Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34343 | −1.65706 | −0.828528 | − | 0.559948i | \(-0.810821\pi\) | ||||
−0.828528 | + | 0.559948i | \(0.810821\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.49167 | 1.74583 | ||||||||
\(5\) | 2.63222 | 1.17716 | 0.588582 | − | 0.808438i | \(-0.299687\pi\) | ||||
0.588582 | + | 0.808438i | \(0.299687\pi\) | |||||||
\(6\) | −2.34343 | −0.956702 | ||||||||
\(7\) | 1.69426 | 0.640369 | 0.320184 | − | 0.947355i | \(-0.396255\pi\) | ||||
0.320184 | + | 0.947355i | \(0.396255\pi\) | |||||||
\(8\) | −3.49562 | −1.23589 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.16842 | −1.95063 | ||||||||
\(11\) | −1.32194 | −0.398579 | −0.199289 | − | 0.979941i | \(-0.563863\pi\) | ||||
−0.199289 | + | 0.979941i | \(0.563863\pi\) | |||||||
\(12\) | 3.49167 | 1.00796 | ||||||||
\(13\) | 4.21493 | 1.16901 | 0.584506 | − | 0.811389i | \(-0.301288\pi\) | ||||
0.584506 | + | 0.811389i | \(0.301288\pi\) | |||||||
\(14\) | −3.97037 | −1.06113 | ||||||||
\(15\) | 2.63222 | 0.679636 | ||||||||
\(16\) | 1.20841 | 0.302101 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.34343 | −0.552352 | ||||||||
\(19\) | 0.200368 | 0.0459676 | 0.0229838 | − | 0.999736i | \(-0.492683\pi\) | ||||
0.0229838 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(20\) | 9.19083 | 2.05513 | ||||||||
\(21\) | 1.69426 | 0.369717 | ||||||||
\(22\) | 3.09787 | 0.660467 | ||||||||
\(23\) | −3.01962 | −0.629635 | −0.314818 | − | 0.949152i | \(-0.601943\pi\) | ||||
−0.314818 | + | 0.949152i | \(0.601943\pi\) | |||||||
\(24\) | −3.49562 | −0.713540 | ||||||||
\(25\) | 1.92857 | 0.385713 | ||||||||
\(26\) | −9.87740 | −1.93712 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.91578 | 1.11798 | ||||||||
\(29\) | 5.81319 | 1.07948 | 0.539741 | − | 0.841831i | \(-0.318522\pi\) | ||||
0.539741 | + | 0.841831i | \(0.318522\pi\) | |||||||
\(30\) | −6.16842 | −1.12619 | ||||||||
\(31\) | −8.08840 | −1.45272 | −0.726360 | − | 0.687315i | \(-0.758789\pi\) | ||||
−0.726360 | + | 0.687315i | \(0.758789\pi\) | |||||||
\(32\) | 4.15942 | 0.735289 | ||||||||
\(33\) | −1.32194 | −0.230120 | ||||||||
\(34\) | −2.34343 | −0.401895 | ||||||||
\(35\) | 4.45965 | 0.753819 | ||||||||
\(36\) | 3.49167 | 0.581945 | ||||||||
\(37\) | −3.41483 | −0.561395 | −0.280698 | − | 0.959796i | \(-0.590566\pi\) | ||||
−0.280698 | + | 0.959796i | \(0.590566\pi\) | |||||||
\(38\) | −0.469548 | −0.0761708 | ||||||||
\(39\) | 4.21493 | 0.674929 | ||||||||
\(40\) | −9.20123 | −1.45484 | ||||||||
\(41\) | 2.29353 | 0.358190 | 0.179095 | − | 0.983832i | \(-0.442683\pi\) | ||||
0.179095 | + | 0.983832i | \(0.442683\pi\) | |||||||
\(42\) | −3.97037 | −0.612642 | ||||||||
\(43\) | 0.581734 | 0.0887136 | 0.0443568 | − | 0.999016i | \(-0.485876\pi\) | ||||
0.0443568 | + | 0.999016i | \(0.485876\pi\) | |||||||
\(44\) | −4.61576 | −0.695852 | ||||||||
\(45\) | 2.63222 | 0.392388 | ||||||||
\(46\) | 7.07628 | 1.04334 | ||||||||
\(47\) | 8.80652 | 1.28456 | 0.642282 | − | 0.766469i | \(-0.277988\pi\) | ||||
0.642282 | + | 0.766469i | \(0.277988\pi\) | |||||||
\(48\) | 1.20841 | 0.174418 | ||||||||
\(49\) | −4.12949 | −0.589928 | ||||||||
\(50\) | −4.51946 | −0.639149 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 14.7171 | 2.04090 | ||||||||
\(53\) | 0.940952 | 0.129250 | 0.0646249 | − | 0.997910i | \(-0.479415\pi\) | ||||
0.0646249 | + | 0.997910i | \(0.479415\pi\) | |||||||
\(54\) | −2.34343 | −0.318901 | ||||||||
\(55\) | −3.47962 | −0.469192 | ||||||||
\(56\) | −5.92248 | −0.791424 | ||||||||
\(57\) | 0.200368 | 0.0265394 | ||||||||
\(58\) | −13.6228 | −1.78876 | ||||||||
\(59\) | −0.347504 | −0.0452412 | −0.0226206 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226206 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(60\) | 9.19083 | 1.18653 | ||||||||
\(61\) | 5.96624 | 0.763898 | 0.381949 | − | 0.924183i | \(-0.375253\pi\) | ||||
0.381949 | + | 0.924183i | \(0.375253\pi\) | |||||||
\(62\) | 18.9546 | 2.40724 | ||||||||
\(63\) | 1.69426 | 0.213456 | ||||||||
\(64\) | −12.1641 | −1.52052 | ||||||||
\(65\) | 11.0946 | 1.37612 | ||||||||
\(66\) | 3.09787 | 0.381321 | ||||||||
\(67\) | −0.333659 | −0.0407629 | −0.0203815 | − | 0.999792i | \(-0.506488\pi\) | ||||
−0.0203815 | + | 0.999792i | \(0.506488\pi\) | |||||||
\(68\) | 3.49167 | 0.423427 | ||||||||
\(69\) | −3.01962 | −0.363520 | ||||||||
\(70\) | −10.4509 | −1.24912 | ||||||||
\(71\) | 5.17052 | 0.613628 | 0.306814 | − | 0.951770i | \(-0.400737\pi\) | ||||
0.306814 | + | 0.951770i | \(0.400737\pi\) | |||||||
\(72\) | −3.49562 | −0.411963 | ||||||||
\(73\) | −8.65040 | −1.01245 | −0.506226 | − | 0.862401i | \(-0.668960\pi\) | ||||
−0.506226 | + | 0.862401i | \(0.668960\pi\) | |||||||
\(74\) | 8.00242 | 0.930263 | ||||||||
\(75\) | 1.92857 | 0.222692 | ||||||||
\(76\) | 0.699618 | 0.0802517 | ||||||||
\(77\) | −2.23970 | −0.255237 | ||||||||
\(78\) | −9.87740 | −1.11840 | ||||||||
\(79\) | 5.40248 | 0.607827 | 0.303913 | − | 0.952700i | \(-0.401707\pi\) | ||||
0.303913 | + | 0.952700i | \(0.401707\pi\) | |||||||
\(80\) | 3.18078 | 0.355623 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.37474 | −0.593540 | ||||||||
\(83\) | 4.12163 | 0.452408 | 0.226204 | − | 0.974080i | \(-0.427368\pi\) | ||||
0.226204 | + | 0.974080i | \(0.427368\pi\) | |||||||
\(84\) | 5.91578 | 0.645465 | ||||||||
\(85\) | 2.63222 | 0.285504 | ||||||||
\(86\) | −1.36325 | −0.147003 | ||||||||
\(87\) | 5.81319 | 0.623239 | ||||||||
\(88\) | 4.62098 | 0.492599 | ||||||||
\(89\) | 11.1722 | 1.18425 | 0.592126 | − | 0.805845i | \(-0.298289\pi\) | ||||
0.592126 | + | 0.805845i | \(0.298289\pi\) | |||||||
\(90\) | −6.16842 | −0.650208 | ||||||||
\(91\) | 7.14118 | 0.748599 | ||||||||
\(92\) | −10.5435 | −1.09924 | ||||||||
\(93\) | −8.08840 | −0.838728 | ||||||||
\(94\) | −20.6375 | −2.12859 | ||||||||
\(95\) | 0.527412 | 0.0541113 | ||||||||
\(96\) | 4.15942 | 0.424519 | ||||||||
\(97\) | −16.3073 | −1.65576 | −0.827879 | − | 0.560907i | \(-0.810452\pi\) | ||||
−0.827879 | + | 0.560907i | \(0.810452\pi\) | |||||||
\(98\) | 9.67718 | 0.977543 | ||||||||
\(99\) | −1.32194 | −0.132860 | ||||||||
\(100\) | 6.73392 | 0.673392 | ||||||||
\(101\) | 12.5834 | 1.25210 | 0.626049 | − | 0.779783i | \(-0.284671\pi\) | ||||
0.626049 | + | 0.779783i | \(0.284671\pi\) | |||||||
\(102\) | −2.34343 | −0.232034 | ||||||||
\(103\) | 13.9393 | 1.37348 | 0.686738 | − | 0.726905i | \(-0.259042\pi\) | ||||
0.686738 | + | 0.726905i | \(0.259042\pi\) | |||||||
\(104\) | −14.7338 | −1.44477 | ||||||||
\(105\) | 4.45965 | 0.435218 | ||||||||
\(106\) | −2.20506 | −0.214174 | ||||||||
\(107\) | −20.2486 | −1.95751 | −0.978755 | − | 0.205035i | \(-0.934269\pi\) | ||||
−0.978755 | + | 0.205035i | \(0.934269\pi\) | |||||||
\(108\) | 3.49167 | 0.335986 | ||||||||
\(109\) | 10.7016 | 1.02502 | 0.512512 | − | 0.858680i | \(-0.328715\pi\) | ||||
0.512512 | + | 0.858680i | \(0.328715\pi\) | |||||||
\(110\) | 8.15426 | 0.777478 | ||||||||
\(111\) | −3.41483 | −0.324122 | ||||||||
\(112\) | 2.04735 | 0.193456 | ||||||||
