Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(0\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.78315 | −1.96799 | −0.983993 | − | 0.178205i | \(-0.942971\pi\) | ||||
−0.983993 | + | 0.178205i | \(0.942971\pi\) | |||||||
\(3\) | −1.65667 | −0.956480 | −0.478240 | − | 0.878229i | \(-0.658725\pi\) | ||||
−0.478240 | + | 0.878229i | \(0.658725\pi\) | |||||||
\(4\) | 5.74594 | 2.87297 | ||||||||
\(5\) | 3.71472 | 1.66127 | 0.830637 | − | 0.556814i | \(-0.187977\pi\) | ||||
0.830637 | + | 0.556814i | \(0.187977\pi\) | |||||||
\(6\) | 4.61077 | 1.88234 | ||||||||
\(7\) | 4.59606 | 1.73715 | 0.868573 | − | 0.495561i | \(-0.165038\pi\) | ||||
0.868573 | + | 0.495561i | \(0.165038\pi\) | |||||||
\(8\) | −10.4255 | −3.68598 | ||||||||
\(9\) | −0.255436 | −0.0851453 | ||||||||
\(10\) | −10.3386 | −3.26936 | ||||||||
\(11\) | −1.10295 | −0.332552 | −0.166276 | − | 0.986079i | \(-0.553174\pi\) | ||||
−0.166276 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(12\) | −9.51915 | −2.74794 | ||||||||
\(13\) | −2.71799 | −0.753836 | −0.376918 | − | 0.926247i | \(-0.623016\pi\) | ||||
−0.376918 | + | 0.926247i | \(0.623016\pi\) | |||||||
\(14\) | −12.7915 | −3.41868 | ||||||||
\(15\) | −6.15408 | −1.58898 | ||||||||
\(16\) | 17.5240 | 4.38099 | ||||||||
\(17\) | 6.21211 | 1.50666 | 0.753329 | − | 0.657643i | \(-0.228447\pi\) | ||||
0.753329 | + | 0.657643i | \(0.228447\pi\) | |||||||
\(18\) | 0.710918 | 0.167565 | ||||||||
\(19\) | 5.35804 | 1.22922 | 0.614609 | − | 0.788832i | \(-0.289314\pi\) | ||||
0.614609 | + | 0.788832i | \(0.289314\pi\) | |||||||
\(20\) | 21.3446 | 4.77279 | ||||||||
\(21\) | −7.61416 | −1.66155 | ||||||||
\(22\) | 3.06968 | 0.654459 | ||||||||
\(23\) | 5.61663 | 1.17115 | 0.585575 | − | 0.810618i | \(-0.300869\pi\) | ||||
0.585575 | + | 0.810618i | \(0.300869\pi\) | |||||||
\(24\) | 17.2717 | 3.52557 | ||||||||
\(25\) | 8.79915 | 1.75983 | ||||||||
\(26\) | 7.56460 | 1.48354 | ||||||||
\(27\) | 5.39319 | 1.03792 | ||||||||
\(28\) | 26.4087 | 4.99077 | ||||||||
\(29\) | −5.18366 | −0.962581 | −0.481291 | − | 0.876561i | \(-0.659832\pi\) | ||||
−0.481291 | + | 0.876561i | \(0.659832\pi\) | |||||||
\(30\) | 17.1277 | 3.12708 | ||||||||
\(31\) | −7.32311 | −1.31527 | −0.657635 | − | 0.753337i | \(-0.728443\pi\) | ||||
−0.657635 | + | 0.753337i | \(0.728443\pi\) | |||||||
\(32\) | −27.9208 | −4.93575 | ||||||||
\(33\) | 1.82723 | 0.318080 | ||||||||
\(34\) | −17.2893 | −2.96508 | ||||||||
\(35\) | 17.0731 | 2.88587 | ||||||||
\(36\) | −1.46772 | −0.244620 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −14.9122 | −2.41909 | ||||||||
\(39\) | 4.50283 | 0.721029 | ||||||||
\(40\) | −38.7280 | −6.12343 | ||||||||
\(41\) | 10.9705 | 1.71331 | 0.856653 | − | 0.515893i | \(-0.172540\pi\) | ||||
0.856653 | + | 0.515893i | \(0.172540\pi\) | |||||||
\(42\) | 21.1914 | 3.26990 | ||||||||
\(43\) | −9.15768 | −1.39653 | −0.698266 | − | 0.715838i | \(-0.746045\pi\) | ||||
−0.698266 | + | 0.715838i | \(0.746045\pi\) | |||||||
\(44\) | −6.33750 | −0.955414 | ||||||||
\(45\) | −0.948873 | −0.141450 | ||||||||
\(46\) | −15.6320 | −2.30481 | ||||||||
\(47\) | 3.92533 | 0.572569 | 0.286284 | − | 0.958145i | \(-0.407580\pi\) | ||||
0.286284 | + | 0.958145i | \(0.407580\pi\) | |||||||
\(48\) | −29.0315 | −4.19033 | ||||||||
\(49\) | 14.1237 | 2.01768 | ||||||||
\(50\) | −24.4894 | −3.46332 | ||||||||
\(51\) | −10.2914 | −1.44109 | ||||||||
\(52\) | −15.6174 | −2.16575 | ||||||||
\(53\) | 6.94608 | 0.954118 | 0.477059 | − | 0.878871i | \(-0.341703\pi\) | ||||
0.477059 | + | 0.878871i | \(0.341703\pi\) | |||||||
\(54\) | −15.0101 | −2.04261 | ||||||||
\(55\) | −4.09716 | −0.552461 | ||||||||
\(56\) | −47.9163 | −6.40309 | ||||||||
\(57\) | −8.87652 | −1.17572 | ||||||||
\(58\) | 14.4269 | 1.89435 | ||||||||
\(59\) | 7.51309 | 0.978120 | 0.489060 | − | 0.872250i | \(-0.337340\pi\) | ||||
0.489060 | + | 0.872250i | \(0.337340\pi\) | |||||||
\(60\) | −35.3610 | −4.56508 | ||||||||
\(61\) | −3.73546 | −0.478277 | −0.239138 | − | 0.970985i | \(-0.576865\pi\) | ||||
−0.239138 | + | 0.970985i | \(0.576865\pi\) | |||||||
\(62\) | 20.3813 | 2.58843 | ||||||||
\(63\) | −1.17400 | −0.147910 | ||||||||
\(64\) | 42.6600 | 5.33251 | ||||||||
\(65\) | −10.0966 | −1.25233 | ||||||||
\(66\) | −5.08546 | −0.625977 | ||||||||
\(67\) | −7.82975 | −0.956557 | −0.478278 | − | 0.878208i | \(-0.658739\pi\) | ||||
−0.478278 | + | 0.878208i | \(0.658739\pi\) | |||||||
\(68\) | 35.6945 | 4.32859 | ||||||||
\(69\) | −9.30492 | −1.12018 | ||||||||
\(70\) | −47.5170 | −5.67936 | ||||||||
\(71\) | 4.16909 | 0.494780 | 0.247390 | − | 0.968916i | \(-0.420427\pi\) | ||||
0.247390 | + | 0.968916i | \(0.420427\pi\) | |||||||
\(72\) | 2.66306 | 0.313844 | ||||||||
\(73\) | −13.3367 | −1.56095 | −0.780473 | − | 0.625189i | \(-0.785022\pi\) | ||||
−0.780473 | + | 0.625189i | \(0.785022\pi\) | |||||||
\(74\) | −2.78315 | −0.323535 | ||||||||
\(75\) | −14.5773 | −1.68324 | ||||||||
\(76\) | 30.7870 | 3.53151 | ||||||||
\(77\) | −5.06923 | −0.577692 | ||||||||
\(78\) | −12.5321 | −1.41898 | ||||||||
\(79\) | 0.552624 | 0.0621751 | 0.0310876 | − | 0.999517i | \(-0.490103\pi\) | ||||
0.0310876 | + | 0.999517i | \(0.490103\pi\) | |||||||
\(80\) | 65.0967 | 7.27803 | ||||||||
\(81\) | −8.16844 | −0.907605 | ||||||||
\(82\) | −30.5326 | −3.37176 | ||||||||
\(83\) | 10.1877 | 1.11824 | 0.559122 | − | 0.829086i | \(-0.311138\pi\) | ||||
0.559122 | + | 0.829086i | \(0.311138\pi\) | |||||||
\(84\) | −43.7505 | −4.77357 | ||||||||
\(85\) | 23.0763 | 2.50297 | ||||||||
\(86\) | 25.4872 | 2.74836 | ||||||||
\(87\) | 8.58763 | 0.920690 | ||||||||
\(88\) | 11.4989 | 1.22578 | ||||||||
\(89\) | −1.31198 | −0.139070 | −0.0695349 | − | 0.997580i | \(-0.522152\pi\) | ||||
−0.0695349 | + | 0.997580i | \(0.522152\pi\) | |||||||
\(90\) | 2.64086 | 0.278371 | ||||||||
\(91\) | −12.4921 | −1.30952 | ||||||||
\(92\) | 32.2729 | 3.36468 | ||||||||
\(93\) | 12.1320 | 1.25803 | ||||||||
\(94\) | −10.9248 | −1.12681 | ||||||||
\(95\) | 19.9036 | 2.04207 | ||||||||
\(96\) | 46.2557 | 4.72095 | ||||||||
\(97\) | 1.24177 | 0.126083 | 0.0630415 | − | 0.998011i | \(-0.479920\pi\) | ||||
0.0630415 | + | 0.998011i | \(0.479920\pi\) | |||||||
\(98\) | −39.3085 | −3.97076 | ||||||||
\(99\) | 0.281734 | 0.0283153 | ||||||||
\(100\) | 50.5594 | 5.05594 | ||||||||
\(101\) | 13.7793 | 1.37110 | 0.685548 | − | 0.728028i | \(-0.259563\pi\) | ||||
0.685548 | + | 0.728028i | \(0.259563\pi\) | |||||||
\(102\) | 28.6427 | 2.83605 | ||||||||
\(103\) | −11.8949 | −1.17204 | −0.586021 | − | 0.810296i | \(-0.699306\pi\) | ||||
−0.586021 | + | 0.810296i | \(0.699306\pi\) | |||||||
\(104\) | 28.3365 | 2.77863 | ||||||||
\(105\) | −28.2845 | −2.76028 | ||||||||
\(106\) | −19.3320 | −1.87769 | ||||||||
\(107\) | 2.12286 | 0.205224 | 0.102612 | − | 0.994721i | \(-0.467280\pi\) | ||||
0.102612 | + | 0.994721i | \(0.467280\pi\) | |||||||
\(108\) | 30.9890 | 2.98192 | ||||||||
\(109\) | 6.57732 | 0.629993 | 0.314997 | − | 0.949093i | \(-0.397997\pi\) | ||||
0.314997 | + | 0.949093i | \(0.397997\pi\) | |||||||
