Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, 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("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.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: | \(64.1438279437\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62862 | −1.85871 | −0.929356 | − | 0.369184i | \(-0.879637\pi\) | ||||
−0.929356 | + | 0.369184i | \(0.879637\pi\) | |||||||
\(3\) | 3.02798 | 1.74821 | 0.874103 | − | 0.485741i | \(-0.161450\pi\) | ||||
0.874103 | + | 0.485741i | \(0.161450\pi\) | |||||||
\(4\) | 4.90963 | 2.45481 | ||||||||
\(5\) | 2.24361 | 1.00337 | 0.501687 | − | 0.865049i | \(-0.332713\pi\) | ||||
0.501687 | + | 0.865049i | \(0.332713\pi\) | |||||||
\(6\) | −7.95940 | −3.24941 | ||||||||
\(7\) | −3.55148 | −1.34233 | −0.671166 | − | 0.741307i | \(-0.734206\pi\) | ||||
−0.671166 | + | 0.741307i | \(0.734206\pi\) | |||||||
\(8\) | −7.64830 | −2.70408 | ||||||||
\(9\) | 6.16867 | 2.05622 | ||||||||
\(10\) | −5.89760 | −1.86498 | ||||||||
\(11\) | 4.02450 | 1.21343 | 0.606717 | − | 0.794918i | \(-0.292486\pi\) | ||||
0.606717 | + | 0.794918i | \(0.292486\pi\) | |||||||
\(12\) | 14.8663 | 4.29152 | ||||||||
\(13\) | −2.03015 | −0.563063 | −0.281532 | − | 0.959552i | \(-0.590842\pi\) | ||||
−0.281532 | + | 0.959552i | \(0.590842\pi\) | |||||||
\(14\) | 9.33547 | 2.49501 | ||||||||
\(15\) | 6.79362 | 1.75410 | ||||||||
\(16\) | 10.2852 | 2.57130 | ||||||||
\(17\) | −7.13861 | −1.73137 | −0.865683 | − | 0.500592i | \(-0.833116\pi\) | ||||
−0.865683 | + | 0.500592i | \(0.833116\pi\) | |||||||
\(18\) | −16.2151 | −3.82193 | ||||||||
\(19\) | −4.32009 | −0.991096 | −0.495548 | − | 0.868581i | \(-0.665033\pi\) | ||||
−0.495548 | + | 0.868581i | \(0.665033\pi\) | |||||||
\(20\) | 11.0153 | 2.46310 | ||||||||
\(21\) | −10.7538 | −2.34667 | ||||||||
\(22\) | −10.5789 | −2.25542 | ||||||||
\(23\) | −4.46785 | −0.931612 | −0.465806 | − | 0.884887i | \(-0.654235\pi\) | ||||
−0.465806 | + | 0.884887i | \(0.654235\pi\) | |||||||
\(24\) | −23.1589 | −4.72729 | ||||||||
\(25\) | 0.0337976 | 0.00675952 | ||||||||
\(26\) | 5.33650 | 1.04657 | ||||||||
\(27\) | 9.59469 | 1.84650 | ||||||||
\(28\) | −17.4364 | −3.29518 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −17.8578 | −3.26038 | ||||||||
\(31\) | −0.124315 | −0.0223277 | −0.0111638 | − | 0.999938i | \(-0.503554\pi\) | ||||
−0.0111638 | + | 0.999938i | \(0.503554\pi\) | |||||||
\(32\) | −11.7392 | −2.07522 | ||||||||
\(33\) | 12.1861 | 2.12133 | ||||||||
\(34\) | 18.7647 | 3.21811 | ||||||||
\(35\) | −7.96814 | −1.34686 | ||||||||
\(36\) | 30.2859 | 5.04765 | ||||||||
\(37\) | 1.06662 | 0.175351 | 0.0876754 | − | 0.996149i | \(-0.472056\pi\) | ||||
0.0876754 | + | 0.996149i | \(0.472056\pi\) | |||||||
\(38\) | 11.3559 | 1.84216 | ||||||||
\(39\) | −6.14727 | −0.984351 | ||||||||
\(40\) | −17.1598 | −2.71320 | ||||||||
\(41\) | 0.321628 | 0.0502299 | 0.0251149 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251149 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(42\) | 28.2676 | 4.36179 | ||||||||
\(43\) | 4.21144 | 0.642238 | 0.321119 | − | 0.947039i | \(-0.395941\pi\) | ||||
0.321119 | + | 0.947039i | \(0.395941\pi\) | |||||||
\(44\) | 19.7588 | 2.97875 | ||||||||
\(45\) | 13.8401 | 2.06316 | ||||||||
\(46\) | 11.7443 | 1.73160 | ||||||||
\(47\) | −6.24344 | −0.910699 | −0.455350 | − | 0.890313i | \(-0.650486\pi\) | ||||
−0.455350 | + | 0.890313i | \(0.650486\pi\) | |||||||
\(48\) | 31.1434 | 4.49516 | ||||||||
\(49\) | 5.61299 | 0.801856 | ||||||||
\(50\) | −0.0888409 | −0.0125640 | ||||||||
\(51\) | −21.6156 | −3.02678 | ||||||||
\(52\) | −9.96730 | −1.38222 | ||||||||
\(53\) | 1.21606 | 0.167038 | 0.0835190 | − | 0.996506i | \(-0.473384\pi\) | ||||
0.0835190 | + | 0.996506i | \(0.473384\pi\) | |||||||
\(54\) | −25.2208 | −3.43211 | ||||||||
\(55\) | 9.02943 | 1.21753 | ||||||||
\(56\) | 27.1627 | 3.62977 | ||||||||
\(57\) | −13.0811 | −1.73264 | ||||||||
\(58\) | 2.62862 | 0.345154 | ||||||||
\(59\) | 2.09684 | 0.272986 | 0.136493 | − | 0.990641i | \(-0.456417\pi\) | ||||
0.136493 | + | 0.990641i | \(0.456417\pi\) | |||||||
\(60\) | 33.3541 | 4.30600 | ||||||||
\(61\) | 5.39164 | 0.690328 | 0.345164 | − | 0.938542i | \(-0.387823\pi\) | ||||
0.345164 | + | 0.938542i | \(0.387823\pi\) | |||||||
\(62\) | 0.326777 | 0.0415007 | ||||||||
\(63\) | −21.9079 | −2.76014 | ||||||||
\(64\) | 10.2875 | 1.28594 | ||||||||
\(65\) | −4.55488 | −0.564963 | ||||||||
\(66\) | −32.0327 | −3.94295 | ||||||||
\(67\) | 11.1623 | 1.36369 | 0.681847 | − | 0.731495i | \(-0.261177\pi\) | ||||
0.681847 | + | 0.731495i | \(0.261177\pi\) | |||||||
\(68\) | −35.0479 | −4.25018 | ||||||||
\(69\) | −13.5286 | −1.62865 | ||||||||
\(70\) | 20.9452 | 2.50343 | ||||||||
\(71\) | −1.49342 | −0.177237 | −0.0886183 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886183 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(72\) | −47.1798 | −5.56020 | ||||||||
\(73\) | −13.6425 | −1.59673 | −0.798365 | − | 0.602173i | \(-0.794302\pi\) | ||||
−0.798365 | + | 0.602173i | \(0.794302\pi\) | |||||||
\(74\) | −2.80373 | −0.325927 | ||||||||
\(75\) | 0.102338 | 0.0118170 | ||||||||
\(76\) | −21.2100 | −2.43296 | ||||||||
\(77\) | −14.2929 | −1.62883 | ||||||||
\(78\) | 16.1588 | 1.82962 | ||||||||
\(79\) | 6.70219 | 0.754055 | 0.377028 | − | 0.926202i | \(-0.376946\pi\) | ||||
0.377028 | + | 0.926202i | \(0.376946\pi\) | |||||||
\(80\) | 23.0760 | 2.57997 | ||||||||
\(81\) | 10.5465 | 1.17183 | ||||||||
\(82\) | −0.845437 | −0.0933629 | ||||||||
\(83\) | 4.10285 | 0.450346 | 0.225173 | − | 0.974319i | \(-0.427705\pi\) | ||||
0.225173 | + | 0.974319i | \(0.427705\pi\) | |||||||
\(84\) | −52.7972 | −5.76065 | ||||||||
\(85\) | −16.0163 | −1.73721 | ||||||||
\(86\) | −11.0703 | −1.19374 | ||||||||
\(87\) | −3.02798 | −0.324634 | ||||||||
\(88\) | −30.7806 | −3.28122 | ||||||||
\(89\) | −12.0251 | −1.27465 | −0.637326 | − | 0.770594i | \(-0.719960\pi\) | ||||
−0.637326 | + | 0.770594i | \(0.719960\pi\) | |||||||
\(90\) | −36.3804 | −3.83483 | ||||||||
\(91\) | 7.21004 | 0.755818 | ||||||||
\(92\) | −21.9355 | −2.28693 | ||||||||
\(93\) | −0.376424 | −0.0390334 | ||||||||
\(94\) | 16.4116 | 1.69273 | ||||||||
\(95\) | −9.69260 | −0.994440 | ||||||||
\(96\) | −35.5461 | −3.62791 | ||||||||
\(97\) | 12.4420 | 1.26329 | 0.631646 | − | 0.775257i | \(-0.282379\pi\) | ||||
0.631646 | + | 0.775257i | \(0.282379\pi\) | |||||||
\(98\) | −14.7544 | −1.49042 | ||||||||
\(99\) | 24.8259 | 2.49509 | ||||||||
\(100\) | 0.165934 | 0.0165934 | ||||||||
\(101\) | −7.91237 | −0.787310 | −0.393655 | − | 0.919258i | \(-0.628790\pi\) | ||||
−0.393655 | + | 0.919258i | \(0.628790\pi\) | |||||||
\(102\) | 56.8190 | 5.62592 | ||||||||
\(103\) | −0.883298 | −0.0870340 | −0.0435170 | − | 0.999053i | \(-0.513856\pi\) | ||||
−0.0435170 | + | 0.999053i | \(0.513856\pi\) | |||||||
\(104\) | 15.5272 | 1.52257 | ||||||||
\(105\) | −24.1274 | −2.35459 | ||||||||
\(106\) | −3.19654 | −0.310476 | ||||||||
\(107\) | −8.42006 | −0.813998 | −0.406999 | − | 0.913429i | \(-0.633425\pi\) | ||||
−0.406999 | + | 0.913429i | \(0.633425\pi\) | |||||||
\(108\) | 47.1063 | 4.53281 | ||||||||
\(109\) | −4.73249 | −0.453291 | −0.226645 | − | 0.973977i | \(-0.572776\pi\) | ||||
−0.226645 | + | 0.973977i | \(0.572776\pi\) | |||||||
\(110\) | −23.7349 | −2.26303 | ||||||||
\(111\) | 3.22970 | 0.306549 | ||||||||
\(112\) | −36.5276 | −3.45153 | ||||||||
\(113\) | −5.21987 | −0.491044 | −0.245522 | − | 0.969391i | \(-0.578959\pi\) | ||||
−0.245522 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(114\) | 34.3853 | 3.22048 | ||||||||
\(115\) | −10.0241 | −0.934755 | ||||||||
\(116\) | −4.90963 | −0.455847 | ||||||||
\(117\) | −12.5234 | −1.15778 | ||||||||
\(118\) | −5.51180 | −0.507402 | ||||||||
\(119\) | 25.3526 | 2.32407 | ||||||||
\(120\) | −51.9596 | −4.74324 | ||||||||
\(121\) | 5.19664 | 0.472421 | ||||||||
\(122\) | −14.1725 | −1.28312 | ||||||||
\(123\) | 0.973884 | 0.0878121 | ||||||||
\(124\) | −0.610342 | −0.0548103 | ||||||||
\(125\) | −11.1422 | −0.996592 | ||||||||
\(126\) | 57.5875 | 5.13030 | ||||||||
\(127\) | −15.1814 | −1.34713 | −0.673565 | − | 0.739128i | \(-0.735238\pi\) | ||||
−0.673565 | + | 0.739128i | \(0.735238\pi\) | |||||||
\(128\) | −3.56358 | −0.314979 | ||||||||
\(129\) | 12.7522 | 1.12276 | ||||||||
\(130\) | 11.9730 | 1.05010 | ||||||||
\(131\) | 18.5401 | 1.61986 | 0.809928 | − | 0.586529i | \(-0.199506\pi\) | ||||
0.809928 | + | 0.586529i | \(0.199506\pi\) | |||||||
\(132\) | 59.8293 | 5.20748 | ||||||||
\(133\) | 15.3427 | 1.33038 | ||||||||
\(134\) | −29.3415 | −2.53472 | ||||||||
\(135\) | 21.5268 | 1.85273 | ||||||||
\(136\) | 54.5982 | 4.68175 | ||||||||
\(137\) | 4.91278 | 0.419727 | 0.209864 | − | 0.977731i | \(-0.432698\pi\) | ||||
0.209864 | + | 0.977731i | \(0.432698\pi\) | |||||||
\(138\) | 35.5614 | 3.02719 | ||||||||
\(139\) | −9.83617 | −0.834293 | −0.417146 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417146 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(140\) | −39.1206 | −3.30629 | ||||||||
\(141\) | −18.9050 | −1.59209 | ||||||||
\(142\) | 3.92563 | 0.329432 | ||||||||
\(143\) | −8.17036 | −0.683240 | ||||||||
\(144\) | 63.4459 | 5.28716 | ||||||||
\(145\) | −2.24361 | −0.186322 | ||||||||
\(146\) | 35.8608 | 2.96786 | ||||||||
\(147\) | 16.9960 | 1.40181 | ||||||||
\(148\) | 5.23669 | 0.430453 | ||||||||
\(149\) | 7.43738 | 0.609294 | 0.304647 | − | 0.952465i | \(-0.401462\pi\) | ||||
0.304647 | + | 0.952465i | \(0.401462\pi\) | |||||||
\(150\) | −0.269009 | −0.0219645 | ||||||||
\(151\) | −11.2375 | −0.914496 | −0.457248 | − | 0.889339i | \(-0.651165\pi\) | ||||
−0.457248 | + | 0.889339i | \(0.651165\pi\) | |||||||
\(152\) | 33.0413 | 2.68000 | ||||||||
\(153\) | −44.0357 | −3.56008 | ||||||||
\(154\) | 37.5707 | 3.02753 | ||||||||
\(155\) | −0.278915 | −0.0224030 | ||||||||
\(156\) | −30.1808 | −2.41640 | ||||||||
\(157\) | −17.0684 | −1.36220 | −0.681102 | − | 0.732188i | \(-0.738499\pi\) | ||||
−0.681102 | + | 0.732188i | \(0.738499\pi\) | |||||||
\(158\) | −17.6175 | −1.40157 | ||||||||
\(159\) | 3.68219 | 0.292017 | ||||||||
\(160\) | −26.3383 | −2.08222 | ||||||||
\(161\) | 15.8675 | 1.25053 | ||||||||
\(162\) | −27.7227 | −2.17810 | ||||||||
\(163\) | 7.59726 | 0.595063 | 0.297532 | − | 0.954712i | \(-0.403837\pi\) | ||||
0.297532 | + | 0.954712i | \(0.403837\pi\) | |||||||
\(164\) | 1.57907 | 0.123305 | ||||||||
\(165\) | 27.3409 | 2.12849 | ||||||||
\(166\) | −10.7848 | −0.837065 | ||||||||
\(167\) | −20.7071 | −1.60236 | −0.801182 | − | 0.598420i | \(-0.795795\pi\) | ||||
−0.801182 | + | 0.598420i | \(0.795795\pi\) | |||||||
\(168\) | 82.2483 | 6.34559 | ||||||||
\(169\) | −8.87848 | −0.682960 | ||||||||
\(170\) | 42.1006 | 3.22897 | ||||||||
\(171\) | −26.6492 | −2.03792 | ||||||||
\(172\) | 20.6766 | 1.57657 | ||||||||
\(173\) | 18.0870 | 1.37513 | 0.687564 | − | 0.726124i | \(-0.258680\pi\) | ||||
0.687564 | + | 0.726124i | \(0.258680\pi\) | |||||||
\(174\) | 7.95940 | 0.603401 | ||||||||
\(175\) | −0.120031 | −0.00907352 | ||||||||
\(176\) | 41.3928 | 3.12010 | ||||||||
\(177\) | 6.34920 | 0.477235 | ||||||||
\(178\) | 31.6093 | 2.36921 | ||||||||
\(179\) | −3.80591 | −0.284467 | −0.142233 | − | 0.989833i | \(-0.545428\pi\) | ||||
−0.142233 | + | 0.989833i | \(0.545428\pi\) | |||||||
\(180\) | 67.9498 | 5.06468 | ||||||||
\(181\) | −8.75462 | −0.650725 | −0.325363 | − | 0.945589i | \(-0.605486\pi\) | ||||
−0.325363 | + | 0.945589i | \(0.605486\pi\) | |||||||
\(182\) | −18.9524 | −1.40485 | ||||||||
\(183\) | 16.3258 | 1.20684 | ||||||||
\(184\) | 34.1715 | 2.51915 | ||||||||
\(185\) | 2.39308 | 0.175942 | ||||||||
\(186\) | 0.989475 | 0.0725518 | ||||||||
\(187\) | −28.7294 | −2.10090 | ||||||||
\(188\) | −30.6530 | −2.23560 | ||||||||
\(189\) | −34.0753 | −2.47861 | ||||||||
\(190\) | 25.4781 | 1.84838 | ||||||||
\(191\) | −2.89359 | −0.209373 | −0.104687 | − | 0.994505i | \(-0.533384\pi\) | ||||
−0.104687 | + | 0.994505i | \(0.533384\pi\) | |||||||
\(192\) | 31.1505 | 2.24809 | ||||||||
\(193\) | 11.0955 | 0.798670 | 0.399335 | − | 0.916805i | \(-0.369241\pi\) | ||||
0.399335 | + | 0.916805i | \(0.369241\pi\) | |||||||
\(194\) | −32.7052 | −2.34810 | ||||||||
\(195\) | −13.7921 | −0.987672 | ||||||||
\(196\) | 27.5577 | 1.96841 | ||||||||
\(197\) | −1.72833 | −0.123139 | −0.0615693 | − | 0.998103i | \(-0.519611\pi\) | ||||
−0.0615693 | + | 0.998103i | \(0.519611\pi\) | |||||||
\(198\) | −65.2577 | −4.63766 | ||||||||
\(199\) | −23.6554 | −1.67689 | −0.838444 | − | 0.544988i | \(-0.816534\pi\) | ||||
−0.838444 | + | 0.544988i | \(0.816534\pi\) | |||||||
\(200\) | −0.258494 | −0.0182783 | ||||||||
\(201\) | 33.7993 | 2.38402 | ||||||||
\(202\) | 20.7986 | 1.46338 | ||||||||
\(203\) | 3.55148 | 0.249265 | ||||||||
\(204\) | −106.124 | −7.43019 | ||||||||
\(205\) | 0.721609 | 0.0503993 | ||||||||
\(206\) | 2.32185 | 0.161771 | ||||||||
\(207\) | −27.5607 | −1.91560 | ||||||||
\(208\) | −20.8805 | −1.44780 | ||||||||
\(209\) | −17.3862 | −1.20263 | ||||||||
\(210\) | 63.4216 | 4.37651 | ||||||||
\(211\) | 1.76161 | 0.121274 | 0.0606372 | − | 0.998160i | \(-0.480687\pi\) | ||||
0.0606372 | + | 0.998160i | \(0.480687\pi\) | |||||||
\(212\) | 5.97038 | 0.410047 | ||||||||
\(213\) | −4.52205 | −0.309846 | ||||||||
\(214\) | 22.1331 | 1.51299 | ||||||||
\(215\) | 9.44883 | 0.644405 | ||||||||
\(216\) | −73.3830 | −4.99308 | ||||||||
\(217\) | 0.441503 | 0.0299712 | ||||||||
\(218\) | 12.4399 | 0.842537 | ||||||||
\(219\) | −41.3092 | −2.79141 | ||||||||
\(220\) | 44.3311 | 2.98880 | ||||||||
\(221\) | 14.4925 | 0.974869 | ||||||||
\(222\) | −8.48964 | −0.569787 | ||||||||
\(223\) | −24.0428 | −1.61002 | −0.805012 | − | 0.593258i | \(-0.797841\pi\) | ||||
−0.805012 | + | 0.593258i | \(0.797841\pi\) | |||||||
\(224\) | 41.6916 | 2.78564 | ||||||||
\(225\) | 0.208486 | 0.0138991 | ||||||||
\(226\) | 13.7210 | 0.912710 | ||||||||
\(227\) | 16.4501 | 1.09183 | 0.545916 | − | 0.837840i | \(-0.316182\pi\) | ||||
0.545916 | + | 0.837840i | \(0.316182\pi\) | |||||||
\(228\) | −64.2236 | −4.25331 | ||||||||
\(229\) | −12.5342 | −0.828283 | −0.414142 | − | 0.910212i | \(-0.635918\pi\) | ||||
−0.414142 | + | 0.910212i | \(0.635918\pi\) | |||||||
\(230\) | 26.3496 | 1.73744 | ||||||||
