Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.715815\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.715815 | 0.506158 | 0.253079 | − | 0.967446i | \(-0.418557\pi\) | ||||
0.253079 | + | 0.967446i | \(0.418557\pi\) | |||||||
\(3\) | 3.10981 | 1.79545 | 0.897725 | − | 0.440556i | \(-0.145219\pi\) | ||||
0.897725 | + | 0.440556i | \(0.145219\pi\) | |||||||
\(4\) | −1.48761 | −0.743804 | ||||||||
\(5\) | 0.799569 | 0.357578 | 0.178789 | − | 0.983887i | \(-0.442782\pi\) | ||||
0.178789 | + | 0.983887i | \(0.442782\pi\) | |||||||
\(6\) | 2.22605 | 0.908781 | ||||||||
\(7\) | −0.891306 | −0.336882 | −0.168441 | − | 0.985712i | \(-0.553873\pi\) | ||||
−0.168441 | + | 0.985712i | \(0.553873\pi\) | |||||||
\(8\) | −2.49648 | −0.882640 | ||||||||
\(9\) | 6.67092 | 2.22364 | ||||||||
\(10\) | 0.572344 | 0.180991 | ||||||||
\(11\) | 0.790116 | 0.238229 | 0.119115 | − | 0.992881i | \(-0.461994\pi\) | ||||
0.119115 | + | 0.992881i | \(0.461994\pi\) | |||||||
\(12\) | −4.62618 | −1.33546 | ||||||||
\(13\) | 6.94611 | 1.92650 | 0.963252 | − | 0.268599i | \(-0.0865606\pi\) | ||||
0.963252 | + | 0.268599i | \(0.0865606\pi\) | |||||||
\(14\) | −0.638011 | −0.170515 | ||||||||
\(15\) | 2.48651 | 0.642014 | ||||||||
\(16\) | 1.18819 | 0.297049 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 4.77515 | 1.12551 | ||||||||
\(19\) | −0.850729 | −0.195171 | −0.0975854 | − | 0.995227i | \(-0.531112\pi\) | ||||
−0.0975854 | + | 0.995227i | \(0.531112\pi\) | |||||||
\(20\) | −1.18945 | −0.265968 | ||||||||
\(21\) | −2.77179 | −0.604855 | ||||||||
\(22\) | 0.565577 | 0.120582 | ||||||||
\(23\) | −3.83267 | −0.799167 | −0.399583 | − | 0.916697i | \(-0.630845\pi\) | ||||
−0.399583 | + | 0.916697i | \(0.630845\pi\) | |||||||
\(24\) | −7.76359 | −1.58474 | ||||||||
\(25\) | −4.36069 | −0.872138 | ||||||||
\(26\) | 4.97213 | 0.975115 | ||||||||
\(27\) | 11.4159 | 2.19699 | ||||||||
\(28\) | 1.32591 | 0.250574 | ||||||||
\(29\) | 2.63271 | 0.488882 | 0.244441 | − | 0.969664i | \(-0.421396\pi\) | ||||
0.244441 | + | 0.969664i | \(0.421396\pi\) | |||||||
\(30\) | 1.77988 | 0.324960 | ||||||||
\(31\) | −3.46979 | −0.623193 | −0.311597 | − | 0.950214i | \(-0.600864\pi\) | ||||
−0.311597 | + | 0.950214i | \(0.600864\pi\) | |||||||
\(32\) | 5.84350 | 1.03299 | ||||||||
\(33\) | 2.45711 | 0.427728 | ||||||||
\(34\) | 0.715815 | 0.122761 | ||||||||
\(35\) | −0.712661 | −0.120462 | ||||||||
\(36\) | −9.92372 | −1.65395 | ||||||||
\(37\) | −0.234677 | −0.0385807 | −0.0192904 | − | 0.999814i | \(-0.506141\pi\) | ||||
−0.0192904 | + | 0.999814i | \(0.506141\pi\) | |||||||
\(38\) | −0.608965 | −0.0987872 | ||||||||
\(39\) | 21.6011 | 3.45894 | ||||||||
\(40\) | −1.99611 | −0.315613 | ||||||||
\(41\) | 5.91551 | 0.923847 | 0.461924 | − | 0.886920i | \(-0.347159\pi\) | ||||
0.461924 | + | 0.886920i | \(0.347159\pi\) | |||||||
\(42\) | −1.98409 | −0.306152 | ||||||||
\(43\) | 0.280745 | 0.0428132 | 0.0214066 | − | 0.999771i | \(-0.493186\pi\) | ||||
0.0214066 | + | 0.999771i | \(0.493186\pi\) | |||||||
\(44\) | −1.17538 | −0.177196 | ||||||||
\(45\) | 5.33387 | 0.795126 | ||||||||
\(46\) | −2.74348 | −0.404505 | ||||||||
\(47\) | −1.88384 | −0.274786 | −0.137393 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137393 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(48\) | 3.69506 | 0.533336 | ||||||||
\(49\) | −6.20557 | −0.886511 | ||||||||
\(50\) | −3.12145 | −0.441439 | ||||||||
\(51\) | 3.10981 | 0.435461 | ||||||||
\(52\) | −10.3331 | −1.43294 | ||||||||
\(53\) | 4.91196 | 0.674710 | 0.337355 | − | 0.941378i | \(-0.390468\pi\) | ||||
0.337355 | + | 0.941378i | \(0.390468\pi\) | |||||||
\(54\) | 8.17166 | 1.11202 | ||||||||
\(55\) | 0.631753 | 0.0851855 | ||||||||
\(56\) | 2.22513 | 0.297346 | ||||||||
\(57\) | −2.64561 | −0.350419 | ||||||||
\(58\) | 1.88453 | 0.247451 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −3.69895 | −0.477533 | ||||||||
\(61\) | 7.96668 | 1.02003 | 0.510014 | − | 0.860166i | \(-0.329640\pi\) | ||||
0.510014 | + | 0.860166i | \(0.329640\pi\) | |||||||
\(62\) | −2.48373 | −0.315434 | ||||||||
\(63\) | −5.94583 | −0.749105 | ||||||||
\(64\) | 1.80647 | 0.225809 | ||||||||
\(65\) | 5.55390 | 0.688876 | ||||||||
\(66\) | 1.75884 | 0.216498 | ||||||||
\(67\) | −9.09272 | −1.11085 | −0.555426 | − | 0.831566i | \(-0.687445\pi\) | ||||
−0.555426 | + | 0.831566i | \(0.687445\pi\) | |||||||
\(68\) | −1.48761 | −0.180399 | ||||||||
\(69\) | −11.9189 | −1.43486 | ||||||||
\(70\) | −0.510134 | −0.0609726 | ||||||||
\(71\) | −11.8155 | −1.40224 | −0.701122 | − | 0.713041i | \(-0.747317\pi\) | ||||
−0.701122 | + | 0.713041i | \(0.747317\pi\) | |||||||
\(72\) | −16.6539 | −1.96268 | ||||||||
\(73\) | 4.12726 | 0.483059 | 0.241529 | − | 0.970393i | \(-0.422351\pi\) | ||||
0.241529 | + | 0.970393i | \(0.422351\pi\) | |||||||
\(74\) | −0.167986 | −0.0195279 | ||||||||
\(75\) | −13.5609 | −1.56588 | ||||||||
\(76\) | 1.26555 | 0.145169 | ||||||||
\(77\) | −0.704235 | −0.0802551 | ||||||||
\(78\) | 15.4624 | 1.75077 | ||||||||
\(79\) | −4.06063 | −0.456857 | −0.228428 | − | 0.973561i | \(-0.573359\pi\) | ||||
−0.228428 | + | 0.973561i | \(0.573359\pi\) | |||||||
\(80\) | 0.950044 | 0.106218 | ||||||||
\(81\) | 15.4885 | 1.72094 | ||||||||
\(82\) | 4.23441 | 0.467613 | ||||||||
\(83\) | −10.4598 | −1.14812 | −0.574059 | − | 0.818814i | \(-0.694632\pi\) | ||||
−0.574059 | + | 0.818814i | \(0.694632\pi\) | |||||||
\(84\) | 4.12334 | 0.449893 | ||||||||
\(85\) | 0.799569 | 0.0867255 | ||||||||
\(86\) | 0.200962 | 0.0216703 | ||||||||
\(87\) | 8.18723 | 0.877763 | ||||||||
\(88\) | −1.97251 | −0.210271 | ||||||||
\(89\) | 10.6636 | 1.13034 | 0.565169 | − | 0.824975i | \(-0.308811\pi\) | ||||
0.565169 | + | 0.824975i | \(0.308811\pi\) | |||||||
\(90\) | 3.81806 | 0.402459 | ||||||||
\(91\) | −6.19111 | −0.649004 | ||||||||
\(92\) | 5.70151 | 0.594424 | ||||||||
\(93\) | −10.7904 | −1.11891 | ||||||||
\(94\) | −1.34848 | −0.139085 | ||||||||
\(95\) | −0.680217 | −0.0697888 | ||||||||
\(96\) | 18.1722 | 1.85469 | ||||||||
\(97\) | −14.6771 | −1.49024 | −0.745119 | − | 0.666932i | \(-0.767607\pi\) | ||||
−0.745119 | + | 0.666932i | \(0.767607\pi\) | |||||||
\(98\) | −4.44205 | −0.448714 | ||||||||
\(99\) | 5.27081 | 0.529736 | ||||||||
\(100\) | 6.48700 | 0.648700 | ||||||||
\(101\) | −19.4512 | −1.93546 | −0.967732 | − | 0.251980i | \(-0.918918\pi\) | ||||
−0.967732 | + | 0.251980i | \(0.918918\pi\) | |||||||
\(102\) | 2.22605 | 0.220412 | ||||||||
\(103\) | 5.50413 | 0.542338 | 0.271169 | − | 0.962532i | \(-0.412590\pi\) | ||||
0.271169 | + | 0.962532i | \(0.412590\pi\) | |||||||
\(104\) | −17.3409 | −1.70041 | ||||||||
\(105\) | −2.21624 | −0.216283 | ||||||||
\(106\) | 3.51606 | 0.341510 | ||||||||
\(107\) | −6.33435 | −0.612364 | −0.306182 | − | 0.951973i | \(-0.599052\pi\) | ||||
−0.306182 | + | 0.951973i | \(0.599052\pi\) | |||||||
\(108\) | −16.9824 | −1.63413 | ||||||||
\(109\) | 16.4229 | 1.57302 | 0.786512 | − | 0.617575i | \(-0.211885\pi\) | ||||
0.786512 | + | 0.617575i | \(0.211885\pi\) | |||||||
\(110\) | 0.452218 | 0.0431173 | ||||||||
\(111\) | −0.729802 | −0.0692698 | ||||||||
\(112\) | −1.05905 | −0.100070 | ||||||||
\(113\) | −6.31664 | −0.594219 | −0.297110 | − | 0.954843i | \(-0.596023\pi\) | ||||
−0.297110 | + | 0.954843i | \(0.596023\pi\) | |||||||
\(114\) | −1.89377 | −0.177368 | ||||||||
\(115\) | −3.06449 | −0.285765 | ||||||||
\(116\) | −3.91644 | −0.363632 | ||||||||
\(117\) | 46.3370 | 4.28385 | ||||||||
\(118\) | −0.715815 | −0.0658962 | ||||||||
\(119\) | −0.891306 | −0.0817059 | ||||||||
\(120\) | −6.20753 | −0.566667 | ||||||||
\(121\) | −10.3757 | −0.943247 | ||||||||
\(122\) | 5.70267 | 0.516295 | ||||||||
\(123\) | 18.3961 | 1.65872 | ||||||||
\(124\) | 5.16169 | 0.463534 | ||||||||
\(125\) | −7.48452 | −0.669436 | ||||||||
\(126\) | −4.25612 | −0.379165 | ||||||||
\(127\) | −15.9169 | −1.41239 | −0.706197 | − | 0.708015i | \(-0.749591\pi\) | ||||
−0.706197 | + | 0.708015i | \(0.749591\pi\) | |||||||
\(128\) | −10.3939 | −0.918699 | ||||||||
\(129\) | 0.873065 | 0.0768691 | ||||||||
\(130\) | 3.97556 | 0.348680 | ||||||||
\(131\) | −10.4847 | −0.916050 | −0.458025 | − | 0.888939i | \(-0.651443\pi\) | ||||
−0.458025 | + | 0.888939i | \(0.651443\pi\) | |||||||
\(132\) | −3.65522 | −0.318146 | ||||||||
\(133\) | 0.758260 | 0.0657495 | ||||||||
\(134\) | −6.50871 | −0.562267 | ||||||||
\(135\) | 9.12779 | 0.785595 | ||||||||
\(136\) | −2.49648 | −0.214072 | ||||||||
\(137\) | −2.36251 | −0.201843 | −0.100921 | − | 0.994894i | \(-0.532179\pi\) | ||||
−0.100921 | + | 0.994894i | \(0.532179\pi\) | |||||||
\(138\) | −8.53172 | −0.726268 | ||||||||
\(139\) | −14.6302 | −1.24091 | −0.620457 | − | 0.784241i | \(-0.713053\pi\) | ||||
−0.620457 | + | 0.784241i | \(0.713053\pi\) | |||||||
\(140\) | 1.06016 | 0.0895999 | ||||||||
\(141\) | −5.85838 | −0.493364 | ||||||||
\(142\) | −8.45773 | −0.709757 | ||||||||
\(143\) | 5.48823 | 0.458949 | ||||||||
\(144\) | 7.92636 | 0.660530 | ||||||||
\(145\) | 2.10503 | 0.174814 | ||||||||
\(146\) | 2.95435 | 0.244504 | ||||||||
\(147\) | −19.2982 | −1.59169 | ||||||||
\(148\) | 0.349108 | 0.0286965 | ||||||||
\(149\) | 0.821269 | 0.0672810 | 0.0336405 | − | 0.999434i | \(-0.489290\pi\) | ||||
0.0336405 | + | 0.999434i | \(0.489290\pi\) | |||||||
\(150\) | −9.70711 | −0.792583 | ||||||||
\(151\) | −4.59418 | −0.373869 | −0.186934 | − | 0.982372i | \(-0.559855\pi\) | ||||
−0.186934 | + | 0.982372i | \(0.559855\pi\) | |||||||
\(152\) | 2.12383 | 0.172266 | ||||||||
\(153\) | 6.67092 | 0.539312 | ||||||||
\(154\) | −0.504103 | −0.0406217 | ||||||||
\(155\) | −2.77434 | −0.222840 | ||||||||
\(156\) | −32.1340 | −2.57278 | ||||||||
\(157\) | 14.9689 | 1.19465 | 0.597325 | − | 0.801999i | \(-0.296230\pi\) | ||||
0.597325 | + | 0.801999i | \(0.296230\pi\) | |||||||
\(158\) | −2.90666 | −0.231242 | ||||||||
\(159\) | 15.2753 | 1.21141 | ||||||||
\(160\) | 4.67228 | 0.369376 | ||||||||
\(161\) | 3.41608 | 0.269225 | ||||||||
\(162\) | 11.0869 | 0.871067 | ||||||||
\(163\) | 15.3919 | 1.20559 | 0.602794 | − | 0.797897i | \(-0.294054\pi\) | ||||
0.602794 | + | 0.797897i | \(0.294054\pi\) | |||||||
\(164\) | −8.79996 | −0.687161 | ||||||||
\(165\) | 1.96463 | 0.152946 | ||||||||
\(166\) | −7.48732 | −0.581129 | ||||||||
\(167\) | 17.0407 | 1.31865 | 0.659326 | − | 0.751857i | \(-0.270842\pi\) | ||||
0.659326 | + | 0.751857i | \(0.270842\pi\) | |||||||
\(168\) | 6.91974 | 0.533869 | ||||||||
\(169\) | 35.2484 | 2.71142 | ||||||||
\(170\) | 0.572344 | 0.0438968 | ||||||||
\(171\) | −5.67515 | −0.433990 | ||||||||
\(172\) | −0.417639 | −0.0318447 | ||||||||
\(173\) | 15.9730 | 1.21441 | 0.607203 | − | 0.794547i | \(-0.292292\pi\) | ||||
0.607203 | + | 0.794547i | \(0.292292\pi\) | |||||||
\(174\) | 5.86054 | 0.444287 | ||||||||
\(175\) | 3.88671 | 0.293807 | ||||||||
\(176\) | 0.938812 | 0.0707656 | ||||||||
\(177\) | −3.10981 | −0.233748 | ||||||||
\(178\) | 7.63315 | 0.572129 | ||||||||
\(179\) | −7.27446 | −0.543719 | −0.271859 | − | 0.962337i | \(-0.587639\pi\) | ||||
−0.271859 | + | 0.962337i | \(0.587639\pi\) | |||||||
\(180\) | −7.93470 | −0.591418 | ||||||||
\(181\) | −16.4972 | −1.22623 | −0.613114 | − | 0.789994i | \(-0.710083\pi\) | ||||
−0.613114 | + | 0.789994i | \(0.710083\pi\) | |||||||
\(182\) | −4.43169 | −0.328499 | ||||||||
\(183\) | 24.7749 | 1.83141 | ||||||||
\(184\) | 9.56820 | 0.705377 | ||||||||
\(185\) | −0.187641 | −0.0137956 | ||||||||
\(186\) | −7.72394 | −0.566347 | ||||||||
\(187\) | 0.790116 | 0.0577790 | ||||||||
\(188\) | 2.80241 | 0.204387 | ||||||||
\(189\) | −10.1750 | −0.740125 | ||||||||
\(190\) | −0.486910 | −0.0353242 | ||||||||
\(191\) | 20.4131 | 1.47704 | 0.738520 | − | 0.674232i | \(-0.235525\pi\) | ||||
0.738520 | + | 0.674232i | \(0.235525\pi\) | |||||||
\(192\) | 5.61780 | 0.405429 | ||||||||
\(193\) | 15.0468 | 1.08309 | 0.541545 | − | 0.840672i | \(-0.317840\pi\) | ||||
0.541545 | + | 0.840672i | \(0.317840\pi\) | |||||||
\(194\) | −10.5061 | −0.754295 | ||||||||
\(195\) | 17.2716 | 1.23684 | ||||||||
\(196\) | 9.23146 | 0.659390 | ||||||||
\(197\) | −23.3199 | −1.66148 | −0.830738 | − | 0.556664i | \(-0.812081\pi\) | ||||
−0.830738 | + | 0.556664i | \(0.812081\pi\) | |||||||
\(198\) | 3.77292 | 0.268130 | ||||||||
\(199\) | −1.36639 | −0.0968607 | −0.0484303 | − | 0.998827i | \(-0.515422\pi\) | ||||
−0.0484303 | + | 0.998827i | \(0.515422\pi\) | |||||||
\(200\) | 10.8864 | 0.769784 | ||||||||
\(201\) | −28.2766 | −1.99448 | ||||||||
\(202\) | −13.9235 | −0.979651 | ||||||||
\(203\) | −2.34655 | −0.164695 | ||||||||
\(204\) | −4.62618 | −0.323897 | ||||||||
\(205\) | 4.72986 | 0.330348 | ||||||||
\(206\) | 3.93994 | 0.274509 | ||||||||
\(207\) | −25.5674 | −1.77706 | ||||||||
\(208\) | 8.25333 | 0.572266 | ||||||||
\(209\) | −0.672175 | −0.0464953 | ||||||||
\(210\) | −1.58642 | −0.109473 | ||||||||
\(211\) | −12.4662 | −0.858207 | −0.429103 | − | 0.903255i | \(-0.641170\pi\) | ||||
−0.429103 | + | 0.903255i | \(0.641170\pi\) | |||||||
\(212\) | −7.30707 | −0.501852 | ||||||||
\(213\) | −36.7440 | −2.51766 | ||||||||
\(214\) | −4.53422 | −0.309953 | ||||||||
\(215\) | 0.224475 | 0.0153091 | ||||||||
\(216\) | −28.4996 | −1.93915 | ||||||||
\(217\) | 3.09265 | 0.209943 | ||||||||
\(218\) | 11.7557 | 0.796199 | ||||||||
\(219\) | 12.8350 | 0.867308 | ||||||||
\(220\) | −0.939801 | −0.0633613 | ||||||||
\(221\) | 6.94611 | 0.467246 | ||||||||
\(222\) | −0.522404 | −0.0350614 | ||||||||
\(223\) | 5.64293 | 0.377878 | 0.188939 | − | 0.981989i | \(-0.439495\pi\) | ||||
0.188939 | + | 0.981989i | \(0.439495\pi\) | |||||||
\(224\) | −5.20834 | −0.347997 | ||||||||
\(225\) | −29.0898 | −1.93932 | ||||||||
\(226\) | −4.52155 | −0.300769 | ||||||||
\(227\) | 12.7965 | 0.849336 | 0.424668 | − | 0.905349i | \(-0.360391\pi\) | ||||
0.424668 | + | 0.905349i | \(0.360391\pi\) | |||||||
\(228\) | 3.93563 | 0.260643 | ||||||||
\(229\) | 2.45284 | 0.162088 | 0.0810442 | − | 0.996711i | \(-0.474174\pi\) | ||||
0.0810442 | + | 0.996711i | \(0.474174\pi\) | |||||||
\(230\) | −2.19361 | −0.144642 | ||||||||
\(231\) | −2.19004 | −0.144094 | ||||||||
\(232\) | −6.57252 | −0.431507 | ||||||||
\(233\) | 3.71566 | 0.243421 | 0.121711 | − | 0.992566i | \(-0.461162\pi\) | ||||
0.121711 | + | 0.992566i | \(0.461162\pi\) | |||||||
\(234\) | 33.1687 | 2.16831 | ||||||||
\(235\) | −1.50626 | −0.0982575 | ||||||||
\(236\) | 1.48761 | 0.0968350 | ||||||||
\(237\) | −12.6278 | −0.820264 | ||||||||
\(238\) | −0.638011 | −0.0413561 | ||||||||
\(239\) | 26.8098 | 1.73418 | 0.867092 | − | 0.498148i | \(-0.165987\pi\) | ||||
0.867092 | + | 0.498148i | \(0.165987\pi\) | |||||||
\(240\) | 2.95446 | 0.190709 | ||||||||
\(241\) | −27.6081 | −1.77839 | −0.889197 | − | 0.457524i | \(-0.848736\pi\) | ||||
−0.889197 | + | 0.457524i | \(0.848736\pi\) | |||||||
\(242\) | −7.42710 | −0.477432 | ||||||||
\(243\) | 13.9185 | 0.892874 | ||||||||
\(244\) | −11.8513 | −0.758701 | ||||||||
\(245\) | −4.96179 | −0.316997 | ||||||||
\(246\) | 13.1682 | 0.839575 | ||||||||
\(247\) | −5.90926 | −0.375997 | ||||||||
\(248\) | 8.66228 | 0.550056 | ||||||||
\(249\) | −32.5281 | −2.06139 | ||||||||
\(250\) | −5.35753 | −0.338840 | ||||||||
\(251\) | 14.1831 | 0.895230 | 0.447615 | − | 0.894226i | \(-0.352274\pi\) | ||||
0.447615 | + | 0.894226i | \(0.352274\pi\) | |||||||
\(252\) | 8.84507 | 0.557187 | ||||||||
\(253\) | −3.02825 | −0.190385 | ||||||||
\(254\) | −11.3935 | −0.714894 | ||||||||
\(255\) | 2.48651 | 0.155711 | ||||||||
\(256\) | −11.0531 | −0.690816 | ||||||||
\(257\) | 3.78188 | 0.235907 | 0.117954 | − | 0.993019i | \(-0.462367\pi\) | ||||
0.117954 | + | 0.993019i | \(0.462367\pi\) | |||||||
\(258\) | 0.624953 | 0.0389079 | ||||||||
\(259\) | 0.209169 | 0.0129971 | ||||||||
\(260\) | −8.26202 | −0.512389 | ||||||||
\(261\) | 17.5626 | 1.08710 | ||||||||
\(262\) | −7.50509 | −0.463666 | ||||||||
\(263\) | 4.18224 | 0.257888 | 0.128944 | − | 0.991652i | \(-0.458841\pi\) | ||||
0.128944 | + | 0.991652i | \(0.458841\pi\) | |||||||
\(264\) | −6.13414 | −0.377530 | ||||||||
\(265\) | 3.92745 | 0.241262 | ||||||||
\(266\) | 0.542774 | 0.0332796 | ||||||||
\(267\) | 33.1617 | 2.02946 | ||||||||
\(268\) | 13.5264 | 0.826256 | ||||||||
\(269\) | 20.4299 | 1.24563 | 0.622815 | − | 0.782369i | \(-0.285989\pi\) | ||||
0.622815 | + | 0.782369i | \(0.285989\pi\) | |||||||
\(270\) | 6.53381 | 0.397635 | ||||||||
\(271\) | 7.62188 | 0.462996 | 0.231498 | − | 0.972835i | \(-0.425637\pi\) | ||||
0.231498 | + | 0.972835i | \(0.425637\pi\) | |||||||
\(272\) | 1.18819 | 0.0720449 | ||||||||
\(273\) | −19.2532 | −1.16526 | ||||||||
\(274\) | −1.69112 | −0.102164 | ||||||||
\(275\) | −3.44545 | −0.207769 | ||||||||
\(276\) | 17.7306 | 1.06726 | ||||||||
\(277\) | 14.2686 | 0.857316 | 0.428658 | − | 0.903467i | \(-0.358986\pi\) | ||||
0.428658 | + | 0.903467i | \(0.358986\pi\) | |||||||
\(278\) | −10.4725 | −0.628098 | ||||||||
\(279\) | −23.1467 | −1.38576 | ||||||||
\(280\) | 1.77915 | 0.106324 | ||||||||
\(281\) | 9.32831 | 0.556480 | 0.278240 | − | 0.960512i | \(-0.410249\pi\) | ||||
0.278240 | + | 0.960512i | \(0.410249\pi\) | |||||||
\(282\) | −4.19352 | −0.249720 | ||||||||
\(283\) | 2.42555 | 0.144184 | 0.0720920 | − | 0.997398i | \(-0.477032\pi\) | ||||
0.0720920 | + | 0.997398i | \(0.477032\pi\) | |||||||
\(284\) | 17.5769 | 1.04299 | ||||||||
\(285\) | −2.11535 | −0.125302 | ||||||||
\(286\) | 3.92856 | 0.232301 | ||||||||
\(287\) | −5.27253 | −0.311228 | ||||||||
\(288\) | 38.9815 | 2.29701 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.50682 | 0.0884833 | ||||||||
\(291\) | −45.6431 | −2.67565 | ||||||||
\(292\) | −6.13974 | −0.359301 | ||||||||
\(293\) | −21.7269 | −1.26930 | −0.634651 | − | 0.772799i | \(-0.718856\pi\) | ||||
−0.634651 | + | 0.772799i | \(0.718856\pi\) | |||||||
\(294\) | −13.8139 | −0.805644 | ||||||||
\(295\) | −0.799569 | −0.0465527 | ||||||||
\(296\) | 0.585868 | 0.0340529 | ||||||||
\(297\) | 9.01987 | 0.523386 | ||||||||
\(298\) | 0.587877 | 0.0340548 | ||||||||
\(299\) | −26.6221 | −1.53960 | ||||||||
\(300\) | 20.1733 | 1.16471 | ||||||||
\(301\) | −0.250230 | −0.0144230 | ||||||||
\(302\) | −3.28858 | −0.189237 | ||||||||
\(303\) | −60.4895 | −3.47503 | ||||||||
\(304\) | −1.01083 | −0.0579752 | ||||||||
\(305\) | 6.36991 | 0.364740 | ||||||||
\(306\) | 4.77515 | 0.272977 | ||||||||
\(307\) | 6.86604 | 0.391866 | 0.195933 | − | 0.980617i | \(-0.437227\pi\) | ||||
0.195933 | + | 0.980617i | \(0.437227\pi\) | |||||||
\(308\) | 1.04763 | 0.0596940 | ||||||||
\(309\) | 17.1168 | 0.973741 | ||||||||
\(310\) | −1.98592 | −0.112792 | ||||||||
\(311\) | 15.3732 | 0.871736 | 0.435868 | − | 0.900011i | \(-0.356441\pi\) | ||||
0.435868 | + | 0.900011i | \(0.356441\pi\) | |||||||
\(312\) | −53.9268 | −3.05300 | ||||||||
\(313\) | −7.41153 | −0.418924 | −0.209462 | − | 0.977817i | \(-0.567171\pi\) | ||||
−0.209462 | + | 0.977817i | \(0.567171\pi\) | |||||||
\(314\) | 10.7150 | 0.604682 | ||||||||
\(315\) | −4.75411 | −0.267864 | ||||||||
\(316\) | 6.04063 | 0.339812 | ||||||||
\(317\) | 0.820916 | 0.0461072 | 0.0230536 | − | 0.999734i | \(-0.492661\pi\) | ||||
0.0230536 | + | 0.999734i | \(0.492661\pi\) | |||||||
\(318\) | 10.9343 | 0.613164 | ||||||||
\(319\) | 2.08015 | 0.116466 | ||||||||
\(320\) | 1.44440 | 0.0807445 | ||||||||
\(321\) | −19.6986 | −1.09947 | ||||||||
\(322\) | 2.44528 | 0.136270 | ||||||||
\(323\) | −0.850729 | −0.0473358 | ||||||||
\(324\) | −23.0408 | −1.28004 | ||||||||
\(325\) | −30.2898 | −1.68018 | ||||||||
\(326\) | 11.0178 | 0.610218 | ||||||||
\(327\) | 51.0720 | 2.82429 | ||||||||
\(328\) | −14.7680 | −0.815425 | ||||||||
\(329\) | 1.67907 | 0.0925704 | ||||||||
\(330\) | 1.40631 | 0.0774150 | ||||||||
\(331\) | −2.09064 | −0.114912 | −0.0574559 | − | 0.998348i | \(-0.518299\pi\) | ||||
−0.0574559 | + | 0.998348i | \(0.518299\pi\) | |||||||
\(332\) | 15.5602 | 0.853974 | ||||||||
\(333\) | −1.56551 | −0.0857897 | ||||||||
\(334\) | 12.1980 | 0.667446 | ||||||||
\(335\) | −7.27026 | −0.397217 | ||||||||
\(336\) | −3.29343 | −0.179671 | ||||||||
\(337\) | −23.3746 | −1.27329 | −0.636647 | − | 0.771155i | \(-0.719679\pi\) | ||||
−0.636647 | + | 0.771155i | \(0.719679\pi\) | |||||||
\(338\) | 25.2314 | 1.37241 | ||||||||
\(339\) | −19.6435 | −1.06689 | ||||||||
\(340\) | −1.18945 | −0.0645068 | ||||||||
\(341\) | −2.74154 | −0.148463 | ||||||||
\(342\) | −4.06236 | −0.219667 | ||||||||
\(343\) | 11.7702 | 0.635531 | ||||||||
\(344\) | −0.700876 | −0.0377887 | ||||||||
\(345\) | −9.52997 | −0.513076 | ||||||||
\(346\) | 11.4337 | 0.614681 | ||||||||
\(347\) | 7.25195 | 0.389305 | 0.194653 | − | 0.980872i | \(-0.437642\pi\) | ||||
0.194653 | + | 0.980872i | \(0.437642\pi\) | |||||||
\(348\) | −12.1794 | −0.652884 | ||||||||
\(349\) | −21.4735 | −1.14945 | −0.574725 | − | 0.818347i | \(-0.694891\pi\) | ||||
−0.574725 | + | 0.818347i | \(0.694891\pi\) | |||||||
\(350\) | 2.78217 | 0.148713 | ||||||||
\(351\) | 79.2959 | 4.23250 | ||||||||
\(352\) | 4.61704 | 0.246089 | ||||||||
\(353\) | 25.3164 | 1.34746 | 0.673728 | − | 0.738979i | \(-0.264692\pi\) | ||||
0.673728 | + | 0.738979i | \(0.264692\pi\) | |||||||
\(354\) | −2.22605 | −0.118313 | ||||||||
\(355\) | −9.44732 | −0.501412 | ||||||||
\(356\) | −15.8632 | −0.840749 | ||||||||
\(357\) | −2.77179 | −0.146699 | ||||||||
\(358\) | −5.20717 | −0.275207 | ||||||||
\(359\) | −2.29751 | −0.121258 | −0.0606288 | − | 0.998160i | \(-0.519311\pi\) | ||||
−0.0606288 | + | 0.998160i | \(0.519311\pi\) | |||||||
\(360\) | −13.3159 | −0.701810 | ||||||||
\(361\) | −18.2763 | −0.961908 | ||||||||
\(362\) | −11.8090 | −0.620665 | ||||||||
\(363\) | −32.2665 | −1.69355 | ||||||||
\(364\) | 9.20994 | 0.482732 | ||||||||
\(365\) | 3.30003 | 0.172731 | ||||||||
\(366\) | 17.7342 | 0.926983 | ||||||||
\(367\) | 0.940489 | 0.0490931 | 0.0245466 | − | 0.999699i | \(-0.492186\pi\) | ||||
0.0245466 | + | 0.999699i | \(0.492186\pi\) | |||||||
\(368\) | −4.55396 | −0.237391 | ||||||||
\(369\) | 39.4619 | 2.05431 | ||||||||
\(370\) | −0.134316 | −0.00698277 | ||||||||
\(371\) | −4.37806 | −0.227298 | ||||||||
\(372\) | 16.0519 | 0.832252 | ||||||||
\(373\) | −24.1158 | −1.24867 | −0.624336 | − | 0.781156i | \(-0.714630\pi\) | ||||
−0.624336 | + | 0.781156i | \(0.714630\pi\) | |||||||
\(374\) | 0.565577 | 0.0292453 | ||||||||
\(375\) | −23.2754 | −1.20194 | ||||||||
\(376\) | 4.70297 | 0.242537 | ||||||||
\(377\) | 18.2871 | 0.941833 | ||||||||
\(378\) | −7.28345 | −0.374620 | ||||||||
\(379\) | −7.43821 | −0.382075 | −0.191037 | − | 0.981583i | \(-0.561185\pi\) | ||||
−0.191037 | + | 0.981583i | \(0.561185\pi\) | |||||||
\(380\) | 1.01190 | 0.0519092 | ||||||||
\(381\) | −49.4985 | −2.53588 | ||||||||
\(382\) | 14.6120 | 0.747615 | ||||||||
\(383\) | −36.7702 | −1.87887 | −0.939435 | − | 0.342728i | \(-0.888649\pi\) | ||||
−0.939435 | + | 0.342728i | \(0.888649\pi\) | |||||||
\(384\) | −32.3230 | −1.64948 | ||||||||
\(385\) | −0.563085 | −0.0286975 | ||||||||
\(386\) | 10.7707 | 0.548214 | ||||||||
\(387\) | 1.87283 | 0.0952013 | ||||||||
\(388\) | 21.8338 | 1.10844 | ||||||||
\(389\) | 20.9619 | 1.06281 | 0.531406 | − | 0.847117i | \(-0.321664\pi\) | ||||
0.531406 | + | 0.847117i | \(0.321664\pi\) | |||||||
\(390\) | 12.3633 | 0.626038 | ||||||||
\(391\) | −3.83267 | −0.193826 | ||||||||
\(392\) | 15.4921 | 0.782470 | ||||||||
\(393\) | −32.6053 | −1.64472 | ||||||||
\(394\) | −16.6928 | −0.840969 | ||||||||
\(395\) | −3.24676 | −0.163362 | ||||||||
\(396\) | −7.84089 | −0.394020 | ||||||||
\(397\) | 31.8689 | 1.59945 | 0.799727 | − | 0.600363i | \(-0.204977\pi\) | ||||
0.799727 | + | 0.600363i | \(0.204977\pi\) | |||||||
\(398\) | −0.978082 | −0.0490268 | ||||||||
\(399\) | 2.35805 | 0.118050 | ||||||||
\(400\) | −5.18135 | −0.259067 | ||||||||
\(401\) | 20.2974 | 1.01360 | 0.506802 | − | 0.862062i | \(-0.330827\pi\) | ||||
0.506802 | + | 0.862062i | \(0.330827\pi\) | |||||||
\(402\) | −20.2408 | −1.00952 | ||||||||
\(403\) | −24.1016 | −1.20058 | ||||||||
\(404\) | 28.9357 | 1.43961 | ||||||||
\(405\) | 12.3841 | 0.615371 | ||||||||
\(406\) | −1.67970 | −0.0833619 | ||||||||
\(407\) | −0.185422 | −0.00919105 | ||||||||
\(408\) | −7.76359 | −0.384355 | ||||||||
\(409\) | −7.30974 | −0.361444 | −0.180722 | − | 0.983534i | \(-0.557843\pi\) | ||||
−0.180722 | + | 0.983534i | \(0.557843\pi\) | |||||||
\(410\) | 3.38571 | 0.167208 | ||||||||
\(411\) | −7.34696 | −0.362399 | ||||||||
\(412\) | −8.18799 | −0.403393 | ||||||||
\(413\) | 0.891306 | 0.0438583 | ||||||||
\(414\) | −18.3016 | −0.899473 | ||||||||
\(415\) | −8.36337 | −0.410542 | ||||||||
\(416\) | 40.5896 | 1.99007 | ||||||||
\(417\) | −45.4970 | −2.22800 | ||||||||
\(418\) | −0.481153 | −0.0235340 | ||||||||
\(419\) | 15.0943 | 0.737404 | 0.368702 | − | 0.929548i | \(-0.379802\pi\) | ||||
0.368702 | + | 0.929548i | \(0.379802\pi\) | |||||||
\(420\) | 3.29690 | 0.160872 | ||||||||
\(421\) | 25.9622 | 1.26532 | 0.632659 | − | 0.774430i | \(-0.281963\pi\) | ||||
0.632659 | + | 0.774430i | \(0.281963\pi\) | |||||||
\(422\) | −8.92348 | −0.434388 | ||||||||
\(423\) | −12.5669 | −0.611025 | ||||||||
\(424\) | −12.2626 | −0.595526 | ||||||||
\(425\) | −4.36069 | −0.211524 | ||||||||
\(426\) | −26.3019 | −1.27433 | ||||||||
\(427\) | −7.10074 | −0.343629 | ||||||||
\(428\) | 9.42303 | 0.455479 | ||||||||
\(429\) | 17.0674 | 0.824020 | ||||||||
\(430\) | 0.160683 | 0.00774882 | ||||||||
\(431\) | 25.7473 | 1.24020 | 0.620102 | − | 0.784521i | \(-0.287091\pi\) | ||||
0.620102 | + | 0.784521i | \(0.287091\pi\) | |||||||
\(432\) | 13.5643 | 0.652612 | ||||||||
\(433\) | −3.64574 | −0.175203 | −0.0876015 | − | 0.996156i | \(-0.527920\pi\) | ||||
−0.0876015 | + | 0.996156i | \(0.527920\pi\) | |||||||
\(434\) | 2.21376 | 0.106264 | ||||||||
\(435\) | 6.54626 | 0.313869 | ||||||||
\(436\) | −24.4308 | −1.17002 | ||||||||
\(437\) | 3.26056 | 0.155974 | ||||||||
\(438\) | 9.18749 | 0.438995 | ||||||||
\(439\) | 15.6504 | 0.746953 | 0.373477 | − | 0.927640i | \(-0.378166\pi\) | ||||
0.373477 | + | 0.927640i | \(0.378166\pi\) | |||||||
\(440\) | −1.57716 | −0.0751882 | ||||||||
\(441\) | −41.3969 | −1.97128 | ||||||||
\(442\) | 4.97213 | 0.236500 | ||||||||
\(443\) | 5.49462 | 0.261057 | 0.130529 | − | 0.991445i | \(-0.458333\pi\) | ||||
0.130529 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(444\) | 1.08566 | 0.0515231 | ||||||||
\(445\) | 8.52627 | 0.404184 | ||||||||
\(446\) | 4.03929 | 0.191266 | ||||||||
\(447\) | 2.55399 | 0.120800 | ||||||||
\(448\) | −1.61012 | −0.0760711 | ||||||||
\(449\) | 25.1710 | 1.18789 | 0.593945 | − | 0.804505i | \(-0.297570\pi\) | ||||
0.593945 | + | 0.804505i | \(0.297570\pi\) | |||||||
\(450\) | −20.8229 | −0.981603 | ||||||||
\(451\) | 4.67394 | 0.220087 | ||||||||
\(452\) | 9.39668 | 0.441983 | ||||||||
\(453\) | −14.2870 | −0.671263 | ||||||||
\(454\) | 9.15996 | 0.429898 | ||||||||
\(455\) | −4.95022 | −0.232070 | ||||||||
\(456\) | 6.60472 | 0.309294 | ||||||||
\(457\) | −24.9340 | −1.16636 | −0.583182 | − | 0.812342i | \(-0.698192\pi\) | ||||
−0.583182 | + | 0.812342i | \(0.698192\pi\) | |||||||
\(458\) | 1.75578 | 0.0820424 | ||||||||
\(459\) | 11.4159 | 0.532848 | ||||||||
\(460\) | 4.55875 | 0.212553 | ||||||||
\(461\) | −1.34109 | −0.0624607 | −0.0312303 | − | 0.999512i | \(-0.509943\pi\) | ||||
−0.0312303 | + | 0.999512i | \(0.509943\pi\) | |||||||
\(462\) | −1.56766 | −0.0729343 | ||||||||
\(463\) | 22.6773 | 1.05390 | 0.526952 | − | 0.849895i | \(-0.323335\pi\) | ||||
0.526952 | + | 0.849895i | \(0.323335\pi\) | |||||||
\(464\) | 3.12817 | 0.145222 | ||||||||
\(465\) | −8.62768 | −0.400099 | ||||||||
\(466\) | 2.65973 | 0.123210 | ||||||||
\(467\) | −13.0318 | −0.603039 | −0.301520 | − | 0.953460i | \(-0.597494\pi\) | ||||
−0.301520 | + | 0.953460i | \(0.597494\pi\) | |||||||
\(468\) | −68.9313 | −3.18635 | ||||||||
\(469\) | 8.10439 | 0.374226 | ||||||||
\(470\) | −1.07820 | −0.0497338 | ||||||||
\(471\) | 46.5505 | 2.14494 | ||||||||
\(472\) | 2.49648 | 0.114910 | ||||||||
\(473\) | 0.221821 | 0.0101994 | ||||||||
\(474\) | −9.03917 | −0.415183 | ||||||||
\(475\) | 3.70977 | 0.170216 | ||||||||
\(476\) | 1.32591 | 0.0607732 | ||||||||
\(477\) | 32.7673 | 1.50031 | ||||||||
\(478\) | 19.1909 | 0.877771 | ||||||||
\(479\) | 7.68206 | 0.351003 | 0.175501 | − | 0.984479i | \(-0.443845\pi\) | ||||
0.175501 | + | 0.984479i | \(0.443845\pi\) | |||||||
\(480\) | 14.5299 | 0.663197 | ||||||||
\(481\) | −1.63009 | −0.0743259 | ||||||||
\(482\) | −19.7623 | −0.900149 | ||||||||
\(483\) | 10.6234 | 0.483380 | ||||||||
\(484\) | 15.4350 | 0.701591 | ||||||||
\(485\) | −11.7354 | −0.532876 | ||||||||
\(486\) | 9.96310 | 0.451935 | ||||||||
\(487\) | 38.2571 | 1.73359 | 0.866797 | − | 0.498661i | \(-0.166175\pi\) | ||||
0.866797 | + | 0.498661i | \(0.166175\pi\) | |||||||
\(488\) | −19.8887 | −0.900318 | ||||||||
\(489\) | 47.8659 | 2.16457 | ||||||||
\(490\) | −3.55172 | −0.160451 | ||||||||
\(491\) | 25.5145 | 1.15145 | 0.575727 | − | 0.817642i | \(-0.304719\pi\) | ||||
0.575727 | + | 0.817642i | \(0.304719\pi\) | |||||||
\(492\) | −27.3662 | −1.23376 | ||||||||
\(493\) | 2.63271 | 0.118571 | ||||||||
\(494\) | −4.22994 | −0.190314 | ||||||||
\(495\) | 4.21437 | 0.189422 | ||||||||
\(496\) | −4.12279 | −0.185119 | ||||||||
\(497\) | 10.5312 | 0.472391 | ||||||||
\(498\) | −23.2841 | −1.04339 | ||||||||
\(499\) | 12.9521 | 0.579814 | 0.289907 | − | 0.957055i | \(-0.406376\pi\) | ||||
0.289907 | + | 0.957055i | \(0.406376\pi\) | |||||||
\(500\) | 11.1340 | 0.497929 | ||||||||
\(501\) | 52.9935 | 2.36757 | ||||||||
\(502\) | 10.1525 | 0.453128 | ||||||||
\(503\) | −35.4930 | −1.58256 | −0.791278 | − | 0.611457i | \(-0.790584\pi\) | ||||
−0.791278 | + | 0.611457i | \(0.790584\pi\) | |||||||
\(504\) | 14.8437 | 0.661190 | ||||||||
\(505\) | −15.5526 | −0.692080 | ||||||||
\(506\) | −2.16767 | −0.0963648 | ||||||||
\(507\) | 109.616 | 4.86822 | ||||||||
\(508\) | 23.6781 | 1.05054 | ||||||||
\(509\) | 12.6517 | 0.560777 | 0.280388 | − | 0.959887i | \(-0.409537\pi\) | ||||
0.280388 | + | 0.959887i | \(0.409537\pi\) | |||||||
\(510\) | 1.77988 | 0.0788145 | ||||||||
\(511\) | −3.67865 | −0.162734 | ||||||||
\(512\) | 12.8758 | 0.569037 | ||||||||
\(513\) | −9.71182 | −0.428788 | ||||||||
\(514\) | 2.70713 | 0.119406 | ||||||||
\(515\) | 4.40093 | 0.193928 | ||||||||
\(516\) | −1.29878 | −0.0571755 | ||||||||
\(517\) | −1.48845 | −0.0654620 | ||||||||
\(518\) | 0.149727 | 0.00657861 | ||||||||
\(519\) | 49.6731 | 2.18041 | ||||||||
\(520\) | −13.8652 | −0.608030 | ||||||||
\(521\) | −30.5330 | −1.33767 | −0.668837 | − | 0.743409i | \(-0.733208\pi\) | ||||
−0.668837 | + | 0.743409i | \(0.733208\pi\) | |||||||
\(522\) | 12.5716 | 0.550243 | ||||||||
\(523\) | 14.7528 | 0.645094 | 0.322547 | − | 0.946554i | \(-0.395461\pi\) | ||||
0.322547 | + | 0.946554i | \(0.395461\pi\) | |||||||
\(524\) | 15.5971 | 0.681362 | ||||||||
\(525\) | 12.0869 | 0.527517 | ||||||||
\(526\) | 2.99372 | 0.130532 | ||||||||
\(527\) | −3.46979 | −0.151147 | ||||||||
\(528\) | 2.91953 | 0.127056 | ||||||||
\(529\) | −8.31064 | −0.361332 | ||||||||
\(530\) | 2.81133 | 0.122116 | ||||||||
\(531\) | −6.67092 | −0.289493 | ||||||||
\(532\) | −1.12799 | −0.0489047 | ||||||||
\(533\) | 41.0898 | 1.77980 | ||||||||
\(534\) | 23.7377 | 1.02723 | ||||||||
\(535\) | −5.06475 | −0.218968 | ||||||||
\(536\) | 22.6998 | 0.980483 | ||||||||
\(537\) | −22.6222 | −0.976220 | ||||||||
\(538\) | 14.6240 | 0.630486 | ||||||||
\(539\) | −4.90313 | −0.211193 | ||||||||
\(540\) | −13.5786 | −0.584329 | ||||||||
\(541\) | 28.0775 | 1.20715 | 0.603573 | − | 0.797307i | \(-0.293743\pi\) | ||||
0.603573 | + | 0.797307i | \(0.293743\pi\) | |||||||
\(542\) | 5.45586 | 0.234349 | ||||||||
\(543\) | −51.3032 | −2.20163 | ||||||||
\(544\) | 5.84350 | 0.250538 | ||||||||
\(545\) | 13.1312 | 0.562479 | ||||||||
\(546\) | −13.7817 | −0.589803 | ||||||||
\(547\) | −12.7368 | −0.544585 | −0.272292 | − | 0.962215i | \(-0.587782\pi\) | ||||
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(548\) | 3.51449 | 0.150132 | ||||||||
\(549\) | 53.1451 | 2.26818 | ||||||||
\(550\) | −2.46631 | −0.105164 | ||||||||
\(551\) | −2.23972 | −0.0954154 | ||||||||
\(552\) | 29.7553 | 1.26647 | ||||||||
\(553\) | 3.61927 | 0.153907 | ||||||||
\(554\) | 10.2137 | 0.433938 | ||||||||
\(555\) | −0.583527 | −0.0247694 | ||||||||
\(556\) | 21.7639 | 0.922996 | ||||||||
\(557\) | 3.73776 | 0.158374 | 0.0791870 | − | 0.996860i | \(-0.474768\pi\) | ||||
0.0791870 | + | 0.996860i | \(0.474768\pi\) | |||||||
\(558\) | −16.5688 | −0.701413 | ||||||||
\(559\) | 1.95009 | 0.0824799 | ||||||||
\(560\) | −0.846780 | −0.0357830 | ||||||||
\(561\) | 2.45711 | 0.103739 | ||||||||
\(562\) | 6.67735 | 0.281667 | ||||||||
\(563\) | −27.4474 | −1.15677 | −0.578386 | − | 0.815763i | \(-0.696317\pi\) | ||||
−0.578386 | + | 0.815763i | \(0.696317\pi\) | |||||||
\(564\) | 8.71497 | 0.366966 | ||||||||
\(565\) | −5.05059 | −0.212480 | ||||||||
\(566\) | 1.73625 | 0.0729799 | ||||||||
\(567\) | −13.8050 | −0.579753 | ||||||||
\(568\) | 29.4972 | 1.23768 | ||||||||
\(569\) | 30.4921 | 1.27830 | 0.639148 | − | 0.769084i | \(-0.279287\pi\) | ||||
0.639148 | + | 0.769084i | \(0.279287\pi\) | |||||||
\(570\) | −1.51420 | −0.0634228 | ||||||||
\(571\) | −22.8460 | −0.956076 | −0.478038 | − | 0.878339i | \(-0.658652\pi\) | ||||
−0.478038 | + | 0.878339i | \(0.658652\pi\) | |||||||
\(572\) | −8.16434 | −0.341368 | ||||||||
\(573\) | 63.4809 | 2.65195 | ||||||||
\(574\) | −3.77416 | −0.157530 | ||||||||
\(575\) | 16.7131 | 0.696984 | ||||||||
\(576\) | 12.0509 | 0.502119 | ||||||||
\(577\) | −46.1756 | −1.92232 | −0.961158 | − | 0.275998i | \(-0.910992\pi\) | ||||
−0.961158 | + | 0.275998i | \(0.910992\pi\) | |||||||
\(578\) | 0.715815 | 0.0297740 | ||||||||
\(579\) | 46.7926 | 1.94463 | ||||||||
\(580\) | −3.13147 | −0.130027 | ||||||||
\(581\) | 9.32292 | 0.386780 | ||||||||
\(582\) | −32.6720 | −1.35430 | ||||||||
\(583\) | 3.88102 | 0.160735 | ||||||||
\(584\) | −10.3036 | −0.426367 | ||||||||
\(585\) | 37.0496 | 1.53181 | ||||||||
\(586\) | −15.5525 | −0.642467 | ||||||||
\(587\) | 9.81827 | 0.405243 | 0.202622 | − | 0.979257i | \(-0.435054\pi\) | ||||
0.202622 | + | 0.979257i | \(0.435054\pi\) | |||||||
\(588\) | 28.7081 | 1.18390 | ||||||||
\(589\) | 2.95186 | 0.121629 | ||||||||
\(590\) | −0.572344 | −0.0235630 | ||||||||
\(591\) | −72.5206 | −2.98310 | ||||||||
\(592\) | −0.278842 | −0.0114604 | ||||||||
\(593\) | −2.65979 | −0.109225 | −0.0546123 | − | 0.998508i | \(-0.517392\pi\) | ||||
−0.0546123 | + | 0.998508i | \(0.517392\pi\) | |||||||
\(594\) | 6.45656 | 0.264916 | ||||||||
\(595\) | −0.712661 | −0.0292162 | ||||||||
\(596\) | −1.22173 | −0.0500439 | ||||||||
\(597\) | −4.24921 | −0.173909 | ||||||||
\(598\) | −19.0565 | −0.779280 | ||||||||
\(599\) | 36.6206 | 1.49628 | 0.748139 | − | 0.663542i | \(-0.230948\pi\) | ||||
0.748139 | + | 0.663542i | \(0.230948\pi\) | |||||||
\(600\) | 33.8546 | 1.38211 | ||||||||
\(601\) | 15.8491 | 0.646499 | 0.323249 | − | 0.946314i | \(-0.395225\pi\) | ||||
0.323249 | + | 0.946314i | \(0.395225\pi\) | |||||||
\(602\) | −0.179118 | −0.00730032 | ||||||||
\(603\) | −60.6568 | −2.47014 | ||||||||
\(604\) | 6.83434 | 0.278085 | ||||||||
\(605\) | −8.29610 | −0.337285 | ||||||||
\(606\) | −43.2993 | −1.75891 | ||||||||
\(607\) | −10.9358 | −0.443870 | −0.221935 | − | 0.975061i | \(-0.571237\pi\) | ||||
−0.221935 | + | 0.975061i | \(0.571237\pi\) | |||||||
\(608\) | −4.97123 | −0.201610 | ||||||||
\(609\) | −7.29732 | −0.295703 | ||||||||
\(610\) | 4.55968 | 0.184616 | ||||||||
\(611\) | −13.0853 | −0.529376 | ||||||||
\(612\) | −9.92372 | −0.401143 | ||||||||
\(613\) | −12.6890 | −0.512504 | −0.256252 | − | 0.966610i | \(-0.582488\pi\) | ||||
−0.256252 | + | 0.966610i | \(0.582488\pi\) | |||||||
\(614\) | 4.91482 | 0.198346 | ||||||||
\(615\) | 14.7090 | 0.593123 | ||||||||
\(616\) | 1.75811 | 0.0708364 | ||||||||
\(617\) | 22.6233 | 0.910782 | 0.455391 | − | 0.890292i | \(-0.349500\pi\) | ||||
0.455391 | + | 0.890292i | \(0.349500\pi\) | |||||||
\(618\) | 12.2525 | 0.492867 | ||||||||
\(619\) | −44.0689 | −1.77128 | −0.885640 | − | 0.464372i | \(-0.846280\pi\) | ||||
−0.885640 | + | 0.464372i | \(0.846280\pi\) | |||||||
\(620\) | 4.12713 | 0.165750 | ||||||||
\(621\) | −43.7533 | −1.75576 | ||||||||
\(622\) | 11.0044 | 0.441236 | ||||||||
\(623\) | −9.50451 | −0.380790 | ||||||||
\(624\) | 25.6663 | 1.02747 | ||||||||
\(625\) | 15.8191 | 0.632762 | ||||||||
\(626\) | −5.30529 | −0.212042 | ||||||||
\(627\) | −2.09034 | −0.0834800 | ||||||||
\(628\) | −22.2679 | −0.888586 | ||||||||
\(629\) | −0.234677 | −0.00935720 | ||||||||
\(630\) | −3.40306 | −0.135581 | ||||||||
\(631\) | 14.9403 | 0.594763 | 0.297382 | − | 0.954759i | \(-0.403887\pi\) | ||||
0.297382 | + | 0.954759i | \(0.403887\pi\) | |||||||
\(632\) | 10.1373 | 0.403240 | ||||||||
\(633\) | −38.7674 | −1.54087 | ||||||||
\(634\) | 0.587624 | 0.0233375 | ||||||||
\(635\) | −12.7266 | −0.505041 | ||||||||
\(636\) | −22.7236 | −0.901050 | ||||||||
\(637\) | −43.1046 | −1.70787 | ||||||||
\(638\) | 1.48900 | 0.0589501 | ||||||||
\(639\) | −78.8204 | −3.11809 | ||||||||
\(640\) | −8.31064 | −0.328507 | ||||||||
\(641\) | 25.9747 | 1.02594 | 0.512969 | − | 0.858407i | \(-0.328546\pi\) | ||||
0.512969 | + | 0.858407i | \(0.328546\pi\) | |||||||
\(642\) | −14.1006 | −0.556505 | ||||||||
\(643\) | 15.9245 | 0.628003 | 0.314001 | − | 0.949423i | \(-0.398330\pi\) | ||||
0.314001 | + | 0.949423i | \(0.398330\pi\) | |||||||
\(644\) | −5.08179 | −0.200251 | ||||||||
\(645\) | 0.698076 | 0.0274867 | ||||||||
\(646\) | −0.608965 | −0.0239594 | ||||||||
\(647\) | −1.39182 | −0.0547179 | −0.0273590 | − | 0.999626i | \(-0.508710\pi\) | ||||
−0.0273590 | + | 0.999626i | \(0.508710\pi\) | |||||||
\(648\) | −38.6667 | −1.51897 | ||||||||
\(649\) | −0.790116 | −0.0310148 | ||||||||
\(650\) | −21.6819 | −0.850435 | ||||||||
\(651\) | 9.61755 | 0.376941 | ||||||||
\(652\) | −22.8971 | −0.896721 | ||||||||
\(653\) | −11.2631 | −0.440758 | −0.220379 | − | 0.975414i | \(-0.570729\pi\) | ||||
−0.220379 | + | 0.975414i | \(0.570729\pi\) | |||||||
\(654\) | 36.5581 | 1.42953 | ||||||||
\(655\) | −8.38322 | −0.327560 | ||||||||
\(656\) | 7.02878 | 0.274428 | ||||||||
\(657\) | 27.5326 | 1.07415 | ||||||||
\(658\) | 1.20191 | 0.0468552 | ||||||||
\(659\) | 32.5692 | 1.26872 | 0.634359 | − | 0.773039i | \(-0.281264\pi\) | ||||
0.634359 | + | 0.773039i | \(0.281264\pi\) | |||||||
\(660\) | −2.92260 | −0.113762 | ||||||||
\(661\) | −2.40477 | −0.0935347 | −0.0467673 | − | 0.998906i | \(-0.514892\pi\) | ||||
−0.0467673 | + | 0.998906i | \(0.514892\pi\) | |||||||
\(662\) | −1.49651 | −0.0581635 | ||||||||
\(663\) | 21.6011 | 0.838917 | ||||||||
\(664\) | 26.1128 | 1.01337 | ||||||||
\(665\) | 0.606282 | 0.0235106 | ||||||||
\(666\) | −1.12062 | −0.0434231 | ||||||||
\(667\) | −10.0903 | −0.390698 | ||||||||
\(668\) | −25.3499 | −0.980818 | ||||||||
\(669\) | 17.5484 | 0.678462 | ||||||||
\(670\) | −5.20416 | −0.201054 | ||||||||
\(671\) | 6.29460 | 0.243000 | ||||||||
\(672\) | −16.1970 | −0.624811 | ||||||||
\(673\) | 2.19677 | 0.0846794 | 0.0423397 | − | 0.999103i | \(-0.486519\pi\) | ||||
0.0423397 | + | 0.999103i | \(0.486519\pi\) | |||||||
\(674\) | −16.7319 | −0.644488 | ||||||||
\(675\) | −49.7811 | −1.91608 | ||||||||
\(676\) | −52.4359 | −2.01676 | ||||||||
\(677\) | −13.8425 | −0.532012 | −0.266006 | − | 0.963971i | \(-0.585704\pi\) | ||||
−0.266006 | + | 0.963971i | \(0.585704\pi\) | |||||||
\(678\) | −14.0612 | −0.540015 | ||||||||
\(679\) | 13.0818 | 0.502034 | ||||||||
\(680\) | −1.99611 | −0.0765474 | ||||||||
\(681\) | 39.7948 | 1.52494 | ||||||||
\(682\) | −1.96244 | −0.0751456 | ||||||||
\(683\) | −3.40731 | −0.130377 | −0.0651886 | − | 0.997873i | \(-0.520765\pi\) | ||||
−0.0651886 | + | 0.997873i | \(0.520765\pi\) | |||||||
\(684\) | 8.44240 | 0.322803 | ||||||||
\(685\) | −1.88899 | −0.0721746 | ||||||||
\(686\) | 8.42529 | 0.321679 | ||||||||
\(687\) | 7.62788 | 0.291022 | ||||||||
\(688\) | 0.333580 | 0.0127176 | ||||||||
\(689\) | 34.1190 | 1.29983 | ||||||||
\(690\) | −6.82170 | −0.259698 | ||||||||
\(691\) | 5.80499 | 0.220832 | 0.110416 | − | 0.993885i | \(-0.464782\pi\) | ||||
0.110416 | + | 0.993885i | \(0.464782\pi\) | |||||||
\(692\) | −23.7616 | −0.903280 | ||||||||
\(693\) | −4.69790 | −0.178458 | ||||||||
\(694\) | 5.19106 | 0.197050 | ||||||||
\(695\) | −11.6978 | −0.443724 | ||||||||
\(696\) | −20.4393 | −0.774749 | ||||||||
\(697\) | 5.91551 | 0.224066 | ||||||||
\(698\) | −15.3711 | −0.581803 | ||||||||
\(699\) | 11.5550 | 0.437051 | ||||||||
\(700\) | −5.78190 | −0.218535 | ||||||||
\(701\) | −50.8512 | −1.92062 | −0.960311 | − | 0.278931i | \(-0.910020\pi\) | ||||
−0.960311 | + | 0.278931i | \(0.910020\pi\) | |||||||
\(702\) | 56.7613 | 2.14232 | ||||||||
\(703\) | 0.199647 | 0.00752983 | ||||||||
\(704\) | 1.42733 | 0.0537943 | ||||||||
\(705\) | −4.68418 | −0.176416 | ||||||||
\(706\) | 18.1219 | 0.682026 | ||||||||
\(707\) | 17.3370 | 0.652023 | ||||||||
\(708\) | 4.62618 | 0.173863 | ||||||||
\(709\) | −28.8897 | −1.08498 | −0.542488 | − | 0.840064i | \(-0.682518\pi\) | ||||
−0.542488 | + | 0.840064i | \(0.682518\pi\) | |||||||
\(710\) | −6.76254 | −0.253794 | ||||||||
\(711\) | −27.0882 | −1.01589 | ||||||||
\(712\) | −26.6215 | −0.997681 | ||||||||
\(713\) | 13.2986 | 0.498035 | ||||||||
\(714\) | −1.98409 | −0.0742528 | ||||||||
\(715\) | 4.38822 | 0.164110 | ||||||||
\(716\) | 10.8215 | 0.404420 | ||||||||
\(717\) | 83.3735 | 3.11364 | ||||||||
\(718\) | −1.64459 | −0.0613755 | ||||||||
\(719\) | −2.32635 | −0.0867583 | −0.0433792 | − | 0.999059i | \(-0.513812\pi\) | ||||
−0.0433792 | + | 0.999059i | \(0.513812\pi\) | |||||||
\(720\) | 6.33767 | 0.236191 | ||||||||
\(721\) | −4.90586 | −0.182704 | ||||||||
\(722\) | −13.0824 | −0.486878 | ||||||||
\(723\) | −85.8560 | −3.19302 | ||||||||
\(724\) | 24.5414 | 0.912073 | ||||||||
\(725\) | −11.4804 | −0.426372 | ||||||||
\(726\) | −23.0969 | −0.857205 | ||||||||
\(727\) | −12.0056 | −0.445261 | −0.222631 | − | 0.974903i | \(-0.571464\pi\) | ||||
−0.222631 | + | 0.974903i | \(0.571464\pi\) | |||||||
\(728\) | 15.4560 | 0.572838 | ||||||||
\(729\) | −3.18138 | −0.117829 | ||||||||
\(730\) | 2.36221 | 0.0874294 | ||||||||
\(731\) | 0.280745 | 0.0103837 | ||||||||
\(732\) | −36.8553 | −1.36221 | ||||||||
\(733\) | −8.13720 | −0.300554 | −0.150277 | − | 0.988644i | \(-0.548017\pi\) | ||||
−0.150277 | + | 0.988644i | \(0.548017\pi\) | |||||||
\(734\) | 0.673216 | 0.0248489 | ||||||||
\(735\) | −15.4302 | −0.569152 | ||||||||
\(736\) | −22.3962 | −0.825535 | ||||||||
\(737\) | −7.18430 | −0.264637 | ||||||||
\(738\) | 28.2474 | 1.03980 | ||||||||
\(739\) | −41.8009 | −1.53767 | −0.768835 | − | 0.639447i | \(-0.779163\pi\) | ||||
−0.768835 | + | 0.639447i | \(0.779163\pi\) | |||||||
\(740\) | 0.279136 | 0.0102612 | ||||||||
\(741\) | −18.3767 | −0.675084 | ||||||||
\(742\) | −3.13388 | −0.115048 | ||||||||
\(743\) | −36.1795 | −1.32730 | −0.663648 | − | 0.748045i | \(-0.730993\pi\) | ||||
−0.663648 | + | 0.748045i | \(0.730993\pi\) | |||||||
\(744\) | 26.9381 | 0.987597 | ||||||||
\(745\) | 0.656662 | 0.0240582 | ||||||||
\(746\) | −17.2625 | −0.632025 | ||||||||
\(747\) | −69.7768 | −2.55300 | ||||||||
\(748\) | −1.17538 | −0.0429763 | ||||||||
\(749\) | 5.64584 | 0.206295 | ||||||||
\(750\) | −16.6609 | −0.608371 | ||||||||
\(751\) | 45.4698 | 1.65922 | 0.829608 | − | 0.558346i | \(-0.188564\pi\) | ||||
0.829608 | + | 0.558346i | \(0.188564\pi\) | |||||||
\(752\) | −2.23837 | −0.0816248 | ||||||||
\(753\) | 44.1068 | 1.60734 | ||||||||
\(754\) | 13.0902 | 0.476716 | ||||||||
\(755\) | −3.67336 | −0.133687 | ||||||||
\(756\) | 15.1365 | 0.550508 | ||||||||
\(757\) | 42.3508 | 1.53926 | 0.769632 | − | 0.638488i | \(-0.220440\pi\) | ||||
0.769632 | + | 0.638488i | \(0.220440\pi\) | |||||||
\(758\) | −5.32438 | −0.193390 | ||||||||
\(759\) | −9.41730 | −0.341826 | ||||||||
\(760\) | 1.69815 | 0.0615984 | ||||||||
\(761\) | −18.6990 | −0.677838 | −0.338919 | − | 0.940816i | \(-0.610061\pi\) | ||||
−0.338919 | + | 0.940816i | \(0.610061\pi\) | |||||||
\(762\) | −35.4318 | −1.28356 | ||||||||
\(763\) | −14.6378 | −0.529923 | ||||||||
\(764\) | −30.3667 | −1.09863 | ||||||||
\(765\) | 5.33387 | 0.192846 | ||||||||
\(766\) | −26.3207 | −0.951005 | ||||||||
\(767\) | −6.94611 | −0.250809 | ||||||||
\(768\) | −34.3729 | −1.24033 | ||||||||
\(769\) | −7.99058 | −0.288148 | −0.144074 | − | 0.989567i | \(-0.546020\pi\) | ||||
−0.144074 | + | 0.989567i | \(0.546020\pi\) | |||||||
\(770\) | −0.403065 | −0.0145255 | ||||||||
\(771\) | 11.7609 | 0.423560 | ||||||||
\(772\) | −22.3837 | −0.805607 | ||||||||
\(773\) | 35.8990 | 1.29120 | 0.645599 | − | 0.763677i | \(-0.276608\pi\) | ||||
0.645599 | + | 0.763677i | \(0.276608\pi\) | |||||||
\(774\) | 1.34060 | 0.0481869 | ||||||||
\(775\) | 15.1307 | 0.543510 | ||||||||
\(776\) | 36.6412 | 1.31534 | ||||||||
\(777\) | 0.650477 | 0.0233357 | ||||||||
\(778\) | 15.0049 | 0.537951 | ||||||||
\(779\) | −5.03250 | −0.180308 | ||||||||
\(780\) | −25.6933 | −0.919969 | ||||||||
\(781\) | −9.33563 | −0.334055 | ||||||||
\(782\) | −2.74348 | −0.0981068 | ||||||||
\(783\) | 30.0547 | 1.07407 | ||||||||
\(784\) | −7.37343 | −0.263337 | ||||||||
\(785\) | 11.9687 | 0.427181 | ||||||||
\(786\) | −23.3394 | −0.832489 | ||||||||
\(787\) | −34.7580 | −1.23899 | −0.619494 | − | 0.785002i | \(-0.712662\pi\) | ||||
−0.619494 | + | 0.785002i | \(0.712662\pi\) | |||||||
\(788\) | 34.6909 | 1.23581 | ||||||||
\(789\) | 13.0060 | 0.463026 | ||||||||
\(790\) | −2.32408 | −0.0826870 | ||||||||
\(791\) | 5.63005 | 0.200182 | ||||||||
\(792\) | −13.1585 | −0.467566 | ||||||||
\(793\) | 55.3374 | 1.96509 | ||||||||
\(794\) | 22.8123 | 0.809577 | ||||||||
\(795\) | 12.2136 | 0.433173 | ||||||||
\(796\) | 2.03265 | 0.0720454 | ||||||||
\(797\) | −48.4969 | −1.71785 | −0.858925 | − | 0.512102i | \(-0.828867\pi\) | ||||
−0.858925 | + | 0.512102i | \(0.828867\pi\) | |||||||
\(798\) | 1.68793 | 0.0597519 | ||||||||
\(799\) | −1.88384 | −0.0666454 | ||||||||
\(800\) | −25.4817 | −0.900913 | ||||||||
\(801\) | 71.1359 | 2.51346 | ||||||||
\(802\) | 14.5292 | 0.513044 | ||||||||
\(803\) | 3.26101 | 0.115079 | ||||||||
\(804\) | 42.0645 | 1.48350 | ||||||||
\(805\) | 2.73139 | 0.0962690 | ||||||||
\(806\) | −17.2523 | −0.607685 | ||||||||
\(807\) | 63.5330 | 2.23647 | ||||||||
\(808\) | 48.5596 | 1.70832 | ||||||||
\(809\) | 17.0653 | 0.599985 | 0.299992 | − | 0.953942i | \(-0.403016\pi\) | ||||
0.299992 | + | 0.953942i | \(0.403016\pi\) | |||||||
\(810\) | 8.86473 | 0.311475 | ||||||||
\(811\) | −27.7125 | −0.973119 | −0.486559 | − | 0.873648i | \(-0.661748\pi\) | ||||
−0.486559 | + | 0.873648i | \(0.661748\pi\) | |||||||
\(812\) | 3.49075 | 0.122501 | ||||||||
\(813\) | 23.7026 | 0.831286 | ||||||||
\(814\) | −0.132728 | −0.00465212 | ||||||||
\(815\) | 12.3069 | 0.431092 | ||||||||
\(816\) | 3.69506 | 0.129353 | ||||||||
\(817\) | −0.238838 | −0.00835589 | ||||||||
\(818\) | −5.23243 | −0.182948 | ||||||||
\(819\) | −41.3004 | −1.44315 | ||||||||
\(820\) | −7.03618 | −0.245714 | ||||||||
\(821\) | −2.90597 | −0.101419 | −0.0507095 | − | 0.998713i | \(-0.516148\pi\) | ||||
−0.0507095 | + | 0.998713i | \(0.516148\pi\) | |||||||
\(822\) | −5.25907 | −0.183431 | ||||||||
\(823\) | 23.5490 | 0.820867 | 0.410433 | − | 0.911891i | \(-0.365377\pi\) | ||||
0.410433 | + | 0.911891i | \(0.365377\pi\) | |||||||
\(824\) | −13.7410 | −0.478689 | ||||||||
\(825\) | −10.7147 | −0.373038 | ||||||||
\(826\) | 0.638011 | 0.0221992 | ||||||||
\(827\) | 17.0705 | 0.593600 | 0.296800 | − | 0.954940i | \(-0.404080\pi\) | ||||
0.296800 | + | 0.954940i | \(0.404080\pi\) | |||||||
\(828\) | 38.0343 | 1.32178 | ||||||||
\(829\) | −33.4324 | −1.16116 | −0.580578 | − | 0.814205i | \(-0.697173\pi\) | ||||
−0.580578 | + | 0.814205i | \(0.697173\pi\) | |||||||
\(830\) | −5.98663 | −0.207799 | ||||||||
\(831\) | 44.3726 | 1.53927 | ||||||||
\(832\) | 12.5480 | 0.435023 | ||||||||
\(833\) | −6.20557 | −0.215010 | ||||||||
\(834\) | −32.5675 | −1.12772 | ||||||||
\(835\) | 13.6252 | 0.471521 | ||||||||
\(836\) | 0.999933 | 0.0345834 | ||||||||
\(837\) | −39.6107 | −1.36915 | ||||||||
\(838\) | 10.8047 | 0.373243 | ||||||||
\(839\) | −11.6884 | −0.403528 | −0.201764 | − | 0.979434i | \(-0.564667\pi\) | ||||
−0.201764 | + | 0.979434i | \(0.564667\pi\) | |||||||
\(840\) | 5.53281 | 0.190900 | ||||||||
\(841\) | −22.0688 | −0.760995 | ||||||||
\(842\) | 18.5841 | 0.640451 | ||||||||
\(843\) | 29.0093 | 0.999132 | ||||||||
\(844\) | 18.5448 | 0.638338 | ||||||||
\(845\) | 28.1836 | 0.969544 | ||||||||
\(846\) | −8.99560 | −0.309275 | ||||||||
\(847\) | 9.24794 | 0.317763 | ||||||||
\(848\) | 5.83637 | 0.200422 | ||||||||
\(849\) | 7.54300 | 0.258875 | ||||||||
\(850\) | −3.12145 | −0.107065 | ||||||||
\(851\) | 0.899441 | 0.0308324 | ||||||||
\(852\) | 54.6607 | 1.87265 | ||||||||
\(853\) | −26.8548 | −0.919490 | −0.459745 | − | 0.888051i | \(-0.652059\pi\) | ||||
−0.459745 | + | 0.888051i | \(0.652059\pi\) | |||||||
\(854\) | −5.08282 | −0.173931 | ||||||||
\(855\) | −4.53768 | −0.155185 | ||||||||
\(856\) | 15.8136 | 0.540498 | ||||||||
\(857\) | 55.1307 | 1.88323 | 0.941615 | − | 0.336692i | \(-0.109308\pi\) | ||||
0.941615 | + | 0.336692i | \(0.109308\pi\) | |||||||
\(858\) | 12.2171 | 0.417084 | ||||||||
\(859\) | 44.2264 | 1.50898 | 0.754492 | − | 0.656309i | \(-0.227883\pi\) | ||||
0.754492 | + | 0.656309i | \(0.227883\pi\) | |||||||
\(860\) | −0.333931 | −0.0113870 | ||||||||
\(861\) | −16.3966 | −0.558793 | ||||||||
\(862\) | 18.4303 | 0.627739 | ||||||||
\(863\) | 35.4084 | 1.20532 | 0.602658 | − | 0.798000i | \(-0.294108\pi\) | ||||
0.602658 | + | 0.798000i | \(0.294108\pi\) | |||||||
\(864\) | 66.7086 | 2.26947 | ||||||||
\(865\) | 12.7715 | 0.434245 | ||||||||
\(866\) | −2.60967 | −0.0886803 | ||||||||
\(867\) | 3.10981 | 0.105615 | ||||||||
\(868\) | −4.60065 | −0.156156 | ||||||||
\(869\) | −3.20837 | −0.108837 | ||||||||
\(870\) | 4.68591 | 0.158867 | ||||||||
\(871\) | −63.1590 | −2.14006 | ||||||||
\(872\) | −40.9994 | −1.38841 | ||||||||
\(873\) | −97.9100 | −3.31375 | ||||||||
\(874\) | 2.33396 | 0.0789475 | ||||||||
\(875\) | 6.67100 | 0.225521 | ||||||||
\(876\) | −19.0934 | −0.645108 | ||||||||
\(877\) | 13.6997 | 0.462607 | 0.231304 | − | 0.972882i | \(-0.425701\pi\) | ||||
0.231304 | + | 0.972882i | \(0.425701\pi\) | |||||||
\(878\) | 11.2028 | 0.378076 | ||||||||
\(879\) | −67.5667 | −2.27897 | ||||||||
\(880\) | 0.750645 | 0.0253043 | ||||||||
\(881\) | 1.46429 | 0.0493332 | 0.0246666 | − | 0.999696i | \(-0.492148\pi\) | ||||
0.0246666 | + | 0.999696i | \(0.492148\pi\) | |||||||
\(882\) | −29.6325 | −0.997780 | ||||||||
\(883\) | −4.32189 | −0.145443 | −0.0727216 | − | 0.997352i | \(-0.523168\pi\) | ||||
−0.0727216 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(884\) | −10.3331 | −0.347539 | ||||||||
\(885\) | −2.48651 | −0.0835831 | ||||||||
\(886\) | 3.93313 | 0.132136 | ||||||||
\(887\) | −35.5692 | −1.19430 | −0.597149 | − | 0.802131i | \(-0.703700\pi\) | ||||
−0.597149 | + | 0.802131i | \(0.703700\pi\) | |||||||
\(888\) | 1.82194 | 0.0611403 | ||||||||
\(889\) | 14.1868 | 0.475810 | ||||||||
\(890\) | 6.10324 | 0.204581 | ||||||||
\(891\) | 12.2377 | 0.409978 | ||||||||
\(892\) | −8.39447 | −0.281067 | ||||||||
\(893\) | 1.60264 | 0.0536302 | ||||||||
\(894\) | 1.82819 | 0.0611437 | ||||||||
\(895\) | −5.81643 | −0.194422 | ||||||||
\(896\) | 9.26413 | 0.309493 | ||||||||
\(897\) | −82.7898 | −2.76427 | ||||||||
\(898\) | 18.0178 | 0.601260 | ||||||||
\(899\) | −9.13496 | −0.304668 | ||||||||
\(900\) | 43.2743 | 1.44248 | ||||||||
\(901\) | 4.91196 | 0.163641 | ||||||||
\(902\) | 3.34568 | 0.111399 | ||||||||
\(903\) | −0.778168 | −0.0258958 | ||||||||
\(904\) | 15.7694 | 0.524482 | ||||||||
\(905\) | −13.1907 | −0.438473 | ||||||||
\(906\) | −10.2269 | −0.339765 | ||||||||
\(907\) | −57.0712 | −1.89502 | −0.947509 | − | 0.319728i | \(-0.896409\pi\) | ||||
−0.947509 | + | 0.319728i | \(0.896409\pi\) | |||||||
\(908\) | −19.0362 | −0.631740 | ||||||||
\(909\) | −129.757 | −4.30378 | ||||||||
\(910\) | −3.54344 | −0.117464 | ||||||||
\(911\) | −53.1533 | −1.76105 | −0.880524 | − | 0.474001i | \(-0.842809\pi\) | ||||
−0.880524 | + | 0.474001i | \(0.842809\pi\) | |||||||
\(912\) | −3.14350 | −0.104092 | ||||||||
\(913\) | −8.26450 | −0.273515 | ||||||||
\(914\) | −17.8481 | −0.590364 | ||||||||
\(915\) | 19.8092 | 0.654872 | ||||||||
\(916\) | −3.64887 | −0.120562 | ||||||||
\(917\) | 9.34505 | 0.308601 | ||||||||
\(918\) | 8.17166 | 0.269705 | ||||||||
\(919\) | −53.0861 | −1.75115 | −0.875574 | − | 0.483085i | \(-0.839516\pi\) | ||||
−0.875574 | + | 0.483085i | \(0.839516\pi\) | |||||||
\(920\) | 7.65044 | 0.252227 | ||||||||
\(921\) | 21.3521 | 0.703575 | ||||||||
\(922\) | −0.959971 | −0.0316150 | ||||||||
\(923\) | −82.0719 | −2.70143 | ||||||||
\(924\) | 3.25792 | 0.107178 | ||||||||
\(925\) | 1.02335 | 0.0336477 | ||||||||
\(926\) | 16.2328 | 0.533441 | ||||||||
\(927\) | 36.7176 | 1.20596 | ||||||||
\(928\) | 15.3842 | 0.505012 | ||||||||
\(929\) | 27.6780 | 0.908085 | 0.454042 | − | 0.890980i | \(-0.349982\pi\) | ||||
0.454042 | + | 0.890980i | \(0.349982\pi\) | |||||||
\(930\) | −6.17582 | −0.202513 | ||||||||
\(931\) | 5.27926 | 0.173021 | ||||||||
\(932\) | −5.52745 | −0.181058 | ||||||||
\(933\) | 47.8079 | 1.56516 | ||||||||
\(934\) | −9.32836 | −0.305233 | ||||||||
\(935\) | 0.631753 | 0.0206605 | ||||||||
\(936\) | −115.679 | −3.78110 | ||||||||
\(937\) | −59.4736 | −1.94292 | −0.971459 | − | 0.237210i | \(-0.923767\pi\) | ||||
−0.971459 | + | 0.237210i | \(0.923767\pi\) | |||||||
\(938\) | 5.80125 | 0.189417 | ||||||||
\(939\) | −23.0485 | −0.752158 | ||||||||
\(940\) | 2.24072 | 0.0730843 | ||||||||
\(941\) | 40.9723 | 1.33566 | 0.667830 | − | 0.744314i | \(-0.267223\pi\) | ||||
0.667830 | + | 0.744314i | \(0.267223\pi\) | |||||||
\(942\) | 33.3216 | 1.08568 | ||||||||
\(943\) | −22.6722 | −0.738308 | ||||||||
\(944\) | −1.18819 | −0.0386724 | ||||||||
\(945\) | −8.13565 | −0.264653 | ||||||||
\(946\) | 0.158783 | 0.00516249 | ||||||||
\(947\) | −22.1080 | −0.718413 | −0.359207 | − | 0.933258i | \(-0.616953\pi\) | ||||
−0.359207 | + | 0.933258i | \(0.616953\pi\) | |||||||
\(948\) | 18.7852 | 0.610116 | ||||||||
\(949\) | 28.6684 | 0.930615 | ||||||||
\(950\) | 2.65551 | 0.0861561 | ||||||||
\(951\) | 2.55289 | 0.0827832 | ||||||||
\(952\) | 2.22513 | 0.0721169 | ||||||||
\(953\) | 39.6897 | 1.28568 | 0.642838 | − | 0.766003i | \(-0.277757\pi\) | ||||
0.642838 | + | 0.766003i | \(0.277757\pi\) | |||||||
\(954\) | 23.4554 | 0.759395 | ||||||||
\(955\) | 16.3217 | 0.528157 | ||||||||
\(956\) | −39.8825 | −1.28989 | ||||||||
\(957\) | 6.46886 | 0.209109 | ||||||||
\(958\) | 5.49894 | 0.177663 | ||||||||
\(959\) | 2.10572 | 0.0679972 | ||||||||
\(960\) | 4.49182 | 0.144973 | ||||||||
\(961\) | −18.9605 | −0.611630 | ||||||||
\(962\) | −1.16685 | −0.0376207 | ||||||||
\(963\) | −42.2559 | −1.36168 | ||||||||
\(964\) | 41.0701 | 1.32278 | ||||||||
\(965\) | 12.0309 | 0.387289 | ||||||||
\(966\) | 7.60437 | 0.244667 | ||||||||
\(967\) | 0.779501 | 0.0250670 | 0.0125335 | − | 0.999921i | \(-0.496010\pi\) | ||||
0.0125335 | + | 0.999921i | \(0.496010\pi\) | |||||||
\(968\) | 25.9028 | 0.832548 | ||||||||
\(969\) | −2.64561 | −0.0849892 | ||||||||
\(970\) | −8.40037 | −0.269720 | ||||||||
\(971\) | −41.7108 | −1.33856 | −0.669282 | − | 0.743008i | \(-0.733398\pi\) | ||||
−0.669282 | + | 0.743008i | \(0.733398\pi\) | |||||||
\(972\) | −20.7053 | −0.664123 | ||||||||
\(973\) | 13.0399 | 0.418041 | ||||||||
\(974\) | 27.3850 | 0.877473 | ||||||||
\(975\) | −94.1956 | −3.01667 | ||||||||
\(976\) | 9.46596 | 0.302998 | ||||||||
\(977\) | 39.1788 | 1.25344 | 0.626720 | − | 0.779245i | \(-0.284397\pi\) | ||||
0.626720 | + | 0.779245i | \(0.284397\pi\) | |||||||
\(978\) | 34.2632 | 1.09562 | ||||||||
\(979\) | 8.42547 | 0.269279 | ||||||||
\(980\) | 7.38119 | 0.235784 | ||||||||
\(981\) | 109.556 | 3.49784 | ||||||||
\(982\) | 18.2637 | 0.582817 | ||||||||
\(983\) | 37.7820 | 1.20506 | 0.602530 | − | 0.798096i | \(-0.294159\pi\) | ||||
0.602530 | + | 0.798096i | \(0.294159\pi\) | |||||||
\(984\) | −45.9256 | −1.46405 | ||||||||
\(985\) | −18.6459 | −0.594108 | ||||||||
\(986\) | 1.88453 | 0.0600158 | ||||||||
\(987\) | 5.22161 | 0.166206 | ||||||||
\(988\) | 8.79066 | 0.279668 | ||||||||
\(989\) | −1.07600 | −0.0342149 | ||||||||
\(990\) | 3.01671 | 0.0958775 | ||||||||
\(991\) | 58.2792 | 1.85130 | 0.925650 | − | 0.378381i | \(-0.123519\pi\) | ||||
0.925650 | + | 0.378381i | \(0.123519\pi\) | |||||||
\(992\) | −20.2757 | −0.643755 | ||||||||
\(993\) | −6.50148 | −0.206318 | ||||||||
\(994\) | 7.53842 | 0.239104 | ||||||||
\(995\) | −1.09252 | −0.0346353 | ||||||||
\(996\) | 48.3891 | 1.53327 | ||||||||
\(997\) | 28.9808 | 0.917832 | 0.458916 | − | 0.888480i | \(-0.348238\pi\) | ||||
0.458916 | + | 0.888480i | \(0.348238\pi\) | |||||||
\(998\) | 9.27128 | 0.293477 | ||||||||
\(999\) | −2.67905 | −0.0847613 |
(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 | 1003.2.a.i.1.10 | ✓ | 18 | |
3.2 | odd | 2 | 9027.2.a.q.1.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.i.1.10 | ✓ | 18 | 1.1 | even | 1 | trivial | |
9027.2.a.q.1.9 | 18 | 3.2 | odd | 2 |