Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.976160\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.976160 | −0.436552 | −0.218276 | − | 0.975887i | \(-0.570043\pi\) | ||||
−0.218276 | + | 0.975887i | \(0.570043\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.87477 | −1.46453 | −0.732264 | − | 0.681021i | \(-0.761536\pi\) | ||||
−0.732264 | + | 0.681021i | \(0.761536\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.976160 | 0.308689 | ||||||||
\(11\) | −0.0200581 | −0.00604776 | −0.00302388 | − | 0.999995i | \(-0.500963\pi\) | ||||
−0.00302388 | + | 0.999995i | \(0.500963\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.09284 | 1.13515 | 0.567574 | − | 0.823322i | \(-0.307882\pi\) | ||||
0.567574 | + | 0.823322i | \(0.307882\pi\) | |||||||
\(14\) | 3.87477 | 1.03558 | ||||||||
\(15\) | 0.976160 | 0.252043 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.76012 | 1.09205 | 0.546024 | − | 0.837770i | \(-0.316141\pi\) | ||||
0.546024 | + | 0.837770i | \(0.316141\pi\) | |||||||
\(20\) | −0.976160 | −0.218276 | ||||||||
\(21\) | 3.87477 | 0.845545 | ||||||||
\(22\) | 0.0200581 | 0.00427641 | ||||||||
\(23\) | −0.204808 | −0.0427054 | −0.0213527 | − | 0.999772i | \(-0.506797\pi\) | ||||
−0.0213527 | + | 0.999772i | \(0.506797\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.04711 | −0.809422 | ||||||||
\(26\) | −4.09284 | −0.802671 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.87477 | −0.732264 | ||||||||
\(29\) | −6.91994 | −1.28500 | −0.642500 | − | 0.766285i | \(-0.722103\pi\) | ||||
−0.642500 | + | 0.766285i | \(0.722103\pi\) | |||||||
\(30\) | −0.976160 | −0.178222 | ||||||||
\(31\) | 1.87253 | 0.336315 | 0.168158 | − | 0.985760i | \(-0.446218\pi\) | ||||
0.168158 | + | 0.985760i | \(0.446218\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.0200581 | 0.00349167 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 3.78240 | 0.639342 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.0763691 | −0.0125550 | −0.00627750 | − | 0.999980i | \(-0.501998\pi\) | ||||
−0.00627750 | + | 0.999980i | \(0.501998\pi\) | |||||||
\(38\) | −4.76012 | −0.772194 | ||||||||
\(39\) | −4.09284 | −0.655378 | ||||||||
\(40\) | 0.976160 | 0.154344 | ||||||||
\(41\) | 1.72765 | 0.269814 | 0.134907 | − | 0.990858i | \(-0.456926\pi\) | ||||
0.134907 | + | 0.990858i | \(0.456926\pi\) | |||||||
\(42\) | −3.87477 | −0.597891 | ||||||||
\(43\) | 0.671491 | 0.102401 | 0.0512007 | − | 0.998688i | \(-0.483695\pi\) | ||||
0.0512007 | + | 0.998688i | \(0.483695\pi\) | |||||||
\(44\) | −0.0200581 | −0.00302388 | ||||||||
\(45\) | −0.976160 | −0.145517 | ||||||||
\(46\) | 0.204808 | 0.0301973 | ||||||||
\(47\) | 10.7654 | 1.57029 | 0.785145 | − | 0.619312i | \(-0.212588\pi\) | ||||
0.785145 | + | 0.619312i | \(0.212588\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 8.01388 | 1.14484 | ||||||||
\(50\) | 4.04711 | 0.572348 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 4.09284 | 0.567574 | ||||||||
\(53\) | −3.54134 | −0.486440 | −0.243220 | − | 0.969971i | \(-0.578204\pi\) | ||||
−0.243220 | + | 0.969971i | \(0.578204\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.0195800 | 0.00264016 | ||||||||
\(56\) | 3.87477 | 0.517789 | ||||||||
\(57\) | −4.76012 | −0.630494 | ||||||||
\(58\) | 6.91994 | 0.908633 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0.976160 | 0.126022 | ||||||||
\(61\) | −6.17734 | −0.790928 | −0.395464 | − | 0.918482i | \(-0.629416\pi\) | ||||
−0.395464 | + | 0.918482i | \(0.629416\pi\) | |||||||
\(62\) | −1.87253 | −0.237811 | ||||||||
\(63\) | −3.87477 | −0.488176 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.99526 | −0.495551 | ||||||||
\(66\) | −0.0200581 | −0.00246899 | ||||||||
\(67\) | −2.36212 | −0.288579 | −0.144290 | − | 0.989535i | \(-0.546090\pi\) | ||||
−0.144290 | + | 0.989535i | \(0.546090\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 0.204808 | 0.0246560 | ||||||||
\(70\) | −3.78240 | −0.452083 | ||||||||
\(71\) | −10.9512 | −1.29967 | −0.649837 | − | 0.760074i | \(-0.725163\pi\) | ||||
−0.649837 | + | 0.760074i | \(0.725163\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.32488 | 0.389147 | 0.194574 | − | 0.980888i | \(-0.437668\pi\) | ||||
0.194574 | + | 0.980888i | \(0.437668\pi\) | |||||||
\(74\) | 0.0763691 | 0.00887773 | ||||||||
\(75\) | 4.04711 | 0.467320 | ||||||||
\(76\) | 4.76012 | 0.546024 | ||||||||
\(77\) | 0.0777208 | 0.00885710 | ||||||||
\(78\) | 4.09284 | 0.463422 | ||||||||
\(79\) | −9.33941 | −1.05077 | −0.525383 | − | 0.850866i | \(-0.676078\pi\) | ||||
−0.525383 | + | 0.850866i | \(0.676078\pi\) | |||||||
\(80\) | −0.976160 | −0.109138 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.72765 | −0.190787 | ||||||||
\(83\) | −2.90996 | −0.319409 | −0.159705 | − | 0.987165i | \(-0.551054\pi\) | ||||
−0.159705 | + | 0.987165i | \(0.551054\pi\) | |||||||
\(84\) | 3.87477 | 0.422773 | ||||||||
\(85\) | −0.976160 | −0.105879 | ||||||||
\(86\) | −0.671491 | −0.0724088 | ||||||||
\(87\) | 6.91994 | 0.741895 | ||||||||
\(88\) | 0.0200581 | 0.00213820 | ||||||||
\(89\) | −13.8917 | −1.47252 | −0.736261 | − | 0.676698i | \(-0.763410\pi\) | ||||
−0.736261 | + | 0.676698i | \(0.763410\pi\) | |||||||
\(90\) | 0.976160 | 0.102896 | ||||||||
\(91\) | −15.8588 | −1.66246 | ||||||||
\(92\) | −0.204808 | −0.0213527 | ||||||||
\(93\) | −1.87253 | −0.194172 | ||||||||
\(94\) | −10.7654 | −1.11036 | ||||||||
\(95\) | −4.64664 | −0.476736 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.56510 | 0.666584 | 0.333292 | − | 0.942824i | \(-0.391840\pi\) | ||||
0.333292 | + | 0.942824i | \(0.391840\pi\) | |||||||
\(98\) | −8.01388 | −0.809524 | ||||||||
\(99\) | −0.0200581 | −0.00201592 | ||||||||
\(100\) | −4.04711 | −0.404711 | ||||||||
\(101\) | 2.28999 | 0.227862 | 0.113931 | − | 0.993489i | \(-0.463656\pi\) | ||||
0.113931 | + | 0.993489i | \(0.463656\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 9.40392 | 0.926596 | 0.463298 | − | 0.886203i | \(-0.346666\pi\) | ||||
0.463298 | + | 0.886203i | \(0.346666\pi\) | |||||||
\(104\) | −4.09284 | −0.401336 | ||||||||
\(105\) | −3.78240 | −0.369125 | ||||||||
\(106\) | 3.54134 | 0.343965 | ||||||||
\(107\) | −10.6637 | −1.03090 | −0.515451 | − | 0.856919i | \(-0.672376\pi\) | ||||
−0.515451 | + | 0.856919i | \(0.672376\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −10.2720 | −0.983879 | −0.491940 | − | 0.870629i | \(-0.663712\pi\) | ||||
−0.491940 | + | 0.870629i | \(0.663712\pi\) | |||||||
\(110\) | −0.0195800 | −0.00186688 | ||||||||
\(111\) | 0.0763691 | 0.00724864 | ||||||||
\(112\) | −3.87477 | −0.366132 | ||||||||
\(113\) | −14.4538 | −1.35970 | −0.679848 | − | 0.733353i | \(-0.737954\pi\) | ||||
−0.679848 | + | 0.733353i | \(0.737954\pi\) | |||||||
\(114\) | 4.76012 | 0.445827 | ||||||||
\(115\) | 0.199925 | 0.0186431 | ||||||||
\(116\) | −6.91994 | −0.642500 | ||||||||
\(117\) | 4.09284 | 0.378383 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −3.87477 | −0.355200 | ||||||||
\(120\) | −0.976160 | −0.0891108 | ||||||||
\(121\) | −10.9996 | −0.999963 | ||||||||
