Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 16 x^{13} + 123 x^{12} - 76 x^{11} - 630 x^{10} + 937 x^{9} + 1083 x^{8} - 2602 x^{7} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.10632\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | −2.74294 | −1.58364 | −0.791820 | − | 0.610755i | \(-0.790866\pi\) | ||||
−0.791820 | + | 0.610755i | \(0.790866\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.560055 | −0.250464 | −0.125232 | − | 0.992127i | \(-0.539968\pi\) | ||||
−0.125232 | + | 0.992127i | \(0.539968\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03063 | 0.389541 | 0.194771 | − | 0.980849i | \(-0.437604\pi\) | ||||
0.194771 | + | 0.980849i | \(0.437604\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.52374 | 1.50791 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.17316 | 1.55977 | 0.779883 | − | 0.625926i | \(-0.215279\pi\) | ||||
0.779883 | + | 0.625926i | \(0.215279\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.63284 | −1.28492 | −0.642459 | − | 0.766320i | \(-0.722086\pi\) | ||||
−0.642459 | + | 0.766320i | \(0.722086\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.53620 | 0.396645 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.68154 | −1.76227 | −0.881133 | − | 0.472868i | \(-0.843219\pi\) | ||||
−0.881133 | + | 0.472868i | \(0.843219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82696 | −0.616893 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46716 | 0.305925 | 0.152963 | − | 0.988232i | \(-0.451119\pi\) | ||||
0.152963 | + | 0.988232i | \(0.451119\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.68634 | −0.937268 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.17954 | −0.804354 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.77275 | 1.44336 | 0.721682 | − | 0.692225i | \(-0.243370\pi\) | ||||
0.721682 | + | 0.692225i | \(0.243370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.95059 | 0.529941 | 0.264971 | − | 0.964256i | \(-0.414638\pi\) | ||||
0.264971 | + | 0.964256i | \(0.414638\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.1897 | −2.47011 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.577209 | −0.0975661 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.08993 | −0.179183 | −0.0895917 | − | 0.995979i | \(-0.528556\pi\) | ||||
−0.0895917 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.7076 | 2.03485 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.08800 | −0.326090 | −0.163045 | − | 0.986619i | \(-0.552132\pi\) | ||||
−0.163045 | + | 0.986619i | \(0.552132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.40274 | −0.518913 | −0.259456 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259456 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.53354 | −0.377678 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.02441 | −1.31635 | −0.658173 | − | 0.752867i | \(-0.728670\pi\) | ||||
−0.658173 | + | 0.752867i | \(0.728670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.93780 | −0.848258 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.74294 | −0.384089 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.6020 | 1.86838 | 0.934191 | − | 0.356773i | \(-0.116123\pi\) | ||||
0.934191 | + | 0.356773i | \(0.116123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.89725 | −0.390665 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21.0700 | 2.79080 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.43003 | 0.183097 | 0.0915485 | − | 0.995801i | \(-0.470818\pi\) | ||||
0.0915485 | + | 0.995801i | \(0.470818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.66230 | 0.587395 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.59464 | 0.321826 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5158 | 1.65122 | 0.825609 | − | 0.564243i | \(-0.190832\pi\) | ||||
0.825609 | + | 0.564243i | \(0.190832\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.02435 | −0.484475 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0700800 | −0.00831697 | −0.00415848 | − | 0.999991i | \(-0.501324\pi\) | ||||
−0.00415848 | + | 0.999991i | \(0.501324\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.70938 | 0.551191 | 0.275596 | − | 0.961274i | \(-0.411125\pi\) | ||||
0.275596 | + | 0.961274i | \(0.411125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.8544 | 1.48429 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.33161 | 0.607593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.5699 | −1.86426 | −0.932132 | − | 0.362119i | \(-0.882053\pi\) | ||||
−0.932132 | + | 0.362119i | \(0.882053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.10698 | −0.234108 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2382 | 1.23356 | 0.616779 | − | 0.787137i | \(-0.288437\pi\) | ||||
0.616779 | + | 0.787137i | \(0.288437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.560055 | −0.0607465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.3202 | −2.28577 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.66413 | −0.388397 | −0.194199 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194199 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.77474 | −0.500529 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.09330 | −0.839236 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.30208 | 0.441384 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1576 | 1.23442 | 0.617208 | − | 0.786800i | \(-0.288264\pi\) | ||||
0.617208 | + | 0.786800i | \(0.288264\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.4020 | 2.35199 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.67881 | 0.963078 | 0.481539 | − | 0.876425i | \(-0.340078\pi\) | ||||
0.481539 | + | 0.876425i | \(0.340078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.31042 | −0.621784 | −0.310892 | − | 0.950445i | \(-0.600628\pi\) | ||||
−0.310892 | + | 0.950445i | \(0.600628\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.58325 | 0.154510 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.66901 | −0.644718 | −0.322359 | − | 0.946618i | \(-0.604476\pi\) | ||||
−0.322359 | + | 0.946618i | \(0.604476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.76973 | 0.839988 | 0.419994 | − | 0.907527i | \(-0.362032\pi\) | ||||
0.419994 | + | 0.907527i | \(0.362032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.98962 | 0.283762 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5511 | −1.18071 | −0.590354 | − | 0.807144i | \(-0.701012\pi\) | ||||