\(110\) | 11.4030 | 1.08724 | ||||||||
\(111\) | −1.65667 | −0.157244 | ||||||||
\(112\) | 80.5412 | 7.61043 | ||||||||
\(113\) | −15.3313 | −1.44225 | −0.721126 | − | 0.692804i | \(-0.756375\pi\) | ||||
−0.721126 | + | 0.692804i | \(0.756375\pi\) | |||||||
\(114\) | 24.7047 | 2.31381 | ||||||||
\(115\) | 20.8642 | 1.94560 | ||||||||
\(116\) | −29.7850 | −2.76547 | ||||||||
\(117\) | 0.694274 | 0.0641856 | ||||||||
\(118\) | −20.9101 | −1.92493 | ||||||||
\(119\) | 28.5512 | 2.61729 | ||||||||
\(120\) | 64.1595 | 5.85694 | ||||||||
\(121\) | −9.78350 | −0.889409 | ||||||||
\(122\) | 10.3964 | 0.941243 | ||||||||
\(123\) | −18.1745 | −1.63874 | ||||||||
\(124\) | −42.0782 | −3.77873 | ||||||||
\(125\) | 14.1128 | 1.26229 | ||||||||
\(126\) | 3.26742 | 0.291085 | ||||||||
\(127\) | 4.49641 | 0.398991 | 0.199496 | − | 0.979899i | \(-0.436070\pi\) | ||||
0.199496 | + | 0.979899i | \(0.436070\pi\) | |||||||
\(128\) | −62.8878 | −5.55855 | ||||||||
\(129\) | 15.1713 | 1.33576 | ||||||||
\(130\) | 28.1004 | 2.46457 | ||||||||
\(131\) | 5.97529 | 0.522064 | 0.261032 | − | 0.965330i | \(-0.415937\pi\) | ||||
0.261032 | + | 0.965330i | \(0.415937\pi\) | |||||||
\(132\) | 10.4992 | 0.913834 | ||||||||
\(133\) | 24.6259 | 2.13533 | ||||||||
\(134\) | 21.7914 | 1.88249 | ||||||||
\(135\) | 20.0342 | 1.72427 | ||||||||
\(136\) | −64.7646 | −5.55352 | ||||||||
\(137\) | −5.20287 | −0.444511 | −0.222256 | − | 0.974988i | \(-0.571342\pi\) | ||||
−0.222256 | + | 0.974988i | \(0.571342\pi\) | |||||||
\(138\) | 25.8970 | 2.20450 | ||||||||
\(139\) | 13.3120 | 1.12911 | 0.564557 | − | 0.825394i | \(-0.309047\pi\) | ||||
0.564557 | + | 0.825394i | \(0.309047\pi\) | |||||||
\(140\) | 98.1009 | 8.29104 | ||||||||
\(141\) | −6.50299 | −0.547651 | ||||||||
\(142\) | −11.6032 | −0.973721 | ||||||||
\(143\) | 2.99782 | 0.250690 | ||||||||
\(144\) | −4.47625 | −0.373021 | ||||||||
\(145\) | −19.2558 | −1.59911 | ||||||||
\(146\) | 37.1182 | 3.07192 | ||||||||
\(147\) | −23.3984 | −1.92987 | ||||||||
\(148\) | 5.74594 | 0.472314 | ||||||||
\(149\) | −6.24671 | −0.511751 | −0.255875 | − | 0.966710i | \(-0.582364\pi\) | ||||
−0.255875 | + | 0.966710i | \(0.582364\pi\) | |||||||
\(150\) | 40.5709 | 3.31260 | ||||||||
\(151\) | 16.3668 | 1.33191 | 0.665957 | − | 0.745990i | \(-0.268023\pi\) | ||||
0.665957 | + | 0.745990i | \(0.268023\pi\) | |||||||
\(152\) | −55.8604 | −4.53088 | ||||||||
\(153\) | −1.58680 | −0.128285 | ||||||||
\(154\) | 14.1084 | 1.13689 | ||||||||
\(155\) | −27.2033 | −2.18502 | ||||||||
\(156\) | 25.8730 | 2.07150 | ||||||||
\(157\) | 3.38381 | 0.270057 | 0.135029 | − | 0.990842i | \(-0.456887\pi\) | ||||
0.135029 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(158\) | −1.53804 | −0.122360 | ||||||||
\(159\) | −11.5074 | −0.912595 | ||||||||
\(160\) | −103.718 | −8.19964 | ||||||||
\(161\) | 25.8144 | 2.03446 | ||||||||
\(162\) | 22.7340 | 1.78615 | ||||||||
\(163\) | −1.00000 | −0.0783260 | ||||||||
\(164\) | 63.0359 | 4.92228 | ||||||||
\(165\) | 6.78765 | 0.528418 | ||||||||
\(166\) | −28.3539 | −2.20069 | ||||||||
\(167\) | −2.19759 | −0.170055 | −0.0850274 | − | 0.996379i | \(-0.527098\pi\) | ||||
−0.0850274 | + | 0.996379i | \(0.527098\pi\) | |||||||
\(168\) | 79.3817 | 6.12443 | ||||||||
\(169\) | −5.61251 | −0.431731 | ||||||||
\(170\) | −64.2248 | −4.92582 | ||||||||
\(171\) | −1.36864 | −0.104662 | ||||||||
\(172\) | −52.6195 | −4.01220 | ||||||||
\(173\) | 20.1207 | 1.52975 | 0.764873 | − | 0.644181i | \(-0.222802\pi\) | ||||
0.764873 | + | 0.644181i | \(0.222802\pi\) | |||||||
\(174\) | −23.9007 | −1.81191 | ||||||||
\(175\) | 40.4414 | 3.05708 | ||||||||
\(176\) | −19.3281 | −1.45691 | ||||||||
\(177\) | −12.4467 | −0.935553 | ||||||||
\(178\) | 3.65145 | 0.273688 | ||||||||
\(179\) | 20.3025 | 1.51748 | 0.758738 | − | 0.651395i | \(-0.225816\pi\) | ||||
0.758738 | + | 0.651395i | \(0.225816\pi\) | |||||||
\(180\) | −5.45217 | −0.406381 | ||||||||
\(181\) | −1.25951 | −0.0936190 | −0.0468095 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468095 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(182\) | 34.7673 | 2.57712 | ||||||||
\(183\) | 6.18844 | 0.457462 | ||||||||
\(184\) | −58.5564 | −4.31684 | ||||||||
\(185\) | 3.71472 | 0.273112 | ||||||||
\(186\) | −33.7652 | −2.47579 | ||||||||
\(187\) | −6.85166 | −0.501043 | ||||||||
\(188\) | 22.5547 | 1.64497 | ||||||||
\(189\) | 24.7874 | 1.80302 | ||||||||
\(190\) | −55.3948 | −4.01876 | ||||||||
\(191\) | 7.25715 | 0.525109 | 0.262554 | − | 0.964917i | \(-0.415435\pi\) | ||||
0.262554 | + | 0.964917i | \(0.415435\pi\) | |||||||
\(192\) | −70.6737 | −5.10044 | ||||||||
\(193\) | 24.6473 | 1.77416 | 0.887078 | − | 0.461621i | \(-0.152732\pi\) | ||||
0.887078 | + | 0.461621i | \(0.152732\pi\) | |||||||
\(194\) | −3.45605 | −0.248130 | ||||||||
\(195\) | 16.7267 | 1.19783 | ||||||||
\(196\) | 81.1541 | 5.79672 | ||||||||
\(197\) | −3.80347 | −0.270986 | −0.135493 | − | 0.990778i | \(-0.543262\pi\) | ||||
−0.135493 | + | 0.990778i | \(0.543262\pi\) | |||||||
\(198\) | −0.784108 | −0.0557241 | ||||||||
\(199\) | −13.7326 | −0.973481 | −0.486741 | − | 0.873547i | \(-0.661814\pi\) | ||||
−0.486741 | + | 0.873547i | \(0.661814\pi\) | |||||||
\(200\) | −91.7359 | −6.48671 | ||||||||
\(201\) | 12.9713 | 0.914928 | ||||||||
\(202\) | −38.3500 | −2.69830 | ||||||||
\(203\) | −23.8244 | −1.67214 | ||||||||
\(204\) | −59.1340 | −4.14021 | ||||||||
\(205\) | 40.7524 | 2.84627 | ||||||||
\(206\) | 33.1054 | 2.30656 | ||||||||
\(207\) | −1.43469 | −0.0997179 | ||||||||
\(208\) | −47.6301 | −3.30255 | ||||||||
\(209\) | −5.90966 | −0.408780 | ||||||||
\(210\) | 78.7200 | 5.43220 | ||||||||
\(211\) | −18.3345 | −1.26220 | −0.631099 | − | 0.775702i | \(-0.717396\pi\) | ||||
−0.631099 | + | 0.775702i | \(0.717396\pi\) | |||||||
\(212\) | 39.9118 | 2.74115 | ||||||||
\(213\) | −6.90682 | −0.473247 | ||||||||
\(214\) | −5.90824 | −0.403879 | ||||||||
\(215\) | −34.0182 | −2.32002 | ||||||||
\(216\) | −56.2269 | −3.82576 | ||||||||
\(217\) | −33.6574 | −2.28482 | ||||||||
\(218\) | −18.3057 | −1.23982 | ||||||||
\(219\) | 22.0946 | 1.49301 | ||||||||
\(220\) | −23.5420 | −1.58720 | ||||||||
\(221\) | −16.8845 | −1.13577 | ||||||||
\(222\) | 4.61077 | 0.309455 | ||||||||
\(223\) | −14.8830 | −0.996637 | −0.498319 | − | 0.866994i | \(-0.666049\pi\) | ||||
−0.498319 | + | 0.866994i | \(0.666049\pi\) | |||||||
\(224\) | −128.326 | −8.57413 | ||||||||
\(225\) | −2.24762 | −0.149841 | ||||||||
\(226\) | 42.6695 | 2.83833 | ||||||||
\(227\) | −22.2425 | −1.47629 | −0.738143 | − | 0.674644i | \(-0.764297\pi\) | ||||
−0.738143 | + | 0.674644i | \(0.764297\pi\) | |||||||
\(228\) | −51.0040 | −3.37782 | ||||||||
\(229\) | −3.57791 | −0.236435 | −0.118217 | − | 0.992988i | \(-0.537718\pi\) | ||||
−0.118217 | + | 0.992988i | \(0.537718\pi\) | |||||||
\(230\) | −58.0684 | −3.82891 | ||||||||
\(231\) | 8.39805 | 0.552551 | ||||||||
\(232\) | 54.0424 | 3.54806 | ||||||||
\(233\) | 1.56507 | 0.102531 | 0.0512655 | − | 0.998685i | \(-0.483675\pi\) | ||||
0.0512655 | + | 0.998685i | \(0.483675\pi\) | |||||||
