Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8040,2,Mod(1,8040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8040, 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("8040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8040.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 15x^{5} + 3x^{4} + 43x^{3} - 6x^{2} - 29x + 6 \) |
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 | 1.5 | ||
Root | \(0.211675\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.61083 | 1.36477 | 0.682383 | − | 0.730995i | \(-0.260944\pi\) | ||||
0.682383 | + | 0.730995i | \(0.260944\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.95191 | −1.19155 | −0.595773 | − | 0.803153i | \(-0.703154\pi\) | ||||
−0.595773 | + | 0.803153i | \(0.703154\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.10788 | 1.41667 | 0.708336 | − | 0.705875i | \(-0.249446\pi\) | ||||
0.708336 | + | 0.705875i | \(0.249446\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.16687 | 1.01061 | 0.505307 | − | 0.862940i | \(-0.331379\pi\) | ||||
0.505307 | + | 0.862940i | \(0.331379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.79100 | 0.640299 | 0.320149 | − | 0.947367i | \(-0.396267\pi\) | ||||
0.320149 | + | 0.947367i | \(0.396267\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.61083 | 0.787948 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.13197 | 0.653061 | 0.326530 | − | 0.945187i | \(-0.394120\pi\) | ||||
0.326530 | + | 0.945187i | \(0.394120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00339 | −0.186325 | −0.0931623 | − | 0.995651i | \(-0.529698\pi\) | ||||
−0.0931623 | + | 0.995651i | \(0.529698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.03151 | 0.364870 | 0.182435 | − | 0.983218i | \(-0.441602\pi\) | ||||
0.182435 | + | 0.983218i | \(0.441602\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.95191 | −0.687940 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.61083 | −0.610342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.39738 | −1.05172 | −0.525861 | − | 0.850570i | \(-0.676257\pi\) | ||||
−0.525861 | + | 0.850570i | \(0.676257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.10788 | 0.817916 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0315111 | −0.00492120 | −0.00246060 | − | 0.999997i | \(-0.500783\pi\) | ||||
−0.00246060 | + | 0.999997i | \(0.500783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.97592 | 0.301324 | 0.150662 | − | 0.988585i | \(-0.451859\pi\) | ||||
0.150662 | + | 0.988585i | \(0.451859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.94924 | 0.576056 | 0.288028 | − | 0.957622i | \(-0.407000\pi\) | ||||
0.288028 | + | 0.957622i | \(0.407000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03811 | 0.862588 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.16687 | 0.583478 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.86080 | −0.392960 | −0.196480 | − | 0.980508i | \(-0.562951\pi\) | ||||
−0.196480 | + | 0.980508i | \(0.562951\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.95191 | 0.532876 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.79100 | 0.369677 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.52446 | −0.458845 | −0.229423 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229423 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00606 | 0.384886 | 0.192443 | − | 0.981308i | \(-0.438359\pi\) | ||||
0.192443 | + | 0.981308i | \(0.438359\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.61083 | 0.454922 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.10788 | −0.633555 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.13197 | 0.377045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2515 | 1.57266 | 0.786332 | − | 0.617804i | \(-0.211977\pi\) | ||||
0.786332 | + | 0.617804i | \(0.211977\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.27398 | 0.500231 | 0.250116 | − | 0.968216i | \(-0.419531\pi\) | ||||
0.250116 | + | 0.968216i | \(0.419531\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.2697 | −1.62618 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34696 | −0.264054 | −0.132027 | − | 0.991246i | \(-0.542149\pi\) | ||||
−0.132027 | + | 0.991246i | \(0.542149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.02480 | −0.112487 | −0.0562433 | − | 0.998417i | \(-0.517912\pi\) | ||||
−0.0562433 | + | 0.998417i | \(0.517912\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.16687 | −0.451960 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00339 | −0.107575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.28609 | 0.348325 | 0.174163 | − | 0.984717i | \(-0.444278\pi\) | ||||
0.174163 | + | 0.984717i | \(0.444278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.4437 | 1.93343 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.03151 | 0.210658 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.79100 | −0.286350 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8180 | 1.60607 | 0.803037 | − | 0.595929i | \(-0.203216\pi\) | ||||
0.803037 | + | 0.595929i | \(0.203216\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.95191 | −0.397182 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4986 | −1.34316 | −0.671580 | − | 0.740932i | \(-0.734384\pi\) | ||||
−0.671580 | + | 0.740932i | \(0.734384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.21508 | −0.907989 | −0.453994 | − | 0.891005i | \(-0.650001\pi\) | ||||
−0.453994 | + | 0.891005i | \(0.650001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.61083 | −0.352381 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.4978 | −1.69157 | −0.845786 | − | 0.533522i | \(-0.820868\pi\) | ||||
−0.845786 | + | 0.533522i | \(0.820868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.36518 | −0.705456 | −0.352728 | − | 0.935726i | \(-0.614746\pi\) | ||||
−0.352728 | + | 0.935726i | \(0.614746\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.39738 | −0.607213 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.23653 | −0.398539 | −0.199270 | − | 0.979945i | \(-0.563857\pi\) | ||||
