Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, 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("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.56310016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 14x^{2} - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.66648\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | ||||||||
\(3\) | −0.750054 | −0.433044 | −0.216522 | − | 0.976278i | \(-0.569471\pi\) | ||||
−0.216522 | + | 0.976278i | \(0.569471\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.872810 | −0.329891 | −0.164946 | − | 0.986303i | \(-0.552745\pi\) | ||||
−0.164946 | + | 0.986303i | \(0.552745\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.43742 | −0.812473 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.11009 | −0.334705 | −0.167353 | − | 0.985897i | \(-0.553522\pi\) | ||||
−0.167353 | + | 0.985897i | \(0.553522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.58290 | −1.27107 | −0.635534 | − | 0.772073i | \(-0.719220\pi\) | ||||
−0.635534 | + | 0.772073i | \(0.719220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.96003 | 0.717914 | 0.358957 | − | 0.933354i | \(-0.383133\pi\) | ||||
0.358957 | + | 0.933354i | \(0.383133\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.654655 | 0.142857 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.83284 | −0.799203 | −0.399602 | − | 0.916689i | \(-0.630852\pi\) | ||||
−0.399602 | + | 0.916689i | \(0.630852\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.07836 | 0.784880 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.56553 | 1.40488 | 0.702442 | − | 0.711741i | \(-0.252093\pi\) | ||||
0.702442 | + | 0.711741i | \(0.252093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.56553 | 1.71802 | 0.859010 | − | 0.511959i | \(-0.171080\pi\) | ||||
0.859010 | + | 0.511959i | \(0.171080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.832629 | 0.144942 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.750054 | −0.123308 | −0.0616540 | − | 0.998098i | \(-0.519638\pi\) | ||||
−0.0616540 | + | 0.998098i | \(0.519638\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.43742 | 0.550428 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.87484 | 1.38602 | 0.693008 | − | 0.720929i | \(-0.256285\pi\) | ||||
0.693008 | + | 0.720929i | \(0.256285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5387 | 1.75964 | 0.879819 | − | 0.475310i | \(-0.157664\pi\) | ||||
0.879819 | + | 0.475310i | \(0.157664\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.53850 | −1.24547 | −0.622734 | − | 0.782434i | \(-0.713978\pi\) | ||||
−0.622734 | + | 0.782434i | \(0.713978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.23820 | −0.891172 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.22018 | −0.310888 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.17023 | −1.12227 | −0.561134 | − | 0.827725i | \(-0.689635\pi\) | ||||
−0.561134 | + | 0.827725i | \(0.689635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.750054 | −0.0993470 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.65465 | 0.605984 | 0.302992 | − | 0.952993i | \(-0.402014\pi\) | ||||
0.302992 | + | 0.952993i | \(0.402014\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.889908 | 0.113941 | 0.0569705 | − | 0.998376i | \(-0.481856\pi\) | ||||
0.0569705 | + | 0.998376i | \(0.481856\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.12740 | 0.268028 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59176 | −0.316634 | −0.158317 | − | 0.987388i | \(-0.550607\pi\) | ||||
−0.158317 | + | 0.987388i | \(0.550607\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.87484 | 0.346090 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.34535 | 0.871732 | 0.435866 | − | 0.900012i | \(-0.356442\pi\) | ||||
0.435866 | + | 0.900012i | \(0.356442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8803 | 1.39049 | 0.695243 | − | 0.718775i | \(-0.255297\pi\) | ||||
0.695243 | + | 0.718775i | \(0.255297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.968900 | 0.110416 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.25327 | 0.472586 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.83284 | 0.420709 | 0.210355 | − | 0.977625i | \(-0.432538\pi\) | ||||
0.210355 | + | 0.977625i | \(0.432538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.67455 | −0.608376 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.34535 | 0.142606 | 0.0713032 | − | 0.997455i | \(-0.477284\pi\) | ||||
0.0713032 | + | 0.997455i | \(0.477284\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.17466 | −0.743978 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.17023 | −0.829561 | −0.414780 | − | 0.909922i | \(-0.636142\pi\) | ||||
−0.414780 | + | 0.909922i | \(0.636142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.70576 | 0.271939 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.43742 | 0.541043 | 0.270522 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270522 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5032 | 1.33051 | 0.665254 | − | 0.746617i | \(-0.268323\pi\) | ||||
0.665254 | + | 0.746617i | \(0.268323\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5030 | −1.01536 | −0.507680 | − | 0.861546i | \(-0.669497\pi\) | ||||
−0.507680 | + | 0.861546i | \(0.669497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.22018 | −0.787351 | −0.393675 | − | 0.919250i | \(-0.628797\pi\) | ||||
−0.393675 | + | 0.919250i | \(0.628797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.562581 | 0.0533978 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.82841 | −0.454219 | −0.227109 | − | 0.973869i | \(-0.572927\pi\) | ||||
−0.227109 | + | 0.973869i | \(0.572927\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.1704 | 1.03271 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.58355 | −0.236833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.76770 | −0.887972 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.65661 | −0.600206 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9161 | 1.14612 | 0.573058 | − | 0.819515i | \(-0.305757\pi\) | ||||
0.573058 | + | 0.819515i | \(0.305757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.65465 | −0.762000 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2022 | 1.15348 | 0.576739 | − | 0.816928i | \(-0.304325\pi\) | ||||
0.576739 | + | 0.816928i | \(0.304325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.872810 | −0.0756822 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.3716 | 1.31328 | 0.656640 | − | 0.754204i | \(-0.271977\pi\) | ||||
0.656640 | + | 0.754204i | \(0.271977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.9849 | 1.35582 | 0.677912 | − | 0.735143i | \(-0.262885\pi\) | ||||
0.677912 | + | 0.735143i | \(0.262885\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.40433 | 0.539342 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.08744 | 0.425433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.67899 | 0.385916 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.11009 | −0.254789 | −0.127394 | − | 0.991852i | \(-0.540661\pi\) | ||||
−0.127394 | + | 0.991852i | \(0.540661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.34535 | −0.272240 | −0.136120 | − | 0.990692i | \(-0.543463\pi\) | ||||
−0.136120 | + | 0.990692i | \(0.543463\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.21484 | −0.583285 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3402 | −1.06467 | −0.532334 | − | 0.846535i | \(-0.678685\pi\) | ||||
−0.532334 | + | 0.846535i | \(0.678685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.12811 | 0.485991 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.34535 | 0.263650 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.33295 | 0.417709 | 0.208854 | − | 0.977947i | \(-0.433026\pi\) | ||||
0.208854 | + | 0.977947i | \(0.433026\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.5906 | 1.43859 | 0.719293 | − | 0.694707i | \(-0.244466\pi\) | ||||
0.719293 | + | 0.694707i | \(0.244466\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.00295 | 0.615611 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.43742 | −0.186394 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.8288 | −0.823301 | −0.411651 | − | 0.911342i | \(-0.635048\pi\) | ||||
−0.411651 | + | 0.911342i | \(0.635048\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.49124 | −0.262418 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.34535 | 0.250043 | 0.125021 | − | 0.992154i | \(-0.460100\pi\) | ||||
0.125021 | + | 0.992154i | \(0.460100\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.667479 | −0.0493415 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.28591 | −0.240290 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.55963 | −0.258925 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.54751 | 0.618476 | 0.309238 | − | 0.950985i | \(-0.399926\pi\) | ||||
0.309238 | + | 0.950985i | \(0.399926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.16980 | −0.156185 | −0.0780927 | − | 0.996946i | \(-0.524883\pi\) | ||||
−0.0780927 | + | 0.996946i | \(0.524883\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3316 | 1.30607 | 0.653036 | − | 0.757327i | \(-0.273495\pi\) | ||||
0.653036 | + | 0.757327i | \(0.273495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.20217 | 0.368772 | 0.184386 | − | 0.982854i | \(-0.440970\pi\) | ||||
0.184386 | + | 0.982854i | \(0.440970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.94396 | 0.137117 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.60327 | −0.463459 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.34225 | 0.649331 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.11009 | −0.0767867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6606 | 1.28465 | 0.642323 | − | 0.766434i | \(-0.277971\pi\) | ||||
0.642323 | + | 0.766434i | \(0.277971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.50940 | −0.377498 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.34889 | −0.566760 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.91087 | −0.602141 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5655 | −0.912516 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.7560 | −1.45689 | −0.728444 | − | 0.685105i | \(-0.759756\pi\) | ||||
−0.728444 | + | 0.685105i | \(0.759756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.58290 | −0.304178 | −0.152089 | − | 0.988367i | \(-0.548600\pi\) | ||||
−0.152089 | + | 0.988367i | \(0.548600\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.6756 | −1.89494 | −0.947469 | − | 0.319847i | \(-0.896368\pi\) | ||||
−0.947469 | + | 0.319847i | \(0.896368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.726727 | −0.0478151 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.3009 | 1.65752 | 0.828759 | − | 0.559605i | \(-0.189047\pi\) | ||||
0.828759 | + | 0.559605i | \(0.189047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.00021 | −0.194885 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.5835 | 1.46081 | 0.730404 | − | 0.683015i | \(-0.239332\pi\) | ||||
0.730404 | + | 0.683015i | \(0.239332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.874839 | 0.0563533 | 0.0281767 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281767 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4253 | −0.989530 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.58290 | −0.291603 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.87484 | −0.182186 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6786 | −0.989623 | −0.494811 | − | 0.869000i | \(-0.664763\pi\) | ||||
−0.494811 | + | 0.869000i | \(0.664763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.25481 | 0.267498 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.1614 | −0.633848 | −0.316924 | − | 0.948451i | \(-0.602650\pi\) | ||||
−0.316924 | + | 0.948451i | \(0.602650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.654655 | 0.0406783 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.4404 | −1.14143 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.29277 | 0.326366 | 0.163183 | − | 0.986596i | \(-0.447824\pi\) | ||||
0.163183 | + | 0.986596i | \(0.447824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.00908 | −0.0617548 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9109 | 0.665248 | 0.332624 | − | 0.943060i | \(-0.392066\pi\) | ||||
0.332624 | + | 0.943060i | \(0.392066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3123 | −1.11239 | −0.556195 | − | 0.831052i | \(-0.687739\pi\) | ||||
−0.556195 | + | 0.831052i | \(0.687739\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.00021 | −0.181581 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8805 | −0.894084 | −0.447042 | − | 0.894513i | \(-0.647523\pi\) | ||||
−0.447042 | + | 0.894513i | \(0.647523\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.3152 | −1.39584 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.8217 | −1.42109 | −0.710543 | − | 0.703654i | \(-0.751551\pi\) | ||||
−0.710543 | + | 0.703654i | \(0.751551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.86394 | −0.170244 | −0.0851219 | − | 0.996371i | \(-0.527128\pi\) | ||||
−0.0851219 | + | 0.996371i | \(0.527128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.74605 | −0.457235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.23820 | −0.484600 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.12811 | 0.359236 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.16980 | −0.126761 | −0.0633805 | − | 0.997989i | \(-0.520188\pi\) | ||||
−0.0633805 | + | 0.997989i | \(0.520188\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.52735 | −0.262704 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.5655 | 1.01584 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0711 | −0.580489 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.07836 | −0.234295 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0978 | 1.43241 | 0.716204 | − | 0.697891i | \(-0.245878\pi\) | ||||
0.716204 | + | 0.697891i | \(0.245878\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1281 | −0.576168 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.3663 | 0.984753 | 0.492377 | − | 0.870382i | \(-0.336128\pi\) | ||||
0.492377 | + | 0.870382i | \(0.336128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.9977 | 1.80862 | 0.904309 | − | 0.426879i | \(-0.140387\pi\) | ||||
0.904309 | + | 0.426879i | \(0.140387\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.1602 | 1.46930 | 0.734652 | − | 0.678444i | \(-0.237345\pi\) | ||||
0.734652 | + | 0.678444i | \(0.237345\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.39843 | −0.470222 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.87779 | 0.439695 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.96003 | 0.164701 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.16558 | 0.340957 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.45249 | 0.410869 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.1841 | −0.669701 | −0.334851 | − | 0.942271i | \(-0.608686\pi\) | ||||
−0.334851 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.82820 | 0.100184 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2401 | −1.10255 | −0.551276 | − | 0.834323i | \(-0.685859\pi\) | ||||
−0.551276 | + | 0.834323i | \(0.685859\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.62157 | 0.196697 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.6186 | −0.575030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5544 | 0.623881 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4676 | −0.830347 | −0.415173 | − | 0.909742i | \(-0.636279\pi\) | ||||
−0.415173 | + | 0.909742i | \(0.636279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.63664 | −0.0876071 | −0.0438036 | − | 0.999040i | \(-0.513948\pi\) | ||||
−0.0438036 | + | 0.999040i | \(0.513948\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.6907 | −0.997635 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.0064 | 1.43740 | 0.718702 | − | 0.695319i | \(-0.244737\pi\) | ||||
0.718702 | + | 0.695319i | \(0.244737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.93780 | 0.102559 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5446 | 0.820411 | 0.410205 | − | 0.911993i | \(-0.365457\pi\) | ||||
0.410205 | + | 0.911993i | \(0.365457\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.32630 | 0.384531 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.1729 | −0.739818 | −0.369909 | − | 0.929068i | \(-0.620611\pi\) | ||||
−0.369909 | + | 0.929068i | \(0.620611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.6317 | −1.12610 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.13106 | 0.370226 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.0019 | 1.44988 | 0.724942 | − | 0.688810i | \(-0.241866\pi\) | ||||
0.724942 | + | 0.688810i | \(0.241866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.6720 | −1.78570 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0950 | −1.49451 | −0.747255 | − | 0.664537i | \(-0.768629\pi\) | ||||
−0.747255 | + | 0.664537i | \(0.768629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.68774 | −0.496318 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.5981 | −1.51239 | −0.756197 | − | 0.654344i | \(-0.772945\pi\) | ||||
−0.756197 | + | 0.654344i | \(0.772945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.1247 | −1.42966 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.6786 | −1.50476 | −0.752382 | − | 0.658727i | \(-0.771095\pi\) | ||||
−0.752382 | + | 0.658727i | \(0.771095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3453 | −0.573759 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.90233 | −0.499507 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.19668 | 0.260814 | 0.130407 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130407 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.654655 | 0.0327737 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.22018 | −0.410496 | −0.205248 | − | 0.978710i | \(-0.565800\pi\) | ||||
−0.205248 | + | 0.978710i | \(0.565800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.8378 | −2.18372 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.832629 | 0.0412719 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.03604 | −0.199569 | −0.0997846 | − | 0.995009i | \(-0.531815\pi\) | ||||
−0.0997846 | + | 0.995009i | \(0.531815\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.5295 | −0.568708 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.06263 | −0.199909 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.9896 | −0.587131 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.30931 | −0.0639639 | −0.0319820 | − | 0.999488i | \(-0.510182\pi\) | ||||
−0.0319820 | + | 0.999488i | \(0.510182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5295 | −0.659387 | −0.329694 | − | 0.944088i | \(-0.606945\pi\) | ||||
−0.329694 | + | 0.944088i | \(0.606945\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.8119 | 1.01191 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.776721 | −0.0375882 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.81585 | −0.184231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3152 | −0.545034 | −0.272517 | − | 0.962151i | \(-0.587856\pi\) | ||||
−0.272517 | + | 0.962151i | \(0.587856\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.1604 | −1.40136 | −0.700680 | − | 0.713475i | \(-0.747120\pi\) | ||||
−0.700680 | + | 0.713475i | \(0.747120\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.83284 | −0.183350 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.9699 | 0.953109 | 0.476555 | − | 0.879145i | \(-0.341885\pi\) | ||||
0.476555 | + | 0.879145i | \(0.341885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.2051 | 0.724053 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.6252 | 1.69261 | 0.846303 | − | 0.532702i | \(-0.178823\pi\) | ||||
0.846303 | + | 0.532702i | \(0.178823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.33274 | 0.110335 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.4043 | 1.52925 | 0.764627 | − | 0.644472i | \(-0.222923\pi\) | ||||
0.764627 | + | 0.644472i | \(0.222923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.85189 | −0.463907 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.50919 | 0.117892 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.20576 | 0.290293 | 0.145147 | − | 0.989410i | \(-0.453635\pi\) | ||||
0.145147 | + | 0.989410i | \(0.453635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.0721 | 0.563476 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.79783 | −0.223457 | −0.111729 | − | 0.993739i | \(-0.535639\pi\) | ||||
−0.111729 | + | 0.993739i | \(0.535639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.5453 | −1.93077 | −0.965387 | − | 0.260823i | \(-0.916006\pi\) | ||||
−0.965387 | + | 0.260823i | \(0.916006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.1953 | 0.841979 | 0.420989 | − | 0.907066i | \(-0.361683\pi\) | ||||
0.420989 | + | 0.907066i | \(0.361683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.26212 | 0.104455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0059 | 0.461047 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.8090 | −0.588960 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.9143 | 0.911812 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.8778 | 1.45653 | 0.728267 | − | 0.685294i | \(-0.240326\pi\) | ||||
0.728267 | + | 0.685294i | \(0.240326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.43742 | 0.156733 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.50919 | −0.114172 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.83749 | 0.264522 | 0.132261 | − | 0.991215i | \(-0.457776\pi\) | ||||
0.132261 | + | 0.991215i | \(0.457776\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.13106 | −0.321820 | −0.160910 | − | 0.986969i | \(-0.551443\pi\) | ||||
−0.160910 | + | 0.986969i | \(0.551443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3942 | 1.00858 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.41109 | −0.287577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.14613 | 0.140840 | 0.0704200 | − | 0.997517i | \(-0.477566\pi\) | ||||
0.0704200 | + | 0.997517i | \(0.477566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9440 | −0.622970 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.1646 | 1.12204 | 0.561018 | − | 0.827804i | \(-0.310410\pi\) | ||||
0.561018 | + | 0.827804i | \(0.310410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00264 | −0.266587 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.9699 | −1.68298 | −0.841492 | − | 0.540269i | \(-0.818322\pi\) | ||||
−0.841492 | + | 0.540269i | \(0.818322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3693 | −0.458709 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.07836 | 0.180064 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.47852 | 0.416865 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.12221 | 0.356526 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.96396 | −0.173664 | −0.0868322 | − | 0.996223i | \(-0.527674\pi\) | ||||
−0.0868322 | + | 0.996223i | \(0.527674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.2557 | 0.754537 | 0.377269 | − | 0.926104i | \(-0.376863\pi\) | ||||
0.377269 | + | 0.926104i | \(0.376863\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.3143 | 1.23339 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.30931 | −0.361274 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.3453 | −0.492346 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.6725 | −1.76172 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.50919 | −0.108279 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.92498 | 0.298280 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2942 | −0.485577 | −0.242789 | − | 0.970079i | \(-0.578062\pi\) | ||||
−0.242789 | + | 0.970079i | \(0.578062\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.50011 | 0.0643758 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1673 | 1.33262 | 0.666309 | − | 0.745676i | \(-0.267873\pi\) | ||||
0.666309 | + | 0.745676i | \(0.267873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.16908 | −0.0925740 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.56553 | 0.322302 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.49124 | −0.148463 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.6266 | 0.958719 | 0.479359 | − | 0.877619i | \(-0.340869\pi\) | ||||
0.479359 | + | 0.877619i | \(0.340869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −52.8807 | −2.23662 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.46461 | 0.104056 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4071 | −0.565041 | −0.282521 | − | 0.959261i | \(-0.591171\pi\) | ||||
−0.282521 | + | 0.959261i | \(0.591171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.71230 | −0.155902 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.6606 | −1.70458 | −0.852290 | − | 0.523070i | \(-0.824786\pi\) | ||||
−0.852290 | + | 0.523070i | \(0.824786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.4433 | −1.73435 | −0.867174 | − | 0.498005i | \(-0.834066\pi\) | ||||
−0.867174 | + | 0.498005i | \(0.834066\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.41109 | −0.267827 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7295 | 1.02950 | 0.514752 | − | 0.857339i | \(-0.327884\pi\) | ||||
0.514752 | + | 0.857339i | \(0.327884\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.62747 | 0.0676351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.34535 | −0.138788 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.06971 | 0.375629 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.03839 | 0.290505 | 0.145253 | − | 0.989395i | \(-0.453600\pi\) | ||||
0.145253 | + | 0.989395i | \(0.453600\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.56553 | 0.394141 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.7497 | −0.565586 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.6484 | 0.724732 | 0.362366 | − | 0.932036i | \(-0.381969\pi\) | ||||
0.362366 | + | 0.932036i | \(0.381969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.90190 | −0.159694 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.5655 | 1.37145 | 0.685725 | − | 0.727861i | \(-0.259485\pi\) | ||||
0.685725 | + | 0.727861i | \(0.259485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0059 | 1.14238 | 0.571192 | − | 0.820816i | \(-0.306481\pi\) | ||||
0.571192 | + | 0.820816i | \(0.306481\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.31722 | 0.257257 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.5802 | 1.24121 | 0.620605 | − | 0.784123i | \(-0.286887\pi\) | ||||
0.620605 | + | 0.784123i | \(0.286887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.95281 | 0.200698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.1311 | 1.58307 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8000 | −0.476596 | −0.238298 | − | 0.971192i | \(-0.576589\pi\) | ||||
−0.238298 | + | 0.971192i | \(0.576589\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7065 | 0.672579 | 0.336289 | − | 0.941759i | \(-0.390828\pi\) | ||||
0.336289 | + | 0.941759i | \(0.390828\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.4433 | −1.02265 | −0.511327 | − | 0.859386i | \(-0.670846\pi\) | ||||
−0.511327 | + | 0.859386i | \(0.670846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.6317 | −0.627279 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.17423 | −0.0470446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.832629 | 0.0332520 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.22018 | −0.0885245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7706 | 1.42401 | 0.712003 | − | 0.702176i | \(-0.247788\pi\) | ||||
0.712003 | + | 0.702176i | \(0.247788\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.9964 | −0.556308 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.5890 | 1.13274 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.9037 | −0.708259 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.3512 | 1.23830 | 0.619150 | − | 0.785273i | \(-0.287477\pi\) | ||||
0.619150 | + | 0.785273i | \(0.287477\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.5626 | −1.24471 | −0.622353 | − | 0.782736i | \(-0.713823\pi\) | ||||
−0.622353 | + | 0.782736i | \(0.713823\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.4649 | −1.63015 | −0.815077 | − | 0.579352i | \(-0.803306\pi\) | ||||
−0.815077 | + | 0.579352i | \(0.803306\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.16710 | −0.202826 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.26212 | 0.245432 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.19668 | 0.203362 | 0.101681 | − | 0.994817i | \(-0.467578\pi\) | ||||
0.101681 | + | 0.994817i | \(0.467578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.9573 | −1.12973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2202 | 0.709758 | 0.354879 | − | 0.934912i | \(-0.384522\pi\) | ||||
0.354879 | + | 0.934912i | \(0.384522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.9109 | −0.735548 | −0.367774 | − | 0.929915i | \(-0.619880\pi\) | ||||
−0.367774 | + | 0.929915i | \(0.619880\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.1749 | 0.395159 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.9975 | −1.12279 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.3182 | 0.630896 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.987880 | −0.0381367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.82841 | 0.186122 | 0.0930608 | − | 0.995660i | \(-0.470335\pi\) | ||||
0.0930608 | + | 0.995660i | \(0.470335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.4042 | −1.39913 | −0.699563 | − | 0.714571i | \(-0.746622\pi\) | ||||
−0.699563 | + | 0.714571i | \(0.746622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.13106 | 0.273665 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.43742 | 0.131722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.1762 | 1.11639 | 0.558197 | − | 0.829708i | \(-0.311493\pi\) | ||||
0.558197 | + | 0.829708i | \(0.311493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.5083 | 0.820591 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.4433 | 1.42648 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.413504 | 0.0157304 | 0.00786521 | − | 0.999969i | \(-0.497496\pi\) | ||||
0.00786521 | + | 0.999969i | \(0.497496\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.36162 | −0.0897103 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.2698 | 0.995040 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.9770 | −0.717778 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.2592 | −0.878487 | −0.439243 | − | 0.898368i | \(-0.644753\pi\) | ||||
−0.439243 | + | 0.898368i | \(0.644753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.750054 | −0.0282888 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.74584 | −0.178486 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.8748 | 1.08442 | 0.542209 | − | 0.840244i | \(-0.317588\pi\) | ||||
0.542209 | + | 0.840244i | \(0.317588\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.74968 | −0.365641 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.6632 | −1.37305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.9389 | −0.632594 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.4613 | −0.986841 | −0.493421 | − | 0.869791i | \(-0.664254\pi\) | ||||
−0.493421 | + | 0.869791i | \(0.664254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.7857 | −0.438923 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.656176 | −0.0244035 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.61886 | 0.319656 | 0.159828 | − | 0.987145i | \(-0.448906\pi\) | ||||
0.159828 | + | 0.987145i | \(0.448906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.19005 | −0.0440758 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.1550 | 1.26327 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.82620 | −0.178260 | −0.0891299 | − | 0.996020i | \(-0.528409\pi\) | ||||
−0.0891299 | + | 0.996020i | \(0.528409\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.87710 | 0.105979 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.4525 | 1.00986 | 0.504928 | − | 0.863161i | \(-0.331519\pi\) | ||||
0.504928 | + | 0.863161i | \(0.331519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.43742 | 0.126277 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.830417 | −0.0304650 | −0.0152325 | − | 0.999884i | \(-0.504849\pi\) | ||||
−0.0152325 | + | 0.999884i | \(0.504849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.34225 | −0.341815 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.16710 | 0.334958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.12516 | −0.332982 | −0.166491 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.7598 | 0.428550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.04926 | −0.0381361 | −0.0190681 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190681 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.19134 | −0.115838 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2353 | 0.443528 | 0.221764 | − | 0.975100i | \(-0.428819\pi\) | ||||
0.221764 | + | 0.975100i | \(0.428819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.17466 | 0.259740 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.3318 | −0.770247 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0741 | −0.904194 | −0.452097 | − | 0.891969i | \(-0.649324\pi\) | ||||
−0.452097 | + | 0.891969i | \(0.649324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.62157 | 0.274484 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.6696 | 1.13908 | 0.569539 | − | 0.821965i | \(-0.307122\pi\) | ||||
0.569539 | + | 0.821965i | \(0.307122\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.491026 | −0.0176155 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.87484 | 0.317974 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.15401 | −0.291773 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.8549 | 1.10267 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.1593 | −1.60975 | −0.804877 | − | 0.593441i | \(-0.797769\pi\) | ||||
−0.804877 | + | 0.593441i | \(0.797769\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.96986 | −0.141331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.21429 | 0.149843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.07836 | −0.144827 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.32144 | 0.0468079 | 0.0234040 | − | 0.999726i | \(-0.492550\pi\) | ||||
0.0234040 | + | 0.999726i | \(0.492550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.2742 | −0.894138 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.27917 | −0.115864 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1882 | −0.465403 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.18374 | −0.288081 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.8267 | 1.54086 | 0.770432 | − | 0.637522i | \(-0.220041\pi\) | ||||
0.770432 | + | 0.637522i | \(0.220041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.1959 | 1.83285 | 0.916424 | − | 0.400209i | \(-0.131063\pi\) | ||||
0.916424 | + | 0.400209i | \(0.131063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.7352 | 0.481714 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5387 | 0.403688 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.74968 | −0.340681 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.02392 | 0.314937 | 0.157468 | − | 0.987524i | \(-0.449667\pi\) | ||||
0.157468 | + | 0.987524i | \(0.449667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0304 | 0.733073 | 0.366537 | − | 0.930404i | \(-0.380543\pi\) | ||||
0.366537 | + | 0.930404i | \(0.380543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.3430 | −1.85492 | −0.927459 | − | 0.373924i | \(-0.878012\pi\) | ||||
−0.927459 | + | 0.373924i | \(0.878012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.0419 | −0.348771 | −0.174385 | − | 0.984677i | \(-0.555794\pi\) | ||||
−0.174385 | + | 0.984677i | \(0.555794\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.1612 | 0.387178 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.4653 | −0.639784 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.0116 | 1.34844 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.4043 | 1.60206 | 0.801028 | − | 0.598627i | \(-0.204287\pi\) | ||||
0.801028 | + | 0.598627i | \(0.204287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.2372 | 0.973698 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.8676 | 0.615393 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.52535 | 0.292934 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.14811 | 0.0737230 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.87484 | 0.0985482 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.5063 | 0.873317 | 0.436659 | − | 0.899627i | \(-0.356162\pi\) | ||||
0.436659 | + | 0.899627i | \(0.356162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.5993 | 0.464542 | 0.232271 | − | 0.972651i | \(-0.425384\pi\) | ||||
0.232271 | + | 0.972651i | \(0.425384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.83387 | 0.164930 | 0.0824648 | − | 0.996594i | \(-0.473721\pi\) | ||||
0.0824648 | + | 0.996594i | \(0.473721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.80995 | 0.198003 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.73254 | −0.263219 | −0.131609 | − | 0.991302i | \(-0.542014\pi\) | ||||
−0.131609 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.17909 | 0.209853 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.44037 | −0.150629 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.8778 | 0.402463 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.9143 | 0.673996 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.2804 | −1.66408 | −0.832040 | − | 0.554715i | \(-0.812827\pi\) | ||||
−0.832040 | + | 0.554715i | \(0.812827\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.62747 | 0.0548930 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.9908 | 1.61685 | 0.808426 | − | 0.588598i | \(-0.200320\pi\) | ||||
0.808426 | + | 0.588598i | \(0.200320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.1422 | −0.711492 | −0.355746 | − | 0.934583i | \(-0.615773\pi\) | ||||
−0.355746 | + | 0.934583i | \(0.615773\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.8175 | −1.40409 | −0.702047 | − | 0.712131i | \(-0.747730\pi\) | ||||
−0.702047 | + | 0.712131i | \(0.747730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.2733 | −0.378093 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.72152 | −0.158177 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.53850 | −0.285730 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.1751 | −0.439903 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 72.3683 | 2.41362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.1841 | −0.805691 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.55387 | 0.251377 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.0809 | 1.36407 | 0.682035 | − | 0.731320i | \(-0.261095\pi\) | ||||
0.682035 | + | 0.731320i | \(0.261095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.2533 | −0.439583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8388 | 0.425369 | 0.212684 | − | 0.977121i | \(-0.431779\pi\) | ||||
0.212684 | + | 0.977121i | \(0.431779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.25481 | −0.140814 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.5230 | −0.380523 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.8807 | 0.952688 | 0.476344 | − | 0.879259i | \(-0.341962\pi\) | ||||
0.476344 | + | 0.879259i | \(0.341962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.8247 | −0.620295 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.6630 | −1.10803 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.9129 | −1.08100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.6966 | 1.53207 | 0.766033 | − | 0.642802i | \(-0.222228\pi\) | ||||
0.766033 | + | 0.642802i | \(0.222228\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.23820 | −0.204449 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.0257 | −0.426441 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.0370 | 0.654581 | 0.327291 | − | 0.944924i | \(-0.393864\pi\) | ||||
0.327291 | + | 0.944924i | \(0.393864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.0000 | −0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.13106 | −0.167268 | −0.0836339 | − | 0.996497i | \(-0.526653\pi\) | ||||
−0.0836339 | + | 0.996497i | \(0.526653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.0159 | −1.10771 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.0044 | 1.00751 | 0.503753 | − | 0.863848i | \(-0.331952\pi\) | ||||
0.503753 | + | 0.863848i | \(0.331952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −54.4463 | −1.76740 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6216 | −0.636273 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.4845 | 1.18185 | 0.590925 | − | 0.806727i | \(-0.298763\pi\) | ||||
0.590925 | + | 0.806727i | \(0.298763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.29928 | 0.203627 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.4165 | −0.433240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.4994 | 1.95159 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.6001 | 0.824953 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.34182 | −0.107466 | −0.0537328 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537328 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.22018 | −0.0713226 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.1311 | −0.357213 | −0.178606 | − | 0.983921i | \(-0.557159\pi\) | ||||
−0.178606 | + | 0.983921i | \(0.557159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.9518 | −0.447275 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.2695 | 1.76823 | 0.884114 | − | 0.467271i | \(-0.154763\pi\) | ||||
0.884114 | + | 0.467271i | \(0.154763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.49346 | −0.0477311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.0360 | 0.639701 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.3971 | 1.00141 | 0.500706 | − | 0.865618i | \(-0.333074\pi\) | ||||
0.500706 | + | 0.865618i | \(0.333074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.58977 | −0.177924 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.2261 | −1.40631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2143 | 0.515064 | 0.257532 | − | 0.966270i | \(-0.417091\pi\) | ||||
0.257532 | + | 0.966270i | \(0.417091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.13877 | 0.290010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.30850 | −0.168122 | −0.0840609 | − | 0.996461i | \(-0.526789\pi\) | ||||
−0.0840609 | + | 0.996461i | \(0.526789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.05899 | −0.0967821 |
(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 | 1900.2.a.k.1.3 | 6 | ||
4.3 | odd | 2 | 7600.2.a.cj.1.4 | 6 | |||
5.2 | odd | 4 | 380.2.c.b.229.4 | yes | 6 | ||
5.3 | odd | 4 | 380.2.c.b.229.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 1900.2.a.k.1.4 | 6 | ||
15.2 | even | 4 | 3420.2.f.c.1369.3 | 6 | |||
15.8 | even | 4 | 3420.2.f.c.1369.4 | 6 | |||
20.3 | even | 4 | 1520.2.d.i.609.4 | 6 | |||
20.7 | even | 4 | 1520.2.d.i.609.3 | 6 | |||
20.19 | odd | 2 | 7600.2.a.cj.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.b.229.3 | ✓ | 6 | 5.3 | odd | 4 | ||
380.2.c.b.229.4 | yes | 6 | 5.2 | odd | 4 | ||
1520.2.d.i.609.3 | 6 | 20.7 | even | 4 | |||
1520.2.d.i.609.4 | 6 | 20.3 | even | 4 | |||
1900.2.a.k.1.3 | 6 | 1.1 | even | 1 | trivial | ||
1900.2.a.k.1.4 | 6 | 5.4 | even | 2 | inner | ||
3420.2.f.c.1369.3 | 6 | 15.2 | even | 4 | |||
3420.2.f.c.1369.4 | 6 | 15.8 | even | 4 | |||
7600.2.a.cj.1.3 | 6 | 20.19 | odd | 2 | |||
7600.2.a.cj.1.4 | 6 | 4.3 | odd | 2 |