\(234\) | −1.93227 | −0.126316 | ||||||||
\(235\) | 14.5815 | 0.951193 | ||||||||
\(236\) | 43.1698 | 2.81011 | ||||||||
\(237\) | −0.915518 | −0.0594693 | ||||||||
\(238\) | −79.4624 | −5.15078 | ||||||||
\(239\) | −15.3179 | −0.990830 | −0.495415 | − | 0.868656i | \(-0.664984\pi\) | ||||
−0.495415 | + | 0.868656i | \(0.664984\pi\) | |||||||
\(240\) | −107.844 | −6.96129 | ||||||||
\(241\) | 27.0631 | 1.74329 | 0.871645 | − | 0.490138i | \(-0.163054\pi\) | ||||
0.871645 | + | 0.490138i | \(0.163054\pi\) | |||||||
\(242\) | 27.2290 | 1.75034 | ||||||||
\(243\) | −2.64714 | −0.169814 | ||||||||
\(244\) | −21.4638 | −1.37408 | ||||||||
\(245\) | 52.4657 | 3.35191 | ||||||||
\(246\) | 50.5826 | 3.22503 | ||||||||
\(247\) | −14.5631 | −0.926630 | ||||||||
\(248\) | 76.3474 | 4.84806 | ||||||||
\(249\) | −16.8777 | −1.06958 | ||||||||
\(250\) | −39.2781 | −2.48416 | ||||||||
\(251\) | −28.5112 | −1.79961 | −0.899806 | − | 0.436290i | \(-0.856292\pi\) | ||||
−0.899806 | + | 0.436290i | \(0.856292\pi\) | |||||||
\(252\) | −6.74573 | −0.424941 | ||||||||
\(253\) | −6.19488 | −0.389469 | ||||||||
\(254\) | −12.5142 | −0.785210 | ||||||||
\(255\) | −38.2298 | −2.39404 | ||||||||
\(256\) | 89.7062 | 5.60664 | ||||||||
\(257\) | −3.33751 | −0.208188 | −0.104094 | − | 0.994567i | \(-0.533194\pi\) | ||||
−0.104094 | + | 0.994567i | \(0.533194\pi\) | |||||||
\(258\) | −42.2240 | −2.62875 | ||||||||
\(259\) | 4.59606 | 0.285585 | ||||||||
\(260\) | −58.0144 | −3.59790 | ||||||||
\(261\) | 1.32409 | 0.0819593 | ||||||||
\(262\) | −16.6302 | −1.02741 | ||||||||
\(263\) | −13.9384 | −0.859480 | −0.429740 | − | 0.902953i | \(-0.641395\pi\) | ||||
−0.429740 | + | 0.902953i | \(0.641395\pi\) | |||||||
\(264\) | −19.0498 | −1.17244 | ||||||||
\(265\) | 25.8028 | 1.58505 | ||||||||
\(266\) | −68.5375 | −4.20231 | ||||||||
\(267\) | 2.17352 | 0.133018 | ||||||||
\(268\) | −44.9893 | −2.74816 | ||||||||
\(269\) | 7.90192 | 0.481788 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(270\) | −55.7583 | −3.39334 | ||||||||
\(271\) | 13.8091 | 0.838845 | 0.419422 | − | 0.907791i | \(-0.362233\pi\) | ||||
0.419422 | + | 0.907791i | \(0.362233\pi\) | |||||||
\(272\) | 108.861 | 6.60066 | ||||||||
\(273\) | 20.6952 | 1.25253 | ||||||||
\(274\) | 14.4804 | 0.874792 | ||||||||
\(275\) | −9.70504 | −0.585236 | ||||||||
\(276\) | −53.4656 | −3.21825 | ||||||||
\(277\) | 12.4308 | 0.746894 | 0.373447 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373447 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(278\) | −37.0495 | −2.22208 | ||||||||
\(279\) | 1.87059 | 0.111989 | ||||||||
\(280\) | −177.996 | −10.6373 | ||||||||
\(281\) | 0.422354 | 0.0251955 | 0.0125978 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125978 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(282\) | 18.0988 | 1.07777 | ||||||||
\(283\) | 4.48772 | 0.266767 | 0.133384 | − | 0.991064i | \(-0.457416\pi\) | ||||
0.133384 | + | 0.991064i | \(0.457416\pi\) | |||||||
\(284\) | 23.9554 | 1.42149 | ||||||||
\(285\) | −32.9738 | −1.95320 | ||||||||
\(286\) | −8.34338 | −0.493355 | ||||||||
\(287\) | 50.4211 | 2.97626 | ||||||||
\(288\) | 7.13199 | 0.420256 | ||||||||
\(289\) | 21.5904 | 1.27002 | ||||||||
\(290\) | 53.5920 | 3.14703 | ||||||||
\(291\) | −2.05721 | −0.120596 | ||||||||
\(292\) | −76.6321 | −4.48455 | ||||||||
\(293\) | 2.60823 | 0.152374 | 0.0761871 | − | 0.997094i | \(-0.475725\pi\) | ||||
0.0761871 | + | 0.997094i | \(0.475725\pi\) | |||||||
\(294\) | 65.1213 | 3.79795 | ||||||||
\(295\) | 27.9090 | 1.62493 | ||||||||
\(296\) | −10.4255 | −0.605972 | ||||||||
\(297\) | −5.94843 | −0.345163 | ||||||||
\(298\) | 17.3856 | 1.00712 | ||||||||
\(299\) | −15.2660 | −0.882855 | ||||||||
\(300\) | −83.7604 | −4.83591 | ||||||||
\(301\) | −42.0892 | −2.42598 | ||||||||
\(302\) | −45.5514 | −2.62119 | ||||||||
\(303\) | −22.8278 | −1.31143 | ||||||||
\(304\) | 93.8942 | 5.38520 | ||||||||
\(305\) | −13.8762 | −0.794549 | ||||||||
\(306\) | 4.41630 | 0.252463 | ||||||||
\(307\) | −34.7728 | −1.98459 | −0.992295 | − | 0.123894i | \(-0.960462\pi\) | ||||
−0.992295 | + | 0.123894i | \(0.960462\pi\) | |||||||
\(308\) | −29.1275 | −1.65969 | ||||||||
\(309\) | 19.7060 | 1.12104 | ||||||||
\(310\) | 75.7110 | 4.30010 | ||||||||
\(311\) | −11.7094 | −0.663980 | −0.331990 | − | 0.943283i | \(-0.607720\pi\) | ||||
−0.331990 | + | 0.943283i | \(0.607720\pi\) | |||||||
\(312\) | −46.9444 | −2.65770 | ||||||||
\(313\) | 31.8928 | 1.80269 | 0.901345 | − | 0.433103i | \(-0.142581\pi\) | ||||
0.901345 | + | 0.433103i | \(0.142581\pi\) | |||||||
\(314\) | −9.41766 | −0.531469 | ||||||||
\(315\) | −4.36108 | −0.245719 | ||||||||
\(316\) | 3.17535 | 0.178627 | ||||||||
\(317\) | −13.3177 | −0.747998 | −0.373999 | − | 0.927429i | \(-0.622014\pi\) | ||||
−0.373999 | + | 0.927429i | \(0.622014\pi\) | |||||||
\(318\) | 32.0268 | 1.79598 | ||||||||
\(319\) | 5.71733 | 0.320109 | ||||||||
\(320\) | 158.470 | 8.85875 | ||||||||
\(321\) | −3.51688 | −0.196293 | ||||||||
\(322\) | −71.8453 | −4.00378 | ||||||||
\(323\) | 33.2848 | 1.85201 | ||||||||
\(324\) | −46.9354 | −2.60752 | ||||||||
\(325\) | −23.9160 | −1.32662 | ||||||||
\(326\) | 2.78315 | 0.154145 | ||||||||
\(327\) | −10.8965 | −0.602576 | ||||||||
\(328\) | −114.373 | −6.31522 | ||||||||
\(329\) | 18.0410 | 0.994635 | ||||||||
\(330\) | −18.8911 | −1.03992 | ||||||||
\(331\) | 19.9617 | 1.09720 | 0.548598 | − | 0.836086i | \(-0.315162\pi\) | ||||
0.548598 | + | 0.836086i | \(0.315162\pi\) | |||||||
\(332\) | 58.5378 | 3.21268 | ||||||||
\(333\) | −0.255436 | −0.0139978 | ||||||||
\(334\) | 6.11623 | 0.334665 | ||||||||
\(335\) | −29.0854 | −1.58910 | ||||||||
\(336\) | −133.430 | −7.27922 | ||||||||
\(337\) | −21.4557 | −1.16877 | −0.584383 | − | 0.811478i | \(-0.698663\pi\) | ||||
−0.584383 | + | 0.811478i | \(0.698663\pi\) | |||||||
\(338\) | 15.6205 | 0.849641 | ||||||||
\(339\) | 25.3990 | 1.37949 | ||||||||
\(340\) | 132.595 | 7.19097 | ||||||||
\(341\) | 8.07704 | 0.437396 | ||||||||
\(342\) | 3.80913 | 0.205974 | ||||||||
\(343\) | 32.7411 | 1.76785 | ||||||||
\(344\) | 95.4737 | 5.14760 | ||||||||
\(345\) | −34.5652 | −1.86093 | ||||||||
\(346\) | −55.9989 | −3.01052 | ||||||||
\(347\) | −11.4970 | −0.617190 | −0.308595 | − | 0.951194i | \(-0.599859\pi\) | ||||
−0.308595 | + | 0.951194i | \(0.599859\pi\) | |||||||
\(348\) | 49.3440 | 2.64512 | ||||||||
\(349\) | 1.04098 | 0.0557225 | 0.0278613 | − | 0.999612i | \(-0.491130\pi\) | ||||
0.0278613 | + | 0.999612i | \(0.491130\pi\) | |||||||
\(350\) | −112.555 | −6.01630 | ||||||||
\(351\) | −14.6587 | −0.782422 | ||||||||
\(352\) | 30.7953 | 1.64140 | ||||||||
\(353\) | 15.3784 | 0.818508 | 0.409254 | − | 0.912420i | \(-0.365789\pi\) | ||||
0.409254 | + | 0.912420i | \(0.365789\pi\) | |||||||
\(354\) | 34.6411 | 1.84116 | ||||||||
\(355\) | 15.4870 | 0.821965 | ||||||||
\(356\) | −7.53857 | −0.399544 | ||||||||
\(357\) | −47.3000 | −2.50338 | ||||||||
\(358\) | −56.5048 | −2.98637 | ||||||||
\(359\) | 9.50535 | 0.501673 | 0.250836 | − | 0.968029i | \(-0.419294\pi\) | ||||
0.250836 | + | 0.968029i | \(0.419294\pi\) | |||||||
\(360\) | 9.89251 | 0.521381 | ||||||||
\(361\) | 9.70860 | 0.510979 | ||||||||
\(362\) | 3.50542 | 0.184241 | ||||||||
\(363\) | 16.2081 | 0.850702 | ||||||||
\(364\) | −71.7786 | −3.76222 | ||||||||
\(365\) | −49.5422 | −2.59316 | ||||||||
\(366\) | −17.2234 | −0.900280 | ||||||||
\(367\) | 25.9002 | 1.35198 | 0.675990 | − | 0.736911i | \(-0.263716\pi\) | ||||
0.675990 | + | 0.736911i | \(0.263716\pi\) | |||||||
\(368\) | 98.4258 | 5.13080 | ||||||||
\(369\) | −2.80226 | −0.145880 | ||||||||
\(370\) | −10.3386 | −0.537480 | ||||||||
\(371\) | 31.9246 | 1.65744 | ||||||||
\(372\) | 69.7098 | 3.61428 | ||||||||
\(373\) | −4.34848 | −0.225156 | −0.112578 | − | 0.993643i | \(-0.535911\pi\) | ||||
−0.112578 | + | 0.993643i | \(0.535911\pi\) | |||||||
\(374\) | 19.0692 | 0.986046 | ||||||||
\(375\) | −23.3803 | −1.20735 | ||||||||
\(376\) | −40.9237 | −2.11048 | ||||||||
\(377\) | 14.0892 | 0.725629 | ||||||||
\(378\) | −68.9872 | −3.54832 | ||||||||
\(379\) | 3.73722 | 0.191968 | 0.0959839 | − | 0.995383i | \(-0.469400\pi\) | ||||
0.0959839 | + | 0.995383i | \(0.469400\pi\) | |||||||
\(380\) | 114.365 | 5.86681 | ||||||||
\(381\) | −7.44907 | −0.381628 | ||||||||
\(382\) | −20.1978 | −1.03341 | ||||||||
\(383\) | −3.61440 | −0.184687 | −0.0923437 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923437 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(384\) | 104.184 | 5.31664 | ||||||||
\(385\) | −18.8308 | −0.959705 | ||||||||
\(386\) | −68.5974 | −3.49151 | ||||||||
\(387\) | 2.33920 | 0.118908 | ||||||||
\(388\) | 7.13516 | 0.362233 | ||||||||
\(389\) | 19.6635 | 0.996980 | 0.498490 | − | 0.866895i | \(-0.333888\pi\) | ||||
0.498490 | + | 0.866895i | \(0.333888\pi\) | |||||||
\(390\) | −46.5531 | −2.35731 | ||||||||
\(391\) | 34.8912 | 1.76452 | ||||||||
\(392\) | −147.247 | −7.43712 | ||||||||
\(393\) | −9.89910 | −0.499344 | ||||||||
\(394\) | 10.5856 | 0.533297 | ||||||||
\(395\) | 2.05285 | 0.103290 | ||||||||
\(396\) | 1.61882 | 0.0813490 | ||||||||
\(397\) | −36.3959 | −1.82666 | −0.913328 | − | 0.407225i | \(-0.866497\pi\) | ||||
−0.913328 | + | 0.407225i | \(0.866497\pi\) | |||||||
\(398\) | 38.2200 | 1.91580 | ||||||||
\(399\) | −40.7970 | −2.04240 | ||||||||
\(400\) | 154.196 | 7.70981 | ||||||||
\(401\) | 35.1406 | 1.75484 | 0.877418 | − | 0.479726i | \(-0.159264\pi\) | ||||
0.877418 | + | 0.479726i | \(0.159264\pi\) | |||||||
\(402\) | −36.1012 | −1.80057 | ||||||||
\(403\) | 19.9042 | 0.991498 | ||||||||
\(404\) | 79.1753 | 3.93912 | ||||||||
\(405\) | −30.3435 | −1.50778 | ||||||||
\(406\) | 66.3069 | 3.29076 | ||||||||
\(407\) | −1.10295 | −0.0546713 | ||||||||
\(408\) | 107.294 | 5.31183 | ||||||||
\(409\) | 15.3877 | 0.760875 | 0.380438 | − | 0.924807i | \(-0.375773\pi\) | ||||
0.380438 | + | 0.924807i | \(0.375773\pi\) | |||||||
\(410\) | −113.420 | −5.60142 | ||||||||
\(411\) | 8.61945 | 0.425166 | ||||||||
\(412\) | −68.3476 | −3.36724 | ||||||||
\(413\) | 34.5306 | 1.69914 | ||||||||
\(414\) | 3.99296 | 0.196243 | ||||||||
\(415\) | 37.8444 | 1.85771 | ||||||||
\(416\) | 75.8887 | 3.72075 | ||||||||
\(417\) | −22.0537 | −1.07997 | ||||||||
\(418\) | 16.4475 | 0.804473 | ||||||||
\(419\) | 20.8875 | 1.02042 | 0.510210 | − | 0.860050i | \(-0.329568\pi\) | ||||
0.510210 | + | 0.860050i | \(0.329568\pi\) | |||||||
\(420\) | −162.521 | −7.93021 | ||||||||
\(421\) | −10.1900 | −0.496630 | −0.248315 | − | 0.968679i | \(-0.579877\pi\) | ||||
−0.248315 | + | 0.968679i | \(0.579877\pi\) | |||||||
\(422\) | 51.0277 | 2.48399 | ||||||||
\(423\) | −1.00267 | −0.0487515 | ||||||||
\(424\) | −72.4166 | −3.51686 | ||||||||
\(425\) | 54.6613 | 2.65146 | ||||||||
\(426\) | 19.2227 | 0.931345 | ||||||||
\(427\) | −17.1684 | −0.830837 | ||||||||
\(428\) | 12.1978 | 0.589604 | ||||||||
\(429\) | −4.96640 | −0.239780 | ||||||||
\(430\) | 94.6779 | 4.56578 | ||||||||
\(431\) | 19.0243 | 0.916367 | 0.458183 | − | 0.888858i | \(-0.348500\pi\) | ||||
0.458183 | + | 0.888858i | \(0.348500\pi\) | |||||||
\(432\) | 94.5102 | 4.54712 | ||||||||
\(433\) | −15.3699 | −0.738628 | −0.369314 | − | 0.929305i | \(-0.620407\pi\) | ||||
−0.369314 | + | 0.929305i | \(0.620407\pi\) | |||||||
\(434\) | 93.6738 | 4.49649 | ||||||||
\(435\) | 31.9006 | 1.52952 | ||||||||
\(436\) | 37.7929 | 1.80995 | ||||||||
\(437\) | 30.0942 | 1.43960 | ||||||||
\(438\) | −61.4926 | −2.93823 | ||||||||
\(439\) | −12.3834 | −0.591026 | −0.295513 | − | 0.955339i | \(-0.595491\pi\) | ||||
−0.295513 | + | 0.955339i | \(0.595491\pi\) | |||||||
\(440\) | 42.7151 | 2.03636 | ||||||||
\(441\) | −3.60771 | −0.171796 | ||||||||
\(442\) | 46.9921 | 2.23519 | ||||||||
\(443\) | −38.2137 | −1.81559 | −0.907795 | − | 0.419414i | \(-0.862235\pi\) | ||||
−0.907795 | + | 0.419414i | \(0.862235\pi\) | |||||||
\(444\) | −9.51915 | −0.451759 | ||||||||
\(445\) | −4.87365 | −0.231033 | ||||||||
\(446\) | 41.4216 | 1.96137 | ||||||||
\(447\) | 10.3488 | 0.489479 | ||||||||
\(448\) | 196.068 | 9.26334 | ||||||||
\(449\) | 2.35482 | 0.111131 | 0.0555654 | − | 0.998455i | \(-0.482304\pi\) | ||||
0.0555654 | + | 0.998455i | \(0.482304\pi\) | |||||||
\(450\) | 6.25547 | 0.294886 | ||||||||
\(451\) | −12.0999 | −0.569764 | ||||||||
\(452\) | −88.0930 | −4.14355 | ||||||||
\(453\) | −27.1145 | −1.27395 | ||||||||
\(454\) | 61.9043 | 2.90531 | ||||||||
\(455\) | −46.4045 | −2.17548 | ||||||||
\(456\) | 92.5425 | 4.33370 | ||||||||
\(457\) | −28.2696 | −1.32240 | −0.661198 | − | 0.750211i | \(-0.729952\pi\) | ||||
−0.661198 | + | 0.750211i | \(0.729952\pi\) | |||||||
\(458\) | 9.95787 | 0.465301 | ||||||||
\(459\) | 33.5031 | 1.56379 | ||||||||
\(460\) | 119.885 | 5.58965 | ||||||||
\(461\) | −29.3839 | −1.36854 | −0.684272 | − | 0.729227i | \(-0.739880\pi\) | ||||
−0.684272 | + | 0.729227i | \(0.739880\pi\) | |||||||
\(462\) | −23.3731 | −1.08741 | ||||||||
\(463\) | 34.8385 | 1.61908 | 0.809542 | − | 0.587062i | \(-0.199715\pi\) | ||||
0.809542 | + | 0.587062i | \(0.199715\pi\) | |||||||
\(464\) | −90.8383 | −4.21706 | ||||||||
\(465\) | 45.0670 | 2.08993 | ||||||||
\(466\) | −4.35583 | −0.201780 | ||||||||
\(467\) | −18.6112 | −0.861224 | −0.430612 | − | 0.902537i | \(-0.641702\pi\) | ||||
−0.430612 | + | 0.902537i | \(0.641702\pi\) | |||||||
\(468\) | 3.98926 | 0.184403 | ||||||||
\(469\) | −35.9860 | −1.66168 | ||||||||
\(470\) | −40.5826 | −1.87194 | ||||||||
\(471\) | −5.60587 | −0.258305 | ||||||||
\(472\) | −78.3279 | −3.60534 | ||||||||
\(473\) | 10.1005 | 0.464420 | ||||||||
\(474\) | 2.54803 | 0.117035 | ||||||||
\(475\) | 47.1462 | 2.16322 | ||||||||
\(476\) | 164.054 | 7.51939 | ||||||||
\(477\) | −1.77428 | −0.0812387 | ||||||||
\(478\) | 42.6320 | 1.94994 | ||||||||
\(479\) | −20.9626 | −0.957807 | −0.478904 | − | 0.877867i | \(-0.658966\pi\) | ||||
−0.478904 | + | 0.877867i | \(0.658966\pi\) | |||||||
\(480\) | 171.827 | 7.84279 | ||||||||
\(481\) | −2.71799 | −0.123930 | ||||||||
\(482\) | −75.3208 | −3.43077 | ||||||||
\(483\) | −42.7660 | −1.94592 | ||||||||
\(484\) | −56.2154 | −2.55525 | ||||||||
\(485\) | 4.61285 | 0.209459 | ||||||||
\(486\) | 7.36739 | 0.334191 | ||||||||
\(487\) | −22.7736 | −1.03197 | −0.515985 | − | 0.856598i | \(-0.672574\pi\) | ||||
−0.515985 | + | 0.856598i | \(0.672574\pi\) | |||||||
\(488\) | 38.9442 | 1.76292 | ||||||||
\(489\) | 1.65667 | 0.0749173 | ||||||||
\(490\) | −146.020 | −6.59652 | ||||||||
\(491\) | −4.39156 | −0.198188 | −0.0990941 | − | 0.995078i | \(-0.531594\pi\) | ||||
−0.0990941 | + | 0.995078i | \(0.531594\pi\) | |||||||
\(492\) | −104.430 | −4.70806 | ||||||||
\(493\) | −32.2015 | −1.45028 | ||||||||
\(494\) | 40.5314 | 1.82359 | ||||||||
\(495\) | 1.04656 | 0.0470394 | ||||||||
\(496\) | −128.330 | −5.76219 | ||||||||
\(497\) | 19.1614 | 0.859505 | ||||||||
\(498\) | 46.9731 | 2.10492 | ||||||||
\(499\) | 16.2976 | 0.729579 | 0.364789 | − | 0.931090i | \(-0.381141\pi\) | ||||
0.364789 | + | 0.931090i | \(0.381141\pi\) | |||||||
\(500\) | 81.0913 | 3.62651 | ||||||||
\(501\) | 3.64069 | 0.162654 | ||||||||
\(502\) | 79.3511 | 3.54161 | ||||||||
\(503\) | −9.85567 | −0.439442 | −0.219721 | − | 0.975563i | \(-0.570515\pi\) | ||||
−0.219721 | + | 0.975563i | \(0.570515\pi\) | |||||||
\(504\) | 12.2396 | 0.545193 | ||||||||
\(505\) | 51.1864 | 2.27776 | ||||||||
\(506\) | 17.2413 | 0.766469 | ||||||||
\(507\) | 9.29808 | 0.412942 | ||||||||
\(508\) | 25.8361 | 1.14629 | ||||||||
\(509\) | −40.5627 | −1.79791 | −0.898956 | − | 0.438039i | \(-0.855673\pi\) | ||||
−0.898956 | + | 0.438039i | \(0.855673\pi\) | |||||||
\(510\) | 106.399 | 4.71145 | ||||||||
\(511\) | −61.2964 | −2.71159 | ||||||||
\(512\) | −123.891 | −5.47524 | ||||||||
\(513\) | 28.8969 | 1.27583 | ||||||||
\(514\) | 9.28881 | 0.409712 | ||||||||
\(515\) | −44.1863 | −1.94708 | ||||||||
\(516\) | 87.1733 | 3.83759 | ||||||||
\(517\) | −4.32945 | −0.190409 | ||||||||
\(518\) | −12.7915 | −0.562028 | ||||||||
\(519\) | −33.3334 | −1.46317 | ||||||||
\(520\) | 105.262 | 4.61606 | ||||||||
\(521\) | 7.83018 | 0.343046 | 0.171523 | − | 0.985180i | \(-0.445131\pi\) | ||||
0.171523 | + | 0.985180i | \(0.445131\pi\) | |||||||
\(522\) | −3.68515 | −0.161295 | ||||||||
\(523\) | 8.73951 | 0.382152 | 0.191076 | − | 0.981575i | \(-0.438802\pi\) | ||||
0.191076 | + | 0.981575i | \(0.438802\pi\) | |||||||
\(524\) | 34.3337 | 1.49987 | ||||||||
\(525\) | −66.9982 | −2.92404 | ||||||||
\(526\) | 38.7928 | 1.69144 | ||||||||
\(527\) | −45.4920 | −1.98166 | ||||||||
\(528\) | 32.0203 | 1.39351 | ||||||||
\(529\) | 8.54659 | 0.371591 | ||||||||
\(530\) | −71.8131 | −3.11936 | ||||||||
\(531\) | −1.91911 | −0.0832824 | ||||||||
\(532\) | 141.499 | 6.13475 | ||||||||
\(533\) | −29.8178 | −1.29155 | ||||||||
\(534\) | −6.04925 | −0.261777 | ||||||||
\(535\) | 7.88582 | 0.340934 | ||||||||
\(536\) | 81.6294 | 3.52585 | ||||||||
\(537\) | −33.6345 | −1.45144 | ||||||||
\(538\) | −21.9922 | −0.948153 | ||||||||
\(539\) | −15.5778 | −0.670983 | ||||||||
\(540\) | 115.115 | 4.95378 | ||||||||
\(541\) | 19.7353 | 0.848488 | 0.424244 | − | 0.905548i | \(-0.360540\pi\) | ||||
0.424244 | + | 0.905548i | \(0.360540\pi\) | |||||||
\(542\) | −38.4329 | −1.65084 | ||||||||
\(543\) | 2.08660 | 0.0895447 | ||||||||
\(544\) | −173.447 | −7.43650 | ||||||||
\(545\) | 24.4329 | 1.04659 | ||||||||
\(546\) | −57.5980 | −2.46497 | ||||||||
\(547\) | −11.0721 | −0.473409 | −0.236705 | − | 0.971582i | \(-0.576067\pi\) | ||||
−0.236705 | + | 0.971582i | \(0.576067\pi\) | |||||||
\(548\) | −29.8954 | −1.27707 | ||||||||
\(549\) | 0.954171 | 0.0407230 | ||||||||
\(550\) | 27.0106 | 1.15174 | ||||||||
\(551\) | −27.7743 | −1.18322 | ||||||||
\(552\) | 97.0088 | 4.12897 | ||||||||
\(553\) | 2.53989 | 0.108007 | ||||||||
\(554\) | −34.5968 | −1.46988 | ||||||||
\(555\) | −6.15408 | −0.261226 | ||||||||
\(556\) | 76.4903 | 3.24391 | ||||||||
\(557\) | −20.4802 | −0.867773 | −0.433887 | − | 0.900967i | \(-0.642858\pi\) | ||||
−0.433887 | + | 0.900967i | \(0.642858\pi\) | |||||||
\(558\) | −5.20613 | −0.220393 | ||||||||
\(559\) | 24.8905 | 1.05276 | ||||||||
\(560\) | 299.188 | 12.6430 | ||||||||
\(561\) | 11.3510 | 0.479238 | ||||||||
\(562\) | −1.17548 | −0.0495845 | ||||||||
\(563\) | −22.8590 | −0.963392 | −0.481696 | − | 0.876338i | \(-0.659979\pi\) | ||||
−0.481696 | + | 0.876338i | \(0.659979\pi\) | |||||||
\(564\) | −37.3658 | −1.57338 | ||||||||
\(565\) | −56.9517 | −2.39597 | ||||||||
\(566\) | −12.4900 | −0.524995 | ||||||||
\(567\) | −37.5426 | −1.57664 | ||||||||
\(568\) | −43.4650 | −1.82375 | ||||||||
\(569\) | 35.1365 | 1.47300 | 0.736499 | − | 0.676438i | \(-0.236477\pi\) | ||||
0.736499 | + | 0.676438i | \(0.236477\pi\) | |||||||
\(570\) | 91.7711 | 3.84387 | ||||||||
\(571\) | −31.8750 | −1.33393 | −0.666965 | − | 0.745089i | \(-0.732407\pi\) | ||||
−0.666965 | + | 0.745089i | \(0.732407\pi\) | |||||||
\(572\) | 17.2253 | 0.720225 | ||||||||
\(573\) | −12.0227 | −0.502256 | ||||||||
\(574\) | −140.330 | −5.85725 | ||||||||
\(575\) | 49.4216 | 2.06102 | ||||||||
\(576\) | −10.8969 | −0.454038 | ||||||||
\(577\) | −6.06522 | −0.252499 | −0.126249 | − | 0.991999i | \(-0.540294\pi\) | ||||
−0.126249 | + | 0.991999i | \(0.540294\pi\) | |||||||
\(578\) | −60.0893 | −2.49938 | ||||||||
\(579\) | −40.8326 | −1.69694 | ||||||||
\(580\) | −110.643 | −4.59420 | ||||||||
\(581\) | 46.8232 | 1.94255 | ||||||||
\(582\) | 5.72554 | 0.237331 | ||||||||
\(583\) | −7.66120 | −0.317294 | ||||||||
\(584\) | 139.043 | 5.75362 | ||||||||
\(585\) | 2.57903 | 0.106630 | ||||||||
\(586\) | −7.25910 | −0.299871 | ||||||||
\(587\) | −40.4724 | −1.67047 | −0.835236 | − | 0.549891i | \(-0.814669\pi\) | ||||
−0.835236 | + | 0.549891i | \(0.814669\pi\) | |||||||
\(588\) | −134.446 | −5.54445 | ||||||||
\(589\) | −39.2375 | −1.61675 | ||||||||
\(590\) | −77.6751 | −3.19783 | ||||||||
\(591\) | 6.30111 | 0.259193 | ||||||||
\(592\) | 17.5240 | 0.720231 | ||||||||
\(593\) | 8.81828 | 0.362123 | 0.181062 | − | 0.983472i | \(-0.442047\pi\) | ||||
0.181062 | + | 0.983472i | \(0.442047\pi\) | |||||||
\(594\) | 16.5554 | 0.679276 | ||||||||
\(595\) | 106.060 | 4.34803 | ||||||||
\(596\) | −35.8933 | −1.47025 | ||||||||
\(597\) | 22.7505 | 0.931116 | ||||||||
\(598\) | 42.4876 | 1.73745 | ||||||||
\(599\) | 17.4213 | 0.711815 | 0.355907 | − | 0.934521i | \(-0.384172\pi\) | ||||
0.355907 | + | 0.934521i | \(0.384172\pi\) | |||||||
\(600\) | 151.976 | 6.20441 | ||||||||
\(601\) | 30.6270 | 1.24930 | 0.624651 | − | 0.780904i | \(-0.285241\pi\) | ||||
0.624651 | + | 0.780904i | \(0.285241\pi\) | |||||||
\(602\) | 117.141 | 4.77430 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 94.0429 | 3.82655 | ||||||||
\(605\) | −36.3430 | −1.47755 | ||||||||
\(606\) | 63.5334 | 2.58087 | ||||||||
\(607\) | 12.4350 | 0.504720 | 0.252360 | − | 0.967633i | \(-0.418793\pi\) | ||||
0.252360 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(608\) | −149.601 | −6.06712 | ||||||||
\(609\) | 39.4692 | 1.59937 | ||||||||
\(610\) | 38.6196 | 1.56366 | ||||||||
\(611\) | −10.6690 | −0.431623 | ||||||||
\(612\) | −9.11765 | −0.368559 | ||||||||
\(613\) | −8.84033 | −0.357057 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(614\) | 96.7782 | 3.90565 | ||||||||
\(615\) | −67.5134 | −2.72240 | ||||||||
\(616\) | 52.8494 | 2.12936 | ||||||||
\(617\) | 19.7128 | 0.793609 | 0.396805 | − | 0.917903i | \(-0.370119\pi\) | ||||
0.396805 | + | 0.917903i | \(0.370119\pi\) | |||||||
\(618\) | −54.8448 | −2.20618 | ||||||||
\(619\) | −4.42275 | −0.177765 | −0.0888827 | − | 0.996042i | \(-0.528330\pi\) | ||||
−0.0888827 | + | 0.996042i | \(0.528330\pi\) | |||||||
\(620\) | −156.309 | −6.27751 | ||||||||
\(621\) | 30.2916 | 1.21556 | ||||||||
\(622\) | 32.5891 | 1.30670 | ||||||||
\(623\) | −6.02994 | −0.241585 | ||||||||
\(624\) | 78.9074 | 3.15883 | ||||||||
\(625\) | 8.42932 | 0.337173 | ||||||||
\(626\) | −88.7626 | −3.54767 | ||||||||
\(627\) | 9.79037 | 0.390990 | ||||||||
\(628\) | 19.4432 | 0.775867 | ||||||||
\(629\) | 6.21211 | 0.247693 | ||||||||
\(630\) | 12.1375 | 0.483571 | ||||||||
\(631\) | −48.3101 | −1.92319 | −0.961597 | − | 0.274466i | \(-0.911499\pi\) | ||||
−0.961597 | + | 0.274466i | \(0.911499\pi\) | |||||||
\(632\) | −5.76141 | −0.229176 | ||||||||
\(633\) | 30.3743 | 1.20727 | ||||||||
\(634\) | 37.0653 | 1.47205 | ||||||||
\(635\) | 16.7029 | 0.662834 | ||||||||
\(636\) | −66.1208 | −2.62186 | ||||||||
\(637\) | −38.3882 | −1.52100 | ||||||||
\(638\) | −15.9122 | −0.629970 | ||||||||
\(639\) | −1.06494 | −0.0421282 | ||||||||
\(640\) | −233.610 | −9.23427 | ||||||||
\(641\) | 6.08065 | 0.240171 | 0.120086 | − | 0.992764i | \(-0.461683\pi\) | ||||
0.120086 | + | 0.992764i | \(0.461683\pi\) | |||||||
\(642\) | 9.78801 | 0.386302 | ||||||||
\(643\) | −25.5937 | −1.00932 | −0.504659 | − | 0.863319i | \(-0.668382\pi\) | ||||
−0.504659 | + | 0.863319i | \(0.668382\pi\) | |||||||
\(644\) | 148.328 | 5.84494 | ||||||||
\(645\) | 56.3571 | 2.21906 | ||||||||
\(646\) | −92.6366 | −3.64474 | ||||||||
\(647\) | −14.4522 | −0.568175 | −0.284088 | − | 0.958798i | \(-0.591691\pi\) | ||||
−0.284088 | + | 0.958798i | \(0.591691\pi\) | |||||||
\(648\) | 85.1604 | 3.34542 | ||||||||
\(649\) | −8.28657 | −0.325276 | ||||||||
\(650\) | 66.5620 | 2.61078 | ||||||||
\(651\) | 55.7593 | 2.18538 | ||||||||
\(652\) | −5.74594 | −0.225028 | ||||||||
\(653\) | 19.9622 | 0.781183 | 0.390591 | − | 0.920564i | \(-0.372271\pi\) | ||||
0.390591 | + | 0.920564i | \(0.372271\pi\) | |||||||
\(654\) | 30.3265 | 1.18586 | ||||||||
\(655\) | 22.1965 | 0.867291 | ||||||||
\(656\) | 192.247 | 7.50598 | ||||||||
\(657\) | 3.40668 | 0.132907 | ||||||||
\(658\) | −50.2110 | −1.95743 | ||||||||
\(659\) | 39.3158 | 1.53153 | 0.765764 | − | 0.643122i | \(-0.222361\pi\) | ||||
0.765764 | + | 0.643122i | \(0.222361\pi\) | |||||||
\(660\) | 39.0014 | 1.51813 | ||||||||
\(661\) | 16.6710 | 0.648429 | 0.324214 | − | 0.945984i | \(-0.394900\pi\) | ||||
0.324214 | + | 0.945984i | \(0.394900\pi\) | |||||||
\(662\) | −55.5565 | −2.15927 | ||||||||
\(663\) | 27.9721 | 1.08635 | ||||||||
\(664\) | −106.212 | −4.12183 | ||||||||
\(665\) | 91.4782 | 3.54737 | ||||||||
\(666\) | 0.710918 | 0.0275475 | ||||||||
\(667\) | −29.1147 | −1.12733 | ||||||||
\(668\) | −12.6272 | −0.488562 | ||||||||
\(669\) | 24.6562 | 0.953264 | ||||||||
\(670\) | 80.9490 | 3.12733 | ||||||||
\(671\) | 4.12003 | 0.159052 | ||||||||
\(672\) | 212.594 | 8.20098 | ||||||||
\(673\) | 13.5098 | 0.520766 | 0.260383 | − | 0.965505i | \(-0.416151\pi\) | ||||
0.260383 | + | 0.965505i | \(0.416151\pi\) | |||||||
\(674\) | 59.7145 | 2.30012 | ||||||||
\(675\) | 47.4555 | 1.82656 | ||||||||
\(676\) | −32.2491 | −1.24035 | ||||||||
\(677\) | 0.844641 | 0.0324622 | 0.0162311 | − | 0.999868i | \(-0.494833\pi\) | ||||
0.0162311 | + | 0.999868i | \(0.494833\pi\) | |||||||
\(678\) | −70.6894 | −2.71481 | ||||||||
\(679\) | 5.70726 | 0.219025 | ||||||||
\(680\) | −240.582 | −9.22592 | ||||||||
\(681\) | 36.8485 | 1.41204 | ||||||||
\(682\) | −22.4796 | −0.860790 | ||||||||
\(683\) | −14.4323 | −0.552238 | −0.276119 | − | 0.961123i | \(-0.589048\pi\) | ||||
−0.276119 | + | 0.961123i | \(0.589048\pi\) | |||||||
\(684\) | −7.86411 | −0.300692 | ||||||||
\(685\) | −19.3272 | −0.738455 | ||||||||
\(686\) | −91.1234 | −3.47911 | ||||||||
\(687\) | 5.92742 | 0.226145 | ||||||||
\(688\) | −160.479 | −6.11820 | ||||||||
\(689\) | −18.8794 | −0.719249 | ||||||||
\(690\) | 96.2003 | 3.66228 | ||||||||
\(691\) | 9.69410 | 0.368781 | 0.184390 | − | 0.982853i | \(-0.440969\pi\) | ||||
0.184390 | + | 0.982853i | \(0.440969\pi\) | |||||||
\(692\) | 115.612 | 4.39492 | ||||||||
\(693\) | 1.29486 | 0.0491878 | ||||||||
\(694\) | 31.9978 | 1.21462 | ||||||||
\(695\) | 49.4506 | 1.87577 | ||||||||
\(696\) | −89.5306 | −3.39365 | ||||||||
\(697\) | 68.1501 | 2.58137 | ||||||||
\(698\) | −2.89722 | −0.109661 | ||||||||
\(699\) | −2.59281 | −0.0980690 | ||||||||
\(700\) | 232.374 | 8.78291 | ||||||||
\(701\) | 24.0594 | 0.908709 | 0.454355 | − | 0.890821i | \(-0.349870\pi\) | ||||
0.454355 | + | 0.890821i | \(0.349870\pi\) | |||||||
\(702\) | 40.7973 | 1.53980 | ||||||||
\(703\) | 5.35804 | 0.202082 | ||||||||
\(704\) | −47.0520 | −1.77334 | ||||||||
\(705\) | −24.1568 | −0.909798 | ||||||||
\(706\) | −42.8004 | −1.61081 | ||||||||
\(707\) | 63.3306 | 2.38179 | ||||||||
\(708\) | −71.5182 | −2.68782 | ||||||||
\(709\) | −27.6717 | −1.03923 | −0.519617 | − | 0.854399i | \(-0.673925\pi\) | ||||
−0.519617 | + | 0.854399i | \(0.673925\pi\) | |||||||
\(710\) | −43.1027 | −1.61762 | ||||||||
\(711\) | −0.141160 | −0.00529392 | ||||||||
\(712\) | 13.6781 | 0.512609 | ||||||||
\(713\) | −41.1312 | −1.54038 | ||||||||
\(714\) | 131.643 | 4.92662 | ||||||||
\(715\) | 11.1361 | 0.416465 | ||||||||
\(716\) | 116.657 | 4.35967 | ||||||||
\(717\) | 25.3767 | 0.947710 | ||||||||
\(718\) | −26.4548 | −0.987286 | ||||||||
\(719\) | 34.0154 | 1.26856 | 0.634280 | − | 0.773104i | \(-0.281297\pi\) | ||||
0.634280 | + | 0.773104i | \(0.281297\pi\) | |||||||
\(720\) | −16.6280 | −0.619690 | ||||||||
\(721\) | −54.6697 | −2.03601 | ||||||||
\(722\) | −27.0205 | −1.00560 | ||||||||
\(723\) | −44.8347 | −1.66742 | ||||||||
\(724\) | −7.23710 | −0.268965 | ||||||||
\(725\) | −45.6118 | −1.69398 | ||||||||
\(726\) | −45.1095 | −1.67417 | ||||||||
\(727\) | 21.5273 | 0.798405 | 0.399202 | − | 0.916863i | \(-0.369287\pi\) | ||||
0.399202 | + | 0.916863i | \(0.369287\pi\) | |||||||
\(728\) | 130.236 | 4.82688 | ||||||||
\(729\) | 28.8908 | 1.07003 | ||||||||
\(730\) | 137.884 | 5.10330 | ||||||||
\(731\) | −56.8885 | −2.10410 | ||||||||
\(732\) | 35.5584 | 1.31428 | ||||||||
\(733\) | 40.3845 | 1.49164 | 0.745818 | − | 0.666149i | \(-0.232059\pi\) | ||||
0.745818 | + | 0.666149i | \(0.232059\pi\) | |||||||
\(734\) | −72.0842 | −2.66068 | ||||||||
\(735\) | −86.9185 | −3.20604 | ||||||||
\(736\) | −156.821 | −5.78051 | ||||||||
\(737\) | 8.63584 | 0.318105 | ||||||||
\(738\) | 7.79913 | 0.287090 | ||||||||
\(739\) | −20.2544 | −0.745069 | −0.372535 | − | 0.928018i | \(-0.621511\pi\) | ||||
−0.372535 | + | 0.928018i | \(0.621511\pi\) | |||||||
\(740\) | 21.3446 | 0.784642 | ||||||||
\(741\) | 24.1263 | 0.886303 | ||||||||
\(742\) | −88.8510 | −3.26182 | ||||||||
\(743\) | 21.0539 | 0.772393 | 0.386197 | − | 0.922417i | \(-0.373789\pi\) | ||||
0.386197 | + | 0.922417i | \(0.373789\pi\) | |||||||
\(744\) | −126.483 | −4.63708 | ||||||||
\(745\) | −23.2048 | −0.850158 | ||||||||
\(746\) | 12.1025 | 0.443104 | ||||||||
\(747\) | −2.60230 | −0.0952132 | ||||||||
\(748\) | −39.3693 | −1.43948 | ||||||||
\(749\) | 9.75677 | 0.356505 | ||||||||
\(750\) | 65.0709 | 2.37605 | ||||||||
\(751\) | 20.0221 | 0.730618 | 0.365309 | − | 0.930886i | \(-0.380963\pi\) | ||||
0.365309 | + | 0.930886i | \(0.380963\pi\) | |||||||
\(752\) | 68.7874 | 2.50842 | ||||||||
\(753\) | 47.2337 | 1.72129 | ||||||||
\(754\) | −39.2123 | −1.42803 | ||||||||
\(755\) | 60.7982 | 2.21267 | ||||||||
\(756\) | 142.427 | 5.18002 | ||||||||
\(757\) | 22.6342 | 0.822653 | 0.411327 | − | 0.911488i | \(-0.365066\pi\) | ||||
0.411327 | + | 0.911488i | \(0.365066\pi\) | |||||||
\(758\) | −10.4012 | −0.377790 | ||||||||
\(759\) | 10.2629 | 0.372519 | ||||||||
\(760\) | −207.506 | −7.52703 | ||||||||
\(761\) | −9.07442 | −0.328948 | −0.164474 | − | 0.986381i | \(-0.552593\pi\) | ||||
−0.164474 | + | 0.986381i | \(0.552593\pi\) | |||||||
\(762\) | 20.7319 | 0.751038 | ||||||||
\(763\) | 30.2297 | 1.09439 | ||||||||
\(764\) | 41.6992 | 1.50862 | ||||||||
\(765\) | −5.89451 | −0.213116 | ||||||||
\(766\) | 10.0594 | 0.363462 | ||||||||
\(767\) | −20.4205 | −0.737343 | ||||||||
\(768\) | −148.614 | −5.36264 | ||||||||
\(769\) | −38.1413 | −1.37541 | −0.687706 | − | 0.725989i | \(-0.741382\pi\) | ||||
−0.687706 | + | 0.725989i | \(0.741382\pi\) | |||||||
\(770\) | 52.4089 | 1.88869 | ||||||||
\(771\) | 5.52916 | 0.199128 | ||||||||
\(772\) | 141.622 | 5.09710 | ||||||||
\(773\) | 42.4191 | 1.52571 | 0.762854 | − | 0.646570i | \(-0.223797\pi\) | ||||
0.762854 | + | 0.646570i | \(0.223797\pi\) | |||||||
\(774\) | −6.51035 | −0.234010 | ||||||||
\(775\) | −64.4372 | −2.31465 | ||||||||
\(776\) | −12.9462 | −0.464740 | ||||||||
\(777\) | −7.61416 | −0.273156 | ||||||||
\(778\) | −54.7266 | −1.96204 | ||||||||
\(779\) | 58.7805 | 2.10603 | ||||||||
\(780\) | 96.1109 | 3.44132 | ||||||||
\(781\) | −4.59831 | −0.164540 | ||||||||
\(782\) | −97.1075 | −3.47256 | ||||||||
\(783\) | −27.9565 | −0.999083 | ||||||||
\(784\) | 247.504 | 8.83942 | ||||||||
\(785\) | 12.5699 | 0.448639 | ||||||||
\(786\) | 27.5507 | 0.982702 | ||||||||
\(787\) | 24.9380 | 0.888943 | 0.444472 | − | 0.895793i | \(-0.353391\pi\) | ||||
0.444472 | + | 0.895793i | \(0.353391\pi\) | |||||||
\(788\) | −21.8545 | −0.778536 | ||||||||
\(789\) | 23.0914 | 0.822076 | ||||||||
\(790\) | −5.71338 | −0.203273 | ||||||||
\(791\) | −70.4637 | −2.50540 | ||||||||
\(792\) | −2.93722 | −0.104370 | ||||||||
\(793\) | 10.1530 | 0.360542 | ||||||||
\(794\) | 101.295 | 3.59483 | ||||||||
\(795\) | −42.7467 | −1.51607 | ||||||||
\(796\) | −78.9070 | −2.79678 | ||||||||
\(797\) | −39.9954 | −1.41671 | −0.708355 | − | 0.705857i | \(-0.750562\pi\) | ||||
−0.708355 | + | 0.705857i | \(0.750562\pi\) | |||||||
\(798\) | 113.544 | 4.01942 | ||||||||
\(799\) | 24.3846 | 0.862666 | ||||||||
\(800\) | −245.680 | −8.68609 | ||||||||
\(801\) | 0.335127 | 0.0118411 | ||||||||
\(802\) | −97.8016 | −3.45349 | ||||||||
\(803\) | 14.7098 | 0.519096 | ||||||||
\(804\) | 74.5326 | 2.62856 | ||||||||
\(805\) | 95.8932 | 3.37979 | ||||||||
\(806\) | −55.3964 | −1.95125 | ||||||||
\(807\) | −13.0909 | −0.460821 | ||||||||
\(808\) | −143.657 | −5.05383 | ||||||||
\(809\) | −21.9738 | −0.772559 | −0.386280 | − | 0.922382i | \(-0.626240\pi\) | ||||
−0.386280 | + | 0.922382i | \(0.626240\pi\) | |||||||
\(810\) | 84.4506 | 2.96729 | ||||||||
\(811\) | 14.4954 | 0.509004 | 0.254502 | − | 0.967072i | \(-0.418088\pi\) | ||||
0.254502 | + | 0.967072i | \(0.418088\pi\) | |||||||
\(812\) | −136.894 | −4.80402 | ||||||||
\(813\) | −22.8772 | −0.802339 | ||||||||
\(814\) | 3.06968 | 0.107592 | ||||||||
\(815\) | −3.71472 | −0.130121 | ||||||||
\(816\) | −180.347 | −6.31340 | ||||||||
\(817\) | −49.0672 | −1.71664 | ||||||||
\(818\) | −42.8265 | −1.49739 | ||||||||
\(819\) | 3.19092 | 0.111500 | ||||||||
\(820\) | 234.161 | 8.17725 | ||||||||
\(821\) | −35.2799 | −1.23128 | −0.615638 | − | 0.788029i | \(-0.711102\pi\) | ||||
−0.615638 | + | 0.788029i | \(0.711102\pi\) | |||||||
\(822\) | −23.9893 | −0.836721 | ||||||||
\(823\) | −22.3090 | −0.777644 | −0.388822 | − | 0.921313i | \(-0.627118\pi\) | ||||
−0.388822 | + | 0.921313i | \(0.627118\pi\) | |||||||
\(824\) | 124.011 | 4.32013 | ||||||||
\(825\) | 16.0781 | 0.559767 | ||||||||
\(826\) | −96.1039 | −3.34388 | ||||||||
\(827\) | −12.4067 | −0.431424 | −0.215712 | − | 0.976457i | \(-0.569207\pi\) | ||||
−0.215712 | + | 0.976457i | \(0.569207\pi\) | |||||||
\(828\) | −8.24365 | −0.286487 | ||||||||
\(829\) | 1.80212 | 0.0625902 | 0.0312951 | − | 0.999510i | \(-0.490037\pi\) | ||||
0.0312951 | + | 0.999510i | \(0.490037\pi\) | |||||||
\(830\) | −105.327 | −3.65595 | ||||||||
\(831\) | −20.5937 | −0.714389 | ||||||||
\(832\) | −115.950 | −4.01984 | ||||||||
\(833\) | 87.7382 | 3.03995 | ||||||||
\(834\) | 61.3789 | 2.12538 | ||||||||
\(835\) | −8.16344 | −0.282507 | ||||||||
\(836\) | −33.9566 | −1.17441 | ||||||||
\(837\) | −39.4949 | −1.36515 | ||||||||
\(838\) | −58.1330 | −2.00817 | ||||||||
\(839\) | 12.2814 | 0.424003 | 0.212001 | − | 0.977269i | \(-0.432002\pi\) | ||||
0.212001 | + | 0.977269i | \(0.432002\pi\) | |||||||
\(840\) | 294.881 | 10.1744 | ||||||||
\(841\) | −2.12968 | −0.0734371 | ||||||||
\(842\) | 28.3603 | 0.977362 | ||||||||
\(843\) | −0.699703 | −0.0240990 | ||||||||
\(844\) | −105.349 | −3.62626 | ||||||||
\(845\) | −20.8489 | −0.717224 | ||||||||
\(846\) | 2.79059 | 0.0959424 | ||||||||
\(847\) | −44.9655 | −1.54503 | ||||||||
\(848\) | 121.723 | 4.17999 | ||||||||
\(849\) | −7.43469 | −0.255158 | ||||||||
\(850\) | −152.131 | −5.21805 | ||||||||
\(851\) | 5.61663 | 0.192536 | ||||||||
\(852\) | −39.6862 | −1.35963 | ||||||||
\(853\) | −11.0752 | −0.379209 | −0.189605 | − | 0.981861i | \(-0.560721\pi\) | ||||
−0.189605 | + | 0.981861i | \(0.560721\pi\) | |||||||
\(854\) | 47.7823 | 1.63508 | ||||||||
\(855\) | −5.08410 | −0.173873 | ||||||||
\(856\) | −22.1319 | −0.756453 | ||||||||
\(857\) | −9.86369 | −0.336937 | −0.168469 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168469 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(858\) | 13.8223 | 0.471884 | ||||||||
\(859\) | 5.01395 | 0.171074 | 0.0855368 | − | 0.996335i | \(-0.472739\pi\) | ||||
0.0855368 | + | 0.996335i | \(0.472739\pi\) | |||||||
\(860\) | −195.467 | −6.66536 | ||||||||
\(861\) | −83.5312 | −2.84674 | ||||||||
\(862\) | −52.9474 | −1.80340 | ||||||||
\(863\) | −13.4895 | −0.459188 | −0.229594 | − | 0.973286i | \(-0.573740\pi\) | ||||
−0.229594 | + | 0.973286i | \(0.573740\pi\) | |||||||
\(864\) | −150.582 | −5.12292 | ||||||||
\(865\) | 74.7427 | 2.54133 | ||||||||
\(866\) | 42.7767 | 1.45361 | ||||||||
\(867\) | −35.7681 | −1.21475 | ||||||||
\(868\) | −193.394 | −6.56421 | ||||||||
\(869\) | −0.609518 | −0.0206765 | ||||||||
\(870\) | −88.7844 | −3.01007 | ||||||||
\(871\) | 21.2812 | 0.721087 | ||||||||
\(872\) | −68.5721 | −2.32214 | ||||||||
\(873\) | −0.317194 | −0.0107354 | ||||||||
\(874\) | −83.7567 | −2.83311 | ||||||||
\(875\) | 64.8632 | 2.19278 | ||||||||
\(876\) | 126.954 | 4.28939 | ||||||||
\(877\) | −24.8006 | −0.837457 | −0.418728 | − | 0.908112i | \(-0.637524\pi\) | ||||
−0.418728 | + | 0.908112i | \(0.637524\pi\) | |||||||
\(878\) | 34.4648 | 1.16313 | ||||||||
\(879\) | −4.32098 | −0.145743 | ||||||||
\(880\) | −71.7985 | −2.42033 | ||||||||
\(881\) | −19.3182 | −0.650846 | −0.325423 | − | 0.945569i | \(-0.605507\pi\) | ||||
−0.325423 | + | 0.945569i | \(0.605507\pi\) | |||||||
\(882\) | 10.0408 | 0.338092 | ||||||||
\(883\) | 9.84949 | 0.331462 | 0.165731 | − | 0.986171i | \(-0.447002\pi\) | ||||
0.165731 | + | 0.986171i | \(0.447002\pi\) | |||||||
\(884\) | −97.0173 | −3.26305 | ||||||||
\(885\) | −46.2361 | −1.55421 | ||||||||
\(886\) | 106.355 | 3.57306 | ||||||||
\(887\) | 14.6169 | 0.490786 | 0.245393 | − | 0.969424i | \(-0.421083\pi\) | ||||
0.245393 | + | 0.969424i | \(0.421083\pi\) | |||||||
\(888\) | 17.2717 | 0.579600 | ||||||||
\(889\) | 20.6657 | 0.693106 | ||||||||
\(890\) | 13.5641 | 0.454670 | ||||||||
\(891\) | 9.00940 | 0.301826 | ||||||||
\(892\) | −85.5167 | −2.86331 | ||||||||
\(893\) | 21.0321 | 0.703812 | ||||||||
\(894\) | −28.8022 | −0.963289 | ||||||||
\(895\) | 75.4180 | 2.52094 | ||||||||
\(896\) | −289.036 | −9.65600 | ||||||||
\(897\) | 25.2907 | 0.844433 | ||||||||
\(898\) | −6.55382 | −0.218704 | ||||||||
\(899\) | 37.9605 | 1.26605 | ||||||||
\(900\) | −12.9147 | −0.430490 | ||||||||
\(901\) | 43.1499 | 1.43753 | ||||||||
\(902\) | 33.6760 | 1.12129 | ||||||||
\(903\) | 69.7280 | 2.32040 | ||||||||
\(904\) | 159.837 | 5.31611 | ||||||||
\(905\) | −4.67875 | −0.155527 | ||||||||
\(906\) | 75.4638 | 2.50712 | ||||||||
\(907\) | −28.6113 | −0.950021 | −0.475011 | − | 0.879980i | \(-0.657556\pi\) | ||||
−0.475011 | + | 0.879980i | \(0.657556\pi\) | |||||||
\(908\) | −127.804 | −4.24133 | ||||||||
\(909\) | −3.51974 | −0.116742 | ||||||||
\(910\) | 129.151 | 4.28131 | ||||||||
\(911\) | −31.3655 | −1.03919 | −0.519593 | − | 0.854414i | \(-0.673916\pi\) | ||||
−0.519593 | + | 0.854414i | \(0.673916\pi\) | |||||||
\(912\) | −155.552 | −5.15084 | ||||||||
\(913\) | −11.2365 | −0.371875 | ||||||||
\(914\) | 78.6786 | 2.60246 | ||||||||
\(915\) | 22.9883 | 0.759970 | ||||||||
\(916\) | −20.5585 | −0.679271 | ||||||||
\(917\) | 27.4628 | 0.906901 | ||||||||
\(918\) | −93.2443 | −3.07752 | ||||||||
\(919\) | 2.89897 | 0.0956282 | 0.0478141 | − | 0.998856i | \(-0.484775\pi\) | ||||
0.0478141 | + | 0.998856i | \(0.484775\pi\) | |||||||
\(920\) | −217.521 | −7.17145 | ||||||||
\(921\) | 57.6072 | 1.89822 | ||||||||
\(922\) | 81.7799 | 2.69328 | ||||||||
\(923\) | −11.3316 | −0.372983 | ||||||||
\(924\) | 48.2547 | 1.58746 | ||||||||
\(925\) | 8.79915 | 0.289314 | ||||||||
\(926\) | −96.9610 | −3.18634 | ||||||||
\(927\) | 3.03839 | 0.0997939 | ||||||||
\(928\) | 144.732 | 4.75107 | ||||||||
\(929\) | −30.2605 | −0.992816 | −0.496408 | − | 0.868089i | \(-0.665348\pi\) | ||||
−0.496408 | + | 0.868089i | \(0.665348\pi\) | |||||||
\(930\) | −125.428 | −4.11296 | ||||||||
\(931\) | 75.6755 | 2.48017 | ||||||||
\(932\) | 8.99280 | 0.294569 | ||||||||
\(933\) | 19.3987 | 0.635084 | ||||||||
\(934\) | 51.7978 | 1.69488 | ||||||||
\(935\) | −25.4520 | −0.832370 | ||||||||
\(936\) | −7.23817 | −0.236587 | ||||||||
\(937\) | 35.2479 | 1.15150 | 0.575749 | − | 0.817627i | \(-0.304711\pi\) | ||||
0.575749 | + | 0.817627i | \(0.304711\pi\) | |||||||
\(938\) | 100.155 | 3.27016 | ||||||||
\(939\) | −52.8360 | −1.72424 | ||||||||
\(940\) | 83.7846 | 2.73275 | ||||||||
\(941\) | 47.7928 | 1.55800 | 0.779000 | − | 0.627024i | \(-0.215727\pi\) | ||||
0.779000 | + | 0.627024i | \(0.215727\pi\) | |||||||
\(942\) | 15.6020 | 0.508340 | ||||||||
\(943\) | 61.6174 | 2.00654 | ||||||||
\(944\) | 131.659 | 4.28514 | ||||||||
\(945\) | 92.0783 | 2.99531 | ||||||||
\(946\) | −28.1112 | −0.913973 | ||||||||
\(947\) | 7.37722 | 0.239728 | 0.119864 | − | 0.992790i | \(-0.461754\pi\) | ||||
0.119864 | + | 0.992790i | \(0.461754\pi\) | |||||||
\(948\) | −5.26051 | −0.170854 | ||||||||
\(949\) | 36.2492 | 1.17670 | ||||||||
\(950\) | −131.215 | −4.25718 | ||||||||
\(951\) | 22.0631 | 0.715446 | ||||||||
\(952\) | −297.662 | −9.64727 | ||||||||
\(953\) | 51.8927 | 1.68097 | 0.840484 | − | 0.541836i | \(-0.182271\pi\) | ||||
0.840484 | + | 0.541836i | \(0.182271\pi\) | |||||||
\(954\) | 4.93809 | 0.159877 | ||||||||
\(955\) | 26.9583 | 0.872349 | ||||||||
\(956\) | −88.0156 | −2.84663 | ||||||||
\(957\) | −9.47174 | −0.306178 | ||||||||
\(958\) | 58.3422 | 1.88495 | ||||||||
\(959\) | −23.9127 | −0.772181 | ||||||||
\(960\) | −262.533 | −8.47322 | ||||||||
\(961\) | 22.6280 | 0.729935 | ||||||||
\(962\) | 7.56460 | 0.243892 | ||||||||
\(963\) | −0.542254 | −0.0174739 | ||||||||
\(964\) | 155.503 | 5.00842 | ||||||||
\(965\) | 91.5580 | 2.94736 | ||||||||
\(966\) | 119.024 | 3.82954 | ||||||||
\(967\) | 11.6437 | 0.374436 | 0.187218 | − | 0.982318i | \(-0.440053\pi\) | ||||
0.187218 | + | 0.982318i | \(0.440053\pi\) | |||||||
\(968\) | 101.998 | 3.27835 | ||||||||
\(969\) | −55.1419 | −1.77141 | ||||||||
\(970\) | −12.8383 | −0.412212 | ||||||||
\(971\) | −40.9212 | −1.31322 | −0.656611 | − | 0.754229i | \(-0.728011\pi\) | ||||
−0.656611 | + | 0.754229i | \(0.728011\pi\) | |||||||
\(972\) | −15.2103 | −0.487870 | ||||||||
\(973\) | 61.1829 | 1.96143 | ||||||||
\(974\) | 63.3824 | 2.03090 | ||||||||
\(975\) | 39.6211 | 1.26889 | ||||||||
\(976\) | −65.4601 | −2.09533 | ||||||||
\(977\) | 33.5888 | 1.07460 | 0.537300 | − | 0.843391i | \(-0.319444\pi\) | ||||
0.537300 | + | 0.843391i | \(0.319444\pi\) | |||||||
\(978\) | −4.61077 | −0.147436 | ||||||||
\(979\) | 1.44705 | 0.0462480 | ||||||||
\(980\) | 301.465 | 9.62995 | ||||||||
\(981\) | −1.68008 | −0.0536410 | ||||||||
\(982\) | 12.2224 | 0.390032 | ||||||||
\(983\) | −6.19480 | −0.197583 | −0.0987917 | − | 0.995108i | \(-0.531498\pi\) | ||||
−0.0987917 | + | 0.995108i | \(0.531498\pi\) | |||||||
\(984\) | 189.479 | 6.04038 | ||||||||
\(985\) | −14.1288 | −0.450182 | ||||||||
\(986\) | 89.6217 | 2.85414 | ||||||||
\(987\) | −29.8881 | −0.951349 | ||||||||
\(988\) | −83.6789 | −2.66218 | ||||||||
\(989\) | −51.4353 | −1.63555 | ||||||||
\(990\) | −2.91274 | −0.0925730 | ||||||||
\(991\) | −40.8533 | −1.29775 | −0.648873 | − | 0.760897i | \(-0.724759\pi\) | ||||
−0.648873 | + | 0.760897i | \(0.724759\pi\) | |||||||
\(992\) | 204.467 | 6.49185 | ||||||||
\(993\) | −33.0700 | −1.04945 | ||||||||
\(994\) | −53.3291 | −1.69149 | ||||||||
\(995\) | −51.0129 | −1.61722 | ||||||||
\(996\) | −96.9780 | −3.07287 | ||||||||
\(997\) | −55.9686 | −1.77254 | −0.886272 | − | 0.463164i | \(-0.846714\pi\) | ||||
−0.886272 | + | 0.463164i | \(0.846714\pi\) | |||||||
\(998\) | −45.3586 | −1.43580 | ||||||||
\(999\) | 5.39319 | 0.170633 |
(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 | 6031.2.a.e.1.1 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.e.1.1 | ✓ | 134 | 1.1 | even | 1 | trivial |