Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(1.74152\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.741521 | 0.428117 | 0.214059 | − | 0.976821i | \(-0.431332\pi\) | ||||
0.214059 | + | 0.976821i | \(0.431332\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.741521 | 0.302725 | ||||||||
\(7\) | −2.92320 | −1.10486 | −0.552432 | − | 0.833558i | \(-0.686300\pi\) | ||||
−0.552432 | + | 0.833558i | \(0.686300\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.45015 | −0.816716 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.78605 | 1.14154 | 0.570768 | − | 0.821111i | \(-0.306646\pi\) | ||||
0.570768 | + | 0.821111i | \(0.306646\pi\) | |||||||
\(12\) | 0.741521 | 0.214059 | ||||||||
\(13\) | −1.20674 | −0.334688 | −0.167344 | − | 0.985899i | \(-0.553519\pi\) | ||||
−0.167344 | + | 0.985899i | \(0.553519\pi\) | |||||||
\(14\) | −2.92320 | −0.781257 | ||||||||
\(15\) | 0.741521 | 0.191460 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.24040 | 0.543378 | 0.271689 | − | 0.962385i | \(-0.412418\pi\) | ||||
0.271689 | + | 0.962385i | \(0.412418\pi\) | |||||||
\(18\) | −2.45015 | −0.577505 | ||||||||
\(19\) | −6.75626 | −1.54999 | −0.774996 | − | 0.631967i | \(-0.782248\pi\) | ||||
−0.774996 | + | 0.631967i | \(0.782248\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.16761 | −0.473011 | ||||||||
\(22\) | 3.78605 | 0.807188 | ||||||||
\(23\) | −2.16212 | −0.450833 | −0.225416 | − | 0.974263i | \(-0.572374\pi\) | ||||
−0.225416 | + | 0.974263i | \(0.572374\pi\) | |||||||
\(24\) | 0.741521 | 0.151362 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.20674 | −0.236660 | ||||||||
\(27\) | −4.04140 | −0.777767 | ||||||||
\(28\) | −2.92320 | −0.552432 | ||||||||
\(29\) | −7.43472 | −1.38059 | −0.690297 | − | 0.723527i | \(-0.742520\pi\) | ||||
−0.690297 | + | 0.723527i | \(0.742520\pi\) | |||||||
\(30\) | 0.741521 | 0.135383 | ||||||||
\(31\) | 2.54924 | 0.457856 | 0.228928 | − | 0.973443i | \(-0.426478\pi\) | ||||
0.228928 | + | 0.973443i | \(0.426478\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.80743 | 0.488711 | ||||||||
\(34\) | 2.24040 | 0.384226 | ||||||||
\(35\) | −2.92320 | −0.494110 | ||||||||
\(36\) | −2.45015 | −0.408358 | ||||||||
\(37\) | −2.16013 | −0.355124 | −0.177562 | − | 0.984110i | \(-0.556821\pi\) | ||||
−0.177562 | + | 0.984110i | \(0.556821\pi\) | |||||||
\(38\) | −6.75626 | −1.09601 | ||||||||
\(39\) | −0.894820 | −0.143286 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −4.79426 | −0.748737 | −0.374369 | − | 0.927280i | \(-0.622141\pi\) | ||||
−0.374369 | + | 0.927280i | \(0.622141\pi\) | |||||||
\(42\) | −2.16761 | −0.334470 | ||||||||
\(43\) | 2.62620 | 0.400492 | 0.200246 | − | 0.979746i | \(-0.435826\pi\) | ||||
0.200246 | + | 0.979746i | \(0.435826\pi\) | |||||||
\(44\) | 3.78605 | 0.570768 | ||||||||
\(45\) | −2.45015 | −0.365246 | ||||||||
\(46\) | −2.16212 | −0.318787 | ||||||||
\(47\) | −9.28939 | −1.35500 | −0.677499 | − | 0.735524i | \(-0.736936\pi\) | ||||
−0.677499 | + | 0.735524i | \(0.736936\pi\) | |||||||
\(48\) | 0.741521 | 0.107029 | ||||||||
\(49\) | 1.54507 | 0.220724 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.66131 | 0.232629 | ||||||||
\(52\) | −1.20674 | −0.167344 | ||||||||
\(53\) | −4.24197 | −0.582680 | −0.291340 | − | 0.956620i | \(-0.594101\pi\) | ||||
−0.291340 | + | 0.956620i | \(0.594101\pi\) | |||||||
\(54\) | −4.04140 | −0.549965 | ||||||||
\(55\) | 3.78605 | 0.510510 | ||||||||
\(56\) | −2.92320 | −0.390628 | ||||||||
\(57\) | −5.00990 | −0.663578 | ||||||||
\(58\) | −7.43472 | −0.976227 | ||||||||
\(59\) | −2.50293 | −0.325854 | −0.162927 | − | 0.986638i | \(-0.552094\pi\) | ||||
−0.162927 | + | 0.986638i | \(0.552094\pi\) | |||||||
\(60\) | 0.741521 | 0.0957299 | ||||||||
\(61\) | −2.21161 | −0.283167 | −0.141584 | − | 0.989926i | \(-0.545219\pi\) | ||||
−0.141584 | + | 0.989926i | \(0.545219\pi\) | |||||||
\(62\) | 2.54924 | 0.323753 | ||||||||
\(63\) | 7.16226 | 0.902359 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.20674 | −0.149677 | ||||||||
\(66\) | 2.80743 | 0.345571 | ||||||||
\(67\) | −6.47843 | −0.791467 | −0.395733 | − | 0.918365i | \(-0.629510\pi\) | ||||
−0.395733 | + | 0.918365i | \(0.629510\pi\) | |||||||
\(68\) | 2.24040 | 0.271689 | ||||||||
\(69\) | −1.60326 | −0.193009 | ||||||||
\(70\) | −2.92320 | −0.349389 | ||||||||
\(71\) | 3.13750 | 0.372352 | 0.186176 | − | 0.982516i | \(-0.440390\pi\) | ||||
0.186176 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(72\) | −2.45015 | −0.288753 | ||||||||
\(73\) | 7.55686 | 0.884464 | 0.442232 | − | 0.896901i | \(-0.354187\pi\) | ||||
0.442232 | + | 0.896901i | \(0.354187\pi\) | |||||||
\(74\) | −2.16013 | −0.251110 | ||||||||
\(75\) | 0.741521 | 0.0856235 | ||||||||
\(76\) | −6.75626 | −0.774996 | ||||||||
\(77\) | −11.0674 | −1.26124 | ||||||||
\(78\) | −0.894820 | −0.101318 | ||||||||
\(79\) | −7.16658 | −0.806303 | −0.403152 | − | 0.915133i | \(-0.632085\pi\) | ||||
−0.403152 | + | 0.915133i | \(0.632085\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 4.35366 | 0.483740 | ||||||||
\(82\) | −4.79426 | −0.529437 | ||||||||
\(83\) | 14.7455 | 1.61852 | 0.809262 | − | 0.587447i | \(-0.199867\pi\) | ||||
0.809262 | + | 0.587447i | \(0.199867\pi\) | |||||||
\(84\) | −2.16761 | −0.236506 | ||||||||
\(85\) | 2.24040 | 0.243006 | ||||||||
\(86\) | 2.62620 | 0.283191 | ||||||||
\(87\) | −5.51300 | −0.591056 | ||||||||
\(88\) | 3.78605 | 0.403594 | ||||||||
\(89\) | 10.3519 | 1.09730 | 0.548652 | − | 0.836051i | \(-0.315141\pi\) | ||||
0.548652 | + | 0.836051i | \(0.315141\pi\) | |||||||
\(90\) | −2.45015 | −0.258268 | ||||||||
\(91\) | 3.52753 | 0.369785 | ||||||||
\(92\) | −2.16212 | −0.225416 | ||||||||
\(93\) | 1.89031 | 0.196016 | ||||||||
\(94\) | −9.28939 | −0.958128 | ||||||||
\(95\) | −6.75626 | −0.693177 | ||||||||
\(96\) | 0.741521 | 0.0756812 | ||||||||
\(97\) | −6.45797 | −0.655708 | −0.327854 | − | 0.944728i | \(-0.606325\pi\) | ||||
−0.327854 | + | 0.944728i | \(0.606325\pi\) | |||||||
\(98\) | 1.54507 | 0.156076 | ||||||||
\(99\) | −9.27637 | −0.932310 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.69551 | 0.367717 | 0.183858 | − | 0.982953i | \(-0.441141\pi\) | ||||
0.183858 | + | 0.982953i | \(0.441141\pi\) | |||||||
\(102\) | 1.66131 | 0.164494 | ||||||||
\(103\) | 6.19576 | 0.610487 | 0.305243 | − | 0.952274i | \(-0.401262\pi\) | ||||
0.305243 | + | 0.952274i | \(0.401262\pi\) | |||||||
\(104\) | −1.20674 | −0.118330 | ||||||||
\(105\) | −2.16761 | −0.211537 | ||||||||
\(106\) | −4.24197 | −0.412017 | ||||||||
\(107\) | −4.26814 | −0.412617 | −0.206309 | − | 0.978487i | \(-0.566145\pi\) | ||||
−0.206309 | + | 0.978487i | \(0.566145\pi\) | |||||||
\(108\) | −4.04140 | −0.388884 | ||||||||
\(109\) | −6.78094 | −0.649496 | −0.324748 | − | 0.945800i | \(-0.605280\pi\) | ||||
−0.324748 | + | 0.945800i | \(0.605280\pi\) | |||||||
\(110\) | 3.78605 | 0.360985 | ||||||||
\(111\) | −1.60178 | −0.152035 | ||||||||
\(112\) | −2.92320 | −0.276216 | ||||||||
\(113\) | −12.8387 | −1.20776 | −0.603881 | − | 0.797075i | \(-0.706380\pi\) | ||||
−0.603881 | + | 0.797075i | \(0.706380\pi\) | |||||||
\(114\) | −5.00990 | −0.469221 | ||||||||
\(115\) | −2.16212 | −0.201619 | ||||||||
\(116\) | −7.43472 | −0.690297 | ||||||||
\(117\) | 2.95668 | 0.273345 | ||||||||
\(118\) | −2.50293 | −0.230414 | ||||||||
\(119\) | −6.54914 | −0.600358 | ||||||||
\(120\) | 0.741521 | 0.0676913 | ||||||||
\(121\) | 3.33415 | 0.303105 | ||||||||
\(122\) | −2.21161 | −0.200229 | ||||||||
\(123\) | −3.55504 | −0.320547 | ||||||||
\(124\) | 2.54924 | 0.228928 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.16226 | 0.638065 | ||||||||
\(127\) | −21.5834 | −1.91522 | −0.957610 | − | 0.288069i | \(-0.906987\pi\) | ||||
−0.957610 | + | 0.288069i | \(0.906987\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.94739 | 0.171458 | ||||||||
\(130\) | −1.20674 | −0.105838 | ||||||||
\(131\) | −1.86617 | −0.163048 | −0.0815242 | − | 0.996671i | \(-0.525979\pi\) | ||||
−0.0815242 | + | 0.996671i | \(0.525979\pi\) | |||||||
\(132\) | 2.80743 | 0.244356 | ||||||||
\(133\) | 19.7499 | 1.71253 | ||||||||
\(134\) | −6.47843 | −0.559651 | ||||||||
\(135\) | −4.04140 | −0.347828 | ||||||||
\(136\) | 2.24040 | 0.192113 | ||||||||
\(137\) | 16.5456 | 1.41358 | 0.706792 | − | 0.707421i | \(-0.250141\pi\) | ||||
0.706792 | + | 0.707421i | \(0.250141\pi\) | |||||||
\(138\) | −1.60326 | −0.136478 | ||||||||
\(139\) | 17.7109 | 1.50222 | 0.751111 | − | 0.660176i | \(-0.229518\pi\) | ||||
0.751111 | + | 0.660176i | \(0.229518\pi\) | |||||||
\(140\) | −2.92320 | −0.247055 | ||||||||
\(141\) | −6.88828 | −0.580098 | ||||||||
\(142\) | 3.13750 | 0.263293 | ||||||||
\(143\) | −4.56876 | −0.382059 | ||||||||
\(144\) | −2.45015 | −0.204179 | ||||||||
\(145\) | −7.43472 | −0.617420 | ||||||||
\(146\) | 7.55686 | 0.625410 | ||||||||
\(147\) | 1.14570 | 0.0944958 | ||||||||
\(148\) | −2.16013 | −0.177562 | ||||||||
\(149\) | −6.38704 | −0.523246 | −0.261623 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261623 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(150\) | 0.741521 | 0.0605449 | ||||||||
\(151\) | −3.63992 | −0.296213 | −0.148106 | − | 0.988971i | \(-0.547318\pi\) | ||||
−0.148106 | + | 0.988971i | \(0.547318\pi\) | |||||||
\(152\) | −6.75626 | −0.548005 | ||||||||
\(153\) | −5.48932 | −0.443785 | ||||||||
\(154\) | −11.0674 | −0.891833 | ||||||||
\(155\) | 2.54924 | 0.204760 | ||||||||
\(156\) | −0.894820 | −0.0716430 | ||||||||
\(157\) | −3.48148 | −0.277852 | −0.138926 | − | 0.990303i | \(-0.544365\pi\) | ||||
−0.138926 | + | 0.990303i | \(0.544365\pi\) | |||||||
\(158\) | −7.16658 | −0.570142 | ||||||||
\(159\) | −3.14551 | −0.249455 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.32029 | 0.498109 | ||||||||
\(162\) | 4.35366 | 0.342056 | ||||||||
\(163\) | −7.48872 | −0.586562 | −0.293281 | − | 0.956026i | \(-0.594747\pi\) | ||||
−0.293281 | + | 0.956026i | \(0.594747\pi\) | |||||||
\(164\) | −4.79426 | −0.374369 | ||||||||
\(165\) | 2.80743 | 0.218558 | ||||||||
\(166\) | 14.7455 | 1.14447 | ||||||||
\(167\) | 0.756944 | 0.0585741 | 0.0292870 | − | 0.999571i | \(-0.490676\pi\) | ||||
0.0292870 | + | 0.999571i | \(0.490676\pi\) | |||||||
\(168\) | −2.16761 | −0.167235 | ||||||||
\(169\) | −11.5438 | −0.887984 | ||||||||
\(170\) | 2.24040 | 0.171831 | ||||||||
\(171\) | 16.5538 | 1.26590 | ||||||||
\(172\) | 2.62620 | 0.200246 | ||||||||
\(173\) | −18.3173 | −1.39264 | −0.696321 | − | 0.717730i | \(-0.745181\pi\) | ||||
−0.696321 | + | 0.717730i | \(0.745181\pi\) | |||||||
\(174\) | −5.51300 | −0.417940 | ||||||||
\(175\) | −2.92320 | −0.220973 | ||||||||
\(176\) | 3.78605 | 0.285384 | ||||||||
\(177\) | −1.85598 | −0.139504 | ||||||||
\(178\) | 10.3519 | 0.775911 | ||||||||
\(179\) | 2.24990 | 0.168166 | 0.0840829 | − | 0.996459i | \(-0.473204\pi\) | ||||
0.0840829 | + | 0.996459i | \(0.473204\pi\) | |||||||
\(180\) | −2.45015 | −0.182623 | ||||||||
\(181\) | −9.62422 | −0.715363 | −0.357681 | − | 0.933844i | \(-0.616433\pi\) | ||||
−0.357681 | + | 0.933844i | \(0.616433\pi\) | |||||||
\(182\) | 3.52753 | 0.261478 | ||||||||
\(183\) | −1.63995 | −0.121229 | ||||||||
\(184\) | −2.16212 | −0.159393 | ||||||||
\(185\) | −2.16013 | −0.158816 | ||||||||
\(186\) | 1.89031 | 0.138604 | ||||||||
\(187\) | 8.48227 | 0.620285 | ||||||||
\(188\) | −9.28939 | −0.677499 | ||||||||
\(189\) | 11.8138 | 0.859327 | ||||||||
\(190\) | −6.75626 | −0.490150 | ||||||||
\(191\) | 1.03740 | 0.0750638 | 0.0375319 | − | 0.999295i | \(-0.488050\pi\) | ||||
0.0375319 | + | 0.999295i | \(0.488050\pi\) | |||||||
\(192\) | 0.741521 | 0.0535147 | ||||||||
\(193\) | −12.0456 | −0.867064 | −0.433532 | − | 0.901138i | \(-0.642733\pi\) | ||||
−0.433532 | + | 0.901138i | \(0.642733\pi\) | |||||||
\(194\) | −6.45797 | −0.463656 | ||||||||
\(195\) | −0.894820 | −0.0640794 | ||||||||
\(196\) | 1.54507 | 0.110362 | ||||||||
\(197\) | 15.0764 | 1.07415 | 0.537073 | − | 0.843536i | \(-0.319530\pi\) | ||||
0.537073 | + | 0.843536i | \(0.319530\pi\) | |||||||
\(198\) | −9.27637 | −0.659243 | ||||||||
\(199\) | 0.396256 | 0.0280899 | 0.0140449 | − | 0.999901i | \(-0.495529\pi\) | ||||
0.0140449 | + | 0.999901i | \(0.495529\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −4.80390 | −0.338841 | ||||||||
\(202\) | 3.69551 | 0.260015 | ||||||||
\(203\) | 21.7331 | 1.52537 | ||||||||
\(204\) | 1.66131 | 0.116315 | ||||||||
\(205\) | −4.79426 | −0.334846 | ||||||||
\(206\) | 6.19576 | 0.431679 | ||||||||
\(207\) | 5.29751 | 0.368202 | ||||||||
\(208\) | −1.20674 | −0.0836721 | ||||||||
\(209\) | −25.5795 | −1.76937 | ||||||||
\(210\) | −2.16761 | −0.149579 | ||||||||
\(211\) | 18.2045 | 1.25325 | 0.626624 | − | 0.779322i | \(-0.284436\pi\) | ||||
0.626624 | + | 0.779322i | \(0.284436\pi\) | |||||||
\(212\) | −4.24197 | −0.291340 | ||||||||
\(213\) | 2.32652 | 0.159410 | ||||||||
\(214\) | −4.26814 | −0.291764 | ||||||||
\(215\) | 2.62620 | 0.179106 | ||||||||
\(216\) | −4.04140 | −0.274982 | ||||||||
\(217\) | −7.45192 | −0.505869 | ||||||||
\(218\) | −6.78094 | −0.459263 | ||||||||
\(219\) | 5.60357 | 0.378654 | ||||||||
\(220\) | 3.78605 | 0.255255 | ||||||||
\(221\) | −2.70358 | −0.181862 | ||||||||
\(222\) | −1.60178 | −0.107505 | ||||||||
\(223\) | −9.99886 | −0.669573 | −0.334787 | − | 0.942294i | \(-0.608664\pi\) | ||||
−0.334787 | + | 0.942294i | \(0.608664\pi\) | |||||||
\(224\) | −2.92320 | −0.195314 | ||||||||
\(225\) | −2.45015 | −0.163343 | ||||||||
\(226\) | −12.8387 | −0.854016 | ||||||||
\(227\) | −8.02690 | −0.532764 | −0.266382 | − | 0.963868i | \(-0.585828\pi\) | ||||
−0.266382 | + | 0.963868i | \(0.585828\pi\) | |||||||
\(228\) | −5.00990 | −0.331789 | ||||||||
\(229\) | −25.6126 | −1.69253 | −0.846264 | − | 0.532763i | \(-0.821154\pi\) | ||||
−0.846264 | + | 0.532763i | \(0.821154\pi\) | |||||||
\(230\) | −2.16212 | −0.142566 | ||||||||
\(231\) | −8.20667 | −0.539960 | ||||||||
\(232\) | −7.43472 | −0.488113 | ||||||||
\(233\) | 8.36069 | 0.547727 | 0.273864 | − | 0.961769i | \(-0.411698\pi\) | ||||
0.273864 | + | 0.961769i | \(0.411698\pi\) | |||||||
\(234\) | 2.95668 | 0.193284 | ||||||||
\(235\) | −9.28939 | −0.605973 | ||||||||
\(236\) | −2.50293 | −0.162927 | ||||||||
\(237\) | −5.31417 | −0.345192 | ||||||||
\(238\) | −6.54914 | −0.424517 | ||||||||
\(239\) | −5.94177 | −0.384341 | −0.192171 | − | 0.981362i | \(-0.561553\pi\) | ||||
−0.192171 | + | 0.981362i | \(0.561553\pi\) | |||||||
\(240\) | 0.741521 | 0.0478650 | ||||||||
\(241\) | −28.2635 | −1.82061 | −0.910307 | − | 0.413933i | \(-0.864155\pi\) | ||||
−0.910307 | + | 0.413933i | \(0.864155\pi\) | |||||||
\(242\) | 3.33415 | 0.214327 | ||||||||
\(243\) | 15.3525 | 0.984865 | ||||||||
\(244\) | −2.21161 | −0.141584 | ||||||||
\(245\) | 1.54507 | 0.0987108 | ||||||||
\(246\) | −3.55504 | −0.226661 | ||||||||
\(247\) | 8.15302 | 0.518764 | ||||||||
\(248\) | 2.54924 | 0.161877 | ||||||||
\(249\) | 10.9341 | 0.692919 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 1.54250 | 0.0973619 | 0.0486810 | − | 0.998814i | \(-0.484498\pi\) | ||||
0.0486810 | + | 0.998814i | \(0.484498\pi\) | |||||||
\(252\) | 7.16226 | 0.451180 | ||||||||
\(253\) | −8.18588 | −0.514642 | ||||||||
\(254\) | −21.5834 | −1.35426 | ||||||||
\(255\) | 1.66131 | 0.104035 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.2344 | 0.763159 | 0.381580 | − | 0.924336i | \(-0.375380\pi\) | ||||
0.381580 | + | 0.924336i | \(0.375380\pi\) | |||||||
\(258\) | 1.94739 | 0.121239 | ||||||||
\(259\) | 6.31449 | 0.392363 | ||||||||
\(260\) | −1.20674 | −0.0748386 | ||||||||
\(261\) | 18.2162 | 1.12755 | ||||||||
\(262\) | −1.86617 | −0.115293 | ||||||||
\(263\) | 6.05174 | 0.373167 | 0.186583 | − | 0.982439i | \(-0.440259\pi\) | ||||
0.186583 | + | 0.982439i | \(0.440259\pi\) | |||||||
\(264\) | 2.80743 | 0.172786 | ||||||||
\(265\) | −4.24197 | −0.260582 | ||||||||
\(266\) | 19.7499 | 1.21094 | ||||||||
\(267\) | 7.67618 | 0.469775 | ||||||||
\(268\) | −6.47843 | −0.395733 | ||||||||
\(269\) | 15.8007 | 0.963388 | 0.481694 | − | 0.876339i | \(-0.340022\pi\) | ||||
0.481694 | + | 0.876339i | \(0.340022\pi\) | |||||||
\(270\) | −4.04140 | −0.245952 | ||||||||
\(271\) | 5.49046 | 0.333522 | 0.166761 | − | 0.985997i | \(-0.446669\pi\) | ||||
0.166761 | + | 0.985997i | \(0.446669\pi\) | |||||||
\(272\) | 2.24040 | 0.135844 | ||||||||
\(273\) | 2.61573 | 0.158311 | ||||||||
\(274\) | 16.5456 | 0.999556 | ||||||||
\(275\) | 3.78605 | 0.228307 | ||||||||
\(276\) | −1.60326 | −0.0965046 | ||||||||
\(277\) | 12.6922 | 0.762601 | 0.381301 | − | 0.924451i | \(-0.375476\pi\) | ||||
0.381301 | + | 0.924451i | \(0.375476\pi\) | |||||||
\(278\) | 17.7109 | 1.06223 | ||||||||
\(279\) | −6.24600 | −0.373938 | ||||||||
\(280\) | −2.92320 | −0.174694 | ||||||||
\(281\) | −11.4113 | −0.680739 | −0.340369 | − | 0.940292i | \(-0.610552\pi\) | ||||
−0.340369 | + | 0.940292i | \(0.610552\pi\) | |||||||
\(282\) | −6.88828 | −0.410191 | ||||||||
\(283\) | −2.68041 | −0.159334 | −0.0796668 | − | 0.996822i | \(-0.525386\pi\) | ||||
−0.0796668 | + | 0.996822i | \(0.525386\pi\) | |||||||
\(284\) | 3.13750 | 0.186176 | ||||||||
\(285\) | −5.00990 | −0.296761 | ||||||||
\(286\) | −4.56876 | −0.270156 | ||||||||
\(287\) | 14.0146 | 0.827253 | ||||||||
\(288\) | −2.45015 | −0.144376 | ||||||||
\(289\) | −11.9806 | −0.704741 | ||||||||
\(290\) | −7.43472 | −0.436582 | ||||||||
\(291\) | −4.78872 | −0.280720 | ||||||||
\(292\) | 7.55686 | 0.442232 | ||||||||
\(293\) | 20.4478 | 1.19457 | 0.597285 | − | 0.802029i | \(-0.296246\pi\) | ||||
0.597285 | + | 0.802029i | \(0.296246\pi\) | |||||||
\(294\) | 1.14570 | 0.0668187 | ||||||||
\(295\) | −2.50293 | −0.145726 | ||||||||
\(296\) | −2.16013 | −0.125555 | ||||||||
\(297\) | −15.3009 | −0.887850 | ||||||||
\(298\) | −6.38704 | −0.369991 | ||||||||
\(299\) | 2.60911 | 0.150888 | ||||||||
\(300\) | 0.741521 | 0.0428117 | ||||||||
\(301\) | −7.67691 | −0.442490 | ||||||||
\(302\) | −3.63992 | −0.209454 | ||||||||
\(303\) | 2.74030 | 0.157426 | ||||||||
\(304\) | −6.75626 | −0.387498 | ||||||||
\(305\) | −2.21161 | −0.126636 | ||||||||
\(306\) | −5.48932 | −0.313803 | ||||||||
\(307\) | −21.7246 | −1.23989 | −0.619943 | − | 0.784647i | \(-0.712844\pi\) | ||||
−0.619943 | + | 0.784647i | \(0.712844\pi\) | |||||||
\(308\) | −11.0674 | −0.630621 | ||||||||
\(309\) | 4.59429 | 0.261360 | ||||||||
\(310\) | 2.54924 | 0.144787 | ||||||||
\(311\) | −21.9236 | −1.24317 | −0.621586 | − | 0.783346i | \(-0.713511\pi\) | ||||
−0.621586 | + | 0.783346i | \(0.713511\pi\) | |||||||
\(312\) | −0.894820 | −0.0506592 | ||||||||
\(313\) | −13.4995 | −0.763039 | −0.381520 | − | 0.924361i | \(-0.624599\pi\) | ||||
−0.381520 | + | 0.924361i | \(0.624599\pi\) | |||||||
\(314\) | −3.48148 | −0.196471 | ||||||||
\(315\) | 7.16226 | 0.403547 | ||||||||
\(316\) | −7.16658 | −0.403152 | ||||||||
\(317\) | 22.9412 | 1.28851 | 0.644254 | − | 0.764811i | \(-0.277168\pi\) | ||||
0.644254 | + | 0.764811i | \(0.277168\pi\) | |||||||
\(318\) | −3.14551 | −0.176391 | ||||||||
\(319\) | −28.1482 | −1.57600 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.16492 | −0.176649 | ||||||||
\(322\) | 6.32029 | 0.352216 | ||||||||
\(323\) | −15.1367 | −0.842231 | ||||||||
\(324\) | 4.35366 | 0.241870 | ||||||||
\(325\) | −1.20674 | −0.0669377 | ||||||||
\(326\) | −7.48872 | −0.414762 | ||||||||
\(327\) | −5.02821 | −0.278061 | ||||||||
\(328\) | −4.79426 | −0.264719 | ||||||||
\(329\) | 27.1547 | 1.49709 | ||||||||
\(330\) | 2.80743 | 0.154544 | ||||||||
\(331\) | −20.8164 | −1.14417 | −0.572086 | − | 0.820194i | \(-0.693866\pi\) | ||||
−0.572086 | + | 0.820194i | \(0.693866\pi\) | |||||||
\(332\) | 14.7455 | 0.809262 | ||||||||
\(333\) | 5.29264 | 0.290035 | ||||||||
\(334\) | 0.756944 | 0.0414181 | ||||||||
\(335\) | −6.47843 | −0.353955 | ||||||||
\(336\) | −2.16761 | −0.118253 | ||||||||
\(337\) | 13.2746 | 0.723114 | 0.361557 | − | 0.932350i | \(-0.382245\pi\) | ||||
0.361557 | + | 0.932350i | \(0.382245\pi\) | |||||||
\(338\) | −11.5438 | −0.627899 | ||||||||
\(339\) | −9.52015 | −0.517063 | ||||||||
\(340\) | 2.24040 | 0.121503 | ||||||||
\(341\) | 9.65153 | 0.522660 | ||||||||
\(342\) | 16.5538 | 0.895128 | ||||||||
\(343\) | 15.9458 | 0.860994 | ||||||||
\(344\) | 2.62620 | 0.141595 | ||||||||
\(345\) | −1.60326 | −0.0863164 | ||||||||
\(346\) | −18.3173 | −0.984747 | ||||||||
\(347\) | 2.90152 | 0.155762 | 0.0778809 | − | 0.996963i | \(-0.475185\pi\) | ||||
0.0778809 | + | 0.996963i | \(0.475185\pi\) | |||||||
\(348\) | −5.51300 | −0.295528 | ||||||||
\(349\) | −2.22064 | −0.118868 | −0.0594341 | − | 0.998232i | \(-0.518930\pi\) | ||||
−0.0594341 | + | 0.998232i | \(0.518930\pi\) | |||||||
\(350\) | −2.92320 | −0.156251 | ||||||||
\(351\) | 4.87690 | 0.260310 | ||||||||
\(352\) | 3.78605 | 0.201797 | ||||||||
\(353\) | 18.6751 | 0.993974 | 0.496987 | − | 0.867758i | \(-0.334440\pi\) | ||||
0.496987 | + | 0.867758i | \(0.334440\pi\) | |||||||
\(354\) | −1.85598 | −0.0986441 | ||||||||
\(355\) | 3.13750 | 0.166521 | ||||||||
\(356\) | 10.3519 | 0.548652 | ||||||||
\(357\) | −4.85632 | −0.257024 | ||||||||
\(358\) | 2.24990 | 0.118911 | ||||||||
\(359\) | 10.0962 | 0.532856 | 0.266428 | − | 0.963855i | \(-0.414157\pi\) | ||||
0.266428 | + | 0.963855i | \(0.414157\pi\) | |||||||
\(360\) | −2.45015 | −0.129134 | ||||||||
\(361\) | 26.6470 | 1.40247 | ||||||||
\(362\) | −9.62422 | −0.505838 | ||||||||
\(363\) | 2.47234 | 0.129764 | ||||||||
\(364\) | 3.52753 | 0.184893 | ||||||||
\(365\) | 7.55686 | 0.395544 | ||||||||
\(366\) | −1.63995 | −0.0857217 | ||||||||
\(367\) | 13.3188 | 0.695236 | 0.347618 | − | 0.937636i | \(-0.386991\pi\) | ||||
0.347618 | + | 0.937636i | \(0.386991\pi\) | |||||||
\(368\) | −2.16212 | −0.112708 | ||||||||
\(369\) | 11.7466 | 0.611505 | ||||||||
\(370\) | −2.16013 | −0.112300 | ||||||||
\(371\) | 12.4001 | 0.643782 | ||||||||
\(372\) | 1.89031 | 0.0980081 | ||||||||
\(373\) | −7.01034 | −0.362981 | −0.181491 | − | 0.983393i | \(-0.558092\pi\) | ||||
−0.181491 | + | 0.983393i | \(0.558092\pi\) | |||||||
\(374\) | 8.48227 | 0.438608 | ||||||||
\(375\) | 0.741521 | 0.0382920 | ||||||||
\(376\) | −9.28939 | −0.479064 | ||||||||
\(377\) | 8.97175 | 0.462069 | ||||||||
\(378\) | 11.8138 | 0.607636 | ||||||||
\(379\) | −11.3530 | −0.583166 | −0.291583 | − | 0.956546i | \(-0.594182\pi\) | ||||
−0.291583 | + | 0.956546i | \(0.594182\pi\) | |||||||
\(380\) | −6.75626 | −0.346589 | ||||||||
\(381\) | −16.0046 | −0.819939 | ||||||||
\(382\) | 1.03740 | 0.0530781 | ||||||||
\(383\) | −1.90171 | −0.0971729 | −0.0485865 | − | 0.998819i | \(-0.515472\pi\) | ||||
−0.0485865 | + | 0.998819i | \(0.515472\pi\) | |||||||
\(384\) | 0.741521 | 0.0378406 | ||||||||
\(385\) | −11.0674 | −0.564045 | ||||||||
\(386\) | −12.0456 | −0.613107 | ||||||||
\(387\) | −6.43459 | −0.327088 | ||||||||
\(388\) | −6.45797 | −0.327854 | ||||||||
\(389\) | 16.4178 | 0.832418 | 0.416209 | − | 0.909269i | \(-0.363358\pi\) | ||||
0.416209 | + | 0.909269i | \(0.363358\pi\) | |||||||
\(390\) | −0.894820 | −0.0453110 | ||||||||
\(391\) | −4.84402 | −0.244972 | ||||||||
\(392\) | 1.54507 | 0.0780378 | ||||||||
\(393\) | −1.38381 | −0.0698038 | ||||||||
\(394\) | 15.0764 | 0.759536 | ||||||||
\(395\) | −7.16658 | −0.360590 | ||||||||
\(396\) | −9.27637 | −0.466155 | ||||||||
\(397\) | 0.399823 | 0.0200666 | 0.0100333 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100333 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(398\) | 0.396256 | 0.0198625 | ||||||||
\(399\) | 14.6449 | 0.733163 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 12.1723 | 0.607856 | 0.303928 | − | 0.952695i | \(-0.401702\pi\) | ||||
0.303928 | + | 0.952695i | \(0.401702\pi\) | |||||||
\(402\) | −4.80390 | −0.239597 | ||||||||
\(403\) | −3.07626 | −0.153239 | ||||||||
\(404\) | 3.69551 | 0.183858 | ||||||||
\(405\) | 4.35366 | 0.216335 | ||||||||
\(406\) | 21.7331 | 1.07860 | ||||||||
\(407\) | −8.17836 | −0.405386 | ||||||||
\(408\) | 1.66131 | 0.0822469 | ||||||||
\(409\) | −33.4856 | −1.65575 | −0.827877 | − | 0.560909i | \(-0.810452\pi\) | ||||
−0.827877 | + | 0.560909i | \(0.810452\pi\) | |||||||
\(410\) | −4.79426 | −0.236772 | ||||||||
\(411\) | 12.2689 | 0.605180 | ||||||||
\(412\) | 6.19576 | 0.305243 | ||||||||
\(413\) | 7.31656 | 0.360025 | ||||||||
\(414\) | 5.29751 | 0.260358 | ||||||||
\(415\) | 14.7455 | 0.723826 | ||||||||
\(416\) | −1.20674 | −0.0591651 | ||||||||
\(417\) | 13.1330 | 0.643127 | ||||||||
\(418\) | −25.5795 | −1.25113 | ||||||||
\(419\) | 9.60020 | 0.469001 | 0.234500 | − | 0.972116i | \(-0.424655\pi\) | ||||
0.234500 | + | 0.972116i | \(0.424655\pi\) | |||||||
\(420\) | −2.16761 | −0.105769 | ||||||||
\(421\) | −5.78529 | −0.281958 | −0.140979 | − | 0.990013i | \(-0.545025\pi\) | ||||
−0.140979 | + | 0.990013i | \(0.545025\pi\) | |||||||
\(422\) | 18.2045 | 0.886180 | ||||||||
\(423\) | 22.7604 | 1.10665 | ||||||||
\(424\) | −4.24197 | −0.206008 | ||||||||
\(425\) | 2.24040 | 0.108676 | ||||||||
\(426\) | 2.32652 | 0.112720 | ||||||||
\(427\) | 6.46496 | 0.312861 | ||||||||
\(428\) | −4.26814 | −0.206309 | ||||||||
\(429\) | −3.38783 | −0.163566 | ||||||||
\(430\) | 2.62620 | 0.126647 | ||||||||
\(431\) | 19.4632 | 0.937509 | 0.468754 | − | 0.883329i | \(-0.344703\pi\) | ||||
0.468754 | + | 0.883329i | \(0.344703\pi\) | |||||||
\(432\) | −4.04140 | −0.194442 | ||||||||
\(433\) | −2.27704 | −0.109428 | −0.0547138 | − | 0.998502i | \(-0.517425\pi\) | ||||
−0.0547138 | + | 0.998502i | \(0.517425\pi\) | |||||||
\(434\) | −7.45192 | −0.357703 | ||||||||
\(435\) | −5.51300 | −0.264328 | ||||||||
\(436\) | −6.78094 | −0.324748 | ||||||||
\(437\) | 14.6078 | 0.698787 | ||||||||
\(438\) | 5.60357 | 0.267749 | ||||||||
\(439\) | 4.72610 | 0.225565 | 0.112782 | − | 0.993620i | \(-0.464024\pi\) | ||||
0.112782 | + | 0.993620i | \(0.464024\pi\) | |||||||
\(440\) | 3.78605 | 0.180493 | ||||||||
\(441\) | −3.78565 | −0.180269 | ||||||||
\(442\) | −2.70358 | −0.128596 | ||||||||
\(443\) | 26.4606 | 1.25718 | 0.628590 | − | 0.777736i | \(-0.283632\pi\) | ||||
0.628590 | + | 0.777736i | \(0.283632\pi\) | |||||||
\(444\) | −1.60178 | −0.0760173 | ||||||||
\(445\) | 10.3519 | 0.490729 | ||||||||
\(446\) | −9.99886 | −0.473460 | ||||||||
\(447\) | −4.73612 | −0.224011 | ||||||||
\(448\) | −2.92320 | −0.138108 | ||||||||
\(449\) | 6.77324 | 0.319649 | 0.159825 | − | 0.987145i | \(-0.448907\pi\) | ||||
0.159825 | + | 0.987145i | \(0.448907\pi\) | |||||||
\(450\) | −2.45015 | −0.115501 | ||||||||
\(451\) | −18.1513 | −0.854711 | ||||||||
\(452\) | −12.8387 | −0.603881 | ||||||||
\(453\) | −2.69908 | −0.126814 | ||||||||
\(454\) | −8.02690 | −0.376721 | ||||||||
\(455\) | 3.52753 | 0.165373 | ||||||||
\(456\) | −5.00990 | −0.234610 | ||||||||
\(457\) | 26.8513 | 1.25605 | 0.628026 | − | 0.778193i | \(-0.283863\pi\) | ||||
0.628026 | + | 0.778193i | \(0.283863\pi\) | |||||||
\(458\) | −25.6126 | −1.19680 | ||||||||
\(459\) | −9.05436 | −0.422621 | ||||||||
\(460\) | −2.16212 | −0.100809 | ||||||||
\(461\) | −5.33116 | −0.248297 | −0.124148 | − | 0.992264i | \(-0.539620\pi\) | ||||
−0.124148 | + | 0.992264i | \(0.539620\pi\) | |||||||
\(462\) | −8.20667 | −0.381809 | ||||||||
\(463\) | 23.2851 | 1.08215 | 0.541076 | − | 0.840974i | \(-0.318017\pi\) | ||||
0.541076 | + | 0.840974i | \(0.318017\pi\) | |||||||
\(464\) | −7.43472 | −0.345148 | ||||||||
\(465\) | 1.89031 | 0.0876611 | ||||||||
\(466\) | 8.36069 | 0.387302 | ||||||||
\(467\) | −3.15723 | −0.146099 | −0.0730495 | − | 0.997328i | \(-0.523273\pi\) | ||||
−0.0730495 | + | 0.997328i | \(0.523273\pi\) | |||||||
\(468\) | 2.95668 | 0.136673 | ||||||||
\(469\) | 18.9377 | 0.874463 | ||||||||
\(470\) | −9.28939 | −0.428488 | ||||||||
\(471\) | −2.58159 | −0.118953 | ||||||||
\(472\) | −2.50293 | −0.115207 | ||||||||
\(473\) | 9.94293 | 0.457177 | ||||||||
\(474\) | −5.31417 | −0.244088 | ||||||||
\(475\) | −6.75626 | −0.309998 | ||||||||
\(476\) | −6.54914 | −0.300179 | ||||||||
\(477\) | 10.3935 | 0.475883 | ||||||||
\(478\) | −5.94177 | −0.271770 | ||||||||
\(479\) | 17.2512 | 0.788226 | 0.394113 | − | 0.919062i | \(-0.371052\pi\) | ||||
0.394113 | + | 0.919062i | \(0.371052\pi\) | |||||||
\(480\) | 0.741521 | 0.0338456 | ||||||||
\(481\) | 2.60671 | 0.118856 | ||||||||
\(482\) | −28.2635 | −1.28737 | ||||||||
\(483\) | 4.68663 | 0.213249 | ||||||||
\(484\) | 3.33415 | 0.151552 | ||||||||
\(485\) | −6.45797 | −0.293242 | ||||||||
\(486\) | 15.3525 | 0.696405 | ||||||||
\(487\) | 14.1137 | 0.639555 | 0.319777 | − | 0.947493i | \(-0.396392\pi\) | ||||
0.319777 | + | 0.947493i | \(0.396392\pi\) | |||||||
\(488\) | −2.21161 | −0.100115 | ||||||||
\(489\) | −5.55305 | −0.251117 | ||||||||
\(490\) | 1.54507 | 0.0697991 | ||||||||
\(491\) | 5.58698 | 0.252137 | 0.126068 | − | 0.992022i | \(-0.459764\pi\) | ||||
0.126068 | + | 0.992022i | \(0.459764\pi\) | |||||||
\(492\) | −3.55504 | −0.160274 | ||||||||
\(493\) | −16.6568 | −0.750184 | ||||||||
\(494\) | 8.15302 | 0.366822 | ||||||||
\(495\) | −9.27637 | −0.416942 | ||||||||
\(496\) | 2.54924 | 0.114464 | ||||||||
\(497\) | −9.17151 | −0.411399 | ||||||||
\(498\) | 10.9341 | 0.489967 | ||||||||
\(499\) | 31.5338 | 1.41165 | 0.705824 | − | 0.708387i | \(-0.250577\pi\) | ||||
0.705824 | + | 0.708387i | \(0.250577\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0.561290 | 0.0250766 | ||||||||
\(502\) | 1.54250 | 0.0688453 | ||||||||
\(503\) | −33.9558 | −1.51402 | −0.757008 | − | 0.653406i | \(-0.773339\pi\) | ||||
−0.757008 | + | 0.653406i | \(0.773339\pi\) | |||||||
\(504\) | 7.16226 | 0.319032 | ||||||||
\(505\) | 3.69551 | 0.164448 | ||||||||
\(506\) | −8.18588 | −0.363907 | ||||||||
\(507\) | −8.55996 | −0.380161 | ||||||||
\(508\) | −21.5834 | −0.957610 | ||||||||
\(509\) | −25.9636 | −1.15081 | −0.575407 | − | 0.817867i | \(-0.695156\pi\) | ||||
−0.575407 | + | 0.817867i | \(0.695156\pi\) | |||||||
\(510\) | 1.66131 | 0.0735639 | ||||||||
\(511\) | −22.0902 | −0.977212 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 27.3047 | 1.20553 | ||||||||
\(514\) | 12.2344 | 0.539635 | ||||||||
\(515\) | 6.19576 | 0.273018 | ||||||||
\(516\) | 1.94739 | 0.0857289 | ||||||||
\(517\) | −35.1701 | −1.54678 | ||||||||
\(518\) | 6.31449 | 0.277443 | ||||||||
\(519\) | −13.5827 | −0.596214 | ||||||||
\(520\) | −1.20674 | −0.0529189 | ||||||||
\(521\) | 19.3369 | 0.847165 | 0.423582 | − | 0.905858i | \(-0.360772\pi\) | ||||
0.423582 | + | 0.905858i | \(0.360772\pi\) | |||||||
\(522\) | 18.2162 | 0.797300 | ||||||||
\(523\) | 21.9848 | 0.961328 | 0.480664 | − | 0.876905i | \(-0.340396\pi\) | ||||
0.480664 | + | 0.876905i | \(0.340396\pi\) | |||||||
\(524\) | −1.86617 | −0.0815242 | ||||||||
\(525\) | −2.16761 | −0.0946023 | ||||||||
\(526\) | 6.05174 | 0.263869 | ||||||||
\(527\) | 5.71132 | 0.248789 | ||||||||
\(528\) | 2.80743 | 0.122178 | ||||||||
\(529\) | −18.3252 | −0.796750 | ||||||||
\(530\) | −4.24197 | −0.184259 | ||||||||
\(531\) | 6.13256 | 0.266130 | ||||||||
\(532\) | 19.7499 | 0.856265 | ||||||||
\(533\) | 5.78541 | 0.250594 | ||||||||
\(534\) | 7.67618 | 0.332181 | ||||||||
\(535\) | −4.26814 | −0.184528 | ||||||||
\(536\) | −6.47843 | −0.279826 | ||||||||
\(537\) | 1.66835 | 0.0719947 | ||||||||
\(538\) | 15.8007 | 0.681218 | ||||||||
\(539\) | 5.84970 | 0.251965 | ||||||||
\(540\) | −4.04140 | −0.173914 | ||||||||
\(541\) | −1.17590 | −0.0505558 | −0.0252779 | − | 0.999680i | \(-0.508047\pi\) | ||||
−0.0252779 | + | 0.999680i | \(0.508047\pi\) | |||||||
\(542\) | 5.49046 | 0.235835 | ||||||||
\(543\) | −7.13656 | −0.306259 | ||||||||
\(544\) | 2.24040 | 0.0960565 | ||||||||
\(545\) | −6.78094 | −0.290464 | ||||||||
\(546\) | 2.61573 | 0.111943 | ||||||||
\(547\) | −1.59787 | −0.0683201 | −0.0341601 | − | 0.999416i | \(-0.510876\pi\) | ||||
−0.0341601 | + | 0.999416i | \(0.510876\pi\) | |||||||
\(548\) | 16.5456 | 0.706792 | ||||||||
\(549\) | 5.41876 | 0.231267 | ||||||||
\(550\) | 3.78605 | 0.161438 | ||||||||
\(551\) | 50.2309 | 2.13991 | ||||||||
\(552\) | −1.60326 | −0.0682391 | ||||||||
\(553\) | 20.9493 | 0.890855 | ||||||||
\(554\) | 12.6922 | 0.539241 | ||||||||
\(555\) | −1.60178 | −0.0679919 | ||||||||
\(556\) | 17.7109 | 0.751111 | ||||||||
\(557\) | 6.99965 | 0.296585 | 0.148292 | − | 0.988944i | \(-0.452622\pi\) | ||||
0.148292 | + | 0.988944i | \(0.452622\pi\) | |||||||
\(558\) | −6.24600 | −0.264414 | ||||||||
\(559\) | −3.16914 | −0.134040 | ||||||||
\(560\) | −2.92320 | −0.123528 | ||||||||
\(561\) | 6.28978 | 0.265555 | ||||||||
\(562\) | −11.4113 | −0.481355 | ||||||||
\(563\) | −0.539470 | −0.0227359 | −0.0113680 | − | 0.999935i | \(-0.503619\pi\) | ||||
−0.0113680 | + | 0.999935i | \(0.503619\pi\) | |||||||
\(564\) | −6.88828 | −0.290049 | ||||||||
\(565\) | −12.8387 | −0.540127 | ||||||||
\(566\) | −2.68041 | −0.112666 | ||||||||
\(567\) | −12.7266 | −0.534467 | ||||||||
\(568\) | 3.13750 | 0.131646 | ||||||||
\(569\) | −21.5821 | −0.904770 | −0.452385 | − | 0.891823i | \(-0.649427\pi\) | ||||
−0.452385 | + | 0.891823i | \(0.649427\pi\) | |||||||
\(570\) | −5.00990 | −0.209842 | ||||||||
\(571\) | 28.9663 | 1.21220 | 0.606102 | − | 0.795387i | \(-0.292732\pi\) | ||||
0.606102 | + | 0.795387i | \(0.292732\pi\) | |||||||
\(572\) | −4.56876 | −0.191029 | ||||||||
\(573\) | 0.769255 | 0.0321361 | ||||||||
\(574\) | 14.0146 | 0.584956 | ||||||||
\(575\) | −2.16212 | −0.0901665 | ||||||||
\(576\) | −2.45015 | −0.102089 | ||||||||
\(577\) | 28.1175 | 1.17055 | 0.585273 | − | 0.810837i | \(-0.300987\pi\) | ||||
0.585273 | + | 0.810837i | \(0.300987\pi\) | |||||||
\(578\) | −11.9806 | −0.498327 | ||||||||
\(579\) | −8.93209 | −0.371205 | ||||||||
\(580\) | −7.43472 | −0.308710 | ||||||||
\(581\) | −43.1039 | −1.78825 | ||||||||
\(582\) | −4.78872 | −0.198499 | ||||||||
\(583\) | −16.0603 | −0.665150 | ||||||||
\(584\) | 7.55686 | 0.312705 | ||||||||
\(585\) | 2.95668 | 0.122244 | ||||||||
\(586\) | 20.4478 | 0.844689 | ||||||||
\(587\) | 5.04201 | 0.208106 | 0.104053 | − | 0.994572i | \(-0.466819\pi\) | ||||
0.104053 | + | 0.994572i | \(0.466819\pi\) | |||||||
\(588\) | 1.14570 | 0.0472479 | ||||||||
\(589\) | −17.2233 | −0.709673 | ||||||||
\(590\) | −2.50293 | −0.103044 | ||||||||
\(591\) | 11.1794 | 0.459861 | ||||||||
\(592\) | −2.16013 | −0.0887809 | ||||||||
\(593\) | 15.1369 | 0.621597 | 0.310799 | − | 0.950476i | \(-0.399403\pi\) | ||||
0.310799 | + | 0.950476i | \(0.399403\pi\) | |||||||
\(594\) | −15.3009 | −0.627804 | ||||||||
\(595\) | −6.54914 | −0.268488 | ||||||||
\(596\) | −6.38704 | −0.261623 | ||||||||
\(597\) | 0.293832 | 0.0120258 | ||||||||
\(598\) | 2.60911 | 0.106694 | ||||||||
\(599\) | 20.9884 | 0.857563 | 0.428782 | − | 0.903408i | \(-0.358943\pi\) | ||||
0.428782 | + | 0.903408i | \(0.358943\pi\) | |||||||
\(600\) | 0.741521 | 0.0302725 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −7.67691 | −0.312887 | ||||||||
\(603\) | 15.8731 | 0.646403 | ||||||||
\(604\) | −3.63992 | −0.148106 | ||||||||
\(605\) | 3.33415 | 0.135552 | ||||||||
\(606\) | 2.74030 | 0.111317 | ||||||||
\(607\) | 26.7289 | 1.08489 | 0.542446 | − | 0.840091i | \(-0.317498\pi\) | ||||
0.542446 | + | 0.840091i | \(0.317498\pi\) | |||||||
\(608\) | −6.75626 | −0.274002 | ||||||||
\(609\) | 16.1156 | 0.653036 | ||||||||
\(610\) | −2.21161 | −0.0895453 | ||||||||
\(611\) | 11.2098 | 0.453502 | ||||||||
\(612\) | −5.48932 | −0.221893 | ||||||||
\(613\) | 5.68225 | 0.229504 | 0.114752 | − | 0.993394i | \(-0.463393\pi\) | ||||
0.114752 | + | 0.993394i | \(0.463393\pi\) | |||||||
\(614\) | −21.7246 | −0.876732 | ||||||||
\(615\) | −3.55504 | −0.143353 | ||||||||
\(616\) | −11.0674 | −0.445916 | ||||||||
\(617\) | 37.6119 | 1.51420 | 0.757099 | − | 0.653300i | \(-0.226616\pi\) | ||||
0.757099 | + | 0.653300i | \(0.226616\pi\) | |||||||
\(618\) | 4.59429 | 0.184809 | ||||||||
\(619\) | 20.0050 | 0.804069 | 0.402035 | − | 0.915624i | \(-0.368303\pi\) | ||||
0.402035 | + | 0.915624i | \(0.368303\pi\) | |||||||
\(620\) | 2.54924 | 0.102380 | ||||||||
\(621\) | 8.73798 | 0.350643 | ||||||||
\(622\) | −21.9236 | −0.879055 | ||||||||
\(623\) | −30.2607 | −1.21237 | ||||||||
\(624\) | −0.894820 | −0.0358215 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.4995 | −0.539550 | ||||||||
\(627\) | −18.9677 | −0.757498 | ||||||||
\(628\) | −3.48148 | −0.138926 | ||||||||
\(629\) | −4.83957 | −0.192966 | ||||||||
\(630\) | 7.16226 | 0.285351 | ||||||||
\(631\) | 0.0444024 | 0.00176763 | 0.000883817 | − | 1.00000i | \(-0.499719\pi\) | ||||
0.000883817 | 1.00000i | \(0.499719\pi\) | ||||||||
\(632\) | −7.16658 | −0.285071 | ||||||||
\(633\) | 13.4990 | 0.536537 | ||||||||
\(634\) | 22.9412 | 0.911113 | ||||||||
\(635\) | −21.5834 | −0.856512 | ||||||||
\(636\) | −3.14551 | −0.124728 | ||||||||
\(637\) | −1.86449 | −0.0738738 | ||||||||
\(638\) | −28.1482 | −1.11440 | ||||||||
\(639\) | −7.68733 | −0.304106 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −23.1116 | −0.912852 | −0.456426 | − | 0.889761i | \(-0.650871\pi\) | ||||
−0.456426 | + | 0.889761i | \(0.650871\pi\) | |||||||
\(642\) | −3.16492 | −0.124909 | ||||||||
\(643\) | −6.57273 | −0.259203 | −0.129602 | − | 0.991566i | \(-0.541370\pi\) | ||||
−0.129602 | + | 0.991566i | \(0.541370\pi\) | |||||||
\(644\) | 6.32029 | 0.249054 | ||||||||
\(645\) | 1.94739 | 0.0766782 | ||||||||
\(646\) | −15.1367 | −0.595547 | ||||||||
\(647\) | −16.7970 | −0.660359 | −0.330180 | − | 0.943918i | \(-0.607109\pi\) | ||||
−0.330180 | + | 0.943918i | \(0.607109\pi\) | |||||||
\(648\) | 4.35366 | 0.171028 | ||||||||
\(649\) | −9.47622 | −0.371974 | ||||||||
\(650\) | −1.20674 | −0.0473321 | ||||||||
\(651\) | −5.52575 | −0.216571 | ||||||||
\(652\) | −7.48872 | −0.293281 | ||||||||
\(653\) | −20.2827 | −0.793722 | −0.396861 | − | 0.917879i | \(-0.629901\pi\) | ||||
−0.396861 | + | 0.917879i | \(0.629901\pi\) | |||||||
\(654\) | −5.02821 | −0.196619 | ||||||||
\(655\) | −1.86617 | −0.0729174 | ||||||||
\(656\) | −4.79426 | −0.187184 | ||||||||
\(657\) | −18.5154 | −0.722355 | ||||||||
\(658\) | 27.1547 | 1.05860 | ||||||||
\(659\) | 8.34781 | 0.325185 | 0.162592 | − | 0.986693i | \(-0.448014\pi\) | ||||
0.162592 | + | 0.986693i | \(0.448014\pi\) | |||||||
\(660\) | 2.80743 | 0.109279 | ||||||||
\(661\) | −17.1480 | −0.666981 | −0.333490 | − | 0.942754i | \(-0.608226\pi\) | ||||
−0.333490 | + | 0.942754i | \(0.608226\pi\) | |||||||
\(662\) | −20.8164 | −0.809052 | ||||||||
\(663\) | −2.00476 | −0.0778584 | ||||||||
\(664\) | 14.7455 | 0.572235 | ||||||||
\(665\) | 19.7499 | 0.765866 | ||||||||
\(666\) | 5.29264 | 0.205086 | ||||||||
\(667\) | 16.0747 | 0.622417 | ||||||||
\(668\) | 0.756944 | 0.0292870 | ||||||||
\(669\) | −7.41436 | −0.286656 | ||||||||
\(670\) | −6.47843 | −0.250284 | ||||||||
\(671\) | −8.37325 | −0.323246 | ||||||||
\(672\) | −2.16761 | −0.0836174 | ||||||||
\(673\) | −0.527550 | −0.0203356 | −0.0101678 | − | 0.999948i | \(-0.503237\pi\) | ||||
−0.0101678 | + | 0.999948i | \(0.503237\pi\) | |||||||
\(674\) | 13.2746 | 0.511319 | ||||||||
\(675\) | −4.04140 | −0.155553 | ||||||||
\(676\) | −11.5438 | −0.443992 | ||||||||
\(677\) | −21.8328 | −0.839105 | −0.419552 | − | 0.907731i | \(-0.637813\pi\) | ||||
−0.419552 | + | 0.907731i | \(0.637813\pi\) | |||||||
\(678\) | −9.52015 | −0.365619 | ||||||||
\(679\) | 18.8779 | 0.724468 | ||||||||
\(680\) | 2.24040 | 0.0859156 | ||||||||
\(681\) | −5.95211 | −0.228085 | ||||||||
\(682\) | 9.65153 | 0.369576 | ||||||||
\(683\) | −25.5697 | −0.978398 | −0.489199 | − | 0.872172i | \(-0.662711\pi\) | ||||
−0.489199 | + | 0.872172i | \(0.662711\pi\) | |||||||
\(684\) | 16.5538 | 0.632951 | ||||||||
\(685\) | 16.5456 | 0.632174 | ||||||||
\(686\) | 15.9458 | 0.608814 | ||||||||
\(687\) | −18.9923 | −0.724601 | ||||||||
\(688\) | 2.62620 | 0.100123 | ||||||||
\(689\) | 5.11894 | 0.195016 | ||||||||
\(690\) | −1.60326 | −0.0610349 | ||||||||
\(691\) | 39.4532 | 1.50087 | 0.750436 | − | 0.660943i | \(-0.229844\pi\) | ||||
0.750436 | + | 0.660943i | \(0.229844\pi\) | |||||||
\(692\) | −18.3173 | −0.696321 | ||||||||
\(693\) | 27.1166 | 1.03008 | ||||||||
\(694\) | 2.90152 | 0.110140 | ||||||||
\(695\) | 17.7109 | 0.671814 | ||||||||
\(696\) | −5.51300 | −0.208970 | ||||||||
\(697\) | −10.7411 | −0.406847 | ||||||||
\(698\) | −2.22064 | −0.0840526 | ||||||||
\(699\) | 6.19963 | 0.234491 | ||||||||
\(700\) | −2.92320 | −0.110486 | ||||||||
\(701\) | 15.2977 | 0.577785 | 0.288893 | − | 0.957361i | \(-0.406713\pi\) | ||||
0.288893 | + | 0.957361i | \(0.406713\pi\) | |||||||
\(702\) | 4.87690 | 0.184067 | ||||||||
\(703\) | 14.5944 | 0.550438 | ||||||||
\(704\) | 3.78605 | 0.142692 | ||||||||
\(705\) | −6.88828 | −0.259428 | ||||||||
\(706\) | 18.6751 | 0.702846 | ||||||||
\(707\) | −10.8027 | −0.406277 | ||||||||
\(708\) | −1.85598 | −0.0697519 | ||||||||
\(709\) | −8.37724 | −0.314614 | −0.157307 | − | 0.987550i | \(-0.550281\pi\) | ||||
−0.157307 | + | 0.987550i | \(0.550281\pi\) | |||||||
\(710\) | 3.13750 | 0.117748 | ||||||||
\(711\) | 17.5592 | 0.658520 | ||||||||
\(712\) | 10.3519 | 0.387955 | ||||||||
\(713\) | −5.51175 | −0.206417 | ||||||||
\(714\) | −4.85632 | −0.181743 | ||||||||
\(715\) | −4.56876 | −0.170862 | ||||||||
\(716\) | 2.24990 | 0.0840829 | ||||||||
\(717\) | −4.40595 | −0.164543 | ||||||||
\(718\) | 10.0962 | 0.376786 | ||||||||
\(719\) | 20.9443 | 0.781090 | 0.390545 | − | 0.920584i | \(-0.372287\pi\) | ||||
0.390545 | + | 0.920584i | \(0.372287\pi\) | |||||||
\(720\) | −2.45015 | −0.0913116 | ||||||||
\(721\) | −18.1114 | −0.674505 | ||||||||
\(722\) | 26.6470 | 0.991698 | ||||||||
\(723\) | −20.9580 | −0.779437 | ||||||||
\(724\) | −9.62422 | −0.357681 | ||||||||
\(725\) | −7.43472 | −0.276119 | ||||||||
\(726\) | 2.47234 | 0.0917572 | ||||||||
\(727\) | −23.8660 | −0.885140 | −0.442570 | − | 0.896734i | \(-0.645933\pi\) | ||||
−0.442570 | + | 0.896734i | \(0.645933\pi\) | |||||||
\(728\) | 3.52753 | 0.130739 | ||||||||
\(729\) | −1.67676 | −0.0621021 | ||||||||
\(730\) | 7.55686 | 0.279692 | ||||||||
\(731\) | 5.88376 | 0.217619 | ||||||||
\(732\) | −1.63995 | −0.0606144 | ||||||||
\(733\) | 14.3164 | 0.528787 | 0.264394 | − | 0.964415i | \(-0.414828\pi\) | ||||
0.264394 | + | 0.964415i | \(0.414828\pi\) | |||||||
\(734\) | 13.3188 | 0.491606 | ||||||||
\(735\) | 1.14570 | 0.0422598 | ||||||||
\(736\) | −2.16212 | −0.0796967 | ||||||||
\(737\) | −24.5277 | −0.903488 | ||||||||
\(738\) | 11.7466 | 0.432400 | ||||||||
\(739\) | −41.9894 | −1.54461 | −0.772303 | − | 0.635255i | \(-0.780895\pi\) | ||||
−0.772303 | + | 0.635255i | \(0.780895\pi\) | |||||||
\(740\) | −2.16013 | −0.0794080 | ||||||||
\(741\) | 6.04563 | 0.222092 | ||||||||
\(742\) | 12.4001 | 0.455222 | ||||||||
\(743\) | 2.19212 | 0.0804212 | 0.0402106 | − | 0.999191i | \(-0.487197\pi\) | ||||
0.0402106 | + | 0.999191i | \(0.487197\pi\) | |||||||
\(744\) | 1.89031 | 0.0693022 | ||||||||
\(745\) | −6.38704 | −0.234003 | ||||||||
\(746\) | −7.01034 | −0.256667 | ||||||||
\(747\) | −36.1285 | −1.32187 | ||||||||
\(748\) | 8.48227 | 0.310143 | ||||||||
\(749\) | 12.4766 | 0.455886 | ||||||||
\(750\) | 0.741521 | 0.0270765 | ||||||||
\(751\) | −6.65765 | −0.242941 | −0.121470 | − | 0.992595i | \(-0.538761\pi\) | ||||
−0.121470 | + | 0.992595i | \(0.538761\pi\) | |||||||
\(752\) | −9.28939 | −0.338749 | ||||||||
\(753\) | 1.14380 | 0.0416823 | ||||||||
\(754\) | 8.97175 | 0.326732 | ||||||||
\(755\) | −3.63992 | −0.132470 | ||||||||
\(756\) | 11.8138 | 0.429664 | ||||||||
\(757\) | −8.18191 | −0.297377 | −0.148688 | − | 0.988884i | \(-0.547505\pi\) | ||||
−0.148688 | + | 0.988884i | \(0.547505\pi\) | |||||||
\(758\) | −11.3530 | −0.412361 | ||||||||
\(759\) | −6.07000 | −0.220327 | ||||||||
\(760\) | −6.75626 | −0.245075 | ||||||||
\(761\) | −46.9481 | −1.70187 | −0.850934 | − | 0.525272i | \(-0.823964\pi\) | ||||
−0.850934 | + | 0.525272i | \(0.823964\pi\) | |||||||
\(762\) | −16.0046 | −0.579784 | ||||||||
\(763\) | 19.8220 | 0.717605 | ||||||||
\(764\) | 1.03740 | 0.0375319 | ||||||||
\(765\) | −5.48932 | −0.198467 | ||||||||
\(766\) | −1.90171 | −0.0687116 | ||||||||
\(767\) | 3.02038 | 0.109060 | ||||||||
\(768\) | 0.741521 | 0.0267573 | ||||||||
\(769\) | −41.5242 | −1.49740 | −0.748700 | − | 0.662909i | \(-0.769322\pi\) | ||||
−0.748700 | + | 0.662909i | \(0.769322\pi\) | |||||||
\(770\) | −11.0674 | −0.398840 | ||||||||
\(771\) | 9.07204 | 0.326722 | ||||||||
\(772\) | −12.0456 | −0.433532 | ||||||||
\(773\) | −11.1666 | −0.401635 | −0.200818 | − | 0.979629i | \(-0.564360\pi\) | ||||
−0.200818 | + | 0.979629i | \(0.564360\pi\) | |||||||
\(774\) | −6.43459 | −0.231286 | ||||||||
\(775\) | 2.54924 | 0.0915713 | ||||||||
\(776\) | −6.45797 | −0.231828 | ||||||||
\(777\) | 4.68232 | 0.167977 | ||||||||
\(778\) | 16.4178 | 0.588608 | ||||||||
\(779\) | 32.3912 | 1.16054 | ||||||||
\(780\) | −0.894820 | −0.0320397 | ||||||||
\(781\) | 11.8787 | 0.425054 | ||||||||
\(782\) | −4.84402 | −0.173222 | ||||||||
\(783\) | 30.0467 | 1.07378 | ||||||||
\(784\) | 1.54507 | 0.0551810 | ||||||||
\(785\) | −3.48148 | −0.124259 | ||||||||
\(786\) | −1.38381 | −0.0493588 | ||||||||
\(787\) | 18.9384 | 0.675081 | 0.337540 | − | 0.941311i | \(-0.390405\pi\) | ||||
0.337540 | + | 0.941311i | \(0.390405\pi\) | |||||||
\(788\) | 15.0764 | 0.537073 | ||||||||
\(789\) | 4.48750 | 0.159759 | ||||||||
\(790\) | −7.16658 | −0.254975 | ||||||||
\(791\) | 37.5300 | 1.33441 | ||||||||
\(792\) | −9.27637 | −0.329621 | ||||||||
\(793\) | 2.66883 | 0.0947728 | ||||||||
\(794\) | 0.399823 | 0.0141892 | ||||||||
\(795\) | −3.14551 | −0.111560 | ||||||||
\(796\) | 0.396256 | 0.0140449 | ||||||||
\(797\) | −45.5372 | −1.61301 | −0.806506 | − | 0.591226i | \(-0.798644\pi\) | ||||
−0.806506 | + | 0.591226i | \(0.798644\pi\) | |||||||
\(798\) | 14.6449 | 0.518425 | ||||||||
\(799\) | −20.8120 | −0.736275 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −25.3638 | −0.896185 | ||||||||
\(802\) | 12.1723 | 0.429819 | ||||||||
\(803\) | 28.6106 | 1.00965 | ||||||||
\(804\) | −4.80390 | −0.169420 | ||||||||
\(805\) | 6.32029 | 0.222761 | ||||||||
\(806\) | −3.07626 | −0.108357 | ||||||||
\(807\) | 11.7166 | 0.412443 | ||||||||
\(808\) | 3.69551 | 0.130008 | ||||||||
\(809\) | 13.0849 | 0.460041 | 0.230021 | − | 0.973186i | \(-0.426121\pi\) | ||||
0.230021 | + | 0.973186i | \(0.426121\pi\) | |||||||
\(810\) | 4.35366 | 0.152972 | ||||||||
\(811\) | −52.3893 | −1.83964 | −0.919819 | − | 0.392343i | \(-0.871665\pi\) | ||||
−0.919819 | + | 0.392343i | \(0.871665\pi\) | |||||||
\(812\) | 21.7331 | 0.762684 | ||||||||
\(813\) | 4.07129 | 0.142786 | ||||||||
\(814\) | −8.17836 | −0.286651 | ||||||||
\(815\) | −7.48872 | −0.262319 | ||||||||
\(816\) | 1.66131 | 0.0581574 | ||||||||
\(817\) | −17.7433 | −0.620760 | ||||||||
\(818\) | −33.4856 | −1.17080 | ||||||||
\(819\) | −8.64295 | −0.302009 | ||||||||
\(820\) | −4.79426 | −0.167423 | ||||||||
\(821\) | −53.0479 | −1.85138 | −0.925691 | − | 0.378280i | \(-0.876516\pi\) | ||||
−0.925691 | + | 0.378280i | \(0.876516\pi\) | |||||||
\(822\) | 12.2689 | 0.427927 | ||||||||
\(823\) | 50.1815 | 1.74922 | 0.874608 | − | 0.484830i | \(-0.161119\pi\) | ||||
0.874608 | + | 0.484830i | \(0.161119\pi\) | |||||||
\(824\) | 6.19576 | 0.215840 | ||||||||
\(825\) | 2.80743 | 0.0977423 | ||||||||
\(826\) | 7.31656 | 0.254576 | ||||||||
\(827\) | −37.8153 | −1.31497 | −0.657483 | − | 0.753470i | \(-0.728379\pi\) | ||||
−0.657483 | + | 0.753470i | \(0.728379\pi\) | |||||||
\(828\) | 5.29751 | 0.184101 | ||||||||
\(829\) | 39.7175 | 1.37945 | 0.689723 | − | 0.724074i | \(-0.257732\pi\) | ||||
0.689723 | + | 0.724074i | \(0.257732\pi\) | |||||||
\(830\) | 14.7455 | 0.511823 | ||||||||
\(831\) | 9.41154 | 0.326483 | ||||||||
\(832\) | −1.20674 | −0.0418361 | ||||||||
\(833\) | 3.46158 | 0.119937 | ||||||||
\(834\) | 13.1330 | 0.454760 | ||||||||
\(835\) | 0.756944 | 0.0261951 | ||||||||
\(836\) | −25.5795 | −0.884685 | ||||||||
\(837\) | −10.3025 | −0.356106 | ||||||||
\(838\) | 9.60020 | 0.331634 | ||||||||
\(839\) | −32.3825 | −1.11797 | −0.558985 | − | 0.829178i | \(-0.688809\pi\) | ||||
−0.558985 | + | 0.829178i | \(0.688809\pi\) | |||||||
\(840\) | −2.16761 | −0.0747897 | ||||||||
\(841\) | 26.2751 | 0.906038 | ||||||||
\(842\) | −5.78529 | −0.199374 | ||||||||
\(843\) | −8.46169 | −0.291436 | ||||||||
\(844\) | 18.2045 | 0.626624 | ||||||||
\(845\) | −11.5438 | −0.397118 | ||||||||
\(846\) | 22.7604 | 0.782518 | ||||||||
\(847\) | −9.74637 | −0.334889 | ||||||||
\(848\) | −4.24197 | −0.145670 | ||||||||
\(849\) | −1.98758 | −0.0682135 | ||||||||
\(850\) | 2.24040 | 0.0768452 | ||||||||
\(851\) | 4.67046 | 0.160101 | ||||||||
\(852\) | 2.32652 | 0.0797052 | ||||||||
\(853\) | 4.06971 | 0.139344 | 0.0696720 | − | 0.997570i | \(-0.477805\pi\) | ||||
0.0696720 | + | 0.997570i | \(0.477805\pi\) | |||||||
\(854\) | 6.46496 | 0.221226 | ||||||||
\(855\) | 16.5538 | 0.566129 | ||||||||
\(856\) | −4.26814 | −0.145882 | ||||||||
\(857\) | 44.2655 | 1.51208 | 0.756039 | − | 0.654526i | \(-0.227132\pi\) | ||||
0.756039 | + | 0.654526i | \(0.227132\pi\) | |||||||
\(858\) | −3.38783 | −0.115659 | ||||||||
\(859\) | −36.6492 | −1.25046 | −0.625228 | − | 0.780442i | \(-0.714994\pi\) | ||||
−0.625228 | + | 0.780442i | \(0.714994\pi\) | |||||||
\(860\) | 2.62620 | 0.0895528 | ||||||||
\(861\) | 10.3921 | 0.354161 | ||||||||
\(862\) | 19.4632 | 0.662919 | ||||||||
\(863\) | −36.5565 | −1.24440 | −0.622198 | − | 0.782860i | \(-0.713760\pi\) | ||||
−0.622198 | + | 0.782860i | \(0.713760\pi\) | |||||||
\(864\) | −4.04140 | −0.137491 | ||||||||
\(865\) | −18.3173 | −0.622809 | ||||||||
\(866\) | −2.27704 | −0.0773770 | ||||||||
\(867\) | −8.88386 | −0.301712 | ||||||||
\(868\) | −7.45192 | −0.252935 | ||||||||
\(869\) | −27.1330 | −0.920424 | ||||||||
\(870\) | −5.51300 | −0.186908 | ||||||||
\(871\) | 7.81776 | 0.264895 | ||||||||
\(872\) | −6.78094 | −0.229632 | ||||||||
\(873\) | 15.8230 | 0.535527 | ||||||||
\(874\) | 14.6078 | 0.494117 | ||||||||
\(875\) | −2.92320 | −0.0988220 | ||||||||
\(876\) | 5.60357 | 0.189327 | ||||||||
\(877\) | −36.0907 | −1.21870 | −0.609349 | − | 0.792902i | \(-0.708569\pi\) | ||||
−0.609349 | + | 0.792902i | \(0.708569\pi\) | |||||||
\(878\) | 4.72610 | 0.159498 | ||||||||
\(879\) | 15.1624 | 0.511416 | ||||||||
\(880\) | 3.78605 | 0.127628 | ||||||||
\(881\) | 32.4769 | 1.09417 | 0.547087 | − | 0.837076i | \(-0.315737\pi\) | ||||
0.547087 | + | 0.837076i | \(0.315737\pi\) | |||||||
\(882\) | −3.78565 | −0.127469 | ||||||||
\(883\) | 28.1173 | 0.946223 | 0.473111 | − | 0.881003i | \(-0.343131\pi\) | ||||
0.473111 | + | 0.881003i | \(0.343131\pi\) | |||||||
\(884\) | −2.70358 | −0.0909311 | ||||||||
\(885\) | −1.85598 | −0.0623880 | ||||||||
\(886\) | 26.4606 | 0.888961 | ||||||||
\(887\) | −31.1536 | −1.04604 | −0.523018 | − | 0.852321i | \(-0.675194\pi\) | ||||
−0.523018 | + | 0.852321i | \(0.675194\pi\) | |||||||
\(888\) | −1.60178 | −0.0537523 | ||||||||
\(889\) | 63.0926 | 2.11606 | ||||||||
\(890\) | 10.3519 | 0.346998 | ||||||||
\(891\) | 16.4832 | 0.552206 | ||||||||
\(892\) | −9.99886 | −0.334787 | ||||||||
\(893\) | 62.7615 | 2.10023 | ||||||||
\(894\) | −4.73612 | −0.158400 | ||||||||
\(895\) | 2.24990 | 0.0752060 | ||||||||
\(896\) | −2.92320 | −0.0976571 | ||||||||
\(897\) | 1.93471 | 0.0645980 | ||||||||
\(898\) | 6.77324 | 0.226026 | ||||||||
\(899\) | −18.9529 | −0.632113 | ||||||||
\(900\) | −2.45015 | −0.0816716 | ||||||||
\(901\) | −9.50373 | −0.316615 | ||||||||
\(902\) | −18.1513 | −0.604372 | ||||||||
\(903\) | −5.69259 | −0.189437 | ||||||||
\(904\) | −12.8387 | −0.427008 | ||||||||
\(905\) | −9.62422 | −0.319920 | ||||||||
\(906\) | −2.69908 | −0.0896708 | ||||||||
\(907\) | 1.65719 | 0.0550262 | 0.0275131 | − | 0.999621i | \(-0.491241\pi\) | ||||
0.0275131 | + | 0.999621i | \(0.491241\pi\) | |||||||
\(908\) | −8.02690 | −0.266382 | ||||||||
\(909\) | −9.05454 | −0.300320 | ||||||||
\(910\) | 3.52753 | 0.116936 | ||||||||
\(911\) | −32.9676 | −1.09227 | −0.546133 | − | 0.837698i | \(-0.683901\pi\) | ||||
−0.546133 | + | 0.837698i | \(0.683901\pi\) | |||||||
\(912\) | −5.00990 | −0.165895 | ||||||||
\(913\) | 55.8270 | 1.84760 | ||||||||
\(914\) | 26.8513 | 0.888163 | ||||||||
\(915\) | −1.63995 | −0.0542152 | ||||||||
\(916\) | −25.6126 | −0.846264 | ||||||||
\(917\) | 5.45519 | 0.180146 | ||||||||
\(918\) | −9.05436 | −0.298839 | ||||||||
\(919\) | 31.2474 | 1.03076 | 0.515379 | − | 0.856963i | \(-0.327651\pi\) | ||||
0.515379 | + | 0.856963i | \(0.327651\pi\) | |||||||
\(920\) | −2.16212 | −0.0712829 | ||||||||
\(921\) | −16.1092 | −0.530817 | ||||||||
\(922\) | −5.33116 | −0.175572 | ||||||||
\(923\) | −3.78613 | −0.124622 | ||||||||
\(924\) | −8.20667 | −0.269980 | ||||||||
\(925\) | −2.16013 | −0.0710247 | ||||||||
\(926\) | 23.2851 | 0.765197 | ||||||||
\(927\) | −15.1805 | −0.498594 | ||||||||
\(928\) | −7.43472 | −0.244057 | ||||||||
\(929\) | −25.9809 | −0.852404 | −0.426202 | − | 0.904628i | \(-0.640149\pi\) | ||||
−0.426202 | + | 0.904628i | \(0.640149\pi\) | |||||||
\(930\) | 1.89031 | 0.0619858 | ||||||||
\(931\) | −10.4389 | −0.342121 | ||||||||
\(932\) | 8.36069 | 0.273864 | ||||||||
\(933\) | −16.2568 | −0.532224 | ||||||||
\(934\) | −3.15723 | −0.103308 | ||||||||
\(935\) | 8.48227 | 0.277400 | ||||||||
\(936\) | 2.95668 | 0.0966421 | ||||||||
\(937\) | −54.3313 | −1.77492 | −0.887462 | − | 0.460880i | \(-0.847534\pi\) | ||||
−0.887462 | + | 0.460880i | \(0.847534\pi\) | |||||||
\(938\) | 18.9377 | 0.618339 | ||||||||
\(939\) | −10.0102 | −0.326670 | ||||||||
\(940\) | −9.28939 | −0.302987 | ||||||||
\(941\) | −0.654760 | −0.0213446 | −0.0106723 | − | 0.999943i | \(-0.503397\pi\) | ||||
−0.0106723 | + | 0.999943i | \(0.503397\pi\) | |||||||
\(942\) | −2.58159 | −0.0841128 | ||||||||
\(943\) | 10.3658 | 0.337555 | ||||||||
\(944\) | −2.50293 | −0.0814636 | ||||||||
\(945\) | 11.8138 | 0.384303 | ||||||||
\(946\) | 9.94293 | 0.323273 | ||||||||
\(947\) | 19.0893 | 0.620318 | 0.310159 | − | 0.950685i | \(-0.399618\pi\) | ||||
0.310159 | + | 0.950685i | \(0.399618\pi\) | |||||||
\(948\) | −5.31417 | −0.172596 | ||||||||
\(949\) | −9.11914 | −0.296020 | ||||||||
\(950\) | −6.75626 | −0.219202 | ||||||||
\(951\) | 17.0114 | 0.551633 | ||||||||
\(952\) | −6.54914 | −0.212259 | ||||||||
\(953\) | −53.7847 | −1.74226 | −0.871129 | − | 0.491054i | \(-0.836612\pi\) | ||||
−0.871129 | + | 0.491054i | \(0.836612\pi\) | |||||||
\(954\) | 10.3935 | 0.336500 | ||||||||
\(955\) | 1.03740 | 0.0335695 | ||||||||
\(956\) | −5.94177 | −0.192171 | ||||||||
\(957\) | −20.8725 | −0.674712 | ||||||||
\(958\) | 17.2512 | 0.557360 | ||||||||
\(959\) | −48.3660 | −1.56182 | ||||||||
\(960\) | 0.741521 | 0.0239325 | ||||||||
\(961\) | −24.5014 | −0.790368 | ||||||||
\(962\) | 2.60671 | 0.0840437 | ||||||||
\(963\) | 10.4576 | 0.336991 | ||||||||
\(964\) | −28.2635 | −0.910307 | ||||||||
\(965\) | −12.0456 | −0.387763 | ||||||||
\(966\) | 4.68663 | 0.150790 | ||||||||
\(967\) | −26.8623 | −0.863835 | −0.431917 | − | 0.901913i | \(-0.642163\pi\) | ||||
−0.431917 | + | 0.901913i | \(0.642163\pi\) | |||||||
\(968\) | 3.33415 | 0.107164 | ||||||||
\(969\) | −11.2242 | −0.360574 | ||||||||
\(970\) | −6.45797 | −0.207353 | ||||||||
\(971\) | 54.4207 | 1.74644 | 0.873222 | − | 0.487322i | \(-0.162026\pi\) | ||||
0.873222 | + | 0.487322i | \(0.162026\pi\) | |||||||
\(972\) | 15.3525 | 0.492432 | ||||||||
\(973\) | −51.7725 | −1.65975 | ||||||||
\(974\) | 14.1137 | 0.452233 | ||||||||
\(975\) | −0.894820 | −0.0286572 | ||||||||
\(976\) | −2.21161 | −0.0707918 | ||||||||
\(977\) | 18.4818 | 0.591284 | 0.295642 | − | 0.955299i | \(-0.404466\pi\) | ||||
0.295642 | + | 0.955299i | \(0.404466\pi\) | |||||||
\(978\) | −5.55305 | −0.177567 | ||||||||
\(979\) | 39.1929 | 1.25261 | ||||||||
\(980\) | 1.54507 | 0.0493554 | ||||||||
\(981\) | 16.6143 | 0.530454 | ||||||||
\(982\) | 5.58698 | 0.178288 | ||||||||
\(983\) | 31.3006 | 0.998333 | 0.499166 | − | 0.866506i | \(-0.333640\pi\) | ||||
0.499166 | + | 0.866506i | \(0.333640\pi\) | |||||||
\(984\) | −3.55504 | −0.113331 | ||||||||
\(985\) | 15.0764 | 0.480373 | ||||||||
\(986\) | −16.6568 | −0.530460 | ||||||||
\(987\) | 20.1358 | 0.640929 | ||||||||
\(988\) | 8.15302 | 0.259382 | ||||||||
\(989\) | −5.67816 | −0.180555 | ||||||||
\(990\) | −9.27637 | −0.294822 | ||||||||
\(991\) | 0.691328 | 0.0219608 | 0.0109804 | − | 0.999940i | \(-0.496505\pi\) | ||||
0.0109804 | + | 0.999940i | \(0.496505\pi\) | |||||||
\(992\) | 2.54924 | 0.0809383 | ||||||||
\(993\) | −15.4358 | −0.489840 | ||||||||
\(994\) | −9.17151 | −0.290903 | ||||||||
\(995\) | 0.396256 | 0.0125622 | ||||||||
\(996\) | 10.9341 | 0.346459 | ||||||||
\(997\) | −28.0981 | −0.889877 | −0.444938 | − | 0.895561i | \(-0.646774\pi\) | ||||
−0.444938 | + | 0.895561i | \(0.646774\pi\) | |||||||
\(998\) | 31.5338 | 0.998186 | ||||||||
\(999\) | 8.72995 | 0.276203 |
(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 | 6010.2.a.c.1.12 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.12 | ✓ | 16 | 1.1 | even | 1 | trivial |