Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1932) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(5\) | −1.38197 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.09017 | −1.68911 | −0.844555 | − | 0.535469i | \(-0.820135\pi\) | ||||
−0.844555 | + | 0.535469i | \(0.820135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.38197 | 0.356822 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.47214 | −1.25539 | −0.627697 | − | 0.778458i | \(-0.716002\pi\) | ||||
−0.627697 | + | 0.778458i | \(0.716002\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.09017 | −0.618034 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.76393 | −0.327554 | −0.163777 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163777 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.70820 | −0.845618 | −0.422809 | − | 0.906219i | \(-0.638956\pi\) | ||||
−0.422809 | + | 0.906219i | \(0.638956\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.38197 | 0.233595 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.47214 | −1.22841 | −0.614206 | − | 0.789146i | \(-0.710524\pi\) | ||||
−0.614206 | + | 0.789146i | \(0.710524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.09017 | 0.975208 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2361 | −1.59861 | −0.799303 | − | 0.600929i | \(-0.794798\pi\) | ||||
−0.799303 | + | 0.600929i | \(0.794798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.32624 | 1.42224 | 0.711119 | − | 0.703072i | \(-0.248189\pi\) | ||||
0.711119 | + | 0.703072i | \(0.248189\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.38197 | −0.206011 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.70820 | 1.41609 | 0.708044 | − | 0.706169i | \(-0.249578\pi\) | ||||
0.708044 | + | 0.706169i | \(0.249578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.61803 | 0.359615 | 0.179807 | − | 0.983702i | \(-0.442453\pi\) | ||||
0.179807 | + | 0.983702i | \(0.442453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.38197 | −0.186344 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.47214 | 0.724802 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.38197 | 0.179917 | 0.0899583 | − | 0.995946i | \(-0.471327\pi\) | ||||
0.0899583 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5623 | 1.60844 | 0.804219 | − | 0.594333i | \(-0.202584\pi\) | ||||
0.804219 | + | 0.594333i | \(0.202584\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.41641 | 1.04393 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.32624 | −1.01721 | −0.508606 | − | 0.860999i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.860999i | \(0.669839\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3262 | −1.34418 | −0.672089 | − | 0.740471i | \(-0.734603\pi\) | ||||
−0.672089 | + | 0.740471i | \(0.734603\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.47214 | −1.10863 | −0.554315 | − | 0.832307i | \(-0.687020\pi\) | ||||
−0.554315 | + | 0.832307i | \(0.687020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.09017 | 0.356822 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.70820 | −0.304697 | −0.152348 | − | 0.988327i | \(-0.548684\pi\) | ||||
−0.152348 | + | 0.988327i | \(0.548684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1803 | 1.44673 | 0.723365 | − | 0.690466i | \(-0.242594\pi\) | ||||
0.723365 | + | 0.690466i | \(0.242594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.90983 | 0.749476 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.76393 | 0.189113 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3820 | −1.52449 | −0.762243 | − | 0.647291i | \(-0.775902\pi\) | ||||
−0.762243 | + | 0.647291i | \(0.775902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.09017 | 0.638423 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.70820 | 0.488218 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.56231 | 0.775876 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.76393 | −0.788308 | −0.394154 | − | 0.919044i | \(-0.628962\pi\) | ||||
−0.394154 | + | 0.919044i | \(0.628962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.38197 | −0.336518 | −0.168259 | − | 0.985743i | \(-0.553815\pi\) | ||||
−0.168259 | + | 0.985743i | \(0.553815\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.47214 | 0.637719 | 0.318859 | − | 0.947802i | \(-0.396700\pi\) | ||||
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.38197 | −0.134866 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3820 | 1.19701 | 0.598505 | − | 0.801119i | \(-0.295762\pi\) | ||||
0.598505 | + | 0.801119i | \(0.295762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.5066 | 1.96417 | 0.982087 | − | 0.188428i | \(-0.0603393\pi\) | ||||
0.982087 | + | 0.188428i | \(0.0603393\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.47214 | 0.709224 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.85410 | 0.926996 | 0.463498 | − | 0.886098i | \(-0.346594\pi\) | ||||
0.463498 | + | 0.886098i | \(0.346594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.38197 | 0.128869 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.09017 | −0.563036 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.00000 | 0.458349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.2361 | 0.922955 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.38197 | −0.211365 | −0.105683 | − | 0.994400i | \(-0.533703\pi\) | ||||
−0.105683 | + | 0.994400i | \(0.533703\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.32624 | −0.821129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1803 | −1.15157 | −0.575786 | − | 0.817601i | \(-0.695304\pi\) | ||||
−0.575786 | + | 0.817601i | \(0.695304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.47214 | 0.474494 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.38197 | 0.118941 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4721 | −1.15100 | −0.575501 | − | 0.817801i | \(-0.695193\pi\) | ||||
−0.575501 | + | 0.817801i | \(0.695193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.3262 | −1.38477 | −0.692387 | − | 0.721527i | \(-0.743441\pi\) | ||||
−0.692387 | + | 0.721527i | \(0.743441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.70820 | −0.817578 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.09017 | −0.509286 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.43769 | 0.202439 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.1246 | −1.73060 | −0.865298 | − | 0.501258i | \(-0.832871\pi\) | ||||
−0.865298 | + | 0.501258i | \(0.832871\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.763932 | −0.0621679 | −0.0310840 | − | 0.999517i | \(-0.509896\pi\) | ||||
−0.0310840 | + | 0.999517i | \(0.509896\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.50658 | 0.522621 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6525 | −1.32901 | −0.664506 | − | 0.747283i | \(-0.731358\pi\) | ||||
−0.664506 | + | 0.747283i | \(0.731358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.61803 | −0.207624 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.90983 | 0.227915 | 0.113958 | − | 0.993486i | \(-0.463647\pi\) | ||||
0.113958 | + | 0.993486i | \(0.463647\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.38197 | 0.107586 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1803 | −1.48422 | −0.742110 | − | 0.670279i | \(-0.766175\pi\) | ||||
−0.742110 | + | 0.670279i | \(0.766175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0902 | 1.85309 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.47214 | −0.418465 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.1803 | −1.00208 | −0.501041 | − | 0.865423i | \(-0.667050\pi\) | ||||
−0.501041 | + | 0.865423i | \(0.667050\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.09017 | 0.233595 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.38197 | −0.103875 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.2705 | 1.73932 | 0.869660 | − | 0.493652i | \(-0.164338\pi\) | ||||
0.869660 | + | 0.493652i | \(0.164338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.23607 | 0.314864 | 0.157432 | − | 0.987530i | \(-0.449678\pi\) | ||||
0.157432 | + | 0.987530i | \(0.449678\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5623 | −0.928632 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.3262 | 0.759200 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.00000 | −0.365636 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6525 | 1.06022 | 0.530108 | − | 0.847930i | \(-0.322151\pi\) | ||||
0.530108 | + | 0.847930i | \(0.322151\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.29180 | 0.596857 | 0.298428 | − | 0.954432i | \(-0.403538\pi\) | ||||
0.298428 | + | 0.954432i | \(0.403538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.41641 | −0.602711 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3820 | 1.45215 | 0.726077 | − | 0.687613i | \(-0.241341\pi\) | ||||
0.726077 | + | 0.687613i | \(0.241341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7984 | 1.47436 | 0.737179 | − | 0.675698i | \(-0.236158\pi\) | ||||
0.737179 | + | 0.675698i | \(0.236158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.32624 | 0.587288 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.76393 | 0.123804 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.1459 | 0.987992 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.47214 | −0.378516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7639 | −0.947548 | −0.473774 | − | 0.880646i | \(-0.657109\pi\) | ||||
−0.473774 | + | 0.880646i | \(0.657109\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.3262 | 0.776061 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.8885 | −0.878991 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.70820 | 0.319614 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.47214 | 0.640068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.4508 | 2.04835 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.56231 | 0.640339 | 0.320170 | − | 0.947360i | \(-0.396260\pi\) | ||||
0.320170 | + | 0.947360i | \(0.396260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.09017 | −0.206011 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.1459 | 0.673407 | 0.336703 | − | 0.941611i | \(-0.390688\pi\) | ||||
0.336703 | + | 0.941611i | \(0.390688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7984 | 1.11007 | 0.555034 | − | 0.831828i | \(-0.312705\pi\) | ||||
0.555034 | + | 0.831828i | \(0.312705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.56231 | −0.102350 | −0.0511750 | − | 0.998690i | \(-0.516297\pi\) | ||||
−0.0511750 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.4164 | −0.875190 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.70820 | 0.175917 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.3262 | −1.83227 | −0.916136 | − | 0.400868i | \(-0.868709\pi\) | ||||
−0.916136 | + | 0.400868i | \(0.868709\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.65248 | 0.364108 | 0.182054 | − | 0.983289i | \(-0.441725\pi\) | ||||
0.182054 | + | 0.983289i | \(0.441725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.38197 | −0.0882906 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.3262 | 2.12050 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.1803 | −0.835270 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.1803 | −1.65249 | −0.826244 | − | 0.563312i | \(-0.809527\pi\) | ||||
−0.826244 | + | 0.563312i | \(0.809527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.90983 | −0.432710 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7082 | −0.855094 | −0.427547 | − | 0.903993i | \(-0.640622\pi\) | ||||
−0.427547 | + | 0.903993i | \(0.640622\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.47214 | 0.464296 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.76393 | −0.109185 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.81966 | 0.297193 | 0.148596 | − | 0.988898i | \(-0.452524\pi\) | ||||
0.148596 | + | 0.988898i | \(0.452524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.61803 | −0.222254 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3820 | 0.880162 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1459 | 0.801520 | 0.400760 | − | 0.916183i | \(-0.368746\pi\) | ||||
0.400760 | + | 0.916183i | \(0.368746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4721 | 0.939865 | 0.469933 | − | 0.882702i | \(-0.344278\pi\) | ||||
0.469933 | + | 0.882702i | \(0.344278\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.09017 | −0.368594 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.09017 | −0.186344 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9098 | 1.19627 | 0.598133 | − | 0.801397i | \(-0.295909\pi\) | ||||
0.598133 | + | 0.801397i | \(0.295909\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.70820 | −0.281873 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1803 | −0.845928 | −0.422964 | − | 0.906146i | \(-0.639010\pi\) | ||||
−0.422964 | + | 0.906146i | \(0.639010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.0344 | −1.90425 | −0.952125 | − | 0.305709i | \(-0.901106\pi\) | ||||
−0.952125 | + | 0.305709i | \(0.901106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.56231 | −0.447952 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.2361 | 0.604216 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.76393 | 0.455130 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.47214 | −0.378106 | −0.189053 | − | 0.981967i | \(-0.560542\pi\) | ||||
−0.189053 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.90983 | −0.111195 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.09017 | 0.352204 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.32624 | −0.537555 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.38197 | 0.194289 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.3607 | −0.994070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.0689 | 1.65905 | 0.829524 | − | 0.558470i | \(-0.188612\pi\) | ||||
0.829524 | + | 0.558470i | \(0.188612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.47214 | −0.368187 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.90983 | 0.221706 | 0.110853 | − | 0.993837i | \(-0.464642\pi\) | ||||
0.110853 | + | 0.993837i | \(0.464642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.4164 | −1.54967 | −0.774833 | − | 0.632165i | \(-0.782166\pi\) | ||||
−0.774833 | + | 0.632165i | \(0.782166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.38197 | 0.0778650 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.6180 | 1.60735 | 0.803674 | − | 0.595069i | \(-0.202875\pi\) | ||||
0.803674 | + | 0.595069i | \(0.202875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.76393 | −0.0987612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3820 | −0.691094 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.3607 | 1.52239 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8197 | 1.04393 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.5066 | −1.13402 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.70820 | −0.535231 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.58359 | 0.361867 | 0.180933 | − | 0.983495i | \(-0.442088\pi\) | ||||
0.180933 | + | 0.983495i | \(0.442088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.47214 | −0.409471 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.5066 | 0.628672 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.9787 | 1.85094 | 0.925469 | − | 0.378823i | \(-0.123671\pi\) | ||||
0.925469 | + | 0.378823i | \(0.123671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.85410 | −0.535201 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.70820 | −0.254964 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.38197 | −0.0744025 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.3050 | −1.51949 | −0.759745 | − | 0.650221i | \(-0.774676\pi\) | ||||
−0.759745 | + | 0.650221i | \(0.774676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.0344 | 1.71476 | 0.857382 | − | 0.514680i | \(-0.172089\pi\) | ||||
0.857382 | + | 0.514680i | \(0.172089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.09017 | 0.325069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6525 | 0.833097 | 0.416549 | − | 0.909113i | \(-0.363240\pi\) | ||||
0.416549 | + | 0.909113i | \(0.363240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.6525 | 0.830747 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.00000 | −0.264628 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.56231 | −0.188011 | −0.0940057 | − | 0.995572i | \(-0.529967\pi\) | ||||
−0.0940057 | + | 0.995572i | \(0.529967\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.9443 | 0.576014 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.0902 | 0.685171 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.27051 | −0.327318 | −0.163659 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163659 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.2361 | −0.532868 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.61803 | −0.135922 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.88854 | −0.149563 | −0.0747816 | − | 0.997200i | \(-0.523826\pi\) | ||||
−0.0747816 | + | 0.997200i | \(0.523826\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1803 | −0.577350 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.7426 | 0.553274 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8885 | −0.918873 | −0.459436 | − | 0.888211i | \(-0.651949\pi\) | ||||
−0.459436 | + | 0.888211i | \(0.651949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.38197 | 0.122032 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7639 | 0.601109 | 0.300554 | − | 0.953765i | \(-0.402828\pi\) | ||||
0.300554 | + | 0.953765i | \(0.402828\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.38197 | 0.0704315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.32624 | 0.474079 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.1246 | −1.02036 | −0.510179 | − | 0.860068i | \(-0.670421\pi\) | ||||
−0.510179 | + | 0.860068i | \(0.670421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.00000 | 0.252861 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.1803 | 0.664860 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.74265 | 0.188313 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.1803 | 1.01282 | 0.506411 | − | 0.862292i | \(-0.330972\pi\) | ||||
0.506411 | + | 0.862292i | \(0.330972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.47214 | −0.273949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7082 | 0.634617 | 0.317309 | − | 0.948322i | \(-0.397221\pi\) | ||||
0.317309 | + | 0.948322i | \(0.397221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.6738 | 1.42834 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.38197 | −0.0686704 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.47214 | −0.370380 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.81966 | 0.139423 | 0.0697116 | − | 0.997567i | \(-0.477792\pi\) | ||||
0.0697116 | + | 0.997567i | \(0.477792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4721 | 0.664531 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.38197 | −0.0680021 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2148 | −0.894128 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.3262 | 0.799499 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.85410 | 0.481404 | 0.240702 | − | 0.970599i | \(-0.422622\pi\) | ||||
0.240702 | + | 0.970599i | \(0.422622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.96556 | 0.436955 | 0.218477 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218477 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.70820 | 0.472029 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.4508 | 0.749476 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.5623 | −0.607933 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.09017 | 0.294036 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0344 | 0.531510 | 0.265755 | − | 0.964041i | \(-0.414379\pi\) | ||||
0.265755 | + | 0.964041i | \(0.414379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.70820 | 0.370433 | 0.185216 | − | 0.982698i | \(-0.440701\pi\) | ||||
0.185216 | + | 0.982698i | \(0.440701\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.43769 | −0.116878 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.47214 | 0.261768 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.2918 | 0.729838 | 0.364919 | − | 0.931039i | \(-0.381097\pi\) | ||||
0.364919 | + | 0.931039i | \(0.381097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.94427 | −0.424955 | −0.212478 | − | 0.977166i | \(-0.568153\pi\) | ||||
−0.212478 | + | 0.977166i | \(0.568153\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.8754 | 0.942184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.1246 | 0.999160 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.8541 | −1.22013 | −0.610065 | − | 0.792351i | \(-0.708857\pi\) | ||||
−0.610065 | + | 0.792351i | \(0.708857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2361 | −0.481998 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.763932 | 0.0358927 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.41641 | −0.394567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2705 | 1.27566 | 0.637830 | − | 0.770177i | \(-0.279832\pi\) | ||||
0.637830 | + | 0.770177i | \(0.279832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.00000 | 0.233380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.2705 | −1.73586 | −0.867930 | − | 0.496686i | \(-0.834550\pi\) | ||||
−0.867930 | + | 0.496686i | \(0.834550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4721 | −1.46263 | −0.731317 | − | 0.682038i | \(-0.761094\pi\) | ||||
−0.731317 | + | 0.682038i | \(0.761094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.50658 | −0.301735 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.5967 | 0.675457 | 0.337728 | − | 0.941244i | \(-0.390341\pi\) | ||||
0.337728 | + | 0.941244i | \(0.390341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.32624 | 0.384470 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.6525 | 0.767306 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.32624 | 0.428821 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9098 | 0.775876 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.61803 | 0.119872 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.8885 | −0.497510 | −0.248755 | − | 0.968566i | \(-0.580021\pi\) | ||||
−0.248755 | + | 0.968566i | \(0.580021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.5066 | 2.07492 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.7295 | 0.487201 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7771 | 1.30401 | 0.652007 | − | 0.758213i | \(-0.273927\pi\) | ||||
0.652007 | + | 0.758213i | \(0.273927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.90983 | −0.131587 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.09017 | 0.274846 | 0.137423 | − | 0.990512i | \(-0.456118\pi\) | ||||
0.137423 | + | 0.990512i | \(0.456118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.81966 | 0.397218 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.38197 | −0.0621148 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.3262 | 0.508051 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.03444 | −0.359671 | −0.179836 | − | 0.983697i | \(-0.557557\pi\) | ||||
−0.179836 | + | 0.983697i | \(0.557557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.1803 | 0.856914 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.67376 | 0.163805 | 0.0819025 | − | 0.996640i | \(-0.473900\pi\) | ||||
0.0819025 | + | 0.996640i | \(0.473900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.67376 | 0.207980 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.0902 | −1.06988 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2361 | 0.498030 | 0.249015 | − | 0.968500i | \(-0.419893\pi\) | ||||
0.249015 | + | 0.968500i | \(0.419893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.47214 | 0.419023 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.47214 | 0.241601 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.94427 | −0.394132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.70820 | 0.426966 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.1803 | 0.578553 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.3050 | −1.37149 | −0.685747 | − | 0.727840i | \(-0.740525\pi\) | ||||
−0.685747 | + | 0.727840i | \(0.740525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.472136 | −0.0206451 | −0.0103225 | − | 0.999947i | \(-0.503286\pi\) | ||||
−0.0103225 | + | 0.999947i | \(0.503286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.09017 | −0.134866 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.5410 | 1.02546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.38197 | 0.0599722 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 62.3394 | 2.70022 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.1115 | −0.739793 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.2705 | −1.00420 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.763932 | −0.0328440 | −0.0164220 | − | 0.999865i | \(-0.505228\pi\) | ||||
−0.0164220 | + | 0.999865i | \(0.505228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.23607 | −0.181787 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.3394 | −1.21393 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.4508 | −1.00269 | −0.501343 | − | 0.865249i | \(-0.667160\pi\) | ||||
−0.501343 | + | 0.865249i | \(0.667160\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.5623 | 0.536146 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.65248 | 0.411209 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.70820 | 0.115165 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.3262 | −0.438324 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.81966 | −0.0771015 | −0.0385507 | − | 0.999257i | \(-0.512274\pi\) | ||||
−0.0385507 | + | 0.999257i | \(0.512274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.7984 | −2.40232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.00000 | 0.211100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.4377 | −0.734911 | −0.367456 | − | 0.930041i | \(-0.619771\pi\) | ||||
−0.367456 | + | 0.930041i | \(0.619771\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6180 | −0.572915 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.11146 | −0.256206 | −0.128103 | − | 0.991761i | \(-0.540889\pi\) | ||||
−0.128103 | + | 0.991761i | \(0.540889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.18034 | 0.0493957 | 0.0246978 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246978 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.6525 | −0.612116 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.09017 | 0.128869 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4164 | 0.891577 | 0.445788 | − | 0.895138i | \(-0.352923\pi\) | ||||
0.445788 | + | 0.895138i | \(0.352923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.29180 | −0.344595 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.1803 | −0.546813 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.61803 | 0.108428 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.41641 | 0.347976 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.3820 | 1.66674 | 0.833371 | − | 0.552714i | \(-0.186408\pi\) | ||||
0.833371 | + | 0.552714i | \(0.186408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.7639 | 1.06158 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.3820 | −0.838402 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.0132 | 1.68421 | 0.842104 | − | 0.539315i | \(-0.181317\pi\) | ||||
0.842104 | + | 0.539315i | \(0.181317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.90983 | −0.283275 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.7984 | −0.851221 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.7984 | −0.808940 | −0.404470 | − | 0.914551i | \(-0.632544\pi\) | ||||
−0.404470 | + | 0.914551i | \(0.632544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.0902 | −1.67610 | −0.838051 | − | 0.545591i | \(-0.816305\pi\) | ||||
−0.838051 | + | 0.545591i | \(0.816305\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.32624 | −0.339071 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.8197 | 0.561849 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.3394 | 1.88086 | 0.940429 | − | 0.339990i | \(-0.110424\pi\) | ||||
0.940429 | + | 0.339990i | \(0.110424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.76393 | −0.0714781 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −59.1246 | −2.39193 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0689 | −0.850964 | −0.425482 | − | 0.904967i | \(-0.639895\pi\) | ||||
−0.425482 | + | 0.904967i | \(0.639895\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.1459 | −0.570418 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.965558 | −0.0388719 | −0.0194360 | − | 0.999811i | \(-0.506187\pi\) | ||||
−0.0194360 | + | 0.999811i | \(0.506187\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.9230 | 1.80561 | 0.902804 | − | 0.430053i | \(-0.141505\pi\) | ||||
0.902804 | + | 0.430053i | \(0.141505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.3820 | 0.576201 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.47214 | 0.218536 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37.3607 | 1.48967 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.47214 | −0.377080 | −0.188540 | − | 0.982066i | \(-0.560375\pi\) | ||||
−0.188540 | + | 0.982066i | \(0.560375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.7639 | 0.547067 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.29180 | 0.130631 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.09017 | −0.241301 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3262 | −0.448059 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.3820 | −0.568054 | −0.284027 | − | 0.958816i | \(-0.591670\pi\) | ||||
−0.284027 | + | 0.958816i | \(0.591670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0902 | 0.871151 | 0.435576 | − | 0.900152i | \(-0.356545\pi\) | ||||
0.435576 | + | 0.900152i | \(0.356545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.8885 | 0.507486 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.0902 | −1.06502 | −0.532512 | − | 0.846422i | \(-0.678752\pi\) | ||||
−0.532512 | + | 0.846422i | \(0.678752\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.38197 | 0.0542469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.70820 | −0.184529 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.4377 | 0.564991 | 0.282495 | − | 0.959269i | \(-0.408838\pi\) | ||||
0.282495 | + | 0.959269i | \(0.408838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.2148 | 0.711710 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.47214 | −0.369543 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.00000 | 0.0389545 | 0.0194772 | − | 0.999810i | \(-0.493800\pi\) | ||||
0.0194772 | + | 0.999810i | \(0.493800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.2918 | −0.983737 | −0.491868 | − | 0.870670i | \(-0.663686\pi\) | ||||
−0.491868 | + | 0.870670i | \(0.663686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.4508 | −1.18261 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.56231 | −0.293254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.76393 | 0.0682997 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.56231 | −0.369700 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.5623 | 0.484962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0557 | 0.464714 | 0.232357 | − | 0.972631i | \(-0.425356\pi\) | ||||
0.232357 | + | 0.972631i | \(0.425356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.09017 | 0.118941 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.5623 | −0.790274 | −0.395137 | − | 0.918622i | \(-0.629303\pi\) | ||||
−0.395137 | + | 0.918622i | \(0.629303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.76393 | 0.297952 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1459 | −0.388792 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.94427 | −0.0743955 | −0.0371977 | − | 0.999308i | \(-0.511843\pi\) | ||||
−0.0371977 | + | 0.999308i | \(0.511843\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.6180 | 0.711359 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.7984 | −0.640898 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.9443 | −0.607428 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.2148 | 1.41572 | 0.707859 | − | 0.706354i | \(-0.249661\pi\) | ||||
0.707859 | + | 0.706354i | \(0.249661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.5623 | 0.855837 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51.1803 | 1.93859 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.56231 | 0.0590918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.0902 | −1.40088 | −0.700438 | − | 0.713713i | \(-0.747012\pi\) | ||||
−0.700438 | + | 0.713713i | \(0.747012\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.8885 | 1.54214 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.4164 | 0.505291 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.38197 | 0.127192 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.1591 | −1.58332 | −0.791658 | − | 0.610964i | \(-0.790782\pi\) | ||||
−0.791658 | + | 0.610964i | \(0.790782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.70820 | −0.101566 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.70820 | 0.176324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.41641 | 0.314756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.3262 | 1.05786 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.7771 | −1.89367 | −0.946833 | − | 0.321726i | \(-0.895737\pi\) | ||||
−0.946833 | + | 0.321726i | \(0.895737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.47214 | −0.241035 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.65248 | −0.210218 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.45085 | 0.202439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.2492 | −1.60402 | −0.802012 | − | 0.597307i | \(-0.796237\pi\) | ||||
−0.802012 | + | 0.597307i | \(0.796237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.6312 | −1.72472 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7082 | 0.580196 | 0.290098 | − | 0.956997i | \(-0.406312\pi\) | ||||
0.290098 | + | 0.956997i | \(0.406312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.38197 | 0.0509746 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.32624 | −0.306701 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7639 | 0.579886 | 0.289943 | − | 0.957044i | \(-0.406364\pi\) | ||||
0.289943 | + | 0.957044i | \(0.406364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.3262 | −1.22427 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.145898 | −0.00535248 | −0.00267624 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267624 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.1935 | 1.06957 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.1803 | 0.482243 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.3820 | −0.452427 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.3262 | 1.39854 | 0.699272 | − | 0.714856i | \(-0.253508\pi\) | ||||
0.699272 | + | 0.714856i | \(0.253508\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.1803 | 0.954065 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.05573 | 0.0384219 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.4164 | −0.378591 | −0.189295 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189295 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00000 | 0.0362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9443 | −0.904229 | −0.452115 | − | 0.891960i | \(-0.649330\pi\) | ||||
−0.452115 | + | 0.891960i | \(0.649330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.5066 | −0.742388 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.90983 | 0.249825 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.41641 | −0.303899 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.6525 | −1.61021 | −0.805105 | − | 0.593133i | \(-0.797891\pi\) | ||||
−0.805105 | + | 0.593133i | \(0.797891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.7082 | 0.493689 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.7082 | −0.529017 | −0.264509 | − | 0.964383i | \(-0.585210\pi\) | ||||
−0.264509 | + | 0.964383i | \(0.585210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.5492 | 0.522621 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.47214 | −0.268061 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 56.0132 | 2.00688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3262 | −0.405285 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.76393 | 0.0630378 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.0132 | 0.821375 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7426 | 0.632457 | 0.316229 | − | 0.948683i | \(-0.397583\pi\) | ||||
0.316229 | + | 0.948683i | \(0.397583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.81966 | −0.171584 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.85410 | −0.350372 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −76.5066 | −2.71683 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.61803 | 0.128318 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.0689 | −0.640033 | −0.320016 | − | 0.947412i | \(-0.603688\pi\) | ||||
−0.320016 | + | 0.947412i | \(0.603688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.5410 | −1.71726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.3820 | −0.508162 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.47214 | −0.334264 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.38197 | −0.0487079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.1459 | −0.462758 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.6180 | 1.74448 | 0.872239 | − | 0.489081i | \(-0.162668\pi\) | ||||
0.872239 | + | 0.489081i | \(0.162668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.63932 | 0.0926791 | 0.0463395 | − | 0.998926i | \(-0.485244\pi\) | ||||
0.0463395 | + | 0.998926i | \(0.485244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.4721 | −0.542631 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.02129 | −0.140860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.0344 | −1.78547 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.09017 | 0.212808 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.6525 | 1.34898 | 0.674490 | − | 0.738284i | \(-0.264363\pi\) | ||||
0.674490 | + | 0.738284i | \(0.264363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.7984 | −0.376408 | −0.188204 | − | 0.982130i | \(-0.560267\pi\) | ||||
−0.188204 | + | 0.982130i | \(0.560267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.09017 | 0.107586 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.2016 | −1.01544 | −0.507720 | − | 0.861522i | \(-0.669512\pi\) | ||||
−0.507720 | + | 0.861522i | \(0.669512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.236068 | 0.00819898 | 0.00409949 | − | 0.999992i | \(-0.498695\pi\) | ||||
0.00409949 | + | 0.999992i | \(0.498695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.9098 | −0.690664 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.00000 | −0.173240 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.5066 | 0.917298 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.70820 | 0.162739 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.2705 | −0.906959 | −0.453479 | − | 0.891267i | \(-0.649817\pi\) | ||||
−0.453479 | + | 0.891267i | \(0.649817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8885 | −0.892708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.1803 | 0.488397 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.2918 | −1.14527 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.0344 | 1.09942 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.47214 | 0.256142 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5410 | 0.771790 | 0.385895 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385895 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.56231 | 0.258625 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.65248 | −0.295563 | −0.147781 | − | 0.989020i | \(-0.547213\pi\) | ||||
−0.147781 | + | 0.989020i | \(0.547213\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8885 | 0.405632 | 0.202816 | − | 0.979217i | \(-0.434991\pi\) | ||||
0.202816 | + | 0.979217i | \(0.434991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.2361 | −0.348844 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.4853 | −1.07177 | −0.535886 | − | 0.844290i | \(-0.680022\pi\) | ||||
−0.535886 | + | 0.844290i | \(0.680022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.2148 | 0.619321 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.70820 | −0.0918695 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.7082 | 1.71818 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.76393 | −0.262769 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.30495 | 0.179135 | 0.0895677 | − | 0.995981i | \(-0.471451\pi\) | ||||
0.0895677 | + | 0.995981i | \(0.471451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.47214 | 0.218300 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.1246 | −1.72243 | −0.861216 | − | 0.508239i | \(-0.830297\pi\) | ||||
−0.861216 | + | 0.508239i | \(0.830297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6738 | −0.359201 | −0.179600 | − | 0.983740i | \(-0.557480\pi\) | ||||
−0.179600 | + | 0.983740i | \(0.557480\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.90983 | 0.0641982 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.2705 | 1.62077 | 0.810383 | − | 0.585901i | \(-0.199259\pi\) | ||||
0.810383 | + | 0.585901i | \(0.199259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.38197 | 0.0798886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −53.1246 | −1.77775 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.1591 | −1.07496 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.09017 | −0.203345 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.30495 | 0.276986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.0902 | −0.436097 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.32624 | 0.310358 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.85410 | −0.194597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.9230 | −0.528714 | −0.264357 | − | 0.964425i | \(-0.585160\pi\) | ||||
−0.264357 | + | 0.964425i | \(0.585160\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.38197 | −0.112173 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5410 | 0.813080 | 0.406540 | − | 0.913633i | \(-0.366735\pi\) | ||||
0.406540 | + | 0.913633i | \(0.366735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.1803 | 0.436206 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.3607 | 0.573926 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1803 | 0.435253 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.0000 | −0.626752 | −0.313376 | − | 0.949629i | \(-0.601460\pi\) | ||||
−0.313376 | + | 0.949629i | \(0.601460\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.0689 | −0.957852 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68.9787 | 2.27046 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.0902 | 0.759200 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.47214 | 0.212573 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.96556 | 0.326959 | 0.163480 | − | 0.986547i | \(-0.447728\pi\) | ||||
0.163480 | + | 0.986547i | \(0.447728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.47214 | −0.179342 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.90983 | −0.128002 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.90983 | 0.225976 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0000 | −0.424691 | −0.212346 | − | 0.977195i | \(-0.568110\pi\) | ||||
−0.212346 | + | 0.977195i | \(0.568110\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.4164 | 0.894701 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.8328 | 1.39631 | 0.698155 | − | 0.715947i | \(-0.254005\pi\) | ||||
0.698155 | + | 0.715947i | \(0.254005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.2361 | 0.333332 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.38197 | −0.0449554 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.3607 | 1.37654 | 0.688269 | − | 0.725456i | \(-0.258371\pi\) | ||||
0.688269 | + | 0.725456i | \(0.258371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.6869 | 1.87260 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.6180 | −0.928003 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.6312 | −1.76968 | −0.884839 | − | 0.465897i | \(-0.845732\pi\) | ||||
−0.884839 | + | 0.465897i | \(0.845732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.2492 | −0.655249 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.76393 | 0.0570198 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.4721 | 0.435038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.83282 | −0.284930 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.3820 | 0.399003 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.4590 | −0.368878 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.0557 | 0.934369 | 0.467185 | − | 0.884160i | \(-0.345268\pi\) | ||||
0.467185 | + | 0.884160i | \(0.345268\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.3607 | −0.878952 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.7426 | 0.858212 | 0.429106 | − | 0.903254i | \(-0.358829\pi\) | ||||
0.429106 | + | 0.903254i | \(0.358829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.3262 | 0.523395 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.8197 | −0.602711 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.2574 | 0.552112 | 0.276056 | − | 0.961142i | \(-0.410973\pi\) | ||||
0.276056 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.3820 | −0.459650 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.5066 | 0.654725 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.70820 | 0.150168 | 0.0750842 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750842 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.1672 | −0.897481 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.70820 | 0.309016 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.32624 | −0.296557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.2705 | 1.40630 | 0.703150 | − | 0.711042i | \(-0.251776\pi\) | ||||
0.703150 | + | 0.711042i | \(0.251776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.58359 | −0.208924 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.7426 | −0.911203 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.2361 | −0.704223 | −0.352112 | − | 0.935958i | \(-0.614536\pi\) | ||||
−0.352112 | + | 0.935958i | \(0.614536\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.47214 | 0.236408 |
(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 | 7728.2.a.w.1.2 | 2 | ||
4.3 | odd | 2 | 1932.2.a.f.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 5796.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.f.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
5796.2.a.n.1.1 | 2 | 12.11 | even | 2 | |||
7728.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial |