Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2695680219\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81361 | −1.28241 | −0.641207 | − | 0.767368i | \(-0.721566\pi\) | ||||
−0.641207 | + | 0.767368i | \(0.721566\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.28917 | 0.644584 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.81361 | −0.740402 | ||||||||
\(7\) | 4.81361 | 1.81937 | 0.909686 | − | 0.415296i | \(-0.136322\pi\) | ||||
0.909686 | + | 0.415296i | \(0.136322\pi\) | |||||||
\(8\) | 1.28917 | 0.455790 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.81361 | −0.573513 | ||||||||
\(11\) | 5.62721 | 1.69667 | 0.848334 | − | 0.529461i | \(-0.177606\pi\) | ||||
0.848334 | + | 0.529461i | \(0.177606\pi\) | |||||||
\(12\) | 1.28917 | 0.372151 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −8.72999 | −2.33319 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.91638 | −1.22910 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | −1.81361 | −0.427471 | ||||||||
\(19\) | 1.47556 | 0.338517 | 0.169259 | − | 0.985572i | \(-0.445863\pi\) | ||||
0.169259 | + | 0.985572i | \(0.445863\pi\) | |||||||
\(20\) | 1.28917 | 0.288267 | ||||||||
\(21\) | 4.81361 | 1.05042 | ||||||||
\(22\) | −10.2056 | −2.17583 | ||||||||
\(23\) | −1.62721 | −0.339297 | −0.169649 | − | 0.985505i | \(-0.554263\pi\) | ||||
−0.169649 | + | 0.985505i | \(0.554263\pi\) | |||||||
\(24\) | 1.28917 | 0.263150 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.81361 | −0.355677 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 6.20555 | 1.17274 | ||||||||
\(29\) | −3.39194 | −0.629868 | −0.314934 | − | 0.949114i | \(-0.601982\pi\) | ||||
−0.314934 | + | 0.949114i | \(0.601982\pi\) | |||||||
\(30\) | −1.81361 | −0.331118 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 6.33804 | 1.12042 | ||||||||
\(33\) | 5.62721 | 0.979572 | ||||||||
\(34\) | −3.62721 | −0.622062 | ||||||||
\(35\) | 4.81361 | 0.813648 | ||||||||
\(36\) | 1.28917 | 0.214861 | ||||||||
\(37\) | −8.20555 | −1.34898 | −0.674492 | − | 0.738282i | \(-0.735637\pi\) | ||||
−0.674492 | + | 0.738282i | \(0.735637\pi\) | |||||||
\(38\) | −2.67609 | −0.434119 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 1.28917 | 0.203835 | ||||||||
\(41\) | 1.76473 | 0.275605 | 0.137802 | − | 0.990460i | \(-0.455996\pi\) | ||||
0.137802 | + | 0.990460i | \(0.455996\pi\) | |||||||
\(42\) | −8.72999 | −1.34707 | ||||||||
\(43\) | 8.81361 | 1.34406 | 0.672031 | − | 0.740523i | \(-0.265422\pi\) | ||||
0.672031 | + | 0.740523i | \(0.265422\pi\) | |||||||
\(44\) | 7.25443 | 1.09365 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 2.95112 | 0.435120 | ||||||||
\(47\) | 0.729988 | 0.106480 | 0.0532399 | − | 0.998582i | \(-0.483045\pi\) | ||||
0.0532399 | + | 0.998582i | \(0.483045\pi\) | |||||||
\(48\) | −4.91638 | −0.709619 | ||||||||
\(49\) | 16.1708 | 2.31012 | ||||||||
\(50\) | −1.81361 | −0.256483 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 1.28917 | 0.178776 | ||||||||
\(53\) | 1.68111 | 0.230919 | 0.115459 | − | 0.993312i | \(-0.463166\pi\) | ||||
0.115459 | + | 0.993312i | \(0.463166\pi\) | |||||||
\(54\) | −1.81361 | −0.246801 | ||||||||
\(55\) | 5.62721 | 0.758773 | ||||||||
\(56\) | 6.20555 | 0.829252 | ||||||||
\(57\) | 1.47556 | 0.195443 | ||||||||
\(58\) | 6.15165 | 0.807751 | ||||||||
\(59\) | −5.39194 | −0.701971 | −0.350986 | − | 0.936381i | \(-0.614153\pi\) | ||||
−0.350986 | + | 0.936381i | \(0.614153\pi\) | |||||||
\(60\) | 1.28917 | 0.166431 | ||||||||
\(61\) | 7.88666 | 1.00978 | 0.504892 | − | 0.863183i | \(-0.331532\pi\) | ||||
0.504892 | + | 0.863183i | \(0.331532\pi\) | |||||||
\(62\) | 1.81361 | 0.230328 | ||||||||
\(63\) | 4.81361 | 0.606457 | ||||||||
\(64\) | −1.66196 | −0.207744 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −10.2056 | −1.25622 | ||||||||
\(67\) | −4.23527 | −0.517421 | −0.258710 | − | 0.965955i | \(-0.583297\pi\) | ||||
−0.258710 | + | 0.965955i | \(0.583297\pi\) | |||||||
\(68\) | 2.57834 | 0.312669 | ||||||||
\(69\) | −1.62721 | −0.195893 | ||||||||
\(70\) | −8.72999 | −1.04343 | ||||||||
\(71\) | 11.2544 | 1.33565 | 0.667827 | − | 0.744316i | \(-0.267224\pi\) | ||||
0.667827 | + | 0.744316i | \(0.267224\pi\) | |||||||
\(72\) | 1.28917 | 0.151930 | ||||||||
\(73\) | −6.25945 | −0.732613 | −0.366307 | − | 0.930494i | \(-0.619378\pi\) | ||||
−0.366307 | + | 0.930494i | \(0.619378\pi\) | |||||||
\(74\) | 14.8816 | 1.72996 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 1.90225 | 0.218203 | ||||||||
\(77\) | 27.0872 | 3.08687 | ||||||||
\(78\) | −1.81361 | −0.205350 | ||||||||
\(79\) | −5.30833 | −0.597233 | −0.298617 | − | 0.954373i | \(-0.596525\pi\) | ||||
−0.298617 | + | 0.954373i | \(0.596525\pi\) | |||||||
\(80\) | −4.91638 | −0.549668 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.20053 | −0.353439 | ||||||||
\(83\) | 4.66196 | 0.511716 | 0.255858 | − | 0.966714i | \(-0.417642\pi\) | ||||
0.255858 | + | 0.966714i | \(0.417642\pi\) | |||||||
\(84\) | 6.20555 | 0.677081 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | −15.9844 | −1.72364 | ||||||||
\(87\) | −3.39194 | −0.363655 | ||||||||
\(88\) | 7.25443 | 0.773324 | ||||||||
\(89\) | −4.20555 | −0.445787 | −0.222894 | − | 0.974843i | \(-0.571550\pi\) | ||||
−0.222894 | + | 0.974843i | \(0.571550\pi\) | |||||||
\(90\) | −1.81361 | −0.191171 | ||||||||
\(91\) | 4.81361 | 0.504603 | ||||||||
\(92\) | −2.09775 | −0.218706 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −1.32391 | −0.136551 | ||||||||
\(95\) | 1.47556 | 0.151389 | ||||||||
\(96\) | 6.33804 | 0.646874 | ||||||||
\(97\) | −14.0680 | −1.42839 | −0.714196 | − | 0.699946i | \(-0.753208\pi\) | ||||
−0.714196 | + | 0.699946i | \(0.753208\pi\) | |||||||
\(98\) | −29.3275 | −2.96252 | ||||||||
\(99\) | 5.62721 | 0.565556 | ||||||||
\(100\) | 1.28917 | 0.128917 | ||||||||
\(101\) | −1.10278 | −0.109730 | −0.0548651 | − | 0.998494i | \(-0.517473\pi\) | ||||
−0.0548651 | + | 0.998494i | \(0.517473\pi\) | |||||||
\(102\) | −3.62721 | −0.359148 | ||||||||
\(103\) | −5.47556 | −0.539523 | −0.269762 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269762 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(104\) | 1.28917 | 0.126413 | ||||||||
\(105\) | 4.81361 | 0.469760 | ||||||||
\(106\) | −3.04888 | −0.296133 | ||||||||
\(107\) | 6.28917 | 0.607997 | 0.303998 | − | 0.952673i | \(-0.401678\pi\) | ||||
0.303998 | + | 0.952673i | \(0.401678\pi\) | |||||||
\(108\) | 1.28917 | 0.124050 | ||||||||
\(109\) | −0.935538 | −0.0896083 | −0.0448042 | − | 0.998996i | \(-0.514266\pi\) | ||||
−0.0448042 | + | 0.998996i | \(0.514266\pi\) | |||||||
\(110\) | −10.2056 | −0.973061 | ||||||||
\(111\) | −8.20555 | −0.778836 | ||||||||
\(112\) | −23.6655 | −2.23618 | ||||||||
\(113\) | 12.7597 | 1.20033 | 0.600166 | − | 0.799875i | \(-0.295101\pi\) | ||||
0.600166 | + | 0.799875i | \(0.295101\pi\) | |||||||
\(114\) | −2.67609 | −0.250639 | ||||||||
\(115\) | −1.62721 | −0.151738 | ||||||||
\(116\) | −4.37279 | −0.406003 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 9.77886 | 0.900217 | ||||||||
\(119\) | 9.62721 | 0.882525 | ||||||||
\(120\) | 1.28917 | 0.117684 | ||||||||
\(121\) | 20.6655 | 1.87868 | ||||||||
\(122\) | −14.3033 | −1.29496 | ||||||||
\(123\) | 1.76473 | 0.159120 | ||||||||
\(124\) | −1.28917 | −0.115771 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −8.72999 | −0.777729 | ||||||||
\(127\) | 3.18639 | 0.282747 | 0.141373 | − | 0.989956i | \(-0.454848\pi\) | ||||
0.141373 | + | 0.989956i | \(0.454848\pi\) | |||||||
\(128\) | −9.66196 | −0.854004 | ||||||||
\(129\) | 8.81361 | 0.775995 | ||||||||
\(130\) | −1.81361 | −0.159064 | ||||||||
\(131\) | 6.52444 | 0.570043 | 0.285021 | − | 0.958521i | \(-0.407999\pi\) | ||||
0.285021 | + | 0.958521i | \(0.407999\pi\) | |||||||
\(132\) | 7.25443 | 0.631417 | ||||||||
\(133\) | 7.10278 | 0.615889 | ||||||||
\(134\) | 7.68111 | 0.663547 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 2.57834 | 0.221091 | ||||||||
\(137\) | 0.372787 | 0.0318493 | 0.0159247 | − | 0.999873i | \(-0.494931\pi\) | ||||
0.0159247 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(138\) | 2.95112 | 0.251216 | ||||||||
\(139\) | −1.47556 | −0.125156 | −0.0625778 | − | 0.998040i | \(-0.519932\pi\) | ||||
−0.0625778 | + | 0.998040i | \(0.519932\pi\) | |||||||
\(140\) | 6.20555 | 0.524465 | ||||||||
\(141\) | 0.729988 | 0.0614761 | ||||||||
\(142\) | −20.4111 | −1.71286 | ||||||||
\(143\) | 5.62721 | 0.470571 | ||||||||
\(144\) | −4.91638 | −0.409698 | ||||||||
\(145\) | −3.39194 | −0.281686 | ||||||||
\(146\) | 11.3522 | 0.939513 | ||||||||
\(147\) | 16.1708 | 1.33375 | ||||||||
\(148\) | −10.5783 | −0.869534 | ||||||||
\(149\) | 12.4408 | 1.01919 | 0.509596 | − | 0.860414i | \(-0.329795\pi\) | ||||
0.509596 | + | 0.860414i | \(0.329795\pi\) | |||||||
\(150\) | −1.81361 | −0.148080 | ||||||||
\(151\) | −9.13249 | −0.743192 | −0.371596 | − | 0.928395i | \(-0.621189\pi\) | ||||
−0.371596 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(152\) | 1.90225 | 0.154293 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | −49.1255 | −3.95865 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 1.28917 | 0.103216 | ||||||||
\(157\) | −11.1567 | −0.890400 | −0.445200 | − | 0.895431i | \(-0.646867\pi\) | ||||
−0.445200 | + | 0.895431i | \(0.646867\pi\) | |||||||
\(158\) | 9.62721 | 0.765900 | ||||||||
\(159\) | 1.68111 | 0.133321 | ||||||||
\(160\) | 6.33804 | 0.501066 | ||||||||
\(161\) | −7.83276 | −0.617308 | ||||||||
\(162\) | −1.81361 | −0.142490 | ||||||||
\(163\) | −19.3622 | −1.51657 | −0.758283 | − | 0.651925i | \(-0.773962\pi\) | ||||
−0.758283 | + | 0.651925i | \(0.773962\pi\) | |||||||
\(164\) | 2.27504 | 0.177650 | ||||||||
\(165\) | 5.62721 | 0.438078 | ||||||||
\(166\) | −8.45495 | −0.656232 | ||||||||
\(167\) | 1.62721 | 0.125918 | 0.0629588 | − | 0.998016i | \(-0.479946\pi\) | ||||
0.0629588 | + | 0.998016i | \(0.479946\pi\) | |||||||
\(168\) | 6.20555 | 0.478769 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.62721 | −0.278195 | ||||||||
\(171\) | 1.47556 | 0.112839 | ||||||||
\(172\) | 11.3622 | 0.866361 | ||||||||
\(173\) | −13.2786 | −1.00955 | −0.504777 | − | 0.863250i | \(-0.668425\pi\) | ||||
−0.504777 | + | 0.863250i | \(0.668425\pi\) | |||||||
\(174\) | 6.15165 | 0.466355 | ||||||||
\(175\) | 4.81361 | 0.363874 | ||||||||
\(176\) | −27.6655 | −2.08537 | ||||||||
\(177\) | −5.39194 | −0.405283 | ||||||||
\(178\) | 7.62721 | 0.571684 | ||||||||
\(179\) | −18.9114 | −1.41350 | −0.706751 | − | 0.707463i | \(-0.749840\pi\) | ||||
−0.706751 | + | 0.707463i | \(0.749840\pi\) | |||||||
\(180\) | 1.28917 | 0.0960890 | ||||||||
\(181\) | −22.8816 | −1.70078 | −0.850389 | − | 0.526154i | \(-0.823634\pi\) | ||||
−0.850389 | + | 0.526154i | \(0.823634\pi\) | |||||||
\(182\) | −8.72999 | −0.647110 | ||||||||
\(183\) | 7.88666 | 0.582999 | ||||||||
\(184\) | −2.09775 | −0.154648 | ||||||||
\(185\) | −8.20555 | −0.603284 | ||||||||
\(186\) | 1.81361 | 0.132980 | ||||||||
\(187\) | 11.2544 | 0.823005 | ||||||||
\(188\) | 0.941078 | 0.0686351 | ||||||||
\(189\) | 4.81361 | 0.350138 | ||||||||
\(190\) | −2.67609 | −0.194144 | ||||||||
\(191\) | −25.2927 | −1.83012 | −0.915059 | − | 0.403320i | \(-0.867856\pi\) | ||||
−0.915059 | + | 0.403320i | \(0.867856\pi\) | |||||||
\(192\) | −1.66196 | −0.119941 | ||||||||
\(193\) | −10.4791 | −0.754304 | −0.377152 | − | 0.926151i | \(-0.623097\pi\) | ||||
−0.377152 | + | 0.926151i | \(0.623097\pi\) | |||||||
\(194\) | 25.5139 | 1.83179 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 20.8469 | 1.48906 | ||||||||
\(197\) | 12.2297 | 0.871332 | 0.435666 | − | 0.900108i | \(-0.356513\pi\) | ||||
0.435666 | + | 0.900108i | \(0.356513\pi\) | |||||||
\(198\) | −10.2056 | −0.725277 | ||||||||
\(199\) | −6.20555 | −0.439900 | −0.219950 | − | 0.975511i | \(-0.570589\pi\) | ||||
−0.219950 | + | 0.975511i | \(0.570589\pi\) | |||||||
\(200\) | 1.28917 | 0.0911580 | ||||||||
\(201\) | −4.23527 | −0.298733 | ||||||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | −16.3275 | −1.14596 | ||||||||
\(204\) | 2.57834 | 0.180520 | ||||||||
\(205\) | 1.76473 | 0.123254 | ||||||||
\(206\) | 9.93051 | 0.691892 | ||||||||
\(207\) | −1.62721 | −0.113099 | ||||||||
\(208\) | −4.91638 | −0.340890 | ||||||||
\(209\) | 8.30330 | 0.574351 | ||||||||
\(210\) | −8.72999 | −0.602426 | ||||||||
\(211\) | −13.6514 | −0.939801 | −0.469900 | − | 0.882719i | \(-0.655710\pi\) | ||||
−0.469900 | + | 0.882719i | \(0.655710\pi\) | |||||||
\(212\) | 2.16724 | 0.148846 | ||||||||
\(213\) | 11.2544 | 0.771141 | ||||||||
\(214\) | −11.4061 | −0.779703 | ||||||||
\(215\) | 8.81361 | 0.601083 | ||||||||
\(216\) | 1.28917 | 0.0877168 | ||||||||
\(217\) | −4.81361 | −0.326769 | ||||||||
\(218\) | 1.69670 | 0.114915 | ||||||||
\(219\) | −6.25945 | −0.422974 | ||||||||
\(220\) | 7.25443 | 0.489093 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 14.8816 | 0.998790 | ||||||||
\(223\) | −23.5733 | −1.57859 | −0.789293 | − | 0.614017i | \(-0.789553\pi\) | ||||
−0.789293 | + | 0.614017i | \(0.789553\pi\) | |||||||
\(224\) | 30.5089 | 2.03846 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −23.1411 | −1.53932 | ||||||||
\(227\) | 18.6761 | 1.23958 | 0.619788 | − | 0.784769i | \(-0.287219\pi\) | ||||
0.619788 | + | 0.784769i | \(0.287219\pi\) | |||||||
\(228\) | 1.90225 | 0.125979 | ||||||||
\(229\) | 13.8328 | 0.914095 | 0.457047 | − | 0.889442i | \(-0.348907\pi\) | ||||
0.457047 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(230\) | 2.95112 | 0.194591 | ||||||||
\(231\) | 27.0872 | 1.78221 | ||||||||
\(232\) | −4.37279 | −0.287088 | ||||||||
\(233\) | 10.3275 | 0.676576 | 0.338288 | − | 0.941043i | \(-0.390152\pi\) | ||||
0.338288 | + | 0.941043i | \(0.390152\pi\) | |||||||
\(234\) | −1.81361 | −0.118559 | ||||||||
\(235\) | 0.729988 | 0.0476192 | ||||||||
\(236\) | −6.95112 | −0.452480 | ||||||||
\(237\) | −5.30833 | −0.344813 | ||||||||
\(238\) | −17.4600 | −1.13176 | ||||||||
\(239\) | 11.6811 | 0.755588 | 0.377794 | − | 0.925890i | \(-0.376683\pi\) | ||||
0.377794 | + | 0.925890i | \(0.376683\pi\) | |||||||
\(240\) | −4.91638 | −0.317351 | ||||||||
\(241\) | −13.0036 | −0.837634 | −0.418817 | − | 0.908071i | \(-0.637555\pi\) | ||||
−0.418817 | + | 0.908071i | \(0.637555\pi\) | |||||||
\(242\) | −37.4791 | −2.40925 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.1672 | 0.650891 | ||||||||
\(245\) | 16.1708 | 1.03311 | ||||||||
\(246\) | −3.20053 | −0.204058 | ||||||||
\(247\) | 1.47556 | 0.0938878 | ||||||||
\(248\) | −1.28917 | −0.0818623 | ||||||||
\(249\) | 4.66196 | 0.295439 | ||||||||
\(250\) | −1.81361 | −0.114703 | ||||||||
\(251\) | 24.9497 | 1.57481 | 0.787405 | − | 0.616436i | \(-0.211424\pi\) | ||||
0.787405 | + | 0.616436i | \(0.211424\pi\) | |||||||
\(252\) | 6.20555 | 0.390913 | ||||||||
\(253\) | −9.15667 | −0.575675 | ||||||||
\(254\) | −5.77886 | −0.362598 | ||||||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | 20.8469 | 1.30293 | ||||||||
\(257\) | 20.4494 | 1.27560 | 0.637800 | − | 0.770202i | \(-0.279845\pi\) | ||||
0.637800 | + | 0.770202i | \(0.279845\pi\) | |||||||
\(258\) | −15.9844 | −0.995146 | ||||||||
\(259\) | −39.4983 | −2.45430 | ||||||||
\(260\) | 1.28917 | 0.0799508 | ||||||||
\(261\) | −3.39194 | −0.209956 | ||||||||
\(262\) | −11.8328 | −0.731031 | ||||||||
\(263\) | −6.93554 | −0.427664 | −0.213832 | − | 0.976870i | \(-0.568594\pi\) | ||||
−0.213832 | + | 0.976870i | \(0.568594\pi\) | |||||||
\(264\) | 7.25443 | 0.446479 | ||||||||
\(265\) | 1.68111 | 0.103270 | ||||||||
\(266\) | −12.8816 | −0.789824 | ||||||||
\(267\) | −4.20555 | −0.257375 | ||||||||
\(268\) | −5.45998 | −0.333521 | ||||||||
\(269\) | −11.1567 | −0.680234 | −0.340117 | − | 0.940383i | \(-0.610467\pi\) | ||||
−0.340117 | + | 0.940383i | \(0.610467\pi\) | |||||||
\(270\) | −1.81361 | −0.110373 | ||||||||
\(271\) | 17.2686 | 1.04899 | 0.524495 | − | 0.851413i | \(-0.324254\pi\) | ||||
0.524495 | + | 0.851413i | \(0.324254\pi\) | |||||||
\(272\) | −9.83276 | −0.596199 | ||||||||
\(273\) | 4.81361 | 0.291333 | ||||||||
\(274\) | −0.676089 | −0.0408440 | ||||||||
\(275\) | 5.62721 | 0.339334 | ||||||||
\(276\) | −2.09775 | −0.126270 | ||||||||
\(277\) | −0.304754 | −0.0183109 | −0.00915546 | − | 0.999958i | \(-0.502914\pi\) | ||||
−0.00915546 | + | 0.999958i | \(0.502914\pi\) | |||||||
\(278\) | 2.67609 | 0.160501 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 6.20555 | 0.370853 | ||||||||
\(281\) | 13.6569 | 0.814704 | 0.407352 | − | 0.913271i | \(-0.366452\pi\) | ||||
0.407352 | + | 0.913271i | \(0.366452\pi\) | |||||||
\(282\) | −1.32391 | −0.0788378 | ||||||||
\(283\) | 15.9844 | 0.950175 | 0.475087 | − | 0.879939i | \(-0.342416\pi\) | ||||
0.475087 | + | 0.879939i | \(0.342416\pi\) | |||||||
\(284\) | 14.5089 | 0.860942 | ||||||||
\(285\) | 1.47556 | 0.0874048 | ||||||||
\(286\) | −10.2056 | −0.603467 | ||||||||
\(287\) | 8.49472 | 0.501427 | ||||||||
\(288\) | 6.33804 | 0.373473 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 6.15165 | 0.361237 | ||||||||
\(291\) | −14.0680 | −0.824683 | ||||||||
\(292\) | −8.06949 | −0.472231 | ||||||||
\(293\) | 5.40608 | 0.315826 | 0.157913 | − | 0.987453i | \(-0.449523\pi\) | ||||
0.157913 | + | 0.987453i | \(0.449523\pi\) | |||||||
\(294\) | −29.3275 | −1.71041 | ||||||||
\(295\) | −5.39194 | −0.313931 | ||||||||
\(296\) | −10.5783 | −0.614853 | ||||||||
\(297\) | 5.62721 | 0.326524 | ||||||||
\(298\) | −22.5628 | −1.30703 | ||||||||
\(299\) | −1.62721 | −0.0941042 | ||||||||
\(300\) | 1.28917 | 0.0744302 | ||||||||
\(301\) | 42.4252 | 2.44535 | ||||||||
\(302\) | 16.5628 | 0.953079 | ||||||||
\(303\) | −1.10278 | −0.0633528 | ||||||||
\(304\) | −7.25443 | −0.416070 | ||||||||
\(305\) | 7.88666 | 0.451589 | ||||||||
\(306\) | −3.62721 | −0.207354 | ||||||||
\(307\) | −20.3517 | −1.16153 | −0.580765 | − | 0.814071i | \(-0.697247\pi\) | ||||
−0.580765 | + | 0.814071i | \(0.697247\pi\) | |||||||
\(308\) | 34.9200 | 1.98975 | ||||||||
\(309\) | −5.47556 | −0.311494 | ||||||||
\(310\) | 1.81361 | 0.103006 | ||||||||
\(311\) | −11.2544 | −0.638180 | −0.319090 | − | 0.947724i | \(-0.603377\pi\) | ||||
−0.319090 | + | 0.947724i | \(0.603377\pi\) | |||||||
\(312\) | 1.28917 | 0.0729848 | ||||||||
\(313\) | 30.6464 | 1.73224 | 0.866118 | − | 0.499840i | \(-0.166608\pi\) | ||||
0.866118 | + | 0.499840i | \(0.166608\pi\) | |||||||
\(314\) | 20.2338 | 1.14186 | ||||||||
\(315\) | 4.81361 | 0.271216 | ||||||||
\(316\) | −6.84333 | −0.384967 | ||||||||
\(317\) | −26.8972 | −1.51070 | −0.755349 | − | 0.655322i | \(-0.772533\pi\) | ||||
−0.755349 | + | 0.655322i | \(0.772533\pi\) | |||||||
\(318\) | −3.04888 | −0.170972 | ||||||||
\(319\) | −19.0872 | −1.06868 | ||||||||
\(320\) | −1.66196 | −0.0929061 | ||||||||
\(321\) | 6.28917 | 0.351027 | ||||||||
\(322\) | 14.2056 | 0.791644 | ||||||||
\(323\) | 2.95112 | 0.164205 | ||||||||
\(324\) | 1.28917 | 0.0716205 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 35.1155 | 1.94487 | ||||||||
\(327\) | −0.935538 | −0.0517354 | ||||||||
\(328\) | 2.27504 | 0.125618 | ||||||||
\(329\) | 3.51388 | 0.193726 | ||||||||
\(330\) | −10.2056 | −0.561797 | ||||||||
\(331\) | 14.5925 | 0.802075 | 0.401037 | − | 0.916062i | \(-0.368650\pi\) | ||||
0.401037 | + | 0.916062i | \(0.368650\pi\) | |||||||
\(332\) | 6.01005 | 0.329844 | ||||||||
\(333\) | −8.20555 | −0.449661 | ||||||||
\(334\) | −2.95112 | −0.161478 | ||||||||
\(335\) | −4.23527 | −0.231397 | ||||||||
\(336\) | −23.6655 | −1.29106 | ||||||||
\(337\) | 19.4600 | 1.06005 | 0.530026 | − | 0.847981i | \(-0.322182\pi\) | ||||
0.530026 | + | 0.847981i | \(0.322182\pi\) | |||||||
\(338\) | −1.81361 | −0.0986472 | ||||||||
\(339\) | 12.7597 | 0.693012 | ||||||||
\(340\) | 2.57834 | 0.139830 | ||||||||
\(341\) | −5.62721 | −0.304731 | ||||||||
\(342\) | −2.67609 | −0.144706 | ||||||||
\(343\) | 44.1447 | 2.38359 | ||||||||
\(344\) | 11.3622 | 0.612610 | ||||||||
\(345\) | −1.62721 | −0.0876062 | ||||||||
\(346\) | 24.0822 | 1.29467 | ||||||||
\(347\) | −33.1411 | −1.77911 | −0.889553 | − | 0.456831i | \(-0.848984\pi\) | ||||
−0.889553 | + | 0.456831i | \(0.848984\pi\) | |||||||
\(348\) | −4.37279 | −0.234406 | ||||||||
\(349\) | −12.6167 | −0.675354 | −0.337677 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337677 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(350\) | −8.72999 | −0.466637 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 35.6655 | 1.90098 | ||||||||
\(353\) | 2.66196 | 0.141682 | 0.0708408 | − | 0.997488i | \(-0.477432\pi\) | ||||
0.0708408 | + | 0.997488i | \(0.477432\pi\) | |||||||
\(354\) | 9.77886 | 0.519741 | ||||||||
\(355\) | 11.2544 | 0.597323 | ||||||||
\(356\) | −5.42166 | −0.287348 | ||||||||
\(357\) | 9.62721 | 0.509526 | ||||||||
\(358\) | 34.2978 | 1.81269 | ||||||||
\(359\) | −10.3814 | −0.547908 | −0.273954 | − | 0.961743i | \(-0.588332\pi\) | ||||
−0.273954 | + | 0.961743i | \(0.588332\pi\) | |||||||
\(360\) | 1.28917 | 0.0679451 | ||||||||
\(361\) | −16.8227 | −0.885406 | ||||||||
\(362\) | 41.4983 | 2.18110 | ||||||||
\(363\) | 20.6655 | 1.08466 | ||||||||
\(364\) | 6.20555 | 0.325259 | ||||||||
\(365\) | −6.25945 | −0.327635 | ||||||||
