Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 42 x^{12} + 70 x^{11} + 680 x^{10} - 882 x^{9} - 5559 x^{8} + 5066 x^{7} + \cdots - 7083 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(4.30228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.30228 | 1.92404 | 0.962020 | − | 0.272979i | \(-0.0880090\pi\) | ||||
0.962020 | + | 0.272979i | \(0.0880090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.58072 | −0.975420 | −0.487710 | − | 0.873006i | \(-0.662168\pi\) | ||||
−0.487710 | + | 0.873006i | \(0.662168\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.30228 | 1.36050 | ||||||||
\(11\) | −2.36140 | −0.711989 | −0.355994 | − | 0.934488i | \(-0.615858\pi\) | ||||
−0.355994 | + | 0.934488i | \(0.615858\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34794 | −1.20590 | −0.602950 | − | 0.797779i | \(-0.706008\pi\) | ||||
−0.602950 | + | 0.797779i | \(0.706008\pi\) | |||||||
\(14\) | −2.58072 | −0.689726 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.59971 | −1.11559 | −0.557797 | − | 0.829977i | \(-0.688353\pi\) | ||||
−0.557797 | + | 0.829977i | \(0.688353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.77611 | 1.09571 | 0.547857 | − | 0.836572i | \(-0.315444\pi\) | ||||
0.547857 | + | 0.836572i | \(0.315444\pi\) | |||||||
\(20\) | 4.30228 | 0.962020 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36140 | −0.503452 | ||||||||
\(23\) | 6.85875 | 1.43015 | 0.715074 | − | 0.699049i | \(-0.246393\pi\) | ||||
0.715074 | + | 0.699049i | \(0.246393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.5096 | 2.70193 | ||||||||
\(26\) | −4.34794 | −0.852701 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.58072 | −0.487710 | ||||||||
\(29\) | 9.68846 | 1.79910 | 0.899551 | − | 0.436817i | \(-0.143894\pi\) | ||||
0.899551 | + | 0.436817i | \(0.143894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83005 | 0.867503 | 0.433751 | − | 0.901033i | \(-0.357190\pi\) | ||||
0.433751 | + | 0.901033i | \(0.357190\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.59971 | −0.788845 | ||||||||
\(35\) | −11.1030 | −1.87675 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.41878 | −0.726443 | −0.363222 | − | 0.931703i | \(-0.618323\pi\) | ||||
−0.363222 | + | 0.931703i | \(0.618323\pi\) | |||||||
\(38\) | 4.77611 | 0.774787 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.30228 | 0.680251 | ||||||||
\(41\) | 4.47634 | 0.699087 | 0.349543 | − | 0.936920i | \(-0.386337\pi\) | ||||
0.349543 | + | 0.936920i | \(0.386337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.56055 | −0.542979 | −0.271490 | − | 0.962441i | \(-0.587516\pi\) | ||||
−0.271490 | + | 0.962441i | \(0.587516\pi\) | |||||||
\(44\) | −2.36140 | −0.355994 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.85875 | 1.01127 | ||||||||
\(47\) | 6.92253 | 1.00976 | 0.504878 | − | 0.863191i | \(-0.331538\pi\) | ||||
0.504878 | + | 0.863191i | \(0.331538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.339891 | −0.0485558 | ||||||||
\(50\) | 13.5096 | 1.91055 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.34794 | −0.602950 | ||||||||
\(53\) | −2.33828 | −0.321187 | −0.160594 | − | 0.987021i | \(-0.551341\pi\) | ||||
−0.160594 | + | 0.987021i | \(0.551341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.1594 | −1.36989 | ||||||||
\(56\) | −2.58072 | −0.344863 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.68846 | 1.27216 | ||||||||
\(59\) | 3.02010 | 0.393184 | 0.196592 | − | 0.980485i | \(-0.437013\pi\) | ||||
0.196592 | + | 0.980485i | \(0.437013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.66465 | −0.213136 | −0.106568 | − | 0.994305i | \(-0.533986\pi\) | ||||
−0.106568 | + | 0.994305i | \(0.533986\pi\) | |||||||
\(62\) | 4.83005 | 0.613417 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −18.7061 | −2.32020 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9222 | −1.82303 | −0.911516 | − | 0.411264i | \(-0.865088\pi\) | ||||
−0.911516 | + | 0.411264i | \(0.865088\pi\) | |||||||
\(68\) | −4.59971 | −0.557797 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.1030 | −1.32706 | ||||||||
\(71\) | −1.22986 | −0.145958 | −0.0729788 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729788 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5077 | 1.93208 | 0.966038 | − | 0.258399i | \(-0.0831950\pi\) | ||||
0.966038 | + | 0.258399i | \(0.0831950\pi\) | |||||||
\(74\) | −4.41878 | −0.513673 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.77611 | 0.547857 | ||||||||
\(77\) | 6.09411 | 0.694488 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.926115 | 0.104196 | 0.0520980 | − | 0.998642i | \(-0.483409\pi\) | ||||
0.0520980 | + | 0.998642i | \(0.483409\pi\) | |||||||
\(80\) | 4.30228 | 0.481010 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.47634 | 0.494329 | ||||||||
\(83\) | 16.1043 | 1.76767 | 0.883837 | − | 0.467795i | \(-0.154951\pi\) | ||||
0.883837 | + | 0.467795i | \(0.154951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.7893 | −2.14645 | ||||||||
\(86\) | −3.56055 | −0.383944 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.36140 | −0.251726 | ||||||||
\(89\) | 2.40888 | 0.255341 | 0.127671 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127671 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2208 | 1.17626 | ||||||||
\(92\) | 6.85875 | 0.715074 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.92253 | 0.714005 | ||||||||
\(95\) | 20.5482 | 2.10820 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.91733 | −1.00695 | −0.503476 | − | 0.864009i | \(-0.667946\pi\) | ||||
−0.503476 | + | 0.864009i | \(0.667946\pi\) | |||||||
\(98\) | −0.339891 | −0.0343341 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.5096 | 1.35096 | ||||||||
\(101\) | 12.8905 | 1.28266 | 0.641328 | − | 0.767266i | \(-0.278384\pi\) | ||||
0.641328 | + | 0.767266i | \(0.278384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0474 | 1.08854 | 0.544268 | − | 0.838911i | \(-0.316807\pi\) | ||||
0.544268 | + | 0.838911i | \(0.316807\pi\) | |||||||
\(104\) | −4.34794 | −0.426350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.33828 | −0.227114 | ||||||||
\(107\) | 13.6167 | 1.31638 | 0.658190 | − | 0.752852i | \(-0.271322\pi\) | ||||
0.658190 | + | 0.752852i | \(0.271322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.0796 | −1.92327 | −0.961637 | − | 0.274326i | \(-0.911545\pi\) | ||||
−0.961637 | + | 0.274326i | \(0.911545\pi\) | |||||||
\(110\) | −10.1594 | −0.968662 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.58072 | −0.243855 | ||||||||
\(113\) | −3.00799 | −0.282968 | −0.141484 | − | 0.989941i | \(-0.545187\pi\) | ||||
−0.141484 | + | 0.989941i | \(0.545187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29.5083 | 2.75166 | ||||||||
\(116\) | 9.68846 | 0.899551 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.02010 | 0.278023 | ||||||||
\(119\) | 11.8706 | 1.08817 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.42380 | −0.493072 | ||||||||
\(122\) | −1.66465 | −0.150710 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.83005 | 0.433751 | ||||||||
\(125\) | 36.6109 | 3.27458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6905 | 1.30357 | 0.651787 | − | 0.758402i | \(-0.274020\pi\) | ||||
0.651787 | + | 0.758402i | \(0.274020\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.7061 | −1.64063 | ||||||||
\(131\) | −7.27060 | −0.635235 | −0.317618 | − | 0.948219i | \(-0.602883\pi\) | ||||
−0.317618 | + | 0.948219i | \(0.602883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.3258 | −1.06878 | ||||||||
\(134\) | −14.9222 | −1.28908 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.59971 | −0.394422 | ||||||||
\(137\) | −5.25460 | −0.448931 | −0.224465 | − | 0.974482i | \(-0.572064\pi\) | ||||
−0.224465 | + | 0.974482i | \(0.572064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.8385 | 1.34341 | 0.671703 | − | 0.740821i | \(-0.265563\pi\) | ||||
0.671703 | + | 0.740821i | \(0.265563\pi\) | |||||||
\(140\) | −11.1030 | −0.938374 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.22986 | −0.103208 | ||||||||
\(143\) | 10.2672 | 0.858587 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 41.6825 | 3.46154 | ||||||||
\(146\) | 16.5077 | 1.36618 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.41878 | −0.363222 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.79221 | 0.552742 | 0.276371 | − | 0.961051i | \(-0.410868\pi\) | ||||
0.276371 | + | 0.961051i | \(0.410868\pi\) | |||||||
\(152\) | 4.77611 | 0.387394 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.09411 | 0.491077 | ||||||||
\(155\) | 20.7802 | 1.66911 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.19817 | −0.494668 | −0.247334 | − | 0.968930i | \(-0.579554\pi\) | ||||
−0.247334 | + | 0.968930i | \(0.579554\pi\) | |||||||
\(158\) | 0.926115 | 0.0736777 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.30228 | 0.340125 | ||||||||
\(161\) | −17.7005 | −1.39499 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.35527 | 0.262805 | 0.131402 | − | 0.991329i | \(-0.458052\pi\) | ||||
0.131402 | + | 0.991329i | \(0.458052\pi\) | |||||||
\(164\) | 4.47634 | 0.349543 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.1043 | 1.24993 | ||||||||
\(167\) | −3.18225 | −0.246250 | −0.123125 | − | 0.992391i | \(-0.539292\pi\) | ||||
−0.123125 | + | 0.992391i | \(0.539292\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.90455 | 0.454196 | ||||||||
\(170\) | −19.7893 | −1.51777 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.56055 | −0.271490 | ||||||||
\(173\) | 1.29626 | 0.0985526 | 0.0492763 | − | 0.998785i | \(-0.484309\pi\) | ||||
0.0492763 | + | 0.998785i | \(0.484309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −34.8646 | −2.63552 | ||||||||
\(176\) | −2.36140 | −0.177997 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.40888 | 0.180553 | ||||||||
\(179\) | 5.70933 | 0.426735 | 0.213368 | − | 0.976972i | \(-0.431557\pi\) | ||||
0.213368 | + | 0.976972i | \(0.431557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9052 | 1.18222 | 0.591112 | − | 0.806590i | \(-0.298689\pi\) | ||||
0.591112 | + | 0.806590i | \(0.298689\pi\) | |||||||
\(182\) | 11.2208 | 0.831741 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.85875 | 0.505633 | ||||||||
\(185\) | −19.0109 | −1.39771 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8618 | 0.794291 | ||||||||
\(188\) | 6.92253 | 0.504878 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.5482 | 1.49072 | ||||||||
\(191\) | 1.86430 | 0.134896 | 0.0674479 | − | 0.997723i | \(-0.478514\pi\) | ||||
0.0674479 | + | 0.997723i | \(0.478514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.9932 | −1.22320 | −0.611599 | − | 0.791168i | \(-0.709473\pi\) | ||||
−0.611599 | + | 0.791168i | \(0.709473\pi\) | |||||||
\(194\) | −9.91733 | −0.712023 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.339891 | −0.0242779 | ||||||||
\(197\) | 8.68393 | 0.618704 | 0.309352 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309352 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0290 | −0.781823 | −0.390911 | − | 0.920428i | \(-0.627840\pi\) | ||||
−0.390911 | + | 0.920428i | \(0.627840\pi\) | |||||||
\(200\) | 13.5096 | 0.955276 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.8905 | 0.906975 | ||||||||
\(203\) | −25.0032 | −1.75488 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.2585 | 1.34507 | ||||||||
\(206\) | 11.0474 | 0.769711 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.34794 | −0.301475 | ||||||||
\(209\) | −11.2783 | −0.780136 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.71092 | 0.255470 | 0.127735 | − | 0.991808i | \(-0.459229\pi\) | ||||
0.127735 | + | 0.991808i | \(0.459229\pi\) | |||||||
\(212\) | −2.33828 | −0.160594 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.6167 | 0.930822 | ||||||||
\(215\) | −15.3185 | −1.04471 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.4650 | −0.846179 | ||||||||
\(218\) | −20.0796 | −1.35996 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.1594 | −0.684947 | ||||||||
\(221\) | 19.9993 | 1.34530 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.31235 | 0.154846 | 0.0774230 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774230 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(224\) | −2.58072 | −0.172432 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00799 | −0.200088 | ||||||||
\(227\) | 9.48105 | 0.629280 | 0.314640 | − | 0.949211i | \(-0.398116\pi\) | ||||
0.314640 | + | 0.949211i | \(0.398116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1183 | −1.13121 | −0.565605 | − | 0.824676i | \(-0.691357\pi\) | ||||
−0.565605 | + | 0.824676i | \(0.691357\pi\) | |||||||
\(230\) | 29.5083 | 1.94572 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.68846 | 0.636078 | ||||||||
\(233\) | 1.89499 | 0.124145 | 0.0620725 | − | 0.998072i | \(-0.480229\pi\) | ||||
0.0620725 | + | 0.998072i | \(0.480229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.7827 | 1.94281 | ||||||||
\(236\) | 3.02010 | 0.196592 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.8706 | 0.769455 | ||||||||
