Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6015,2,Mod(1,6015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0300168158\) |
Analytic rank: | \(0\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17202 | −1.53585 | −0.767925 | − | 0.640540i | \(-0.778711\pi\) | ||||
−0.767925 | + | 0.640540i | \(0.778711\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.71767 | 1.35884 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.17202 | −0.886723 | ||||||||
\(7\) | −0.722026 | −0.272900 | −0.136450 | − | 0.990647i | \(-0.543569\pi\) | ||||
−0.136450 | + | 0.990647i | \(0.543569\pi\) | |||||||
\(8\) | −1.55879 | −0.551117 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.17202 | 0.686853 | ||||||||
\(11\) | 3.51451 | 1.05966 | 0.529832 | − | 0.848102i | \(-0.322255\pi\) | ||||
0.529832 | + | 0.848102i | \(0.322255\pi\) | |||||||
\(12\) | 2.71767 | 0.784524 | ||||||||
\(13\) | 5.21945 | 1.44761 | 0.723807 | − | 0.690002i | \(-0.242390\pi\) | ||||
0.723807 | + | 0.690002i | \(0.242390\pi\) | |||||||
\(14\) | 1.56825 | 0.419134 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −2.04961 | −0.512402 | ||||||||
\(17\) | 2.33888 | 0.567261 | 0.283630 | − | 0.958934i | \(-0.408461\pi\) | ||||
0.283630 | + | 0.958934i | \(0.408461\pi\) | |||||||
\(18\) | −2.17202 | −0.511950 | ||||||||
\(19\) | 7.25112 | 1.66352 | 0.831760 | − | 0.555135i | \(-0.187334\pi\) | ||||
0.831760 | + | 0.555135i | \(0.187334\pi\) | |||||||
\(20\) | −2.71767 | −0.607690 | ||||||||
\(21\) | −0.722026 | −0.157559 | ||||||||
\(22\) | −7.63359 | −1.62749 | ||||||||
\(23\) | 1.16716 | 0.243371 | 0.121685 | − | 0.992569i | \(-0.461170\pi\) | ||||
0.121685 | + | 0.992569i | \(0.461170\pi\) | |||||||
\(24\) | −1.55879 | −0.318188 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.3367 | −2.22332 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.96223 | −0.370826 | ||||||||
\(29\) | −10.5614 | −1.96120 | −0.980600 | − | 0.196022i | \(-0.937198\pi\) | ||||
−0.980600 | + | 0.196022i | \(0.937198\pi\) | |||||||
\(30\) | 2.17202 | 0.396555 | ||||||||
\(31\) | 6.42467 | 1.15391 | 0.576953 | − | 0.816778i | \(-0.304242\pi\) | ||||
0.576953 | + | 0.816778i | \(0.304242\pi\) | |||||||
\(32\) | 7.56938 | 1.33809 | ||||||||
\(33\) | 3.51451 | 0.611798 | ||||||||
\(34\) | −5.08008 | −0.871227 | ||||||||
\(35\) | 0.722026 | 0.122045 | ||||||||
\(36\) | 2.71767 | 0.452945 | ||||||||
\(37\) | −0.191811 | −0.0315335 | −0.0157667 | − | 0.999876i | \(-0.505019\pi\) | ||||
−0.0157667 | + | 0.999876i | \(0.505019\pi\) | |||||||
\(38\) | −15.7496 | −2.55492 | ||||||||
\(39\) | 5.21945 | 0.835781 | ||||||||
\(40\) | 1.55879 | 0.246467 | ||||||||
\(41\) | 8.24409 | 1.28751 | 0.643756 | − | 0.765231i | \(-0.277375\pi\) | ||||
0.643756 | + | 0.765231i | \(0.277375\pi\) | |||||||
\(42\) | 1.56825 | 0.241987 | ||||||||
\(43\) | 6.00834 | 0.916263 | 0.458132 | − | 0.888884i | \(-0.348519\pi\) | ||||
0.458132 | + | 0.888884i | \(0.348519\pi\) | |||||||
\(44\) | 9.55128 | 1.43991 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −2.53510 | −0.373781 | ||||||||
\(47\) | 10.6156 | 1.54845 | 0.774225 | − | 0.632910i | \(-0.218140\pi\) | ||||
0.774225 | + | 0.632910i | \(0.218140\pi\) | |||||||
\(48\) | −2.04961 | −0.295835 | ||||||||
\(49\) | −6.47868 | −0.925526 | ||||||||
\(50\) | −2.17202 | −0.307170 | ||||||||
\(51\) | 2.33888 | 0.327508 | ||||||||
\(52\) | 14.1847 | 1.96707 | ||||||||
\(53\) | −7.42761 | −1.02026 | −0.510131 | − | 0.860097i | \(-0.670403\pi\) | ||||
−0.510131 | + | 0.860097i | \(0.670403\pi\) | |||||||
\(54\) | −2.17202 | −0.295574 | ||||||||
\(55\) | −3.51451 | −0.473896 | ||||||||
\(56\) | 1.12549 | 0.150400 | ||||||||
\(57\) | 7.25112 | 0.960434 | ||||||||
\(58\) | 22.9395 | 3.01211 | ||||||||
\(59\) | 3.93902 | 0.512816 | 0.256408 | − | 0.966569i | \(-0.417461\pi\) | ||||
0.256408 | + | 0.966569i | \(0.417461\pi\) | |||||||
\(60\) | −2.71767 | −0.350850 | ||||||||
\(61\) | 8.42212 | 1.07834 | 0.539171 | − | 0.842197i | \(-0.318738\pi\) | ||||
0.539171 | + | 0.842197i | \(0.318738\pi\) | |||||||
\(62\) | −13.9545 | −1.77223 | ||||||||
\(63\) | −0.722026 | −0.0909667 | ||||||||
\(64\) | −12.3416 | −1.54270 | ||||||||
\(65\) | −5.21945 | −0.647393 | ||||||||
\(66\) | −7.63359 | −0.939629 | ||||||||
\(67\) | 0.356294 | 0.0435283 | 0.0217641 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217641 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(68\) | 6.35629 | 0.770814 | ||||||||
\(69\) | 1.16716 | 0.140510 | ||||||||
\(70\) | −1.56825 | −0.187442 | ||||||||
\(71\) | 12.4798 | 1.48107 | 0.740537 | − | 0.672015i | \(-0.234571\pi\) | ||||
0.740537 | + | 0.672015i | \(0.234571\pi\) | |||||||
\(72\) | −1.55879 | −0.183706 | ||||||||
\(73\) | 1.19724 | 0.140126 | 0.0700630 | − | 0.997543i | \(-0.477680\pi\) | ||||
0.0700630 | + | 0.997543i | \(0.477680\pi\) | |||||||
\(74\) | 0.416616 | 0.0484307 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 19.7061 | 2.26045 | ||||||||
\(77\) | −2.53757 | −0.289183 | ||||||||
\(78\) | −11.3367 | −1.28363 | ||||||||
\(79\) | 9.01975 | 1.01480 | 0.507401 | − | 0.861710i | \(-0.330606\pi\) | ||||
0.507401 | + | 0.861710i | \(0.330606\pi\) | |||||||
\(80\) | 2.04961 | 0.229153 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.9063 | −1.97742 | ||||||||
\(83\) | 0.233260 | 0.0256036 | 0.0128018 | − | 0.999918i | \(-0.495925\pi\) | ||||
0.0128018 | + | 0.999918i | \(0.495925\pi\) | |||||||
\(84\) | −1.96223 | −0.214097 | ||||||||
\(85\) | −2.33888 | −0.253687 | ||||||||
\(86\) | −13.0502 | −1.40724 | ||||||||
\(87\) | −10.5614 | −1.13230 | ||||||||
\(88\) | −5.47840 | −0.583999 | ||||||||
\(89\) | −6.48999 | −0.687938 | −0.343969 | − | 0.938981i | \(-0.611771\pi\) | ||||
−0.343969 | + | 0.938981i | \(0.611771\pi\) | |||||||
\(90\) | 2.17202 | 0.228951 | ||||||||
\(91\) | −3.76858 | −0.395054 | ||||||||
\(92\) | 3.17197 | 0.330700 | ||||||||
\(93\) | 6.42467 | 0.666208 | ||||||||
\(94\) | −23.0574 | −2.37819 | ||||||||
\(95\) | −7.25112 | −0.743949 | ||||||||
\(96\) | 7.56938 | 0.772547 | ||||||||
\(97\) | −1.29315 | −0.131300 | −0.0656500 | − | 0.997843i | \(-0.520912\pi\) | ||||
−0.0656500 | + | 0.997843i | \(0.520912\pi\) | |||||||
\(98\) | 14.0718 | 1.42147 | ||||||||
\(99\) | 3.51451 | 0.353222 | ||||||||
\(100\) | 2.71767 | 0.271767 | ||||||||
\(101\) | −18.0463 | −1.79567 | −0.897836 | − | 0.440329i | \(-0.854862\pi\) | ||||
−0.897836 | + | 0.440329i | \(0.854862\pi\) | |||||||
\(102\) | −5.08008 | −0.503003 | ||||||||
\(103\) | 18.6362 | 1.83627 | 0.918137 | − | 0.396262i | \(-0.129693\pi\) | ||||
0.918137 | + | 0.396262i | \(0.129693\pi\) | |||||||
\(104\) | −8.13605 | −0.797805 | ||||||||
\(105\) | 0.722026 | 0.0704625 | ||||||||
\(106\) | 16.1329 | 1.56697 | ||||||||
\(107\) | −7.26136 | −0.701982 | −0.350991 | − | 0.936379i | \(-0.614155\pi\) | ||||
−0.350991 | + | 0.936379i | \(0.614155\pi\) | |||||||
\(108\) | 2.71767 | 0.261508 | ||||||||
\(109\) | −19.9690 | −1.91268 | −0.956341 | − | 0.292252i | \(-0.905595\pi\) | ||||
−0.956341 | + | 0.292252i | \(0.905595\pi\) | |||||||
\(110\) | 7.63359 | 0.727834 | ||||||||
\(111\) | −0.191811 | −0.0182059 | ||||||||
\(112\) | 1.47987 | 0.139835 | ||||||||
\(113\) | −14.9558 | −1.40692 | −0.703462 | − | 0.710732i | \(-0.748364\pi\) | ||||
−0.703462 | + | 0.710732i | \(0.748364\pi\) | |||||||
\(114\) | −15.7496 | −1.47508 | ||||||||
\(115\) | −1.16716 | −0.108839 | ||||||||
\(116\) | −28.7023 | −2.66495 | ||||||||
\(117\) | 5.21945 | 0.482538 | ||||||||
\(118\) | −8.55562 | −0.787609 | ||||||||
\(119\) | −1.68873 | −0.154805 | ||||||||
\(120\) | 1.55879 | 0.142298 | ||||||||
\(121\) | 1.35178 | 0.122889 | ||||||||
\(122\) | −18.2930 | −1.65617 | ||||||||
\(123\) | 8.24409 | 0.743345 | ||||||||
\(124\) | 17.4601 | 1.56797 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.56825 | 0.139711 | ||||||||
\(127\) | −5.64314 | −0.500748 | −0.250374 | − | 0.968149i | \(-0.580554\pi\) | ||||
−0.250374 | + | 0.968149i | \(0.580554\pi\) | |||||||
\(128\) | 11.6675 | 1.03127 | ||||||||
\(129\) | 6.00834 | 0.529005 | ||||||||
\(130\) | 11.3367 | 0.994299 | ||||||||
\(131\) | −19.3517 | −1.69077 | −0.845384 | − | 0.534159i | \(-0.820628\pi\) | ||||
−0.845384 | + | 0.534159i | \(0.820628\pi\) | |||||||
\(132\) | 9.55128 | 0.831332 | ||||||||
\(133\) | −5.23549 | −0.453975 | ||||||||
\(134\) | −0.773878 | −0.0668529 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −3.64583 | −0.312627 | ||||||||
\(137\) | 15.6380 | 1.33604 | 0.668021 | − | 0.744142i | \(-0.267142\pi\) | ||||
0.668021 | + | 0.744142i | \(0.267142\pi\) | |||||||
\(138\) | −2.53510 | −0.215802 | ||||||||
\(139\) | −8.60340 | −0.729731 | −0.364865 | − | 0.931060i | \(-0.618885\pi\) | ||||
−0.364865 | + | 0.931060i | \(0.618885\pi\) | |||||||
\(140\) | 1.96223 | 0.165839 | ||||||||
\(141\) | 10.6156 | 0.893998 | ||||||||
\(142\) | −27.1063 | −2.27471 | ||||||||
\(143\) | 18.3438 | 1.53399 | ||||||||
\(144\) | −2.04961 | −0.170801 | ||||||||
\(145\) | 10.5614 | 0.877075 | ||||||||
\(146\) | −2.60042 | −0.215213 | ||||||||
\(147\) | −6.47868 | −0.534352 | ||||||||
\(148\) | −0.521278 | −0.0428488 | ||||||||
\(149\) | −7.84552 | −0.642730 | −0.321365 | − | 0.946955i | \(-0.604142\pi\) | ||||
−0.321365 | + | 0.946955i | \(0.604142\pi\) | |||||||
\(150\) | −2.17202 | −0.177345 | ||||||||
\(151\) | 4.43824 | 0.361179 | 0.180589 | − | 0.983559i | \(-0.442199\pi\) | ||||
0.180589 | + | 0.983559i | \(0.442199\pi\) | |||||||
\(152\) | −11.3030 | −0.916794 | ||||||||
\(153\) | 2.33888 | 0.189087 | ||||||||
\(154\) | 5.51164 | 0.444141 | ||||||||
\(155\) | −6.42467 | −0.516042 | ||||||||
\(156\) | 14.1847 | 1.13569 | ||||||||
\(157\) | −18.1790 | −1.45084 | −0.725421 | − | 0.688306i | \(-0.758355\pi\) | ||||
−0.725421 | + | 0.688306i | \(0.758355\pi\) | |||||||
\(158\) | −19.5911 | −1.55858 | ||||||||
\(159\) | −7.42761 | −0.589048 | ||||||||
\(160\) | −7.56938 | −0.598412 | ||||||||
\(161\) | −0.842722 | −0.0664158 | ||||||||
\(162\) | −2.17202 | −0.170650 | ||||||||
\(163\) | 18.8798 | 1.47878 | 0.739389 | − | 0.673279i | \(-0.235115\pi\) | ||||
0.739389 | + | 0.673279i | \(0.235115\pi\) | |||||||
\(164\) | 22.4047 | 1.74952 | ||||||||
\(165\) | −3.51451 | −0.273604 | ||||||||
\(166\) | −0.506646 | −0.0393234 | ||||||||
\(167\) | 3.82014 | 0.295611 | 0.147806 | − | 0.989016i | \(-0.452779\pi\) | ||||
0.147806 | + | 0.989016i | \(0.452779\pi\) | |||||||
\(168\) | 1.12549 | 0.0868334 | ||||||||
\(169\) | 14.2427 | 1.09559 | ||||||||
\(170\) | 5.08008 | 0.389625 | ||||||||
\(171\) | 7.25112 | 0.554507 | ||||||||
\(172\) | 16.3287 | 1.24505 | ||||||||
\(173\) | −0.147794 | −0.0112366 | −0.00561829 | − | 0.999984i | \(-0.501788\pi\) | ||||
−0.00561829 | + | 0.999984i | \(0.501788\pi\) | |||||||
\(174\) | 22.9395 | 1.73904 | ||||||||
\(175\) | −0.722026 | −0.0545800 | ||||||||
\(176\) | −7.20337 | −0.542974 | ||||||||
\(177\) | 3.93902 | 0.296075 | ||||||||
\(178\) | 14.0964 | 1.05657 | ||||||||
\(179\) | −25.0399 | −1.87157 | −0.935785 | − | 0.352572i | \(-0.885307\pi\) | ||||
−0.935785 | + | 0.352572i | \(0.885307\pi\) | |||||||
\(180\) | −2.71767 | −0.202563 | ||||||||
\(181\) | −18.7119 | −1.39085 | −0.695423 | − | 0.718601i | \(-0.744783\pi\) | ||||
−0.695423 | + | 0.718601i | \(0.744783\pi\) | |||||||
\(182\) | 8.18542 | 0.606744 | ||||||||
\(183\) | 8.42212 | 0.622581 | ||||||||
\(184\) | −1.81937 | −0.134126 | ||||||||
\(185\) | 0.191811 | 0.0141022 | ||||||||
\(186\) | −13.9545 | −1.02319 | ||||||||
\(187\) | 8.22000 | 0.601106 | ||||||||
\(188\) | 28.8498 | 2.10409 | ||||||||
\(189\) | −0.722026 | −0.0525196 | ||||||||
\(190\) | 15.7496 | 1.14259 | ||||||||
\(191\) | 18.8448 | 1.36356 | 0.681781 | − | 0.731556i | \(-0.261206\pi\) | ||||
0.681781 | + | 0.731556i | \(0.261206\pi\) | |||||||
\(192\) | −12.3416 | −0.890680 | ||||||||
\(193\) | 5.55334 | 0.399738 | 0.199869 | − | 0.979823i | \(-0.435948\pi\) | ||||
0.199869 | + | 0.979823i | \(0.435948\pi\) | |||||||
\(194\) | 2.80876 | 0.201657 | ||||||||
\(195\) | −5.21945 | −0.373773 | ||||||||
\(196\) | −17.6069 | −1.25764 | ||||||||
\(197\) | −5.45935 | −0.388963 | −0.194481 | − | 0.980906i | \(-0.562302\pi\) | ||||
−0.194481 | + | 0.980906i | \(0.562302\pi\) | |||||||
\(198\) | −7.63359 | −0.542495 | ||||||||
\(199\) | 0.256761 | 0.0182013 | 0.00910066 | − | 0.999959i | \(-0.497103\pi\) | ||||
0.00910066 | + | 0.999959i | \(0.497103\pi\) | |||||||
\(200\) | −1.55879 | −0.110223 | ||||||||
\(201\) | 0.356294 | 0.0251310 | ||||||||
\(202\) | 39.1969 | 2.75788 | ||||||||
\(203\) | 7.62559 | 0.535211 | ||||||||
\(204\) | 6.35629 | 0.445029 | ||||||||
\(205\) | −8.24409 | −0.575793 | ||||||||
\(206\) | −40.4781 | −2.82024 | ||||||||
\(207\) | 1.16716 | 0.0811235 | ||||||||
\(208\) | −10.6978 | −0.741761 | ||||||||
\(209\) | 25.4841 | 1.76277 | ||||||||
\(210\) | −1.56825 | −0.108220 | ||||||||
\(211\) | 19.5219 | 1.34395 | 0.671973 | − | 0.740576i | \(-0.265447\pi\) | ||||
0.671973 | + | 0.740576i | \(0.265447\pi\) | |||||||
\(212\) | −20.1858 | −1.38637 | ||||||||
\(213\) | 12.4798 | 0.855099 | ||||||||
\(214\) | 15.7718 | 1.07814 | ||||||||
\(215\) | −6.00834 | −0.409765 | ||||||||
\(216\) | −1.55879 | −0.106063 | ||||||||
\(217\) | −4.63878 | −0.314901 | ||||||||
\(218\) | 43.3730 | 2.93759 | ||||||||
\(219\) | 1.19724 | 0.0809018 | ||||||||
\(220\) | −9.55128 | −0.643947 | ||||||||
\(221\) | 12.2076 | 0.821175 | ||||||||
\(222\) | 0.416616 | 0.0279615 | ||||||||
\(223\) | 15.8677 | 1.06258 | 0.531291 | − | 0.847190i | \(-0.321707\pi\) | ||||
0.531291 | + | 0.847190i | \(0.321707\pi\) | |||||||
\(224\) | −5.46529 | −0.365165 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 32.4843 | 2.16083 | ||||||||
\(227\) | −24.2538 | −1.60978 | −0.804890 | − | 0.593424i | \(-0.797776\pi\) | ||||
−0.804890 | + | 0.593424i | \(0.797776\pi\) | |||||||
\(228\) | 19.7061 | 1.30507 | ||||||||
\(229\) | −10.4032 | −0.687464 | −0.343732 | − | 0.939068i | \(-0.611691\pi\) | ||||
−0.343732 | + | 0.939068i | \(0.611691\pi\) | |||||||
\(230\) | 2.53510 | 0.167160 | ||||||||
\(231\) | −2.53757 | −0.166960 | ||||||||
\(232\) | 16.4630 | 1.08085 | ||||||||
\(233\) | −11.0431 | −0.723456 | −0.361728 | − | 0.932284i | \(-0.617813\pi\) | ||||
−0.361728 | + | 0.932284i | \(0.617813\pi\) | |||||||
\(234\) | −11.3367 | −0.741106 | ||||||||
\(235\) | −10.6156 | −0.692488 | ||||||||
\(236\) | 10.7050 | 0.696833 | ||||||||
\(237\) | 9.01975 | 0.585896 | ||||||||
\(238\) | 3.66795 | 0.237758 | ||||||||
\(239\) | −22.4165 | −1.45000 | −0.725002 | − | 0.688747i | \(-0.758161\pi\) | ||||
−0.725002 | + | 0.688747i | \(0.758161\pi\) | |||||||
\(240\) | 2.04961 | 0.132302 | ||||||||
\(241\) | 19.6497 | 1.26575 | 0.632874 | − | 0.774255i | \(-0.281875\pi\) | ||||
0.632874 | + | 0.774255i | \(0.281875\pi\) | |||||||
\(242\) | −2.93609 | −0.188739 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 22.8885 | 1.46529 | ||||||||
\(245\) | 6.47868 | 0.413908 | ||||||||
\(246\) | −17.9063 | −1.14167 | ||||||||
\(247\) | 37.8468 | 2.40814 | ||||||||
\(248\) | −10.0147 | −0.635937 | ||||||||
\(249\) | 0.233260 | 0.0147823 | ||||||||
\(250\) | 2.17202 | 0.137371 | ||||||||
\(251\) | −3.21617 | −0.203003 | −0.101501 | − | 0.994835i | \(-0.532365\pi\) | ||||
−0.101501 | + | 0.994835i | \(0.532365\pi\) | |||||||
\(252\) | −1.96223 | −0.123609 | ||||||||
\(253\) | 4.10201 | 0.257891 | ||||||||
\(254\) | 12.2570 | 0.769073 | ||||||||
\(255\) | −2.33888 | −0.146466 | ||||||||
\(256\) | −0.658785 | −0.0411741 | ||||||||
\(257\) | 5.25537 | 0.327821 | 0.163910 | − | 0.986475i | \(-0.447589\pi\) | ||||
0.163910 | + | 0.986475i | \(0.447589\pi\) | |||||||
\(258\) | −13.0502 | −0.812472 | ||||||||
\(259\) | 0.138492 | 0.00860548 | ||||||||
\(260\) | −14.1847 | −0.879701 | ||||||||
\(261\) | −10.5614 | −0.653733 | ||||||||
\(262\) | 42.0323 | 2.59677 | ||||||||
\(263\) | 15.9986 | 0.986517 | 0.493259 | − | 0.869883i | \(-0.335806\pi\) | ||||
0.493259 | + | 0.869883i | \(0.335806\pi\) | |||||||
\(264\) | −5.47840 | −0.337172 | ||||||||
\(265\) | 7.42761 | 0.456275 | ||||||||
\(266\) | 11.3716 | 0.697237 | ||||||||
\(267\) | −6.48999 | −0.397181 | ||||||||
\(268\) | 0.968290 | 0.0591477 | ||||||||
\(269\) | −21.2447 | −1.29531 | −0.647656 | − | 0.761933i | \(-0.724250\pi\) | ||||
−0.647656 | + | 0.761933i | \(0.724250\pi\) | |||||||
\(270\) | 2.17202 | 0.132185 | ||||||||
\(271\) | 7.31997 | 0.444656 | 0.222328 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222328 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(272\) | −4.79378 | −0.290666 | ||||||||
\(273\) | −3.76858 | −0.228085 | ||||||||
\(274\) | −33.9660 | −2.05196 | ||||||||
\(275\) | 3.51451 | 0.211933 | ||||||||
\(276\) | 3.17197 | 0.190930 | ||||||||
\(277\) | 23.3805 | 1.40480 | 0.702399 | − | 0.711784i | \(-0.252112\pi\) | ||||
0.702399 | + | 0.711784i | \(0.252112\pi\) | |||||||
\(278\) | 18.6867 | 1.12076 | ||||||||
\(279\) | 6.42467 | 0.384635 | ||||||||
\(280\) | −1.12549 | −0.0672609 | ||||||||
\(281\) | 22.1189 | 1.31951 | 0.659753 | − | 0.751483i | \(-0.270661\pi\) | ||||
0.659753 | + | 0.751483i | \(0.270661\pi\) | |||||||
\(282\) | −23.0574 | −1.37305 | ||||||||
\(283\) | 10.3373 | 0.614488 | 0.307244 | − | 0.951631i | \(-0.400593\pi\) | ||||
0.307244 | + | 0.951631i | \(0.400593\pi\) | |||||||
\(284\) | 33.9159 | 2.01254 | ||||||||
\(285\) | −7.25112 | −0.429519 | ||||||||
\(286\) | −39.8431 | −2.35597 | ||||||||
\(287\) | −5.95245 | −0.351362 | ||||||||
\(288\) | 7.56938 | 0.446030 | ||||||||
\(289\) | −11.5297 | −0.678215 | ||||||||
\(290\) | −22.9395 | −1.34706 | ||||||||
\(291\) | −1.29315 | −0.0758060 | ||||||||
\(292\) | 3.25370 | 0.190408 | ||||||||
\(293\) | −9.28607 | −0.542498 | −0.271249 | − | 0.962509i | \(-0.587437\pi\) | ||||
−0.271249 | + | 0.962509i | \(0.587437\pi\) | |||||||
\(294\) | 14.0718 | 0.820685 | ||||||||
\(295\) | −3.93902 | −0.229338 | ||||||||
\(296\) | 0.298993 | 0.0173786 | ||||||||
\(297\) | 3.51451 | 0.203933 | ||||||||
\(298\) | 17.0406 | 0.987137 | ||||||||
\(299\) | 6.09195 | 0.352307 | ||||||||
\(300\) | 2.71767 | 0.156905 | ||||||||
\(301\) | −4.33817 | −0.250048 | ||||||||
\(302\) | −9.63995 | −0.554717 | ||||||||
\(303\) | −18.0463 | −1.03673 | ||||||||
\(304\) | −14.8619 | −0.852391 | ||||||||
\(305\) | −8.42212 | −0.482249 | ||||||||
\(306\) | −5.08008 | −0.290409 | ||||||||
\(307\) | −8.15718 | −0.465555 | −0.232778 | − | 0.972530i | \(-0.574781\pi\) | ||||
−0.232778 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(308\) | −6.89627 | −0.392951 | ||||||||
\(309\) | 18.6362 | 1.06017 | ||||||||
\(310\) | 13.9545 | 0.792563 | ||||||||
\(311\) | −23.8355 | −1.35158 | −0.675792 | − | 0.737092i | \(-0.736198\pi\) | ||||
−0.675792 | + | 0.737092i | \(0.736198\pi\) | |||||||
\(312\) | −8.13605 | −0.460613 | ||||||||
\(313\) | 2.03645 | 0.115107 | 0.0575535 | − | 0.998342i | \(-0.481670\pi\) | ||||
0.0575535 | + | 0.998342i | \(0.481670\pi\) | |||||||
\(314\) | 39.4851 | 2.22827 | ||||||||
\(315\) | 0.722026 | 0.0406815 | ||||||||
\(316\) | 24.5127 | 1.37895 | ||||||||
\(317\) | 8.85082 | 0.497111 | 0.248556 | − | 0.968618i | \(-0.420044\pi\) | ||||
0.248556 | + | 0.968618i | \(0.420044\pi\) | |||||||
\(318\) | 16.1329 | 0.904690 | ||||||||
\(319\) | −37.1181 | −2.07821 | ||||||||
\(320\) | 12.3416 | 0.689918 | ||||||||
\(321\) | −7.26136 | −0.405290 | ||||||||
\(322\) | 1.83041 | 0.102005 | ||||||||
\(323\) | 16.9595 | 0.943649 | ||||||||
\(324\) | 2.71767 | 0.150982 | ||||||||
\(325\) | 5.21945 | 0.289523 | ||||||||
\(326\) | −41.0072 | −2.27118 | ||||||||
\(327\) | −19.9690 | −1.10429 | ||||||||
\(328\) | −12.8508 | −0.709569 | ||||||||
\(329\) | −7.66477 | −0.422572 | ||||||||
\(330\) | 7.63359 | 0.420215 | ||||||||
\(331\) | 3.21020 | 0.176449 | 0.0882244 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882244 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(332\) | 0.633925 | 0.0347911 | ||||||||
\(333\) | −0.191811 | −0.0105112 | ||||||||
\(334\) | −8.29742 | −0.454014 | ||||||||
\(335\) | −0.356294 | −0.0194664 | ||||||||
\(336\) | 1.47987 | 0.0807335 | ||||||||
\(337\) | 5.44134 | 0.296409 | 0.148204 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148204 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(338\) | −30.9353 | −1.68266 | ||||||||
\(339\) | −14.9558 | −0.812289 | ||||||||
\(340\) | −6.35629 | −0.344718 | ||||||||
\(341\) | 22.5796 | 1.22275 | ||||||||
\(342\) | −15.7496 | −0.851639 | ||||||||
\(343\) | 9.73195 | 0.525476 | ||||||||
\(344\) | −9.36576 | −0.504968 | ||||||||
\(345\) | −1.16716 | −0.0628380 | ||||||||
\(346\) | 0.321012 | 0.0172577 | ||||||||
\(347\) | 25.5060 | 1.36923 | 0.684617 | − | 0.728903i | \(-0.259969\pi\) | ||||
0.684617 | + | 0.728903i | \(0.259969\pi\) | |||||||
\(348\) | −28.7023 | −1.53861 | ||||||||
\(349\) | 7.62761 | 0.408297 | 0.204148 | − | 0.978940i | \(-0.434557\pi\) | ||||
0.204148 | + | 0.978940i | \(0.434557\pi\) | |||||||
\(350\) | 1.56825 | 0.0838267 | ||||||||
\(351\) | 5.21945 | 0.278594 | ||||||||
\(352\) | 26.6027 | 1.41793 | ||||||||
\(353\) | −19.7452 | −1.05093 | −0.525467 | − | 0.850814i | \(-0.676109\pi\) | ||||
−0.525467 | + | 0.850814i | \(0.676109\pi\) | |||||||
\(354\) | −8.55562 | −0.454726 | ||||||||
\(355\) | −12.4798 | −0.662357 | ||||||||
\(356\) | −17.6377 | −0.934794 | ||||||||
\(357\) | −1.68873 | −0.0893770 | ||||||||
\(358\) | 54.3871 | 2.87445 | ||||||||
\(359\) | −25.1554 | −1.32765 | −0.663825 | − | 0.747888i | \(-0.731068\pi\) | ||||
−0.663825 | + | 0.747888i | \(0.731068\pi\) | |||||||
\(360\) | 1.55879 | 0.0821557 | ||||||||
\(361\) | 33.5787 | 1.76730 | ||||||||
\(362\) | 40.6426 | 2.13613 | ||||||||
\(363\) | 1.35178 | 0.0709500 | ||||||||
\(364\) | −10.2417 | −0.536814 | ||||||||
\(365\) | −1.19724 | −0.0626663 | ||||||||
\(366\) | −18.2930 | −0.956191 | ||||||||
\(367\) | 26.5211 | 1.38439 | 0.692196 | − | 0.721709i | \(-0.256643\pi\) | ||||
0.692196 | + | 0.721709i | \(0.256643\pi\) | |||||||
\(368\) | −2.39223 | −0.124704 | ||||||||
\(369\) | 8.24409 | 0.429170 | ||||||||
\(370\) | −0.416616 | −0.0216589 | ||||||||
\(371\) | 5.36293 | 0.278429 | ||||||||
\(372\) | 17.4601 | 0.905266 | ||||||||
\(373\) | −21.1068 | −1.09287 | −0.546436 | − | 0.837501i | \(-0.684016\pi\) | ||||
−0.546436 | + | 0.837501i | \(0.684016\pi\) | |||||||
\(374\) | −17.8540 | −0.923209 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −16.5476 | −0.853377 | ||||||||
\(377\) | −55.1246 | −2.83906 | ||||||||
\(378\) | 1.56825 | 0.0806623 | ||||||||
\(379\) | 2.55660 | 0.131324 | 0.0656619 | − | 0.997842i | \(-0.479084\pi\) | ||||
0.0656619 | + | 0.997842i | \(0.479084\pi\) | |||||||
\(380\) | −19.7061 | −1.01090 | ||||||||
\(381\) | −5.64314 | −0.289107 | ||||||||
\(382\) | −40.9313 | −2.09423 | ||||||||
\(383\) | −28.1678 | −1.43931 | −0.719654 | − | 0.694333i | \(-0.755699\pi\) | ||||
−0.719654 | + | 0.694333i | \(0.755699\pi\) | |||||||
\(384\) | 11.6675 | 0.595404 | ||||||||
\(385\) | 2.53757 | 0.129326 | ||||||||
\(386\) | −12.0620 | −0.613938 | ||||||||
\(387\) | 6.00834 | 0.305421 | ||||||||
\(388\) | −3.51437 | −0.178415 | ||||||||
\(389\) | 14.4020 | 0.730212 | 0.365106 | − | 0.930966i | \(-0.381033\pi\) | ||||
0.365106 | + | 0.930966i | \(0.381033\pi\) | |||||||
\(390\) | 11.3367 | 0.574059 | ||||||||
\(391\) | 2.72985 | 0.138055 | ||||||||
\(392\) | 10.0989 | 0.510073 | ||||||||
\(393\) | −19.3517 | −0.976165 | ||||||||
\(394\) | 11.8578 | 0.597389 | ||||||||
\(395\) | −9.01975 | −0.453833 | ||||||||
\(396\) | 9.55128 | 0.479970 | ||||||||
\(397\) | −3.75089 | −0.188252 | −0.0941258 | − | 0.995560i | \(-0.530006\pi\) | ||||
−0.0941258 | + | 0.995560i | \(0.530006\pi\) | |||||||
\(398\) | −0.557690 | −0.0279545 | ||||||||
\(399\) | −5.23549 | −0.262102 | ||||||||
\(400\) | −2.04961 | −0.102480 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −0.773878 | −0.0385975 | ||||||||
\(403\) | 33.5333 | 1.67041 | ||||||||
\(404\) | −49.0439 | −2.44002 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −16.5629 | −0.822004 | ||||||||
\(407\) | −0.674120 | −0.0334149 | ||||||||
\(408\) | −3.64583 | −0.180495 | ||||||||
\(409\) | 19.7524 | 0.976694 | 0.488347 | − | 0.872649i | \(-0.337600\pi\) | ||||
0.488347 | + | 0.872649i | \(0.337600\pi\) | |||||||
\(410\) | 17.9063 | 0.884331 | ||||||||
\(411\) | 15.6380 | 0.771364 | ||||||||
\(412\) | 50.6469 | 2.49520 | ||||||||
\(413\) | −2.84407 | −0.139948 | ||||||||
\(414\) | −2.53510 | −0.124594 | ||||||||
\(415\) | −0.233260 | −0.0114503 | ||||||||
\(416\) | 39.5080 | 1.93704 | ||||||||
\(417\) | −8.60340 | −0.421310 | ||||||||
\(418\) | −55.3520 | −2.70736 | ||||||||
\(419\) | 20.4807 | 1.00055 | 0.500273 | − | 0.865868i | \(-0.333233\pi\) | ||||
0.500273 | + | 0.865868i | \(0.333233\pi\) | |||||||
\(420\) | 1.96223 | 0.0957469 | ||||||||
\(421\) | −15.6326 | −0.761888 | −0.380944 | − | 0.924598i | \(-0.624401\pi\) | ||||
−0.380944 | + | 0.924598i | \(0.624401\pi\) | |||||||
\(422\) | −42.4021 | −2.06410 | ||||||||
\(423\) | 10.6156 | 0.516150 | ||||||||
\(424\) | 11.5781 | 0.562283 | ||||||||
\(425\) | 2.33888 | 0.113452 | ||||||||
\(426\) | −27.1063 | −1.31330 | ||||||||
\(427\) | −6.08098 | −0.294279 | ||||||||
\(428\) | −19.7340 | −0.953878 | ||||||||
\(429\) | 18.3438 | 0.885647 | ||||||||
\(430\) | 13.0502 | 0.629338 | ||||||||
\(431\) | −4.24956 | −0.204694 | −0.102347 | − | 0.994749i | \(-0.532635\pi\) | ||||
−0.102347 | + | 0.994749i | \(0.532635\pi\) | |||||||
\(432\) | −2.04961 | −0.0986118 | ||||||||
\(433\) | 11.5596 | 0.555520 | 0.277760 | − | 0.960650i | \(-0.410408\pi\) | ||||
0.277760 | + | 0.960650i | \(0.410408\pi\) | |||||||
\(434\) | 10.0755 | 0.483640 | ||||||||
\(435\) | 10.5614 | 0.506379 | ||||||||
\(436\) | −54.2691 | −2.59902 | ||||||||
\(437\) | 8.46324 | 0.404852 | ||||||||
\(438\) | −2.60042 | −0.124253 | ||||||||
\(439\) | −23.9398 | −1.14259 | −0.571293 | − | 0.820746i | \(-0.693558\pi\) | ||||
−0.571293 | + | 0.820746i | \(0.693558\pi\) | |||||||
\(440\) | 5.47840 | 0.261172 | ||||||||
\(441\) | −6.47868 | −0.308509 | ||||||||
\(442\) | −26.5152 | −1.26120 | ||||||||
\(443\) | −40.6637 | −1.93199 | −0.965996 | − | 0.258558i | \(-0.916753\pi\) | ||||
−0.965996 | + | 0.258558i | \(0.916753\pi\) | |||||||
\(444\) | −0.521278 | −0.0247388 | ||||||||
\(445\) | 6.48999 | 0.307655 | ||||||||
\(446\) | −34.4650 | −1.63197 | ||||||||
\(447\) | −7.84552 | −0.371080 | ||||||||
\(448\) | 8.91097 | 0.421004 | ||||||||
\(449\) | 24.4439 | 1.15358 | 0.576788 | − | 0.816894i | \(-0.304306\pi\) | ||||
0.576788 | + | 0.816894i | \(0.304306\pi\) | |||||||
\(450\) | −2.17202 | −0.102390 | ||||||||
\(451\) | 28.9740 | 1.36433 | ||||||||
\(452\) | −40.6450 | −1.91178 | ||||||||
\(453\) | 4.43824 | 0.208527 | ||||||||
\(454\) | 52.6797 | 2.47238 | ||||||||
\(455\) | 3.76858 | 0.176674 | ||||||||
\(456\) | −11.3030 | −0.529311 | ||||||||
\(457\) | −6.94927 | −0.325073 | −0.162536 | − | 0.986703i | \(-0.551968\pi\) | ||||
−0.162536 | + | 0.986703i | \(0.551968\pi\) | |||||||
\(458\) | 22.5960 | 1.05584 | ||||||||
\(459\) | 2.33888 | 0.109169 | ||||||||
\(460\) | −3.17197 | −0.147894 | ||||||||
\(461\) | 22.7309 | 1.05868 | 0.529342 | − | 0.848408i | \(-0.322439\pi\) | ||||
0.529342 | + | 0.848408i | \(0.322439\pi\) | |||||||
\(462\) | 5.51164 | 0.256425 | ||||||||
\(463\) | 15.7905 | 0.733847 | 0.366923 | − | 0.930251i | \(-0.380411\pi\) | ||||
0.366923 | + | 0.930251i | \(0.380411\pi\) | |||||||
\(464\) | 21.6467 | 1.00492 | ||||||||
\(465\) | −6.42467 | −0.297937 | ||||||||
\(466\) | 23.9858 | 1.11112 | ||||||||
\(467\) | 16.2694 | 0.752859 | 0.376429 | − | 0.926445i | \(-0.377152\pi\) | ||||
0.376429 | + | 0.926445i | \(0.377152\pi\) | |||||||
\(468\) | 14.1847 | 0.655690 | ||||||||
\(469\) | −0.257253 | −0.0118789 | ||||||||
\(470\) | 23.0574 | 1.06356 | ||||||||
\(471\) | −18.1790 | −0.837644 | ||||||||
\(472\) | −6.14012 | −0.282622 | ||||||||
\(473\) | 21.1164 | 0.970931 | ||||||||
\(474\) | −19.5911 | −0.899848 | ||||||||
\(475\) | 7.25112 | 0.332704 | ||||||||
\(476\) | −4.58941 | −0.210355 | ||||||||
\(477\) | −7.42761 | −0.340087 | ||||||||
\(478\) | 48.6891 | 2.22699 | ||||||||
\(479\) | −15.9673 | −0.729564 | −0.364782 | − | 0.931093i | \(-0.618857\pi\) | ||||
−0.364782 | + | 0.931093i | \(0.618857\pi\) | |||||||
\(480\) | −7.56938 | −0.345493 | ||||||||
\(481\) | −1.00115 | −0.0456483 | ||||||||
\(482\) | −42.6795 | −1.94400 | ||||||||
\(483\) | −0.842722 | −0.0383452 | ||||||||
\(484\) | 3.67369 | 0.166986 | ||||||||
\(485\) | 1.29315 | 0.0587191 | ||||||||
\(486\) | −2.17202 | −0.0985248 | ||||||||
\(487\) | 23.1357 | 1.04838 | 0.524188 | − | 0.851602i | \(-0.324369\pi\) | ||||
0.524188 | + | 0.851602i | \(0.324369\pi\) | |||||||
\(488\) | −13.1283 | −0.594292 | ||||||||
\(489\) | 18.8798 | 0.853773 | ||||||||
\(490\) | −14.0718 | −0.635700 | ||||||||
\(491\) | 17.8683 | 0.806384 | 0.403192 | − | 0.915115i | \(-0.367901\pi\) | ||||
0.403192 | + | 0.915115i | \(0.367901\pi\) | |||||||
\(492\) | 22.4047 | 1.01008 | ||||||||
\(493\) | −24.7018 | −1.11251 | ||||||||
\(494\) | −82.2041 | −3.69854 | ||||||||
\(495\) | −3.51451 | −0.157965 | ||||||||
\(496\) | −13.1681 | −0.591264 | ||||||||
\(497\) | −9.01071 | −0.404185 | ||||||||
\(498\) | −0.506646 | −0.0227034 | ||||||||
\(499\) | −37.5643 | −1.68161 | −0.840805 | − | 0.541338i | \(-0.817918\pi\) | ||||
−0.840805 | + | 0.541338i | \(0.817918\pi\) | |||||||
\(500\) | −2.71767 | −0.121538 | ||||||||
\(501\) | 3.82014 | 0.170671 | ||||||||
\(502\) | 6.98558 | 0.311782 | ||||||||
\(503\) | 6.05063 | 0.269784 | 0.134892 | − | 0.990860i | \(-0.456931\pi\) | ||||
0.134892 | + | 0.990860i | \(0.456931\pi\) | |||||||
\(504\) | 1.12549 | 0.0501333 | ||||||||
\(505\) | 18.0463 | 0.803049 | ||||||||
\(506\) | −8.90965 | −0.396082 | ||||||||
\(507\) | 14.2427 | 0.632539 | ||||||||
\(508\) | −15.3362 | −0.680433 | ||||||||
\(509\) | 16.0628 | 0.711972 | 0.355986 | − | 0.934491i | \(-0.384145\pi\) | ||||
0.355986 | + | 0.934491i | \(0.384145\pi\) | |||||||
\(510\) | 5.08008 | 0.224950 | ||||||||
\(511\) | −0.864437 | −0.0382404 | ||||||||
\(512\) | −21.9041 | −0.968034 | ||||||||
\(513\) | 7.25112 | 0.320145 | ||||||||
\(514\) | −11.4148 | −0.503484 | ||||||||
\(515\) | −18.6362 | −0.821207 | ||||||||
\(516\) | 16.3287 | 0.718830 | ||||||||
\(517\) | 37.3088 | 1.64084 | ||||||||
\(518\) | −0.300808 | −0.0132167 | ||||||||
\(519\) | −0.147794 | −0.00648745 | ||||||||
\(520\) | 8.13605 | 0.356789 | ||||||||
\(521\) | 15.0359 | 0.658736 | 0.329368 | − | 0.944202i | \(-0.393164\pi\) | ||||
0.329368 | + | 0.944202i | \(0.393164\pi\) | |||||||
\(522\) | 22.9395 | 1.00404 | ||||||||
\(523\) | 41.7342 | 1.82491 | 0.912454 | − | 0.409178i | \(-0.134185\pi\) | ||||
0.912454 | + | 0.409178i | \(0.134185\pi\) | |||||||
\(524\) | −52.5916 | −2.29747 | ||||||||
\(525\) | −0.722026 | −0.0315118 | ||||||||
\(526\) | −34.7493 | −1.51514 | ||||||||
\(527\) | 15.0265 | 0.654565 | ||||||||
\(528\) | −7.20337 | −0.313486 | ||||||||
\(529\) | −21.6377 | −0.940771 | ||||||||
\(530\) | −16.1329 | −0.700769 | ||||||||
\(531\) | 3.93902 | 0.170939 | ||||||||
\(532\) | −14.2283 | −0.616877 | ||||||||
\(533\) | 43.0296 | 1.86382 | ||||||||
\(534\) | 14.0964 | 0.610010 | ||||||||
\(535\) | 7.26136 | 0.313936 | ||||||||
\(536\) | −0.555389 | −0.0239892 | ||||||||
\(537\) | −25.0399 | −1.08055 | ||||||||
\(538\) | 46.1439 | 1.98940 | ||||||||
\(539\) | −22.7694 | −0.980747 | ||||||||
\(540\) | −2.71767 | −0.116950 | ||||||||
\(541\) | −42.8386 | −1.84178 | −0.920888 | − | 0.389828i | \(-0.872535\pi\) | ||||
−0.920888 | + | 0.389828i | \(0.872535\pi\) | |||||||
\(542\) | −15.8991 | −0.682925 | ||||||||
\(543\) | −18.7119 | −0.803005 | ||||||||
\(544\) | 17.7038 | 0.759046 | ||||||||
\(545\) | 19.9690 | 0.855378 | ||||||||
\(546\) | 8.18542 | 0.350304 | ||||||||
\(547\) | −27.5055 | −1.17605 | −0.588024 | − | 0.808843i | \(-0.700094\pi\) | ||||
−0.588024 | + | 0.808843i | \(0.700094\pi\) | |||||||
\(548\) | 42.4989 | 1.81546 | ||||||||
\(549\) | 8.42212 | 0.359447 | ||||||||
\(550\) | −7.63359 | −0.325497 | ||||||||
\(551\) | −76.5818 | −3.26249 | ||||||||
\(552\) | −1.81937 | −0.0774375 | ||||||||
\(553\) | −6.51249 | −0.276939 | ||||||||
\(554\) | −50.7829 | −2.15756 | ||||||||
\(555\) | 0.191811 | 0.00814190 | ||||||||
\(556\) | −23.3812 | −0.991584 | ||||||||
\(557\) | 30.1333 | 1.27679 | 0.638394 | − | 0.769709i | \(-0.279599\pi\) | ||||
0.638394 | + | 0.769709i | \(0.279599\pi\) | |||||||
\(558\) | −13.9545 | −0.590742 | ||||||||
\(559\) | 31.3602 | 1.32640 | ||||||||
\(560\) | −1.47987 | −0.0625359 | ||||||||
\(561\) | 8.22000 | 0.347049 | ||||||||
\(562\) | −48.0428 | −2.02656 | ||||||||
\(563\) | −8.65025 | −0.364565 | −0.182282 | − | 0.983246i | \(-0.558348\pi\) | ||||
−0.182282 | + | 0.983246i | \(0.558348\pi\) | |||||||
\(564\) | 28.8498 | 1.21480 | ||||||||
\(565\) | 14.9558 | 0.629196 | ||||||||
\(566\) | −22.4528 | −0.943761 | ||||||||
\(567\) | −0.722026 | −0.0303222 | ||||||||
\(568\) | −19.4534 | −0.816246 | ||||||||
\(569\) | 26.2282 | 1.09954 | 0.549772 | − | 0.835315i | \(-0.314715\pi\) | ||||
0.549772 | + | 0.835315i | \(0.314715\pi\) | |||||||
\(570\) | 15.7496 | 0.659677 | ||||||||
\(571\) | −1.50787 | −0.0631025 | −0.0315512 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315512 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(572\) | 49.8524 | 2.08443 | ||||||||
\(573\) | 18.8448 | 0.787253 | ||||||||
\(574\) | 12.9288 | 0.539639 | ||||||||
\(575\) | 1.16716 | 0.0486741 | ||||||||
\(576\) | −12.3416 | −0.514234 | ||||||||
\(577\) | 9.85368 | 0.410214 | 0.205107 | − | 0.978740i | \(-0.434246\pi\) | ||||
0.205107 | + | 0.978740i | \(0.434246\pi\) | |||||||
\(578\) | 25.0427 | 1.04164 | ||||||||
\(579\) | 5.55334 | 0.230789 | ||||||||
\(580\) | 28.7023 | 1.19180 | ||||||||
\(581\) | −0.168420 | −0.00698724 | ||||||||
\(582\) | 2.80876 | 0.116427 | ||||||||
\(583\) | −26.1044 | −1.08113 | ||||||||
\(584\) | −1.86625 | −0.0772259 | ||||||||
\(585\) | −5.21945 | −0.215798 | ||||||||
\(586\) | 20.1695 | 0.833195 | ||||||||
\(587\) | 25.1616 | 1.03853 | 0.519265 | − | 0.854613i | \(-0.326206\pi\) | ||||
0.519265 | + | 0.854613i | \(0.326206\pi\) | |||||||
\(588\) | −17.6069 | −0.726097 | ||||||||
\(589\) | 46.5860 | 1.91954 | ||||||||
\(590\) | 8.55562 | 0.352229 | ||||||||
\(591\) | −5.45935 | −0.224568 | ||||||||
\(592\) | 0.393137 | 0.0161578 | ||||||||
\(593\) | 30.2239 | 1.24115 | 0.620574 | − | 0.784148i | \(-0.286900\pi\) | ||||
0.620574 | + | 0.784148i | \(0.286900\pi\) | |||||||
\(594\) | −7.63359 | −0.313210 | ||||||||
\(595\) | 1.68873 | 0.0692311 | ||||||||
\(596\) | −21.3215 | −0.873364 | ||||||||
\(597\) | 0.256761 | 0.0105085 | ||||||||
\(598\) | −13.2318 | −0.541090 | ||||||||
\(599\) | 16.4438 | 0.671875 | 0.335937 | − | 0.941884i | \(-0.390947\pi\) | ||||
0.335937 | + | 0.941884i | \(0.390947\pi\) | |||||||
\(600\) | −1.55879 | −0.0636375 | ||||||||
\(601\) | −36.4102 | −1.48520 | −0.742602 | − | 0.669733i | \(-0.766408\pi\) | ||||
−0.742602 | + | 0.669733i | \(0.766408\pi\) | |||||||
\(602\) | 9.42260 | 0.384037 | ||||||||
\(603\) | 0.356294 | 0.0145094 | ||||||||
\(604\) | 12.0617 | 0.490783 | ||||||||
\(605\) | −1.35178 | −0.0549577 | ||||||||
\(606\) | 39.1969 | 1.59227 | ||||||||
\(607\) | −20.8364 | −0.845725 | −0.422862 | − | 0.906194i | \(-0.638975\pi\) | ||||
−0.422862 | + | 0.906194i | \(0.638975\pi\) | |||||||
\(608\) | 54.8864 | 2.22594 | ||||||||
\(609\) | 7.62559 | 0.309004 | ||||||||
\(610\) | 18.2930 | 0.740662 | ||||||||
\(611\) | 55.4078 | 2.24156 | ||||||||
\(612\) | 6.35629 | 0.256938 | ||||||||
\(613\) | 12.6732 | 0.511867 | 0.255933 | − | 0.966694i | \(-0.417617\pi\) | ||||
0.255933 | + | 0.966694i | \(0.417617\pi\) | |||||||
\(614\) | 17.7176 | 0.715023 | ||||||||
\(615\) | −8.24409 | −0.332434 | ||||||||
\(616\) | 3.95554 | 0.159373 | ||||||||
\(617\) | 7.11050 | 0.286258 | 0.143129 | − | 0.989704i | \(-0.454284\pi\) | ||||
0.143129 | + | 0.989704i | \(0.454284\pi\) | |||||||
\(618\) | −40.4781 | −1.62827 | ||||||||
\(619\) | 22.6606 | 0.910808 | 0.455404 | − | 0.890285i | \(-0.349495\pi\) | ||||
0.455404 | + | 0.890285i | \(0.349495\pi\) | |||||||
\(620\) | −17.4601 | −0.701216 | ||||||||
\(621\) | 1.16716 | 0.0468367 | ||||||||
\(622\) | 51.7711 | 2.07583 | ||||||||
\(623\) | 4.68594 | 0.187738 | ||||||||
\(624\) | −10.6978 | −0.428256 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.42321 | −0.176787 | ||||||||
\(627\) | 25.4841 | 1.01774 | ||||||||
\(628\) | −49.4045 | −1.97145 | ||||||||
\(629\) | −0.448621 | −0.0178877 | ||||||||
\(630\) | −1.56825 | −0.0624807 | ||||||||
\(631\) | −18.4454 | −0.734300 | −0.367150 | − | 0.930162i | \(-0.619666\pi\) | ||||
−0.367150 | + | 0.930162i | \(0.619666\pi\) | |||||||
\(632\) | −14.0599 | −0.559274 | ||||||||
\(633\) | 19.5219 | 0.775928 | ||||||||
\(634\) | −19.2241 | −0.763488 | ||||||||
\(635\) | 5.64314 | 0.223941 | ||||||||
\(636\) | −20.1858 | −0.800419 | ||||||||
\(637\) | −33.8151 | −1.33980 | ||||||||
\(638\) | 80.6212 | 3.19182 | ||||||||
\(639\) | 12.4798 | 0.493692 | ||||||||
\(640\) | −11.6675 | −0.461198 | ||||||||
\(641\) | 10.9976 | 0.434378 | 0.217189 | − | 0.976130i | \(-0.430311\pi\) | ||||
0.217189 | + | 0.976130i | \(0.430311\pi\) | |||||||
\(642\) | 15.7718 | 0.622464 | ||||||||
\(643\) | 6.83077 | 0.269379 | 0.134690 | − | 0.990888i | \(-0.456996\pi\) | ||||
0.134690 | + | 0.990888i | \(0.456996\pi\) | |||||||
\(644\) | −2.29024 | −0.0902482 | ||||||||
\(645\) | −6.00834 | −0.236578 | ||||||||
\(646\) | −36.8363 | −1.44930 | ||||||||
\(647\) | 1.61068 | 0.0633222 | 0.0316611 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316611 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(648\) | −1.55879 | −0.0612352 | ||||||||
\(649\) | 13.8437 | 0.543413 | ||||||||
\(650\) | −11.3367 | −0.444664 | ||||||||
\(651\) | −4.63878 | −0.181808 | ||||||||
\(652\) | 51.3090 | 2.00941 | ||||||||
\(653\) | 41.6120 | 1.62840 | 0.814202 | − | 0.580581i | \(-0.197175\pi\) | ||||
0.814202 | + | 0.580581i | \(0.197175\pi\) | |||||||
\(654\) | 43.3730 | 1.69602 | ||||||||
\(655\) | 19.3517 | 0.756134 | ||||||||
\(656\) | −16.8972 | −0.659723 | ||||||||
\(657\) | 1.19724 | 0.0467087 | ||||||||
\(658\) | 16.6480 | 0.649007 | ||||||||
\(659\) | 19.5281 | 0.760708 | 0.380354 | − | 0.924841i | \(-0.375802\pi\) | ||||
0.380354 | + | 0.924841i | \(0.375802\pi\) | |||||||
\(660\) | −9.55128 | −0.371783 | ||||||||
\(661\) | −49.4617 | −1.92384 | −0.961919 | − | 0.273335i | \(-0.911873\pi\) | ||||
−0.961919 | + | 0.273335i | \(0.911873\pi\) | |||||||
\(662\) | −6.97262 | −0.270999 | ||||||||
\(663\) | 12.2076 | 0.474106 | ||||||||
\(664\) | −0.363605 | −0.0141106 | ||||||||
\(665\) | 5.23549 | 0.203024 | ||||||||
\(666\) | 0.416616 | 0.0161436 | ||||||||
\(667\) | −12.3269 | −0.477298 | ||||||||
\(668\) | 10.3819 | 0.401687 | ||||||||
\(669\) | 15.8677 | 0.613482 | ||||||||
\(670\) | 0.773878 | 0.0298975 | ||||||||
\(671\) | 29.5996 | 1.14268 | ||||||||
\(672\) | −5.46529 | −0.210828 | ||||||||
\(673\) | −13.8834 | −0.535166 | −0.267583 | − | 0.963535i | \(-0.586225\pi\) | ||||
−0.267583 | + | 0.963535i | \(0.586225\pi\) | |||||||
\(674\) | −11.8187 | −0.455240 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 38.7068 | 1.48872 | ||||||||
\(677\) | −43.7910 | −1.68303 | −0.841513 | − | 0.540237i | \(-0.818335\pi\) | ||||
−0.841513 | + | 0.540237i | \(0.818335\pi\) | |||||||
\(678\) | 32.4843 | 1.24755 | ||||||||
\(679\) | 0.933690 | 0.0358318 | ||||||||
\(680\) | 3.64583 | 0.139811 | ||||||||
\(681\) | −24.2538 | −0.929407 | ||||||||
\(682\) | −49.0433 | −1.87796 | ||||||||
\(683\) | 44.6719 | 1.70932 | 0.854662 | − | 0.519186i | \(-0.173765\pi\) | ||||
0.854662 | + | 0.519186i | \(0.173765\pi\) | |||||||
\(684\) | 19.7061 | 0.753483 | ||||||||
\(685\) | −15.6380 | −0.597496 | ||||||||
\(686\) | −21.1380 | −0.807052 | ||||||||
\(687\) | −10.4032 | −0.396907 | ||||||||
\(688\) | −12.3147 | −0.469495 | ||||||||
\(689\) | −38.7681 | −1.47695 | ||||||||
\(690\) | 2.53510 | 0.0965097 | ||||||||
\(691\) | −12.0169 | −0.457145 | −0.228573 | − | 0.973527i | \(-0.573406\pi\) | ||||
−0.228573 | + | 0.973527i | \(0.573406\pi\) | |||||||
\(692\) | −0.401656 | −0.0152687 | ||||||||
\(693\) | −2.53757 | −0.0963942 | ||||||||
\(694\) | −55.3996 | −2.10294 | ||||||||
\(695\) | 8.60340 | 0.326345 | ||||||||
\(696\) | 16.4630 | 0.624029 | ||||||||
\(697\) | 19.2819 | 0.730354 | ||||||||
\(698\) | −16.5673 | −0.627083 | ||||||||
\(699\) | −11.0431 | −0.417688 | ||||||||
\(700\) | −1.96223 | −0.0741652 | ||||||||
\(701\) | −17.3718 | −0.656124 | −0.328062 | − | 0.944656i | \(-0.606396\pi\) | ||||
−0.328062 | + | 0.944656i | \(0.606396\pi\) | |||||||
\(702\) | −11.3367 | −0.427878 | ||||||||
\(703\) | −1.39084 | −0.0524565 | ||||||||
\(704\) | −43.3748 | −1.63475 | ||||||||
\(705\) | −10.6156 | −0.399808 | ||||||||
\(706\) | 42.8871 | 1.61408 | ||||||||
\(707\) | 13.0299 | 0.490039 | ||||||||
\(708\) | 10.7050 | 0.402317 | ||||||||
\(709\) | 10.1634 | 0.381696 | 0.190848 | − | 0.981620i | \(-0.438876\pi\) | ||||
0.190848 | + | 0.981620i | \(0.438876\pi\) | |||||||
\(710\) | 27.1063 | 1.01728 | ||||||||
\(711\) | 9.01975 | 0.338267 | ||||||||
\(712\) | 10.1166 | 0.379134 | ||||||||
\(713\) | 7.49865 | 0.280827 | ||||||||
\(714\) | 3.66795 | 0.137270 | ||||||||
\(715\) | −18.3438 | −0.686020 | ||||||||
\(716\) | −68.0502 | −2.54315 | ||||||||
\(717\) | −22.4165 | −0.837160 | ||||||||
\(718\) | 54.6380 | 2.03907 | ||||||||
\(719\) | 1.00051 | 0.0373126 | 0.0186563 | − | 0.999826i | \(-0.494061\pi\) | ||||
0.0186563 | + | 0.999826i | \(0.494061\pi\) | |||||||
\(720\) | 2.04961 | 0.0763844 | ||||||||
\(721\) | −13.4558 | −0.501120 | ||||||||
\(722\) | −72.9335 | −2.71431 | ||||||||
\(723\) | 19.6497 | 0.730779 | ||||||||
\(724\) | −50.8528 | −1.88993 | ||||||||
\(725\) | −10.5614 | −0.392240 | ||||||||
\(726\) | −2.93609 | −0.108969 | ||||||||
\(727\) | −39.5004 | −1.46499 | −0.732495 | − | 0.680772i | \(-0.761644\pi\) | ||||
−0.732495 | + | 0.680772i | \(0.761644\pi\) | |||||||
\(728\) | 5.87444 | 0.217721 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.60042 | 0.0962460 | ||||||||
\(731\) | 14.0528 | 0.519760 | ||||||||
\(732\) | 22.8885 | 0.845985 | ||||||||
\(733\) | −26.3517 | −0.973321 | −0.486661 | − | 0.873591i | \(-0.661785\pi\) | ||||
−0.486661 | + | 0.873591i | \(0.661785\pi\) | |||||||
\(734\) | −57.6045 | −2.12622 | ||||||||
\(735\) | 6.47868 | 0.238970 | ||||||||
\(736\) | 8.83471 | 0.325652 | ||||||||
\(737\) | 1.25220 | 0.0461253 | ||||||||
\(738\) | −17.9063 | −0.659141 | ||||||||
\(739\) | −51.1032 | −1.87986 | −0.939931 | − | 0.341365i | \(-0.889111\pi\) | ||||
−0.939931 | + | 0.341365i | \(0.889111\pi\) | |||||||
\(740\) | 0.521278 | 0.0191626 | ||||||||
\(741\) | 37.8468 | 1.39034 | ||||||||
\(742\) | −11.6484 | −0.427626 | ||||||||
\(743\) | 30.4132 | 1.11575 | 0.557876 | − | 0.829924i | \(-0.311616\pi\) | ||||
0.557876 | + | 0.829924i | \(0.311616\pi\) | |||||||
\(744\) | −10.0147 | −0.367158 | ||||||||
\(745\) | 7.84552 | 0.287438 | ||||||||
\(746\) | 45.8445 | 1.67849 | ||||||||
\(747\) | 0.233260 | 0.00853455 | ||||||||
\(748\) | 22.3393 | 0.816804 | ||||||||
\(749\) | 5.24289 | 0.191571 | ||||||||
\(750\) | 2.17202 | 0.0793110 | ||||||||
\(751\) | −5.35980 | −0.195582 | −0.0977910 | − | 0.995207i | \(-0.531178\pi\) | ||||
−0.0977910 | + | 0.995207i | \(0.531178\pi\) | |||||||
\(752\) | −21.7579 | −0.793429 | ||||||||
\(753\) | −3.21617 | −0.117204 | ||||||||
\(754\) | 119.732 | 4.36037 | ||||||||
\(755\) | −4.43824 | −0.161524 | ||||||||
\(756\) | −1.96223 | −0.0713655 | ||||||||
\(757\) | 1.34520 | 0.0488923 | 0.0244461 | − | 0.999701i | \(-0.492218\pi\) | ||||
0.0244461 | + | 0.999701i | \(0.492218\pi\) | |||||||
\(758\) | −5.55299 | −0.201694 | ||||||||
\(759\) | 4.10201 | 0.148894 | ||||||||
\(760\) | 11.3030 | 0.410003 | ||||||||
\(761\) | 7.75272 | 0.281036 | 0.140518 | − | 0.990078i | \(-0.455123\pi\) | ||||
0.140518 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(762\) | 12.2570 | 0.444025 | ||||||||
\(763\) | 14.4181 | 0.521971 | ||||||||
\(764\) | 51.2140 | 1.85286 | ||||||||
\(765\) | −2.33888 | −0.0845622 | ||||||||
\(766\) | 61.1810 | 2.21056 | ||||||||
\(767\) | 20.5595 | 0.742361 | ||||||||
\(768\) | −0.658785 | −0.0237719 | ||||||||
\(769\) | 12.9556 | 0.467190 | 0.233595 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233595 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(770\) | −5.51164 | −0.198626 | ||||||||
\(771\) | 5.25537 | 0.189267 | ||||||||
\(772\) | 15.0922 | 0.543179 | ||||||||
\(773\) | 4.89841 | 0.176184 | 0.0880918 | − | 0.996112i | \(-0.471923\pi\) | ||||
0.0880918 | + | 0.996112i | \(0.471923\pi\) | |||||||
\(774\) | −13.0502 | −0.469081 | ||||||||
\(775\) | 6.42467 | 0.230781 | ||||||||
\(776\) | 2.01576 | 0.0723616 | ||||||||
\(777\) | 0.138492 | 0.00496838 | ||||||||
\(778\) | −31.2815 | −1.12150 | ||||||||
\(779\) | 59.7789 | 2.14180 | ||||||||
\(780\) | −14.1847 | −0.507895 | ||||||||
\(781\) | 43.8602 | 1.56944 | ||||||||
\(782\) | −5.92929 | −0.212031 | ||||||||
\(783\) | −10.5614 | −0.377433 | ||||||||
\(784\) | 13.2788 | 0.474241 | ||||||||
\(785\) | 18.1790 | 0.648836 | ||||||||
\(786\) | 42.0323 | 1.49924 | ||||||||
\(787\) | −35.2759 | −1.25745 | −0.628725 | − | 0.777628i | \(-0.716423\pi\) | ||||
−0.628725 | + | 0.777628i | \(0.716423\pi\) | |||||||
\(788\) | −14.8367 | −0.528536 | ||||||||
\(789\) | 15.9986 | 0.569566 | ||||||||
\(790\) | 19.5911 | 0.697019 | ||||||||
\(791\) | 10.7985 | 0.383950 | ||||||||
\(792\) | −5.47840 | −0.194666 | ||||||||
\(793\) | 43.9588 | 1.56102 | ||||||||
\(794\) | 8.14700 | 0.289126 | ||||||||
\(795\) | 7.42761 | 0.263430 | ||||||||
\(796\) | 0.697792 | 0.0247326 | ||||||||
\(797\) | −3.55618 | −0.125966 | −0.0629832 | − | 0.998015i | \(-0.520061\pi\) | ||||
−0.0629832 | + | 0.998015i | \(0.520061\pi\) | |||||||
\(798\) | 11.3716 | 0.402550 | ||||||||
\(799\) | 24.8287 | 0.878375 | ||||||||
\(800\) | 7.56938 | 0.267618 | ||||||||
\(801\) | −6.48999 | −0.229313 | ||||||||
\(802\) | 2.17202 | 0.0766967 | ||||||||
\(803\) | 4.20770 | 0.148487 | ||||||||
\(804\) | 0.968290 | 0.0341490 | ||||||||
\(805\) | 0.842722 | 0.0297021 | ||||||||
\(806\) | −72.8349 | −2.56550 | ||||||||
\(807\) | −21.2447 | −0.747848 | ||||||||
\(808\) | 28.1305 | 0.989626 | ||||||||
\(809\) | 14.7947 | 0.520153 | 0.260076 | − | 0.965588i | \(-0.416252\pi\) | ||||
0.260076 | + | 0.965588i | \(0.416252\pi\) | |||||||
\(810\) | 2.17202 | 0.0763170 | ||||||||
\(811\) | 13.0169 | 0.457084 | 0.228542 | − | 0.973534i | \(-0.426604\pi\) | ||||
0.228542 | + | 0.973534i | \(0.426604\pi\) | |||||||
\(812\) | 20.7238 | 0.727264 | ||||||||
\(813\) | 7.31997 | 0.256722 | ||||||||
\(814\) | 1.46420 | 0.0513203 | ||||||||
\(815\) | −18.8798 | −0.661329 | ||||||||
\(816\) | −4.79378 | −0.167816 | ||||||||
\(817\) | 43.5672 | 1.52422 | ||||||||
\(818\) | −42.9027 | −1.50006 | ||||||||
\(819\) | −3.76858 | −0.131685 | ||||||||
\(820\) | −22.4047 | −0.782407 | ||||||||
\(821\) | −51.4546 | −1.79578 | −0.897889 | − | 0.440223i | \(-0.854899\pi\) | ||||
−0.897889 | + | 0.440223i | \(0.854899\pi\) | |||||||
\(822\) | −33.9660 | −1.18470 | ||||||||
\(823\) | 25.9205 | 0.903532 | 0.451766 | − | 0.892137i | \(-0.350794\pi\) | ||||
0.451766 | + | 0.892137i | \(0.350794\pi\) | |||||||
\(824\) | −29.0499 | −1.01200 | ||||||||
\(825\) | 3.51451 | 0.122360 | ||||||||
\(826\) | 6.17738 | 0.214939 | ||||||||
\(827\) | 30.2104 | 1.05052 | 0.525259 | − | 0.850942i | \(-0.323968\pi\) | ||||
0.525259 | + | 0.850942i | \(0.323968\pi\) | |||||||
\(828\) | 3.17197 | 0.110233 | ||||||||
\(829\) | 52.4610 | 1.82205 | 0.911023 | − | 0.412355i | \(-0.135294\pi\) | ||||
0.911023 | + | 0.412355i | \(0.135294\pi\) | |||||||
\(830\) | 0.506646 | 0.0175859 | ||||||||
\(831\) | 23.3805 | 0.811060 | ||||||||
\(832\) | −64.4165 | −2.23324 | ||||||||
\(833\) | −15.1528 | −0.525014 | ||||||||
\(834\) | 18.6867 | 0.647069 | ||||||||
\(835\) | −3.82014 | −0.132201 | ||||||||
\(836\) | 69.2574 | 2.39532 | ||||||||
\(837\) | 6.42467 | 0.222069 | ||||||||
\(838\) | −44.4844 | −1.53669 | ||||||||
\(839\) | −5.14899 | −0.177763 | −0.0888815 | − | 0.996042i | \(-0.528329\pi\) | ||||
−0.0888815 | + | 0.996042i | \(0.528329\pi\) | |||||||
\(840\) | −1.12549 | −0.0388331 | ||||||||
\(841\) | 82.5427 | 2.84630 | ||||||||
\(842\) | 33.9544 | 1.17015 | ||||||||
\(843\) | 22.1189 | 0.761817 | ||||||||
\(844\) | 53.0542 | 1.82620 | ||||||||
\(845\) | −14.2427 | −0.489962 | ||||||||
\(846\) | −23.0574 | −0.792729 | ||||||||
\(847\) | −0.976020 | −0.0335364 | ||||||||
\(848\) | 15.2237 | 0.522784 | ||||||||
\(849\) | 10.3373 | 0.354775 | ||||||||
\(850\) | −5.08008 | −0.174245 | ||||||||
\(851\) | −0.223874 | −0.00767431 | ||||||||
\(852\) | 33.9159 | 1.16194 | ||||||||
\(853\) | 37.3951 | 1.28038 | 0.640192 | − | 0.768215i | \(-0.278855\pi\) | ||||
0.640192 | + | 0.768215i | \(0.278855\pi\) | |||||||
\(854\) | 13.2080 | 0.451969 | ||||||||
\(855\) | −7.25112 | −0.247983 | ||||||||
\(856\) | 11.3190 | 0.386874 | ||||||||
\(857\) | 49.7681 | 1.70004 | 0.850022 | − | 0.526746i | \(-0.176588\pi\) | ||||
0.850022 | + | 0.526746i | \(0.176588\pi\) | |||||||
\(858\) | −39.8431 | −1.36022 | ||||||||
\(859\) | −18.9741 | −0.647388 | −0.323694 | − | 0.946162i | \(-0.604925\pi\) | ||||
−0.323694 | + | 0.946162i | \(0.604925\pi\) | |||||||
\(860\) | −16.3287 | −0.556803 | ||||||||
\(861\) | −5.95245 | −0.202859 | ||||||||
\(862\) | 9.23014 | 0.314380 | ||||||||
\(863\) | −44.4758 | −1.51397 | −0.756986 | − | 0.653431i | \(-0.773329\pi\) | ||||
−0.756986 | + | 0.653431i | \(0.773329\pi\) | |||||||
\(864\) | 7.56938 | 0.257516 | ||||||||
\(865\) | 0.147794 | 0.00502515 | ||||||||
\(866\) | −25.1077 | −0.853196 | ||||||||
\(867\) | −11.5297 | −0.391568 | ||||||||
\(868\) | −12.6067 | −0.427898 | ||||||||
\(869\) | 31.7000 | 1.07535 | ||||||||
\(870\) | −22.9395 | −0.777723 | ||||||||
\(871\) | 1.85966 | 0.0630121 | ||||||||
\(872\) | 31.1276 | 1.05411 | ||||||||
\(873\) | −1.29315 | −0.0437666 | ||||||||
\(874\) | −18.3823 | −0.621791 | ||||||||
\(875\) | 0.722026 | 0.0244089 | ||||||||
\(876\) | 3.25370 | 0.109932 | ||||||||
\(877\) | 8.25483 | 0.278746 | 0.139373 | − | 0.990240i | \(-0.455491\pi\) | ||||
0.139373 | + | 0.990240i | \(0.455491\pi\) | |||||||
\(878\) | 51.9978 | 1.75484 | ||||||||
\(879\) | −9.28607 | −0.313211 | ||||||||
\(880\) | 7.20337 | 0.242826 | ||||||||
\(881\) | 30.8699 | 1.04003 | 0.520017 | − | 0.854156i | \(-0.325925\pi\) | ||||
0.520017 | + | 0.854156i | \(0.325925\pi\) | |||||||
\(882\) | 14.0718 | 0.473823 | ||||||||
\(883\) | 11.9203 | 0.401149 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(884\) | 33.1764 | 1.11584 | ||||||||
\(885\) | −3.93902 | −0.132409 | ||||||||
\(886\) | 88.3224 | 2.96725 | ||||||||
\(887\) | 34.4944 | 1.15821 | 0.579105 | − | 0.815253i | \(-0.303402\pi\) | ||||
0.579105 | + | 0.815253i | \(0.303402\pi\) | |||||||
\(888\) | 0.298993 | 0.0100336 | ||||||||
\(889\) | 4.07449 | 0.136654 | ||||||||
\(890\) | −14.0964 | −0.472512 | ||||||||
\(891\) | 3.51451 | 0.117741 | ||||||||
\(892\) | 43.1232 | 1.44387 | ||||||||
\(893\) | 76.9752 | 2.57588 | ||||||||
\(894\) | 17.0406 | 0.569924 | ||||||||
\(895\) | 25.0399 | 0.836991 | ||||||||
\(896\) | −8.42423 | −0.281434 | ||||||||
\(897\) | 6.09195 | 0.203404 | ||||||||
\(898\) | −53.0925 | −1.77172 | ||||||||
\(899\) | −67.8534 | −2.26304 | ||||||||
\(900\) | 2.71767 | 0.0905890 | ||||||||
\(901\) | −17.3723 | −0.578754 | ||||||||
\(902\) | −62.9320 | −2.09541 | ||||||||
\(903\) | −4.33817 | −0.144365 | ||||||||
\(904\) | 23.3130 | 0.775380 | ||||||||
\(905\) | 18.7119 | 0.622005 | ||||||||
\(906\) | −9.63995 | −0.320266 | ||||||||
\(907\) | 16.8500 | 0.559496 | 0.279748 | − | 0.960073i | \(-0.409749\pi\) | ||||
0.279748 | + | 0.960073i | \(0.409749\pi\) | |||||||
\(908\) | −65.9138 | −2.18743 | ||||||||
\(909\) | −18.0463 | −0.598558 | ||||||||
\(910\) | −8.18542 | −0.271344 | ||||||||
\(911\) | −50.7377 | −1.68102 | −0.840508 | − | 0.541799i | \(-0.817743\pi\) | ||||
−0.840508 | + | 0.541799i | \(0.817743\pi\) | |||||||
\(912\) | −14.8619 | −0.492128 | ||||||||
\(913\) | 0.819796 | 0.0271313 | ||||||||
\(914\) | 15.0939 | 0.499263 | ||||||||
\(915\) | −8.42212 | −0.278427 | ||||||||
\(916\) | −28.2725 | −0.934150 | ||||||||
\(917\) | 13.9724 | 0.461411 | ||||||||
\(918\) | −5.08008 | −0.167668 | ||||||||
\(919\) | 6.38035 | 0.210468 | 0.105234 | − | 0.994447i | \(-0.466441\pi\) | ||||
0.105234 | + | 0.994447i | \(0.466441\pi\) | |||||||
\(920\) | 1.81937 | 0.0599828 | ||||||||
\(921\) | −8.15718 | −0.268788 | ||||||||
\(922\) | −49.3720 | −1.62598 | ||||||||
\(923\) | 65.1375 | 2.14403 | ||||||||
\(924\) | −6.89627 | −0.226871 | ||||||||
\(925\) | −0.191811 | −0.00630669 | ||||||||
\(926\) | −34.2973 | −1.12708 | ||||||||
\(927\) | 18.6362 | 0.612092 | ||||||||
\(928\) | −79.9431 | −2.62426 | ||||||||
\(929\) | −17.4190 | −0.571500 | −0.285750 | − | 0.958304i | \(-0.592243\pi\) | ||||
−0.285750 | + | 0.958304i | \(0.592243\pi\) | |||||||
\(930\) | 13.9545 | 0.457587 | ||||||||
\(931\) | −46.9776 | −1.53963 | ||||||||
\(932\) | −30.0114 | −0.983057 | ||||||||
\(933\) | −23.8355 | −0.780338 | ||||||||
\(934\) | −35.3375 | −1.15628 | ||||||||
\(935\) | −8.22000 | −0.268823 | ||||||||
\(936\) | −8.13605 | −0.265935 | ||||||||
\(937\) | −9.10341 | −0.297395 | −0.148698 | − | 0.988883i | \(-0.547508\pi\) | ||||
−0.148698 | + | 0.988883i | \(0.547508\pi\) | |||||||
\(938\) | 0.558760 | 0.0182442 | ||||||||
\(939\) | 2.03645 | 0.0664571 | ||||||||
\(940\) | −28.8498 | −0.940977 | ||||||||
\(941\) | −25.7667 | −0.839971 | −0.419985 | − | 0.907531i | \(-0.637965\pi\) | ||||
−0.419985 | + | 0.907531i | \(0.637965\pi\) | |||||||
\(942\) | 39.4851 | 1.28649 | ||||||||
\(943\) | 9.62221 | 0.313342 | ||||||||
\(944\) | −8.07344 | −0.262768 | ||||||||
\(945\) | 0.722026 | 0.0234875 | ||||||||
\(946\) | −45.8652 | −1.49121 | ||||||||
\(947\) | 54.4199 | 1.76841 | 0.884205 | − | 0.467100i | \(-0.154701\pi\) | ||||
0.884205 | + | 0.467100i | \(0.154701\pi\) | |||||||
\(948\) | 24.5127 | 0.796136 | ||||||||
\(949\) | 6.24892 | 0.202849 | ||||||||
\(950\) | −15.7496 | −0.510983 | ||||||||
\(951\) | 8.85082 | 0.287007 | ||||||||
\(952\) | 2.63238 | 0.0853159 | ||||||||
\(953\) | 8.99170 | 0.291270 | 0.145635 | − | 0.989338i | \(-0.453478\pi\) | ||||
0.145635 | + | 0.989338i | \(0.453478\pi\) | |||||||
\(954\) | 16.1329 | 0.522323 | ||||||||
\(955\) | −18.8448 | −0.609804 | ||||||||
\(956\) | −60.9207 | −1.97032 | ||||||||
\(957\) | −37.1181 | −1.19986 | ||||||||
\(958\) | 34.6813 | 1.12050 | ||||||||
\(959\) | −11.2910 | −0.364606 | ||||||||
\(960\) | 12.3416 | 0.398324 | ||||||||
\(961\) | 10.2764 | 0.331498 | ||||||||
\(962\) | 2.17451 | 0.0701090 | ||||||||
\(963\) | −7.26136 | −0.233994 | ||||||||
\(964\) | 53.4014 | 1.71994 | ||||||||
\(965\) | −5.55334 | −0.178768 | ||||||||
\(966\) | 1.83041 | 0.0588925 | ||||||||
\(967\) | 0.437339 | 0.0140639 | 0.00703193 | − | 0.999975i | \(-0.497762\pi\) | ||||
0.00703193 | + | 0.999975i | \(0.497762\pi\) | |||||||
\(968\) | −2.10715 | −0.0677263 | ||||||||
\(969\) | 16.9595 | 0.544816 | ||||||||
\(970\) | −2.80876 | −0.0901837 | ||||||||
\(971\) | 27.0620 | 0.868460 | 0.434230 | − | 0.900802i | \(-0.357021\pi\) | ||||
0.434230 | + | 0.900802i | \(0.357021\pi\) | |||||||
\(972\) | 2.71767 | 0.0871693 | ||||||||
\(973\) | 6.21187 | 0.199144 | ||||||||
\(974\) | −50.2511 | −1.61015 | ||||||||
\(975\) | 5.21945 | 0.167156 | ||||||||
\(976\) | −17.2620 | −0.552544 | ||||||||
\(977\) | 22.9883 | 0.735459 | 0.367730 | − | 0.929933i | \(-0.380135\pi\) | ||||
0.367730 | + | 0.929933i | \(0.380135\pi\) | |||||||
\(978\) | −41.0072 | −1.31127 | ||||||||
\(979\) | −22.8091 | −0.728983 | ||||||||
\(980\) | 17.6069 | 0.562432 | ||||||||
\(981\) | −19.9690 | −0.637561 | ||||||||
\(982\) | −38.8103 | −1.23849 | ||||||||
\(983\) | 59.2130 | 1.88860 | 0.944300 | − | 0.329085i | \(-0.106740\pi\) | ||||
0.944300 | + | 0.329085i | \(0.106740\pi\) | |||||||
\(984\) | −12.8508 | −0.409670 | ||||||||
\(985\) | 5.45935 | 0.173949 | ||||||||
\(986\) | 53.6527 | 1.70865 | ||||||||
\(987\) | −7.66477 | −0.243972 | ||||||||
\(988\) | 102.855 | 3.27226 | ||||||||
\(989\) | 7.01272 | 0.222991 | ||||||||
\(990\) | 7.63359 | 0.242611 | ||||||||
\(991\) | 1.43875 | 0.0457035 | 0.0228518 | − | 0.999739i | \(-0.492725\pi\) | ||||
0.0228518 | + | 0.999739i | \(0.492725\pi\) | |||||||
\(992\) | 48.6308 | 1.54403 | ||||||||
\(993\) | 3.21020 | 0.101873 | ||||||||
\(994\) | 19.5714 | 0.620768 | ||||||||
\(995\) | −0.256761 | −0.00813988 | ||||||||
\(996\) | 0.633925 | 0.0200867 | ||||||||
\(997\) | 13.6594 | 0.432596 | 0.216298 | − | 0.976327i | \(-0.430602\pi\) | ||||
0.216298 | + | 0.976327i | \(0.430602\pi\) | |||||||
\(998\) | 81.5905 | 2.58270 | ||||||||
\(999\) | −0.191811 | −0.00606862 |
(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 | 6015.2.a.h.1.7 | ✓ | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6015.2.a.h.1.7 | ✓ | 39 | 1.1 | even | 1 | trivial |