Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, 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("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.18857\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18857 | 0.840443 | 0.420222 | − | 0.907422i | \(-0.361952\pi\) | ||||
0.420222 | + | 0.907422i | \(0.361952\pi\) | |||||||
\(3\) | −2.80137 | −1.61737 | −0.808685 | − | 0.588242i | \(-0.799820\pi\) | ||||
−0.808685 | + | 0.588242i | \(0.799820\pi\) | |||||||
\(4\) | −0.587311 | −0.293655 | ||||||||
\(5\) | −2.45282 | −1.09693 | −0.548467 | − | 0.836172i | \(-0.684788\pi\) | ||||
−0.548467 | + | 0.836172i | \(0.684788\pi\) | |||||||
\(6\) | −3.32961 | −1.35931 | ||||||||
\(7\) | −2.24002 | −0.846648 | −0.423324 | − | 0.905978i | \(-0.639137\pi\) | ||||
−0.423324 | + | 0.905978i | \(0.639137\pi\) | |||||||
\(8\) | −3.07519 | −1.08724 | ||||||||
\(9\) | 4.84766 | 1.61589 | ||||||||
\(10\) | −2.91534 | −0.921910 | ||||||||
\(11\) | −0.270482 | −0.0815535 | −0.0407767 | − | 0.999168i | \(-0.512983\pi\) | ||||
−0.0407767 | + | 0.999168i | \(0.512983\pi\) | |||||||
\(12\) | 1.64527 | 0.474950 | ||||||||
\(13\) | 5.10390 | 1.41557 | 0.707784 | − | 0.706429i | \(-0.249695\pi\) | ||||
0.707784 | + | 0.706429i | \(0.249695\pi\) | |||||||
\(14\) | −2.66241 | −0.711559 | ||||||||
\(15\) | 6.87124 | 1.77415 | ||||||||
\(16\) | −2.48044 | −0.620111 | ||||||||
\(17\) | 3.58126 | 0.868583 | 0.434291 | − | 0.900772i | \(-0.356999\pi\) | ||||
0.434291 | + | 0.900772i | \(0.356999\pi\) | |||||||
\(18\) | 5.76177 | 1.35806 | ||||||||
\(19\) | 0.250632 | 0.0574989 | 0.0287494 | − | 0.999587i | \(-0.490848\pi\) | ||||
0.0287494 | + | 0.999587i | \(0.490848\pi\) | |||||||
\(20\) | 1.44057 | 0.322121 | ||||||||
\(21\) | 6.27512 | 1.36934 | ||||||||
\(22\) | −0.321486 | −0.0685411 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 8.61474 | 1.75848 | ||||||||
\(25\) | 1.01632 | 0.203263 | ||||||||
\(26\) | 6.06632 | 1.18970 | ||||||||
\(27\) | −5.17598 | −0.996118 | ||||||||
\(28\) | 1.31559 | 0.248623 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 8.16693 | 1.49107 | ||||||||
\(31\) | −4.65149 | −0.835433 | −0.417717 | − | 0.908577i | \(-0.637169\pi\) | ||||
−0.417717 | + | 0.908577i | \(0.637169\pi\) | |||||||
\(32\) | 3.20221 | 0.566076 | ||||||||
\(33\) | 0.757721 | 0.131902 | ||||||||
\(34\) | 4.25656 | 0.729994 | ||||||||
\(35\) | 5.49436 | 0.928716 | ||||||||
\(36\) | −2.84708 | −0.474514 | ||||||||
\(37\) | 3.58910 | 0.590045 | 0.295022 | − | 0.955490i | \(-0.404673\pi\) | ||||
0.295022 | + | 0.955490i | \(0.404673\pi\) | |||||||
\(38\) | 0.297893 | 0.0483245 | ||||||||
\(39\) | −14.2979 | −2.28950 | ||||||||
\(40\) | 7.54288 | 1.19263 | ||||||||
\(41\) | 3.14829 | 0.491681 | 0.245840 | − | 0.969310i | \(-0.420936\pi\) | ||||
0.245840 | + | 0.969310i | \(0.420936\pi\) | |||||||
\(42\) | 7.45839 | 1.15085 | ||||||||
\(43\) | −4.04337 | −0.616608 | −0.308304 | − | 0.951288i | \(-0.599761\pi\) | ||||
−0.308304 | + | 0.951288i | \(0.599761\pi\) | |||||||
\(44\) | 0.158857 | 0.0239486 | ||||||||
\(45\) | −11.8904 | −1.77252 | ||||||||
\(46\) | −1.18857 | −0.175244 | ||||||||
\(47\) | 0.357493 | 0.0521457 | 0.0260729 | − | 0.999660i | \(-0.491700\pi\) | ||||
0.0260729 | + | 0.999660i | \(0.491700\pi\) | |||||||
\(48\) | 6.94864 | 1.00295 | ||||||||
\(49\) | −1.98231 | −0.283187 | ||||||||
\(50\) | 1.20796 | 0.170831 | ||||||||
\(51\) | −10.0324 | −1.40482 | ||||||||
\(52\) | −2.99758 | −0.415689 | ||||||||
\(53\) | 6.68748 | 0.918596 | 0.459298 | − | 0.888282i | \(-0.348101\pi\) | ||||
0.459298 | + | 0.888282i | \(0.348101\pi\) | |||||||
\(54\) | −6.15199 | −0.837180 | ||||||||
\(55\) | 0.663444 | 0.0894588 | ||||||||
\(56\) | 6.88849 | 0.920513 | ||||||||
\(57\) | −0.702112 | −0.0929970 | ||||||||
\(58\) | 1.18857 | 0.156066 | ||||||||
\(59\) | 8.05588 | 1.04879 | 0.524393 | − | 0.851476i | \(-0.324292\pi\) | ||||
0.524393 | + | 0.851476i | \(0.324292\pi\) | |||||||
\(60\) | −4.03556 | −0.520988 | ||||||||
\(61\) | 0.731406 | 0.0936470 | 0.0468235 | − | 0.998903i | \(-0.485090\pi\) | ||||
0.0468235 | + | 0.998903i | \(0.485090\pi\) | |||||||
\(62\) | −5.52861 | −0.702134 | ||||||||
\(63\) | −10.8589 | −1.36809 | ||||||||
\(64\) | 8.76692 | 1.09587 | ||||||||
\(65\) | −12.5189 | −1.55278 | ||||||||
\(66\) | 0.900601 | 0.110856 | ||||||||
\(67\) | 1.58166 | 0.193230 | 0.0966150 | − | 0.995322i | \(-0.469198\pi\) | ||||
0.0966150 | + | 0.995322i | \(0.469198\pi\) | |||||||
\(68\) | −2.10331 | −0.255064 | ||||||||
\(69\) | 2.80137 | 0.337245 | ||||||||
\(70\) | 6.53041 | 0.780533 | ||||||||
\(71\) | −3.90259 | −0.463152 | −0.231576 | − | 0.972817i | \(-0.574388\pi\) | ||||
−0.231576 | + | 0.972817i | \(0.574388\pi\) | |||||||
\(72\) | −14.9075 | −1.75686 | ||||||||
\(73\) | −8.90294 | −1.04201 | −0.521005 | − | 0.853554i | \(-0.674443\pi\) | ||||
−0.521005 | + | 0.853554i | \(0.674443\pi\) | |||||||
\(74\) | 4.26589 | 0.495899 | ||||||||
\(75\) | −2.84707 | −0.328752 | ||||||||
\(76\) | −0.147199 | −0.0168849 | ||||||||
\(77\) | 0.605886 | 0.0690471 | ||||||||
\(78\) | −16.9940 | −1.92419 | ||||||||
\(79\) | 13.5151 | 1.52056 | 0.760281 | − | 0.649594i | \(-0.225061\pi\) | ||||
0.760281 | + | 0.649594i | \(0.225061\pi\) | |||||||
\(80\) | 6.08408 | 0.680221 | ||||||||
\(81\) | −0.0431602 | −0.00479558 | ||||||||
\(82\) | 3.74195 | 0.413230 | ||||||||
\(83\) | 11.3724 | 1.24828 | 0.624142 | − | 0.781311i | \(-0.285449\pi\) | ||||
0.624142 | + | 0.781311i | \(0.285449\pi\) | |||||||
\(84\) | −3.68545 | −0.402115 | ||||||||
\(85\) | −8.78417 | −0.952777 | ||||||||
\(86\) | −4.80581 | −0.518224 | ||||||||
\(87\) | −2.80137 | −0.300338 | ||||||||
\(88\) | 0.831784 | 0.0886685 | ||||||||
\(89\) | 11.2229 | 1.18962 | 0.594812 | − | 0.803865i | \(-0.297226\pi\) | ||||
0.594812 | + | 0.803865i | \(0.297226\pi\) | |||||||
\(90\) | −14.1326 | −1.48970 | ||||||||
\(91\) | −11.4328 | −1.19849 | ||||||||
\(92\) | 0.587311 | 0.0612314 | ||||||||
\(93\) | 13.0305 | 1.35120 | ||||||||
\(94\) | 0.424904 | 0.0438255 | ||||||||
\(95\) | −0.614754 | −0.0630725 | ||||||||
\(96\) | −8.97056 | −0.915554 | ||||||||
\(97\) | 11.5510 | 1.17283 | 0.586416 | − | 0.810010i | \(-0.300539\pi\) | ||||
0.586416 | + | 0.810010i | \(0.300539\pi\) | |||||||
\(98\) | −2.35611 | −0.238003 | ||||||||
\(99\) | −1.31121 | −0.131781 | ||||||||
\(100\) | −0.596893 | −0.0596893 | ||||||||
\(101\) | 8.44579 | 0.840388 | 0.420194 | − | 0.907434i | \(-0.361962\pi\) | ||||
0.420194 | + | 0.907434i | \(0.361962\pi\) | |||||||
\(102\) | −11.9242 | −1.18067 | ||||||||
\(103\) | 15.3708 | 1.51453 | 0.757265 | − | 0.653107i | \(-0.226535\pi\) | ||||
0.757265 | + | 0.653107i | \(0.226535\pi\) | |||||||
\(104\) | −15.6955 | −1.53907 | ||||||||
\(105\) | −15.3917 | −1.50208 | ||||||||
\(106\) | 7.94851 | 0.772028 | ||||||||
\(107\) | −6.78017 | −0.655464 | −0.327732 | − | 0.944771i | \(-0.606284\pi\) | ||||
−0.327732 | + | 0.944771i | \(0.606284\pi\) | |||||||
\(108\) | 3.03991 | 0.292515 | ||||||||
\(109\) | −15.4197 | −1.47694 | −0.738470 | − | 0.674287i | \(-0.764451\pi\) | ||||
−0.738470 | + | 0.674287i | \(0.764451\pi\) | |||||||
\(110\) | 0.788547 | 0.0751850 | ||||||||
\(111\) | −10.0544 | −0.954321 | ||||||||
\(112\) | 5.55624 | 0.525016 | ||||||||
\(113\) | 7.79673 | 0.733454 | 0.366727 | − | 0.930329i | \(-0.380478\pi\) | ||||
0.366727 | + | 0.930329i | \(0.380478\pi\) | |||||||
\(114\) | −0.834507 | −0.0781587 | ||||||||
\(115\) | 2.45282 | 0.228726 | ||||||||
\(116\) | −0.587311 | −0.0545304 | ||||||||
\(117\) | 24.7420 | 2.28740 | ||||||||
\(118\) | 9.57494 | 0.881445 | ||||||||
\(119\) | −8.02209 | −0.735384 | ||||||||
\(120\) | −21.1304 | −1.92893 | ||||||||
\(121\) | −10.9268 | −0.993349 | ||||||||
\(122\) | 0.869325 | 0.0787050 | ||||||||
\(123\) | −8.81953 | −0.795230 | ||||||||
\(124\) | 2.73187 | 0.245329 | ||||||||
\(125\) | 9.77125 | 0.873967 | ||||||||
\(126\) | −12.9065 | −1.14980 | ||||||||
\(127\) | 5.60983 | 0.497792 | 0.248896 | − | 0.968530i | \(-0.419932\pi\) | ||||
0.248896 | + | 0.968530i | \(0.419932\pi\) | |||||||
\(128\) | 4.01565 | 0.354937 | ||||||||
\(129\) | 11.3270 | 0.997284 | ||||||||
\(130\) | −14.8796 | −1.30503 | ||||||||
\(131\) | −12.3992 | −1.08332 | −0.541661 | − | 0.840597i | \(-0.682204\pi\) | ||||
−0.541661 | + | 0.840597i | \(0.682204\pi\) | |||||||
\(132\) | −0.445018 | −0.0387338 | ||||||||
\(133\) | −0.561420 | −0.0486813 | ||||||||
\(134\) | 1.87990 | 0.162399 | ||||||||
\(135\) | 12.6957 | 1.09268 | ||||||||
\(136\) | −11.0130 | −0.944361 | ||||||||
\(137\) | −6.81840 | −0.582535 | −0.291267 | − | 0.956642i | \(-0.594077\pi\) | ||||
−0.291267 | + | 0.956642i | \(0.594077\pi\) | |||||||
\(138\) | 3.32961 | 0.283435 | ||||||||
\(139\) | 11.5227 | 0.977340 | 0.488670 | − | 0.872469i | \(-0.337482\pi\) | ||||
0.488670 | + | 0.872469i | \(0.337482\pi\) | |||||||
\(140\) | −3.22690 | −0.272723 | ||||||||
\(141\) | −1.00147 | −0.0843390 | ||||||||
\(142\) | −4.63849 | −0.389253 | ||||||||
\(143\) | −1.38052 | −0.115444 | ||||||||
\(144\) | −12.0244 | −1.00203 | ||||||||
\(145\) | −2.45282 | −0.203695 | ||||||||
\(146\) | −10.5817 | −0.875750 | ||||||||
\(147\) | 5.55319 | 0.458019 | ||||||||
\(148\) | −2.10792 | −0.173270 | ||||||||
\(149\) | 5.48395 | 0.449262 | 0.224631 | − | 0.974444i | \(-0.427882\pi\) | ||||
0.224631 | + | 0.974444i | \(0.427882\pi\) | |||||||
\(150\) | −3.38393 | −0.276297 | ||||||||
\(151\) | −7.48853 | −0.609408 | −0.304704 | − | 0.952447i | \(-0.598557\pi\) | ||||
−0.304704 | + | 0.952447i | \(0.598557\pi\) | |||||||
\(152\) | −0.770741 | −0.0625153 | ||||||||
\(153\) | 17.3607 | 1.40353 | ||||||||
\(154\) | 0.720135 | 0.0580301 | ||||||||
\(155\) | 11.4093 | 0.916414 | ||||||||
\(156\) | 8.39732 | 0.672323 | ||||||||
\(157\) | −4.50112 | −0.359229 | −0.179614 | − | 0.983737i | \(-0.557485\pi\) | ||||
−0.179614 | + | 0.983737i | \(0.557485\pi\) | |||||||
\(158\) | 16.0635 | 1.27795 | ||||||||
\(159\) | −18.7341 | −1.48571 | ||||||||
\(160\) | −7.85443 | −0.620947 | ||||||||
\(161\) | 2.24002 | 0.176538 | ||||||||
\(162\) | −0.0512988 | −0.00403041 | ||||||||
\(163\) | −8.47294 | −0.663652 | −0.331826 | − | 0.943341i | \(-0.607665\pi\) | ||||
−0.331826 | + | 0.943341i | \(0.607665\pi\) | |||||||
\(164\) | −1.84903 | −0.144385 | ||||||||
\(165\) | −1.85855 | −0.144688 | ||||||||
\(166\) | 13.5169 | 1.04911 | ||||||||
\(167\) | −18.8068 | −1.45531 | −0.727655 | − | 0.685943i | \(-0.759390\pi\) | ||||
−0.727655 | + | 0.685943i | \(0.759390\pi\) | |||||||
\(168\) | −19.2972 | −1.48881 | ||||||||
\(169\) | 13.0498 | 1.00383 | ||||||||
\(170\) | −10.4406 | −0.800755 | ||||||||
\(171\) | 1.21498 | 0.0929117 | ||||||||
\(172\) | 2.37472 | 0.181070 | ||||||||
\(173\) | 22.0804 | 1.67874 | 0.839370 | − | 0.543560i | \(-0.182924\pi\) | ||||
0.839370 | + | 0.543560i | \(0.182924\pi\) | |||||||
\(174\) | −3.32961 | −0.252417 | ||||||||
\(175\) | −2.27657 | −0.172092 | ||||||||
\(176\) | 0.670916 | 0.0505722 | ||||||||
\(177\) | −22.5675 | −1.69628 | ||||||||
\(178\) | 13.3391 | 0.999811 | ||||||||
\(179\) | 9.54901 | 0.713726 | 0.356863 | − | 0.934157i | \(-0.383846\pi\) | ||||
0.356863 | + | 0.934157i | \(0.383846\pi\) | |||||||
\(180\) | 6.98338 | 0.520510 | ||||||||
\(181\) | −0.785526 | −0.0583877 | −0.0291938 | − | 0.999574i | \(-0.509294\pi\) | ||||
−0.0291938 | + | 0.999574i | \(0.509294\pi\) | |||||||
\(182\) | −13.5887 | −1.00726 | ||||||||
\(183\) | −2.04894 | −0.151462 | ||||||||
\(184\) | 3.07519 | 0.226706 | ||||||||
\(185\) | −8.80341 | −0.647240 | ||||||||
\(186\) | 15.4877 | 1.13561 | ||||||||
\(187\) | −0.968667 | −0.0708359 | ||||||||
\(188\) | −0.209960 | −0.0153129 | ||||||||
\(189\) | 11.5943 | 0.843361 | ||||||||
\(190\) | −0.730676 | −0.0530088 | ||||||||
\(191\) | −18.4700 | −1.33644 | −0.668221 | − | 0.743963i | \(-0.732944\pi\) | ||||
−0.668221 | + | 0.743963i | \(0.732944\pi\) | |||||||
\(192\) | −24.5594 | −1.77242 | ||||||||
\(193\) | 9.01839 | 0.649158 | 0.324579 | − | 0.945859i | \(-0.394777\pi\) | ||||
0.324579 | + | 0.945859i | \(0.394777\pi\) | |||||||
\(194\) | 13.7292 | 0.985698 | ||||||||
\(195\) | 35.0702 | 2.51143 | ||||||||
\(196\) | 1.16423 | 0.0831595 | ||||||||
\(197\) | 18.5072 | 1.31859 | 0.659293 | − | 0.751886i | \(-0.270856\pi\) | ||||
0.659293 | + | 0.751886i | \(0.270856\pi\) | |||||||
\(198\) | −1.55846 | −0.110755 | ||||||||
\(199\) | −12.9100 | −0.915168 | −0.457584 | − | 0.889166i | \(-0.651285\pi\) | ||||
−0.457584 | + | 0.889166i | \(0.651285\pi\) | |||||||
\(200\) | −3.12536 | −0.220996 | ||||||||
\(201\) | −4.43080 | −0.312525 | ||||||||
\(202\) | 10.0384 | 0.706298 | ||||||||
\(203\) | −2.24002 | −0.157219 | ||||||||
\(204\) | 5.89215 | 0.412533 | ||||||||
\(205\) | −7.72219 | −0.539341 | ||||||||
\(206\) | 18.2692 | 1.27288 | ||||||||
\(207\) | −4.84766 | −0.336936 | ||||||||
\(208\) | −12.6599 | −0.877809 | ||||||||
\(209\) | −0.0677915 | −0.00468924 | ||||||||
\(210\) | −18.2941 | −1.26241 | ||||||||
\(211\) | 7.21884 | 0.496966 | 0.248483 | − | 0.968636i | \(-0.420068\pi\) | ||||
0.248483 | + | 0.968636i | \(0.420068\pi\) | |||||||
\(212\) | −3.92763 | −0.269751 | ||||||||
\(213\) | 10.9326 | 0.749089 | ||||||||
\(214\) | −8.05868 | −0.550880 | ||||||||
\(215\) | 9.91765 | 0.676378 | ||||||||
\(216\) | 15.9171 | 1.08302 | ||||||||
\(217\) | 10.4194 | 0.707318 | ||||||||
\(218\) | −18.3273 | −1.24128 | ||||||||
\(219\) | 24.9404 | 1.68532 | ||||||||
\(220\) | −0.389648 | −0.0262701 | ||||||||
\(221\) | 18.2784 | 1.22954 | ||||||||
\(222\) | −11.9503 | −0.802053 | ||||||||
\(223\) | 22.1908 | 1.48601 | 0.743004 | − | 0.669287i | \(-0.233400\pi\) | ||||
0.743004 | + | 0.669287i | \(0.233400\pi\) | |||||||
\(224\) | −7.17301 | −0.479267 | ||||||||
\(225\) | 4.92675 | 0.328450 | ||||||||
\(226\) | 9.26692 | 0.616427 | ||||||||
\(227\) | 12.9479 | 0.859384 | 0.429692 | − | 0.902976i | \(-0.358622\pi\) | ||||
0.429692 | + | 0.902976i | \(0.358622\pi\) | |||||||
\(228\) | 0.412358 | 0.0273091 | ||||||||
\(229\) | 13.3468 | 0.881984 | 0.440992 | − | 0.897511i | \(-0.354627\pi\) | ||||
0.440992 | + | 0.897511i | \(0.354627\pi\) | |||||||
\(230\) | 2.91534 | 0.192232 | ||||||||
\(231\) | −1.69731 | −0.111675 | ||||||||
\(232\) | −3.07519 | −0.201896 | ||||||||
\(233\) | 14.9611 | 0.980136 | 0.490068 | − | 0.871684i | \(-0.336972\pi\) | ||||
0.490068 | + | 0.871684i | \(0.336972\pi\) | |||||||
\(234\) | 29.4075 | 1.92243 | ||||||||
\(235\) | −0.876865 | −0.0572004 | ||||||||
\(236\) | −4.73131 | −0.307982 | ||||||||
\(237\) | −37.8606 | −2.45931 | ||||||||
\(238\) | −9.53478 | −0.618048 | ||||||||
\(239\) | −30.3026 | −1.96011 | −0.980057 | − | 0.198716i | \(-0.936323\pi\) | ||||
−0.980057 | + | 0.198716i | \(0.936323\pi\) | |||||||
\(240\) | −17.0437 | −1.10017 | ||||||||
\(241\) | −14.4573 | −0.931276 | −0.465638 | − | 0.884975i | \(-0.654175\pi\) | ||||
−0.465638 | + | 0.884975i | \(0.654175\pi\) | |||||||
\(242\) | −12.9873 | −0.834853 | ||||||||
\(243\) | 15.6488 | 1.00387 | ||||||||
\(244\) | −0.429563 | −0.0275000 | ||||||||
\(245\) | 4.86225 | 0.310638 | ||||||||
\(246\) | −10.4826 | −0.668346 | ||||||||
\(247\) | 1.27920 | 0.0813936 | ||||||||
\(248\) | 14.3042 | 0.908319 | ||||||||
\(249\) | −31.8583 | −2.01894 | ||||||||
\(250\) | 11.6138 | 0.734520 | ||||||||
\(251\) | 25.7720 | 1.62671 | 0.813356 | − | 0.581766i | \(-0.197638\pi\) | ||||
0.813356 | + | 0.581766i | \(0.197638\pi\) | |||||||
\(252\) | 6.37753 | 0.401746 | ||||||||
\(253\) | 0.270482 | 0.0170051 | ||||||||
\(254\) | 6.66766 | 0.418366 | ||||||||
\(255\) | 24.6077 | 1.54099 | ||||||||
\(256\) | −12.7610 | −0.797561 | ||||||||
\(257\) | 24.8104 | 1.54763 | 0.773815 | − | 0.633411i | \(-0.218346\pi\) | ||||
0.773815 | + | 0.633411i | \(0.218346\pi\) | |||||||
\(258\) | 13.4629 | 0.838161 | ||||||||
\(259\) | −8.03966 | −0.499560 | ||||||||
\(260\) | 7.35251 | 0.455983 | ||||||||
\(261\) | 4.84766 | 0.300063 | ||||||||
\(262\) | −14.7373 | −0.910471 | ||||||||
\(263\) | 13.5794 | 0.837341 | 0.418671 | − | 0.908138i | \(-0.362496\pi\) | ||||
0.418671 | + | 0.908138i | \(0.362496\pi\) | |||||||
\(264\) | −2.33013 | −0.143410 | ||||||||
\(265\) | −16.4032 | −1.00764 | ||||||||
\(266\) | −0.667285 | −0.0409139 | ||||||||
\(267\) | −31.4394 | −1.92406 | ||||||||
\(268\) | −0.928924 | −0.0567431 | ||||||||
\(269\) | 24.0089 | 1.46385 | 0.731924 | − | 0.681386i | \(-0.238622\pi\) | ||||
0.731924 | + | 0.681386i | \(0.238622\pi\) | |||||||
\(270\) | 15.0897 | 0.918331 | ||||||||
\(271\) | 6.94160 | 0.421672 | 0.210836 | − | 0.977521i | \(-0.432381\pi\) | ||||
0.210836 | + | 0.977521i | \(0.432381\pi\) | |||||||
\(272\) | −8.88311 | −0.538618 | ||||||||
\(273\) | 32.0276 | 1.93840 | ||||||||
\(274\) | −8.10411 | −0.489587 | ||||||||
\(275\) | −0.274895 | −0.0165768 | ||||||||
\(276\) | −1.64527 | −0.0990339 | ||||||||
\(277\) | 16.0603 | 0.964969 | 0.482485 | − | 0.875904i | \(-0.339734\pi\) | ||||
0.482485 | + | 0.875904i | \(0.339734\pi\) | |||||||
\(278\) | 13.6955 | 0.821399 | ||||||||
\(279\) | −22.5489 | −1.34997 | ||||||||
\(280\) | −16.8962 | −1.00974 | ||||||||
\(281\) | −19.5284 | −1.16497 | −0.582484 | − | 0.812842i | \(-0.697919\pi\) | ||||
−0.582484 | + | 0.812842i | \(0.697919\pi\) | |||||||
\(282\) | −1.19031 | −0.0708821 | ||||||||
\(283\) | −20.8211 | −1.23769 | −0.618843 | − | 0.785514i | \(-0.712398\pi\) | ||||
−0.618843 | + | 0.785514i | \(0.712398\pi\) | |||||||
\(284\) | 2.29203 | 0.136007 | ||||||||
\(285\) | 1.72215 | 0.102012 | ||||||||
\(286\) | −1.64083 | −0.0970245 | ||||||||
\(287\) | −7.05224 | −0.416280 | ||||||||
\(288\) | 15.5232 | 0.914715 | ||||||||
\(289\) | −4.17459 | −0.245564 | ||||||||
\(290\) | −2.91534 | −0.171194 | ||||||||
\(291\) | −32.3587 | −1.89690 | ||||||||
\(292\) | 5.22879 | 0.305992 | ||||||||
\(293\) | 15.0317 | 0.878160 | 0.439080 | − | 0.898448i | \(-0.355304\pi\) | ||||
0.439080 | + | 0.898448i | \(0.355304\pi\) | |||||||
\(294\) | 6.60033 | 0.384939 | ||||||||
\(295\) | −19.7596 | −1.15045 | ||||||||
\(296\) | −11.0372 | −0.641523 | ||||||||
\(297\) | 1.40001 | 0.0812369 | ||||||||
\(298\) | 6.51803 | 0.377579 | ||||||||
\(299\) | −5.10390 | −0.295166 | ||||||||
\(300\) | 1.67212 | 0.0965397 | ||||||||
\(301\) | 9.05723 | 0.522050 | ||||||||
\(302\) | −8.90061 | −0.512172 | ||||||||
\(303\) | −23.6598 | −1.35922 | ||||||||
\(304\) | −0.621678 | −0.0356557 | ||||||||
\(305\) | −1.79401 | −0.102725 | ||||||||
\(306\) | 20.6344 | 1.17959 | ||||||||
\(307\) | 23.5758 | 1.34554 | 0.672771 | − | 0.739851i | \(-0.265104\pi\) | ||||
0.672771 | + | 0.739851i | \(0.265104\pi\) | |||||||
\(308\) | −0.355843 | −0.0202761 | ||||||||
\(309\) | −43.0593 | −2.44956 | ||||||||
\(310\) | 13.5607 | 0.770194 | ||||||||
\(311\) | −26.6440 | −1.51084 | −0.755420 | − | 0.655241i | \(-0.772567\pi\) | ||||
−0.755420 | + | 0.655241i | \(0.772567\pi\) | |||||||
\(312\) | 43.9688 | 2.48924 | ||||||||
\(313\) | −23.0068 | −1.30042 | −0.650211 | − | 0.759753i | \(-0.725320\pi\) | ||||
−0.650211 | + | 0.759753i | \(0.725320\pi\) | |||||||
\(314\) | −5.34988 | −0.301911 | ||||||||
\(315\) | 26.6348 | 1.50070 | ||||||||
\(316\) | −7.93754 | −0.446521 | ||||||||
\(317\) | −28.2169 | −1.58482 | −0.792410 | − | 0.609989i | \(-0.791174\pi\) | ||||
−0.792410 | + | 0.609989i | \(0.791174\pi\) | |||||||
\(318\) | −22.2667 | −1.24866 | ||||||||
\(319\) | −0.270482 | −0.0151441 | ||||||||
\(320\) | −21.5037 | −1.20209 | ||||||||
\(321\) | 18.9938 | 1.06013 | ||||||||
\(322\) | 2.66241 | 0.148370 | ||||||||
\(323\) | 0.897577 | 0.0499425 | ||||||||
\(324\) | 0.0253485 | 0.00140825 | ||||||||
\(325\) | 5.18717 | 0.287733 | ||||||||
\(326\) | −10.0706 | −0.557762 | ||||||||
\(327\) | 43.1963 | 2.38876 | ||||||||
\(328\) | −9.68160 | −0.534577 | ||||||||
\(329\) | −0.800791 | −0.0441491 | ||||||||
\(330\) | −2.20901 | −0.121602 | ||||||||
\(331\) | −22.7095 | −1.24823 | −0.624114 | − | 0.781333i | \(-0.714540\pi\) | ||||
−0.624114 | + | 0.781333i | \(0.714540\pi\) | |||||||
\(332\) | −6.67914 | −0.366565 | ||||||||
\(333\) | 17.3988 | 0.953446 | ||||||||
\(334\) | −22.3531 | −1.22311 | ||||||||
\(335\) | −3.87951 | −0.211960 | ||||||||
\(336\) | −15.5651 | −0.849145 | ||||||||
\(337\) | −14.1878 | −0.772856 | −0.386428 | − | 0.922320i | \(-0.626291\pi\) | ||||
−0.386428 | + | 0.922320i | \(0.626291\pi\) | |||||||
\(338\) | 15.5106 | 0.843663 | ||||||||
\(339\) | −21.8415 | −1.18627 | ||||||||
\(340\) | 5.15904 | 0.279788 | ||||||||
\(341\) | 1.25815 | 0.0681325 | ||||||||
\(342\) | 1.44408 | 0.0780870 | ||||||||
\(343\) | 20.1206 | 1.08641 | ||||||||
\(344\) | 12.4341 | 0.670404 | ||||||||
\(345\) | −6.87124 | −0.369935 | ||||||||
\(346\) | 26.2440 | 1.41089 | ||||||||
\(347\) | −28.5481 | −1.53254 | −0.766270 | − | 0.642519i | \(-0.777889\pi\) | ||||
−0.766270 | + | 0.642519i | \(0.777889\pi\) | |||||||
\(348\) | 1.64527 | 0.0881959 | ||||||||
\(349\) | −17.1768 | −0.919453 | −0.459726 | − | 0.888061i | \(-0.652052\pi\) | ||||
−0.459726 | + | 0.888061i | \(0.652052\pi\) | |||||||
\(350\) | −2.70585 | −0.144634 | ||||||||
\(351\) | −26.4177 | −1.41007 | ||||||||
\(352\) | −0.866141 | −0.0461655 | ||||||||
\(353\) | −7.41216 | −0.394509 | −0.197255 | − | 0.980352i | \(-0.563203\pi\) | ||||
−0.197255 | + | 0.980352i | \(0.563203\pi\) | |||||||
\(354\) | −26.8229 | −1.42562 | ||||||||
\(355\) | 9.57234 | 0.508047 | ||||||||
\(356\) | −6.59133 | −0.349340 | ||||||||
\(357\) | 22.4728 | 1.18939 | ||||||||
\(358\) | 11.3496 | 0.599846 | ||||||||
\(359\) | 31.1387 | 1.64344 | 0.821720 | − | 0.569892i | \(-0.193015\pi\) | ||||
0.821720 | + | 0.569892i | \(0.193015\pi\) | |||||||
\(360\) | 36.5653 | 1.92716 | ||||||||
\(361\) | −18.9372 | −0.996694 | ||||||||
\(362\) | −0.933649 | −0.0490715 | ||||||||
\(363\) | 30.6101 | 1.60661 | ||||||||
\(364\) | 6.71463 | 0.351942 | ||||||||
\(365\) | 21.8373 | 1.14302 | ||||||||
\(366\) | −2.43530 | −0.127295 | ||||||||
\(367\) | 7.17549 | 0.374558 | 0.187279 | − | 0.982307i | \(-0.440033\pi\) | ||||
0.187279 | + | 0.982307i | \(0.440033\pi\) | |||||||
\(368\) | 2.48044 | 0.129302 | ||||||||
\(369\) | 15.2619 | 0.794501 | ||||||||
\(370\) | −10.4634 | −0.543968 | ||||||||
\(371\) | −14.9801 | −0.777728 | ||||||||
\(372\) | −7.65298 | −0.396789 | ||||||||
\(373\) | 33.9245 | 1.75654 | 0.878272 | − | 0.478162i | \(-0.158697\pi\) | ||||
0.878272 | + | 0.478162i | \(0.158697\pi\) | |||||||
\(374\) | −1.15132 | −0.0595336 | ||||||||
\(375\) | −27.3729 | −1.41353 | ||||||||
\(376\) | −1.09936 | −0.0566951 | ||||||||
\(377\) | 5.10390 | 0.262864 | ||||||||
\(378\) | 13.7806 | 0.708797 | ||||||||
\(379\) | 28.2639 | 1.45182 | 0.725909 | − | 0.687791i | \(-0.241419\pi\) | ||||
0.725909 | + | 0.687791i | \(0.241419\pi\) | |||||||
\(380\) | 0.361052 | 0.0185216 | ||||||||
\(381\) | −15.7152 | −0.805114 | ||||||||
\(382\) | −21.9528 | −1.12320 | ||||||||
\(383\) | 37.4192 | 1.91203 | 0.956015 | − | 0.293318i | \(-0.0947596\pi\) | ||||
0.956015 | + | 0.293318i | \(0.0947596\pi\) | |||||||
\(384\) | −11.2493 | −0.574064 | ||||||||
\(385\) | −1.48613 | −0.0757401 | ||||||||
\(386\) | 10.7189 | 0.545580 | ||||||||
\(387\) | −19.6009 | −0.996370 | ||||||||
\(388\) | −6.78406 | −0.344408 | ||||||||
\(389\) | −10.5424 | −0.534523 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(390\) | 41.6832 | 2.11071 | ||||||||
\(391\) | −3.58126 | −0.181112 | ||||||||
\(392\) | 6.09599 | 0.307894 | ||||||||
\(393\) | 34.7347 | 1.75213 | ||||||||
\(394\) | 21.9971 | 1.10820 | ||||||||
\(395\) | −33.1500 | −1.66796 | ||||||||
\(396\) | 0.770086 | 0.0386983 | ||||||||
\(397\) | 28.4890 | 1.42982 | 0.714911 | − | 0.699215i | \(-0.246467\pi\) | ||||
0.714911 | + | 0.699215i | \(0.246467\pi\) | |||||||
\(398\) | −15.3444 | −0.769147 | ||||||||
\(399\) | 1.57274 | 0.0787357 | ||||||||
\(400\) | −2.52091 | −0.126046 | ||||||||
\(401\) | 8.12691 | 0.405838 | 0.202919 | − | 0.979195i | \(-0.434957\pi\) | ||||
0.202919 | + | 0.979195i | \(0.434957\pi\) | |||||||
\(402\) | −5.26630 | −0.262659 | ||||||||
\(403\) | −23.7408 | −1.18261 | ||||||||
\(404\) | −4.96031 | −0.246784 | ||||||||
\(405\) | 0.105864 | 0.00526043 | ||||||||
\(406\) | −2.66241 | −0.132133 | ||||||||
\(407\) | −0.970789 | −0.0481202 | ||||||||
\(408\) | 30.8516 | 1.52738 | ||||||||
\(409\) | −32.4682 | −1.60545 | −0.802725 | − | 0.596349i | \(-0.796618\pi\) | ||||
−0.802725 | + | 0.596349i | \(0.796618\pi\) | |||||||
\(410\) | −9.17833 | −0.453286 | ||||||||
\(411\) | 19.1008 | 0.942175 | ||||||||
\(412\) | −9.02744 | −0.444750 | ||||||||
\(413\) | −18.0453 | −0.887952 | ||||||||
\(414\) | −5.76177 | −0.283175 | ||||||||
\(415\) | −27.8944 | −1.36928 | ||||||||
\(416\) | 16.3438 | 0.801319 | ||||||||
\(417\) | −32.2792 | −1.58072 | ||||||||
\(418\) | −0.0805747 | −0.00394104 | ||||||||
\(419\) | −1.56846 | −0.0766242 | −0.0383121 | − | 0.999266i | \(-0.512198\pi\) | ||||
−0.0383121 | + | 0.999266i | \(0.512198\pi\) | |||||||
\(420\) | 9.03973 | 0.441094 | ||||||||
\(421\) | 30.1884 | 1.47129 | 0.735645 | − | 0.677367i | \(-0.236879\pi\) | ||||
0.735645 | + | 0.677367i | \(0.236879\pi\) | |||||||
\(422\) | 8.58007 | 0.417671 | ||||||||
\(423\) | 1.73301 | 0.0842616 | ||||||||
\(424\) | −20.5653 | −0.998738 | ||||||||
\(425\) | 3.63969 | 0.176551 | ||||||||
\(426\) | 12.9941 | 0.629566 | ||||||||
\(427\) | −1.63836 | −0.0792860 | ||||||||
\(428\) | 3.98207 | 0.192481 | ||||||||
\(429\) | 3.86733 | 0.186717 | ||||||||
\(430\) | 11.7878 | 0.568458 | ||||||||
\(431\) | 23.0917 | 1.11229 | 0.556144 | − | 0.831086i | \(-0.312280\pi\) | ||||
0.556144 | + | 0.831086i | \(0.312280\pi\) | |||||||
\(432\) | 12.8387 | 0.617704 | ||||||||
\(433\) | −29.0918 | −1.39806 | −0.699030 | − | 0.715092i | \(-0.746385\pi\) | ||||
−0.699030 | + | 0.715092i | \(0.746385\pi\) | |||||||
\(434\) | 12.3842 | 0.594460 | ||||||||
\(435\) | 6.87124 | 0.329451 | ||||||||
\(436\) | 9.05616 | 0.433711 | ||||||||
\(437\) | −0.250632 | −0.0119893 | ||||||||
\(438\) | 29.6433 | 1.41641 | ||||||||
\(439\) | −20.5340 | −0.980035 | −0.490017 | − | 0.871713i | \(-0.663010\pi\) | ||||
−0.490017 | + | 0.871713i | \(0.663010\pi\) | |||||||
\(440\) | −2.04022 | −0.0972635 | ||||||||
\(441\) | −9.60958 | −0.457599 | ||||||||
\(442\) | 21.7251 | 1.03336 | ||||||||
\(443\) | 13.6309 | 0.647625 | 0.323813 | − | 0.946121i | \(-0.395035\pi\) | ||||
0.323813 | + | 0.946121i | \(0.395035\pi\) | |||||||
\(444\) | 5.90506 | 0.280242 | ||||||||
\(445\) | −27.5277 | −1.30494 | ||||||||
\(446\) | 26.3753 | 1.24891 | ||||||||
\(447\) | −15.3626 | −0.726624 | ||||||||
\(448\) | −19.6381 | −0.927812 | ||||||||
\(449\) | 3.61395 | 0.170553 | 0.0852763 | − | 0.996357i | \(-0.472823\pi\) | ||||
0.0852763 | + | 0.996357i | \(0.472823\pi\) | |||||||
\(450\) | 5.85577 | 0.276044 | ||||||||
\(451\) | −0.851558 | −0.0400983 | ||||||||
\(452\) | −4.57910 | −0.215383 | ||||||||
\(453\) | 20.9781 | 0.985638 | ||||||||
\(454\) | 15.3895 | 0.722263 | ||||||||
\(455\) | 28.0427 | 1.31466 | ||||||||
\(456\) | 2.15913 | 0.101110 | ||||||||
\(457\) | 7.64767 | 0.357743 | 0.178871 | − | 0.983872i | \(-0.442755\pi\) | ||||
0.178871 | + | 0.983872i | \(0.442755\pi\) | |||||||
\(458\) | 15.8636 | 0.741258 | ||||||||
\(459\) | −18.5365 | −0.865211 | ||||||||
\(460\) | −1.44057 | −0.0671668 | ||||||||
\(461\) | 1.84092 | 0.0857400 | 0.0428700 | − | 0.999081i | \(-0.486350\pi\) | ||||
0.0428700 | + | 0.999081i | \(0.486350\pi\) | |||||||
\(462\) | −2.01736 | −0.0938562 | ||||||||
\(463\) | −31.8243 | −1.47900 | −0.739501 | − | 0.673156i | \(-0.764938\pi\) | ||||
−0.739501 | + | 0.673156i | \(0.764938\pi\) | |||||||
\(464\) | −2.48044 | −0.115152 | ||||||||
\(465\) | −31.9616 | −1.48218 | ||||||||
\(466\) | 17.7823 | 0.823748 | ||||||||
\(467\) | 19.5865 | 0.906355 | 0.453178 | − | 0.891420i | \(-0.350290\pi\) | ||||
0.453178 | + | 0.891420i | \(0.350290\pi\) | |||||||
\(468\) | −14.5312 | −0.671707 | ||||||||
\(469\) | −3.54294 | −0.163598 | ||||||||
\(470\) | −1.04221 | −0.0480737 | ||||||||
\(471\) | 12.6093 | 0.581006 | ||||||||
\(472\) | −24.7734 | −1.14029 | ||||||||
\(473\) | 1.09366 | 0.0502866 | ||||||||
\(474\) | −44.9999 | −2.06691 | ||||||||
\(475\) | 0.254721 | 0.0116874 | ||||||||
\(476\) | 4.71146 | 0.215949 | ||||||||
\(477\) | 32.4187 | 1.48435 | ||||||||
\(478\) | −36.0167 | −1.64736 | ||||||||
\(479\) | −24.2519 | −1.10810 | −0.554049 | − | 0.832484i | \(-0.686918\pi\) | ||||
−0.554049 | + | 0.832484i | \(0.686918\pi\) | |||||||
\(480\) | 22.0032 | 1.00430 | ||||||||
\(481\) | 18.3184 | 0.835248 | ||||||||
\(482\) | −17.1835 | −0.782685 | ||||||||
\(483\) | −6.27512 | −0.285528 | ||||||||
\(484\) | 6.41745 | 0.291702 | ||||||||
\(485\) | −28.3326 | −1.28652 | ||||||||
\(486\) | 18.5997 | 0.843699 | ||||||||
\(487\) | −16.8555 | −0.763796 | −0.381898 | − | 0.924204i | \(-0.624729\pi\) | ||||
−0.381898 | + | 0.924204i | \(0.624729\pi\) | |||||||
\(488\) | −2.24921 | −0.101817 | ||||||||
\(489\) | 23.7358 | 1.07337 | ||||||||
\(490\) | 5.77911 | 0.261073 | ||||||||
\(491\) | 20.8116 | 0.939212 | 0.469606 | − | 0.882876i | \(-0.344396\pi\) | ||||
0.469606 | + | 0.882876i | \(0.344396\pi\) | |||||||
\(492\) | 5.17980 | 0.233524 | ||||||||
\(493\) | 3.58126 | 0.161292 | ||||||||
\(494\) | 1.52041 | 0.0684067 | ||||||||
\(495\) | 3.21615 | 0.144555 | ||||||||
\(496\) | 11.5378 | 0.518061 | ||||||||
\(497\) | 8.74188 | 0.392127 | ||||||||
\(498\) | −37.8657 | −1.69680 | ||||||||
\(499\) | 6.70326 | 0.300079 | 0.150040 | − | 0.988680i | \(-0.452060\pi\) | ||||
0.150040 | + | 0.988680i | \(0.452060\pi\) | |||||||
\(500\) | −5.73876 | −0.256645 | ||||||||
\(501\) | 52.6846 | 2.35378 | ||||||||
\(502\) | 30.6317 | 1.36716 | ||||||||
\(503\) | 31.5150 | 1.40518 | 0.702592 | − | 0.711593i | \(-0.252026\pi\) | ||||
0.702592 | + | 0.711593i | \(0.252026\pi\) | |||||||
\(504\) | 33.3930 | 1.48744 | ||||||||
\(505\) | −20.7160 | −0.921850 | ||||||||
\(506\) | 0.321486 | 0.0142918 | ||||||||
\(507\) | −36.5573 | −1.62357 | ||||||||
\(508\) | −3.29472 | −0.146179 | ||||||||
\(509\) | 15.8028 | 0.700447 | 0.350223 | − | 0.936666i | \(-0.386106\pi\) | ||||
0.350223 | + | 0.936666i | \(0.386106\pi\) | |||||||
\(510\) | 29.2479 | 1.29512 | ||||||||
\(511\) | 19.9428 | 0.882216 | ||||||||
\(512\) | −23.1986 | −1.02524 | ||||||||
\(513\) | −1.29727 | −0.0572757 | ||||||||
\(514\) | 29.4888 | 1.30070 | ||||||||
\(515\) | −37.7018 | −1.66134 | ||||||||
\(516\) | −6.65245 | −0.292858 | ||||||||
\(517\) | −0.0966956 | −0.00425267 | ||||||||
\(518\) | −9.55567 | −0.419852 | ||||||||
\(519\) | −61.8553 | −2.71514 | ||||||||
\(520\) | 38.4981 | 1.68825 | ||||||||
\(521\) | 28.3329 | 1.24129 | 0.620643 | − | 0.784094i | \(-0.286872\pi\) | ||||
0.620643 | + | 0.784094i | \(0.286872\pi\) | |||||||
\(522\) | 5.76177 | 0.252186 | ||||||||
\(523\) | 3.98741 | 0.174357 | 0.0871787 | − | 0.996193i | \(-0.472215\pi\) | ||||
0.0871787 | + | 0.996193i | \(0.472215\pi\) | |||||||
\(524\) | 7.28218 | 0.318124 | ||||||||
\(525\) | 6.37750 | 0.278337 | ||||||||
\(526\) | 16.1400 | 0.703738 | ||||||||
\(527\) | −16.6582 | −0.725643 | ||||||||
\(528\) | −1.87948 | −0.0817940 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −19.4963 | −0.846863 | ||||||||
\(531\) | 39.0522 | 1.69472 | ||||||||
\(532\) | 0.329728 | 0.0142955 | ||||||||
\(533\) | 16.0686 | 0.696007 | ||||||||
\(534\) | −37.3679 | −1.61707 | ||||||||
\(535\) | 16.6305 | 0.719000 | ||||||||
\(536\) | −4.86389 | −0.210088 | ||||||||
\(537\) | −26.7503 | −1.15436 | ||||||||
\(538\) | 28.5362 | 1.23028 | ||||||||
\(539\) | 0.536180 | 0.0230949 | ||||||||
\(540\) | −7.45634 | −0.320870 | ||||||||
\(541\) | 17.8138 | 0.765873 | 0.382937 | − | 0.923775i | \(-0.374913\pi\) | ||||
0.382937 | + | 0.923775i | \(0.374913\pi\) | |||||||
\(542\) | 8.25055 | 0.354392 | ||||||||
\(543\) | 2.20055 | 0.0944345 | ||||||||
\(544\) | 11.4679 | 0.491684 | ||||||||
\(545\) | 37.8217 | 1.62010 | ||||||||
\(546\) | 38.0669 | 1.62911 | ||||||||
\(547\) | −13.1541 | −0.562429 | −0.281214 | − | 0.959645i | \(-0.590737\pi\) | ||||
−0.281214 | + | 0.959645i | \(0.590737\pi\) | |||||||
\(548\) | 4.00452 | 0.171065 | ||||||||
\(549\) | 3.54561 | 0.151323 | ||||||||
\(550\) | −0.326731 | −0.0139319 | ||||||||
\(551\) | 0.250632 | 0.0106773 | ||||||||
\(552\) | −8.61474 | −0.366668 | ||||||||
\(553\) | −30.2740 | −1.28738 | ||||||||
\(554\) | 19.0887 | 0.811002 | ||||||||
\(555\) | 24.6616 | 1.04683 | ||||||||
\(556\) | −6.76739 | −0.287001 | ||||||||
\(557\) | −40.6143 | −1.72088 | −0.860442 | − | 0.509549i | \(-0.829812\pi\) | ||||
−0.860442 | + | 0.509549i | \(0.829812\pi\) | |||||||
\(558\) | −26.8008 | −1.13457 | ||||||||
\(559\) | −20.6370 | −0.872851 | ||||||||
\(560\) | −13.6285 | −0.575907 | ||||||||
\(561\) | 2.71359 | 0.114568 | ||||||||
\(562\) | −23.2108 | −0.979089 | ||||||||
\(563\) | 13.0949 | 0.551882 | 0.275941 | − | 0.961175i | \(-0.411010\pi\) | ||||
0.275941 | + | 0.961175i | \(0.411010\pi\) | |||||||
\(564\) | 0.588174 | 0.0247666 | ||||||||
\(565\) | −19.1240 | −0.804551 | ||||||||
\(566\) | −24.7473 | −1.04021 | ||||||||
\(567\) | 0.0966798 | 0.00406017 | ||||||||
\(568\) | 12.0012 | 0.503559 | ||||||||
\(569\) | −14.8300 | −0.621706 | −0.310853 | − | 0.950458i | \(-0.600615\pi\) | ||||
−0.310853 | + | 0.950458i | \(0.600615\pi\) | |||||||
\(570\) | 2.04689 | 0.0857349 | ||||||||
\(571\) | −33.0155 | −1.38166 | −0.690828 | − | 0.723019i | \(-0.742754\pi\) | ||||
−0.690828 | + | 0.723019i | \(0.742754\pi\) | |||||||
\(572\) | 0.810792 | 0.0339009 | ||||||||
\(573\) | 51.7412 | 2.16152 | ||||||||
\(574\) | −8.38205 | −0.349860 | ||||||||
\(575\) | −1.01632 | −0.0423833 | ||||||||
\(576\) | 42.4991 | 1.77080 | ||||||||
\(577\) | 5.82980 | 0.242698 | 0.121349 | − | 0.992610i | \(-0.461278\pi\) | ||||
0.121349 | + | 0.992610i | \(0.461278\pi\) | |||||||
\(578\) | −4.96178 | −0.206383 | ||||||||
\(579\) | −25.2638 | −1.04993 | ||||||||
\(580\) | 1.44057 | 0.0598163 | ||||||||
\(581\) | −25.4744 | −1.05686 | ||||||||
\(582\) | −38.4605 | −1.59424 | ||||||||
\(583\) | −1.80885 | −0.0749147 | ||||||||
\(584\) | 27.3782 | 1.13292 | ||||||||
\(585\) | −60.6876 | −2.50912 | ||||||||
\(586\) | 17.8661 | 0.738044 | ||||||||
\(587\) | −13.1706 | −0.543608 | −0.271804 | − | 0.962353i | \(-0.587620\pi\) | ||||
−0.271804 | + | 0.962353i | \(0.587620\pi\) | |||||||
\(588\) | −3.26145 | −0.134500 | ||||||||
\(589\) | −1.16581 | −0.0480365 | ||||||||
\(590\) | −23.4856 | −0.966886 | ||||||||
\(591\) | −51.8456 | −2.13264 | ||||||||
\(592\) | −8.90257 | −0.365893 | ||||||||
\(593\) | 19.1559 | 0.786637 | 0.393319 | − | 0.919402i | \(-0.371327\pi\) | ||||
0.393319 | + | 0.919402i | \(0.371327\pi\) | |||||||
\(594\) | 1.66401 | 0.0682750 | ||||||||
\(595\) | 19.6767 | 0.806667 | ||||||||
\(596\) | −3.22078 | −0.131928 | ||||||||
\(597\) | 36.1658 | 1.48017 | ||||||||
\(598\) | −6.06632 | −0.248070 | ||||||||
\(599\) | 46.4926 | 1.89964 | 0.949819 | − | 0.312800i | \(-0.101267\pi\) | ||||
0.949819 | + | 0.312800i | \(0.101267\pi\) | |||||||
\(600\) | 8.75529 | 0.357433 | ||||||||
\(601\) | −22.1735 | −0.904474 | −0.452237 | − | 0.891898i | \(-0.649374\pi\) | ||||
−0.452237 | + | 0.891898i | \(0.649374\pi\) | |||||||
\(602\) | 10.7651 | 0.438753 | ||||||||
\(603\) | 7.66733 | 0.312238 | ||||||||
\(604\) | 4.39809 | 0.178956 | ||||||||
\(605\) | 26.8015 | 1.08964 | ||||||||
\(606\) | −28.1212 | −1.14235 | ||||||||
\(607\) | −26.1701 | −1.06221 | −0.531106 | − | 0.847305i | \(-0.678223\pi\) | ||||
−0.531106 | + | 0.847305i | \(0.678223\pi\) | |||||||
\(608\) | 0.802575 | 0.0325487 | ||||||||
\(609\) | 6.27512 | 0.254281 | ||||||||
\(610\) | −2.13230 | −0.0863341 | ||||||||
\(611\) | 1.82461 | 0.0738158 | ||||||||
\(612\) | −10.1961 | −0.412155 | ||||||||
\(613\) | −12.8789 | −0.520173 | −0.260086 | − | 0.965585i | \(-0.583751\pi\) | ||||
−0.260086 | + | 0.965585i | \(0.583751\pi\) | |||||||
\(614\) | 28.0214 | 1.13085 | ||||||||
\(615\) | 21.6327 | 0.872314 | ||||||||
\(616\) | −1.86321 | −0.0750710 | ||||||||
\(617\) | 22.6128 | 0.910358 | 0.455179 | − | 0.890400i | \(-0.349575\pi\) | ||||
0.455179 | + | 0.890400i | \(0.349575\pi\) | |||||||
\(618\) | −51.1788 | −2.05871 | ||||||||
\(619\) | 2.79837 | 0.112476 | 0.0562380 | − | 0.998417i | \(-0.482089\pi\) | ||||
0.0562380 | + | 0.998417i | \(0.482089\pi\) | |||||||
\(620\) | −6.70079 | −0.269110 | ||||||||
\(621\) | 5.17598 | 0.207705 | ||||||||
\(622\) | −31.6681 | −1.26978 | ||||||||
\(623\) | −25.1395 | −1.00719 | ||||||||
\(624\) | 35.4652 | 1.41974 | ||||||||
\(625\) | −29.0487 | −1.16195 | ||||||||
\(626\) | −27.3451 | −1.09293 | ||||||||
\(627\) | 0.189909 | 0.00758423 | ||||||||
\(628\) | 2.64356 | 0.105489 | ||||||||
\(629\) | 12.8535 | 0.512503 | ||||||||
\(630\) | 31.6572 | 1.26125 | ||||||||
\(631\) | 11.8215 | 0.470606 | 0.235303 | − | 0.971922i | \(-0.424392\pi\) | ||||
0.235303 | + | 0.971922i | \(0.424392\pi\) | |||||||
\(632\) | −41.5613 | −1.65322 | ||||||||
\(633\) | −20.2226 | −0.803778 | ||||||||
\(634\) | −33.5377 | −1.33195 | ||||||||
\(635\) | −13.7599 | −0.546045 | ||||||||
\(636\) | 11.0027 | 0.436287 | ||||||||
\(637\) | −10.1175 | −0.400871 | ||||||||
\(638\) | −0.321486 | −0.0127278 | ||||||||
\(639\) | −18.9184 | −0.748402 | ||||||||
\(640\) | −9.84966 | −0.389342 | ||||||||
\(641\) | 8.74272 | 0.345317 | 0.172658 | − | 0.984982i | \(-0.444764\pi\) | ||||
0.172658 | + | 0.984982i | \(0.444764\pi\) | |||||||
\(642\) | 22.5753 | 0.890977 | ||||||||
\(643\) | −33.9965 | −1.34069 | −0.670346 | − | 0.742049i | \(-0.733854\pi\) | ||||
−0.670346 | + | 0.742049i | \(0.733854\pi\) | |||||||
\(644\) | −1.31559 | −0.0518414 | ||||||||
\(645\) | −27.7830 | −1.09395 | ||||||||
\(646\) | 1.06683 | 0.0419739 | ||||||||
\(647\) | −33.8286 | −1.32994 | −0.664970 | − | 0.746870i | \(-0.731556\pi\) | ||||
−0.664970 | + | 0.746870i | \(0.731556\pi\) | |||||||
\(648\) | 0.132726 | 0.00521397 | ||||||||
\(649\) | −2.17897 | −0.0855322 | ||||||||
\(650\) | 6.16530 | 0.241823 | ||||||||
\(651\) | −29.1887 | −1.14399 | ||||||||
\(652\) | 4.97625 | 0.194885 | ||||||||
\(653\) | −6.65479 | −0.260422 | −0.130211 | − | 0.991486i | \(-0.541565\pi\) | ||||
−0.130211 | + | 0.991486i | \(0.541565\pi\) | |||||||
\(654\) | 51.3416 | 2.00762 | ||||||||
\(655\) | 30.4130 | 1.18833 | ||||||||
\(656\) | −7.80917 | −0.304897 | ||||||||
\(657\) | −43.1584 | −1.68377 | ||||||||
\(658\) | −0.951793 | −0.0371048 | ||||||||
\(659\) | −30.7096 | −1.19628 | −0.598138 | − | 0.801393i | \(-0.704093\pi\) | ||||
−0.598138 | + | 0.801393i | \(0.704093\pi\) | |||||||
\(660\) | 1.09155 | 0.0424884 | ||||||||
\(661\) | −37.0799 | −1.44224 | −0.721120 | − | 0.692810i | \(-0.756372\pi\) | ||||
−0.721120 | + | 0.692810i | \(0.756372\pi\) | |||||||
\(662\) | −26.9918 | −1.04906 | ||||||||
\(663\) | −51.2045 | −1.98862 | ||||||||
\(664\) | −34.9723 | −1.35719 | ||||||||
\(665\) | 1.37706 | 0.0534002 | ||||||||
\(666\) | 20.6796 | 0.801317 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 11.0454 | 0.427360 | ||||||||
\(669\) | −62.1647 | −2.40343 | ||||||||
\(670\) | −4.61106 | −0.178141 | ||||||||
\(671\) | −0.197833 | −0.00763724 | ||||||||
\(672\) | 20.0942 | 0.775152 | ||||||||
\(673\) | 13.1912 | 0.508483 | 0.254241 | − | 0.967141i | \(-0.418174\pi\) | ||||
0.254241 | + | 0.967141i | \(0.418174\pi\) | |||||||
\(674\) | −16.8631 | −0.649542 | ||||||||
\(675\) | −5.26043 | −0.202474 | ||||||||
\(676\) | −7.66430 | −0.294781 | ||||||||
\(677\) | 9.75914 | 0.375074 | 0.187537 | − | 0.982258i | \(-0.439949\pi\) | ||||
0.187537 | + | 0.982258i | \(0.439949\pi\) | |||||||
\(678\) | −25.9601 | −0.996990 | ||||||||
\(679\) | −25.8746 | −0.992975 | ||||||||
\(680\) | 27.0130 | 1.03590 | ||||||||
\(681\) | −36.2719 | −1.38994 | ||||||||
\(682\) | 1.49539 | 0.0572615 | ||||||||
\(683\) | 4.12121 | 0.157694 | 0.0788469 | − | 0.996887i | \(-0.474876\pi\) | ||||
0.0788469 | + | 0.996887i | \(0.474876\pi\) | |||||||
\(684\) | −0.713570 | −0.0272840 | ||||||||
\(685\) | 16.7243 | 0.639002 | ||||||||
\(686\) | 23.9146 | 0.913064 | ||||||||
\(687\) | −37.3894 | −1.42650 | ||||||||
\(688\) | 10.0294 | 0.382366 | ||||||||
\(689\) | 34.1323 | 1.30034 | ||||||||
\(690\) | −8.16693 | −0.310910 | ||||||||
\(691\) | −47.3810 | −1.80246 | −0.901228 | − | 0.433344i | \(-0.857333\pi\) | ||||
−0.901228 | + | 0.433344i | \(0.857333\pi\) | |||||||
\(692\) | −12.9680 | −0.492971 | ||||||||
\(693\) | 2.93713 | 0.111572 | ||||||||
\(694\) | −33.9312 | −1.28801 | ||||||||
\(695\) | −28.2630 | −1.07208 | ||||||||
\(696\) | 8.61474 | 0.326541 | ||||||||
\(697\) | 11.2749 | 0.427065 | ||||||||
\(698\) | −20.4158 | −0.772748 | ||||||||
\(699\) | −41.9116 | −1.58524 | ||||||||
\(700\) | 1.33705 | 0.0505358 | ||||||||
\(701\) | 0.536333 | 0.0202570 | 0.0101285 | − | 0.999949i | \(-0.496776\pi\) | ||||
0.0101285 | + | 0.999949i | \(0.496776\pi\) | |||||||
\(702\) | −31.3992 | −1.18509 | ||||||||
\(703\) | 0.899544 | 0.0339269 | ||||||||
\(704\) | −2.37130 | −0.0893717 | ||||||||
\(705\) | 2.45642 | 0.0925142 | ||||||||
\(706\) | −8.80984 | −0.331563 | ||||||||
\(707\) | −18.9187 | −0.711513 | ||||||||
\(708\) | 13.2541 | 0.498121 | ||||||||
\(709\) | 12.7191 | 0.477677 | 0.238839 | − | 0.971059i | \(-0.423233\pi\) | ||||
0.238839 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(710\) | 11.3774 | 0.426985 | ||||||||
\(711\) | 65.5164 | 2.45706 | ||||||||
\(712\) | −34.5125 | −1.29341 | ||||||||
\(713\) | 4.65149 | 0.174200 | ||||||||
\(714\) | 26.7104 | 0.999613 | ||||||||
\(715\) | 3.38615 | 0.126635 | ||||||||
\(716\) | −5.60824 | −0.209590 | ||||||||
\(717\) | 84.8888 | 3.17023 | ||||||||
\(718\) | 37.0104 | 1.38122 | ||||||||
\(719\) | 0.927663 | 0.0345960 | 0.0172980 | − | 0.999850i | \(-0.494494\pi\) | ||||
0.0172980 | + | 0.999850i | \(0.494494\pi\) | |||||||
\(720\) | 29.4935 | 1.09916 | ||||||||
\(721\) | −34.4309 | −1.28227 | ||||||||
\(722\) | −22.5081 | −0.837664 | ||||||||
\(723\) | 40.5002 | 1.50622 | ||||||||
\(724\) | 0.461348 | 0.0171459 | ||||||||
\(725\) | 1.01632 | 0.0377450 | ||||||||
\(726\) | 36.3821 | 1.35027 | ||||||||
\(727\) | 12.8206 | 0.475488 | 0.237744 | − | 0.971328i | \(-0.423592\pi\) | ||||
0.237744 | + | 0.971328i | \(0.423592\pi\) | |||||||
\(728\) | 35.1582 | 1.30305 | ||||||||
\(729\) | −43.7087 | −1.61884 | ||||||||
\(730\) | 25.9551 | 0.960640 | ||||||||
\(731\) | −14.4804 | −0.535575 | ||||||||
\(732\) | 1.20336 | 0.0444776 | ||||||||
\(733\) | −18.7464 | −0.692413 | −0.346207 | − | 0.938158i | \(-0.612530\pi\) | ||||
−0.346207 | + | 0.938158i | \(0.612530\pi\) | |||||||
\(734\) | 8.52855 | 0.314794 | ||||||||
\(735\) | −13.6210 | −0.502416 | ||||||||
\(736\) | −3.20221 | −0.118035 | ||||||||
\(737\) | −0.427810 | −0.0157586 | ||||||||
\(738\) | 18.1397 | 0.667733 | ||||||||
\(739\) | −1.73116 | −0.0636819 | −0.0318409 | − | 0.999493i | \(-0.510137\pi\) | ||||
−0.0318409 | + | 0.999493i | \(0.510137\pi\) | |||||||
\(740\) | 5.17034 | 0.190066 | ||||||||
\(741\) | −3.58351 | −0.131644 | ||||||||
\(742\) | −17.8048 | −0.653636 | ||||||||
\(743\) | 37.2951 | 1.36822 | 0.684112 | − | 0.729377i | \(-0.260190\pi\) | ||||
0.684112 | + | 0.729377i | \(0.260190\pi\) | |||||||
\(744\) | −40.0714 | −1.46909 | ||||||||
\(745\) | −13.4511 | −0.492811 | ||||||||
\(746\) | 40.3215 | 1.47627 | ||||||||
\(747\) | 55.1296 | 2.01709 | ||||||||
\(748\) | 0.568909 | 0.0208014 | ||||||||
\(749\) | 15.1877 | 0.554947 | ||||||||
\(750\) | −32.5345 | −1.18799 | ||||||||
\(751\) | 28.6370 | 1.04498 | 0.522489 | − | 0.852646i | \(-0.325004\pi\) | ||||
0.522489 | + | 0.852646i | \(0.325004\pi\) | |||||||
\(752\) | −0.886742 | −0.0323361 | ||||||||
\(753\) | −72.1968 | −2.63100 | ||||||||
\(754\) | 6.06632 | 0.220922 | ||||||||
\(755\) | 18.3680 | 0.668480 | ||||||||
\(756\) | −6.80946 | −0.247658 | ||||||||
\(757\) | 3.71936 | 0.135182 | 0.0675912 | − | 0.997713i | \(-0.478469\pi\) | ||||
0.0675912 | + | 0.997713i | \(0.478469\pi\) | |||||||
\(758\) | 33.5935 | 1.22017 | ||||||||
\(759\) | −0.757721 | −0.0275035 | ||||||||
\(760\) | 1.89049 | 0.0685751 | ||||||||
\(761\) | −11.7584 | −0.426243 | −0.213122 | − | 0.977026i | \(-0.568363\pi\) | ||||
−0.213122 | + | 0.977026i | \(0.568363\pi\) | |||||||
\(762\) | −18.6786 | −0.676653 | ||||||||
\(763\) | 34.5404 | 1.25045 | ||||||||
\(764\) | 10.8476 | 0.392453 | ||||||||
\(765\) | −42.5827 | −1.53958 | ||||||||
\(766\) | 44.4751 | 1.60695 | ||||||||
\(767\) | 41.1164 | 1.48463 | ||||||||
\(768\) | 35.7482 | 1.28995 | ||||||||
\(769\) | 8.27470 | 0.298393 | 0.149197 | − | 0.988808i | \(-0.452331\pi\) | ||||
0.149197 | + | 0.988808i | \(0.452331\pi\) | |||||||
\(770\) | −1.76636 | −0.0636552 | ||||||||
\(771\) | −69.5031 | −2.50309 | ||||||||
\(772\) | −5.29660 | −0.190629 | ||||||||
\(773\) | −10.8503 | −0.390257 | −0.195129 | − | 0.980778i | \(-0.562512\pi\) | ||||
−0.195129 | + | 0.980778i | \(0.562512\pi\) | |||||||
\(774\) | −23.2970 | −0.837392 | ||||||||
\(775\) | −4.72738 | −0.169813 | ||||||||
\(776\) | −35.5217 | −1.27515 | ||||||||
\(777\) | 22.5220 | 0.807974 | ||||||||
\(778\) | −12.5304 | −0.449236 | ||||||||
\(779\) | 0.789063 | 0.0282711 | ||||||||
\(780\) | −20.5971 | −0.737494 | ||||||||
\(781\) | 1.05558 | 0.0377717 | ||||||||
\(782\) | −4.25656 | −0.152214 | ||||||||
\(783\) | −5.17598 | −0.184974 | ||||||||
\(784\) | 4.91701 | 0.175608 | ||||||||
\(785\) | 11.0404 | 0.394050 | ||||||||
\(786\) | 41.2845 | 1.47257 | ||||||||
\(787\) | −2.85603 | −0.101806 | −0.0509032 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509032 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(788\) | −10.8695 | −0.387210 | ||||||||
\(789\) | −38.0409 | −1.35429 | ||||||||
\(790\) | −39.4009 | −1.40182 | ||||||||
\(791\) | −17.4648 | −0.620978 | ||||||||
\(792\) | 4.03221 | 0.143278 | ||||||||
\(793\) | 3.73303 | 0.132564 | ||||||||
\(794\) | 33.8611 | 1.20168 | ||||||||
\(795\) | 45.9513 | 1.62973 | ||||||||
\(796\) | 7.58220 | 0.268744 | ||||||||
\(797\) | 10.7229 | 0.379826 | 0.189913 | − | 0.981801i | \(-0.439179\pi\) | ||||
0.189913 | + | 0.981801i | \(0.439179\pi\) | |||||||
\(798\) | 1.86931 | 0.0661729 | ||||||||
\(799\) | 1.28027 | 0.0452929 | ||||||||
\(800\) | 3.25445 | 0.115062 | ||||||||
\(801\) | 54.4048 | 1.92230 | ||||||||
\(802\) | 9.65937 | 0.341084 | ||||||||
\(803\) | 2.40809 | 0.0849796 | ||||||||
\(804\) | 2.60226 | 0.0917745 | ||||||||
\(805\) | −5.49436 | −0.193651 | ||||||||
\(806\) | −28.2175 | −0.993918 | ||||||||
\(807\) | −67.2578 | −2.36759 | ||||||||
\(808\) | −25.9724 | −0.913706 | ||||||||
\(809\) | 45.7098 | 1.60707 | 0.803535 | − | 0.595258i | \(-0.202950\pi\) | ||||
0.803535 | + | 0.595258i | \(0.202950\pi\) | |||||||
\(810\) | 0.125827 | 0.00442110 | ||||||||
\(811\) | 24.2070 | 0.850023 | 0.425011 | − | 0.905188i | \(-0.360270\pi\) | ||||
0.425011 | + | 0.905188i | \(0.360270\pi\) | |||||||
\(812\) | 1.31559 | 0.0461681 | ||||||||
\(813\) | −19.4460 | −0.682000 | ||||||||
\(814\) | −1.15385 | −0.0404423 | ||||||||
\(815\) | 20.7826 | 0.727982 | ||||||||
\(816\) | 24.8849 | 0.871144 | ||||||||
\(817\) | −1.01340 | −0.0354543 | ||||||||
\(818\) | −38.5906 | −1.34929 | ||||||||
\(819\) | −55.4225 | −1.93662 | ||||||||
\(820\) | 4.53533 | 0.158380 | ||||||||
\(821\) | 27.6627 | 0.965436 | 0.482718 | − | 0.875776i | \(-0.339650\pi\) | ||||
0.482718 | + | 0.875776i | \(0.339650\pi\) | |||||||
\(822\) | 22.7026 | 0.791844 | ||||||||
\(823\) | 25.9299 | 0.903861 | 0.451930 | − | 0.892053i | \(-0.350736\pi\) | ||||
0.451930 | + | 0.892053i | \(0.350736\pi\) | |||||||
\(824\) | −47.2681 | −1.64666 | ||||||||
\(825\) | 0.770083 | 0.0268108 | ||||||||
\(826\) | −21.4481 | −0.746273 | ||||||||
\(827\) | 49.6826 | 1.72763 | 0.863817 | − | 0.503805i | \(-0.168067\pi\) | ||||
0.863817 | + | 0.503805i | \(0.168067\pi\) | |||||||
\(828\) | 2.84708 | 0.0989430 | ||||||||
\(829\) | 56.8151 | 1.97327 | 0.986634 | − | 0.162950i | \(-0.0521009\pi\) | ||||
0.986634 | + | 0.162950i | \(0.0521009\pi\) | |||||||
\(830\) | −33.1544 | −1.15081 | ||||||||
\(831\) | −44.9908 | −1.56071 | ||||||||
\(832\) | 44.7455 | 1.55127 | ||||||||
\(833\) | −7.09917 | −0.245972 | ||||||||
\(834\) | −38.3660 | −1.32851 | ||||||||
\(835\) | 46.1295 | 1.59638 | ||||||||
\(836\) | 0.0398147 | 0.00137702 | ||||||||
\(837\) | 24.0760 | 0.832190 | ||||||||
\(838\) | −1.86422 | −0.0643983 | ||||||||
\(839\) | −5.02733 | −0.173563 | −0.0867813 | − | 0.996227i | \(-0.527658\pi\) | ||||
−0.0867813 | + | 0.996227i | \(0.527658\pi\) | |||||||
\(840\) | 47.3325 | 1.63313 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 35.8809 | 1.23654 | ||||||||
\(843\) | 54.7063 | 1.88418 | ||||||||
\(844\) | −4.23971 | −0.145937 | ||||||||
\(845\) | −32.0088 | −1.10114 | ||||||||
\(846\) | 2.05979 | 0.0708171 | ||||||||
\(847\) | 24.4763 | 0.841017 | ||||||||
\(848\) | −16.5879 | −0.569632 | ||||||||
\(849\) | 58.3276 | 2.00180 | ||||||||
\(850\) | 4.32601 | 0.148381 | ||||||||
\(851\) | −3.58910 | −0.123033 | ||||||||
\(852\) | −6.42083 | −0.219974 | ||||||||
\(853\) | −41.9131 | −1.43508 | −0.717539 | − | 0.696518i | \(-0.754732\pi\) | ||||
−0.717539 | + | 0.696518i | \(0.754732\pi\) | |||||||
\(854\) | −1.94730 | −0.0666354 | ||||||||
\(855\) | −2.98012 | −0.101918 | ||||||||
\(856\) | 20.8503 | 0.712649 | ||||||||
\(857\) | 12.9893 | 0.443707 | 0.221853 | − | 0.975080i | \(-0.428789\pi\) | ||||
0.221853 | + | 0.975080i | \(0.428789\pi\) | |||||||
\(858\) | 4.59658 | 0.156925 | ||||||||
\(859\) | 27.9391 | 0.953269 | 0.476634 | − | 0.879102i | \(-0.341857\pi\) | ||||
0.476634 | + | 0.879102i | \(0.341857\pi\) | |||||||
\(860\) | −5.82475 | −0.198622 | ||||||||
\(861\) | 19.7559 | 0.673280 | ||||||||
\(862\) | 27.4460 | 0.934815 | ||||||||
\(863\) | 50.0500 | 1.70372 | 0.851861 | − | 0.523768i | \(-0.175474\pi\) | ||||
0.851861 | + | 0.523768i | \(0.175474\pi\) | |||||||
\(864\) | −16.5746 | −0.563878 | ||||||||
\(865\) | −54.1591 | −1.84147 | ||||||||
\(866\) | −34.5775 | −1.17499 | ||||||||
\(867\) | 11.6946 | 0.397168 | ||||||||
\(868\) | −6.11945 | −0.207708 | ||||||||
\(869\) | −3.65558 | −0.124007 | ||||||||
\(870\) | 8.16693 | 0.276885 | ||||||||
\(871\) | 8.07262 | 0.273530 | ||||||||
\(872\) | 47.4185 | 1.60579 | ||||||||
\(873\) | 55.9956 | 1.89516 | ||||||||
\(874\) | −0.297893 | −0.0100764 | ||||||||
\(875\) | −21.8878 | −0.739943 | ||||||||
\(876\) | −14.6478 | −0.494902 | ||||||||
\(877\) | −22.5778 | −0.762398 | −0.381199 | − | 0.924493i | \(-0.624489\pi\) | ||||
−0.381199 | + | 0.924493i | \(0.624489\pi\) | |||||||
\(878\) | −24.4060 | −0.823663 | ||||||||
\(879\) | −42.1093 | −1.42031 | ||||||||
\(880\) | −1.64564 | −0.0554744 | ||||||||
\(881\) | 1.26810 | 0.0427232 | 0.0213616 | − | 0.999772i | \(-0.493200\pi\) | ||||
0.0213616 | + | 0.999772i | \(0.493200\pi\) | |||||||
\(882\) | −11.4216 | −0.384586 | ||||||||
\(883\) | −49.6727 | −1.67162 | −0.835809 | − | 0.549020i | \(-0.815001\pi\) | ||||
−0.835809 | + | 0.549020i | \(0.815001\pi\) | |||||||
\(884\) | −10.7351 | −0.361060 | ||||||||
\(885\) | 55.3539 | 1.86070 | ||||||||
\(886\) | 16.2013 | 0.544292 | ||||||||
\(887\) | −35.3059 | −1.18545 | −0.592727 | − | 0.805403i | \(-0.701949\pi\) | ||||
−0.592727 | + | 0.805403i | \(0.701949\pi\) | |||||||
\(888\) | 30.9192 | 1.03758 | ||||||||
\(889\) | −12.5661 | −0.421455 | ||||||||
\(890\) | −32.7185 | −1.09673 | ||||||||
\(891\) | 0.0116741 | 0.000391096 0 | ||||||||
\(892\) | −13.0329 | −0.436375 | ||||||||
\(893\) | 0.0895992 | 0.00299832 | ||||||||
\(894\) | −18.2594 | −0.610686 | ||||||||
\(895\) | −23.4220 | −0.782910 | ||||||||
\(896\) | −8.99514 | −0.300506 | ||||||||
\(897\) | 14.2979 | 0.477393 | ||||||||
\(898\) | 4.29541 | 0.143340 | ||||||||
\(899\) | −4.65149 | −0.155136 | ||||||||
\(900\) | −2.89354 | −0.0964512 | ||||||||
\(901\) | 23.9496 | 0.797877 | ||||||||
\(902\) | −1.01213 | −0.0337003 | ||||||||
\(903\) | −25.3726 | −0.844349 | ||||||||
\(904\) | −23.9764 | −0.797444 | ||||||||
\(905\) | 1.92675 | 0.0640474 | ||||||||
\(906\) | 24.9339 | 0.828373 | ||||||||
\(907\) | 34.9622 | 1.16090 | 0.580450 | − | 0.814296i | \(-0.302877\pi\) | ||||
0.580450 | + | 0.814296i | \(0.302877\pi\) | |||||||
\(908\) | −7.60446 | −0.252363 | ||||||||
\(909\) | 40.9423 | 1.35797 | ||||||||
\(910\) | 33.3306 | 1.10490 | ||||||||
\(911\) | −8.92983 | −0.295858 | −0.147929 | − | 0.988998i | \(-0.547261\pi\) | ||||
−0.147929 | + | 0.988998i | \(0.547261\pi\) | |||||||
\(912\) | 1.74155 | 0.0576685 | ||||||||
\(913\) | −3.07603 | −0.101802 | ||||||||
\(914\) | 9.08976 | 0.300663 | ||||||||
\(915\) | 5.02567 | 0.166144 | ||||||||
\(916\) | −7.83875 | −0.259000 | ||||||||
\(917\) | 27.7744 | 0.917193 | ||||||||
\(918\) | −22.0319 | −0.727160 | ||||||||
\(919\) | 48.3753 | 1.59576 | 0.797878 | − | 0.602819i | \(-0.205956\pi\) | ||||
0.797878 | + | 0.602819i | \(0.205956\pi\) | |||||||
\(920\) | −7.54288 | −0.248681 | ||||||||
\(921\) | −66.0445 | −2.17624 | ||||||||
\(922\) | 2.18805 | 0.0720596 | ||||||||
\(923\) | −19.9184 | −0.655623 | ||||||||
\(924\) | 0.996848 | 0.0327939 | ||||||||
\(925\) | 3.64766 | 0.119934 | ||||||||
\(926\) | −37.8253 | −1.24302 | ||||||||
\(927\) | 74.5125 | 2.44731 | ||||||||
\(928\) | 3.20221 | 0.105118 | ||||||||
\(929\) | −9.45683 | −0.310268 | −0.155134 | − | 0.987893i | \(-0.549581\pi\) | ||||
−0.155134 | + | 0.987893i | \(0.549581\pi\) | |||||||
\(930\) | −37.9884 | −1.24569 | ||||||||
\(931\) | −0.496831 | −0.0162830 | ||||||||
\(932\) | −8.78683 | −0.287822 | ||||||||
\(933\) | 74.6395 | 2.44359 | ||||||||
\(934\) | 23.2798 | 0.761740 | ||||||||
\(935\) | 2.37596 | 0.0777023 | ||||||||
\(936\) | −76.0863 | −2.48696 | ||||||||
\(937\) | 47.8421 | 1.56293 | 0.781466 | − | 0.623948i | \(-0.214472\pi\) | ||||
0.781466 | + | 0.623948i | \(0.214472\pi\) | |||||||
\(938\) | −4.21102 | −0.137495 | ||||||||
\(939\) | 64.4506 | 2.10326 | ||||||||
\(940\) | 0.514993 | 0.0167972 | ||||||||
\(941\) | −40.1070 | −1.30745 | −0.653726 | − | 0.756732i | \(-0.726795\pi\) | ||||
−0.653726 | + | 0.756732i | \(0.726795\pi\) | |||||||
\(942\) | 14.9870 | 0.488302 | ||||||||
\(943\) | −3.14829 | −0.102523 | ||||||||
\(944\) | −19.9822 | −0.650364 | ||||||||
\(945\) | −28.4387 | −0.925111 | ||||||||
\(946\) | 1.29989 | 0.0422630 | ||||||||
\(947\) | 1.28470 | 0.0417471 | 0.0208735 | − | 0.999782i | \(-0.493355\pi\) | ||||
0.0208735 | + | 0.999782i | \(0.493355\pi\) | |||||||
\(948\) | 22.2360 | 0.722190 | ||||||||
\(949\) | −45.4397 | −1.47504 | ||||||||
\(950\) | 0.302753 | 0.00982260 | ||||||||
\(951\) | 79.0460 | 2.56324 | ||||||||
\(952\) | 24.6694 | 0.799541 | ||||||||
\(953\) | −15.8789 | −0.514367 | −0.257184 | − | 0.966363i | \(-0.582795\pi\) | ||||
−0.257184 | + | 0.966363i | \(0.582795\pi\) | |||||||
\(954\) | 38.5317 | 1.24751 | ||||||||
\(955\) | 45.3035 | 1.46599 | ||||||||
\(956\) | 17.7971 | 0.575598 | ||||||||
\(957\) | 0.757721 | 0.0244936 | ||||||||
\(958\) | −28.8250 | −0.931294 | ||||||||
\(959\) | 15.2733 | 0.493202 | ||||||||
\(960\) | 60.2397 | 1.94423 | ||||||||
\(961\) | −9.36360 | −0.302052 | ||||||||
\(962\) | 21.7727 | 0.701979 | ||||||||
\(963\) | −32.8680 | −1.05916 | ||||||||
\(964\) | 8.49093 | 0.273474 | ||||||||
\(965\) | −22.1205 | −0.712083 | ||||||||
\(966\) | −7.45839 | −0.239970 | ||||||||
\(967\) | 2.03647 | 0.0654886 | 0.0327443 | − | 0.999464i | \(-0.489575\pi\) | ||||
0.0327443 | + | 0.999464i | \(0.489575\pi\) | |||||||
\(968\) | 33.6021 | 1.08001 | ||||||||
\(969\) | −2.51444 | −0.0807756 | ||||||||
\(970\) | −33.6752 | −1.08124 | ||||||||
\(971\) | 22.1428 | 0.710598 | 0.355299 | − | 0.934753i | \(-0.384379\pi\) | ||||
0.355299 | + | 0.934753i | \(0.384379\pi\) | |||||||
\(972\) | −9.19074 | −0.294793 | ||||||||
\(973\) | −25.8110 | −0.827463 | ||||||||
\(974\) | −20.0339 | −0.641927 | ||||||||
\(975\) | −14.5312 | −0.465370 | ||||||||
\(976\) | −1.81421 | −0.0580715 | ||||||||
\(977\) | −6.21388 | −0.198800 | −0.0993999 | − | 0.995048i | \(-0.531692\pi\) | ||||
−0.0993999 | + | 0.995048i | \(0.531692\pi\) | |||||||
\(978\) | 28.2116 | 0.902107 | ||||||||
\(979\) | −3.03559 | −0.0970180 | ||||||||
\(980\) | −2.85565 | −0.0912205 | ||||||||
\(981\) | −74.7495 | −2.38657 | ||||||||
\(982\) | 24.7359 | 0.789355 | ||||||||
\(983\) | −14.9800 | −0.477789 | −0.238894 | − | 0.971046i | \(-0.576785\pi\) | ||||
−0.238894 | + | 0.971046i | \(0.576785\pi\) | |||||||
\(984\) | 27.1217 | 0.864609 | ||||||||
\(985\) | −45.3949 | −1.44640 | ||||||||
\(986\) | 4.25656 | 0.135557 | ||||||||
\(987\) | 2.24331 | 0.0714054 | ||||||||
\(988\) | −0.751288 | −0.0239017 | ||||||||
\(989\) | 4.04337 | 0.128572 | ||||||||
\(990\) | 3.82261 | 0.121490 | ||||||||
\(991\) | 32.2880 | 1.02566 | 0.512831 | − | 0.858489i | \(-0.328597\pi\) | ||||
0.512831 | + | 0.858489i | \(0.328597\pi\) | |||||||
\(992\) | −14.8951 | −0.472918 | ||||||||
\(993\) | 63.6177 | 2.01885 | ||||||||
\(994\) | 10.3903 | 0.329560 | ||||||||
\(995\) | 31.6660 | 1.00388 | ||||||||
\(996\) | 18.7107 | 0.592872 | ||||||||
\(997\) | 8.79624 | 0.278580 | 0.139290 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139290 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(998\) | 7.96727 | 0.252199 | ||||||||
\(999\) | −18.5771 | −0.587754 |
(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 | 667.2.a.c.1.8 | ✓ | 13 | |
3.2 | odd | 2 | 6003.2.a.o.1.6 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.c.1.8 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6003.2.a.o.1.6 | 13 | 3.2 | odd | 2 |