Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44806 | −1.73104 | −0.865521 | − | 0.500873i | \(-0.833012\pi\) | ||||
−0.865521 | + | 0.500873i | \(0.833012\pi\) | |||||||
\(3\) | 0.638947 | 0.368896 | 0.184448 | − | 0.982842i | \(-0.440950\pi\) | ||||
0.184448 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(4\) | 3.99301 | 1.99650 | ||||||||
\(5\) | 2.71697 | 1.21507 | 0.607534 | − | 0.794294i | \(-0.292159\pi\) | ||||
0.607534 | + | 0.794294i | \(0.292159\pi\) | |||||||
\(6\) | −1.56418 | −0.638574 | ||||||||
\(7\) | −2.58742 | −0.977954 | −0.488977 | − | 0.872297i | \(-0.662630\pi\) | ||||
−0.488977 | + | 0.872297i | \(0.662630\pi\) | |||||||
\(8\) | −4.87901 | −1.72499 | ||||||||
\(9\) | −2.59175 | −0.863916 | ||||||||
\(10\) | −6.65132 | −2.10333 | ||||||||
\(11\) | −1.21810 | −0.367270 | −0.183635 | − | 0.982994i | \(-0.558786\pi\) | ||||
−0.183635 | + | 0.982994i | \(0.558786\pi\) | |||||||
\(12\) | 2.55132 | 0.736502 | ||||||||
\(13\) | 3.03775 | 0.842520 | 0.421260 | − | 0.906940i | \(-0.361588\pi\) | ||||
0.421260 | + | 0.906940i | \(0.361588\pi\) | |||||||
\(14\) | 6.33417 | 1.69288 | ||||||||
\(15\) | 1.73600 | 0.448234 | ||||||||
\(16\) | 3.95809 | 0.989523 | ||||||||
\(17\) | −7.02111 | −1.70287 | −0.851434 | − | 0.524461i | \(-0.824267\pi\) | ||||
−0.851434 | + | 0.524461i | \(0.824267\pi\) | |||||||
\(18\) | 6.34476 | 1.49547 | ||||||||
\(19\) | −2.68795 | −0.616657 | −0.308329 | − | 0.951280i | \(-0.599770\pi\) | ||||
−0.308329 | + | 0.951280i | \(0.599770\pi\) | |||||||
\(20\) | 10.8489 | 2.42589 | ||||||||
\(21\) | −1.65323 | −0.360763 | ||||||||
\(22\) | 2.98198 | 0.635760 | ||||||||
\(23\) | 3.79072 | 0.790420 | 0.395210 | − | 0.918591i | \(-0.370672\pi\) | ||||
0.395210 | + | 0.918591i | \(0.370672\pi\) | |||||||
\(24\) | −3.11742 | −0.636342 | ||||||||
\(25\) | 2.38195 | 0.476390 | ||||||||
\(26\) | −7.43660 | −1.45844 | ||||||||
\(27\) | −3.57283 | −0.687591 | ||||||||
\(28\) | −10.3316 | −1.95249 | ||||||||
\(29\) | 2.04796 | 0.380297 | 0.190149 | − | 0.981755i | \(-0.439103\pi\) | ||||
0.190149 | + | 0.981755i | \(0.439103\pi\) | |||||||
\(30\) | −4.24984 | −0.775911 | ||||||||
\(31\) | 1.27817 | 0.229567 | 0.114783 | − | 0.993391i | \(-0.463383\pi\) | ||||
0.114783 | + | 0.993391i | \(0.463383\pi\) | |||||||
\(32\) | 0.0683552 | 0.0120836 | ||||||||
\(33\) | −0.778299 | −0.135484 | ||||||||
\(34\) | 17.1881 | 2.94774 | ||||||||
\(35\) | −7.02997 | −1.18828 | ||||||||
\(36\) | −10.3489 | −1.72481 | ||||||||
\(37\) | −1.90866 | −0.313781 | −0.156891 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156891 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(38\) | 6.58026 | 1.06746 | ||||||||
\(39\) | 1.94096 | 0.310802 | ||||||||
\(40\) | −13.2561 | −2.09598 | ||||||||
\(41\) | 5.31602 | 0.830223 | 0.415112 | − | 0.909770i | \(-0.363742\pi\) | ||||
0.415112 | + | 0.909770i | \(0.363742\pi\) | |||||||
\(42\) | 4.04720 | 0.624496 | ||||||||
\(43\) | 10.0162 | 1.52745 | 0.763727 | − | 0.645539i | \(-0.223367\pi\) | ||||
0.763727 | + | 0.645539i | \(0.223367\pi\) | |||||||
\(44\) | −4.86387 | −0.733256 | ||||||||
\(45\) | −7.04171 | −1.04972 | ||||||||
\(46\) | −9.27992 | −1.36825 | ||||||||
\(47\) | −0.542905 | −0.0791909 | −0.0395954 | − | 0.999216i | \(-0.512607\pi\) | ||||
−0.0395954 | + | 0.999216i | \(0.512607\pi\) | |||||||
\(48\) | 2.52901 | 0.365031 | ||||||||
\(49\) | −0.305236 | −0.0436052 | ||||||||
\(50\) | −5.83116 | −0.824651 | ||||||||
\(51\) | −4.48611 | −0.628182 | ||||||||
\(52\) | 12.1298 | 1.68209 | ||||||||
\(53\) | −0.780766 | −0.107246 | −0.0536232 | − | 0.998561i | \(-0.517077\pi\) | ||||
−0.0536232 | + | 0.998561i | \(0.517077\pi\) | |||||||
\(54\) | 8.74650 | 1.19025 | ||||||||
\(55\) | −3.30954 | −0.446258 | ||||||||
\(56\) | 12.6241 | 1.68696 | ||||||||
\(57\) | −1.71745 | −0.227482 | ||||||||
\(58\) | −5.01354 | −0.658310 | ||||||||
\(59\) | 1.67584 | 0.218176 | 0.109088 | − | 0.994032i | \(-0.465207\pi\) | ||||
0.109088 | + | 0.994032i | \(0.465207\pi\) | |||||||
\(60\) | 6.93187 | 0.894900 | ||||||||
\(61\) | 3.68160 | 0.471380 | 0.235690 | − | 0.971828i | \(-0.424265\pi\) | ||||
0.235690 | + | 0.971828i | \(0.424265\pi\) | |||||||
\(62\) | −3.12905 | −0.397390 | ||||||||
\(63\) | 6.70595 | 0.844870 | ||||||||
\(64\) | −8.08352 | −1.01044 | ||||||||
\(65\) | 8.25349 | 1.02372 | ||||||||
\(66\) | 1.90532 | 0.234529 | ||||||||
\(67\) | −3.02607 | −0.369694 | −0.184847 | − | 0.982767i | \(-0.559179\pi\) | ||||
−0.184847 | + | 0.982767i | \(0.559179\pi\) | |||||||
\(68\) | −28.0353 | −3.39978 | ||||||||
\(69\) | 2.42207 | 0.291583 | ||||||||
\(70\) | 17.2098 | 2.05696 | ||||||||
\(71\) | −6.94609 | −0.824350 | −0.412175 | − | 0.911105i | \(-0.635231\pi\) | ||||
−0.412175 | + | 0.911105i | \(0.635231\pi\) | |||||||
\(72\) | 12.6451 | 1.49024 | ||||||||
\(73\) | −9.17151 | −1.07344 | −0.536722 | − | 0.843759i | \(-0.680338\pi\) | ||||
−0.536722 | + | 0.843759i | \(0.680338\pi\) | |||||||
\(74\) | 4.67251 | 0.543168 | ||||||||
\(75\) | 1.52194 | 0.175738 | ||||||||
\(76\) | −10.7330 | −1.23116 | ||||||||
\(77\) | 3.15173 | 0.359173 | ||||||||
\(78\) | −4.75159 | −0.538012 | ||||||||
\(79\) | −10.3060 | −1.15952 | −0.579760 | − | 0.814787i | \(-0.696854\pi\) | ||||
−0.579760 | + | 0.814787i | \(0.696854\pi\) | |||||||
\(80\) | 10.7540 | 1.20234 | ||||||||
\(81\) | 5.49240 | 0.610266 | ||||||||
\(82\) | −13.0140 | −1.43715 | ||||||||
\(83\) | 2.04260 | 0.224204 | 0.112102 | − | 0.993697i | \(-0.464242\pi\) | ||||
0.112102 | + | 0.993697i | \(0.464242\pi\) | |||||||
\(84\) | −6.60134 | −0.720266 | ||||||||
\(85\) | −19.0762 | −2.06910 | ||||||||
\(86\) | −24.5203 | −2.64409 | ||||||||
\(87\) | 1.30854 | 0.140290 | ||||||||
\(88\) | 5.94310 | 0.633537 | ||||||||
\(89\) | 7.64182 | 0.810031 | 0.405016 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405016 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(90\) | 17.2385 | 1.81710 | ||||||||
\(91\) | −7.85995 | −0.823946 | ||||||||
\(92\) | 15.1364 | 1.57808 | ||||||||
\(93\) | 0.816685 | 0.0846863 | ||||||||
\(94\) | 1.32907 | 0.137083 | ||||||||
\(95\) | −7.30308 | −0.749280 | ||||||||
\(96\) | 0.0436753 | 0.00445759 | ||||||||
\(97\) | 10.5494 | 1.07113 | 0.535564 | − | 0.844495i | \(-0.320099\pi\) | ||||
0.535564 | + | 0.844495i | \(0.320099\pi\) | |||||||
\(98\) | 0.747237 | 0.0754823 | ||||||||
\(99\) | 3.15700 | 0.317290 | ||||||||
\(100\) | 9.51114 | 0.951114 | ||||||||
\(101\) | −14.3572 | −1.42860 | −0.714298 | − | 0.699842i | \(-0.753254\pi\) | ||||
−0.714298 | + | 0.699842i | \(0.753254\pi\) | |||||||
\(102\) | 10.9823 | 1.08741 | ||||||||
\(103\) | 2.84322 | 0.280150 | 0.140075 | − | 0.990141i | \(-0.455266\pi\) | ||||
0.140075 | + | 0.990141i | \(0.455266\pi\) | |||||||
\(104\) | −14.8212 | −1.45334 | ||||||||
\(105\) | −4.49177 | −0.438352 | ||||||||
\(106\) | 1.91136 | 0.185648 | ||||||||
\(107\) | −5.30612 | −0.512962 | −0.256481 | − | 0.966549i | \(-0.582563\pi\) | ||||
−0.256481 | + | 0.966549i | \(0.582563\pi\) | |||||||
\(108\) | −14.2663 | −1.37278 | ||||||||
\(109\) | 14.6961 | 1.40763 | 0.703816 | − | 0.710382i | \(-0.251478\pi\) | ||||
0.703816 | + | 0.710382i | \(0.251478\pi\) | |||||||
