Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1279733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.33192\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90785 | 1.34905 | 0.674527 | − | 0.738250i | \(-0.264348\pi\) | ||||
0.674527 | + | 0.738250i | \(0.264348\pi\) | |||||||
\(3\) | −1.08494 | −0.626388 | −0.313194 | − | 0.949689i | \(-0.601399\pi\) | ||||
−0.313194 | + | 0.949689i | \(0.601399\pi\) | |||||||
\(4\) | 1.63989 | 0.819947 | ||||||||
\(5\) | −1.10591 | −0.494579 | −0.247290 | − | 0.968942i | \(-0.579540\pi\) | ||||
−0.247290 | + | 0.968942i | \(0.579540\pi\) | |||||||
\(6\) | −2.06989 | −0.845031 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.687029 | −0.242902 | ||||||||
\(9\) | −1.82292 | −0.607638 | ||||||||
\(10\) | −2.10992 | −0.667214 | ||||||||
\(11\) | −0.799816 | −0.241154 | −0.120577 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120577 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(12\) | −1.77918 | −0.513605 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.90785 | 0.509894 | ||||||||
\(15\) | 1.19984 | 0.309798 | ||||||||
\(16\) | −4.59054 | −1.14763 | ||||||||
\(17\) | 2.63979 | 0.640244 | 0.320122 | − | 0.947376i | \(-0.396276\pi\) | ||||
0.320122 | + | 0.947376i | \(0.396276\pi\) | |||||||
\(18\) | −3.47785 | −0.819737 | ||||||||
\(19\) | −1.84186 | −0.422552 | −0.211276 | − | 0.977426i | \(-0.567762\pi\) | ||||
−0.211276 | + | 0.977426i | \(0.567762\pi\) | |||||||
\(20\) | −1.81358 | −0.405529 | ||||||||
\(21\) | −1.08494 | −0.236752 | ||||||||
\(22\) | −1.52593 | −0.325329 | ||||||||
\(23\) | −3.82692 | −0.797968 | −0.398984 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398984 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(24\) | 0.745382 | 0.152151 | ||||||||
\(25\) | −3.77696 | −0.755391 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.23255 | 1.00701 | ||||||||
\(28\) | 1.63989 | 0.309911 | ||||||||
\(29\) | −7.54322 | −1.40074 | −0.700370 | − | 0.713780i | \(-0.746982\pi\) | ||||
−0.700370 | + | 0.713780i | \(0.746982\pi\) | |||||||
\(30\) | 2.28912 | 0.417935 | ||||||||
\(31\) | −7.86730 | −1.41301 | −0.706505 | − | 0.707708i | \(-0.749729\pi\) | ||||
−0.706505 | + | 0.707708i | \(0.749729\pi\) | |||||||
\(32\) | −7.38400 | −1.30532 | ||||||||
\(33\) | 0.867749 | 0.151056 | ||||||||
\(34\) | 5.03633 | 0.863724 | ||||||||
\(35\) | −1.10591 | −0.186933 | ||||||||
\(36\) | −2.98939 | −0.498231 | ||||||||
\(37\) | 3.45786 | 0.568469 | 0.284234 | − | 0.958755i | \(-0.408261\pi\) | ||||
0.284234 | + | 0.958755i | \(0.408261\pi\) | |||||||
\(38\) | −3.51399 | −0.570045 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.759794 | 0.120134 | ||||||||
\(41\) | −10.9578 | −1.71133 | −0.855664 | − | 0.517532i | \(-0.826851\pi\) | ||||
−0.855664 | + | 0.517532i | \(0.826851\pi\) | |||||||
\(42\) | −2.06989 | −0.319392 | ||||||||
\(43\) | −2.63910 | −0.402459 | −0.201230 | − | 0.979544i | \(-0.564494\pi\) | ||||
−0.201230 | + | 0.979544i | \(0.564494\pi\) | |||||||
\(44\) | −1.31161 | −0.197733 | ||||||||
\(45\) | 2.01599 | 0.300525 | ||||||||
\(46\) | −7.30119 | −1.07650 | ||||||||
\(47\) | 5.22430 | 0.762043 | 0.381021 | − | 0.924566i | \(-0.375572\pi\) | ||||
0.381021 | + | 0.924566i | \(0.375572\pi\) | |||||||
\(48\) | 4.98044 | 0.718864 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.20587 | −1.01906 | ||||||||
\(51\) | −2.86401 | −0.401041 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.15957 | 0.846082 | 0.423041 | − | 0.906111i | \(-0.360963\pi\) | ||||
0.423041 | + | 0.906111i | \(0.360963\pi\) | |||||||
\(54\) | 9.98293 | 1.35850 | ||||||||
\(55\) | 0.884527 | 0.119270 | ||||||||
\(56\) | −0.687029 | −0.0918081 | ||||||||
\(57\) | 1.99830 | 0.264681 | ||||||||
\(58\) | −14.3913 | −1.88967 | ||||||||
\(59\) | 5.10250 | 0.664288 | 0.332144 | − | 0.943229i | \(-0.392228\pi\) | ||||
0.332144 | + | 0.943229i | \(0.392228\pi\) | |||||||
\(60\) | 1.96762 | 0.254018 | ||||||||
\(61\) | 3.31543 | 0.424498 | 0.212249 | − | 0.977216i | \(-0.431921\pi\) | ||||
0.212249 | + | 0.977216i | \(0.431921\pi\) | |||||||
\(62\) | −15.0096 | −1.90623 | ||||||||
\(63\) | −1.82292 | −0.229666 | ||||||||
\(64\) | −4.90649 | −0.613312 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.65553 | 0.203782 | ||||||||
\(67\) | −13.9305 | −1.70188 | −0.850942 | − | 0.525260i | \(-0.823968\pi\) | ||||
−0.850942 | + | 0.525260i | \(0.823968\pi\) | |||||||
\(68\) | 4.32898 | 0.524966 | ||||||||
\(69\) | 4.15196 | 0.499837 | ||||||||
\(70\) | −2.10992 | −0.252183 | ||||||||
\(71\) | 6.69004 | 0.793962 | 0.396981 | − | 0.917827i | \(-0.370058\pi\) | ||||
0.396981 | + | 0.917827i | \(0.370058\pi\) | |||||||
\(72\) | 1.25240 | 0.147596 | ||||||||
\(73\) | 15.0774 | 1.76467 | 0.882336 | − | 0.470619i | \(-0.155969\pi\) | ||||
0.882336 | + | 0.470619i | \(0.155969\pi\) | |||||||
\(74\) | 6.59708 | 0.766895 | ||||||||
\(75\) | 4.09775 | 0.473168 | ||||||||
\(76\) | −3.02045 | −0.346470 | ||||||||
\(77\) | −0.799816 | −0.0911475 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.10529 | −0.911916 | −0.455958 | − | 0.890001i | \(-0.650703\pi\) | ||||
−0.455958 | + | 0.890001i | \(0.650703\pi\) | |||||||
\(80\) | 5.07673 | 0.567596 | ||||||||
\(81\) | −0.208236 | −0.0231373 | ||||||||
\(82\) | −20.9059 | −2.30867 | ||||||||
\(83\) | 15.6338 | 1.71603 | 0.858016 | − | 0.513623i | \(-0.171697\pi\) | ||||
0.858016 | + | 0.513623i | \(0.171697\pi\) | |||||||
\(84\) | −1.77918 | −0.194124 | ||||||||
\(85\) | −2.91938 | −0.316651 | ||||||||
\(86\) | −5.03501 | −0.542939 | ||||||||
\(87\) | 8.18390 | 0.877407 | ||||||||
\(88\) | 0.549497 | 0.0585766 | ||||||||
\(89\) | −2.27897 | −0.241570 | −0.120785 | − | 0.992679i | \(-0.538541\pi\) | ||||
−0.120785 | + | 0.992679i | \(0.538541\pi\) | |||||||
\(90\) | 3.84620 | 0.405425 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.27574 | −0.654291 | ||||||||
\(93\) | 8.53552 | 0.885092 | ||||||||
\(94\) | 9.96718 | 1.02804 | ||||||||
\(95\) | 2.03694 | 0.208985 | ||||||||
\(96\) | 8.01116 | 0.817636 | ||||||||
\(97\) | 16.4949 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184073\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184073\pi\) | |||||||
\(98\) | 1.90785 | 0.192722 | ||||||||
\(99\) | 1.45800 | 0.146534 | ||||||||
\(100\) | −6.19381 | −0.619381 | ||||||||
\(101\) | −14.0686 | −1.39988 | −0.699940 | − | 0.714201i | \(-0.746790\pi\) | ||||
−0.699940 | + | 0.714201i | \(0.746790\pi\) | |||||||
\(102\) | −5.46409 | −0.541026 | ||||||||
\(103\) | 0.110230 | 0.0108613 | 0.00543063 | − | 0.999985i | \(-0.498271\pi\) | ||||
0.00543063 | + | 0.999985i | \(0.498271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.19984 | 0.117093 | ||||||||
\(106\) | 11.7515 | 1.14141 | ||||||||
\(107\) | −13.8071 | −1.33478 | −0.667389 | − | 0.744709i | \(-0.732588\pi\) | ||||
−0.667389 | + | 0.744709i | \(0.732588\pi\) | |||||||
\(108\) | 8.58083 | 0.825691 | ||||||||
\(109\) | −2.17385 | −0.208217 | −0.104108 | − | 0.994566i | \(-0.533199\pi\) | ||||
−0.104108 | + | 0.994566i | \(0.533199\pi\) | |||||||
\(110\) | 1.68754 | 0.160901 | ||||||||
\(111\) | −3.75156 | −0.356082 | ||||||||
\(112\) | −4.59054 | −0.433765 | ||||||||
\(113\) | −16.2026 | −1.52421 | −0.762105 | − | 0.647453i | \(-0.775834\pi\) | ||||
−0.762105 | + | 0.647453i | \(0.775834\pi\) | |||||||
\(114\) | 3.81245 | 0.357069 | ||||||||
\(115\) | 4.23224 | 0.394658 | ||||||||
\(116\) | −12.3701 | −1.14853 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.73480 | 0.896161 | ||||||||
\(119\) | 2.63979 | 0.241989 | ||||||||
\(120\) | −0.824328 | −0.0752505 | ||||||||
\(121\) | −10.3603 | −0.941845 | ||||||||
\(122\) | 6.32535 | 0.572670 | ||||||||
\(123\) | 11.8886 | 1.07195 | ||||||||
\(124\) | −12.9015 | −1.15859 | ||||||||
\(125\) | 9.70655 | 0.868180 | ||||||||
\(126\) | −3.47785 | −0.309831 | ||||||||
\(127\) | 19.9799 | 1.77293 | 0.886463 | − | 0.462800i | \(-0.153155\pi\) | ||||
0.886463 | + | 0.462800i | \(0.153155\pi\) | |||||||
\(128\) | 5.40714 | 0.477928 | ||||||||
\(129\) | 2.86325 | 0.252095 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.3019 | −1.59905 | −0.799524 | − | 0.600634i | \(-0.794915\pi\) | ||||
−0.799524 | + | 0.600634i | \(0.794915\pi\) | |||||||
\(132\) | 1.42302 | 0.123858 | ||||||||
\(133\) | −1.84186 | −0.159709 | ||||||||
\(134\) | −26.5773 | −2.29593 | ||||||||
\(135\) | −5.78675 | −0.498044 | ||||||||
\(136\) | −1.81362 | −0.155516 | ||||||||
\(137\) | 1.03858 | 0.0887322 | 0.0443661 | − | 0.999015i | \(-0.485873\pi\) | ||||
0.0443661 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(138\) | 7.92132 | 0.674307 | ||||||||
\(139\) | 16.0516 | 1.36148 | 0.680738 | − | 0.732527i | \(-0.261659\pi\) | ||||
0.680738 | + | 0.732527i | \(0.261659\pi\) | |||||||
\(140\) | −1.81358 | −0.153275 | ||||||||
\(141\) | −5.66803 | −0.477334 | ||||||||
\(142\) | 12.7636 | 1.07110 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.36816 | 0.697346 | ||||||||
\(145\) | 8.34214 | 0.692777 | ||||||||
\(146\) | 28.7654 | 2.38064 | ||||||||
\(147\) | −1.08494 | −0.0894840 | ||||||||
\(148\) | 5.67052 | 0.466114 | ||||||||
\(149\) | −0.376052 | −0.0308074 | −0.0154037 | − | 0.999881i | \(-0.504903\pi\) | ||||
−0.0154037 | + | 0.999881i | \(0.504903\pi\) | |||||||
\(150\) | 7.81790 | 0.638329 | ||||||||
\(151\) | −0.149749 | −0.0121864 | −0.00609321 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609321 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(152\) | 1.26541 | 0.102638 | ||||||||
\(153\) | −4.81212 | −0.389037 | ||||||||
\(154\) | −1.52593 | −0.122963 | ||||||||
\(155\) | 8.70055 | 0.698845 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.22397 | −0.576536 | −0.288268 | − | 0.957550i | \(-0.593079\pi\) | ||||
−0.288268 | + | 0.957550i | \(0.593079\pi\) | |||||||
\(158\) | −15.4637 | −1.23022 | ||||||||
\(159\) | −6.68274 | −0.529976 | ||||||||
\(160\) | 8.16606 | 0.645584 | ||||||||
\(161\) | −3.82692 | −0.301603 | ||||||||
\(162\) | −0.397282 | −0.0312134 | ||||||||
\(163\) | 3.83171 | 0.300123 | 0.150062 | − | 0.988677i | \(-0.452053\pi\) | ||||
0.150062 | + | 0.988677i | \(0.452053\pi\) | |||||||
\(164\) | −17.9697 | −1.40320 | ||||||||
\(165\) | −0.959654 | −0.0747090 | ||||||||
\(166\) | 29.8269 | 2.31502 | ||||||||
\(167\) | 1.83270 | 0.141819 | 0.0709094 | − | 0.997483i | \(-0.477410\pi\) | ||||
0.0709094 | + | 0.997483i | \(0.477410\pi\) | |||||||
\(168\) | 0.745382 | 0.0575075 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −5.56974 | −0.427180 | ||||||||
\(171\) | 3.35755 | 0.256759 | ||||||||
\(172\) | −4.32784 | −0.329995 | ||||||||
\(173\) | −22.0343 | −1.67524 | −0.837618 | − | 0.546256i | \(-0.816053\pi\) | ||||
−0.837618 | + | 0.546256i | \(0.816053\pi\) | |||||||
\(174\) | 15.6137 | 1.18367 | ||||||||
\(175\) | −3.77696 | −0.285511 | ||||||||
\(176\) | 3.67158 | 0.276756 | ||||||||
\(177\) | −5.53588 | −0.416102 | ||||||||
\(178\) | −4.34793 | −0.325891 | ||||||||
\(179\) | 5.62164 | 0.420181 | 0.210091 | − | 0.977682i | \(-0.432624\pi\) | ||||
0.210091 | + | 0.977682i | \(0.432624\pi\) | |||||||
\(180\) | 3.30600 | 0.246415 | ||||||||
\(181\) | −4.44007 | −0.330028 | −0.165014 | − | 0.986291i | \(-0.552767\pi\) | ||||
−0.165014 | + | 0.986291i | \(0.552767\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.59703 | −0.265900 | ||||||||
\(184\) | 2.62920 | 0.193828 | ||||||||
\(185\) | −3.82409 | −0.281153 | ||||||||
\(186\) | 16.2845 | 1.19404 | ||||||||
\(187\) | −2.11135 | −0.154397 | ||||||||
\(188\) | 8.56730 | 0.624834 | ||||||||
\(189\) | 5.23255 | 0.380612 | ||||||||
\(190\) | 3.88617 | 0.281932 | ||||||||
\(191\) | −4.39741 | −0.318186 | −0.159093 | − | 0.987264i | \(-0.550857\pi\) | ||||
−0.159093 | + | 0.987264i | \(0.550857\pi\) | |||||||
\(192\) | 5.32323 | 0.384171 | ||||||||
\(193\) | 25.2708 | 1.81903 | 0.909516 | − | 0.415669i | \(-0.136452\pi\) | ||||
0.909516 | + | 0.415669i | \(0.136452\pi\) | |||||||
\(194\) | 31.4699 | 2.25941 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.63989 | 0.117135 | ||||||||
\(197\) | 6.91860 | 0.492930 | 0.246465 | − | 0.969152i | \(-0.420731\pi\) | ||||
0.246465 | + | 0.969152i | \(0.420731\pi\) | |||||||
\(198\) | 2.78164 | 0.197683 | ||||||||
\(199\) | 17.3958 | 1.23315 | 0.616577 | − | 0.787295i | \(-0.288519\pi\) | ||||
0.616577 | + | 0.787295i | \(0.288519\pi\) | |||||||
\(200\) | 2.59488 | 0.183486 | ||||||||
\(201\) | 15.1137 | 1.06604 | ||||||||
\(202\) | −26.8408 | −1.88851 | ||||||||
\(203\) | −7.54322 | −0.529430 | ||||||||
\(204\) | −4.69666 | −0.328832 | ||||||||
\(205\) | 12.1184 | 0.846387 | ||||||||
\(206\) | 0.210302 | 0.0146524 | ||||||||
\(207\) | 6.97615 | 0.484876 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.47315 | 0.101900 | ||||||||
\(210\) | 2.28912 | 0.157964 | ||||||||
\(211\) | 7.50167 | 0.516436 | 0.258218 | − | 0.966087i | \(-0.416865\pi\) | ||||
0.258218 | + | 0.966087i | \(0.416865\pi\) | |||||||
\(212\) | 10.1010 | 0.693742 | ||||||||
\(213\) | −7.25826 | −0.497328 | ||||||||
\(214\) | −26.3418 | −1.80069 | ||||||||
\(215\) | 2.91862 | 0.199048 | ||||||||
\(216\) | −3.59492 | −0.244603 | ||||||||
\(217\) | −7.86730 | −0.534067 | ||||||||
\(218\) | −4.14738 | −0.280896 | ||||||||
\(219\) | −16.3580 | −1.10537 | ||||||||
\(220\) | 1.45053 | 0.0977947 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.15741 | −0.480374 | ||||||||
\(223\) | −25.8645 | −1.73201 | −0.866007 | − | 0.500032i | \(-0.833322\pi\) | ||||
−0.866007 | + | 0.500032i | \(0.833322\pi\) | |||||||
\(224\) | −7.38400 | −0.493364 | ||||||||
\(225\) | 6.88507 | 0.459005 | ||||||||
\(226\) | −30.9121 | −2.05624 | ||||||||
\(227\) | 5.19695 | 0.344933 | 0.172467 | − | 0.985015i | \(-0.444826\pi\) | ||||
0.172467 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(228\) | 3.27700 | 0.217024 | ||||||||
\(229\) | 5.03722 | 0.332869 | 0.166434 | − | 0.986053i | \(-0.446775\pi\) | ||||
0.166434 | + | 0.986053i | \(0.446775\pi\) | |||||||
\(230\) | 8.07448 | 0.532415 | ||||||||
\(231\) | 0.867749 | 0.0570937 | ||||||||
\(232\) | 5.18241 | 0.340242 | ||||||||
\(233\) | −16.2022 | −1.06144 | −0.530721 | − | 0.847546i | \(-0.678079\pi\) | ||||
−0.530721 | + | 0.847546i | \(0.678079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.77762 | −0.376890 | ||||||||
\(236\) | 8.36755 | 0.544681 | ||||||||
\(237\) | 8.79372 | 0.571213 | ||||||||
\(238\) | 5.03633 | 0.326457 | ||||||||
\(239\) | 3.22405 | 0.208546 | 0.104273 | − | 0.994549i | \(-0.466748\pi\) | ||||
0.104273 | + | 0.994549i | \(0.466748\pi\) | |||||||
\(240\) | −5.50793 | −0.355535 | ||||||||
\(241\) | −17.2522 | −1.11131 | −0.555655 | − | 0.831413i | \(-0.687532\pi\) | ||||
−0.555655 | + | 0.831413i | \(0.687532\pi\) | |||||||
\(242\) | −19.7659 | −1.27060 | ||||||||
\(243\) | −15.4717 | −0.992512 | ||||||||
\(244\) | 5.43696 | 0.348065 | ||||||||
\(245\) | −1.10591 | −0.0706542 | ||||||||
\(246\) | 22.6816 | 1.44613 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.40507 | 0.343222 | ||||||||
\(249\) | −16.9617 | −1.07490 | ||||||||
\(250\) | 18.5186 | 1.17122 | ||||||||
\(251\) | 17.3864 | 1.09742 | 0.548711 | − | 0.836012i | \(-0.315119\pi\) | ||||
0.548711 | + | 0.836012i | \(0.315119\pi\) | |||||||
\(252\) | −2.98939 | −0.188314 | ||||||||
\(253\) | 3.06083 | 0.192433 | ||||||||
\(254\) | 38.1186 | 2.39177 | ||||||||
\(255\) | 3.16734 | 0.198347 | ||||||||
\(256\) | 20.1290 | 1.25806 | ||||||||
\(257\) | −14.6189 | −0.911901 | −0.455950 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455950 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(258\) | 5.46266 | 0.340090 | ||||||||
\(259\) | 3.45786 | 0.214861 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.7506 | 0.851143 | ||||||||
\(262\) | −34.9174 | −2.15720 | ||||||||
\(263\) | 7.41229 | 0.457061 | 0.228531 | − | 0.973537i | \(-0.426608\pi\) | ||||
0.228531 | + | 0.973537i | \(0.426608\pi\) | |||||||
\(264\) | −0.596169 | −0.0366916 | ||||||||
\(265\) | −6.81195 | −0.418455 | ||||||||
\(266\) | −3.51399 | −0.215457 | ||||||||
\(267\) | 2.47253 | 0.151317 | ||||||||
\(268\) | −22.8446 | −1.39545 | ||||||||
\(269\) | −4.58385 | −0.279482 | −0.139741 | − | 0.990188i | \(-0.544627\pi\) | ||||
−0.139741 | + | 0.990188i | \(0.544627\pi\) | |||||||
\(270\) | −11.0402 | −0.671888 | ||||||||
\(271\) | −3.62768 | −0.220366 | −0.110183 | − | 0.993911i | \(-0.535144\pi\) | ||||
−0.110183 | + | 0.993911i | \(0.535144\pi\) | |||||||
\(272\) | −12.1181 | −0.734766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.98146 | 0.119705 | ||||||||
\(275\) | 3.02087 | 0.182165 | ||||||||
\(276\) | 6.80877 | 0.409840 | ||||||||
\(277\) | 23.6739 | 1.42242 | 0.711212 | − | 0.702978i | \(-0.248147\pi\) | ||||
0.711212 | + | 0.702978i | \(0.248147\pi\) | |||||||
\(278\) | 30.6240 | 1.83670 | ||||||||
\(279\) | 14.3414 | 0.858599 | ||||||||
\(280\) | 0.759794 | 0.0454064 | ||||||||
\(281\) | −25.5415 | −1.52368 | −0.761838 | − | 0.647768i | \(-0.775703\pi\) | ||||
−0.761838 | + | 0.647768i | \(0.775703\pi\) | |||||||
\(282\) | −10.8138 | −0.643950 | ||||||||
\(283\) | −2.95356 | −0.175571 | −0.0877855 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877855 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(284\) | 10.9710 | 0.651006 | ||||||||
\(285\) | −2.20994 | −0.130906 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.9578 | −0.646821 | ||||||||
\(288\) | 13.4604 | 0.793162 | ||||||||
\(289\) | −10.0315 | −0.590088 | ||||||||
\(290\) | 15.9156 | 0.934594 | ||||||||
\(291\) | −17.8959 | −1.04908 | ||||||||
\(292\) | 24.7253 | 1.44694 | ||||||||
\(293\) | 22.6667 | 1.32420 | 0.662102 | − | 0.749414i | \(-0.269665\pi\) | ||||
0.662102 | + | 0.749414i | \(0.269665\pi\) | |||||||
\(294\) | −2.06989 | −0.120719 | ||||||||
\(295\) | −5.64291 | −0.328543 | ||||||||
\(296\) | −2.37565 | −0.138082 | ||||||||
\(297\) | −4.18508 | −0.242843 | ||||||||
\(298\) | −0.717451 | −0.0415608 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.71988 | 0.387973 | ||||||||
\(301\) | −2.63910 | −0.152115 | ||||||||
\(302\) | −0.285699 | −0.0164401 | ||||||||
\(303\) | 15.2636 | 0.876868 | ||||||||
\(304\) | 8.45512 | 0.484934 | ||||||||
\(305\) | −3.66658 | −0.209948 | ||||||||
\(306\) | −9.18080 | −0.524832 | ||||||||
\(307\) | 2.04932 | 0.116961 | 0.0584805 | − | 0.998289i | \(-0.481374\pi\) | ||||
0.0584805 | + | 0.998289i | \(0.481374\pi\) | |||||||
\(308\) | −1.31161 | −0.0747361 | ||||||||
\(309\) | −0.119592 | −0.00680336 | ||||||||
\(310\) | 16.5994 | 0.942780 | ||||||||
\(311\) | −15.4445 | −0.875776 | −0.437888 | − | 0.899030i | \(-0.644273\pi\) | ||||
−0.437888 | + | 0.899030i | \(0.644273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.59184 | −0.372593 | −0.186296 | − | 0.982494i | \(-0.559648\pi\) | ||||
−0.186296 | + | 0.982494i | \(0.559648\pi\) | |||||||
\(314\) | −13.7823 | −0.777778 | ||||||||
\(315\) | 2.01599 | 0.113588 | ||||||||
\(316\) | −13.2918 | −0.747723 | ||||||||
\(317\) | −17.6182 | −0.989536 | −0.494768 | − | 0.869025i | \(-0.664747\pi\) | ||||
−0.494768 | + | 0.869025i | \(0.664747\pi\) | |||||||
\(318\) | −12.7497 | −0.714966 | ||||||||
\(319\) | 6.03319 | 0.337794 | ||||||||
\(320\) | 5.42615 | 0.303331 | ||||||||
\(321\) | 14.9798 | 0.836089 | ||||||||
\(322\) | −7.30119 | −0.406879 | ||||||||
\(323\) | −4.86213 | −0.270536 | ||||||||
\(324\) | −0.341484 | −0.0189713 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.31034 | 0.404882 | ||||||||
\(327\) | 2.35848 | 0.130424 | ||||||||
\(328\) | 7.52836 | 0.415684 | ||||||||
\(329\) | 5.22430 | 0.288025 | ||||||||
\(330\) | −1.83088 | −0.100786 | ||||||||
\(331\) | −14.0822 | −0.774027 | −0.387014 | − | 0.922074i | \(-0.626493\pi\) | ||||
−0.387014 | + | 0.922074i | \(0.626493\pi\) | |||||||
\(332\) | 25.6378 | 1.40706 | ||||||||
\(333\) | −6.30339 | −0.345423 | ||||||||
\(334\) | 3.49652 | 0.191321 | ||||||||
\(335\) | 15.4059 | 0.841716 | ||||||||
\(336\) | 4.98044 | 0.271705 | ||||||||
\(337\) | 2.73318 | 0.148886 | 0.0744429 | − | 0.997225i | \(-0.476282\pi\) | ||||
0.0744429 | + | 0.997225i | \(0.476282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.5788 | 0.954747 | ||||||||
\(340\) | −4.78747 | −0.259637 | ||||||||
\(341\) | 6.29240 | 0.340752 | ||||||||
\(342\) | 6.40571 | 0.346381 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.81314 | 0.0977579 | ||||||||
\(345\) | −4.59171 | −0.247209 | ||||||||
\(346\) | −42.0382 | −2.25999 | ||||||||
\(347\) | −2.90684 | −0.156047 | −0.0780236 | − | 0.996952i | \(-0.524861\pi\) | ||||
−0.0780236 | + | 0.996952i | \(0.524861\pi\) | |||||||
\(348\) | 13.4207 | 0.719427 | ||||||||
\(349\) | 7.10583 | 0.380366 | 0.190183 | − | 0.981749i | \(-0.439092\pi\) | ||||
0.190183 | + | 0.981749i | \(0.439092\pi\) | |||||||
\(350\) | −7.20587 | −0.385170 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.90584 | 0.314782 | ||||||||
\(353\) | −6.18844 | −0.329378 | −0.164689 | − | 0.986346i | \(-0.552662\pi\) | ||||
−0.164689 | + | 0.986346i | \(0.552662\pi\) | |||||||
\(354\) | −10.5616 | −0.561344 | ||||||||
\(355\) | −7.39860 | −0.392677 | ||||||||
\(356\) | −3.73726 | −0.198075 | ||||||||
\(357\) | −2.86401 | −0.151579 | ||||||||
\(358\) | 10.7253 | 0.566847 | ||||||||
\(359\) | −25.8517 | −1.36440 | −0.682201 | − | 0.731165i | \(-0.738977\pi\) | ||||
−0.682201 | + | 0.731165i | \(0.738977\pi\) | |||||||
\(360\) | −1.38504 | −0.0729981 | ||||||||
\(361\) | −15.6076 | −0.821450 | ||||||||
\(362\) | −8.47099 | −0.445225 | ||||||||
\(363\) | 11.2403 | 0.589960 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.6743 | −0.872770 | ||||||||
\(366\) | −6.86260 | −0.358714 | ||||||||
\(367\) | −34.7499 | −1.81393 | −0.906964 | − | 0.421207i | \(-0.861606\pi\) | ||||
−0.906964 | + | 0.421207i | \(0.861606\pi\) | |||||||
\(368\) | 17.5676 | 0.915775 | ||||||||
\(369\) | 19.9752 | 1.03987 | ||||||||
\(370\) | −7.29580 | −0.379290 | ||||||||
\(371\) | 6.15957 | 0.319789 | ||||||||
\(372\) | 13.9973 | 0.725728 | ||||||||
\(373\) | −26.1368 | −1.35331 | −0.676656 | − | 0.736299i | \(-0.736572\pi\) | ||||
−0.676656 | + | 0.736299i | \(0.736572\pi\) | |||||||
\(374\) | −4.02814 | −0.208290 | ||||||||
\(375\) | −10.5310 | −0.543817 | ||||||||
\(376\) | −3.58925 | −0.185101 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 9.98293 | 0.513466 | ||||||||
\(379\) | 18.1562 | 0.932623 | 0.466311 | − | 0.884621i | \(-0.345583\pi\) | ||||
0.466311 | + | 0.884621i | \(0.345583\pi\) | |||||||
\(380\) | 3.34036 | 0.171357 | ||||||||
\(381\) | −21.6769 | −1.11054 | ||||||||
\(382\) | −8.38961 | −0.429250 | ||||||||
\(383\) | −7.68219 | −0.392541 | −0.196271 | − | 0.980550i | \(-0.562883\pi\) | ||||
−0.196271 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(384\) | −5.86640 | −0.299368 | ||||||||
\(385\) | 0.884527 | 0.0450797 | ||||||||
\(386\) | 48.2129 | 2.45397 | ||||||||
\(387\) | 4.81086 | 0.244550 | ||||||||
\(388\) | 27.0499 | 1.37325 | ||||||||
\(389\) | −9.23745 | −0.468357 | −0.234179 | − | 0.972194i | \(-0.575240\pi\) | ||||
−0.234179 | + | 0.972194i | \(0.575240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.1023 | −0.510894 | ||||||||
\(392\) | −0.687029 | −0.0347002 | ||||||||
\(393\) | 19.8564 | 1.00162 | ||||||||
\(394\) | 13.1997 | 0.664989 | ||||||||
\(395\) | 8.96374 | 0.451015 | ||||||||
\(396\) | 2.39096 | 0.120150 | ||||||||
\(397\) | −16.7052 | −0.838410 | −0.419205 | − | 0.907892i | \(-0.637691\pi\) | ||||
−0.419205 | + | 0.907892i | \(0.637691\pi\) | |||||||
\(398\) | 33.1885 | 1.66359 | ||||||||
\(399\) | 1.99830 | 0.100040 | ||||||||
\(400\) | 17.3383 | 0.866913 | ||||||||
\(401\) | −28.3934 | −1.41790 | −0.708950 | − | 0.705258i | \(-0.750831\pi\) | ||||
−0.708950 | + | 0.705258i | \(0.750831\pi\) | |||||||
\(402\) | 28.8347 | 1.43814 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −23.0710 | −1.14783 | ||||||||
\(405\) | 0.230290 | 0.0114432 | ||||||||
\(406\) | −14.3913 | −0.714230 | ||||||||
\(407\) | −2.76565 | −0.137088 | ||||||||
\(408\) | 1.96766 | 0.0974135 | ||||||||
\(409\) | −25.8721 | −1.27929 | −0.639647 | − | 0.768669i | \(-0.720919\pi\) | ||||
−0.639647 | + | 0.768669i | \(0.720919\pi\) | |||||||
\(410\) | 23.1201 | 1.14182 | ||||||||
\(411\) | −1.12680 | −0.0555808 | ||||||||
\(412\) | 0.180765 | 0.00890565 | ||||||||
\(413\) | 5.10250 | 0.251077 | ||||||||
\(414\) | 13.3094 | 0.654124 | ||||||||
\(415\) | −17.2896 | −0.848714 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4149 | −0.852811 | ||||||||
\(418\) | 2.81055 | 0.137468 | ||||||||
\(419\) | −6.55673 | −0.320317 | −0.160158 | − | 0.987091i | \(-0.551201\pi\) | ||||
−0.160158 | + | 0.987091i | \(0.551201\pi\) | |||||||
\(420\) | 1.96762 | 0.0960099 | ||||||||
\(421\) | −14.4100 | −0.702300 | −0.351150 | − | 0.936319i | \(-0.614209\pi\) | ||||
−0.351150 | + | 0.936319i | \(0.614209\pi\) | |||||||
\(422\) | 14.3121 | 0.696700 | ||||||||
\(423\) | −9.52346 | −0.463046 | ||||||||
\(424\) | −4.23181 | −0.205515 | ||||||||
\(425\) | −9.97039 | −0.483635 | ||||||||
\(426\) | −13.8477 | −0.670922 | ||||||||
\(427\) | 3.31543 | 0.160445 | ||||||||
\(428\) | −22.6421 | −1.09445 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.56828 | 0.268526 | ||||||||
\(431\) | 14.7027 | 0.708204 | 0.354102 | − | 0.935207i | \(-0.384787\pi\) | ||||
0.354102 | + | 0.935207i | \(0.384787\pi\) | |||||||
\(432\) | −24.0202 | −1.15567 | ||||||||
\(433\) | −20.6178 | −0.990830 | −0.495415 | − | 0.868656i | \(-0.664984\pi\) | ||||
−0.495415 | + | 0.868656i | \(0.664984\pi\) | |||||||
\(434\) | −15.0096 | −0.720486 | ||||||||
\(435\) | −9.05068 | −0.433947 | ||||||||
\(436\) | −3.56488 | −0.170727 | ||||||||
\(437\) | 7.04865 | 0.337182 | ||||||||
\(438\) | −31.2086 | −1.49120 | ||||||||
\(439\) | 20.3424 | 0.970892 | 0.485446 | − | 0.874267i | \(-0.338657\pi\) | ||||
0.485446 | + | 0.874267i | \(0.338657\pi\) | |||||||
\(440\) | −0.607696 | −0.0289708 | ||||||||
\(441\) | −1.82292 | −0.0868055 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8195 | 0.656582 | 0.328291 | − | 0.944577i | \(-0.393527\pi\) | ||||
0.328291 | + | 0.944577i | \(0.393527\pi\) | |||||||
\(444\) | −6.15215 | −0.291968 | ||||||||
\(445\) | 2.52034 | 0.119476 | ||||||||
\(446\) | −49.3456 | −2.33658 | ||||||||
\(447\) | 0.407992 | 0.0192974 | ||||||||
\(448\) | −4.90649 | −0.231810 | ||||||||
\(449\) | −18.2060 | −0.859193 | −0.429596 | − | 0.903021i | \(-0.641344\pi\) | ||||
−0.429596 | + | 0.903021i | \(0.641344\pi\) | |||||||
\(450\) | 13.1357 | 0.619222 | ||||||||
\(451\) | 8.76426 | 0.412693 | ||||||||
\(452\) | −26.5705 | −1.24977 | ||||||||
\(453\) | 0.162468 | 0.00763342 | ||||||||
\(454\) | 9.91500 | 0.465334 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.37289 | −0.0642914 | ||||||||
\(457\) | −8.94689 | −0.418518 | −0.209259 | − | 0.977860i | \(-0.567105\pi\) | ||||
−0.209259 | + | 0.977860i | \(0.567105\pi\) | |||||||
\(458\) | 9.61025 | 0.449058 | ||||||||
\(459\) | 13.8129 | 0.644729 | ||||||||
\(460\) | 6.94042 | 0.323599 | ||||||||
\(461\) | 8.68811 | 0.404645 | 0.202323 | − | 0.979319i | \(-0.435151\pi\) | ||||
0.202323 | + | 0.979319i | \(0.435151\pi\) | |||||||
\(462\) | 1.65553 | 0.0770225 | ||||||||
\(463\) | 20.2019 | 0.938864 | 0.469432 | − | 0.882969i | \(-0.344459\pi\) | ||||
0.469432 | + | 0.882969i | \(0.344459\pi\) | |||||||
\(464\) | 34.6274 | 1.60754 | ||||||||
\(465\) | −9.43954 | −0.437748 | ||||||||
\(466\) | −30.9114 | −1.43194 | ||||||||
\(467\) | −10.5588 | −0.488601 | −0.244300 | − | 0.969700i | \(-0.578558\pi\) | ||||
−0.244300 | + | 0.969700i | \(0.578558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.9305 | −0.643252 | ||||||||
\(470\) | −11.0228 | −0.508446 | ||||||||
\(471\) | 7.83754 | 0.361135 | ||||||||
\(472\) | −3.50556 | −0.161357 | ||||||||
\(473\) | 2.11079 | 0.0970545 | ||||||||
\(474\) | 16.7771 | 0.770597 | ||||||||
\(475\) | 6.95662 | 0.319192 | ||||||||
\(476\) | 4.32898 | 0.198418 | ||||||||
\(477\) | −11.2284 | −0.514112 | ||||||||
\(478\) | 6.15100 | 0.281340 | ||||||||
\(479\) | −38.1404 | −1.74268 | −0.871340 | − | 0.490680i | \(-0.836748\pi\) | ||||
−0.871340 | + | 0.490680i | \(0.836748\pi\) | |||||||
\(480\) | −8.85965 | −0.404386 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −32.9146 | −1.49922 | ||||||||
\(483\) | 4.15196 | 0.188921 | ||||||||
\(484\) | −16.9898 | −0.772263 | ||||||||
\(485\) | −18.2420 | −0.828325 | ||||||||
\(486\) | −29.5178 | −1.33895 | ||||||||
\(487\) | −4.23947 | −0.192109 | −0.0960544 | − | 0.995376i | \(-0.530622\pi\) | ||||
−0.0960544 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(488\) | −2.27780 | −0.103111 | ||||||||
\(489\) | −4.15716 | −0.187993 | ||||||||
\(490\) | −2.10992 | −0.0953163 | ||||||||
\(491\) | 16.0662 | 0.725057 | 0.362529 | − | 0.931973i | \(-0.381913\pi\) | ||||
0.362529 | + | 0.931973i | \(0.381913\pi\) | |||||||
\(492\) | 19.4960 | 0.878946 | ||||||||
\(493\) | −19.9125 | −0.896815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.61242 | −0.0724728 | ||||||||
\(496\) | 36.1151 | 1.62162 | ||||||||
\(497\) | 6.69004 | 0.300089 | ||||||||
\(498\) | −32.3603 | −1.45010 | ||||||||
\(499\) | 28.9437 | 1.29570 | 0.647848 | − | 0.761769i | \(-0.275669\pi\) | ||||
0.647848 | + | 0.761769i | \(0.275669\pi\) | |||||||
\(500\) | 15.9177 | 0.711862 | ||||||||
\(501\) | −1.98837 | −0.0888336 | ||||||||
\(502\) | 33.1707 | 1.48048 | ||||||||
\(503\) | −26.9087 | −1.19980 | −0.599901 | − | 0.800075i | \(-0.704793\pi\) | ||||
−0.599901 | + | 0.800075i | \(0.704793\pi\) | |||||||
\(504\) | 1.25240 | 0.0557861 | ||||||||
\(505\) | 15.5587 | 0.692352 | ||||||||
\(506\) | 5.83961 | 0.259602 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.7648 | 1.45370 | ||||||||
\(509\) | 20.0963 | 0.890755 | 0.445377 | − | 0.895343i | \(-0.353070\pi\) | ||||
0.445377 | + | 0.895343i | \(0.353070\pi\) | |||||||
\(510\) | 6.04281 | 0.267580 | ||||||||
\(511\) | 15.0774 | 0.666984 | ||||||||
\(512\) | 27.5888 | 1.21927 | ||||||||
\(513\) | −9.63762 | −0.425511 | ||||||||
\(514\) | −27.8906 | −1.23020 | ||||||||
\(515\) | −0.121904 | −0.00537175 | ||||||||
\(516\) | 4.69543 | 0.206705 | ||||||||
\(517\) | −4.17848 | −0.183769 | ||||||||
\(518\) | 6.59708 | 0.289859 | ||||||||
\(519\) | 23.9058 | 1.04935 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.2678 | 1.32605 | 0.663027 | − | 0.748595i | \(-0.269271\pi\) | ||||
0.663027 | + | 0.748595i | \(0.269271\pi\) | |||||||
\(522\) | 26.2342 | 1.14824 | ||||||||
\(523\) | 41.6444 | 1.82098 | 0.910491 | − | 0.413529i | \(-0.135704\pi\) | ||||
0.910491 | + | 0.413529i | \(0.135704\pi\) | |||||||
\(524\) | −30.0132 | −1.31113 | ||||||||
\(525\) | 4.09775 | 0.178841 | ||||||||
\(526\) | 14.1415 | 0.616600 | ||||||||
\(527\) | −20.7681 | −0.904671 | ||||||||
\(528\) | −3.98343 | −0.173357 | ||||||||
\(529\) | −8.35469 | −0.363248 | ||||||||
\(530\) | −12.9962 | −0.564518 | ||||||||
\(531\) | −9.30142 | −0.403647 | ||||||||
\(532\) | −3.02045 | −0.130953 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.71722 | 0.204134 | ||||||||
\(535\) | 15.2694 | 0.660154 | ||||||||
\(536\) | 9.57067 | 0.413390 | ||||||||
\(537\) | −6.09912 | −0.263196 | ||||||||
\(538\) | −8.74531 | −0.377037 | ||||||||
\(539\) | −0.799816 | −0.0344505 | ||||||||
\(540\) | −9.48965 | −0.408369 | ||||||||
\(541\) | 9.64131 | 0.414512 | 0.207256 | − | 0.978287i | \(-0.433547\pi\) | ||||
0.207256 | + | 0.978287i | \(0.433547\pi\) | |||||||
\(542\) | −6.92107 | −0.297285 | ||||||||
\(543\) | 4.81719 | 0.206725 | ||||||||
\(544\) | −19.4922 | −0.835723 | ||||||||
\(545\) | 2.40409 | 0.102980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0811 | −0.901362 | −0.450681 | − | 0.892685i | \(-0.648819\pi\) | ||||
−0.450681 | + | 0.892685i | \(0.648819\pi\) | |||||||
\(548\) | 1.70317 | 0.0727557 | ||||||||
\(549\) | −6.04375 | −0.257941 | ||||||||
\(550\) | 5.76337 | 0.245751 | ||||||||
\(551\) | 13.8935 | 0.591885 | ||||||||
\(552\) | −2.85252 | −0.121411 | ||||||||
\(553\) | −8.10529 | −0.344672 | ||||||||
\(554\) | 45.1662 | 1.91893 | ||||||||
\(555\) | 4.14889 | 0.176111 | ||||||||
\(556\) | 26.3228 | 1.11634 | ||||||||
\(557\) | 16.5044 | 0.699313 | 0.349657 | − | 0.936878i | \(-0.386298\pi\) | ||||
0.349657 | + | 0.936878i | \(0.386298\pi\) | |||||||
\(558\) | 27.3613 | 1.15830 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5.07673 | 0.214531 | ||||||||
\(561\) | 2.29068 | 0.0967125 | ||||||||
\(562\) | −48.7293 | −2.05552 | ||||||||
\(563\) | −10.7950 | −0.454954 | −0.227477 | − | 0.973784i | \(-0.573048\pi\) | ||||
−0.227477 | + | 0.973784i | \(0.573048\pi\) | |||||||
\(564\) | −9.29496 | −0.391389 | ||||||||
\(565\) | 17.9186 | 0.753843 | ||||||||
\(566\) | −5.63495 | −0.236855 | ||||||||
\(567\) | −0.208236 | −0.00874507 | ||||||||
\(568\) | −4.59625 | −0.192854 | ||||||||
\(569\) | −39.8672 | −1.67132 | −0.835660 | − | 0.549247i | \(-0.814915\pi\) | ||||
−0.835660 | + | 0.549247i | \(0.814915\pi\) | |||||||
\(570\) | −4.21624 | −0.176599 | ||||||||
\(571\) | 42.8074 | 1.79143 | 0.895717 | − | 0.444624i | \(-0.146663\pi\) | ||||
0.895717 | + | 0.444624i | \(0.146663\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.77091 | 0.199308 | ||||||||
\(574\) | −20.9059 | −0.872597 | ||||||||
\(575\) | 14.4541 | 0.602778 | ||||||||
\(576\) | 8.94412 | 0.372672 | ||||||||
\(577\) | 0.199664 | 0.00831211 | 0.00415606 | − | 0.999991i | \(-0.498677\pi\) | ||||
0.00415606 | + | 0.999991i | \(0.498677\pi\) | |||||||
\(578\) | −19.1386 | −0.796060 | ||||||||
\(579\) | −27.4172 | −1.13942 | ||||||||
\(580\) | 13.6802 | 0.568040 | ||||||||
\(581\) | 15.6338 | 0.648599 | ||||||||
\(582\) | −34.1428 | −1.41526 | ||||||||
\(583\) | −4.92652 | −0.204036 | ||||||||
\(584\) | −10.3586 | −0.428642 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.2447 | 1.78642 | ||||||||
\(587\) | 1.12962 | 0.0466244 | 0.0233122 | − | 0.999728i | \(-0.492579\pi\) | ||||
0.0233122 | + | 0.999728i | \(0.492579\pi\) | |||||||
\(588\) | −1.77918 | −0.0733721 | ||||||||
\(589\) | 14.4905 | 0.597069 | ||||||||
\(590\) | −10.7658 | −0.443223 | ||||||||
\(591\) | −7.50624 | −0.308765 | ||||||||
\(592\) | −15.8734 | −0.652394 | ||||||||
\(593\) | 16.5142 | 0.678158 | 0.339079 | − | 0.940758i | \(-0.389885\pi\) | ||||
0.339079 | + | 0.940758i | \(0.389885\pi\) | |||||||
\(594\) | −7.98450 | −0.327608 | ||||||||
\(595\) | −2.91938 | −0.119683 | ||||||||
\(596\) | −0.616685 | −0.0252604 | ||||||||
\(597\) | −18.8733 | −0.772432 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.44907 | 0.304361 | 0.152180 | − | 0.988353i | \(-0.451371\pi\) | ||||
0.152180 | + | 0.988353i | \(0.451371\pi\) | |||||||
\(600\) | −2.81528 | −0.114933 | ||||||||
\(601\) | −20.8286 | −0.849618 | −0.424809 | − | 0.905283i | \(-0.639659\pi\) | ||||
−0.424809 | + | 0.905283i | \(0.639659\pi\) | |||||||
\(602\) | −5.03501 | −0.205212 | ||||||||
\(603\) | 25.3942 | 1.03413 | ||||||||
\(604\) | −0.245573 | −0.00999221 | ||||||||
\(605\) | 11.4576 | 0.465817 | ||||||||
\(606\) | 29.1206 | 1.18294 | ||||||||
\(607\) | 35.4304 | 1.43808 | 0.719038 | − | 0.694970i | \(-0.244583\pi\) | ||||
0.719038 | + | 0.694970i | \(0.244583\pi\) | |||||||
\(608\) | 13.6003 | 0.551564 | ||||||||
\(609\) | 8.18390 | 0.331628 | ||||||||
\(610\) | −6.99529 | −0.283231 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.89136 | −0.318989 | ||||||||
\(613\) | 19.1451 | 0.773263 | 0.386632 | − | 0.922234i | \(-0.373638\pi\) | ||||
0.386632 | + | 0.922234i | \(0.373638\pi\) | |||||||
\(614\) | 3.90980 | 0.157787 | ||||||||
\(615\) | −13.1477 | −0.530167 | ||||||||
\(616\) | 0.549497 | 0.0221399 | ||||||||
\(617\) | 3.52481 | 0.141904 | 0.0709518 | − | 0.997480i | \(-0.477396\pi\) | ||||
0.0709518 | + | 0.997480i | \(0.477396\pi\) | |||||||
\(618\) | −0.228164 | −0.00917810 | ||||||||
\(619\) | 40.1768 | 1.61484 | 0.807421 | − | 0.589976i | \(-0.200863\pi\) | ||||
0.807421 | + | 0.589976i | \(0.200863\pi\) | |||||||
\(620\) | 14.2680 | 0.573016 | ||||||||
\(621\) | −20.0245 | −0.803557 | ||||||||
\(622\) | −29.4657 | −1.18147 | ||||||||
\(623\) | −2.27897 | −0.0913049 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.15019 | 0.326008 | ||||||||
\(626\) | −12.5762 | −0.502648 | ||||||||
\(627\) | −1.59827 | −0.0638288 | ||||||||
\(628\) | −11.8465 | −0.472728 | ||||||||
\(629\) | 9.12804 | 0.363959 | ||||||||
\(630\) | 3.84620 | 0.153236 | ||||||||
\(631\) | −6.33561 | −0.252217 | −0.126108 | − | 0.992016i | \(-0.540249\pi\) | ||||
−0.126108 | + | 0.992016i | \(0.540249\pi\) | |||||||
\(632\) | 5.56857 | 0.221506 | ||||||||
\(633\) | −8.13883 | −0.323489 | ||||||||
\(634\) | −33.6129 | −1.33494 | ||||||||
\(635\) | −22.0960 | −0.876852 | ||||||||
\(636\) | −10.9590 | −0.434552 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.5104 | 0.455702 | ||||||||
\(639\) | −12.1954 | −0.482442 | ||||||||
\(640\) | −5.97983 | −0.236373 | ||||||||
\(641\) | −27.5697 | −1.08894 | −0.544469 | − | 0.838781i | \(-0.683269\pi\) | ||||
−0.544469 | + | 0.838781i | \(0.683269\pi\) | |||||||
\(642\) | 28.5792 | 1.12793 | ||||||||
\(643\) | −15.7718 | −0.621977 | −0.310989 | − | 0.950414i | \(-0.600660\pi\) | ||||
−0.310989 | + | 0.950414i | \(0.600660\pi\) | |||||||
\(644\) | −6.27574 | −0.247299 | ||||||||
\(645\) | −3.16651 | −0.124681 | ||||||||
\(646\) | −9.27621 | −0.364968 | ||||||||
\(647\) | 7.55988 | 0.297210 | 0.148605 | − | 0.988897i | \(-0.452522\pi\) | ||||
0.148605 | + | 0.988897i | \(0.452522\pi\) | |||||||
\(648\) | 0.143064 | 0.00562008 | ||||||||
\(649\) | −4.08106 | −0.160196 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.53552 | 0.334533 | ||||||||
\(652\) | 6.28360 | 0.246085 | ||||||||
\(653\) | 27.2957 | 1.06816 | 0.534082 | − | 0.845432i | \(-0.320657\pi\) | ||||
0.534082 | + | 0.845432i | \(0.320657\pi\) | |||||||
\(654\) | 4.49964 | 0.175950 | ||||||||
\(655\) | 20.2403 | 0.790856 | ||||||||
\(656\) | 50.3024 | 1.96398 | ||||||||
\(657\) | −27.4848 | −1.07228 | ||||||||
\(658\) | 9.96718 | 0.388561 | ||||||||
\(659\) | 26.4906 | 1.03193 | 0.515963 | − | 0.856611i | \(-0.327434\pi\) | ||||
0.515963 | + | 0.856611i | \(0.327434\pi\) | |||||||
\(660\) | −1.57373 | −0.0612574 | ||||||||
\(661\) | 9.13946 | 0.355484 | 0.177742 | − | 0.984077i | \(-0.443121\pi\) | ||||
0.177742 | + | 0.984077i | \(0.443121\pi\) | |||||||
\(662\) | −26.8667 | −1.04420 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.7409 | −0.416827 | ||||||||
\(665\) | 2.03694 | 0.0789890 | ||||||||
\(666\) | −12.0259 | −0.465995 | ||||||||
\(667\) | 28.8673 | 1.11775 | ||||||||
\(668\) | 3.00544 | 0.116284 | ||||||||
\(669\) | 28.0613 | 1.08491 | ||||||||
\(670\) | 29.3922 | 1.13552 | ||||||||
\(671\) | −2.65174 | −0.102369 | ||||||||
\(672\) | 8.01116 | 0.309037 | ||||||||
\(673\) | −9.03859 | −0.348412 | −0.174206 | − | 0.984709i | \(-0.555736\pi\) | ||||
−0.174206 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(674\) | 5.21450 | 0.200855 | ||||||||
\(675\) | −19.7631 | −0.760683 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.04397 | −0.232289 | −0.116144 | − | 0.993232i | \(-0.537054\pi\) | ||||
−0.116144 | + | 0.993232i | \(0.537054\pi\) | |||||||
\(678\) | 33.5376 | 1.28800 | ||||||||
\(679\) | 16.4949 | 0.633018 | ||||||||
\(680\) | 2.00570 | 0.0769151 | ||||||||
\(681\) | −5.63835 | −0.216062 | ||||||||
\(682\) | 12.0050 | 0.459693 | ||||||||
\(683\) | 43.9978 | 1.68353 | 0.841764 | − | 0.539846i | \(-0.181518\pi\) | ||||
0.841764 | + | 0.539846i | \(0.181518\pi\) | |||||||
\(684\) | 5.50603 | 0.210528 | ||||||||
\(685\) | −1.14858 | −0.0438851 | ||||||||
\(686\) | 1.90785 | 0.0728421 | ||||||||
\(687\) | −5.46505 | −0.208505 | ||||||||
\(688\) | 12.1149 | 0.461876 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.76029 | −0.333498 | ||||||||
\(691\) | 22.7816 | 0.866651 | 0.433326 | − | 0.901237i | \(-0.357340\pi\) | ||||
0.433326 | + | 0.901237i | \(0.357340\pi\) | |||||||
\(692\) | −36.1339 | −1.37361 | ||||||||
\(693\) | 1.45800 | 0.0553847 | ||||||||
\(694\) | −5.54581 | −0.210516 | ||||||||
\(695\) | −17.7516 | −0.673357 | ||||||||
\(696\) | −5.62258 | −0.213123 | ||||||||
\(697\) | −28.9264 | −1.09567 | ||||||||
\(698\) | 13.5569 | 0.513135 | ||||||||
\(699\) | 17.5784 | 0.664875 | ||||||||
\(700\) | −6.19381 | −0.234104 | ||||||||
\(701\) | −30.4001 | −1.14820 | −0.574098 | − | 0.818786i | \(-0.694647\pi\) | ||||
−0.574098 | + | 0.818786i | \(0.694647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.36889 | −0.240207 | ||||||||
\(704\) | 3.92429 | 0.147902 | ||||||||
\(705\) | 6.26835 | 0.236080 | ||||||||
\(706\) | −11.8066 | −0.444348 | ||||||||
\(707\) | −14.0686 | −0.529105 | ||||||||
\(708\) | −9.07825 | −0.341182 | ||||||||
\(709\) | −30.0571 | −1.12882 | −0.564409 | − | 0.825495i | \(-0.690896\pi\) | ||||
−0.564409 | + | 0.825495i | \(0.690896\pi\) | |||||||
\(710\) | −14.1154 | −0.529742 | ||||||||
\(711\) | 14.7753 | 0.554115 | ||||||||
\(712\) | 1.56572 | 0.0586777 | ||||||||
\(713\) | 30.1075 | 1.12754 | ||||||||
\(714\) | −5.46409 | −0.204489 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.21890 | 0.344526 | ||||||||
\(717\) | −3.49789 | −0.130631 | ||||||||
\(718\) | −49.3212 | −1.84065 | ||||||||
\(719\) | 17.5716 | 0.655308 | 0.327654 | − | 0.944798i | \(-0.393742\pi\) | ||||
0.327654 | + | 0.944798i | \(0.393742\pi\) | |||||||
\(720\) | −9.25445 | −0.344893 | ||||||||
\(721\) | 0.110230 | 0.00410517 | ||||||||
\(722\) | −29.7769 | −1.10818 | ||||||||
\(723\) | 18.7175 | 0.696111 | ||||||||
\(724\) | −7.28124 | −0.270605 | ||||||||
\(725\) | 28.4904 | 1.05811 | ||||||||
\(726\) | 21.4447 | 0.795888 | ||||||||
\(727\) | 24.8988 | 0.923446 | 0.461723 | − | 0.887024i | \(-0.347231\pi\) | ||||
0.461723 | + | 0.887024i | \(0.347231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.4105 | 0.644835 | ||||||||
\(730\) | −31.8120 | −1.17741 | ||||||||
\(731\) | −6.96668 | −0.257672 | ||||||||
\(732\) | −5.89875 | −0.218024 | ||||||||
\(733\) | −31.8923 | −1.17797 | −0.588984 | − | 0.808145i | \(-0.700472\pi\) | ||||
−0.588984 | + | 0.808145i | \(0.700472\pi\) | |||||||
\(734\) | −66.2976 | −2.44709 | ||||||||
\(735\) | 1.19984 | 0.0442569 | ||||||||
\(736\) | 28.2580 | 1.04160 | ||||||||
\(737\) | 11.1419 | 0.410415 | ||||||||
\(738\) | 38.1097 | 1.40284 | ||||||||
\(739\) | 18.0548 | 0.664157 | 0.332078 | − | 0.943252i | \(-0.392250\pi\) | ||||
0.332078 | + | 0.943252i | \(0.392250\pi\) | |||||||
\(740\) | −6.27110 | −0.230530 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7515 | 0.431413 | ||||||||
\(743\) | −43.5109 | −1.59626 | −0.798129 | − | 0.602486i | \(-0.794177\pi\) | ||||
−0.798129 | + | 0.602486i | \(0.794177\pi\) | |||||||
\(744\) | −5.86415 | −0.214990 | ||||||||
\(745\) | 0.415881 | 0.0152367 | ||||||||
\(746\) | −49.8651 | −1.82569 | ||||||||
\(747\) | −28.4991 | −1.04273 | ||||||||
\(748\) | −3.46239 | −0.126597 | ||||||||
\(749\) | −13.8071 | −0.504499 | ||||||||
\(750\) | −20.0915 | −0.733639 | ||||||||
\(751\) | −49.5788 | −1.80916 | −0.904578 | − | 0.426307i | \(-0.859814\pi\) | ||||
−0.904578 | + | 0.426307i | \(0.859814\pi\) | |||||||
\(752\) | −23.9823 | −0.874546 | ||||||||
\(753\) | −18.8632 | −0.687412 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.165610 | 0.00602715 | ||||||||
\(756\) | 8.58083 | 0.312082 | ||||||||
\(757\) | 51.8824 | 1.88570 | 0.942850 | − | 0.333218i | \(-0.108135\pi\) | ||||
0.942850 | + | 0.333218i | \(0.108135\pi\) | |||||||
\(758\) | 34.6394 | 1.25816 | ||||||||
\(759\) | −3.32080 | −0.120538 | ||||||||
\(760\) | −1.39943 | −0.0507628 | ||||||||
\(761\) | −8.00874 | −0.290317 | −0.145158 | − | 0.989408i | \(-0.546369\pi\) | ||||
−0.145158 | + | 0.989408i | \(0.546369\pi\) | |||||||
\(762\) | −41.3562 | −1.49818 | ||||||||
\(763\) | −2.17385 | −0.0786986 | ||||||||
\(764\) | −7.21129 | −0.260895 | ||||||||
\(765\) | 5.32178 | 0.192410 | ||||||||
\(766\) | −14.6565 | −0.529560 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −21.8387 | −0.788035 | ||||||||
\(769\) | 22.7156 | 0.819147 | 0.409573 | − | 0.912277i | \(-0.365678\pi\) | ||||
0.409573 | + | 0.912277i | \(0.365678\pi\) | |||||||
\(770\) | 1.68754 | 0.0608149 | ||||||||
\(771\) | 15.8605 | 0.571204 | ||||||||
\(772\) | 41.4414 | 1.49151 | ||||||||
\(773\) | −24.4370 | −0.878937 | −0.439468 | − | 0.898258i | \(-0.644833\pi\) | ||||
−0.439468 | + | 0.898258i | \(0.644833\pi\) | |||||||
\(774\) | 9.17839 | 0.329911 | ||||||||
\(775\) | 29.7145 | 1.06738 | ||||||||
\(776\) | −11.3325 | −0.406813 | ||||||||
\(777\) | −3.75156 | −0.134586 | ||||||||
\(778\) | −17.6237 | −0.631839 | ||||||||
\(779\) | 20.1828 | 0.723124 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.35080 | −0.191467 | ||||||||
\(782\) | −19.2736 | −0.689224 | ||||||||
\(783\) | −39.4703 | −1.41055 | ||||||||
\(784\) | −4.59054 | −0.163948 | ||||||||
\(785\) | 7.98908 | 0.285142 | ||||||||
\(786\) | 37.8831 | 1.35124 | ||||||||
\(787\) | 3.70522 | 0.132077 | 0.0660385 | − | 0.997817i | \(-0.478964\pi\) | ||||
0.0660385 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(788\) | 11.3458 | 0.404176 | ||||||||
\(789\) | −8.04186 | −0.286298 | ||||||||
\(790\) | 17.1015 | 0.608443 | ||||||||
\(791\) | −16.2026 | −0.576097 | ||||||||
\(792\) | −1.00169 | −0.0355934 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −31.8710 | −1.13106 | ||||||||
\(795\) | 7.39052 | 0.262115 | ||||||||
\(796\) | 28.5272 | 1.01112 | ||||||||
\(797\) | −47.2016 | −1.67197 | −0.835984 | − | 0.548754i | \(-0.815102\pi\) | ||||
−0.835984 | + | 0.548754i | \(0.815102\pi\) | |||||||
\(798\) | 3.81245 | 0.134959 | ||||||||
\(799\) | 13.7911 | 0.487893 | ||||||||
\(800\) | 27.8890 | 0.986027 | ||||||||
\(801\) | 4.15436 | 0.146787 | ||||||||
\(802\) | −54.1704 | −1.91282 | ||||||||
\(803\) | −12.0591 | −0.425557 | ||||||||
\(804\) | 24.7849 | 0.874095 | ||||||||
\(805\) | 4.23224 | 0.149167 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.97319 | 0.175064 | ||||||||
\(808\) | 9.66556 | 0.340033 | ||||||||
\(809\) | −15.3631 | −0.540139 | −0.270070 | − | 0.962841i | \(-0.587047\pi\) | ||||
−0.270070 | + | 0.962841i | \(0.587047\pi\) | |||||||
\(810\) | 0.439359 | 0.0154375 | ||||||||
\(811\) | −38.2892 | −1.34452 | −0.672258 | − | 0.740317i | \(-0.734676\pi\) | ||||
−0.672258 | + | 0.740317i | \(0.734676\pi\) | |||||||
\(812\) | −12.3701 | −0.434104 | ||||||||
\(813\) | 3.93580 | 0.138034 | ||||||||
\(814\) | −5.27645 | −0.184940 | ||||||||
\(815\) | −4.23754 | −0.148435 | ||||||||
\(816\) | 13.1473 | 0.460248 | ||||||||
\(817\) | 4.86085 | 0.170060 | ||||||||
\(818\) | −49.3601 | −1.72584 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.8729 | 0.693993 | ||||||||
\(821\) | −18.0178 | −0.628824 | −0.314412 | − | 0.949287i | \(-0.601807\pi\) | ||||
−0.314412 | + | 0.949287i | \(0.601807\pi\) | |||||||
\(822\) | −2.14976 | −0.0749815 | ||||||||
\(823\) | 12.2209 | 0.425995 | 0.212998 | − | 0.977053i | \(-0.431677\pi\) | ||||
0.212998 | + | 0.977053i | \(0.431677\pi\) | |||||||
\(824\) | −0.0757310 | −0.00263821 | ||||||||
\(825\) | −3.27745 | −0.114106 | ||||||||
\(826\) | 9.73480 | 0.338717 | ||||||||
\(827\) | −50.2854 | −1.74859 | −0.874297 | − | 0.485390i | \(-0.838677\pi\) | ||||
−0.874297 | + | 0.485390i | \(0.838677\pi\) | |||||||
\(828\) | 11.4401 | 0.397572 | ||||||||
\(829\) | −41.3255 | −1.43530 | −0.717648 | − | 0.696407i | \(-0.754781\pi\) | ||||
−0.717648 | + | 0.696407i | \(0.754781\pi\) | |||||||
\(830\) | −32.9860 | −1.14496 | ||||||||
\(831\) | −25.6846 | −0.890989 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.63979 | 0.0914634 | ||||||||
\(834\) | −33.2250 | −1.15049 | ||||||||
\(835\) | −2.02681 | −0.0701407 | ||||||||
\(836\) | 2.41581 | 0.0835524 | ||||||||
\(837\) | −41.1661 | −1.42291 | ||||||||
\(838\) | −12.5093 | −0.432125 | ||||||||
\(839\) | 44.8612 | 1.54878 | 0.774391 | − | 0.632708i | \(-0.218057\pi\) | ||||
0.774391 | + | 0.632708i | \(0.218057\pi\) | |||||||
\(840\) | −0.824328 | −0.0284420 | ||||||||
\(841\) | 27.9001 | 0.962073 | ||||||||
\(842\) | −27.4921 | −0.947441 | ||||||||
\(843\) | 27.7108 | 0.954412 | ||||||||
\(844\) | 12.3019 | 0.423450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.1693 | −0.624674 | ||||||||
\(847\) | −10.3603 | −0.355984 | ||||||||
\(848\) | −28.2757 | −0.970993 | ||||||||
\(849\) | 3.20442 | 0.109976 | ||||||||
\(850\) | −19.0220 | −0.652449 | ||||||||
\(851\) | −13.2330 | −0.453620 | ||||||||
\(852\) | −11.9028 | −0.407782 | ||||||||
\(853\) | −38.3749 | −1.31393 | −0.656966 | − | 0.753920i | \(-0.728160\pi\) | ||||
−0.656966 | + | 0.753920i | \(0.728160\pi\) | |||||||
\(854\) | 6.32535 | 0.216449 | ||||||||
\(855\) | −3.71316 | −0.126987 | ||||||||
\(856\) | 9.48585 | 0.324220 | ||||||||
\(857\) | 6.20663 | 0.212015 | 0.106007 | − | 0.994365i | \(-0.466193\pi\) | ||||
0.106007 | + | 0.994365i | \(0.466193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.0183 | 1.46777 | 0.733884 | − | 0.679275i | \(-0.237706\pi\) | ||||
0.733884 | + | 0.679275i | \(0.237706\pi\) | |||||||
\(860\) | 4.78622 | 0.163209 | ||||||||
\(861\) | 11.8886 | 0.405161 | ||||||||
\(862\) | 28.0506 | 0.955406 | ||||||||
\(863\) | 19.4927 | 0.663540 | 0.331770 | − | 0.943360i | \(-0.392354\pi\) | ||||
0.331770 | + | 0.943360i | \(0.392354\pi\) | |||||||
\(864\) | −38.6372 | −1.31446 | ||||||||
\(865\) | 24.3680 | 0.828537 | ||||||||
\(866\) | −39.3358 | −1.33668 | ||||||||
\(867\) | 10.8835 | 0.369624 | ||||||||
\(868\) | −12.9015 | −0.437907 | ||||||||
\(869\) | 6.48274 | 0.219912 | ||||||||
\(870\) | −17.2674 | −0.585418 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.49350 | 0.0505762 | ||||||||
\(873\) | −30.0689 | −1.01768 | ||||||||
\(874\) | 13.4478 | 0.454877 | ||||||||
\(875\) | 9.70655 | 0.328141 | ||||||||
\(876\) | −26.8253 | −0.906344 | ||||||||
\(877\) | −33.2003 | −1.12109 | −0.560547 | − | 0.828123i | \(-0.689409\pi\) | ||||
−0.560547 | + | 0.828123i | \(0.689409\pi\) | |||||||
\(878\) | 38.8103 | 1.30979 | ||||||||
\(879\) | −24.5919 | −0.829465 | ||||||||
\(880\) | −4.06045 | −0.136878 | ||||||||
\(881\) | 50.5588 | 1.70337 | 0.851684 | − | 0.524055i | \(-0.175582\pi\) | ||||
0.851684 | + | 0.524055i | \(0.175582\pi\) | |||||||
\(882\) | −3.47785 | −0.117105 | ||||||||
\(883\) | 7.17013 | 0.241294 | 0.120647 | − | 0.992695i | \(-0.461503\pi\) | ||||
0.120647 | + | 0.992695i | \(0.461503\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.12220 | 0.205795 | ||||||||
\(886\) | 26.3654 | 0.885764 | ||||||||
\(887\) | −31.0525 | −1.04264 | −0.521320 | − | 0.853361i | \(-0.674560\pi\) | ||||
−0.521320 | + | 0.853361i | \(0.674560\pi\) | |||||||
\(888\) | 2.57743 | 0.0864928 | ||||||||
\(889\) | 19.9799 | 0.670103 | ||||||||
\(890\) | 4.80843 | 0.161179 | ||||||||
\(891\) | 0.166550 | 0.00557964 | ||||||||
\(892\) | −42.4150 | −1.42016 | ||||||||
\(893\) | −9.62243 | −0.322002 | ||||||||
\(894\) | 0.778388 | 0.0260332 | ||||||||
\(895\) | −6.21705 | −0.207813 | ||||||||
\(896\) | 5.40714 | 0.180640 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.7343 | −1.15910 | ||||||||
\(899\) | 59.3448 | 1.97926 | ||||||||
\(900\) | 11.2908 | 0.376359 | ||||||||
\(901\) | 16.2600 | 0.541699 | ||||||||
\(902\) | 16.7209 | 0.556745 | ||||||||
\(903\) | 2.86325 | 0.0952831 | ||||||||
\(904\) | 11.1316 | 0.370233 | ||||||||
\(905\) | 4.91033 | 0.163225 | ||||||||
\(906\) | 0.309965 | 0.0102979 | ||||||||
\(907\) | −21.6888 | −0.720165 | −0.360082 | − | 0.932921i | \(-0.617251\pi\) | ||||
−0.360082 | + | 0.932921i | \(0.617251\pi\) | |||||||
\(908\) | 8.52244 | 0.282827 | ||||||||
\(909\) | 25.6459 | 0.850621 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0626 | −0.929756 | −0.464878 | − | 0.885375i | \(-0.653902\pi\) | ||||
−0.464878 | + | 0.885375i | \(0.653902\pi\) | |||||||
\(912\) | −9.17326 | −0.303757 | ||||||||
\(913\) | −12.5042 | −0.413827 | ||||||||
\(914\) | −17.0693 | −0.564603 | ||||||||
\(915\) | 3.97800 | 0.131509 | ||||||||
\(916\) | 8.26050 | 0.272935 | ||||||||
\(917\) | −18.3019 | −0.604383 | ||||||||
\(918\) | 26.3529 | 0.869774 | ||||||||
\(919\) | −1.09050 | −0.0359724 | −0.0179862 | − | 0.999838i | \(-0.505725\pi\) | ||||
−0.0179862 | + | 0.999838i | \(0.505725\pi\) | |||||||
\(920\) | −2.90767 | −0.0958631 | ||||||||
\(921\) | −2.22338 | −0.0732629 | ||||||||
\(922\) | 16.5756 | 0.545889 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.42302 | 0.0468138 | ||||||||
\(925\) | −13.0602 | −0.429416 | ||||||||
\(926\) | 38.5423 | 1.26658 | ||||||||
\(927\) | −0.200939 | −0.00659971 | ||||||||
\(928\) | 55.6991 | 1.82841 | ||||||||
\(929\) | −25.7716 | −0.845540 | −0.422770 | − | 0.906237i | \(-0.638942\pi\) | ||||
−0.422770 | + | 0.906237i | \(0.638942\pi\) | |||||||
\(930\) | −18.0092 | −0.590546 | ||||||||
\(931\) | −1.84186 | −0.0603645 | ||||||||
\(932\) | −26.5699 | −0.870327 | ||||||||
\(933\) | 16.7563 | 0.548575 | ||||||||
\(934\) | −20.1445 | −0.659149 | ||||||||
\(935\) | 2.33497 | 0.0763616 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.39284 | −0.176176 | −0.0880882 | − | 0.996113i | \(-0.528076\pi\) | ||||
−0.0880882 | + | 0.996113i | \(0.528076\pi\) | |||||||
\(938\) | −26.5773 | −0.867781 | ||||||||
\(939\) | 7.15172 | 0.233388 | ||||||||
\(940\) | −9.47468 | −0.309030 | ||||||||
\(941\) | −59.3354 | −1.93428 | −0.967139 | − | 0.254248i | \(-0.918172\pi\) | ||||
−0.967139 | + | 0.254248i | \(0.918172\pi\) | |||||||
\(942\) | 14.9529 | 0.487190 | ||||||||
\(943\) | 41.9348 | 1.36558 | ||||||||
\(944\) | −23.4232 | −0.762360 | ||||||||
\(945\) | −5.78675 | −0.188243 | ||||||||
\(946\) | 4.02708 | 0.130932 | ||||||||
\(947\) | −29.0891 | −0.945270 | −0.472635 | − | 0.881258i | \(-0.656697\pi\) | ||||
−0.472635 | + | 0.881258i | \(0.656697\pi\) | |||||||
\(948\) | 14.4208 | 0.468364 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 13.2722 | 0.430607 | ||||||||
\(951\) | 19.1146 | 0.619833 | ||||||||
\(952\) | −1.81362 | −0.0587796 | ||||||||
\(953\) | 11.0404 | 0.357633 | 0.178816 | − | 0.983882i | \(-0.442773\pi\) | ||||
0.178816 | + | 0.983882i | \(0.442773\pi\) | |||||||
\(954\) | −21.4221 | −0.693565 | ||||||||
\(955\) | 4.86315 | 0.157368 | ||||||||
\(956\) | 5.28710 | 0.170997 | ||||||||
\(957\) | −6.54562 | −0.211590 | ||||||||
\(958\) | −72.7662 | −2.35097 | ||||||||
\(959\) | 1.03858 | 0.0335376 | ||||||||
\(960\) | −5.88703 | −0.190003 | ||||||||
\(961\) | 30.8945 | 0.996596 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.1691 | 0.811063 | ||||||||
\(964\) | −28.2917 | −0.911215 | ||||||||
\(965\) | −27.9473 | −0.899656 | ||||||||
\(966\) | 7.92132 | 0.254864 | ||||||||
\(967\) | 15.3720 | 0.494330 | 0.247165 | − | 0.968973i | \(-0.420501\pi\) | ||||
0.247165 | + | 0.968973i | \(0.420501\pi\) | |||||||
\(968\) | 7.11782 | 0.228776 | ||||||||
\(969\) | 5.27510 | 0.169460 | ||||||||
\(970\) | −34.8029 | −1.11745 | ||||||||
\(971\) | 45.8252 | 1.47060 | 0.735300 | − | 0.677741i | \(-0.237041\pi\) | ||||
0.735300 | + | 0.677741i | \(0.237041\pi\) | |||||||
\(972\) | −25.3720 | −0.813807 | ||||||||
\(973\) | 16.0516 | 0.514589 | ||||||||
\(974\) | −8.08828 | −0.259165 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.2196 | −0.487168 | ||||||||
\(977\) | −30.9623 | −0.990572 | −0.495286 | − | 0.868730i | \(-0.664937\pi\) | ||||
−0.495286 | + | 0.868730i | \(0.664937\pi\) | |||||||
\(978\) | −7.93125 | −0.253613 | ||||||||
\(979\) | 1.82275 | 0.0582555 | ||||||||
\(980\) | −1.81358 | −0.0579327 | ||||||||
\(981\) | 3.96274 | 0.126521 | ||||||||
\(982\) | 30.6519 | 0.978142 | ||||||||
\(983\) | 27.6460 | 0.881769 | 0.440884 | − | 0.897564i | \(-0.354665\pi\) | ||||
0.440884 | + | 0.897564i | \(0.354665\pi\) | |||||||
\(984\) | −8.16778 | −0.260379 | ||||||||
\(985\) | −7.65137 | −0.243793 | ||||||||
\(986\) | −37.9901 | −1.20985 | ||||||||
\(987\) | −5.66803 | −0.180415 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.0996 | 0.321149 | ||||||||
\(990\) | −3.07625 | −0.0977697 | ||||||||
\(991\) | −29.7267 | −0.944301 | −0.472151 | − | 0.881518i | \(-0.656522\pi\) | ||||
−0.472151 | + | 0.881518i | \(0.656522\pi\) | |||||||
\(992\) | 58.0922 | 1.84443 | ||||||||
\(993\) | 15.2783 | 0.484841 | ||||||||
\(994\) | 12.7636 | 0.404837 | ||||||||
\(995\) | −19.2382 | −0.609892 | ||||||||
\(996\) | −27.8153 | −0.881362 | ||||||||
\(997\) | 24.6552 | 0.780838 | 0.390419 | − | 0.920637i | \(-0.372330\pi\) | ||||
0.390419 | + | 0.920637i | \(0.372330\pi\) | |||||||
\(998\) | 55.2202 | 1.74797 | ||||||||
\(999\) | 18.0934 | 0.572451 |
(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 | 1183.2.a.n.1.5 | ✓ | 6 | |
7.6 | odd | 2 | 8281.2.a.cb.1.5 | 6 | |||
13.5 | odd | 4 | 1183.2.c.h.337.4 | 12 | |||
13.8 | odd | 4 | 1183.2.c.h.337.9 | 12 | |||
13.12 | even | 2 | 1183.2.a.o.1.2 | yes | 6 | ||
91.90 | odd | 2 | 8281.2.a.cg.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.n.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1183.2.a.o.1.2 | yes | 6 | 13.12 | even | 2 | ||
1183.2.c.h.337.4 | 12 | 13.5 | odd | 4 | |||
1183.2.c.h.337.9 | 12 | 13.8 | odd | 4 | |||
8281.2.a.cb.1.5 | 6 | 7.6 | odd | 2 | |||
8281.2.a.cg.1.2 | 6 | 91.90 | odd | 2 |