Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4013,2,Mod(1,4013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4013.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: | \(32.0439663311\) |
Analytic rank: | \(1\) |
Dimension: | \(157\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81982 | −1.99392 | −0.996958 | − | 0.0779447i | \(-0.975164\pi\) | ||||
−0.996958 | + | 0.0779447i | \(0.975164\pi\) | |||||||
\(3\) | 1.03159 | 0.595591 | 0.297796 | − | 0.954630i | \(-0.403749\pi\) | ||||
0.297796 | + | 0.954630i | \(0.403749\pi\) | |||||||
\(4\) | 5.95140 | 2.97570 | ||||||||
\(5\) | 1.63220 | 0.729943 | 0.364971 | − | 0.931019i | \(-0.381079\pi\) | ||||
0.364971 | + | 0.931019i | \(0.381079\pi\) | |||||||
\(6\) | −2.90891 | −1.18756 | ||||||||
\(7\) | 3.00127 | 1.13437 | 0.567187 | − | 0.823589i | \(-0.308032\pi\) | ||||
0.567187 | + | 0.823589i | \(0.308032\pi\) | |||||||
\(8\) | −11.1422 | −3.93938 | ||||||||
\(9\) | −1.93581 | −0.645271 | ||||||||
\(10\) | −4.60252 | −1.45544 | ||||||||
\(11\) | 4.90998 | 1.48041 | 0.740207 | − | 0.672379i | \(-0.234728\pi\) | ||||
0.740207 | + | 0.672379i | \(0.234728\pi\) | |||||||
\(12\) | 6.13943 | 1.77230 | ||||||||
\(13\) | −5.47917 | −1.51965 | −0.759824 | − | 0.650129i | \(-0.774715\pi\) | ||||
−0.759824 | + | 0.650129i | \(0.774715\pi\) | |||||||
\(14\) | −8.46305 | −2.26185 | ||||||||
\(15\) | 1.68377 | 0.434748 | ||||||||
\(16\) | 19.5163 | 4.87908 | ||||||||
\(17\) | −6.48207 | −1.57213 | −0.786067 | − | 0.618141i | \(-0.787886\pi\) | ||||
−0.786067 | + | 0.618141i | \(0.787886\pi\) | |||||||
\(18\) | 5.45865 | 1.28662 | ||||||||
\(19\) | −4.81887 | −1.10552 | −0.552762 | − | 0.833339i | \(-0.686426\pi\) | ||||
−0.552762 | + | 0.833339i | \(0.686426\pi\) | |||||||
\(20\) | 9.71388 | 2.17209 | ||||||||
\(21\) | 3.09610 | 0.675624 | ||||||||
\(22\) | −13.8453 | −2.95182 | ||||||||
\(23\) | −0.298932 | −0.0623315 | −0.0311658 | − | 0.999514i | \(-0.509922\pi\) | ||||
−0.0311658 | + | 0.999514i | \(0.509922\pi\) | |||||||
\(24\) | −11.4943 | −2.34626 | ||||||||
\(25\) | −2.33592 | −0.467183 | ||||||||
\(26\) | 15.4503 | 3.03005 | ||||||||
\(27\) | −5.09176 | −0.979909 | ||||||||
\(28\) | 17.8618 | 3.37556 | ||||||||
\(29\) | 7.24040 | 1.34451 | 0.672254 | − | 0.740320i | \(-0.265326\pi\) | ||||
0.672254 | + | 0.740320i | \(0.265326\pi\) | |||||||
\(30\) | −4.74793 | −0.866850 | ||||||||
\(31\) | −6.64697 | −1.19383 | −0.596916 | − | 0.802304i | \(-0.703607\pi\) | ||||
−0.596916 | + | 0.802304i | \(0.703607\pi\) | |||||||
\(32\) | −32.7481 | −5.78910 | ||||||||
\(33\) | 5.06510 | 0.881721 | ||||||||
\(34\) | 18.2783 | 3.13470 | ||||||||
\(35\) | 4.89868 | 0.828029 | ||||||||
\(36\) | −11.5208 | −1.92013 | ||||||||
\(37\) | 4.71805 | 0.775642 | 0.387821 | − | 0.921735i | \(-0.373228\pi\) | ||||
0.387821 | + | 0.921735i | \(0.373228\pi\) | |||||||
\(38\) | 13.5883 | 2.20432 | ||||||||
\(39\) | −5.65228 | −0.905089 | ||||||||
\(40\) | −18.1864 | −2.87552 | ||||||||
\(41\) | 2.11712 | 0.330639 | 0.165319 | − | 0.986240i | \(-0.447134\pi\) | ||||
0.165319 | + | 0.986240i | \(0.447134\pi\) | |||||||
\(42\) | −8.73044 | −1.34714 | ||||||||
\(43\) | −3.63811 | −0.554807 | −0.277404 | − | 0.960753i | \(-0.589474\pi\) | ||||
−0.277404 | + | 0.960753i | \(0.589474\pi\) | |||||||
\(44\) | 29.2212 | 4.40526 | ||||||||
\(45\) | −3.15964 | −0.471011 | ||||||||
\(46\) | 0.842934 | 0.124284 | ||||||||
\(47\) | −4.84762 | −0.707097 | −0.353549 | − | 0.935416i | \(-0.615025\pi\) | ||||
−0.353549 | + | 0.935416i | \(0.615025\pi\) | |||||||
\(48\) | 20.1329 | 2.90594 | ||||||||
\(49\) | 2.00764 | 0.286805 | ||||||||
\(50\) | 6.58687 | 0.931524 | ||||||||
\(51\) | −6.68687 | −0.936349 | ||||||||
\(52\) | −32.6087 | −4.52201 | ||||||||
\(53\) | 2.37433 | 0.326139 | 0.163070 | − | 0.986615i | \(-0.447860\pi\) | ||||
0.163070 | + | 0.986615i | \(0.447860\pi\) | |||||||
\(54\) | 14.3579 | 1.95386 | ||||||||
\(55\) | 8.01407 | 1.08062 | ||||||||
\(56\) | −33.4409 | −4.46873 | ||||||||
\(57\) | −4.97112 | −0.658440 | ||||||||
\(58\) | −20.4166 | −2.68084 | ||||||||
\(59\) | 7.57648 | 0.986374 | 0.493187 | − | 0.869923i | \(-0.335832\pi\) | ||||
0.493187 | + | 0.869923i | \(0.335832\pi\) | |||||||
\(60\) | 10.0208 | 1.29368 | ||||||||
\(61\) | −6.90355 | −0.883909 | −0.441955 | − | 0.897037i | \(-0.645715\pi\) | ||||
−0.441955 | + | 0.897037i | \(0.645715\pi\) | |||||||
\(62\) | 18.7433 | 2.38040 | ||||||||
\(63\) | −5.80990 | −0.731979 | ||||||||
\(64\) | 53.3112 | 6.66390 | ||||||||
\(65\) | −8.94311 | −1.10926 | ||||||||
\(66\) | −14.2827 | −1.75808 | ||||||||
\(67\) | −0.975192 | −0.119139 | −0.0595693 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595693 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(68\) | −38.5774 | −4.67820 | ||||||||
\(69\) | −0.308376 | −0.0371241 | ||||||||
\(70\) | −13.8134 | −1.65102 | ||||||||
\(71\) | 9.25846 | 1.09878 | 0.549389 | − | 0.835567i | \(-0.314861\pi\) | ||||
0.549389 | + | 0.835567i | \(0.314861\pi\) | |||||||
\(72\) | 21.5693 | 2.54196 | ||||||||
\(73\) | −11.2782 | −1.32001 | −0.660004 | − | 0.751262i | \(-0.729445\pi\) | ||||
−0.660004 | + | 0.751262i | \(0.729445\pi\) | |||||||
\(74\) | −13.3040 | −1.54656 | ||||||||
\(75\) | −2.40972 | −0.278250 | ||||||||
\(76\) | −28.6790 | −3.28971 | ||||||||
\(77\) | 14.7362 | 1.67934 | ||||||||
\(78\) | 15.9384 | 1.80467 | ||||||||
\(79\) | 11.5118 | 1.29517 | 0.647587 | − | 0.761992i | \(-0.275778\pi\) | ||||
0.647587 | + | 0.761992i | \(0.275778\pi\) | |||||||
\(80\) | 31.8546 | 3.56145 | ||||||||
\(81\) | 0.554809 | 0.0616454 | ||||||||
\(82\) | −5.96991 | −0.659266 | ||||||||
\(83\) | 10.2684 | 1.12711 | 0.563554 | − | 0.826080i | \(-0.309434\pi\) | ||||
0.563554 | + | 0.826080i | \(0.309434\pi\) | |||||||
\(84\) | 18.4261 | 2.01045 | ||||||||
\(85\) | −10.5801 | −1.14757 | ||||||||
\(86\) | 10.2588 | 1.10624 | ||||||||
\(87\) | 7.46916 | 0.800778 | ||||||||
\(88\) | −54.7081 | −5.83190 | ||||||||
\(89\) | −14.4094 | −1.52739 | −0.763697 | − | 0.645574i | \(-0.776618\pi\) | ||||
−0.763697 | + | 0.645574i | \(0.776618\pi\) | |||||||
\(90\) | 8.90962 | 0.939156 | ||||||||
\(91\) | −16.4445 | −1.72385 | ||||||||
\(92\) | −1.77906 | −0.185480 | ||||||||
\(93\) | −6.85698 | −0.711036 | ||||||||
\(94\) | 13.6694 | 1.40989 | ||||||||
\(95\) | −7.86536 | −0.806969 | ||||||||
\(96\) | −33.7828 | −3.44794 | ||||||||
\(97\) | −17.5407 | −1.78098 | −0.890492 | − | 0.454998i | \(-0.849640\pi\) | ||||
−0.890492 | + | 0.454998i | \(0.849640\pi\) | |||||||
\(98\) | −5.66118 | −0.571865 | ||||||||
\(99\) | −9.50479 | −0.955268 | ||||||||
\(100\) | −13.9020 | −1.39020 | ||||||||
\(101\) | −13.0898 | −1.30248 | −0.651242 | − | 0.758870i | \(-0.725752\pi\) | ||||
−0.651242 | + | 0.758870i | \(0.725752\pi\) | |||||||
\(102\) | 18.8558 | 1.86700 | ||||||||
\(103\) | −11.9455 | −1.17702 | −0.588511 | − | 0.808489i | \(-0.700286\pi\) | ||||
−0.588511 | + | 0.808489i | \(0.700286\pi\) | |||||||
\(104\) | 61.0502 | 5.98646 | ||||||||
\(105\) | 5.05345 | 0.493167 | ||||||||
\(106\) | −6.69519 | −0.650294 | ||||||||
\(107\) | 3.55055 | 0.343245 | 0.171623 | − | 0.985163i | \(-0.445099\pi\) | ||||