\(239\) | −10.4414 | −0.675400 | −0.337700 | − | 0.941254i | \(-0.609649\pi\) | ||||
−0.337700 | + | 0.941254i | \(0.609649\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.96284 | 0.641763 | 0.320882 | − | 0.947119i | \(-0.396021\pi\) | ||||
0.320882 | + | 0.947119i | \(0.396021\pi\) | |||||||
\(242\) | −5.42380 | −0.348655 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.66465 | −0.106568 | ||||||||
\(245\) | −1.46231 | −0.0934233 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.7662 | −1.32132 | ||||||||
\(248\) | 4.83005 | 0.306708 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 36.6109 | 2.31548 | ||||||||
\(251\) | 13.6358 | 0.860681 | 0.430341 | − | 0.902667i | \(-0.358393\pi\) | ||||
0.430341 | + | 0.902667i | \(0.358393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.1962 | −1.01825 | ||||||||
\(254\) | 14.6905 | 0.921766 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.3175 | 0.830724 | 0.415362 | − | 0.909656i | \(-0.363655\pi\) | ||||
0.415362 | + | 0.909656i | \(0.363655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4036 | 0.708587 | ||||||||
\(260\) | −18.7061 | −1.16010 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.27060 | −0.449179 | ||||||||
\(263\) | −1.11201 | −0.0685698 | −0.0342849 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342849 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0599 | −0.617977 | ||||||||
\(266\) | −12.3258 | −0.755743 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.9222 | −0.911516 | ||||||||
\(269\) | −27.6181 | −1.68390 | −0.841952 | − | 0.539553i | \(-0.818593\pi\) | ||||
−0.841952 | + | 0.539553i | \(0.818593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0063 | 1.03306 | 0.516528 | − | 0.856270i | \(-0.327224\pi\) | ||||
0.516528 | + | 0.856270i | \(0.327224\pi\) | |||||||
\(272\) | −4.59971 | −0.278899 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.25460 | −0.317442 | ||||||||
\(275\) | −31.9017 | −1.92374 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3266 | −0.800717 | −0.400358 | − | 0.916359i | \(-0.631114\pi\) | ||||
−0.400358 | + | 0.916359i | \(0.631114\pi\) | |||||||
\(278\) | 15.8385 | 0.949931 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.1030 | −0.663530 | ||||||||
\(281\) | −3.48845 | −0.208104 | −0.104052 | − | 0.994572i | \(-0.533181\pi\) | ||||
−0.104052 | + | 0.994572i | \(0.533181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7321 | 0.816291 | 0.408145 | − | 0.912917i | \(-0.366176\pi\) | ||||
0.408145 | + | 0.912917i | \(0.366176\pi\) | |||||||
\(284\) | −1.22986 | −0.0729788 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.2672 | 0.607113 | ||||||||
\(287\) | −11.5522 | −0.681903 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.15737 | 0.244551 | ||||||||
\(290\) | 41.6825 | 2.44768 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.5077 | 0.966038 | ||||||||
\(293\) | 7.12602 | 0.416307 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9933 | 0.756502 | ||||||||
\(296\) | −4.41878 | −0.256837 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −29.8214 | −1.72462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.18878 | 0.529633 | ||||||||
\(302\) | 6.79221 | 0.390848 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.77611 | 0.273929 | ||||||||
\(305\) | −7.16178 | −0.410082 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.7190 | −1.75323 | −0.876614 | − | 0.481195i | \(-0.840203\pi\) | ||||
−0.876614 | + | 0.481195i | \(0.840203\pi\) | |||||||
\(308\) | 6.09411 | 0.347244 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.7802 | 1.18024 | ||||||||
\(311\) | −28.4027 | −1.61057 | −0.805283 | − | 0.592890i | \(-0.797987\pi\) | ||||
−0.805283 | + | 0.592890i | \(0.797987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4329 | 0.646225 | 0.323113 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323113 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(314\) | −6.19817 | −0.349783 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.926115 | 0.0520980 | ||||||||
\(317\) | −28.0375 | −1.57474 | −0.787370 | − | 0.616480i | \(-0.788558\pi\) | ||||
−0.787370 | + | 0.616480i | \(0.788558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.8783 | −1.28094 | ||||||||
\(320\) | 4.30228 | 0.240505 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.7005 | −0.986410 | ||||||||
\(323\) | −21.9687 | −1.22237 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −58.7391 | −3.25826 | ||||||||
\(326\) | 3.35527 | 0.185831 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.47634 | 0.247165 | ||||||||
\(329\) | −17.8651 | −0.984935 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.4851 | 1.40079 | 0.700395 | − | 0.713756i | \(-0.253007\pi\) | ||||
0.700395 | + | 0.713756i | \(0.253007\pi\) | |||||||
\(332\) | 16.1043 | 0.883837 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.18225 | −0.174125 | ||||||||
\(335\) | −64.1994 | −3.50759 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.13084 | −0.388441 | −0.194221 | − | 0.980958i | \(-0.562218\pi\) | ||||
−0.194221 | + | 0.980958i | \(0.562218\pi\) | |||||||
\(338\) | 5.90455 | 0.321165 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.7893 | −1.07322 | ||||||||
\(341\) | −11.4057 | −0.617652 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.9422 | 1.02278 | ||||||||
\(344\) | −3.56055 | −0.191972 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.29626 | 0.0696872 | ||||||||
\(347\) | −21.4199 | −1.14988 | −0.574941 | − | 0.818195i | \(-0.694975\pi\) | ||||
−0.574941 | + | 0.818195i | \(0.694975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9563 | 0.854122 | 0.427061 | − | 0.904223i | \(-0.359549\pi\) | ||||
0.427061 | + | 0.904223i | \(0.359549\pi\) | |||||||
\(350\) | −34.8646 | −1.86359 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.36140 | −0.125863 | ||||||||
\(353\) | −11.7388 | −0.624792 | −0.312396 | − | 0.949952i | \(-0.601132\pi\) | ||||
−0.312396 | + | 0.949952i | \(0.601132\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.29121 | −0.280828 | ||||||||
\(356\) | 2.40888 | 0.127671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.70933 | 0.301747 | ||||||||
\(359\) | −31.1311 | −1.64303 | −0.821517 | − | 0.570184i | \(-0.806872\pi\) | ||||
−0.821517 | + | 0.570184i | \(0.806872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.81122 | 0.200590 | ||||||||
\(362\) | 15.9052 | 0.835959 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.2208 | 0.588130 | ||||||||