−0.199270 | + | 0.979945i | \(0.563857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.13197 | −0.292058 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.10788 | 0.472224 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.0459 | 1.37925 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.61761 | 0.419783 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0315111 | −0.00284126 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1095 | −1.16328 | −0.581642 | − | 0.813445i | \(-0.697589\pi\) | ||||
−0.581642 | + | 0.813445i | \(0.697589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.97592 | 0.173970 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.93669 | 0.868172 | 0.434086 | − | 0.900871i | \(-0.357071\pi\) | ||||
0.434086 | + | 0.900871i | \(0.357071\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0778 | 0.873858 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.49781 | 0.640581 | 0.320290 | − | 0.947319i | \(-0.396219\pi\) | ||||
0.320290 | + | 0.947319i | \(0.396219\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.33834 | 0.622430 | 0.311215 | − | 0.950340i | \(-0.399264\pi\) | ||||
0.311215 | + | 0.950340i | \(0.399264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.94924 | 0.332586 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.1859 | −1.68803 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00339 | 0.0833269 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.03811 | 0.498015 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1055 | −1.15557 | −0.577784 | − | 0.816190i | \(-0.696082\pi\) | ||||
−0.577784 | + | 0.816190i | \(0.696082\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.577475 | −0.0469942 | −0.0234971 | − | 0.999724i | \(-0.507480\pi\) | ||||
−0.0234971 | + | 0.999724i | \(0.507480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.16687 | 0.336871 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.03151 | −0.163175 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7978 | 0.941566 | 0.470783 | − | 0.882249i | \(-0.343971\pi\) | ||||
0.470783 | + | 0.882249i | \(0.343971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.86080 | −0.226876 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3090 | 0.891275 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7219 | 1.46641 | 0.733204 | − | 0.680008i | \(-0.238024\pi\) | ||||
0.733204 | + | 0.680008i | \(0.238024\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.95191 | 0.307656 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.7169 | −1.13883 | −0.569416 | − | 0.822050i | \(-0.692830\pi\) | ||||
−0.569416 | + | 0.822050i | \(0.692830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0905 | 1.00696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.79100 | 0.213433 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.1994 | −1.61176 | −0.805880 | − | 0.592079i | \(-0.798307\pi\) | ||||
−0.805880 | + | 0.592079i | \(0.798307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61083 | 0.272953 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.52446 | −0.264914 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.65922 | 0.721964 | 0.360982 | − | 0.932573i | \(-0.382442\pi\) | ||||
0.360982 | + | 0.932573i | \(0.382442\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6152 | 0.937684 | 0.468842 | − | 0.883282i | \(-0.344671\pi\) | ||||
0.468842 | + | 0.883282i | \(0.344671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.00606 | 0.222214 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.39738 | 0.470345 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.4671 | −1.20419 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.61083 | 0.262649 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.9695 | 0.793724 | 0.396862 | − | 0.917878i | \(-0.370099\pi\) | ||||
0.396862 | + | 0.917878i | \(0.370099\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.722848 | 0.0520317 | 0.0260159 | − | 0.999662i | \(-0.491718\pi\) | ||||
0.0260159 | + | 0.999662i | \(0.491718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.10788 | −0.365783 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.6212 | 1.32671 | 0.663354 | − | 0.748306i | \(-0.269133\pi\) | ||||
0.663354 | + | 0.748306i | \(0.269133\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9803 | 1.48725 | 0.743626 | − | 0.668596i | \(-0.233104\pi\) | ||||
0.743626 | + | 0.668596i | \(0.233104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.62307 | −0.254290 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0315111 | 0.00220083 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.13197 | 0.217687 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.0298 | −0.762945 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2534 | 1.32546 | 0.662729 | − | 0.748859i | \(-0.269398\pi\) | ||||
0.662729 | + | 0.748859i | \(0.269398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.2515 | 0.907978 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.97592 | −0.134756 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.33545 | 0.497963 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.27398 | 0.288809 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.2839 | 1.43171 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0434167 | −0.00290740 | −0.00145370 | − | 0.999999i | \(-0.500463\pi\) | ||||
−0.00145370 | + | 0.999999i | \(0.500463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.1183 | −1.60079 | −0.800393 | − | 0.599476i | \(-0.795376\pi\) | ||||
−0.800393 | + | 0.599476i | \(0.795376\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.1106 | 0.998539 | 0.499270 | − | 0.866447i | \(-0.333602\pi\) | ||||
0.499270 | + | 0.866447i | \(0.333602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.2697 | −0.938877 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.5699 | −0.692457 | −0.346228 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346228 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.94924 | −0.257620 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.34696 | −0.152452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5167 | 0.809640 | 0.404820 | − | 0.914396i | \(-0.367334\pi\) | ||||
0.404820 | + | 0.914396i | \(0.367334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.76911 | 0.564868 | 0.282434 | − | 0.959287i | \(-0.408858\pi\) | ||||