0.171623 | + | 0.985163i | \(0.445099\pi\) | |||||||
\(108\) | −30.3031 | −2.91591 | ||||||||
\(109\) | −14.0076 | −1.34168 | −0.670842 | − | 0.741600i | \(-0.734067\pi\) | ||||
−0.670842 | + | 0.741600i | \(0.734067\pi\) | |||||||
\(110\) | −22.5983 | −2.15466 | ||||||||
\(111\) | 4.86711 | 0.461966 | ||||||||
\(112\) | 58.5738 | 5.53471 | ||||||||
\(113\) | −4.46545 | −0.420074 | −0.210037 | − | 0.977693i | \(-0.567358\pi\) | ||||
−0.210037 | + | 0.977693i | \(0.567358\pi\) | |||||||
\(114\) | 14.0177 | 1.31287 | ||||||||
\(115\) | −0.487917 | −0.0454985 | ||||||||
\(116\) | 43.0905 | 4.00085 | ||||||||
\(117\) | 10.6066 | 0.980584 | ||||||||
\(118\) | −21.3643 | −1.96675 | ||||||||
\(119\) | −19.4545 | −1.78339 | ||||||||
\(120\) | −18.7610 | −1.71263 | ||||||||
\(121\) | 13.1079 | 1.19162 | ||||||||
\(122\) | 19.4668 | 1.76244 | ||||||||
\(123\) | 2.18401 | 0.196926 | ||||||||
\(124\) | −39.5588 | −3.55248 | ||||||||
\(125\) | −11.9737 | −1.07096 | ||||||||
\(126\) | 16.3829 | 1.45950 | ||||||||
\(127\) | −5.69251 | −0.505128 | −0.252564 | − | 0.967580i | \(-0.581274\pi\) | ||||
−0.252564 | + | 0.967580i | \(0.581274\pi\) | |||||||
\(128\) | −84.8318 | −7.49815 | ||||||||
\(129\) | −3.75306 | −0.330438 | ||||||||
\(130\) | 25.2180 | 2.21176 | ||||||||
\(131\) | −6.12789 | −0.535397 | −0.267698 | − | 0.963503i | \(-0.586263\pi\) | ||||
−0.267698 | + | 0.963503i | \(0.586263\pi\) | |||||||
\(132\) | 30.1444 | 2.62374 | ||||||||
\(133\) | −14.4627 | −1.25408 | ||||||||
\(134\) | 2.74987 | 0.237552 | ||||||||
\(135\) | −8.31078 | −0.715278 | ||||||||
\(136\) | 72.2248 | 6.19323 | ||||||||
\(137\) | 4.66038 | 0.398163 | 0.199082 | − | 0.979983i | \(-0.436204\pi\) | ||||
0.199082 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(138\) | 0.869566 | 0.0740224 | ||||||||
\(139\) | 10.7876 | 0.914994 | 0.457497 | − | 0.889211i | \(-0.348746\pi\) | ||||
0.457497 | + | 0.889211i | \(0.348746\pi\) | |||||||
\(140\) | 29.1540 | 2.46396 | ||||||||
\(141\) | −5.00077 | −0.421141 | ||||||||
\(142\) | −26.1072 | −2.19087 | ||||||||
\(143\) | −26.9026 | −2.24971 | ||||||||
\(144\) | −37.7800 | −3.14833 | ||||||||
\(145\) | 11.8178 | 0.981415 | ||||||||
\(146\) | 31.8024 | 2.63198 | ||||||||
\(147\) | 2.07107 | 0.170819 | ||||||||
\(148\) | 28.0790 | 2.30808 | ||||||||
\(149\) | −11.9737 | −0.980926 | −0.490463 | − | 0.871462i | \(-0.663172\pi\) | ||||
−0.490463 | + | 0.871462i | \(0.663172\pi\) | |||||||
\(150\) | 6.79498 | 0.554808 | ||||||||
\(151\) | −12.3400 | −1.00421 | −0.502107 | − | 0.864805i | \(-0.667442\pi\) | ||||
−0.502107 | + | 0.864805i | \(0.667442\pi\) | |||||||
\(152\) | 53.6929 | 4.35507 | ||||||||
\(153\) | 12.5481 | 1.01445 | ||||||||
\(154\) | −41.5534 | −3.34847 | ||||||||
\(155\) | −10.8492 | −0.871429 | ||||||||
\(156\) | −33.6390 | −2.69327 | ||||||||
\(157\) | −8.94198 | −0.713648 | −0.356824 | − | 0.934172i | \(-0.616140\pi\) | ||||
−0.356824 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(158\) | −32.4611 | −2.58247 | ||||||||
\(159\) | 2.44934 | 0.194246 | ||||||||
\(160\) | −53.4515 | −4.22572 | ||||||||
\(161\) | −0.897175 | −0.0707073 | ||||||||
\(162\) | −1.56446 | −0.122916 | ||||||||
\(163\) | 10.8844 | 0.852535 | 0.426267 | − | 0.904597i | \(-0.359828\pi\) | ||||
0.426267 | + | 0.904597i | \(0.359828\pi\) | |||||||
\(164\) | 12.5998 | 0.983882 | ||||||||
\(165\) | 8.26727 | 0.643606 | ||||||||
\(166\) | −28.9552 | −2.24736 | ||||||||
\(167\) | −7.35515 | −0.569159 | −0.284579 | − | 0.958653i | \(-0.591854\pi\) | ||||
−0.284579 | + | 0.958653i | \(0.591854\pi\) | |||||||
\(168\) | −34.4974 | −2.66154 | ||||||||
\(169\) | 17.0213 | 1.30933 | ||||||||
\(170\) | 29.8339 | 2.28815 | ||||||||
\(171\) | 9.32842 | 0.713362 | ||||||||
\(172\) | −21.6519 | −1.65094 | ||||||||
\(173\) | −7.00564 | −0.532629 | −0.266314 | − | 0.963886i | \(-0.585806\pi\) | ||||
−0.266314 | + | 0.963886i | \(0.585806\pi\) | |||||||
\(174\) | −21.0617 | −1.59668 | ||||||||
\(175\) | −7.01072 | −0.529961 | ||||||||
\(176\) | 95.8247 | 7.22306 | ||||||||
\(177\) | 7.81586 | 0.587476 | ||||||||
\(178\) | 40.6320 | 3.04550 | ||||||||
\(179\) | −2.90858 | −0.217397 | −0.108699 | − | 0.994075i | \(-0.534668\pi\) | ||||
−0.108699 | + | 0.994075i | \(0.534668\pi\) | |||||||
\(180\) | −18.8043 | −1.40159 | ||||||||
\(181\) | −13.0636 | −0.971008 | −0.485504 | − | 0.874235i | \(-0.661364\pi\) | ||||
−0.485504 | + | 0.874235i | \(0.661364\pi\) | |||||||
\(182\) | 46.3705 | 3.43721 | ||||||||
\(183\) | −7.12167 | −0.526449 | ||||||||
\(184\) | 3.33077 | 0.245547 | ||||||||
\(185\) | 7.70080 | 0.566174 | ||||||||
\(186\) | 19.3355 | 1.41775 | ||||||||
\(187\) | −31.8268 | −2.32741 | ||||||||
\(188\) | −28.8501 | −2.10411 | ||||||||
\(189\) | −15.2818 | −1.11158 | ||||||||
\(190\) | 22.1789 | 1.60903 | ||||||||
\(191\) | 14.5844 | 1.05529 | 0.527646 | − | 0.849464i | \(-0.323075\pi\) | ||||
0.527646 | + | 0.849464i | \(0.323075\pi\) | |||||||
\(192\) | 54.9955 | 3.96896 | ||||||||
\(193\) | −3.72783 | −0.268335 | −0.134167 | − | 0.990959i | \(-0.542836\pi\) | ||||
−0.134167 | + | 0.990959i | \(0.542836\pi\) | |||||||
\(194\) | 49.4615 | 3.55113 | ||||||||
\(195\) | −9.22566 | −0.660663 | ||||||||
\(196\) | 11.9482 | 0.853446 | ||||||||
\(197\) | 23.8734 | 1.70091 | 0.850455 | − | 0.526048i | \(-0.176327\pi\) | ||||
0.850455 | + | 0.526048i | \(0.176327\pi\) | |||||||
\(198\) | 26.8018 | 1.90472 | ||||||||
\(199\) | 19.0289 | 1.34892 | 0.674462 | − | 0.738310i | \(-0.264376\pi\) | ||||
0.674462 | + | 0.738310i | \(0.264376\pi\) | |||||||
\(200\) | 26.0273 | 1.84041 | ||||||||
\(201\) | −1.00600 | −0.0709579 | ||||||||
\(202\) | 36.9109 | 2.59704 | ||||||||
\(203\) | 21.7304 | 1.52518 | ||||||||
\(204\) | −39.7962 | −2.78629 | ||||||||
\(205\) | 3.45557 | 0.241348 | ||||||||
\(206\) | 33.6841 | 2.34688 | ||||||||
\(207\) | 0.578675 | 0.0402207 | ||||||||
\(208\) | −106.933 | −7.41449 | ||||||||
\(209\) | −23.6605 | −1.63663 | ||||||||
\(210\) | −14.2498 | −0.983333 | ||||||||
\(211\) | 5.29850 | 0.364764 | 0.182382 | − | 0.983228i | \(-0.441619\pi\) | ||||
0.182382 | + | 0.983228i | \(0.441619\pi\) | |||||||
\(212\) | 14.1306 | 0.970492 | ||||||||
\(213\) | 9.55098 | 0.654422 | ||||||||
\(214\) | −10.0119 | −0.684402 | ||||||||
\(215\) | −5.93814 | −0.404978 | ||||||||
\(216\) | 56.7336 | 3.86023 | ||||||||
\(217\) | −19.9494 | −1.35425 | ||||||||
\(218\) | 39.4989 | 2.67521 | ||||||||
\(219\) | −11.6345 | −0.786185 | ||||||||
\(220\) | 47.6949 | 3.21559 | ||||||||
\(221\) | 35.5164 | 2.38909 | ||||||||
\(222\) | −13.7244 | −0.921120 | ||||||||
\(223\) | −2.49768 | −0.167257 | −0.0836286 | − | 0.996497i | \(-0.526651\pi\) | ||||
−0.0836286 | + | 0.996497i | \(0.526651\pi\) | |||||||
\(224\) | −98.2860 | −6.56701 | ||||||||
\(225\) | 4.52190 | 0.301460 | ||||||||
\(226\) | 12.5918 | 0.837592 | ||||||||
\(227\) | 16.8104 | 1.11574 | 0.557872 | − | 0.829927i | \(-0.311618\pi\) | ||||
0.557872 | + | 0.829927i | \(0.311618\pi\) | |||||||
\(228\) | −29.5851 | −1.95932 | ||||||||
\(229\) | 23.0956 | 1.52620 | 0.763100 | − | 0.646280i | \(-0.223676\pi\) | ||||
0.763100 | + | 0.646280i | \(0.223676\pi\) | |||||||
