Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75915 | −1.95101 | −0.975505 | − | 0.219976i | \(-0.929402\pi\) | ||||
−0.975505 | + | 0.219976i | \(0.929402\pi\) | |||||||
\(3\) | 3.04798 | 1.75975 | 0.879876 | − | 0.475202i | \(-0.157625\pi\) | ||||
0.879876 | + | 0.475202i | \(0.157625\pi\) | |||||||
\(4\) | 5.61289 | 2.80644 | ||||||||
\(5\) | −2.57270 | −1.15055 | −0.575274 | − | 0.817961i | \(-0.695105\pi\) | ||||
−0.575274 | + | 0.817961i | \(0.695105\pi\) | |||||||
\(6\) | −8.40983 | −3.43330 | ||||||||
\(7\) | −0.275912 | −0.104285 | −0.0521424 | − | 0.998640i | \(-0.516605\pi\) | ||||
−0.0521424 | + | 0.998640i | \(0.516605\pi\) | |||||||
\(8\) | −9.96848 | −3.52439 | ||||||||
\(9\) | 6.29019 | 2.09673 | ||||||||
\(10\) | 7.09847 | 2.24473 | ||||||||
\(11\) | 1.07656 | 0.324595 | 0.162298 | − | 0.986742i | \(-0.448109\pi\) | ||||
0.162298 | + | 0.986742i | \(0.448109\pi\) | |||||||
\(12\) | 17.1080 | 4.93865 | ||||||||
\(13\) | 3.84543 | 1.06653 | 0.533265 | − | 0.845948i | \(-0.320965\pi\) | ||||
0.533265 | + | 0.845948i | \(0.320965\pi\) | |||||||
\(14\) | 0.761280 | 0.203461 | ||||||||
\(15\) | −7.84156 | −2.02468 | ||||||||
\(16\) | 16.2787 | 4.06968 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −17.3556 | −4.09074 | ||||||||
\(19\) | −8.39562 | −1.92609 | −0.963044 | − | 0.269345i | \(-0.913193\pi\) | ||||
−0.963044 | + | 0.269345i | \(0.913193\pi\) | |||||||
\(20\) | −14.4403 | −3.22895 | ||||||||
\(21\) | −0.840974 | −0.183515 | ||||||||
\(22\) | −2.97039 | −0.633289 | ||||||||
\(23\) | −5.83447 | −1.21657 | −0.608285 | − | 0.793719i | \(-0.708142\pi\) | ||||
−0.608285 | + | 0.793719i | \(0.708142\pi\) | |||||||
\(24\) | −30.3837 | −6.20205 | ||||||||
\(25\) | 1.61881 | 0.323762 | ||||||||
\(26\) | −10.6101 | −2.08081 | ||||||||
\(27\) | 10.0284 | 1.92997 | ||||||||
\(28\) | −1.54866 | −0.292669 | ||||||||
\(29\) | 9.83543 | 1.82639 | 0.913197 | − | 0.407519i | \(-0.133606\pi\) | ||||
0.913197 | + | 0.407519i | \(0.133606\pi\) | |||||||
\(30\) | 21.6360 | 3.95017 | ||||||||
\(31\) | −0.683059 | −0.122681 | −0.0613405 | − | 0.998117i | \(-0.519538\pi\) | ||||
−0.0613405 | + | 0.998117i | \(0.519538\pi\) | |||||||
\(32\) | −24.9784 | −4.41560 | ||||||||
\(33\) | 3.28134 | 0.571208 | ||||||||
\(34\) | −2.75915 | −0.473190 | ||||||||
\(35\) | 0.709839 | 0.119985 | ||||||||
\(36\) | 35.3061 | 5.88435 | ||||||||
\(37\) | 2.82254 | 0.464022 | 0.232011 | − | 0.972713i | \(-0.425469\pi\) | ||||
0.232011 | + | 0.972713i | \(0.425469\pi\) | |||||||
\(38\) | 23.1647 | 3.75782 | ||||||||
\(39\) | 11.7208 | 1.87683 | ||||||||
\(40\) | 25.6459 | 4.05498 | ||||||||
\(41\) | −11.8657 | −1.85311 | −0.926557 | − | 0.376154i | \(-0.877247\pi\) | ||||
−0.926557 | + | 0.376154i | \(0.877247\pi\) | |||||||
\(42\) | 2.32037 | 0.358041 | ||||||||
\(43\) | 1.63044 | 0.248640 | 0.124320 | − | 0.992242i | \(-0.460325\pi\) | ||||
0.124320 | + | 0.992242i | \(0.460325\pi\) | |||||||
\(44\) | 6.04262 | 0.910959 | ||||||||
\(45\) | −16.1828 | −2.41239 | ||||||||
\(46\) | 16.0981 | 2.37354 | ||||||||
\(47\) | −8.40296 | −1.22570 | −0.612849 | − | 0.790200i | \(-0.709977\pi\) | ||||
−0.612849 | + | 0.790200i | \(0.709977\pi\) | |||||||
\(48\) | 49.6172 | 7.16163 | ||||||||
\(49\) | −6.92387 | −0.989125 | ||||||||
\(50\) | −4.46653 | −0.631663 | ||||||||
\(51\) | 3.04798 | 0.426803 | ||||||||
\(52\) | 21.5840 | 2.99316 | ||||||||
\(53\) | −8.09454 | −1.11187 | −0.555936 | − | 0.831225i | \(-0.687640\pi\) | ||||
−0.555936 | + | 0.831225i | \(0.687640\pi\) | |||||||
\(54\) | −27.6699 | −3.76540 | ||||||||
\(55\) | −2.76967 | −0.373463 | ||||||||
\(56\) | 2.75042 | 0.367540 | ||||||||
\(57\) | −25.5897 | −3.38944 | ||||||||
\(58\) | −27.1374 | −3.56331 | ||||||||
\(59\) | −4.19090 | −0.545608 | −0.272804 | − | 0.962070i | \(-0.587951\pi\) | ||||
−0.272804 | + | 0.962070i | \(0.587951\pi\) | |||||||
\(60\) | −44.0138 | −5.68215 | ||||||||
\(61\) | 7.21910 | 0.924310 | 0.462155 | − | 0.886799i | \(-0.347076\pi\) | ||||
0.462155 | + | 0.886799i | \(0.347076\pi\) | |||||||
\(62\) | 1.88466 | 0.239352 | ||||||||
\(63\) | −1.73554 | −0.218657 | ||||||||
\(64\) | 36.3616 | 4.54520 | ||||||||
\(65\) | −9.89316 | −1.22709 | ||||||||
\(66\) | −9.05369 | −1.11443 | ||||||||
\(67\) | −3.59814 | −0.439582 | −0.219791 | − | 0.975547i | \(-0.570538\pi\) | ||||
−0.219791 | + | 0.975547i | \(0.570538\pi\) | |||||||
\(68\) | 5.61289 | 0.680662 | ||||||||
\(69\) | −17.7833 | −2.14086 | ||||||||
\(70\) | −1.95855 | −0.234091 | ||||||||
\(71\) | −6.33421 | −0.751733 | −0.375866 | − | 0.926674i | \(-0.622655\pi\) | ||||
−0.375866 | + | 0.926674i | \(0.622655\pi\) | |||||||
\(72\) | −62.7036 | −7.38969 | ||||||||
\(73\) | 0.910127 | 0.106522 | 0.0532611 | − | 0.998581i | \(-0.483038\pi\) | ||||
0.0532611 | + | 0.998581i | \(0.483038\pi\) | |||||||
\(74\) | −7.78779 | −0.905313 | ||||||||
\(75\) | 4.93410 | 0.569741 | ||||||||
\(76\) | −47.1237 | −5.40545 | ||||||||
\(77\) | −0.297036 | −0.0338504 | ||||||||
\(78\) | −32.3394 | −3.66172 | ||||||||
\(79\) | −4.28754 | −0.482386 | −0.241193 | − | 0.970477i | \(-0.577539\pi\) | ||||
−0.241193 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(80\) | −41.8803 | −4.68236 | ||||||||
\(81\) | 11.6959 | 1.29955 | ||||||||
\(82\) | 32.7393 | 3.61545 | ||||||||
\(83\) | −4.00061 | −0.439124 | −0.219562 | − | 0.975599i | \(-0.570463\pi\) | ||||
−0.219562 | + | 0.975599i | \(0.570463\pi\) | |||||||
\(84\) | −4.72029 | −0.515026 | ||||||||
\(85\) | −2.57270 | −0.279049 | ||||||||
\(86\) | −4.49863 | −0.485100 | ||||||||
\(87\) | 29.9782 | 3.21400 | ||||||||
\(88\) | −10.7317 | −1.14400 | ||||||||
\(89\) | 12.2425 | 1.29771 | 0.648853 | − | 0.760914i | \(-0.275249\pi\) | ||||
0.648853 | + | 0.760914i | \(0.275249\pi\) | |||||||
\(90\) | 44.6507 | 4.70660 | ||||||||
\(91\) | −1.06100 | −0.111223 | ||||||||
\(92\) | −32.7482 | −3.41424 | ||||||||
\(93\) | −2.08195 | −0.215888 | ||||||||
\(94\) | 23.1850 | 2.39135 | ||||||||
\(95\) | 21.5995 | 2.21606 | ||||||||
\(96\) | −76.1337 | −7.77036 | ||||||||
\(97\) | 15.4252 | 1.56619 | 0.783094 | − | 0.621904i | \(-0.213640\pi\) | ||||
0.783094 | + | 0.621904i | \(0.213640\pi\) | |||||||
\(98\) | 19.1040 | 1.92979 | ||||||||
\(99\) | 6.77178 | 0.680589 | ||||||||
\(100\) | 9.08619 | 0.908619 | ||||||||
\(101\) | −18.8474 | −1.87539 | −0.937695 | − | 0.347458i | \(-0.887045\pi\) | ||||
−0.937695 | + | 0.347458i | \(0.887045\pi\) | |||||||
\(102\) | −8.40983 | −0.832697 | ||||||||
\(103\) | −11.2789 | −1.11135 | −0.555673 | − | 0.831401i | \(-0.687539\pi\) | ||||
−0.555673 | + | 0.831401i | \(0.687539\pi\) | |||||||
\(104\) | −38.3331 | −3.75887 | ||||||||
\(105\) | 2.16358 | 0.211143 | ||||||||
\(106\) | 22.3340 | 2.16927 | ||||||||
\(107\) | 4.07973 | 0.394402 | 0.197201 | − | 0.980363i | \(-0.436815\pi\) | ||||
0.197201 | + | 0.980363i | \(0.436815\pi\) | |||||||
\(108\) | 56.2885 | 5.41636 | ||||||||
\(109\) | 0.691996 | 0.0662812 | 0.0331406 | − | 0.999451i | \(-0.489449\pi\) | ||||
0.0331406 | + | 0.999451i | \(0.489449\pi\) | |||||||
\(110\) | 7.64194 | 0.728630 | ||||||||
\(111\) | 8.60304 | 0.816565 | ||||||||
