Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.42288\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.10747 | 1.83692 | 0.918458 | − | 0.395519i | \(-0.129435\pi\) | ||||
0.918458 | + | 0.395519i | \(0.129435\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.42288 | −0.537800 | −0.268900 | − | 0.963168i | \(-0.586660\pi\) | ||||
−0.268900 | + | 0.963168i | \(0.586660\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.10747 | 1.29890 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.35771 | 0.376560 | 0.188280 | − | 0.982115i | \(-0.439709\pi\) | ||||
0.188280 | + | 0.982115i | \(0.439709\pi\) | |||||||
\(14\) | −1.42288 | −0.380282 | ||||||||
\(15\) | 4.10747 | 1.06054 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.83039 | 0.929006 | 0.464503 | − | 0.885572i | \(-0.346233\pi\) | ||||
0.464503 | + | 0.885572i | \(0.346233\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.67648 | −0.843443 | −0.421721 | − | 0.906726i | \(-0.638574\pi\) | ||||
−0.421721 | + | 0.906726i | \(0.638574\pi\) | |||||||
\(20\) | 4.10747 | 0.918458 | ||||||||
\(21\) | −1.42288 | −0.310499 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 2.60600 | 0.543388 | 0.271694 | − | 0.962384i | \(-0.412416\pi\) | ||||
0.271694 | + | 0.962384i | \(0.412416\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 11.8713 | 2.37426 | ||||||||
\(26\) | 1.35771 | 0.266268 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.42288 | −0.268900 | ||||||||
\(29\) | 5.91127 | 1.09770 | 0.548848 | − | 0.835922i | \(-0.315067\pi\) | ||||
0.548848 | + | 0.835922i | \(0.315067\pi\) | |||||||
\(30\) | 4.10747 | 0.749918 | ||||||||
\(31\) | −4.71346 | −0.846563 | −0.423282 | − | 0.905998i | \(-0.639122\pi\) | ||||
−0.423282 | + | 0.905998i | \(0.639122\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 3.83039 | 0.656906 | ||||||||
\(35\) | −5.84445 | −0.987892 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.0578 | −1.81789 | −0.908946 | − | 0.416913i | \(-0.863112\pi\) | ||||
−0.908946 | + | 0.416913i | \(0.863112\pi\) | |||||||
\(38\) | −3.67648 | −0.596404 | ||||||||
\(39\) | 1.35771 | 0.217407 | ||||||||
\(40\) | 4.10747 | 0.649448 | ||||||||
\(41\) | 4.99190 | 0.779603 | 0.389802 | − | 0.920899i | \(-0.372544\pi\) | ||||
0.389802 | + | 0.920899i | \(0.372544\pi\) | |||||||
\(42\) | −1.42288 | −0.219556 | ||||||||
\(43\) | 10.2658 | 1.56551 | 0.782757 | − | 0.622328i | \(-0.213813\pi\) | ||||
0.782757 | + | 0.622328i | \(0.213813\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 4.10747 | 0.612305 | ||||||||
\(46\) | 2.60600 | 0.384233 | ||||||||
\(47\) | −13.0197 | −1.89912 | −0.949558 | − | 0.313592i | \(-0.898468\pi\) | ||||
−0.949558 | + | 0.313592i | \(0.898468\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.97540 | −0.710771 | ||||||||
\(50\) | 11.8713 | 1.67885 | ||||||||
\(51\) | 3.83039 | 0.536362 | ||||||||
\(52\) | 1.35771 | 0.188280 | ||||||||
\(53\) | 11.1134 | 1.52655 | 0.763273 | − | 0.646076i | \(-0.223591\pi\) | ||||
0.763273 | + | 0.646076i | \(0.223591\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.10747 | −0.553851 | ||||||||
\(56\) | −1.42288 | −0.190141 | ||||||||
\(57\) | −3.67648 | −0.486962 | ||||||||
\(58\) | 5.91127 | 0.776188 | ||||||||
\(59\) | −10.0544 | −1.30897 | −0.654486 | − | 0.756074i | \(-0.727115\pi\) | ||||
−0.654486 | + | 0.756074i | \(0.727115\pi\) | |||||||
\(60\) | 4.10747 | 0.530272 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −4.71346 | −0.598610 | ||||||||
\(63\) | −1.42288 | −0.179267 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.57674 | 0.691710 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −6.68998 | −0.817311 | −0.408656 | − | 0.912689i | \(-0.634002\pi\) | ||||
−0.408656 | + | 0.912689i | \(0.634002\pi\) | |||||||
\(68\) | 3.83039 | 0.464503 | ||||||||
\(69\) | 2.60600 | 0.313725 | ||||||||
\(70\) | −5.84445 | −0.698545 | ||||||||
\(71\) | 12.7780 | 1.51647 | 0.758235 | − | 0.651981i | \(-0.226062\pi\) | ||||
0.758235 | + | 0.651981i | \(0.226062\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.832592 | 0.0974476 | 0.0487238 | − | 0.998812i | \(-0.484485\pi\) | ||||
0.0487238 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(74\) | −11.0578 | −1.28544 | ||||||||
\(75\) | 11.8713 | 1.37078 | ||||||||
\(76\) | −3.67648 | −0.421721 | ||||||||
\(77\) | 1.42288 | 0.162153 | ||||||||
\(78\) | 1.35771 | 0.153730 | ||||||||
\(79\) | −3.15180 | −0.354605 | −0.177303 | − | 0.984156i | \(-0.556737\pi\) | ||||
−0.177303 | + | 0.984156i | \(0.556737\pi\) | |||||||
\(80\) | 4.10747 | 0.459229 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.99190 | 0.551263 | ||||||||
\(83\) | 13.9256 | 1.52854 | 0.764269 | − | 0.644898i | \(-0.223100\pi\) | ||||
0.764269 | + | 0.644898i | \(0.223100\pi\) | |||||||
\(84\) | −1.42288 | −0.155249 | ||||||||
\(85\) | 15.7332 | 1.70650 | ||||||||
\(86\) | 10.2658 | 1.10699 | ||||||||
\(87\) | 5.91127 | 0.633755 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 5.54212 | 0.587464 | 0.293732 | − | 0.955888i | \(-0.405103\pi\) | ||||
0.293732 | + | 0.955888i | \(0.405103\pi\) | |||||||
\(90\) | 4.10747 | 0.432965 | ||||||||
\(91\) | −1.93186 | −0.202514 | ||||||||
\(92\) | 2.60600 | 0.271694 | ||||||||
\(93\) | −4.71346 | −0.488763 | ||||||||
\(94\) | −13.0197 | −1.34288 | ||||||||
\(95\) | −15.1010 | −1.54933 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.11901 | −0.722826 | −0.361413 | − | 0.932406i | \(-0.617706\pi\) | ||||
−0.361413 | + | 0.932406i | \(0.617706\pi\) | |||||||
\(98\) | −4.97540 | −0.502591 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 11.8713 | 1.18713 | ||||||||
\(101\) | 7.29628 | 0.726007 | 0.363004 | − | 0.931788i | \(-0.381751\pi\) | ||||
0.363004 | + | 0.931788i | \(0.381751\pi\) | |||||||
\(102\) | 3.83039 | 0.379265 | ||||||||
\(103\) | 12.2396 | 1.20600 | 0.603000 | − | 0.797742i | \(-0.293972\pi\) | ||||
0.603000 | + | 0.797742i | \(0.293972\pi\) | |||||||
\(104\) | 1.35771 | 0.133134 | ||||||||
\(105\) | −5.84445 | −0.570360 | ||||||||
\(106\) | 11.1134 | 1.07943 | ||||||||
\(107\) | −14.3397 | −1.38627 | −0.693134 | − | 0.720809i | \(-0.743771\pi\) | ||||
−0.693134 | + | 0.720809i | \(0.743771\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −10.7776 | −1.03230 | −0.516152 | − | 0.856497i | \(-0.672636\pi\) | ||||
−0.516152 | + | 0.856497i | \(0.672636\pi\) | |||||||
\(110\) | −4.10747 | −0.391632 | ||||||||
\(111\) | −11.0578 | −1.04956 | ||||||||
\(112\) | −1.42288 | −0.134450 | ||||||||
\(113\) | −3.15790 | −0.297070 | −0.148535 | − | 0.988907i | \(-0.547456\pi\) | ||||
−0.148535 | + | 0.988907i | \(0.547456\pi\) | |||||||
\(114\) | −3.67648 | −0.344334 | ||||||||
\(115\) | 10.7040 | 0.998157 | ||||||||
\(116\) | 5.91127 | 0.548848 | ||||||||
\(117\) | 1.35771 | 0.125520 | ||||||||
\(118\) | −10.0544 | −0.925583 | ||||||||
\(119\) | −5.45020 | −0.499619 | ||||||||
\(120\) | 4.10747 | 0.374959 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 4.99190 | 0.450104 | ||||||||
\(124\) | −4.71346 | −0.423282 | ||||||||
\(125\) | 28.2236 | 2.52440 | ||||||||
\(126\) | −1.42288 | −0.126761 | ||||||||
\(127\) | −10.3986 | −0.922727 | −0.461364 | − | 0.887211i | \(-0.652640\pi\) | ||||
−0.461364 | + | 0.887211i | \(0.652640\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.2658 | 0.903850 | ||||||||
\(130\) | 5.57674 | 0.489113 | ||||||||
\(131\) | −2.37667 | −0.207651 | −0.103825 | − | 0.994596i | \(-0.533108\pi\) | ||||
−0.103825 | + | 0.994596i | \(0.533108\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 5.23121 | 0.453603 | ||||||||
\(134\) | −6.68998 | −0.577926 | ||||||||
\(135\) | 4.10747 | 0.353515 | ||||||||
\(136\) | 3.83039 | 0.328453 | ||||||||
\(137\) | 3.23285 | 0.276201 | 0.138100 | − | 0.990418i | \(-0.455900\pi\) | ||||
0.138100 | + | 0.990418i | \(0.455900\pi\) | |||||||
\(138\) | 2.60600 | 0.221837 | ||||||||
\(139\) | −6.86229 | −0.582052 | −0.291026 | − | 0.956715i | \(-0.593997\pi\) | ||||
−0.291026 | + | 0.956715i | \(0.593997\pi\) | |||||||
\(140\) | −5.84445 | −0.493946 | ||||||||
\(141\) | −13.0197 | −1.09646 | ||||||||
\(142\) | 12.7780 | 1.07231 | ||||||||
\(143\) | −1.35771 | −0.113537 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 24.2803 | 2.01637 | ||||||||
\(146\) | 0.832592 | 0.0689058 | ||||||||
\(147\) | −4.97540 | −0.410364 | ||||||||
\(148\) | −11.0578 | −0.908946 | ||||||||
\(149\) | −2.54990 | −0.208896 | −0.104448 | − | 0.994530i | \(-0.533308\pi\) | ||||
−0.104448 | + | 0.994530i | \(0.533308\pi\) | |||||||
\(150\) | 11.8713 | 0.969287 | ||||||||
\(151\) | −6.94441 | −0.565128 | −0.282564 | − | 0.959248i | \(-0.591185\pi\) | ||||
−0.282564 | + | 0.959248i | \(0.591185\pi\) | |||||||
\(152\) | −3.67648 | −0.298202 | ||||||||
\(153\) | 3.83039 | 0.309669 | ||||||||
\(154\) | 1.42288 | 0.114659 | ||||||||
\(155\) | −19.3604 | −1.55506 | ||||||||
\(156\) | 1.35771 | 0.108704 | ||||||||
\(157\) | −13.2590 | −1.05819 | −0.529093 | − | 0.848564i | \(-0.677468\pi\) | ||||
−0.529093 | + | 0.848564i | \(0.677468\pi\) | |||||||
\(158\) | −3.15180 | −0.250744 | ||||||||
\(159\) | 11.1134 | 0.881352 | ||||||||
\(160\) | 4.10747 | 0.324724 | ||||||||
\(161\) | −3.70803 | −0.292234 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −21.6257 | −1.69386 | −0.846929 | − | 0.531706i | \(-0.821551\pi\) | ||||
−0.846929 | + | 0.531706i | \(0.821551\pi\) | |||||||
\(164\) | 4.99190 | 0.389802 | ||||||||
\(165\) | −4.10747 | −0.319766 | ||||||||
\(166\) | 13.9256 | 1.08084 | ||||||||
\(167\) | 7.91006 | 0.612098 | 0.306049 | − | 0.952016i | \(-0.400993\pi\) | ||||
0.306049 | + | 0.952016i | \(0.400993\pi\) | |||||||
\(168\) | −1.42288 | −0.109778 | ||||||||
\(169\) | −11.1566 | −0.858202 | ||||||||
\(170\) | 15.7332 | 1.20668 | ||||||||
\(171\) | −3.67648 | −0.281148 | ||||||||
\(172\) | 10.2658 | 0.782757 | ||||||||
\(173\) | 13.6471 | 1.03757 | 0.518786 | − | 0.854904i | \(-0.326384\pi\) | ||||
0.518786 | + | 0.854904i | \(0.326384\pi\) | |||||||
\(174\) | 5.91127 | 0.448132 | ||||||||
\(175\) | −16.8915 | −1.27688 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −10.0544 | −0.755735 | ||||||||
\(178\) | 5.54212 | 0.415400 | ||||||||
\(179\) | −11.8058 | −0.882406 | −0.441203 | − | 0.897407i | \(-0.645448\pi\) | ||||
−0.441203 | + | 0.897407i | \(0.645448\pi\) | |||||||
\(180\) | 4.10747 | 0.306153 | ||||||||
\(181\) | 1.97489 | 0.146793 | 0.0733963 | − | 0.997303i | \(-0.476616\pi\) | ||||
0.0733963 | + | 0.997303i | \(0.476616\pi\) | |||||||
\(182\) | −1.93186 | −0.143199 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 2.60600 | 0.192117 | ||||||||
\(185\) | −45.4196 | −3.33931 | ||||||||
\(186\) | −4.71346 | −0.345608 | ||||||||
\(187\) | −3.83039 | −0.280106 | ||||||||
\(188\) | −13.0197 | −0.949558 | ||||||||
\(189\) | −1.42288 | −0.103500 | ||||||||
\(190\) | −15.1010 | −1.09554 | ||||||||
\(191\) | −11.8090 | −0.854469 | −0.427234 | − | 0.904141i | \(-0.640512\pi\) | ||||
−0.427234 | + | 0.904141i | \(0.640512\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −23.8698 | −1.71819 | −0.859094 | − | 0.511818i | \(-0.828972\pi\) | ||||
−0.859094 | + | 0.511818i | \(0.828972\pi\) | |||||||
\(194\) | −7.11901 | −0.511115 | ||||||||
\(195\) | 5.57674 | 0.399359 | ||||||||
\(196\) | −4.97540 | −0.355386 | ||||||||
\(197\) | 7.36122 | 0.524465 | 0.262233 | − | 0.965005i | \(-0.415541\pi\) | ||||
0.262233 | + | 0.965005i | \(0.415541\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 12.5538 | 0.889915 | 0.444958 | − | 0.895552i | \(-0.353219\pi\) | ||||
0.444958 | + | 0.895552i | \(0.353219\pi\) | |||||||
\(200\) | 11.8713 | 0.839427 | ||||||||
\(201\) | −6.68998 | −0.471875 | ||||||||
\(202\) | 7.29628 | 0.513365 | ||||||||
\(203\) | −8.41105 | −0.590340 | ||||||||
\(204\) | 3.83039 | 0.268181 | ||||||||
\(205\) | 20.5041 | 1.43207 | ||||||||
\(206\) | 12.2396 | 0.852770 | ||||||||
\(207\) | 2.60600 | 0.181129 | ||||||||
\(208\) | 1.35771 | 0.0941401 | ||||||||
\(209\) | 3.67648 | 0.254308 | ||||||||
\(210\) | −5.84445 | −0.403305 | ||||||||
\(211\) | 19.1327 | 1.31715 | 0.658575 | − | 0.752515i | \(-0.271159\pi\) | ||||
0.658575 | + | 0.752515i | \(0.271159\pi\) | |||||||
\(212\) | 11.1134 | 0.763273 | ||||||||
\(213\) | 12.7780 | 0.875535 | ||||||||
\(214\) | −14.3397 | −0.980240 | ||||||||
\(215\) | 42.1663 | 2.87572 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 6.70671 | 0.455281 | ||||||||
\(218\) | −10.7776 | −0.729949 | ||||||||
\(219\) | 0.832592 | 0.0562614 | ||||||||
\(220\) | −4.10747 | −0.276925 | ||||||||
\(221\) | 5.20055 | 0.349827 | ||||||||
\(222\) | −11.0578 | −0.742152 | ||||||||
\(223\) | 5.86877 | 0.393002 | 0.196501 | − | 0.980504i | \(-0.437042\pi\) | ||||
0.196501 | + | 0.980504i | \(0.437042\pi\) | |||||||
\(224\) | −1.42288 | −0.0950705 | ||||||||
\(225\) | 11.8713 | 0.791419 | ||||||||
\(226\) | −3.15790 | −0.210060 | ||||||||
\(227\) | 16.8179 | 1.11624 | 0.558120 | − | 0.829760i | \(-0.311523\pi\) | ||||
0.558120 | + | 0.829760i | \(0.311523\pi\) | |||||||
\(228\) | −3.67648 | −0.243481 | ||||||||
\(229\) | −21.5733 | −1.42560 | −0.712802 | − | 0.701365i | \(-0.752574\pi\) | ||||
−0.712802 | + | 0.701365i | \(0.752574\pi\) | |||||||
\(230\) | 10.7040 | 0.705804 | ||||||||
\(231\) | 1.42288 | 0.0936189 | ||||||||
\(232\) | 5.91127 | 0.388094 | ||||||||
\(233\) | −11.7417 | −0.769227 | −0.384614 | − | 0.923078i | \(-0.625665\pi\) | ||||
−0.384614 | + | 0.923078i | \(0.625665\pi\) | |||||||
\(234\) | 1.35771 | 0.0887561 | ||||||||
\(235\) | −53.4779 | −3.48852 | ||||||||
\(236\) | −10.0544 | −0.654486 | ||||||||
\(237\) | −3.15180 | −0.204731 | ||||||||
\(238\) | −5.45020 | −0.353284 | ||||||||
\(239\) | 23.1597 | 1.49808 | 0.749038 | − | 0.662528i | \(-0.230516\pi\) | ||||
0.749038 | + | 0.662528i | \(0.230516\pi\) | |||||||
\(240\) | 4.10747 | 0.265136 | ||||||||
\(241\) | 9.55766 | 0.615663 | 0.307831 | − | 0.951441i | \(-0.400397\pi\) | ||||
0.307831 | + | 0.951441i | \(0.400397\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −20.4363 | −1.30563 | ||||||||
\(246\) | 4.99190 | 0.318272 | ||||||||
\(247\) | −4.99159 | −0.317607 | ||||||||
\(248\) | −4.71346 | −0.299305 | ||||||||
\(249\) | 13.9256 | 0.882502 | ||||||||
\(250\) | 28.2236 | 1.78502 | ||||||||
\(251\) | −0.638796 | −0.0403205 | −0.0201602 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201602 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(252\) | −1.42288 | −0.0896333 | ||||||||
\(253\) | −2.60600 | −0.163838 | ||||||||
\(254\) | −10.3986 | −0.652467 | ||||||||
\(255\) | 15.7332 | 0.985251 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.7374 | 1.48070 | 0.740350 | − | 0.672221i | \(-0.234660\pi\) | ||||
0.740350 | + | 0.672221i | \(0.234660\pi\) | |||||||
\(258\) | 10.2658 | 0.639118 | ||||||||
\(259\) | 15.7340 | 0.977662 | ||||||||
\(260\) | 5.57674 | 0.345855 | ||||||||
\(261\) | 5.91127 | 0.365898 | ||||||||
\(262\) | −2.37667 | −0.146831 | ||||||||
\(263\) | 16.5229 | 1.01884 | 0.509422 | − | 0.860517i | \(-0.329859\pi\) | ||||
0.509422 | + | 0.860517i | \(0.329859\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 45.6480 | 2.80414 | ||||||||
\(266\) | 5.23121 | 0.320746 | ||||||||
\(267\) | 5.54212 | 0.339172 | ||||||||
\(268\) | −6.68998 | −0.408656 | ||||||||
\(269\) | −7.99577 | −0.487511 | −0.243755 | − | 0.969837i | \(-0.578379\pi\) | ||||
−0.243755 | + | 0.969837i | \(0.578379\pi\) | |||||||
\(270\) | 4.10747 | 0.249973 | ||||||||
\(271\) | −4.76725 | −0.289590 | −0.144795 | − | 0.989462i | \(-0.546252\pi\) | ||||
−0.144795 | + | 0.989462i | \(0.546252\pi\) | |||||||
\(272\) | 3.83039 | 0.232251 | ||||||||
\(273\) | −1.93186 | −0.116922 | ||||||||
\(274\) | 3.23285 | 0.195304 | ||||||||
\(275\) | −11.8713 | −0.715866 | ||||||||
\(276\) | 2.60600 | 0.156863 | ||||||||
\(277\) | −16.9682 | −1.01952 | −0.509761 | − | 0.860316i | \(-0.670266\pi\) | ||||
−0.509761 | + | 0.860316i | \(0.670266\pi\) | |||||||
\(278\) | −6.86229 | −0.411573 | ||||||||
\(279\) | −4.71346 | −0.282188 | ||||||||
\(280\) | −5.84445 | −0.349273 | ||||||||
\(281\) | −13.4780 | −0.804031 | −0.402015 | − | 0.915633i | \(-0.631690\pi\) | ||||
−0.402015 | + | 0.915633i | \(0.631690\pi\) | |||||||
\(282\) | −13.0197 | −0.775311 | ||||||||
\(283\) | −31.7376 | −1.88661 | −0.943303 | − | 0.331934i | \(-0.892299\pi\) | ||||
−0.943303 | + | 0.331934i | \(0.892299\pi\) | |||||||
\(284\) | 12.7780 | 0.758235 | ||||||||
\(285\) | −15.1010 | −0.894508 | ||||||||
\(286\) | −1.35771 | −0.0802829 | ||||||||
\(287\) | −7.10289 | −0.419271 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −2.32812 | −0.136948 | ||||||||
\(290\) | 24.2803 | 1.42579 | ||||||||
\(291\) | −7.11901 | −0.417324 | ||||||||
\(292\) | 0.832592 | 0.0487238 | ||||||||
\(293\) | −29.0309 | −1.69601 | −0.848003 | − | 0.529992i | \(-0.822195\pi\) | ||||
−0.848003 | + | 0.529992i | \(0.822195\pi\) | |||||||
\(294\) | −4.97540 | −0.290171 | ||||||||
\(295\) | −41.2981 | −2.40447 | ||||||||
\(296\) | −11.0578 | −0.642722 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −2.54990 | −0.147712 | ||||||||
\(299\) | 3.53818 | 0.204618 | ||||||||
\(300\) | 11.8713 | 0.685389 | ||||||||
\(301\) | −14.6070 | −0.841933 | ||||||||
\(302\) | −6.94441 | −0.399606 | ||||||||
\(303\) | 7.29628 | 0.419160 | ||||||||
\(304\) | −3.67648 | −0.210861 | ||||||||
\(305\) | 4.10747 | 0.235193 | ||||||||
\(306\) | 3.83039 | 0.218969 | ||||||||
\(307\) | −1.57252 | −0.0897484 | −0.0448742 | − | 0.998993i | \(-0.514289\pi\) | ||||
−0.0448742 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(308\) | 1.42288 | 0.0810764 | ||||||||
\(309\) | 12.2396 | 0.696284 | ||||||||
\(310\) | −19.3604 | −1.09960 | ||||||||
\(311\) | −26.9163 | −1.52628 | −0.763142 | − | 0.646231i | \(-0.776344\pi\) | ||||
−0.763142 | + | 0.646231i | \(0.776344\pi\) | |||||||
\(312\) | 1.35771 | 0.0768651 | ||||||||
\(313\) | 9.09300 | 0.513967 | 0.256983 | − | 0.966416i | \(-0.417271\pi\) | ||||
0.256983 | + | 0.966416i | \(0.417271\pi\) | |||||||
\(314\) | −13.2590 | −0.748250 | ||||||||
\(315\) | −5.84445 | −0.329297 | ||||||||
\(316\) | −3.15180 | −0.177303 | ||||||||
\(317\) | 19.7222 | 1.10771 | 0.553856 | − | 0.832613i | \(-0.313156\pi\) | ||||
0.553856 | + | 0.832613i | \(0.313156\pi\) | |||||||
\(318\) | 11.1134 | 0.623210 | ||||||||
\(319\) | −5.91127 | −0.330968 | ||||||||
\(320\) | 4.10747 | 0.229614 | ||||||||
\(321\) | −14.3397 | −0.800362 | ||||||||
\(322\) | −3.70803 | −0.206640 | ||||||||
\(323\) | −14.0824 | −0.783563 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 16.1177 | 0.894052 | ||||||||
\(326\) | −21.6257 | −1.19774 | ||||||||
\(327\) | −10.7776 | −0.596001 | ||||||||
\(328\) | 4.99190 | 0.275631 | ||||||||
\(329\) | 18.5255 | 1.02134 | ||||||||
\(330\) | −4.10747 | −0.226109 | ||||||||
\(331\) | 17.4514 | 0.959214 | 0.479607 | − | 0.877483i | \(-0.340779\pi\) | ||||
0.479607 | + | 0.877483i | \(0.340779\pi\) | |||||||
\(332\) | 13.9256 | 0.764269 | ||||||||
\(333\) | −11.0578 | −0.605964 | ||||||||
\(334\) | 7.91006 | 0.432819 | ||||||||
\(335\) | −27.4789 | −1.50133 | ||||||||
\(336\) | −1.42288 | −0.0776247 | ||||||||
\(337\) | 31.2281 | 1.70110 | 0.850551 | − | 0.525893i | \(-0.176269\pi\) | ||||
0.850551 | + | 0.525893i | \(0.176269\pi\) | |||||||
\(338\) | −11.1566 | −0.606841 | ||||||||
\(339\) | −3.15790 | −0.171513 | ||||||||
\(340\) | 15.7332 | 0.853252 | ||||||||
\(341\) | 4.71346 | 0.255248 | ||||||||
\(342\) | −3.67648 | −0.198801 | ||||||||
\(343\) | 17.0396 | 0.920052 | ||||||||
\(344\) | 10.2658 | 0.553493 | ||||||||
\(345\) | 10.7040 | 0.576286 | ||||||||
\(346\) | 13.6471 | 0.733675 | ||||||||
\(347\) | −7.77055 | −0.417145 | −0.208573 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208573 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(348\) | 5.91127 | 0.316877 | ||||||||
\(349\) | −10.9441 | −0.585824 | −0.292912 | − | 0.956139i | \(-0.594624\pi\) | ||||
−0.292912 | + | 0.956139i | \(0.594624\pi\) | |||||||
\(350\) | −16.8915 | −0.902887 | ||||||||
\(351\) | 1.35771 | 0.0724691 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 17.6048 | 0.937007 | 0.468504 | − | 0.883462i | \(-0.344793\pi\) | ||||
0.468504 | + | 0.883462i | \(0.344793\pi\) | |||||||
\(354\) | −10.0544 | −0.534385 | ||||||||
\(355\) | 52.4853 | 2.78563 | ||||||||
\(356\) | 5.54212 | 0.293732 | ||||||||
\(357\) | −5.45020 | −0.288455 | ||||||||
\(358\) | −11.8058 | −0.623955 | ||||||||
\(359\) | −9.83321 | −0.518977 | −0.259488 | − | 0.965746i | \(-0.583554\pi\) | ||||
−0.259488 | + | 0.965746i | \(0.583554\pi\) | |||||||
\(360\) | 4.10747 | 0.216483 | ||||||||
\(361\) | −5.48349 | −0.288605 | ||||||||
\(362\) | 1.97489 | 0.103798 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −1.93186 | −0.101257 | ||||||||
\(365\) | 3.41985 | 0.179003 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −20.7128 | −1.08120 | −0.540600 | − | 0.841280i | \(-0.681803\pi\) | ||||
−0.540600 | + | 0.841280i | \(0.681803\pi\) | |||||||
\(368\) | 2.60600 | 0.135847 | ||||||||
\(369\) | 4.99190 | 0.259868 | ||||||||