\(230\) | 1.37584 | 0.0907201 | ||||||||
\(231\) | 15.2018 | 1.00020 | ||||||||
\(232\) | −80.6743 | −5.29653 | ||||||||
\(233\) | −28.0004 | −1.83437 | −0.917183 | − | 0.398467i | \(-0.869542\pi\) | ||||
−0.917183 | + | 0.398467i | \(0.869542\pi\) | |||||||
\(234\) | −29.9088 | −1.95520 | ||||||||
\(235\) | −7.91229 | −0.516141 | ||||||||
\(236\) | 45.0907 | 2.93515 | ||||||||
\(237\) | 11.8755 | 0.771394 | ||||||||
\(238\) | 54.8581 | 3.55593 | ||||||||
\(239\) | −5.86560 | −0.379414 | −0.189707 | − | 0.981841i | \(-0.560754\pi\) | ||||
−0.189707 | + | 0.981841i | \(0.560754\pi\) | |||||||
\(240\) | 32.8610 | 2.12117 | ||||||||
\(241\) | 1.30460 | 0.0840366 | 0.0420183 | − | 0.999117i | \(-0.486621\pi\) | ||||
0.0420183 | + | 0.999117i | \(0.486621\pi\) | |||||||
\(242\) | −36.9618 | −2.37600 | ||||||||
\(243\) | 15.8476 | 1.01662 | ||||||||
\(244\) | −41.0858 | −2.63025 | ||||||||
\(245\) | 3.27687 | 0.209351 | ||||||||
\(246\) | −6.15852 | −0.392653 | ||||||||
\(247\) | 26.4034 | 1.68001 | ||||||||
\(248\) | 74.0622 | 4.70295 | ||||||||
\(249\) | 10.5929 | 0.671295 | ||||||||
\(250\) | 33.7637 | 2.13540 | ||||||||
\(251\) | 28.8995 | 1.82412 | 0.912059 | − | 0.410060i | \(-0.134492\pi\) | ||||
0.912059 | + | 0.410060i | \(0.134492\pi\) | |||||||
\(252\) | −34.5770 | −2.17815 | ||||||||
\(253\) | −1.46775 | −0.0922764 | ||||||||
\(254\) | 16.0519 | 1.00718 | ||||||||
\(255\) | −10.9143 | −0.683482 | ||||||||
\(256\) | 132.588 | 8.28677 | ||||||||
\(257\) | 9.90390 | 0.617788 | 0.308894 | − | 0.951096i | \(-0.400041\pi\) | ||||
0.308894 | + | 0.951096i | \(0.400041\pi\) | |||||||
\(258\) | 10.5830 | 0.658866 | ||||||||
\(259\) | 14.1601 | 0.879868 | ||||||||
\(260\) | −53.2240 | −3.30081 | ||||||||
\(261\) | −14.0161 | −0.867572 | ||||||||
\(262\) | 17.2796 | 1.06754 | ||||||||
\(263\) | 10.2382 | 0.631316 | 0.315658 | − | 0.948873i | \(-0.397775\pi\) | ||||
0.315658 | + | 0.948873i | \(0.397775\pi\) | |||||||
\(264\) | −56.4366 | −3.47343 | ||||||||
\(265\) | 3.87538 | 0.238063 | ||||||||
\(266\) | 40.7823 | 2.50052 | ||||||||
\(267\) | −14.8647 | −0.909703 | ||||||||
\(268\) | −5.80375 | −0.354521 | ||||||||
\(269\) | −9.88154 | −0.602488 | −0.301244 | − | 0.953547i | \(-0.597402\pi\) | ||||
−0.301244 | + | 0.953547i | \(0.597402\pi\) | |||||||
\(270\) | 23.4349 | 1.42620 | ||||||||
\(271\) | −22.9893 | −1.39650 | −0.698250 | − | 0.715854i | \(-0.746037\pi\) | ||||
−0.698250 | + | 0.715854i | \(0.746037\pi\) | |||||||
\(272\) | −126.506 | −7.67057 | ||||||||
\(273\) | −16.9640 | −1.02671 | ||||||||
\(274\) | −13.1414 | −0.793904 | ||||||||
\(275\) | −11.4693 | −0.691624 | ||||||||
\(276\) | −1.83527 | −0.110470 | ||||||||
\(277\) | 2.97484 | 0.178741 | 0.0893705 | − | 0.995998i | \(-0.471514\pi\) | ||||
0.0893705 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(278\) | −30.4192 | −1.82442 | ||||||||
\(279\) | 12.8673 | 0.770345 | ||||||||
\(280\) | −54.5823 | −3.26192 | ||||||||
\(281\) | −25.0556 | −1.49469 | −0.747346 | − | 0.664435i | \(-0.768672\pi\) | ||||
−0.747346 | + | 0.664435i | \(0.768672\pi\) | |||||||
\(282\) | 14.1013 | 0.839720 | ||||||||
\(283\) | 22.8372 | 1.35753 | 0.678766 | − | 0.734355i | \(-0.262515\pi\) | ||||
0.678766 | + | 0.734355i | \(0.262515\pi\) | |||||||
\(284\) | 55.1008 | 3.26963 | ||||||||
\(285\) | −8.11387 | −0.480624 | ||||||||
\(286\) | 75.8605 | 4.48572 | ||||||||
\(287\) | 6.35406 | 0.375068 | ||||||||
\(288\) | 63.3942 | 3.73554 | ||||||||
\(289\) | 25.0173 | 1.47160 | ||||||||
\(290\) | −33.3241 | −1.95686 | ||||||||
\(291\) | −18.0949 | −1.06074 | ||||||||
\(292\) | −67.1208 | −3.92794 | ||||||||
\(293\) | −28.3112 | −1.65396 | −0.826978 | − | 0.562235i | \(-0.809942\pi\) | ||||
−0.826978 | + | 0.562235i | \(0.809942\pi\) | |||||||
\(294\) | −5.84004 | −0.340598 | ||||||||
\(295\) | 12.3664 | 0.719997 | ||||||||
\(296\) | −52.5696 | −3.05554 | ||||||||
\(297\) | −25.0004 | −1.45067 | ||||||||
\(298\) | 33.7638 | 1.95588 | ||||||||
\(299\) | 1.63790 | 0.0947220 | ||||||||
\(300\) | −14.3412 | −0.827989 | ||||||||
\(301\) | −10.9190 | −0.629359 | ||||||||
\(302\) | 34.7966 | 2.00232 | ||||||||
\(303\) | −13.5034 | −0.775749 | ||||||||
\(304\) | −94.0466 | −5.39394 | ||||||||
\(305\) | −11.2680 | −0.645203 | ||||||||
\(306\) | −35.3834 | −2.02273 | ||||||||
\(307\) | −12.6484 | −0.721882 | −0.360941 | − | 0.932589i | \(-0.617544\pi\) | ||||
−0.360941 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(308\) | 87.7008 | 4.99722 | ||||||||
\(309\) | −12.3229 | −0.701024 | ||||||||
\(310\) | 30.5928 | 1.73756 | ||||||||
\(311\) | −0.962252 | −0.0545643 | −0.0272822 | − | 0.999628i | \(-0.508685\pi\) | ||||
−0.0272822 | + | 0.999628i | \(0.508685\pi\) | |||||||
\(312\) | 62.9790 | 3.56549 | ||||||||
\(313\) | −14.3470 | −0.810938 | −0.405469 | − | 0.914109i | \(-0.632892\pi\) | ||||
−0.405469 | + | 0.914109i | \(0.632892\pi\) | |||||||
\(314\) | 25.2148 | 1.42295 | ||||||||
\(315\) | −9.48293 | −0.534303 | ||||||||
\(316\) | 68.5110 | 3.85405 | ||||||||
\(317\) | 21.0823 | 1.18410 | 0.592049 | − | 0.805902i | \(-0.298319\pi\) | ||||
0.592049 | + | 0.805902i | \(0.298319\pi\) | |||||||
\(318\) | −6.90672 | −0.387309 | ||||||||
\(319\) | 35.5502 | 1.99043 | ||||||||
\(320\) | 87.0146 | 4.86427 | ||||||||
\(321\) | 3.66273 | 0.204434 | ||||||||
\(322\) | 2.52987 | 0.140984 | ||||||||
\(323\) | 31.2362 | 1.73803 | ||||||||
\(324\) | 3.30189 | 0.183438 | ||||||||
\(325\) | 12.7989 | 0.709954 | ||||||||
\(326\) | −30.6922 | −1.69988 | ||||||||
\(327\) | −14.4502 | −0.799096 | ||||||||
\(328\) | −23.5895 | −1.30251 | ||||||||
\(329\) | −14.5490 | −0.802113 | ||||||||
\(330\) | −23.3122 | −1.28330 | ||||||||
\(331\) | −3.09575 | −0.170158 | −0.0850790 | − | 0.996374i | \(-0.527114\pi\) | ||||
−0.0850790 | + | 0.996374i | \(0.527114\pi\) | |||||||
\(332\) | 61.1115 | 3.35393 | ||||||||
\(333\) | −9.13325 | −0.500499 | ||||||||
\(334\) | 20.7402 | 1.13485 | ||||||||
\(335\) | −1.59171 | −0.0869644 | ||||||||
\(336\) | 60.4244 | 3.29642 | ||||||||
\(337\) | −4.30290 | −0.234394 | −0.117197 | − | 0.993109i | \(-0.537391\pi\) | ||||
−0.117197 | + | 0.993109i | \(0.537391\pi\) | |||||||
\(338\) | −47.9970 | −2.61069 | ||||||||
\(339\) | −4.60653 | −0.250192 | ||||||||
\(340\) | −62.9661 | −3.41482 | ||||||||
\(341\) | −32.6365 | −1.76736 | ||||||||
\(342\) | −26.3045 | −1.42238 | ||||||||
\(343\) | −14.9834 | −0.809030 | ||||||||
\(344\) | 40.5367 | 2.18559 | ||||||||
\(345\) | −0.503332 | −0.0270985 | ||||||||
\(346\) | 19.7547 | 1.06202 | ||||||||
\(347\) | 6.23494 | 0.334709 | 0.167355 | − | 0.985897i | \(-0.446478\pi\) | ||||
0.167355 | + | 0.985897i | \(0.446478\pi\) | |||||||
\(348\) | 44.4519 | 2.38287 | ||||||||
\(349\) | −16.8738 | −0.903232 | −0.451616 | − | 0.892212i | \(-0.649152\pi\) | ||||
−0.451616 | + | 0.892212i | \(0.649152\pi\) | |||||||
\(350\) | 19.7690 | 1.05670 | ||||||||
\(351\) | 27.8986 | 1.48912 | ||||||||
\(352\) | −160.792 | −8.57027 | ||||||||
\(353\) | 2.28194 | 0.121455 | 0.0607276 | − | 0.998154i | \(-0.480658\pi\) | ||||
0.0607276 | + | 0.998154i | \(0.480658\pi\) | |||||||
\(354\) | −22.0393 | −1.17138 | ||||||||
