Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, 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("1792.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 896) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1 |
$q$-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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.4721 | 2.70389 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.23607 | 0.742405 | 0.371202 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371202 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23607 | 0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4721 | 1.94463 | 0.972313 | − | 0.233681i | \(-0.0750770\pi\) | ||||
0.972313 | + | 0.233681i | \(0.0750770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.9443 | 2.25331 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23607 | 0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47214 | −0.406417 | −0.203208 | − | 0.979136i | \(-0.565137\pi\) | ||||
−0.203208 | + | 0.979136i | \(0.565137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.4721 | −1.67688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427 | 1.36399 | 0.681994 | − | 0.731357i | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731357i | \(0.261113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −24.1803 | −3.60459 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.94427 | −0.721196 | −0.360598 | − | 0.932721i | \(-0.617427\pi\) | ||||
−0.360598 | + | 0.932721i | \(0.617427\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.47214 | 0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.94427 | 1.22859 | 0.614295 | − | 0.789076i | \(-0.289440\pi\) | ||||
0.614295 | + | 0.789076i | \(0.289440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.9443 | 1.74541 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.4721 | −1.38707 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.76393 | −0.620211 | −0.310106 | − | 0.950702i | \(-0.600364\pi\) | ||||
−0.310106 | + | 0.950702i | \(0.600364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.23607 | −0.414336 | −0.207168 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207168 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.47214 | −0.941401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4721 | −1.29891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4721 | −1.27938 | −0.639688 | − | 0.768635i | \(-0.720936\pi\) | ||||
−0.639688 | + | 0.768635i | \(0.720936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9443 | −1.53620 | −0.768101 | − | 0.640328i | \(-0.778798\pi\) | ||||
−0.768101 | + | 0.640328i | \(0.778798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.94427 | −0.344601 | −0.172300 | − | 0.985044i | \(-0.555120\pi\) | ||||
−0.172300 | + | 0.985044i | \(0.555120\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.7082 | −2.04477 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.76393 | −0.522909 | −0.261455 | − | 0.965216i | \(-0.584202\pi\) | ||||
−0.261455 | + | 0.965216i | \(0.584202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.47214 | 0.702002 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −33.8885 | −3.63323 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | −0.339232 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.4721 | −1.07442 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.94427 | −0.705084 | −0.352542 | − | 0.935796i | \(-0.614683\pi\) | ||||
−0.352542 | + | 0.935796i | \(0.614683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −29.8885 | −3.00391 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.18034 | −0.813974 | −0.406987 | − | 0.913434i | \(-0.633421\pi\) | ||||
−0.406987 | + | 0.913434i | \(0.633421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.4721 | −1.02198 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.4721 | −1.78577 | −0.892884 | − | 0.450286i | \(-0.851322\pi\) | ||||
−0.892884 | + | 0.450286i | \(0.851322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4721 | 1.00305 | 0.501524 | − | 0.865144i | \(-0.332773\pi\) | ||||
0.501524 | + | 0.865144i | \(0.332773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.4164 | −1.26211 | −0.631055 | − | 0.775738i | \(-0.717378\pi\) | ||||
−0.631055 | + | 0.775738i | \(0.717378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | −0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.1803 | 2.23547 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.47214 | 0.583573 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.41641 | 0.658100 | 0.329050 | − | 0.944313i | \(-0.393272\pi\) | ||||
0.329050 | + | 0.944313i | \(0.393272\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.9443 | −2.54840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.18034 | 0.714720 | 0.357360 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357360 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.23607 | −0.280603 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 46.8328 | 4.03073 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7639 | 1.08262 | 0.541311 | − | 0.840822i | \(-0.317928\pi\) | ||||
0.541311 | + | 0.840822i | \(0.317928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0000 | 1.34744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.9443 | −1.08245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8885 | −2.81429 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.23607 | −0.266906 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.944272 | −0.0773578 | −0.0386789 | − | 0.999252i | \(-0.512315\pi\) | ||||
