Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20952 | −1.56237 | −0.781184 | − | 0.624301i | \(-0.785384\pi\) | ||||
−0.781184 | + | 0.624301i | \(0.785384\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.88199 | 1.44099 | ||||||||
\(5\) | −2.30853 | −1.03241 | −0.516204 | − | 0.856466i | \(-0.672655\pi\) | ||||
−0.516204 | + | 0.856466i | \(0.672655\pi\) | |||||||
\(6\) | 2.20952 | 0.902033 | ||||||||
\(7\) | −2.22002 | −0.839090 | −0.419545 | − | 0.907735i | \(-0.637810\pi\) | ||||
−0.419545 | + | 0.907735i | \(0.637810\pi\) | |||||||
\(8\) | −1.94877 | −0.688993 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.10076 | 1.61300 | ||||||||
\(11\) | −3.84505 | −1.15933 | −0.579663 | − | 0.814856i | \(-0.696816\pi\) | ||||
−0.579663 | + | 0.814856i | \(0.696816\pi\) | |||||||
\(12\) | −2.88199 | −0.831958 | ||||||||
\(13\) | −1.58168 | −0.438680 | −0.219340 | − | 0.975648i | \(-0.570390\pi\) | ||||
−0.219340 | + | 0.975648i | \(0.570390\pi\) | |||||||
\(14\) | 4.90519 | 1.31097 | ||||||||
\(15\) | 2.30853 | 0.596061 | ||||||||
\(16\) | −1.45813 | −0.364533 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.20952 | −0.520789 | ||||||||
\(19\) | −0.738095 | −0.169331 | −0.0846653 | − | 0.996409i | \(-0.526982\pi\) | ||||
−0.0846653 | + | 0.996409i | \(0.526982\pi\) | |||||||
\(20\) | −6.65316 | −1.48769 | ||||||||
\(21\) | 2.22002 | 0.484449 | ||||||||
\(22\) | 8.49572 | 1.81129 | ||||||||
\(23\) | −4.94002 | −1.03007 | −0.515033 | − | 0.857171i | \(-0.672220\pi\) | ||||
−0.515033 | + | 0.857171i | \(0.672220\pi\) | |||||||
\(24\) | 1.94877 | 0.397790 | ||||||||
\(25\) | 0.329329 | 0.0658658 | ||||||||
\(26\) | 3.49477 | 0.685380 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −6.39808 | −1.20912 | ||||||||
\(29\) | 10.1642 | 1.88744 | 0.943720 | − | 0.330744i | \(-0.107300\pi\) | ||||
0.943720 | + | 0.330744i | \(0.107300\pi\) | |||||||
\(30\) | −5.10076 | −0.931266 | ||||||||
\(31\) | −0.840905 | −0.151031 | −0.0755155 | − | 0.997145i | \(-0.524060\pi\) | ||||
−0.0755155 | + | 0.997145i | \(0.524060\pi\) | |||||||
\(32\) | 7.11930 | 1.25853 | ||||||||
\(33\) | 3.84505 | 0.669337 | ||||||||
\(34\) | −2.20952 | −0.378930 | ||||||||
\(35\) | 5.12500 | 0.866283 | ||||||||
\(36\) | 2.88199 | 0.480331 | ||||||||
\(37\) | −8.92908 | −1.46793 | −0.733966 | − | 0.679186i | \(-0.762333\pi\) | ||||
−0.733966 | + | 0.679186i | \(0.762333\pi\) | |||||||
\(38\) | 1.63084 | 0.264557 | ||||||||
\(39\) | 1.58168 | 0.253272 | ||||||||
\(40\) | 4.49879 | 0.711322 | ||||||||
\(41\) | 0.805630 | 0.125818 | 0.0629091 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629091 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(42\) | −4.90519 | −0.756887 | ||||||||
\(43\) | −1.73261 | −0.264221 | −0.132110 | − | 0.991235i | \(-0.542175\pi\) | ||||
−0.132110 | + | 0.991235i | \(0.542175\pi\) | |||||||
\(44\) | −11.0814 | −1.67058 | ||||||||
\(45\) | −2.30853 | −0.344136 | ||||||||
\(46\) | 10.9151 | 1.60934 | ||||||||
\(47\) | −3.65706 | −0.533437 | −0.266718 | − | 0.963774i | \(-0.585939\pi\) | ||||
−0.266718 | + | 0.963774i | \(0.585939\pi\) | |||||||
\(48\) | 1.45813 | 0.210463 | ||||||||
\(49\) | −2.07149 | −0.295928 | ||||||||
\(50\) | −0.727660 | −0.102907 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −4.55839 | −0.632135 | ||||||||
\(53\) | 0.966170 | 0.132714 | 0.0663568 | − | 0.997796i | \(-0.478862\pi\) | ||||
0.0663568 | + | 0.997796i | \(0.478862\pi\) | |||||||
\(54\) | 2.20952 | 0.300678 | ||||||||
\(55\) | 8.87642 | 1.19690 | ||||||||
\(56\) | 4.32631 | 0.578127 | ||||||||
\(57\) | 0.738095 | 0.0977631 | ||||||||
\(58\) | −22.4580 | −2.94888 | ||||||||
\(59\) | 13.0182 | 1.69483 | 0.847415 | − | 0.530931i | \(-0.178158\pi\) | ||||
0.847415 | + | 0.530931i | \(0.178158\pi\) | |||||||
\(60\) | 6.65316 | 0.858919 | ||||||||
\(61\) | 2.83262 | 0.362679 | 0.181340 | − | 0.983421i | \(-0.441957\pi\) | ||||
0.181340 | + | 0.983421i | \(0.441957\pi\) | |||||||
\(62\) | 1.85800 | 0.235966 | ||||||||
\(63\) | −2.22002 | −0.279697 | ||||||||
\(64\) | −12.8140 | −1.60175 | ||||||||
\(65\) | 3.65137 | 0.452897 | ||||||||
\(66\) | −8.49572 | −1.04575 | ||||||||
\(67\) | −1.20484 | −0.147195 | −0.0735974 | − | 0.997288i | \(-0.523448\pi\) | ||||
−0.0735974 | + | 0.997288i | \(0.523448\pi\) | |||||||
\(68\) | 2.88199 | 0.349492 | ||||||||
\(69\) | 4.94002 | 0.594708 | ||||||||
\(70\) | −11.3238 | −1.35345 | ||||||||
\(71\) | 14.3800 | 1.70660 | 0.853298 | − | 0.521423i | \(-0.174599\pi\) | ||||
0.853298 | + | 0.521423i | \(0.174599\pi\) | |||||||
\(72\) | −1.94877 | −0.229664 | ||||||||
\(73\) | −4.59489 | −0.537791 | −0.268895 | − | 0.963169i | \(-0.586659\pi\) | ||||
−0.268895 | + | 0.963169i | \(0.586659\pi\) | |||||||
\(74\) | 19.7290 | 2.29345 | ||||||||
\(75\) | −0.329329 | −0.0380276 | ||||||||
\(76\) | −2.12718 | −0.244004 | ||||||||
\(77\) | 8.53610 | 0.972779 | ||||||||
\(78\) | −3.49477 | −0.395704 | ||||||||
\(79\) | 7.33466 | 0.825214 | 0.412607 | − | 0.910909i | \(-0.364618\pi\) | ||||
0.412607 | + | 0.910909i | \(0.364618\pi\) | |||||||
\(80\) | 3.36614 | 0.376346 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.78006 | −0.196574 | ||||||||
\(83\) | −0.714138 | −0.0783868 | −0.0391934 | − | 0.999232i | \(-0.512479\pi\) | ||||
−0.0391934 | + | 0.999232i | \(0.512479\pi\) | |||||||
\(84\) | 6.39808 | 0.698087 | ||||||||
\(85\) | −2.30853 | −0.250396 | ||||||||
\(86\) | 3.82824 | 0.412810 | ||||||||
\(87\) | −10.1642 | −1.08971 | ||||||||
\(88\) | 7.49310 | 0.798767 | ||||||||
\(89\) | −3.74781 | −0.397267 | −0.198633 | − | 0.980074i | \(-0.563650\pi\) | ||||
−0.198633 | + | 0.980074i | \(0.563650\pi\) | |||||||
\(90\) | 5.10076 | 0.537667 | ||||||||
\(91\) | 3.51138 | 0.368092 | ||||||||
\(92\) | −14.2371 | −1.48432 | ||||||||
\(93\) | 0.840905 | 0.0871978 | ||||||||
\(94\) | 8.08035 | 0.833425 | ||||||||
\(95\) | 1.70392 | 0.174818 | ||||||||
\(96\) | −7.11930 | −0.726611 | ||||||||
\(97\) | 18.5380 | 1.88224 | 0.941122 | − | 0.338067i | \(-0.109773\pi\) | ||||
0.941122 | + | 0.338067i | \(0.109773\pi\) | |||||||
\(98\) | 4.57701 | 0.462348 | ||||||||
\(99\) | −3.84505 | −0.386442 | ||||||||
\(100\) | 0.949122 | 0.0949122 | ||||||||
\(101\) | −13.8732 | −1.38043 | −0.690216 | − | 0.723604i | \(-0.742484\pi\) | ||||
−0.690216 | + | 0.723604i | \(0.742484\pi\) | |||||||
\(102\) | 2.20952 | 0.218775 | ||||||||
\(103\) | 2.31242 | 0.227849 | 0.113925 | − | 0.993489i | \(-0.463658\pi\) | ||||
0.113925 | + | 0.993489i | \(0.463658\pi\) | |||||||
\(104\) | 3.08233 | 0.302248 | ||||||||
\(105\) | −5.12500 | −0.500149 | ||||||||
\(106\) | −2.13477 | −0.207348 | ||||||||
\(107\) | −1.17716 | −0.113800 | −0.0569001 | − | 0.998380i | \(-0.518122\pi\) | ||||
−0.0569001 | + | 0.998380i | \(0.518122\pi\) | |||||||
\(108\) | −2.88199 | −0.277319 | ||||||||
\(109\) | −19.9146 | −1.90747 | −0.953734 | − | 0.300650i | \(-0.902796\pi\) | ||||
−0.953734 | + | 0.300650i | \(0.902796\pi\) | |||||||
\(110\) | −19.6127 | −1.86999 | ||||||||
\(111\) | 8.92908 | 0.847511 | ||||||||
\(112\) | 3.23708 | 0.305876 | ||||||||
\(113\) | 9.41079 | 0.885293 | 0.442646 | − | 0.896696i | \(-0.354040\pi\) | ||||
0.442646 | + | 0.896696i | \(0.354040\pi\) | |||||||
\(114\) | −1.63084 | −0.152742 | ||||||||
\(115\) | 11.4042 | 1.06345 | ||||||||
\(116\) | 29.2930 | 2.71979 | ||||||||
\(117\) | −1.58168 | −0.146227 | ||||||||
\(118\) | −28.7641 | −2.64795 | ||||||||
\(119\) | −2.22002 | −0.203509 | ||||||||
\(120\) | −4.49879 | −0.410682 | ||||||||
\(121\) | 3.78439 | 0.344036 | ||||||||
\(122\) | −6.25873 | −0.566639 | ||||||||
\(123\) | −0.805630 | −0.0726412 | ||||||||
\(124\) | −2.42348 | −0.217635 | ||||||||
\(125\) | 10.7824 | 0.964407 | ||||||||
\(126\) | 4.90519 | 0.436989 | ||||||||
\(127\) | −5.42283 | −0.481199 | −0.240599 | − | 0.970625i | \(-0.577344\pi\) | ||||
−0.240599 | + | 0.970625i | \(0.577344\pi\) | |||||||
\(128\) | 14.0742 | 1.24399 | ||||||||
\(129\) | 1.73261 | 0.152548 | ||||||||
\(130\) | −8.06779 | −0.707592 | ||||||||
\(131\) | −5.15483 | −0.450379 | −0.225190 | − | 0.974315i | \(-0.572300\pi\) | ||||
−0.225190 | + | 0.974315i | \(0.572300\pi\) | |||||||
\(132\) | 11.0814 | 0.964510 | ||||||||
\(133\) | 1.63859 | 0.142084 | ||||||||
\(134\) | 2.66212 | 0.229973 | ||||||||
\(135\) | 2.30853 | 0.198687 | ||||||||
\(136\) | −1.94877 | −0.167105 | ||||||||
\(137\) | 1.80324 | 0.154061 | 0.0770307 | − | 0.997029i | \(-0.475456\pi\) | ||||
0.0770307 | + | 0.997029i | \(0.475456\pi\) | |||||||
\(138\) | −10.9151 | −0.929153 | ||||||||
\(139\) | 8.52112 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(140\) | 14.7702 | 1.24831 | ||||||||
\(141\) | 3.65706 | 0.307980 | ||||||||
\(142\) | −31.7730 | −2.66633 | ||||||||
\(143\) | 6.08165 | 0.508574 | ||||||||
\(144\) | −1.45813 | −0.121511 | ||||||||
\(145\) | −23.4644 | −1.94861 | ||||||||
\(146\) | 10.1525 | 0.840227 | ||||||||
\(147\) | 2.07149 | 0.170854 | ||||||||
\(148\) | −25.7335 | −2.11528 | ||||||||
\(149\) | 21.9483 | 1.79808 | 0.899038 | − | 0.437870i | \(-0.144267\pi\) | ||||
0.899038 | + | 0.437870i | \(0.144267\pi\) | |||||||
\(150\) | 0.727660 | 0.0594132 | ||||||||
\(151\) | 6.83500 | 0.556224 | 0.278112 | − | 0.960549i | \(-0.410291\pi\) | ||||
0.278112 | + | 0.960549i | \(0.410291\pi\) | |||||||
\(152\) | 1.43837 | 0.116668 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −18.8607 | −1.51984 | ||||||||
\(155\) | 1.94126 | 0.155926 | ||||||||
\(156\) | 4.55839 | 0.364964 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −16.2061 | −1.28929 | ||||||||
\(159\) | −0.966170 | −0.0766223 | ||||||||
\(160\) | −16.4352 | −1.29931 | ||||||||
\(161\) | 10.9670 | 0.864317 | ||||||||
\(162\) | −2.20952 | −0.173596 | ||||||||
\(163\) | 7.96902 | 0.624182 | 0.312091 | − | 0.950052i | \(-0.398971\pi\) | ||||
0.312091 | + | 0.950052i | \(0.398971\pi\) | |||||||
\(164\) | 2.32181 | 0.181303 | ||||||||
\(165\) | −8.87642 | −0.691029 | ||||||||
\(166\) | 1.57790 | 0.122469 | ||||||||
\(167\) | 6.96414 | 0.538901 | 0.269450 | − | 0.963014i | \(-0.413158\pi\) | ||||
0.269450 | + | 0.963014i | \(0.413158\pi\) | |||||||
\(168\) | −4.32631 | −0.333782 | ||||||||
\(169\) | −10.4983 | −0.807559 | ||||||||
\(170\) | 5.10076 | 0.391210 | ||||||||
\(171\) | −0.738095 | −0.0564435 | ||||||||
\(172\) | −4.99336 | −0.380740 | ||||||||
\(173\) | −4.40945 | −0.335244 | −0.167622 | − | 0.985851i | \(-0.553609\pi\) | ||||
−0.167622 | + | 0.985851i | \(0.553609\pi\) | |||||||
\(174\) | 22.4580 | 1.70253 | ||||||||
\(175\) | −0.731118 | −0.0552674 | ||||||||
\(176\) | 5.60658 | 0.422612 | ||||||||
\(177\) | −13.0182 | −0.978510 | ||||||||
\(178\) | 8.28086 | 0.620677 | ||||||||
\(179\) | 7.09049 | 0.529968 | 0.264984 | − | 0.964253i | \(-0.414633\pi\) | ||||
0.264984 | + | 0.964253i | \(0.414633\pi\) | |||||||
\(180\) | −6.65316 | −0.495897 | ||||||||
\(181\) | 3.58628 | 0.266566 | 0.133283 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133283 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(182\) | −7.75847 | −0.575096 | ||||||||
\(183\) | −2.83262 | −0.209393 | ||||||||
\(184\) | 9.62694 | 0.709707 | ||||||||
\(185\) | 20.6131 | 1.51550 | ||||||||
\(186\) | −1.85800 | −0.136235 | ||||||||
\(187\) | −3.84505 | −0.281178 | ||||||||
\(188\) | −10.5396 | −0.768679 | ||||||||
\(189\) | 2.22002 | 0.161483 | ||||||||
\(190\) | −3.76484 | −0.273130 | ||||||||
\(191\) | −10.7272 | −0.776194 | −0.388097 | − | 0.921619i | \(-0.626867\pi\) | ||||
−0.388097 | + | 0.921619i | \(0.626867\pi\) | |||||||
\(192\) | 12.8140 | 0.924770 | ||||||||
\(193\) | −17.2369 | −1.24074 | −0.620370 | − | 0.784309i | \(-0.713017\pi\) | ||||
−0.620370 | + | 0.784309i | \(0.713017\pi\) | |||||||
\(194\) | −40.9600 | −2.94076 | ||||||||
\(195\) | −3.65137 | −0.261480 | ||||||||
\(196\) | −5.97002 | −0.426430 | ||||||||
\(197\) | 23.5952 | 1.68109 | 0.840545 | − | 0.541741i | \(-0.182235\pi\) | ||||
0.840545 | + | 0.541741i | \(0.182235\pi\) | |||||||
\(198\) | 8.49572 | 0.603764 | ||||||||
\(199\) | 2.59595 | 0.184022 | 0.0920110 | − | 0.995758i | \(-0.470671\pi\) | ||||
0.0920110 | + | 0.995758i | \(0.470671\pi\) | |||||||
\(200\) | −0.641785 | −0.0453811 | ||||||||
\(201\) | 1.20484 | 0.0849830 | ||||||||
\(202\) | 30.6531 | 2.15674 | ||||||||
\(203\) | −22.5647 | −1.58373 | ||||||||
\(204\) | −2.88199 | −0.201779 | ||||||||
\(205\) | −1.85982 | −0.129896 | ||||||||
\(206\) | −5.10934 | −0.355985 | ||||||||
\(207\) | −4.94002 | −0.343355 | ||||||||
\(208\) | 2.30630 | 0.159913 | ||||||||
\(209\) | 2.83801 | 0.196309 | ||||||||
\(210\) | 11.3238 | 0.781416 | ||||||||
\(211\) | 26.1164 | 1.79793 | 0.898963 | − | 0.438025i | \(-0.144322\pi\) | ||||
0.898963 | + | 0.438025i | \(0.144322\pi\) | |||||||
\(212\) | 2.78449 | 0.191239 | ||||||||
\(213\) | −14.3800 | −0.985304 | ||||||||
\(214\) | 2.60096 | 0.177798 | ||||||||
\(215\) | 3.99979 | 0.272783 | ||||||||
\(216\) | 1.94877 | 0.132597 | ||||||||
\(217\) | 1.86683 | 0.126729 | ||||||||
\(218\) | 44.0016 | 2.98017 | ||||||||
\(219\) | 4.59489 | 0.310494 | ||||||||
\(220\) | 25.5817 | 1.72472 | ||||||||
\(221\) | −1.58168 | −0.106396 | ||||||||
\(222\) | −19.7290 | −1.32412 | ||||||||
\(223\) | 11.2118 | 0.750798 | 0.375399 | − | 0.926863i | \(-0.377506\pi\) | ||||
0.375399 | + | 0.926863i | \(0.377506\pi\) | |||||||
\(224\) | −15.8050 | −1.05602 | ||||||||
\(225\) | 0.329329 | 0.0219553 | ||||||||
\(226\) | −20.7933 | −1.38315 | ||||||||
\(227\) | 16.0179 | 1.06314 | 0.531572 | − | 0.847013i | \(-0.321602\pi\) | ||||
0.531572 | + | 0.847013i | \(0.321602\pi\) | |||||||
\(228\) | 2.12718 | 0.140876 | ||||||||
\(229\) | −8.93746 | −0.590604 | −0.295302 | − | 0.955404i | \(-0.595420\pi\) | ||||
−0.295302 | + | 0.955404i | \(0.595420\pi\) | |||||||
\(230\) | −25.1978 | −1.66150 | ||||||||
\(231\) | −8.53610 | −0.561634 | ||||||||
\(232\) | −19.8076 | −1.30043 | ||||||||
\(233\) | −1.19361 | −0.0781958 | −0.0390979 | − | 0.999235i | \(-0.512448\pi\) | ||||
−0.0390979 | + | 0.999235i | \(0.512448\pi\) | |||||||
\(234\) | 3.49477 | 0.228460 | ||||||||
\(235\) | 8.44245 | 0.550724 | ||||||||
\(236\) | 37.5184 | 2.44224 | ||||||||
\(237\) | −7.33466 | −0.476438 | ||||||||
\(238\) | 4.90519 | 0.317956 | ||||||||
\(239\) | 26.4181 | 1.70885 | 0.854423 | − | 0.519578i | \(-0.173911\pi\) | ||||
0.854423 | + | 0.519578i | \(0.173911\pi\) | |||||||
\(240\) | −3.36614 | −0.217284 | ||||||||
\(241\) | 8.65381 | 0.557441 | 0.278720 | − | 0.960372i | \(-0.410090\pi\) | ||||
0.278720 | + | 0.960372i | \(0.410090\pi\) | |||||||
\(242\) | −8.36170 | −0.537510 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.16356 | 0.522618 | ||||||||
\(245\) | 4.78212 | 0.305518 | ||||||||
\(246\) | 1.78006 | 0.113492 | ||||||||
\(247\) | 1.16743 | 0.0742820 | ||||||||
\(248\) | 1.63873 | 0.104059 | ||||||||
\(249\) | 0.714138 | 0.0452566 | ||||||||
\(250\) | −23.8240 | −1.50676 | ||||||||
\(251\) | −13.1035 | −0.827083 | −0.413541 | − | 0.910485i | \(-0.635708\pi\) | ||||
−0.413541 | + | 0.910485i | \(0.635708\pi\) | |||||||
\(252\) | −6.39808 | −0.403041 | ||||||||
\(253\) | 18.9946 | 1.19418 | ||||||||
\(254\) | 11.9819 | 0.751809 | ||||||||
\(255\) | 2.30853 | 0.144566 | ||||||||
\(256\) | −5.46923 | −0.341827 | ||||||||
\(257\) | −6.26798 | −0.390986 | −0.195493 | − | 0.980705i | \(-0.562631\pi\) | ||||
−0.195493 | + | 0.980705i | \(0.562631\pi\) | |||||||
\(258\) | −3.82824 | −0.238336 | ||||||||
\(259\) | 19.8228 | 1.23173 | ||||||||
\(260\) | 10.5232 | 0.652621 | ||||||||
\(261\) | 10.1642 | 0.629147 | ||||||||
\(262\) | 11.3897 | 0.703658 | ||||||||
\(263\) | −25.6283 | −1.58031 | −0.790155 | − | 0.612907i | \(-0.790000\pi\) | ||||
−0.790155 | + | 0.612907i | \(0.790000\pi\) | |||||||
\(264\) | −7.49310 | −0.461168 | ||||||||
\(265\) | −2.23044 | −0.137015 | ||||||||
\(266\) | −3.62050 | −0.221987 | ||||||||
\(267\) | 3.74781 | 0.229362 | ||||||||
\(268\) | −3.47234 | −0.212107 | ||||||||
\(269\) | −27.5743 | −1.68123 | −0.840617 | − | 0.541631i | \(-0.817807\pi\) | ||||
−0.840617 | + | 0.541631i | \(0.817807\pi\) | |||||||
\(270\) | −5.10076 | −0.310422 | ||||||||
\(271\) | 25.5444 | 1.55171 | 0.775857 | − | 0.630908i | \(-0.217318\pi\) | ||||
0.775857 | + | 0.630908i | \(0.217318\pi\) | |||||||
\(272\) | −1.45813 | −0.0884122 | ||||||||
\(273\) | −3.51138 | −0.212518 | ||||||||
\(274\) | −3.98430 | −0.240701 | ||||||||
\(275\) | −1.26629 | −0.0763599 | ||||||||
\(276\) | 14.2371 | 0.856970 | ||||||||
\(277\) | 4.16094 | 0.250006 | 0.125003 | − | 0.992156i | \(-0.460106\pi\) | ||||
0.125003 | + | 0.992156i | \(0.460106\pi\) | |||||||
\(278\) | −18.8276 | −1.12920 | ||||||||
\(279\) | −0.840905 | −0.0503437 | ||||||||
\(280\) | −9.98743 | −0.596863 | ||||||||
\(281\) | −24.7320 | −1.47539 | −0.737693 | − | 0.675136i | \(-0.764085\pi\) | ||||
−0.737693 | + | 0.675136i | \(0.764085\pi\) | |||||||
\(282\) | −8.08035 | −0.481178 | ||||||||
\(283\) | 26.0154 | 1.54645 | 0.773226 | − | 0.634130i | \(-0.218642\pi\) | ||||
0.773226 | + | 0.634130i | \(0.218642\pi\) | |||||||
\(284\) | 41.4431 | 2.45919 | ||||||||
\(285\) | −1.70392 | −0.100931 | ||||||||
\(286\) | −13.4375 | −0.794579 | ||||||||
\(287\) | −1.78852 | −0.105573 | ||||||||
\(288\) | 7.11930 | 0.419509 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 51.8450 | 3.04444 | ||||||||
\(291\) | −18.5380 | −1.08671 | ||||||||
\(292\) | −13.2424 | −0.774953 | ||||||||
\(293\) | −19.0533 | −1.11310 | −0.556552 | − | 0.830813i | \(-0.687876\pi\) | ||||
−0.556552 | + | 0.830813i | \(0.687876\pi\) | |||||||
\(294\) | −4.57701 | −0.266937 | ||||||||
\(295\) | −30.0530 | −1.74976 | ||||||||
\(296\) | 17.4007 | 1.01139 | ||||||||
\(297\) | 3.84505 | 0.223112 | ||||||||
\(298\) | −48.4953 | −2.80926 | ||||||||
\(299\) | 7.81355 | 0.451869 | ||||||||
\(300\) | −0.949122 | −0.0547976 | ||||||||
\(301\) | 3.84643 | 0.221705 | ||||||||
\(302\) | −15.1021 | −0.869027 | ||||||||
\(303\) | 13.8732 | 0.796993 | ||||||||
\(304\) | 1.07624 | 0.0617265 | ||||||||
\(305\) | −6.53919 | −0.374433 | ||||||||
\(306\) | −2.20952 | −0.126310 | ||||||||
\(307\) | −24.7473 | −1.41240 | −0.706201 | − | 0.708012i | \(-0.749592\pi\) | ||||
−0.706201 | + | 0.708012i | \(0.749592\pi\) | |||||||
\(308\) | 24.6009 | 1.40177 | ||||||||
\(309\) | −2.31242 | −0.131549 | ||||||||
\(310\) | −4.28925 | −0.243613 | ||||||||
\(311\) | 19.3519 | 1.09735 | 0.548673 | − | 0.836037i | \(-0.315133\pi\) | ||||
0.548673 | + | 0.836037i | \(0.315133\pi\) | |||||||
\(312\) | −3.08233 | −0.174503 | ||||||||
\(313\) | −22.0735 | −1.24767 | −0.623834 | − | 0.781557i | \(-0.714426\pi\) | ||||
−0.623834 | + | 0.781557i | \(0.714426\pi\) | |||||||
\(314\) | −2.20952 | −0.124691 | ||||||||
\(315\) | 5.12500 | 0.288761 | ||||||||
\(316\) | 21.1384 | 1.18913 | ||||||||
\(317\) | 17.5284 | 0.984491 | 0.492246 | − | 0.870456i | \(-0.336176\pi\) | ||||
0.492246 | + | 0.870456i | \(0.336176\pi\) | |||||||
\(318\) | 2.13477 | 0.119712 | ||||||||
\(319\) | −39.0818 | −2.18816 | ||||||||
\(320\) | 29.5815 | 1.65366 | ||||||||
\(321\) | 1.17716 | 0.0657026 | ||||||||
\(322\) | −24.2317 | −1.35038 | ||||||||
\(323\) | −0.738095 | −0.0410687 | ||||||||
\(324\) | 2.88199 | 0.160110 | ||||||||
\(325\) | −0.520895 | −0.0288940 | ||||||||
\(326\) | −17.6077 | −0.975202 | ||||||||
\(327\) | 19.9146 | 1.10128 | ||||||||
\(328\) | −1.56998 | −0.0866879 | ||||||||
\(329\) | 8.11876 | 0.447602 | ||||||||
\(330\) | 19.6127 | 1.07964 | ||||||||
\(331\) | 6.98992 | 0.384201 | 0.192100 | − | 0.981375i | \(-0.438470\pi\) | ||||
0.192100 | + | 0.981375i | \(0.438470\pi\) | |||||||
\(332\) | −2.05813 | −0.112955 | ||||||||
\(333\) | −8.92908 | −0.489311 | ||||||||
\(334\) | −15.3874 | −0.841961 | ||||||||
\(335\) | 2.78142 | 0.151965 | ||||||||
\(336\) | −3.23708 | −0.176597 | ||||||||
\(337\) | −6.01148 | −0.327466 | −0.163733 | − | 0.986505i | \(-0.552354\pi\) | ||||
−0.163733 | + | 0.986505i | \(0.552354\pi\) | |||||||
\(338\) | 23.1962 | 1.26170 | ||||||||
\(339\) | −9.41079 | −0.511124 | ||||||||
\(340\) | −6.65316 | −0.360818 | ||||||||
\(341\) | 3.23332 | 0.175094 | ||||||||
\(342\) | 1.63084 | 0.0881855 | ||||||||
\(343\) | 20.1389 | 1.08740 | ||||||||
\(344\) | 3.37645 | 0.182046 | ||||||||
\(345\) | −11.4042 | −0.613981 | ||||||||
\(346\) | 9.74277 | 0.523775 | ||||||||
\(347\) | 5.53277 | 0.297014 | 0.148507 | − | 0.988911i | \(-0.452553\pi\) | ||||
0.148507 | + | 0.988911i | \(0.452553\pi\) | |||||||
\(348\) | −29.2930 | −1.57027 | ||||||||
\(349\) | 10.0050 | 0.535557 | 0.267779 | − | 0.963480i | \(-0.413710\pi\) | ||||
0.267779 | + | 0.963480i | \(0.413710\pi\) | |||||||
\(350\) | 1.61542 | 0.0863479 | ||||||||
\(351\) | 1.58168 | 0.0844241 | ||||||||
\(352\) | −27.3741 | −1.45904 | ||||||||
\(353\) | −2.60373 | −0.138582 | −0.0692912 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692912 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(354\) | 28.7641 | 1.52879 | ||||||||
\(355\) | −33.1968 | −1.76190 | ||||||||
\(356\) | −10.8011 | −0.572459 | ||||||||
\(357\) | 2.22002 | 0.117496 | ||||||||
\(358\) | −15.6666 | −0.828005 | ||||||||
\(359\) | −9.61828 | −0.507633 | −0.253817 | − | 0.967252i | \(-0.581686\pi\) | ||||
−0.253817 | + | 0.967252i | \(0.581686\pi\) | |||||||
\(360\) | 4.49879 | 0.237107 | ||||||||
\(361\) | −18.4552 | −0.971327 | ||||||||
\(362\) | −7.92396 | −0.416474 | ||||||||
\(363\) | −3.78439 | −0.198629 | ||||||||
\(364\) | 10.1197 | 0.530419 | ||||||||
\(365\) | 10.6075 | 0.555220 | ||||||||
\(366\) | 6.25873 | 0.327149 | ||||||||
\(367\) | −10.0218 | −0.523136 | −0.261568 | − | 0.965185i | \(-0.584240\pi\) | ||||
−0.261568 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(368\) | 7.20319 | 0.375492 | ||||||||
\(369\) | 0.805630 | 0.0419394 | ||||||||
\(370\) | −45.5451 | −2.36778 | ||||||||
\(371\) | −2.14492 | −0.111359 | ||||||||
\(372\) | 2.42348 | 0.125651 | ||||||||
\(373\) | −5.66337 | −0.293238 | −0.146619 | − | 0.989193i | \(-0.546839\pi\) | ||||
−0.146619 | + | 0.989193i | \(0.546839\pi\) | |||||||
\(374\) | 8.49572 | 0.439303 | ||||||||
\(375\) | −10.7824 | −0.556801 | ||||||||
\(376\) | 7.12675 | 0.367534 | ||||||||
\(377\) | −16.0765 | −0.827983 | ||||||||
\(378\) | −4.90519 | −0.252296 | ||||||||
\(379\) | 10.8505 | 0.557352 | 0.278676 | − | 0.960385i | \(-0.410104\pi\) | ||||
0.278676 | + | 0.960385i | \(0.410104\pi\) | |||||||
\(380\) | 4.91066 | 0.251912 | ||||||||
\(381\) | 5.42283 | 0.277820 | ||||||||
\(382\) | 23.7020 | 1.21270 | ||||||||
\(383\) | 34.6746 | 1.77179 | 0.885895 | − | 0.463885i | \(-0.153545\pi\) | ||||
0.885895 | + | 0.463885i | \(0.153545\pi\) | |||||||
\(384\) | −14.0742 | −0.718220 | ||||||||
\(385\) | −19.7059 | −1.00430 | ||||||||
\(386\) | 38.0853 | 1.93849 | ||||||||
\(387\) | −1.73261 | −0.0880735 | ||||||||
\(388\) | 53.4261 | 2.71230 | ||||||||
\(389\) | 2.83589 | 0.143785 | 0.0718927 | − | 0.997412i | \(-0.477096\pi\) | ||||
0.0718927 | + | 0.997412i | \(0.477096\pi\) | |||||||
\(390\) | 8.06779 | 0.408528 | ||||||||
\(391\) | −4.94002 | −0.249827 | ||||||||
\(392\) | 4.03686 | 0.203892 | ||||||||
\(393\) | 5.15483 | 0.260027 | ||||||||
\(394\) | −52.1342 | −2.62648 | ||||||||
\(395\) | −16.9323 | −0.851957 | ||||||||
\(396\) | −11.0814 | −0.556860 | ||||||||
\(397\) | 25.4417 | 1.27688 | 0.638440 | − | 0.769672i | \(-0.279580\pi\) | ||||
0.638440 | + | 0.769672i | \(0.279580\pi\) | |||||||
\(398\) | −5.73580 | −0.287510 | ||||||||
\(399\) | −1.63859 | −0.0820320 | ||||||||
\(400\) | −0.480205 | −0.0240102 | ||||||||
\(401\) | 22.7176 | 1.13446 | 0.567232 | − | 0.823558i | \(-0.308014\pi\) | ||||
0.567232 | + | 0.823558i | \(0.308014\pi\) | |||||||
\(402\) | −2.66212 | −0.132775 | ||||||||
\(403\) | 1.33005 | 0.0662544 | ||||||||
\(404\) | −39.9823 | −1.98919 | ||||||||
\(405\) | −2.30853 | −0.114712 | ||||||||
\(406\) | 49.8572 | 2.47437 | ||||||||
\(407\) | 34.3328 | 1.70181 | ||||||||
\(408\) | 1.94877 | 0.0964783 | ||||||||
\(409\) | −14.6619 | −0.724983 | −0.362491 | − | 0.931987i | \(-0.618074\pi\) | ||||
−0.362491 | + | 0.931987i | \(0.618074\pi\) | |||||||
\(410\) | 4.10932 | 0.202945 | ||||||||
\(411\) | −1.80324 | −0.0889474 | ||||||||
\(412\) | 6.66436 | 0.328329 | ||||||||
\(413\) | −28.9008 | −1.42212 | ||||||||
\(414\) | 10.9151 | 0.536447 | ||||||||
\(415\) | 1.64861 | 0.0809271 | ||||||||
\(416\) | −11.2605 | −0.552091 | ||||||||
\(417\) | −8.52112 | −0.417281 | ||||||||
\(418\) | −6.27065 | −0.306707 | ||||||||
\(419\) | 29.9080 | 1.46110 | 0.730550 | − | 0.682859i | \(-0.239264\pi\) | ||||
0.730550 | + | 0.682859i | \(0.239264\pi\) | |||||||
\(420\) | −14.7702 | −0.720711 | ||||||||
\(421\) | −0.799668 | −0.0389734 | −0.0194867 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194867 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(422\) | −57.7047 | −2.80902 | ||||||||
\(423\) | −3.65706 | −0.177812 | ||||||||
\(424\) | −1.88284 | −0.0914388 | ||||||||
\(425\) | 0.329329 | 0.0159748 | ||||||||
\(426\) | 31.7730 | 1.53941 | ||||||||
\(427\) | −6.28848 | −0.304321 | ||||||||
\(428\) | −3.39255 | −0.163985 | ||||||||
\(429\) | −6.08165 | −0.293625 | ||||||||
\(430\) | −8.83762 | −0.426188 | ||||||||
\(431\) | 17.5388 | 0.844812 | 0.422406 | − | 0.906407i | \(-0.361186\pi\) | ||||
0.422406 | + | 0.906407i | \(0.361186\pi\) | |||||||
\(432\) | 1.45813 | 0.0701543 | ||||||||
\(433\) | −15.2755 | −0.734096 | −0.367048 | − | 0.930202i | \(-0.619632\pi\) | ||||
−0.367048 | + | 0.930202i | \(0.619632\pi\) | |||||||
\(434\) | −4.12480 | −0.197997 | ||||||||
\(435\) | 23.4644 | 1.12503 | ||||||||
\(436\) | −57.3935 | −2.74865 | ||||||||
\(437\) | 3.64620 | 0.174422 | ||||||||
\(438\) | −10.1525 | −0.485105 | ||||||||
\(439\) | −17.6320 | −0.841529 | −0.420764 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420764 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(440\) | −17.2981 | −0.824653 | ||||||||
\(441\) | −2.07149 | −0.0986426 | ||||||||
\(442\) | 3.49477 | 0.166229 | ||||||||
\(443\) | 2.01022 | 0.0955083 | 0.0477542 | − | 0.998859i | \(-0.484794\pi\) | ||||
0.0477542 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(444\) | 25.7335 | 1.22126 | ||||||||
\(445\) | 8.65194 | 0.410141 | ||||||||
\(446\) | −24.7727 | −1.17302 | ||||||||
\(447\) | −21.9483 | −1.03812 | ||||||||
\(448\) | 28.4474 | 1.34401 | ||||||||
\(449\) | 7.55031 | 0.356321 | 0.178161 | − | 0.984001i | \(-0.442985\pi\) | ||||
0.178161 | + | 0.984001i | \(0.442985\pi\) | |||||||
\(450\) | −0.727660 | −0.0343022 | ||||||||
\(451\) | −3.09769 | −0.145864 | ||||||||
\(452\) | 27.1218 | 1.27570 | ||||||||
\(453\) | −6.83500 | −0.321136 | ||||||||
\(454\) | −35.3918 | −1.66102 | ||||||||
\(455\) | −8.10614 | −0.380022 | ||||||||
\(456\) | −1.43837 | −0.0673580 | ||||||||
\(457\) | −2.56504 | −0.119988 | −0.0599938 | − | 0.998199i | \(-0.519108\pi\) | ||||
−0.0599938 | + | 0.998199i | \(0.519108\pi\) | |||||||
\(458\) | 19.7475 | 0.922741 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 32.8667 | 1.53242 | ||||||||
\(461\) | −19.3695 | −0.902127 | −0.451064 | − | 0.892492i | \(-0.648955\pi\) | ||||
−0.451064 | + | 0.892492i | \(0.648955\pi\) | |||||||
\(462\) | 18.8607 | 0.877479 | ||||||||
\(463\) | 12.2330 | 0.568515 | 0.284257 | − | 0.958748i | \(-0.408253\pi\) | ||||
0.284257 | + | 0.958748i | \(0.408253\pi\) | |||||||
\(464\) | −14.8207 | −0.688034 | ||||||||
\(465\) | −1.94126 | −0.0900237 | ||||||||
\(466\) | 2.63730 | 0.122171 | ||||||||
\(467\) | 10.2642 | 0.474972 | 0.237486 | − | 0.971391i | \(-0.423677\pi\) | ||||
0.237486 | + | 0.971391i | \(0.423677\pi\) | |||||||
\(468\) | −4.55839 | −0.210712 | ||||||||
\(469\) | 2.67478 | 0.123510 | ||||||||
\(470\) | −18.6538 | −0.860434 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −25.3695 | −1.16773 | ||||||||
\(473\) | 6.66197 | 0.306318 | ||||||||
\(474\) | 16.2061 | 0.744371 | ||||||||
\(475\) | −0.243076 | −0.0111531 | ||||||||
\(476\) | −6.39808 | −0.293255 | ||||||||
\(477\) | 0.966170 | 0.0442379 | ||||||||
\(478\) | −58.3714 | −2.66985 | ||||||||
\(479\) | 10.5901 | 0.483874 | 0.241937 | − | 0.970292i | \(-0.422217\pi\) | ||||
0.241937 | + | 0.970292i | \(0.422217\pi\) | |||||||
\(480\) | 16.4352 | 0.750159 | ||||||||
\(481\) | 14.1230 | 0.643953 | ||||||||
\(482\) | −19.1208 | −0.870928 | ||||||||
\(483\) | −10.9670 | −0.499014 | ||||||||
\(484\) | 10.9066 | 0.495753 | ||||||||
\(485\) | −42.7955 | −1.94324 | ||||||||
\(486\) | 2.20952 | 0.100226 | ||||||||
\(487\) | 6.55707 | 0.297129 | 0.148565 | − | 0.988903i | \(-0.452535\pi\) | ||||
0.148565 | + | 0.988903i | \(0.452535\pi\) | |||||||
\(488\) | −5.52011 | −0.249883 | ||||||||
\(489\) | −7.96902 | −0.360372 | ||||||||
\(490\) | −10.5662 | −0.477332 | ||||||||
\(491\) | 22.9432 | 1.03541 | 0.517705 | − | 0.855559i | \(-0.326786\pi\) | ||||
0.517705 | + | 0.855559i | \(0.326786\pi\) | |||||||
\(492\) | −2.32181 | −0.104675 | ||||||||
\(493\) | 10.1642 | 0.457772 | ||||||||
\(494\) | −2.57947 | −0.116056 | ||||||||
\(495\) | 8.87642 | 0.398966 | ||||||||
\(496\) | 1.22615 | 0.0550557 | ||||||||
\(497\) | −31.9240 | −1.43199 | ||||||||
\(498\) | −1.57790 | −0.0707075 | ||||||||
\(499\) | 11.6637 | 0.522137 | 0.261069 | − | 0.965320i | \(-0.415925\pi\) | ||||
0.261069 | + | 0.965320i | \(0.415925\pi\) | |||||||
\(500\) | 31.0747 | 1.38970 | ||||||||
\(501\) | −6.96414 | −0.311135 | ||||||||
\(502\) | 28.9524 | 1.29221 | ||||||||
\(503\) | −5.18372 | −0.231130 | −0.115565 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115565 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(504\) | 4.32631 | 0.192709 | ||||||||
\(505\) | 32.0267 | 1.42517 | ||||||||
\(506\) | −41.9690 | −1.86575 | ||||||||
\(507\) | 10.4983 | 0.466245 | ||||||||
\(508\) | −15.6285 | −0.693404 | ||||||||
\(509\) | 2.41208 | 0.106914 | 0.0534568 | − | 0.998570i | \(-0.482976\pi\) | ||||
0.0534568 | + | 0.998570i | \(0.482976\pi\) | |||||||
\(510\) | −5.10076 | −0.225865 | ||||||||
\(511\) | 10.2008 | 0.451255 | ||||||||
\(512\) | −16.0640 | −0.709934 | ||||||||
\(513\) | 0.738095 | 0.0325877 | ||||||||
\(514\) | 13.8492 | 0.610863 | ||||||||
\(515\) | −5.33830 | −0.235233 | ||||||||
\(516\) | 4.99336 | 0.219820 | ||||||||
\(517\) | 14.0616 | 0.618427 | ||||||||
\(518\) | −43.7989 | −1.92441 | ||||||||
\(519\) | 4.40945 | 0.193553 | ||||||||
\(520\) | −7.11567 | −0.312043 | ||||||||
\(521\) | 18.1932 | 0.797058 | 0.398529 | − | 0.917156i | \(-0.369521\pi\) | ||||
0.398529 | + | 0.917156i | \(0.369521\pi\) | |||||||
\(522\) | −22.4580 | −0.982959 | ||||||||
\(523\) | −20.7596 | −0.907755 | −0.453878 | − | 0.891064i | \(-0.649960\pi\) | ||||
−0.453878 | + | 0.891064i | \(0.649960\pi\) | |||||||
\(524\) | −14.8561 | −0.648993 | ||||||||
\(525\) | 0.731118 | 0.0319086 | ||||||||
\(526\) | 56.6263 | 2.46903 | ||||||||
\(527\) | −0.840905 | −0.0366304 | ||||||||
\(528\) | −5.60658 | −0.243995 | ||||||||
\(529\) | 1.40378 | 0.0610340 | ||||||||
\(530\) | 4.92820 | 0.214067 | ||||||||
\(531\) | 13.0182 | 0.564943 | ||||||||
\(532\) | 4.72239 | 0.204741 | ||||||||
\(533\) | −1.27425 | −0.0551940 | ||||||||
\(534\) | −8.28086 | −0.358348 | ||||||||
\(535\) | 2.71751 | 0.117488 | ||||||||
\(536\) | 2.34796 | 0.101416 | ||||||||
\(537\) | −7.09049 | −0.305977 | ||||||||
\(538\) | 60.9260 | 2.62670 | ||||||||
\(539\) | 7.96500 | 0.343077 | ||||||||
\(540\) | 6.65316 | 0.286306 | ||||||||
\(541\) | −9.05763 | −0.389418 | −0.194709 | − | 0.980861i | \(-0.562376\pi\) | ||||
−0.194709 | + | 0.980861i | \(0.562376\pi\) | |||||||
\(542\) | −56.4410 | −2.42435 | ||||||||
\(543\) | −3.58628 | −0.153902 | ||||||||
\(544\) | 7.11930 | 0.305238 | ||||||||
\(545\) | 45.9734 | 1.96929 | ||||||||
\(546\) | 7.75847 | 0.332032 | ||||||||
\(547\) | −18.4935 | −0.790727 | −0.395364 | − | 0.918525i | \(-0.629381\pi\) | ||||
−0.395364 | + | 0.918525i | \(0.629381\pi\) | |||||||
\(548\) | 5.19692 | 0.222001 | ||||||||
\(549\) | 2.83262 | 0.120893 | ||||||||
\(550\) | 2.79789 | 0.119302 | ||||||||
\(551\) | −7.50213 | −0.319601 | ||||||||
\(552\) | −9.62694 | −0.409750 | ||||||||
\(553\) | −16.2831 | −0.692429 | ||||||||
\(554\) | −9.19368 | −0.390602 | ||||||||
\(555\) | −20.6131 | −0.874977 | ||||||||
\(556\) | 24.5577 | 1.04148 | ||||||||
\(557\) | 12.9092 | 0.546981 | 0.273491 | − | 0.961875i | \(-0.411822\pi\) | ||||
0.273491 | + | 0.961875i | \(0.411822\pi\) | |||||||
\(558\) | 1.85800 | 0.0786553 | ||||||||
\(559\) | 2.74044 | 0.115908 | ||||||||
\(560\) | −7.47292 | −0.315788 | ||||||||
\(561\) | 3.84505 | 0.162338 | ||||||||
\(562\) | 54.6458 | 2.30510 | ||||||||
\(563\) | −16.5522 | −0.697593 | −0.348796 | − | 0.937199i | \(-0.613410\pi\) | ||||
−0.348796 | + | 0.937199i | \(0.613410\pi\) | |||||||
\(564\) | 10.5396 | 0.443797 | ||||||||
\(565\) | −21.7251 | −0.913983 | ||||||||
\(566\) | −57.4815 | −2.41613 | ||||||||
\(567\) | −2.22002 | −0.0932322 | ||||||||
\(568\) | −28.0233 | −1.17583 | ||||||||
\(569\) | −28.5553 | −1.19710 | −0.598550 | − | 0.801086i | \(-0.704256\pi\) | ||||
−0.598550 | + | 0.801086i | \(0.704256\pi\) | |||||||
\(570\) | 3.76484 | 0.157692 | ||||||||
\(571\) | 27.1517 | 1.13626 | 0.568132 | − | 0.822937i | \(-0.307666\pi\) | ||||
0.568132 | + | 0.822937i | \(0.307666\pi\) | |||||||
\(572\) | 17.5272 | 0.732851 | ||||||||
\(573\) | 10.7272 | 0.448136 | ||||||||
\(574\) | 3.95177 | 0.164944 | ||||||||
\(575\) | −1.62689 | −0.0678461 | ||||||||
\(576\) | −12.8140 | −0.533916 | ||||||||
\(577\) | −9.37529 | −0.390298 | −0.195149 | − | 0.980774i | \(-0.562519\pi\) | ||||
−0.195149 | + | 0.980774i | \(0.562519\pi\) | |||||||
\(578\) | −2.20952 | −0.0919040 | ||||||||
\(579\) | 17.2369 | 0.716341 | ||||||||
\(580\) | −67.6239 | −2.80793 | ||||||||
\(581\) | 1.58540 | 0.0657736 | ||||||||
\(582\) | 40.9600 | 1.69785 | ||||||||
\(583\) | −3.71497 | −0.153858 | ||||||||
\(584\) | 8.95436 | 0.370534 | ||||||||
\(585\) | 3.65137 | 0.150966 | ||||||||
\(586\) | 42.0986 | 1.73908 | ||||||||
\(587\) | 43.4149 | 1.79192 | 0.895962 | − | 0.444131i | \(-0.146487\pi\) | ||||
0.895962 | + | 0.444131i | \(0.146487\pi\) | |||||||
\(588\) | 5.97002 | 0.246199 | ||||||||
\(589\) | 0.620668 | 0.0255742 | ||||||||
\(590\) | 66.4028 | 2.73376 | ||||||||
\(591\) | −23.5952 | −0.970578 | ||||||||
\(592\) | 13.0198 | 0.535109 | ||||||||
\(593\) | −35.4407 | −1.45538 | −0.727688 | − | 0.685908i | \(-0.759405\pi\) | ||||
−0.727688 | + | 0.685908i | \(0.759405\pi\) | |||||||
\(594\) | −8.49572 | −0.348583 | ||||||||
\(595\) | 5.12500 | 0.210105 | ||||||||
\(596\) | 63.2547 | 2.59102 | ||||||||
\(597\) | −2.59595 | −0.106245 | ||||||||
\(598\) | −17.2642 | −0.705986 | ||||||||
\(599\) | −40.3090 | −1.64698 | −0.823490 | − | 0.567330i | \(-0.807976\pi\) | ||||
−0.823490 | + | 0.567330i | \(0.807976\pi\) | |||||||
\(600\) | 0.641785 | 0.0262008 | ||||||||
\(601\) | 9.33407 | 0.380745 | 0.190372 | − | 0.981712i | \(-0.439030\pi\) | ||||
0.190372 | + | 0.981712i | \(0.439030\pi\) | |||||||
\(602\) | −8.49878 | −0.346384 | ||||||||
\(603\) | −1.20484 | −0.0490650 | ||||||||
\(604\) | 19.6984 | 0.801515 | ||||||||
\(605\) | −8.73640 | −0.355185 | ||||||||
\(606\) | −30.6531 | −1.24520 | ||||||||
\(607\) | −23.1494 | −0.939605 | −0.469802 | − | 0.882772i | \(-0.655675\pi\) | ||||
−0.469802 | + | 0.882772i | \(0.655675\pi\) | |||||||
\(608\) | −5.25472 | −0.213107 | ||||||||
\(609\) | 22.5647 | 0.914369 | ||||||||
\(610\) | 14.4485 | 0.585002 | ||||||||
\(611\) | 5.78432 | 0.234008 | ||||||||
\(612\) | 2.88199 | 0.116497 | ||||||||
\(613\) | −25.7877 | −1.04155 | −0.520777 | − | 0.853693i | \(-0.674358\pi\) | ||||
−0.520777 | + | 0.853693i | \(0.674358\pi\) | |||||||
\(614\) | 54.6796 | 2.20669 | ||||||||
\(615\) | 1.85982 | 0.0749954 | ||||||||
\(616\) | −16.6349 | −0.670238 | ||||||||
\(617\) | 5.01790 | 0.202013 | 0.101007 | − | 0.994886i | \(-0.467794\pi\) | ||||
0.101007 | + | 0.994886i | \(0.467794\pi\) | |||||||
\(618\) | 5.10934 | 0.205528 | ||||||||
\(619\) | −24.1372 | −0.970156 | −0.485078 | − | 0.874471i | \(-0.661209\pi\) | ||||
−0.485078 | + | 0.874471i | \(0.661209\pi\) | |||||||
\(620\) | 5.59468 | 0.224688 | ||||||||
\(621\) | 4.94002 | 0.198236 | ||||||||
\(622\) | −42.7584 | −1.71446 | ||||||||
\(623\) | 8.32022 | 0.333343 | ||||||||
\(624\) | −2.30630 | −0.0923260 | ||||||||
\(625\) | −26.5382 | −1.06153 | ||||||||
\(626\) | 48.7718 | 1.94932 | ||||||||
\(627\) | −2.83801 | −0.113339 | ||||||||
\(628\) | 2.88199 | 0.115004 | ||||||||
\(629\) | −8.92908 | −0.356026 | ||||||||
\(630\) | −11.3238 | −0.451151 | ||||||||
\(631\) | 36.2545 | 1.44327 | 0.721635 | − | 0.692274i | \(-0.243391\pi\) | ||||
0.721635 | + | 0.692274i | \(0.243391\pi\) | |||||||
\(632\) | −14.2935 | −0.568567 | ||||||||
\(633\) | −26.1164 | −1.03803 | ||||||||
\(634\) | −38.7293 | −1.53814 | ||||||||
\(635\) | 12.5188 | 0.496793 | ||||||||
\(636\) | −2.78449 | −0.110412 | ||||||||
\(637\) | 3.27645 | 0.129818 | ||||||||
\(638\) | 86.3520 | 3.41871 | ||||||||
\(639\) | 14.3800 | 0.568866 | ||||||||
\(640\) | −32.4907 | −1.28431 | ||||||||
\(641\) | −22.4900 | −0.888303 | −0.444151 | − | 0.895952i | \(-0.646495\pi\) | ||||
−0.444151 | + | 0.895952i | \(0.646495\pi\) | |||||||
\(642\) | −2.60096 | −0.102652 | ||||||||
\(643\) | −31.6183 | −1.24690 | −0.623452 | − | 0.781862i | \(-0.714270\pi\) | ||||
−0.623452 | + | 0.781862i | \(0.714270\pi\) | |||||||
\(644\) | 31.6066 | 1.24548 | ||||||||
\(645\) | −3.99979 | −0.157492 | ||||||||
\(646\) | 1.63084 | 0.0641644 | ||||||||
\(647\) | −32.6741 | −1.28455 | −0.642275 | − | 0.766474i | \(-0.722009\pi\) | ||||
−0.642275 | + | 0.766474i | \(0.722009\pi\) | |||||||
\(648\) | −1.94877 | −0.0765548 | ||||||||
\(649\) | −50.0557 | −1.96486 | ||||||||
\(650\) | 1.15093 | 0.0451431 | ||||||||
\(651\) | −1.86683 | −0.0731668 | ||||||||
\(652\) | 22.9666 | 0.899442 | ||||||||
\(653\) | −1.21932 | −0.0477157 | −0.0238579 | − | 0.999715i | \(-0.507595\pi\) | ||||
−0.0238579 | + | 0.999715i | \(0.507595\pi\) | |||||||
\(654\) | −44.0016 | −1.72060 | ||||||||
\(655\) | 11.9001 | 0.464975 | ||||||||
\(656\) | −1.17471 | −0.0458649 | ||||||||
\(657\) | −4.59489 | −0.179264 | ||||||||
\(658\) | −17.9386 | −0.699318 | ||||||||
\(659\) | 22.5867 | 0.879854 | 0.439927 | − | 0.898033i | \(-0.355004\pi\) | ||||
0.439927 | + | 0.898033i | \(0.355004\pi\) | |||||||
\(660\) | −25.5817 | −0.995767 | ||||||||
\(661\) | 21.1970 | 0.824466 | 0.412233 | − | 0.911078i | \(-0.364749\pi\) | ||||
0.412233 | + | 0.911078i | \(0.364749\pi\) | |||||||
\(662\) | −15.4444 | −0.600263 | ||||||||
\(663\) | 1.58168 | 0.0614276 | ||||||||
\(664\) | 1.39169 | 0.0540079 | ||||||||
\(665\) | −3.78274 | −0.146688 | ||||||||
\(666\) | 19.7290 | 0.764483 | ||||||||
\(667\) | −50.2112 | −1.94419 | ||||||||
\(668\) | 20.0705 | 0.776552 | ||||||||
\(669\) | −11.2118 | −0.433473 | ||||||||
\(670\) | −6.14560 | −0.237425 | ||||||||
\(671\) | −10.8915 | −0.420463 | ||||||||
\(672\) | 15.8050 | 0.609692 | ||||||||
\(673\) | −41.1885 | −1.58770 | −0.793851 | − | 0.608113i | \(-0.791927\pi\) | ||||
−0.793851 | + | 0.608113i | \(0.791927\pi\) | |||||||
\(674\) | 13.2825 | 0.511622 | ||||||||
\(675\) | −0.329329 | −0.0126759 | ||||||||
\(676\) | −30.2559 | −1.16369 | ||||||||
\(677\) | 22.6867 | 0.871920 | 0.435960 | − | 0.899966i | \(-0.356409\pi\) | ||||
0.435960 | + | 0.899966i | \(0.356409\pi\) | |||||||
\(678\) | 20.7933 | 0.798564 | ||||||||
\(679\) | −41.1547 | −1.57937 | ||||||||
\(680\) | 4.49879 | 0.172521 | ||||||||
\(681\) | −16.0179 | −0.613806 | ||||||||
\(682\) | −7.14409 | −0.273561 | ||||||||
\(683\) | −21.3664 | −0.817562 | −0.408781 | − | 0.912632i | \(-0.634046\pi\) | ||||
−0.408781 | + | 0.912632i | \(0.634046\pi\) | |||||||
\(684\) | −2.12718 | −0.0813347 | ||||||||
\(685\) | −4.16285 | −0.159054 | ||||||||
\(686\) | −44.4974 | −1.69892 | ||||||||
\(687\) | 8.93746 | 0.340985 | ||||||||
\(688\) | 2.52637 | 0.0963170 | ||||||||
\(689\) | −1.52818 | −0.0582189 | ||||||||
\(690\) | 25.1978 | 0.959265 | ||||||||
\(691\) | −50.4409 | −1.91886 | −0.959432 | − | 0.281940i | \(-0.909022\pi\) | ||||
−0.959432 | + | 0.281940i | \(0.909022\pi\) | |||||||
\(692\) | −12.7080 | −0.483085 | ||||||||
\(693\) | 8.53610 | 0.324260 | ||||||||
\(694\) | −12.2248 | −0.464046 | ||||||||
\(695\) | −19.6713 | −0.746174 | ||||||||
\(696\) | 19.8076 | 0.750805 | ||||||||
\(697\) | 0.805630 | 0.0305154 | ||||||||
\(698\) | −22.1063 | −0.836738 | ||||||||
\(699\) | 1.19361 | 0.0451463 | ||||||||
\(700\) | −2.10707 | −0.0796399 | ||||||||
\(701\) | −19.9321 | −0.752824 | −0.376412 | − | 0.926452i | \(-0.622842\pi\) | ||||
−0.376412 | + | 0.926452i | \(0.622842\pi\) | |||||||
\(702\) | −3.49477 | −0.131901 | ||||||||
\(703\) | 6.59051 | 0.248566 | ||||||||
\(704\) | 49.2704 | 1.85695 | ||||||||
\(705\) | −8.44245 | −0.317961 | ||||||||
\(706\) | 5.75299 | 0.216517 | ||||||||
\(707\) | 30.7988 | 1.15831 | ||||||||
\(708\) | −37.5184 | −1.41003 | ||||||||
\(709\) | 2.87595 | 0.108009 | 0.0540044 | − | 0.998541i | \(-0.482802\pi\) | ||||
0.0540044 | + | 0.998541i | \(0.482802\pi\) | |||||||
\(710\) | 73.3491 | 2.75274 | ||||||||
\(711\) | 7.33466 | 0.275071 | ||||||||
\(712\) | 7.30360 | 0.273714 | ||||||||
\(713\) | 4.15409 | 0.155572 | ||||||||
\(714\) | −4.90519 | −0.183572 | ||||||||
\(715\) | −14.0397 | −0.525055 | ||||||||
\(716\) | 20.4347 | 0.763680 | ||||||||
\(717\) | −26.4181 | −0.986603 | ||||||||
\(718\) | 21.2518 | 0.793110 | ||||||||
\(719\) | −33.1529 | −1.23640 | −0.618198 | − | 0.786022i | \(-0.712137\pi\) | ||||
−0.618198 | + | 0.786022i | \(0.712137\pi\) | |||||||
\(720\) | 3.36614 | 0.125449 | ||||||||
\(721\) | −5.13362 | −0.191186 | ||||||||
\(722\) | 40.7772 | 1.51757 | ||||||||
\(723\) | −8.65381 | −0.321839 | ||||||||
\(724\) | 10.3356 | 0.384120 | ||||||||
\(725\) | 3.34736 | 0.124318 | ||||||||
\(726\) | 8.36170 | 0.310332 | ||||||||
\(727\) | 0.721276 | 0.0267507 | 0.0133753 | − | 0.999911i | \(-0.495742\pi\) | ||||
0.0133753 | + | 0.999911i | \(0.495742\pi\) | |||||||
\(728\) | −6.84285 | −0.253613 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.4374 | −0.867457 | ||||||||
\(731\) | −1.73261 | −0.0640829 | ||||||||
\(732\) | −8.16356 | −0.301734 | ||||||||
\(733\) | 8.87008 | 0.327624 | 0.163812 | − | 0.986492i | \(-0.447621\pi\) | ||||
0.163812 | + | 0.986492i | \(0.447621\pi\) | |||||||
\(734\) | 22.1435 | 0.817330 | ||||||||
\(735\) | −4.78212 | −0.176391 | ||||||||
\(736\) | −35.1695 | −1.29636 | ||||||||
\(737\) | 4.63268 | 0.170647 | ||||||||
\(738\) | −1.78006 | −0.0655248 | ||||||||
\(739\) | −27.6014 | −1.01533 | −0.507667 | − | 0.861554i | \(-0.669492\pi\) | ||||
−0.507667 | + | 0.861554i | \(0.669492\pi\) | |||||||
\(740\) | 59.4066 | 2.18383 | ||||||||
\(741\) | −1.16743 | −0.0428867 | ||||||||
\(742\) | 4.73925 | 0.173983 | ||||||||
\(743\) | −33.0066 | −1.21089 | −0.605447 | − | 0.795885i | \(-0.707006\pi\) | ||||