\(355\) | 15.1117 | 0.802045 | ||||||||
\(356\) | −85.7561 | −4.54507 | ||||||||
\(357\) | −20.0691 | −1.06217 | ||||||||
\(358\) | 8.20167 | 0.433472 | ||||||||
\(359\) | −22.1412 | −1.16857 | −0.584283 | − | 0.811550i | \(-0.698624\pi\) | ||||
−0.584283 | + | 0.811550i | \(0.698624\pi\) | |||||||
\(360\) | 35.2054 | 1.85549 | ||||||||
\(361\) | 4.22147 | 0.222183 | ||||||||
\(362\) | 36.8369 | 1.93611 | ||||||||
\(363\) | 13.5220 | 0.709721 | ||||||||
\(364\) | −97.8676 | −5.12966 | ||||||||
\(365\) | −18.4082 | −0.963530 | ||||||||
\(366\) | 20.0818 | 1.04969 | ||||||||
\(367\) | 4.05357 | 0.211595 | 0.105797 | − | 0.994388i | \(-0.466260\pi\) | ||||
0.105797 | + | 0.994388i | \(0.466260\pi\) | |||||||
\(368\) | −5.83405 | −0.304121 | ||||||||
\(369\) | −4.09835 | −0.213352 | ||||||||
\(370\) | −21.7149 | −1.12890 | ||||||||
\(371\) | 7.12601 | 0.369964 | ||||||||
\(372\) | −40.8086 | −2.11583 | ||||||||
\(373\) | −3.35329 | −0.173627 | −0.0868133 | − | 0.996225i | \(-0.527668\pi\) | ||||
−0.0868133 | + | 0.996225i | \(0.527668\pi\) | |||||||
\(374\) | 89.7460 | 4.64065 | ||||||||
\(375\) | −12.3520 | −0.637855 | ||||||||
\(376\) | 54.0133 | 2.78552 | ||||||||
\(377\) | −39.6714 | −2.04318 | ||||||||
\(378\) | 43.0918 | 2.21640 | ||||||||
\(379\) | −5.00597 | −0.257139 | −0.128570 | − | 0.991700i | \(-0.541039\pi\) | ||||
−0.128570 | + | 0.991700i | \(0.541039\pi\) | |||||||
\(380\) | −46.8099 | −2.40130 | ||||||||
\(381\) | −5.87236 | −0.300850 | ||||||||
\(382\) | −41.1255 | −2.10416 | ||||||||
\(383\) | 8.96283 | 0.457979 | 0.228990 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228990 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(384\) | −87.5121 | −4.46583 | ||||||||
\(385\) | 24.0524 | 1.22582 | ||||||||
\(386\) | 10.5118 | 0.535037 | ||||||||
\(387\) | 7.04271 | 0.358001 | ||||||||
\(388\) | −104.391 | −5.29967 | ||||||||
\(389\) | −24.7213 | −1.25342 | −0.626710 | − | 0.779253i | \(-0.715599\pi\) | ||||
−0.626710 | + | 0.779253i | \(0.715599\pi\) | |||||||
\(390\) | 26.0147 | 1.31731 | ||||||||
\(391\) | 1.93770 | 0.0979935 | ||||||||
\(392\) | −22.3696 | −1.12983 | ||||||||
\(393\) | −6.32150 | −0.318878 | ||||||||
\(394\) | −67.3188 | −3.39147 | ||||||||
\(395\) | 18.7895 | 0.945403 | ||||||||
\(396\) | −56.5668 | −2.84259 | ||||||||
\(397\) | 20.2495 | 1.01629 | 0.508147 | − | 0.861270i | \(-0.330331\pi\) | ||||
0.508147 | + | 0.861270i | \(0.330331\pi\) | |||||||
\(398\) | −53.6582 | −2.68964 | ||||||||
\(399\) | −14.9197 | −0.746918 | ||||||||
\(400\) | −45.5885 | −2.27943 | ||||||||
\(401\) | 20.9110 | 1.04425 | 0.522123 | − | 0.852870i | \(-0.325140\pi\) | ||||
0.522123 | + | 0.852870i | \(0.325140\pi\) | |||||||
\(402\) | 2.83675 | 0.141484 | ||||||||
\(403\) | 36.4199 | 1.81420 | ||||||||
\(404\) | −77.9027 | −3.87580 | ||||||||
\(405\) | 0.905560 | 0.0449977 | ||||||||
\(406\) | −61.2759 | −3.04107 | ||||||||
\(407\) | 23.1655 | 1.14827 | ||||||||
\(408\) | 74.5067 | 3.68863 | ||||||||
\(409\) | −15.1092 | −0.747102 | −0.373551 | − | 0.927610i | \(-0.621860\pi\) | ||||
−0.373551 | + | 0.927610i | \(0.621860\pi\) | |||||||
\(410\) | −9.74409 | −0.481227 | ||||||||
\(411\) | 4.80762 | 0.237143 | ||||||||
\(412\) | −71.0922 | −3.50246 | ||||||||
\(413\) | 22.7391 | 1.11892 | ||||||||
\(414\) | −1.63176 | −0.0801967 | ||||||||
\(415\) | 16.7602 | 0.822724 | ||||||||
\(416\) | 179.432 | 8.79740 | ||||||||
\(417\) | 11.1285 | 0.544963 | ||||||||
\(418\) | 66.7184 | 3.26331 | ||||||||
\(419\) | 22.0687 | 1.07813 | 0.539063 | − | 0.842265i | \(-0.318778\pi\) | ||||
0.539063 | + | 0.842265i | \(0.318778\pi\) | |||||||
\(420\) | 30.0751 | 1.46752 | ||||||||
\(421\) | −40.0155 | −1.95024 | −0.975118 | − | 0.221689i | \(-0.928843\pi\) | ||||
−0.975118 | + | 0.221689i | \(0.928843\pi\) | |||||||
\(422\) | −14.9408 | −0.727308 | ||||||||
\(423\) | 9.38408 | 0.456269 | ||||||||
\(424\) | −26.4553 | −1.28478 | ||||||||
\(425\) | 15.1416 | 0.734475 | ||||||||
\(426\) | −26.9321 | −1.30486 | ||||||||
\(427\) | −20.7194 | −1.00268 | ||||||||
\(428\) | 21.1308 | 1.02139 | ||||||||
\(429\) | −27.7526 | −1.33991 | ||||||||
\(430\) | 16.7445 | 0.807491 | ||||||||
\(431\) | −31.4461 | −1.51471 | −0.757353 | − | 0.653005i | \(-0.773508\pi\) | ||||
−0.757353 | + | 0.653005i | \(0.773508\pi\) | |||||||
\(432\) | −99.3724 | −4.78106 | ||||||||
\(433\) | −27.0905 | −1.30189 | −0.650944 | − | 0.759126i | \(-0.725627\pi\) | ||||
−0.650944 | + | 0.759126i | \(0.725627\pi\) | |||||||
\(434\) | 56.2537 | 2.70026 | ||||||||
\(435\) | 12.1912 | 0.584522 | ||||||||
\(436\) | −83.3648 | −3.99245 | ||||||||
\(437\) | 1.44051 | 0.0689090 | ||||||||
\(438\) | 32.8072 | 1.56759 | ||||||||
\(439\) | −7.96189 | −0.380000 | −0.190000 | − | 0.981784i | \(-0.560849\pi\) | ||||
−0.190000 | + | 0.981784i | \(0.560849\pi\) | |||||||
\(440\) | −89.2947 | −4.25696 | ||||||||
\(441\) | −3.88641 | −0.185067 | ||||||||
\(442\) | −100.150 | −4.76364 | ||||||||
\(443\) | 32.3402 | 1.53653 | 0.768264 | − | 0.640133i | \(-0.221121\pi\) | ||||
0.768264 | + | 0.640133i | \(0.221121\pi\) | |||||||
\(444\) | 28.9661 | 1.37467 | ||||||||
\(445\) | −23.5191 | −1.11491 | ||||||||
\(446\) | 7.04302 | 0.333497 | ||||||||
\(447\) | −12.3520 | −0.584231 | ||||||||
\(448\) | 160.001 | 7.55936 | ||||||||
\(449\) | −8.57427 | −0.404645 | −0.202322 | − | 0.979319i | \(-0.564849\pi\) | ||||
−0.202322 | + | 0.979319i | \(0.564849\pi\) | |||||||
\(450\) | −12.7509 | −0.601085 | ||||||||
\(451\) | 10.3950 | 0.489482 | ||||||||
\(452\) | −26.5756 | −1.25001 | ||||||||
\(453\) | −12.7299 | −0.598102 | ||||||||
\(454\) | −47.4022 | −2.22470 | ||||||||
\(455\) | −26.8407 | −1.25831 | ||||||||
\(456\) | 55.3894 | 2.59384 | ||||||||
\(457\) | 13.8460 | 0.647688 | 0.323844 | − | 0.946110i | \(-0.395025\pi\) | ||||
0.323844 | + | 0.946110i | \(0.395025\pi\) | |||||||
\(458\) | −65.1255 | −3.04312 | ||||||||
\(459\) | 33.0051 | 1.54055 | ||||||||
\(460\) | −2.90379 | −0.135390 | ||||||||
\(461\) | 25.2053 | 1.17393 | 0.586964 | − | 0.809613i | \(-0.300323\pi\) | ||||
0.586964 | + | 0.809613i | \(0.300323\pi\) | |||||||
\(462\) | −42.8663 | −1.99432 | ||||||||
\(463\) | 14.9530 | 0.694925 | 0.347462 | − | 0.937694i | \(-0.387043\pi\) | ||||
0.347462 | + | 0.937694i | \(0.387043\pi\) | |||||||
\(464\) | 141.306 | 6.55997 | ||||||||
\(465\) | −11.1920 | −0.519016 | ||||||||
\(466\) | 78.9561 | 3.65757 | ||||||||
\(467\) | −11.7295 | −0.542777 | −0.271389 | − | 0.962470i | \(-0.587483\pi\) | ||||
−0.271389 | + | 0.962470i | \(0.587483\pi\) | |||||||
\(468\) | 63.1243 | 2.91792 | ||||||||
\(469\) | −2.92682 | −0.135148 | ||||||||
\(470\) | 22.3112 | 1.02914 | ||||||||
\(471\) | −9.22450 | −0.425042 | ||||||||
\(472\) | −84.4190 | −3.88570 | ||||||||
\(473\) | −17.8631 | −0.821344 | ||||||||
\(474\) | −33.4867 | −1.53809 | ||||||||
\(475\) | 11.2565 | 0.516482 | ||||||||
\(476\) | −115.781 | −5.30683 | ||||||||
\(477\) | −4.59626 | −0.210448 | ||||||||
\(478\) | 16.5399 | 0.756519 | ||||||||
\(479\) | −30.8541 | −1.40976 | −0.704880 | − | 0.709326i | \(-0.748999\pi\) | ||||
−0.704880 | + | 0.709326i | \(0.748999\pi\) | |||||||
\(480\) | −55.1403 | −2.51680 | ||||||||
