Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(1,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, 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("731.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + 7816 x^{11} - 19517 x^{10} - 13527 x^{9} + 40173 x^{8} + 8942 x^{7} - 41911 x^{6} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.86082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86082 | −1.31580 | −0.657900 | − | 0.753105i | \(-0.728555\pi\) | ||||
−0.657900 | + | 0.753105i | \(0.728555\pi\) | |||||||
\(3\) | 2.21039 | 1.27617 | 0.638085 | − | 0.769966i | \(-0.279727\pi\) | ||||
0.638085 | + | 0.769966i | \(0.279727\pi\) | |||||||
\(4\) | 1.46266 | 0.731331 | ||||||||
\(5\) | 1.15323 | 0.515739 | 0.257869 | − | 0.966180i | \(-0.416980\pi\) | ||||
0.257869 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(6\) | −4.11315 | −1.67919 | ||||||||
\(7\) | 2.59124 | 0.979396 | 0.489698 | − | 0.871892i | \(-0.337107\pi\) | ||||
0.489698 | + | 0.871892i | \(0.337107\pi\) | |||||||
\(8\) | 0.999890 | 0.353514 | ||||||||
\(9\) | 1.88583 | 0.628611 | ||||||||
\(10\) | −2.14595 | −0.678609 | ||||||||
\(11\) | 3.01488 | 0.909019 | 0.454510 | − | 0.890742i | \(-0.349814\pi\) | ||||
0.454510 | + | 0.890742i | \(0.349814\pi\) | |||||||
\(12\) | 3.23306 | 0.933303 | ||||||||
\(13\) | 0.191815 | 0.0531999 | 0.0265999 | − | 0.999646i | \(-0.491532\pi\) | ||||
0.0265999 | + | 0.999646i | \(0.491532\pi\) | |||||||
\(14\) | −4.82184 | −1.28869 | ||||||||
\(15\) | 2.54908 | 0.658170 | ||||||||
\(16\) | −4.78594 | −1.19649 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −3.50920 | −0.827126 | ||||||||
\(19\) | 2.18357 | 0.500945 | 0.250473 | − | 0.968124i | \(-0.419414\pi\) | ||||
0.250473 | + | 0.968124i | \(0.419414\pi\) | |||||||
\(20\) | 1.68678 | 0.377176 | ||||||||
\(21\) | 5.72765 | 1.24988 | ||||||||
\(22\) | −5.61015 | −1.19609 | ||||||||
\(23\) | 1.33614 | 0.278603 | 0.139302 | − | 0.990250i | \(-0.455514\pi\) | ||||
0.139302 | + | 0.990250i | \(0.455514\pi\) | |||||||
\(24\) | 2.21015 | 0.451145 | ||||||||
\(25\) | −3.67007 | −0.734014 | ||||||||
\(26\) | −0.356934 | −0.0700005 | ||||||||
\(27\) | −2.46275 | −0.473956 | ||||||||
\(28\) | 3.79011 | 0.716263 | ||||||||
\(29\) | −8.81546 | −1.63699 | −0.818495 | − | 0.574513i | \(-0.805191\pi\) | ||||
−0.818495 | + | 0.574513i | \(0.805191\pi\) | |||||||
\(30\) | −4.74339 | −0.866021 | ||||||||
\(31\) | 4.89012 | 0.878291 | 0.439146 | − | 0.898416i | \(-0.355281\pi\) | ||||
0.439146 | + | 0.898416i | \(0.355281\pi\) | |||||||
\(32\) | 6.90601 | 1.22082 | ||||||||
\(33\) | 6.66406 | 1.16006 | ||||||||
\(34\) | −1.86082 | −0.319129 | ||||||||
\(35\) | 2.98829 | 0.505113 | ||||||||
\(36\) | 2.75834 | 0.459723 | ||||||||
\(37\) | 11.1412 | 1.83161 | 0.915804 | − | 0.401624i | \(-0.131554\pi\) | ||||
0.915804 | + | 0.401624i | \(0.131554\pi\) | |||||||
\(38\) | −4.06324 | −0.659144 | ||||||||
\(39\) | 0.423986 | 0.0678921 | ||||||||
\(40\) | 1.15310 | 0.182321 | ||||||||
\(41\) | −3.89827 | −0.608808 | −0.304404 | − | 0.952543i | \(-0.598457\pi\) | ||||
−0.304404 | + | 0.952543i | \(0.598457\pi\) | |||||||
\(42\) | −10.6582 | −1.64459 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 4.40975 | 0.664794 | ||||||||
\(45\) | 2.17479 | 0.324199 | ||||||||
\(46\) | −2.48631 | −0.366587 | ||||||||
\(47\) | −4.39530 | −0.641120 | −0.320560 | − | 0.947228i | \(-0.603871\pi\) | ||||
−0.320560 | + | 0.947228i | \(0.603871\pi\) | |||||||
\(48\) | −10.5788 | −1.52692 | ||||||||
\(49\) | −0.285478 | −0.0407826 | ||||||||
\(50\) | 6.82935 | 0.965816 | ||||||||
\(51\) | 2.21039 | 0.309517 | ||||||||
\(52\) | 0.280561 | 0.0389067 | ||||||||
\(53\) | −12.1032 | −1.66251 | −0.831254 | − | 0.555893i | \(-0.812376\pi\) | ||||
−0.831254 | + | 0.555893i | \(0.812376\pi\) | |||||||
\(54\) | 4.58274 | 0.623632 | ||||||||
\(55\) | 3.47684 | 0.468816 | ||||||||
\(56\) | 2.59095 | 0.346231 | ||||||||
\(57\) | 4.82654 | 0.639291 | ||||||||
\(58\) | 16.4040 | 2.15395 | ||||||||
\(59\) | 3.10264 | 0.403930 | 0.201965 | − | 0.979393i | \(-0.435267\pi\) | ||||
0.201965 | + | 0.979393i | \(0.435267\pi\) | |||||||
\(60\) | 3.72845 | 0.481341 | ||||||||
\(61\) | −6.37651 | −0.816429 | −0.408215 | − | 0.912886i | \(-0.633848\pi\) | ||||
−0.408215 | + | 0.912886i | \(0.633848\pi\) | |||||||
\(62\) | −9.09965 | −1.15566 | ||||||||
\(63\) | 4.88664 | 0.615659 | ||||||||
\(64\) | −3.27898 | −0.409873 | ||||||||
\(65\) | 0.221206 | 0.0274372 | ||||||||
\(66\) | −12.4006 | −1.52641 | ||||||||
\(67\) | 10.6005 | 1.29505 | 0.647526 | − | 0.762043i | \(-0.275804\pi\) | ||||
0.647526 | + | 0.762043i | \(0.275804\pi\) | |||||||
\(68\) | 1.46266 | 0.177374 | ||||||||
\(69\) | 2.95338 | 0.355545 | ||||||||
\(70\) | −5.56067 | −0.664627 | ||||||||
\(71\) | 2.29264 | 0.272086 | 0.136043 | − | 0.990703i | \(-0.456561\pi\) | ||||
0.136043 | + | 0.990703i | \(0.456561\pi\) | |||||||
\(72\) | 1.88562 | 0.222223 | ||||||||
\(73\) | 7.91542 | 0.926430 | 0.463215 | − | 0.886246i | \(-0.346696\pi\) | ||||
0.463215 | + | 0.886246i | \(0.346696\pi\) | |||||||
\(74\) | −20.7319 | −2.41003 | ||||||||
\(75\) | −8.11229 | −0.936726 | ||||||||
\(76\) | 3.19383 | 0.366357 | ||||||||
\(77\) | 7.81227 | 0.890290 | ||||||||
\(78\) | −0.788963 | −0.0893325 | ||||||||
\(79\) | 1.86796 | 0.210162 | 0.105081 | − | 0.994464i | \(-0.466490\pi\) | ||||
0.105081 | + | 0.994464i | \(0.466490\pi\) | |||||||
\(80\) | −5.51928 | −0.617074 | ||||||||
\(81\) | −11.1011 | −1.23346 | ||||||||
\(82\) | 7.25400 | 0.801070 | ||||||||
\(83\) | 0.538979 | 0.0591607 | 0.0295803 | − | 0.999562i | \(-0.490583\pi\) | ||||
0.0295803 | + | 0.999562i | \(0.490583\pi\) | |||||||
\(84\) | 8.37763 | 0.914074 | ||||||||
\(85\) | 1.15323 | 0.125085 | ||||||||
\(86\) | 1.86082 | 0.200658 | ||||||||
\(87\) | −19.4856 | −2.08908 | ||||||||
\(88\) | 3.01454 | 0.321352 | ||||||||
\(89\) | −2.83673 | −0.300692 | −0.150346 | − | 0.988633i | \(-0.548039\pi\) | ||||
−0.150346 | + | 0.988633i | \(0.548039\pi\) | |||||||
\(90\) | −4.04690 | −0.426581 | ||||||||
\(91\) | 0.497038 | 0.0521038 | ||||||||
\(92\) | 1.95431 | 0.203751 | ||||||||
\(93\) | 10.8091 | 1.12085 | ||||||||
\(94\) | 8.17887 | 0.843586 | ||||||||
\(95\) | 2.51815 | 0.258357 | ||||||||
\(96\) | 15.2650 | 1.55798 | ||||||||
\(97\) | 16.5114 | 1.67648 | 0.838240 | − | 0.545301i | \(-0.183585\pi\) | ||||
0.838240 | + | 0.545301i | \(0.183585\pi\) | |||||||
\(98\) | 0.531225 | 0.0536618 | ||||||||
\(99\) | 5.68555 | 0.571419 | ||||||||
\(100\) | −5.36807 | −0.536807 | ||||||||
\(101\) | 16.7864 | 1.67031 | 0.835154 | − | 0.550017i | \(-0.185379\pi\) | ||||
0.835154 | + | 0.550017i | \(0.185379\pi\) | |||||||
\(102\) | −4.11315 | −0.407262 | ||||||||
\(103\) | 8.37286 | 0.825003 | 0.412501 | − | 0.910957i | \(-0.364655\pi\) | ||||
0.412501 | + | 0.910957i | \(0.364655\pi\) | |||||||
\(104\) | 0.191794 | 0.0188069 | ||||||||
\(105\) | 6.60528 | 0.644610 | ||||||||
\(106\) | 22.5220 | 2.18753 | ||||||||
\(107\) | 3.40454 | 0.329129 | 0.164565 | − | 0.986366i | \(-0.447378\pi\) | ||||
0.164565 | + | 0.986366i | \(0.447378\pi\) | |||||||
\(108\) | −3.60217 | −0.346619 | ||||||||
\(109\) | −2.52873 | −0.242208 | −0.121104 | − | 0.992640i | \(-0.538643\pi\) | ||||
−0.121104 | + | 0.992640i | \(0.538643\pi\) | |||||||
\(110\) | −6.46978 | −0.616869 | ||||||||
\(111\) | 24.6265 | 2.33744 | ||||||||
\(112\) | −12.4015 | −1.17183 | ||||||||
\(113\) | −15.5311 | −1.46104 | −0.730520 | − | 0.682891i | \(-0.760722\pi\) | ||||
−0.730520 | + | 0.682891i | \(0.760722\pi\) | |||||||
\(114\) | −8.98134 | −0.841180 | ||||||||
\(115\) | 1.54087 | 0.143687 | ||||||||
\(116\) | −12.8941 | −1.19718 | ||||||||
\(117\) | 0.361731 | 0.0334420 | ||||||||
\(118\) | −5.77347 | −0.531491 | ||||||||
\(119\) | 2.59124 | 0.237539 | ||||||||
\(120\) | 2.54880 | 0.232673 | ||||||||
\(121\) | −1.91052 | −0.173684 | ||||||||
\(122\) | 11.8656 | 1.07426 | ||||||||
\(123\) | −8.61671 | −0.776943 | ||||||||
\(124\) | 7.15259 | 0.642322 | ||||||||
\(125\) | −9.99855 | −0.894298 | ||||||||
\(126\) | −9.09318 | −0.810085 | ||||||||
\(127\) | 8.65498 | 0.768005 | 0.384003 | − | 0.923332i | \(-0.374545\pi\) | ||||
0.384003 | + | 0.923332i | \(0.374545\pi\) | |||||||
\(128\) | −7.71042 | −0.681511 | ||||||||
\(129\) | −2.21039 | −0.194614 | ||||||||
\(130\) | −0.411625 | −0.0361019 | ||||||||
\(131\) | 11.4313 | 0.998760 | 0.499380 | − | 0.866383i | \(-0.333561\pi\) | ||||
0.499380 | + | 0.866383i | \(0.333561\pi\) | |||||||
\(132\) | 9.74727 | 0.848391 | ||||||||
\(133\) | 5.65815 | 0.490624 | ||||||||
\(134\) | −19.7256 | −1.70403 | ||||||||
\(135\) | −2.84011 | −0.244437 | ||||||||
\(136\) | 0.999890 | 0.0857398 | ||||||||
\(137\) | −11.7956 | −1.00777 | −0.503883 | − | 0.863772i | \(-0.668096\pi\) | ||||
−0.503883 | + | 0.863772i | \(0.668096\pi\) | |||||||
\(138\) | −5.49572 | −0.467827 | ||||||||
\(139\) | −3.10983 | −0.263772 | −0.131886 | − | 0.991265i | \(-0.542103\pi\) | ||||
−0.131886 | + | 0.991265i | \(0.542103\pi\) | |||||||
\(140\) | 4.37085 | 0.369405 | ||||||||
\(141\) | −9.71533 | −0.818179 | ||||||||
\(142\) | −4.26619 | −0.358011 | ||||||||
\(143\) | 0.578298 | 0.0483597 | ||||||||
\(144\) | −9.02549 | −0.752124 | ||||||||
\(145\) | −10.1662 | −0.844259 | ||||||||
\(146\) | −14.7292 | −1.21900 | ||||||||
\(147\) | −0.631019 | −0.0520456 | ||||||||
\(148\) | 16.2959 | 1.33951 | ||||||||
\(149\) | −7.03103 | −0.576004 | −0.288002 | − | 0.957630i | \(-0.592991\pi\) | ||||
−0.288002 | + | 0.957630i | \(0.592991\pi\) | |||||||
\(150\) | 15.0955 | 1.23255 | ||||||||
\(151\) | −11.5008 | −0.935920 | −0.467960 | − | 0.883750i | \(-0.655011\pi\) | ||||
−0.467960 | + | 0.883750i | \(0.655011\pi\) | |||||||
\(152\) | 2.18333 | 0.177091 | ||||||||
\(153\) | 1.88583 | 0.152460 | ||||||||
\(154\) | −14.5372 | −1.17144 | ||||||||
\(155\) | 5.63941 | 0.452969 | ||||||||
\(156\) | 0.620149 | 0.0496516 | ||||||||
\(157\) | 8.25034 | 0.658449 | 0.329224 | − | 0.944252i | \(-0.393213\pi\) | ||||
0.329224 | + | 0.944252i | \(0.393213\pi\) | |||||||
\(158\) | −3.47594 | −0.276531 | ||||||||
\(159\) | −26.7529 | −2.12164 | ||||||||
\(160\) | 7.96420 | 0.629625 | ||||||||
\(161\) | 3.46225 | 0.272863 | ||||||||
\(162\) | 20.6572 | 1.62299 | ||||||||
\(163\) | −17.3187 | −1.35650 | −0.678251 | − | 0.734830i | \(-0.737262\pi\) | ||||
−0.678251 | + | 0.734830i | \(0.737262\pi\) | |||||||
\(164\) | −5.70186 | −0.445240 | ||||||||
\(165\) | 7.68517 | 0.598290 | ||||||||
\(166\) | −1.00295 | −0.0778436 | ||||||||
\(167\) | −12.6615 | −0.979776 | −0.489888 | − | 0.871785i | \(-0.662962\pi\) | ||||
−0.489888 | + | 0.871785i | \(0.662962\pi\) | |||||||
\(168\) | 5.72702 | 0.441849 | ||||||||
\(169\) | −12.9632 | −0.997170 | ||||||||
\(170\) | −2.14595 | −0.164587 | ||||||||
\(171\) | 4.11785 | 0.314899 | ||||||||
\(172\) | −1.46266 | −0.111527 | ||||||||
\(173\) | −19.4401 | −1.47800 | −0.739001 | − | 0.673705i | \(-0.764702\pi\) | ||||
−0.739001 | + | 0.673705i | \(0.764702\pi\) | |||||||
\(174\) | 36.2593 | 2.74881 | ||||||||
\(175\) | −9.51003 | −0.718890 | ||||||||
\(176\) | −14.4290 | −1.08763 | ||||||||
\(177\) | 6.85806 | 0.515483 | ||||||||
\(178\) | 5.27864 | 0.395651 | ||||||||
\(179\) | −25.0226 | −1.87028 | −0.935139 | − | 0.354282i | \(-0.884725\pi\) | ||||
−0.935139 | + | 0.354282i | \(0.884725\pi\) | |||||||
\(180\) | 3.18099 | 0.237097 | ||||||||
\(181\) | −17.5185 | −1.30214 | −0.651072 | − | 0.759016i | \(-0.725680\pi\) | ||||
−0.651072 | + | 0.759016i | \(0.725680\pi\) | |||||||
\(182\) | −0.924901 | −0.0685582 | ||||||||
\(183\) | −14.0946 | −1.04190 | ||||||||
\(184\) | 1.33599 | 0.0984903 | ||||||||
\(185\) | 12.8484 | 0.944631 | ||||||||
\(186\) | −20.1138 | −1.47481 | ||||||||
\(187\) | 3.01488 | 0.220470 | ||||||||
\(188\) | −6.42884 | −0.468871 | ||||||||
\(189\) | −6.38157 | −0.464191 | ||||||||
\(190\) | −4.68583 | −0.339946 | ||||||||
\(191\) | 21.9856 | 1.59082 | 0.795411 | − | 0.606071i | \(-0.207255\pi\) | ||||
0.795411 | + | 0.606071i | \(0.207255\pi\) | |||||||
\(192\) | −7.24784 | −0.523068 | ||||||||
\(193\) | −0.291360 | −0.0209726 | −0.0104863 | − | 0.999945i | \(-0.503338\pi\) | ||||
−0.0104863 | + | 0.999945i | \(0.503338\pi\) | |||||||
\(194\) | −30.7248 | −2.20591 | ||||||||
\(195\) | 0.488952 | 0.0350146 | ||||||||
\(196\) | −0.417559 | −0.0298256 | ||||||||
\(197\) | 17.9480 | 1.27875 | 0.639373 | − | 0.768897i | \(-0.279194\pi\) | ||||
0.639373 | + | 0.768897i | \(0.279194\pi\) | |||||||
\(198\) | −10.5798 | −0.751874 | ||||||||
\(199\) | −7.63630 | −0.541323 | −0.270662 | − | 0.962675i | \(-0.587242\pi\) | ||||
−0.270662 | + | 0.962675i | \(0.587242\pi\) | |||||||
\(200\) | −3.66966 | −0.259484 | ||||||||
\(201\) | 23.4312 | 1.65271 | ||||||||
\(202\) | −31.2365 | −2.19779 | ||||||||
\(203\) | −22.8430 | −1.60326 | ||||||||
\(204\) | 3.23306 | 0.226359 | ||||||||
\(205\) | −4.49559 | −0.313986 | ||||||||
\(206\) | −15.5804 | −1.08554 | ||||||||
\(207\) | 2.51973 | 0.175133 | ||||||||
\(208\) | −0.918015 | −0.0636529 | ||||||||
\(209\) | 6.58319 | 0.455369 | ||||||||
\(210\) | −12.2913 | −0.848178 | ||||||||
\(211\) | 2.88473 | 0.198593 | 0.0992965 | − | 0.995058i | \(-0.468341\pi\) | ||||
0.0992965 | + | 0.995058i | \(0.468341\pi\) | |||||||
\(212\) | −17.7030 | −1.21584 | ||||||||
\(213\) | 5.06762 | 0.347228 | ||||||||
\(214\) | −6.33525 | −0.433068 | ||||||||
\(215\) | −1.15323 | −0.0786494 | ||||||||
\(216\) | −2.46248 | −0.167550 | ||||||||
\(217\) | 12.6715 | 0.860195 | ||||||||
\(218\) | 4.70551 | 0.318698 | ||||||||
\(219\) | 17.4962 | 1.18228 | ||||||||
\(220\) | 5.08544 | 0.342860 | ||||||||
\(221\) | 0.191815 | 0.0129029 | ||||||||
\(222\) | −45.8256 | −3.07561 | ||||||||
\(223\) | −7.16709 | −0.479944 | −0.239972 | − | 0.970780i | \(-0.577138\pi\) | ||||
−0.239972 | + | 0.970780i | \(0.577138\pi\) | |||||||
\(224\) | 17.8951 | 1.19567 | ||||||||
\(225\) | −6.92113 | −0.461409 | ||||||||
\(226\) | 28.9006 | 1.92244 | ||||||||
\(227\) | −9.36637 | −0.621668 | −0.310834 | − | 0.950464i | \(-0.600608\pi\) | ||||
−0.310834 | + | 0.950464i | \(0.600608\pi\) | |||||||
\(228\) | 7.05961 | 0.467534 | ||||||||
\(229\) | −5.96945 | −0.394473 | −0.197236 | − | 0.980356i | \(-0.563197\pi\) | ||||
−0.197236 | + | 0.980356i | \(0.563197\pi\) | |||||||
\(230\) | −2.86728 | −0.189063 | ||||||||
\(231\) | 17.2682 | 1.13616 | ||||||||
\(232\) | −8.81449 | −0.578700 | ||||||||
\(233\) | 0.474582 | 0.0310909 | 0.0155455 | − | 0.999879i | \(-0.495052\pi\) | ||||
0.0155455 | + | 0.999879i | \(0.495052\pi\) | |||||||
\(234\) | −0.673117 | −0.0440030 | ||||||||
\(235\) | −5.06878 | −0.330650 | ||||||||
\(236\) | 4.53812 | 0.295407 | ||||||||
\(237\) | 4.12892 | 0.268202 | ||||||||
\(238\) | −4.82184 | −0.312553 | ||||||||
\(239\) | 4.97411 | 0.321748 | 0.160874 | − | 0.986975i | \(-0.448569\pi\) | ||||
0.160874 | + | 0.986975i | \(0.448569\pi\) | |||||||
\(240\) | −12.1998 | −0.787491 | ||||||||
\(241\) | −7.55048 | −0.486369 | −0.243185 | − | 0.969980i | \(-0.578192\pi\) | ||||
−0.243185 | + | 0.969980i | \(0.578192\pi\) | |||||||
\(242\) | 3.55514 | 0.228533 | ||||||||
\(243\) | −17.1496 | −1.10015 | ||||||||
\(244\) | −9.32669 | −0.597080 | ||||||||
\(245\) | −0.329221 | −0.0210332 | ||||||||
\(246\) | 16.0342 | 1.02230 | ||||||||
\(247\) | 0.418841 | 0.0266502 | ||||||||
\(248\) | 4.88958 | 0.310489 | ||||||||
\(249\) | 1.19136 | 0.0754991 | ||||||||
\(250\) | 18.6055 | 1.17672 | ||||||||
\(251\) | −8.98211 | −0.566946 | −0.283473 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283473 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(252\) | 7.14751 | 0.450251 | ||||||||
\(253\) | 4.02828 | 0.253256 | ||||||||
\(254\) | −16.1054 | −1.01054 | ||||||||
\(255\) | 2.54908 | 0.159630 | ||||||||
\(256\) | 20.9057 | 1.30661 | ||||||||
\(257\) | −17.0074 | −1.06089 | −0.530445 | − | 0.847719i | \(-0.677975\pi\) | ||||
−0.530445 | + | 0.847719i | \(0.677975\pi\) | |||||||
\(258\) | 4.11315 | 0.256073 | ||||||||
\(259\) | 28.8696 | 1.79387 | ||||||||
\(260\) | 0.323550 | 0.0200657 | ||||||||
\(261\) | −16.6245 | −1.02903 | ||||||||
\(262\) | −21.2717 | −1.31417 | ||||||||
\(263\) | −0.191449 | −0.0118052 | −0.00590262 | − | 0.999983i | \(-0.501879\pi\) | ||||
−0.00590262 | + | 0.999983i | \(0.501879\pi\) | |||||||
\(264\) | 6.66332 | 0.410099 | ||||||||
\(265\) | −13.9578 | −0.857419 | ||||||||
\(266\) | −10.5288 | −0.645563 | ||||||||
\(267\) | −6.27028 | −0.383735 | ||||||||
\(268\) | 15.5049 | 0.947113 | ||||||||
\(269\) | 12.2886 | 0.749246 | 0.374623 | − | 0.927177i | \(-0.377772\pi\) | ||||
0.374623 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(270\) | 5.28494 | 0.321631 | ||||||||
\(271\) | 23.4369 | 1.42369 | 0.711845 | − | 0.702336i | \(-0.247860\pi\) | ||||
0.711845 | + | 0.702336i | \(0.247860\pi\) | |||||||
\(272\) | −4.78594 | −0.290190 | ||||||||
\(273\) | 1.09865 | 0.0664933 | ||||||||
\(274\) | 21.9495 | 1.32602 | ||||||||
\(275\) | −11.0648 | −0.667233 | ||||||||
\(276\) | 4.31980 | 0.260021 | ||||||||
\(277\) | −4.42361 | −0.265789 | −0.132894 | − | 0.991130i | \(-0.542427\pi\) | ||||
−0.132894 | + | 0.991130i | \(0.542427\pi\) | |||||||
\(278\) | 5.78684 | 0.347071 | ||||||||
\(279\) | 9.22194 | 0.552103 | ||||||||
\(280\) | 2.98796 | 0.178565 | ||||||||
\(281\) | 28.2876 | 1.68750 | 0.843749 | − | 0.536738i | \(-0.180344\pi\) | ||||
0.843749 | + | 0.536738i | \(0.180344\pi\) | |||||||
\(282\) | 18.0785 | 1.07656 | ||||||||
\(283\) | 2.71894 | 0.161624 | 0.0808120 | − | 0.996729i | \(-0.474249\pi\) | ||||
0.0808120 | + | 0.996729i | \(0.474249\pi\) | |||||||
\(284\) | 3.35335 | 0.198985 | ||||||||
\(285\) | 5.56610 | 0.329707 | ||||||||
\(286\) | −1.07611 | −0.0636318 | ||||||||
\(287\) | −10.1014 | −0.596264 | ||||||||
\(288\) | 13.0236 | 0.767422 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 18.9176 | 1.11088 | ||||||||
\(291\) | 36.4967 | 2.13947 | ||||||||
\(292\) | 11.5776 | 0.677527 | ||||||||
\(293\) | −6.67166 | −0.389763 | −0.194881 | − | 0.980827i | \(-0.562432\pi\) | ||||
−0.194881 | + | 0.980827i | \(0.562432\pi\) | |||||||
\(294\) | 1.17422 | 0.0684816 | ||||||||
\(295\) | 3.57805 | 0.208322 | ||||||||
\(296\) | 11.1400 | 0.647500 | ||||||||
\(297\) | −7.42488 | −0.430835 | ||||||||
\(298\) | 13.0835 | 0.757907 | ||||||||
\(299\) | 0.256291 | 0.0148217 | ||||||||
\(300\) | −11.8655 | −0.685057 | ||||||||
\(301\) | −2.59124 | −0.149357 | ||||||||
\(302\) | 21.4009 | 1.23148 | ||||||||
\(303\) | 37.1045 | 2.13160 | ||||||||
\(304\) | −10.4504 | −0.599374 | ||||||||
\(305\) | −7.35357 | −0.421064 | ||||||||
\(306\) | −3.50920 | −0.200608 | ||||||||
\(307\) | 12.8275 | 0.732105 | 0.366052 | − | 0.930594i | \(-0.380709\pi\) | ||||
0.366052 | + | 0.930594i | \(0.380709\pi\) | |||||||
\(308\) | 11.4267 | 0.651097 | ||||||||
\(309\) | 18.5073 | 1.05284 | ||||||||
\(310\) | −10.4940 | −0.596017 | ||||||||
\(311\) | −23.8066 | −1.34995 | −0.674975 | − | 0.737840i | \(-0.735846\pi\) | ||||
−0.674975 | + | 0.737840i | \(0.735846\pi\) | |||||||
\(312\) | 0.423939 | 0.0240008 | ||||||||
\(313\) | −3.55619 | −0.201008 | −0.100504 | − | 0.994937i | \(-0.532046\pi\) | ||||
−0.100504 | + | 0.994937i | \(0.532046\pi\) | |||||||
\(314\) | −15.3524 | −0.866388 | ||||||||
\(315\) | 5.63541 | 0.317519 | ||||||||
\(316\) | 2.73219 | 0.153698 | ||||||||
\(317\) | −26.7591 | −1.50294 | −0.751471 | − | 0.659766i | \(-0.770655\pi\) | ||||
−0.751471 | + | 0.659766i | \(0.770655\pi\) | |||||||
\(318\) | 49.7824 | 2.79166 | ||||||||
\(319\) | −26.5775 | −1.48806 | ||||||||
\(320\) | −3.78141 | −0.211387 | ||||||||
\(321\) | 7.52537 | 0.420025 | ||||||||
\(322\) | −6.44263 | −0.359034 | ||||||||
\(323\) | 2.18357 | 0.121497 | ||||||||
\(324\) | −16.2372 | −0.902067 | ||||||||
\(325\) | −0.703974 | −0.0390495 | ||||||||
\(326\) | 32.2270 | 1.78489 | ||||||||
\(327\) | −5.58948 | −0.309099 | ||||||||
\(328\) | −3.89784 | −0.215222 | ||||||||
\(329\) | −11.3893 | −0.627911 | ||||||||
\(330\) | −14.3007 | −0.787230 | ||||||||
\(331\) | 11.5361 | 0.634082 | 0.317041 | − | 0.948412i | \(-0.397311\pi\) | ||||
0.317041 | + | 0.948412i | \(0.397311\pi\) | |||||||
\(332\) | 0.788345 | 0.0432661 | ||||||||
\(333\) | 21.0105 | 1.15137 | ||||||||
\(334\) | 23.5608 | 1.28919 | ||||||||
\(335\) | 12.2247 | 0.667909 | ||||||||
\(336\) | −27.4122 | −1.49546 | ||||||||
\(337\) | 13.1860 | 0.718289 | 0.359144 | − | 0.933282i | \(-0.383069\pi\) | ||||
0.359144 | + | 0.933282i | \(0.383069\pi\) | |||||||
\(338\) | 24.1222 | 1.31208 | ||||||||
\(339\) | −34.3297 | −1.86454 | ||||||||
\(340\) | 1.68678 | 0.0914786 | ||||||||
\(341\) | 14.7431 | 0.798384 | ||||||||
\(342\) | −7.66258 | −0.414345 | ||||||||
\(343\) | −18.8784 | −1.01934 | ||||||||
\(344\) | −0.999890 | −0.0539104 | ||||||||
\(345\) | 3.40592 | 0.183369 | ||||||||
\(346\) | 36.1745 | 1.94476 | ||||||||
\(347\) | −3.19155 | −0.171332 | −0.0856658 | − | 0.996324i | \(-0.527302\pi\) | ||||
−0.0856658 | + | 0.996324i | \(0.527302\pi\) | |||||||
\(348\) | −28.5009 | −1.52781 | ||||||||
\(349\) | 28.5816 | 1.52994 | 0.764969 | − | 0.644067i | \(-0.222754\pi\) | ||||
0.764969 | + | 0.644067i | \(0.222754\pi\) | |||||||
\(350\) | 17.6965 | 0.945916 | ||||||||
\(351\) | −0.472392 | −0.0252144 | ||||||||
\(352\) | 20.8208 | 1.10975 | ||||||||
\(353\) | −35.4420 | −1.88639 | −0.943193 | − | 0.332244i | \(-0.892194\pi\) | ||||
−0.943193 | + | 0.332244i | \(0.892194\pi\) | |||||||
\(354\) | −12.7616 | −0.678273 | ||||||||
\(355\) | 2.64393 | 0.140325 | ||||||||
\(356\) | −4.14917 | −0.219906 | ||||||||
\(357\) | 5.72765 | 0.303140 | ||||||||
\(358\) | 46.5626 | 2.46091 | ||||||||
