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: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68791 | −1.90064 | −0.950320 | − | 0.311276i | \(-0.899244\pi\) | ||||
−0.950320 | + | 0.311276i | \(0.899244\pi\) | |||||||
\(3\) | −2.90985 | −1.68000 | −0.840002 | − | 0.542583i | \(-0.817446\pi\) | ||||
−0.840002 | + | 0.542583i | \(0.817446\pi\) | |||||||
\(4\) | 5.22486 | 2.61243 | ||||||||
\(5\) | −3.09378 | −1.38358 | −0.691790 | − | 0.722098i | \(-0.743178\pi\) | ||||
−0.691790 | + | 0.722098i | \(0.743178\pi\) | |||||||
\(6\) | 7.82142 | 3.19308 | ||||||||
\(7\) | −1.70397 | −0.644039 | −0.322020 | − | 0.946733i | \(-0.604362\pi\) | ||||
−0.322020 | + | 0.946733i | \(0.604362\pi\) | |||||||
\(8\) | −8.66813 | −3.06465 | ||||||||
\(9\) | 5.46725 | 1.82242 | ||||||||
\(10\) | 8.31580 | 2.62969 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −15.2036 | −4.38889 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.58011 | 1.22409 | ||||||||
\(15\) | 9.00245 | 2.32442 | ||||||||
\(16\) | 12.8494 | 3.21236 | ||||||||
\(17\) | 1.04237 | 0.252811 | 0.126406 | − | 0.991979i | \(-0.459656\pi\) | ||||
0.126406 | + | 0.991979i | \(0.459656\pi\) | |||||||
\(18\) | −14.6955 | −3.46375 | ||||||||
\(19\) | 0.291109 | 0.0667850 | 0.0333925 | − | 0.999442i | \(-0.489369\pi\) | ||||
0.0333925 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(20\) | −16.1646 | −3.61451 | ||||||||
\(21\) | 4.95829 | 1.08199 | ||||||||
\(22\) | 2.68791 | 0.573064 | ||||||||
\(23\) | −7.88320 | −1.64376 | −0.821880 | − | 0.569661i | \(-0.807075\pi\) | ||||
−0.821880 | + | 0.569661i | \(0.807075\pi\) | |||||||
\(24\) | 25.2230 | 5.14862 | ||||||||
\(25\) | 4.57148 | 0.914296 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.17933 | −1.38166 | ||||||||
\(28\) | −8.90299 | −1.68251 | ||||||||
\(29\) | −0.935722 | −0.173759 | −0.0868796 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868796 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(30\) | −24.1978 | −4.41789 | ||||||||
\(31\) | −1.01935 | −0.183080 | −0.0915399 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915399 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(32\) | −17.2019 | −3.04089 | ||||||||
\(33\) | 2.90985 | 0.506540 | ||||||||
\(34\) | −2.80179 | −0.480503 | ||||||||
\(35\) | 5.27170 | 0.891080 | ||||||||
\(36\) | 28.5656 | 4.76093 | ||||||||
\(37\) | 6.79609 | 1.11727 | 0.558635 | − | 0.829414i | \(-0.311325\pi\) | ||||
0.558635 | + | 0.829414i | \(0.311325\pi\) | |||||||
\(38\) | −0.782475 | −0.126934 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26.8173 | 4.24019 | ||||||||
\(41\) | −4.76040 | −0.743450 | −0.371725 | − | 0.928343i | \(-0.621234\pi\) | ||||
−0.371725 | + | 0.928343i | \(0.621234\pi\) | |||||||
\(42\) | −13.3274 | −2.05647 | ||||||||
\(43\) | −10.1591 | −1.54926 | −0.774628 | − | 0.632418i | \(-0.782063\pi\) | ||||
−0.774628 | + | 0.632418i | \(0.782063\pi\) | |||||||
\(44\) | −5.22486 | −0.787677 | ||||||||
\(45\) | −16.9145 | −2.52146 | ||||||||
\(46\) | 21.1893 | 3.12419 | ||||||||
\(47\) | −2.04588 | −0.298422 | −0.149211 | − | 0.988805i | \(-0.547673\pi\) | ||||
−0.149211 | + | 0.988805i | \(0.547673\pi\) | |||||||
\(48\) | −37.3900 | −5.39678 | ||||||||
\(49\) | −4.09650 | −0.585214 | ||||||||
\(50\) | −12.2877 | −1.73775 | ||||||||
\(51\) | −3.03314 | −0.424724 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.76011 | −0.653851 | −0.326926 | − | 0.945050i | \(-0.606013\pi\) | ||||
−0.326926 | + | 0.945050i | \(0.606013\pi\) | |||||||
\(54\) | 19.2974 | 2.62604 | ||||||||
\(55\) | 3.09378 | 0.417165 | ||||||||
\(56\) | 14.7702 | 1.97375 | ||||||||
\(57\) | −0.847085 | −0.112199 | ||||||||
\(58\) | 2.51514 | 0.330254 | ||||||||
\(59\) | −11.6149 | −1.51212 | −0.756062 | − | 0.654500i | \(-0.772879\pi\) | ||||
−0.756062 | + | 0.654500i | \(0.772879\pi\) | |||||||
\(60\) | 47.0365 | 6.07239 | ||||||||
\(61\) | 9.48390 | 1.21429 | 0.607145 | − | 0.794591i | \(-0.292315\pi\) | ||||
0.607145 | + | 0.794591i | \(0.292315\pi\) | |||||||
\(62\) | 2.73991 | 0.347969 | ||||||||
\(63\) | −9.31601 | −1.17371 | ||||||||
\(64\) | 20.5382 | 2.56727 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.82142 | −0.962751 | ||||||||
\(67\) | −9.43031 | −1.15210 | −0.576048 | − | 0.817416i | \(-0.695406\pi\) | ||||
−0.576048 | + | 0.817416i | \(0.695406\pi\) | |||||||
\(68\) | 5.44623 | 0.660452 | ||||||||
\(69\) | 22.9389 | 2.76152 | ||||||||
\(70\) | −14.1699 | −1.69362 | ||||||||
\(71\) | −0.582928 | −0.0691808 | −0.0345904 | − | 0.999402i | \(-0.511013\pi\) | ||||
−0.0345904 | + | 0.999402i | \(0.511013\pi\) | |||||||
\(72\) | −47.3908 | −5.58506 | ||||||||
\(73\) | −15.8198 | −1.85157 | −0.925784 | − | 0.378053i | \(-0.876594\pi\) | ||||
−0.925784 | + | 0.378053i | \(0.876594\pi\) | |||||||
\(74\) | −18.2673 | −2.12353 | ||||||||
\(75\) | −13.3023 | −1.53602 | ||||||||
\(76\) | 1.52100 | 0.174471 | ||||||||
\(77\) | 1.70397 | 0.194185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2976 | −1.38358 | −0.691792 | − | 0.722097i | \(-0.743179\pi\) | ||||
−0.691792 | + | 0.722097i | \(0.743179\pi\) | |||||||
\(80\) | −39.7533 | −4.44456 | ||||||||
\(81\) | 4.48905 | 0.498783 | ||||||||
\(82\) | 12.7955 | 1.41303 | ||||||||
\(83\) | 10.5008 | 1.15261 | 0.576305 | − | 0.817235i | \(-0.304494\pi\) | ||||
0.576305 | + | 0.817235i | \(0.304494\pi\) | |||||||
\(84\) | 25.9064 | 2.82662 | ||||||||
\(85\) | −3.22486 | −0.349785 | ||||||||
\(86\) | 27.3069 | 2.94458 | ||||||||
\(87\) | 2.72281 | 0.291916 | ||||||||
\(88\) | 8.66813 | 0.924026 | ||||||||
\(89\) | −5.79180 | −0.613930 | −0.306965 | − | 0.951721i | \(-0.599313\pi\) | ||||
−0.306965 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(90\) | 45.4646 | 4.79238 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −41.1886 | −4.29421 | ||||||||
\(93\) | 2.96615 | 0.307575 | ||||||||
\(94\) | 5.49914 | 0.567193 | ||||||||
\(95\) | −0.900628 | −0.0924025 | ||||||||
\(96\) | 50.0549 | 5.10870 | ||||||||
\(97\) | 0.922801 | 0.0936963 | 0.0468481 | − | 0.998902i | \(-0.485082\pi\) | ||||
0.0468481 | + | 0.998902i | \(0.485082\pi\) | |||||||
\(98\) | 11.0110 | 1.11228 | ||||||||
\(99\) | −5.46725 | −0.549479 | ||||||||
\(100\) | 23.8853 | 2.38853 | ||||||||
\(101\) | −12.8629 | −1.27990 | −0.639951 | − | 0.768415i | \(-0.721046\pi\) | ||||
−0.639951 | + | 0.768415i | \(0.721046\pi\) | |||||||
\(102\) | 8.15280 | 0.807248 | ||||||||
\(103\) | −16.8954 | −1.66475 | −0.832377 | − | 0.554210i | \(-0.813021\pi\) | ||||
−0.832377 | + | 0.554210i | \(0.813021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.3399 | −1.49702 | ||||||||
\(106\) | 12.7947 | 1.24274 | ||||||||
\(107\) | 4.69227 | 0.453619 | 0.226809 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226809 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(108\) | −37.5110 | −3.60949 | ||||||||
\(109\) | −13.7724 | −1.31916 | −0.659580 | − | 0.751634i | \(-0.729266\pi\) | ||||
−0.659580 | + | 0.751634i | \(0.729266\pi\) | |||||||
\(110\) | −8.31580 | −0.792881 | ||||||||
