Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66059 | −1.88132 | −0.940662 | − | 0.339345i | \(-0.889795\pi\) | ||||
−0.940662 | + | 0.339345i | \(0.889795\pi\) | |||||||
\(3\) | −0.870455 | −0.502557 | −0.251279 | − | 0.967915i | \(-0.580851\pi\) | ||||
−0.251279 | + | 0.967915i | \(0.580851\pi\) | |||||||
\(4\) | 5.07876 | 2.53938 | ||||||||
\(5\) | −2.53728 | −1.13471 | −0.567353 | − | 0.823475i | \(-0.692032\pi\) | ||||
−0.567353 | + | 0.823475i | \(0.692032\pi\) | |||||||
\(6\) | 2.31593 | 0.945474 | ||||||||
\(7\) | 1.57807 | 0.596453 | 0.298227 | − | 0.954495i | \(-0.403605\pi\) | ||||
0.298227 | + | 0.954495i | \(0.403605\pi\) | |||||||
\(8\) | −8.19134 | −2.89607 | ||||||||
\(9\) | −2.24231 | −0.747436 | ||||||||
\(10\) | 6.75067 | 2.13475 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.42083 | −1.27618 | ||||||||
\(13\) | −5.54559 | −1.53807 | −0.769035 | − | 0.639206i | \(-0.779263\pi\) | ||||
−0.769035 | + | 0.639206i | \(0.779263\pi\) | |||||||
\(14\) | −4.19860 | −1.12212 | ||||||||
\(15\) | 2.20859 | 0.570255 | ||||||||
\(16\) | 11.6363 | 2.90907 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 5.96587 | 1.40617 | ||||||||
\(19\) | −7.29705 | −1.67406 | −0.837029 | − | 0.547159i | \(-0.815709\pi\) | ||||
−0.837029 | + | 0.547159i | \(0.815709\pi\) | |||||||
\(20\) | −12.8862 | −2.88145 | ||||||||
\(21\) | −1.37364 | −0.299752 | ||||||||
\(22\) | −2.66059 | −0.567241 | ||||||||
\(23\) | 7.87110 | 1.64124 | 0.820619 | − | 0.571476i | \(-0.193629\pi\) | ||||
0.820619 | + | 0.571476i | \(0.193629\pi\) | |||||||
\(24\) | 7.13019 | 1.45544 | ||||||||
\(25\) | 1.43779 | 0.287558 | ||||||||
\(26\) | 14.7546 | 2.89361 | ||||||||
\(27\) | 4.56319 | 0.878187 | ||||||||
\(28\) | 8.01463 | 1.51462 | ||||||||
\(29\) | 1.60580 | 0.298189 | 0.149095 | − | 0.988823i | \(-0.452364\pi\) | ||||
0.149095 | + | 0.988823i | \(0.452364\pi\) | |||||||
\(30\) | −5.87616 | −1.07283 | ||||||||
\(31\) | 5.64012 | 1.01300 | 0.506498 | − | 0.862241i | \(-0.330940\pi\) | ||||
0.506498 | + | 0.862241i | \(0.330940\pi\) | |||||||
\(32\) | −14.5768 | −2.57684 | ||||||||
\(33\) | −0.870455 | −0.151527 | ||||||||
\(34\) | 2.66059 | 0.456288 | ||||||||
\(35\) | −4.00400 | −0.676799 | ||||||||
\(36\) | −11.3881 | −1.89802 | ||||||||
\(37\) | −2.01159 | −0.330703 | −0.165351 | − | 0.986235i | \(-0.552876\pi\) | ||||
−0.165351 | + | 0.986235i | \(0.552876\pi\) | |||||||
\(38\) | 19.4145 | 3.14945 | ||||||||
\(39\) | 4.82719 | 0.772969 | ||||||||
\(40\) | 20.7837 | 3.28619 | ||||||||
\(41\) | −8.14727 | −1.27239 | −0.636195 | − | 0.771528i | \(-0.719493\pi\) | ||||
−0.636195 | + | 0.771528i | \(0.719493\pi\) | |||||||
\(42\) | 3.65469 | 0.563931 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 5.07876 | 0.765652 | ||||||||
\(45\) | 5.68936 | 0.848120 | ||||||||
\(46\) | −20.9418 | −3.08770 | ||||||||
\(47\) | 3.48904 | 0.508929 | 0.254464 | − | 0.967082i | \(-0.418101\pi\) | ||||
0.254464 | + | 0.967082i | \(0.418101\pi\) | |||||||
\(48\) | −10.1289 | −1.46198 | ||||||||
\(49\) | −4.50970 | −0.644243 | ||||||||
\(50\) | −3.82537 | −0.540989 | ||||||||
\(51\) | 0.870455 | 0.121888 | ||||||||
\(52\) | −28.1647 | −3.90575 | ||||||||
\(53\) | −4.47992 | −0.615364 | −0.307682 | − | 0.951489i | \(-0.599553\pi\) | ||||
−0.307682 | + | 0.951489i | \(0.599553\pi\) | |||||||
\(54\) | −12.1408 | −1.65215 | ||||||||
\(55\) | −2.53728 | −0.342127 | ||||||||
\(56\) | −12.9265 | −1.72737 | ||||||||
\(57\) | 6.35175 | 0.841310 | ||||||||
\(58\) | −4.27238 | −0.560990 | ||||||||
\(59\) | 4.63908 | 0.603956 | 0.301978 | − | 0.953315i | \(-0.402353\pi\) | ||||
0.301978 | + | 0.953315i | \(0.402353\pi\) | |||||||
\(60\) | 11.2169 | 1.44809 | ||||||||
\(61\) | 1.59035 | 0.203624 | 0.101812 | − | 0.994804i | \(-0.467536\pi\) | ||||
0.101812 | + | 0.994804i | \(0.467536\pi\) | |||||||
\(62\) | −15.0061 | −1.90577 | ||||||||
\(63\) | −3.53851 | −0.445811 | ||||||||
\(64\) | 15.5103 | 1.93879 | ||||||||
\(65\) | 14.0707 | 1.74526 | ||||||||
\(66\) | 2.31593 | 0.285071 | ||||||||
\(67\) | −14.5722 | −1.78028 | −0.890139 | − | 0.455689i | \(-0.849393\pi\) | ||||
−0.890139 | + | 0.455689i | \(0.849393\pi\) | |||||||
\(68\) | −5.07876 | −0.615890 | ||||||||
\(69\) | −6.85144 | −0.824816 | ||||||||
\(70\) | 10.6530 | 1.27328 | ||||||||
\(71\) | −2.40885 | −0.285877 | −0.142939 | − | 0.989732i | \(-0.545655\pi\) | ||||
−0.142939 | + | 0.989732i | \(0.545655\pi\) | |||||||
\(72\) | 18.3675 | 2.16463 | ||||||||
\(73\) | −12.2347 | −1.43196 | −0.715980 | − | 0.698121i | \(-0.754020\pi\) | ||||
−0.715980 | + | 0.698121i | \(0.754020\pi\) | |||||||
\(74\) | 5.35202 | 0.622159 | ||||||||
\(75\) | −1.25153 | −0.144514 | ||||||||
\(76\) | −37.0600 | −4.25107 | ||||||||
\(77\) | 1.57807 | 0.179837 | ||||||||
\(78\) | −12.8432 | −1.45420 | ||||||||
\(79\) | −12.1757 | −1.36987 | −0.684935 | − | 0.728604i | \(-0.740169\pi\) | ||||
−0.684935 | + | 0.728604i | \(0.740169\pi\) | |||||||
\(80\) | −29.5245 | −3.30094 | ||||||||
\(81\) | 2.75487 | 0.306097 | ||||||||
\(82\) | 21.6766 | 2.39378 | ||||||||
\(83\) | −4.85369 | −0.532762 | −0.266381 | − | 0.963868i | \(-0.585828\pi\) | ||||
−0.266381 | + | 0.963868i | \(0.585828\pi\) | |||||||
\(84\) | −6.97637 | −0.761185 | ||||||||
\(85\) | 2.53728 | 0.275207 | ||||||||
\(86\) | 2.66059 | 0.286899 | ||||||||
\(87\) | −1.39777 | −0.149857 | ||||||||
\(88\) | −8.19134 | −0.873199 | ||||||||
\(89\) | 18.3671 | 1.94690 | 0.973452 | − | 0.228891i | \(-0.0735098\pi\) | ||||
0.973452 | + | 0.228891i | \(0.0735098\pi\) | |||||||
\(90\) | −15.1371 | −1.59559 | ||||||||
\(91\) | −8.75132 | −0.917387 | ||||||||
\(92\) | 39.9754 | 4.16773 | ||||||||
\(93\) | −4.90947 | −0.509089 | ||||||||
\(94\) | −9.28292 | −0.957460 | ||||||||
\(95\) | 18.5147 | 1.89956 | ||||||||
\(96\) | 12.6884 | 1.29501 | ||||||||
\(97\) | −2.70432 | −0.274582 | −0.137291 | − | 0.990531i | \(-0.543840\pi\) | ||||
−0.137291 | + | 0.990531i | \(0.543840\pi\) | |||||||
\(98\) | 11.9985 | 1.21203 | ||||||||
\(99\) | −2.24231 | −0.225360 | ||||||||
\(100\) | 7.30218 | 0.730218 | ||||||||
\(101\) | −15.5569 | −1.54797 | −0.773986 | − | 0.633202i | \(-0.781740\pi\) | ||||
−0.773986 | + | 0.633202i | \(0.781740\pi\) | |||||||
\(102\) | −2.31593 | −0.229311 | ||||||||
\(103\) | −10.3576 | −1.02056 | −0.510282 | − | 0.860007i | \(-0.670459\pi\) | ||||
−0.510282 | + | 0.860007i | \(0.670459\pi\) | |||||||
\(104\) | 45.4258 | 4.45437 | ||||||||
\(105\) | 3.48530 | 0.340130 | ||||||||
\(106\) | 11.9193 | 1.15770 | ||||||||
\(107\) | −10.5750 | −1.02232 | −0.511161 | − | 0.859485i | \(-0.670784\pi\) | ||||
−0.511161 | + | 0.859485i | \(0.670784\pi\) | |||||||
\(108\) | 23.1754 | 2.23005 | ||||||||
\(109\) | −10.7814 | −1.03267 | −0.516333 | − | 0.856388i | \(-0.672703\pi\) | ||||
−0.516333 | + | 0.856388i | \(0.672703\pi\) | |||||||
\(110\) | 6.75067 | 0.643651 | ||||||||
\(111\) | 1.75100 | 0.166197 | ||||||||
\(112\) | 18.3629 | 1.73513 | ||||||||
\(113\) | 15.4711 | 1.45540 | 0.727701 | − | 0.685894i | \(-0.240589\pi\) | ||||
0.727701 | + | 0.685894i | \(0.240589\pi\) | |||||||
\(114\) | −16.8994 | −1.58278 | ||||||||
\(115\) | −19.9712 | −1.86232 | ||||||||
\(116\) | 8.15546 | 0.757216 | ||||||||
\(117\) | 12.4349 | 1.14961 | ||||||||
\(118\) | −12.3427 | −1.13624 | ||||||||
\(119\) | −1.57807 | −0.144661 | ||||||||
\(120\) | −18.0913 | −1.65150 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.23128 | −0.383082 | ||||||||
\(123\) | 7.09184 | 0.639449 | ||||||||
\(124\) | 28.6448 | 2.57238 | ||||||||
\(125\) | 9.03833 | 0.808413 | ||||||||
\(126\) | 9.41455 | 0.838714 | ||||||||
\(127\) | 17.1175 | 1.51893 | 0.759467 | − | 0.650546i | \(-0.225460\pi\) | ||||
0.759467 | + | 0.650546i | \(0.225460\pi\) | |||||||
\(128\) | −12.1131 | −1.07066 | ||||||||
\(129\) | 0.870455 | 0.0766393 | ||||||||
\(130\) | −37.4365 | −3.28340 | ||||||||
\(131\) | −0.830164 | −0.0725318 | −0.0362659 | − | 0.999342i | \(-0.511546\pi\) | ||||
−0.0362659 | + | 0.999342i | \(0.511546\pi\) | |||||||
\(132\) | −4.42083 | −0.384784 | ||||||||
\(133\) | −11.5152 | −0.998497 | ||||||||
\(134\) | 38.7707 | 3.34928 | ||||||||
\(135\) | −11.5781 | −0.996484 | ||||||||
\(136\) | 8.19134 | 0.702401 | ||||||||
\(137\) | −14.4097 | −1.23110 | −0.615550 | − | 0.788098i | \(-0.711066\pi\) | ||||
−0.615550 | + | 0.788098i | \(0.711066\pi\) | |||||||
\(138\) | 18.2289 | 1.55175 | ||||||||
\(139\) | −19.3602 | −1.64211 | −0.821053 | − | 0.570851i | \(-0.806613\pi\) | ||||
−0.821053 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(140\) | −20.3354 | −1.71865 | ||||||||
\(141\) | −3.03705 | −0.255766 | ||||||||
\(142\) | 6.40896 | 0.537828 | ||||||||
\(143\) | −5.54559 | −0.463746 | ||||||||
\(144\) | −26.0922 | −2.17435 | ||||||||
\(145\) | −4.07436 | −0.338357 | ||||||||
\(146\) | 32.5515 | 2.69398 | ||||||||
\(147\) | 3.92549 | 0.323769 | ||||||||
\(148\) | −10.2164 | −0.839780 | ||||||||
\(149\) | 19.9891 | 1.63757 | 0.818786 | − | 0.574099i | \(-0.194648\pi\) | ||||
0.818786 | + | 0.574099i | \(0.194648\pi\) | |||||||
\(150\) | 3.32981 | 0.271878 | ||||||||
\(151\) | 16.8923 | 1.37468 | 0.687338 | − | 0.726337i | \(-0.258779\pi\) | ||||
0.687338 | + | 0.726337i | \(0.258779\pi\) | |||||||
\(152\) | 59.7726 | 4.84820 | ||||||||
\(153\) | 2.24231 | 0.181280 | ||||||||
\(154\) | −4.19860 | −0.338333 | ||||||||
\(155\) | −14.3106 | −1.14945 | ||||||||
\(156\) | 24.5161 | 1.96286 | ||||||||
\(157\) | −16.6329 | −1.32745 | −0.663726 | − | 0.747976i | \(-0.731026\pi\) | ||||
−0.663726 | + | 0.747976i | \(0.731026\pi\) | |||||||
\(158\) | 32.3945 | 2.57717 | ||||||||
\(159\) | 3.89957 | 0.309256 | ||||||||
\(160\) | 36.9854 | 2.92395 | ||||||||
\(161\) | 12.4211 | 0.978921 | ||||||||
\(162\) | −7.32959 | −0.575867 | ||||||||
\(163\) | −13.0658 | −1.02339 | −0.511694 | − | 0.859168i | \(-0.670982\pi\) | ||||
−0.511694 | + | 0.859168i | \(0.670982\pi\) | |||||||
\(164\) | −41.3781 | −3.23108 | ||||||||
\(165\) | 2.20859 | 0.171938 | ||||||||
\(166\) | 12.9137 | 1.00230 | ||||||||
\(167\) | −18.8842 | −1.46131 | −0.730653 | − | 0.682749i | \(-0.760784\pi\) | ||||
−0.730653 | + | 0.682749i | \(0.760784\pi\) | |||||||
\(168\) | 11.2519 | 0.868104 | ||||||||
\(169\) | 17.7536 | 1.36566 | ||||||||
\(170\) | −6.75067 | −0.517753 | ||||||||
\(171\) | 16.3622 | 1.25125 | ||||||||
\(172\) | −5.07876 | −0.387252 | ||||||||
\(173\) | −13.9903 | −1.06366 | −0.531832 | − | 0.846850i | \(-0.678496\pi\) | ||||
−0.531832 | + | 0.846850i | \(0.678496\pi\) | |||||||
\(174\) | 3.71891 | 0.281930 | ||||||||
\(175\) | 2.26893 | 0.171515 | ||||||||
\(176\) | 11.6363 | 0.877119 | ||||||||
\(177\) | −4.03811 | −0.303523 | ||||||||
\(178\) | −48.8673 | −3.66276 | ||||||||
\(179\) | 5.09962 | 0.381163 | 0.190582 | − | 0.981671i | \(-0.438963\pi\) | ||||
0.190582 | + | 0.981671i | \(0.438963\pi\) | |||||||
\(180\) | 28.8949 | 2.15370 | ||||||||
\(181\) | −15.7689 | −1.17209 | −0.586046 | − | 0.810277i | \(-0.699316\pi\) | ||||
−0.586046 | + | 0.810277i | \(0.699316\pi\) | |||||||
\(182\) | 23.2837 | 1.72590 | ||||||||
\(183\) | −1.38433 | −0.102333 | ||||||||
\(184\) | −64.4748 | −4.75315 | ||||||||
\(185\) | 5.10396 | 0.375250 | ||||||||
\(186\) | 13.0621 | 0.957761 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 17.7200 | 1.29236 | ||||||||
\(189\) | 7.20103 | 0.523798 | ||||||||
\(190\) | −49.2600 | −3.57369 | ||||||||
\(191\) | −24.3575 | −1.76245 | −0.881223 | − | 0.472702i | \(-0.843279\pi\) | ||||
−0.881223 | + | 0.472702i | \(0.843279\pi\) | |||||||
\(192\) | −13.5011 | −0.974355 | ||||||||
\(193\) | 6.37501 | 0.458883 | 0.229442 | − | 0.973322i | \(-0.426310\pi\) | ||||
0.229442 | + | 0.973322i | \(0.426310\pi\) | |||||||
\(194\) | 7.19510 | 0.516578 | ||||||||
\(195\) | −12.2479 | −0.877092 | ||||||||
\(196\) | −22.9037 | −1.63598 | ||||||||
\(197\) | 3.81198 | 0.271592 | 0.135796 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135796 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(198\) | 5.96587 | 0.423976 | ||||||||
\(199\) | −17.0808 | −1.21082 | −0.605412 | − | 0.795913i | \(-0.706991\pi\) | ||||
−0.605412 | + | 0.795913i | \(0.706991\pi\) | |||||||
\(200\) | −11.7774 | −0.832788 | ||||||||
\(201\) | 12.6844 | 0.894692 | ||||||||
\(202\) | 41.3907 | 2.91224 | ||||||||
\(203\) | 2.53406 | 0.177856 | ||||||||
\(204\) | 4.42083 | 0.309520 | ||||||||
\(205\) | 20.6719 | 1.44379 | ||||||||
\(206\) | 27.5574 | 1.92001 | ||||||||
\(207\) | −17.6494 | −1.22672 | ||||||||
\(208\) | −64.5302 | −4.47436 | ||||||||
\(209\) | −7.29705 | −0.504747 | ||||||||
\(210\) | −9.27297 | −0.639896 | ||||||||
\(211\) | 21.9914 | 1.51395 | 0.756977 | − | 0.653442i | \(-0.226676\pi\) | ||||
0.756977 | + | 0.653442i | \(0.226676\pi\) | |||||||
\(212\) | −22.7525 | −1.56264 | ||||||||
\(213\) | 2.09679 | 0.143670 | ||||||||
\(214\) | 28.1357 | 1.92332 | ||||||||
\(215\) | 2.53728 | 0.173041 | ||||||||
\(216\) | −37.3787 | −2.54330 | ||||||||
\(217\) | 8.90049 | 0.604205 | ||||||||
\(218\) | 28.6848 | 1.94278 | ||||||||
\(219\) | 10.6497 | 0.719642 | ||||||||
\(220\) | −12.8862 | −0.868790 | ||||||||
\(221\) | 5.54559 | 0.373037 | ||||||||
\(222\) | −4.65869 | −0.312671 | ||||||||
\(223\) | 13.4686 | 0.901926 | 0.450963 | − | 0.892543i | \(-0.351081\pi\) | ||||
0.450963 | + | 0.892543i | \(0.351081\pi\) | |||||||
\(224\) | −23.0032 | −1.53696 | ||||||||
\(225\) | −3.22396 | −0.214931 | ||||||||
\(226\) | −41.1624 | −2.73808 | ||||||||
\(227\) | −7.93654 | −0.526767 | −0.263383 | − | 0.964691i | \(-0.584838\pi\) | ||||
−0.263383 | + | 0.964691i | \(0.584838\pi\) | |||||||
\(228\) | 32.2590 | 2.13641 | ||||||||
\(229\) | 4.11295 | 0.271792 | 0.135896 | − | 0.990723i | \(-0.456609\pi\) | ||||
0.135896 | + | 0.990723i | \(0.456609\pi\) | |||||||
\(230\) | 53.1352 | 3.50363 | ||||||||
\(231\) | −1.37364 | −0.0903787 | ||||||||
\(232\) | −13.1536 | −0.863578 | ||||||||
\(233\) | 11.7614 | 0.770517 | 0.385258 | − | 0.922809i | \(-0.374112\pi\) | ||||
0.385258 | + | 0.922809i | \(0.374112\pi\) | |||||||
\(234\) | −33.0843 | −2.16279 | ||||||||
\(235\) | −8.85267 | −0.577484 | ||||||||
\(236\) | 23.5608 | 1.53368 | ||||||||
\(237\) | 10.5984 | 0.688438 | ||||||||
\(238\) | 4.19860 | 0.272155 | ||||||||
\(239\) | 22.2846 | 1.44147 | 0.720737 | − | 0.693209i | \(-0.243804\pi\) | ||||
0.720737 | + | 0.693209i | \(0.243804\pi\) | |||||||
\(240\) | 25.6998 | 1.65891 | ||||||||
\(241\) | 20.2341 | 1.30339 | 0.651695 | − | 0.758481i | \(-0.274058\pi\) | ||||
0.651695 | + | 0.758481i | \(0.274058\pi\) | |||||||
\(242\) | −2.66059 | −0.171029 | ||||||||
\(243\) | −16.0876 | −1.03202 | ||||||||
\(244\) | 8.07702 | 0.517078 | ||||||||
\(245\) | 11.4424 | 0.731027 | ||||||||
\(246\) | −18.8685 | −1.20301 | ||||||||
\(247\) | 40.4664 | 2.57482 | ||||||||
\(248\) | −46.2001 | −2.93371 | ||||||||
\(249\) | 4.22492 | 0.267743 | ||||||||
\(250\) | −24.0473 | −1.52089 | ||||||||
\(251\) | 9.69461 | 0.611918 | 0.305959 | − | 0.952045i | \(-0.401023\pi\) | ||||
0.305959 | + | 0.952045i | \(0.401023\pi\) | |||||||
\(252\) | −17.9713 | −1.13208 | ||||||||
\(253\) | 7.87110 | 0.494852 | ||||||||
\(254\) | −45.5428 | −2.85761 | ||||||||
\(255\) | −2.20859 | −0.138307 | ||||||||
\(256\) | 1.20747 | 0.0754671 | ||||||||
\(257\) | −26.8705 | −1.67613 | −0.838067 | − | 0.545568i | \(-0.816314\pi\) | ||||
−0.838067 | + | 0.545568i | \(0.816314\pi\) | |||||||
\(258\) | −2.31593 | −0.144183 | ||||||||
\(259\) | −3.17442 | −0.197249 | ||||||||
\(260\) | 71.4618 | 4.43187 | ||||||||
\(261\) | −3.60069 | −0.222877 | ||||||||
\(262\) | 2.20873 | 0.136456 | ||||||||
\(263\) | −30.2390 | −1.86461 | −0.932307 | − | 0.361668i | \(-0.882207\pi\) | ||||
−0.932307 | + | 0.361668i | \(0.882207\pi\) | |||||||
\(264\) | 7.13019 | 0.438833 | ||||||||
\(265\) | 11.3668 | 0.698258 | ||||||||
\(266\) | 30.6374 | 1.87850 | ||||||||
\(267\) | −15.9877 | −0.978431 | ||||||||
\(268\) | −74.0088 | −4.52080 | ||||||||
\(269\) | −15.5140 | −0.945903 | −0.472952 | − | 0.881088i | \(-0.656811\pi\) | ||||
−0.472952 | + | 0.881088i | \(0.656811\pi\) | |||||||
\(270\) | 30.8046 | 1.87471 | ||||||||
\(271\) | −14.6783 | −0.891644 | −0.445822 | − | 0.895122i | \(-0.647088\pi\) | ||||
−0.445822 | + | 0.895122i | \(0.647088\pi\) | |||||||
\(272\) | −11.6363 | −0.705554 | ||||||||
\(273\) | 7.61763 | 0.461040 | ||||||||
\(274\) | 38.3383 | 2.31610 | ||||||||
\(275\) | 1.43779 | 0.0867019 | ||||||||
\(276\) | −34.7968 | −2.09452 | ||||||||
\(277\) | −3.14366 | −0.188884 | −0.0944422 | − | 0.995530i | \(-0.530107\pi\) | ||||
−0.0944422 | + | 0.995530i | \(0.530107\pi\) | |||||||
\(278\) | 51.5095 | 3.08934 | ||||||||
\(279\) | −12.6469 | −0.757150 | ||||||||
\(280\) | 32.7981 | 1.96006 | ||||||||
\(281\) | 1.01999 | 0.0608473 | 0.0304236 | − | 0.999537i | \(-0.490314\pi\) | ||||
0.0304236 | + | 0.999537i | \(0.490314\pi\) | |||||||
\(282\) | 8.08036 | 0.481178 | ||||||||
\(283\) | 3.69869 | 0.219865 | 0.109932 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109932 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(284\) | −12.2340 | −0.725952 | ||||||||
\(285\) | −16.1162 | −0.954640 | ||||||||
\(286\) | 14.7546 | 0.872456 | ||||||||
\(287\) | −12.8569 | −0.758921 | ||||||||
\(288\) | 32.6857 | 1.92602 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 10.8402 | 0.636559 | ||||||||
\(291\) | 2.35399 | 0.137993 | ||||||||
\(292\) | −62.1370 | −3.63629 | ||||||||
\(293\) | 1.45167 | 0.0848075 | 0.0424037 | − | 0.999101i | \(-0.486498\pi\) | ||||
0.0424037 | + | 0.999101i | \(0.486498\pi\) | |||||||
\(294\) | −10.4441 | −0.609115 | ||||||||
\(295\) | −11.7706 | −0.685313 | ||||||||
\(296\) | 16.4776 | 0.957740 | ||||||||
\(297\) | 4.56319 | 0.264783 | ||||||||
\(298\) | −53.1829 | −3.08080 | ||||||||
\(299\) | −43.6499 | −2.52434 | ||||||||
\(300\) | −6.35622 | −0.366977 | ||||||||
\(301\) | −1.57807 | −0.0909583 | ||||||||
\(302\) | −44.9436 | −2.58621 | ||||||||
\(303\) | 13.5416 | 0.777945 | ||||||||
\(304\) | −84.9106 | −4.86996 | ||||||||
\(305\) | −4.03517 | −0.231053 | ||||||||
\(306\) | −5.96587 | −0.341046 | ||||||||
\(307\) | 8.53719 | 0.487243 | 0.243622 | − | 0.969870i | \(-0.421664\pi\) | ||||
0.243622 | + | 0.969870i | \(0.421664\pi\) | |||||||
\(308\) | 8.01463 | 0.456676 | ||||||||
\(309\) | 9.01582 | 0.512892 | ||||||||
\(310\) | 38.0746 | 2.16249 | ||||||||
\(311\) | 10.0213 | 0.568258 | 0.284129 | − | 0.958786i | \(-0.408296\pi\) | ||||
0.284129 | + | 0.958786i | \(0.408296\pi\) | |||||||
\(312\) | −39.5411 | −2.23858 | ||||||||
\(313\) | 14.2659 | 0.806359 | 0.403180 | − | 0.915121i | \(-0.367905\pi\) | ||||
0.403180 | + | 0.915121i | \(0.367905\pi\) | |||||||
\(314\) | 44.2535 | 2.49737 | ||||||||
\(315\) | 8.97820 | 0.505864 | ||||||||
\(316\) | −61.8373 | −3.47862 | ||||||||
\(317\) | −23.8586 | −1.34003 | −0.670015 | − | 0.742347i | \(-0.733713\pi\) | ||||
−0.670015 | + | 0.742347i | \(0.733713\pi\) | |||||||
\(318\) | −10.3752 | −0.581811 | ||||||||
\(319\) | 1.60580 | 0.0899074 | ||||||||
\(320\) | −39.3541 | −2.19996 | ||||||||
\(321\) | 9.20504 | 0.513775 | ||||||||
\(322\) | −33.0476 | −1.84167 | ||||||||
\(323\) | 7.29705 | 0.406019 | ||||||||
\(324\) | 13.9913 | 0.777296 | ||||||||
\(325\) | −7.97338 | −0.442284 | ||||||||
\(326\) | 34.7627 | 1.92533 | ||||||||
\(327\) | 9.38469 | 0.518974 | ||||||||
\(328\) | 66.7371 | 3.68494 | ||||||||
\(329\) | 5.50594 | 0.303552 | ||||||||
\(330\) | −5.87616 | −0.323472 | ||||||||
\(331\) | 23.6822 | 1.30169 | 0.650846 | − | 0.759210i | \(-0.274414\pi\) | ||||
0.650846 | + | 0.759210i | \(0.274414\pi\) | |||||||
\(332\) | −24.6507 | −1.35288 | ||||||||
\(333\) | 4.51060 | 0.247179 | ||||||||
\(334\) | 50.2433 | 2.74919 | ||||||||
\(335\) | 36.9738 | 2.02009 | ||||||||
\(336\) | −15.9840 | −0.872001 | ||||||||
\(337\) | −7.38517 | −0.402296 | −0.201148 | − | 0.979561i | \(-0.564467\pi\) | ||||
−0.201148 | + | 0.979561i | \(0.564467\pi\) | |||||||
\(338\) | −47.2351 | −2.56925 | ||||||||
\(339\) | −13.4669 | −0.731423 | ||||||||
\(340\) | 12.8862 | 0.698854 | ||||||||
\(341\) | 5.64012 | 0.305430 | ||||||||
\(342\) | −43.5333 | −2.35401 | ||||||||
\(343\) | −18.1631 | −0.980714 | ||||||||
\(344\) | 8.19134 | 0.441647 | ||||||||
\(345\) | 17.3840 | 0.935924 | ||||||||
\(346\) | 37.2225 | 2.00110 | ||||||||
\(347\) | −25.9513 | −1.39314 | −0.696570 | − | 0.717489i | \(-0.745291\pi\) | ||||
−0.696570 | + | 0.717489i | \(0.745291\pi\) | |||||||
\(348\) | −7.09896 | −0.380544 | ||||||||
\(349\) | 3.22080 | 0.172405 | 0.0862027 | − | 0.996278i | \(-0.472527\pi\) | ||||
0.0862027 | + | 0.996278i | \(0.472527\pi\) | |||||||
\(350\) | −6.03669 | −0.322675 | ||||||||
\(351\) | −25.3056 | −1.35071 | ||||||||
\(352\) | −14.5768 | −0.776946 | ||||||||
\(353\) | 17.6835 | 0.941198 | 0.470599 | − | 0.882347i | \(-0.344038\pi\) | ||||
0.470599 | + | 0.882347i | \(0.344038\pi\) | |||||||
\(354\) | 10.7438 | 0.571025 | ||||||||
\(355\) | 6.11192 | 0.324387 | ||||||||
\(356\) | 93.2819 | 4.94393 | ||||||||
\(357\) | 1.37364 | 0.0727006 | ||||||||
\(358\) | −13.5680 | −0.717092 | ||||||||
\(359\) | 0.130807 | 0.00690375 | 0.00345187 | − | 0.999994i | \(-0.498901\pi\) | ||||
0.00345187 | + | 0.999994i | \(0.498901\pi\) | |||||||
\(360\) | −46.6035 | −2.45622 | ||||||||
\(361\) | 34.2469 | 1.80247 | ||||||||
\(362\) | 41.9546 | 2.20509 | ||||||||
\(363\) | −0.870455 | −0.0456870 | ||||||||
\(364\) | −44.4459 | −2.32960 | ||||||||
\(365\) | 31.0428 | 1.62485 | ||||||||
\(366\) | 3.68314 | 0.192521 | ||||||||
\(367\) | −2.06773 | −0.107935 | −0.0539673 | − | 0.998543i | \(-0.517187\pi\) | ||||
−0.0539673 | + | 0.998543i | \(0.517187\pi\) | |||||||
\(368\) | 91.5904 | 4.77448 | ||||||||
\(369\) | 18.2687 | 0.951030 | ||||||||
\(370\) | −13.5796 | −0.705968 | ||||||||
\(371\) | −7.06962 | −0.367036 | ||||||||
\(372\) | −24.9340 | −1.29277 | ||||||||
\(373\) | 3.04369 | 0.157596 | 0.0787982 | − | 0.996891i | \(-0.474892\pi\) | ||||
0.0787982 | + | 0.996891i | \(0.474892\pi\) | |||||||
\(374\) | 2.66059 | 0.137576 | ||||||||
\(375\) | −7.86746 | −0.406274 | ||||||||
\(376\) | −28.5799 | −1.47390 | ||||||||
\(377\) | −8.90510 | −0.458636 | ||||||||
\(378\) | −19.1590 | −0.985433 | ||||||||
\(379\) | −19.1476 | −0.983545 | −0.491772 | − | 0.870724i | \(-0.663651\pi\) | ||||
−0.491772 | + | 0.870724i | \(0.663651\pi\) | |||||||
\(380\) | 94.0315 | 4.82371 | ||||||||
\(381\) | −14.9000 | −0.763352 | ||||||||
\(382\) | 64.8054 | 3.31573 | ||||||||
\(383\) | −27.1862 | −1.38915 | −0.694574 | − | 0.719421i | \(-0.744407\pi\) | ||||
−0.694574 | + | 0.719421i | \(0.744407\pi\) | |||||||
\(384\) | 10.5440 | 0.538069 | ||||||||
\(385\) | −4.00400 | −0.204063 | ||||||||
\(386\) | −16.9613 | −0.863308 | ||||||||
\(387\) | 2.24231 | 0.113983 | ||||||||
\(388\) | −13.7346 | −0.697269 | ||||||||
\(389\) | −11.6206 | −0.589190 | −0.294595 | − | 0.955622i | \(-0.595185\pi\) | ||||
−0.294595 | + | 0.955622i | \(0.595185\pi\) | |||||||
\(390\) | 32.5868 | 1.65009 | ||||||||
\(391\) | −7.87110 | −0.398058 | ||||||||
\(392\) | 36.9405 | 1.86578 | ||||||||
\(393\) | 0.722621 | 0.0364514 | ||||||||
\(394\) | −10.1421 | −0.510953 | ||||||||
\(395\) | 30.8931 | 1.55440 | ||||||||
\(396\) | −11.3881 | −0.572276 | ||||||||
\(397\) | −2.83727 | −0.142398 | −0.0711992 | − | 0.997462i | \(-0.522683\pi\) | ||||
−0.0711992 | + | 0.997462i | \(0.522683\pi\) | |||||||
\(398\) | 45.4450 | 2.27795 | ||||||||
\(399\) | 10.0235 | 0.501802 | ||||||||
\(400\) | 16.7305 | 0.836526 | ||||||||
\(401\) | 28.6063 | 1.42853 | 0.714265 | − | 0.699876i | \(-0.246761\pi\) | ||||
0.714265 | + | 0.699876i | \(0.246761\pi\) | |||||||
\(402\) | −33.7482 | −1.68321 | ||||||||
\(403\) | −31.2778 | −1.55806 | ||||||||
\(404\) | −79.0099 | −3.93089 | ||||||||
\(405\) | −6.98987 | −0.347330 | ||||||||
\(406\) | −6.74210 | −0.334605 | ||||||||
\(407\) | −2.01159 | −0.0997106 | ||||||||
\(408\) | −7.13019 | −0.352997 | ||||||||
\(409\) | 7.05543 | 0.348868 | 0.174434 | − | 0.984669i | \(-0.444190\pi\) | ||||
0.174434 | + | 0.984669i | \(0.444190\pi\) | |||||||
\(410\) | −54.9996 | −2.71624 | ||||||||
\(411\) | 12.5430 | 0.618699 | ||||||||
\(412\) | −52.6038 | −2.59160 | ||||||||
\(413\) | 7.32077 | 0.360232 | ||||||||
\(414\) | 46.9580 | 2.30786 | ||||||||
\(415\) | 12.3152 | 0.604528 | ||||||||
\(416\) | 80.8370 | 3.96336 | ||||||||
\(417\) | 16.8521 | 0.825253 | ||||||||
\(418\) | 19.4145 | 0.949593 | ||||||||
\(419\) | 16.6105 | 0.811478 | 0.405739 | − | 0.913989i | \(-0.367014\pi\) | ||||
0.405739 | + | 0.913989i | \(0.367014\pi\) | |||||||
\(420\) | 17.7010 | 0.863721 | ||||||||
\(421\) | 34.4380 | 1.67840 | 0.839202 | − | 0.543819i | \(-0.183022\pi\) | ||||
0.839202 | + | 0.543819i | \(0.183022\pi\) | |||||||
\(422\) | −58.5103 | −2.84824 | ||||||||
\(423\) | −7.82350 | −0.380391 | ||||||||
\(424\) | 36.6965 | 1.78214 | ||||||||
\(425\) | −1.43779 | −0.0697430 | ||||||||
\(426\) | −5.57871 | −0.270290 | ||||||||
\(427\) | 2.50968 | 0.121452 | ||||||||
\(428\) | −53.7078 | −2.59606 | ||||||||
\(429\) | 4.82719 | 0.233059 | ||||||||
\(430\) | −6.75067 | −0.325546 | ||||||||
\(431\) | 12.9384 | 0.623220 | 0.311610 | − | 0.950210i | \(-0.399132\pi\) | ||||
0.311610 | + | 0.950210i | \(0.399132\pi\) | |||||||
\(432\) | 53.0987 | 2.55471 | ||||||||
\(433\) | 23.7005 | 1.13897 | 0.569486 | − | 0.822001i | \(-0.307142\pi\) | ||||
0.569486 | + | 0.822001i | \(0.307142\pi\) | |||||||
\(434\) | −23.6806 | −1.13671 | ||||||||
\(435\) | 3.54654 | 0.170044 | ||||||||
\(436\) | −54.7560 | −2.62233 | ||||||||
\(437\) | −57.4358 | −2.74753 | ||||||||
\(438\) | −28.3346 | −1.35388 | ||||||||
\(439\) | −12.5017 | −0.596674 | −0.298337 | − | 0.954461i | \(-0.596432\pi\) | ||||
−0.298337 | + | 0.954461i | \(0.596432\pi\) | |||||||
\(440\) | 20.7837 | 0.990825 | ||||||||
\(441\) | 10.1121 | 0.481531 | ||||||||
\(442\) | −14.7546 | −0.701803 | ||||||||
\(443\) | 28.6698 | 1.36214 | 0.681072 | − | 0.732217i | \(-0.261514\pi\) | ||||
0.681072 | + | 0.732217i | \(0.261514\pi\) | |||||||
\(444\) | 8.89289 | 0.422038 | ||||||||
\(445\) | −46.6024 | −2.20916 | ||||||||
\(446\) | −35.8345 | −1.69682 | ||||||||
\(447\) | −17.3996 | −0.822974 | ||||||||
\(448\) | 24.4764 | 1.15640 | ||||||||
\(449\) | −19.9595 | −0.941945 | −0.470972 | − | 0.882148i | \(-0.656097\pi\) | ||||
−0.470972 | + | 0.882148i | \(0.656097\pi\) | |||||||
\(450\) | 8.57766 | 0.404355 | ||||||||
\(451\) | −8.14727 | −0.383640 | ||||||||
\(452\) | 78.5742 | 3.69582 | ||||||||
\(453\) | −14.7040 | −0.690854 | ||||||||
\(454\) | 21.1159 | 0.991019 | ||||||||
\(455\) | 22.2045 | 1.04096 | ||||||||
\(456\) | −52.0293 | −2.43650 | ||||||||
\(457\) | −26.9453 | −1.26045 | −0.630224 | − | 0.776414i | \(-0.717037\pi\) | ||||
−0.630224 | + | 0.776414i | \(0.717037\pi\) | |||||||
\(458\) | −10.9429 | −0.511328 | ||||||||
\(459\) | −4.56319 | −0.212992 | ||||||||
\(460\) | −101.429 | −4.72914 | ||||||||
\(461\) | −26.1593 | −1.21836 | −0.609179 | − | 0.793033i | \(-0.708501\pi\) | ||||
−0.609179 | + | 0.793033i | \(0.708501\pi\) | |||||||
\(462\) | 3.65469 | 0.170032 | ||||||||
\(463\) | −30.0923 | −1.39851 | −0.699254 | − | 0.714873i | \(-0.746484\pi\) | ||||
−0.699254 | + | 0.714873i | \(0.746484\pi\) | |||||||
\(464\) | 18.6855 | 0.867454 | ||||||||
\(465\) | 12.4567 | 0.577666 | ||||||||
\(466\) | −31.2924 | −1.44959 | ||||||||
\(467\) | −38.0326 | −1.75994 | −0.879969 | − | 0.475031i | \(-0.842437\pi\) | ||||
−0.879969 | + | 0.475031i | \(0.842437\pi\) | |||||||
\(468\) | 63.1540 | 2.91930 | ||||||||
\(469\) | −22.9959 | −1.06185 | ||||||||
\(470\) | 23.5534 | 1.08644 | ||||||||
\(471\) | 14.4782 | 0.667121 | ||||||||
\(472\) | −38.0002 | −1.74910 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −28.1980 | −1.29518 | ||||||||
\(475\) | −10.4916 | −0.481388 | ||||||||
\(476\) | −8.01463 | −0.367350 | ||||||||
\(477\) | 10.0454 | 0.459946 | ||||||||
\(478\) | −59.2904 | −2.71188 | ||||||||
\(479\) | −15.3441 | −0.701090 | −0.350545 | − | 0.936546i | \(-0.614004\pi\) | ||||
−0.350545 | + | 0.936546i | \(0.614004\pi\) | |||||||
\(480\) | −32.1941 | −1.46945 | ||||||||
\(481\) | 11.1554 | 0.508644 | ||||||||
\(482\) | −53.8346 | −2.45210 | ||||||||
\(483\) | −10.8120 | −0.491964 | ||||||||
\(484\) | 5.07876 | 0.230853 | ||||||||
\(485\) | 6.86162 | 0.311570 | ||||||||
\(486\) | 42.8025 | 1.94156 | ||||||||
\(487\) | −4.98060 | −0.225693 | −0.112846 | − | 0.993612i | \(-0.535997\pi\) | ||||
−0.112846 | + | 0.993612i | \(0.535997\pi\) | |||||||
\(488\) | −13.0271 | −0.589710 | ||||||||
\(489\) | 11.3731 | 0.514312 | ||||||||
\(490\) | −30.4435 | −1.37530 | ||||||||
\(491\) | 24.3655 | 1.09960 | 0.549801 | − | 0.835296i | \(-0.314704\pi\) | ||||
0.549801 | + | 0.835296i | \(0.314704\pi\) | |||||||
\(492\) | 36.0177 | 1.62381 | ||||||||
\(493\) | −1.60580 | −0.0723215 | ||||||||
\(494\) | −107.665 | −4.84407 | ||||||||
\(495\) | 5.68936 | 0.255718 | ||||||||
\(496\) | 65.6302 | 2.94688 | ||||||||
\(497\) | −3.80132 | −0.170513 | ||||||||
\(498\) | −11.2408 | −0.503712 | ||||||||
\(499\) | −15.6279 | −0.699599 | −0.349800 | − | 0.936825i | \(-0.613750\pi\) | ||||
−0.349800 | + | 0.936825i | \(0.613750\pi\) | |||||||
\(500\) | 45.9035 | 2.05287 | ||||||||
\(501\) | 16.4379 | 0.734390 | ||||||||
\(502\) | −25.7934 | −1.15122 | ||||||||
\(503\) | −4.60234 | −0.205208 | −0.102604 | − | 0.994722i | \(-0.532717\pi\) | ||||
−0.102604 | + | 0.994722i | \(0.532717\pi\) | |||||||
\(504\) | 28.9851 | 1.29110 | ||||||||
\(505\) | 39.4723 | 1.75649 | ||||||||
\(506\) | −20.9418 | −0.930976 | ||||||||
\(507\) | −15.4537 | −0.686323 | ||||||||
\(508\) | 86.9358 | 3.85715 | ||||||||
\(509\) | 18.2928 | 0.810816 | 0.405408 | − | 0.914136i | \(-0.367130\pi\) | ||||
0.405408 | + | 0.914136i | \(0.367130\pi\) | |||||||
\(510\) | 5.87616 | 0.260201 | ||||||||
\(511\) | −19.3071 | −0.854097 | ||||||||
\(512\) | 21.0137 | 0.928683 | ||||||||
\(513\) | −33.2978 | −1.47014 | ||||||||
\(514\) | 71.4914 | 3.15335 | ||||||||
\(515\) | 26.2801 | 1.15804 | ||||||||
\(516\) | 4.42083 | 0.194616 | ||||||||
\(517\) | 3.48904 | 0.153448 | ||||||||
\(518\) | 8.44584 | 0.371089 | ||||||||
\(519\) | 12.1779 | 0.534552 | ||||||||
\(520\) | −115.258 | −5.05440 | ||||||||
\(521\) | −2.19257 | −0.0960584 | −0.0480292 | − | 0.998846i | \(-0.515294\pi\) | ||||
−0.0480292 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(522\) | 9.57998 | 0.419304 | ||||||||
\(523\) | 13.2329 | 0.578636 | 0.289318 | − | 0.957233i | \(-0.406571\pi\) | ||||
0.289318 | + | 0.957233i | \(0.406571\pi\) | |||||||
\(524\) | −4.21621 | −0.184186 | ||||||||
\(525\) | −1.97500 | −0.0861960 | ||||||||
\(526\) | 80.4536 | 3.50794 | ||||||||
\(527\) | −5.64012 | −0.245688 | ||||||||
\(528\) | −10.1289 | −0.440803 | ||||||||
\(529\) | 38.9542 | 1.69366 | ||||||||
\(530\) | −30.2425 | −1.31365 | ||||||||
\(531\) | −10.4022 | −0.451419 | ||||||||
\(532\) | −58.4831 | −2.53556 | ||||||||
\(533\) | 45.1815 | 1.95703 | ||||||||
\(534\) | 42.5368 | 1.84075 | ||||||||
\(535\) | 26.8317 | 1.16003 | ||||||||
\(536\) | 119.366 | 5.15582 | ||||||||
\(537\) | −4.43899 | −0.191556 | ||||||||
\(538\) | 41.2764 | 1.77955 | ||||||||
\(539\) | −4.50970 | −0.194247 | ||||||||
\(540\) | −58.8024 | −2.53045 | ||||||||
\(541\) | −14.6820 | −0.631228 | −0.315614 | − | 0.948888i | \(-0.602211\pi\) | ||||
−0.315614 | + | 0.948888i | \(0.602211\pi\) | |||||||
\(542\) | 39.0530 | 1.67747 | ||||||||
\(543\) | 13.7261 | 0.589044 | ||||||||
\(544\) | 14.5768 | 0.624975 | ||||||||
\(545\) | 27.3553 | 1.17177 | ||||||||
\(546\) | −20.2674 | −0.867365 | ||||||||
\(547\) | −0.0899527 | −0.00384610 | −0.00192305 | − | 0.999998i | \(-0.500612\pi\) | ||||
−0.00192305 | + | 0.999998i | \(0.500612\pi\) | |||||||
\(548\) | −73.1832 | −3.12623 | ||||||||
\(549\) | −3.56606 | −0.152196 | ||||||||
\(550\) | −3.82537 | −0.163114 | ||||||||
\(551\) | −11.7176 | −0.499186 | ||||||||
\(552\) | 56.1224 | 2.38873 | ||||||||
\(553\) | −19.2140 | −0.817063 | ||||||||
\(554\) | 8.36401 | 0.355353 | ||||||||
\(555\) | −4.44277 | −0.188585 | ||||||||
\(556\) | −98.3256 | −4.16993 | ||||||||
\(557\) | 21.5747 | 0.914150 | 0.457075 | − | 0.889428i | \(-0.348897\pi\) | ||||
0.457075 | + | 0.889428i | \(0.348897\pi\) | |||||||
\(558\) | 33.6482 | 1.42444 | ||||||||
\(559\) | 5.54559 | 0.234554 | ||||||||
\(560\) | −46.5917 | −1.96886 | ||||||||
\(561\) | 0.870455 | 0.0367506 | ||||||||
\(562\) | −2.71377 | −0.114473 | ||||||||
\(563\) | 18.8013 | 0.792382 | 0.396191 | − | 0.918168i | \(-0.370332\pi\) | ||||
0.396191 | + | 0.918168i | \(0.370332\pi\) | |||||||
\(564\) | −15.4245 | −0.649487 | ||||||||
\(565\) | −39.2546 | −1.65145 | ||||||||
\(566\) | −9.84072 | −0.413637 | ||||||||
\(567\) | 4.34737 | 0.182572 | ||||||||
\(568\) | 19.7317 | 0.827923 | ||||||||
\(569\) | −26.6804 | −1.11850 | −0.559251 | − | 0.828998i | \(-0.688911\pi\) | ||||
−0.559251 | + | 0.828998i | \(0.688911\pi\) | |||||||
\(570\) | 42.8786 | 1.79599 | ||||||||
\(571\) | −3.77200 | −0.157853 | −0.0789267 | − | 0.996880i | \(-0.525149\pi\) | ||||
−0.0789267 | + | 0.996880i | \(0.525149\pi\) | |||||||
\(572\) | −28.1647 | −1.17763 | ||||||||
\(573\) | 21.2021 | 0.885730 | ||||||||
\(574\) | 34.2071 | 1.42778 | ||||||||
\(575\) | 11.3170 | 0.471950 | ||||||||
\(576\) | −34.7790 | −1.44912 | ||||||||
\(577\) | −21.6186 | −0.899994 | −0.449997 | − | 0.893030i | \(-0.648575\pi\) | ||||
−0.449997 | + | 0.893030i | \(0.648575\pi\) | |||||||
\(578\) | −2.66059 | −0.110666 | ||||||||
\(579\) | −5.54916 | −0.230615 | ||||||||
\(580\) | −20.6927 | −0.859217 | ||||||||
\(581\) | −7.65945 | −0.317767 | ||||||||
\(582\) | −6.26301 | −0.259610 | ||||||||
\(583\) | −4.47992 | −0.185539 | ||||||||
\(584\) | 100.218 | 4.14706 | ||||||||
\(585\) | −31.5509 | −1.30447 | ||||||||
\(586\) | −3.86231 | −0.159550 | ||||||||
\(587\) | −24.0630 | −0.993187 | −0.496594 | − | 0.867983i | \(-0.665416\pi\) | ||||
−0.496594 | + | 0.867983i | \(0.665416\pi\) | |||||||
\(588\) | 19.9367 | 0.822174 | ||||||||
\(589\) | −41.1562 | −1.69581 | ||||||||
\(590\) | 31.3169 | 1.28930 | ||||||||
\(591\) | −3.31816 | −0.136491 | ||||||||
\(592\) | −23.4074 | −0.962039 | ||||||||
\(593\) | 22.3368 | 0.917264 | 0.458632 | − | 0.888626i | \(-0.348340\pi\) | ||||
0.458632 | + | 0.888626i | \(0.348340\pi\) | |||||||
\(594\) | −12.1408 | −0.498143 | ||||||||
\(595\) | 4.00400 | 0.164148 | ||||||||
\(596\) | 101.520 | 4.15842 | ||||||||
\(597\) | 14.8680 | 0.608508 | ||||||||
\(598\) | 116.135 | 4.74910 | ||||||||
\(599\) | 18.5635 | 0.758484 | 0.379242 | − | 0.925297i | \(-0.376185\pi\) | ||||
0.379242 | + | 0.925297i | \(0.376185\pi\) | |||||||
\(600\) | 10.2517 | 0.418524 | ||||||||
\(601\) | −2.90206 | −0.118377 | −0.0591887 | − | 0.998247i | \(-0.518851\pi\) | ||||
−0.0591887 | + | 0.998247i | \(0.518851\pi\) | |||||||
\(602\) | 4.19860 | 0.171122 | ||||||||
\(603\) | 32.6754 | 1.33064 | ||||||||
\(604\) | 85.7920 | 3.49083 | ||||||||
\(605\) | −2.53728 | −0.103155 | ||||||||
\(606\) | −36.0287 | −1.46357 | ||||||||
\(607\) | −34.9208 | −1.41739 | −0.708696 | − | 0.705514i | \(-0.750716\pi\) | ||||
−0.708696 | + | 0.705514i | \(0.750716\pi\) | |||||||
\(608\) | 106.368 | 4.31378 | ||||||||
\(609\) | −2.20578 | −0.0893828 | ||||||||
\(610\) | 10.7359 | 0.434686 | ||||||||
\(611\) | −19.3488 | −0.782768 | ||||||||
\(612\) | 11.3881 | 0.460339 | ||||||||
\(613\) | −32.4176 | −1.30934 | −0.654668 | − | 0.755917i | \(-0.727191\pi\) | ||||
−0.654668 | + | 0.755917i | \(0.727191\pi\) | |||||||
\(614\) | −22.7140 | −0.916663 | ||||||||
\(615\) | −17.9940 | −0.725587 | ||||||||
\(616\) | −12.9265 | −0.520823 | ||||||||
\(617\) | 0.469553 | 0.0189035 | 0.00945174 | − | 0.999955i | \(-0.496991\pi\) | ||||
0.00945174 | + | 0.999955i | \(0.496991\pi\) | |||||||
\(618\) | −23.9874 | −0.964916 | ||||||||
\(619\) | 33.4134 | 1.34300 | 0.671500 | − | 0.741005i | \(-0.265650\pi\) | ||||
0.671500 | + | 0.741005i | \(0.265650\pi\) | |||||||
\(620\) | −72.6800 | −2.91890 | ||||||||
\(621\) | 35.9173 | 1.44131 | ||||||||
\(622\) | −26.6627 | −1.06908 | ||||||||
\(623\) | 28.9845 | 1.16124 | ||||||||
\(624\) | 56.1706 | 2.24862 | ||||||||
\(625\) | −30.1217 | −1.20487 | ||||||||
\(626\) | −37.9559 | −1.51702 | ||||||||
\(627\) | 6.35175 | 0.253665 | ||||||||
\(628\) | −84.4747 | −3.37091 | ||||||||
\(629\) | 2.01159 | 0.0802072 | ||||||||
\(630\) | −23.8873 | −0.951694 | ||||||||
\(631\) | 33.8593 | 1.34792 | 0.673959 | − | 0.738769i | \(-0.264592\pi\) | ||||
0.673959 | + | 0.738769i | \(0.264592\pi\) | |||||||
\(632\) | 99.7350 | 3.96724 | ||||||||
\(633\) | −19.1426 | −0.760849 | ||||||||
\(634\) | 63.4780 | 2.52103 | ||||||||
\(635\) | −43.4319 | −1.72354 | ||||||||
\(636\) | 19.8050 | 0.785319 | ||||||||
\(637\) | 25.0090 | 0.990892 | ||||||||
\(638\) | −4.27238 | −0.169145 | ||||||||
\(639\) | 5.40138 | 0.213675 | ||||||||
\(640\) | 30.7344 | 1.21489 | ||||||||
\(641\) | 6.38117 | 0.252041 | 0.126021 | − | 0.992028i | \(-0.459779\pi\) | ||||
0.126021 | + | 0.992028i | \(0.459779\pi\) | |||||||
\(642\) | −24.4909 | −0.966578 | ||||||||
\(643\) | 17.3845 | 0.685577 | 0.342788 | − | 0.939413i | \(-0.388629\pi\) | ||||
0.342788 | + | 0.939413i | \(0.388629\pi\) | |||||||
\(644\) | 63.0839 | 2.48585 | ||||||||
\(645\) | −2.20859 | −0.0869631 | ||||||||
\(646\) | −19.4145 | −0.763853 | ||||||||
\(647\) | 18.5926 | 0.730949 | 0.365475 | − | 0.930821i | \(-0.380907\pi\) | ||||
0.365475 | + | 0.930821i | \(0.380907\pi\) | |||||||
\(648\) | −22.5661 | −0.886478 | ||||||||
\(649\) | 4.63908 | 0.182100 | ||||||||
\(650\) | 21.2139 | 0.832079 | ||||||||
\(651\) | −7.74748 | −0.303648 | ||||||||
\(652\) | −66.3578 | −2.59877 | ||||||||
\(653\) | 40.0788 | 1.56840 | 0.784202 | − | 0.620505i | \(-0.213073\pi\) | ||||
0.784202 | + | 0.620505i | \(0.213073\pi\) | |||||||
\(654\) | −24.9688 | −0.976359 | ||||||||
\(655\) | 2.10636 | 0.0823023 | ||||||||
\(656\) | −94.8041 | −3.70148 | ||||||||
\(657\) | 27.4339 | 1.07030 | ||||||||
\(658\) | −14.6491 | −0.571080 | ||||||||
\(659\) | −36.6028 | −1.42584 | −0.712921 | − | 0.701244i | \(-0.752628\pi\) | ||||
−0.712921 | + | 0.701244i | \(0.752628\pi\) | |||||||
\(660\) | 11.2169 | 0.436617 | ||||||||
\(661\) | −12.3226 | −0.479293 | −0.239646 | − | 0.970860i | \(-0.577031\pi\) | ||||
−0.239646 | + | 0.970860i | \(0.577031\pi\) | |||||||
\(662\) | −63.0087 | −2.44890 | ||||||||
\(663\) | −4.82719 | −0.187472 | ||||||||
\(664\) | 39.7582 | 1.54292 | ||||||||
\(665\) | 29.2174 | 1.13300 | ||||||||
\(666\) | −12.0009 | −0.465024 | ||||||||
\(667\) | 12.6394 | 0.489399 | ||||||||
\(668\) | −95.9085 | −3.71081 | ||||||||
\(669\) | −11.7238 | −0.453270 | ||||||||
\(670\) | −98.3722 | −3.80045 | ||||||||
\(671\) | 1.59035 | 0.0613949 | ||||||||
\(672\) | 20.0232 | 0.772413 | ||||||||
\(673\) | 47.4646 | 1.82962 | 0.914812 | − | 0.403880i | \(-0.132339\pi\) | ||||
0.914812 | + | 0.403880i | \(0.132339\pi\) | |||||||
\(674\) | 19.6489 | 0.756849 | ||||||||
\(675\) | 6.56090 | 0.252529 | ||||||||
\(676\) | 90.1662 | 3.46793 | ||||||||
\(677\) | 0.548743 | 0.0210899 | 0.0105449 | − | 0.999944i | \(-0.496643\pi\) | ||||
0.0105449 | + | 0.999944i | \(0.496643\pi\) | |||||||
\(678\) | 35.8300 | 1.37604 | ||||||||
\(679\) | −4.26760 | −0.163776 | ||||||||
\(680\) | −20.7837 | −0.797019 | ||||||||
\(681\) | 6.90840 | 0.264731 | ||||||||
\(682\) | −15.0061 | −0.574612 | ||||||||
\(683\) | 14.6486 | 0.560512 | 0.280256 | − | 0.959925i | \(-0.409581\pi\) | ||||
0.280256 | + | 0.959925i | \(0.409581\pi\) | |||||||
\(684\) | 83.0999 | 3.17740 | ||||||||
\(685\) | 36.5613 | 1.39694 | ||||||||
\(686\) | 48.3246 | 1.84504 | ||||||||
\(687\) | −3.58014 | −0.136591 | ||||||||
\(688\) | −11.6363 | −0.443630 | ||||||||
\(689\) | 24.8438 | 0.946474 | ||||||||
\(690\) | −46.2518 | −1.76078 | ||||||||
\(691\) | −30.2219 | −1.14969 | −0.574847 | − | 0.818261i | \(-0.694939\pi\) | ||||
−0.574847 | + | 0.818261i | \(0.694939\pi\) | |||||||
\(692\) | −71.0534 | −2.70105 | ||||||||
\(693\) | −3.53851 | −0.134417 | ||||||||
\(694\) | 69.0459 | 2.62095 | ||||||||
\(695\) | 49.1221 | 1.86331 | ||||||||
\(696\) | 11.4496 | 0.433998 | ||||||||
\(697\) | 8.14727 | 0.308600 | ||||||||
\(698\) | −8.56924 | −0.324350 | ||||||||
\(699\) | −10.2378 | −0.387229 | ||||||||
\(700\) | 11.5233 | 0.435541 | ||||||||
\(701\) | −46.9706 | −1.77406 | −0.887028 | − | 0.461716i | \(-0.847234\pi\) | ||||
−0.887028 | + | 0.461716i | \(0.847234\pi\) | |||||||
\(702\) | 67.3280 | 2.54113 | ||||||||
\(703\) | 14.6786 | 0.553616 | ||||||||
\(704\) | 15.5103 | 0.584568 | ||||||||
\(705\) | 7.70585 | 0.290219 | ||||||||
\(706\) | −47.0486 | −1.77070 | ||||||||
\(707\) | −24.5499 | −0.923293 | ||||||||
\(708\) | −20.5086 | −0.770760 | ||||||||
\(709\) | 35.2164 | 1.32258 | 0.661290 | − | 0.750130i | \(-0.270009\pi\) | ||||
0.661290 | + | 0.750130i | \(0.270009\pi\) | |||||||
\(710\) | −16.2613 | −0.610277 | ||||||||
\(711\) | 27.3016 | 1.02389 | ||||||||
\(712\) | −150.451 | −5.63838 | ||||||||
\(713\) | 44.3940 | 1.66257 | ||||||||
\(714\) | −3.65469 | −0.136773 | ||||||||
\(715\) | 14.0707 | 0.526215 | ||||||||
\(716\) | 25.8997 | 0.967919 | ||||||||
\(717\) | −19.3978 | −0.724423 | ||||||||
\(718\) | −0.348025 | −0.0129882 | ||||||||
\(719\) | 42.6654 | 1.59115 | 0.795576 | − | 0.605854i | \(-0.207168\pi\) | ||||
0.795576 | + | 0.605854i | \(0.207168\pi\) | |||||||
\(720\) | 66.2031 | 2.46724 | ||||||||
\(721\) | −16.3450 | −0.608719 | ||||||||
\(722\) | −91.1171 | −3.39103 | ||||||||
\(723\) | −17.6128 | −0.655029 | ||||||||
\(724\) | −80.0865 | −2.97639 | ||||||||
\(725\) | 2.30880 | 0.0857465 | ||||||||
\(726\) | 2.31593 | 0.0859521 | ||||||||
\(727\) | −41.1159 | −1.52490 | −0.762452 | − | 0.647045i | \(-0.776005\pi\) | ||||
−0.762452 | + | 0.647045i | \(0.776005\pi\) | |||||||
\(728\) | 71.6850 | 2.65682 | ||||||||
\(729\) | 5.73890 | 0.212552 | ||||||||
\(730\) | −82.5922 | −3.05688 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −7.03068 | −0.259862 | ||||||||
\(733\) | 29.0554 | 1.07319 | 0.536593 | − | 0.843841i | \(-0.319711\pi\) | ||||
0.536593 | + | 0.843841i | \(0.319711\pi\) | |||||||
\(734\) | 5.50139 | 0.203060 | ||||||||
\(735\) | −9.96008 | −0.367383 | ||||||||
\(736\) | −114.735 | −4.22920 | ||||||||
\(737\) | −14.5722 | −0.536774 | ||||||||
\(738\) | −48.6056 | −1.78920 | ||||||||
\(739\) | 15.3390 | 0.564253 | 0.282127 | − | 0.959377i | \(-0.408960\pi\) | ||||
0.282127 | + | 0.959377i | \(0.408960\pi\) | |||||||
\(740\) | 25.9218 | 0.952904 | ||||||||
\(741\) | −35.2242 | −1.29399 | ||||||||
\(742\) | 18.8094 | 0.690514 | ||||||||
\(743\) | −7.58541 | −0.278282 | −0.139141 | − | 0.990273i | \(-0.544434\pi\) | ||||
−0.139141 | + | 0.990273i | \(0.544434\pi\) | |||||||
\(744\) | 40.2151 | 1.47436 | ||||||||
\(745\) | −50.7179 | −1.85816 | ||||||||
\(746\) | −8.09803 | −0.296490 | ||||||||
\(747\) | 10.8835 | 0.398205 | ||||||||
\(748\) | −5.07876 | −0.185698 | ||||||||
\(749\) | −16.6880 | −0.609767 | ||||||||
\(750\) | 20.9321 | 0.764333 | ||||||||
\(751\) | 22.8706 | 0.834559 | 0.417279 | − | 0.908778i | \(-0.362984\pi\) | ||||
0.417279 | + | 0.908778i | \(0.362984\pi\) | |||||||
\(752\) | 40.5995 | 1.48051 | ||||||||
\(753\) | −8.43872 | −0.307524 | ||||||||
\(754\) | 23.6928 | 0.862843 | ||||||||
\(755\) | −42.8605 | −1.55985 | ||||||||
\(756\) | 36.5723 | 1.33012 | ||||||||
\(757\) | −32.4872 | −1.18077 | −0.590384 | − | 0.807123i | \(-0.701024\pi\) | ||||
−0.590384 | + | 0.807123i | \(0.701024\pi\) | |||||||
\(758\) | 50.9439 | 1.85037 | ||||||||
\(759\) | −6.85144 | −0.248691 | ||||||||
\(760\) | −151.660 | −5.50128 | ||||||||
\(761\) | 38.9926 | 1.41348 | 0.706740 | − | 0.707474i | \(-0.250165\pi\) | ||||
0.706740 | + | 0.707474i | \(0.250165\pi\) | |||||||
\(762\) | 39.6429 | 1.43611 | ||||||||
\(763\) | −17.0137 | −0.615938 | ||||||||
\(764\) | −123.706 | −4.47552 | ||||||||
\(765\) | −5.68936 | −0.205699 | ||||||||
\(766\) | 72.3313 | 2.61344 | ||||||||
\(767\) | −25.7264 | −0.928927 | ||||||||
\(768\) | −1.05105 | −0.0379265 | ||||||||
\(769\) | −9.05845 | −0.326656 | −0.163328 | − | 0.986572i | \(-0.552223\pi\) | ||||
−0.163328 | + | 0.986572i | \(0.552223\pi\) | |||||||
\(770\) | 10.6530 | 0.383908 | ||||||||
\(771\) | 23.3895 | 0.842353 | ||||||||
\(772\) | 32.3771 | 1.16528 | ||||||||
\(773\) | −5.78595 | −0.208106 | −0.104053 | − | 0.994572i | \(-0.533181\pi\) | ||||
−0.104053 | + | 0.994572i | \(0.533181\pi\) | |||||||
\(774\) | −5.96587 | −0.214439 | ||||||||
\(775\) | 8.10930 | 0.291295 | ||||||||
\(776\) | 22.1520 | 0.795211 | ||||||||
\(777\) | 2.76319 | 0.0991289 | ||||||||
\(778\) | 30.9178 | 1.10846 | ||||||||
\(779\) | 59.4510 | 2.13005 | ||||||||
\(780\) | −62.2043 | −2.22727 | ||||||||
\(781\) | −2.40885 | −0.0861953 | ||||||||
\(782\) | 20.9418 | 0.748877 | ||||||||
\(783\) | 7.32756 | 0.261866 | ||||||||
\(784\) | −52.4763 | −1.87415 | ||||||||
\(785\) | 42.2024 | 1.50627 | ||||||||
\(786\) | −1.92260 | −0.0685769 | ||||||||
\(787\) | −13.3593 | −0.476207 | −0.238104 | − | 0.971240i | \(-0.576526\pi\) | ||||
−0.238104 | + | 0.971240i | \(0.576526\pi\) | |||||||
\(788\) | 19.3601 | 0.689676 | ||||||||
\(789\) | 26.3217 | 0.937076 | ||||||||
\(790\) | −82.1939 | −2.92433 | ||||||||
\(791\) | 24.4145 | 0.868079 | ||||||||
\(792\) | 18.3675 | 0.652661 | ||||||||
\(793\) | −8.81944 | −0.313188 | ||||||||
\(794\) | 7.54882 | 0.267898 | ||||||||
\(795\) | −9.89430 | −0.350915 | ||||||||
\(796\) | −86.7491 | −3.07474 | ||||||||
\(797\) | 8.87297 | 0.314297 | 0.157148 | − | 0.987575i | \(-0.449770\pi\) | ||||
0.157148 | + | 0.987575i | \(0.449770\pi\) | |||||||
\(798\) | −26.6684 | −0.944053 | ||||||||
\(799\) | −3.48904 | −0.123433 | ||||||||
\(800\) | −20.9583 | −0.740989 | ||||||||
\(801\) | −41.1846 | −1.45519 | ||||||||
\(802\) | −76.1097 | −2.68753 | ||||||||
\(803\) | −12.2347 | −0.431752 | ||||||||
\(804\) | 64.4213 | 2.27196 | ||||||||
\(805\) | −31.5159 | −1.11079 | ||||||||
\(806\) | 83.2176 | 2.93121 | ||||||||
\(807\) | 13.5042 | 0.475371 | ||||||||
\(808\) | 127.432 | 4.48304 | ||||||||
\(809\) | −12.3372 | −0.433754 | −0.216877 | − | 0.976199i | \(-0.569587\pi\) | ||||
−0.216877 | + | 0.976199i | \(0.569587\pi\) | |||||||
\(810\) | 18.5972 | 0.653440 | ||||||||
\(811\) | 31.3233 | 1.09991 | 0.549955 | − | 0.835194i | \(-0.314645\pi\) | ||||
0.549955 | + | 0.835194i | \(0.314645\pi\) | |||||||
\(812\) | 12.8699 | 0.451644 | ||||||||
\(813\) | 12.7768 | 0.448102 | ||||||||
\(814\) | 5.35202 | 0.187588 | ||||||||
\(815\) | 33.1515 | 1.16125 | ||||||||
\(816\) | 10.1289 | 0.354582 | ||||||||
\(817\) | 7.29705 | 0.255291 | ||||||||
\(818\) | −18.7716 | −0.656335 | ||||||||
\(819\) | 19.6231 | 0.685688 | ||||||||
\(820\) | 104.988 | 3.66633 | ||||||||
\(821\) | 56.9650 | 1.98809 | 0.994047 | − | 0.108956i | \(-0.0347507\pi\) | ||||
0.994047 | + | 0.108956i | \(0.0347507\pi\) | |||||||
\(822\) | −33.3717 | −1.16397 | ||||||||
\(823\) | −6.52318 | −0.227384 | −0.113692 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113692 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(824\) | 84.8425 | 2.95563 | ||||||||
\(825\) | −1.25153 | −0.0435727 | ||||||||
\(826\) | −19.4776 | −0.677713 | ||||||||
\(827\) | 34.5198 | 1.20037 | 0.600185 | − | 0.799861i | \(-0.295093\pi\) | ||||
0.600185 | + | 0.799861i | \(0.295093\pi\) | |||||||
\(828\) | −89.6372 | −3.11511 | ||||||||
\(829\) | 13.1429 | 0.456473 | 0.228237 | − | 0.973606i | \(-0.426704\pi\) | ||||
0.228237 | + | 0.973606i | \(0.426704\pi\) | |||||||
\(830\) | −32.7657 | −1.13731 | ||||||||
\(831\) | 2.73642 | 0.0949253 | ||||||||
\(832\) | −86.0141 | −2.98200 | ||||||||
\(833\) | 4.50970 | 0.156252 | ||||||||
\(834\) | −44.8367 | −1.55257 | ||||||||
\(835\) | 47.9146 | 1.65815 | ||||||||
\(836\) | −37.0600 | −1.28175 | ||||||||
\(837\) | 25.7370 | 0.889600 | ||||||||
\(838\) | −44.1939 | −1.52665 | ||||||||
\(839\) | 29.5728 | 1.02097 | 0.510483 | − | 0.859888i | \(-0.329467\pi\) | ||||
0.510483 | + | 0.859888i | \(0.329467\pi\) | |||||||
\(840\) | −28.5493 | −0.985043 | ||||||||
\(841\) | −26.4214 | −0.911083 | ||||||||
\(842\) | −91.6255 | −3.15762 | ||||||||
\(843\) | −0.887852 | −0.0305792 | ||||||||
\(844\) | 111.689 | 3.84450 | ||||||||
\(845\) | −45.0458 | −1.54962 | ||||||||
\(846\) | 20.8152 | 0.715640 | ||||||||
\(847\) | 1.57807 | 0.0542230 | ||||||||
\(848\) | −52.1297 | −1.79014 | ||||||||
\(849\) | −3.21955 | −0.110495 | ||||||||
\(850\) | 3.82537 | 0.131209 | ||||||||
\(851\) | −15.8334 | −0.542762 | ||||||||
\(852\) | 10.6491 | 0.364833 | ||||||||
\(853\) | 29.4565 | 1.00857 | 0.504285 | − | 0.863537i | \(-0.331756\pi\) | ||||
0.504285 | + | 0.863537i | \(0.331756\pi\) | |||||||
\(854\) | −6.67725 | −0.228491 | ||||||||
\(855\) | −41.5155 | −1.41980 | ||||||||
\(856\) | 86.6232 | 2.96072 | ||||||||
\(857\) | 15.0929 | 0.515564 | 0.257782 | − | 0.966203i | \(-0.417008\pi\) | ||||
0.257782 | + | 0.966203i | \(0.417008\pi\) | |||||||
\(858\) | −12.8432 | −0.438459 | ||||||||
\(859\) | 8.36317 | 0.285348 | 0.142674 | − | 0.989770i | \(-0.454430\pi\) | ||||
0.142674 | + | 0.989770i | \(0.454430\pi\) | |||||||
\(860\) | 12.8862 | 0.439417 | ||||||||
\(861\) | 11.1914 | 0.381402 | ||||||||
\(862\) | −34.4238 | −1.17248 | ||||||||
\(863\) | 3.72873 | 0.126927 | 0.0634637 | − | 0.997984i | \(-0.479785\pi\) | ||||
0.0634637 | + | 0.997984i | \(0.479785\pi\) | |||||||
\(864\) | −66.5168 | −2.26295 | ||||||||
\(865\) | 35.4973 | 1.20694 | ||||||||
\(866\) | −63.0574 | −2.14278 | ||||||||
\(867\) | −0.870455 | −0.0295622 | ||||||||
\(868\) | 45.2035 | 1.53431 | ||||||||
\(869\) | −12.1757 | −0.413031 | ||||||||
\(870\) | −9.43592 | −0.319908 | ||||||||
\(871\) | 80.8115 | 2.73819 | ||||||||