\(113\) | 6.67043 | 0.627502 | 0.313751 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313751 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(114\) | −0.469548 | −0.0439772 | ||||||||
\(115\) | −7.94831 | −0.741183 | ||||||||
\(116\) | 20.2977 | 1.88460 | ||||||||
\(117\) | 4.21493 | 0.389671 | ||||||||
\(118\) | 0.814351 | 0.0749671 | ||||||||
\(119\) | 1.69426 | 0.155312 | ||||||||
\(120\) | −9.20123 | −0.839953 | ||||||||
\(121\) | −9.25248 | −0.841135 | ||||||||
\(122\) | −13.9815 | −1.26582 | ||||||||
\(123\) | 2.29353 | 0.206801 | ||||||||
\(124\) | −28.2420 | −2.53621 | ||||||||
\(125\) | −8.08468 | −0.723116 | ||||||||
\(126\) | −3.97037 | −0.353709 | ||||||||
\(127\) | 17.4233 | 1.54607 | 0.773035 | − | 0.634364i | \(-0.218738\pi\) | ||||
0.773035 | + | 0.634364i | \(0.218738\pi\) | |||||||
\(128\) | 20.1869 | 1.78429 | ||||||||
\(129\) | 0.581734 | 0.0512188 | ||||||||
\(130\) | −25.9995 | −2.28030 | ||||||||
\(131\) | −6.85121 | −0.598593 | −0.299296 | − | 0.954160i | \(-0.596752\pi\) | ||||
−0.299296 | + | 0.954160i | \(0.596752\pi\) | |||||||
\(132\) | −4.61576 | −0.401750 | ||||||||
\(133\) | 0.339475 | 0.0294362 | ||||||||
\(134\) | 0.781906 | 0.0675464 | ||||||||
\(135\) | 2.63222 | 0.226545 | ||||||||
\(136\) | −3.49562 | −0.299747 | ||||||||
\(137\) | 10.3764 | 0.886512 | 0.443256 | − | 0.896395i | \(-0.353823\pi\) | ||||
0.443256 | + | 0.896395i | \(0.353823\pi\) | |||||||
\(138\) | 7.07628 | 0.602373 | ||||||||
\(139\) | 6.74346 | 0.571973 | 0.285986 | − | 0.958234i | \(-0.407679\pi\) | ||||
0.285986 | + | 0.958234i | \(0.407679\pi\) | |||||||
\(140\) | 15.5716 | 1.31604 | ||||||||
\(141\) | 8.80652 | 0.741643 | ||||||||
\(142\) | −12.1168 | −1.01682 | ||||||||
\(143\) | −5.57187 | −0.465943 | ||||||||
\(144\) | 1.20841 | 0.100700 | ||||||||
\(145\) | 15.3016 | 1.27073 | ||||||||
\(146\) | 20.2716 | 1.67769 | ||||||||
\(147\) | −4.12949 | −0.340595 | ||||||||
\(148\) | −11.9235 | −0.980102 | ||||||||
\(149\) | 7.13928 | 0.584872 | 0.292436 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292436 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(150\) | −4.51946 | −0.369013 | ||||||||
\(151\) | 17.3354 | 1.41073 | 0.705367 | − | 0.708842i | \(-0.250782\pi\) | ||||
0.705367 | + | 0.708842i | \(0.250782\pi\) | |||||||
\(152\) | −0.700410 | −0.0568107 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 5.24858 | 0.422943 | ||||||||
\(155\) | −21.2904 | −1.71009 | ||||||||
\(156\) | 14.7171 | 1.17831 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −12.6603 | −1.00720 | ||||||||
\(159\) | 0.940952 | 0.0746224 | ||||||||
\(160\) | 10.9485 | 0.865555 | ||||||||
\(161\) | −5.11602 | −0.403199 | ||||||||
\(162\) | −2.34343 | −0.184117 | ||||||||
\(163\) | 21.3736 | 1.67411 | 0.837053 | − | 0.547122i | \(-0.184276\pi\) | ||||
0.837053 | + | 0.547122i | \(0.184276\pi\) | |||||||
\(164\) | 8.00825 | 0.625340 | ||||||||
\(165\) | −3.47962 | −0.270888 | ||||||||
\(166\) | −9.65875 | −0.749664 | ||||||||
\(167\) | −22.2209 | −1.71950 | −0.859752 | − | 0.510712i | \(-0.829382\pi\) | ||||
−0.859752 | + | 0.510712i | \(0.829382\pi\) | |||||||
\(168\) | −5.92248 | −0.456929 | ||||||||
\(169\) | 4.76566 | 0.366589 | ||||||||
\(170\) | −6.16842 | −0.473096 | ||||||||
\(171\) | 0.200368 | 0.0153225 | ||||||||
\(172\) | 2.03122 | 0.154879 | ||||||||
\(173\) | 8.90582 | 0.677097 | 0.338548 | − | 0.940949i | \(-0.390064\pi\) | ||||
0.338548 | + | 0.940949i | \(0.390064\pi\) | |||||||
\(174\) | −13.6228 | −1.03274 | ||||||||
\(175\) | 3.26749 | 0.246999 | ||||||||
\(176\) | −1.59743 | −0.120411 | ||||||||
\(177\) | −0.347504 | −0.0261200 | ||||||||
\(178\) | −26.1813 | −1.96237 | ||||||||
\(179\) | 20.6630 | 1.54443 | 0.772214 | − | 0.635362i | \(-0.219149\pi\) | ||||
0.772214 | + | 0.635362i | \(0.219149\pi\) | |||||||
\(180\) | 9.19083 | 0.685044 | ||||||||
\(181\) | 10.7691 | 0.800458 | 0.400229 | − | 0.916415i | \(-0.368931\pi\) | ||||
0.400229 | + | 0.916415i | \(0.368931\pi\) | |||||||
\(182\) | −16.7349 | −1.24047 | ||||||||
\(183\) | 5.96624 | 0.441037 | ||||||||
\(184\) | 10.5555 | 0.778158 | ||||||||
\(185\) | −8.98858 | −0.660854 | ||||||||
\(186\) | 18.9546 | 1.38982 | ||||||||
\(187\) | −1.32194 | −0.0966696 | ||||||||
\(188\) | 30.7495 | 2.24263 | ||||||||
\(189\) | 1.69426 | 0.123239 | ||||||||
\(190\) | −1.23595 | −0.0896655 | ||||||||
\(191\) | 16.4057 | 1.18707 | 0.593536 | − | 0.804808i | \(-0.297732\pi\) | ||||
0.593536 | + | 0.804808i | \(0.297732\pi\) | |||||||
\(192\) | −12.1641 | −0.877870 | ||||||||
\(193\) | 10.1229 | 0.728664 | 0.364332 | − | 0.931269i | \(-0.381297\pi\) | ||||
0.364332 | + | 0.931269i | \(0.381297\pi\) | |||||||
\(194\) | 38.2151 | 2.74368 | ||||||||
\(195\) | 11.0946 | 0.794502 | ||||||||
\(196\) | −14.4188 | −1.02992 | ||||||||
\(197\) | 9.56610 | 0.681556 | 0.340778 | − | 0.940144i | \(-0.389309\pi\) | ||||
0.340778 | + | 0.940144i | \(0.389309\pi\) | |||||||
\(198\) | 3.09787 | 0.220156 | ||||||||
\(199\) | −18.9114 | −1.34059 | −0.670297 | − | 0.742093i | \(-0.733833\pi\) | ||||
−0.670297 | + | 0.742093i | \(0.733833\pi\) | |||||||
\(200\) | −6.74154 | −0.476699 | ||||||||
\(201\) | −0.333659 | −0.0235345 | ||||||||
\(202\) | −29.4884 | −2.07480 | ||||||||
\(203\) | 9.84904 | 0.691267 | ||||||||
\(204\) | 3.49167 | 0.244466 | ||||||||
\(205\) | 6.03708 | 0.421648 | ||||||||
\(206\) | −32.6657 | −2.27593 | ||||||||
\(207\) | −3.01962 | −0.209878 | ||||||||
\(208\) | 5.09335 | 0.353160 | ||||||||
\(209\) | −0.264874 | −0.0183217 | ||||||||
\(210\) | −10.4509 | −0.721180 | ||||||||
\(211\) | 11.1000 | 0.764158 | 0.382079 | − | 0.924130i | \(-0.375208\pi\) | ||||
0.382079 | + | 0.924130i | \(0.375208\pi\) | |||||||
\(212\) | 3.28549 | 0.225649 | ||||||||
\(213\) | 5.17052 | 0.354278 | ||||||||
\(214\) | 47.4513 | 3.24370 | ||||||||
\(215\) | 1.53125 | 0.104430 | ||||||||
\(216\) | −3.49562 | −0.237847 | ||||||||
\(217\) | −13.7038 | −0.930277 | ||||||||
\(218\) | −25.0784 | −1.69852 | ||||||||
\(219\) | −8.65040 | −0.584540 | ||||||||
\(220\) | −12.1497 | −0.819132 | ||||||||
\(221\) | 4.21493 | 0.283527 | ||||||||
\(222\) | 8.00242 | 0.537088 | ||||||||
\(223\) | −11.8262 | −0.791943 | −0.395971 | − | 0.918263i | \(-0.629592\pi\) | ||||
−0.395971 | + | 0.918263i | \(0.629592\pi\) | |||||||
\(224\) | 7.04713 | 0.470856 | ||||||||
\(225\) | 1.92857 | 0.128571 | ||||||||
\(226\) | −15.6317 | −1.03981 | ||||||||
\(227\) | −10.0902 | −0.669710 | −0.334855 | − | 0.942270i | \(-0.608687\pi\) | ||||
−0.334855 | + | 0.942270i | \(0.608687\pi\) | |||||||
\(228\) | 0.699618 | 0.0463333 | ||||||||
\(229\) | −2.86997 | −0.189653 | −0.0948266 | − | 0.995494i | \(-0.530230\pi\) | ||||
−0.0948266 | + | 0.995494i | \(0.530230\pi\) | |||||||
\(230\) | 18.6263 | 1.22818 | ||||||||
\(231\) | −2.23970 | −0.147361 | ||||||||
\(232\) | −20.3207 | −1.33412 | ||||||||
\(233\) | 21.0685 | 1.38024 | 0.690121 | − | 0.723694i | \(-0.257557\pi\) | ||||
0.690121 | + | 0.723694i | \(0.257557\pi\) | |||||||
\(234\) | −9.87740 | −0.645706 | ||||||||
\(235\) | 23.1807 | 1.51214 | ||||||||
\(236\) | −1.21337 | −0.0789835 | ||||||||
\(237\) | 5.40248 | 0.350929 | ||||||||
\(238\) | −3.97037 | −0.257361 | ||||||||