−0.590354 | + | 0.807144i | \(0.701012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.821692 | −0.0766232 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.9578 | −1.93755 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.03063 | 0.0944777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.7616 | 1.43287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.72726 | 0.516409 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.42488 | 0.485216 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.3605 | −1.98418 | −0.992088 | − | 0.125544i | \(-0.959932\pi\) | ||||
−0.992088 | + | 0.125544i | \(0.959932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.33352 | 0.821770 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.5643 | 1.70934 | 0.854671 | − | 0.519169i | \(-0.173759\pi\) | ||||
0.854671 | + | 0.519169i | \(0.173759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.91682 | −0.686476 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.34077 | 0.201462 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.54575 | 0.730113 | 0.365056 | − | 0.930985i | \(-0.381050\pi\) | ||||
0.365056 | + | 0.930985i | \(0.381050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2947 | −1.46692 | −0.733458 | − | 0.679735i | \(-0.762095\pi\) | ||||
−0.733458 | + | 0.679735i | \(0.762095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.7535 | 2.08462 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.9664 | −2.00417 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.35316 | −0.361511 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.2871 | 1.34333 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6391 | 1.11736 | 0.558678 | − | 0.829385i | \(-0.311309\pi\) | ||||
0.558678 | + | 0.829385i | \(0.311309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.05070 | 0.492399 | 0.246200 | − | 0.969219i | \(-0.420818\pi\) | ||||
0.246200 | + | 0.969219i | \(0.420818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.52374 | 0.365723 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.65249 | −0.132731 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6913 | −1.41192 | −0.705958 | − | 0.708253i | \(-0.749483\pi\) | ||||
−0.705958 | + | 0.708253i | \(0.749483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −37.3096 | −2.95884 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.51210 | 0.119170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0257 | −1.49021 | −0.745105 | − | 0.666947i | \(-0.767601\pi\) | ||||
−0.745105 | + | 0.666947i | \(0.767601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.94700 | 0.618673 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0370 | −1.08622 | −0.543109 | − | 0.839662i | \(-0.682753\pi\) | ||||
−0.543109 | + | 0.839662i | \(0.682753\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.46318 | 0.651014 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.7493 | −2.65735 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.3611 | −1.24391 | −0.621957 | − | 0.783051i | \(-0.713662\pi\) | ||||
−0.621957 | + | 0.783051i | \(0.713662\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.82988 | −0.365105 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.74294 | 0.206172 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.57781 | 0.342162 | 0.171081 | − | 0.985257i | \(-0.445274\pi\) | ||||
0.171081 | + | 0.985257i | \(0.445274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.629353 | −0.0467794 | −0.0233897 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233897 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.92250 | −0.289960 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.610420 | 0.0448790 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.17316 | 0.378299 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.30756 | −0.313329 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0394 | −1.30528 | −0.652641 | − | 0.757667i | \(-0.726339\pi\) | ||||
−0.652641 | + | 0.757667i | \(0.726339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.8263 | −1.13921 | −0.569603 | − | 0.821920i | \(-0.692903\pi\) | ||||
−0.569603 | + | 0.821920i | \(0.692903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.11696 | −0.509656 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.97810 | −0.283428 | −0.141714 | − | 0.989908i | \(-0.545261\pi\) | ||||
−0.141714 | + | 0.989908i | \(0.545261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.706120 | 0.0500555 | 0.0250278 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250278 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.0731 | −2.61493 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.01082 | 0.562250 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.16939 | 0.0816739 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.63708 | 0.461309 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −39.7378 | −2.74872 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.81305 | 0.262501 | 0.131251 | − | 0.991349i | \(-0.458101\pi\) | ||||
0.131251 | + | 0.991349i | \(0.458101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.192226 | 0.0131711 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.90572 | 0.129969 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.04096 | 0.206434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.9176 | −0.872889 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.63284 | −0.311638 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.7895 | −1.99485 | −0.997425 | − | 0.0717198i | \(-0.977151\pi\) | ||||
−0.997425 | + | 0.0717198i | \(0.977151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.1998 | −1.41332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.3939 | −1.55271 | −0.776354 | − | 0.630297i | \(-0.782933\pi\) | ||||
−0.776354 | + | 0.630297i | \(0.782933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9389 | −1.18543 | −0.592717 | − | 0.805410i | \(-0.701945\pi\) | ||||
−0.592717 | + | 0.805410i | \(0.701945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.6243 | −0.962209 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.47483 | −0.489692 | −0.244846 | − | 0.969562i | \(-0.578737\pi\) | ||||
