Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.05490\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 2.05490 | 1.18640 | 0.593198 | − | 0.805056i | \(-0.297865\pi\) | ||||
0.593198 | + | 0.805056i | \(0.297865\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.929320 | 0.415604 | 0.207802 | − | 0.978171i | \(-0.433369\pi\) | ||||
0.207802 | + | 0.978171i | \(0.433369\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.22261 | 0.407537 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.90966 | 0.493072 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.05388 | −1.22575 | −0.612873 | − | 0.790181i | \(-0.709986\pi\) | ||||
−0.612873 | + | 0.790181i | \(0.709986\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.52180 | 1.03737 | 0.518686 | − | 0.854965i | \(-0.326421\pi\) | ||||
0.518686 | + | 0.854965i | \(0.326421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.05490 | 0.448416 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.13093 | −0.652843 | −0.326422 | − | 0.945224i | \(-0.605843\pi\) | ||||
−0.326422 | + | 0.945224i | \(0.605843\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.13637 | −0.827273 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.65235 | −0.702896 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.89235 | −0.722791 | −0.361395 | − | 0.932413i | \(-0.617700\pi\) | ||||
−0.361395 | + | 0.932413i | \(0.617700\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.650557 | −0.116844 | −0.0584218 | − | 0.998292i | \(-0.518607\pi\) | ||||
−0.0584218 | + | 0.998292i | \(0.518607\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.05490 | −0.357712 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.929320 | 0.157084 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58094 | −1.08190 | −0.540950 | − | 0.841055i | \(-0.681935\pi\) | ||||
−0.540950 | + | 0.841055i | \(0.681935\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.05490 | −0.329047 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3620 | −1.77444 | −0.887220 | − | 0.461346i | \(-0.847367\pi\) | ||||
−0.887220 | + | 0.461346i | \(0.847367\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.86287 | −1.35158 | −0.675788 | − | 0.737096i | \(-0.736196\pi\) | ||||
−0.675788 | + | 0.737096i | \(0.736196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.13620 | 0.169374 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.96562 | 1.16191 | 0.580953 | − | 0.813937i | \(-0.302680\pi\) | ||||
0.580953 | + | 0.813937i | \(0.302680\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.3852 | −1.45422 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.49550 | −1.30431 | −0.652154 | − | 0.758087i | \(-0.726134\pi\) | ||||
−0.652154 | + | 0.758087i | \(0.726134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.929320 | −0.125309 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.29185 | 1.23074 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4166 | 1.61650 | 0.808251 | − | 0.588838i | \(-0.200414\pi\) | ||||
0.808251 | + | 0.588838i | \(0.200414\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.70412 | −0.986411 | −0.493206 | − | 0.869913i | \(-0.664175\pi\) | ||||
−0.493206 | + | 0.869913i | \(0.664175\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.22261 | 0.154035 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.929320 | −0.115268 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8613 | −1.57125 | −0.785626 | − | 0.618702i | \(-0.787659\pi\) | ||||
−0.785626 | + | 0.618702i | \(0.787659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.43374 | −0.774531 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0543 | −1.19322 | −0.596612 | − | 0.802530i | \(-0.703487\pi\) | ||||
−0.596612 | + | 0.802530i | \(0.703487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.4339 | 1.80640 | 0.903199 | − | 0.429222i | \(-0.141212\pi\) | ||||
0.903199 | + | 0.429222i | \(0.141212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.49981 | −0.981474 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2793 | −1.15652 | −0.578258 | − | 0.815854i | \(-0.696267\pi\) | ||||
−0.578258 | + | 0.815854i | \(0.696267\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1731 | −1.24145 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.85960 | 0.972468 | 0.486234 | − | 0.873829i | \(-0.338370\pi\) | ||||
0.486234 | + | 0.873829i | \(0.338370\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.69667 | −0.509425 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.99838 | −0.857517 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.21794 | −0.129101 | −0.0645506 | − | 0.997914i | \(-0.520561\pi\) | ||||
−0.0645506 | + | 0.997914i | \(0.520561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.33683 | −0.138623 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.20220 | 0.431136 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.19616 | 0.629125 | 0.314563 | − | 0.949237i | \(-0.398142\pi\) | ||||
0.314563 | + | 0.949237i | \(0.398142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.22261 | −0.122877 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.27848 | −0.425725 | −0.212863 | − | 0.977082i | \(-0.568279\pi\) | ||||
−0.212863 | + | 0.977082i | \(0.568279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0901 | 1.68393 | 0.841966 | − | 0.539530i | \(-0.181398\pi\) | ||||
0.841966 | + | 0.539530i | \(0.181398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.90966 | 0.186364 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9650 | 1.64006 | 0.820032 | − | 0.572318i | \(-0.193956\pi\) | ||||
0.820032 | + | 0.572318i | \(0.193956\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2886 | 1.36860 | 0.684298 | − | 0.729202i | \(-0.260109\pi\) | ||||
0.684298 | + | 0.729202i | \(0.260109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.5232 | −1.28356 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.28934 | −0.497579 | −0.248790 | − | 0.968558i | \(-0.580033\pi\) | ||||
