Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32373 | −0.936016 | −0.468008 | − | 0.883724i | \(-0.655028\pi\) | ||||
−0.468008 | + | 0.883724i | \(0.655028\pi\) | |||||||
\(3\) | −3.06819 | −1.77142 | −0.885710 | − | 0.464238i | \(-0.846328\pi\) | ||||
−0.885710 | + | 0.464238i | \(0.846328\pi\) | |||||||
\(4\) | −0.247749 | −0.123875 | ||||||||
\(5\) | 3.29067 | 1.47163 | 0.735815 | − | 0.677182i | \(-0.236799\pi\) | ||||
0.735815 | + | 0.677182i | \(0.236799\pi\) | |||||||
\(6\) | 4.06144 | 1.65808 | ||||||||
\(7\) | −2.61144 | −0.987032 | −0.493516 | − | 0.869737i | \(-0.664289\pi\) | ||||
−0.493516 | + | 0.869737i | \(0.664289\pi\) | |||||||
\(8\) | 2.97540 | 1.05196 | ||||||||
\(9\) | 6.41379 | 2.13793 | ||||||||
\(10\) | −4.35594 | −1.37747 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.760142 | 0.219434 | ||||||||
\(13\) | 5.06631 | 1.40514 | 0.702571 | − | 0.711614i | \(-0.252035\pi\) | ||||
0.702571 | + | 0.711614i | \(0.252035\pi\) | |||||||
\(14\) | 3.45683 | 0.923877 | ||||||||
\(15\) | −10.0964 | −2.60688 | ||||||||
\(16\) | −3.44312 | −0.860780 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −8.49010 | −2.00114 | ||||||||
\(19\) | 5.54578 | 1.27229 | 0.636145 | − | 0.771570i | \(-0.280528\pi\) | ||||
0.636145 | + | 0.771570i | \(0.280528\pi\) | |||||||
\(20\) | −0.815260 | −0.182298 | ||||||||
\(21\) | 8.01240 | 1.74845 | ||||||||
\(22\) | −1.32373 | −0.282219 | ||||||||
\(23\) | 1.26421 | 0.263606 | 0.131803 | − | 0.991276i | \(-0.457923\pi\) | ||||
0.131803 | + | 0.991276i | \(0.457923\pi\) | |||||||
\(24\) | −9.12911 | −1.86347 | ||||||||
\(25\) | 5.82848 | 1.16570 | ||||||||
\(26\) | −6.70641 | −1.31523 | ||||||||
\(27\) | −10.4742 | −2.01575 | ||||||||
\(28\) | 0.646983 | 0.122268 | ||||||||
\(29\) | −5.31625 | −0.987202 | −0.493601 | − | 0.869688i | \(-0.664320\pi\) | ||||
−0.493601 | + | 0.869688i | \(0.664320\pi\) | |||||||
\(30\) | 13.3649 | 2.44008 | ||||||||
\(31\) | 5.32587 | 0.956554 | 0.478277 | − | 0.878209i | \(-0.341261\pi\) | ||||
0.478277 | + | 0.878209i | \(0.341261\pi\) | |||||||
\(32\) | −1.39306 | −0.246260 | ||||||||
\(33\) | −3.06819 | −0.534103 | ||||||||
\(34\) | −1.32373 | −0.227017 | ||||||||
\(35\) | −8.59338 | −1.45255 | ||||||||
\(36\) | −1.58901 | −0.264835 | ||||||||
\(37\) | 11.0730 | 1.82039 | 0.910193 | − | 0.414183i | \(-0.135933\pi\) | ||||
0.910193 | + | 0.414183i | \(0.135933\pi\) | |||||||
\(38\) | −7.34109 | −1.19088 | ||||||||
\(39\) | −15.5444 | −2.48910 | ||||||||
\(40\) | 9.79106 | 1.54810 | ||||||||
\(41\) | −7.71007 | −1.20411 | −0.602055 | − | 0.798454i | \(-0.705651\pi\) | ||||
−0.602055 | + | 0.798454i | \(0.705651\pi\) | |||||||
\(42\) | −10.6062 | −1.63658 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −0.247749 | −0.0373496 | ||||||||
\(45\) | 21.1056 | 3.14624 | ||||||||
\(46\) | −1.67347 | −0.246739 | ||||||||
\(47\) | −7.04648 | −1.02783 | −0.513917 | − | 0.857840i | \(-0.671806\pi\) | ||||
−0.513917 | + | 0.857840i | \(0.671806\pi\) | |||||||
\(48\) | 10.5642 | 1.52480 | ||||||||
\(49\) | −0.180376 | −0.0257679 | ||||||||
\(50\) | −7.71531 | −1.09111 | ||||||||
\(51\) | −3.06819 | −0.429633 | ||||||||
\(52\) | −1.25517 | −0.174061 | ||||||||
\(53\) | −2.42816 | −0.333533 | −0.166767 | − | 0.985996i | \(-0.553333\pi\) | ||||
−0.166767 | + | 0.985996i | \(0.553333\pi\) | |||||||
\(54\) | 13.8649 | 1.88678 | ||||||||
\(55\) | 3.29067 | 0.443713 | ||||||||
\(56\) | −7.77009 | −1.03832 | ||||||||
\(57\) | −17.0155 | −2.25376 | ||||||||
\(58\) | 7.03725 | 0.924037 | ||||||||
\(59\) | 0.973284 | 0.126711 | 0.0633554 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633554 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(60\) | 2.50137 | 0.322926 | ||||||||
\(61\) | −8.10682 | −1.03797 | −0.518986 | − | 0.854783i | \(-0.673690\pi\) | ||||
−0.518986 | + | 0.854783i | \(0.673690\pi\) | |||||||
\(62\) | −7.04999 | −0.895350 | ||||||||
\(63\) | −16.7492 | −2.11021 | ||||||||
\(64\) | 8.73027 | 1.09128 | ||||||||
\(65\) | 16.6715 | 2.06785 | ||||||||
\(66\) | 4.06144 | 0.499929 | ||||||||
\(67\) | −10.8514 | −1.32571 | −0.662854 | − | 0.748749i | \(-0.730655\pi\) | ||||
−0.662854 | + | 0.748749i | \(0.730655\pi\) | |||||||
\(68\) | −0.247749 | −0.0300440 | ||||||||
\(69\) | −3.87884 | −0.466957 | ||||||||
\(70\) | 11.3753 | 1.35961 | ||||||||
\(71\) | −12.4014 | −1.47178 | −0.735890 | − | 0.677101i | \(-0.763236\pi\) | ||||
−0.735890 | + | 0.677101i | \(0.763236\pi\) | |||||||
\(72\) | 19.0836 | 2.24903 | ||||||||
\(73\) | 10.2699 | 1.20200 | 0.601000 | − | 0.799249i | \(-0.294769\pi\) | ||||
0.601000 | + | 0.799249i | \(0.294769\pi\) | |||||||
\(74\) | −14.6576 | −1.70391 | ||||||||
\(75\) | −17.8829 | −2.06494 | ||||||||
\(76\) | −1.37396 | −0.157604 | ||||||||
\(77\) | −2.61144 | −0.297601 | ||||||||
\(78\) | 20.5765 | 2.32983 | ||||||||
\(79\) | −4.52430 | −0.509024 | −0.254512 | − | 0.967070i | \(-0.581915\pi\) | ||||
−0.254512 | + | 0.967070i | \(0.581915\pi\) | |||||||
\(80\) | −11.3302 | −1.26675 | ||||||||
\(81\) | 12.8954 | 1.43282 | ||||||||
\(82\) | 10.2060 | 1.12707 | ||||||||
\(83\) | −15.1729 | −1.66544 | −0.832721 | − | 0.553693i | \(-0.813218\pi\) | ||||
−0.832721 | + | 0.553693i | \(0.813218\pi\) | |||||||
\(84\) | −1.98507 | −0.216588 | ||||||||
\(85\) | 3.29067 | 0.356923 | ||||||||
\(86\) | 1.32373 | 0.142741 | ||||||||
\(87\) | 16.3113 | 1.74875 | ||||||||
\(88\) | 2.97540 | 0.317179 | ||||||||
\(89\) | −16.7185 | −1.77216 | −0.886079 | − | 0.463533i | \(-0.846581\pi\) | ||||
−0.886079 | + | 0.463533i | \(0.846581\pi\) | |||||||
\(90\) | −27.9381 | −2.94493 | ||||||||
\(91\) | −13.2304 | −1.38692 | ||||||||
\(92\) | −0.313207 | −0.0326541 | ||||||||
\(93\) | −16.3408 | −1.69446 | ||||||||
\(94\) | 9.32761 | 0.962069 | ||||||||
\(95\) | 18.2493 | 1.87234 | ||||||||
\(96\) | 4.27417 | 0.436231 | ||||||||
\(97\) | 0.313815 | 0.0318631 | 0.0159316 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159316 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(98\) | 0.238768 | 0.0241192 | ||||||||
\(99\) | 6.41379 | 0.644610 | ||||||||
\(100\) | −1.44400 | −0.144400 | ||||||||
\(101\) | −7.44088 | −0.740395 | −0.370198 | − | 0.928953i | \(-0.620710\pi\) | ||||
−0.370198 | + | 0.928953i | \(0.620710\pi\) | |||||||
\(102\) | 4.06144 | 0.402143 | ||||||||
\(103\) | −1.17331 | −0.115610 | −0.0578049 | − | 0.998328i | \(-0.518410\pi\) | ||||
−0.0578049 | + | 0.998328i | \(0.518410\pi\) | |||||||
\(104\) | 15.0743 | 1.47816 | ||||||||
\(105\) | 26.3661 | 2.57307 | ||||||||
\(106\) | 3.21422 | 0.312193 | ||||||||
\(107\) | −11.4399 | −1.10594 | −0.552970 | − | 0.833201i | \(-0.686505\pi\) | ||||
−0.552970 | + | 0.833201i | \(0.686505\pi\) | |||||||
\(108\) | 2.59497 | 0.249701 | ||||||||
\(109\) | 9.33134 | 0.893780 | 0.446890 | − | 0.894589i | \(-0.352532\pi\) | ||||
0.446890 | + | 0.894589i | \(0.352532\pi\) | |||||||
\(110\) | −4.35594 | −0.415323 | ||||||||
\(111\) | −33.9740 | −3.22467 | ||||||||
\(112\) | 8.99151 | 0.849618 | ||||||||
\(113\) | −12.7753 | −1.20180 | −0.600898 | − | 0.799326i | \(-0.705190\pi\) | ||||
−0.600898 | + | 0.799326i | \(0.705190\pi\) | |||||||
\(114\) | 22.5239 | 2.10955 | ||||||||
\(115\) | 4.16009 | 0.387930 | ||||||||
\(116\) | 1.31710 | 0.122289 | ||||||||
\(117\) | 32.4943 | 3.00410 | ||||||||
\(118\) | −1.28836 | −0.118603 | ||||||||
\(119\) | −2.61144 | −0.239390 | ||||||||
\(120\) | −30.0408 | −2.74234 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 10.7312 | 0.971558 | ||||||||
\(123\) | 23.6560 | 2.13299 | ||||||||
\(124\) | −1.31948 | −0.118493 | ||||||||
\(125\) | 2.72625 | 0.243843 | ||||||||
\(126\) | 22.1714 | 1.97519 | ||||||||
\(127\) | −3.00321 | −0.266492 | −0.133246 | − | 0.991083i | \(-0.542540\pi\) | ||||
−0.133246 | + | 0.991083i | \(0.542540\pi\) | |||||||
\(128\) | −8.77037 | −0.775199 | ||||||||
\(129\) | 3.06819 | 0.270139 | ||||||||
\(130\) | −22.0685 | −1.93554 | ||||||||
\(131\) | 8.95047 | 0.782006 | 0.391003 | − | 0.920389i | \(-0.372128\pi\) | ||||
0.391003 | + | 0.920389i | \(0.372128\pi\) | |||||||
\(132\) | 0.760142 | 0.0661619 | ||||||||
\(133\) | −14.4825 | −1.25579 | ||||||||
\(134\) | 14.3643 | 1.24088 | ||||||||
\(135\) | −34.4670 | −2.96645 | ||||||||
\(136\) | 2.97540 | 0.255139 | ||||||||
\(137\) | −14.4207 | −1.23204 | −0.616020 | − | 0.787731i | \(-0.711256\pi\) | ||||
−0.616020 | + | 0.787731i | \(0.711256\pi\) | |||||||
\(138\) | 5.13452 | 0.437079 | ||||||||
\(139\) | −21.3866 | −1.81399 | −0.906994 | − | 0.421144i | \(-0.861629\pi\) | ||||
−0.906994 | + | 0.421144i | \(0.861629\pi\) | |||||||
\(140\) | 2.12900 | 0.179934 | ||||||||
\(141\) | 21.6199 | 1.82073 | ||||||||
\(142\) | 16.4161 | 1.37761 | ||||||||
\(143\) | 5.06631 | 0.423666 | ||||||||
\(144\) | −22.0835 | −1.84029 | ||||||||
\(145\) | −17.4940 | −1.45280 | ||||||||
\(146\) | −13.5945 | −1.12509 | ||||||||
\(147\) | 0.553427 | 0.0456458 | ||||||||
\(148\) | −2.74332 | −0.225500 | ||||||||
\(149\) | 14.6922 | 1.20363 | 0.601816 | − | 0.798634i | \(-0.294444\pi\) | ||||
0.601816 | + | 0.798634i | \(0.294444\pi\) | |||||||
\(150\) | 23.6720 | 1.93281 | ||||||||
\(151\) | −0.122631 | −0.00997955 | −0.00498977 | − | 0.999988i | \(-0.501588\pi\) | ||||
−0.00498977 | + | 0.999988i | \(0.501588\pi\) | |||||||
\(152\) | 16.5009 | 1.33840 | ||||||||
\(153\) | 6.41379 | 0.518524 | ||||||||
\(154\) | 3.45683 | 0.278560 | ||||||||
\(155\) | 17.5257 | 1.40769 | ||||||||
\(156\) | 3.85112 | 0.308336 | ||||||||
\(157\) | −10.0524 | −0.802266 | −0.401133 | − | 0.916020i | \(-0.631384\pi\) | ||||
−0.401133 | + | 0.916020i | \(0.631384\pi\) | |||||||
\(158\) | 5.98894 | 0.476454 | ||||||||
\(159\) | 7.45006 | 0.590828 | ||||||||
\(160\) | −4.58409 | −0.362404 | ||||||||
\(161\) | −3.30141 | −0.260187 | ||||||||
\(162\) | −17.0699 | −1.34114 | ||||||||
\(163\) | −5.30239 | −0.415316 | −0.207658 | − | 0.978202i | \(-0.566584\pi\) | ||||
−0.207658 | + | 0.978202i | \(0.566584\pi\) | |||||||
\(164\) | 1.91016 | 0.149159 | ||||||||
\(165\) | −10.0964 | −0.786003 | ||||||||
\(166\) | 20.0848 | 1.55888 | ||||||||
\(167\) | 12.9321 | 1.00071 | 0.500356 | − | 0.865820i | \(-0.333202\pi\) | ||||
0.500356 | + | 0.865820i | \(0.333202\pi\) | |||||||
\(168\) | 23.8401 | 1.83931 | ||||||||
\(169\) | 12.6675 | 0.974424 | ||||||||
\(170\) | −4.35594 | −0.334085 | ||||||||
\(171\) | 35.5695 | 2.72007 | ||||||||
\(172\) | 0.247749 | 0.0188907 | ||||||||
\(173\) | −3.39988 | −0.258488 | −0.129244 | − | 0.991613i | \(-0.541255\pi\) | ||||
−0.129244 | + | 0.991613i | \(0.541255\pi\) | |||||||
\(174\) | −21.5916 | −1.63686 | ||||||||
\(175\) | −15.2207 | −1.15058 | ||||||||
\(176\) | −3.44312 | −0.259535 | ||||||||
\(177\) | −2.98622 | −0.224458 | ||||||||
\(178\) | 22.1307 | 1.65877 | ||||||||
\(179\) | −5.87314 | −0.438979 | −0.219490 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219490 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(180\) | −5.22891 | −0.389740 | ||||||||
\(181\) | −1.69841 | −0.126242 | −0.0631208 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631208 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(182\) | 17.5134 | 1.29818 | ||||||||
\(183\) | 24.8733 | 1.83868 | ||||||||
\(184\) | 3.76153 | 0.277304 | ||||||||
\(185\) | 36.4375 | 2.67894 | ||||||||
\(186\) | 21.6307 | 1.58604 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 1.74576 | 0.127323 | ||||||||
\(189\) | 27.3527 | 1.98961 | ||||||||
\(190\) | −24.1571 | −1.75254 | ||||||||
\(191\) | −8.94524 | −0.647255 | −0.323627 | − | 0.946185i | \(-0.604902\pi\) | ||||
−0.323627 | + | 0.946185i | \(0.604902\pi\) | |||||||
\(192\) | −26.7861 | −1.93312 | ||||||||
\(193\) | 8.63763 | 0.621750 | 0.310875 | − | 0.950451i | \(-0.399378\pi\) | ||||
0.310875 | + | 0.950451i | \(0.399378\pi\) | |||||||
\(194\) | −0.415406 | −0.0298244 | ||||||||
\(195\) | −51.1514 | −3.66303 | ||||||||
\(196\) | 0.0446879 | 0.00319199 | ||||||||
\(197\) | 0.920019 | 0.0655487 | 0.0327743 | − | 0.999463i | \(-0.489566\pi\) | ||||
0.0327743 | + | 0.999463i | \(0.489566\pi\) | |||||||
\(198\) | −8.49010 | −0.603365 | ||||||||
\(199\) | 5.49924 | 0.389831 | 0.194915 | − | 0.980820i | \(-0.437557\pi\) | ||||
0.194915 | + | 0.980820i | \(0.437557\pi\) | |||||||
\(200\) | 17.3421 | 1.22627 | ||||||||
\(201\) | 33.2941 | 2.34839 | ||||||||
\(202\) | 9.84968 | 0.693021 | ||||||||
\(203\) | 13.8831 | 0.974400 | ||||||||
\(204\) | 0.760142 | 0.0532206 | ||||||||
\(205\) | −25.3713 | −1.77201 | ||||||||
\(206\) | 1.55314 | 0.108213 | ||||||||
\(207\) | 8.10838 | 0.563571 | ||||||||
\(208\) | −17.4439 | −1.20952 | ||||||||
\(209\) | 5.54578 | 0.383610 | ||||||||
\(210\) | −34.9015 | −2.40843 | ||||||||
\(211\) | −20.5953 | −1.41784 | −0.708921 | − | 0.705288i | \(-0.750818\pi\) | ||||
−0.708921 | + | 0.705288i | \(0.750818\pi\) | |||||||
\(212\) | 0.601575 | 0.0413163 | ||||||||
\(213\) | 38.0500 | 2.60714 | ||||||||
\(214\) | 15.1433 | 1.03518 | ||||||||
\(215\) | −3.29067 | −0.224422 | ||||||||
\(216\) | −31.1649 | −2.12050 | ||||||||
\(217\) | −13.9082 | −0.944150 | ||||||||
\(218\) | −12.3521 | −0.836592 | ||||||||
\(219\) | −31.5100 | −2.12925 | ||||||||
\(220\) | −0.815260 | −0.0549648 | ||||||||
\(221\) | 5.06631 | 0.340797 | ||||||||
\(222\) | 44.9723 | 3.01834 | ||||||||
\(223\) | −12.5594 | −0.841040 | −0.420520 | − | 0.907283i | \(-0.638152\pi\) | ||||
−0.420520 | + | 0.907283i | \(0.638152\pi\) | |||||||
\(224\) | 3.63789 | 0.243067 | ||||||||
\(225\) | 37.3827 | 2.49218 | ||||||||
\(226\) | 16.9109 | 1.12490 | ||||||||
\(227\) | −19.5012 | −1.29434 | −0.647169 | − | 0.762347i | \(-0.724047\pi\) | ||||
−0.647169 | + | 0.762347i | \(0.724047\pi\) | |||||||
\(228\) | 4.21558 | 0.279184 | ||||||||
\(229\) | 6.23187 | 0.411814 | 0.205907 | − | 0.978572i | \(-0.433986\pi\) | ||||
0.205907 | + | 0.978572i | \(0.433986\pi\) | |||||||
\(230\) | −5.50682 | −0.363109 | ||||||||
\(231\) | 8.01240 | 0.527177 | ||||||||
\(232\) | −15.8180 | −1.03850 | ||||||||
\(233\) | 3.71757 | 0.243546 | 0.121773 | − | 0.992558i | \(-0.461142\pi\) | ||||
0.121773 | + | 0.992558i | \(0.461142\pi\) | |||||||
\(234\) | −43.0135 | −2.81188 | ||||||||
\(235\) | −23.1876 | −1.51259 | ||||||||
\(236\) | −0.241130 | −0.0156962 | ||||||||
\(237\) | 13.8814 | 0.901695 | ||||||||
\(238\) | 3.45683 | 0.224073 | ||||||||
\(239\) | −3.50632 | −0.226805 | −0.113403 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113403 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(240\) | 34.7631 | 2.24395 | ||||||||
\(241\) | −3.37137 | −0.217169 | −0.108585 | − | 0.994087i | \(-0.534632\pi\) | ||||
−0.108585 | + | 0.994087i | \(0.534632\pi\) | |||||||
\(242\) | −1.32373 | −0.0850923 | ||||||||
\(243\) | −8.14291 | −0.522368 | ||||||||
\(244\) | 2.00846 | 0.128578 | ||||||||
\(245\) | −0.593556 | −0.0379209 | ||||||||
\(246\) | −31.3140 | −1.99651 | ||||||||
\(247\) | 28.0966 | 1.78775 | ||||||||
\(248\) | 15.8466 | 1.00626 | ||||||||
\(249\) | 46.5533 | 2.95020 | ||||||||
\(250\) | −3.60881 | −0.228241 | ||||||||
\(251\) | 0.348846 | 0.0220190 | 0.0110095 | − | 0.999939i | \(-0.496496\pi\) | ||||
0.0110095 | + | 0.999939i | \(0.496496\pi\) | |||||||
\(252\) | 4.14961 | 0.261401 | ||||||||
\(253\) | 1.26421 | 0.0794802 | ||||||||
\(254\) | 3.97542 | 0.249440 | ||||||||
\(255\) | −10.0964 | −0.632260 | ||||||||
\(256\) | −5.85097 | −0.365686 | ||||||||
\(257\) | 20.2449 | 1.26284 | 0.631422 | − | 0.775439i | \(-0.282472\pi\) | ||||
0.631422 | + | 0.775439i | \(0.282472\pi\) | |||||||
\(258\) | −4.06144 | −0.252854 | ||||||||
\(259\) | −28.9164 | −1.79678 | ||||||||
\(260\) | −4.13036 | −0.256154 | ||||||||
\(261\) | −34.0973 | −2.11057 | ||||||||
\(262\) | −11.8480 | −0.731970 | ||||||||
\(263\) | −13.3935 | −0.825877 | −0.412939 | − | 0.910759i | \(-0.635498\pi\) | ||||
−0.412939 | + | 0.910759i | \(0.635498\pi\) | |||||||
\(264\) | −9.12911 | −0.561858 | ||||||||
\(265\) | −7.99026 | −0.490838 | ||||||||
\(266\) | 19.1708 | 1.17544 | ||||||||
\(267\) | 51.2956 | 3.13924 | ||||||||
\(268\) | 2.68842 | 0.164222 | ||||||||
\(269\) | 10.5138 | 0.641040 | 0.320520 | − | 0.947242i | \(-0.396142\pi\) | ||||
0.320520 | + | 0.947242i | \(0.396142\pi\) | |||||||
\(270\) | 45.6248 | 2.77664 | ||||||||
\(271\) | −16.3128 | −0.990930 | −0.495465 | − | 0.868628i | \(-0.665002\pi\) | ||||
−0.495465 | + | 0.868628i | \(0.665002\pi\) | |||||||
\(272\) | −3.44312 | −0.208770 | ||||||||
\(273\) | 40.5933 | 2.45682 | ||||||||
\(274\) | 19.0890 | 1.15321 | ||||||||
\(275\) | 5.82848 | 0.351471 | ||||||||
\(276\) | 0.960979 | 0.0578441 | ||||||||
\(277\) | 26.7626 | 1.60801 | 0.804003 | − | 0.594625i | \(-0.202699\pi\) | ||||
0.804003 | + | 0.594625i | \(0.202699\pi\) | |||||||
\(278\) | 28.3100 | 1.69792 | ||||||||
\(279\) | 34.1590 | 2.04505 | ||||||||
\(280\) | −25.5688 | −1.52803 | ||||||||
\(281\) | −2.21316 | −0.132026 | −0.0660131 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660131 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(282\) | −28.6189 | −1.70423 | ||||||||
\(283\) | −2.87234 | −0.170743 | −0.0853715 | − | 0.996349i | \(-0.527208\pi\) | ||||
−0.0853715 | + | 0.996349i | \(0.527208\pi\) | |||||||
\(284\) | 3.07245 | 0.182316 | ||||||||
\(285\) | −55.9924 | −3.31670 | ||||||||
\(286\) | −6.70641 | −0.396558 | ||||||||
\(287\) | 20.1344 | 1.18850 | ||||||||
\(288\) | −8.93479 | −0.526487 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 23.1572 | 1.35984 | ||||||||
\(291\) | −0.962845 | −0.0564430 | ||||||||
\(292\) | −2.54436 | −0.148897 | ||||||||
\(293\) | 12.6167 | 0.737078 | 0.368539 | − | 0.929612i | \(-0.379858\pi\) | ||||
0.368539 | + | 0.929612i | \(0.379858\pi\) | |||||||
\(294\) | −0.732585 | −0.0427252 | ||||||||
\(295\) | 3.20275 | 0.186471 | ||||||||
\(296\) | 32.9466 | 1.91498 | ||||||||
\(297\) | −10.4742 | −0.607773 | ||||||||
\(298\) | −19.4485 | −1.12662 | ||||||||
\(299\) | 6.40488 | 0.370404 | ||||||||
\(300\) | 4.43047 | 0.255793 | ||||||||
\(301\) | 2.61144 | 0.150521 | ||||||||
\(302\) | 0.162330 | 0.00934101 | ||||||||
\(303\) | 22.8300 | 1.31155 | ||||||||
\(304\) | −19.0948 | −1.09516 | ||||||||
\(305\) | −26.6768 | −1.52751 | ||||||||
\(306\) | −8.49010 | −0.485347 | ||||||||
\(307\) | 28.9978 | 1.65499 | 0.827496 | − | 0.561471i | \(-0.189764\pi\) | ||||
0.827496 | + | 0.561471i | \(0.189764\pi\) | |||||||
\(308\) | 0.646983 | 0.0368653 | ||||||||
\(309\) | 3.59994 | 0.204794 | ||||||||
\(310\) | −23.1992 | −1.31762 | ||||||||
\(311\) | −9.26842 | −0.525564 | −0.262782 | − | 0.964855i | \(-0.584640\pi\) | ||||
−0.262782 | + | 0.964855i | \(0.584640\pi\) | |||||||
\(312\) | −46.2509 | −2.61844 | ||||||||
\(313\) | 9.89724 | 0.559425 | 0.279713 | − | 0.960084i | \(-0.409761\pi\) | ||||
0.279713 | + | 0.960084i | \(0.409761\pi\) | |||||||
\(314\) | 13.3066 | 0.750934 | ||||||||
\(315\) | −55.1162 | −3.10544 | ||||||||
\(316\) | 1.12089 | 0.0630551 | ||||||||
\(317\) | 21.2221 | 1.19195 | 0.595976 | − | 0.803002i | \(-0.296765\pi\) | ||||
0.595976 | + | 0.803002i | \(0.296765\pi\) | |||||||
\(318\) | −9.86184 | −0.553024 | ||||||||
\(319\) | −5.31625 | −0.297653 | ||||||||
\(320\) | 28.7284 | 1.60597 | ||||||||
\(321\) | 35.0999 | 1.95908 | ||||||||
\(322\) | 4.37016 | 0.243540 | ||||||||
\(323\) | 5.54578 | 0.308575 | ||||||||
\(324\) | −3.19481 | −0.177490 | ||||||||
\(325\) | 29.5289 | 1.63797 | ||||||||
\(326\) | 7.01892 | 0.388742 | ||||||||
\(327\) | −28.6303 | −1.58326 | ||||||||
\(328\) | −22.9406 | −1.26668 | ||||||||
\(329\) | 18.4015 | 1.01451 | ||||||||
\(330\) | 13.3649 | 0.735711 | ||||||||
\(331\) | −30.1059 | −1.65477 | −0.827384 | − | 0.561637i | \(-0.810172\pi\) | ||||
−0.827384 | + | 0.561637i | \(0.810172\pi\) | |||||||
\(332\) | 3.75907 | 0.206306 | ||||||||
\(333\) | 71.0198 | 3.89186 | ||||||||
\(334\) | −17.1185 | −0.936683 | ||||||||
\(335\) | −35.7083 | −1.95095 | ||||||||
\(336\) | −27.5877 | −1.50503 | ||||||||
\(337\) | 12.3346 | 0.671909 | 0.335955 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335955 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(338\) | −16.7683 | −0.912076 | ||||||||
\(339\) | 39.1969 | 2.12889 | ||||||||
\(340\) | −0.815260 | −0.0442137 | ||||||||
\(341\) | 5.32587 | 0.288412 | ||||||||
\(342\) | −47.0843 | −2.54602 | ||||||||
\(343\) | 18.7511 | 1.01247 | ||||||||
\(344\) | −2.97540 | −0.160423 | ||||||||
\(345\) | −12.7640 | −0.687188 | ||||||||
\(346\) | 4.50051 | 0.241949 | ||||||||
\(347\) | −28.4883 | −1.52933 | −0.764666 | − | 0.644426i | \(-0.777096\pi\) | ||||
−0.764666 | + | 0.644426i | \(0.777096\pi\) | |||||||
\(348\) | −4.04110 | −0.216626 | ||||||||
\(349\) | −2.57991 | −0.138100 | −0.0690498 | − | 0.997613i | \(-0.521997\pi\) | ||||
−0.0690498 | + | 0.997613i | \(0.521997\pi\) | |||||||
\(350\) | 20.1481 | 1.07696 | ||||||||
\(351\) | −53.0654 | −2.83242 | ||||||||
\(352\) | −1.39306 | −0.0742503 | ||||||||
\(353\) | −24.8428 | −1.32225 | −0.661123 | − | 0.750277i | \(-0.729920\pi\) | ||||
−0.661123 | + | 0.750277i | \(0.729920\pi\) | |||||||
\(354\) | 3.95294 | 0.210096 | ||||||||
\(355\) | −40.8090 | −2.16592 | ||||||||
\(356\) | 4.14200 | 0.219526 | ||||||||
\(357\) | 8.01240 | 0.424061 | ||||||||
\(358\) | 7.77443 | 0.410891 | ||||||||
\(359\) | −24.8131 | −1.30959 | −0.654794 | − | 0.755808i | \(-0.727245\pi\) | ||||
−0.654794 | + | 0.755808i | \(0.727245\pi\) | |||||||
\(360\) | 62.7978 | 3.30974 | ||||||||
\(361\) | 11.7557 | 0.618720 | ||||||||
\(362\) | 2.24823 | 0.118164 | ||||||||
\(363\) | −3.06819 | −0.161038 | ||||||||
\(364\) | 3.27781 | 0.171804 | ||||||||
\(365\) | 33.7948 | 1.76890 | ||||||||
\(366\) | −32.9254 | −1.72104 | ||||||||
\(367\) | 37.4816 | 1.95653 | 0.978263 | − | 0.207370i | \(-0.0664903\pi\) | ||||
0.978263 | + | 0.207370i | \(0.0664903\pi\) | |||||||
\(368\) | −4.35283 | −0.226907 | ||||||||
\(369\) | −49.4508 | −2.57431 | ||||||||
\(370\) | −48.2332 | −2.50753 | ||||||||
\(371\) | 6.34100 | 0.329208 | ||||||||
\(372\) | 4.04842 | 0.209901 | ||||||||
\(373\) | −21.4703 | −1.11169 | −0.555845 | − | 0.831286i | \(-0.687605\pi\) | ||||
−0.555845 | + | 0.831286i | \(0.687605\pi\) | |||||||
\(374\) | −1.32373 | −0.0684482 | ||||||||
\(375\) | −8.36466 | −0.431949 | ||||||||
\(376\) | −20.9661 | −1.08125 | ||||||||
\(377\) | −26.9338 | −1.38716 | ||||||||
\(378\) | −36.2074 | −1.86231 | ||||||||
\(379\) | 22.6124 | 1.16152 | 0.580762 | − | 0.814074i | \(-0.302755\pi\) | ||||
0.580762 | + | 0.814074i | \(0.302755\pi\) | |||||||
\(380\) | −4.52125 | −0.231935 | ||||||||
\(381\) | 9.21441 | 0.472069 | ||||||||
\(382\) | 11.8410 | 0.605841 | ||||||||
\(383\) | 5.48800 | 0.280424 | 0.140212 | − | 0.990122i | \(-0.455222\pi\) | ||||
0.140212 | + | 0.990122i | \(0.455222\pi\) | |||||||
\(384\) | 26.9092 | 1.37320 | ||||||||
\(385\) | −8.59338 | −0.437959 | ||||||||
\(386\) | −11.4339 | −0.581968 | ||||||||
\(387\) | −6.41379 | −0.326031 | ||||||||
\(388\) | −0.0777475 | −0.00394703 | ||||||||
\(389\) | 22.9128 | 1.16173 | 0.580864 | − | 0.814001i | \(-0.302715\pi\) | ||||
0.580864 | + | 0.814001i | \(0.302715\pi\) | |||||||
\(390\) | 67.7105 | 3.42865 | ||||||||
\(391\) | 1.26421 | 0.0639338 | ||||||||
\(392\) | −0.536690 | −0.0271069 | ||||||||
\(393\) | −27.4617 | −1.38526 | ||||||||
\(394\) | −1.21785 | −0.0613546 | ||||||||
\(395\) | −14.8880 | −0.749095 | ||||||||
\(396\) | −1.58901 | −0.0798509 | ||||||||
\(397\) | −3.77228 | −0.189325 | −0.0946627 | − | 0.995509i | \(-0.530177\pi\) | ||||
−0.0946627 | + | 0.995509i | \(0.530177\pi\) | |||||||
\(398\) | −7.27949 | −0.364888 | ||||||||
\(399\) | 44.4350 | 2.22453 | ||||||||
\(400\) | −20.0682 | −1.00341 | ||||||||
\(401\) | 9.10387 | 0.454626 | 0.227313 | − | 0.973822i | \(-0.427006\pi\) | ||||
0.227313 | + | 0.973822i | \(0.427006\pi\) | |||||||
\(402\) | −44.0723 | −2.19813 | ||||||||
\(403\) | 26.9825 | 1.34409 | ||||||||
\(404\) | 1.84347 | 0.0917162 | ||||||||
\(405\) | 42.4343 | 2.10858 | ||||||||
\(406\) | −18.3774 | −0.912054 | ||||||||
\(407\) | 11.0730 | 0.548867 | ||||||||
\(408\) | −9.12911 | −0.451958 | ||||||||
\(409\) | −20.6221 | −1.01970 | −0.509849 | − | 0.860264i | \(-0.670299\pi\) | ||||
−0.509849 | + | 0.860264i | \(0.670299\pi\) | |||||||
\(410\) | 33.5846 | 1.65863 | ||||||||
\(411\) | 44.2453 | 2.18246 | ||||||||
\(412\) | 0.290687 | 0.0143211 | ||||||||
\(413\) | −2.54167 | −0.125068 | ||||||||
\(414\) | −10.7333 | −0.527512 | ||||||||
\(415\) | −49.9289 | −2.45091 | ||||||||
\(416\) | −7.05767 | −0.346031 | ||||||||
\(417\) | 65.6182 | 3.21334 | ||||||||
\(418\) | −7.34109 | −0.359065 | ||||||||
\(419\) | −29.5803 | −1.44509 | −0.722546 | − | 0.691323i | \(-0.757028\pi\) | ||||
−0.722546 | + | 0.691323i | \(0.757028\pi\) | |||||||
\(420\) | −6.53219 | −0.318738 | ||||||||
\(421\) | −40.1253 | −1.95559 | −0.977795 | − | 0.209564i | \(-0.932796\pi\) | ||||
−0.977795 | + | 0.209564i | \(0.932796\pi\) | |||||||
\(422\) | 27.2626 | 1.32712 | ||||||||
\(423\) | −45.1947 | −2.19744 | ||||||||
\(424\) | −7.22476 | −0.350865 | ||||||||
\(425\) | 5.82848 | 0.282723 | ||||||||
\(426\) | −50.3678 | −2.44033 | ||||||||
\(427\) | 21.1705 | 1.02451 | ||||||||
\(428\) | 2.83423 | 0.136998 | ||||||||
\(429\) | −15.5444 | −0.750491 | ||||||||
\(430\) | 4.35594 | 0.210062 | ||||||||
\(431\) | 2.21544 | 0.106714 | 0.0533571 | − | 0.998575i | \(-0.483008\pi\) | ||||
0.0533571 | + | 0.998575i | \(0.483008\pi\) | |||||||
\(432\) | 36.0638 | 1.73512 | ||||||||
\(433\) | −18.2480 | −0.876944 | −0.438472 | − | 0.898745i | \(-0.644480\pi\) | ||||
−0.438472 | + | 0.898745i | \(0.644480\pi\) | |||||||
\(434\) | 18.4106 | 0.883739 | ||||||||
\(435\) | 53.6749 | 2.57351 | ||||||||
\(436\) | −2.31183 | −0.110717 | ||||||||
\(437\) | 7.01103 | 0.335383 | ||||||||
\(438\) | 41.7106 | 1.99301 | ||||||||
\(439\) | 18.4083 | 0.878578 | 0.439289 | − | 0.898346i | \(-0.355230\pi\) | ||||
0.439289 | + | 0.898346i | \(0.355230\pi\) | |||||||
\(440\) | 9.79106 | 0.466771 | ||||||||
\(441\) | −1.15689 | −0.0550901 | ||||||||
\(442\) | −6.70641 | −0.318991 | ||||||||
\(443\) | −18.7295 | −0.889863 | −0.444932 | − | 0.895564i | \(-0.646772\pi\) | ||||
−0.444932 | + | 0.895564i | \(0.646772\pi\) | |||||||
\(444\) | 8.41704 | 0.399455 | ||||||||
\(445\) | −55.0150 | −2.60796 | ||||||||
\(446\) | 16.6252 | 0.787226 | ||||||||
\(447\) | −45.0785 | −2.13214 | ||||||||
\(448\) | −22.7986 | −1.07713 | ||||||||
\(449\) | −12.3196 | −0.581400 | −0.290700 | − | 0.956814i | \(-0.593888\pi\) | ||||
−0.290700 | + | 0.956814i | \(0.593888\pi\) | |||||||
\(450\) | −49.4844 | −2.33272 | ||||||||
\(451\) | −7.71007 | −0.363053 | ||||||||
\(452\) | 3.16506 | 0.148872 | ||||||||
\(453\) | 0.376255 | 0.0176780 | ||||||||
\(454\) | 25.8142 | 1.21152 | ||||||||
\(455\) | −43.5367 | −2.04103 | ||||||||
\(456\) | −50.6280 | −2.37087 | ||||||||
\(457\) | −26.0552 | −1.21881 | −0.609407 | − | 0.792858i | \(-0.708592\pi\) | ||||
−0.609407 | + | 0.792858i | \(0.708592\pi\) | |||||||
\(458\) | −8.24929 | −0.385464 | ||||||||
\(459\) | −10.4742 | −0.488892 | ||||||||
\(460\) | −1.03066 | −0.0480547 | ||||||||
\(461\) | −10.8724 | −0.506380 | −0.253190 | − | 0.967417i | \(-0.581480\pi\) | ||||
−0.253190 | + | 0.967417i | \(0.581480\pi\) | |||||||
\(462\) | −10.6062 | −0.493446 | ||||||||
\(463\) | 35.0402 | 1.62846 | 0.814229 | − | 0.580544i | \(-0.197160\pi\) | ||||
0.814229 | + | 0.580544i | \(0.197160\pi\) | |||||||
\(464\) | 18.3045 | 0.849764 | ||||||||
\(465\) | −53.7720 | −2.49362 | ||||||||
\(466\) | −4.92104 | −0.227963 | ||||||||
\(467\) | −14.1930 | −0.656773 | −0.328386 | − | 0.944543i | \(-0.606505\pi\) | ||||
−0.328386 | + | 0.944543i | \(0.606505\pi\) | |||||||
\(468\) | −8.05043 | −0.372131 | ||||||||
\(469\) | 28.3377 | 1.30852 | ||||||||
\(470\) | 30.6940 | 1.41581 | ||||||||
\(471\) | 30.8426 | 1.42115 | ||||||||
\(472\) | 2.89591 | 0.133295 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −18.3752 | −0.844001 | ||||||||
\(475\) | 32.3235 | 1.48310 | ||||||||
\(476\) | 0.646983 | 0.0296544 | ||||||||
\(477\) | −15.5737 | −0.713071 | ||||||||
\(478\) | 4.64141 | 0.212293 | ||||||||
\(479\) | −3.57255 | −0.163234 | −0.0816171 | − | 0.996664i | \(-0.526008\pi\) | ||||
−0.0816171 | + | 0.996664i | \(0.526008\pi\) | |||||||
\(480\) | 14.0649 | 0.641970 | ||||||||
\(481\) | 56.0992 | 2.55790 | ||||||||
\(482\) | 4.46277 | 0.203274 | ||||||||
\(483\) | 10.1294 | 0.460901 | ||||||||
\(484\) | −0.247749 | −0.0112613 | ||||||||
\(485\) | 1.03266 | 0.0468907 | ||||||||
\(486\) | 10.7790 | 0.488945 | ||||||||
\(487\) | 38.9110 | 1.76323 | 0.881613 | − | 0.471972i | \(-0.156458\pi\) | ||||
0.881613 | + | 0.471972i | \(0.156458\pi\) | |||||||
\(488\) | −24.1211 | −1.09191 | ||||||||
\(489\) | 16.2688 | 0.735699 | ||||||||
\(490\) | 0.785705 | 0.0354945 | ||||||||
\(491\) | −24.3200 | −1.09755 | −0.548773 | − | 0.835972i | \(-0.684905\pi\) | ||||
−0.548773 | + | 0.835972i | \(0.684905\pi\) | |||||||
\(492\) | −5.86075 | −0.264223 | ||||||||
\(493\) | −5.31625 | −0.239432 | ||||||||
\(494\) | −37.1923 | −1.67336 | ||||||||
\(495\) | 21.1056 | 0.948628 | ||||||||
\(496\) | −18.3376 | −0.823383 | ||||||||
\(497\) | 32.3856 | 1.45269 | ||||||||
\(498\) | −61.6239 | −2.76143 | ||||||||
\(499\) | −33.9940 | −1.52178 | −0.760891 | − | 0.648880i | \(-0.775238\pi\) | ||||
−0.760891 | + | 0.648880i | \(0.775238\pi\) | |||||||
\(500\) | −0.675427 | −0.0302060 | ||||||||
\(501\) | −39.6780 | −1.77268 | ||||||||
\(502\) | −0.461776 | −0.0206101 | ||||||||
\(503\) | −9.22831 | −0.411470 | −0.205735 | − | 0.978608i | \(-0.565958\pi\) | ||||
−0.205735 | + | 0.978608i | \(0.565958\pi\) | |||||||
\(504\) | −49.8358 | −2.21986 | ||||||||
\(505\) | −24.4854 | −1.08959 | ||||||||
\(506\) | −1.67347 | −0.0743947 | ||||||||
\(507\) | −38.8663 | −1.72611 | ||||||||
\(508\) | 0.744042 | 0.0330115 | ||||||||
\(509\) | −27.6150 | −1.22401 | −0.612006 | − | 0.790853i | \(-0.709637\pi\) | ||||
−0.612006 | + | 0.790853i | \(0.709637\pi\) | |||||||
\(510\) | 13.3649 | 0.591806 | ||||||||
\(511\) | −26.8192 | −1.18641 | ||||||||
\(512\) | 25.2858 | 1.11749 | ||||||||
\(513\) | −58.0874 | −2.56462 | ||||||||
\(514\) | −26.7987 | −1.18204 | ||||||||
\(515\) | −3.86097 | −0.170135 | ||||||||
\(516\) | −0.760142 | −0.0334634 | ||||||||
\(517\) | −7.04648 | −0.309904 | ||||||||
\(518\) | 38.2774 | 1.68181 | ||||||||
\(519\) | 10.4315 | 0.457891 | ||||||||
\(520\) | 49.6046 | 2.17530 | ||||||||
\(521\) | −43.3674 | −1.89996 | −0.949980 | − | 0.312310i | \(-0.898897\pi\) | ||||
−0.949980 | + | 0.312310i | \(0.898897\pi\) | |||||||
\(522\) | 45.1355 | 1.97553 | ||||||||
\(523\) | −0.658755 | −0.0288054 | −0.0144027 | − | 0.999896i | \(-0.504585\pi\) | ||||
−0.0144027 | + | 0.999896i | \(0.504585\pi\) | |||||||
\(524\) | −2.21747 | −0.0968707 | ||||||||
\(525\) | 46.7001 | 2.03816 | ||||||||
\(526\) | 17.7293 | 0.773034 | ||||||||
\(527\) | 5.32587 | 0.231998 | ||||||||
\(528\) | 10.5642 | 0.459746 | ||||||||
\(529\) | −21.4018 | −0.930512 | ||||||||
\(530\) | 10.5769 | 0.459432 | ||||||||
\(531\) | 6.24244 | 0.270899 | ||||||||
\(532\) | 3.58802 | 0.155561 | ||||||||
\(533\) | −39.0616 | −1.69195 | ||||||||
\(534\) | −67.9013 | −2.93838 | ||||||||
\(535\) | −37.6450 | −1.62753 | ||||||||
\(536\) | −32.2873 | −1.39460 | ||||||||
\(537\) | 18.0199 | 0.777617 | ||||||||
\(538\) | −13.9174 | −0.600023 | ||||||||
\(539\) | −0.180376 | −0.00776932 | ||||||||
\(540\) | 8.53917 | 0.367467 | ||||||||
\(541\) | −3.01235 | −0.129511 | −0.0647555 | − | 0.997901i | \(-0.520627\pi\) | ||||
−0.0647555 | + | 0.997901i | \(0.520627\pi\) | |||||||
\(542\) | 21.5936 | 0.927526 | ||||||||
\(543\) | 5.21104 | 0.223627 | ||||||||
\(544\) | −1.39306 | −0.0597269 | ||||||||
\(545\) | 30.7063 | 1.31531 | ||||||||
\(546\) | −53.7344 | −2.29962 | ||||||||
\(547\) | 27.7750 | 1.18757 | 0.593786 | − | 0.804623i | \(-0.297633\pi\) | ||||
0.593786 | + | 0.804623i | \(0.297633\pi\) | |||||||
\(548\) | 3.57271 | 0.152618 | ||||||||
\(549\) | −51.9954 | −2.21911 | ||||||||
\(550\) | −7.71531 | −0.328982 | ||||||||
\(551\) | −29.4827 | −1.25601 | ||||||||
\(552\) | −11.5411 | −0.491222 | ||||||||
\(553\) | 11.8150 | 0.502423 | ||||||||
\(554\) | −35.4263 | −1.50512 | ||||||||
\(555\) | −111.797 | −4.74552 | ||||||||
\(556\) | 5.29851 | 0.224707 | ||||||||
\(557\) | −4.19375 | −0.177695 | −0.0888474 | − | 0.996045i | \(-0.528318\pi\) | ||||
−0.0888474 | + | 0.996045i | \(0.528318\pi\) | |||||||
\(558\) | −45.2172 | −1.91420 | ||||||||
\(559\) | −5.06631 | −0.214282 | ||||||||
\(560\) | 29.5881 | 1.25032 | ||||||||
\(561\) | −3.06819 | −0.129539 | ||||||||
\(562\) | 2.92962 | 0.123579 | ||||||||
\(563\) | −9.14152 | −0.385269 | −0.192635 | − | 0.981271i | \(-0.561703\pi\) | ||||
−0.192635 | + | 0.981271i | \(0.561703\pi\) | |||||||
\(564\) | −5.35632 | −0.225542 | ||||||||
\(565\) | −42.0391 | −1.76860 | ||||||||
\(566\) | 3.80220 | 0.159818 | ||||||||
\(567\) | −33.6755 | −1.41424 | ||||||||
\(568\) | −36.8993 | −1.54826 | ||||||||
\(569\) | 21.5988 | 0.905469 | 0.452735 | − | 0.891645i | \(-0.350448\pi\) | ||||
0.452735 | + | 0.891645i | \(0.350448\pi\) | |||||||
\(570\) | 74.1185 | 3.10448 | ||||||||
\(571\) | 32.2692 | 1.35042 | 0.675211 | − | 0.737624i | \(-0.264052\pi\) | ||||
0.675211 | + | 0.737624i | \(0.264052\pi\) | |||||||
\(572\) | −1.25517 | −0.0524815 | ||||||||
\(573\) | 27.4457 | 1.14656 | ||||||||
\(574\) | −26.6524 | −1.11245 | ||||||||
\(575\) | 7.36842 | 0.307284 | ||||||||
\(576\) | 55.9941 | 2.33309 | ||||||||
\(577\) | 15.1275 | 0.629767 | 0.314883 | − | 0.949130i | \(-0.398035\pi\) | ||||
0.314883 | + | 0.949130i | \(0.398035\pi\) | |||||||
\(578\) | −1.32373 | −0.0550597 | ||||||||
\(579\) | −26.5019 | −1.10138 | ||||||||
\(580\) | 4.33412 | 0.179965 | ||||||||
\(581\) | 39.6231 | 1.64384 | ||||||||
\(582\) | 1.27454 | 0.0528315 | ||||||||
\(583\) | −2.42816 | −0.100564 | ||||||||
\(584\) | 30.5571 | 1.26446 | ||||||||
\(585\) | 106.928 | 4.42092 | ||||||||
\(586\) | −16.7011 | −0.689917 | ||||||||
\(587\) | 31.5834 | 1.30359 | 0.651793 | − | 0.758397i | \(-0.274017\pi\) | ||||
0.651793 | + | 0.758397i | \(0.274017\pi\) | |||||||
\(588\) | −0.137111 | −0.00565436 | ||||||||
\(589\) | 29.5361 | 1.21701 | ||||||||
\(590\) | −4.23957 | −0.174540 | ||||||||
\(591\) | −2.82279 | −0.116114 | ||||||||
\(592\) | −38.1256 | −1.56695 | ||||||||
\(593\) | 14.2537 | 0.585329 | 0.292665 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292665 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(594\) | 13.8649 | 0.568885 | ||||||||
\(595\) | −8.59338 | −0.352294 | ||||||||
\(596\) | −3.63998 | −0.149100 | ||||||||
\(597\) | −16.8727 | −0.690554 | ||||||||
\(598\) | −8.47831 | −0.346704 | ||||||||
\(599\) | 12.4437 | 0.508436 | 0.254218 | − | 0.967147i | \(-0.418182\pi\) | ||||
0.254218 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(600\) | −53.2088 | −2.17224 | ||||||||
\(601\) | 44.3406 | 1.80869 | 0.904346 | − | 0.426801i | \(-0.140359\pi\) | ||||
0.904346 | + | 0.426801i | \(0.140359\pi\) | |||||||
\(602\) | −3.45683 | −0.140890 | ||||||||
\(603\) | −69.5985 | −2.83427 | ||||||||
\(604\) | 0.0303817 | 0.00123621 | ||||||||
\(605\) | 3.29067 | 0.133785 | ||||||||
\(606\) | −30.2207 | −1.22763 | ||||||||
\(607\) | −26.9200 | −1.09265 | −0.546325 | − | 0.837574i | \(-0.683973\pi\) | ||||
−0.546325 | + | 0.837574i | \(0.683973\pi\) | |||||||
\(608\) | −7.72560 | −0.313314 | ||||||||
\(609\) | −42.5959 | −1.72607 | ||||||||
\(610\) | 35.3128 | 1.42977 | ||||||||
\(611\) | −35.6997 | −1.44425 | ||||||||
\(612\) | −1.58901 | −0.0642320 | ||||||||
\(613\) | −27.2210 | −1.09945 | −0.549724 | − | 0.835346i | \(-0.685267\pi\) | ||||
−0.549724 | + | 0.835346i | \(0.685267\pi\) | |||||||
\(614\) | −38.3852 | −1.54910 | ||||||||
\(615\) | 77.8439 | 3.13897 | ||||||||
\(616\) | −7.77009 | −0.313066 | ||||||||
\(617\) | 14.3210 | 0.576543 | 0.288271 | − | 0.957549i | \(-0.406919\pi\) | ||||
0.288271 | + | 0.957549i | \(0.406919\pi\) | |||||||
\(618\) | −4.76534 | −0.191690 | ||||||||
\(619\) | −45.7670 | −1.83953 | −0.919766 | − | 0.392468i | \(-0.871621\pi\) | ||||
−0.919766 | + | 0.392468i | \(0.871621\pi\) | |||||||
\(620\) | −4.34197 | −0.174378 | ||||||||
\(621\) | −13.2415 | −0.531365 | ||||||||
\(622\) | 12.2689 | 0.491936 | ||||||||
\(623\) | 43.6594 | 1.74918 | ||||||||
\(624\) | 53.5213 | 2.14257 | ||||||||
\(625\) | −20.1712 | −0.806849 | ||||||||
\(626\) | −13.1012 | −0.523631 | ||||||||
\(627\) | −17.0155 | −0.679534 | ||||||||
\(628\) | 2.49047 | 0.0993804 | ||||||||
\(629\) | 11.0730 | 0.441509 | ||||||||
\(630\) | 72.9587 | 2.90674 | ||||||||
\(631\) | 25.6636 | 1.02165 | 0.510825 | − | 0.859685i | \(-0.329340\pi\) | ||||
0.510825 | + | 0.859685i | \(0.329340\pi\) | |||||||
\(632\) | −13.4616 | −0.535475 | ||||||||
\(633\) | 63.1904 | 2.51159 | ||||||||
\(634\) | −28.0922 | −1.11569 | ||||||||
\(635\) | −9.88255 | −0.392177 | ||||||||
\(636\) | −1.84575 | −0.0731886 | ||||||||
\(637\) | −0.913839 | −0.0362076 | ||||||||
\(638\) | 7.03725 | 0.278607 | ||||||||
\(639\) | −79.5403 | −3.14657 | ||||||||
\(640\) | −28.8604 | −1.14081 | ||||||||
\(641\) | −14.6785 | −0.579767 | −0.289883 | − | 0.957062i | \(-0.593617\pi\) | ||||
−0.289883 | + | 0.957062i | \(0.593617\pi\) | |||||||
\(642\) | −46.4626 | −1.83373 | ||||||||
\(643\) | −6.69048 | −0.263847 | −0.131923 | − | 0.991260i | \(-0.542115\pi\) | ||||
−0.131923 | + | 0.991260i | \(0.542115\pi\) | |||||||
\(644\) | 0.817922 | 0.0322306 | ||||||||
\(645\) | 10.0964 | 0.397545 | ||||||||
\(646\) | −7.34109 | −0.288831 | ||||||||
\(647\) | 1.06123 | 0.0417211 | 0.0208605 | − | 0.999782i | \(-0.493359\pi\) | ||||
0.0208605 | + | 0.999782i | \(0.493359\pi\) | |||||||
\(648\) | 38.3689 | 1.50727 | ||||||||
\(649\) | 0.973284 | 0.0382047 | ||||||||
\(650\) | −39.0882 | −1.53316 | ||||||||
\(651\) | 42.6730 | 1.67249 | ||||||||
\(652\) | 1.31366 | 0.0514471 | ||||||||
\(653\) | 27.2507 | 1.06640 | 0.533201 | − | 0.845988i | \(-0.320989\pi\) | ||||
0.533201 | + | 0.845988i | \(0.320989\pi\) | |||||||
\(654\) | 37.8987 | 1.48196 | ||||||||
\(655\) | 29.4530 | 1.15082 | ||||||||
\(656\) | 26.5467 | 1.03648 | ||||||||
\(657\) | 65.8690 | 2.56979 | ||||||||
\(658\) | −24.3585 | −0.949593 | ||||||||
\(659\) | 3.12236 | 0.121630 | 0.0608149 | − | 0.998149i | \(-0.480630\pi\) | ||||
0.0608149 | + | 0.998149i | \(0.480630\pi\) | |||||||
\(660\) | 2.50137 | 0.0973658 | ||||||||
\(661\) | −27.4025 | −1.06584 | −0.532918 | − | 0.846167i | \(-0.678904\pi\) | ||||
−0.532918 | + | 0.846167i | \(0.678904\pi\) | |||||||
\(662\) | 39.8519 | 1.54889 | ||||||||
\(663\) | −15.5444 | −0.603695 | ||||||||
\(664\) | −45.1455 | −1.75199 | ||||||||
\(665\) | −47.6570 | −1.84806 | ||||||||
\(666\) | −94.0108 | −3.64284 | ||||||||
\(667\) | −6.72085 | −0.260232 | ||||||||
\(668\) | −3.20391 | −0.123963 | ||||||||
\(669\) | 38.5346 | 1.48983 | ||||||||
\(670\) | 47.2680 | 1.82612 | ||||||||
\(671\) | −8.10682 | −0.312960 | ||||||||
\(672\) | −11.1617 | −0.430573 | ||||||||
\(673\) | −28.4613 | −1.09710 | −0.548551 | − | 0.836117i | \(-0.684820\pi\) | ||||
−0.548551 | + | 0.836117i | \(0.684820\pi\) | |||||||
\(674\) | −16.3276 | −0.628917 | ||||||||
\(675\) | −61.0485 | −2.34976 | ||||||||
\(676\) | −3.13837 | −0.120706 | ||||||||
\(677\) | −12.2744 | −0.471744 | −0.235872 | − | 0.971784i | \(-0.575795\pi\) | ||||
−0.235872 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(678\) | −51.8860 | −1.99267 | ||||||||
\(679\) | −0.819510 | −0.0314499 | ||||||||
\(680\) | 9.79106 | 0.375470 | ||||||||
\(681\) | 59.8333 | 2.29282 | ||||||||
\(682\) | −7.04999 | −0.269958 | ||||||||
\(683\) | 40.6350 | 1.55486 | 0.777428 | − | 0.628972i | \(-0.216524\pi\) | ||||
0.777428 | + | 0.628972i | \(0.216524\pi\) | |||||||
\(684\) | −8.81231 | −0.336947 | ||||||||
\(685\) | −47.4535 | −1.81311 | ||||||||
\(686\) | −24.8214 | −0.947684 | ||||||||
\(687\) | −19.1206 | −0.729495 | ||||||||
\(688\) | 3.44312 | 0.131268 | ||||||||
\(689\) | −12.3018 | −0.468662 | ||||||||
\(690\) | 16.8960 | 0.643219 | ||||||||
\(691\) | −3.97248 | −0.151120 | −0.0755601 | − | 0.997141i | \(-0.524074\pi\) | ||||
−0.0755601 | + | 0.997141i | \(0.524074\pi\) | |||||||
\(692\) | 0.842318 | 0.0320201 | ||||||||
\(693\) | −16.7492 | −0.636251 | ||||||||
\(694\) | 37.7107 | 1.43148 | ||||||||
\(695\) | −70.3762 | −2.66952 | ||||||||
\(696\) | 48.5326 | 1.83962 | ||||||||
\(697\) | −7.71007 | −0.292040 | ||||||||
\(698\) | 3.41510 | 0.129263 | ||||||||
\(699\) | −11.4062 | −0.431422 | ||||||||
\(700\) | 3.77093 | 0.142528 | ||||||||
\(701\) | 13.2868 | 0.501837 | 0.250919 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250919 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(702\) | 70.2440 | 2.65119 | ||||||||
\(703\) | 61.4083 | 2.31606 | ||||||||
\(704\) | 8.73027 | 0.329034 | ||||||||
\(705\) | 71.1440 | 2.67944 | ||||||||
\(706\) | 32.8850 | 1.23764 | ||||||||
\(707\) | 19.4314 | 0.730794 | ||||||||
\(708\) | 0.739834 | 0.0278047 | ||||||||
\(709\) | −7.95956 | −0.298928 | −0.149464 | − | 0.988767i | \(-0.547755\pi\) | ||||
−0.149464 | + | 0.988767i | \(0.547755\pi\) | |||||||
\(710\) | 54.0199 | 2.02733 | ||||||||
\(711\) | −29.0179 | −1.08826 | ||||||||
\(712\) | −49.7443 | −1.86425 | ||||||||
\(713\) | 6.73301 | 0.252153 | ||||||||
\(714\) | −10.6062 | −0.396928 | ||||||||
\(715\) | 16.6715 | 0.623480 | ||||||||
\(716\) | 1.45507 | 0.0543784 | ||||||||
\(717\) | 10.7581 | 0.401767 | ||||||||
\(718\) | 32.8458 | 1.22579 | ||||||||
\(719\) | 12.5936 | 0.469662 | 0.234831 | − | 0.972036i | \(-0.424546\pi\) | ||||
0.234831 | + | 0.972036i | \(0.424546\pi\) | |||||||
\(720\) | −72.6693 | −2.70823 | ||||||||
\(721\) | 3.06403 | 0.114111 | ||||||||
\(722\) | −15.5613 | −0.579131 | ||||||||
\(723\) | 10.3440 | 0.384698 | ||||||||
\(724\) | 0.420779 | 0.0156381 | ||||||||
\(725\) | −30.9856 | −1.15078 | ||||||||
\(726\) | 4.06144 | 0.150734 | ||||||||
\(727\) | 47.9025 | 1.77661 | 0.888303 | − | 0.459257i | \(-0.151884\pi\) | ||||
0.888303 | + | 0.459257i | \(0.151884\pi\) | |||||||
\(728\) | −39.3657 | −1.45899 | ||||||||
\(729\) | −13.7021 | −0.507484 | ||||||||
\(730\) | −44.7350 | −1.65572 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −6.16233 | −0.227766 | ||||||||
\(733\) | 28.5751 | 1.05545 | 0.527723 | − | 0.849416i | \(-0.323046\pi\) | ||||
0.527723 | + | 0.849416i | \(0.323046\pi\) | |||||||
\(734\) | −49.6154 | −1.83134 | ||||||||
\(735\) | 1.82114 | 0.0671738 | ||||||||
\(736\) | −1.76112 | −0.0649157 | ||||||||
\(737\) | −10.8514 | −0.399716 | ||||||||
\(738\) | 65.4593 | 2.40959 | ||||||||
\(739\) | −53.8455 | −1.98074 | −0.990368 | − | 0.138457i | \(-0.955786\pi\) | ||||
−0.990368 | + | 0.138457i | \(0.955786\pi\) | |||||||
\(740\) | −9.02736 | −0.331852 | ||||||||
\(741\) | −86.2059 | −3.16685 | ||||||||
\(742\) | −8.39374 | −0.308144 | ||||||||
\(743\) | −25.5932 | −0.938924 | −0.469462 | − | 0.882953i | \(-0.655552\pi\) | ||||
−0.469462 | + | 0.882953i | \(0.655552\pi\) | |||||||
\(744\) | −48.6204 | −1.78251 | ||||||||
\(745\) | 48.3472 | 1.77130 | ||||||||
\(746\) | 28.4208 | 1.04056 | ||||||||
\(747\) | −97.3158 | −3.56060 | ||||||||
\(748\) | −0.247749 | −0.00905861 | ||||||||
\(749\) | 29.8747 | 1.09160 | ||||||||
\(750\) | 11.0725 | 0.404311 | ||||||||
\(751\) | −22.3213 | −0.814514 | −0.407257 | − | 0.913314i | \(-0.633515\pi\) | ||||
−0.407257 | + | 0.913314i | \(0.633515\pi\) | |||||||
\(752\) | 24.2619 | 0.884740 | ||||||||
\(753\) | −1.07033 | −0.0390048 | ||||||||
\(754\) | 35.6529 | 1.29840 | ||||||||
\(755\) | −0.403537 | −0.0146862 | ||||||||
\(756\) | −6.77660 | −0.246463 | ||||||||
\(757\) | −33.2148 | −1.20721 | −0.603606 | − | 0.797283i | \(-0.706270\pi\) | ||||
−0.603606 | + | 0.797283i | \(0.706270\pi\) | |||||||
\(758\) | −29.9327 | −1.08720 | ||||||||
\(759\) | −3.87884 | −0.140793 | ||||||||
\(760\) | 54.2991 | 1.96963 | ||||||||
\(761\) | −33.1364 | −1.20119 | −0.600597 | − | 0.799552i | \(-0.705070\pi\) | ||||
−0.600597 | + | 0.799552i | \(0.705070\pi\) | |||||||
\(762\) | −12.1974 | −0.441864 | ||||||||
\(763\) | −24.3682 | −0.882190 | ||||||||
\(764\) | 2.21618 | 0.0801785 | ||||||||
\(765\) | 21.1056 | 0.763076 | ||||||||
\(766\) | −7.26461 | −0.262481 | ||||||||
\(767\) | 4.93096 | 0.178047 | ||||||||
\(768\) | 17.9519 | 0.647783 | ||||||||
\(769\) | −29.2335 | −1.05419 | −0.527093 | − | 0.849807i | \(-0.676718\pi\) | ||||
−0.527093 | + | 0.849807i | \(0.676718\pi\) | |||||||
\(770\) | 11.3753 | 0.409937 | ||||||||
\(771\) | −62.1153 | −2.23703 | ||||||||
\(772\) | −2.13997 | −0.0770190 | ||||||||
\(773\) | 13.6889 | 0.492354 | 0.246177 | − | 0.969225i | \(-0.420825\pi\) | ||||
0.246177 | + | 0.969225i | \(0.420825\pi\) | |||||||
\(774\) | 8.49010 | 0.305171 | ||||||||
\(775\) | 31.0417 | 1.11505 | ||||||||
\(776\) | 0.933728 | 0.0335189 | ||||||||
\(777\) | 88.7211 | 3.18285 | ||||||||
\(778\) | −30.3303 | −1.08739 | ||||||||
\(779\) | −42.7584 | −1.53198 | ||||||||
\(780\) | 12.6727 | 0.453757 | ||||||||
\(781\) | −12.4014 | −0.443759 | ||||||||
\(782\) | −1.67347 | −0.0598431 | ||||||||
\(783\) | 55.6832 | 1.98996 | ||||||||
\(784\) | 0.621055 | 0.0221805 | ||||||||
\(785\) | −33.0790 | −1.18064 | ||||||||
\(786\) | 36.3518 | 1.29663 | ||||||||
\(787\) | −3.01198 | −0.107366 | −0.0536828 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536828 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(788\) | −0.227934 | −0.00811981 | ||||||||
\(789\) | 41.0937 | 1.46298 | ||||||||
\(790\) | 19.7076 | 0.701165 | ||||||||
\(791\) | 33.3618 | 1.18621 | ||||||||
\(792\) | 19.0836 | 0.678107 | ||||||||
\(793\) | −41.0717 | −1.45850 | ||||||||
\(794\) | 4.99347 | 0.177212 | ||||||||
\(795\) | 24.5157 | 0.869481 | ||||||||
\(796\) | −1.36243 | −0.0482901 | ||||||||
\(797\) | −27.4119 | −0.970981 | −0.485490 | − | 0.874242i | \(-0.661359\pi\) | ||||
−0.485490 | + | 0.874242i | \(0.661359\pi\) | |||||||
\(798\) | −58.8198 | −2.08220 | ||||||||
\(799\) | −7.04648 | −0.249287 | ||||||||
\(800\) | −8.11941 | −0.287065 | ||||||||
\(801\) | −107.229 | −3.78875 | ||||||||
\(802\) | −12.0510 | −0.425537 | ||||||||
\(803\) | 10.2699 | 0.362417 | ||||||||
\(804\) | −8.24859 | −0.290905 | ||||||||
\(805\) | −10.8638 | −0.382900 | ||||||||
\(806\) | −35.7175 | −1.25809 | ||||||||
\(807\) | −32.2584 | −1.13555 | ||||||||
\(808\) | −22.1396 | −0.778869 | ||||||||
\(809\) | 29.0679 | 1.02197 | 0.510986 | − | 0.859589i | \(-0.329280\pi\) | ||||
0.510986 | + | 0.859589i | \(0.329280\pi\) | |||||||
\(810\) | −56.1714 | −1.97366 | ||||||||
\(811\) | −45.1234 | −1.58450 | −0.792249 | − | 0.610198i | \(-0.791090\pi\) | ||||
−0.792249 | + | 0.610198i | \(0.791090\pi\) | |||||||
\(812\) | −3.43952 | −0.120703 | ||||||||
\(813\) | 50.0507 | 1.75535 | ||||||||
\(814\) | −14.6576 | −0.513748 | ||||||||
\(815\) | −17.4484 | −0.611191 | ||||||||
\(816\) | 10.5642 | 0.369819 | ||||||||
\(817\) | −5.54578 | −0.194022 | ||||||||
\(818\) | 27.2980 | 0.954453 | ||||||||
\(819\) | −84.8569 | −2.96514 | ||||||||
\(820\) | 6.28571 | 0.219507 | ||||||||
\(821\) | 14.8790 | 0.519279 | 0.259640 | − | 0.965706i | \(-0.416396\pi\) | ||||
0.259640 | + | 0.965706i | \(0.416396\pi\) | |||||||
\(822\) | −58.5687 | −2.04282 | ||||||||
\(823\) | 49.1389 | 1.71287 | 0.856437 | − | 0.516251i | \(-0.172673\pi\) | ||||
0.856437 | + | 0.516251i | \(0.172673\pi\) | |||||||
\(824\) | −3.49107 | −0.121617 | ||||||||
\(825\) | −17.8829 | −0.622602 | ||||||||
\(826\) | 3.36448 | 0.117065 | ||||||||
\(827\) | 35.6216 | 1.23868 | 0.619342 | − | 0.785121i | \(-0.287399\pi\) | ||||
0.619342 | + | 0.785121i | \(0.287399\pi\) | |||||||
\(828\) | −2.00884 | −0.0698122 | ||||||||
\(829\) | −18.2847 | −0.635052 | −0.317526 | − | 0.948249i | \(-0.602852\pi\) | ||||
−0.317526 | + | 0.948249i | \(0.602852\pi\) | |||||||
\(830\) | 66.0922 | 2.29409 | ||||||||
\(831\) | −82.1127 | −2.84846 | ||||||||
\(832\) | 44.2303 | 1.53341 | ||||||||
\(833\) | −0.180376 | −0.00624964 | ||||||||
\(834\) | −86.8605 | −3.00773 | ||||||||
\(835\) | 42.5551 | 1.47268 | ||||||||
\(836\) | −1.37396 | −0.0475195 | ||||||||
\(837\) | −55.7840 | −1.92818 | ||||||||
\(838\) | 39.1562 | 1.35263 | ||||||||
\(839\) | 50.2858 | 1.73606 | 0.868029 | − | 0.496514i | \(-0.165387\pi\) | ||||
0.868029 | + | 0.496514i | \(0.165387\pi\) | |||||||
\(840\) | 78.4499 | 2.70678 | ||||||||
\(841\) | −0.737536 | −0.0254323 | ||||||||
\(842\) | 53.1150 | 1.83046 | ||||||||
\(843\) | 6.79040 | 0.233874 | ||||||||
\(844\) | 5.10248 | 0.175635 | ||||||||
\(845\) | 41.6845 | 1.43399 | ||||||||
\(846\) | 59.8254 | 2.05684 | ||||||||
\(847\) | −2.61144 | −0.0897302 | ||||||||
\(848\) | 8.36045 | 0.287099 | ||||||||
\(849\) | 8.81290 | 0.302458 | ||||||||
\(850\) | −7.71531 | −0.264633 | ||||||||
\(851\) | 13.9986 | 0.479865 | ||||||||
\(852\) | −9.42686 | −0.322959 | ||||||||
\(853\) | 40.6167 | 1.39069 | 0.695345 | − | 0.718676i | \(-0.255252\pi\) | ||||
0.695345 | + | 0.718676i | \(0.255252\pi\) | |||||||
\(854\) | −28.0239 | −0.958959 | ||||||||
\(855\) | 117.047 | 4.00293 | ||||||||
\(856\) | −34.0384 | −1.16341 | ||||||||
\(857\) | −19.3959 | −0.662550 | −0.331275 | − | 0.943534i | \(-0.607479\pi\) | ||||
−0.331275 | + | 0.943534i | \(0.607479\pi\) | |||||||
\(858\) | 20.5765 | 0.702471 | ||||||||
\(859\) | 11.5975 | 0.395701 | 0.197851 | − | 0.980232i | \(-0.436604\pi\) | ||||
0.197851 | + | 0.980232i | \(0.436604\pi\) | |||||||
\(860\) | 0.815260 | 0.0278001 | ||||||||
\(861\) | −61.7762 | −2.10533 | ||||||||
\(862\) | −2.93264 | −0.0998861 | ||||||||
\(863\) | −22.9365 | −0.780769 | −0.390385 | − | 0.920652i | \(-0.627658\pi\) | ||||
−0.390385 | + | 0.920652i | \(0.627658\pi\) | |||||||
\(864\) | 14.5911 | 0.496400 | ||||||||
\(865\) | −11.1879 | −0.380399 | ||||||||
\(866\) | 24.1554 | 0.820834 | ||||||||
\(867\) | −3.06819 | −0.104201 | ||||||||
\(868\) | 3.44574 | 0.116956 | ||||||||
\(869\) | −4.52430 | −0.153476 | ||||||||
\(870\) | −71.0508 | −2.40885 | ||||||||
\(871\) | −54.9765 | −1.86281 | ||||||||
\(872\) | 27.7645 | 0.940225 | ||||||||
\(873\) | 2.01275 | 0.0681212 | ||||||||
\(874\) | −9.28068 | −0.313924 | ||||||||
\(875\) | −7.11945 | −0.240681 | ||||||||
\(876\) | 7.80658 | 0.263760 | ||||||||
\(877\) | 3.94279 | 0.133139 | 0.0665694 | − | 0.997782i | \(-0.478795\pi\) | ||||
0.0665694 | + | 0.997782i | \(0.478795\pi\) | |||||||
\(878\) | −24.3675 | −0.822363 | ||||||||
\(879\) | −38.7106 | −1.30568 | ||||||||
\(880\) | −11.3302 | −0.381940 | ||||||||
\(881\) | 23.1435 | 0.779725 | 0.389863 | − | 0.920873i | \(-0.372522\pi\) | ||||
0.389863 | + | 0.920873i | \(0.372522\pi\) | |||||||
\(882\) | 1.53141 | 0.0515652 | ||||||||
\(883\) | 27.3514 | 0.920447 | 0.460223 | − | 0.887803i | \(-0.347769\pi\) | ||||
0.460223 | + | 0.887803i | \(0.347769\pi\) | |||||||
\(884\) | −1.25517 | −0.0422161 | ||||||||
\(885\) | −9.82665 | −0.330319 | ||||||||
\(886\) | 24.7927 | 0.832926 | ||||||||
\(887\) | −5.94032 | −0.199457 | −0.0997283 | − | 0.995015i | \(-0.531797\pi\) | ||||
−0.0997283 | + | 0.995015i | \(0.531797\pi\) | |||||||
\(888\) | −101.086 | −3.39224 | ||||||||
\(889\) | 7.84270 | 0.263036 | ||||||||
\(890\) | 72.8248 | 2.44109 | ||||||||
\(891\) | 12.8954 | 0.432011 | ||||||||
\(892\) | 3.11158 | 0.104183 | ||||||||
\(893\) | −39.0782 | −1.30770 | ||||||||
\(894\) | 59.6716 | 1.99572 | ||||||||
\(895\) | −19.3265 | −0.646015 | ||||||||
\(896\) | 22.9033 | 0.765146 | ||||||||
\(897\) | −19.6514 | −0.656141 | ||||||||
\(898\) | 16.3078 | 0.544199 | ||||||||
\(899\) | −28.3136 | −0.944312 | ||||||||
\(900\) | −9.26153 | −0.308718 | ||||||||
\(901\) | −2.42816 | −0.0808937 | ||||||||
\(902\) | 10.2060 | 0.339823 | ||||||||
\(903\) | −8.01240 | −0.266636 | ||||||||
\(904\) | −38.0116 | −1.26425 | ||||||||
\(905\) | −5.58889 | −0.185781 | ||||||||
\(906\) | −0.498058 | −0.0165469 | ||||||||
\(907\) | −41.4801 | −1.37732 | −0.688662 | − | 0.725082i | \(-0.741802\pi\) | ||||
−0.688662 | + | 0.725082i | \(0.741802\pi\) | |||||||
\(908\) | 4.83140 | 0.160336 | ||||||||
\(909\) | −47.7242 | −1.58291 | ||||||||
\(910\) | 57.6307 | 1.91044 | ||||||||
\(911\) | −38.2395 | −1.26693 | −0.633466 | − | 0.773770i | \(-0.718368\pi\) | ||||
−0.633466 | + | 0.773770i | \(0.718368\pi\) | |||||||
\(912\) | 58.5865 | 1.93999 | ||||||||
\(913\) | −15.1729 | −0.502150 | ||||||||
\(914\) | 34.4900 | 1.14083 | ||||||||
\(915\) | 81.8496 | 2.70586 | ||||||||
\(916\) | −1.54394 | −0.0510133 | ||||||||
\(917\) | −23.3736 | −0.771865 | ||||||||
\(918\) | 13.8649 | 0.457611 | ||||||||
\(919\) | 52.5976 | 1.73503 | 0.867517 | − | 0.497407i | \(-0.165715\pi\) | ||||
0.867517 | + | 0.497407i | \(0.165715\pi\) | |||||||
\(920\) | 12.3780 | 0.408089 | ||||||||
\(921\) | −88.9708 | −2.93169 | ||||||||
\(922\) | 14.3921 | 0.473979 | ||||||||
\(923\) | −62.8296 | −2.06806 | ||||||||
\(924\) | −1.98507 | −0.0653039 | ||||||||
\(925\) | 64.5387 | 2.12202 | ||||||||
\(926\) | −46.3837 | −1.52426 | ||||||||
\(927\) | −7.52537 | −0.247166 | ||||||||
\(928\) | 7.40584 | 0.243109 | ||||||||
\(929\) | −7.29117 | −0.239215 | −0.119608 | − | 0.992821i | \(-0.538164\pi\) | ||||
−0.119608 | + | 0.992821i | \(0.538164\pi\) | |||||||
\(930\) | 71.1795 | 2.33407 | ||||||||
\(931\) | −1.00032 | −0.0327843 | ||||||||
\(932\) | −0.921024 | −0.0301691 | ||||||||
\(933\) | 28.4373 | 0.930995 | ||||||||
\(934\) | 18.7876 | 0.614750 | ||||||||
\(935\) | 3.29067 | 0.107616 | ||||||||
\(936\) | 96.6836 | 3.16020 | ||||||||
\(937\) | −22.6136 | −0.738756 | −0.369378 | − | 0.929279i | \(-0.620429\pi\) | ||||
−0.369378 | + | 0.929279i | \(0.620429\pi\) | |||||||
\(938\) | −37.5114 | −1.22479 | ||||||||
\(939\) | −30.3666 | −0.990977 | ||||||||
\(940\) | 5.74471 | 0.187372 | ||||||||
\(941\) | 44.6558 | 1.45574 | 0.727868 | − | 0.685717i | \(-0.240511\pi\) | ||||
0.727868 | + | 0.685717i | \(0.240511\pi\) | |||||||
\(942\) | −40.8271 | −1.33022 | ||||||||
\(943\) | −9.74715 | −0.317411 | ||||||||
\(944\) | −3.35113 | −0.109070 | ||||||||
\(945\) | 90.0085 | 2.92798 | ||||||||
\(946\) | 1.32373 | 0.0430380 | ||||||||
\(947\) | 6.21336 | 0.201907 | 0.100953 | − | 0.994891i | \(-0.467811\pi\) | ||||
0.100953 | + | 0.994891i | \(0.467811\pi\) | |||||||
\(948\) | −3.43911 | −0.111697 | ||||||||
\(949\) | 52.0305 | 1.68898 | ||||||||
\(950\) | −42.7874 | −1.38821 | ||||||||
\(951\) | −65.1134 | −2.11145 | ||||||||
\(952\) | −7.77009 | −0.251830 | ||||||||
\(953\) | −8.97776 | −0.290818 | −0.145409 | − | 0.989372i | \(-0.546450\pi\) | ||||
−0.145409 | + | 0.989372i | \(0.546450\pi\) | |||||||
\(954\) | 20.6153 | 0.667446 | ||||||||
\(955\) | −29.4358 | −0.952520 | ||||||||
\(956\) | 0.868689 | 0.0280954 | ||||||||
\(957\) | 16.3113 | 0.527268 | ||||||||
\(958\) | 4.72908 | 0.152790 | ||||||||
\(959\) | 37.6587 | 1.21606 | ||||||||
\(960\) | −88.1442 | −2.84484 | ||||||||
\(961\) | −2.63512 | −0.0850039 | ||||||||
\(962\) | −74.2599 | −2.39424 | ||||||||
\(963\) | −73.3733 | −2.36442 | ||||||||
\(964\) | 0.835255 | 0.0269017 | ||||||||
\(965\) | 28.4235 | 0.914986 | ||||||||
\(966\) | −13.4085 | −0.431411 | ||||||||
\(967\) | 32.1152 | 1.03275 | 0.516377 | − | 0.856361i | \(-0.327280\pi\) | ||||
0.516377 | + | 0.856361i | \(0.327280\pi\) | |||||||
\(968\) | 2.97540 | 0.0956331 | ||||||||
\(969\) | −17.0155 | −0.546617 | ||||||||
\(970\) | −1.36696 | −0.0438905 | ||||||||
\(971\) | −25.3868 | −0.814702 | −0.407351 | − | 0.913272i | \(-0.633547\pi\) | ||||
−0.407351 | + | 0.913272i | \(0.633547\pi\) | |||||||
\(972\) | 2.01740 | 0.0647082 | ||||||||
\(973\) | 55.8499 | 1.79046 | ||||||||
\(974\) | −51.5075 | −1.65041 | ||||||||
\(975\) | −90.6003 | −2.90153 | ||||||||
\(976\) | 27.9128 | 0.893466 | ||||||||
\(977\) | 60.5451 | 1.93701 | 0.968505 | − | 0.248994i | \(-0.0801000\pi\) | ||||
0.968505 | + | 0.248994i | \(0.0801000\pi\) | |||||||
\(978\) | −21.5354 | −0.688625 | ||||||||
\(979\) | −16.7185 | −0.534326 | ||||||||
\(980\) | 0.147053 | 0.00469743 | ||||||||
\(981\) | 59.8493 | 1.91084 | ||||||||
\(982\) | 32.1930 | 1.02732 | ||||||||
\(983\) | 4.25333 | 0.135660 | 0.0678301 | − | 0.997697i | \(-0.478392\pi\) | ||||
0.0678301 | + | 0.997697i | \(0.478392\pi\) | |||||||
\(984\) | 70.3861 | 2.24383 | ||||||||
\(985\) | 3.02748 | 0.0964634 | ||||||||
\(986\) | 7.03725 | 0.224112 | ||||||||
\(987\) | −56.4592 | −1.79712 | ||||||||
\(988\) | −6.96092 | −0.221456 | ||||||||
\(989\) | −1.26421 | −0.0401995 | ||||||||
\(990\) | −27.9381 | −0.887931 | ||||||||
\(991\) | −5.11660 | −0.162534 | −0.0812671 | − | 0.996692i | \(-0.525897\pi\) | ||||
−0.0812671 | + | 0.996692i | \(0.525897\pi\) | |||||||
\(992\) | −7.41925 | −0.235561 | ||||||||
\(993\) | 92.3705 | 2.93129 | ||||||||
\(994\) | −42.8697 | −1.35974 | ||||||||
\(995\) | 18.0962 | 0.573687 | ||||||||
\(996\) | −11.5336 | −0.365455 | ||||||||
\(997\) | 23.4779 | 0.743553 | 0.371777 | − | 0.928322i | \(-0.378749\pi\) | ||||
0.371777 | + | 0.928322i | \(0.378749\pi\) | |||||||
\(998\) | 44.9988 | 1.42441 | ||||||||
\(999\) | −115.980 | −3.66945 |
(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 | 8041.2.a.c.1.19 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.c.1.19 | ✓ | 60 | 1.1 | even | 1 | trivial |