\(112\) | −4.49149 | −0.424406 | ||||||||
\(113\) | 5.40994 | 0.508924 | 0.254462 | − | 0.967083i | \(-0.418102\pi\) | ||||
0.254462 | + | 0.967083i | \(0.418102\pi\) | |||||||
\(114\) | 70.6057 | 6.61283 | ||||||||
\(115\) | 15.0104 | 1.39972 | ||||||||
\(116\) | 55.2051 | 5.12567 | ||||||||
\(117\) | 24.1885 | 2.23623 | ||||||||
\(118\) | 11.5633 | 1.06449 | ||||||||
\(119\) | −0.275912 | −0.0252928 | ||||||||
\(120\) | 78.1684 | 7.13576 | ||||||||
\(121\) | −9.84102 | −0.894638 | ||||||||
\(122\) | −19.9185 | −1.80334 | ||||||||
\(123\) | −36.1665 | −3.26102 | ||||||||
\(124\) | −3.83393 | −0.344297 | ||||||||
\(125\) | 8.69881 | 0.778045 | ||||||||
\(126\) | 4.78860 | 0.426602 | ||||||||
\(127\) | 10.4288 | 0.925409 | 0.462704 | − | 0.886513i | \(-0.346879\pi\) | ||||
0.462704 | + | 0.886513i | \(0.346879\pi\) | |||||||
\(128\) | −50.3701 | −4.45213 | ||||||||
\(129\) | 4.96956 | 0.437545 | ||||||||
\(130\) | 27.2967 | 2.39408 | ||||||||
\(131\) | −14.4178 | −1.25969 | −0.629844 | − | 0.776722i | \(-0.716881\pi\) | ||||
−0.629844 | + | 0.776722i | \(0.716881\pi\) | |||||||
\(132\) | 18.4178 | 1.60306 | ||||||||
\(133\) | 2.31645 | 0.200862 | ||||||||
\(134\) | 9.92778 | 0.857630 | ||||||||
\(135\) | −25.8002 | −2.22053 | ||||||||
\(136\) | −9.96848 | −0.854790 | ||||||||
\(137\) | −1.87616 | −0.160291 | −0.0801455 | − | 0.996783i | \(-0.525539\pi\) | ||||
−0.0801455 | + | 0.996783i | \(0.525539\pi\) | |||||||
\(138\) | 49.0668 | 4.17685 | ||||||||
\(139\) | 14.4187 | 1.22298 | 0.611489 | − | 0.791253i | \(-0.290571\pi\) | ||||
0.611489 | + | 0.791253i | \(0.290571\pi\) | |||||||
\(140\) | 3.98425 | 0.336730 | ||||||||
\(141\) | −25.6121 | −2.15693 | ||||||||
\(142\) | 17.4770 | 1.46664 | ||||||||
\(143\) | 4.13984 | 0.346191 | ||||||||
\(144\) | 102.396 | 8.53302 | ||||||||
\(145\) | −25.3037 | −2.10135 | ||||||||
\(146\) | −2.51117 | −0.207826 | ||||||||
\(147\) | −21.1038 | −1.74062 | ||||||||
\(148\) | 15.8426 | 1.30225 | ||||||||
\(149\) | −7.10481 | −0.582048 | −0.291024 | − | 0.956716i | \(-0.593996\pi\) | ||||
−0.291024 | + | 0.956716i | \(0.593996\pi\) | |||||||
\(150\) | −13.6139 | −1.11157 | ||||||||
\(151\) | 17.7945 | 1.44809 | 0.724046 | − | 0.689751i | \(-0.242280\pi\) | ||||
0.724046 | + | 0.689751i | \(0.242280\pi\) | |||||||
\(152\) | 83.6916 | 6.78828 | ||||||||
\(153\) | 6.29019 | 0.508532 | ||||||||
\(154\) | 0.819565 | 0.0660424 | ||||||||
\(155\) | 1.75731 | 0.141150 | ||||||||
\(156\) | 65.7875 | 5.26722 | ||||||||
\(157\) | −11.4463 | −0.913514 | −0.456757 | − | 0.889591i | \(-0.650989\pi\) | ||||
−0.456757 | + | 0.889591i | \(0.650989\pi\) | |||||||
\(158\) | 11.8299 | 0.941140 | ||||||||
\(159\) | −24.6720 | −1.95662 | ||||||||
\(160\) | 64.2620 | 5.08036 | ||||||||
\(161\) | 1.60980 | 0.126870 | ||||||||
\(162\) | −32.2708 | −2.53543 | ||||||||
\(163\) | −17.1323 | −1.34190 | −0.670951 | − | 0.741502i | \(-0.734114\pi\) | ||||
−0.670951 | + | 0.741502i | \(0.734114\pi\) | |||||||
\(164\) | −66.6009 | −5.20066 | ||||||||
\(165\) | −8.44192 | −0.657202 | ||||||||
\(166\) | 11.0383 | 0.856735 | ||||||||
\(167\) | −16.1998 | −1.25358 | −0.626789 | − | 0.779189i | \(-0.715631\pi\) | ||||
−0.626789 | + | 0.779189i | \(0.715631\pi\) | |||||||
\(168\) | 8.38323 | 0.646780 | ||||||||
\(169\) | 1.78733 | 0.137487 | ||||||||
\(170\) | 7.09847 | 0.544428 | ||||||||
\(171\) | −52.8101 | −4.03849 | ||||||||
\(172\) | 9.15149 | 0.697794 | ||||||||
\(173\) | −0.995702 | −0.0757018 | −0.0378509 | − | 0.999283i | \(-0.512051\pi\) | ||||
−0.0378509 | + | 0.999283i | \(0.512051\pi\) | |||||||
\(174\) | −82.7142 | −6.27055 | ||||||||
\(175\) | −0.446648 | −0.0337634 | ||||||||
\(176\) | 17.5250 | 1.32100 | ||||||||
\(177\) | −12.7738 | −0.960136 | ||||||||
\(178\) | −33.7789 | −2.53184 | ||||||||
\(179\) | 3.74695 | 0.280060 | 0.140030 | − | 0.990147i | \(-0.455280\pi\) | ||||
0.140030 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(180\) | −90.8322 | −6.77023 | ||||||||
\(181\) | 3.00371 | 0.223264 | 0.111632 | − | 0.993750i | \(-0.464392\pi\) | ||||
0.111632 | + | 0.993750i | \(0.464392\pi\) | |||||||
\(182\) | 2.92745 | 0.216997 | ||||||||
\(183\) | 22.0037 | 1.62656 | ||||||||
\(184\) | 58.1608 | 4.28767 | ||||||||
\(185\) | −7.26156 | −0.533880 | ||||||||
\(186\) | 5.74440 | 0.421200 | ||||||||
\(187\) | 1.07656 | 0.0787260 | ||||||||
\(188\) | −47.1649 | −3.43985 | ||||||||
\(189\) | −2.76696 | −0.201267 | ||||||||
\(190\) | −59.5960 | −4.32355 | ||||||||
\(191\) | −11.1324 | −0.805515 | −0.402757 | − | 0.915307i | \(-0.631948\pi\) | ||||
−0.402757 | + | 0.915307i | \(0.631948\pi\) | |||||||
\(192\) | 110.829 | 7.99842 | ||||||||
\(193\) | 22.9052 | 1.64875 | 0.824375 | − | 0.566045i | \(-0.191527\pi\) | ||||
0.824375 | + | 0.566045i | \(0.191527\pi\) | |||||||
\(194\) | −42.5603 | −3.05565 | ||||||||
\(195\) | −30.1542 | −2.15938 | ||||||||
\(196\) | −38.8629 | −2.77592 | ||||||||
\(197\) | 16.2607 | 1.15852 | 0.579262 | − | 0.815141i | \(-0.303341\pi\) | ||||
0.579262 | + | 0.815141i | \(0.303341\pi\) | |||||||
\(198\) | −18.6843 | −1.32784 | ||||||||
\(199\) | −13.4673 | −0.954671 | −0.477335 | − | 0.878721i | \(-0.658397\pi\) | ||||
−0.477335 | + | 0.878721i | \(0.658397\pi\) | |||||||
\(200\) | −16.1371 | −1.14106 | ||||||||
\(201\) | −10.9671 | −0.773556 | ||||||||
\(202\) | 52.0029 | 3.65891 | ||||||||
\(203\) | −2.71371 | −0.190465 | ||||||||
\(204\) | 17.1080 | 1.19780 | ||||||||
\(205\) | 30.5270 | 2.13210 | ||||||||
\(206\) | 31.1202 | 2.16825 | ||||||||
\(207\) | −36.6999 | −2.55082 | ||||||||
\(208\) | 62.5986 | 4.34043 | ||||||||
\(209\) | −9.03840 | −0.625199 | ||||||||
\(210\) | −5.96962 | −0.411943 | ||||||||
\(211\) | 7.68654 | 0.529164 | 0.264582 | − | 0.964363i | \(-0.414766\pi\) | ||||
0.264582 | + | 0.964363i | \(0.414766\pi\) | |||||||
\(212\) | −45.4337 | −3.12040 | ||||||||
\(213\) | −19.3066 | −1.32286 | ||||||||
\(214\) | −11.2566 | −0.769483 | ||||||||
\(215\) | −4.19465 | −0.286073 | ||||||||
\(216\) | −99.9683 | −6.80198 | ||||||||
\(217\) | 0.188464 | 0.0127938 | ||||||||
\(218\) | −1.90932 | −0.129315 | ||||||||
\(219\) | 2.77405 | 0.187453 | ||||||||
\(220\) | −15.5459 | −1.04810 | ||||||||
\(221\) | 3.84543 | 0.258672 | ||||||||
\(222\) | −23.7371 | −1.59313 | ||||||||
\(223\) | 11.3649 | 0.761051 | 0.380525 | − | 0.924770i | \(-0.375743\pi\) | ||||
0.380525 | + | 0.924770i | \(0.375743\pi\) | |||||||
\(224\) | 6.89183 | 0.460480 | ||||||||
\(225\) | 10.1826 | 0.678841 | ||||||||
\(226\) | −14.9268 | −0.992917 | ||||||||
\(227\) | 8.68896 | 0.576706 | 0.288353 | − | 0.957524i | \(-0.406892\pi\) | ||||
0.288353 | + | 0.957524i | \(0.406892\pi\) | |||||||
\(228\) | −143.632 | −9.51226 | ||||||||
\(229\) | −18.4536 | −1.21945 | −0.609723 | − | 0.792614i | \(-0.708720\pi\) | ||||
−0.609723 | + | 0.792614i | \(0.708720\pi\) | |||||||
\(230\) | −41.4158 | −2.73088 | ||||||||
\(231\) | −0.905360 | −0.0595683 | ||||||||
\(232\) | −98.0442 | −6.43692 | ||||||||
\(233\) | 3.53003 | 0.231260 | 0.115630 | − | 0.993292i | \(-0.463111\pi\) | ||||
0.115630 | + | 0.993292i | \(0.463111\pi\) | |||||||
\(234\) | −66.7396 | −4.36290 | ||||||||
\(235\) | 21.6183 | 1.41022 | ||||||||
\(236\) | −23.5230 | −1.53122 | ||||||||
\(237\) | −13.0683 | −0.848880 | ||||||||
\(238\) | 0.761280 | 0.0493465 | ||||||||
\(239\) | −21.0528 | −1.36179 | −0.680896 | − | 0.732380i | \(-0.738409\pi\) | ||||
−0.680896 | + | 0.732380i | \(0.738409\pi\) | |||||||
\(240\) | −127.650 | −8.23980 | ||||||||
\(241\) | 12.1773 | 0.784411 | 0.392205 | − | 0.919878i | \(-0.371712\pi\) | ||||
0.392205 | + | 0.919878i | \(0.371712\pi\) | |||||||
\(242\) | 27.1528 | 1.74545 | ||||||||
\(243\) | 5.56367 | 0.356910 | ||||||||
\(244\) | 40.5200 | 2.59402 | ||||||||
\(245\) | 17.8131 | 1.13804 | ||||||||
\(246\) | 99.7887 | 6.36229 | ||||||||
\(247\) | −32.2848 | −2.05423 | ||||||||
\(248\) | 6.80905 | 0.432375 | ||||||||
\(249\) | −12.1938 | −0.772749 | ||||||||
\(250\) | −24.0013 | −1.51797 | ||||||||
\(251\) | 30.0993 | 1.89985 | 0.949925 | − | 0.312478i | \(-0.101159\pi\) | ||||
0.949925 | + | 0.312478i | \(0.101159\pi\) | |||||||
\(252\) | −9.74137 | −0.613649 | ||||||||
\(253\) | −6.28116 | −0.394893 | ||||||||
\(254\) | −28.7747 | −1.80548 | ||||||||
\(255\) | −7.84156 | −0.491057 | ||||||||
\(256\) | 66.2554 | 4.14096 | ||||||||
\(257\) | 5.68256 | 0.354469 | 0.177234 | − | 0.984169i | \(-0.443285\pi\) | ||||
0.177234 | + | 0.984169i | \(0.443285\pi\) | |||||||
\(258\) | −13.7117 | −0.853656 | ||||||||
\(259\) | −0.778771 | −0.0483905 | ||||||||
\(260\) | −55.5291 | −3.44377 | ||||||||
\(261\) | 61.8667 | 3.82945 | ||||||||
\(262\) | 39.7808 | 2.45766 | ||||||||
\(263\) | −31.4541 | −1.93955 | −0.969773 | − | 0.244010i | \(-0.921537\pi\) | ||||
−0.969773 | + | 0.244010i | \(0.921537\pi\) | |||||||
\(264\) | −32.7100 | −2.01316 | ||||||||
\(265\) | 20.8249 | 1.27926 | ||||||||
\(266\) | −6.39142 | −0.391883 | ||||||||
\(267\) | 37.3150 | 2.28364 | ||||||||
\(268\) | −20.1959 | −1.23366 | ||||||||
\(269\) | −0.00307033 | −0.000187202 0 | −9.36008e−5 | − | 1.00000i | \(-0.500030\pi\) | ||||
−9.36008e−5 | 1.00000i | \(0.500030\pi\) | ||||||||
\(270\) | 71.1866 | 4.33228 | ||||||||
\(271\) | −21.5107 | −1.30668 | −0.653342 | − | 0.757063i | \(-0.726634\pi\) | ||||
−0.653342 | + | 0.757063i | \(0.726634\pi\) | |||||||
\(272\) | 16.2787 | 0.987042 | ||||||||
\(273\) | −3.23390 | −0.195725 | ||||||||
\(274\) | 5.17659 | 0.312730 | ||||||||
\(275\) | 1.74275 | 0.105092 | ||||||||
\(276\) | −99.8159 | −6.00821 | ||||||||
\(277\) | −2.50556 | −0.150544 | −0.0752721 | − | 0.997163i | \(-0.523983\pi\) | ||||
−0.0752721 | + | 0.997163i | \(0.523983\pi\) | |||||||
\(278\) | −39.7833 | −2.38604 | ||||||||
\(279\) | −4.29657 | −0.257229 | ||||||||
\(280\) | −7.07602 | −0.422873 | ||||||||
\(281\) | 4.17035 | 0.248782 | 0.124391 | − | 0.992233i | \(-0.460302\pi\) | ||||
0.124391 | + | 0.992233i | \(0.460302\pi\) | |||||||
\(282\) | 70.6674 | 4.20818 | ||||||||
\(283\) | −13.9039 | −0.826500 | −0.413250 | − | 0.910618i | \(-0.635606\pi\) | ||||
−0.413250 | + | 0.910618i | \(0.635606\pi\) | |||||||
\(284\) | −35.5532 | −2.10970 | ||||||||
\(285\) | 65.8347 | 3.89971 | ||||||||
\(286\) | −11.4224 | −0.675422 | ||||||||
\(287\) | 3.27389 | 0.193252 | ||||||||
\(288\) | −157.119 | −9.25832 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 69.8165 | 4.09976 | ||||||||
\(291\) | 47.0156 | 2.75610 | ||||||||
\(292\) | 5.10844 | 0.298949 | ||||||||
\(293\) | 22.9731 | 1.34210 | 0.671051 | − | 0.741411i | \(-0.265843\pi\) | ||||
0.671051 | + | 0.741411i | \(0.265843\pi\) | |||||||
\(294\) | 58.2286 | 3.39596 | ||||||||
\(295\) | 10.7819 | 0.627749 | ||||||||
\(296\) | −28.1364 | −1.63540 | ||||||||
\(297\) | 10.7962 | 0.626461 | ||||||||
\(298\) | 19.6032 | 1.13558 | ||||||||
\(299\) | −22.4360 | −1.29751 | ||||||||
\(300\) | 27.6945 | 1.59895 | ||||||||
\(301\) | −0.449858 | −0.0259294 | ||||||||
\(302\) | −49.0975 | −2.82524 | ||||||||
\(303\) | −57.4467 | −3.30022 | ||||||||
\(304\) | −136.670 | −7.83856 | ||||||||
\(305\) | −18.5726 | −1.06346 | ||||||||
\(306\) | −17.3556 | −0.992151 | ||||||||
\(307\) | −7.31766 | −0.417641 | −0.208821 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208821 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(308\) | −1.66723 | −0.0949991 | ||||||||
\(309\) | −34.3780 | −1.95570 | ||||||||
\(310\) | −4.84867 | −0.275386 | ||||||||
\(311\) | −1.04860 | −0.0594606 | −0.0297303 | − | 0.999558i | \(-0.509465\pi\) | ||||
−0.0297303 | + | 0.999558i | \(0.509465\pi\) | |||||||
\(312\) | −116.839 | −6.61468 | ||||||||
\(313\) | −9.22256 | −0.521290 | −0.260645 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260645 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(314\) | 31.5820 | 1.78228 | ||||||||
\(315\) | 4.46502 | 0.251576 | ||||||||
\(316\) | −24.0655 | −1.35379 | ||||||||
\(317\) | 2.43246 | 0.136621 | 0.0683104 | − | 0.997664i | \(-0.478239\pi\) | ||||
0.0683104 | + | 0.997664i | \(0.478239\pi\) | |||||||
\(318\) | 68.0737 | 3.81738 | ||||||||
\(319\) | 10.5884 | 0.592839 | ||||||||
\(320\) | −93.5476 | −5.22947 | ||||||||
\(321\) | 12.4349 | 0.694050 | ||||||||
\(322\) | −4.44167 | −0.247524 | ||||||||
\(323\) | −8.39562 | −0.467145 | ||||||||
\(324\) | 65.6480 | 3.64711 | ||||||||
\(325\) | 6.22502 | 0.345302 | ||||||||
\(326\) | 47.2704 | 2.61807 | ||||||||
\(327\) | 2.10919 | 0.116639 | ||||||||
\(328\) | 118.283 | 6.53110 | ||||||||
\(329\) | 2.31847 | 0.127822 | ||||||||
\(330\) | 23.2925 | 1.28221 | ||||||||
\(331\) | −17.2043 | −0.945636 | −0.472818 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472818 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(332\) | −22.4549 | −1.23238 | ||||||||
\(333\) | 17.7543 | 0.972930 | ||||||||
\(334\) | 44.6976 | 2.44574 | ||||||||
\(335\) | 9.25694 | 0.505761 | ||||||||
\(336\) | −13.6900 | −0.746849 | ||||||||
\(337\) | −21.2747 | −1.15891 | −0.579453 | − | 0.815005i | \(-0.696734\pi\) | ||||
−0.579453 | + | 0.815005i | \(0.696734\pi\) | |||||||
\(338\) | −4.93151 | −0.268239 | ||||||||
\(339\) | 16.4894 | 0.895581 | ||||||||
\(340\) | −14.4403 | −0.783135 | ||||||||
\(341\) | −0.735355 | −0.0398217 | ||||||||
\(342\) | 145.711 | 7.87913 | ||||||||
\(343\) | 3.84176 | 0.207435 | ||||||||
\(344\) | −16.2530 | −0.876305 | ||||||||
\(345\) | 45.7513 | 2.46317 | ||||||||
\(346\) | 2.74729 | 0.147695 | ||||||||
\(347\) | −21.9439 | −1.17801 | −0.589004 | − | 0.808130i | \(-0.700480\pi\) | ||||
−0.589004 | + | 0.808130i | \(0.700480\pi\) | |||||||
\(348\) | 168.264 | 9.01991 | ||||||||
\(349\) | −9.63635 | −0.515822 | −0.257911 | − | 0.966169i | \(-0.583034\pi\) | ||||
−0.257911 | + | 0.966169i | \(0.583034\pi\) | |||||||
\(350\) | 1.23237 | 0.0658728 | ||||||||
\(351\) | 38.5637 | 2.05838 | ||||||||
\(352\) | −26.8908 | −1.43328 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 35.2447 | 1.87324 | ||||||||
\(355\) | 16.2961 | 0.864905 | ||||||||
\(356\) | 68.7159 | 3.64194 | ||||||||
\(357\) | −0.840974 | −0.0445090 | ||||||||
\(358\) | −10.3384 | −0.546401 | ||||||||
\(359\) | −29.5758 | −1.56095 | −0.780476 | − | 0.625185i | \(-0.785023\pi\) | ||||
−0.780476 | + | 0.625185i | \(0.785023\pi\) | |||||||
\(360\) | 161.318 | 8.50220 | ||||||||