−0.248790 | + | 0.968558i | \(0.580033\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.90963 | −0.271325 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.22261 | −0.113031 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.05388 | −0.463289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.3477 | −2.10519 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.49060 | −0.759423 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.76890 | 0.511907 | 0.255953 | − | 0.966689i | \(-0.417611\pi\) | ||||
0.255953 | + | 0.966689i | \(0.417611\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.2123 | −1.60350 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3283 | −0.989762 | −0.494881 | − | 0.868961i | \(-0.664788\pi\) | ||||
−0.494881 | + | 0.868961i | \(0.664788\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.52180 | 0.392090 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.39420 | −0.292127 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.6510 | −0.995409 | −0.497704 | − | 0.867347i | \(-0.665824\pi\) | ||||
−0.497704 | + | 0.867347i | \(0.665824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.37197 | −0.710101 | −0.355051 | − | 0.934847i | \(-0.615536\pi\) | ||||
−0.355051 | + | 0.934847i | \(0.615536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3685 | 1.37848 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.61724 | −0.300395 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.05490 | 0.169485 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.9193 | 1.05839 | 0.529196 | − | 0.848499i | \(-0.322494\pi\) | ||||
0.529196 | + | 0.848499i | \(0.322494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1077 | 1.06669 | 0.533346 | − | 0.845897i | \(-0.320934\pi\) | ||||
0.533346 | + | 0.845897i | \(0.320934\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.17894 | −0.499537 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.604575 | −0.0485607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.26949 | 0.659978 | 0.329989 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329989 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.5123 | −1.54743 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.13093 | −0.246752 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.91977 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.90966 | −0.148667 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.44439 | 0.266535 | 0.133267 | − | 0.991080i | \(-0.457453\pi\) | ||||
0.133267 | + | 0.991080i | \(0.457453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.52841 | 0.422768 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2236 | 1.23346 | 0.616729 | − | 0.787176i | \(-0.288457\pi\) | ||||
0.616729 | + | 0.787176i | \(0.288457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.13637 | −0.312680 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.5148 | 1.91781 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.4581 | 1.30488 | 0.652441 | − | 0.757839i | \(-0.273745\pi\) | ||||
0.652441 | + | 0.757839i | \(0.273745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.20535 | −0.535569 | −0.267785 | − | 0.963479i | \(-0.586292\pi\) | ||||
−0.267785 | + | 0.963479i | \(0.586292\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.8312 | −1.17028 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.11580 | −0.449642 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.05388 | 0.369576 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.65235 | −0.265670 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7213 | −1.57170 | −0.785848 | − | 0.618420i | \(-0.787773\pi\) | ||||
−0.785848 | + | 0.618420i | \(0.787773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.29040 | 0.308829 | 0.154415 | − | 0.988006i | \(-0.450651\pi\) | ||||
0.154415 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.90966 | −0.136753 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.83071 | −0.486668 | −0.243334 | − | 0.969943i | \(-0.578241\pi\) | ||||
−0.243334 | + | 0.969943i | \(0.578241\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.16560 | 0.578844 | 0.289422 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289422 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.4286 | −1.86413 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.89235 | −0.273189 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5589 | −0.737465 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.82791 | −0.266058 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.52180 | −0.312779 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.07057 | 0.417915 | 0.208958 | − | 0.977925i | \(-0.432993\pi\) | ||||
0.208958 | + | 0.977925i | \(0.432993\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.6605 | −1.41564 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.23644 | −0.561721 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.650557 | −0.0441627 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.7151 | 2.14310 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.05388 | 0.339961 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.1208 | −0.744705 | −0.372353 | − | 0.928091i | \(-0.621449\pi\) | ||||
−0.372353 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.05717 | −0.337145 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.64172 | 0.573571 | 0.286786 | − | 0.957995i | \(-0.407413\pi\) | ||||
0.286786 | + | 0.957995i | \(0.407413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.3645 | −1.54397 | −0.771984 | − | 0.635642i | \(-0.780735\pi\) | ||||
−0.771984 | + | 0.635642i | \(0.780735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.05490 | −0.135202 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.3459 | −1.66046 | −0.830231 | − | 0.557419i | \(-0.811792\pi\) | ||||
−0.830231 | + | 0.557419i | \(0.811792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.40261 | 0.482893 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.1230 | −1.37209 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.5131 | −1.45625 | −0.728125 | − | 0.685444i | \(-0.759608\pi\) | ||||
−0.728125 | + | 0.685444i | \(0.759608\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5802 | 1.06803 | 0.534013 | − | 0.845476i | \(-0.320683\pi\) | ||||
0.534013 | + | 0.845476i | \(0.320683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.0024 | −0.769957 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.929320 | 0.0593720 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.52180 | −0.287715 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.2056 | 1.15373 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.6471 | −0.672037 | −0.336019 | − | 0.941855i | \(-0.609080\pi\) | ||||
−0.336019 | + | 0.941855i | \(0.609080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.13093 | 0.196840 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.65119 | −0.604381 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.22557 | 0.325962 | 0.162981 | − | 0.986629i | \(-0.447889\pi\) | ||||
0.162981 | + | 0.986629i | \(0.447889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.58094 | −0.408920 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.75883 | −0.294564 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00459 | −0.493584 | −0.246792 | − | 0.969068i | \(-0.579376\pi\) | ||||
−0.246792 | + | 0.969068i | \(0.579376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.82436 | −0.542076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.50274 | −0.153165 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.9168 | 0.726581 | 0.363291 | − | 0.931676i | \(-0.381653\pi\) | ||||
0.363291 | + | 0.931676i | \(0.381653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1920 | 0.619122 | 0.309561 | − | 0.950880i | \(-0.399818\pi\) | ||||
0.309561 | + | 0.950880i | \(0.399818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.05490 | −0.124368 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.13637 | 0.249432 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5066 | 1.05187 | 0.525934 | − | 0.850526i | \(-0.323716\pi\) | ||||
0.525934 | + | 0.850526i | \(0.323716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.795379 | −0.0476181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.56131 | −0.391415 | −0.195707 | − | 0.980662i | \(-0.562700\pi\) | ||||
−0.195707 | + | 0.980662i | \(0.562700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00778 | 0.297681 | 0.148841 | − | 0.988861i | \(-0.452446\pi\) | ||||
0.148841 | + | 0.988861i | \(0.452446\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.63509 | 0.511499 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3620 | −0.670676 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.54172 | 0.502454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7325 | 0.746392 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8927 | 0.986883 | 0.493441 | − | 0.869779i | \(-0.335739\pi\) | ||||
0.493441 | + | 0.869779i | \(0.335739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5390 | 0.671825 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.65235 | 0.211931 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.13093 | 0.181066 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.86287 | −0.510847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.79186 | −0.505079 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.15959 | −0.409957 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.17232 | 0.295200 | 0.147600 | − | 0.989047i | \(-0.452845\pi\) | ||||
0.147600 | + | 0.989047i | \(0.452845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.1183 | 1.99781 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.9152 | 0.789059 | 0.394530 | − | 0.918883i | \(-0.370908\pi\) | ||||
0.394530 | + | 0.918883i | \(0.370908\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9020 | 0.898831 | 0.449416 | − | 0.893323i | \(-0.351632\pi\) | ||||
0.449416 | + | 0.893323i | \(0.351632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.13620 | 0.0640175 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.6516 | −0.822918 | −0.411459 | − | 0.911428i | \(-0.634981\pi\) | ||||
−0.411459 | + | 0.911428i | \(0.634981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.89235 | 0.217930 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.8613 | 1.94577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8526 | −1.27156 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.13637 | 0.229444 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.3616 | 1.62370 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.96562 | 0.439159 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5219 | 1.34784 | 0.673922 | − | 0.738803i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738803i | \(0.264608\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.04594 | −0.440915 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.9522 | −0.653019 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.125969 | −0.00686198 | −0.00343099 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00343099 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.8691 | −0.590327 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.650557 | 0.0352296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.97900 | −0.321899 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.1881 | −1.83531 | −0.917656 | − | 0.397375i | \(-0.869921\pi\) | ||||
−0.917656 | + | 0.397375i | \(0.869921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.95886 | 0.265442 | 0.132721 | − | 0.991153i | \(-0.457629\pi\) | ||||
0.132721 | + | 0.991153i | \(0.457629\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.65235 | 0.194948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.1296 | −1.55041 | −0.775207 | − | 0.631707i | \(-0.782355\pi\) | ||||
−0.775207 | + | 0.631707i | \(0.782355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.34364 | −0.495909 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.3852 | −0.549644 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.21670 | 0.0642150 | 0.0321075 | − | 0.999484i | \(-0.489778\pi\) | ||||
0.0321075 | + | 0.999484i | \(0.489778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44668 | 0.0761411 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.05490 | 0.107854 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3430 | 0.750747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.4543 | −0.754508 | −0.377254 | − | 0.926110i | \(-0.623132\pi\) | ||||
−0.377254 | + | 0.926110i | \(0.623132\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.8913 | −0.723151 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.49550 | −0.492982 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.7743 | −1.17921 | −0.589605 | − | 0.807692i | \(-0.700716\pi\) | ||||
−0.589605 | + | 0.807692i | \(0.700716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.4473 | −0.900977 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.89235 | 0.200466 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4702 | 0.640551 | 0.320275 | − | 0.947324i | \(-0.396225\pi\) | ||||
0.320275 | + | 0.947324i | \(0.396225\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.8545 | 0.607325 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.2679 | 1.08674 | 0.543371 | − | 0.839493i | \(-0.317148\pi\) | ||||
0.543371 | + | 0.839493i | \(0.317148\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.929320 | −0.0473625 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8359 | −0.550817 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.7751 | 1.61106 | 0.805530 | − | 0.592555i | \(-0.201881\pi\) | ||||
0.805530 | + | 0.592555i | \(0.201881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8233 | 0.800220 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.2786 | −1.17425 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.55280 | −0.480653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.8096 | −0.642895 | −0.321448 | − | 0.946927i | \(-0.604169\pi\) | ||||
−0.321448 | + | 0.946927i | \(0.604169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.29185 | 0.465174 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.6309 | −1.72939 | −0.864693 | − | 0.502300i | \(-0.832487\pi\) | ||||
−0.864693 | + | 0.502300i | \(0.832487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.650557 | 0.0324066 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.3833 | −0.515952 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.58094 | 0.326205 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.9173 | −1.77600 | −0.887998 | − | 0.459847i | \(-0.847904\pi\) | ||||
−0.887998 | + | 0.459847i | \(0.847904\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.9416 | −1.18095 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.4166 | 0.610980 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.23340 | 0.404162 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.2036 | −0.842462 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0102 | −0.928708 | −0.464354 | − | 0.885650i | \(-0.653713\pi\) | ||||
−0.464354 | + | 0.885650i | \(0.653713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2677 | 1.52389 | 0.761947 | − | 0.647639i | \(-0.224244\pi\) | ||||
0.761947 | + | 0.647639i | \(0.224244\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.73886 | 0.473520 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.9047 | 1.01403 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.70412 | −0.372828 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.05490 | 0.0992115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0409 | −0.676326 | −0.338163 | − | 0.941088i | \(-0.609805\pi\) | ||||
−0.338163 | + | 0.941088i | \(0.609805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8510 | 0.953980 | 0.476990 | − | 0.878909i | \(-0.341728\pi\) | ||||
0.476990 | + | 0.878909i | \(0.341728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.43305 | −0.356388 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.1574 | −0.677242 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7936 | 1.04015 | 0.520076 | − | 0.854120i | \(-0.325904\pi\) | ||||
0.520076 | + | 0.854120i | \(0.325904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.22261 | 0.0582196 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.4482 | −1.01903 | −0.509516 | − | 0.860461i | \(-0.670176\pi\) | ||||
−0.509516 | + | 0.860461i | \(0.670176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.13185 | −0.0536550 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.5479 | 1.25567 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.1215 | 1.37433 | 0.687164 | − | 0.726503i | \(-0.258856\pi\) | ||||
0.687164 | + | 0.726503i | \(0.258856\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3620 | 0.535014 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.9351 | 1.26552 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.929320 | −0.0435672 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.7601 | −1.43890 | −0.719449 | − | 0.694545i | \(-0.755606\pi\) | ||||
−0.719449 | + | 0.694545i | \(0.755606\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4586 | 0.861572 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.34317 | 0.342006 | 0.171003 | − | 0.985271i | \(-0.445299\pi\) | ||||
0.171003 | + | 0.985271i | \(0.445299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.40181 | 0.158095 | 0.0790477 | − | 0.996871i | \(-0.474812\pi\) | ||||
0.0790477 | + | 0.996871i | \(0.474812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.24234 | −0.0576122 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.03680 | −0.0942521 | −0.0471260 | − | 0.998889i | \(-0.515006\pi\) | ||||
−0.0471260 | + | 0.998889i | \(0.515006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8613 | −0.593877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9930 | 0.782995 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.86287 | 0.407515 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7038 | −0.858190 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.6093 | −0.531554 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.5052 | 0.571379 | 0.285690 | − | 0.958322i | \(-0.407777\pi\) | ||||
0.285690 | + | 0.958322i | \(0.407777\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.58094 | 0.300065 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.43374 | −0.292745 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.75822 | 0.261467 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.7529 | −0.668518 | −0.334259 | − | 0.942481i | \(-0.608486\pi\) | ||||
−0.334259 | + | 0.942481i | \(0.608486\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.1096 | −0.457173 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0293564 | −0.00132483 | −0.000662417 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000662417 | 1.00000i | \(0.500211\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.6715 | 0.885958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.13620 | −0.0510683 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.0543 | −0.450996 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.6586 | −1.41723 | −0.708617 | − | 0.705593i | \(-0.750681\pi\) | ||||
−0.708617 | + | 0.705593i | \(0.750681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.07787 | 0.316216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.47377 | 0.288651 | 0.144326 | − | 0.989530i | \(-0.453899\pi\) | ||||
0.144326 | + | 0.989530i | \(0.453899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.97608 | −0.176933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.05490 | 0.0912613 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2339 | 1.16280 | 0.581400 | − | 0.813618i | \(-0.302505\pi\) | ||||
0.581400 | + | 0.813618i | \(0.302505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4339 | 0.682754 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.5152 | −0.729165 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.8821 | 0.699850 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.96562 | −0.350328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.3379 | 1.46337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.50570 | −0.109777 | −0.0548883 | − | 0.998492i | \(-0.517480\pi\) | ||||
−0.0548883 | + | 0.998492i | \(0.517480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.325724 | −0.0142429 | −0.00712146 | − | 0.999975i | \(-0.502267\pi\) | ||||
−0.00712146 | + | 0.999975i | \(0.502267\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.49981 | −0.370962 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.28784 | 0.143220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.1973 | −0.573796 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.1807 | 0.658785 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3620 | 0.492141 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7659 | 0.681618 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.8747 | 1.54811 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.7800 | −1.40932 | −0.704662 | − | 0.709543i | \(-0.748901\pi\) | ||||
−0.704662 | + | 0.709543i | \(0.748901\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.8063 | −0.635398 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.2786 | 0.568795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.5393 | 0.963710 | 0.481855 | − | 0.876251i | \(-0.339963\pi\) | ||||
0.481855 | + | 0.876251i | \(0.339963\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.41915 | −0.401999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.6004 | −0.749803 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2793 | −0.437122 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.5673 | −0.533454 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.0145 | −1.56835 | −0.784177 | − | 0.620538i | \(-0.786914\pi\) | ||||
−0.784177 | + | 0.620538i | \(0.786914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.86287 | 0.374860 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.3852 | 0.438464 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8927 | 0.459074 | 0.229537 | − | 0.973300i | \(-0.426279\pi\) | ||||
0.229537 | + | 0.973300i | \(0.426279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.91549 | −0.206796 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.1731 | −0.469224 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.1624 | −0.426028 | −0.213014 | − | 0.977049i | \(-0.568328\pi\) | ||||
−0.213014 | + | 0.977049i | \(0.568328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7132 | −0.950516 | −0.475258 | − | 0.879846i | \(-0.657645\pi\) | ||||
−0.475258 | + | 0.879846i | \(0.657645\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.6350 | −1.86466 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.9507 | 0.540080 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2471 | −0.551485 | −0.275743 | − | 0.961231i | \(-0.588924\pi\) | ||||
−0.275743 | + | 0.961231i | \(0.588924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.81633 | 0.366394 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.85960 | 0.367558 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.49550 | 0.393264 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.13620 | −0.0469760 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.7195 | −0.731361 | −0.365680 | − | 0.930741i | \(-0.619164\pi\) | ||||
−0.365680 | + | 0.930741i | \(0.619164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.94169 | −0.121210 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0364 | −0.577382 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0647 | 0.618635 | 0.309317 | − | 0.950959i | \(-0.399899\pi\) | ||||
0.309317 | + | 0.950959i | \(0.399899\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.69667 | −0.192545 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.7795 | 0.686739 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.88585 | −0.322207 | −0.161103 | − | 0.986938i | \(-0.551505\pi\) | ||||
−0.161103 | + | 0.986938i | \(0.551505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00278 | −0.285649 | −0.142825 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142825 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.7243 | −0.640344 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.929320 | 0.0377822 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.40076 | 0.219210 | 0.109605 | − | 0.993975i | \(-0.465041\pi\) | ||||
0.109605 | + | 0.993975i | \(0.465041\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.99838 | −0.324111 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.96562 | −0.322254 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.8522 | 1.12494 | 0.562470 | − | 0.826817i | \(-0.309851\pi\) | ||||
0.562470 | + | 0.826817i | \(0.309851\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.6975 | −0.874927 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.6574 | 1.35499 | 0.677497 | − | 0.735525i | \(-0.263065\pi\) | ||||
0.677497 | + | 0.735525i | \(0.263065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.0524 | −1.56965 | −0.784824 | − | 0.619719i | \(-0.787246\pi\) | ||||
−0.784824 | + | 0.619719i | \(0.787246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.4353 | 0.458881 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.21794 | −0.0487957 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.7913 | 0.511654 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.29185 | −0.371081 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.2593 | 1.32613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8663 | 1.42781 | 0.713907 | − | 0.700240i | \(-0.246924\pi\) | ||||
0.713907 | + | 0.700240i | \(0.246924\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.4744 | 0.495814 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.36115 | 0.212751 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.2925 | −0.486283 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.1431 | −0.795606 | −0.397803 | − | 0.917471i | \(-0.630227\pi\) | ||||
−0.397803 | + | 0.917471i | \(0.630227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.8212 | −1.60983 | −0.804916 | − | 0.593389i | \(-0.797790\pi\) | ||||
−0.804916 | + | 0.593389i | \(0.797790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.9251 | −0.666423 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.47095 | −0.175771 | −0.0878857 | − | 0.996131i | \(-0.528011\pi\) | ||||
−0.0878857 | + | 0.996131i | \(0.528011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.4166 | −0.487394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.33683 | −0.0523945 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.15206 | 0.319015 | 0.159507 | − | 0.987197i | \(-0.449009\pi\) | ||||
0.159507 | + | 0.987197i | \(0.449009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5276 | −0.411349 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.8696 | 0.736175 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.7186 | 1.07976 | 0.539881 | − | 0.841741i | \(-0.318469\pi\) | ||||
0.539881 | + | 0.841741i | \(0.318469\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5438 | 0.565689 | 0.282845 | − | 0.959166i | \(-0.408722\pi\) | ||||
0.282845 | + | 0.959166i | \(0.408722\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.3852 | 0.403328 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.20220 | 0.162954 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.1867 | 0.471869 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.8522 | −0.883516 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.70412 | 0.297414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.94442 | −0.306235 | −0.153117 | − | 0.988208i | \(-0.548931\pi\) | ||||
−0.153117 | + | 0.988208i | \(0.548931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.1075 | 0.581487 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.9244 | −0.535159 | −0.267579 | − | 0.963536i | \(-0.586224\pi\) | ||||
−0.267579 | + | 0.963536i | \(0.586224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.19616 | 0.237787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.7579 | 0.680483 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1515 | −0.962396 | −0.481198 | − | 0.876612i | \(-0.659798\pi\) | ||||
−0.481198 | + | 0.876612i | \(0.659798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.8275 | −0.413696 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.0116 | −1.83176 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.49550 | 0.361750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.16034 | −0.0441416 | −0.0220708 | − | 0.999756i | \(-0.507026\pi\) | ||||
−0.0220708 | + | 0.999756i | \(0.507026\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.22261 | −0.0464432 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.78023 | −0.295121 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 57.4220 | 2.17501 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −52.0832 | −1.96997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8732 | 0.788370 | 0.394185 | − | 0.919031i | \(-0.371027\pi\) | ||||
0.394185 | + | 0.919031i | \(0.371027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.7577 | −1.12233 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.2116 | 0.572902 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.27848 | −0.160909 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3585 | 0.464132 | 0.232066 | − | 0.972700i | \(-0.425451\pi\) | ||||
0.232066 | + | 0.972700i | \(0.425451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.5677 | −0.471324 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.03685 | 0.0762805 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.929320 | 0.0347546 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.2621 | −1.72769 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.2310 | −0.717195 | −0.358598 | − | 0.933492i | \(-0.616745\pi\) | ||||
−0.358598 | + | 0.933492i | \(0.616745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.0901 | 0.636467 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.0707 | 1.26710 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.1002 | 0.597945 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.36247 | 0.347235 | 0.173617 | − | 0.984813i | \(-0.444454\pi\) | ||||
0.173617 | + | 0.984813i | \(0.444454\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.85535 | 0.327976 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.7919 | 1.65669 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.4130 | −1.27107 | −0.635537 | − | 0.772070i | \(-0.719221\pi\) | ||||
−0.635537 | + | 0.772070i | \(0.719221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.90966 | 0.0704388 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.8613 | 0.473750 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.6474 | 0.502027 | 0.251013 | − | 0.967984i | \(-0.419236\pi\) | ||||
0.251013 | + | 0.967984i | \(0.419236\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.29185 | −0.341344 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.7957 | 1.31322 | 0.656608 | − | 0.754232i | \(-0.271991\pi\) | ||||
0.656608 | + | 0.754232i | \(0.271991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0062 | 0.439872 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8319 | 0.396317 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9650 | 0.619886 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.5922 | −1.37176 | −0.685879 | − | 0.727716i | \(-0.740582\pi\) | ||||
−0.685879 | + | 0.727716i | \(0.740582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.8787 | −0.797303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1813 | 0.443322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.4938 | −0.454095 | −0.227048 | − | 0.973884i | \(-0.572907\pi\) | ||||
−0.227048 | + | 0.973884i | \(0.572907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.43374 | 0.233530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.6874 | 1.18492 | 0.592458 | − | 0.805601i | \(-0.298158\pi\) | ||||
0.592458 | + | 0.805601i | \(0.298158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2886 | 0.517281 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.74221 | −0.207610 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.4166 | −0.448337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.1192 | −0.437030 | −0.218515 | − | 0.975834i | \(-0.570121\pi\) | ||||
−0.218515 | + | 0.975834i | \(0.570121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.7380 | 0.386720 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.8912 | −1.90236 | −0.951182 | − | 0.308631i | \(-0.900129\pi\) | ||||
−0.951182 | + | 0.308631i | \(0.900129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.69094 | 0.0966615 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5232 | −0.485141 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.3765 | −1.84076 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0543 | 0.359770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.2162 | 0.508047 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.68500 | 0.274290 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.99290 | −0.0710392 | −0.0355196 | − | 0.999369i | \(-0.511309\pi\) | ||||
−0.0355196 | + | 0.999369i | \(0.511309\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.4486 | −0.585586 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.28934 | −0.188067 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.70412 | 0.273581 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.1332 | −0.643117 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.8825 | −0.845962 | −0.422981 | − | 0.906139i | \(-0.639016\pi\) | ||||
−0.422981 | + | 0.906139i | \(0.639016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.2573 | −1.42420 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.48907 | −0.0526136 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.4339 | −0.544650 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.90963 | −0.102551 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.4879 | 0.862014 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.0178 | −1.30148 | −0.650739 | − | 0.759302i | \(-0.725541\pi\) | ||||
−0.650739 | + | 0.759302i | \(0.725541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6575 | 0.900957 | 0.450478 | − | 0.892787i | \(-0.351253\pi\) | ||||
0.450478 | + | 0.892787i | \(0.351253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.9436 | 0.734524 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.57203 | −0.160151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.0761 | −1.40209 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.22261 | −0.0427215 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.2467 | 0.811316 | 0.405658 | − | 0.914025i | \(-0.367042\pi\) | ||||
0.405658 | + | 0.914025i | \(0.367042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.8583 | −1.31966 | −0.659829 | − | 0.751416i | \(-0.729371\pi\) | ||||
−0.659829 | + | 0.751416i | \(0.729371\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.49981 | 0.295926 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.9460 | −0.971778 | −0.485889 | − | 0.874021i | \(-0.661504\pi\) | ||||
−0.485889 | + | 0.874021i | \(0.661504\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.6059 | 1.13245 | 0.566225 | − | 0.824251i | \(-0.308404\pi\) | ||||
0.566225 | + | 0.824251i | \(0.308404\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.9742 | 1.24793 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.05388 | −0.175107 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.20094 | 0.110773 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.37606 | 0.0821288 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.4877 | −1.08708 | −0.543538 | − | 0.839385i | \(-0.682916\pi\) | ||||
−0.543538 | + | 0.839385i | \(0.682916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.8496 | −0.477573 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.4828 | −0.464373 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.929320 | 0.0319696 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.2905 | 0.353168 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.6044 | 0.706311 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.2557 | 1.75496 | 0.877480 | − | 0.479612i | \(-0.159223\pi\) | ||||
0.877480 | + | 0.479612i | \(0.159223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.13766 | 0.175704 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.9404 | 1.02275 | 0.511373 | − | 0.859359i | \(-0.329137\pi\) | ||||
0.511373 | + | 0.859359i | \(0.329137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.94140 | 0.339196 | 0.169598 | − | 0.985513i | \(-0.445753\pi\) | ||||
0.169598 | + | 0.985513i | \(0.445753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.3477 | −0.795687 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.3903 | 0.898335 | 0.449168 | − | 0.893448i | \(-0.351721\pi\) | ||||
0.449168 | + | 0.893448i | \(0.351721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0769 | 0.512630 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.5524 | 0.596110 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.2793 | 0.348703 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.8613 | 0.435787 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.57550 | 0.256392 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.49060 | −0.287035 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.0860 | 1.62375 | 0.811875 | − | 0.583831i | \(-0.198447\pi\) | ||||
0.811875 | + | 0.583831i | \(0.198447\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.7128 | 1.17083 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.5152 | 1.73559 | 0.867795 | − | 0.496922i | \(-0.165536\pi\) | ||||
0.867795 | + | 0.496922i | \(0.165536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.2091 | −1.62236 | −0.811182 | − | 0.584793i | \(-0.801176\pi\) | ||||
−0.811182 | + | 0.584793i | \(0.801176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.7114 | 0.797051 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.4825 | 1.22496 | 0.612481 | − | 0.790485i | \(-0.290171\pi\) | ||||
0.612481 | + | 0.790485i | \(0.290171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.76890 | 0.193483 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.1731 | 0.374311 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.0189 | 1.20533 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.2242 | 0.542315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.43374 | 0.214816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.53219 | 0.0844534 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.9892 | 1.59875 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.2123 | −0.606068 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.69607 | −0.222585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.6480 | −1.28329 | −0.641643 | − | 0.767003i | \(-0.721747\pi\) | ||||
−0.641643 | + | 0.767003i | \(0.721747\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.23093 | −0.173499 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.0649 | −1.42680 | −0.713402 | − | 0.700755i | \(-0.752847\pi\) | ||||
−0.713402 | + | 0.700755i | \(0.752847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.85960 | −0.293210 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.7122 | −0.486371 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.3283 | −0.374095 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0454 | 0.463314 | 0.231657 | − | 0.972798i | \(-0.425585\pi\) | ||||
0.231657 | + | 0.972798i | \(0.425585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.6286 | 0.350224 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0543 | 0.330941 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.2212 | 0.895027 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.8945 | 0.686265 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.3509 | −0.372411 | −0.186205 | − | 0.982511i | \(-0.559619\pi\) | ||||
−0.186205 | + | 0.982511i | \(0.559619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.52180 | 0.148196 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.5944 | 0.936137 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.69667 | 0.153598 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.2212 | 0.889279 | 0.444640 | − | 0.895710i | \(-0.353332\pi\) | ||||
0.444640 | + | 0.895710i | \(0.353332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.6769 | 1.06637 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.64879 | 0.0863479 | 0.0431740 | − | 0.999068i | \(-0.486253\pi\) | ||||
0.0431740 | + | 0.999068i | \(0.486253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.5735 | 1.15843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.39420 | −0.110413 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.8007 | −1.48832 | −0.744161 | − | 0.668000i | \(-0.767150\pi\) | ||||
−0.744161 | + | 0.668000i | \(0.767150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4339 | −0.501005 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.1076 | −0.976307 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.2570 | 0.494224 | 0.247112 | − | 0.968987i | \(-0.420518\pi\) | ||||
0.247112 | + | 0.968987i | \(0.420518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.1860 | −0.653204 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.99838 | 0.258551 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6510 | −0.376229 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5768 | −0.986348 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.7416 | 0.668387 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.98715 | 0.128351 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.77630 | 0.0571220 | 0.0285610 | − | 0.999592i | \(-0.490908\pi\) | ||||
0.0285610 | + | 0.999592i | \(0.490908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −46.9599 | −1.50857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.4161 | −0.430544 | −0.215272 | − | 0.976554i | \(-0.569064\pi\) | ||||
−0.215272 | + | 0.976554i | \(0.569064\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.37197 | −0.268393 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.49981 | 0.272212 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.1992 | −0.326302 | −0.163151 | − | 0.986601i | \(-0.552166\pi\) | ||||
−0.163151 | + | 0.986601i | \(0.552166\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.21794 | 0.0389255 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4694 | 0.557754 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.9526 | −0.349335 | −0.174667 | − | 0.984627i | \(-0.555885\pi\) | ||||
−0.174667 | + | 0.984627i | \(0.555885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.34792 | −0.202261 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.3685 | 0.521017 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7490 | 0.882367 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.4006 | −1.25160 | −0.625800 | − | 0.779983i | \(-0.715228\pi\) | ||||
−0.625800 | + | 0.779983i | \(0.715228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50.3900 | 1.59908 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.58846 | 0.240570 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5869 | 0.873687 | 0.436843 | − | 0.899538i | \(-0.356096\pi\) | ||||
0.436843 | + | 0.899538i | \(0.356096\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.0359 | 0.760463 |
(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 | 8008.2.a.y.1.12 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.12 | ✓ | 14 | 1.1 | even | 1 | trivial |