\(239\) | 27.0493 | 1.74967 | 0.874836 | − | 0.484419i | \(-0.160969\pi\) | ||||
0.874836 | + | 0.484419i | \(0.160969\pi\) | |||||||
\(240\) | 3.18078 | 0.205319 | ||||||||
\(241\) | 15.2582 | 0.982868 | 0.491434 | − | 0.870915i | \(-0.336473\pi\) | ||||
0.491434 | + | 0.870915i | \(0.336473\pi\) | |||||||
\(242\) | 21.6826 | 1.39381 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 20.8321 | 1.33364 | ||||||||
\(245\) | −10.8697 | −0.694441 | ||||||||
\(246\) | −5.37474 | −0.342681 | ||||||||
\(247\) | 0.844537 | 0.0537366 | ||||||||
\(248\) | 28.2740 | 1.79540 | ||||||||
\(249\) | 4.12163 | 0.261198 | ||||||||
\(250\) | 18.9459 | 1.19824 | ||||||||
\(251\) | −31.1231 | −1.96447 | −0.982236 | − | 0.187648i | \(-0.939914\pi\) | ||||
−0.982236 | + | 0.187648i | \(0.939914\pi\) | |||||||
\(252\) | 5.91578 | 0.372659 | ||||||||
\(253\) | 3.99175 | 0.250959 | ||||||||
\(254\) | −40.8303 | −2.56192 | ||||||||
\(255\) | 2.63222 | 0.164836 | ||||||||
\(256\) | −22.9785 | −1.43615 | ||||||||
\(257\) | 3.94888 | 0.246324 | 0.123162 | − | 0.992387i | \(-0.460696\pi\) | ||||
0.123162 | + | 0.992387i | \(0.460696\pi\) | |||||||
\(258\) | −1.36325 | −0.0848724 | ||||||||
\(259\) | −5.78560 | −0.359500 | ||||||||
\(260\) | 38.7387 | 2.40247 | ||||||||
\(261\) | 5.81319 | 0.359827 | ||||||||
\(262\) | 16.0553 | 0.991902 | ||||||||
\(263\) | 14.1209 | 0.870733 | 0.435366 | − | 0.900253i | \(-0.356619\pi\) | ||||
0.435366 | + | 0.900253i | \(0.356619\pi\) | |||||||
\(264\) | 4.62098 | 0.284402 | ||||||||
\(265\) | 2.47679 | 0.152148 | ||||||||
\(266\) | −0.795535 | −0.0487774 | ||||||||
\(267\) | 11.1722 | 0.683728 | ||||||||
\(268\) | −1.16503 | −0.0711653 | ||||||||
\(269\) | 23.8881 | 1.45648 | 0.728241 | − | 0.685321i | \(-0.240338\pi\) | ||||
0.728241 | + | 0.685321i | \(0.240338\pi\) | |||||||
\(270\) | −6.16842 | −0.375398 | ||||||||
\(271\) | −17.5817 | −1.06801 | −0.534005 | − | 0.845481i | \(-0.679314\pi\) | ||||
−0.534005 | + | 0.845481i | \(0.679314\pi\) | |||||||
\(272\) | 1.20841 | 0.0732703 | ||||||||
\(273\) | 7.14118 | 0.432204 | ||||||||
\(274\) | −24.3163 | −1.46900 | ||||||||
\(275\) | −2.54944 | −0.153737 | ||||||||
\(276\) | −10.5435 | −0.634645 | ||||||||
\(277\) | −16.3152 | −0.980286 | −0.490143 | − | 0.871642i | \(-0.663055\pi\) | ||||
−0.490143 | + | 0.871642i | \(0.663055\pi\) | |||||||
\(278\) | −15.8028 | −0.947790 | ||||||||
\(279\) | −8.08840 | −0.484240 | ||||||||
\(280\) | −15.5892 | −0.931635 | ||||||||
\(281\) | 15.5401 | 0.927045 | 0.463522 | − | 0.886085i | \(-0.346585\pi\) | ||||
0.463522 | + | 0.886085i | \(0.346585\pi\) | |||||||
\(282\) | −20.6375 | −1.22894 | ||||||||
\(283\) | −5.24539 | −0.311806 | −0.155903 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155903 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(284\) | 18.0537 | 1.07129 | ||||||||
\(285\) | 0.527412 | 0.0312412 | ||||||||
\(286\) | 13.0573 | 0.772094 | ||||||||
\(287\) | 3.88583 | 0.229374 | ||||||||
\(288\) | 4.15942 | 0.245096 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −35.8582 | −2.10567 | ||||||||
\(291\) | −16.3073 | −0.955952 | ||||||||
\(292\) | −30.2043 | −1.76757 | ||||||||
\(293\) | −14.5139 | −0.847910 | −0.423955 | − | 0.905683i | \(-0.639358\pi\) | ||||
−0.423955 | + | 0.905683i | \(0.639358\pi\) | |||||||
\(294\) | 9.67718 | 0.564385 | ||||||||
\(295\) | −0.914706 | −0.0532562 | ||||||||
\(296\) | 11.9370 | 0.693821 | ||||||||
\(297\) | −1.32194 | −0.0767065 | ||||||||
\(298\) | −16.7304 | −0.969166 | ||||||||
\(299\) | −12.7275 | −0.736051 | ||||||||
\(300\) | 6.73392 | 0.388783 | ||||||||
\(301\) | 0.985607 | 0.0568094 | ||||||||
\(302\) | −40.6243 | −2.33766 | ||||||||
\(303\) | 12.5834 | 0.722900 | ||||||||
\(304\) | 0.242126 | 0.0138869 | ||||||||
\(305\) | 15.7044 | 0.899233 | ||||||||
\(306\) | −2.34343 | −0.133965 | ||||||||
\(307\) | −15.7810 | −0.900667 | −0.450334 | − | 0.892860i | \(-0.648695\pi\) | ||||
−0.450334 | + | 0.892860i | \(0.648695\pi\) | |||||||
\(308\) | −7.82029 | −0.445602 | ||||||||
\(309\) | 13.9393 | 0.792977 | ||||||||
\(310\) | 49.8926 | 2.83371 | ||||||||
\(311\) | 17.2449 | 0.977867 | 0.488933 | − | 0.872321i | \(-0.337386\pi\) | ||||
0.488933 | + | 0.872321i | \(0.337386\pi\) | |||||||
\(312\) | −14.7338 | −0.834137 | ||||||||
\(313\) | −1.31450 | −0.0742997 | −0.0371499 | − | 0.999310i | \(-0.511828\pi\) | ||||
−0.0371499 | + | 0.999310i | \(0.511828\pi\) | |||||||
\(314\) | −2.34343 | −0.132247 | ||||||||
\(315\) | 4.45965 | 0.251273 | ||||||||
\(316\) | 18.8637 | 1.06116 | ||||||||
\(317\) | 25.3157 | 1.42187 | 0.710937 | − | 0.703256i | \(-0.248271\pi\) | ||||
0.710937 | + | 0.703256i | \(0.248271\pi\) | |||||||
\(318\) | −2.20506 | −0.123653 | ||||||||
\(319\) | −7.68467 | −0.430259 | ||||||||
\(320\) | −32.0186 | −1.78990 | ||||||||
\(321\) | −20.2486 | −1.13017 | ||||||||
\(322\) | 11.9890 | 0.668123 | ||||||||
\(323\) | 0.200368 | 0.0111488 | ||||||||
\(324\) | 3.49167 | 0.193982 | ||||||||
\(325\) | 8.12878 | 0.450904 | ||||||||
\(326\) | −50.0875 | −2.77409 | ||||||||
\(327\) | 10.7016 | 0.591798 | ||||||||
\(328\) | −8.01732 | −0.442682 | ||||||||
\(329\) | 14.9205 | 0.822595 | ||||||||
\(330\) | 8.15426 | 0.448877 | ||||||||
\(331\) | −8.93826 | −0.491291 | −0.245646 | − | 0.969360i | \(-0.579000\pi\) | ||||
−0.245646 | + | 0.969360i | \(0.579000\pi\) | |||||||
\(332\) | 14.3914 | 0.789828 | ||||||||
\(333\) | −3.41483 | −0.187132 | ||||||||
\(334\) | 52.0731 | 2.84931 | ||||||||
\(335\) | −0.878263 | −0.0479846 | ||||||||
\(336\) | 2.04735 | 0.111692 | ||||||||
\(337\) | −21.3670 | −1.16394 | −0.581968 | − | 0.813212i | \(-0.697717\pi\) | ||||
−0.581968 | + | 0.813212i | \(0.697717\pi\) | |||||||
\(338\) | −11.1680 | −0.607459 | ||||||||
\(339\) | 6.67043 | 0.362288 | ||||||||
\(340\) | 9.19083 | 0.498443 | ||||||||
\(341\) | 10.6924 | 0.579023 | ||||||||
\(342\) | −0.469548 | −0.0253903 | ||||||||
\(343\) | −18.8562 | −1.01814 | ||||||||
\(344\) | −2.03352 | −0.109640 | ||||||||
\(345\) | −7.94831 | −0.427922 | ||||||||
\(346\) | −20.8702 | −1.12199 | ||||||||
\(347\) | −8.11833 | −0.435815 | −0.217907 | − | 0.975969i | \(-0.569923\pi\) | ||||
−0.217907 | + | 0.975969i | \(0.569923\pi\) | |||||||
\(348\) | 20.2977 | 1.08807 | ||||||||
\(349\) | −23.8501 | −1.27667 | −0.638334 | − | 0.769759i | \(-0.720376\pi\) | ||||
−0.638334 | + | 0.769759i | \(0.720376\pi\) | |||||||
\(350\) | −7.65713 | −0.409291 | ||||||||
\(351\) | 4.21493 | 0.224976 | ||||||||
\(352\) | −5.49849 | −0.293071 | ||||||||
\(353\) | 13.0359 | 0.693833 | 0.346916 | − | 0.937896i | \(-0.387229\pi\) | ||||
0.346916 | + | 0.937896i | \(0.387229\pi\) | |||||||
\(354\) | 0.814351 | 0.0432823 | ||||||||
\(355\) | 13.6099 | 0.722340 | ||||||||
\(356\) | 39.0096 | 2.06751 | ||||||||
\(357\) | 1.69426 | 0.0896696 | ||||||||
\(358\) | −48.4224 | −2.55920 | ||||||||
\(359\) | 12.7269 | 0.671698 | 0.335849 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335849 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(360\) | −9.20123 | −0.484947 | ||||||||
\(361\) | −18.9599 | −0.997887 | ||||||||
\(362\) | −25.2365 | −1.32640 | ||||||||