−0.0386789 | + | 0.999252i | \(0.512315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.47214 | −0.201180 | −0.100590 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100590 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.9443 | −1.20817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.180340 | 0.0143927 | 0.00719634 | − | 0.999974i | \(-0.497709\pi\) | ||||
0.00719634 | + | 0.999974i | \(0.497709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.9443 | −2.29543 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.47214 | −0.194832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −41.8885 | −3.26102 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9443 | 1.00166 | 0.500829 | − | 0.865546i | \(-0.333029\pi\) | ||||
0.500829 | + | 0.865546i | \(0.333029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.1803 | 1.84912 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.70820 | −0.738101 | −0.369051 | − | 0.929409i | \(-0.620317\pi\) | ||||
−0.369051 | + | 0.929409i | \(0.620317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.47214 | −0.413655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4164 | 1.15877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.47214 | 0.184776 | 0.0923881 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923881 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.7639 | −1.54337 | −0.771685 | − | 0.636004i | \(-0.780586\pi\) | ||||
−0.771685 | + | 0.636004i | \(0.780586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4721 | 0.774123 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.4721 | 1.05269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.8885 | 1.29437 | 0.647185 | − | 0.762333i | \(-0.275946\pi\) | ||||
0.647185 | + | 0.762333i | \(0.275946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.52786 | 0.253941 | 0.126971 | − | 0.991906i | \(-0.459475\pi\) | ||||
0.126971 | + | 0.991906i | \(0.459475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 33.8885 | 2.42681 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.00000 | −0.284988 | −0.142494 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142494 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 33.8885 | 2.39031 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.4721 | −0.735000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.47214 | 0.452034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.4721 | 1.28390 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.9443 | −0.895374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4164 | 1.06131 | 0.530655 | − | 0.847588i | \(-0.321946\pi\) | ||||
0.530655 | + | 0.847588i | \(0.321946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.8885 | 2.87016 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.9443 | −1.97398 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.52786 | 0.643833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.47214 | −0.435363 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0557 | −0.740346 | −0.370173 | − | 0.928963i | \(-0.620702\pi\) | ||||
−0.370173 | + | 0.928963i | \(0.620702\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.8885 | 2.72590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.70820 | −0.644356 | −0.322178 | − | 0.946679i | \(-0.604415\pi\) | ||||
−0.322178 | + | 0.946679i | \(0.604415\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.65248 | −0.439608 | −0.219804 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219804 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.9443 | −0.851671 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8885 | −1.04089 | −0.520447 | − | 0.853894i | \(-0.674235\pi\) | ||||
−0.520447 | + | 0.853894i | \(0.674235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −41.8885 | −2.72095 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.4721 | 1.19486 | 0.597432 | − | 0.801920i | \(-0.296188\pi\) | ||||
0.597432 | + | 0.801920i | \(0.296188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.94427 | 0.189657 | 0.0948286 | − | 0.995494i | \(-0.469770\pi\) | ||||
0.0948286 | + | 0.995494i | \(0.469770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.23607 | −0.206745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4721 | 0.666326 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4164 | 0.976975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6525 | 0.924856 | 0.462428 | − | 0.886657i | \(-0.346978\pi\) | ||||
0.462428 | + | 0.886657i | \(0.346978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.88854 | −0.621687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.9443 | −1.31158 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.8885 | 1.73964 | 0.869820 | − | 0.493370i | \(-0.164235\pi\) | ||||
0.869820 | + | 0.493370i | \(0.164235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.47214 | 0.153611 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 78.2492 | 4.84351 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.05573 | 0.188424 | 0.0942121 | − | 0.995552i | \(-0.469967\pi\) | ||||
0.0942121 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.9443 | −1.77803 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.47214 | −0.396088 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1246 | 0.800222 | 0.400111 | − | 0.916467i | \(-0.368972\pi\) | ||||
0.400111 | + | 0.916467i | \(0.368972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.9443 | −1.27227 | −0.636137 | − | 0.771576i | \(-0.719469\pi\) | ||||
−0.636137 | + | 0.771576i | \(0.719469\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.4721 | 0.633803 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.8885 | −1.31993 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.0000 | −1.20168 | −0.600842 | − | 0.799368i | \(-0.705168\pi\) | ||||
−0.600842 | + | 0.799368i | \(0.705168\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.65248 | −0.395449 | −0.197724 | − | 0.980258i | \(-0.563355\pi\) | ||||
−0.197724 | + | 0.980258i | \(0.563355\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.8885 | 2.00738 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.4721 | 1.31734 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.2918 | −0.834936 | −0.417468 | − | 0.908692i | \(-0.637082\pi\) | ||||
−0.417468 | + | 0.908692i | \(0.637082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.4164 | 0.897578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 57.8885 | 3.35903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.4721 | 1.52078 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4721 | 0.599633 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.5967 | −1.57503 | −0.787515 | − | 0.616296i | \(-0.788633\pi\) | ||||
−0.787515 | + | 0.616296i | \(0.788633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.8885 | −1.47275 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.8885 | −1.57635 | −0.788177 | − | 0.615449i | \(-0.788975\pi\) | ||||
−0.788177 | + | 0.615449i | \(0.788975\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.1803 | 1.36241 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8885 | −0.780058 | −0.390029 | − | 0.920803i | \(-0.627535\pi\) | ||||
−0.390029 | + | 0.920803i | \(0.627535\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.8885 | −2.34531 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 59.7771 | 3.33643 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.47214 | −0.360119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.7082 | 0.982274 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.8885 | −1.87404 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.94427 | 0.272587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9443 | 1.37106 | 0.685531 | − | 0.728044i | \(-0.259570\pi\) | ||||
0.685531 | + | 0.728044i | \(0.259570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.4721 | −1.01227 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.8885 | 1.85153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4164 | 0.948732 | 0.474366 | − | 0.880328i | \(-0.342677\pi\) | ||||
0.474366 | + | 0.880328i | \(0.342677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.4164 | 2.35806 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.8885 | 1.39379 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.9443 | −1.76854 | −0.884271 | − | 0.466975i | \(-0.845344\pi\) | ||||
−0.884271 | + | 0.466975i | \(0.845344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7082 | −0.947898 | −0.473949 | − | 0.880552i | \(-0.657172\pi\) | ||||
−0.473949 | + | 0.880552i | \(0.657172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −46.8328 | −2.49975 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.9443 | −1.85990 | −0.929948 | − | 0.367691i | \(-0.880148\pi\) | ||||
−0.929948 | + | 0.367691i | \(0.880148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 41.8885 | 2.22321 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.47214 | −0.342542 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.4164 | −1.23587 | −0.617935 | − | 0.786229i | \(-0.712031\pi\) | ||||
−0.617935 | + | 0.786229i | \(0.712031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.1803 | −0.849248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.52786 | 0.498711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0557 | 0.577104 | 0.288552 | − | 0.957464i | \(-0.406826\pi\) | ||||
0.288552 | + | 0.957464i | \(0.406826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.9443 | −0.777968 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.94427 | −0.464363 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0557 | 0.779556 | 0.389778 | − | 0.920909i | \(-0.372552\pi\) | ||||
0.389778 | + | 0.920909i | \(0.372552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.94427 | 0.255321 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33.8885 | 1.74535 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.11146 | 0.108458 | 0.0542291 | − | 0.998529i | \(-0.482730\pi\) | ||||
0.0542291 | + | 0.998529i | \(0.482730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0000 | −1.22956 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.9443 | 1.07020 | 0.535101 | − | 0.844788i | \(-0.320273\pi\) | ||||
0.535101 | + | 0.844788i | \(0.320273\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.9443 | −0.659701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 66.8328 | 3.39730 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.41641 | 0.376027 | 0.188013 | − | 0.982166i | \(-0.439795\pi\) | ||||
0.188013 | + | 0.982166i | \(0.439795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94427 | −0.250043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.4721 | −1.33534 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.8885 | −2.10764 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.1246 | 1.86323 | 0.931615 | − | 0.363446i | \(-0.118400\pi\) | ||||
0.931615 | + | 0.363446i | \(0.118400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.4721 | 0.524263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.47214 | 0.423078 | 0.211539 | − | 0.977370i | \(-0.432152\pi\) | ||||
0.211539 | + | 0.977370i | \(0.432152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −79.0132 | −3.92620 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.88854 | 0.490157 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.94427 | 0.145585 | 0.0727924 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727924 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.3607 | 1.59623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.76393 | 0.234418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4164 | 0.756762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.3050 | −2.02271 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.1803 | −0.790461 | −0.395231 | − | 0.918582i | \(-0.629335\pi\) | ||||
−0.395231 | + | 0.918582i | \(0.629335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0000 | 0.584844 | 0.292422 | − | 0.956289i | \(-0.405539\pi\) | ||||
0.292422 | + | 0.956289i | \(0.405539\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.9443 | −1.79629 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.9443 | −0.530875 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.23607 | 0.156604 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.8885 | 2.02240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3607 | −0.595393 | −0.297696 | − | 0.954661i | \(-0.596218\pi\) | ||||
−0.297696 | + | 0.954661i | \(0.596218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 109.666 | 5.25806 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000 | 0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.05573 | 0.145842 | 0.0729210 | − | 0.997338i | \(-0.476768\pi\) | ||||
0.0729210 | + | 0.997338i | \(0.476768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.3607 | 0.967365 | 0.483683 | − | 0.875244i | \(-0.339299\pi\) | ||||
0.483683 | + | 0.875244i | \(0.339299\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.47214 | −0.306809 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.05573 | 0.144531 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.8885 | −0.561055 | −0.280528 | − | 0.959846i | \(-0.590509\pi\) | ||||
−0.280528 | + | 0.959846i | \(0.590509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | 0.375873 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4721 | 0.490941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5279 | 0.539251 | 0.269625 | − | 0.962965i | \(-0.413100\pi\) | ||||
0.269625 | + | 0.962965i | \(0.413100\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.9443 | 1.35100 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0689 | 0.841552 | 0.420776 | − | 0.907165i | \(-0.361758\pi\) | ||||
0.420776 | + | 0.907165i | \(0.361758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.8885 | −1.57493 | −0.787467 | − | 0.616357i | \(-0.788608\pi\) | ||||
−0.787467 | + | 0.616357i | \(0.788608\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.65248 | −0.307840 | −0.153920 | − | 0.988083i | \(-0.549190\pi\) | ||||
−0.153920 | + | 0.988083i | \(0.549190\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4721 | 0.483558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.583592 | −0.0268905 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.7771 | −1.64503 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.7082 | 0.812508 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 66.8328 | 3.06006 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | −0.731059 | −0.365529 | − | 0.930800i | \(-0.619112\pi\) | ||||
−0.365529 | + | 0.930800i | \(0.619112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.00000 | 0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.4721 | 1.02041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5279 | −0.613006 | −0.306503 | − | 0.951870i | \(-0.599159\pi\) | ||||
−0.306503 | + | 0.951870i | \(0.599159\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 38.8328 | 1.75608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.52786 | −0.249469 | −0.124735 | − | 0.992190i | \(-0.539808\pi\) | ||||
−0.124735 | + | 0.992190i | \(0.539808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.9443 | −0.943283 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 96.7214 | 4.34730 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.9443 | 0.580630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3607 | −0.911469 | −0.455735 | − | 0.890116i | \(-0.650623\pi\) | ||||
−0.455735 | + | 0.890116i | \(0.650623\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.8885 | −1.87144 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.9443 | −1.29056 | −0.645281 | − | 0.763946i | \(-0.723260\pi\) | ||||
−0.645281 | + | 0.763946i | \(0.723260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.4721 | 1.17799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.18034 | 0.363302 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.6525 | −1.35865 | −0.679324 | − | 0.733839i | \(-0.737727\pi\) | ||||
−0.679324 | + | 0.733839i | \(0.737727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.94427 | 0.130247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.8328 | −2.06772 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.8885 | −1.14079 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.7771 | 0.869795 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.4164 | 1.37903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.05573 | 0.396739 | 0.198369 | − | 0.980127i | \(-0.436435\pi\) | ||||
0.198369 | + | 0.980127i | \(0.436435\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1803 | 1.05733 | 0.528666 | − | 0.848830i | \(-0.322692\pi\) | ||||
0.528666 | + | 0.848830i | \(0.322692\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.7082 | 0.772849 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.5967 | −1.54477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.47214 | −0.280339 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.7771 | 2.58439 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.9443 | −0.728491 | −0.364246 | − | 0.931303i | \(-0.618673\pi\) | ||||
−0.364246 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 67.1935 | 2.88355 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.8885 | −1.45163 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8328 | −0.805233 | −0.402617 | − | 0.915369i | \(-0.631899\pi\) | ||||
−0.402617 | + | 0.915369i | \(0.631899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.1803 | −1.03199 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.8885 | 1.44370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9443 | −0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.8885 | −1.09891 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.8885 | −1.26642 | −0.633209 | − | 0.773981i | \(-0.718263\pi\) | ||||
−0.633209 | + | 0.773981i | \(0.718263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.9443 | 1.22421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.8885 | −1.09302 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.5410 | 1.03428 | 0.517140 | − | 0.855901i | \(-0.326997\pi\) | ||||
0.517140 | + | 0.855901i | \(0.326997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.4164 | 1.82654 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.4164 | −1.02539 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.4164 | −1.73627 | −0.868133 | − | 0.496332i | \(-0.834680\pi\) | ||||
−0.868133 | + | 0.496332i | \(0.834680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.7771 | −1.66462 | −0.832310 | − | 0.554311i | \(-0.812982\pi\) | ||||
−0.832310 | + | 0.554311i | \(0.812982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −57.8885 | −2.41833 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5279 | 0.564151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.8328 | 1.36685 | 0.683424 | − | 0.730022i | \(-0.260490\pi\) | ||||
0.683424 | + | 0.730022i | \(0.260490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.4164 | −0.474450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.76393 | 0.197641 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.7771 | −1.48174 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −78.2492 | −3.23521 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.2361 | −0.793957 | −0.396979 | − | 0.917828i | \(-0.629941\pi\) | ||||
−0.396979 | + | 0.917828i | \(0.629941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.9443 | 0.532456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.47214 | −0.265332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −77.6656 | −3.17864 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.8885 | −1.62709 | −0.813544 | − | 0.581504i | \(-0.802465\pi\) | ||||
−0.813544 | + | 0.581504i | \(0.802465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −78.2492 | −3.18655 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.1803 | −0.657824 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8885 | −1.05078 | −0.525392 | − | 0.850860i | \(-0.676081\pi\) | ||||
−0.525392 | + | 0.850860i | \(0.676081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.8885 | 1.37323 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.52786 | −0.223268 | −0.111634 | − | 0.993749i | \(-0.535608\pi\) | ||||
−0.111634 | + | 0.993749i | \(0.535608\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.9443 | −0.844555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.4721 | −1.30728 | −0.653639 | − | 0.756806i | \(-0.726759\pi\) | ||||
−0.653639 | + | 0.756806i | \(0.726759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1803 | 1.29344 | 0.646719 | − | 0.762729i | \(-0.276141\pi\) | ||||
0.646719 | + | 0.762729i | \(0.276141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.7771 | −1.43569 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.8885 | 1.67287 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.94427 | 0.197141 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8885 | −0.712132 | −0.356066 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356066 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −49.8885 | −1.98289 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | −0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23607 | 0.128218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −96.7214 | −3.82624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.3607 | 1.35717 | 0.678583 | − | 0.734524i | \(-0.262595\pi\) | ||||
0.678583 | + | 0.734524i | \(0.262595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.5410 | 1.59878 | 0.799391 | − | 0.600811i | \(-0.205156\pi\) | ||||
0.799391 | + | 0.600811i | \(0.205156\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 93.6656 | 3.68808 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8885 | 0.703271 | 0.351636 | − | 0.936137i | \(-0.385626\pi\) | ||||
0.351636 | + | 0.936137i | \(0.385626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0557 | 0.748003 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.4164 | 1.54248 | 0.771242 | − | 0.636543i | \(-0.219636\pi\) | ||||
0.771242 | + | 0.636543i | \(0.219636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.4721 | −1.03435 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.0000 | −0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8328 | 0.421987 | 0.210993 | − | 0.977488i | \(-0.432330\pi\) | ||||
0.210993 | + | 0.977488i | \(0.432330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.2361 | −1.05936 | −0.529680 | − | 0.848197i | \(-0.677688\pi\) | ||||
−0.529680 | + | 0.848197i | \(0.677688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.9443 | 0.813408 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.4721 | 0.406092 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.8885 | 1.00241 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.7771 | 1.38322 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.9443 | 0.499708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8885 | 0.920836 | 0.460418 | − | 0.887702i | \(-0.347700\pi\) | ||||
0.460418 | + | 0.887702i | \(0.347700\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −79.1935 | −3.04816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.1246 | 0.811885 | 0.405942 | − | 0.913899i | \(-0.366943\pi\) | ||||
0.405942 | + | 0.913899i | \(0.366943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.94427 | 0.266497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.4164 | 1.20388 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.5279 | −0.823741 | −0.411870 | − | 0.911242i | \(-0.635124\pi\) | ||||
−0.411870 | + | 0.911242i | \(0.635124\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.3607 | 1.23644 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.5279 | 0.821339 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.9443 | 1.10269 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7082 | −1.28232 | −0.641160 | − | 0.767407i | \(-0.721547\pi\) | ||||
−0.641160 | + | 0.767407i | \(0.721547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.8885 | 1.13537 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.3050 | −1.56679 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.4164 | 1.94475 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.3607 | −1.07117 | −0.535584 | − | 0.844482i | \(-0.679908\pi\) | ||||
−0.535584 | + | 0.844482i | \(0.679908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −51.7771 | −1.95004 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.18034 | 0.307653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.47214 | −0.0928430 | −0.0464215 | − | 0.998922i | \(-0.514782\pi\) | ||||
−0.0464215 | + | 0.998922i | \(0.514782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 96.7214 | 3.62733 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.8885 | 1.56654 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −59.7771 | −2.23242 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.9443 | −1.37779 | −0.688894 | − | 0.724862i | \(-0.741904\pi\) | ||||
−0.688894 | + | 0.724862i | \(0.741904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.52786 | −0.354345 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 57.3050 | 2.12825 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.8328 | −1.44023 | −0.720115 | − | 0.693855i | \(-0.755911\pi\) | ||||
−0.720115 | + | 0.693855i | \(0.755911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0689 | −0.962876 | −0.481438 | − | 0.876480i | \(-0.659885\pi\) | ||||
−0.481438 | + | 0.876480i | \(0.659885\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.4721 | 0.386271 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.8885 | 1.54298 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.8885 | 0.510898 | 0.255449 | − | 0.966822i | \(-0.417777\pi\) | ||||
0.255449 | + | 0.966822i | \(0.417777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.8885 | −1.24493 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.4721 | 1.26466 | 0.632330 | − | 0.774699i | \(-0.282099\pi\) | ||||
0.632330 | + | 0.774699i | \(0.282099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.05573 | 0.111953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.5967 | −1.30242 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.4721 | 0.674957 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.3607 | −1.03490 | −0.517448 | − | 0.855715i | \(-0.673118\pi\) | ||||
−0.517448 | + | 0.855715i | \(0.673118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −47.4164 | −1.72795 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.5836 | 0.602741 | 0.301370 | − | 0.953507i | \(-0.402556\pi\) | ||||
0.301370 | + | 0.953507i | \(0.402556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.0000 | 1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.88854 | 0.285959 | 0.142980 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142980 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4721 | −0.379117 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.3607 | 1.74848 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.4164 | −0.556654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.9443 | 1.26012 | 0.630061 | − | 0.776545i | \(-0.283030\pi\) | ||||