\(366\) | −14.3033 | −0.747646 | ||||||||
\(367\) | −15.1950 | −0.793172 | −0.396586 | − | 0.917998i | \(-0.629805\pi\) | ||||
−0.396586 | + | 0.917998i | \(0.629805\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | 1.76473 | 0.0918682 | ||||||||
\(370\) | 14.8816 | 0.773660 | ||||||||
\(371\) | 8.09221 | 0.420127 | ||||||||
\(372\) | −1.28917 | −0.0668403 | ||||||||
\(373\) | 4.20555 | 0.217755 | 0.108878 | − | 0.994055i | \(-0.465274\pi\) | ||||
0.108878 | + | 0.994055i | \(0.465274\pi\) | |||||||
\(374\) | −20.4111 | −1.05543 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0.941078 | 0.0485324 | ||||||||
\(377\) | −3.39194 | −0.174694 | ||||||||
\(378\) | −8.72999 | −0.449022 | ||||||||
\(379\) | −26.7683 | −1.37500 | −0.687498 | − | 0.726187i | \(-0.741291\pi\) | ||||
−0.687498 | + | 0.726187i | \(0.741291\pi\) | |||||||
\(380\) | 1.90225 | 0.0975833 | ||||||||
\(381\) | 3.18639 | 0.163244 | ||||||||
\(382\) | 45.8711 | 2.34697 | ||||||||
\(383\) | 32.4635 | 1.65881 | 0.829405 | − | 0.558648i | \(-0.188680\pi\) | ||||
0.829405 | + | 0.558648i | \(0.188680\pi\) | |||||||
\(384\) | −9.66196 | −0.493060 | ||||||||
\(385\) | 27.0872 | 1.38049 | ||||||||
\(386\) | 19.0050 | 0.967330 | ||||||||
\(387\) | 8.81361 | 0.448021 | ||||||||
\(388\) | −18.1361 | −0.920719 | ||||||||
\(389\) | −21.5381 | −1.09202 | −0.546011 | − | 0.837778i | \(-0.683854\pi\) | ||||
−0.546011 | + | 0.837778i | \(0.683854\pi\) | |||||||
\(390\) | −1.81361 | −0.0918355 | ||||||||
\(391\) | −3.25443 | −0.164583 | ||||||||
\(392\) | 20.8469 | 1.05293 | ||||||||
\(393\) | 6.52444 | 0.329114 | ||||||||
\(394\) | −22.1799 | −1.11741 | ||||||||
\(395\) | −5.30833 | −0.267091 | ||||||||
\(396\) | 7.25443 | 0.364549 | ||||||||
\(397\) | −4.31335 | −0.216481 | −0.108240 | − | 0.994125i | \(-0.534522\pi\) | ||||
−0.108240 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(398\) | 11.2544 | 0.564133 | ||||||||
\(399\) | 7.10278 | 0.355584 | ||||||||
\(400\) | −4.91638 | −0.245819 | ||||||||
\(401\) | −2.31889 | −0.115800 | −0.0578999 | − | 0.998322i | \(-0.518440\pi\) | ||||
−0.0578999 | + | 0.998322i | \(0.518440\pi\) | |||||||
\(402\) | 7.68111 | 0.383099 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | −1.42166 | −0.0707304 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 29.6116 | 1.46960 | ||||||||
\(407\) | −46.1744 | −2.28878 | ||||||||
\(408\) | 2.57834 | 0.127647 | ||||||||
\(409\) | −0.759707 | −0.0375651 | −0.0187826 | − | 0.999824i | \(-0.505979\pi\) | ||||
−0.0187826 | + | 0.999824i | \(0.505979\pi\) | |||||||
\(410\) | −3.20053 | −0.158063 | ||||||||
\(411\) | 0.372787 | 0.0183882 | ||||||||
\(412\) | −7.05892 | −0.347768 | ||||||||
\(413\) | −25.9547 | −1.27715 | ||||||||
\(414\) | 2.95112 | 0.145040 | ||||||||
\(415\) | 4.66196 | 0.228846 | ||||||||
\(416\) | 6.33804 | 0.310748 | ||||||||
\(417\) | −1.47556 | −0.0722586 | ||||||||
\(418\) | −15.0589 | −0.736556 | ||||||||
\(419\) | −36.9583 | −1.80553 | −0.902765 | − | 0.430135i | \(-0.858466\pi\) | ||||
−0.902765 | + | 0.430135i | \(0.858466\pi\) | |||||||
\(420\) | 6.20555 | 0.302800 | ||||||||
\(421\) | 4.67609 | 0.227899 | 0.113949 | − | 0.993487i | \(-0.463650\pi\) | ||||
0.113949 | + | 0.993487i | \(0.463650\pi\) | |||||||
\(422\) | 24.7583 | 1.20521 | ||||||||
\(423\) | 0.729988 | 0.0354932 | ||||||||
\(424\) | 2.16724 | 0.105250 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | −20.4111 | −0.988921 | ||||||||
\(427\) | 37.9633 | 1.83717 | ||||||||
\(428\) | 8.10780 | 0.391905 | ||||||||
\(429\) | 5.62721 | 0.271684 | ||||||||
\(430\) | −15.9844 | −0.770837 | ||||||||
\(431\) | −16.0680 | −0.773970 | −0.386985 | − | 0.922086i | \(-0.626483\pi\) | ||||
−0.386985 | + | 0.922086i | \(0.626483\pi\) | |||||||
\(432\) | −4.91638 | −0.236540 | ||||||||
\(433\) | −7.22471 | −0.347197 | −0.173599 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173599 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(434\) | 8.72999 | 0.419053 | ||||||||
\(435\) | −3.39194 | −0.162631 | ||||||||
\(436\) | −1.20607 | −0.0577601 | ||||||||
\(437\) | −2.40105 | −0.114858 | ||||||||
\(438\) | 11.3522 | 0.542428 | ||||||||
\(439\) | −31.6897 | −1.51247 | −0.756234 | − | 0.654302i | \(-0.772963\pi\) | ||||
−0.756234 | + | 0.654302i | \(0.772963\pi\) | |||||||
\(440\) | 7.25443 | 0.345841 | ||||||||
\(441\) | 16.1708 | 0.770038 | ||||||||
\(442\) | −3.62721 | −0.172529 | ||||||||
\(443\) | 3.97582 | 0.188897 | 0.0944485 | − | 0.995530i | \(-0.469891\pi\) | ||||
0.0944485 | + | 0.995530i | \(0.469891\pi\) | |||||||
\(444\) | −10.5783 | −0.502026 | ||||||||
\(445\) | −4.20555 | −0.199362 | ||||||||
\(446\) | 42.7527 | 2.02440 | ||||||||
\(447\) | 12.4408 | 0.588431 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | −11.9461 | −0.563771 | −0.281886 | − | 0.959448i | \(-0.590960\pi\) | ||||
−0.281886 | + | 0.959448i | \(0.590960\pi\) | |||||||
\(450\) | −1.81361 | −0.0854942 | ||||||||
\(451\) | 9.93051 | 0.467610 | ||||||||
\(452\) | 16.4494 | 0.773715 | ||||||||
\(453\) | −9.13249 | −0.429082 | ||||||||
\(454\) | −33.8711 | −1.58965 | ||||||||
\(455\) | 4.81361 | 0.225665 | ||||||||
\(456\) | 1.90225 | 0.0890809 | ||||||||
\(457\) | 21.3466 | 0.998554 | 0.499277 | − | 0.866443i | \(-0.333599\pi\) | ||||
0.499277 | + | 0.866443i | \(0.333599\pi\) | |||||||
\(458\) | −25.0872 | −1.17225 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | −2.09775 | −0.0978082 | ||||||||
\(461\) | 28.6761 | 1.33558 | 0.667789 | − | 0.744350i | \(-0.267241\pi\) | ||||
0.667789 | + | 0.744350i | \(0.267241\pi\) | |||||||
\(462\) | −49.1255 | −2.28553 | ||||||||
\(463\) | −26.6167 | −1.23698 | −0.618490 | − | 0.785792i | \(-0.712255\pi\) | ||||
−0.618490 | + | 0.785792i | \(0.712255\pi\) | |||||||
\(464\) | 16.6761 | 0.774168 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | −18.7300 | −0.867650 | ||||||||
\(467\) | 16.2680 | 0.752795 | 0.376398 | − | 0.926458i | \(-0.377163\pi\) | ||||
0.376398 | + | 0.926458i | \(0.377163\pi\) | |||||||
\(468\) | 1.28917 | 0.0595918 | ||||||||
\(469\) | −20.3869 | −0.941381 | ||||||||
\(470\) | −1.32391 | −0.0610675 | ||||||||
\(471\) | −11.1567 | −0.514072 | ||||||||
\(472\) | −6.95112 | −0.319951 | ||||||||
\(473\) | 49.5960 | 2.28043 | ||||||||
\(474\) | 9.62721 | 0.442193 | ||||||||
\(475\) | 1.47556 | 0.0677034 | ||||||||
\(476\) | 12.4111 | 0.568862 | ||||||||
\(477\) | 1.68111 | 0.0769728 | ||||||||
\(478\) | −21.1849 | −0.968977 | ||||||||
\(479\) | 10.0297 | 0.458270 | 0.229135 | − | 0.973395i | \(-0.426410\pi\) | ||||
0.229135 | + | 0.973395i | \(0.426410\pi\) | |||||||
\(480\) | 6.33804 | 0.289291 | ||||||||
\(481\) | −8.20555 | −0.374141 | ||||||||
\(482\) | 23.5834 | 1.07419 | ||||||||
\(483\) | −7.83276 | −0.356403 | ||||||||
\(484\) | 26.6413 | 1.21097 | ||||||||
\(485\) | −14.0680 | −0.638796 | ||||||||
\(486\) | −1.81361 | −0.0822669 | ||||||||
\(487\) | −16.8972 | −0.765686 | −0.382843 | − | 0.923813i | \(-0.625055\pi\) | ||||
−0.382843 | + | 0.923813i | \(0.625055\pi\) | |||||||
\(488\) | 10.1672 | 0.460249 | ||||||||
\(489\) | −19.3622 | −0.875590 | ||||||||
\(490\) | −29.3275 | −1.32488 | ||||||||
\(491\) | −1.66698 | −0.0752297 | −0.0376148 | − | 0.999292i | \(-0.511976\pi\) | ||||
−0.0376148 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(492\) | 2.27504 | 0.102567 | ||||||||
\(493\) | −6.78389 | −0.305531 | ||||||||
\(494\) | −2.67609 | −0.120403 | ||||||||
\(495\) | 5.62721 | 0.252924 | ||||||||
\(496\) | 4.91638 | 0.220752 | ||||||||
\(497\) | 54.1744 | 2.43005 | ||||||||
\(498\) | −8.45495 | −0.378875 | ||||||||
\(499\) | 24.4353 | 1.09387 | 0.546937 | − | 0.837174i | \(-0.315794\pi\) | ||||
0.546937 | + | 0.837174i | \(0.315794\pi\) | |||||||
\(500\) | 1.28917 | 0.0576534 | ||||||||
\(501\) | 1.62721 | 0.0726985 | ||||||||
\(502\) | −45.2489 | −2.01956 | ||||||||
\(503\) | 9.65139 | 0.430334 | 0.215167 | − | 0.976577i | \(-0.430970\pi\) | ||||
0.215167 | + | 0.976577i | \(0.430970\pi\) | |||||||
\(504\) | 6.20555 | 0.276417 | ||||||||
\(505\) | −1.10278 | −0.0490728 | ||||||||
\(506\) | 16.6066 | 0.738254 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 4.10780 | 0.182254 | ||||||||
\(509\) | −32.5527 | −1.44287 | −0.721437 | − | 0.692480i | \(-0.756518\pi\) | ||||
−0.721437 | + | 0.692480i | \(0.756518\pi\) | |||||||
\(510\) | −3.62721 | −0.160616 | ||||||||
\(511\) | −30.1305 | −1.33290 | ||||||||
\(512\) | −18.4842 | −0.816892 | ||||||||
\(513\) | 1.47556 | 0.0651477 | ||||||||
\(514\) | −37.0872 | −1.63585 | ||||||||
\(515\) | −5.47556 | −0.241282 | ||||||||
\(516\) | 11.3622 | 0.500194 | ||||||||
\(517\) | 4.10780 | 0.180661 | ||||||||
\(518\) | 71.6344 | 3.14743 | ||||||||
\(519\) | −13.2786 | −0.582866 | ||||||||
\(520\) | 1.28917 | 0.0565338 | ||||||||
\(521\) | −11.8272 | −0.518160 | −0.259080 | − | 0.965856i | \(-0.583419\pi\) | ||||
−0.259080 | + | 0.965856i | \(0.583419\pi\) | |||||||
\(522\) | 6.15165 | 0.269250 | ||||||||
\(523\) | 29.3919 | 1.28522 | 0.642610 | − | 0.766193i | \(-0.277852\pi\) | ||||
0.642610 | + | 0.766193i | \(0.277852\pi\) | |||||||
\(524\) | 8.41110 | 0.367441 | ||||||||
\(525\) | 4.81361 | 0.210083 | ||||||||
\(526\) | 12.5783 | 0.548442 | ||||||||
\(527\) | −2.00000 | −0.0871214 | ||||||||
\(528\) | −27.6655 | −1.20399 | ||||||||
\(529\) | −20.3522 | −0.884877 | ||||||||
\(530\) | −3.04888 | −0.132435 | ||||||||
\(531\) | −5.39194 | −0.233990 | ||||||||
\(532\) | 9.15667 | 0.396992 | ||||||||
\(533\) | 1.76473 | 0.0764390 | ||||||||
\(534\) | 7.62721 | 0.330062 | ||||||||
\(535\) | 6.28917 | 0.271904 | ||||||||
\(536\) | −5.45998 | −0.235835 | ||||||||
\(537\) | −18.9114 | −0.816085 | ||||||||
\(538\) | 20.2338 | 0.872342 | ||||||||
\(539\) | 90.9966 | 3.91950 | ||||||||
\(540\) | 1.28917 | 0.0554770 | ||||||||
\(541\) | 32.9200 | 1.41534 | 0.707670 | − | 0.706543i | \(-0.249747\pi\) | ||||
0.707670 | + | 0.706543i | \(0.249747\pi\) | |||||||
\(542\) | −31.3184 | −1.34524 | ||||||||
\(543\) | −22.8816 | −0.981945 | ||||||||
\(544\) | 12.6761 | 0.543483 | ||||||||
\(545\) | −0.935538 | −0.0400741 | ||||||||
\(546\) | −8.72999 | −0.373609 | ||||||||
\(547\) | −1.25997 | −0.0538722 | −0.0269361 | − | 0.999637i | \(-0.508575\pi\) | ||||
−0.0269361 | + | 0.999637i | \(0.508575\pi\) | |||||||
\(548\) | 0.480585 | 0.0205296 | ||||||||
\(549\) | 7.88666 | 0.336595 | ||||||||
\(550\) | −10.2056 | −0.435166 | ||||||||
\(551\) | −5.00502 | −0.213221 | ||||||||
\(552\) | −2.09775 | −0.0892862 | ||||||||
\(553\) | −25.5522 | −1.08659 | ||||||||
\(554\) | 0.552705 | 0.0234822 | ||||||||
\(555\) | −8.20555 | −0.348306 | ||||||||
\(556\) | −1.90225 | −0.0806733 | ||||||||
\(557\) | 33.7250 | 1.42897 | 0.714486 | − | 0.699649i | \(-0.246660\pi\) | ||||
0.714486 | + | 0.699649i | \(0.246660\pi\) | |||||||
\(558\) | 1.81361 | 0.0767761 | ||||||||
\(559\) | 8.81361 | 0.372776 | ||||||||
\(560\) | −23.6655 | −1.00005 | ||||||||
\(561\) | 11.2544 | 0.475162 | ||||||||
\(562\) | −24.7683 | −1.04479 | ||||||||
\(563\) | 3.86393 | 0.162845 | 0.0814227 | − | 0.996680i | \(-0.474054\pi\) | ||||
0.0814227 | + | 0.996680i | \(0.474054\pi\) | |||||||
\(564\) | 0.941078 | 0.0396265 | ||||||||
\(565\) | 12.7597 | 0.536805 | ||||||||
\(566\) | −28.9894 | −1.21852 | ||||||||
\(567\) | 4.81361 | 0.202152 | ||||||||
\(568\) | 14.5089 | 0.608778 | ||||||||
\(569\) | 31.5194 | 1.32136 | 0.660681 | − | 0.750667i | \(-0.270267\pi\) | ||||
0.660681 | + | 0.750667i | \(0.270267\pi\) | |||||||
\(570\) | −2.67609 | −0.112089 | ||||||||
\(571\) | 5.67557 | 0.237515 | 0.118758 | − | 0.992923i | \(-0.462109\pi\) | ||||
0.118758 | + | 0.992923i | \(0.462109\pi\) | |||||||
\(572\) | 7.25443 | 0.303323 | ||||||||
\(573\) | −25.2927 | −1.05662 | ||||||||
\(574\) | −15.4061 | −0.643037 | ||||||||
\(575\) | −1.62721 | −0.0678595 | ||||||||
\(576\) | −1.66196 | −0.0692481 | ||||||||
\(577\) | −36.5089 | −1.51988 | −0.759942 | − | 0.649991i | \(-0.774773\pi\) | ||||
−0.759942 | + | 0.649991i | \(0.774773\pi\) | |||||||
\(578\) | 23.5769 | 0.980669 | ||||||||
\(579\) | −10.4791 | −0.435498 | ||||||||
\(580\) | −4.37279 | −0.181570 | ||||||||
\(581\) | 22.4408 | 0.931002 | ||||||||
\(582\) | 25.5139 | 1.05758 | ||||||||
\(583\) | 9.45998 | 0.391792 | ||||||||
\(584\) | −8.06949 | −0.333918 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | −9.80450 | −0.405020 | ||||||||
\(587\) | 4.49472 | 0.185517 | 0.0927584 | − | 0.995689i | \(-0.470432\pi\) | ||||
0.0927584 | + | 0.995689i | \(0.470432\pi\) | |||||||
\(588\) | 20.8469 | 0.859712 | ||||||||
\(589\) | −1.47556 | −0.0607995 | ||||||||
\(590\) | 9.77886 | 0.402589 | ||||||||
\(591\) | 12.2297 | 0.503064 | ||||||||
\(592\) | 40.3416 | 1.65803 | ||||||||
\(593\) | −4.24940 | −0.174502 | −0.0872510 | − | 0.996186i | \(-0.527808\pi\) | ||||
−0.0872510 | + | 0.996186i | \(0.527808\pi\) | |||||||
\(594\) | −10.2056 | −0.418739 | ||||||||
\(595\) | 9.62721 | 0.394677 | ||||||||
\(596\) | 16.0383 | 0.656955 | ||||||||
\(597\) | −6.20555 | −0.253976 | ||||||||
\(598\) | 2.95112 | 0.120680 | ||||||||
\(599\) | −26.4011 | −1.07872 | −0.539359 | − | 0.842076i | \(-0.681333\pi\) | ||||
−0.539359 | + | 0.842076i | \(0.681333\pi\) | |||||||
\(600\) | 1.28917 | 0.0526301 | ||||||||
\(601\) | 46.6394 | 1.90246 | 0.951230 | − | 0.308483i | \(-0.0998212\pi\) | ||||
0.951230 | + | 0.308483i | \(0.0998212\pi\) | |||||||
\(602\) | −76.9427 | −3.13595 | ||||||||
\(603\) | −4.23527 | −0.172474 | ||||||||
\(604\) | −11.7733 | −0.479050 | ||||||||
\(605\) | 20.6655 | 0.840173 | ||||||||
\(606\) | 2.00000 | 0.0812444 | ||||||||
\(607\) | 45.4005 | 1.84275 | 0.921375 | − | 0.388674i | \(-0.127067\pi\) | ||||
0.921375 | + | 0.388674i | \(0.127067\pi\) | |||||||
\(608\) | 9.35218 | 0.379281 | ||||||||
\(609\) | −16.3275 | −0.661623 | ||||||||
\(610\) | −14.3033 | −0.579124 | ||||||||
\(611\) | 0.729988 | 0.0295322 | ||||||||
\(612\) | 2.57834 | 0.104223 | ||||||||
\(613\) | 21.6655 | 0.875062 | 0.437531 | − | 0.899203i | \(-0.355853\pi\) | ||||
0.437531 | + | 0.899203i | \(0.355853\pi\) | |||||||
\(614\) | 36.9099 | 1.48956 | ||||||||
\(615\) | 1.76473 | 0.0711608 | ||||||||
\(616\) | 34.9200 | 1.40696 | ||||||||
\(617\) | −5.52946 | −0.222608 | −0.111304 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111304 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(618\) | 9.93051 | 0.399464 | ||||||||
\(619\) | −28.1602 | −1.13186 | −0.565928 | − | 0.824455i | \(-0.691482\pi\) | ||||
−0.565928 | + | 0.824455i | \(0.691482\pi\) | |||||||
\(620\) | −1.28917 | −0.0517743 | ||||||||
\(621\) | −1.62721 | −0.0652978 | ||||||||
\(622\) | 20.4111 | 0.818411 | ||||||||
\(623\) | −20.2439 | −0.811053 | ||||||||
\(624\) | −4.91638 | −0.196813 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −55.5805 | −2.22144 | ||||||||
\(627\) | 8.30330 | 0.331602 | ||||||||
\(628\) | −14.3828 | −0.573938 | ||||||||
\(629\) | −16.4111 | −0.654353 | ||||||||
\(630\) | −8.72999 | −0.347811 | ||||||||
\(631\) | −26.8716 | −1.06974 | −0.534871 | − | 0.844934i | \(-0.679640\pi\) | ||||
−0.534871 | + | 0.844934i | \(0.679640\pi\) | |||||||
\(632\) | −6.84333 | −0.272213 | ||||||||
\(633\) | −13.6514 | −0.542594 | ||||||||
\(634\) | 48.7810 | 1.93734 | ||||||||
\(635\) | 3.18639 | 0.126448 | ||||||||
\(636\) | 2.16724 | 0.0859365 | ||||||||
\(637\) | 16.1708 | 0.640711 | ||||||||
\(638\) | 34.6167 | 1.37049 | ||||||||
\(639\) | 11.2544 | 0.445218 | ||||||||
\(640\) | −9.66196 | −0.381922 | ||||||||
\(641\) | −11.3325 | −0.447607 | −0.223804 | − | 0.974634i | \(-0.571847\pi\) | ||||
−0.223804 | + | 0.974634i | \(0.571847\pi\) | |||||||
\(642\) | −11.4061 | −0.450162 | ||||||||
\(643\) | −1.25997 | −0.0496882 | −0.0248441 | − | 0.999691i | \(-0.507909\pi\) | ||||
−0.0248441 | + | 0.999691i | \(0.507909\pi\) | |||||||
\(644\) | −10.0978 | −0.397907 | ||||||||
\(645\) | 8.81361 | 0.347035 | ||||||||
\(646\) | −5.35218 | −0.210579 | ||||||||
\(647\) | −21.1411 | −0.831142 | −0.415571 | − | 0.909561i | \(-0.636418\pi\) | ||||
−0.415571 | + | 0.909561i | \(0.636418\pi\) | |||||||
\(648\) | 1.28917 | 0.0506433 | ||||||||
\(649\) | −30.3416 | −1.19101 | ||||||||
\(650\) | −1.81361 | −0.0711355 | ||||||||
\(651\) | −4.81361 | −0.188660 | ||||||||
\(652\) | −24.9612 | −0.977555 | ||||||||
\(653\) | 28.1502 | 1.10160 | 0.550801 | − | 0.834636i | \(-0.314322\pi\) | ||||
0.550801 | + | 0.834636i | \(0.314322\pi\) | |||||||
\(654\) | 1.69670 | 0.0663461 | ||||||||
\(655\) | 6.52444 | 0.254931 | ||||||||
\(656\) | −8.67609 | −0.338744 | ||||||||
\(657\) | −6.25945 | −0.244204 | ||||||||
\(658\) | −6.37279 | −0.248437 | ||||||||
\(659\) | 11.6217 | 0.452716 | 0.226358 | − | 0.974044i | \(-0.427318\pi\) | ||||
0.226358 | + | 0.974044i | \(0.427318\pi\) | |||||||
\(660\) | 7.25443 | 0.282378 | ||||||||
\(661\) | −4.95112 | −0.192576 | −0.0962882 | − | 0.995353i | \(-0.530697\pi\) | ||||
−0.0962882 | + | 0.995353i | \(0.530697\pi\) | |||||||
\(662\) | −26.4650 | −1.02859 | ||||||||
\(663\) | 2.00000 | 0.0776736 | ||||||||
\(664\) | 6.01005 | 0.233235 | ||||||||
\(665\) | 7.10278 | 0.275434 | ||||||||
\(666\) | 14.8816 | 0.576652 | ||||||||
\(667\) | 5.51941 | 0.213713 | ||||||||
\(668\) | 2.09775 | 0.0811645 | ||||||||
\(669\) | −23.5733 | −0.911397 | ||||||||
\(670\) | 7.68111 | 0.296747 | ||||||||
\(671\) | 44.3799 | 1.71327 | ||||||||
\(672\) | 30.5089 | 1.17690 | ||||||||
\(673\) | 30.1447 | 1.16199 | 0.580996 | − | 0.813907i | \(-0.302663\pi\) | ||||
0.580996 | + | 0.813907i | \(0.302663\pi\) | |||||||
\(674\) | −35.2927 | −1.35943 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 1.28917 | 0.0495834 | ||||||||
\(677\) | −30.1205 | −1.15762 | −0.578812 | − | 0.815461i | \(-0.696484\pi\) | ||||
−0.578812 | + | 0.815461i | \(0.696484\pi\) | |||||||
\(678\) | −23.1411 | −0.888728 | ||||||||
\(679\) | −67.7180 | −2.59878 | ||||||||
\(680\) | 2.57834 | 0.0988747 | ||||||||
\(681\) | 18.6761 | 0.715669 | ||||||||
\(682\) | 10.2056 | 0.390791 | ||||||||
\(683\) | 39.2716 | 1.50269 | 0.751343 | − | 0.659912i | \(-0.229406\pi\) | ||||
0.751343 | + | 0.659912i | \(0.229406\pi\) | |||||||
\(684\) | 1.90225 | 0.0727343 | ||||||||
\(685\) | 0.372787 | 0.0142435 | ||||||||
\(686\) | −80.0610 | −3.05674 | ||||||||
\(687\) | 13.8328 | 0.527753 | ||||||||
\(688\) | −43.3311 | −1.65198 | ||||||||
\(689\) | 1.68111 | 0.0640453 | ||||||||
\(690\) | 2.95112 | 0.112347 | ||||||||
\(691\) | 16.5472 | 0.629484 | 0.314742 | − | 0.949177i | \(-0.398082\pi\) | ||||
0.314742 | + | 0.949177i | \(0.398082\pi\) | |||||||
\(692\) | −17.1184 | −0.650742 | ||||||||
\(693\) | 27.0872 | 1.02896 | ||||||||
\(694\) | 60.1049 | 2.28155 | ||||||||
\(695\) | −1.47556 | −0.0559713 | ||||||||
\(696\) | −4.37279 | −0.165750 | ||||||||
\(697\) | 3.52946 | 0.133688 | ||||||||
\(698\) | 22.8816 | 0.866083 | ||||||||
\(699\) | 10.3275 | 0.390621 | ||||||||
\(700\) | 6.20555 | 0.234548 | ||||||||
\(701\) | 22.8222 | 0.861983 | 0.430991 | − | 0.902356i | \(-0.358164\pi\) | ||||
0.430991 | + | 0.902356i | \(0.358164\pi\) | |||||||
\(702\) | −1.81361 | −0.0684502 | ||||||||
\(703\) | −12.1078 | −0.456654 | ||||||||
\(704\) | −9.35218 | −0.352473 | ||||||||
\(705\) | 0.729988 | 0.0274929 | ||||||||
\(706\) | −4.82774 | −0.181694 | ||||||||
\(707\) | −5.30833 | −0.199640 | ||||||||
\(708\) | −6.95112 | −0.261239 | ||||||||
\(709\) | −42.4705 | −1.59501 | −0.797507 | − | 0.603309i | \(-0.793848\pi\) | ||||
−0.797507 | + | 0.603309i | \(0.793848\pi\) | |||||||
\(710\) | −20.4111 | −0.766015 | ||||||||
\(711\) | −5.30833 | −0.199078 | ||||||||
\(712\) | −5.42166 | −0.203185 | ||||||||
\(713\) | 1.62721 | 0.0609396 | ||||||||
\(714\) | −17.4600 | −0.653423 | ||||||||
\(715\) | 5.62721 | 0.210446 | ||||||||
\(716\) | −24.3799 | −0.911121 | ||||||||
\(717\) | 11.6811 | 0.436239 | ||||||||
\(718\) | 18.8277 | 0.702645 | ||||||||
\(719\) | 12.2947 | 0.458515 | 0.229258 | − | 0.973366i | \(-0.426370\pi\) | ||||
0.229258 | + | 0.973366i | \(0.426370\pi\) | |||||||
\(720\) | −4.91638 | −0.183223 | ||||||||
\(721\) | −26.3572 | −0.981593 | ||||||||
\(722\) | 30.5098 | 1.13546 | ||||||||
\(723\) | −13.0036 | −0.483608 | ||||||||
\(724\) | −29.4983 | −1.09630 | ||||||||
\(725\) | −3.39194 | −0.125974 | ||||||||
\(726\) | −37.4791 | −1.39098 | ||||||||
\(727\) | 7.07160 | 0.262271 | 0.131136 | − | 0.991364i | \(-0.458138\pi\) | ||||
0.131136 | + | 0.991364i | \(0.458138\pi\) | |||||||
\(728\) | 6.20555 | 0.229993 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.3522 | 0.420163 | ||||||||
\(731\) | 17.6272 | 0.651966 | ||||||||
\(732\) | 10.1672 | 0.375792 | ||||||||
\(733\) | −12.5003 | −0.461708 | −0.230854 | − | 0.972988i | \(-0.574152\pi\) | ||||
−0.230854 | + | 0.972988i | \(0.574152\pi\) | |||||||
\(734\) | 27.5577 | 1.01717 | ||||||||
\(735\) | 16.1708 | 0.596469 | ||||||||
\(736\) | −10.3133 | −0.380155 | ||||||||
\(737\) | −23.8328 | −0.877891 | ||||||||
\(738\) | −3.20053 | −0.117813 | ||||||||
\(739\) | −46.8716 | −1.72420 | −0.862100 | − | 0.506739i | \(-0.830851\pi\) | ||||
−0.862100 | + | 0.506739i | \(0.830851\pi\) | |||||||
\(740\) | −10.5783 | −0.388867 | ||||||||
\(741\) | 1.47556 | 0.0542061 | ||||||||
\(742\) | −14.6761 | −0.538776 | ||||||||
\(743\) | 0.358654 | 0.0131577 | 0.00657886 | − | 0.999978i | \(-0.497906\pi\) | ||||
0.00657886 | + | 0.999978i | \(0.497906\pi\) | |||||||
\(744\) | −1.28917 | −0.0472632 | ||||||||
\(745\) | 12.4408 | 0.455796 | ||||||||
\(746\) | −7.62721 | −0.279252 | ||||||||
\(747\) | 4.66196 | 0.170572 | ||||||||
\(748\) | 14.5089 | 0.530496 | ||||||||
\(749\) | 30.2736 | 1.10617 | ||||||||
\(750\) | −1.81361 | −0.0662235 | ||||||||
\(751\) | 14.8675 | 0.542523 | 0.271261 | − | 0.962506i | \(-0.412559\pi\) | ||||
0.271261 | + | 0.962506i | \(0.412559\pi\) | |||||||
\(752\) | −3.58890 | −0.130874 | ||||||||
\(753\) | 24.9497 | 0.909217 | ||||||||
\(754\) | 6.15165 | 0.224030 | ||||||||
\(755\) | −9.13249 | −0.332365 | ||||||||
\(756\) | 6.20555 | 0.225694 | ||||||||
\(757\) | 47.3608 | 1.72136 | 0.860678 | − | 0.509149i | \(-0.170040\pi\) | ||||
0.860678 | + | 0.509149i | \(0.170040\pi\) | |||||||
\(758\) | 48.5472 | 1.76331 | ||||||||
\(759\) | −9.15667 | −0.332366 | ||||||||
\(760\) | 1.90225 | 0.0690018 | ||||||||
\(761\) | 42.8661 | 1.55389 | 0.776947 | − | 0.629566i | \(-0.216767\pi\) | ||||
0.776947 | + | 0.629566i | \(0.216767\pi\) | |||||||
\(762\) | −5.77886 | −0.209346 | ||||||||
\(763\) | −4.50331 | −0.163031 | ||||||||
\(764\) | −32.6066 | −1.17967 | ||||||||
\(765\) | 2.00000 | 0.0723102 | ||||||||
\(766\) | −58.8761 | −2.12728 | ||||||||
\(767\) | −5.39194 | −0.194692 | ||||||||
\(768\) | 20.8469 | 0.752248 | ||||||||
\(769\) | −7.88666 | −0.284400 | −0.142200 | − | 0.989838i | \(-0.545418\pi\) | ||||
−0.142200 | + | 0.989838i | \(0.545418\pi\) | |||||||
\(770\) | −49.1255 | −1.77036 | ||||||||
\(771\) | 20.4494 | 0.736468 | ||||||||
\(772\) | −13.5094 | −0.486213 | ||||||||
\(773\) | 12.3658 | 0.444767 | 0.222383 | − | 0.974959i | \(-0.428616\pi\) | ||||
0.222383 | + | 0.974959i | \(0.428616\pi\) | |||||||
\(774\) | −15.9844 | −0.574548 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | −18.1361 | −0.651047 | ||||||||
\(777\) | −39.4983 | −1.41699 | ||||||||
\(778\) | 39.0616 | 1.40042 | ||||||||
\(779\) | 2.60397 | 0.0932969 | ||||||||
\(780\) | 1.28917 | 0.0461596 | ||||||||
\(781\) | 63.3311 | 2.26616 | ||||||||
\(782\) | 5.90225 | 0.211064 | ||||||||
\(783\) | −3.39194 | −0.121218 | ||||||||
\(784\) | −79.5019 | −2.83935 | ||||||||
\(785\) | −11.1567 | −0.398199 | ||||||||
\(786\) | −11.8328 | −0.422061 | ||||||||
\(787\) | 33.9945 | 1.21177 | 0.605886 | − | 0.795552i | \(-0.292819\pi\) | ||||
0.605886 | + | 0.795552i | \(0.292819\pi\) | |||||||
\(788\) | 15.7662 | 0.561647 | ||||||||
\(789\) | −6.93554 | −0.246912 | ||||||||
\(790\) | 9.62721 | 0.342521 | ||||||||
\(791\) | 61.4202 | 2.18385 | ||||||||
\(792\) | 7.25443 | 0.257775 | ||||||||
\(793\) | 7.88666 | 0.280064 | ||||||||
\(794\) | 7.82272 | 0.277618 | ||||||||
\(795\) | 1.68111 | 0.0596229 | ||||||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | 1.04334 | 0.0369569 | 0.0184784 | − | 0.999829i | \(-0.494118\pi\) | ||||
0.0184784 | + | 0.999829i | \(0.494118\pi\) | |||||||
\(798\) | −12.8816 | −0.456005 | ||||||||
\(799\) | 1.45998 | 0.0516502 | ||||||||
\(800\) | 6.33804 | 0.224084 | ||||||||
\(801\) | −4.20555 | −0.148596 | ||||||||
\(802\) | 4.20555 | 0.148503 | ||||||||
\(803\) | −35.2233 | −1.24300 | ||||||||
\(804\) | −5.45998 | −0.192559 | ||||||||
\(805\) | −7.83276 | −0.276069 | ||||||||
\(806\) | 1.81361 | 0.0638816 | ||||||||
\(807\) | −11.1567 | −0.392734 | ||||||||
\(808\) | −1.42166 | −0.0500139 | ||||||||
\(809\) | 14.3119 | 0.503179 | 0.251590 | − | 0.967834i | \(-0.419047\pi\) | ||||
0.251590 | + | 0.967834i | \(0.419047\pi\) | |||||||
\(810\) | −1.81361 | −0.0637236 | ||||||||
\(811\) | −14.2211 | −0.499372 | −0.249686 | − | 0.968327i | \(-0.580327\pi\) | ||||
−0.249686 | + | 0.968327i | \(0.580327\pi\) | |||||||
\(812\) | −21.0489 | −0.738671 | ||||||||
\(813\) | 17.2686 | 0.605635 | ||||||||
\(814\) | 83.7422 | 2.93516 | ||||||||
\(815\) | −19.3622 | −0.678229 | ||||||||
\(816\) | −9.83276 | −0.344216 | ||||||||
\(817\) | 13.0050 | 0.454988 | ||||||||
\(818\) | 1.37781 | 0.0481740 | ||||||||
\(819\) | 4.81361 | 0.168201 | ||||||||
\(820\) | 2.27504 | 0.0794477 | ||||||||
\(821\) | −24.8122 | −0.865950 | −0.432975 | − | 0.901406i | \(-0.642536\pi\) | ||||
−0.432975 | + | 0.901406i | \(0.642536\pi\) | |||||||
\(822\) | −0.676089 | −0.0235813 | ||||||||
\(823\) | −9.05747 | −0.315724 | −0.157862 | − | 0.987461i | \(-0.550460\pi\) | ||||
−0.157862 | + | 0.987461i | \(0.550460\pi\) | |||||||
\(824\) | −7.05892 | −0.245909 | ||||||||
\(825\) | 5.62721 | 0.195914 | ||||||||
\(826\) | 47.0716 | 1.63783 | ||||||||
\(827\) | −38.7285 | −1.34672 | −0.673362 | − | 0.739313i | \(-0.735150\pi\) | ||||
−0.673362 | + | 0.739313i | \(0.735150\pi\) | |||||||
\(828\) | −2.09775 | −0.0729019 | ||||||||
\(829\) | 39.2927 | 1.36469 | 0.682347 | − | 0.731029i | \(-0.260960\pi\) | ||||
0.682347 | + | 0.731029i | \(0.260960\pi\) | |||||||
\(830\) | −8.45495 | −0.293476 | ||||||||
\(831\) | −0.304754 | −0.0105718 | ||||||||
\(832\) | −1.66196 | −0.0576179 | ||||||||
\(833\) | 32.3416 | 1.12057 | ||||||||
\(834\) | 2.67609 | 0.0926654 | ||||||||
\(835\) | 1.62721 | 0.0563120 | ||||||||
\(836\) | 10.7044 | 0.370218 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 67.0278 | 2.31544 | ||||||||
\(839\) | −0.569743 | −0.0196697 | −0.00983486 | − | 0.999952i | \(-0.503131\pi\) | ||||
−0.00983486 | + | 0.999952i | \(0.503131\pi\) | |||||||
\(840\) | 6.20555 | 0.214112 | ||||||||
\(841\) | −17.4947 | −0.603266 | ||||||||
\(842\) | −8.48059 | −0.292260 | ||||||||
\(843\) | 13.6569 | 0.470370 | ||||||||
\(844\) | −17.5989 | −0.605781 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −1.32391 | −0.0455170 | ||||||||
\(847\) | 99.4757 | 3.41803 | ||||||||
\(848\) | −8.26499 | −0.283821 | ||||||||
\(849\) | 15.9844 | 0.548584 | ||||||||
\(850\) | −3.62721 | −0.124412 | ||||||||
\(851\) | 13.3522 | 0.457707 | ||||||||
\(852\) | 14.5089 | 0.497065 | ||||||||
\(853\) | −8.79248 | −0.301049 | −0.150524 | − | 0.988606i | \(-0.548096\pi\) | ||||
−0.150524 | + | 0.988606i | \(0.548096\pi\) | |||||||
\(854\) | −68.8505 | −2.35601 | ||||||||
\(855\) | 1.47556 | 0.0504632 | ||||||||
\(856\) | 8.10780 | 0.277119 | ||||||||
\(857\) | −26.5783 | −0.907899 | −0.453949 | − | 0.891027i | \(-0.649985\pi\) | ||||
−0.453949 | + | 0.891027i | \(0.649985\pi\) | |||||||
\(858\) | −10.2056 | −0.348412 | ||||||||
\(859\) | −30.7044 | −1.04762 | −0.523810 | − | 0.851835i | \(-0.675490\pi\) | ||||
−0.523810 | + | 0.851835i | \(0.675490\pi\) | |||||||
\(860\) | 11.3622 | 0.387449 | ||||||||
\(861\) | 8.49472 | 0.289499 | ||||||||
\(862\) | 29.1411 | 0.992549 | ||||||||
\(863\) | 25.0136 | 0.851473 | 0.425737 | − | 0.904847i | \(-0.360015\pi\) | ||||
0.425737 | + | 0.904847i | \(0.360015\pi\) | |||||||
\(864\) | 6.33804 | 0.215625 | ||||||||
\(865\) | −13.2786 | −0.451486 | ||||||||
\(866\) | 13.1028 | 0.445250 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | −6.20555 | −0.210630 | ||||||||
\(869\) | −29.8711 | −1.01331 | ||||||||
\(870\) | 6.15165 | 0.208561 | ||||||||
\(871\) | −4.23527 | −0.143507 | ||||||||
\(872\) | −1.20607 | −0.0408426 | ||||||||
\(873\) | −14.0680 | −0.476131 | ||||||||
\(874\) | 4.35457 | 0.147295 | ||||||||
\(875\) | 4.81361 | 0.162730 | ||||||||
\(876\) | −8.06949 | −0.272643 | ||||||||
\(877\) | 50.3799 | 1.70121 | 0.850605 | − | 0.525806i | \(-0.176236\pi\) | ||||
0.850605 | + | 0.525806i | \(0.176236\pi\) | |||||||
\(878\) | 57.4727 | 1.93961 | ||||||||
\(879\) | 5.40608 | 0.182342 | ||||||||
\(880\) | −27.6655 | −0.932605 | ||||||||
\(881\) | 9.43026 | 0.317713 | 0.158857 | − | 0.987302i | \(-0.449219\pi\) | ||||
0.158857 | + | 0.987302i | \(0.449219\pi\) | |||||||
\(882\) | −29.3275 | −0.987508 | ||||||||
\(883\) | 2.22522 | 0.0748847 | 0.0374424 | − | 0.999299i | \(-0.488079\pi\) | ||||
0.0374424 | + | 0.999299i | \(0.488079\pi\) | |||||||
\(884\) | 2.57834 | 0.0867189 | ||||||||
\(885\) | −5.39194 | −0.181248 | ||||||||
\(886\) | −7.21057 | −0.242244 | ||||||||
\(887\) | 19.7491 | 0.663111 | 0.331556 | − | 0.943436i | \(-0.392427\pi\) | ||||
0.331556 | + | 0.943436i | \(0.392427\pi\) | |||||||
\(888\) | −10.5783 | −0.354986 | ||||||||
\(889\) | 15.3380 | 0.514422 | ||||||||
\(890\) | 7.62721 | 0.255665 | ||||||||
\(891\) | 5.62721 | 0.188519 | ||||||||
\(892\) | −30.3900 | −1.01753 | ||||||||
\(893\) | 1.07714 | 0.0360452 | ||||||||
\(894\) | −22.5628 | −0.754611 | ||||||||
\(895\) | −18.9114 | −0.632137 | ||||||||
\(896\) | −46.5089 | −1.55375 | ||||||||
\(897\) | −1.62721 | −0.0543311 | ||||||||
\(898\) | 21.6655 | 0.722988 | ||||||||
\(899\) | 3.39194 | 0.113128 | ||||||||
\(900\) | 1.28917 | 0.0429723 | ||||||||
\(901\) | 3.36222 | 0.112012 | ||||||||
\(902\) | −18.0100 | −0.599669 | ||||||||
\(903\) | 42.4252 | 1.41182 | ||||||||
\(904\) | 16.4494 | 0.547099 | ||||||||
\(905\) | −22.8816 | −0.760611 | ||||||||
\(906\) | 16.5628 | 0.550261 | ||||||||
\(907\) | 7.89220 | 0.262056 | 0.131028 | − | 0.991379i | \(-0.458172\pi\) | ||||
0.131028 | + | 0.991379i | \(0.458172\pi\) | |||||||
\(908\) | 24.0766 | 0.799011 | ||||||||
\(909\) | −1.10278 | −0.0365767 | ||||||||
\(910\) | −8.72999 | −0.289396 | ||||||||
\(911\) | −53.1653 | −1.76144 | −0.880722 | − | 0.473634i | \(-0.842942\pi\) | ||||
−0.880722 | + | 0.473634i | \(0.842942\pi\) | |||||||
\(912\) | −7.25443 | −0.240218 | ||||||||
\(913\) | 26.2338 | 0.868213 | ||||||||
\(914\) | −38.7144 | −1.28056 | ||||||||
\(915\) | 7.88666 | 0.260725 | ||||||||
\(916\) | 17.8328 | 0.589211 | ||||||||
\(917\) | 31.4061 | 1.03712 | ||||||||
\(918\) | −3.62721 | −0.119716 | ||||||||
\(919\) | −37.1608 | −1.22582 | −0.612910 | − | 0.790153i | \(-0.710001\pi\) | ||||
−0.612910 | + | 0.790153i | \(0.710001\pi\) | |||||||
\(920\) | −2.09775 | −0.0691608 | ||||||||
\(921\) | −20.3517 | −0.670610 | ||||||||
\(922\) | −52.0071 | −1.71276 | ||||||||
\(923\) | 11.2544 | 0.370444 | ||||||||
\(924\) | 34.9200 | 1.14878 | ||||||||
\(925\) | −8.20555 | −0.269797 | ||||||||
\(926\) | 48.2721 | 1.58632 | ||||||||
\(927\) | −5.47556 | −0.179841 | ||||||||
\(928\) | −21.4983 | −0.705716 | ||||||||
\(929\) | 21.6499 | 0.710311 | 0.355156 | − | 0.934807i | \(-0.384428\pi\) | ||||
0.355156 | + | 0.934807i | \(0.384428\pi\) | |||||||
\(930\) | 1.81361 | 0.0594705 | ||||||||
\(931\) | 23.8610 | 0.782014 | ||||||||
\(932\) | 13.3139 | 0.436110 | ||||||||
\(933\) | −11.2544 | −0.368453 | ||||||||
\(934\) | −29.5038 | −0.965395 | ||||||||
\(935\) | 11.2544 | 0.368059 | ||||||||
\(936\) | 1.28917 | 0.0421378 | ||||||||
\(937\) | 22.0766 | 0.721212 | 0.360606 | − | 0.932718i | \(-0.382570\pi\) | ||||
0.360606 | + | 0.932718i | \(0.382570\pi\) | |||||||
\(938\) | 36.9739 | 1.20724 | ||||||||
\(939\) | 30.6464 | 1.00011 | ||||||||
\(940\) | 0.941078 | 0.0306946 | ||||||||
\(941\) | −29.8172 | −0.972012 | −0.486006 | − | 0.873955i | \(-0.661547\pi\) | ||||
−0.486006 | + | 0.873955i | \(0.661547\pi\) | |||||||
\(942\) | 20.2338 | 0.659253 | ||||||||
\(943\) | −2.87159 | −0.0935119 | ||||||||
\(944\) | 26.5089 | 0.862790 | ||||||||
\(945\) | 4.81361 | 0.156587 | ||||||||
\(946\) | −89.9477 | −2.92445 | ||||||||
\(947\) | 3.52946 | 0.114692 | 0.0573460 | − | 0.998354i | \(-0.481736\pi\) | ||||
0.0573460 | + | 0.998354i | \(0.481736\pi\) | |||||||
\(948\) | −6.84333 | −0.222261 | ||||||||
\(949\) | −6.25945 | −0.203190 | ||||||||
\(950\) | −2.67609 | −0.0868238 | ||||||||
\(951\) | −26.8972 | −0.872202 | ||||||||
\(952\) | 12.4111 | 0.402246 | ||||||||
\(953\) | 24.5527 | 0.795340 | 0.397670 | − | 0.917528i | \(-0.369819\pi\) | ||||
0.397670 | + | 0.917528i | \(0.369819\pi\) | |||||||
\(954\) | −3.04888 | −0.0987110 | ||||||||
\(955\) | −25.2927 | −0.818454 | ||||||||
\(956\) | 15.0589 | 0.487040 | ||||||||
\(957\) | −19.0872 | −0.617001 | ||||||||
\(958\) | −18.1900 | −0.587691 | ||||||||
\(959\) | 1.79445 | 0.0579458 | ||||||||
\(960\) | −1.66196 | −0.0536394 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 14.8816 | 0.479803 | ||||||||
\(963\) | 6.28917 | 0.202666 | ||||||||
\(964\) | −16.7638 | −0.539925 | ||||||||
\(965\) | −10.4791 | −0.337335 | ||||||||
\(966\) | 14.2056 | 0.457056 | ||||||||
\(967\) | 29.6555 | 0.953656 | 0.476828 | − | 0.878997i | \(-0.341786\pi\) | ||||
0.476828 | + | 0.878997i | \(0.341786\pi\) | |||||||
\(968\) | 26.6413 | 0.856285 | ||||||||
\(969\) | 2.95112 | 0.0948038 | ||||||||
\(970\) | 25.5139 | 0.819201 | ||||||||
\(971\) | 36.7738 | 1.18013 | 0.590064 | − | 0.807356i | \(-0.299102\pi\) | ||||
0.590064 | + | 0.807356i | \(0.299102\pi\) | |||||||
\(972\) | 1.28917 | 0.0413501 | ||||||||
\(973\) | −7.10278 | −0.227705 | ||||||||
\(974\) | 30.6449 | 0.981926 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | −38.7738 | −1.24112 | ||||||||
\(977\) | 35.5083 | 1.13601 | 0.568006 | − | 0.823024i | \(-0.307715\pi\) | ||||
0.568006 | + | 0.823024i | \(0.307715\pi\) | |||||||
\(978\) | 35.1155 | 1.12287 | ||||||||
\(979\) | −23.6655 | −0.756353 | ||||||||
\(980\) | 20.8469 | 0.665930 | ||||||||
\(981\) | −0.935538 | −0.0298694 | ||||||||
\(982\) | 3.02324 | 0.0964756 | ||||||||
\(983\) | 8.66196 | 0.276273 | 0.138137 | − | 0.990413i | \(-0.455889\pi\) | ||||
0.138137 | + | 0.990413i | \(0.455889\pi\) | |||||||
\(984\) | 2.27504 | 0.0725255 | ||||||||
\(985\) | 12.2297 | 0.389672 | ||||||||
\(986\) | 12.3033 | 0.391817 | ||||||||
\(987\) | 3.51388 | 0.111848 | ||||||||
\(988\) | 1.90225 | 0.0605186 | ||||||||
\(989\) | −14.3416 | −0.456037 | ||||||||
\(990\) | −10.2056 | −0.324354 | ||||||||
\(991\) | −1.53500 | −0.0487609 | −0.0243805 | − | 0.999703i | \(-0.507761\pi\) | ||||
−0.0243805 | + | 0.999703i | \(0.507761\pi\) | |||||||
\(992\) | −6.33804 | −0.201233 | ||||||||
\(993\) | 14.5925 | 0.463078 | ||||||||
\(994\) | −98.2510 | −3.11633 | ||||||||
\(995\) | −6.20555 | −0.196729 | ||||||||
\(996\) | 6.01005 | 0.190436 | ||||||||
\(997\) | −41.8766 | −1.32625 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(998\) | −44.3160 | −1.40280 | ||||||||
\(999\) | −8.20555 | −0.259612 |
(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 | 6045.2.a.r.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.r.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |