Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64605 | −1.87104 | −0.935521 | − | 0.353272i | \(-0.885069\pi\) | ||||
−0.935521 | + | 0.353272i | \(0.885069\pi\) | |||||||
\(3\) | −0.0865598 | −0.0499753 | −0.0249877 | − | 0.999688i | \(-0.507955\pi\) | ||||
−0.0249877 | + | 0.999688i | \(0.507955\pi\) | |||||||
\(4\) | 5.00159 | 2.50079 | ||||||||
\(5\) | −1.46630 | −0.655748 | −0.327874 | − | 0.944721i | \(-0.606332\pi\) | ||||
−0.327874 | + | 0.944721i | \(0.606332\pi\) | |||||||
\(6\) | 0.229042 | 0.0935059 | ||||||||
\(7\) | −4.80741 | −1.81703 | −0.908515 | − | 0.417852i | \(-0.862783\pi\) | ||||
−0.908515 | + | 0.417852i | \(0.862783\pi\) | |||||||
\(8\) | −7.94236 | −2.80805 | ||||||||
\(9\) | −2.99251 | −0.997502 | ||||||||
\(10\) | 3.87990 | 1.22693 | ||||||||
\(11\) | 2.57564 | 0.776585 | 0.388292 | − | 0.921536i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921536i | \(0.373065\pi\) | |||||||
\(12\) | −0.432937 | −0.124978 | ||||||||
\(13\) | 4.36416 | 1.21040 | 0.605200 | − | 0.796074i | \(-0.293093\pi\) | ||||
0.605200 | + | 0.796074i | \(0.293093\pi\) | |||||||
\(14\) | 12.7207 | 3.39974 | ||||||||
\(15\) | 0.126922 | 0.0327712 | ||||||||
\(16\) | 11.0127 | 2.75318 | ||||||||
\(17\) | 5.06362 | 1.22811 | 0.614054 | − | 0.789264i | \(-0.289538\pi\) | ||||
0.614054 | + | 0.789264i | \(0.289538\pi\) | |||||||
\(18\) | 7.91833 | 1.86637 | ||||||||
\(19\) | 3.86716 | 0.887187 | 0.443593 | − | 0.896228i | \(-0.353703\pi\) | ||||
0.443593 | + | 0.896228i | \(0.353703\pi\) | |||||||
\(20\) | −7.33382 | −1.63989 | ||||||||
\(21\) | 0.416129 | 0.0908067 | ||||||||
\(22\) | −6.81528 | −1.45302 | ||||||||
\(23\) | 5.72586 | 1.19392 | 0.596962 | − | 0.802270i | \(-0.296374\pi\) | ||||
0.596962 | + | 0.802270i | \(0.296374\pi\) | |||||||
\(24\) | 0.687489 | 0.140333 | ||||||||
\(25\) | −2.84997 | −0.569994 | ||||||||
\(26\) | −11.5478 | −2.26471 | ||||||||
\(27\) | 0.518710 | 0.0998259 | ||||||||
\(28\) | −24.0447 | −4.54402 | ||||||||
\(29\) | 4.16537 | 0.773490 | 0.386745 | − | 0.922187i | \(-0.373599\pi\) | ||||
0.386745 | + | 0.922187i | \(0.373599\pi\) | |||||||
\(30\) | −0.335843 | −0.0613163 | ||||||||
\(31\) | 1.73342 | 0.311331 | 0.155665 | − | 0.987810i | \(-0.450248\pi\) | ||||
0.155665 | + | 0.987810i | \(0.450248\pi\) | |||||||
\(32\) | −13.2555 | −2.34326 | ||||||||
\(33\) | −0.222947 | −0.0388101 | ||||||||
\(34\) | −13.3986 | −2.29784 | ||||||||
\(35\) | 7.04909 | 1.19151 | ||||||||
\(36\) | −14.9673 | −2.49455 | ||||||||
\(37\) | 6.26985 | 1.03076 | 0.515379 | − | 0.856962i | \(-0.327651\pi\) | ||||
0.515379 | + | 0.856962i | \(0.327651\pi\) | |||||||
\(38\) | −10.2327 | −1.65996 | ||||||||
\(39\) | −0.377761 | −0.0604901 | ||||||||
\(40\) | 11.6459 | 1.84137 | ||||||||
\(41\) | −5.65631 | −0.883367 | −0.441683 | − | 0.897171i | \(-0.645619\pi\) | ||||
−0.441683 | + | 0.897171i | \(0.645619\pi\) | |||||||
\(42\) | −1.10110 | −0.169903 | ||||||||
\(43\) | 3.61517 | 0.551308 | 0.275654 | − | 0.961257i | \(-0.411106\pi\) | ||||
0.275654 | + | 0.961257i | \(0.411106\pi\) | |||||||
\(44\) | 12.8823 | 1.94208 | ||||||||
\(45\) | 4.38791 | 0.654110 | ||||||||
\(46\) | −15.1509 | −2.23388 | ||||||||
\(47\) | −3.93319 | −0.573715 | −0.286858 | − | 0.957973i | \(-0.592611\pi\) | ||||
−0.286858 | + | 0.957973i | \(0.592611\pi\) | |||||||
\(48\) | −0.953259 | −0.137591 | ||||||||
\(49\) | 16.1112 | 2.30160 | ||||||||
\(50\) | 7.54117 | 1.06648 | ||||||||
\(51\) | −0.438306 | −0.0613751 | ||||||||
\(52\) | 21.8277 | 3.02696 | ||||||||
\(53\) | −0.0159586 | −0.00219208 | −0.00109604 | − | 0.999999i | \(-0.500349\pi\) | ||||
−0.00109604 | + | 0.999999i | \(0.500349\pi\) | |||||||
\(54\) | −1.37253 | −0.186778 | ||||||||
\(55\) | −3.77666 | −0.509244 | ||||||||
\(56\) | 38.1822 | 5.10231 | ||||||||
\(57\) | −0.334741 | −0.0443375 | ||||||||
\(58\) | −11.0218 | −1.44723 | ||||||||
\(59\) | 9.52594 | 1.24017 | 0.620086 | − | 0.784534i | \(-0.287098\pi\) | ||||
0.620086 | + | 0.784534i | \(0.287098\pi\) | |||||||
\(60\) | 0.634814 | 0.0819541 | ||||||||
\(61\) | −5.30684 | −0.679471 | −0.339736 | − | 0.940521i | \(-0.610338\pi\) | ||||
−0.339736 | + | 0.940521i | \(0.610338\pi\) | |||||||
\(62\) | −4.58671 | −0.582513 | ||||||||
\(63\) | 14.3862 | 1.81249 | ||||||||
\(64\) | 13.0493 | 1.63116 | ||||||||
\(65\) | −6.39915 | −0.793717 | ||||||||
\(66\) | 0.589929 | 0.0726153 | ||||||||
\(67\) | 6.24632 | 0.763109 | 0.381555 | − | 0.924346i | \(-0.375389\pi\) | ||||
0.381555 | + | 0.924346i | \(0.375389\pi\) | |||||||
\(68\) | 25.3261 | 3.07125 | ||||||||
\(69\) | −0.495629 | −0.0596667 | ||||||||
\(70\) | −18.6523 | −2.22937 | ||||||||
\(71\) | 3.50484 | 0.415948 | 0.207974 | − | 0.978134i | \(-0.433313\pi\) | ||||
0.207974 | + | 0.978134i | \(0.433313\pi\) | |||||||
\(72\) | 23.7676 | 2.80104 | ||||||||
\(73\) | 7.45362 | 0.872381 | 0.436190 | − | 0.899854i | \(-0.356327\pi\) | ||||
0.436190 | + | 0.899854i | \(0.356327\pi\) | |||||||
\(74\) | −16.5904 | −1.92859 | ||||||||
\(75\) | 0.246693 | 0.0284857 | ||||||||
\(76\) | 19.3419 | 2.21867 | ||||||||
\(77\) | −12.3822 | −1.41108 | ||||||||
\(78\) | 0.999574 | 0.113179 | ||||||||
\(79\) | 5.44143 | 0.612209 | 0.306104 | − | 0.951998i | \(-0.400974\pi\) | ||||
0.306104 | + | 0.951998i | \(0.400974\pi\) | |||||||
\(80\) | −16.1479 | −1.80539 | ||||||||
\(81\) | 8.93262 | 0.992514 | ||||||||
\(82\) | 14.9669 | 1.65282 | ||||||||
\(83\) | −15.8453 | −1.73924 | −0.869621 | − | 0.493720i | \(-0.835637\pi\) | ||||
−0.869621 | + | 0.493720i | \(0.835637\pi\) | |||||||
\(84\) | 2.08130 | 0.227089 | ||||||||
\(85\) | −7.42477 | −0.805330 | ||||||||
\(86\) | −9.56593 | −1.03152 | ||||||||
\(87\) | −0.360554 | −0.0386554 | ||||||||
\(88\) | −20.4567 | −2.18069 | ||||||||
\(89\) | 4.26134 | 0.451701 | 0.225851 | − | 0.974162i | \(-0.427484\pi\) | ||||
0.225851 | + | 0.974162i | \(0.427484\pi\) | |||||||
\(90\) | −11.6106 | −1.22387 | ||||||||
\(91\) | −20.9803 | −2.19933 | ||||||||
\(92\) | 28.6384 | 2.98576 | ||||||||
\(93\) | −0.150044 | −0.0155589 | ||||||||
\(94\) | 10.4074 | 1.07344 | ||||||||
\(95\) | −5.67041 | −0.581771 | ||||||||
\(96\) | 1.14739 | 0.117105 | ||||||||
\(97\) | −9.83726 | −0.998822 | −0.499411 | − | 0.866365i | \(-0.666450\pi\) | ||||
−0.499411 | + | 0.866365i | \(0.666450\pi\) | |||||||
\(98\) | −42.6310 | −4.30638 | ||||||||
\(99\) | −7.70762 | −0.774645 | ||||||||
\(100\) | −14.2544 | −1.42544 | ||||||||
\(101\) | 3.82878 | 0.380977 | 0.190489 | − | 0.981689i | \(-0.438993\pi\) | ||||
0.190489 | + | 0.981689i | \(0.438993\pi\) | |||||||
\(102\) | 1.15978 | 0.114835 | ||||||||
\(103\) | −14.2637 | −1.40544 | −0.702720 | − | 0.711467i | \(-0.748031\pi\) | ||||
−0.702720 | + | 0.711467i | \(0.748031\pi\) | |||||||
\(104\) | −34.6617 | −3.39886 | ||||||||
\(105\) | −0.610168 | −0.0595463 | ||||||||
\(106\) | 0.0422272 | 0.00410147 | ||||||||
\(107\) | 3.05407 | 0.295249 | 0.147624 | − | 0.989044i | \(-0.452837\pi\) | ||||
0.147624 | + | 0.989044i | \(0.452837\pi\) | |||||||
\(108\) | 2.59438 | 0.249644 | ||||||||
\(109\) | 3.96121 | 0.379415 | 0.189707 | − | 0.981841i | \(-0.439246\pi\) | ||||
0.189707 | + | 0.981841i | \(0.439246\pi\) | |||||||