0.630061 | + | 0.776545i | \(0.283030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −90.2492 | −3.25025 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.1246 | −1.04754 | −0.523770 | − | 0.851860i | \(-0.675475\pi\) | ||||
−0.523770 | + | 0.851860i | \(0.675475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.00000 | −0.286998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.47214 | −0.231888 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.7771 | 1.85273 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −151.554 | −5.41610 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.583592 | −0.0208293 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.1246 | 1.60852 | 0.804259 | − | 0.594278i | \(-0.202562\pi\) | ||||
0.804259 | + | 0.594278i | \(0.202562\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.88854 | −0.352041 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4164 | 0.477033 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4721 | −0.371876 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 93.6656 | 3.32198 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.7639 | −1.01887 | −0.509435 | − | 0.860509i | \(-0.670146\pi\) | ||||
−0.509435 | + | 0.860509i | \(0.670146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.88854 | 0.349832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.9443 | 0.528030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7771 | 0.415604 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42.4721 | −1.49509 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.4164 | 0.752961 | 0.376480 | − | 0.926425i | \(-0.377134\pi\) | ||||
0.376480 | + | 0.926425i | \(0.377134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1246 | 0.460867 | 0.230434 | − | 0.973088i | \(-0.425986\pi\) | ||||
0.230434 | + | 0.973088i | \(0.425986\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 67.7771 | 2.37705 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.8328 | 1.36025 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.9443 | 1.01263 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.1803 | −0.844929 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.00000 | −0.139601 | −0.0698005 | − | 0.997561i | \(-0.522236\pi\) | ||||
−0.0698005 | + | 0.997561i | \(0.522236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8328 | −0.795902 | −0.397951 | − | 0.917407i | \(-0.630279\pi\) | ||||
−0.397951 | + | 0.917407i | \(0.630279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 70.8328 | 2.46608 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.58359 | −0.298481 | −0.149240 | − | 0.988801i | \(-0.547683\pi\) | ||||
−0.149240 | + | 0.988801i | \(0.547683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.1246 | −0.455837 | −0.227918 | − | 0.973680i | \(-0.573192\pi\) | ||||
−0.227918 | + | 0.973680i | \(0.573192\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 64.7214 | 2.24516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.8885 | −1.44961 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.6656 | 2.78157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.4164 | 0.668737 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.18034 | 0.281412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.5279 | 0.738834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.11146 | −0.209498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.7639 | −0.984858 | −0.492429 | − | 0.870353i | \(-0.663891\pi\) | ||||
−0.492429 | + | 0.870353i | \(0.663891\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −78.2492 | −2.67607 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.16718 | −0.108189 | −0.0540945 | − | 0.998536i | \(-0.517227\pi\) | ||||
−0.0540945 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.81966 | 0.266803 | 0.133402 | − | 0.991062i | \(-0.457410\pi\) | ||||
0.133402 | + | 0.991062i | \(0.457410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.47214 | −0.220570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.88854 | −0.0642868 | −0.0321434 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321434 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.4164 | 1.06819 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.0689 | 1.42873 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.7771 | −1.75642 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.8885 | −1.14827 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −51.8885 | −1.75616 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.52786 | 0.0516512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.3607 | −1.49795 | −0.748977 | − | 0.662596i | \(-0.769455\pi\) | ||||
−0.748977 | + | 0.662596i | \(0.769455\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.2492 | 1.55995 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.8328 | 1.10617 | 0.553083 | − | 0.833126i | \(-0.313451\pi\) | ||||
0.553083 | + | 0.833126i | \(0.313451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.5279 | −0.993692 | −0.496846 | − | 0.867839i | \(-0.665509\pi\) | ||||
−0.496846 | + | 0.867839i | \(0.665509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.8885 | −1.67699 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.8328 | 1.30388 | 0.651939 | − | 0.758271i | \(-0.273956\pi\) | ||||