\(111\) | −19.7756 | −1.87702 | ||||||||
\(112\) | −21.8950 | −2.06888 | ||||||||
\(113\) | −8.36051 | −0.786491 | −0.393245 | − | 0.919434i | \(-0.628648\pi\) | ||||
−0.393245 | + | 0.919434i | \(0.628648\pi\) | |||||||
\(114\) | 2.27689 | 0.213250 | ||||||||
\(115\) | 24.3889 | 2.27428 | ||||||||
\(116\) | −4.88902 | −0.453934 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 31.2197 | 2.87400 | ||||||||
\(119\) | −1.77616 | −0.162820 | ||||||||
\(120\) | −78.0344 | −7.12353 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −25.4919 | −2.30793 | ||||||||
\(123\) | 13.8521 | 1.24900 | ||||||||
\(124\) | −5.32594 | −0.478283 | ||||||||
\(125\) | 1.32574 | 0.118578 | ||||||||
\(126\) | 25.0406 | 2.23079 | ||||||||
\(127\) | −4.09166 | −0.363076 | −0.181538 | − | 0.983384i | \(-0.558107\pi\) | ||||
−0.181538 | + | 0.983384i | \(0.558107\pi\) | |||||||
\(128\) | −20.8010 | −1.83857 | ||||||||
\(129\) | 29.5616 | 2.60276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.63924 | −0.143221 | −0.0716104 | − | 0.997433i | \(-0.522814\pi\) | ||||
−0.0716104 | + | 0.997433i | \(0.522814\pi\) | |||||||
\(132\) | 15.2036 | 1.32330 | ||||||||
\(133\) | −0.496041 | −0.0430122 | ||||||||
\(134\) | 25.3478 | 2.18972 | ||||||||
\(135\) | 22.2113 | 1.91164 | ||||||||
\(136\) | −9.03538 | −0.774778 | ||||||||
\(137\) | −7.27779 | −0.621783 | −0.310892 | − | 0.950445i | \(-0.600628\pi\) | ||||
−0.310892 | + | 0.950445i | \(0.600628\pi\) | |||||||
\(138\) | −61.6578 | −5.24866 | ||||||||
\(139\) | 11.0849 | 0.940212 | 0.470106 | − | 0.882610i | \(-0.344216\pi\) | ||||
0.470106 | + | 0.882610i | \(0.344216\pi\) | |||||||
\(140\) | 27.5439 | 2.32788 | ||||||||
\(141\) | 5.95321 | 0.501351 | ||||||||
\(142\) | 1.56686 | 0.131488 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 70.2510 | 5.85425 | ||||||||
\(145\) | 2.89492 | 0.240410 | ||||||||
\(146\) | 42.5222 | 3.51916 | ||||||||
\(147\) | 11.9202 | 0.983162 | ||||||||
\(148\) | 35.5086 | 2.91879 | ||||||||
\(149\) | −0.116636 | −0.00955523 | −0.00477761 | − | 0.999989i | \(-0.501521\pi\) | ||||
−0.00477761 | + | 0.999989i | \(0.501521\pi\) | |||||||
\(150\) | 35.7555 | 2.91942 | ||||||||
\(151\) | 9.89456 | 0.805208 | 0.402604 | − | 0.915374i | \(-0.368105\pi\) | ||||
0.402604 | + | 0.915374i | \(0.368105\pi\) | |||||||
\(152\) | −2.52337 | −0.204673 | ||||||||
\(153\) | 5.69888 | 0.460727 | ||||||||
\(154\) | −4.58011 | −0.369076 | ||||||||
\(155\) | 3.15363 | 0.253306 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.33594 | 0.585472 | 0.292736 | − | 0.956193i | \(-0.405434\pi\) | ||||
0.292736 | + | 0.956193i | \(0.405434\pi\) | |||||||
\(158\) | 33.0547 | 2.62969 | ||||||||
\(159\) | 13.8512 | 1.09847 | ||||||||
\(160\) | 53.2188 | 4.20731 | ||||||||
\(161\) | 13.4327 | 1.05865 | ||||||||
\(162\) | −12.0661 | −0.948006 | ||||||||
\(163\) | 20.1802 | 1.58064 | 0.790318 | − | 0.612696i | \(-0.209915\pi\) | ||||
0.790318 | + | 0.612696i | \(0.209915\pi\) | |||||||
\(164\) | −24.8724 | −1.94221 | ||||||||
\(165\) | −9.00245 | −0.700840 | ||||||||
\(166\) | −28.2251 | −2.19069 | ||||||||
\(167\) | 4.95156 | 0.383163 | 0.191582 | − | 0.981477i | \(-0.438638\pi\) | ||||
0.191582 | + | 0.981477i | \(0.438638\pi\) | |||||||
\(168\) | −42.9791 | −3.31591 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.66813 | 0.664815 | ||||||||
\(171\) | 1.59157 | 0.121710 | ||||||||
\(172\) | −53.0801 | −4.04732 | ||||||||
\(173\) | 21.1077 | 1.60479 | 0.802394 | − | 0.596795i | \(-0.203560\pi\) | ||||
0.802394 | + | 0.596795i | \(0.203560\pi\) | |||||||
\(174\) | −7.31868 | −0.554828 | ||||||||
\(175\) | −7.78965 | −0.588842 | ||||||||
\(176\) | −12.8494 | −0.968562 | ||||||||
\(177\) | 33.7975 | 2.54038 | ||||||||
\(178\) | 15.5678 | 1.16686 | ||||||||
\(179\) | 1.06432 | 0.0795513 | 0.0397757 | − | 0.999209i | \(-0.487336\pi\) | ||||
0.0397757 | + | 0.999209i | \(0.487336\pi\) | |||||||
\(180\) | −88.3757 | −6.58713 | ||||||||
\(181\) | 18.7869 | 1.39642 | 0.698210 | − | 0.715893i | \(-0.253980\pi\) | ||||
0.698210 | + | 0.715893i | \(0.253980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.5968 | −2.04001 | ||||||||
\(184\) | 68.3326 | 5.03754 | ||||||||
\(185\) | −21.0256 | −1.54583 | ||||||||
\(186\) | −7.97273 | −0.584589 | ||||||||
\(187\) | −1.04237 | −0.0762255 | ||||||||
\(188\) | −10.6894 | −0.779608 | ||||||||
\(189\) | 12.2333 | 0.889844 | ||||||||
\(190\) | 2.42081 | 0.175624 | ||||||||
\(191\) | −19.2897 | −1.39575 | −0.697876 | − | 0.716219i | \(-0.745871\pi\) | ||||
−0.697876 | + | 0.716219i | \(0.745871\pi\) | |||||||
\(192\) | −59.7630 | −4.31303 | ||||||||
\(193\) | −10.4036 | −0.748864 | −0.374432 | − | 0.927254i | \(-0.622162\pi\) | ||||
−0.374432 | + | 0.927254i | \(0.622162\pi\) | |||||||
\(194\) | −2.48041 | −0.178083 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.4036 | −1.52883 | ||||||||
\(197\) | −9.93369 | −0.707746 | −0.353873 | − | 0.935293i | \(-0.615136\pi\) | ||||
−0.353873 | + | 0.935293i | \(0.615136\pi\) | |||||||
\(198\) | 14.6955 | 1.04436 | ||||||||
\(199\) | −12.7227 | −0.901886 | −0.450943 | − | 0.892553i | \(-0.648912\pi\) | ||||
−0.450943 | + | 0.892553i | \(0.648912\pi\) | |||||||
\(200\) | −39.6262 | −2.80199 | ||||||||
\(201\) | 27.4408 | 1.93553 | ||||||||
\(202\) | 34.5742 | 2.43263 | ||||||||
\(203\) | 1.59444 | 0.111908 | ||||||||
\(204\) | −15.8477 | −1.10956 | ||||||||
\(205\) | 14.7276 | 1.02862 | ||||||||
\(206\) | 45.4133 | 3.16410 | ||||||||
\(207\) | −43.0994 | −2.99561 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.291109 | −0.0201364 | ||||||||
\(210\) | 41.2322 | 2.84529 | ||||||||
\(211\) | 2.00015 | 0.137696 | 0.0688480 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688480 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(212\) | −24.8709 | −1.70814 | ||||||||
\(213\) | 1.69623 | 0.116224 | ||||||||
\(214\) | −12.6124 | −0.862166 | ||||||||
\(215\) | 31.4302 | 2.14352 | ||||||||
\(216\) | 62.2313 | 4.23431 | ||||||||
\(217\) | 1.73693 | 0.117911 | ||||||||
\(218\) | 37.0191 | 2.50725 | ||||||||
\(219\) | 46.0333 | 3.11064 | ||||||||
\(220\) | 16.1646 | 1.08981 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 53.1551 | 3.56753 | ||||||||
\(223\) | 3.25053 | 0.217672 | 0.108836 | − | 0.994060i | \(-0.465288\pi\) | ||||
0.108836 | + | 0.994060i | \(0.465288\pi\) | |||||||
\(224\) | 29.3114 | 1.95845 | ||||||||
\(225\) | 24.9934 | 1.66623 | ||||||||
\(226\) | 22.4723 | 1.49483 | ||||||||
\(227\) | 17.3081 | 1.14878 | 0.574388 | − | 0.818583i | \(-0.305240\pi\) | ||||
0.574388 | + | 0.818583i | \(0.305240\pi\) | |||||||
\(228\) | −4.42590 | −0.293112 | ||||||||
\(229\) | 12.2229 | 0.807712 | 0.403856 | − | 0.914822i | \(-0.367670\pi\) | ||||
0.403856 | + | 0.914822i | \(0.367670\pi\) | |||||||
\(230\) | −65.5551 | −4.32258 | ||||||||
\(231\) | −4.95829 | −0.326232 | ||||||||
\(232\) | 8.11096 | 0.532511 | ||||||||
\(233\) | 0.275611 | 0.0180558 | 0.00902792 | − | 0.999959i | \(-0.497126\pi\) | ||||
0.00902792 | + | 0.999959i | \(0.497126\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.32951 | 0.412892 | ||||||||
\(236\) | −60.6860 | −3.95032 | ||||||||
\(237\) | 35.7841 | 2.32443 | ||||||||
\(238\) | 4.77416 | 0.309463 | ||||||||
\(239\) | −22.4425 | −1.45168 | −0.725841 | − | 0.687863i | \(-0.758549\pi\) | ||||
−0.725841 | + | 0.687863i | \(0.758549\pi\) | |||||||
\(240\) | 115.676 | 7.46688 | ||||||||
\(241\) | 17.7396 | 1.14271 | 0.571353 | − | 0.820705i | \(-0.306419\pi\) | ||||
0.571353 | + | 0.820705i | \(0.306419\pi\) | |||||||
\(242\) | −2.68791 | −0.172785 | ||||||||
\(243\) | 8.47551 | 0.543704 | ||||||||
\(244\) | 49.5521 | 3.17225 | ||||||||
\(245\) | 12.6737 | 0.809691 | ||||||||
\(246\) | −37.2331 | −2.37390 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.83582 | 0.561075 | ||||||||
\(249\) | −30.5557 | −1.93639 | ||||||||
\(250\) | −3.56348 | −0.225374 | ||||||||
\(251\) | −20.5224 | −1.29537 | −0.647683 | − | 0.761910i | \(-0.724262\pi\) | ||||
−0.647683 | + | 0.761910i | \(0.724262\pi\) | |||||||
\(252\) | −48.6748 | −3.06623 | ||||||||
\(253\) | 7.88320 | 0.495612 | ||||||||
\(254\) | 10.9980 | 0.690076 | ||||||||
\(255\) | 9.38387 | 0.587641 | ||||||||
\(256\) | 14.8350 | 0.927185 | ||||||||
\(257\) | −10.1295 | −0.631862 | −0.315931 | − | 0.948782i | \(-0.602317\pi\) | ||||
−0.315931 | + | 0.948782i | \(0.602317\pi\) | |||||||
\(258\) | −79.4590 | −4.94690 | ||||||||
\(259\) | −11.5803 | −0.719565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.11583 | −0.316662 | ||||||||
\(262\) | 4.40612 | 0.272211 | ||||||||
\(263\) | 0.0974277 | 0.00600765 | 0.00300383 | − | 0.999995i | \(-0.499044\pi\) | ||||
0.00300383 | + | 0.999995i | \(0.499044\pi\) | |||||||
\(264\) | −25.2230 | −1.55237 | ||||||||
\(265\) | 14.7267 | 0.904656 | ||||||||
\(266\) | 1.33331 | 0.0817506 | ||||||||
\(267\) | 16.8533 | 1.03140 | ||||||||
\(268\) | −49.2721 | −3.00977 | ||||||||
\(269\) | −3.50796 | −0.213884 | −0.106942 | − | 0.994265i | \(-0.534106\pi\) | ||||
−0.106942 | + | 0.994265i | \(0.534106\pi\) | |||||||
\(270\) | −59.7019 | −3.63334 | ||||||||
\(271\) | −15.3135 | −0.930230 | −0.465115 | − | 0.885250i | \(-0.653987\pi\) | ||||
−0.465115 | + | 0.885250i | \(0.653987\pi\) | |||||||
\(272\) | 13.3938 | 0.812121 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.5620 | 1.18179 | ||||||||
\(275\) | −4.57148 | −0.275671 | ||||||||
\(276\) | 119.853 | 7.21429 | ||||||||
\(277\) | −20.6695 | −1.24191 | −0.620954 | − | 0.783847i | \(-0.713255\pi\) | ||||
−0.620954 | + | 0.783847i | \(0.713255\pi\) | |||||||
\(278\) | −29.7953 | −1.78700 | ||||||||
\(279\) | −5.57301 | −0.333648 | ||||||||
\(280\) | −45.6958 | −2.73085 | ||||||||
\(281\) | 28.7750 | 1.71657 | 0.858286 | − | 0.513172i | \(-0.171530\pi\) | ||||
0.858286 | + | 0.513172i | \(0.171530\pi\) | |||||||
\(282\) | −16.0017 | −0.952887 | ||||||||
\(283\) | −30.2757 | −1.79971 | −0.899853 | − | 0.436193i | \(-0.856326\pi\) | ||||
−0.899853 | + | 0.436193i | \(0.856326\pi\) | |||||||
\(284\) | −3.04571 | −0.180730 | ||||||||
\(285\) | 2.62070 | 0.155237 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.11157 | 0.478811 | ||||||||
\(288\) | −94.0468 | −5.54176 | ||||||||
\(289\) | −15.9135 | −0.936086 | ||||||||
\(290\) | −7.78128 | −0.456933 | ||||||||
\(291\) | −2.68522 | −0.157410 | ||||||||
\(292\) | −82.6562 | −4.83709 | ||||||||
\(293\) | 11.0766 | 0.647100 | 0.323550 | − | 0.946211i | \(-0.395124\pi\) | ||||
0.323550 | + | 0.946211i | \(0.395124\pi\) | |||||||
\(294\) | −32.0404 | −1.86864 | ||||||||
\(295\) | 35.9338 | 2.09215 | ||||||||
\(296\) | −58.9094 | −3.42404 | ||||||||
\(297\) | 7.17933 | 0.416587 | ||||||||
\(298\) | 0.313508 | 0.0181610 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −69.5028 | −4.01275 | ||||||||
\(301\) | 17.3108 | 0.997781 | ||||||||
\(302\) | −26.5957 | −1.53041 | ||||||||
\(303\) | 37.4291 | 2.15024 | ||||||||
\(304\) | 3.74059 | 0.214537 | ||||||||
\(305\) | −29.3411 | −1.68007 | ||||||||
\(306\) | −15.3181 | −0.875677 | ||||||||
\(307\) | 5.13474 | 0.293055 | 0.146528 | − | 0.989207i | \(-0.453190\pi\) | ||||
0.146528 | + | 0.989207i | \(0.453190\pi\) | |||||||
\(308\) | 8.90299 | 0.507295 | ||||||||
\(309\) | 49.1632 | 2.79679 | ||||||||
\(310\) | −8.47668 | −0.481443 | ||||||||
\(311\) | 21.3788 | 1.21228 | 0.606141 | − | 0.795357i | \(-0.292717\pi\) | ||||
0.606141 | + | 0.795357i | \(0.292717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.92078 | 0.108569 | 0.0542845 | − | 0.998526i | \(-0.482712\pi\) | ||||
0.0542845 | + | 0.998526i | \(0.482712\pi\) | |||||||
\(314\) | −19.7183 | −1.11277 | ||||||||
\(315\) | 28.8217 | 1.62392 | ||||||||
\(316\) | −64.2530 | −3.61452 | ||||||||
\(317\) | −8.45359 | −0.474801 | −0.237400 | − | 0.971412i | \(-0.576295\pi\) | ||||
−0.237400 | + | 0.971412i | \(0.576295\pi\) | |||||||
\(318\) | −37.2308 | −2.08780 | ||||||||
\(319\) | 0.935722 | 0.0523904 | ||||||||
\(320\) | −63.5406 | −3.55203 | ||||||||
\(321\) | −13.6538 | −0.762082 | ||||||||
\(322\) | −36.1059 | −2.01210 | ||||||||
\(323\) | 0.303443 | 0.0168840 | ||||||||
\(324\) | 23.4546 | 1.30303 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −54.2426 | −3.00422 | ||||||||
\(327\) | 40.0758 | 2.21619 | ||||||||
\(328\) | 41.2638 | 2.27841 | ||||||||
\(329\) | 3.48611 | 0.192196 | ||||||||
\(330\) | 24.1978 | 1.33204 | ||||||||
\(331\) | −24.7021 | −1.35775 | −0.678874 | − | 0.734255i | \(-0.737532\pi\) | ||||
−0.678874 | + | 0.734255i | \(0.737532\pi\) | |||||||
\(332\) | 54.8651 | 3.01111 | ||||||||
\(333\) | 37.1559 | 2.03613 | ||||||||
\(334\) | −13.3093 | −0.728255 | ||||||||
\(335\) | 29.1753 | 1.59402 | ||||||||
\(336\) | 63.7113 | 3.47573 | ||||||||
\(337\) | 25.8404 | 1.40762 | 0.703809 | − | 0.710389i | \(-0.251481\pi\) | ||||
0.703809 | + | 0.710389i | \(0.251481\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.3279 | 1.32131 | ||||||||
\(340\) | −16.8494 | −0.913789 | ||||||||
\(341\) | 1.01935 | 0.0552007 | ||||||||
\(342\) | −4.27799 | −0.231327 | ||||||||
\(343\) | 18.9081 | 1.02094 | ||||||||
\(344\) | 88.0608 | 4.74792 | ||||||||
\(345\) | −70.9681 | −3.82079 | ||||||||
\(346\) | −56.7355 | −3.05012 | ||||||||
\(347\) | 1.98790 | 0.106716 | 0.0533580 | − | 0.998575i | \(-0.483008\pi\) | ||||
0.0533580 | + | 0.998575i | \(0.483008\pi\) | |||||||
\(348\) | 14.2263 | 0.762611 | ||||||||
\(349\) | 9.65372 | 0.516752 | 0.258376 | − | 0.966044i | \(-0.416813\pi\) | ||||
0.258376 | + | 0.966044i | \(0.416813\pi\) | |||||||
\(350\) | 20.9379 | 1.11918 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 17.2019 | 0.916862 | ||||||||
\(353\) | −4.97653 | −0.264874 | −0.132437 | − | 0.991191i | \(-0.542280\pi\) | ||||
−0.132437 | + | 0.991191i | \(0.542280\pi\) | |||||||
\(354\) | −90.8447 | −4.82834 | ||||||||
\(355\) | 1.80345 | 0.0957172 | ||||||||
\(356\) | −30.2614 | −1.60385 | ||||||||
\(357\) | 5.16837 | 0.273539 | ||||||||
\(358\) | −2.86081 | −0.151198 | ||||||||
\(359\) | −15.8428 | −0.836149 | −0.418075 | − | 0.908413i | \(-0.637295\pi\) | ||||
−0.418075 | + | 0.908413i | \(0.637295\pi\) | |||||||
\(360\) | 146.617 | 7.72738 | ||||||||
\(361\) | −18.9153 | −0.995540 | ||||||||
\(362\) | −50.4975 | −2.65409 | ||||||||
\(363\) | −2.90985 | −0.152728 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.9430 | 2.56179 | ||||||||
\(366\) | 74.1776 | 3.87733 | ||||||||
\(367\) | −4.23360 | −0.220992 | −0.110496 | − | 0.993877i | \(-0.535244\pi\) | ||||
−0.110496 | + | 0.993877i | \(0.535244\pi\) | |||||||
\(368\) | −101.295 | −5.28035 | ||||||||
\(369\) | −26.0263 | −1.35488 | ||||||||
\(370\) | 56.5149 | 2.93807 | ||||||||
\(371\) | 8.11107 | 0.421106 | ||||||||
\(372\) | 15.4977 | 0.803518 | ||||||||
\(373\) | −3.24566 | −0.168054 | −0.0840269 | − | 0.996463i | \(-0.526778\pi\) | ||||
−0.0840269 | + | 0.996463i | \(0.526778\pi\) | |||||||
\(374\) | 2.80179 | 0.144877 | ||||||||
\(375\) | −3.85772 | −0.199212 | ||||||||
\(376\) | 17.7340 | 0.914559 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −32.8821 | −1.69127 | ||||||||
\(379\) | −20.8566 | −1.07133 | −0.535666 | − | 0.844430i | \(-0.679940\pi\) | ||||
−0.535666 | + | 0.844430i | \(0.679940\pi\) | |||||||
\(380\) | −4.70565 | −0.241395 | ||||||||
\(381\) | 11.9061 | 0.609969 | ||||||||
\(382\) | 51.8489 | 2.65282 | ||||||||
\(383\) | −25.6788 | −1.31213 | −0.656063 | − | 0.754706i | \(-0.727780\pi\) | ||||
−0.656063 | + | 0.754706i | \(0.727780\pi\) | |||||||
\(384\) | 60.5279 | 3.08880 | ||||||||
\(385\) | −5.27170 | −0.268671 | ||||||||
\(386\) | 27.9638 | 1.42332 | ||||||||
\(387\) | −55.5426 | −2.82339 | ||||||||
\(388\) | 4.82151 | 0.244775 | ||||||||
\(389\) | 16.8280 | 0.853214 | 0.426607 | − | 0.904437i | \(-0.359709\pi\) | ||||
0.426607 | + | 0.904437i | \(0.359709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.21719 | −0.415561 | ||||||||
\(392\) | 35.5090 | 1.79347 | ||||||||
\(393\) | 4.76994 | 0.240611 | ||||||||
\(394\) | 26.7009 | 1.34517 | ||||||||
\(395\) | 38.0460 | 1.91430 | ||||||||
\(396\) | −28.5656 | −1.43547 | ||||||||
\(397\) | −3.41837 | −0.171563 | −0.0857817 | − | 0.996314i | \(-0.527339\pi\) | ||||
−0.0857817 | + | 0.996314i | \(0.527339\pi\) | |||||||
\(398\) | 34.1974 | 1.71416 | ||||||||
\(399\) | 1.44341 | 0.0722606 | ||||||||
\(400\) | 58.7409 | 2.93705 | ||||||||
\(401\) | 5.82738 | 0.291005 | 0.145503 | − | 0.989358i | \(-0.453520\pi\) | ||||
0.145503 | + | 0.989358i | \(0.453520\pi\) | |||||||
\(402\) | −73.7585 | −3.67874 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −67.2067 | −3.34366 | ||||||||
\(405\) | −13.8881 | −0.690106 | ||||||||
\(406\) | −4.28571 | −0.212696 | ||||||||
\(407\) | −6.79609 | −0.336870 | ||||||||
\(408\) | 26.2916 | 1.30163 | ||||||||
\(409\) | 13.4473 | 0.664927 | 0.332464 | − | 0.943116i | \(-0.392120\pi\) | ||||
0.332464 | + | 0.943116i | \(0.392120\pi\) | |||||||
\(410\) | −39.5866 | −1.95504 | ||||||||
\(411\) | 21.1773 | 1.04460 | ||||||||
\(412\) | −88.2761 | −4.34905 | ||||||||
\(413\) | 19.7913 | 0.973867 | ||||||||
\(414\) | 115.847 | 5.69358 | ||||||||
\(415\) | −32.4871 | −1.59473 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −32.2555 | −1.57956 | ||||||||
\(418\) | 0.782475 | 0.0382721 | ||||||||
\(419\) | −25.5596 | −1.24867 | −0.624335 | − | 0.781157i | \(-0.714630\pi\) | ||||
−0.624335 | + | 0.781157i | \(0.714630\pi\) | |||||||
\(420\) | −80.1487 | −3.91086 | ||||||||
\(421\) | −30.5005 | −1.48650 | −0.743251 | − | 0.669013i | \(-0.766717\pi\) | ||||
−0.743251 | + | 0.669013i | \(0.766717\pi\) | |||||||
\(422\) | −5.37622 | −0.261710 | ||||||||
\(423\) | −11.1853 | −0.543850 | ||||||||
\(424\) | 41.2613 | 2.00382 | ||||||||
\(425\) | 4.76517 | 0.231145 | ||||||||
\(426\) | −4.55932 | −0.220900 | ||||||||
\(427\) | −16.1603 | −0.782050 | ||||||||
\(428\) | 24.5164 | 1.18505 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −84.4815 | −4.07406 | ||||||||
\(431\) | 9.03274 | 0.435092 | 0.217546 | − | 0.976050i | \(-0.430195\pi\) | ||||
0.217546 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(432\) | −92.2503 | −4.43839 | ||||||||
\(433\) | −20.8135 | −1.00023 | −0.500116 | − | 0.865958i | \(-0.666709\pi\) | ||||
−0.500116 | + | 0.865958i | \(0.666709\pi\) | |||||||
\(434\) | −4.66872 | −0.224106 | ||||||||
\(435\) | −8.42379 | −0.403890 | ||||||||
\(436\) | −71.9590 | −3.44621 | ||||||||
\(437\) | −2.29487 | −0.109779 | ||||||||
\(438\) | −123.733 | −5.91221 | ||||||||
\(439\) | 25.1827 | 1.20191 | 0.600953 | − | 0.799284i | \(-0.294788\pi\) | ||||
0.600953 | + | 0.799284i | \(0.294788\pi\) | |||||||
\(440\) | −26.8173 | −1.27846 | ||||||||
\(441\) | −22.3966 | −1.06650 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.6126 | 1.78703 | 0.893513 | − | 0.449037i | \(-0.148233\pi\) | ||||
0.893513 | + | 0.449037i | \(0.148233\pi\) | |||||||
\(444\) | −103.325 | −4.90358 | ||||||||
\(445\) | 17.9186 | 0.849422 | ||||||||
\(446\) | −8.73714 | −0.413715 | ||||||||
\(447\) | 0.339395 | 0.0160528 | ||||||||
\(448\) | −34.9964 | −1.65342 | ||||||||
\(449\) | −9.31247 | −0.439482 | −0.219741 | − | 0.975558i | \(-0.570521\pi\) | ||||
−0.219741 | + | 0.975558i | \(0.570521\pi\) | |||||||
\(450\) | −67.1800 | −3.16690 | ||||||||
\(451\) | 4.76040 | 0.224159 | ||||||||
\(452\) | −43.6825 | −2.05465 | ||||||||
\(453\) | −28.7917 | −1.35275 | ||||||||
\(454\) | −46.5225 | −2.18341 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34264 | 0.343851 | ||||||||
\(457\) | 24.0367 | 1.12439 | 0.562194 | − | 0.827005i | \(-0.309957\pi\) | ||||
0.562194 | + | 0.827005i | \(0.309957\pi\) | |||||||
\(458\) | −32.8541 | −1.53517 | ||||||||
\(459\) | −7.48350 | −0.349300 | ||||||||
\(460\) | 127.428 | 5.94138 | ||||||||
\(461\) | 26.9815 | 1.25665 | 0.628327 | − | 0.777949i | \(-0.283740\pi\) | ||||
0.628327 | + | 0.777949i | \(0.283740\pi\) | |||||||
\(462\) | 13.3274 | 0.620049 | ||||||||
\(463\) | −32.5496 | −1.51271 | −0.756355 | − | 0.654161i | \(-0.773022\pi\) | ||||
−0.756355 | + | 0.654161i | \(0.773022\pi\) | |||||||
\(464\) | −12.0235 | −0.558177 | ||||||||
\(465\) | −9.17661 | −0.425555 | ||||||||
\(466\) | −0.740816 | −0.0343177 | ||||||||
\(467\) | −20.5962 | −0.953077 | −0.476538 | − | 0.879154i | \(-0.658109\pi\) | ||||
−0.476538 | + | 0.879154i | \(0.658109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0689 | 0.741995 | ||||||||
\(470\) | −17.0131 | −0.784758 | ||||||||
\(471\) | −21.3465 | −0.983595 | ||||||||
\(472\) | 100.679 | 4.63413 | ||||||||
\(473\) | 10.1591 | 0.467118 | ||||||||
\(474\) | −96.1845 | −4.41790 | ||||||||
\(475\) | 1.33080 | 0.0610613 | ||||||||
\(476\) | −9.28019 | −0.425357 | ||||||||
\(477\) | −26.0247 | −1.19159 | ||||||||
\(478\) | 60.3233 | 2.75912 | ||||||||
\(479\) | −11.7511 | −0.536923 | −0.268461 | − | 0.963290i | \(-0.586515\pi\) | ||||
−0.268461 | + | 0.963290i | \(0.586515\pi\) | |||||||
\(480\) | −154.859 | −7.06830 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −47.6823 | −2.17187 | ||||||||
\(483\) | −39.0872 | −1.77853 | ||||||||
\(484\) | 5.22486 | 0.237494 | ||||||||
\(485\) | −2.85495 | −0.129636 | ||||||||
\(486\) | −22.7814 | −1.03339 | ||||||||
\(487\) | −9.45558 | −0.428473 | −0.214237 | − | 0.976782i | \(-0.568726\pi\) | ||||
−0.214237 | + | 0.976782i | \(0.568726\pi\) | |||||||
\(488\) | −82.2077 | −3.72137 | ||||||||
\(489\) | −58.7215 | −2.65548 | ||||||||
\(490\) | −34.0657 | −1.53893 | ||||||||
\(491\) | 16.0978 | 0.726482 | 0.363241 | − | 0.931695i | \(-0.381670\pi\) | ||||
0.363241 | + | 0.931695i | \(0.381670\pi\) | |||||||
\(492\) | 72.3751 | 3.26292 | ||||||||
\(493\) | −0.975367 | −0.0439283 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.9145 | 0.760249 | ||||||||
\(496\) | −13.0980 | −0.588118 | ||||||||
\(497\) | 0.993290 | 0.0445551 | ||||||||
\(498\) | 82.1310 | 3.68038 | ||||||||
\(499\) | −30.5933 | −1.36954 | −0.684772 | − | 0.728758i | \(-0.740098\pi\) | ||||
−0.684772 | + | 0.728758i | \(0.740098\pi\) | |||||||
\(500\) | 6.92683 | 0.309777 | ||||||||
\(501\) | −14.4083 | −0.643716 | ||||||||
\(502\) | 55.1625 | 2.46202 | ||||||||
\(503\) | 26.5348 | 1.18313 | 0.591563 | − | 0.806259i | \(-0.298511\pi\) | ||||
0.591563 | + | 0.806259i | \(0.298511\pi\) | |||||||
\(504\) | 80.7524 | 3.59700 | ||||||||
\(505\) | 39.7949 | 1.77085 | ||||||||
\(506\) | −21.1893 | −0.941980 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.3783 | −0.948510 | ||||||||
\(509\) | −22.5513 | −0.999570 | −0.499785 | − | 0.866149i | \(-0.666588\pi\) | ||||
−0.499785 | + | 0.866149i | \(0.666588\pi\) | |||||||
\(510\) | −25.2230 | −1.11689 | ||||||||
\(511\) | 26.9564 | 1.19248 | ||||||||
\(512\) | 1.72704 | 0.0763250 | ||||||||
\(513\) | −2.08997 | −0.0922743 | ||||||||
\(514\) | 27.2272 | 1.20094 | ||||||||
\(515\) | 52.2707 | 2.30332 | ||||||||
\(516\) | 154.455 | 6.79952 | ||||||||
\(517\) | 2.04588 | 0.0899777 | ||||||||
\(518\) | 31.1268 | 1.36763 | ||||||||
\(519\) | −61.4203 | −2.69605 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4510 | 0.720732 | 0.360366 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360366 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(522\) | 13.7509 | 0.601859 | ||||||||
\(523\) | −10.0678 | −0.440234 | −0.220117 | − | 0.975473i | \(-0.570644\pi\) | ||||
−0.220117 | + | 0.975473i | \(0.570644\pi\) | |||||||
\(524\) | −8.56478 | −0.374154 | ||||||||
\(525\) | 22.6667 | 0.989258 | ||||||||
\(526\) | −0.261877 | −0.0114184 | ||||||||
\(527\) | −1.06253 | −0.0462847 | ||||||||
\(528\) | 37.3900 | 1.62719 | ||||||||
\(529\) | 39.1448 | 1.70195 | ||||||||
\(530\) | −39.5841 | −1.71943 | ||||||||
\(531\) | −63.5013 | −2.75572 | ||||||||
\(532\) | −2.59174 | −0.112366 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −45.3001 | −1.96033 | ||||||||
\(535\) | −14.5169 | −0.627618 | ||||||||
\(536\) | 81.7432 | 3.53077 | ||||||||
\(537\) | −3.09703 | −0.133647 | ||||||||
\(538\) | 9.42909 | 0.406517 | ||||||||
\(539\) | 4.09650 | 0.176449 | ||||||||
\(540\) | 116.051 | 4.99403 | ||||||||
\(541\) | −3.30312 | −0.142012 | −0.0710060 | − | 0.997476i | \(-0.522621\pi\) | ||||
−0.0710060 | + | 0.997476i | \(0.522621\pi\) | |||||||
\(542\) | 41.1614 | 1.76803 | ||||||||
\(543\) | −54.6672 | −2.34599 | ||||||||
\(544\) | −17.9307 | −0.768771 | ||||||||
\(545\) | 42.6089 | 1.82516 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.05777 | 0.173498 | 0.0867489 | − | 0.996230i | \(-0.472352\pi\) | ||||
0.0867489 | + | 0.996230i | \(0.472352\pi\) | |||||||
\(548\) | −38.0254 | −1.62436 | ||||||||
\(549\) | 51.8508 | 2.21294 | ||||||||
\(550\) | 12.2877 | 0.523950 | ||||||||
\(551\) | −0.272397 | −0.0116045 | ||||||||
\(552\) | −198.838 | −8.46310 | ||||||||
\(553\) | 20.9546 | 0.891082 | ||||||||
\(554\) | 55.5577 | 2.36042 | ||||||||
\(555\) | 61.1814 | 2.59701 | ||||||||
\(556\) | 57.9172 | 2.45624 | ||||||||
\(557\) | 6.10464 | 0.258662 | 0.129331 | − | 0.991601i | \(-0.458717\pi\) | ||||
0.129331 | + | 0.991601i | \(0.458717\pi\) | |||||||
\(558\) | 14.9798 | 0.634144 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 67.7384 | 2.86247 | ||||||||
\(561\) | 3.03314 | 0.128059 | ||||||||
\(562\) | −77.3446 | −3.26258 | ||||||||
\(563\) | −17.0418 | −0.718225 | −0.359112 | − | 0.933294i | \(-0.616921\pi\) | ||||
−0.359112 | + | 0.933294i | \(0.616921\pi\) | |||||||
\(564\) | 31.1047 | 1.30974 | ||||||||
\(565\) | 25.8656 | 1.08817 | ||||||||
\(566\) | 81.3785 | 3.42059 | ||||||||
\(567\) | −7.64919 | −0.321236 | ||||||||
\(568\) | 5.05289 | 0.212015 | ||||||||
\(569\) | −7.42389 | −0.311226 | −0.155613 | − | 0.987818i | \(-0.549735\pi\) | ||||
−0.155613 | + | 0.987818i | \(0.549735\pi\) | |||||||
\(570\) | −7.04419 | −0.295049 | ||||||||
\(571\) | 10.9772 | 0.459382 | 0.229691 | − | 0.973264i | \(-0.426228\pi\) | ||||
0.229691 | + | 0.973264i | \(0.426228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 56.1301 | 2.34487 | ||||||||
\(574\) | −21.8032 | −0.910047 | ||||||||
\(575\) | −36.0379 | −1.50288 | ||||||||
\(576\) | 112.287 | 4.67863 | ||||||||
\(577\) | 3.74826 | 0.156042 | 0.0780211 | − | 0.996952i | \(-0.475140\pi\) | ||||
0.0780211 | + | 0.996952i | \(0.475140\pi\) | |||||||
\(578\) | 42.7740 | 1.77916 | ||||||||
\(579\) | 30.2728 | 1.25810 | ||||||||
\(580\) | 15.1255 | 0.628054 | ||||||||
\(581\) | −17.8930 | −0.742326 | ||||||||
\(582\) | 7.21762 | 0.299180 | ||||||||
\(583\) | 4.76011 | 0.197144 | ||||||||
\(584\) | 137.128 | 5.67440 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.7728 | −1.22990 | ||||||||
\(587\) | −20.5788 | −0.849377 | −0.424688 | − | 0.905340i | \(-0.639616\pi\) | ||||
−0.424688 | + | 0.905340i | \(0.639616\pi\) | |||||||
\(588\) | 62.2814 | 2.56844 | ||||||||
\(589\) | −0.296741 | −0.0122270 | ||||||||
\(590\) | −96.5868 | −3.97642 | ||||||||
\(591\) | 28.9056 | 1.18902 | ||||||||
\(592\) | 87.3258 | 3.58907 | ||||||||
\(593\) | −6.50155 | −0.266986 | −0.133493 | − | 0.991050i | \(-0.542619\pi\) | ||||
−0.133493 | + | 0.991050i | \(0.542619\pi\) | |||||||
\(594\) | −19.2974 | −0.791781 | ||||||||
\(595\) | 5.49505 | 0.225275 | ||||||||
\(596\) | −0.609409 | −0.0249624 | ||||||||
\(597\) | 37.0211 | 1.51517 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.5421 | −0.921045 | −0.460522 | − | 0.887648i | \(-0.652338\pi\) | ||||
−0.460522 | + | 0.887648i | \(0.652338\pi\) | |||||||
\(600\) | 115.306 | 4.70736 | ||||||||
\(601\) | 42.5783 | 1.73680 | 0.868402 | − | 0.495860i | \(-0.165147\pi\) | ||||
0.868402 | + | 0.495860i | \(0.165147\pi\) | |||||||
\(602\) | −46.5300 | −1.89642 | ||||||||
\(603\) | −51.5578 | −2.09960 | ||||||||
\(604\) | 51.6977 | 2.10355 | ||||||||
\(605\) | −3.09378 | −0.125780 | ||||||||
\(606\) | −100.606 | −4.08684 | ||||||||
\(607\) | 25.3486 | 1.02887 | 0.514434 | − | 0.857530i | \(-0.328002\pi\) | ||||
0.514434 | + | 0.857530i | \(0.328002\pi\) | |||||||
\(608\) | −5.00762 | −0.203086 | ||||||||
\(609\) | −4.63959 | −0.188006 | ||||||||
\(610\) | 78.8663 | 3.19320 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 29.7759 | 1.20362 | ||||||||
\(613\) | −16.9842 | −0.685985 | −0.342992 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342992 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(614\) | −13.8017 | −0.556992 | ||||||||
\(615\) | −42.8553 | −1.72809 | ||||||||
\(616\) | −14.7702 | −0.595109 | ||||||||
\(617\) | 44.9940 | 1.81139 | 0.905695 | − | 0.423929i | \(-0.139350\pi\) | ||||
0.905695 | + | 0.423929i | \(0.139350\pi\) | |||||||
\(618\) | −132.146 | −5.31570 | ||||||||
\(619\) | 11.3275 | 0.455292 | 0.227646 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227646 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(620\) | 16.4773 | 0.661744 | ||||||||
\(621\) | 56.5960 | 2.27112 | ||||||||
\(622\) | −57.4644 | −2.30411 | ||||||||
\(623\) | 9.86904 | 0.395395 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.9590 | −1.07836 | ||||||||
\(626\) | −5.16289 | −0.206351 | ||||||||
\(627\) | 0.847085 | 0.0338293 | ||||||||
\(628\) | 38.3293 | 1.52950 | ||||||||
\(629\) | 7.08402 | 0.282459 | ||||||||
\(630\) | −77.4701 | −3.08648 | ||||||||
\(631\) | 3.00798 | 0.119746 | 0.0598730 | − | 0.998206i | \(-0.480930\pi\) | ||||
0.0598730 | + | 0.998206i | \(0.480930\pi\) | |||||||
\(632\) | 106.597 | 4.24020 | ||||||||
\(633\) | −5.82014 | −0.231330 | ||||||||
\(634\) | 22.7225 | 0.902425 | ||||||||
\(635\) | 12.6587 | 0.502345 | ||||||||
\(636\) | 72.3707 | 2.86968 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.51514 | −0.0995752 | ||||||||
\(639\) | −3.18701 | −0.126076 | ||||||||
\(640\) | 64.3538 | 2.54381 | ||||||||
\(641\) | −15.0695 | −0.595208 | −0.297604 | − | 0.954689i | \(-0.596188\pi\) | ||||
−0.297604 | + | 0.954689i | \(0.596188\pi\) | |||||||
\(642\) | 36.7002 | 1.44844 | ||||||||
\(643\) | 16.4528 | 0.648833 | 0.324417 | − | 0.945914i | \(-0.394832\pi\) | ||||
0.324417 | + | 0.945914i | \(0.394832\pi\) | |||||||
\(644\) | 70.1840 | 2.76564 | ||||||||
\(645\) | −91.4572 | −3.60112 | ||||||||
\(646\) | −0.815627 | −0.0320904 | ||||||||
\(647\) | 30.2788 | 1.19038 | 0.595191 | − | 0.803585i | \(-0.297077\pi\) | ||||
0.595191 | + | 0.803585i | \(0.297077\pi\) | |||||||
\(648\) | −38.9116 | −1.52859 | ||||||||
\(649\) | 11.6149 | 0.455923 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.05422 | −0.198090 | ||||||||
\(652\) | 105.439 | 4.12930 | ||||||||
\(653\) | 23.8518 | 0.933394 | 0.466697 | − | 0.884417i | \(-0.345444\pi\) | ||||
0.466697 | + | 0.884417i | \(0.345444\pi\) | |||||||
\(654\) | −107.720 | −4.21219 | ||||||||
\(655\) | 5.07144 | 0.198157 | ||||||||
\(656\) | −61.1685 | −2.38823 | ||||||||
\(657\) | −86.4908 | −3.37433 | ||||||||
\(658\) | −9.37036 | −0.365295 | ||||||||
\(659\) | −11.9043 | −0.463727 | −0.231863 | − | 0.972748i | \(-0.574482\pi\) | ||||
−0.231863 | + | 0.972748i | \(0.574482\pi\) | |||||||
\(660\) | −47.0365 | −1.83089 | ||||||||
\(661\) | 4.50059 | 0.175053 | 0.0875263 | − | 0.996162i | \(-0.472104\pi\) | ||||
0.0875263 | + | 0.996162i | \(0.472104\pi\) | |||||||
\(662\) | 66.3969 | 2.58059 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −91.0221 | −3.53234 | ||||||||
\(665\) | 1.53464 | 0.0595108 | ||||||||
\(666\) | −99.8717 | −3.86995 | ||||||||
\(667\) | 7.37648 | 0.285619 | ||||||||
\(668\) | 25.8712 | 1.00099 | ||||||||
\(669\) | −9.45857 | −0.365690 | ||||||||
\(670\) | −78.4206 | −3.02965 | ||||||||
\(671\) | −9.48390 | −0.366122 | ||||||||
\(672\) | −85.2918 | −3.29020 | ||||||||
\(673\) | −9.30191 | −0.358562 | −0.179281 | − | 0.983798i | \(-0.557377\pi\) | ||||
−0.179281 | + | 0.983798i | \(0.557377\pi\) | |||||||
\(674\) | −69.4568 | −2.67538 | ||||||||
\(675\) | −32.8202 | −1.26325 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.0200 | 1.69183 | 0.845913 | − | 0.533322i | \(-0.179056\pi\) | ||||
0.845913 | + | 0.533322i | \(0.179056\pi\) | |||||||
\(678\) | −65.3911 | −2.51133 | ||||||||
\(679\) | −1.57242 | −0.0603441 | ||||||||
\(680\) | 27.9535 | 1.07197 | ||||||||
\(681\) | −50.3639 | −1.92995 | ||||||||
\(682\) | −2.73991 | −0.104917 | ||||||||
\(683\) | −17.7684 | −0.679891 | −0.339945 | − | 0.940445i | \(-0.610409\pi\) | ||||
−0.339945 | + | 0.940445i | \(0.610409\pi\) | |||||||
\(684\) | 8.31571 | 0.317959 | ||||||||
\(685\) | 22.5159 | 0.860287 | ||||||||
\(686\) | −50.8232 | −1.94044 | ||||||||
\(687\) | −35.5669 | −1.35696 | ||||||||
\(688\) | −130.539 | −4.97676 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 190.756 | 7.26195 | ||||||||
\(691\) | −6.75142 | −0.256836 | −0.128418 | − | 0.991720i | \(-0.540990\pi\) | ||||
−0.128418 | + | 0.991720i | \(0.540990\pi\) | |||||||
\(692\) | 110.285 | 4.19239 | ||||||||
\(693\) | 9.31601 | 0.353886 | ||||||||
\(694\) | −5.34329 | −0.202829 | ||||||||
\(695\) | −34.2943 | −1.30086 | ||||||||
\(696\) | −23.6017 | −0.894621 | ||||||||
\(697\) | −4.96209 | −0.187953 | ||||||||
\(698\) | −25.9483 | −0.982159 | ||||||||
\(699\) | −0.801986 | −0.0303339 | ||||||||
\(700\) | −40.6998 | −1.53831 | ||||||||
\(701\) | −10.2838 | −0.388412 | −0.194206 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194206 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.97840 | 0.0746169 | ||||||||
\(704\) | −20.5382 | −0.774061 | ||||||||
\(705\) | −18.4179 | −0.693660 | ||||||||
\(706\) | 13.3765 | 0.503430 | ||||||||
\(707\) | 21.9179 | 0.824307 | ||||||||
\(708\) | 176.587 | 6.63655 | ||||||||
\(709\) | 26.3616 | 0.990029 | 0.495015 | − | 0.868885i | \(-0.335163\pi\) | ||||
0.495015 | + | 0.868885i | \(0.335163\pi\) | |||||||
\(710\) | −4.84751 | −0.181924 | ||||||||
\(711\) | −67.2338 | −2.52147 | ||||||||
\(712\) | 50.2041 | 1.88148 | ||||||||
\(713\) | 8.03570 | 0.300939 | ||||||||
\(714\) | −13.8921 | −0.519899 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.56094 | 0.207822 | ||||||||
\(717\) | 65.3043 | 2.43883 | ||||||||
\(718\) | 42.5839 | 1.58922 | ||||||||
\(719\) | 31.9625 | 1.19200 | 0.596000 | − | 0.802984i | \(-0.296756\pi\) | ||||
0.596000 | + | 0.802984i | \(0.296756\pi\) | |||||||
\(720\) | −217.341 | −8.09983 | ||||||||
\(721\) | 28.7892 | 1.07217 | ||||||||
\(722\) | 50.8425 | 1.89216 | ||||||||
\(723\) | −51.6195 | −1.91975 | ||||||||
\(724\) | 98.1590 | 3.64805 | ||||||||
\(725\) | −4.27764 | −0.158867 | ||||||||
\(726\) | 7.82142 | 0.290280 | ||||||||
\(727\) | −6.35132 | −0.235557 | −0.117779 | − | 0.993040i | \(-0.537577\pi\) | ||||
−0.117779 | + | 0.993040i | \(0.537577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.1296 | −1.41221 | ||||||||
\(730\) | −131.554 | −4.86905 | ||||||||
\(731\) | −10.5896 | −0.391669 | ||||||||
\(732\) | −144.189 | −5.32939 | ||||||||
\(733\) | −33.9768 | −1.25496 | −0.627481 | − | 0.778632i | \(-0.715914\pi\) | ||||
−0.627481 | + | 0.778632i | \(0.715914\pi\) | |||||||
\(734\) | 11.3795 | 0.420026 | ||||||||
\(735\) | −36.8785 | −1.36028 | ||||||||
\(736\) | 135.606 | 4.99849 | ||||||||
\(737\) | 9.43031 | 0.347370 | ||||||||
\(738\) | 69.9563 | 2.57513 | ||||||||
\(739\) | −31.1540 | −1.14602 | −0.573009 | − | 0.819549i | \(-0.694224\pi\) | ||||
−0.573009 | + | 0.819549i | \(0.694224\pi\) | |||||||
\(740\) | −109.856 | −4.03838 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −21.8018 | −0.800370 | ||||||||
\(743\) | 39.1173 | 1.43507 | 0.717537 | − | 0.696520i | \(-0.245269\pi\) | ||||
0.717537 | + | 0.696520i | \(0.245269\pi\) | |||||||
\(744\) | −25.7109 | −0.942609 | ||||||||
\(745\) | 0.360847 | 0.0132204 | ||||||||
\(746\) | 8.72403 | 0.319410 | ||||||||
\(747\) | 57.4103 | 2.10053 | ||||||||
\(748\) | −5.44623 | −0.199134 | ||||||||
\(749\) | −7.99547 | −0.292148 | ||||||||
\(750\) | 10.3692 | 0.378630 | ||||||||
\(751\) | −2.15947 | −0.0788001 | −0.0394000 | − | 0.999224i | \(-0.512545\pi\) | ||||
−0.0394000 | + | 0.999224i | \(0.512545\pi\) | |||||||
\(752\) | −26.2884 | −0.958640 | ||||||||
\(753\) | 59.7173 | 2.17622 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.6116 | −1.11407 | ||||||||
\(756\) | 63.9174 | 2.32466 | ||||||||
\(757\) | −0.315358 | −0.0114619 | −0.00573094 | − | 0.999984i | \(-0.501824\pi\) | ||||
−0.00573094 | + | 0.999984i | \(0.501824\pi\) | |||||||
\(758\) | 56.0607 | 2.03622 | ||||||||
\(759\) | −22.9389 | −0.832631 | ||||||||
\(760\) | 7.80676 | 0.283181 | ||||||||
\(761\) | 20.6516 | 0.748622 | 0.374311 | − | 0.927303i | \(-0.377879\pi\) | ||||
0.374311 | + | 0.927303i | \(0.377879\pi\) | |||||||
\(762\) | −32.0026 | −1.15933 | ||||||||
\(763\) | 23.4678 | 0.849590 | ||||||||
\(764\) | −100.786 | −3.64630 | ||||||||
\(765\) | −17.6311 | −0.637454 | ||||||||
\(766\) | 69.0223 | 2.49388 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −43.1675 | −1.55767 | ||||||||
\(769\) | −12.7162 | −0.458559 | −0.229280 | − | 0.973361i | \(-0.573637\pi\) | ||||
−0.229280 | + | 0.973361i | \(0.573637\pi\) | |||||||
\(770\) | 14.1699 | 0.510646 | ||||||||
\(771\) | 29.4754 | 1.06153 | ||||||||
\(772\) | −54.3571 | −1.95635 | ||||||||
\(773\) | 8.70103 | 0.312954 | 0.156477 | − | 0.987682i | \(-0.449986\pi\) | ||||
0.156477 | + | 0.987682i | \(0.449986\pi\) | |||||||
\(774\) | 149.293 | 5.36624 | ||||||||
\(775\) | −4.65992 | −0.167389 | ||||||||
\(776\) | −7.99896 | −0.287146 | ||||||||
\(777\) | 33.6970 | 1.20887 | ||||||||
\(778\) | −45.2322 | −1.62165 | ||||||||
\(779\) | −1.38580 | −0.0496513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.582928 | 0.0208588 | ||||||||
\(782\) | 22.0871 | 0.789832 | ||||||||
\(783\) | 6.71786 | 0.240077 | ||||||||
\(784\) | −52.6376 | −1.87992 | ||||||||
\(785\) | −22.6958 | −0.810048 | ||||||||
\(786\) | −12.8212 | −0.457316 | ||||||||
\(787\) | −36.4098 | −1.29787 | −0.648934 | − | 0.760845i | \(-0.724785\pi\) | ||||
−0.648934 | + | 0.760845i | \(0.724785\pi\) | |||||||
\(788\) | −51.9021 | −1.84894 | ||||||||
\(789\) | −0.283500 | −0.0100929 | ||||||||
\(790\) | −102.264 | −3.63840 | ||||||||
\(791\) | 14.2460 | 0.506531 | ||||||||
\(792\) | 47.3908 | 1.68396 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.18828 | 0.326080 | ||||||||
\(795\) | −42.8527 | −1.51983 | ||||||||
\(796\) | −66.4741 | −2.35611 | ||||||||
\(797\) | 3.32151 | 0.117654 | 0.0588270 | − | 0.998268i | \(-0.481264\pi\) | ||||
0.0588270 | + | 0.998268i | \(0.481264\pi\) | |||||||
\(798\) | −3.87974 | −0.137341 | ||||||||
\(799\) | −2.13256 | −0.0754446 | ||||||||
\(800\) | −78.6379 | −2.78027 | ||||||||
\(801\) | −31.6652 | −1.11884 | ||||||||
\(802\) | −15.6635 | −0.553096 | ||||||||
\(803\) | 15.8198 | 0.558269 | ||||||||
\(804\) | 143.374 | 5.05643 | ||||||||
\(805\) | −41.5579 | −1.46472 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2077 | 0.359327 | ||||||||
\(808\) | 111.497 | 3.92245 | ||||||||
\(809\) | 7.94177 | 0.279218 | 0.139609 | − | 0.990207i | \(-0.455415\pi\) | ||||
0.139609 | + | 0.990207i | \(0.455415\pi\) | |||||||
\(810\) | 37.3300 | 1.31164 | ||||||||
\(811\) | −18.5407 | −0.651052 | −0.325526 | − | 0.945533i | \(-0.605541\pi\) | ||||
−0.325526 | + | 0.945533i | \(0.605541\pi\) | |||||||
\(812\) | 8.33072 | 0.292351 | ||||||||
\(813\) | 44.5601 | 1.56279 | ||||||||
\(814\) | 18.2673 | 0.640267 | ||||||||
\(815\) | −62.4332 | −2.18694 | ||||||||
\(816\) | −38.9741 | −1.36437 | ||||||||
\(817\) | −2.95742 | −0.103467 | ||||||||
\(818\) | −36.1452 | −1.26379 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 76.9499 | 2.68721 | ||||||||
\(821\) | −26.9214 | −0.939565 | −0.469782 | − | 0.882782i | \(-0.655668\pi\) | ||||
−0.469782 | + | 0.882782i | \(0.655668\pi\) | |||||||
\(822\) | −56.9226 | −1.98541 | ||||||||
\(823\) | −48.5760 | −1.69325 | −0.846626 | − | 0.532188i | \(-0.821370\pi\) | ||||
−0.846626 | + | 0.532188i | \(0.821370\pi\) | |||||||
\(824\) | 146.452 | 5.10188 | ||||||||
\(825\) | 13.3023 | 0.463128 | ||||||||
\(826\) | −53.1973 | −1.85097 | ||||||||
\(827\) | 47.6008 | 1.65524 | 0.827621 | − | 0.561287i | \(-0.189694\pi\) | ||||
0.827621 | + | 0.561287i | \(0.189694\pi\) | |||||||
\(828\) | −225.188 | −7.82583 | ||||||||
\(829\) | −3.40020 | −0.118094 | −0.0590470 | − | 0.998255i | \(-0.518806\pi\) | ||||
−0.0590470 | + | 0.998255i | \(0.518806\pi\) | |||||||
\(830\) | 87.3224 | 3.03100 | ||||||||
\(831\) | 60.1451 | 2.08641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.27006 | −0.147949 | ||||||||
\(834\) | 86.6999 | 3.00217 | ||||||||
\(835\) | −15.3190 | −0.530137 | ||||||||
\(836\) | −1.52100 | −0.0526050 | ||||||||
\(837\) | 7.31822 | 0.252955 | ||||||||
\(838\) | 68.7020 | 2.37327 | ||||||||
\(839\) | 42.8825 | 1.48047 | 0.740233 | − | 0.672350i | \(-0.234715\pi\) | ||||
0.740233 | + | 0.672350i | \(0.234715\pi\) | |||||||
\(840\) | 132.968 | 4.58783 | ||||||||
\(841\) | −28.1244 | −0.969808 | ||||||||
\(842\) | 81.9825 | 2.82530 | ||||||||
\(843\) | −83.7310 | −2.88385 | ||||||||
\(844\) | 10.4505 | 0.359721 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 30.0652 | 1.03366 | ||||||||
\(847\) | −1.70397 | −0.0585490 | ||||||||
\(848\) | −61.1647 | −2.10040 | ||||||||
\(849\) | 88.0980 | 3.02351 | ||||||||
\(850\) | −12.8083 | −0.439322 | ||||||||
\(851\) | −53.5749 | −1.83652 | ||||||||
\(852\) | 8.86258 | 0.303627 | ||||||||
\(853\) | 41.0285 | 1.40479 | 0.702395 | − | 0.711787i | \(-0.252114\pi\) | ||||
0.702395 | + | 0.711787i | \(0.252114\pi\) | |||||||
\(854\) | 43.4373 | 1.48639 | ||||||||
\(855\) | −4.92396 | −0.168396 | ||||||||
\(856\) | −40.6732 | −1.39018 | ||||||||
\(857\) | −46.7316 | −1.59632 | −0.798161 | − | 0.602444i | \(-0.794194\pi\) | ||||
−0.798161 | + | 0.602444i | \(0.794194\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.18746 | 0.176994 | 0.0884970 | − | 0.996076i | \(-0.471794\pi\) | ||||
0.0884970 | + | 0.996076i | \(0.471794\pi\) | |||||||
\(860\) | 164.218 | 5.59979 | ||||||||
\(861\) | −23.6035 | −0.804405 | ||||||||
\(862\) | −24.2792 | −0.826953 | ||||||||
\(863\) | 44.3316 | 1.50907 | 0.754533 | − | 0.656262i | \(-0.227864\pi\) | ||||
0.754533 | + | 0.656262i | \(0.227864\pi\) | |||||||
\(864\) | 123.498 | 4.20148 | ||||||||
\(865\) | −65.3025 | −2.22035 | ||||||||
\(866\) | 55.9448 | 1.90108 | ||||||||
\(867\) | 46.3059 | 1.57263 | ||||||||
\(868\) | 9.07522 | 0.308033 | ||||||||
\(869\) | 12.2976 | 0.417166 | ||||||||
\(870\) | 22.6424 | 0.767649 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 119.381 | 4.04276 | ||||||||
\(873\) | 5.04518 | 0.170754 | ||||||||
\(874\) | 6.16841 | 0.208649 | ||||||||
\(875\) | −2.25902 | −0.0763690 | ||||||||
\(876\) | 240.518 | 8.12633 | ||||||||
\(877\) | −28.7343 | −0.970288 | −0.485144 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485144 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(878\) | −67.6889 | −2.28439 | ||||||||
\(879\) | −32.2312 | −1.08713 | ||||||||
\(880\) | 39.7533 | 1.34008 | ||||||||
\(881\) | 3.46294 | 0.116669 | 0.0583347 | − | 0.998297i | \(-0.481421\pi\) | ||||
0.0583347 | + | 0.998297i | \(0.481421\pi\) | |||||||
\(882\) | 60.1999 | 2.02704 | ||||||||
\(883\) | −25.7431 | −0.866326 | −0.433163 | − | 0.901316i | \(-0.642602\pi\) | ||||
−0.433163 | + | 0.901316i | \(0.642602\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −104.562 | −3.51482 | ||||||||
\(886\) | −101.099 | −3.39649 | ||||||||
\(887\) | 56.3033 | 1.89048 | 0.945240 | − | 0.326375i | \(-0.105827\pi\) | ||||
0.945240 | + | 0.326375i | \(0.105827\pi\) | |||||||
\(888\) | 171.418 | 5.75240 | ||||||||
\(889\) | 6.97205 | 0.233835 | ||||||||
\(890\) | −48.1635 | −1.61444 | ||||||||
\(891\) | −4.48905 | −0.150389 | ||||||||
\(892\) | 16.9836 | 0.568652 | ||||||||
\(893\) | −0.595575 | −0.0199302 | ||||||||
\(894\) | −0.912263 | −0.0305106 | ||||||||
\(895\) | −3.29279 | −0.110066 | ||||||||
\(896\) | 35.4443 | 1.18411 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.0311 | 0.835298 | ||||||||
\(899\) | 0.953825 | 0.0318118 | ||||||||
\(900\) | 130.587 | 4.35290 | ||||||||
\(901\) | −4.96179 | −0.165301 | ||||||||
\(902\) | −12.7955 | −0.426045 | ||||||||
\(903\) | −50.3720 | −1.67628 | ||||||||
\(904\) | 72.4700 | 2.41032 | ||||||||
\(905\) | −58.1226 | −1.93206 | ||||||||
\(906\) | 77.3896 | 2.57110 | ||||||||
\(907\) | 25.6494 | 0.851676 | 0.425838 | − | 0.904799i | \(-0.359979\pi\) | ||||
0.425838 | + | 0.904799i | \(0.359979\pi\) | |||||||
\(908\) | 90.4322 | 3.00110 | ||||||||
\(909\) | −70.3245 | −2.33251 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.7349 | 1.18395 | 0.591975 | − | 0.805957i | \(-0.298349\pi\) | ||||
0.591975 | + | 0.805957i | \(0.298349\pi\) | |||||||
\(912\) | −10.8846 | −0.360424 | ||||||||
\(913\) | −10.5008 | −0.347525 | ||||||||
\(914\) | −64.6084 | −2.13706 | ||||||||
\(915\) | 85.3784 | 2.82252 | ||||||||
\(916\) | 63.8630 | 2.11009 | ||||||||
\(917\) | 2.79320 | 0.0922397 | ||||||||
\(918\) | 20.1150 | 0.663893 | ||||||||
\(919\) | −7.42382 | −0.244889 | −0.122445 | − | 0.992475i | \(-0.539073\pi\) | ||||
−0.122445 | + | 0.992475i | \(0.539073\pi\) | |||||||
\(920\) | −211.406 | −6.96985 | ||||||||
\(921\) | −14.9414 | −0.492334 | ||||||||
\(922\) | −72.5238 | −2.38845 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −25.9064 | −0.852258 | ||||||||
\(925\) | 31.0682 | 1.02152 | ||||||||
\(926\) | 87.4905 | 2.87512 | ||||||||
\(927\) | −92.3714 | −3.03387 | ||||||||
\(928\) | 16.0962 | 0.528382 | ||||||||
\(929\) | −28.5106 | −0.935403 | −0.467702 | − | 0.883886i | \(-0.654918\pi\) | ||||
−0.467702 | + | 0.883886i | \(0.654918\pi\) | |||||||
\(930\) | 24.6659 | 0.808827 | ||||||||
\(931\) | −1.19253 | −0.0390835 | ||||||||
\(932\) | 1.44003 | 0.0471696 | ||||||||
\(933\) | −62.2093 | −2.03664 | ||||||||
\(934\) | 55.3606 | 1.81146 | ||||||||
\(935\) | 3.22486 | 0.105464 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.3343 | 0.468280 | 0.234140 | − | 0.972203i | \(-0.424773\pi\) | ||||
0.234140 | + | 0.972203i | \(0.424773\pi\) | |||||||
\(938\) | −43.1919 | −1.41026 | ||||||||
\(939\) | −5.58920 | −0.182396 | ||||||||
\(940\) | 33.0708 | 1.07865 | ||||||||
\(941\) | 26.5519 | 0.865568 | 0.432784 | − | 0.901498i | \(-0.357531\pi\) | ||||
0.432784 | + | 0.901498i | \(0.357531\pi\) | |||||||
\(942\) | 57.3775 | 1.86946 | ||||||||
\(943\) | 37.5272 | 1.22205 | ||||||||
\(944\) | −149.244 | −4.85749 | ||||||||
\(945\) | −37.8473 | −1.23117 | ||||||||
\(946\) | −27.3069 | −0.887823 | ||||||||
\(947\) | −51.3198 | −1.66767 | −0.833835 | − | 0.552013i | \(-0.813860\pi\) | ||||
−0.833835 | + | 0.552013i | \(0.813860\pi\) | |||||||
\(948\) | 186.967 | 6.07240 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.57707 | −0.116055 | ||||||||
\(951\) | 24.5987 | 0.797668 | ||||||||
\(952\) | 15.3960 | 0.498987 | ||||||||
\(953\) | 32.8316 | 1.06352 | 0.531759 | − | 0.846895i | \(-0.321531\pi\) | ||||
0.531759 | + | 0.846895i | \(0.321531\pi\) | |||||||
\(954\) | 69.9520 | 2.26478 | ||||||||
\(955\) | 59.6780 | 1.93113 | ||||||||
\(956\) | −117.259 | −3.79242 | ||||||||
\(957\) | −2.72281 | −0.0880161 | ||||||||
\(958\) | 31.5860 | 1.02050 | ||||||||
\(959\) | 12.4011 | 0.400453 | ||||||||
\(960\) | 184.894 | 5.96742 | ||||||||
\(961\) | −29.9609 | −0.966482 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.6538 | 0.826682 | ||||||||
\(964\) | 92.6867 | 2.98524 | ||||||||
\(965\) | 32.1863 | 1.03611 | ||||||||
\(966\) | 105.063 | 3.38034 | ||||||||
\(967\) | 26.5335 | 0.853259 | 0.426630 | − | 0.904426i | \(-0.359701\pi\) | ||||
0.426630 | + | 0.904426i | \(0.359701\pi\) | |||||||
\(968\) | −8.66813 | −0.278604 | ||||||||
\(969\) | −0.882975 | −0.0283652 | ||||||||
\(970\) | 7.67384 | 0.246392 | ||||||||
\(971\) | 0.504385 | 0.0161865 | 0.00809324 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809324 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(972\) | 44.2834 | 1.42039 | ||||||||
\(973\) | −18.8884 | −0.605533 | ||||||||
\(974\) | 25.4157 | 0.814373 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 121.863 | 3.90073 | ||||||||
\(977\) | −19.3758 | −0.619886 | −0.309943 | − | 0.950755i | \(-0.600310\pi\) | ||||
−0.309943 | + | 0.950755i | \(0.600310\pi\) | |||||||
\(978\) | 157.838 | 5.04710 | ||||||||
\(979\) | 5.79180 | 0.185107 | ||||||||
\(980\) | 66.2181 | 2.11526 | ||||||||
\(981\) | −75.2973 | −2.40406 | ||||||||
\(982\) | −43.2693 | −1.38078 | ||||||||
\(983\) | 10.6735 | 0.340432 | 0.170216 | − | 0.985407i | \(-0.445554\pi\) | ||||
0.170216 | + | 0.985407i | \(0.445554\pi\) | |||||||
\(984\) | −120.072 | −3.82774 | ||||||||
\(985\) | 30.7327 | 0.979224 | ||||||||
\(986\) | 2.62170 | 0.0834919 | ||||||||
\(987\) | −10.1441 | −0.322890 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 80.0865 | 2.54660 | ||||||||
\(990\) | −45.4646 | −1.44496 | ||||||||
\(991\) | −8.52193 | −0.270708 | −0.135354 | − | 0.990797i | \(-0.543217\pi\) | ||||
−0.135354 | + | 0.990797i | \(0.543217\pi\) | |||||||
\(992\) | 17.5346 | 0.556725 | ||||||||
\(993\) | 71.8794 | 2.28102 | ||||||||
\(994\) | −2.66987 | −0.0846832 | ||||||||
\(995\) | 39.3611 | 1.24783 | ||||||||
\(996\) | −159.649 | −5.05868 | ||||||||
\(997\) | −35.8287 | −1.13471 | −0.567354 | − | 0.823474i | \(-0.692033\pi\) | ||||
−0.567354 | + | 0.823474i | \(0.692033\pi\) | |||||||
\(998\) | 82.2320 | 2.60301 | ||||||||
\(999\) | −48.7913 | −1.54369 |
(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.s.1.1 | ✓ | 21 | |
13.12 | even | 2 | 1859.2.a.t.1.21 | yes | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.1 | ✓ | 21 | 1.1 | even | 1 | trivial | |
1859.2.a.t.1.21 | yes | 21 | 13.12 | even | 2 |