\(359\) | 8.26077 | 0.435987 | 0.217993 | − | 0.975950i | \(-0.430049\pi\) | ||||
0.217993 | + | 0.975950i | \(0.430049\pi\) | |||||||
\(360\) | 2.17455 | 0.114609 | ||||||||
\(361\) | −14.2320 | −0.749054 | ||||||||
\(362\) | 32.5989 | 1.71336 | ||||||||
\(363\) | −4.22300 | −0.221650 | ||||||||
\(364\) | 0.727000 | 0.0381051 | ||||||||
\(365\) | 9.12828 | 0.477796 | ||||||||
\(366\) | 26.2276 | 1.37094 | ||||||||
\(367\) | −30.7382 | −1.60452 | −0.802261 | − | 0.596974i | \(-0.796370\pi\) | ||||
−0.802261 | + | 0.596974i | \(0.796370\pi\) | |||||||
\(368\) | −6.39467 | −0.333345 | ||||||||
\(369\) | −7.35149 | −0.382703 | ||||||||
\(370\) | −23.9086 | −1.24295 | ||||||||
\(371\) | −31.3624 | −1.62825 | ||||||||
\(372\) | 15.8100 | 0.819712 | ||||||||
\(373\) | 4.17451 | 0.216148 | 0.108074 | − | 0.994143i | \(-0.465532\pi\) | ||||
0.108074 | + | 0.994143i | \(0.465532\pi\) | |||||||
\(374\) | −5.61015 | −0.290094 | ||||||||
\(375\) | −22.1007 | −1.14128 | ||||||||
\(376\) | −4.39481 | −0.226645 | ||||||||
\(377\) | −1.69094 | −0.0870877 | ||||||||
\(378\) | 11.8750 | 0.610783 | ||||||||
\(379\) | −30.5234 | −1.56788 | −0.783942 | − | 0.620834i | \(-0.786794\pi\) | ||||
−0.783942 | + | 0.620834i | \(0.786794\pi\) | |||||||
\(380\) | 3.68320 | 0.188944 | ||||||||
\(381\) | 19.1309 | 0.980106 | ||||||||
\(382\) | −40.9113 | −2.09320 | ||||||||
\(383\) | 22.6816 | 1.15897 | 0.579487 | − | 0.814982i | \(-0.303253\pi\) | ||||
0.579487 | + | 0.814982i | \(0.303253\pi\) | |||||||
\(384\) | −17.0430 | −0.869724 | ||||||||
\(385\) | 9.00931 | 0.459157 | ||||||||
\(386\) | 0.542170 | 0.0275957 | ||||||||
\(387\) | −1.88583 | −0.0958622 | ||||||||
\(388\) | 24.1506 | 1.22606 | ||||||||
\(389\) | −3.56215 | −0.180608 | −0.0903040 | − | 0.995914i | \(-0.528784\pi\) | ||||
−0.0903040 | + | 0.995914i | \(0.528784\pi\) | |||||||
\(390\) | −0.909853 | −0.0460722 | ||||||||
\(391\) | 1.33614 | 0.0675713 | ||||||||
\(392\) | −0.285447 | −0.0144173 | ||||||||
\(393\) | 25.2677 | 1.27459 | ||||||||
\(394\) | −33.3981 | −1.68257 | ||||||||
\(395\) | 2.15418 | 0.108388 | ||||||||
\(396\) | 8.31604 | 0.417897 | ||||||||
\(397\) | −2.35072 | −0.117979 | −0.0589897 | − | 0.998259i | \(-0.518788\pi\) | ||||
−0.0589897 | + | 0.998259i | \(0.518788\pi\) | |||||||
\(398\) | 14.2098 | 0.712273 | ||||||||
\(399\) | 12.5067 | 0.626120 | ||||||||
\(400\) | 17.5647 | 0.878237 | ||||||||
\(401\) | −5.37666 | −0.268498 | −0.134249 | − | 0.990948i | \(-0.542862\pi\) | ||||
−0.134249 | + | 0.990948i | \(0.542862\pi\) | |||||||
\(402\) | −43.6013 | −2.17463 | ||||||||
\(403\) | 0.937998 | 0.0467250 | ||||||||
\(404\) | 24.5528 | 1.22155 | ||||||||
\(405\) | −12.8021 | −0.636143 | ||||||||
\(406\) | 42.5067 | 2.10957 | ||||||||
\(407\) | 33.5895 | 1.66497 | ||||||||
\(408\) | 2.21015 | 0.109419 | ||||||||
\(409\) | 26.2887 | 1.29989 | 0.649945 | − | 0.759981i | \(-0.274792\pi\) | ||||
0.649945 | + | 0.759981i | \(0.274792\pi\) | |||||||
\(410\) | 8.36550 | 0.413143 | ||||||||
\(411\) | −26.0729 | −1.28608 | ||||||||
\(412\) | 12.2467 | 0.603350 | ||||||||
\(413\) | 8.03970 | 0.395608 | ||||||||
\(414\) | −4.68876 | −0.230440 | ||||||||
\(415\) | 0.621565 | 0.0305114 | ||||||||
\(416\) | 1.32468 | 0.0649476 | ||||||||
\(417\) | −6.87394 | −0.336618 | ||||||||
\(418\) | −12.2502 | −0.599175 | ||||||||
\(419\) | −10.0868 | −0.492771 | −0.246385 | − | 0.969172i | \(-0.579243\pi\) | ||||
−0.246385 | + | 0.969172i | \(0.579243\pi\) | |||||||
\(420\) | 9.66130 | 0.471423 | ||||||||
\(421\) | 34.9786 | 1.70475 | 0.852377 | − | 0.522927i | \(-0.175160\pi\) | ||||
0.852377 | + | 0.522927i | \(0.175160\pi\) | |||||||
\(422\) | −5.36797 | −0.261309 | ||||||||
\(423\) | −8.28880 | −0.403015 | ||||||||
\(424\) | −12.1019 | −0.587720 | ||||||||
\(425\) | −3.67007 | −0.178024 | ||||||||
\(426\) | −9.42995 | −0.456883 | ||||||||
\(427\) | −16.5231 | −0.799608 | ||||||||
\(428\) | 4.97969 | 0.240703 | ||||||||
\(429\) | 1.27827 | 0.0617153 | ||||||||
\(430\) | 2.14595 | 0.103487 | ||||||||
\(431\) | 32.8038 | 1.58010 | 0.790052 | − | 0.613040i | \(-0.210053\pi\) | ||||
0.790052 | + | 0.613040i | \(0.210053\pi\) | |||||||
\(432\) | 11.7866 | 0.567082 | ||||||||
\(433\) | 7.56622 | 0.363610 | 0.181805 | − | 0.983335i | \(-0.441806\pi\) | ||||
0.181805 | + | 0.983335i | \(0.441806\pi\) | |||||||
\(434\) | −23.5794 | −1.13185 | ||||||||
\(435\) | −22.4713 | −1.07742 | ||||||||
\(436\) | −3.69867 | −0.177134 | ||||||||
\(437\) | 2.91754 | 0.139565 | ||||||||
\(438\) | −32.5573 | −1.55565 | ||||||||
\(439\) | 11.1980 | 0.534449 | 0.267225 | − | 0.963634i | \(-0.413893\pi\) | ||||
0.267225 | + | 0.963634i | \(0.413893\pi\) | |||||||
\(440\) | 3.47645 | 0.165733 | ||||||||
\(441\) | −0.538364 | −0.0256364 | ||||||||
\(442\) | −0.356934 | −0.0169776 | ||||||||
\(443\) | −6.53265 | −0.310375 | −0.155188 | − | 0.987885i | \(-0.549598\pi\) | ||||
−0.155188 | + | 0.987885i | \(0.549598\pi\) | |||||||
\(444\) | 36.0203 | 1.70945 | ||||||||
\(445\) | −3.27139 | −0.155079 | ||||||||
\(446\) | 13.3367 | 0.631511 | ||||||||
\(447\) | −15.5413 | −0.735080 | ||||||||
\(448\) | −8.49663 | −0.401428 | ||||||||
\(449\) | 8.52043 | 0.402104 | 0.201052 | − | 0.979581i | \(-0.435564\pi\) | ||||
0.201052 | + | 0.979581i | \(0.435564\pi\) | |||||||
\(450\) | 12.8790 | 0.607122 | ||||||||
\(451\) | −11.7528 | −0.553418 | ||||||||
\(452\) | −22.7167 | −1.06850 | ||||||||
\(453\) | −25.4212 | −1.19439 | ||||||||
\(454\) | 17.4292 | 0.817991 | ||||||||
\(455\) | 0.573198 | 0.0268719 | ||||||||
\(456\) | 4.82601 | 0.225999 | ||||||||
\(457\) | −33.0112 | −1.54420 | −0.772099 | − | 0.635503i | \(-0.780793\pi\) | ||||
−0.772099 | + | 0.635503i | \(0.780793\pi\) | |||||||
\(458\) | 11.1081 | 0.519047 | ||||||||
\(459\) | −2.46275 | −0.114951 | ||||||||
\(460\) | 2.25377 | 0.105082 | ||||||||
\(461\) | 36.3799 | 1.69438 | 0.847190 | − | 0.531291i | \(-0.178293\pi\) | ||||
0.847190 | + | 0.531291i | \(0.178293\pi\) | |||||||
\(462\) | −32.1330 | −1.49496 | ||||||||
\(463\) | 25.0230 | 1.16292 | 0.581459 | − | 0.813576i | \(-0.302482\pi\) | ||||
0.581459 | + | 0.813576i | \(0.302482\pi\) | |||||||
\(464\) | 42.1903 | 1.95864 | ||||||||
\(465\) | 12.4653 | 0.578065 | ||||||||
\(466\) | −0.883113 | −0.0409094 | ||||||||
\(467\) | 8.41010 | 0.389173 | 0.194586 | − | 0.980885i | \(-0.437664\pi\) | ||||
0.194586 | + | 0.980885i | \(0.437664\pi\) | |||||||
\(468\) | 0.529090 | 0.0244572 | ||||||||
\(469\) | 27.4683 | 1.26837 | ||||||||
\(470\) | 9.43209 | 0.435070 | ||||||||
\(471\) | 18.2365 | 0.840293 | ||||||||
\(472\) | 3.10230 | 0.142795 | ||||||||
\(473\) | −3.01488 | −0.138624 | ||||||||
\(474\) | −7.68319 | −0.352900 | ||||||||
\(475\) | −8.01385 | −0.367701 | ||||||||
\(476\) | 3.79011 | 0.173719 | ||||||||
\(477\) | −22.8247 | −1.04507 | ||||||||
\(478\) | −9.25594 | −0.423357 | ||||||||
\(479\) | −24.8649 | −1.13611 | −0.568053 | − | 0.822992i | \(-0.692303\pi\) | ||||
−0.568053 | + | 0.822992i | \(0.692303\pi\) | |||||||
\(480\) | 17.6040 | 0.803509 | ||||||||
\(481\) | 2.13706 | 0.0974414 | ||||||||
\(482\) | 14.0501 | 0.639965 | ||||||||
\(483\) | 7.65292 | 0.348220 | ||||||||
\(484\) | −2.79445 | −0.127020 | ||||||||
