Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63095 | −1.15326 | −0.576630 | − | 0.817006i | \(-0.695632\pi\) | ||||
−0.576630 | + | 0.817006i | \(0.695632\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.660014 | 0.330007 | ||||||||
\(5\) | 1.38859 | 0.620996 | 0.310498 | − | 0.950574i | \(-0.399504\pi\) | ||||
0.310498 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(6\) | 1.63095 | 0.665835 | ||||||||
\(7\) | 2.37558 | 0.897885 | 0.448942 | − | 0.893561i | \(-0.351801\pi\) | ||||
0.448942 | + | 0.893561i | \(0.351801\pi\) | |||||||
\(8\) | 2.18546 | 0.772676 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.26473 | −0.716169 | ||||||||
\(11\) | −1.95226 | −0.588628 | −0.294314 | − | 0.955709i | \(-0.595091\pi\) | ||||
−0.294314 | + | 0.955709i | \(0.595091\pi\) | |||||||
\(12\) | −0.660014 | −0.190530 | ||||||||
\(13\) | −2.02534 | −0.561728 | −0.280864 | − | 0.959748i | \(-0.590621\pi\) | ||||
−0.280864 | + | 0.959748i | \(0.590621\pi\) | |||||||
\(14\) | −3.87446 | −1.03549 | ||||||||
\(15\) | −1.38859 | −0.358532 | ||||||||
\(16\) | −4.88441 | −1.22110 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.63095 | −0.384420 | ||||||||
\(19\) | 2.21429 | 0.507994 | 0.253997 | − | 0.967205i | \(-0.418255\pi\) | ||||
0.253997 | + | 0.967205i | \(0.418255\pi\) | |||||||
\(20\) | 0.916488 | 0.204933 | ||||||||
\(21\) | −2.37558 | −0.518394 | ||||||||
\(22\) | 3.18404 | 0.678840 | ||||||||
\(23\) | 3.80128 | 0.792621 | 0.396310 | − | 0.918117i | \(-0.370290\pi\) | ||||
0.396310 | + | 0.918117i | \(0.370290\pi\) | |||||||
\(24\) | −2.18546 | −0.446105 | ||||||||
\(25\) | −3.07182 | −0.614364 | ||||||||
\(26\) | 3.30323 | 0.647817 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.56792 | 0.296308 | ||||||||
\(29\) | −7.93340 | −1.47320 | −0.736598 | − | 0.676331i | \(-0.763569\pi\) | ||||
−0.736598 | + | 0.676331i | \(0.763569\pi\) | |||||||
\(30\) | 2.26473 | 0.413481 | ||||||||
\(31\) | −3.32374 | −0.596961 | −0.298480 | − | 0.954416i | \(-0.596480\pi\) | ||||
−0.298480 | + | 0.954416i | \(0.596480\pi\) | |||||||
\(32\) | 3.59534 | 0.635572 | ||||||||
\(33\) | 1.95226 | 0.339844 | ||||||||
\(34\) | −1.63095 | −0.279706 | ||||||||
\(35\) | 3.29871 | 0.557583 | ||||||||
\(36\) | 0.660014 | 0.110002 | ||||||||
\(37\) | 11.1954 | 1.84052 | 0.920258 | − | 0.391311i | \(-0.127978\pi\) | ||||
0.920258 | + | 0.391311i | \(0.127978\pi\) | |||||||
\(38\) | −3.61141 | −0.585849 | ||||||||
\(39\) | 2.02534 | 0.324314 | ||||||||
\(40\) | 3.03470 | 0.479829 | ||||||||
\(41\) | 4.09779 | 0.639967 | 0.319983 | − | 0.947423i | \(-0.396323\pi\) | ||||
0.319983 | + | 0.947423i | \(0.396323\pi\) | |||||||
\(42\) | 3.87446 | 0.597843 | ||||||||
\(43\) | 3.60885 | 0.550344 | 0.275172 | − | 0.961395i | \(-0.411265\pi\) | ||||
0.275172 | + | 0.961395i | \(0.411265\pi\) | |||||||
\(44\) | −1.28852 | −0.194251 | ||||||||
\(45\) | 1.38859 | 0.206999 | ||||||||
\(46\) | −6.19971 | −0.914097 | ||||||||
\(47\) | −0.0414365 | −0.00604414 | −0.00302207 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302207 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(48\) | 4.88441 | 0.705004 | ||||||||
\(49\) | −1.35662 | −0.193803 | ||||||||
\(50\) | 5.01000 | 0.708521 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.33675 | −0.185374 | ||||||||
\(53\) | 2.03991 | 0.280203 | 0.140102 | − | 0.990137i | \(-0.455257\pi\) | ||||
0.140102 | + | 0.990137i | \(0.455257\pi\) | |||||||
\(54\) | 1.63095 | 0.221945 | ||||||||
\(55\) | −2.71088 | −0.365535 | ||||||||
\(56\) | 5.19173 | 0.693774 | ||||||||
\(57\) | −2.21429 | −0.293290 | ||||||||
\(58\) | 12.9390 | 1.69898 | ||||||||
\(59\) | −0.596046 | −0.0775986 | −0.0387993 | − | 0.999247i | \(-0.512353\pi\) | ||||
−0.0387993 | + | 0.999247i | \(0.512353\pi\) | |||||||
\(60\) | −0.916488 | −0.118318 | ||||||||
\(61\) | −5.88020 | −0.752882 | −0.376441 | − | 0.926441i | \(-0.622852\pi\) | ||||
−0.376441 | + | 0.926441i | \(0.622852\pi\) | |||||||
\(62\) | 5.42087 | 0.688451 | ||||||||
\(63\) | 2.37558 | 0.299295 | ||||||||
\(64\) | 3.90499 | 0.488123 | ||||||||
\(65\) | −2.81236 | −0.348831 | ||||||||
\(66\) | −3.18404 | −0.391929 | ||||||||
\(67\) | −4.79611 | −0.585939 | −0.292969 | − | 0.956122i | \(-0.594643\pi\) | ||||
−0.292969 | + | 0.956122i | \(0.594643\pi\) | |||||||
\(68\) | 0.660014 | 0.0800384 | ||||||||
\(69\) | −3.80128 | −0.457620 | ||||||||
\(70\) | −5.38004 | −0.643038 | ||||||||
\(71\) | −4.60483 | −0.546493 | −0.273247 | − | 0.961944i | \(-0.588097\pi\) | ||||
−0.273247 | + | 0.961944i | \(0.588097\pi\) | |||||||
\(72\) | 2.18546 | 0.257559 | ||||||||
\(73\) | −10.9519 | −1.28182 | −0.640909 | − | 0.767616i | \(-0.721443\pi\) | ||||
−0.640909 | + | 0.767616i | \(0.721443\pi\) | |||||||
\(74\) | −18.2592 | −2.12259 | ||||||||
\(75\) | 3.07182 | 0.354703 | ||||||||
\(76\) | 1.46146 | 0.167641 | ||||||||
\(77\) | −4.63774 | −0.528520 | ||||||||
\(78\) | −3.30323 | −0.374018 | ||||||||
\(79\) | −1.83474 | −0.206425 | −0.103212 | − | 0.994659i | \(-0.532912\pi\) | ||||
−0.103212 | + | 0.994659i | \(0.532912\pi\) | |||||||
\(80\) | −6.78244 | −0.758300 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.68331 | −0.738048 | ||||||||
\(83\) | −12.4574 | −1.36738 | −0.683689 | − | 0.729773i | \(-0.739626\pi\) | ||||
−0.683689 | + | 0.729773i | \(0.739626\pi\) | |||||||
\(84\) | −1.56792 | −0.171074 | ||||||||
\(85\) | 1.38859 | 0.150614 | ||||||||
\(86\) | −5.88586 | −0.634689 | ||||||||
\(87\) | 7.93340 | 0.850550 | ||||||||
\(88\) | −4.26657 | −0.454818 | ||||||||
\(89\) | −9.18735 | −0.973858 | −0.486929 | − | 0.873442i | \(-0.661883\pi\) | ||||
−0.486929 | + | 0.873442i | \(0.661883\pi\) | |||||||
\(90\) | −2.26473 | −0.238723 | ||||||||
\(91\) | −4.81135 | −0.504367 | ||||||||
\(92\) | 2.50889 | 0.261570 | ||||||||
\(93\) | 3.32374 | 0.344656 | ||||||||
\(94\) | 0.0675811 | 0.00697046 | ||||||||
\(95\) | 3.07475 | 0.315462 | ||||||||
\(96\) | −3.59534 | −0.366948 | ||||||||
\(97\) | 3.30682 | 0.335756 | 0.167878 | − | 0.985808i | \(-0.446308\pi\) | ||||
0.167878 | + | 0.985808i | \(0.446308\pi\) | |||||||
\(98\) | 2.21258 | 0.223505 | ||||||||
\(99\) | −1.95226 | −0.196209 | ||||||||
\(100\) | −2.02744 | −0.202744 | ||||||||
\(101\) | −1.74442 | −0.173577 | −0.0867884 | − | 0.996227i | \(-0.527660\pi\) | ||||
−0.0867884 | + | 0.996227i | \(0.527660\pi\) | |||||||
\(102\) | 1.63095 | 0.161489 | ||||||||
\(103\) | 10.1173 | 0.996885 | 0.498443 | − | 0.866923i | \(-0.333905\pi\) | ||||
0.498443 | + | 0.866923i | \(0.333905\pi\) | |||||||
\(104\) | −4.42629 | −0.434033 | ||||||||
\(105\) | −3.29871 | −0.321921 | ||||||||
\(106\) | −3.32700 | −0.323147 | ||||||||
\(107\) | −10.6795 | −1.03242 | −0.516212 | − | 0.856461i | \(-0.672658\pi\) | ||||
−0.516212 | + | 0.856461i | \(0.672658\pi\) | |||||||
\(108\) | −0.660014 | −0.0635098 | ||||||||
\(109\) | −5.11875 | −0.490287 | −0.245144 | − | 0.969487i | \(-0.578835\pi\) | ||||
−0.245144 | + | 0.969487i | \(0.578835\pi\) | |||||||
\(110\) | 4.42133 | 0.421557 | ||||||||
\(111\) | −11.1954 | −1.06262 | ||||||||
\(112\) | −11.6033 | −1.09641 | ||||||||
\(113\) | 7.96643 | 0.749419 | 0.374709 | − | 0.927142i | \(-0.377742\pi\) | ||||
0.374709 | + | 0.927142i | \(0.377742\pi\) | |||||||
\(114\) | 3.61141 | 0.338240 | ||||||||
\(115\) | 5.27841 | 0.492214 | ||||||||
\(116\) | −5.23615 | −0.486165 | ||||||||
\(117\) | −2.02534 | −0.187243 | ||||||||
\(118\) | 0.972124 | 0.0894912 | ||||||||
\(119\) | 2.37558 | 0.217769 | ||||||||
\(120\) | −3.03470 | −0.277029 | ||||||||
\(121\) | −7.18869 | −0.653518 | ||||||||
\(122\) | 9.59034 | 0.868268 | ||||||||
\(123\) | −4.09779 | −0.369485 | ||||||||
\(124\) | −2.19371 | −0.197001 | ||||||||
\(125\) | −11.2084 | −1.00251 | ||||||||
\(126\) | −3.87446 | −0.345165 | ||||||||
\(127\) | −6.54251 | −0.580554 | −0.290277 | − | 0.956943i | \(-0.593747\pi\) | ||||
−0.290277 | + | 0.956943i | \(0.593747\pi\) | |||||||
\(128\) | −13.5595 | −1.19850 | ||||||||
\(129\) | −3.60885 | −0.317741 | ||||||||
\(130\) | 4.58684 | 0.402292 | ||||||||
\(131\) | 8.63455 | 0.754404 | 0.377202 | − | 0.926131i | \(-0.376886\pi\) | ||||
0.377202 | + | 0.926131i | \(0.376886\pi\) | |||||||
\(132\) | 1.28852 | 0.112151 | ||||||||
\(133\) | 5.26023 | 0.456120 | ||||||||
\(134\) | 7.82225 | 0.675739 | ||||||||
\(135\) | −1.38859 | −0.119511 | ||||||||
\(136\) | 2.18546 | 0.187401 | ||||||||
\(137\) | 21.8727 | 1.86872 | 0.934358 | − | 0.356337i | \(-0.115974\pi\) | ||||
0.934358 | + | 0.356337i | \(0.115974\pi\) | |||||||
\(138\) | 6.19971 | 0.527754 | ||||||||
\(139\) | −3.71694 | −0.315267 | −0.157633 | − | 0.987498i | \(-0.550386\pi\) | ||||
−0.157633 | + | 0.987498i | \(0.550386\pi\) | |||||||
\(140\) | 2.17719 | 0.184006 | ||||||||
\(141\) | 0.0414365 | 0.00348959 | ||||||||
\(142\) | 7.51028 | 0.630248 | ||||||||
\(143\) | 3.95398 | 0.330648 | ||||||||
\(144\) | −4.88441 | −0.407034 | ||||||||
\(145\) | −11.0162 | −0.914849 | ||||||||
\(146\) | 17.8620 | 1.47827 | ||||||||
\(147\) | 1.35662 | 0.111892 | ||||||||
\(148\) | 7.38913 | 0.607383 | ||||||||
\(149\) | 14.7784 | 1.21069 | 0.605347 | − | 0.795962i | \(-0.293034\pi\) | ||||
0.605347 | + | 0.795962i | \(0.293034\pi\) | |||||||
\(150\) | −5.01000 | −0.409065 | ||||||||
\(151\) | −23.1761 | −1.88604 | −0.943021 | − | 0.332732i | \(-0.892030\pi\) | ||||
−0.943021 | + | 0.332732i | \(0.892030\pi\) | |||||||
\(152\) | 4.83925 | 0.392515 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 7.56395 | 0.609520 | ||||||||
\(155\) | −4.61531 | −0.370710 | ||||||||
\(156\) | 1.33675 | 0.107026 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 2.99238 | 0.238061 | ||||||||
\(159\) | −2.03991 | −0.161775 | ||||||||
\(160\) | 4.99245 | 0.394688 | ||||||||
\(161\) | 9.03024 | 0.711682 | ||||||||
\(162\) | −1.63095 | −0.128140 | ||||||||
\(163\) | −16.5974 | −1.30001 | −0.650005 | − | 0.759930i | \(-0.725233\pi\) | ||||
−0.650005 | + | 0.759930i | \(0.725233\pi\) | |||||||
\(164\) | 2.70460 | 0.211193 | ||||||||
\(165\) | 2.71088 | 0.211042 | ||||||||
\(166\) | 20.3175 | 1.57694 | ||||||||
\(167\) | −7.95155 | −0.615309 | −0.307655 | − | 0.951498i | \(-0.599544\pi\) | ||||
−0.307655 | + | 0.951498i | \(0.599544\pi\) | |||||||
\(168\) | −5.19173 | −0.400551 | ||||||||
\(169\) | −8.89801 | −0.684462 | ||||||||
\(170\) | −2.26473 | −0.173697 | ||||||||
\(171\) | 2.21429 | 0.169331 | ||||||||
\(172\) | 2.38189 | 0.181617 | ||||||||
\(173\) | 16.8262 | 1.27927 | 0.639636 | − | 0.768678i | \(-0.279085\pi\) | ||||
0.639636 | + | 0.768678i | \(0.279085\pi\) | |||||||
\(174\) | −12.9390 | −0.980905 | ||||||||
\(175\) | −7.29735 | −0.551628 | ||||||||
\(176\) | 9.53562 | 0.718775 | ||||||||
\(177\) | 0.596046 | 0.0448015 | ||||||||
\(178\) | 14.9842 | 1.12311 | ||||||||
\(179\) | 1.12061 | 0.0837585 | 0.0418792 | − | 0.999123i | \(-0.486666\pi\) | ||||
0.0418792 | + | 0.999123i | \(0.486666\pi\) | |||||||
\(180\) | 0.916488 | 0.0683110 | ||||||||
\(181\) | −23.7229 | −1.76331 | −0.881655 | − | 0.471894i | \(-0.843571\pi\) | ||||
−0.881655 | + | 0.471894i | \(0.843571\pi\) | |||||||
\(182\) | 7.84710 | 0.581666 | ||||||||
\(183\) | 5.88020 | 0.434677 | ||||||||
\(184\) | 8.30753 | 0.612439 | ||||||||
\(185\) | 15.5459 | 1.14295 | ||||||||
\(186\) | −5.42087 | −0.397477 | ||||||||
\(187\) | −1.95226 | −0.142763 | ||||||||
\(188\) | −0.0273487 | −0.00199461 | ||||||||
\(189\) | −2.37558 | −0.172798 | ||||||||
\(190\) | −5.01477 | −0.363810 | ||||||||
\(191\) | −1.08853 | −0.0787636 | −0.0393818 | − | 0.999224i | \(-0.512539\pi\) | ||||
−0.0393818 | + | 0.999224i | \(0.512539\pi\) | |||||||
\(192\) | −3.90499 | −0.281818 | ||||||||
\(193\) | 24.2440 | 1.74512 | 0.872560 | − | 0.488507i | \(-0.162458\pi\) | ||||
0.872560 | + | 0.488507i | \(0.162458\pi\) | |||||||
\(194\) | −5.39327 | −0.387214 | ||||||||
\(195\) | 2.81236 | 0.201397 | ||||||||
\(196\) | −0.895387 | −0.0639562 | ||||||||
\(197\) | 4.48344 | 0.319432 | 0.159716 | − | 0.987163i | \(-0.448942\pi\) | ||||
0.159716 | + | 0.987163i | \(0.448942\pi\) | |||||||
\(198\) | 3.18404 | 0.226280 | ||||||||
\(199\) | −6.77236 | −0.480080 | −0.240040 | − | 0.970763i | \(-0.577161\pi\) | ||||
−0.240040 | + | 0.970763i | \(0.577161\pi\) | |||||||
\(200\) | −6.71333 | −0.474704 | ||||||||
\(201\) | 4.79611 | 0.338292 | ||||||||
\(202\) | 2.84508 | 0.200179 | ||||||||
\(203\) | −18.8464 | −1.32276 | ||||||||
\(204\) | −0.660014 | −0.0462102 | ||||||||
\(205\) | 5.69014 | 0.397417 | ||||||||
\(206\) | −16.5008 | −1.14967 | ||||||||
\(207\) | 3.80128 | 0.264207 | ||||||||
\(208\) | 9.89258 | 0.685927 | ||||||||
\(209\) | −4.32287 | −0.299019 | ||||||||
\(210\) | 5.38004 | 0.371258 | ||||||||
\(211\) | 2.52702 | 0.173967 | 0.0869836 | − | 0.996210i | \(-0.472277\pi\) | ||||
0.0869836 | + | 0.996210i | \(0.472277\pi\) | |||||||
\(212\) | 1.34637 | 0.0924690 | ||||||||
\(213\) | 4.60483 | 0.315518 | ||||||||
\(214\) | 17.4178 | 1.19065 | ||||||||
\(215\) | 5.01120 | 0.341761 | ||||||||
\(216\) | −2.18546 | −0.148702 | ||||||||
\(217\) | −7.89580 | −0.536002 | ||||||||
\(218\) | 8.34845 | 0.565428 | ||||||||
\(219\) | 10.9519 | 0.740059 | ||||||||
\(220\) | −1.78922 | −0.120629 | ||||||||
\(221\) | −2.02534 | −0.136239 | ||||||||
\(222\) | 18.2592 | 1.22548 | ||||||||
\(223\) | −5.56077 | −0.372377 | −0.186188 | − | 0.982514i | \(-0.559613\pi\) | ||||
−0.186188 | + | 0.982514i | \(0.559613\pi\) | |||||||
\(224\) | 8.54101 | 0.570670 | ||||||||
\(225\) | −3.07182 | −0.204788 | ||||||||
\(226\) | −12.9929 | −0.864274 | ||||||||
\(227\) | 27.1183 | 1.79990 | 0.899952 | − | 0.435989i | \(-0.143601\pi\) | ||||
0.899952 | + | 0.435989i | \(0.143601\pi\) | |||||||
\(228\) | −1.46146 | −0.0967879 | ||||||||
\(229\) | 10.3903 | 0.686611 | 0.343305 | − | 0.939224i | \(-0.388453\pi\) | ||||
0.343305 | + | 0.939224i | \(0.388453\pi\) | |||||||
\(230\) | −8.60885 | −0.567651 | ||||||||
\(231\) | 4.63774 | 0.305141 | ||||||||
\(232\) | −17.3381 | −1.13830 | ||||||||
\(233\) | −19.5398 | −1.28009 | −0.640047 | − | 0.768336i | \(-0.721085\pi\) | ||||
−0.640047 | + | 0.768336i | \(0.721085\pi\) | |||||||
\(234\) | 3.30323 | 0.215939 | ||||||||
\(235\) | −0.0575383 | −0.00375339 | ||||||||
\(236\) | −0.393398 | −0.0256081 | ||||||||
\(237\) | 1.83474 | 0.119179 | ||||||||
\(238\) | −3.87446 | −0.251144 | ||||||||
\(239\) | −12.5770 | −0.813541 | −0.406770 | − | 0.913530i | \(-0.633345\pi\) | ||||
−0.406770 | + | 0.913530i | \(0.633345\pi\) | |||||||
\(240\) | 6.78244 | 0.437805 | ||||||||
\(241\) | −2.92636 | −0.188503 | −0.0942517 | − | 0.995548i | \(-0.530046\pi\) | ||||
−0.0942517 | + | 0.995548i | \(0.530046\pi\) | |||||||
\(242\) | 11.7244 | 0.753675 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.88101 | −0.248456 | ||||||||
\(245\) | −1.88379 | −0.120351 | ||||||||
\(246\) | 6.68331 | 0.426112 | ||||||||
\(247\) | −4.48469 | −0.285354 | ||||||||
\(248\) | −7.26389 | −0.461257 | ||||||||
\(249\) | 12.4574 | 0.789456 | ||||||||
\(250\) | 18.2805 | 1.15616 | ||||||||
\(251\) | −19.3774 | −1.22309 | −0.611546 | − | 0.791209i | \(-0.709452\pi\) | ||||
−0.611546 | + | 0.791209i | \(0.709452\pi\) | |||||||
\(252\) | 1.56792 | 0.0987694 | ||||||||
\(253\) | −7.42107 | −0.466558 | ||||||||
\(254\) | 10.6705 | 0.669529 | ||||||||
\(255\) | −1.38859 | −0.0869568 | ||||||||
\(256\) | 14.3050 | 0.894063 | ||||||||
\(257\) | 0.665979 | 0.0415426 | 0.0207713 | − | 0.999784i | \(-0.493388\pi\) | ||||
0.0207713 | + | 0.999784i | \(0.493388\pi\) | |||||||
\(258\) | 5.88586 | 0.366438 | ||||||||
\(259\) | 26.5956 | 1.65257 | ||||||||
\(260\) | −1.85620 | −0.115116 | ||||||||
\(261\) | −7.93340 | −0.491065 | ||||||||
\(262\) | −14.0826 | −0.870024 | ||||||||
\(263\) | 0.249822 | 0.0154047 | 0.00770235 | − | 0.999970i | \(-0.497548\pi\) | ||||
0.00770235 | + | 0.999970i | \(0.497548\pi\) | |||||||
\(264\) | 4.26657 | 0.262589 | ||||||||
\(265\) | 2.83260 | 0.174005 | ||||||||
\(266\) | −8.57920 | −0.526025 | ||||||||
\(267\) | 9.18735 | 0.562257 | ||||||||
\(268\) | −3.16550 | −0.193364 | ||||||||
\(269\) | −21.3703 | −1.30297 | −0.651485 | − | 0.758661i | \(-0.725854\pi\) | ||||
−0.651485 | + | 0.758661i | \(0.725854\pi\) | |||||||
\(270\) | 2.26473 | 0.137827 | ||||||||
\(271\) | −11.1217 | −0.675597 | −0.337798 | − | 0.941219i | \(-0.609682\pi\) | ||||
−0.337798 | + | 0.941219i | \(0.609682\pi\) | |||||||
\(272\) | −4.88441 | −0.296161 | ||||||||
\(273\) | 4.81135 | 0.291196 | ||||||||
\(274\) | −35.6735 | −2.15511 | ||||||||
\(275\) | 5.99698 | 0.361632 | ||||||||
\(276\) | −2.50889 | −0.151018 | ||||||||
\(277\) | 25.3139 | 1.52097 | 0.760483 | − | 0.649358i | \(-0.224962\pi\) | ||||
0.760483 | + | 0.649358i | \(0.224962\pi\) | |||||||
\(278\) | 6.06217 | 0.363585 | ||||||||
\(279\) | −3.32374 | −0.198987 | ||||||||
\(280\) | 7.20918 | 0.430831 | ||||||||
\(281\) | 1.34523 | 0.0802494 | 0.0401247 | − | 0.999195i | \(-0.487224\pi\) | ||||
0.0401247 | + | 0.999195i | \(0.487224\pi\) | |||||||
\(282\) | −0.0675811 | −0.00402440 | ||||||||
\(283\) | 20.3342 | 1.20875 | 0.604373 | − | 0.796702i | \(-0.293424\pi\) | ||||
0.604373 | + | 0.796702i | \(0.293424\pi\) | |||||||
\(284\) | −3.03925 | −0.180346 | ||||||||
\(285\) | −3.07475 | −0.182132 | ||||||||
\(286\) | −6.44876 | −0.381323 | ||||||||
\(287\) | 9.73462 | 0.574617 | ||||||||
\(288\) | 3.59534 | 0.211857 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 17.9670 | 1.05506 | ||||||||
\(291\) | −3.30682 | −0.193849 | ||||||||
\(292\) | −7.22838 | −0.423009 | ||||||||
\(293\) | 18.2670 | 1.06717 | 0.533586 | − | 0.845746i | \(-0.320844\pi\) | ||||
0.533586 | + | 0.845746i | \(0.320844\pi\) | |||||||
\(294\) | −2.21258 | −0.129041 | ||||||||
\(295\) | −0.827663 | −0.0481884 | ||||||||
\(296\) | 24.4671 | 1.42212 | ||||||||
\(297\) | 1.95226 | 0.113281 | ||||||||
\(298\) | −24.1029 | −1.39624 | ||||||||
\(299\) | −7.69887 | −0.445237 | ||||||||
\(300\) | 2.02744 | 0.117054 | ||||||||
\(301\) | 8.57310 | 0.494145 | ||||||||
\(302\) | 37.7991 | 2.17510 | ||||||||
\(303\) | 1.74442 | 0.100215 | ||||||||
\(304\) | −10.8155 | −0.620313 | ||||||||
\(305\) | −8.16518 | −0.467537 | ||||||||
\(306\) | −1.63095 | −0.0932355 | ||||||||
\(307\) | 20.9522 | 1.19581 | 0.597904 | − | 0.801568i | \(-0.296000\pi\) | ||||
0.597904 | + | 0.801568i | \(0.296000\pi\) | |||||||
\(308\) | −3.06097 | −0.174415 | ||||||||
\(309\) | −10.1173 | −0.575552 | ||||||||
\(310\) | 7.52736 | 0.427525 | ||||||||
\(311\) | 32.3282 | 1.83316 | 0.916582 | − | 0.399848i | \(-0.130937\pi\) | ||||
0.916582 | + | 0.399848i | \(0.130937\pi\) | |||||||
\(312\) | 4.42629 | 0.250589 | ||||||||
\(313\) | −34.3294 | −1.94041 | −0.970205 | − | 0.242284i | \(-0.922103\pi\) | ||||
−0.970205 | + | 0.242284i | \(0.922103\pi\) | |||||||
\(314\) | −1.63095 | −0.0920401 | ||||||||
\(315\) | 3.29871 | 0.185861 | ||||||||
\(316\) | −1.21095 | −0.0681215 | ||||||||
\(317\) | −1.91871 | −0.107766 | −0.0538829 | − | 0.998547i | \(-0.517160\pi\) | ||||
−0.0538829 | + | 0.998547i | \(0.517160\pi\) | |||||||
\(318\) | 3.32700 | 0.186569 | ||||||||
\(319\) | 15.4880 | 0.867164 | ||||||||
\(320\) | 5.42242 | 0.303123 | ||||||||
\(321\) | 10.6795 | 0.596071 | ||||||||
\(322\) | −14.7279 | −0.820754 | ||||||||
\(323\) | 2.21429 | 0.123207 | ||||||||
\(324\) | 0.660014 | 0.0366674 | ||||||||
\(325\) | 6.22147 | 0.345105 | ||||||||
\(326\) | 27.0696 | 1.49925 | ||||||||
\(327\) | 5.11875 | 0.283068 | ||||||||
\(328\) | 8.95554 | 0.494487 | ||||||||
\(329\) | −0.0984358 | −0.00542694 | ||||||||
\(330\) | −4.42133 | −0.243386 | ||||||||
\(331\) | 23.8782 | 1.31246 | 0.656231 | − | 0.754560i | \(-0.272150\pi\) | ||||
0.656231 | + | 0.754560i | \(0.272150\pi\) | |||||||
\(332\) | −8.22206 | −0.451244 | ||||||||
\(333\) | 11.1954 | 0.613506 | ||||||||
\(334\) | 12.9686 | 0.709611 | ||||||||
\(335\) | −6.65983 | −0.363866 | ||||||||
\(336\) | 11.6033 | 0.633012 | ||||||||
\(337\) | −13.3733 | −0.728489 | −0.364245 | − | 0.931303i | \(-0.618673\pi\) | ||||
−0.364245 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(338\) | 14.5122 | 0.789362 | ||||||||
\(339\) | −7.96643 | −0.432677 | ||||||||
\(340\) | 0.916488 | 0.0497035 | ||||||||
\(341\) | 6.48879 | 0.351388 | ||||||||
\(342\) | −3.61141 | −0.195283 | ||||||||
\(343\) | −19.8518 | −1.07190 | ||||||||
\(344\) | 7.88698 | 0.425237 | ||||||||
\(345\) | −5.27841 | −0.284180 | ||||||||
\(346\) | −27.4428 | −1.47533 | ||||||||
\(347\) | −16.4594 | −0.883588 | −0.441794 | − | 0.897117i | \(-0.645658\pi\) | ||||
−0.441794 | + | 0.897117i | \(0.645658\pi\) | |||||||
\(348\) | 5.23615 | 0.280687 | ||||||||
\(349\) | 30.3631 | 1.62530 | 0.812650 | − | 0.582753i | \(-0.198024\pi\) | ||||
0.812650 | + | 0.582753i | \(0.198024\pi\) | |||||||
\(350\) | 11.9017 | 0.636170 | ||||||||
\(351\) | 2.02534 | 0.108105 | ||||||||
\(352\) | −7.01902 | −0.374115 | ||||||||
\(353\) | 12.7752 | 0.679956 | 0.339978 | − | 0.940433i | \(-0.389580\pi\) | ||||
0.339978 | + | 0.940433i | \(0.389580\pi\) | |||||||
\(354\) | −0.972124 | −0.0516678 | ||||||||
\(355\) | −6.39422 | −0.339370 | ||||||||
\(356\) | −6.06378 | −0.321380 | ||||||||
\(357\) | −2.37558 | −0.125729 | ||||||||
\(358\) | −1.82767 | −0.0965953 | ||||||||
\(359\) | 20.4202 | 1.07774 | 0.538868 | − | 0.842390i | \(-0.318852\pi\) | ||||
0.538868 | + | 0.842390i | \(0.318852\pi\) | |||||||
\(360\) | 3.03470 | 0.159943 | ||||||||
\(361\) | −14.0969 | −0.741942 | ||||||||
\(362\) | 38.6910 | 2.03355 | ||||||||
\(363\) | 7.18869 | 0.377309 | ||||||||
\(364\) | −3.17556 | −0.166444 | ||||||||
\(365\) | −15.2076 | −0.796004 | ||||||||
\(366\) | −9.59034 | −0.501295 | ||||||||
\(367\) | −8.00192 | −0.417697 | −0.208848 | − | 0.977948i | \(-0.566972\pi\) | ||||
−0.208848 | + | 0.977948i | \(0.566972\pi\) | |||||||
\(368\) | −18.5670 | −0.967871 | ||||||||
\(369\) | 4.09779 | 0.213322 | ||||||||
\(370\) | −25.3546 | −1.31812 | ||||||||
\(371\) | 4.84597 | 0.251590 | ||||||||
\(372\) | 2.19371 | 0.113739 | ||||||||
\(373\) | −7.08890 | −0.367050 | −0.183525 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183525 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(374\) | 3.18404 | 0.164643 | ||||||||
\(375\) | 11.2084 | 0.578801 | ||||||||
\(376\) | −0.0905578 | −0.00467016 | ||||||||
\(377\) | 16.0678 | 0.827535 | ||||||||
\(378\) | 3.87446 | 0.199281 | ||||||||
\(379\) | −22.1308 | −1.13678 | −0.568391 | − | 0.822759i | \(-0.692434\pi\) | ||||
−0.568391 | + | 0.822759i | \(0.692434\pi\) | |||||||
\(380\) | 2.02937 | 0.104105 | ||||||||
\(381\) | 6.54251 | 0.335183 | ||||||||
\(382\) | 1.77535 | 0.0908349 | ||||||||
\(383\) | 2.60313 | 0.133013 | 0.0665067 | − | 0.997786i | \(-0.478815\pi\) | ||||
0.0665067 | + | 0.997786i | \(0.478815\pi\) | |||||||
\(384\) | 13.5595 | 0.691957 | ||||||||
\(385\) | −6.43992 | −0.328209 | ||||||||
\(386\) | −39.5408 | −2.01258 | ||||||||
\(387\) | 3.60885 | 0.183448 | ||||||||
\(388\) | 2.18254 | 0.110802 | ||||||||
\(389\) | −23.4684 | −1.18989 | −0.594946 | − | 0.803765i | \(-0.702827\pi\) | ||||
−0.594946 | + | 0.803765i | \(0.702827\pi\) | |||||||
\(390\) | −4.58684 | −0.232263 | ||||||||
\(391\) | 3.80128 | 0.192239 | ||||||||
\(392\) | −2.96483 | −0.149747 | ||||||||
\(393\) | −8.63455 | −0.435555 | ||||||||
\(394\) | −7.31229 | −0.368388 | ||||||||
\(395\) | −2.54770 | −0.128189 | ||||||||
\(396\) | −1.28852 | −0.0647504 | ||||||||
\(397\) | −13.0697 | −0.655947 | −0.327974 | − | 0.944687i | \(-0.606366\pi\) | ||||
−0.327974 | + | 0.944687i | \(0.606366\pi\) | |||||||
\(398\) | 11.0454 | 0.553657 | ||||||||
\(399\) | −5.26023 | −0.263341 | ||||||||
\(400\) | 15.0040 | 0.750201 | ||||||||
\(401\) | 5.58643 | 0.278973 | 0.139486 | − | 0.990224i | \(-0.455455\pi\) | ||||
0.139486 | + | 0.990224i | \(0.455455\pi\) | |||||||
\(402\) | −7.82225 | −0.390138 | ||||||||
\(403\) | 6.73169 | 0.335329 | ||||||||
\(404\) | −1.15134 | −0.0572815 | ||||||||
\(405\) | 1.38859 | 0.0689996 | ||||||||
\(406\) | 30.7377 | 1.52549 | ||||||||
\(407\) | −21.8563 | −1.08338 | ||||||||
\(408\) | −2.18546 | −0.108196 | ||||||||
\(409\) | 9.45533 | 0.467536 | 0.233768 | − | 0.972292i | \(-0.424894\pi\) | ||||
0.233768 | + | 0.972292i | \(0.424894\pi\) | |||||||
\(410\) | −9.28037 | −0.458325 | ||||||||
\(411\) | −21.8727 | −1.07890 | ||||||||
\(412\) | 6.67754 | 0.328979 | ||||||||
\(413\) | −1.41595 | −0.0696746 | ||||||||
\(414\) | −6.19971 | −0.304699 | ||||||||
\(415\) | −17.2982 | −0.849136 | ||||||||
\(416\) | −7.28177 | −0.357018 | ||||||||
\(417\) | 3.71694 | 0.182019 | ||||||||
\(418\) | 7.05041 | 0.344847 | ||||||||
\(419\) | 2.38129 | 0.116333 | 0.0581667 | − | 0.998307i | \(-0.481475\pi\) | ||||
0.0581667 | + | 0.998307i | \(0.481475\pi\) | |||||||
\(420\) | −2.17719 | −0.106236 | ||||||||
\(421\) | −17.7632 | −0.865724 | −0.432862 | − | 0.901460i | \(-0.642496\pi\) | ||||
−0.432862 | + | 0.901460i | \(0.642496\pi\) | |||||||
\(422\) | −4.12146 | −0.200629 | ||||||||
\(423\) | −0.0414365 | −0.00201471 | ||||||||
\(424\) | 4.45814 | 0.216506 | ||||||||
\(425\) | −3.07182 | −0.149005 | ||||||||
\(426\) | −7.51028 | −0.363874 | ||||||||
\(427\) | −13.9689 | −0.676002 | ||||||||
\(428\) | −7.04861 | −0.340707 | ||||||||
\(429\) | −3.95398 | −0.190900 | ||||||||
\(430\) | −8.17305 | −0.394139 | ||||||||
\(431\) | 36.7215 | 1.76881 | 0.884407 | − | 0.466717i | \(-0.154563\pi\) | ||||
0.884407 | + | 0.466717i | \(0.154563\pi\) | |||||||
\(432\) | 4.88441 | 0.235001 | ||||||||
\(433\) | −35.2394 | −1.69350 | −0.846749 | − | 0.531992i | \(-0.821444\pi\) | ||||
−0.846749 | + | 0.531992i | \(0.821444\pi\) | |||||||
\(434\) | 12.8777 | 0.618149 | ||||||||
\(435\) | 11.0162 | 0.528188 | ||||||||
\(436\) | −3.37845 | −0.161798 | ||||||||
\(437\) | 8.41714 | 0.402647 | ||||||||
\(438\) | −17.8620 | −0.853479 | ||||||||
\(439\) | −24.3683 | −1.16304 | −0.581518 | − | 0.813534i | \(-0.697541\pi\) | ||||
−0.581518 | + | 0.813534i | \(0.697541\pi\) | |||||||
\(440\) | −5.92452 | −0.282440 | ||||||||
\(441\) | −1.35662 | −0.0646009 | ||||||||
\(442\) | 3.30323 | 0.157119 | ||||||||
\(443\) | 14.5156 | 0.689658 | 0.344829 | − | 0.938665i | \(-0.387937\pi\) | ||||
0.344829 | + | 0.938665i | \(0.387937\pi\) | |||||||
\(444\) | −7.38913 | −0.350673 | ||||||||
\(445\) | −12.7575 | −0.604762 | ||||||||
\(446\) | 9.06937 | 0.429447 | ||||||||
\(447\) | −14.7784 | −0.698995 | ||||||||
\(448\) | 9.27661 | 0.438279 | ||||||||
\(449\) | −14.6717 | −0.692399 | −0.346200 | − | 0.938161i | \(-0.612528\pi\) | ||||
−0.346200 | + | 0.938161i | \(0.612528\pi\) | |||||||
\(450\) | 5.01000 | 0.236174 | ||||||||
\(451\) | −7.99993 | −0.376702 | ||||||||
\(452\) | 5.25795 | 0.247313 | ||||||||
\(453\) | 23.1761 | 1.08891 | ||||||||
\(454\) | −44.2287 | −2.07576 | ||||||||
\(455\) | −6.68099 | −0.313210 | ||||||||
\(456\) | −4.83925 | −0.226618 | ||||||||
\(457\) | −23.4238 | −1.09572 | −0.547859 | − | 0.836571i | \(-0.684557\pi\) | ||||
−0.547859 | + | 0.836571i | \(0.684557\pi\) | |||||||
\(458\) | −16.9461 | −0.791840 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 3.48382 | 0.162434 | ||||||||
\(461\) | −35.8457 | −1.66950 | −0.834752 | − | 0.550627i | \(-0.814389\pi\) | ||||
−0.834752 | + | 0.550627i | \(0.814389\pi\) | |||||||
\(462\) | −7.56395 | −0.351907 | ||||||||
\(463\) | 0.0315112 | 0.00146445 | 0.000732225 | − | 1.00000i | \(-0.499767\pi\) | ||||
0.000732225 | 1.00000i | \(0.499767\pi\) | ||||||||
\(464\) | 38.7500 | 1.79892 | ||||||||
\(465\) | 4.61531 | 0.214030 | ||||||||
\(466\) | 31.8685 | 1.47628 | ||||||||
\(467\) | 29.6850 | 1.37366 | 0.686829 | − | 0.726819i | \(-0.259002\pi\) | ||||
0.686829 | + | 0.726819i | \(0.259002\pi\) | |||||||
\(468\) | −1.33675 | −0.0617913 | ||||||||
\(469\) | −11.3936 | −0.526105 | ||||||||
\(470\) | 0.0938424 | 0.00432863 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −1.30263 | −0.0599585 | ||||||||
\(473\) | −7.04539 | −0.323948 | ||||||||
\(474\) | −2.99238 | −0.137445 | ||||||||
\(475\) | −6.80191 | −0.312093 | ||||||||
\(476\) | 1.56792 | 0.0718653 | ||||||||
\(477\) | 2.03991 | 0.0934011 | ||||||||
\(478\) | 20.5126 | 0.938224 | ||||||||
\(479\) | 30.6535 | 1.40059 | 0.700296 | − | 0.713852i | \(-0.253051\pi\) | ||||
0.700296 | + | 0.713852i | \(0.253051\pi\) | |||||||
\(480\) | −4.99245 | −0.227873 | ||||||||
\(481\) | −22.6745 | −1.03387 | ||||||||
\(482\) | 4.77276 | 0.217393 | ||||||||
\(483\) | −9.03024 | −0.410890 | ||||||||
\(484\) | −4.74464 | −0.215665 | ||||||||
\(485\) | 4.59181 | 0.208503 | ||||||||
\(486\) | 1.63095 | 0.0739816 | ||||||||
\(487\) | −21.6657 | −0.981766 | −0.490883 | − | 0.871226i | \(-0.663326\pi\) | ||||
−0.490883 | + | 0.871226i | \(0.663326\pi\) | |||||||
\(488\) | −12.8509 | −0.581734 | ||||||||
\(489\) | 16.5974 | 0.750561 | ||||||||
\(490\) | 3.07237 | 0.138796 | ||||||||
\(491\) | 10.2333 | 0.461820 | 0.230910 | − | 0.972975i | \(-0.425830\pi\) | ||||
0.230910 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(492\) | −2.70460 | −0.121933 | ||||||||
\(493\) | −7.93340 | −0.357302 | ||||||||
\(494\) | 7.31433 | 0.329087 | ||||||||
\(495\) | −2.71088 | −0.121845 | ||||||||
\(496\) | 16.2345 | 0.728950 | ||||||||
\(497\) | −10.9392 | −0.490688 | ||||||||
\(498\) | −20.3175 | −0.910448 | ||||||||
\(499\) | 9.67331 | 0.433037 | 0.216518 | − | 0.976279i | \(-0.430530\pi\) | ||||
0.216518 | + | 0.976279i | \(0.430530\pi\) | |||||||
\(500\) | −7.39773 | −0.330836 | ||||||||
\(501\) | 7.95155 | 0.355249 | ||||||||
\(502\) | 31.6037 | 1.41054 | ||||||||
\(503\) | −24.0496 | −1.07232 | −0.536159 | − | 0.844117i | \(-0.680125\pi\) | ||||
−0.536159 | + | 0.844117i | \(0.680125\pi\) | |||||||
\(504\) | 5.19173 | 0.231258 | ||||||||
\(505\) | −2.42229 | −0.107790 | ||||||||
\(506\) | 12.1034 | 0.538063 | ||||||||
\(507\) | 8.89801 | 0.395174 | ||||||||
\(508\) | −4.31814 | −0.191587 | ||||||||
\(509\) | −23.5613 | −1.04433 | −0.522167 | − | 0.852843i | \(-0.674876\pi\) | ||||
−0.522167 | + | 0.852843i | \(0.674876\pi\) | |||||||
\(510\) | 2.26473 | 0.100284 | ||||||||
\(511\) | −26.0170 | −1.15093 | ||||||||
\(512\) | 3.78824 | 0.167418 | ||||||||
\(513\) | −2.21429 | −0.0977635 | ||||||||
\(514\) | −1.08618 | −0.0479094 | ||||||||
\(515\) | 14.0487 | 0.619062 | ||||||||
\(516\) | −2.38189 | −0.104857 | ||||||||
\(517\) | 0.0808948 | 0.00355775 | ||||||||
\(518\) | −43.3763 | −1.90584 | ||||||||
\(519\) | −16.8262 | −0.738588 | ||||||||
\(520\) | −6.14630 | −0.269533 | ||||||||
\(521\) | 2.46091 | 0.107815 | 0.0539073 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539073 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(522\) | 12.9390 | 0.566326 | ||||||||
\(523\) | 11.1734 | 0.488579 | 0.244290 | − | 0.969702i | \(-0.421445\pi\) | ||||
0.244290 | + | 0.969702i | \(0.421445\pi\) | |||||||
\(524\) | 5.69892 | 0.248959 | ||||||||
\(525\) | 7.29735 | 0.318483 | ||||||||
\(526\) | −0.407449 | −0.0177656 | ||||||||
\(527\) | −3.32374 | −0.144784 | ||||||||
\(528\) | −9.53562 | −0.414985 | ||||||||
\(529\) | −8.55030 | −0.371752 | ||||||||
\(530\) | −4.61984 | −0.200673 | ||||||||
\(531\) | −0.596046 | −0.0258662 | ||||||||
\(532\) | 3.47183 | 0.150523 | ||||||||
\(533\) | −8.29940 | −0.359487 | ||||||||
\(534\) | −14.9842 | −0.648428 | ||||||||
\(535\) | −14.8294 | −0.641132 | ||||||||
\(536\) | −10.4817 | −0.452741 | ||||||||
\(537\) | −1.12061 | −0.0483580 | ||||||||
\(538\) | 34.8540 | 1.50266 | ||||||||
\(539\) | 2.64847 | 0.114078 | ||||||||
\(540\) | −0.916488 | −0.0394394 | ||||||||
\(541\) | −27.8397 | −1.19692 | −0.598462 | − | 0.801151i | \(-0.704221\pi\) | ||||
−0.598462 | + | 0.801151i | \(0.704221\pi\) | |||||||
\(542\) | 18.1390 | 0.779138 | ||||||||
\(543\) | 23.7229 | 1.01805 | ||||||||
\(544\) | 3.59534 | 0.154149 | ||||||||
\(545\) | −7.10784 | −0.304467 | ||||||||
\(546\) | −7.84710 | −0.335825 | ||||||||
\(547\) | 18.4066 | 0.787007 | 0.393504 | − | 0.919323i | \(-0.371263\pi\) | ||||
0.393504 | + | 0.919323i | \(0.371263\pi\) | |||||||
\(548\) | 14.4363 | 0.616689 | ||||||||
\(549\) | −5.88020 | −0.250961 | ||||||||
\(550\) | −9.78081 | −0.417055 | ||||||||
\(551\) | −17.5669 | −0.748375 | ||||||||
\(552\) | −8.30753 | −0.353592 | ||||||||
\(553\) | −4.35858 | −0.185346 | ||||||||
\(554\) | −41.2858 | −1.75407 | ||||||||
\(555\) | −15.5459 | −0.659885 | ||||||||
\(556\) | −2.45323 | −0.104040 | ||||||||
\(557\) | −4.57492 | −0.193846 | −0.0969229 | − | 0.995292i | \(-0.530900\pi\) | ||||
−0.0969229 | + | 0.995292i | \(0.530900\pi\) | |||||||
\(558\) | 5.42087 | 0.229484 | ||||||||
\(559\) | −7.30913 | −0.309143 | ||||||||
\(560\) | −16.1122 | −0.680866 | ||||||||
\(561\) | 1.95226 | 0.0824243 | ||||||||
\(562\) | −2.19400 | −0.0925484 | ||||||||
\(563\) | 28.4996 | 1.20112 | 0.600558 | − | 0.799581i | \(-0.294945\pi\) | ||||
0.600558 | + | 0.799581i | \(0.294945\pi\) | |||||||
\(564\) | 0.0273487 | 0.00115159 | ||||||||
\(565\) | 11.0621 | 0.465386 | ||||||||
\(566\) | −33.1642 | −1.39400 | ||||||||
\(567\) | 2.37558 | 0.0997650 | ||||||||
\(568\) | −10.0637 | −0.422262 | ||||||||
\(569\) | 1.71526 | 0.0719073 | 0.0359536 | − | 0.999353i | \(-0.488553\pi\) | ||||
0.0359536 | + | 0.999353i | \(0.488553\pi\) | |||||||
\(570\) | 5.01477 | 0.210046 | ||||||||
\(571\) | −14.4910 | −0.606432 | −0.303216 | − | 0.952922i | \(-0.598060\pi\) | ||||
−0.303216 | + | 0.952922i | \(0.598060\pi\) | |||||||
\(572\) | 2.60968 | 0.109116 | ||||||||
\(573\) | 1.08853 | 0.0454742 | ||||||||
\(574\) | −15.8767 | −0.662682 | ||||||||
\(575\) | −11.6768 | −0.486958 | ||||||||
\(576\) | 3.90499 | 0.162708 | ||||||||
\(577\) | −12.1257 | −0.504799 | −0.252399 | − | 0.967623i | \(-0.581220\pi\) | ||||
−0.252399 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(578\) | −1.63095 | −0.0678388 | ||||||||
\(579\) | −24.2440 | −1.00755 | ||||||||
\(580\) | −7.27087 | −0.301906 | ||||||||
\(581\) | −29.5936 | −1.22775 | ||||||||
\(582\) | 5.39327 | 0.223558 | ||||||||
\(583\) | −3.98243 | −0.164935 | ||||||||
\(584\) | −23.9348 | −0.990430 | ||||||||
\(585\) | −2.81236 | −0.116277 | ||||||||
\(586\) | −29.7927 | −1.23073 | ||||||||
\(587\) | −15.1958 | −0.627198 | −0.313599 | − | 0.949555i | \(-0.601535\pi\) | ||||
−0.313599 | + | 0.949555i | \(0.601535\pi\) | |||||||
\(588\) | 0.895387 | 0.0369251 | ||||||||
\(589\) | −7.35973 | −0.303253 | ||||||||
\(590\) | 1.34988 | 0.0555737 | ||||||||
\(591\) | −4.48344 | −0.184424 | ||||||||
\(592\) | −54.6830 | −2.24746 | ||||||||
\(593\) | 17.5232 | 0.719592 | 0.359796 | − | 0.933031i | \(-0.382846\pi\) | ||||
0.359796 | + | 0.933031i | \(0.382846\pi\) | |||||||
\(594\) | −3.18404 | −0.130643 | ||||||||
\(595\) | 3.29871 | 0.135234 | ||||||||
\(596\) | 9.75395 | 0.399537 | ||||||||
\(597\) | 6.77236 | 0.277174 | ||||||||
\(598\) | 12.5565 | 0.513474 | ||||||||
\(599\) | −10.7969 | −0.441148 | −0.220574 | − | 0.975370i | \(-0.570793\pi\) | ||||
−0.220574 | + | 0.975370i | \(0.570793\pi\) | |||||||
\(600\) | 6.71333 | 0.274071 | ||||||||
\(601\) | 7.82972 | 0.319381 | 0.159690 | − | 0.987167i | \(-0.448950\pi\) | ||||
0.159690 | + | 0.987167i | \(0.448950\pi\) | |||||||
\(602\) | −13.9823 | −0.569878 | ||||||||
\(603\) | −4.79611 | −0.195313 | ||||||||
\(604\) | −15.2965 | −0.622407 | ||||||||
\(605\) | −9.98214 | −0.405832 | ||||||||
\(606\) | −2.84508 | −0.115573 | ||||||||
\(607\) | −29.6897 | −1.20507 | −0.602534 | − | 0.798093i | \(-0.705842\pi\) | ||||
−0.602534 | + | 0.798093i | \(0.705842\pi\) | |||||||
\(608\) | 7.96113 | 0.322867 | ||||||||
\(609\) | 18.8464 | 0.763696 | ||||||||
\(610\) | 13.3170 | 0.539191 | ||||||||
\(611\) | 0.0839230 | 0.00339516 | ||||||||
\(612\) | 0.660014 | 0.0266795 | ||||||||
\(613\) | −41.2587 | −1.66642 | −0.833212 | − | 0.552954i | \(-0.813500\pi\) | ||||
−0.833212 | + | 0.552954i | \(0.813500\pi\) | |||||||
\(614\) | −34.1722 | −1.37908 | ||||||||
\(615\) | −5.69014 | −0.229449 | ||||||||
\(616\) | −10.1356 | −0.408374 | ||||||||
\(617\) | −9.63876 | −0.388042 | −0.194021 | − | 0.980997i | \(-0.562153\pi\) | ||||
−0.194021 | + | 0.980997i | \(0.562153\pi\) | |||||||
\(618\) | 16.5008 | 0.663761 | ||||||||
\(619\) | −21.6398 | −0.869777 | −0.434888 | − | 0.900484i | \(-0.643212\pi\) | ||||
−0.434888 | + | 0.900484i | \(0.643212\pi\) | |||||||
\(620\) | −3.04617 | −0.122337 | ||||||||
\(621\) | −3.80128 | −0.152540 | ||||||||
\(622\) | −52.7258 | −2.11411 | ||||||||
\(623\) | −21.8253 | −0.874412 | ||||||||
\(624\) | −9.89258 | −0.396020 | ||||||||
\(625\) | −0.204825 | −0.00819300 | ||||||||
\(626\) | 55.9897 | 2.23780 | ||||||||
\(627\) | 4.32287 | 0.172639 | ||||||||
\(628\) | 0.660014 | 0.0263374 | ||||||||
\(629\) | 11.1954 | 0.446391 | ||||||||
\(630\) | −5.38004 | −0.214346 | ||||||||
\(631\) | 23.0891 | 0.919164 | 0.459582 | − | 0.888135i | \(-0.347999\pi\) | ||||
0.459582 | + | 0.888135i | \(0.347999\pi\) | |||||||
\(632\) | −4.00975 | −0.159499 | ||||||||
\(633\) | −2.52702 | −0.100440 | ||||||||
\(634\) | 3.12934 | 0.124282 | ||||||||
\(635\) | −9.08486 | −0.360522 | ||||||||
\(636\) | −1.34637 | −0.0533870 | ||||||||
\(637\) | 2.74761 | 0.108864 | ||||||||
\(638\) | −25.2603 | −1.00006 | ||||||||
\(639\) | −4.60483 | −0.182164 | ||||||||
\(640\) | −18.8286 | −0.744267 | ||||||||
\(641\) | −21.2261 | −0.838381 | −0.419191 | − | 0.907898i | \(-0.637686\pi\) | ||||
−0.419191 | + | 0.907898i | \(0.637686\pi\) | |||||||
\(642\) | −17.4178 | −0.687424 | ||||||||
\(643\) | −28.8546 | −1.13791 | −0.568957 | − | 0.822367i | \(-0.692653\pi\) | ||||
−0.568957 | + | 0.822367i | \(0.692653\pi\) | |||||||
\(644\) | 5.96008 | 0.234860 | ||||||||
\(645\) | −5.01120 | −0.197316 | ||||||||
\(646\) | −3.61141 | −0.142089 | ||||||||
\(647\) | 14.0367 | 0.551841 | 0.275921 | − | 0.961180i | \(-0.411017\pi\) | ||||
0.275921 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(648\) | 2.18546 | 0.0858529 | ||||||||
\(649\) | 1.16363 | 0.0456766 | ||||||||
\(650\) | −10.1469 | −0.397996 | ||||||||
\(651\) | 7.89580 | 0.309461 | ||||||||
\(652\) | −10.9545 | −0.429012 | ||||||||
\(653\) | 29.8587 | 1.16846 | 0.584230 | − | 0.811588i | \(-0.301397\pi\) | ||||
0.584230 | + | 0.811588i | \(0.301397\pi\) | |||||||
\(654\) | −8.34845 | −0.326450 | ||||||||
\(655\) | 11.9898 | 0.468482 | ||||||||
\(656\) | −20.0153 | −0.781465 | ||||||||
\(657\) | −10.9519 | −0.427273 | ||||||||
\(658\) | 0.160544 | 0.00625867 | ||||||||
\(659\) | −44.9933 | −1.75269 | −0.876345 | − | 0.481685i | \(-0.840025\pi\) | ||||
−0.876345 | + | 0.481685i | \(0.840025\pi\) | |||||||
\(660\) | 1.78922 | 0.0696453 | ||||||||
\(661\) | −5.28863 | −0.205704 | −0.102852 | − | 0.994697i | \(-0.532797\pi\) | ||||
−0.102852 | + | 0.994697i | \(0.532797\pi\) | |||||||
\(662\) | −38.9442 | −1.51361 | ||||||||
\(663\) | 2.02534 | 0.0786576 | ||||||||
\(664\) | −27.2251 | −1.05654 | ||||||||
\(665\) | 7.30430 | 0.283249 | ||||||||
\(666\) | −18.2592 | −0.707531 | ||||||||
\(667\) | −30.1571 | −1.16769 | ||||||||
\(668\) | −5.24813 | −0.203056 | ||||||||
\(669\) | 5.56077 | 0.214992 | ||||||||
\(670\) | 10.8619 | 0.419631 | ||||||||
\(671\) | 11.4797 | 0.443167 | ||||||||
\(672\) | −8.54101 | −0.329477 | ||||||||
\(673\) | −18.5041 | −0.713282 | −0.356641 | − | 0.934242i | \(-0.616078\pi\) | ||||
−0.356641 | + | 0.934242i | \(0.616078\pi\) | |||||||
\(674\) | 21.8112 | 0.840137 | ||||||||
\(675\) | 3.07182 | 0.118234 | ||||||||
\(676\) | −5.87281 | −0.225877 | ||||||||
\(677\) | 31.7699 | 1.22102 | 0.610509 | − | 0.792009i | \(-0.290965\pi\) | ||||
0.610509 | + | 0.792009i | \(0.290965\pi\) | |||||||
\(678\) | 12.9929 | 0.498989 | ||||||||
\(679\) | 7.85561 | 0.301471 | ||||||||
\(680\) | 3.03470 | 0.116376 | ||||||||
\(681\) | −27.1183 | −1.03918 | ||||||||
\(682\) | −10.5829 | −0.405241 | ||||||||
\(683\) | −32.0534 | −1.22649 | −0.613245 | − | 0.789893i | \(-0.710136\pi\) | ||||
−0.613245 | + | 0.789893i | \(0.710136\pi\) | |||||||
\(684\) | 1.46146 | 0.0558805 | ||||||||
\(685\) | 30.3723 | 1.16046 | ||||||||
\(686\) | 32.3774 | 1.23618 | ||||||||
\(687\) | −10.3903 | −0.396415 | ||||||||
\(688\) | −17.6271 | −0.672026 | ||||||||
\(689\) | −4.13151 | −0.157398 | ||||||||
\(690\) | 8.60885 | 0.327733 | ||||||||
\(691\) | 17.7689 | 0.675959 | 0.337979 | − | 0.941153i | \(-0.390257\pi\) | ||||
0.337979 | + | 0.941153i | \(0.390257\pi\) | |||||||
\(692\) | 11.1055 | 0.422168 | ||||||||
\(693\) | −4.63774 | −0.176173 | ||||||||
\(694\) | 26.8446 | 1.01901 | ||||||||
\(695\) | −5.16131 | −0.195780 | ||||||||
\(696\) | 17.3381 | 0.657199 | ||||||||
\(697\) | 4.09779 | 0.155215 | ||||||||
\(698\) | −49.5208 | −1.87439 | ||||||||
\(699\) | 19.5398 | 0.739062 | ||||||||
\(700\) | −4.81635 | −0.182041 | ||||||||
\(701\) | −25.8698 | −0.977087 | −0.488544 | − | 0.872539i | \(-0.662472\pi\) | ||||
−0.488544 | + | 0.872539i | \(0.662472\pi\) | |||||||
\(702\) | −3.30323 | −0.124673 | ||||||||
\(703\) | 24.7900 | 0.934972 | ||||||||
\(704\) | −7.62354 | −0.287323 | ||||||||
\(705\) | 0.0575383 | 0.00216702 | ||||||||
\(706\) | −20.8358 | −0.784165 | ||||||||
\(707\) | −4.14402 | −0.155852 | ||||||||
\(708\) | 0.393398 | 0.0147848 | ||||||||
\(709\) | 24.5893 | 0.923469 | 0.461734 | − | 0.887018i | \(-0.347227\pi\) | ||||
0.461734 | + | 0.887018i | \(0.347227\pi\) | |||||||
\(710\) | 10.4287 | 0.391382 | ||||||||
\(711\) | −1.83474 | −0.0688082 | ||||||||
\(712\) | −20.0786 | −0.752476 | ||||||||
\(713\) | −12.6344 | −0.473164 | ||||||||
\(714\) | 3.87446 | 0.144998 | ||||||||
\(715\) | 5.49045 | 0.205331 | ||||||||
\(716\) | 0.739619 | 0.0276409 | ||||||||
\(717\) | 12.5770 | 0.469698 | ||||||||
\(718\) | −33.3044 | −1.24291 | ||||||||
\(719\) | 34.7811 | 1.29712 | 0.648558 | − | 0.761165i | \(-0.275372\pi\) | ||||
0.648558 | + | 0.761165i | \(0.275372\pi\) | |||||||
\(720\) | −6.78244 | −0.252767 | ||||||||
\(721\) | 24.0344 | 0.895088 | ||||||||
\(722\) | 22.9914 | 0.855652 | ||||||||
\(723\) | 2.92636 | 0.108833 | ||||||||
\(724\) | −15.6575 | −0.581905 | ||||||||
\(725\) | 24.3700 | 0.905078 | ||||||||
\(726\) | −11.7244 | −0.435135 | ||||||||
\(727\) | 32.5468 | 1.20709 | 0.603546 | − | 0.797328i | \(-0.293754\pi\) | ||||
0.603546 | + | 0.797328i | \(0.293754\pi\) | |||||||
\(728\) | −10.5150 | −0.389712 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 24.8030 | 0.917999 | ||||||||
\(731\) | 3.60885 | 0.133478 | ||||||||
\(732\) | 3.88101 | 0.143446 | ||||||||
\(733\) | −18.8236 | −0.695266 | −0.347633 | − | 0.937631i | \(-0.613014\pi\) | ||||
−0.347633 | + | 0.937631i | \(0.613014\pi\) | |||||||
\(734\) | 13.0508 | 0.481713 | ||||||||
\(735\) | 1.88379 | 0.0694845 | ||||||||
\(736\) | 13.6669 | 0.503767 | ||||||||
\(737\) | 9.36325 | 0.344900 | ||||||||
\(738\) | −6.68331 | −0.246016 | ||||||||
\(739\) | −17.0080 | −0.625648 | −0.312824 | − | 0.949811i | \(-0.601275\pi\) | ||||
−0.312824 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(740\) | 10.2605 | 0.377183 | ||||||||
\(741\) | 4.48469 | 0.164749 | ||||||||
\(742\) | −7.90356 | −0.290149 | ||||||||
\(743\) | −39.8288 | −1.46118 | −0.730589 | − | 0.682818i | \(-0.760754\pi\) | ||||
−0.730589 | + | 0.682818i | \(0.760754\pi\) | |||||||
\(744\) | 7.26389 | 0.266307 | ||||||||
\(745\) | 20.5211 | 0.751836 | ||||||||
\(746\) | 11.5617 | 0.423303 | ||||||||
\(747\) | −12.4574 | −0.455793 | ||||||||
\(748\) | −1.28852 | −0.0471128 | ||||||||
\(749\) | −25.3700 | −0.926999 | ||||||||
\(750\) | −18.2805 | −0.667508 | ||||||||
\(751\) | 8.36466 | 0.305231 | 0.152615 | − | 0.988286i | \(-0.451230\pi\) | ||||
0.152615 | + | 0.988286i | \(0.451230\pi\) | |||||||
\(752\) | 0.202393 | 0.00738052 | ||||||||
\(753\) | 19.3774 | 0.706153 | ||||||||
\(754\) | −26.2059 | −0.954362 | ||||||||
\(755\) | −32.1821 | −1.17123 | ||||||||
\(756\) | −1.56792 | −0.0570245 | ||||||||
\(757\) | −12.6034 | −0.458077 | −0.229039 | − | 0.973417i | \(-0.573558\pi\) | ||||
−0.229039 | + | 0.973417i | \(0.573558\pi\) | |||||||
\(758\) | 36.0943 | 1.31100 | ||||||||
\(759\) | 7.42107 | 0.269368 | ||||||||
\(760\) | 6.71973 | 0.243750 | ||||||||
\(761\) | −4.11791 | −0.149274 | −0.0746371 | − | 0.997211i | \(-0.523780\pi\) | ||||
−0.0746371 | + | 0.997211i | \(0.523780\pi\) | |||||||
\(762\) | −10.6705 | −0.386553 | ||||||||
\(763\) | −12.1600 | −0.440222 | ||||||||
\(764\) | −0.718448 | −0.0259925 | ||||||||
\(765\) | 1.38859 | 0.0502046 | ||||||||
\(766\) | −4.24558 | −0.153399 | ||||||||
\(767\) | 1.20719 | 0.0435892 | ||||||||
\(768\) | −14.3050 | −0.516188 | ||||||||
\(769\) | −10.1725 | −0.366829 | −0.183415 | − | 0.983036i | \(-0.558715\pi\) | ||||
−0.183415 | + | 0.983036i | \(0.558715\pi\) | |||||||
\(770\) | 10.5032 | 0.378510 | ||||||||
\(771\) | −0.665979 | −0.0239846 | ||||||||
\(772\) | 16.0014 | 0.575902 | ||||||||
\(773\) | 0.364381 | 0.0131059 | 0.00655293 | − | 0.999979i | \(-0.497914\pi\) | ||||
0.00655293 | + | 0.999979i | \(0.497914\pi\) | |||||||
\(774\) | −5.88586 | −0.211563 | ||||||||
\(775\) | 10.2099 | 0.366751 | ||||||||
\(776\) | 7.22691 | 0.259431 | ||||||||
\(777\) | −26.5956 | −0.954113 | ||||||||
\(778\) | 38.2758 | 1.37225 | ||||||||
\(779\) | 9.07371 | 0.325099 | ||||||||
\(780\) | 1.85620 | 0.0664625 | ||||||||
\(781\) | 8.98982 | 0.321681 | ||||||||
\(782\) | −6.19971 | −0.221701 | ||||||||
\(783\) | 7.93340 | 0.283517 | ||||||||
\(784\) | 6.62628 | 0.236653 | ||||||||
\(785\) | 1.38859 | 0.0495609 | ||||||||
\(786\) | 14.0826 | 0.502308 | ||||||||
\(787\) | −49.0372 | −1.74799 | −0.873994 | − | 0.485937i | \(-0.838479\pi\) | ||||
−0.873994 | + | 0.485937i | \(0.838479\pi\) | |||||||
\(788\) | 2.95913 | 0.105415 | ||||||||
\(789\) | −0.249822 | −0.00889391 | ||||||||
\(790\) | 4.15519 | 0.147835 | ||||||||
\(791\) | 18.9249 | 0.672892 | ||||||||
\(792\) | −4.26657 | −0.151606 | ||||||||
\(793\) | 11.9094 | 0.422915 | ||||||||
\(794\) | 21.3160 | 0.756477 | ||||||||
\(795\) | −2.83260 | −0.100462 | ||||||||
\(796\) | −4.46985 | −0.158430 | ||||||||
\(797\) | 14.1931 | 0.502744 | 0.251372 | − | 0.967890i | \(-0.419118\pi\) | ||||
0.251372 | + | 0.967890i | \(0.419118\pi\) | |||||||
\(798\) | 8.57920 | 0.303701 | ||||||||
\(799\) | −0.0414365 | −0.00146592 | ||||||||
\(800\) | −11.0442 | −0.390472 | ||||||||
\(801\) | −9.18735 | −0.324619 | ||||||||
\(802\) | −9.11121 | −0.321728 | ||||||||
\(803\) | 21.3809 | 0.754514 | ||||||||
\(804\) | 3.16550 | 0.111639 | ||||||||
\(805\) | 12.5393 | 0.441952 | ||||||||
\(806\) | −10.9791 | −0.386722 | ||||||||
\(807\) | 21.3703 | 0.752270 | ||||||||
\(808\) | −3.81237 | −0.134119 | ||||||||
\(809\) | 7.88086 | 0.277076 | 0.138538 | − | 0.990357i | \(-0.455760\pi\) | ||||
0.138538 | + | 0.990357i | \(0.455760\pi\) | |||||||
\(810\) | −2.26473 | −0.0795744 | ||||||||
\(811\) | −4.67120 | −0.164028 | −0.0820141 | − | 0.996631i | \(-0.526135\pi\) | ||||
−0.0820141 | + | 0.996631i | \(0.526135\pi\) | |||||||
\(812\) | −12.4389 | −0.436520 | ||||||||
\(813\) | 11.1217 | 0.390056 | ||||||||
\(814\) | 35.6467 | 1.24942 | ||||||||
\(815\) | −23.0470 | −0.807301 | ||||||||
\(816\) | 4.88441 | 0.170989 | ||||||||
\(817\) | 7.99105 | 0.279571 | ||||||||
\(818\) | −15.4212 | −0.539190 | ||||||||
\(819\) | −4.81135 | −0.168122 | ||||||||
\(820\) | 3.75557 | 0.131150 | ||||||||
\(821\) | −7.64967 | −0.266975 | −0.133488 | − | 0.991050i | \(-0.542618\pi\) | ||||
−0.133488 | + | 0.991050i | \(0.542618\pi\) | |||||||
\(822\) | 35.6735 | 1.24425 | ||||||||
\(823\) | −21.3014 | −0.742519 | −0.371259 | − | 0.928529i | \(-0.621074\pi\) | ||||
−0.371259 | + | 0.928529i | \(0.621074\pi\) | |||||||
\(824\) | 22.1109 | 0.770269 | ||||||||
\(825\) | −5.99698 | −0.208788 | ||||||||
\(826\) | 2.30936 | 0.0803528 | ||||||||
\(827\) | 27.0958 | 0.942214 | 0.471107 | − | 0.882076i | \(-0.343855\pi\) | ||||
0.471107 | + | 0.882076i | \(0.343855\pi\) | |||||||
\(828\) | 2.50889 | 0.0871901 | ||||||||
\(829\) | −12.0102 | −0.417132 | −0.208566 | − | 0.978008i | \(-0.566880\pi\) | ||||
