Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.16228 | 1.19523 | 0.597614 | − | 0.801784i | \(-0.296115\pi\) | ||||
0.597614 | + | 0.801784i | \(0.296115\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.16228 | 1.25497 | 0.627487 | − | 0.778627i | \(-0.284084\pi\) | ||||
0.627487 | + | 0.778627i | \(0.284084\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.16228 | 1.43176 | 0.715879 | − | 0.698224i | \(-0.246026\pi\) | ||||
0.715879 | + | 0.698224i | \(0.246026\pi\) | |||||||
\(14\) | 3.16228 | 0.845154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.837722 | 0.203178 | 0.101589 | − | 0.994826i | \(-0.467607\pi\) | ||||
0.101589 | + | 0.994826i | \(0.467607\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.16228 | −0.690066 | ||||||||
\(22\) | 4.16228 | 0.887401 | ||||||||
\(23\) | −5.32456 | −1.11025 | −0.555123 | − | 0.831768i | \(-0.687329\pi\) | ||||
−0.555123 | + | 0.831768i | \(0.687329\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.16228 | 1.01241 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.16228 | 0.597614 | ||||||||
\(29\) | −3.83772 | −0.712647 | −0.356324 | − | 0.934363i | \(-0.615970\pi\) | ||||
−0.356324 | + | 0.934363i | \(0.615970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.32456 | 0.956318 | 0.478159 | − | 0.878273i | \(-0.341304\pi\) | ||||
0.478159 | + | 0.878273i | \(0.341304\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.16228 | −0.724560 | ||||||||
\(34\) | 0.837722 | 0.143668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −5.16228 | −0.826626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.32456 | −0.987730 | −0.493865 | − | 0.869539i | \(-0.664416\pi\) | ||||
−0.493865 | + | 0.869539i | \(0.664416\pi\) | |||||||
\(42\) | −3.16228 | −0.487950 | ||||||||
\(43\) | −9.16228 | −1.39723 | −0.698617 | − | 0.715496i | \(-0.746201\pi\) | ||||
−0.698617 | + | 0.715496i | \(0.746201\pi\) | |||||||
\(44\) | 4.16228 | 0.627487 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.32456 | −0.785063 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.837722 | −0.117305 | ||||||||
\(52\) | 5.16228 | 0.715879 | ||||||||
\(53\) | 1.83772 | 0.252431 | 0.126215 | − | 0.992003i | \(-0.459717\pi\) | ||||
0.126215 | + | 0.992003i | \(0.459717\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.16228 | 0.422577 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −3.83772 | −0.503918 | ||||||||
\(59\) | −7.48683 | −0.974703 | −0.487351 | − | 0.873206i | \(-0.662037\pi\) | ||||
−0.487351 | + | 0.873206i | \(0.662037\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.16228 | −0.532925 | −0.266463 | − | 0.963845i | \(-0.585855\pi\) | ||||
−0.266463 | + | 0.963845i | \(0.585855\pi\) | |||||||
\(62\) | 5.32456 | 0.676219 | ||||||||
\(63\) | 3.16228 | 0.398410 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.16228 | −0.512341 | ||||||||
\(67\) | −6.48683 | −0.792493 | −0.396246 | − | 0.918144i | \(-0.629687\pi\) | ||||
−0.396246 | + | 0.918144i | \(0.629687\pi\) | |||||||
\(68\) | 0.837722 | 0.101589 | ||||||||
\(69\) | 5.32456 | 0.641001 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.16228 | 0.137937 | 0.0689685 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689685 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 13.1623 | 1.49998 | ||||||||
\(78\) | −5.16228 | −0.584513 | ||||||||
\(79\) | −5.32456 | −0.599059 | −0.299530 | − | 0.954087i | \(-0.596830\pi\) | ||||
−0.299530 | + | 0.954087i | \(0.596830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.32456 | −0.698430 | ||||||||
\(83\) | 6.48683 | 0.712022 | 0.356011 | − | 0.934482i | \(-0.384136\pi\) | ||||
0.356011 | + | 0.934482i | \(0.384136\pi\) | |||||||
\(84\) | −3.16228 | −0.345033 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.16228 | −0.987994 | ||||||||
\(87\) | 3.83772 | 0.411447 | ||||||||
\(88\) | 4.16228 | 0.443700 | ||||||||
\(89\) | −7.32456 | −0.776401 | −0.388201 | − | 0.921575i | \(-0.626903\pi\) | ||||
−0.388201 | + | 0.921575i | \(0.626903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3246 | 1.71128 | ||||||||
\(92\) | −5.32456 | −0.555123 | ||||||||
\(93\) | −5.32456 | −0.552131 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.513167 | 0.0521042 | 0.0260521 | − | 0.999661i | \(-0.491706\pi\) | ||||
0.0260521 | + | 0.999661i | \(0.491706\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | 4.16228 | 0.418325 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8114 | −1.37428 | −0.687142 | − | 0.726523i | \(-0.741135\pi\) | ||||
−0.687142 | + | 0.726523i | \(0.741135\pi\) | |||||||
\(102\) | −0.837722 | −0.0829469 | ||||||||
\(103\) | 15.6491 | 1.54195 | 0.770976 | − | 0.636864i | \(-0.219769\pi\) | ||||
0.770976 | + | 0.636864i | \(0.219769\pi\) | |||||||
\(104\) | 5.16228 | 0.506203 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.83772 | 0.178495 | ||||||||
\(107\) | 12.8377 | 1.24107 | 0.620535 | − | 0.784179i | \(-0.286916\pi\) | ||||
0.620535 | + | 0.784179i | \(0.286916\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 7.67544 | 0.735174 | 0.367587 | − | 0.929989i | \(-0.380184\pi\) | ||||
0.367587 | + | 0.929989i | \(0.380184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 3.16228 | 0.298807 | ||||||||
\(113\) | 9.64911 | 0.907712 | 0.453856 | − | 0.891075i | \(-0.350048\pi\) | ||||
0.453856 | + | 0.891075i | \(0.350048\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.83772 | −0.356324 | ||||||||
\(117\) | 5.16228 | 0.477253 | ||||||||
\(118\) | −7.48683 | −0.689219 | ||||||||
\(119\) | 2.64911 | 0.242844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.32456 | 0.574960 | ||||||||
\(122\) | −4.16228 | −0.376835 | ||||||||
\(123\) | 6.32456 | 0.570266 | ||||||||
\(124\) | 5.32456 | 0.478159 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.16228 | 0.281718 | ||||||||
\(127\) | 15.6491 | 1.38863 | 0.694317 | − | 0.719669i | \(-0.255707\pi\) | ||||
0.694317 | + | 0.719669i | \(0.255707\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.16228 | 0.806694 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4868 | −1.09098 | −0.545490 | − | 0.838117i | \(-0.683656\pi\) | ||||
−0.545490 | + | 0.838117i | \(0.683656\pi\) | |||||||
\(132\) | −4.16228 | −0.362280 | ||||||||
\(133\) | −3.16228 | −0.274204 | ||||||||
\(134\) | −6.48683 | −0.560377 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.837722 | 0.0718341 | ||||||||
\(137\) | 2.32456 | 0.198600 | 0.0993001 | − | 0.995058i | \(-0.468340\pi\) | ||||
0.0993001 | + | 0.995058i | \(0.468340\pi\) | |||||||
\(138\) | 5.32456 | 0.453256 | ||||||||
\(139\) | 21.4868 | 1.82249 | 0.911245 | − | 0.411865i | \(-0.135123\pi\) | ||||
0.911245 | + | 0.411865i | \(0.135123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 1.16228 | 0.0975362 | ||||||||
\(143\) | 21.4868 | 1.79682 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00000 | −0.0827606 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | 10.0000 | 0.821995 | ||||||||
\(149\) | 16.6491 | 1.36395 | 0.681974 | − | 0.731376i | \(-0.261122\pi\) | ||||
0.681974 | + | 0.731376i | \(0.261122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0.837722 | 0.0677258 | ||||||||
\(154\) | 13.1623 | 1.06065 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.16228 | −0.413313 | ||||||||
\(157\) | 18.3246 | 1.46246 | 0.731229 | − | 0.682132i | \(-0.238947\pi\) | ||||
0.731229 | + | 0.682132i | \(0.238947\pi\) | |||||||
\(158\) | −5.32456 | −0.423599 | ||||||||
\(159\) | −1.83772 | −0.145741 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.8377 | −1.32700 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −22.6491 | −1.77402 | −0.887008 | − | 0.461755i | \(-0.847220\pi\) | ||||
−0.887008 | + | 0.461755i | \(0.847220\pi\) | |||||||
\(164\) | −6.32456 | −0.493865 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.48683 | 0.503476 | ||||||||
\(167\) | 2.64911 | 0.204994 | 0.102497 | − | 0.994733i | \(-0.467317\pi\) | ||||
0.102497 | + | 0.994733i | \(0.467317\pi\) | |||||||
\(168\) | −3.16228 | −0.243975 | ||||||||
\(169\) | 13.6491 | 1.04993 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −9.16228 | −0.698617 | ||||||||
\(173\) | −2.16228 | −0.164395 | −0.0821975 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821975 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(174\) | 3.83772 | 0.290937 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.16228 | 0.313743 | ||||||||
\(177\) | 7.48683 | 0.562745 | ||||||||
\(178\) | −7.32456 | −0.548999 | ||||||||
\(179\) | −20.6491 | −1.54339 | −0.771693 | − | 0.635995i | \(-0.780590\pi\) | ||||
−0.771693 | + | 0.635995i | \(0.780590\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.16228 | 0.681027 | 0.340513 | − | 0.940240i | \(-0.389399\pi\) | ||||
0.340513 | + | 0.940240i | \(0.389399\pi\) | |||||||
\(182\) | 16.3246 | 1.21006 | ||||||||
\(183\) | 4.16228 | 0.307684 | ||||||||
\(184\) | −5.32456 | −0.392531 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.32456 | −0.390415 | ||||||||
\(187\) | 3.48683 | 0.254982 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | −3.16228 | −0.230022 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6491 | 1.56647 | 0.783237 | − | 0.621723i | \(-0.213567\pi\) | ||||
0.783237 | + | 0.621723i | \(0.213567\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −9.16228 | −0.659515 | −0.329758 | − | 0.944066i | \(-0.606967\pi\) | ||||
−0.329758 | + | 0.944066i | \(0.606967\pi\) | |||||||
\(194\) | 0.513167 | 0.0368432 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −24.1359 | −1.71961 | −0.859807 | − | 0.510618i | \(-0.829416\pi\) | ||||
−0.859807 | + | 0.510618i | \(0.829416\pi\) | |||||||
\(198\) | 4.16228 | 0.295800 | ||||||||
\(199\) | −18.6491 | −1.32200 | −0.661000 | − | 0.750386i | \(-0.729868\pi\) | ||||
−0.661000 | + | 0.750386i | \(0.729868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.48683 | 0.457546 | ||||||||
\(202\) | −13.8114 | −0.971766 | ||||||||
\(203\) | −12.1359 | −0.851776 | ||||||||
\(204\) | −0.837722 | −0.0586523 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6491 | 1.09033 | ||||||||
\(207\) | −5.32456 | −0.370082 | ||||||||
\(208\) | 5.16228 | 0.357940 | ||||||||
\(209\) | −4.16228 | −0.287911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8114 | −1.29503 | −0.647515 | − | 0.762053i | \(-0.724192\pi\) | ||||
−0.647515 | + | 0.762053i | \(0.724192\pi\) | |||||||
\(212\) | 1.83772 | 0.126215 | ||||||||
\(213\) | −1.16228 | −0.0796380 | ||||||||
\(214\) | 12.8377 | 0.877569 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 16.8377 | 1.14302 | ||||||||
\(218\) | 7.67544 | 0.519847 | ||||||||
\(219\) | 1.00000 | 0.0675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.32456 | 0.290901 | ||||||||
\(222\) | −10.0000 | −0.671156 | ||||||||
\(223\) | −25.6491 | −1.71759 | −0.858796 | − | 0.512318i | \(-0.828787\pi\) | ||||
−0.858796 | + | 0.512318i | \(0.828787\pi\) | |||||||
\(224\) | 3.16228 | 0.211289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.64911 | 0.641849 | ||||||||
\(227\) | −2.00000 | −0.132745 | −0.0663723 | − | 0.997795i | \(-0.521143\pi\) | ||||
−0.0663723 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 8.16228 | 0.539378 | 0.269689 | − | 0.962947i | \(-0.413079\pi\) | ||||
0.269689 | + | 0.962947i | \(0.413079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1623 | −0.866014 | ||||||||
\(232\) | −3.83772 | −0.251959 | ||||||||
\(233\) | −11.8114 | −0.773790 | −0.386895 | − | 0.922124i | \(-0.626452\pi\) | ||||
−0.386895 | + | 0.922124i | \(0.626452\pi\) | |||||||
\(234\) | 5.16228 | 0.337469 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.48683 | −0.487351 | ||||||||
\(237\) | 5.32456 | 0.345867 | ||||||||
\(238\) | 2.64911 | 0.171716 | ||||||||
\(239\) | −24.3246 | −1.57342 | −0.786712 | − | 0.617320i | \(-0.788218\pi\) | ||||
−0.786712 | + | 0.617320i | \(0.788218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5132 | 0.677213 | 0.338606 | − | 0.940928i | \(-0.390045\pi\) | ||||
0.338606 | + | 0.940928i | \(0.390045\pi\) | |||||||
\(242\) | 6.32456 | 0.406558 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.16228 | −0.266463 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.32456 | 0.403239 | ||||||||
\(247\) | −5.16228 | −0.328468 | ||||||||
\(248\) | 5.32456 | 0.338110 | ||||||||
\(249\) | −6.48683 | −0.411086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.6491 | −0.672166 | −0.336083 | − | 0.941832i | \(-0.609102\pi\) | ||||
−0.336083 | + | 0.941832i | \(0.609102\pi\) | |||||||
\(252\) | 3.16228 | 0.199205 | ||||||||
\(253\) | −22.1623 | −1.39333 | ||||||||
\(254\) | 15.6491 | 0.981913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.3246 | −1.20543 | −0.602716 | − | 0.797956i | \(-0.705915\pi\) | ||||
−0.602716 | + | 0.797956i | \(0.705915\pi\) | |||||||
\(258\) | 9.16228 | 0.570418 | ||||||||
\(259\) | 31.6228 | 1.96494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.83772 | −0.237549 | ||||||||
\(262\) | −12.4868 | −0.771439 | ||||||||
\(263\) | 31.9737 | 1.97158 | 0.985790 | − | 0.167980i | \(-0.0537245\pi\) | ||||
0.985790 | + | 0.167980i | \(0.0537245\pi\) | |||||||
\(264\) | −4.16228 | −0.256170 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.16228 | −0.193892 | ||||||||
\(267\) | 7.32456 | 0.448256 | ||||||||
\(268\) | −6.48683 | −0.396246 | ||||||||
\(269\) | 12.3246 | 0.751441 | 0.375721 | − | 0.926733i | \(-0.377395\pi\) | ||||
0.375721 | + | 0.926733i | \(0.377395\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.16228 | −0.0706033 | −0.0353017 | − | 0.999377i | \(-0.511239\pi\) | ||||
−0.0353017 | + | 0.999377i | \(0.511239\pi\) | |||||||
\(272\) | 0.837722 | 0.0507944 | ||||||||
\(273\) | −16.3246 | −0.988007 | ||||||||
\(274\) | 2.32456 | 0.140432 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.32456 | 0.320501 | ||||||||
\(277\) | 24.8114 | 1.49077 | 0.745386 | − | 0.666633i | \(-0.232265\pi\) | ||||
0.745386 | + | 0.666633i | \(0.232265\pi\) | |||||||
\(278\) | 21.4868 | 1.28869 | ||||||||
\(279\) | 5.32456 | 0.318773 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.64911 | 0.456308 | 0.228154 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228154 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(282\) | −6.00000 | −0.357295 | ||||||||
\(283\) | 24.6491 | 1.46524 | 0.732619 | − | 0.680639i | \(-0.238298\pi\) | ||||
0.732619 | + | 0.680639i | \(0.238298\pi\) | |||||||
\(284\) | 1.16228 | 0.0689685 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.4868 | 1.27054 | ||||||||
\(287\) | −20.0000 | −1.18056 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.2982 | −0.958719 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.513167 | −0.0300824 | ||||||||
\(292\) | −1.00000 | −0.0585206 | ||||||||
\(293\) | 16.4868 | 0.963171 | 0.481586 | − | 0.876399i | \(-0.340061\pi\) | ||||
0.481586 | + | 0.876399i | \(0.340061\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.0000 | 0.581238 | ||||||||
\(297\) | −4.16228 | −0.241520 | ||||||||
\(298\) | 16.6491 | 0.964457 | ||||||||
\(299\) | −27.4868 | −1.58960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.9737 | −1.67001 | ||||||||
\(302\) | −10.0000 | −0.575435 | ||||||||
\(303\) | 13.8114 | 0.793444 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.837722 | 0.0478894 | ||||||||
\(307\) | 13.5132 | 0.771237 | 0.385619 | − | 0.922658i | \(-0.373988\pi\) | ||||
0.385619 | + | 0.922658i | \(0.373988\pi\) | |||||||
\(308\) | 13.1623 | 0.749990 | ||||||||
\(309\) | −15.6491 | −0.890247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.0000 | −1.47432 | −0.737162 | − | 0.675716i | \(-0.763835\pi\) | ||||
−0.737162 | + | 0.675716i | \(0.763835\pi\) | |||||||
\(312\) | −5.16228 | −0.292256 | ||||||||
\(313\) | −10.6754 | −0.603412 | −0.301706 | − | 0.953401i | \(-0.597556\pi\) | ||||
−0.301706 | + | 0.953401i | \(0.597556\pi\) | |||||||
\(314\) | 18.3246 | 1.03411 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.32456 | −0.299530 | ||||||||
\(317\) | 4.16228 | 0.233777 | 0.116888 | − | 0.993145i | \(-0.462708\pi\) | ||||
0.116888 | + | 0.993145i | \(0.462708\pi\) | |||||||
\(318\) | −1.83772 | −0.103054 | ||||||||
\(319\) | −15.9737 | −0.894354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8377 | −0.716532 | ||||||||
\(322\) | −16.8377 | −0.938330 | ||||||||
\(323\) | −0.837722 | −0.0466121 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.6491 | −1.25442 | ||||||||
\(327\) | −7.67544 | −0.424453 | ||||||||
\(328\) | −6.32456 | −0.349215 | ||||||||
\(329\) | 18.9737 | 1.04605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.18861 | −0.175262 | −0.0876310 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876310 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(332\) | 6.48683 | 0.356011 | ||||||||
\(333\) | 10.0000 | 0.547997 | ||||||||
\(334\) | 2.64911 | 0.144953 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.16228 | −0.172516 | ||||||||
\(337\) | −2.97367 | −0.161986 | −0.0809930 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809930 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(338\) | 13.6491 | 0.742414 | ||||||||
\(339\) | −9.64911 | −0.524068 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.1623 | 1.20015 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −12.6491 | −0.682988 | ||||||||
\(344\) | −9.16228 | −0.493997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.16228 | −0.116245 | ||||||||
\(347\) | −20.0000 | −1.07366 | −0.536828 | − | 0.843692i | \(-0.680378\pi\) | ||||
−0.536828 | + | 0.843692i | \(0.680378\pi\) | |||||||
\(348\) | 3.83772 | 0.205724 | ||||||||
\(349\) | −17.8377 | −0.954831 | −0.477416 | − | 0.878678i | \(-0.658426\pi\) | ||||
−0.477416 | + | 0.878678i | \(0.658426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.16228 | −0.275542 | ||||||||
\(352\) | 4.16228 | 0.221850 | ||||||||
\(353\) | 23.8114 | 1.26735 | 0.633676 | − | 0.773598i | \(-0.281545\pi\) | ||||
0.633676 | + | 0.773598i | \(0.281545\pi\) | |||||||
\(354\) | 7.48683 | 0.397921 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.32456 | −0.388201 | ||||||||
\(357\) | −2.64911 | −0.140206 | ||||||||
\(358\) | −20.6491 | −1.09134 | ||||||||
\(359\) | −11.6754 | −0.616206 | −0.308103 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308103 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 9.16228 | 0.481559 | ||||||||
\(363\) | −6.32456 | −0.331953 | ||||||||
\(364\) | 16.3246 | 0.855639 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.16228 | 0.217566 | ||||||||
\(367\) | −7.48683 | −0.390810 | −0.195405 | − | 0.980723i | \(-0.562602\pi\) | ||||
−0.195405 | + | 0.980723i | \(0.562602\pi\) | |||||||
\(368\) | −5.32456 | −0.277562 | ||||||||
\(369\) | −6.32456 | −0.329243 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.81139 | 0.301712 | ||||||||
\(372\) | −5.32456 | −0.276065 | ||||||||
\(373\) | −16.1359 | −0.835487 | −0.417744 | − | 0.908565i | \(-0.637179\pi\) | ||||
−0.417744 | + | 0.908565i | \(0.637179\pi\) | |||||||
\(374\) | 3.48683 | 0.180300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −19.8114 | −1.02034 | ||||||||
\(378\) | −3.16228 | −0.162650 | ||||||||
\(379\) | 22.9737 | 1.18008 | 0.590039 | − | 0.807375i | \(-0.299112\pi\) | ||||
0.590039 | + | 0.807375i | \(0.299112\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6491 | −0.801728 | ||||||||
\(382\) | 21.6491 | 1.10766 | ||||||||
\(383\) | −3.48683 | −0.178169 | −0.0890844 | − | 0.996024i | \(-0.528394\pi\) | ||||
−0.0890844 | + | 0.996024i | \(0.528394\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.16228 | −0.466348 | ||||||||
\(387\) | −9.16228 | −0.465745 | ||||||||
\(388\) | 0.513167 | 0.0260521 | ||||||||
\(389\) | −34.6491 | −1.75678 | −0.878390 | − | 0.477945i | \(-0.841382\pi\) | ||||
−0.878390 | + | 0.477945i | \(0.841382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.46050 | −0.225577 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 12.4868 | 0.629877 | ||||||||
\(394\) | −24.1359 | −1.21595 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.16228 | 0.209162 | ||||||||
\(397\) | 17.1359 | 0.860028 | 0.430014 | − | 0.902822i | \(-0.358509\pi\) | ||||
0.430014 | + | 0.902822i | \(0.358509\pi\) | |||||||
\(398\) | −18.6491 | −0.934795 | ||||||||
\(399\) | 3.16228 | 0.158312 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6491 | 0.681604 | 0.340802 | − | 0.940135i | \(-0.389301\pi\) | ||||
0.340802 | + | 0.940135i | \(0.389301\pi\) | |||||||
\(402\) | 6.48683 | 0.323534 | ||||||||
\(403\) | 27.4868 | 1.36922 | ||||||||
\(404\) | −13.8114 | −0.687142 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.1359 | −0.602297 | ||||||||
\(407\) | 41.6228 | 2.06316 | ||||||||
\(408\) | −0.837722 | −0.0414734 | ||||||||
\(409\) | −7.67544 | −0.379526 | −0.189763 | − | 0.981830i | \(-0.560772\pi\) | ||||
−0.189763 | + | 0.981830i | \(0.560772\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.32456 | −0.114662 | ||||||||
\(412\) | 15.6491 | 0.770976 | ||||||||
\(413\) | −23.6754 | −1.16499 | ||||||||
\(414\) | −5.32456 | −0.261688 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.16228 | 0.253101 | ||||||||
\(417\) | −21.4868 | −1.05221 | ||||||||
\(418\) | −4.16228 | −0.203584 | ||||||||
\(419\) | 8.00000 | 0.390826 | 0.195413 | − | 0.980721i | \(-0.437395\pi\) | ||||
0.195413 | + | 0.980721i | \(0.437395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6491 | 0.908902 | 0.454451 | − | 0.890772i | \(-0.349835\pi\) | ||||
0.454451 | + | 0.890772i | \(0.349835\pi\) | |||||||
\(422\) | −18.8114 | −0.915724 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 1.83772 | 0.0892477 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.16228 | −0.0563125 | ||||||||
\(427\) | −13.1623 | −0.636967 | ||||||||
\(428\) | 12.8377 | 0.620535 | ||||||||
\(429\) | −21.4868 | −1.03739 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.324555 | −0.0156333 | −0.00781664 | − | 0.999969i | \(-0.502488\pi\) | ||||
−0.00781664 | + | 0.999969i | \(0.502488\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 28.1359 | 1.35213 | 0.676064 | − | 0.736843i | \(-0.263684\pi\) | ||||
0.676064 | + | 0.736843i | \(0.263684\pi\) | |||||||
\(434\) | 16.8377 | 0.808237 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.67544 | 0.367587 | ||||||||
\(437\) | 5.32456 | 0.254708 | ||||||||
\(438\) | 1.00000 | 0.0477818 | ||||||||
\(439\) | 13.6491 | 0.651437 | 0.325718 | − | 0.945467i | \(-0.394394\pi\) | ||||
0.325718 | + | 0.945467i | \(0.394394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 4.32456 | 0.205698 | ||||||||
\(443\) | −11.8377 | −0.562427 | −0.281214 | − | 0.959645i | \(-0.590737\pi\) | ||||
−0.281214 | + | 0.959645i | \(0.590737\pi\) | |||||||
\(444\) | −10.0000 | −0.474579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.6491 | −1.21452 | ||||||||
\(447\) | −16.6491 | −0.787476 | ||||||||
\(448\) | 3.16228 | 0.149404 | ||||||||
\(449\) | −11.0000 | −0.519122 | −0.259561 | − | 0.965727i | \(-0.583578\pi\) | ||||
−0.259561 | + | 0.965727i | \(0.583578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.3246 | −1.23957 | ||||||||
\(452\) | 9.64911 | 0.453856 | ||||||||
\(453\) | 10.0000 | 0.469841 | ||||||||
\(454\) | −2.00000 | −0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 9.67544 | 0.452598 | 0.226299 | − | 0.974058i | \(-0.427337\pi\) | ||||
0.226299 | + | 0.974058i | \(0.427337\pi\) | |||||||
\(458\) | 8.16228 | 0.381398 | ||||||||
\(459\) | −0.837722 | −0.0391015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | −13.1623 | −0.612365 | ||||||||
\(463\) | −21.6754 | −1.00734 | −0.503672 | − | 0.863895i | \(-0.668018\pi\) | ||||
−0.503672 | + | 0.863895i | \(0.668018\pi\) | |||||||
\(464\) | −3.83772 | −0.178162 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.8114 | −0.547152 | ||||||||
\(467\) | −37.1359 | −1.71845 | −0.859223 | − | 0.511601i | \(-0.829053\pi\) | ||||
−0.859223 | + | 0.511601i | \(0.829053\pi\) | |||||||
\(468\) | 5.16228 | 0.238626 | ||||||||
\(469\) | −20.5132 | −0.947210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3246 | −0.844351 | ||||||||
\(472\) | −7.48683 | −0.344609 | ||||||||
\(473\) | −38.1359 | −1.75349 | ||||||||
\(474\) | 5.32456 | 0.244565 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.64911 | 0.121422 | ||||||||
\(477\) | 1.83772 | 0.0841435 | ||||||||
\(478\) | −24.3246 | −1.11258 | ||||||||
\(479\) | −39.9737 | −1.82644 | −0.913222 | − | 0.407463i | \(-0.866414\pi\) | ||||
−0.913222 | + | 0.407463i | \(0.866414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.6228 | 2.35380 | ||||||||
\(482\) | 10.5132 | 0.478862 | ||||||||
\(483\) | 16.8377 | 0.766143 | ||||||||
\(484\) | 6.32456 | 0.287480 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −28.6491 | −1.29822 | −0.649108 | − | 0.760697i | \(-0.724857\pi\) | ||||
−0.649108 | + | 0.760697i | \(0.724857\pi\) | |||||||
\(488\) | −4.16228 | −0.188417 | ||||||||
\(489\) | 22.6491 | 1.02423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 6.32456 | 0.285133 | ||||||||
\(493\) | −3.21495 | −0.144794 | ||||||||
\(494\) | −5.16228 | −0.232262 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.32456 | 0.239080 | ||||||||
\(497\) | 3.67544 | 0.164866 | ||||||||
\(498\) | −6.48683 | −0.290682 | ||||||||
\(499\) | −5.81139 | −0.260153 | −0.130077 | − | 0.991504i | \(-0.541522\pi\) | ||||
−0.130077 | + | 0.991504i | \(0.541522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.64911 | −0.118354 | ||||||||
\(502\) | −10.6491 | −0.475293 | ||||||||
\(503\) | −29.2982 | −1.30634 | −0.653172 | − | 0.757210i | \(-0.726562\pi\) | ||||
−0.653172 | + | 0.757210i | \(0.726562\pi\) | |||||||
\(504\) | 3.16228 | 0.140859 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.1623 | −0.985233 | ||||||||
\(507\) | −13.6491 | −0.606178 | ||||||||
\(508\) | 15.6491 | 0.694317 | ||||||||
\(509\) | 16.8114 | 0.745152 | 0.372576 | − | 0.928002i | \(-0.378475\pi\) | ||||
0.372576 | + | 0.928002i | \(0.378475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.16228 | −0.139891 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −19.3246 | −0.852370 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.16228 | 0.403347 | ||||||||
\(517\) | 24.9737 | 1.09834 | ||||||||
\(518\) | 31.6228 | 1.38943 | ||||||||
\(519\) | 2.16228 | 0.0949135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.9737 | 0.875062 | 0.437531 | − | 0.899203i | \(-0.355853\pi\) | ||||
0.437531 | + | 0.899203i | \(0.355853\pi\) | |||||||
\(522\) | −3.83772 | −0.167973 | ||||||||
\(523\) | −16.6491 | −0.728015 | −0.364007 | − | 0.931396i | \(-0.618592\pi\) | ||||
−0.364007 | + | 0.931396i | \(0.618592\pi\) | |||||||
\(524\) | −12.4868 | −0.545490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.9737 | 1.39412 | ||||||||
\(527\) | 4.46050 | 0.194302 | ||||||||
\(528\) | −4.16228 | −0.181140 | ||||||||
\(529\) | 5.35089 | 0.232647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.48683 | −0.324901 | ||||||||
\(532\) | −3.16228 | −0.137102 | ||||||||
\(533\) | −32.6491 | −1.41419 | ||||||||
\(534\) | 7.32456 | 0.316965 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.48683 | −0.280189 | ||||||||
\(537\) | 20.6491 | 0.891075 | ||||||||
\(538\) | 12.3246 | 0.531349 | ||||||||
\(539\) | 12.4868 | 0.537846 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.162278 | −0.00697686 | −0.00348843 | − | 0.999994i | \(-0.501110\pi\) | ||||
−0.00348843 | + | 0.999994i | \(0.501110\pi\) | |||||||
\(542\) | −1.16228 | −0.0499241 | ||||||||
\(543\) | −9.16228 | −0.393191 | ||||||||
\(544\) | 0.837722 | 0.0359170 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.3246 | −0.698626 | ||||||||
\(547\) | −16.8114 | −0.718803 | −0.359402 | − | 0.933183i | \(-0.617019\pi\) | ||||
−0.359402 | + | 0.933183i | \(0.617019\pi\) | |||||||
\(548\) | 2.32456 | 0.0993001 | ||||||||
\(549\) | −4.16228 | −0.177642 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.83772 | 0.163492 | ||||||||
\(552\) | 5.32456 | 0.226628 | ||||||||
\(553\) | −16.8377 | −0.716013 | ||||||||
\(554\) | 24.8114 | 1.05413 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.4868 | 0.911245 | ||||||||
\(557\) | −22.8377 | −0.967665 | −0.483833 | − | 0.875161i | \(-0.660756\pi\) | ||||
−0.483833 | + | 0.875161i | \(0.660756\pi\) | |||||||
\(558\) | 5.32456 | 0.225406 | ||||||||
\(559\) | −47.2982 | −2.00050 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.48683 | −0.147214 | ||||||||
\(562\) | 7.64911 | 0.322658 | ||||||||
\(563\) | 31.1623 | 1.31333 | 0.656667 | − | 0.754181i | \(-0.271966\pi\) | ||||
0.656667 | + | 0.754181i | \(0.271966\pi\) | |||||||
\(564\) | −6.00000 | −0.252646 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.6491 | 1.03608 | ||||||||
\(567\) | 3.16228 | 0.132803 | ||||||||
\(568\) | 1.16228 | 0.0487681 | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8114 | −0.661686 | −0.330843 | − | 0.943686i | \(-0.607333\pi\) | ||||
−0.330843 | + | 0.943686i | \(0.607333\pi\) | |||||||
\(572\) | 21.4868 | 0.898410 | ||||||||
\(573\) | −21.6491 | −0.904405 | ||||||||
\(574\) | −20.0000 | −0.834784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −16.6754 | −0.694208 | −0.347104 | − | 0.937827i | \(-0.612835\pi\) | ||||
−0.347104 | + | 0.937827i | \(0.612835\pi\) | |||||||
\(578\) | −16.2982 | −0.677917 | ||||||||
\(579\) | 9.16228 | 0.380771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.5132 | 0.851030 | ||||||||
\(582\) | −0.513167 | −0.0212715 | ||||||||
\(583\) | 7.64911 | 0.316794 | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.4868 | 0.681065 | ||||||||
\(587\) | −18.8114 | −0.776429 | −0.388215 | − | 0.921569i | \(-0.626908\pi\) | ||||
−0.388215 | + | 0.921569i | \(0.626908\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | −5.32456 | −0.219394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.1359 | 0.992820 | ||||||||
\(592\) | 10.0000 | 0.410997 | ||||||||
\(593\) | −2.32456 | −0.0954580 | −0.0477290 | − | 0.998860i | \(-0.515198\pi\) | ||||
−0.0477290 | + | 0.998860i | \(0.515198\pi\) | |||||||
\(594\) | −4.16228 | −0.170780 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6491 | 0.681974 | ||||||||
\(597\) | 18.6491 | 0.763257 | ||||||||
\(598\) | −27.4868 | −1.12402 | ||||||||
\(599\) | −4.18861 | −0.171142 | −0.0855710 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855710 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.8114 | 1.86869 | 0.934343 | − | 0.356376i | \(-0.115988\pi\) | ||||
0.934343 | + | 0.356376i | \(0.115988\pi\) | |||||||
\(602\) | −28.9737 | −1.18088 | ||||||||
\(603\) | −6.48683 | −0.264164 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.8114 | 0.561049 | ||||||||
\(607\) | 2.02633 | 0.0822464 | 0.0411232 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411232 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 12.1359 | 0.491773 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9737 | 1.25306 | ||||||||
\(612\) | 0.837722 | 0.0338629 | ||||||||
\(613\) | −27.2982 | −1.10256 | −0.551282 | − | 0.834319i | \(-0.685861\pi\) | ||||
−0.551282 | + | 0.834319i | \(0.685861\pi\) | |||||||
\(614\) | 13.5132 | 0.545347 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.1623 | 0.530323 | ||||||||
\(617\) | −11.6754 | −0.470036 | −0.235018 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235018 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(618\) | −15.6491 | −0.629500 | ||||||||
\(619\) | 10.8377 | 0.435605 | 0.217802 | − | 0.975993i | \(-0.430111\pi\) | ||||
0.217802 | + | 0.975993i | \(0.430111\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.32456 | 0.213667 | ||||||||
\(622\) | −26.0000 | −1.04251 | ||||||||
\(623\) | −23.1623 | −0.927977 | ||||||||
\(624\) | −5.16228 | −0.206656 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.6754 | −0.426677 | ||||||||
\(627\) | 4.16228 | 0.166225 | ||||||||
\(628\) | 18.3246 | 0.731229 | ||||||||
\(629\) | 8.37722 | 0.334022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.2982 | 1.80329 | 0.901647 | − | 0.432473i | \(-0.142359\pi\) | ||||
0.901647 | + | 0.432473i | \(0.142359\pi\) | |||||||
\(632\) | −5.32456 | −0.211799 | ||||||||
\(633\) | 18.8114 | 0.747686 | ||||||||
\(634\) | 4.16228 | 0.165305 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.83772 | −0.0728704 | ||||||||
\(637\) | 15.4868 | 0.613611 | ||||||||
\(638\) | −15.9737 | −0.632403 | ||||||||
\(639\) | 1.16228 | 0.0459790 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.2982 | −1.47319 | −0.736596 | − | 0.676333i | \(-0.763568\pi\) | ||||
−0.736596 | + | 0.676333i | \(0.763568\pi\) | |||||||
\(642\) | −12.8377 | −0.506664 | ||||||||
\(643\) | 6.64911 | 0.262215 | 0.131108 | − | 0.991368i | \(-0.458147\pi\) | ||||
0.131108 | + | 0.991368i | \(0.458147\pi\) | |||||||
\(644\) | −16.8377 | −0.663499 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.837722 | −0.0329597 | ||||||||
\(647\) | −9.00000 | −0.353827 | −0.176913 | − | 0.984226i | \(-0.556611\pi\) | ||||
−0.176913 | + | 0.984226i | \(0.556611\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −31.1623 | −1.22323 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.8377 | −0.659922 | ||||||||
\(652\) | −22.6491 | −0.887008 | ||||||||
\(653\) | 6.97367 | 0.272901 | 0.136450 | − | 0.990647i | \(-0.456431\pi\) | ||||
0.136450 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(654\) | −7.67544 | −0.300134 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.32456 | −0.246932 | ||||||||
\(657\) | −1.00000 | −0.0390137 | ||||||||
\(658\) | 18.9737 | 0.739671 | ||||||||
\(659\) | −49.8114 | −1.94038 | −0.970188 | − | 0.242353i | \(-0.922081\pi\) | ||||
−0.970188 | + | 0.242353i | \(0.922081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.2982 | 1.45073 | 0.725366 | − | 0.688363i | \(-0.241670\pi\) | ||||
0.725366 | + | 0.688363i | \(0.241670\pi\) | |||||||
\(662\) | −3.18861 | −0.123929 | ||||||||
\(663\) | −4.32456 | −0.167952 | ||||||||
\(664\) | 6.48683 | 0.251738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0000 | 0.387492 | ||||||||
\(667\) | 20.4342 | 0.791214 | ||||||||
\(668\) | 2.64911 | 0.102497 | ||||||||
\(669\) | 25.6491 | 0.991652 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3246 | −0.668807 | ||||||||
\(672\) | −3.16228 | −0.121988 | ||||||||
\(673\) | −32.4605 | −1.25126 | −0.625630 | − | 0.780120i | \(-0.715158\pi\) | ||||
−0.625630 | + | 0.780120i | \(0.715158\pi\) | |||||||
\(674\) | −2.97367 | −0.114541 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.6491 | 0.524966 | ||||||||
\(677\) | 18.4868 | 0.710507 | 0.355253 | − | 0.934770i | \(-0.384395\pi\) | ||||
0.355253 | + | 0.934770i | \(0.384395\pi\) | |||||||
\(678\) | −9.64911 | −0.370572 | ||||||||
\(679\) | 1.62278 | 0.0622765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.00000 | 0.0766402 | ||||||||
\(682\) | 22.1623 | 0.848637 | ||||||||
\(683\) | −37.1096 | −1.41996 | −0.709980 | − | 0.704222i | \(-0.751296\pi\) | ||||
−0.709980 | + | 0.704222i | \(0.751296\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.6491 | −0.482945 | ||||||||
\(687\) | −8.16228 | −0.311410 | ||||||||
\(688\) | −9.16228 | −0.349309 | ||||||||
\(689\) | 9.48683 | 0.361420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4868 | 0.513063 | 0.256532 | − | 0.966536i | \(-0.417420\pi\) | ||||
0.256532 | + | 0.966536i | \(0.417420\pi\) | |||||||
\(692\) | −2.16228 | −0.0821975 | ||||||||
\(693\) | 13.1623 | 0.499994 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.83772 | 0.145468 | ||||||||
\(697\) | −5.29822 | −0.200684 | ||||||||
\(698\) | −17.8377 | −0.675168 | ||||||||
\(699\) | 11.8114 | 0.446748 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9737 | −1.16986 | −0.584930 | − | 0.811084i | \(-0.698878\pi\) | ||||
−0.584930 | + | 0.811084i | \(0.698878\pi\) | |||||||
\(702\) | −5.16228 | −0.194838 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | 4.16228 | 0.156872 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.8114 | 0.896153 | ||||||||
\(707\) | −43.6754 | −1.64258 | ||||||||
\(708\) | 7.48683 | 0.281372 | ||||||||
\(709\) | 23.5132 | 0.883056 | 0.441528 | − | 0.897248i | \(-0.354437\pi\) | ||||
0.441528 | + | 0.897248i | \(0.354437\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32456 | −0.199686 | ||||||||
\(712\) | −7.32456 | −0.274499 | ||||||||
\(713\) | −28.3509 | −1.06175 | ||||||||
\(714\) | −2.64911 | −0.0991405 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.6491 | −0.771693 | ||||||||
\(717\) | 24.3246 | 0.908417 | ||||||||
\(718\) | −11.6754 | −0.435724 | ||||||||
\(719\) | 19.3246 | 0.720684 | 0.360342 | − | 0.932820i | \(-0.382660\pi\) | ||||
0.360342 | + | 0.932820i | \(0.382660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.4868 | 1.84299 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −10.5132 | −0.390989 | ||||||||
\(724\) | 9.16228 | 0.340513 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.32456 | −0.234726 | ||||||||
\(727\) | −49.6228 | −1.84041 | −0.920203 | − | 0.391440i | \(-0.871977\pi\) | ||||
−0.920203 | + | 0.391440i | \(0.871977\pi\) | |||||||
\(728\) | 16.3246 | 0.605028 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.67544 | −0.283887 | ||||||||
\(732\) | 4.16228 | 0.153842 | ||||||||
\(733\) | 50.4868 | 1.86477 | 0.932387 | − | 0.361462i | \(-0.117722\pi\) | ||||
0.932387 | + | 0.361462i | \(0.117722\pi\) | |||||||
\(734\) | −7.48683 | −0.276344 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.32456 | −0.196266 | ||||||||
\(737\) | −27.0000 | −0.994558 | ||||||||
\(738\) | −6.32456 | −0.232810 | ||||||||
\(739\) | 6.32456 | 0.232653 | 0.116326 | − | 0.993211i | \(-0.462888\pi\) | ||||
0.116326 | + | 0.993211i | \(0.462888\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.16228 | 0.189641 | ||||||||
\(742\) | 5.81139 | 0.213343 | ||||||||
\(743\) | 4.64911 | 0.170559 | 0.0852797 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852797 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(744\) | −5.32456 | −0.195208 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.1359 | −0.590779 | ||||||||
\(747\) | 6.48683 | 0.237341 | ||||||||
\(748\) | 3.48683 | 0.127491 | ||||||||
\(749\) | 40.5964 | 1.48336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.0000 | −0.948753 | −0.474377 | − | 0.880322i | \(-0.657327\pi\) | ||||
−0.474377 | + | 0.880322i | \(0.657327\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | 10.6491 | 0.388075 | ||||||||
\(754\) | −19.8114 | −0.721488 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.16228 | −0.115011 | ||||||||
\(757\) | −4.86406 | −0.176787 | −0.0883936 | − | 0.996086i | \(-0.528173\pi\) | ||||
−0.0883936 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(758\) | 22.9737 | 0.834441 | ||||||||
\(759\) | 22.1623 | 0.804440 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.4868 | −1.43140 | −0.715698 | − | 0.698410i | \(-0.753891\pi\) | ||||
−0.715698 | + | 0.698410i | \(0.753891\pi\) | |||||||
\(762\) | −15.6491 | −0.566907 | ||||||||
\(763\) | 24.2719 | 0.878701 | ||||||||
\(764\) | 21.6491 | 0.783237 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.48683 | −0.125984 | ||||||||
\(767\) | −38.6491 | −1.39554 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 34.6754 | 1.25043 | 0.625214 | − | 0.780453i | \(-0.285012\pi\) | ||||
0.625214 | + | 0.780453i | \(0.285012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.3246 | 0.695957 | ||||||||
\(772\) | −9.16228 | −0.329758 | ||||||||
\(773\) | 8.97367 | 0.322760 | 0.161380 | − | 0.986892i | \(-0.448405\pi\) | ||||
0.161380 | + | 0.986892i | \(0.448405\pi\) | |||||||
\(774\) | −9.16228 | −0.329331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.513167 | 0.0184216 | ||||||||
\(777\) | −31.6228 | −1.13446 | ||||||||
\(778\) | −34.6491 | −1.24223 | ||||||||
\(779\) | 6.32456 | 0.226601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.83772 | 0.173107 | ||||||||
\(782\) | −4.46050 | −0.159507 | ||||||||
\(783\) | 3.83772 | 0.137149 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.4868 | 0.445391 | ||||||||
\(787\) | 34.4868 | 1.22932 | 0.614661 | − | 0.788791i | \(-0.289293\pi\) | ||||
0.614661 | + | 0.788791i | \(0.289293\pi\) | |||||||
\(788\) | −24.1359 | −0.859807 | ||||||||
\(789\) | −31.9737 | −1.13829 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.5132 | 1.08492 | ||||||||
\(792\) | 4.16228 | 0.147900 | ||||||||
\(793\) | −21.4868 | −0.763020 | ||||||||
\(794\) | 17.1359 | 0.608132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.6491 | −0.661000 | ||||||||
\(797\) | 47.6228 | 1.68689 | 0.843443 | − | 0.537219i | \(-0.180525\pi\) | ||||
0.843443 | + | 0.537219i | \(0.180525\pi\) | |||||||
\(798\) | 3.16228 | 0.111943 | ||||||||
\(799\) | 5.02633 | 0.177819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.32456 | −0.258800 | ||||||||
\(802\) | 13.6491 | 0.481967 | ||||||||
\(803\) | −4.16228 | −0.146884 | ||||||||
\(804\) | 6.48683 | 0.228773 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.4868 | 0.968182 | ||||||||
\(807\) | −12.3246 | −0.433845 | ||||||||
\(808\) | −13.8114 | −0.485883 | ||||||||
\(809\) | −23.1623 | −0.814342 | −0.407171 | − | 0.913352i | \(-0.633485\pi\) | ||||
−0.407171 | + | 0.913352i | \(0.633485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.1886 | 0.392885 | 0.196443 | − | 0.980515i | \(-0.437061\pi\) | ||||
0.196443 | + | 0.980515i | \(0.437061\pi\) | |||||||
\(812\) | −12.1359 | −0.425888 | ||||||||
\(813\) | 1.16228 | 0.0407629 | ||||||||
\(814\) | 41.6228 | 1.45888 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.837722 | −0.0293261 | ||||||||
\(817\) | 9.16228 | 0.320548 | ||||||||
\(818\) | −7.67544 | −0.268366 | ||||||||
\(819\) | 16.3246 | 0.570426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8377 | 1.28565 | 0.642823 | − | 0.766015i | \(-0.277763\pi\) | ||||
0.642823 | + | 0.766015i | \(0.277763\pi\) | |||||||
\(822\) | −2.32456 | −0.0810782 | ||||||||
\(823\) | −27.2982 | −0.951556 | −0.475778 | − | 0.879565i | \(-0.657833\pi\) | ||||
−0.475778 | + | 0.879565i | \(0.657833\pi\) | |||||||
\(824\) | 15.6491 | 0.545163 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.6754 | −0.823774 | ||||||||
\(827\) | 5.16228 | 0.179510 | 0.0897550 | − | 0.995964i | \(-0.471392\pi\) | ||||
0.0897550 | + | 0.995964i | \(0.471392\pi\) | |||||||
\(828\) | −5.32456 | −0.185041 | ||||||||
\(829\) | −22.7851 | −0.791358 | −0.395679 | − | 0.918389i | \(-0.629491\pi\) | ||||
−0.395679 | + | 0.918389i | \(0.629491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.8114 | −0.860698 | ||||||||
\(832\) | 5.16228 | 0.178970 | ||||||||
\(833\) | 2.51317 | 0.0870761 | ||||||||
\(834\) | −21.4868 | −0.744028 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.16228 | −0.143955 | ||||||||
\(837\) | −5.32456 | −0.184044 | ||||||||
\(838\) | 8.00000 | 0.276355 | ||||||||
\(839\) | −12.8377 | −0.443207 | −0.221604 | − | 0.975137i | \(-0.571129\pi\) | ||||
−0.221604 | + | 0.975137i | \(0.571129\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.2719 | −0.492134 | ||||||||
\(842\) | 18.6491 | 0.642691 | ||||||||
\(843\) | −7.64911 | −0.263449 | ||||||||
\(844\) | −18.8114 | −0.647515 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 20.0000 | 0.687208 | ||||||||
\(848\) | 1.83772 | 0.0631076 | ||||||||
\(849\) | −24.6491 | −0.845955 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.2456 | −1.82523 | ||||||||
\(852\) | −1.16228 | −0.0398190 | ||||||||
\(853\) | 32.3246 | 1.10677 | 0.553386 | − | 0.832925i | \(-0.313336\pi\) | ||||
0.553386 | + | 0.832925i | \(0.313336\pi\) | |||||||
\(854\) | −13.1623 | −0.450404 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.8377 | 0.438784 | ||||||||
\(857\) | 25.6754 | 0.877056 | 0.438528 | − | 0.898717i | \(-0.355500\pi\) | ||||
0.438528 | + | 0.898717i | \(0.355500\pi\) | |||||||
\(858\) | −21.4868 | −0.733548 | ||||||||
\(859\) | −5.35089 | −0.182570 | −0.0912850 | − | 0.995825i | \(-0.529097\pi\) | ||||
−0.0912850 | + | 0.995825i | \(0.529097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | 0.681598 | ||||||||
\(862\) | −0.324555 | −0.0110544 | ||||||||
\(863\) | 54.9737 | 1.87133 | 0.935663 | − | 0.352896i | \(-0.114803\pi\) | ||||
0.935663 | + | 0.352896i | \(0.114803\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 28.1359 | 0.956098 | ||||||||
\(867\) | 16.2982 | 0.553517 | ||||||||
\(868\) | 16.8377 | 0.571510 | ||||||||
\(869\) | −22.1623 | −0.751804 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4868 | −1.13466 | ||||||||
\(872\) | 7.67544 | 0.259923 | ||||||||
\(873\) | 0.513167 | 0.0173681 | ||||||||
\(874\) | 5.32456 | 0.180106 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.00000 | 0.0337869 | ||||||||
\(877\) | 45.6228 | 1.54057 | 0.770286 | − | 0.637699i | \(-0.220114\pi\) | ||||
0.770286 | + | 0.637699i | \(0.220114\pi\) | |||||||
\(878\) | 13.6491 | 0.460635 | ||||||||
\(879\) | −16.4868 | −0.556087 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.3246 | 0.482607 | 0.241303 | − | 0.970450i | \(-0.422425\pi\) | ||||
0.241303 | + | 0.970450i | \(0.422425\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | −29.4868 | −0.992311 | −0.496155 | − | 0.868234i | \(-0.665255\pi\) | ||||
−0.496155 | + | 0.868234i | \(0.665255\pi\) | |||||||
\(884\) | 4.32456 | 0.145451 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.8377 | −0.397696 | ||||||||
\(887\) | 21.6754 | 0.727790 | 0.363895 | − | 0.931440i | \(-0.381447\pi\) | ||||
0.363895 | + | 0.931440i | \(0.381447\pi\) | |||||||
\(888\) | −10.0000 | −0.335578 | ||||||||
\(889\) | 49.4868 | 1.65974 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.16228 | 0.139442 | ||||||||
\(892\) | −25.6491 | −0.858796 | ||||||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | −16.6491 | −0.556830 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.16228 | 0.105644 | ||||||||
\(897\) | 27.4868 | 0.917759 | ||||||||
\(898\) | −11.0000 | −0.367075 | ||||||||
\(899\) | −20.4342 | −0.681518 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.53950 | 0.0512882 | ||||||||
\(902\) | −26.3246 | −0.876512 | ||||||||
\(903\) | 28.9737 | 0.964183 | ||||||||
\(904\) | 9.64911 | 0.320925 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.0000 | 0.332228 | ||||||||
\(907\) | −38.6491 | −1.28332 | −0.641661 | − | 0.766988i | \(-0.721755\pi\) | ||||
−0.641661 | + | 0.766988i | \(0.721755\pi\) | |||||||
\(908\) | −2.00000 | −0.0663723 | ||||||||
\(909\) | −13.8114 | −0.458095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.02633 | −0.232793 | −0.116396 | − | 0.993203i | \(-0.537134\pi\) | ||||
−0.116396 | + | 0.993203i | \(0.537134\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 27.0000 | 0.893570 | ||||||||
\(914\) | 9.67544 | 0.320035 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.16228 | 0.269689 | ||||||||
\(917\) | −39.4868 | −1.30397 | ||||||||
\(918\) | −0.837722 | −0.0276490 | ||||||||
\(919\) | −18.8377 | −0.621399 | −0.310700 | − | 0.950508i | \(-0.600563\pi\) | ||||
−0.310700 | + | 0.950508i | \(0.600563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5132 | −0.445274 | ||||||||
\(922\) | 12.0000 | 0.395199 | ||||||||
\(923\) | 6.00000 | 0.197492 | ||||||||
\(924\) | −13.1623 | −0.433007 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.6754 | −0.712299 | ||||||||
\(927\) | 15.6491 | 0.513984 | ||||||||
\(928\) | −3.83772 | −0.125979 | ||||||||
\(929\) | −37.2982 | −1.22371 | −0.611857 | − | 0.790968i | \(-0.709577\pi\) | ||||
−0.611857 | + | 0.790968i | \(0.709577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | −11.8114 | −0.386895 | ||||||||
\(933\) | 26.0000 | 0.851202 | ||||||||
\(934\) | −37.1359 | −1.21513 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.16228 | 0.168734 | ||||||||
\(937\) | −26.6491 | −0.870588 | −0.435294 | − | 0.900288i | \(-0.643356\pi\) | ||||
−0.435294 | + | 0.900288i | \(0.643356\pi\) | |||||||
\(938\) | −20.5132 | −0.669779 | ||||||||
\(939\) | 10.6754 | 0.348380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.8114 | 1.06962 | 0.534810 | − | 0.844972i | \(-0.320383\pi\) | ||||
0.534810 | + | 0.844972i | \(0.320383\pi\) | |||||||
\(942\) | −18.3246 | −0.597046 | ||||||||
\(943\) | 33.6754 | 1.09662 | ||||||||
\(944\) | −7.48683 | −0.243676 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.1359 | −1.23991 | ||||||||
\(947\) | −48.0000 | −1.55979 | −0.779895 | − | 0.625910i | \(-0.784728\pi\) | ||||
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(948\) | 5.32456 | 0.172934 | ||||||||
\(949\) | −5.16228 | −0.167575 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.16228 | −0.134971 | ||||||||
\(952\) | 2.64911 | 0.0858582 | ||||||||
\(953\) | −40.6754 | −1.31761 | −0.658803 | − | 0.752315i | \(-0.728937\pi\) | ||||
−0.658803 | + | 0.752315i | \(0.728937\pi\) | |||||||
\(954\) | 1.83772 | 0.0594985 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.3246 | −0.786712 | ||||||||
\(957\) | 15.9737 | 0.516355 | ||||||||
\(958\) | −39.9737 | −1.29149 | ||||||||
\(959\) | 7.35089 | 0.237373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64911 | −0.0854552 | ||||||||
\(962\) | 51.6228 | 1.66439 | ||||||||
\(963\) | 12.8377 | 0.413690 | ||||||||
\(964\) | 10.5132 | 0.338606 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.8377 | 0.541745 | ||||||||
\(967\) | 24.3246 | 0.782225 | 0.391112 | − | 0.920343i | \(-0.372090\pi\) | ||||
0.391112 | + | 0.920343i | \(0.372090\pi\) | |||||||
\(968\) | 6.32456 | 0.203279 | ||||||||
\(969\) | 0.837722 | 0.0269115 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5132 | 0.401567 | 0.200783 | − | 0.979636i | \(-0.435651\pi\) | ||||
0.200783 | + | 0.979636i | \(0.435651\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 67.9473 | 2.17829 | ||||||||
\(974\) | −28.6491 | −0.917977 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.16228 | −0.133231 | ||||||||
\(977\) | −53.9473 | −1.72593 | −0.862964 | − | 0.505265i | \(-0.831395\pi\) | ||||
−0.862964 | + | 0.505265i | \(0.831395\pi\) | |||||||
\(978\) | 22.6491 | 0.724239 | ||||||||
\(979\) | −30.4868 | −0.974363 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.67544 | 0.245058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.1359 | −1.15256 | −0.576279 | − | 0.817253i | \(-0.695496\pi\) | ||||
−0.576279 | + | 0.817253i | \(0.695496\pi\) | |||||||
\(984\) | 6.32456 | 0.201619 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.21495 | −0.102385 | ||||||||
\(987\) | −18.9737 | −0.603938 | ||||||||
\(988\) | −5.16228 | −0.164234 | ||||||||
\(989\) | 48.7851 | 1.55127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2982 | 0.771858 | 0.385929 | − | 0.922528i | \(-0.373881\pi\) | ||||
0.385929 | + | 0.922528i | \(0.373881\pi\) | |||||||
\(992\) | 5.32456 | 0.169055 | ||||||||
\(993\) | 3.18861 | 0.101188 | ||||||||
\(994\) | 3.67544 | 0.116578 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.48683 | −0.205543 | ||||||||
\(997\) | 13.5132 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(998\) | −5.81139 | −0.183956 | ||||||||
\(999\) | −10.0000 | −0.316386 |
(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 | 2850.2.a.bg.1.2 | yes | 2 | |
3.2 | odd | 2 | 8550.2.a.bq.1.2 | 2 | |||
5.2 | odd | 4 | 2850.2.d.v.799.4 | 4 | |||
5.3 | odd | 4 | 2850.2.d.v.799.1 | 4 | |||
5.4 | even | 2 | 2850.2.a.bf.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 8550.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bf.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
2850.2.a.bg.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
2850.2.d.v.799.1 | 4 | 5.3 | odd | 4 | |||
2850.2.d.v.799.4 | 4 | 5.2 | odd | 4 | |||
8550.2.a.bq.1.2 | 2 | 3.2 | odd | 2 | |||
8550.2.a.ca.1.1 | 2 | 15.14 | odd | 2 |