0.282434 | + | 0.959287i | \(0.408858\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.03811 | −0.385761 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2561 | 0.907093 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.02480 | −0.0649442 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7157 | −0.991965 | −0.495982 | − | 0.868333i | \(-0.665192\pi\) | ||||
−0.495982 | + | 0.868333i | \(0.665192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3773 | −0.778152 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.16687 | −0.260939 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.71788 | 0.419050 | 0.209525 | − | 0.977803i | \(-0.432808\pi\) | ||||
0.209525 | + | 0.977803i | \(0.432808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.0999 | −1.43536 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00339 | −0.0621082 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.6126 | 1.33269 | 0.666346 | − | 0.745642i | \(-0.267857\pi\) | ||||
0.666346 | + | 0.745642i | \(0.267857\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.86080 | 0.175737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.28609 | 0.201106 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.1299 | 1.83705 | 0.918527 | − | 0.395359i | \(-0.129380\pi\) | ||||
0.918527 | + | 0.395359i | \(0.129380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7627 | −0.775279 | −0.387640 | − | 0.921811i | \(-0.626710\pi\) | ||||
−0.387640 | + | 0.921811i | \(0.626710\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.4437 | 1.11626 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.95191 | −0.238309 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.1883 | 0.852490 | 0.426245 | − | 0.904608i | \(-0.359836\pi\) | ||||
0.426245 | + | 0.904608i | \(0.359836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.03151 | 0.121623 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6888 | 0.697296 | 0.348648 | − | 0.937254i | \(-0.386641\pi\) | ||||
0.348648 | + | 0.937254i | \(0.386641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3802 | 0.854813 | 0.427407 | − | 0.904060i | \(-0.359427\pi\) | ||||
0.427407 | + | 0.904060i | \(0.359427\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.79100 | −0.165324 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.113781 | −0.00671629 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.362793 | 0.0213408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.8180 | 0.927267 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.3640 | −0.780733 | −0.390366 | − | 0.920660i | \(-0.627652\pi\) | ||||
−0.390366 | + | 0.920660i | \(0.627652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.52446 | 0.205202 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.95191 | −0.229313 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.9977 | 0.925173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.13470 | 0.411237 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.4986 | −0.775474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00606 | −0.172126 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.55156 | −0.145625 | −0.0728125 | − | 0.997346i | \(-0.523197\pi\) | ||||
−0.0728125 | + | 0.997346i | \(0.523197\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.21508 | −0.524228 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.0850 | −1.59255 | −0.796276 | − | 0.604933i | \(-0.793200\pi\) | ||||
−0.796276 | + | 0.604933i | \(0.793200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.73874 | −0.324372 | −0.162186 | − | 0.986760i | \(-0.551855\pi\) | ||||
−0.162186 | + | 0.986760i | \(0.551855\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.61083 | −0.203447 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6975 | 0.769330 | 0.384665 | − | 0.923056i | \(-0.374317\pi\) | ||||
0.384665 | + | 0.923056i | \(0.374317\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.96530 | 0.222014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.4978 | −0.976630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6297 | 0.647095 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.10788 | 0.283334 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.36518 | −0.407295 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.2600 | 0.786182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.77430 | 0.317384 | 0.158692 | − | 0.987328i | \(-0.449272\pi\) | ||||
0.158692 | + | 0.987328i | \(0.449272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.39738 | −0.350574 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.9573 | −0.651358 | −0.325679 | − | 0.945480i | \(-0.605593\pi\) | ||||
−0.325679 | + | 0.945480i | \(0.605593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.23653 | −0.230097 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.02835 | −0.434760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.47321 | −0.187536 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.13197 | −0.168620 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.1534 | −1.13557 | −0.567787 | − | 0.823176i | \(-0.692200\pi\) | ||||
−0.567787 | + | 0.823176i | \(0.692200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9858 | −0.588056 | −0.294028 | − | 0.955797i | \(-0.594996\pi\) | ||||
−0.294028 | + | 0.955797i | \(0.594996\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.10788 | 0.272639 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.7880 | −0.999986 | −0.499993 | − | 0.866029i | \(-0.666664\pi\) | ||||
−0.499993 | + | 0.866029i | \(0.666664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2515 | −0.703317 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.0459 | 0.796312 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.24991 | 0.277080 | 0.138540 | − | 0.990357i | \(-0.455759\pi\) | ||||
0.138540 | + | 0.990357i | \(0.455759\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2103 | −0.590018 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.61761 | 0.242362 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.27398 | −0.223710 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.3062 | 1.52977 | 0.764885 | − | 0.644167i | \(-0.222796\pi\) | ||||