\(231\) | −43.2787 | −2.84753 | ||||||||
\(232\) | 7.64830 | 0.502135 | ||||||||
\(233\) | −27.1534 | −1.77888 | −0.889441 | − | 0.457051i | \(-0.848906\pi\) | ||||
−0.889441 | + | 0.457051i | \(0.848906\pi\) | |||||||
\(234\) | 32.9191 | 2.15199 | ||||||||
\(235\) | −14.0079 | −0.913772 | ||||||||
\(236\) | 10.2947 | 0.670129 | ||||||||
\(237\) | 20.2941 | 1.31824 | ||||||||
\(238\) | −66.6423 | −4.31978 | ||||||||
\(239\) | −7.94928 | −0.514196 | −0.257098 | − | 0.966385i | \(-0.582766\pi\) | ||||
−0.257098 | + | 0.966385i | \(0.582766\pi\) | |||||||
\(240\) | 69.8736 | 4.51032 | ||||||||
\(241\) | 24.5705 | 1.58273 | 0.791364 | − | 0.611346i | \(-0.209371\pi\) | ||||
0.791364 | + | 0.611346i | \(0.209371\pi\) | |||||||
\(242\) | −13.6600 | −0.878096 | ||||||||
\(243\) | 3.15059 | 0.202110 | ||||||||
\(244\) | 26.4709 | 1.69463 | ||||||||
\(245\) | 12.5934 | 0.804561 | ||||||||
\(246\) | −2.55997 | −0.163218 | ||||||||
\(247\) | 8.77044 | 0.558050 | ||||||||
\(248\) | 0.950800 | 0.0603758 | ||||||||
\(249\) | 12.4234 | 0.787298 | ||||||||
\(250\) | 29.2887 | 1.85238 | ||||||||
\(251\) | 1.28499 | 0.0811075 | 0.0405538 | − | 0.999177i | \(-0.487088\pi\) | ||||
0.0405538 | + | 0.999177i | \(0.487088\pi\) | |||||||
\(252\) | −107.560 | −6.77562 | ||||||||
\(253\) | −17.9809 | −1.13045 | ||||||||
\(254\) | 39.9060 | 2.50393 | ||||||||
\(255\) | −48.4970 | −3.03700 | ||||||||
\(256\) | −11.2078 | −0.700489 | ||||||||
\(257\) | −22.6435 | −1.41246 | −0.706231 | − | 0.707982i | \(-0.749606\pi\) | ||||
−0.706231 | + | 0.707982i | \(0.749606\pi\) | |||||||
\(258\) | −33.5205 | −2.08690 | ||||||||
\(259\) | −3.78807 | −0.235379 | ||||||||
\(260\) | −22.3628 | −1.38688 | ||||||||
\(261\) | −6.16867 | −0.381831 | ||||||||
\(262\) | −48.7348 | −3.01085 | ||||||||
\(263\) | 19.1202 | 1.17900 | 0.589501 | − | 0.807767i | \(-0.299324\pi\) | ||||
0.589501 | + | 0.807767i | \(0.299324\pi\) | |||||||
\(264\) | −93.2031 | −5.73625 | ||||||||
\(265\) | 2.72836 | 0.167602 | ||||||||
\(266\) | −40.3301 | −2.47279 | ||||||||
\(267\) | −36.4116 | −2.22836 | ||||||||
\(268\) | 54.8028 | 3.34762 | ||||||||
\(269\) | −14.6549 | −0.893527 | −0.446763 | − | 0.894652i | \(-0.647423\pi\) | ||||
−0.446763 | + | 0.894652i | \(0.647423\pi\) | |||||||
\(270\) | −56.5856 | −3.44369 | ||||||||
\(271\) | −25.1373 | −1.52698 | −0.763490 | − | 0.645820i | \(-0.776516\pi\) | ||||
−0.763490 | + | 0.645820i | \(0.776516\pi\) | |||||||
\(272\) | −73.4219 | −4.45186 | ||||||||
\(273\) | 21.8319 | 1.32133 | ||||||||
\(274\) | −12.9138 | −0.780153 | ||||||||
\(275\) | 0.136019 | 0.00820223 | ||||||||
\(276\) | −66.4203 | −3.99803 | ||||||||
\(277\) | −1.00000 | −0.0600842 | ||||||||
\(278\) | 25.8555 | 1.55071 | ||||||||
\(279\) | −0.766860 | −0.0459107 | ||||||||
\(280\) | 60.9427 | 3.64202 | ||||||||
\(281\) | −13.9716 | −0.833474 | −0.416737 | − | 0.909027i | \(-0.636826\pi\) | ||||
−0.416737 | + | 0.909027i | \(0.636826\pi\) | |||||||
\(282\) | 49.6941 | 2.95924 | ||||||||
\(283\) | −5.60095 | −0.332942 | −0.166471 | − | 0.986046i | \(-0.553237\pi\) | ||||
−0.166471 | + | 0.986046i | \(0.553237\pi\) | |||||||
\(284\) | −7.33214 | −0.435083 | ||||||||
\(285\) | −29.3490 | −1.73849 | ||||||||
\(286\) | 21.4767 | 1.26995 | ||||||||
\(287\) | −1.14225 | −0.0674252 | ||||||||
\(288\) | −72.4154 | −4.26712 | ||||||||
\(289\) | 33.9597 | 1.99763 | ||||||||
\(290\) | 5.89760 | 0.346319 | ||||||||
\(291\) | 37.6741 | 2.20850 | ||||||||
\(292\) | −66.9795 | −3.91968 | ||||||||
\(293\) | −26.9202 | −1.57269 | −0.786346 | − | 0.617786i | \(-0.788030\pi\) | ||||
−0.786346 | + | 0.617786i | \(0.788030\pi\) | |||||||
\(294\) | −44.6761 | −2.60556 | ||||||||
\(295\) | 4.70450 | 0.273907 | ||||||||
\(296\) | −8.15780 | −0.474163 | ||||||||
\(297\) | 38.6139 | 2.24060 | ||||||||
\(298\) | −19.5500 | −1.13250 | ||||||||
\(299\) | 9.07043 | 0.524556 | ||||||||
\(300\) | 0.502444 | 0.0290086 | ||||||||
\(301\) | −14.9568 | −0.862097 | ||||||||
\(302\) | 29.5391 | 1.69979 | ||||||||
\(303\) | −23.9585 | −1.37638 | ||||||||
\(304\) | −44.4329 | −2.54840 | ||||||||
\(305\) | 12.0967 | 0.692658 | ||||||||
\(306\) | 115.753 | 6.61716 | ||||||||
\(307\) | −9.42974 | −0.538184 | −0.269092 | − | 0.963115i | \(-0.586724\pi\) | ||||
−0.269092 | + | 0.963115i | \(0.586724\pi\) | |||||||
\(308\) | −70.1730 | −3.99848 | ||||||||
\(309\) | −2.67461 | −0.152153 | ||||||||
\(310\) | 0.733161 | 0.0416408 | ||||||||
\(311\) | 4.35408 | 0.246897 | 0.123449 | − | 0.992351i | \(-0.460605\pi\) | ||||
0.123449 | + | 0.992351i | \(0.460605\pi\) | |||||||
\(312\) | 47.0161 | 2.66176 | ||||||||
\(313\) | 17.4888 | 0.988528 | 0.494264 | − | 0.869312i | \(-0.335438\pi\) | ||||
0.494264 | + | 0.869312i | \(0.335438\pi\) | |||||||
\(314\) | 44.8662 | 2.53195 | ||||||||
\(315\) | −49.1528 | −2.76945 | ||||||||
\(316\) | 32.9053 | 1.85107 | ||||||||
\(317\) | −0.666177 | −0.0374162 | −0.0187081 | − | 0.999825i | \(-0.505955\pi\) | ||||
−0.0187081 | + | 0.999825i | \(0.505955\pi\) | |||||||
\(318\) | −9.67908 | −0.542776 | ||||||||
\(319\) | −4.02450 | −0.225329 | ||||||||
\(320\) | 23.0813 | 1.29028 | ||||||||
\(321\) | −25.4958 | −1.42304 | ||||||||
\(322\) | −41.7095 | −2.32438 | ||||||||
\(323\) | 30.8394 | 1.71595 | ||||||||
\(324\) | 51.7794 | 2.87664 | ||||||||
\(325\) | −0.0686143 | −0.00380604 | ||||||||
\(326\) | −19.9703 | −1.10605 | ||||||||
\(327\) | −14.3299 | −0.792445 | ||||||||
\(328\) | −2.45991 | −0.135826 | ||||||||
\(329\) | 22.1734 | 1.22246 | ||||||||
\(330\) | −71.8689 | −3.95625 | ||||||||
\(331\) | −33.4301 | −1.83749 | −0.918743 | − | 0.394855i | \(-0.870795\pi\) | ||||
−0.918743 | + | 0.394855i | \(0.870795\pi\) | |||||||
\(332\) | 20.1435 | 1.10552 | ||||||||
\(333\) | 6.57961 | 0.360560 | ||||||||
\(334\) | 54.4311 | 2.97834 | ||||||||
\(335\) | 25.0439 | 1.36830 | ||||||||
\(336\) | −110.605 | −6.03399 | ||||||||
\(337\) | −26.2482 | −1.42983 | −0.714916 | − | 0.699210i | \(-0.753535\pi\) | ||||
−0.714916 | + | 0.699210i | \(0.753535\pi\) | |||||||
\(338\) | 23.3381 | 1.26943 | ||||||||
\(339\) | −15.8057 | −0.858447 | ||||||||
\(340\) | −78.6339 | −4.26452 | ||||||||
\(341\) | −0.500307 | −0.0270932 | ||||||||
\(342\) | 70.0506 | 3.78790 | ||||||||
\(343\) | 4.92593 | 0.265975 | ||||||||
\(344\) | −32.2103 | −1.73666 | ||||||||
\(345\) | −30.3529 | −1.63414 | ||||||||
\(346\) | −47.5438 | −2.55597 | ||||||||
\(347\) | 2.19961 | 0.118081 | 0.0590407 | − | 0.998256i | \(-0.481196\pi\) | ||||
0.0590407 | + | 0.998256i | \(0.481196\pi\) | |||||||
\(348\) | −14.8663 | −0.796915 | ||||||||
\(349\) | 6.65676 | 0.356328 | 0.178164 | − | 0.984001i | \(-0.442984\pi\) | ||||
0.178164 | + | 0.984001i | \(0.442984\pi\) | |||||||
\(350\) | 0.315516 | 0.0168651 | ||||||||
\(351\) | −19.4787 | −1.03970 | ||||||||
\(352\) | −47.2445 | −2.51814 | ||||||||
\(353\) | −23.3662 | −1.24366 | −0.621828 | − | 0.783154i | \(-0.713610\pi\) | ||||
−0.621828 | + | 0.783154i | \(0.713610\pi\) | |||||||
\(354\) | −16.6896 | −0.887043 | ||||||||
\(355\) | −3.35066 | −0.177835 | ||||||||
\(356\) | −59.0385 | −3.12904 | ||||||||
\(357\) | 76.7672 | 4.06295 | ||||||||