−0.244846 | + | 0.969562i | \(0.578737\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.05416 | 0.329697 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.4504 | 2.95232 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8015 | 0.892742 | 0.446371 | − | 0.894848i | \(-0.352716\pi\) | ||||
0.446371 | + | 0.894848i | \(0.352716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.3075 | 1.88786 | 0.943932 | − | 0.330141i | \(-0.107096\pi\) | ||||
0.943932 | + | 0.330141i | \(0.107096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.3179 | 1.17510 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.32549 | 0.212458 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.5873 | 2.26437 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.8259 | −1.95351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.67144 | 0.168620 | 0.0843099 | − | 0.996440i | \(-0.473131\pi\) | ||||
0.0843099 | + | 0.996440i | \(0.473131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.58987 | 0.477171 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.53620 | 0.0962005 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.6689 | −1.28929 | −0.644645 | − | 0.764482i | \(-0.722995\pi\) | ||||
−0.644645 | + | 0.764482i | \(0.722995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.12331 | −0.0697993 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 35.1619 | 2.17647 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.0641 | −1.60718 | −0.803592 | − | 0.595181i | \(-0.797080\pi\) | ||||
−0.803592 | + | 0.595181i | \(0.797080\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.61788 | −0.467962 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0505 | 0.615082 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4578 | −0.637622 | −0.318811 | − | 0.947818i | \(-0.603284\pi\) | ||||
−0.318811 | + | 0.947818i | \(0.603284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8115 | −1.26421 | −0.632104 | − | 0.774883i | \(-0.717809\pi\) | ||||
−0.632104 | + | 0.774883i | \(0.717809\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.0968 | 0.792657 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.2432 | −1.46192 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3796 | −0.623649 | −0.311824 | − | 0.950140i | \(-0.600940\pi\) | ||||
−0.311824 | + | 0.950140i | \(0.600940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.3477 | 0.799106 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.52394 | −0.269875 | −0.134938 | − | 0.990854i | \(-0.543083\pi\) | ||||
−0.134938 | + | 0.990854i | \(0.543083\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0440 | −0.656499 | −0.328250 | − | 0.944591i | \(-0.606459\pi\) | ||||
−0.328250 | + | 0.944591i | \(0.606459\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.8004 | −0.698994 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.15195 | −0.127026 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.3476 | −1.95487 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9859 | 1.10917 | 0.554585 | − | 0.832127i | \(-0.312877\pi\) | ||||
0.554585 | + | 0.832127i | \(0.312877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.560055 | 0.0326076 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.6214 | −1.25460 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.79714 | −0.393089 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.50696 | −0.202138 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.5484 | −1.52517 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.800897 | −0.0458592 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.4129 | −1.56454 | −0.782268 | − | 0.622942i | \(-0.785937\pi\) | ||||
−0.782268 | + | 0.622942i | \(0.785937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.3091 | 0.984682 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.0768449 | −0.00435748 | −0.00217874 | − | 0.999998i | \(-0.500694\pi\) | ||||
−0.00217874 | + | 0.999998i | \(0.500694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.9528 | −1.46694 | −0.733471 | − | 0.679721i | \(-0.762101\pi\) | ||||
−0.733471 | + | 0.679721i | \(0.762101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.61114 | −0.147121 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.72878 | 0.490257 | 0.245129 | − | 0.969491i | \(-0.421170\pi\) | ||||
0.245129 | + | 0.969491i | \(0.421170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.2097 | 2.25131 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.2927 | 1.02100 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.68154 | −0.427412 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.7110 | 1.20431 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.0549 | −1.33024 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.30083 | −0.512771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.10057 | −0.280352 | −0.140176 | − | 0.990127i | \(-0.544767\pi\) | ||||
−0.140176 | + | 0.990127i | \(0.544767\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.93056 | −0.270193 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.56959 | −0.413571 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.3220 | 1.05254 | 0.526268 | − | 0.850319i | \(-0.323591\pi\) | ||||
0.526268 | + | 0.850319i | \(0.323591\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.4270 | 1.86982 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2639 | 0.826584 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.3341 | −0.719973 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.25386 | 0.121344 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.7702 | −0.953954 | −0.476977 | − | 0.878916i | \(-0.658268\pi\) | ||||
−0.476977 | + | 0.878916i | \(0.658268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1565 | 1.66777 | 0.833884 | − | 0.551940i | \(-0.186112\pi\) | ||||
0.833884 | + | 0.551940i | \(0.186112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3631 | 1.03353 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.29069 | −0.281595 | −0.140798 | − | 0.990038i | \(-0.544967\pi\) | ||||
−0.140798 | + | 0.990038i | \(0.544967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0392486 | 0.00208310 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.82696 | −0.149619 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0854 | 0.743398 | 0.371699 | − | 0.928353i | \(-0.378775\pi\) | ||||
0.371699 | + | 0.928353i | \(0.378775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.0061 | 2.10558 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −43.2331 | −2.26915 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.63751 | −0.138054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.09151 | −0.422373 | −0.211187 | − | 0.977446i | \(-0.567733\pi\) | ||||
−0.211187 | + | 0.977446i | \(0.567733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.44556 | −0.491716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0187 | 0.727812 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.4470 | −1.68004 | −0.840021 | − | 0.542553i | \(-0.817458\pi\) | ||||
−0.840021 | + | 0.542553i | \(0.817458\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.8801 | −0.768407 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.0099 | −1.85460 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2667 | 1.09239 | 0.546197 | − | 0.837656i | \(-0.316075\pi\) | ||||
0.546197 | + | 0.837656i | \(0.316075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 61.3337 | 3.14222 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3781 | 1.39896 | 0.699479 | − | 0.714653i | \(-0.253415\pi\) | ||||
0.699479 | + | 0.714653i | \(0.253415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.98599 | −0.152180 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.3931 | −0.782476 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.1858 | −1.37837 | −0.689187 | − | 0.724584i | \(-0.742032\pi\) | ||||
−0.689187 | + | 0.724584i | \(0.742032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.46716 | 0.0741977 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −53.6638 | −2.70698 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.28007 | 0.466931 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7457 | 1.09139 | 0.545694 | − | 0.837985i | \(-0.316266\pi\) | ||||
0.545694 | + | 0.837985i | \(0.316266\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.7154 | 1.08713 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.8629 | 1.79091 | 0.895453 | − | 0.445156i | \(-0.146852\pi\) | ||||
0.895453 | + | 0.445156i | \(0.146852\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.6696 | −0.680931 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.18002 | 0.0586357 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.63838 | −0.279484 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.6180 | 1.01949 | 0.509746 | − | 0.860325i | \(-0.329739\pi\) | ||||
0.509746 | + | 0.860325i | \(0.329739\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.4405 | −1.15624 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.03063 | −0.0507140 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.29403 | −0.308962 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.4384 | 2.32307 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.1953 | −0.937749 | −0.468875 | − | 0.883265i | \(-0.655340\pi\) | ||||
−0.468875 | + | 0.883265i | \(0.655340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.7932 | 1.30582 | 0.652910 | − | 0.757436i | \(-0.273548\pi\) | ||||
0.652910 | + | 0.757436i | \(0.273548\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −40.8241 | −1.98494 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.68634 | −0.227321 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.47383 | 0.0713239 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 65.7385 | 3.17388 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.22702 | 0.107272 | 0.0536359 | − | 0.998561i | \(-0.482919\pi\) | ||||
0.0536359 | + | 0.998561i | \(0.482919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.3534 | −1.02618 | −0.513090 | − | 0.858335i | \(-0.671499\pi\) | ||||
−0.513090 | + | 0.858335i | \(0.671499\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.9405 | 0.572502 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.2701 | −0.539121 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7867 | 1.18301 | 0.591503 | − | 0.806303i | \(-0.298535\pi\) | ||||
0.591503 | + | 0.806303i | \(0.298535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.8611 | −1.27910 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8726 | 0.659108 | 0.329554 | − | 0.944137i | \(-0.393102\pi\) | ||||
0.329554 | + | 0.944137i | \(0.393102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.05212 | 0.0972796 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.4112 | −1.76949 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1634 | 0.809992 | 0.404996 | − | 0.914318i | \(-0.367273\pi\) | ||||
0.404996 | + | 0.914318i | \(0.367273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8015 | −0.508624 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.5967 | −0.779783 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.67411 | 0.125364 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.91385 | 0.136304 | 0.0681520 | − | 0.997675i | \(-0.478290\pi\) | ||||
0.0681520 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.17954 | −0.195084 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.4628 | −0.999624 | −0.499812 | − | 0.866134i | \(-0.666598\pi\) | ||||
−0.499812 | + | 0.866134i | \(0.666598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.9897 | 1.39374 | 0.696869 | − | 0.717198i | \(-0.254576\pi\) | ||||
0.696869 | + | 0.717198i | \(0.254576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.53269 | 0.210198 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.3030 | −0.939512 | −0.469756 | − | 0.882796i | \(-0.655658\pi\) | ||||
−0.469756 | + | 0.882796i | \(0.655658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.9298 | 0.643218 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.5261 | 2.23597 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.6029 | −0.809382 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.9983 | 1.65172 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 61.5321 | 2.81736 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.1851 | −0.739518 | −0.369759 | − | 0.929128i | \(-0.620560\pi\) | ||||
−0.369759 | + | 0.929128i | \(0.620560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.04947 | 0.230236 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.14762 | −0.188723 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.80891 | −0.309177 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.47282 | −0.112054 | −0.0560270 | − | 0.998429i | \(-0.517843\pi\) | ||||