\(481\) | −25.8510 | −1.17870 | ||||||||
\(482\) | −3.67874 | −0.167562 | ||||||||
\(483\) | −0.925521 | −0.0421127 | ||||||||
\(484\) | 78.0101 | 3.54591 | ||||||||
\(485\) | −28.6299 | −1.30002 | ||||||||
\(486\) | −44.6874 | −2.02706 | ||||||||
\(487\) | 24.9298 | 1.12968 | 0.564840 | − | 0.825201i | \(-0.308938\pi\) | ||||
0.564840 | + | 0.825201i | \(0.308938\pi\) | |||||||
\(488\) | 76.9210 | 3.48205 | ||||||||
\(489\) | 11.2283 | 0.507762 | ||||||||
\(490\) | −9.24018 | −0.417429 | ||||||||
\(491\) | 2.50375 | 0.112992 | 0.0564962 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564962 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(492\) | 12.9979 | 0.585991 | ||||||||
\(493\) | −46.9328 | −2.11375 | ||||||||
\(494\) | −74.4528 | −3.34979 | ||||||||
\(495\) | −15.5137 | −0.697291 | ||||||||
\(496\) | −129.725 | −5.82480 | ||||||||
\(497\) | 27.7872 | 1.24642 | ||||||||
\(498\) | −29.8700 | −1.33851 | ||||||||
\(499\) | 42.0583 | 1.88279 | 0.941394 | − | 0.337310i | \(-0.109517\pi\) | ||||
0.941394 | + | 0.337310i | \(0.109517\pi\) | |||||||
\(500\) | −71.2602 | −3.18685 | ||||||||
\(501\) | −7.58753 | −0.338986 | ||||||||
\(502\) | −81.4913 | −3.63714 | ||||||||
\(503\) | 23.5105 | 1.04828 | 0.524142 | − | 0.851631i | \(-0.324386\pi\) | ||||
0.524142 | + | 0.851631i | \(0.324386\pi\) | |||||||
\(504\) | 64.7353 | 2.88354 | ||||||||
\(505\) | −21.3652 | −0.950740 | ||||||||
\(506\) | 4.13878 | 0.183991 | ||||||||
\(507\) | 17.5591 | 0.779825 | ||||||||
\(508\) | −33.8784 | −1.50311 | ||||||||
\(509\) | 33.5711 | 1.48801 | 0.744007 | − | 0.668171i | \(-0.232923\pi\) | ||||
0.744007 | + | 0.668171i | \(0.232923\pi\) | |||||||
\(510\) | 30.7765 | 1.36280 | ||||||||
\(511\) | −33.8488 | −1.49738 | ||||||||
\(512\) | −204.212 | −9.02497 | ||||||||
\(513\) | 24.5365 | 1.08331 | ||||||||
\(514\) | −27.9272 | −1.23182 | ||||||||
\(515\) | −19.4974 | −0.859159 | ||||||||
\(516\) | −22.3359 | −0.983285 | ||||||||
\(517\) | −23.8017 | −1.04680 | ||||||||
\(518\) | −39.9291 | −1.75438 | ||||||||
\(519\) | −7.22698 | −0.317229 | ||||||||
\(520\) | 99.6462 | 4.36978 | ||||||||
\(521\) | 19.6828 | 0.862319 | 0.431159 | − | 0.902276i | \(-0.358105\pi\) | ||||
0.431159 | + | 0.902276i | \(0.358105\pi\) | |||||||
\(522\) | 39.5228 | 1.72987 | ||||||||
\(523\) | −24.5399 | −1.07305 | −0.536527 | − | 0.843883i | \(-0.680264\pi\) | ||||
−0.536527 | + | 0.843883i | \(0.680264\pi\) | |||||||
\(524\) | −36.4695 | −1.59318 | ||||||||
\(525\) | −7.23222 | −0.315640 | ||||||||
\(526\) | −28.8700 | −1.25879 | ||||||||
\(527\) | 43.0862 | 1.87686 | ||||||||
\(528\) | 98.8523 | 4.30199 | ||||||||
\(529\) | −22.9106 | −0.996115 | ||||||||
\(530\) | −10.9279 | −0.474677 | ||||||||
\(531\) | −14.6667 | −0.636478 | ||||||||
\(532\) | −86.0734 | −3.73176 | ||||||||
\(533\) | −11.6001 | −0.502455 | ||||||||
\(534\) | 41.9157 | 1.81387 | ||||||||
\(535\) | 5.79522 | 0.250549 | ||||||||
\(536\) | 10.8658 | 0.469332 | ||||||||
\(537\) | −3.00047 | −0.129480 | ||||||||
\(538\) | 27.8642 | 1.20131 | ||||||||
\(539\) | 9.85744 | 0.424590 | ||||||||
\(540\) | −49.4607 | −2.12845 | ||||||||
\(541\) | −2.70038 | −0.116098 | −0.0580492 | − | 0.998314i | \(-0.518488\pi\) | ||||
−0.0580492 | + | 0.998314i | \(0.518488\pi\) | |||||||
\(542\) | 64.8257 | 2.78450 | ||||||||
\(543\) | −13.4763 | −0.578324 | ||||||||
\(544\) | 212.276 | 9.10124 | ||||||||
\(545\) | −22.8632 | −0.979353 | ||||||||
\(546\) | 47.8355 | 2.04717 | ||||||||
\(547\) | −7.84479 | −0.335419 | −0.167709 | − | 0.985836i | \(-0.553637\pi\) | ||||
−0.167709 | + | 0.985836i | \(0.553637\pi\) | |||||||
\(548\) | 27.7358 | 1.18481 | ||||||||
\(549\) | 13.3640 | 0.570361 | ||||||||
\(550\) | 32.3414 | 1.37904 | ||||||||
\(551\) | −34.8905 | −1.48639 | ||||||||
\(552\) | 3.43600 | 0.146246 | ||||||||
\(553\) | 34.5499 | 1.46921 | ||||||||
\(554\) | −8.38853 | −0.356394 | ||||||||
\(555\) | 7.94411 | 0.337209 | ||||||||
\(556\) | 64.2014 | 2.72275 | ||||||||
\(557\) | 34.0031 | 1.44076 | 0.720378 | − | 0.693582i | \(-0.243968\pi\) | ||||
0.720378 | + | 0.693582i | \(0.243968\pi\) | |||||||
\(558\) | −36.2835 | −1.53600 | ||||||||
\(559\) | 19.9338 | 0.843111 | ||||||||
\(560\) | 95.6043 | 4.04002 | ||||||||
\(561\) | −32.8324 | −1.38618 | ||||||||
\(562\) | 70.6524 | 2.98029 | ||||||||
\(563\) | −7.67566 | −0.323490 | −0.161745 | − | 0.986833i | \(-0.551712\pi\) | ||||
−0.161745 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(564\) | −29.7616 | −1.25319 | ||||||||
\(565\) | −7.28851 | −0.306630 | ||||||||
\(566\) | −64.3969 | −2.70680 | ||||||||
\(567\) | 1.66513 | 0.0699290 | ||||||||
\(568\) | −103.160 | −4.32850 | ||||||||
\(569\) | 7.21892 | 0.302633 | 0.151316 | − | 0.988485i | \(-0.451649\pi\) | ||||
0.151316 | + | 0.988485i | \(0.451649\pi\) | |||||||
\(570\) | 22.8797 | 0.958323 | ||||||||
\(571\) | 36.6934 | 1.53557 | 0.767786 | − | 0.640707i | \(-0.221359\pi\) | ||||
0.767786 | + | 0.640707i | \(0.221359\pi\) | |||||||
\(572\) | −160.108 | −6.69445 | ||||||||
\(573\) | 15.0452 | 0.628523 | ||||||||
\(574\) | −17.9173 | −0.747854 | ||||||||
\(575\) | 0.698279 | 0.0291202 | ||||||||
\(576\) | −103.200 | −4.30002 | ||||||||
\(577\) | 26.6827 | 1.11082 | 0.555408 | − | 0.831578i | \(-0.312562\pi\) | ||||
0.555408 | + | 0.831578i | \(0.312562\pi\) | |||||||
\(578\) | −70.5443 | −2.93426 | ||||||||
\(579\) | −3.84560 | −0.159818 | ||||||||
\(580\) | 70.3324 | 2.92039 | ||||||||
\(581\) | 30.8184 | 1.27856 | ||||||||
\(582\) | 51.0243 | 2.11502 | ||||||||
\(583\) | 11.6579 | 0.482821 | ||||||||
\(584\) | 125.664 | 5.20001 | ||||||||
\(585\) | 17.3122 | 0.715771 | ||||||||
\(586\) | 79.8324 | 3.29785 | ||||||||
\(587\) | −14.4442 | −0.596175 | −0.298088 | − | 0.954539i | \(-0.596349\pi\) | ||||
−0.298088 | + | 0.954539i | \(0.596349\pi\) | |||||||
\(588\) | 12.3257 | 0.508305 | ||||||||
\(589\) | 32.0309 | 1.31981 | ||||||||
\(590\) | −34.8709 | −1.43561 | ||||||||
\(591\) | 24.6277 | 1.01305 | ||||||||
\(592\) | 92.0789 | 3.78442 | ||||||||
\(593\) | 7.89910 | 0.324377 | 0.162189 | − | 0.986760i | \(-0.448145\pi\) | ||||
0.162189 | + | 0.986760i | \(0.448145\pi\) | |||||||
\(594\) | 70.4967 | 2.89251 | ||||||||
\(595\) | −31.7536 | −1.30177 | ||||||||
\(596\) | −71.2604 | −2.91894 | ||||||||
\(597\) | 19.6301 | 0.803408 | ||||||||
\(598\) | −4.61857 | −0.188868 | ||||||||
\(599\) | −44.8641 | −1.83310 | −0.916549 | − | 0.399922i | \(-0.869037\pi\) | ||||
−0.916549 | + | 0.399922i | \(0.869037\pi\) | |||||||
\(600\) | 26.8497 | 1.09613 | ||||||||
\(601\) | 10.0406 | 0.409566 | 0.204783 | − | 0.978807i | \(-0.434351\pi\) | ||||
0.204783 | + | 0.978807i | \(0.434351\pi\) | |||||||
\(602\) | 30.7896 | 1.25489 | ||||||||
\(603\) | 1.88779 | 0.0768767 | ||||||||
\(604\) | −73.4402 | −2.98824 | ||||||||
\(605\) | 21.3947 | 0.869817 | ||||||||
\(606\) | 38.0771 | 1.54678 | ||||||||
\(607\) | −18.6721 | −0.757876 | −0.378938 | − | 0.925422i | \(-0.623711\pi\) | ||||
−0.378938 | + | 0.925422i | \(0.623711\pi\) | |||||||
\(608\) | 157.809 | 6.39999 | ||||||||
\(609\) | 22.4170 | 0.908382 | ||||||||
\(610\) | 31.7737 | 1.28648 | ||||||||
\(611\) | 26.5609 | 1.07454 | ||||||||