\(363\) | −9.25248 | −0.485629 | ||||||||
\(364\) | 24.9346 | 1.30693 | ||||||||
\(365\) | −22.7697 | −1.19182 | ||||||||
\(366\) | −13.9815 | −0.730823 | ||||||||
\(367\) | −33.8498 | −1.76695 | −0.883473 | − | 0.468482i | \(-0.844801\pi\) | ||||
−0.883473 | + | 0.468482i | \(0.844801\pi\) | |||||||
\(368\) | −3.64893 | −0.190214 | ||||||||
\(369\) | 2.29353 | 0.119397 | ||||||||
\(370\) | 21.0641 | 1.09507 | ||||||||
\(371\) | 1.59421 | 0.0827675 | ||||||||
\(372\) | −28.2420 | −1.46428 | ||||||||
\(373\) | 30.4444 | 1.57635 | 0.788175 | − | 0.615451i | \(-0.211026\pi\) | ||||
0.788175 | + | 0.615451i | \(0.211026\pi\) | |||||||
\(374\) | 3.09787 | 0.160187 | ||||||||
\(375\) | −8.08468 | −0.417491 | ||||||||
\(376\) | −30.7843 | −1.58758 | ||||||||
\(377\) | 24.5022 | 1.26193 | ||||||||
\(378\) | −3.97037 | −0.204214 | ||||||||
\(379\) | −26.8570 | −1.37955 | −0.689775 | − | 0.724024i | \(-0.742291\pi\) | ||||
−0.689775 | + | 0.724024i | \(0.742291\pi\) | |||||||
\(380\) | 1.84155 | 0.0944693 | ||||||||
\(381\) | 17.4233 | 0.892624 | ||||||||
\(382\) | −38.4455 | −1.96704 | ||||||||
\(383\) | 19.4573 | 0.994219 | 0.497110 | − | 0.867688i | \(-0.334395\pi\) | ||||
0.497110 | + | 0.867688i | \(0.334395\pi\) | |||||||
\(384\) | 20.1869 | 1.03016 | ||||||||
\(385\) | −5.89538 | −0.300456 | ||||||||
\(386\) | −23.7224 | −1.20744 | ||||||||
\(387\) | 0.581734 | 0.0295712 | ||||||||
\(388\) | −56.9397 | −2.89068 | ||||||||
\(389\) | −14.8086 | −0.750826 | −0.375413 | − | 0.926858i | \(-0.622499\pi\) | ||||
−0.375413 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(390\) | −25.9995 | −1.31653 | ||||||||
\(391\) | −3.01962 | −0.152709 | ||||||||
\(392\) | 14.4351 | 0.729084 | ||||||||
\(393\) | −6.85121 | −0.345598 | ||||||||
\(394\) | −22.4175 | −1.12938 | ||||||||
\(395\) | 14.2205 | 0.715511 | ||||||||
\(396\) | −4.61576 | −0.231951 | ||||||||
\(397\) | 7.40718 | 0.371756 | 0.185878 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185878 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(398\) | 44.3176 | 2.22144 | ||||||||
\(399\) | 0.339475 | 0.0169950 | ||||||||
\(400\) | 2.33049 | 0.116525 | ||||||||
\(401\) | −20.7838 | −1.03789 | −0.518947 | − | 0.854806i | \(-0.673676\pi\) | ||||
−0.518947 | + | 0.854806i | \(0.673676\pi\) | |||||||
\(402\) | 0.781906 | 0.0389979 | ||||||||
\(403\) | −34.0921 | −1.69825 | ||||||||
\(404\) | 43.9372 | 2.18596 | ||||||||
\(405\) | 2.63222 | 0.130796 | ||||||||
\(406\) | −23.0805 | −1.14547 | ||||||||
\(407\) | 4.51419 | 0.223760 | ||||||||
\(408\) | −3.49562 | −0.173059 | ||||||||
\(409\) | −4.19752 | −0.207554 | −0.103777 | − | 0.994601i | \(-0.533093\pi\) | ||||
−0.103777 | + | 0.994601i | \(0.533093\pi\) | |||||||
\(410\) | −14.1475 | −0.698694 | ||||||||
\(411\) | 10.3764 | 0.511828 | ||||||||
\(412\) | 48.6713 | 2.39786 | ||||||||
\(413\) | −0.588761 | −0.0289710 | ||||||||
\(414\) | 7.07628 | 0.347780 | ||||||||
\(415\) | 10.8490 | 0.532558 | ||||||||
\(416\) | 17.5317 | 0.859562 | ||||||||
\(417\) | 6.74346 | 0.330228 | ||||||||
\(418\) | 0.620713 | 0.0303601 | ||||||||
\(419\) | −26.6237 | −1.30065 | −0.650325 | − | 0.759656i | \(-0.725367\pi\) | ||||
−0.650325 | + | 0.759656i | \(0.725367\pi\) | |||||||
\(420\) | 15.5716 | 0.759817 | ||||||||
\(421\) | 2.43007 | 0.118435 | 0.0592173 | − | 0.998245i | \(-0.481140\pi\) | ||||
0.0592173 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(422\) | −26.0122 | −1.26625 | ||||||||
\(423\) | 8.80652 | 0.428188 | ||||||||
\(424\) | −3.28921 | −0.159738 | ||||||||
\(425\) | 1.92857 | 0.0935493 | ||||||||
\(426\) | −12.1168 | −0.587059 | ||||||||
\(427\) | 10.1083 | 0.489177 | ||||||||
\(428\) | −70.7015 | −3.41749 | ||||||||
\(429\) | −5.57187 | −0.269013 | ||||||||
\(430\) | −3.58838 | −0.173047 | ||||||||
\(431\) | −38.5352 | −1.85618 | −0.928088 | − | 0.372360i | \(-0.878549\pi\) | ||||
−0.928088 | + | 0.372360i | \(0.878549\pi\) | |||||||
\(432\) | 1.20841 | 0.0581394 | ||||||||
\(433\) | −9.47365 | −0.455274 | −0.227637 | − | 0.973746i | \(-0.573100\pi\) | ||||
−0.227637 | + | 0.973746i | \(0.573100\pi\) | |||||||
\(434\) | 32.1140 | 1.54152 | ||||||||
\(435\) | 15.3016 | 0.733655 | ||||||||
\(436\) | 37.3663 | 1.78952 | ||||||||
\(437\) | −0.605036 | −0.0289428 | ||||||||
\(438\) | 20.2716 | 0.968615 | ||||||||
\(439\) | −5.98904 | −0.285841 | −0.142921 | − | 0.989734i | \(-0.545649\pi\) | ||||
−0.142921 | + | 0.989734i | \(0.545649\pi\) | |||||||
\(440\) | 12.1634 | 0.579869 | ||||||||
\(441\) | −4.12949 | −0.196643 | ||||||||
\(442\) | −9.87740 | −0.469820 | ||||||||
\(443\) | −2.36813 | −0.112513 | −0.0562567 | − | 0.998416i | \(-0.517917\pi\) | ||||
−0.0562567 | + | 0.998416i | \(0.517917\pi\) | |||||||
\(444\) | −11.9235 | −0.565862 | ||||||||
\(445\) | 29.4077 | 1.39406 | ||||||||
\(446\) | 27.7139 | 1.31229 | ||||||||
\(447\) | 7.13928 | 0.337676 | ||||||||
\(448\) | −20.6092 | −0.973691 | ||||||||
\(449\) | −7.35402 | −0.347058 | −0.173529 | − | 0.984829i | \(-0.555517\pi\) | ||||
−0.173529 | + | 0.984829i | \(0.555517\pi\) | |||||||
\(450\) | −4.51946 | −0.213050 | ||||||||
\(451\) | −3.03190 | −0.142767 | ||||||||
\(452\) | 23.2909 | 1.09551 | ||||||||
\(453\) | 17.3354 | 0.814488 | ||||||||
\(454\) | 23.6457 | 1.10975 | ||||||||
\(455\) | 18.7971 | 0.881223 | ||||||||
\(456\) | −0.700410 | −0.0327997 | ||||||||
\(457\) | 6.92939 | 0.324143 | 0.162072 | − | 0.986779i | \(-0.448182\pi\) | ||||
0.162072 | + | 0.986779i | \(0.448182\pi\) | |||||||
\(458\) | 6.72559 | 0.314266 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −27.7528 | −1.29398 | ||||||||
\(461\) | −10.3910 | −0.483955 | −0.241978 | − | 0.970282i | \(-0.577796\pi\) | ||||
−0.241978 | + | 0.970282i | \(0.577796\pi\) | |||||||
\(462\) | 5.24858 | 0.244186 | ||||||||
\(463\) | 9.57768 | 0.445113 | 0.222556 | − | 0.974920i | \(-0.428560\pi\) | ||||
0.222556 | + | 0.974920i | \(0.428560\pi\) | |||||||
\(464\) | 7.02469 | 0.326113 | ||||||||
\(465\) | −21.2904 | −0.987320 | ||||||||
\(466\) | −49.3725 | −2.28714 | ||||||||
\(467\) | 14.8538 | 0.687354 | 0.343677 | − | 0.939088i | \(-0.388327\pi\) | ||||
0.343677 | + | 0.939088i | \(0.388327\pi\) | |||||||
\(468\) | 14.7171 | 0.680300 | ||||||||
\(469\) | −0.565304 | −0.0261033 | ||||||||
\(470\) | −54.3223 | −2.50570 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 1.21474 | 0.0559130 | ||||||||
\(473\) | −0.769015 | −0.0353593 | ||||||||
\(474\) | −12.6603 | −0.581509 | ||||||||
\(475\) | 0.386423 | 0.0177303 | ||||||||
\(476\) | 5.91578 | 0.271149 | ||||||||
\(477\) | 0.940952 | 0.0430832 | ||||||||
\(478\) | −63.3881 | −2.89931 | ||||||||
\(479\) | −24.2328 | −1.10723 | −0.553613 | − | 0.832774i | \(-0.686751\pi\) | ||||
−0.553613 | + | 0.832774i | \(0.686751\pi\) | |||||||
\(480\) | 10.9485 | 0.499729 | ||||||||
\(481\) | −14.3933 | −0.656278 | ||||||||
\(482\) | −35.7566 | −1.62867 | ||||||||
\(483\) | −5.11602 | −0.232787 | ||||||||
\(484\) | −32.3066 | −1.46848 | ||||||||
\(485\) | −42.9244 | −1.94910 | ||||||||
\(486\) | −2.34343 | −0.106300 | ||||||||
\(487\) | −33.5072 | −1.51836 | −0.759178 | − | 0.650883i | \(-0.774399\pi\) | ||||
−0.759178 | + | 0.650883i | \(0.774399\pi\) | |||||||
\(488\) | −20.8557 | −0.944093 | ||||||||
\(489\) | 21.3736 | 0.966546 | ||||||||
\(490\) | 25.4724 | 1.15073 | ||||||||
\(491\) | 5.11611 | 0.230887 | 0.115443 | − | 0.993314i | \(-0.463171\pi\) | ||||
0.115443 | + | 0.993314i | \(0.463171\pi\) | |||||||
\(492\) | 8.00825 | 0.361040 | ||||||||
\(493\) | 5.81319 | 0.261813 | ||||||||
\(494\) | −1.97911 | −0.0890446 | ||||||||
\(495\) | −3.47962 | −0.156397 | ||||||||
\(496\) | −9.77407 | −0.438868 | ||||||||
\(497\) | 8.76019 | 0.392948 | ||||||||
\(498\) | −9.65875 | −0.432819 | ||||||||
\(499\) | 17.9381 | 0.803021 | 0.401511 | − | 0.915854i | \(-0.368485\pi\) | ||||
0.401511 | + | 0.915854i | \(0.368485\pi\) | |||||||
\(500\) | −28.2290 | −1.26244 | ||||||||
\(501\) | −22.2209 | −0.992756 | ||||||||
\(502\) | 72.9348 | 3.25524 | ||||||||
\(503\) | −27.3128 | −1.21782 | −0.608909 | − | 0.793240i | \(-0.708393\pi\) | ||||
−0.608909 | + | 0.793240i | \(0.708393\pi\) | |||||||
\(504\) | −5.92248 | −0.263808 | ||||||||
\(505\) | 33.1223 | 1.47392 | ||||||||
\(506\) | −9.35439 | −0.415853 | ||||||||
\(507\) | 4.76566 | 0.211651 | ||||||||
\(508\) | 60.8364 | 2.69918 | ||||||||
\(509\) | 23.1250 | 1.02500 | 0.512499 | − | 0.858688i | \(-0.328720\pi\) | ||||
0.512499 | + | 0.858688i | \(0.328720\pi\) | |||||||
\(510\) | −6.16842 | −0.273142 | ||||||||
\(511\) | −14.6560 | −0.648343 | ||||||||
\(512\) | 13.4745 | 0.595495 | ||||||||
\(513\) | 0.200368 | 0.00884646 | ||||||||
\(514\) | −9.25392 | −0.408173 | ||||||||
\(515\) | 36.6912 | 1.61681 | ||||||||
\(516\) | 2.03122 | 0.0894195 | ||||||||
\(517\) | −11.6417 | −0.512000 | ||||||||
\(518\) | 13.5582 | 0.595711 | ||||||||
\(519\) | 8.90582 | 0.390922 | ||||||||
\(520\) | −38.7826 | −1.70073 | ||||||||
\(521\) | −4.75568 | −0.208350 | −0.104175 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104175 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(522\) | −13.6228 | −0.596254 | ||||||||
\(523\) | −7.81714 | −0.341820 | −0.170910 | − | 0.985287i | \(-0.554671\pi\) | ||||
−0.170910 | + | 0.985287i | \(0.554671\pi\) | |||||||
\(524\) | −23.9221 | −1.04504 | ||||||||
\(525\) | 3.26749 | 0.142605 | ||||||||
\(526\) | −33.0914 | −1.44285 | ||||||||
\(527\) | −8.08840 | −0.352336 | ||||||||
\(528\) | −1.59743 | −0.0695194 | ||||||||
\(529\) | −13.8819 | −0.603560 | ||||||||
\(530\) | −5.80419 | −0.252118 | ||||||||
\(531\) | −0.347504 | −0.0150804 | ||||||||
\(532\) | 1.18533 | 0.0513907 | ||||||||
\(533\) | 9.66709 | 0.418728 | ||||||||
\(534\) | −26.1813 | −1.13298 | ||||||||
\(535\) | −53.2988 | −2.30431 | ||||||||
\(536\) | 1.16634 | 0.0503784 | ||||||||
\(537\) | 20.6630 | 0.891676 | ||||||||
\(538\) | −55.9801 | −2.41347 | ||||||||
\(539\) | 5.45893 | 0.235133 | ||||||||
\(540\) | 9.19083 | 0.395510 | ||||||||
\(541\) | 5.59802 | 0.240678 | 0.120339 | − | 0.992733i | \(-0.461602\pi\) | ||||
0.120339 | + | 0.992733i | \(0.461602\pi\) | |||||||
\(542\) | 41.2014 | 1.76975 | ||||||||
\(543\) | 10.7691 | 0.462145 | ||||||||
\(544\) | 4.15942 | 0.178334 | ||||||||
\(545\) | 28.1688 | 1.20662 | ||||||||
\(546\) | −16.7349 | −0.716186 | ||||||||
\(547\) | 27.8189 | 1.18945 | 0.594725 | − | 0.803929i | \(-0.297261\pi\) | ||||
0.594725 | + | 0.803929i | \(0.297261\pi\) | |||||||
\(548\) | 36.2308 | 1.54770 | ||||||||
\(549\) | 5.96624 | 0.254633 | ||||||||
\(550\) | 5.97444 | 0.254751 | ||||||||
\(551\) | 1.16478 | 0.0496212 | ||||||||
\(552\) | 10.5555 | 0.449270 | ||||||||
\(553\) | 9.15319 | 0.389233 | ||||||||
\(554\) | 38.2336 | 1.62439 | ||||||||
\(555\) | −8.98858 | −0.381544 | ||||||||
\(556\) | 23.5459 | 0.998569 | ||||||||
\(557\) | 19.2020 | 0.813616 | 0.406808 | − | 0.913514i | \(-0.366642\pi\) | ||||
0.406808 | + | 0.913514i | \(0.366642\pi\) | |||||||
\(558\) | 18.9546 | 0.802412 | ||||||||
\(559\) | 2.45197 | 0.103707 | ||||||||
\(560\) | 5.38907 | 0.227730 | ||||||||
\(561\) | −1.32194 | −0.0558122 | ||||||||
\(562\) | −36.4172 | −1.53616 | ||||||||
\(563\) | −27.9107 | −1.17630 | −0.588149 | − | 0.808753i | \(-0.700143\pi\) | ||||
−0.588149 | + | 0.808753i | \(0.700143\pi\) | |||||||
\(564\) | 30.7495 | 1.29479 | ||||||||
\(565\) | 17.5580 | 0.738672 | ||||||||
\(566\) | 12.2922 | 0.516680 | ||||||||
\(567\) | 1.69426 | 0.0711521 | ||||||||
\(568\) | −18.0742 | −0.758375 | ||||||||
\(569\) | −26.9919 | −1.13156 | −0.565780 | − | 0.824556i | \(-0.691425\pi\) | ||||
−0.565780 | + | 0.824556i | \(0.691425\pi\) | |||||||
\(570\) | −1.23595 | −0.0517684 | ||||||||
\(571\) | 5.03627 | 0.210761 | 0.105381 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105381 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(572\) | −19.4551 | −0.813460 | ||||||||
\(573\) | 16.4057 | 0.685356 | ||||||||
\(574\) | −9.10618 | −0.380085 | ||||||||
\(575\) | −5.82355 | −0.242859 | ||||||||
\(576\) | −12.1641 | −0.506839 | ||||||||
\(577\) | −9.76393 | −0.406478 | −0.203239 | − | 0.979129i | \(-0.565147\pi\) | ||||
−0.203239 | + | 0.979129i | \(0.565147\pi\) | |||||||
\(578\) | −2.34343 | −0.0974739 | ||||||||
\(579\) | 10.1229 | 0.420694 | ||||||||
\(580\) | 53.4280 | 2.21848 | ||||||||
\(581\) | 6.98310 | 0.289708 | ||||||||
\(582\) | 38.2151 | 1.58407 | ||||||||
\(583\) | −1.24388 | −0.0515162 | ||||||||
\(584\) | 30.2385 | 1.25128 | ||||||||
\(585\) | 11.0946 | 0.458706 | ||||||||
\(586\) | 34.0123 | 1.40503 | ||||||||
\(587\) | −28.0390 | −1.15729 | −0.578647 | − | 0.815578i | \(-0.696419\pi\) | ||||
−0.578647 | + | 0.815578i | \(0.696419\pi\) | |||||||
\(588\) | −14.4188 | −0.594622 | ||||||||
\(589\) | −1.62066 | −0.0667780 | ||||||||
\(590\) | 2.14355 | 0.0882485 | ||||||||
\(591\) | 9.56610 | 0.393497 | ||||||||
\(592\) | −4.12650 | −0.169598 | ||||||||
\(593\) | 20.0367 | 0.822810 | 0.411405 | − | 0.911453i | \(-0.365038\pi\) | ||||
0.411405 | + | 0.911453i | \(0.365038\pi\) | |||||||
\(594\) | 3.09787 | 0.127107 | ||||||||
\(595\) | 4.45965 | 0.182828 | ||||||||
\(596\) | 24.9280 | 1.02109 | ||||||||
\(597\) | −18.9114 | −0.773992 | ||||||||
\(598\) | 29.8260 | 1.21968 | ||||||||
\(599\) | 2.39580 | 0.0978898 | 0.0489449 | − | 0.998801i | \(-0.484414\pi\) | ||||
0.0489449 | + | 0.998801i | \(0.484414\pi\) | |||||||
\(600\) | −6.74154 | −0.275222 | ||||||||
\(601\) | 6.14181 | 0.250530 | 0.125265 | − | 0.992123i | \(-0.460022\pi\) | ||||
0.125265 | + | 0.992123i | \(0.460022\pi\) | |||||||
\(602\) | −2.30970 | −0.0941364 | ||||||||
\(603\) | −0.333659 | −0.0135876 | ||||||||
\(604\) | 60.5294 | 2.46291 | ||||||||
\(605\) | −24.3545 | −0.990153 | ||||||||
\(606\) | −29.4884 | −1.19788 | ||||||||
\(607\) | −31.3457 | −1.27228 | −0.636141 | − | 0.771573i | \(-0.719470\pi\) | ||||
−0.636141 | + | 0.771573i | \(0.719470\pi\) | |||||||
\(608\) | 0.833415 | 0.0337994 | ||||||||
\(609\) | 9.84904 | 0.399103 | ||||||||
\(610\) | −36.8022 | −1.49008 | ||||||||
\(611\) | 37.1189 | 1.50167 | ||||||||
\(612\) | 3.49167 | 0.141142 | ||||||||
\(613\) | 29.5265 | 1.19257 | 0.596283 | − | 0.802775i | \(-0.296644\pi\) | ||||
0.596283 | + | 0.802775i | \(0.296644\pi\) | |||||||
\(614\) | 36.9816 | 1.49246 | ||||||||
