Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 \) |
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 | 1.7 | ||
Root | \(1.54977\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54977 | −1.09585 | −0.547925 | − | 0.836527i | \(-0.684582\pi\) | ||||
−0.547925 | + | 0.836527i | \(0.684582\pi\) | |||||||
\(3\) | −3.21447 | −1.85588 | −0.927939 | − | 0.372732i | \(-0.878421\pi\) | ||||
−0.927939 | + | 0.372732i | \(0.878421\pi\) | |||||||
\(4\) | 0.401778 | 0.200889 | ||||||||
\(5\) | −2.07911 | −0.929805 | −0.464903 | − | 0.885362i | \(-0.653911\pi\) | ||||
−0.464903 | + | 0.885362i | \(0.653911\pi\) | |||||||
\(6\) | 4.98169 | 2.03377 | ||||||||
\(7\) | 0.871568 | 0.329422 | 0.164711 | − | 0.986342i | \(-0.447331\pi\) | ||||
0.164711 | + | 0.986342i | \(0.447331\pi\) | |||||||
\(8\) | 2.47687 | 0.875706 | ||||||||
\(9\) | 7.33285 | 2.44428 | ||||||||
\(10\) | 3.22213 | 1.01893 | ||||||||
\(11\) | 0.118796 | 0.0358185 | 0.0179092 | − | 0.999840i | \(-0.494299\pi\) | ||||
0.0179092 | + | 0.999840i | \(0.494299\pi\) | |||||||
\(12\) | −1.29151 | −0.372826 | ||||||||
\(13\) | −1.17173 | −0.324978 | −0.162489 | − | 0.986710i | \(-0.551952\pi\) | ||||
−0.162489 | + | 0.986710i | \(0.551952\pi\) | |||||||
\(14\) | −1.35073 | −0.360997 | ||||||||
\(15\) | 6.68324 | 1.72560 | ||||||||
\(16\) | −4.64213 | −1.16053 | ||||||||
\(17\) | 6.72101 | 1.63008 | 0.815042 | − | 0.579402i | \(-0.196714\pi\) | ||||
0.815042 | + | 0.579402i | \(0.196714\pi\) | |||||||
\(18\) | −11.3642 | −2.67857 | ||||||||
\(19\) | 4.91679 | 1.12799 | 0.563995 | − | 0.825778i | \(-0.309264\pi\) | ||||
0.563995 | + | 0.825778i | \(0.309264\pi\) | |||||||
\(20\) | −0.835340 | −0.186788 | ||||||||
\(21\) | −2.80163 | −0.611366 | ||||||||
\(22\) | −0.184107 | −0.0392517 | ||||||||
\(23\) | 2.58561 | 0.539136 | 0.269568 | − | 0.962981i | \(-0.413119\pi\) | ||||
0.269568 | + | 0.962981i | \(0.413119\pi\) | |||||||
\(24\) | −7.96184 | −1.62520 | ||||||||
\(25\) | −0.677311 | −0.135462 | ||||||||
\(26\) | 1.81590 | 0.356127 | ||||||||
\(27\) | −13.9278 | −2.68041 | ||||||||
\(28\) | 0.350177 | 0.0661772 | ||||||||
\(29\) | 0.929188 | 0.172546 | 0.0862729 | − | 0.996272i | \(-0.472504\pi\) | ||||
0.0862729 | + | 0.996272i | \(0.472504\pi\) | |||||||
\(30\) | −10.3575 | −1.89101 | ||||||||
\(31\) | 6.92176 | 1.24318 | 0.621592 | − | 0.783341i | \(-0.286486\pi\) | ||||
0.621592 | + | 0.783341i | \(0.286486\pi\) | |||||||
\(32\) | 2.24048 | 0.396064 | ||||||||
\(33\) | −0.381868 | −0.0664747 | ||||||||
\(34\) | −10.4160 | −1.78633 | ||||||||
\(35\) | −1.81208 | −0.306298 | ||||||||
\(36\) | 2.94618 | 0.491030 | ||||||||
\(37\) | −0.871716 | −0.143309 | −0.0716546 | − | 0.997430i | \(-0.522828\pi\) | ||||
−0.0716546 | + | 0.997430i | \(0.522828\pi\) | |||||||
\(38\) | −7.61988 | −1.23611 | ||||||||
\(39\) | 3.76648 | 0.603120 | ||||||||
\(40\) | −5.14968 | −0.814236 | ||||||||
\(41\) | 1.73741 | 0.271338 | 0.135669 | − | 0.990754i | \(-0.456682\pi\) | ||||
0.135669 | + | 0.990754i | \(0.456682\pi\) | |||||||
\(42\) | 4.34188 | 0.669966 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 0.0477298 | 0.00719554 | ||||||||
\(45\) | −15.2458 | −2.27271 | ||||||||
\(46\) | −4.00709 | −0.590813 | ||||||||
\(47\) | −9.72016 | −1.41783 | −0.708916 | − | 0.705293i | \(-0.750815\pi\) | ||||
−0.708916 | + | 0.705293i | \(0.750815\pi\) | |||||||
\(48\) | 14.9220 | 2.15381 | ||||||||
\(49\) | −6.24037 | −0.891481 | ||||||||
\(50\) | 1.04967 | 0.148446 | ||||||||
\(51\) | −21.6045 | −3.02524 | ||||||||
\(52\) | −0.470774 | −0.0652846 | ||||||||
\(53\) | −5.24926 | −0.721041 | −0.360520 | − | 0.932751i | \(-0.617401\pi\) | ||||
−0.360520 | + | 0.932751i | \(0.617401\pi\) | |||||||
\(54\) | 21.5849 | 2.93733 | ||||||||
\(55\) | −0.246991 | −0.0333042 | ||||||||
\(56\) | 2.15876 | 0.288477 | ||||||||
\(57\) | −15.8049 | −2.09341 | ||||||||
\(58\) | −1.44003 | −0.189085 | ||||||||
\(59\) | −3.87260 | −0.504169 | −0.252085 | − | 0.967705i | \(-0.581116\pi\) | ||||
−0.252085 | + | 0.967705i | \(0.581116\pi\) | |||||||
\(60\) | 2.68518 | 0.346655 | ||||||||
\(61\) | −2.03937 | −0.261114 | −0.130557 | − | 0.991441i | \(-0.541677\pi\) | ||||
−0.130557 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(62\) | −10.7271 | −1.36234 | ||||||||
\(63\) | 6.39107 | 0.805200 | ||||||||
\(64\) | 5.81204 | 0.726505 | ||||||||
\(65\) | 2.43614 | 0.302166 | ||||||||
\(66\) | 0.591807 | 0.0728464 | ||||||||
\(67\) | −1.82807 | −0.223335 | −0.111667 | − | 0.993746i | \(-0.535619\pi\) | ||||
−0.111667 | + | 0.993746i | \(0.535619\pi\) | |||||||
\(68\) | 2.70036 | 0.327466 | ||||||||
\(69\) | −8.31136 | −1.00057 | ||||||||
\(70\) | 2.80831 | 0.335657 | ||||||||
\(71\) | 12.5462 | 1.48896 | 0.744481 | − | 0.667644i | \(-0.232697\pi\) | ||||
0.744481 | + | 0.667644i | \(0.232697\pi\) | |||||||
\(72\) | 18.1625 | 2.14047 | ||||||||
\(73\) | 3.30592 | 0.386928 | 0.193464 | − | 0.981107i | \(-0.438028\pi\) | ||||
0.193464 | + | 0.981107i | \(0.438028\pi\) | |||||||
\(74\) | 1.35096 | 0.157046 | ||||||||
\(75\) | 2.17720 | 0.251401 | ||||||||
\(76\) | 1.97546 | 0.226601 | ||||||||
\(77\) | 0.103539 | 0.0117994 | ||||||||
\(78\) | −5.83717 | −0.660929 | ||||||||
\(79\) | 6.32506 | 0.711625 | 0.355813 | − | 0.934557i | \(-0.384204\pi\) | ||||
0.355813 | + | 0.934557i | \(0.384204\pi\) | |||||||
\(80\) | 9.65149 | 1.07907 | ||||||||
\(81\) | 22.7721 | 2.53023 | ||||||||
\(82\) | −2.69258 | −0.297346 | ||||||||
\(83\) | −2.34720 | −0.257639 | −0.128820 | − | 0.991668i | \(-0.541119\pi\) | ||||
−0.128820 | + | 0.991668i | \(0.541119\pi\) | |||||||
\(84\) | −1.12564 | −0.122817 | ||||||||
\(85\) | −13.9737 | −1.51566 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.98685 | −0.320224 | ||||||||
\(88\) | 0.294244 | 0.0313665 | ||||||||
\(89\) | 7.20924 | 0.764178 | 0.382089 | − | 0.924126i | \(-0.375205\pi\) | ||||
0.382089 | + | 0.924126i | \(0.375205\pi\) | |||||||
\(90\) | 23.6274 | 2.49055 | ||||||||
\(91\) | −1.02124 | −0.107055 | ||||||||
\(92\) | 1.03884 | 0.108307 | ||||||||
\(93\) | −22.2498 | −2.30720 | ||||||||
\(94\) | 15.0640 | 1.55373 | ||||||||
\(95\) | −10.2225 | −1.04881 | ||||||||
\(96\) | −7.20196 | −0.735047 | ||||||||
\(97\) | −12.2645 | −1.24527 | −0.622637 | − | 0.782511i | \(-0.713939\pi\) | ||||
−0.622637 | + | 0.782511i | \(0.713939\pi\) | |||||||
\(98\) | 9.67112 | 0.976931 | ||||||||
\(99\) | 0.871116 | 0.0875505 | ||||||||
\(100\) | −0.272129 | −0.0272129 | ||||||||
\(101\) | 15.0311 | 1.49565 | 0.747823 | − | 0.663898i | \(-0.231099\pi\) | ||||
0.747823 | + | 0.663898i | \(0.231099\pi\) | |||||||
\(102\) | 33.4820 | 3.31521 | ||||||||
\(103\) | 5.37576 | 0.529690 | 0.264845 | − | 0.964291i | \(-0.414679\pi\) | ||||
0.264845 | + | 0.964291i | \(0.414679\pi\) | |||||||
\(104\) | −2.90221 | −0.284585 | ||||||||
\(105\) | 5.82490 | 0.568452 | ||||||||
\(106\) | 8.13512 | 0.790153 | ||||||||
\(107\) | 4.18065 | 0.404159 | 0.202079 | − | 0.979369i | \(-0.435230\pi\) | ||||
0.202079 | + | 0.979369i | \(0.435230\pi\) | |||||||
\(108\) | −5.59590 | −0.538465 | ||||||||
\(109\) | −15.0109 | −1.43778 | −0.718892 | − | 0.695122i | \(-0.755350\pi\) | ||||