0.651939 | + | 0.758271i | \(0.273956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.41641 | −0.248738 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −97.6656 | −3.27192 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.8885 | −0.864393 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.8885 | −0.595954 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.9443 | 0.963205 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.1935 | 2.23359 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.58359 | −0.285013 | −0.142507 | − | 0.989794i | \(-0.545516\pi\) | ||||
−0.142507 | + | 0.989794i | \(0.545516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −61.1246 | −2.02738 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.5279 | −1.50841 | −0.754203 | − | 0.656642i | \(-0.771976\pi\) | ||||
−0.754203 | + | 0.656642i | \(0.771976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.0557 | 0.630653 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −33.8885 | −1.12032 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.18034 | −0.270139 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.83282 | −0.225394 | −0.112697 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112697 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 89.3050 | 2.94270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41.8885 | −1.37878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.5279 | −0.444793 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 59.7771 | 1.96334 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.88854 | 0.258815 | 0.129407 | − | 0.991592i | \(-0.458693\pi\) | ||||
0.129407 | + | 0.991592i | \(0.458693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.23607 | 0.106058 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.8885 | 0.847553 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.8885 | −0.846646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.05573 | −0.295838 | −0.147919 | − | 0.988999i | \(-0.547257\pi\) | ||||
−0.147919 | + | 0.988999i | \(0.547257\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 90.2492 | 2.94517 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.6525 | 0.999242 | 0.499621 | − | 0.866244i | \(-0.333473\pi\) | ||||
0.499621 | + | 0.866244i | \(0.333473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.94427 | −0.161008 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −46.8328 | −1.52347 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.9443 | −1.85044 | −0.925220 | − | 0.379431i | \(-0.876120\pi\) | ||||
−0.925220 | + | 0.379431i | \(0.876120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.52786 | −0.309288 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.9443 | 1.45742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.88854 | −0.125962 | −0.0629811 | − | 0.998015i | \(-0.520061\pi\) | ||||
−0.0629811 | + | 0.998015i | \(0.520061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −57.8885 | −1.87323 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 135.554 | 4.38184 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −138.026 | −4.44784 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.4164 | −0.367507 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.4164 | −1.26755 | −0.633773 | − | 0.773519i | \(-0.718495\pi\) | ||||
−0.633773 | + | 0.773519i | \(0.718495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.9443 | 0.672827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.6525 | −1.49715 | −0.748575 | − | 0.663051i | \(-0.769261\pi\) | ||||
−0.748575 | + | 0.663051i | \(0.769261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7639 | −0.409193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −57.3050 | −1.83523 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 78.2492 | 2.49831 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.7771 | 1.39627 | 0.698136 | − | 0.715965i | \(-0.254013\pi\) | ||||
0.698136 | + | 0.715965i | \(0.254013\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.9443 | 0.412439 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0000 | −0.509286 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.1115 | 0.703103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8328 | −0.725308 | −0.362654 | − | 0.931924i | \(-0.618129\pi\) | ||||
−0.362654 | + | 0.931924i | \(0.618129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −80.7214 | −2.56161 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −77.6656 | −2.46217 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.2361 | −1.11594 | −0.557969 | − | 0.829862i | \(-0.688419\pi\) | ||||
−0.557969 | + | 0.829862i | \(0.688419\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.7771 | 1.13194 |
(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 | 1792.2.a.j.1.1 | 2 | ||
4.3 | odd | 2 | 1792.2.a.r.1.2 | 2 | |||
8.3 | odd | 2 | 1792.2.a.l.1.1 | 2 | |||
8.5 | even | 2 | 1792.2.a.t.1.2 | 2 | |||
16.3 | odd | 4 | 896.2.b.e.449.4 | yes | 4 | ||
16.5 | even | 4 | 896.2.b.g.449.4 | yes | 4 | ||
16.11 | odd | 4 | 896.2.b.e.449.1 | ✓ | 4 | ||
16.13 | even | 4 | 896.2.b.g.449.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.e.449.1 | ✓ | 4 | 16.11 | odd | 4 | ||
896.2.b.e.449.4 | yes | 4 | 16.3 | odd | 4 | ||
896.2.b.g.449.1 | yes | 4 | 16.13 | even | 4 | ||
896.2.b.g.449.4 | yes | 4 | 16.5 | even | 4 | ||
1792.2.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1792.2.a.l.1.1 | 2 | 8.3 | odd | 2 | |||
1792.2.a.r.1.2 | 2 | 4.3 | odd | 2 | |||
1792.2.a.t.1.2 | 2 | 8.5 | even | 2 |