\(872\) | 88.3137 | 2.99068 | ||||||||
\(873\) | 6.06392 | 0.205233 | ||||||||
\(874\) | 152.813 | 5.16899 | ||||||||
\(875\) | 14.2631 | 0.482180 | ||||||||
\(876\) | 54.0875 | 1.82745 | ||||||||
\(877\) | 42.0489 | 1.41989 | 0.709945 | − | 0.704257i | \(-0.248720\pi\) | ||||
0.709945 | + | 0.704257i | \(0.248720\pi\) | |||||||
\(878\) | 33.2620 | 1.12254 | ||||||||
\(879\) | −1.26361 | −0.0426206 | ||||||||
\(880\) | −29.5245 | −0.995272 | ||||||||
\(881\) | 3.70250 | 0.124740 | 0.0623702 | − | 0.998053i | \(-0.480134\pi\) | ||||
0.0623702 | + | 0.998053i | \(0.480134\pi\) | |||||||
\(882\) | −26.9043 | −0.905915 | ||||||||
\(883\) | 5.52888 | 0.186062 | 0.0930309 | − | 0.995663i | \(-0.470344\pi\) | ||||
0.0930309 | + | 0.995663i | \(0.470344\pi\) | |||||||
\(884\) | 28.1647 | 0.947283 | ||||||||
\(885\) | 10.2458 | 0.344409 | ||||||||
\(886\) | −76.2787 | −2.56263 | ||||||||
\(887\) | 38.8050 | 1.30294 | 0.651472 | − | 0.758673i | \(-0.274152\pi\) | ||||
0.651472 | + | 0.758673i | \(0.274152\pi\) | |||||||
\(888\) | −14.3430 | −0.481319 | ||||||||
\(889\) | 27.0126 | 0.905973 | ||||||||
\(890\) | 123.990 | 4.15615 | ||||||||
\(891\) | 2.75487 | 0.0922916 | ||||||||
\(892\) | 68.4039 | 2.29033 | ||||||||
\(893\) | −25.4597 | −0.851976 | ||||||||
\(894\) | 46.2933 | 1.54828 | ||||||||
\(895\) | −12.9392 | −0.432508 | ||||||||
\(896\) | −19.1154 | −0.638599 | ||||||||
\(897\) | 37.9953 | 1.26863 | ||||||||
\(898\) | 53.1040 | 1.77210 | ||||||||
\(899\) | 9.05689 | 0.302064 | ||||||||
\(900\) | −16.3737 | −0.545791 | ||||||||
\(901\) | 4.47992 | 0.149248 | ||||||||
\(902\) | 21.6766 | 0.721751 | ||||||||
\(903\) | 1.37364 | 0.0457118 | ||||||||
\(904\) | −126.729 | −4.21495 | ||||||||
\(905\) | 40.0101 | 1.32998 | ||||||||
\(906\) | 39.1214 | 1.29972 | ||||||||
\(907\) | 15.8936 | 0.527737 | 0.263869 | − | 0.964559i | \(-0.415001\pi\) | ||||
0.263869 | + | 0.964559i | \(0.415001\pi\) | |||||||
\(908\) | −40.3078 | −1.33766 | ||||||||
\(909\) | 34.8834 | 1.15701 | ||||||||
\(910\) | −59.0773 | −1.95839 | ||||||||
\(911\) | −17.9616 | −0.595094 | −0.297547 | − | 0.954707i | \(-0.596169\pi\) | ||||
−0.297547 | + | 0.954707i | \(0.596169\pi\) | |||||||
\(912\) | 73.9109 | 2.44743 | ||||||||
\(913\) | −4.85369 | −0.160634 | ||||||||
\(914\) | 71.6905 | 2.37131 | ||||||||
\(915\) | 3.51243 | 0.116117 | ||||||||
\(916\) | 20.8887 | 0.690182 | ||||||||
\(917\) | −1.31006 | −0.0432618 | ||||||||
\(918\) | 12.1408 | 0.400706 | ||||||||
\(919\) | −49.0097 | −1.61668 | −0.808340 | − | 0.588715i | \(-0.799634\pi\) | ||||
−0.808340 | + | 0.588715i | \(0.799634\pi\) | |||||||
\(920\) | 163.591 | 5.39342 | ||||||||
\(921\) | −7.43124 | −0.244868 | ||||||||
\(922\) | 69.5992 | 2.29213 | ||||||||
\(923\) | 13.3585 | 0.439700 | ||||||||
\(924\) | −6.97637 | −0.229506 | ||||||||
\(925\) | −2.89223 | −0.0950961 | ||||||||
\(926\) | 80.0635 | 2.63105 | ||||||||
\(927\) | 23.2249 | 0.762806 | ||||||||
\(928\) | −23.4074 | −0.768385 | ||||||||
\(929\) | −27.1642 | −0.891228 | −0.445614 | − | 0.895225i | \(-0.647015\pi\) | ||||
−0.445614 | + | 0.895225i | \(0.647015\pi\) | |||||||
\(930\) | −33.1422 | −1.08678 | ||||||||
\(931\) | 32.9075 | 1.07850 | ||||||||
\(932\) | 59.7335 | 1.95664 | ||||||||
\(933\) | −8.72313 | −0.285582 | ||||||||
\(934\) | 101.189 | 3.31101 | ||||||||
\(935\) | 2.53728 | 0.0829779 | ||||||||
\(936\) | −101.859 | −3.32935 | ||||||||
\(937\) | 19.4721 | 0.636124 | 0.318062 | − | 0.948070i | \(-0.396968\pi\) | ||||
0.318062 | + | 0.948070i | \(0.396968\pi\) | |||||||
\(938\) | 61.1828 | 1.99769 | ||||||||
\(939\) | −12.4179 | −0.405242 | ||||||||
\(940\) | −44.9606 | −1.46645 | ||||||||
\(941\) | 31.3309 | 1.02136 | 0.510679 | − | 0.859772i | \(-0.329394\pi\) | ||||
0.510679 | + | 0.859772i | \(0.329394\pi\) | |||||||
\(942\) | −38.5206 | −1.25507 | ||||||||
\(943\) | −64.1280 | −2.08829 | ||||||||
\(944\) | 53.9817 | 1.75695 | ||||||||
\(945\) | −18.2710 | −0.594356 | ||||||||
\(946\) | 2.66059 | 0.0865034 | ||||||||
\(947\) | 14.5406 | 0.472505 | 0.236253 | − | 0.971692i | \(-0.424081\pi\) | ||||
0.236253 | + | 0.971692i | \(0.424081\pi\) | |||||||
\(948\) | 53.8266 | 1.74821 | ||||||||
\(949\) | 67.8485 | 2.20246 | ||||||||
\(950\) | 27.9139 | 0.905647 | ||||||||
\(951\) | 20.7678 | 0.673443 | ||||||||
\(952\) | 12.9265 | 0.418950 | ||||||||
\(953\) | 30.6007 | 0.991254 | 0.495627 | − | 0.868535i | \(-0.334938\pi\) | ||||
0.495627 | + | 0.868535i | \(0.334938\pi\) | |||||||
\(954\) | −26.7266 | −0.865307 | ||||||||
\(955\) | 61.8017 | 1.99986 | ||||||||
\(956\) | 113.178 | 3.66045 | ||||||||
\(957\) | −1.39777 | −0.0451836 | ||||||||
\(958\) | 40.8244 | 1.31898 | ||||||||
\(959\) | −22.7394 | −0.734294 | ||||||||
\(960\) | 34.2560 | 1.10561 | ||||||||
\(961\) | 0.810984 | 0.0261608 | ||||||||
\(962\) | −29.6801 | −0.956925 | ||||||||
\(963\) | 23.7124 | 0.764120 | ||||||||
\(964\) | 102.764 | 3.30981 | ||||||||
\(965\) | −16.1752 | −0.520697 | ||||||||
\(966\) | 28.7664 | 0.925544 | ||||||||
\(967\) | 23.5641 | 0.757770 | 0.378885 | − | 0.925444i | \(-0.376308\pi\) | ||||
0.378885 | + | 0.925444i | \(0.376308\pi\) | |||||||
\(968\) | −8.19134 | −0.263280 | ||||||||
\(969\) | −6.35175 | −0.204048 | ||||||||
\(970\) | −18.2560 | −0.586165 | ||||||||
\(971\) | 25.4869 | 0.817913 | 0.408957 | − | 0.912554i | \(-0.365893\pi\) | ||||
0.408957 | + | 0.912554i | \(0.365893\pi\) | |||||||
\(972\) | −81.7049 | −2.62069 | ||||||||
\(973\) | −30.5516 | −0.979440 | ||||||||
\(974\) | 13.2514 | 0.424601 | ||||||||
\(975\) | 6.94047 | 0.222273 | ||||||||
\(976\) | 18.5058 | 0.592357 | ||||||||
\(977\) | 17.4287 | 0.557592 | 0.278796 | − | 0.960350i | \(-0.410065\pi\) | ||||
0.278796 | + | 0.960350i | \(0.410065\pi\) | |||||||
\(978\) | −30.2593 | −0.967587 | ||||||||
\(979\) | 18.3671 | 0.587014 | ||||||||
\(980\) | 58.1131 | 1.85636 | ||||||||
\(981\) | 24.1751 | 0.771852 | ||||||||
\(982\) | −64.8268 | −2.06871 | ||||||||
\(983\) | 24.3019 | 0.775110 | 0.387555 | − | 0.921847i | \(-0.373320\pi\) | ||||
0.387555 | + | 0.921847i | \(0.373320\pi\) | |||||||
\(984\) | −58.0916 | −1.85189 | ||||||||
\(985\) | −9.67206 | −0.308177 | ||||||||
\(986\) | 4.27238 | 0.136060 | ||||||||
\(987\) | −4.79267 | −0.152552 | ||||||||
\(988\) | 205.519 | 6.53845 | ||||||||
\(989\) | −7.87110 | −0.250286 | ||||||||
\(990\) | −15.1371 | −0.481088 | ||||||||
\(991\) | 46.5378 | 1.47832 | 0.739161 | − | 0.673529i | \(-0.235222\pi\) | ||||
0.739161 | + | 0.673529i | \(0.235222\pi\) | |||||||
\(992\) | −82.2149 | −2.61033 | ||||||||
\(993\) | −20.6143 | −0.654175 | ||||||||
\(994\) | 10.1138 | 0.320789 | ||||||||
\(995\) | 43.3387 | 1.37393 | ||||||||
\(996\) | 21.4574 | 0.679902 | ||||||||
\(997\) | −52.3932 | −1.65931 | −0.829654 | − | 0.558278i | \(-0.811462\pi\) | ||||
−0.829654 | + | 0.558278i | \(0.811462\pi\) | |||||||
\(998\) | 41.5794 | 1.31617 | ||||||||
\(999\) | −9.17926 | −0.290419 |
(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 | 8041.2.a.i.1.3 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.i.1.3 | ✓ | 78 | 1.1 | even | 1 | trivial |