Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1476,2,Mod(1,1476)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1476, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1476.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1476.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: | \(11.7859193383\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 164) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.31526\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1476.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.17025 | −0.523350 | −0.261675 | − | 0.965156i | \(-0.584275\pi\) | ||||
−0.261675 | + | 0.965156i | \(0.584275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.14501 | 1.18870 | 0.594352 | − | 0.804205i | \(-0.297409\pi\) | ||||
0.594352 | + | 0.804205i | \(0.297409\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67570 | 0.505241 | 0.252621 | − | 0.967565i | \(-0.418708\pi\) | ||||
0.252621 | + | 0.967565i | \(0.418708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.63052 | 1.83898 | 0.919488 | − | 0.393118i | \(-0.128604\pi\) | ||||
0.919488 | + | 0.393118i | \(0.128604\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.16120 | −1.25178 | −0.625888 | − | 0.779913i | \(-0.715263\pi\) | ||||
−0.625888 | + | 0.779913i | \(0.715263\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.72562 | −1.08413 | −0.542065 | − | 0.840336i | \(-0.682357\pi\) | ||||
−0.542065 | + | 0.840336i | \(0.682357\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.82071 | 1.83925 | 0.919623 | − | 0.392803i | \(-0.128495\pi\) | ||||
0.919623 | + | 0.392803i | \(0.128495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.63052 | −0.726104 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.80981 | 0.336074 | 0.168037 | − | 0.985781i | \(-0.446257\pi\) | ||||
0.168037 | + | 0.985781i | \(0.446257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.65951 | −0.298056 | −0.149028 | − | 0.988833i | \(-0.547614\pi\) | ||||
−0.149028 | + | 0.988833i | \(0.547614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.68044 | −0.622108 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.99096 | −0.327311 | −0.163656 | − | 0.986518i | \(-0.552329\pi\) | ||||
−0.163656 | + | 0.986518i | \(0.552329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.46932 | 0.224069 | 0.112034 | − | 0.993704i | \(-0.464263\pi\) | ||||
0.112034 | + | 0.993704i | \(0.464263\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.53543 | 1.24502 | 0.622510 | − | 0.782612i | \(-0.286113\pi\) | ||||
0.622510 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.89112 | 0.413017 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.35139 | 1.28451 | 0.642256 | − | 0.766490i | \(-0.277999\pi\) | ||||
0.642256 | + | 0.766490i | \(0.277999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.96098 | −0.264418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.82071 | −1.14836 | −0.574179 | − | 0.818730i | \(-0.694679\pi\) | ||||
−0.574179 | + | 0.818730i | \(0.694679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6305 | 1.61717 | 0.808586 | − | 0.588378i | \(-0.200233\pi\) | ||||
0.808586 | + | 0.588378i | \(0.200233\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.75935 | −0.962429 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.67570 | 1.18207 | 0.591037 | − | 0.806644i | \(-0.298719\pi\) | ||||
0.591037 | + | 0.806644i | \(0.298719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.776081 | 0.0921039 | 0.0460519 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460519 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.33145 | 0.975123 | 0.487561 | − | 0.873089i | \(-0.337887\pi\) | ||||
0.487561 | + | 0.873089i | \(0.337887\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.27009 | 0.600582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.915804 | 0.103036 | 0.0515180 | − | 0.998672i | \(-0.483594\pi\) | ||||
0.0515180 | + | 0.998672i | \(0.483594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0998 | 1.10860 | 0.554301 | − | 0.832316i | \(-0.312986\pi\) | ||||
0.554301 | + | 0.832316i | \(0.312986\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.03988 | 0.655117 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.44033 | 0.682674 | 0.341337 | − | 0.939941i | \(-0.389120\pi\) | ||||
0.341337 | + | 0.939941i | \(0.389120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.8531 | 2.18600 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.53014 | 0.567380 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.32241 | −0.845012 | −0.422506 | − | 0.906360i | \(-0.638850\pi\) | ||||
−0.422506 | + | 0.906360i | \(0.638850\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.79173 | −0.974313 | −0.487157 | − | 0.873315i | \(-0.661966\pi\) | ||||
−0.487157 | + | 0.873315i | \(0.661966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.648608 | −0.0639093 | −0.0319546 | − | 0.999489i | \(-0.510173\pi\) | ||||
−0.0319546 | + | 0.999489i | \(0.510173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8026 | −1.62437 | −0.812186 | − | 0.583399i | \(-0.801722\pi\) | ||||
−0.812186 | + | 0.583399i | \(0.801722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.84969 | 0.368734 | 0.184367 | − | 0.982857i | \(-0.440977\pi\) | ||||
0.184367 | + | 0.982857i | \(0.440977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.65046 | 0.719695 | 0.359848 | − | 0.933011i | \(-0.382829\pi\) | ||||
0.359848 | + | 0.933011i | \(0.382829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3224 | −0.962569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.2321 | −1.48799 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.19204 | −0.744731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0998 | 0.903357 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9206 | 1.32398 | 0.661992 | − | 0.749511i | \(-0.269711\pi\) | ||||
0.661992 | + | 0.749511i | \(0.269711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.19019 | −0.366098 | −0.183049 | − | 0.983104i | \(-0.558597\pi\) | ||||
−0.183049 | + | 0.983104i | \(0.558597\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.8621 | −1.28871 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.09984 | −0.350273 | −0.175137 | − | 0.984544i | \(-0.556037\pi\) | ||||
−0.175137 | + | 0.984544i | \(0.556037\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.9819 | −1.01629 | −0.508146 | − | 0.861271i | \(-0.669669\pi\) | ||||
−0.508146 | + | 0.861271i | \(0.669669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.1107 | 0.929127 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.11793 | −0.175884 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.80981 | 0.148266 | 0.0741328 | − | 0.997248i | \(-0.476381\pi\) | ||||
0.0741328 | + | 0.997248i | \(0.476381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3561 | −1.73794 | −0.868969 | − | 0.494867i | \(-0.835217\pi\) | ||||
−0.868969 | + | 0.494867i | \(0.835217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.94203 | 0.155988 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1107 | 1.04635 | 0.523175 | − | 0.852225i | \(-0.324747\pi\) | ||||
0.523175 | + | 0.852225i | \(0.324747\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.7413 | 2.18632 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7808 | 0.844420 | 0.422210 | − | 0.906498i | \(-0.361255\pi\) | ||||
0.422210 | + | 0.906498i | \(0.361255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6757 | −1.05826 | −0.529129 | − | 0.848542i | \(-0.677481\pi\) | ||||
−0.529129 | + | 0.848542i | \(0.677481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.9638 | 2.38183 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5801 | −0.804387 | −0.402193 | − | 0.915555i | \(-0.631752\pi\) | ||||
−0.402193 | + | 0.915555i | \(0.631752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4180 | −0.863123 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.23536 | 0.0923352 | 0.0461676 | − | 0.998934i | \(-0.485299\pi\) | ||||
0.0461676 | + | 0.998934i | \(0.485299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.90965 | −0.290602 | −0.145301 | − | 0.989387i | \(-0.546415\pi\) | ||||
−0.145301 | + | 0.989387i | \(0.546415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.32991 | 0.171298 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.64861 | −0.632449 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.31712 | 0.529448 | 0.264724 | − | 0.964324i | \(-0.414719\pi\) | ||||
0.264724 | + | 0.964324i | \(0.414719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3009 | −0.957422 | −0.478711 | − | 0.877973i | \(-0.658896\pi\) | ||||
−0.478711 | + | 0.877973i | \(0.658896\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5692 | 1.10926 | 0.554628 | − | 0.832098i | \(-0.312860\pi\) | ||||
0.554628 | + | 0.832098i | \(0.312860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.8972 | −1.97758 | −0.988789 | − | 0.149319i | \(-0.952292\pi\) | ||||
−0.988789 | + | 0.149319i | \(0.952292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.69189 | 0.399492 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.17025 | −0.0817336 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.91870 | −0.547748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1484 | 1.24939 | 0.624694 | − | 0.780870i | \(-0.285224\pi\) | ||||
0.624694 | + | 0.780870i | \(0.285224\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.71947 | −0.117267 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.21917 | −0.354300 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.2215 | −2.30199 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.55826 | −0.439174 | −0.219587 | − | 0.975593i | \(-0.570471\pi\) | ||||
−0.219587 | + | 0.975593i | \(0.570471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4884 | −1.55898 | −0.779489 | − | 0.626416i | \(-0.784521\pi\) | ||||
−0.779489 | + | 0.626416i | \(0.784521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1503 | 0.802915 | 0.401457 | − | 0.915878i | \(-0.368504\pi\) | ||||
0.401457 | + | 0.915878i | \(0.368504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.8422 | 1.43093 | 0.715465 | − | 0.698649i | \(-0.246215\pi\) | ||||
0.715465 | + | 0.698649i | \(0.246215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.98856 | −0.651582 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.5968 | −1.39698 | −0.698490 | − | 0.715620i | \(-0.746144\pi\) | ||||
−0.698490 | + | 0.715620i | \(0.746144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6305 | 0.813603 | 0.406802 | − | 0.913516i | \(-0.366644\pi\) | ||||
0.406802 | + | 0.913516i | \(0.366644\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.38332 | −0.216152 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.3333 | −1.99369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.7702 | −1.31101 | −0.655503 | − | 0.755192i | \(-0.727543\pi\) | ||||
−0.655503 | + | 0.755192i | \(0.727543\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7808 | 0.929263 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.8207 | −0.924491 | −0.462245 | − | 0.886752i | \(-0.652956\pi\) | ||||
−0.462245 | + | 0.886752i | \(0.652956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.26159 | −0.389076 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.4175 | −1.13567 | −0.567836 | − | 0.823142i | \(-0.692219\pi\) | ||||
−0.567836 | + | 0.823142i | \(0.692219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.9434 | −0.672250 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8916 | 1.57864 | 0.789318 | − | 0.613984i | \(-0.210434\pi\) | ||||
0.789318 | + | 0.613984i | \(0.210434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5017 | −1.06315 | −0.531576 | − | 0.847010i | \(-0.678400\pi\) | ||||
−0.531576 | + | 0.847010i | \(0.678400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.08365 | −0.366858 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.77179 | 0.527045 | 0.263523 | − | 0.964653i | \(-0.415116\pi\) | ||||
0.263523 | + | 0.964653i | \(0.415116\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.2215 | −0.967692 | −0.483846 | − | 0.875153i | \(-0.660761\pi\) | ||||
−0.483846 | + | 0.875153i | \(0.660761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.9819 | −0.712251 | −0.356125 | − | 0.934438i | \(-0.615902\pi\) | ||||
−0.356125 | + | 0.934438i | \(0.615902\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.14501 | 0.185644 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.63803 | 0.566943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2516 | 0.657323 | 0.328661 | − | 0.944448i | \(-0.393403\pi\) | ||||
0.328661 | + | 0.944448i | \(0.393403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3224 | 0.600994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 58.4859 | 3.38233 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.62103 | 0.266352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.7808 | −0.846348 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.61244 | 0.491538 | 0.245769 | − | 0.969328i | \(-0.420960\pi\) | ||||
0.245769 | + | 0.969328i | \(0.420960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.7575 | −1.80080 | −0.900400 | − | 0.435063i | \(-0.856726\pi\) | ||||
−0.900400 | + | 0.435063i | \(0.856726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.21777 | 0.125356 | 0.0626778 | − | 0.998034i | \(-0.480036\pi\) | ||||
0.0626778 | + | 0.998034i | \(0.480036\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3947 | 1.03315 | 0.516574 | − | 0.856243i | \(-0.327207\pi\) | ||||
0.516574 | + | 0.856243i | \(0.327207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.03269 | 0.169798 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.3899 | 1.35709 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0723 | −1.33529 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.8440 | 1.47996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1160 | 0.556027 | 0.278014 | − | 0.960577i | \(-0.410324\pi\) | ||||
0.278014 | + | 0.960577i | \(0.410324\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3230 | −0.618639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.81135 | 0.425511 | 0.212756 | − | 0.977105i | \(-0.431756\pi\) | ||||
0.212756 | + | 0.977105i | \(0.431756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.78083 | −0.150590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.9225 | −0.697749 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6281 | 0.838959 | 0.419480 | − | 0.907765i | \(-0.362213\pi\) | ||||
0.419480 | + | 0.907765i | \(0.362213\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.49265 | 0.401073 | 0.200536 | − | 0.979686i | \(-0.435732\pi\) | ||||
0.200536 | + | 0.979686i | \(0.435732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.4313 | −1.19390 | −0.596949 | − | 0.802279i | \(-0.703620\pi\) | ||||
−0.596949 | + | 0.802279i | \(0.703620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.908206 | −0.0482026 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6196 | 0.824372 | 0.412186 | − | 0.911100i | \(-0.364765\pi\) | ||||
0.412186 | + | 0.911100i | \(0.364765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.33145 | 0.175340 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.74985 | −0.510331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.82790 | −0.199815 | −0.0999073 | − | 0.994997i | \(-0.531855\pi\) | ||||
−0.0999073 | + | 0.994997i | \(0.531855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.4103 | 1.52690 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1997 | −0.942344 | −0.471172 | − | 0.882041i | \(-0.656169\pi\) | ||||
−0.471172 | + | 0.882041i | \(0.656169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7627 | −0.758311 | −0.379156 | − | 0.925333i | \(-0.623785\pi\) | ||||
−0.379156 | + | 0.925333i | \(0.623785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.75406 | −0.242921 | −0.121460 | − | 0.992596i | \(-0.538758\pi\) | ||||
−0.121460 | + | 0.992596i | \(0.538758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.16730 | −0.314315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.3804 | −0.729114 | −0.364557 | − | 0.931181i | \(-0.618780\pi\) | ||||
−0.364557 | + | 0.931181i | \(0.618780\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.5255 | −2.30232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.07172 | −0.0539239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.9311 | −0.548618 | −0.274309 | − | 0.961642i | \(-0.588449\pi\) | ||||
−0.274309 | + | 0.961642i | \(0.588449\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.4132 | −1.51876 | −0.759382 | − | 0.650646i | \(-0.774498\pi\) | ||||
−0.759382 | + | 0.650646i | \(0.774498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0034 | −0.548118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.33624 | −0.165371 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3100 | 0.658136 | 0.329068 | − | 0.944306i | \(-0.393266\pi\) | ||||
0.329068 | + | 0.944306i | \(0.393266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.7413 | −1.36506 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.8193 | −0.580187 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.7917 | −0.771476 | −0.385738 | − | 0.922608i | \(-0.626053\pi\) | ||||
−0.385738 | + | 0.922608i | \(0.626053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.4317 | −1.67810 | −0.839050 | − | 0.544054i | \(-0.816889\pi\) | ||||
−0.839050 | + | 0.544054i | \(0.816889\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.7379 | 0.908920 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.7232 | 1.92234 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.69189 | −0.274168 | −0.137084 | − | 0.990559i | \(-0.543773\pi\) | ||||
−0.137084 | + | 0.990559i | \(0.543773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0034 | −0.624903 | −0.312452 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312452 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.6833 | −1.99398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.59593 | 0.457989 | 0.228994 | − | 0.973428i | \(-0.426456\pi\) | ||||
0.228994 | + | 0.973428i | \(0.426456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.47072 | 0.117388 | 0.0586938 | − | 0.998276i | \(-0.481306\pi\) | ||||
0.0586938 | + | 0.998276i | \(0.481306\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.53678 | −0.357278 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.2324 | −1.66272 | −0.831359 | − | 0.555735i | \(-0.812437\pi\) | ||||
−0.831359 | + | 0.555735i | \(0.812437\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67570 | 0.0789054 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.4033 | −1.14404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.0241 | −1.73191 | −0.865957 | − | 0.500118i | \(-0.833290\pi\) | ||||
−0.865957 | + | 0.500118i | \(0.833290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.6324 | 1.28697 | 0.643484 | − | 0.765460i | \(-0.277488\pi\) | ||||
0.643484 | + | 0.765460i | \(0.277488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1877 | 1.07763 | 0.538813 | − | 0.842425i | \(-0.318873\pi\) | ||||
0.538813 | + | 0.842425i | \(0.318873\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.5235 | 1.27364 | 0.636818 | − | 0.771014i | \(-0.280250\pi\) | ||||
0.636818 | + | 0.771014i | \(0.280250\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.4302 | 1.40514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.46213 | 0.113209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.1565 | 0.787192 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.1088 | −0.507576 | −0.253788 | − | 0.967260i | \(-0.581677\pi\) | ||||
−0.253788 | + | 0.967260i | \(0.581677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.2011 | −0.601918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.73927 | 0.442238 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3933 | −1.42256 | −0.711282 | − | 0.702906i | \(-0.751885\pi\) | ||||
−0.711282 | + | 0.702906i | \(0.751885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.9590 | −1.80333 | −0.901663 | − | 0.432440i | \(-0.857653\pi\) | ||||
−0.901663 | + | 0.432440i | \(0.857653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.34081 | −0.420689 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.44079 | 0.109484 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0951 | 0.720515 | 0.360258 | − | 0.932853i | \(-0.382689\pi\) | ||||
0.360258 | + | 0.932853i | \(0.382689\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.97717 | −0.266509 | −0.133254 | − | 0.991082i | \(-0.542543\pi\) | ||||
−0.133254 | + | 0.991082i | \(0.542543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4587 | 0.509907 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5726 | 0.557269 | 0.278634 | − | 0.960397i | \(-0.410118\pi\) | ||||
0.278634 | + | 0.960397i | \(0.410118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.2025 | 1.15913 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.759032 | 0.0334469 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3028 | 0.629036 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.6233 | 1.38544 | 0.692722 | − | 0.721205i | \(-0.256411\pi\) | ||||
0.692722 | + | 0.721205i | \(0.256411\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.5405 | −0.941900 | −0.470950 | − | 0.882160i | \(-0.656089\pi\) | ||||
−0.470950 | + | 0.882160i | \(0.656089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.56505 | 0.373099 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.8049 | 2.38282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.63052 | 0.287200 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.6632 | 0.850115 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.84463 | 0.208673 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4927 | 1.35397 | 0.676987 | − | 0.735995i | \(-0.263285\pi\) | ||||
0.676987 | + | 0.735995i | \(0.263285\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.50509 | −0.192977 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6861 | −0.756201 | −0.378100 | − | 0.925765i | \(-0.623423\pi\) | ||||
−0.378100 | + | 0.925765i | \(0.623423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.55248 | −0.364348 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.88022 | 0.122479 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.3296 | 0.819021 | 0.409511 | − | 0.912305i | \(-0.365699\pi\) | ||||
0.409511 | + | 0.912305i | \(0.365699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.74235 | 0.412057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7299 | −1.50583 | −0.752917 | − | 0.658115i | \(-0.771354\pi\) | ||||
−0.752917 | + | 0.658115i | \(0.771354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.95293 | −0.376653 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.65187 | −0.195016 | −0.0975082 | − | 0.995235i | \(-0.531087\pi\) | ||||
−0.0975082 | + | 0.995235i | \(0.531087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6791 | −0.865393 | −0.432697 | − | 0.901540i | \(-0.642438\pi\) | ||||
−0.432697 | + | 0.901540i | \(0.642438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.0238 | −1.33548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7808 | −1.03164 | −0.515820 | − | 0.856697i | \(-0.672513\pi\) | ||||
−0.515820 | + | 0.856697i | \(0.672513\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7641 | 1.31780 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.6701 | 0.648989 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.4027 | 0.553187 | 0.276594 | − | 0.960987i | \(-0.410794\pi\) | ||||
0.276594 | + | 0.960987i | \(0.410794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.84219 | 0.323132 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.83911 | 0.0755233 | 0.0377616 | − | 0.999287i | \(-0.487977\pi\) | ||||
0.0377616 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.9955 | 0.778740 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.9457 | 1.46870 | 0.734352 | − | 0.678769i | \(-0.237486\pi\) | ||||
0.734352 | + | 0.678769i | \(0.237486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8858 | −1.21907 | −0.609533 | − | 0.792760i | \(-0.708643\pi\) | ||||
−0.609533 | + | 0.792760i | \(0.708643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.58671 | 0.389755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.25015 | 0.172508 | 0.0862541 | − | 0.996273i | \(-0.472510\pi\) | ||||
0.0862541 | + | 0.996273i | \(0.472510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 56.5944 | 2.28956 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.35184 | −0.377717 | −0.188859 | − | 0.982004i | \(-0.560479\pi\) | ||||
−0.188859 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6019 | −0.507332 | −0.253666 | − | 0.967292i | \(-0.581636\pi\) | ||||
−0.253666 | + | 0.967292i | \(0.581636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.54018 | −0.102098 | −0.0510491 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510491 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.2549 | 0.811497 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.33331 | 0.253332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.2757 | 0.409720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.0057 | 1.91108 | 0.955538 | − | 0.294867i | \(-0.0952752\pi\) | ||||
0.955538 | + | 0.294867i | \(0.0952752\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.4607 | −0.692908 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.1696 | 0.759528 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.02148 | −0.0403461 | −0.0201730 | − | 0.999797i | \(-0.506422\pi\) | ||||
−0.0201730 | + | 0.999797i | \(0.506422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.40606 | −0.331503 | −0.165751 | − | 0.986168i | \(-0.553005\pi\) | ||||
−0.165751 | + | 0.986168i | \(0.553005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.86778 | −0.230686 | −0.115343 | − | 0.993326i | \(-0.536797\pi\) | ||||
−0.115343 | + | 0.993326i | \(0.536797\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.7808 | −0.580198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5749 | −1.47042 | −0.735209 | − | 0.677841i | \(-0.762916\pi\) | ||||
−0.735209 | + | 0.677841i | \(0.762916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.90355 | 0.191598 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8360 | 0.655839 | 0.327919 | − | 0.944706i | \(-0.393653\pi\) | ||||
0.327919 | + | 0.944706i | \(0.393653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.84983 | 0.188637 | 0.0943183 | − | 0.995542i | \(-0.469933\pi\) | ||||
0.0943183 | + | 0.995542i | \(0.469933\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.3924 | 0.674447 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9638 | 0.618122 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1649 | 0.817062 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.24065 | 0.240559 | 0.120280 | − | 0.992740i | \(-0.461621\pi\) | ||||
0.120280 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3566 | 1.12827 | 0.564134 | − | 0.825683i | \(-0.309210\pi\) | ||||
0.564134 | + | 0.825683i | \(0.309210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.1741 | −1.00447 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.6861 | 0.982849 | 0.491425 | − | 0.870920i | \(-0.336476\pi\) | ||||
0.491425 | + | 0.870920i | \(0.336476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.79783 | 0.183316 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 62.0046 | 2.36219 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.77128 | 0.333675 | 0.166838 | − | 0.985984i | \(-0.446644\pi\) | ||||
0.166838 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0218 | 0.531877 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.16120 | −0.195495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.1075 | 0.570602 | 0.285301 | − | 0.958438i | \(-0.407906\pi\) | ||||
0.285301 | + | 0.958438i | \(0.407906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.40850 | 0.354848 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.7951 | −1.15817 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0132 | −0.451165 | −0.225583 | − | 0.974224i | \(-0.572429\pi\) | ||||
−0.225583 | + | 0.974224i | \(0.572429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.6380 | −0.548198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.0023 | −0.486259 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.27778 | 0.0849468 | 0.0424734 | − | 0.999098i | \(-0.486476\pi\) | ||||
0.0424734 | + | 0.999098i | \(0.486476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.03988 | −0.0759692 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.57056 | −0.244025 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.71952 | 0.286301 | 0.143151 | − | 0.989701i | \(-0.454277\pi\) | ||||
0.143151 | + | 0.989701i | \(0.454277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.58345 | −0.280484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.2753 | 1.22905 | 0.614526 | − | 0.788896i | \(-0.289347\pi\) | ||||
0.614526 | + | 0.788896i | \(0.289347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.2135 | 0.597233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.0057 | 1.76592 | 0.882959 | − | 0.469450i | \(-0.155548\pi\) | ||||
0.882959 | + | 0.469450i | \(0.155548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.1345 | −1.58245 | −0.791226 | − | 0.611524i | \(-0.790557\pi\) | ||||
−0.791226 | + | 0.611524i | \(0.790557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.11793 | −0.0775948 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.8445 | −1.93090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.46883 | −0.236051 | −0.118025 | − | 0.993011i | \(-0.537656\pi\) | ||||
−0.118025 | + | 0.993011i | \(0.537656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.9920 | 0.909550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.5531 | −1.43758 | −0.718790 | − | 0.695227i | \(-0.755304\pi\) | ||||
−0.718790 | + | 0.695227i | \(0.755304\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5130 | −1.03360 | −0.516799 | − | 0.856107i | \(-0.672876\pi\) | ||||
−0.516799 | + | 0.856107i | \(0.672876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1073 | 0.438315 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.4859 | −2.11180 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.7184 | 1.79289 | 0.896445 | − | 0.443154i | \(-0.146141\pi\) | ||||
0.896445 | + | 0.443154i | \(0.146141\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.2539 | 0.872351 | 0.436175 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436175 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.02488 | 0.216420 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.72562 | −0.169313 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.30048 | 0.0465347 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3428 | −0.547608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.907346 | 0.0323434 | 0.0161717 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161717 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0608 | 0.855504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 83.7470 | 2.97394 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.4934 | 1.15098 | 0.575488 | − | 0.817810i | \(-0.304812\pi\) | ||||
0.575488 | + | 0.817810i | \(0.304812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.0531 | −1.55849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9610 | 0.492672 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.4641 | −1.14421 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.07804 | 0.0730602 | 0.0365301 | − | 0.999333i | \(-0.488370\pi\) | ||||
0.0365301 | + | 0.999333i | \(0.488370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.7518 | −0.482893 | −0.241446 | − | 0.970414i | \(-0.577622\pi\) | ||||
−0.241446 | + | 0.970414i | \(0.577622\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.6162 | −0.441927 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.94344 | −0.242920 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.76979 | −0.236267 | −0.118134 | − | 0.992998i | \(-0.537691\pi\) | ||||
−0.118134 | + | 0.992998i | \(0.537691\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.3575 | 0.779335 | 0.389667 | − | 0.920956i | \(-0.372590\pi\) | ||||
0.389667 | + | 0.920956i | \(0.372590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.1160 | −0.908143 | −0.454072 | − | 0.890965i | \(-0.650029\pi\) | ||||
−0.454072 | + | 0.890965i | \(0.650029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7540 | −0.686085 | −0.343043 | − | 0.939320i | \(-0.611458\pi\) | ||||
−0.343043 | + | 0.939320i | \(0.611458\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.9216 | −0.517004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0039 | 0.553839 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.8188 | −0.718745 | −0.359373 | − | 0.933194i | \(-0.617009\pi\) | ||||
−0.359373 | + | 0.933194i | \(0.617009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7246 | −0.887054 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.2353 | −1.24653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.7641 | −0.885265 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.5617 | −0.602006 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.6666 | 1.66631 | 0.833157 | − | 0.553037i | \(-0.186531\pi\) | ||||
0.833157 | + | 0.553037i | \(0.186531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.8515 | 0.439001 | 0.219500 | − | 0.975612i | \(-0.429557\pi\) | ||||
0.219500 | + | 0.975612i | \(0.429557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.60904 | −0.0548998 | −0.0274499 | − | 0.999623i | \(-0.508739\pi\) | ||||
−0.0274499 | + | 0.999623i | \(0.508739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.0494 | 1.56754 | 0.783770 | − | 0.621052i | \(-0.213294\pi\) | ||||
0.783770 | + | 0.621052i | \(0.213294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3813 | 0.420976 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.53461 | 0.0520581 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.1549 | 2.17381 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.7641 | 1.07382 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.63392 | 0.122709 | 0.0613543 | − | 0.998116i | \(-0.480458\pi\) | ||||
0.0613543 | + | 0.998116i | \(0.480458\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.2426 | −0.951519 | −0.475759 | − | 0.879575i | \(-0.657827\pi\) | ||||
−0.475759 | + | 0.879575i | \(0.657827\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.23962 | −0.142674 | −0.0713372 | − | 0.997452i | \(-0.522727\pi\) | ||||
−0.0713372 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.4003 | 1.55797 | 0.778984 | − | 0.627043i | \(-0.215735\pi\) | ||||
0.778984 | + | 0.627043i | \(0.215735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.9254 | 1.57383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40.3352 | −1.34976 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.44568 | −0.0483237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.00339 | −0.100169 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.2644 | −1.60792 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.57526 | 0.152087 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0358 | −0.897708 | −0.448854 | − | 0.893605i | \(-0.648168\pi\) | ||||
−0.448854 | + | 0.893605i | \(0.648168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.3500 | 1.40312 | 0.701559 | − | 0.712612i | \(-0.252488\pi\) | ||||
0.701559 | + | 0.712612i | \(0.252488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9243 | 0.560111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.1782 | −0.435183 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.17400 | 0.269635 | 0.134818 | − | 0.990870i | \(-0.456955\pi\) | ||||
0.134818 | + | 0.990870i | \(0.456955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.14582 | 0.169377 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.22821 | 0.237662 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.2596 | −1.38649 | −0.693247 | − | 0.720700i | \(-0.743820\pi\) | ||||
−0.693247 | + | 0.720700i | \(0.743820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.6623 | −0.447764 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.1210 | 0.330992 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.16600 | 0.0380917 | 0.0190458 | − | 0.999819i | \(-0.493937\pi\) | ||||
0.0190458 | + | 0.999819i | \(0.493937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.93864 | −0.160995 | −0.0804975 | − | 0.996755i | \(-0.525651\pi\) | ||||
−0.0804975 | + | 0.996755i | \(0.525651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.82071 | 0.287242 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.3210 | −0.822822 | −0.411411 | − | 0.911450i | \(-0.634964\pi\) | ||||
−0.411411 | + | 0.911450i | \(0.634964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.2419 | 1.79323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.6143 | 1.54238 | 0.771189 | − | 0.636606i | \(-0.219662\pi\) | ||||
0.771189 | + | 0.636606i | \(0.219662\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.56283 | −0.277087 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.8941 | −0.416371 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2460 | −0.911163 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.5654 | 0.501067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.9763 | −0.835342 | −0.417671 | − | 0.908598i | \(-0.637153\pi\) | ||||
−0.417671 | + | 0.908598i | \(0.637153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.8687 | 1.79291 | 0.896457 | − | 0.443132i | \(-0.146133\pi\) | ||||
0.896457 | + | 0.443132i | \(0.146133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.6833 | −1.20807 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.5241 | 1.36047 | 0.680233 | − | 0.732996i | \(-0.261879\pi\) | ||||
0.680233 | + | 0.732996i | \(0.261879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.7920 | 0.344915 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.8977 | −1.62338 | −0.811692 | − | 0.584086i | \(-0.801453\pi\) | ||||
−0.811692 | + | 0.584086i | \(0.801453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.2198 | −0.580530 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.9604 | 0.412118 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7147 | −0.880387 | −0.440194 | − | 0.897903i | \(-0.645090\pi\) | ||||
−0.440194 | + | 0.897903i | \(0.645090\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.6466 | 1.03497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.3480 | −0.707768 | −0.353884 | − | 0.935289i | \(-0.615139\pi\) | ||||
−0.353884 | + | 0.935289i | \(0.615139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1476.2.a.g.1.3 | 4 | ||
3.2 | odd | 2 | 164.2.a.a.1.2 | ✓ | 4 | ||
4.3 | odd | 2 | 5904.2.a.bp.1.3 | 4 | |||
12.11 | even | 2 | 656.2.a.i.1.3 | 4 | |||
15.2 | even | 4 | 4100.2.d.c.1149.4 | 8 | |||
15.8 | even | 4 | 4100.2.d.c.1149.5 | 8 | |||
15.14 | odd | 2 | 4100.2.a.c.1.3 | 4 | |||
21.20 | even | 2 | 8036.2.a.i.1.3 | 4 | |||
24.5 | odd | 2 | 2624.2.a.v.1.3 | 4 | |||
24.11 | even | 2 | 2624.2.a.y.1.2 | 4 | |||
123.122 | odd | 2 | 6724.2.a.c.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
656.2.a.i.1.3 | 4 | 12.11 | even | 2 | |||
1476.2.a.g.1.3 | 4 | 1.1 | even | 1 | trivial | ||
2624.2.a.v.1.3 | 4 | 24.5 | odd | 2 | |||
2624.2.a.y.1.2 | 4 | 24.11 | even | 2 | |||
4100.2.a.c.1.3 | 4 | 15.14 | odd | 2 | |||
4100.2.d.c.1149.4 | 8 | 15.2 | even | 4 | |||
4100.2.d.c.1149.5 | 8 | 15.8 | even | 4 | |||
5904.2.a.bp.1.3 | 4 | 4.3 | odd | 2 | |||
6724.2.a.c.1.3 | 4 | 123.122 | odd | 2 | |||
8036.2.a.i.1.3 | 4 | 21.20 | even | 2 |