Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, 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("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(1\) |
Dimension: | \(309\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67443 | −1.89111 | −0.945554 | − | 0.325466i | \(-0.894479\pi\) | ||||
−0.945554 | + | 0.325466i | \(0.894479\pi\) | |||||||
\(3\) | −1.89818 | −1.09591 | −0.547956 | − | 0.836507i | \(-0.684594\pi\) | ||||
−0.547956 | + | 0.836507i | \(0.684594\pi\) | |||||||
\(4\) | 5.15257 | 2.57629 | ||||||||
\(5\) | −2.43152 | −1.08741 | −0.543705 | − | 0.839276i | \(-0.682979\pi\) | ||||
−0.543705 | + | 0.839276i | \(0.682979\pi\) | |||||||
\(6\) | 5.07654 | 2.07249 | ||||||||
\(7\) | 2.86566 | 1.08312 | 0.541559 | − | 0.840663i | \(-0.317834\pi\) | ||||
0.541559 | + | 0.840663i | \(0.317834\pi\) | |||||||
\(8\) | −8.43133 | −2.98093 | ||||||||
\(9\) | 0.603070 | 0.201023 | ||||||||
\(10\) | 6.50294 | 2.05641 | ||||||||
\(11\) | 4.27299 | 1.28835 | 0.644177 | − | 0.764877i | \(-0.277200\pi\) | ||||
0.644177 | + | 0.764877i | \(0.277200\pi\) | |||||||
\(12\) | −9.78049 | −2.82338 | ||||||||
\(13\) | 0.189678 | 0.0526071 | 0.0263036 | − | 0.999654i | \(-0.491626\pi\) | ||||
0.0263036 | + | 0.999654i | \(0.491626\pi\) | |||||||
\(14\) | −7.66401 | −2.04829 | ||||||||
\(15\) | 4.61546 | 1.19171 | ||||||||
\(16\) | 12.2439 | 3.06096 | ||||||||
\(17\) | 1.12106 | 0.271896 | 0.135948 | − | 0.990716i | \(-0.456592\pi\) | ||||
0.135948 | + | 0.990716i | \(0.456592\pi\) | |||||||
\(18\) | −1.61287 | −0.380156 | ||||||||
\(19\) | −7.55968 | −1.73431 | −0.867155 | − | 0.498038i | \(-0.834054\pi\) | ||||
−0.867155 | + | 0.498038i | \(0.834054\pi\) | |||||||
\(20\) | −12.5286 | −2.80148 | ||||||||
\(21\) | −5.43953 | −1.18700 | ||||||||
\(22\) | −11.4278 | −2.43641 | ||||||||
\(23\) | −7.54256 | −1.57273 | −0.786367 | − | 0.617760i | \(-0.788040\pi\) | ||||
−0.786367 | + | 0.617760i | \(0.788040\pi\) | |||||||
\(24\) | 16.0041 | 3.26683 | ||||||||
\(25\) | 0.912304 | 0.182461 | ||||||||
\(26\) | −0.507280 | −0.0994857 | ||||||||
\(27\) | 4.54979 | 0.875608 | ||||||||
\(28\) | 14.7655 | 2.79042 | ||||||||
\(29\) | 6.13120 | 1.13853 | 0.569267 | − | 0.822152i | \(-0.307227\pi\) | ||||
0.569267 | + | 0.822152i | \(0.307227\pi\) | |||||||
\(30\) | −12.3437 | −2.25364 | ||||||||
\(31\) | 3.70580 | 0.665581 | 0.332791 | − | 0.943001i | \(-0.392010\pi\) | ||||
0.332791 | + | 0.943001i | \(0.392010\pi\) | |||||||
\(32\) | −15.8827 | −2.80769 | ||||||||
\(33\) | −8.11087 | −1.41192 | ||||||||
\(34\) | −2.99819 | −0.514185 | ||||||||
\(35\) | −6.96792 | −1.17779 | ||||||||
\(36\) | 3.10736 | 0.517893 | ||||||||
\(37\) | 8.03245 | 1.32053 | 0.660264 | − | 0.751034i | \(-0.270445\pi\) | ||||
0.660264 | + | 0.751034i | \(0.270445\pi\) | |||||||
\(38\) | 20.2178 | 3.27977 | ||||||||
\(39\) | −0.360042 | −0.0576528 | ||||||||
\(40\) | 20.5010 | 3.24149 | ||||||||
\(41\) | −3.65263 | −0.570445 | −0.285223 | − | 0.958461i | \(-0.592068\pi\) | ||||
−0.285223 | + | 0.958461i | \(0.592068\pi\) | |||||||
\(42\) | 14.5476 | 2.24475 | ||||||||
\(43\) | 10.2794 | 1.56760 | 0.783798 | − | 0.621016i | \(-0.213280\pi\) | ||||
0.783798 | + | 0.621016i | \(0.213280\pi\) | |||||||
\(44\) | 22.0169 | 3.31917 | ||||||||
\(45\) | −1.46638 | −0.218595 | ||||||||
\(46\) | 20.1721 | 2.97421 | ||||||||
\(47\) | 4.94177 | 0.720831 | 0.360415 | − | 0.932792i | \(-0.382635\pi\) | ||||
0.360415 | + | 0.932792i | \(0.382635\pi\) | |||||||
\(48\) | −23.2410 | −3.35455 | ||||||||
\(49\) | 1.21202 | 0.173146 | ||||||||
\(50\) | −2.43989 | −0.345053 | ||||||||
\(51\) | −2.12796 | −0.297974 | ||||||||
\(52\) | 0.977328 | 0.135531 | ||||||||
\(53\) | −8.88480 | −1.22042 | −0.610211 | − | 0.792239i | \(-0.708915\pi\) | ||||
−0.610211 | + | 0.792239i | \(0.708915\pi\) | |||||||
\(54\) | −12.1681 | −1.65587 | ||||||||
\(55\) | −10.3899 | −1.40097 | ||||||||
\(56\) | −24.1614 | −3.22870 | ||||||||
\(57\) | 14.3496 | 1.90065 | ||||||||
\(58\) | −16.3975 | −2.15309 | ||||||||
\(59\) | −7.85765 | −1.02298 | −0.511489 | − | 0.859290i | \(-0.670906\pi\) | ||||
−0.511489 | + | 0.859290i | \(0.670906\pi\) | |||||||
\(60\) | 23.7815 | 3.07018 | ||||||||
\(61\) | 3.20740 | 0.410666 | 0.205333 | − | 0.978692i | \(-0.434172\pi\) | ||||
0.205333 | + | 0.978692i | \(0.434172\pi\) | |||||||
\(62\) | −9.91090 | −1.25869 | ||||||||
\(63\) | 1.72819 | 0.217732 | ||||||||
\(64\) | 17.9894 | 2.24867 | ||||||||
\(65\) | −0.461206 | −0.0572055 | ||||||||
\(66\) | 21.6920 | 2.67010 | ||||||||
\(67\) | 8.07005 | 0.985913 | 0.492957 | − | 0.870054i | \(-0.335916\pi\) | ||||
0.492957 | + | 0.870054i | \(0.335916\pi\) | |||||||
\(68\) | 5.77633 | 0.700482 | ||||||||
\(69\) | 14.3171 | 1.72358 | ||||||||
\(70\) | 18.6352 | 2.22734 | ||||||||
\(71\) | 1.63264 | 0.193759 | 0.0968796 | − | 0.995296i | \(-0.469114\pi\) | ||||
0.0968796 | + | 0.995296i | \(0.469114\pi\) | |||||||
\(72\) | −5.08468 | −0.599235 | ||||||||
\(73\) | −3.90267 | −0.456772 | −0.228386 | − | 0.973571i | \(-0.573345\pi\) | ||||
−0.228386 | + | 0.973571i | \(0.573345\pi\) | |||||||
\(74\) | −21.4822 | −2.49726 | ||||||||
\(75\) | −1.73171 | −0.199961 | ||||||||
\(76\) | −38.9518 | −4.46808 | ||||||||
\(77\) | 12.2449 | 1.39544 | ||||||||
\(78\) | 0.962906 | 0.109028 | ||||||||
\(79\) | −16.1114 | −1.81267 | −0.906336 | − | 0.422558i | \(-0.861132\pi\) | ||||
−0.906336 | + | 0.422558i | \(0.861132\pi\) | |||||||
\(80\) | −29.7712 | −3.32852 | ||||||||
\(81\) | −10.4455 | −1.16061 | ||||||||
\(82\) | 9.76870 | 1.07877 | ||||||||
\(83\) | −7.98861 | −0.876864 | −0.438432 | − | 0.898764i | \(-0.644466\pi\) | ||||
−0.438432 | + | 0.898764i | \(0.644466\pi\) | |||||||
\(84\) | −28.0276 | −3.05806 | ||||||||
\(85\) | −2.72588 | −0.295663 | ||||||||
\(86\) | −27.4916 | −2.96449 | ||||||||
\(87\) | −11.6381 | −1.24773 | ||||||||
\(88\) | −36.0270 | −3.84049 | ||||||||
\(89\) | −15.0225 | −1.59238 | −0.796189 | − | 0.605048i | \(-0.793154\pi\) | ||||
−0.796189 | + | 0.605048i | \(0.793154\pi\) | |||||||
\(90\) | 3.92172 | 0.413386 | ||||||||
\(91\) | 0.543552 | 0.0569798 | ||||||||
\(92\) | −38.8636 | −4.05181 | ||||||||
\(93\) | −7.03426 | −0.729418 | ||||||||
\(94\) | −13.2164 | −1.36317 | ||||||||
\(95\) | 18.3815 | 1.88591 | ||||||||
\(96\) | 30.1481 | 3.07698 | ||||||||
\(97\) | 5.56650 | 0.565192 | 0.282596 | − | 0.959239i | \(-0.408804\pi\) | ||||
0.282596 | + | 0.959239i | \(0.408804\pi\) | |||||||
\(98\) | −3.24147 | −0.327438 | ||||||||
\(99\) | 2.57691 | 0.258989 | ||||||||
\(100\) | 4.70071 | 0.470071 | ||||||||
\(101\) | −2.09406 | −0.208366 | −0.104183 | − | 0.994558i | \(-0.533223\pi\) | ||||
−0.104183 | + | 0.994558i | \(0.533223\pi\) | |||||||
\(102\) | 5.69108 | 0.563501 | ||||||||
\(103\) | 9.41699 | 0.927883 | 0.463942 | − | 0.885866i | \(-0.346435\pi\) | ||||
0.463942 | + | 0.885866i | \(0.346435\pi\) | |||||||
\(104\) | −1.59924 | −0.156818 | ||||||||
\(105\) | 13.2263 | 1.29076 | ||||||||
\(106\) | 23.7618 | 2.30795 | ||||||||
\(107\) | −5.75346 | −0.556207 | −0.278104 | − | 0.960551i | \(-0.589706\pi\) | ||||
−0.278104 | + | 0.960551i | \(0.589706\pi\) | |||||||
\(108\) | 23.4431 | 2.25582 | ||||||||
\(109\) | −5.94102 | −0.569047 | −0.284523 | − | 0.958669i | \(-0.591835\pi\) | ||||
−0.284523 | + | 0.958669i | \(0.591835\pi\) | |||||||
\(110\) | 27.7870 | 2.64938 | ||||||||
\(111\) | −15.2470 | −1.44718 | ||||||||
\(112\) | 35.0868 | 3.31539 | ||||||||
\(113\) | −4.08957 | −0.384714 | −0.192357 | − | 0.981325i | \(-0.561613\pi\) | ||||
−0.192357 | + | 0.981325i | \(0.561613\pi\) | |||||||
\(114\) | −38.3770 | −3.59434 | ||||||||
\(115\) | 18.3399 | 1.71021 | ||||||||
\(116\) | 31.5914 | 2.93319 | ||||||||
\(117\) | 0.114389 | 0.0105753 | ||||||||
\(118\) | 21.0147 | 1.93456 | ||||||||
\(119\) | 3.21257 | 0.294496 | ||||||||
\(120\) | −38.9145 | −3.55239 | ||||||||
\(121\) | 7.25840 | 0.659855 | ||||||||
\(122\) | −8.57798 | −0.776614 | ||||||||
\(123\) | 6.93333 | 0.625158 | ||||||||
\(124\) | 19.0944 | 1.71473 | ||||||||
\(125\) | 9.93933 | 0.889000 | ||||||||
\(126\) | −4.62193 | −0.411754 | ||||||||
\(127\) | 13.1736 | 1.16896 | 0.584482 | − | 0.811407i | \(-0.301298\pi\) | ||||
0.584482 | + | 0.811407i | \(0.301298\pi\) | |||||||
\(128\) | −16.3459 | −1.44479 | ||||||||
\(129\) | −19.5121 | −1.71795 | ||||||||
\(130\) | 1.23346 | 0.108182 | ||||||||
\(131\) | −10.7144 | −0.936121 | −0.468061 | − | 0.883696i | \(-0.655047\pi\) | ||||
−0.468061 | + | 0.883696i | \(0.655047\pi\) | |||||||
\(132\) | −41.7919 | −3.63752 | ||||||||
\(133\) | −21.6635 | −1.87846 | ||||||||
\(134\) | −21.5828 | −1.86447 | ||||||||
\(135\) | −11.0629 | −0.952145 | ||||||||
\(136\) | −9.45200 | −0.810503 | ||||||||
\(137\) | 1.07823 | 0.0921191 | 0.0460595 | − | 0.998939i | \(-0.485334\pi\) | ||||
0.0460595 | + | 0.998939i | \(0.485334\pi\) | |||||||
\(138\) | −38.2901 | −3.25947 | ||||||||
\(139\) | 17.8734 | 1.51600 | 0.757999 | − | 0.652256i | \(-0.226177\pi\) | ||||
0.757999 | + | 0.652256i | \(0.226177\pi\) | |||||||
\(140\) | −35.9027 | −3.03434 | ||||||||
\(141\) | −9.38034 | −0.789967 | ||||||||
\(142\) | −4.36639 | −0.366419 | ||||||||
\(143\) | 0.810490 | 0.0677766 | ||||||||
\(144\) | 7.38390 | 0.615325 | ||||||||
\(145\) | −14.9081 | −1.23805 | ||||||||
\(146\) | 10.4374 | 0.863806 | ||||||||
\(147\) | −2.30063 | −0.189753 | ||||||||
\(148\) | 41.3878 | 3.40206 | ||||||||
\(149\) | 11.7423 | 0.961965 | 0.480983 | − | 0.876730i | \(-0.340280\pi\) | ||||
0.480983 | + | 0.876730i | \(0.340280\pi\) | |||||||
\(150\) | 4.63134 | 0.378148 | ||||||||
\(151\) | 1.26006 | 0.102542 | 0.0512710 | − | 0.998685i | \(-0.483673\pi\) | ||||
0.0512710 | + | 0.998685i | \(0.483673\pi\) | |||||||
\(152\) | 63.7382 | 5.16985 | ||||||||
\(153\) | 0.676075 | 0.0546574 | ||||||||
\(154\) | −32.7482 | −2.63893 | ||||||||
\(155\) | −9.01074 | −0.723760 | ||||||||
\(156\) | −1.85514 | −0.148530 | ||||||||
\(157\) | −11.8205 | −0.943382 | −0.471691 | − | 0.881764i | \(-0.656356\pi\) | ||||
−0.471691 | + | 0.881764i | \(0.656356\pi\) | |||||||
\(158\) | 43.0887 | 3.42796 | ||||||||
\(159\) | 16.8649 | 1.33747 | ||||||||
\(160\) | 38.6191 | 3.05311 | ||||||||
\(161\) | −21.6144 | −1.70346 | ||||||||
\(162\) | 27.9358 | 2.19484 | ||||||||
\(163\) | −24.4130 | −1.91217 | −0.956085 | − | 0.293088i | \(-0.905317\pi\) | ||||
−0.956085 | + | 0.293088i | \(0.905317\pi\) | |||||||
\(164\) | −18.8204 | −1.46963 | ||||||||
\(165\) | 19.7218 | 1.53534 | ||||||||
\(166\) | 21.3650 | 1.65824 | ||||||||
\(167\) | 15.0925 | 1.16790 | 0.583948 | − | 0.811791i | \(-0.301507\pi\) | ||||
0.583948 | + | 0.811791i | \(0.301507\pi\) | |||||||
\(168\) | 45.8625 | 3.53837 | ||||||||
\(169\) | −12.9640 | −0.997232 | ||||||||
\(170\) | 7.29016 | 0.559130 | ||||||||
\(171\) | −4.55902 | −0.348637 | ||||||||
\(172\) | 52.9654 | 4.03858 | ||||||||
\(173\) | −0.580461 | −0.0441317 | −0.0220658 | − | 0.999757i | \(-0.507024\pi\) | ||||
−0.0220658 | + | 0.999757i | \(0.507024\pi\) | |||||||
\(174\) | 31.1252 | 2.35960 | ||||||||
\(175\) | 2.61435 | 0.197627 | ||||||||
\(176\) | 52.3178 | 3.94360 | ||||||||
\(177\) | 14.9152 | 1.12109 | ||||||||
\(178\) | 40.1765 | 3.01136 | ||||||||
\(179\) | −15.7726 | −1.17890 | −0.589450 | − | 0.807805i | \(-0.700655\pi\) | ||||
−0.589450 | + | 0.807805i | \(0.700655\pi\) | |||||||
\(180\) | −7.55562 | −0.563162 | ||||||||
\(181\) | 22.9087 | 1.70279 | 0.851395 | − | 0.524525i | \(-0.175757\pi\) | ||||
0.851395 | + | 0.524525i | \(0.175757\pi\) | |||||||
\(182\) | −1.45369 | −0.107755 | ||||||||
\(183\) | −6.08822 | −0.450054 | ||||||||
\(184\) | 63.5939 | 4.68820 | ||||||||
\(185\) | −19.5311 | −1.43595 | ||||||||
\(186\) | 18.8126 | 1.37941 | ||||||||
\(187\) | 4.79026 | 0.350298 | ||||||||
\(188\) | 25.4628 | 1.85707 | ||||||||
\(189\) | 13.0382 | 0.948388 | ||||||||
\(190\) | −49.1601 | −3.56645 | ||||||||
\(191\) | −18.4589 | −1.33564 | −0.667818 | − | 0.744325i | \(-0.732772\pi\) | ||||
−0.667818 | + | 0.744325i | \(0.732772\pi\) | |||||||
\(192\) | −34.1470 | −2.46435 | ||||||||
\(193\) | −5.36127 | −0.385912 | −0.192956 | − | 0.981207i | \(-0.561808\pi\) | ||||
−0.192956 | + | 0.981207i | \(0.561808\pi\) | |||||||
\(194\) | −14.8872 | −1.06884 | ||||||||
\(195\) | 0.875449 | 0.0626922 | ||||||||
\(196\) | 6.24504 | 0.446074 | ||||||||
\(197\) | 24.2824 | 1.73005 | 0.865023 | − | 0.501732i | \(-0.167304\pi\) | ||||
0.865023 | + | 0.501732i | \(0.167304\pi\) | |||||||
\(198\) | −6.89176 | −0.489776 | ||||||||
\(199\) | 22.8423 | 1.61924 | 0.809622 | − | 0.586951i | \(-0.199672\pi\) | ||||
0.809622 | + | 0.586951i | \(0.199672\pi\) | |||||||
\(200\) | −7.69194 | −0.543902 | ||||||||
\(201\) | −15.3184 | −1.08047 | ||||||||
\(202\) | 5.60041 | 0.394043 | ||||||||
\(203\) | 17.5699 | 1.23317 | ||||||||
\(204\) | −10.9645 | −0.767667 | ||||||||
\(205\) | 8.88145 | 0.620308 | ||||||||
\(206\) | −25.1851 | −1.75473 | ||||||||
\(207\) | −4.54869 | −0.316156 | ||||||||
\(208\) | 2.32239 | 0.161029 | ||||||||
\(209\) | −32.3024 | −2.23441 | ||||||||
\(210\) | −35.3729 | −2.44096 | ||||||||
\(211\) | −20.4977 | −1.41112 | −0.705560 | − | 0.708650i | \(-0.749305\pi\) | ||||
−0.705560 | + | 0.708650i | \(0.749305\pi\) | |||||||
\(212\) | −45.7796 | −3.14415 | ||||||||
\(213\) | −3.09904 | −0.212343 | ||||||||
\(214\) | 15.3872 | 1.05185 | ||||||||
\(215\) | −24.9946 | −1.70462 | ||||||||
\(216\) | −38.3608 | −2.61012 | ||||||||
\(217\) | 10.6196 | 0.720903 | ||||||||
\(218\) | 15.8889 | 1.07613 | ||||||||
\(219\) | 7.40794 | 0.500582 | ||||||||
\(220\) | −53.5345 | −3.60930 | ||||||||
\(221\) | 0.212640 | 0.0143037 | ||||||||
\(222\) | 40.7770 | 2.73678 | ||||||||
\(223\) | 26.0517 | 1.74455 | 0.872275 | − | 0.489015i | \(-0.162644\pi\) | ||||
0.872275 | + | 0.489015i | \(0.162644\pi\) | |||||||
\(224\) | −45.5144 | −3.04106 | ||||||||
\(225\) | 0.550183 | 0.0366788 | ||||||||
\(226\) | 10.9373 | 0.727536 | ||||||||
\(227\) | −19.9624 | −1.32495 | −0.662475 | − | 0.749084i | \(-0.730494\pi\) | ||||
−0.662475 | + | 0.749084i | \(0.730494\pi\) | |||||||
\(228\) | 73.9374 | 4.89662 | ||||||||
\(229\) | −21.5385 | −1.42330 | −0.711651 | − | 0.702533i | \(-0.752052\pi\) | ||||
−0.711651 | + | 0.702533i | \(0.752052\pi\) | |||||||
\(230\) | −49.0488 | −3.23418 | ||||||||
\(231\) | −23.2430 | −1.52928 | ||||||||
\(232\) | −51.6942 | −3.39389 | ||||||||
\(233\) | 3.27507 | 0.214557 | 0.107279 | − | 0.994229i | \(-0.465786\pi\) | ||||
0.107279 | + | 0.994229i | \(0.465786\pi\) | |||||||
\(234\) | −0.305925 | −0.0199989 | ||||||||
\(235\) | −12.0160 | −0.783839 | ||||||||
\(236\) | −40.4871 | −2.63549 | ||||||||
\(237\) | 30.5822 | 1.98653 | ||||||||
\(238\) | −8.59179 | −0.556923 | ||||||||
\(239\) | −26.2737 | −1.69950 | −0.849752 | − | 0.527182i | \(-0.823249\pi\) | ||||
−0.849752 | + | 0.527182i | \(0.823249\pi\) | |||||||
\(240\) | 56.5110 | 3.64777 | ||||||||
\(241\) | 1.75603 | 0.113116 | 0.0565580 | − | 0.998399i | \(-0.481987\pi\) | ||||
0.0565580 | + | 0.998399i | \(0.481987\pi\) | |||||||
\(242\) | −19.4121 | −1.24786 | ||||||||
\(243\) | 6.17804 | 0.396321 | ||||||||
\(244\) | 16.5264 | 1.05799 | ||||||||
\(245\) | −2.94706 | −0.188281 | ||||||||
\(246\) | −18.5427 | −1.18224 | ||||||||
\(247\) | −1.43390 | −0.0912371 | ||||||||
\(248\) | −31.2448 | −1.98405 | ||||||||
\(249\) | 15.1638 | 0.960966 | ||||||||
\(250\) | −26.5820 | −1.68120 | ||||||||
\(251\) | 0.464826 | 0.0293395 | 0.0146698 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146698 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(252\) | 8.90464 | 0.560940 | ||||||||
\(253\) | −32.2293 | −2.02624 | ||||||||
\(254\) | −35.2317 | −2.21064 | ||||||||
\(255\) | 5.17419 | 0.324020 | ||||||||
\(256\) | 7.73734 | 0.483584 | ||||||||
\(257\) | 27.6326 | 1.72368 | 0.861838 | − | 0.507184i | \(-0.169314\pi\) | ||||
0.861838 | + | 0.507184i | \(0.169314\pi\) | |||||||
\(258\) | 52.1838 | 3.24882 | ||||||||
\(259\) | 23.0183 | 1.43029 | ||||||||
\(260\) | −2.37640 | −0.147378 | ||||||||
\(261\) | 3.69754 | 0.228872 | ||||||||
\(262\) | 28.6549 | 1.77031 | ||||||||
\(263\) | 9.09253 | 0.560669 | 0.280335 | − | 0.959902i | \(-0.409555\pi\) | ||||
0.280335 | + | 0.959902i | \(0.409555\pi\) | |||||||
\(264\) | 68.3855 | 4.20884 | ||||||||
\(265\) | 21.6036 | 1.32710 | ||||||||
\(266\) | 57.9375 | 3.55238 | ||||||||
\(267\) | 28.5153 | 1.74511 | ||||||||
\(268\) | 41.5815 | 2.53999 | ||||||||
\(269\) | 24.5820 | 1.49879 | 0.749395 | − | 0.662123i | \(-0.230344\pi\) | ||||
0.749395 | + | 0.662123i | \(0.230344\pi\) | |||||||
\(270\) | 29.5870 | 1.80061 | ||||||||
\(271\) | 29.8402 | 1.81266 | 0.906331 | − | 0.422567i | \(-0.138871\pi\) | ||||
0.906331 | + | 0.422567i | \(0.138871\pi\) | |||||||
\(272\) | 13.7261 | 0.832265 | ||||||||
\(273\) | −1.03176 | −0.0624448 | ||||||||
\(274\) | −2.88364 | −0.174207 | ||||||||
\(275\) | 3.89826 | 0.235074 | ||||||||
\(276\) | 73.7699 | 4.44043 | ||||||||
\(277\) | −0.921441 | −0.0553640 | −0.0276820 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276820 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(278\) | −47.8010 | −2.86692 | ||||||||
\(279\) | 2.23485 | 0.133797 | ||||||||
\(280\) | 58.7489 | 3.51092 | ||||||||
\(281\) | −1.49617 | −0.0892541 | −0.0446270 | − | 0.999004i | \(-0.514210\pi\) | ||||
−0.0446270 | + | 0.999004i | \(0.514210\pi\) | |||||||
\(282\) | 25.0871 | 1.49391 | ||||||||
\(283\) | 12.8917 | 0.766334 | 0.383167 | − | 0.923679i | \(-0.374833\pi\) | ||||
0.383167 | + | 0.923679i | \(0.374833\pi\) | |||||||
\(284\) | 8.41231 | 0.499179 | ||||||||
\(285\) | −34.8914 | −2.06679 | ||||||||
\(286\) | −2.16760 | −0.128173 | ||||||||
\(287\) | −10.4672 | −0.617860 | ||||||||
\(288\) | −9.57836 | −0.564410 | ||||||||
\(289\) | −15.7432 | −0.926072 | ||||||||
\(290\) | 39.8708 | 2.34129 | ||||||||
\(291\) | −10.5662 | −0.619401 | ||||||||
\(292\) | −20.1088 | −1.17678 | ||||||||
\(293\) | 3.73575 | 0.218245 | 0.109122 | − | 0.994028i | \(-0.465196\pi\) | ||||
0.109122 | + | 0.994028i | \(0.465196\pi\) | |||||||
\(294\) | 6.15288 | 0.358843 | ||||||||
\(295\) | 19.1060 | 1.11240 | ||||||||
\(296\) | −67.7243 | −3.93639 | ||||||||
\(297\) | 19.4412 | 1.12809 | ||||||||
\(298\) | −31.4039 | −1.81918 | ||||||||
\(299\) | −1.43066 | −0.0827370 | ||||||||
\(300\) | −8.92277 | −0.515157 | ||||||||
\(301\) | 29.4573 | 1.69789 | ||||||||
\(302\) | −3.36993 | −0.193918 | ||||||||
\(303\) | 3.97489 | 0.228351 | ||||||||
\(304\) | −92.5597 | −5.30866 | ||||||||
\(305\) | −7.79888 | −0.446562 | ||||||||
\(306\) | −1.80812 | −0.103363 | ||||||||
\(307\) | −19.8036 | −1.13025 | −0.565126 | − | 0.825005i | \(-0.691172\pi\) | ||||
−0.565126 | + | 0.825005i | \(0.691172\pi\) | |||||||
\(308\) | 63.0929 | 3.59505 | ||||||||
\(309\) | −17.8751 | −1.01688 | ||||||||
\(310\) | 24.0986 | 1.36871 | ||||||||
\(311\) | 30.9600 | 1.75558 | 0.877791 | − | 0.479043i | \(-0.159016\pi\) | ||||
0.877791 | + | 0.479043i | \(0.159016\pi\) | |||||||
\(312\) | 3.03563 | 0.171859 | ||||||||
\(313\) | −13.5594 | −0.766420 | −0.383210 | − | 0.923661i | \(-0.625181\pi\) | ||||
−0.383210 | + | 0.923661i | \(0.625181\pi\) | |||||||
\(314\) | 31.6132 | 1.78404 | ||||||||
\(315\) | −4.20214 | −0.236764 | ||||||||
\(316\) | −83.0150 | −4.66996 | ||||||||
\(317\) | 11.2934 | 0.634301 | 0.317151 | − | 0.948375i | \(-0.397274\pi\) | ||||
0.317151 | + | 0.948375i | \(0.397274\pi\) | |||||||
\(318\) | −45.1040 | −2.52931 | ||||||||
\(319\) | 26.1985 | 1.46684 | ||||||||
\(320\) | −43.7416 | −2.44523 | ||||||||
\(321\) | 10.9211 | 0.609554 | ||||||||
\(322\) | 57.8063 | 3.22142 | ||||||||
\(323\) | −8.47484 | −0.471552 | ||||||||
\(324\) | −53.8213 | −2.99007 | ||||||||
\(325\) | 0.173044 | 0.00959874 | ||||||||
\(326\) | 65.2907 | 3.61612 | ||||||||
\(327\) | 11.2771 | 0.623625 | ||||||||
\(328\) | 30.7965 | 1.70045 | ||||||||
\(329\) | 14.1614 | 0.780745 | ||||||||
\(330\) | −52.7445 | −2.90349 | ||||||||
\(331\) | 1.20630 | 0.0663041 | 0.0331521 | − | 0.999450i | \(-0.489445\pi\) | ||||
0.0331521 | + | 0.999450i | \(0.489445\pi\) | |||||||
\(332\) | −41.1619 | −2.25905 | ||||||||
\(333\) | 4.84413 | 0.265457 | ||||||||
\(334\) | −40.3640 | −2.20862 | ||||||||
\(335\) | −19.6225 | −1.07209 | ||||||||
\(336\) | −66.6008 | −3.63337 | ||||||||
\(337\) | −3.94495 | −0.214895 | −0.107448 | − | 0.994211i | \(-0.534268\pi\) | ||||
−0.107448 | + | 0.994211i | \(0.534268\pi\) | |||||||
\(338\) | 34.6714 | 1.88587 | ||||||||
\(339\) | 7.76272 | 0.421613 | ||||||||
\(340\) | −14.0453 | −0.761712 | ||||||||
\(341\) | 15.8348 | 0.857504 | ||||||||
\(342\) | 12.1928 | 0.659309 | ||||||||
\(343\) | −16.5864 | −0.895581 | ||||||||
\(344\) | −86.6692 | −4.67289 | ||||||||
\(345\) | −34.8124 | −1.87424 | ||||||||
\(346\) | 1.55240 | 0.0834577 | ||||||||
\(347\) | 15.3008 | 0.821388 | 0.410694 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410694 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(348\) | −59.9661 | −3.21452 | ||||||||
\(349\) | 3.13791 | 0.167969 | 0.0839844 | − | 0.996467i | \(-0.473235\pi\) | ||||
0.0839844 | + | 0.996467i | \(0.473235\pi\) | |||||||
\(350\) | −6.99191 | −0.373733 | ||||||||
\(351\) | 0.862995 | 0.0460633 | ||||||||
\(352\) | −67.8664 | −3.61729 | ||||||||
\(353\) | 27.0654 | 1.44054 | 0.720272 | − | 0.693692i | \(-0.244017\pi\) | ||||
0.720272 | + | 0.693692i | \(0.244017\pi\) | |||||||
\(354\) | −39.8896 | −2.12011 | ||||||||
\(355\) | −3.96981 | −0.210696 | ||||||||
\(356\) | −77.4044 | −4.10242 | ||||||||
\(357\) | −6.09802 | −0.322742 | ||||||||
\(358\) | 42.1827 | 2.22943 | ||||||||
\(359\) | 6.82906 | 0.360424 | 0.180212 | − | 0.983628i | \(-0.442322\pi\) | ||||
0.180212 | + | 0.983628i | \(0.442322\pi\) | |||||||
\(360\) | 12.3635 | 0.651615 | ||||||||
\(361\) | 38.1488 | 2.00783 | ||||||||
\(362\) | −61.2677 | −3.22016 | ||||||||
\(363\) | −13.7777 | −0.723143 | ||||||||
\(364\) | 2.80069 | 0.146796 | ||||||||
\(365\) | 9.48942 | 0.496699 | ||||||||
\(366\) | 16.2825 | 0.851100 | ||||||||
\(367\) | −27.2296 | −1.42137 | −0.710687 | − | 0.703508i | \(-0.751616\pi\) | ||||
−0.710687 | + | 0.703508i | \(0.751616\pi\) | |||||||
\(368\) | −92.3501 | −4.81408 | ||||||||
\(369\) | −2.20279 | −0.114673 | ||||||||
\(370\) | 52.2345 | 2.71554 | ||||||||
\(371\) | −25.4608 | −1.32186 | ||||||||
\(372\) | −36.2445 | −1.87919 | ||||||||
\(373\) | 18.8394 | 0.975466 | 0.487733 | − | 0.872993i | \(-0.337824\pi\) | ||||
0.487733 | + | 0.872993i | \(0.337824\pi\) | |||||||
\(374\) | −12.8112 | −0.662452 | ||||||||
\(375\) | −18.8666 | −0.974266 | ||||||||
\(376\) | −41.6657 | −2.14874 | ||||||||
\(377\) | 1.16295 | 0.0598951 | ||||||||
\(378\) | −34.8697 | −1.79350 | ||||||||
\(379\) | −0.301390 | −0.0154814 | −0.00774069 | − | 0.999970i | \(-0.502464\pi\) | ||||
−0.00774069 | + | 0.999970i | \(0.502464\pi\) | |||||||
\(380\) | 94.7123 | 4.85864 | ||||||||
\(381\) | −25.0057 | −1.28108 | ||||||||
\(382\) | 49.3669 | 2.52583 | ||||||||
\(383\) | −7.99148 | −0.408346 | −0.204173 | − | 0.978935i | \(-0.565450\pi\) | ||||
−0.204173 | + | 0.978935i | \(0.565450\pi\) | |||||||
\(384\) | 31.0275 | 1.58336 | ||||||||
\(385\) | −29.7738 | −1.51742 | ||||||||
\(386\) | 14.3383 | 0.729802 | ||||||||
\(387\) | 6.19920 | 0.315123 | ||||||||
\(388\) | 28.6818 | 1.45610 | ||||||||
\(389\) | 5.29913 | 0.268677 | 0.134338 | − | 0.990936i | \(-0.457109\pi\) | ||||
0.134338 | + | 0.990936i | \(0.457109\pi\) | |||||||
\(390\) | −2.34133 | −0.118558 | ||||||||
\(391\) | −8.45564 | −0.427620 | ||||||||
\(392\) | −10.2190 | −0.516136 | ||||||||
\(393\) | 20.3378 | 1.02591 | ||||||||
\(394\) | −64.9415 | −3.27170 | ||||||||
\(395\) | 39.1752 | 1.97112 | ||||||||
\(396\) | 13.2777 | 0.667230 | ||||||||
\(397\) | −17.1476 | −0.860615 | −0.430307 | − | 0.902682i | \(-0.641595\pi\) | ||||
−0.430307 | + | 0.902682i | \(0.641595\pi\) | |||||||
\(398\) | −61.0900 | −3.06216 | ||||||||
\(399\) | 41.1211 | 2.05863 | ||||||||
\(400\) | 11.1701 | 0.558506 | ||||||||
\(401\) | 8.42097 | 0.420523 | 0.210262 | − | 0.977645i | \(-0.432568\pi\) | ||||
0.210262 | + | 0.977645i | \(0.432568\pi\) | |||||||
\(402\) | 40.9679 | 2.04329 | ||||||||
\(403\) | 0.702908 | 0.0350143 | ||||||||
\(404\) | −10.7898 | −0.536811 | ||||||||
\(405\) | 25.3985 | 1.26206 | ||||||||
\(406\) | −46.9896 | −2.33205 | ||||||||
\(407\) | 34.3226 | 1.70131 | ||||||||
\(408\) | 17.9416 | 0.888239 | ||||||||
\(409\) | 13.2027 | 0.652832 | 0.326416 | − | 0.945226i | \(-0.394159\pi\) | ||||
0.326416 | + | 0.945226i | \(0.394159\pi\) | |||||||
\(410\) | −23.7528 | −1.17307 | ||||||||
\(411\) | −2.04666 | −0.100954 | ||||||||
\(412\) | 48.5217 | 2.39049 | ||||||||
\(413\) | −22.5174 | −1.10801 | ||||||||
\(414\) | 12.1652 | 0.597885 | ||||||||
\(415\) | 19.4245 | 0.953511 | ||||||||
\(416\) | −3.01259 | −0.147704 | ||||||||
\(417\) | −33.9268 | −1.66140 | ||||||||
\(418\) | 86.3905 | 4.22550 | ||||||||
\(419\) | 1.55567 | 0.0759994 | 0.0379997 | − | 0.999278i | \(-0.487901\pi\) | ||||
0.0379997 | + | 0.999278i | \(0.487901\pi\) | |||||||
\(420\) | 68.1497 | 3.32536 | ||||||||
\(421\) | −9.34657 | −0.455524 | −0.227762 | − | 0.973717i | \(-0.573141\pi\) | ||||
−0.227762 | + | 0.973717i | \(0.573141\pi\) | |||||||
\(422\) | 54.8197 | 2.66858 | ||||||||
\(423\) | 2.98023 | 0.144904 | ||||||||
\(424\) | 74.9107 | 3.63799 | ||||||||
\(425\) | 1.02274 | 0.0496104 | ||||||||
\(426\) | 8.28817 | 0.401563 | ||||||||
\(427\) | 9.19134 | 0.444800 | ||||||||
\(428\) | −29.6451 | −1.43295 | ||||||||
\(429\) | −1.53845 | −0.0742772 | ||||||||
\(430\) | 66.8464 | 3.22362 | ||||||||
\(431\) | −33.2187 | −1.60009 | −0.800044 | − | 0.599941i | \(-0.795191\pi\) | ||||
−0.800044 | + | 0.599941i | \(0.795191\pi\) | |||||||
\(432\) | 55.7070 | 2.68021 | ||||||||
\(433\) | 23.9988 | 1.15331 | 0.576655 | − | 0.816988i | \(-0.304358\pi\) | ||||
0.576655 | + | 0.816988i | \(0.304358\pi\) | |||||||
\(434\) | −28.4013 | −1.36331 | ||||||||
\(435\) | 28.2983 | 1.35680 | ||||||||
\(436\) | −30.6116 | −1.46603 | ||||||||
\(437\) | 57.0194 | 2.72761 | ||||||||
\(438\) | −19.8120 | −0.946655 | ||||||||
\(439\) | −21.4411 | −1.02333 | −0.511664 | − | 0.859186i | \(-0.670971\pi\) | ||||
−0.511664 | + | 0.859186i | \(0.670971\pi\) | |||||||
\(440\) | 87.6004 | 4.17618 | ||||||||
\(441\) | 0.730934 | 0.0348064 | ||||||||
\(442\) | −0.568689 | −0.0270498 | ||||||||
\(443\) | −40.2156 | −1.91070 | −0.955351 | − | 0.295474i | \(-0.904523\pi\) | ||||
−0.955351 | + | 0.295474i | \(0.904523\pi\) | |||||||
\(444\) | −78.5613 | −3.72835 | ||||||||
\(445\) | 36.5275 | 1.73157 | ||||||||
\(446\) | −69.6734 | −3.29913 | ||||||||
\(447\) | −22.2889 | −1.05423 | ||||||||
\(448\) | 51.5515 | 2.43558 | ||||||||
\(449\) | 7.52202 | 0.354986 | 0.177493 | − | 0.984122i | \(-0.443201\pi\) | ||||
0.177493 | + | 0.984122i | \(0.443201\pi\) | |||||||
\(450\) | −1.47142 | −0.0693636 | ||||||||
\(451\) | −15.6076 | −0.734935 | ||||||||
\(452\) | −21.0718 | −0.991135 | ||||||||
\(453\) | −2.39181 | −0.112377 | ||||||||
\(454\) | 53.3880 | 2.50562 | ||||||||
\(455\) | −1.32166 | −0.0619604 | ||||||||
\(456\) | −120.986 | −5.66570 | ||||||||
\(457\) | −5.96681 | −0.279115 | −0.139558 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139558 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(458\) | 57.6031 | 2.69162 | ||||||||
\(459\) | 5.10058 | 0.238075 | ||||||||
\(460\) | 94.4977 | 4.40598 | ||||||||
\(461\) | −34.2658 | −1.59592 | −0.797959 | − | 0.602712i | \(-0.794087\pi\) | ||||
−0.797959 | + | 0.602712i | \(0.794087\pi\) | |||||||
\(462\) | 62.1618 | 2.89203 | ||||||||
\(463\) | 13.2956 | 0.617901 | 0.308950 | − | 0.951078i | \(-0.400022\pi\) | ||||
0.308950 | + | 0.951078i | \(0.400022\pi\) | |||||||
\(464\) | 75.0695 | 3.48502 | ||||||||
\(465\) | 17.1040 | 0.793177 | ||||||||
\(466\) | −8.75895 | −0.405750 | ||||||||
\(467\) | 17.1853 | 0.795241 | 0.397621 | − | 0.917550i | \(-0.369836\pi\) | ||||
0.397621 | + | 0.917550i | \(0.369836\pi\) | |||||||
\(468\) | 0.589397 | 0.0272449 | ||||||||
\(469\) | 23.1260 | 1.06786 | ||||||||
\(470\) | 32.1360 | 1.48232 | ||||||||
\(471\) | 22.4375 | 1.03386 | ||||||||
\(472\) | 66.2504 | 3.04942 | ||||||||
\(473\) | 43.9238 | 2.01962 | ||||||||
\(474\) | −81.7900 | −3.75674 | ||||||||
\(475\) | −6.89673 | −0.316444 | ||||||||
\(476\) | 16.5530 | 0.758706 | ||||||||
\(477\) | −5.35815 | −0.245333 | ||||||||
\(478\) | 70.2672 | 3.21395 | ||||||||
\(479\) | 29.5529 | 1.35031 | 0.675153 | − | 0.737677i | \(-0.264077\pi\) | ||||
0.675153 | + | 0.737677i | \(0.264077\pi\) | |||||||
\(480\) | −73.3058 | −3.34594 | ||||||||
\(481\) | 1.52358 | 0.0694692 | ||||||||
\(482\) | −4.69638 | −0.213914 | ||||||||
\(483\) | 41.0280 | 1.86684 | ||||||||
\(484\) | 37.3994 | 1.69997 | ||||||||
\(485\) | −13.5351 | −0.614596 | ||||||||
\(486\) | −16.5227 | −0.749486 | ||||||||
\(487\) | −22.5082 | −1.01994 | −0.509972 | − | 0.860191i | \(-0.670344\pi\) | ||||
−0.509972 | + | 0.860191i | \(0.670344\pi\) | |||||||
\(488\) | −27.0427 | −1.22417 | ||||||||
\(489\) | 46.3401 | 2.09557 | ||||||||
\(490\) | 7.88171 | 0.356059 | ||||||||
\(491\) | −25.5461 | −1.15288 | −0.576440 | − | 0.817139i | \(-0.695559\pi\) | ||||
−0.576440 | + | 0.817139i | \(0.695559\pi\) | |||||||
\(492\) | 35.7245 | 1.61058 | ||||||||
\(493\) | 6.87342 | 0.309563 | ||||||||
\(494\) | 3.83487 | 0.172539 | ||||||||
\(495\) | −6.26581 | −0.281627 | ||||||||
\(496\) | 45.3733 | 2.03732 | ||||||||
\(497\) | 4.67861 | 0.209864 | ||||||||
\(498\) | −40.5545 | −1.81729 | ||||||||
\(499\) | −27.0222 | −1.20968 | −0.604839 | − | 0.796348i | \(-0.706763\pi\) | ||||
−0.604839 | + | 0.796348i | \(0.706763\pi\) | |||||||
\(500\) | 51.2131 | 2.29032 | ||||||||
\(501\) | −28.6483 | −1.27991 | ||||||||
\(502\) | −1.24314 | −0.0554842 | ||||||||
\(503\) | −33.2675 | −1.48333 | −0.741663 | − | 0.670773i | \(-0.765963\pi\) | ||||
−0.741663 | + | 0.670773i | \(0.765963\pi\) | |||||||
\(504\) | −14.5710 | −0.649043 | ||||||||
\(505\) | 5.09175 | 0.226580 | ||||||||
\(506\) | 86.1949 | 3.83183 | ||||||||
\(507\) | 24.6080 | 1.09288 | ||||||||
\(508\) | 67.8777 | 3.01158 | ||||||||
\(509\) | 13.7336 | 0.608731 | 0.304365 | − | 0.952555i | \(-0.401556\pi\) | ||||
0.304365 | + | 0.952555i | \(0.401556\pi\) | |||||||
\(510\) | −13.8380 | −0.612757 | ||||||||
\(511\) | −11.1837 | −0.494739 | ||||||||
\(512\) | 11.9989 | 0.530282 | ||||||||
\(513\) | −34.3950 | −1.51858 | ||||||||
\(514\) | −73.9015 | −3.25965 | ||||||||
\(515\) | −22.8976 | −1.00899 | ||||||||
\(516\) | −100.538 | −4.42592 | ||||||||
\(517\) | 21.1161 | 0.928685 | ||||||||
\(518\) | −61.5608 | −2.70483 | ||||||||
\(519\) | 1.10182 | 0.0483644 | ||||||||
\(520\) | 3.88858 | 0.170525 | ||||||||
\(521\) | 14.5729 | 0.638450 | 0.319225 | − | 0.947679i | \(-0.396577\pi\) | ||||
0.319225 | + | 0.947679i | \(0.396577\pi\) | |||||||
\(522\) | −9.88881 | −0.432821 | ||||||||
\(523\) | −7.99304 | −0.349511 | −0.174756 | − | 0.984612i | \(-0.555914\pi\) | ||||
−0.174756 | + | 0.984612i | \(0.555914\pi\) | |||||||
\(524\) | −55.2067 | −2.41172 | ||||||||
\(525\) | −4.96250 | −0.216581 | ||||||||
\(526\) | −24.3173 | −1.06029 | ||||||||
\(527\) | 4.15441 | 0.180969 | ||||||||
\(528\) | −99.3084 | −4.32184 | ||||||||
\(529\) | 33.8903 | 1.47349 | ||||||||
\(530\) | −57.7773 | −2.50969 | ||||||||
\(531\) | −4.73871 | −0.205642 | ||||||||
\(532\) | −111.623 | −4.83946 | ||||||||
\(533\) | −0.692823 | −0.0300095 | ||||||||
\(534\) | −76.2621 | −3.30018 | ||||||||
\(535\) | 13.9897 | 0.604826 | ||||||||
\(536\) | −68.0413 | −2.93893 | ||||||||
\(537\) | 29.9392 | 1.29197 | ||||||||
\(538\) | −65.7428 | −2.83437 | ||||||||
\(539\) | 5.17896 | 0.223073 | ||||||||
\(540\) | −57.0025 | −2.45300 | ||||||||
\(541\) | 13.0723 | 0.562023 | 0.281012 | − | 0.959704i | \(-0.409330\pi\) | ||||
0.281012 | + | 0.959704i | \(0.409330\pi\) | |||||||
\(542\) | −79.8055 | −3.42794 | ||||||||
\(543\) | −43.4847 | −1.86611 | ||||||||
\(544\) | −17.8054 | −0.763399 | ||||||||
\(545\) | 14.4457 | 0.618787 | ||||||||
\(546\) | 2.75936 | 0.118090 | ||||||||
\(547\) | 34.6375 | 1.48099 | 0.740495 | − | 0.672062i | \(-0.234591\pi\) | ||||
0.740495 | + | 0.672062i | \(0.234591\pi\) | |||||||
\(548\) | 5.55564 | 0.237325 | ||||||||
\(549\) | 1.93429 | 0.0825534 | ||||||||
\(550\) | −10.4256 | −0.444550 | ||||||||
\(551\) | −46.3499 | −1.97457 | ||||||||
\(552\) | −120.712 | −5.13786 | ||||||||
\(553\) | −46.1698 | −1.96334 | ||||||||
\(554\) | 2.46433 | 0.104699 | ||||||||
\(555\) | 37.0734 | 1.57368 | ||||||||
\(556\) | 92.0938 | 3.90565 | ||||||||
\(557\) | −15.5134 | −0.657322 | −0.328661 | − | 0.944448i | \(-0.606597\pi\) | ||||
−0.328661 | + | 0.944448i | \(0.606597\pi\) | |||||||
\(558\) | −5.97696 | −0.253025 | ||||||||
\(559\) | 1.94978 | 0.0824667 | ||||||||
\(560\) | −85.3143 | −3.60519 | ||||||||
\(561\) | −9.09275 | −0.383896 | ||||||||
\(562\) | 4.00140 | 0.168789 | ||||||||
\(563\) | −19.5000 | −0.821826 | −0.410913 | − | 0.911675i | \(-0.634790\pi\) | ||||
−0.410913 | + | 0.911675i | \(0.634790\pi\) | |||||||
\(564\) | −48.3329 | −2.03518 | ||||||||
\(565\) | 9.94389 | 0.418342 | ||||||||
\(566\) | −34.4780 | −1.44922 | ||||||||
\(567\) | −29.9333 | −1.25708 | ||||||||
\(568\) | −13.7654 | −0.577582 | ||||||||
\(569\) | 16.4359 | 0.689027 | 0.344514 | − | 0.938781i | \(-0.388044\pi\) | ||||
0.344514 | + | 0.938781i | \(0.388044\pi\) | |||||||
\(570\) | 93.3146 | 3.90852 | ||||||||
\(571\) | 34.6767 | 1.45118 | 0.725588 | − | 0.688130i | \(-0.241568\pi\) | ||||
0.725588 | + | 0.688130i | \(0.241568\pi\) | |||||||
\(572\) | 4.17611 | 0.174612 | ||||||||
\(573\) | 35.0381 | 1.46374 | ||||||||
\(574\) | 27.9938 | 1.16844 | ||||||||
\(575\) | −6.88111 | −0.286962 | ||||||||
\(576\) | 10.8488 | 0.452035 | ||||||||
\(577\) | 36.4051 | 1.51556 | 0.757782 | − | 0.652507i | \(-0.226283\pi\) | ||||
0.757782 | + | 0.652507i | \(0.226283\pi\) | |||||||
\(578\) | 42.1042 | 1.75130 | ||||||||
\(579\) | 10.1766 | 0.422926 | ||||||||
\(580\) | −76.8153 | −3.18958 | ||||||||
\(581\) | −22.8927 | −0.949748 | ||||||||
\(582\) | 28.2585 | 1.17135 | ||||||||
\(583\) | −37.9646 | −1.57233 | ||||||||
\(584\) | 32.9047 | 1.36161 | ||||||||
\(585\) | −0.278139 | −0.0114996 | ||||||||
\(586\) | −9.99100 | −0.412725 | ||||||||
\(587\) | 15.4475 | 0.637588 | 0.318794 | − | 0.947824i | \(-0.396722\pi\) | ||||
0.318794 | + | 0.947824i | \(0.396722\pi\) | |||||||
\(588\) | −11.8542 | −0.488858 | ||||||||
\(589\) | −28.0147 | −1.15432 | ||||||||
\(590\) | −51.0978 | −2.10366 | ||||||||
\(591\) | −46.0922 | −1.89598 | ||||||||
\(592\) | 98.3482 | 4.04209 | ||||||||
\(593\) | −38.5590 | −1.58343 | −0.791713 | − | 0.610893i | \(-0.790811\pi\) | ||||
−0.791713 | + | 0.610893i | \(0.790811\pi\) | |||||||
\(594\) | −51.9941 | −2.13334 | ||||||||
\(595\) | −7.81144 | −0.320238 | ||||||||
\(596\) | 60.5030 | 2.47830 | ||||||||
\(597\) | −43.3586 | −1.77455 | ||||||||
\(598\) | 3.82619 | 0.156465 | ||||||||
\(599\) | 24.5528 | 1.00320 | 0.501600 | − | 0.865100i | \(-0.332745\pi\) | ||||
0.501600 | + | 0.865100i | \(0.332745\pi\) | |||||||
\(600\) | 14.6006 | 0.596069 | ||||||||
\(601\) | 22.6814 | 0.925193 | 0.462596 | − | 0.886569i | \(-0.346918\pi\) | ||||
0.462596 | + | 0.886569i | \(0.346918\pi\) | |||||||
\(602\) | −78.7815 | −3.21090 | ||||||||
\(603\) | 4.86680 | 0.198191 | ||||||||
\(604\) | 6.49253 | 0.264177 | ||||||||
\(605\) | −17.6490 | −0.717533 | ||||||||
\(606\) | −10.6306 | −0.431837 | ||||||||
\(607\) | 33.1908 | 1.34717 | 0.673586 | − | 0.739109i | \(-0.264753\pi\) | ||||
0.673586 | + | 0.739109i | \(0.264753\pi\) | |||||||
\(608\) | 120.068 | 4.86940 | ||||||||
\(609\) | −33.3508 | −1.35144 | ||||||||
\(610\) | 20.8575 | 0.844497 | ||||||||
\(611\) | 0.937343 | 0.0379209 | ||||||||
\(612\) | 3.48353 | 0.140813 | ||||||||
\(613\) | 27.8533 | 1.12498 | 0.562492 | − | 0.826803i | \(-0.309843\pi\) | ||||
0.562492 | + | 0.826803i | \(0.309843\pi\) | |||||||
\(614\) | 52.9634 | 2.13743 | ||||||||
\(615\) | −16.8586 | −0.679803 | ||||||||
\(616\) | −103.241 | −4.15970 | ||||||||
\(617\) | −10.2016 | −0.410699 | −0.205350 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205350 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(618\) | 47.8057 | 1.92303 | ||||||||
\(619\) | −38.3478 | −1.54133 | −0.770664 | − | 0.637242i | \(-0.780075\pi\) | ||||
−0.770664 | + | 0.637242i | \(0.780075\pi\) | |||||||
\(620\) | −46.4285 | −1.86461 | ||||||||
\(621\) | −34.3171 | −1.37710 | ||||||||
\(622\) | −82.8004 | −3.32000 | ||||||||
\(623\) | −43.0493 | −1.72473 | ||||||||
\(624\) | −4.40830 | −0.176473 | ||||||||
\(625\) | −28.7292 | −1.14917 | ||||||||
\(626\) | 36.2635 | 1.44938 | ||||||||
\(627\) | 61.3157 | 2.44871 | ||||||||
\(628\) | −60.9062 | −2.43042 | ||||||||
\(629\) | 9.00484 | 0.359046 | ||||||||
\(630\) | 11.2383 | 0.447746 | ||||||||
\(631\) | −27.0621 | −1.07732 | −0.538662 | − | 0.842522i | \(-0.681070\pi\) | ||||
−0.538662 | + | 0.842522i | \(0.681070\pi\) | |||||||
\(632\) | 135.840 | 5.40344 | ||||||||
\(633\) | 38.9083 | 1.54646 | ||||||||
\(634\) | −30.2034 | −1.19953 | ||||||||
\(635\) | −32.0318 | −1.27114 | ||||||||
\(636\) | 86.8977 | 3.44572 | ||||||||
\(637\) | 0.229894 | 0.00910872 | ||||||||
\(638\) | −70.0661 | −2.77394 | ||||||||
\(639\) | 0.984598 | 0.0389501 | ||||||||
\(640\) | 39.7455 | 1.57108 | ||||||||
\(641\) | −28.2050 | −1.11403 | −0.557015 | − | 0.830503i | \(-0.688053\pi\) | ||||
−0.557015 | + | 0.830503i | \(0.688053\pi\) | |||||||
\(642\) | −29.2076 | −1.15273 | ||||||||
\(643\) | 25.3480 | 0.999629 | 0.499815 | − | 0.866132i | \(-0.333401\pi\) | ||||
0.499815 | + | 0.866132i | \(0.333401\pi\) | |||||||
\(644\) | −111.370 | −4.38859 | ||||||||
\(645\) | 47.4442 | 1.86811 | ||||||||
\(646\) | 22.6653 | 0.891756 | ||||||||
\(647\) | −7.02393 | −0.276139 | −0.138070 | − | 0.990423i | \(-0.544090\pi\) | ||||
−0.138070 | + | 0.990423i | \(0.544090\pi\) | |||||||
\(648\) | 88.0696 | 3.45970 | ||||||||
\(649\) | −33.5756 | −1.31796 | ||||||||
\(650\) | −0.462793 | −0.0181522 | ||||||||
\(651\) | −20.1578 | −0.790047 | ||||||||
\(652\) | −125.790 | −4.92630 | ||||||||
\(653\) | −42.6366 | −1.66850 | −0.834249 | − | 0.551388i | \(-0.814098\pi\) | ||||
−0.834249 | + | 0.551388i | \(0.814098\pi\) | |||||||
\(654\) | −30.1598 | −1.17934 | ||||||||
\(655\) | 26.0523 | 1.01795 | ||||||||
\(656\) | −44.7223 | −1.74611 | ||||||||
\(657\) | −2.35358 | −0.0918219 | ||||||||
\(658\) | −37.8738 | −1.47647 | ||||||||
\(659\) | −26.9096 | −1.04825 | −0.524124 | − | 0.851642i | \(-0.675607\pi\) | ||||
−0.524124 | + | 0.851642i | \(0.675607\pi\) | |||||||
\(660\) | 101.618 | 3.95547 | ||||||||
\(661\) | 41.0374 | 1.59617 | 0.798085 | − | 0.602544i | \(-0.205846\pi\) | ||||
0.798085 | + | 0.602544i | \(0.205846\pi\) | |||||||
\(662\) | −3.22616 | −0.125388 | ||||||||
\(663\) | −0.403627 | −0.0156756 | ||||||||
\(664\) | 67.3546 | 2.61387 | ||||||||
\(665\) | 52.6753 | 2.04266 | ||||||||
\(666\) | −12.9553 | −0.502007 | ||||||||
\(667\) | −46.2449 | −1.79061 | ||||||||
\(668\) | 77.7654 | 3.00884 | ||||||||
\(669\) | −49.4507 | −1.91187 | ||||||||
\(670\) | 52.4790 | 2.02744 | ||||||||
\(671\) | 13.7052 | 0.529083 | ||||||||
\(672\) | 86.3943 | 3.33273 | ||||||||
\(673\) | −23.3272 | −0.899199 | −0.449600 | − | 0.893230i | \(-0.648433\pi\) | ||||
−0.449600 | + | 0.893230i | \(0.648433\pi\) | |||||||
\(674\) | 10.5505 | 0.406390 | ||||||||
\(675\) | 4.15079 | 0.159764 | ||||||||
\(676\) | −66.7981 | −2.56916 | ||||||||
\(677\) | −3.54650 | −0.136303 | −0.0681515 | − | 0.997675i | \(-0.521710\pi\) | ||||
−0.0681515 | + | 0.997675i | \(0.521710\pi\) | |||||||
\(678\) | −20.7609 | −0.797316 | ||||||||
\(679\) | 15.9517 | 0.612170 | ||||||||
\(680\) | 22.9828 | 0.881349 | ||||||||
\(681\) | 37.8921 | 1.45203 | ||||||||
\(682\) | −42.3491 | −1.62163 | ||||||||
\(683\) | −18.5294 | −0.709007 | −0.354504 | − | 0.935055i | \(-0.615350\pi\) | ||||
−0.354504 | + | 0.935055i | \(0.615350\pi\) | |||||||
\(684\) | −23.4907 | −0.898188 | ||||||||
\(685\) | −2.62173 | −0.100171 | ||||||||
\(686\) | 44.3591 | 1.69364 | ||||||||
\(687\) | 40.8838 | 1.55981 | ||||||||
\(688\) | 125.860 | 4.79836 | ||||||||
\(689\) | −1.68525 | −0.0642029 | ||||||||
\(690\) | 93.1032 | 3.54438 | ||||||||
\(691\) | −11.1841 | −0.425464 | −0.212732 | − | 0.977111i | \(-0.568236\pi\) | ||||
−0.212732 | + | 0.977111i | \(0.568236\pi\) | |||||||
\(692\) | −2.99087 | −0.113696 | ||||||||
\(693\) | 7.38455 | 0.280516 | ||||||||
\(694\) | −40.9208 | −1.55333 | ||||||||
\(695\) | −43.4595 | −1.64851 | ||||||||
\(696\) | 98.1246 | 3.71940 | ||||||||
\(697\) | −4.09481 | −0.155102 | ||||||||
\(698\) | −8.39213 | −0.317647 | ||||||||
\(699\) | −6.21666 | −0.235136 | ||||||||
\(700\) | 13.4707 | 0.509143 | ||||||||
\(701\) | −37.3875 | −1.41211 | −0.706054 | − | 0.708158i | \(-0.749526\pi\) | ||||
−0.706054 | + | 0.708158i | \(0.749526\pi\) | |||||||
\(702\) | −2.30802 | −0.0871105 | ||||||||
\(703\) | −60.7228 | −2.29020 | ||||||||
\(704\) | 76.8683 | 2.89708 | ||||||||
\(705\) | 22.8085 | 0.859018 | ||||||||
\(706\) | −72.3844 | −2.72422 | ||||||||
\(707\) | −6.00086 | −0.225686 | ||||||||
\(708\) | 76.8516 | 2.88826 | ||||||||
\(709\) | −29.8194 | −1.11989 | −0.559945 | − | 0.828530i | \(-0.689178\pi\) | ||||
−0.559945 | + | 0.828530i | \(0.689178\pi\) | |||||||
\(710\) | 10.6170 | 0.398448 | ||||||||
\(711\) | −9.71628 | −0.364389 | ||||||||
\(712\) | 126.659 | 4.74676 | ||||||||
\(713\) | −27.9512 | −1.04678 | ||||||||
\(714\) | 16.3087 | 0.610339 | ||||||||
\(715\) | −1.97073 | −0.0737010 | ||||||||
\(716\) | −81.2695 | −3.03718 | ||||||||
\(717\) | 49.8721 | 1.86251 | ||||||||
\(718\) | −18.2638 | −0.681601 | ||||||||
\(719\) | 14.8603 | 0.554196 | 0.277098 | − | 0.960842i | \(-0.410627\pi\) | ||||
0.277098 | + | 0.960842i | \(0.410627\pi\) | |||||||
\(720\) | −17.9541 | −0.669111 | ||||||||
\(721\) | 26.9859 | 1.00501 | ||||||||
\(722\) | −102.026 | −3.79703 | ||||||||
\(723\) | −3.33326 | −0.123965 | ||||||||
\(724\) | 118.039 | 4.38688 | ||||||||
\(725\) | 5.59352 | 0.207738 | ||||||||
\(726\) | 36.8475 | 1.36754 | ||||||||
\(727\) | −16.3593 | −0.606732 | −0.303366 | − | 0.952874i | \(-0.598111\pi\) | ||||
−0.303366 | + | 0.952874i | \(0.598111\pi\) | |||||||
\(728\) | −4.58287 | −0.169853 | ||||||||
\(729\) | 19.6095 | 0.726280 | ||||||||
\(730\) | −25.3788 | −0.939311 | ||||||||
\(731\) | 11.5238 | 0.426223 | ||||||||
\(732\) | −31.3700 | −1.15947 | ||||||||
\(733\) | 12.6695 | 0.467960 | 0.233980 | − | 0.972241i | \(-0.424825\pi\) | ||||
0.233980 | + | 0.972241i | \(0.424825\pi\) | |||||||
\(734\) | 72.8237 | 2.68797 | ||||||||
\(735\) | 5.59404 | 0.206339 | ||||||||
\(736\) | 119.796 | 4.41574 | ||||||||
\(737\) | 34.4832 | 1.27020 | ||||||||
\(738\) | 5.89121 | 0.216858 | ||||||||
\(739\) | −7.46822 | −0.274723 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(740\) | −100.635 | −3.69943 | ||||||||
\(741\) | 2.72180 | 0.0999879 | ||||||||
\(742\) | 68.0932 | 2.49978 | ||||||||
\(743\) | 17.8826 | 0.656051 | 0.328025 | − | 0.944669i | \(-0.393617\pi\) | ||||
0.328025 | + | 0.944669i | \(0.393617\pi\) | |||||||
\(744\) | 59.3082 | 2.17434 | ||||||||
\(745\) | −28.5516 | −1.04605 | ||||||||
\(746\) | −50.3846 | −1.84471 | ||||||||
\(747\) | −4.81769 | −0.176270 | ||||||||
\(748\) | 24.6822 | 0.902469 | ||||||||
\(749\) | −16.4875 | −0.602439 | ||||||||
\(750\) | 50.4574 | 1.84244 | ||||||||
\(751\) | 3.70986 | 0.135375 | 0.0676874 | − | 0.997707i | \(-0.478438\pi\) | ||||
0.0676874 | + | 0.997707i | \(0.478438\pi\) | |||||||
\(752\) | 60.5063 | 2.20644 | ||||||||
\(753\) | −0.882321 | −0.0321536 | ||||||||
\(754\) | −3.11023 | −0.113268 | ||||||||
\(755\) | −3.06386 | −0.111505 | ||||||||
\(756\) | 67.1801 | 2.44332 | ||||||||
\(757\) | −48.0669 | −1.74702 | −0.873510 | − | 0.486807i | \(-0.838162\pi\) | ||||
−0.873510 | + | 0.486807i | \(0.838162\pi\) | |||||||
\(758\) | 0.806048 | 0.0292770 | ||||||||
\(759\) | 61.1768 | 2.22058 | ||||||||
\(760\) | −154.981 | −5.62175 | ||||||||
\(761\) | 0.514146 | 0.0186378 | 0.00931890 | − | 0.999957i | \(-0.497034\pi\) | ||||
0.00931890 | + | 0.999957i | \(0.497034\pi\) | |||||||
\(762\) | 66.8760 | 2.42266 | ||||||||
\(763\) | −17.0250 | −0.616345 | ||||||||
\(764\) | −95.1106 | −3.44098 | ||||||||
\(765\) | −1.64389 | −0.0594351 | ||||||||
\(766\) | 21.3727 | 0.772225 | ||||||||
\(767\) | −1.49042 | −0.0538160 | ||||||||
\(768\) | −14.6868 | −0.529966 | ||||||||
\(769\) | 15.4661 | 0.557723 | 0.278862 | − | 0.960331i | \(-0.410043\pi\) | ||||
0.278862 | + | 0.960331i | \(0.410043\pi\) | |||||||
\(770\) | 79.6280 | 2.86959 | ||||||||
\(771\) | −52.4516 | −1.88900 | ||||||||
\(772\) | −27.6243 | −0.994221 | ||||||||
\(773\) | −14.9912 | −0.539197 | −0.269599 | − | 0.962973i | \(-0.586891\pi\) | ||||
−0.269599 | + | 0.962973i | \(0.586891\pi\) | |||||||
\(774\) | −16.5793 | −0.595932 | ||||||||
\(775\) | 3.38081 | 0.121442 | ||||||||
\(776\) | −46.9330 | −1.68480 | ||||||||
\(777\) | −43.6928 | −1.56747 | ||||||||
\(778\) | −14.1722 | −0.508097 | ||||||||
\(779\) | 27.6127 | 0.989329 | ||||||||
\(780\) | 4.51082 | 0.161513 | ||||||||
\(781\) | 6.97626 | 0.249630 | ||||||||
\(782\) | 22.6140 | 0.808676 | ||||||||
\(783\) | 27.8957 | 0.996911 | ||||||||
\(784\) | 14.8398 | 0.529994 | ||||||||
\(785\) | 28.7419 | 1.02584 | ||||||||
\(786\) | −54.3920 | −1.94010 | ||||||||
\(787\) | −26.0738 | −0.929430 | −0.464715 | − | 0.885460i | \(-0.653843\pi\) | ||||
−0.464715 | + | 0.885460i | \(0.653843\pi\) | |||||||
\(788\) | 125.117 | 4.45710 | ||||||||
\(789\) | −17.2592 | −0.614444 | ||||||||
\(790\) | −104.771 | −3.72759 | ||||||||
\(791\) | −11.7193 | −0.416691 | ||||||||
\(792\) | −21.7268 | −0.772027 | ||||||||
\(793\) | 0.608373 | 0.0216040 | ||||||||
\(794\) | 45.8601 | 1.62751 | ||||||||
\(795\) | −41.0074 | −1.45438 | ||||||||
\(796\) | 117.696 | 4.17164 | ||||||||
\(797\) | −30.1737 | −1.06881 | −0.534403 | − | 0.845230i | \(-0.679464\pi\) | ||||
−0.534403 | + | 0.845230i | \(0.679464\pi\) | |||||||
\(798\) | −109.976 | −3.89309 | ||||||||
\(799\) | 5.54000 | 0.195991 | ||||||||
\(800\) | −14.4898 | −0.512293 | ||||||||
\(801\) | −9.05959 | −0.320105 | ||||||||
\(802\) | −22.5213 | −0.795255 | ||||||||
\(803\) | −16.6760 | −0.588484 | ||||||||
\(804\) | −78.9290 | −2.78361 | ||||||||
\(805\) | 52.5560 | 1.85236 | ||||||||
\(806\) | −1.87988 | −0.0662158 | ||||||||
\(807\) | −46.6609 | −1.64254 | ||||||||
\(808\) | 17.6557 | 0.621125 | ||||||||
\(809\) | −55.1431 | −1.93873 | −0.969364 | − | 0.245630i | \(-0.921005\pi\) | ||||
−0.969364 | + | 0.245630i | \(0.921005\pi\) | |||||||
\(810\) | −67.9265 | −2.38669 | ||||||||
\(811\) | −19.0594 | −0.669265 | −0.334633 | − | 0.942349i | \(-0.608612\pi\) | ||||
−0.334633 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(812\) | 90.5304 | 3.17699 | ||||||||
\(813\) | −56.6419 | −1.98652 | ||||||||
\(814\) | −91.7933 | −3.21735 | ||||||||
\(815\) | 59.3607 | 2.07931 | ||||||||
\(816\) | −26.0545 | −0.912089 | ||||||||
\(817\) | −77.7091 | −2.71870 | ||||||||
\(818\) | −35.3097 | −1.23458 | ||||||||
\(819\) | 0.327800 | 0.0114543 | ||||||||
\(820\) | 45.7623 | 1.59809 | ||||||||
\(821\) | −9.79040 | −0.341687 | −0.170844 | − | 0.985298i | \(-0.554649\pi\) | ||||
−0.170844 | + | 0.985298i | \(0.554649\pi\) | |||||||
\(822\) | 5.47365 | 0.190916 | ||||||||
\(823\) | 4.78542 | 0.166809 | 0.0834046 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834046 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(824\) | −79.3978 | −2.76595 | ||||||||
\(825\) | −7.39958 | −0.257620 | ||||||||
\(826\) | 60.2211 | 2.09536 | ||||||||
\(827\) | 12.6197 | 0.438832 | 0.219416 | − | 0.975631i | \(-0.429585\pi\) | ||||
0.219416 | + | 0.975631i | \(0.429585\pi\) | |||||||
\(828\) | −23.4375 | −0.814508 | ||||||||
\(829\) | 4.46812 | 0.155184 | 0.0775922 | − | 0.996985i | \(-0.475277\pi\) | ||||
0.0775922 | + | 0.996985i | \(0.475277\pi\) | |||||||
\(830\) | −51.9494 | −1.80319 | ||||||||
\(831\) | 1.74906 | 0.0606741 | ||||||||
\(832\) | 3.41218 | 0.118296 | ||||||||
\(833\) | 1.35875 | 0.0470778 | ||||||||
\(834\) | 90.7347 | 3.14189 | ||||||||
\(835\) | −36.6979 | −1.26998 | ||||||||
\(836\) | −166.441 | −5.75647 | ||||||||
\(837\) | 16.8606 | 0.582788 | ||||||||
\(838\) | −4.16053 | −0.143723 | ||||||||
\(839\) | 6.17131 | 0.213057 | 0.106529 | − | 0.994310i | \(-0.466026\pi\) | ||||
0.106529 | + | 0.994310i | \(0.466026\pi\) | |||||||
\(840\) | −111.516 | −3.84766 | ||||||||
\(841\) | 8.59159 | 0.296262 | ||||||||
\(842\) | 24.9967 | 0.861445 | ||||||||
\(843\) | 2.83999 | 0.0978146 | ||||||||
\(844\) | −105.616 | −3.63545 | ||||||||
\(845\) | 31.5223 | 1.08440 | ||||||||
\(846\) | −7.97041 | −0.274028 | ||||||||
\(847\) | 20.8001 | 0.714701 | ||||||||
\(848\) | −108.784 | −3.73567 | ||||||||
\(849\) | −24.4708 | −0.839835 | ||||||||
\(850\) | −2.73526 | −0.0938186 | ||||||||
\(851\) | −60.5853 | −2.07684 | ||||||||
\(852\) | −15.9680 | −0.547056 | ||||||||
\(853\) | −45.2450 | −1.54916 | −0.774580 | − | 0.632476i | \(-0.782039\pi\) | ||||
−0.774580 | + | 0.632476i | \(0.782039\pi\) | |||||||
\(854\) | −24.5816 | −0.841165 | ||||||||
\(855\) | 11.0854 | 0.379111 | ||||||||
\(856\) | 48.5093 | 1.65801 | ||||||||
\(857\) | 41.7727 | 1.42693 | 0.713464 | − | 0.700691i | \(-0.247125\pi\) | ||||
0.713464 | + | 0.700691i | \(0.247125\pi\) | |||||||
\(858\) | 4.11448 | 0.140466 | ||||||||
\(859\) | −28.1620 | −0.960875 | −0.480438 | − | 0.877029i | \(-0.659522\pi\) | ||||
−0.480438 | + | 0.877029i | \(0.659522\pi\) | |||||||
\(860\) | −128.787 | −4.39159 | ||||||||
\(861\) | 19.8686 | 0.677120 | ||||||||
\(862\) | 88.8411 | 3.02594 | ||||||||
\(863\) | −42.1317 | −1.43418 | −0.717090 | − | 0.696981i | \(-0.754526\pi\) | ||||
−0.717090 | + | 0.696981i | \(0.754526\pi\) | |||||||
\(864\) | −72.2629 | −2.45843 | ||||||||
\(865\) | 1.41141 | 0.0479892 | ||||||||
\(866\) | −64.1832 | −2.18103 | ||||||||
\(867\) | 29.8834 | 1.01489 | ||||||||
\(868\) | 54.7181 | 1.85725 | ||||||||
\(869\) | −68.8437 | −2.33536 | ||||||||
\(870\) | −75.6817 | −2.56585 | ||||||||
\(871\) | 1.53071 | 0.0518661 | ||||||||
\(872\) | 50.0908 | 1.69629 | ||||||||
\(873\) | 3.35698 | 0.113617 | ||||||||
\(874\) | −152.494 | −5.15820 | ||||||||
\(875\) | 28.4828 | 0.962893 | ||||||||
\(876\) | 38.1700 | 1.28964 | ||||||||
\(877\) | −14.0536 | −0.474557 | −0.237279 | − | 0.971442i | \(-0.576255\pi\) | ||||
−0.237279 | + | 0.971442i | \(0.576255\pi\) | |||||||
\(878\) | 57.3427 | 1.93522 | ||||||||
\(879\) | −7.09111 | −0.239177 | ||||||||
\(880\) | −127.212 | −4.28832 | ||||||||
\(881\) | −19.8655 | −0.669285 | −0.334642 | − | 0.942345i | \(-0.608616\pi\) | ||||
−0.334642 | + | 0.942345i | \(0.608616\pi\) | |||||||
\(882\) | −1.95483 | −0.0658226 | ||||||||
\(883\) | 14.9354 | 0.502616 | 0.251308 | − | 0.967907i | \(-0.419139\pi\) | ||||
0.251308 | + | 0.967907i | \(0.419139\pi\) | |||||||
\(884\) | 1.09564 | 0.0368504 | ||||||||
\(885\) | −36.2666 | −1.21909 | ||||||||
\(886\) | 107.554 | 3.61334 | ||||||||
\(887\) | 51.6223 | 1.73331 | 0.866654 | − | 0.498910i | \(-0.166266\pi\) | ||||
0.866654 | + | 0.498910i | \(0.166266\pi\) | |||||||
\(888\) | 128.553 | 4.31394 | ||||||||
\(889\) | 37.7510 | 1.26613 | ||||||||
\(890\) | −97.6902 | −3.27458 | ||||||||
\(891\) | −44.6335 | −1.49528 | ||||||||
\(892\) | 134.233 | 4.49446 | ||||||||
\(893\) | −37.3582 | −1.25014 | ||||||||
\(894\) | 59.6101 | 1.99366 | ||||||||
\(895\) | 38.3514 | 1.28195 | ||||||||
\(896\) | −46.8420 | −1.56488 | ||||||||
\(897\) | 2.71564 | 0.0906725 | ||||||||
\(898\) | −20.1171 | −0.671317 | ||||||||
\(899\) | 22.7210 | 0.757787 | ||||||||
\(900\) | 2.83486 | 0.0944952 | ||||||||
\(901\) | −9.96037 | −0.331828 | ||||||||
\(902\) | 41.7415 | 1.38984 | ||||||||
\(903\) | −55.9152 | −1.86074 | ||||||||
\(904\) | 34.4805 | 1.14681 | ||||||||
\(905\) | −55.7030 | −1.85163 | ||||||||
\(906\) | 6.39672 | 0.212517 | ||||||||
\(907\) | −18.8826 | −0.626985 | −0.313493 | − | 0.949591i | \(-0.601499\pi\) | ||||
−0.313493 | + | 0.949591i | \(0.601499\pi\) | |||||||
\(908\) | −102.858 | −3.41345 | ||||||||
\(909\) | −1.26286 | −0.0418865 | ||||||||
\(910\) | 3.53469 | 0.117174 | ||||||||
\(911\) | 37.1336 | 1.23029 | 0.615145 | − | 0.788414i | \(-0.289097\pi\) | ||||
0.615145 | + | 0.788414i | \(0.289097\pi\) | |||||||
\(912\) | 175.695 | 5.81783 | ||||||||
\(913\) | −34.1352 | −1.12971 | ||||||||
\(914\) | 15.9578 | 0.527837 | ||||||||
\(915\) | 14.8036 | 0.489393 | ||||||||
\(916\) | −110.978 | −3.66683 | ||||||||
\(917\) | −30.7038 | −1.01393 | ||||||||
\(918\) | −13.6411 | −0.450225 | ||||||||
\(919\) | 5.35187 | 0.176542 | 0.0882710 | − | 0.996097i | \(-0.471866\pi\) | ||||
0.0882710 | + | 0.996097i | \(0.471866\pi\) | |||||||
\(920\) | −154.630 | −5.09800 | ||||||||
\(921\) | 37.5907 | 1.23866 | ||||||||
\(922\) | 91.6415 | 3.01805 | ||||||||
\(923\) | 0.309676 | 0.0101931 | ||||||||
\(924\) | −119.761 | −3.93986 | ||||||||
\(925\) | 7.32804 | 0.240944 | ||||||||
\(926\) | −35.5582 | −1.16852 | ||||||||
\(927\) | 5.67910 | 0.186526 | ||||||||
\(928\) | −97.3798 | −3.19665 | ||||||||
\(929\) | −36.8448 | −1.20884 | −0.604419 | − | 0.796666i | \(-0.706595\pi\) | ||||
−0.604419 | + | 0.796666i | \(0.706595\pi\) | |||||||
\(930\) | −45.7433 | −1.49998 | ||||||||
\(931\) | −9.16251 | −0.300289 | ||||||||
\(932\) | 16.8750 | 0.552760 | ||||||||
\(933\) | −58.7676 | −1.92396 | ||||||||
\(934\) | −45.9609 | −1.50389 | ||||||||
\(935\) | −11.6476 | −0.380918 | ||||||||
\(936\) | −0.964451 | −0.0315241 | ||||||||
\(937\) | 17.0304 | 0.556357 | 0.278179 | − | 0.960529i | \(-0.410269\pi\) | ||||
0.278179 | + | 0.960529i | \(0.410269\pi\) | |||||||
\(938\) | −61.8490 | −2.01944 | ||||||||
\(939\) | 25.7380 | 0.839929 | ||||||||
\(940\) | −61.9134 | −2.01939 | ||||||||
\(941\) | −3.02953 | −0.0987598 | −0.0493799 | − | 0.998780i | \(-0.515725\pi\) | ||||
−0.0493799 | + | 0.998780i | \(0.515725\pi\) | |||||||
\(942\) | −60.0074 | −1.95515 | ||||||||
\(943\) | 27.5502 | 0.897158 | ||||||||
\(944\) | −96.2079 | −3.13130 | ||||||||
\(945\) | −31.7026 | −1.03129 | ||||||||
\(946\) | −117.471 | −3.81931 | ||||||||
\(947\) | 57.9829 | 1.88419 | 0.942096 | − | 0.335345i | \(-0.108853\pi\) | ||||
0.942096 | + | 0.335345i | \(0.108853\pi\) | |||||||
\(948\) | 157.577 | 5.11787 | ||||||||
\(949\) | −0.740249 | −0.0240295 | ||||||||
\(950\) | 18.4448 | 0.598429 | ||||||||
\(951\) | −21.4369 | −0.695139 | ||||||||
\(952\) | −27.0863 | −0.877870 | ||||||||
\(953\) | −7.37054 | −0.238755 | −0.119378 | − | 0.992849i | \(-0.538090\pi\) | ||||
−0.119378 | + | 0.992849i | \(0.538090\pi\) | |||||||
\(954\) | 14.3300 | 0.463951 | ||||||||
\(955\) | 44.8831 | 1.45238 | ||||||||
\(956\) | −135.377 | −4.37841 | ||||||||
\(957\) | −49.7294 | −1.60752 | ||||||||
\(958\) | −79.0372 | −2.55357 | ||||||||
\(959\) | 3.08983 | 0.0997759 | ||||||||
\(960\) | 83.0291 | 2.67975 | ||||||||
\(961\) | −17.2671 | −0.557002 | ||||||||
\(962\) | −4.07470 | −0.131374 | ||||||||
\(963\) | −3.46973 | −0.111811 | ||||||||
\(964\) | 9.04808 | 0.291419 | ||||||||
\(965\) | 13.0360 | 0.419645 | ||||||||
\(966\) | −109.726 | −3.53039 | ||||||||
\(967\) | 14.7334 | 0.473793 | 0.236897 | − | 0.971535i | \(-0.423870\pi\) | ||||
0.236897 | + | 0.971535i | \(0.423870\pi\) | |||||||
\(968\) | −61.1980 | −1.96698 | ||||||||
\(969\) | 16.0867 | 0.516780 | ||||||||
\(970\) | 36.1986 | 1.16227 | ||||||||
\(971\) | −2.43397 | −0.0781097 | −0.0390548 | − | 0.999237i | \(-0.512435\pi\) | ||||
−0.0390548 | + | 0.999237i | \(0.512435\pi\) | |||||||
\(972\) | 31.8328 | 1.02104 | ||||||||
\(973\) | 51.2190 | 1.64201 | ||||||||
\(974\) | 60.1966 | 1.92882 | ||||||||
\(975\) | −0.328467 | −0.0105194 | ||||||||
\(976\) | 39.2710 | 1.25703 | ||||||||
\(977\) | −35.0855 | −1.12248 | −0.561242 | − | 0.827651i | \(-0.689676\pi\) | ||||
−0.561242 | + | 0.827651i | \(0.689676\pi\) | |||||||
\(978\) | −123.933 | −3.96295 | ||||||||
\(979\) | −64.1908 | −2.05155 | ||||||||
\(980\) | −15.1849 | −0.485065 | ||||||||
\(981\) | −3.58285 | −0.114392 | ||||||||
\(982\) | 68.3213 | 2.18022 | ||||||||
\(983\) | 39.0926 | 1.24686 | 0.623431 | − | 0.781879i | \(-0.285738\pi\) | ||||
0.623431 | + | 0.781879i | \(0.285738\pi\) | |||||||
\(984\) | −58.4572 | −1.86355 | ||||||||
\(985\) | −59.0431 | −1.88127 | ||||||||
\(986\) | −18.3825 | −0.585417 | ||||||||
\(987\) | −26.8809 | −0.855628 | ||||||||
\(988\) | −7.38829 | −0.235053 | ||||||||
\(989\) | −77.5331 | −2.46541 | ||||||||
\(990\) | 16.7575 | 0.532587 | ||||||||
\(991\) | −6.90753 | −0.219425 | −0.109712 | − | 0.993963i | \(-0.534993\pi\) | ||||
−0.109712 | + | 0.993963i | \(0.534993\pi\) | |||||||
\(992\) | −58.8580 | −1.86874 | ||||||||
\(993\) | −2.28977 | −0.0726635 | ||||||||
\(994\) | −12.5126 | −0.396876 | ||||||||
\(995\) | −55.5415 | −1.76078 | ||||||||
\(996\) | 78.1325 | 2.47572 | ||||||||
\(997\) | 34.3234 | 1.08703 | 0.543517 | − | 0.839398i | \(-0.317092\pi\) | ||||
0.543517 | + | 0.839398i | \(0.317092\pi\) | |||||||
\(998\) | 72.2689 | 2.28763 | ||||||||
\(999\) | 36.5460 | 1.15626 |
(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 | 8011.2.a.a.1.10 | ✓ | 309 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.a.1.10 | ✓ | 309 | 1.1 | even | 1 | trivial |