\(612\) | 74.6786 | 3.01870 | ||||||||
\(613\) | 10.1753 | 0.410976 | 0.205488 | − | 0.978660i | \(-0.434122\pi\) | ||||
0.205488 | + | 0.978660i | \(0.434122\pi\) | |||||||
\(614\) | 35.6662 | 1.43937 | ||||||||
\(615\) | 3.56475 | 0.143745 | ||||||||
\(616\) | −164.194 | −6.61556 | ||||||||
\(617\) | −48.1240 | −1.93740 | −0.968700 | − | 0.248233i | \(-0.920150\pi\) | ||||
−0.968700 | + | 0.248233i | \(0.920150\pi\) | |||||||
\(618\) | 34.7483 | 1.39778 | ||||||||
\(619\) | 42.3661 | 1.70284 | 0.851418 | − | 0.524487i | \(-0.175743\pi\) | ||||
0.851418 | + | 0.524487i | \(0.175743\pi\) | |||||||
\(620\) | −64.5679 | −2.59311 | ||||||||
\(621\) | 1.52209 | 0.0610792 | ||||||||
\(622\) | 2.71338 | 0.108797 | ||||||||
\(623\) | −43.2466 | −1.73264 | ||||||||
\(624\) | −110.312 | −4.41600 | ||||||||
\(625\) | −7.86391 | −0.314557 | ||||||||
\(626\) | 40.4558 | 1.61694 | ||||||||
\(627\) | −24.4081 | −0.974764 | ||||||||
\(628\) | −53.2173 | −2.12360 | ||||||||
\(629\) | −30.5827 | −1.21941 | ||||||||
\(630\) | 26.7402 | 1.06535 | ||||||||
\(631\) | 16.1789 | 0.644071 | 0.322036 | − | 0.946728i | \(-0.395633\pi\) | ||||
0.322036 | + | 0.946728i | \(0.395633\pi\) | |||||||
\(632\) | −128.267 | −5.10217 | ||||||||
\(633\) | 5.46591 | 0.217250 | ||||||||
\(634\) | −59.4483 | −2.36099 | ||||||||
\(635\) | −9.29132 | −0.368715 | ||||||||
\(636\) | 14.5770 | 0.578017 | ||||||||
\(637\) | −11.0002 | −0.435843 | ||||||||
\(638\) | −100.245 | −3.96875 | ||||||||
\(639\) | −17.9227 | −0.709009 | ||||||||
\(640\) | −138.463 | −5.47322 | ||||||||
\(641\) | −26.4679 | −1.04542 | −0.522710 | − | 0.852511i | \(-0.675079\pi\) | ||||
−0.522710 | + | 0.852511i | \(0.675079\pi\) | |||||||
\(642\) | −10.3283 | −0.407624 | ||||||||
\(643\) | −32.7273 | −1.29064 | −0.645319 | − | 0.763913i | \(-0.723276\pi\) | ||||
−0.645319 | + | 0.763913i | \(0.723276\pi\) | |||||||
\(644\) | −5.33944 | −0.210404 | ||||||||
\(645\) | −6.12575 | −0.241201 | ||||||||
\(646\) | −88.0807 | −3.46549 | ||||||||
\(647\) | 21.9733 | 0.863861 | 0.431930 | − | 0.901907i | \(-0.357833\pi\) | ||||
0.431930 | + | 0.901907i | \(0.357833\pi\) | |||||||
\(648\) | −6.18181 | −0.242845 | ||||||||
\(649\) | 37.2003 | 1.46024 | ||||||||
\(650\) | −36.0906 | −1.41559 | ||||||||
\(651\) | −20.5797 | −0.806581 | ||||||||
\(652\) | 64.7776 | 2.53689 | ||||||||
\(653\) | −25.8305 | −1.01083 | −0.505413 | − | 0.862878i | \(-0.668660\pi\) | ||||
−0.505413 | + | 0.862878i | \(0.668660\pi\) | |||||||
\(654\) | 40.7469 | 1.59333 | ||||||||
\(655\) | −10.0020 | −0.390809 | ||||||||
\(656\) | 41.3185 | 1.61321 | ||||||||
\(657\) | 21.8324 | 0.851763 | ||||||||
\(658\) | 41.0256 | 1.59935 | ||||||||
\(659\) | 27.4121 | 1.06782 | 0.533912 | − | 0.845540i | \(-0.320721\pi\) | ||||
0.533912 | + | 0.845540i | \(0.320721\pi\) | |||||||
\(660\) | 49.2018 | 1.91518 | ||||||||
\(661\) | 4.67037 | 0.181657 | 0.0908283 | − | 0.995867i | \(-0.471049\pi\) | ||||
0.0908283 | + | 0.995867i | \(0.471049\pi\) | |||||||
\(662\) | 8.72948 | 0.339281 | ||||||||
\(663\) | 36.6385 | 1.42292 | ||||||||
\(664\) | −114.413 | −4.44010 | ||||||||
\(665\) | −23.6061 | −0.915405 | ||||||||
\(666\) | 25.7541 | 0.997953 | ||||||||
\(667\) | −2.16438 | −0.0838053 | ||||||||
\(668\) | −43.7734 | −1.69364 | ||||||||
\(669\) | −2.57660 | −0.0996170 | ||||||||
\(670\) | 4.48834 | 0.173400 | ||||||||
\(671\) | −33.8963 | −1.30855 | ||||||||
\(672\) | −101.391 | −3.91125 | ||||||||
\(673\) | −34.6556 | −1.33587 | −0.667937 | − | 0.744218i | \(-0.732823\pi\) | ||||
−0.667937 | + | 0.744218i | \(0.732823\pi\) | |||||||
\(674\) | 12.1334 | 0.467362 | ||||||||
\(675\) | 11.8939 | 0.457797 | ||||||||
\(676\) | 101.300 | 3.89617 | ||||||||
\(677\) | 0.880503 | 0.0338405 | 0.0169202 | − | 0.999857i | \(-0.494614\pi\) | ||||
0.0169202 | + | 0.999857i | \(0.494614\pi\) | |||||||
\(678\) | 12.9896 | 0.498862 | ||||||||
\(679\) | −52.6443 | −2.02030 | ||||||||
\(680\) | 117.885 | 4.52070 | ||||||||
\(681\) | 17.3415 | 0.664527 | ||||||||
\(682\) | 92.0291 | 3.52398 | ||||||||
\(683\) | −26.9586 | −1.03154 | −0.515772 | − | 0.856726i | \(-0.672495\pi\) | ||||
−0.515772 | + | 0.856726i | \(0.672495\pi\) | |||||||
\(684\) | 55.5171 | 2.12275 | ||||||||
\(685\) | 7.60668 | 0.290636 | ||||||||
\(686\) | 42.2506 | 1.61314 | ||||||||
\(687\) | 23.8253 | 0.908992 | ||||||||
\(688\) | −71.0027 | −2.70695 | ||||||||
\(689\) | −13.0093 | −0.495617 | ||||||||
\(690\) | 1.41931 | 0.0540321 | ||||||||
\(691\) | 4.01561 | 0.152761 | 0.0763805 | − | 0.997079i | \(-0.475664\pi\) | ||||
0.0763805 | + | 0.997079i | \(0.475664\pi\) | |||||||
\(692\) | −41.6933 | −1.58494 | ||||||||
\(693\) | −28.5265 | −1.08363 | ||||||||
\(694\) | −17.5814 | −0.667382 | ||||||||
\(695\) | 17.6076 | 0.667894 | ||||||||
\(696\) | −83.2231 | −3.15456 | ||||||||
\(697\) | −13.7233 | −0.519809 | ||||||||
\(698\) | 47.5810 | 1.80097 | ||||||||
\(699\) | −28.8850 | −1.09253 | ||||||||
\(700\) | −41.7236 | −1.57700 | ||||||||
\(701\) | −12.9604 | −0.489508 | −0.244754 | − | 0.969585i | \(-0.578707\pi\) | ||||
−0.244754 | + | 0.969585i | \(0.578707\pi\) | |||||||
\(702\) | −78.6691 | −2.96917 | ||||||||
\(703\) | −22.7356 | −0.857491 | ||||||||
\(704\) | 261.757 | 9.86532 | ||||||||
\(705\) | −8.16227 | −0.307409 | ||||||||
\(706\) | −6.43466 | −0.242171 | ||||||||
\(707\) | −39.2861 | −1.47751 | ||||||||
\(708\) | 46.5153 | 1.74815 | ||||||||
\(709\) | −22.8221 | −0.857103 | −0.428552 | − | 0.903517i | \(-0.640976\pi\) | ||||
−0.428552 | + | 0.903517i | \(0.640976\pi\) | |||||||
\(710\) | −42.6123 | −1.59921 | ||||||||
\(711\) | −22.2846 | −0.835738 | ||||||||
\(712\) | 160.553 | 6.01698 | ||||||||
\(713\) | 1.98699 | 0.0744134 | ||||||||
\(714\) | 56.5914 | 2.11788 | ||||||||
\(715\) | −43.9104 | −1.64216 | ||||||||
\(716\) | −17.3101 | −0.646909 | ||||||||
\(717\) | −6.05092 | −0.225976 | ||||||||
\(718\) | 62.4342 | 2.33002 | ||||||||
\(719\) | 15.8102 | 0.589620 | 0.294810 | − | 0.955556i | \(-0.404744\pi\) | ||||
0.294810 | + | 0.955556i | \(0.404744\pi\) | |||||||
\(720\) | −61.6645 | −2.29810 | ||||||||
\(721\) | −35.8516 | −1.33518 | ||||||||
\(722\) | −11.9038 | −0.443013 | ||||||||
\(723\) | 1.34582 | 0.0500515 | ||||||||
\(724\) | −77.7465 | −2.88943 | ||||||||
\(725\) | −16.9130 | −0.628132 | ||||||||
\(726\) | −38.1296 | −1.41512 | ||||||||
\(727\) | −22.1698 | −0.822232 | −0.411116 | − | 0.911583i | \(-0.634861\pi\) | ||||
−0.411116 | + | 0.911583i | \(0.634861\pi\) | |||||||
\(728\) | 183.228 | 6.79089 | ||||||||
\(729\) | 14.6839 | 0.543847 | ||||||||
\(730\) | 51.9079 | 1.92120 | ||||||||
\(731\) | 23.5825 | 0.872231 | ||||||||
\(732\) | −42.3839 | −1.56655 | ||||||||
\(733\) | −20.6038 | −0.761019 | −0.380510 | − | 0.924777i | \(-0.624251\pi\) | ||||
−0.380510 | + | 0.924777i | \(0.624251\pi\) | |||||||
\(734\) | −11.4304 | −0.421902 | ||||||||
\(735\) | 3.38040 | 0.124688 | ||||||||
\(736\) | 9.78944 | 0.360844 | ||||||||
\(737\) | −4.78817 | −0.176374 | ||||||||
\(738\) | 11.5566 | 0.425405 | ||||||||
\(739\) | 10.6714 | 0.392554 | 0.196277 | − | 0.980549i | \(-0.437115\pi\) | ||||
0.196277 | + | 0.980549i | \(0.437115\pi\) | |||||||