\(110\) | 8.10196 | 0.772491 | ||||||||
\(111\) | −1.21953 | −0.115753 | ||||||||
\(112\) | −10.2413 | −0.967708 | ||||||||
\(113\) | 6.47672 | 0.609279 | 0.304639 | − | 0.952468i | \(-0.401464\pi\) | ||||
0.304639 | + | 0.952468i | \(0.401464\pi\) | |||||||
\(114\) | 4.20443 | 0.393781 | ||||||||
\(115\) | 10.2993 | 0.960414 | ||||||||
\(116\) | 8.17754 | 0.759265 | ||||||||
\(117\) | −7.87308 | −0.727866 | ||||||||
\(118\) | −4.10256 | −0.377671 | ||||||||
\(119\) | 18.1666 | 1.66533 | ||||||||
\(120\) | −8.46996 | −0.773198 | ||||||||
\(121\) | −9.51624 | −0.865113 | ||||||||
\(122\) | −9.01278 | −0.815979 | ||||||||
\(123\) | 3.39666 | 0.306266 | ||||||||
\(124\) | 5.10376 | 0.458331 | ||||||||
\(125\) | −7.11317 | −0.636222 | ||||||||
\(126\) | −16.4166 | −1.46251 | ||||||||
\(127\) | 21.4938 | 1.90726 | 0.953632 | − | 0.300975i | \(-0.0973122\pi\) | ||||
0.953632 | + | 0.300975i | \(0.0973122\pi\) | |||||||
\(128\) | 19.6523 | 1.73703 | ||||||||
\(129\) | 6.39981 | 0.563472 | ||||||||
\(130\) | −20.2050 | −1.77210 | ||||||||
\(131\) | 17.9998 | 1.57265 | 0.786323 | − | 0.617816i | \(-0.211982\pi\) | ||||
0.786323 | + | 0.617816i | \(0.211982\pi\) | |||||||
\(132\) | −3.10775 | −0.270495 | ||||||||
\(133\) | 6.95486 | 0.603063 | ||||||||
\(134\) | 7.40801 | 0.639955 | ||||||||
\(135\) | −9.70728 | −0.835470 | ||||||||
\(136\) | 34.2560 | 2.93743 | ||||||||
\(137\) | −20.2559 | −1.73058 | −0.865291 | − | 0.501270i | \(-0.832866\pi\) | ||||
−0.865291 | + | 0.501270i | \(0.832866\pi\) | |||||||
\(138\) | −5.92937 | −0.504742 | ||||||||
\(139\) | 19.5490 | 1.65813 | 0.829063 | − | 0.559155i | \(-0.188874\pi\) | ||||
0.829063 | + | 0.559155i | \(0.188874\pi\) | |||||||
\(140\) | −28.0707 | −2.37241 | ||||||||
\(141\) | −0.346887 | −0.0292132 | ||||||||
\(142\) | 17.0045 | 1.42698 | ||||||||
\(143\) | −3.70027 | −0.309432 | ||||||||
\(144\) | −10.2584 | −0.854865 | ||||||||
\(145\) | 5.56427 | 0.462087 | ||||||||
\(146\) | 22.4524 | 1.85818 | ||||||||
\(147\) | −0.195030 | −0.0160858 | ||||||||
\(148\) | −7.62128 | −0.626465 | ||||||||
\(149\) | 23.8697 | 1.95548 | 0.977739 | − | 0.209825i | \(-0.0672893\pi\) | ||||
0.977739 | + | 0.209825i | \(0.0672893\pi\) | |||||||
\(150\) | −3.72580 | −0.304210 | ||||||||
\(151\) | 3.46765 | 0.282193 | 0.141096 | − | 0.989996i | \(-0.454937\pi\) | ||||
0.141096 | + | 0.989996i | \(0.454937\pi\) | |||||||
\(152\) | 13.1145 | 1.06373 | ||||||||
\(153\) | 18.1969 | 1.47114 | ||||||||
\(154\) | −7.71564 | −0.621744 | ||||||||
\(155\) | 3.47277 | 0.278939 | ||||||||
\(156\) | 7.75027 | 0.620518 | ||||||||
\(157\) | −14.7265 | −1.17531 | −0.587653 | − | 0.809113i | \(-0.699948\pi\) | ||||
−0.587653 | + | 0.809113i | \(0.699948\pi\) | |||||||
\(158\) | 25.2298 | 2.00718 | ||||||||
\(159\) | −0.498868 | −0.0395628 | ||||||||
\(160\) | 0.185719 | 0.0146824 | ||||||||
\(161\) | −9.80820 | −0.772995 | ||||||||
\(162\) | −13.4457 | −1.05640 | ||||||||
\(163\) | −15.3276 | −1.20055 | −0.600274 | − | 0.799795i | \(-0.704942\pi\) | ||||
−0.600274 | + | 0.799795i | \(0.704942\pi\) | |||||||
\(164\) | 21.2269 | 1.65754 | ||||||||
\(165\) | −2.11462 | −0.164623 | ||||||||
\(166\) | −5.00040 | −0.388107 | ||||||||
\(167\) | 16.4302 | 1.27141 | 0.635705 | − | 0.771932i | \(-0.280709\pi\) | ||||
0.635705 | + | 0.771932i | \(0.280709\pi\) | |||||||
\(168\) | 8.06610 | 0.622313 | ||||||||
\(169\) | −3.77208 | −0.290160 | ||||||||
\(170\) | 46.6996 | 3.58170 | ||||||||
\(171\) | 6.96648 | 0.532740 | ||||||||
\(172\) | 39.9947 | 3.04957 | ||||||||
\(173\) | 18.0974 | 1.37592 | 0.687959 | − | 0.725749i | \(-0.258507\pi\) | ||||
0.687959 | + | 0.725749i | \(0.258507\pi\) | |||||||
\(174\) | −3.20339 | −0.242848 | ||||||||
\(175\) | −6.16312 | −0.465888 | ||||||||
\(176\) | −4.82134 | −0.363422 | ||||||||
\(177\) | 1.07077 | 0.0804842 | ||||||||
\(178\) | −18.7077 | −1.40220 | ||||||||
\(179\) | −13.6150 | −1.01763 | −0.508815 | − | 0.860876i | \(-0.669916\pi\) | ||||
−0.508815 | + | 0.860876i | \(0.669916\pi\) | |||||||
\(180\) | −28.1176 | −2.09576 | ||||||||
\(181\) | 18.8659 | 1.40229 | 0.701144 | − | 0.713019i | \(-0.252673\pi\) | ||||
0.701144 | + | 0.713019i | \(0.252673\pi\) | |||||||
\(182\) | 19.2416 | 1.42628 | ||||||||
\(183\) | 2.35234 | 0.173890 | ||||||||
\(184\) | −18.4949 | −1.36347 | ||||||||
\(185\) | −5.18577 | −0.381265 | ||||||||
\(186\) | −1.99930 | −0.146596 | ||||||||
\(187\) | 8.55239 | 0.625413 | ||||||||
\(188\) | −2.16782 | −0.158105 | ||||||||
\(189\) | 9.24442 | 0.672433 | ||||||||
\(190\) | 17.8784 | 1.29704 | ||||||||
\(191\) | 24.6849 | 1.78614 | 0.893070 | − | 0.449918i | \(-0.148547\pi\) | ||||
0.893070 | + | 0.449918i | \(0.148547\pi\) | |||||||
\(192\) | −5.16494 | −0.372747 | ||||||||
\(193\) | 4.00533 | 0.288310 | 0.144155 | − | 0.989555i | \(-0.453954\pi\) | ||||
0.144155 | + | 0.989555i | \(0.453954\pi\) | |||||||
\(194\) | −25.8255 | −1.85417 | ||||||||
\(195\) | 5.27354 | 0.377646 | ||||||||
\(196\) | −1.21881 | −0.0870579 | ||||||||
\(197\) | 12.4603 | 0.887762 | 0.443881 | − | 0.896086i | \(-0.353601\pi\) | ||||
0.443881 | + | 0.896086i | \(0.353601\pi\) | |||||||
\(198\) | −7.72853 | −0.549243 | ||||||||
\(199\) | −8.10231 | −0.574358 | −0.287179 | − | 0.957877i | \(-0.592717\pi\) | ||||
−0.287179 | + | 0.957877i | \(0.592717\pi\) | |||||||
\(200\) | −11.6215 | −0.821768 | ||||||||
\(201\) | −1.93350 | −0.136378 | ||||||||
\(202\) | 35.1473 | 2.47296 | ||||||||
\(203\) | −5.29895 | −0.371913 | ||||||||
\(204\) | −17.9131 | −1.25417 | ||||||||
\(205\) | 14.4435 | 1.00878 | ||||||||
\(206\) | −6.96037 | −0.484952 | ||||||||
\(207\) | −9.82459 | −0.682856 | ||||||||
\(208\) | 12.0237 | 0.833693 | ||||||||
\(209\) | 3.27418 | 0.226480 | ||||||||
\(210\) | 10.9961 | 0.758806 | ||||||||
\(211\) | −1.81191 | −0.124737 | −0.0623685 | − | 0.998053i | \(-0.519865\pi\) | ||||
−0.0623685 | + | 0.998053i | \(0.519865\pi\) | |||||||
\(212\) | −3.11760 | −0.214118 | ||||||||
\(213\) | −4.43818 | −0.304099 | ||||||||
\(214\) | 12.9897 | 0.887959 | ||||||||
\(215\) | 27.2137 | 1.85596 | ||||||||
\(216\) | 17.4318 | 1.18609 | ||||||||
\(217\) | −3.30718 | −0.224506 | ||||||||
\(218\) | −35.9770 | −2.43667 | ||||||||
\(219\) | −5.86010 | −0.395989 | ||||||||
\(220\) | −13.2150 | −0.890956 | ||||||||
\(221\) | −21.3284 | −1.43470 | ||||||||
\(222\) | 2.98548 | 0.200373 | ||||||||
\(223\) | 15.7492 | 1.05464 | 0.527321 | − | 0.849666i | \(-0.323196\pi\) | ||||
0.527321 | + | 0.849666i | \(0.323196\pi\) | |||||||
\(224\) | −0.176864 | −0.0118172 | ||||||||
\(225\) | −6.17341 | −0.411561 | ||||||||
\(226\) | −15.8554 | −1.05469 | ||||||||
\(227\) | 28.2574 | 1.87551 | 0.937755 | − | 0.347298i | \(-0.112901\pi\) | ||||
0.937755 | + | 0.347298i | \(0.112901\pi\) | |||||||
\(228\) | −6.85781 | −0.454169 | ||||||||
\(229\) | 4.06379 | 0.268543 | 0.134271 | − | 0.990945i | \(-0.457131\pi\) | ||||
0.134271 | + | 0.990945i | \(0.457131\pi\) | |||||||
\(230\) | −25.2133 | −1.66252 | ||||||||
\(231\) | 2.01379 | 0.132498 | ||||||||
\(232\) | −9.99203 | −0.656009 | ||||||||
\(233\) | −12.5962 | −0.825205 | −0.412603 | − | 0.910911i | \(-0.635380\pi\) | ||||
