Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60210 | −1.83997 | −0.919983 | − | 0.391959i | \(-0.871797\pi\) | ||||
−0.919983 | + | 0.391959i | \(0.871797\pi\) | |||||||
\(3\) | −3.36394 | −1.94217 | −0.971084 | − | 0.238736i | \(-0.923267\pi\) | ||||
−0.971084 | + | 0.238736i | \(0.923267\pi\) | |||||||
\(4\) | 4.77094 | 2.38547 | ||||||||
\(5\) | 3.49358 | 1.56238 | 0.781188 | − | 0.624295i | \(-0.214614\pi\) | ||||
0.781188 | + | 0.624295i | \(0.214614\pi\) | |||||||
\(6\) | 8.75331 | 3.57352 | ||||||||
\(7\) | 4.61670 | 1.74495 | 0.872474 | − | 0.488660i | \(-0.162514\pi\) | ||||
0.872474 | + | 0.488660i | \(0.162514\pi\) | |||||||
\(8\) | −7.21028 | −2.54922 | ||||||||
\(9\) | 8.31606 | 2.77202 | ||||||||
\(10\) | −9.09066 | −2.87472 | ||||||||
\(11\) | 5.76146 | 1.73715 | 0.868573 | − | 0.495561i | \(-0.165038\pi\) | ||||
0.868573 | + | 0.495561i | \(0.165038\pi\) | |||||||
\(12\) | −16.0491 | −4.63299 | ||||||||
\(13\) | −3.60496 | −0.999836 | −0.499918 | − | 0.866073i | \(-0.666637\pi\) | ||||
−0.499918 | + | 0.866073i | \(0.666637\pi\) | |||||||
\(14\) | −12.0131 | −3.21065 | ||||||||
\(15\) | −11.7522 | −3.03440 | ||||||||
\(16\) | 9.22002 | 2.30500 | ||||||||
\(17\) | −6.25498 | −1.51706 | −0.758528 | − | 0.651640i | \(-0.774081\pi\) | ||||
−0.758528 | + | 0.651640i | \(0.774081\pi\) | |||||||
\(18\) | −21.6393 | −5.10042 | ||||||||
\(19\) | 1.10055 | 0.252485 | 0.126242 | − | 0.991999i | \(-0.459708\pi\) | ||||
0.126242 | + | 0.991999i | \(0.459708\pi\) | |||||||
\(20\) | 16.6677 | 3.72701 | ||||||||
\(21\) | −15.5303 | −3.38899 | ||||||||
\(22\) | −14.9919 | −3.19629 | ||||||||
\(23\) | −5.25956 | −1.09669 | −0.548347 | − | 0.836251i | \(-0.684743\pi\) | ||||
−0.548347 | + | 0.836251i | \(0.684743\pi\) | |||||||
\(24\) | 24.2549 | 4.95102 | ||||||||
\(25\) | 7.20511 | 1.44102 | ||||||||
\(26\) | 9.38048 | 1.83966 | ||||||||
\(27\) | −17.8829 | −3.44156 | ||||||||
\(28\) | 22.0260 | 4.16253 | ||||||||
\(29\) | −0.286773 | −0.0532524 | −0.0266262 | − | 0.999645i | \(-0.508476\pi\) | ||||
−0.0266262 | + | 0.999645i | \(0.508476\pi\) | |||||||
\(30\) | 30.5804 | 5.58319 | ||||||||
\(31\) | −5.82152 | −1.04558 | −0.522788 | − | 0.852463i | \(-0.675108\pi\) | ||||
−0.522788 | + | 0.852463i | \(0.675108\pi\) | |||||||
\(32\) | −9.57088 | −1.69191 | ||||||||
\(33\) | −19.3812 | −3.37383 | ||||||||
\(34\) | 16.2761 | 2.79133 | ||||||||
\(35\) | 16.1288 | 2.72627 | ||||||||
\(36\) | 39.6755 | 6.61258 | ||||||||
\(37\) | 6.50400 | 1.06925 | 0.534625 | − | 0.845089i | \(-0.320453\pi\) | ||||
0.534625 | + | 0.845089i | \(0.320453\pi\) | |||||||
\(38\) | −2.86376 | −0.464563 | ||||||||
\(39\) | 12.1269 | 1.94185 | ||||||||
\(40\) | −25.1897 | −3.98284 | ||||||||
\(41\) | 1.67633 | 0.261799 | 0.130899 | − | 0.991396i | \(-0.458214\pi\) | ||||
0.130899 | + | 0.991396i | \(0.458214\pi\) | |||||||
\(42\) | 40.4114 | 6.23562 | ||||||||
\(43\) | −6.74649 | −1.02883 | −0.514415 | − | 0.857542i | \(-0.671991\pi\) | ||||
−0.514415 | + | 0.857542i | \(0.671991\pi\) | |||||||
\(44\) | 27.4876 | 4.14391 | ||||||||
\(45\) | 29.0528 | 4.33094 | ||||||||
\(46\) | 13.6859 | 2.01788 | ||||||||
\(47\) | −6.65750 | −0.971097 | −0.485548 | − | 0.874210i | \(-0.661380\pi\) | ||||
−0.485548 | + | 0.874210i | \(0.661380\pi\) | |||||||
\(48\) | −31.0155 | −4.47671 | ||||||||
\(49\) | 14.3139 | 2.04485 | ||||||||
\(50\) | −18.7484 | −2.65143 | ||||||||
\(51\) | 21.0414 | 2.94638 | ||||||||
\(52\) | −17.1991 | −2.38508 | ||||||||
\(53\) | −8.93512 | −1.22733 | −0.613667 | − | 0.789565i | \(-0.710306\pi\) | ||||
−0.613667 | + | 0.789565i | \(0.710306\pi\) | |||||||
\(54\) | 46.5331 | 6.33236 | ||||||||
\(55\) | 20.1281 | 2.71408 | ||||||||
\(56\) | −33.2877 | −4.44826 | ||||||||
\(57\) | −3.70219 | −0.490368 | ||||||||
\(58\) | 0.746213 | 0.0979826 | ||||||||
\(59\) | 0.421069 | 0.0548186 | 0.0274093 | − | 0.999624i | \(-0.491274\pi\) | ||||
0.0274093 | + | 0.999624i | \(0.491274\pi\) | |||||||
\(60\) | −56.0690 | −7.23848 | ||||||||
\(61\) | −5.32593 | −0.681916 | −0.340958 | − | 0.940079i | \(-0.610751\pi\) | ||||
−0.340958 | + | 0.940079i | \(0.610751\pi\) | |||||||
\(62\) | 15.1482 | 1.92382 | ||||||||
\(63\) | 38.3928 | 4.83703 | ||||||||
\(64\) | 6.46438 | 0.808047 | ||||||||
\(65\) | −12.5942 | −1.56212 | ||||||||
\(66\) | 50.4318 | 6.20773 | ||||||||
\(67\) | −4.40120 | −0.537692 | −0.268846 | − | 0.963183i | \(-0.586642\pi\) | ||||
−0.268846 | + | 0.963183i | \(0.586642\pi\) | |||||||
\(68\) | −29.8422 | −3.61890 | ||||||||
\(69\) | 17.6928 | 2.12996 | ||||||||
\(70\) | −41.9689 | −5.01624 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −59.9612 | −7.06649 | ||||||||
\(73\) | −5.64956 | −0.661231 | −0.330615 | − | 0.943766i | \(-0.607256\pi\) | ||||
−0.330615 | + | 0.943766i | \(0.607256\pi\) | |||||||
\(74\) | −16.9241 | −1.96738 | ||||||||
\(75\) | −24.2375 | −2.79871 | ||||||||
\(76\) | 5.25068 | 0.602295 | ||||||||
\(77\) | 26.5989 | 3.03123 | ||||||||
\(78\) | −31.5553 | −3.57294 | ||||||||
\(79\) | −10.1255 | −1.13920 | −0.569602 | − | 0.821921i | \(-0.692903\pi\) | ||||
−0.569602 | + | 0.821921i | \(0.692903\pi\) | |||||||
\(80\) | 32.2109 | 3.60129 | ||||||||
\(81\) | 35.2087 | 3.91208 | ||||||||
\(82\) | −4.36198 | −0.481700 | ||||||||
\(83\) | 9.41179 | 1.03308 | 0.516539 | − | 0.856264i | \(-0.327220\pi\) | ||||
0.516539 | + | 0.856264i | \(0.327220\pi\) | |||||||
\(84\) | −74.0941 | −8.08433 | ||||||||
\(85\) | −21.8523 | −2.37021 | ||||||||
\(86\) | 17.5551 | 1.89301 | ||||||||
\(87\) | 0.964686 | 0.103425 | ||||||||
\(88\) | −41.5418 | −4.42837 | ||||||||
\(89\) | −5.01685 | −0.531785 | −0.265892 | − | 0.964003i | \(-0.585667\pi\) | ||||
−0.265892 | + | 0.964003i | \(0.585667\pi\) | |||||||
\(90\) | −75.5985 | −7.96878 | ||||||||
\(91\) | −16.6430 | −1.74466 | ||||||||
\(92\) | −25.0930 | −2.61613 | ||||||||
\(93\) | 19.5832 | 2.03069 | ||||||||
\(94\) | 17.3235 | 1.78678 | ||||||||
\(95\) | 3.84488 | 0.394476 | ||||||||
\(96\) | 32.1958 | 3.28597 | ||||||||
\(97\) | −5.93740 | −0.602851 | −0.301426 | − | 0.953490i | \(-0.597463\pi\) | ||||
−0.301426 | + | 0.953490i | \(0.597463\pi\) | |||||||
\(98\) | −37.2463 | −3.76245 | ||||||||
\(99\) | 47.9127 | 4.81540 | ||||||||
\(100\) | 34.3752 | 3.43752 | ||||||||
\(101\) | −13.0117 | −1.29471 | −0.647354 | − | 0.762189i | \(-0.724124\pi\) | ||||
−0.647354 | + | 0.762189i | \(0.724124\pi\) | |||||||
\(102\) | −54.7518 | −5.42124 | ||||||||
\(103\) | 15.1364 | 1.49144 | 0.745719 | − | 0.666260i | \(-0.232106\pi\) | ||||
0.745719 | + | 0.666260i | \(0.232106\pi\) | |||||||
\(104\) | 25.9928 | 2.54880 | ||||||||
\(105\) | −54.2563 | −5.29487 | ||||||||
\(106\) | 23.2501 | 2.25825 | ||||||||
\(107\) | −8.20679 | −0.793381 | −0.396690 | − | 0.917953i | \(-0.629841\pi\) | ||||
−0.396690 | + | 0.917953i | \(0.629841\pi\) | |||||||
\(108\) | −85.3182 | −8.20975 | ||||||||
\(109\) | −12.6905 | −1.21553 | −0.607767 | − | 0.794116i | \(-0.707934\pi\) | ||||
−0.607767 | + | 0.794116i | \(0.707934\pi\) | |||||||
\(110\) | −52.3755 | −4.99381 | ||||||||
\(111\) | −21.8790 | −2.07667 | ||||||||
\(112\) | 42.5661 | 4.02212 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 9.63349 | 0.902259 | ||||||||
\(115\) | −18.3747 | −1.71345 | ||||||||
\(116\) | −1.36818 | −0.127032 | ||||||||
\(117\) | −29.9791 | −2.77157 | ||||||||
\(118\) | −1.09567 | −0.100864 | ||||||||
\(119\) | −28.8774 | −2.64719 | ||||||||
\(120\) | 84.7365 | 7.73535 | ||||||||
\(121\) | 22.1944 | 2.01768 | ||||||||
\(122\) | 13.8586 | 1.25470 | ||||||||
\(123\) | −5.63906 | −0.508457 | ||||||||
\(124\) | −27.7742 | −2.49419 | ||||||||
\(125\) | 7.70371 | 0.689041 | ||||||||
\(126\) | −99.9020 | −8.89997 | ||||||||
\(127\) | 21.9765 | 1.95010 | 0.975049 | − | 0.221988i | \(-0.0712546\pi\) | ||||
0.975049 | + | 0.221988i | \(0.0712546\pi\) | |||||||
\(128\) | 2.32077 | 0.205129 | ||||||||
\(129\) | 22.6947 | 1.99816 | ||||||||
\(130\) | 32.7715 | 2.87425 | ||||||||
\(131\) | −12.3591 | −1.07982 | −0.539909 | − | 0.841723i | \(-0.681541\pi\) | ||||
−0.539909 | + | 0.841723i | \(0.681541\pi\) | |||||||
\(132\) | −92.4665 | −8.04818 | ||||||||
\(133\) | 5.08093 | 0.440573 | ||||||||
\(134\) | 11.4524 | 0.989335 | ||||||||
\(135\) | −62.4753 | −5.37702 | ||||||||
\(136\) | 45.1002 | 3.86731 | ||||||||
\(137\) | −7.92953 | −0.677465 | −0.338733 | − | 0.940883i | \(-0.609998\pi\) | ||||
−0.338733 | + | 0.940883i | \(0.609998\pi\) | |||||||
\(138\) | −46.0385 | −3.91906 | ||||||||
\(139\) | −9.59529 | −0.813862 | −0.406931 | − | 0.913459i | \(-0.633401\pi\) | ||||
−0.406931 | + | 0.913459i | \(0.633401\pi\) | |||||||
\(140\) | 76.9497 | 6.50343 | ||||||||
\(141\) | 22.3954 | 1.88603 | ||||||||
\(142\) | 2.60210 | 0.218364 | ||||||||
\(143\) | −20.7698 | −1.73686 | ||||||||
\(144\) | 76.6742 | 6.38952 | ||||||||
\(145\) | −1.00187 | −0.0832004 | ||||||||
\(146\) | 14.7007 | 1.21664 | ||||||||
\(147\) | −48.1511 | −3.97144 | ||||||||
\(148\) | 31.0302 | 2.55067 | ||||||||
\(149\) | 6.19872 | 0.507819 | 0.253909 | − | 0.967228i | \(-0.418284\pi\) | ||||
0.253909 | + | 0.967228i | \(0.418284\pi\) | |||||||
\(150\) | 63.0685 | 5.14952 | ||||||||
\(151\) | −0.0475608 | −0.00387044 | −0.00193522 | − | 0.999998i | \(-0.500616\pi\) | ||||
−0.00193522 | + | 0.999998i | \(0.500616\pi\) | |||||||
\(152\) | −7.93531 | −0.643639 | ||||||||
\(153\) | −52.0168 | −4.20531 | ||||||||
\(154\) | −69.2132 | −5.57736 | ||||||||
\(155\) | −20.3380 | −1.63358 | ||||||||
\(156\) | 57.8565 | 4.63223 | ||||||||
\(157\) | −0.151653 | −0.0121032 | −0.00605161 | − | 0.999982i | \(-0.501926\pi\) | ||||
−0.00605161 | + | 0.999982i | \(0.501926\pi\) | |||||||
\(158\) | 26.3475 | 2.09610 | ||||||||
\(159\) | 30.0572 | 2.38369 | ||||||||
\(160\) | −33.4366 | −2.64340 | ||||||||
\(161\) | −24.2818 | −1.91367 | ||||||||
\(162\) | −91.6167 | −7.19808 | ||||||||
\(163\) | 20.1194 | 1.57587 | 0.787936 | − | 0.615757i | \(-0.211150\pi\) | ||||
0.787936 | + | 0.615757i | \(0.211150\pi\) | |||||||
\(164\) | 7.99767 | 0.624513 | ||||||||
\(165\) | −67.7097 | −5.27119 | ||||||||
\(166\) | −24.4904 | −1.90083 | ||||||||
\(167\) | −14.3182 | −1.10797 | −0.553986 | − | 0.832526i | \(-0.686894\pi\) | ||||
−0.553986 | + | 0.832526i | \(0.686894\pi\) | |||||||
\(168\) | 111.978 | 8.63927 | ||||||||
\(169\) | −0.00425693 | −0.000327457 0 | ||||||||
\(170\) | 56.8619 | 4.36111 | ||||||||
\(171\) | 9.15228 | 0.699892 | ||||||||
\(172\) | −32.1871 | −2.45424 | ||||||||
\(173\) | 1.29430 | 0.0984042 | 0.0492021 | − | 0.998789i | \(-0.484332\pi\) | ||||
0.0492021 | + | 0.998789i | \(0.484332\pi\) | |||||||
\(174\) | −2.51021 | −0.190299 | ||||||||
\(175\) | 33.2638 | 2.51451 | ||||||||
\(176\) | 53.1208 | 4.00413 | ||||||||
\(177\) | −1.41645 | −0.106467 | ||||||||
\(178\) | 13.0544 | 0.978466 | ||||||||
\(179\) | 20.3183 | 1.51866 | 0.759329 | − | 0.650707i | \(-0.225527\pi\) | ||||
0.759329 | + | 0.650707i | \(0.225527\pi\) | |||||||
\(180\) | 138.609 | 10.3313 | ||||||||
\(181\) | −4.71899 | −0.350760 | −0.175380 | − | 0.984501i | \(-0.556115\pi\) | ||||
−0.175380 | + | 0.984501i | \(0.556115\pi\) | |||||||
\(182\) | 43.3069 | 3.21012 | ||||||||
\(183\) | 17.9161 | 1.32440 | ||||||||
\(184\) | 37.9229 | 2.79571 | ||||||||
\(185\) | 22.7222 | 1.67057 | ||||||||
\(186\) | −50.9576 | −3.73639 | ||||||||
\(187\) | −36.0378 | −2.63535 | ||||||||
\(188\) | −31.7626 | −2.31652 | ||||||||
\(189\) | −82.5599 | −6.00535 | ||||||||
\(190\) | −10.0048 | −0.725822 | ||||||||
\(191\) | −9.41762 | −0.681435 | −0.340718 | − | 0.940166i | \(-0.610670\pi\) | ||||
−0.340718 | + | 0.940166i | \(0.610670\pi\) | |||||||
\(192\) | −21.7457 | −1.56936 | ||||||||
\(193\) | −3.23023 | −0.232517 | −0.116259 | − | 0.993219i | \(-0.537090\pi\) | ||||
−0.116259 | + | 0.993219i | \(0.537090\pi\) | |||||||
\(194\) | 15.4497 | 1.10923 | ||||||||
\(195\) | 42.3661 | 3.03390 | ||||||||
\(196\) | 68.2909 | 4.87792 | ||||||||
\(197\) | −21.9713 | −1.56539 | −0.782697 | − | 0.622403i | \(-0.786156\pi\) | ||||
−0.782697 | + | 0.622403i | \(0.786156\pi\) | |||||||
\(198\) | −124.674 | −8.86017 | ||||||||
\(199\) | −11.7698 | −0.834341 | −0.417171 | − | 0.908828i | \(-0.636978\pi\) | ||||
−0.417171 | + | 0.908828i | \(0.636978\pi\) | |||||||
\(200\) | −51.9508 | −3.67348 | ||||||||
\(201\) | 14.8054 | 1.04429 | ||||||||
\(202\) | 33.8577 | 2.38222 | ||||||||
\(203\) | −1.32395 | −0.0929228 | ||||||||
\(204\) | 100.387 | 7.02851 | ||||||||
\(205\) | 5.85639 | 0.409028 | ||||||||
\(206\) | −39.3866 | −2.74419 | ||||||||
\(207\) | −43.7388 | −3.04006 | ||||||||
\(208\) | −33.2378 | −2.30463 | ||||||||
\(209\) | 6.34080 | 0.438602 | ||||||||
\(210\) | 141.181 | 9.74238 | ||||||||
\(211\) | −23.7673 | −1.63621 | −0.818104 | − | 0.575070i | \(-0.804975\pi\) | ||||
−0.818104 | + | 0.575070i | \(0.804975\pi\) | |||||||
\(212\) | −42.6290 | −2.92777 | ||||||||
\(213\) | 3.36394 | 0.230493 | ||||||||
\(214\) | 21.3549 | 1.45979 | ||||||||
\(215\) | −23.5694 | −1.60742 | ||||||||
\(216\) | 128.941 | 8.77330 | ||||||||
\(217\) | −26.8762 | −1.82448 | ||||||||
\(218\) | 33.0221 | 2.23654 | ||||||||
\(219\) | 19.0048 | 1.28422 | ||||||||
\(220\) | 96.0302 | 6.47435 | ||||||||
\(221\) | 22.5490 | 1.51681 | ||||||||
\(222\) | 56.9315 | 3.82099 | ||||||||
\(223\) | 11.9856 | 0.802613 | 0.401307 | − | 0.915944i | \(-0.368556\pi\) | ||||
0.401307 | + | 0.915944i | \(0.368556\pi\) | |||||||
\(224\) | −44.1859 | −2.95229 | ||||||||
\(225\) | 59.9181 | 3.99454 | ||||||||
\(226\) | 2.60210 | 0.173089 | ||||||||
\(227\) | 1.07170 | 0.0711311 | 0.0355655 | − | 0.999367i | \(-0.488677\pi\) | ||||
0.0355655 | + | 0.999367i | \(0.488677\pi\) | |||||||
\(228\) | −17.6630 | −1.16976 | ||||||||
\(229\) | 6.90899 | 0.456559 | 0.228280 | − | 0.973596i | \(-0.426690\pi\) | ||||
0.228280 | + | 0.973596i | \(0.426690\pi\) | |||||||
\(230\) | 47.8128 | 3.15268 | ||||||||
\(231\) | −89.4771 | −5.88716 | ||||||||
\(232\) | 2.06772 | 0.135752 | ||||||||
\(233\) | 8.51296 | 0.557702 | 0.278851 | − | 0.960334i | \(-0.410046\pi\) | ||||
0.278851 | + | 0.960334i | \(0.410046\pi\) | |||||||
\(234\) | 78.0087 | 5.09959 | ||||||||
\(235\) | −23.2585 | −1.51722 | ||||||||
\(236\) | 2.00890 | 0.130768 | ||||||||
\(237\) | 34.0614 | 2.21253 | ||||||||
\(238\) | 75.1420 | 4.87073 | ||||||||
\(239\) | −25.4717 | −1.64762 | −0.823812 | − | 0.566863i | \(-0.808157\pi\) | ||||
−0.823812 | + | 0.566863i | \(0.808157\pi\) | |||||||
\(240\) | −108.355 | −6.99430 | ||||||||
\(241\) | 6.62060 | 0.426470 | 0.213235 | − | 0.977001i | \(-0.431600\pi\) | ||||
0.213235 | + | 0.977001i | \(0.431600\pi\) | |||||||
\(242\) | −57.7522 | −3.71245 | ||||||||
\(243\) | −64.7911 | −4.15635 | ||||||||
\(244\) | −25.4097 | −1.62669 | ||||||||
\(245\) | 50.0069 | 3.19482 | ||||||||
\(246\) | 14.6734 | 0.935543 | ||||||||
\(247\) | −3.96746 | −0.252443 | ||||||||
\(248\) | 41.9748 | 2.66541 | ||||||||
\(249\) | −31.6606 | −2.00641 | ||||||||
\(250\) | −20.0459 | −1.26781 | ||||||||
\(251\) | −25.8699 | −1.63290 | −0.816448 | − | 0.577419i | \(-0.804060\pi\) | ||||
−0.816448 | + | 0.577419i | \(0.804060\pi\) | |||||||
\(252\) | 183.170 | 11.5386 | ||||||||
\(253\) | −30.3027 | −1.90512 | ||||||||
\(254\) | −57.1851 | −3.58811 | ||||||||
\(255\) | 73.5097 | 4.60336 | ||||||||
\(256\) | −18.9676 | −1.18548 | ||||||||
\(257\) | −26.5578 | −1.65663 | −0.828315 | − | 0.560263i | \(-0.810700\pi\) | ||||
−0.828315 | + | 0.560263i | \(0.810700\pi\) | |||||||
\(258\) | −59.0541 | −3.67655 | ||||||||
\(259\) | 30.0270 | 1.86579 | ||||||||
\(260\) | −60.0863 | −3.72640 | ||||||||
\(261\) | −2.38482 | −0.147617 | ||||||||
\(262\) | 32.1596 | 1.98683 | ||||||||
\(263\) | −0.925928 | −0.0570952 | −0.0285476 | − | 0.999592i | \(-0.509088\pi\) | ||||
−0.0285476 | + | 0.999592i | \(0.509088\pi\) | |||||||
\(264\) | 139.744 | 8.60064 | ||||||||
\(265\) | −31.2156 | −1.91756 | ||||||||
\(266\) | −13.2211 | −0.810638 | ||||||||
\(267\) | 16.8764 | 1.03282 | ||||||||
\(268\) | −20.9979 | −1.28265 | ||||||||
\(269\) | −1.46557 | −0.0893571 | −0.0446785 | − | 0.999001i | \(-0.514226\pi\) | ||||
−0.0446785 | + | 0.999001i | \(0.514226\pi\) | |||||||
\(270\) | 162.567 | 9.89353 | ||||||||
\(271\) | 12.4067 | 0.753654 | 0.376827 | − | 0.926284i | \(-0.377015\pi\) | ||||
0.376827 | + | 0.926284i | \(0.377015\pi\) | |||||||
\(272\) | −57.6711 | −3.49682 | ||||||||
\(273\) | 55.9861 | 3.38843 | ||||||||
\(274\) | 20.6334 | 1.24651 | ||||||||
\(275\) | 41.5119 | 2.50326 | ||||||||
\(276\) | 84.4114 | 5.08097 | ||||||||
\(277\) | 0.381825 | 0.0229417 | 0.0114708 | − | 0.999934i | \(-0.496349\pi\) | ||||
0.0114708 | + | 0.999934i | \(0.496349\pi\) | |||||||
\(278\) | 24.9679 | 1.49748 | ||||||||
\(279\) | −48.4122 | −2.89836 | ||||||||
\(280\) | −116.293 | −6.94986 | ||||||||
\(281\) | 12.7609 | 0.761250 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(282\) | −58.2752 | −3.47024 | ||||||||
\(283\) | 9.54306 | 0.567276 | 0.283638 | − | 0.958931i | \(-0.408459\pi\) | ||||
0.283638 | + | 0.958931i | \(0.408459\pi\) | |||||||
\(284\) | −4.77094 | −0.283103 | ||||||||
\(285\) | −12.9339 | −0.766139 | ||||||||
\(286\) | 54.0453 | 3.19576 | ||||||||
\(287\) | 7.73911 | 0.456825 | ||||||||
\(288\) | −79.5920 | −4.69000 | ||||||||
\(289\) | 22.1248 | 1.30146 | ||||||||
\(290\) | 2.60696 | 0.153086 | ||||||||
\(291\) | 19.9730 | 1.17084 | ||||||||
\(292\) | −26.9537 | −1.57735 | ||||||||
\(293\) | −23.7162 | −1.38551 | −0.692757 | − | 0.721171i | \(-0.743604\pi\) | ||||
−0.692757 | + | 0.721171i | \(0.743604\pi\) | |||||||
\(294\) | 125.294 | 7.30731 | ||||||||
\(295\) | 1.47104 | 0.0856472 | ||||||||
\(296\) | −46.8957 | −2.72576 | ||||||||
\(297\) | −103.032 | −5.97850 | ||||||||
\(298\) | −16.1297 | −0.934369 | ||||||||
\(299\) | 18.9605 | 1.09651 | ||||||||
\(300\) | −115.636 | −6.67624 | ||||||||
\(301\) | −31.1465 | −1.79525 | ||||||||
\(302\) | 0.123758 | 0.00712148 | ||||||||
\(303\) | 43.7704 | 2.51454 | ||||||||
\(304\) | 10.1471 | 0.581978 | ||||||||
\(305\) | −18.6066 | −1.06541 | ||||||||
\(306\) | 135.353 | 7.73763 | ||||||||
\(307\) | 30.9024 | 1.76370 | 0.881848 | − | 0.471534i | \(-0.156300\pi\) | ||||
0.881848 | + | 0.471534i | \(0.156300\pi\) | |||||||
\(308\) | 126.902 | 7.23092 | ||||||||
\(309\) | −50.9180 | −2.89663 | ||||||||
\(310\) | 52.9215 | 3.00574 | ||||||||
\(311\) | 15.1817 | 0.860874 | 0.430437 | − | 0.902621i | \(-0.358359\pi\) | ||||
0.430437 | + | 0.902621i | \(0.358359\pi\) | |||||||
\(312\) | −87.4381 | −4.95021 | ||||||||
\(313\) | 6.32076 | 0.357271 | 0.178635 | − | 0.983915i | \(-0.442832\pi\) | ||||
0.178635 | + | 0.983915i | \(0.442832\pi\) | |||||||
\(314\) | 0.394616 | 0.0222695 | ||||||||
\(315\) | 134.128 | 7.55727 | ||||||||
\(316\) | −48.3080 | −2.71754 | ||||||||
\(317\) | 28.3071 | 1.58988 | 0.794941 | − | 0.606687i | \(-0.207502\pi\) | ||||
0.794941 | + | 0.606687i | \(0.207502\pi\) | |||||||
\(318\) | −78.2119 | −4.38590 | ||||||||
\(319\) | −1.65223 | −0.0925072 | ||||||||
\(320\) | 22.5838 | 1.26247 | ||||||||
\(321\) | 27.6071 | 1.54088 | ||||||||
\(322\) | 63.1838 | 3.52109 | ||||||||
\(323\) | −6.88395 | −0.383033 | ||||||||
\(324\) | 167.979 | 9.33215 | ||||||||
\(325\) | −25.9741 | −1.44079 | ||||||||
\(326\) | −52.3527 | −2.89955 | ||||||||
\(327\) | 42.6901 | 2.36077 | ||||||||
\(328\) | −12.0868 | −0.667382 | ||||||||
\(329\) | −30.7357 | −1.69451 | ||||||||
\(330\) | 176.188 | 9.69881 | ||||||||
\(331\) | −5.78196 | −0.317805 | −0.158903 | − | 0.987294i | \(-0.550796\pi\) | ||||
−0.158903 | + | 0.987294i | \(0.550796\pi\) | |||||||
\(332\) | 44.9031 | 2.46438 | ||||||||
\(333\) | 54.0877 | 2.96399 | ||||||||
\(334\) | 37.2573 | 2.03863 | ||||||||
\(335\) | −15.3760 | −0.840078 | ||||||||
\(336\) | −143.189 | −7.81163 | ||||||||
\(337\) | −16.5683 | −0.902532 | −0.451266 | − | 0.892390i | \(-0.649027\pi\) | ||||
−0.451266 | + | 0.892390i | \(0.649027\pi\) | |||||||
\(338\) | 0.0110770 | 0.000602509 0 | ||||||||
\(339\) | 3.36394 | 0.182704 | ||||||||
\(340\) | −104.256 | −5.65408 | ||||||||
\(341\) | −33.5405 | −1.81632 | ||||||||
\(342\) | −23.8152 | −1.28778 | ||||||||
\(343\) | 33.7662 | 1.82320 | ||||||||
\(344\) | 48.6441 | 2.62271 | ||||||||
\(345\) | 61.8112 | 3.32781 | ||||||||
\(346\) | −3.36792 | −0.181060 | ||||||||
\(347\) | 15.5392 | 0.834186 | 0.417093 | − | 0.908864i | \(-0.363049\pi\) | ||||
0.417093 | + | 0.908864i | \(0.363049\pi\) | |||||||
\(348\) | 4.60246 | 0.246718 | ||||||||
\(349\) | −19.3686 | −1.03678 | −0.518388 | − | 0.855146i | \(-0.673468\pi\) | ||||
−0.518388 | + | 0.855146i | \(0.673468\pi\) | |||||||
\(350\) | −86.5559 | −4.62661 | ||||||||
\(351\) | 64.4671 | 3.44100 | ||||||||
\(352\) | −55.1422 | −2.93909 | ||||||||
\(353\) | −5.50452 | −0.292976 | −0.146488 | − | 0.989212i | \(-0.546797\pi\) | ||||
−0.146488 | + | 0.989212i | \(0.546797\pi\) | |||||||
\(354\) | 3.68575 | 0.195895 | ||||||||
\(355\) | −3.49358 | −0.185420 | ||||||||
\(356\) | −23.9351 | −1.26856 | ||||||||
\(357\) | 97.1417 | 5.14128 | ||||||||
\(358\) | −52.8702 | −2.79428 | ||||||||
\(359\) | −17.1453 | −0.904894 | −0.452447 | − | 0.891791i | \(-0.649449\pi\) | ||||
−0.452447 | + | 0.891791i | \(0.649449\pi\) | |||||||
\(360\) | −209.479 | −11.0405 | ||||||||
\(361\) | −17.7888 | −0.936252 | ||||||||
\(362\) | 12.2793 | 0.645386 | ||||||||
\(363\) | −74.6606 | −3.91867 | ||||||||
\(364\) | −79.4029 | −4.16185 | ||||||||
\(365\) | −19.7372 | −1.03309 | ||||||||
\(366\) | −46.6195 | −2.43684 | ||||||||
\(367\) | −11.7232 | −0.611947 | −0.305973 | − | 0.952040i | \(-0.598982\pi\) | ||||
−0.305973 | + | 0.952040i | \(0.598982\pi\) | |||||||
\(368\) | −48.4932 | −2.52788 | ||||||||
\(369\) | 13.9405 | 0.725711 | ||||||||
\(370\) | −59.1256 | −3.07380 | ||||||||
\(371\) | −41.2508 | −2.14163 | ||||||||
\(372\) | 93.4305 | 4.84415 | ||||||||
\(373\) | 7.34320 | 0.380217 | 0.190108 | − | 0.981763i | \(-0.439116\pi\) | ||||
0.190108 | + | 0.981763i | \(0.439116\pi\) | |||||||
\(374\) | 93.7742 | 4.84895 | ||||||||
\(375\) | −25.9148 | −1.33823 | ||||||||
\(376\) | 48.0025 | 2.47554 | ||||||||
\(377\) | 1.03381 | 0.0532437 | ||||||||
\(378\) | 214.830 | 11.0496 | ||||||||
\(379\) | −22.1987 | −1.14027 | −0.570135 | − | 0.821551i | \(-0.693109\pi\) | ||||
−0.570135 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(380\) | 18.3437 | 0.941011 | ||||||||
\(381\) | −73.9275 | −3.78742 | ||||||||
\(382\) | 24.5056 | 1.25382 | ||||||||
\(383\) | 0.507200 | 0.0259167 | 0.0129583 | − | 0.999916i | \(-0.495875\pi\) | ||||
0.0129583 | + | 0.999916i | \(0.495875\pi\) | |||||||
\(384\) | −7.80693 | −0.398396 | ||||||||
\(385\) | 92.9255 | 4.73592 | ||||||||
\(386\) | 8.40540 | 0.427824 | ||||||||
\(387\) | −56.1042 | −2.85194 | ||||||||
\(388\) | −28.3270 | −1.43808 | ||||||||
\(389\) | 4.95049 | 0.251000 | 0.125500 | − | 0.992094i | \(-0.459947\pi\) | ||||
0.125500 | + | 0.992094i | \(0.459947\pi\) | |||||||
\(390\) | −110.241 | −5.58228 | ||||||||
\(391\) | 32.8984 | 1.66375 | ||||||||
\(392\) | −103.207 | −5.21276 | ||||||||
\(393\) | 41.5752 | 2.09719 | ||||||||
\(394\) | 57.1717 | 2.88027 | ||||||||
\(395\) | −35.3741 | −1.77987 | ||||||||
\(396\) | 228.589 | 11.4870 | ||||||||
\(397\) | −12.8861 | −0.646734 | −0.323367 | − | 0.946274i | \(-0.604815\pi\) | ||||
−0.323367 | + | 0.946274i | \(0.604815\pi\) | |||||||
\(398\) | 30.6263 | 1.53516 | ||||||||
\(399\) | −17.0919 | −0.855666 | ||||||||
\(400\) | 66.4312 | 3.32156 | ||||||||
\(401\) | 31.1149 | 1.55380 | 0.776901 | − | 0.629623i | \(-0.216791\pi\) | ||||
0.776901 | + | 0.629623i | \(0.216791\pi\) | |||||||
\(402\) | −38.5251 | −1.92146 | ||||||||
\(403\) | 20.9864 | 1.04541 | ||||||||
\(404\) | −62.0779 | −3.08849 | ||||||||
\(405\) | 123.004 | 6.11214 | ||||||||
\(406\) | 3.44504 | 0.170975 | ||||||||
\(407\) | 37.4725 | 1.85744 | ||||||||
\(408\) | −151.714 | −7.51097 | ||||||||
\(409\) | −12.3617 | −0.611245 | −0.305623 | − | 0.952153i | \(-0.598865\pi\) | ||||
−0.305623 | + | 0.952153i | \(0.598865\pi\) | |||||||
\(410\) | −15.2389 | −0.752597 | ||||||||
\(411\) | 26.6744 | 1.31575 | ||||||||
\(412\) | 72.2151 | 3.55778 | ||||||||
\(413\) | 1.94395 | 0.0956556 | ||||||||
\(414\) | 113.813 | 5.59360 | ||||||||
\(415\) | 32.8808 | 1.61406 | ||||||||
\(416\) | 34.5026 | 1.69163 | ||||||||
\(417\) | 32.2779 | 1.58066 | ||||||||
\(418\) | −16.4994 | −0.807013 | ||||||||
\(419\) | 14.6550 | 0.715945 | 0.357973 | − | 0.933732i | \(-0.383468\pi\) | ||||
0.357973 | + | 0.933732i | \(0.383468\pi\) | |||||||
\(420\) | −258.854 | −12.6308 | ||||||||
\(421\) | −14.1174 | −0.688038 | −0.344019 | − | 0.938963i | \(-0.611789\pi\) | ||||
−0.344019 | + | 0.938963i | \(0.611789\pi\) | |||||||
\(422\) | 61.8450 | 3.01057 | ||||||||
\(423\) | −55.3642 | −2.69190 | ||||||||
\(424\) | 64.4248 | 3.12874 | ||||||||
\(425\) | −45.0678 | −2.18611 | ||||||||
\(426\) | −8.75331 | −0.424099 | ||||||||
\(427\) | −24.5882 | −1.18991 | ||||||||
\(428\) | −39.1541 | −1.89259 | ||||||||
\(429\) | 69.8684 | 3.37328 | ||||||||
\(430\) | 61.3300 | 2.95760 | ||||||||
\(431\) | −11.7049 | −0.563804 | −0.281902 | − | 0.959443i | \(-0.590965\pi\) | ||||
−0.281902 | + | 0.959443i | \(0.590965\pi\) | |||||||
\(432\) | −164.881 | −7.93282 | ||||||||
\(433\) | 25.3699 | 1.21920 | 0.609599 | − | 0.792710i | \(-0.291330\pi\) | ||||
0.609599 | + | 0.792710i | \(0.291330\pi\) | |||||||
\(434\) | 69.9348 | 3.35698 | ||||||||
\(435\) | 3.37021 | 0.161589 | ||||||||
\(436\) | −60.5458 | −2.89962 | ||||||||
\(437\) | −5.78843 | −0.276898 | ||||||||
\(438\) | −49.4523 | −2.36292 | ||||||||
\(439\) | −0.759129 | −0.0362312 | −0.0181156 | − | 0.999836i | \(-0.505767\pi\) | ||||
−0.0181156 | + | 0.999836i | \(0.505767\pi\) | |||||||
\(440\) | −145.130 | −6.91878 | ||||||||
\(441\) | 119.036 | 5.66836 | ||||||||
\(442\) | −58.6748 | −2.79087 | ||||||||
\(443\) | 9.26568 | 0.440226 | 0.220113 | − | 0.975474i | \(-0.429357\pi\) | ||||
0.220113 | + | 0.975474i | \(0.429357\pi\) | |||||||
\(444\) | −104.384 | −4.95383 | ||||||||
\(445\) | −17.5268 | −0.830848 | ||||||||
\(446\) | −31.1877 | −1.47678 | ||||||||
\(447\) | −20.8521 | −0.986270 | ||||||||
\(448\) | 29.8441 | 1.41000 | ||||||||
\(449\) | −33.0167 | −1.55815 | −0.779077 | − | 0.626928i | \(-0.784312\pi\) | ||||
−0.779077 | + | 0.626928i | \(0.784312\pi\) | |||||||
\(450\) | −155.913 | −7.34981 | ||||||||
\(451\) | 9.65810 | 0.454782 | ||||||||
\(452\) | −4.77094 | −0.224406 | ||||||||
\(453\) | 0.159991 | 0.00751705 | ||||||||
\(454\) | −2.78867 | −0.130879 | ||||||||
\(455\) | −58.1438 | −2.72582 | ||||||||
\(456\) | 26.6939 | 1.25005 | ||||||||
\(457\) | 2.28127 | 0.106713 | 0.0533566 | − | 0.998576i | \(-0.483008\pi\) | ||||
0.0533566 | + | 0.998576i | \(0.483008\pi\) | |||||||
\(458\) | −17.9779 | −0.840053 | ||||||||
\(459\) | 111.857 | 5.22105 | ||||||||
\(460\) | −87.6646 | −4.08738 | ||||||||
\(461\) | −12.7426 | −0.593484 | −0.296742 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296742 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(462\) | 232.829 | 10.8322 | ||||||||
\(463\) | 28.0052 | 1.30151 | 0.650755 | − | 0.759288i | \(-0.274452\pi\) | ||||
0.650755 | + | 0.759288i | \(0.274452\pi\) | |||||||
\(464\) | −2.64405 | −0.122747 | ||||||||
\(465\) | 68.4156 | 3.17270 | ||||||||
\(466\) | −22.1516 | −1.02615 | ||||||||
\(467\) | 32.5484 | 1.50616 | 0.753080 | − | 0.657929i | \(-0.228567\pi\) | ||||
0.753080 | + | 0.657929i | \(0.228567\pi\) | |||||||
\(468\) | −143.028 | −6.61149 | ||||||||
\(469\) | −20.3190 | −0.938246 | ||||||||
\(470\) | 60.5211 | 2.79163 | ||||||||
\(471\) | 0.510150 | 0.0235065 | ||||||||
\(472\) | −3.03603 | −0.139745 | ||||||||
\(473\) | −38.8696 | −1.78723 | ||||||||
\(474\) | −88.6314 | −4.07097 | ||||||||
\(475\) | 7.92961 | 0.363835 | ||||||||
\(476\) | −137.772 | −6.31479 | ||||||||
\(477\) | −74.3050 | −3.40219 | ||||||||
\(478\) | 66.2799 | 3.03157 | ||||||||
\(479\) | −23.3134 | −1.06522 | −0.532609 | − | 0.846361i | \(-0.678788\pi\) | ||||
−0.532609 | + | 0.846361i | \(0.678788\pi\) | |||||||
\(480\) | 112.479 | 5.13392 | ||||||||
\(481\) | −23.4467 | −1.06908 | ||||||||
\(482\) | −17.2275 | −0.784690 | ||||||||
\(483\) | 81.6824 | 3.71668 | ||||||||
\(484\) | 105.888 | 4.81311 | ||||||||
\(485\) | −20.7428 | −0.941881 | ||||||||
\(486\) | 168.593 | 7.64754 | ||||||||
\(487\) | −29.1496 | −1.32089 | −0.660447 | − | 0.750873i | \(-0.729633\pi\) | ||||
−0.660447 | + | 0.750873i | \(0.729633\pi\) | |||||||
\(488\) | 38.4015 | 1.73835 | ||||||||
\(489\) | −67.6803 | −3.06061 | ||||||||
\(490\) | −130.123 | −5.87836 | ||||||||
\(491\) | −18.3627 | −0.828696 | −0.414348 | − | 0.910119i | \(-0.635990\pi\) | ||||
−0.414348 | + | 0.910119i | \(0.635990\pi\) | |||||||
\(492\) | −26.9036 | −1.21291 | ||||||||
\(493\) | 1.79376 | 0.0807870 | ||||||||
\(494\) | 10.3237 | 0.464487 | ||||||||
\(495\) | 167.387 | 7.52347 | ||||||||
\(496\) | −53.6746 | −2.41006 | ||||||||
\(497\) | −4.61670 | −0.207087 | ||||||||
\(498\) | 82.3843 | 3.69173 | ||||||||
\(499\) | 10.7663 | 0.481968 | 0.240984 | − | 0.970529i | \(-0.422530\pi\) | ||||
0.240984 | + | 0.970529i | \(0.422530\pi\) | |||||||
\(500\) | 36.7540 | 1.64369 | ||||||||
\(501\) | 48.1654 | 2.15187 | ||||||||
\(502\) | 67.3162 | 3.00447 | ||||||||
\(503\) | −4.90844 | −0.218857 | −0.109428 | − | 0.993995i | \(-0.534902\pi\) | ||||
−0.109428 | + | 0.993995i | \(0.534902\pi\) | |||||||
\(504\) | −276.823 | −12.3307 | ||||||||
\(505\) | −45.4573 | −2.02282 | ||||||||
\(506\) | 78.8508 | 3.50535 | ||||||||
\(507\) | 0.0143201 | 0.000635976 0 | ||||||||
\(508\) | 104.849 | 4.65191 | ||||||||
\(509\) | −19.5874 | −0.868197 | −0.434099 | − | 0.900865i | \(-0.642933\pi\) | ||||
−0.434099 | + | 0.900865i | \(0.642933\pi\) | |||||||
\(510\) | −191.280 | −8.47001 | ||||||||
\(511\) | −26.0823 | −1.15381 | ||||||||
\(512\) | 44.7142 | 1.97611 | ||||||||
\(513\) | −19.6811 | −0.868941 | ||||||||
\(514\) | 69.1061 | 3.04814 | ||||||||
\(515\) | 52.8804 | 2.33019 | ||||||||
\(516\) | 108.275 | 4.76656 | ||||||||
\(517\) | −38.3569 | −1.68694 | ||||||||
\(518\) | −78.1334 | −3.43299 | ||||||||
\(519\) | −4.35396 | −0.191118 | ||||||||
\(520\) | 90.8079 | 3.98219 | ||||||||
\(521\) | 6.59752 | 0.289043 | 0.144521 | − | 0.989502i | \(-0.453836\pi\) | ||||
0.144521 | + | 0.989502i | \(0.453836\pi\) | |||||||
\(522\) | 6.20556 | 0.271610 | ||||||||
\(523\) | 25.4889 | 1.11455 | 0.557277 | − | 0.830327i | \(-0.311846\pi\) | ||||
0.557277 | + | 0.830327i | \(0.311846\pi\) | |||||||
\(524\) | −58.9645 | −2.57588 | ||||||||
\(525\) | −111.897 | −4.88360 | ||||||||
\(526\) | 2.40936 | 0.105053 | ||||||||
\(527\) | 36.4135 | 1.58620 | ||||||||
\(528\) | −178.695 | −7.77669 | ||||||||
\(529\) | 4.66293 | 0.202736 | ||||||||
\(530\) | 81.2261 | 3.52824 | ||||||||
\(531\) | 3.50164 | 0.151958 | ||||||||
\(532\) | 24.2408 | 1.05097 | ||||||||
\(533\) | −6.04310 | −0.261756 | ||||||||
\(534\) | −43.9140 | −1.90035 | ||||||||
\(535\) | −28.6711 | −1.23956 | ||||||||
\(536\) | 31.7339 | 1.37070 | ||||||||
\(537\) | −68.3493 | −2.94949 | ||||||||
\(538\) | 3.81355 | 0.164414 | ||||||||
\(539\) | 82.4691 | 3.55220 | ||||||||
\(540\) | −298.066 | −12.8267 | ||||||||
\(541\) | 20.6224 | 0.886625 | 0.443313 | − | 0.896367i | \(-0.353803\pi\) | ||||
0.443313 | + | 0.896367i | \(0.353803\pi\) | |||||||
\(542\) | −32.2836 | −1.38670 | ||||||||
\(543\) | 15.8744 | 0.681235 | ||||||||
\(544\) | 59.8657 | 2.56672 | ||||||||
\(545\) | −44.3354 | −1.89912 | ||||||||
\(546\) | −145.682 | −6.23459 | ||||||||
\(547\) | 39.2785 | 1.67943 | 0.839714 | − | 0.543028i | \(-0.182722\pi\) | ||||
0.839714 | + | 0.543028i | \(0.182722\pi\) | |||||||
\(548\) | −37.8313 | −1.61607 | ||||||||
\(549\) | −44.2908 | −1.89028 | ||||||||
\(550\) | −108.018 | −4.60592 | ||||||||
\(551\) | −0.315609 | −0.0134454 | ||||||||
\(552\) | −127.570 | −5.42975 | ||||||||
\(553\) | −46.7463 | −1.98785 | ||||||||
\(554\) | −0.993550 | −0.0422119 | ||||||||
\(555\) | −76.4362 | −3.24453 | ||||||||
\(556\) | −45.7786 | −1.94144 | ||||||||
\(557\) | −45.1309 | −1.91226 | −0.956129 | − | 0.292947i | \(-0.905364\pi\) | ||||
−0.956129 | + | 0.292947i | \(0.905364\pi\) | |||||||
\(558\) | 125.973 | 5.33288 | ||||||||
\(559\) | 24.3208 | 1.02866 | ||||||||
\(560\) | 148.708 | 6.28406 | ||||||||
\(561\) | 121.229 | 5.11829 | ||||||||
\(562\) | −33.2051 | −1.40067 | ||||||||
\(563\) | −26.3040 | −1.10858 | −0.554291 | − | 0.832323i | \(-0.687010\pi\) | ||||
−0.554291 | + | 0.832323i | \(0.687010\pi\) | |||||||
\(564\) | 106.847 | 4.49908 | ||||||||
\(565\) | −3.49358 | −0.146976 | ||||||||
\(566\) | −24.8320 | −1.04377 | ||||||||
\(567\) | 162.548 | 6.82637 | ||||||||
\(568\) | 7.21028 | 0.302537 | ||||||||
\(569\) | 28.2473 | 1.18419 | 0.592094 | − | 0.805869i | \(-0.298302\pi\) | ||||
0.592094 | + | 0.805869i | \(0.298302\pi\) | |||||||
\(570\) | 33.6554 | 1.40967 | ||||||||
\(571\) | −8.28304 | −0.346634 | −0.173317 | − | 0.984866i | \(-0.555449\pi\) | ||||
−0.173317 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(572\) | −99.0917 | −4.14323 | ||||||||
\(573\) | 31.6803 | 1.32346 | ||||||||
\(574\) | −20.1380 | −0.840542 | ||||||||
\(575\) | −37.8957 | −1.58036 | ||||||||
\(576\) | 53.7581 | 2.23992 | ||||||||
\(577\) | −26.4974 | −1.10310 | −0.551551 | − | 0.834141i | \(-0.685964\pi\) | ||||
−0.551551 | + | 0.834141i | \(0.685964\pi\) | |||||||
\(578\) | −57.5711 | −2.39464 | ||||||||
\(579\) | 10.8663 | 0.451588 | ||||||||
\(580\) | −4.77984 | −0.198472 | ||||||||
\(581\) | 43.4514 | 1.80267 | ||||||||
\(582\) | −51.9719 | −2.15430 | ||||||||
\(583\) | −51.4794 | −2.13206 | ||||||||
\(584\) | 40.7349 | 1.68562 | ||||||||
\(585\) | −104.734 | −4.33023 | ||||||||
\(586\) | 61.7119 | 2.54930 | ||||||||
\(587\) | −5.11979 | −0.211316 | −0.105658 | − | 0.994403i | \(-0.533695\pi\) | ||||
−0.105658 | + | 0.994403i | \(0.533695\pi\) | |||||||
\(588\) | −229.726 | −9.47375 | ||||||||
\(589\) | −6.40690 | −0.263992 | ||||||||
\(590\) | −3.82780 | −0.157588 | ||||||||
\(591\) | 73.9102 | 3.04026 | ||||||||
\(592\) | 59.9670 | 2.46463 | ||||||||
\(593\) | −31.1582 | −1.27951 | −0.639756 | − | 0.768578i | \(-0.720965\pi\) | ||||
−0.639756 | + | 0.768578i | \(0.720965\pi\) | |||||||
\(594\) | 268.099 | 11.0002 | ||||||||
\(595\) | −100.886 | −4.13590 | ||||||||
\(596\) | 29.5737 | 1.21139 | ||||||||
\(597\) | 39.5930 | 1.62043 | ||||||||
\(598\) | −49.3372 | −2.01755 | ||||||||
\(599\) | −8.85367 | −0.361751 | −0.180875 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180875 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(600\) | 174.759 | 7.13452 | ||||||||
\(601\) | 10.7159 | 0.437112 | 0.218556 | − | 0.975824i | \(-0.429865\pi\) | ||||
0.218556 | + | 0.975824i | \(0.429865\pi\) | |||||||
\(602\) | 81.0464 | 3.30321 | ||||||||
\(603\) | −36.6007 | −1.49049 | ||||||||
\(604\) | −0.226910 | −0.00923283 | ||||||||
\(605\) | 77.5380 | 3.15237 | ||||||||
\(606\) | −113.895 | −4.62667 | ||||||||
\(607\) | 36.9484 | 1.49969 | 0.749844 | − | 0.661615i | \(-0.230129\pi\) | ||||
0.749844 | + | 0.661615i | \(0.230129\pi\) | |||||||
\(608\) | −10.5333 | −0.427181 | ||||||||
\(609\) | 4.45367 | 0.180472 | ||||||||
\(610\) | 48.4162 | 1.96032 | ||||||||
\(611\) | 24.0000 | 0.970938 | ||||||||
\(612\) | −248.169 | −10.0317 | ||||||||
\(613\) | −6.31769 | −0.255169 | −0.127584 | − | 0.991828i | \(-0.540722\pi\) | ||||
−0.127584 | + | 0.991828i | \(0.540722\pi\) | |||||||
\(614\) | −80.4114 | −3.24514 | ||||||||
\(615\) | −19.7005 | −0.794402 | ||||||||
\(616\) | −191.786 | −7.72727 | ||||||||
\(617\) | 4.53669 | 0.182640 | 0.0913202 | − | 0.995822i | \(-0.470891\pi\) | ||||
0.0913202 | + | 0.995822i | \(0.470891\pi\) | |||||||
\(618\) | 132.494 | 5.32969 | ||||||||
\(619\) | −31.7078 | −1.27445 | −0.637223 | − | 0.770679i | \(-0.719917\pi\) | ||||
−0.637223 | + | 0.770679i | \(0.719917\pi\) | |||||||
\(620\) | −97.0313 | −3.89687 | ||||||||
\(621\) | 94.0560 | 3.77434 | ||||||||
\(622\) | −39.5043 | −1.58398 | ||||||||
\(623\) | −23.1613 | −0.927937 | ||||||||
\(624\) | 111.810 | 4.47598 | ||||||||
\(625\) | −9.11199 | −0.364479 | ||||||||
\(626\) | −16.4473 | −0.657366 | ||||||||
\(627\) | −21.3300 | −0.851840 | ||||||||
\(628\) | −0.723527 | −0.0288719 | ||||||||
\(629\) | −40.6824 | −1.62211 | ||||||||
\(630\) | −349.016 | −13.9051 | ||||||||
\(631\) | 13.9395 | 0.554922 | 0.277461 | − | 0.960737i | \(-0.410507\pi\) | ||||
0.277461 | + | 0.960737i | \(0.410507\pi\) | |||||||
\(632\) | 73.0075 | 2.90408 | ||||||||
\(633\) | 79.9517 | 3.17779 | ||||||||
\(634\) | −73.6579 | −2.92533 | ||||||||
\(635\) | 76.7767 | 3.04679 | ||||||||
\(636\) | 143.401 | 5.68622 | ||||||||
\(637\) | −51.6012 | −2.04451 | ||||||||
\(638\) | 4.29928 | 0.170210 | ||||||||
\(639\) | −8.31606 | −0.328978 | ||||||||
\(640\) | 8.10781 | 0.320489 | ||||||||
\(641\) | −13.8794 | −0.548205 | −0.274103 | − | 0.961700i | \(-0.588381\pi\) | ||||
−0.274103 | + | 0.961700i | \(0.588381\pi\) | |||||||
\(642\) | −71.8366 | −2.83516 | ||||||||
\(643\) | 6.51654 | 0.256987 | 0.128494 | − | 0.991710i | \(-0.458986\pi\) | ||||
0.128494 | + | 0.991710i | \(0.458986\pi\) | |||||||
\(644\) | −115.847 | −4.56502 | ||||||||
\(645\) | 79.2859 | 3.12188 | ||||||||
\(646\) | 17.9128 | 0.704768 | ||||||||
\(647\) | 18.8360 | 0.740519 | 0.370259 | − | 0.928928i | \(-0.379269\pi\) | ||||
0.370259 | + | 0.928928i | \(0.379269\pi\) | |||||||
\(648\) | −253.865 | −9.97274 | ||||||||
\(649\) | 2.42597 | 0.0952278 | ||||||||
\(650\) | 67.5874 | 2.65099 | ||||||||
\(651\) | 90.4099 | 3.54344 | ||||||||
\(652\) | 95.9885 | 3.75920 | ||||||||
\(653\) | −42.7094 | −1.67135 | −0.835674 | − | 0.549226i | \(-0.814923\pi\) | ||||
−0.835674 | + | 0.549226i | \(0.814923\pi\) | |||||||
\(654\) | −111.084 | −4.34374 | ||||||||
\(655\) | −43.1775 | −1.68708 | ||||||||
\(656\) | 15.4558 | 0.603447 | ||||||||
\(657\) | −46.9821 | −1.83295 | ||||||||
\(658\) | 79.9775 | 3.11785 | ||||||||
\(659\) | 13.5203 | 0.526675 | 0.263338 | − | 0.964704i | \(-0.415177\pi\) | ||||
0.263338 | + | 0.964704i | \(0.415177\pi\) | |||||||
\(660\) | −323.039 | −12.5743 | ||||||||
\(661\) | 22.3097 | 0.867746 | 0.433873 | − | 0.900974i | \(-0.357147\pi\) | ||||
0.433873 | + | 0.900974i | \(0.357147\pi\) | |||||||
\(662\) | 15.0453 | 0.584751 | ||||||||
\(663\) | −75.8533 | −2.94590 | ||||||||
\(664\) | −67.8616 | −2.63354 | ||||||||
\(665\) | 17.7506 | 0.688340 | ||||||||
\(666\) | −140.742 | −5.45363 | ||||||||
\(667\) | 1.50830 | 0.0584016 | ||||||||
\(668\) | −68.3111 | −2.64304 | ||||||||
\(669\) | −40.3187 | −1.55881 | ||||||||
\(670\) | 40.0098 | 1.54571 | ||||||||
\(671\) | −30.6851 | −1.18459 | ||||||||
\(672\) | 148.638 | 5.73385 | ||||||||
\(673\) | 5.72025 | 0.220499 | 0.110250 | − | 0.993904i | \(-0.464835\pi\) | ||||
0.110250 | + | 0.993904i | \(0.464835\pi\) | |||||||
\(674\) | 43.1124 | 1.66063 | ||||||||
\(675\) | −128.848 | −4.95936 | ||||||||
\(676\) | −0.0203096 | −0.000781138 0 | ||||||||
\(677\) | 1.02100 | 0.0392404 | 0.0196202 | − | 0.999808i | \(-0.493754\pi\) | ||||
0.0196202 | + | 0.999808i | \(0.493754\pi\) | |||||||
\(678\) | −8.75331 | −0.336169 | ||||||||
\(679\) | −27.4112 | −1.05194 | ||||||||
\(680\) | 157.561 | 6.04220 | ||||||||
\(681\) | −3.60512 | −0.138149 | ||||||||
\(682\) | 87.2758 | 3.34196 | ||||||||
\(683\) | 43.7709 | 1.67485 | 0.837423 | − | 0.546555i | \(-0.184061\pi\) | ||||
0.837423 | + | 0.546555i | \(0.184061\pi\) | |||||||
\(684\) | 43.6650 | 1.66957 | ||||||||
\(685\) | −27.7024 | −1.05846 | ||||||||
\(686\) | −87.8632 | −3.35463 | ||||||||
\(687\) | −23.2414 | −0.886715 | ||||||||
\(688\) | −62.2027 | −2.37146 | ||||||||
\(689\) | 32.2108 | 1.22713 | ||||||||
\(690\) | −160.839 | −6.12305 | ||||||||
\(691\) | 44.5879 | 1.69621 | 0.848103 | − | 0.529832i | \(-0.177745\pi\) | ||||
0.848103 | + | 0.529832i | \(0.177745\pi\) | |||||||
\(692\) | 6.17506 | 0.234740 | ||||||||
\(693\) | 221.198 | 8.40263 | ||||||||
\(694\) | −40.4345 | −1.53487 | ||||||||
\(695\) | −33.5219 | −1.27156 | ||||||||
\(696\) | −6.95566 | −0.263654 | ||||||||
\(697\) | −10.4854 | −0.397163 | ||||||||
\(698\) | 50.3990 | 1.90763 | ||||||||
\(699\) | −28.6370 | −1.08315 | ||||||||
\(700\) | 158.700 | 5.99829 | ||||||||
\(701\) | −3.02534 | −0.114266 | −0.0571328 | − | 0.998367i | \(-0.518196\pi\) | ||||
−0.0571328 | + | 0.998367i | \(0.518196\pi\) | |||||||
\(702\) | −167.750 | −6.33132 | ||||||||
\(703\) | 7.15801 | 0.269969 | ||||||||
\(704\) | 37.2442 | 1.40370 | ||||||||
\(705\) | 78.2402 | 2.94670 | ||||||||
\(706\) | 14.3233 | 0.539066 | ||||||||
\(707\) | −60.0709 | −2.25920 | ||||||||
\(708\) | −6.75780 | −0.253974 | ||||||||
\(709\) | −17.4752 | −0.656294 | −0.328147 | − | 0.944627i | \(-0.606424\pi\) | ||||
−0.328147 | + | 0.944627i | \(0.606424\pi\) | |||||||
\(710\) | 9.09066 | 0.341166 | ||||||||
\(711\) | −84.2040 | −3.15790 | ||||||||
\(712\) | 36.1729 | 1.35564 | ||||||||
\(713\) | 30.6186 | 1.14668 | ||||||||
\(714\) | −252.773 | −9.45978 | ||||||||
\(715\) | −72.5611 | −2.71363 | ||||||||
\(716\) | 96.9372 | 3.62271 | ||||||||
\(717\) | 85.6850 | 3.19997 | ||||||||
\(718\) | 44.6138 | 1.66497 | ||||||||
\(719\) | 44.2919 | 1.65181 | 0.825905 | − | 0.563809i | \(-0.190665\pi\) | ||||
0.825905 | + | 0.563809i | \(0.190665\pi\) | |||||||
\(720\) | 267.868 | 9.98284 | ||||||||
\(721\) | 69.8804 | 2.60248 | ||||||||
\(722\) | 46.2883 | 1.72267 | ||||||||
\(723\) | −22.2713 | −0.828277 | ||||||||
\(724\) | −22.5140 | −0.836728 | ||||||||
\(725\) | −2.06623 | −0.0767379 | ||||||||
\(726\) | 194.275 | 7.21021 | ||||||||
\(727\) | 2.33574 | 0.0866278 | 0.0433139 | − | 0.999062i | \(-0.486208\pi\) | ||||
0.0433139 | + | 0.999062i | \(0.486208\pi\) | |||||||
\(728\) | 120.001 | 4.44753 | ||||||||
\(729\) | 112.327 | 4.16026 | ||||||||
\(730\) | 51.3582 | 1.90085 | ||||||||
\(731\) | 42.1992 | 1.56079 | ||||||||
\(732\) | 85.4767 | 3.15931 | ||||||||
\(733\) | 28.4414 | 1.05051 | 0.525254 | − | 0.850946i | \(-0.323970\pi\) | ||||
0.525254 | + | 0.850946i | \(0.323970\pi\) | |||||||
\(734\) | 30.5050 | 1.12596 | ||||||||
\(735\) | −168.220 | −6.20488 | ||||||||
\(736\) | 50.3386 | 1.85550 | ||||||||
\(737\) | −25.3574 | −0.934050 | ||||||||
\(738\) | −36.2745 | −1.33528 | ||||||||
\(739\) | 44.6834 | 1.64371 | 0.821853 | − | 0.569700i | \(-0.192941\pi\) | ||||
0.821853 | + | 0.569700i | \(0.192941\pi\) | |||||||
\(740\) | 108.407 | 3.98510 | ||||||||
\(741\) | 13.3463 | 0.490287 | ||||||||
\(742\) | 107.339 | 3.94053 | ||||||||
\(743\) | 9.16128 | 0.336095 | 0.168047 | − | 0.985779i | \(-0.446254\pi\) | ||||
0.168047 | + | 0.985779i | \(0.446254\pi\) | |||||||
\(744\) | −141.201 | −5.17667 | ||||||||
\(745\) | 21.6557 | 0.793404 | ||||||||
\(746\) | −19.1078 | −0.699585 | ||||||||
\(747\) | 78.2690 | 2.86371 | ||||||||
\(748\) | −171.935 | −6.28655 | ||||||||
\(749\) | −37.8883 | −1.38441 | ||||||||
\(750\) | 67.4330 | 2.46230 | ||||||||
\(751\) | 41.1496 | 1.50157 | 0.750785 | − | 0.660547i | \(-0.229676\pi\) | ||||
0.750785 | + | 0.660547i | \(0.229676\pi\) | |||||||
\(752\) | −61.3823 | −2.23838 | ||||||||
\(753\) | 87.0248 | 3.17136 | ||||||||
\(754\) | −2.69007 | −0.0979666 | ||||||||
\(755\) | −0.166157 | −0.00604709 | ||||||||
\(756\) | −393.889 | −14.3256 | ||||||||
\(757\) | 24.7802 | 0.900651 | 0.450325 | − | 0.892864i | \(-0.351308\pi\) | ||||
0.450325 | + | 0.892864i | \(0.351308\pi\) | |||||||
\(758\) | 57.7633 | 2.09806 | ||||||||
\(759\) | 101.936 | 3.70006 | ||||||||
\(760\) | −27.7226 | −1.00561 | ||||||||
\(761\) | −44.9674 | −1.63007 | −0.815034 | − | 0.579414i | \(-0.803282\pi\) | ||||
−0.815034 | + | 0.579414i | \(0.803282\pi\) | |||||||
\(762\) | 192.367 | 6.96872 | ||||||||
\(763\) | −58.5884 | −2.12104 | ||||||||
\(764\) | −44.9309 | −1.62554 | ||||||||
\(765\) | −181.725 | −6.57028 | ||||||||
\(766\) | −1.31979 | −0.0476858 | ||||||||
\(767\) | −1.51794 | −0.0548096 | ||||||||
\(768\) | 63.8059 | 2.30240 | ||||||||
\(769\) | −3.47686 | −0.125379 | −0.0626893 | − | 0.998033i | \(-0.519968\pi\) | ||||
−0.0626893 | + | 0.998033i | \(0.519968\pi\) | |||||||
\(770\) | −241.802 | −8.71394 | ||||||||
\(771\) | 89.3387 | 3.21745 | ||||||||
\(772\) | −15.4113 | −0.554663 | ||||||||
\(773\) | −22.6372 | −0.814204 | −0.407102 | − | 0.913383i | \(-0.633461\pi\) | ||||
−0.407102 | + | 0.913383i | \(0.633461\pi\) | |||||||
\(774\) | 145.989 | 5.24746 | ||||||||
\(775\) | −41.9447 | −1.50670 | ||||||||
\(776\) | 42.8103 | 1.53680 | ||||||||
\(777\) | −101.009 | −3.62368 | ||||||||
\(778\) | −12.8817 | −0.461831 | ||||||||
\(779\) | 1.84489 | 0.0661001 | ||||||||
\(780\) | 202.127 | 7.23729 | ||||||||
\(781\) | −5.76146 | −0.206161 | ||||||||
\(782\) | −85.6052 | −3.06123 | ||||||||
\(783\) | 5.12833 | 0.183272 | ||||||||
\(784\) | 131.975 | 4.71338 | ||||||||
\(785\) | −0.529811 | −0.0189098 | ||||||||
\(786\) | −108.183 | −3.85876 | ||||||||
\(787\) | 3.54946 | 0.126525 | 0.0632624 | − | 0.997997i | \(-0.479850\pi\) | ||||
0.0632624 | + | 0.997997i | \(0.479850\pi\) | |||||||
\(788\) | −104.824 | −3.73420 | ||||||||
\(789\) | 3.11476 | 0.110888 | ||||||||
\(790\) | 92.0472 | 3.27489 | ||||||||
\(791\) | −4.61670 | −0.164151 | ||||||||
\(792\) | −345.464 | −12.2755 | ||||||||
\(793\) | 19.1998 | 0.681804 | ||||||||
\(794\) | 33.5309 | 1.18997 | ||||||||
\(795\) | 105.007 | 3.72422 | ||||||||
\(796\) | −56.1532 | −1.99030 | ||||||||
\(797\) | −22.8919 | −0.810871 | −0.405436 | − | 0.914124i | \(-0.632880\pi\) | ||||
−0.405436 | + | 0.914124i | \(0.632880\pi\) | |||||||
\(798\) | 44.4750 | 1.57440 | ||||||||
\(799\) | 41.6426 | 1.47321 | ||||||||
\(800\) | −68.9592 | −2.43807 | ||||||||
\(801\) | −41.7204 | −1.47412 | ||||||||
\(802\) | −80.9641 | −2.85894 | ||||||||
\(803\) | −32.5497 | −1.14865 | ||||||||
\(804\) | 70.6355 | 2.49112 | ||||||||
\(805\) | −84.8304 | −2.98988 | ||||||||
\(806\) | −54.6087 | −1.92351 | ||||||||
\(807\) | 4.93007 | 0.173547 | ||||||||
\(808\) | 93.8177 | 3.30050 | ||||||||
\(809\) | 46.9371 | 1.65022 | 0.825110 | − | 0.564972i | \(-0.191113\pi\) | ||||
0.825110 | + | 0.564972i | \(0.191113\pi\) | |||||||
\(810\) | −320.070 | −11.2461 | ||||||||
\(811\) | 46.4110 | 1.62971 | 0.814855 | − | 0.579664i | \(-0.196816\pi\) | ||||
0.814855 | + | 0.579664i | \(0.196816\pi\) | |||||||
\(812\) | −6.31647 | −0.221665 | ||||||||
\(813\) | −41.7354 | −1.46372 | ||||||||
\(814\) | −97.5074 | −3.41763 | ||||||||
\(815\) | 70.2887 | 2.46211 | ||||||||
\(816\) | 194.002 | 6.79142 | ||||||||
\(817\) | −7.42487 | −0.259763 | ||||||||
\(818\) | 32.1663 | 1.12467 | ||||||||
\(819\) | −138.404 | −4.83624 | ||||||||
\(820\) | 27.9405 | 0.975725 | ||||||||
\(821\) | −25.4774 | −0.889168 | −0.444584 | − | 0.895737i | \(-0.646649\pi\) | ||||
−0.444584 | + | 0.895737i | \(0.646649\pi\) | |||||||
\(822\) | −69.4096 | −2.42094 | ||||||||
\(823\) | 22.4718 | 0.783318 | 0.391659 | − | 0.920111i | \(-0.371901\pi\) | ||||
0.391659 | + | 0.920111i | \(0.371901\pi\) | |||||||
\(824\) | −109.138 | −3.80200 | ||||||||
\(825\) | −139.643 | −4.86176 | ||||||||
\(826\) | −5.05836 | −0.176003 | ||||||||
\(827\) | −27.1017 | −0.942417 | −0.471208 | − | 0.882022i | \(-0.656182\pi\) | ||||
−0.471208 | + | 0.882022i | \(0.656182\pi\) | |||||||
\(828\) | −208.675 | −7.25197 | ||||||||
\(829\) | 26.2755 | 0.912584 | 0.456292 | − | 0.889830i | \(-0.349177\pi\) | ||||
0.456292 | + | 0.889830i | \(0.349177\pi\) | |||||||
\(830\) | −85.5593 | −2.96981 | ||||||||
\(831\) | −1.28444 | −0.0445566 | ||||||||
\(832\) | −23.3038 | −0.807915 | ||||||||
\(833\) | −89.5334 | −3.10215 | ||||||||
\(834\) | −83.9905 | −2.90835 | ||||||||
\(835\) | −50.0216 | −1.73107 | ||||||||
\(836\) | 30.2516 | 1.04627 | ||||||||
\(837\) | 104.106 | 3.59842 | ||||||||
\(838\) | −38.1339 | −1.31731 | ||||||||
\(839\) | −21.9814 | −0.758883 | −0.379441 | − | 0.925216i | \(-0.623884\pi\) | ||||
−0.379441 | + | 0.925216i | \(0.623884\pi\) | |||||||
\(840\) | 391.203 | 13.4978 | ||||||||
\(841\) | −28.9178 | −0.997164 | ||||||||
\(842\) | 36.7349 | 1.26597 | ||||||||
\(843\) | −42.9267 | −1.47848 | ||||||||
\(844\) | −113.392 | −3.90313 | ||||||||
\(845\) | −0.0148719 | −0.000511610 0 | ||||||||
\(846\) | 144.063 | 4.95300 | ||||||||
\(847\) | 102.465 | 3.52074 | ||||||||
\(848\) | −82.3820 | −2.82901 | ||||||||
\(849\) | −32.1022 | −1.10175 | ||||||||
\(850\) | 117.271 | 4.02237 | ||||||||
\(851\) | −34.2082 | −1.17264 | ||||||||
\(852\) | 16.0491 | 0.549835 | ||||||||
\(853\) | −10.3915 | −0.355797 | −0.177898 | − | 0.984049i | \(-0.556930\pi\) | ||||
−0.177898 | + | 0.984049i | \(0.556930\pi\) | |||||||
\(854\) | 63.9811 | 2.18939 | ||||||||
\(855\) | 31.9742 | 1.09350 | ||||||||
\(856\) | 59.1733 | 2.02250 | ||||||||
\(857\) | −24.2506 | −0.828384 | −0.414192 | − | 0.910190i | \(-0.635936\pi\) | ||||
−0.414192 | + | 0.910190i | \(0.635936\pi\) | |||||||
\(858\) | −181.805 | −6.20671 | ||||||||
\(859\) | −48.5643 | −1.65699 | −0.828497 | − | 0.559994i | \(-0.810803\pi\) | ||||
−0.828497 | + | 0.559994i | \(0.810803\pi\) | |||||||
\(860\) | −112.448 | −3.83445 | ||||||||
\(861\) | −26.0339 | −0.887232 | ||||||||
\(862\) | 30.4573 | 1.03738 | ||||||||
\(863\) | −31.2733 | −1.06455 | −0.532277 | − | 0.846570i | \(-0.678664\pi\) | ||||
−0.532277 | + | 0.846570i | \(0.678664\pi\) | |||||||
\(864\) | 171.155 | 5.82281 | ||||||||
\(865\) | 4.52176 | 0.153744 | ||||||||
\(866\) | −66.0150 | −2.24328 | ||||||||
\(867\) | −74.4265 | −2.52766 | ||||||||
\(868\) | −128.225 | −4.35224 | ||||||||
\(869\) | −58.3375 | −1.97896 | ||||||||
\(870\) | −8.76963 | −0.297318 | ||||||||
\(871\) | 15.8662 | 0.537604 | ||||||||
\(872\) | 91.5024 | 3.09866 | ||||||||
\(873\) | −49.3758 | −1.67112 | ||||||||
\(874\) | 15.0621 | 0.509483 | ||||||||
\(875\) | 35.5657 | 1.20234 | ||||||||
\(876\) | 90.6706 | 3.06348 | ||||||||
\(877\) | 58.8247 | 1.98637 | 0.993184 | − | 0.116556i | \(-0.0371856\pi\) | ||||
0.993184 | + | 0.116556i | \(0.0371856\pi\) | |||||||
\(878\) | 1.97533 | 0.0666642 | ||||||||
\(879\) | 79.7797 | 2.69090 | ||||||||
\(880\) | 185.582 | 6.25596 | ||||||||
\(881\) | −39.1516 | −1.31905 | −0.659525 | − | 0.751682i | \(-0.729243\pi\) | ||||
−0.659525 | + | 0.751682i | \(0.729243\pi\) | |||||||
\(882\) | −309.743 | −10.4296 | ||||||||
\(883\) | 4.39632 | 0.147948 | 0.0739740 | − | 0.997260i | \(-0.476432\pi\) | ||||
0.0739740 | + | 0.997260i | \(0.476432\pi\) | |||||||
\(884\) | 107.580 | 3.61830 | ||||||||
\(885\) | −4.94848 | −0.166341 | ||||||||
\(886\) | −24.1103 | −0.810000 | ||||||||
\(887\) | 17.5656 | 0.589796 | 0.294898 | − | 0.955529i | \(-0.404714\pi\) | ||||
0.294898 | + | 0.955529i | \(0.404714\pi\) | |||||||
\(888\) | 157.754 | 5.29388 | ||||||||
\(889\) | 101.459 | 3.40282 | ||||||||
\(890\) | 45.6065 | 1.52873 | ||||||||
\(891\) | 202.853 | 6.79585 | ||||||||
\(892\) | 57.1825 | 1.91461 | ||||||||
\(893\) | −7.32695 | −0.245187 | ||||||||
\(894\) | 54.2593 | 1.81470 | ||||||||
\(895\) | 70.9835 | 2.37272 | ||||||||
\(896\) | 10.7143 | 0.357940 | ||||||||
\(897\) | −63.7819 | −2.12961 | ||||||||
\(898\) | 85.9129 | 2.86695 | ||||||||
\(899\) | 1.66946 | 0.0556795 | ||||||||
\(900\) | 285.866 | 9.52886 | ||||||||
\(901\) | 55.8890 | 1.86193 | ||||||||
\(902\) | −25.1314 | −0.836784 | ||||||||
\(903\) | 104.775 | 3.48669 | ||||||||
\(904\) | 7.21028 | 0.239810 | ||||||||
\(905\) | −16.4862 | −0.548019 | ||||||||
\(906\) | −0.416314 | −0.0138311 | ||||||||
\(907\) | 8.08787 | 0.268553 | 0.134277 | − | 0.990944i | \(-0.457129\pi\) | ||||
0.134277 | + | 0.990944i | \(0.457129\pi\) | |||||||
\(908\) | 5.11301 | 0.169681 | ||||||||
\(909\) | −108.206 | −3.58896 | ||||||||
\(910\) | 151.296 | 5.01542 | ||||||||
\(911\) | −46.1273 | −1.52826 | −0.764132 | − | 0.645060i | \(-0.776832\pi\) | ||||
−0.764132 | + | 0.645060i | \(0.776832\pi\) | |||||||
\(912\) | −34.1343 | −1.13030 | ||||||||
\(913\) | 54.2256 | 1.79461 | ||||||||
\(914\) | −5.93610 | −0.196349 | ||||||||
\(915\) | 62.5913 | 2.06920 | ||||||||
\(916\) | 32.9624 | 1.08911 | ||||||||
\(917\) | −57.0582 | −1.88423 | ||||||||
\(918\) | −291.064 | −9.60654 | ||||||||
\(919\) | −20.0091 | −0.660040 | −0.330020 | − | 0.943974i | \(-0.607056\pi\) | ||||
−0.330020 | + | 0.943974i | \(0.607056\pi\) | |||||||
\(920\) | 132.487 | 4.36796 | ||||||||
\(921\) | −103.954 | −3.42540 | ||||||||
\(922\) | 33.1577 | 1.09199 | ||||||||
\(923\) | 3.60496 | 0.118659 | ||||||||
\(924\) | −426.890 | −14.0437 | ||||||||
\(925\) | 46.8620 | 1.54081 | ||||||||
\(926\) | −72.8723 | −2.39473 | ||||||||
\(927\) | 125.876 | 4.13430 | ||||||||
\(928\) | 2.74467 | 0.0900982 | ||||||||
\(929\) | 35.6807 | 1.17065 | 0.585323 | − | 0.810800i | \(-0.300968\pi\) | ||||
0.585323 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(930\) | −178.024 | −5.83765 | ||||||||
\(931\) | 15.7533 | 0.516292 | ||||||||
\(932\) | 40.6148 | 1.33038 | ||||||||
\(933\) | −51.0702 | −1.67196 | ||||||||
\(934\) | −84.6943 | −2.77128 | ||||||||
\(935\) | −125.901 | −4.11741 | ||||||||
\(936\) | 216.158 | 7.06533 | ||||||||
\(937\) | −49.3387 | −1.61182 | −0.805912 | − | 0.592036i | \(-0.798324\pi\) | ||||
−0.805912 | + | 0.592036i | \(0.798324\pi\) | |||||||
\(938\) | 52.8722 | 1.72634 | ||||||||
\(939\) | −21.2626 | −0.693880 | ||||||||
\(940\) | −110.965 | −3.61928 | ||||||||
\(941\) | 2.79330 | 0.0910590 | 0.0455295 | − | 0.998963i | \(-0.485502\pi\) | ||||
0.0455295 | + | 0.998963i | \(0.485502\pi\) | |||||||
\(942\) | −1.32746 | −0.0432511 | ||||||||
\(943\) | −8.81675 | −0.287113 | ||||||||
\(944\) | 3.88227 | 0.126357 | ||||||||
\(945\) | −288.430 | −9.38262 | ||||||||
\(946\) | 101.143 | 3.28843 | ||||||||
\(947\) | −19.3674 | −0.629357 | −0.314678 | − | 0.949198i | \(-0.601897\pi\) | ||||
−0.314678 | + | 0.949198i | \(0.601897\pi\) | |||||||
\(948\) | 162.505 | 5.27792 | ||||||||
\(949\) | 20.3664 | 0.661123 | ||||||||
\(950\) | −20.6337 | −0.669445 | ||||||||
\(951\) | −95.2231 | −3.08782 | ||||||||
\(952\) | 208.214 | 6.74826 | ||||||||
\(953\) | −3.64981 | −0.118229 | −0.0591145 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591145 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(954\) | 193.349 | 6.25992 | ||||||||
\(955\) | −32.9012 | −1.06466 | ||||||||
\(956\) | −121.524 | −3.93036 | ||||||||
\(957\) | 5.55800 | 0.179665 | ||||||||
\(958\) | 60.6640 | 1.95997 | ||||||||
\(959\) | −36.6082 | −1.18214 | ||||||||
\(960\) | −75.9705 | −2.45194 | ||||||||
\(961\) | 2.89015 | 0.0932305 | ||||||||
\(962\) | 61.0107 | 1.96706 | ||||||||
\(963\) | −68.2482 | −2.19927 | ||||||||
\(964\) | 31.5865 | 1.01733 | ||||||||
\(965\) | −11.2851 | −0.363279 | ||||||||
\(966\) | −212.546 | −6.83856 | ||||||||
\(967\) | −42.0133 | −1.35106 | −0.675528 | − | 0.737334i | \(-0.736084\pi\) | ||||
−0.675528 | + | 0.737334i | \(0.736084\pi\) | |||||||
\(968\) | −160.028 | −5.14350 | ||||||||
\(969\) | 23.1572 | 0.743915 | ||||||||
\(970\) | 53.9748 | 1.73303 | ||||||||
\(971\) | 0.606672 | 0.0194690 | 0.00973451 | − | 0.999953i | \(-0.496901\pi\) | ||||
0.00973451 | + | 0.999953i | \(0.496901\pi\) | |||||||
\(972\) | −309.115 | −9.91486 | ||||||||
\(973\) | −44.2986 | −1.42015 | ||||||||
\(974\) | 75.8503 | 2.43040 | ||||||||
\(975\) | 87.3753 | 2.79825 | ||||||||
\(976\) | −49.1052 | −1.57182 | ||||||||
\(977\) | −39.5593 | −1.26561 | −0.632807 | − | 0.774310i | \(-0.718097\pi\) | ||||
−0.632807 | + | 0.774310i | \(0.718097\pi\) | |||||||
\(978\) | 176.111 | 5.63142 | ||||||||
\(979\) | −28.9044 | −0.923788 | ||||||||
\(980\) | 238.580 | 7.62116 | ||||||||
\(981\) | −105.535 | −3.36948 | ||||||||
\(982\) | 47.7816 | 1.52477 | ||||||||
\(983\) | 32.9685 | 1.05153 | 0.525766 | − | 0.850629i | \(-0.323779\pi\) | ||||
0.525766 | + | 0.850629i | \(0.323779\pi\) | |||||||
\(984\) | 40.6592 | 1.29617 | ||||||||
\(985\) | −76.7586 | −2.44573 | ||||||||
\(986\) | −4.66755 | −0.148645 | ||||||||
\(987\) | 103.393 | 3.29103 | ||||||||
\(988\) | −18.9285 | −0.602196 | ||||||||
\(989\) | 35.4835 | 1.12831 | ||||||||
\(990\) | −435.558 | −13.8429 | ||||||||
\(991\) | 4.88552 | 0.155194 | 0.0775969 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775969 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(992\) | 55.7171 | 1.76902 | ||||||||
\(993\) | 19.4501 | 0.617232 | ||||||||
\(994\) | 12.0131 | 0.381034 | ||||||||
\(995\) | −41.1189 | −1.30356 | ||||||||
\(996\) | −151.051 | −4.78624 | ||||||||
\(997\) | −5.65953 | −0.179239 | −0.0896195 | − | 0.995976i | \(-0.528565\pi\) | ||||
−0.0896195 | + | 0.995976i | \(0.528565\pi\) | |||||||
\(998\) | −28.0151 | −0.886804 | ||||||||
\(999\) | −116.310 | −3.67989 |
(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 | 8023.2.a.c.1.11 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.11 | ✓ | 158 | 1.1 | even | 1 | trivial |