\(615\) | 6.03708 | 0.243438 | ||||||||
\(616\) | 7.82914 | 0.315445 | ||||||||
\(617\) | −2.38840 | −0.0961535 | −0.0480767 | − | 0.998844i | \(-0.515309\pi\) | ||||
−0.0480767 | + | 0.998844i | \(0.515309\pi\) | |||||||
\(618\) | −32.6657 | −1.31401 | ||||||||
\(619\) | 20.6316 | 0.829255 | 0.414627 | − | 0.909991i | \(-0.363912\pi\) | ||||
0.414627 | + | 0.909991i | \(0.363912\pi\) | |||||||
\(620\) | −74.3391 | −2.98553 | ||||||||
\(621\) | −3.01962 | −0.121173 | ||||||||
\(622\) | −40.4122 | −1.62038 | ||||||||
\(623\) | 18.9286 | 0.758358 | ||||||||
\(624\) | 5.09335 | 0.203897 | ||||||||
\(625\) | −30.9235 | −1.23694 | ||||||||
\(626\) | 3.08043 | 0.123119 | ||||||||
\(627\) | −0.264874 | −0.0105780 | ||||||||
\(628\) | 3.49167 | 0.139333 | ||||||||
\(629\) | −3.41483 | −0.136158 | ||||||||
\(630\) | −10.4509 | −0.416373 | ||||||||
\(631\) | 43.2137 | 1.72031 | 0.860154 | − | 0.510034i | \(-0.170367\pi\) | ||||
0.860154 | + | 0.510034i | \(0.170367\pi\) | |||||||
\(632\) | −18.8850 | −0.751206 | ||||||||
\(633\) | 11.1000 | 0.441187 | ||||||||
\(634\) | −59.3257 | −2.35612 | ||||||||
\(635\) | 45.8620 | 1.81998 | ||||||||
\(636\) | 3.28549 | 0.130278 | ||||||||
\(637\) | −17.4055 | −0.689633 | ||||||||
\(638\) | 18.0085 | 0.712963 | ||||||||
\(639\) | 5.17052 | 0.204543 | ||||||||
\(640\) | 53.1364 | 2.10040 | ||||||||
\(641\) | −39.6883 | −1.56759 | −0.783797 | − | 0.621017i | \(-0.786720\pi\) | ||||
−0.783797 | + | 0.621017i | \(0.786720\pi\) | |||||||
\(642\) | 47.4513 | 1.87275 | ||||||||
\(643\) | −47.1409 | −1.85905 | −0.929527 | − | 0.368754i | \(-0.879784\pi\) | ||||
−0.929527 | + | 0.368754i | \(0.879784\pi\) | |||||||
\(644\) | −17.8634 | −0.703918 | ||||||||
\(645\) | 1.53125 | 0.0602929 | ||||||||
\(646\) | −0.469548 | −0.0184741 | ||||||||
\(647\) | −9.83543 | −0.386671 | −0.193335 | − | 0.981133i | \(-0.561931\pi\) | ||||
−0.193335 | + | 0.981133i | \(0.561931\pi\) | |||||||
\(648\) | −3.49562 | −0.137321 | ||||||||
\(649\) | 0.459378 | 0.0180322 | ||||||||
\(650\) | −19.0492 | −0.747173 | ||||||||
\(651\) | −13.7038 | −0.537095 | ||||||||
\(652\) | 74.6294 | 2.92271 | ||||||||
\(653\) | 41.3384 | 1.61769 | 0.808847 | − | 0.588018i | \(-0.200092\pi\) | ||||
0.808847 | + | 0.588018i | \(0.200092\pi\) | |||||||
\(654\) | −25.0784 | −0.980642 | ||||||||
\(655\) | −18.0339 | −0.704641 | ||||||||
\(656\) | 2.77152 | 0.108210 | ||||||||
\(657\) | −8.65040 | −0.337484 | ||||||||
\(658\) | −34.9652 | −1.36309 | ||||||||
\(659\) | −32.6987 | −1.27376 | −0.636880 | − | 0.770963i | \(-0.719775\pi\) | ||||
−0.636880 | + | 0.770963i | \(0.719775\pi\) | |||||||
\(660\) | −12.1497 | −0.472926 | ||||||||
\(661\) | 18.6623 | 0.725879 | 0.362939 | − | 0.931813i | \(-0.381773\pi\) | ||||
0.362939 | + | 0.931813i | \(0.381773\pi\) | |||||||
\(662\) | 20.9462 | 0.814097 | ||||||||
\(663\) | 4.21493 | 0.163694 | ||||||||
\(664\) | −14.4076 | −0.559125 | ||||||||
\(665\) | 0.893571 | 0.0346512 | ||||||||
\(666\) | 8.00242 | 0.310088 | ||||||||
\(667\) | −17.5536 | −0.679680 | ||||||||
\(668\) | −77.5879 | −3.00197 | ||||||||
\(669\) | −11.8262 | −0.457228 | ||||||||
\(670\) | 2.05815 | 0.0795132 | ||||||||
\(671\) | −7.88699 | −0.304474 | ||||||||
\(672\) | 7.04713 | 0.271849 | ||||||||
\(673\) | −6.58598 | −0.253871 | −0.126935 | − | 0.991911i | \(-0.540514\pi\) | ||||
−0.126935 | + | 0.991911i | \(0.540514\pi\) | |||||||
\(674\) | 50.0721 | 1.92871 | ||||||||
\(675\) | 1.92857 | 0.0742306 | ||||||||
\(676\) | 16.6401 | 0.640004 | ||||||||
\(677\) | 23.7157 | 0.911467 | 0.455734 | − | 0.890116i | \(-0.349377\pi\) | ||||
0.455734 | + | 0.890116i | \(0.349377\pi\) | |||||||
\(678\) | −15.6317 | −0.600332 | ||||||||
\(679\) | −27.6288 | −1.06030 | ||||||||
\(680\) | −9.20123 | −0.352851 | ||||||||
\(681\) | −10.0902 | −0.386657 | ||||||||
\(682\) | −25.0568 | −0.959474 | ||||||||
\(683\) | 16.5588 | 0.633606 | 0.316803 | − | 0.948491i | \(-0.397391\pi\) | ||||
0.316803 | + | 0.948491i | \(0.397391\pi\) | |||||||
\(684\) | 0.699618 | 0.0267506 | ||||||||
\(685\) | 27.3128 | 1.04357 | ||||||||
\(686\) | 44.1882 | 1.68712 | ||||||||
\(687\) | −2.86997 | −0.109496 | ||||||||
\(688\) | 0.702970 | 0.0268005 | ||||||||
\(689\) | 3.96605 | 0.151095 | ||||||||
\(690\) | 18.6263 | 0.709091 | ||||||||
\(691\) | −46.2055 | −1.75774 | −0.878869 | − | 0.477063i | \(-0.841701\pi\) | ||||
−0.878869 | + | 0.477063i | \(0.841701\pi\) | |||||||
\(692\) | 31.0962 | 1.18210 | ||||||||
\(693\) | −2.23970 | −0.0850792 | ||||||||
\(694\) | 19.0248 | 0.722170 | ||||||||
\(695\) | 17.7502 | 0.673305 | ||||||||
\(696\) | −20.3207 | −0.770254 | ||||||||
\(697\) | 2.29353 | 0.0868738 | ||||||||
\(698\) | 55.8911 | 2.11551 | ||||||||
\(699\) | 21.0685 | 0.796883 | ||||||||
\(700\) | 11.4090 | 0.431219 | ||||||||
\(701\) | 17.3662 | 0.655910 | 0.327955 | − | 0.944693i | \(-0.393640\pi\) | ||||
0.327955 | + | 0.944693i | \(0.393640\pi\) | |||||||
\(702\) | −9.87740 | −0.372799 | ||||||||
\(703\) | −0.684223 | −0.0258060 | ||||||||
\(704\) | 16.0802 | 0.606046 | ||||||||
\(705\) | 23.1807 | 0.873035 | ||||||||
\(706\) | −30.5488 | −1.14972 | ||||||||
\(707\) | 21.3196 | 0.801805 | ||||||||
\(708\) | −1.21337 | −0.0456012 | ||||||||
\(709\) | −16.4449 | −0.617600 | −0.308800 | − | 0.951127i | \(-0.599927\pi\) | ||||
−0.308800 | + | 0.951127i | \(0.599927\pi\) | |||||||
\(710\) | −31.8939 | −1.19696 | ||||||||
\(711\) | 5.40248 | 0.202609 | ||||||||
\(712\) | −39.0538 | −1.46360 | ||||||||
\(713\) | 24.4239 | 0.914683 | ||||||||
\(714\) | −3.97037 | −0.148588 | ||||||||
\(715\) | −14.6664 | −0.548492 | ||||||||
\(716\) | 72.1485 | 2.69631 | ||||||||
\(717\) | 27.0493 | 1.01017 | ||||||||
\(718\) | −29.8245 | −1.11304 | ||||||||
\(719\) | 1.35352 | 0.0504779 | 0.0252389 | − | 0.999681i | \(-0.491965\pi\) | ||||
0.0252389 | + | 0.999681i | \(0.491965\pi\) | |||||||
\(720\) | 3.18078 | 0.118541 | ||||||||
\(721\) | 23.6167 | 0.879531 | ||||||||
\(722\) | 44.4311 | 1.65355 | ||||||||
\(723\) | 15.2582 | 0.567459 | ||||||||
\(724\) | 37.6020 | 1.39747 | ||||||||
\(725\) | 11.2111 | 0.416371 | ||||||||
\(726\) | 21.6826 | 0.804715 | ||||||||
\(727\) | 34.9133 | 1.29486 | 0.647431 | − | 0.762124i | \(-0.275844\pi\) | ||||
0.647431 | + | 0.762124i | \(0.275844\pi\) | |||||||
\(728\) | −24.9628 | −0.925184 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 53.3593 | 1.97491 | ||||||||
\(731\) | 0.581734 | 0.0215162 | ||||||||
\(732\) | 20.8321 | 0.769977 | ||||||||
\(733\) | −33.8932 | −1.25187 | −0.625937 | − | 0.779874i | \(-0.715283\pi\) | ||||
−0.625937 | + | 0.779874i | \(0.715283\pi\) | |||||||
\(734\) | 79.3247 | 2.92793 | ||||||||
\(735\) | −10.8697 | −0.400936 | ||||||||
\(736\) | −12.5599 | −0.462964 | ||||||||
\(737\) | 0.441076 | 0.0162472 | ||||||||
\(738\) | −5.37474 | −0.197847 | ||||||||
\(739\) | −21.7263 | −0.799215 | −0.399608 | − | 0.916686i | \(-0.630854\pi\) | ||||
−0.399608 | + | 0.916686i | \(0.630854\pi\) | |||||||
\(740\) | −31.3851 | −1.15374 | ||||||||
\(741\) | 0.844537 | 0.0310249 | ||||||||
\(742\) | −3.73593 | −0.137150 | ||||||||
\(743\) | −6.63705 | −0.243490 | −0.121745 | − | 0.992561i | \(-0.538849\pi\) | ||||
−0.121745 | + | 0.992561i | \(0.538849\pi\) | |||||||
\(744\) | 28.2740 | 1.03657 | ||||||||
\(745\) | 18.7921 | 0.688490 | ||||||||
\(746\) | −71.3443 | −2.61210 | ||||||||
\(747\) | 4.12163 | 0.150803 | ||||||||
\(748\) | −4.61576 | −0.168769 | ||||||||
\(749\) | −34.3064 | −1.25353 | ||||||||
\(750\) | 18.9459 | 0.691806 | ||||||||
\(751\) | 4.82655 | 0.176123 | 0.0880617 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880617 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(752\) | 10.6418 | 0.388068 | ||||||||
\(753\) | −31.1231 | −1.13419 | ||||||||
\(754\) | −57.4192 | −2.09108 | ||||||||
\(755\) | 45.6305 | 1.66066 | ||||||||
\(756\) | 5.91578 | 0.215155 | ||||||||
\(757\) | 26.5789 | 0.966028 | 0.483014 | − | 0.875613i | \(-0.339542\pi\) | ||||
0.483014 | + | 0.875613i | \(0.339542\pi\) | |||||||
\(758\) | 62.9374 | 2.28599 | ||||||||
\(759\) | 3.99175 | 0.144891 | ||||||||
\(760\) | −1.84363 | −0.0668755 | ||||||||
\(761\) | 16.2352 | 0.588526 | 0.294263 | − | 0.955724i | \(-0.404926\pi\) | ||||
0.294263 | + | 0.955724i | \(0.404926\pi\) | |||||||
\(762\) | −40.8303 | −1.47913 | ||||||||
\(763\) | 18.1312 | 0.656394 | ||||||||
\(764\) | 57.2831 | 2.07243 | ||||||||
\(765\) | 2.63222 | 0.0951680 | ||||||||
\(766\) | −45.5967 | −1.64748 | ||||||||
\(767\) | −1.46471 | −0.0528875 | ||||||||
\(768\) | −22.9785 | −0.829164 | ||||||||
\(769\) | −24.8260 | −0.895249 | −0.447624 | − | 0.894222i | \(-0.647730\pi\) | ||||
−0.447624 | + | 0.894222i | \(0.647730\pi\) | |||||||
\(770\) | 13.8154 | 0.497873 | ||||||||
\(771\) | 3.94888 | 0.142215 | ||||||||
\(772\) | 35.3459 | 1.27213 | ||||||||
\(773\) | 3.20794 | 0.115382 | 0.0576909 | − | 0.998334i | \(-0.481626\pi\) | ||||
0.0576909 | + | 0.998334i | \(0.481626\pi\) | |||||||
\(774\) | −1.36325 | −0.0490011 | ||||||||
\(775\) | −15.5990 | −0.560334 | ||||||||
\(776\) | 57.0042 | 2.04633 | ||||||||
\(777\) | −5.78560 | −0.207557 | ||||||||
\(778\) | 34.7029 | 1.24416 | ||||||||
\(779\) | 0.459550 | 0.0164651 | ||||||||
\(780\) | 38.7387 | 1.38707 | ||||||||
\(781\) | −6.83510 | −0.244579 | ||||||||
\(782\) | 7.07628 | 0.253047 | ||||||||
\(783\) | 5.81319 | 0.207746 | ||||||||
\(784\) | −4.99010 | −0.178218 | ||||||||
\(785\) | 2.63222 | 0.0939479 | ||||||||
\(786\) | 16.0553 | 0.572675 | ||||||||
\(787\) | 27.9067 | 0.994766 | 0.497383 | − | 0.867531i | \(-0.334294\pi\) | ||||
0.497383 | + | 0.867531i | \(0.334294\pi\) | |||||||
\(788\) | 33.4016 | 1.18988 | ||||||||
\(789\) | 14.1209 | 0.502718 | ||||||||
\(790\) | −33.3248 | −1.18564 | ||||||||
\(791\) | 11.3014 | 0.401833 | ||||||||
\(792\) | 4.62098 | 0.164200 | ||||||||
\(793\) | 25.1473 | 0.893007 | ||||||||
\(794\) | −17.3582 | −0.616020 | ||||||||
\(795\) | 2.47679 | 0.0878427 | ||||||||
\(796\) | −66.0323 | −2.34045 | ||||||||
\(797\) | 35.3877 | 1.25350 | 0.626749 | − | 0.779222i | \(-0.284385\pi\) | ||||
0.626749 | + | 0.779222i | \(0.284385\pi\) | |||||||
\(798\) | −0.795535 | −0.0281617 | ||||||||
\(799\) | 8.80652 | 0.311552 | ||||||||
\(800\) | 8.02173 | 0.283611 | ||||||||
\(801\) | 11.1722 | 0.394751 | ||||||||
\(802\) | 48.7055 | 1.71985 | ||||||||
\(803\) | 11.4353 | 0.403542 | ||||||||
\(804\) | −1.16503 | −0.0410873 | ||||||||
\(805\) | −13.4665 | −0.474631 | ||||||||
\(806\) | 79.8924 | 2.81409 | ||||||||
\(807\) | 23.8881 | 0.840901 | ||||||||
\(808\) | −43.9869 | −1.54745 | ||||||||
\(809\) | −15.1711 | −0.533388 | −0.266694 | − | 0.963781i | \(-0.585931\pi\) | ||||
−0.266694 | + | 0.963781i | \(0.585931\pi\) | |||||||
\(810\) | −6.16842 | −0.216736 | ||||||||
\(811\) | −40.8498 | −1.43443 | −0.717216 | − | 0.696851i | \(-0.754584\pi\) | ||||
−0.717216 | + | 0.696851i | \(0.754584\pi\) | |||||||
\(812\) | 34.3896 | 1.20684 | ||||||||
\(813\) | −17.5817 | −0.616616 | ||||||||
\(814\) | −10.5787 | −0.370783 | ||||||||
\(815\) | 56.2598 | 1.97070 | ||||||||
\(816\) | 1.20841 | 0.0423026 | ||||||||
\(817\) | 0.116561 | 0.00407795 | ||||||||
\(818\) | 9.83659 | 0.343928 | ||||||||
\(819\) | 7.14118 | 0.249533 | ||||||||
\(820\) | 21.0795 | 0.736127 | ||||||||
\(821\) | −53.0547 | −1.85162 | −0.925811 | − | 0.377987i | \(-0.876616\pi\) | ||||
−0.925811 | + | 0.377987i | \(0.876616\pi\) | |||||||
\(822\) | −24.3163 | −0.848128 | ||||||||
\(823\) | 20.5826 | 0.717463 | 0.358732 | − | 0.933441i | \(-0.383209\pi\) | ||||
0.358732 | + | 0.933441i | \(0.383209\pi\) | |||||||
\(824\) | −48.7263 | −1.69746 | ||||||||
\(825\) | −2.54944 | −0.0887602 | ||||||||
\(826\) | 1.37972 | 0.0480066 | ||||||||
\(827\) | −23.5729 | −0.819710 | −0.409855 | − | 0.912151i | \(-0.634421\pi\) | ||||
−0.409855 | + | 0.912151i | \(0.634421\pi\) | |||||||
\(828\) | −10.5435 | −0.366413 | ||||||||
\(829\) | 21.1595 | 0.734900 | 0.367450 | − | 0.930043i | \(-0.380231\pi\) | ||||
0.367450 | + | 0.930043i | \(0.380231\pi\) | |||||||
\(830\) | −25.4239 | −0.882477 | ||||||||
\(831\) | −16.3152 | −0.565968 | ||||||||
\(832\) | −51.2710 | −1.77750 | ||||||||
\(833\) | −4.12949 | −0.143078 | ||||||||
\(834\) | −15.8028 | −0.547207 | ||||||||
\(835\) | −58.4902 | −2.02414 | ||||||||
\(836\) | −0.924850 | −0.0319866 | ||||||||
\(837\) | −8.08840 | −0.279576 | ||||||||
\(838\) | 62.3907 | 2.15525 | ||||||||
\(839\) | −31.9427 | −1.10278 | −0.551392 | − | 0.834246i | \(-0.685903\pi\) | ||||
−0.551392 | + | 0.834246i | \(0.685903\pi\) | |||||||
\(840\) | −15.5892 | −0.537880 | ||||||||
\(841\) | 4.79318 | 0.165282 | ||||||||
\(842\) | −5.69471 | −0.196253 | ||||||||
\(843\) | 15.5401 | 0.535230 | ||||||||
\(844\) | 38.7577 | 1.33409 | ||||||||
\(845\) | 12.5443 | 0.431536 | ||||||||
\(846\) | −20.6375 | −0.709531 | ||||||||
\(847\) | −15.6761 | −0.538637 | ||||||||
\(848\) | 1.13705 | 0.0390465 | ||||||||
\(849\) | −5.24539 | −0.180021 | ||||||||
\(850\) | −4.51946 | −0.155016 | ||||||||
\(851\) | 10.3115 | 0.353474 | ||||||||
\(852\) | 18.0537 | 0.618511 | ||||||||
\(853\) | 9.13920 | 0.312920 | 0.156460 | − | 0.987684i | \(-0.449992\pi\) | ||||
0.156460 | + | 0.987684i | \(0.449992\pi\) | |||||||
\(854\) | −23.6882 | −0.810593 | ||||||||
\(855\) | 0.527412 | 0.0180371 | ||||||||
\(856\) | 70.7815 | 2.41926 | ||||||||
\(857\) | −27.9302 | −0.954079 | −0.477040 | − | 0.878882i | \(-0.658290\pi\) | ||||
−0.477040 | + | 0.878882i | \(0.658290\pi\) | |||||||
\(858\) | 13.0573 | 0.445769 | ||||||||
\(859\) | 29.9001 | 1.02018 | 0.510090 | − | 0.860121i | \(-0.329612\pi\) | ||||
0.510090 | + | 0.860121i | \(0.329612\pi\) | |||||||
\(860\) | 5.34661 | 0.182318 | ||||||||
\(861\) | 3.88583 | 0.132429 | ||||||||
\(862\) | 90.3046 | 3.07579 | ||||||||
\(863\) | 10.0814 | 0.343173 | 0.171587 | − | 0.985169i | \(-0.445111\pi\) | ||||
0.171587 | + | 0.985169i | \(0.445111\pi\) | |||||||
\(864\) | 4.15942 | 0.141506 | ||||||||
\(865\) | 23.4420 | 0.797054 | ||||||||
\(866\) | 22.2008 | 0.754415 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −47.8492 | −1.62411 | ||||||||
\(869\) | −7.14174 | −0.242267 | ||||||||
\(870\) | −35.8582 | −1.21571 | ||||||||
\(871\) | −1.40635 | −0.0476523 | ||||||||
\(872\) | −37.4086 | −1.26681 | ||||||||
\(873\) | −16.3073 | −0.551919 | ||||||||
\(874\) | 1.41786 | 0.0479598 | ||||||||
\(875\) | −13.6975 | −0.463061 | ||||||||
\(876\) | −30.2043 | −1.02051 | ||||||||
\(877\) | 40.4003 | 1.36422 | 0.682110 | − | 0.731249i | \(-0.261062\pi\) | ||||
0.682110 | + | 0.731249i | \(0.261062\pi\) | |||||||
\(878\) | 14.0349 | 0.473655 | ||||||||
\(879\) | −14.5139 | −0.489541 | ||||||||
\(880\) | −4.20479 | −0.141744 | ||||||||
\(881\) | 27.0800 | 0.912350 | 0.456175 | − | 0.889890i | \(-0.349219\pi\) | ||||
0.456175 | + | 0.889890i | \(0.349219\pi\) | |||||||
\(882\) | 9.67718 | 0.325848 | ||||||||
\(883\) | −1.84057 | −0.0619403 | −0.0309701 | − | 0.999520i | \(-0.509860\pi\) | ||||
−0.0309701 | + | 0.999520i | \(0.509860\pi\) | |||||||
\(884\) | 14.7171 | 0.494991 | ||||||||
\(885\) | −0.914706 | −0.0307475 | ||||||||
\(886\) | 5.54956 | 0.186441 | ||||||||
\(887\) | −8.19905 | −0.275297 | −0.137649 | − | 0.990481i | \(-0.543954\pi\) | ||||
−0.137649 | + | 0.990481i | \(0.543954\pi\) | |||||||
\(888\) | 11.9370 | 0.400578 | ||||||||
\(889\) | 29.5196 | 0.990055 | ||||||||
\(890\) | −68.9149 | −2.31003 | ||||||||
\(891\) | −1.32194 | −0.0442865 | ||||||||
\(892\) | −41.2933 | −1.38260 | ||||||||
\(893\) | 1.76454 | 0.0590482 | ||||||||
\(894\) | −16.7304 | −0.559548 | ||||||||
\(895\) | 54.3896 | 1.81804 | ||||||||
\(896\) | 34.2019 | 1.14260 | ||||||||
\(897\) | −12.7275 | −0.424959 | ||||||||
\(898\) | 17.2336 | 0.575094 | ||||||||
\(899\) | −47.0194 | −1.56819 | ||||||||
\(900\) | 6.73392 | 0.224464 | ||||||||
\(901\) | 0.940952 | 0.0313477 | ||||||||
\(902\) | 7.10506 | 0.236573 | ||||||||
\(903\) | 0.985607 | 0.0327989 | ||||||||
\(904\) | −23.3173 | −0.775522 | ||||||||
\(905\) | 28.3465 | 0.942270 | ||||||||
\(906\) | −40.6243 | −1.34965 | ||||||||
\(907\) | 54.7096 | 1.81660 | 0.908302 | − | 0.418316i | \(-0.137380\pi\) | ||||
0.908302 | + | 0.418316i | \(0.137380\pi\) | |||||||
\(908\) | −35.2316 | −1.16920 | ||||||||
\(909\) | 12.5834 | 0.417366 | ||||||||
\(910\) | −44.0498 | −1.46024 | ||||||||
\(911\) | −21.7271 | −0.719852 | −0.359926 | − | 0.932981i | \(-0.617198\pi\) | ||||
−0.359926 | + | 0.932981i | \(0.617198\pi\) | |||||||
\(912\) | 0.242126 | 0.00801758 | ||||||||
\(913\) | −5.44853 | −0.180320 | ||||||||
\(914\) | −16.2385 | −0.537123 | ||||||||
\(915\) | 15.7044 | 0.519173 | ||||||||
\(916\) | −10.0210 | −0.331103 | ||||||||
\(917\) | −11.6077 | −0.383320 | ||||||||
\(918\) | −2.34343 | −0.0773447 | ||||||||
\(919\) | 53.7107 | 1.77175 | 0.885875 | − | 0.463923i | \(-0.153559\pi\) | ||||
0.885875 | + | 0.463923i | \(0.153559\pi\) | |||||||
\(920\) | 27.7842 | 0.916019 | ||||||||
\(921\) | −15.7810 | −0.520000 | ||||||||
\(922\) | 24.3505 | 0.801941 | ||||||||
\(923\) | 21.7934 | 0.717338 | ||||||||
\(924\) | −7.82029 | −0.257269 | ||||||||
\(925\) | −6.58573 | −0.216538 | ||||||||
\(926\) | −22.4446 | −0.737576 | ||||||||
\(927\) | 13.9393 | 0.457825 | ||||||||
\(928\) | 24.1795 | 0.793732 | ||||||||
\(929\) | −21.9632 | −0.720591 | −0.360295 | − | 0.932838i | \(-0.617324\pi\) | ||||
−0.360295 | + | 0.932838i | \(0.617324\pi\) | |||||||
\(930\) | 49.8926 | 1.63604 | ||||||||
\(931\) | −0.827418 | −0.0271175 | ||||||||
\(932\) | 73.5641 | 2.40967 | ||||||||
\(933\) | 17.2449 | 0.564572 | ||||||||
\(934\) | −34.8090 | −1.13898 | ||||||||
\(935\) | −3.47962 | −0.113796 | ||||||||
\(936\) | −14.7338 | −0.481589 | ||||||||
\(937\) | −34.3407 | −1.12186 | −0.560931 | − | 0.827863i | \(-0.689557\pi\) | ||||
−0.560931 | + | 0.827863i | \(0.689557\pi\) | |||||||
\(938\) | 1.32475 | 0.0432546 | ||||||||
\(939\) | −1.31450 | −0.0428970 | ||||||||
\(940\) | 80.9392 | 2.63995 | ||||||||
\(941\) | −37.7683 | −1.23121 | −0.615607 | − | 0.788054i | \(-0.711089\pi\) | ||||
−0.615607 | + | 0.788054i | \(0.711089\pi\) | |||||||
\(942\) | −2.34343 | −0.0763531 | ||||||||
\(943\) | −6.92561 | −0.225529 | ||||||||
\(944\) | −0.419925 | −0.0136674 | ||||||||
\(945\) | 4.45965 | 0.145073 | ||||||||
\(946\) | 1.80213 | 0.0585924 | ||||||||
\(947\) | −25.9868 | −0.844457 | −0.422229 | − | 0.906489i | \(-0.638752\pi\) | ||||
−0.422229 | + | 0.906489i | \(0.638752\pi\) | |||||||
\(948\) | 18.8637 | 0.612664 | ||||||||
\(949\) | −36.4608 | −1.18357 | ||||||||
\(950\) | −0.905556 | −0.0293801 | ||||||||
\(951\) | 25.3157 | 0.820919 | ||||||||
\(952\) | −5.92248 | −0.191949 | ||||||||
\(953\) | −15.7304 | −0.509559 | −0.254779 | − | 0.966999i | \(-0.582003\pi\) | ||||
−0.254779 | + | 0.966999i | \(0.582003\pi\) | |||||||
\(954\) | −2.20506 | −0.0713913 | ||||||||
\(955\) | 43.1833 | 1.39738 | ||||||||
\(956\) | 94.4471 | 3.05464 | ||||||||
\(957\) | −7.68467 | −0.248410 | ||||||||
\(958\) | 56.7879 | 1.83473 | ||||||||
\(959\) | 17.5802 | 0.567695 | ||||||||
\(960\) | −32.0186 | −1.03340 | ||||||||
\(961\) | 34.4222 | 1.11039 | ||||||||
\(962\) | 33.7297 | 1.08749 | ||||||||
\(963\) | −20.2486 | −0.652503 | ||||||||
\(964\) | 53.2766 | 1.71592 | ||||||||
\(965\) | 26.6457 | 0.857757 | ||||||||
\(966\) | 11.9890 | 0.385741 | ||||||||
\(967\) | 50.1371 | 1.61230 | 0.806150 | − | 0.591711i | \(-0.201547\pi\) | ||||
0.806150 | + | 0.591711i | \(0.201547\pi\) | |||||||
\(968\) | 32.3432 | 1.03955 | ||||||||
\(969\) | 0.200368 | 0.00643674 | ||||||||
\(970\) | 100.590 | 3.22976 | ||||||||
\(971\) | 38.1545 | 1.22443 | 0.612217 | − | 0.790689i | \(-0.290278\pi\) | ||||
0.612217 | + | 0.790689i | \(0.290278\pi\) | |||||||
\(972\) | 3.49167 | 0.111995 | ||||||||
\(973\) | 11.4251 | 0.366273 | ||||||||
\(974\) | 78.5218 | 2.51600 | ||||||||
\(975\) | 8.12878 | 0.260329 | ||||||||
\(976\) | 7.20963 | 0.230775 | ||||||||
\(977\) | 23.0721 | 0.738141 | 0.369071 | − | 0.929401i | \(-0.379676\pi\) | ||||
0.369071 | + | 0.929401i | \(0.379676\pi\) | |||||||
\(978\) | −50.0875 | −1.60162 | ||||||||
\(979\) | −14.7690 | −0.472018 | ||||||||
\(980\) | −37.9535 | −1.21238 | ||||||||
\(981\) | 10.7016 | 0.341675 | ||||||||
\(982\) | −11.9892 | −0.382592 | ||||||||
\(983\) | −40.6354 | −1.29607 | −0.648034 | − | 0.761612i | \(-0.724408\pi\) | ||||
−0.648034 | + | 0.761612i | \(0.724408\pi\) | |||||||
\(984\) | −8.01732 | −0.255583 | ||||||||
\(985\) | 25.1801 | 0.802303 | ||||||||
\(986\) | −13.6228 | −0.433839 | ||||||||
\(987\) | 14.9205 | 0.474925 | ||||||||
\(988\) | 2.94884 | 0.0938152 | ||||||||
\(989\) | −1.75662 | −0.0558572 | ||||||||
\(990\) | 8.15426 | 0.259159 | ||||||||
\(991\) | −38.1690 | −1.21248 | −0.606239 | − | 0.795282i | \(-0.707323\pi\) | ||||
−0.606239 | + | 0.795282i | \(0.707323\pi\) | |||||||
\(992\) | −33.6431 | −1.06817 | ||||||||
\(993\) | −8.93826 | −0.283647 | ||||||||
\(994\) | −20.5289 | −0.651137 | ||||||||
\(995\) | −49.7789 | −1.57810 | ||||||||
\(996\) | 14.3914 | 0.456008 | ||||||||
\(997\) | −53.7168 | −1.70123 | −0.850615 | − | 0.525789i | \(-0.823770\pi\) | ||||
−0.850615 | + | 0.525789i | \(0.823770\pi\) | |||||||
\(998\) | −42.0368 | −1.33065 | ||||||||
\(999\) | −3.41483 | −0.108041 |
(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 | 8007.2.a.i.1.5 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.i.1.5 | ✓ | 63 | 1.1 | even | 1 | trivial |