−0.605447 | + | 0.795885i | \(0.707006\pi\) | |||||||
\(744\) | −1.63873 | −0.0600787 | ||||||||
\(745\) | −50.6684 | −1.85635 | ||||||||
\(746\) | 12.5133 | 0.458146 | ||||||||
\(747\) | −0.714138 | −0.0261289 | ||||||||
\(748\) | −11.0814 | −0.405175 | ||||||||
\(749\) | 2.61332 | 0.0954887 | ||||||||
\(750\) | 23.8240 | 0.869928 | ||||||||
\(751\) | 44.7830 | 1.63416 | 0.817078 | − | 0.576528i | \(-0.195593\pi\) | ||||
0.817078 | + | 0.576528i | \(0.195593\pi\) | |||||||
\(752\) | 5.33247 | 0.194455 | ||||||||
\(753\) | 13.1035 | 0.477516 | ||||||||
\(754\) | 35.5214 | 1.29361 | ||||||||
\(755\) | −15.7788 | −0.574250 | ||||||||
\(756\) | 6.39808 | 0.232696 | ||||||||
\(757\) | −7.22520 | −0.262604 | −0.131302 | − | 0.991342i | \(-0.541916\pi\) | ||||
−0.131302 | + | 0.991342i | \(0.541916\pi\) | |||||||
\(758\) | −23.9744 | −0.870789 | ||||||||
\(759\) | −18.9946 | −0.689461 | ||||||||
\(760\) | −3.32054 | −0.120448 | ||||||||
\(761\) | 8.01954 | 0.290708 | 0.145354 | − | 0.989380i | \(-0.453568\pi\) | ||||
0.145354 | + | 0.989380i | \(0.453568\pi\) | |||||||
\(762\) | −11.9819 | −0.434057 | ||||||||
\(763\) | 44.2108 | 1.60054 | ||||||||
\(764\) | −30.9157 | −1.11849 | ||||||||
\(765\) | −2.30853 | −0.0834652 | ||||||||
\(766\) | −76.6143 | −2.76819 | ||||||||
\(767\) | −20.5907 | −0.743489 | ||||||||
\(768\) | 5.46923 | 0.197354 | ||||||||
\(769\) | 46.9365 | 1.69257 | 0.846287 | − | 0.532726i | \(-0.178833\pi\) | ||||
0.846287 | + | 0.532726i | \(0.178833\pi\) | |||||||
\(770\) | 43.5405 | 1.56909 | ||||||||
\(771\) | 6.26798 | 0.225736 | ||||||||
\(772\) | −49.6765 | −1.78790 | ||||||||
\(773\) | 8.07146 | 0.290310 | 0.145155 | − | 0.989409i | \(-0.453632\pi\) | ||||
0.145155 | + | 0.989409i | \(0.453632\pi\) | |||||||
\(774\) | 3.82824 | 0.137603 | ||||||||
\(775\) | −0.276935 | −0.00994778 | ||||||||
\(776\) | −36.1261 | −1.29685 | ||||||||
\(777\) | −19.8228 | −0.711138 | ||||||||
\(778\) | −6.26596 | −0.224646 | ||||||||
\(779\) | −0.594632 | −0.0213049 | ||||||||
\(780\) | −10.5232 | −0.376791 | ||||||||
\(781\) | −55.2920 | −1.97850 | ||||||||
\(782\) | 10.9151 | 0.390322 | ||||||||
\(783\) | −10.1642 | −0.363238 | ||||||||
\(784\) | 3.02051 | 0.107875 | ||||||||
\(785\) | −2.30853 | −0.0823951 | ||||||||
\(786\) | −11.3897 | −0.406257 | ||||||||
\(787\) | 11.5758 | 0.412632 | 0.206316 | − | 0.978485i | \(-0.433853\pi\) | ||||
0.206316 | + | 0.978485i | \(0.433853\pi\) | |||||||
\(788\) | 68.0011 | 2.42244 | ||||||||
\(789\) | 25.6283 | 0.912392 | ||||||||
\(790\) | 37.4123 | 1.33107 | ||||||||
\(791\) | −20.8922 | −0.742841 | ||||||||
\(792\) | 7.49310 | 0.266256 | ||||||||
\(793\) | −4.48031 | −0.159100 | ||||||||
\(794\) | −56.2139 | −1.99496 | ||||||||
\(795\) | 2.23044 | 0.0791054 | ||||||||
\(796\) | 7.48149 | 0.265174 | ||||||||
\(797\) | −31.6105 | −1.11970 | −0.559851 | − | 0.828594i | \(-0.689141\pi\) | ||||
−0.559851 | + | 0.828594i | \(0.689141\pi\) | |||||||
\(798\) | 3.62050 | 0.128164 | ||||||||
\(799\) | −3.65706 | −0.129377 | ||||||||
\(800\) | 2.34459 | 0.0828939 | ||||||||
\(801\) | −3.74781 | −0.132422 | ||||||||
\(802\) | −50.1950 | −1.77245 | ||||||||
\(803\) | 17.6676 | 0.623475 | ||||||||
\(804\) | 3.47234 | 0.122460 | ||||||||
\(805\) | −25.3176 | −0.892328 | ||||||||
\(806\) | −2.93877 | −0.103514 | ||||||||
\(807\) | 27.5743 | 0.970661 | ||||||||
\(808\) | 27.0356 | 0.951108 | ||||||||
\(809\) | 18.2386 | 0.641237 | 0.320618 | − | 0.947208i | \(-0.396109\pi\) | ||||
0.320618 | + | 0.947208i | \(0.396109\pi\) | |||||||
\(810\) | 5.10076 | 0.179222 | ||||||||
\(811\) | −56.8141 | −1.99501 | −0.997507 | − | 0.0705716i | \(-0.977518\pi\) | ||||
−0.997507 | + | 0.0705716i | \(0.977518\pi\) | |||||||
\(812\) | −65.0312 | −2.28215 | ||||||||
\(813\) | −25.5444 | −0.895883 | ||||||||
\(814\) | −75.8590 | −2.65886 | ||||||||
\(815\) | −18.3968 | −0.644410 | ||||||||
\(816\) | 1.45813 | 0.0510448 | ||||||||
\(817\) | 1.27883 | 0.0447406 | ||||||||
\(818\) | 32.3957 | 1.13269 | ||||||||
\(819\) | 3.51138 | 0.122697 | ||||||||
\(820\) | −5.35999 | −0.187179 | ||||||||
\(821\) | −9.61418 | −0.335537 | −0.167769 | − | 0.985826i | \(-0.553656\pi\) | ||||
−0.167769 | + | 0.985826i | \(0.553656\pi\) | |||||||
\(822\) | 3.98430 | 0.138969 | ||||||||
\(823\) | −18.9976 | −0.662215 | −0.331107 | − | 0.943593i | \(-0.607422\pi\) | ||||
−0.331107 | + | 0.943593i | \(0.607422\pi\) | |||||||
\(824\) | −4.50636 | −0.156987 | ||||||||
\(825\) | 1.26629 | 0.0440864 | ||||||||
\(826\) | 63.8569 | 2.22187 | ||||||||
\(827\) | −46.1651 | −1.60532 | −0.802659 | − | 0.596438i | \(-0.796582\pi\) | ||||
−0.802659 | + | 0.596438i | \(0.796582\pi\) | |||||||
\(828\) | −14.2371 | −0.494772 | ||||||||
\(829\) | −46.1714 | −1.60360 | −0.801800 | − | 0.597592i | \(-0.796124\pi\) | ||||
−0.801800 | + | 0.597592i | \(0.796124\pi\) | |||||||
\(830\) | −3.64264 | −0.126438 | ||||||||
\(831\) | −4.16094 | −0.144341 | ||||||||
\(832\) | 20.2677 | 0.702656 | ||||||||
\(833\) | −2.07149 | −0.0717730 | ||||||||
\(834\) | 18.8276 | 0.651946 | ||||||||
\(835\) | −16.0769 | −0.556366 | ||||||||
\(836\) | 8.17911 | 0.282880 | ||||||||
\(837\) | 0.840905 | 0.0290659 | ||||||||
\(838\) | −66.0823 | −2.28277 | ||||||||
\(839\) | 17.6093 | 0.607941 | 0.303971 | − | 0.952681i | \(-0.401688\pi\) | ||||
0.303971 | + | 0.952681i | \(0.401688\pi\) | |||||||
\(840\) | 9.98743 | 0.344599 | ||||||||
\(841\) | 74.3106 | 2.56243 | ||||||||
\(842\) | 1.76688 | 0.0608908 | ||||||||
\(843\) | 24.7320 | 0.851814 | ||||||||
\(844\) | 75.2670 | 2.59080 | ||||||||
\(845\) | 24.2356 | 0.833731 | ||||||||
\(846\) | 8.08035 | 0.277808 | ||||||||
\(847\) | −8.40145 | −0.288677 | ||||||||
\(848\) | −1.40880 | −0.0483785 | ||||||||
\(849\) | −26.0154 | −0.892845 | ||||||||
\(850\) | −0.727660 | −0.0249585 | ||||||||
\(851\) | 44.1098 | 1.51207 | ||||||||
\(852\) | −41.4431 | −1.41982 | ||||||||
\(853\) | −16.2066 | −0.554904 | −0.277452 | − | 0.960740i | \(-0.589490\pi\) | ||||
−0.277452 | + | 0.960740i | \(0.589490\pi\) | |||||||
\(854\) | 13.8945 | 0.475461 | ||||||||
\(855\) | 1.70392 | 0.0582727 | ||||||||
\(856\) | 2.29401 | 0.0784075 | ||||||||
\(857\) | −34.2031 | −1.16836 | −0.584178 | − | 0.811626i | \(-0.698583\pi\) | ||||
−0.584178 | + | 0.811626i | \(0.698583\pi\) | |||||||
\(858\) | 13.4375 | 0.458750 | ||||||||
\(859\) | 22.7029 | 0.774613 | 0.387306 | − | 0.921951i | \(-0.373406\pi\) | ||||
0.387306 | + | 0.921951i | \(0.373406\pi\) | |||||||
\(860\) | 11.5273 | 0.393079 | ||||||||
\(861\) | 1.78852 | 0.0609525 | ||||||||
\(862\) | −38.7523 | −1.31991 | ||||||||
\(863\) | −21.9545 | −0.747340 | −0.373670 | − | 0.927562i | \(-0.621901\pi\) | ||||
−0.373670 | + | 0.927562i | \(0.621901\pi\) | |||||||
\(864\) | −7.11930 | −0.242204 | ||||||||
\(865\) | 10.1794 | 0.346109 | ||||||||
\(866\) | 33.7517 | 1.14693 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 5.38018 | 0.182615 | ||||||||
\(869\) | −28.2021 | −0.956692 | ||||||||
\(870\) | −51.8450 | −1.75771 | ||||||||
\(871\) | 1.90568 | 0.0645715 | ||||||||
\(872\) | 38.8088 | 1.31423 | ||||||||
\(873\) | 18.5380 | 0.627415 | ||||||||
\(874\) | −8.05636 | −0.272511 | ||||||||
\(875\) | −23.9372 | −0.809225 | ||||||||
\(876\) | 13.2424 | 0.447419 | ||||||||
\(877\) | 18.2044 | 0.614719 | 0.307360 | − | 0.951593i | \(-0.400555\pi\) | ||||
0.307360 | + | 0.951593i | \(0.400555\pi\) | |||||||
\(878\) | 38.9583 | 1.31478 | ||||||||
\(879\) | 19.0533 | 0.642651 | ||||||||
\(880\) | −12.9430 | −0.436308 | ||||||||
\(881\) | −17.1771 | −0.578711 | −0.289356 | − | 0.957222i | \(-0.593441\pi\) | ||||
−0.289356 | + | 0.957222i | \(0.593441\pi\) | |||||||
\(882\) | 4.57701 | 0.154116 | ||||||||
\(883\) | −49.8843 | −1.67874 | −0.839370 | − | 0.543561i | \(-0.817076\pi\) | ||||
−0.839370 | + | 0.543561i | \(0.817076\pi\) | |||||||
\(884\) | −4.55839 | −0.153315 | ||||||||
\(885\) | 30.0530 | 1.01022 | ||||||||
\(886\) | −4.44162 | −0.149219 | ||||||||
\(887\) | −26.7693 | −0.898825 | −0.449413 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449413 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(888\) | −17.4007 | −0.583929 | ||||||||
\(889\) | 12.0388 | 0.403769 | ||||||||
\(890\) | −19.1167 | −0.640792 | ||||||||
\(891\) | −3.84505 | −0.128814 | ||||||||
\(892\) | 32.3123 | 1.08189 | ||||||||
\(893\) | 2.69926 | 0.0903272 | ||||||||
\(894\) | 48.4953 | 1.62193 | ||||||||
\(895\) | −16.3686 | −0.547143 | ||||||||
\(896\) | −31.2450 | −1.04382 | ||||||||
\(897\) | −7.81355 | −0.260887 | ||||||||
\(898\) | −16.6826 | −0.556705 | ||||||||
\(899\) | −8.54711 | −0.285062 | ||||||||
\(900\) | 0.949122 | 0.0316374 | ||||||||
\(901\) | 0.966170 | 0.0321878 | ||||||||
\(902\) | 6.84441 | 0.227894 | ||||||||
\(903\) | −3.84643 | −0.128001 | ||||||||
\(904\) | −18.3394 | −0.609960 | ||||||||
\(905\) | −8.27905 | −0.275205 | ||||||||
\(906\) | 15.1021 | 0.501733 | ||||||||
\(907\) | −23.7621 | −0.789007 | −0.394503 | − | 0.918894i | \(-0.629083\pi\) | ||||
−0.394503 | + | 0.918894i | \(0.629083\pi\) | |||||||
\(908\) | 46.1633 | 1.53198 | ||||||||
\(909\) | −13.8732 | −0.460144 | ||||||||
\(910\) | 17.9107 | 0.593733 | ||||||||
\(911\) | −8.54566 | −0.283130 | −0.141565 | − | 0.989929i | \(-0.545213\pi\) | ||||
−0.141565 | + | 0.989929i | \(0.545213\pi\) | |||||||
\(912\) | −1.07624 | −0.0356378 | ||||||||
\(913\) | 2.74589 | 0.0908758 | ||||||||
\(914\) | 5.66752 | 0.187465 | ||||||||
\(915\) | 6.53919 | 0.216179 | ||||||||
\(916\) | −25.7576 | −0.851056 | ||||||||
\(917\) | 11.4438 | 0.377909 | ||||||||
\(918\) | 2.20952 | 0.0729251 | ||||||||
\(919\) | −16.1680 | −0.533334 | −0.266667 | − | 0.963789i | \(-0.585922\pi\) | ||||
−0.266667 | + | 0.963789i | \(0.585922\pi\) | |||||||
\(920\) | −22.2241 | −0.732707 | ||||||||
\(921\) | 24.7473 | 0.815450 | ||||||||
\(922\) | 42.7973 | 1.40945 | ||||||||
\(923\) | −22.7447 | −0.748651 | ||||||||
\(924\) | −24.6009 | −0.809311 | ||||||||
\(925\) | −2.94061 | −0.0966866 | ||||||||
\(926\) | −27.0290 | −0.888229 | ||||||||
\(927\) | 2.31242 | 0.0759498 | ||||||||
\(928\) | 72.3619 | 2.37539 | ||||||||
\(929\) | −36.0783 | −1.18369 | −0.591845 | − | 0.806052i | \(-0.701600\pi\) | ||||
−0.591845 | + | 0.806052i | \(0.701600\pi\) | |||||||
\(930\) | 4.28925 | 0.140650 | ||||||||
\(931\) | 1.52896 | 0.0501096 | ||||||||
\(932\) | −3.43996 | −0.112680 | ||||||||
\(933\) | −19.3519 | −0.633553 | ||||||||
\(934\) | −22.6790 | −0.742080 | ||||||||
\(935\) | 8.87642 | 0.290290 | ||||||||
\(936\) | 3.08233 | 0.100749 | ||||||||
\(937\) | 20.1577 | 0.658524 | 0.329262 | − | 0.944239i | \(-0.393200\pi\) | ||||
0.329262 | + | 0.944239i | \(0.393200\pi\) | |||||||
\(938\) | −5.90998 | −0.192968 | ||||||||
\(939\) | 22.0735 | 0.720341 | ||||||||
\(940\) | 24.3310 | 0.793590 | ||||||||
\(941\) | 19.2928 | 0.628926 | 0.314463 | − | 0.949270i | \(-0.398176\pi\) | ||||
0.314463 | + | 0.949270i | \(0.398176\pi\) | |||||||
\(942\) | 2.20952 | 0.0719901 | ||||||||
\(943\) | −3.97983 | −0.129601 | ||||||||
\(944\) | −18.9823 | −0.617821 | ||||||||
\(945\) | −5.12500 | −0.166716 | ||||||||
\(946\) | −14.7198 | −0.478581 | ||||||||
\(947\) | 10.3285 | 0.335631 | 0.167816 | − | 0.985818i | \(-0.446329\pi\) | ||||
0.167816 | + | 0.985818i | \(0.446329\pi\) | |||||||
\(948\) | −21.1384 | −0.686543 | ||||||||
\(949\) | 7.26766 | 0.235918 | ||||||||
\(950\) | 0.537082 | 0.0174252 | ||||||||
\(951\) | −17.5284 | −0.568396 | ||||||||
\(952\) | 4.32631 | 0.140216 | ||||||||
\(953\) | −14.1433 | −0.458148 | −0.229074 | − | 0.973409i | \(-0.573570\pi\) | ||||
−0.229074 | + | 0.973409i | \(0.573570\pi\) | |||||||
\(954\) | −2.13477 | −0.0691158 | ||||||||
\(955\) | 24.7641 | 0.801349 | ||||||||
\(956\) | 76.1366 | 2.46243 | ||||||||
\(957\) | 39.0818 | 1.26333 | ||||||||
\(958\) | −23.3991 | −0.755989 | ||||||||
\(959\) | −4.00324 | −0.129271 | ||||||||
\(960\) | −29.5815 | −0.954740 | ||||||||
\(961\) | −30.2929 | −0.977190 | ||||||||
\(962\) | −31.2051 | −1.00609 | ||||||||
\(963\) | −1.17716 | −0.0379334 | ||||||||
\(964\) | 24.9402 | 0.803268 | ||||||||
\(965\) | 39.7920 | 1.28095 | ||||||||
\(966\) | 24.2317 | 0.779643 | ||||||||
\(967\) | −33.2309 | −1.06863 | −0.534317 | − | 0.845284i | \(-0.679431\pi\) | ||||
−0.534317 | + | 0.845284i | \(0.679431\pi\) | |||||||
\(968\) | −7.37490 | −0.237038 | ||||||||
\(969\) | 0.738095 | 0.0237110 | ||||||||
\(970\) | 94.5576 | 3.03606 | ||||||||
\(971\) | 13.7675 | 0.441821 | 0.220910 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220910 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(972\) | −2.88199 | −0.0924397 | ||||||||
\(973\) | −18.9171 | −0.606454 | ||||||||
\(974\) | −14.4880 | −0.464225 | ||||||||
\(975\) | 0.520895 | 0.0166820 | ||||||||
\(976\) | −4.13032 | −0.132208 | ||||||||
\(977\) | 16.4974 | 0.527800 | 0.263900 | − | 0.964550i | \(-0.414991\pi\) | ||||
0.263900 | + | 0.964550i | \(0.414991\pi\) | |||||||
\(978\) | 17.6077 | 0.563033 | ||||||||
\(979\) | 14.4105 | 0.460562 | ||||||||
\(980\) | 13.7820 | 0.440249 | ||||||||
\(981\) | −19.9146 | −0.635823 | ||||||||
\(982\) | −50.6934 | −1.61769 | ||||||||
\(983\) | −26.9699 | −0.860205 | −0.430102 | − | 0.902780i | \(-0.641523\pi\) | ||||
−0.430102 | + | 0.902780i | \(0.641523\pi\) | |||||||
\(984\) | 1.56998 | 0.0500493 | ||||||||
\(985\) | −54.4704 | −1.73557 | ||||||||
\(986\) | −22.4580 | −0.715208 | ||||||||
\(987\) | −8.11876 | −0.258423 | ||||||||
\(988\) | 3.36453 | 0.107040 | ||||||||
\(989\) | 8.55912 | 0.272164 | ||||||||
\(990\) | −19.6127 | −0.623331 | ||||||||
\(991\) | 45.0013 | 1.42951 | 0.714756 | − | 0.699373i | \(-0.246538\pi\) | ||||
0.714756 | + | 0.699373i | \(0.246538\pi\) | |||||||
\(992\) | −5.98666 | −0.190077 | ||||||||
\(993\) | −6.98992 | −0.221818 | ||||||||
\(994\) | 70.5368 | 2.23729 | ||||||||
\(995\) | −5.99284 | −0.189986 | ||||||||
\(996\) | 2.05813 | 0.0652145 | ||||||||
\(997\) | −37.7485 | −1.19551 | −0.597754 | − | 0.801679i | \(-0.703940\pi\) | ||||
−0.597754 | + | 0.801679i | \(0.703940\pi\) | |||||||
\(998\) | −25.7711 | −0.815770 | ||||||||
\(999\) | 8.92908 | 0.282504 |
(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 | 8007.2.a.c.1.5 | ✓ | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.c.1.5 | ✓ | 39 | 1.1 | even | 1 | trivial |