Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.28561300.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.35258\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.53464 | 1.79226 | 0.896131 | − | 0.443789i | \(-0.146366\pi\) | ||||
0.896131 | + | 0.443789i | \(0.146366\pi\) | |||||||
\(3\) | −2.99024 | −1.72642 | −0.863208 | − | 0.504849i | \(-0.831548\pi\) | ||||
−0.863208 | + | 0.504849i | \(0.831548\pi\) | |||||||
\(4\) | 4.42441 | 2.21221 | ||||||||
\(5\) | −3.35258 | −1.49932 | −0.749660 | − | 0.661823i | \(-0.769783\pi\) | ||||
−0.749660 | + | 0.661823i | \(0.769783\pi\) | |||||||
\(6\) | −7.57919 | −3.09419 | ||||||||
\(7\) | 1.91841 | 0.725091 | 0.362545 | − | 0.931966i | \(-0.381908\pi\) | ||||
0.362545 | + | 0.931966i | \(0.381908\pi\) | |||||||
\(8\) | 6.14501 | 2.17259 | ||||||||
\(9\) | 5.94153 | 1.98051 | ||||||||
\(10\) | −8.49760 | −2.68718 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −13.2300 | −3.81919 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.86248 | 1.29955 | ||||||||
\(15\) | 10.0250 | 2.58845 | ||||||||
\(16\) | 6.72659 | 1.68165 | ||||||||
\(17\) | −1.97271 | −0.478454 | −0.239227 | − | 0.970964i | \(-0.576894\pi\) | ||||
−0.239227 | + | 0.970964i | \(0.576894\pi\) | |||||||
\(18\) | 15.0596 | 3.54959 | ||||||||
\(19\) | −2.82126 | −0.647240 | −0.323620 | − | 0.946187i | \(-0.604900\pi\) | ||||
−0.323620 | + | 0.946187i | \(0.604900\pi\) | |||||||
\(20\) | −14.8332 | −3.31680 | ||||||||
\(21\) | −5.73650 | −1.25181 | ||||||||
\(22\) | −2.53464 | −0.540388 | ||||||||
\(23\) | −0.439850 | −0.0917150 | −0.0458575 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458575 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(24\) | −18.3751 | −3.75079 | ||||||||
\(25\) | 6.23981 | 1.24796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.79587 | −1.69277 | ||||||||
\(28\) | 8.48783 | 1.60405 | ||||||||
\(29\) | 2.49845 | 0.463950 | 0.231975 | − | 0.972722i | \(-0.425481\pi\) | ||||
0.231975 | + | 0.972722i | \(0.425481\pi\) | |||||||
\(30\) | 25.4098 | 4.63918 | ||||||||
\(31\) | −4.63180 | −0.831895 | −0.415948 | − | 0.909389i | \(-0.636550\pi\) | ||||
−0.415948 | + | 0.909389i | \(0.636550\pi\) | |||||||
\(32\) | 4.75947 | 0.841363 | ||||||||
\(33\) | 2.99024 | 0.520534 | ||||||||
\(34\) | −5.00013 | −0.857514 | ||||||||
\(35\) | −6.43163 | −1.08714 | ||||||||
\(36\) | 26.2878 | 4.38129 | ||||||||
\(37\) | −7.79007 | −1.28068 | −0.640340 | − | 0.768092i | \(-0.721206\pi\) | ||||
−0.640340 | + | 0.768092i | \(0.721206\pi\) | |||||||
\(38\) | −7.15087 | −1.16002 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.6017 | −3.25741 | ||||||||
\(41\) | −9.71084 | −1.51658 | −0.758289 | − | 0.651918i | \(-0.773965\pi\) | ||||
−0.758289 | + | 0.651918i | \(0.773965\pi\) | |||||||
\(42\) | −14.5400 | −2.24357 | ||||||||
\(43\) | −6.59493 | −1.00572 | −0.502859 | − | 0.864369i | \(-0.667718\pi\) | ||||
−0.502859 | + | 0.864369i | \(0.667718\pi\) | |||||||
\(44\) | −4.42441 | −0.667005 | ||||||||
\(45\) | −19.9195 | −2.96942 | ||||||||
\(46\) | −1.11486 | −0.164377 | ||||||||
\(47\) | −0.104554 | −0.0152507 | −0.00762536 | − | 0.999971i | \(-0.502427\pi\) | ||||
−0.00762536 | + | 0.999971i | \(0.502427\pi\) | |||||||
\(48\) | −20.1141 | −2.90322 | ||||||||
\(49\) | −3.31970 | −0.474243 | ||||||||
\(50\) | 15.8157 | 2.23667 | ||||||||
\(51\) | 5.89889 | 0.826010 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.381991 | 0.0524705 | 0.0262352 | − | 0.999656i | \(-0.491648\pi\) | ||||
0.0262352 | + | 0.999656i | \(0.491648\pi\) | |||||||
\(54\) | −22.2944 | −3.03388 | ||||||||
\(55\) | 3.35258 | 0.452062 | ||||||||
\(56\) | 11.7887 | 1.57533 | ||||||||
\(57\) | 8.43623 | 1.11741 | ||||||||
\(58\) | 6.33267 | 0.831520 | ||||||||
\(59\) | −1.03254 | −0.134426 | −0.0672128 | − | 0.997739i | \(-0.521411\pi\) | ||||
−0.0672128 | + | 0.997739i | \(0.521411\pi\) | |||||||
\(60\) | 44.3548 | 5.72618 | ||||||||
\(61\) | −5.73635 | −0.734464 | −0.367232 | − | 0.930129i | \(-0.619695\pi\) | ||||
−0.367232 | + | 0.930129i | \(0.619695\pi\) | |||||||
\(62\) | −11.7399 | −1.49097 | ||||||||
\(63\) | 11.3983 | 1.43605 | ||||||||
\(64\) | −1.38963 | −0.173704 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.57919 | 0.932933 | ||||||||
\(67\) | −7.25193 | −0.885964 | −0.442982 | − | 0.896530i | \(-0.646079\pi\) | ||||
−0.442982 | + | 0.896530i | \(0.646079\pi\) | |||||||
\(68\) | −8.72810 | −1.05844 | ||||||||
\(69\) | 1.31526 | 0.158338 | ||||||||
\(70\) | −16.3019 | −1.94845 | ||||||||
\(71\) | 11.2672 | 1.33717 | 0.668586 | − | 0.743635i | \(-0.266900\pi\) | ||||
0.668586 | + | 0.743635i | \(0.266900\pi\) | |||||||
\(72\) | 36.5108 | 4.30284 | ||||||||
\(73\) | 0.808179 | 0.0945902 | 0.0472951 | − | 0.998881i | \(-0.484940\pi\) | ||||
0.0472951 | + | 0.998881i | \(0.484940\pi\) | |||||||
\(74\) | −19.7450 | −2.29531 | ||||||||
\(75\) | −18.6585 | −2.15450 | ||||||||
\(76\) | −12.4824 | −1.43183 | ||||||||
\(77\) | −1.91841 | −0.218623 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.04501 | −0.792625 | −0.396313 | − | 0.918116i | \(-0.629710\pi\) | ||||
−0.396313 | + | 0.918116i | \(0.629710\pi\) | |||||||
\(80\) | −22.5514 | −2.52133 | ||||||||
\(81\) | 8.47718 | 0.941908 | ||||||||
\(82\) | −24.6135 | −2.71811 | ||||||||
\(83\) | 8.70830 | 0.955860 | 0.477930 | − | 0.878398i | \(-0.341387\pi\) | ||||
0.477930 | + | 0.878398i | \(0.341387\pi\) | |||||||
\(84\) | −25.3807 | −2.76926 | ||||||||
\(85\) | 6.61369 | 0.717355 | ||||||||
\(86\) | −16.7158 | −1.80251 | ||||||||
\(87\) | −7.47095 | −0.800970 | ||||||||
\(88\) | −6.14501 | −0.655061 | ||||||||
\(89\) | 10.3321 | 1.09520 | 0.547599 | − | 0.836741i | \(-0.315542\pi\) | ||||
0.547599 | + | 0.836741i | \(0.315542\pi\) | |||||||
\(90\) | −50.4887 | −5.32198 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.94608 | −0.202892 | ||||||||
\(93\) | 13.8502 | 1.43620 | ||||||||
\(94\) | −0.265006 | −0.0273333 | ||||||||
\(95\) | 9.45849 | 0.970421 | ||||||||
\(96\) | −14.2319 | −1.45254 | ||||||||
\(97\) | −19.3846 | −1.96821 | −0.984106 | − | 0.177583i | \(-0.943172\pi\) | ||||
−0.984106 | + | 0.177583i | \(0.943172\pi\) | |||||||
\(98\) | −8.41426 | −0.849968 | ||||||||
\(99\) | −5.94153 | −0.597146 | ||||||||
\(100\) | 27.6075 | 2.76075 | ||||||||
\(101\) | 3.34654 | 0.332993 | 0.166497 | − | 0.986042i | \(-0.446755\pi\) | ||||
0.166497 | + | 0.986042i | \(0.446755\pi\) | |||||||
\(102\) | 14.9516 | 1.48043 | ||||||||
\(103\) | 18.4647 | 1.81939 | 0.909693 | − | 0.415282i | \(-0.136317\pi\) | ||||
0.909693 | + | 0.415282i | \(0.136317\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.2321 | 1.87686 | ||||||||
\(106\) | 0.968210 | 0.0940409 | ||||||||
\(107\) | −12.3949 | −1.19826 | −0.599132 | − | 0.800650i | \(-0.704488\pi\) | ||||
−0.599132 | + | 0.800650i | \(0.704488\pi\) | |||||||
\(108\) | −38.9166 | −3.74475 | ||||||||
\(109\) | −3.51113 | −0.336305 | −0.168153 | − | 0.985761i | \(-0.553780\pi\) | ||||
−0.168153 | + | 0.985761i | \(0.553780\pi\) | |||||||
\(110\) | 8.49760 | 0.810214 | ||||||||
\(111\) | 23.2942 | 2.21098 | ||||||||
\(112\) | 12.9044 | 1.21935 | ||||||||
\(113\) | 17.0302 | 1.60206 | 0.801031 | − | 0.598623i | \(-0.204285\pi\) | ||||
0.801031 | + | 0.598623i | \(0.204285\pi\) | |||||||
\(114\) | 21.3828 | 2.00268 | ||||||||
\(115\) | 1.47463 | 0.137510 | ||||||||
\(116\) | 11.0542 | 1.02635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.61712 | −0.240926 | ||||||||
\(119\) | −3.78448 | −0.346922 | ||||||||
\(120\) | 61.6039 | 5.62364 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −14.5396 | −1.31635 | ||||||||
\(123\) | 29.0377 | 2.61824 | ||||||||
\(124\) | −20.4930 | −1.84032 | ||||||||
\(125\) | −4.15655 | −0.371773 | ||||||||
\(126\) | 28.8906 | 2.57378 | ||||||||
\(127\) | 2.56073 | 0.227228 | 0.113614 | − | 0.993525i | \(-0.463757\pi\) | ||||
0.113614 | + | 0.993525i | \(0.463757\pi\) | |||||||
\(128\) | −13.0411 | −1.15269 | ||||||||
\(129\) | 19.7204 | 1.73629 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.1666 | −1.06300 | −0.531499 | − | 0.847059i | \(-0.678371\pi\) | ||||
−0.531499 | + | 0.847059i | \(0.678371\pi\) | |||||||
\(132\) | 13.2300 | 1.15153 | ||||||||
\(133\) | −5.41233 | −0.469308 | ||||||||
\(134\) | −18.3810 | −1.58788 | ||||||||
\(135\) | 29.4889 | 2.53800 | ||||||||
\(136\) | −12.1224 | −1.03948 | ||||||||
\(137\) | 10.9394 | 0.934620 | 0.467310 | − | 0.884094i | \(-0.345223\pi\) | ||||
0.467310 | + | 0.884094i | \(0.345223\pi\) | |||||||
\(138\) | 3.33370 | 0.283784 | ||||||||
\(139\) | −6.00780 | −0.509575 | −0.254788 | − | 0.966997i | \(-0.582006\pi\) | ||||
−0.254788 | + | 0.966997i | \(0.582006\pi\) | |||||||
\(140\) | −28.4562 | −2.40498 | ||||||||
\(141\) | 0.312640 | 0.0263291 | ||||||||
\(142\) | 28.5584 | 2.39656 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 39.9662 | 3.33052 | ||||||||
\(145\) | −8.37625 | −0.695609 | ||||||||
\(146\) | 2.04844 | 0.169530 | ||||||||
\(147\) | 9.92670 | 0.818741 | ||||||||
\(148\) | −34.4665 | −2.83313 | ||||||||
\(149\) | −13.4382 | −1.10090 | −0.550448 | − | 0.834869i | \(-0.685543\pi\) | ||||
−0.550448 | + | 0.834869i | \(0.685543\pi\) | |||||||
\(150\) | −47.2926 | −3.86143 | ||||||||
\(151\) | −7.46127 | −0.607190 | −0.303595 | − | 0.952801i | \(-0.598187\pi\) | ||||
−0.303595 | + | 0.952801i | \(0.598187\pi\) | |||||||
\(152\) | −17.3367 | −1.40619 | ||||||||
\(153\) | −11.7209 | −0.947582 | ||||||||
\(154\) | −4.86248 | −0.391830 | ||||||||
\(155\) | 15.5285 | 1.24728 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7742 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(158\) | −17.8566 | −1.42059 | ||||||||
\(159\) | −1.14224 | −0.0905858 | ||||||||
\(160\) | −15.9565 | −1.26147 | ||||||||
\(161\) | −0.843812 | −0.0665017 | ||||||||
\(162\) | 21.4866 | 1.68815 | ||||||||
\(163\) | −15.8386 | −1.24058 | −0.620289 | − | 0.784374i | \(-0.712985\pi\) | ||||
−0.620289 | + | 0.784374i | \(0.712985\pi\) | |||||||
\(164\) | −42.9648 | −3.35498 | ||||||||
\(165\) | −10.0250 | −0.780447 | ||||||||
\(166\) | 22.0724 | 1.71315 | ||||||||
\(167\) | 19.2946 | 1.49306 | 0.746530 | − | 0.665352i | \(-0.231719\pi\) | ||||
0.746530 | + | 0.665352i | \(0.231719\pi\) | |||||||
\(168\) | −35.2509 | −2.71967 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 16.7633 | 1.28569 | ||||||||
\(171\) | −16.7626 | −1.28187 | ||||||||
\(172\) | −29.1787 | −2.22485 | ||||||||
\(173\) | −16.0251 | −1.21837 | −0.609185 | − | 0.793028i | \(-0.708503\pi\) | ||||
−0.609185 | + | 0.793028i | \(0.708503\pi\) | |||||||
\(174\) | −18.9362 | −1.43555 | ||||||||
\(175\) | 11.9705 | 0.904885 | ||||||||
\(176\) | −6.72659 | −0.507036 | ||||||||
\(177\) | 3.08755 | 0.232074 | ||||||||
\(178\) | 26.1881 | 1.96288 | ||||||||
\(179\) | 10.0656 | 0.752339 | 0.376169 | − | 0.926551i | \(-0.377241\pi\) | ||||
0.376169 | + | 0.926551i | \(0.377241\pi\) | |||||||
\(180\) | −88.1319 | −6.56896 | ||||||||
\(181\) | −9.77673 | −0.726698 | −0.363349 | − | 0.931653i | \(-0.618367\pi\) | ||||
−0.363349 | + | 0.931653i | \(0.618367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.1531 | 1.26799 | ||||||||
\(184\) | −2.70288 | −0.199259 | ||||||||
\(185\) | 26.1168 | 1.92015 | ||||||||
\(186\) | 35.1052 | 2.57404 | ||||||||
\(187\) | 1.97271 | 0.144259 | ||||||||
\(188\) | −0.462588 | −0.0337377 | ||||||||
\(189\) | −16.8741 | −1.22741 | ||||||||
\(190\) | 23.9739 | 1.73925 | ||||||||
\(191\) | −1.02585 | −0.0742276 | −0.0371138 | − | 0.999311i | \(-0.511816\pi\) | ||||
−0.0371138 | + | 0.999311i | \(0.511816\pi\) | |||||||
\(192\) | 4.15532 | 0.299884 | ||||||||
\(193\) | −20.8263 | −1.49911 | −0.749554 | − | 0.661944i | \(-0.769732\pi\) | ||||
−0.749554 | + | 0.661944i | \(0.769732\pi\) | |||||||
\(194\) | −49.1331 | −3.52755 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.6877 | −1.04912 | ||||||||
\(197\) | 8.05501 | 0.573896 | 0.286948 | − | 0.957946i | \(-0.407359\pi\) | ||||
0.286948 | + | 0.957946i | \(0.407359\pi\) | |||||||
\(198\) | −15.0596 | −1.07024 | ||||||||
\(199\) | 19.0290 | 1.34893 | 0.674466 | − | 0.738306i | \(-0.264374\pi\) | ||||
0.674466 | + | 0.738306i | \(0.264374\pi\) | |||||||
\(200\) | 38.3437 | 2.71131 | ||||||||
\(201\) | 21.6850 | 1.52954 | ||||||||
\(202\) | 8.48228 | 0.596811 | ||||||||
\(203\) | 4.79305 | 0.336406 | ||||||||
\(204\) | 26.0991 | 1.82730 | ||||||||
\(205\) | 32.5564 | 2.27384 | ||||||||
\(206\) | 46.8015 | 3.26082 | ||||||||
\(207\) | −2.61338 | −0.181642 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82126 | 0.195150 | ||||||||
\(210\) | 48.7465 | 3.36383 | ||||||||
\(211\) | 18.5614 | 1.27782 | 0.638909 | − | 0.769282i | \(-0.279386\pi\) | ||||
0.638909 | + | 0.769282i | \(0.279386\pi\) | |||||||
\(212\) | 1.69008 | 0.116075 | ||||||||
\(213\) | −33.6917 | −2.30852 | ||||||||
\(214\) | −31.4167 | −2.14760 | ||||||||
\(215\) | 22.1101 | 1.50789 | ||||||||
\(216\) | −54.0508 | −3.67769 | ||||||||
\(217\) | −8.88569 | −0.603200 | ||||||||
\(218\) | −8.89946 | −0.602748 | ||||||||
\(219\) | −2.41665 | −0.163302 | ||||||||
\(220\) | 14.8332 | 1.00005 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 59.0424 | 3.96267 | ||||||||
\(223\) | 2.55638 | 0.171188 | 0.0855938 | − | 0.996330i | \(-0.472721\pi\) | ||||
0.0855938 | + | 0.996330i | \(0.472721\pi\) | |||||||
\(224\) | 9.13061 | 0.610065 | ||||||||
\(225\) | 37.0740 | 2.47160 | ||||||||
\(226\) | 43.1654 | 2.87132 | ||||||||
\(227\) | 10.1765 | 0.675440 | 0.337720 | − | 0.941247i | \(-0.390344\pi\) | ||||
0.337720 | + | 0.941247i | \(0.390344\pi\) | |||||||
\(228\) | 37.3253 | 2.47193 | ||||||||
\(229\) | 23.7436 | 1.56902 | 0.784510 | − | 0.620117i | \(-0.212915\pi\) | ||||
0.784510 | + | 0.620117i | \(0.212915\pi\) | |||||||
\(230\) | 3.73766 | 0.246454 | ||||||||
\(231\) | 5.73650 | 0.377434 | ||||||||
\(232\) | 15.3530 | 1.00797 | ||||||||
\(233\) | 12.7702 | 0.836607 | 0.418303 | − | 0.908307i | \(-0.362625\pi\) | ||||
0.418303 | + | 0.908307i | \(0.362625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.350525 | 0.0228657 | ||||||||
\(236\) | −4.56839 | −0.297377 | ||||||||
\(237\) | 21.0663 | 1.36840 | ||||||||
\(238\) | −9.59229 | −0.621776 | ||||||||
\(239\) | −28.0301 | −1.81312 | −0.906558 | − | 0.422081i | \(-0.861300\pi\) | ||||
−0.906558 | + | 0.422081i | \(0.861300\pi\) | |||||||
\(240\) | 67.4342 | 4.35286 | ||||||||
\(241\) | −6.06670 | −0.390790 | −0.195395 | − | 0.980725i | \(-0.562599\pi\) | ||||
−0.195395 | + | 0.980725i | \(0.562599\pi\) | |||||||
\(242\) | 2.53464 | 0.162933 | ||||||||
\(243\) | 1.03884 | 0.0666415 | ||||||||
\(244\) | −25.3800 | −1.62479 | ||||||||
\(245\) | 11.1296 | 0.711042 | ||||||||
\(246\) | 73.6003 | 4.69258 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −28.4625 | −1.80737 | ||||||||
\(249\) | −26.0399 | −1.65021 | ||||||||
\(250\) | −10.5354 | −0.666315 | ||||||||
\(251\) | 16.3142 | 1.02974 | 0.514870 | − | 0.857268i | \(-0.327840\pi\) | ||||
0.514870 | + | 0.857268i | \(0.327840\pi\) | |||||||
\(252\) | 50.4307 | 3.17684 | ||||||||
\(253\) | 0.439850 | 0.0276531 | ||||||||
\(254\) | 6.49052 | 0.407252 | ||||||||
\(255\) | −19.7765 | −1.23845 | ||||||||
\(256\) | −30.2754 | −1.89221 | ||||||||
\(257\) | 12.5358 | 0.781964 | 0.390982 | − | 0.920398i | \(-0.372135\pi\) | ||||
0.390982 | + | 0.920398i | \(0.372135\pi\) | |||||||
\(258\) | 49.9842 | 3.11188 | ||||||||
\(259\) | −14.9445 | −0.928609 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.8446 | 0.918857 | ||||||||
\(262\) | −30.8379 | −1.90517 | ||||||||
\(263\) | −13.5122 | −0.833199 | −0.416599 | − | 0.909090i | \(-0.636778\pi\) | ||||
−0.416599 | + | 0.909090i | \(0.636778\pi\) | |||||||
\(264\) | 18.3751 | 1.13091 | ||||||||
\(265\) | −1.28066 | −0.0786701 | ||||||||
\(266\) | −13.7183 | −0.841124 | ||||||||
\(267\) | −30.8954 | −1.89077 | ||||||||
\(268\) | −32.0855 | −1.95993 | ||||||||
\(269\) | −11.9388 | −0.727924 | −0.363962 | − | 0.931414i | \(-0.618576\pi\) | ||||
−0.363962 | + | 0.931414i | \(0.618576\pi\) | |||||||
\(270\) | 74.7438 | 4.54876 | ||||||||
\(271\) | 0.798793 | 0.0485232 | 0.0242616 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242616 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(272\) | −13.2696 | −0.804590 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.7276 | 1.67508 | ||||||||
\(275\) | −6.23981 | −0.376274 | ||||||||
\(276\) | 5.81923 | 0.350276 | ||||||||
\(277\) | 14.4989 | 0.871155 | 0.435578 | − | 0.900151i | \(-0.356544\pi\) | ||||
0.435578 | + | 0.900151i | \(0.356544\pi\) | |||||||
\(278\) | −15.2276 | −0.913292 | ||||||||
\(279\) | −27.5200 | −1.64758 | ||||||||
\(280\) | −39.5224 | −2.36192 | ||||||||
\(281\) | 12.0278 | 0.717520 | 0.358760 | − | 0.933430i | \(-0.383200\pi\) | ||||
0.358760 | + | 0.933430i | \(0.383200\pi\) | |||||||
\(282\) | 0.792432 | 0.0471886 | ||||||||
\(283\) | 13.0157 | 0.773701 | 0.386850 | − | 0.922143i | \(-0.373563\pi\) | ||||
0.386850 | + | 0.922143i | \(0.373563\pi\) | |||||||
\(284\) | 49.8508 | 2.95810 | ||||||||
\(285\) | −28.2832 | −1.67535 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.6294 | −1.09966 | ||||||||
\(288\) | 28.2785 | 1.66633 | ||||||||
\(289\) | −13.1084 | −0.771082 | ||||||||
\(290\) | −21.2308 | −1.24671 | ||||||||
\(291\) | 57.9647 | 3.39795 | ||||||||
\(292\) | 3.57571 | 0.209253 | ||||||||
\(293\) | −9.35716 | −0.546651 | −0.273326 | − | 0.961922i | \(-0.588124\pi\) | ||||
−0.273326 | + | 0.961922i | \(0.588124\pi\) | |||||||
\(294\) | 25.1606 | 1.46740 | ||||||||
\(295\) | 3.46168 | 0.201547 | ||||||||
\(296\) | −47.8701 | −2.78239 | ||||||||
\(297\) | 8.79587 | 0.510388 | ||||||||
\(298\) | −34.0609 | −1.97310 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −82.5529 | −4.76619 | ||||||||
\(301\) | −12.6518 | −0.729237 | ||||||||
\(302\) | −18.9117 | −1.08824 | ||||||||
\(303\) | −10.0070 | −0.574884 | ||||||||
\(304\) | −18.9774 | −1.08843 | ||||||||
\(305\) | 19.2316 | 1.10120 | ||||||||
\(306\) | −29.7084 | −1.69832 | ||||||||
\(307\) | −14.3957 | −0.821604 | −0.410802 | − | 0.911725i | \(-0.634751\pi\) | ||||
−0.410802 | + | 0.911725i | \(0.634751\pi\) | |||||||
\(308\) | −8.48783 | −0.483639 | ||||||||
\(309\) | −55.2140 | −3.14102 | ||||||||
\(310\) | 39.3591 | 2.23545 | ||||||||
\(311\) | 18.9376 | 1.07385 | 0.536926 | − | 0.843629i | \(-0.319585\pi\) | ||||
0.536926 | + | 0.843629i | \(0.319585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9761 | −0.903024 | −0.451512 | − | 0.892265i | \(-0.649115\pi\) | ||||
−0.451512 | + | 0.892265i | \(0.649115\pi\) | |||||||
\(314\) | 34.9126 | 1.97023 | ||||||||
\(315\) | −38.2137 | −2.15310 | ||||||||
\(316\) | −31.1700 | −1.75345 | ||||||||
\(317\) | 12.0125 | 0.674691 | 0.337346 | − | 0.941381i | \(-0.390471\pi\) | ||||
0.337346 | + | 0.941381i | \(0.390471\pi\) | |||||||
\(318\) | −2.89518 | −0.162354 | ||||||||
\(319\) | −2.49845 | −0.139886 | ||||||||
\(320\) | 4.65884 | 0.260437 | ||||||||
\(321\) | 37.0638 | 2.06870 | ||||||||
\(322\) | −2.13876 | −0.119189 | ||||||||
\(323\) | 5.56553 | 0.309675 | ||||||||
\(324\) | 37.5065 | 2.08369 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −40.1453 | −2.22344 | ||||||||
\(327\) | 10.4991 | 0.580603 | ||||||||
\(328\) | −59.6733 | −3.29490 | ||||||||
\(329\) | −0.200577 | −0.0110582 | ||||||||
\(330\) | −25.4098 | −1.39877 | ||||||||
\(331\) | −21.1500 | −1.16251 | −0.581256 | − | 0.813721i | \(-0.697438\pi\) | ||||
−0.581256 | + | 0.813721i | \(0.697438\pi\) | |||||||
\(332\) | 38.5291 | 2.11456 | ||||||||
\(333\) | −46.2849 | −2.53640 | ||||||||
\(334\) | 48.9048 | 2.67595 | ||||||||
\(335\) | 24.3127 | 1.32834 | ||||||||
\(336\) | −38.5871 | −2.10510 | ||||||||
\(337\) | 6.26056 | 0.341034 | 0.170517 | − | 0.985355i | \(-0.445456\pi\) | ||||
0.170517 | + | 0.985355i | \(0.445456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −50.9242 | −2.76582 | ||||||||
\(340\) | 29.2617 | 1.58694 | ||||||||
\(341\) | 4.63180 | 0.250826 | ||||||||
\(342\) | −42.4871 | −2.29744 | ||||||||
\(343\) | −19.7974 | −1.06896 | ||||||||
\(344\) | −40.5260 | −2.18501 | ||||||||
\(345\) | −4.40950 | −0.237400 | ||||||||
\(346\) | −40.6180 | −2.18364 | ||||||||
\(347\) | −10.4099 | −0.558834 | −0.279417 | − | 0.960170i | \(-0.590141\pi\) | ||||
−0.279417 | + | 0.960170i | \(0.590141\pi\) | |||||||
\(348\) | −33.0546 | −1.77191 | ||||||||
\(349\) | −27.5513 | −1.47479 | −0.737394 | − | 0.675462i | \(-0.763944\pi\) | ||||
−0.737394 | + | 0.675462i | \(0.763944\pi\) | |||||||
\(350\) | 30.3410 | 1.62179 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.75947 | −0.253681 | ||||||||
\(353\) | −5.28628 | −0.281360 | −0.140680 | − | 0.990055i | \(-0.544929\pi\) | ||||
−0.140680 | + | 0.990055i | \(0.544929\pi\) | |||||||
\(354\) | 7.82583 | 0.415938 | ||||||||
\(355\) | −37.7743 | −2.00485 | ||||||||
\(356\) | 45.7134 | 2.42280 | ||||||||
\(357\) | 11.3165 | 0.598932 | ||||||||
\(358\) | 25.5127 | 1.34839 | ||||||||
\(359\) | 23.0174 | 1.21481 | 0.607407 | − | 0.794391i | \(-0.292210\pi\) | ||||
0.607407 | + | 0.794391i | \(0.292210\pi\) | |||||||
\(360\) | −122.405 | −6.45133 | ||||||||
\(361\) | −11.0405 | −0.581080 | ||||||||
\(362\) | −24.7805 | −1.30243 | ||||||||
\(363\) | −2.99024 | −0.156947 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.70949 | −0.141821 | ||||||||
\(366\) | 43.4769 | 2.27257 | ||||||||
\(367\) | 18.6338 | 0.972677 | 0.486339 | − | 0.873770i | \(-0.338332\pi\) | ||||
0.486339 | + | 0.873770i | \(0.338332\pi\) | |||||||
\(368\) | −2.95869 | −0.154232 | ||||||||
\(369\) | −57.6972 | −3.00360 | ||||||||
\(370\) | 66.1969 | 3.44141 | ||||||||
\(371\) | 0.732815 | 0.0380459 | ||||||||
\(372\) | 61.2789 | 3.17716 | ||||||||
\(373\) | 0.434255 | 0.0224849 | 0.0112424 | − | 0.999937i | \(-0.496421\pi\) | ||||
0.0112424 | + | 0.999937i | \(0.496421\pi\) | |||||||
\(374\) | 5.00013 | 0.258550 | ||||||||
\(375\) | 12.4291 | 0.641835 | ||||||||
\(376\) | −0.642484 | −0.0331336 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −42.7698 | −2.19984 | ||||||||
\(379\) | 19.1999 | 0.986231 | 0.493115 | − | 0.869964i | \(-0.335858\pi\) | ||||
0.493115 | + | 0.869964i | \(0.335858\pi\) | |||||||
\(380\) | 41.8483 | 2.14677 | ||||||||
\(381\) | −7.65718 | −0.392289 | ||||||||
\(382\) | −2.60015 | −0.133035 | ||||||||
\(383\) | 5.79295 | 0.296006 | 0.148003 | − | 0.988987i | \(-0.452716\pi\) | ||||
0.148003 | + | 0.988987i | \(0.452716\pi\) | |||||||
\(384\) | 38.9961 | 1.99001 | ||||||||
\(385\) | 6.43163 | 0.327786 | ||||||||
\(386\) | −52.7871 | −2.68679 | ||||||||
\(387\) | −39.1840 | −1.99183 | ||||||||
\(388\) | −85.7656 | −4.35409 | ||||||||
\(389\) | 22.3481 | 1.13309 | 0.566546 | − | 0.824030i | \(-0.308279\pi\) | ||||
0.566546 | + | 0.824030i | \(0.308279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.867698 | 0.0438814 | ||||||||
\(392\) | −20.3996 | −1.03034 | ||||||||
\(393\) | 36.3809 | 1.83518 | ||||||||
\(394\) | 20.4166 | 1.02857 | ||||||||
\(395\) | 23.6190 | 1.18840 | ||||||||
\(396\) | −26.2878 | −1.32101 | ||||||||
\(397\) | −32.7283 | −1.64259 | −0.821294 | − | 0.570506i | \(-0.806747\pi\) | ||||
−0.821294 | + | 0.570506i | \(0.806747\pi\) | |||||||
\(398\) | 48.2318 | 2.41764 | ||||||||
\(399\) | 16.1841 | 0.810221 | ||||||||
\(400\) | 41.9726 | 2.09863 | ||||||||
\(401\) | −18.2188 | −0.909801 | −0.454901 | − | 0.890542i | \(-0.650325\pi\) | ||||
−0.454901 | + | 0.890542i | \(0.650325\pi\) | |||||||
\(402\) | 54.9637 | 2.74134 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.8065 | 0.736649 | ||||||||
\(405\) | −28.4204 | −1.41222 | ||||||||
\(406\) | 12.1487 | 0.602928 | ||||||||
\(407\) | 7.79007 | 0.386139 | ||||||||
\(408\) | 36.2487 | 1.79458 | ||||||||
\(409\) | −39.2971 | −1.94312 | −0.971558 | − | 0.236802i | \(-0.923901\pi\) | ||||
−0.971558 | + | 0.236802i | \(0.923901\pi\) | |||||||
\(410\) | 82.5188 | 4.07531 | ||||||||
\(411\) | −32.7116 | −1.61354 | ||||||||
\(412\) | 81.6956 | 4.02486 | ||||||||
\(413\) | −1.98084 | −0.0974707 | ||||||||
\(414\) | −6.62398 | −0.325551 | ||||||||
\(415\) | −29.1953 | −1.43314 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.9648 | 0.879738 | ||||||||
\(418\) | 7.15087 | 0.349761 | ||||||||
\(419\) | −1.57695 | −0.0770388 | −0.0385194 | − | 0.999258i | \(-0.512264\pi\) | ||||
−0.0385194 | + | 0.999258i | \(0.512264\pi\) | |||||||
\(420\) | 85.0907 | 4.15200 | ||||||||
\(421\) | −10.0373 | −0.489189 | −0.244595 | − | 0.969625i | \(-0.578655\pi\) | ||||
−0.244595 | + | 0.969625i | \(0.578655\pi\) | |||||||
\(422\) | 47.0465 | 2.29019 | ||||||||
\(423\) | −0.621209 | −0.0302042 | ||||||||
\(424\) | 2.34734 | 0.113997 | ||||||||
\(425\) | −12.3094 | −0.597092 | ||||||||
\(426\) | −85.3963 | −4.13747 | ||||||||
\(427\) | −11.0047 | −0.532553 | ||||||||
\(428\) | −54.8403 | −2.65081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 56.0411 | 2.70254 | ||||||||
\(431\) | −1.00444 | −0.0483821 | −0.0241911 | − | 0.999707i | \(-0.507701\pi\) | ||||
−0.0241911 | + | 0.999707i | \(0.507701\pi\) | |||||||
\(432\) | −59.1662 | −2.84664 | ||||||||
\(433\) | −4.11273 | −0.197645 | −0.0988225 | − | 0.995105i | \(-0.531508\pi\) | ||||
−0.0988225 | + | 0.995105i | \(0.531508\pi\) | |||||||
\(434\) | −22.5220 | −1.08109 | ||||||||
\(435\) | 25.0470 | 1.20091 | ||||||||
\(436\) | −15.5347 | −0.743977 | ||||||||
\(437\) | 1.24093 | 0.0593616 | ||||||||
\(438\) | −6.12534 | −0.292680 | ||||||||
\(439\) | 4.14317 | 0.197743 | 0.0988713 | − | 0.995100i | \(-0.468477\pi\) | ||||
0.0988713 | + | 0.995100i | \(0.468477\pi\) | |||||||
\(440\) | 20.6017 | 0.982146 | ||||||||
\(441\) | −19.7241 | −0.939243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3516 | −0.491821 | −0.245911 | − | 0.969293i | \(-0.579087\pi\) | ||||
−0.245911 | + | 0.969293i | \(0.579087\pi\) | |||||||
\(444\) | 103.063 | 4.89115 | ||||||||
\(445\) | −34.6392 | −1.64205 | ||||||||
\(446\) | 6.47950 | 0.306813 | ||||||||
\(447\) | 40.1833 | 1.90061 | ||||||||
\(448\) | −2.66588 | −0.125951 | ||||||||
\(449\) | 9.13794 | 0.431246 | 0.215623 | − | 0.976477i | \(-0.430822\pi\) | ||||
0.215623 | + | 0.976477i | \(0.430822\pi\) | |||||||
\(450\) | 93.9693 | 4.42975 | ||||||||
\(451\) | 9.71084 | 0.457266 | ||||||||
\(452\) | 75.3484 | 3.54409 | ||||||||
\(453\) | 22.3110 | 1.04826 | ||||||||
\(454\) | 25.7939 | 1.21057 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 51.8407 | 2.42767 | ||||||||
\(457\) | −1.43933 | −0.0673288 | −0.0336644 | − | 0.999433i | \(-0.510718\pi\) | ||||
−0.0336644 | + | 0.999433i | \(0.510718\pi\) | |||||||
\(458\) | 60.1814 | 2.81209 | ||||||||
\(459\) | 17.3517 | 0.809910 | ||||||||
\(460\) | 6.52438 | 0.304201 | ||||||||
\(461\) | −25.1927 | −1.17334 | −0.586671 | − | 0.809825i | \(-0.699562\pi\) | ||||
−0.586671 | + | 0.809825i | \(0.699562\pi\) | |||||||
\(462\) | 14.5400 | 0.676461 | ||||||||
\(463\) | 14.1428 | 0.657271 | 0.328635 | − | 0.944457i | \(-0.393411\pi\) | ||||
0.328635 | + | 0.944457i | \(0.393411\pi\) | |||||||
\(464\) | 16.8060 | 0.780200 | ||||||||
\(465\) | −46.4339 | −2.15332 | ||||||||
\(466\) | 32.3680 | 1.49942 | ||||||||
\(467\) | 18.4384 | 0.853228 | 0.426614 | − | 0.904434i | \(-0.359706\pi\) | ||||
0.426614 | + | 0.904434i | \(0.359706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.9122 | −0.642405 | ||||||||
\(470\) | 0.888455 | 0.0409814 | ||||||||
\(471\) | −41.1881 | −1.89785 | ||||||||
\(472\) | −6.34499 | −0.292052 | ||||||||
\(473\) | 6.59493 | 0.303235 | ||||||||
\(474\) | 53.3954 | 2.45253 | ||||||||
\(475\) | −17.6041 | −0.807731 | ||||||||
\(476\) | −16.7441 | −0.767463 | ||||||||
\(477\) | 2.26961 | 0.103918 | ||||||||
\(478\) | −71.0462 | −3.24958 | ||||||||
\(479\) | −28.2221 | −1.28950 | −0.644750 | − | 0.764394i | \(-0.723038\pi\) | ||||
−0.644750 | + | 0.764394i | \(0.723038\pi\) | |||||||
\(480\) | 47.7138 | 2.17783 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −15.3769 | −0.700399 | ||||||||
\(483\) | 2.52320 | 0.114810 | ||||||||
\(484\) | 4.42441 | 0.201110 | ||||||||
\(485\) | 64.9886 | 2.95098 | ||||||||
\(486\) | 2.63308 | 0.119439 | ||||||||
\(487\) | 12.1754 | 0.551720 | 0.275860 | − | 0.961198i | \(-0.411037\pi\) | ||||
0.275860 | + | 0.961198i | \(0.411037\pi\) | |||||||
\(488\) | −35.2499 | −1.59569 | ||||||||
\(489\) | 47.3613 | 2.14175 | ||||||||
\(490\) | 28.2095 | 1.27437 | ||||||||
\(491\) | 35.0308 | 1.58092 | 0.790458 | − | 0.612516i | \(-0.209842\pi\) | ||||
0.790458 | + | 0.612516i | \(0.209842\pi\) | |||||||
\(492\) | 128.475 | 5.79209 | ||||||||
\(493\) | −4.92872 | −0.221978 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.9195 | 0.895313 | ||||||||
\(496\) | −31.1562 | −1.39895 | ||||||||
\(497\) | 21.6151 | 0.969572 | ||||||||
\(498\) | −66.0018 | −2.95761 | ||||||||
\(499\) | −7.22186 | −0.323295 | −0.161648 | − | 0.986849i | \(-0.551681\pi\) | ||||
−0.161648 | + | 0.986849i | \(0.551681\pi\) | |||||||
\(500\) | −18.3903 | −0.822439 | ||||||||
\(501\) | −57.6954 | −2.57764 | ||||||||
\(502\) | 41.3505 | 1.84556 | ||||||||
\(503\) | 15.4630 | 0.689460 | 0.344730 | − | 0.938702i | \(-0.387970\pi\) | ||||
0.344730 | + | 0.938702i | \(0.387970\pi\) | |||||||
\(504\) | 70.0426 | 3.11995 | ||||||||
\(505\) | −11.2195 | −0.499263 | ||||||||
\(506\) | 1.11486 | 0.0495616 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.3297 | 0.502674 | ||||||||
\(509\) | −33.2042 | −1.47175 | −0.735876 | − | 0.677117i | \(-0.763229\pi\) | ||||
−0.735876 | + | 0.677117i | \(0.763229\pi\) | |||||||
\(510\) | −50.1264 | −2.21963 | ||||||||
\(511\) | 1.55042 | 0.0685865 | ||||||||
\(512\) | −50.6550 | −2.23865 | ||||||||
\(513\) | 24.8154 | 1.09563 | ||||||||
\(514\) | 31.7739 | 1.40149 | ||||||||
\(515\) | −61.9046 | −2.72784 | ||||||||
\(516\) | 87.2513 | 3.84102 | ||||||||
\(517\) | 0.104554 | 0.00459826 | ||||||||
\(518\) | −37.8791 | −1.66431 | ||||||||
\(519\) | 47.9190 | 2.10341 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0340 | −0.965325 | −0.482663 | − | 0.875806i | \(-0.660330\pi\) | ||||
−0.482663 | + | 0.875806i | \(0.660330\pi\) | |||||||
\(522\) | 37.6257 | 1.64683 | ||||||||
\(523\) | 28.8453 | 1.26132 | 0.630658 | − | 0.776061i | \(-0.282785\pi\) | ||||
0.630658 | + | 0.776061i | \(0.282785\pi\) | |||||||
\(524\) | −53.8299 | −2.35157 | ||||||||
\(525\) | −35.7947 | −1.56221 | ||||||||
\(526\) | −34.2486 | −1.49331 | ||||||||
\(527\) | 9.13721 | 0.398023 | ||||||||
\(528\) | 20.1141 | 0.875354 | ||||||||
\(529\) | −22.8065 | −0.991588 | ||||||||
\(530\) | −3.24600 | −0.140997 | ||||||||
\(531\) | −6.13488 | −0.266231 | ||||||||
\(532\) | −23.9464 | −1.03821 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −78.3088 | −3.38875 | ||||||||
\(535\) | 41.5551 | 1.79658 | ||||||||
\(536\) | −44.5632 | −1.92484 | ||||||||
\(537\) | −30.0986 | −1.29885 | ||||||||
\(538\) | −30.2607 | −1.30463 | ||||||||
\(539\) | 3.31970 | 0.142990 | ||||||||
\(540\) | 130.471 | 5.61458 | ||||||||
\(541\) | −19.3752 | −0.833007 | −0.416503 | − | 0.909134i | \(-0.636745\pi\) | ||||
−0.416503 | + | 0.909134i | \(0.636745\pi\) | |||||||
\(542\) | 2.02465 | 0.0869664 | ||||||||
\(543\) | 29.2347 | 1.25458 | ||||||||
\(544\) | −9.38907 | −0.402553 | ||||||||
\(545\) | 11.7714 | 0.504230 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.4512 | 1.34475 | 0.672377 | − | 0.740209i | \(-0.265273\pi\) | ||||
0.672377 | + | 0.740209i | \(0.265273\pi\) | |||||||
\(548\) | 48.4006 | 2.06757 | ||||||||
\(549\) | −34.0827 | −1.45461 | ||||||||
\(550\) | −15.8157 | −0.674383 | ||||||||
\(551\) | −7.04876 | −0.300287 | ||||||||
\(552\) | 8.08226 | 0.344004 | ||||||||
\(553\) | −13.5152 | −0.574725 | ||||||||
\(554\) | 36.7496 | 1.56134 | ||||||||
\(555\) | −78.0956 | −3.31497 | ||||||||
\(556\) | −26.5810 | −1.12728 | ||||||||
\(557\) | −24.1266 | −1.02228 | −0.511138 | − | 0.859499i | \(-0.670776\pi\) | ||||
−0.511138 | + | 0.859499i | \(0.670776\pi\) | |||||||
\(558\) | −69.7532 | −2.95289 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −43.2629 | −1.82819 | ||||||||
\(561\) | −5.89889 | −0.249051 | ||||||||
\(562\) | 30.4863 | 1.28598 | ||||||||
\(563\) | −7.74375 | −0.326360 | −0.163180 | − | 0.986596i | \(-0.552175\pi\) | ||||
−0.163180 | + | 0.986596i | \(0.552175\pi\) | |||||||
\(564\) | 1.38325 | 0.0582453 | ||||||||
\(565\) | −57.0950 | −2.40200 | ||||||||
\(566\) | 32.9900 | 1.38667 | ||||||||
\(567\) | 16.2627 | 0.682969 | ||||||||
\(568\) | 69.2372 | 2.90513 | ||||||||
\(569\) | −18.3952 | −0.771167 | −0.385583 | − | 0.922673i | \(-0.626000\pi\) | ||||
−0.385583 | + | 0.922673i | \(0.626000\pi\) | |||||||
\(570\) | −71.6877 | −3.00267 | ||||||||
\(571\) | −9.57839 | −0.400843 | −0.200422 | − | 0.979710i | \(-0.564231\pi\) | ||||
−0.200422 | + | 0.979710i | \(0.564231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.06752 | 0.128148 | ||||||||
\(574\) | −47.2188 | −1.97087 | ||||||||
\(575\) | −2.74458 | −0.114457 | ||||||||
\(576\) | −8.25652 | −0.344022 | ||||||||
\(577\) | 12.1259 | 0.504808 | 0.252404 | − | 0.967622i | \(-0.418779\pi\) | ||||
0.252404 | + | 0.967622i | \(0.418779\pi\) | |||||||
\(578\) | −33.2251 | −1.38198 | ||||||||
\(579\) | 62.2755 | 2.58808 | ||||||||
\(580\) | −37.0600 | −1.53883 | ||||||||
\(581\) | 16.7061 | 0.693085 | ||||||||
\(582\) | 146.920 | 6.09002 | ||||||||
\(583\) | −0.381991 | −0.0158204 | ||||||||
\(584\) | 4.96627 | 0.205506 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.7171 | −0.979742 | ||||||||
\(587\) | −25.3026 | −1.04435 | −0.522175 | − | 0.852838i | \(-0.674879\pi\) | ||||
−0.522175 | + | 0.852838i | \(0.674879\pi\) | |||||||
\(588\) | 43.9198 | 1.81122 | ||||||||
\(589\) | 13.0675 | 0.538436 | ||||||||
\(590\) | 8.77413 | 0.361225 | ||||||||
\(591\) | −24.0864 | −0.990783 | ||||||||
\(592\) | −52.4006 | −2.15365 | ||||||||
\(593\) | −2.55502 | −0.104922 | −0.0524610 | − | 0.998623i | \(-0.516707\pi\) | ||||
−0.0524610 | + | 0.998623i | \(0.516707\pi\) | |||||||
\(594\) | 22.2944 | 0.914750 | ||||||||
\(595\) | 12.6878 | 0.520148 | ||||||||
\(596\) | −59.4559 | −2.43541 | ||||||||
\(597\) | −56.9013 | −2.32882 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.3849 | 1.77266 | 0.886329 | − | 0.463055i | \(-0.153247\pi\) | ||||
0.886329 | + | 0.463055i | \(0.153247\pi\) | |||||||
\(600\) | −114.657 | −4.68084 | ||||||||
\(601\) | 9.55136 | 0.389608 | 0.194804 | − | 0.980842i | \(-0.437593\pi\) | ||||
0.194804 | + | 0.980842i | \(0.437593\pi\) | |||||||
\(602\) | −32.0677 | −1.30698 | ||||||||
\(603\) | −43.0875 | −1.75466 | ||||||||
\(604\) | −33.0117 | −1.34323 | ||||||||
\(605\) | −3.35258 | −0.136302 | ||||||||
\(606\) | −25.3640 | −1.03034 | ||||||||
\(607\) | 3.77022 | 0.153028 | 0.0765142 | − | 0.997068i | \(-0.475621\pi\) | ||||
0.0765142 | + | 0.997068i | \(0.475621\pi\) | |||||||
\(608\) | −13.4277 | −0.544564 | ||||||||
\(609\) | −14.3324 | −0.580776 | ||||||||
\(610\) | 48.7452 | 1.97363 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −51.8583 | −2.09625 | ||||||||
\(613\) | 39.3763 | 1.59039 | 0.795197 | − | 0.606352i | \(-0.207368\pi\) | ||||
0.795197 | + | 0.606352i | \(0.207368\pi\) | |||||||
\(614\) | −36.4879 | −1.47253 | ||||||||
\(615\) | −97.3514 | −3.92559 | ||||||||
\(616\) | −11.7887 | −0.474979 | ||||||||
\(617\) | −26.9832 | −1.08630 | −0.543152 | − | 0.839635i | \(-0.682769\pi\) | ||||
−0.543152 | + | 0.839635i | \(0.682769\pi\) | |||||||
\(618\) | −139.948 | −5.62952 | ||||||||
\(619\) | −19.3050 | −0.775932 | −0.387966 | − | 0.921674i | \(-0.626822\pi\) | ||||
−0.387966 | + | 0.921674i | \(0.626822\pi\) | |||||||
\(620\) | 68.7044 | 2.75923 | ||||||||
\(621\) | 3.86886 | 0.155252 | ||||||||
\(622\) | 48.0000 | 1.92463 | ||||||||
\(623\) | 19.8212 | 0.794119 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2638 | −0.690554 | ||||||||
\(626\) | −40.4938 | −1.61846 | ||||||||
\(627\) | −8.43623 | −0.336911 | ||||||||
\(628\) | 60.9426 | 2.43188 | ||||||||
\(629\) | 15.3676 | 0.612746 | ||||||||
\(630\) | −96.8580 | −3.85892 | ||||||||
\(631\) | 15.3139 | 0.609636 | 0.304818 | − | 0.952411i | \(-0.401404\pi\) | ||||
0.304818 | + | 0.952411i | \(0.401404\pi\) | |||||||
\(632\) | −43.2917 | −1.72205 | ||||||||
\(633\) | −55.5030 | −2.20604 | ||||||||
\(634\) | 30.4475 | 1.20922 | ||||||||
\(635\) | −8.58504 | −0.340687 | ||||||||
\(636\) | −5.05376 | −0.200395 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.33267 | −0.250713 | ||||||||
\(639\) | 66.9445 | 2.64828 | ||||||||
\(640\) | 43.7215 | 1.72824 | ||||||||
\(641\) | 29.3891 | 1.16080 | 0.580400 | − | 0.814332i | \(-0.302896\pi\) | ||||
0.580400 | + | 0.814332i | \(0.302896\pi\) | |||||||
\(642\) | 93.9436 | 3.70766 | ||||||||
\(643\) | 44.7293 | 1.76395 | 0.881976 | − | 0.471295i | \(-0.156213\pi\) | ||||
0.881976 | + | 0.471295i | \(0.156213\pi\) | |||||||
\(644\) | −3.73337 | −0.147115 | ||||||||
\(645\) | −66.1143 | −2.60325 | ||||||||
\(646\) | 14.1066 | 0.555018 | ||||||||
\(647\) | 16.1126 | 0.633452 | 0.316726 | − | 0.948517i | \(-0.397416\pi\) | ||||
0.316726 | + | 0.948517i | \(0.397416\pi\) | |||||||
\(648\) | 52.0924 | 2.04638 | ||||||||
\(649\) | 1.03254 | 0.0405308 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.5703 | 1.04137 | ||||||||
\(652\) | −70.0766 | −2.74441 | ||||||||
\(653\) | −38.5815 | −1.50981 | −0.754905 | − | 0.655835i | \(-0.772317\pi\) | ||||
−0.754905 | + | 0.655835i | \(0.772317\pi\) | |||||||
\(654\) | 26.6115 | 1.04059 | ||||||||
\(655\) | 40.7894 | 1.59377 | ||||||||
\(656\) | −65.3208 | −2.55035 | ||||||||
\(657\) | 4.80182 | 0.187337 | ||||||||
\(658\) | −0.508390 | −0.0198191 | ||||||||
\(659\) | −18.5716 | −0.723447 | −0.361723 | − | 0.932285i | \(-0.617812\pi\) | ||||
−0.361723 | + | 0.932285i | \(0.617812\pi\) | |||||||
\(660\) | −44.3548 | −1.72651 | ||||||||
\(661\) | −12.0249 | −0.467714 | −0.233857 | − | 0.972271i | \(-0.575135\pi\) | ||||
−0.233857 | + | 0.972271i | \(0.575135\pi\) | |||||||
\(662\) | −53.6078 | −2.08353 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 53.5126 | 2.07669 | ||||||||
\(665\) | 18.1453 | 0.703643 | ||||||||
\(666\) | −117.316 | −4.54589 | ||||||||
\(667\) | −1.09894 | −0.0425512 | ||||||||
\(668\) | 85.3671 | 3.30295 | ||||||||
\(669\) | −7.64417 | −0.295541 | ||||||||
\(670\) | 61.6240 | 2.38074 | ||||||||
\(671\) | 5.73635 | 0.221449 | ||||||||
\(672\) | −27.3027 | −1.05323 | ||||||||
\(673\) | −39.9547 | −1.54014 | −0.770071 | − | 0.637958i | \(-0.779779\pi\) | ||||
−0.770071 | + | 0.637958i | \(0.779779\pi\) | |||||||
\(674\) | 15.8683 | 0.611223 | ||||||||
\(675\) | −54.8845 | −2.11251 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.34058 | −0.0515226 | −0.0257613 | − | 0.999668i | \(-0.508201\pi\) | ||||
−0.0257613 | + | 0.999668i | \(0.508201\pi\) | |||||||
\(678\) | −129.075 | −4.95708 | ||||||||
\(679\) | −37.1877 | −1.42713 | ||||||||
\(680\) | 40.6412 | 1.55852 | ||||||||
\(681\) | −30.4303 | −1.16609 | ||||||||
\(682\) | 11.7399 | 0.449546 | ||||||||
\(683\) | 17.6692 | 0.676092 | 0.338046 | − | 0.941130i | \(-0.390234\pi\) | ||||
0.338046 | + | 0.941130i | \(0.390234\pi\) | |||||||
\(684\) | −74.1645 | −2.83575 | ||||||||
\(685\) | −36.6754 | −1.40129 | ||||||||
\(686\) | −50.1794 | −1.91586 | ||||||||
\(687\) | −70.9989 | −2.70878 | ||||||||
\(688\) | −44.3614 | −1.69126 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −11.1765 | −0.425482 | ||||||||
\(691\) | 21.4216 | 0.814915 | 0.407458 | − | 0.913224i | \(-0.366415\pi\) | ||||
0.407458 | + | 0.913224i | \(0.366415\pi\) | |||||||
\(692\) | −70.9018 | −2.69528 | ||||||||
\(693\) | −11.3983 | −0.432985 | ||||||||
\(694\) | −26.3854 | −1.00158 | ||||||||
\(695\) | 20.1416 | 0.764016 | ||||||||
\(696\) | −45.9091 | −1.74018 | ||||||||
\(697\) | 19.1567 | 0.725612 | ||||||||
\(698\) | −69.8328 | −2.64321 | ||||||||
\(699\) | −38.1861 | −1.44433 | ||||||||
\(700\) | 52.9624 | 2.00179 | ||||||||
\(701\) | 7.83629 | 0.295972 | 0.147986 | − | 0.988989i | \(-0.452721\pi\) | ||||
0.147986 | + | 0.988989i | \(0.452721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.9778 | 0.828908 | ||||||||
\(704\) | 1.38963 | 0.0523736 | ||||||||
\(705\) | −1.04815 | −0.0394757 | ||||||||
\(706\) | −13.3988 | −0.504272 | ||||||||
\(707\) | 6.42003 | 0.241450 | ||||||||
\(708\) | 13.6606 | 0.513396 | ||||||||
\(709\) | 5.09790 | 0.191456 | 0.0957279 | − | 0.995408i | \(-0.469482\pi\) | ||||
0.0957279 | + | 0.995408i | \(0.469482\pi\) | |||||||
\(710\) | −95.7443 | −3.59322 | ||||||||
\(711\) | −41.8581 | −1.56980 | ||||||||
\(712\) | 63.4908 | 2.37942 | ||||||||
\(713\) | 2.03729 | 0.0762972 | ||||||||
\(714\) | 28.6832 | 1.07344 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 44.5344 | 1.66433 | ||||||||
\(717\) | 83.8167 | 3.13019 | ||||||||
\(718\) | 58.3410 | 2.17727 | ||||||||
\(719\) | −19.0066 | −0.708827 | −0.354413 | − | 0.935089i | \(-0.615319\pi\) | ||||
−0.354413 | + | 0.935089i | \(0.615319\pi\) | |||||||
\(720\) | −133.990 | −4.99351 | ||||||||
\(721\) | 35.4230 | 1.31922 | ||||||||
\(722\) | −27.9838 | −1.04145 | ||||||||
\(723\) | 18.1409 | 0.674666 | ||||||||
\(724\) | −43.2563 | −1.60761 | ||||||||
\(725\) | 15.5898 | 0.578991 | ||||||||
\(726\) | −7.57919 | −0.281290 | ||||||||
\(727\) | 4.60308 | 0.170719 | 0.0853595 | − | 0.996350i | \(-0.472796\pi\) | ||||
0.0853595 | + | 0.996350i | \(0.472796\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.5379 | −1.05696 | ||||||||
\(730\) | −6.86758 | −0.254180 | ||||||||
\(731\) | 13.0099 | 0.481189 | ||||||||
\(732\) | 75.8922 | 2.80506 | ||||||||
\(733\) | 22.9104 | 0.846213 | 0.423107 | − | 0.906080i | \(-0.360940\pi\) | ||||
0.423107 | + | 0.906080i | \(0.360940\pi\) | |||||||
\(734\) | 47.2300 | 1.74329 | ||||||||
\(735\) | −33.2801 | −1.22755 | ||||||||
\(736\) | −2.09345 | −0.0771656 | ||||||||
\(737\) | 7.25193 | 0.267128 | ||||||||
\(738\) | −146.242 | −5.38324 | ||||||||
\(739\) | 2.63363 | 0.0968797 | 0.0484398 | − | 0.998826i | \(-0.484575\pi\) | ||||
0.0484398 | + | 0.998826i | \(0.484575\pi\) | |||||||
\(740\) | 115.552 | 4.24776 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.85742 | 0.0681882 | ||||||||
\(743\) | 6.05846 | 0.222263 | 0.111132 | − | 0.993806i | \(-0.464552\pi\) | ||||
0.111132 | + | 0.993806i | \(0.464552\pi\) | |||||||
\(744\) | 85.1095 | 3.12027 | ||||||||
\(745\) | 45.0525 | 1.65060 | ||||||||
\(746\) | 1.10068 | 0.0402988 | ||||||||
\(747\) | 51.7406 | 1.89309 | ||||||||
\(748\) | 8.72810 | 0.319131 | ||||||||
\(749\) | −23.7786 | −0.868851 | ||||||||
\(750\) | 31.5033 | 1.15034 | ||||||||
\(751\) | −12.7774 | −0.466255 | −0.233127 | − | 0.972446i | \(-0.574896\pi\) | ||||
−0.233127 | + | 0.972446i | \(0.574896\pi\) | |||||||
\(752\) | −0.703290 | −0.0256463 | ||||||||
\(753\) | −48.7832 | −1.77776 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.0145 | 0.910372 | ||||||||
\(756\) | −74.6579 | −2.71528 | ||||||||
\(757\) | 38.7827 | 1.40958 | 0.704791 | − | 0.709415i | \(-0.251041\pi\) | ||||
0.704791 | + | 0.709415i | \(0.251041\pi\) | |||||||
\(758\) | 48.6648 | 1.76758 | ||||||||
\(759\) | −1.31526 | −0.0477407 | ||||||||
\(760\) | 58.1226 | 2.10833 | ||||||||
\(761\) | 40.5551 | 1.47012 | 0.735061 | − | 0.678001i | \(-0.237154\pi\) | ||||
0.735061 | + | 0.678001i | \(0.237154\pi\) | |||||||
\(762\) | −19.4082 | −0.703086 | ||||||||
\(763\) | −6.73579 | −0.243852 | ||||||||
\(764\) | −4.53876 | −0.164207 | ||||||||
\(765\) | 39.2954 | 1.42073 | ||||||||
\(766\) | 14.6830 | 0.530520 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 90.5306 | 3.26674 | ||||||||
\(769\) | 26.4805 | 0.954910 | 0.477455 | − | 0.878656i | \(-0.341559\pi\) | ||||
0.477455 | + | 0.878656i | \(0.341559\pi\) | |||||||
\(770\) | 16.3019 | 0.587479 | ||||||||
\(771\) | −37.4852 | −1.34999 | ||||||||
\(772\) | −92.1439 | −3.31633 | ||||||||
\(773\) | −14.2498 | −0.512530 | −0.256265 | − | 0.966607i | \(-0.582492\pi\) | ||||
−0.256265 | + | 0.966607i | \(0.582492\pi\) | |||||||
\(774\) | −99.3174 | −3.56989 | ||||||||
\(775\) | −28.9015 | −1.03817 | ||||||||
\(776\) | −119.119 | −4.27612 | ||||||||
\(777\) | 44.6878 | 1.60316 | ||||||||
\(778\) | 56.6444 | 2.03080 | ||||||||
\(779\) | 27.3968 | 0.981591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2672 | −0.403173 | ||||||||
\(782\) | 2.19930 | 0.0786469 | ||||||||
\(783\) | −21.9760 | −0.785359 | ||||||||
\(784\) | −22.3303 | −0.797510 | ||||||||
\(785\) | −46.1791 | −1.64820 | ||||||||
\(786\) | 92.2126 | 3.28912 | ||||||||
\(787\) | 54.1394 | 1.92986 | 0.964931 | − | 0.262503i | \(-0.0845480\pi\) | ||||
0.964931 | + | 0.262503i | \(0.0845480\pi\) | |||||||
\(788\) | 35.6387 | 1.26958 | ||||||||
\(789\) | 40.4047 | 1.43845 | ||||||||
\(790\) | 59.8656 | 2.12992 | ||||||||
\(791\) | 32.6708 | 1.16164 | ||||||||
\(792\) | −36.5108 | −1.29735 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −82.9546 | −2.94395 | ||||||||
\(795\) | 3.82947 | 0.135817 | ||||||||
\(796\) | 84.1922 | 2.98411 | ||||||||
\(797\) | −19.7774 | −0.700553 | −0.350276 | − | 0.936646i | \(-0.613912\pi\) | ||||
−0.350276 | + | 0.936646i | \(0.613912\pi\) | |||||||
\(798\) | 41.0210 | 1.45213 | ||||||||
\(799\) | 0.206255 | 0.00729676 | ||||||||
\(800\) | 29.6982 | 1.04999 | ||||||||
\(801\) | 61.3884 | 2.16905 | ||||||||
\(802\) | −46.1780 | −1.63060 | ||||||||
\(803\) | −0.808179 | −0.0285200 | ||||||||
\(804\) | 95.9433 | 3.38366 | ||||||||
\(805\) | 2.82895 | 0.0997073 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.7000 | 1.25670 | ||||||||
\(808\) | 20.5645 | 0.723458 | ||||||||
\(809\) | 7.57611 | 0.266362 | 0.133181 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133181 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(810\) | −72.0356 | −2.53107 | ||||||||
\(811\) | −36.2578 | −1.27318 | −0.636592 | − | 0.771201i | \(-0.719657\pi\) | ||||
−0.636592 | + | 0.771201i | \(0.719657\pi\) | |||||||
\(812\) | 21.2064 | 0.744199 | ||||||||
\(813\) | −2.38858 | −0.0837712 | ||||||||
\(814\) | 19.7450 | 0.692063 | ||||||||
\(815\) | 53.1003 | 1.86002 | ||||||||
\(816\) | 39.6794 | 1.38906 | ||||||||
\(817\) | 18.6060 | 0.650941 | ||||||||
\(818\) | −99.6040 | −3.48257 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 144.043 | 5.03019 | ||||||||
\(821\) | 28.6271 | 0.999093 | 0.499547 | − | 0.866287i | \(-0.333500\pi\) | ||||
0.499547 | + | 0.866287i | \(0.333500\pi\) | |||||||
\(822\) | −82.9121 | −2.89189 | ||||||||
\(823\) | −19.5200 | −0.680424 | −0.340212 | − | 0.940349i | \(-0.610499\pi\) | ||||
−0.340212 | + | 0.940349i | \(0.610499\pi\) | |||||||
\(824\) | 113.466 | 3.95278 | ||||||||
\(825\) | 18.6585 | 0.649606 | ||||||||
\(826\) | −5.02072 | −0.174693 | ||||||||
\(827\) | 4.68925 | 0.163061 | 0.0815306 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815306 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(828\) | −11.5627 | −0.401830 | ||||||||
\(829\) | −20.9053 | −0.726071 | −0.363036 | − | 0.931775i | \(-0.618260\pi\) | ||||
−0.363036 | + | 0.931775i | \(0.618260\pi\) | |||||||
\(830\) | −73.9996 | −2.56856 | ||||||||
\(831\) | −43.3552 | −1.50398 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.54883 | 0.226903 | ||||||||
\(834\) | 45.5342 | 1.57672 | ||||||||
\(835\) | −64.6867 | −2.23857 | ||||||||
\(836\) | 12.4824 | 0.431713 | ||||||||
\(837\) | 40.7407 | 1.40820 | ||||||||
\(838\) | −3.99699 | −0.138074 | ||||||||
\(839\) | −47.0179 | −1.62324 | −0.811618 | − | 0.584188i | \(-0.801413\pi\) | ||||
−0.811618 | + | 0.584188i | \(0.801413\pi\) | |||||||
\(840\) | 118.182 | 4.07765 | ||||||||
\(841\) | −22.7578 | −0.784751 | ||||||||
\(842\) | −25.4410 | −0.876756 | ||||||||
\(843\) | −35.9661 | −1.23874 | ||||||||
\(844\) | 82.1232 | 2.82680 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.57454 | −0.0541338 | ||||||||
\(847\) | 1.91841 | 0.0659174 | ||||||||
\(848\) | 2.56950 | 0.0882369 | ||||||||
\(849\) | −38.9199 | −1.33573 | ||||||||
\(850\) | −31.1998 | −1.07014 | ||||||||
\(851\) | 3.42646 | 0.117458 | ||||||||
\(852\) | −149.066 | −5.10691 | ||||||||
\(853\) | −48.7942 | −1.67068 | −0.835340 | − | 0.549733i | \(-0.814729\pi\) | ||||
−0.835340 | + | 0.549733i | \(0.814729\pi\) | |||||||
\(854\) | −27.8929 | −0.954476 | ||||||||
\(855\) | 56.1979 | 1.92193 | ||||||||
\(856\) | −76.1671 | −2.60334 | ||||||||
\(857\) | −48.2335 | −1.64762 | −0.823812 | − | 0.566863i | \(-0.808157\pi\) | ||||
−0.823812 | + | 0.566863i | \(0.808157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.2337 | 0.895082 | 0.447541 | − | 0.894263i | \(-0.352300\pi\) | ||||
0.447541 | + | 0.894263i | \(0.352300\pi\) | |||||||
\(860\) | 97.8240 | 3.33577 | ||||||||
\(861\) | 55.7063 | 1.89847 | ||||||||
\(862\) | −2.54589 | −0.0867135 | ||||||||
\(863\) | −28.5207 | −0.970857 | −0.485428 | − | 0.874276i | \(-0.661336\pi\) | ||||
−0.485428 | + | 0.874276i | \(0.661336\pi\) | |||||||
\(864\) | −41.8637 | −1.42423 | ||||||||
\(865\) | 53.7256 | 1.82673 | ||||||||
\(866\) | −10.4243 | −0.354232 | ||||||||
\(867\) | 39.1972 | 1.33121 | ||||||||
\(868\) | −39.3139 | −1.33440 | ||||||||
\(869\) | 7.04501 | 0.238985 | ||||||||
\(870\) | 63.4851 | 2.15235 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −21.5760 | −0.730654 | ||||||||
\(873\) | −115.174 | −3.89806 | ||||||||
\(874\) | 3.14531 | 0.106392 | ||||||||
\(875\) | −7.97397 | −0.269569 | ||||||||
\(876\) | −10.6922 | −0.361257 | ||||||||
\(877\) | 0.365718 | 0.0123494 | 0.00617472 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617472 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(878\) | 10.5014 | 0.354407 | ||||||||
\(879\) | 27.9801 | 0.943747 | ||||||||
\(880\) | 22.5514 | 0.760209 | ||||||||
\(881\) | 8.48901 | 0.286002 | 0.143001 | − | 0.989723i | \(-0.454325\pi\) | ||||
0.143001 | + | 0.989723i | \(0.454325\pi\) | |||||||
\(882\) | −49.9936 | −1.68337 | ||||||||
\(883\) | −12.2202 | −0.411244 | −0.205622 | − | 0.978632i | \(-0.565922\pi\) | ||||
−0.205622 | + | 0.978632i | \(0.565922\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.3513 | −0.347954 | ||||||||
\(886\) | −26.2377 | −0.881473 | ||||||||
\(887\) | −17.1979 | −0.577447 | −0.288724 | − | 0.957412i | \(-0.593231\pi\) | ||||
−0.288724 | + | 0.957412i | \(0.593231\pi\) | |||||||
\(888\) | 143.143 | 4.80356 | ||||||||
\(889\) | 4.91252 | 0.164761 | ||||||||
\(890\) | −87.7979 | −2.94299 | ||||||||
\(891\) | −8.47718 | −0.283996 | ||||||||
\(892\) | 11.3105 | 0.378702 | ||||||||
\(893\) | 0.294973 | 0.00987088 | ||||||||
\(894\) | 101.850 | 3.40638 | ||||||||
\(895\) | −33.7458 | −1.12800 | ||||||||
\(896\) | −25.0183 | −0.835802 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.1614 | 0.772906 | ||||||||
\(899\) | −11.5723 | −0.385958 | ||||||||
\(900\) | 164.031 | 5.46768 | ||||||||
\(901\) | −0.753559 | −0.0251047 | ||||||||
\(902\) | 24.6135 | 0.819540 | ||||||||
\(903\) | 37.8319 | 1.25897 | ||||||||
\(904\) | 104.651 | 3.48063 | ||||||||
\(905\) | 32.7773 | 1.08955 | ||||||||
\(906\) | 56.5504 | 1.87876 | ||||||||
\(907\) | −4.69802 | −0.155995 | −0.0779976 | − | 0.996954i | \(-0.524853\pi\) | ||||
−0.0779976 | + | 0.996954i | \(0.524853\pi\) | |||||||
\(908\) | 45.0252 | 1.49421 | ||||||||
\(909\) | 19.8836 | 0.659496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.8968 | −1.02366 | −0.511828 | − | 0.859088i | \(-0.671032\pi\) | ||||
−0.511828 | + | 0.859088i | \(0.671032\pi\) | |||||||
\(912\) | 56.7470 | 1.87908 | ||||||||
\(913\) | −8.70830 | −0.288203 | ||||||||
\(914\) | −3.64817 | −0.120671 | ||||||||
\(915\) | −57.5070 | −1.90112 | ||||||||
\(916\) | 105.051 | 3.47099 | ||||||||
\(917\) | −23.3405 | −0.770770 | ||||||||
\(918\) | 43.9805 | 1.45157 | ||||||||
\(919\) | 52.6196 | 1.73576 | 0.867880 | − | 0.496773i | \(-0.165482\pi\) | ||||
0.867880 | + | 0.496773i | \(0.165482\pi\) | |||||||
\(920\) | 9.06163 | 0.298753 | ||||||||
\(921\) | 43.0465 | 1.41843 | ||||||||
\(922\) | −63.8545 | −2.10294 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 25.3807 | 0.834962 | ||||||||
\(925\) | −48.6085 | −1.59824 | ||||||||
\(926\) | 35.8469 | 1.17800 | ||||||||
\(927\) | 109.709 | 3.60331 | ||||||||
\(928\) | 11.8913 | 0.390350 | ||||||||
\(929\) | −12.3906 | −0.406522 | −0.203261 | − | 0.979125i | \(-0.565154\pi\) | ||||
−0.203261 | + | 0.979125i | \(0.565154\pi\) | |||||||
\(930\) | −117.693 | −3.85931 | ||||||||
\(931\) | 9.36573 | 0.306949 | ||||||||
\(932\) | 56.5008 | 1.85075 | ||||||||
\(933\) | −56.6279 | −1.85392 | ||||||||
\(934\) | 46.7348 | 1.52921 | ||||||||
\(935\) | −6.61369 | −0.216291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5056 | 0.604551 | 0.302275 | − | 0.953221i | \(-0.402254\pi\) | ||||
0.302275 | + | 0.953221i | \(0.402254\pi\) | |||||||
\(938\) | −35.2624 | −1.15136 | ||||||||
\(939\) | 47.7725 | 1.55900 | ||||||||
\(940\) | 1.55087 | 0.0505837 | ||||||||
\(941\) | 40.0842 | 1.30671 | 0.653353 | − | 0.757053i | \(-0.273362\pi\) | ||||
0.653353 | + | 0.757053i | \(0.273362\pi\) | |||||||
\(942\) | −104.397 | −3.40144 | ||||||||
\(943\) | 4.27131 | 0.139093 | ||||||||
\(944\) | −6.94549 | −0.226056 | ||||||||
\(945\) | 56.5718 | 1.84028 | ||||||||
\(946\) | 16.7158 | 0.543477 | ||||||||
\(947\) | −28.6413 | −0.930716 | −0.465358 | − | 0.885123i | \(-0.654074\pi\) | ||||
−0.465358 | + | 0.885123i | \(0.654074\pi\) | |||||||
\(948\) | 93.2058 | 3.02718 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −44.6201 | −1.44767 | ||||||||
\(951\) | −35.9203 | −1.16480 | ||||||||
\(952\) | −23.2557 | −0.753720 | ||||||||
\(953\) | 18.6739 | 0.604907 | 0.302453 | − | 0.953164i | \(-0.402194\pi\) | ||||
0.302453 | + | 0.953164i | \(0.402194\pi\) | |||||||
\(954\) | 5.75265 | 0.186249 | ||||||||
\(955\) | 3.43923 | 0.111291 | ||||||||
\(956\) | −124.017 | −4.01098 | ||||||||
\(957\) | 7.47095 | 0.241502 | ||||||||
\(958\) | −71.5329 | −2.31112 | ||||||||
\(959\) | 20.9863 | 0.677684 | ||||||||
\(960\) | −13.9311 | −0.449623 | ||||||||
\(961\) | −9.54646 | −0.307950 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −73.6449 | −2.37317 | ||||||||
\(964\) | −26.8416 | −0.864508 | ||||||||
\(965\) | 69.8218 | 2.24764 | ||||||||
\(966\) | 6.39541 | 0.205769 | ||||||||
\(967\) | −0.163454 | −0.00525631 | −0.00262816 | − | 0.999997i | \(-0.500837\pi\) | ||||
−0.00262816 | + | 0.999997i | \(0.500837\pi\) | |||||||
\(968\) | 6.14501 | 0.197508 | ||||||||
\(969\) | −16.6423 | −0.534627 | ||||||||
\(970\) | 164.723 | 5.28893 | ||||||||
\(971\) | −24.4462 | −0.784514 | −0.392257 | − | 0.919856i | \(-0.628306\pi\) | ||||
−0.392257 | + | 0.919856i | \(0.628306\pi\) | |||||||
\(972\) | 4.59624 | 0.147425 | ||||||||
\(973\) | −11.5254 | −0.369488 | ||||||||
\(974\) | 30.8603 | 0.988826 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.5861 | −1.23511 | ||||||||
\(977\) | −11.6592 | −0.373012 | −0.186506 | − | 0.982454i | \(-0.559716\pi\) | ||||
−0.186506 | + | 0.982454i | \(0.559716\pi\) | |||||||
\(978\) | 120.044 | 3.83858 | ||||||||
\(979\) | −10.3321 | −0.330215 | ||||||||
\(980\) | 49.2418 | 1.57297 | ||||||||
\(981\) | −20.8615 | −0.666056 | ||||||||
\(982\) | 88.7905 | 2.83342 | ||||||||
\(983\) | 32.6779 | 1.04226 | 0.521132 | − | 0.853476i | \(-0.325510\pi\) | ||||
0.521132 | + | 0.853476i | \(0.325510\pi\) | |||||||
\(984\) | 178.437 | 5.68837 | ||||||||
\(985\) | −27.0051 | −0.860454 | ||||||||
\(986\) | −12.4925 | −0.397844 | ||||||||
\(987\) | 0.599773 | 0.0190910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.90078 | 0.0922394 | ||||||||
\(990\) | 50.4887 | 1.60464 | ||||||||
\(991\) | 42.7697 | 1.35862 | 0.679312 | − | 0.733850i | \(-0.262278\pi\) | ||||
0.679312 | + | 0.733850i | \(0.262278\pi\) | |||||||
\(992\) | −22.0449 | −0.699926 | ||||||||
\(993\) | 63.2437 | 2.00698 | ||||||||
\(994\) | 54.7867 | 1.73773 | ||||||||
\(995\) | −63.7964 | −2.02248 | ||||||||
\(996\) | −115.211 | −3.65061 | ||||||||
\(997\) | 30.9571 | 0.980422 | 0.490211 | − | 0.871604i | \(-0.336920\pi\) | ||||
0.490211 | + | 0.871604i | \(0.336920\pi\) | |||||||
\(998\) | −18.3048 | −0.579430 | ||||||||
\(999\) | 68.5205 | 2.16789 |
(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 | 1859.2.a.k.1.6 | 6 | ||
13.3 | even | 3 | 143.2.e.c.100.1 | ✓ | 12 | ||
13.9 | even | 3 | 143.2.e.c.133.1 | yes | 12 | ||
13.12 | even | 2 | 1859.2.a.l.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.c.100.1 | ✓ | 12 | 13.3 | even | 3 | ||
143.2.e.c.133.1 | yes | 12 | 13.9 | even | 3 | ||
1859.2.a.k.1.6 | 6 | 1.1 | even | 1 | trivial | ||
1859.2.a.l.1.1 | 6 | 13.12 | even | 2 |