Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08292 | −0.765739 | −0.382869 | − | 0.923803i | \(-0.625064\pi\) | ||||
−0.382869 | + | 0.923803i | \(0.625064\pi\) | |||||||
\(3\) | −0.496145 | −0.286450 | −0.143225 | − | 0.989690i | \(-0.545747\pi\) | ||||
−0.143225 | + | 0.989690i | \(0.545747\pi\) | |||||||
\(4\) | −0.827289 | −0.413644 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.537284 | 0.219345 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.06172 | 1.08248 | ||||||||
\(9\) | −2.75384 | −0.917947 | ||||||||
\(10\) | −1.08292 | −0.342449 | ||||||||
\(11\) | 0.0921526 | 0.0277850 | 0.0138925 | − | 0.999903i | \(-0.495578\pi\) | ||||
0.0138925 | + | 0.999903i | \(0.495578\pi\) | |||||||
\(12\) | 0.410455 | 0.118488 | ||||||||
\(13\) | 3.58582 | 0.994527 | 0.497264 | − | 0.867600i | \(-0.334338\pi\) | ||||
0.497264 | + | 0.867600i | \(0.334338\pi\) | |||||||
\(14\) | −1.08292 | −0.289422 | ||||||||
\(15\) | −0.496145 | −0.128104 | ||||||||
\(16\) | −1.66102 | −0.415254 | ||||||||
\(17\) | 4.47425 | 1.08517 | 0.542583 | − | 0.840002i | \(-0.317446\pi\) | ||||
0.542583 | + | 0.840002i | \(0.317446\pi\) | |||||||
\(18\) | 2.98218 | 0.702907 | ||||||||
\(19\) | 0.525247 | 0.120500 | 0.0602499 | − | 0.998183i | \(-0.480810\pi\) | ||||
0.0602499 | + | 0.998183i | \(0.480810\pi\) | |||||||
\(20\) | −0.827289 | −0.184987 | ||||||||
\(21\) | −0.496145 | −0.108268 | ||||||||
\(22\) | −0.0997937 | −0.0212761 | ||||||||
\(23\) | −6.03693 | −1.25879 | −0.629393 | − | 0.777087i | \(-0.716697\pi\) | ||||
−0.629393 | + | 0.777087i | \(0.716697\pi\) | |||||||
\(24\) | −1.51906 | −0.310076 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.88315 | −0.761548 | ||||||||
\(27\) | 2.85474 | 0.549395 | ||||||||
\(28\) | −0.827289 | −0.156343 | ||||||||
\(29\) | 6.16008 | 1.14390 | 0.571950 | − | 0.820289i | \(-0.306187\pi\) | ||||
0.571950 | + | 0.820289i | \(0.306187\pi\) | |||||||
\(30\) | 0.537284 | 0.0980943 | ||||||||
\(31\) | −6.08228 | −1.09241 | −0.546205 | − | 0.837651i | \(-0.683928\pi\) | ||||
−0.546205 | + | 0.837651i | \(0.683928\pi\) | |||||||
\(32\) | −4.32470 | −0.764506 | ||||||||
\(33\) | −0.0457210 | −0.00795901 | ||||||||
\(34\) | −4.84525 | −0.830953 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.27822 | 0.379703 | ||||||||
\(37\) | −10.0087 | −1.64542 | −0.822712 | − | 0.568459i | \(-0.807540\pi\) | ||||
−0.822712 | + | 0.568459i | \(0.807540\pi\) | |||||||
\(38\) | −0.568799 | −0.0922714 | ||||||||
\(39\) | −1.77909 | −0.284882 | ||||||||
\(40\) | 3.06172 | 0.484101 | ||||||||
\(41\) | 2.71787 | 0.424460 | 0.212230 | − | 0.977220i | \(-0.431927\pi\) | ||||
0.212230 | + | 0.977220i | \(0.431927\pi\) | |||||||
\(42\) | 0.537284 | 0.0829048 | ||||||||
\(43\) | 1.91268 | 0.291681 | 0.145841 | − | 0.989308i | \(-0.453411\pi\) | ||||
0.145841 | + | 0.989308i | \(0.453411\pi\) | |||||||
\(44\) | −0.0762367 | −0.0114931 | ||||||||
\(45\) | −2.75384 | −0.410518 | ||||||||
\(46\) | 6.53750 | 0.963902 | ||||||||
\(47\) | −8.05017 | −1.17424 | −0.587119 | − | 0.809501i | \(-0.699738\pi\) | ||||
−0.587119 | + | 0.809501i | \(0.699738\pi\) | |||||||
\(48\) | 0.824105 | 0.118949 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.08292 | −0.153148 | ||||||||
\(51\) | −2.21988 | −0.310845 | ||||||||
\(52\) | −2.96651 | −0.411380 | ||||||||
\(53\) | −6.29211 | −0.864287 | −0.432144 | − | 0.901805i | \(-0.642243\pi\) | ||||
−0.432144 | + | 0.901805i | \(0.642243\pi\) | |||||||
\(54\) | −3.09145 | −0.420693 | ||||||||
\(55\) | 0.0921526 | 0.0124258 | ||||||||
\(56\) | 3.06172 | 0.409140 | ||||||||
\(57\) | −0.260599 | −0.0345171 | ||||||||
\(58\) | −6.67087 | −0.875928 | ||||||||
\(59\) | −0.398133 | −0.0518325 | −0.0259163 | − | 0.999664i | \(-0.508250\pi\) | ||||
−0.0259163 | + | 0.999664i | \(0.508250\pi\) | |||||||
\(60\) | 0.410455 | 0.0529895 | ||||||||
\(61\) | −6.33993 | −0.811744 | −0.405872 | − | 0.913930i | \(-0.633032\pi\) | ||||
−0.405872 | + | 0.913930i | \(0.633032\pi\) | |||||||
\(62\) | 6.58661 | 0.836501 | ||||||||
\(63\) | −2.75384 | −0.346951 | ||||||||
\(64\) | 8.00533 | 1.00067 | ||||||||
\(65\) | 3.58582 | 0.444766 | ||||||||
\(66\) | 0.0495121 | 0.00609452 | ||||||||
\(67\) | 9.17925 | 1.12142 | 0.560712 | − | 0.828011i | \(-0.310528\pi\) | ||||
0.560712 | + | 0.828011i | \(0.310528\pi\) | |||||||
\(68\) | −3.70150 | −0.448873 | ||||||||
\(69\) | 2.99519 | 0.360579 | ||||||||
\(70\) | −1.08292 | −0.129433 | ||||||||
\(71\) | −5.90674 | −0.701001 | −0.350501 | − | 0.936563i | \(-0.613989\pi\) | ||||
−0.350501 | + | 0.936563i | \(0.613989\pi\) | |||||||
\(72\) | −8.43149 | −0.993661 | ||||||||
\(73\) | −2.48079 | −0.290355 | −0.145177 | − | 0.989406i | \(-0.546375\pi\) | ||||
−0.145177 | + | 0.989406i | \(0.546375\pi\) | |||||||
\(74\) | 10.8386 | 1.25996 | ||||||||
\(75\) | −0.496145 | −0.0572899 | ||||||||
\(76\) | −0.434531 | −0.0498441 | ||||||||
\(77\) | 0.0921526 | 0.0105018 | ||||||||
\(78\) | 1.92660 | 0.218145 | ||||||||
\(79\) | −4.11562 | −0.463044 | −0.231522 | − | 0.972830i | \(-0.574371\pi\) | ||||
−0.231522 | + | 0.972830i | \(0.574371\pi\) | |||||||
\(80\) | −1.66102 | −0.185707 | ||||||||
\(81\) | 6.84516 | 0.760573 | ||||||||
\(82\) | −2.94323 | −0.325025 | ||||||||
\(83\) | 7.53603 | 0.827187 | 0.413593 | − | 0.910462i | \(-0.364273\pi\) | ||||
0.413593 | + | 0.910462i | \(0.364273\pi\) | |||||||
\(84\) | 0.410455 | 0.0447843 | ||||||||
\(85\) | 4.47425 | 0.485301 | ||||||||
\(86\) | −2.07128 | −0.223352 | ||||||||
\(87\) | −3.05630 | −0.327669 | ||||||||
\(88\) | 0.282145 | 0.0300768 | ||||||||
\(89\) | −5.34892 | −0.566985 | −0.283492 | − | 0.958975i | \(-0.591493\pi\) | ||||
−0.283492 | + | 0.958975i | \(0.591493\pi\) | |||||||
\(90\) | 2.98218 | 0.314350 | ||||||||
\(91\) | 3.58582 | 0.375896 | ||||||||
\(92\) | 4.99428 | 0.520690 | ||||||||
\(93\) | 3.01769 | 0.312920 | ||||||||
\(94\) | 8.71767 | 0.899159 | ||||||||
\(95\) | 0.525247 | 0.0538892 | ||||||||
\(96\) | 2.14568 | 0.218992 | ||||||||
\(97\) | −3.97960 | −0.404067 | −0.202034 | − | 0.979379i | \(-0.564755\pi\) | ||||
−0.202034 | + | 0.979379i | \(0.564755\pi\) | |||||||
\(98\) | −1.08292 | −0.109391 | ||||||||
\(99\) | −0.253773 | −0.0255052 | ||||||||
\(100\) | −0.827289 | −0.0827289 | ||||||||
\(101\) | −6.84384 | −0.680987 | −0.340494 | − | 0.940247i | \(-0.610594\pi\) | ||||
−0.340494 | + | 0.940247i | \(0.610594\pi\) | |||||||
\(102\) | 2.40395 | 0.238026 | ||||||||
\(103\) | 7.42107 | 0.731219 | 0.365610 | − | 0.930768i | \(-0.380860\pi\) | ||||
0.365610 | + | 0.930768i | \(0.380860\pi\) | |||||||
\(104\) | 10.9788 | 1.07656 | ||||||||
\(105\) | −0.496145 | −0.0484188 | ||||||||
\(106\) | 6.81384 | 0.661818 | ||||||||
\(107\) | −7.58183 | −0.732963 | −0.366482 | − | 0.930425i | \(-0.619438\pi\) | ||||
−0.366482 | + | 0.930425i | \(0.619438\pi\) | |||||||
\(108\) | −2.36169 | −0.227254 | ||||||||
\(109\) | 5.16970 | 0.495167 | 0.247584 | − | 0.968867i | \(-0.420364\pi\) | ||||
0.247584 | + | 0.968867i | \(0.420364\pi\) | |||||||
\(110\) | −0.0997937 | −0.00951495 | ||||||||
\(111\) | 4.96578 | 0.471331 | ||||||||
\(112\) | −1.66102 | −0.156951 | ||||||||
\(113\) | −18.3481 | −1.72604 | −0.863022 | − | 0.505166i | \(-0.831431\pi\) | ||||
−0.863022 | + | 0.505166i | \(0.831431\pi\) | |||||||
\(114\) | 0.282207 | 0.0264311 | ||||||||
\(115\) | −6.03693 | −0.562946 | ||||||||
\(116\) | −5.09617 | −0.473167 | ||||||||
\(117\) | −9.87477 | −0.912923 | ||||||||
\(118\) | 0.431146 | 0.0396902 | ||||||||
\(119\) | 4.47425 | 0.410154 | ||||||||
\(120\) | −1.51906 | −0.138670 | ||||||||
\(121\) | −10.9915 | −0.999228 | ||||||||
\(122\) | 6.86562 | 0.621584 | ||||||||
\(123\) | −1.34846 | −0.121586 | ||||||||
\(124\) | 5.03180 | 0.451869 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.98218 | 0.265674 | ||||||||
\(127\) | 2.92115 | 0.259210 | 0.129605 | − | 0.991566i | \(-0.458629\pi\) | ||||
0.129605 | + | 0.991566i | \(0.458629\pi\) | |||||||
\(128\) | −0.0197165 | −0.00174271 | ||||||||
\(129\) | −0.948968 | −0.0835519 | ||||||||
\(130\) | −3.88315 | −0.340575 | ||||||||
\(131\) | 13.6122 | 1.18931 | 0.594653 | − | 0.803982i | \(-0.297289\pi\) | ||||
0.594653 | + | 0.803982i | \(0.297289\pi\) | |||||||
\(132\) | 0.0378245 | 0.00329220 | ||||||||
\(133\) | 0.525247 | 0.0455447 | ||||||||
\(134\) | −9.94038 | −0.858718 | ||||||||
\(135\) | 2.85474 | 0.245697 | ||||||||
\(136\) | 13.6989 | 1.17467 | ||||||||
\(137\) | 7.59167 | 0.648600 | 0.324300 | − | 0.945954i | \(-0.394871\pi\) | ||||
0.324300 | + | 0.945954i | \(0.394871\pi\) | |||||||
\(138\) | −3.24355 | −0.276109 | ||||||||
\(139\) | 21.4764 | 1.82161 | 0.910803 | − | 0.412841i | \(-0.135463\pi\) | ||||
0.910803 | + | 0.412841i | \(0.135463\pi\) | |||||||
\(140\) | −0.827289 | −0.0699186 | ||||||||
\(141\) | 3.99405 | 0.336360 | ||||||||
\(142\) | 6.39652 | 0.536784 | ||||||||
\(143\) | 0.330442 | 0.0276330 | ||||||||
\(144\) | 4.57417 | 0.381181 | ||||||||
\(145\) | 6.16008 | 0.511567 | ||||||||
\(146\) | 2.68649 | 0.222336 | ||||||||
\(147\) | −0.496145 | −0.0409214 | ||||||||
\(148\) | 8.28010 | 0.680620 | ||||||||
\(149\) | 7.02415 | 0.575441 | 0.287720 | − | 0.957714i | \(-0.407103\pi\) | ||||
0.287720 | + | 0.957714i | \(0.407103\pi\) | |||||||
\(150\) | 0.537284 | 0.0438691 | ||||||||
\(151\) | −1.40307 | −0.114180 | −0.0570900 | − | 0.998369i | \(-0.518182\pi\) | ||||
−0.0570900 | + | 0.998369i | \(0.518182\pi\) | |||||||
\(152\) | 1.60816 | 0.130439 | ||||||||
\(153\) | −12.3214 | −0.996124 | ||||||||
\(154\) | −0.0997937 | −0.00804160 | ||||||||
\(155\) | −6.08228 | −0.488541 | ||||||||
\(156\) | 1.47182 | 0.117840 | ||||||||
\(157\) | −14.2383 | −1.13634 | −0.568171 | − | 0.822910i | \(-0.692349\pi\) | ||||
−0.568171 | + | 0.822910i | \(0.692349\pi\) | |||||||
\(158\) | 4.45688 | 0.354571 | ||||||||
\(159\) | 3.12180 | 0.247575 | ||||||||
\(160\) | −4.32470 | −0.341897 | ||||||||
\(161\) | −6.03693 | −0.475777 | ||||||||
\(162\) | −7.41274 | −0.582400 | ||||||||
\(163\) | 6.82867 | 0.534863 | 0.267431 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267431 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(164\) | −2.24846 | −0.175575 | ||||||||
\(165\) | −0.0457210 | −0.00355938 | ||||||||
\(166\) | −8.16090 | −0.633409 | ||||||||
\(167\) | −14.0012 | −1.08344 | −0.541722 | − | 0.840558i | \(-0.682227\pi\) | ||||
−0.541722 | + | 0.840558i | \(0.682227\pi\) | |||||||
\(168\) | −1.51906 | −0.117198 | ||||||||
\(169\) | −0.141908 | −0.0109160 | ||||||||
\(170\) | −4.84525 | −0.371614 | ||||||||
\(171\) | −1.44645 | −0.110612 | ||||||||
\(172\) | −1.58234 | −0.120652 | ||||||||
\(173\) | −13.1344 | −0.998588 | −0.499294 | − | 0.866433i | \(-0.666407\pi\) | ||||
−0.499294 | + | 0.866433i | \(0.666407\pi\) | |||||||
\(174\) | 3.30972 | 0.250909 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −0.153067 | −0.0115379 | ||||||||
\(177\) | 0.197532 | 0.0148474 | ||||||||
\(178\) | 5.79244 | 0.434162 | ||||||||
\(179\) | −2.91378 | −0.217786 | −0.108893 | − | 0.994053i | \(-0.534731\pi\) | ||||
−0.108893 | + | 0.994053i | \(0.534731\pi\) | |||||||
\(180\) | 2.27822 | 0.169809 | ||||||||
\(181\) | −17.9103 | −1.33126 | −0.665630 | − | 0.746282i | \(-0.731837\pi\) | ||||
−0.665630 | + | 0.746282i | \(0.731837\pi\) | |||||||
\(182\) | −3.88315 | −0.287838 | ||||||||
\(183\) | 3.14552 | 0.232524 | ||||||||
\(184\) | −18.4834 | −1.36261 | ||||||||
\(185\) | −10.0087 | −0.735856 | ||||||||
\(186\) | −3.26792 | −0.239615 | ||||||||
\(187\) | 0.412314 | 0.0301514 | ||||||||
\(188\) | 6.65981 | 0.485717 | ||||||||
\(189\) | 2.85474 | 0.207652 | ||||||||
\(190\) | −0.568799 | −0.0412650 | ||||||||
\(191\) | 20.3533 | 1.47271 | 0.736356 | − | 0.676594i | \(-0.236545\pi\) | ||||
0.736356 | + | 0.676594i | \(0.236545\pi\) | |||||||
\(192\) | −3.97180 | −0.286640 | ||||||||
\(193\) | 12.9449 | 0.931794 | 0.465897 | − | 0.884839i | \(-0.345732\pi\) | ||||
0.465897 | + | 0.884839i | \(0.345732\pi\) | |||||||
\(194\) | 4.30958 | 0.309410 | ||||||||
\(195\) | −1.77909 | −0.127403 | ||||||||
\(196\) | −0.827289 | −0.0590920 | ||||||||
\(197\) | 8.99708 | 0.641015 | 0.320508 | − | 0.947246i | \(-0.396146\pi\) | ||||
0.320508 | + | 0.947246i | \(0.396146\pi\) | |||||||
\(198\) | 0.274816 | 0.0195303 | ||||||||
\(199\) | 16.0890 | 1.14052 | 0.570260 | − | 0.821465i | \(-0.306843\pi\) | ||||
0.570260 | + | 0.821465i | \(0.306843\pi\) | |||||||
\(200\) | 3.06172 | 0.216496 | ||||||||
\(201\) | −4.55424 | −0.321231 | ||||||||
\(202\) | 7.41132 | 0.521458 | ||||||||
\(203\) | 6.16008 | 0.432353 | ||||||||
\(204\) | 1.83648 | 0.128579 | ||||||||
\(205\) | 2.71787 | 0.189824 | ||||||||
\(206\) | −8.03641 | −0.559923 | ||||||||
\(207\) | 16.6247 | 1.15550 | ||||||||
\(208\) | −5.95610 | −0.412981 | ||||||||
\(209\) | 0.0484028 | 0.00334809 | ||||||||
\(210\) | 0.537284 | 0.0370762 | ||||||||
\(211\) | −26.8260 | −1.84678 | −0.923390 | − | 0.383864i | \(-0.874593\pi\) | ||||
−0.923390 | + | 0.383864i | \(0.874593\pi\) | |||||||
\(212\) | 5.20539 | 0.357508 | ||||||||
\(213\) | 2.93060 | 0.200801 | ||||||||
\(214\) | 8.21050 | 0.561258 | ||||||||
\(215\) | 1.91268 | 0.130444 | ||||||||
\(216\) | 8.74042 | 0.594710 | ||||||||
\(217\) | −6.08228 | −0.412892 | ||||||||
\(218\) | −5.59836 | −0.379169 | ||||||||
\(219\) | 1.23083 | 0.0831720 | ||||||||
\(220\) | −0.0762367 | −0.00513988 | ||||||||
\(221\) | 16.0439 | 1.07923 | ||||||||
\(222\) | −5.37753 | −0.360916 | ||||||||
\(223\) | −19.5248 | −1.30748 | −0.653740 | − | 0.756719i | \(-0.726801\pi\) | ||||
−0.653740 | + | 0.756719i | \(0.726801\pi\) | |||||||
\(224\) | −4.32470 | −0.288956 | ||||||||
\(225\) | −2.75384 | −0.183589 | ||||||||
\(226\) | 19.8695 | 1.32170 | ||||||||
\(227\) | −12.1273 | −0.804920 | −0.402460 | − | 0.915438i | \(-0.631845\pi\) | ||||
−0.402460 | + | 0.915438i | \(0.631845\pi\) | |||||||
\(228\) | 0.215590 | 0.0142778 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 6.53750 | 0.431070 | ||||||||
\(231\) | −0.0457210 | −0.00300822 | ||||||||
\(232\) | 18.8605 | 1.23825 | ||||||||
\(233\) | 7.40295 | 0.484983 | 0.242492 | − | 0.970154i | \(-0.422035\pi\) | ||||
0.242492 | + | 0.970154i | \(0.422035\pi\) | |||||||
\(234\) | 10.6936 | 0.699060 | ||||||||
\(235\) | −8.05017 | −0.525135 | ||||||||
\(236\) | 0.329371 | 0.0214402 | ||||||||
\(237\) | 2.04195 | 0.132639 | ||||||||
\(238\) | −4.84525 | −0.314071 | ||||||||
\(239\) | 21.7879 | 1.40934 | 0.704672 | − | 0.709534i | \(-0.251094\pi\) | ||||
0.704672 | + | 0.709534i | \(0.251094\pi\) | |||||||
\(240\) | 0.824105 | 0.0531958 | ||||||||
\(241\) | −4.08529 | −0.263157 | −0.131578 | − | 0.991306i | \(-0.542005\pi\) | ||||
−0.131578 | + | 0.991306i | \(0.542005\pi\) | |||||||
\(242\) | 11.9029 | 0.765148 | ||||||||
\(243\) | −11.9604 | −0.767261 | ||||||||
\(244\) | 5.24495 | 0.335773 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 1.46027 | 0.0931033 | ||||||||
\(247\) | 1.88344 | 0.119840 | ||||||||
\(248\) | −18.6223 | −1.18251 | ||||||||
\(249\) | −3.73897 | −0.236947 | ||||||||
\(250\) | −1.08292 | −0.0684898 | ||||||||
\(251\) | −11.8988 | −0.751045 | −0.375522 | − | 0.926813i | \(-0.622537\pi\) | ||||
−0.375522 | + | 0.926813i | \(0.622537\pi\) | |||||||
\(252\) | 2.27822 | 0.143514 | ||||||||
\(253\) | −0.556318 | −0.0349754 | ||||||||
\(254\) | −3.16337 | −0.198487 | ||||||||
\(255\) | −2.21988 | −0.139014 | ||||||||
\(256\) | −15.9893 | −0.999331 | ||||||||
\(257\) | −10.4278 | −0.650466 | −0.325233 | − | 0.945634i | \(-0.605443\pi\) | ||||
−0.325233 | + | 0.945634i | \(0.605443\pi\) | |||||||
\(258\) | 1.02765 | 0.0639790 | ||||||||
\(259\) | −10.0087 | −0.621912 | ||||||||
\(260\) | −2.96651 | −0.183975 | ||||||||
\(261\) | −16.9639 | −1.05004 | ||||||||
\(262\) | −14.7409 | −0.910698 | ||||||||
\(263\) | 20.7297 | 1.27825 | 0.639123 | − | 0.769105i | \(-0.279298\pi\) | ||||
0.639123 | + | 0.769105i | \(0.279298\pi\) | |||||||
\(264\) | −0.139985 | −0.00861549 | ||||||||
\(265\) | −6.29211 | −0.386521 | ||||||||
\(266\) | −0.568799 | −0.0348753 | ||||||||
\(267\) | 2.65384 | 0.162412 | ||||||||
\(268\) | −7.59389 | −0.463871 | ||||||||
\(269\) | −17.8263 | −1.08689 | −0.543443 | − | 0.839446i | \(-0.682880\pi\) | ||||
−0.543443 | + | 0.839446i | \(0.682880\pi\) | |||||||
\(270\) | −3.09145 | −0.188140 | ||||||||
\(271\) | 25.9613 | 1.57704 | 0.788518 | − | 0.615012i | \(-0.210849\pi\) | ||||
0.788518 | + | 0.615012i | \(0.210849\pi\) | |||||||
\(272\) | −7.43181 | −0.450620 | ||||||||
\(273\) | −1.77909 | −0.107675 | ||||||||
\(274\) | −8.22115 | −0.496658 | ||||||||
\(275\) | 0.0921526 | 0.00555701 | ||||||||
\(276\) | −2.47789 | −0.149151 | ||||||||
\(277\) | 4.33183 | 0.260275 | 0.130137 | − | 0.991496i | \(-0.458458\pi\) | ||||
0.130137 | + | 0.991496i | \(0.458458\pi\) | |||||||
\(278\) | −23.2572 | −1.39487 | ||||||||
\(279\) | 16.7496 | 1.00277 | ||||||||
\(280\) | 3.06172 | 0.182973 | ||||||||
\(281\) | 0.643321 | 0.0383773 | 0.0191886 | − | 0.999816i | \(-0.493892\pi\) | ||||
0.0191886 | + | 0.999816i | \(0.493892\pi\) | |||||||
\(282\) | −4.32523 | −0.257564 | ||||||||
\(283\) | −0.351072 | −0.0208691 | −0.0104345 | − | 0.999946i | \(-0.503321\pi\) | ||||
−0.0104345 | + | 0.999946i | \(0.503321\pi\) | |||||||
\(284\) | 4.88658 | 0.289965 | ||||||||
\(285\) | −0.260599 | −0.0154365 | ||||||||
\(286\) | −0.357842 | −0.0211596 | ||||||||
\(287\) | 2.71787 | 0.160431 | ||||||||
\(288\) | 11.9095 | 0.701776 | ||||||||
\(289\) | 3.01894 | 0.177585 | ||||||||
\(290\) | −6.67087 | −0.391727 | ||||||||
\(291\) | 1.97446 | 0.115745 | ||||||||
\(292\) | 2.05233 | 0.120104 | ||||||||
\(293\) | −7.05482 | −0.412147 | −0.206073 | − | 0.978537i | \(-0.566069\pi\) | ||||
−0.206073 | + | 0.978537i | \(0.566069\pi\) | |||||||
\(294\) | 0.537284 | 0.0313351 | ||||||||
\(295\) | −0.398133 | −0.0231802 | ||||||||
\(296\) | −30.6439 | −1.78114 | ||||||||
\(297\) | 0.263072 | 0.0152650 | ||||||||
\(298\) | −7.60658 | −0.440637 | ||||||||
\(299\) | −21.6473 | −1.25190 | ||||||||
\(300\) | 0.410455 | 0.0236976 | ||||||||
\(301\) | 1.91268 | 0.110245 | ||||||||
\(302\) | 1.51941 | 0.0874321 | ||||||||
\(303\) | 3.39554 | 0.195068 | ||||||||
\(304\) | −0.872444 | −0.0500381 | ||||||||
\(305\) | −6.33993 | −0.363023 | ||||||||
\(306\) | 13.3430 | 0.762771 | ||||||||
\(307\) | −19.2504 | −1.09868 | −0.549340 | − | 0.835599i | \(-0.685121\pi\) | ||||
−0.549340 | + | 0.835599i | \(0.685121\pi\) | |||||||
\(308\) | −0.0762367 | −0.00434399 | ||||||||
\(309\) | −3.68193 | −0.209457 | ||||||||
\(310\) | 6.58661 | 0.374094 | ||||||||
\(311\) | 17.0756 | 0.968268 | 0.484134 | − | 0.874994i | \(-0.339135\pi\) | ||||
0.484134 | + | 0.874994i | \(0.339135\pi\) | |||||||
\(312\) | −5.44707 | −0.308379 | ||||||||
\(313\) | −14.8552 | −0.839664 | −0.419832 | − | 0.907602i | \(-0.637911\pi\) | ||||
−0.419832 | + | 0.907602i | \(0.637911\pi\) | |||||||
\(314\) | 15.4189 | 0.870141 | ||||||||
\(315\) | −2.75384 | −0.155161 | ||||||||
\(316\) | 3.40481 | 0.191535 | ||||||||
\(317\) | −34.4682 | −1.93593 | −0.967964 | − | 0.251091i | \(-0.919211\pi\) | ||||
−0.967964 | + | 0.251091i | \(0.919211\pi\) | |||||||
\(318\) | −3.38065 | −0.189578 | ||||||||
\(319\) | 0.567668 | 0.0317833 | ||||||||
\(320\) | 8.00533 | 0.447511 | ||||||||
\(321\) | 3.76169 | 0.209957 | ||||||||
\(322\) | 6.53750 | 0.364321 | ||||||||
\(323\) | 2.35009 | 0.130762 | ||||||||
\(324\) | −5.66292 | −0.314607 | ||||||||
\(325\) | 3.58582 | 0.198905 | ||||||||
\(326\) | −7.39489 | −0.409565 | ||||||||
\(327\) | −2.56492 | −0.141840 | ||||||||
\(328\) | 8.32136 | 0.459470 | ||||||||
\(329\) | −8.05017 | −0.443820 | ||||||||
\(330\) | 0.0495121 | 0.00272555 | ||||||||
\(331\) | −34.5310 | −1.89799 | −0.948997 | − | 0.315284i | \(-0.897900\pi\) | ||||
−0.948997 | + | 0.315284i | \(0.897900\pi\) | |||||||
\(332\) | −6.23447 | −0.342161 | ||||||||
\(333\) | 27.5624 | 1.51041 | ||||||||
\(334\) | 15.1621 | 0.829634 | ||||||||
\(335\) | 9.17925 | 0.501516 | ||||||||
\(336\) | 0.824105 | 0.0449586 | ||||||||
\(337\) | 5.60713 | 0.305440 | 0.152720 | − | 0.988269i | \(-0.451197\pi\) | ||||
0.152720 | + | 0.988269i | \(0.451197\pi\) | |||||||
\(338\) | 0.153675 | 0.00835882 | ||||||||
\(339\) | 9.10332 | 0.494425 | ||||||||
\(340\) | −3.70150 | −0.200742 | ||||||||
\(341\) | −0.560498 | −0.0303527 | ||||||||
\(342\) | 1.56638 | 0.0847002 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.85610 | 0.315740 | ||||||||
\(345\) | 2.99519 | 0.161256 | ||||||||
\(346\) | 14.2234 | 0.764657 | ||||||||
\(347\) | 32.1558 | 1.72621 | 0.863106 | − | 0.505024i | \(-0.168516\pi\) | ||||
0.863106 | + | 0.505024i | \(0.168516\pi\) | |||||||
\(348\) | 2.52844 | 0.135539 | ||||||||
\(349\) | −5.42746 | −0.290525 | −0.145263 | − | 0.989393i | \(-0.546403\pi\) | ||||
−0.145263 | + | 0.989393i | \(0.546403\pi\) | |||||||
\(350\) | −1.08292 | −0.0578844 | ||||||||
\(351\) | 10.2366 | 0.546388 | ||||||||
\(352\) | −0.398532 | −0.0212418 | ||||||||
\(353\) | 11.6349 | 0.619262 | 0.309631 | − | 0.950857i | \(-0.399794\pi\) | ||||
0.309631 | + | 0.950857i | \(0.399794\pi\) | |||||||
\(354\) | −0.213911 | −0.0113692 | ||||||||
\(355\) | −5.90674 | −0.313497 | ||||||||
\(356\) | 4.42510 | 0.234530 | ||||||||
\(357\) | −2.21988 | −0.117488 | ||||||||
\(358\) | 3.15539 | 0.166768 | ||||||||
\(359\) | 34.1213 | 1.80085 | 0.900426 | − | 0.435009i | \(-0.143255\pi\) | ||||
0.900426 | + | 0.435009i | \(0.143255\pi\) | |||||||
\(360\) | −8.43149 | −0.444379 | ||||||||
\(361\) | −18.7241 | −0.985480 | ||||||||
\(362\) | 19.3954 | 1.01940 | ||||||||
\(363\) | 5.45338 | 0.286228 | ||||||||
\(364\) | −2.96651 | −0.155487 | ||||||||
\(365\) | −2.48079 | −0.129851 | ||||||||
\(366\) | −3.40634 | −0.178052 | ||||||||
\(367\) | 3.22270 | 0.168224 | 0.0841118 | − | 0.996456i | \(-0.473195\pi\) | ||||
0.0841118 | + | 0.996456i | \(0.473195\pi\) | |||||||
\(368\) | 10.0274 | 0.522716 | ||||||||
\(369\) | −7.48458 | −0.389631 | ||||||||
\(370\) | 10.8386 | 0.563473 | ||||||||
\(371\) | −6.29211 | −0.326670 | ||||||||
\(372\) | −2.49650 | −0.129438 | ||||||||
\(373\) | 13.3019 | 0.688745 | 0.344373 | − | 0.938833i | \(-0.388092\pi\) | ||||
0.344373 | + | 0.938833i | \(0.388092\pi\) | |||||||
\(374\) | −0.446502 | −0.0230881 | ||||||||
\(375\) | −0.496145 | −0.0256208 | ||||||||
\(376\) | −24.6474 | −1.27109 | ||||||||
\(377\) | 22.0889 | 1.13764 | ||||||||
\(378\) | −3.09145 | −0.159007 | ||||||||
\(379\) | 10.4707 | 0.537842 | 0.268921 | − | 0.963162i | \(-0.413333\pi\) | ||||
0.268921 | + | 0.963162i | \(0.413333\pi\) | |||||||
\(380\) | −0.434531 | −0.0222909 | ||||||||
\(381\) | −1.44931 | −0.0742506 | ||||||||
\(382\) | −22.0409 | −1.12771 | ||||||||
\(383\) | −6.11139 | −0.312277 | −0.156139 | − | 0.987735i | \(-0.549905\pi\) | ||||
−0.156139 | + | 0.987735i | \(0.549905\pi\) | |||||||
\(384\) | 0.00978226 | 0.000499199 0 | ||||||||
\(385\) | 0.0921526 | 0.00469653 | ||||||||
\(386\) | −14.0183 | −0.713511 | ||||||||
\(387\) | −5.26722 | −0.267748 | ||||||||
\(388\) | 3.29228 | 0.167140 | ||||||||
\(389\) | 14.3076 | 0.725422 | 0.362711 | − | 0.931902i | \(-0.381851\pi\) | ||||
0.362711 | + | 0.931902i | \(0.381851\pi\) | |||||||
\(390\) | 1.92660 | 0.0975574 | ||||||||
\(391\) | −27.0107 | −1.36599 | ||||||||
\(392\) | 3.06172 | 0.154640 | ||||||||
\(393\) | −6.75364 | −0.340676 | ||||||||
\(394\) | −9.74310 | −0.490850 | ||||||||
\(395\) | −4.11562 | −0.207080 | ||||||||
\(396\) | 0.209944 | 0.0105501 | ||||||||
\(397\) | 9.29598 | 0.466552 | 0.233276 | − | 0.972411i | \(-0.425055\pi\) | ||||
0.233276 | + | 0.972411i | \(0.425055\pi\) | |||||||
\(398\) | −17.4231 | −0.873340 | ||||||||
\(399\) | −0.260599 | −0.0130462 | ||||||||
\(400\) | −1.66102 | −0.0830508 | ||||||||
\(401\) | −28.1185 | −1.40417 | −0.702084 | − | 0.712094i | \(-0.747747\pi\) | ||||
−0.702084 | + | 0.712094i | \(0.747747\pi\) | |||||||
\(402\) | 4.93187 | 0.245979 | ||||||||
\(403\) | −21.8100 | −1.08643 | ||||||||
\(404\) | 5.66183 | 0.281686 | ||||||||
\(405\) | 6.84516 | 0.340138 | ||||||||
\(406\) | −6.67087 | −0.331070 | ||||||||
\(407\) | −0.922329 | −0.0457182 | ||||||||
\(408\) | −6.79665 | −0.336484 | ||||||||
\(409\) | −3.62949 | −0.179467 | −0.0897333 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897333 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(410\) | −2.94323 | −0.145356 | ||||||||
\(411\) | −3.76657 | −0.185791 | ||||||||
\(412\) | −6.13936 | −0.302465 | ||||||||
\(413\) | −0.398133 | −0.0195909 | ||||||||
\(414\) | −18.0032 | −0.884810 | ||||||||
\(415\) | 7.53603 | 0.369929 | ||||||||
\(416\) | −15.5076 | −0.760322 | ||||||||
\(417\) | −10.6554 | −0.521798 | ||||||||
\(418\) | −0.0524163 | −0.00256376 | ||||||||
\(419\) | −5.43796 | −0.265662 | −0.132831 | − | 0.991139i | \(-0.542407\pi\) | ||||
−0.132831 | + | 0.991139i | \(0.542407\pi\) | |||||||
\(420\) | 0.410455 | 0.0200282 | ||||||||
\(421\) | −10.6001 | −0.516618 | −0.258309 | − | 0.966062i | \(-0.583165\pi\) | ||||
−0.258309 | + | 0.966062i | \(0.583165\pi\) | |||||||
\(422\) | 29.0504 | 1.41415 | ||||||||
\(423\) | 22.1689 | 1.07789 | ||||||||
\(424\) | −19.2647 | −0.935576 | ||||||||
\(425\) | 4.47425 | 0.217033 | ||||||||
\(426\) | −3.17360 | −0.153761 | ||||||||
\(427\) | −6.33993 | −0.306811 | ||||||||
\(428\) | 6.27236 | 0.303186 | ||||||||
\(429\) | −0.163947 | −0.00791545 | ||||||||
\(430\) | −2.07128 | −0.0998859 | ||||||||
\(431\) | −24.1090 | −1.16129 | −0.580644 | − | 0.814158i | \(-0.697199\pi\) | ||||
−0.580644 | + | 0.814158i | \(0.697199\pi\) | |||||||
\(432\) | −4.74177 | −0.228139 | ||||||||
\(433\) | 5.07998 | 0.244128 | 0.122064 | − | 0.992522i | \(-0.461049\pi\) | ||||
0.122064 | + | 0.992522i | \(0.461049\pi\) | |||||||
\(434\) | 6.58661 | 0.316168 | ||||||||
\(435\) | −3.05630 | −0.146538 | ||||||||
\(436\) | −4.27683 | −0.204823 | ||||||||
\(437\) | −3.17088 | −0.151684 | ||||||||
\(438\) | −1.33289 | −0.0636880 | ||||||||
\(439\) | 23.4909 | 1.12116 | 0.560579 | − | 0.828101i | \(-0.310579\pi\) | ||||
0.560579 | + | 0.828101i | \(0.310579\pi\) | |||||||
\(440\) | 0.282145 | 0.0134508 | ||||||||
\(441\) | −2.75384 | −0.131135 | ||||||||
\(442\) | −17.3742 | −0.826406 | ||||||||
\(443\) | −10.5882 | −0.503063 | −0.251531 | − | 0.967849i | \(-0.580934\pi\) | ||||
−0.251531 | + | 0.967849i | \(0.580934\pi\) | |||||||
\(444\) | −4.10813 | −0.194963 | ||||||||
\(445\) | −5.34892 | −0.253563 | ||||||||
\(446\) | 21.1438 | 1.00119 | ||||||||
\(447\) | −3.48500 | −0.164835 | ||||||||
\(448\) | 8.00533 | 0.378216 | ||||||||
\(449\) | −7.52686 | −0.355214 | −0.177607 | − | 0.984101i | \(-0.556836\pi\) | ||||
−0.177607 | + | 0.984101i | \(0.556836\pi\) | |||||||
\(450\) | 2.98218 | 0.140581 | ||||||||
\(451\) | 0.250459 | 0.0117936 | ||||||||
\(452\) | 15.1792 | 0.713968 | ||||||||
\(453\) | 0.696125 | 0.0327068 | ||||||||
\(454\) | 13.1329 | 0.616358 | ||||||||
\(455\) | 3.58582 | 0.168106 | ||||||||
\(456\) | −0.797880 | −0.0373642 | ||||||||
\(457\) | 31.8197 | 1.48846 | 0.744232 | − | 0.667922i | \(-0.232816\pi\) | ||||
0.744232 | + | 0.667922i | \(0.232816\pi\) | |||||||
\(458\) | 1.08292 | 0.0506014 | ||||||||
\(459\) | 12.7728 | 0.596185 | ||||||||
\(460\) | 4.99428 | 0.232860 | ||||||||
\(461\) | −5.79119 | −0.269723 | −0.134861 | − | 0.990864i | \(-0.543059\pi\) | ||||
−0.134861 | + | 0.990864i | \(0.543059\pi\) | |||||||
\(462\) | 0.0495121 | 0.00230351 | ||||||||
\(463\) | 11.2474 | 0.522712 | 0.261356 | − | 0.965243i | \(-0.415830\pi\) | ||||
0.261356 | + | 0.965243i | \(0.415830\pi\) | |||||||
\(464\) | −10.2320 | −0.475009 | ||||||||
\(465\) | 3.01769 | 0.139942 | ||||||||
\(466\) | −8.01678 | −0.371370 | ||||||||
\(467\) | −7.91399 | −0.366216 | −0.183108 | − | 0.983093i | \(-0.558616\pi\) | ||||
−0.183108 | + | 0.983093i | \(0.558616\pi\) | |||||||
\(468\) | 8.16928 | 0.377625 | ||||||||
\(469\) | 9.17925 | 0.423858 | ||||||||
\(470\) | 8.71767 | 0.402116 | ||||||||
\(471\) | 7.06428 | 0.325505 | ||||||||
\(472\) | −1.21897 | −0.0561078 | ||||||||
\(473\) | 0.176259 | 0.00810437 | ||||||||
\(474\) | −2.21126 | −0.101567 | ||||||||
\(475\) | 0.525247 | 0.0241000 | ||||||||
\(476\) | −3.70150 | −0.169658 | ||||||||
\(477\) | 17.3275 | 0.793370 | ||||||||
\(478\) | −23.5945 | −1.07919 | ||||||||
\(479\) | −35.2829 | −1.61212 | −0.806059 | − | 0.591836i | \(-0.798403\pi\) | ||||
−0.806059 | + | 0.591836i | \(0.798403\pi\) | |||||||
\(480\) | 2.14568 | 0.0979364 | ||||||||
\(481\) | −35.8895 | −1.63642 | ||||||||
\(482\) | 4.42404 | 0.201509 | ||||||||
\(483\) | 2.99519 | 0.136286 | ||||||||
\(484\) | 9.09315 | 0.413325 | ||||||||
\(485\) | −3.97960 | −0.180704 | ||||||||
\(486\) | 12.9521 | 0.587521 | ||||||||
\(487\) | 27.4557 | 1.24414 | 0.622068 | − | 0.782963i | \(-0.286293\pi\) | ||||
0.622068 | + | 0.782963i | \(0.286293\pi\) | |||||||
\(488\) | −19.4111 | −0.878699 | ||||||||
\(489\) | −3.38801 | −0.153211 | ||||||||
\(490\) | −1.08292 | −0.0489213 | ||||||||
\(491\) | −39.9202 | −1.80158 | −0.900788 | − | 0.434260i | \(-0.857010\pi\) | ||||
−0.900788 | + | 0.434260i | \(0.857010\pi\) | |||||||
\(492\) | 1.11556 | 0.0502935 | ||||||||
\(493\) | 27.5618 | 1.24132 | ||||||||
\(494\) | −2.03961 | −0.0917664 | ||||||||
\(495\) | −0.253773 | −0.0114063 | ||||||||
\(496\) | 10.1028 | 0.453628 | ||||||||
\(497\) | −5.90674 | −0.264954 | ||||||||
\(498\) | 4.04899 | 0.181440 | ||||||||
\(499\) | −32.0474 | −1.43464 | −0.717318 | − | 0.696746i | \(-0.754631\pi\) | ||||
−0.717318 | + | 0.696746i | \(0.754631\pi\) | |||||||
\(500\) | −0.827289 | −0.0369975 | ||||||||
\(501\) | 6.94661 | 0.310352 | ||||||||
\(502\) | 12.8854 | 0.575104 | ||||||||
\(503\) | 27.6593 | 1.23327 | 0.616634 | − | 0.787250i | \(-0.288496\pi\) | ||||
0.616634 | + | 0.787250i | \(0.288496\pi\) | |||||||
\(504\) | −8.43149 | −0.375568 | ||||||||
\(505\) | −6.84384 | −0.304547 | ||||||||
\(506\) | 0.602447 | 0.0267820 | ||||||||
\(507\) | 0.0704071 | 0.00312689 | ||||||||
\(508\) | −2.41663 | −0.107221 | ||||||||
\(509\) | −20.6035 | −0.913232 | −0.456616 | − | 0.889664i | \(-0.650939\pi\) | ||||
−0.456616 | + | 0.889664i | \(0.650939\pi\) | |||||||
\(510\) | 2.40395 | 0.106449 | ||||||||
\(511\) | −2.48079 | −0.109744 | ||||||||
\(512\) | 17.3545 | 0.766969 | ||||||||
\(513\) | 1.49944 | 0.0662020 | ||||||||
\(514\) | 11.2924 | 0.498087 | ||||||||
\(515\) | 7.42107 | 0.327011 | ||||||||
\(516\) | 0.785070 | 0.0345608 | ||||||||
\(517\) | −0.741844 | −0.0326262 | ||||||||
\(518\) | 10.8386 | 0.476222 | ||||||||
\(519\) | 6.51655 | 0.286045 | ||||||||
\(520\) | 10.9788 | 0.481451 | ||||||||
\(521\) | −13.9391 | −0.610684 | −0.305342 | − | 0.952243i | \(-0.598771\pi\) | ||||
−0.305342 | + | 0.952243i | \(0.598771\pi\) | |||||||
\(522\) | 18.3705 | 0.804055 | ||||||||
\(523\) | 2.19327 | 0.0959049 | 0.0479525 | − | 0.998850i | \(-0.484730\pi\) | ||||
0.0479525 | + | 0.998850i | \(0.484730\pi\) | |||||||
\(524\) | −11.2612 | −0.491950 | ||||||||
\(525\) | −0.496145 | −0.0216535 | ||||||||
\(526\) | −22.4485 | −0.978802 | ||||||||
\(527\) | −27.2137 | −1.18545 | ||||||||
\(528\) | 0.0759434 | 0.00330501 | ||||||||
\(529\) | 13.4445 | 0.584544 | ||||||||
\(530\) | 6.81384 | 0.295974 | ||||||||
\(531\) | 1.09640 | 0.0475795 | ||||||||
\(532\) | −0.434531 | −0.0188393 | ||||||||
\(533\) | 9.74578 | 0.422137 | ||||||||
\(534\) | −2.87389 | −0.124366 | ||||||||
\(535\) | −7.58183 | −0.327791 | ||||||||
\(536\) | 28.1043 | 1.21392 | ||||||||
\(537\) | 1.44566 | 0.0623848 | ||||||||
\(538\) | 19.3044 | 0.832271 | ||||||||
\(539\) | 0.0921526 | 0.00396929 | ||||||||
\(540\) | −2.36169 | −0.101631 | ||||||||
\(541\) | −14.2180 | −0.611281 | −0.305640 | − | 0.952147i | \(-0.598871\pi\) | ||||
−0.305640 | + | 0.952147i | \(0.598871\pi\) | |||||||
\(542\) | −28.1139 | −1.20760 | ||||||||
\(543\) | 8.88610 | 0.381339 | ||||||||
\(544\) | −19.3498 | −0.829616 | ||||||||
\(545\) | 5.16970 | 0.221446 | ||||||||
\(546\) | 1.92660 | 0.0824511 | ||||||||
\(547\) | 25.9106 | 1.10786 | 0.553928 | − | 0.832565i | \(-0.313128\pi\) | ||||
0.553928 | + | 0.832565i | \(0.313128\pi\) | |||||||
\(548\) | −6.28050 | −0.268290 | ||||||||
\(549\) | 17.4591 | 0.745138 | ||||||||
\(550\) | −0.0997937 | −0.00425522 | ||||||||
\(551\) | 3.23556 | 0.137840 | ||||||||
\(552\) | 9.17045 | 0.390320 | ||||||||
\(553\) | −4.11562 | −0.175014 | ||||||||
\(554\) | −4.69102 | −0.199302 | ||||||||
\(555\) | 4.96578 | 0.210786 | ||||||||
\(556\) | −17.7672 | −0.753497 | ||||||||
\(557\) | −38.5855 | −1.63492 | −0.817459 | − | 0.575987i | \(-0.804618\pi\) | ||||
−0.817459 | + | 0.575987i | \(0.804618\pi\) | |||||||
\(558\) | −18.1385 | −0.767863 | ||||||||
\(559\) | 6.85853 | 0.290085 | ||||||||
\(560\) | −1.66102 | −0.0701908 | ||||||||
\(561\) | −0.204567 | −0.00863685 | ||||||||
\(562\) | −0.696663 | −0.0293870 | ||||||||
\(563\) | −17.2874 | −0.728575 | −0.364288 | − | 0.931286i | \(-0.618687\pi\) | ||||
−0.364288 | + | 0.931286i | \(0.618687\pi\) | |||||||
\(564\) | −3.30423 | −0.139133 | ||||||||
\(565\) | −18.3481 | −0.771911 | ||||||||
\(566\) | 0.380182 | 0.0159802 | ||||||||
\(567\) | 6.84516 | 0.287469 | ||||||||
\(568\) | −18.0848 | −0.758821 | ||||||||
\(569\) | 13.9836 | 0.586224 | 0.293112 | − | 0.956078i | \(-0.405309\pi\) | ||||
0.293112 | + | 0.956078i | \(0.405309\pi\) | |||||||
\(570\) | 0.282207 | 0.0118203 | ||||||||
\(571\) | −32.9814 | −1.38023 | −0.690114 | − | 0.723701i | \(-0.742439\pi\) | ||||
−0.690114 | + | 0.723701i | \(0.742439\pi\) | |||||||
\(572\) | −0.273371 | −0.0114302 | ||||||||
\(573\) | −10.0982 | −0.421858 | ||||||||
\(574\) | −2.94323 | −0.122848 | ||||||||
\(575\) | −6.03693 | −0.251757 | ||||||||
\(576\) | −22.0454 | −0.918558 | ||||||||
\(577\) | 8.21231 | 0.341883 | 0.170941 | − | 0.985281i | \(-0.445319\pi\) | ||||
0.170941 | + | 0.985281i | \(0.445319\pi\) | |||||||
\(578\) | −3.26926 | −0.135983 | ||||||||
\(579\) | −6.42255 | −0.266912 | ||||||||
\(580\) | −5.09617 | −0.211607 | ||||||||
\(581\) | 7.53603 | 0.312647 | ||||||||
\(582\) | −2.13818 | −0.0886303 | ||||||||
\(583\) | −0.579834 | −0.0240143 | ||||||||
\(584\) | −7.59549 | −0.314304 | ||||||||
\(585\) | −9.87477 | −0.408271 | ||||||||
\(586\) | 7.63979 | 0.315597 | ||||||||
\(587\) | −20.5589 | −0.848558 | −0.424279 | − | 0.905532i | \(-0.639472\pi\) | ||||
−0.424279 | + | 0.905532i | \(0.639472\pi\) | |||||||
\(588\) | 0.410455 | 0.0169269 | ||||||||
\(589\) | −3.19470 | −0.131635 | ||||||||
\(590\) | 0.431146 | 0.0177500 | ||||||||
\(591\) | −4.46386 | −0.183619 | ||||||||
\(592\) | 16.6247 | 0.683269 | ||||||||
\(593\) | −7.79482 | −0.320095 | −0.160048 | − | 0.987109i | \(-0.551165\pi\) | ||||
−0.160048 | + | 0.987109i | \(0.551165\pi\) | |||||||
\(594\) | −0.284885 | −0.0116890 | ||||||||
\(595\) | 4.47425 | 0.183426 | ||||||||
\(596\) | −5.81100 | −0.238028 | ||||||||
\(597\) | −7.98248 | −0.326701 | ||||||||
\(598\) | 23.4423 | 0.958626 | ||||||||
\(599\) | −16.4055 | −0.670311 | −0.335156 | − | 0.942163i | \(-0.608789\pi\) | ||||
−0.335156 | + | 0.942163i | \(0.608789\pi\) | |||||||
\(600\) | −1.51906 | −0.0620153 | ||||||||
\(601\) | −33.6730 | −1.37355 | −0.686776 | − | 0.726869i | \(-0.740975\pi\) | ||||
−0.686776 | + | 0.726869i | \(0.740975\pi\) | |||||||
\(602\) | −2.07128 | −0.0844190 | ||||||||
\(603\) | −25.2782 | −1.02941 | ||||||||
\(604\) | 1.16074 | 0.0472299 | ||||||||
\(605\) | −10.9915 | −0.446868 | ||||||||
\(606\) | −3.67709 | −0.149371 | ||||||||
\(607\) | −36.3829 | −1.47674 | −0.738368 | − | 0.674398i | \(-0.764403\pi\) | ||||
−0.738368 | + | 0.674398i | \(0.764403\pi\) | |||||||
\(608\) | −2.27153 | −0.0921229 | ||||||||
\(609\) | −3.05630 | −0.123847 | ||||||||
\(610\) | 6.86562 | 0.277981 | ||||||||
\(611\) | −28.8664 | −1.16781 | ||||||||
\(612\) | 10.1933 | 0.412041 | ||||||||
\(613\) | 6.31778 | 0.255173 | 0.127586 | − | 0.991827i | \(-0.459277\pi\) | ||||
0.127586 | + | 0.991827i | \(0.459277\pi\) | |||||||
\(614\) | 20.8466 | 0.841302 | ||||||||
\(615\) | −1.34846 | −0.0543750 | ||||||||
\(616\) | 0.282145 | 0.0113680 | ||||||||
\(617\) | −43.1501 | −1.73716 | −0.868578 | − | 0.495552i | \(-0.834966\pi\) | ||||
−0.868578 | + | 0.495552i | \(0.834966\pi\) | |||||||
\(618\) | 3.98722 | 0.160390 | ||||||||
\(619\) | −37.5255 | −1.50828 | −0.754140 | − | 0.656714i | \(-0.771946\pi\) | ||||
−0.754140 | + | 0.656714i | \(0.771946\pi\) | |||||||
\(620\) | 5.03180 | 0.202082 | ||||||||
\(621\) | −17.2339 | −0.691571 | ||||||||
\(622\) | −18.4915 | −0.741440 | ||||||||
\(623\) | −5.34892 | −0.214300 | ||||||||
\(624\) | 2.95509 | 0.118298 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.0869 | 0.642964 | ||||||||
\(627\) | −0.0240148 | −0.000959060 0 | ||||||||
\(628\) | 11.7792 | 0.470042 | ||||||||
\(629\) | −44.7816 | −1.78556 | ||||||||
\(630\) | 2.98218 | 0.118813 | ||||||||
\(631\) | −28.3186 | −1.12735 | −0.563673 | − | 0.825998i | \(-0.690612\pi\) | ||||
−0.563673 | + | 0.825998i | \(0.690612\pi\) | |||||||
\(632\) | −12.6009 | −0.501237 | ||||||||
\(633\) | 13.3096 | 0.529009 | ||||||||
\(634\) | 37.3262 | 1.48241 | ||||||||
\(635\) | 2.92115 | 0.115922 | ||||||||
\(636\) | −2.58263 | −0.102408 | ||||||||
\(637\) | 3.58582 | 0.142075 | ||||||||
\(638\) | −0.614737 | −0.0243377 | ||||||||
\(639\) | 16.2662 | 0.643482 | ||||||||
\(640\) | −0.0197165 | −0.000779365 0 | ||||||||
\(641\) | −9.73555 | −0.384531 | −0.192266 | − | 0.981343i | \(-0.561584\pi\) | ||||
−0.192266 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(642\) | −4.07360 | −0.160772 | ||||||||
\(643\) | 2.03037 | 0.0800699 | 0.0400350 | − | 0.999198i | \(-0.487253\pi\) | ||||
0.0400350 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(644\) | 4.99428 | 0.196802 | ||||||||
\(645\) | −0.948968 | −0.0373656 | ||||||||
\(646\) | −2.54495 | −0.100130 | ||||||||
\(647\) | 12.0928 | 0.475419 | 0.237709 | − | 0.971336i | \(-0.423603\pi\) | ||||
0.237709 | + | 0.971336i | \(0.423603\pi\) | |||||||
\(648\) | 20.9580 | 0.823306 | ||||||||
\(649\) | −0.0366890 | −0.00144017 | ||||||||
\(650\) | −3.88315 | −0.152310 | ||||||||
\(651\) | 3.01769 | 0.118273 | ||||||||
\(652\) | −5.64928 | −0.221243 | ||||||||
\(653\) | 26.9774 | 1.05571 | 0.527854 | − | 0.849335i | \(-0.322997\pi\) | ||||
0.527854 | + | 0.849335i | \(0.322997\pi\) | |||||||
\(654\) | 2.77760 | 0.108613 | ||||||||
\(655\) | 13.6122 | 0.531874 | ||||||||
\(656\) | −4.51443 | −0.176259 | ||||||||
\(657\) | 6.83170 | 0.266530 | ||||||||
\(658\) | 8.71767 | 0.339850 | ||||||||
\(659\) | −11.4446 | −0.445817 | −0.222909 | − | 0.974839i | \(-0.571555\pi\) | ||||
−0.222909 | + | 0.974839i | \(0.571555\pi\) | |||||||
\(660\) | 0.0378245 | 0.00147232 | ||||||||
\(661\) | −9.38431 | −0.365007 | −0.182504 | − | 0.983205i | \(-0.558420\pi\) | ||||
−0.182504 | + | 0.983205i | \(0.558420\pi\) | |||||||
\(662\) | 37.3942 | 1.45337 | ||||||||
\(663\) | −7.96008 | −0.309144 | ||||||||
\(664\) | 23.0732 | 0.895415 | ||||||||
\(665\) | 0.525247 | 0.0203682 | ||||||||
\(666\) | −29.8478 | −1.15658 | ||||||||
\(667\) | −37.1880 | −1.43992 | ||||||||
\(668\) | 11.5830 | 0.448160 | ||||||||
\(669\) | 9.68716 | 0.374527 | ||||||||
\(670\) | −9.94038 | −0.384030 | ||||||||
\(671\) | −0.584240 | −0.0225543 | ||||||||
\(672\) | 2.14568 | 0.0827713 | ||||||||
\(673\) | −0.676710 | −0.0260853 | −0.0130426 | − | 0.999915i | \(-0.504152\pi\) | ||||
−0.0130426 | + | 0.999915i | \(0.504152\pi\) | |||||||
\(674\) | −6.07207 | −0.233887 | ||||||||
\(675\) | 2.85474 | 0.109879 | ||||||||
\(676\) | 0.117399 | 0.00451535 | ||||||||
\(677\) | −1.76667 | −0.0678988 | −0.0339494 | − | 0.999424i | \(-0.510809\pi\) | ||||
−0.0339494 | + | 0.999424i | \(0.510809\pi\) | |||||||
\(678\) | −9.85815 | −0.378600 | ||||||||
\(679\) | −3.97960 | −0.152723 | ||||||||
\(680\) | 13.6989 | 0.525330 | ||||||||
\(681\) | 6.01692 | 0.230569 | ||||||||
\(682\) | 0.606973 | 0.0232422 | ||||||||
\(683\) | 29.9167 | 1.14473 | 0.572365 | − | 0.819999i | \(-0.306026\pi\) | ||||
0.572365 | + | 0.819999i | \(0.306026\pi\) | |||||||
\(684\) | 1.19663 | 0.0457542 | ||||||||
\(685\) | 7.59167 | 0.290063 | ||||||||
\(686\) | −1.08292 | −0.0413460 | ||||||||
\(687\) | 0.496145 | 0.0189291 | ||||||||
\(688\) | −3.17700 | −0.121122 | ||||||||
\(689\) | −22.5624 | −0.859557 | ||||||||
\(690\) | −3.24355 | −0.123480 | ||||||||
\(691\) | 27.3310 | 1.03972 | 0.519861 | − | 0.854251i | \(-0.325984\pi\) | ||||
0.519861 | + | 0.854251i | \(0.325984\pi\) | |||||||
\(692\) | 10.8659 | 0.413060 | ||||||||
\(693\) | −0.253773 | −0.00964005 | ||||||||
\(694\) | −34.8220 | −1.32183 | ||||||||
\(695\) | 21.4764 | 0.814647 | ||||||||
\(696\) | −9.35753 | −0.354696 | ||||||||
\(697\) | 12.1604 | 0.460609 | ||||||||
\(698\) | 5.87749 | 0.222466 | ||||||||
\(699\) | −3.67294 | −0.138923 | ||||||||
\(700\) | −0.827289 | −0.0312686 | ||||||||
\(701\) | 7.06259 | 0.266750 | 0.133375 | − | 0.991066i | \(-0.457418\pi\) | ||||
0.133375 | + | 0.991066i | \(0.457418\pi\) | |||||||
\(702\) | −11.0854 | −0.418390 | ||||||||
\(703\) | −5.25705 | −0.198273 | ||||||||
\(704\) | 0.737711 | 0.0278035 | ||||||||
\(705\) | 3.99405 | 0.150425 | ||||||||
\(706\) | −12.5996 | −0.474193 | ||||||||
\(707\) | −6.84384 | −0.257389 | ||||||||
\(708\) | −0.163416 | −0.00614154 | ||||||||
\(709\) | 13.7222 | 0.515349 | 0.257674 | − | 0.966232i | \(-0.417044\pi\) | ||||
0.257674 | + | 0.966232i | \(0.417044\pi\) | |||||||
\(710\) | 6.39652 | 0.240057 | ||||||||
\(711\) | 11.3338 | 0.425050 | ||||||||
\(712\) | −16.3769 | −0.613751 | ||||||||
\(713\) | 36.7183 | 1.37511 | ||||||||
\(714\) | 2.40395 | 0.0899654 | ||||||||
\(715\) | 0.330442 | 0.0123578 | ||||||||
\(716\) | 2.41054 | 0.0900861 | ||||||||
\(717\) | −10.8100 | −0.403706 | ||||||||
\(718\) | −36.9505 | −1.37898 | ||||||||
\(719\) | 13.0806 | 0.487823 | 0.243911 | − | 0.969798i | \(-0.421569\pi\) | ||||
0.243911 | + | 0.969798i | \(0.421569\pi\) | |||||||
\(720\) | 4.57417 | 0.170469 | ||||||||
\(721\) | 7.42107 | 0.276375 | ||||||||
\(722\) | 20.2767 | 0.754620 | ||||||||
\(723\) | 2.02690 | 0.0753812 | ||||||||
\(724\) | 14.8170 | 0.550668 | ||||||||
\(725\) | 6.16008 | 0.228780 | ||||||||
\(726\) | −5.90557 | −0.219176 | ||||||||
\(727\) | −21.6440 | −0.802730 | −0.401365 | − | 0.915918i | \(-0.631464\pi\) | ||||
−0.401365 | + | 0.915918i | \(0.631464\pi\) | |||||||
\(728\) | 10.9788 | 0.406901 | ||||||||
\(729\) | −14.6014 | −0.540791 | ||||||||
\(730\) | 2.68649 | 0.0994316 | ||||||||
\(731\) | 8.55782 | 0.316522 | ||||||||
\(732\) | −2.60226 | −0.0961821 | ||||||||
\(733\) | −26.3017 | −0.971476 | −0.485738 | − | 0.874105i | \(-0.661449\pi\) | ||||
−0.485738 | + | 0.874105i | \(0.661449\pi\) | |||||||
\(734\) | −3.48992 | −0.128815 | ||||||||
\(735\) | −0.496145 | −0.0183006 | ||||||||
\(736\) | 26.1079 | 0.962350 | ||||||||
\(737\) | 0.845891 | 0.0311588 | ||||||||
\(738\) | 8.10518 | 0.298356 | ||||||||
\(739\) | −25.1474 | −0.925062 | −0.462531 | − | 0.886603i | \(-0.653059\pi\) | ||||
−0.462531 | + | 0.886603i | \(0.653059\pi\) | |||||||
\(740\) | 8.28010 | 0.304383 | ||||||||
\(741\) | −0.934459 | −0.0343282 | ||||||||
\(742\) | 6.81384 | 0.250144 | ||||||||
\(743\) | −33.0359 | −1.21197 | −0.605985 | − | 0.795476i | \(-0.707221\pi\) | ||||
−0.605985 | + | 0.795476i | \(0.707221\pi\) | |||||||
\(744\) | 9.23934 | 0.338731 | ||||||||
\(745\) | 7.02415 | 0.257345 | ||||||||
\(746\) | −14.4048 | −0.527399 | ||||||||
\(747\) | −20.7530 | −0.759313 | ||||||||
\(748\) | −0.341102 | −0.0124719 | ||||||||
\(749\) | −7.58183 | −0.277034 | ||||||||
\(750\) | 0.537284 | 0.0196189 | ||||||||
\(751\) | −24.1765 | −0.882215 | −0.441107 | − | 0.897454i | \(-0.645414\pi\) | ||||
−0.441107 | + | 0.897454i | \(0.645414\pi\) | |||||||
\(752\) | 13.3715 | 0.487607 | ||||||||
\(753\) | 5.90352 | 0.215136 | ||||||||
\(754\) | −23.9205 | −0.871134 | ||||||||
\(755\) | −1.40307 | −0.0510629 | ||||||||
\(756\) | −2.36169 | −0.0858940 | ||||||||
\(757\) | 25.0399 | 0.910091 | 0.455046 | − | 0.890468i | \(-0.349623\pi\) | ||||
0.455046 | + | 0.890468i | \(0.349623\pi\) | |||||||
\(758\) | −11.3389 | −0.411846 | ||||||||
\(759\) | 0.276015 | 0.0100187 | ||||||||
\(760\) | 1.60816 | 0.0583341 | ||||||||
\(761\) | −34.1549 | −1.23811 | −0.619057 | − | 0.785346i | \(-0.712485\pi\) | ||||
−0.619057 | + | 0.785346i | \(0.712485\pi\) | |||||||
\(762\) | 1.56949 | 0.0568566 | ||||||||
\(763\) | 5.16970 | 0.187156 | ||||||||
\(764\) | −16.8380 | −0.609179 | ||||||||
\(765\) | −12.3214 | −0.445480 | ||||||||
\(766\) | 6.61813 | 0.239123 | ||||||||
\(767\) | −1.42763 | −0.0515489 | ||||||||
\(768\) | 7.93301 | 0.286258 | ||||||||
\(769\) | −40.3438 | −1.45483 | −0.727417 | − | 0.686196i | \(-0.759279\pi\) | ||||
−0.727417 | + | 0.686196i | \(0.759279\pi\) | |||||||
\(770\) | −0.0997937 | −0.00359631 | ||||||||
\(771\) | 5.17368 | 0.186326 | ||||||||
\(772\) | −10.7092 | −0.385431 | ||||||||
\(773\) | 12.9638 | 0.466276 | 0.233138 | − | 0.972444i | \(-0.425101\pi\) | ||||
0.233138 | + | 0.972444i | \(0.425101\pi\) | |||||||
\(774\) | 5.70397 | 0.205025 | ||||||||
\(775\) | −6.08228 | −0.218482 | ||||||||
\(776\) | −12.1844 | −0.437395 | ||||||||
\(777\) | 4.96578 | 0.178146 | ||||||||
\(778\) | −15.4939 | −0.555484 | ||||||||
\(779\) | 1.42755 | 0.0511473 | ||||||||
\(780\) | 1.47182 | 0.0526995 | ||||||||
\(781\) | −0.544321 | −0.0194773 | ||||||||
\(782\) | 29.2504 | 1.04599 | ||||||||
\(783\) | 17.5854 | 0.628452 | ||||||||
\(784\) | −1.66102 | −0.0593220 | ||||||||
\(785\) | −14.2383 | −0.508188 | ||||||||
\(786\) | 7.31364 | 0.260869 | ||||||||
\(787\) | 6.33820 | 0.225932 | 0.112966 | − | 0.993599i | \(-0.463965\pi\) | ||||
0.112966 | + | 0.993599i | \(0.463965\pi\) | |||||||
\(788\) | −7.44318 | −0.265152 | ||||||||
\(789\) | −10.2849 | −0.366153 | ||||||||
\(790\) | 4.45688 | 0.158569 | ||||||||
\(791\) | −18.3481 | −0.652383 | ||||||||
\(792\) | −0.776984 | −0.0276089 | ||||||||
\(793\) | −22.7338 | −0.807302 | ||||||||
\(794\) | −10.0668 | −0.357257 | ||||||||
\(795\) | 3.12180 | 0.110719 | ||||||||
\(796\) | −13.3102 | −0.471769 | ||||||||
\(797\) | −1.25700 | −0.0445253 | −0.0222626 | − | 0.999752i | \(-0.507087\pi\) | ||||
−0.0222626 | + | 0.999752i | \(0.507087\pi\) | |||||||
\(798\) | 0.282207 | 0.00999002 | ||||||||
\(799\) | −36.0185 | −1.27424 | ||||||||
\(800\) | −4.32470 | −0.152901 | ||||||||
\(801\) | 14.7301 | 0.520462 | ||||||||
\(802\) | 30.4500 | 1.07523 | ||||||||
\(803\) | −0.228611 | −0.00806752 | ||||||||
\(804\) | 3.76767 | 0.132875 | ||||||||
\(805\) | −6.03693 | −0.212774 | ||||||||
\(806\) | 23.6184 | 0.831923 | ||||||||
\(807\) | 8.84441 | 0.311338 | ||||||||
\(808\) | −20.9539 | −0.737157 | ||||||||
\(809\) | −14.8380 | −0.521677 | −0.260838 | − | 0.965382i | \(-0.583999\pi\) | ||||
−0.260838 | + | 0.965382i | \(0.583999\pi\) | |||||||
\(810\) | −7.41274 | −0.260457 | ||||||||
\(811\) | 32.0316 | 1.12478 | 0.562391 | − | 0.826871i | \(-0.309882\pi\) | ||||
0.562391 | + | 0.826871i | \(0.309882\pi\) | |||||||
\(812\) | −5.09617 | −0.178840 | ||||||||
\(813\) | −12.8806 | −0.451741 | ||||||||
\(814\) | 0.998807 | 0.0350082 | ||||||||
\(815\) | 6.82867 | 0.239198 | ||||||||
\(816\) | 3.68726 | 0.129080 | ||||||||
\(817\) | 1.00463 | 0.0351475 | ||||||||
\(818\) | 3.93044 | 0.137425 | ||||||||
\(819\) | −9.87477 | −0.345052 | ||||||||
\(820\) | −2.24846 | −0.0785197 | ||||||||
\(821\) | −3.11135 | −0.108587 | −0.0542935 | − | 0.998525i | \(-0.517291\pi\) | ||||
−0.0542935 | + | 0.998525i | \(0.517291\pi\) | |||||||
\(822\) | 4.07888 | 0.142267 | ||||||||
\(823\) | −4.42018 | −0.154078 | −0.0770389 | − | 0.997028i | \(-0.524547\pi\) | ||||
−0.0770389 | + | 0.997028i | \(0.524547\pi\) | |||||||
\(824\) | 22.7212 | 0.791532 | ||||||||
\(825\) | −0.0457210 | −0.00159180 | ||||||||
\(826\) | 0.431146 | 0.0150015 | ||||||||
\(827\) | −18.7164 | −0.650834 | −0.325417 | − | 0.945571i | \(-0.605505\pi\) | ||||
−0.325417 | + | 0.945571i | \(0.605505\pi\) | |||||||
\(828\) | −13.7535 | −0.477966 | ||||||||
\(829\) | −45.0927 | −1.56613 | −0.783067 | − | 0.621938i | \(-0.786346\pi\) | ||||
−0.783067 | + | 0.621938i | \(0.786346\pi\) | |||||||
\(830\) | −8.16090 | −0.283269 | ||||||||
\(831\) | −2.14922 | −0.0745556 | ||||||||
\(832\) | 28.7056 | 0.995189 | ||||||||
\(833\) | 4.47425 | 0.155024 | ||||||||
\(834\) | 11.5389 | 0.399561 | ||||||||
\(835\) | −14.0012 | −0.484531 | ||||||||
\(836\) | −0.0400431 | −0.00138492 | ||||||||
\(837\) | −17.3633 | −0.600165 | ||||||||
\(838\) | 5.88887 | 0.203427 | ||||||||
\(839\) | 23.2397 | 0.802322 | 0.401161 | − | 0.916008i | \(-0.368607\pi\) | ||||
0.401161 | + | 0.916008i | \(0.368607\pi\) | |||||||
\(840\) | −1.51906 | −0.0524125 | ||||||||
\(841\) | 8.94665 | 0.308505 | ||||||||
\(842\) | 11.4791 | 0.395595 | ||||||||
\(843\) | −0.319180 | −0.0109932 | ||||||||
\(844\) | 22.1929 | 0.763910 | ||||||||
\(845\) | −0.141908 | −0.00488179 | ||||||||
\(846\) | −24.0071 | −0.825380 | ||||||||
\(847\) | −10.9915 | −0.377673 | ||||||||
\(848\) | 10.4513 | 0.358899 | ||||||||
\(849\) | 0.174183 | 0.00597793 | ||||||||
\(850\) | −4.84525 | −0.166191 | ||||||||
\(851\) | 60.4219 | 2.07124 | ||||||||
\(852\) | −2.42445 | −0.0830604 | ||||||||
\(853\) | 19.3513 | 0.662577 | 0.331289 | − | 0.943529i | \(-0.392517\pi\) | ||||
0.331289 | + | 0.943529i | \(0.392517\pi\) | |||||||
\(854\) | 6.86562 | 0.234937 | ||||||||
\(855\) | −1.44645 | −0.0494674 | ||||||||
\(856\) | −23.2135 | −0.793419 | ||||||||
\(857\) | −50.6166 | −1.72903 | −0.864515 | − | 0.502606i | \(-0.832375\pi\) | ||||
−0.864515 | + | 0.502606i | \(0.832375\pi\) | |||||||
\(858\) | 0.177542 | 0.00606117 | ||||||||
\(859\) | −45.5330 | −1.55356 | −0.776782 | − | 0.629769i | \(-0.783150\pi\) | ||||
−0.776782 | + | 0.629769i | \(0.783150\pi\) | |||||||
\(860\) | −1.58234 | −0.0539573 | ||||||||
\(861\) | −1.34846 | −0.0459553 | ||||||||
\(862\) | 26.1080 | 0.889243 | ||||||||
\(863\) | −25.5847 | −0.870912 | −0.435456 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435456 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(864\) | −12.3459 | −0.420016 | ||||||||
\(865\) | −13.1344 | −0.446582 | ||||||||
\(866\) | −5.50120 | −0.186938 | ||||||||
\(867\) | −1.49783 | −0.0508690 | ||||||||
\(868\) | 5.03180 | 0.170790 | ||||||||
\(869\) | −0.379265 | −0.0128657 | ||||||||
\(870\) | 3.30972 | 0.112210 | ||||||||
\(871\) | 32.9151 | 1.11529 | ||||||||
\(872\) | 15.8282 | 0.536010 | ||||||||
\(873\) | 10.9592 | 0.370912 | ||||||||
\(874\) | 3.43380 | 0.116150 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −1.01825 | −0.0344036 | ||||||||
\(877\) | −1.43205 | −0.0483570 | −0.0241785 | − | 0.999708i | \(-0.507697\pi\) | ||||
−0.0241785 | + | 0.999708i | \(0.507697\pi\) | |||||||
\(878\) | −25.4387 | −0.858514 | ||||||||
\(879\) | 3.50021 | 0.118059 | ||||||||
\(880\) | −0.153067 | −0.00515989 | ||||||||
\(881\) | −23.8094 | −0.802157 | −0.401079 | − | 0.916044i | \(-0.631365\pi\) | ||||
−0.401079 | + | 0.916044i | \(0.631365\pi\) | |||||||
\(882\) | 2.98218 | 0.100415 | ||||||||
\(883\) | −5.39787 | −0.181653 | −0.0908264 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908264 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(884\) | −13.2729 | −0.446416 | ||||||||
\(885\) | 0.197532 | 0.00663996 | ||||||||
\(886\) | 11.4662 | 0.385215 | ||||||||
\(887\) | 45.6190 | 1.53173 | 0.765867 | − | 0.642999i | \(-0.222310\pi\) | ||||
0.765867 | + | 0.642999i | \(0.222310\pi\) | |||||||
\(888\) | 15.2038 | 0.510207 | ||||||||
\(889\) | 2.92115 | 0.0979722 | ||||||||
\(890\) | 5.79244 | 0.194163 | ||||||||
\(891\) | 0.630799 | 0.0211325 | ||||||||
\(892\) | 16.1527 | 0.540832 | ||||||||
\(893\) | −4.22833 | −0.141496 | ||||||||
\(894\) | 3.77397 | 0.126220 | ||||||||
\(895\) | −2.91378 | −0.0973971 | ||||||||
\(896\) | −0.0197165 | −0.000658683 0 | ||||||||
\(897\) | 10.7402 | 0.358605 | ||||||||
\(898\) | 8.15097 | 0.272001 | ||||||||
\(899\) | −37.4674 | −1.24961 | ||||||||
\(900\) | 2.27822 | 0.0759407 | ||||||||
\(901\) | −28.1525 | −0.937895 | ||||||||
\(902\) | −0.271226 | −0.00903084 | ||||||||
\(903\) | −0.948968 | −0.0315797 | ||||||||
\(904\) | −56.1768 | −1.86841 | ||||||||
\(905\) | −17.9103 | −0.595358 | ||||||||
\(906\) | −0.753846 | −0.0250449 | ||||||||
\(907\) | 24.0144 | 0.797385 | 0.398693 | − | 0.917085i | \(-0.369464\pi\) | ||||
0.398693 | + | 0.917085i | \(0.369464\pi\) | |||||||
\(908\) | 10.0328 | 0.332951 | ||||||||
\(909\) | 18.8468 | 0.625110 | ||||||||
\(910\) | −3.88315 | −0.128725 | ||||||||
\(911\) | 10.3576 | 0.343162 | 0.171581 | − | 0.985170i | \(-0.445112\pi\) | ||||
0.171581 | + | 0.985170i | \(0.445112\pi\) | |||||||
\(912\) | 0.432859 | 0.0143334 | ||||||||
\(913\) | 0.694465 | 0.0229834 | ||||||||
\(914\) | −34.4581 | −1.13977 | ||||||||
\(915\) | 3.14552 | 0.103988 | ||||||||
\(916\) | 0.827289 | 0.0273344 | ||||||||
\(917\) | 13.6122 | 0.449516 | ||||||||
\(918\) | −13.8319 | −0.456522 | ||||||||
\(919\) | −31.3961 | −1.03566 | −0.517830 | − | 0.855483i | \(-0.673260\pi\) | ||||
−0.517830 | + | 0.855483i | \(0.673260\pi\) | |||||||
\(920\) | −18.4834 | −0.609379 | ||||||||
\(921\) | 9.55100 | 0.314716 | ||||||||
\(922\) | 6.27139 | 0.206537 | ||||||||
\(923\) | −21.1805 | −0.697165 | ||||||||
\(924\) | 0.0378245 | 0.00124433 | ||||||||
\(925\) | −10.0087 | −0.329085 | ||||||||
\(926\) | −12.1800 | −0.400261 | ||||||||
\(927\) | −20.4364 | −0.671220 | ||||||||
\(928\) | −26.6405 | −0.874518 | ||||||||
\(929\) | 31.6122 | 1.03716 | 0.518581 | − | 0.855028i | \(-0.326460\pi\) | ||||
0.518581 | + | 0.855028i | \(0.326460\pi\) | |||||||
\(930\) | −3.26792 | −0.107159 | ||||||||
\(931\) | 0.525247 | 0.0172143 | ||||||||
\(932\) | −6.12437 | −0.200610 | ||||||||
\(933\) | −8.47197 | −0.277360 | ||||||||
\(934\) | 8.57020 | 0.280426 | ||||||||
\(935\) | 0.412314 | 0.0134841 | ||||||||
\(936\) | −30.2338 | −0.988223 | ||||||||
\(937\) | −8.18678 | −0.267450 | −0.133725 | − | 0.991018i | \(-0.542694\pi\) | ||||
−0.133725 | + | 0.991018i | \(0.542694\pi\) | |||||||
\(938\) | −9.94038 | −0.324565 | ||||||||
\(939\) | 7.37032 | 0.240521 | ||||||||
\(940\) | 6.65981 | 0.217219 | ||||||||
\(941\) | 10.4548 | 0.340817 | 0.170408 | − | 0.985374i | \(-0.445491\pi\) | ||||
0.170408 | + | 0.985374i | \(0.445491\pi\) | |||||||
\(942\) | −7.65003 | −0.249252 | ||||||||
\(943\) | −16.4076 | −0.534304 | ||||||||
\(944\) | 0.661306 | 0.0215237 | ||||||||
\(945\) | 2.85474 | 0.0928647 | ||||||||
\(946\) | −0.190874 | −0.00620583 | ||||||||
\(947\) | 28.5930 | 0.929149 | 0.464574 | − | 0.885534i | \(-0.346207\pi\) | ||||
0.464574 | + | 0.885534i | \(0.346207\pi\) | |||||||
\(948\) | −1.68928 | −0.0548652 | ||||||||
\(949\) | −8.89567 | −0.288766 | ||||||||
\(950\) | −0.568799 | −0.0184543 | ||||||||
\(951\) | 17.1012 | 0.554545 | ||||||||
\(952\) | 13.6989 | 0.443984 | ||||||||
\(953\) | −50.0926 | −1.62266 | −0.811330 | − | 0.584589i | \(-0.801256\pi\) | ||||
−0.811330 | + | 0.584589i | \(0.801256\pi\) | |||||||
\(954\) | −18.7642 | −0.607514 | ||||||||
\(955\) | 20.3533 | 0.658617 | ||||||||
\(956\) | −18.0249 | −0.582967 | ||||||||
\(957\) | −0.281645 | −0.00910431 | ||||||||
\(958\) | 38.2085 | 1.23446 | ||||||||
\(959\) | 7.59167 | 0.245148 | ||||||||
\(960\) | −3.97180 | −0.128189 | ||||||||
\(961\) | 5.99416 | 0.193360 | ||||||||
\(962\) | 38.8653 | 1.25307 | ||||||||
\(963\) | 20.8791 | 0.672821 | ||||||||
\(964\) | 3.37972 | 0.108853 | ||||||||
\(965\) | 12.9449 | 0.416711 | ||||||||
\(966\) | −3.24355 | −0.104359 | ||||||||
\(967\) | 35.1678 | 1.13092 | 0.565459 | − | 0.824776i | \(-0.308699\pi\) | ||||
0.565459 | + | 0.824776i | \(0.308699\pi\) | |||||||
\(968\) | −33.6529 | −1.08165 | ||||||||
\(969\) | −1.16598 | −0.0374568 | ||||||||
\(970\) | 4.30958 | 0.138372 | ||||||||
\(971\) | 44.8228 | 1.43843 | 0.719216 | − | 0.694787i | \(-0.244501\pi\) | ||||
0.719216 | + | 0.694787i | \(0.244501\pi\) | |||||||
\(972\) | 9.89471 | 0.317373 | ||||||||
\(973\) | 21.4764 | 0.688503 | ||||||||
\(974\) | −29.7323 | −0.952683 | ||||||||
\(975\) | −1.77909 | −0.0569764 | ||||||||
\(976\) | 10.5307 | 0.337080 | ||||||||
\(977\) | −2.07108 | −0.0662598 | −0.0331299 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331299 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(978\) | 3.66894 | 0.117320 | ||||||||
\(979\) | −0.492917 | −0.0157537 | ||||||||
\(980\) | −0.827289 | −0.0264268 | ||||||||
\(981\) | −14.2365 | −0.454537 | ||||||||
\(982\) | 43.2303 | 1.37954 | ||||||||
\(983\) | −20.8932 | −0.666390 | −0.333195 | − | 0.942858i | \(-0.608127\pi\) | ||||
−0.333195 | + | 0.942858i | \(0.608127\pi\) | |||||||
\(984\) | −4.12860 | −0.131615 | ||||||||
\(985\) | 8.99708 | 0.286671 | ||||||||
\(986\) | −29.8471 | −0.950527 | ||||||||
\(987\) | 3.99405 | 0.127132 | ||||||||
\(988\) | −1.55815 | −0.0495713 | ||||||||
\(989\) | −11.5467 | −0.367164 | ||||||||
\(990\) | 0.274816 | 0.00873422 | ||||||||
\(991\) | 32.1016 | 1.01974 | 0.509870 | − | 0.860251i | \(-0.329693\pi\) | ||||
0.509870 | + | 0.860251i | \(0.329693\pi\) | |||||||
\(992\) | 26.3040 | 0.835154 | ||||||||
\(993\) | 17.1324 | 0.543680 | ||||||||
\(994\) | 6.39652 | 0.202885 | ||||||||
\(995\) | 16.0890 | 0.510056 | ||||||||
\(996\) | 3.09320 | 0.0980119 | ||||||||
\(997\) | −3.83217 | −0.121366 | −0.0606829 | − | 0.998157i | \(-0.519328\pi\) | ||||
−0.0606829 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(998\) | 34.7047 | 1.09856 | ||||||||
\(999\) | −28.5723 | −0.903987 |
(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 | 8015.2.a.h.1.14 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.h.1.14 | ✓ | 38 | 1.1 | even | 1 | trivial |