−0.0560270 | + | 0.998429i | \(0.517843\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.1865 | 2.35996 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.1435 | −1.90191 | −0.950954 | − | 0.309332i | \(-0.899895\pi\) | ||||
−0.950954 | + | 0.309332i | \(0.899895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.77275 | 0.350067 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.1064 | −0.589090 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0722265 | −0.00323980 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.3301 | −1.13393 | −0.566966 | − | 0.823741i | \(-0.691883\pi\) | ||||
−0.566966 | + | 0.823741i | \(0.691883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.5028 | 1.72018 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.6671 | −1.94702 | −0.973510 | − | 0.228644i | \(-0.926571\pi\) | ||||
−0.973510 | + | 0.228644i | \(0.926571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.42066 | −0.241216 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.2140 | −1.03097 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.9653 | 0.574676 | 0.287338 | − | 0.957829i | \(-0.407230\pi\) | ||||
0.287338 | + | 0.957829i | \(0.407230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.85363 | 0.214712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.1053 | 1.41749 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.53418 | 0.155735 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.6847 | −2.05319 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.8777 | 1.96991 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.7874 | −0.866902 | −0.433451 | − | 0.901177i | \(-0.642704\pi\) | ||||
−0.433451 | + | 0.901177i | \(0.642704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9107 | 0.608272 | 0.304136 | − | 0.952629i | \(-0.401632\pi\) | ||||
0.304136 | + | 0.952629i | \(0.401632\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.2481 | 0.578194 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.95059 | 0.128530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8474 | −0.906410 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.52374 | −0.196314 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.67335 | 0.418999 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.73501 | 0.161479 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.5567 | −0.541861 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.7172 | −1.32308 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.501110 | −0.0215444 | −0.0107722 | − | 0.999942i | \(-0.503429\pi\) | ||||
−0.0107722 | + | 0.999942i | \(0.503429\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.72628 | 0.0740818 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.91153 | −0.210387 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.9283 | 1.32240 | 0.661200 | − | 0.750210i | \(-0.270047\pi\) | ||||
0.661200 | + | 0.750210i | \(0.270047\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.46910 | 0.276095 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.7067 | −2.54359 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.0775 | −0.726208 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.67435 | −0.0710721 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.8586 | 0.544838 | 0.272419 | − | 0.962179i | \(-0.412176\pi\) | ||||
0.272419 | + | 0.962179i | \(0.412176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.7643 | 0.666760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1897 | −0.599089 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.72190 | 0.409729 | 0.204865 | − | 0.978790i | \(-0.434325\pi\) | ||||
0.204865 | + | 0.978790i | \(0.434325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.02930 | 0.295725 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.17151 | −0.0911949 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.8753 | −1.71358 | −0.856792 | − | 0.515663i | \(-0.827546\pi\) | ||||
−0.856792 | + | 0.515663i | \(0.827546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.23472 | −0.219066 | −0.109533 | − | 0.993983i | \(-0.534936\pi\) | ||||
−0.109533 | + | 0.993983i | \(0.534936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 49.4810 | 2.06710 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.87563 | −0.286734 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.13205 | −0.255280 | −0.127640 | − | 0.991821i | \(-0.540740\pi\) | ||||
−0.127640 | + | 0.991821i | \(0.540740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 43.4108 | 1.80409 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.5825 | 0.480522 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 70.3654 | 2.91424 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.7375 | 0.485286 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.3823 | −0.552347 | −0.276173 | − | 0.961108i | \(-0.589066\pi\) | ||||
−0.276173 | + | 0.961108i | \(0.589066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.6651 | −0.933898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.9117 | 0.448848 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.9068 | 1.31026 | 0.655128 | − | 0.755518i | \(-0.272615\pi\) | ||||
0.655128 | + | 0.755518i | \(0.272615\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.577209 | −0.0236633 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.93685 | −0.0792699 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.0947 | −0.902765 | −0.451383 | − | 0.892331i | \(-0.649069\pi\) | ||||
−0.451383 | + | 0.892331i | \(0.649069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.5468 | −1.69473 | −0.847366 | − | 0.531010i | \(-0.821813\pi\) | ||||
−0.847366 | + | 0.531010i | \(0.821813\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 61.1420 | 2.48990 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.82733 | −0.358882 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2686 | 0.538556 | 0.269278 | − | 0.963063i | \(-0.413215\pi\) | ||||
0.269278 | + | 0.963063i | \(0.413215\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.9732 | −0.890401 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.8086 | 1.69140 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0521 | −1.13301 | −0.566506 | − | 0.824057i | \(-0.691705\pi\) | ||||
−0.566506 | + | 0.824057i | \(0.691705\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.20758 | −0.129342 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.5791 | 0.828485 | 0.414243 | − | 0.910167i | \(-0.364047\pi\) | ||||
0.414243 | + | 0.910167i | \(0.364047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.81346 | −0.354243 | −0.177121 | − | 0.984189i | \(-0.556679\pi\) | ||||
−0.177121 | + | 0.984189i | \(0.556679\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.13208 | −0.246072 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.77637 | −0.151297 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3935 | 0.815739 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 108.999 | 4.35299 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.08993 | −0.0434583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1613 | 0.563752 | 0.281876 | − | 0.959451i | \(-0.409043\pi\) | ||||
0.281876 | + | 0.959451i | \(0.409043\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.4590 | −0.415707 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.5231 | 0.496965 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.5089 | 1.08994 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.317024 | −0.0125413 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.93575 | 0.155453 | 0.0777263 | − | 0.996975i | \(-0.475234\pi\) | ||||
0.0777263 | + | 0.996975i | \(0.475234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9249 | −0.430837 | −0.215419 | − | 0.976522i | \(-0.569112\pi\) | ||||
−0.215419 | + | 0.976522i | \(0.569112\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.22728 | −0.205824 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6497 | 0.969078 | 0.484539 | − | 0.874770i | \(-0.338987\pi\) | ||||
0.484539 | + | 0.874770i | \(0.338987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.17316 | −0.203064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.34119 | −0.326917 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.1759 | −1.53307 | −0.766535 | − | 0.642203i | \(-0.778021\pi\) | ||||
−0.766535 | + | 0.642203i | \(0.778021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9571 | −0.428129 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.3040 | 0.831149 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3417 | −0.753446 | −0.376723 | − | 0.926326i | \(-0.622949\pi\) | ||||
−0.376723 | + | 0.926326i | \(0.622949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4720 | −0.523999 | −0.261999 | − | 0.965068i | \(-0.584382\pi\) | ||||
−0.261999 | + | 0.965068i | \(0.584382\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.7076 | 0.493523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.43385 | 0.171937 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4039 | 0.441561 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 81.7108 | 3.15912 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.39779 | 0.285588 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.8425 | −1.76710 | −0.883549 | − | 0.468339i | \(-0.844853\pi\) | ||||
−0.883549 | + | 0.468339i | \(0.844853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.5868 | 0.753895 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.2310 | −0.508510 | −0.254255 | − | 0.967137i | \(-0.581830\pi\) | ||||
−0.254255 | + | 0.967137i | \(0.581830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5300 | 0.480856 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 64.1682 | 2.45893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.9161 | −0.570750 | −0.285375 | − | 0.958416i | \(-0.592118\pi\) | ||||
−0.285375 | + | 0.958416i | \(0.592118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.78609 | −0.182867 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.2054 | 1.87730 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −63.0160 | −2.40072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.22718 | −0.198851 | −0.0994256 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994256 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.1188 | 0.916199 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.68597 | 0.367410 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.08800 | −0.0790885 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.5030 | 0.775496 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.7273 | 0.896168 | 0.448084 | − | 0.893991i | \(-0.352106\pi\) | ||||
0.448084 | + | 0.893991i | \(0.352106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.37234 | 0.315769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8633 | −0.522122 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.97527 | 0.375159 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.3049 | −0.387008 | −0.193504 | − | 0.981100i | \(-0.561985\pi\) | ||||
−0.193504 | + | 0.981100i | \(0.561985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −74.9581 | −2.81115 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.32900 | 0.162122 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.4225 | 0.501973 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.8566 | −1.41378 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.2574 | −1.83699 | −0.918495 | − | 0.395433i | \(-0.870595\pi\) | ||||
−0.918495 | + | 0.395433i | \(0.870595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.50371 | −0.242211 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −80.3889 | −2.98970 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.4257 | −1.35282 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.0358 | −1.11396 | −0.556982 | − | 0.830524i | \(-0.688041\pi\) | ||||
−0.556982 | + | 0.830524i | \(0.688041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9242 | −1.62682 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.40274 | −0.125855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2926 | 0.417100 | 0.208550 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208550 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.12164 | −0.336457 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 69.9194 | 2.57551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6692 | −0.539616 | −0.269808 | − | 0.962914i | \(-0.586960\pi\) | ||||
−0.269808 | + | 0.962914i | \(0.586960\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −97.6141 | −3.58594 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.75273 | 0.284420 | 0.142210 | − | 0.989837i | \(-0.454579\pi\) | ||||
0.142210 | + | 0.989837i | \(0.454579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.63862 | −0.279857 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 50.8389 | 1.86010 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.87328 | −0.251144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4696 | 0.819926 | 0.409963 | − | 0.912102i | \(-0.365542\pi\) | ||||
0.409963 | + | 0.912102i | \(0.365542\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.32761 | −0.267033 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.38872 | −0.123328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.360873 | −0.0131162 | −0.00655808 | − | 0.999978i | \(-0.502088\pi\) | ||||
−0.00655808 | + | 0.999978i | \(0.502088\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.8186 | −0.755667 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.3247 | −0.773020 | −0.386510 | − | 0.922285i | \(-0.626320\pi\) | ||||
−0.386510 | + | 0.922285i | \(0.626320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.03835 | 0.327210 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.53354 | −0.0916005 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.63284 | 0.167282 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.1098 | 0.653056 | 0.326528 | − | 0.945188i | \(-0.394121\pi\) | ||||
0.326528 | + | 0.945188i | \(0.394121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.6936 | 2.04177 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.3622 | 0.552540 | 0.276270 | − | 0.961080i | \(-0.410902\pi\) | ||||
0.276270 | + | 0.961080i | \(0.410902\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.8275 | −0.496697 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.08119 | 0.110537 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0390 | 0.574658 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.362535 | −0.0129725 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.4865 | −1.16097 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.90807 | 0.353634 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6165 | 1.19830 | 0.599149 | − | 0.800638i | \(-0.295506\pi\) | ||||
0.599149 | + | 0.800638i | \(0.295506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 71.4925 | 2.54520 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9355 | −0.459935 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.62511 | −0.235265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.8954 | 0.741084 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.83433 | 0.206663 | 0.103331 | − | 0.994647i | \(-0.467050\pi\) | ||||
0.103331 | + | 0.994647i | \(0.467050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.02441 | −0.319261 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.5756 | −0.585670 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.3624 | 0.859729 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.846861 | −0.0298479 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.6851 | 1.00976 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.2284 | 0.781509 | 0.390754 | − | 0.920495i | \(-0.372214\pi\) | ||||
0.390754 | + | 0.920495i | \(0.372214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.9505 | 1.50820 | 0.754098 | − | 0.656762i | \(-0.228074\pi\) | ||||
0.754098 | + | 0.656762i | \(0.228074\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 57.0848 | 2.00205 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.6554 | 0.373244 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.1383 | 0.914462 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.5997 | −0.754754 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0324 | 0.350135 | 0.175067 | − | 0.984556i | \(-0.443986\pi\) | ||||
0.175067 | + | 0.984556i | \(0.443986\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8604 | 0.448284 | 0.224142 | − | 0.974556i | \(-0.428042\pi\) | ||||
0.224142 | + | 0.974556i | \(0.428042\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 66.4977 | 2.31515 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.7358 | −1.65994 | −0.829969 | − | 0.557810i | \(-0.811642\pi\) | ||||
−0.829969 | + | 0.557810i | \(0.811642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.72445 | −0.233550 | −0.116775 | − | 0.993158i | \(-0.537256\pi\) | ||||
−0.116775 | + | 0.993158i | \(0.537256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.4706 | 0.987635 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.93780 | −0.205733 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.86151 | 0.272059 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.3321 | −0.426260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.1140 | 1.73013 | 0.865063 | − | 0.501663i | \(-0.167278\pi\) | ||||
0.865063 | + | 0.501663i | \(0.167278\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.4156 | 1.08330 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4089 | 0.427385 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.73984 | −0.163056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.2443 | 0.558162 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.2931 | 1.03966 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.59911 | −0.0548167 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.8061 | −1.32869 | −0.664347 | − | 0.747424i | \(-0.731290\pi\) | ||||
−0.664347 | + | 0.747424i | \(0.731290\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.4615 | 0.665570 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.5880 | 1.14734 | 0.573672 | − | 0.819085i | \(-0.305518\pi\) | ||||
0.573672 | + | 0.819085i | \(0.305518\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.9315 | −0.509455 | −0.254727 | − | 0.967013i | \(-0.581986\pi\) | ||||
−0.254727 | + | 0.967013i | \(0.581986\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.90268 | 0.201163 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9450 | −0.644894 | −0.322447 | − | 0.946588i | \(-0.604505\pi\) | ||||
−0.322447 | + | 0.946588i | \(0.604505\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.16313 | 0.311556 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.74294 | −0.0931553 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −85.7189 | −2.90781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62.6165 | −2.12168 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 54.9978 | 1.86139 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.59104 | 0.189012 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.3344 | −0.551574 | −0.275787 | − | 0.961219i | \(-0.588938\pi\) | ||||
−0.275787 | + | 0.961219i | \(0.588938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52.0773 | −1.75652 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.41565 | 0.182458 | 0.0912289 | − | 0.995830i | \(-0.470920\pi\) | ||||
0.0912289 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.7329 | −0.731370 | −0.365685 | − | 0.930739i | \(-0.619165\pi\) | ||||
−0.365685 | + | 0.930739i | \(0.619165\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.53620 | −0.0516388 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1177 | 0.641909 | 0.320954 | − | 0.947095i | \(-0.395996\pi\) | ||||
0.320954 | + | 0.947095i | \(0.395996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.0454 | −0.772919 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8997 | −0.365154 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 69.3214 | 2.31975 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.56382 | −0.0856992 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.6442 | 0.622511 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.9342 | 0.764898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6020 | 0.453149 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.61940 | 0.320114 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.352472 | 0.0117166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.4624 | 1.27712 | 0.638561 | − | 0.769571i | \(-0.279530\pi\) | ||||
0.638561 | + | 0.769571i | \(0.279530\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.7845 | 1.45224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.8912 | −0.924078 | −0.462039 | − | 0.886860i | \(-0.652882\pi\) | ||||
−0.462039 | + | 0.886860i | \(0.652882\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58.1372 | 1.92406 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.19682 | 0.0726245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.1636 | 0.665860 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.6029 | 1.17443 | 0.587215 | − | 0.809431i | \(-0.300224\pi\) | ||||
0.587215 | + | 0.809431i | \(0.300224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.1921 | 2.47766 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.324669 | 0.0106866 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.10778 | 0.167943 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.5467 | −0.937597 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.9694 | 0.720794 | 0.360397 | − | 0.932799i | \(-0.382641\pi\) | ||||
0.360397 | + | 0.932799i | \(0.382641\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.6115 | 1.49486 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.210781 | 0.00690067 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.89725 | −0.0947502 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.1936 | 0.986381 | 0.493191 | − | 0.869921i | \(-0.335831\pi\) | ||||
0.493191 | + | 0.869921i | \(0.335831\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 71.1872 | 2.32311 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.1344 | 1.40614 | 0.703071 | − | 0.711120i | \(-0.251812\pi\) | ||||
0.703071 | + | 0.711120i | \(0.251812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.06343 | −0.0997592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.41247 | 0.0784776 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.8584 | −1.16524 | −0.582620 | − | 0.812744i | \(-0.697973\pi\) | ||||
−0.582620 | + | 0.812744i | \(0.697973\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.8178 | −0.708236 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.9426 | −0.776391 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.8915 | −1.74572 | −0.872859 | − | 0.487972i | \(-0.837737\pi\) | ||||
−0.872859 | + | 0.487972i | \(0.837737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.1030 | 0.326926 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −110.293 | −3.56526 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.80750 | 0.284409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2940 | −0.719162 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.1689 | −0.972179 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.86362 | 0.285330 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0384 | 0.515760 | 0.257880 | − | 0.966177i | \(-0.416976\pi\) | ||||
0.257880 | + | 0.966177i | \(0.416976\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0700 | 0.676867 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.4983 | 1.46011 | 0.730054 | − | 0.683389i | \(-0.239495\pi\) | ||||
0.730054 | + | 0.683389i | \(0.239495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.8244 | −0.571424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −59.5522 | −1.90720 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.1604 | 1.50879 | 0.754397 | − | 0.656418i | \(-0.227929\pi\) | ||||
0.754397 | + | 0.656418i | \(0.227929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9551 | −0.605809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.6720 | 1.26663 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.90408 | 0.124521 | 0.0622605 | − | 0.998060i | \(-0.480169\pi\) | ||||
0.0622605 | + | 0.998060i | \(0.480169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.22796 | 0.0709886 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.5116 | 0.812045 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.99238 | −0.158748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.53543 | 0.175839 | 0.0879194 | − | 0.996128i | \(-0.471978\pi\) | ||||
0.0879194 | + | 0.996128i | \(0.471978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.9906 | 0.443977 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.395466 | −0.0125371 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.9740 | 0.822606 | 0.411303 | − | 0.911499i | \(-0.365074\pi\) | ||||
0.411303 | + | 0.911499i | \(0.365074\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.55541 | 0.144127 |
(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 | 4012.2.a.h.1.2 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.h.1.2 | ✓ | 15 | 1.1 | even | 1 | trivial |