Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
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: | \( x^{8} - 2x^{7} - 8x^{6} + 15x^{5} + 19x^{4} - 31x^{3} - 13x^{2} + 14x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 501) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.63639\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.62511 | −1.62120 | −0.810598 | − | 0.585603i | \(-0.800858\pi\) | ||||
−0.810598 | + | 0.585603i | \(0.800858\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70865 | 0.645810 | 0.322905 | − | 0.946431i | \(-0.395340\pi\) | ||||
0.322905 | + | 0.946431i | \(0.395340\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.73929 | 1.12744 | 0.563720 | − | 0.825966i | \(-0.309370\pi\) | ||||
0.563720 | + | 0.825966i | \(0.309370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.28262 | −1.46514 | −0.732568 | − | 0.680694i | \(-0.761678\pi\) | ||||
−0.732568 | + | 0.680694i | \(0.761678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.62511 | −0.935998 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.55148 | −0.618825 | −0.309413 | − | 0.950928i | \(-0.600132\pi\) | ||||
−0.309413 | + | 0.950928i | \(0.600132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.63986 | −1.75271 | −0.876353 | − | 0.481670i | \(-0.840030\pi\) | ||||
−0.876353 | + | 0.481670i | \(0.840030\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.70865 | 0.372859 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.71726 | 1.40064 | 0.700322 | − | 0.713827i | \(-0.253040\pi\) | ||||
0.700322 | + | 0.713827i | \(0.253040\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.14139 | 1.62828 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.10123 | 0.390189 | 0.195095 | − | 0.980784i | \(-0.437499\pi\) | ||||
0.195095 | + | 0.980784i | \(0.437499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.01919 | 1.44029 | 0.720145 | − | 0.693824i | \(-0.244075\pi\) | ||||
0.720145 | + | 0.693824i | \(0.244075\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.73929 | 0.650928 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.19405 | −1.04699 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.23604 | 0.860799 | 0.430400 | − | 0.902638i | \(-0.358373\pi\) | ||||
0.430400 | + | 0.902638i | \(0.358373\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.28262 | −0.845896 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.40689 | 0.844414 | 0.422207 | − | 0.906499i | \(-0.361256\pi\) | ||||
0.422207 | + | 0.906499i | \(0.361256\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.04679 | −0.922127 | −0.461063 | − | 0.887367i | \(-0.652532\pi\) | ||||
−0.461063 | + | 0.887367i | \(0.652532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.62511 | −0.540399 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.03434 | −0.588469 | −0.294235 | − | 0.955733i | \(-0.595065\pi\) | ||||
−0.294235 | + | 0.955733i | \(0.595065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.08050 | −0.582929 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.55148 | −0.357279 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.29196 | −0.452186 | −0.226093 | − | 0.974106i | \(-0.572595\pi\) | ||||
−0.226093 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.5553 | −1.82780 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.63986 | −1.01192 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8952 | −1.67881 | −0.839403 | − | 0.543510i | \(-0.817095\pi\) | ||||
−0.839403 | + | 0.543510i | \(0.817095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2877 | 1.44524 | 0.722620 | − | 0.691245i | \(-0.242938\pi\) | ||||
0.722620 | + | 0.691245i | \(0.242938\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.70865 | 0.215270 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.1501 | 2.37527 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.08146 | 0.742969 | 0.371485 | − | 0.928439i | \(-0.378849\pi\) | ||||
0.371485 | + | 0.928439i | \(0.378849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.71726 | 0.808663 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.88309 | −0.579517 | −0.289758 | − | 0.957100i | \(-0.593575\pi\) | ||||
−0.289758 | + | 0.957100i | \(0.593575\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.70680 | −0.433848 | −0.216924 | − | 0.976188i | \(-0.569602\pi\) | ||||
−0.216924 | + | 0.976188i | \(0.569602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.14139 | 0.940087 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.38916 | 0.728112 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7416 | 1.32103 | 0.660515 | − | 0.750813i | \(-0.270338\pi\) | ||||
0.660515 | + | 0.750813i | \(0.270338\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6696 | −1.71996 | −0.859981 | − | 0.510326i | \(-0.829525\pi\) | ||||
−0.859981 | + | 0.510326i | \(0.829525\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.24939 | 1.00324 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.10123 | 0.225276 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.46878 | 0.261690 | 0.130845 | − | 0.991403i | \(-0.458231\pi\) | ||||
0.130845 | + | 0.991403i | \(0.458231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.02617 | −0.946200 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.01919 | 0.831551 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27.6953 | 2.84148 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.76227 | −0.483536 | −0.241768 | − | 0.970334i | \(-0.577727\pi\) | ||||
−0.241768 | + | 0.970334i | \(0.577727\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.73929 | 0.375813 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9847 | −1.49104 | −0.745518 | − | 0.666485i | \(-0.767798\pi\) | ||||
−0.745518 | + | 0.666485i | \(0.767798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.40203 | −0.236679 | −0.118340 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118340 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.19405 | −0.604477 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.24916 | 0.410782 | 0.205391 | − | 0.978680i | \(-0.434153\pi\) | ||||
0.205391 | + | 0.978680i | \(0.434153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.5656 | −1.49091 | −0.745457 | − | 0.666554i | \(-0.767769\pi\) | ||||
−0.745457 | + | 0.666554i | \(0.767769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.23604 | 0.496983 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.57378 | −0.806553 | −0.403276 | − | 0.915078i | \(-0.632129\pi\) | ||||
−0.403276 | + | 0.915078i | \(0.632129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.3508 | −2.27072 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.28262 | −0.488379 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.35960 | −0.399644 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.98232 | 0.271120 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.40689 | 0.487523 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3879 | −1.01856 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6163 | 1.82940 | 0.914702 | − | 0.404129i | \(-0.132425\pi\) | ||||
0.914702 | + | 0.404129i | \(0.132425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.04679 | −0.532390 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00607 | −0.262642 | −0.131321 | − | 0.991340i | \(-0.541922\pi\) | ||||
−0.131321 | + | 0.991340i | \(0.541922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.0539 | −1.13192 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.62511 | −0.311999 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.9358 | −1.27605 | −0.638025 | − | 0.770016i | \(-0.720248\pi\) | ||||
−0.638025 | + | 0.770016i | \(0.720248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9035 | −1.60338 | −0.801689 | − | 0.597742i | \(-0.796065\pi\) | ||||
−0.801689 | + | 0.597742i | \(0.796065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.03434 | −0.339753 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.7533 | −1.65185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.61719 | −0.632573 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.08050 | −0.336554 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.964909 | −0.0790484 | −0.0395242 | − | 0.999219i | \(-0.512584\pi\) | ||||
−0.0395242 | + | 0.999219i | \(0.512584\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9141 | −1.53921 | −0.769605 | − | 0.638520i | \(-0.779547\pi\) | ||||
−0.769605 | + | 0.638520i | \(0.779547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.55148 | −0.206275 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29.0704 | −2.33499 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.36667 | 0.268690 | 0.134345 | − | 0.990935i | \(-0.457107\pi\) | ||||
0.134345 | + | 0.990935i | \(0.457107\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.29196 | −0.261070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4775 | 0.904551 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.681465 | 0.0533765 | 0.0266882 | − | 0.999644i | \(-0.491504\pi\) | ||||
0.0266882 | + | 0.999644i | \(0.491504\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.5553 | −1.05528 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.9061 | 1.14662 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.63986 | −0.584235 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.04156 | 0.383303 | 0.191651 | − | 0.981463i | \(-0.438616\pi\) | ||||
0.191651 | + | 0.981463i | \(0.438616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.9108 | 1.05156 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.8952 | −0.969259 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.14897 | 0.683826 | 0.341913 | − | 0.939732i | \(-0.388925\pi\) | ||||
0.341913 | + | 0.939732i | \(0.388925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2259 | 0.908748 | 0.454374 | − | 0.890811i | \(-0.349863\pi\) | ||||
0.454374 | + | 0.890811i | \(0.349863\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2877 | 0.834410 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.9812 | −1.39552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.54074 | −0.697688 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.70865 | 0.124286 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6142 | −1.20216 | −0.601080 | − | 0.799189i | \(-0.705263\pi\) | ||||
−0.601080 | + | 0.799189i | \(0.705263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.78696 | 0.560518 | 0.280259 | − | 0.959924i | \(-0.409580\pi\) | ||||
0.280259 | + | 0.959924i | \(0.409580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19.1501 | 1.37136 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.7525 | 0.837328 | 0.418664 | − | 0.908141i | \(-0.362499\pi\) | ||||
0.418664 | + | 0.908141i | \(0.362499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.51873 | 0.462101 | 0.231050 | − | 0.972942i | \(-0.425784\pi\) | ||||
0.231050 | + | 0.972942i | \(0.425784\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.08146 | 0.428953 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.59028 | 0.251988 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.6005 | −1.36896 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.71726 | 0.466882 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −28.5677 | −1.97607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2143 | 0.909711 | 0.454856 | − | 0.890565i | \(-0.349691\pi\) | ||||
0.454856 | + | 0.890565i | \(0.349691\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.88309 | −0.334584 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.9202 | 1.49495 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.7020 | 0.930154 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.70680 | −0.250482 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4785 | 0.906663 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.9483 | −1.06797 | −0.533987 | − | 0.845493i | \(-0.679307\pi\) | ||||
−0.533987 | + | 0.845493i | \(0.679307\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.14139 | 0.542759 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.27727 | 0.0847754 | 0.0423877 | − | 0.999101i | \(-0.486504\pi\) | ||||
0.0423877 | + | 0.999101i | \(0.486504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.75137 | 0.181816 | 0.0909078 | − | 0.995859i | \(-0.471023\pi\) | ||||
0.0909078 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.38916 | 0.420376 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.73207 | −0.178984 | −0.0894921 | − | 0.995988i | \(-0.528524\pi\) | ||||
−0.0894921 | + | 0.995988i | \(0.528524\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.6249 | 0.954025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.7416 | 0.762697 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.1609 | −1.75689 | −0.878445 | − | 0.477843i | \(-0.841419\pi\) | ||||
−0.878445 | + | 0.477843i | \(0.841419\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.73684 | −0.627205 | −0.313603 | − | 0.949554i | \(-0.601536\pi\) | ||||
−0.313603 | + | 0.949554i | \(0.601536\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.7923 | 0.945042 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.3585 | 2.56795 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.6696 | −0.993020 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.8215 | −1.18800 | −0.594001 | − | 0.804464i | \(-0.702452\pi\) | ||||
−0.594001 | + | 0.804464i | \(0.702452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.1178 | 1.57914 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.24939 | 0.579219 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.66522 | 0.166252 | 0.0831259 | − | 0.996539i | \(-0.473510\pi\) | ||||
0.0831259 | + | 0.996539i | \(0.473510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.94658 | 0.555913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.10123 | 0.130063 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.38514 | −0.578712 | −0.289356 | − | 0.957221i | \(-0.593441\pi\) | ||||
−0.289356 | + | 0.957221i | \(0.593441\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.9337 | 0.733082 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.46878 | 0.151087 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2658 | 0.686890 | 0.343445 | − | 0.939173i | \(-0.388406\pi\) | ||||
0.343445 | + | 0.939173i | \(0.388406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4755 | 1.18305 | 0.591527 | − | 0.806285i | \(-0.298525\pi\) | ||||
0.591527 | + | 0.806285i | \(0.298525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.02617 | −0.546289 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.4430 | 1.83578 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.75098 | 0.465711 | 0.232856 | − | 0.972511i | \(-0.425193\pi\) | ||||
0.232856 | + | 0.972511i | \(0.425193\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.01919 | 0.480096 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.9976 | −1.19295 | −0.596477 | − | 0.802630i | \(-0.703433\pi\) | ||||
−0.596477 | + | 0.802630i | \(0.703433\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.99842 | −0.118793 | −0.0593967 | − | 0.998234i | \(-0.518918\pi\) | ||||
−0.0593967 | + | 0.998234i | \(0.518918\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 27.6953 | 1.64053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.23850 | 0.545331 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4899 | −0.617055 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.76227 | −0.279169 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1462 | −0.768008 | −0.384004 | − | 0.923331i | \(-0.625455\pi\) | ||||
−0.384004 | + | 0.923331i | \(0.625455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 46.7463 | 2.72167 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.73929 | 0.216976 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.4847 | −2.05213 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3319 | −0.595519 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.9847 | −0.860851 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.9191 | −2.34302 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0378 | −1.08654 | −0.543272 | − | 0.839557i | \(-0.682815\pi\) | ||||
−0.543272 | + | 0.839557i | \(0.682815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.40203 | −0.136647 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.31774 | −0.414951 | −0.207475 | − | 0.978240i | \(-0.566525\pi\) | ||||
−0.207475 | + | 0.978240i | \(0.566525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.5818 | −1.21987 | −0.609937 | − | 0.792450i | \(-0.708805\pi\) | ||||
−0.609937 | + | 0.792450i | \(0.708805\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.19405 | −0.348995 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.2702 | −1.08232 | −0.541162 | − | 0.840918i | \(-0.682016\pi\) | ||||
−0.541162 | + | 0.840918i | \(0.682016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.85713 | 0.439915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.24916 | 0.237165 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4930 | 1.08462 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −43.0079 | −2.38565 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5656 | −0.860780 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.89330 | −0.380040 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.0258 | −1.48547 | −0.742737 | − | 0.669583i | \(-0.766473\pi\) | ||||
−0.742737 | + | 0.669583i | \(0.766473\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.23604 | 0.286933 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.0459 | −1.20450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0867 | 1.47550 | 0.737752 | − | 0.675072i | \(-0.235887\pi\) | ||||
0.737752 | + | 0.675072i | \(0.235887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.57378 | −0.465664 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.9861 | 1.62384 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.9327 | −1.02227 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.3508 | −1.31100 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.04990 | −0.0563618 | −0.0281809 | − | 0.999603i | \(-0.508971\pi\) | ||||
−0.0281809 | + | 0.999603i | \(0.508971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.79660 | −0.256756 | −0.128378 | − | 0.991725i | \(-0.540977\pi\) | ||||
−0.128378 | + | 0.991725i | \(0.540977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.28262 | −0.281965 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.1349 | −0.539425 | −0.269713 | − | 0.962941i | \(-0.586929\pi\) | ||||
−0.269713 | + | 0.962941i | \(0.586929\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7017 | 0.939510 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.35960 | −0.230734 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.68943 | 0.353055 | 0.176527 | − | 0.984296i | \(-0.443514\pi\) | ||||
0.176527 | + | 0.984296i | \(0.443514\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.3675 | 2.07197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.98232 | 0.156531 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4375 | 0.703353 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.32088 | 0.277748 | 0.138874 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138874 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.40689 | 0.281471 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.62483 | −0.292026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.9039 | −1.13414 | −0.567071 | − | 0.823669i | \(-0.691924\pi\) | ||||
−0.567071 | + | 0.823669i | \(0.691924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.3879 | −0.588067 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.1000 | −0.571680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1233 | −0.982300 | −0.491150 | − | 0.871075i | \(-0.663423\pi\) | ||||
−0.491150 | + | 0.871075i | \(0.663423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.6163 | 1.05621 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.4789 | −1.60850 | −0.804248 | − | 0.594293i | \(-0.797432\pi\) | ||||
−0.804248 | + | 0.594293i | \(0.797432\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.1614 | −1.18041 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.04679 | −0.307376 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.5326 | −1.75087 | −0.875435 | − | 0.483335i | \(-0.839425\pi\) | ||||
−0.875435 | + | 0.483335i | \(0.839425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.1390 | −0.866755 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00607 | −0.151636 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.5644 | −2.14165 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.0959 | 1.51047 | 0.755234 | − | 0.655455i | \(-0.227523\pi\) | ||||
0.755234 | + | 0.655455i | \(0.227523\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.0539 | −0.653512 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9203 | 0.695146 | 0.347573 | − | 0.937653i | \(-0.387006\pi\) | ||||
0.347573 | + | 0.937653i | \(0.387006\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.3624 | −2.11022 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.62511 | −0.180133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.5791 | 0.970499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.684344 | −0.0338386 | −0.0169193 | − | 0.999857i | \(-0.505386\pi\) | ||||
−0.0169193 | + | 0.999857i | \(0.505386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.9358 | −0.736728 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.0333 | −1.08419 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 56.8039 | 2.78840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.9035 | −0.925710 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0874 | −0.590508 | −0.295254 | − | 0.955419i | \(-0.595404\pi\) | ||||
−0.295254 | + | 0.955419i | \(0.595404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.7142 | 1.25324 | 0.626618 | − | 0.779327i | \(-0.284439\pi\) | ||||
0.626618 | + | 0.779327i | \(0.284439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.03434 | −0.196156 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.7726 | −1.00762 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.2868 | 0.933351 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.7533 | −0.953697 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2017 | −1.21392 | −0.606961 | − | 0.794731i | \(-0.707612\pi\) | ||||
−0.606961 | + | 0.794731i | \(0.707612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.89916 | 0.331553 | 0.165776 | − | 0.986163i | \(-0.446987\pi\) | ||||
0.165776 | + | 0.986163i | \(0.446987\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.61719 | −0.365216 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −51.3189 | −2.45492 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.6783 | 1.89374 | 0.946871 | − | 0.321615i | \(-0.104226\pi\) | ||||
0.946871 | + | 0.321615i | \(0.104226\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.08050 | −0.194310 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.33342 | 0.443444 | 0.221722 | − | 0.975110i | \(-0.428832\pi\) | ||||
0.221722 | + | 0.975110i | \(0.428832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.94958 | −0.424251 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.964909 | −0.0456386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2858 | −0.579805 | −0.289902 | − | 0.957056i | \(-0.593623\pi\) | ||||
−0.289902 | + | 0.957056i | \(0.593623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.2179 | 0.952026 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.9141 | −0.888664 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.7208 | 1.53398 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.3360 | 1.32550 | 0.662751 | − | 0.748840i | \(-0.269389\pi\) | ||||
0.662751 | + | 0.748840i | \(0.269389\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.55148 | −0.119093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.1768 | −1.12603 | −0.563014 | − | 0.826447i | \(-0.690358\pi\) | ||||
−0.563014 | + | 0.826447i | \(0.690358\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.08154 | −0.143211 | −0.0716057 | − | 0.997433i | \(-0.522812\pi\) | ||||
−0.0716057 | + | 0.997433i | \(0.522812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −29.0704 | −1.34811 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.43216 | 0.343919 | 0.171960 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171960 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3911 | 0.479817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.36667 | 0.155128 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.6107 | −1.03964 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −62.1991 | −2.85389 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.29196 | −0.150729 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6251 | 0.759619 | 0.379810 | − | 0.925065i | \(-0.375989\pi\) | ||||
0.379810 | + | 0.925065i | \(0.375989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.6600 | −1.26119 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.4775 | 0.522243 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.2637 | 0.783906 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.5765 | −1.38555 | −0.692777 | − | 0.721152i | \(-0.743613\pi\) | ||||
−0.692777 | + | 0.721152i | \(0.743613\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.681465 | 0.0308169 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.79196 | 0.216258 | 0.108129 | − | 0.994137i | \(-0.465514\pi\) | ||||
0.108129 | + | 0.994137i | \(0.465514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.36126 | −0.241459 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.5553 | −0.609267 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.34352 | −0.374258 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.15628 | 0.141294 | 0.0706472 | − | 0.997501i | \(-0.477494\pi\) | ||||
0.0706472 | + | 0.997501i | \(0.477494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.0941 | −1.34183 | −0.670916 | − | 0.741534i | \(-0.734099\pi\) | ||||
−0.670916 | + | 0.741534i | \(0.734099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.3212 | 2.41726 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.9061 | 0.662003 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8120 | −0.878152 | −0.439076 | − | 0.898450i | \(-0.644694\pi\) | ||||
−0.439076 | + | 0.898450i | \(0.644694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.33364 | −0.280184 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.63986 | −0.337308 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.70761 | 0.383703 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0856 | −0.663464 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.04156 | 0.221300 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.3463 | −0.847579 | −0.423789 | − | 0.905761i | \(-0.639300\pi\) | ||||
−0.423789 | + | 0.905761i | \(0.639300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9423 | −1.26556 | −0.632778 | − | 0.774333i | \(-0.718086\pi\) | ||||
−0.632778 | + | 0.774333i | \(0.718086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.9108 | 0.607118 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.4608 | −0.891287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1215 | 0.961806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8952 | −0.559602 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.5625 | −1.23718 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4037 | −0.665959 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.14897 | 0.394807 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.2582 | −0.657217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.6947 | −1.27667 | −0.638336 | − | 0.769757i | \(-0.720377\pi\) | ||||
−0.638336 | + | 0.769757i | \(0.720377\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.2259 | 0.524666 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 56.4269 | 2.41706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.38735 | 0.144833 | 0.0724163 | − | 0.997374i | \(-0.476929\pi\) | ||||
0.0724163 | + | 0.997374i | \(0.476929\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.2877 | 0.481747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.0531 | −0.683887 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0623 | 0.853135 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.9812 | −0.805707 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.24723 | 0.222332 | 0.111166 | − | 0.993802i | \(-0.464541\pi\) | ||||
0.111166 | + | 0.993802i | \(0.464541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.9429 | 1.35104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.54074 | −0.402810 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.1413 | −0.553840 | −0.276920 | − | 0.960893i | \(-0.589314\pi\) | ||||
−0.276920 | + | 0.960893i | \(0.589314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.0808 | 1.30758 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.70865 | 0.0717567 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.1300 | 1.13735 | 0.568675 | − | 0.822562i | \(-0.307456\pi\) | ||||
0.568675 | + | 0.822562i | \(0.307456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.07458 | 0.337911 | 0.168955 | − | 0.985624i | \(-0.445961\pi\) | ||||
0.168955 | + | 0.985624i | \(0.445961\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.6142 | −0.694068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 54.6878 | 2.28064 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.7649 | 0.697931 | 0.348965 | − | 0.937136i | \(-0.386533\pi\) | ||||
0.348965 | + | 0.937136i | \(0.386533\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.78696 | 0.323615 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.7739 | −1.11077 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.3096 | −0.509812 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.1501 | 0.791758 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.1028 | 1.49012 | 0.745061 | − | 0.666996i | \(-0.232420\pi\) | ||||
0.745061 | + | 0.666996i | \(0.232420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −61.2655 | −2.52440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.7525 | 0.483431 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.6934 | 1.17830 | 0.589148 | − | 0.808025i | \(-0.299463\pi\) | ||||
0.589148 | + | 0.808025i | \(0.299463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.8040 | 0.647901 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.51873 | 0.266794 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.2332 | −0.990141 | −0.495071 | − | 0.868853i | \(-0.664858\pi\) | ||||
−0.495071 | + | 0.868853i | \(0.664858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.5123 | −1.20383 | −0.601917 | − | 0.798559i | \(-0.705596\pi\) | ||||
−0.601917 | + | 0.798559i | \(0.705596\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.08146 | 0.247656 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8112 | −0.439539 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.1543 | −1.30510 | −0.652552 | − | 0.757744i | \(-0.726302\pi\) | ||||
−0.652552 | + | 0.757744i | \(0.726302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.59028 | 0.145486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.3119 | 0.862188 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7926 | 0.637857 | 0.318928 | − | 0.947779i | \(-0.396677\pi\) | ||||
0.318928 | + | 0.947779i | \(0.396677\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.6005 | −0.790370 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.6167 | −0.709220 | −0.354610 | − | 0.935014i | \(-0.615386\pi\) | ||||
−0.354610 | + | 0.935014i | \(0.615386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.58374 | 0.103849 | 0.0519246 | − | 0.998651i | \(-0.483464\pi\) | ||||
0.0519246 | + | 0.998651i | \(0.483464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.71726 | 0.269554 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.21829 | 0.169002 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.575264 | 0.0230105 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.5677 | −1.14088 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.3597 | −0.532684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0988 | −0.800120 | −0.400060 | − | 0.916489i | \(-0.631011\pi\) | ||||
−0.400060 | + | 0.916489i | \(0.631011\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.2143 | 0.525222 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −74.7364 | −2.96582 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.5558 | 0.854070 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.88309 | −0.193172 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.2904 | −1.39389 | −0.696943 | − | 0.717126i | \(-0.745457\pi\) | ||||
−0.696943 | + | 0.717126i | \(0.745457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.1897 | −0.480715 | −0.240357 | − | 0.970684i | \(-0.577265\pi\) | ||||
−0.240357 | + | 0.970684i | \(0.577265\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.9202 | 0.863109 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.13850 | −0.359272 | −0.179636 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179636 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.2188 | −1.89275 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.7020 | 0.537025 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3695 | 0.405792 | 0.202896 | − | 0.979200i | \(-0.434965\pi\) | ||||
0.202896 | + | 0.979200i | \(0.434965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8973 | 0.425794 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.70680 | −0.144616 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.5378 | 1.61808 | 0.809042 | − | 0.587751i | \(-0.199987\pi\) | ||||
0.809042 | + | 0.587751i | \(0.199987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.3751 | 1.76489 | 0.882443 | − | 0.470419i | \(-0.155897\pi\) | ||||
0.882443 | + | 0.470419i | \(0.155897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.4785 | 0.523462 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 47.3217 | 1.83506 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1145 | 0.546517 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.9483 | −0.616595 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.2080 | 1.62942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.658734 | −0.0253923 | −0.0126962 | − | 0.999919i | \(-0.504041\pi\) | ||||
−0.0126962 | + | 0.999919i | \(0.504041\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.14139 | 0.313362 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.87746 | 0.0721566 | 0.0360783 | − | 0.999349i | \(-0.488513\pi\) | ||||
0.0360783 | + | 0.999349i | \(0.488513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.13708 | −0.312272 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.27727 | 0.0489451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0783 | 1.49529 | 0.747644 | − | 0.664099i | \(-0.231185\pi\) | ||||
0.747644 | + | 0.664099i | \(0.231185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54.1438 | 2.06873 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.75137 | 0.104971 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.3902 | 0.662514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.5443 | −0.705458 | −0.352729 | − | 0.935725i | \(-0.614746\pi\) | ||||
−0.352729 | + | 0.935725i | \(0.614746\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.38916 | 0.242704 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 68.5273 | 2.59939 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.7956 | −0.522545 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.73207 | −0.103337 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.92644 | 0.299378 | 0.149689 | − | 0.988733i | \(-0.452173\pi\) | ||||
0.149689 | + | 0.988733i | \(0.452173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.0026 | −1.50873 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.6249 | 0.550806 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.6037 | −0.962927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.5390 | −1.82292 | −0.911461 | − | 0.411387i | \(-0.865044\pi\) | ||||
−0.911461 | + | 0.411387i | \(0.865044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.7416 | 0.440343 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 53.8670 | 2.01733 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 71.6077 | 2.67798 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.1609 | −1.01434 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.98110 | 0.223057 | 0.111529 | − | 0.993761i | \(-0.464425\pi\) | ||||
0.111529 | + | 0.993761i | \(0.464425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.10424 | −0.152850 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.73684 | −0.362117 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.1070 | 0.635336 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.978393 | −0.0362866 | −0.0181433 | − | 0.999835i | \(-0.505776\pi\) | ||||
−0.0181433 | + | 0.999835i | \(0.505776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4283 | 0.570635 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.7386 | 1.80020 | 0.900101 | − | 0.435681i | \(-0.143492\pi\) | ||||
0.900101 | + | 0.435681i | \(0.143492\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.7923 | 0.545620 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.7404 | 0.837653 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.8810 | −0.694549 | −0.347275 | − | 0.937763i | \(-0.612893\pi\) | ||||
−0.347275 | + | 0.937763i | \(0.612893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.3585 | 1.48261 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.54298 | 0.350098 | 0.175049 | − | 0.984560i | \(-0.443992\pi\) | ||||
0.175049 | + | 0.984560i | \(0.443992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.49790 | 0.128153 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.6696 | −0.573321 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.26035 | 0.265287 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7014 | −1.41223 | −0.706117 | − | 0.708096i | \(-0.749555\pi\) | ||||
−0.706117 | + | 0.708096i | \(0.749555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.8215 | −0.685893 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 68.5657 | 2.49536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.4031 | 1.83193 | 0.915965 | − | 0.401257i | \(-0.131427\pi\) | ||||
0.915965 | + | 0.401257i | \(0.131427\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.1178 | 0.911718 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1763 | 0.840141 | 0.420070 | − | 0.907492i | \(-0.362005\pi\) | ||||
0.420070 | + | 0.907492i | \(0.362005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.5962 | −0.962848 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.24939 | 0.334412 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 68.1202 | 2.45968 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0045 | 0.973808 | 0.486904 | − | 0.873455i | \(-0.338126\pi\) | ||||
0.486904 | + | 0.873455i | \(0.338126\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.66522 | 0.0959855 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.4965 | 1.52849 | 0.764246 | − | 0.644925i | \(-0.223112\pi\) | ||||
0.764246 | + | 0.644925i | \(0.223112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65.2873 | 2.34519 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.94658 | 0.320957 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.3079 | −1.48001 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2593 | −0.653370 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.10123 | 0.0750920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.2046 | −0.435599 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.2673 | 1.61361 | 0.806803 | − | 0.590821i | \(-0.201196\pi\) | ||||
0.806803 | + | 0.590821i | \(0.201196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.38514 | −0.334120 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6496 | −0.520880 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −59.6286 | −2.11747 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.9337 | 0.423245 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.7500 | −0.380783 | −0.190392 | − | 0.981708i | \(-0.560976\pi\) | ||||
−0.190392 | + | 0.981708i | \(0.560976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2936 | 0.364160 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.46878 | 0.0872300 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.8608 | −0.489137 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.6070 | −1.46645 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.2658 | 0.396576 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.5809 | 0.758743 | 0.379371 | − | 0.925244i | \(-0.376140\pi\) | ||||
0.379371 | + | 0.925244i | \(0.376140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3625 | 0.995943 | 0.497972 | − | 0.867193i | \(-0.334078\pi\) | ||||
0.497972 | + | 0.867193i | \(0.334078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.4755 | 0.683037 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.47038 | −0.0865338 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.1966 | 1.61622 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.02617 | −0.315400 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.3162 | −0.709039 | −0.354519 | − | 0.935049i | \(-0.615356\pi\) | ||||
−0.354519 | + | 0.935049i | \(0.615356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.9449 | −0.520948 | −0.260474 | − | 0.965481i | \(-0.583879\pi\) | ||||
−0.260474 | + | 0.965481i | \(0.583879\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.4430 | 1.05989 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.9501 | −0.693734 | −0.346867 | − | 0.937914i | \(-0.612754\pi\) | ||||
−0.346867 | + | 0.937914i | \(0.612754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.0430 | −1.80753 | −0.903765 | − | 0.428029i | \(-0.859208\pi\) | ||||
−0.903765 | + | 0.428029i | \(0.859208\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.75098 | 0.268878 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.4113 | 0.360731 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.62511 | 0.125452 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.01919 | 0.277184 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.3093 | −0.563058 | −0.281529 | − | 0.959553i | \(-0.590842\pi\) | ||||
−0.281529 | + | 0.959553i | \(0.590842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5848 | −0.847752 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.9976 | −0.688753 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −54.0362 | −1.85890 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.09575 | 0.175092 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.99842 | −0.0685855 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.1718 | 1.20567 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.499221 | −0.0170930 | −0.00854649 | − | 0.999963i | \(-0.502720\pi\) | ||||
−0.00854649 | + | 0.999963i | \(0.502720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 27.6953 | 0.947160 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5417 | 0.667531 | 0.333765 | − | 0.942656i | \(-0.391681\pi\) | ||||
0.333765 | + | 0.942656i | \(0.391681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.17233 | −0.176478 | −0.0882389 | − | 0.996099i | \(-0.528124\pi\) | ||||
−0.0882389 | + | 0.996099i | \(0.528124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.23850 | 0.314847 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.4457 | −1.75123 | −0.875615 | − | 0.483009i | \(-0.839544\pi\) | ||||
−0.875615 | + | 0.483009i | \(0.839544\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.2762 | −0.621409 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.4899 | −0.356257 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.9052 | 1.48938 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.1261 | −1.08855 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.76227 | −0.161179 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.4579 | −0.657798 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.5013 | −0.827350 | −0.413675 | − | 0.910425i | \(-0.635755\pi\) | ||||
−0.413675 | + | 0.910425i | \(0.635755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.1462 | −0.443409 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.3995 | −0.485132 | −0.242566 | − | 0.970135i | \(-0.577989\pi\) | ||||
−0.242566 | + | 0.970135i | \(0.577989\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.38774 | −0.181312 | −0.0906559 | − | 0.995882i | \(-0.528896\pi\) | ||||
−0.0906559 | + | 0.995882i | \(0.528896\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.7463 | 1.57136 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.97543 | −0.267789 | −0.133894 | − | 0.990996i | \(-0.542748\pi\) | ||||
−0.133894 | + | 0.990996i | \(0.542748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.2262 | 1.18145 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.73929 | 0.125271 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.8218 | 1.03141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.1660 | −1.10862 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35.4847 | −1.18480 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.8502 | 0.561985 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.39939 | 0.279824 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.3319 | −0.343823 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.3204 | −1.47326 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.9048 | −1.59065 | −0.795326 | − | 0.606182i | \(-0.792700\pi\) | ||||
−0.795326 | + | 0.606182i | \(0.792700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.9847 | −0.497012 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.3844 | −1.10607 | −0.553037 | − | 0.833157i | \(-0.686531\pi\) | ||||
−0.553037 | + | 0.833157i | \(0.686531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.5932 | −1.93915 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −40.9191 | −1.35274 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.13634 | −0.169617 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.31358 | 0.142292 | 0.0711459 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711459 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.0378 | −0.627317 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.7955 | 0.849070 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.6286 | 1.40162 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.40203 | −0.0788930 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.8838 | 1.30854 | 0.654272 | − | 0.756259i | \(-0.272975\pi\) | ||||
0.654272 | + | 0.756259i | \(0.272975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.1745 | 1.02170 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.31774 | −0.239572 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.5862 | 1.13109 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.4960 | −0.800250 | −0.400125 | − | 0.916461i | \(-0.631033\pi\) | ||||
−0.400125 | + | 0.916461i | \(0.631033\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.5818 | −0.704294 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.5676 | 0.670486 | 0.335243 | − | 0.942132i | \(-0.391182\pi\) | ||||
0.335243 | + | 0.942132i | \(0.391182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.3195 | 1.18272 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.19405 | −0.201492 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.7521 | −0.349395 | −0.174697 | − | 0.984622i | \(-0.555895\pi\) | ||||
−0.174697 | + | 0.984622i | \(0.555895\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5816 | 0.635646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.2702 | −0.624880 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.8772 | 1.06500 | 0.532499 | − | 0.846431i | \(-0.321253\pi\) | ||||
0.532499 | + | 0.846431i | \(0.321253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.2282 | 1.94894 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.85713 | 0.253985 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.5201 | −0.824086 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.3074 | 1.07443 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.24916 | 0.136927 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.2286 | −0.908710 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0286 | 1.60881 | 0.804405 | − | 0.594081i | \(-0.202484\pi\) | ||||
0.804405 | + | 0.594081i | \(0.202484\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.4930 | 0.626205 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.37248 | −0.204503 | −0.102251 | − | 0.994759i | \(-0.532605\pi\) | ||||
−0.102251 | + | 0.994759i | \(0.532605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.2996 | −1.03548 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −43.0079 | −1.37735 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.12270 | 0.163890 | 0.0819448 | − | 0.996637i | \(-0.473887\pi\) | ||||
0.0819448 | + | 0.996637i | \(0.473887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.23148 | 0.295040 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.5656 | −0.496971 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.608262 | −0.0194006 | −0.00970028 | − | 0.999953i | \(-0.503088\pi\) | ||||
−0.00970028 | + | 0.999953i | \(0.503088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.6039 | −1.35747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.89330 | −0.219416 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.6178 | −1.29157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.9745 | 1.17453 | 0.587267 | − | 0.809393i | \(-0.300204\pi\) | ||||
0.587267 | + | 0.809393i | \(0.300204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.0258 | −0.857639 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6311 | −0.749156 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.1927 | 1.87465 | 0.937326 | − | 0.348454i | \(-0.113293\pi\) | ||||
0.937326 | + | 0.348454i | \(0.113293\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.23604 | 0.165661 |
(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 | 8016.2.a.z.1.1 | 8 | ||
4.3 | odd | 2 | 501.2.a.d.1.2 | ✓ | 8 | ||
12.11 | even | 2 | 1503.2.a.f.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
501.2.a.d.1.2 | ✓ | 8 | 4.3 | odd | 2 | ||
1503.2.a.f.1.7 | 8 | 12.11 | even | 2 | |||
8016.2.a.z.1.1 | 8 | 1.1 | even | 1 | trivial |