0.764885 | + | 0.644167i | \(0.222796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0315111 | −0.00164040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3299 | −0.536299 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5199 | −0.648257 | −0.324129 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324129 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.12519 | −0.263961 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.4168 | −1.76787 | −0.883936 | − | 0.467609i | \(-0.845116\pi\) | ||||
−0.883936 | + | 0.467609i | \(0.845116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1095 | −0.671622 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.25280 | −0.472796 | −0.236398 | − | 0.971656i | \(-0.575967\pi\) | ||||
−0.236398 | + | 0.971656i | \(0.575967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.2697 | 0.727251 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.97592 | 0.100441 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.256374 | −0.0129987 | −0.00649934 | − | 0.999979i | \(-0.502069\pi\) | ||||
−0.00649934 | + | 0.999979i | \(0.502069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.0505 | 0.659992 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.93669 | 0.501240 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.34696 | 0.118089 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.6329 | −1.68799 | −0.843994 | − | 0.536352i | \(-0.819802\pi\) | ||||
−0.843994 | + | 0.536352i | \(0.819802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0778 | 0.504522 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.467824 | −0.0233620 | −0.0116810 | − | 0.999932i | \(-0.503718\pi\) | ||||
−0.0116810 | + | 0.999932i | \(0.503718\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3767 | 0.516901 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.2819 | 1.25318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.09058 | −0.152819 | −0.0764096 | − | 0.997077i | \(-0.524346\pi\) | ||||
−0.0764096 | + | 0.997077i | \(0.524346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.49781 | 0.369840 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.7262 | −0.626217 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.02480 | 0.0503055 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.33834 | 0.359360 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.43962 | −0.0703298 | −0.0351649 | − | 0.999382i | \(-0.511196\pi\) | ||||
−0.0351649 | + | 0.999382i | \(0.511196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2803 | 0.598507 | 0.299253 | − | 0.954174i | \(-0.403262\pi\) | ||||
0.299253 | + | 0.954174i | \(0.403262\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.94924 | 0.192019 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.16687 | 0.202123 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8544 | 0.525280 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.1859 | −0.974585 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.1887 | 1.21330 | 0.606649 | − | 0.794970i | \(-0.292513\pi\) | ||||
0.606649 | + | 0.794970i | \(0.292513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.8480 | 1.09800 | 0.549001 | − | 0.835822i | \(-0.315008\pi\) | ||||
0.549001 | + | 0.835822i | \(0.315008\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.00339 | 0.0481088 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.74131 | 0.418154 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.7813 | 1.70775 | 0.853875 | − | 0.520478i | \(-0.174246\pi\) | ||||
0.853875 | + | 0.520478i | \(0.174246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.03811 | 0.287529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5541 | 0.786509 | 0.393255 | − | 0.919430i | \(-0.371349\pi\) | ||||
0.393255 | + | 0.919430i | \(0.371349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.28609 | −0.155776 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1055 | −0.667167 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.552445 | −0.0260715 | −0.0130357 | − | 0.999915i | \(-0.504150\pi\) | ||||
−0.0130357 | + | 0.999915i | \(0.504150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.124529 | 0.00586384 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.577475 | −0.0271321 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.4437 | −0.864655 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3560 | −0.718322 | −0.359161 | − | 0.933276i | \(-0.616937\pi\) | ||||
−0.359161 | + | 0.933276i | \(0.616937\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.16687 | 0.194493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.6577 | −0.822401 | −0.411201 | − | 0.911545i | \(-0.634890\pi\) | ||||
−0.411201 | + | 0.911545i | \(0.634890\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0420 | −0.699060 | −0.349530 | − | 0.936925i | \(-0.613659\pi\) | ||||
−0.349530 | + | 0.936925i | \(0.613659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.03151 | −0.0942091 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.60120 | 0.166644 | 0.0833218 | − | 0.996523i | \(-0.473447\pi\) | ||||
0.0833218 | + | 0.996523i | \(0.473447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.61083 | 0.166733 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.7978 | 0.543613 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.80864 | −0.359042 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.79100 | 0.128060 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.86080 | −0.130987 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.78569 | 0.355737 | 0.177869 | − | 0.984054i | \(-0.443080\pi\) | ||||
0.177869 | + | 0.984054i | \(0.443080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.6771 | −1.48995 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3090 | 0.514578 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8180 | −0.718258 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0734 | 0.547098 | 0.273549 | − | 0.961858i | \(-0.411802\pi\) | ||||
0.273549 | + | 0.961858i | \(0.411802\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.7219 | 0.846632 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8500 | 1.57276 | 0.786378 | − | 0.617745i | \(-0.211954\pi\) | ||||
0.786378 | + | 0.617745i | \(0.211954\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.18099 | −0.188302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.95191 | 0.177625 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.8490 | 2.14632 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.4794 | 1.45398 | 0.726989 | − | 0.686649i | \(-0.240919\pi\) | ||||
0.726989 | + | 0.686649i | \(0.240919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.7169 | −0.657504 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.5356 | 1.22775 | 0.613875 | − | 0.789403i | \(-0.289610\pi\) | ||||
0.613875 | + | 0.789403i | \(0.289610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.4986 | 0.600680 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.0905 | 0.581369 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.8007 | −1.09927 | −0.549636 | − | 0.835404i | \(-0.685233\pi\) | ||||
−0.549636 | + | 0.835404i | \(0.685233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4326 | 0.682699 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.79100 | 0.123226 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.21508 | 0.406065 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.6071 | −0.686397 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.1994 | −0.930550 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.88070 | 0.301449 | 0.150724 | − | 0.988576i | \(-0.451839\pi\) | ||||
0.150724 | + | 0.988576i | \(0.451839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.50396 | −0.196944 | −0.0984722 | − | 0.995140i | \(-0.531396\pi\) | ||||
−0.0984722 | + | 0.995140i | \(0.531396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.61083 | 0.157590 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.46504 | 0.368743 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.1908 | −0.573512 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.52446 | −0.152948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.160955 | −0.00697173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.4978 | 0.756494 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.65922 | 0.416826 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.8621 | −1.02781 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.1324 | −0.478619 | −0.239310 | − | 0.970943i | \(-0.576921\pi\) | ||||
−0.239310 | + | 0.970943i | \(0.576921\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6152 | 0.541372 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.36518 | 0.315490 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.2028 | 0.735538 | 0.367769 | − | 0.929917i | \(-0.380122\pi\) | ||||
0.367769 | + | 0.929917i | \(0.380122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.00606 | 0.128295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.80045 | −0.119303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.47450 | −0.360372 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.39738 | 0.271554 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3509 | 0.438582 | 0.219291 | − | 0.975660i | \(-0.429626\pi\) | ||||
0.219291 | + | 0.975660i | \(0.429626\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0927 | 0.426878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.4671 | −0.695241 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6520 | −0.912521 | −0.456261 | − | 0.889846i | \(-0.650812\pi\) | ||||
−0.456261 | + | 0.889846i | \(0.650812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.23653 | 0.178232 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.61083 | 0.151641 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.15642 | 0.258090 | 0.129045 | − | 0.991639i | \(-0.458809\pi\) | ||||
0.129045 | + | 0.991639i | \(0.458809\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.4090 | −1.06333 | −0.531667 | − | 0.846954i | \(-0.678434\pi\) | ||||
−0.531667 | + | 0.846954i | \(0.678434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.9695 | 0.458257 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.13197 | 0.130612 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.7616 | −1.90508 | −0.952541 | − | 0.304411i | \(-0.901540\pi\) | ||||
−0.952541 | + | 0.304411i | \(0.901540\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.722848 | 0.0300405 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.70039 | −0.153518 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3056 | 0.468231 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.10788 | −0.211185 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.9664 | 1.52577 | 0.762883 | − | 0.646536i | \(-0.223783\pi\) | ||||
0.762883 | + | 0.646536i | \(0.223783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.66994 | 0.233626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.6212 | 0.765975 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.8852 | −0.857652 | −0.428826 | − | 0.903387i | \(-0.641073\pi\) | ||||
−0.428826 | + | 0.903387i | \(0.641073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0459 | −0.616820 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.9803 | 0.858666 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.27017 | −0.297051 | −0.148526 | − | 0.988909i | \(-0.547453\pi\) | ||||
−0.148526 | + | 0.988909i | \(0.547453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.2676 | −1.84650 | −0.923252 | − | 0.384195i | \(-0.874479\pi\) | ||||
−0.923252 | + | 0.384195i | \(0.874479\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.61761 | −0.187733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.9016 | −0.970136 | −0.485068 | − | 0.874476i | \(-0.661205\pi\) | ||||
−0.485068 | + | 0.874476i | \(0.661205\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.62307 | −0.146814 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.1723 | 0.816083 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.1502 | 1.54087 | 0.770435 | − | 0.637518i | \(-0.220039\pi\) | ||||
0.770435 | + | 0.637518i | \(0.220039\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0315111 | 0.00127065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.40259 | 0.338276 | 0.169138 | − | 0.985592i | \(-0.445902\pi\) | ||||
0.169138 | + | 0.985592i | \(0.445902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.60518 | 0.345871 | 0.172936 | − | 0.984933i | \(-0.444675\pi\) | ||||
0.172936 | + | 0.984933i | \(0.444675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.13197 | 0.125682 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8655 | 0.475383 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.0298 | −0.440487 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.6570 | −1.06289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2734 | 0.886692 | 0.443346 | − | 0.896351i | \(-0.353791\pi\) | ||||
0.443346 | + | 0.896351i | \(0.353791\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.2534 | 0.765254 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.1095 | 0.520236 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.8420 | 1.22200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2515 | 0.524221 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.06312 | 0.120986 | 0.0604930 | − | 0.998169i | \(-0.480733\pi\) | ||||
0.0604930 | + | 0.998169i | \(0.480733\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.68139 | −0.0663074 | −0.0331537 | − | 0.999450i | \(-0.510555\pi\) | ||||
−0.0331537 | + | 0.999450i | \(0.510555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.97592 | −0.0778016 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.0726 | 1.61473 | 0.807366 | − | 0.590051i | \(-0.200892\pi\) | ||||
0.807366 | + | 0.590051i | \(0.200892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.9283 | 0.546735 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.33545 | 0.287499 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.2381 | 1.02677 | 0.513387 | − | 0.858157i | \(-0.328390\pi\) | ||||
0.513387 | + | 0.858157i | \(0.328390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.93669 | −0.388259 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.27398 | 0.166744 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.61523 | 0.0629203 | 0.0314602 | − | 0.999505i | \(-0.489984\pi\) | ||||
0.0314602 | + | 0.999505i | \(0.489984\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.7656 | −1.50781 | −0.753904 | − | 0.656985i | \(-0.771831\pi\) | ||||
−0.753904 | + | 0.656985i | \(0.771831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.2839 | 0.826598 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0778 | −0.390801 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.14258 | −0.121681 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0434167 | −0.00167859 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.8797 | −0.458610 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.441903 | −0.0170341 | −0.00851705 | − | 0.999964i | \(-0.502711\pi\) | ||||
−0.00851705 | + | 0.999964i | \(0.502711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.6075 | 0.753578 | 0.376789 | − | 0.926299i | \(-0.377028\pi\) | ||||
0.376789 | + | 0.926299i | \(0.377028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 57.1161 | 2.19192 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.1183 | −0.924214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.12846 | 0.349291 | 0.174645 | − | 0.984631i | \(-0.444122\pi\) | ||||
0.174645 | + | 0.984631i | \(0.444122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.49781 | −0.286477 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.1106 | 0.576507 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.6126 | −0.556696 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.0546 | −1.48571 | −0.742853 | − | 0.669454i | \(-0.766528\pi\) | ||||
−0.742853 | + | 0.669454i | \(0.766528\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.2697 | −0.542061 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.33834 | −0.278359 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.131302 | −0.00497343 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.5699 | −0.399790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.8561 | −0.976570 | −0.488285 | − | 0.872684i | \(-0.662377\pi\) | ||||
−0.488285 | + | 0.872684i | \(0.662377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.8551 | −0.673417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.94924 | −0.148737 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −48.7412 | −1.83310 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8391 | 0.857742 | 0.428871 | − | 0.903366i | \(-0.358912\pi\) | ||||
0.428871 | + | 0.903366i | \(0.358912\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34696 | −0.0880180 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.36263 | 0.238282 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.1859 | 0.754910 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.5167 | 0.467446 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.1305 | 0.452390 | 0.226195 | − | 0.974082i | \(-0.427371\pi\) | ||||
0.226195 | + | 0.974082i | \(0.427371\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.2741 | −1.23919 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.76911 | 0.326127 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00339 | −0.0372649 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.6088 | 1.17230 | 0.586152 | − | 0.810201i | \(-0.300642\pi\) | ||||
0.586152 | + | 0.810201i | \(0.300642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.23338 | 0.304523 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.22504 | 0.340735 | 0.170367 | − | 0.985381i | \(-0.445505\pi\) | ||||
0.170367 | + | 0.985381i | \(0.445505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.03811 | −0.222719 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.95191 | −0.145571 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.9265 | 1.17443 | 0.587217 | − | 0.809430i | \(-0.300224\pi\) | ||||
0.587217 | + | 0.809430i | \(0.300224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.2561 | 0.523710 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.41981 | −0.308893 | −0.154446 | − | 0.988001i | \(-0.549359\pi\) | ||||
−0.154446 | + | 0.988001i | \(0.549359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1055 | 0.516785 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.02480 | −0.0374955 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −63.1815 | −2.30860 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.3140 | −0.485833 | −0.242917 | − | 0.970047i | \(-0.578104\pi\) | ||||
−0.242917 | + | 0.970047i | \(0.578104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.7157 | −0.572711 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.577475 | 0.0210165 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.3061 | −0.374581 | −0.187291 | − | 0.982305i | \(-0.559971\pi\) | ||||
−0.187291 | + | 0.982305i | \(0.559971\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.3773 | −0.449266 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6664 | −0.930406 | −0.465203 | − | 0.885204i | \(-0.654019\pi\) | ||||
−0.465203 | + | 0.885204i | \(0.654019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.5944 | −0.962783 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.16687 | −0.150653 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0025 | −0.650033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.6427 | 0.924700 | 0.462350 | − | 0.886698i | \(-0.347006\pi\) | ||||
0.462350 | + | 0.886698i | \(0.347006\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.71788 | 0.241939 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.2347 | −1.30327 | −0.651635 | − | 0.758532i | \(-0.725917\pi\) | ||||
−0.651635 | + | 0.758532i | \(0.725917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.03151 | 0.0729740 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.0999 | −0.828703 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0879472 | −0.00315104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.3688 | −1.87390 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00339 | −0.0358582 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.7978 | −0.421081 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7835 | 0.455682 | 0.227841 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227841 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.6126 | 0.769431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.2974 | −0.543913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.3546 | 0.545258 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.86080 | 0.101462 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.44142 | −0.157323 | −0.0786615 | − | 0.996901i | \(-0.525065\pi\) | ||||
−0.0786615 | + | 0.996901i | \(0.525065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.4560 | 0.582170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.28609 | 0.116108 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.8904 | −0.596049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.3090 | −0.398590 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.1299 | 1.06062 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.965317 | 0.0339387 | 0.0169694 | − | 0.999856i | \(-0.494598\pi\) | ||||
0.0169694 | + | 0.999856i | \(0.494598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.30046 | 0.256354 | 0.128177 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128177 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.7627 | −0.447608 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7219 | −0.655798 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.51477 | 0.192937 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.4437 | 0.644476 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.8343 | −0.936525 | −0.468263 | − | 0.883589i | \(-0.655120\pi\) | ||||
−0.468263 | + | 0.883589i | \(0.655120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.2105 | 0.530206 | 0.265103 | − | 0.964220i | \(-0.414594\pi\) | ||||
0.265103 | + | 0.964220i | \(0.414594\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.95191 | −0.137588 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.8677 | −0.690868 | −0.345434 | − | 0.938443i | \(-0.612268\pi\) | ||||
−0.345434 | + | 0.938443i | \(0.612268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1836 | −0.527347 | −0.263673 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263673 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.1883 | 0.492185 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.1600 | 0.871743 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.7169 | 0.509301 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.03151 | 0.0702193 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.7563 | 1.61421 | 0.807104 | − | 0.590409i | \(-0.201034\pi\) | ||||
0.807104 | + | 0.590409i | \(0.201034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9932 | −0.965283 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.6888 | 0.402584 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.0905 | −0.450326 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.6734 | 0.572905 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.3802 | 0.493527 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.0364 | −0.686839 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.6156 | −0.603148 | −0.301574 | − | 0.953443i | \(-0.597512\pi\) | ||||
−0.301574 | + | 0.953443i | \(0.597512\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.79100 | −0.0954501 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.7808 | 1.49552 | 0.747762 | − | 0.663967i | \(-0.231128\pi\) | ||||
0.747762 | + | 0.663967i | \(0.231128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.6898 | 1.08124 | 0.540622 | − | 0.841266i | \(-0.318189\pi\) | ||||
0.540622 | + | 0.841266i | \(0.318189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.113781 | −0.00387765 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5685 | 0.666119 | 0.333059 | − | 0.942906i | \(-0.391919\pi\) | ||||
0.333059 | + | 0.942906i | \(0.391919\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1994 | 0.720801 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.362793 | 0.0123211 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.27500 | 0.314633 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.10788 | 0.173074 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.8180 | 0.535358 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.61083 | −0.122068 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.9226 | 0.909112 | 0.454556 | − | 0.890718i | \(-0.349798\pi\) | ||||
0.454556 | + | 0.890718i | \(0.349798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.3640 | −0.450756 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.9281 | 0.570323 | 0.285162 | − | 0.958479i | \(-0.407953\pi\) | ||||
0.285162 | + | 0.958479i | \(0.407953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0415 | −0.640798 | −0.320399 | − | 0.947283i | \(-0.603817\pi\) | ||||
−0.320399 | + | 0.947283i | \(0.603817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.52446 | 0.118473 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.80958 | −0.0943364 | −0.0471682 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471682 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.3363 | −1.58761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.95191 | −0.132394 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.0223 | 0.368848 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.65922 | −0.322872 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9977 | 0.534149 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.03839 | −0.0679843 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.9206 | −0.397131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.13470 | 0.237428 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.6152 | −0.419345 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.8586 | −1.05785 | −0.528923 | − | 0.848670i | \(-0.677404\pi\) | ||||
−0.528923 | + | 0.848670i | \(0.677404\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.4986 | −0.447720 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.9667 | −1.42355 | −0.711775 | − | 0.702407i | \(-0.752109\pi\) | ||||
−0.711775 | + | 0.702407i | \(0.752109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.04993 | 0.134033 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.00606 | −0.0993773 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35.8797 | 1.18485 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0441 | 0.430284 | 0.215142 | − | 0.976583i | \(-0.430979\pi\) | ||||
0.215142 | + | 0.976583i | \(0.430979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.55156 | −0.0840766 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.6872 | 2.22795 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.39738 | −0.210345 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.21508 | −0.302663 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.0287500 | −0.000943257 0 | −0.000471629 | − | 1.00000i | \(-0.500150\pi\) | ||||
−0.000471629 | 1.00000i | \(0.500150\pi\) | ||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.8524 | 0.552314 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.0850 | −0.919460 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.4671 | 0.538532 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.2736 | −0.727648 | −0.363824 | − | 0.931468i | \(-0.618529\pi\) | ||||
−0.363824 | + | 0.931468i | \(0.618529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.73874 | −0.187277 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.2045 | 0.528253 | 0.264126 | − | 0.964488i | \(-0.414916\pi\) | ||||
0.264126 | + | 0.964488i | \(0.414916\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0986916 | −0.00321384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.61083 | −0.117460 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.07154 | −0.0998117 | −0.0499059 | − | 0.998754i | \(-0.515892\pi\) | ||||
−0.0499059 | + | 0.998754i | \(0.515892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.8310 | 0.708664 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.6975 | 0.444173 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.3892 | 0.822437 | 0.411219 | − | 0.911537i | \(-0.365103\pi\) | ||||
0.411219 | + | 0.911537i | \(0.365103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.9695 | −0.354964 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.96530 | 0.128180 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.0733 | 0.874243 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8730 | −0.866870 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.4978 | −0.563857 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.722848 | −0.0232693 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.48762 | 0.208628 | 0.104314 | − | 0.994544i | \(-0.466735\pi\) | ||||
0.104314 | + | 0.994544i | \(0.466735\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.6297 | 0.373600 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5113 | −1.13961 | −0.569806 | − | 0.821779i | \(-0.692982\pi\) | ||||
−0.569806 | + | 0.821779i | \(0.692982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.4975 | 0.849472 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.10788 | 0.163583 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.88536 | −0.188289 | −0.0941447 | − | 0.995559i | \(-0.530012\pi\) | ||||
−0.0941447 | + | 0.995559i | \(0.530012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.9864 | −0.415046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.36518 | −0.235152 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.21530 | 0.0706571 | 0.0353285 | − | 0.999376i | \(-0.488752\pi\) | ||||
0.0353285 | + | 0.999376i | \(0.488752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.6212 | −0.593321 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.2600 | 0.453902 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.18851 | 0.196783 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.2636 | −1.81904 | −0.909519 | − | 0.415663i | \(-0.863550\pi\) | ||||
−0.909519 | + | 0.415663i | \(0.863550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.77430 | 0.183242 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.9803 | −0.665120 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.19804 | 0.0379423 | 0.0189711 | − | 0.999820i | \(-0.493961\pi\) | ||||
0.0189711 | + | 0.999820i | \(0.493961\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.39738 | −0.202404 |
(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 | 8040.2.a.t.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8040.2.a.t.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial |