Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, 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("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.738482 | 0.522186 | 0.261093 | − | 0.965314i | \(-0.415917\pi\) | ||||
0.261093 | + | 0.965314i | \(0.415917\pi\) | |||||||
\(3\) | 2.27911 | 1.31585 | 0.657923 | − | 0.753085i | \(-0.271435\pi\) | ||||
0.657923 | + | 0.753085i | \(0.271435\pi\) | |||||||
\(4\) | −1.45464 | −0.727322 | ||||||||
\(5\) | 3.79116 | 1.69546 | 0.847729 | − | 0.530430i | \(-0.177970\pi\) | ||||
0.847729 | + | 0.530430i | \(0.177970\pi\) | |||||||
\(6\) | 1.68308 | 0.687116 | ||||||||
\(7\) | 4.03115 | 1.52363 | 0.761815 | − | 0.647794i | \(-0.224308\pi\) | ||||
0.761815 | + | 0.647794i | \(0.224308\pi\) | |||||||
\(8\) | −2.55119 | −0.901983 | ||||||||
\(9\) | 2.19436 | 0.731452 | ||||||||
\(10\) | 2.79970 | 0.885343 | ||||||||
\(11\) | −4.62241 | −1.39371 | −0.696855 | − | 0.717212i | \(-0.745418\pi\) | ||||
−0.696855 | + | 0.717212i | \(0.745418\pi\) | |||||||
\(12\) | −3.31530 | −0.957044 | ||||||||
\(13\) | −3.86363 | −1.07158 | −0.535788 | − | 0.844352i | \(-0.679986\pi\) | ||||
−0.535788 | + | 0.844352i | \(0.679986\pi\) | |||||||
\(14\) | 2.97693 | 0.795618 | ||||||||
\(15\) | 8.64048 | 2.23096 | ||||||||
\(16\) | 1.02528 | 0.256320 | ||||||||
\(17\) | 1.73504 | 0.420810 | 0.210405 | − | 0.977614i | \(-0.432522\pi\) | ||||
0.210405 | + | 0.977614i | \(0.432522\pi\) | |||||||
\(18\) | 1.62049 | 0.381954 | ||||||||
\(19\) | −4.30211 | −0.986971 | −0.493485 | − | 0.869754i | \(-0.664277\pi\) | ||||
−0.493485 | + | 0.869754i | \(0.664277\pi\) | |||||||
\(20\) | −5.51479 | −1.23314 | ||||||||
\(21\) | 9.18744 | 2.00486 | ||||||||
\(22\) | −3.41357 | −0.727775 | ||||||||
\(23\) | −7.16718 | −1.49446 | −0.747230 | − | 0.664566i | \(-0.768617\pi\) | ||||
−0.747230 | + | 0.664566i | \(0.768617\pi\) | |||||||
\(24\) | −5.81446 | −1.18687 | ||||||||
\(25\) | 9.37288 | 1.87458 | ||||||||
\(26\) | −2.85322 | −0.559562 | ||||||||
\(27\) | −1.83615 | −0.353368 | ||||||||
\(28\) | −5.86389 | −1.10817 | ||||||||
\(29\) | −3.40299 | −0.631919 | −0.315960 | − | 0.948773i | \(-0.602326\pi\) | ||||
−0.315960 | + | 0.948773i | \(0.602326\pi\) | |||||||
\(30\) | 6.38084 | 1.16498 | ||||||||
\(31\) | 1.29624 | 0.232812 | 0.116406 | − | 0.993202i | \(-0.462863\pi\) | ||||
0.116406 | + | 0.993202i | \(0.462863\pi\) | |||||||
\(32\) | 5.85954 | 1.03583 | ||||||||
\(33\) | −10.5350 | −1.83391 | ||||||||
\(34\) | 1.28130 | 0.219741 | ||||||||
\(35\) | 15.2827 | 2.58325 | ||||||||
\(36\) | −3.19201 | −0.532002 | ||||||||
\(37\) | 11.4689 | 1.88548 | 0.942738 | − | 0.333535i | \(-0.108242\pi\) | ||||
0.942738 | + | 0.333535i | \(0.108242\pi\) | |||||||
\(38\) | −3.17703 | −0.515382 | ||||||||
\(39\) | −8.80564 | −1.41003 | ||||||||
\(40\) | −9.67197 | −1.52927 | ||||||||
\(41\) | −6.76299 | −1.05620 | −0.528101 | − | 0.849182i | \(-0.677096\pi\) | ||||
−0.528101 | + | 0.849182i | \(0.677096\pi\) | |||||||
\(42\) | 6.78476 | 1.04691 | ||||||||
\(43\) | 1.28015 | 0.195221 | 0.0976104 | − | 0.995225i | \(-0.468880\pi\) | ||||
0.0976104 | + | 0.995225i | \(0.468880\pi\) | |||||||
\(44\) | 6.72397 | 1.01368 | ||||||||
\(45\) | 8.31915 | 1.24015 | ||||||||
\(46\) | −5.29283 | −0.780385 | ||||||||
\(47\) | 8.34021 | 1.21654 | 0.608272 | − | 0.793728i | \(-0.291863\pi\) | ||||
0.608272 | + | 0.793728i | \(0.291863\pi\) | |||||||
\(48\) | 2.33673 | 0.337278 | ||||||||
\(49\) | 9.25015 | 1.32145 | ||||||||
\(50\) | 6.92170 | 0.978876 | ||||||||
\(51\) | 3.95436 | 0.553722 | ||||||||
\(52\) | 5.62020 | 0.779382 | ||||||||
\(53\) | 9.55893 | 1.31302 | 0.656510 | − | 0.754317i | \(-0.272032\pi\) | ||||
0.656510 | + | 0.754317i | \(0.272032\pi\) | |||||||
\(54\) | −1.35596 | −0.184523 | ||||||||
\(55\) | −17.5243 | −2.36298 | ||||||||
\(56\) | −10.2842 | −1.37429 | ||||||||
\(57\) | −9.80499 | −1.29870 | ||||||||
\(58\) | −2.51305 | −0.329979 | ||||||||
\(59\) | 3.24630 | 0.422632 | 0.211316 | − | 0.977418i | \(-0.432225\pi\) | ||||
0.211316 | + | 0.977418i | \(0.432225\pi\) | |||||||
\(60\) | −12.5688 | −1.62263 | ||||||||
\(61\) | −12.3562 | −1.58205 | −0.791025 | − | 0.611784i | \(-0.790452\pi\) | ||||
−0.791025 | + | 0.611784i | \(0.790452\pi\) | |||||||
\(62\) | 0.957253 | 0.121571 | ||||||||
\(63\) | 8.84578 | 1.11446 | ||||||||
\(64\) | 2.27660 | 0.284575 | ||||||||
\(65\) | −14.6476 | −1.81681 | ||||||||
\(66\) | −7.77991 | −0.957641 | ||||||||
\(67\) | −12.1005 | −1.47832 | −0.739158 | − | 0.673532i | \(-0.764777\pi\) | ||||
−0.739158 | + | 0.673532i | \(0.764777\pi\) | |||||||
\(68\) | −2.52387 | −0.306065 | ||||||||
\(69\) | −16.3348 | −1.96648 | ||||||||
\(70\) | 11.2860 | 1.34894 | ||||||||
\(71\) | 7.17544 | 0.851568 | 0.425784 | − | 0.904825i | \(-0.359998\pi\) | ||||
0.425784 | + | 0.904825i | \(0.359998\pi\) | |||||||
\(72\) | −5.59823 | −0.659757 | ||||||||
\(73\) | 4.96822 | 0.581486 | 0.290743 | − | 0.956801i | \(-0.406098\pi\) | ||||
0.290743 | + | 0.956801i | \(0.406098\pi\) | |||||||
\(74\) | 8.46958 | 0.984568 | ||||||||
\(75\) | 21.3619 | 2.46665 | ||||||||
\(76\) | 6.25804 | 0.717846 | ||||||||
\(77\) | −18.6336 | −2.12350 | ||||||||
\(78\) | −6.50281 | −0.736298 | ||||||||
\(79\) | 10.6927 | 1.20303 | 0.601514 | − | 0.798862i | \(-0.294564\pi\) | ||||
0.601514 | + | 0.798862i | \(0.294564\pi\) | |||||||
\(80\) | 3.88700 | 0.434579 | ||||||||
\(81\) | −10.7679 | −1.19643 | ||||||||
\(82\) | −4.99435 | −0.551533 | ||||||||
\(83\) | −5.83442 | −0.640411 | −0.320206 | − | 0.947348i | \(-0.603752\pi\) | ||||
−0.320206 | + | 0.947348i | \(0.603752\pi\) | |||||||
\(84\) | −13.3645 | −1.45818 | ||||||||
\(85\) | 6.57783 | 0.713466 | ||||||||
\(86\) | 0.945366 | 0.101941 | ||||||||
\(87\) | −7.75580 | −0.831509 | ||||||||
\(88\) | 11.7927 | 1.25710 | ||||||||
\(89\) | 6.64931 | 0.704826 | 0.352413 | − | 0.935845i | \(-0.385361\pi\) | ||||
0.352413 | + | 0.935845i | \(0.385361\pi\) | |||||||
\(90\) | 6.14354 | 0.647586 | ||||||||
\(91\) | −15.5748 | −1.63269 | ||||||||
\(92\) | 10.4257 | 1.08695 | ||||||||
\(93\) | 2.95429 | 0.306345 | ||||||||
\(94\) | 6.15909 | 0.635262 | ||||||||
\(95\) | −16.3100 | −1.67337 | ||||||||
\(96\) | 13.3545 | 1.36299 | ||||||||
\(97\) | −10.1113 | −1.02665 | −0.513323 | − | 0.858195i | \(-0.671586\pi\) | ||||
−0.513323 | + | 0.858195i | \(0.671586\pi\) | |||||||
\(98\) | 6.83107 | 0.690042 | ||||||||
\(99\) | −10.1432 | −1.01943 | ||||||||
\(100\) | −13.6342 | −1.36342 | ||||||||
\(101\) | 5.70553 | 0.567721 | 0.283861 | − | 0.958866i | \(-0.408385\pi\) | ||||
0.283861 | + | 0.958866i | \(0.408385\pi\) | |||||||
\(102\) | 2.92023 | 0.289145 | ||||||||
\(103\) | 9.24132 | 0.910575 | 0.455287 | − | 0.890345i | \(-0.349537\pi\) | ||||
0.455287 | + | 0.890345i | \(0.349537\pi\) | |||||||
\(104\) | 9.85685 | 0.966544 | ||||||||
\(105\) | 34.8310 | 3.39916 | ||||||||
\(106\) | 7.05910 | 0.685640 | ||||||||
\(107\) | −15.0186 | −1.45190 | −0.725951 | − | 0.687746i | \(-0.758600\pi\) | ||||
−0.725951 | + | 0.687746i | \(0.758600\pi\) | |||||||
\(108\) | 2.67095 | 0.257012 | ||||||||
\(109\) | −2.99448 | −0.286819 | −0.143409 | − | 0.989663i | \(-0.545807\pi\) | ||||
−0.143409 | + | 0.989663i | \(0.545807\pi\) | |||||||
\(110\) | −12.9414 | −1.23391 | ||||||||
\(111\) | 26.1389 | 2.48100 | ||||||||
\(112\) | 4.13305 | 0.390537 | ||||||||
\(113\) | −2.05064 | −0.192908 | −0.0964539 | − | 0.995337i | \(-0.530750\pi\) | ||||
−0.0964539 | + | 0.995337i | \(0.530750\pi\) | |||||||
\(114\) | −7.24081 | −0.678164 | ||||||||
\(115\) | −27.1719 | −2.53379 | ||||||||
\(116\) | 4.95014 | 0.459609 | ||||||||
\(117\) | −8.47817 | −0.783807 | ||||||||
\(118\) | 2.39733 | 0.220692 | ||||||||
\(119\) | 6.99422 | 0.641159 | ||||||||
\(120\) | −22.0435 | −2.01229 | ||||||||
\(121\) | 10.3667 | 0.942427 | ||||||||
\(122\) | −9.12483 | −0.826124 | ||||||||
\(123\) | −15.4136 | −1.38980 | ||||||||
\(124\) | −1.88558 | −0.169330 | ||||||||
\(125\) | 16.5783 | 1.48281 | ||||||||
\(126\) | 6.53245 | 0.581957 | ||||||||
\(127\) | −2.63530 | −0.233845 | −0.116923 | − | 0.993141i | \(-0.537303\pi\) | ||||
−0.116923 | + | 0.993141i | \(0.537303\pi\) | |||||||
\(128\) | −10.0378 | −0.887228 | ||||||||
\(129\) | 2.91760 | 0.256881 | ||||||||
\(130\) | −10.8170 | −0.948713 | ||||||||
\(131\) | −9.66184 | −0.844159 | −0.422080 | − | 0.906559i | \(-0.638700\pi\) | ||||
−0.422080 | + | 0.906559i | \(0.638700\pi\) | |||||||
\(132\) | 15.3247 | 1.33384 | ||||||||
\(133\) | −17.3424 | −1.50378 | ||||||||
\(134\) | −8.93603 | −0.771956 | ||||||||
\(135\) | −6.96114 | −0.599120 | ||||||||
\(136\) | −4.42643 | −0.379564 | ||||||||
\(137\) | 3.82672 | 0.326939 | 0.163469 | − | 0.986548i | \(-0.447732\pi\) | ||||
0.163469 | + | 0.986548i | \(0.447732\pi\) | |||||||
\(138\) | −12.0630 | −1.02687 | ||||||||
\(139\) | 12.8713 | 1.09173 | 0.545863 | − | 0.837875i | \(-0.316202\pi\) | ||||
0.545863 | + | 0.837875i | \(0.316202\pi\) | |||||||
\(140\) | −22.2309 | −1.87886 | ||||||||
\(141\) | 19.0083 | 1.60079 | ||||||||
\(142\) | 5.29893 | 0.444677 | ||||||||
\(143\) | 17.8593 | 1.49347 | ||||||||
\(144\) | 2.24983 | 0.187486 | ||||||||
\(145\) | −12.9013 | −1.07139 | ||||||||
\(146\) | 3.66894 | 0.303644 | ||||||||
\(147\) | 21.0821 | 1.73883 | ||||||||
\(148\) | −16.6832 | −1.37135 | ||||||||
\(149\) | 15.0108 | 1.22973 | 0.614867 | − | 0.788631i | \(-0.289210\pi\) | ||||
0.614867 | + | 0.788631i | \(0.289210\pi\) | |||||||
\(150\) | 15.7753 | 1.28805 | ||||||||
\(151\) | 7.14463 | 0.581422 | 0.290711 | − | 0.956811i | \(-0.406108\pi\) | ||||
0.290711 | + | 0.956811i | \(0.406108\pi\) | |||||||
\(152\) | 10.9755 | 0.890231 | ||||||||
\(153\) | 3.80731 | 0.307803 | ||||||||
\(154\) | −13.7606 | −1.10886 | ||||||||
\(155\) | 4.91427 | 0.394724 | ||||||||
\(156\) | 12.8091 | 1.02555 | ||||||||
\(157\) | −3.67900 | −0.293616 | −0.146808 | − | 0.989165i | \(-0.546900\pi\) | ||||
−0.146808 | + | 0.989165i | \(0.546900\pi\) | |||||||
\(158\) | 7.89640 | 0.628204 | ||||||||
\(159\) | 21.7859 | 1.72773 | ||||||||
\(160\) | 22.2144 | 1.75620 | ||||||||
\(161\) | −28.8920 | −2.27700 | ||||||||
\(162\) | −7.95188 | −0.624758 | ||||||||
\(163\) | −6.36798 | −0.498779 | −0.249389 | − | 0.968403i | \(-0.580230\pi\) | ||||
−0.249389 | + | 0.968403i | \(0.580230\pi\) | |||||||
\(164\) | 9.83775 | 0.768199 | ||||||||
\(165\) | −39.9399 | −3.10931 | ||||||||
\(166\) | −4.30862 | −0.334413 | ||||||||
\(167\) | −1.87848 | −0.145361 | −0.0726804 | − | 0.997355i | \(-0.523155\pi\) | ||||
−0.0726804 | + | 0.997355i | \(0.523155\pi\) | |||||||
\(168\) | −23.4389 | −1.80835 | ||||||||
\(169\) | 1.92760 | 0.148277 | ||||||||
\(170\) | 4.85761 | 0.372562 | ||||||||
\(171\) | −9.44036 | −0.721922 | ||||||||
\(172\) | −1.86216 | −0.141988 | ||||||||
\(173\) | −10.0104 | −0.761080 | −0.380540 | − | 0.924764i | \(-0.624262\pi\) | ||||
−0.380540 | + | 0.924764i | \(0.624262\pi\) | |||||||
\(174\) | −5.72752 | −0.434202 | ||||||||
\(175\) | 37.7835 | 2.85616 | ||||||||
\(176\) | −4.73926 | −0.357235 | ||||||||
\(177\) | 7.39868 | 0.556118 | ||||||||
\(178\) | 4.91040 | 0.368050 | ||||||||
\(179\) | −9.09399 | −0.679717 | −0.339858 | − | 0.940477i | \(-0.610379\pi\) | ||||
−0.339858 | + | 0.940477i | \(0.610379\pi\) | |||||||
\(180\) | −12.1014 | −0.901986 | ||||||||
\(181\) | 24.7002 | 1.83595 | 0.917976 | − | 0.396635i | \(-0.129822\pi\) | ||||
0.917976 | + | 0.396635i | \(0.129822\pi\) | |||||||
\(182\) | −11.5017 | −0.852566 | ||||||||
\(183\) | −28.1612 | −2.08173 | ||||||||
\(184\) | 18.2848 | 1.34798 | ||||||||
\(185\) | 43.4804 | 3.19674 | ||||||||
\(186\) | 2.18169 | 0.159969 | ||||||||
\(187\) | −8.02009 | −0.586487 | ||||||||
\(188\) | −12.1320 | −0.884820 | ||||||||
\(189\) | −7.40180 | −0.538402 | ||||||||
\(190\) | −12.0446 | −0.873808 | ||||||||
\(191\) | −13.2841 | −0.961204 | −0.480602 | − | 0.876939i | \(-0.659582\pi\) | ||||
−0.480602 | + | 0.876939i | \(0.659582\pi\) | |||||||
\(192\) | 5.18864 | 0.374457 | ||||||||
\(193\) | 26.6666 | 1.91950 | 0.959750 | − | 0.280855i | \(-0.0906180\pi\) | ||||
0.959750 | + | 0.280855i | \(0.0906180\pi\) | |||||||
\(194\) | −7.46701 | −0.536100 | ||||||||
\(195\) | −33.3836 | −2.39065 | ||||||||
\(196\) | −13.4557 | −0.961120 | ||||||||
\(197\) | 3.65462 | 0.260381 | 0.130190 | − | 0.991489i | \(-0.458441\pi\) | ||||
0.130190 | + | 0.991489i | \(0.458441\pi\) | |||||||
\(198\) | −7.49059 | −0.532333 | ||||||||
\(199\) | 18.6263 | 1.32038 | 0.660191 | − | 0.751098i | \(-0.270475\pi\) | ||||
0.660191 | + | 0.751098i | \(0.270475\pi\) | |||||||
\(200\) | −23.9120 | −1.69083 | ||||||||
\(201\) | −27.5785 | −1.94524 | ||||||||
\(202\) | 4.21343 | 0.296456 | ||||||||
\(203\) | −13.7180 | −0.962811 | ||||||||
\(204\) | −5.75219 | −0.402734 | ||||||||
\(205\) | −25.6396 | −1.79074 | ||||||||
\(206\) | 6.82455 | 0.475489 | ||||||||
\(207\) | −15.7273 | −1.09313 | ||||||||
\(208\) | −3.96129 | −0.274666 | ||||||||
\(209\) | 19.8861 | 1.37555 | ||||||||
\(210\) | 25.7221 | 1.77499 | ||||||||
\(211\) | −3.17606 | −0.218649 | −0.109325 | − | 0.994006i | \(-0.534869\pi\) | ||||
−0.109325 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(212\) | −13.9048 | −0.954989 | ||||||||
\(213\) | 16.3536 | 1.12053 | ||||||||
\(214\) | −11.0910 | −0.758162 | ||||||||
\(215\) | 4.85324 | 0.330988 | ||||||||
\(216\) | 4.68438 | 0.318731 | ||||||||
\(217\) | 5.22535 | 0.354720 | ||||||||
\(218\) | −2.21137 | −0.149773 | ||||||||
\(219\) | 11.3231 | 0.765146 | ||||||||
\(220\) | 25.4916 | 1.71864 | ||||||||
\(221\) | −6.70356 | −0.450930 | ||||||||
\(222\) | 19.3031 | 1.29554 | ||||||||
\(223\) | −12.4850 | −0.836059 | −0.418030 | − | 0.908433i | \(-0.637279\pi\) | ||||
−0.418030 | + | 0.908433i | \(0.637279\pi\) | |||||||
\(224\) | 23.6207 | 1.57822 | ||||||||
\(225\) | 20.5674 | 1.37116 | ||||||||
\(226\) | −1.51436 | −0.100734 | ||||||||
\(227\) | −16.1748 | −1.07356 | −0.536778 | − | 0.843723i | \(-0.680359\pi\) | ||||
−0.536778 | + | 0.843723i | \(0.680359\pi\) | |||||||
\(228\) | 14.2628 | 0.944575 | ||||||||
\(229\) | −22.6012 | −1.49353 | −0.746765 | − | 0.665088i | \(-0.768394\pi\) | ||||
−0.746765 | + | 0.665088i | \(0.768394\pi\) | |||||||
\(230\) | −20.0660 | −1.32311 | ||||||||
\(231\) | −42.4682 | −2.79420 | ||||||||
\(232\) | 8.68168 | 0.569980 | ||||||||
\(233\) | −3.70258 | −0.242564 | −0.121282 | − | 0.992618i | \(-0.538701\pi\) | ||||
−0.121282 | + | 0.992618i | \(0.538701\pi\) | |||||||
\(234\) | −6.26098 | −0.409293 | ||||||||
\(235\) | 31.6191 | 2.06260 | ||||||||
\(236\) | −4.72221 | −0.307389 | ||||||||
\(237\) | 24.3700 | 1.58300 | ||||||||
\(238\) | 5.16511 | 0.334804 | ||||||||
\(239\) | 5.99222 | 0.387604 | 0.193802 | − | 0.981041i | \(-0.437918\pi\) | ||||
0.193802 | + | 0.981041i | \(0.437918\pi\) | |||||||
\(240\) | 8.85890 | 0.571840 | ||||||||
\(241\) | 19.9256 | 1.28352 | 0.641760 | − | 0.766905i | \(-0.278204\pi\) | ||||
0.641760 | + | 0.766905i | \(0.278204\pi\) | |||||||
\(242\) | 7.65562 | 0.492122 | ||||||||
\(243\) | −19.0327 | −1.22095 | ||||||||
\(244\) | 17.9739 | 1.15066 | ||||||||
\(245\) | 35.0688 | 2.24046 | ||||||||
\(246\) | −11.3827 | −0.725733 | ||||||||
\(247\) | 16.6217 | 1.05762 | ||||||||
\(248\) | −3.30697 | −0.209993 | ||||||||
\(249\) | −13.2973 | −0.842683 | ||||||||
\(250\) | 12.2428 | 0.774300 | ||||||||
\(251\) | 5.43776 | 0.343228 | 0.171614 | − | 0.985164i | \(-0.445102\pi\) | ||||
0.171614 | + | 0.985164i | \(0.445102\pi\) | |||||||
\(252\) | −12.8675 | −0.810574 | ||||||||
\(253\) | 33.1297 | 2.08284 | ||||||||
\(254\) | −1.94612 | −0.122111 | ||||||||
\(255\) | 14.9916 | 0.938811 | ||||||||
\(256\) | −11.9660 | −0.747873 | ||||||||
\(257\) | 16.9275 | 1.05591 | 0.527954 | − | 0.849273i | \(-0.322959\pi\) | ||||
0.527954 | + | 0.849273i | \(0.322959\pi\) | |||||||
\(258\) | 2.15460 | 0.134139 | ||||||||
\(259\) | 46.2328 | 2.87277 | ||||||||
\(260\) | 21.3071 | 1.32141 | ||||||||
\(261\) | −7.46737 | −0.462219 | ||||||||
\(262\) | −7.13510 | −0.440808 | ||||||||
\(263\) | −14.2305 | −0.877489 | −0.438744 | − | 0.898612i | \(-0.644577\pi\) | ||||
−0.438744 | + | 0.898612i | \(0.644577\pi\) | |||||||
\(264\) | 26.8768 | 1.65415 | ||||||||
\(265\) | 36.2394 | 2.22617 | ||||||||
\(266\) | −12.8071 | −0.785252 | ||||||||
\(267\) | 15.1545 | 0.927443 | ||||||||
\(268\) | 17.6020 | 1.07521 | ||||||||
\(269\) | 4.78021 | 0.291455 | 0.145727 | − | 0.989325i | \(-0.453448\pi\) | ||||
0.145727 | + | 0.989325i | \(0.453448\pi\) | |||||||
\(270\) | −5.14068 | −0.312852 | ||||||||
\(271\) | 22.8296 | 1.38680 | 0.693399 | − | 0.720554i | \(-0.256112\pi\) | ||||
0.693399 | + | 0.720554i | \(0.256112\pi\) | |||||||
\(272\) | 1.77891 | 0.107862 | ||||||||
\(273\) | −35.4968 | −2.14837 | ||||||||
\(274\) | 2.82596 | 0.170723 | ||||||||
\(275\) | −43.3253 | −2.61261 | ||||||||
\(276\) | 23.7613 | 1.43026 | ||||||||
\(277\) | 2.84440 | 0.170903 | 0.0854516 | − | 0.996342i | \(-0.472767\pi\) | ||||
0.0854516 | + | 0.996342i | \(0.472767\pi\) | |||||||
\(278\) | 9.50519 | 0.570083 | ||||||||
\(279\) | 2.84442 | 0.170291 | ||||||||
\(280\) | −38.9892 | −2.33005 | ||||||||
\(281\) | −8.70598 | −0.519356 | −0.259678 | − | 0.965695i | \(-0.583616\pi\) | ||||
−0.259678 | + | 0.965695i | \(0.583616\pi\) | |||||||
\(282\) | 14.0373 | 0.835907 | ||||||||
\(283\) | 28.5870 | 1.69932 | 0.849659 | − | 0.527333i | \(-0.176808\pi\) | ||||
0.849659 | + | 0.527333i | \(0.176808\pi\) | |||||||
\(284\) | −10.4377 | −0.619364 | ||||||||
\(285\) | −37.1723 | −2.20189 | ||||||||
\(286\) | 13.1887 | 0.779867 | ||||||||
\(287\) | −27.2626 | −1.60926 | ||||||||
\(288\) | 12.8579 | 0.757660 | ||||||||
\(289\) | −13.9896 | −0.822919 | ||||||||
\(290\) | −9.52735 | −0.559465 | ||||||||
\(291\) | −23.0448 | −1.35091 | ||||||||
\(292\) | −7.22699 | −0.422928 | ||||||||
\(293\) | −7.13843 | −0.417032 | −0.208516 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208516 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(294\) | 15.5688 | 0.907990 | ||||||||
\(295\) | 12.3072 | 0.716554 | ||||||||
\(296\) | −29.2594 | −1.70067 | ||||||||
\(297\) | 8.48745 | 0.492492 | ||||||||
\(298\) | 11.0852 | 0.642149 | ||||||||
\(299\) | 27.6913 | 1.60143 | ||||||||
\(300\) | −31.0739 | −1.79405 | ||||||||
\(301\) | 5.16047 | 0.297444 | ||||||||
\(302\) | 5.27618 | 0.303610 | ||||||||
\(303\) | 13.0035 | 0.747034 | ||||||||
\(304\) | −4.41086 | −0.252980 | ||||||||
\(305\) | −46.8443 | −2.68230 | ||||||||
\(306\) | 2.81163 | 0.160730 | ||||||||
\(307\) | 4.76214 | 0.271790 | 0.135895 | − | 0.990723i | \(-0.456609\pi\) | ||||
0.135895 | + | 0.990723i | \(0.456609\pi\) | |||||||
\(308\) | 27.1053 | 1.54447 | ||||||||
\(309\) | 21.0620 | 1.19818 | ||||||||
\(310\) | 3.62910 | 0.206119 | ||||||||
\(311\) | −29.6663 | −1.68222 | −0.841111 | − | 0.540862i | \(-0.818098\pi\) | ||||
−0.841111 | + | 0.540862i | \(0.818098\pi\) | |||||||
\(312\) | 22.4649 | 1.27182 | ||||||||
\(313\) | 3.14569 | 0.177805 | 0.0889025 | − | 0.996040i | \(-0.471664\pi\) | ||||
0.0889025 | + | 0.996040i | \(0.471664\pi\) | |||||||
\(314\) | −2.71687 | −0.153322 | ||||||||
\(315\) | 33.5357 | 1.88952 | ||||||||
\(316\) | −15.5541 | −0.874989 | ||||||||
\(317\) | −4.87154 | −0.273613 | −0.136806 | − | 0.990598i | \(-0.543684\pi\) | ||||
−0.136806 | + | 0.990598i | \(0.543684\pi\) | |||||||
\(318\) | 16.0885 | 0.902197 | ||||||||
\(319\) | 15.7300 | 0.880712 | ||||||||
\(320\) | 8.63096 | 0.482485 | ||||||||
\(321\) | −34.2291 | −1.91048 | ||||||||
\(322\) | −21.3362 | −1.18902 | ||||||||
\(323\) | −7.46435 | −0.415327 | ||||||||
\(324\) | 15.6634 | 0.870190 | ||||||||
\(325\) | −36.2133 | −2.00875 | ||||||||
\(326\) | −4.70264 | −0.260455 | ||||||||
\(327\) | −6.82475 | −0.377410 | ||||||||
\(328\) | 17.2537 | 0.952676 | ||||||||
\(329\) | 33.6206 | 1.85356 | ||||||||
\(330\) | −29.4949 | −1.62364 | ||||||||
\(331\) | 19.7091 | 1.08331 | 0.541655 | − | 0.840601i | \(-0.317798\pi\) | ||||
0.541655 | + | 0.840601i | \(0.317798\pi\) | |||||||
\(332\) | 8.48701 | 0.465785 | ||||||||
\(333\) | 25.1669 | 1.37914 | ||||||||
\(334\) | −1.38722 | −0.0759053 | ||||||||
\(335\) | −45.8751 | −2.50642 | ||||||||
\(336\) | 9.41969 | 0.513886 | ||||||||
\(337\) | 6.18352 | 0.336838 | 0.168419 | − | 0.985716i | \(-0.446134\pi\) | ||||
0.168419 | + | 0.985716i | \(0.446134\pi\) | |||||||
\(338\) | 1.42350 | 0.0774280 | ||||||||
\(339\) | −4.67364 | −0.253837 | ||||||||
\(340\) | −9.56840 | −0.518919 | ||||||||
\(341\) | −5.99178 | −0.324473 | ||||||||
\(342\) | −6.97153 | −0.376977 | ||||||||
\(343\) | 9.07070 | 0.489772 | ||||||||
\(344\) | −3.26590 | −0.176086 | ||||||||
\(345\) | −61.9278 | −3.33408 | ||||||||
\(346\) | −7.39253 | −0.397425 | ||||||||
\(347\) | −16.8542 | −0.904783 | −0.452392 | − | 0.891819i | \(-0.649429\pi\) | ||||
−0.452392 | + | 0.891819i | \(0.649429\pi\) | |||||||
\(348\) | 11.2819 | 0.604775 | ||||||||
\(349\) | 0.876469 | 0.0469163 | 0.0234581 | − | 0.999725i | \(-0.492532\pi\) | ||||
0.0234581 | + | 0.999725i | \(0.492532\pi\) | |||||||
\(350\) | 27.9024 | 1.49145 | ||||||||
\(351\) | 7.09420 | 0.378660 | ||||||||
\(352\) | −27.0852 | −1.44365 | ||||||||
\(353\) | −26.5298 | −1.41204 | −0.706020 | − | 0.708192i | \(-0.749511\pi\) | ||||
−0.706020 | + | 0.708192i | \(0.749511\pi\) | |||||||
\(354\) | 5.46379 | 0.290397 | ||||||||
\(355\) | 27.2032 | 1.44380 | ||||||||
\(356\) | −9.67239 | −0.512635 | ||||||||
\(357\) | 15.9406 | 0.843667 | ||||||||
\(358\) | −6.71575 | −0.354938 | ||||||||
\(359\) | 5.36111 | 0.282949 | 0.141474 | − | 0.989942i | \(-0.454816\pi\) | ||||
0.141474 | + | 0.989942i | \(0.454816\pi\) | |||||||
\(360\) | −21.2238 | −1.11859 | ||||||||
\(361\) | −0.491879 | −0.0258884 | ||||||||
\(362\) | 18.2407 | 0.958708 | ||||||||
\(363\) | 23.6269 | 1.24009 | ||||||||
\(364\) | 22.6559 | 1.18749 | ||||||||
\(365\) | 18.8353 | 0.985885 | ||||||||
\(366\) | −20.7965 | −1.08705 | ||||||||
\(367\) | 24.9627 | 1.30304 | 0.651520 | − | 0.758632i | \(-0.274132\pi\) | ||||
0.651520 | + | 0.758632i | \(0.274132\pi\) | |||||||
\(368\) | −7.34836 | −0.383060 | ||||||||
\(369\) | −14.8404 | −0.772561 | ||||||||
\(370\) | 32.1095 | 1.66929 | ||||||||
\(371\) | 38.5335 | 2.00056 | ||||||||
\(372\) | −4.29744 | −0.222812 | ||||||||
\(373\) | −15.0785 | −0.780734 | −0.390367 | − | 0.920659i | \(-0.627652\pi\) | ||||
−0.390367 | + | 0.920659i | \(0.627652\pi\) | |||||||
\(374\) | −5.92269 | −0.306255 | ||||||||
\(375\) | 37.7838 | 1.95114 | ||||||||
\(376\) | −21.2775 | −1.09730 | ||||||||
\(377\) | 13.1479 | 0.677150 | ||||||||
\(378\) | −5.46609 | −0.281146 | ||||||||
\(379\) | −14.0283 | −0.720587 | −0.360294 | − | 0.932839i | \(-0.617324\pi\) | ||||
−0.360294 | + | 0.932839i | \(0.617324\pi\) | |||||||
\(380\) | 23.7252 | 1.21708 | ||||||||
\(381\) | −6.00616 | −0.307705 | ||||||||
\(382\) | −9.81007 | −0.501927 | ||||||||
\(383\) | −13.2932 | −0.679253 | −0.339626 | − | 0.940560i | \(-0.610301\pi\) | ||||
−0.339626 | + | 0.940560i | \(0.610301\pi\) | |||||||
\(384\) | −22.8774 | −1.16746 | ||||||||
\(385\) | −70.6430 | −3.60030 | ||||||||
\(386\) | 19.6928 | 1.00234 | ||||||||
\(387\) | 2.80910 | 0.142795 | ||||||||
\(388\) | 14.7083 | 0.746703 | ||||||||
\(389\) | 24.9812 | 1.26660 | 0.633298 | − | 0.773908i | \(-0.281701\pi\) | ||||
0.633298 | + | 0.773908i | \(0.281701\pi\) | |||||||
\(390\) | −24.6532 | −1.24836 | ||||||||
\(391\) | −12.4354 | −0.628884 | ||||||||
\(392\) | −23.5989 | −1.19193 | ||||||||
\(393\) | −22.0204 | −1.11078 | ||||||||
\(394\) | 2.69887 | 0.135967 | ||||||||
\(395\) | 40.5379 | 2.03968 | ||||||||
\(396\) | 14.7548 | 0.741456 | ||||||||
\(397\) | −16.3754 | −0.821860 | −0.410930 | − | 0.911667i | \(-0.634796\pi\) | ||||
−0.410930 | + | 0.911667i | \(0.634796\pi\) | |||||||
\(398\) | 13.7552 | 0.689485 | ||||||||
\(399\) | −39.5254 | −1.97874 | ||||||||
\(400\) | 9.60982 | 0.480491 | ||||||||
\(401\) | 28.3698 | 1.41672 | 0.708360 | − | 0.705851i | \(-0.249435\pi\) | ||||
0.708360 | + | 0.705851i | \(0.249435\pi\) | |||||||
\(402\) | −20.3662 | −1.01578 | ||||||||
\(403\) | −5.00820 | −0.249476 | ||||||||
\(404\) | −8.29951 | −0.412916 | ||||||||
\(405\) | −40.8227 | −2.02850 | ||||||||
\(406\) | −10.1305 | −0.502766 | ||||||||
\(407\) | −53.0140 | −2.62781 | ||||||||
\(408\) | −10.0883 | −0.499447 | ||||||||
\(409\) | 25.0188 | 1.23710 | 0.618549 | − | 0.785746i | \(-0.287721\pi\) | ||||
0.618549 | + | 0.785746i | \(0.287721\pi\) | |||||||
\(410\) | −18.9344 | −0.935101 | ||||||||
\(411\) | 8.72152 | 0.430201 | ||||||||
\(412\) | −13.4428 | −0.662281 | ||||||||
\(413\) | 13.0863 | 0.643935 | ||||||||
\(414\) | −11.6144 | −0.570815 | ||||||||
\(415\) | −22.1192 | −1.08579 | ||||||||
\(416\) | −22.6390 | −1.10997 | ||||||||
\(417\) | 29.3350 | 1.43654 | ||||||||
\(418\) | 14.6855 | 0.718293 | ||||||||
\(419\) | 16.2484 | 0.793788 | 0.396894 | − | 0.917865i | \(-0.370088\pi\) | ||||
0.396894 | + | 0.917865i | \(0.370088\pi\) | |||||||
\(420\) | −50.6668 | −2.47229 | ||||||||
\(421\) | 27.6483 | 1.34750 | 0.673748 | − | 0.738961i | \(-0.264683\pi\) | ||||
0.673748 | + | 0.738961i | \(0.264683\pi\) | |||||||
\(422\) | −2.34547 | −0.114175 | ||||||||
\(423\) | 18.3014 | 0.889844 | ||||||||
\(424\) | −24.3867 | −1.18432 | ||||||||
\(425\) | 16.2624 | 0.788841 | ||||||||
\(426\) | 12.0769 | 0.585126 | ||||||||
\(427\) | −49.8097 | −2.41046 | ||||||||
\(428\) | 21.8467 | 1.05600 | ||||||||
\(429\) | 40.7033 | 1.96517 | ||||||||
\(430\) | 3.58403 | 0.172837 | ||||||||
\(431\) | −30.8322 | −1.48514 | −0.742568 | − | 0.669771i | \(-0.766392\pi\) | ||||
−0.742568 | + | 0.669771i | \(0.766392\pi\) | |||||||
\(432\) | −1.88257 | −0.0905751 | ||||||||
\(433\) | −20.9217 | −1.00543 | −0.502716 | − | 0.864452i | \(-0.667666\pi\) | ||||
−0.502716 | + | 0.864452i | \(0.667666\pi\) | |||||||
\(434\) | 3.85883 | 0.185230 | ||||||||
\(435\) | −29.4034 | −1.40979 | ||||||||
\(436\) | 4.35590 | 0.208610 | ||||||||
\(437\) | 30.8340 | 1.47499 | ||||||||
\(438\) | 8.36193 | 0.399548 | ||||||||
\(439\) | −34.0600 | −1.62560 | −0.812798 | − | 0.582546i | \(-0.802057\pi\) | ||||
−0.812798 | + | 0.582546i | \(0.802057\pi\) | |||||||
\(440\) | 44.7079 | 2.13136 | ||||||||
\(441\) | 20.2981 | 0.966578 | ||||||||
\(442\) | −4.95046 | −0.235469 | ||||||||
\(443\) | −28.7016 | −1.36366 | −0.681828 | − | 0.731513i | \(-0.738815\pi\) | ||||
−0.681828 | + | 0.731513i | \(0.738815\pi\) | |||||||
\(444\) | −38.0228 | −1.80448 | ||||||||
\(445\) | 25.2086 | 1.19500 | ||||||||
\(446\) | −9.21997 | −0.436578 | ||||||||
\(447\) | 34.2113 | 1.61814 | ||||||||
\(448\) | 9.17732 | 0.433588 | ||||||||
\(449\) | 35.9605 | 1.69708 | 0.848541 | − | 0.529130i | \(-0.177482\pi\) | ||||
0.848541 | + | 0.529130i | \(0.177482\pi\) | |||||||
\(450\) | 15.1887 | 0.716001 | ||||||||
\(451\) | 31.2613 | 1.47204 | ||||||||
\(452\) | 2.98295 | 0.140306 | ||||||||
\(453\) | 16.2834 | 0.765062 | ||||||||
\(454\) | −11.9448 | −0.560596 | ||||||||
\(455\) | −59.0467 | −2.76815 | ||||||||
\(456\) | 25.0144 | 1.17141 | ||||||||
\(457\) | 8.41951 | 0.393848 | 0.196924 | − | 0.980419i | \(-0.436905\pi\) | ||||
0.196924 | + | 0.980419i | \(0.436905\pi\) | |||||||
\(458\) | −16.6906 | −0.779900 | ||||||||
\(459\) | −3.18581 | −0.148701 | ||||||||
\(460\) | 39.5255 | 1.84288 | ||||||||
\(461\) | 16.3496 | 0.761476 | 0.380738 | − | 0.924683i | \(-0.375670\pi\) | ||||
0.380738 | + | 0.924683i | \(0.375670\pi\) | |||||||
\(462\) | −31.3620 | −1.45909 | ||||||||
\(463\) | −25.5880 | −1.18918 | −0.594589 | − | 0.804030i | \(-0.702685\pi\) | ||||
−0.594589 | + | 0.804030i | \(0.702685\pi\) | |||||||
\(464\) | −3.48901 | −0.161973 | ||||||||
\(465\) | 11.2002 | 0.519396 | ||||||||
\(466\) | −2.73429 | −0.126663 | ||||||||
\(467\) | 36.2732 | 1.67852 | 0.839261 | − | 0.543729i | \(-0.182988\pi\) | ||||
0.839261 | + | 0.543729i | \(0.182988\pi\) | |||||||
\(468\) | 12.3327 | 0.570080 | ||||||||
\(469\) | −48.7791 | −2.25241 | ||||||||
\(470\) | 23.3501 | 1.07706 | ||||||||
\(471\) | −8.38485 | −0.386354 | ||||||||
\(472\) | −8.28193 | −0.381207 | ||||||||
\(473\) | −5.91737 | −0.272081 | ||||||||
\(474\) | 17.9968 | 0.826620 | ||||||||
\(475\) | −40.3231 | −1.85015 | ||||||||
\(476\) | −10.1741 | −0.466329 | ||||||||
\(477\) | 20.9757 | 0.960412 | ||||||||
\(478\) | 4.42514 | 0.202401 | ||||||||
\(479\) | −20.8433 | −0.952357 | −0.476178 | − | 0.879349i | \(-0.657978\pi\) | ||||
−0.476178 | + | 0.879349i | \(0.657978\pi\) | |||||||
\(480\) | 50.6292 | 2.31090 | ||||||||
\(481\) | −44.3115 | −2.02043 | ||||||||
\(482\) | 14.7147 | 0.670236 | ||||||||
\(483\) | −65.8480 | −2.99619 | ||||||||
\(484\) | −15.0799 | −0.685448 | ||||||||
\(485\) | −38.3335 | −1.74064 | ||||||||
\(486\) | −14.0553 | −0.637563 | ||||||||
\(487\) | −1.61935 | −0.0733798 | −0.0366899 | − | 0.999327i | \(-0.511681\pi\) | ||||
−0.0366899 | + | 0.999327i | \(0.511681\pi\) | |||||||
\(488\) | 31.5231 | 1.42698 | ||||||||
\(489\) | −14.5133 | −0.656316 | ||||||||
\(490\) | 25.8977 | 1.16994 | ||||||||
\(491\) | −18.4080 | −0.830741 | −0.415371 | − | 0.909652i | \(-0.636348\pi\) | ||||
−0.415371 | + | 0.909652i | \(0.636348\pi\) | |||||||
\(492\) | 22.4213 | 1.01083 | ||||||||
\(493\) | −5.90434 | −0.265918 | ||||||||
\(494\) | 12.2748 | 0.552271 | ||||||||
\(495\) | −38.4546 | −1.72840 | ||||||||
\(496\) | 1.32901 | 0.0596744 | ||||||||
\(497\) | 28.9253 | 1.29748 | ||||||||
\(498\) | −9.81982 | −0.440037 | ||||||||
\(499\) | −8.70198 | −0.389554 | −0.194777 | − | 0.980848i | \(-0.562398\pi\) | ||||
−0.194777 | + | 0.980848i | \(0.562398\pi\) | |||||||
\(500\) | −24.1155 | −1.07848 | ||||||||
\(501\) | −4.28126 | −0.191273 | ||||||||
\(502\) | 4.01569 | 0.179229 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | −22.5673 | −1.00523 | ||||||||
\(505\) | 21.6306 | 0.962547 | ||||||||
\(506\) | 24.4656 | 1.08763 | ||||||||
\(507\) | 4.39322 | 0.195110 | ||||||||
\(508\) | 3.83343 | 0.170081 | ||||||||
\(509\) | −6.56992 | −0.291206 | −0.145603 | − | 0.989343i | \(-0.546512\pi\) | ||||
−0.145603 | + | 0.989343i | \(0.546512\pi\) | |||||||
\(510\) | 11.0710 | 0.490234 | ||||||||
\(511\) | 20.0276 | 0.885970 | ||||||||
\(512\) | 11.2390 | 0.496700 | ||||||||
\(513\) | 7.89932 | 0.348764 | ||||||||
\(514\) | 12.5006 | 0.551380 | ||||||||
\(515\) | 35.0353 | 1.54384 | ||||||||
\(516\) | −4.24407 | −0.186835 | ||||||||
\(517\) | −38.5519 | −1.69551 | ||||||||
\(518\) | 34.1421 | 1.50012 | ||||||||
\(519\) | −22.8149 | −1.00146 | ||||||||
\(520\) | 37.3689 | 1.63873 | ||||||||
\(521\) | −25.8155 | −1.13100 | −0.565499 | − | 0.824749i | \(-0.691316\pi\) | ||||
−0.565499 | + | 0.824749i | \(0.691316\pi\) | |||||||
\(522\) | −5.51452 | −0.241364 | ||||||||
\(523\) | −0.711015 | −0.0310905 | −0.0155453 | − | 0.999879i | \(-0.504948\pi\) | ||||
−0.0155453 | + | 0.999879i | \(0.504948\pi\) | |||||||
\(524\) | 14.0545 | 0.613976 | ||||||||
\(525\) | 86.1128 | 3.75827 | ||||||||
\(526\) | −10.5090 | −0.458212 | ||||||||
\(527\) | 2.24904 | 0.0979698 | ||||||||
\(528\) | −10.8013 | −0.470067 | ||||||||
\(529\) | 28.3684 | 1.23341 | ||||||||
\(530\) | 26.7622 | 1.16247 | ||||||||
\(531\) | 7.12353 | 0.309135 | ||||||||
\(532\) | 25.2271 | 1.09373 | ||||||||
\(533\) | 26.1297 | 1.13180 | ||||||||
\(534\) | 11.1914 | 0.484297 | ||||||||
\(535\) | −56.9379 | −2.46164 | ||||||||
\(536\) | 30.8708 | 1.33342 | ||||||||
\(537\) | −20.7262 | −0.894403 | ||||||||
\(538\) | 3.53010 | 0.152193 | ||||||||
\(539\) | −42.7580 | −1.84172 | ||||||||
\(540\) | 10.1260 | 0.435753 | ||||||||
\(541\) | 12.4754 | 0.536358 | 0.268179 | − | 0.963369i | \(-0.413578\pi\) | ||||
0.268179 | + | 0.963369i | \(0.413578\pi\) | |||||||
\(542\) | 16.8592 | 0.724166 | ||||||||
\(543\) | 56.2946 | 2.41583 | ||||||||
\(544\) | 10.1666 | 0.435888 | ||||||||
\(545\) | −11.3525 | −0.486289 | ||||||||
\(546\) | −26.2138 | −1.12185 | ||||||||
\(547\) | −2.52452 | −0.107941 | −0.0539704 | − | 0.998543i | \(-0.517188\pi\) | ||||
−0.0539704 | + | 0.998543i | \(0.517188\pi\) | |||||||
\(548\) | −5.56651 | −0.237790 | ||||||||
\(549\) | −27.1139 | −1.15719 | ||||||||
\(550\) | −31.9950 | −1.36427 | ||||||||
\(551\) | 14.6400 | 0.623686 | ||||||||
\(552\) | 41.6732 | 1.77373 | ||||||||
\(553\) | 43.1041 | 1.83297 | ||||||||
\(554\) | 2.10054 | 0.0892432 | ||||||||
\(555\) | 99.0968 | 4.20642 | ||||||||
\(556\) | −18.7231 | −0.794036 | ||||||||
\(557\) | −18.5546 | −0.786184 | −0.393092 | − | 0.919499i | \(-0.628595\pi\) | ||||
−0.393092 | + | 0.919499i | \(0.628595\pi\) | |||||||
\(558\) | 2.10056 | 0.0889236 | ||||||||
\(559\) | −4.94601 | −0.209194 | ||||||||
\(560\) | 15.6691 | 0.662138 | ||||||||
\(561\) | −18.2787 | −0.771727 | ||||||||
\(562\) | −6.42921 | −0.271200 | ||||||||
\(563\) | −33.9002 | −1.42872 | −0.714362 | − | 0.699777i | \(-0.753283\pi\) | ||||
−0.714362 | + | 0.699777i | \(0.753283\pi\) | |||||||
\(564\) | −27.6503 | −1.16429 | ||||||||
\(565\) | −7.77430 | −0.327067 | ||||||||
\(566\) | 21.1109 | 0.887359 | ||||||||
\(567\) | −43.4069 | −1.82292 | ||||||||
\(568\) | −18.3059 | −0.768100 | ||||||||
\(569\) | −12.6955 | −0.532223 | −0.266111 | − | 0.963942i | \(-0.585739\pi\) | ||||
−0.266111 | + | 0.963942i | \(0.585739\pi\) | |||||||
\(570\) | −27.4510 | −1.14980 | ||||||||
\(571\) | −12.3436 | −0.516562 | −0.258281 | − | 0.966070i | \(-0.583156\pi\) | ||||
−0.258281 | + | 0.966070i | \(0.583156\pi\) | |||||||
\(572\) | −25.9789 | −1.08623 | ||||||||
\(573\) | −30.2760 | −1.26480 | ||||||||
\(574\) | −20.1329 | −0.840333 | ||||||||
\(575\) | −67.1771 | −2.80148 | ||||||||
\(576\) | 4.99568 | 0.208153 | ||||||||
\(577\) | 32.8671 | 1.36828 | 0.684138 | − | 0.729353i | \(-0.260179\pi\) | ||||
0.684138 | + | 0.729353i | \(0.260179\pi\) | |||||||
\(578\) | −10.3311 | −0.429716 | ||||||||
\(579\) | 60.7761 | 2.52577 | ||||||||
\(580\) | 18.7668 | 0.779247 | ||||||||
\(581\) | −23.5194 | −0.975750 | ||||||||
\(582\) | −17.0182 | −0.705426 | ||||||||
\(583\) | −44.1853 | −1.82997 | ||||||||
\(584\) | −12.6749 | −0.524490 | ||||||||
\(585\) | −32.1421 | −1.32891 | ||||||||
\(586\) | −5.27160 | −0.217768 | ||||||||
\(587\) | −29.7918 | −1.22964 | −0.614819 | − | 0.788668i | \(-0.710771\pi\) | ||||
−0.614819 | + | 0.788668i | \(0.710771\pi\) | |||||||
\(588\) | −30.6670 | −1.26469 | ||||||||
\(589\) | −5.57658 | −0.229779 | ||||||||
\(590\) | 9.08866 | 0.374174 | ||||||||
\(591\) | 8.32929 | 0.342621 | ||||||||
\(592\) | 11.7588 | 0.483285 | ||||||||
\(593\) | 45.0621 | 1.85048 | 0.925240 | − | 0.379383i | \(-0.123864\pi\) | ||||
0.925240 | + | 0.379383i | \(0.123864\pi\) | |||||||
\(594\) | 6.26783 | 0.257172 | ||||||||
\(595\) | 26.5162 | 1.08706 | ||||||||
\(596\) | −21.8354 | −0.894412 | ||||||||
\(597\) | 42.4514 | 1.73742 | ||||||||
\(598\) | 20.4495 | 0.836243 | ||||||||
\(599\) | −41.5406 | −1.69730 | −0.848652 | − | 0.528952i | \(-0.822585\pi\) | ||||
−0.848652 | + | 0.528952i | \(0.822585\pi\) | |||||||
\(600\) | −54.4982 | −2.22488 | ||||||||
\(601\) | 14.4075 | 0.587694 | 0.293847 | − | 0.955852i | \(-0.405064\pi\) | ||||
0.293847 | + | 0.955852i | \(0.405064\pi\) | |||||||
\(602\) | 3.81091 | 0.155321 | ||||||||
\(603\) | −26.5529 | −1.08132 | ||||||||
\(604\) | −10.3929 | −0.422881 | ||||||||
\(605\) | 39.3018 | 1.59785 | ||||||||
\(606\) | 9.60288 | 0.390090 | ||||||||
\(607\) | −18.5714 | −0.753790 | −0.376895 | − | 0.926256i | \(-0.623008\pi\) | ||||
−0.376895 | + | 0.926256i | \(0.623008\pi\) | |||||||
\(608\) | −25.2083 | −1.02233 | ||||||||
\(609\) | −31.2648 | −1.26691 | ||||||||
\(610\) | −34.5937 | −1.40066 | ||||||||
\(611\) | −32.2234 | −1.30362 | ||||||||
\(612\) | −5.53828 | −0.223872 | ||||||||
\(613\) | −19.5200 | −0.788404 | −0.394202 | − | 0.919024i | \(-0.628979\pi\) | ||||
−0.394202 | + | 0.919024i | \(0.628979\pi\) | |||||||
\(614\) | 3.51675 | 0.141925 | ||||||||
\(615\) | −58.4355 | −2.35635 | ||||||||
\(616\) | 47.5380 | 1.91536 | ||||||||
\(617\) | 43.6158 | 1.75591 | 0.877954 | − | 0.478745i | \(-0.158908\pi\) | ||||
0.877954 | + | 0.478745i | \(0.158908\pi\) | |||||||
\(618\) | 15.5539 | 0.625671 | ||||||||
\(619\) | −15.7737 | −0.633999 | −0.317000 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.317000 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(620\) | −7.14851 | −0.287091 | ||||||||
\(621\) | 13.1600 | 0.528094 | ||||||||
\(622\) | −21.9080 | −0.878432 | ||||||||
\(623\) | 26.8044 | 1.07389 | ||||||||
\(624\) | −9.02824 | −0.361419 | ||||||||
\(625\) | 15.9865 | 0.639458 | ||||||||
\(626\) | 2.32304 | 0.0928472 | ||||||||
\(627\) | 45.3227 | 1.81001 | ||||||||
\(628\) | 5.35163 | 0.213553 | ||||||||
\(629\) | 19.8991 | 0.793427 | ||||||||
\(630\) | 24.7655 | 0.986683 | ||||||||
\(631\) | 20.1102 | 0.800575 | 0.400288 | − | 0.916390i | \(-0.368910\pi\) | ||||
0.400288 | + | 0.916390i | \(0.368910\pi\) | |||||||
\(632\) | −27.2793 | −1.08511 | ||||||||
\(633\) | −7.23861 | −0.287709 | ||||||||
\(634\) | −3.59754 | −0.142877 | ||||||||
\(635\) | −9.99085 | −0.396475 | ||||||||
\(636\) | −31.6907 | −1.25662 | ||||||||
\(637\) | −35.7391 | −1.41604 | ||||||||
\(638\) | 11.6163 | 0.459895 | ||||||||
\(639\) | 15.7455 | 0.622882 | ||||||||
\(640\) | −38.0550 | −1.50426 | ||||||||
\(641\) | −16.7023 | −0.659701 | −0.329850 | − | 0.944033i | \(-0.606998\pi\) | ||||
−0.329850 | + | 0.944033i | \(0.606998\pi\) | |||||||
\(642\) | −25.2776 | −0.997625 | ||||||||
\(643\) | 11.8118 | 0.465811 | 0.232905 | − | 0.972499i | \(-0.425177\pi\) | ||||
0.232905 | + | 0.972499i | \(0.425177\pi\) | |||||||
\(644\) | 42.0275 | 1.65612 | ||||||||
\(645\) | 11.0611 | 0.435530 | ||||||||
\(646\) | −5.51229 | −0.216878 | ||||||||
\(647\) | −5.72612 | −0.225117 | −0.112558 | − | 0.993645i | \(-0.535905\pi\) | ||||
−0.112558 | + | 0.993645i | \(0.535905\pi\) | |||||||
\(648\) | 27.4709 | 1.07916 | ||||||||
\(649\) | −15.0057 | −0.589026 | ||||||||
\(650\) | −26.7429 | −1.04894 | ||||||||
\(651\) | 11.9092 | 0.466757 | ||||||||
\(652\) | 9.26315 | 0.362773 | ||||||||
\(653\) | 25.6377 | 1.00328 | 0.501640 | − | 0.865076i | \(-0.332730\pi\) | ||||
0.501640 | + | 0.865076i | \(0.332730\pi\) | |||||||
\(654\) | −5.03996 | −0.197078 | ||||||||
\(655\) | −36.6296 | −1.43124 | ||||||||
\(656\) | −6.93395 | −0.270725 | ||||||||
\(657\) | 10.9020 | 0.425329 | ||||||||
\(658\) | 24.8282 | 0.967905 | ||||||||
\(659\) | −19.6150 | −0.764091 | −0.382045 | − | 0.924144i | \(-0.624780\pi\) | ||||
−0.382045 | + | 0.924144i | \(0.624780\pi\) | |||||||
\(660\) | 58.0983 | 2.26147 | ||||||||
\(661\) | 6.71840 | 0.261316 | 0.130658 | − | 0.991428i | \(-0.458291\pi\) | ||||
0.130658 | + | 0.991428i | \(0.458291\pi\) | |||||||
\(662\) | 14.5548 | 0.565689 | ||||||||
\(663\) | −15.2782 | −0.593355 | ||||||||
\(664\) | 14.8847 | 0.577640 | ||||||||
\(665\) | −65.7479 | −2.54959 | ||||||||
\(666\) | 18.5853 | 0.720165 | ||||||||
\(667\) | 24.3898 | 0.944378 | ||||||||
\(668\) | 2.73251 | 0.105724 | ||||||||
\(669\) | −28.4548 | −1.10013 | ||||||||
\(670\) | −33.8779 | −1.30882 | ||||||||
\(671\) | 57.1155 | 2.20492 | ||||||||
\(672\) | 53.8341 | 2.07670 | ||||||||
\(673\) | 0.657038 | 0.0253270 | 0.0126635 | − | 0.999920i | \(-0.495969\pi\) | ||||
0.0126635 | + | 0.999920i | \(0.495969\pi\) | |||||||
\(674\) | 4.56642 | 0.175892 | ||||||||
\(675\) | −17.2100 | −0.662414 | ||||||||
\(676\) | −2.80397 | −0.107845 | ||||||||
\(677\) | 7.87250 | 0.302565 | 0.151282 | − | 0.988491i | \(-0.451660\pi\) | ||||
0.151282 | + | 0.988491i | \(0.451660\pi\) | |||||||
\(678\) | −3.45140 | −0.132550 | ||||||||
\(679\) | −40.7601 | −1.56423 | ||||||||
\(680\) | −16.7813 | −0.643534 | ||||||||
\(681\) | −36.8641 | −1.41264 | ||||||||
\(682\) | −4.42482 | −0.169435 | ||||||||
\(683\) | 16.5842 | 0.634576 | 0.317288 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317288 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(684\) | 13.7324 | 0.525070 | ||||||||
\(685\) | 14.5077 | 0.554310 | ||||||||
\(686\) | 6.69855 | 0.255752 | ||||||||
\(687\) | −51.5107 | −1.96526 | ||||||||
\(688\) | 1.31251 | 0.0500389 | ||||||||
\(689\) | −36.9321 | −1.40700 | ||||||||
\(690\) | −45.7326 | −1.74101 | ||||||||
\(691\) | 22.9396 | 0.872664 | 0.436332 | − | 0.899786i | \(-0.356277\pi\) | ||||
0.436332 | + | 0.899786i | \(0.356277\pi\) | |||||||
\(692\) | 14.5616 | 0.553550 | ||||||||
\(693\) | −40.8888 | −1.55324 | ||||||||
\(694\) | −12.4466 | −0.472465 | ||||||||
\(695\) | 48.7970 | 1.85097 | ||||||||
\(696\) | 19.7865 | 0.750007 | ||||||||
\(697\) | −11.7341 | −0.444460 | ||||||||
\(698\) | 0.647256 | 0.0244990 | ||||||||
\(699\) | −8.43859 | −0.319177 | ||||||||
\(700\) | −54.9615 | −2.07735 | ||||||||
\(701\) | −38.2990 | −1.44653 | −0.723266 | − | 0.690569i | \(-0.757360\pi\) | ||||
−0.723266 | + | 0.690569i | \(0.757360\pi\) | |||||||
\(702\) | 5.23894 | 0.197731 | ||||||||
\(703\) | −49.3404 | −1.86091 | ||||||||
\(704\) | −10.5234 | −0.396615 | ||||||||
\(705\) | 72.0634 | 2.71406 | ||||||||
\(706\) | −19.5918 | −0.737347 | ||||||||
\(707\) | 22.9998 | 0.864998 | ||||||||
\(708\) | −10.7624 | −0.404477 | ||||||||
\(709\) | 13.9055 | 0.522232 | 0.261116 | − | 0.965307i | \(-0.415909\pi\) | ||||
0.261116 | + | 0.965307i | \(0.415909\pi\) | |||||||
\(710\) | 20.0891 | 0.753930 | ||||||||
\(711\) | 23.4637 | 0.879958 | ||||||||
\(712\) | −16.9637 | −0.635741 | ||||||||
\(713\) | −9.29042 | −0.347929 | ||||||||
\(714\) | 11.7719 | 0.440551 | ||||||||
\(715\) | 67.7073 | 2.53211 | ||||||||
\(716\) | 13.2285 | 0.494373 | ||||||||
\(717\) | 13.6569 | 0.510028 | ||||||||
\(718\) | 3.95908 | 0.147752 | ||||||||
\(719\) | −1.36261 | −0.0508166 | −0.0254083 | − | 0.999677i | \(-0.508089\pi\) | ||||
−0.0254083 | + | 0.999677i | \(0.508089\pi\) | |||||||
\(720\) | 8.52946 | 0.317874 | ||||||||
\(721\) | 37.2531 | 1.38738 | ||||||||
\(722\) | −0.363244 | −0.0135185 | ||||||||
\(723\) | 45.4127 | 1.68892 | ||||||||
\(724\) | −35.9300 | −1.33533 | ||||||||
\(725\) | −31.8958 | −1.18458 | ||||||||
\(726\) | 17.4480 | 0.647557 | ||||||||
\(727\) | 23.4016 | 0.867918 | 0.433959 | − | 0.900933i | \(-0.357116\pi\) | ||||
0.433959 | + | 0.900933i | \(0.357116\pi\) | |||||||
\(728\) | 39.7344 | 1.47266 | ||||||||
\(729\) | −11.0742 | −0.410154 | ||||||||
\(730\) | 13.9095 | 0.514815 | ||||||||
\(731\) | 2.22111 | 0.0821509 | ||||||||
\(732\) | 40.9645 | 1.51409 | ||||||||
\(733\) | −9.99331 | −0.369111 | −0.184556 | − | 0.982822i | \(-0.559085\pi\) | ||||
−0.184556 | + | 0.982822i | \(0.559085\pi\) | |||||||
\(734\) | 18.4345 | 0.680429 | ||||||||
\(735\) | 79.9257 | 2.94811 | ||||||||
\(736\) | −41.9963 | −1.54801 | ||||||||
\(737\) | 55.9337 | 2.06034 | ||||||||
\(738\) | −10.9594 | −0.403420 | ||||||||
\(739\) | 23.1704 | 0.852335 | 0.426168 | − | 0.904644i | \(-0.359863\pi\) | ||||
0.426168 | + | 0.904644i | \(0.359863\pi\) | |||||||
\(740\) | −63.2485 | −2.32506 | ||||||||
\(741\) | 37.8828 | 1.39166 | ||||||||
\(742\) | 28.4563 | 1.04466 | ||||||||
\(743\) | 20.2086 | 0.741383 | 0.370691 | − | 0.928756i | \(-0.379121\pi\) | ||||
0.370691 | + | 0.928756i | \(0.379121\pi\) | |||||||
\(744\) | −7.53696 | −0.276318 | ||||||||
\(745\) | 56.9083 | 2.08496 | ||||||||
\(746\) | −11.1352 | −0.407688 | ||||||||
\(747\) | −12.8028 | −0.468430 | ||||||||
\(748\) | 11.6664 | 0.426565 | ||||||||
\(749\) | −60.5422 | −2.21216 | ||||||||
\(750\) | 27.9026 | 1.01886 | ||||||||
\(751\) | 11.5168 | 0.420253 | 0.210127 | − | 0.977674i | \(-0.432612\pi\) | ||||
0.210127 | + | 0.977674i | \(0.432612\pi\) | |||||||
\(752\) | 8.55104 | 0.311824 | ||||||||
\(753\) | 12.3933 | 0.451636 | ||||||||
\(754\) | 9.70947 | 0.353598 | ||||||||
\(755\) | 27.0864 | 0.985776 | ||||||||
\(756\) | 10.7670 | 0.391591 | ||||||||
\(757\) | 39.7268 | 1.44390 | 0.721948 | − | 0.691947i | \(-0.243247\pi\) | ||||
0.721948 | + | 0.691947i | \(0.243247\pi\) | |||||||
\(758\) | −10.3597 | −0.376280 | ||||||||
\(759\) | 75.5062 | 2.74070 | ||||||||
\(760\) | 41.6099 | 1.50935 | ||||||||
\(761\) | −22.6597 | −0.821415 | −0.410708 | − | 0.911767i | \(-0.634718\pi\) | ||||
−0.410708 | + | 0.911767i | \(0.634718\pi\) | |||||||
\(762\) | −4.43544 | −0.160679 | ||||||||
\(763\) | −12.0712 | −0.437006 | ||||||||
\(764\) | 19.3236 | 0.699105 | ||||||||
\(765\) | 14.4341 | 0.521866 | ||||||||
\(766\) | −9.81682 | −0.354696 | ||||||||
\(767\) | −12.5425 | −0.452882 | ||||||||
\(768\) | −27.2718 | −0.984086 | ||||||||
\(769\) | 17.6004 | 0.634688 | 0.317344 | − | 0.948311i | \(-0.397209\pi\) | ||||
0.317344 | + | 0.948311i | \(0.397209\pi\) | |||||||
\(770\) | −52.1686 | −1.88003 | ||||||||
\(771\) | 38.5797 | 1.38941 | ||||||||
\(772\) | −38.7904 | −1.39610 | ||||||||
\(773\) | 45.8392 | 1.64872 | 0.824361 | − | 0.566064i | \(-0.191535\pi\) | ||||
0.824361 | + | 0.566064i | \(0.191535\pi\) | |||||||
\(774\) | 2.07447 | 0.0745653 | ||||||||
\(775\) | 12.1495 | 0.436424 | ||||||||
\(776\) | 25.7959 | 0.926018 | ||||||||
\(777\) | 105.370 | 3.78012 | ||||||||
\(778\) | 18.4481 | 0.661398 | ||||||||
\(779\) | 29.0951 | 1.04244 | ||||||||
\(780\) | 48.5612 | 1.73877 | ||||||||
\(781\) | −33.1678 | −1.18684 | ||||||||
\(782\) | −9.18330 | −0.328394 | ||||||||
\(783\) | 6.24840 | 0.223300 | ||||||||
\(784\) | 9.48399 | 0.338714 | ||||||||
\(785\) | −13.9477 | −0.497813 | ||||||||
\(786\) | −16.2617 | −0.580035 | ||||||||
\(787\) | −17.4603 | −0.622391 | −0.311196 | − | 0.950346i | \(-0.600729\pi\) | ||||
−0.311196 | + | 0.950346i | \(0.600729\pi\) | |||||||
\(788\) | −5.31617 | −0.189381 | ||||||||
\(789\) | −32.4329 | −1.15464 | ||||||||
\(790\) | 29.9365 | 1.06509 | ||||||||
\(791\) | −8.26643 | −0.293920 | ||||||||
\(792\) | 25.8773 | 0.919510 | ||||||||
\(793\) | 47.7397 | 1.69529 | ||||||||
\(794\) | −12.0930 | −0.429163 | ||||||||
\(795\) | 82.5937 | 2.92930 | ||||||||
\(796\) | −27.0946 | −0.960343 | ||||||||
\(797\) | 7.37081 | 0.261087 | 0.130544 | − | 0.991443i | \(-0.458328\pi\) | ||||
0.130544 | + | 0.991443i | \(0.458328\pi\) | |||||||
\(798\) | −29.1888 | −1.03327 | ||||||||
\(799\) | 14.4706 | 0.511934 | ||||||||
\(800\) | 54.9207 | 1.94174 | ||||||||
\(801\) | 14.5910 | 0.515546 | ||||||||
\(802\) | 20.9506 | 0.739791 | ||||||||
\(803\) | −22.9652 | −0.810423 | ||||||||
\(804\) | 40.1169 | 1.41482 | ||||||||
\(805\) | −109.534 | −3.86056 | ||||||||
\(806\) | −3.69847 | −0.130273 | ||||||||
\(807\) | 10.8946 | 0.383510 | ||||||||
\(808\) | −14.5559 | −0.512075 | ||||||||
\(809\) | −7.04747 | −0.247776 | −0.123888 | − | 0.992296i | \(-0.539536\pi\) | ||||
−0.123888 | + | 0.992296i | \(0.539536\pi\) | |||||||
\(810\) | −30.1468 | −1.05925 | ||||||||
\(811\) | −52.9606 | −1.85970 | −0.929849 | − | 0.367941i | \(-0.880063\pi\) | ||||
−0.929849 | + | 0.367941i | \(0.880063\pi\) | |||||||
\(812\) | 19.9547 | 0.700274 | ||||||||
\(813\) | 52.0312 | 1.82481 | ||||||||
\(814\) | −39.1499 | −1.37220 | ||||||||
\(815\) | −24.1420 | −0.845658 | ||||||||
\(816\) | 4.05433 | 0.141930 | ||||||||
\(817\) | −5.50733 | −0.192677 | ||||||||
\(818\) | 18.4759 | 0.645995 | ||||||||
\(819\) | −34.1768 | −1.19423 | ||||||||
\(820\) | 37.2964 | 1.30245 | ||||||||
\(821\) | −32.9925 | −1.15145 | −0.575724 | − | 0.817644i | \(-0.695280\pi\) | ||||
−0.575724 | + | 0.817644i | \(0.695280\pi\) | |||||||
\(822\) | 6.44069 | 0.224645 | ||||||||
\(823\) | 9.98952 | 0.348213 | 0.174106 | − | 0.984727i | \(-0.444296\pi\) | ||||
0.174106 | + | 0.984727i | \(0.444296\pi\) | |||||||
\(824\) | −23.5764 | −0.821323 | ||||||||
\(825\) | −98.7433 | −3.43780 | ||||||||
\(826\) | 9.66399 | 0.336253 | ||||||||
\(827\) | 18.2097 | 0.633213 | 0.316607 | − | 0.948557i | \(-0.397456\pi\) | ||||
0.316607 | + | 0.948557i | \(0.397456\pi\) | |||||||
\(828\) | 22.8777 | 0.795055 | ||||||||
\(829\) | −9.44705 | −0.328110 | −0.164055 | − | 0.986451i | \(-0.552457\pi\) | ||||
−0.164055 | + | 0.986451i | \(0.552457\pi\) | |||||||
\(830\) | −16.3346 | −0.566984 | ||||||||
\(831\) | 6.48270 | 0.224882 | ||||||||
\(832\) | −8.79594 | −0.304944 | ||||||||
\(833\) | 16.0494 | 0.556080 | ||||||||
\(834\) | 21.6634 | 0.750142 | ||||||||
\(835\) | −7.12160 | −0.246453 | ||||||||
\(836\) | −28.9272 | −1.00047 | ||||||||
\(837\) | −2.38010 | −0.0822684 | ||||||||
\(838\) | 11.9992 | 0.414504 | ||||||||
\(839\) | 23.5644 | 0.813533 | 0.406766 | − | 0.913532i | \(-0.366656\pi\) | ||||
0.406766 | + | 0.913532i | \(0.366656\pi\) | |||||||
\(840\) | −88.8607 | −3.06599 | ||||||||
\(841\) | −17.4197 | −0.600678 | ||||||||
\(842\) | 20.4178 | 0.703643 | ||||||||
\(843\) | −19.8419 | −0.683392 | ||||||||
\(844\) | 4.62004 | 0.159028 | ||||||||
\(845\) | 7.30783 | 0.251397 | ||||||||
\(846\) | 13.5153 | 0.464664 | ||||||||
\(847\) | 41.7897 | 1.43591 | ||||||||
\(848\) | 9.80057 | 0.336553 | ||||||||
\(849\) | 65.1529 | 2.23604 | ||||||||
\(850\) | 12.0095 | 0.411921 | ||||||||
\(851\) | −82.1996 | −2.81777 | ||||||||
\(852\) | −23.7887 | −0.814989 | ||||||||
\(853\) | −52.2667 | −1.78958 | −0.894789 | − | 0.446490i | \(-0.852674\pi\) | ||||
−0.894789 | + | 0.446490i | \(0.852674\pi\) | |||||||
\(854\) | −36.7836 | −1.25871 | ||||||||
\(855\) | −35.7899 | −1.22399 | ||||||||
\(856\) | 38.3153 | 1.30959 | ||||||||
\(857\) | −23.7734 | −0.812083 | −0.406041 | − | 0.913855i | \(-0.633091\pi\) | ||||
−0.406041 | + | 0.913855i | \(0.633091\pi\) | |||||||
\(858\) | 30.0587 | 1.02619 | ||||||||
\(859\) | 16.6060 | 0.566588 | 0.283294 | − | 0.959033i | \(-0.408573\pi\) | ||||
0.283294 | + | 0.959033i | \(0.408573\pi\) | |||||||
\(860\) | −7.05974 | −0.240735 | ||||||||
\(861\) | −62.1346 | −2.11754 | ||||||||
\(862\) | −22.7690 | −0.775517 | ||||||||
\(863\) | 30.5826 | 1.04104 | 0.520521 | − | 0.853849i | \(-0.325738\pi\) | ||||
0.520521 | + | 0.853849i | \(0.325738\pi\) | |||||||
\(864\) | −10.7590 | −0.366028 | ||||||||
\(865\) | −37.9512 | −1.29038 | ||||||||
\(866\) | −15.4503 | −0.525022 | ||||||||
\(867\) | −31.8839 | −1.08283 | ||||||||
\(868\) | −7.60103 | −0.257996 | ||||||||
\(869\) | −49.4263 | −1.67667 | ||||||||
\(870\) | −21.7139 | −0.736171 | ||||||||
\(871\) | 46.7520 | 1.58413 | ||||||||
\(872\) | 7.63949 | 0.258706 | ||||||||
\(873\) | −22.1878 | −0.750943 | ||||||||
\(874\) | 22.7703 | 0.770218 | ||||||||
\(875\) | 66.8295 | 2.25925 | ||||||||
\(876\) | −16.4711 | −0.556508 | ||||||||
\(877\) | 45.7382 | 1.54447 | 0.772235 | − | 0.635337i | \(-0.219139\pi\) | ||||
0.772235 | + | 0.635337i | \(0.219139\pi\) | |||||||
\(878\) | −25.1527 | −0.848863 | ||||||||
\(879\) | −16.2693 | −0.548750 | ||||||||
\(880\) | −17.9673 | −0.605677 | ||||||||
\(881\) | −9.93887 | −0.334849 | −0.167425 | − | 0.985885i | \(-0.553545\pi\) | ||||
−0.167425 | + | 0.985885i | \(0.553545\pi\) | |||||||
\(882\) | 14.9898 | 0.504733 | ||||||||
\(883\) | −29.0582 | −0.977886 | −0.488943 | − | 0.872316i | \(-0.662617\pi\) | ||||
−0.488943 | + | 0.872316i | \(0.662617\pi\) | |||||||
\(884\) | 9.75130 | 0.327972 | ||||||||
\(885\) | 28.0495 | 0.942875 | ||||||||
\(886\) | −21.1956 | −0.712081 | ||||||||
\(887\) | −41.7824 | −1.40291 | −0.701457 | − | 0.712712i | \(-0.747467\pi\) | ||||
−0.701457 | + | 0.712712i | \(0.747467\pi\) | |||||||
\(888\) | −66.6854 | −2.23782 | ||||||||
\(889\) | −10.6233 | −0.356294 | ||||||||
\(890\) | 18.6161 | 0.624013 | ||||||||
\(891\) | 49.7735 | 1.66748 | ||||||||
\(892\) | 18.1613 | 0.608084 | ||||||||
\(893\) | −35.8805 | −1.20069 | ||||||||
\(894\) | 25.2644 | 0.844970 | ||||||||
\(895\) | −34.4767 | −1.15243 | ||||||||
\(896\) | −40.4640 | −1.35181 | ||||||||
\(897\) | 63.1116 | 2.10723 | ||||||||
\(898\) | 26.5562 | 0.886191 | ||||||||
\(899\) | −4.41111 | −0.147119 | ||||||||
\(900\) | −29.9183 | −0.997277 | ||||||||
\(901\) | 16.5852 | 0.552532 | ||||||||
\(902\) | 23.0859 | 0.768677 | ||||||||
\(903\) | 11.7613 | 0.391391 | ||||||||
\(904\) | 5.23157 | 0.174000 | ||||||||
\(905\) | 93.6424 | 3.11278 | ||||||||
\(906\) | 12.0250 | 0.399504 | ||||||||
\(907\) | −15.3714 | −0.510397 | −0.255199 | − | 0.966889i | \(-0.582141\pi\) | ||||
−0.255199 | + | 0.966889i | \(0.582141\pi\) | |||||||
\(908\) | 23.5285 | 0.780821 | ||||||||
\(909\) | 12.5200 | 0.415261 | ||||||||
\(910\) | −43.6049 | −1.44549 | ||||||||
\(911\) | 10.3340 | 0.342382 | 0.171191 | − | 0.985238i | \(-0.445238\pi\) | ||||
0.171191 | + | 0.985238i | \(0.445238\pi\) | |||||||
\(912\) | −10.0529 | −0.332883 | ||||||||
\(913\) | 26.9691 | 0.892547 | ||||||||
\(914\) | 6.21766 | 0.205662 | ||||||||
\(915\) | −106.764 | −3.52949 | ||||||||
\(916\) | 32.8767 | 1.08628 | ||||||||
\(917\) | −38.9483 | −1.28619 | ||||||||
\(918\) | −2.35266 | −0.0776493 | ||||||||
\(919\) | 45.0421 | 1.48580 | 0.742901 | − | 0.669401i | \(-0.233449\pi\) | ||||
0.742901 | + | 0.669401i | \(0.233449\pi\) | |||||||
\(920\) | 69.3207 | 2.28544 | ||||||||
\(921\) | 10.8535 | 0.357634 | ||||||||
\(922\) | 12.0739 | 0.397632 | ||||||||
\(923\) | −27.7232 | −0.912521 | ||||||||
\(924\) | 61.7761 | 2.03228 | ||||||||
\(925\) | 107.497 | 3.53447 | ||||||||
\(926\) | −18.8963 | −0.620971 | ||||||||
\(927\) | 20.2788 | 0.666042 | ||||||||
\(928\) | −19.9399 | −0.654560 | ||||||||
\(929\) | −14.7997 | −0.485562 | −0.242781 | − | 0.970081i | \(-0.578060\pi\) | ||||
−0.242781 | + | 0.970081i | \(0.578060\pi\) | |||||||
\(930\) | 8.27113 | 0.271221 | ||||||||
\(931\) | −39.7951 | −1.30423 | ||||||||
\(932\) | 5.38593 | 0.176422 | ||||||||
\(933\) | −67.6129 | −2.21355 | ||||||||
\(934\) | 26.7871 | 0.876500 | ||||||||
\(935\) | −30.4054 | −0.994364 | ||||||||
\(936\) | 21.6295 | 0.706981 | ||||||||
\(937\) | 3.42126 | 0.111768 | 0.0558839 | − | 0.998437i | \(-0.482202\pi\) | ||||
0.0558839 | + | 0.998437i | \(0.482202\pi\) | |||||||
\(938\) | −36.0225 | −1.17618 | ||||||||
\(939\) | 7.16939 | 0.233964 | ||||||||
\(940\) | −45.9945 | −1.50017 | ||||||||
\(941\) | 17.9750 | 0.585968 | 0.292984 | − | 0.956117i | \(-0.405352\pi\) | ||||
0.292984 | + | 0.956117i | \(0.405352\pi\) | |||||||
\(942\) | −6.19206 | −0.201748 | ||||||||
\(943\) | 48.4715 | 1.57845 | ||||||||
\(944\) | 3.32836 | 0.108329 | ||||||||
\(945\) | −28.0614 | −0.912837 | ||||||||
\(946\) | −4.36987 | −0.142077 | ||||||||
\(947\) | −9.49653 | −0.308596 | −0.154298 | − | 0.988024i | \(-0.549312\pi\) | ||||
−0.154298 | + | 0.988024i | \(0.549312\pi\) | |||||||
\(948\) | −35.4497 | −1.15135 | ||||||||
\(949\) | −19.1953 | −0.623107 | ||||||||
\(950\) | −29.7779 | −0.966123 | ||||||||
\(951\) | −11.1028 | −0.360033 | ||||||||
\(952\) | −17.8436 | −0.578315 | ||||||||
\(953\) | −48.6172 | −1.57487 | −0.787433 | − | 0.616401i | \(-0.788590\pi\) | ||||
−0.787433 | + | 0.616401i | \(0.788590\pi\) | |||||||
\(954\) | 15.4902 | 0.501513 | ||||||||
\(955\) | −50.3621 | −1.62968 | ||||||||
\(956\) | −8.71655 | −0.281913 | ||||||||
\(957\) | 35.8505 | 1.15888 | ||||||||
\(958\) | −15.3924 | −0.497307 | ||||||||
\(959\) | 15.4261 | 0.498134 | ||||||||
\(960\) | 19.6709 | 0.634877 | ||||||||
\(961\) | −29.3197 | −0.945798 | ||||||||
\(962\) | −32.7233 | −1.05504 | ||||||||
\(963\) | −32.9562 | −1.06200 | ||||||||
\(964\) | −28.9847 | −0.933533 | ||||||||
\(965\) | 101.097 | 3.25443 | ||||||||
\(966\) | −48.6276 | −1.56457 | ||||||||
\(967\) | 36.9048 | 1.18678 | 0.593389 | − | 0.804916i | \(-0.297789\pi\) | ||||
0.593389 | + | 0.804916i | \(0.297789\pi\) | |||||||
\(968\) | −26.4474 | −0.850053 | ||||||||
\(969\) | −17.0121 | −0.546507 | ||||||||
\(970\) | −28.3086 | −0.908935 | ||||||||
\(971\) | 39.9682 | 1.28264 | 0.641321 | − | 0.767273i | \(-0.278387\pi\) | ||||
0.641321 | + | 0.767273i | \(0.278387\pi\) | |||||||
\(972\) | 27.6859 | 0.888024 | ||||||||
\(973\) | 51.8859 | 1.66339 | ||||||||
\(974\) | −1.19586 | −0.0383179 | ||||||||
\(975\) | −82.5342 | −2.64321 | ||||||||
\(976\) | −12.6686 | −0.405511 | ||||||||
\(977\) | 54.4292 | 1.74134 | 0.870672 | − | 0.491864i | \(-0.163684\pi\) | ||||
0.870672 | + | 0.491864i | \(0.163684\pi\) | |||||||
\(978\) | −10.7178 | −0.342719 | ||||||||
\(979\) | −30.7359 | −0.982323 | ||||||||
\(980\) | −51.0126 | −1.62954 | ||||||||
\(981\) | −6.57095 | −0.209794 | ||||||||
\(982\) | −13.5940 | −0.433801 | ||||||||
\(983\) | −47.7647 | −1.52346 | −0.761728 | − | 0.647897i | \(-0.775649\pi\) | ||||
−0.761728 | + | 0.647897i | \(0.775649\pi\) | |||||||
\(984\) | 39.3231 | 1.25357 | ||||||||
\(985\) | 13.8552 | 0.441464 | ||||||||
\(986\) | −4.36025 | −0.138859 | ||||||||
\(987\) | 76.6252 | 2.43901 | ||||||||
\(988\) | −24.1787 | −0.769227 | ||||||||
\(989\) | −9.17505 | −0.291750 | ||||||||
\(990\) | −28.3980 | −0.902548 | ||||||||
\(991\) | 18.5959 | 0.590717 | 0.295359 | − | 0.955386i | \(-0.404561\pi\) | ||||
0.295359 | + | 0.955386i | \(0.404561\pi\) | |||||||
\(992\) | 7.59539 | 0.241154 | ||||||||
\(993\) | 44.9193 | 1.42547 | ||||||||
\(994\) | 21.3608 | 0.677523 | ||||||||
\(995\) | 70.6152 | 2.23865 | ||||||||
\(996\) | 19.3429 | 0.612902 | ||||||||
\(997\) | 3.78354 | 0.119826 | 0.0599129 | − | 0.998204i | \(-0.480918\pi\) | ||||
0.0599129 | + | 0.998204i | \(0.480918\pi\) | |||||||
\(998\) | −6.42625 | −0.203420 | ||||||||
\(999\) | −21.0586 | −0.666266 |
(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 | 503.2.a.f.1.16 | ✓ | 26 | |
3.2 | odd | 2 | 4527.2.a.o.1.11 | 26 | |||
4.3 | odd | 2 | 8048.2.a.u.1.7 | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.f.1.16 | ✓ | 26 | 1.1 | even | 1 | trivial | |
4527.2.a.o.1.11 | 26 | 3.2 | odd | 2 | |||
8048.2.a.u.1.7 | 26 | 4.3 | odd | 2 |