−0.718892 | + | 0.695122i | \(0.755350\pi\) | |||||||
\(110\) | 0.382778 | 0.0364965 | ||||||||
\(111\) | 2.80211 | 0.265964 | ||||||||
\(112\) | −4.04593 | −0.382305 | ||||||||
\(113\) | 10.5214 | 0.989772 | 0.494886 | − | 0.868958i | \(-0.335210\pi\) | ||||
0.494886 | + | 0.868958i | \(0.335210\pi\) | |||||||
\(114\) | 24.4939 | 2.29407 | ||||||||
\(115\) | −5.37575 | −0.501292 | ||||||||
\(116\) | 0.373328 | 0.0346626 | ||||||||
\(117\) | −8.59208 | −0.794338 | ||||||||
\(118\) | 6.00163 | 0.552494 | ||||||||
\(119\) | 5.85782 | 0.536985 | ||||||||
\(120\) | 16.5535 | 1.51112 | ||||||||
\(121\) | −10.9859 | −0.998717 | ||||||||
\(122\) | 3.16054 | 0.286142 | ||||||||
\(123\) | −5.58486 | −0.503570 | ||||||||
\(124\) | 2.78101 | 0.249742 | ||||||||
\(125\) | 11.8037 | 1.05576 | ||||||||
\(126\) | −9.90468 | −0.882379 | ||||||||
\(127\) | 18.5498 | 1.64603 | 0.823016 | − | 0.568018i | \(-0.192290\pi\) | ||||
0.823016 | + | 0.568018i | \(0.192290\pi\) | |||||||
\(128\) | −13.4883 | −1.19221 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.77545 | −0.331129 | ||||||||
\(131\) | 19.2658 | 1.68326 | 0.841628 | − | 0.540057i | \(-0.181597\pi\) | ||||
0.841628 | + | 0.540057i | \(0.181597\pi\) | |||||||
\(132\) | −0.153426 | −0.0133541 | ||||||||
\(133\) | 4.28532 | 0.371584 | ||||||||
\(134\) | 2.83309 | 0.244741 | ||||||||
\(135\) | 28.9574 | 2.49226 | ||||||||
\(136\) | 16.6471 | 1.42748 | ||||||||
\(137\) | 10.4252 | 0.890685 | 0.445343 | − | 0.895360i | \(-0.353082\pi\) | ||||
0.445343 | + | 0.895360i | \(0.353082\pi\) | |||||||
\(138\) | 12.8807 | 1.09648 | ||||||||
\(139\) | 12.6616 | 1.07394 | 0.536972 | − | 0.843600i | \(-0.319568\pi\) | ||||
0.536972 | + | 0.843600i | \(0.319568\pi\) | |||||||
\(140\) | −0.728056 | −0.0615319 | ||||||||
\(141\) | 31.2452 | 2.63132 | ||||||||
\(142\) | −19.4437 | −1.63168 | ||||||||
\(143\) | −0.139197 | −0.0116402 | ||||||||
\(144\) | −34.0400 | −2.83667 | ||||||||
\(145\) | −1.93188 | −0.160434 | ||||||||
\(146\) | −5.12340 | −0.424016 | ||||||||
\(147\) | 20.0595 | 1.65448 | ||||||||
\(148\) | −0.350237 | −0.0287893 | ||||||||
\(149\) | −5.73581 | −0.469896 | −0.234948 | − | 0.972008i | \(-0.575492\pi\) | ||||
−0.234948 | + | 0.972008i | \(0.575492\pi\) | |||||||
\(150\) | −3.37415 | −0.275498 | ||||||||
\(151\) | −12.0649 | −0.981827 | −0.490913 | − | 0.871208i | \(-0.663337\pi\) | ||||
−0.490913 | + | 0.871208i | \(0.663337\pi\) | |||||||
\(152\) | 12.1783 | 0.987788 | ||||||||
\(153\) | 49.2841 | 3.98439 | ||||||||
\(154\) | −0.160462 | −0.0129304 | ||||||||
\(155\) | −14.3911 | −1.15592 | ||||||||
\(156\) | 1.51329 | 0.121160 | ||||||||
\(157\) | −17.9121 | −1.42954 | −0.714772 | − | 0.699357i | \(-0.753470\pi\) | ||||
−0.714772 | + | 0.699357i | \(0.753470\pi\) | |||||||
\(158\) | −9.80238 | −0.779835 | ||||||||
\(159\) | 16.8736 | 1.33816 | ||||||||
\(160\) | −4.65820 | −0.368263 | ||||||||
\(161\) | 2.25353 | 0.177603 | ||||||||
\(162\) | −35.2915 | −2.77276 | ||||||||
\(163\) | −14.2861 | −1.11898 | −0.559489 | − | 0.828838i | \(-0.689002\pi\) | ||||
−0.559489 | + | 0.828838i | \(0.689002\pi\) | |||||||
\(164\) | 0.698053 | 0.0545088 | ||||||||
\(165\) | 0.793945 | 0.0618086 | ||||||||
\(166\) | 3.63762 | 0.282334 | ||||||||
\(167\) | −3.46008 | −0.267749 | −0.133874 | − | 0.990998i | \(-0.542742\pi\) | ||||
−0.133874 | + | 0.990998i | \(0.542742\pi\) | |||||||
\(168\) | −6.93928 | −0.535377 | ||||||||
\(169\) | −11.6271 | −0.894389 | ||||||||
\(170\) | 21.6560 | 1.66094 | ||||||||
\(171\) | 36.0541 | 2.75712 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9867 | 0.835304 | 0.417652 | − | 0.908607i | \(-0.362853\pi\) | ||||
0.417652 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(174\) | 4.62892 | 0.350918 | ||||||||
\(175\) | −0.590323 | −0.0446242 | ||||||||
\(176\) | −0.551469 | −0.0415685 | ||||||||
\(177\) | 12.4484 | 0.935677 | ||||||||
\(178\) | −11.1726 | −0.837425 | ||||||||
\(179\) | −10.2806 | −0.768412 | −0.384206 | − | 0.923247i | \(-0.625525\pi\) | ||||
−0.384206 | + | 0.923247i | \(0.625525\pi\) | |||||||
\(180\) | −6.12542 | −0.456562 | ||||||||
\(181\) | −13.1597 | −0.978154 | −0.489077 | − | 0.872241i | \(-0.662666\pi\) | ||||
−0.489077 | + | 0.872241i | \(0.662666\pi\) | |||||||
\(182\) | 1.58268 | 0.117316 | ||||||||
\(183\) | 6.55549 | 0.484596 | ||||||||
\(184\) | 6.40421 | 0.472125 | ||||||||
\(185\) | 1.81239 | 0.133250 | ||||||||
\(186\) | 34.4820 | 2.52834 | ||||||||
\(187\) | 0.798432 | 0.0583872 | ||||||||
\(188\) | −3.90535 | −0.284827 | ||||||||
\(189\) | −12.1390 | −0.882986 | ||||||||
\(190\) | 15.8426 | 1.14934 | ||||||||
\(191\) | 6.04540 | 0.437430 | 0.218715 | − | 0.975789i | \(-0.429814\pi\) | ||||
0.218715 | + | 0.975789i | \(0.429814\pi\) | |||||||
\(192\) | −18.6827 | −1.34830 | ||||||||
\(193\) | −23.6408 | −1.70170 | −0.850852 | − | 0.525406i | \(-0.823913\pi\) | ||||
−0.850852 | + | 0.525406i | \(0.823913\pi\) | |||||||
\(194\) | 19.0072 | 1.36463 | ||||||||
\(195\) | −7.83092 | −0.560784 | ||||||||
\(196\) | −2.50724 | −0.179089 | ||||||||
\(197\) | 2.96314 | 0.211115 | 0.105558 | − | 0.994413i | \(-0.466337\pi\) | ||||
0.105558 | + | 0.994413i | \(0.466337\pi\) | |||||||
\(198\) | −1.35003 | −0.0959423 | ||||||||
\(199\) | −21.4455 | −1.52023 | −0.760117 | − | 0.649786i | \(-0.774858\pi\) | ||||
−0.760117 | + | 0.649786i | \(0.774858\pi\) | |||||||
\(200\) | −1.67761 | −0.118625 | ||||||||
\(201\) | 5.87629 | 0.414482 | ||||||||
\(202\) | −23.2946 | −1.63900 | ||||||||
\(203\) | 0.809850 | 0.0568404 | ||||||||
\(204\) | −8.68022 | −0.607737 | ||||||||
\(205\) | −3.61226 | −0.252291 | ||||||||
\(206\) | −8.33118 | −0.580461 | ||||||||
\(207\) | 18.9599 | 1.31780 | ||||||||
\(208\) | 5.43930 | 0.377148 | ||||||||
\(209\) | 0.584098 | 0.0404029 | ||||||||
\(210\) | −9.02723 | −0.622938 | ||||||||
\(211\) | −1.41265 | −0.0972506 | −0.0486253 | − | 0.998817i | \(-0.515484\pi\) | ||||
−0.0486253 | + | 0.998817i | \(0.515484\pi\) | |||||||
\(212\) | −2.10904 | −0.144849 | ||||||||
\(213\) | −40.3295 | −2.76333 | ||||||||
\(214\) | −6.47903 | −0.442898 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −34.4974 | −2.34725 | ||||||||
\(217\) | 6.03278 | 0.409532 | ||||||||
\(218\) | 23.2634 | 1.57560 | ||||||||
\(219\) | −10.6268 | −0.718092 | ||||||||
\(220\) | −0.0992355 | −0.00669046 | ||||||||
\(221\) | −7.87518 | −0.529742 | ||||||||
\(222\) | −4.34262 | −0.291457 | ||||||||
\(223\) | 18.4579 | 1.23603 | 0.618016 | − | 0.786166i | \(-0.287937\pi\) | ||||
0.618016 | + | 0.786166i | \(0.287937\pi\) | |||||||
\(224\) | 1.95273 | 0.130472 | ||||||||
\(225\) | −4.96662 | −0.331108 | ||||||||
\(226\) | −16.3058 | −1.08464 | ||||||||
\(227\) | −17.4397 | −1.15752 | −0.578758 | − | 0.815499i | \(-0.696462\pi\) | ||||
−0.578758 | + | 0.815499i | \(0.696462\pi\) | |||||||
\(228\) | −6.35007 | −0.420543 | ||||||||
\(229\) | 16.5342 | 1.09261 | 0.546306 | − | 0.837586i | \(-0.316034\pi\) | ||||
0.546306 | + | 0.837586i | \(0.316034\pi\) | |||||||
\(230\) | 8.33117 | 0.549341 | ||||||||
\(231\) | −0.332824 | −0.0218982 | ||||||||
\(232\) | 2.30148 | 0.151100 | ||||||||
\(233\) | −10.5158 | −0.688914 | −0.344457 | − | 0.938802i | \(-0.611937\pi\) | ||||
−0.344457 | + | 0.938802i | \(0.611937\pi\) | |||||||
\(234\) | 13.3157 | 0.870476 | ||||||||
\(235\) | 20.2093 | 1.31831 | ||||||||
\(236\) | −1.55593 | −0.101282 | ||||||||
\(237\) | −20.3318 | −1.32069 | ||||||||
\(238\) | −9.07825 | −0.588456 | ||||||||
\(239\) | −2.10552 | −0.136195 | −0.0680973 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680973 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(240\) | −31.0245 | −2.00262 | ||||||||
\(241\) | 24.9373 | 1.60635 | 0.803176 | − | 0.595742i | \(-0.203142\pi\) | ||||
0.803176 | + | 0.595742i | \(0.203142\pi\) | |||||||
\(242\) | 17.0256 | 1.09444 | ||||||||
\(243\) | −31.4169 | −2.01539 | ||||||||
\(244\) | −0.819373 | −0.0524550 | ||||||||
\(245\) | 12.9744 | 0.828904 | ||||||||
\(246\) | 8.65523 | 0.551837 | ||||||||
\(247\) | −5.76113 | −0.366572 | ||||||||
\(248\) | 17.1443 | 1.08866 | ||||||||
\(249\) | 7.54502 | 0.478147 | ||||||||
\(250\) | −18.2931 | −1.15695 | ||||||||
\(251\) | 26.0926 | 1.64695 | 0.823474 | − | 0.567354i | \(-0.192033\pi\) | ||||
0.823474 | + | 0.567354i | \(0.192033\pi\) | |||||||
\(252\) | 2.56779 | 0.161756 | ||||||||
\(253\) | 0.307161 | 0.0193110 | ||||||||
\(254\) | −28.7479 | −1.80381 | ||||||||
\(255\) | 44.9181 | 2.81288 | ||||||||
\(256\) | 9.27959 | 0.579975 | ||||||||
\(257\) | 0.883164 | 0.0550903 | 0.0275451 | − | 0.999621i | \(-0.491231\pi\) | ||||
0.0275451 | + | 0.999621i | \(0.491231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.759760 | −0.0472092 | ||||||||
\(260\) | 0.978789 | 0.0607019 | ||||||||
\(261\) | 6.81359 | 0.421751 | ||||||||
\(262\) | −29.8574 | −1.84460 | ||||||||
\(263\) | 2.92298 | 0.180239 | 0.0901193 | − | 0.995931i | \(-0.471275\pi\) | ||||
0.0901193 | + | 0.995931i | \(0.471275\pi\) | |||||||
\(264\) | −0.945839 | −0.0582123 | ||||||||
\(265\) | 10.9138 | 0.670427 | ||||||||
\(266\) | −6.64125 | −0.407201 | ||||||||
\(267\) | −23.1739 | −1.41822 | ||||||||
\(268\) | −0.734479 | −0.0448655 | ||||||||
\(269\) | −5.32307 | −0.324553 | −0.162277 | − | 0.986745i | \(-0.551884\pi\) | ||||
−0.162277 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(270\) | −44.8773 | −2.73115 | ||||||||
\(271\) | 17.9472 | 1.09022 | 0.545108 | − | 0.838366i | \(-0.316489\pi\) | ||||
0.545108 | + | 0.838366i | \(0.316489\pi\) | |||||||
\(272\) | −31.1998 | −1.89177 | ||||||||
\(273\) | 3.28274 | 0.198681 | ||||||||
\(274\) | −16.1566 | −0.976058 | ||||||||
\(275\) | −0.0804622 | −0.00485205 | ||||||||
\(276\) | −3.33933 | −0.201004 | ||||||||
\(277\) | −24.6071 | −1.47850 | −0.739249 | − | 0.673432i | \(-0.764819\pi\) | ||||
−0.739249 | + | 0.673432i | \(0.764819\pi\) | |||||||
\(278\) | −19.6226 | −1.17688 | ||||||||
\(279\) | 50.7562 | 3.03869 | ||||||||
\(280\) | −4.48830 | −0.268227 | ||||||||
\(281\) | 21.3772 | 1.27526 | 0.637629 | − | 0.770344i | \(-0.279915\pi\) | ||||
0.637629 | + | 0.770344i | \(0.279915\pi\) | |||||||
\(282\) | −48.4228 | −2.88354 | ||||||||
\(283\) | −9.40482 | −0.559059 | −0.279529 | − | 0.960137i | \(-0.590178\pi\) | ||||
−0.279529 | + | 0.960137i | \(0.590178\pi\) | |||||||
\(284\) | 5.04080 | 0.299116 | ||||||||
\(285\) | 32.8601 | 1.94646 | ||||||||
\(286\) | 0.215723 | 0.0127559 | ||||||||
\(287\) | 1.51427 | 0.0893845 | ||||||||
\(288\) | 16.4291 | 0.968093 | ||||||||
\(289\) | 28.1720 | 1.65717 | ||||||||
\(290\) | 2.99397 | 0.175812 | ||||||||
\(291\) | 39.4240 | 2.31108 | ||||||||
\(292\) | 1.32825 | 0.0777297 | ||||||||
\(293\) | −6.07616 | −0.354973 | −0.177486 | − | 0.984123i | \(-0.556797\pi\) | ||||
−0.177486 | + | 0.984123i | \(0.556797\pi\) | |||||||
\(294\) | −31.0876 | −1.81306 | ||||||||
\(295\) | 8.05155 | 0.468779 | ||||||||
\(296\) | −2.15913 | −0.125497 | ||||||||
\(297\) | −1.65458 | −0.0960083 | ||||||||
\(298\) | 8.88916 | 0.514935 | ||||||||
\(299\) | −3.02962 | −0.175207 | ||||||||
\(300\) | 0.874752 | 0.0505038 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.6978 | 1.07594 | ||||||||
\(303\) | −48.3169 | −2.77574 | ||||||||
\(304\) | −22.8244 | −1.30907 | ||||||||
\(305\) | 4.24006 | 0.242785 | ||||||||
\(306\) | −76.3789 | −4.36629 | ||||||||
\(307\) | 19.0136 | 1.08516 | 0.542582 | − | 0.840003i | \(-0.317447\pi\) | ||||
0.542582 | + | 0.840003i | \(0.317447\pi\) | |||||||
\(308\) | 0.0415998 | 0.00237037 | ||||||||
\(309\) | −17.2803 | −0.983039 | ||||||||
\(310\) | 22.3028 | 1.26671 | ||||||||
\(311\) | 8.92295 | 0.505974 | 0.252987 | − | 0.967470i | \(-0.418587\pi\) | ||||
0.252987 | + | 0.967470i | \(0.418587\pi\) | |||||||
\(312\) | 9.32909 | 0.528156 | ||||||||
\(313\) | −25.4924 | −1.44092 | −0.720458 | − | 0.693499i | \(-0.756068\pi\) | ||||
−0.720458 | + | 0.693499i | \(0.756068\pi\) | |||||||
\(314\) | 27.7597 | 1.56657 | ||||||||
\(315\) | −13.2877 | −0.748679 | ||||||||
\(316\) | 2.54127 | 0.142958 | ||||||||
\(317\) | 0.227021 | 0.0127508 | 0.00637539 | − | 0.999980i | \(-0.497971\pi\) | ||||
0.00637539 | + | 0.999980i | \(0.497971\pi\) | |||||||
\(318\) | −26.1501 | −1.46643 | ||||||||
\(319\) | 0.110384 | 0.00618033 | ||||||||
\(320\) | −12.0839 | −0.675508 | ||||||||
\(321\) | −13.4386 | −0.750069 | ||||||||
\(322\) | −3.49245 | −0.194627 | ||||||||
\(323\) | 33.0458 | 1.83872 | ||||||||
\(324\) | 9.14933 | 0.508296 | ||||||||
\(325\) | 0.793623 | 0.0440223 | ||||||||
\(326\) | 22.1402 | 1.22623 | ||||||||
\(327\) | 48.2522 | 2.66835 | ||||||||
\(328\) | 4.30334 | 0.237612 | ||||||||
\(329\) | −8.47178 | −0.467065 | ||||||||
\(330\) | −1.23043 | −0.0677330 | ||||||||
\(331\) | 9.38415 | 0.515799 | 0.257900 | − | 0.966172i | \(-0.416970\pi\) | ||||
0.257900 | + | 0.966172i | \(0.416970\pi\) | |||||||
\(332\) | −0.943055 | −0.0517569 | ||||||||
\(333\) | −6.39216 | −0.350288 | ||||||||
\(334\) | 5.36232 | 0.293413 | ||||||||
\(335\) | 3.80076 | 0.207658 | ||||||||
\(336\) | 13.0055 | 0.709511 | ||||||||
\(337\) | −6.36872 | −0.346926 | −0.173463 | − | 0.984840i | \(-0.555496\pi\) | ||||
−0.173463 | + | 0.984840i | \(0.555496\pi\) | |||||||
\(338\) | 18.0192 | 0.980117 | ||||||||
\(339\) | −33.8208 | −1.83690 | ||||||||
\(340\) | −5.61433 | −0.304480 | ||||||||
\(341\) | 0.822280 | 0.0445290 | ||||||||
\(342\) | −55.8754 | −3.02140 | ||||||||
\(343\) | −11.5399 | −0.623095 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.2802 | 0.930336 | ||||||||
\(346\) | −17.0268 | −0.915369 | ||||||||
\(347\) | −13.6088 | −0.730556 | −0.365278 | − | 0.930898i | \(-0.619026\pi\) | ||||
−0.365278 | + | 0.930898i | \(0.619026\pi\) | |||||||
\(348\) | −1.20005 | −0.0643295 | ||||||||
\(349\) | 21.5883 | 1.15560 | 0.577799 | − | 0.816179i | \(-0.303912\pi\) | ||||
0.577799 | + | 0.816179i | \(0.303912\pi\) | |||||||
\(350\) | 0.914863 | 0.0489015 | ||||||||
\(351\) | 16.3196 | 0.871075 | ||||||||
\(352\) | 0.266161 | 0.0141864 | ||||||||
\(353\) | 2.59435 | 0.138083 | 0.0690416 | − | 0.997614i | \(-0.478006\pi\) | ||||
0.0690416 | + | 0.997614i | \(0.478006\pi\) | |||||||
\(354\) | −19.2921 | −1.02536 | ||||||||
\(355\) | −26.0849 | −1.38444 | ||||||||
\(356\) | 2.89652 | 0.153515 | ||||||||
\(357\) | −18.8298 | −0.996579 | ||||||||
\(358\) | 15.9326 | 0.842065 | ||||||||
\(359\) | 21.7304 | 1.14689 | 0.573445 | − | 0.819244i | \(-0.305607\pi\) | ||||
0.573445 | + | 0.819244i | \(0.305607\pi\) | |||||||
\(360\) | −37.7618 | −1.99022 | ||||||||
\(361\) | 5.17485 | 0.272361 | ||||||||
\(362\) | 20.3945 | 1.07191 | ||||||||
\(363\) | 35.3139 | 1.85350 | ||||||||
\(364\) | −0.410311 | −0.0215062 | ||||||||
\(365\) | −6.87336 | −0.359768 | ||||||||
\(366\) | −10.1595 | −0.531044 | ||||||||
\(367\) | −7.28324 | −0.380182 | −0.190091 | − | 0.981766i | \(-0.560878\pi\) | ||||
−0.190091 | + | 0.981766i | \(0.560878\pi\) | |||||||
\(368\) | −12.0027 | −0.625685 | ||||||||
\(369\) | 12.7402 | 0.663226 | ||||||||
\(370\) | −2.80879 | −0.146022 | ||||||||
\(371\) | −4.57508 | −0.237526 | ||||||||
\(372\) | −8.93949 | −0.463491 | ||||||||
\(373\) | 15.2019 | 0.787124 | 0.393562 | − | 0.919298i | \(-0.371243\pi\) | ||||
0.393562 | + | 0.919298i | \(0.371243\pi\) | |||||||
\(374\) | −1.23738 | −0.0639836 | ||||||||
\(375\) | −37.9428 | −1.95936 | ||||||||
\(376\) | −24.0756 | −1.24160 | ||||||||
\(377\) | −1.08875 | −0.0560736 | ||||||||
\(378\) | 18.8127 | 0.967621 | ||||||||
\(379\) | 20.5398 | 1.05506 | 0.527529 | − | 0.849537i | \(-0.323118\pi\) | ||||
0.527529 | + | 0.849537i | \(0.323118\pi\) | |||||||
\(380\) | −4.10719 | −0.210695 | ||||||||
\(381\) | −59.6280 | −3.05483 | ||||||||
\(382\) | −9.36896 | −0.479358 | ||||||||
\(383\) | −8.07630 | −0.412680 | −0.206340 | − | 0.978480i | \(-0.566155\pi\) | ||||
−0.206340 | + | 0.978480i | \(0.566155\pi\) | |||||||
\(384\) | 43.3577 | 2.21259 | ||||||||
\(385\) | −0.215269 | −0.0109711 | ||||||||
\(386\) | 36.6378 | 1.86481 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.92762 | −0.250162 | ||||||||
\(389\) | 33.5847 | 1.70281 | 0.851406 | − | 0.524507i | \(-0.175751\pi\) | ||||
0.851406 | + | 0.524507i | \(0.175751\pi\) | |||||||
\(390\) | 12.1361 | 0.614535 | ||||||||
\(391\) | 17.3779 | 0.878837 | ||||||||
\(392\) | −15.4566 | −0.780676 | ||||||||
\(393\) | −61.9293 | −3.12392 | ||||||||
\(394\) | −4.59218 | −0.231351 | ||||||||
\(395\) | −13.1505 | −0.661673 | ||||||||
\(396\) | 0.349996 | 0.0175879 | ||||||||
\(397\) | 23.7641 | 1.19269 | 0.596343 | − | 0.802730i | \(-0.296620\pi\) | ||||
0.596343 | + | 0.802730i | \(0.296620\pi\) | |||||||
\(398\) | 33.2356 | 1.66595 | ||||||||
\(399\) | −13.7750 | −0.689615 | ||||||||
\(400\) | 3.14417 | 0.157208 | ||||||||
\(401\) | 5.89139 | 0.294202 | 0.147101 | − | 0.989121i | \(-0.453006\pi\) | ||||
0.147101 | + | 0.989121i | \(0.453006\pi\) | |||||||
\(402\) | −9.10688 | −0.454210 | ||||||||
\(403\) | −8.11040 | −0.404008 | ||||||||
\(404\) | 6.03915 | 0.300459 | ||||||||
\(405\) | −47.3456 | −2.35262 | ||||||||
\(406\) | −1.25508 | −0.0622886 | ||||||||
\(407\) | −0.103557 | −0.00513312 | ||||||||
\(408\) | −53.5116 | −2.64922 | ||||||||
\(409\) | 15.8785 | 0.785144 | 0.392572 | − | 0.919721i | \(-0.371585\pi\) | ||||
0.392572 | + | 0.919721i | \(0.371585\pi\) | |||||||
\(410\) | 5.59816 | 0.276474 | ||||||||
\(411\) | −33.5116 | −1.65300 | ||||||||
\(412\) | 2.15987 | 0.106409 | ||||||||
\(413\) | −3.37523 | −0.166084 | ||||||||
\(414\) | −29.3834 | −1.44411 | ||||||||
\(415\) | 4.88009 | 0.239554 | ||||||||
\(416\) | −2.62522 | −0.128712 | ||||||||
\(417\) | −40.7005 | −1.99311 | ||||||||
\(418\) | −0.905215 | −0.0442755 | ||||||||
\(419\) | 35.1526 | 1.71731 | 0.858657 | − | 0.512550i | \(-0.171299\pi\) | ||||
0.858657 | + | 0.512550i | \(0.171299\pi\) | |||||||
\(420\) | 2.34032 | 0.114196 | ||||||||
\(421\) | −5.89826 | −0.287464 | −0.143732 | − | 0.989617i | \(-0.545910\pi\) | ||||
−0.143732 | + | 0.989617i | \(0.545910\pi\) | |||||||
\(422\) | 2.18927 | 0.106572 | ||||||||
\(423\) | −71.2765 | −3.46558 | ||||||||
\(424\) | −13.0017 | −0.631420 | ||||||||
\(425\) | −4.55222 | −0.220815 | ||||||||
\(426\) | 62.5013 | 3.02820 | ||||||||
\(427\) | −1.77745 | −0.0860166 | ||||||||
\(428\) | 1.67969 | 0.0811911 | ||||||||
\(429\) | 0.447445 | 0.0216028 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6191 | 0.848684 | 0.424342 | − | 0.905502i | \(-0.360505\pi\) | ||||
0.424342 | + | 0.905502i | \(0.360505\pi\) | |||||||
\(432\) | 64.6548 | 3.11070 | ||||||||
\(433\) | −12.1201 | −0.582456 | −0.291228 | − | 0.956654i | \(-0.594064\pi\) | ||||
−0.291228 | + | 0.956654i | \(0.594064\pi\) | |||||||
\(434\) | −9.34941 | −0.448786 | ||||||||
\(435\) | 6.20998 | 0.297746 | ||||||||
\(436\) | −6.03105 | −0.288835 | ||||||||
\(437\) | 12.7129 | 0.608140 | ||||||||
\(438\) | 16.4690 | 0.786922 | ||||||||
\(439\) | 25.2649 | 1.20583 | 0.602915 | − | 0.797806i | \(-0.294006\pi\) | ||||
0.602915 | + | 0.797806i | \(0.294006\pi\) | |||||||
\(440\) | −0.611764 | −0.0291647 | ||||||||
\(441\) | −45.7597 | −2.17903 | ||||||||
\(442\) | 12.2047 | 0.580518 | ||||||||
\(443\) | −19.5814 | −0.930339 | −0.465170 | − | 0.885222i | \(-0.654007\pi\) | ||||
−0.465170 | + | 0.885222i | \(0.654007\pi\) | |||||||
\(444\) | 1.12583 | 0.0534294 | ||||||||
\(445\) | −14.9888 | −0.710537 | ||||||||
\(446\) | −28.6054 | −1.35451 | ||||||||
\(447\) | 18.4376 | 0.872069 | ||||||||
\(448\) | 5.06559 | 0.239327 | ||||||||
\(449\) | −1.44077 | −0.0679943 | −0.0339971 | − | 0.999422i | \(-0.510824\pi\) | ||||
−0.0339971 | + | 0.999422i | \(0.510824\pi\) | |||||||
\(450\) | 7.69711 | 0.362845 | ||||||||
\(451\) | 0.206398 | 0.00971891 | ||||||||
\(452\) | 4.22728 | 0.198834 | ||||||||
\(453\) | 38.7823 | 1.82215 | ||||||||
\(454\) | 27.0275 | 1.26846 | ||||||||
\(455\) | 2.12326 | 0.0995401 | ||||||||
\(456\) | −39.1467 | −1.83321 | ||||||||
\(457\) | −27.8686 | −1.30364 | −0.651820 | − | 0.758374i | \(-0.725994\pi\) | ||||
−0.651820 | + | 0.758374i | \(0.725994\pi\) | |||||||
\(458\) | −25.6242 | −1.19734 | ||||||||
\(459\) | −93.6090 | −4.36930 | ||||||||
\(460\) | −2.15986 | −0.100704 | ||||||||
\(461\) | −41.5360 | −1.93452 | −0.967262 | − | 0.253780i | \(-0.918326\pi\) | ||||
−0.967262 | + | 0.253780i | \(0.918326\pi\) | |||||||
\(462\) | 0.515800 | 0.0239972 | ||||||||
\(463\) | −27.7716 | −1.29066 | −0.645328 | − | 0.763906i | \(-0.723279\pi\) | ||||
−0.645328 | + | 0.763906i | \(0.723279\pi\) | |||||||
\(464\) | −4.31341 | −0.200245 | ||||||||
\(465\) | 46.2597 | 2.14524 | ||||||||
\(466\) | 16.2971 | 0.754947 | ||||||||
\(467\) | 33.0499 | 1.52937 | 0.764684 | − | 0.644405i | \(-0.222895\pi\) | ||||
0.764684 | + | 0.644405i | \(0.222895\pi\) | |||||||
\(468\) | −3.45211 | −0.159574 | ||||||||
\(469\) | −1.59329 | −0.0735712 | ||||||||
\(470\) | −31.3197 | −1.44467 | ||||||||
\(471\) | 57.5781 | 2.65306 | ||||||||
\(472\) | −9.59193 | −0.441504 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 31.5095 | 1.44728 | ||||||||
\(475\) | −3.33020 | −0.152800 | ||||||||
\(476\) | 2.35354 | 0.107874 | ||||||||
\(477\) | −38.4920 | −1.76243 | ||||||||
\(478\) | 3.26306 | 0.149249 | ||||||||
\(479\) | −3.48410 | −0.159192 | −0.0795962 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795962 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(480\) | 14.9737 | 0.683451 | ||||||||
\(481\) | 1.02141 | 0.0465724 | ||||||||
\(482\) | −38.6470 | −1.76032 | ||||||||
\(483\) | −7.24392 | −0.329610 | ||||||||
\(484\) | −4.41389 | −0.200631 | ||||||||
\(485\) | 25.4993 | 1.15786 | ||||||||
\(486\) | 48.6888 | 2.20857 | ||||||||
\(487\) | 31.0843 | 1.40856 | 0.704282 | − | 0.709920i | \(-0.251269\pi\) | ||||
0.704282 | + | 0.709920i | \(0.251269\pi\) | |||||||
\(488\) | −5.05125 | −0.228659 | ||||||||
\(489\) | 45.9225 | 2.07669 | ||||||||
\(490\) | −20.1073 | −0.908355 | ||||||||
\(491\) | −5.96490 | −0.269192 | −0.134596 | − | 0.990901i | \(-0.542974\pi\) | ||||
−0.134596 | + | 0.990901i | \(0.542974\pi\) | |||||||
\(492\) | −2.24387 | −0.101162 | ||||||||
\(493\) | 6.24508 | 0.281264 | ||||||||
\(494\) | 8.92841 | 0.401708 | ||||||||
\(495\) | −1.81114 | −0.0814049 | ||||||||
\(496\) | −32.1317 | −1.44276 | ||||||||
\(497\) | 10.9349 | 0.490496 | ||||||||
\(498\) | −11.6930 | −0.523977 | ||||||||
\(499\) | −5.77735 | −0.258630 | −0.129315 | − | 0.991604i | \(-0.541278\pi\) | ||||
−0.129315 | + | 0.991604i | \(0.541278\pi\) | |||||||
\(500\) | 4.74249 | 0.212090 | ||||||||
\(501\) | 11.1223 | 0.496909 | ||||||||
\(502\) | −40.4374 | −1.80481 | ||||||||
\(503\) | 9.74952 | 0.434710 | 0.217355 | − | 0.976093i | \(-0.430257\pi\) | ||||
0.217355 | + | 0.976093i | \(0.430257\pi\) | |||||||
\(504\) | 15.8299 | 0.705118 | ||||||||
\(505\) | −31.2512 | −1.39066 | ||||||||
\(506\) | −0.476028 | −0.0211620 | ||||||||
\(507\) | 37.3749 | 1.65988 | ||||||||
\(508\) | 7.45292 | 0.330670 | ||||||||
\(509\) | −8.21780 | −0.364248 | −0.182124 | − | 0.983276i | \(-0.558297\pi\) | ||||
−0.182124 | + | 0.983276i | \(0.558297\pi\) | |||||||
\(510\) | −69.6126 | −3.08250 | ||||||||
\(511\) | 2.88133 | 0.127463 | ||||||||
\(512\) | 12.5953 | 0.556640 | ||||||||
\(513\) | −68.4802 | −3.02348 | ||||||||
\(514\) | −1.36870 | −0.0603707 | ||||||||
\(515\) | −11.1768 | −0.492508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.15472 | −0.0507846 | ||||||||
\(518\) | 1.17745 | 0.0517342 | ||||||||
\(519\) | −35.3165 | −1.55022 | ||||||||
\(520\) | 6.03401 | 0.264609 | ||||||||
\(521\) | −36.6124 | −1.60402 | −0.802010 | − | 0.597311i | \(-0.796236\pi\) | ||||
−0.802010 | + | 0.597311i | \(0.796236\pi\) | |||||||
\(522\) | −10.5595 | −0.462176 | ||||||||
\(523\) | 16.0999 | 0.704002 | 0.352001 | − | 0.936000i | \(-0.385501\pi\) | ||||
0.352001 | + | 0.936000i | \(0.385501\pi\) | |||||||
\(524\) | 7.74056 | 0.338148 | ||||||||
\(525\) | 1.89758 | 0.0828171 | ||||||||
\(526\) | −4.52994 | −0.197515 | ||||||||
\(527\) | 46.5212 | 2.02649 | ||||||||
\(528\) | 1.77268 | 0.0771461 | ||||||||
\(529\) | −16.3146 | −0.709332 | ||||||||
\(530\) | −16.9138 | −0.734688 | ||||||||
\(531\) | −28.3972 | −1.23233 | ||||||||
\(532\) | 1.72175 | 0.0746472 | ||||||||
\(533\) | −2.03577 | −0.0881788 | ||||||||
\(534\) | 35.9142 | 1.55416 | ||||||||
\(535\) | −8.69202 | −0.375789 | ||||||||
\(536\) | −4.52790 | −0.195575 | ||||||||
\(537\) | 33.0469 | 1.42608 | ||||||||
\(538\) | 8.24952 | 0.355662 | ||||||||
\(539\) | −0.741334 | −0.0319315 | ||||||||
\(540\) | 11.6345 | 0.500668 | ||||||||
\(541\) | 35.3518 | 1.51989 | 0.759946 | − | 0.649986i | \(-0.225225\pi\) | ||||
0.759946 | + | 0.649986i | \(0.225225\pi\) | |||||||
\(542\) | −27.8140 | −1.19471 | ||||||||
\(543\) | 42.3016 | 1.81533 | ||||||||
\(544\) | 15.0583 | 0.645618 | ||||||||
\(545\) | 31.2093 | 1.33686 | ||||||||
\(546\) | −5.08749 | −0.217724 | ||||||||
\(547\) | 8.12884 | 0.347564 | 0.173782 | − | 0.984784i | \(-0.444401\pi\) | ||||
0.173782 | + | 0.984784i | \(0.444401\pi\) | |||||||
\(548\) | 4.18862 | 0.178929 | ||||||||
\(549\) | −14.9544 | −0.638236 | ||||||||
\(550\) | 0.124698 | 0.00531713 | ||||||||
\(551\) | 4.56862 | 0.194630 | ||||||||
\(552\) | −20.5862 | −0.876206 | ||||||||
\(553\) | 5.51272 | 0.234425 | ||||||||
\(554\) | 38.1353 | 1.62021 | ||||||||
\(555\) | −5.82589 | −0.247295 | ||||||||
\(556\) | 5.08716 | 0.215744 | ||||||||
\(557\) | −25.5405 | −1.08219 | −0.541093 | − | 0.840963i | \(-0.681989\pi\) | ||||
−0.541093 | + | 0.840963i | \(0.681989\pi\) | |||||||
\(558\) | −78.6603 | −3.32995 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.41193 | 0.355469 | ||||||||
\(561\) | −2.56654 | −0.108359 | ||||||||
\(562\) | −33.1297 | −1.39749 | ||||||||
\(563\) | 33.8216 | 1.42541 | 0.712706 | − | 0.701463i | \(-0.247469\pi\) | ||||
0.712706 | + | 0.701463i | \(0.247469\pi\) | |||||||
\(564\) | 12.5537 | 0.528604 | ||||||||
\(565\) | −21.8752 | −0.920295 | ||||||||
\(566\) | 14.5753 | 0.612645 | ||||||||
\(567\) | 19.8474 | 0.833514 | ||||||||
\(568\) | 31.0754 | 1.30389 | ||||||||
\(569\) | −6.18173 | −0.259151 | −0.129576 | − | 0.991570i | \(-0.541362\pi\) | ||||
−0.129576 | + | 0.991570i | \(0.541362\pi\) | |||||||
\(570\) | −50.9255 | −2.13303 | ||||||||
\(571\) | −3.78544 | −0.158416 | −0.0792079 | − | 0.996858i | \(-0.525239\pi\) | ||||
−0.0792079 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(572\) | −0.0559263 | −0.00233839 | ||||||||
\(573\) | −19.4328 | −0.811816 | ||||||||
\(574\) | −2.34677 | −0.0979521 | ||||||||
\(575\) | −1.75126 | −0.0730326 | ||||||||
\(576\) | 42.6188 | 1.77578 | ||||||||
\(577\) | 9.43111 | 0.392622 | 0.196311 | − | 0.980542i | \(-0.437104\pi\) | ||||
0.196311 | + | 0.980542i | \(0.437104\pi\) | |||||||
\(578\) | −43.6600 | −1.81602 | ||||||||
\(579\) | 75.9928 | 3.15815 | ||||||||
\(580\) | −0.776188 | −0.0322295 | ||||||||
\(581\) | −2.04575 | −0.0848719 | ||||||||
\(582\) | −61.0980 | −2.53259 | ||||||||
\(583\) | −0.623593 | −0.0258266 | ||||||||
\(584\) | 8.18833 | 0.338836 | ||||||||
\(585\) | 17.8639 | 0.738580 | ||||||||
\(586\) | 9.41663 | 0.388997 | ||||||||
\(587\) | −0.925629 | −0.0382048 | −0.0191024 | − | 0.999818i | \(-0.506081\pi\) | ||||
−0.0191024 | + | 0.999818i | \(0.506081\pi\) | |||||||
\(588\) | 8.05947 | 0.332367 | ||||||||
\(589\) | 34.0328 | 1.40230 | ||||||||
\(590\) | −12.4780 | −0.513712 | ||||||||
\(591\) | −9.52495 | −0.391804 | ||||||||
\(592\) | 4.04662 | 0.166315 | ||||||||
\(593\) | 18.9168 | 0.776820 | 0.388410 | − | 0.921487i | \(-0.373024\pi\) | ||||
0.388410 | + | 0.921487i | \(0.373024\pi\) | |||||||
\(594\) | 2.56421 | 0.105211 | ||||||||
\(595\) | −12.1790 | −0.499292 | ||||||||
\(596\) | −2.30452 | −0.0943969 | ||||||||
\(597\) | 68.9361 | 2.82137 | ||||||||
\(598\) | 4.69520 | 0.192001 | ||||||||
\(599\) | 25.8820 | 1.05751 | 0.528754 | − | 0.848775i | \(-0.322659\pi\) | ||||
0.528754 | + | 0.848775i | \(0.322659\pi\) | |||||||
\(600\) | 5.39265 | 0.220154 | ||||||||
\(601\) | 26.9085 | 1.09762 | 0.548809 | − | 0.835948i | \(-0.315081\pi\) | ||||
0.548809 | + | 0.835948i | \(0.315081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.4050 | −0.545893 | ||||||||
\(604\) | −4.84741 | −0.197238 | ||||||||
\(605\) | 22.8408 | 0.928612 | ||||||||
\(606\) | 74.8800 | 3.04179 | ||||||||
\(607\) | 38.4078 | 1.55893 | 0.779463 | − | 0.626448i | \(-0.215492\pi\) | ||||
0.779463 | + | 0.626448i | \(0.215492\pi\) | |||||||
\(608\) | 11.0160 | 0.446757 | ||||||||
\(609\) | −2.60324 | −0.105489 | ||||||||
\(610\) | −6.57111 | −0.266056 | ||||||||
\(611\) | 11.3894 | 0.460764 | ||||||||
\(612\) | 19.8013 | 0.800420 | ||||||||
\(613\) | −19.8510 | −0.801775 | −0.400887 | − | 0.916127i | \(-0.631298\pi\) | ||||
−0.400887 | + | 0.916127i | \(0.631298\pi\) | |||||||
\(614\) | −29.4667 | −1.18918 | ||||||||
\(615\) | 11.6115 | 0.468222 | ||||||||
\(616\) | 0.256453 | 0.0103328 | ||||||||
\(617\) | 22.7681 | 0.916611 | 0.458306 | − | 0.888795i | \(-0.348457\pi\) | ||||
0.458306 | + | 0.888795i | \(0.348457\pi\) | |||||||
\(618\) | 26.7804 | 1.07726 | ||||||||
\(619\) | −13.0377 | −0.524031 | −0.262015 | − | 0.965064i | \(-0.584387\pi\) | ||||
−0.262015 | + | 0.965064i | \(0.584387\pi\) | |||||||
\(620\) | −5.78202 | −0.232212 | ||||||||
\(621\) | −36.0119 | −1.44511 | ||||||||
\(622\) | −13.8285 | −0.554472 | ||||||||
\(623\) | 6.28334 | 0.251737 | ||||||||
\(624\) | −17.4845 | −0.699940 | ||||||||
\(625\) | −21.1547 | −0.846188 | ||||||||
\(626\) | 39.5073 | 1.57903 | ||||||||
\(627\) | −1.87757 | −0.0749828 | ||||||||
\(628\) | −7.19671 | −0.287180 | ||||||||
\(629\) | −5.85881 | −0.233606 | ||||||||
\(630\) | 20.5929 | 0.820440 | ||||||||
\(631\) | 36.4675 | 1.45175 | 0.725874 | − | 0.687827i | \(-0.241435\pi\) | ||||
0.725874 | + | 0.687827i | \(0.241435\pi\) | |||||||
\(632\) | 15.6664 | 0.623175 | ||||||||
\(633\) | 4.54092 | 0.180485 | ||||||||
\(634\) | −0.351830 | −0.0139730 | ||||||||
\(635\) | −38.5671 | −1.53049 | ||||||||
\(636\) | 6.77945 | 0.268822 | ||||||||
\(637\) | 7.31200 | 0.289712 | ||||||||
\(638\) | −0.171070 | −0.00677272 | ||||||||
\(639\) | 91.9995 | 3.63944 | ||||||||
\(640\) | 28.0436 | 1.10852 | ||||||||
\(641\) | −29.0371 | −1.14690 | −0.573449 | − | 0.819241i | \(-0.694395\pi\) | ||||
−0.573449 | + | 0.819241i | \(0.694395\pi\) | |||||||
\(642\) | 20.8267 | 0.821964 | ||||||||
\(643\) | −37.8479 | −1.49257 | −0.746287 | − | 0.665624i | \(-0.768165\pi\) | ||||
−0.746287 | + | 0.665624i | \(0.768165\pi\) | |||||||
\(644\) | 0.905420 | 0.0356785 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −51.2133 | −2.01496 | ||||||||
\(647\) | 22.5991 | 0.888461 | 0.444230 | − | 0.895913i | \(-0.353477\pi\) | ||||
0.444230 | + | 0.895913i | \(0.353477\pi\) | |||||||
\(648\) | 56.4036 | 2.21574 | ||||||||
\(649\) | −0.460051 | −0.0180586 | ||||||||
\(650\) | −1.22993 | −0.0482418 | ||||||||
\(651\) | −19.3922 | −0.760041 | ||||||||
\(652\) | −5.73986 | −0.224790 | ||||||||
\(653\) | 5.01382 | 0.196206 | 0.0981030 | − | 0.995176i | \(-0.468723\pi\) | ||||
0.0981030 | + | 0.995176i | \(0.468723\pi\) | |||||||
\(654\) | −74.7796 | −2.92411 | ||||||||
\(655\) | −40.0556 | −1.56510 | ||||||||
\(656\) | −8.06528 | −0.314896 | ||||||||
\(657\) | 24.2418 | 0.945762 | ||||||||
\(658\) | 13.1293 | 0.511833 | ||||||||
\(659\) | −29.6913 | −1.15661 | −0.578304 | − | 0.815821i | \(-0.696285\pi\) | ||||
−0.578304 | + | 0.815821i | \(0.696285\pi\) | |||||||
\(660\) | 0.318990 | 0.0124167 | ||||||||
\(661\) | 25.1099 | 0.976660 | 0.488330 | − | 0.872659i | \(-0.337606\pi\) | ||||
0.488330 | + | 0.872659i | \(0.337606\pi\) | |||||||
\(662\) | −14.5432 | −0.565239 | ||||||||
\(663\) | 25.3146 | 0.983136 | ||||||||
\(664\) | −5.81372 | −0.225616 | ||||||||
\(665\) | −8.90964 | −0.345501 | ||||||||
\(666\) | 9.90636 | 0.383864 | ||||||||
\(667\) | 2.40251 | 0.0930257 | ||||||||
\(668\) | −1.39018 | −0.0537879 | ||||||||
\(669\) | −59.3324 | −2.29392 | ||||||||
\(670\) | −5.89029 | −0.227562 | ||||||||
\(671\) | −0.242269 | −0.00935271 | ||||||||
\(672\) | −6.27700 | −0.242140 | ||||||||
\(673\) | 14.6041 | 0.562948 | 0.281474 | − | 0.959569i | \(-0.409177\pi\) | ||||
0.281474 | + | 0.959569i | \(0.409177\pi\) | |||||||
\(674\) | 9.87003 | 0.380179 | ||||||||
\(675\) | 9.43347 | 0.363095 | ||||||||
\(676\) | −4.67150 | −0.179673 | ||||||||
\(677\) | −31.6070 | −1.21476 | −0.607379 | − | 0.794412i | \(-0.707779\pi\) | ||||
−0.607379 | + | 0.794412i | \(0.707779\pi\) | |||||||
\(678\) | 52.4144 | 2.01296 | ||||||||
\(679\) | −10.6894 | −0.410220 | ||||||||
\(680\) | −34.6111 | −1.32727 | ||||||||
\(681\) | 56.0596 | 2.14821 | ||||||||
\(682\) | −1.27434 | −0.0487971 | ||||||||
\(683\) | −17.3172 | −0.662626 | −0.331313 | − | 0.943521i | \(-0.607492\pi\) | ||||
−0.331313 | + | 0.943521i | \(0.607492\pi\) | |||||||
\(684\) | 14.4857 | 0.553876 | ||||||||
\(685\) | −21.6751 | −0.828164 | ||||||||
\(686\) | 17.8841 | 0.682819 | ||||||||
\(687\) | −53.1488 | −2.02775 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.15068 | 0.234322 | ||||||||
\(690\) | −26.7803 | −1.01951 | ||||||||
\(691\) | 12.5940 | 0.479099 | 0.239549 | − | 0.970884i | \(-0.423000\pi\) | ||||
0.239549 | + | 0.970884i | \(0.423000\pi\) | |||||||
\(692\) | 4.41422 | 0.167804 | ||||||||
\(693\) | 0.759237 | 0.0288410 | ||||||||
\(694\) | 21.0904 | 0.800581 | ||||||||
\(695\) | −26.3249 | −0.998559 | ||||||||
\(696\) | −7.39805 | −0.280422 | ||||||||
\(697\) | 11.6771 | 0.442303 | ||||||||
\(698\) | −33.4569 | −1.26636 | ||||||||
\(699\) | 33.8028 | 1.27854 | ||||||||
\(700\) | −0.237179 | −0.00896452 | ||||||||
\(701\) | 44.2374 | 1.67082 | 0.835412 | − | 0.549625i | \(-0.185229\pi\) | ||||
0.835412 | + | 0.549625i | \(0.185229\pi\) | |||||||
\(702\) | −25.2916 | −0.954568 | ||||||||
\(703\) | −4.28605 | −0.161651 | ||||||||
\(704\) | 0.690450 | 0.0260223 | ||||||||
\(705\) | −64.9622 | −2.44662 | ||||||||
\(706\) | −4.02063 | −0.151318 | ||||||||
\(707\) | 13.1006 | 0.492698 | ||||||||
\(708\) | 5.00148 | 0.187967 | ||||||||
\(709\) | −3.57636 | −0.134313 | −0.0671565 | − | 0.997742i | \(-0.521393\pi\) | ||||
−0.0671565 | + | 0.997742i | \(0.521393\pi\) | |||||||
\(710\) | 40.4256 | 1.51714 | ||||||||
\(711\) | 46.3807 | 1.73941 | ||||||||
\(712\) | 17.8564 | 0.669196 | ||||||||
\(713\) | 17.8969 | 0.670245 | ||||||||
\(714\) | 29.1818 | 1.09210 | ||||||||
\(715\) | 0.289405 | 0.0108231 | ||||||||
\(716\) | −4.13054 | −0.154366 | ||||||||
\(717\) | 6.76814 | 0.252761 | ||||||||
\(718\) | −33.6771 | −1.25682 | ||||||||
\(719\) | −42.4273 | −1.58227 | −0.791136 | − | 0.611641i | \(-0.790510\pi\) | ||||
−0.791136 | + | 0.611641i | \(0.790510\pi\) | |||||||
\(720\) | 70.7729 | 2.63755 | ||||||||
\(721\) | 4.68534 | 0.174491 | ||||||||
\(722\) | −8.01981 | −0.298467 | ||||||||
\(723\) | −80.1603 | −2.98119 | ||||||||
\(724\) | −5.28729 | −0.196501 | ||||||||
\(725\) | −0.629350 | −0.0233735 | ||||||||
\(726\) | −54.7283 | −2.03116 | ||||||||
\(727\) | 22.2087 | 0.823673 | 0.411837 | − | 0.911258i | \(-0.364887\pi\) | ||||
0.411837 | + | 0.911258i | \(0.364887\pi\) | |||||||
\(728\) | −2.52948 | −0.0937486 | ||||||||
\(729\) | 32.6724 | 1.21009 | ||||||||
\(730\) | 10.6521 | 0.394252 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.63385 | 0.0973500 | ||||||||
\(733\) | 2.51655 | 0.0929509 | 0.0464754 | − | 0.998919i | \(-0.485201\pi\) | ||||
0.0464754 | + | 0.998919i | \(0.485201\pi\) | |||||||
\(734\) | 11.2873 | 0.416623 | ||||||||
\(735\) | −41.7059 | −1.53834 | ||||||||
\(736\) | 5.79299 | 0.213533 | ||||||||
\(737\) | −0.217168 | −0.00799950 | ||||||||
\(738\) | −19.7443 | −0.726797 | ||||||||
\(739\) | −36.3733 | −1.33801 | −0.669006 | − | 0.743257i | \(-0.733280\pi\) | ||||
−0.669006 | + | 0.743257i | \(0.733280\pi\) | |||||||
\(740\) | 0.728180 | 0.0267684 | ||||||||
\(741\) | 18.5190 | 0.680313 | ||||||||
\(742\) | 7.09031 | 0.260294 | ||||||||
\(743\) | −7.15992 | −0.262672 | −0.131336 | − | 0.991338i | \(-0.541927\pi\) | ||||
−0.131336 | + | 0.991338i | \(0.541927\pi\) | |||||||
\(744\) | −55.1099 | −2.02043 | ||||||||
\(745\) | 11.9254 | 0.436911 | ||||||||
\(746\) | −23.5594 | −0.862570 | ||||||||
\(747\) | −17.2117 | −0.629742 | ||||||||
\(748\) | 0.320793 | 0.0117293 | ||||||||
\(749\) | 3.64372 | 0.133139 | ||||||||
\(750\) | 58.8025 | 2.14717 | ||||||||
\(751\) | 33.6779 | 1.22892 | 0.614461 | − | 0.788947i | \(-0.289373\pi\) | ||||
0.614461 | + | 0.788947i | \(0.289373\pi\) | |||||||
\(752\) | 45.1223 | 1.64544 | ||||||||
\(753\) | −83.8739 | −3.05653 | ||||||||
\(754\) | 1.68731 | 0.0614483 | ||||||||
\(755\) | 25.0842 | 0.912908 | ||||||||
\(756\) | −4.87720 | −0.177382 | ||||||||
\(757\) | 11.1908 | 0.406738 | 0.203369 | − | 0.979102i | \(-0.434811\pi\) | ||||
0.203369 | + | 0.979102i | \(0.434811\pi\) | |||||||
\(758\) | −31.8319 | −1.15619 | ||||||||
\(759\) | −0.987361 | −0.0358389 | ||||||||
\(760\) | −25.3199 | −0.918450 | ||||||||
\(761\) | −18.5968 | −0.674134 | −0.337067 | − | 0.941481i | \(-0.609435\pi\) | ||||
−0.337067 | + | 0.941481i | \(0.609435\pi\) | |||||||
\(762\) | 92.4095 | 3.34764 | ||||||||
\(763\) | −13.0830 | −0.473637 | ||||||||
\(764\) | 2.42891 | 0.0878749 | ||||||||
\(765\) | −102.467 | −3.70470 | ||||||||
\(766\) | 12.5164 | 0.452235 | ||||||||
\(767\) | 4.53762 | 0.163844 | ||||||||
\(768\) | −29.8290 | −1.07636 | ||||||||
\(769\) | −16.4974 | −0.594912 | −0.297456 | − | 0.954736i | \(-0.596138\pi\) | ||||
−0.297456 | + | 0.954736i | \(0.596138\pi\) | |||||||
\(770\) | 0.333617 | 0.0120227 | ||||||||
\(771\) | −2.83891 | −0.102241 | ||||||||
\(772\) | −9.49837 | −0.341854 | ||||||||
\(773\) | 24.9319 | 0.896740 | 0.448370 | − | 0.893848i | \(-0.352005\pi\) | ||||
0.448370 | + | 0.893848i | \(0.352005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.68818 | −0.168405 | ||||||||
\(776\) | −30.3777 | −1.09049 | ||||||||
\(777\) | 2.44223 | 0.0876145 | ||||||||
\(778\) | −52.0485 | −1.86603 | ||||||||
\(779\) | 8.54248 | 0.306066 | ||||||||
\(780\) | −3.14629 | −0.112655 | ||||||||
\(781\) | 1.49045 | 0.0533324 | ||||||||
\(782\) | −26.9317 | −0.963075 | ||||||||
\(783\) | −12.9416 | −0.462494 | ||||||||
\(784\) | 28.9686 | 1.03459 | ||||||||
\(785\) | 37.2413 | 1.32920 | ||||||||
\(786\) | 95.9760 | 3.42335 | ||||||||
\(787\) | −18.6314 | −0.664137 | −0.332068 | − | 0.943255i | \(-0.607746\pi\) | ||||
−0.332068 | + | 0.943255i | \(0.607746\pi\) | |||||||
\(788\) | 1.19053 | 0.0424108 | ||||||||
\(789\) | −9.39584 | −0.334501 | ||||||||
\(790\) | 20.3802 | 0.725095 | ||||||||
\(791\) | 9.17013 | 0.326052 | ||||||||
\(792\) | 2.15764 | 0.0766685 | ||||||||
\(793\) | 2.38958 | 0.0848563 | ||||||||
\(794\) | −36.8288 | −1.30701 | ||||||||
\(795\) | −35.0820 | −1.24423 | ||||||||
\(796\) | −8.61635 | −0.305398 | ||||||||
\(797\) | 54.0840 | 1.91575 | 0.957876 | − | 0.287181i | \(-0.0927181\pi\) | ||||
0.957876 | + | 0.287181i | \(0.0927181\pi\) | |||||||
\(798\) | 21.3481 | 0.755715 | ||||||||
\(799\) | −65.3293 | −2.31119 | ||||||||
\(800\) | −1.51750 | −0.0536518 | ||||||||
\(801\) | 52.8643 | 1.86787 | ||||||||
\(802\) | −9.13028 | −0.322401 | ||||||||
\(803\) | 0.392731 | 0.0138592 | ||||||||
\(804\) | 2.36097 | 0.0832648 | ||||||||
\(805\) | −4.68533 | −0.165136 | ||||||||
\(806\) | 12.5692 | 0.442732 | ||||||||
\(807\) | 17.1109 | 0.602332 | ||||||||
\(808\) | 37.2300 | 1.30975 | ||||||||
\(809\) | 27.7176 | 0.974499 | 0.487249 | − | 0.873263i | \(-0.338000\pi\) | ||||
0.487249 | + | 0.873263i | \(0.338000\pi\) | |||||||
\(810\) | 73.3747 | 2.57813 | ||||||||
\(811\) | 1.13784 | 0.0399551 | 0.0199776 | − | 0.999800i | \(-0.493641\pi\) | ||||
0.0199776 | + | 0.999800i | \(0.493641\pi\) | |||||||
\(812\) | 0.325380 | 0.0114186 | ||||||||
\(813\) | −57.6909 | −2.02331 | ||||||||
\(814\) | 0.160489 | 0.00562513 | ||||||||
\(815\) | 29.7024 | 1.04043 | ||||||||
\(816\) | 100.291 | 3.51089 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −24.6080 | −0.860400 | ||||||||
\(819\) | −7.48858 | −0.261672 | ||||||||
\(820\) | −1.45133 | −0.0506826 | ||||||||
\(821\) | 1.25444 | 0.0437803 | 0.0218902 | − | 0.999760i | \(-0.493032\pi\) | ||||
0.0218902 | + | 0.999760i | \(0.493032\pi\) | |||||||
\(822\) | 51.9351 | 1.81144 | ||||||||
\(823\) | 41.3981 | 1.44305 | 0.721523 | − | 0.692391i | \(-0.243443\pi\) | ||||
0.721523 | + | 0.692391i | \(0.243443\pi\) | |||||||
\(824\) | 13.3151 | 0.463853 | ||||||||
\(825\) | 0.258644 | 0.00900482 | ||||||||
\(826\) | 5.23082 | 0.182004 | ||||||||
\(827\) | 25.2468 | 0.877918 | 0.438959 | − | 0.898507i | \(-0.355347\pi\) | ||||
0.438959 | + | 0.898507i | \(0.355347\pi\) | |||||||
\(828\) | 7.61766 | 0.264732 | ||||||||
\(829\) | −6.34472 | −0.220361 | −0.110181 | − | 0.993912i | \(-0.535143\pi\) | ||||
−0.110181 | + | 0.993912i | \(0.535143\pi\) | |||||||
\(830\) | −7.56300 | −0.262516 | ||||||||
\(831\) | 79.0989 | 2.74391 | ||||||||
\(832\) | −6.81011 | −0.236098 | ||||||||
\(833\) | −41.9416 | −1.45319 | ||||||||
\(834\) | 63.0762 | 2.18415 | ||||||||
\(835\) | 7.19388 | 0.248954 | ||||||||
\(836\) | 0.234678 | 0.00811650 | ||||||||
\(837\) | −96.4050 | −3.33224 | ||||||||
\(838\) | −54.4783 | −1.88192 | ||||||||
\(839\) | −3.18926 | −0.110106 | −0.0550528 | − | 0.998483i | \(-0.517533\pi\) | ||||
−0.0550528 | + | 0.998483i | \(0.517533\pi\) | |||||||
\(840\) | 14.4275 | 0.497797 | ||||||||
\(841\) | −28.1366 | −0.970228 | ||||||||
\(842\) | 9.14094 | 0.315018 | ||||||||
\(843\) | −68.7165 | −2.36672 | ||||||||
\(844\) | −0.567571 | −0.0195366 | ||||||||
\(845\) | 24.1739 | 0.831608 | ||||||||
\(846\) | 110.462 | 3.79776 | ||||||||
\(847\) | −9.57495 | −0.328999 | ||||||||
\(848\) | 24.3677 | 0.836791 | ||||||||
\(849\) | 30.2316 | 1.03754 | ||||||||
\(850\) | 7.05488 | 0.241980 | ||||||||
\(851\) | −2.25391 | −0.0772632 | ||||||||
\(852\) | −16.2035 | −0.555123 | ||||||||
\(853\) | 5.14257 | 0.176078 | 0.0880391 | − | 0.996117i | \(-0.471940\pi\) | ||||
0.0880391 | + | 0.996117i | \(0.471940\pi\) | |||||||
\(854\) | 2.75463 | 0.0942614 | ||||||||
\(855\) | −74.9603 | −2.56359 | ||||||||
\(856\) | 10.3549 | 0.353924 | ||||||||
\(857\) | 26.9541 | 0.920736 | 0.460368 | − | 0.887728i | \(-0.347717\pi\) | ||||
0.460368 | + | 0.887728i | \(0.347717\pi\) | |||||||
\(858\) | −0.693435 | −0.0236735 | ||||||||
\(859\) | 31.7257 | 1.08247 | 0.541234 | − | 0.840872i | \(-0.317957\pi\) | ||||
0.541234 | + | 0.840872i | \(0.317957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.86758 | −0.165887 | ||||||||
\(862\) | −27.3056 | −0.930031 | ||||||||
\(863\) | 34.4558 | 1.17289 | 0.586445 | − | 0.809989i | \(-0.300527\pi\) | ||||
0.586445 | + | 0.809989i | \(0.300527\pi\) | |||||||
\(864\) | −31.2050 | −1.06162 | ||||||||
\(865\) | −22.8426 | −0.776670 | ||||||||
\(866\) | 18.7834 | 0.638285 | ||||||||
\(867\) | −90.5581 | −3.07551 | ||||||||
\(868\) | 2.42384 | 0.0822705 | ||||||||
\(869\) | 0.751395 | 0.0254893 | ||||||||
\(870\) | −9.62403 | −0.326285 | ||||||||
\(871\) | 2.14200 | 0.0725788 | ||||||||
\(872\) | −37.1801 | −1.25908 | ||||||||
\(873\) | −89.9339 | −3.04380 | ||||||||
\(874\) | −19.7020 | −0.666431 | ||||||||
\(875\) | 10.2878 | 0.347790 | ||||||||
\(876\) | −4.26961 | −0.144257 | ||||||||
\(877\) | 33.8882 | 1.14432 | 0.572161 | − | 0.820141i | \(-0.306105\pi\) | ||||
0.572161 | + | 0.820141i | \(0.306105\pi\) | |||||||
\(878\) | −39.1548 | −1.32141 | ||||||||
\(879\) | 19.5317 | 0.658786 | ||||||||
\(880\) | 1.14656 | 0.0386506 | ||||||||
\(881\) | −26.2950 | −0.885901 | −0.442950 | − | 0.896546i | \(-0.646068\pi\) | ||||
−0.442950 | + | 0.896546i | \(0.646068\pi\) | |||||||
\(882\) | 70.9168 | 2.38789 | ||||||||
\(883\) | −5.79598 | −0.195050 | −0.0975252 | − | 0.995233i | \(-0.531093\pi\) | ||||
−0.0975252 | + | 0.995233i | \(0.531093\pi\) | |||||||
\(884\) | −3.16407 | −0.106419 | ||||||||
\(885\) | −25.8815 | −0.869997 | ||||||||
\(886\) | 30.3466 | 1.01951 | ||||||||
\(887\) | −11.4913 | −0.385840 | −0.192920 | − | 0.981214i | \(-0.561796\pi\) | ||||
−0.192920 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(888\) | 6.94046 | 0.232907 | ||||||||
\(889\) | 16.1674 | 0.542239 | ||||||||
\(890\) | 23.2291 | 0.778642 | ||||||||
\(891\) | 2.70525 | 0.0906291 | ||||||||
\(892\) | 7.41598 | 0.248305 | ||||||||
\(893\) | −47.7920 | −1.59930 | ||||||||
\(894\) | −28.5740 | −0.955657 | ||||||||
\(895\) | 21.3746 | 0.714473 | ||||||||
\(896\) | −11.7559 | −0.392738 | ||||||||
\(897\) | 9.73863 | 0.325164 | ||||||||
\(898\) | 2.23286 | 0.0745116 | ||||||||
\(899\) | 6.43161 | 0.214506 | ||||||||
\(900\) | −1.99548 | −0.0665160 | ||||||||
\(901\) | −35.2803 | −1.17536 | ||||||||
\(902\) | −0.319869 | −0.0106505 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.0602 | 0.866750 | ||||||||
\(905\) | 27.3605 | 0.909493 | ||||||||
\(906\) | −60.1035 | −1.99681 | ||||||||
\(907\) | 47.6023 | 1.58061 | 0.790304 | − | 0.612716i | \(-0.209923\pi\) | ||||
0.790304 | + | 0.612716i | \(0.209923\pi\) | |||||||
\(908\) | −7.00691 | −0.232532 | ||||||||
\(909\) | 110.220 | 3.65578 | ||||||||
\(910\) | −3.29056 | −0.109081 | ||||||||
\(911\) | 30.6746 | 1.01629 | 0.508147 | − | 0.861271i | \(-0.330331\pi\) | ||||
0.508147 | + | 0.861271i | \(0.330331\pi\) | |||||||
\(912\) | 73.3684 | 2.42947 | ||||||||
\(913\) | −0.278839 | −0.00922824 | ||||||||
\(914\) | 43.1899 | 1.42859 | ||||||||
\(915\) | −13.6296 | −0.450579 | ||||||||
\(916\) | 6.64309 | 0.219494 | ||||||||
\(917\) | 16.7914 | 0.554501 | ||||||||
\(918\) | 145.072 | 4.78810 | ||||||||
\(919\) | 26.9074 | 0.887594 | 0.443797 | − | 0.896127i | \(-0.353631\pi\) | ||||
0.443797 | + | 0.896127i | \(0.353631\pi\) | |||||||
\(920\) | −13.3150 | −0.438984 | ||||||||
\(921\) | −61.1188 | −2.01393 | ||||||||
\(922\) | 64.3711 | 2.11995 | ||||||||
\(923\) | −14.7007 | −0.483880 | ||||||||
\(924\) | −0.133721 | −0.00439911 | ||||||||
\(925\) | 0.590423 | 0.0194130 | ||||||||
\(926\) | 43.0395 | 1.41437 | ||||||||
\(927\) | 39.4197 | 1.29471 | ||||||||
\(928\) | 2.08183 | 0.0683393 | ||||||||
\(929\) | 23.8762 | 0.783354 | 0.391677 | − | 0.920103i | \(-0.371895\pi\) | ||||
0.391677 | + | 0.920103i | \(0.371895\pi\) | |||||||
\(930\) | −71.6918 | −2.35087 | ||||||||
\(931\) | −30.6826 | −1.00558 | ||||||||
\(932\) | −4.22503 | −0.138395 | ||||||||
\(933\) | −28.6826 | −0.939026 | ||||||||
\(934\) | −51.2197 | −1.67596 | ||||||||
\(935\) | −1.66003 | −0.0542887 | ||||||||
\(936\) | −21.2815 | −0.695607 | ||||||||
\(937\) | 15.6416 | 0.510990 | 0.255495 | − | 0.966810i | \(-0.417762\pi\) | ||||
0.255495 | + | 0.966810i | \(0.417762\pi\) | |||||||
\(938\) | 2.46923 | 0.0806231 | ||||||||
\(939\) | 81.9447 | 2.67416 | ||||||||
\(940\) | 8.11964 | 0.264834 | ||||||||
\(941\) | 52.3791 | 1.70751 | 0.853755 | − | 0.520675i | \(-0.174320\pi\) | ||||
0.853755 | + | 0.520675i | \(0.174320\pi\) | |||||||
\(942\) | −89.2327 | −2.90736 | ||||||||
\(943\) | 4.49225 | 0.146288 | ||||||||
\(944\) | 17.9771 | 0.585105 | ||||||||
\(945\) | 25.2384 | 0.821005 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.92049 | 0.0949031 | 0.0474516 | − | 0.998874i | \(-0.484890\pi\) | ||||
0.0474516 | + | 0.998874i | \(0.484890\pi\) | |||||||
\(948\) | −8.16886 | −0.265312 | ||||||||
\(949\) | −3.87363 | −0.125743 | ||||||||
\(950\) | 5.16103 | 0.167446 | ||||||||
\(951\) | −0.729754 | −0.0236639 | ||||||||
\(952\) | 14.5091 | 0.470241 | ||||||||
\(953\) | 4.41502 | 0.143016 | 0.0715082 | − | 0.997440i | \(-0.477219\pi\) | ||||
0.0715082 | + | 0.997440i | \(0.477219\pi\) | |||||||
\(954\) | 59.6536 | 1.93136 | ||||||||
\(955\) | −12.5690 | −0.406724 | ||||||||
\(956\) | −0.845951 | −0.0273600 | ||||||||
\(957\) | −0.354827 | −0.0114699 | ||||||||
\(958\) | 5.39954 | 0.174451 | ||||||||
\(959\) | 9.08627 | 0.293411 | ||||||||
\(960\) | 38.8433 | 1.25366 | ||||||||
\(961\) | 16.9107 | 0.545507 | ||||||||
\(962\) | −1.58295 | −0.0510364 | ||||||||
\(963\) | 30.6561 | 0.987878 | ||||||||
\(964\) | 10.0193 | 0.322699 | ||||||||
\(965\) | 49.1518 | 1.58225 | ||||||||
\(966\) | 11.2264 | 0.361203 | ||||||||
\(967\) | 10.7653 | 0.346190 | 0.173095 | − | 0.984905i | \(-0.444623\pi\) | ||||
0.173095 | + | 0.984905i | \(0.444623\pi\) | |||||||
\(968\) | −27.2106 | −0.874583 | ||||||||
\(969\) | −106.225 | −3.41244 | ||||||||
\(970\) | −39.5179 | −1.26884 | ||||||||
\(971\) | −3.67115 | −0.117813 | −0.0589064 | − | 0.998264i | \(-0.518761\pi\) | ||||
−0.0589064 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(972\) | −12.6226 | −0.404870 | ||||||||
\(973\) | 11.0355 | 0.353781 | ||||||||
\(974\) | −48.1734 | −1.54358 | ||||||||
\(975\) | −2.55108 | −0.0816999 | ||||||||
\(976\) | 9.46700 | 0.303031 | ||||||||
\(977\) | 47.0516 | 1.50531 | 0.752657 | − | 0.658413i | \(-0.228772\pi\) | ||||
0.752657 | + | 0.658413i | \(0.228772\pi\) | |||||||
\(978\) | −71.1691 | −2.27574 | ||||||||
\(979\) | 0.856432 | 0.0273717 | ||||||||
\(980\) | 5.21283 | 0.166518 | ||||||||
\(981\) | −110.073 | −3.51435 | ||||||||
\(982\) | 9.24420 | 0.294994 | ||||||||
\(983\) | −32.3172 | −1.03076 | −0.515379 | − | 0.856962i | \(-0.672349\pi\) | ||||
−0.515379 | + | 0.856962i | \(0.672349\pi\) | |||||||
\(984\) | −13.8330 | −0.440979 | ||||||||
\(985\) | −6.16069 | −0.196296 | ||||||||
\(986\) | −9.67842 | −0.308224 | ||||||||
\(987\) | 27.2323 | 0.866815 | ||||||||
\(988\) | −2.31470 | −0.0736403 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 2.80685 | 0.0892076 | ||||||||
\(991\) | −46.2290 | −1.46851 | −0.734256 | − | 0.678873i | \(-0.762469\pi\) | ||||
−0.734256 | + | 0.678873i | \(0.762469\pi\) | |||||||
\(992\) | 15.5080 | 0.492381 | ||||||||
\(993\) | −30.1651 | −0.957261 | ||||||||
\(994\) | −16.9465 | −0.537511 | ||||||||
\(995\) | 44.5876 | 1.41352 | ||||||||
\(996\) | 3.03143 | 0.0960544 | ||||||||
\(997\) | 30.7575 | 0.974100 | 0.487050 | − | 0.873374i | \(-0.338073\pi\) | ||||
0.487050 | + | 0.873374i | \(0.338073\pi\) | |||||||
\(998\) | 8.95354 | 0.283420 | ||||||||
\(999\) | 12.1411 | 0.384128 |
(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 | 1849.2.a.p.1.7 | ✓ | 20 | |
43.42 | odd | 2 | 1849.2.a.r.1.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.p.1.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1849.2.a.r.1.14 | yes | 20 | 43.42 | odd | 2 |