\(358\) | 10.0043 | 0.528742 | ||||||||
\(359\) | 26.2202 | 1.38385 | 0.691924 | − | 0.721970i | \(-0.256763\pi\) | ||||
0.691924 | + | 0.721970i | \(0.256763\pi\) | |||||||
\(360\) | −105.853 | −5.57896 | ||||||||
\(361\) | −0.336842 | −0.0177285 | ||||||||
\(362\) | 23.0125 | 1.20951 | ||||||||
\(363\) | 15.7353 | 0.825890 | ||||||||
\(364\) | 35.3986 | 1.85539 | ||||||||
\(365\) | −30.6084 | −1.60212 | ||||||||
\(366\) | −42.9142 | −2.24316 | ||||||||
\(367\) | −23.2231 | −1.21223 | −0.606117 | − | 0.795376i | \(-0.707274\pi\) | ||||
−0.606117 | + | 0.795376i | \(0.707274\pi\) | |||||||
\(368\) | −45.9527 | −2.39545 | ||||||||
\(369\) | 1.98402 | 0.103284 | ||||||||
\(370\) | −6.29048 | −0.327026 | ||||||||
\(371\) | −4.31879 | −0.224221 | ||||||||
\(372\) | −1.84810 | −0.0958197 | ||||||||
\(373\) | 5.29004 | 0.273908 | 0.136954 | − | 0.990577i | \(-0.456269\pi\) | ||||
0.136954 | + | 0.990577i | \(0.456269\pi\) | |||||||
\(374\) | 75.5185 | 3.90497 | ||||||||
\(375\) | −33.7385 | −1.74225 | ||||||||
\(376\) | 47.7517 | 2.46260 | ||||||||
\(377\) | 2.03015 | 0.104558 | ||||||||
\(378\) | 89.5709 | 4.60703 | ||||||||
\(379\) | 4.89341 | 0.251358 | 0.125679 | − | 0.992071i | \(-0.459889\pi\) | ||||
0.125679 | + | 0.992071i | \(0.459889\pi\) | |||||||
\(380\) | −47.5871 | −2.44117 | ||||||||
\(381\) | −45.9689 | −2.35506 | ||||||||
\(382\) | 7.60615 | 0.389164 | ||||||||
\(383\) | −1.22634 | −0.0626630 | −0.0313315 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313315 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(384\) | −10.7904 | −0.550647 | ||||||||
\(385\) | −32.0678 | −1.63433 | ||||||||
\(386\) | −29.1658 | −1.48450 | ||||||||
\(387\) | 25.9790 | 1.32059 | ||||||||
\(388\) | 61.0855 | 3.10115 | ||||||||
\(389\) | 9.73216 | 0.493440 | 0.246720 | − | 0.969087i | \(-0.420647\pi\) | ||||
0.246720 | + | 0.969087i | \(0.420647\pi\) | |||||||
\(390\) | 36.2541 | 1.83580 | ||||||||
\(391\) | 31.8942 | 1.61296 | ||||||||
\(392\) | −42.9298 | −2.16828 | ||||||||
\(393\) | 56.1391 | 2.83184 | ||||||||
\(394\) | 4.54313 | 0.228879 | ||||||||
\(395\) | 15.0371 | 0.756599 | ||||||||
\(396\) | 121.886 | 6.12499 | ||||||||
\(397\) | 8.41018 | 0.422095 | 0.211047 | − | 0.977476i | \(-0.432313\pi\) | ||||
0.211047 | + | 0.977476i | \(0.432313\pi\) | |||||||
\(398\) | 62.1810 | 3.11685 | ||||||||
\(399\) | 46.4574 | 2.32578 | ||||||||
\(400\) | 0.347614 | 0.0173807 | ||||||||
\(401\) | 27.1012 | 1.35337 | 0.676685 | − | 0.736273i | \(-0.263416\pi\) | ||||
0.676685 | + | 0.736273i | \(0.263416\pi\) | |||||||
\(402\) | −88.8454 | −4.43121 | ||||||||
\(403\) | 0.252379 | 0.0125719 | ||||||||
\(404\) | −38.8468 | −1.93270 | ||||||||
\(405\) | 23.6623 | 1.17579 | ||||||||
\(406\) | −9.33547 | −0.463312 | ||||||||
\(407\) | 4.29260 | 0.212777 | ||||||||
\(408\) | 165.322 | 8.18467 | ||||||||
\(409\) | −31.1136 | −1.53847 | −0.769234 | − | 0.638967i | \(-0.779362\pi\) | ||||
−0.769234 | + | 0.638967i | \(0.779362\pi\) | |||||||
\(410\) | −1.89683 | −0.0936779 | ||||||||
\(411\) | 14.8758 | 0.733770 | ||||||||
\(412\) | −4.33667 | −0.213652 | ||||||||
\(413\) | −7.44689 | −0.366437 | ||||||||
\(414\) | 72.4466 | 3.56056 | ||||||||
\(415\) | 9.20521 | 0.451866 | ||||||||
\(416\) | 23.8324 | 1.16848 | ||||||||
\(417\) | −29.7837 | −1.45852 | ||||||||
\(418\) | 45.7017 | 2.23534 | ||||||||
\(419\) | 12.4010 | 0.605826 | 0.302913 | − | 0.953018i | \(-0.402041\pi\) | ||||
0.302913 | + | 0.953018i | \(0.402041\pi\) | |||||||
\(420\) | −118.456 | −5.78008 | ||||||||
\(421\) | 9.86836 | 0.480954 | 0.240477 | − | 0.970655i | \(-0.422696\pi\) | ||||
0.240477 | + | 0.970655i | \(0.422696\pi\) | |||||||
\(422\) | −4.63060 | −0.225414 | ||||||||
\(423\) | −38.5137 | −1.87260 | ||||||||
\(424\) | −9.30075 | −0.451685 | ||||||||
\(425\) | −0.241268 | −0.0117032 | ||||||||
\(426\) | 11.8867 | 0.575915 | ||||||||
\(427\) | −19.1483 | −0.926650 | ||||||||
\(428\) | −41.3393 | −1.99821 | ||||||||
\(429\) | −24.7397 | −1.19444 | ||||||||
\(430\) | −24.8374 | −1.19776 | ||||||||
\(431\) | 31.8135 | 1.53240 | 0.766200 | − | 0.642602i | \(-0.222145\pi\) | ||||
0.766200 | + | 0.642602i | \(0.222145\pi\) | |||||||
\(432\) | 98.6831 | 4.74789 | ||||||||
\(433\) | −24.7488 | −1.18935 | −0.594677 | − | 0.803965i | \(-0.702720\pi\) | ||||
−0.594677 | + | 0.803965i | \(0.702720\pi\) | |||||||
\(434\) | −1.16054 | −0.0557078 | ||||||||
\(435\) | −6.79362 | −0.325729 | ||||||||
\(436\) | −23.2348 | −1.11274 | ||||||||
\(437\) | 19.3015 | 0.923317 | ||||||||
\(438\) | 108.586 | 5.18844 | ||||||||
\(439\) | 5.10896 | 0.243837 | 0.121919 | − | 0.992540i | \(-0.461095\pi\) | ||||
0.121919 | + | 0.992540i | \(0.461095\pi\) | |||||||
\(440\) | −69.0597 | −3.29229 | ||||||||
\(441\) | 34.6247 | 1.64880 | ||||||||
\(442\) | −38.0951 | −1.81200 | ||||||||
\(443\) | 35.0742 | 1.66642 | 0.833212 | − | 0.552954i | \(-0.186499\pi\) | ||||
0.833212 | + | 0.552954i | \(0.186499\pi\) | |||||||
\(444\) | 15.8566 | 0.752521 | ||||||||
\(445\) | −26.9796 | −1.27895 | ||||||||
\(446\) | 63.1993 | 2.99257 | ||||||||
\(447\) | 22.5202 | 1.06517 | ||||||||
\(448\) | −36.5360 | −1.72616 | ||||||||
\(449\) | 10.5709 | 0.498870 | 0.249435 | − | 0.968392i | \(-0.419755\pi\) | ||||
0.249435 | + | 0.968392i | \(0.419755\pi\) | |||||||
\(450\) | −0.548031 | −0.0258344 | ||||||||
\(451\) | 1.29439 | 0.0609506 | ||||||||
\(452\) | −25.6276 | −1.20542 | ||||||||
\(453\) | −34.0270 | −1.59873 | ||||||||
\(454\) | −43.2411 | −2.02940 | ||||||||
\(455\) | 16.1765 | 0.758368 | ||||||||
\(456\) | 100.048 | 4.68520 | ||||||||
\(457\) | 29.0183 | 1.35742 | 0.678709 | − | 0.734407i | \(-0.262540\pi\) | ||||
0.678709 | + | 0.734407i | \(0.262540\pi\) | |||||||
\(458\) | 32.9476 | 1.53954 | ||||||||
\(459\) | −68.4927 | −3.19696 | ||||||||
\(460\) | −49.2147 | −2.29465 | ||||||||
\(461\) | 26.0885 | 1.21506 | 0.607532 | − | 0.794295i | \(-0.292160\pi\) | ||||
0.607532 | + | 0.794295i | \(0.292160\pi\) | |||||||
\(462\) | 113.763 | 5.29275 | ||||||||
\(463\) | 9.98755 | 0.464161 | 0.232080 | − | 0.972697i | \(-0.425447\pi\) | ||||
0.232080 | + | 0.972697i | \(0.425447\pi\) | |||||||
\(464\) | −10.2852 | −0.477478 | ||||||||
\(465\) | −0.844550 | −0.0391651 | ||||||||
\(466\) | 71.3760 | 3.30643 | ||||||||
\(467\) | −41.8477 | −1.93648 | −0.968240 | − | 0.250024i | \(-0.919562\pi\) | ||||
−0.968240 | + | 0.250024i | \(0.919562\pi\) | |||||||
\(468\) | −61.4850 | −2.84214 | ||||||||
\(469\) | −39.6427 | −1.83053 | ||||||||
\(470\) | 36.8213 | 1.69844 | ||||||||
\(471\) | −51.6827 | −2.38141 | ||||||||
\(472\) | −16.0373 | −0.738175 | ||||||||
\(473\) | 16.9489 | 0.779313 | ||||||||
\(474\) | −53.3454 | −2.45024 | ||||||||
\(475\) | −0.146009 | −0.00669933 | ||||||||
\(476\) | 124.472 | 5.70516 | ||||||||
\(477\) | 7.50145 | 0.343468 | ||||||||
\(478\) | 20.8956 | 0.955743 | ||||||||
\(479\) | 19.6771 | 0.899071 | 0.449536 | − | 0.893262i | \(-0.351589\pi\) | ||||
0.449536 | + | 0.893262i | \(0.351589\pi\) | |||||||
\(480\) | −79.7518 | −3.64015 | ||||||||
\(481\) | −2.16540 | −0.0987336 | ||||||||
\(482\) | −64.5865 | −2.94184 | ||||||||
\(483\) | 48.0464 | 2.18619 | ||||||||
\(484\) | 25.5135 | 1.15971 | ||||||||
\(485\) | 27.9150 | 1.26756 | ||||||||
\(486\) | −8.28169 | −0.375665 | ||||||||
\(487\) | −41.0333 | −1.85940 | −0.929699 | − | 0.368320i | \(-0.879933\pi\) | ||||
−0.929699 | + | 0.368320i | \(0.879933\pi\) | |||||||
\(488\) | −41.2368 | −1.86670 | ||||||||
\(489\) | 23.0044 | 1.04029 | ||||||||
\(490\) | −33.1032 | −1.49545 | ||||||||
\(491\) | 29.0552 | 1.31124 | 0.655621 | − | 0.755090i | \(-0.272407\pi\) | ||||
0.655621 | + | 0.755090i | \(0.272407\pi\) | |||||||
\(492\) | 4.78141 | 0.215562 | ||||||||
\(493\) | 7.13861 | 0.321507 | ||||||||
\(494\) | −23.0541 | −1.03725 | ||||||||
\(495\) | 55.6996 | 2.50351 | ||||||||
\(496\) | −1.27861 | −0.0574111 | ||||||||
\(497\) | 5.30385 | 0.237910 | ||||||||
\(498\) | −32.6562 | −1.46336 | ||||||||
\(499\) | 42.2250 | 1.89025 | 0.945125 | − | 0.326708i | \(-0.105939\pi\) | ||||
0.945125 | + | 0.326708i | \(0.105939\pi\) | |||||||
\(500\) | −54.7042 | −2.44645 | ||||||||
\(501\) | −62.7008 | −2.80126 | ||||||||
\(502\) | −3.37773 | −0.150756 | ||||||||
\(503\) | 36.1451 | 1.61163 | 0.805815 | − | 0.592168i | \(-0.201728\pi\) | ||||
0.805815 | + | 0.592168i | \(0.201728\pi\) | |||||||
\(504\) | 167.558 | 7.46363 | ||||||||
\(505\) | −17.7523 | −0.789967 | ||||||||
\(506\) | 47.2649 | 2.10118 | ||||||||
\(507\) | −26.8839 | −1.19395 | ||||||||
\(508\) | −74.5349 | −3.30695 | ||||||||
\(509\) | 19.2978 | 0.855362 | 0.427681 | − | 0.903930i | \(-0.359331\pi\) | ||||
0.427681 | + | 0.903930i | \(0.359331\pi\) | |||||||
\(510\) | 127.480 | 5.64491 | ||||||||
\(511\) | 48.4509 | 2.14334 | ||||||||
\(512\) | 36.5882 | 1.61699 | ||||||||
\(513\) | −41.4499 | −1.83006 | ||||||||
\(514\) | 59.5210 | 2.62536 | ||||||||
\(515\) | −1.98178 | −0.0873276 | ||||||||
\(516\) | 62.6083 | 2.75618 | ||||||||
\(517\) | −25.1267 | −1.10507 | ||||||||
\(518\) | 9.95737 | 0.437502 | ||||||||
\(519\) | 54.7671 | 2.40401 | ||||||||
\(520\) | 34.8370 | 1.52771 | ||||||||
\(521\) | 11.0548 | 0.484318 | 0.242159 | − | 0.970237i | \(-0.422144\pi\) | ||||
0.242159 | + | 0.970237i | \(0.422144\pi\) | |||||||
\(522\) | 16.2151 | 0.709715 | ||||||||
\(523\) | 29.3926 | 1.28525 | 0.642623 | − | 0.766182i | \(-0.277846\pi\) | ||||
0.642623 | + | 0.766182i | \(0.277846\pi\) | |||||||
\(524\) | 91.0250 | 3.97645 | ||||||||
\(525\) | −0.363453 | −0.0158624 | ||||||||
\(526\) | −50.2597 | −2.19143 | ||||||||
\(527\) | 0.887437 | 0.0386574 | ||||||||
\(528\) | 125.337 | 5.45457 | ||||||||
\(529\) | −3.03829 | −0.132100 | ||||||||
\(530\) | −7.17181 | −0.311523 | ||||||||
\(531\) | 12.9347 | 0.561320 | ||||||||
\(532\) | 75.3269 | 3.26584 | ||||||||
\(533\) | −0.652954 | −0.0282826 | ||||||||
\(534\) | 95.7122 | 4.14187 | ||||||||
\(535\) | −18.8913 | −0.816744 | ||||||||
\(536\) | −85.3727 | −3.68754 | ||||||||
\(537\) | −11.5242 | −0.497307 | ||||||||
\(538\) | 38.5222 | 1.66081 | ||||||||
\(539\) | 22.5895 | 0.972999 | ||||||||
\(540\) | 105.688 | 4.54810 | ||||||||
\(541\) | 39.5024 | 1.69834 | 0.849171 | − | 0.528118i | \(-0.177102\pi\) | ||||
0.849171 | + | 0.528118i | \(0.177102\pi\) | |||||||
\(542\) | 66.0762 | 2.83822 | ||||||||
\(543\) | −26.5088 | −1.13760 | ||||||||
\(544\) | 83.8017 | 3.59297 | ||||||||
\(545\) | −10.6179 | −0.454820 | ||||||||
\(546\) | −57.3876 | −2.45596 | ||||||||
\(547\) | −33.4027 | −1.42820 | −0.714098 | − | 0.700046i | \(-0.753163\pi\) | ||||
−0.714098 | + | 0.700046i | \(0.753163\pi\) | |||||||
\(548\) | 24.1199 | 1.03035 | ||||||||
\(549\) | 33.2593 | 1.41947 | ||||||||
\(550\) | −0.357541 | −0.0152456 | ||||||||
\(551\) | 4.32009 | 0.184042 | ||||||||
\(552\) | 103.471 | 4.40400 | ||||||||
\(553\) | −23.8027 | −1.01219 | ||||||||
\(554\) | 2.62862 | 0.111679 | ||||||||
\(555\) | 7.24619 | 0.307584 | ||||||||
\(556\) | −48.2919 | −2.04803 | ||||||||
\(557\) | −7.42457 | −0.314589 | −0.157294 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157294 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(558\) | 2.01578 | 0.0853348 | ||||||||
\(559\) | −8.54986 | −0.361621 | ||||||||
\(560\) | −81.9538 | −3.46318 | ||||||||
\(561\) | −86.9919 | −3.67280 | ||||||||
\(562\) | 36.7259 | 1.54919 | ||||||||
\(563\) | −12.5824 | −0.530284 | −0.265142 | − | 0.964209i | \(-0.585419\pi\) | ||||
−0.265142 | + | 0.964209i | \(0.585419\pi\) | |||||||
\(564\) | −92.8166 | −3.90828 | ||||||||
\(565\) | −11.7114 | −0.492701 | ||||||||
\(566\) | 14.7228 | 0.618844 | ||||||||
\(567\) | −37.4557 | −1.57299 | ||||||||
\(568\) | 11.4221 | 0.479262 | ||||||||
\(569\) | 19.6994 | 0.825843 | 0.412921 | − | 0.910767i | \(-0.364508\pi\) | ||||
0.412921 | + | 0.910767i | \(0.364508\pi\) | |||||||
\(570\) | 77.1473 | 3.23135 | ||||||||
\(571\) | −10.4133 | −0.435784 | −0.217892 | − | 0.975973i | \(-0.569918\pi\) | ||||
−0.217892 | + | 0.975973i | \(0.569918\pi\) | |||||||
\(572\) | −40.1134 | −1.67723 | ||||||||
\(573\) | −8.76175 | −0.366027 | ||||||||
\(574\) | 3.00255 | 0.125324 | ||||||||
\(575\) | −0.151003 | −0.00629725 | ||||||||
\(576\) | 63.4605 | 2.64419 | ||||||||
\(577\) | −31.9524 | −1.33020 | −0.665098 | − | 0.746756i | \(-0.731610\pi\) | ||||
−0.665098 | + | 0.746756i | \(0.731610\pi\) | |||||||
\(578\) | −89.2670 | −3.71302 | ||||||||
\(579\) | 33.5969 | 1.39624 | ||||||||
\(580\) | −11.0153 | −0.457386 | ||||||||
\(581\) | −14.5712 | −0.604514 | ||||||||
\(582\) | −99.0308 | −4.10496 | ||||||||
\(583\) | 4.89402 | 0.202690 | ||||||||
\(584\) | 104.342 | 4.31769 | ||||||||
\(585\) | −28.0976 | −1.16169 | ||||||||
\(586\) | 70.7628 | 2.92318 | ||||||||
\(587\) | −31.7717 | −1.31136 | −0.655680 | − | 0.755039i | \(-0.727618\pi\) | ||||
−0.655680 | + | 0.755039i | \(0.727618\pi\) | |||||||
\(588\) | 83.4442 | 3.44118 | ||||||||
\(589\) | 0.537053 | 0.0221289 | ||||||||
\(590\) | −12.3663 | −0.509114 | ||||||||
\(591\) | −5.23336 | −0.215272 | ||||||||
\(592\) | 10.9704 | 0.450879 | ||||||||
\(593\) | −15.4064 | −0.632665 | −0.316333 | − | 0.948648i | \(-0.602452\pi\) | ||||
−0.316333 | + | 0.948648i | \(0.602452\pi\) | |||||||
\(594\) | −101.501 | −4.16464 | ||||||||
\(595\) | 56.8814 | 2.33191 | ||||||||
\(596\) | 36.5148 | 1.49570 | ||||||||
\(597\) | −71.6282 | −2.93155 | ||||||||
\(598\) | −23.8427 | −0.974999 | ||||||||
\(599\) | −21.0518 | −0.860155 | −0.430078 | − | 0.902792i | \(-0.641514\pi\) | ||||
−0.430078 | + | 0.902792i | \(0.641514\pi\) | |||||||
\(600\) | −0.782715 | −0.0319542 | ||||||||
\(601\) | −27.4790 | −1.12089 | −0.560446 | − | 0.828191i | \(-0.689370\pi\) | ||||
−0.560446 | + | 0.828191i | \(0.689370\pi\) | |||||||
\(602\) | 39.3158 | 1.60239 | ||||||||
\(603\) | 68.8567 | 2.80406 | ||||||||
\(604\) | −55.1720 | −2.24492 | ||||||||
\(605\) | 11.6592 | 0.474015 | ||||||||
\(606\) | 62.9778 | 2.55830 | ||||||||
\(607\) | −47.2220 | −1.91668 | −0.958341 | − | 0.285625i | \(-0.907799\pi\) | ||||
−0.958341 | + | 0.285625i | \(0.907799\pi\) | |||||||
\(608\) | 50.7145 | 2.05674 | ||||||||
\(609\) | 10.7538 | 0.435766 | ||||||||
\(610\) | −31.7977 | −1.28745 | ||||||||
\(611\) | 12.6751 | 0.512781 | ||||||||
\(612\) | −216.199 | −8.73933 | ||||||||
\(613\) | 18.0691 | 0.729803 | 0.364902 | − | 0.931046i | \(-0.381103\pi\) | ||||
0.364902 | + | 0.931046i | \(0.381103\pi\) | |||||||
\(614\) | 24.7872 | 1.00033 | ||||||||
\(615\) | 2.18502 | 0.0881084 | ||||||||
\(616\) | 109.317 | 4.40449 | ||||||||
\(617\) | 7.74046 | 0.311619 | 0.155810 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155810 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(618\) | 7.03053 | 0.282809 | ||||||||
\(619\) | −9.02740 | −0.362842 | −0.181421 | − | 0.983406i | \(-0.558070\pi\) | ||||
−0.181421 | + | 0.983406i | \(0.558070\pi\) | |||||||
\(620\) | −1.36937 | −0.0549952 | ||||||||
\(621\) | −42.8676 | −1.72022 | ||||||||
\(622\) | −11.4452 | −0.458912 | ||||||||
\(623\) | 42.7067 | 1.71101 | ||||||||
\(624\) | −63.2258 | −2.53106 | ||||||||
\(625\) | −25.1678 | −1.00671 | ||||||||
\(626\) | −45.9715 | −1.83739 | ||||||||
\(627\) | −52.6451 | −2.10244 | ||||||||
\(628\) | −83.7994 | −3.34396 | ||||||||
\(629\) | −7.61416 | −0.303596 | ||||||||
\(630\) | 129.204 | 5.14761 | ||||||||
\(631\) | 41.0017 | 1.63225 | 0.816126 | − | 0.577874i | \(-0.196117\pi\) | ||||
0.816126 | + | 0.577874i | \(0.196117\pi\) | |||||||
\(632\) | −51.2603 | −2.03903 | ||||||||
\(633\) | 5.33413 | 0.212013 | ||||||||
\(634\) | 1.75112 | 0.0695460 | ||||||||
\(635\) | −34.0611 | −1.35168 | ||||||||
\(636\) | 18.0782 | 0.716847 | ||||||||
\(637\) | −11.3952 | −0.451495 | ||||||||
\(638\) | 10.5789 | 0.418822 | ||||||||
\(639\) | −9.21243 | −0.364438 | ||||||||
\(640\) | −7.99528 | −0.316041 | ||||||||
\(641\) | 46.1016 | 1.82090 | 0.910451 | − | 0.413616i | \(-0.135734\pi\) | ||||
0.910451 | + | 0.413616i | \(0.135734\pi\) | |||||||
\(642\) | 67.0186 | 2.64501 | ||||||||
\(643\) | 4.40584 | 0.173749 | 0.0868747 | − | 0.996219i | \(-0.472312\pi\) | ||||
0.0868747 | + | 0.996219i | \(0.472312\pi\) | |||||||
\(644\) | 77.9034 | 3.06982 | ||||||||
\(645\) | 28.6109 | 1.12655 | ||||||||
\(646\) | −81.0650 | −3.18946 | ||||||||
\(647\) | −14.6659 | −0.576576 | −0.288288 | − | 0.957544i | \(-0.593086\pi\) | ||||
−0.288288 | + | 0.957544i | \(0.593086\pi\) | |||||||
\(648\) | −80.6628 | −3.16874 | ||||||||
\(649\) | 8.43875 | 0.331250 | ||||||||
\(650\) | 0.180361 | 0.00707433 | ||||||||
\(651\) | 1.33686 | 0.0523958 | ||||||||
\(652\) | 37.2997 | 1.46077 | ||||||||
\(653\) | 13.8140 | 0.540583 | 0.270292 | − | 0.962779i | \(-0.412880\pi\) | ||||
0.270292 | + | 0.962779i | \(0.412880\pi\) | |||||||
\(654\) | 37.6678 | 1.47293 | ||||||||
\(655\) | 41.5968 | 1.62532 | ||||||||
\(656\) | 3.30800 | 0.129156 | ||||||||
\(657\) | −84.1560 | −3.28324 | ||||||||
\(658\) | −58.2855 | −2.27220 | ||||||||
\(659\) | 25.8540 | 1.00713 | 0.503565 | − | 0.863957i | \(-0.332021\pi\) | ||||
0.503565 | + | 0.863957i | \(0.332021\pi\) | |||||||
\(660\) | 134.234 | 5.22505 | ||||||||
\(661\) | 12.5580 | 0.488450 | 0.244225 | − | 0.969719i | \(-0.421467\pi\) | ||||
0.244225 | + | 0.969719i | \(0.421467\pi\) | |||||||
\(662\) | 87.8750 | 3.41536 | ||||||||
\(663\) | 43.8829 | 1.70427 | ||||||||
\(664\) | −31.3798 | −1.21777 | ||||||||
\(665\) | 34.4231 | 1.33487 | ||||||||
\(666\) | −17.2953 | −0.670178 | ||||||||
\(667\) | 4.46785 | 0.172996 | ||||||||
\(668\) | −101.664 | −3.93351 | ||||||||
\(669\) | −72.8011 | −2.81465 | ||||||||
\(670\) | −65.8309 | −2.54327 | ||||||||
\(671\) | 21.6987 | 0.837668 | ||||||||
\(672\) | 126.241 | 4.86987 | ||||||||
\(673\) | −9.30043 | −0.358505 | −0.179253 | − | 0.983803i | \(-0.557368\pi\) | ||||
−0.179253 | + | 0.983803i | \(0.557368\pi\) | |||||||
\(674\) | 68.9966 | 2.65765 | ||||||||
\(675\) | 0.324277 | 0.0124814 | ||||||||
\(676\) | −43.5900 | −1.67654 | ||||||||
\(677\) | 16.2598 | 0.624914 | 0.312457 | − | 0.949932i | \(-0.398848\pi\) | ||||
0.312457 | + | 0.949932i | \(0.398848\pi\) | |||||||
\(678\) | 41.5471 | 1.59561 | ||||||||
\(679\) | −44.1875 | −1.69576 | ||||||||
\(680\) | 122.497 | 4.69755 | ||||||||
\(681\) | 49.8107 | 1.90875 | ||||||||
\(682\) | 1.31512 | 0.0503584 | ||||||||
\(683\) | −15.2953 | −0.585260 | −0.292630 | − | 0.956226i | \(-0.594530\pi\) | ||||
−0.292630 | + | 0.956226i | \(0.594530\pi\) | |||||||
\(684\) | −130.838 | −5.00270 | ||||||||
\(685\) | 11.0224 | 0.421144 | ||||||||
\(686\) | −12.9484 | −0.494372 | ||||||||
\(687\) | −37.9533 | −1.44801 | ||||||||
\(688\) | 43.3154 | 1.65138 | ||||||||
\(689\) | −2.46878 | −0.0940530 | ||||||||
\(690\) | 79.7861 | 3.03741 | ||||||||
\(691\) | 28.1357 | 1.07033 | 0.535167 | − | 0.844746i | \(-0.320249\pi\) | ||||
0.535167 | + | 0.844746i | \(0.320249\pi\) | |||||||
\(692\) | 88.8004 | 3.37568 | ||||||||
\(693\) | −88.1685 | −3.34924 | ||||||||
\(694\) | −5.78194 | −0.219480 | ||||||||
\(695\) | −22.0686 | −0.837108 | ||||||||
\(696\) | 23.1589 | 0.877836 | ||||||||
\(697\) | −2.29598 | −0.0869663 | ||||||||
\(698\) | −17.4981 | −0.662312 | ||||||||
\(699\) | −82.2201 | −3.10985 | ||||||||
\(700\) | −0.589309 | −0.0222738 | ||||||||
\(701\) | −18.8307 | −0.711226 | −0.355613 | − | 0.934633i | \(-0.615728\pi\) | ||||
−0.355613 | + | 0.934633i | \(0.615728\pi\) | |||||||
\(702\) | 51.2020 | 1.93249 | ||||||||
\(703\) | −4.60788 | −0.173789 | ||||||||
\(704\) | 41.4023 | 1.56041 | ||||||||
\(705\) | −42.4155 | −1.59746 | ||||||||
\(706\) | 61.4207 | 2.31160 | ||||||||
\(707\) | 28.1006 | 1.05683 | ||||||||
\(708\) | 31.1722 | 1.17152 | ||||||||
\(709\) | 35.6439 | 1.33864 | 0.669318 | − | 0.742976i | \(-0.266586\pi\) | ||||
0.669318 | + | 0.742976i | \(0.266586\pi\) | |||||||
\(710\) | 8.80760 | 0.330543 | ||||||||
\(711\) | 41.3436 | 1.55051 | ||||||||
\(712\) | 91.9712 | 3.44676 | ||||||||
\(713\) | 0.555422 | 0.0208007 | ||||||||
\(714\) | −201.792 | −7.55186 | ||||||||
\(715\) | −18.3311 | −0.685545 | ||||||||
\(716\) | −18.6856 | −0.698313 | ||||||||
\(717\) | −24.0703 | −0.898921 | ||||||||
\(718\) | −68.9228 | −2.57218 | ||||||||
\(719\) | −2.69021 | −0.100328 | −0.0501639 | − | 0.998741i | \(-0.515974\pi\) | ||||
−0.0501639 | + | 0.998741i | \(0.515974\pi\) | |||||||
\(720\) | 142.348 | 5.30500 | ||||||||
\(721\) | 3.13701 | 0.116829 | ||||||||
\(722\) | 0.885429 | 0.0329523 | ||||||||
\(723\) | 74.3991 | 2.76693 | ||||||||
\(724\) | −42.9819 | −1.59741 | ||||||||
\(725\) | −0.0337976 | −0.00125521 | ||||||||
\(726\) | −41.3621 | −1.53509 | ||||||||
\(727\) | −5.04604 | −0.187147 | −0.0935737 | − | 0.995612i | \(-0.529829\pi\) | ||||
−0.0935737 | + | 0.995612i | \(0.529829\pi\) | |||||||
\(728\) | −55.1445 | −2.04379 | ||||||||
\(729\) | −22.0996 | −0.818504 | ||||||||
\(730\) | 80.4578 | 2.97788 | ||||||||
\(731\) | −30.0638 | −1.11195 | ||||||||
\(732\) | 80.1535 | 2.96256 | ||||||||
\(733\) | −15.3664 | −0.567570 | −0.283785 | − | 0.958888i | \(-0.591590\pi\) | ||||
−0.283785 | + | 0.958888i | \(0.591590\pi\) | |||||||
\(734\) | 61.0445 | 2.25319 | ||||||||
\(735\) | 38.1325 | 1.40654 | ||||||||
\(736\) | 52.4491 | 1.93330 | ||||||||
\(737\) | 44.9228 | 1.65475 | ||||||||
\(738\) | −5.21522 | −0.191975 | ||||||||
\(739\) | 9.10492 | 0.334930 | 0.167465 | − | 0.985878i | \(-0.446442\pi\) | ||||
0.167465 | + | 0.985878i | \(0.446442\pi\) | |||||||
\(740\) | 11.7491 | 0.431906 | ||||||||
\(741\) | 26.5567 | 0.975586 | ||||||||
\(742\) | 11.3525 | 0.416762 | ||||||||
\(743\) | 22.2951 | 0.817929 | 0.408964 | − | 0.912550i | \(-0.365890\pi\) | ||||
0.408964 | + | 0.912550i | \(0.365890\pi\) | |||||||
\(744\) | 2.87900 | 0.105549 | ||||||||
\(745\) | 16.6866 | 0.611350 | ||||||||
\(746\) | −13.9055 | −0.509116 | ||||||||
\(747\) | 25.3091 | 0.926013 | ||||||||
\(748\) | −141.050 | −5.15731 | ||||||||
\(749\) | 29.9036 | 1.09266 | ||||||||
\(750\) | 88.6855 | 3.23834 | ||||||||
\(751\) | −10.5708 | −0.385733 | −0.192866 | − | 0.981225i | \(-0.561778\pi\) | ||||
−0.192866 | + | 0.981225i | \(0.561778\pi\) | |||||||
\(752\) | −64.2149 | −2.34168 | ||||||||
\(753\) | 3.89091 | 0.141793 | ||||||||
\(754\) | −5.33650 | −0.194344 | ||||||||
\(755\) | −25.2126 | −0.917581 | ||||||||
\(756\) | −167.297 | −6.08453 | ||||||||
\(757\) | 9.60956 | 0.349265 | 0.174633 | − | 0.984634i | \(-0.444126\pi\) | ||||
0.174633 | + | 0.984634i | \(0.444126\pi\) | |||||||
\(758\) | −12.8629 | −0.467202 | ||||||||
\(759\) | −54.4458 | −1.97626 | ||||||||
\(760\) | 74.1319 | 2.68905 | ||||||||
\(761\) | −15.0353 | −0.545029 | −0.272514 | − | 0.962152i | \(-0.587855\pi\) | ||||
−0.272514 | + | 0.962152i | \(0.587855\pi\) | |||||||
\(762\) | 120.835 | 4.37738 | ||||||||
\(763\) | 16.8073 | 0.608467 | ||||||||
\(764\) | −14.2065 | −0.513972 | ||||||||
\(765\) | −98.7991 | −3.57209 | ||||||||
\(766\) | 3.22357 | 0.116472 | ||||||||
\(767\) | −4.25691 | −0.153708 | ||||||||
\(768\) | −33.9371 | −1.22460 | ||||||||
\(769\) | 39.4562 | 1.42283 | 0.711414 | − | 0.702773i | \(-0.248055\pi\) | ||||
0.711414 | + | 0.702773i | \(0.248055\pi\) | |||||||
\(770\) | 84.2940 | 3.03774 | ||||||||
\(771\) | −68.5640 | −2.46927 | ||||||||
\(772\) | 54.4747 | 1.96059 | ||||||||
\(773\) | 50.1342 | 1.80320 | 0.901601 | − | 0.432569i | \(-0.142393\pi\) | ||||
0.901601 | + | 0.432569i | \(0.142393\pi\) | |||||||
\(774\) | −68.2888 | −2.45459 | ||||||||
\(775\) | −0.00420156 | −0.000150924 0 | ||||||||
\(776\) | −95.1600 | −3.41605 | ||||||||
\(777\) | −11.4702 | −0.411491 | ||||||||
\(778\) | −25.5821 | −0.917164 | ||||||||
\(779\) | −1.38946 | −0.0497826 | ||||||||
\(780\) | −67.7140 | −2.42455 | ||||||||
\(781\) | −6.01028 | −0.215065 | ||||||||
\(782\) | −83.8377 | −2.99803 | ||||||||
\(783\) | −9.59469 | −0.342886 | ||||||||
\(784\) | 57.7306 | 2.06181 | ||||||||
\(785\) | −38.2948 | −1.36680 | ||||||||
\(786\) | −147.568 | −5.26358 | ||||||||
\(787\) | 49.0931 | 1.74998 | 0.874990 | − | 0.484142i | \(-0.160868\pi\) | ||||
0.874990 | + | 0.484142i | \(0.160868\pi\) | |||||||
\(788\) | −8.48547 | −0.302283 | ||||||||
\(789\) | 57.8957 | 2.06114 | ||||||||
\(790\) | −39.5268 | −1.40630 | ||||||||
\(791\) | 18.5383 | 0.659145 | ||||||||
\(792\) | −189.875 | −6.74693 | ||||||||
\(793\) | −10.9459 | −0.388699 | ||||||||
\(794\) | −22.1071 | −0.784553 | ||||||||
\(795\) | 8.26142 | 0.293002 | ||||||||
\(796\) | −116.139 | −4.11645 | ||||||||
\(797\) | −26.4428 | −0.936651 | −0.468325 | − | 0.883556i | \(-0.655142\pi\) | ||||
−0.468325 | + | 0.883556i | \(0.655142\pi\) | |||||||
\(798\) | −122.119 | −4.32295 | ||||||||
\(799\) | 44.5694 | 1.57675 | ||||||||
\(800\) | −0.396757 | −0.0140275 | ||||||||
\(801\) | −74.1786 | −2.62097 | ||||||||
\(802\) | −71.2387 | −2.51553 | ||||||||
\(803\) | −54.9042 | −1.93753 | ||||||||
\(804\) | 165.942 | 5.85232 | ||||||||
\(805\) | 35.6005 | 1.25475 | ||||||||
\(806\) | −0.663408 | −0.0233675 | ||||||||
\(807\) | −44.3749 | −1.56207 | ||||||||
\(808\) | 60.5162 | 2.12895 | ||||||||
\(809\) | 52.2726 | 1.83781 | 0.918903 | − | 0.394484i | \(-0.129077\pi\) | ||||
0.918903 | + | 0.394484i | \(0.129077\pi\) | |||||||
\(810\) | −62.1991 | −2.18545 | ||||||||
\(811\) | −10.3865 | −0.364721 | −0.182360 | − | 0.983232i | \(-0.558374\pi\) | ||||
−0.182360 | + | 0.983232i | \(0.558374\pi\) | |||||||
\(812\) | 17.4364 | 0.611899 | ||||||||
\(813\) | −76.1151 | −2.66947 | ||||||||
\(814\) | −11.2836 | −0.395490 | ||||||||
\(815\) | 17.0453 | 0.597071 | ||||||||
\(816\) | −222.320 | −7.78276 | ||||||||
\(817\) | −18.1938 | −0.636520 | ||||||||
\(818\) | 81.7857 | 2.85957 | ||||||||
\(819\) | 44.4764 | 1.55413 | ||||||||
\(820\) | 3.54283 | 0.123721 | ||||||||
\(821\) | −32.2228 | −1.12458 | −0.562291 | − | 0.826939i | \(-0.690080\pi\) | ||||
−0.562291 | + | 0.826939i | \(0.690080\pi\) | |||||||
\(822\) | −39.1028 | −1.36387 | ||||||||
\(823\) | −30.1346 | −1.05043 | −0.525213 | − | 0.850971i | \(-0.676014\pi\) | ||||
−0.525213 | + | 0.850971i | \(0.676014\pi\) | |||||||
\(824\) | 6.75573 | 0.235347 | ||||||||
\(825\) | 0.411862 | 0.0143392 | ||||||||
\(826\) | 19.5750 | 0.681102 | ||||||||
\(827\) | −29.0327 | −1.00957 | −0.504784 | − | 0.863246i | \(-0.668428\pi\) | ||||
−0.504784 | + | 0.863246i | \(0.668428\pi\) | |||||||
\(828\) | −135.313 | −4.70245 | ||||||||
\(829\) | −7.90200 | −0.274448 | −0.137224 | − | 0.990540i | \(-0.543818\pi\) | ||||
−0.137224 | + | 0.990540i | \(0.543818\pi\) | |||||||
\(830\) | −24.1970 | −0.839889 | ||||||||
\(831\) | −3.02798 | −0.105040 | ||||||||
\(832\) | −20.8853 | −0.724067 | ||||||||
\(833\) | −40.0689 | −1.38831 | ||||||||
\(834\) | 78.2900 | 2.71096 | ||||||||
\(835\) | −46.4587 | −1.60777 | ||||||||
\(836\) | −85.3598 | −2.95223 | ||||||||
\(837\) | −1.19277 | −0.0412280 | ||||||||
\(838\) | −32.5974 | −1.12606 | ||||||||
\(839\) | 37.8130 | 1.30545 | 0.652725 | − | 0.757595i | \(-0.273626\pi\) | ||||
0.652725 | + | 0.757595i | \(0.273626\pi\) | |||||||
\(840\) | 184.533 | 6.36700 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −25.9401 | −0.893956 | ||||||||
\(843\) | −42.3056 | −1.45708 | ||||||||
\(844\) | 8.64886 | 0.297706 | ||||||||
\(845\) | −19.9199 | −0.685264 | ||||||||
\(846\) | 101.238 | 3.48063 | ||||||||
\(847\) | −18.4557 | −0.634147 | ||||||||
\(848\) | 12.5074 | 0.429504 | ||||||||
\(849\) | −16.9596 | −0.582051 | ||||||||
\(850\) | 0.634200 | 0.0217529 | ||||||||
\(851\) | −4.76549 | −0.163359 | ||||||||
\(852\) | −22.2016 | −0.760614 | ||||||||
\(853\) | 10.5224 | 0.360279 | 0.180139 | − | 0.983641i | \(-0.442345\pi\) | ||||
0.180139 | + | 0.983641i | \(0.442345\pi\) | |||||||
\(854\) | 50.3335 | 1.72238 | ||||||||
\(855\) | −59.7905 | −2.04479 | ||||||||
\(856\) | 64.3991 | 2.20112 | ||||||||
\(857\) | 16.1404 | 0.551346 | 0.275673 | − | 0.961251i | \(-0.411099\pi\) | ||||
0.275673 | + | 0.961251i | \(0.411099\pi\) | |||||||
\(858\) | 65.0312 | 2.22013 | ||||||||
\(859\) | 19.5149 | 0.665841 | 0.332921 | − | 0.942955i | \(-0.391966\pi\) | ||||
0.332921 | + | 0.942955i | \(0.391966\pi\) | |||||||
\(860\) | 46.3902 | 1.58189 | ||||||||
\(861\) | −3.45873 | −0.117873 | ||||||||
\(862\) | −83.6254 | −2.84829 | ||||||||
\(863\) | −17.7448 | −0.604040 | −0.302020 | − | 0.953302i | \(-0.597661\pi\) | ||||
−0.302020 | + | 0.953302i | \(0.597661\pi\) | |||||||
\(864\) | −112.634 | −3.83189 | ||||||||
\(865\) | 40.5802 | 1.37977 | ||||||||
\(866\) | 65.0552 | 2.21067 | ||||||||
\(867\) | 102.829 | 3.49227 | ||||||||
\(868\) | 2.16761 | 0.0735736 | ||||||||
\(869\) | 26.9730 | 0.914996 | ||||||||
\(870\) | 17.8578 | 0.605437 | ||||||||
\(871\) | −22.6612 | −0.767846 | ||||||||
\(872\) | 36.1955 | 1.22573 | ||||||||
\(873\) | 76.7506 | 2.59761 | ||||||||
\(874\) | −50.7363 | −1.71618 | ||||||||
\(875\) | 39.5714 | 1.33776 | ||||||||
\(876\) | −202.813 | −6.85240 | ||||||||
\(877\) | 13.1896 | 0.445382 | 0.222691 | − | 0.974889i | \(-0.428516\pi\) | ||||
0.222691 | + | 0.974889i | \(0.428516\pi\) | |||||||
\(878\) | −13.4295 | −0.453224 | ||||||||
\(879\) | −81.5138 | −2.74939 | ||||||||
\(880\) | 92.8694 | 3.13063 | ||||||||
\(881\) | 47.5500 | 1.60200 | 0.801000 | − | 0.598665i | \(-0.204302\pi\) | ||||
0.801000 | + | 0.598665i | \(0.204302\pi\) | |||||||
\(882\) | −91.0151 | −3.06464 | ||||||||
\(883\) | 29.6255 | 0.996976 | 0.498488 | − | 0.866897i | \(-0.333889\pi\) | ||||
0.498488 | + | 0.866897i | \(0.333889\pi\) | |||||||
\(884\) | 71.1526 | 2.39312 | ||||||||
\(885\) | 14.2451 | 0.478845 | ||||||||
\(886\) | −92.1966 | −3.09740 | ||||||||
\(887\) | −11.4122 | −0.383185 | −0.191593 | − | 0.981475i | \(-0.561365\pi\) | ||||
−0.191593 | + | 0.981475i | \(0.561365\pi\) | |||||||
\(888\) | −24.7017 | −0.828934 | ||||||||
\(889\) | 53.9163 | 1.80830 | ||||||||
\(890\) | 70.9189 | 2.37721 | ||||||||
\(891\) | 42.4445 | 1.42194 | ||||||||
\(892\) | −118.041 | −3.95231 | ||||||||
\(893\) | 26.9722 | 0.902590 | ||||||||
\(894\) | −59.1971 | −1.97985 | ||||||||
\(895\) | −8.53898 | −0.285427 | ||||||||
\(896\) | 12.6560 | 0.422806 | ||||||||
\(897\) | 27.4651 | 0.917032 | ||||||||
\(898\) | −27.7868 | −0.927256 | ||||||||
\(899\) | 0.124315 | 0.00414615 | ||||||||
\(900\) | 1.02359 | 0.0341197 | ||||||||
\(901\) | −8.68094 | −0.289204 | ||||||||
\(902\) | −3.40246 | −0.113290 | ||||||||
\(903\) | −45.2890 | −1.50712 | ||||||||
\(904\) | 39.9231 | 1.32782 | ||||||||
\(905\) | −19.6420 | −0.652921 | ||||||||
\(906\) | 89.4439 | 2.97158 | ||||||||
\(907\) | 19.6318 | 0.651863 | 0.325932 | − | 0.945393i | \(-0.394322\pi\) | ||||
0.325932 | + | 0.945393i | \(0.394322\pi\) | |||||||
\(908\) | 80.7640 | 2.68025 | ||||||||
\(909\) | −48.8088 | −1.61889 | ||||||||
\(910\) | −42.5219 | −1.40959 | ||||||||
\(911\) | −54.5174 | −1.80624 | −0.903120 | − | 0.429388i | \(-0.858729\pi\) | ||||
−0.903120 | + | 0.429388i | \(0.858729\pi\) | |||||||
\(912\) | −134.542 | −4.45513 | ||||||||
\(913\) | 16.5119 | 0.546465 | ||||||||
\(914\) | −76.2780 | −2.52305 | ||||||||
\(915\) | 36.6287 | 1.21091 | ||||||||
\(916\) | −61.5382 | −2.03328 | ||||||||
\(917\) | −65.8448 | −2.17439 | ||||||||
\(918\) | 180.041 | 5.94224 | ||||||||
\(919\) | −38.4425 | −1.26810 | −0.634050 | − | 0.773292i | \(-0.718609\pi\) | ||||
−0.634050 | + | 0.773292i | \(0.718609\pi\) | |||||||
\(920\) | 76.6675 | 2.52765 | ||||||||
\(921\) | −28.5531 | −0.940856 | ||||||||
\(922\) | −68.5767 | −2.25845 | ||||||||
\(923\) | 3.03187 | 0.0997954 | ||||||||
\(924\) | −212.483 | −6.99016 | ||||||||
\(925\) | 0.0360491 | 0.00118529 | ||||||||
\(926\) | −26.2534 | −0.862741 | ||||||||
\(927\) | −5.44878 | −0.178961 | ||||||||
\(928\) | 11.7392 | 0.385359 | ||||||||
\(929\) | 8.01060 | 0.262819 | 0.131410 | − | 0.991328i | \(-0.458050\pi\) | ||||
0.131410 | + | 0.991328i | \(0.458050\pi\) | |||||||
\(930\) | 2.22000 | 0.0727966 | ||||||||
\(931\) | −24.2486 | −0.794716 | ||||||||
\(932\) | −133.313 | −4.36682 | ||||||||
\(933\) | 13.1841 | 0.431628 | ||||||||
\(934\) | 110.002 | 3.59936 | ||||||||
\(935\) | −64.4575 | −2.10799 | ||||||||
\(936\) | 95.7823 | 3.13074 | ||||||||
\(937\) | −10.8673 | −0.355020 | −0.177510 | − | 0.984119i | \(-0.556804\pi\) | ||||
−0.177510 | + | 0.984119i | \(0.556804\pi\) | |||||||
\(938\) | 104.206 | 3.40243 | ||||||||
\(939\) | 52.9559 | 1.72815 | ||||||||
\(940\) | −68.7734 | −2.24314 | ||||||||
\(941\) | 19.2075 | 0.626146 | 0.313073 | − | 0.949729i | \(-0.398642\pi\) | ||||
0.313073 | + | 0.949729i | \(0.398642\pi\) | |||||||
\(942\) | 135.854 | 4.42637 | ||||||||
\(943\) | −1.43699 | −0.0467947 | ||||||||
\(944\) | 21.5664 | 0.701927 | ||||||||
\(945\) | −76.4518 | −2.48698 | ||||||||
\(946\) | −44.5523 | −1.44852 | ||||||||
\(947\) | 31.1723 | 1.01296 | 0.506481 | − | 0.862251i | \(-0.330946\pi\) | ||||
0.506481 | + | 0.862251i | \(0.330946\pi\) | |||||||
\(948\) | 99.6365 | 3.23604 | ||||||||
\(949\) | 27.6963 | 0.899060 | ||||||||
\(950\) | 0.383801 | 0.0124521 | ||||||||
\(951\) | −2.01717 | −0.0654113 | ||||||||
\(952\) | −193.904 | −6.28447 | ||||||||
\(953\) | 48.6926 | 1.57731 | 0.788654 | − | 0.614837i | \(-0.210778\pi\) | ||||
0.788654 | + | 0.614837i | \(0.210778\pi\) | |||||||
\(954\) | −19.7184 | −0.638408 | ||||||||
\(955\) | −6.49210 | −0.210079 | ||||||||
\(956\) | −39.0280 | −1.26226 | ||||||||
\(957\) | −12.1861 | −0.393922 | ||||||||
\(958\) | −51.7237 | −1.67112 | ||||||||
\(959\) | −17.4476 | −0.563414 | ||||||||
\(960\) | 69.8897 | 2.25568 | ||||||||
\(961\) | −30.9845 | −0.999501 | ||||||||
\(962\) | 5.69200 | 0.183517 | ||||||||
\(963\) | −51.9406 | −1.67376 | ||||||||
\(964\) | 120.632 | 3.88530 | ||||||||
\(965\) | 24.8940 | 0.801365 | ||||||||
\(966\) | −126.296 | −4.06350 | ||||||||
\(967\) | 46.2894 | 1.48857 | 0.744284 | − | 0.667864i | \(-0.232791\pi\) | ||||
0.744284 | + | 0.667864i | \(0.232791\pi\) | |||||||
\(968\) | −39.7454 | −1.27747 | ||||||||
\(969\) | 93.3811 | 2.99983 | ||||||||
\(970\) | −73.3779 | −2.35602 | ||||||||
\(971\) | −15.6421 | −0.501979 | −0.250989 | − | 0.967990i | \(-0.580756\pi\) | ||||
−0.250989 | + | 0.967990i | \(0.580756\pi\) | |||||||
\(972\) | 15.4682 | 0.496143 | ||||||||
\(973\) | 34.9329 | 1.11990 | ||||||||
\(974\) | 107.861 | 3.45609 | ||||||||
\(975\) | −0.207763 | −0.00665373 | ||||||||
\(976\) | 55.4540 | 1.77504 | ||||||||
\(977\) | −28.5396 | −0.913062 | −0.456531 | − | 0.889707i | \(-0.650908\pi\) | ||||
−0.456531 | + | 0.889707i | \(0.650908\pi\) | |||||||
\(978\) | −60.4696 | −1.93361 | ||||||||
\(979\) | −48.3949 | −1.54671 | ||||||||
\(980\) | 61.8288 | 1.97505 | ||||||||
\(981\) | −29.1932 | −0.932067 | ||||||||
\(982\) | −76.3749 | −2.43722 | ||||||||
\(983\) | 26.6019 | 0.848469 | 0.424234 | − | 0.905552i | \(-0.360543\pi\) | ||||
0.424234 | + | 0.905552i | \(0.360543\pi\) | |||||||
\(984\) | −7.44855 | −0.237451 | ||||||||
\(985\) | −3.87771 | −0.123554 | ||||||||
\(986\) | −18.7647 | −0.597589 | ||||||||
\(987\) | 67.1407 | 2.13711 | ||||||||
\(988\) | 43.0596 | 1.36991 | ||||||||
\(989\) | −18.8161 | −0.598317 | ||||||||
\(990\) | −146.413 | −4.65331 | ||||||||
\(991\) | −24.0184 | −0.762969 | −0.381485 | − | 0.924375i | \(-0.624587\pi\) | ||||
−0.381485 | + | 0.924375i | \(0.624587\pi\) | |||||||
\(992\) | 1.45936 | 0.0463349 | ||||||||
\(993\) | −101.226 | −3.21231 | ||||||||
\(994\) | −13.9418 | −0.442207 | ||||||||
\(995\) | −53.0736 | −1.68255 | ||||||||
\(996\) | 60.9941 | 1.93267 | ||||||||
\(997\) | −0.274695 | −0.00869969 | −0.00434984 | − | 0.999991i | \(-0.501385\pi\) | ||||
−0.00434984 | + | 0.999991i | \(0.501385\pi\) | |||||||
\(998\) | −110.993 | −3.51343 | ||||||||
\(999\) | 10.2339 | 0.323785 |
(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 | 8033.2.a.b.1.5 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8033.2.a.b.1.5 | ✓ | 153 | 1.1 | even | 1 | trivial |