−0.412603 | + | 0.910911i | \(0.635380\pi\) | |||||||
\(234\) | 19.2738 | 1.25997 | ||||||||
\(235\) | −1.47506 | −0.0962223 | ||||||||
\(236\) | 6.69164 | 0.435589 | ||||||||
\(237\) | −6.58501 | −0.427742 | ||||||||
\(238\) | −44.4729 | −2.88275 | ||||||||
\(239\) | −9.72816 | −0.629263 | −0.314631 | − | 0.949214i | \(-0.601881\pi\) | ||||
−0.314631 | + | 0.949214i | \(0.601881\pi\) | |||||||
\(240\) | 6.87126 | 0.443538 | ||||||||
\(241\) | −3.20338 | −0.206348 | −0.103174 | − | 0.994663i | \(-0.532900\pi\) | ||||
−0.103174 | + | 0.994663i | \(0.532900\pi\) | |||||||
\(242\) | 23.2963 | 1.49755 | ||||||||
\(243\) | 14.2278 | 0.912716 | ||||||||
\(244\) | 14.7006 | 0.941112 | ||||||||
\(245\) | −0.829319 | −0.0529832 | ||||||||
\(246\) | −8.31522 | −0.530159 | ||||||||
\(247\) | −8.16531 | −0.519546 | ||||||||
\(248\) | −6.23622 | −0.396000 | ||||||||
\(249\) | 1.30511 | 0.0827080 | ||||||||
\(250\) | 17.4135 | 1.10133 | ||||||||
\(251\) | −6.66846 | −0.420909 | −0.210455 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210455 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(252\) | 26.7769 | 1.68679 | ||||||||
\(253\) | −4.61747 | −0.290298 | ||||||||
\(254\) | −52.6181 | −3.30155 | ||||||||
\(255\) | −12.1887 | −0.763283 | ||||||||
\(256\) | −31.9429 | −1.99643 | ||||||||
\(257\) | 13.3549 | 0.833057 | 0.416529 | − | 0.909123i | \(-0.363247\pi\) | ||||
0.416529 | + | 0.909123i | \(0.363247\pi\) | |||||||
\(258\) | −15.6671 | −0.975393 | ||||||||
\(259\) | 4.93850 | 0.306864 | ||||||||
\(260\) | 32.9562 | 2.04386 | ||||||||
\(261\) | −5.30780 | −0.328545 | ||||||||
\(262\) | −44.0645 | −2.72231 | ||||||||
\(263\) | 4.48350 | 0.276464 | 0.138232 | − | 0.990400i | \(-0.455858\pi\) | ||||
0.138232 | + | 0.990400i | \(0.455858\pi\) | |||||||
\(264\) | 3.79733 | 0.233709 | ||||||||
\(265\) | −2.12132 | −0.130312 | ||||||||
\(266\) | −17.0259 | −1.04393 | ||||||||
\(267\) | 4.88272 | 0.298817 | ||||||||
\(268\) | −12.0831 | −0.738095 | ||||||||
\(269\) | 7.97761 | 0.486404 | 0.243202 | − | 0.969976i | \(-0.421802\pi\) | ||||
0.243202 | + | 0.969976i | \(0.421802\pi\) | |||||||
\(270\) | 23.7640 | 1.44623 | ||||||||
\(271\) | −29.8671 | −1.81430 | −0.907148 | − | 0.420812i | \(-0.861745\pi\) | ||||
−0.907148 | + | 0.420812i | \(0.861745\pi\) | |||||||
\(272\) | −27.7902 | −1.68503 | ||||||||
\(273\) | −5.02209 | −0.303950 | ||||||||
\(274\) | 49.5878 | 2.99571 | ||||||||
\(275\) | −2.90145 | −0.174964 | ||||||||
\(276\) | 9.67133 | 0.582146 | ||||||||
\(277\) | 29.3875 | 1.76573 | 0.882863 | − | 0.469631i | \(-0.155613\pi\) | ||||
0.882863 | + | 0.469631i | \(0.155613\pi\) | |||||||
\(278\) | −47.8572 | −2.87029 | ||||||||
\(279\) | −3.31271 | −0.198326 | ||||||||
\(280\) | 34.2992 | 2.04977 | ||||||||
\(281\) | 19.0313 | 1.13531 | 0.567655 | − | 0.823266i | \(-0.307851\pi\) | ||||
0.567655 | + | 0.823266i | \(0.307851\pi\) | |||||||
\(282\) | 0.849202 | 0.0505692 | ||||||||
\(283\) | 10.1295 | 0.602137 | 0.301068 | − | 0.953603i | \(-0.402657\pi\) | ||||
0.301068 | + | 0.953603i | \(0.402657\pi\) | |||||||
\(284\) | −27.7358 | −1.64582 | ||||||||
\(285\) | −4.66628 | −0.276407 | ||||||||
\(286\) | 9.05850 | 0.535640 | ||||||||
\(287\) | −13.7548 | −0.811921 | ||||||||
\(288\) | −0.177159 | −0.0104392 | ||||||||
\(289\) | 32.2960 | 1.89976 | ||||||||
\(290\) | −13.6217 | −0.799892 | ||||||||
\(291\) | 6.74049 | 0.395135 | ||||||||
\(292\) | −36.6219 | −2.14313 | ||||||||
\(293\) | 5.97991 | 0.349350 | 0.174675 | − | 0.984626i | \(-0.444113\pi\) | ||||
0.174675 | + | 0.984626i | \(0.444113\pi\) | |||||||
\(294\) | 0.477445 | 0.0278451 | ||||||||
\(295\) | 4.55322 | 0.265099 | ||||||||
\(296\) | 9.31234 | 0.541269 | ||||||||
\(297\) | 4.35205 | 0.252532 | ||||||||
\(298\) | −58.4344 | −3.38501 | ||||||||
\(299\) | 11.5153 | 0.665945 | ||||||||
\(300\) | 6.07711 | 0.350862 | ||||||||
\(301\) | −25.9161 | −1.49378 | ||||||||
\(302\) | −8.48901 | −0.488488 | ||||||||
\(303\) | −9.17349 | −0.527003 | ||||||||
\(304\) | −10.6391 | −0.610197 | ||||||||
\(305\) | 10.0028 | 0.572759 | ||||||||
\(306\) | −44.5472 | −2.54660 | ||||||||
\(307\) | −6.15134 | −0.351076 | −0.175538 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175538 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(308\) | 12.5849 | 0.717091 | ||||||||
\(309\) | 1.81666 | 0.103346 | ||||||||
\(310\) | −8.50155 | −0.482856 | ||||||||
\(311\) | −18.2099 | −1.03259 | −0.516294 | − | 0.856411i | \(-0.672689\pi\) | ||||
−0.516294 | + | 0.856411i | \(0.672689\pi\) | |||||||
\(312\) | −9.46995 | −0.536131 | ||||||||
\(313\) | −4.30348 | −0.243247 | −0.121624 | − | 0.992576i | \(-0.538810\pi\) | ||||
−0.121624 | + | 0.992576i | \(0.538810\pi\) | |||||||
\(314\) | 36.0515 | 2.03450 | ||||||||
\(315\) | 18.2199 | 1.02657 | ||||||||
\(316\) | −41.1521 | −2.31498 | ||||||||
\(317\) | 4.32905 | 0.243144 | 0.121572 | − | 0.992583i | \(-0.461207\pi\) | ||||
0.121572 | + | 0.992583i | \(0.461207\pi\) | |||||||
\(318\) | 1.22126 | 0.0684848 | ||||||||
\(319\) | −2.49462 | −0.139672 | ||||||||
\(320\) | −21.9627 | −1.22775 | ||||||||
\(321\) | −3.39033 | −0.189230 | ||||||||
\(322\) | 24.0111 | 1.33809 | ||||||||
\(323\) | 18.8724 | 1.05009 | ||||||||
\(324\) | 21.9312 | 1.21840 | ||||||||
\(325\) | 7.23577 | 0.401368 | ||||||||
\(326\) | 37.5228 | 2.07820 | ||||||||
\(327\) | 9.39003 | 0.519270 | ||||||||
\(328\) | −25.9369 | −1.43213 | ||||||||
\(329\) | 1.40473 | 0.0774450 | ||||||||
\(330\) | 5.17672 | 0.284969 | ||||||||
\(331\) | −22.7375 | −1.24977 | −0.624883 | − | 0.780718i | \(-0.714853\pi\) | ||||
−0.624883 | + | 0.780718i | \(0.714853\pi\) | |||||||
\(332\) | 8.15610 | 0.447624 | ||||||||
\(333\) | 4.94675 | 0.271080 | ||||||||
\(334\) | −40.2222 | −2.20086 | ||||||||
\(335\) | −8.22176 | −0.449203 | ||||||||
\(336\) | −6.54362 | −0.356984 | ||||||||
\(337\) | −26.8457 | −1.46238 | −0.731190 | − | 0.682174i | \(-0.761035\pi\) | ||||
−0.731190 | + | 0.682174i | \(0.761035\pi\) | |||||||
\(338\) | 9.23428 | 0.502279 | ||||||||
\(339\) | 4.13828 | 0.224761 | ||||||||
\(340\) | −76.1713 | −4.13097 | ||||||||
\(341\) | −1.55694 | −0.0843131 | ||||||||
\(342\) | −17.0544 | −0.922195 | ||||||||
\(343\) | 18.9017 | 1.02060 | ||||||||
\(344\) | −48.8690 | −2.63484 | ||||||||
\(345\) | 6.58070 | 0.354293 | ||||||||
\(346\) | −44.3035 | −2.38177 | ||||||||
\(347\) | 0.623186 | 0.0334544 | 0.0167272 | − | 0.999860i | \(-0.494675\pi\) | ||||
0.0167272 | + | 0.999860i | \(0.494675\pi\) | |||||||
\(348\) | 5.22501 | 0.280090 | ||||||||
\(349\) | −21.0827 | −1.12853 | −0.564266 | − | 0.825593i | \(-0.690841\pi\) | ||||
−0.564266 | + | 0.825593i | \(0.690841\pi\) | |||||||
\(350\) | 15.0877 | 0.806471 | ||||||||
\(351\) | −10.8534 | −0.579309 | ||||||||
\(352\) | −0.0832632 | −0.00443795 | ||||||||
\(353\) | −13.9529 | −0.742637 | −0.371319 | − | 0.928506i | \(-0.621094\pi\) | ||||
−0.371319 | + | 0.928506i | \(0.621094\pi\) | |||||||
\(354\) | −2.62132 | −0.139321 | ||||||||
\(355\) | −18.8724 | −1.00164 | ||||||||
\(356\) | 30.5138 | 1.61723 | ||||||||
\(357\) | 11.6075 | 0.614333 | ||||||||
\(358\) | 33.3303 | 1.76156 | ||||||||
\(359\) | 9.05258 | 0.477777 | 0.238888 | − | 0.971047i | \(-0.423217\pi\) | ||||
0.238888 | + | 0.971047i | \(0.423217\pi\) | |||||||
\(360\) | 34.3565 | 1.81075 | ||||||||
\(361\) | −11.7749 | −0.619734 | ||||||||
\(362\) | −46.1848 | −2.42742 | ||||||||
\(363\) | −6.08037 | −0.319137 | ||||||||
\(364\) | −31.3848 | −1.64501 | ||||||||
\(365\) | −24.9188 | −1.30431 | ||||||||
\(366\) | −5.75868 | −0.301011 | ||||||||
\(367\) | 19.7610 | 1.03152 | 0.515758 | − | 0.856734i | \(-0.327510\pi\) | ||||
0.515758 | + | 0.856734i | \(0.327510\pi\) | |||||||
\(368\) | 15.0040 | 0.782139 | ||||||||
\(369\) | −13.7778 | −0.717243 | ||||||||
\(370\) | 12.6951 | 0.659986 | ||||||||
\(371\) | 2.02017 | 0.104882 | ||||||||
\(372\) | 3.26103 | 0.169077 | ||||||||
\(373\) | 5.28206 | 0.273495 | 0.136747 | − | 0.990606i | \(-0.456335\pi\) | ||||
0.136747 | + | 0.990606i | \(0.456335\pi\) | |||||||
\(374\) | −20.9368 | −1.08262 | ||||||||
\(375\) | −4.54494 | −0.234700 | ||||||||
\(376\) | 2.64884 | 0.136603 | ||||||||
\(377\) | 6.22120 | 0.320408 | ||||||||
\(378\) | −22.6309 | −1.16401 | ||||||||
\(379\) | 4.91493 | 0.252463 | 0.126232 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126232 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(380\) | −29.1613 | −1.49594 | ||||||||
\(381\) | 13.7334 | 0.703582 | ||||||||
\(382\) | −60.4303 | −3.09188 | ||||||||
\(383\) | 12.4502 | 0.636175 | 0.318087 | − | 0.948061i | \(-0.396959\pi\) | ||||
0.318087 | + | 0.948061i | \(0.396959\pi\) | |||||||
\(384\) | 12.5567 | 0.640784 | ||||||||
\(385\) | 8.56318 | 0.436420 | ||||||||
\(386\) | −9.80529 | −0.499076 | ||||||||
\(387\) | −25.9594 | −1.31959 | ||||||||
\(388\) | 42.1238 | 2.13851 | ||||||||
\(389\) | 5.73019 | 0.290532 | 0.145266 | − | 0.989393i | \(-0.453596\pi\) | ||||
0.145266 | + | 0.989393i | \(0.453596\pi\) | |||||||
\(390\) | −12.9099 | −0.653721 | ||||||||
\(391\) | −26.6151 | −1.34598 | ||||||||
\(392\) | 1.48925 | 0.0752184 | ||||||||
\(393\) | 11.5009 | 0.580143 | ||||||||
\(394\) | −30.5037 | −1.53675 | ||||||||
\(395\) | −28.0012 | −1.40889 | ||||||||
\(396\) | 12.6059 | 0.633472 | ||||||||
\(397\) | 24.0411 | 1.20659 | 0.603295 | − | 0.797518i | \(-0.293854\pi\) | ||||
0.603295 | + | 0.797518i | \(0.293854\pi\) | |||||||
\(398\) | 19.8350 | 0.994237 | ||||||||
\(399\) | 4.44378 | 0.222467 | ||||||||
\(400\) | 9.42798 | 0.471399 | ||||||||
\(401\) | −19.7439 | −0.985963 | −0.492981 | − | 0.870040i | \(-0.664093\pi\) | ||||
−0.492981 | + | 0.870040i | \(0.664093\pi\) | |||||||
\(402\) | 4.73332 | 0.236077 | ||||||||
\(403\) | 3.88277 | 0.193415 | ||||||||
\(404\) | −57.3285 | −2.85220 | ||||||||
\(405\) | 14.9227 | 0.741515 | ||||||||
\(406\) | 12.9722 | 0.643798 | ||||||||
\(407\) | 2.32493 | 0.115242 | ||||||||
\(408\) | 21.8878 | 1.08361 | ||||||||
\(409\) | −24.3986 | −1.20643 | −0.603216 | − | 0.797578i | \(-0.706114\pi\) | ||||
−0.603216 | + | 0.797578i | \(0.706114\pi\) | |||||||
\(410\) | −35.3586 | −1.74624 | ||||||||
\(411\) | −12.9425 | −0.638405 | ||||||||
\(412\) | 11.3530 | 0.559321 | ||||||||
\(413\) | −4.33611 | −0.213366 | ||||||||
\(414\) | 24.0512 | 1.18205 | ||||||||
\(415\) | 5.54968 | 0.272423 | ||||||||
\(416\) | 0.207646 | 0.0101807 | ||||||||
\(417\) | 12.4908 | 0.611676 | ||||||||
\(418\) | −8.01540 | −0.392046 | ||||||||
\(419\) | 27.3441 | 1.33585 | 0.667923 | − | 0.744231i | \(-0.267184\pi\) | ||||
0.667923 | + | 0.744231i | \(0.267184\pi\) | |||||||
\(420\) | −17.9357 | −0.875172 | ||||||||
\(421\) | −19.0243 | −0.927190 | −0.463595 | − | 0.886047i | \(-0.653441\pi\) | ||||
−0.463595 | + | 0.886047i | \(0.653441\pi\) | |||||||
\(422\) | 4.43567 | 0.215925 | ||||||||
\(423\) | 1.40707 | 0.0684142 | ||||||||
\(424\) | 3.80936 | 0.184999 | ||||||||
\(425\) | −16.7239 | −0.811230 | ||||||||
\(426\) | 10.8649 | 0.526408 | ||||||||
\(427\) | −9.52585 | −0.460988 | ||||||||
\(428\) | −21.1874 | −1.02413 | ||||||||
\(429\) | −2.36428 | −0.114148 | ||||||||
\(430\) | −66.6209 | −3.21275 | ||||||||
\(431\) | 26.9087 | 1.29615 | 0.648074 | − | 0.761577i | \(-0.275575\pi\) | ||||
0.648074 | + | 0.761577i | \(0.275575\pi\) | |||||||
\(432\) | −14.1416 | −0.680387 | ||||||||
\(433\) | 1.64122 | 0.0788718 | 0.0394359 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394359 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(434\) | 8.09618 | 0.388629 | ||||||||
\(435\) | 3.55527 | 0.170462 | ||||||||
\(436\) | 58.6817 | 2.81034 | ||||||||
\(437\) | −10.1893 | −0.487418 | ||||||||
\(438\) | 14.3459 | 0.685474 | ||||||||
\(439\) | 2.23271 | 0.106562 | 0.0532808 | − | 0.998580i | \(-0.483032\pi\) | ||||
0.0532808 | + | 0.998580i | \(0.483032\pi\) | |||||||
\(440\) | 16.1473 | 0.769790 | ||||||||
\(441\) | 0.791095 | 0.0376712 | ||||||||
\(442\) | 52.2132 | 2.48353 | ||||||||
\(443\) | −16.8275 | −0.799497 | −0.399749 | − | 0.916625i | \(-0.630903\pi\) | ||||
−0.399749 | + | 0.916625i | \(0.630903\pi\) | |||||||
\(444\) | −4.86959 | −0.231101 | ||||||||
\(445\) | 20.7626 | 0.984243 | ||||||||
\(446\) | −38.5550 | −1.82563 | ||||||||
\(447\) | 15.2514 | 0.721368 | ||||||||
\(448\) | 20.9155 | 0.988165 | ||||||||
\(449\) | −25.1524 | −1.18702 | −0.593508 | − | 0.804828i | \(-0.702258\pi\) | ||||
−0.593508 | + | 0.804828i | \(0.702258\pi\) | |||||||
\(450\) | 15.1129 | 0.712429 | ||||||||
\(451\) | −6.47543 | −0.304916 | ||||||||
\(452\) | 25.8616 | 1.21643 | ||||||||
\(453\) | 2.21564 | 0.104100 | ||||||||
\(454\) | −69.1759 | −3.24658 | ||||||||
\(455\) | −21.3553 | −1.00115 | ||||||||
\(456\) | 8.37947 | 0.392405 | ||||||||
\(457\) | 6.34089 | 0.296614 | 0.148307 | − | 0.988941i | \(-0.452618\pi\) | ||||
0.148307 | + | 0.988941i | \(0.452618\pi\) | |||||||
\(458\) | −9.94841 | −0.464859 | ||||||||
\(459\) | 25.0852 | 1.17088 | ||||||||
\(460\) | 41.1251 | 1.91747 | ||||||||
\(461\) | 36.9823 | 1.72244 | 0.861220 | − | 0.508233i | \(-0.169701\pi\) | ||||
0.861220 | + | 0.508233i | \(0.169701\pi\) | |||||||
\(462\) | −4.92988 | −0.229359 | ||||||||
\(463\) | 2.01797 | 0.0937829 | 0.0468915 | − | 0.998900i | \(-0.485069\pi\) | ||||
0.0468915 | + | 0.998900i | \(0.485069\pi\) | |||||||
\(464\) | 8.10603 | 0.376313 | ||||||||
\(465\) | 2.21891 | 0.102900 | ||||||||
\(466\) | 30.8363 | 1.42846 | ||||||||
\(467\) | 10.4813 | 0.485017 | 0.242508 | − | 0.970149i | \(-0.422030\pi\) | ||||
0.242508 | + | 0.970149i | \(0.422030\pi\) | |||||||
\(468\) | −31.4373 | −1.45319 | ||||||||
\(469\) | 7.82973 | 0.361543 | ||||||||
\(470\) | 3.61104 | 0.166565 | ||||||||
\(471\) | −9.40947 | −0.433566 | ||||||||
\(472\) | −8.17644 | −0.376351 | ||||||||
\(473\) | −12.2007 | −0.560988 | ||||||||
\(474\) | 16.1205 | 0.740439 | ||||||||
\(475\) | −6.40255 | −0.293769 | ||||||||
\(476\) | 72.5393 | 3.32483 | ||||||||
\(477\) | 2.02355 | 0.0926519 | ||||||||
\(478\) | 23.8151 | 1.08928 | ||||||||
\(479\) | 3.18121 | 0.145353 | 0.0726766 | − | 0.997356i | \(-0.476846\pi\) | ||||
0.0726766 | + | 0.997356i | \(0.476846\pi\) | |||||||
\(480\) | 0.118665 | 0.00541628 | ||||||||
\(481\) | −5.79802 | −0.264367 | ||||||||
\(482\) | 7.84207 | 0.357197 | ||||||||
\(483\) | −6.26692 | −0.285155 | ||||||||
\(484\) | −37.9984 | −1.72720 | ||||||||
\(485\) | 28.6624 | 1.30149 | ||||||||
\(486\) | −34.8306 | −1.57995 | ||||||||
\(487\) | 19.3044 | 0.874765 | 0.437383 | − | 0.899276i | \(-0.355906\pi\) | ||||
0.437383 | + | 0.899276i | \(0.355906\pi\) | |||||||
\(488\) | −17.9625 | −0.813126 | ||||||||
\(489\) | −9.79350 | −0.442877 | ||||||||
\(490\) | 2.03022 | 0.0917162 | ||||||||
\(491\) | 11.5390 | 0.520747 | 0.260373 | − | 0.965508i | \(-0.416154\pi\) | ||||
0.260373 | + | 0.965508i | \(0.416154\pi\) | |||||||
\(492\) | 13.5629 | 0.611461 | ||||||||
\(493\) | −14.3790 | −0.647597 | ||||||||
\(494\) | 19.9892 | 0.899356 | ||||||||
\(495\) | 8.57749 | 0.385529 | ||||||||
\(496\) | 5.05913 | 0.227162 | ||||||||
\(497\) | 17.9725 | 0.806176 | ||||||||
\(498\) | −3.19499 | −0.143171 | ||||||||
\(499\) | 14.8497 | 0.664764 | 0.332382 | − | 0.943145i | \(-0.392148\pi\) | ||||
0.332382 | + | 0.943145i | \(0.392148\pi\) | |||||||
\(500\) | −28.4030 | −1.27022 | ||||||||
\(501\) | 10.4980 | 0.469018 | ||||||||
\(502\) | 16.3248 | 0.728612 | ||||||||
\(503\) | 26.7758 | 1.19387 | 0.596937 | − | 0.802288i | \(-0.296384\pi\) | ||||
0.596937 | + | 0.802288i | \(0.296384\pi\) | |||||||
\(504\) | −32.7184 | −1.45739 | ||||||||
\(505\) | −39.0082 | −1.73584 | ||||||||
\(506\) | 11.3038 | 0.502517 | ||||||||
\(507\) | −2.41016 | −0.107039 | ||||||||
\(508\) | 85.8248 | 3.80786 | ||||||||
\(509\) | 3.91792 | 0.173659 | 0.0868294 | − | 0.996223i | \(-0.472326\pi\) | ||||
0.0868294 | + | 0.996223i | \(0.472326\pi\) | |||||||
\(510\) | 29.8386 | 1.32127 | ||||||||
\(511\) | 23.7306 | 1.04978 | ||||||||
\(512\) | 38.8937 | 1.71887 | ||||||||
\(513\) | 9.60357 | 0.424008 | ||||||||
\(514\) | −32.6937 | −1.44206 | ||||||||
\(515\) | 7.72495 | 0.340402 | ||||||||
\(516\) | 25.5545 | 1.12497 | ||||||||
\(517\) | 0.661311 | 0.0290844 | ||||||||
\(518\) | −12.0898 | −0.531194 | ||||||||
\(519\) | 11.5633 | 0.507571 | ||||||||
\(520\) | −40.2688 | −1.76590 | ||||||||
\(521\) | 22.1673 | 0.971168 | 0.485584 | − | 0.874190i | \(-0.338607\pi\) | ||||
0.485584 | + | 0.874190i | \(0.338607\pi\) | |||||||
\(522\) | 12.9938 | 0.568725 | ||||||||
\(523\) | 16.9234 | 0.740010 | 0.370005 | − | 0.929030i | \(-0.379356\pi\) | ||||
0.370005 | + | 0.929030i | \(0.379356\pi\) | |||||||
\(524\) | 71.8731 | 3.13979 | ||||||||
\(525\) | −3.93790 | −0.171864 | ||||||||
\(526\) | −10.9759 | −0.478571 | ||||||||
\(527\) | −8.97420 | −0.390922 | ||||||||
\(528\) | −3.08058 | −0.134065 | ||||||||
\(529\) | −8.63044 | −0.375237 | ||||||||
\(530\) | 5.19313 | 0.225575 | ||||||||
\(531\) | −4.34336 | −0.188486 | ||||||||
\(532\) | 27.7708 | 1.20402 | ||||||||
\(533\) | 16.1487 | 0.699480 | ||||||||
\(534\) | −11.9532 | −0.517265 | ||||||||
\(535\) | −14.4166 | −0.623284 | ||||||||
\(536\) | 14.7642 | 0.637717 | ||||||||
\(537\) | −8.69924 | −0.375400 | ||||||||
\(538\) | −19.5297 | −0.841985 | ||||||||
\(539\) | 0.371807 | 0.0160149 | ||||||||
\(540\) | −38.7613 | −1.66802 | ||||||||
\(541\) | 4.86672 | 0.209236 | 0.104618 | − | 0.994512i | \(-0.466638\pi\) | ||||
0.104618 | + | 0.994512i | \(0.466638\pi\) | |||||||
\(542\) | 73.1165 | 3.14062 | ||||||||
\(543\) | 12.0543 | 0.517299 | ||||||||
\(544\) | −0.479929 | −0.0205768 | ||||||||
\(545\) | 39.9290 | 1.71037 | ||||||||
\(546\) | 12.2944 | 0.526151 | ||||||||
\(547\) | 39.9013 | 1.70606 | 0.853028 | − | 0.521866i | \(-0.174764\pi\) | ||||
0.853028 | + | 0.521866i | \(0.174764\pi\) | |||||||
\(548\) | −80.8821 | −3.45511 | ||||||||
\(549\) | −9.54177 | −0.407233 | ||||||||
\(550\) | 7.10292 | 0.302870 | ||||||||
\(551\) | −5.50482 | −0.234513 | ||||||||
\(552\) | −11.8173 | −0.502977 | ||||||||
\(553\) | 26.6661 | 1.13396 | ||||||||
\(554\) | −71.9425 | −3.05654 | ||||||||
\(555\) | −3.31343 | −0.140647 | ||||||||
\(556\) | 78.0594 | 3.31046 | ||||||||
\(557\) | −15.0197 | −0.636407 | −0.318204 | − | 0.948022i | \(-0.603080\pi\) | ||||
−0.318204 | + | 0.948022i | \(0.603080\pi\) | |||||||
\(558\) | 8.10971 | 0.343311 | ||||||||
\(559\) | 30.4267 | 1.28691 | ||||||||
\(560\) | −27.8253 | −1.17583 | ||||||||
\(561\) | 5.46452 | 0.230712 | ||||||||
\(562\) | −46.5897 | −1.96527 | ||||||||
\(563\) | −4.39769 | −0.185340 | −0.0926702 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926702 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(564\) | −1.38512 | −0.0583242 | ||||||||
\(565\) | 17.5971 | 0.740315 | ||||||||
\(566\) | −24.7977 | −1.04232 | ||||||||
\(567\) | −14.2112 | −0.596812 | ||||||||
\(568\) | 33.8900 | 1.42199 | ||||||||
\(569\) | −0.103258 | −0.00432879 | −0.00216439 | − | 0.999998i | \(-0.500689\pi\) | ||||
−0.00216439 | + | 0.999998i | \(0.500689\pi\) | |||||||
\(570\) | 11.4233 | 0.478471 | ||||||||
\(571\) | −20.3614 | −0.852099 | −0.426050 | − | 0.904700i | \(-0.640095\pi\) | ||||
−0.426050 | + | 0.904700i | \(0.640095\pi\) | |||||||
\(572\) | −14.7752 | −0.617783 | ||||||||
\(573\) | 15.7724 | 0.658900 | ||||||||
\(574\) | 33.6726 | 1.40547 | ||||||||
\(575\) | 9.02931 | 0.376548 | ||||||||
\(576\) | 20.9504 | 0.872935 | ||||||||
\(577\) | 0.522539 | 0.0217536 | 0.0108768 | − | 0.999941i | \(-0.496538\pi\) | ||||
0.0108768 | + | 0.999941i | \(0.496538\pi\) | |||||||
\(578\) | −79.0625 | −3.28857 | ||||||||
\(579\) | 2.55919 | 0.106356 | ||||||||
\(580\) | 22.2182 | 0.922559 | ||||||||
\(581\) | −5.28506 | −0.219261 | ||||||||
\(582\) | −16.5011 | −0.683994 | ||||||||
\(583\) | 0.951049 | 0.0393884 | ||||||||
\(584\) | 44.7478 | 1.85168 | ||||||||
\(585\) | −21.3910 | −0.884407 | ||||||||
\(586\) | −14.6392 | −0.604739 | ||||||||
\(587\) | −8.92951 | −0.368560 | −0.184280 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184280 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(588\) | −0.778755 | −0.0321153 | ||||||||
\(589\) | −3.43566 | −0.141564 | ||||||||
\(590\) | −11.1466 | −0.458896 | ||||||||
\(591\) | 7.96149 | 0.327492 | ||||||||
\(592\) | −7.55464 | −0.310494 | ||||||||
\(593\) | 34.6067 | 1.42113 | 0.710563 | − | 0.703634i | \(-0.248440\pi\) | ||||
0.710563 | + | 0.703634i | \(0.248440\pi\) | |||||||
\(594\) | −10.6541 | −0.437143 | ||||||||
\(595\) | 49.3581 | 2.02349 | ||||||||
\(596\) | 95.3117 | 3.90412 | ||||||||
\(597\) | −5.17695 | −0.211878 | ||||||||
\(598\) | −28.1901 | −1.15278 | ||||||||
\(599\) | 3.81199 | 0.155754 | 0.0778768 | − | 0.996963i | \(-0.475186\pi\) | ||||
0.0778768 | + | 0.996963i | \(0.475186\pi\) | |||||||
\(600\) | −7.42555 | −0.303147 | ||||||||
\(601\) | 25.1906 | 1.02755 | 0.513773 | − | 0.857926i | \(-0.328247\pi\) | ||||
0.513773 | + | 0.857926i | \(0.328247\pi\) | |||||||
\(602\) | 63.4443 | 2.58580 | ||||||||
\(603\) | 7.84281 | 0.319384 | ||||||||
\(604\) | 13.8463 | 0.563399 | ||||||||
\(605\) | −25.8554 | −1.05117 | ||||||||
\(606\) | 22.4573 | 0.912265 | ||||||||
\(607\) | 17.8056 | 0.722707 | 0.361353 | − | 0.932429i | \(-0.382315\pi\) | ||||
0.361353 | + | 0.932429i | \(0.382315\pi\) | |||||||
\(608\) | −0.183735 | −0.00745144 | ||||||||
\(609\) | −3.38575 | −0.137197 | ||||||||
\(610\) | −24.4875 | −0.991469 | ||||||||
\(611\) | −1.64921 | −0.0667199 | ||||||||
\(612\) | 72.6605 | 2.93713 | ||||||||
\(613\) | −35.7770 | −1.44502 | −0.722510 | − | 0.691361i | \(-0.757012\pi\) | ||||
−0.722510 | + | 0.691361i | \(0.757012\pi\) | |||||||
\(614\) | 15.0589 | 0.607726 | ||||||||
\(615\) | 9.22863 | 0.372134 | ||||||||
\(616\) | −15.3773 | −0.619570 | ||||||||
\(617\) | 33.8685 | 1.36349 | 0.681747 | − | 0.731588i | \(-0.261220\pi\) | ||||
0.681747 | + | 0.731588i | \(0.261220\pi\) | |||||||
\(618\) | −4.44731 | −0.178897 | ||||||||
\(619\) | 11.4125 | 0.458708 | 0.229354 | − | 0.973343i | \(-0.426339\pi\) | ||||
0.229354 | + | 0.973343i | \(0.426339\pi\) | |||||||
\(620\) | 13.8668 | 0.556904 | ||||||||
\(621\) | −13.5436 | −0.543486 | ||||||||
\(622\) | 44.5790 | 1.78745 | ||||||||
\(623\) | −19.7726 | −0.792174 | ||||||||
\(624\) | 7.68250 | 0.307546 | ||||||||
\(625\) | −31.2361 | −1.24944 | ||||||||
\(626\) | 10.5352 | 0.421071 | ||||||||
\(627\) | 2.09203 | 0.0835475 | ||||||||
\(628\) | −58.8032 | −2.34650 | ||||||||
\(629\) | 13.4009 | 0.534328 | ||||||||
\(630\) | −44.6034 | −1.77704 | ||||||||
\(631\) | −14.0788 | −0.560470 | −0.280235 | − | 0.959931i | \(-0.590412\pi\) | ||||
−0.280235 | + | 0.959931i | \(0.590412\pi\) | |||||||
\(632\) | 50.2832 | 2.00016 | ||||||||
\(633\) | −1.15771 | −0.0460150 | ||||||||
\(634\) | −10.5978 | −0.420892 | ||||||||
\(635\) | 58.3980 | 2.31746 | ||||||||
\(636\) | −1.99198 | −0.0789873 | ||||||||
\(637\) | −0.927231 | −0.0367382 | ||||||||
\(638\) | 6.10698 | 0.241778 | ||||||||
\(639\) | 18.0025 | 0.712169 | ||||||||
\(640\) | 53.3947 | 2.11061 | ||||||||
\(641\) | 4.23496 | 0.167271 | 0.0836355 | − | 0.996496i | \(-0.473347\pi\) | ||||
0.0836355 | + | 0.996496i | \(0.473347\pi\) | |||||||
\(642\) | 8.29974 | 0.327565 | ||||||||
\(643\) | −28.9268 | −1.14076 | −0.570382 | − | 0.821380i | \(-0.693205\pi\) | ||||
−0.570382 | + | 0.821380i | \(0.693205\pi\) | |||||||
\(644\) | −39.1642 | −1.54329 | ||||||||
\(645\) | 17.3881 | 0.684657 | ||||||||
\(646\) | −46.2007 | −1.81774 | ||||||||
\(647\) | 37.9455 | 1.49179 | 0.745897 | − | 0.666062i | \(-0.232021\pi\) | ||||
0.745897 | + | 0.666062i | \(0.232021\pi\) | |||||||
\(648\) | −26.7974 | −1.05270 | ||||||||
\(649\) | −2.04134 | −0.0801295 | ||||||||
\(650\) | −17.7136 | −0.694785 | ||||||||
\(651\) | −2.11311 | −0.0828194 | ||||||||
\(652\) | −61.2031 | −2.39690 | ||||||||
\(653\) | 7.20271 | 0.281864 | 0.140932 | − | 0.990019i | \(-0.454990\pi\) | ||||
0.140932 | + | 0.990019i | \(0.454990\pi\) | |||||||
\(654\) | −22.9874 | −0.898877 | ||||||||
\(655\) | 48.9049 | 1.91087 | ||||||||
\(656\) | 21.0413 | 0.821525 | ||||||||
\(657\) | 23.7702 | 0.927365 | ||||||||
\(658\) | −3.43886 | −0.134061 | ||||||||
\(659\) | 15.8633 | 0.617945 | 0.308972 | − | 0.951071i | \(-0.400015\pi\) | ||||
0.308972 | + | 0.951071i | \(0.400015\pi\) | |||||||
\(660\) | −8.44369 | −0.328670 | ||||||||
\(661\) | −11.9083 | −0.463179 | −0.231589 | − | 0.972814i | \(-0.574393\pi\) | ||||
−0.231589 | + | 0.972814i | \(0.574393\pi\) | |||||||
\(662\) | 55.6628 | 2.16340 | ||||||||
\(663\) | −13.6277 | −0.529256 | ||||||||
\(664\) | −9.96584 | −0.386750 | ||||||||
\(665\) | 18.8962 | 0.732762 | ||||||||
\(666\) | −12.1100 | −0.469251 | ||||||||
\(667\) | 7.76326 | 0.300595 | ||||||||
\(668\) | 65.6061 | 2.53838 | ||||||||
\(669\) | 10.0629 | 0.389054 | ||||||||
\(670\) | 20.1274 | 0.777589 | ||||||||
\(671\) | −4.48454 | −0.173124 | ||||||||
\(672\) | −0.113007 | −0.00435932 | ||||||||
\(673\) | −34.1140 | −1.31500 | −0.657499 | − | 0.753455i | \(-0.728386\pi\) | ||||
−0.657499 | + | 0.753455i | \(0.728386\pi\) | |||||||
\(674\) | 65.7200 | 2.53144 | ||||||||
\(675\) | −8.51030 | −0.327562 | ||||||||
\(676\) | −15.0619 | −0.579305 | ||||||||
\(677\) | −8.36864 | −0.321633 | −0.160816 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160816 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(678\) | −10.1308 | −0.389070 | ||||||||
\(679\) | −27.2957 | −1.04751 | ||||||||
\(680\) | 93.0727 | 3.56918 | ||||||||
\(681\) | 18.0550 | 0.691868 | ||||||||
\(682\) | 3.81149 | 0.145949 | ||||||||
\(683\) | −5.73012 | −0.219257 | −0.109628 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109628 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(684\) | 27.8172 | 1.06362 | ||||||||
\(685\) | −55.0349 | −2.10277 | ||||||||
\(686\) | −46.2726 | −1.76670 | ||||||||
\(687\) | 2.59655 | 0.0990644 | ||||||||
\(688\) | 39.6450 | 1.51145 | ||||||||
\(689\) | −2.37177 | −0.0903573 | ||||||||
\(690\) | −16.1100 | −0.613295 | ||||||||
\(691\) | −39.9477 | −1.51968 | −0.759840 | − | 0.650110i | \(-0.774723\pi\) | ||||
−0.759840 | + | 0.650110i | \(0.774723\pi\) | |||||||
\(692\) | 72.2630 | 2.74703 | ||||||||
\(693\) | −8.16850 | −0.310296 | ||||||||
\(694\) | −1.52560 | −0.0579109 | ||||||||
\(695\) | 53.1142 | 2.01474 | ||||||||
\(696\) | −6.38437 | −0.241999 | ||||||||
\(697\) | −37.3244 | −1.41376 | ||||||||
\(698\) | 51.6118 | 1.95354 | ||||||||
\(699\) | −8.04831 | −0.304415 | ||||||||
\(700\) | −24.6094 | −0.930147 | ||||||||
\(701\) | −46.1558 | −1.74328 | −0.871639 | − | 0.490148i | \(-0.836943\pi\) | ||||
−0.871639 | + | 0.490148i | \(0.836943\pi\) | |||||||
\(702\) | 26.5697 | 1.00281 | ||||||||
\(703\) | 5.13037 | 0.193495 | ||||||||
\(704\) | 9.84652 | 0.371105 | ||||||||
\(705\) | −0.942484 | −0.0354960 | ||||||||
\(706\) | 34.1575 | 1.28554 | ||||||||
\(707\) | 37.1482 | 1.39710 | ||||||||
\(708\) | 4.27560 | 0.160687 | ||||||||
\(709\) | 29.9827 | 1.12602 | 0.563011 | − | 0.826449i | \(-0.309643\pi\) | ||||
0.563011 | + | 0.826449i | \(0.309643\pi\) | |||||||
\(710\) | 46.2007 | 1.73388 | ||||||||
\(711\) | 26.7106 | 1.00173 | ||||||||
\(712\) | −37.2845 | −1.39730 | ||||||||
\(713\) | 4.84520 | 0.181454 | ||||||||
\(714\) | −28.4158 | −1.06344 | ||||||||
\(715\) | −10.0536 | −0.375981 | ||||||||
\(716\) | −54.3647 | −2.03170 | ||||||||
\(717\) | −6.21578 | −0.232132 | ||||||||
\(718\) | −22.1613 | −0.827052 | ||||||||
\(719\) | −14.2178 | −0.530234 | −0.265117 | − | 0.964216i | \(-0.585411\pi\) | ||||
−0.265117 | + | 0.964216i | \(0.585411\pi\) | |||||||
\(720\) | −27.8717 | −1.03872 | ||||||||
\(721\) | −7.35661 | −0.273974 | ||||||||
\(722\) | 28.8258 | 1.07278 | ||||||||
\(723\) | −2.04679 | −0.0761209 | ||||||||
\(724\) | 75.3315 | 2.79967 | ||||||||
\(725\) | 4.87815 | 0.181170 | ||||||||
\(726\) | 14.8851 | 0.552439 | ||||||||
\(727\) | −12.0364 | −0.446406 | −0.223203 | − | 0.974772i | \(-0.571651\pi\) | ||||
−0.223203 | + | 0.974772i | \(0.571651\pi\) | |||||||
\(728\) | 38.3487 | 1.42130 | ||||||||
\(729\) | −7.38636 | −0.273569 | ||||||||
\(730\) | 61.0027 | 2.25781 | ||||||||
\(731\) | −70.3247 | −2.60105 | ||||||||
\(732\) | 9.39293 | 0.347173 | ||||||||
\(733\) | −24.0115 | −0.886886 | −0.443443 | − | 0.896303i | \(-0.646243\pi\) | ||||
−0.443443 | + | 0.896303i | \(0.646243\pi\) | |||||||
\(734\) | −48.3762 | −1.78560 | ||||||||
\(735\) | −0.529890 | −0.0195453 | ||||||||
\(736\) | 0.259115 | 0.00955112 | ||||||||
\(737\) | 3.68605 | 0.135777 | ||||||||
\(738\) | 33.7289 | 1.24158 | ||||||||
\(739\) | −17.3153 | −0.636952 | −0.318476 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318476 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(740\) | −20.7068 | −0.761198 | ||||||||
\(741\) | −5.21720 | −0.191658 | ||||||||
\(742\) | −4.94551 | −0.181555 | ||||||||
\(743\) | 42.7128 | 1.56698 | 0.783490 | − | 0.621404i | \(-0.213437\pi\) | ||||
0.783490 | + | 0.621404i | \(0.213437\pi\) | |||||||
\(744\) | −3.98461 | −0.146083 | ||||||||
\(745\) | 64.8532 | 2.37604 | ||||||||
\(746\) | −12.9308 | −0.473431 | ||||||||
\(747\) | −5.29389 | −0.193693 | ||||||||
\(748\) | 34.1498 | 1.24864 | ||||||||
\(749\) | 13.7292 | 0.501654 | ||||||||
\(750\) | 11.1263 | 0.406275 | ||||||||
\(751\) | −0.177872 | −0.00649063 | −0.00324532 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324532 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(752\) | −2.14887 | −0.0783612 | ||||||||
\(753\) | −4.26079 | −0.155272 | ||||||||
\(754\) | −15.2299 | −0.554640 | ||||||||
\(755\) | 9.42150 | 0.342884 | ||||||||
\(756\) | 36.9130 | 1.34251 | ||||||||
\(757\) | −34.5227 | −1.25475 | −0.627374 | − | 0.778718i | \(-0.715870\pi\) | ||||
−0.627374 | + | 0.778718i | \(0.715870\pi\) | |||||||
\(758\) | −12.0321 | −0.437024 | ||||||||
\(759\) | −2.95031 | −0.107090 | ||||||||
\(760\) | 35.6318 | 1.29250 | ||||||||
\(761\) | −7.64193 | −0.277020 | −0.138510 | − | 0.990361i | \(-0.544231\pi\) | ||||
−0.138510 | + | 0.990361i | \(0.544231\pi\) | |||||||
\(762\) | −33.6201 | −1.21793 | ||||||||
\(763\) | −38.0251 | −1.37660 | ||||||||
\(764\) | 98.5672 | 3.56603 | ||||||||
\(765\) | 49.4406 | 1.78753 | ||||||||
\(766\) | −30.4788 | −1.10124 | ||||||||
\(767\) | 5.09078 | 0.183818 | ||||||||
\(768\) | −20.4098 | −0.736475 | ||||||||
\(769\) | −46.0228 | −1.65962 | −0.829812 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829812 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(770\) | −20.9632 | −0.755461 | ||||||||
\(771\) | 8.53308 | 0.307311 | ||||||||
\(772\) | 15.9933 | 0.575612 | ||||||||
\(773\) | 34.0479 | 1.22462 | 0.612309 | − | 0.790619i | \(-0.290241\pi\) | ||||
0.612309 | + | 0.790619i | \(0.290241\pi\) | |||||||
\(774\) | 63.5503 | 2.28427 | ||||||||
\(775\) | 3.04455 | 0.109363 | ||||||||
\(776\) | −51.4705 | −1.84768 | ||||||||
\(777\) | 3.15544 | 0.113201 | ||||||||
\(778\) | −14.0279 | −0.502923 | ||||||||
\(779\) | −14.2892 | −0.511963 | ||||||||
\(780\) | 21.0573 | 0.753971 | ||||||||
\(781\) | 8.46102 | 0.302759 | ||||||||
\(782\) | 65.1553 | 2.32995 | ||||||||
\(783\) | −7.31702 | −0.261489 | ||||||||
\(784\) | −1.20815 | −0.0431483 | ||||||||
\(785\) | −40.0116 | −1.42808 | ||||||||
\(786\) | −28.1549 | −1.00425 | ||||||||
\(787\) | 16.6027 | 0.591821 | 0.295910 | − | 0.955216i | \(-0.404377\pi\) | ||||
0.295910 | + | 0.955216i | \(0.404377\pi\) | |||||||
\(788\) | 49.7542 | 1.77242 | ||||||||
\(789\) | 2.86472 | 0.101987 | ||||||||
\(790\) | 68.5488 | 2.43886 | ||||||||
\(791\) | −16.7580 | −0.595847 | ||||||||
\(792\) | −15.4030 | −0.547322 | ||||||||
\(793\) | 11.1838 | 0.397147 | ||||||||
\(794\) | −58.8542 | −2.08866 | ||||||||
\(795\) | −1.35541 | −0.0480715 | ||||||||
\(796\) | −32.3526 | −1.14671 | ||||||||
\(797\) | 40.0029 | 1.41698 | 0.708488 | − | 0.705723i | \(-0.249378\pi\) | ||||
0.708488 | + | 0.705723i | \(0.249378\pi\) | |||||||
\(798\) | −10.8787 | −0.385100 | ||||||||
\(799\) | 3.81180 | 0.134852 | ||||||||
\(800\) | 0.162819 | 0.00575651 | ||||||||
\(801\) | −19.8057 | −0.699799 | ||||||||
\(802\) | 48.3343 | 1.70674 | ||||||||
\(803\) | 11.1718 | 0.394244 | ||||||||
\(804\) | −7.72047 | −0.272280 | ||||||||
\(805\) | −26.6486 | −0.939241 | ||||||||
\(806\) | −9.50527 | −0.334809 | ||||||||
\(807\) | 5.09727 | 0.179432 | ||||||||
\(808\) | 70.0489 | 2.46431 | ||||||||
\(809\) | −18.6479 | −0.655626 | −0.327813 | − | 0.944743i | \(-0.606312\pi\) | ||||
−0.327813 | + | 0.944743i | \(0.606312\pi\) | |||||||
\(810\) | −36.5317 | −1.28359 | ||||||||
\(811\) | 4.36721 | 0.153354 | 0.0766768 | − | 0.997056i | \(-0.475569\pi\) | ||||
0.0766768 | + | 0.997056i | \(0.475569\pi\) | |||||||
\(812\) | −21.1588 | −0.742527 | ||||||||
\(813\) | −19.0835 | −0.669287 | ||||||||
\(814\) | −5.69157 | −0.199489 | ||||||||
\(815\) | −41.6446 | −1.45875 | ||||||||
\(816\) | −17.7565 | −0.621600 | ||||||||
\(817\) | −26.9230 | −0.941916 | ||||||||
\(818\) | 59.7292 | 2.08838 | ||||||||
\(819\) | 20.3710 | 0.711820 | ||||||||
\(820\) | 57.6730 | 2.01403 | ||||||||
\(821\) | 55.9785 | 1.95366 | 0.976831 | − | 0.214011i | \(-0.0686530\pi\) | ||||
0.976831 | + | 0.214011i | \(0.0686530\pi\) | |||||||
\(822\) | 31.6839 | 1.10510 | ||||||||
\(823\) | 49.9579 | 1.74142 | 0.870711 | − | 0.491795i | \(-0.163659\pi\) | ||||
0.870711 | + | 0.491795i | \(0.163659\pi\) | |||||||
\(824\) | −13.8721 | −0.483256 | ||||||||
\(825\) | −1.85387 | −0.0645435 | ||||||||
\(826\) | 10.6151 | 0.369345 | ||||||||
\(827\) | 35.3047 | 1.22767 | 0.613833 | − | 0.789436i | \(-0.289627\pi\) | ||||
0.613833 | + | 0.789436i | \(0.289627\pi\) | |||||||
\(828\) | −39.2297 | −1.36332 | ||||||||
\(829\) | 38.9067 | 1.35129 | 0.675643 | − | 0.737229i | \(-0.263866\pi\) | ||||
0.675643 | + | 0.737229i | \(0.263866\pi\) | |||||||
\(830\) | −13.5860 | −0.471576 | ||||||||
\(831\) | 18.7771 | 0.651369 | ||||||||
\(832\) | −24.5557 | −0.851316 | ||||||||
\(833\) | 2.14310 | 0.0742539 | ||||||||
\(834\) | −30.5782 | −1.05884 | ||||||||
\(835\) | 44.6405 | 1.54485 | ||||||||
\(836\) | 13.0738 | 0.452168 | ||||||||
\(837\) | −4.56670 | −0.157848 | ||||||||
\(838\) | −66.9400 | −2.31240 | ||||||||
\(839\) | 28.2054 | 0.973759 | 0.486880 | − | 0.873469i | \(-0.338135\pi\) | ||||
0.486880 | + | 0.873469i | \(0.338135\pi\) | |||||||
\(840\) | 21.9154 | 0.756153 | ||||||||
\(841\) | −24.8058 | −0.855374 | ||||||||
\(842\) | 46.5728 | 1.60500 | ||||||||
\(843\) | 12.1600 | 0.418811 | ||||||||
\(844\) | −7.23497 | −0.249038 | ||||||||
\(845\) | −10.2486 | −0.352564 | ||||||||
\(846\) | −3.44460 | −0.118428 | ||||||||
\(847\) | 24.6225 | 0.846041 | ||||||||
\(848\) | −3.09034 | −0.106123 | ||||||||
\(849\) | 6.47222 | 0.222126 | ||||||||
\(850\) | 40.9412 | 1.40427 | ||||||||
\(851\) | −7.23518 | −0.248019 | ||||||||
\(852\) | −17.7217 | −0.607135 | ||||||||
\(853\) | 37.3608 | 1.27921 | 0.639604 | − | 0.768705i | \(-0.279098\pi\) | ||||
0.639604 | + | 0.768705i | \(0.279098\pi\) | |||||||
\(854\) | 23.3199 | 0.797990 | ||||||||
\(855\) | 18.9277 | 0.647315 | ||||||||
\(856\) | 25.8886 | 0.884854 | ||||||||
\(857\) | −30.0266 | −1.02569 | −0.512844 | − | 0.858482i | \(-0.671408\pi\) | ||||
−0.512844 | + | 0.858482i | \(0.671408\pi\) | |||||||
\(858\) | 5.78790 | 0.197596 | ||||||||
\(859\) | −12.2446 | −0.417780 | −0.208890 | − | 0.977939i | \(-0.566985\pi\) | ||||
−0.208890 | + | 0.977939i | \(0.566985\pi\) | |||||||
\(860\) | 108.665 | 3.70543 | ||||||||
\(861\) | −8.78859 | −0.299514 | ||||||||
\(862\) | −65.8743 | −2.24369 | ||||||||
\(863\) | 42.7517 | 1.45529 | 0.727643 | − | 0.685956i | \(-0.240616\pi\) | ||||
0.727643 | + | 0.685956i | \(0.240616\pi\) | |||||||
\(864\) | −0.244221 | −0.00830858 | ||||||||
\(865\) | 49.1701 | 1.67183 | ||||||||
\(866\) | −4.01780 | −0.136530 | ||||||||
\(867\) | 20.6354 | 0.700815 | ||||||||
\(868\) | −13.2056 | −0.448227 | ||||||||
\(869\) | 12.5538 | 0.425857 | ||||||||
\(870\) | −8.70352 | −0.295077 | ||||||||
\(871\) | −9.19245 | −0.311474 | ||||||||
\(872\) | −71.7024 | −2.42815 | ||||||||
\(873\) | −27.3413 | −0.925364 | ||||||||
\(874\) | 24.9439 | 0.843741 | ||||||||
\(875\) | 18.4048 | 0.622196 | ||||||||
\(876\) | −23.3994 | −0.790594 | ||||||||
\(877\) | −11.1387 | −0.376128 | −0.188064 | − | 0.982157i | \(-0.560221\pi\) | ||||
−0.188064 | + | 0.982157i | \(0.560221\pi\) | |||||||
\(878\) | −5.46582 | −0.184462 | ||||||||
\(879\) | 3.82084 | 0.128874 | ||||||||
\(880\) | −13.0995 | −0.441583 | ||||||||
\(881\) | −20.6608 | −0.696080 | −0.348040 | − | 0.937480i | \(-0.613153\pi\) | ||||
−0.348040 | + | 0.937480i | \(0.613153\pi\) | |||||||
\(882\) | −1.93665 | −0.0652104 | ||||||||
\(883\) | −31.2664 | −1.05220 | −0.526099 | − | 0.850423i | \(-0.676346\pi\) | ||||
−0.526099 | + | 0.850423i | \(0.676346\pi\) | |||||||
\(884\) | −85.1643 | −2.86439 | ||||||||
\(885\) | 2.90926 | 0.0977938 | ||||||||
\(886\) | 41.1947 | 1.38396 | ||||||||
\(887\) | 18.9698 | 0.636942 | 0.318471 | − | 0.947933i | \(-0.396831\pi\) | ||||
0.318471 | + | 0.947933i | \(0.396831\pi\) | |||||||
\(888\) | 5.95009 | 0.199672 | ||||||||
\(889\) | −55.6135 | −1.86522 | ||||||||
\(890\) | −50.8282 | −1.70377 | ||||||||
\(891\) | −6.69027 | −0.224133 | ||||||||
\(892\) | 62.8866 | 2.10560 | ||||||||
\(893\) | 1.45930 | 0.0488336 | ||||||||
\(894\) | −37.3365 | −1.24872 | ||||||||
\(895\) | −36.9915 | −1.23649 | ||||||||
\(896\) | −50.8487 | −1.69874 | ||||||||
\(897\) | 7.35764 | 0.245664 | ||||||||
\(898\) | 61.5747 | 2.05477 | ||||||||
\(899\) | 2.61766 | 0.0873037 | ||||||||
\(900\) | −24.6505 | −0.821683 | ||||||||
\(901\) | 5.48184 | 0.182627 | ||||||||
\(902\) | 15.8523 | 0.527823 | ||||||||
\(903\) | −16.5590 | −0.551050 | ||||||||
\(904\) | −31.6000 | −1.05100 | ||||||||
\(905\) | 51.2581 | 1.70388 | ||||||||
\(906\) | −5.42403 | −0.180201 | ||||||||
\(907\) | 3.60840 | 0.119815 | 0.0599075 | − | 0.998204i | \(-0.480919\pi\) | ||||
0.0599075 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(908\) | 112.832 | 3.74446 | ||||||||
\(909\) | 37.2103 | 1.23419 | ||||||||
\(910\) | 52.2790 | 1.73303 | ||||||||
\(911\) | −20.8948 | −0.692276 | −0.346138 | − | 0.938184i | \(-0.612507\pi\) | ||||
−0.346138 | + | 0.938184i | \(0.612507\pi\) | |||||||
\(912\) | −6.79784 | −0.225099 | ||||||||
\(913\) | −2.48808 | −0.0823435 | ||||||||
\(914\) | −15.5229 | −0.513451 | ||||||||
\(915\) | 6.39126 | 0.211288 | ||||||||
\(916\) | 16.2267 | 0.536147 | ||||||||
\(917\) | −46.5730 | −1.53798 | ||||||||
\(918\) | −61.4102 | −2.02684 | ||||||||
\(919\) | 3.58842 | 0.118371 | 0.0591855 | − | 0.998247i | \(-0.481150\pi\) | ||||
0.0591855 | + | 0.998247i | \(0.481150\pi\) | |||||||
\(920\) | −50.2503 | −1.65670 | ||||||||
\(921\) | −3.93038 | −0.129510 | ||||||||
\(922\) | −90.5351 | −2.98161 | ||||||||
\(923\) | −21.1005 | −0.694531 | ||||||||
\(924\) | 8.04108 | 0.264532 | ||||||||
\(925\) | −4.54632 | −0.149482 | ||||||||
\(926\) | −4.94011 | −0.162342 | ||||||||
\(927\) | −7.36890 | −0.242026 | ||||||||
\(928\) | 0.139989 | 0.00459536 | ||||||||
\(929\) | 23.8636 | 0.782938 | 0.391469 | − | 0.920191i | \(-0.371967\pi\) | ||||
0.391469 | + | 0.920191i | \(0.371967\pi\) | |||||||
\(930\) | −5.43204 | −0.178124 | ||||||||
\(931\) | 0.820458 | 0.0268894 | ||||||||
\(932\) | −50.2968 | −1.64752 | ||||||||
\(933\) | −11.6352 | −0.380918 | ||||||||
\(934\) | −25.6589 | −0.839584 | ||||||||
\(935\) | 23.2366 | 0.759919 | ||||||||
\(936\) | 38.4128 | 1.25556 | ||||||||
\(937\) | −9.58015 | −0.312970 | −0.156485 | − | 0.987680i | \(-0.550016\pi\) | ||||
−0.156485 | + | 0.987680i | \(0.550016\pi\) | |||||||
\(938\) | −19.1677 | −0.625847 | ||||||||
\(939\) | −2.74970 | −0.0897330 | ||||||||
\(940\) | −5.88992 | −0.192108 | ||||||||
\(941\) | −20.9329 | −0.682393 | −0.341197 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341197 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(942\) | 23.0350 | 0.750520 | ||||||||
\(943\) | 20.1516 | 0.656225 | ||||||||
\(944\) | 6.63313 | 0.215890 | ||||||||
\(945\) | 25.1169 | 0.817051 | ||||||||
\(946\) | 29.8681 | 0.971094 | ||||||||
\(947\) | −5.83448 | −0.189595 | −0.0947976 | − | 0.995497i | \(-0.530220\pi\) | ||||
−0.0947976 | + | 0.995497i | \(0.530220\pi\) | |||||||
\(948\) | −26.2940 | −0.853989 | ||||||||
\(949\) | −27.8607 | −0.904398 | ||||||||
\(950\) | 15.6739 | 0.508527 | ||||||||
\(951\) | 2.76603 | 0.0896947 | ||||||||
\(952\) | −88.6349 | −2.87267 | ||||||||
\(953\) | −25.6994 | −0.832484 | −0.416242 | − | 0.909254i | \(-0.636653\pi\) | ||||
−0.416242 | + | 0.909254i | \(0.636653\pi\) | |||||||
\(954\) | −4.95377 | −0.160384 | ||||||||
\(955\) | 67.0684 | 2.17028 | ||||||||
\(956\) | −38.8446 | −1.25633 | ||||||||
\(957\) | −1.59393 | −0.0515244 | ||||||||
\(958\) | −7.78779 | −0.251612 | ||||||||
\(959\) | 52.4107 | 1.69243 | ||||||||
\(960\) | −14.0330 | −0.452913 | ||||||||
\(961\) | −29.3663 | −0.947299 | ||||||||
\(962\) | 14.1939 | 0.457630 | ||||||||
\(963\) | 13.7521 | 0.443156 | ||||||||
\(964\) | −12.7911 | −0.411974 | ||||||||
\(965\) | 10.8824 | 0.350316 | ||||||||
\(966\) | 15.3418 | 0.493614 | ||||||||
\(967\) | −45.6525 | −1.46808 | −0.734042 | − | 0.679104i | \(-0.762369\pi\) | ||||
−0.734042 | + | 0.679104i | \(0.762369\pi\) | |||||||
\(968\) | 46.4298 | 1.49231 | ||||||||
\(969\) | 12.0584 | 0.387373 | ||||||||
\(970\) | −70.1673 | −2.25294 | ||||||||
\(971\) | 17.4439 | 0.559802 | 0.279901 | − | 0.960029i | \(-0.409698\pi\) | ||||
0.279901 | + | 0.960029i | \(0.409698\pi\) | |||||||
\(972\) | 56.8118 | 1.82224 | ||||||||
\(973\) | −50.5816 | −1.62157 | ||||||||
\(974\) | −47.2583 | −1.51425 | ||||||||
\(975\) | 4.62327 | 0.148063 | ||||||||
\(976\) | 14.5721 | 0.466442 | ||||||||
\(977\) | 23.6939 | 0.758035 | 0.379018 | − | 0.925389i | \(-0.376262\pi\) | ||||
0.379018 | + | 0.925389i | \(0.376262\pi\) | |||||||
\(978\) | 23.9751 | 0.766639 | ||||||||
\(979\) | −9.30848 | −0.297500 | ||||||||
\(980\) | −3.31148 | −0.105781 | ||||||||
\(981\) | −38.0886 | −1.21608 | ||||||||
\(982\) | −28.2481 | −0.901434 | ||||||||
\(983\) | −8.88218 | −0.283298 | −0.141649 | − | 0.989917i | \(-0.545240\pi\) | ||||
−0.141649 | + | 0.989917i | \(0.545240\pi\) | |||||||
\(984\) | −16.5723 | −0.528306 | ||||||||
\(985\) | 33.8544 | 1.07869 | ||||||||
\(986\) | 35.2006 | 1.12102 | ||||||||
\(987\) | 0.897545 | 0.0285692 | ||||||||
\(988\) | −32.6041 | −1.03728 | ||||||||
\(989\) | 37.9686 | 1.20733 | ||||||||
\(990\) | −20.9982 | −0.667367 | ||||||||
\(991\) | 36.1718 | 1.14904 | 0.574518 | − | 0.818492i | \(-0.305190\pi\) | ||||
0.574518 | + | 0.818492i | \(0.305190\pi\) | |||||||
\(992\) | 0.0873698 | 0.00277399 | ||||||||
\(993\) | −14.5281 | −0.461034 | ||||||||
\(994\) | −43.9978 | −1.39552 | ||||||||
\(995\) | −22.0138 | −0.697884 | ||||||||
\(996\) | 5.21131 | 0.165127 | ||||||||
\(997\) | 37.4471 | 1.18596 | 0.592980 | − | 0.805217i | \(-0.297951\pi\) | ||||
0.592980 | + | 0.805217i | \(0.297951\pi\) | |||||||
\(998\) | −36.3530 | −1.15073 | ||||||||
\(999\) | 6.81930 | 0.215753 |
(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 | 6037.2.a.b.1.16 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.16 | ✓ | 259 | 1.1 | even | 1 | trivial |