\(740\) | 45.8305 | 1.68476 | ||||||||
\(741\) | 27.2376 | 1.00060 | ||||||||
\(742\) | −20.0941 | −0.737677 | ||||||||
\(743\) | 6.38222 | 0.234141 | 0.117070 | − | 0.993124i | \(-0.462650\pi\) | ||||
0.117070 | + | 0.993124i | \(0.462650\pi\) | |||||||
\(744\) | 76.4021 | 2.80104 | ||||||||
\(745\) | −19.5435 | −0.716020 | ||||||||
\(746\) | 9.45567 | 0.346197 | ||||||||
\(747\) | −19.8778 | −0.727289 | ||||||||
\(748\) | −189.414 | −6.92566 | ||||||||
\(749\) | 10.6562 | 0.389368 | ||||||||
\(750\) | 34.8304 | 1.27183 | ||||||||
\(751\) | −17.3836 | −0.634337 | −0.317169 | − | 0.948369i | \(-0.602732\pi\) | ||||
−0.317169 | + | 0.948369i | \(0.602732\pi\) | |||||||
\(752\) | −94.6077 | −3.44999 | ||||||||
\(753\) | 29.8125 | 1.08643 | ||||||||
\(754\) | 111.866 | 4.07393 | ||||||||
\(755\) | −20.1414 | −0.733020 | ||||||||
\(756\) | −90.9478 | −3.30774 | ||||||||
\(757\) | 37.9814 | 1.38046 | 0.690229 | − | 0.723591i | \(-0.257510\pi\) | ||||
0.690229 | + | 0.723591i | \(0.257510\pi\) | |||||||
\(758\) | 14.1159 | 0.512714 | ||||||||
\(759\) | −1.51412 | −0.0549591 | ||||||||
\(760\) | 87.6377 | 3.17896 | ||||||||
\(761\) | 25.7815 | 0.934577 | 0.467289 | − | 0.884105i | \(-0.345231\pi\) | ||||
0.467289 | + | 0.884105i | \(0.345231\pi\) | |||||||
\(762\) | 16.5590 | 0.599869 | ||||||||
\(763\) | −42.0406 | −1.52197 | ||||||||
\(764\) | 86.7977 | 3.14023 | ||||||||
\(765\) | 20.4810 | 0.740492 | ||||||||
\(766\) | −25.2736 | −0.913171 | ||||||||
\(767\) | −41.5128 | −1.49894 | ||||||||
\(768\) | 136.777 | 4.93553 | ||||||||
\(769\) | 37.2405 | 1.34293 | 0.671463 | − | 0.741039i | \(-0.265666\pi\) | ||||
0.671463 | + | 0.741039i | \(0.265666\pi\) | |||||||
\(770\) | −67.8235 | −2.44419 | ||||||||
\(771\) | 10.2168 | 0.367949 | ||||||||
\(772\) | −22.1858 | −0.798483 | ||||||||
\(773\) | 27.8431 | 1.00145 | 0.500723 | − | 0.865608i | \(-0.333068\pi\) | ||||
0.500723 | + | 0.865608i | \(0.333068\pi\) | |||||||
\(774\) | −19.8592 | −0.713824 | ||||||||
\(775\) | 15.5268 | 0.557738 | ||||||||
\(776\) | 195.442 | 7.01597 | ||||||||
\(777\) | 14.6075 | 0.524042 | ||||||||
\(778\) | 69.7097 | 2.49921 | ||||||||
\(779\) | −10.2021 | −0.365529 | ||||||||
\(780\) | −54.9056 | −1.96593 | ||||||||
\(781\) | 45.4588 | 1.62664 | ||||||||
\(782\) | −5.46396 | −0.195391 | ||||||||
\(783\) | −36.8664 | −1.31750 | ||||||||
\(784\) | 39.1817 | 1.39935 | ||||||||
\(785\) | −14.5951 | −0.520922 | ||||||||
\(786\) | 17.8255 | 0.635815 | ||||||||
\(787\) | 45.1279 | 1.60864 | 0.804318 | − | 0.594199i | \(-0.202531\pi\) | ||||
0.804318 | + | 0.594199i | \(0.202531\pi\) | |||||||
\(788\) | 142.080 | 5.06140 | ||||||||
\(789\) | 10.5617 | 0.376007 | ||||||||
\(790\) | −52.9831 | −1.88505 | ||||||||
\(791\) | −13.4020 | −0.476521 | ||||||||
\(792\) | 105.905 | 3.76316 | ||||||||
\(793\) | 37.8257 | 1.34323 | ||||||||
\(794\) | −57.1000 | −2.02640 | ||||||||
\(795\) | 3.99783 | 0.141788 | ||||||||
\(796\) | 113.249 | 4.01399 | ||||||||
\(797\) | 0.519595 | 0.0184050 | 0.00920250 | − | 0.999958i | \(-0.497071\pi\) | ||||
0.00920250 | + | 0.999958i | \(0.497071\pi\) | |||||||
\(798\) | 42.0708 | 1.48929 | ||||||||
\(799\) | 31.4226 | 1.11165 | ||||||||
\(800\) | 76.4968 | 2.70457 | ||||||||
\(801\) | 27.8939 | 0.985583 | ||||||||
\(802\) | −58.9654 | −2.08214 | ||||||||
\(803\) | −55.3754 | −1.95416 | ||||||||
\(804\) | −5.98712 | −0.211149 | ||||||||
\(805\) | −1.46437 | −0.0516123 | ||||||||
\(806\) | −102.698 | −3.61737 | ||||||||
\(807\) | −10.1937 | −0.358837 | ||||||||
\(808\) | 145.850 | 5.13098 | ||||||||
\(809\) | −11.4395 | −0.402192 | −0.201096 | − | 0.979571i | \(-0.564450\pi\) | ||||
−0.201096 | + | 0.979571i | \(0.564450\pi\) | |||||||
\(810\) | −2.55352 | −0.0897215 | ||||||||
\(811\) | −20.8150 | −0.730912 | −0.365456 | − | 0.930829i | \(-0.619087\pi\) | ||||
−0.365456 | + | 0.930829i | \(0.619087\pi\) | |||||||
\(812\) | 129.326 | 4.53846 | ||||||||
\(813\) | −23.7156 | −0.831743 | ||||||||
\(814\) | −65.3226 | −2.28955 | ||||||||
\(815\) | 17.7656 | 0.622302 | ||||||||
\(816\) | −130.503 | −4.56853 | ||||||||
\(817\) | 17.5316 | 0.613353 | ||||||||
\(818\) | 42.6053 | 1.48966 | ||||||||
\(819\) | 31.8334 | 1.11235 | ||||||||
\(820\) | 20.5655 | 0.718177 | ||||||||
\(821\) | −10.1073 | −0.352748 | −0.176374 | − | 0.984323i | \(-0.556437\pi\) | ||||
−0.176374 | + | 0.984323i | \(0.556437\pi\) | |||||||
\(822\) | −13.5566 | −0.472842 | ||||||||
\(823\) | 21.4947 | 0.749257 | 0.374628 | − | 0.927175i | \(-0.377770\pi\) | ||||
0.374628 | + | 0.927175i | \(0.377770\pi\) | |||||||
\(824\) | 133.099 | 4.63673 | ||||||||
\(825\) | −11.8317 | −0.411926 | ||||||||
\(826\) | −64.1202 | −2.23103 | ||||||||
\(827\) | 30.5221 | 1.06136 | 0.530679 | − | 0.847573i | \(-0.321937\pi\) | ||||
0.530679 | + | 0.847573i | \(0.321937\pi\) | |||||||
\(828\) | 3.44393 | 0.119685 | ||||||||
\(829\) | 23.1867 | 0.805308 | 0.402654 | − | 0.915352i | \(-0.368088\pi\) | ||||
0.402654 | + | 0.915352i | \(0.368088\pi\) | |||||||
\(830\) | −47.2607 | −1.64044 | ||||||||
\(831\) | 3.06883 | 0.106457 | ||||||||
\(832\) | −292.101 | −10.1268 | ||||||||
\(833\) | −13.0136 | −0.450896 | ||||||||
\(834\) | −31.3803 | −1.08661 | ||||||||
\(835\) | −12.0051 | −0.415453 | ||||||||
\(836\) | −140.813 | −4.87012 | ||||||||
\(837\) | 33.8448 | 1.16985 | ||||||||
\(838\) | −62.2298 | −2.14969 | ||||||||
\(839\) | −40.1019 | −1.38447 | −0.692235 | − | 0.721672i | \(-0.743374\pi\) | ||||
−0.692235 | + | 0.721672i | \(0.743374\pi\) | |||||||
\(840\) | −56.3068 | −1.94277 | ||||||||
\(841\) | 23.4234 | 0.807704 | ||||||||
\(842\) | 112.837 | 3.88860 | ||||||||
\(843\) | −25.8472 | −0.890226 | ||||||||
\(844\) | 31.5335 | 1.08543 | ||||||||
\(845\) | 27.7822 | 0.955735 | ||||||||
\(846\) | −26.4614 | −0.909763 | ||||||||
\(847\) | 39.3403 | 1.35175 | ||||||||
\(848\) | 46.3382 | 1.59126 | ||||||||
\(849\) | 23.5588 | 0.808535 | ||||||||
\(850\) | −42.6966 | −1.46448 | ||||||||
\(851\) | −1.41037 | −0.0483469 | ||||||||
\(852\) | 56.8417 | 1.94736 | ||||||||
\(853\) | 28.1507 | 0.963861 | 0.481930 | − | 0.876210i | \(-0.339936\pi\) | ||||
0.481930 | + | 0.876210i | \(0.339936\pi\) | |||||||
\(854\) | 58.4251 | 1.99927 | ||||||||
\(855\) | 15.2259 | 0.520714 | ||||||||
\(856\) | −39.5611 | −1.35217 | ||||||||
\(857\) | −45.2090 | −1.54431 | −0.772155 | − | 0.635434i | \(-0.780821\pi\) | ||||
−0.772155 | + | 0.635434i | \(0.780821\pi\) | |||||||
\(858\) | 78.2573 | 2.67166 | ||||||||
\(859\) | −5.37755 | −0.183480 | −0.0917399 | − | 0.995783i | \(-0.529243\pi\) | ||||
−0.0917399 | + | 0.995783i | \(0.529243\pi\) | |||||||
\(860\) | −35.3402 | −1.20509 | ||||||||
\(861\) | 6.55481 | 0.223387 | ||||||||
\(862\) | 88.6725 | 3.02020 | ||||||||
\(863\) | −18.1486 | −0.617784 | −0.308892 | − | 0.951097i | \(-0.599958\pi\) | ||||
−0.308892 | + | 0.951097i | \(0.599958\pi\) | |||||||
\(864\) | 166.745 | 5.67280 | ||||||||
\(865\) | −11.4346 | −0.388789 | ||||||||
\(866\) | 76.3904 | 2.59585 | ||||||||
\(867\) | 25.8077 | 0.876475 | ||||||||
\(868\) | −118.727 | −4.02985 | ||||||||
\(869\) | 56.5224 | 1.91739 | ||||||||
\(870\) | −34.3770 | −1.16549 | ||||||||