\(370\) | −45.4196 | −2.36125 | ||||||||
\(371\) | −15.8131 | −0.820976 | ||||||||
\(372\) | −4.71346 | −0.244382 | ||||||||
\(373\) | 22.9216 | 1.18684 | 0.593418 | − | 0.804894i | \(-0.297778\pi\) | ||||
0.593418 | + | 0.804894i | \(0.297778\pi\) | |||||||
\(374\) | −3.83039 | −0.198065 | ||||||||
\(375\) | 28.2236 | 1.45746 | ||||||||
\(376\) | −13.0197 | −0.671439 | ||||||||
\(377\) | 8.02578 | 0.413349 | ||||||||
\(378\) | −1.42288 | −0.0731853 | ||||||||
\(379\) | 3.58342 | 0.184068 | 0.0920339 | − | 0.995756i | \(-0.470663\pi\) | ||||
0.0920339 | + | 0.995756i | \(0.470663\pi\) | |||||||
\(380\) | −15.1010 | −0.774666 | ||||||||
\(381\) | −10.3986 | −0.532737 | ||||||||
\(382\) | −11.8090 | −0.604201 | ||||||||
\(383\) | −36.2661 | −1.85311 | −0.926556 | − | 0.376158i | \(-0.877245\pi\) | ||||
−0.926556 | + | 0.376158i | \(0.877245\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 5.84445 | 0.297861 | ||||||||
\(386\) | −23.8698 | −1.21494 | ||||||||
\(387\) | 10.2658 | 0.521838 | ||||||||
\(388\) | −7.11901 | −0.361413 | ||||||||
\(389\) | −26.9353 | −1.36567 | −0.682836 | − | 0.730572i | \(-0.739254\pi\) | ||||
−0.682836 | + | 0.730572i | \(0.739254\pi\) | |||||||
\(390\) | 5.57674 | 0.282389 | ||||||||
\(391\) | 9.98198 | 0.504810 | ||||||||
\(392\) | −4.97540 | −0.251296 | ||||||||
\(393\) | −2.37667 | −0.119887 | ||||||||
\(394\) | 7.36122 | 0.370853 | ||||||||
\(395\) | −12.9459 | −0.651380 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 6.90455 | 0.346530 | 0.173265 | − | 0.984875i | \(-0.444568\pi\) | ||||
0.173265 | + | 0.984875i | \(0.444568\pi\) | |||||||
\(398\) | 12.5538 | 0.629265 | ||||||||
\(399\) | 5.23121 | 0.261888 | ||||||||
\(400\) | 11.8713 | 0.593564 | ||||||||
\(401\) | 15.3687 | 0.767476 | 0.383738 | − | 0.923442i | \(-0.374637\pi\) | ||||
0.383738 | + | 0.923442i | \(0.374637\pi\) | |||||||
\(402\) | −6.68998 | −0.333666 | ||||||||
\(403\) | −6.39951 | −0.318782 | ||||||||
\(404\) | 7.29628 | 0.363004 | ||||||||
\(405\) | 4.10747 | 0.204102 | ||||||||
\(406\) | −8.41105 | −0.417433 | ||||||||
\(407\) | 11.0578 | 0.548115 | ||||||||
\(408\) | 3.83039 | 0.189632 | ||||||||
\(409\) | −11.1119 | −0.549448 | −0.274724 | − | 0.961523i | \(-0.588587\pi\) | ||||
−0.274724 | + | 0.961523i | \(0.588587\pi\) | |||||||
\(410\) | 20.5041 | 1.01262 | ||||||||
\(411\) | 3.23285 | 0.159465 | ||||||||
\(412\) | 12.2396 | 0.603000 | ||||||||
\(413\) | 14.3062 | 0.703964 | ||||||||
\(414\) | 2.60600 | 0.128078 | ||||||||
\(415\) | 57.1991 | 2.80779 | ||||||||
\(416\) | 1.35771 | 0.0665671 | ||||||||
\(417\) | −6.86229 | −0.336048 | ||||||||
\(418\) | 3.67648 | 0.179823 | ||||||||
\(419\) | 18.5086 | 0.904204 | 0.452102 | − | 0.891966i | \(-0.350674\pi\) | ||||
0.452102 | + | 0.891966i | \(0.350674\pi\) | |||||||
\(420\) | −5.84445 | −0.285180 | ||||||||
\(421\) | −25.2737 | −1.23177 | −0.615883 | − | 0.787837i | \(-0.711201\pi\) | ||||
−0.615883 | + | 0.787837i | \(0.711201\pi\) | |||||||
\(422\) | 19.1327 | 0.931366 | ||||||||
\(423\) | −13.0197 | −0.633039 | ||||||||
\(424\) | 11.1134 | 0.539716 | ||||||||
\(425\) | 45.4717 | 2.20570 | ||||||||
\(426\) | 12.7780 | 0.619097 | ||||||||
\(427\) | −1.42288 | −0.0688582 | ||||||||
\(428\) | −14.3397 | −0.693134 | ||||||||
\(429\) | −1.35771 | −0.0655508 | ||||||||
\(430\) | 42.1663 | 2.03344 | ||||||||
\(431\) | 10.5667 | 0.508979 | 0.254490 | − | 0.967076i | \(-0.418093\pi\) | ||||
0.254490 | + | 0.967076i | \(0.418093\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 3.13640 | 0.150726 | 0.0753629 | − | 0.997156i | \(-0.475988\pi\) | ||||
0.0753629 | + | 0.997156i | \(0.475988\pi\) | |||||||
\(434\) | 6.70671 | 0.321933 | ||||||||
\(435\) | 24.2803 | 1.16415 | ||||||||
\(436\) | −10.7776 | −0.516152 | ||||||||
\(437\) | −9.58089 | −0.458316 | ||||||||
\(438\) | 0.832592 | 0.0397828 | ||||||||
\(439\) | −18.6958 | −0.892303 | −0.446151 | − | 0.894957i | \(-0.647206\pi\) | ||||
−0.446151 | + | 0.894957i | \(0.647206\pi\) | |||||||
\(440\) | −4.10747 | −0.195816 | ||||||||
\(441\) | −4.97540 | −0.236924 | ||||||||
\(442\) | 5.20055 | 0.247365 | ||||||||
\(443\) | −3.94422 | −0.187396 | −0.0936978 | − | 0.995601i | \(-0.529869\pi\) | ||||
−0.0936978 | + | 0.995601i | \(0.529869\pi\) | |||||||
\(444\) | −11.0578 | −0.524780 | ||||||||
\(445\) | 22.7641 | 1.07912 | ||||||||
\(446\) | 5.86877 | 0.277895 | ||||||||
\(447\) | −2.54990 | −0.120606 | ||||||||
\(448\) | −1.42288 | −0.0672250 | ||||||||
\(449\) | −35.3741 | −1.66941 | −0.834704 | − | 0.550699i | \(-0.814361\pi\) | ||||
−0.834704 | + | 0.550699i | \(0.814361\pi\) | |||||||
\(450\) | 11.8713 | 0.559618 | ||||||||
\(451\) | −4.99190 | −0.235059 | ||||||||
\(452\) | −3.15790 | −0.148535 | ||||||||
\(453\) | −6.94441 | −0.326277 | ||||||||
\(454\) | 16.8179 | 0.789301 | ||||||||
\(455\) | −7.93506 | −0.372001 | ||||||||
\(456\) | −3.67648 | −0.172167 | ||||||||
\(457\) | 34.1323 | 1.59664 | 0.798321 | − | 0.602232i | \(-0.205722\pi\) | ||||
0.798321 | + | 0.602232i | \(0.205722\pi\) | |||||||
\(458\) | −21.5733 | −1.00805 | ||||||||
\(459\) | 3.83039 | 0.178787 | ||||||||
\(460\) | 10.7040 | 0.499079 | ||||||||
\(461\) | 29.0729 | 1.35406 | 0.677030 | − | 0.735956i | \(-0.263267\pi\) | ||||
0.677030 | + | 0.735956i | \(0.263267\pi\) | |||||||
\(462\) | 1.42288 | 0.0661986 | ||||||||
\(463\) | 15.8931 | 0.738617 | 0.369309 | − | 0.929307i | \(-0.379595\pi\) | ||||
0.369309 | + | 0.929307i | \(0.379595\pi\) | |||||||
\(464\) | 5.91127 | 0.274424 | ||||||||
\(465\) | −19.3604 | −0.897817 | ||||||||
\(466\) | −11.7417 | −0.543926 | ||||||||
\(467\) | −6.87174 | −0.317986 | −0.158993 | − | 0.987280i | \(-0.550825\pi\) | ||||
−0.158993 | + | 0.987280i | \(0.550825\pi\) | |||||||
\(468\) | 1.35771 | 0.0627601 | ||||||||
\(469\) | 9.51907 | 0.439550 | ||||||||
\(470\) | −53.4779 | −2.46675 | ||||||||
\(471\) | −13.2590 | −0.610943 | ||||||||
\(472\) | −10.0544 | −0.462791 | ||||||||
\(473\) | −10.2658 | −0.472020 | ||||||||
\(474\) | −3.15180 | −0.144767 | ||||||||
\(475\) | −43.6446 | −2.00255 | ||||||||
\(476\) | −5.45020 | −0.249809 | ||||||||
\(477\) | 11.1134 | 0.508849 | ||||||||
\(478\) | 23.1597 | 1.05930 | ||||||||
\(479\) | −12.0445 | −0.550329 | −0.275165 | − | 0.961397i | \(-0.588732\pi\) | ||||
−0.275165 | + | 0.961397i | \(0.588732\pi\) | |||||||
\(480\) | 4.10747 | 0.187479 | ||||||||
\(481\) | −15.0133 | −0.684546 | ||||||||
\(482\) | 9.55766 | 0.435339 | ||||||||
\(483\) | −3.70803 | −0.168721 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −29.2411 | −1.32777 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 17.1802 | 0.778511 | 0.389255 | − | 0.921130i | \(-0.372732\pi\) | ||||
0.389255 | + | 0.921130i | \(0.372732\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −21.6257 | −0.977949 | ||||||||
\(490\) | −20.4363 | −0.923218 | ||||||||
\(491\) | 10.5248 | 0.474978 | 0.237489 | − | 0.971390i | \(-0.423676\pi\) | ||||
0.237489 | + | 0.971390i | \(0.423676\pi\) | |||||||
\(492\) | 4.99190 | 0.225052 | ||||||||
\(493\) | 22.6425 | 1.01976 | ||||||||
\(494\) | −4.99159 | −0.224582 | ||||||||
\(495\) | −4.10747 | −0.184617 | ||||||||
\(496\) | −4.71346 | −0.211641 | ||||||||
\(497\) | −18.1816 | −0.815557 | ||||||||
\(498\) | 13.9256 | 0.624023 | ||||||||
\(499\) | 28.7356 | 1.28638 | 0.643192 | − | 0.765705i | \(-0.277610\pi\) | ||||
0.643192 | + | 0.765705i | \(0.277610\pi\) | |||||||
\(500\) | 28.2236 | 1.26220 | ||||||||
\(501\) | 7.91006 | 0.353395 | ||||||||
\(502\) | −0.638796 | −0.0285109 | ||||||||
\(503\) | 1.24265 | 0.0554071 | 0.0277035 | − | 0.999616i | \(-0.491181\pi\) | ||||
0.0277035 | + | 0.999616i | \(0.491181\pi\) | |||||||
\(504\) | −1.42288 | −0.0633803 | ||||||||
\(505\) | 29.9692 | 1.33361 | ||||||||
\(506\) | −2.60600 | −0.115851 | ||||||||
\(507\) | −11.1566 | −0.495483 | ||||||||
\(508\) | −10.3986 | −0.461364 | ||||||||
\(509\) | −25.9689 | −1.15105 | −0.575526 | − | 0.817783i | \(-0.695203\pi\) | ||||
−0.575526 | + | 0.817783i | \(0.695203\pi\) | |||||||
\(510\) | 15.7332 | 0.696678 | ||||||||
\(511\) | −1.18468 | −0.0524073 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.67648 | −0.162321 | ||||||||
\(514\) | 23.7374 | 1.04701 | ||||||||
\(515\) | 50.2736 | 2.21532 | ||||||||
\(516\) | 10.2658 | 0.451925 | ||||||||
\(517\) | 13.0197 | 0.572605 | ||||||||
\(518\) | 15.7340 | 0.691311 | ||||||||
\(519\) | 13.6471 | 0.599043 | ||||||||
\(520\) | 5.57674 | 0.244556 | ||||||||
\(521\) | 16.2047 | 0.709939 | 0.354970 | − | 0.934878i | \(-0.384491\pi\) | ||||
0.354970 | + | 0.934878i | \(0.384491\pi\) | |||||||
\(522\) | 5.91127 | 0.258729 | ||||||||
\(523\) | 28.2588 | 1.23567 | 0.617835 | − | 0.786308i | \(-0.288010\pi\) | ||||
0.617835 | + | 0.786308i | \(0.288010\pi\) | |||||||
\(524\) | −2.37667 | −0.103825 | ||||||||
\(525\) | −16.8915 | −0.737204 | ||||||||
\(526\) | 16.5229 | 0.720431 | ||||||||
\(527\) | −18.0544 | −0.786462 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −16.2088 | −0.704730 | ||||||||
\(530\) | 45.6480 | 1.98282 | ||||||||
\(531\) | −10.0544 | −0.436324 | ||||||||
\(532\) | 5.23121 | 0.226802 | ||||||||
\(533\) | 6.77754 | 0.293568 | ||||||||
\(534\) | 5.54212 | 0.239831 | ||||||||
\(535\) | −58.8997 | −2.54646 | ||||||||
\(536\) | −6.68998 | −0.288963 | ||||||||
\(537\) | −11.8058 | −0.509457 | ||||||||
\(538\) | −7.99577 | −0.344722 | ||||||||
\(539\) | 4.97540 | 0.214306 | ||||||||
\(540\) | 4.10747 | 0.176757 | ||||||||
\(541\) | 31.7978 | 1.36709 | 0.683547 | − | 0.729907i | \(-0.260436\pi\) | ||||
0.683547 | + | 0.729907i | \(0.260436\pi\) | |||||||
\(542\) | −4.76725 | −0.204771 | ||||||||
\(543\) | 1.97489 | 0.0847507 | ||||||||
\(544\) | 3.83039 | 0.164227 | ||||||||
\(545\) | −44.2685 | −1.89626 | ||||||||
\(546\) | −1.93186 | −0.0826760 | ||||||||
\(547\) | −23.9072 | −1.02220 | −0.511100 | − | 0.859521i | \(-0.670762\pi\) | ||||
−0.511100 | + | 0.859521i | \(0.670762\pi\) | |||||||
\(548\) | 3.23285 | 0.138100 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −11.8713 | −0.506193 | ||||||||
\(551\) | −21.7327 | −0.925843 | ||||||||
\(552\) | 2.60600 | 0.110919 | ||||||||
\(553\) | 4.48465 | 0.190707 | ||||||||
\(554\) | −16.9682 | −0.720910 | ||||||||
\(555\) | −45.4196 | −1.92795 | ||||||||
\(556\) | −6.86229 | −0.291026 | ||||||||
\(557\) | −21.7193 | −0.920278 | −0.460139 | − | 0.887847i | \(-0.652200\pi\) | ||||
−0.460139 | + | 0.887847i | \(0.652200\pi\) | |||||||
\(558\) | −4.71346 | −0.199537 | ||||||||
\(559\) | 13.9379 | 0.589510 | ||||||||
\(560\) | −5.84445 | −0.246973 | ||||||||
\(561\) | −3.83039 | −0.161719 | ||||||||
\(562\) | −13.4780 | −0.568536 | ||||||||
\(563\) | −14.4630 | −0.609543 | −0.304772 | − | 0.952425i | \(-0.598580\pi\) | ||||
−0.304772 | + | 0.952425i | \(0.598580\pi\) | |||||||
\(564\) | −13.0197 | −0.548228 | ||||||||
\(565\) | −12.9710 | −0.545692 | ||||||||
\(566\) | −31.7376 | −1.33403 | ||||||||
\(567\) | −1.42288 | −0.0597555 | ||||||||
\(568\) | 12.7780 | 0.536153 | ||||||||
\(569\) | 12.1466 | 0.509210 | 0.254605 | − | 0.967045i | \(-0.418055\pi\) | ||||
0.254605 | + | 0.967045i | \(0.418055\pi\) | |||||||
\(570\) | −15.1010 | −0.632512 | ||||||||
\(571\) | 11.4183 | 0.477839 | 0.238920 | − | 0.971039i | \(-0.423207\pi\) | ||||
0.238920 | + | 0.971039i | \(0.423207\pi\) | |||||||
\(572\) | −1.35771 | −0.0567686 | ||||||||
\(573\) | −11.8090 | −0.493328 | ||||||||
\(574\) | −7.10289 | −0.296469 | ||||||||
\(575\) | 30.9365 | 1.29014 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.6000 | 0.691067 | 0.345534 | − | 0.938406i | \(-0.387698\pi\) | ||||
0.345534 | + | 0.938406i | \(0.387698\pi\) | |||||||
\(578\) | −2.32812 | −0.0968372 | ||||||||
\(579\) | −23.8698 | −0.991996 | ||||||||
\(580\) | 24.2803 | 1.00819 | ||||||||
\(581\) | −19.8146 | −0.822047 | ||||||||
\(582\) | −7.11901 | −0.295092 | ||||||||
\(583\) | −11.1134 | −0.460271 | ||||||||
\(584\) | 0.832592 | 0.0344529 | ||||||||
\(585\) | 5.57674 | 0.230570 | ||||||||
\(586\) | −29.0309 | −1.19926 | ||||||||
\(587\) | 3.05147 | 0.125948 | 0.0629738 | − | 0.998015i | \(-0.479942\pi\) | ||||
0.0629738 | + | 0.998015i | \(0.479942\pi\) | |||||||
\(588\) | −4.97540 | −0.205182 | ||||||||
\(589\) | 17.3290 | 0.714027 | ||||||||
\(590\) | −41.2981 | −1.70022 | ||||||||
\(591\) | 7.36122 | 0.302800 | ||||||||
\(592\) | −11.0578 | −0.454473 | ||||||||
\(593\) | −14.7290 | −0.604848 | −0.302424 | − | 0.953173i | \(-0.597796\pi\) | ||||
−0.302424 | + | 0.953173i | \(0.597796\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −22.3865 | −0.917758 | ||||||||
\(596\) | −2.54990 | −0.104448 | ||||||||
\(597\) | 12.5538 | 0.513793 | ||||||||
\(598\) | 3.53818 | 0.144687 | ||||||||
\(599\) | 45.3750 | 1.85397 | 0.926987 | − | 0.375094i | \(-0.122389\pi\) | ||||
0.926987 | + | 0.375094i | \(0.122389\pi\) | |||||||
\(600\) | 11.8713 | 0.484643 | ||||||||
\(601\) | −17.3276 | −0.706807 | −0.353404 | − | 0.935471i | \(-0.614976\pi\) | ||||
−0.353404 | + | 0.935471i | \(0.614976\pi\) | |||||||
\(602\) | −14.6070 | −0.595336 | ||||||||
\(603\) | −6.68998 | −0.272437 | ||||||||
\(604\) | −6.94441 | −0.282564 | ||||||||
\(605\) | 4.10747 | 0.166992 | ||||||||
\(606\) | 7.29628 | 0.296391 | ||||||||
\(607\) | 34.5021 | 1.40040 | 0.700199 | − | 0.713948i | \(-0.253095\pi\) | ||||
0.700199 | + | 0.713948i | \(0.253095\pi\) | |||||||
\(608\) | −3.67648 | −0.149101 | ||||||||
\(609\) | −8.41105 | −0.340833 | ||||||||
\(610\) | 4.10747 | 0.166306 | ||||||||
\(611\) | −17.6769 | −0.715132 | ||||||||
\(612\) | 3.83039 | 0.154834 | ||||||||
\(613\) | 25.2513 | 1.01989 | 0.509946 | − | 0.860207i | \(-0.329665\pi\) | ||||
0.509946 | + | 0.860207i | \(0.329665\pi\) | |||||||
\(614\) | −1.57252 | −0.0634617 | ||||||||
\(615\) | 20.5041 | 0.826803 | ||||||||
\(616\) | 1.42288 | 0.0573296 | ||||||||
\(617\) | −28.3837 | −1.14268 | −0.571342 | − | 0.820712i | \(-0.693577\pi\) | ||||
−0.571342 | + | 0.820712i | \(0.693577\pi\) | |||||||
\(618\) | 12.2396 | 0.492347 | ||||||||
\(619\) | 17.3561 | 0.697599 | 0.348800 | − | 0.937197i | \(-0.386589\pi\) | ||||
0.348800 | + | 0.937197i | \(0.386589\pi\) | |||||||
\(620\) | −19.3604 | −0.777532 | ||||||||
\(621\) | 2.60600 | 0.104575 | ||||||||
\(622\) | −26.9163 | −1.07925 | ||||||||
\(623\) | −7.88580 | −0.315938 | ||||||||
\(624\) | 1.35771 | 0.0543518 | ||||||||
\(625\) | 56.5711 | 2.26284 | ||||||||
\(626\) | 9.09300 | 0.363430 | ||||||||
\(627\) | 3.67648 | 0.146825 | ||||||||
\(628\) | −13.2590 | −0.529093 | ||||||||
\(629\) | −42.3557 | −1.68883 | ||||||||
\(630\) | −5.84445 | −0.232848 | ||||||||
\(631\) | −23.1140 | −0.920156 | −0.460078 | − | 0.887879i | \(-0.652178\pi\) | ||||
−0.460078 | + | 0.887879i | \(0.652178\pi\) | |||||||
\(632\) | −3.15180 | −0.125372 | ||||||||
\(633\) | 19.1327 | 0.760457 | ||||||||
\(634\) | 19.7222 | 0.783271 | ||||||||
\(635\) | −42.7119 | −1.69497 | ||||||||
\(636\) | 11.1134 | 0.440676 | ||||||||
\(637\) | −6.75514 | −0.267648 | ||||||||
\(638\) | −5.91127 | −0.234029 | ||||||||
\(639\) | 12.7780 | 0.505490 | ||||||||
\(640\) | 4.10747 | 0.162362 | ||||||||
\(641\) | −32.9678 | −1.30215 | −0.651075 | − | 0.759013i | \(-0.725682\pi\) | ||||
−0.651075 | + | 0.759013i | \(0.725682\pi\) | |||||||
\(642\) | −14.3397 | −0.565942 | ||||||||
\(643\) | 38.4964 | 1.51815 | 0.759075 | − | 0.651004i | \(-0.225652\pi\) | ||||
0.759075 | + | 0.651004i | \(0.225652\pi\) | |||||||
\(644\) | −3.70803 | −0.146117 | ||||||||
\(645\) | 42.1663 | 1.66030 | ||||||||
\(646\) | −14.0824 | −0.554063 | ||||||||
\(647\) | −27.4947 | −1.08093 | −0.540464 | − | 0.841367i | \(-0.681751\pi\) | ||||
−0.540464 | + | 0.841367i | \(0.681751\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 10.0544 | 0.394670 | ||||||||
\(650\) | 16.1177 | 0.632190 | ||||||||
\(651\) | 6.70671 | 0.262857 | ||||||||
\(652\) | −21.6257 | −0.846929 | ||||||||
\(653\) | 16.4779 | 0.644830 | 0.322415 | − | 0.946598i | \(-0.395505\pi\) | ||||
0.322415 | + | 0.946598i | \(0.395505\pi\) | |||||||
\(654\) | −10.7776 | −0.421436 | ||||||||
\(655\) | −9.76210 | −0.381437 | ||||||||
\(656\) | 4.99190 | 0.194901 | ||||||||
\(657\) | 0.832592 | 0.0324825 | ||||||||
\(658\) | 18.5255 | 0.722199 | ||||||||
\(659\) | −42.8787 | −1.67032 | −0.835159 | − | 0.550008i | \(-0.814625\pi\) | ||||
−0.835159 | + | 0.550008i | \(0.814625\pi\) | |||||||
\(660\) | −4.10747 | −0.159883 | ||||||||
\(661\) | −23.3718 | −0.909057 | −0.454528 | − | 0.890732i | \(-0.650192\pi\) | ||||
−0.454528 | + | 0.890732i | \(0.650192\pi\) | |||||||
\(662\) | 17.4514 | 0.678267 | ||||||||
\(663\) | 5.20055 | 0.201973 | ||||||||
\(664\) | 13.9256 | 0.540420 | ||||||||
\(665\) | 21.4870 | 0.833231 | ||||||||
\(666\) | −11.0578 | −0.428481 | ||||||||
\(667\) | 15.4047 | 0.596474 | ||||||||
\(668\) | 7.91006 | 0.306049 | ||||||||
\(669\) | 5.86877 | 0.226900 | ||||||||
\(670\) | −27.4789 | −1.06160 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −1.42288 | −0.0548890 | ||||||||
\(673\) | 34.9598 | 1.34760 | 0.673801 | − | 0.738913i | \(-0.264661\pi\) | ||||
0.673801 | + | 0.738913i | \(0.264661\pi\) | |||||||
\(674\) | 31.2281 | 1.20286 | ||||||||
\(675\) | 11.8713 | 0.456926 | ||||||||
\(676\) | −11.1566 | −0.429101 | ||||||||
\(677\) | −21.3537 | −0.820689 | −0.410344 | − | 0.911931i | \(-0.634592\pi\) | ||||
−0.410344 | + | 0.911931i | \(0.634592\pi\) | |||||||
\(678\) | −3.15790 | −0.121278 | ||||||||
\(679\) | 10.1295 | 0.388736 | ||||||||
\(680\) | 15.7332 | 0.603341 | ||||||||
\(681\) | 16.8179 | 0.644462 | ||||||||
\(682\) | 4.71346 | 0.180488 | ||||||||
\(683\) | −39.9344 | −1.52805 | −0.764023 | − | 0.645189i | \(-0.776779\pi\) | ||||
−0.764023 | + | 0.645189i | \(0.776779\pi\) | |||||||
\(684\) | −3.67648 | −0.140574 | ||||||||
\(685\) | 13.2788 | 0.507358 | ||||||||
\(686\) | 17.0396 | 0.650575 | ||||||||
\(687\) | −21.5733 | −0.823073 | ||||||||
\(688\) | 10.2658 | 0.391378 | ||||||||
\(689\) | 15.0888 | 0.574837 | ||||||||
\(690\) | 10.7040 | 0.407496 | ||||||||
\(691\) | −43.3431 | −1.64885 | −0.824425 | − | 0.565971i | \(-0.808502\pi\) | ||||
−0.824425 | + | 0.565971i | \(0.808502\pi\) | |||||||
\(692\) | 13.6471 | 0.518786 | ||||||||
\(693\) | 1.42288 | 0.0540509 | ||||||||
\(694\) | −7.77055 | −0.294966 | ||||||||
\(695\) | −28.1866 | −1.06918 | ||||||||
\(696\) | 5.91127 | 0.224066 | ||||||||
\(697\) | 19.1209 | 0.724256 | ||||||||
\(698\) | −10.9441 | −0.414240 | ||||||||
\(699\) | −11.7417 | −0.444114 | ||||||||
\(700\) | −16.8915 | −0.638438 | ||||||||
\(701\) | −8.10204 | −0.306010 | −0.153005 | − | 0.988225i | \(-0.548895\pi\) | ||||
−0.153005 | + | 0.988225i | \(0.548895\pi\) | |||||||
\(702\) | 1.35771 | 0.0512434 | ||||||||
\(703\) | 40.6538 | 1.53329 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −53.4779 | −2.01410 | ||||||||
\(706\) | 17.6048 | 0.662564 | ||||||||
\(707\) | −10.3818 | −0.390446 | ||||||||
\(708\) | −10.0544 | −0.377868 | ||||||||
\(709\) | −46.0294 | −1.72867 | −0.864335 | − | 0.502917i | \(-0.832260\pi\) | ||||
−0.864335 | + | 0.502917i | \(0.832260\pi\) | |||||||
\(710\) | 52.4853 | 1.96974 | ||||||||
\(711\) | −3.15180 | −0.118202 | ||||||||
\(712\) | 5.54212 | 0.207700 | ||||||||
\(713\) | −12.2833 | −0.460012 | ||||||||
\(714\) | −5.45020 | −0.203969 | ||||||||
\(715\) | −5.57674 | −0.208558 | ||||||||
\(716\) | −11.8058 | −0.441203 | ||||||||
\(717\) | 23.1597 | 0.864914 | ||||||||
\(718\) | −9.83321 | −0.366972 | ||||||||
\(719\) | 39.9491 | 1.48985 | 0.744926 | − | 0.667147i | \(-0.232485\pi\) | ||||
0.744926 | + | 0.667147i | \(0.232485\pi\) | |||||||
\(720\) | 4.10747 | 0.153076 | ||||||||
\(721\) | −17.4155 | −0.648586 | ||||||||
\(722\) | −5.48349 | −0.204074 | ||||||||
\(723\) | 9.55766 | 0.355453 | ||||||||
\(724\) | 1.97489 | 0.0733963 | ||||||||
\(725\) | 70.1744 | 2.60621 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −24.4008 | −0.904976 | −0.452488 | − | 0.891771i | \(-0.649463\pi\) | ||||
−0.452488 | + | 0.891771i | \(0.649463\pi\) | |||||||
\(728\) | −1.93186 | −0.0715995 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.41985 | 0.126574 | ||||||||
\(731\) | 39.3218 | 1.45437 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | −38.9607 | −1.43904 | −0.719522 | − | 0.694469i | \(-0.755639\pi\) | ||||
−0.719522 | + | 0.694469i | \(0.755639\pi\) | |||||||
\(734\) | −20.7128 | −0.764524 | ||||||||
\(735\) | −20.4363 | −0.753804 | ||||||||
\(736\) | 2.60600 | 0.0960583 | ||||||||
\(737\) | 6.68998 | 0.246429 | ||||||||
\(738\) | 4.99190 | 0.183754 | ||||||||
\(739\) | 19.0974 | 0.702510 | 0.351255 | − | 0.936280i | \(-0.385755\pi\) | ||||
0.351255 | + | 0.936280i | \(0.385755\pi\) | |||||||
\(740\) | −45.4196 | −1.66966 | ||||||||
\(741\) | −4.99159 | −0.183371 | ||||||||
\(742\) | −15.8131 | −0.580518 | ||||||||
\(743\) | −9.78625 | −0.359023 | −0.179511 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179511 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(744\) | −4.71346 | −0.172804 | ||||||||
\(745\) | −10.4736 | −0.383724 | ||||||||
\(746\) | 22.9216 | 0.839220 | ||||||||