\(365\) | 71.0207 | 3.71739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0585 | −0.733845 | −0.366923 | − | 0.930251i | \(-0.619589\pi\) | ||||
−0.366923 | + | 0.930251i | \(0.619589\pi\) | |||||||
\(368\) | 6.85875 | 0.357537 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.0109 | −0.988327 | ||||||||
\(371\) | 6.03444 | 0.313292 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.1993 | 1.87433 | 0.937165 | − | 0.348886i | \(-0.113440\pi\) | ||||
0.937165 | + | 0.348886i | \(0.113440\pi\) | |||||||
\(374\) | 10.8618 | 0.561648 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92253 | 0.357002 | ||||||||
\(377\) | −42.1248 | −2.16954 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.83323 | 0.402366 | 0.201183 | − | 0.979554i | \(-0.435521\pi\) | ||||
0.201183 | + | 0.979554i | \(0.435521\pi\) | |||||||
\(380\) | 20.5482 | 1.05410 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.86430 | 0.0953857 | ||||||||
\(383\) | −28.6388 | −1.46338 | −0.731688 | − | 0.681639i | \(-0.761267\pi\) | ||||
−0.731688 | + | 0.681639i | \(0.761267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.2186 | 1.33622 | ||||||||
\(386\) | −16.9932 | −0.864932 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.91733 | −0.503476 | ||||||||
\(389\) | −29.8923 | −1.51560 | −0.757800 | − | 0.652487i | \(-0.773726\pi\) | ||||
−0.757800 | + | 0.652487i | \(0.773726\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.5483 | −1.59546 | ||||||||
\(392\) | −0.339891 | −0.0171671 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.68393 | 0.437490 | ||||||||
\(395\) | 3.98441 | 0.200477 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.71141 | 0.286648 | 0.143324 | − | 0.989676i | \(-0.454221\pi\) | ||||
0.143324 | + | 0.989676i | \(0.454221\pi\) | |||||||
\(398\) | −11.0290 | −0.552832 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.5096 | 0.675482 | ||||||||
\(401\) | 0.176944 | 0.00883618 | 0.00441809 | − | 0.999990i | \(-0.498594\pi\) | ||||
0.00441809 | + | 0.999990i | \(0.498594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.0008 | −1.04612 | ||||||||
\(404\) | 12.8905 | 0.641328 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.0032 | −1.24089 | ||||||||
\(407\) | 10.4345 | 0.517219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5360 | 0.520973 | 0.260487 | − | 0.965477i | \(-0.416117\pi\) | ||||
0.260487 | + | 0.965477i | \(0.416117\pi\) | |||||||
\(410\) | 19.2585 | 0.951109 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.0474 | 0.544268 | ||||||||
\(413\) | −7.79404 | −0.383520 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 69.2852 | 3.40108 | ||||||||
\(416\) | −4.34794 | −0.213175 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.2783 | −0.551640 | ||||||||
\(419\) | −4.42760 | −0.216302 | −0.108151 | − | 0.994134i | \(-0.534493\pi\) | ||||
−0.108151 | + | 0.994134i | \(0.534493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8257 | 0.576350 | 0.288175 | − | 0.957578i | \(-0.406951\pi\) | ||||
0.288175 | + | 0.957578i | \(0.406951\pi\) | |||||||
\(422\) | 3.71092 | 0.180645 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.33828 | −0.113557 | ||||||||
\(425\) | −62.1405 | −3.01426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.29598 | 0.207897 | ||||||||
\(428\) | 13.6167 | 0.658190 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.3185 | −0.738724 | ||||||||
\(431\) | 16.9221 | 0.815108 | 0.407554 | − | 0.913181i | \(-0.366382\pi\) | ||||
0.407554 | + | 0.913181i | \(0.366382\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.7977 | −0.999475 | −0.499737 | − | 0.866177i | \(-0.666570\pi\) | ||||
−0.499737 | + | 0.866177i | \(0.666570\pi\) | |||||||
\(434\) | −12.4650 | −0.598339 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.0796 | −0.961637 | ||||||||
\(437\) | 32.7581 | 1.56703 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.52842 | 0.168402 | 0.0842011 | − | 0.996449i | \(-0.473166\pi\) | ||||
0.0842011 | + | 0.996449i | \(0.473166\pi\) | |||||||
\(440\) | −10.1594 | −0.484331 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.9993 | 0.951268 | ||||||||
\(443\) | 31.0514 | 1.47530 | 0.737648 | − | 0.675186i | \(-0.235937\pi\) | ||||
0.737648 | + | 0.675186i | \(0.235937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.3637 | 0.491286 | ||||||||
\(446\) | 2.31235 | 0.109493 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.58072 | −0.121928 | ||||||||
\(449\) | 23.2911 | 1.09918 | 0.549588 | − | 0.835436i | \(-0.314785\pi\) | ||||
0.549588 | + | 0.835436i | \(0.314785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5704 | −0.497742 | ||||||||
\(452\) | −3.00799 | −0.141484 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.48105 | 0.444968 | ||||||||
\(455\) | 48.2751 | 2.26317 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.4856 | −1.65995 | −0.829973 | − | 0.557803i | \(-0.811645\pi\) | ||||
−0.829973 | + | 0.557803i | \(0.811645\pi\) | |||||||
\(458\) | −17.1183 | −0.799886 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 29.5083 | 1.37583 | ||||||||
\(461\) | −11.5348 | −0.537229 | −0.268614 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268614 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6842 | −1.00775 | −0.503874 | − | 0.863777i | \(-0.668093\pi\) | ||||
−0.503874 | + | 0.863777i | \(0.668093\pi\) | |||||||
\(464\) | 9.68846 | 0.449775 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.89499 | 0.0877838 | ||||||||
\(467\) | −2.36171 | −0.109287 | −0.0546434 | − | 0.998506i | \(-0.517402\pi\) | ||||
−0.0546434 | + | 0.998506i | \(0.517402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.5099 | 1.77822 | ||||||||
\(470\) | 29.7827 | 1.37377 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.02010 | 0.139012 | ||||||||
\(473\) | 8.40788 | 0.386595 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 64.5236 | 2.96054 | ||||||||
\(476\) | 11.8706 | 0.544087 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.4414 | −0.477580 | ||||||||
\(479\) | 29.8556 | 1.36414 | 0.682069 | − | 0.731287i | \(-0.261080\pi\) | ||||
0.682069 | + | 0.731287i | \(0.261080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.2126 | 0.876019 | ||||||||
\(482\) | 9.96284 | 0.453795 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.42380 | −0.246536 | ||||||||
\(485\) | −42.6672 | −1.93742 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0354 | −0.545375 | −0.272687 | − | 0.962103i | \(-0.587912\pi\) | ||||
−0.272687 | + | 0.962103i | \(0.587912\pi\) | |||||||
\(488\) | −1.66465 | −0.0753550 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.46231 | −0.0660602 | ||||||||
\(491\) | 36.1930 | 1.63337 | 0.816684 | − | 0.577085i | \(-0.195810\pi\) | ||||
0.816684 | + | 0.577085i | \(0.195810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.5641 | −2.00707 | ||||||||
\(494\) | −20.7662 | −0.934316 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.83005 | 0.216876 | ||||||||
\(497\) | 3.17393 | 0.142370 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.7640 | 0.750461 | 0.375231 | − | 0.926931i | \(-0.377563\pi\) | ||||
0.375231 | + | 0.926931i | \(0.377563\pi\) | |||||||
\(500\) | 36.6109 | 1.63729 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.6358 | 0.608594 | ||||||||
\(503\) | 16.8621 | 0.751845 | 0.375923 | − | 0.926651i | \(-0.377326\pi\) | ||||
0.375923 | + | 0.926651i | \(0.377326\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.4588 | 2.46788 | ||||||||
\(506\) | −16.1962 | −0.720010 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.6905 | 0.651787 | ||||||||
\(509\) | 0.689284 | 0.0305520 | 0.0152760 | − | 0.999883i | \(-0.495137\pi\) | ||||
0.0152760 | + | 0.999883i | \(0.495137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.6016 | −1.88459 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.3175 | 0.587410 | ||||||||
\(515\) | 47.5292 | 2.09439 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.3469 | −0.718934 | ||||||||
\(518\) | 11.4036 | 0.501047 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.7061 | −0.820315 | ||||||||
\(521\) | 39.6190 | 1.73574 | 0.867869 | − | 0.496793i | \(-0.165489\pi\) | ||||
0.867869 | + | 0.496793i | \(0.165489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.8746 | −0.781600 | −0.390800 | − | 0.920476i | \(-0.627802\pi\) | ||||
−0.390800 | + | 0.920476i | \(0.627802\pi\) | |||||||
\(524\) | −7.27060 | −0.317618 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.11201 | −0.0484862 | ||||||||
\(527\) | −22.2169 | −0.967781 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.0424 | 1.04532 | ||||||||
\(530\) | −10.0599 | −0.436976 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.3258 | −0.534391 | ||||||||
\(533\) | −19.4628 | −0.843029 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 58.5831 | 2.53277 | ||||||||
\(536\) | −14.9222 | −0.644539 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.6181 | −1.19070 | ||||||||
\(539\) | 0.802617 | 0.0345712 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.3068 | 1.56095 | 0.780476 | − | 0.625186i | \(-0.214977\pi\) | ||||
0.780476 | + | 0.625186i | \(0.214977\pi\) | |||||||
\(542\) | 17.0063 | 0.730481 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.59971 | −0.197211 | ||||||||
\(545\) | −86.3880 | −3.70045 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7836 | 1.14518 | 0.572592 | − | 0.819840i | \(-0.305938\pi\) | ||||
0.572592 | + | 0.819840i | \(0.305938\pi\) | |||||||
\(548\) | −5.25460 | −0.224465 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.9017 | −1.36029 | ||||||||
\(551\) | 46.2731 | 1.97130 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.39004 | −0.101635 | ||||||||
\(554\) | −13.3266 | −0.566192 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.8385 | 0.671703 | ||||||||
\(557\) | −28.9109 | −1.22499 | −0.612496 | − | 0.790474i | \(-0.709835\pi\) | ||||
−0.612496 | + | 0.790474i | \(0.709835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4811 | 0.654779 | ||||||||
\(560\) | −11.1030 | −0.469187 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.48845 | −0.147151 | ||||||||
\(563\) | −29.1613 | −1.22900 | −0.614502 | − | 0.788915i | \(-0.710643\pi\) | ||||
−0.614502 | + | 0.788915i | \(0.710643\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.9412 | −0.544441 | ||||||||
\(566\) | 13.7321 | 0.577205 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.22986 | −0.0516038 | ||||||||
\(569\) | −2.95408 | −0.123841 | −0.0619207 | − | 0.998081i | \(-0.519723\pi\) | ||||
−0.0619207 | + | 0.998081i | \(0.519723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9821 | 0.459588 | 0.229794 | − | 0.973239i | \(-0.426195\pi\) | ||||
0.229794 | + | 0.973239i | \(0.426195\pi\) | |||||||
\(572\) | 10.2672 | 0.429294 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.5522 | −0.482178 | ||||||||
\(575\) | 92.6592 | 3.86416 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.3780 | −1.63933 | −0.819664 | − | 0.572845i | \(-0.805840\pi\) | ||||
−0.819664 | + | 0.572845i | \(0.805840\pi\) | |||||||
\(578\) | 4.15737 | 0.172924 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 41.6825 | 1.73077 | ||||||||
\(581\) | −41.5606 | −1.72422 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.52161 | 0.228682 | ||||||||
\(584\) | 16.5077 | 0.683092 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.12602 | 0.294373 | ||||||||
\(587\) | −25.0820 | −1.03525 | −0.517623 | − | 0.855609i | \(-0.673183\pi\) | ||||
−0.517623 | + | 0.855609i | \(0.673183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.0688 | 0.950535 | ||||||||
\(590\) | 12.9933 | 0.534927 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.41878 | −0.181611 | ||||||||
\(593\) | 41.9959 | 1.72456 | 0.862282 | − | 0.506428i | \(-0.169034\pi\) | ||||
0.862282 | + | 0.506428i | \(0.169034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 51.0706 | 2.09369 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −29.8214 | −1.21949 | ||||||||
\(599\) | 20.7536 | 0.847969 | 0.423984 | − | 0.905670i | \(-0.360631\pi\) | ||||
0.423984 | + | 0.905670i | \(0.360631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8460 | −0.442416 | −0.221208 | − | 0.975227i | \(-0.571000\pi\) | ||||
−0.221208 | + | 0.975227i | \(0.571000\pi\) | |||||||
\(602\) | 9.18878 | 0.374507 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.79221 | 0.276371 | ||||||||
\(605\) | −23.3347 | −0.948691 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.16725 | −0.128555 | −0.0642775 | − | 0.997932i | \(-0.520474\pi\) | ||||
−0.0642775 | + | 0.997932i | \(0.520474\pi\) | |||||||
\(608\) | 4.77611 | 0.193697 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.16178 | −0.289972 | ||||||||
\(611\) | −30.0987 | −1.21766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.5898 | −1.76058 | −0.880288 | − | 0.474439i | \(-0.842651\pi\) | ||||
−0.880288 | + | 0.474439i | \(0.842651\pi\) | |||||||
\(614\) | −30.7190 | −1.23972 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.09411 | 0.245539 | ||||||||
\(617\) | −37.8700 | −1.52459 | −0.762295 | − | 0.647230i | \(-0.775927\pi\) | ||||
−0.762295 | + | 0.647230i | \(0.775927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.40979 | −0.257631 | −0.128816 | − | 0.991669i | \(-0.541118\pi\) | ||||
−0.128816 | + | 0.991669i | \(0.541118\pi\) | |||||||
\(620\) | 20.7802 | 0.834555 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.4027 | −1.13884 | ||||||||
\(623\) | −6.21665 | −0.249065 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.9624 | 3.59849 | ||||||||
\(626\) | 11.4329 | 0.456950 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.19817 | −0.247334 | ||||||||
\(629\) | 20.3251 | 0.810416 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.6878 | −1.14204 | −0.571021 | − | 0.820935i | \(-0.693453\pi\) | ||||
−0.571021 | + | 0.820935i | \(0.693453\pi\) | |||||||
\(632\) | 0.926115 | 0.0368389 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.0375 | −1.11351 | ||||||||
\(635\) | 63.2028 | 2.50813 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.47782 | 0.0585535 | ||||||||
\(638\) | −22.8783 | −0.905761 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.30228 | 0.170063 | ||||||||
\(641\) | −17.8921 | −0.706697 | −0.353348 | − | 0.935492i | \(-0.614957\pi\) | ||||
−0.353348 | + | 0.935492i | \(0.614957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.6114 | −1.28607 | −0.643035 | − | 0.765837i | \(-0.722325\pi\) | ||||
−0.643035 | + | 0.765837i | \(0.722325\pi\) | |||||||
\(644\) | −17.7005 | −0.697497 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.9687 | −0.864348 | ||||||||
\(647\) | 4.88499 | 0.192049 | 0.0960243 | − | 0.995379i | \(-0.469387\pi\) | ||||
0.0960243 | + | 0.995379i | \(0.469387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.13167 | −0.279942 | ||||||||
\(650\) | −58.7391 | −2.30394 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.35527 | 0.131402 | ||||||||
\(653\) | −6.49092 | −0.254009 | −0.127005 | − | 0.991902i | \(-0.540536\pi\) | ||||
−0.127005 | + | 0.991902i | \(0.540536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.2802 | −1.22222 | ||||||||
\(656\) | 4.47634 | 0.174772 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.8651 | −0.696455 | ||||||||
\(659\) | −26.7244 | −1.04104 | −0.520518 | − | 0.853851i | \(-0.674261\pi\) | ||||
−0.520518 | + | 0.853851i | \(0.674261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.2623 | −1.52713 | −0.763563 | − | 0.645733i | \(-0.776552\pi\) | ||||
−0.763563 | + | 0.645733i | \(0.776552\pi\) | |||||||
\(662\) | 25.4851 | 0.990508 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.1043 | 0.624967 | ||||||||
\(665\) | −53.0291 | −2.05638 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 66.4507 | 2.57298 | ||||||||
\(668\) | −3.18225 | −0.123125 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −64.1994 | −2.48024 | ||||||||
\(671\) | 3.93089 | 0.151750 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1320 | −0.583295 | −0.291647 | − | 0.956526i | \(-0.594203\pi\) | ||||
−0.291647 | + | 0.956526i | \(0.594203\pi\) | |||||||
\(674\) | −7.13084 | −0.274670 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.90455 | 0.227098 | ||||||||
\(677\) | 24.6721 | 0.948225 | 0.474113 | − | 0.880464i | \(-0.342769\pi\) | ||||
0.474113 | + | 0.880464i | \(0.342769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.5939 | 0.982202 | ||||||||
\(680\) | −19.7893 | −0.758884 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.4057 | −0.436746 | ||||||||
\(683\) | −47.6165 | −1.82199 | −0.910997 | − | 0.412413i | \(-0.864686\pi\) | ||||
−0.910997 | + | 0.412413i | \(0.864686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.6068 | −0.863761 | ||||||||
\(686\) | 18.9422 | 0.723216 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.56055 | −0.135745 | ||||||||
\(689\) | 10.1667 | 0.387320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4242 | −0.700889 | −0.350444 | − | 0.936584i | \(-0.613969\pi\) | ||||
−0.350444 | + | 0.936584i | \(0.613969\pi\) | |||||||
\(692\) | 1.29626 | 0.0492763 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.4199 | −0.813090 | ||||||||
\(695\) | 68.1418 | 2.58477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.5899 | −0.779898 | ||||||||
\(698\) | 15.9563 | 0.603955 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −34.8646 | −1.31776 | ||||||||
\(701\) | −5.10936 | −0.192978 | −0.0964890 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964890 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.1046 | −0.795975 | ||||||||
\(704\) | −2.36140 | −0.0889986 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.7388 | −0.441794 | ||||||||
\(707\) | −33.2669 | −1.25113 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.6730 | 1.30217 | 0.651085 | − | 0.759005i | \(-0.274314\pi\) | ||||
0.651085 | + | 0.759005i | \(0.274314\pi\) | |||||||
\(710\) | −5.29121 | −0.198576 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.40888 | 0.0902767 | ||||||||
\(713\) | 33.1281 | 1.24066 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.1725 | 1.65196 | ||||||||
\(716\) | 5.70933 | 0.213368 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.1311 | −1.16180 | ||||||||
\(719\) | −48.0107 | −1.79050 | −0.895248 | − | 0.445567i | \(-0.853002\pi\) | ||||
−0.895248 | + | 0.445567i | \(0.853002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.5103 | −1.06178 | ||||||||
\(722\) | 3.81122 | 0.141839 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.9052 | 0.591112 | ||||||||
\(725\) | 130.888 | 4.86105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.3222 | 1.12459 | 0.562293 | − | 0.826938i | \(-0.309919\pi\) | ||||
0.562293 | + | 0.826938i | \(0.309919\pi\) | |||||||
\(728\) | 11.2208 | 0.415871 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 71.0207 | 2.62859 | ||||||||
\(731\) | 16.3775 | 0.605745 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.69123 | −0.173275 | −0.0866373 | − | 0.996240i | \(-0.527612\pi\) | ||||
−0.0866373 | + | 0.996240i | \(0.527612\pi\) | |||||||
\(734\) | −14.0585 | −0.518907 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.85875 | 0.252817 | ||||||||
\(737\) | 35.2372 | 1.29798 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8461 | 1.06112 | 0.530561 | − | 0.847647i | \(-0.321981\pi\) | ||||
0.530561 | + | 0.847647i | \(0.321981\pi\) | |||||||
\(740\) | −19.0109 | −0.698853 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.03444 | 0.221531 | ||||||||
\(743\) | −23.7767 | −0.872281 | −0.436141 | − | 0.899878i | \(-0.643655\pi\) | ||||
−0.436141 | + | 0.899878i | \(0.643655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.30228 | 0.157623 | ||||||||
\(746\) | 36.1993 | 1.32535 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.8618 | 0.397145 | ||||||||
\(749\) | −35.1410 | −1.28402 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8466 | −0.614743 | −0.307371 | − | 0.951590i | \(-0.599449\pi\) | ||||
−0.307371 | + | 0.951590i | \(0.599449\pi\) | |||||||
\(752\) | 6.92253 | 0.252439 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −42.1248 | −1.53409 | ||||||||
\(755\) | 29.2220 | 1.06350 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.2260 | 0.444362 | 0.222181 | − | 0.975005i | \(-0.428682\pi\) | ||||
0.222181 | + | 0.975005i | \(0.428682\pi\) | |||||||
\(758\) | 7.83323 | 0.284516 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.5482 | 0.745361 | ||||||||
\(761\) | −18.2371 | −0.661093 | −0.330546 | − | 0.943790i | \(-0.607233\pi\) | ||||
−0.330546 | + | 0.943790i | \(0.607233\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.8197 | 1.87600 | ||||||||
\(764\) | 1.86430 | 0.0674479 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.6388 | −1.03476 | ||||||||
\(767\) | −13.1312 | −0.474141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.5926 | −1.10320 | −0.551598 | − | 0.834110i | \(-0.685982\pi\) | ||||
−0.551598 | + | 0.834110i | \(0.685982\pi\) | |||||||
\(770\) | 26.2186 | 0.944852 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.9932 | −0.611599 | ||||||||
\(773\) | −37.6037 | −1.35251 | −0.676255 | − | 0.736667i | \(-0.736398\pi\) | ||||
−0.676255 | + | 0.736667i | \(0.736398\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65.2523 | 2.34393 | ||||||||
\(776\) | −9.91733 | −0.356012 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.8923 | −1.07169 | ||||||||
\(779\) | 21.3795 | 0.766000 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.90419 | 0.103920 | ||||||||
\(782\) | −31.5483 | −1.12816 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.339891 | −0.0121389 | ||||||||
\(785\) | −26.6663 | −0.951760 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.42552 | 0.0508145 | 0.0254072 | − | 0.999677i | \(-0.491912\pi\) | ||||
0.0254072 | + | 0.999677i | \(0.491912\pi\) | |||||||
\(788\) | 8.68393 | 0.309352 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.98441 | 0.141759 | ||||||||
\(791\) | 7.76277 | 0.276012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.23778 | 0.257021 | ||||||||
\(794\) | 5.71141 | 0.202691 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0290 | −0.390911 | ||||||||
\(797\) | 6.20525 | 0.219801 | 0.109901 | − | 0.993943i | \(-0.464947\pi\) | ||||
0.109901 | + | 0.993943i | \(0.464947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.8417 | −1.12648 | ||||||||
\(800\) | 13.5096 | 0.477638 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.176944 | 0.00624812 | ||||||||
\(803\) | −38.9812 | −1.37562 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −76.1526 | −2.68402 | ||||||||
\(806\) | −21.0008 | −0.739720 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.8905 | 0.453488 | ||||||||
\(809\) | −43.4131 | −1.52632 | −0.763161 | − | 0.646208i | \(-0.776354\pi\) | ||||
−0.763161 | + | 0.646208i | \(0.776354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.38440 | −0.329531 | −0.164765 | − | 0.986333i | \(-0.552687\pi\) | ||||
−0.164765 | + | 0.986333i | \(0.552687\pi\) | |||||||
\(812\) | −25.0032 | −0.877440 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.4345 | 0.365729 | ||||||||
\(815\) | 14.4353 | 0.505647 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.0056 | −0.594950 | ||||||||
\(818\) | 10.5360 | 0.368384 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.2585 | 0.672535 | ||||||||
\(821\) | −17.2247 | −0.601146 | −0.300573 | − | 0.953759i | \(-0.597178\pi\) | ||||
−0.300573 | + | 0.953759i | \(0.597178\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.3874 | −1.37296 | −0.686478 | − | 0.727150i | \(-0.740844\pi\) | ||||
−0.686478 | + | 0.727150i | \(0.740844\pi\) | |||||||
\(824\) | 11.0474 | 0.384856 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.79404 | −0.271189 | ||||||||
\(827\) | −10.1788 | −0.353953 | −0.176977 | − | 0.984215i | \(-0.556632\pi\) | ||||
−0.176977 | + | 0.984215i | \(0.556632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3518 | −0.394264 | −0.197132 | − | 0.980377i | \(-0.563163\pi\) | ||||
−0.197132 | + | 0.980377i | \(0.563163\pi\) | |||||||
\(830\) | 69.2852 | 2.40492 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.34794 | −0.150738 | ||||||||
\(833\) | 1.56340 | 0.0541686 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.6909 | −0.473794 | ||||||||
\(836\) | −11.2783 | −0.390068 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.42760 | −0.152949 | ||||||||
\(839\) | −2.73753 | −0.0945099 | −0.0472549 | − | 0.998883i | \(-0.515047\pi\) | ||||
−0.0472549 | + | 0.998883i | \(0.515047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.8662 | 2.23677 | ||||||||
\(842\) | 11.8257 | 0.407541 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.71092 | 0.127735 | ||||||||
\(845\) | 25.4031 | 0.873892 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.9973 | 0.480953 | ||||||||
\(848\) | −2.33828 | −0.0802968 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −62.1405 | −2.13140 | ||||||||
\(851\) | −30.3073 | −1.03892 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3394 | −0.525211 | −0.262605 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262605 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(854\) | 4.29598 | 0.147006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.6167 | 0.465411 | ||||||||
\(857\) | −9.87398 | −0.337289 | −0.168644 | − | 0.985677i | \(-0.553939\pi\) | ||||
−0.168644 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.1268 | −1.81266 | −0.906332 | − | 0.422566i | \(-0.861130\pi\) | ||||
−0.906332 | + | 0.422566i | \(0.861130\pi\) | |||||||
\(860\) | −15.3185 | −0.522357 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.9221 | 0.576369 | ||||||||
\(863\) | 2.81682 | 0.0958856 | 0.0479428 | − | 0.998850i | \(-0.484733\pi\) | ||||
0.0479428 | + | 0.998850i | \(0.484733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.57687 | 0.189619 | ||||||||
\(866\) | −20.7977 | −0.706735 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.4650 | −0.423090 | ||||||||
\(869\) | −2.18693 | −0.0741864 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.8806 | 2.19840 | ||||||||
\(872\) | −20.0796 | −0.679980 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.7581 | 1.10806 | ||||||||
\(875\) | −94.4825 | −3.19409 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.8402 | −0.771258 | −0.385629 | − | 0.922654i | \(-0.626016\pi\) | ||||
−0.385629 | + | 0.922654i | \(0.626016\pi\) | |||||||
\(878\) | 3.52842 | 0.119078 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.1594 | −0.342474 | ||||||||
\(881\) | 48.7811 | 1.64348 | 0.821738 | − | 0.569865i | \(-0.193005\pi\) | ||||
0.821738 | + | 0.569865i | \(0.193005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0519 | 1.14594 | 0.572969 | − | 0.819577i | \(-0.305792\pi\) | ||||
0.572969 | + | 0.819577i | \(0.305792\pi\) | |||||||
\(884\) | 19.9993 | 0.672648 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.0514 | 1.04319 | ||||||||
\(887\) | 18.7194 | 0.628535 | 0.314268 | − | 0.949334i | \(-0.398241\pi\) | ||||
0.314268 | + | 0.949334i | \(0.398241\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.9121 | −1.27153 | ||||||||
\(890\) | 10.3637 | 0.347392 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.31235 | 0.0774230 | ||||||||
\(893\) | 33.0628 | 1.10640 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.5631 | 0.821055 | ||||||||
\(896\) | −2.58072 | −0.0862158 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.2911 | 0.777235 | ||||||||
\(899\) | 46.7957 | 1.56072 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7554 | 0.358315 | ||||||||
\(902\) | −10.5704 | −0.351957 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00799 | −0.100044 | ||||||||
\(905\) | 68.4287 | 2.27465 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.9204 | 1.55796 | 0.778982 | − | 0.627046i | \(-0.215736\pi\) | ||||
0.778982 | + | 0.627046i | \(0.215736\pi\) | |||||||
\(908\) | 9.48105 | 0.314640 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 48.2751 | 1.60030 | ||||||||
\(911\) | −58.8767 | −1.95067 | −0.975337 | − | 0.220722i | \(-0.929159\pi\) | ||||
−0.975337 | + | 0.220722i | \(0.929159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.0286 | −1.25856 | ||||||||
\(914\) | −35.4856 | −1.17376 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.1183 | −0.565605 | ||||||||
\(917\) | 18.7634 | 0.619621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.8315 | 1.54483 | 0.772414 | − | 0.635120i | \(-0.219049\pi\) | ||||
0.772414 | + | 0.635120i | \(0.219049\pi\) | |||||||
\(920\) | 29.5083 | 0.972859 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.5348 | −0.379878 | ||||||||
\(923\) | 5.34736 | 0.176010 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.6962 | −1.96280 | ||||||||
\(926\) | −21.6842 | −0.712586 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.68846 | 0.318039 | ||||||||
\(929\) | −51.9419 | −1.70416 | −0.852080 | − | 0.523412i | \(-0.824659\pi\) | ||||
−0.852080 | + | 0.523412i | \(0.824659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.62335 | −0.0532033 | ||||||||
\(932\) | 1.89499 | 0.0620725 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.36171 | −0.0772774 | ||||||||
\(935\) | 46.7304 | 1.52825 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2778 | −0.597109 | −0.298555 | − | 0.954393i | \(-0.596505\pi\) | ||||
−0.298555 | + | 0.954393i | \(0.596505\pi\) | |||||||
\(938\) | 38.5099 | 1.25739 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.7827 | 0.971405 | ||||||||
\(941\) | 28.2186 | 0.919900 | 0.459950 | − | 0.887945i | \(-0.347867\pi\) | ||||
0.459950 | + | 0.887945i | \(0.347867\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.7021 | 0.999797 | ||||||||
\(944\) | 3.02010 | 0.0982960 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.40788 | 0.273364 | ||||||||
\(947\) | −24.9199 | −0.809788 | −0.404894 | − | 0.914364i | \(-0.632692\pi\) | ||||
−0.404894 | + | 0.914364i | \(0.632692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −71.7743 | −2.32989 | ||||||||
\(950\) | 64.5236 | 2.09342 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.8706 | 0.384727 | ||||||||
\(953\) | 26.5397 | 0.859705 | 0.429853 | − | 0.902899i | \(-0.358565\pi\) | ||||
0.429853 | + | 0.902899i | \(0.358565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.02073 | 0.259545 | ||||||||
\(956\) | −10.4414 | −0.337700 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.8556 | 0.964592 | ||||||||
\(959\) | 13.5606 | 0.437896 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.67062 | −0.247439 | ||||||||
\(962\) | 19.2126 | 0.619439 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.96284 | 0.320882 | ||||||||
\(965\) | −73.1096 | −2.35348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.13455 | −0.165116 | −0.0825580 | − | 0.996586i | \(-0.526309\pi\) | ||||
−0.0825580 | + | 0.996586i | \(0.526309\pi\) | |||||||
\(968\) | −5.42380 | −0.174327 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −42.6672 | −1.36996 | ||||||||
\(971\) | 43.7968 | 1.40551 | 0.702753 | − | 0.711434i | \(-0.251954\pi\) | ||||
0.702753 | + | 0.711434i | \(0.251954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.8748 | −1.31039 | ||||||||
\(974\) | −12.0354 | −0.385638 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.66465 | −0.0532840 | ||||||||
\(977\) | −24.0519 | −0.769488 | −0.384744 | − | 0.923023i | \(-0.625710\pi\) | ||||
−0.384744 | + | 0.923023i | \(0.625710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.68833 | −0.181800 | ||||||||
\(980\) | −1.46231 | −0.0467116 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.1930 | 1.15497 | ||||||||
\(983\) | 4.05611 | 0.129370 | 0.0646849 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646849 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.3607 | 1.19041 | ||||||||
\(986\) | −44.5641 | −1.41921 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.7662 | −0.660661 | ||||||||
\(989\) | −24.4209 | −0.776540 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.1610 | 0.545136 | 0.272568 | − | 0.962136i | \(-0.412127\pi\) | ||||
0.272568 | + | 0.962136i | \(0.412127\pi\) | |||||||
\(992\) | 4.83005 | 0.153354 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.17393 | 0.100671 | ||||||||
\(995\) | −47.4497 | −1.50426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.9829 | −1.32961 | −0.664806 | − | 0.747016i | \(-0.731486\pi\) | ||||
−0.664806 | + | 0.747016i | \(0.731486\pi\) | |||||||
\(998\) | 16.7640 | 0.530656 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.r.1.14 | yes | 14 | |
3.2 | odd | 2 | 8046.2.a.q.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.q.1.1 | ✓ | 14 | 3.2 | odd | 2 | ||
8046.2.a.r.1.14 | yes | 14 | 1.1 | even | 1 | trivial |