Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,4,Mod(129,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.129");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(9.44030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.359712057600.22 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 17x^{6} + 82x^{4} + 96x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.4 | ||
Root | \(2.47107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.129 |
Dual form | 160.4.c.d.129.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 4.30169i | − | 0.827861i | −0.910309 | − | 0.413930i | \(-0.864156\pi\) | ||
0.910309 | − | 0.413930i | \(-0.135844\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.58258 | + | 7.16515i | 0.767649 | + | 0.640871i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.3162i | 1.52893i | 0.644664 | + | 0.764466i | \(0.276997\pi\) | ||||
−0.644664 | + | 0.764466i | \(0.723003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.49545 | 0.314646 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −65.2358 | −1.78812 | −0.894061 | − | 0.447946i | \(-0.852156\pi\) | ||||
−0.894061 | + | 0.447946i | \(0.852156\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33.6697i | 0.718330i | 0.933274 | + | 0.359165i | \(0.116939\pi\) | ||||
−0.933274 | + | 0.359165i | \(0.883061\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 30.8223 | − | 36.9196i | 0.530552 | − | 0.635506i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 73.3212i | 1.04606i | 0.852315 | + | 0.523030i | \(0.175198\pi\) | ||||
−0.852315 | + | 0.523030i | \(0.824802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 134.063 | 1.61874 | 0.809372 | − | 0.587297i | \(-0.199808\pi\) | ||||
0.809372 | + | 0.587297i | \(0.199808\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 121.808 | 1.26574 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.7007i | 0.133274i | 0.997777 | + | 0.0666371i | \(0.0212270\pi\) | ||||
−0.997777 | + | 0.0666371i | \(0.978773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.3212 | + | 122.991i | 0.178570 | + | 0.983927i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 152.690i | − | 1.08834i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 224.642 | 1.43845 | 0.719225 | − | 0.694777i | \(-0.244497\pi\) | ||||
0.719225 | + | 0.694777i | \(0.244497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −68.8271 | −0.398765 | −0.199382 | − | 0.979922i | \(-0.563894\pi\) | ||||
−0.199382 | + | 0.979922i | \(0.563894\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 280.624i | 1.48032i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −202.890 | + | 243.026i | −0.979847 | + | 1.17368i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 196.312i | − | 0.872257i | −0.899884 | − | 0.436129i | \(-0.856349\pi\) | ||
0.899884 | − | 0.436129i | \(-0.143651\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 144.837 | 0.594678 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −143.147 | −0.545263 | −0.272632 | − | 0.962118i | \(-0.587894\pi\) | ||||
−0.272632 | + | 0.962118i | \(0.587894\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 15.0755i | − | 0.0534648i | −0.999643 | − | 0.0267324i | \(-0.991490\pi\) | ||
0.999643 | − | 0.0267324i | \(-0.00851021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 72.9129 | + | 60.8712i | 0.241538 | + | 0.201648i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 134.399i | 0.417107i | 0.978011 | + | 0.208554i | \(0.0668756\pi\) | ||||
−0.978011 | + | 0.208554i | \(0.933124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −458.808 | −1.33763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 315.405 | 0.865991 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 262.955i | − | 0.681502i | −0.940154 | − | 0.340751i | \(-0.889319\pi\) | ||
0.940154 | − | 0.340751i | \(-0.110681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −559.891 | − | 467.424i | −1.37265 | − | 1.14595i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 576.697i | − | 1.34009i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −119.698 | −0.264124 | −0.132062 | − | 0.991241i | \(-0.542160\pi\) | ||||
−0.132062 | + | 0.991241i | \(0.542160\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16.5409 | 0.0347188 | 0.0173594 | − | 0.999849i | \(-0.494474\pi\) | ||||
0.0173594 | + | 0.999849i | \(0.494474\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 240.559i | 0.481073i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −241.248 | + | 288.973i | −0.460357 | + | 0.551425i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 545.565i | 0.994797i | 0.867522 | + | 0.497399i | \(0.165711\pi\) | ||||
−0.867522 | + | 0.497399i | \(0.834289\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 63.2379 | 0.110333 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 199.299 | 0.333132 | 0.166566 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166566 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 43.2667i | − | 0.0693696i | −0.999398 | − | 0.0346848i | \(-0.988957\pi\) | ||
0.999398 | − | 0.0346848i | \(-0.0110427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 529.069 | − | 96.0190i | 0.814555 | − | 0.147831i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1847.23i | − | 2.73391i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 438.694 | 0.624772 | 0.312386 | − | 0.949955i | \(-0.398872\pi\) | ||||
0.312386 | + | 0.949955i | \(0.398872\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −427.450 | −0.586351 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1220.89i | − | 1.61458i | −0.590154 | − | 0.807291i | \(-0.700933\pi\) | ||
0.590154 | − | 0.807291i | \(-0.299067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −525.358 | + | 629.285i | −0.670389 | + | 0.803006i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 966.342i | − | 1.19084i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −723.212 | −0.861352 | −0.430676 | − | 0.902507i | \(-0.641725\pi\) | ||||
−0.430676 | + | 0.902507i | \(0.641725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −953.398 | −1.09828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 296.073i | 0.330122i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1150.60 | + | 960.581i | 1.24263 | + | 1.03741i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1136.00i | − | 1.18911i | −0.804056 | − | 0.594553i | \(-0.797329\pi\) | ||
0.804056 | − | 0.594553i | \(-0.202671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −554.208 | −0.562626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1175.21 | −1.15780 | −0.578901 | − | 0.815398i | \(-0.696518\pi\) | ||||
−0.578901 | + | 0.815398i | \(0.696518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1752.43i | 1.67643i | 0.545344 | + | 0.838213i | \(0.316399\pi\) | ||||
−0.545344 | + | 0.838213i | \(0.683601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1045.42 | + | 872.770i | 0.971646 | + | 0.811177i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 94.5981i | 0.0854686i | 0.999086 | + | 0.0427343i | \(0.0136069\pi\) | ||||
−0.999086 | + | 0.0427343i | \(0.986393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1349.68 | 1.18602 | 0.593009 | − | 0.805196i | \(-0.297940\pi\) | ||||
0.593009 | + | 0.805196i | \(0.297940\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −844.474 | −0.722108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 529.248i | 0.440597i | 0.975432 | + | 0.220299i | \(0.0707032\pi\) | ||||
−0.975432 | + | 0.220299i | \(0.929297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −105.333 | + | 126.170i | −0.0854116 | + | 0.102308i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 286.039i | 0.226020i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2076.18 | −1.59935 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2924.71 | 2.19738 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 615.774i | 0.451402i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −689.675 | + | 1215.51i | −0.493491 | + | 0.869751i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 814.066i | − | 0.568793i | −0.958707 | − | 0.284396i | \(-0.908207\pi\) | ||
0.958707 | − | 0.284396i | \(-0.0917931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −64.8500 | −0.0442614 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1329.85 | 0.886946 | 0.443473 | − | 0.896288i | \(-0.353746\pi\) | ||||
0.443473 | + | 0.896288i | \(0.353746\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3796.15i | 2.47495i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1094.05 | − | 1310.48i | 0.697488 | − | 0.835466i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2906.98i | − | 1.81284i | −0.422373 | − | 0.906422i | \(-0.638803\pi\) | ||
0.422373 | − | 0.906422i | \(-0.361197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 921.077 | 0.562048 | 0.281024 | − | 0.959701i | \(-0.409326\pi\) | ||||
0.281024 | + | 0.959701i | \(0.409326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 578.141 | 0.345307 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2196.47i | − | 1.28446i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1928.01 | + | 1609.60i | 1.10422 | + | 0.921860i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1973.65i | 1.10737i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −265.259 | −0.145845 | −0.0729224 | − | 0.997338i | \(-0.523233\pi\) | ||||
−0.0729224 | + | 0.997338i | \(0.523233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2507.69 | 1.35148 | 0.675738 | − | 0.737142i | \(-0.263825\pi\) | ||||
0.675738 | + | 0.737142i | \(0.263825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 622.897i | 0.329139i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −590.713 | − | 493.156i | −0.306111 | − | 0.255557i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8818i | 0.00756495i | 0.999993 | + | 0.00378248i | \(0.00120400\pi\) | ||||
−0.999993 | + | 0.00378248i | \(0.998796\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1131.15 | −0.564188 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −416.268 | −0.203767 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1184.23i | − | 0.569055i | −0.958668 | − | 0.284528i | \(-0.908163\pi\) | ||
0.958668 | − | 0.284528i | \(-0.0918368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2010.72 | + | 2408.48i | −0.948691 | + | 1.13636i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2688.78i | 1.24589i | 0.782266 | + | 0.622945i | \(0.214064\pi\) | ||||
−0.782266 | + | 0.622945i | \(0.785936\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1063.35 | 0.484002 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1138.92 | 0.509332 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1940.72i | − | 0.852891i | −0.904513 | − | 0.426445i | \(-0.859766\pi\) | ||
0.904513 | − | 0.426445i | \(-0.140234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3482.64 | + | 632.052i | −1.50436 | + | 0.273021i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 514.903i | 0.218658i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1580.62 | −0.660005 | −0.330002 | − | 0.943980i | \(-0.607050\pi\) | ||||
−0.330002 | + | 0.943980i | \(0.607050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2561.93 | −1.05208 | −0.526040 | − | 0.850460i | \(-0.676324\pi\) | ||||
−0.526040 | + | 0.850460i | \(0.676324\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 71.1539i | − | 0.0287423i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1406.61 | − | 1684.86i | 0.559004 | − | 0.669587i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4783.17i | − | 1.87048i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4323.62 | 1.66400 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 137.654 | 0.0521482 | 0.0260741 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260741 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 845.503i | 0.315340i | 0.987492 | + | 0.157670i | \(0.0503982\pi\) | ||||
−0.987492 | + | 0.157670i | \(0.949602\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1243.07 | + | 1037.78i | 0.456504 | + | 0.381111i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2733.63i | − | 0.988646i | −0.869278 | − | 0.494323i | \(-0.835416\pi\) | ||
0.869278 | − | 0.494323i | \(-0.164584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4649.70 | 1.65632 | 0.828162 | − | 0.560489i | \(-0.189387\pi\) | ||||
0.828162 | + | 0.560489i | \(0.189387\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2346.85 | 0.823553 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6361.02i | 2.19929i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1228.57 | − | 1025.67i | −0.418571 | − | 0.349443i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 124.889i | 0.0419343i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8745.70 | −2.89451 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3845.91 | −1.25480 | −0.627402 | − | 0.778696i | \(-0.715882\pi\) | ||||
−0.627402 | + | 0.778696i | \(0.715882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 857.321i | − | 0.275787i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 108.018 | − | 129.386i | 0.0342640 | − | 0.0410422i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1948.92i | − | 0.609684i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −186.120 | −0.0574284 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2468.70 | −0.751416 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1460.74i | − | 0.438648i | −0.975652 | − | 0.219324i | \(-0.929615\pi\) | ||
0.975652 | − | 0.219324i | \(-0.0703851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 189.629 | + | 1044.86i | 0.0561863 | + | 0.309589i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3435.16i | − | 1.00440i | −0.864750 | − | 0.502202i | \(-0.832523\pi\) | ||
0.864750 | − | 0.502202i | \(-0.167477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 595.358 | 0.171801 | 0.0859003 | − | 0.996304i | \(-0.472623\pi\) | ||||
0.0859003 | + | 0.996304i | \(0.472623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7946.21 | −2.26330 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5432.62i | − | 1.52748i | −0.645523 | − | 0.763740i | \(-0.723361\pi\) | ||
0.645523 | − | 0.763740i | \(-0.276639\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −962.986 | + | 1153.49i | −0.267312 | + | 0.320192i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1887.13i | − | 0.517224i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3931.51 | 1.06405 | 0.532026 | − | 0.846728i | \(-0.321431\pi\) | ||||
0.532026 | + | 0.846728i | \(0.321431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2587.88 | −0.691701 | −0.345851 | − | 0.938290i | \(-0.612410\pi\) | ||||
−0.345851 | + | 0.938290i | \(0.612410\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 2283.89i | − | 0.602927i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3937.75 | − | 3287.43i | −1.02683 | − | 0.857249i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4513.86i | 1.16279i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5251.90 | −1.33665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2231.79 | 0.561232 | 0.280616 | − | 0.959820i | \(-0.409461\pi\) | ||||
0.280616 | + | 0.959820i | \(0.409461\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 959.012i | − | 0.238311i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2706.99 | + | 2259.93i | 0.664777 | + | 0.554988i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2477.07i | 0.601226i | 0.953746 | + | 0.300613i | \(0.0971913\pi\) | ||||
−0.953746 | + | 0.300613i | \(0.902809\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5558.81 | 1.33362 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1908.44 | 0.452603 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4865.27i | − | 1.14071i | −0.821400 | − | 0.570353i | \(-0.806806\pi\) | ||
0.821400 | − | 0.570353i | \(-0.193194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1884.11 | − | 2256.83i | 0.436754 | − | 0.523154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3111.04i | 0.713080i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6753.93 | 1.53084 | 0.765418 | − | 0.643534i | \(-0.222532\pi\) | ||||
0.765418 | + | 0.643534i | \(0.222532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4315.74 | 0.967390 | 0.483695 | − | 0.875237i | \(-0.339294\pi\) | ||||
0.483695 | + | 0.875237i | \(0.339294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4101.22i | 0.909221i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1456.14 | − | 8023.41i | −0.319304 | − | 1.75938i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5799.07i | 1.25788i | 0.777454 | + | 0.628939i | \(0.216511\pi\) | ||||
−0.777454 | + | 0.628939i | \(0.783489\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −584.717 | −0.125470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −538.674 | −0.114358 | −0.0571790 | − | 0.998364i | \(-0.518211\pi\) | ||||
−0.0571790 | + | 0.998364i | \(0.518211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1648.50i | − | 0.346265i | −0.984899 | − | 0.173133i | \(-0.944611\pi\) | ||
0.984899 | − | 0.173133i | \(-0.0553889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4132.12 | − | 4949.55i | 0.858827 | − | 1.02872i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4053.38i | − | 0.833670i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −463.000 | −0.0942398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4886.72 | −0.984415 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4963.73i | − | 0.989707i | −0.868976 | − | 0.494854i | \(-0.835222\pi\) | ||
0.868976 | − | 0.494854i | \(-0.164778\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1027.32 | − | 857.653i | −0.202755 | − | 0.169269i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9960.88i | 1.94609i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −494.968 | −0.0957350 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 426.880 | 0.0817441 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5055.40i | 0.958499i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 141.964 | + | 118.518i | 0.0266518 | + | 0.0222503i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9906.61i | 1.84169i | 0.389925 | + | 0.920847i | \(0.372501\pi\) | ||||
−0.389925 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7538.40 | 1.38785 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3477.27 | 0.634012 | 0.317006 | − | 0.948424i | \(-0.397323\pi\) | ||||
0.317006 | + | 0.948424i | \(0.397323\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3958.27i | 0.714808i | 0.933950 | + | 0.357404i | \(0.116338\pi\) | ||||
−0.933950 | + | 0.357404i | \(0.883662\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1723.64 | + | 2064.62i | −0.308305 | + | 0.369295i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3296.86i | 0.584132i | 0.956398 | + | 0.292066i | \(0.0943428\pi\) | ||||
−0.956398 | + | 0.292066i | \(0.905657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14654.7 | −2.57212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 406.932 | 0.0707561 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9829.65i | 1.69330i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4141.07 | + | 751.548i | −0.706785 | + | 0.128272i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5805.91i | − | 0.981858i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3805.66 | −0.637728 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6048.38 | 1.00438 | 0.502189 | − | 0.864758i | \(-0.332528\pi\) | ||||
0.502189 | + | 0.864758i | \(0.332528\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1667.76i | − | 0.274453i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3909.06 | + | 4682.35i | −0.637536 | + | 0.763655i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8539.53i | 1.38035i | 0.723643 | + | 0.690175i | \(0.242466\pi\) | ||||
−0.723643 | + | 0.690175i | \(0.757534\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2276.66 | 0.364753 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4489.99 | 0.713040 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3279.23i | − | 0.516215i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 542.744 | + | 453.109i | 0.0846967 | + | 0.0707089i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6610.79i | − | 1.02273i | −0.859365 | − | 0.511363i | \(-0.829141\pi\) | ||
0.859365 | − | 0.511363i | \(-0.170859\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2491.07 | 0.382074 | 0.191037 | − | 0.981583i | \(-0.438815\pi\) | ||||
0.191037 | + | 0.981583i | \(0.438815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5141.04 | 0.781791 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3383.35i | − | 0.510134i | −0.966923 | − | 0.255067i | \(-0.917902\pi\) | ||
0.966923 | − | 0.255067i | \(-0.0820975\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1710.50 | + | 1428.00i | 0.255729 | + | 0.213495i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8931.08i | 1.32404i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1303.53 | −0.191637 | −0.0958185 | − | 0.995399i | \(-0.530547\pi\) | ||||
−0.0958185 | + | 0.995399i | \(0.530547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11113.8 | 1.62033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 12581.2i | − | 1.81912i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 310.012 | − | 371.339i | 0.0444569 | − | 0.0532515i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6672.42i | − | 0.949040i | −0.880245 | − | 0.474520i | \(-0.842622\pi\) | ||
0.880245 | − | 0.474520i | \(-0.157378\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1216.10 | −0.171565 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7445.88 | 1.04197 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5945.42i | 0.825314i | 0.910886 | + | 0.412657i | \(0.135399\pi\) | ||||
−0.910886 | + | 0.412657i | \(0.864601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5228.76 | + | 2966.77i | 0.720033 | + | 0.408542i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7563.64i | 1.03328i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12553.4 | −1.70139 | −0.850693 | − | 0.525663i | \(-0.823817\pi\) | ||||
−0.850693 | + | 0.525663i | \(0.823817\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3501.86 | −0.470881 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7602.57i | 1.01429i | 0.861861 | + | 0.507145i | \(0.169299\pi\) | ||||
−0.861861 | + | 0.507145i | \(0.830701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13235.7 | − | 15854.0i | 1.75209 | − | 2.09869i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 128.073i | − | 0.0168225i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 484.765 | 0.0631840 | 0.0315920 | − | 0.999501i | \(-0.489942\pi\) | ||||
0.0315920 | + | 0.999501i | \(0.489942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1077.87 | −0.139413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5720.62i | − | 0.734268i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3765.13 | + | 3143.31i | 0.479605 | + | 0.400398i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9367.85i | 1.18428i | 0.805835 | + | 0.592140i | \(0.201717\pi\) | ||||
−0.805835 | + | 0.592140i | \(0.798283\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16329.9 | 2.04891 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6650.48 | −0.828203 | −0.414101 | − | 0.910231i | \(-0.635904\pi\) | ||||
−0.414101 | + | 0.910231i | \(0.635904\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2317.39i | − | 0.286445i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3668.62 | − | 3062.74i | −0.450112 | − | 0.375775i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12806.6i | 1.55970i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1615.31 | 0.195286 | 0.0976432 | − | 0.995221i | \(-0.468870\pi\) | ||||
0.0976432 | + | 0.995221i | \(0.468870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12504.9 | −1.50078 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3389.39i | − | 0.403828i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8747.87 | − | 10478.4i | 1.03474 | − | 1.23943i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3962.19i | − | 0.465298i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10181.0 | −1.18705 | −0.593526 | − | 0.804815i | \(-0.702264\pi\) | ||||
−0.593526 | + | 0.804815i | \(0.702264\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4145.13 | −0.479860 | −0.239930 | − | 0.970790i | \(-0.577124\pi\) | ||||
−0.239930 | + | 0.970790i | \(0.577124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1141.78i | 0.131241i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9017.84 | + | 1636.62i | −1.02925 | + | 0.186794i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 468.376i | 0.0530827i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9448.53 | −1.06336 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14283.0 | −1.59627 | −0.798133 | − | 0.602482i | \(-0.794179\pi\) | ||||
−0.798133 | + | 0.602482i | \(0.794179\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7773.88i | − | 0.862792i | −0.902163 | − | 0.431396i | \(-0.858021\pi\) | ||
0.902163 | − | 0.431396i | \(-0.141979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6923.99 | − | 8293.71i | 0.763172 | − | 0.914144i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1970.82i | 0.215737i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3841.14 | −0.417602 | −0.208801 | − | 0.977958i | \(-0.566956\pi\) | ||||
−0.208801 | + | 0.977958i | \(0.566956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3897.78 | −0.420881 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2955.34i | − | 0.316958i | −0.987362 | − | 0.158479i | \(-0.949341\pi\) | ||
0.987362 | − | 0.158479i | \(-0.0506590\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6207.02 | − | 5181.92i | −0.661216 | − | 0.552015i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1141.06i | 0.120739i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10786.9 | 1.13377 | 0.566886 | − | 0.823796i | \(-0.308148\pi\) | ||||
0.566886 | + | 0.823796i | \(0.308148\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9338.31 | 0.974997 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 10787.3i | − | 1.11883i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8182.61 | − | 6831.24i | −0.843092 | − | 0.703854i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15384.9i | − | 1.57479i | −0.616451 | − | 0.787393i | \(-0.711430\pi\) | ||
0.616451 | − | 0.787393i | \(-0.288570\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11195.5 | 1.13847 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14590.9 | −1.47411 | −0.737057 | − | 0.675830i | \(-0.763785\pi\) | ||||
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8828.72i | 0.886188i | 0.896475 | + | 0.443094i | \(0.146119\pi\) | ||||
−0.896475 | + | 0.443094i | \(0.853881\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2121.41 | + | 2541.07i | −0.211565 | + | 0.253418i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4110.64i | 0.407319i | 0.979042 | + | 0.203659i | \(0.0652835\pi\) | ||||
−0.979042 | + | 0.203659i | \(0.934716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15448.3 | −1.52098 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 64.0169 | 0.00626273 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 983.461i | 0.0956016i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2992.45 | + | 16488.5i | 0.289059 | + | 1.59273i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2233.92i | − | 0.214432i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1852.96 | 0.176751 | 0.0883757 | − | 0.996087i | \(-0.471832\pi\) | ||||
0.0883757 | + | 0.996087i | \(0.471832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6609.77 | 0.626569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1790.66i | 0.168691i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8139.61 | − | 9749.81i | 0.762063 | − | 0.912816i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5285.78i | 0.491831i | 0.969291 | + | 0.245915i | \(0.0790885\pi\) | ||||
−0.969291 | + | 0.245915i | \(0.920912\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5094.19 | −0.471099 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12149.4 | −1.11669 | −0.558347 | − | 0.829608i | \(-0.688564\pi\) | ||||
−0.558347 | + | 0.829608i | \(0.688564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16471.1i | 1.50470i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4756.53 | − | 3970.98i | −0.431899 | − | 0.360570i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5643.38i | 0.509337i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3587.97 | −0.321883 | −0.160941 | − | 0.986964i | \(-0.551453\pi\) | ||||
−0.160941 | + | 0.986964i | \(0.551453\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11566.3 | 1.03142 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 18351.9i | − | 1.62678i | −0.581720 | − | 0.813389i | \(-0.697620\pi\) | ||
0.581720 | − | 0.813389i | \(-0.302380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10086.3 | − | 8420.57i | −0.888785 | − | 0.742001i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4574.21i | − | 0.400686i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −992.521 | −0.0864297 | −0.0432149 | − | 0.999066i | \(-0.513760\pi\) | ||||
−0.0432149 | + | 0.999066i | \(0.513760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1225.15 | 0.106061 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 20470.1i | − | 1.76175i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12556.4 | + | 15040.3i | −1.07437 | + | 1.28691i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8767.59i | − | 0.745838i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8348.37 | −0.706075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11192.3 | 0.941155 | 0.470577 | − | 0.882359i | \(-0.344046\pi\) | ||||
0.470577 | + | 0.882359i | \(0.344046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4959.46i | 0.414650i | 0.978272 | + | 0.207325i | \(0.0664758\pi\) | ||||
−0.978272 | + | 0.207325i | \(0.933524\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2718.89 | + | 14981.2i | 0.226023 | + | 1.24540i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5046.48i | − | 0.417131i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11950.9 | 0.982238 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1016.89 | −0.0831057 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4819.72i | − | 0.391679i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −677.810 | + | 811.895i | −0.0547743 | + | 0.0656099i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6799.33i | 0.546392i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29930.7 | 2.39185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18555.9 | −1.47464 | −0.737319 | − | 0.675545i | \(-0.763908\pi\) | ||||
−0.737319 | + | 0.675545i | \(0.763908\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11020.6i | 0.870976i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11583.7 | + | 9670.66i | 0.910445 | + | 0.760084i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24604.8i | − | 1.92326i | −0.274345 | − | 0.961631i | \(-0.588461\pi\) | ||
0.274345 | − | 0.961631i | \(-0.411539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 140.523 | 0.0109241 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30116.2 | 2.32848 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12422.2i | 0.955233i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7247.76 | − | 6050.78i | −0.554325 | − | 0.462777i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13010.2i | 0.989694i | 0.868980 | + | 0.494847i | \(0.164776\pi\) | ||||
−0.868980 | + | 0.494847i | \(0.835224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 507.587 | 0.0384054 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20575.7 | −1.54850 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 9751.95i | − | 0.730010i | −0.931006 | − | 0.365005i | \(-0.881067\pi\) | ||
0.931006 | − | 0.365005i | \(-0.118933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3792.15 | + | 4542.32i | −0.282366 | + | 0.338224i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 12103.8i | − | 0.896491i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5645.90 | −0.415973 | −0.207986 | − | 0.978132i | \(-0.566691\pi\) | ||||
−0.207986 | + | 0.978132i | \(0.566691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17188.1 | 1.25972 | 0.629860 | − | 0.776709i | \(-0.283112\pi\) | ||||
0.629860 | + | 0.776709i | \(0.283112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 592.145i | − | 0.0431714i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1808.05 | + | 328.138i | −0.131132 | + | 0.0237987i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 23294.0i | − | 1.68066i | −0.542076 | − | 0.840330i | \(-0.682361\pi\) | ||
0.542076 | − | 0.840330i | \(-0.317639\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3637.09 | 0.261058 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34571.0 | 2.46858 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17154.0i | 1.21861i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2049.52 | + | 2454.95i | −0.144850 | + | 0.173504i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15182.5i | 1.06754i | 0.845629 | + | 0.533771i | \(0.179226\pi\) | ||||
−0.845629 | + | 0.533771i | \(0.820774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9227.15 | −0.645498 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11759.2 | −0.818461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26734.6i | 1.85137i | 0.378301 | + | 0.925683i | \(0.376508\pi\) | ||||
−0.378301 | + | 0.925683i | \(0.623492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17819.0 | − | 14876.1i | −1.22774 | − | 1.02498i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 20001.6i | − | 1.37121i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2868.56 | 0.195670 | 0.0978350 | − | 0.995203i | \(-0.468808\pi\) | ||||
0.0978350 | + | 0.995203i | \(0.468808\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4242.60 | −0.287952 | −0.143976 | − | 0.989581i | \(-0.545989\pi\) | ||||
−0.143976 | + | 0.989581i | \(0.545989\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4634.82i | 0.313009i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25101.5 | + | 20956.0i | 1.68681 | + | 1.40823i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2058.87i | 0.137672i | 0.997628 | + | 0.0688361i | \(0.0219285\pi\) | ||||
−0.997628 | + | 0.0688361i | \(0.978071\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27363.1 | 1.82071 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4525.16 | −0.299621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16492.5i | 1.08667i | 0.839518 | + | 0.543333i | \(0.182838\pi\) | ||||
−0.839518 | + | 0.543333i | \(0.817162\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4412.11 | + | 5284.93i | −0.289290 | + | 0.346518i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12562.1i | 0.819662i | 0.912161 | + | 0.409831i | \(0.134412\pi\) | ||||
−0.912161 | + | 0.409831i | \(0.865588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18297.2 | −1.18809 | −0.594043 | − | 0.804434i | \(-0.702469\pi\) | ||||
−0.594043 | + | 0.804434i | \(0.702469\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2244.66 | 0.145048 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 20478.6i | − | 1.31695i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14628.5 | + | 5490.61i | −0.936226 | + | 0.351399i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 37621.3i | 2.39625i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14393.8 | 0.912433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25681.4 | −1.62022 | −0.810112 | − | 0.586275i | \(-0.800594\pi\) | ||||
−0.810112 | + | 0.586275i | \(0.800594\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16543.9i | 1.03880i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5832.90 | − | 6986.78i | 0.364522 | − | 0.436633i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 15447.9i | − | 0.960861i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1693.13 | 0.104819 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12994.7 | 0.800720 | 0.400360 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400360 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4625.71i | − | 0.283701i | −0.989888 | − | 0.141851i | \(-0.954695\pi\) | ||
0.989888 | − | 0.141851i | \(-0.0453053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −556.580 | − | 464.660i | −0.0339773 | − | 0.0283659i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8771.72i | 0.533002i | 0.963835 | + | 0.266501i | \(0.0858675\pi\) | ||||
−0.963835 | + | 0.266501i | \(0.914132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7808.58 | 0.472286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8383.66 | −0.504733 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2239.49i | − | 0.134209i | −0.997746 | − | 0.0671043i | \(-0.978624\pi\) | ||
0.997746 | − | 0.0671043i | \(-0.0213760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11413.6 | + | 9528.61i | 0.680863 | + | 0.568418i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 367.570i | − | 0.0218269i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4539.62 | 0.268344 | 0.134172 | − | 0.990958i | \(-0.457163\pi\) | ||||
0.134172 | + | 0.990958i | \(0.457163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28228.4 | 1.66105 | 0.830526 | − | 0.556980i | \(-0.188040\pi\) | ||||
0.830526 | + | 0.556980i | \(0.188040\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10619.6i | 0.622068i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27200.0 | + | 32580.8i | −1.58612 | + | 1.89989i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3302.40i | 0.191708i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6283.65 | −0.363139 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1079.06 | −0.0620814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7649.89i | 0.438160i | 0.975707 | + | 0.219080i | \(0.0703056\pi\) | ||||
−0.975707 | + | 0.219080i | \(0.929694\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18779.5 | − | 3408.24i | 1.07085 | − | 0.194345i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12087.9i | − | 0.686228i | −0.939294 | − | 0.343114i | \(-0.888518\pi\) | ||
0.939294 | − | 0.343114i | \(-0.111482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32167.2 | 1.81806 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14777.0 | −0.831506 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 8827.56i | − | 0.494549i | −0.968945 | − | 0.247275i | \(-0.920465\pi\) | ||
0.968945 | − | 0.247275i | \(-0.0795350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20828.9 | − | 24949.3i | 1.16180 | − | 1.39163i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2561.04i | − | 0.142227i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8853.60 | 0.489543 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12913.1 | −0.710908 | −0.355454 | − | 0.934694i | \(-0.615674\pi\) | ||||
−0.355454 | + | 0.934694i | \(0.615674\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 15693.1i | − | 0.860217i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7905.21 | + | 6599.65i | 0.431456 | + | 0.360200i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10495.7i | − | 0.570378i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23369.5 | −1.26454 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12297.2 | −0.662567 | −0.331283 | − | 0.943531i | \(-0.607482\pi\) | ||||
−0.331283 | + | 0.943531i | \(0.607482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 26318.2i | − | 1.41196i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4961.94 | + | 4142.47i | 0.265074 | + | 0.221297i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 33277.5i | − | 1.77020i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34308.2 | −1.81731 | −0.908653 | − | 0.417552i | \(-0.862888\pi\) | ||||
−0.908653 | + | 0.417552i | \(0.862888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3726.91 | 0.196582 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1011.81i | − | 0.0531451i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15738.0 | − | 18851.4i | 0.823174 | − | 0.986016i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 16912.1i | − | 0.880887i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21631.4 | −1.12200 | −0.560999 | − | 0.827817i | \(-0.689583\pi\) | ||||
−0.560999 | + | 0.827817i | \(0.689583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49622.1 | −2.56314 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11132.3i | 0.572632i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5014.29 | + | 27629.0i | 0.256864 | + | 1.41533i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12049.8i | − | 0.614723i | −0.951593 | − | 0.307361i | \(-0.900554\pi\) | ||
0.951593 | − | 0.307361i | \(-0.0994460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21365.7 | −1.08549 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1105.35 | 0.0559274 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15221.6i | 0.767017i | 0.923537 | + | 0.383508i | \(0.125284\pi\) | ||||
−0.923537 | + | 0.383508i | \(0.874716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14141.5 | + | 16939.0i | −0.709683 | + | 0.850073i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 35590.4i | − | 1.77882i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9845.80 | 0.490099 | 0.245050 | − | 0.969511i | \(-0.421196\pi\) | ||||
0.245050 | + | 0.969511i | \(0.421196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19417.2 | 0.962630 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35081.5i | 1.73219i | 0.499881 | + | 0.866094i | \(0.333377\pi\) | ||||
−0.499881 | + | 0.866094i | \(0.666623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2276.61 | − | 1900.62i | −0.111958 | − | 0.0934676i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 10372.0i | − | 0.508022i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2678.66 | −0.130676 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20007.7 | 0.972158 | 0.486079 | − | 0.873915i | \(-0.338427\pi\) | ||||
0.486079 | + | 0.873915i | \(0.338427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9600.47i | − | 0.464622i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21522.4 | + | 17968.0i | 1.03746 | + | 0.866122i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33478.7i | − | 1.60741i | −0.595031 | − | 0.803703i | \(-0.702860\pi\) | ||
0.595031 | − | 0.803703i | \(-0.297140\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4125.37 | −0.197288 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12728.1 | 0.606298 | 0.303149 | − | 0.952943i | \(-0.401962\pi\) | ||||
0.303149 | + | 0.952943i | \(0.401962\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38217.8i | 1.81334i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4463.15 | + | 5346.06i | −0.210935 | + | 0.252663i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4030.19i | − | 0.189728i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20061.4 | 0.940747 | 0.470373 | − | 0.882468i | \(-0.344119\pi\) | ||||
0.470373 | + | 0.882468i | \(0.344119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10655.6 | 0.497732 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 672.445i | − | 0.0312887i | −0.999878 | − | 0.0156444i | \(-0.995020\pi\) | ||
0.999878 | − | 0.0156444i | \(-0.00497996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1536.30 | − | 8465.10i | −0.0712073 | − | 0.392355i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 23912.3i | − | 1.10405i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19190.7 | −0.882642 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13001.4 | −0.595681 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 34300.8i | − | 1.56553i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −106.630 | + | 127.724i | −0.00484816 | + | 0.00580723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7928.23i | 0.359099i | 0.983749 | + | 0.179550i | \(0.0574640\pi\) | ||||
−0.983749 | + | 0.179550i | \(0.942536\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20928.9 | −0.944346 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14986.3 | −0.673643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 556.928i | 0.0249396i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9708.17 | − | 8104.86i | −0.433099 | − | 0.361572i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3196.35i | − | 0.142059i | −0.997474 | − | 0.0710293i | \(-0.977372\pi\) | ||
0.997474 | − | 0.0710293i | \(-0.0226284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9854.26 | −0.436319 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6144.02 | −0.271021 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2822.54i | 0.124041i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3572.65 | − | 2982.62i | −0.156422 | − | 0.130588i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 29053.3i | − | 1.26732i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15278.6 | 0.663987 | 0.331993 | − | 0.943282i | \(-0.392279\pi\) | ||||
0.331993 | + | 0.943282i | \(0.392279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27275.2 | 1.18096 | 0.590482 | − | 0.807051i | \(-0.298938\pi\) | ||||
0.590482 | + | 0.807051i | \(0.298938\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 18565.0i | − | 0.800864i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8485.18 | − | 10163.7i | 0.364691 | − | 0.436835i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2021.06i | − | 0.0865459i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8099.55 | −0.345569 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11047.6 | −0.469627 | −0.234814 | − | 0.972040i | \(-0.575448\pi\) | ||||
−0.234814 | + | 0.972040i | \(0.575448\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 46589.2i | − | 1.97327i | −0.162959 | − | 0.986633i | \(-0.552104\pi\) | ||
0.162959 | − | 0.986633i | \(-0.447896\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34514.2 | + | 6263.87i | −1.45652 | + | 0.264339i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7622.29i | 0.320499i | 0.987077 | + | 0.160250i | \(0.0512299\pi\) | ||||
−0.987077 | + | 0.160250i | \(0.948770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 637.729 | 0.0267180 | 0.0133590 | − | 0.999911i | \(-0.495748\pi\) | ||||
0.0133590 | + | 0.999911i | \(0.495748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24945.8 | 1.04135 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 33640.3i | − | 1.39924i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19265.5 | + | 23076.6i | −0.798454 | + | 0.956406i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10509.2i | 0.433993i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38563.3 | −1.58683 | −0.793417 | − | 0.608679i | \(-0.791700\pi\) | ||||
−0.793417 | + | 0.608679i | \(0.791700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26075.2 | 1.06914 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2317.21i | 0.0946725i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9126.29 | + | 7619.07i | 0.371543 | + | 0.310182i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 82816.7i | 3.35964i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7091.33 | −0.286660 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2885.93 | 0.116249 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21077.3i | 0.846040i | 0.906120 | + | 0.423020i | \(0.139030\pi\) | ||||
−0.906120 | + | 0.423020i | \(0.860970\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9774.91 | + | 8160.57i | 0.390988 | + | 0.326416i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24424.6i | 0.973546i | 0.873528 | + | 0.486773i | \(0.161826\pi\) | ||||
−0.873528 | + | 0.486773i | \(0.838174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25649.1 | 1.01878 | 0.509392 | − | 0.860534i | \(-0.329870\pi\) | ||||
0.509392 | + | 0.860534i | \(0.329870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17436.4 | −0.690163 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31095.6i | 1.22654i | 0.789872 | + | 0.613272i | \(0.210147\pi\) | ||||
−0.789872 | + | 0.613272i | \(0.789853\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13905.5 | − | 16656.4i | 0.546593 | − | 0.654721i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1991.68i | 0.0780174i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28618.6 | −1.11717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18369.0 | −0.714593 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9650.84i | − | 0.374148i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34418.7 | − | 19529.0i | −1.32979 | − | 0.754514i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26626.0i | − | 1.02519i | −0.858630 | − | 0.512597i | \(-0.828684\pi\) | ||
0.858630 | − | 0.512597i | \(-0.171316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21352.4 | −0.819340 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18538.6 | −0.708945 | −0.354472 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354472 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16994.0i | − | 0.647672i | −0.946113 | − | 0.323836i | \(-0.895027\pi\) | ||
0.946113 | − | 0.323836i | \(-0.104973\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3689.36 | + | 4419.19i | −0.140132 | + | 0.167853i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19948.2i | 0.755126i | 0.925984 | + | 0.377563i | \(0.123238\pi\) | ||||
−0.925984 | + | 0.377563i | \(0.876762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23051.3 | 0.869645 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27885.0 | 1.04847 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18017.8i | 0.675190i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13565.8 | − | 11325.4i | −0.506652 | − | 0.422978i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2129.20i | 0.0792552i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15461.5 | −0.573603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19280.1 | 0.712891 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1836.31i | − | 0.0676727i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21987.9 | − | 18356.6i | −0.807628 | − | 0.674247i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 31481.3i | − | 1.15250i | −0.817273 | − | 0.576251i | \(-0.804515\pi\) | ||
0.817273 | − | 0.576251i | \(-0.195485\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9983.96 | −0.364298 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29685.8 | 1.07962 | 0.539811 | − | 0.841787i | \(-0.318496\pi\) | ||||
0.539811 | + | 0.841787i | \(0.318496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 79645.8i | 2.88707i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 509.828 | − | 610.684i | 0.0184201 | − | 0.0220640i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37656.4i | 1.35608i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21804.9 | 0.782673 | 0.391336 | − | 0.920248i | \(-0.372013\pi\) | ||||
0.391336 | + | 0.920248i | \(0.372013\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42615.2 | 1.52467 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6710.33i | 0.239299i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24144.6 | − | 4381.92i | 0.858238 | − | 0.155759i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14887.7i | 0.527481i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49150.1 | 1.73580 | 0.867902 | − | 0.496735i | \(-0.165468\pi\) | ||||
0.867902 | + | 0.496735i | \(0.165468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −61509.1 | −2.16528 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 14958.1i | − | 0.524873i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34272.1 | − | 41051.9i | 1.19874 | − | 1.43587i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 33165.6i | − | 1.15632i | −0.815922 | − | 0.578161i | \(-0.803770\pi\) | ||
0.815922 | − | 0.578161i | \(-0.196230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17027.3 | 0.591761 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15184.8 | −0.526048 | −0.263024 | − | 0.964789i | \(-0.584720\pi\) | ||||
−0.263024 | + | 0.964789i | \(0.584720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2104.36i | − | 0.0726696i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37107.8 | + | 30979.4i | 1.27737 | + | 1.06641i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 44341.2i | − | 1.52154i | −0.649023 | − | 0.760769i | \(-0.724822\pi\) | ||
0.649023 | − | 0.760769i | \(-0.275178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1456.78 | 0.0498303 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14182.1 | 0.483580 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31056.8i | − | 1.05564i | −0.849356 | − | 0.527821i | \(-0.823009\pi\) | ||
0.849356 | − | 0.527821i | \(-0.176991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1181.43 | + | 986.313i | 0.0400315 | + | 0.0334202i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 63040.1i | 2.12936i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 82314.5 | 2.77171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25053.8 | −0.840987 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 803.654i | 0.0268924i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6058.16 | + | 7256.59i | −0.202092 | + | 0.242070i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40508.8i | − | 1.34713i | −0.739128 | − | 0.673564i | \(-0.764762\pi\) | ||
0.739128 | − | 0.673564i | \(-0.235238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42284.1 | 1.40182 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36986.9 | −1.22242 | −0.611208 | − | 0.791470i | \(-0.709316\pi\) | ||||
−0.611208 | + | 0.791470i | \(0.709316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26081.4i | 0.859333i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3232.93 | + | 17813.6i | 0.106191 | + | 0.585119i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28979.9i | 0.948975i | 0.880262 | + | 0.474488i | \(0.157367\pi\) | ||||
−0.880262 | + | 0.474488i | \(0.842633\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47179.3 | 1.54020 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11466.1 | 0.373176 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31114.6i | 1.00956i | 0.863247 | + | 0.504782i | \(0.168427\pi\) | ||||
−0.863247 | + | 0.504782i | \(0.831573\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19586.9 | − | 23461.6i | 0.633594 | − | 0.758933i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16370.8i | 0.527950i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 221.620 | 0.00712549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44477.8 | −1.42571 | −0.712857 | − | 0.701309i | \(-0.752599\pi\) | ||||
−0.712857 | + | 0.701309i | \(0.752599\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 26018.3i | − | 0.831485i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39906.4 | + | 33315.8i | 1.27147 | + | 1.06149i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57489.4i | 1.82619i | 0.407752 | + | 0.913093i | \(0.366313\pi\) | ||||
−0.407752 | + | 0.913093i | \(0.633687\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29975.0 | −0.949316 |
(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 | 160.4.c.d.129.4 | yes | 8 | |
3.2 | odd | 2 | 1440.4.f.k.289.2 | 8 | |||
4.3 | odd | 2 | inner | 160.4.c.d.129.6 | yes | 8 | |
5.2 | odd | 4 | 800.4.a.z.1.2 | 4 | |||
5.3 | odd | 4 | 800.4.a.y.1.3 | 4 | |||
5.4 | even | 2 | inner | 160.4.c.d.129.5 | yes | 8 | |
8.3 | odd | 2 | 320.4.c.j.129.3 | 8 | |||
8.5 | even | 2 | 320.4.c.j.129.5 | 8 | |||
12.11 | even | 2 | 1440.4.f.k.289.1 | 8 | |||
15.14 | odd | 2 | 1440.4.f.k.289.3 | 8 | |||
20.3 | even | 4 | 800.4.a.y.1.2 | 4 | |||
20.7 | even | 4 | 800.4.a.z.1.3 | 4 | |||
20.19 | odd | 2 | inner | 160.4.c.d.129.3 | ✓ | 8 | |
40.3 | even | 4 | 1600.4.a.cv.1.3 | 4 | |||
40.13 | odd | 4 | 1600.4.a.cv.1.2 | 4 | |||
40.19 | odd | 2 | 320.4.c.j.129.6 | 8 | |||
40.27 | even | 4 | 1600.4.a.cu.1.2 | 4 | |||
40.29 | even | 2 | 320.4.c.j.129.4 | 8 | |||
40.37 | odd | 4 | 1600.4.a.cu.1.3 | 4 | |||
60.59 | even | 2 | 1440.4.f.k.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.c.d.129.3 | ✓ | 8 | 20.19 | odd | 2 | inner | |
160.4.c.d.129.4 | yes | 8 | 1.1 | even | 1 | trivial | |
160.4.c.d.129.5 | yes | 8 | 5.4 | even | 2 | inner | |
160.4.c.d.129.6 | yes | 8 | 4.3 | odd | 2 | inner | |
320.4.c.j.129.3 | 8 | 8.3 | odd | 2 | |||
320.4.c.j.129.4 | 8 | 40.29 | even | 2 | |||
320.4.c.j.129.5 | 8 | 8.5 | even | 2 | |||
320.4.c.j.129.6 | 8 | 40.19 | odd | 2 | |||
800.4.a.y.1.2 | 4 | 20.3 | even | 4 | |||
800.4.a.y.1.3 | 4 | 5.3 | odd | 4 | |||
800.4.a.z.1.2 | 4 | 5.2 | odd | 4 | |||
800.4.a.z.1.3 | 4 | 20.7 | even | 4 | |||
1440.4.f.k.289.1 | 8 | 12.11 | even | 2 | |||
1440.4.f.k.289.2 | 8 | 3.2 | odd | 2 | |||
1440.4.f.k.289.3 | 8 | 15.14 | odd | 2 | |||
1440.4.f.k.289.4 | 8 | 60.59 | even | 2 | |||
1600.4.a.cu.1.2 | 4 | 40.27 | even | 4 | |||
1600.4.a.cu.1.3 | 4 | 40.37 | odd | 4 | |||
1600.4.a.cv.1.2 | 4 | 40.13 | odd | 4 | |||
1600.4.a.cv.1.3 | 4 | 40.3 | even | 4 |