\(122\) | 6.17734 | 0.559270 | ||||||||
\(123\) | −1.72765 | −0.155777 | ||||||||
\(124\) | 1.87253 | 0.168158 | ||||||||
\(125\) | 8.83143 | 0.789907 | ||||||||
\(126\) | 3.87477 | 0.345192 | ||||||||
\(127\) | 11.0071 | 0.976724 | 0.488362 | − | 0.872641i | \(-0.337594\pi\) | ||||
0.488362 | + | 0.872641i | \(0.337594\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.671491 | −0.0591215 | ||||||||
\(130\) | 3.99526 | 0.350408 | ||||||||
\(131\) | 9.73289 | 0.850367 | 0.425183 | − | 0.905107i | \(-0.360210\pi\) | ||||
0.425183 | + | 0.905107i | \(0.360210\pi\) | |||||||
\(132\) | 0.0200581 | 0.00174584 | ||||||||
\(133\) | −18.4444 | −1.59933 | ||||||||
\(134\) | 2.36212 | 0.204056 | ||||||||
\(135\) | 0.976160 | 0.0840145 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 17.5945 | 1.50320 | 0.751602 | − | 0.659617i | \(-0.229282\pi\) | ||||
0.751602 | + | 0.659617i | \(0.229282\pi\) | |||||||
\(138\) | −0.204808 | −0.0174344 | ||||||||
\(139\) | 18.6395 | 1.58098 | 0.790489 | − | 0.612476i | \(-0.209826\pi\) | ||||
0.790489 | + | 0.612476i | \(0.209826\pi\) | |||||||
\(140\) | 3.78240 | 0.319671 | ||||||||
\(141\) | −10.7654 | −0.906607 | ||||||||
\(142\) | 10.9512 | 0.919008 | ||||||||
\(143\) | −0.0820947 | −0.00686510 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.75497 | 0.560970 | ||||||||
\(146\) | −3.32488 | −0.275169 | ||||||||
\(147\) | −8.01388 | −0.660974 | ||||||||
\(148\) | −0.0763691 | −0.00627750 | ||||||||
\(149\) | 11.1125 | 0.910374 | 0.455187 | − | 0.890396i | \(-0.349572\pi\) | ||||
0.455187 | + | 0.890396i | \(0.349572\pi\) | |||||||
\(150\) | −4.04711 | −0.330445 | ||||||||
\(151\) | 15.4133 | 1.25432 | 0.627159 | − | 0.778891i | \(-0.284218\pi\) | ||||
0.627159 | + | 0.778891i | \(0.284218\pi\) | |||||||
\(152\) | −4.76012 | −0.386097 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.0777208 | −0.00626292 | ||||||||
\(155\) | −1.82788 | −0.146819 | ||||||||
\(156\) | −4.09284 | −0.327689 | ||||||||
\(157\) | −1.24776 | −0.0995818 | −0.0497909 | − | 0.998760i | \(-0.515855\pi\) | ||||
−0.0497909 | + | 0.998760i | \(0.515855\pi\) | |||||||
\(158\) | 9.33941 | 0.743003 | ||||||||
\(159\) | 3.54134 | 0.280847 | ||||||||
\(160\) | 0.976160 | 0.0771722 | ||||||||
\(161\) | 0.793584 | 0.0625432 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 7.89843 | 0.618653 | 0.309327 | − | 0.950956i | \(-0.399896\pi\) | ||||
0.309327 | + | 0.950956i | \(0.399896\pi\) | |||||||
\(164\) | 1.72765 | 0.134907 | ||||||||
\(165\) | −0.0195800 | −0.00152430 | ||||||||
\(166\) | 2.90996 | 0.225856 | ||||||||
\(167\) | −23.7000 | −1.83396 | −0.916980 | − | 0.398934i | \(-0.869380\pi\) | ||||
−0.916980 | + | 0.398934i | \(0.869380\pi\) | |||||||
\(168\) | −3.87477 | −0.298945 | ||||||||
\(169\) | 3.75130 | 0.288562 | ||||||||
\(170\) | 0.976160 | 0.0748681 | ||||||||
\(171\) | 4.76012 | 0.364016 | ||||||||
\(172\) | 0.671491 | 0.0512007 | ||||||||
\(173\) | 24.3272 | 1.84956 | 0.924780 | − | 0.380501i | \(-0.124249\pi\) | ||||
0.924780 | + | 0.380501i | \(0.124249\pi\) | |||||||
\(174\) | −6.91994 | −0.524599 | ||||||||
\(175\) | 15.6816 | 1.18542 | ||||||||
\(176\) | −0.0200581 | −0.00151194 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 13.8917 | 1.04123 | ||||||||
\(179\) | −26.2696 | −1.96348 | −0.981741 | − | 0.190222i | \(-0.939079\pi\) | ||||
−0.981741 | + | 0.190222i | \(0.939079\pi\) | |||||||
\(180\) | −0.976160 | −0.0727587 | ||||||||
\(181\) | −10.5798 | −0.786390 | −0.393195 | − | 0.919455i | \(-0.628630\pi\) | ||||
−0.393195 | + | 0.919455i | \(0.628630\pi\) | |||||||
\(182\) | 15.8588 | 1.17553 | ||||||||
\(183\) | 6.17734 | 0.456642 | ||||||||
\(184\) | 0.204808 | 0.0150986 | ||||||||
\(185\) | 0.0745485 | 0.00548091 | ||||||||
\(186\) | 1.87253 | 0.137300 | ||||||||
\(187\) | −0.0200581 | −0.00146680 | ||||||||
\(188\) | 10.7654 | 0.785145 | ||||||||
\(189\) | 3.87477 | 0.281848 | ||||||||
\(190\) | 4.64664 | 0.337103 | ||||||||
\(191\) | 18.5956 | 1.34553 | 0.672767 | − | 0.739854i | \(-0.265106\pi\) | ||||
0.672767 | + | 0.739854i | \(0.265106\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −10.0613 | −0.724226 | −0.362113 | − | 0.932134i | \(-0.617945\pi\) | ||||
−0.362113 | + | 0.932134i | \(0.617945\pi\) | |||||||
\(194\) | −6.56510 | −0.471346 | ||||||||
\(195\) | 3.99526 | 0.286107 | ||||||||
\(196\) | 8.01388 | 0.572420 | ||||||||
\(197\) | 12.4837 | 0.889424 | 0.444712 | − | 0.895674i | \(-0.353306\pi\) | ||||
0.444712 | + | 0.895674i | \(0.353306\pi\) | |||||||
\(198\) | 0.0200581 | 0.00142547 | ||||||||
\(199\) | 12.8824 | 0.913208 | 0.456604 | − | 0.889670i | \(-0.349066\pi\) | ||||
0.456604 | + | 0.889670i | \(0.349066\pi\) | |||||||
\(200\) | 4.04711 | 0.286174 | ||||||||
\(201\) | 2.36212 | 0.166611 | ||||||||
\(202\) | −2.28999 | −0.161123 | ||||||||
\(203\) | 26.8132 | 1.88192 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −1.68647 | −0.117788 | ||||||||
\(206\) | −9.40392 | −0.655202 | ||||||||
\(207\) | −0.204808 | −0.0142351 | ||||||||
\(208\) | 4.09284 | 0.283787 | ||||||||
\(209\) | −0.0954792 | −0.00660444 | ||||||||
\(210\) | 3.78240 | 0.261010 | ||||||||
\(211\) | 21.2253 | 1.46121 | 0.730606 | − | 0.682799i | \(-0.239237\pi\) | ||||
0.730606 | + | 0.682799i | \(0.239237\pi\) | |||||||
\(212\) | −3.54134 | −0.243220 | ||||||||
\(213\) | 10.9512 | 0.750367 | ||||||||
\(214\) | 10.6637 | 0.728958 | ||||||||
\(215\) | −0.655483 | −0.0447036 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −7.25561 | −0.492543 | ||||||||
\(218\) | 10.2720 | 0.695708 | ||||||||
\(219\) | −3.32488 | −0.224674 | ||||||||
\(220\) | 0.0195800 | 0.00132008 | ||||||||
\(221\) | 4.09284 | 0.275314 | ||||||||
\(222\) | −0.0763691 | −0.00512556 | ||||||||
\(223\) | 24.7471 | 1.65719 | 0.828595 | − | 0.559848i | \(-0.189140\pi\) | ||||
0.828595 | + | 0.559848i | \(0.189140\pi\) | |||||||
\(224\) | 3.87477 | 0.258894 | ||||||||
\(225\) | −4.04711 | −0.269807 | ||||||||
\(226\) | 14.4538 | 0.961451 | ||||||||
\(227\) | 0.782040 | 0.0519058 | 0.0259529 | − | 0.999663i | \(-0.491738\pi\) | ||||
0.0259529 | + | 0.999663i | \(0.491738\pi\) | |||||||
\(228\) | −4.76012 | −0.315247 | ||||||||
\(229\) | 1.67635 | 0.110776 | 0.0553882 | − | 0.998465i | \(-0.482360\pi\) | ||||
0.0553882 | + | 0.998465i | \(0.482360\pi\) | |||||||
\(230\) | −0.199925 | −0.0131827 | ||||||||
\(231\) | −0.0777208 | −0.00511365 | ||||||||
\(232\) | 6.91994 | 0.454316 | ||||||||
\(233\) | −2.77060 | −0.181508 | −0.0907539 | − | 0.995873i | \(-0.528928\pi\) | ||||
−0.0907539 | + | 0.995873i | \(0.528928\pi\) | |||||||
\(234\) | −4.09284 | −0.267557 | ||||||||
\(235\) | −10.5087 | −0.685513 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 9.33941 | 0.606660 | ||||||||
\(238\) | 3.87477 | 0.251164 | ||||||||
\(239\) | −0.488210 | −0.0315796 | −0.0157898 | − | 0.999875i | \(-0.505026\pi\) | ||||
−0.0157898 | + | 0.999875i | \(0.505026\pi\) | |||||||
\(240\) | 0.976160 | 0.0630109 | ||||||||
\(241\) | −18.6888 | −1.20385 | −0.601925 | − | 0.798553i | \(-0.705599\pi\) | ||||
−0.601925 | + | 0.798553i | \(0.705599\pi\) | |||||||
\(242\) | 10.9996 | 0.707081 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.17734 | −0.395464 | ||||||||
\(245\) | −7.82283 | −0.499782 | ||||||||
\(246\) | 1.72765 | 0.110151 | ||||||||
\(247\) | 19.4824 | 1.23964 | ||||||||
\(248\) | −1.87253 | −0.118905 | ||||||||
\(249\) | 2.90996 | 0.184411 | ||||||||
\(250\) | −8.83143 | −0.558549 | ||||||||
\(251\) | −9.79196 | −0.618063 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(252\) | −3.87477 | −0.244088 | ||||||||
\(253\) | 0.00410806 | 0.000258272 0 | ||||||||
\(254\) | −11.0071 | −0.690648 | ||||||||
\(255\) | 0.976160 | 0.0611295 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.93389 | −0.370146 | −0.185073 | − | 0.982725i | \(-0.559252\pi\) | ||||
−0.185073 | + | 0.982725i | \(0.559252\pi\) | |||||||
\(258\) | 0.671491 | 0.0418052 | ||||||||
\(259\) | 0.295913 | 0.0183872 | ||||||||
\(260\) | −3.99526 | −0.247776 | ||||||||
\(261\) | −6.91994 | −0.428334 | ||||||||
\(262\) | −9.73289 | −0.601300 | ||||||||
\(263\) | 0.685091 | 0.0422445 | 0.0211223 | − | 0.999777i | \(-0.493276\pi\) | ||||
0.0211223 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(264\) | −0.0200581 | −0.00123449 | ||||||||
\(265\) | 3.45692 | 0.212357 | ||||||||
\(266\) | 18.4444 | 1.13090 | ||||||||
\(267\) | 13.8917 | 0.850161 | ||||||||
\(268\) | −2.36212 | −0.144290 | ||||||||
\(269\) | 5.05267 | 0.308067 | 0.154034 | − | 0.988066i | \(-0.450774\pi\) | ||||
0.154034 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(270\) | −0.976160 | −0.0594072 | ||||||||
\(271\) | −19.1778 | −1.16497 | −0.582485 | − | 0.812841i | \(-0.697920\pi\) | ||||
−0.582485 | + | 0.812841i | \(0.697920\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 15.8588 | 0.959819 | ||||||||
\(274\) | −17.5945 | −1.06293 | ||||||||
\(275\) | 0.0811775 | 0.00489519 | ||||||||
\(276\) | 0.204808 | 0.0123280 | ||||||||
\(277\) | 5.02496 | 0.301921 | 0.150960 | − | 0.988540i | \(-0.451763\pi\) | ||||
0.150960 | + | 0.988540i | \(0.451763\pi\) | |||||||
\(278\) | −18.6395 | −1.11792 | ||||||||
\(279\) | 1.87253 | 0.112105 | ||||||||
\(280\) | −3.78240 | −0.226042 | ||||||||
\(281\) | −29.8736 | −1.78211 | −0.891055 | − | 0.453895i | \(-0.850034\pi\) | ||||
−0.891055 | + | 0.453895i | \(0.850034\pi\) | |||||||
\(282\) | 10.7654 | 0.641068 | ||||||||
\(283\) | 9.35241 | 0.555943 | 0.277971 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277971 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(284\) | −10.9512 | −0.649837 | ||||||||
\(285\) | 4.64664 | 0.275243 | ||||||||
\(286\) | 0.0820947 | 0.00485436 | ||||||||
\(287\) | −6.69427 | −0.395150 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.75497 | −0.396665 | ||||||||
\(291\) | −6.56510 | −0.384853 | ||||||||
\(292\) | 3.32488 | 0.194574 | ||||||||
\(293\) | −19.7447 | −1.15350 | −0.576749 | − | 0.816921i | \(-0.695679\pi\) | ||||
−0.576749 | + | 0.816921i | \(0.695679\pi\) | |||||||
\(294\) | 8.01388 | 0.467379 | ||||||||
\(295\) | 0.976160 | 0.0568342 | ||||||||
\(296\) | 0.0763691 | 0.00443887 | ||||||||
\(297\) | 0.0200581 | 0.00116389 | ||||||||
\(298\) | −11.1125 | −0.643732 | ||||||||
\(299\) | −0.838244 | −0.0484769 | ||||||||
\(300\) | 4.04711 | 0.233660 | ||||||||
\(301\) | −2.60188 | −0.149970 | ||||||||
\(302\) | −15.4133 | −0.886936 | ||||||||
\(303\) | −2.28999 | −0.131556 | ||||||||
\(304\) | 4.76012 | 0.273012 | ||||||||
\(305\) | 6.03008 | 0.345281 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 26.3420 | 1.50342 | 0.751708 | − | 0.659497i | \(-0.229230\pi\) | ||||
0.751708 | + | 0.659497i | \(0.229230\pi\) | |||||||
\(308\) | 0.0777208 | 0.00442855 | ||||||||
\(309\) | −9.40392 | −0.534970 | ||||||||
\(310\) | 1.82788 | 0.103817 | ||||||||
\(311\) | 22.5144 | 1.27668 | 0.638338 | − | 0.769756i | \(-0.279622\pi\) | ||||
0.638338 | + | 0.769756i | \(0.279622\pi\) | |||||||
\(312\) | 4.09284 | 0.231711 | ||||||||
\(313\) | 16.9101 | 0.955814 | 0.477907 | − | 0.878411i | \(-0.341396\pi\) | ||||
0.477907 | + | 0.878411i | \(0.341396\pi\) | |||||||
\(314\) | 1.24776 | 0.0704150 | ||||||||
\(315\) | 3.78240 | 0.213114 | ||||||||
\(316\) | −9.33941 | −0.525383 | ||||||||
\(317\) | −1.50973 | −0.0847947 | −0.0423974 | − | 0.999101i | \(-0.513500\pi\) | ||||
−0.0423974 | + | 0.999101i | \(0.513500\pi\) | |||||||
\(318\) | −3.54134 | −0.198588 | ||||||||
\(319\) | 0.138801 | 0.00777137 | ||||||||
\(320\) | −0.976160 | −0.0545690 | ||||||||
\(321\) | 10.6637 | 0.595191 | ||||||||
\(322\) | −0.793584 | −0.0442247 | ||||||||
\(323\) | 4.76012 | 0.264860 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −16.5642 | −0.918814 | ||||||||
\(326\) | −7.89843 | −0.437454 | ||||||||
\(327\) | 10.2720 | 0.568043 | ||||||||
\(328\) | −1.72765 | −0.0953937 | ||||||||
\(329\) | −41.7134 | −2.29973 | ||||||||
\(330\) | 0.0195800 | 0.00107784 | ||||||||
\(331\) | 14.9957 | 0.824239 | 0.412120 | − | 0.911130i | \(-0.364789\pi\) | ||||
0.412120 | + | 0.911130i | \(0.364789\pi\) | |||||||
\(332\) | −2.90996 | −0.159705 | ||||||||
\(333\) | −0.0763691 | −0.00418500 | ||||||||
\(334\) | 23.7000 | 1.29681 | ||||||||
\(335\) | 2.30581 | 0.125980 | ||||||||
\(336\) | 3.87477 | 0.211386 | ||||||||
\(337\) | −32.0030 | −1.74331 | −0.871657 | − | 0.490117i | \(-0.836954\pi\) | ||||
−0.871657 | + | 0.490117i | \(0.836954\pi\) | |||||||
\(338\) | −3.75130 | −0.204044 | ||||||||
\(339\) | 14.4538 | 0.785021 | ||||||||
\(340\) | −0.976160 | −0.0529397 | ||||||||
\(341\) | −0.0375594 | −0.00203395 | ||||||||
\(342\) | −4.76012 | −0.257398 | ||||||||
\(343\) | −3.92855 | −0.212122 | ||||||||
\(344\) | −0.671491 | −0.0362044 | ||||||||
\(345\) | −0.199925 | −0.0107636 | ||||||||
\(346\) | −24.3272 | −1.30784 | ||||||||
\(347\) | 7.08683 | 0.380441 | 0.190220 | − | 0.981741i | \(-0.439080\pi\) | ||||
0.190220 | + | 0.981741i | \(0.439080\pi\) | |||||||
\(348\) | 6.91994 | 0.370948 | ||||||||
\(349\) | 35.6085 | 1.90608 | 0.953040 | − | 0.302845i | \(-0.0979365\pi\) | ||||
0.953040 | + | 0.302845i | \(0.0979365\pi\) | |||||||
\(350\) | −15.6816 | −0.838219 | ||||||||
\(351\) | −4.09284 | −0.218459 | ||||||||
\(352\) | 0.0200581 | 0.00106910 | ||||||||
\(353\) | 32.3000 | 1.71916 | 0.859579 | − | 0.511003i | \(-0.170726\pi\) | ||||
0.859579 | + | 0.511003i | \(0.170726\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 10.6902 | 0.567376 | ||||||||
\(356\) | −13.8917 | −0.736261 | ||||||||
\(357\) | 3.87477 | 0.205075 | ||||||||
\(358\) | 26.2696 | 1.38839 | ||||||||
\(359\) | −25.2748 | −1.33395 | −0.666976 | − | 0.745079i | \(-0.732412\pi\) | ||||
−0.666976 | + | 0.745079i | \(0.732412\pi\) | |||||||
\(360\) | 0.976160 | 0.0514482 | ||||||||
\(361\) | 3.65879 | 0.192568 | ||||||||
\(362\) | 10.5798 | 0.556061 | ||||||||
\(363\) | 10.9996 | 0.577329 | ||||||||
\(364\) | −15.8588 | −0.831228 | ||||||||
\(365\) | −3.24561 | −0.169883 | ||||||||
\(366\) | −6.17734 | −0.322895 | ||||||||
\(367\) | 16.9270 | 0.883580 | 0.441790 | − | 0.897119i | \(-0.354344\pi\) | ||||
0.441790 | + | 0.897119i | \(0.354344\pi\) | |||||||
\(368\) | −0.204808 | −0.0106763 | ||||||||
\(369\) | 1.72765 | 0.0899381 | ||||||||
\(370\) | −0.0745485 | −0.00387559 | ||||||||
\(371\) | 13.7219 | 0.712405 | ||||||||
\(372\) | −1.87253 | −0.0970859 | ||||||||
\(373\) | −1.60953 | −0.0833383 | −0.0416691 | − | 0.999131i | \(-0.513268\pi\) | ||||
−0.0416691 | + | 0.999131i | \(0.513268\pi\) | |||||||
\(374\) | 0.0200581 | 0.00103718 | ||||||||
\(375\) | −8.83143 | −0.456053 | ||||||||
\(376\) | −10.7654 | −0.555181 | ||||||||
\(377\) | −28.3222 | −1.45867 | ||||||||
\(378\) | −3.87477 | −0.199297 | ||||||||
\(379\) | −5.76769 | −0.296266 | −0.148133 | − | 0.988967i | \(-0.547326\pi\) | ||||
−0.148133 | + | 0.988967i | \(0.547326\pi\) | |||||||
\(380\) | −4.64664 | −0.238368 | ||||||||
\(381\) | −11.0071 | −0.563912 | ||||||||
\(382\) | −18.5956 | −0.951436 | ||||||||
\(383\) | 29.1366 | 1.48881 | 0.744405 | − | 0.667728i | \(-0.232733\pi\) | ||||
0.744405 | + | 0.667728i | \(0.232733\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.0758679 | −0.00386659 | ||||||||
\(386\) | 10.0613 | 0.512105 | ||||||||
\(387\) | 0.671491 | 0.0341338 | ||||||||
\(388\) | 6.56510 | 0.333292 | ||||||||
\(389\) | 15.2183 | 0.771600 | 0.385800 | − | 0.922582i | \(-0.373925\pi\) | ||||
0.385800 | + | 0.922582i | \(0.373925\pi\) | |||||||
\(390\) | −3.99526 | −0.202308 | ||||||||
\(391\) | −0.204808 | −0.0103576 | ||||||||
\(392\) | −8.01388 | −0.404762 | ||||||||
\(393\) | −9.73289 | −0.490960 | ||||||||
\(394\) | −12.4837 | −0.628918 | ||||||||
\(395\) | 9.11676 | 0.458714 | ||||||||
\(396\) | −0.0200581 | −0.00100796 | ||||||||
\(397\) | 34.3140 | 1.72217 | 0.861086 | − | 0.508459i | \(-0.169785\pi\) | ||||
0.861086 | + | 0.508459i | \(0.169785\pi\) | |||||||
\(398\) | −12.8824 | −0.645735 | ||||||||
\(399\) | 18.4444 | 0.923376 | ||||||||
\(400\) | −4.04711 | −0.202356 | ||||||||
\(401\) | −15.4362 | −0.770845 | −0.385422 | − | 0.922740i | \(-0.625944\pi\) | ||||
−0.385422 | + | 0.922740i | \(0.625944\pi\) | |||||||
\(402\) | −2.36212 | −0.117812 | ||||||||
\(403\) | 7.66394 | 0.381768 | ||||||||
\(404\) | 2.28999 | 0.113931 | ||||||||
\(405\) | −0.976160 | −0.0485058 | ||||||||
\(406\) | −26.8132 | −1.33072 | ||||||||
\(407\) | 0.00153182 | 7.59296e−5 0 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 26.4843 | 1.30956 | 0.654781 | − | 0.755819i | \(-0.272761\pi\) | ||||
0.654781 | + | 0.755819i | \(0.272761\pi\) | |||||||
\(410\) | 1.68647 | 0.0832886 | ||||||||
\(411\) | −17.5945 | −0.867875 | ||||||||
\(412\) | 9.40392 | 0.463298 | ||||||||
\(413\) | 3.87477 | 0.190665 | ||||||||
\(414\) | 0.204808 | 0.0100658 | ||||||||
\(415\) | 2.84058 | 0.139439 | ||||||||
\(416\) | −4.09284 | −0.200668 | ||||||||
\(417\) | −18.6395 | −0.912779 | ||||||||
\(418\) | 0.0954792 | 0.00467004 | ||||||||
\(419\) | 33.8253 | 1.65248 | 0.826238 | − | 0.563321i | \(-0.190477\pi\) | ||||
0.826238 | + | 0.563321i | \(0.190477\pi\) | |||||||
\(420\) | −3.78240 | −0.184562 | ||||||||
\(421\) | 8.88019 | 0.432794 | 0.216397 | − | 0.976305i | \(-0.430569\pi\) | ||||
0.216397 | + | 0.976305i | \(0.430569\pi\) | |||||||
\(422\) | −21.2253 | −1.03323 | ||||||||
\(423\) | 10.7654 | 0.523430 | ||||||||
\(424\) | 3.54134 | 0.171983 | ||||||||
\(425\) | −4.04711 | −0.196314 | ||||||||
\(426\) | −10.9512 | −0.530590 | ||||||||
\(427\) | 23.9358 | 1.15834 | ||||||||
\(428\) | −10.6637 | −0.515451 | ||||||||
\(429\) | 0.0820947 | 0.00396357 | ||||||||
\(430\) | 0.655483 | 0.0316102 | ||||||||
\(431\) | −1.60947 | −0.0775256 | −0.0387628 | − | 0.999248i | \(-0.512342\pi\) | ||||
−0.0387628 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 10.3342 | 0.496631 | 0.248315 | − | 0.968679i | \(-0.420123\pi\) | ||||
0.248315 | + | 0.968679i | \(0.420123\pi\) | |||||||
\(434\) | 7.25561 | 0.348281 | ||||||||
\(435\) | −6.75497 | −0.323876 | ||||||||
\(436\) | −10.2720 | −0.491940 | ||||||||
\(437\) | −0.974910 | −0.0466363 | ||||||||
\(438\) | 3.32488 | 0.158869 | ||||||||
\(439\) | 5.92289 | 0.282684 | 0.141342 | − | 0.989961i | \(-0.454858\pi\) | ||||
0.141342 | + | 0.989961i | \(0.454858\pi\) | |||||||
\(440\) | −0.0195800 | −0.000933438 0 | ||||||||
\(441\) | 8.01388 | 0.381613 | ||||||||
\(442\) | −4.09284 | −0.194676 | ||||||||
\(443\) | −3.78046 | −0.179615 | −0.0898076 | − | 0.995959i | \(-0.528625\pi\) | ||||
−0.0898076 | + | 0.995959i | \(0.528625\pi\) | |||||||
\(444\) | 0.0763691 | 0.00362432 | ||||||||
\(445\) | 13.5606 | 0.642833 | ||||||||
\(446\) | −24.7471 | −1.17181 | ||||||||
\(447\) | −11.1125 | −0.525605 | ||||||||
\(448\) | −3.87477 | −0.183066 | ||||||||
\(449\) | −25.1981 | −1.18917 | −0.594586 | − | 0.804032i | \(-0.702684\pi\) | ||||
−0.594586 | + | 0.804032i | \(0.702684\pi\) | |||||||
\(450\) | 4.04711 | 0.190783 | ||||||||
\(451\) | −0.0346535 | −0.00163177 | ||||||||
\(452\) | −14.4538 | −0.679848 | ||||||||
\(453\) | −15.4133 | −0.724181 | ||||||||
\(454\) | −0.782040 | −0.0367030 | ||||||||
\(455\) | 15.4807 | 0.725749 | ||||||||
\(456\) | 4.76012 | 0.222913 | ||||||||
\(457\) | 13.0744 | 0.611594 | 0.305797 | − | 0.952097i | \(-0.401077\pi\) | ||||
0.305797 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(458\) | −1.67635 | −0.0783308 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0.199925 | 0.00932156 | ||||||||
\(461\) | 2.93939 | 0.136901 | 0.0684505 | − | 0.997655i | \(-0.478194\pi\) | ||||
0.0684505 | + | 0.997655i | \(0.478194\pi\) | |||||||
\(462\) | 0.0777208 | 0.00361590 | ||||||||
\(463\) | 37.6944 | 1.75181 | 0.875903 | − | 0.482488i | \(-0.160267\pi\) | ||||
0.875903 | + | 0.482488i | \(0.160267\pi\) | |||||||
\(464\) | −6.91994 | −0.321250 | ||||||||
\(465\) | 1.82788 | 0.0847661 | ||||||||
\(466\) | 2.77060 | 0.128345 | ||||||||
\(467\) | −15.4296 | −0.713999 | −0.356999 | − | 0.934105i | \(-0.616200\pi\) | ||||
−0.356999 | + | 0.934105i | \(0.616200\pi\) | |||||||
\(468\) | 4.09284 | 0.189191 | ||||||||
\(469\) | 9.15270 | 0.422632 | ||||||||
\(470\) | 10.5087 | 0.484731 | ||||||||
\(471\) | 1.24776 | 0.0574936 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | −0.0134689 | −0.000619299 0 | ||||||||
\(474\) | −9.33941 | −0.428973 | ||||||||
\(475\) | −19.2648 | −0.883928 | ||||||||
\(476\) | −3.87477 | −0.177600 | ||||||||
\(477\) | −3.54134 | −0.162147 | ||||||||
\(478\) | 0.488210 | 0.0223302 | ||||||||
\(479\) | 16.5292 | 0.755237 | 0.377618 | − | 0.925961i | \(-0.376743\pi\) | ||||
0.377618 | + | 0.925961i | \(0.376743\pi\) | |||||||
\(480\) | −0.976160 | −0.0445554 | ||||||||
\(481\) | −0.312566 | −0.0142518 | ||||||||
\(482\) | 18.6888 | 0.851250 | ||||||||
\(483\) | −0.793584 | −0.0361093 | ||||||||
\(484\) | −10.9996 | −0.499982 | ||||||||
\(485\) | −6.40858 | −0.290999 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −4.64275 | −0.210383 | −0.105192 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105192 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(488\) | 6.17734 | 0.279635 | ||||||||
\(489\) | −7.89843 | −0.357180 | ||||||||
\(490\) | 7.82283 | 0.353399 | ||||||||
\(491\) | −10.2849 | −0.464152 | −0.232076 | − | 0.972698i | \(-0.574552\pi\) | ||||
−0.232076 | + | 0.972698i | \(0.574552\pi\) | |||||||
\(492\) | −1.72765 | −0.0778886 | ||||||||
\(493\) | −6.91994 | −0.311658 | ||||||||
\(494\) | −19.4824 | −0.876555 | ||||||||
\(495\) | 0.0195800 | 0.000880053 0 | ||||||||
\(496\) | 1.87253 | 0.0840789 | ||||||||
\(497\) | 42.4336 | 1.90341 | ||||||||
\(498\) | −2.90996 | −0.130398 | ||||||||
\(499\) | −2.71766 | −0.121659 | −0.0608295 | − | 0.998148i | \(-0.519375\pi\) | ||||
−0.0608295 | + | 0.998148i | \(0.519375\pi\) | |||||||
\(500\) | 8.83143 | 0.394954 | ||||||||
\(501\) | 23.7000 | 1.05884 | ||||||||
\(502\) | 9.79196 | 0.437037 | ||||||||
\(503\) | 44.1857 | 1.97014 | 0.985071 | − | 0.172147i | \(-0.0550703\pi\) | ||||
0.985071 | + | 0.172147i | \(0.0550703\pi\) | |||||||
\(504\) | 3.87477 | 0.172596 | ||||||||
\(505\) | −2.23540 | −0.0994738 | ||||||||
\(506\) | −0.00410806 | −0.000182626 0 | ||||||||
\(507\) | −3.75130 | −0.166601 | ||||||||
\(508\) | 11.0071 | 0.488362 | ||||||||
\(509\) | −32.5057 | −1.44079 | −0.720394 | − | 0.693565i | \(-0.756039\pi\) | ||||
−0.720394 | + | 0.693565i | \(0.756039\pi\) | |||||||
\(510\) | −0.976160 | −0.0432251 | ||||||||
\(511\) | −12.8831 | −0.569917 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.76012 | −0.210165 | ||||||||
\(514\) | 5.93389 | 0.261733 | ||||||||
\(515\) | −9.17974 | −0.404507 | ||||||||
\(516\) | −0.671491 | −0.0295608 | ||||||||
\(517\) | −0.215933 | −0.00949673 | ||||||||
\(518\) | −0.295913 | −0.0130017 | ||||||||
\(519\) | −24.3272 | −1.06784 | ||||||||
\(520\) | 3.99526 | 0.175204 | ||||||||
\(521\) | −15.6998 | −0.687821 | −0.343911 | − | 0.939002i | \(-0.611752\pi\) | ||||
−0.343911 | + | 0.939002i | \(0.611752\pi\) | |||||||
\(522\) | 6.91994 | 0.302878 | ||||||||
\(523\) | 14.6944 | 0.642542 | 0.321271 | − | 0.946987i | \(-0.395890\pi\) | ||||
0.321271 | + | 0.946987i | \(0.395890\pi\) | |||||||
\(524\) | 9.73289 | 0.425183 | ||||||||
\(525\) | −15.6816 | −0.684403 | ||||||||
\(526\) | −0.685091 | −0.0298714 | ||||||||
\(527\) | 1.87253 | 0.0815685 | ||||||||
\(528\) | 0.0200581 | 0.000872918 0 | ||||||||
\(529\) | −22.9581 | −0.998176 | ||||||||
\(530\) | −3.45692 | −0.150159 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | −18.4444 | −0.799667 | ||||||||
\(533\) | 7.07100 | 0.306279 | ||||||||
\(534\) | −13.8917 | −0.601155 | ||||||||
\(535\) | 10.4095 | 0.450042 | ||||||||
\(536\) | 2.36212 | 0.102028 | ||||||||
\(537\) | 26.2696 | 1.13362 | ||||||||
\(538\) | −5.05267 | −0.217836 | ||||||||
\(539\) | −0.160743 | −0.00692371 | ||||||||
\(540\) | 0.976160 | 0.0420072 | ||||||||
\(541\) | 40.9475 | 1.76047 | 0.880234 | − | 0.474539i | \(-0.157385\pi\) | ||||
0.880234 | + | 0.474539i | \(0.157385\pi\) | |||||||
\(542\) | 19.1778 | 0.823759 | ||||||||
\(543\) | 10.5798 | 0.454022 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 10.0271 | 0.429514 | ||||||||
\(546\) | −15.8588 | −0.678695 | ||||||||
\(547\) | 43.1212 | 1.84373 | 0.921864 | − | 0.387514i | \(-0.126666\pi\) | ||||
0.921864 | + | 0.387514i | \(0.126666\pi\) | |||||||
\(548\) | 17.5945 | 0.751602 | ||||||||
\(549\) | −6.17734 | −0.263643 | ||||||||
\(550\) | −0.0811775 | −0.00346142 | ||||||||
\(551\) | −32.9398 | −1.40328 | ||||||||
\(552\) | −0.204808 | −0.00871720 | ||||||||
\(553\) | 36.1881 | 1.53887 | ||||||||
\(554\) | −5.02496 | −0.213490 | ||||||||
\(555\) | −0.0745485 | −0.00316441 | ||||||||
\(556\) | 18.6395 | 0.790489 | ||||||||
\(557\) | −40.9288 | −1.73421 | −0.867105 | − | 0.498125i | \(-0.834022\pi\) | ||||
−0.867105 | + | 0.498125i | \(0.834022\pi\) | |||||||
\(558\) | −1.87253 | −0.0792703 | ||||||||
\(559\) | 2.74830 | 0.116241 | ||||||||
\(560\) | 3.78240 | 0.159836 | ||||||||
\(561\) | 0.0200581 | 0.000846855 0 | ||||||||
\(562\) | 29.8736 | 1.26014 | ||||||||
\(563\) | −3.58242 | −0.150981 | −0.0754906 | − | 0.997147i | \(-0.524052\pi\) | ||||
−0.0754906 | + | 0.997147i | \(0.524052\pi\) | |||||||
\(564\) | −10.7654 | −0.453304 | ||||||||
\(565\) | 14.1092 | 0.593579 | ||||||||
\(566\) | −9.35241 | −0.393111 | ||||||||
\(567\) | −3.87477 | −0.162725 | ||||||||
\(568\) | 10.9512 | 0.459504 | ||||||||
\(569\) | 17.1405 | 0.718567 | 0.359284 | − | 0.933228i | \(-0.383021\pi\) | ||||
0.359284 | + | 0.933228i | \(0.383021\pi\) | |||||||
\(570\) | −4.64664 | −0.194627 | ||||||||
\(571\) | 22.8089 | 0.954522 | 0.477261 | − | 0.878762i | \(-0.341630\pi\) | ||||
0.477261 | + | 0.878762i | \(0.341630\pi\) | |||||||
\(572\) | −0.0820947 | −0.00343255 | ||||||||
\(573\) | −18.5956 | −0.776844 | ||||||||
\(574\) | 6.69427 | 0.279413 | ||||||||
\(575\) | 0.828880 | 0.0345667 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.8241 | −0.950178 | −0.475089 | − | 0.879938i | \(-0.657584\pi\) | ||||
−0.475089 | + | 0.879938i | \(0.657584\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 10.0613 | 0.418132 | ||||||||
\(580\) | 6.75497 | 0.280485 | ||||||||
\(581\) | 11.2754 | 0.467784 | ||||||||
\(582\) | 6.56510 | 0.272132 | ||||||||
\(583\) | 0.0710327 | 0.00294187 | ||||||||
\(584\) | −3.32488 | −0.137584 | ||||||||
\(585\) | −3.99526 | −0.165184 | ||||||||
\(586\) | 19.7447 | 0.815647 | ||||||||
\(587\) | −21.6300 | −0.892767 | −0.446384 | − | 0.894842i | \(-0.647288\pi\) | ||||
−0.446384 | + | 0.894842i | \(0.647288\pi\) | |||||||
\(588\) | −8.01388 | −0.330487 | ||||||||
\(589\) | 8.91345 | 0.367272 | ||||||||
\(590\) | −0.976160 | −0.0401879 | ||||||||
\(591\) | −12.4837 | −0.513509 | ||||||||
\(592\) | −0.0763691 | −0.00313875 | ||||||||
\(593\) | 37.4157 | 1.53648 | 0.768238 | − | 0.640164i | \(-0.221134\pi\) | ||||
0.768238 | + | 0.640164i | \(0.221134\pi\) | |||||||
\(594\) | −0.0200581 | −0.000822995 0 | ||||||||
\(595\) | 3.78240 | 0.155063 | ||||||||
\(596\) | 11.1125 | 0.455187 | ||||||||
\(597\) | −12.8824 | −0.527241 | ||||||||
\(598\) | 0.838244 | 0.0342784 | ||||||||
\(599\) | −22.2390 | −0.908660 | −0.454330 | − | 0.890833i | \(-0.650121\pi\) | ||||
−0.454330 | + | 0.890833i | \(0.650121\pi\) | |||||||
\(600\) | −4.04711 | −0.165223 | ||||||||
\(601\) | −3.99369 | −0.162906 | −0.0814531 | − | 0.996677i | \(-0.525956\pi\) | ||||
−0.0814531 | + | 0.996677i | \(0.525956\pi\) | |||||||
\(602\) | 2.60188 | 0.106045 | ||||||||
\(603\) | −2.36212 | −0.0961931 | ||||||||
\(604\) | 15.4133 | 0.627159 | ||||||||
\(605\) | 10.7374 | 0.436536 | ||||||||
\(606\) | 2.28999 | 0.0930245 | ||||||||
\(607\) | −10.8577 | −0.440701 | −0.220351 | − | 0.975421i | \(-0.570720\pi\) | ||||
−0.220351 | + | 0.975421i | \(0.570720\pi\) | |||||||
\(608\) | −4.76012 | −0.193049 | ||||||||
\(609\) | −26.8132 | −1.08653 | ||||||||
\(610\) | −6.03008 | −0.244151 | ||||||||
\(611\) | 44.0609 | 1.78251 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 19.0462 | 0.769270 | 0.384635 | − | 0.923069i | \(-0.374327\pi\) | ||||
0.384635 | + | 0.923069i | \(0.374327\pi\) | |||||||
\(614\) | −26.3420 | −1.06308 | ||||||||
\(615\) | 1.68647 | 0.0680049 | ||||||||
\(616\) | −0.0777208 | −0.00313146 | ||||||||
\(617\) | 29.4380 | 1.18513 | 0.592565 | − | 0.805522i | \(-0.298115\pi\) | ||||
0.592565 | + | 0.805522i | \(0.298115\pi\) | |||||||
\(618\) | 9.40392 | 0.378281 | ||||||||
\(619\) | 14.2727 | 0.573669 | 0.286835 | − | 0.957980i | \(-0.407397\pi\) | ||||
0.286835 | + | 0.957980i | \(0.407397\pi\) | |||||||
\(620\) | −1.82788 | −0.0734096 | ||||||||
\(621\) | 0.204808 | 0.00821865 | ||||||||
\(622\) | −22.5144 | −0.902746 | ||||||||
\(623\) | 53.8274 | 2.15655 | ||||||||
\(624\) | −4.09284 | −0.163845 | ||||||||
\(625\) | 11.6147 | 0.464587 | ||||||||
\(626\) | −16.9101 | −0.675862 | ||||||||
\(627\) | 0.0954792 | 0.00381307 | ||||||||
\(628\) | −1.24776 | −0.0497909 | ||||||||
\(629\) | −0.0763691 | −0.00304504 | ||||||||
\(630\) | −3.78240 | −0.150694 | ||||||||
\(631\) | 4.18663 | 0.166667 | 0.0833336 | − | 0.996522i | \(-0.473443\pi\) | ||||
0.0833336 | + | 0.996522i | \(0.473443\pi\) | |||||||
\(632\) | 9.33941 | 0.371502 | ||||||||
\(633\) | −21.2253 | −0.843632 | ||||||||
\(634\) | 1.50973 | 0.0599589 | ||||||||
\(635\) | −10.7447 | −0.426391 | ||||||||
\(636\) | 3.54134 | 0.140423 | ||||||||
\(637\) | 32.7995 | 1.29956 | ||||||||
\(638\) | −0.138801 | −0.00549519 | ||||||||
\(639\) | −10.9512 | −0.433225 | ||||||||
\(640\) | 0.976160 | 0.0385861 | ||||||||
\(641\) | 20.7493 | 0.819549 | 0.409775 | − | 0.912187i | \(-0.365607\pi\) | ||||
0.409775 | + | 0.912187i | \(0.365607\pi\) | |||||||
\(642\) | −10.6637 | −0.420864 | ||||||||
\(643\) | −39.7523 | −1.56768 | −0.783840 | − | 0.620963i | \(-0.786742\pi\) | ||||
−0.783840 | + | 0.620963i | \(0.786742\pi\) | |||||||
\(644\) | 0.793584 | 0.0312716 | ||||||||
\(645\) | 0.655483 | 0.0258096 | ||||||||
\(646\) | −4.76012 | −0.187285 | ||||||||
\(647\) | 0.414841 | 0.0163091 | 0.00815453 | − | 0.999967i | \(-0.497404\pi\) | ||||
0.00815453 | + | 0.999967i | \(0.497404\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.0200581 | 0.000787351 0 | ||||||||
\(650\) | 16.5642 | 0.649700 | ||||||||
\(651\) | 7.25561 | 0.284370 | ||||||||
\(652\) | 7.89843 | 0.309327 | ||||||||
\(653\) | 32.0099 | 1.25265 | 0.626323 | − | 0.779564i | \(-0.284559\pi\) | ||||
0.626323 | + | 0.779564i | \(0.284559\pi\) | |||||||
\(654\) | −10.2720 | −0.401667 | ||||||||
\(655\) | −9.50086 | −0.371229 | ||||||||
\(656\) | 1.72765 | 0.0674535 | ||||||||
\(657\) | 3.32488 | 0.129716 | ||||||||
\(658\) | 41.7134 | 1.62616 | ||||||||
\(659\) | −21.5527 | −0.839574 | −0.419787 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419787 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(660\) | −0.0195800 | −0.000762149 0 | ||||||||
\(661\) | −6.61164 | −0.257163 | −0.128582 | − | 0.991699i | \(-0.541042\pi\) | ||||
−0.128582 | + | 0.991699i | \(0.541042\pi\) | |||||||
\(662\) | −14.9957 | −0.582825 | ||||||||
\(663\) | −4.09284 | −0.158953 | ||||||||
\(664\) | 2.90996 | 0.112928 | ||||||||
\(665\) | 18.0047 | 0.698192 | ||||||||
\(666\) | 0.0763691 | 0.00295924 | ||||||||
\(667\) | 1.41726 | 0.0548764 | ||||||||
\(668\) | −23.7000 | −0.916980 | ||||||||
\(669\) | −24.7471 | −0.956779 | ||||||||
\(670\) | −2.30581 | −0.0890813 | ||||||||
\(671\) | 0.123906 | 0.00478334 | ||||||||
\(672\) | −3.87477 | −0.149473 | ||||||||
\(673\) | −19.9294 | −0.768224 | −0.384112 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384112 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(674\) | 32.0030 | 1.23271 | ||||||||
\(675\) | 4.04711 | 0.155773 | ||||||||
\(676\) | 3.75130 | 0.144281 | ||||||||
\(677\) | −20.8723 | −0.802187 | −0.401093 | − | 0.916037i | \(-0.631370\pi\) | ||||
−0.401093 | + | 0.916037i | \(0.631370\pi\) | |||||||
\(678\) | −14.4538 | −0.555094 | ||||||||
\(679\) | −25.4383 | −0.976231 | ||||||||
\(680\) | 0.976160 | 0.0374340 | ||||||||
\(681\) | −0.782040 | −0.0299679 | ||||||||
\(682\) | 0.0375594 | 0.00143822 | ||||||||
\(683\) | 10.6419 | 0.407201 | 0.203601 | − | 0.979054i | \(-0.434736\pi\) | ||||
0.203601 | + | 0.979054i | \(0.434736\pi\) | |||||||
\(684\) | 4.76012 | 0.182008 | ||||||||
\(685\) | −17.1751 | −0.656227 | ||||||||
\(686\) | 3.92855 | 0.149993 | ||||||||
\(687\) | −1.67635 | −0.0639568 | ||||||||
\(688\) | 0.671491 | 0.0256004 | ||||||||
\(689\) | −14.4941 | −0.552182 | ||||||||
\(690\) | 0.199925 | 0.00761102 | ||||||||
\(691\) | −34.3588 | −1.30707 | −0.653535 | − | 0.756896i | \(-0.726715\pi\) | ||||
−0.653535 | + | 0.756896i | \(0.726715\pi\) | |||||||
\(692\) | 24.3272 | 0.924780 | ||||||||
\(693\) | 0.0777208 | 0.00295237 | ||||||||
\(694\) | −7.08683 | −0.269012 | ||||||||
\(695\) | −18.1951 | −0.690180 | ||||||||
\(696\) | −6.91994 | −0.262300 | ||||||||
\(697\) | 1.72765 | 0.0654395 | ||||||||
\(698\) | −35.6085 | −1.34780 | ||||||||
\(699\) | 2.77060 | 0.104794 | ||||||||
\(700\) | 15.6816 | 0.592710 | ||||||||
\(701\) | −1.29257 | −0.0488198 | −0.0244099 | − | 0.999702i | \(-0.507771\pi\) | ||||
−0.0244099 | + | 0.999702i | \(0.507771\pi\) | |||||||
\(702\) | 4.09284 | 0.154474 | ||||||||
\(703\) | −0.363527 | −0.0137107 | ||||||||
\(704\) | −0.0200581 | −0.000755969 0 | ||||||||
\(705\) | 10.5087 | 0.395781 | ||||||||
\(706\) | −32.3000 | −1.21563 | ||||||||
\(707\) | −8.87319 | −0.333711 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −7.83101 | −0.294100 | −0.147050 | − | 0.989129i | \(-0.546978\pi\) | ||||
−0.147050 | + | 0.989129i | \(0.546978\pi\) | |||||||
\(710\) | −10.6902 | −0.401195 | ||||||||
\(711\) | −9.33941 | −0.350255 | ||||||||
\(712\) | 13.8917 | 0.520615 | ||||||||
\(713\) | −0.383508 | −0.0143625 | ||||||||
\(714\) | −3.87477 | −0.145010 | ||||||||
\(715\) | 0.0801375 | 0.00299697 | ||||||||
\(716\) | −26.2696 | −0.981741 | ||||||||
\(717\) | 0.488210 | 0.0182325 | ||||||||
\(718\) | 25.2748 | 0.943247 | ||||||||
\(719\) | −17.6553 | −0.658432 | −0.329216 | − | 0.944255i | \(-0.606784\pi\) | ||||
−0.329216 | + | 0.944255i | \(0.606784\pi\) | |||||||
\(720\) | −0.976160 | −0.0363793 | ||||||||
\(721\) | −36.4381 | −1.35703 | ||||||||
\(722\) | −3.65879 | −0.136166 | ||||||||
\(723\) | 18.6888 | 0.695043 | ||||||||
\(724\) | −10.5798 | −0.393195 | ||||||||
\(725\) | 28.0058 | 1.04011 | ||||||||
\(726\) | −10.9996 | −0.408233 | ||||||||
\(727\) | 38.4302 | 1.42530 | 0.712649 | − | 0.701521i | \(-0.247495\pi\) | ||||
0.712649 | + | 0.701521i | \(0.247495\pi\) | |||||||
\(728\) | 15.8588 | 0.587767 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.24561 | 0.120125 | ||||||||
\(731\) | 0.671491 | 0.0248360 | ||||||||
\(732\) | 6.17734 | 0.228321 | ||||||||
\(733\) | 21.0258 | 0.776605 | 0.388302 | − | 0.921532i | \(-0.373062\pi\) | ||||
0.388302 | + | 0.921532i | \(0.373062\pi\) | |||||||
\(734\) | −16.9270 | −0.624785 | ||||||||
\(735\) | 7.82283 | 0.288549 | ||||||||
\(736\) | 0.204808 | 0.00754931 | ||||||||
\(737\) | 0.0473798 | 0.00174526 | ||||||||
\(738\) | −1.72765 | −0.0635958 | ||||||||
\(739\) | 25.9626 | 0.955051 | 0.477526 | − | 0.878618i | \(-0.341534\pi\) | ||||
0.477526 | + | 0.878618i | \(0.341534\pi\) | |||||||
\(740\) | 0.0745485 | 0.00274046 | ||||||||
\(741\) | −19.4824 | −0.715704 | ||||||||
\(742\) | −13.7219 | −0.503747 | ||||||||
\(743\) | −49.2105 | −1.80536 | −0.902679 | − | 0.430315i | \(-0.858402\pi\) | ||||
−0.902679 | + | 0.430315i | \(0.858402\pi\) | |||||||
\(744\) | 1.87253 | 0.0686501 | ||||||||
\(745\) | −10.8476 | −0.397426 | ||||||||
\(746\) | 1.60953 | 0.0589291 | ||||||||
\(747\) | −2.90996 | −0.106470 | ||||||||
\(748\) | −0.0200581 | −0.000733398 0 | ||||||||
\(749\) | 41.3196 | 1.50978 | ||||||||
\(750\) | 8.83143 | 0.322478 | ||||||||
\(751\) | 11.4941 | 0.419427 | 0.209714 | − | 0.977763i | \(-0.432747\pi\) | ||||
0.209714 | + | 0.977763i | \(0.432747\pi\) | |||||||
\(752\) | 10.7654 | 0.392572 | ||||||||
\(753\) | 9.79196 | 0.356839 | ||||||||
\(754\) | 28.3222 | 1.03143 | ||||||||
\(755\) | −15.0459 | −0.547575 | ||||||||
\(756\) | 3.87477 | 0.140924 | ||||||||
\(757\) | −22.4832 | −0.817167 | −0.408583 | − | 0.912721i | \(-0.633977\pi\) | ||||
−0.408583 | + | 0.912721i | \(0.633977\pi\) | |||||||
\(758\) | 5.76769 | 0.209492 | ||||||||
\(759\) | −0.00410806 | −0.000149113 0 | ||||||||
\(760\) | 4.64664 | 0.168551 | ||||||||
\(761\) | 22.8630 | 0.828784 | 0.414392 | − | 0.910099i | \(-0.363994\pi\) | ||||
0.414392 | + | 0.910099i | \(0.363994\pi\) | |||||||
\(762\) | 11.0071 | 0.398746 | ||||||||
\(763\) | 39.8017 | 1.44092 | ||||||||
\(764\) | 18.5956 | 0.672767 | ||||||||
\(765\) | −0.976160 | −0.0352931 | ||||||||
\(766\) | −29.1366 | −1.05275 | ||||||||
\(767\) | −4.09284 | −0.147784 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 40.5926 | 1.46381 | 0.731903 | − | 0.681409i | \(-0.238633\pi\) | ||||
0.731903 | + | 0.681409i | \(0.238633\pi\) | |||||||
\(770\) | 0.0758679 | 0.00273409 | ||||||||
\(771\) | 5.93389 | 0.213704 | ||||||||
\(772\) | −10.0613 | −0.362113 | ||||||||
\(773\) | −53.2082 | −1.91377 | −0.956883 | − | 0.290474i | \(-0.906187\pi\) | ||||
−0.956883 | + | 0.290474i | \(0.906187\pi\) | |||||||
\(774\) | −0.671491 | −0.0241363 | ||||||||
\(775\) | −7.57832 | −0.272221 | ||||||||
\(776\) | −6.56510 | −0.235673 | ||||||||
\(777\) | −0.295913 | −0.0106158 | ||||||||
\(778\) | −15.2183 | −0.545604 | ||||||||
\(779\) | 8.22385 | 0.294650 | ||||||||
\(780\) | 3.99526 | 0.143053 | ||||||||
\(781\) | 0.219662 | 0.00786011 | ||||||||
\(782\) | 0.204808 | 0.00732391 | ||||||||
\(783\) | 6.91994 | 0.247298 | ||||||||
\(784\) | 8.01388 | 0.286210 | ||||||||
\(785\) | 1.21801 | 0.0434726 | ||||||||
\(786\) | 9.73289 | 0.347161 | ||||||||
\(787\) | 3.24829 | 0.115789 | 0.0578945 | − | 0.998323i | \(-0.481561\pi\) | ||||
0.0578945 | + | 0.998323i | \(0.481561\pi\) | |||||||
\(788\) | 12.4837 | 0.444712 | ||||||||
\(789\) | −0.685091 | −0.0243899 | ||||||||
\(790\) | −9.11676 | −0.324360 | ||||||||
\(791\) | 56.0051 | 1.99131 | ||||||||
\(792\) | 0.0200581 | 0.000712735 0 | ||||||||
\(793\) | −25.2829 | −0.897820 | ||||||||
\(794\) | −34.3140 | −1.21776 | ||||||||
\(795\) | −3.45692 | −0.122604 | ||||||||
\(796\) | 12.8824 | 0.456604 | ||||||||
\(797\) | 21.3316 | 0.755603 | 0.377802 | − | 0.925887i | \(-0.376680\pi\) | ||||
0.377802 | + | 0.925887i | \(0.376680\pi\) | |||||||
\(798\) | −18.4444 | −0.652925 | ||||||||
\(799\) | 10.7654 | 0.380851 | ||||||||
\(800\) | 4.04711 | 0.143087 | ||||||||
\(801\) | −13.8917 | −0.490841 | ||||||||
\(802\) | 15.4362 | 0.545070 | ||||||||
\(803\) | −0.0666908 | −0.00235347 | ||||||||
\(804\) | 2.36212 | 0.0833057 | ||||||||
\(805\) | −0.774665 | −0.0273034 | ||||||||
\(806\) | −7.66394 | −0.269951 | ||||||||
\(807\) | −5.05267 | −0.177863 | ||||||||
\(808\) | −2.28999 | −0.0805615 | ||||||||
\(809\) | −21.3886 | −0.751982 | −0.375991 | − | 0.926623i | \(-0.622698\pi\) | ||||
−0.375991 | + | 0.926623i | \(0.622698\pi\) | |||||||
\(810\) | 0.976160 | 0.0342988 | ||||||||
\(811\) | 25.7158 | 0.903003 | 0.451501 | − | 0.892270i | \(-0.350889\pi\) | ||||
0.451501 | + | 0.892270i | \(0.350889\pi\) | |||||||
\(812\) | 26.8132 | 0.940959 | ||||||||
\(813\) | 19.1778 | 0.672596 | ||||||||
\(814\) | −0.00153182 | −5.36903e−5 0 | ||||||||
\(815\) | −7.71014 | −0.270074 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | 3.19638 | 0.111827 | ||||||||
\(818\) | −26.4843 | −0.926000 | ||||||||
\(819\) | −15.8588 | −0.554152 | ||||||||
\(820\) | −1.68647 | −0.0588940 | ||||||||
\(821\) | 7.09093 | 0.247475 | 0.123738 | − | 0.992315i | \(-0.460512\pi\) | ||||
0.123738 | + | 0.992315i | \(0.460512\pi\) | |||||||
\(822\) | 17.5945 | 0.613680 | ||||||||
\(823\) | −26.0126 | −0.906744 | −0.453372 | − | 0.891321i | \(-0.649779\pi\) | ||||
−0.453372 | + | 0.891321i | \(0.649779\pi\) | |||||||
\(824\) | −9.40392 | −0.327601 | ||||||||
\(825\) | −0.0811775 | −0.00282624 | ||||||||
\(826\) | −3.87477 | −0.134821 | ||||||||
\(827\) | −20.7693 | −0.722218 | −0.361109 | − | 0.932524i | \(-0.617602\pi\) | ||||
−0.361109 | + | 0.932524i | \(0.617602\pi\) | |||||||
\(828\) | −0.204808 | −0.00711756 | ||||||||
\(829\) | 53.2093 | 1.84803 | 0.924017 | − | 0.382351i | \(-0.124886\pi\) | ||||
0.924017 | + | 0.382351i | \(0.124886\pi\) | |||||||
\(830\) | −2.84058 | −0.0985981 | ||||||||
\(831\) | −5.02496 | −0.174314 | ||||||||
\(832\) | 4.09284 | 0.141894 | ||||||||
\(833\) | 8.01388 | 0.277664 | ||||||||
\(834\) | 18.6395 | 0.645432 | ||||||||
\(835\) | 23.1350 | 0.800619 | ||||||||
\(836\) | −0.0954792 | −0.00330222 | ||||||||
\(837\) | −1.87253 | −0.0647239 | ||||||||
\(838\) | −33.8253 | −1.16848 | ||||||||
\(839\) | 22.9755 | 0.793204 | 0.396602 | − | 0.917991i | \(-0.370189\pi\) | ||||
0.396602 | + | 0.917991i | \(0.370189\pi\) | |||||||
\(840\) | 3.78240 | 0.130505 | ||||||||
\(841\) | 18.8856 | 0.651227 | ||||||||
\(842\) | −8.88019 | −0.306032 | ||||||||
\(843\) | 29.8736 | 1.02890 | ||||||||
\(844\) | 21.2253 | 0.730606 | ||||||||
\(845\) | −3.66187 | −0.125972 | ||||||||
\(846\) | −10.7654 | −0.370121 | ||||||||
\(847\) | 42.6210 | 1.46447 | ||||||||
\(848\) | −3.54134 | −0.121610 | ||||||||
\(849\) | −9.35241 | −0.320974 | ||||||||
\(850\) | 4.04711 | 0.138815 | ||||||||
\(851\) | 0.0156410 | 0.000536166 0 | ||||||||
\(852\) | 10.9512 | 0.375184 | ||||||||
\(853\) | 12.4322 | 0.425671 | 0.212836 | − | 0.977088i | \(-0.431730\pi\) | ||||
0.212836 | + | 0.977088i | \(0.431730\pi\) | |||||||
\(854\) | −23.9358 | −0.819067 | ||||||||
\(855\) | −4.64664 | −0.158912 | ||||||||
\(856\) | 10.6637 | 0.364479 | ||||||||
\(857\) | −13.0859 | −0.447005 | −0.223502 | − | 0.974703i | \(-0.571749\pi\) | ||||
−0.223502 | + | 0.974703i | \(0.571749\pi\) | |||||||
\(858\) | −0.0820947 | −0.00280267 | ||||||||
\(859\) | 35.5786 | 1.21393 | 0.606964 | − | 0.794730i | \(-0.292387\pi\) | ||||
0.606964 | + | 0.794730i | \(0.292387\pi\) | |||||||
\(860\) | −0.655483 | −0.0223518 | ||||||||
\(861\) | 6.69427 | 0.228140 | ||||||||
\(862\) | 1.60947 | 0.0548189 | ||||||||
\(863\) | 27.3570 | 0.931243 | 0.465621 | − | 0.884984i | \(-0.345831\pi\) | ||||
0.465621 | + | 0.884984i | \(0.345831\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −23.7472 | −0.807430 | ||||||||
\(866\) | −10.3342 | −0.351171 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −7.25561 | −0.246272 | ||||||||
\(869\) | 0.187331 | 0.00635477 | ||||||||
\(870\) | 6.75497 | 0.229015 | ||||||||
\(871\) | −9.66779 | −0.327580 | ||||||||
\(872\) | 10.2720 | 0.347854 | ||||||||
\(873\) | 6.56510 | 0.222195 | ||||||||
\(874\) | 0.974910 | 0.0329768 | ||||||||
\(875\) | −34.2198 | −1.15684 | ||||||||
\(876\) | −3.32488 | −0.112337 | ||||||||
\(877\) | −7.62407 | −0.257446 | −0.128723 | − | 0.991681i | \(-0.541088\pi\) | ||||
−0.128723 | + | 0.991681i | \(0.541088\pi\) | |||||||
\(878\) | −5.92289 | −0.199888 | ||||||||
\(879\) | 19.7447 | 0.665973 | ||||||||
\(880\) | 0.0195800 | 0.000660040 0 | ||||||||
\(881\) | −17.0712 | −0.575142 | −0.287571 | − | 0.957759i | \(-0.592848\pi\) | ||||
−0.287571 | + | 0.957759i | \(0.592848\pi\) | |||||||
\(882\) | −8.01388 | −0.269841 | ||||||||
\(883\) | 24.7219 | 0.831958 | 0.415979 | − | 0.909374i | \(-0.363439\pi\) | ||||
0.415979 | + | 0.909374i | \(0.363439\pi\) | |||||||
\(884\) | 4.09284 | 0.137657 | ||||||||
\(885\) | −0.976160 | −0.0328133 | ||||||||
\(886\) | 3.78046 | 0.127007 | ||||||||
\(887\) | 25.8472 | 0.867865 | 0.433933 | − | 0.900945i | \(-0.357126\pi\) | ||||
0.433933 | + | 0.900945i | \(0.357126\pi\) | |||||||
\(888\) | −0.0763691 | −0.00256278 | ||||||||
\(889\) | −42.6501 | −1.43044 | ||||||||
\(890\) | −13.5606 | −0.454551 | ||||||||
\(891\) | −0.0200581 | −0.000671973 0 | ||||||||
\(892\) | 24.7471 | 0.828595 | ||||||||
\(893\) | 51.2445 | 1.71483 | ||||||||
\(894\) | 11.1125 | 0.371659 | ||||||||
\(895\) | 25.6433 | 0.857162 | ||||||||
\(896\) | 3.87477 | 0.129447 | ||||||||
\(897\) | 0.838244 | 0.0279882 | ||||||||
\(898\) | 25.1981 | 0.840872 | ||||||||
\(899\) | −12.9578 | −0.432166 | ||||||||
\(900\) | −4.04711 | −0.134904 | ||||||||
\(901\) | −3.54134 | −0.117979 | ||||||||
\(902\) | 0.0346535 | 0.00115384 | ||||||||
\(903\) | 2.60188 | 0.0865850 | ||||||||
\(904\) | 14.4538 | 0.480725 | ||||||||
\(905\) | 10.3276 | 0.343300 | ||||||||
\(906\) | 15.4133 | 0.512073 | ||||||||
\(907\) | −26.1380 | −0.867898 | −0.433949 | − | 0.900937i | \(-0.642880\pi\) | ||||
−0.433949 | + | 0.900937i | \(0.642880\pi\) | |||||||
\(908\) | 0.782040 | 0.0259529 | ||||||||
\(909\) | 2.28999 | 0.0759542 | ||||||||
\(910\) | −15.4807 | −0.513182 | ||||||||
\(911\) | 4.23218 | 0.140218 | 0.0701092 | − | 0.997539i | \(-0.477665\pi\) | ||||
0.0701092 | + | 0.997539i | \(0.477665\pi\) | |||||||
\(912\) | −4.76012 | −0.157623 | ||||||||
\(913\) | 0.0583683 | 0.00193171 | ||||||||
\(914\) | −13.0744 | −0.432462 | ||||||||
\(915\) | −6.03008 | −0.199348 | ||||||||
\(916\) | 1.67635 | 0.0553882 | ||||||||
\(917\) | −37.7128 | −1.24539 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −14.6891 | −0.484547 | −0.242274 | − | 0.970208i | \(-0.577893\pi\) | ||||
−0.242274 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(920\) | −0.199925 | −0.00659134 | ||||||||
\(921\) | −26.3420 | −0.867997 | ||||||||
\(922\) | −2.93939 | −0.0968036 | ||||||||
\(923\) | −44.8217 | −1.47532 | ||||||||
\(924\) | −0.0777208 | −0.00255683 | ||||||||
\(925\) | 0.309074 | 0.0101623 | ||||||||
\(926\) | −37.6944 | −1.23871 | ||||||||
\(927\) | 9.40392 | 0.308865 | ||||||||
\(928\) | 6.91994 | 0.227158 | ||||||||
\(929\) | 4.80777 | 0.157738 | 0.0788689 | − | 0.996885i | \(-0.474869\pi\) | ||||
0.0788689 | + | 0.996885i | \(0.474869\pi\) | |||||||
\(930\) | −1.82788 | −0.0599387 | ||||||||
\(931\) | 38.1471 | 1.25022 | ||||||||
\(932\) | −2.77060 | −0.0907539 | ||||||||
\(933\) | −22.5144 | −0.737089 | ||||||||
\(934\) | 15.4296 | 0.504874 | ||||||||
\(935\) | 0.0195800 | 0.000640333 0 | ||||||||
\(936\) | −4.09284 | −0.133779 | ||||||||
\(937\) | −55.8126 | −1.82332 | −0.911658 | − | 0.410949i | \(-0.865197\pi\) | ||||
−0.911658 | + | 0.410949i | \(0.865197\pi\) | |||||||
\(938\) | −9.15270 | −0.298846 | ||||||||
\(939\) | −16.9101 | −0.551839 | ||||||||
\(940\) | −10.5087 | −0.342757 | ||||||||
\(941\) | 30.8389 | 1.00532 | 0.502661 | − | 0.864484i | \(-0.332355\pi\) | ||||
0.502661 | + | 0.864484i | \(0.332355\pi\) | |||||||
\(942\) | −1.24776 | −0.0406541 | ||||||||
\(943\) | −0.353837 | −0.0115225 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −3.78240 | −0.123042 | ||||||||
\(946\) | 0.0134689 | 0.000437910 0 | ||||||||
\(947\) | 30.7117 | 0.997997 | 0.498999 | − | 0.866603i | \(-0.333701\pi\) | ||||
0.498999 | + | 0.866603i | \(0.333701\pi\) | |||||||
\(948\) | 9.33941 | 0.303330 | ||||||||
\(949\) | 13.6082 | 0.441740 | ||||||||
\(950\) | 19.2648 | 0.625031 | ||||||||
\(951\) | 1.50973 | 0.0489563 | ||||||||
\(952\) | 3.87477 | 0.125582 | ||||||||
\(953\) | 35.9992 | 1.16613 | 0.583065 | − | 0.812426i | \(-0.301853\pi\) | ||||
0.583065 | + | 0.812426i | \(0.301853\pi\) | |||||||
\(954\) | 3.54134 | 0.114655 | ||||||||
\(955\) | −18.1523 | −0.587396 | ||||||||
\(956\) | −0.488210 | −0.0157898 | ||||||||
\(957\) | −0.138801 | −0.00448680 | ||||||||
\(958\) | −16.5292 | −0.534033 | ||||||||
\(959\) | −68.1749 | −2.20148 | ||||||||
\(960\) | 0.976160 | 0.0315054 | ||||||||
\(961\) | −27.4936 | −0.886892 | ||||||||
\(962\) | 0.312566 | 0.0100775 | ||||||||
\(963\) | −10.6637 | −0.343634 | ||||||||
\(964\) | −18.6888 | −0.601925 | ||||||||
\(965\) | 9.82141 | 0.316162 | ||||||||
\(966\) | 0.793584 | 0.0255331 | ||||||||
\(967\) | −57.8042 | −1.85886 | −0.929430 | − | 0.369000i | \(-0.879700\pi\) | ||||
−0.929430 | + | 0.369000i | \(0.879700\pi\) | |||||||
\(968\) | 10.9996 | 0.353540 | ||||||||
\(969\) | −4.76012 | −0.152917 | ||||||||
\(970\) | 6.40858 | 0.205767 | ||||||||
\(971\) | −43.8980 | −1.40875 | −0.704377 | − | 0.709826i | \(-0.748773\pi\) | ||||
−0.704377 | + | 0.709826i | \(0.748773\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −72.2237 | −2.31539 | ||||||||
\(974\) | 4.64275 | 0.148763 | ||||||||
\(975\) | 16.5642 | 0.530478 | ||||||||
\(976\) | −6.17734 | −0.197732 | ||||||||
\(977\) | 32.1070 | 1.02719 | 0.513597 | − | 0.858032i | \(-0.328313\pi\) | ||||
0.513597 | + | 0.858032i | \(0.328313\pi\) | |||||||
\(978\) | 7.89843 | 0.252564 | ||||||||
\(979\) | 0.278642 | 0.00890545 | ||||||||
\(980\) | −7.82283 | −0.249891 | ||||||||
\(981\) | −10.2720 | −0.327960 | ||||||||
\(982\) | 10.2849 | 0.328205 | ||||||||
\(983\) | 38.8987 | 1.24067 | 0.620337 | − | 0.784335i | \(-0.286996\pi\) | ||||
0.620337 | + | 0.784335i | \(0.286996\pi\) | |||||||
\(984\) | 1.72765 | 0.0550756 | ||||||||
\(985\) | −12.1861 | −0.388280 | ||||||||
\(986\) | 6.91994 | 0.220376 | ||||||||
\(987\) | 41.7134 | 1.32775 | ||||||||
\(988\) | 19.4824 | 0.619818 | ||||||||
\(989\) | −0.137527 | −0.00437309 | ||||||||
\(990\) | −0.0195800 | −0.000622292 0 | ||||||||
\(991\) | 58.3009 | 1.85199 | 0.925994 | − | 0.377538i | \(-0.123229\pi\) | ||||
0.925994 | + | 0.377538i | \(0.123229\pi\) | |||||||
\(992\) | −1.87253 | −0.0594527 | ||||||||
\(993\) | −14.9957 | −0.475875 | ||||||||
\(994\) | −42.4336 | −1.34591 | ||||||||
\(995\) | −12.5753 | −0.398663 | ||||||||
\(996\) | 2.90996 | 0.0922055 | ||||||||
\(997\) | −42.3174 | −1.34021 | −0.670103 | − | 0.742268i | \(-0.733750\pi\) | ||||
−0.670103 | + | 0.742268i | \(0.733750\pi\) | |||||||
\(998\) | 2.71766 | 0.0860259 | ||||||||
\(999\) | 0.0763691 | 0.00241621 |
(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 | 6018.2.a.x.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.x.1.4 | ✓ | 10 | 1.1 | even | 1 | trivial |