\(361\) | 51.4865 | 2.70981 | ||||||||
\(362\) | −8.28768 | −0.435591 | ||||||||
\(363\) | −29.9952 | −1.57434 | ||||||||
\(364\) | −5.95526 | −0.312141 | ||||||||
\(365\) | −2.34149 | −0.122559 | ||||||||
\(366\) | −60.7113 | −3.17343 | ||||||||
\(367\) | −14.3792 | −0.750587 | −0.375293 | − | 0.926906i | \(-0.622458\pi\) | ||||
−0.375293 | + | 0.926906i | \(0.622458\pi\) | |||||||
\(368\) | −94.9776 | −4.95105 | ||||||||
\(369\) | −74.6377 | −3.88548 | ||||||||
\(370\) | 20.0357 | 1.04161 | ||||||||
\(371\) | 2.23338 | 0.115951 | ||||||||
\(372\) | −11.6857 | −0.605878 | ||||||||
\(373\) | 23.1709 | 1.19975 | 0.599873 | − | 0.800095i | \(-0.295218\pi\) | ||||
0.599873 | + | 0.800095i | \(0.295218\pi\) | |||||||
\(374\) | −2.97039 | −0.153595 | ||||||||
\(375\) | 26.5138 | 1.36917 | ||||||||
\(376\) | 83.7647 | 4.31984 | ||||||||
\(377\) | 37.8215 | 1.94790 | ||||||||
\(378\) | 7.63446 | 0.392674 | ||||||||
\(379\) | −34.6024 | −1.77741 | −0.888703 | − | 0.458484i | \(-0.848393\pi\) | ||||
−0.888703 | + | 0.458484i | \(0.848393\pi\) | |||||||
\(380\) | 121.235 | 6.21924 | ||||||||
\(381\) | 31.7869 | 1.62849 | ||||||||
\(382\) | 30.7160 | 1.57157 | ||||||||
\(383\) | −8.63991 | −0.441479 | −0.220739 | − | 0.975333i | \(-0.570847\pi\) | ||||
−0.220739 | + | 0.975333i | \(0.570847\pi\) | |||||||
\(384\) | −153.527 | −7.83465 | ||||||||
\(385\) | 0.764185 | 0.0389465 | ||||||||
\(386\) | −63.1987 | −3.21673 | ||||||||
\(387\) | 10.2558 | 0.521331 | ||||||||
\(388\) | 86.5797 | 4.39542 | ||||||||
\(389\) | −22.0077 | −1.11584 | −0.557918 | − | 0.829896i | \(-0.688399\pi\) | ||||
−0.557918 | + | 0.829896i | \(0.688399\pi\) | |||||||
\(390\) | 83.1997 | 4.21298 | ||||||||
\(391\) | −5.83447 | −0.295062 | ||||||||
\(392\) | 69.0205 | 3.48606 | ||||||||
\(393\) | −43.9451 | −2.21674 | ||||||||
\(394\) | −44.8655 | −2.26029 | ||||||||
\(395\) | 11.0306 | 0.555008 | ||||||||
\(396\) | 38.0092 | 1.91003 | ||||||||
\(397\) | −24.9452 | −1.25196 | −0.625981 | − | 0.779838i | \(-0.715301\pi\) | ||||
−0.625981 | + | 0.779838i | \(0.715301\pi\) | |||||||
\(398\) | 37.1582 | 1.86257 | ||||||||
\(399\) | 7.06050 | 0.353467 | ||||||||
\(400\) | 26.3521 | 1.31761 | ||||||||
\(401\) | 0.955194 | 0.0477001 | 0.0238500 | − | 0.999716i | \(-0.492408\pi\) | ||||
0.0238500 | + | 0.999716i | \(0.492408\pi\) | |||||||
\(402\) | 30.2597 | 1.50922 | ||||||||
\(403\) | −2.62665 | −0.130843 | ||||||||
\(404\) | −105.789 | −5.26318 | ||||||||
\(405\) | −30.0902 | −1.49519 | ||||||||
\(406\) | 7.48752 | 0.371599 | ||||||||
\(407\) | 3.03864 | 0.150620 | ||||||||
\(408\) | −30.3837 | −1.50422 | ||||||||
\(409\) | 11.0858 | 0.548156 | 0.274078 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274078 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(410\) | −84.2284 | −4.15975 | ||||||||
\(411\) | −5.71850 | −0.282073 | ||||||||
\(412\) | −63.3074 | −3.11893 | ||||||||
\(413\) | 1.15632 | 0.0568986 | ||||||||
\(414\) | 101.260 | 4.97668 | ||||||||
\(415\) | 10.2924 | 0.505233 | ||||||||
\(416\) | −96.0526 | −4.70937 | ||||||||
\(417\) | 43.9479 | 2.15214 | ||||||||
\(418\) | 24.9383 | 1.21977 | ||||||||
\(419\) | −34.0109 | −1.66154 | −0.830771 | − | 0.556615i | \(-0.812100\pi\) | ||||
−0.830771 | + | 0.556615i | \(0.812100\pi\) | |||||||
\(420\) | 12.1439 | 0.592562 | ||||||||
\(421\) | −28.5556 | −1.39172 | −0.695858 | − | 0.718179i | \(-0.744976\pi\) | ||||
−0.695858 | + | 0.718179i | \(0.744976\pi\) | |||||||
\(422\) | −21.2083 | −1.03240 | ||||||||
\(423\) | −52.8562 | −2.56996 | ||||||||
\(424\) | 80.6903 | 3.91867 | ||||||||
\(425\) | 1.61881 | 0.0785238 | ||||||||
\(426\) | 53.2696 | 2.58092 | ||||||||
\(427\) | −1.99183 | −0.0963915 | ||||||||
\(428\) | 22.8990 | 1.10687 | ||||||||
\(429\) | 12.6182 | 0.609211 | ||||||||
\(430\) | 11.5736 | 0.558131 | ||||||||
\(431\) | 0.135371 | 0.00652058 | 0.00326029 | − | 0.999995i | \(-0.498962\pi\) | ||||
0.00326029 | + | 0.999995i | \(0.498962\pi\) | |||||||
\(432\) | 163.250 | 7.85438 | ||||||||
\(433\) | 5.99029 | 0.287875 | 0.143938 | − | 0.989587i | \(-0.454024\pi\) | ||||
0.143938 | + | 0.989587i | \(0.454024\pi\) | |||||||
\(434\) | −0.519999 | −0.0249608 | ||||||||
\(435\) | −77.1251 | −3.69786 | ||||||||
\(436\) | 3.88410 | 0.186014 | ||||||||
\(437\) | 48.9840 | 2.34322 | ||||||||
\(438\) | −7.65401 | −0.365723 | ||||||||
\(439\) | −0.574794 | −0.0274334 | −0.0137167 | − | 0.999906i | \(-0.504366\pi\) | ||||
−0.0137167 | + | 0.999906i | \(0.504366\pi\) | |||||||
\(440\) | 27.6094 | 1.31623 | ||||||||
\(441\) | −43.5525 | −2.07393 | ||||||||
\(442\) | −10.6101 | −0.504671 | ||||||||
\(443\) | −29.1583 | −1.38535 | −0.692677 | − | 0.721248i | \(-0.743569\pi\) | ||||
−0.692677 | + | 0.721248i | \(0.743569\pi\) | |||||||
\(444\) | 48.2879 | 2.29164 | ||||||||
\(445\) | −31.4964 | −1.49307 | ||||||||
\(446\) | −31.3575 | −1.48482 | ||||||||
\(447\) | −21.6553 | −1.02426 | ||||||||
\(448\) | −10.0326 | −0.473995 | ||||||||
\(449\) | 16.7991 | 0.792798 | 0.396399 | − | 0.918078i | \(-0.370260\pi\) | ||||
0.396399 | + | 0.918078i | \(0.370260\pi\) | |||||||
\(450\) | −28.0953 | −1.32443 | ||||||||
\(451\) | −12.7742 | −0.601513 | ||||||||
\(452\) | 30.3654 | 1.42827 | ||||||||
\(453\) | 54.2372 | 2.54829 | ||||||||
\(454\) | −23.9741 | −1.12516 | ||||||||
\(455\) | 2.72964 | 0.127967 | ||||||||
\(456\) | 255.090 | 11.9457 | ||||||||
\(457\) | 41.7718 | 1.95400 | 0.977001 | − | 0.213235i | \(-0.0684001\pi\) | ||||
0.977001 | + | 0.213235i | \(0.0684001\pi\) | |||||||
\(458\) | 50.9161 | 2.37915 | ||||||||
\(459\) | 10.0284 | 0.468088 | ||||||||
\(460\) | 84.2514 | 3.92824 | ||||||||
\(461\) | −17.5482 | −0.817301 | −0.408650 | − | 0.912691i | \(-0.634000\pi\) | ||||
−0.408650 | + | 0.912691i | \(0.634000\pi\) | |||||||
\(462\) | 2.49802 | 0.116218 | ||||||||
\(463\) | 12.3575 | 0.574304 | 0.287152 | − | 0.957885i | \(-0.407292\pi\) | ||||
0.287152 | + | 0.957885i | \(0.407292\pi\) | |||||||
\(464\) | 160.108 | 7.43283 | ||||||||
\(465\) | 5.35624 | 0.248390 | ||||||||
\(466\) | −9.73987 | −0.451191 | ||||||||
\(467\) | −12.9361 | −0.598611 | −0.299306 | − | 0.954157i | \(-0.596755\pi\) | ||||
−0.299306 | + | 0.954157i | \(0.596755\pi\) | |||||||
\(468\) | 135.767 | 6.27584 | ||||||||
\(469\) | 0.992767 | 0.0458417 | ||||||||
\(470\) | −59.6481 | −2.75136 | ||||||||
\(471\) | −34.8881 | −1.60756 | ||||||||
\(472\) | 41.7769 | 1.92294 | ||||||||
\(473\) | 1.75527 | 0.0807075 | ||||||||
\(474\) | 36.0574 | 1.65617 | ||||||||
\(475\) | −13.5909 | −0.623594 | ||||||||
\(476\) | −1.54866 | −0.0709827 | ||||||||
\(477\) | −50.9162 | −2.33129 | ||||||||
\(478\) | 58.0877 | 2.65687 | ||||||||
\(479\) | 43.2299 | 1.97523 | 0.987613 | − | 0.156911i | \(-0.0501537\pi\) | ||||
0.987613 | + | 0.156911i | \(0.0501537\pi\) | |||||||
\(480\) | 195.869 | 8.94017 | ||||||||
\(481\) | 10.8539 | 0.494894 | ||||||||
\(482\) | −33.5990 | −1.53039 | ||||||||
\(483\) | 4.90663 | 0.223260 | ||||||||
\(484\) | −55.2365 | −2.51075 | ||||||||
\(485\) | −39.6844 | −1.80197 | ||||||||
\(486\) | −15.3510 | −0.696334 | ||||||||
\(487\) | 22.9353 | 1.03930 | 0.519649 | − | 0.854380i | \(-0.326063\pi\) | ||||
0.519649 | + | 0.854380i | \(0.326063\pi\) | |||||||
\(488\) | −71.9634 | −3.25763 | ||||||||
\(489\) | −52.2188 | −2.36142 | ||||||||
\(490\) | −49.1489 | −2.22032 | ||||||||
\(491\) | 36.5922 | 1.65138 | 0.825690 | − | 0.564123i | \(-0.190786\pi\) | ||||
0.825690 | + | 0.564123i | \(0.190786\pi\) | |||||||
\(492\) | −202.998 | −9.15188 | ||||||||
\(493\) | 9.83543 | 0.442965 | ||||||||
\(494\) | 89.0784 | 4.00783 | ||||||||
\(495\) | −17.4218 | −0.783051 | ||||||||
\(496\) | −11.1193 | −0.499272 | ||||||||
\(497\) | 1.74768 | 0.0783943 | ||||||||
\(498\) | 33.6444 | 1.50764 | ||||||||
\(499\) | −4.46293 | −0.199788 | −0.0998940 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998940 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(500\) | 48.8254 | 2.18354 | ||||||||
\(501\) | −49.3767 | −2.20599 | ||||||||
\(502\) | −83.0483 | −3.70663 | ||||||||
\(503\) | 30.0035 | 1.33779 | 0.668896 | − | 0.743356i | \(-0.266767\pi\) | ||||
0.668896 | + | 0.743356i | \(0.266767\pi\) | |||||||
\(504\) | 17.3007 | 0.770633 | ||||||||
\(505\) | 48.4889 | 2.15773 | ||||||||
\(506\) | 17.3306 | 0.770441 | ||||||||
\(507\) | 5.44775 | 0.241943 | ||||||||
\(508\) | 58.5358 | 2.59711 | ||||||||
\(509\) | −7.43252 | −0.329440 | −0.164720 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164720 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(510\) | 21.6360 | 0.958058 | ||||||||
\(511\) | −0.251114 | −0.0111087 | ||||||||
\(512\) | −82.0680 | −3.62693 | ||||||||
\(513\) | −84.1950 | −3.71730 | ||||||||
\(514\) | −15.6790 | −0.691572 | ||||||||
\(515\) | 29.0174 | 1.27866 | ||||||||
\(516\) | 27.8936 | 1.22795 | ||||||||
\(517\) | −9.04630 | −0.397856 | ||||||||
\(518\) | 2.14874 | 0.0944103 | ||||||||
\(519\) | −3.03488 | −0.133217 | ||||||||
\(520\) | 98.6197 | 4.32476 | ||||||||
\(521\) | 35.6418 | 1.56150 | 0.780749 | − | 0.624845i | \(-0.214838\pi\) | ||||
0.780749 | + | 0.624845i | \(0.214838\pi\) | |||||||
\(522\) | −170.699 | −7.47131 | ||||||||
\(523\) | −27.8357 | −1.21717 | −0.608584 | − | 0.793489i | \(-0.708262\pi\) | ||||
−0.608584 | + | 0.793489i | \(0.708262\pi\) | |||||||
\(524\) | −80.9254 | −3.53524 | ||||||||
\(525\) | −1.36138 | −0.0594153 | ||||||||
\(526\) | 86.7866 | 3.78407 | ||||||||
\(527\) | −0.683059 | −0.0297545 | ||||||||
\(528\) | 53.4160 | 2.32463 | ||||||||
\(529\) | 11.0410 | 0.480044 | ||||||||
\(530\) | −57.4589 | −2.49585 | ||||||||
\(531\) | −26.3615 | −1.14399 | ||||||||
\(532\) | 13.0020 | 0.563707 | ||||||||
\(533\) | −45.6288 | −1.97640 | ||||||||
\(534\) | −102.958 | −4.45541 | ||||||||
\(535\) | −10.4959 | −0.453779 | ||||||||
\(536\) | 35.8679 | 1.54926 | ||||||||
\(537\) | 11.4206 | 0.492837 | ||||||||
\(538\) | 0.00847150 | 0.000365232 0 | ||||||||
\(539\) | −7.45397 | −0.321065 | ||||||||
\(540\) | −144.814 | −6.23179 | ||||||||
\(541\) | −11.7582 | −0.505526 | −0.252763 | − | 0.967528i | \(-0.581339\pi\) | ||||
−0.252763 | + | 0.967528i | \(0.581339\pi\) | |||||||
\(542\) | 59.3513 | 2.54936 | ||||||||
\(543\) | 9.15526 | 0.392890 | ||||||||
\(544\) | −24.9784 | −1.07094 | ||||||||
\(545\) | −1.78030 | −0.0762598 | ||||||||
\(546\) | 8.92282 | 0.381861 | ||||||||
\(547\) | 7.34831 | 0.314191 | 0.157095 | − | 0.987583i | \(-0.449787\pi\) | ||||
0.157095 | + | 0.987583i | \(0.449787\pi\) | |||||||
\(548\) | −10.5307 | −0.449848 | ||||||||
\(549\) | 45.4095 | 1.93803 | ||||||||
\(550\) | −4.80850 | −0.205035 | ||||||||
\(551\) | −82.5745 | −3.51779 | ||||||||
\(552\) | 177.273 | 7.54524 | ||||||||
\(553\) | 1.18298 | 0.0503055 | ||||||||
\(554\) | 6.91319 | 0.293713 | ||||||||
\(555\) | −22.1331 | −0.939497 | ||||||||
\(556\) | 80.9305 | 3.43222 | ||||||||
\(557\) | 20.6326 | 0.874233 | 0.437116 | − | 0.899405i | \(-0.356000\pi\) | ||||
0.437116 | + | 0.899405i | \(0.356000\pi\) | |||||||
\(558\) | 11.8549 | 0.501856 | ||||||||
\(559\) | 6.26975 | 0.265182 | ||||||||
\(560\) | 11.5553 | 0.488299 | ||||||||
\(561\) | 3.28134 | 0.138538 | ||||||||
\(562\) | −11.5066 | −0.485376 | ||||||||
\(563\) | −8.99049 | −0.378904 | −0.189452 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189452 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(564\) | −143.758 | −6.05329 | ||||||||
\(565\) | −13.9182 | −0.585542 | ||||||||
\(566\) | 38.3628 | 1.61251 | ||||||||
\(567\) | −3.22705 | −0.135523 | ||||||||
\(568\) | 63.1425 | 2.64940 | ||||||||
\(569\) | 41.9354 | 1.75802 | 0.879011 | − | 0.476801i | \(-0.158204\pi\) | ||||
0.879011 | + | 0.476801i | \(0.158204\pi\) | |||||||
\(570\) | −181.648 | −7.60838 | ||||||||
\(571\) | 12.9947 | 0.543809 | 0.271905 | − | 0.962324i | \(-0.412346\pi\) | ||||
0.271905 | + | 0.962324i | \(0.412346\pi\) | |||||||
\(572\) | 23.2365 | 0.971565 | ||||||||
\(573\) | −33.9315 | −1.41751 | ||||||||
\(574\) | −9.03314 | −0.377036 | ||||||||
\(575\) | −9.44489 | −0.393879 | ||||||||
\(576\) | 228.721 | 9.53005 | ||||||||
\(577\) | −22.0443 | −0.917715 | −0.458858 | − | 0.888510i | \(-0.651741\pi\) | ||||
−0.458858 | + | 0.888510i | \(0.651741\pi\) | |||||||
\(578\) | −2.75915 | −0.114765 | ||||||||
\(579\) | 69.8145 | 2.90139 | ||||||||
\(580\) | −142.027 | −5.89733 | ||||||||
\(581\) | 1.10381 | 0.0457939 | ||||||||
\(582\) | −129.723 | −5.37719 | ||||||||
\(583\) | −8.71427 | −0.360908 | ||||||||
\(584\) | −9.07258 | −0.375426 | ||||||||
\(585\) | −62.2298 | −2.57289 | ||||||||
\(586\) | −63.3861 | −2.61845 | ||||||||
\(587\) | 14.1701 | 0.584864 | 0.292432 | − | 0.956286i | \(-0.405536\pi\) | ||||
0.292432 | + | 0.956286i | \(0.405536\pi\) | |||||||
\(588\) | −118.453 | −4.88494 | ||||||||
\(589\) | 5.73470 | 0.236294 | ||||||||
\(590\) | −29.7489 | −1.22474 | ||||||||
\(591\) | 49.5622 | 2.03872 | ||||||||
\(592\) | 45.9473 | 1.88842 | ||||||||
\(593\) | 9.68032 | 0.397523 | 0.198762 | − | 0.980048i | \(-0.436308\pi\) | ||||
0.198762 | + | 0.980048i | \(0.436308\pi\) | |||||||
\(594\) | −29.7884 | −1.22223 | ||||||||
\(595\) | 0.709839 | 0.0291006 | ||||||||
\(596\) | −39.8785 | −1.63349 | ||||||||
\(597\) | −41.0480 | −1.67998 | ||||||||
\(598\) | 61.9043 | 2.53145 | ||||||||
\(599\) | −17.4311 | −0.712215 | −0.356108 | − | 0.934445i | \(-0.615896\pi\) | ||||
−0.356108 | + | 0.934445i | \(0.615896\pi\) | |||||||
\(600\) | −49.1855 | −2.00799 | ||||||||
\(601\) | −23.6705 | −0.965541 | −0.482770 | − | 0.875747i | \(-0.660369\pi\) | ||||
−0.482770 | + | 0.875747i | \(0.660369\pi\) | |||||||
\(602\) | 1.24122 | 0.0505885 | ||||||||
\(603\) | −22.6330 | −0.921686 | ||||||||
\(604\) | 99.8783 | 4.06399 | ||||||||
\(605\) | 25.3180 | 1.02932 | ||||||||
\(606\) | 158.504 | 6.43877 | ||||||||
\(607\) | 20.4428 | 0.829749 | 0.414874 | − | 0.909879i | \(-0.363825\pi\) | ||||
0.414874 | + | 0.909879i | \(0.363825\pi\) | |||||||
\(608\) | 209.709 | 8.50482 | ||||||||
\(609\) | −8.27134 | −0.335171 | ||||||||
\(610\) | 51.2445 | 2.07483 | ||||||||
\(611\) | −32.3130 | −1.30724 | ||||||||
\(612\) | 35.3061 | 1.42717 | ||||||||
\(613\) | 22.6785 | 0.915974 | 0.457987 | − | 0.888959i | \(-0.348571\pi\) | ||||
0.457987 | + | 0.888959i | \(0.348571\pi\) | |||||||
\(614\) | 20.1905 | 0.814822 | ||||||||
\(615\) | 93.0457 | 3.75197 | ||||||||
\(616\) | 2.96099 | 0.119302 | ||||||||
\(617\) | 5.39690 | 0.217271 | 0.108636 | − | 0.994082i | \(-0.465352\pi\) | ||||
0.108636 | + | 0.994082i | \(0.465352\pi\) | |||||||
\(618\) | 94.8539 | 3.81558 | ||||||||
\(619\) | −15.7245 | −0.632020 | −0.316010 | − | 0.948756i | \(-0.602343\pi\) | ||||
−0.316010 | + | 0.948756i | \(0.602343\pi\) | |||||||
\(620\) | 9.86357 | 0.396130 | ||||||||
\(621\) | −58.5106 | −2.34795 | ||||||||
\(622\) | 2.89324 | 0.116008 | ||||||||
\(623\) | −3.37786 | −0.135331 | ||||||||
\(624\) | 190.800 | 7.63809 | ||||||||
\(625\) | −30.4735 | −1.21894 | ||||||||
\(626\) | 25.4464 | 1.01704 | ||||||||
\(627\) | −27.5489 | −1.10020 | ||||||||
\(628\) | −64.2468 | −2.56373 | ||||||||
\(629\) | 2.82254 | 0.112542 | ||||||||
\(630\) | −12.3197 | −0.490827 | ||||||||
\(631\) | −46.7243 | −1.86006 | −0.930032 | − | 0.367478i | \(-0.880221\pi\) | ||||
−0.930032 | + | 0.367478i | \(0.880221\pi\) | |||||||
\(632\) | 42.7402 | 1.70011 | ||||||||
\(633\) | 23.4284 | 0.931197 | ||||||||
\(634\) | −6.71152 | −0.266549 | ||||||||
\(635\) | −26.8303 | −1.06473 | ||||||||
\(636\) | −138.481 | −5.49114 | ||||||||
\(637\) | −26.6253 | −1.05493 | ||||||||
\(638\) | −29.2151 | −1.15664 | ||||||||
\(639\) | −39.8434 | −1.57618 | ||||||||
\(640\) | 129.587 | 5.12239 | ||||||||
\(641\) | 11.0495 | 0.436427 | 0.218214 | − | 0.975901i | \(-0.429977\pi\) | ||||
0.218214 | + | 0.975901i | \(0.429977\pi\) | |||||||
\(642\) | −34.3098 | −1.35410 | ||||||||
\(643\) | −5.23720 | −0.206535 | −0.103268 | − | 0.994654i | \(-0.532930\pi\) | ||||
−0.103268 | + | 0.994654i | \(0.532930\pi\) | |||||||
\(644\) | 9.03561 | 0.356053 | ||||||||
\(645\) | −12.7852 | −0.503417 | ||||||||
\(646\) | 23.1647 | 0.911405 | ||||||||
\(647\) | −20.0952 | −0.790023 | −0.395012 | − | 0.918676i | \(-0.629259\pi\) | ||||
−0.395012 | + | 0.918676i | \(0.629259\pi\) | |||||||
\(648\) | −116.591 | −4.58011 | ||||||||
\(649\) | −4.51176 | −0.177102 | ||||||||
\(650\) | −17.1757 | −0.673688 | ||||||||
\(651\) | 0.574434 | 0.0225139 | ||||||||
\(652\) | −96.1614 | −3.76597 | ||||||||
\(653\) | −20.7919 | −0.813651 | −0.406826 | − | 0.913506i | \(-0.633364\pi\) | ||||
−0.406826 | + | 0.913506i | \(0.633364\pi\) | |||||||
\(654\) | −5.81957 | −0.227563 | ||||||||
\(655\) | 37.0927 | 1.44933 | ||||||||
\(656\) | −193.159 | −7.54158 | ||||||||
\(657\) | 5.72487 | 0.223348 | ||||||||
\(658\) | −6.39701 | −0.249381 | ||||||||
\(659\) | −29.4240 | −1.14620 | −0.573099 | − | 0.819486i | \(-0.694259\pi\) | ||||
−0.573099 | + | 0.819486i | \(0.694259\pi\) | |||||||
\(660\) | −47.3835 | −1.84440 | ||||||||
\(661\) | 4.41961 | 0.171903 | 0.0859515 | − | 0.996299i | \(-0.472607\pi\) | ||||
0.0859515 | + | 0.996299i | \(0.472607\pi\) | |||||||
\(662\) | 47.4693 | 1.84495 | ||||||||
\(663\) | 11.7208 | 0.455198 | ||||||||
\(664\) | 39.8800 | 1.54764 | ||||||||
\(665\) | −5.95954 | −0.231101 | ||||||||
\(666\) | −48.9867 | −1.89820 | ||||||||
\(667\) | −57.3845 | −2.22194 | ||||||||
\(668\) | −90.9276 | −3.51810 | ||||||||
\(669\) | 34.6400 | 1.33926 | ||||||||
\(670\) | −25.5412 | −0.986744 | ||||||||
\(671\) | 7.77180 | 0.300027 | ||||||||
\(672\) | 21.0062 | 0.810330 | ||||||||
\(673\) | −14.9365 | −0.575761 | −0.287881 | − | 0.957666i | \(-0.592951\pi\) | ||||
−0.287881 | + | 0.957666i | \(0.592951\pi\) | |||||||
\(674\) | 58.7000 | 2.26104 | ||||||||
\(675\) | 16.2341 | 0.624852 | ||||||||
\(676\) | 10.0321 | 0.385849 | ||||||||
\(677\) | 15.6079 | 0.599859 | 0.299929 | − | 0.953961i | \(-0.403037\pi\) | ||||
0.299929 | + | 0.953961i | \(0.403037\pi\) | |||||||
\(678\) | −45.4966 | −1.74729 | ||||||||
\(679\) | −4.25598 | −0.163330 | ||||||||
\(680\) | 25.6459 | 0.983477 | ||||||||
\(681\) | 26.4838 | 1.01486 | ||||||||
\(682\) | 2.02895 | 0.0776925 | ||||||||
\(683\) | 33.0327 | 1.26396 | 0.631981 | − | 0.774984i | \(-0.282242\pi\) | ||||
0.631981 | + | 0.774984i | \(0.282242\pi\) | |||||||
\(684\) | −296.417 | −11.3338 | ||||||||
\(685\) | 4.82680 | 0.184423 | ||||||||
\(686\) | −10.6000 | −0.404709 | ||||||||
\(687\) | −56.2462 | −2.14593 | ||||||||
\(688\) | 26.5415 | 1.01189 | ||||||||
\(689\) | −31.1270 | −1.18584 | ||||||||
\(690\) | −126.235 | −4.80567 | ||||||||
\(691\) | 51.6960 | 1.96661 | 0.983303 | − | 0.181973i | \(-0.0582485\pi\) | ||||
0.983303 | + | 0.181973i | \(0.0582485\pi\) | |||||||
\(692\) | −5.58876 | −0.212453 | ||||||||
\(693\) | −1.86841 | −0.0709751 | ||||||||
\(694\) | 60.5463 | 2.29831 | ||||||||
\(695\) | −37.0951 | −1.40710 | ||||||||
\(696\) | −298.837 | −11.3274 | ||||||||
\(697\) | −11.8657 | −0.449446 | ||||||||
\(698\) | 26.5881 | 1.00637 | ||||||||
\(699\) | 10.7595 | 0.406960 | ||||||||
\(700\) | −2.50699 | −0.0947552 | ||||||||
\(701\) | −27.8846 | −1.05319 | −0.526593 | − | 0.850118i | \(-0.676531\pi\) | ||||
−0.526593 | + | 0.850118i | \(0.676531\pi\) | |||||||
\(702\) | −106.403 | −4.01592 | ||||||||
\(703\) | −23.6970 | −0.893748 | ||||||||
\(704\) | 39.1455 | 1.47535 | ||||||||
\(705\) | 65.8923 | 2.48165 | ||||||||
\(706\) | −2.75915 | −0.103842 | ||||||||
\(707\) | 5.20023 | 0.195575 | ||||||||
\(708\) | −71.6977 | −2.69457 | ||||||||
\(709\) | −8.96482 | −0.336681 | −0.168340 | − | 0.985729i | \(-0.553841\pi\) | ||||
−0.168340 | + | 0.985729i | \(0.553841\pi\) | |||||||
\(710\) | −44.9632 | −1.68744 | ||||||||
\(711\) | −26.9694 | −1.01143 | ||||||||
\(712\) | −122.039 | −4.57362 | ||||||||
\(713\) | 3.98528 | 0.149250 | ||||||||
\(714\) | 2.32037 | 0.0868376 | ||||||||
\(715\) | −10.6506 | −0.398309 | ||||||||
\(716\) | 21.0312 | 0.785973 | ||||||||
\(717\) | −64.1685 | −2.39642 | ||||||||
\(718\) | 81.6040 | 3.04544 | ||||||||
\(719\) | −3.85541 | −0.143783 | −0.0718913 | − | 0.997412i | \(-0.522903\pi\) | ||||
−0.0718913 | + | 0.997412i | \(0.522903\pi\) | |||||||
\(720\) | −263.435 | −9.81765 | ||||||||
\(721\) | 3.11199 | 0.115897 | ||||||||
\(722\) | −142.059 | −5.28687 | ||||||||
\(723\) | 37.1163 | 1.38037 | ||||||||
\(724\) | 16.8595 | 0.626578 | ||||||||
\(725\) | 15.9217 | 0.591316 | ||||||||
\(726\) | 82.7612 | 3.07156 | ||||||||
\(727\) | 45.7272 | 1.69593 | 0.847965 | − | 0.530052i | \(-0.177828\pi\) | ||||
0.847965 | + | 0.530052i | \(0.177828\pi\) | |||||||
\(728\) | 10.5765 | 0.391993 | ||||||||
\(729\) | −18.1298 | −0.671476 | ||||||||
\(730\) | 6.46050 | 0.239114 | ||||||||
\(731\) | 1.63044 | 0.0603041 | ||||||||
\(732\) | 123.504 | 4.56484 | ||||||||
\(733\) | −3.02099 | −0.111583 | −0.0557915 | − | 0.998442i | \(-0.517768\pi\) | ||||
−0.0557915 | + | 0.998442i | \(0.517768\pi\) | |||||||
\(734\) | 39.6742 | 1.46440 | ||||||||
\(735\) | 54.2939 | 2.00266 | ||||||||
\(736\) | 145.736 | 5.37188 | ||||||||
\(737\) | −3.87361 | −0.142686 | ||||||||
\(738\) | 205.936 | 7.58062 | ||||||||
\(739\) | 11.0182 | 0.405310 | 0.202655 | − | 0.979250i | \(-0.435043\pi\) | ||||
0.202655 | + | 0.979250i | \(0.435043\pi\) | |||||||
\(740\) | −40.7583 | −1.49830 | ||||||||
\(741\) | −98.4034 | −3.61494 | ||||||||
\(742\) | −6.16222 | −0.226222 | ||||||||
\(743\) | 11.5163 | 0.422491 | 0.211246 | − | 0.977433i | \(-0.432248\pi\) | ||||
0.211246 | + | 0.977433i | \(0.432248\pi\) | |||||||
\(744\) | 20.7539 | 0.760874 | ||||||||
\(745\) | 18.2786 | 0.669675 | ||||||||
\(746\) | −63.9320 | −2.34072 | ||||||||
\(747\) | −25.1646 | −0.920724 | ||||||||
\(748\) | 6.04262 | 0.220940 | ||||||||
\(749\) | −1.12564 | −0.0411301 | ||||||||
\(750\) | −73.1554 | −2.67126 | ||||||||
\(751\) | −47.3238 | −1.72687 | −0.863435 | − | 0.504459i | \(-0.831692\pi\) | ||||
−0.863435 | + | 0.504459i | \(0.831692\pi\) | |||||||
\(752\) | −136.789 | −4.98820 | ||||||||
\(753\) | 91.7421 | 3.34327 | ||||||||
\(754\) | −104.355 | −3.80038 | ||||||||
\(755\) | −45.7799 | −1.66610 | ||||||||
\(756\) | −15.5307 | −0.564844 | ||||||||
\(757\) | −16.4081 | −0.596363 | −0.298181 | − | 0.954509i | \(-0.596380\pi\) | ||||
−0.298181 | + | 0.954509i | \(0.596380\pi\) | |||||||
\(758\) | 95.4730 | 3.46774 | ||||||||
\(759\) | −19.1449 | −0.694915 | ||||||||
\(760\) | −215.314 | −7.81025 | ||||||||
\(761\) | 41.4233 | 1.50159 | 0.750797 | − | 0.660533i | \(-0.229670\pi\) | ||||
0.750797 | + | 0.660533i | \(0.229670\pi\) | |||||||
\(762\) | −87.7046 | −3.17720 | ||||||||
\(763\) | −0.190930 | −0.00691213 | ||||||||
\(764\) | −62.4851 | −2.26063 | ||||||||
\(765\) | −16.1828 | −0.585091 | ||||||||
\(766\) | 23.8388 | 0.861330 | ||||||||
\(767\) | −16.1158 | −0.581908 | ||||||||
\(768\) | 201.945 | 7.28707 | ||||||||
\(769\) | −14.4630 | −0.521548 | −0.260774 | − | 0.965400i | \(-0.583978\pi\) | ||||
−0.260774 | + | 0.965400i | \(0.583978\pi\) | |||||||
\(770\) | −2.10850 | −0.0759850 | ||||||||
\(771\) | 17.3204 | 0.623777 | ||||||||
\(772\) | 128.564 | 4.62712 | ||||||||
\(773\) | −40.7096 | −1.46422 | −0.732110 | − | 0.681186i | \(-0.761465\pi\) | ||||
−0.732110 | + | 0.681186i | \(0.761465\pi\) | |||||||
\(774\) | −28.2972 | −1.01712 | ||||||||
\(775\) | −1.10574 | −0.0397194 | ||||||||
\(776\) | −153.765 | −5.51985 | ||||||||
\(777\) | −2.37368 | −0.0851553 | ||||||||
\(778\) | 60.7225 | 2.17701 | ||||||||
\(779\) | 99.6201 | 3.56926 | ||||||||
\(780\) | −169.252 | −6.06019 | ||||||||
\(781\) | −6.81917 | −0.244009 | ||||||||
\(782\) | 16.0981 | 0.575668 | ||||||||
\(783\) | 98.6340 | 3.52489 | ||||||||
\(784\) | −112.712 | −4.02542 | ||||||||
\(785\) | 29.4480 | 1.05104 | ||||||||
\(786\) | 121.251 | 4.32488 | ||||||||
\(787\) | −4.48905 | −0.160017 | −0.0800087 | − | 0.996794i | \(-0.525495\pi\) | ||||
−0.0800087 | + | 0.996794i | \(0.525495\pi\) | |||||||
\(788\) | 91.2692 | 3.25133 | ||||||||
\(789\) | −95.8716 | −3.41312 | ||||||||
\(790\) | −30.4349 | −1.08283 | ||||||||
\(791\) | −1.49266 | −0.0530731 | ||||||||
\(792\) | −67.5043 | −2.39866 | ||||||||
\(793\) | 27.7605 | 0.985805 | ||||||||
\(794\) | 68.8274 | 2.44259 | ||||||||
\(795\) | 63.4738 | 2.25118 | ||||||||
\(796\) | −75.5904 | −2.67923 | ||||||||
\(797\) | 16.3443 | 0.578943 | 0.289472 | − | 0.957187i | \(-0.406520\pi\) | ||||
0.289472 | + | 0.957187i | \(0.406520\pi\) | |||||||
\(798\) | −19.4809 | −0.689618 | ||||||||
\(799\) | −8.40296 | −0.297275 | ||||||||
\(800\) | −40.4352 | −1.42960 | ||||||||
\(801\) | 77.0078 | 2.72094 | ||||||||
\(802\) | −2.63552 | −0.0930634 | ||||||||
\(803\) | 0.979807 | 0.0345766 | ||||||||
\(804\) | −61.5568 | −2.17094 | ||||||||
\(805\) | −4.14153 | −0.145970 | ||||||||
\(806\) | 7.24732 | 0.255276 | ||||||||
\(807\) | −0.00935832 | −0.000329429 0 | ||||||||
\(808\) | 187.880 | 6.60961 | ||||||||
\(809\) | 12.4977 | 0.439397 | 0.219698 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219698 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(810\) | 83.0232 | 2.91714 | ||||||||
\(811\) | −16.3057 | −0.572570 | −0.286285 | − | 0.958144i | \(-0.592420\pi\) | ||||
−0.286285 | + | 0.958144i | \(0.592420\pi\) | |||||||
\(812\) | −15.2317 | −0.534529 | ||||||||
\(813\) | −65.5643 | −2.29944 | ||||||||
\(814\) | −8.38404 | −0.293860 | ||||||||
\(815\) | 44.0762 | 1.54392 | ||||||||
\(816\) | 49.6172 | 1.73695 | ||||||||
\(817\) | −13.6886 | −0.478903 | ||||||||
\(818\) | −30.5873 | −1.06946 | ||||||||
\(819\) | −6.67389 | −0.233204 | ||||||||
\(820\) | 171.345 | 5.98361 | ||||||||
\(821\) | 15.4545 | 0.539366 | 0.269683 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269683 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(822\) | 15.7782 | 0.550327 | ||||||||
\(823\) | −29.9671 | −1.04459 | −0.522294 | − | 0.852766i | \(-0.674923\pi\) | ||||
−0.522294 | + | 0.852766i | \(0.674923\pi\) | |||||||
\(824\) | 112.434 | 3.91682 | ||||||||
\(825\) | 5.31186 | 0.184935 | ||||||||
\(826\) | −3.19045 | −0.111010 | ||||||||
\(827\) | 53.3751 | 1.85604 | 0.928018 | − | 0.372536i | \(-0.121512\pi\) | ||||
0.928018 | + | 0.372536i | \(0.121512\pi\) | |||||||
\(828\) | −205.992 | −7.15873 | ||||||||
\(829\) | −50.5535 | −1.75580 | −0.877898 | − | 0.478847i | \(-0.841055\pi\) | ||||
−0.877898 | + | 0.478847i | \(0.841055\pi\) | |||||||
\(830\) | −28.3982 | −0.985715 | ||||||||
\(831\) | −7.63689 | −0.264921 | ||||||||
\(832\) | 139.826 | 4.84759 | ||||||||
\(833\) | −6.92387 | −0.239898 | ||||||||
\(834\) | −121.259 | −4.19885 | ||||||||
\(835\) | 41.6773 | 1.44230 | ||||||||
\(836\) | −50.7315 | −1.75459 | ||||||||
\(837\) | −6.85002 | −0.236771 | ||||||||
\(838\) | 93.8410 | 3.24168 | ||||||||
\(839\) | 24.6800 | 0.852049 | 0.426024 | − | 0.904712i | \(-0.359914\pi\) | ||||
0.426024 | + | 0.904712i | \(0.359914\pi\) | |||||||
\(840\) | −21.5676 | −0.744152 | ||||||||
\(841\) | 67.7357 | 2.33571 | ||||||||
\(842\) | 78.7892 | 2.71525 | ||||||||
\(843\) | 12.7111 | 0.437795 | ||||||||
\(844\) | 43.1437 | 1.48507 | ||||||||
\(845\) | −4.59827 | −0.158185 | ||||||||
\(846\) | 145.838 | 5.01402 | ||||||||
\(847\) | 2.71525 | 0.0932971 | ||||||||
\(848\) | −131.769 | −4.52496 | ||||||||
\(849\) | −42.3788 | −1.45444 | ||||||||
\(850\) | −4.46653 | −0.153201 | ||||||||
\(851\) | −16.4680 | −0.564516 | ||||||||
\(852\) | −108.366 | −3.71254 | ||||||||
\(853\) | 2.12450 | 0.0727414 | 0.0363707 | − | 0.999338i | \(-0.488420\pi\) | ||||
0.0363707 | + | 0.999338i | \(0.488420\pi\) | |||||||
\(854\) | 5.49576 | 0.188061 | ||||||||
\(855\) | 135.865 | 4.64647 | ||||||||
\(856\) | −40.6687 | −1.39003 | ||||||||
\(857\) | −5.50448 | −0.188029 | −0.0940147 | − | 0.995571i | \(-0.529970\pi\) | ||||
−0.0940147 | + | 0.995571i | \(0.529970\pi\) | |||||||
\(858\) | −34.8153 | −1.18858 | ||||||||
\(859\) | −22.9299 | −0.782359 | −0.391179 | − | 0.920314i | \(-0.627933\pi\) | ||||
−0.391179 | + | 0.920314i | \(0.627933\pi\) | |||||||
\(860\) | −23.5441 | −0.802846 | ||||||||
\(861\) | 9.97876 | 0.340075 | ||||||||
\(862\) | −0.373507 | −0.0127217 | ||||||||
\(863\) | 53.4583 | 1.81974 | 0.909871 | − | 0.414892i | \(-0.136180\pi\) | ||||
0.909871 | + | 0.414892i | \(0.136180\pi\) | |||||||
\(864\) | −250.494 | −8.52199 | ||||||||
\(865\) | 2.56165 | 0.0870986 | ||||||||
\(866\) | −16.5281 | −0.561647 | ||||||||
\(867\) | 3.04798 | 0.103515 | ||||||||
\(868\) | 1.05783 | 0.0359050 | ||||||||
\(869\) | −4.61580 | −0.156580 | ||||||||
\(870\) | 212.799 | 7.21457 | ||||||||
\(871\) | −13.8364 | −0.468828 | ||||||||
\(872\) | −6.89815 | −0.233601 | ||||||||
\(873\) | 97.0272 | 3.28387 | ||||||||
\(874\) | −135.154 | −4.57165 | ||||||||
\(875\) | −2.40010 | −0.0811382 | ||||||||
\(876\) | 15.5704 | 0.526076 | ||||||||
\(877\) | −55.6896 | −1.88050 | −0.940252 | − | 0.340478i | \(-0.889411\pi\) | ||||
−0.940252 | + | 0.340478i | \(0.889411\pi\) | |||||||
\(878\) | 1.58594 | 0.0535229 | ||||||||
\(879\) | 70.0215 | 2.36177 | ||||||||
\(880\) | −45.0867 | −1.51987 | ||||||||
\(881\) | 26.8525 | 0.904683 | 0.452342 | − | 0.891845i | \(-0.350589\pi\) | ||||
0.452342 | + | 0.891845i | \(0.350589\pi\) | |||||||
\(882\) | 120.168 | 4.04626 | ||||||||
\(883\) | 9.07472 | 0.305389 | 0.152694 | − | 0.988273i | \(-0.451205\pi\) | ||||
0.152694 | + | 0.988273i | \(0.451205\pi\) | |||||||
\(884\) | 21.5840 | 0.725947 | ||||||||
\(885\) | 32.8631 | 1.10468 | ||||||||
\(886\) | 80.4521 | 2.70284 | ||||||||
\(887\) | −40.0843 | −1.34590 | −0.672950 | − | 0.739688i | \(-0.734973\pi\) | ||||
−0.672950 | + | 0.739688i | \(0.734973\pi\) | |||||||
\(888\) | −85.7593 | −2.87789 | ||||||||
\(889\) | −2.87743 | −0.0965061 | ||||||||
\(890\) | 86.9032 | 2.91300 | ||||||||
\(891\) | 12.5914 | 0.421828 | ||||||||
\(892\) | 63.7900 | 2.13585 | ||||||||
\(893\) | 70.5481 | 2.36080 | ||||||||
\(894\) | 59.7502 | 1.99834 | ||||||||
\(895\) | −9.63980 | −0.322223 | ||||||||
\(896\) | 13.8977 | 0.464290 | ||||||||
\(897\) | −68.3846 | −2.28330 | ||||||||
\(898\) | −46.3511 | −1.54676 | ||||||||
\(899\) | −6.71817 | −0.224064 | ||||||||
\(900\) | 57.1539 | 1.90513 | ||||||||
\(901\) | −8.09454 | −0.269668 | ||||||||
\(902\) | 35.2458 | 1.17356 | ||||||||
\(903\) | −1.37116 | −0.0456293 | ||||||||
\(904\) | −53.9288 | −1.79365 | ||||||||
\(905\) | −7.72767 | −0.256876 | ||||||||
\(906\) | −149.648 | −4.97173 | ||||||||
\(907\) | −13.5350 | −0.449421 | −0.224710 | − | 0.974426i | \(-0.572144\pi\) | ||||
−0.224710 | + | 0.974426i | \(0.572144\pi\) | |||||||
\(908\) | 48.7701 | 1.61849 | ||||||||
\(909\) | −118.554 | −3.93219 | ||||||||
\(910\) | −7.53147 | −0.249666 | ||||||||
\(911\) | −8.64866 | −0.286543 | −0.143271 | − | 0.989683i | \(-0.545762\pi\) | ||||
−0.143271 | + | 0.989683i | \(0.545762\pi\) | |||||||
\(912\) | −416.567 | −13.7939 | ||||||||
\(913\) | −4.30690 | −0.142538 | ||||||||
\(914\) | −115.254 | −3.81228 | ||||||||
\(915\) | −56.6089 | −1.87143 | ||||||||
\(916\) | −103.578 | −3.42231 | ||||||||
\(917\) | 3.97803 | 0.131366 | ||||||||
\(918\) | −27.6699 | −0.913244 | ||||||||
\(919\) | −46.7285 | −1.54143 | −0.770716 | − | 0.637179i | \(-0.780101\pi\) | ||||
−0.770716 | + | 0.637179i | \(0.780101\pi\) | |||||||
\(920\) | −149.630 | −4.93317 | ||||||||
\(921\) | −22.3041 | −0.734945 | ||||||||
\(922\) | 48.4180 | 1.59456 | ||||||||
\(923\) | −24.3578 | −0.801746 | ||||||||
\(924\) | −5.08168 | −0.167175 | ||||||||
\(925\) | 4.56915 | 0.150233 | ||||||||
\(926\) | −34.0963 | −1.12047 | ||||||||
\(927\) | −70.9467 | −2.33019 | ||||||||
\(928\) | −245.673 | −8.06461 | ||||||||
\(929\) | 1.55668 | 0.0510731 | 0.0255365 | − | 0.999674i | \(-0.491871\pi\) | ||||
0.0255365 | + | 0.999674i | \(0.491871\pi\) | |||||||
\(930\) | −14.7787 | −0.484611 | ||||||||
\(931\) | 58.1302 | 1.90514 | ||||||||
\(932\) | 19.8137 | 0.649018 | ||||||||
\(933\) | −3.19611 | −0.104636 | ||||||||
\(934\) | 35.6926 | 1.16790 | ||||||||
\(935\) | −2.76967 | −0.0905780 | ||||||||
\(936\) | −241.122 | −7.88133 | ||||||||
\(937\) | −56.0835 | −1.83217 | −0.916084 | − | 0.400987i | \(-0.868667\pi\) | ||||
−0.916084 | + | 0.400987i | \(0.868667\pi\) | |||||||
\(938\) | −2.73919 | −0.0894377 | ||||||||
\(939\) | −28.1102 | −0.917341 | ||||||||
\(940\) | 121.341 | 3.95772 | ||||||||
\(941\) | −17.2233 | −0.561465 | −0.280733 | − | 0.959786i | \(-0.590577\pi\) | ||||
−0.280733 | + | 0.959786i | \(0.590577\pi\) | |||||||
\(942\) | 96.2614 | 3.13637 | ||||||||
\(943\) | 69.2302 | 2.25444 | ||||||||
\(944\) | −68.2224 | −2.22045 | ||||||||
\(945\) | 7.11858 | 0.231567 | ||||||||
\(946\) | −4.84305 | −0.157461 | ||||||||
\(947\) | −23.2500 | −0.755522 | −0.377761 | − | 0.925903i | \(-0.623306\pi\) | ||||
−0.377761 | + | 0.925903i | \(0.623306\pi\) | |||||||
\(948\) | −73.3511 | −2.38233 | ||||||||
\(949\) | 3.49983 | 0.113609 | ||||||||
\(950\) | 37.4993 | 1.21664 | ||||||||
\(951\) | 7.41410 | 0.240419 | ||||||||
\(952\) | 2.75042 | 0.0891416 | ||||||||
\(953\) | 28.5844 | 0.925938 | 0.462969 | − | 0.886374i | \(-0.346784\pi\) | ||||
0.462969 | + | 0.886374i | \(0.346784\pi\) | |||||||
\(954\) | 140.485 | 4.54838 | ||||||||
\(955\) | 28.6405 | 0.926784 | ||||||||
\(956\) | −118.167 | −3.82179 | ||||||||
\(957\) | 32.2734 | 1.04325 | ||||||||
\(958\) | −119.278 | −3.85369 | ||||||||
\(959\) | 0.517654 | 0.0167159 | ||||||||
\(960\) | −285.131 | −9.20257 | ||||||||
\(961\) | −30.5334 | −0.984949 | ||||||||
\(962\) | −29.9474 | −0.965543 | ||||||||
\(963\) | 25.6623 | 0.826955 | ||||||||
\(964\) | 68.3500 | 2.20140 | ||||||||
\(965\) | −58.9282 | −1.89697 | ||||||||
\(966\) | −13.5381 | −0.435582 | ||||||||
\(967\) | 49.2918 | 1.58512 | 0.792558 | − | 0.609797i | \(-0.208749\pi\) | ||||
0.792558 | + | 0.609797i | \(0.208749\pi\) | |||||||
\(968\) | 98.0999 | 3.15305 | ||||||||
\(969\) | −25.5897 | −0.822060 | ||||||||
\(970\) | 109.495 | 3.51567 | ||||||||
\(971\) | −41.5039 | −1.33192 | −0.665962 | − | 0.745986i | \(-0.731979\pi\) | ||||
−0.665962 | + | 0.745986i | \(0.731979\pi\) | |||||||
\(972\) | 31.2282 | 1.00165 | ||||||||
\(973\) | −3.97829 | −0.127538 | ||||||||
\(974\) | −63.2819 | −2.02768 | ||||||||
\(975\) | 18.9737 | 0.607646 | ||||||||
\(976\) | 117.518 | 3.76165 | ||||||||
\(977\) | −0.630180 | −0.0201613 | −0.0100806 | − | 0.999949i | \(-0.503209\pi\) | ||||
−0.0100806 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(978\) | 144.079 | 4.60715 | ||||||||
\(979\) | 13.1798 | 0.421229 | ||||||||
\(980\) | 99.9828 | 3.19383 | ||||||||
\(981\) | 4.35279 | 0.138974 | ||||||||
\(982\) | −100.963 | −3.22186 | ||||||||
\(983\) | 9.70853 | 0.309654 | 0.154827 | − | 0.987942i | \(-0.450518\pi\) | ||||
0.154827 | + | 0.987942i | \(0.450518\pi\) | |||||||
\(984\) | 360.525 | 11.4931 | ||||||||
\(985\) | −41.8339 | −1.33294 | ||||||||
\(986\) | −27.1374 | −0.864230 | ||||||||
\(987\) | 7.06667 | 0.224935 | ||||||||
\(988\) | −181.211 | −5.76508 | ||||||||
\(989\) | −9.51276 | −0.302488 | ||||||||
\(990\) | 48.0692 | 1.52774 | ||||||||
\(991\) | 32.8600 | 1.04383 | 0.521916 | − | 0.852997i | \(-0.325217\pi\) | ||||
0.521916 | + | 0.852997i | \(0.325217\pi\) | |||||||
\(992\) | 17.0617 | 0.541710 | ||||||||
\(993\) | −52.4385 | −1.66409 | ||||||||
\(994\) | −4.82211 | −0.152948 | ||||||||
\(995\) | 34.6474 | 1.09840 | ||||||||
\(996\) | −68.4423 | −2.16868 | ||||||||
\(997\) | 8.96902 | 0.284052 | 0.142026 | − | 0.989863i | \(-0.454638\pi\) | ||||
0.142026 | + | 0.989863i | \(0.454638\pi\) | |||||||
\(998\) | 12.3139 | 0.389789 | ||||||||
\(999\) | 28.3057 | 0.895552 |
(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 | 6001.2.a.b.1.2 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.2 | ✓ | 114 | 1.1 | even | 1 | trivial |