\(110\) | 9.99323 | 0.952817 | ||||||||
\(111\) | −0.542718 | −0.0515125 | ||||||||
\(112\) | −52.9426 | −5.00261 | ||||||||
\(113\) | −6.37308 | −0.599529 | −0.299765 | − | 0.954013i | \(-0.596908\pi\) | ||||
−0.299765 | + | 0.954013i | \(0.596908\pi\) | |||||||
\(114\) | 0.885741 | 0.0829572 | ||||||||
\(115\) | −8.39581 | −0.782913 | ||||||||
\(116\) | 20.8335 | 1.93434 | ||||||||
\(117\) | −13.0598 | −1.20738 | ||||||||
\(118\) | −25.2061 | −2.32041 | ||||||||
\(119\) | −24.3429 | −2.23151 | ||||||||
\(120\) | −1.00806 | −0.0920232 | ||||||||
\(121\) | −4.36608 | −0.396916 | ||||||||
\(122\) | 14.0422 | 1.27132 | ||||||||
\(123\) | 0.489609 | 0.0441465 | ||||||||
\(124\) | 8.66984 | 0.778575 | ||||||||
\(125\) | 11.5104 | 1.02952 | ||||||||
\(126\) | −38.0667 | −3.39125 | ||||||||
\(127\) | −8.99010 | −0.797743 | −0.398871 | − | 0.917007i | \(-0.630598\pi\) | ||||
−0.398871 | + | 0.917007i | \(0.630598\pi\) | |||||||
\(128\) | −8.01812 | −0.708708 | ||||||||
\(129\) | −0.312928 | −0.0275518 | ||||||||
\(130\) | 16.9325 | 1.48508 | ||||||||
\(131\) | −0.402871 | −0.0351990 | −0.0175995 | − | 0.999845i | \(-0.505602\pi\) | ||||
−0.0175995 | + | 0.999845i | \(0.505602\pi\) | |||||||
\(132\) | −1.11509 | −0.0970561 | ||||||||
\(133\) | −18.5910 | −1.61205 | ||||||||
\(134\) | −16.5281 | −1.42781 | ||||||||
\(135\) | −0.760584 | −0.0654606 | ||||||||
\(136\) | −40.2171 | −3.44859 | ||||||||
\(137\) | 7.30938 | 0.624482 | 0.312241 | − | 0.950003i | \(-0.398920\pi\) | ||||
0.312241 | + | 0.950003i | \(0.398920\pi\) | |||||||
\(138\) | 1.31146 | 0.111639 | ||||||||
\(139\) | 5.86279 | 0.497276 | 0.248638 | − | 0.968597i | \(-0.420017\pi\) | ||||
0.248638 | + | 0.968597i | \(0.420017\pi\) | |||||||
\(140\) | 35.2567 | 2.97973 | ||||||||
\(141\) | 0.340456 | 0.0286716 | ||||||||
\(142\) | −9.27398 | −0.778255 | ||||||||
\(143\) | 11.2405 | 0.939978 | ||||||||
\(144\) | −32.9556 | −2.74630 | ||||||||
\(145\) | −6.10768 | −0.507215 | ||||||||
\(146\) | −19.7227 | −1.63226 | ||||||||
\(147\) | −1.39458 | −0.115023 | ||||||||
\(148\) | 31.3592 | 2.57771 | ||||||||
\(149\) | 20.4152 | 1.67248 | 0.836241 | − | 0.548362i | \(-0.184749\pi\) | ||||
0.836241 | + | 0.548362i | \(0.184749\pi\) | |||||||
\(150\) | −0.652762 | −0.0532978 | ||||||||
\(151\) | −14.0415 | −1.14268 | −0.571342 | − | 0.820712i | \(-0.693577\pi\) | ||||
−0.571342 | + | 0.820712i | \(0.693577\pi\) | |||||||
\(152\) | −30.7144 | −2.49126 | ||||||||
\(153\) | −15.1529 | −1.22504 | ||||||||
\(154\) | 32.7638 | 2.64018 | ||||||||
\(155\) | −2.54171 | −0.204155 | ||||||||
\(156\) | −1.88940 | −0.151273 | ||||||||
\(157\) | −15.8888 | −1.26806 | −0.634031 | − | 0.773308i | \(-0.718601\pi\) | ||||
−0.634031 | + | 0.773308i | \(0.718601\pi\) | |||||||
\(158\) | −14.3983 | −1.14547 | ||||||||
\(159\) | 0.00138137 | 0.000109550 0 | ||||||||
\(160\) | 19.4365 | 1.53659 | ||||||||
\(161\) | −27.5265 | −2.16940 | ||||||||
\(162\) | −23.6362 | −1.85703 | ||||||||
\(163\) | 3.73850 | 0.292822 | 0.146411 | − | 0.989224i | \(-0.453228\pi\) | ||||
0.146411 | + | 0.989224i | \(0.453228\pi\) | |||||||
\(164\) | −28.2905 | −2.20912 | ||||||||
\(165\) | 0.326907 | 0.0254496 | ||||||||
\(166\) | 41.9274 | 3.25419 | ||||||||
\(167\) | 2.35594 | 0.182308 | 0.0911541 | − | 0.995837i | \(-0.470944\pi\) | ||||
0.0911541 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(168\) | −3.30504 | −0.254990 | ||||||||
\(169\) | 6.04586 | 0.465066 | ||||||||
\(170\) | 19.6463 | 1.50680 | ||||||||
\(171\) | −11.5725 | −0.884971 | ||||||||
\(172\) | 18.0816 | 1.37871 | ||||||||
\(173\) | 1.97358 | 0.150048 | 0.0750242 | − | 0.997182i | \(-0.476097\pi\) | ||||
0.0750242 | + | 0.997182i | \(0.476097\pi\) | |||||||
\(174\) | 0.954044 | 0.0723259 | ||||||||
\(175\) | 13.7010 | 1.03570 | ||||||||
\(176\) | 28.3648 | 2.13808 | ||||||||
\(177\) | −0.824564 | −0.0619780 | ||||||||
\(178\) | −11.2757 | −0.845152 | ||||||||
\(179\) | 6.11912 | 0.457365 | 0.228682 | − | 0.973501i | \(-0.426558\pi\) | ||||
0.228682 | + | 0.973501i | \(0.426558\pi\) | |||||||
\(180\) | 21.9465 | 1.63580 | ||||||||
\(181\) | −14.0159 | −1.04180 | −0.520898 | − | 0.853619i | \(-0.674403\pi\) | ||||
−0.520898 | + | 0.853619i | \(0.674403\pi\) | |||||||
\(182\) | 55.5149 | 4.11504 | ||||||||
\(183\) | 0.459359 | 0.0339568 | ||||||||
\(184\) | −45.4768 | −3.35260 | ||||||||
\(185\) | −9.19347 | −0.675918 | ||||||||
\(186\) | 0.397025 | 0.0291113 | ||||||||
\(187\) | 13.0421 | 0.953730 | ||||||||
\(188\) | −19.6722 | −1.43474 | ||||||||
\(189\) | −2.49365 | −0.181387 | ||||||||
\(190\) | 15.0042 | 1.08852 | ||||||||
\(191\) | 3.23956 | 0.234406 | 0.117203 | − | 0.993108i | \(-0.462607\pi\) | ||||
0.117203 | + | 0.993108i | \(0.462607\pi\) | |||||||
\(192\) | −1.12954 | −0.0815179 | ||||||||
\(193\) | −19.8896 | −1.43168 | −0.715842 | − | 0.698262i | \(-0.753957\pi\) | ||||
−0.715842 | + | 0.698262i | \(0.753957\pi\) | |||||||
\(194\) | 26.0299 | 1.86884 | ||||||||
\(195\) | 0.553909 | 0.0396663 | ||||||||
\(196\) | 80.5815 | 5.75582 | ||||||||
\(197\) | 12.2142 | 0.870224 | 0.435112 | − | 0.900376i | \(-0.356709\pi\) | ||||
0.435112 | + | 0.900376i | \(0.356709\pi\) | |||||||
\(198\) | 20.3948 | 1.44939 | ||||||||
\(199\) | 25.5372 | 1.81029 | 0.905143 | − | 0.425108i | \(-0.139764\pi\) | ||||
0.905143 | + | 0.425108i | \(0.139764\pi\) | |||||||
\(200\) | 22.6355 | 1.60057 | ||||||||
\(201\) | −0.540680 | −0.0381367 | ||||||||
\(202\) | −10.1311 | −0.712824 | ||||||||
\(203\) | −20.0247 | −1.40546 | ||||||||
\(204\) | −2.19223 | −0.153487 | ||||||||
\(205\) | 8.29383 | 0.579266 | ||||||||
\(206\) | 37.7424 | 2.62964 | ||||||||
\(207\) | −17.1347 | −1.19094 | ||||||||
\(208\) | 48.0612 | 3.33245 | ||||||||
\(209\) | 9.96041 | 0.688976 | ||||||||
\(210\) | 1.61454 | 0.111414 | ||||||||
\(211\) | 11.1326 | 0.766398 | 0.383199 | − | 0.923666i | \(-0.374822\pi\) | ||||
0.383199 | + | 0.923666i | \(0.374822\pi\) | |||||||
\(212\) | −0.0798183 | −0.00548194 | ||||||||
\(213\) | −0.303378 | −0.0207871 | ||||||||
\(214\) | −8.08124 | −0.552422 | ||||||||
\(215\) | −5.30092 | −0.361519 | ||||||||
\(216\) | −4.11978 | −0.280316 | ||||||||
\(217\) | −8.33325 | −0.565698 | ||||||||
\(218\) | −10.4816 | −0.709901 | ||||||||
\(219\) | −0.645184 | −0.0435975 | ||||||||
\(220\) | −18.8893 | −1.27351 | ||||||||
\(221\) | 22.0984 | 1.48650 | ||||||||
\(222\) | 1.43606 | 0.0963819 | ||||||||
\(223\) | −16.3468 | −1.09466 | −0.547332 | − | 0.836915i | \(-0.684357\pi\) | ||||
−0.547332 | + | 0.836915i | \(0.684357\pi\) | |||||||
\(224\) | 63.7246 | 4.25778 | ||||||||
\(225\) | 8.52856 | 0.568571 | ||||||||
\(226\) | 16.8635 | 1.12174 | ||||||||
\(227\) | −28.6151 | −1.89925 | −0.949627 | − | 0.313383i | \(-0.898538\pi\) | ||||
−0.949627 | + | 0.313383i | \(0.898538\pi\) | |||||||
\(228\) | −1.67423 | −0.110879 | ||||||||
\(229\) | −24.0500 | −1.58927 | −0.794635 | − | 0.607088i | \(-0.792338\pi\) | ||||
−0.794635 | + | 0.607088i | \(0.792338\pi\) | |||||||
\(230\) | 22.2157 | 1.46486 | ||||||||
\(231\) | 1.07180 | 0.0705191 | ||||||||
\(232\) | −33.0829 | −2.17200 | ||||||||
\(233\) | −10.9982 | −0.720517 | −0.360259 | − | 0.932852i | \(-0.617312\pi\) | ||||
−0.360259 | + | 0.932852i | \(0.617312\pi\) | |||||||
\(234\) | 34.5568 | 2.25905 | ||||||||
\(235\) | 5.76723 | 0.376213 | ||||||||
\(236\) | 47.6449 | 3.10142 | ||||||||
\(237\) | −0.471009 | −0.0305953 | ||||||||
\(238\) | 64.4125 | 4.17525 | ||||||||
\(239\) | 0.803309 | 0.0519617 | 0.0259809 | − | 0.999662i | \(-0.491729\pi\) | ||||
0.0259809 | + | 0.999662i | \(0.491729\pi\) | |||||||
\(240\) | 1.39776 | 0.0902251 | ||||||||
\(241\) | 15.1730 | 0.977376 | 0.488688 | − | 0.872459i | \(-0.337476\pi\) | ||||
0.488688 | + | 0.872459i | \(0.337476\pi\) | |||||||
\(242\) | 11.5529 | 0.742646 | ||||||||
\(243\) | −2.32934 | −0.149427 | ||||||||
\(244\) | −26.5426 | −1.69922 | ||||||||
\(245\) | −23.6238 | −1.50927 | ||||||||
\(246\) | −1.29553 | −0.0826000 | ||||||||
\(247\) | 16.8769 | 1.07385 | ||||||||
\(248\) | −13.7674 | −0.874232 | ||||||||
\(249\) | 1.37156 | 0.0869192 | ||||||||
\(250\) | −30.4571 | −1.92628 | ||||||||
\(251\) | 15.3394 | 0.968216 | 0.484108 | − | 0.875008i | \(-0.339144\pi\) | ||||
0.484108 | + | 0.875008i | \(0.339144\pi\) | |||||||
\(252\) | 71.9539 | 4.53267 | ||||||||
\(253\) | 14.7477 | 0.927183 | ||||||||
\(254\) | 23.7883 | 1.49261 | ||||||||
\(255\) | 0.642687 | 0.0402466 | ||||||||
\(256\) | −4.88223 | −0.305140 | ||||||||
\(257\) | 9.78914 | 0.610630 | 0.305315 | − | 0.952251i | \(-0.401238\pi\) | ||||
0.305315 | + | 0.952251i | \(0.401238\pi\) | |||||||
\(258\) | 0.828025 | 0.0515506 | ||||||||
\(259\) | −30.1418 | −1.87292 | ||||||||
\(260\) | −32.0059 | −1.98492 | ||||||||
\(261\) | −12.4649 | −0.771558 | ||||||||
\(262\) | 1.06602 | 0.0658588 | ||||||||
\(263\) | 21.6338 | 1.33399 | 0.666997 | − | 0.745060i | \(-0.267579\pi\) | ||||
0.666997 | + | 0.745060i | \(0.267579\pi\) | |||||||
\(264\) | 1.77073 | 0.108981 | ||||||||
\(265\) | 0.0234000 | 0.00143745 | ||||||||
\(266\) | 49.1928 | 3.01620 | ||||||||
\(267\) | −0.368861 | −0.0225739 | ||||||||
\(268\) | 31.2415 | 1.90838 | ||||||||
\(269\) | 30.2003 | 1.84135 | 0.920674 | − | 0.390333i | \(-0.127640\pi\) | ||||
0.920674 | + | 0.390333i | \(0.127640\pi\) | |||||||
\(270\) | 2.01254 | 0.122480 | ||||||||
\(271\) | −11.1520 | −0.677434 | −0.338717 | − | 0.940888i | \(-0.609993\pi\) | ||||
−0.338717 | + | 0.940888i | \(0.609993\pi\) | |||||||
\(272\) | 55.7642 | 3.38120 | ||||||||
\(273\) | 1.81605 | 0.109912 | ||||||||
\(274\) | −19.3410 | −1.16843 | ||||||||
\(275\) | −7.34050 | −0.442649 | ||||||||
\(276\) | −2.47893 | −0.149214 | ||||||||
\(277\) | 12.5708 | 0.755307 | 0.377653 | − | 0.925947i | \(-0.376731\pi\) | ||||
0.377653 | + | 0.925947i | \(0.376731\pi\) | |||||||
\(278\) | −15.5133 | −0.930423 | ||||||||
\(279\) | −5.18726 | −0.310553 | ||||||||
\(280\) | −55.9864 | −3.34583 | ||||||||
\(281\) | 7.10484 | 0.423839 | 0.211920 | − | 0.977287i | \(-0.432028\pi\) | ||||
0.211920 | + | 0.977287i | \(0.432028\pi\) | |||||||
\(282\) | −0.900865 | −0.0536458 | ||||||||
\(283\) | 13.8382 | 0.822594 | 0.411297 | − | 0.911501i | \(-0.365076\pi\) | ||||
0.411297 | + | 0.911501i | \(0.365076\pi\) | |||||||
\(284\) | 17.5298 | 1.04020 | ||||||||
\(285\) | 0.490829 | 0.0290742 | ||||||||
\(286\) | −29.7429 | −1.75874 | ||||||||
\(287\) | 27.1922 | 1.60510 | ||||||||
\(288\) | 39.6672 | 2.33741 | ||||||||
\(289\) | 8.64024 | 0.508249 | ||||||||
\(290\) | 16.1612 | 0.949020 | ||||||||
\(291\) | 0.851511 | 0.0499165 | ||||||||
\(292\) | 37.2800 | 2.18164 | ||||||||
\(293\) | −18.9420 | −1.10660 | −0.553301 | − | 0.832981i | \(-0.686632\pi\) | ||||
−0.553301 | + | 0.832981i | \(0.686632\pi\) | |||||||
\(294\) | 3.69013 | 0.215213 | ||||||||
\(295\) | −13.9679 | −0.813241 | ||||||||
\(296\) | −49.7974 | −2.89442 | ||||||||
\(297\) | 1.33601 | 0.0775232 | ||||||||
\(298\) | −54.0198 | −3.12928 | ||||||||
\(299\) | 24.9885 | 1.44512 | ||||||||
\(300\) | 1.23386 | 0.0712368 | ||||||||
\(301\) | −17.3796 | −1.00174 | ||||||||
\(302\) | 37.1546 | 2.13801 | ||||||||
\(303\) | −0.331418 | −0.0190395 | ||||||||
\(304\) | 42.5879 | 2.44258 | ||||||||
\(305\) | 7.78140 | 0.445562 | ||||||||
\(306\) | 40.0954 | 2.29210 | ||||||||
\(307\) | −16.6913 | −0.952624 | −0.476312 | − | 0.879276i | \(-0.658027\pi\) | ||||
−0.476312 | + | 0.879276i | \(0.658027\pi\) | |||||||
\(308\) | −61.9305 | −3.52882 | ||||||||
\(309\) | 1.23466 | 0.0702373 | ||||||||
\(310\) | 6.72548 | 0.381982 | ||||||||
\(311\) | 19.5173 | 1.10673 | 0.553364 | − | 0.832940i | \(-0.313344\pi\) | ||||
0.553364 | + | 0.832940i | \(0.313344\pi\) | |||||||
\(312\) | 3.00031 | 0.169859 | ||||||||
\(313\) | −16.3993 | −0.926946 | −0.463473 | − | 0.886111i | \(-0.653397\pi\) | ||||
−0.463473 | + | 0.886111i | \(0.653397\pi\) | |||||||
\(314\) | 42.0425 | 2.37260 | ||||||||
\(315\) | −21.0945 | −1.18854 | ||||||||
\(316\) | 27.2158 | 1.53101 | ||||||||
\(317\) | 4.16664 | 0.234022 | 0.117011 | − | 0.993131i | \(-0.462669\pi\) | ||||
0.117011 | + | 0.993131i | \(0.462669\pi\) | |||||||
\(318\) | −0.00365518 | −0.000204972 0 | ||||||||
\(319\) | 10.7285 | 0.600681 | ||||||||
\(320\) | −19.1342 | −1.06963 | ||||||||
\(321\) | −0.264360 | −0.0147551 | ||||||||
\(322\) | 72.8366 | 4.05903 | ||||||||
\(323\) | 19.5818 | 1.08956 | ||||||||
\(324\) | 44.6773 | 2.48207 | ||||||||
\(325\) | −12.4377 | −0.689921 | ||||||||
\(326\) | −9.89225 | −0.547881 | ||||||||
\(327\) | −0.342881 | −0.0189614 | ||||||||
\(328\) | 44.9244 | 2.48054 | ||||||||
\(329\) | 18.9085 | 1.04246 | ||||||||
\(330\) | −0.865012 | −0.0476173 | ||||||||
\(331\) | 22.3730 | 1.22973 | 0.614865 | − | 0.788632i | \(-0.289210\pi\) | ||||
0.614865 | + | 0.788632i | \(0.289210\pi\) | |||||||
\(332\) | −79.2514 | −4.34949 | ||||||||
\(333\) | −18.7626 | −1.02818 | ||||||||
\(334\) | −6.23394 | −0.341106 | ||||||||
\(335\) | −9.15896 | −0.500408 | ||||||||
\(336\) | 4.58271 | 0.250007 | ||||||||
\(337\) | 20.6946 | 1.12731 | 0.563655 | − | 0.826011i | \(-0.309395\pi\) | ||||
0.563655 | + | 0.826011i | \(0.309395\pi\) | |||||||
\(338\) | −15.9977 | −0.870158 | ||||||||
\(339\) | 0.551653 | 0.0299617 | ||||||||
\(340\) | −37.1357 | −2.01396 | ||||||||
\(341\) | 4.46466 | 0.241775 | ||||||||
\(342\) | 30.6214 | 1.65582 | ||||||||
\(343\) | −43.8012 | −2.36504 | ||||||||
\(344\) | −28.7130 | −1.54810 | ||||||||
\(345\) | 0.726740 | 0.0391264 | ||||||||
\(346\) | −5.22219 | −0.280747 | ||||||||
\(347\) | 11.9336 | 0.640630 | 0.320315 | − | 0.947311i | \(-0.396211\pi\) | ||||
0.320315 | + | 0.947311i | \(0.396211\pi\) | |||||||
\(348\) | −1.80334 | −0.0966693 | ||||||||
\(349\) | −3.21568 | −0.172131 | −0.0860657 | − | 0.996289i | \(-0.527429\pi\) | ||||
−0.0860657 | + | 0.996289i | \(0.527429\pi\) | |||||||
\(350\) | −36.2535 | −1.93783 | ||||||||
\(351\) | 2.26373 | 0.120829 | ||||||||
\(352\) | −34.1414 | −1.81974 | ||||||||
\(353\) | −16.7078 | −0.889268 | −0.444634 | − | 0.895712i | \(-0.646666\pi\) | ||||
−0.444634 | + | 0.895712i | \(0.646666\pi\) | |||||||
\(354\) | 2.18184 | 0.115963 | ||||||||
\(355\) | −5.13913 | −0.272757 | ||||||||
\(356\) | 21.3135 | 1.12961 | ||||||||
\(357\) | 2.10712 | 0.111520 | ||||||||
\(358\) | −16.1915 | −0.855748 | ||||||||
\(359\) | −15.6914 | −0.828160 | −0.414080 | − | 0.910241i | \(-0.635897\pi\) | ||||
−0.414080 | + | 0.910241i | \(0.635897\pi\) | |||||||
\(360\) | −34.8503 | −1.83677 | ||||||||
\(361\) | −4.04509 | −0.212899 | ||||||||
\(362\) | 37.0869 | 1.94924 | ||||||||
\(363\) | 0.377927 | 0.0198360 | ||||||||
\(364\) | −104.935 | −5.50008 | ||||||||
\(365\) | −10.9292 | −0.572062 | ||||||||
\(366\) | −1.21549 | −0.0635346 | ||||||||
\(367\) | −17.2242 | −0.899094 | −0.449547 | − | 0.893257i | \(-0.648415\pi\) | ||||
−0.449547 | + | 0.893257i | \(0.648415\pi\) | |||||||
\(368\) | 63.0572 | 3.28709 | ||||||||
\(369\) | 16.9265 | 0.881160 | ||||||||
\(370\) | 24.3264 | 1.26467 | ||||||||
\(371\) | 0.0767194 | 0.00398307 | ||||||||
\(372\) | −0.750460 | −0.0389095 | ||||||||
\(373\) | 19.2770 | 0.998127 | 0.499063 | − | 0.866565i | \(-0.333677\pi\) | ||||
0.499063 | + | 0.866565i | \(0.333677\pi\) | |||||||
\(374\) | −34.5100 | −1.78447 | ||||||||
\(375\) | −0.996338 | −0.0514507 | ||||||||
\(376\) | 31.2388 | 1.61102 | ||||||||
\(377\) | 18.1783 | 0.936232 | ||||||||
\(378\) | 6.59834 | 0.339382 | ||||||||
\(379\) | −18.8645 | −0.969004 | −0.484502 | − | 0.874790i | \(-0.660999\pi\) | ||||
−0.484502 | + | 0.874790i | \(0.660999\pi\) | |||||||
\(380\) | −28.3610 | −1.45489 | ||||||||
\(381\) | 0.778182 | 0.0398675 | ||||||||
\(382\) | −8.57204 | −0.438584 | ||||||||
\(383\) | 34.7702 | 1.77667 | 0.888337 | − | 0.459192i | \(-0.151861\pi\) | ||||
0.888337 | + | 0.459192i | \(0.151861\pi\) | |||||||
\(384\) | 0.694047 | 0.0354179 | ||||||||
\(385\) | 18.1559 | 0.925312 | ||||||||
\(386\) | 52.6289 | 2.67874 | ||||||||
\(387\) | −10.8184 | −0.549931 | ||||||||
\(388\) | −49.2019 | −2.49785 | ||||||||
\(389\) | 32.2435 | 1.63481 | 0.817406 | − | 0.576062i | \(-0.195411\pi\) | ||||
0.817406 | + | 0.576062i | \(0.195411\pi\) | |||||||
\(390\) | −1.46567 | −0.0742172 | ||||||||
\(391\) | 28.9936 | 1.46627 | ||||||||
\(392\) | −127.961 | −6.46300 | ||||||||
\(393\) | 0.0348724 | 0.00175908 | ||||||||
\(394\) | −32.3194 | −1.62823 | ||||||||
\(395\) | −7.97876 | −0.401455 | ||||||||
\(396\) | −38.5504 | −1.93723 | ||||||||
\(397\) | −9.49168 | −0.476374 | −0.238187 | − | 0.971219i | \(-0.576553\pi\) | ||||
−0.238187 | + | 0.971219i | \(0.576553\pi\) | |||||||
\(398\) | −67.5728 | −3.38712 | ||||||||
\(399\) | 1.60923 | 0.0805625 | ||||||||
\(400\) | −31.3859 | −1.56930 | ||||||||
\(401\) | 5.90272 | 0.294768 | 0.147384 | − | 0.989079i | \(-0.452915\pi\) | ||||
0.147384 | + | 0.989079i | \(0.452915\pi\) | |||||||
\(402\) | 1.43067 | 0.0713552 | ||||||||
\(403\) | 7.56490 | 0.376835 | ||||||||
\(404\) | 19.1500 | 0.952746 | ||||||||
\(405\) | −13.0979 | −0.650839 | ||||||||
\(406\) | 52.9863 | 2.62966 | ||||||||
\(407\) | 16.1489 | 0.800471 | ||||||||
\(408\) | 3.48118 | 0.172344 | ||||||||
\(409\) | −24.3422 | −1.20365 | −0.601823 | − | 0.798629i | \(-0.705559\pi\) | ||||
−0.601823 | + | 0.798629i | \(0.705559\pi\) | |||||||
\(410\) | −21.9459 | −1.08383 | ||||||||
\(411\) | −0.632699 | −0.0312087 | ||||||||
\(412\) | −71.3409 | −3.51472 | ||||||||
\(413\) | −45.7951 | −2.25343 | ||||||||
\(414\) | 45.3392 | 2.22830 | ||||||||
\(415\) | 23.2339 | 1.14051 | ||||||||
\(416\) | −57.8491 | −2.83628 | ||||||||
\(417\) | −0.507482 | −0.0248515 | ||||||||
\(418\) | −26.3558 | −1.28910 | ||||||||
\(419\) | −26.8175 | −1.31012 | −0.655060 | − | 0.755577i | \(-0.727357\pi\) | ||||
−0.655060 | + | 0.755577i | \(0.727357\pi\) | |||||||
\(420\) | −3.05181 | −0.148913 | ||||||||
\(421\) | 0.355718 | 0.0173366 | 0.00866831 | − | 0.999962i | \(-0.497241\pi\) | ||||
0.00866831 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(422\) | −29.4574 | −1.43396 | ||||||||
\(423\) | 11.7701 | 0.572282 | ||||||||
\(424\) | 0.126749 | 0.00615547 | ||||||||
\(425\) | −14.4312 | −0.700015 | ||||||||
\(426\) | 0.802754 | 0.0388936 | ||||||||
\(427\) | 25.5121 | 1.23462 | ||||||||
\(428\) | 15.2752 | 0.738356 | ||||||||
\(429\) | −0.972975 | −0.0469757 | ||||||||
\(430\) | 14.0265 | 0.676418 | ||||||||
\(431\) | 18.4008 | 0.886336 | 0.443168 | − | 0.896439i | \(-0.353855\pi\) | ||||
0.443168 | + | 0.896439i | \(0.353855\pi\) | |||||||
\(432\) | 5.71241 | 0.274838 | ||||||||
\(433\) | 2.81257 | 0.135164 | 0.0675818 | − | 0.997714i | \(-0.478472\pi\) | ||||
0.0675818 | + | 0.997714i | \(0.478472\pi\) | |||||||
\(434\) | 22.0502 | 1.05844 | ||||||||
\(435\) | 0.528679 | 0.0253482 | ||||||||
\(436\) | 19.8123 | 0.948839 | ||||||||
\(437\) | 22.1428 | 1.05923 | ||||||||
\(438\) | 1.70719 | 0.0815727 | ||||||||
\(439\) | 16.8499 | 0.804201 | 0.402101 | − | 0.915595i | \(-0.368280\pi\) | ||||
0.402101 | + | 0.915595i | \(0.368280\pi\) | |||||||
\(440\) | 29.9956 | 1.42998 | ||||||||
\(441\) | −48.2128 | −2.29585 | ||||||||
\(442\) | −58.4736 | −2.78130 | ||||||||
\(443\) | −40.9646 | −1.94629 | −0.973144 | − | 0.230197i | \(-0.926063\pi\) | ||||
−0.973144 | + | 0.230197i | \(0.926063\pi\) | |||||||
\(444\) | −2.71445 | −0.128822 | ||||||||
\(445\) | −6.24839 | −0.296202 | ||||||||
\(446\) | 43.2545 | 2.04816 | ||||||||
\(447\) | −1.76714 | −0.0835828 | ||||||||
\(448\) | −62.7333 | −2.96387 | ||||||||
\(449\) | 25.8064 | 1.21788 | 0.608940 | − | 0.793216i | \(-0.291595\pi\) | ||||
0.608940 | + | 0.793216i | \(0.291595\pi\) | |||||||
\(450\) | −22.5670 | −1.06382 | ||||||||
\(451\) | −14.5686 | −0.686009 | ||||||||
\(452\) | −31.8756 | −1.49930 | ||||||||
\(453\) | 1.21543 | 0.0571060 | ||||||||
\(454\) | 75.7171 | 3.55358 | ||||||||
\(455\) | 30.7633 | 1.44221 | ||||||||
\(456\) | 2.65863 | 0.124502 | ||||||||
\(457\) | 25.9497 | 1.21388 | 0.606939 | − | 0.794748i | \(-0.292397\pi\) | ||||
0.606939 | + | 0.794748i | \(0.292397\pi\) | |||||||
\(458\) | 63.6376 | 2.97359 | ||||||||
\(459\) | 2.62655 | 0.122597 | ||||||||
\(460\) | −41.9924 | −1.95791 | ||||||||
\(461\) | −33.0910 | −1.54120 | −0.770602 | − | 0.637317i | \(-0.780044\pi\) | ||||
−0.770602 | + | 0.637317i | \(0.780044\pi\) | |||||||
\(462\) | −2.83603 | −0.131944 | ||||||||
\(463\) | −0.598540 | −0.0278165 | −0.0139082 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139082 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(464\) | 45.8721 | 2.12956 | ||||||||
\(465\) | 0.220010 | 0.0102027 | ||||||||
\(466\) | 29.1018 | 1.34812 | ||||||||
\(467\) | −14.7382 | −0.682001 | −0.341000 | − | 0.940063i | \(-0.610766\pi\) | ||||
−0.341000 | + | 0.940063i | \(0.610766\pi\) | |||||||
\(468\) | −65.3196 | −3.01940 | ||||||||
\(469\) | −30.0286 | −1.38659 | ||||||||
\(470\) | −15.2604 | −0.703909 | ||||||||
\(471\) | 1.37533 | 0.0633718 | ||||||||
\(472\) | −75.6585 | −3.48246 | ||||||||
\(473\) | 9.31138 | 0.428138 | ||||||||
\(474\) | 1.24632 | 0.0572451 | ||||||||
\(475\) | −11.0213 | −0.505691 | ||||||||
\(476\) | −121.753 | −5.58055 | ||||||||
\(477\) | 0.0477562 | 0.00218660 | ||||||||
\(478\) | −2.12560 | −0.0972225 | ||||||||
\(479\) | −22.7965 | −1.04160 | −0.520800 | − | 0.853679i | \(-0.674366\pi\) | ||||
−0.520800 | + | 0.853679i | \(0.674366\pi\) | |||||||
\(480\) | −1.68242 | −0.0767916 | ||||||||
\(481\) | 27.3626 | 1.24763 | ||||||||
\(482\) | −40.1484 | −1.82871 | ||||||||
\(483\) | 2.38269 | 0.108416 | ||||||||
\(484\) | −21.8373 | −0.992605 | ||||||||
\(485\) | 14.4244 | 0.654976 | ||||||||
\(486\) | 6.16355 | 0.279584 | ||||||||
\(487\) | −33.6072 | −1.52289 | −0.761443 | − | 0.648232i | \(-0.775509\pi\) | ||||
−0.761443 | + | 0.648232i | \(0.775509\pi\) | |||||||
\(488\) | 42.1488 | 1.90799 | ||||||||
\(489\) | −0.323604 | −0.0146339 | ||||||||
\(490\) | 62.5098 | 2.82390 | ||||||||
\(491\) | −17.8021 | −0.803397 | −0.401699 | − | 0.915772i | \(-0.631580\pi\) | ||||
−0.401699 | + | 0.915772i | \(0.631580\pi\) | |||||||
\(492\) | 2.44882 | 0.110401 | ||||||||
\(493\) | 21.0919 | 0.949930 | ||||||||
\(494\) | −44.6571 | −2.00922 | ||||||||
\(495\) | 11.3017 | 0.507972 | ||||||||
\(496\) | 19.0896 | 0.857150 | ||||||||
\(497\) | −16.8492 | −0.755789 | ||||||||
\(498\) | −3.62922 | −0.162629 | ||||||||
\(499\) | 1.92040 | 0.0859691 | 0.0429845 | − | 0.999076i | \(-0.486313\pi\) | ||||
0.0429845 | + | 0.999076i | \(0.486313\pi\) | |||||||
\(500\) | 57.5703 | 2.57462 | ||||||||
\(501\) | −0.203930 | −0.00911092 | ||||||||
\(502\) | −40.5889 | −1.81157 | ||||||||
\(503\) | 24.9087 | 1.11063 | 0.555313 | − | 0.831641i | \(-0.312598\pi\) | ||||
0.555313 | + | 0.831641i | \(0.312598\pi\) | |||||||
\(504\) | −114.260 | −5.08957 | ||||||||
\(505\) | −5.61412 | −0.249825 | ||||||||
\(506\) | −39.0233 | −1.73480 | ||||||||
\(507\) | −0.523329 | −0.0232418 | ||||||||
\(508\) | −44.9648 | −1.99499 | ||||||||
\(509\) | 22.6361 | 1.00333 | 0.501663 | − | 0.865063i | \(-0.332722\pi\) | ||||
0.501663 | + | 0.865063i | \(0.332722\pi\) | |||||||
\(510\) | −1.70058 | −0.0753031 | ||||||||
\(511\) | −35.8326 | −1.58514 | ||||||||
\(512\) | 28.9549 | 1.27964 | ||||||||
\(513\) | 2.00594 | 0.0885642 | ||||||||
\(514\) | −25.9026 | −1.14251 | ||||||||
\(515\) | 20.9148 | 0.921615 | ||||||||
\(516\) | −1.56514 | −0.0689014 | ||||||||
\(517\) | −10.1305 | −0.445538 | ||||||||
\(518\) | 79.7567 | 3.50431 | ||||||||
\(519\) | −0.170833 | −0.00749872 | ||||||||
\(520\) | 50.8244 | 2.22880 | ||||||||
\(521\) | 17.3593 | 0.760526 | 0.380263 | − | 0.924878i | \(-0.375834\pi\) | ||||
0.380263 | + | 0.924878i | \(0.375834\pi\) | |||||||
\(522\) | 32.9828 | 1.44362 | ||||||||
\(523\) | 18.7533 | 0.820027 | 0.410013 | − | 0.912080i | \(-0.365524\pi\) | ||||
0.410013 | + | 0.912080i | \(0.365524\pi\) | |||||||
\(524\) | −2.01499 | −0.0880254 | ||||||||
\(525\) | −1.18595 | −0.0517593 | ||||||||
\(526\) | −57.2441 | −2.49596 | ||||||||
\(527\) | 8.77737 | 0.382348 | ||||||||
\(528\) | −2.45525 | −0.106851 | ||||||||
\(529\) | 9.78544 | 0.425454 | ||||||||
\(530\) | −0.0619177 | −0.00268953 | ||||||||
\(531\) | −28.5065 | −1.23707 | ||||||||
\(532\) | −92.9846 | −4.03139 | ||||||||
\(533\) | −24.6850 | −1.06923 | ||||||||
\(534\) | 0.976025 | 0.0422367 | ||||||||
\(535\) | −4.47818 | −0.193609 | ||||||||
\(536\) | −49.6105 | −2.14285 | ||||||||
\(537\) | −0.529670 | −0.0228570 | ||||||||
\(538\) | −79.9117 | −3.44524 | ||||||||
\(539\) | 41.4966 | 1.78739 | ||||||||
\(540\) | −3.80413 | −0.163704 | ||||||||
\(541\) | 28.3782 | 1.22007 | 0.610037 | − | 0.792373i | \(-0.291155\pi\) | ||||
0.610037 | + | 0.792373i | \(0.291155\pi\) | |||||||
\(542\) | 29.5087 | 1.26751 | ||||||||
\(543\) | 1.21322 | 0.0520641 | ||||||||
\(544\) | −67.1208 | −2.87778 | ||||||||
\(545\) | −5.80831 | −0.248801 | ||||||||
\(546\) | −4.80536 | −0.205650 | ||||||||
\(547\) | −28.9121 | −1.23619 | −0.618097 | − | 0.786102i | \(-0.712096\pi\) | ||||
−0.618097 | + | 0.786102i | \(0.712096\pi\) | |||||||
\(548\) | 36.5585 | 1.56170 | ||||||||
\(549\) | 15.8808 | 0.677774 | ||||||||
\(550\) | 19.4233 | 0.828214 | ||||||||
\(551\) | 16.1082 | 0.686231 | ||||||||
\(552\) | 3.93647 | 0.167547 | ||||||||
\(553\) | −26.1592 | −1.11240 | ||||||||
\(554\) | −33.2630 | −1.41321 | ||||||||
\(555\) | 0.795785 | 0.0337792 | ||||||||
\(556\) | 29.3233 | 1.24358 | ||||||||
\(557\) | 1.35712 | 0.0575032 | 0.0287516 | − | 0.999587i | \(-0.490847\pi\) | ||||
0.0287516 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(558\) | 13.7258 | 0.581058 | ||||||||
\(559\) | 15.7772 | 0.667303 | ||||||||
\(560\) | 77.6297 | 3.28045 | ||||||||
\(561\) | −1.12892 | −0.0476630 | ||||||||
\(562\) | −18.7998 | −0.793021 | ||||||||
\(563\) | 31.0870 | 1.31016 | 0.655080 | − | 0.755559i | \(-0.272635\pi\) | ||||
0.655080 | + | 0.755559i | \(0.272635\pi\) | |||||||
\(564\) | 1.70282 | 0.0717018 | ||||||||
\(565\) | 9.34484 | 0.393140 | ||||||||
\(566\) | −36.6165 | −1.53911 | ||||||||
\(567\) | −42.9428 | −1.80343 | ||||||||
\(568\) | −27.8367 | −1.16800 | ||||||||
\(569\) | 4.28242 | 0.179529 | 0.0897643 | − | 0.995963i | \(-0.471389\pi\) | ||||
0.0897643 | + | 0.995963i | \(0.471389\pi\) | |||||||
\(570\) | −1.29876 | −0.0543991 | ||||||||
\(571\) | 24.1973 | 1.01263 | 0.506313 | − | 0.862350i | \(-0.331008\pi\) | ||||
0.506313 | + | 0.862350i | \(0.331008\pi\) | |||||||
\(572\) | 56.2204 | 2.35069 | ||||||||
\(573\) | −0.280416 | −0.0117145 | ||||||||
\(574\) | −71.9519 | −3.00321 | ||||||||
\(575\) | −16.3185 | −0.680530 | ||||||||
\(576\) | −39.0501 | −1.62709 | ||||||||
\(577\) | −16.8897 | −0.703127 | −0.351563 | − | 0.936164i | \(-0.614350\pi\) | ||||
−0.351563 | + | 0.936164i | \(0.614350\pi\) | |||||||
\(578\) | −22.8625 | −0.950956 | ||||||||
\(579\) | 1.72164 | 0.0715489 | ||||||||
\(580\) | −30.5481 | −1.26844 | ||||||||
\(581\) | 76.1746 | 3.16026 | ||||||||
\(582\) | −2.25314 | −0.0933958 | ||||||||
\(583\) | −0.0411036 | −0.00170234 | ||||||||
\(584\) | −59.1994 | −2.44969 | ||||||||
\(585\) | 19.1495 | 0.791735 | ||||||||
\(586\) | 50.1215 | 2.07050 | ||||||||
\(587\) | 20.6711 | 0.853187 | 0.426593 | − | 0.904444i | \(-0.359714\pi\) | ||||
0.426593 | + | 0.904444i | \(0.359714\pi\) | |||||||
\(588\) | −6.97512 | −0.287649 | ||||||||
\(589\) | 6.70340 | 0.276209 | ||||||||
\(590\) | 36.9597 | 1.52161 | ||||||||
\(591\) | −1.05726 | −0.0434898 | ||||||||
\(592\) | 69.0481 | 2.83786 | ||||||||
\(593\) | 4.89814 | 0.201143 | 0.100571 | − | 0.994930i | \(-0.467933\pi\) | ||||
0.100571 | + | 0.994930i | \(0.467933\pi\) | |||||||
\(594\) | −3.53516 | −0.145049 | ||||||||
\(595\) | 35.6939 | 1.46331 | ||||||||
\(596\) | 102.109 | 4.18253 | ||||||||
\(597\) | −2.21050 | −0.0904696 | ||||||||
\(598\) | −66.1210 | −2.70389 | ||||||||
\(599\) | 46.5479 | 1.90189 | 0.950947 | − | 0.309353i | \(-0.100112\pi\) | ||||
0.950947 | + | 0.309353i | \(0.100112\pi\) | |||||||
\(600\) | −1.95932 | −0.0799891 | ||||||||
\(601\) | 47.8571 | 1.95213 | 0.976066 | − | 0.217473i | \(-0.0697815\pi\) | ||||
0.976066 | + | 0.217473i | \(0.0697815\pi\) | |||||||
\(602\) | 45.9873 | 1.87430 | ||||||||
\(603\) | −18.6922 | −0.761204 | ||||||||
\(604\) | −70.2300 | −2.85762 | ||||||||
\(605\) | 6.40197 | 0.260277 | ||||||||
\(606\) | 0.876949 | 0.0356236 | ||||||||
\(607\) | −43.5880 | −1.76918 | −0.884592 | − | 0.466366i | \(-0.845563\pi\) | ||||
−0.884592 | + | 0.466366i | \(0.845563\pi\) | |||||||
\(608\) | −51.2611 | −2.07891 | ||||||||
\(609\) | 1.73333 | 0.0702381 | ||||||||
\(610\) | −20.5900 | −0.833665 | ||||||||
\(611\) | −17.1651 | −0.694424 | ||||||||
\(612\) | −75.7887 | −3.06358 | ||||||||
\(613\) | −3.76272 | −0.151975 | −0.0759874 | − | 0.997109i | \(-0.524211\pi\) | ||||
−0.0759874 | + | 0.997109i | \(0.524211\pi\) | |||||||
\(614\) | 44.1661 | 1.78240 | ||||||||
\(615\) | −0.717912 | −0.0289490 | ||||||||
\(616\) | 98.3436 | 3.96238 | ||||||||
\(617\) | 0.475122 | 0.0191277 | 0.00956384 | − | 0.999954i | \(-0.496956\pi\) | ||||
0.00956384 | + | 0.999954i | \(0.496956\pi\) | |||||||
\(618\) | −3.26697 | −0.131417 | ||||||||
\(619\) | −33.9193 | −1.36333 | −0.681665 | − | 0.731664i | \(-0.738744\pi\) | ||||
−0.681665 | + | 0.731664i | \(0.738744\pi\) | |||||||
\(620\) | −12.7126 | −0.510549 | ||||||||
\(621\) | 2.97006 | 0.119184 | ||||||||
\(622\) | −51.6439 | −2.07073 | ||||||||
\(623\) | −20.4860 | −0.820755 | ||||||||
\(624\) | −4.16017 | −0.166540 | ||||||||
\(625\) | −2.62781 | −0.105112 | ||||||||
\(626\) | 43.3935 | 1.73435 | ||||||||
\(627\) | −0.862171 | −0.0344318 | ||||||||
\(628\) | −79.4691 | −3.17116 | ||||||||
\(629\) | 31.7482 | 1.26588 | ||||||||
\(630\) | 55.8170 | 2.22380 | ||||||||
\(631\) | −4.28588 | −0.170618 | −0.0853092 | − | 0.996355i | \(-0.527188\pi\) | ||||
−0.0853092 | + | 0.996355i | \(0.527188\pi\) | |||||||
\(632\) | −43.2178 | −1.71911 | ||||||||
\(633\) | −0.963634 | −0.0383010 | ||||||||
\(634\) | −11.0251 | −0.437864 | ||||||||
\(635\) | 13.1822 | 0.523118 | ||||||||
\(636\) | 0.00690905 | 0.000273962 0 | ||||||||
\(637\) | 70.3117 | 2.78585 | ||||||||
\(638\) | −28.3882 | −1.12390 | ||||||||
\(639\) | −10.4883 | −0.414909 | ||||||||
\(640\) | 11.7570 | 0.464734 | ||||||||
\(641\) | 14.7011 | 0.580657 | 0.290329 | − | 0.956927i | \(-0.406235\pi\) | ||||
0.290329 | + | 0.956927i | \(0.406235\pi\) | |||||||
\(642\) | 0.699511 | 0.0276075 | ||||||||
\(643\) | 7.20623 | 0.284186 | 0.142093 | − | 0.989853i | \(-0.454617\pi\) | ||||
0.142093 | + | 0.989853i | \(0.454617\pi\) | |||||||
\(644\) | −137.676 | −5.42521 | ||||||||
\(645\) | 0.458846 | 0.0180671 | ||||||||
\(646\) | −51.8145 | −2.03861 | ||||||||
\(647\) | 38.4156 | 1.51027 | 0.755137 | − | 0.655567i | \(-0.227571\pi\) | ||||
0.755137 | + | 0.655567i | \(0.227571\pi\) | |||||||
\(648\) | −70.9461 | −2.78703 | ||||||||
\(649\) | 24.5354 | 0.963099 | ||||||||
\(650\) | 32.9108 | 1.29087 | ||||||||
\(651\) | 0.721324 | 0.0282709 | ||||||||
\(652\) | 18.6984 | 0.732287 | ||||||||
\(653\) | 9.36327 | 0.366413 | 0.183207 | − | 0.983074i | \(-0.441352\pi\) | ||||
0.183207 | + | 0.983074i | \(0.441352\pi\) | |||||||
\(654\) | 0.907282 | 0.0354775 | ||||||||
\(655\) | 0.590729 | 0.0230817 | ||||||||
\(656\) | −62.2913 | −2.43207 | ||||||||
\(657\) | −22.3050 | −0.870202 | ||||||||
\(658\) | −50.0328 | −1.95048 | ||||||||
\(659\) | 0.773262 | 0.0301220 | 0.0150610 | − | 0.999887i | \(-0.495206\pi\) | ||||
0.0150610 | + | 0.999887i | \(0.495206\pi\) | |||||||
\(660\) | 1.63505 | 0.0636443 | ||||||||
\(661\) | 18.4117 | 0.716130 | 0.358065 | − | 0.933697i | \(-0.383437\pi\) | ||||
0.358065 | + | 0.933697i | \(0.383437\pi\) | |||||||
\(662\) | −59.2001 | −2.30088 | ||||||||
\(663\) | −1.91284 | −0.0742884 | ||||||||
\(664\) | 125.849 | 4.88388 | ||||||||
\(665\) | 27.2600 | 1.05710 | ||||||||
\(666\) | 49.6468 | 1.92377 | ||||||||
\(667\) | 23.8503 | 0.923488 | ||||||||
\(668\) | 11.7835 | 0.455915 | ||||||||
\(669\) | 1.41498 | 0.0547062 | ||||||||
\(670\) | 24.2351 | 0.936283 | ||||||||
\(671\) | −13.6685 | −0.527667 | ||||||||
\(672\) | −5.51599 | −0.212784 | ||||||||
\(673\) | −21.4652 | −0.827424 | −0.413712 | − | 0.910408i | \(-0.635768\pi\) | ||||
−0.413712 | + | 0.910408i | \(0.635768\pi\) | |||||||
\(674\) | −54.7591 | −2.10924 | ||||||||
\(675\) | −1.47831 | −0.0569002 | ||||||||
\(676\) | 30.2389 | 1.16304 | ||||||||
\(677\) | 41.1602 | 1.58191 | 0.790957 | − | 0.611871i | \(-0.209583\pi\) | ||||
0.790957 | + | 0.611871i | \(0.209583\pi\) | |||||||
\(678\) | −1.45970 | −0.0560595 | ||||||||
\(679\) | 47.2917 | 1.81489 | ||||||||
\(680\) | 58.9702 | 2.26140 | ||||||||
\(681\) | 2.47692 | 0.0949158 | ||||||||
\(682\) | −11.8137 | −0.452371 | ||||||||
\(683\) | −21.2727 | −0.813978 | −0.406989 | − | 0.913433i | \(-0.633421\pi\) | ||||
−0.406989 | + | 0.913433i | \(0.633421\pi\) | |||||||
\(684\) | −57.8809 | −2.21313 | ||||||||
\(685\) | −10.7177 | −0.409503 | ||||||||
\(686\) | 115.900 | 4.42509 | ||||||||
\(687\) | 2.08176 | 0.0794243 | ||||||||
\(688\) | 39.8128 | 1.51785 | ||||||||
\(689\) | −0.0696457 | −0.00265329 | ||||||||
\(690\) | −1.92299 | −0.0732070 | ||||||||
\(691\) | −18.9801 | −0.722037 | −0.361018 | − | 0.932559i | \(-0.617571\pi\) | ||||
−0.361018 | + | 0.932559i | \(0.617571\pi\) | |||||||
\(692\) | 9.87103 | 0.375240 | ||||||||
\(693\) | 37.0537 | 1.40755 | ||||||||
\(694\) | −31.5770 | −1.19865 | ||||||||
\(695\) | −8.59660 | −0.326088 | ||||||||
\(696\) | 2.86365 | 0.108546 | ||||||||
\(697\) | −28.6414 | −1.08487 | ||||||||
\(698\) | 8.50885 | 0.322065 | ||||||||
\(699\) | 0.952004 | 0.0360081 | ||||||||
\(700\) | 68.5267 | 2.59006 | ||||||||
\(701\) | 4.59819 | 0.173671 | 0.0868356 | − | 0.996223i | \(-0.472325\pi\) | ||||
0.0868356 | + | 0.996223i | \(0.472325\pi\) | |||||||
\(702\) | −5.98995 | −0.226076 | ||||||||
\(703\) | 24.2465 | 0.914475 | ||||||||
\(704\) | 33.6103 | 1.26674 | ||||||||
\(705\) | −0.499211 | −0.0188014 | ||||||||
\(706\) | 44.2098 | 1.66386 | ||||||||
\(707\) | −18.4065 | −0.692247 | ||||||||
\(708\) | −4.12413 | −0.154994 | ||||||||
\(709\) | 43.3211 | 1.62696 | 0.813480 | − | 0.581593i | \(-0.197570\pi\) | ||||
0.813480 | + | 0.581593i | \(0.197570\pi\) | |||||||
\(710\) | 13.5984 | 0.510339 | ||||||||
\(711\) | −16.2835 | −0.610680 | ||||||||
\(712\) | −33.8451 | −1.26840 | ||||||||
\(713\) | 9.92530 | 0.371705 | ||||||||
\(714\) | −5.57554 | −0.208659 | ||||||||
\(715\) | −16.4819 | −0.616389 | ||||||||
\(716\) | 30.6053 | 1.14378 | ||||||||
\(717\) | −0.0695343 | −0.00259681 | ||||||||
\(718\) | 41.5202 | 1.54952 | ||||||||
\(719\) | 10.3041 | 0.384277 | 0.192139 | − | 0.981368i | \(-0.438458\pi\) | ||||
0.192139 | + | 0.981368i | \(0.438458\pi\) | |||||||
\(720\) | 48.3228 | 1.80088 | ||||||||
\(721\) | 68.5712 | 2.55373 | ||||||||
\(722\) | 10.7035 | 0.398343 | ||||||||
\(723\) | −1.31337 | −0.0488447 | ||||||||
\(724\) | −70.1019 | −2.60532 | ||||||||
\(725\) | −11.8712 | −0.440885 | ||||||||
\(726\) | −1.00001 | −0.0371140 | ||||||||
\(727\) | −22.5526 | −0.836428 | −0.418214 | − | 0.908349i | \(-0.637344\pi\) | ||||
−0.418214 | + | 0.908349i | \(0.637344\pi\) | |||||||
\(728\) | 166.633 | 6.17583 | ||||||||
\(729\) | −26.5962 | −0.985046 | ||||||||
\(730\) | 28.9193 | 1.07035 | ||||||||
\(731\) | 18.3058 | 0.677066 | ||||||||
\(732\) | 2.29753 | 0.0849190 | ||||||||
\(733\) | −46.1682 | −1.70526 | −0.852631 | − | 0.522514i | \(-0.824994\pi\) | ||||
−0.852631 | + | 0.522514i | \(0.824994\pi\) | |||||||
\(734\) | 45.5760 | 1.68224 | ||||||||
\(735\) | 2.04487 | 0.0754262 | ||||||||
\(736\) | −75.8991 | −2.79768 | ||||||||
\(737\) | 16.0883 | 0.592619 | ||||||||
\(738\) | −44.7885 | −1.64869 | ||||||||
\(739\) | −7.16285 | −0.263490 | −0.131745 | − | 0.991284i | \(-0.542058\pi\) | ||||
−0.131745 | + | 0.991284i | \(0.542058\pi\) | |||||||
\(740\) | −45.9820 | −1.69033 | ||||||||
\(741\) | −1.46086 | −0.0536660 | ||||||||
\(742\) | −0.203004 | −0.00745250 | ||||||||
\(743\) | −10.3110 | −0.378274 | −0.189137 | − | 0.981951i | \(-0.560569\pi\) | ||||
−0.189137 | + | 0.981951i | \(0.560569\pi\) | |||||||
\(744\) | 1.19171 | 0.0436901 | ||||||||
\(745\) | −29.9348 | −1.09673 | ||||||||
\(746\) | −51.0080 | −1.86754 | ||||||||
\(747\) | 47.4170 | 1.73490 | ||||||||
\(748\) | 65.2310 | 2.38508 | ||||||||
\(749\) | −14.6822 | −0.536475 | ||||||||
\(750\) | 2.63636 | 0.0962663 | ||||||||
\(751\) | 11.9353 | 0.435525 | 0.217762 | − | 0.976002i | \(-0.430124\pi\) | ||||
0.217762 | + | 0.976002i | \(0.430124\pi\) | |||||||
\(752\) | −43.3151 | −1.57954 | ||||||||
\(753\) | −1.32778 | −0.0483869 | ||||||||
\(754\) | −48.1008 | −1.75173 | ||||||||
\(755\) | 20.5891 | 0.749313 | ||||||||
\(756\) | −12.4722 | −0.453611 | ||||||||
\(757\) | −6.41756 | −0.233250 | −0.116625 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116625 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(758\) | 49.9164 | 1.81305 | ||||||||
\(759\) | −1.27656 | −0.0463363 | ||||||||
\(760\) | 45.0364 | 1.63364 | ||||||||
\(761\) | −8.04158 | −0.291507 | −0.145754 | − | 0.989321i | \(-0.546561\pi\) | ||||
−0.145754 | + | 0.989321i | \(0.546561\pi\) | |||||||
\(762\) | −2.05911 | −0.0745936 | ||||||||
\(763\) | −19.0431 | −0.689408 | ||||||||
\(764\) | 16.2029 | 0.586202 | ||||||||
\(765\) | 22.2187 | 0.803318 | ||||||||
\(766\) | −92.0037 | −3.32423 | ||||||||
\(767\) | 41.5727 | 1.50110 | ||||||||
\(768\) | 0.422605 | 0.0152495 | ||||||||
\(769\) | 34.7266 | 1.25227 | 0.626136 | − | 0.779714i | \(-0.284635\pi\) | ||||
0.626136 | + | 0.779714i | \(0.284635\pi\) | |||||||
\(770\) | −48.0415 | −1.73130 | ||||||||
\(771\) | −0.847347 | −0.0305164 | ||||||||
\(772\) | −99.4796 | −3.58035 | ||||||||
\(773\) | 17.7661 | 0.639002 | 0.319501 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319501 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(774\) | 28.6261 | 1.02894 | ||||||||
\(775\) | −4.94019 | −0.177457 | ||||||||
\(776\) | 78.1311 | 2.80474 | ||||||||
\(777\) | 2.60907 | 0.0935997 | ||||||||
\(778\) | −85.3180 | −3.05880 | ||||||||
\(779\) | −21.8738 | −0.783711 | ||||||||
\(780\) | 2.77043 | 0.0991972 | ||||||||
\(781\) | 9.02720 | 0.323019 | ||||||||
\(782\) | −76.7185 | −2.74345 | ||||||||
\(783\) | 2.16062 | 0.0772143 | ||||||||
\(784\) | 177.428 | 6.33671 | ||||||||
\(785\) | 23.2977 | 0.831529 | ||||||||
\(786\) | −0.0922742 | −0.00329131 | ||||||||
\(787\) | −32.2652 | −1.15013 | −0.575065 | − | 0.818108i | \(-0.695023\pi\) | ||||
−0.575065 | + | 0.818108i | \(0.695023\pi\) | |||||||
\(788\) | 61.0903 | 2.17625 | ||||||||
\(789\) | −1.87261 | −0.0666668 | ||||||||
\(790\) | 21.1122 | 0.751139 | ||||||||
\(791\) | 30.6380 | 1.08936 | ||||||||
\(792\) | 61.2167 | 2.17524 | ||||||||
\(793\) | −23.1599 | −0.822431 | ||||||||
\(794\) | 25.1155 | 0.891315 | ||||||||
\(795\) | −0.00202550 | −7.18372e−5 0 | ||||||||
\(796\) | 127.727 | 4.52715 | ||||||||
\(797\) | 44.4127 | 1.57318 | 0.786590 | − | 0.617476i | \(-0.211845\pi\) | ||||
0.786590 | + | 0.617476i | \(0.211845\pi\) | |||||||
\(798\) | −4.25812 | −0.150736 | ||||||||
\(799\) | −19.9162 | −0.704584 | ||||||||
\(800\) | 37.7778 | 1.33565 | ||||||||
\(801\) | −12.7521 | −0.450573 | ||||||||
\(802\) | −15.6189 | −0.551523 | ||||||||
\(803\) | 19.1979 | 0.677477 | ||||||||
\(804\) | −2.70426 | −0.0953719 | ||||||||
\(805\) | 40.3621 | 1.42258 | ||||||||
\(806\) | −20.0171 | −0.705073 | ||||||||
\(807\) | −2.61414 | −0.0920220 | ||||||||
\(808\) | −30.4095 | −1.06980 | ||||||||
\(809\) | −39.9511 | −1.40461 | −0.702303 | − | 0.711879i | \(-0.747845\pi\) | ||||
−0.702303 | + | 0.711879i | \(0.747845\pi\) | |||||||
\(810\) | 34.6577 | 1.21775 | ||||||||
\(811\) | 23.2696 | 0.817106 | 0.408553 | − | 0.912735i | \(-0.366034\pi\) | ||||
0.408553 | + | 0.912735i | \(0.366034\pi\) | |||||||
\(812\) | −100.155 | −3.51475 | ||||||||
\(813\) | 0.965313 | 0.0338550 | ||||||||
\(814\) | −42.7308 | −1.49771 | ||||||||
\(815\) | −5.48175 | −0.192017 | ||||||||
\(816\) | −4.82694 | −0.168977 | ||||||||
\(817\) | 13.9804 | 0.489114 | ||||||||
\(818\) | 64.4108 | 2.25207 | ||||||||
\(819\) | 62.7837 | 2.19384 | ||||||||
\(820\) | 41.4823 | 1.44863 | ||||||||
\(821\) | −25.7475 | −0.898595 | −0.449298 | − | 0.893382i | \(-0.648326\pi\) | ||||
−0.449298 | + | 0.893382i | \(0.648326\pi\) | |||||||
\(822\) | 1.67415 | 0.0583928 | ||||||||
\(823\) | 44.9842 | 1.56805 | 0.784025 | − | 0.620729i | \(-0.213163\pi\) | ||||
0.784025 | + | 0.620729i | \(0.213163\pi\) | |||||||
\(824\) | 113.287 | 3.94654 | ||||||||
\(825\) | 0.635392 | 0.0221215 | ||||||||
\(826\) | 121.176 | 4.21626 | ||||||||
\(827\) | −35.7382 | −1.24274 | −0.621369 | − | 0.783518i | \(-0.713423\pi\) | ||||
−0.621369 | + | 0.783518i | \(0.713423\pi\) | |||||||
\(828\) | −85.7006 | −2.97830 | ||||||||
\(829\) | −39.2241 | −1.36231 | −0.681154 | − | 0.732140i | \(-0.738522\pi\) | ||||
−0.681154 | + | 0.732140i | \(0.738522\pi\) | |||||||
\(830\) | −61.4780 | −2.13393 | ||||||||
\(831\) | −1.08813 | −0.0377467 | ||||||||
\(832\) | 56.9492 | 1.97436 | ||||||||
\(833\) | 81.5809 | 2.82661 | ||||||||
\(834\) | 1.34282 | 0.0464982 | ||||||||
\(835\) | −3.45451 | −0.119548 | ||||||||
\(836\) | 49.8179 | 1.72299 | ||||||||
\(837\) | 0.899142 | 0.0310789 | ||||||||
\(838\) | 70.9604 | 2.45129 | ||||||||
\(839\) | 13.2223 | 0.456486 | 0.228243 | − | 0.973604i | \(-0.426702\pi\) | ||||
0.228243 | + | 0.973604i | \(0.426702\pi\) | |||||||
\(840\) | 4.84618 | 0.167209 | ||||||||
\(841\) | −11.6497 | −0.401713 | ||||||||
\(842\) | −0.941247 | −0.0324375 | ||||||||
\(843\) | −0.614994 | −0.0211815 | ||||||||
\(844\) | 55.6806 | 1.91660 | ||||||||
\(845\) | −8.86503 | −0.304966 | ||||||||
\(846\) | −31.1443 | −1.07076 | ||||||||
\(847\) | 20.9895 | 0.721208 | ||||||||
\(848\) | −0.175747 | −0.00603519 | ||||||||
\(849\) | −1.19783 | −0.0411094 | ||||||||
\(850\) | 38.1856 | 1.30976 | ||||||||
\(851\) | 35.9003 | 1.23065 | ||||||||
\(852\) | −1.51737 | −0.0519843 | ||||||||
\(853\) | 18.4076 | 0.630264 | 0.315132 | − | 0.949048i | \(-0.397951\pi\) | ||||
0.315132 | + | 0.949048i | \(0.397951\pi\) | |||||||
\(854\) | −67.5065 | −2.31002 | ||||||||
\(855\) | 16.9687 | 0.580318 | ||||||||
\(856\) | −24.2566 | −0.829072 | ||||||||
\(857\) | −6.47183 | −0.221074 | −0.110537 | − | 0.993872i | \(-0.535257\pi\) | ||||
−0.110537 | + | 0.993872i | \(0.535257\pi\) | |||||||
\(858\) | 2.57454 | 0.0878935 | ||||||||
\(859\) | −33.4938 | −1.14280 | −0.571398 | − | 0.820673i | \(-0.693599\pi\) | ||||
−0.571398 | + | 0.820673i | \(0.693599\pi\) | |||||||
\(860\) | −26.5130 | −0.904086 | ||||||||
\(861\) | −2.35375 | −0.0802156 | ||||||||
\(862\) | −48.6895 | −1.65837 | ||||||||
\(863\) | 17.5074 | 0.595960 | 0.297980 | − | 0.954572i | \(-0.403687\pi\) | ||||
0.297980 | + | 0.954572i | \(0.403687\pi\) | |||||||
\(864\) | −6.87576 | −0.233918 | ||||||||
\(865\) | −2.89385 | −0.0983940 | ||||||||
\(866\) | −7.44221 | −0.252896 | ||||||||
\(867\) | −0.747898 | −0.0253999 | ||||||||
\(868\) | −41.6795 | −1.41469 | ||||||||
\(869\) | 14.0152 | 0.475432 | ||||||||
\(870\) | −1.39891 | −0.0474276 | ||||||||
\(871\) | 27.2599 | 0.923667 | ||||||||
\(872\) | −31.4613 | −1.06542 | ||||||||
\(873\) | 29.4381 | 0.996328 | ||||||||
\(874\) | −58.5910 | −1.98187 | ||||||||
\(875\) | −55.3352 | −1.87067 | ||||||||
\(876\) | −3.22695 | −0.109028 | ||||||||
\(877\) | 12.1390 | 0.409905 | 0.204953 | − | 0.978772i | \(-0.434296\pi\) | ||||
0.204953 | + | 0.978772i | \(0.434296\pi\) | |||||||
\(878\) | −44.5857 | −1.50469 | ||||||||
\(879\) | 1.63961 | 0.0553028 | ||||||||
\(880\) | −41.5912 | −1.40204 | ||||||||
\(881\) | 26.4420 | 0.890852 | 0.445426 | − | 0.895319i | \(-0.353052\pi\) | ||||
0.445426 | + | 0.895319i | \(0.353052\pi\) | |||||||
\(882\) | 127.574 | 4.29563 | ||||||||
\(883\) | 12.1855 | 0.410076 | 0.205038 | − | 0.978754i | \(-0.434268\pi\) | ||||
0.205038 | + | 0.978754i | \(0.434268\pi\) | |||||||
\(884\) | 110.527 | 3.71743 | ||||||||
\(885\) | 1.20906 | 0.0406420 | ||||||||
\(886\) | 108.395 | 3.64158 | ||||||||
\(887\) | −16.2777 | −0.546550 | −0.273275 | − | 0.961936i | \(-0.588107\pi\) | ||||
−0.273275 | + | 0.961936i | \(0.588107\pi\) | |||||||
\(888\) | 4.31046 | 0.144650 | ||||||||
\(889\) | 43.2191 | 1.44952 | ||||||||
\(890\) | 16.5336 | 0.554207 | ||||||||
\(891\) | 23.0072 | 0.770771 | ||||||||
\(892\) | −81.7601 | −2.73753 | ||||||||
\(893\) | −15.2103 | −0.508993 | ||||||||
\(894\) | 4.67594 | 0.156387 | ||||||||
\(895\) | −8.97246 | −0.299916 | ||||||||
\(896\) | 38.5464 | 1.28774 | ||||||||
\(897\) | −2.16300 | −0.0722206 | ||||||||
\(898\) | −68.2851 | −2.27870 | ||||||||
\(899\) | 7.22033 | 0.240811 | ||||||||
\(900\) | 42.6564 | 1.42188 | ||||||||
\(901\) | −0.0808082 | −0.00269211 | ||||||||
\(902\) | 38.5493 | 1.28355 | ||||||||
\(903\) | 1.50438 | 0.0500625 | ||||||||
\(904\) | 50.6173 | 1.68351 | ||||||||
\(905\) | 20.5515 | 0.683156 | ||||||||
\(906\) | −3.21610 | −0.106848 | ||||||||
\(907\) | 29.7376 | 0.987421 | 0.493710 | − | 0.869626i | \(-0.335640\pi\) | ||||
0.493710 | + | 0.869626i | \(0.335640\pi\) | |||||||
\(908\) | −143.121 | −4.74964 | ||||||||
\(909\) | −11.4576 | −0.380026 | ||||||||
\(910\) | −81.4014 | −2.69843 | ||||||||
\(911\) | −52.3587 | −1.73472 | −0.867361 | − | 0.497680i | \(-0.834185\pi\) | ||||
−0.867361 | + | 0.497680i | \(0.834185\pi\) | |||||||
\(912\) | −3.68640 | −0.122069 | ||||||||
\(913\) | −40.8117 | −1.35067 | ||||||||
\(914\) | −68.6644 | −2.27122 | ||||||||
\(915\) | −0.673557 | −0.0222671 | ||||||||
\(916\) | −120.288 | −3.97444 | ||||||||
\(917\) | 1.93677 | 0.0639576 | ||||||||
\(918\) | −6.94999 | −0.229384 | ||||||||
\(919\) | 29.1886 | 0.962843 | 0.481421 | − | 0.876489i | \(-0.340121\pi\) | ||||
0.481421 | + | 0.876489i | \(0.340121\pi\) | |||||||
\(920\) | 66.6826 | 2.19846 | ||||||||
\(921\) | 1.44480 | 0.0476077 | ||||||||
\(922\) | 87.5606 | 2.88365 | ||||||||
\(923\) | 15.2957 | 0.503463 | ||||||||
\(924\) | 5.36069 | 0.176354 | ||||||||
\(925\) | −17.8689 | −0.587526 | ||||||||
\(926\) | 1.58377 | 0.0520458 | ||||||||
\(927\) | 42.6841 | 1.40193 | ||||||||
\(928\) | −55.2141 | −1.81249 | ||||||||
\(929\) | −22.9553 | −0.753137 | −0.376569 | − | 0.926389i | \(-0.622896\pi\) | ||||
−0.376569 | + | 0.926389i | \(0.622896\pi\) | |||||||
\(930\) | −0.582157 | −0.0190897 | ||||||||
\(931\) | 62.3045 | 2.04195 | ||||||||
\(932\) | −55.0086 | −1.80187 | ||||||||
\(933\) | −1.68942 | −0.0553091 | ||||||||
\(934\) | 38.9979 | 1.27605 | ||||||||
\(935\) | −19.1235 | −0.625407 | ||||||||
\(936\) | 103.725 | 3.39037 | ||||||||
\(937\) | 35.4762 | 1.15896 | 0.579479 | − | 0.814987i | \(-0.303256\pi\) | ||||
0.579479 | + | 0.814987i | \(0.303256\pi\) | |||||||
\(938\) | 79.4573 | 2.59437 | ||||||||
\(939\) | 1.41952 | 0.0463244 | ||||||||
\(940\) | 28.8453 | 0.940831 | ||||||||
\(941\) | 41.0396 | 1.33785 | 0.668926 | − | 0.743329i | \(-0.266754\pi\) | ||||
0.668926 | + | 0.743329i | \(0.266754\pi\) | |||||||
\(942\) | −3.63919 | −0.118571 | ||||||||
\(943\) | −32.3872 | −1.05467 | ||||||||
\(944\) | 104.907 | 3.41442 | ||||||||
\(945\) | 3.65644 | 0.118944 | ||||||||
\(946\) | −24.6384 | −0.801063 | ||||||||
\(947\) | −57.4401 | −1.86655 | −0.933276 | − | 0.359160i | \(-0.883063\pi\) | ||||
−0.933276 | + | 0.359160i | \(0.883063\pi\) | |||||||
\(948\) | −2.35580 | −0.0765127 | ||||||||
\(949\) | 32.5288 | 1.05593 | ||||||||
\(950\) | 29.1629 | 0.946170 | ||||||||
\(951\) | −0.360663 | −0.0116953 | ||||||||
\(952\) | 193.340 | 6.26619 | ||||||||
\(953\) | 16.6030 | 0.537825 | 0.268913 | − | 0.963165i | \(-0.413336\pi\) | ||||
0.268913 | + | 0.963165i | \(0.413336\pi\) | |||||||
\(954\) | −0.126365 | −0.00409123 | ||||||||
\(955\) | −4.75016 | −0.153711 | ||||||||
\(956\) | 4.01782 | 0.129946 | ||||||||
\(957\) | −0.928657 | −0.0300192 | ||||||||
\(958\) | 60.3208 | 1.94888 | ||||||||
\(959\) | −35.1392 | −1.13470 | ||||||||
\(960\) | 1.65625 | 0.0534552 | ||||||||
\(961\) | −27.9953 | −0.903073 | ||||||||
\(962\) | −72.4029 | −2.33436 | ||||||||
\(963\) | −9.13934 | −0.294511 | ||||||||
\(964\) | 75.8889 | 2.44422 | ||||||||
\(965\) | 29.1641 | 0.938825 | ||||||||
\(966\) | −6.30473 | −0.202851 | ||||||||
\(967\) | 49.2291 | 1.58310 | 0.791550 | − | 0.611104i | \(-0.209274\pi\) | ||||
0.791550 | + | 0.611104i | \(0.209274\pi\) | |||||||
\(968\) | 34.6770 | 1.11456 | ||||||||
\(969\) | −1.69500 | −0.0544512 | ||||||||
\(970\) | −38.1676 | −1.22549 | ||||||||
\(971\) | −15.1993 | −0.487768 | −0.243884 | − | 0.969804i | \(-0.578422\pi\) | ||||
−0.243884 | + | 0.969804i | \(0.578422\pi\) | |||||||
\(972\) | −11.6504 | −0.373686 | ||||||||
\(973\) | −28.1848 | −0.903565 | ||||||||
\(974\) | 88.9263 | 2.84938 | ||||||||
\(975\) | 1.07661 | 0.0344790 | ||||||||
\(976\) | −58.4427 | −1.87071 | ||||||||
\(977\) | −11.8933 | −0.380499 | −0.190250 | − | 0.981736i | \(-0.560930\pi\) | ||||
−0.190250 | + | 0.981736i | \(0.560930\pi\) | |||||||
\(978\) | 0.856272 | 0.0273805 | ||||||||
\(979\) | 10.9757 | 0.350784 | ||||||||
\(980\) | −118.157 | −3.77437 | ||||||||
\(981\) | −11.8539 | −0.378467 | ||||||||
\(982\) | 47.1053 | 1.50319 | ||||||||
\(983\) | −3.44831 | −0.109984 | −0.0549920 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549920 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(984\) | −3.88865 | −0.123966 | ||||||||
\(985\) | −17.9096 | −0.570648 | ||||||||
\(986\) | −55.8102 | −1.77736 | ||||||||
\(987\) | −1.63671 | −0.0520972 | ||||||||
\(988\) | 84.4112 | 2.68548 | ||||||||
\(989\) | 20.6999 | 0.658220 | ||||||||
\(990\) | −29.9048 | −0.950437 | ||||||||
\(991\) | −32.7835 | −1.04140 | −0.520702 | − | 0.853739i | \(-0.674330\pi\) | ||||
−0.520702 | + | 0.853739i | \(0.674330\pi\) | |||||||
\(992\) | −22.9773 | −0.729530 | ||||||||
\(993\) | −1.93660 | −0.0614562 | ||||||||
\(994\) | 44.5838 | 1.41411 | ||||||||
\(995\) | −37.4452 | −1.18709 | ||||||||
\(996\) | 6.85999 | 0.217367 | ||||||||
\(997\) | −47.6704 | −1.50974 | −0.754868 | − | 0.655876i | \(-0.772299\pi\) | ||||
−0.754868 | + | 0.655876i | \(0.772299\pi\) | |||||||
\(998\) | −5.08149 | −0.160852 | ||||||||
\(999\) | 3.25224 | 0.102896 |
(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 | 8011.2.a.b.1.11 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.11 | ✓ | 358 | 1.1 | even | 1 | trivial |