\(871\) | 5.34324 | 0.181049 | ||||||||
\(872\) | 156.076 | 5.28540 | ||||||||
\(873\) | 33.9554 | 1.14922 | ||||||||
\(874\) | −4.06198 | −0.137399 | ||||||||
\(875\) | −35.9363 | −1.21487 | ||||||||
\(876\) | −69.2414 | −2.33945 | ||||||||
\(877\) | 4.16524 | 0.140650 | 0.0703251 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703251 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(878\) | 22.4511 | 0.757688 | ||||||||
\(879\) | −29.2056 | −0.985081 | ||||||||
\(880\) | 156.405 | 5.27242 | ||||||||
\(881\) | −14.7796 | −0.497938 | −0.248969 | − | 0.968511i | \(-0.580092\pi\) | ||||
−0.248969 | + | 0.968511i | \(0.580092\pi\) | |||||||
\(882\) | 10.9590 | 0.369008 | ||||||||
\(883\) | −17.9986 | −0.605702 | −0.302851 | − | 0.953038i | \(-0.597938\pi\) | ||||
−0.302851 | + | 0.953038i | \(0.597938\pi\) | |||||||
\(884\) | 211.372 | 7.10921 | ||||||||
\(885\) | 12.7571 | 0.428824 | ||||||||
\(886\) | −91.1935 | −3.06371 | ||||||||
\(887\) | 45.5760 | 1.53029 | 0.765145 | − | 0.643858i | \(-0.222667\pi\) | ||||
0.765145 | + | 0.643858i | \(0.222667\pi\) | |||||||
\(888\) | −54.2305 | −1.81986 | ||||||||
\(889\) | −17.0848 | −0.573005 | ||||||||
\(890\) | 66.3196 | 2.22304 | ||||||||
\(891\) | 2.72410 | 0.0912607 | ||||||||
\(892\) | −14.8647 | −0.497707 | ||||||||
\(893\) | 23.3600 | 0.781713 | ||||||||
\(894\) | 34.8305 | 1.16491 | ||||||||
\(895\) | −4.74739 | −0.158688 | ||||||||
\(896\) | −254.603 | −8.50570 | ||||||||
\(897\) | 1.68964 | 0.0564156 | ||||||||
\(898\) | 24.1779 | 0.806827 | ||||||||
\(899\) | −48.1268 | −1.60512 | ||||||||
\(900\) | 26.9116 | 0.897053 | ||||||||
\(901\) | −15.3906 | −0.512734 | ||||||||
\(902\) | −29.3121 | −0.975986 | ||||||||
\(903\) | −11.2640 | −0.374841 | ||||||||
\(904\) | 49.7551 | 1.65483 | ||||||||
\(905\) | −21.3224 | −0.708780 | ||||||||
\(906\) | 35.8960 | 1.19256 | ||||||||
\(907\) | −13.1327 | −0.436063 | −0.218032 | − | 0.975942i | \(-0.569964\pi\) | ||||
−0.218032 | + | 0.975942i | \(0.569964\pi\) | |||||||
\(908\) | 100.045 | 3.32012 | ||||||||
\(909\) | 25.3394 | 0.840456 | ||||||||
\(910\) | 75.6860 | 2.50897 | ||||||||
\(911\) | 56.3744 | 1.86777 | 0.933883 | − | 0.357577i | \(-0.116397\pi\) | ||||
0.933883 | + | 0.357577i | \(0.116397\pi\) | |||||||
\(912\) | −97.0179 | −3.21259 | ||||||||
\(913\) | 50.4178 | 1.66858 | ||||||||
\(914\) | −39.0432 | −1.29144 | ||||||||
\(915\) | −11.6240 | −0.384278 | ||||||||
\(916\) | 137.451 | 4.54151 | ||||||||
\(917\) | −18.3915 | −0.607340 | ||||||||
\(918\) | −93.0686 | −3.07172 | ||||||||
\(919\) | −17.0940 | −0.563878 | −0.281939 | − | 0.959432i | \(-0.590977\pi\) | ||||
−0.281939 | + | 0.959432i | \(0.590977\pi\) | |||||||
\(920\) | 5.43648 | 0.179236 | ||||||||
\(921\) | −13.0480 | −0.429947 | ||||||||
\(922\) | −71.0745 | −2.34071 | ||||||||
\(923\) | −50.7287 | −1.66975 | ||||||||
\(924\) | 90.4717 | 2.97630 | ||||||||
\(925\) | −11.0210 | −0.362367 | ||||||||
\(926\) | −42.1648 | −1.38562 | ||||||||
\(927\) | 23.1242 | 0.759498 | ||||||||
\(928\) | −237.109 | −7.78350 | ||||||||
\(929\) | 11.3970 | 0.373923 | 0.186961 | − | 0.982367i | \(-0.440136\pi\) | ||||
0.186961 | + | 0.982367i | \(0.440136\pi\) | |||||||
\(930\) | 31.5594 | 1.03487 | ||||||||
\(931\) | −9.67453 | −0.317070 | ||||||||
\(932\) | −166.641 | −5.45852 | ||||||||
\(933\) | −0.992654 | −0.0324980 | ||||||||
\(934\) | 33.0752 | 1.08225 | ||||||||
\(935\) | −51.9478 | −1.69888 | ||||||||
\(936\) | −118.182 | −3.86289 | ||||||||
\(937\) | −28.3827 | −0.927222 | −0.463611 | − | 0.886039i | \(-0.653447\pi\) | ||||
−0.463611 | + | 0.886039i | \(0.653447\pi\) | |||||||
\(938\) | 8.25310 | 0.269473 | ||||||||
\(939\) | −14.8002 | −0.482987 | ||||||||
\(940\) | −47.0892 | −1.53588 | ||||||||
\(941\) | 20.1284 | 0.656167 | 0.328084 | − | 0.944649i | \(-0.393597\pi\) | ||||
0.328084 | + | 0.944649i | \(0.393597\pi\) | |||||||
\(942\) | 26.0114 | 0.847498 | ||||||||
\(943\) | −0.632874 | −0.0206092 | ||||||||
\(944\) | 147.865 | 4.81260 | ||||||||
\(945\) | −24.9429 | −0.811393 | ||||||||
\(946\) | 50.3706 | 1.63769 | ||||||||
\(947\) | 43.4788 | 1.41287 | 0.706435 | − | 0.707778i | \(-0.250302\pi\) | ||||
0.706435 | + | 0.707778i | \(0.250302\pi\) | |||||||
\(948\) | 70.6756 | 2.29544 | ||||||||
\(949\) | 61.7949 | 2.00595 | ||||||||
\(950\) | −31.7412 | −1.02982 | ||||||||
\(951\) | 21.7484 | 0.705239 | ||||||||
\(952\) | 216.766 | 7.02544 | ||||||||
\(953\) | −30.4139 | −0.985202 | −0.492601 | − | 0.870255i | \(-0.663954\pi\) | ||||
−0.492601 | + | 0.870255i | \(0.663954\pi\) | |||||||
\(954\) | 12.9606 | 0.419616 | ||||||||
\(955\) | 23.8047 | 0.770303 | ||||||||
\(956\) | −34.9085 | −1.12902 | ||||||||
\(957\) | 36.6734 | 1.18548 | ||||||||
\(958\) | 87.0031 | 2.81094 | ||||||||
\(959\) | 13.9871 | 0.451666 | ||||||||
\(960\) | 89.7638 | 2.89711 | ||||||||
\(961\) | 13.1823 | 0.425234 | ||||||||
\(962\) | 72.8951 | 2.35023 | ||||||||
\(963\) | −6.87321 | −0.221486 | ||||||||
\(964\) | 7.76419 | 0.250068 | ||||||||
\(965\) | −6.08456 | −0.195869 | ||||||||
\(966\) | 2.60980 | 0.0839691 | ||||||||
\(967\) | 7.56190 | 0.243174 | 0.121587 | − | 0.992581i | \(-0.461202\pi\) | ||||
0.121587 | + | 0.992581i | \(0.461202\pi\) | |||||||
\(968\) | −146.051 | −4.69425 | ||||||||
\(969\) | 32.2231 | 1.03516 | ||||||||
\(970\) | 80.7312 | 2.59212 | ||||||||
\(971\) | −47.1478 | −1.51305 | −0.756523 | − | 0.653968i | \(-0.773103\pi\) | ||||
−0.756523 | + | 0.653968i | \(0.773103\pi\) | |||||||
\(972\) | 94.3154 | 3.02517 | ||||||||
\(973\) | 32.3766 | 1.03795 | ||||||||
\(974\) | −70.2977 | −2.25248 | ||||||||
\(975\) | 13.2032 | 0.422842 | ||||||||
\(976\) | −134.732 | −4.31267 | ||||||||
\(977\) | −48.3929 | −1.54823 | −0.774114 | − | 0.633046i | \(-0.781804\pi\) | ||||
−0.774114 | + | 0.633046i | \(0.781804\pi\) | |||||||
\(978\) | −31.6619 | −1.01244 | ||||||||
\(979\) | −70.7499 | −2.26118 | ||||||||
\(980\) | 19.5019 | 0.622967 | ||||||||
\(981\) | 27.1161 | 0.865750 | ||||||||
\(982\) | −7.06012 | −0.225297 | ||||||||
\(983\) | 42.6912 | 1.36164 | 0.680819 | − | 0.732452i | \(-0.261624\pi\) | ||||
0.680819 | + | 0.732452i | \(0.261624\pi\) | |||||||
\(984\) | −24.3348 | −0.775764 | ||||||||
\(985\) | 38.9662 | 1.24157 | ||||||||
\(986\) | 132.342 | 4.21463 | ||||||||
\(987\) | −15.0087 | −0.477732 | ||||||||
\(988\) | 157.137 | 4.99919 | ||||||||
\(989\) | 1.08755 | 0.0345820 | ||||||||
\(990\) | 43.7460 | 1.39034 | ||||||||
\(991\) | 12.9519 | 0.411430 | 0.205715 | − | 0.978612i | \(-0.434048\pi\) | ||||
0.205715 | + | 0.978612i | \(0.434048\pi\) | |||||||
\(992\) | 217.676 | 6.91122 | ||||||||
\(993\) | −3.19356 | −0.101345 | ||||||||
\(994\) | −78.3549 | −2.48527 | ||||||||
\(995\) | 31.0590 | 0.984638 | ||||||||
\(996\) | 63.0423 | 1.99757 | ||||||||
\(997\) | −38.3038 | −1.21309 | −0.606546 | − | 0.795048i | \(-0.707445\pi\) | ||||
−0.606546 | + | 0.795048i | \(0.707445\pi\) | |||||||
\(998\) | −118.597 | −3.75412 | ||||||||
\(999\) | −24.0231 | −0.760059 |
(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 | 4013.2.a.b.1.1 | ✓ | 157 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4013.2.a.b.1.1 | ✓ | 157 | 1.1 | even | 1 | trivial |