\(747\) | 13.9256 | 0.509513 | ||||||||
\(748\) | −3.83039 | −0.140053 | ||||||||
\(749\) | 20.4037 | 0.745535 | ||||||||
\(750\) | 28.2236 | 1.03058 | ||||||||
\(751\) | −9.80629 | −0.357837 | −0.178918 | − | 0.983864i | \(-0.557260\pi\) | ||||
−0.178918 | + | 0.983864i | \(0.557260\pi\) | |||||||
\(752\) | −13.0197 | −0.474779 | ||||||||
\(753\) | −0.638796 | −0.0232790 | ||||||||
\(754\) | 8.02578 | 0.292282 | ||||||||
\(755\) | −28.5240 | −1.03809 | ||||||||
\(756\) | −1.42288 | −0.0517498 | ||||||||
\(757\) | 24.9314 | 0.906148 | 0.453074 | − | 0.891473i | \(-0.350327\pi\) | ||||
0.453074 | + | 0.891473i | \(0.350327\pi\) | |||||||
\(758\) | 3.58342 | 0.130156 | ||||||||
\(759\) | −2.60600 | −0.0945917 | ||||||||
\(760\) | −15.1010 | −0.547772 | ||||||||
\(761\) | 18.3660 | 0.665767 | 0.332883 | − | 0.942968i | \(-0.391978\pi\) | ||||
0.332883 | + | 0.942968i | \(0.391978\pi\) | |||||||
\(762\) | −10.3986 | −0.376702 | ||||||||
\(763\) | 15.3352 | 0.555173 | ||||||||
\(764\) | −11.8090 | −0.427234 | ||||||||
\(765\) | 15.7332 | 0.568835 | ||||||||
\(766\) | −36.2661 | −1.31035 | ||||||||
\(767\) | −13.6509 | −0.492907 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 31.4932 | 1.13567 | 0.567837 | − | 0.823141i | \(-0.307780\pi\) | ||||
0.567837 | + | 0.823141i | \(0.307780\pi\) | |||||||
\(770\) | 5.84445 | 0.210619 | ||||||||
\(771\) | 23.7374 | 0.854883 | ||||||||
\(772\) | −23.8698 | −0.859094 | ||||||||
\(773\) | 27.8403 | 1.00135 | 0.500673 | − | 0.865637i | \(-0.333086\pi\) | ||||
0.500673 | + | 0.865637i | \(0.333086\pi\) | |||||||
\(774\) | 10.2658 | 0.368995 | ||||||||
\(775\) | −55.9549 | −2.00996 | ||||||||
\(776\) | −7.11901 | −0.255558 | ||||||||
\(777\) | 15.7340 | 0.564453 | ||||||||
\(778\) | −26.9353 | −0.965676 | ||||||||
\(779\) | −18.3526 | −0.657551 | ||||||||
\(780\) | 5.57674 | 0.199679 | ||||||||
\(781\) | −12.7780 | −0.457233 | ||||||||
\(782\) | 9.98198 | 0.356955 | ||||||||
\(783\) | 5.91127 | 0.211252 | ||||||||
\(784\) | −4.97540 | −0.177693 | ||||||||
\(785\) | −54.4610 | −1.94380 | ||||||||
\(786\) | −2.37667 | −0.0847731 | ||||||||
\(787\) | −27.4533 | −0.978605 | −0.489302 | − | 0.872114i | \(-0.662749\pi\) | ||||
−0.489302 | + | 0.872114i | \(0.662749\pi\) | |||||||
\(788\) | 7.36122 | 0.262233 | ||||||||
\(789\) | 16.5229 | 0.588230 | ||||||||
\(790\) | −12.9459 | −0.460595 | ||||||||
\(791\) | 4.49332 | 0.159764 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 1.35771 | 0.0482136 | ||||||||
\(794\) | 6.90455 | 0.245033 | ||||||||
\(795\) | 45.6480 | 1.61897 | ||||||||
\(796\) | 12.5538 | 0.444958 | ||||||||
\(797\) | −9.07171 | −0.321336 | −0.160668 | − | 0.987008i | \(-0.551365\pi\) | ||||
−0.160668 | + | 0.987008i | \(0.551365\pi\) | |||||||
\(798\) | 5.23121 | 0.185183 | ||||||||
\(799\) | −49.8704 | −1.76429 | ||||||||
\(800\) | 11.8713 | 0.419713 | ||||||||
\(801\) | 5.54212 | 0.195821 | ||||||||
\(802\) | 15.3687 | 0.542688 | ||||||||
\(803\) | −0.832592 | −0.0293815 | ||||||||
\(804\) | −6.68998 | −0.235937 | ||||||||
\(805\) | −15.2306 | −0.536809 | ||||||||
\(806\) | −6.39951 | −0.225413 | ||||||||
\(807\) | −7.99577 | −0.281464 | ||||||||
\(808\) | 7.29628 | 0.256682 | ||||||||
\(809\) | −24.4519 | −0.859682 | −0.429841 | − | 0.902905i | \(-0.641430\pi\) | ||||
−0.429841 | + | 0.902905i | \(0.641430\pi\) | |||||||
\(810\) | 4.10747 | 0.144322 | ||||||||
\(811\) | 43.4625 | 1.52618 | 0.763088 | − | 0.646295i | \(-0.223682\pi\) | ||||
0.763088 | + | 0.646295i | \(0.223682\pi\) | |||||||
\(812\) | −8.41105 | −0.295170 | ||||||||
\(813\) | −4.76725 | −0.167195 | ||||||||
\(814\) | 11.0578 | 0.387576 | ||||||||
\(815\) | −88.8270 | −3.11147 | ||||||||
\(816\) | 3.83039 | 0.134090 | ||||||||
\(817\) | −37.7419 | −1.32042 | ||||||||
\(818\) | −11.1119 | −0.388519 | ||||||||
\(819\) | −1.93186 | −0.0675047 | ||||||||
\(820\) | 20.5041 | 0.716033 | ||||||||
\(821\) | −9.99288 | −0.348754 | −0.174377 | − | 0.984679i | \(-0.555791\pi\) | ||||
−0.174377 | + | 0.984679i | \(0.555791\pi\) | |||||||
\(822\) | 3.23285 | 0.112759 | ||||||||
\(823\) | 47.9700 | 1.67213 | 0.836064 | − | 0.548631i | \(-0.184851\pi\) | ||||
0.836064 | + | 0.548631i | \(0.184851\pi\) | |||||||
\(824\) | 12.2396 | 0.426385 | ||||||||
\(825\) | −11.8713 | −0.413305 | ||||||||
\(826\) | 14.3062 | 0.497778 | ||||||||
\(827\) | 19.1979 | 0.667578 | 0.333789 | − | 0.942648i | \(-0.391673\pi\) | ||||
0.333789 | + | 0.942648i | \(0.391673\pi\) | |||||||
\(828\) | 2.60600 | 0.0905646 | ||||||||
\(829\) | −21.9741 | −0.763193 | −0.381597 | − | 0.924329i | \(-0.624626\pi\) | ||||
−0.381597 | + | 0.924329i | \(0.624626\pi\) | |||||||
\(830\) | 57.1991 | 1.98541 | ||||||||
\(831\) | −16.9682 | −0.588621 | ||||||||
\(832\) | 1.35771 | 0.0470701 | ||||||||
\(833\) | −19.0577 | −0.660311 | ||||||||
\(834\) | −6.86229 | −0.237622 | ||||||||
\(835\) | 32.4903 | 1.12437 | ||||||||
\(836\) | 3.67648 | 0.127154 | ||||||||
\(837\) | −4.71346 | −0.162921 | ||||||||
\(838\) | 18.5086 | 0.639369 | ||||||||
\(839\) | −36.2986 | −1.25317 | −0.626583 | − | 0.779355i | \(-0.715547\pi\) | ||||
−0.626583 | + | 0.779355i | \(0.715547\pi\) | |||||||
\(840\) | −5.84445 | −0.201653 | ||||||||
\(841\) | 5.94310 | 0.204935 | ||||||||
\(842\) | −25.2737 | −0.870991 | ||||||||
\(843\) | −13.4780 | −0.464207 | ||||||||
\(844\) | 19.1327 | 0.658575 | ||||||||
\(845\) | −45.8255 | −1.57644 | ||||||||
\(846\) | −13.0197 | −0.447626 | ||||||||
\(847\) | −1.42288 | −0.0488909 | ||||||||
\(848\) | 11.1134 | 0.381637 | ||||||||
\(849\) | −31.7376 | −1.08923 | ||||||||
\(850\) | 45.4717 | 1.55966 | ||||||||
\(851\) | −28.8166 | −0.987820 | ||||||||
\(852\) | 12.7780 | 0.437767 | ||||||||
\(853\) | −53.6070 | −1.83547 | −0.917734 | − | 0.397195i | \(-0.869984\pi\) | ||||
−0.917734 | + | 0.397195i | \(0.869984\pi\) | |||||||
\(854\) | −1.42288 | −0.0486901 | ||||||||
\(855\) | −15.1010 | −0.516444 | ||||||||
\(856\) | −14.3397 | −0.490120 | ||||||||
\(857\) | −35.4071 | −1.20948 | −0.604742 | − | 0.796422i | \(-0.706724\pi\) | ||||
−0.604742 | + | 0.796422i | \(0.706724\pi\) | |||||||
\(858\) | −1.35771 | −0.0463514 | ||||||||
\(859\) | −12.1934 | −0.416034 | −0.208017 | − | 0.978125i | \(-0.566701\pi\) | ||||
−0.208017 | + | 0.978125i | \(0.566701\pi\) | |||||||
\(860\) | 42.1663 | 1.43786 | ||||||||
\(861\) | −7.10289 | −0.242066 | ||||||||
\(862\) | 10.5667 | 0.359903 | ||||||||
\(863\) | −19.6425 | −0.668637 | −0.334319 | − | 0.942460i | \(-0.608506\pi\) | ||||
−0.334319 | + | 0.942460i | \(0.608506\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 56.0552 | 1.90593 | ||||||||
\(866\) | 3.13640 | 0.106579 | ||||||||
\(867\) | −2.32812 | −0.0790672 | ||||||||
\(868\) | 6.70671 | 0.227641 | ||||||||
\(869\) | 3.15180 | 0.106917 | ||||||||
\(870\) | 24.2803 | 0.823181 | ||||||||
\(871\) | −9.08304 | −0.307767 | ||||||||
\(872\) | −10.7776 | −0.364975 | ||||||||
\(873\) | −7.11901 | −0.240942 | ||||||||
\(874\) | −9.58089 | −0.324079 | ||||||||
\(875\) | −40.1589 | −1.35762 | ||||||||
\(876\) | 0.832592 | 0.0281307 | ||||||||
\(877\) | 28.4046 | 0.959155 | 0.479577 | − | 0.877500i | \(-0.340790\pi\) | ||||
0.479577 | + | 0.877500i | \(0.340790\pi\) | |||||||
\(878\) | −18.6958 | −0.630953 | ||||||||
\(879\) | −29.0309 | −0.979189 | ||||||||
\(880\) | −4.10747 | −0.138463 | ||||||||
\(881\) | 7.07692 | 0.238427 | 0.119214 | − | 0.992869i | \(-0.461963\pi\) | ||||
0.119214 | + | 0.992869i | \(0.461963\pi\) | |||||||
\(882\) | −4.97540 | −0.167530 | ||||||||
\(883\) | 50.2257 | 1.69023 | 0.845115 | − | 0.534584i | \(-0.179532\pi\) | ||||
0.845115 | + | 0.534584i | \(0.179532\pi\) | |||||||
\(884\) | 5.20055 | 0.174913 | ||||||||
\(885\) | −41.2981 | −1.38822 | ||||||||
\(886\) | −3.94422 | −0.132509 | ||||||||
\(887\) | 31.3499 | 1.05263 | 0.526314 | − | 0.850290i | \(-0.323574\pi\) | ||||
0.526314 | + | 0.850290i | \(0.323574\pi\) | |||||||
\(888\) | −11.0578 | −0.371076 | ||||||||
\(889\) | 14.7960 | 0.496242 | ||||||||
\(890\) | 22.7641 | 0.763054 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 5.86877 | 0.196501 | ||||||||
\(893\) | 47.8666 | 1.60180 | ||||||||
\(894\) | −2.54990 | −0.0852813 | ||||||||
\(895\) | −48.4919 | −1.62091 | ||||||||
\(896\) | −1.42288 | −0.0475352 | ||||||||
\(897\) | 3.53818 | 0.118136 | ||||||||
\(898\) | −35.3741 | −1.18045 | ||||||||
\(899\) | −27.8626 | −0.929268 | ||||||||
\(900\) | 11.8713 | 0.395710 | ||||||||
\(901\) | 42.5687 | 1.41817 | ||||||||
\(902\) | −4.99190 | −0.166212 | ||||||||
\(903\) | −14.6070 | −0.486090 | ||||||||
\(904\) | −3.15790 | −0.105030 | ||||||||
\(905\) | 8.11181 | 0.269646 | ||||||||
\(906\) | −6.94441 | −0.230713 | ||||||||
\(907\) | 3.99294 | 0.132583 | 0.0662917 | − | 0.997800i | \(-0.478883\pi\) | ||||
0.0662917 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(908\) | 16.8179 | 0.558120 | ||||||||
\(909\) | 7.29628 | 0.242002 | ||||||||
\(910\) | −7.93506 | −0.263045 | ||||||||
\(911\) | 18.7650 | 0.621711 | 0.310855 | − | 0.950457i | \(-0.399385\pi\) | ||||
0.310855 | + | 0.950457i | \(0.399385\pi\) | |||||||
\(912\) | −3.67648 | −0.121740 | ||||||||
\(913\) | −13.9256 | −0.460872 | ||||||||
\(914\) | 34.1323 | 1.12900 | ||||||||
\(915\) | 4.10747 | 0.135789 | ||||||||
\(916\) | −21.5733 | −0.712802 | ||||||||
\(917\) | 3.38173 | 0.111675 | ||||||||
\(918\) | 3.83039 | 0.126422 | ||||||||
\(919\) | −15.6989 | −0.517858 | −0.258929 | − | 0.965896i | \(-0.583370\pi\) | ||||
−0.258929 | + | 0.965896i | \(0.583370\pi\) | |||||||
\(920\) | 10.7040 | 0.352902 | ||||||||
\(921\) | −1.57252 | −0.0518163 | ||||||||
\(922\) | 29.0729 | 0.957464 | ||||||||
\(923\) | 17.3488 | 0.571043 | ||||||||
\(924\) | 1.42288 | 0.0468095 | ||||||||
\(925\) | −131.270 | −4.31615 | ||||||||
\(926\) | 15.8931 | 0.522281 | ||||||||
\(927\) | 12.2396 | 0.402000 | ||||||||
\(928\) | 5.91127 | 0.194047 | ||||||||
\(929\) | −32.4492 | −1.06463 | −0.532313 | − | 0.846548i | \(-0.678677\pi\) | ||||
−0.532313 | + | 0.846548i | \(0.678677\pi\) | |||||||
\(930\) | −19.3604 | −0.634852 | ||||||||
\(931\) | 18.2920 | 0.599495 | ||||||||
\(932\) | −11.7417 | −0.384614 | ||||||||
\(933\) | −26.9163 | −0.881200 | ||||||||
\(934\) | −6.87174 | −0.224850 | ||||||||
\(935\) | −15.7332 | −0.514531 | ||||||||
\(936\) | 1.35771 | 0.0443781 | ||||||||
\(937\) | −44.6431 | −1.45843 | −0.729214 | − | 0.684286i | \(-0.760114\pi\) | ||||
−0.729214 | + | 0.684286i | \(0.760114\pi\) | |||||||
\(938\) | 9.51907 | 0.310809 | ||||||||
\(939\) | 9.09300 | 0.296739 | ||||||||
\(940\) | −53.4779 | −1.74426 | ||||||||
\(941\) | 38.6171 | 1.25888 | 0.629440 | − | 0.777049i | \(-0.283284\pi\) | ||||
0.629440 | + | 0.777049i | \(0.283284\pi\) | |||||||
\(942\) | −13.2590 | −0.432002 | ||||||||
\(943\) | 13.0089 | 0.423627 | ||||||||
\(944\) | −10.0544 | −0.327243 | ||||||||
\(945\) | −5.84445 | −0.190120 | ||||||||
\(946\) | −10.2658 | −0.333769 | ||||||||
\(947\) | −28.4307 | −0.923873 | −0.461937 | − | 0.886913i | \(-0.652845\pi\) | ||||
−0.461937 | + | 0.886913i | \(0.652845\pi\) | |||||||
\(948\) | −3.15180 | −0.102366 | ||||||||
\(949\) | 1.13042 | 0.0366949 | ||||||||
\(950\) | −43.6446 | −1.41602 | ||||||||
\(951\) | 19.7222 | 0.639538 | ||||||||
\(952\) | −5.45020 | −0.176642 | ||||||||
\(953\) | 27.3787 | 0.886882 | 0.443441 | − | 0.896304i | \(-0.353758\pi\) | ||||
0.443441 | + | 0.896304i | \(0.353758\pi\) | |||||||
\(954\) | 11.1134 | 0.359811 | ||||||||
\(955\) | −48.5051 | −1.56959 | ||||||||
\(956\) | 23.1597 | 0.749038 | ||||||||
\(957\) | −5.91127 | −0.191084 | ||||||||
\(958\) | −12.0445 | −0.389142 | ||||||||
\(959\) | −4.59997 | −0.148541 | ||||||||
\(960\) | 4.10747 | 0.132568 | ||||||||
\(961\) | −8.78326 | −0.283331 | ||||||||
\(962\) | −15.0133 | −0.484047 | ||||||||
\(963\) | −14.3397 | −0.462089 | ||||||||
\(964\) | 9.55766 | 0.307831 | ||||||||
\(965\) | −98.0446 | −3.15617 | ||||||||
\(966\) | −3.70803 | −0.119304 | ||||||||
\(967\) | −18.9518 | −0.609450 | −0.304725 | − | 0.952440i | \(-0.598565\pi\) | ||||
−0.304725 | + | 0.952440i | \(0.598565\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −14.0824 | −0.452390 | ||||||||
\(970\) | −29.2411 | −0.938875 | ||||||||
\(971\) | −7.16615 | −0.229973 | −0.114986 | − | 0.993367i | \(-0.536682\pi\) | ||||
−0.114986 | + | 0.993367i | \(0.536682\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 9.76425 | 0.313027 | ||||||||
\(974\) | 17.1802 | 0.550490 | ||||||||
\(975\) | 16.1177 | 0.516181 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −6.00204 | −0.192022 | −0.0960111 | − | 0.995380i | \(-0.530608\pi\) | ||||
−0.0960111 | + | 0.995380i | \(0.530608\pi\) | |||||||
\(978\) | −21.6257 | −0.691514 | ||||||||
\(979\) | −5.54212 | −0.177127 | ||||||||
\(980\) | −20.4363 | −0.652814 | ||||||||
\(981\) | −10.7776 | −0.344101 | ||||||||
\(982\) | 10.5248 | 0.335860 | ||||||||
\(983\) | −44.5011 | −1.41937 | −0.709683 | − | 0.704522i | \(-0.751162\pi\) | ||||
−0.709683 | + | 0.704522i | \(0.751162\pi\) | |||||||
\(984\) | 4.99190 | 0.159136 | ||||||||
\(985\) | 30.2360 | 0.963398 | ||||||||
\(986\) | 22.6425 | 0.721083 | ||||||||
\(987\) | 18.5255 | 0.589673 | ||||||||
\(988\) | −4.99159 | −0.158804 | ||||||||
\(989\) | 26.7525 | 0.850681 | ||||||||
\(990\) | −4.10747 | −0.130544 | ||||||||
\(991\) | −18.1181 | −0.575540 | −0.287770 | − | 0.957700i | \(-0.592914\pi\) | ||||
−0.287770 | + | 0.957700i | \(0.592914\pi\) | |||||||
\(992\) | −4.71346 | −0.149653 | ||||||||
\(993\) | 17.4514 | 0.553802 | ||||||||
\(994\) | −18.1816 | −0.576686 | ||||||||
\(995\) | 51.5643 | 1.63470 | ||||||||
\(996\) | 13.9256 | 0.441251 | ||||||||
\(997\) | −26.1634 | −0.828603 | −0.414301 | − | 0.910140i | \(-0.635974\pi\) | ||||
−0.414301 | + | 0.910140i | \(0.635974\pi\) | |||||||
\(998\) | 28.7356 | 0.909611 | ||||||||
\(999\) | −11.0578 | −0.349854 |
(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 | 4026.2.a.bb.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.bb.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial |