Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 10x^{5} + 7x^{4} + 27x^{3} - 15x^{2} - 20x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.49844\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 | ||||||||
\(3\) | −0.370477 | −0.213895 | −0.106947 | − | 0.994265i | \(-0.534108\pi\) | ||||
−0.106947 | + | 0.994265i | \(0.534108\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.98038 | 1.33287 | 0.666433 | − | 0.745565i | \(-0.267820\pi\) | ||||
0.666433 | + | 0.745565i | \(0.267820\pi\) | |||||||
\(6\) | 0.370477 | 0.151247 | ||||||||
\(7\) | −2.56529 | −0.969587 | −0.484794 | − | 0.874629i | \(-0.661105\pi\) | ||||
−0.484794 | + | 0.874629i | \(0.661105\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.86275 | −0.954249 | ||||||||
\(10\) | −2.98038 | −0.942478 | ||||||||
\(11\) | −5.77573 | −1.74145 | −0.870724 | − | 0.491772i | \(-0.836349\pi\) | ||||
−0.870724 | + | 0.491772i | \(0.836349\pi\) | |||||||
\(12\) | −0.370477 | −0.106947 | ||||||||
\(13\) | −0.953732 | −0.264518 | −0.132259 | − | 0.991215i | \(-0.542223\pi\) | ||||
−0.132259 | + | 0.991215i | \(0.542223\pi\) | |||||||
\(14\) | 2.56529 | 0.685602 | ||||||||
\(15\) | −1.10416 | −0.285093 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.51668 | 0.610385 | 0.305193 | − | 0.952291i | \(-0.401279\pi\) | ||||
0.305193 | + | 0.952291i | \(0.401279\pi\) | |||||||
\(18\) | 2.86275 | 0.674756 | ||||||||
\(19\) | −7.19922 | −1.65161 | −0.825807 | − | 0.563953i | \(-0.809280\pi\) | ||||
−0.825807 | + | 0.563953i | \(0.809280\pi\) | |||||||
\(20\) | 2.98038 | 0.666433 | ||||||||
\(21\) | 0.950379 | 0.207390 | ||||||||
\(22\) | 5.77573 | 1.23139 | ||||||||
\(23\) | −5.17399 | −1.07885 | −0.539426 | − | 0.842033i | \(-0.681359\pi\) | ||||
−0.539426 | + | 0.842033i | \(0.681359\pi\) | |||||||
\(24\) | 0.370477 | 0.0756233 | ||||||||
\(25\) | 3.88265 | 0.776530 | ||||||||
\(26\) | 0.953732 | 0.187042 | ||||||||
\(27\) | 2.17201 | 0.418004 | ||||||||
\(28\) | −2.56529 | −0.484794 | ||||||||
\(29\) | 4.63236 | 0.860208 | 0.430104 | − | 0.902779i | \(-0.358477\pi\) | ||||
0.430104 | + | 0.902779i | \(0.358477\pi\) | |||||||
\(30\) | 1.10416 | 0.201591 | ||||||||
\(31\) | 8.16921 | 1.46723 | 0.733617 | − | 0.679563i | \(-0.237831\pi\) | ||||
0.733617 | + | 0.679563i | \(0.237831\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.13977 | 0.372487 | ||||||||
\(34\) | −2.51668 | −0.431608 | ||||||||
\(35\) | −7.64552 | −1.29233 | ||||||||
\(36\) | −2.86275 | −0.477124 | ||||||||
\(37\) | −9.43775 | −1.55156 | −0.775778 | − | 0.631006i | \(-0.782642\pi\) | ||||
−0.775778 | + | 0.631006i | \(0.782642\pi\) | |||||||
\(38\) | 7.19922 | 1.16787 | ||||||||
\(39\) | 0.353336 | 0.0565790 | ||||||||
\(40\) | −2.98038 | −0.471239 | ||||||||
\(41\) | 2.46810 | 0.385453 | 0.192726 | − | 0.981253i | \(-0.438267\pi\) | ||||
0.192726 | + | 0.981253i | \(0.438267\pi\) | |||||||
\(42\) | −0.950379 | −0.146647 | ||||||||
\(43\) | 5.86496 | 0.894398 | 0.447199 | − | 0.894435i | \(-0.352422\pi\) | ||||
0.447199 | + | 0.894435i | \(0.352422\pi\) | |||||||
\(44\) | −5.77573 | −0.870724 | ||||||||
\(45\) | −8.53207 | −1.27189 | ||||||||
\(46\) | 5.17399 | 0.762864 | ||||||||
\(47\) | −9.50969 | −1.38713 | −0.693565 | − | 0.720394i | \(-0.743961\pi\) | ||||
−0.693565 | + | 0.720394i | \(0.743961\pi\) | |||||||
\(48\) | −0.370477 | −0.0534737 | ||||||||
\(49\) | −0.419304 | −0.0599006 | ||||||||
\(50\) | −3.88265 | −0.549089 | ||||||||
\(51\) | −0.932373 | −0.130558 | ||||||||
\(52\) | −0.953732 | −0.132259 | ||||||||
\(53\) | −7.51226 | −1.03189 | −0.515944 | − | 0.856622i | \(-0.672559\pi\) | ||||
−0.515944 | + | 0.856622i | \(0.672559\pi\) | |||||||
\(54\) | −2.17201 | −0.295573 | ||||||||
\(55\) | −17.2139 | −2.32112 | ||||||||
\(56\) | 2.56529 | 0.342801 | ||||||||
\(57\) | 2.66714 | 0.353272 | ||||||||
\(58\) | −4.63236 | −0.608259 | ||||||||
\(59\) | −1.01485 | −0.132122 | −0.0660610 | − | 0.997816i | \(-0.521043\pi\) | ||||
−0.0660610 | + | 0.997816i | \(0.521043\pi\) | |||||||
\(60\) | −1.10416 | −0.142547 | ||||||||
\(61\) | −5.86716 | −0.751212 | −0.375606 | − | 0.926779i | \(-0.622565\pi\) | ||||
−0.375606 | + | 0.926779i | \(0.622565\pi\) | |||||||
\(62\) | −8.16921 | −1.03749 | ||||||||
\(63\) | 7.34377 | 0.925228 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.84248 | −0.352566 | ||||||||
\(66\) | −2.13977 | −0.263388 | ||||||||
\(67\) | 12.1288 | 1.48177 | 0.740883 | − | 0.671634i | \(-0.234407\pi\) | ||||
0.740883 | + | 0.671634i | \(0.234407\pi\) | |||||||
\(68\) | 2.51668 | 0.305193 | ||||||||
\(69\) | 1.91685 | 0.230761 | ||||||||
\(70\) | 7.64552 | 0.913815 | ||||||||
\(71\) | −12.3537 | −1.46611 | −0.733057 | − | 0.680167i | \(-0.761907\pi\) | ||||
−0.733057 | + | 0.680167i | \(0.761907\pi\) | |||||||
\(72\) | 2.86275 | 0.337378 | ||||||||
\(73\) | 0.650878 | 0.0761795 | 0.0380897 | − | 0.999274i | \(-0.487873\pi\) | ||||
0.0380897 | + | 0.999274i | \(0.487873\pi\) | |||||||
\(74\) | 9.43775 | 1.09712 | ||||||||
\(75\) | −1.43843 | −0.166096 | ||||||||
\(76\) | −7.19922 | −0.825807 | ||||||||
\(77\) | 14.8164 | 1.68849 | ||||||||
\(78\) | −0.353336 | −0.0400074 | ||||||||
\(79\) | 15.5158 | 1.74567 | 0.872834 | − | 0.488018i | \(-0.162280\pi\) | ||||
0.872834 | + | 0.488018i | \(0.162280\pi\) | |||||||
\(80\) | 2.98038 | 0.333216 | ||||||||
\(81\) | 7.78356 | 0.864840 | ||||||||
\(82\) | −2.46810 | −0.272556 | ||||||||
\(83\) | −8.27171 | −0.907939 | −0.453969 | − | 0.891017i | \(-0.649992\pi\) | ||||
−0.453969 | + | 0.891017i | \(0.649992\pi\) | |||||||
\(84\) | 0.950379 | 0.103695 | ||||||||
\(85\) | 7.50067 | 0.813562 | ||||||||
\(86\) | −5.86496 | −0.632435 | ||||||||
\(87\) | −1.71618 | −0.183994 | ||||||||
\(88\) | 5.77573 | 0.615695 | ||||||||
\(89\) | 2.89852 | 0.307242 | 0.153621 | − | 0.988130i | \(-0.450907\pi\) | ||||
0.153621 | + | 0.988130i | \(0.450907\pi\) | |||||||
\(90\) | 8.53207 | 0.899359 | ||||||||
\(91\) | 2.44660 | 0.256473 | ||||||||
\(92\) | −5.17399 | −0.539426 | ||||||||
\(93\) | −3.02650 | −0.313834 | ||||||||
\(94\) | 9.50969 | 0.980850 | ||||||||
\(95\) | −21.4564 | −2.20138 | ||||||||
\(96\) | 0.370477 | 0.0378116 | ||||||||
\(97\) | 0.956247 | 0.0970922 | 0.0485461 | − | 0.998821i | \(-0.484541\pi\) | ||||
0.0485461 | + | 0.998821i | \(0.484541\pi\) | |||||||
\(98\) | 0.419304 | 0.0423561 | ||||||||
\(99\) | 16.5345 | 1.66178 | ||||||||
\(100\) | 3.88265 | 0.388265 | ||||||||
\(101\) | 5.92549 | 0.589608 | 0.294804 | − | 0.955558i | \(-0.404746\pi\) | ||||
0.294804 | + | 0.955558i | \(0.404746\pi\) | |||||||
\(102\) | 0.932373 | 0.0923187 | ||||||||
\(103\) | −7.57015 | −0.745909 | −0.372955 | − | 0.927850i | \(-0.621655\pi\) | ||||
−0.372955 | + | 0.927850i | \(0.621655\pi\) | |||||||
\(104\) | 0.953732 | 0.0935211 | ||||||||
\(105\) | 2.83249 | 0.276423 | ||||||||
\(106\) | 7.51226 | 0.729655 | ||||||||
\(107\) | 16.0455 | 1.55118 | 0.775589 | − | 0.631238i | \(-0.217453\pi\) | ||||
0.775589 | + | 0.631238i | \(0.217453\pi\) | |||||||
\(108\) | 2.17201 | 0.209002 | ||||||||
\(109\) | 2.50942 | 0.240359 | 0.120179 | − | 0.992752i | \(-0.461653\pi\) | ||||
0.120179 | + | 0.992752i | \(0.461653\pi\) | |||||||
\(110\) | 17.2139 | 1.64128 | ||||||||
\(111\) | 3.49647 | 0.331870 | ||||||||
\(112\) | −2.56529 | −0.242397 | ||||||||
\(113\) | −13.4589 | −1.26611 | −0.633055 | − | 0.774107i | \(-0.718199\pi\) | ||||
−0.633055 | + | 0.774107i | \(0.718199\pi\) | |||||||
\(114\) | −2.66714 | −0.249801 | ||||||||
\(115\) | −15.4205 | −1.43796 | ||||||||
\(116\) | 4.63236 | 0.430104 | ||||||||
\(117\) | 2.73029 | 0.252416 | ||||||||
\(118\) | 1.01485 | 0.0934244 | ||||||||
\(119\) | −6.45602 | −0.591822 | ||||||||
\(120\) | 1.10416 | 0.100796 | ||||||||
\(121\) | 22.3591 | 2.03264 | ||||||||
\(122\) | 5.86716 | 0.531187 | ||||||||
\(123\) | −0.914375 | −0.0824464 | ||||||||
\(124\) | 8.16921 | 0.733617 | ||||||||
\(125\) | −3.33013 | −0.297856 | ||||||||
\(126\) | −7.34377 | −0.654235 | ||||||||
\(127\) | 2.35435 | 0.208915 | 0.104458 | − | 0.994529i | \(-0.466689\pi\) | ||||
0.104458 | + | 0.994529i | \(0.466689\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.17283 | −0.191307 | ||||||||
\(130\) | 2.84248 | 0.249302 | ||||||||
\(131\) | 8.14252 | 0.711415 | 0.355708 | − | 0.934597i | \(-0.384240\pi\) | ||||
0.355708 | + | 0.934597i | \(0.384240\pi\) | |||||||
\(132\) | 2.13977 | 0.186243 | ||||||||
\(133\) | 18.4681 | 1.60138 | ||||||||
\(134\) | −12.1288 | −1.04777 | ||||||||
\(135\) | 6.47342 | 0.557143 | ||||||||
\(136\) | −2.51668 | −0.215804 | ||||||||
\(137\) | −13.5630 | −1.15876 | −0.579382 | − | 0.815056i | \(-0.696706\pi\) | ||||
−0.579382 | + | 0.815056i | \(0.696706\pi\) | |||||||
\(138\) | −1.91685 | −0.163173 | ||||||||
\(139\) | −17.6145 | −1.49405 | −0.747023 | − | 0.664798i | \(-0.768518\pi\) | ||||
−0.747023 | + | 0.664798i | \(0.768518\pi\) | |||||||
\(140\) | −7.64552 | −0.646165 | ||||||||
\(141\) | 3.52312 | 0.296700 | ||||||||
\(142\) | 12.3537 | 1.03670 | ||||||||
\(143\) | 5.50850 | 0.460644 | ||||||||
\(144\) | −2.86275 | −0.238562 | ||||||||
\(145\) | 13.8062 | 1.14654 | ||||||||
\(146\) | −0.650878 | −0.0538670 | ||||||||
\(147\) | 0.155342 | 0.0128124 | ||||||||
\(148\) | −9.43775 | −0.775778 | ||||||||
\(149\) | 4.73354 | 0.387787 | 0.193893 | − | 0.981023i | \(-0.437888\pi\) | ||||
0.193893 | + | 0.981023i | \(0.437888\pi\) | |||||||
\(150\) | 1.43843 | 0.117447 | ||||||||
\(151\) | 18.5426 | 1.50897 | 0.754486 | − | 0.656316i | \(-0.227886\pi\) | ||||
0.754486 | + | 0.656316i | \(0.227886\pi\) | |||||||
\(152\) | 7.19922 | 0.583934 | ||||||||
\(153\) | −7.20463 | −0.582460 | ||||||||
\(154\) | −14.8164 | −1.19394 | ||||||||
\(155\) | 24.3473 | 1.95562 | ||||||||
\(156\) | 0.353336 | 0.0282895 | ||||||||
\(157\) | 6.62583 | 0.528799 | 0.264399 | − | 0.964413i | \(-0.414826\pi\) | ||||
0.264399 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(158\) | −15.5158 | −1.23437 | ||||||||
\(159\) | 2.78312 | 0.220716 | ||||||||
\(160\) | −2.98038 | −0.235620 | ||||||||
\(161\) | 13.2728 | 1.04604 | ||||||||
\(162\) | −7.78356 | −0.611534 | ||||||||
\(163\) | −7.35217 | −0.575867 | −0.287933 | − | 0.957650i | \(-0.592968\pi\) | ||||
−0.287933 | + | 0.957650i | \(0.592968\pi\) | |||||||
\(164\) | 2.46810 | 0.192726 | ||||||||
\(165\) | 6.37734 | 0.496475 | ||||||||
\(166\) | 8.27171 | 0.642010 | ||||||||
\(167\) | −18.4854 | −1.43045 | −0.715223 | − | 0.698896i | \(-0.753675\pi\) | ||||
−0.715223 | + | 0.698896i | \(0.753675\pi\) | |||||||
\(168\) | −0.950379 | −0.0733234 | ||||||||
\(169\) | −12.0904 | −0.930030 | ||||||||
\(170\) | −7.50067 | −0.575275 | ||||||||
\(171\) | 20.6095 | 1.57605 | ||||||||
\(172\) | 5.86496 | 0.447199 | ||||||||
\(173\) | −15.2035 | −1.15590 | −0.577951 | − | 0.816071i | \(-0.696148\pi\) | ||||
−0.577951 | + | 0.816071i | \(0.696148\pi\) | |||||||
\(174\) | 1.71618 | 0.130103 | ||||||||
\(175\) | −9.96011 | −0.752913 | ||||||||
\(176\) | −5.77573 | −0.435362 | ||||||||
\(177\) | 0.375978 | 0.0282602 | ||||||||
\(178\) | −2.89852 | −0.217253 | ||||||||
\(179\) | −8.92937 | −0.667412 | −0.333706 | − | 0.942677i | \(-0.608299\pi\) | ||||
−0.333706 | + | 0.942677i | \(0.608299\pi\) | |||||||
\(180\) | −8.53207 | −0.635943 | ||||||||
\(181\) | 8.96265 | 0.666189 | 0.333094 | − | 0.942894i | \(-0.391907\pi\) | ||||
0.333094 | + | 0.942894i | \(0.391907\pi\) | |||||||
\(182\) | −2.44660 | −0.181354 | ||||||||
\(183\) | 2.17365 | 0.160680 | ||||||||
\(184\) | 5.17399 | 0.381432 | ||||||||
\(185\) | −28.1280 | −2.06802 | ||||||||
\(186\) | 3.02650 | 0.221914 | ||||||||
\(187\) | −14.5357 | −1.06295 | ||||||||
\(188\) | −9.50969 | −0.693565 | ||||||||
\(189\) | −5.57183 | −0.405291 | ||||||||
\(190\) | 21.4564 | 1.55661 | ||||||||
\(191\) | −2.71179 | −0.196218 | −0.0981091 | − | 0.995176i | \(-0.531279\pi\) | ||||
−0.0981091 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(192\) | −0.370477 | −0.0267369 | ||||||||
\(193\) | −10.4616 | −0.753042 | −0.376521 | − | 0.926408i | \(-0.622880\pi\) | ||||
−0.376521 | + | 0.926408i | \(0.622880\pi\) | |||||||
\(194\) | −0.956247 | −0.0686545 | ||||||||
\(195\) | 1.05307 | 0.0754122 | ||||||||
\(196\) | −0.419304 | −0.0299503 | ||||||||
\(197\) | −8.17270 | −0.582280 | −0.291140 | − | 0.956680i | \(-0.594035\pi\) | ||||
−0.291140 | + | 0.956680i | \(0.594035\pi\) | |||||||
\(198\) | −16.5345 | −1.17505 | ||||||||
\(199\) | 23.4576 | 1.66287 | 0.831433 | − | 0.555625i | \(-0.187521\pi\) | ||||
0.831433 | + | 0.555625i | \(0.187521\pi\) | |||||||
\(200\) | −3.88265 | −0.274545 | ||||||||
\(201\) | −4.49343 | −0.316942 | ||||||||
\(202\) | −5.92549 | −0.416916 | ||||||||
\(203\) | −11.8833 | −0.834047 | ||||||||
\(204\) | −0.932373 | −0.0652792 | ||||||||
\(205\) | 7.35587 | 0.513757 | ||||||||
\(206\) | 7.57015 | 0.527437 | ||||||||
\(207\) | 14.8118 | 1.02949 | ||||||||
\(208\) | −0.953732 | −0.0661294 | ||||||||
\(209\) | 41.5807 | 2.87620 | ||||||||
\(210\) | −2.83249 | −0.195460 | ||||||||
\(211\) | 23.7236 | 1.63320 | 0.816600 | − | 0.577203i | \(-0.195856\pi\) | ||||
0.816600 | + | 0.577203i | \(0.195856\pi\) | |||||||
\(212\) | −7.51226 | −0.515944 | ||||||||
\(213\) | 4.57676 | 0.313594 | ||||||||
\(214\) | −16.0455 | −1.09685 | ||||||||
\(215\) | 17.4798 | 1.19211 | ||||||||
\(216\) | −2.17201 | −0.147787 | ||||||||
\(217\) | −20.9564 | −1.42261 | ||||||||
\(218\) | −2.50942 | −0.169959 | ||||||||
\(219\) | −0.241135 | −0.0162944 | ||||||||
\(220\) | −17.2139 | −1.16056 | ||||||||
\(221\) | −2.40024 | −0.161458 | ||||||||
\(222\) | −3.49647 | −0.234667 | ||||||||
\(223\) | −4.63802 | −0.310585 | −0.155292 | − | 0.987869i | \(-0.549632\pi\) | ||||
−0.155292 | + | 0.987869i | \(0.549632\pi\) | |||||||
\(224\) | 2.56529 | 0.171400 | ||||||||
\(225\) | −11.1150 | −0.741003 | ||||||||
\(226\) | 13.4589 | 0.895274 | ||||||||
\(227\) | 2.30295 | 0.152852 | 0.0764261 | − | 0.997075i | \(-0.475649\pi\) | ||||
0.0764261 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(228\) | 2.66714 | 0.176636 | ||||||||
\(229\) | 1.98890 | 0.131430 | 0.0657150 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657150 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(230\) | 15.4205 | 1.01679 | ||||||||
\(231\) | −5.48913 | −0.361159 | ||||||||
\(232\) | −4.63236 | −0.304129 | ||||||||
\(233\) | 5.58928 | 0.366166 | 0.183083 | − | 0.983097i | \(-0.441392\pi\) | ||||
0.183083 | + | 0.983097i | \(0.441392\pi\) | |||||||
\(234\) | −2.73029 | −0.178485 | ||||||||
\(235\) | −28.3425 | −1.84886 | ||||||||
\(236\) | −1.01485 | −0.0660610 | ||||||||
\(237\) | −5.74826 | −0.373389 | ||||||||
\(238\) | 6.45602 | 0.418481 | ||||||||
\(239\) | −3.34553 | −0.216404 | −0.108202 | − | 0.994129i | \(-0.534509\pi\) | ||||
−0.108202 | + | 0.994129i | \(0.534509\pi\) | |||||||
\(240\) | −1.10416 | −0.0712733 | ||||||||
\(241\) | 26.7139 | 1.72079 | 0.860395 | − | 0.509627i | \(-0.170217\pi\) | ||||
0.860395 | + | 0.509627i | \(0.170217\pi\) | |||||||
\(242\) | −22.3591 | −1.43729 | ||||||||
\(243\) | −9.39967 | −0.602989 | ||||||||
\(244\) | −5.86716 | −0.375606 | ||||||||
\(245\) | −1.24968 | −0.0798394 | ||||||||
\(246\) | 0.914375 | 0.0582984 | ||||||||
\(247\) | 6.86613 | 0.436881 | ||||||||
\(248\) | −8.16921 | −0.518745 | ||||||||
\(249\) | 3.06448 | 0.194203 | ||||||||
\(250\) | 3.33013 | 0.210616 | ||||||||
\(251\) | −29.3076 | −1.84988 | −0.924940 | − | 0.380112i | \(-0.875885\pi\) | ||||
−0.924940 | + | 0.380112i | \(0.875885\pi\) | |||||||
\(252\) | 7.34377 | 0.462614 | ||||||||
\(253\) | 29.8836 | 1.87877 | ||||||||
\(254\) | −2.35435 | −0.147725 | ||||||||
\(255\) | −2.77882 | −0.174017 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.3803 | 0.647504 | 0.323752 | − | 0.946142i | \(-0.395056\pi\) | ||||
0.323752 | + | 0.946142i | \(0.395056\pi\) | |||||||
\(258\) | 2.17283 | 0.135275 | ||||||||
\(259\) | 24.2105 | 1.50437 | ||||||||
\(260\) | −2.84248 | −0.176283 | ||||||||
\(261\) | −13.2613 | −0.820853 | ||||||||
\(262\) | −8.14252 | −0.503046 | ||||||||
\(263\) | −8.83916 | −0.545046 | −0.272523 | − | 0.962149i | \(-0.587858\pi\) | ||||
−0.272523 | + | 0.962149i | \(0.587858\pi\) | |||||||
\(264\) | −2.13977 | −0.131694 | ||||||||
\(265\) | −22.3894 | −1.37537 | ||||||||
\(266\) | −18.4681 | −1.13235 | ||||||||
\(267\) | −1.07383 | −0.0657175 | ||||||||
\(268\) | 12.1288 | 0.740883 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | −6.47342 | −0.393960 | ||||||||
\(271\) | 7.39604 | 0.449277 | 0.224639 | − | 0.974442i | \(-0.427880\pi\) | ||||
0.224639 | + | 0.974442i | \(0.427880\pi\) | |||||||
\(272\) | 2.51668 | 0.152596 | ||||||||
\(273\) | −0.906407 | −0.0548583 | ||||||||
\(274\) | 13.5630 | 0.819370 | ||||||||
\(275\) | −22.4251 | −1.35229 | ||||||||
\(276\) | 1.91685 | 0.115381 | ||||||||
\(277\) | 13.5773 | 0.815779 | 0.407890 | − | 0.913031i | \(-0.366265\pi\) | ||||
0.407890 | + | 0.913031i | \(0.366265\pi\) | |||||||
\(278\) | 17.6145 | 1.05645 | ||||||||
\(279\) | −23.3864 | −1.40011 | ||||||||
\(280\) | 7.64552 | 0.456907 | ||||||||
\(281\) | 13.5723 | 0.809653 | 0.404826 | − | 0.914394i | \(-0.367332\pi\) | ||||
0.404826 | + | 0.914394i | \(0.367332\pi\) | |||||||
\(282\) | −3.52312 | −0.209799 | ||||||||
\(283\) | 20.5026 | 1.21875 | 0.609377 | − | 0.792880i | \(-0.291419\pi\) | ||||
0.609377 | + | 0.792880i | \(0.291419\pi\) | |||||||
\(284\) | −12.3537 | −0.733057 | ||||||||
\(285\) | 7.94909 | 0.470864 | ||||||||
\(286\) | −5.50850 | −0.325724 | ||||||||
\(287\) | −6.33139 | −0.373730 | ||||||||
\(288\) | 2.86275 | 0.168689 | ||||||||
\(289\) | −10.6663 | −0.627430 | ||||||||
\(290\) | −13.8062 | −0.810727 | ||||||||
\(291\) | −0.354267 | −0.0207675 | ||||||||
\(292\) | 0.650878 | 0.0380897 | ||||||||
\(293\) | −26.0133 | −1.51971 | −0.759857 | − | 0.650090i | \(-0.774731\pi\) | ||||
−0.759857 | + | 0.650090i | \(0.774731\pi\) | |||||||
\(294\) | −0.155342 | −0.00905976 | ||||||||
\(295\) | −3.02463 | −0.176101 | ||||||||
\(296\) | 9.43775 | 0.548558 | ||||||||
\(297\) | −12.5450 | −0.727932 | ||||||||
\(298\) | −4.73354 | −0.274207 | ||||||||
\(299\) | 4.93460 | 0.285376 | ||||||||
\(300\) | −1.43843 | −0.0830479 | ||||||||
\(301\) | −15.0453 | −0.867197 | ||||||||
\(302\) | −18.5426 | −1.06700 | ||||||||
\(303\) | −2.19526 | −0.126114 | ||||||||
\(304\) | −7.19922 | −0.412903 | ||||||||
\(305\) | −17.4863 | −1.00126 | ||||||||
\(306\) | 7.20463 | 0.411861 | ||||||||
\(307\) | −17.3993 | −0.993031 | −0.496516 | − | 0.868028i | \(-0.665387\pi\) | ||||
−0.496516 | + | 0.868028i | \(0.665387\pi\) | |||||||
\(308\) | 14.8164 | 0.844243 | ||||||||
\(309\) | 2.80457 | 0.159546 | ||||||||
\(310\) | −24.3473 | −1.38284 | ||||||||
\(311\) | −13.4740 | −0.764038 | −0.382019 | − | 0.924155i | \(-0.624771\pi\) | ||||
−0.382019 | + | 0.924155i | \(0.624771\pi\) | |||||||
\(312\) | −0.353336 | −0.0200037 | ||||||||
\(313\) | −9.89195 | −0.559126 | −0.279563 | − | 0.960127i | \(-0.590190\pi\) | ||||
−0.279563 | + | 0.960127i | \(0.590190\pi\) | |||||||
\(314\) | −6.62583 | −0.373917 | ||||||||
\(315\) | 21.8872 | 1.23320 | ||||||||
\(316\) | 15.5158 | 0.872834 | ||||||||
\(317\) | 19.2200 | 1.07950 | 0.539751 | − | 0.841825i | \(-0.318518\pi\) | ||||
0.539751 | + | 0.841825i | \(0.318518\pi\) | |||||||
\(318\) | −2.78312 | −0.156070 | ||||||||
\(319\) | −26.7553 | −1.49801 | ||||||||
\(320\) | 2.98038 | 0.166608 | ||||||||
\(321\) | −5.94449 | −0.331789 | ||||||||
\(322\) | −13.2728 | −0.739663 | ||||||||
\(323\) | −18.1182 | −1.00812 | ||||||||
\(324\) | 7.78356 | 0.432420 | ||||||||
\(325\) | −3.70301 | −0.205406 | ||||||||
\(326\) | 7.35217 | 0.407199 | ||||||||
\(327\) | −0.929682 | −0.0514115 | ||||||||
\(328\) | −2.46810 | −0.136278 | ||||||||
\(329\) | 24.3951 | 1.34494 | ||||||||
\(330\) | −6.37734 | −0.351061 | ||||||||
\(331\) | −10.6168 | −0.583550 | −0.291775 | − | 0.956487i | \(-0.594246\pi\) | ||||
−0.291775 | + | 0.956487i | \(0.594246\pi\) | |||||||
\(332\) | −8.27171 | −0.453969 | ||||||||
\(333\) | 27.0179 | 1.48057 | ||||||||
\(334\) | 18.4854 | 1.01148 | ||||||||
\(335\) | 36.1483 | 1.97499 | ||||||||
\(336\) | 0.950379 | 0.0518474 | ||||||||
\(337\) | −4.73621 | −0.257998 | −0.128999 | − | 0.991645i | \(-0.541176\pi\) | ||||
−0.128999 | + | 0.991645i | \(0.541176\pi\) | |||||||
\(338\) | 12.0904 | 0.657631 | ||||||||
\(339\) | 4.98622 | 0.270814 | ||||||||
\(340\) | 7.50067 | 0.406781 | ||||||||
\(341\) | −47.1832 | −2.55511 | ||||||||
\(342\) | −20.6095 | −1.11444 | ||||||||
\(343\) | 19.0326 | 1.02767 | ||||||||
\(344\) | −5.86496 | −0.316217 | ||||||||
\(345\) | 5.71292 | 0.307573 | ||||||||
\(346\) | 15.2035 | 0.817346 | ||||||||
\(347\) | −9.70333 | −0.520902 | −0.260451 | − | 0.965487i | \(-0.583871\pi\) | ||||
−0.260451 | + | 0.965487i | \(0.583871\pi\) | |||||||
\(348\) | −1.71618 | −0.0919971 | ||||||||
\(349\) | −34.9874 | −1.87283 | −0.936416 | − | 0.350893i | \(-0.885878\pi\) | ||||
−0.936416 | + | 0.350893i | \(0.885878\pi\) | |||||||
\(350\) | 9.96011 | 0.532390 | ||||||||
\(351\) | −2.07152 | −0.110569 | ||||||||
\(352\) | 5.77573 | 0.307847 | ||||||||
\(353\) | 17.9950 | 0.957777 | 0.478888 | − | 0.877876i | \(-0.341040\pi\) | ||||
0.478888 | + | 0.877876i | \(0.341040\pi\) | |||||||
\(354\) | −0.375978 | −0.0199830 | ||||||||
\(355\) | −36.8187 | −1.95413 | ||||||||
\(356\) | 2.89852 | 0.153621 | ||||||||
\(357\) | 2.39180 | 0.126588 | ||||||||
\(358\) | 8.92937 | 0.471932 | ||||||||
\(359\) | −8.64349 | −0.456186 | −0.228093 | − | 0.973639i | \(-0.573249\pi\) | ||||
−0.228093 | + | 0.973639i | \(0.573249\pi\) | |||||||
\(360\) | 8.53207 | 0.449679 | ||||||||
\(361\) | 32.8287 | 1.72783 | ||||||||
\(362\) | −8.96265 | −0.471067 | ||||||||
\(363\) | −8.28351 | −0.434772 | ||||||||
\(364\) | 2.44660 | 0.128236 | ||||||||
\(365\) | 1.93986 | 0.101537 | ||||||||
\(366\) | −2.17365 | −0.113618 | ||||||||
\(367\) | −25.4599 | −1.32899 | −0.664497 | − | 0.747291i | \(-0.731354\pi\) | ||||
−0.664497 | + | 0.747291i | \(0.731354\pi\) | |||||||
\(368\) | −5.17399 | −0.269713 | ||||||||
\(369\) | −7.06555 | −0.367818 | ||||||||
\(370\) | 28.1280 | 1.46231 | ||||||||
\(371\) | 19.2711 | 1.00051 | ||||||||
\(372\) | −3.02650 | −0.156917 | ||||||||
\(373\) | −5.63673 | −0.291859 | −0.145929 | − | 0.989295i | \(-0.546617\pi\) | ||||
−0.145929 | + | 0.989295i | \(0.546617\pi\) | |||||||
\(374\) | 14.5357 | 0.751622 | ||||||||
\(375\) | 1.23374 | 0.0637098 | ||||||||
\(376\) | 9.50969 | 0.490425 | ||||||||
\(377\) | −4.41803 | −0.227540 | ||||||||
\(378\) | 5.57183 | 0.286584 | ||||||||
\(379\) | −16.2741 | −0.835944 | −0.417972 | − | 0.908460i | \(-0.637259\pi\) | ||||
−0.417972 | + | 0.908460i | \(0.637259\pi\) | |||||||
\(380\) | −21.4564 | −1.10069 | ||||||||
\(381\) | −0.872233 | −0.0446859 | ||||||||
\(382\) | 2.71179 | 0.138747 | ||||||||
\(383\) | 17.3292 | 0.885483 | 0.442742 | − | 0.896649i | \(-0.354006\pi\) | ||||
0.442742 | + | 0.896649i | \(0.354006\pi\) | |||||||
\(384\) | 0.370477 | 0.0189058 | ||||||||
\(385\) | 44.1585 | 2.25052 | ||||||||
\(386\) | 10.4616 | 0.532481 | ||||||||
\(387\) | −16.7899 | −0.853478 | ||||||||
\(388\) | 0.956247 | 0.0485461 | ||||||||
\(389\) | 32.7406 | 1.66002 | 0.830008 | − | 0.557752i | \(-0.188336\pi\) | ||||
0.830008 | + | 0.557752i | \(0.188336\pi\) | |||||||
\(390\) | −1.05307 | −0.0533245 | ||||||||
\(391\) | −13.0213 | −0.658516 | ||||||||
\(392\) | 0.419304 | 0.0211781 | ||||||||
\(393\) | −3.01661 | −0.152168 | ||||||||
\(394\) | 8.17270 | 0.411734 | ||||||||
\(395\) | 46.2430 | 2.32674 | ||||||||
\(396\) | 16.5345 | 0.830888 | ||||||||
\(397\) | −10.1894 | −0.511392 | −0.255696 | − | 0.966757i | \(-0.582305\pi\) | ||||
−0.255696 | + | 0.966757i | \(0.582305\pi\) | |||||||
\(398\) | −23.4576 | −1.17582 | ||||||||
\(399\) | −6.84199 | −0.342528 | ||||||||
\(400\) | 3.88265 | 0.194132 | ||||||||
\(401\) | 27.6214 | 1.37935 | 0.689673 | − | 0.724121i | \(-0.257754\pi\) | ||||
0.689673 | + | 0.724121i | \(0.257754\pi\) | |||||||
\(402\) | 4.49343 | 0.224112 | ||||||||
\(403\) | −7.79124 | −0.388109 | ||||||||
\(404\) | 5.92549 | 0.294804 | ||||||||
\(405\) | 23.1979 | 1.15272 | ||||||||
\(406\) | 11.8833 | 0.589760 | ||||||||
\(407\) | 54.5099 | 2.70195 | ||||||||
\(408\) | 0.932373 | 0.0461593 | ||||||||
\(409\) | −32.3617 | −1.60018 | −0.800092 | − | 0.599877i | \(-0.795216\pi\) | ||||
−0.800092 | + | 0.599877i | \(0.795216\pi\) | |||||||
\(410\) | −7.35587 | −0.363281 | ||||||||
\(411\) | 5.02477 | 0.247854 | ||||||||
\(412\) | −7.57015 | −0.372955 | ||||||||
\(413\) | 2.60338 | 0.128104 | ||||||||
\(414\) | −14.8118 | −0.727962 | ||||||||
\(415\) | −24.6528 | −1.21016 | ||||||||
\(416\) | 0.953732 | 0.0467606 | ||||||||
\(417\) | 6.52578 | 0.319569 | ||||||||
\(418\) | −41.5807 | −2.03378 | ||||||||
\(419\) | −20.7391 | −1.01317 | −0.506586 | − | 0.862189i | \(-0.669093\pi\) | ||||
−0.506586 | + | 0.862189i | \(0.669093\pi\) | |||||||
\(420\) | 2.83249 | 0.138211 | ||||||||
\(421\) | −2.74188 | −0.133631 | −0.0668155 | − | 0.997765i | \(-0.521284\pi\) | ||||
−0.0668155 | + | 0.997765i | \(0.521284\pi\) | |||||||
\(422\) | −23.7236 | −1.15485 | ||||||||
\(423\) | 27.2238 | 1.32367 | ||||||||
\(424\) | 7.51226 | 0.364828 | ||||||||
\(425\) | 9.77140 | 0.473983 | ||||||||
\(426\) | −4.57676 | −0.221745 | ||||||||
\(427\) | 15.0509 | 0.728366 | ||||||||
\(428\) | 16.0455 | 0.775589 | ||||||||
\(429\) | −2.04077 | −0.0985294 | ||||||||
\(430\) | −17.4798 | −0.842950 | ||||||||
\(431\) | −1.93294 | −0.0931065 | −0.0465533 | − | 0.998916i | \(-0.514824\pi\) | ||||
−0.0465533 | + | 0.998916i | \(0.514824\pi\) | |||||||
\(432\) | 2.17201 | 0.104501 | ||||||||
\(433\) | 4.35794 | 0.209429 | 0.104715 | − | 0.994502i | \(-0.466607\pi\) | ||||
0.104715 | + | 0.994502i | \(0.466607\pi\) | |||||||
\(434\) | 20.9564 | 1.00594 | ||||||||
\(435\) | −5.11487 | −0.245239 | ||||||||
\(436\) | 2.50942 | 0.120179 | ||||||||
\(437\) | 37.2487 | 1.78185 | ||||||||
\(438\) | 0.241135 | 0.0115219 | ||||||||
\(439\) | 8.19465 | 0.391109 | 0.195555 | − | 0.980693i | \(-0.437349\pi\) | ||||
0.195555 | + | 0.980693i | \(0.437349\pi\) | |||||||
\(440\) | 17.2139 | 0.820638 | ||||||||
\(441\) | 1.20036 | 0.0571601 | ||||||||
\(442\) | 2.40024 | 0.114168 | ||||||||
\(443\) | −5.51425 | −0.261990 | −0.130995 | − | 0.991383i | \(-0.541817\pi\) | ||||
−0.130995 | + | 0.991383i | \(0.541817\pi\) | |||||||
\(444\) | 3.49647 | 0.165935 | ||||||||
\(445\) | 8.63867 | 0.409512 | ||||||||
\(446\) | 4.63802 | 0.219616 | ||||||||
\(447\) | −1.75367 | −0.0829456 | ||||||||
\(448\) | −2.56529 | −0.121198 | ||||||||
\(449\) | −19.1545 | −0.903956 | −0.451978 | − | 0.892029i | \(-0.649281\pi\) | ||||
−0.451978 | + | 0.892029i | \(0.649281\pi\) | |||||||
\(450\) | 11.1150 | 0.523968 | ||||||||
\(451\) | −14.2551 | −0.671246 | ||||||||
\(452\) | −13.4589 | −0.633055 | ||||||||
\(453\) | −6.86959 | −0.322762 | ||||||||
\(454\) | −2.30295 | −0.108083 | ||||||||
\(455\) | 7.29178 | 0.341844 | ||||||||
\(456\) | −2.66714 | −0.124900 | ||||||||
\(457\) | −41.6610 | −1.94882 | −0.974409 | − | 0.224783i | \(-0.927833\pi\) | ||||
−0.974409 | + | 0.224783i | \(0.927833\pi\) | |||||||
\(458\) | −1.98890 | −0.0929350 | ||||||||
\(459\) | 5.46627 | 0.255144 | ||||||||
\(460\) | −15.4205 | −0.718982 | ||||||||
\(461\) | 28.7942 | 1.34108 | 0.670539 | − | 0.741874i | \(-0.266063\pi\) | ||||
0.670539 | + | 0.741874i | \(0.266063\pi\) | |||||||
\(462\) | 5.48913 | 0.255378 | ||||||||
\(463\) | 1.89638 | 0.0881321 | 0.0440660 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440660 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(464\) | 4.63236 | 0.215052 | ||||||||
\(465\) | −9.02012 | −0.418298 | ||||||||
\(466\) | −5.58928 | −0.258918 | ||||||||
\(467\) | −9.53499 | −0.441227 | −0.220613 | − | 0.975361i | \(-0.570806\pi\) | ||||
−0.220613 | + | 0.975361i | \(0.570806\pi\) | |||||||
\(468\) | 2.73029 | 0.126208 | ||||||||
\(469\) | −31.1138 | −1.43670 | ||||||||
\(470\) | 28.3425 | 1.30734 | ||||||||
\(471\) | −2.45472 | −0.113107 | ||||||||
\(472\) | 1.01485 | 0.0467122 | ||||||||
\(473\) | −33.8744 | −1.55755 | ||||||||
\(474\) | 5.74826 | 0.264026 | ||||||||
\(475\) | −27.9520 | −1.28253 | ||||||||
\(476\) | −6.45602 | −0.295911 | ||||||||
\(477\) | 21.5057 | 0.984678 | ||||||||
\(478\) | 3.34553 | 0.153021 | ||||||||
\(479\) | 11.2845 | 0.515602 | 0.257801 | − | 0.966198i | \(-0.417002\pi\) | ||||
0.257801 | + | 0.966198i | \(0.417002\pi\) | |||||||
\(480\) | 1.10416 | 0.0503978 | ||||||||
\(481\) | 9.00108 | 0.410414 | ||||||||
\(482\) | −26.7139 | −1.21678 | ||||||||
\(483\) | −4.91726 | −0.223743 | ||||||||
\(484\) | 22.3591 | 1.01632 | ||||||||
\(485\) | 2.84998 | 0.129411 | ||||||||
\(486\) | 9.39967 | 0.426377 | ||||||||
\(487\) | 13.3515 | 0.605014 | 0.302507 | − | 0.953147i | \(-0.402176\pi\) | ||||
0.302507 | + | 0.953147i | \(0.402176\pi\) | |||||||
\(488\) | 5.86716 | 0.265594 | ||||||||
\(489\) | 2.72381 | 0.123175 | ||||||||
\(490\) | 1.24968 | 0.0564550 | ||||||||
\(491\) | 37.9516 | 1.71273 | 0.856365 | − | 0.516370i | \(-0.172717\pi\) | ||||
0.856365 | + | 0.516370i | \(0.172717\pi\) | |||||||
\(492\) | −0.914375 | −0.0412232 | ||||||||
\(493\) | 11.6582 | 0.525058 | ||||||||
\(494\) | −6.86613 | −0.308922 | ||||||||
\(495\) | 49.2789 | 2.21492 | ||||||||
\(496\) | 8.16921 | 0.366808 | ||||||||
\(497\) | 31.6908 | 1.42153 | ||||||||
\(498\) | −3.06448 | −0.137323 | ||||||||
\(499\) | −27.6365 | −1.23718 | −0.618590 | − | 0.785714i | \(-0.712296\pi\) | ||||
−0.618590 | + | 0.785714i | \(0.712296\pi\) | |||||||
\(500\) | −3.33013 | −0.148928 | ||||||||
\(501\) | 6.84842 | 0.305965 | ||||||||
\(502\) | 29.3076 | 1.30806 | ||||||||
\(503\) | 20.9442 | 0.933855 | 0.466927 | − | 0.884296i | \(-0.345361\pi\) | ||||
0.466927 | + | 0.884296i | \(0.345361\pi\) | |||||||
\(504\) | −7.34377 | −0.327117 | ||||||||
\(505\) | 17.6602 | 0.785868 | ||||||||
\(506\) | −29.8836 | −1.32849 | ||||||||
\(507\) | 4.47921 | 0.198929 | ||||||||
\(508\) | 2.35435 | 0.104458 | ||||||||
\(509\) | −25.5377 | −1.13194 | −0.565969 | − | 0.824426i | \(-0.691498\pi\) | ||||
−0.565969 | + | 0.824426i | \(0.691498\pi\) | |||||||
\(510\) | 2.77882 | 0.123048 | ||||||||
\(511\) | −1.66969 | −0.0738627 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −15.6368 | −0.690381 | ||||||||
\(514\) | −10.3803 | −0.457854 | ||||||||
\(515\) | −22.5619 | −0.994197 | ||||||||
\(516\) | −2.17283 | −0.0956536 | ||||||||
\(517\) | 54.9254 | 2.41562 | ||||||||
\(518\) | −24.2105 | −1.06375 | ||||||||
\(519\) | 5.63255 | 0.247242 | ||||||||
\(520\) | 2.84248 | 0.124651 | ||||||||
\(521\) | −38.8849 | −1.70358 | −0.851788 | − | 0.523886i | \(-0.824482\pi\) | ||||
−0.851788 | + | 0.523886i | \(0.824482\pi\) | |||||||
\(522\) | 13.2613 | 0.580430 | ||||||||
\(523\) | −25.0299 | −1.09448 | −0.547240 | − | 0.836976i | \(-0.684321\pi\) | ||||
−0.547240 | + | 0.836976i | \(0.684321\pi\) | |||||||
\(524\) | 8.14252 | 0.355708 | ||||||||
\(525\) | 3.68999 | 0.161044 | ||||||||
\(526\) | 8.83916 | 0.385406 | ||||||||
\(527\) | 20.5593 | 0.895578 | ||||||||
\(528\) | 2.13977 | 0.0931217 | ||||||||
\(529\) | 3.77022 | 0.163922 | ||||||||
\(530\) | 22.3894 | 0.972532 | ||||||||
\(531\) | 2.90525 | 0.126077 | ||||||||
\(532\) | 18.4681 | 0.800692 | ||||||||
\(533\) | −2.35391 | −0.101959 | ||||||||
\(534\) | 1.07383 | 0.0464693 | ||||||||
\(535\) | 47.8217 | 2.06751 | ||||||||
\(536\) | −12.1288 | −0.523883 | ||||||||
\(537\) | 3.30812 | 0.142756 | ||||||||
\(538\) | 1.00000 | 0.0431131 | ||||||||
\(539\) | 2.42179 | 0.104314 | ||||||||
\(540\) | 6.47342 | 0.278571 | ||||||||
\(541\) | 0.997803 | 0.0428989 | 0.0214494 | − | 0.999770i | \(-0.493172\pi\) | ||||
0.0214494 | + | 0.999770i | \(0.493172\pi\) | |||||||
\(542\) | −7.39604 | −0.317687 | ||||||||
\(543\) | −3.32046 | −0.142494 | ||||||||
\(544\) | −2.51668 | −0.107902 | ||||||||
\(545\) | 7.47902 | 0.320366 | ||||||||
\(546\) | 0.906407 | 0.0387907 | ||||||||
\(547\) | −15.8011 | −0.675608 | −0.337804 | − | 0.941217i | \(-0.609684\pi\) | ||||
−0.337804 | + | 0.941217i | \(0.609684\pi\) | |||||||
\(548\) | −13.5630 | −0.579382 | ||||||||
\(549\) | 16.7962 | 0.716843 | ||||||||
\(550\) | 22.4251 | 0.956211 | ||||||||
\(551\) | −33.3494 | −1.42073 | ||||||||
\(552\) | −1.91685 | −0.0815863 | ||||||||
\(553\) | −39.8026 | −1.69258 | ||||||||
\(554\) | −13.5773 | −0.576843 | ||||||||
\(555\) | 10.4208 | 0.442338 | ||||||||
\(556\) | −17.6145 | −0.747023 | ||||||||
\(557\) | −36.3525 | −1.54031 | −0.770153 | − | 0.637860i | \(-0.779820\pi\) | ||||
−0.770153 | + | 0.637860i | \(0.779820\pi\) | |||||||
\(558\) | 23.3864 | 0.990025 | ||||||||
\(559\) | −5.59360 | −0.236584 | ||||||||
\(560\) | −7.64552 | −0.323082 | ||||||||
\(561\) | 5.38514 | 0.227361 | ||||||||
\(562\) | −13.5723 | −0.572511 | ||||||||
\(563\) | −20.1622 | −0.849736 | −0.424868 | − | 0.905255i | \(-0.639680\pi\) | ||||
−0.424868 | + | 0.905255i | \(0.639680\pi\) | |||||||
\(564\) | 3.52312 | 0.148350 | ||||||||
\(565\) | −40.1127 | −1.68755 | ||||||||
\(566\) | −20.5026 | −0.861790 | ||||||||
\(567\) | −19.9671 | −0.838538 | ||||||||
\(568\) | 12.3537 | 0.518349 | ||||||||
\(569\) | −16.0424 | −0.672530 | −0.336265 | − | 0.941767i | \(-0.609164\pi\) | ||||
−0.336265 | + | 0.941767i | \(0.609164\pi\) | |||||||
\(570\) | −7.94909 | −0.332951 | ||||||||
\(571\) | −32.2187 | −1.34831 | −0.674156 | − | 0.738589i | \(-0.735493\pi\) | ||||
−0.674156 | + | 0.738589i | \(0.735493\pi\) | |||||||
\(572\) | 5.50850 | 0.230322 | ||||||||
\(573\) | 1.00466 | 0.0419701 | ||||||||
\(574\) | 6.33139 | 0.264267 | ||||||||
\(575\) | −20.0888 | −0.837761 | ||||||||
\(576\) | −2.86275 | −0.119281 | ||||||||
\(577\) | 42.6582 | 1.77589 | 0.887943 | − | 0.459954i | \(-0.152134\pi\) | ||||
0.887943 | + | 0.459954i | \(0.152134\pi\) | |||||||
\(578\) | 10.6663 | 0.443660 | ||||||||
\(579\) | 3.87578 | 0.161072 | ||||||||
\(580\) | 13.8062 | 0.573271 | ||||||||
\(581\) | 21.2193 | 0.880326 | ||||||||
\(582\) | 0.354267 | 0.0146849 | ||||||||
\(583\) | 43.3888 | 1.79698 | ||||||||
\(584\) | −0.650878 | −0.0269335 | ||||||||
\(585\) | 8.13731 | 0.336436 | ||||||||
\(586\) | 26.0133 | 1.07460 | ||||||||
\(587\) | −13.8741 | −0.572646 | −0.286323 | − | 0.958133i | \(-0.592433\pi\) | ||||
−0.286323 | + | 0.958133i | \(0.592433\pi\) | |||||||
\(588\) | 0.155342 | 0.00640622 | ||||||||
\(589\) | −58.8119 | −2.42330 | ||||||||
\(590\) | 3.02463 | 0.124522 | ||||||||
\(591\) | 3.02779 | 0.124547 | ||||||||
\(592\) | −9.43775 | −0.387889 | ||||||||
\(593\) | 33.6435 | 1.38157 | 0.690786 | − | 0.723059i | \(-0.257265\pi\) | ||||
0.690786 | + | 0.723059i | \(0.257265\pi\) | |||||||
\(594\) | 12.5450 | 0.514726 | ||||||||
\(595\) | −19.2414 | −0.788819 | ||||||||
\(596\) | 4.73354 | 0.193893 | ||||||||
\(597\) | −8.69051 | −0.355679 | ||||||||
\(598\) | −4.93460 | −0.201791 | ||||||||
\(599\) | 12.8677 | 0.525761 | 0.262881 | − | 0.964828i | \(-0.415327\pi\) | ||||
0.262881 | + | 0.964828i | \(0.415327\pi\) | |||||||
\(600\) | 1.43843 | 0.0587237 | ||||||||
\(601\) | 17.2785 | 0.704804 | 0.352402 | − | 0.935849i | \(-0.385365\pi\) | ||||
0.352402 | + | 0.935849i | \(0.385365\pi\) | |||||||
\(602\) | 15.0453 | 0.613201 | ||||||||
\(603\) | −34.7216 | −1.41397 | ||||||||
\(604\) | 18.5426 | 0.754486 | ||||||||
\(605\) | 66.6384 | 2.70924 | ||||||||
\(606\) | 2.19526 | 0.0891762 | ||||||||
\(607\) | −36.7366 | −1.49109 | −0.745547 | − | 0.666453i | \(-0.767812\pi\) | ||||
−0.745547 | + | 0.666453i | \(0.767812\pi\) | |||||||
\(608\) | 7.19922 | 0.291967 | ||||||||
\(609\) | 4.40250 | 0.178398 | ||||||||
\(610\) | 17.4863 | 0.708001 | ||||||||
\(611\) | 9.06970 | 0.366921 | ||||||||
\(612\) | −7.20463 | −0.291230 | ||||||||
\(613\) | −35.5029 | −1.43395 | −0.716975 | − | 0.697099i | \(-0.754474\pi\) | ||||
−0.716975 | + | 0.697099i | \(0.754474\pi\) | |||||||
\(614\) | 17.3993 | 0.702179 | ||||||||
\(615\) | −2.72518 | −0.109890 | ||||||||
\(616\) | −14.8164 | −0.596970 | ||||||||
\(617\) | 5.97403 | 0.240505 | 0.120253 | − | 0.992743i | \(-0.461630\pi\) | ||||
0.120253 | + | 0.992743i | \(0.461630\pi\) | |||||||
\(618\) | −2.80457 | −0.112816 | ||||||||
\(619\) | 1.54631 | 0.0621513 | 0.0310757 | − | 0.999517i | \(-0.490107\pi\) | ||||
0.0310757 | + | 0.999517i | \(0.490107\pi\) | |||||||
\(620\) | 24.3473 | 0.977812 | ||||||||
\(621\) | −11.2380 | −0.450965 | ||||||||
\(622\) | 13.4740 | 0.540256 | ||||||||
\(623\) | −7.43552 | −0.297898 | ||||||||
\(624\) | 0.353336 | 0.0141447 | ||||||||
\(625\) | −29.3383 | −1.17353 | ||||||||
\(626\) | 9.89195 | 0.395362 | ||||||||
\(627\) | −15.4047 | −0.615205 | ||||||||
\(628\) | 6.62583 | 0.264399 | ||||||||
\(629\) | −23.7518 | −0.947047 | ||||||||
\(630\) | −21.8872 | −0.872007 | ||||||||
\(631\) | 33.5953 | 1.33741 | 0.668705 | − | 0.743528i | \(-0.266849\pi\) | ||||
0.668705 | + | 0.743528i | \(0.266849\pi\) | |||||||
\(632\) | −15.5158 | −0.617187 | ||||||||
\(633\) | −8.78905 | −0.349333 | ||||||||
\(634\) | −19.2200 | −0.763324 | ||||||||
\(635\) | 7.01686 | 0.278456 | ||||||||
\(636\) | 2.78312 | 0.110358 | ||||||||
\(637\) | 0.399904 | 0.0158448 | ||||||||
\(638\) | 26.7553 | 1.05925 | ||||||||
\(639\) | 35.3655 | 1.39904 | ||||||||
\(640\) | −2.98038 | −0.117810 | ||||||||
\(641\) | 22.6820 | 0.895884 | 0.447942 | − | 0.894063i | \(-0.352157\pi\) | ||||
0.447942 | + | 0.894063i | \(0.352157\pi\) | |||||||
\(642\) | 5.94449 | 0.234610 | ||||||||
\(643\) | 35.9742 | 1.41868 | 0.709341 | − | 0.704865i | \(-0.248993\pi\) | ||||
0.709341 | + | 0.704865i | \(0.248993\pi\) | |||||||
\(644\) | 13.2728 | 0.523021 | ||||||||
\(645\) | −6.47586 | −0.254987 | ||||||||
\(646\) | 18.1182 | 0.712849 | ||||||||
\(647\) | −29.8868 | −1.17497 | −0.587485 | − | 0.809235i | \(-0.699882\pi\) | ||||
−0.587485 | + | 0.809235i | \(0.699882\pi\) | |||||||
\(648\) | −7.78356 | −0.305767 | ||||||||
\(649\) | 5.86149 | 0.230084 | ||||||||
\(650\) | 3.70301 | 0.145244 | ||||||||
\(651\) | 7.76385 | 0.304289 | ||||||||
\(652\) | −7.35217 | −0.287933 | ||||||||
\(653\) | −48.1187 | −1.88303 | −0.941516 | − | 0.336968i | \(-0.890598\pi\) | ||||
−0.941516 | + | 0.336968i | \(0.890598\pi\) | |||||||
\(654\) | 0.929682 | 0.0363534 | ||||||||
\(655\) | 24.2678 | 0.948220 | ||||||||
\(656\) | 2.46810 | 0.0963632 | ||||||||
\(657\) | −1.86330 | −0.0726942 | ||||||||
\(658\) | −24.3951 | −0.951019 | ||||||||
\(659\) | −27.3372 | −1.06491 | −0.532454 | − | 0.846459i | \(-0.678730\pi\) | ||||
−0.532454 | + | 0.846459i | \(0.678730\pi\) | |||||||
\(660\) | 6.37734 | 0.248237 | ||||||||
\(661\) | −20.6868 | −0.804623 | −0.402311 | − | 0.915503i | \(-0.631793\pi\) | ||||
−0.402311 | + | 0.915503i | \(0.631793\pi\) | |||||||
\(662\) | 10.6168 | 0.412632 | ||||||||
\(663\) | 0.889234 | 0.0345350 | ||||||||
\(664\) | 8.27171 | 0.321005 | ||||||||
\(665\) | 55.0418 | 2.13443 | ||||||||
\(666\) | −27.0179 | −1.04692 | ||||||||
\(667\) | −23.9678 | −0.928037 | ||||||||
\(668\) | −18.4854 | −0.715223 | ||||||||
\(669\) | 1.71828 | 0.0664325 | ||||||||
\(670\) | −36.1483 | −1.39653 | ||||||||
\(671\) | 33.8871 | 1.30820 | ||||||||
\(672\) | −0.950379 | −0.0366617 | ||||||||
\(673\) | −3.68048 | −0.141872 | −0.0709360 | − | 0.997481i | \(-0.522599\pi\) | ||||
−0.0709360 | + | 0.997481i | \(0.522599\pi\) | |||||||
\(674\) | 4.73621 | 0.182432 | ||||||||
\(675\) | 8.43316 | 0.324593 | ||||||||
\(676\) | −12.0904 | −0.465015 | ||||||||
\(677\) | −17.3358 | −0.666268 | −0.333134 | − | 0.942880i | \(-0.608106\pi\) | ||||
−0.333134 | + | 0.942880i | \(0.608106\pi\) | |||||||
\(678\) | −4.98622 | −0.191495 | ||||||||
\(679\) | −2.45305 | −0.0941393 | ||||||||
\(680\) | −7.50067 | −0.287637 | ||||||||
\(681\) | −0.853190 | −0.0326943 | ||||||||
\(682\) | 47.1832 | 1.80674 | ||||||||
\(683\) | 2.26489 | 0.0866636 | 0.0433318 | − | 0.999061i | \(-0.486203\pi\) | ||||
0.0433318 | + | 0.999061i | \(0.486203\pi\) | |||||||
\(684\) | 20.6095 | 0.788025 | ||||||||
\(685\) | −40.4228 | −1.54448 | ||||||||
\(686\) | −19.0326 | −0.726670 | ||||||||
\(687\) | −0.736840 | −0.0281122 | ||||||||
\(688\) | 5.86496 | 0.223599 | ||||||||
\(689\) | 7.16468 | 0.272953 | ||||||||
\(690\) | −5.71292 | −0.217487 | ||||||||
\(691\) | −34.9262 | −1.32865 | −0.664327 | − | 0.747442i | \(-0.731282\pi\) | ||||
−0.664327 | + | 0.747442i | \(0.731282\pi\) | |||||||
\(692\) | −15.2035 | −0.577951 | ||||||||
\(693\) | −42.4156 | −1.61124 | ||||||||
\(694\) | 9.70333 | 0.368333 | ||||||||
\(695\) | −52.4980 | −1.99136 | ||||||||
\(696\) | 1.71618 | 0.0650517 | ||||||||
\(697\) | 6.21143 | 0.235275 | ||||||||
\(698\) | 34.9874 | 1.32429 | ||||||||
\(699\) | −2.07070 | −0.0783210 | ||||||||
\(700\) | −9.96011 | −0.376457 | ||||||||
\(701\) | −8.67601 | −0.327688 | −0.163844 | − | 0.986486i | \(-0.552389\pi\) | ||||
−0.163844 | + | 0.986486i | \(0.552389\pi\) | |||||||
\(702\) | 2.07152 | 0.0781844 | ||||||||
\(703\) | 67.9444 | 2.56257 | ||||||||
\(704\) | −5.77573 | −0.217681 | ||||||||
\(705\) | 10.5002 | 0.395461 | ||||||||
\(706\) | −17.9950 | −0.677251 | ||||||||
\(707\) | −15.2006 | −0.571676 | ||||||||
\(708\) | 0.375978 | 0.0141301 | ||||||||
\(709\) | −52.4850 | −1.97111 | −0.985557 | − | 0.169342i | \(-0.945836\pi\) | ||||
−0.985557 | + | 0.169342i | \(0.945836\pi\) | |||||||
\(710\) | 36.8187 | 1.38178 | ||||||||
\(711\) | −44.4179 | −1.66580 | ||||||||
\(712\) | −2.89852 | −0.108626 | ||||||||
\(713\) | −42.2675 | −1.58293 | ||||||||
\(714\) | −2.39180 | −0.0895110 | ||||||||
\(715\) | 16.4174 | 0.613976 | ||||||||
\(716\) | −8.92937 | −0.333706 | ||||||||
\(717\) | 1.23944 | 0.0462878 | ||||||||
\(718\) | 8.64349 | 0.322572 | ||||||||
\(719\) | 12.2225 | 0.455822 | 0.227911 | − | 0.973682i | \(-0.426810\pi\) | ||||
0.227911 | + | 0.973682i | \(0.426810\pi\) | |||||||
\(720\) | −8.53207 | −0.317971 | ||||||||
\(721\) | 19.4196 | 0.723224 | ||||||||
\(722\) | −32.8287 | −1.22176 | ||||||||
\(723\) | −9.89686 | −0.368068 | ||||||||
\(724\) | 8.96265 | 0.333094 | ||||||||
\(725\) | 17.9858 | 0.667977 | ||||||||
\(726\) | 8.28351 | 0.307430 | ||||||||
\(727\) | 32.8117 | 1.21692 | 0.608460 | − | 0.793585i | \(-0.291788\pi\) | ||||
0.608460 | + | 0.793585i | \(0.291788\pi\) | |||||||
\(728\) | −2.44660 | −0.0906769 | ||||||||
\(729\) | −19.8683 | −0.735864 | ||||||||
\(730\) | −1.93986 | −0.0717975 | ||||||||
\(731\) | 14.7602 | 0.545927 | ||||||||
\(732\) | 2.17365 | 0.0803402 | ||||||||
\(733\) | −11.8567 | −0.437937 | −0.218968 | − | 0.975732i | \(-0.570269\pi\) | ||||
−0.218968 | + | 0.975732i | \(0.570269\pi\) | |||||||
\(734\) | 25.4599 | 0.939741 | ||||||||
\(735\) | 0.462979 | 0.0170772 | ||||||||
\(736\) | 5.17399 | 0.190716 | ||||||||
\(737\) | −70.0525 | −2.58042 | ||||||||
\(738\) | 7.06555 | 0.260087 | ||||||||
\(739\) | 23.7096 | 0.872173 | 0.436086 | − | 0.899905i | \(-0.356364\pi\) | ||||
0.436086 | + | 0.899905i | \(0.356364\pi\) | |||||||
\(740\) | −28.1280 | −1.03401 | ||||||||
\(741\) | −2.54374 | −0.0934466 | ||||||||
\(742\) | −19.2711 | −0.707464 | ||||||||
\(743\) | 16.3166 | 0.598600 | 0.299300 | − | 0.954159i | \(-0.403247\pi\) | ||||
0.299300 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(744\) | 3.02650 | 0.110957 | ||||||||
\(745\) | 14.1077 | 0.516867 | ||||||||
\(746\) | 5.63673 | 0.206375 | ||||||||
\(747\) | 23.6798 | 0.866399 | ||||||||
\(748\) | −14.5357 | −0.531477 | ||||||||
\(749\) | −41.1613 | −1.50400 | ||||||||
\(750\) | −1.23374 | −0.0450496 | ||||||||
\(751\) | 30.5188 | 1.11365 | 0.556824 | − | 0.830630i | \(-0.312020\pi\) | ||||
0.556824 | + | 0.830630i | \(0.312020\pi\) | |||||||
\(752\) | −9.50969 | −0.346783 | ||||||||
\(753\) | 10.8578 | 0.395680 | ||||||||
\(754\) | 4.41803 | 0.160895 | ||||||||
\(755\) | 55.2639 | 2.01126 | ||||||||
\(756\) | −5.57183 | −0.202646 | ||||||||
\(757\) | 21.0756 | 0.766007 | 0.383003 | − | 0.923747i | \(-0.374890\pi\) | ||||
0.383003 | + | 0.923747i | \(0.374890\pi\) | |||||||
\(758\) | 16.2741 | 0.591101 | ||||||||
\(759\) | −11.0712 | −0.401858 | ||||||||
\(760\) | 21.4564 | 0.778305 | ||||||||
\(761\) | −9.37156 | −0.339719 | −0.169859 | − | 0.985468i | \(-0.554331\pi\) | ||||
−0.169859 | + | 0.985468i | \(0.554331\pi\) | |||||||
\(762\) | 0.872233 | 0.0315977 | ||||||||
\(763\) | −6.43738 | −0.233049 | ||||||||
\(764\) | −2.71179 | −0.0981091 | ||||||||
\(765\) | −21.4725 | −0.776340 | ||||||||
\(766\) | −17.3292 | −0.626131 | ||||||||
\(767\) | 0.967894 | 0.0349486 | ||||||||
\(768\) | −0.370477 | −0.0133684 | ||||||||
\(769\) | 26.9367 | 0.971363 | 0.485681 | − | 0.874136i | \(-0.338572\pi\) | ||||
0.485681 | + | 0.874136i | \(0.338572\pi\) | |||||||
\(770\) | −44.1585 | −1.59136 | ||||||||
\(771\) | −3.84565 | −0.138498 | ||||||||
\(772\) | −10.4616 | −0.376521 | ||||||||
\(773\) | −14.7111 | −0.529121 | −0.264560 | − | 0.964369i | \(-0.585227\pi\) | ||||
−0.264560 | + | 0.964369i | \(0.585227\pi\) | |||||||
\(774\) | 16.7899 | 0.603500 | ||||||||
\(775\) | 31.7182 | 1.13935 | ||||||||
\(776\) | −0.956247 | −0.0343273 | ||||||||
\(777\) | −8.96944 | −0.321777 | ||||||||
\(778\) | −32.7406 | −1.17381 | ||||||||
\(779\) | −17.7684 | −0.636619 | ||||||||
\(780\) | 1.05307 | 0.0377061 | ||||||||
\(781\) | 71.3516 | 2.55316 | ||||||||
\(782\) | 13.0213 | 0.465641 | ||||||||
\(783\) | 10.0615 | 0.359570 | ||||||||
\(784\) | −0.419304 | −0.0149751 | ||||||||
\(785\) | 19.7475 | 0.704818 | ||||||||
\(786\) | 3.01661 | 0.107599 | ||||||||
\(787\) | 3.73905 | 0.133283 | 0.0666414 | − | 0.997777i | \(-0.478772\pi\) | ||||
0.0666414 | + | 0.997777i | \(0.478772\pi\) | |||||||
\(788\) | −8.17270 | −0.291140 | ||||||||
\(789\) | 3.27471 | 0.116583 | ||||||||
\(790\) | −46.2430 | −1.64525 | ||||||||
\(791\) | 34.5260 | 1.22760 | ||||||||
\(792\) | −16.5345 | −0.587526 | ||||||||
\(793\) | 5.59569 | 0.198709 | ||||||||
\(794\) | 10.1894 | 0.361609 | ||||||||
\(795\) | 8.29474 | 0.294184 | ||||||||
\(796\) | 23.4576 | 0.831433 | ||||||||
\(797\) | 7.11196 | 0.251919 | 0.125959 | − | 0.992035i | \(-0.459799\pi\) | ||||
0.125959 | + | 0.992035i | \(0.459799\pi\) | |||||||
\(798\) | 6.84199 | 0.242204 | ||||||||
\(799\) | −23.9329 | −0.846685 | ||||||||
\(800\) | −3.88265 | −0.137272 | ||||||||
\(801\) | −8.29772 | −0.293185 | ||||||||
\(802\) | −27.6214 | −0.975345 | ||||||||
\(803\) | −3.75929 | −0.132663 | ||||||||
\(804\) | −4.49343 | −0.158471 | ||||||||
\(805\) | 39.5579 | 1.39423 | ||||||||
\(806\) | 7.79124 | 0.274435 | ||||||||
\(807\) | 0.370477 | 0.0130414 | ||||||||
\(808\) | −5.92549 | −0.208458 | ||||||||
\(809\) | −10.2508 | −0.360398 | −0.180199 | − | 0.983630i | \(-0.557674\pi\) | ||||
−0.180199 | + | 0.983630i | \(0.557674\pi\) | |||||||
\(810\) | −23.1979 | −0.815093 | ||||||||
\(811\) | −17.6750 | −0.620655 | −0.310327 | − | 0.950630i | \(-0.600439\pi\) | ||||
−0.310327 | + | 0.950630i | \(0.600439\pi\) | |||||||
\(812\) | −11.8833 | −0.417023 | ||||||||
\(813\) | −2.74006 | −0.0960981 | ||||||||
\(814\) | −54.5099 | −1.91057 | ||||||||
\(815\) | −21.9123 | −0.767553 | ||||||||
\(816\) | −0.932373 | −0.0326396 | ||||||||
\(817\) | −42.2231 | −1.47720 | ||||||||
\(818\) | 32.3617 | 1.13150 | ||||||||
\(819\) | −7.00399 | −0.244739 | ||||||||
\(820\) | 7.35587 | 0.256878 | ||||||||
\(821\) | 14.4456 | 0.504153 | 0.252077 | − | 0.967707i | \(-0.418886\pi\) | ||||
0.252077 | + | 0.967707i | \(0.418886\pi\) | |||||||
\(822\) | −5.02477 | −0.175259 | ||||||||
\(823\) | −5.39437 | −0.188036 | −0.0940179 | − | 0.995571i | \(-0.529971\pi\) | ||||
−0.0940179 | + | 0.995571i | \(0.529971\pi\) | |||||||
\(824\) | 7.57015 | 0.263719 | ||||||||
\(825\) | 8.30799 | 0.289247 | ||||||||
\(826\) | −2.60338 | −0.0905831 | ||||||||
\(827\) | −40.7336 | −1.41645 | −0.708223 | − | 0.705989i | \(-0.750503\pi\) | ||||
−0.708223 | + | 0.705989i | \(0.750503\pi\) | |||||||
\(828\) | 14.8118 | 0.514747 | ||||||||
\(829\) | −15.9379 | −0.553547 | −0.276773 | − | 0.960935i | \(-0.589265\pi\) | ||||
−0.276773 | + | 0.960935i | \(0.589265\pi\) | |||||||
\(830\) | 24.6528 | 0.855712 | ||||||||
\(831\) | −5.03007 | −0.174491 | ||||||||
\(832\) | −0.953732 | −0.0330647 | ||||||||
\(833\) | −1.05526 | −0.0365625 | ||||||||
\(834\) | −6.52578 | −0.225969 | ||||||||
\(835\) | −55.0936 | −1.90659 | ||||||||
\(836\) | 41.5807 | 1.43810 | ||||||||
\(837\) | 17.7436 | 0.613309 | ||||||||
\(838\) | 20.7391 | 0.716421 | ||||||||
\(839\) | 47.0290 | 1.62362 | 0.811811 | − | 0.583921i | \(-0.198482\pi\) | ||||
0.811811 | + | 0.583921i | \(0.198482\pi\) | |||||||
\(840\) | −2.83249 | −0.0977302 | ||||||||
\(841\) | −7.54122 | −0.260042 | ||||||||
\(842\) | 2.74188 | 0.0944914 | ||||||||
\(843\) | −5.02821 | −0.173181 | ||||||||
\(844\) | 23.7236 | 0.816600 | ||||||||
\(845\) | −36.0339 | −1.23961 | ||||||||
\(846\) | −27.2238 | −0.935975 | ||||||||
\(847\) | −57.3574 | −1.97082 | ||||||||
\(848\) | −7.51226 | −0.257972 | ||||||||
\(849\) | −7.59575 | −0.260685 | ||||||||
\(850\) | −9.77140 | −0.335156 | ||||||||
\(851\) | 48.8308 | 1.67390 | ||||||||
\(852\) | 4.57676 | 0.156797 | ||||||||
\(853\) | 5.50121 | 0.188358 | 0.0941790 | − | 0.995555i | \(-0.469977\pi\) | ||||
0.0941790 | + | 0.995555i | \(0.469977\pi\) | |||||||
\(854\) | −15.0509 | −0.515032 | ||||||||
\(855\) | 61.4242 | 2.10066 | ||||||||
\(856\) | −16.0455 | −0.548424 | ||||||||
\(857\) | −6.74343 | −0.230351 | −0.115176 | − | 0.993345i | \(-0.536743\pi\) | ||||
−0.115176 | + | 0.993345i | \(0.536743\pi\) | |||||||
\(858\) | 2.04077 | 0.0696708 | ||||||||
\(859\) | 38.3733 | 1.30928 | 0.654641 | − | 0.755940i | \(-0.272820\pi\) | ||||
0.654641 | + | 0.755940i | \(0.272820\pi\) | |||||||
\(860\) | 17.4798 | 0.596056 | ||||||||
\(861\) | 2.34563 | 0.0799390 | ||||||||
\(862\) | 1.93294 | 0.0658363 | ||||||||
\(863\) | 27.5099 | 0.936449 | 0.468224 | − | 0.883610i | \(-0.344894\pi\) | ||||
0.468224 | + | 0.883610i | \(0.344894\pi\) | |||||||
\(864\) | −2.17201 | −0.0738934 | ||||||||
\(865\) | −45.3122 | −1.54066 | ||||||||
\(866\) | −4.35794 | −0.148089 | ||||||||
\(867\) | 3.95162 | 0.134204 | ||||||||
\(868\) | −20.9564 | −0.711306 | ||||||||
\(869\) | −89.6153 | −3.03999 | ||||||||
\(870\) | 5.11487 | 0.173410 | ||||||||
\(871\) | −11.5676 | −0.391953 | ||||||||
\(872\) | −2.50942 | −0.0849797 | ||||||||
\(873\) | −2.73749 | −0.0926501 | ||||||||
\(874\) | −37.2487 | −1.25996 | ||||||||
\(875\) | 8.54273 | 0.288797 | ||||||||
\(876\) | −0.241135 | −0.00814720 | ||||||||
\(877\) | 40.4307 | 1.36525 | 0.682625 | − | 0.730769i | \(-0.260838\pi\) | ||||
0.682625 | + | 0.730769i | \(0.260838\pi\) | |||||||
\(878\) | −8.19465 | −0.276556 | ||||||||
\(879\) | 9.63733 | 0.325059 | ||||||||
\(880\) | −17.2139 | −0.580279 | ||||||||
\(881\) | 14.9852 | 0.504866 | 0.252433 | − | 0.967614i | \(-0.418769\pi\) | ||||
0.252433 | + | 0.967614i | \(0.418769\pi\) | |||||||
\(882\) | −1.20036 | −0.0404183 | ||||||||
\(883\) | 45.8998 | 1.54465 | 0.772325 | − | 0.635227i | \(-0.219094\pi\) | ||||
0.772325 | + | 0.635227i | \(0.219094\pi\) | |||||||
\(884\) | −2.40024 | −0.0807289 | ||||||||
\(885\) | 1.12056 | 0.0376671 | ||||||||
\(886\) | 5.51425 | 0.185255 | ||||||||
\(887\) | 38.4897 | 1.29236 | 0.646179 | − | 0.763186i | \(-0.276366\pi\) | ||||
0.646179 | + | 0.763186i | \(0.276366\pi\) | |||||||
\(888\) | −3.49647 | −0.117334 | ||||||||
\(889\) | −6.03959 | −0.202561 | ||||||||
\(890\) | −8.63867 | −0.289569 | ||||||||
\(891\) | −44.9557 | −1.50607 | ||||||||
\(892\) | −4.63802 | −0.155292 | ||||||||
\(893\) | 68.4623 | 2.29100 | ||||||||
\(894\) | 1.75367 | 0.0586514 | ||||||||
\(895\) | −26.6129 | −0.889570 | ||||||||
\(896\) | 2.56529 | 0.0857002 | ||||||||
\(897\) | −1.82816 | −0.0610404 | ||||||||
\(898\) | 19.1545 | 0.639193 | ||||||||
\(899\) | 37.8427 | 1.26213 | ||||||||
\(900\) | −11.1150 | −0.370501 | ||||||||
\(901\) | −18.9060 | −0.629849 | ||||||||
\(902\) | 14.2551 | 0.474643 | ||||||||
\(903\) | 5.57393 | 0.185489 | ||||||||
\(904\) | 13.4589 | 0.447637 | ||||||||
\(905\) | 26.7121 | 0.887940 | ||||||||
\(906\) | 6.86959 | 0.228227 | ||||||||
\(907\) | −3.30242 | −0.109655 | −0.0548275 | − | 0.998496i | \(-0.517461\pi\) | ||||
−0.0548275 | + | 0.998496i | \(0.517461\pi\) | |||||||
\(908\) | 2.30295 | 0.0764261 | ||||||||
\(909\) | −16.9632 | −0.562633 | ||||||||
\(910\) | −7.29178 | −0.241720 | ||||||||
\(911\) | 0.593599 | 0.0196668 | 0.00983341 | − | 0.999952i | \(-0.496870\pi\) | ||||
0.00983341 | + | 0.999952i | \(0.496870\pi\) | |||||||
\(912\) | 2.66714 | 0.0883180 | ||||||||
\(913\) | 47.7752 | 1.58113 | ||||||||
\(914\) | 41.6610 | 1.37802 | ||||||||
\(915\) | 6.47828 | 0.214165 | ||||||||
\(916\) | 1.98890 | 0.0657150 | ||||||||
\(917\) | −20.8879 | −0.689779 | ||||||||
\(918\) | −5.46627 | −0.180414 | ||||||||
\(919\) | 7.37035 | 0.243125 | 0.121563 | − | 0.992584i | \(-0.461209\pi\) | ||||
0.121563 | + | 0.992584i | \(0.461209\pi\) | |||||||
\(920\) | 15.4205 | 0.508397 | ||||||||
\(921\) | 6.44604 | 0.212404 | ||||||||
\(922\) | −28.7942 | −0.948285 | ||||||||
\(923\) | 11.7821 | 0.387813 | ||||||||
\(924\) | −5.48913 | −0.180579 | ||||||||
\(925\) | −36.6435 | −1.20483 | ||||||||
\(926\) | −1.89638 | −0.0623188 | ||||||||
\(927\) | 21.6714 | 0.711783 | ||||||||
\(928\) | −4.63236 | −0.152065 | ||||||||
\(929\) | 0.386422 | 0.0126781 | 0.00633905 | − | 0.999980i | \(-0.497982\pi\) | ||||
0.00633905 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(930\) | 9.02012 | 0.295782 | ||||||||
\(931\) | 3.01866 | 0.0989327 | ||||||||
\(932\) | 5.58928 | 0.183083 | ||||||||
\(933\) | 4.99179 | 0.163424 | ||||||||
\(934\) | 9.53499 | 0.311994 | ||||||||
\(935\) | −43.3218 | −1.41678 | ||||||||
\(936\) | −2.73029 | −0.0892424 | ||||||||
\(937\) | −29.0617 | −0.949405 | −0.474702 | − | 0.880146i | \(-0.657444\pi\) | ||||
−0.474702 | + | 0.880146i | \(0.657444\pi\) | |||||||
\(938\) | 31.1138 | 1.01590 | ||||||||
\(939\) | 3.66474 | 0.119594 | ||||||||
\(940\) | −28.3425 | −0.924429 | ||||||||
\(941\) | −22.0276 | −0.718081 | −0.359040 | − | 0.933322i | \(-0.616896\pi\) | ||||
−0.359040 | + | 0.933322i | \(0.616896\pi\) | |||||||
\(942\) | 2.45472 | 0.0799790 | ||||||||
\(943\) | −12.7699 | −0.415847 | ||||||||
\(944\) | −1.01485 | −0.0330305 | ||||||||
\(945\) | −16.6062 | −0.540199 | ||||||||
\(946\) | 33.8744 | 1.10135 | ||||||||
\(947\) | −6.64851 | −0.216047 | −0.108024 | − | 0.994148i | \(-0.534452\pi\) | ||||
−0.108024 | + | 0.994148i | \(0.534452\pi\) | |||||||
\(948\) | −5.74826 | −0.186695 | ||||||||
\(949\) | −0.620763 | −0.0201508 | ||||||||
\(950\) | 27.9520 | 0.906884 | ||||||||
\(951\) | −7.12056 | −0.230900 | ||||||||
\(952\) | 6.45602 | 0.209241 | ||||||||
\(953\) | −57.4933 | −1.86239 | −0.931195 | − | 0.364521i | \(-0.881233\pi\) | ||||
−0.931195 | + | 0.364521i | \(0.881233\pi\) | |||||||
\(954\) | −21.5057 | −0.696273 | ||||||||
\(955\) | −8.08216 | −0.261532 | ||||||||
\(956\) | −3.34553 | −0.108202 | ||||||||
\(957\) | 9.91221 | 0.320416 | ||||||||
\(958\) | −11.2845 | −0.364586 | ||||||||
\(959\) | 34.7929 | 1.12352 | ||||||||
\(960\) | −1.10416 | −0.0356366 | ||||||||
\(961\) | 35.7360 | 1.15277 | ||||||||
\(962\) | −9.00108 | −0.290207 | ||||||||
\(963\) | −45.9342 | −1.48021 | ||||||||
\(964\) | 26.7139 | 0.860395 | ||||||||
\(965\) | −31.1795 | −1.00370 | ||||||||
\(966\) | 4.91726 | 0.158210 | ||||||||
\(967\) | 44.0592 | 1.41685 | 0.708424 | − | 0.705788i | \(-0.249407\pi\) | ||||
0.708424 | + | 0.705788i | \(0.249407\pi\) | |||||||
\(968\) | −22.3591 | −0.718647 | ||||||||
\(969\) | 6.71236 | 0.215632 | ||||||||
\(970\) | −2.84998 | −0.0915072 | ||||||||
\(971\) | 25.8900 | 0.830850 | 0.415425 | − | 0.909627i | \(-0.363633\pi\) | ||||
0.415425 | + | 0.909627i | \(0.363633\pi\) | |||||||
\(972\) | −9.39967 | −0.301494 | ||||||||
\(973\) | 45.1864 | 1.44861 | ||||||||
\(974\) | −13.3515 | −0.427810 | ||||||||
\(975\) | 1.37188 | 0.0439353 | ||||||||
\(976\) | −5.86716 | −0.187803 | ||||||||
\(977\) | 16.1799 | 0.517642 | 0.258821 | − | 0.965925i | \(-0.416666\pi\) | ||||
0.258821 | + | 0.965925i | \(0.416666\pi\) | |||||||
\(978\) | −2.72381 | −0.0870979 | ||||||||
\(979\) | −16.7410 | −0.535046 | ||||||||
\(980\) | −1.24968 | −0.0399197 | ||||||||
\(981\) | −7.18383 | −0.229362 | ||||||||
\(982\) | −37.9516 | −1.21108 | ||||||||
\(983\) | −27.7004 | −0.883504 | −0.441752 | − | 0.897137i | \(-0.645643\pi\) | ||||
−0.441752 | + | 0.897137i | \(0.645643\pi\) | |||||||
\(984\) | 0.914375 | 0.0291492 | ||||||||
\(985\) | −24.3577 | −0.776101 | ||||||||
\(986\) | −11.6582 | −0.371272 | ||||||||
\(987\) | −9.03781 | −0.287677 | ||||||||
\(988\) | 6.86613 | 0.218441 | ||||||||
\(989\) | −30.3453 | −0.964923 | ||||||||
\(990\) | −49.2789 | −1.56619 | ||||||||
\(991\) | −15.6306 | −0.496523 | −0.248262 | − | 0.968693i | \(-0.579859\pi\) | ||||
−0.248262 | + | 0.968693i | \(0.579859\pi\) | |||||||
\(992\) | −8.16921 | −0.259373 | ||||||||
\(993\) | 3.93326 | 0.124818 | ||||||||
\(994\) | −31.6908 | −1.00517 | ||||||||
\(995\) | 69.9126 | 2.21638 | ||||||||
\(996\) | 3.06448 | 0.0971017 | ||||||||
\(997\) | 59.0197 | 1.86917 | 0.934586 | − | 0.355737i | \(-0.115770\pi\) | ||||
0.934586 | + | 0.355737i | \(0.115770\pi\) | |||||||
\(998\) | 27.6365 | 0.874819 | ||||||||
\(999\) | −20.4989 | −0.648557 |
(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 | 538.2.a.d.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 4842.2.a.o.1.1 | 7 | |||
4.3 | odd | 2 | 4304.2.a.i.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.d.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
4304.2.a.i.1.4 | 7 | 4.3 | odd | 2 | |||
4842.2.a.o.1.1 | 7 | 3.2 | odd | 2 |