||
\(670\) | 47.0486 | 1.81764 | ||||||||
\(671\) | 1.34175 | 0.0517975 | ||||||||
\(672\) | −7.87309 | −0.303711 | ||||||||
\(673\) | 39.8082 | 1.53449 | 0.767246 | − | 0.641353i | \(-0.221626\pi\) | ||||
0.767246 | + | 0.641353i | \(0.221626\pi\) | |||||||
\(674\) | 23.5805 | 0.908285 | ||||||||
\(675\) | 31.9185 | 1.22854 | ||||||||
\(676\) | −43.3305 | −1.66656 | ||||||||
\(677\) | −38.6297 | −1.48466 | −0.742331 | − | 0.670034i | \(-0.766280\pi\) | ||||
−0.742331 | + | 0.670034i | \(0.766280\pi\) | |||||||
\(678\) | −1.93698 | −0.0743891 | ||||||||
\(679\) | 0.575862 | 0.0220996 | ||||||||
\(680\) | −221.859 | −8.50789 | ||||||||
\(681\) | −24.4939 | −0.938609 | ||||||||
\(682\) | 54.2271 | 2.07646 | ||||||||
\(683\) | 21.3719 | 0.817772 | 0.408886 | − | 0.912586i | \(-0.365917\pi\) | ||||
0.408886 | + | 0.912586i | \(0.365917\pi\) | |||||||
\(684\) | −0.481244 | −0.0184008 | ||||||||
\(685\) | 38.3608 | 1.46569 | ||||||||
\(686\) | −6.80869 | −0.259957 | ||||||||
\(687\) | 4.17474 | 0.159276 | ||||||||
\(688\) | 80.0885 | 3.05335 | ||||||||
\(689\) | −2.31842 | −0.0883247 | ||||||||
\(690\) | 12.8941 | 0.490869 | ||||||||
\(691\) | −38.0668 | −1.44813 | −0.724066 | − | 0.689731i | \(-0.757729\pi\) | ||||
−0.724066 | + | 0.689731i | \(0.757729\pi\) | |||||||
\(692\) | 69.0749 | 2.62583 | ||||||||
\(693\) | 0.0422189 | 0.00160377 | ||||||||
\(694\) | 44.8518 | 1.70255 | ||||||||
\(695\) | −75.9295 | −2.88017 | ||||||||
\(696\) | −27.7594 | −1.05222 | ||||||||
\(697\) | −14.6483 | −0.554843 | ||||||||
\(698\) | 15.8187 | 0.598745 | ||||||||
\(699\) | −15.0620 | −0.569697 | ||||||||
\(700\) | −6.17741 | −0.233484 | ||||||||
\(701\) | −7.84038 | −0.296127 | −0.148064 | − | 0.988978i | \(-0.547304\pi\) | ||||
−0.148064 | + | 0.988978i | \(0.547304\pi\) | |||||||
\(702\) | 32.7185 | 1.23488 | ||||||||
\(703\) | 1.28173 | 0.0483415 | ||||||||
\(704\) | −134.548 | −5.07096 | ||||||||
\(705\) | 13.1108 | 0.493783 | ||||||||
\(706\) | 21.3972 | 0.805293 | ||||||||
\(707\) | −0.576734 | −0.0216903 | ||||||||
\(708\) | −50.7021 | −1.90550 | ||||||||
\(709\) | −16.7361 | −0.628536 | −0.314268 | − | 0.949334i | \(-0.601759\pi\) | ||||
−0.314268 | + | 0.949334i | \(0.601759\pi\) | |||||||
\(710\) | 117.003 | 4.39106 | ||||||||
\(711\) | −0.0311655 | −0.00116880 | ||||||||
\(712\) | −66.4803 | −2.49145 | ||||||||
\(713\) | −4.34531 | −0.162733 | ||||||||
\(714\) | 5.62741 | 0.210601 | ||||||||
\(715\) | −27.7340 | −1.03719 | ||||||||
\(716\) | −119.324 | −4.45933 | ||||||||
\(717\) | −47.3726 | −1.76916 | ||||||||
\(718\) | 1.76902 | 0.0660192 | ||||||||
\(719\) | −36.4046 | −1.35766 | −0.678831 | − | 0.734295i | \(-0.737513\pi\) | ||||
−0.678831 | + | 0.734295i | \(0.737513\pi\) | |||||||
\(720\) | −3.67988 | −0.137141 | ||||||||
\(721\) | 3.40612 | 0.126850 | ||||||||
\(722\) | 47.9650 | 1.78507 | ||||||||
\(723\) | −19.1324 | −0.711540 | ||||||||
\(724\) | 79.3955 | 2.95071 | ||||||||
\(725\) | −9.80163 | −0.364023 | ||||||||
\(726\) | 9.25106 | 0.343339 | ||||||||
\(727\) | 10.9879 | 0.407518 | 0.203759 | − | 0.979021i | \(-0.434684\pi\) | ||||
0.203759 | + | 0.979021i | \(0.434684\pi\) | |||||||
\(728\) | −4.08535 | −0.151413 | ||||||||
\(729\) | 26.3742 | 0.976820 | ||||||||
\(730\) | −95.2491 | −3.52533 | ||||||||
\(731\) | −32.0072 | −1.18383 | ||||||||
\(732\) | 3.68566 | 0.136226 | ||||||||
\(733\) | 1.41767 | 0.0523629 | 0.0261814 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261814 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(734\) | 30.3525 | 1.12033 | ||||||||
\(735\) | −40.8663 | −1.50738 | ||||||||
\(736\) | 20.2816 | 0.747589 | ||||||||
\(737\) | −18.2692 | −0.672954 | ||||||||
\(738\) | −0.408993 | −0.0150552 | ||||||||
\(739\) | 52.0980 | 1.91646 | 0.958228 | − | 0.286006i | \(-0.0923277\pi\) | ||||
0.958228 | + | 0.286006i | \(0.0923277\pi\) | |||||||
\(740\) | 18.8747 | 0.693847 | ||||||||
\(741\) | −5.17339 | −0.190049 | ||||||||
\(742\) | 0.490281 | 0.0179988 | ||||||||
\(743\) | 38.1653 | 1.40015 | 0.700074 | − | 0.714070i | \(-0.253150\pi\) | ||||
0.700074 | + | 0.714070i | \(0.253150\pi\) | |||||||
\(744\) | 96.1024 | 3.52328 | ||||||||
\(745\) | −65.5578 | −2.40185 | ||||||||
\(746\) | −96.1538 | −3.52044 | ||||||||
\(747\) | −0.195760 | −0.00716247 | ||||||||
\(748\) | 133.529 | 4.88231 | ||||||||
\(749\) | −3.24044 | −0.118403 | ||||||||
\(750\) | −19.6665 | −0.718121 | ||||||||
\(751\) | −21.8905 | −0.798796 | −0.399398 | − | 0.916778i | \(-0.630781\pi\) | ||||
−0.399398 | + | 0.916778i | \(0.630781\pi\) | |||||||
\(752\) | 36.8832 | 1.34499 | ||||||||
\(753\) | 3.63304 | 0.132395 | ||||||||
\(754\) | −10.0473 | −0.365900 | ||||||||
\(755\) | −34.7808 | −1.26580 | ||||||||
\(756\) | −5.10694 | −0.185738 | ||||||||
\(757\) | 42.9653 | 1.56160 | 0.780799 | − | 0.624782i | \(-0.214812\pi\) | ||||
0.780799 | + | 0.624782i | \(0.214812\pi\) | |||||||
\(758\) | −14.9109 | −0.541589 | ||||||||
\(759\) | −5.00683 | −0.181736 | ||||||||
\(760\) | −43.1317 | −1.56455 | ||||||||
\(761\) | 18.0950 | 0.655944 | 0.327972 | − | 0.944687i | \(-0.393635\pi\) | ||||
0.327972 | + | 0.944687i | \(0.393635\pi\) | |||||||
\(762\) | −75.1162 | −2.72117 | ||||||||
\(763\) | 0.176382 | 0.00638547 | ||||||||
\(764\) | 102.883 | 3.72219 | ||||||||
\(765\) | 1.47066 | 0.0531717 | ||||||||
\(766\) | 50.8714 | 1.83806 | ||||||||
\(767\) | −11.8396 | −0.427504 | ||||||||
\(768\) | −122.893 | −4.43453 | ||||||||
\(769\) | −45.4054 | −1.63736 | −0.818680 | − | 0.574250i | \(-0.805294\pi\) | ||||
−0.818680 | + | 0.574250i | \(0.805294\pi\) | |||||||
\(770\) | 5.86497 | 0.211359 | ||||||||
\(771\) | −17.7756 | −0.640174 | ||||||||
\(772\) | 91.9162 | 3.30814 | ||||||||
\(773\) | −34.9339 | −1.25649 | −0.628243 | − | 0.778017i | \(-0.716226\pi\) | ||||
−0.628243 | + | 0.778017i | \(0.716226\pi\) | |||||||
\(774\) | −0.893669 | −0.0321223 | ||||||||
\(775\) | 33.9331 | 1.21891 | ||||||||
\(776\) | 32.8087 | 1.17776 | ||||||||
\(777\) | −0.308876 | −0.0110809 | ||||||||
\(778\) | 53.0691 | 1.90262 | ||||||||
\(779\) | −2.84778 | −0.102032 | ||||||||
\(780\) | −76.1829 | −2.72778 | ||||||||
\(781\) | −45.4330 | −1.62572 | ||||||||
\(782\) | −14.4966 | −0.518397 | ||||||||
\(783\) | −8.10313 | −0.289582 | ||||||||
\(784\) | −114.965 | −4.10588 | ||||||||
\(785\) | −24.2041 | −0.863881 | ||||||||
\(786\) | 30.8483 | 1.10032 | ||||||||
\(787\) | −6.56740 | −0.234102 | −0.117051 | − | 0.993126i | \(-0.537344\pi\) | ||||
−0.117051 | + | 0.993126i | \(0.537344\pi\) | |||||||
\(788\) | −48.1007 | −1.71352 | ||||||||
\(789\) | −12.6493 | −0.450328 | ||||||||
\(790\) | −4.32944 | −0.154035 | ||||||||
\(791\) | 0.0705999 | 0.00251024 | ||||||||
\(792\) | 2.40535 | 0.0854703 | ||||||||
\(793\) | 0.860651 | 0.0305626 | ||||||||
\(794\) | −28.7132 | −1.01899 | ||||||||
\(795\) | 5.89856 | 0.209200 | ||||||||
\(796\) | −80.4443 | −2.85127 | ||||||||
\(797\) | 14.1558 | 0.501424 | 0.250712 | − | 0.968062i | \(-0.419335\pi\) | ||||
0.250712 | + | 0.968062i | \(0.419335\pi\) | |||||||
\(798\) | 1.09403 | 0.0387282 | ||||||||
\(799\) | −14.7403 | −0.521474 | ||||||||
\(800\) | −158.381 | −5.59963 | ||||||||
\(801\) | 0.440684 | 0.0155708 | ||||||||
\(802\) | 71.5338 | 2.52595 | ||||||||
\(803\) | 36.9856 | 1.30519 | ||||||||
\(804\) | −50.1838 | −1.76985 | ||||||||
\(805\) | −0.469970 | −0.0165643 | ||||||||
\(806\) | 34.7835 | 1.22520 | ||||||||
\(807\) | 37.8113 | 1.33102 | ||||||||
\(808\) | −32.8584 | −1.15595 | ||||||||
\(809\) | 24.4879 | 0.860950 | 0.430475 | − | 0.902603i | \(-0.358346\pi\) | ||||
0.430475 | + | 0.902603i | \(0.358346\pi\) | |||||||
\(810\) | −85.0922 | −2.98983 | ||||||||
\(811\) | −51.0011 | −1.79089 | −0.895446 | − | 0.445170i | \(-0.853143\pi\) | ||||
−0.895446 | + | 0.445170i | \(0.853143\pi\) | |||||||
\(812\) | 1.56825 | 0.0550349 | ||||||||
\(813\) | −17.4455 | −0.611839 | ||||||||
\(814\) | −9.92974 | −0.348037 | ||||||||
\(815\) | 41.9428 | 1.46919 | ||||||||
\(816\) | 190.462 | 6.66749 | ||||||||
\(817\) | −6.22254 | −0.217699 | ||||||||
\(818\) | 29.0168 | 1.01455 | ||||||||
\(819\) | 0.0270810 | 0.000946285 0 | ||||||||
\(820\) | −41.9361 | −1.46447 | ||||||||
\(821\) | 7.63150 | 0.266341 | 0.133171 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133171 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(822\) | −55.4358 | −1.93355 | ||||||||
\(823\) | −43.7553 | −1.52522 | −0.762608 | − | 0.646861i | \(-0.776081\pi\) | ||||
−0.762608 | + | 0.646861i | \(0.776081\pi\) | |||||||
\(824\) | 194.057 | 6.76031 | ||||||||
\(825\) | 39.0989 | 1.36125 | ||||||||
\(826\) | 2.50375 | 0.0871167 | ||||||||
\(827\) | 19.5733 | 0.680632 | 0.340316 | − | 0.940311i | \(-0.389466\pi\) | ||||
0.340316 | + | 0.940311i | \(0.389466\pi\) | |||||||
\(828\) | −0.298751 | −0.0103823 | ||||||||
\(829\) | 48.5775 | 1.68717 | 0.843584 | − | 0.536998i | \(-0.180442\pi\) | ||||
0.843584 | + | 0.536998i | \(0.180442\pi\) | |||||||
\(830\) | −27.1945 | −0.943936 | ||||||||
\(831\) | 27.5983 | 0.957376 | ||||||||
\(832\) | −86.3045 | −2.99207 | ||||||||
\(833\) | 45.9453 | 1.59191 | ||||||||
\(834\) | 109.727 | 3.79954 | ||||||||
\(835\) | −22.0225 | −0.762119 | ||||||||
\(836\) | 25.9595 | 0.897828 | ||||||||
\(837\) | 28.0529 | 0.969650 | ||||||||
\(838\) | 61.9135 | 2.13877 | ||||||||
\(839\) | −51.4208 | −1.77524 | −0.887622 | − | 0.460572i | \(-0.847644\pi\) | ||||
−0.887622 | + | 0.460572i | \(0.847644\pi\) | |||||||
\(840\) | 10.3940 | 0.358628 | ||||||||
\(841\) | −26.5117 | −0.914195 | ||||||||
\(842\) | −31.5448 | −1.08711 | ||||||||
\(843\) | −38.2792 | −1.31841 | ||||||||
\(844\) | −95.2907 | −3.28004 | ||||||||
\(845\) | 25.7430 | 0.885587 | ||||||||
\(846\) | −0.411562 | −0.0141498 | ||||||||
\(847\) | −0.337187 | −0.0115859 | ||||||||
\(848\) | 16.5937 | 0.569831 | ||||||||
\(849\) | 21.6585 | 0.743316 | ||||||||
\(850\) | 113.206 | 3.88292 | ||||||||
\(851\) | 0.795686 | 0.0272758 | ||||||||
\(852\) | −124.800 | −4.27559 | ||||||||
\(853\) | 27.3523 | 0.936524 | 0.468262 | − | 0.883590i | \(-0.344880\pi\) | ||||
0.468262 | + | 0.883590i | \(0.344880\pi\) | |||||||
\(854\) | −0.182004 | −0.00622804 | ||||||||
\(855\) | 0.285911 | 0.00977796 | ||||||||
\(856\) | −184.618 | −6.31011 | ||||||||
\(857\) | 14.0844 | 0.481113 | 0.240556 | − | 0.970635i | \(-0.422670\pi\) | ||||
0.240556 | + | 0.970635i | \(0.422670\pi\) | |||||||
\(858\) | 40.0789 | 1.36827 | ||||||||
\(859\) | −6.32851 | −0.215926 | −0.107963 | − | 0.994155i | \(-0.534433\pi\) | ||||
−0.107963 | + | 0.994155i | \(0.534433\pi\) | |||||||
\(860\) | −91.6325 | −3.12464 | ||||||||
\(861\) | 0.686268 | 0.0233879 | ||||||||
\(862\) | 80.0683 | 2.72714 | ||||||||
\(863\) | 19.1930 | 0.653337 | 0.326669 | − | 0.945139i | \(-0.394074\pi\) | ||||
0.326669 | + | 0.945139i | \(0.394074\pi\) | |||||||
\(864\) | −130.936 | −4.45453 | ||||||||
\(865\) | −41.0380 | −1.39533 | ||||||||
\(866\) | 25.3867 | 0.862675 | ||||||||
\(867\) | −46.3476 | −1.57405 | ||||||||
\(868\) | −5.42927 | −0.184281 | ||||||||
\(869\) | 1.68114 | 0.0570289 | ||||||||
\(870\) | 25.5625 | 0.866648 | ||||||||
\(871\) | −11.7186 | −0.397069 | ||||||||
\(872\) | 10.0491 | 0.340304 | ||||||||
\(873\) | −0.217482 | −0.00736066 | ||||||||
\(874\) | −2.81829 | −0.0953301 | ||||||||
\(875\) | 0.716816 | 0.0242328 | ||||||||
\(876\) | 101.596 | 3.43262 | ||||||||
\(877\) | −29.0388 | −0.980570 | −0.490285 | − | 0.871562i | \(-0.663107\pi\) | ||||
−0.490285 | + | 0.871562i | \(0.663107\pi\) | |||||||
\(878\) | −47.8748 | −1.61570 | ||||||||
\(879\) | 26.6999 | 0.900566 | ||||||||
\(880\) | 198.502 | 6.69149 | ||||||||
\(881\) | 56.3133 | 1.89724 | 0.948622 | − | 0.316412i | \(-0.102478\pi\) | ||||
0.948622 | + | 0.316412i | \(0.102478\pi\) | |||||||
\(882\) | 1.28283 | 0.0431953 | ||||||||
\(883\) | 50.8746 | 1.71207 | 0.856034 | − | 0.516920i | \(-0.172921\pi\) | ||||
0.856034 | + | 0.516920i | \(0.172921\pi\) | |||||||
\(884\) | 85.6511 | 2.88076 | ||||||||
\(885\) | 30.1226 | 1.01256 | ||||||||
\(886\) | 77.5306 | 2.60469 | ||||||||
\(887\) | −1.99453 | −0.0669698 | −0.0334849 | − | 0.999439i | \(-0.510661\pi\) | ||||
−0.0334849 | + | 0.999439i | \(0.510661\pi\) | |||||||
\(888\) | −17.5977 | −0.590539 | ||||||||
\(889\) | 2.73787 | 0.0918253 | ||||||||
\(890\) | 61.2190 | 2.05206 | ||||||||
\(891\) | 33.0417 | 1.10694 | ||||||||
\(892\) | 101.222 | 3.38915 | ||||||||
\(893\) | −2.86567 | −0.0958960 | ||||||||
\(894\) | 94.7387 | 3.16853 | ||||||||
\(895\) | 70.8912 | 2.36963 | ||||||||
\(896\) | 9.25923 | 0.309329 | ||||||||
\(897\) | −3.21159 | −0.107232 | ||||||||
\(898\) | −21.2085 | −0.707737 | ||||||||
\(899\) | −8.61456 | −0.287312 | ||||||||
\(900\) | 2.33298 | 0.0777661 | ||||||||
\(901\) | −6.63165 | −0.220932 | ||||||||
\(902\) | 22.0621 | 0.734587 | ||||||||
\(903\) | 1.49953 | 0.0499012 | ||||||||
\(904\) | 4.02230 | 0.133780 | ||||||||
\(905\) | −47.1696 | −1.56797 | ||||||||
\(906\) | 50.2623 | 1.66985 | ||||||||
\(907\) | 10.2607 | 0.340701 | 0.170351 | − | 0.985383i | \(-0.445510\pi\) | ||||
0.170351 | + | 0.985383i | \(0.445510\pi\) | |||||||
\(908\) | 78.8380 | 2.61633 | ||||||||
\(909\) | 0.217811 | 0.00722435 | ||||||||
\(910\) | 3.76203 | 0.124710 | ||||||||
\(911\) | 17.1599 | 0.568533 | 0.284266 | − | 0.958745i | \(-0.408250\pi\) | ||||
0.284266 | + | 0.958745i | \(0.408250\pi\) | |||||||
\(912\) | 37.0278 | 1.22611 | ||||||||
\(913\) | 10.5598 | 0.349477 | ||||||||
\(914\) | 62.7500 | 2.07559 | ||||||||
\(915\) | −2.18968 | −0.0723887 | ||||||||
\(916\) | −13.4371 | −0.443975 | ||||||||
\(917\) | −1.12437 | −0.0371301 | ||||||||
\(918\) | 93.5886 | 3.08888 | ||||||||
\(919\) | −38.8770 | −1.28244 | −0.641218 | − | 0.767359i | \(-0.721570\pi\) | ||||
−0.641218 | + | 0.767359i | \(0.721570\pi\) | |||||||
\(920\) | −26.7757 | −0.882768 | ||||||||
\(921\) | −58.6535 | −1.93270 | ||||||||
\(922\) | 5.47744 | 0.180390 | ||||||||
\(923\) | −29.1426 | −0.959239 | ||||||||
\(924\) | −6.25580 | −0.205801 | ||||||||
\(925\) | −6.21361 | −0.204302 | ||||||||
\(926\) | 38.3201 | 1.25928 | ||||||||
\(927\) | −1.28637 | −0.0422498 | ||||||||
\(928\) | 40.2082 | 1.31990 | ||||||||
\(929\) | 41.7187 | 1.36875 | 0.684373 | − | 0.729132i | \(-0.260076\pi\) | ||||
0.684373 | + | 0.729132i | \(0.260076\pi\) | |||||||
\(930\) | −88.4967 | −2.90192 | ||||||||
\(931\) | 8.93226 | 0.292743 | ||||||||
\(932\) | 48.4797 | 1.58800 | ||||||||
\(933\) | 48.8279 | 1.59855 | ||||||||
\(934\) | 57.0410 | 1.86644 | ||||||||
\(935\) | −79.3308 | −2.59440 | ||||||||
\(936\) | 1.54289 | 0.0504309 | ||||||||
\(937\) | −58.8071 | −1.92114 | −0.960571 | − | 0.278034i | \(-0.910317\pi\) | ||||
−0.960571 | + | 0.278034i | \(0.910317\pi\) | |||||||
\(938\) | 2.47816 | 0.0809147 | ||||||||
\(939\) | 35.1076 | 1.14569 | ||||||||
\(940\) | −42.1995 | −1.37640 | ||||||||
\(941\) | 3.86886 | 0.126121 | 0.0630607 | − | 0.998010i | \(-0.479914\pi\) | ||||
0.0630607 | + | 0.998010i | \(0.479914\pi\) | |||||||
\(942\) | 34.9777 | 1.13964 | ||||||||
\(943\) | −1.76787 | −0.0575698 | ||||||||
\(944\) | 84.7403 | 2.75806 | ||||||||
\(945\) | 3.03408 | 0.0986986 | ||||||||
\(946\) | 48.2067 | 1.56734 | ||||||||
\(947\) | −31.6269 | −1.02774 | −0.513868 | − | 0.857870i | \(-0.671788\pi\) | ||||
−0.513868 | + | 0.857870i | \(0.671788\pi\) | |||||||
\(948\) | 4.61795 | 0.149984 | ||||||||
\(949\) | 23.7241 | 0.770117 | ||||||||
\(950\) | 22.0084 | 0.714046 | ||||||||
\(951\) | −11.7914 | −0.382363 | ||||||||
\(952\) | −11.6858 | −0.378739 | ||||||||
\(953\) | 10.8278 | 0.350746 | 0.175373 | − | 0.984502i | \(-0.443887\pi\) | ||||
0.175373 | + | 0.984502i | \(0.443887\pi\) | |||||||
\(954\) | −0.185161 | −0.00599482 | ||||||||
\(955\) | −61.1239 | −1.97792 | ||||||||
\(956\) | 152.477 | 4.93146 | ||||||||
\(957\) | −9.92602 | −0.320863 | ||||||||
\(958\) | 83.0326 | 2.68266 | ||||||||
\(959\) | 2.02055 | 0.0652470 | ||||||||
\(960\) | 219.577 | 7.08683 | ||||||||
\(961\) | −1.17657 | −0.0379538 | ||||||||
\(962\) | −6.36934 | −0.205356 | ||||||||
\(963\) | 1.22380 | 0.0394363 | ||||||||
\(964\) | 61.5809 | 1.98339 | ||||||||
\(965\) | −54.6082 | −1.75790 | ||||||||
\(966\) | 0.679161 | 0.0218517 | ||||||||
\(967\) | −20.5370 | −0.660427 | −0.330213 | − | 0.943906i | \(-0.607121\pi\) | ||||
−0.330213 | + | 0.943906i | \(0.607121\pi\) | |||||||
\(968\) | −19.2106 | −0.617453 | ||||||||
\(969\) | −14.7981 | −0.475383 | ||||||||
\(970\) | −30.2122 | −0.970055 | ||||||||
\(971\) | −31.4658 | −1.00979 | −0.504893 | − | 0.863182i | \(-0.668468\pi\) | ||||
−0.504893 | + | 0.863182i | \(0.668468\pi\) | |||||||
\(972\) | 3.90121 | 0.125131 | ||||||||
\(973\) | −3.99938 | −0.128214 | ||||||||
\(974\) | 1.34191 | 0.0429977 | ||||||||
\(975\) | 25.0797 | 0.803192 | ||||||||
\(976\) | −6.15998 | −0.197176 | ||||||||
\(977\) | −57.3742 | −1.83556 | −0.917782 | − | 0.397084i | \(-0.870022\pi\) | ||||
−0.917782 | + | 0.397084i | \(0.870022\pi\) | |||||||
\(978\) | −60.6123 | −1.93817 | ||||||||
\(979\) | −23.7716 | −0.759744 | ||||||||
\(980\) | 131.536 | 4.20175 | ||||||||
\(981\) | −0.0666133 | −0.00212680 | ||||||||
\(982\) | −116.918 | −3.73099 | ||||||||
\(983\) | 53.3569 | 1.70182 | 0.850910 | − | 0.525312i | \(-0.176051\pi\) | ||||
0.850910 | + | 0.525312i | \(0.176051\pi\) | |||||||
\(984\) | 39.0989 | 1.24643 | ||||||||
\(985\) | 28.5771 | 0.910541 | ||||||||
\(986\) | −28.7394 | −0.915250 | ||||||||
\(987\) | 0.690578 | 0.0219813 | ||||||||
\(988\) | 16.6515 | 0.529754 | ||||||||
\(989\) | −3.86288 | −0.122833 | ||||||||
\(990\) | −2.21499 | −0.0703969 | ||||||||
\(991\) | −44.4308 | −1.41139 | −0.705695 | − | 0.708516i | \(-0.749365\pi\) | ||||
−0.705695 | + | 0.708516i | \(0.749365\pi\) | |||||||
\(992\) | −139.200 | −4.41960 | ||||||||
\(993\) | 2.97456 | 0.0943947 | ||||||||
\(994\) | 6.16285 | 0.195474 | ||||||||
\(995\) | 47.7926 | 1.51513 | ||||||||
\(996\) | 29.0067 | 0.919114 | ||||||||
\(997\) | 52.0182 | 1.64743 | 0.823717 | − | 0.567002i | \(-0.191897\pi\) | ||||
0.823717 | + | 0.567002i | \(0.191897\pi\) | |||||||
\(998\) | −66.3210 | −2.09936 | ||||||||
\(999\) | −5.13687 | −0.162523 |
(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 | 4033.2.a.d.1.3 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.3 | ✓ | 79 | 1.1 | even | 1 | trivial |