\(485\) | 19.0414 | 0.864626 | ||||||||
\(486\) | 31.9124 | 1.44758 | ||||||||
\(487\) | −24.6480 | −1.11691 | −0.558455 | − | 0.829535i | \(-0.688606\pi\) | ||||
−0.558455 | + | 0.829535i | \(0.688606\pi\) | |||||||
\(488\) | −6.37581 | −0.288619 | ||||||||
\(489\) | −38.2810 | −1.73113 | ||||||||
\(490\) | 0.612623 | 0.0276755 | ||||||||
\(491\) | −3.93127 | −0.177416 | −0.0887078 | − | 0.996058i | \(-0.528274\pi\) | ||||
−0.0887078 | + | 0.996058i | \(0.528274\pi\) | |||||||
\(492\) | −12.6033 | −0.568202 | ||||||||
\(493\) | −8.81546 | −0.397029 | ||||||||
\(494\) | −0.779389 | −0.0350664 | ||||||||
\(495\) | 6.55673 | 0.294703 | ||||||||
\(496\) | −23.4038 | −1.05086 | ||||||||
\(497\) | 5.94077 | 0.266480 | ||||||||
\(498\) | −2.21690 | −0.0993418 | ||||||||
\(499\) | 23.2252 | 1.03970 | 0.519852 | − | 0.854256i | \(-0.325987\pi\) | ||||
0.519852 | + | 0.854256i | \(0.325987\pi\) | |||||||
\(500\) | −14.6245 | −0.654028 | ||||||||
\(501\) | −27.9869 | −1.25036 | ||||||||
\(502\) | 16.7141 | 0.745987 | ||||||||
\(503\) | 13.6427 | 0.608300 | 0.304150 | − | 0.952624i | \(-0.401628\pi\) | ||||
0.304150 | + | 0.952624i | \(0.401628\pi\) | |||||||
\(504\) | 4.88610 | 0.217644 | ||||||||
\(505\) | 19.3585 | 0.861442 | ||||||||
\(506\) | −7.49592 | −0.333234 | ||||||||
\(507\) | −28.6538 | −1.27256 | ||||||||
\(508\) | 12.6593 | 0.561666 | ||||||||
\(509\) | 40.3465 | 1.78833 | 0.894164 | − | 0.447740i | \(-0.147771\pi\) | ||||
0.894164 | + | 0.447740i | \(0.147771\pi\) | |||||||
\(510\) | −4.74339 | −0.210041 | ||||||||
\(511\) | 20.5108 | 0.907342 | ||||||||
\(512\) | −23.4810 | −1.03772 | ||||||||
\(513\) | −5.37758 | −0.237426 | ||||||||
\(514\) | 31.6477 | 1.39592 | ||||||||
\(515\) | 9.65581 | 0.425486 | ||||||||
\(516\) | −3.23306 | −0.142327 | ||||||||
\(517\) | −13.2513 | −0.582791 | ||||||||
\(518\) | −53.7213 | −2.36038 | ||||||||
\(519\) | −42.9702 | −1.88618 | ||||||||
\(520\) | 0.221182 | 0.00969946 | ||||||||
\(521\) | 14.6597 | 0.642252 | 0.321126 | − | 0.947036i | \(-0.395939\pi\) | ||||
0.321126 | + | 0.947036i | \(0.395939\pi\) | |||||||
\(522\) | 30.9352 | 1.35400 | ||||||||
\(523\) | −0.499303 | −0.0218330 | −0.0109165 | − | 0.999940i | \(-0.503475\pi\) | ||||
−0.0109165 | + | 0.999940i | \(0.503475\pi\) | |||||||
\(524\) | 16.7202 | 0.730425 | ||||||||
\(525\) | −21.0209 | −0.917427 | ||||||||
\(526\) | 0.356252 | 0.0155333 | ||||||||
\(527\) | 4.89012 | 0.213017 | ||||||||
\(528\) | −31.8938 | −1.38800 | ||||||||
\(529\) | −21.2147 | −0.922380 | ||||||||
\(530\) | 25.9730 | 1.12819 | ||||||||
\(531\) | 5.85107 | 0.253915 | ||||||||
\(532\) | 8.27597 | 0.358809 | ||||||||
\(533\) | −0.747747 | −0.0323885 | ||||||||
\(534\) | 11.6679 | 0.504918 | ||||||||
\(535\) | 3.92621 | 0.169745 | ||||||||
\(536\) | 10.5993 | 0.457820 | ||||||||
\(537\) | −55.3098 | −2.38679 | ||||||||
\(538\) | −22.8668 | −0.985859 | ||||||||
\(539\) | −0.860682 | −0.0370722 | ||||||||
\(540\) | −4.15412 | −0.178765 | ||||||||
\(541\) | −17.2497 | −0.741620 | −0.370810 | − | 0.928709i | \(-0.620920\pi\) | ||||
−0.370810 | + | 0.928709i | \(0.620920\pi\) | |||||||
\(542\) | −43.6119 | −1.87329 | ||||||||
\(543\) | −38.7229 | −1.66176 | ||||||||
\(544\) | 6.90601 | 0.296093 | ||||||||
\(545\) | −2.91620 | −0.124916 | ||||||||
\(546\) | −2.04439 | −0.0874919 | ||||||||
\(547\) | −5.15817 | −0.220547 | −0.110274 | − | 0.993901i | \(-0.535173\pi\) | ||||
−0.110274 | + | 0.993901i | \(0.535173\pi\) | |||||||
\(548\) | −17.2530 | −0.737010 | ||||||||
\(549\) | −12.0250 | −0.513216 | ||||||||
\(550\) | 20.5896 | 0.877945 | ||||||||
\(551\) | −19.2492 | −0.820043 | ||||||||
\(552\) | 2.95306 | 0.125690 | ||||||||
\(553\) | 4.84033 | 0.205832 | ||||||||
\(554\) | 8.23155 | 0.349725 | ||||||||
\(555\) | 28.3999 | 1.20551 | ||||||||
\(556\) | −4.54863 | −0.192905 | ||||||||
\(557\) | −16.5838 | −0.702678 | −0.351339 | − | 0.936248i | \(-0.614273\pi\) | ||||
−0.351339 | + | 0.936248i | \(0.614273\pi\) | |||||||
\(558\) | −17.1604 | −0.726458 | ||||||||
\(559\) | −0.191815 | −0.00811291 | ||||||||
\(560\) | −14.3018 | −0.604360 | ||||||||
\(561\) | 6.66406 | 0.281357 | ||||||||
\(562\) | −52.6383 | −2.22041 | ||||||||
\(563\) | −29.5306 | −1.24457 | −0.622284 | − | 0.782792i | \(-0.713795\pi\) | ||||
−0.622284 | + | 0.782792i | \(0.713795\pi\) | |||||||
\(564\) | −14.2103 | −0.598360 | ||||||||
\(565\) | −17.9108 | −0.753515 | ||||||||
\(566\) | −5.05946 | −0.212665 | ||||||||
\(567\) | −28.7657 | −1.20805 | ||||||||
\(568\) | 2.29238 | 0.0961863 | ||||||||
\(569\) | 10.8038 | 0.452917 | 0.226459 | − | 0.974021i | \(-0.427285\pi\) | ||||
0.226459 | + | 0.974021i | \(0.427285\pi\) | |||||||
\(570\) | −10.3575 | −0.433829 | ||||||||
\(571\) | 10.0624 | 0.421098 | 0.210549 | − | 0.977583i | \(-0.432475\pi\) | ||||
0.210549 | + | 0.977583i | \(0.432475\pi\) | |||||||
\(572\) | 0.845855 | 0.0353670 | ||||||||
\(573\) | 48.5968 | 2.03016 | ||||||||
\(574\) | 18.7968 | 0.784565 | ||||||||
\(575\) | −4.90371 | −0.204499 | ||||||||
\(576\) | −6.18361 | −0.257651 | ||||||||
\(577\) | 7.38883 | 0.307601 | 0.153801 | − | 0.988102i | \(-0.450849\pi\) | ||||
0.153801 | + | 0.988102i | \(0.450849\pi\) | |||||||
\(578\) | −1.86082 | −0.0774000 | ||||||||
\(579\) | −0.644021 | −0.0267646 | ||||||||
\(580\) | −14.8698 | −0.617433 | ||||||||
\(581\) | 1.39662 | 0.0579418 | ||||||||
\(582\) | −67.9139 | −2.81512 | ||||||||
\(583\) | −36.4898 | −1.51125 | ||||||||
\(584\) | 7.91455 | 0.327506 | ||||||||
\(585\) | 0.417158 | 0.0172473 | ||||||||
\(586\) | 12.4148 | 0.512850 | ||||||||
\(587\) | −20.7256 | −0.855435 | −0.427718 | − | 0.903912i | \(-0.640682\pi\) | ||||
−0.427718 | + | 0.903912i | \(0.640682\pi\) | |||||||
\(588\) | −0.922968 | −0.0380626 | ||||||||
\(589\) | 10.6779 | 0.439976 | ||||||||
\(590\) | −6.65812 | −0.274111 | ||||||||
\(591\) | 39.6722 | 1.63190 | ||||||||
\(592\) | −53.3214 | −2.19149 | ||||||||
\(593\) | 9.69414 | 0.398091 | 0.199045 | − | 0.979990i | \(-0.436216\pi\) | ||||
0.199045 | + | 0.979990i | \(0.436216\pi\) | |||||||
\(594\) | 13.8164 | 0.566893 | ||||||||
\(595\) | 2.98829 | 0.122508 | ||||||||
\(596\) | −10.2840 | −0.421250 | ||||||||
\(597\) | −16.8792 | −0.690820 | ||||||||
\(598\) | −0.476912 | −0.0195024 | ||||||||
\(599\) | −27.8397 | −1.13750 | −0.568749 | − | 0.822511i | \(-0.692573\pi\) | ||||
−0.568749 | + | 0.822511i | \(0.692573\pi\) | |||||||
\(600\) | −8.11140 | −0.331146 | ||||||||
\(601\) | 6.13362 | 0.250195 | 0.125098 | − | 0.992144i | \(-0.460076\pi\) | ||||
0.125098 | + | 0.992144i | \(0.460076\pi\) | |||||||
\(602\) | 4.82184 | 0.196523 | ||||||||
\(603\) | 19.9907 | 0.814084 | ||||||||
\(604\) | −16.8218 | −0.684467 | ||||||||
\(605\) | −2.20326 | −0.0895753 | ||||||||
\(606\) | −69.0449 | −2.80476 | ||||||||
\(607\) | 14.7898 | 0.600300 | 0.300150 | − | 0.953892i | \(-0.402963\pi\) | ||||
0.300150 | + | 0.953892i | \(0.402963\pi\) | |||||||
\(608\) | 15.0798 | 0.611565 | ||||||||
\(609\) | −50.4919 | −2.04604 | ||||||||
\(610\) | 13.6837 | 0.554036 | ||||||||
\(611\) | −0.843084 | −0.0341075 | ||||||||
\(612\) | 2.75834 | 0.111499 | ||||||||
\(613\) | −28.1955 | −1.13880 | −0.569402 | − | 0.822059i | \(-0.692825\pi\) | ||||
−0.569402 | + | 0.822059i | \(0.692825\pi\) | |||||||
\(614\) | −23.8697 | −0.963304 | ||||||||
\(615\) | −9.93702 | −0.400699 | ||||||||
\(616\) | 7.81141 | 0.314731 | ||||||||
\(617\) | 25.0163 | 1.00712 | 0.503560 | − | 0.863961i | \(-0.332023\pi\) | ||||
0.503560 | + | 0.863961i | \(0.332023\pi\) | |||||||
\(618\) | −34.4388 | −1.38533 | ||||||||
\(619\) | −10.0045 | −0.402113 | −0.201056 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201056 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(620\) | 8.24856 | 0.331270 | ||||||||
\(621\) | −3.29056 | −0.132046 | ||||||||
\(622\) | 44.2999 | 1.77627 | ||||||||
\(623\) | −7.35064 | −0.294497 | ||||||||
\(624\) | −2.02917 | −0.0812320 | ||||||||
\(625\) | 6.81974 | 0.272790 | ||||||||
\(626\) | 6.61745 | 0.264486 | ||||||||
\(627\) | 14.5514 | 0.581128 | ||||||||
\(628\) | 12.0675 | 0.481544 | ||||||||
\(629\) | 11.1412 | 0.444230 | ||||||||
\(630\) | −10.4865 | −0.417792 | ||||||||
\(631\) | 32.9009 | 1.30976 | 0.654881 | − | 0.755732i | \(-0.272719\pi\) | ||||
0.654881 | + | 0.755732i | \(0.272719\pi\) | |||||||
\(632\) | 1.86775 | 0.0742952 | ||||||||
\(633\) | 6.37638 | 0.253438 | ||||||||
\(634\) | 49.7940 | 1.97757 | ||||||||
\(635\) | 9.98115 | 0.396090 | ||||||||
\(636\) | −39.1305 | −1.55162 | ||||||||
\(637\) | −0.0547590 | −0.00216963 | ||||||||
\(638\) | 49.4561 | 1.95799 | ||||||||
\(639\) | 4.32353 | 0.171036 | ||||||||
\(640\) | −8.89186 | −0.351482 | ||||||||
\(641\) | 6.15705 | 0.243189 | 0.121594 | − | 0.992580i | \(-0.461199\pi\) | ||||
0.121594 | + | 0.992580i | \(0.461199\pi\) | |||||||
\(642\) | −14.0034 | −0.552669 | ||||||||
\(643\) | 3.86650 | 0.152480 | 0.0762399 | − | 0.997090i | \(-0.475709\pi\) | ||||
0.0762399 | + | 0.997090i | \(0.475709\pi\) | |||||||
\(644\) | 5.06410 | 0.199553 | ||||||||
\(645\) | −2.54908 | −0.100370 | ||||||||
\(646\) | −4.06324 | −0.159866 | ||||||||
\(647\) | 0.161858 | 0.00636329 | 0.00318165 | − | 0.999995i | \(-0.498987\pi\) | ||||
0.00318165 | + | 0.999995i | \(0.498987\pi\) | |||||||
\(648\) | −11.0999 | −0.436046 | ||||||||
\(649\) | 9.35409 | 0.367180 | ||||||||
\(650\) | 1.30997 | 0.0513813 | ||||||||
\(651\) | 28.0089 | 1.09776 | ||||||||
\(652\) | −25.3314 | −0.992053 | ||||||||
\(653\) | 28.5286 | 1.11641 | 0.558206 | − | 0.829702i | \(-0.311490\pi\) | ||||
0.558206 | + | 0.829702i | \(0.311490\pi\) | |||||||
\(654\) | 10.4010 | 0.406712 | ||||||||
\(655\) | 13.1829 | 0.515099 | ||||||||
\(656\) | 18.6569 | 0.728430 | ||||||||
\(657\) | 14.9272 | 0.582364 | ||||||||
\(658\) | 21.1934 | 0.826205 | ||||||||
\(659\) | 2.89377 | 0.112725 | 0.0563626 | − | 0.998410i | \(-0.482050\pi\) | ||||
0.0563626 | + | 0.998410i | \(0.482050\pi\) | |||||||
\(660\) | 11.2408 | 0.437548 | ||||||||
\(661\) | 18.2303 | 0.709075 | 0.354537 | − | 0.935042i | \(-0.384638\pi\) | ||||
0.354537 | + | 0.935042i | \(0.384638\pi\) | |||||||
\(662\) | −21.4667 | −0.834325 | ||||||||
\(663\) | 0.423986 | 0.0164663 | ||||||||
\(664\) | 0.538920 | 0.0209142 | ||||||||
\(665\) | 6.52513 | 0.253034 | ||||||||
\(666\) | −39.0968 | −1.51497 | ||||||||
\(667\) | −11.7787 | −0.456071 | ||||||||
\(668\) | −18.5195 | −0.716541 | ||||||||
\(669\) | −15.8421 | −0.612490 | ||||||||
\(670\) | −22.7481 | −0.878835 | ||||||||
\(671\) | −19.2244 | −0.742150 | ||||||||
\(672\) | 39.5553 | 1.52588 | ||||||||
\(673\) | 4.54050 | 0.175023 | 0.0875117 | − | 0.996163i | \(-0.472108\pi\) | ||||
0.0875117 | + | 0.996163i | \(0.472108\pi\) | |||||||
\(674\) | −24.5369 | −0.945125 | ||||||||
\(675\) | 9.03845 | 0.347890 | ||||||||
\(676\) | −18.9608 | −0.729261 | ||||||||
\(677\) | 26.0116 | 0.999707 | 0.499853 | − | 0.866110i | \(-0.333387\pi\) | ||||
0.499853 | + | 0.866110i | \(0.333387\pi\) | |||||||
\(678\) | 63.8816 | 2.45336 | ||||||||
\(679\) | 42.7850 | 1.64194 | ||||||||
\(680\) | 1.15310 | 0.0442193 | ||||||||
\(681\) | −20.7033 | −0.793354 | ||||||||
\(682\) | −27.4343 | −1.05051 | ||||||||
\(683\) | −46.0997 | −1.76396 | −0.881978 | − | 0.471291i | \(-0.843788\pi\) | ||||
−0.881978 | + | 0.471291i | \(0.843788\pi\) | |||||||
\(684\) | 6.02302 | 0.230296 | ||||||||
\(685\) | −13.6030 | −0.519743 | ||||||||
\(686\) | 35.1294 | 1.34125 | ||||||||
\(687\) | −13.1948 | −0.503414 | ||||||||
\(688\) | 4.78594 | 0.182462 | ||||||||
\(689\) | −2.32158 | −0.0884452 | ||||||||
\(690\) | −6.33781 | −0.241276 | ||||||||
\(691\) | −52.2599 | −1.98806 | −0.994029 | − | 0.109114i | \(-0.965199\pi\) | ||||
−0.994029 | + | 0.109114i | \(0.965199\pi\) | |||||||
\(692\) | −28.4343 | −1.08091 | ||||||||
\(693\) | 14.7326 | 0.559646 | ||||||||
\(694\) | 5.93892 | 0.225438 | ||||||||
\(695\) | −3.58633 | −0.136037 | ||||||||
\(696\) | −19.4835 | −0.738520 | ||||||||
\(697\) | −3.89827 | −0.147658 | ||||||||
\(698\) | −53.1853 | −2.01309 | ||||||||
\(699\) | 1.04901 | 0.0396773 | ||||||||
\(700\) | −13.9100 | −0.525747 | ||||||||
\(701\) | −27.9280 | −1.05483 | −0.527413 | − | 0.849609i | \(-0.676838\pi\) | ||||
−0.527413 | + | 0.849609i | \(0.676838\pi\) | |||||||
\(702\) | 0.879038 | 0.0331771 | ||||||||
\(703\) | 24.3277 | 0.917536 | ||||||||
\(704\) | −9.88573 | −0.372583 | ||||||||
\(705\) | −11.2040 | −0.421966 | ||||||||
\(706\) | 65.9513 | 2.48211 | ||||||||
\(707\) | 43.4975 | 1.63589 | ||||||||
\(708\) | 10.0310 | 0.376989 | ||||||||
\(709\) | 5.32357 | 0.199931 | 0.0999655 | − | 0.994991i | \(-0.468127\pi\) | ||||
0.0999655 | + | 0.994991i | \(0.468127\pi\) | |||||||
\(710\) | −4.91988 | −0.184640 | ||||||||
\(711\) | 3.52265 | 0.132110 | ||||||||
\(712\) | −2.83641 | −0.106299 | ||||||||
\(713\) | 6.53386 | 0.244695 | ||||||||
\(714\) | −10.6582 | −0.398871 | ||||||||
\(715\) | 0.666909 | 0.0249410 | ||||||||
\(716\) | −36.5996 | −1.36779 | ||||||||
\(717\) | 10.9947 | 0.410606 | ||||||||
\(718\) | −15.3718 | −0.573672 | ||||||||
\(719\) | 44.8503 | 1.67263 | 0.836317 | − | 0.548246i | \(-0.184704\pi\) | ||||
0.836317 | + | 0.548246i | \(0.184704\pi\) | |||||||
\(720\) | −10.4084 | −0.387899 | ||||||||
\(721\) | 21.6961 | 0.808005 | ||||||||
\(722\) | 26.4833 | 0.985606 | ||||||||
\(723\) | −16.6895 | −0.620690 | ||||||||
\(724\) | −25.6237 | −0.952298 | ||||||||
\(725\) | 32.3534 | 1.20157 | ||||||||
\(726\) | 7.85825 | 0.291647 | ||||||||
\(727\) | −34.5889 | −1.28283 | −0.641416 | − | 0.767193i | \(-0.721653\pi\) | ||||
−0.641416 | + | 0.767193i | \(0.721653\pi\) | |||||||
\(728\) | 0.496984 | 0.0184194 | ||||||||
\(729\) | −4.60396 | −0.170517 | ||||||||
\(730\) | −16.9861 | −0.628684 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −20.6156 | −0.761976 | ||||||||
\(733\) | 1.84897 | 0.0682932 | 0.0341466 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341466 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(734\) | 57.1984 | 2.11123 | ||||||||
\(735\) | −0.727708 | −0.0268419 | ||||||||
\(736\) | 9.22737 | 0.340125 | ||||||||
\(737\) | 31.9591 | 1.17723 | ||||||||
\(738\) | 13.6798 | 0.503561 | ||||||||
\(739\) | 43.8591 | 1.61338 | 0.806692 | − | 0.590973i | \(-0.201256\pi\) | ||||
0.806692 | + | 0.590973i | \(0.201256\pi\) | |||||||
\(740\) | 18.7928 | 0.690839 | ||||||||
\(741\) | 0.925803 | 0.0340102 | ||||||||
\(742\) | 58.3599 | 2.14246 | ||||||||
\(743\) | −22.9024 | −0.840209 | −0.420105 | − | 0.907476i | \(-0.638007\pi\) | ||||
−0.420105 | + | 0.907476i | \(0.638007\pi\) | |||||||
\(744\) | 10.8079 | 0.396236 | ||||||||
\(745\) | −8.10837 | −0.297068 | ||||||||
\(746\) | −7.76803 | −0.284408 | ||||||||
\(747\) | 1.01642 | 0.0371890 | ||||||||
\(748\) | 4.40975 | 0.161236 | ||||||||
\(749\) | 8.82198 | 0.322348 | ||||||||
\(750\) | 41.1255 | 1.50169 | ||||||||
\(751\) | −24.5705 | −0.896589 | −0.448295 | − | 0.893886i | \(-0.647968\pi\) | ||||
−0.448295 | + | 0.893886i | \(0.647968\pi\) | |||||||
\(752\) | 21.0357 | 0.767091 | ||||||||
\(753\) | −19.8540 | −0.723519 | ||||||||
\(754\) | 3.14654 | 0.114590 | ||||||||
\(755\) | −13.2630 | −0.482690 | ||||||||
\(756\) | −9.33408 | −0.339477 | ||||||||
\(757\) | −50.8608 | −1.84857 | −0.924284 | − | 0.381705i | \(-0.875337\pi\) | ||||
−0.924284 | + | 0.381705i | \(0.875337\pi\) | |||||||
\(758\) | 56.7987 | 2.06302 | ||||||||
\(759\) | 8.90408 | 0.323198 | ||||||||
\(760\) | 2.51787 | 0.0913328 | ||||||||
\(761\) | 1.76669 | 0.0640424 | 0.0320212 | − | 0.999487i | \(-0.489806\pi\) | ||||
0.0320212 | + | 0.999487i | \(0.489806\pi\) | |||||||
\(762\) | −35.5992 | −1.28962 | ||||||||
\(763\) | −6.55254 | −0.237218 | ||||||||
\(764\) | 32.1575 | 1.16342 | ||||||||
\(765\) | 2.17479 | 0.0786298 | ||||||||
\(766\) | −42.2064 | −1.52498 | ||||||||
\(767\) | 0.595134 | 0.0214890 | ||||||||
\(768\) | 46.2098 | 1.66745 | ||||||||
\(769\) | 30.9106 | 1.11466 | 0.557332 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557332 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(770\) | −16.7647 | −0.604159 | ||||||||
\(771\) | −37.5929 | −1.35388 | ||||||||
\(772\) | −0.426162 | −0.0153379 | ||||||||
\(773\) | 33.5407 | 1.20637 | 0.603187 | − | 0.797600i | \(-0.293897\pi\) | ||||
0.603187 | + | 0.797600i | \(0.293897\pi\) | |||||||
\(774\) | 3.50920 | 0.126136 | ||||||||
\(775\) | −17.9471 | −0.644678 | ||||||||
\(776\) | 16.5096 | 0.592660 | ||||||||
\(777\) | 63.8132 | 2.28929 | ||||||||
\(778\) | 6.62853 | 0.237644 | ||||||||
\(779\) | −8.51215 | −0.304979 | ||||||||
\(780\) | 0.715172 | 0.0256073 | ||||||||
\(781\) | 6.91202 | 0.247331 | ||||||||
\(782\) | −2.48631 | −0.0889103 | ||||||||
\(783\) | 21.7103 | 0.775862 | ||||||||
\(784\) | 1.36628 | 0.0487958 | ||||||||
\(785\) | 9.51451 | 0.339588 | ||||||||
\(786\) | −47.0188 | −1.67710 | ||||||||
\(787\) | −25.9039 | −0.923375 | −0.461687 | − | 0.887043i | \(-0.652756\pi\) | ||||
−0.461687 | + | 0.887043i | \(0.652756\pi\) | |||||||
\(788\) | 26.2519 | 0.935187 | ||||||||
\(789\) | −0.423177 | −0.0150655 | ||||||||
\(790\) | −4.00855 | −0.142618 | ||||||||
\(791\) | −40.2447 | −1.43094 | ||||||||
\(792\) | 5.68492 | 0.202005 | ||||||||
\(793\) | −1.22311 | −0.0434339 | ||||||||
\(794\) | 4.37428 | 0.155237 | ||||||||
\(795\) | −30.8522 | −1.09421 | ||||||||
\(796\) | −11.1693 | −0.395886 | ||||||||
\(797\) | 15.6298 | 0.553637 | 0.276818 | − | 0.960922i | \(-0.410720\pi\) | ||||
0.276818 | + | 0.960922i | \(0.410720\pi\) | |||||||
\(798\) | −23.2728 | −0.823849 | ||||||||
\(799\) | −4.39530 | −0.155494 | ||||||||
\(800\) | −25.3455 | −0.896100 | ||||||||
\(801\) | −5.34959 | −0.189018 | ||||||||
\(802\) | 10.0050 | 0.353290 | ||||||||
\(803\) | 23.8640 | 0.842143 | ||||||||
\(804\) | 34.2719 | 1.20868 | ||||||||
\(805\) | 3.99275 | 0.140726 | ||||||||
\(806\) | −1.74545 | −0.0614808 | ||||||||
\(807\) | 27.1625 | 0.956166 | ||||||||
\(808\) | 16.7845 | 0.590478 | ||||||||
\(809\) | −40.7498 | −1.43269 | −0.716343 | − | 0.697748i | \(-0.754185\pi\) | ||||
−0.716343 | + | 0.697748i | \(0.754185\pi\) | |||||||
\(810\) | 23.8225 | 0.837037 | ||||||||
\(811\) | 8.27914 | 0.290720 | 0.145360 | − | 0.989379i | \(-0.453566\pi\) | ||||
0.145360 | + | 0.989379i | \(0.453566\pi\) | |||||||
\(812\) | −33.4116 | −1.17252 | ||||||||
\(813\) | 51.8047 | 1.81687 | ||||||||
\(814\) | −62.5041 | −2.19077 | ||||||||
\(815\) | −19.9723 | −0.699601 | ||||||||
\(816\) | −10.5788 | −0.370332 | ||||||||
\(817\) | −2.18357 | −0.0763934 | ||||||||
\(818\) | −48.9185 | −1.71040 | ||||||||
\(819\) | 0.937331 | 0.0327530 | ||||||||
\(820\) | −6.57553 | −0.229628 | ||||||||
\(821\) | 22.7743 | 0.794827 | 0.397414 | − | 0.917640i | \(-0.369908\pi\) | ||||
0.397414 | + | 0.917640i | \(0.369908\pi\) | |||||||
\(822\) | 48.5170 | 1.69222 | ||||||||
\(823\) | 15.6087 | 0.544084 | 0.272042 | − | 0.962285i | \(-0.412301\pi\) | ||||
0.272042 | + | 0.962285i | \(0.412301\pi\) | |||||||
\(824\) | 8.37194 | 0.291650 | ||||||||
\(825\) | −24.4576 | −0.851503 | ||||||||
\(826\) | −14.9605 | −0.520541 | ||||||||
\(827\) | −25.7229 | −0.894472 | −0.447236 | − | 0.894416i | \(-0.647592\pi\) | ||||
−0.447236 | + | 0.894416i | \(0.647592\pi\) | |||||||
\(828\) | 3.68551 | 0.128080 | ||||||||
\(829\) | 5.93206 | 0.206029 | 0.103014 | − | 0.994680i | \(-0.467151\pi\) | ||||
0.103014 | + | 0.994680i | \(0.467151\pi\) | |||||||
\(830\) | −1.15662 | −0.0401470 | ||||||||
\(831\) | −9.77791 | −0.339192 | ||||||||
\(832\) | −0.628958 | −0.0218052 | ||||||||
\(833\) | −0.285478 | −0.00989124 | ||||||||
\(834\) | 12.7912 | 0.442922 | ||||||||
\(835\) | −14.6016 | −0.505308 | ||||||||
\(836\) | 9.62899 | 0.333026 | ||||||||
\(837\) | −12.0431 | −0.416271 | ||||||||
\(838\) | 18.7697 | 0.648388 | ||||||||
\(839\) | 38.7520 | 1.33787 | 0.668934 | − | 0.743322i | \(-0.266751\pi\) | ||||
0.668934 | + | 0.743322i | \(0.266751\pi\) | |||||||
\(840\) | 6.60456 | 0.227879 | ||||||||
\(841\) | 48.7124 | 1.67974 | ||||||||
\(842\) | −65.0891 | −2.24312 | ||||||||
\(843\) | 62.5267 | 2.15353 | ||||||||
\(844\) | 4.21939 | 0.145237 | ||||||||
\(845\) | −14.9495 | −0.514279 | ||||||||
\(846\) | 15.4240 | 0.530287 | ||||||||
\(847\) | −4.95061 | −0.170105 | ||||||||
\(848\) | 57.9254 | 1.98917 | ||||||||
\(849\) | 6.00992 | 0.206260 | ||||||||
\(850\) | 6.82935 | 0.234245 | ||||||||
\(851\) | 14.8862 | 0.510293 | ||||||||
\(852\) | 7.41223 | 0.253939 | ||||||||
\(853\) | 48.1892 | 1.64997 | 0.824984 | − | 0.565157i | \(-0.191184\pi\) | ||||
0.824984 | + | 0.565157i | \(0.191184\pi\) | |||||||
\(854\) | 30.7465 | 1.05212 | ||||||||
\(855\) | 4.74881 | 0.162406 | ||||||||
\(856\) | 3.40416 | 0.116352 | ||||||||
\(857\) | −33.4859 | −1.14386 | −0.571928 | − | 0.820304i | \(-0.693804\pi\) | ||||
−0.571928 | + | 0.820304i | \(0.693804\pi\) | |||||||
\(858\) | −2.37863 | −0.0812050 | ||||||||
\(859\) | −25.2222 | −0.860570 | −0.430285 | − | 0.902693i | \(-0.641587\pi\) | ||||
−0.430285 | + | 0.902693i | \(0.641587\pi\) | |||||||
\(860\) | −1.68678 | −0.0575188 | ||||||||
\(861\) | −22.3280 | −0.760935 | ||||||||
\(862\) | −61.0421 | −2.07910 | ||||||||
\(863\) | 23.9561 | 0.815475 | 0.407738 | − | 0.913099i | \(-0.366318\pi\) | ||||
0.407738 | + | 0.913099i | \(0.366318\pi\) | |||||||
\(864\) | −17.0078 | −0.578616 | ||||||||
\(865\) | −22.4188 | −0.762262 | ||||||||
\(866\) | −14.0794 | −0.478438 | ||||||||
\(867\) | 2.21039 | 0.0750688 | ||||||||
\(868\) | 18.5341 | 0.629088 | ||||||||
\(869\) | 5.63166 | 0.191041 | ||||||||
\(870\) | 41.8152 | 1.41767 | ||||||||
\(871\) | 2.03333 | 0.0688967 | ||||||||
\(872\) | −2.52845 | −0.0856241 | ||||||||
\(873\) | 31.1378 | 1.05385 | ||||||||
\(874\) | −5.42903 | −0.183640 | ||||||||
\(875\) | −25.9086 | −0.875872 | ||||||||
\(876\) | 25.5910 | 0.864640 | ||||||||
\(877\) | 12.2633 | 0.414102 | 0.207051 | − | 0.978330i | \(-0.433613\pi\) | ||||
0.207051 | + | 0.978330i | \(0.433613\pi\) | |||||||
\(878\) | −20.8374 | −0.703228 | ||||||||
\(879\) | −14.7470 | −0.497404 | ||||||||
\(880\) | −16.6399 | −0.560932 | ||||||||
\(881\) | 28.0472 | 0.944935 | 0.472467 | − | 0.881348i | \(-0.343363\pi\) | ||||
0.472467 | + | 0.881348i | \(0.343363\pi\) | |||||||
\(882\) | 1.00180 | 0.0337324 | ||||||||
\(883\) | 0.978787 | 0.0329388 | 0.0164694 | − | 0.999864i | \(-0.494757\pi\) | ||||
0.0164694 | + | 0.999864i | \(0.494757\pi\) | |||||||
\(884\) | 0.280561 | 0.00943627 | ||||||||
\(885\) | 7.90890 | 0.265855 | ||||||||
\(886\) | 12.1561 | 0.408392 | ||||||||
\(887\) | 41.4749 | 1.39259 | 0.696295 | − | 0.717755i | \(-0.254830\pi\) | ||||
0.696295 | + | 0.717755i | \(0.254830\pi\) | |||||||
\(888\) | 24.6238 | 0.826321 | ||||||||
\(889\) | 22.4271 | 0.752182 | ||||||||
\(890\) | 6.08747 | 0.204053 | ||||||||
\(891\) | −33.4685 | −1.12124 | ||||||||
\(892\) | −10.4830 | −0.350998 | ||||||||
\(893\) | −9.59744 | −0.321166 | ||||||||
\(894\) | 28.9197 | 0.967218 | ||||||||
\(895\) | −28.8567 | −0.964574 | ||||||||
\(896\) | −19.9795 | −0.667470 | ||||||||
\(897\) | 0.566503 | 0.0189150 | ||||||||
\(898\) | −15.8550 | −0.529088 | ||||||||
\(899\) | −43.1087 | −1.43775 | ||||||||
\(900\) | −10.1233 | −0.337443 | ||||||||
\(901\) | −12.1032 | −0.403217 | ||||||||
\(902\) | 21.8699 | 0.728188 | ||||||||
\(903\) | −5.72765 | −0.190604 | ||||||||
\(904\) | −15.5294 | −0.516499 | ||||||||
\(905\) | −20.2029 | −0.671566 | ||||||||
\(906\) | 47.3044 | 1.57158 | ||||||||
\(907\) | −40.3469 | −1.33970 | −0.669849 | − | 0.742497i | \(-0.733641\pi\) | ||||
−0.669849 | + | 0.742497i | \(0.733641\pi\) | |||||||
\(908\) | −13.6998 | −0.454645 | ||||||||
\(909\) | 31.6563 | 1.04997 | ||||||||
\(910\) | −1.06662 | −0.0353581 | ||||||||
\(911\) | −11.1429 | −0.369179 | −0.184590 | − | 0.982816i | \(-0.559096\pi\) | ||||
−0.184590 | + | 0.982816i | \(0.559096\pi\) | |||||||
\(912\) | −23.0996 | −0.764903 | ||||||||
\(913\) | 1.62496 | 0.0537782 | ||||||||
\(914\) | 61.4280 | 2.03186 | ||||||||
\(915\) | −16.2543 | −0.537349 | ||||||||
\(916\) | −8.73130 | −0.288490 | ||||||||
\(917\) | 29.6213 | 0.978182 | ||||||||
\(918\) | 4.58274 | 0.151253 | ||||||||
\(919\) | −41.1546 | −1.35757 | −0.678783 | − | 0.734339i | \(-0.737492\pi\) | ||||
−0.678783 | + | 0.734339i | \(0.737492\pi\) | |||||||
\(920\) | 1.54070 | 0.0507953 | ||||||||
\(921\) | 28.3538 | 0.934290 | ||||||||
\(922\) | −67.6965 | −2.22947 | ||||||||
\(923\) | 0.439762 | 0.0144749 | ||||||||
\(924\) | 25.2575 | 0.830911 | ||||||||
\(925\) | −40.8891 | −1.34443 | ||||||||
\(926\) | −46.5634 | −1.53017 | ||||||||
\(927\) | 15.7898 | 0.518606 | ||||||||
\(928\) | −60.8797 | −1.99847 | ||||||||
\(929\) | −2.05473 | −0.0674134 | −0.0337067 | − | 0.999432i | \(-0.510731\pi\) | ||||
−0.0337067 | + | 0.999432i | \(0.510731\pi\) | |||||||
\(930\) | −23.1957 | −0.760619 | ||||||||
\(931\) | −0.623362 | −0.0204299 | ||||||||
\(932\) | 0.694153 | 0.0227378 | ||||||||
\(933\) | −52.6220 | −1.72277 | ||||||||
\(934\) | −15.6497 | −0.512074 | ||||||||
\(935\) | 3.47684 | 0.113705 | ||||||||
\(936\) | 0.361691 | 0.0118222 | ||||||||
\(937\) | −25.0583 | −0.818619 | −0.409310 | − | 0.912395i | \(-0.634230\pi\) | ||||
−0.409310 | + | 0.912395i | \(0.634230\pi\) | |||||||
\(938\) | −51.1137 | −1.66892 | ||||||||
\(939\) | −7.86058 | −0.256520 | ||||||||
\(940\) | −7.41391 | −0.241815 | ||||||||
\(941\) | 25.4764 | 0.830506 | 0.415253 | − | 0.909706i | \(-0.363693\pi\) | ||||
0.415253 | + | 0.909706i | \(0.363693\pi\) | |||||||
\(942\) | −33.9349 | −1.10566 | ||||||||
\(943\) | −5.20862 | −0.169616 | ||||||||
\(944\) | −14.8491 | −0.483296 | ||||||||
\(945\) | −7.35940 | −0.239401 | ||||||||
\(946\) | 5.61015 | 0.182402 | ||||||||
\(947\) | 0.162359 | 0.00527596 | 0.00263798 | − | 0.999997i | \(-0.499160\pi\) | ||||
0.00263798 | + | 0.999997i | \(0.499160\pi\) | |||||||
\(948\) | 6.03921 | 0.196145 | ||||||||
\(949\) | 1.51830 | 0.0492860 | ||||||||
\(950\) | 14.9124 | 0.483821 | ||||||||
\(951\) | −59.1481 | −1.91801 | ||||||||
\(952\) | 2.59095 | 0.0839733 | ||||||||
\(953\) | 1.15049 | 0.0372680 | 0.0186340 | − | 0.999826i | \(-0.494068\pi\) | ||||
0.0186340 | + | 0.999826i | \(0.494068\pi\) | |||||||
\(954\) | 42.4727 | 1.37510 | ||||||||
\(955\) | 25.3544 | 0.820448 | ||||||||
\(956\) | 7.27544 | 0.235305 | ||||||||
\(957\) | −58.7468 | −1.89901 | ||||||||
\(958\) | 46.2692 | 1.49489 | ||||||||
\(959\) | −30.5652 | −0.987002 | ||||||||
\(960\) | −8.35840 | −0.269766 | ||||||||
\(961\) | −7.08674 | −0.228604 | ||||||||
\(962\) | −3.97668 | −0.128213 | ||||||||
\(963\) | 6.42039 | 0.206894 | ||||||||
\(964\) | −11.0438 | −0.355697 | ||||||||
\(965\) | −0.336005 | −0.0108164 | ||||||||
\(966\) | −14.2407 | −0.458188 | ||||||||
\(967\) | 25.5896 | 0.822906 | 0.411453 | − | 0.911431i | \(-0.365021\pi\) | ||||
0.411453 | + | 0.911431i | \(0.365021\pi\) | |||||||
\(968\) | −1.91031 | −0.0613997 | ||||||||
\(969\) | 4.82654 | 0.155051 | ||||||||
\(970\) | −35.4327 | −1.13768 | ||||||||
\(971\) | −6.47776 | −0.207881 | −0.103941 | − | 0.994584i | \(-0.533145\pi\) | ||||
−0.103941 | + | 0.994584i | \(0.533145\pi\) | |||||||
\(972\) | −25.0841 | −0.804573 | ||||||||
\(973\) | −8.05831 | −0.258337 | ||||||||
\(974\) | 45.8657 | 1.46963 | ||||||||
\(975\) | −1.55606 | −0.0498337 | ||||||||
\(976\) | 30.5176 | 0.976846 | ||||||||
\(977\) | 25.2304 | 0.807193 | 0.403597 | − | 0.914937i | \(-0.367760\pi\) | ||||
0.403597 | + | 0.914937i | \(0.367760\pi\) | |||||||
\(978\) | 71.2342 | 2.27782 | ||||||||
\(979\) | −8.55238 | −0.273335 | ||||||||
\(980\) | −0.481540 | −0.0153822 | ||||||||
\(981\) | −4.76875 | −0.152255 | ||||||||
\(982\) | 7.31539 | 0.233443 | ||||||||
\(983\) | 60.2674 | 1.92223 | 0.961116 | − | 0.276146i | \(-0.0890572\pi\) | ||||
0.961116 | + | 0.276146i | \(0.0890572\pi\) | |||||||
\(984\) | −8.61576 | −0.274660 | ||||||||
\(985\) | 20.6982 | 0.659498 | ||||||||
\(986\) | 16.4040 | 0.522410 | ||||||||
\(987\) | −25.1748 | −0.801321 | ||||||||
\(988\) | 0.612623 | 0.0194901 | ||||||||
\(989\) | −1.33614 | −0.0424866 | ||||||||
\(990\) | −12.2009 | −0.387770 | ||||||||
\(991\) | −23.7400 | −0.754127 | −0.377064 | − | 0.926187i | \(-0.623066\pi\) | ||||
−0.377064 | + | 0.926187i | \(0.623066\pi\) | |||||||
\(992\) | 33.7712 | 1.07224 | ||||||||
\(993\) | 25.4993 | 0.809196 | ||||||||
\(994\) | −11.0547 | −0.350634 | ||||||||
\(995\) | −8.80639 | −0.279181 | ||||||||
\(996\) | 1.74255 | 0.0552149 | ||||||||
\(997\) | 41.3805 | 1.31053 | 0.655267 | − | 0.755397i | \(-0.272556\pi\) | ||||
0.655267 | + | 0.755397i | \(0.272556\pi\) | |||||||
\(998\) | −43.2180 | −1.36804 | ||||||||
\(999\) | −27.4381 | −0.868102 |
(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 | 731.2.a.e.1.5 | ✓ | 19 | |
3.2 | odd | 2 | 6579.2.a.t.1.15 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.a.e.1.5 | ✓ | 19 | 1.1 | even | 1 | trivial | |
6579.2.a.t.1.15 | 19 | 3.2 | odd | 2 |