−0.208566 | + | 0.978008i | \(0.566880\pi\) | |||||||
\(830\) | 28.2126 | 0.979274 | ||||||||
\(831\) | −25.3139 | −0.878130 | ||||||||
\(832\) | −7.90892 | −0.274192 | ||||||||
\(833\) | −1.35662 | −0.0470041 | ||||||||
\(834\) | −6.06217 | −0.209916 | ||||||||
\(835\) | −11.0414 | −0.382105 | ||||||||
\(836\) | −2.85315 | −0.0986784 | ||||||||
\(837\) | 3.32374 | 0.114885 | ||||||||
\(838\) | −3.88377 | −0.134163 | ||||||||
\(839\) | 40.8771 | 1.41123 | 0.705617 | − | 0.708593i | \(-0.250670\pi\) | ||||
0.705617 | + | 0.708593i | \(0.250670\pi\) | |||||||
\(840\) | −7.20918 | −0.248740 | ||||||||
\(841\) | 33.9389 | 1.17031 | ||||||||
\(842\) | 28.9709 | 0.998404 | ||||||||
\(843\) | −1.34523 | −0.0463320 | ||||||||
\(844\) | 1.66787 | 0.0574104 | ||||||||
\(845\) | −12.3557 | −0.425048 | ||||||||
\(846\) | 0.0675811 | 0.00232349 | ||||||||
\(847\) | −17.0773 | −0.586784 | ||||||||
\(848\) | −9.96376 | −0.342157 | ||||||||
\(849\) | −20.3342 | −0.697869 | ||||||||
\(850\) | 5.01000 | 0.171842 | ||||||||
\(851\) | 42.5569 | 1.45883 | ||||||||
\(852\) | 3.03925 | 0.104123 | ||||||||
\(853\) | −23.6549 | −0.809927 | −0.404964 | − | 0.914333i | \(-0.632716\pi\) | ||||
−0.404964 | + | 0.914333i | \(0.632716\pi\) | |||||||
\(854\) | 22.7826 | 0.779605 | ||||||||
\(855\) | 3.07475 | 0.105154 | ||||||||
\(856\) | −23.3396 | −0.797730 | ||||||||
\(857\) | 1.84214 | 0.0629264 | 0.0314632 | − | 0.999505i | \(-0.489983\pi\) | ||||
0.0314632 | + | 0.999505i | \(0.489983\pi\) | |||||||
\(858\) | 6.44876 | 0.220157 | ||||||||
\(859\) | −1.64608 | −0.0561635 | −0.0280818 | − | 0.999606i | \(-0.508940\pi\) | ||||
−0.0280818 | + | 0.999606i | \(0.508940\pi\) | |||||||
\(860\) | 3.30746 | 0.112784 | ||||||||
\(861\) | −9.73462 | −0.331755 | ||||||||
\(862\) | −59.8911 | −2.03990 | ||||||||
\(863\) | −43.2392 | −1.47188 | −0.735939 | − | 0.677048i | \(-0.763259\pi\) | ||||
−0.735939 | + | 0.677048i | \(0.763259\pi\) | |||||||
\(864\) | −3.59534 | −0.122316 | ||||||||
\(865\) | 23.3647 | 0.794423 | ||||||||
\(866\) | 57.4739 | 1.95304 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −5.21134 | −0.176884 | ||||||||
\(869\) | 3.58189 | 0.121507 | ||||||||
\(870\) | −17.9670 | −0.609138 | ||||||||
\(871\) | 9.71375 | 0.329138 | ||||||||
\(872\) | −11.1868 | −0.378833 | ||||||||
\(873\) | 3.30682 | 0.111919 | ||||||||
\(874\) | −13.7280 | −0.464356 | ||||||||
\(875\) | −26.6266 | −0.900142 | ||||||||
\(876\) | 7.22838 | 0.244224 | ||||||||
\(877\) | −2.39618 | −0.0809131 | −0.0404566 | − | 0.999181i | \(-0.512881\pi\) | ||||
−0.0404566 | + | 0.999181i | \(0.512881\pi\) | |||||||
\(878\) | 39.7436 | 1.34128 | ||||||||
\(879\) | −18.2670 | −0.616132 | ||||||||
\(880\) | 13.2411 | 0.446356 | ||||||||
\(881\) | 51.5181 | 1.73569 | 0.867845 | − | 0.496835i | \(-0.165505\pi\) | ||||
0.867845 | + | 0.496835i | \(0.165505\pi\) | |||||||
\(882\) | 2.21258 | 0.0745016 | ||||||||
\(883\) | 47.6457 | 1.60341 | 0.801703 | − | 0.597722i | \(-0.203927\pi\) | ||||
0.801703 | + | 0.597722i | \(0.203927\pi\) | |||||||
\(884\) | −1.33675 | −0.0449598 | ||||||||
\(885\) | 0.827663 | 0.0278216 | ||||||||
\(886\) | −23.6743 | −0.795355 | ||||||||
\(887\) | −20.0028 | −0.671627 | −0.335814 | − | 0.941928i | \(-0.609011\pi\) | ||||
−0.335814 | + | 0.941928i | \(0.609011\pi\) | |||||||
\(888\) | −24.4671 | −0.821063 | ||||||||
\(889\) | −15.5423 | −0.521270 | ||||||||
\(890\) | 20.8068 | 0.697447 | ||||||||
\(891\) | −1.95226 | −0.0654031 | ||||||||
\(892\) | −3.67018 | −0.122887 | ||||||||
\(893\) | −0.0917527 | −0.00307039 | ||||||||
\(894\) | 24.1029 | 0.806122 | ||||||||
\(895\) | 1.55607 | 0.0520137 | ||||||||
\(896\) | −32.2118 | −1.07612 | ||||||||
\(897\) | 7.69887 | 0.257058 | ||||||||
\(898\) | 23.9288 | 0.798516 | ||||||||
\(899\) | 26.3685 | 0.879440 | ||||||||
\(900\) | −2.02744 | −0.0675814 | ||||||||
\(901\) | 2.03991 | 0.0679593 | ||||||||
\(902\) | 13.0475 | 0.434435 | ||||||||
\(903\) | −8.57310 | −0.285295 | ||||||||
\(904\) | 17.4103 | 0.579058 | ||||||||
\(905\) | −32.9414 | −1.09501 | ||||||||
\(906\) | −37.7991 | −1.25579 | ||||||||
\(907\) | 32.8164 | 1.08965 | 0.544826 | − | 0.838549i | \(-0.316596\pi\) | ||||
0.544826 | + | 0.838549i | \(0.316596\pi\) | |||||||
\(908\) | 17.8984 | 0.593981 | ||||||||
\(909\) | −1.74442 | −0.0578589 | ||||||||
\(910\) | 10.8964 | 0.361212 | ||||||||
\(911\) | −25.0836 | −0.831056 | −0.415528 | − | 0.909580i | \(-0.636403\pi\) | ||||
−0.415528 | + | 0.909580i | \(0.636403\pi\) | |||||||
\(912\) | 10.8155 | 0.358138 | ||||||||
\(913\) | 24.3201 | 0.804876 | ||||||||
\(914\) | 38.2031 | 1.26365 | ||||||||
\(915\) | 8.16518 | 0.269933 | ||||||||
\(916\) | 6.85774 | 0.226586 | ||||||||
\(917\) | 20.5121 | 0.677368 | ||||||||
\(918\) | 1.63095 | 0.0538295 | ||||||||
\(919\) | 7.87486 | 0.259768 | 0.129884 | − | 0.991529i | \(-0.458540\pi\) | ||||
0.129884 | + | 0.991529i | \(0.458540\pi\) | |||||||
\(920\) | 11.5357 | 0.380322 | ||||||||
\(921\) | −20.9522 | −0.690400 | ||||||||
\(922\) | 58.4628 | 1.92537 | ||||||||
\(923\) | 9.32634 | 0.306980 | ||||||||
\(924\) | 3.06097 | 0.100699 | ||||||||
\(925\) | −34.3903 | −1.13075 | ||||||||
\(926\) | −0.0513933 | −0.00168889 | ||||||||
\(927\) | 10.1173 | 0.332295 | ||||||||
\(928\) | −28.5233 | −0.936322 | ||||||||
\(929\) | 18.8542 | 0.618586 | 0.309293 | − | 0.950967i | \(-0.399908\pi\) | ||||
0.309293 | + | 0.950967i | \(0.399908\pi\) | |||||||
\(930\) | −7.52736 | −0.246832 | ||||||||
\(931\) | −3.00395 | −0.0984506 | ||||||||
\(932\) | −12.8965 | −0.422440 | ||||||||
\(933\) | −32.3282 | −1.05838 | ||||||||
\(934\) | −48.4149 | −1.58418 | ||||||||
\(935\) | −2.71088 | −0.0886554 | ||||||||
\(936\) | −4.42629 | −0.144678 | ||||||||
\(937\) | −32.9832 | −1.07751 | −0.538757 | − | 0.842461i | \(-0.681106\pi\) | ||||
−0.538757 | + | 0.842461i | \(0.681106\pi\) | |||||||
\(938\) | 18.5824 | 0.606736 | ||||||||
\(939\) | 34.3294 | 1.12030 | ||||||||
\(940\) | −0.0379761 | −0.00123864 | ||||||||
\(941\) | −24.9724 | −0.814078 | −0.407039 | − | 0.913411i | \(-0.633439\pi\) | ||||
−0.407039 | + | 0.913411i | \(0.633439\pi\) | |||||||
\(942\) | 1.63095 | 0.0531394 | ||||||||
\(943\) | 15.5768 | 0.507251 | ||||||||
\(944\) | 2.91133 | 0.0947558 | ||||||||
\(945\) | −3.29871 | −0.107307 | ||||||||
\(946\) | 11.4907 | 0.373595 | ||||||||
\(947\) | −24.6507 | −0.801040 | −0.400520 | − | 0.916288i | \(-0.631170\pi\) | ||||
−0.400520 | + | 0.916288i | \(0.631170\pi\) | |||||||
\(948\) | 1.21095 | 0.0393300 | ||||||||
\(949\) | 22.1812 | 0.720033 | ||||||||
\(950\) | 11.0936 | 0.359924 | ||||||||
\(951\) | 1.91871 | 0.0622186 | ||||||||
\(952\) | 5.19173 | 0.168265 | ||||||||
\(953\) | 36.6746 | 1.18801 | 0.594003 | − | 0.804463i | \(-0.297547\pi\) | ||||
0.594003 | + | 0.804463i | \(0.297547\pi\) | |||||||
\(954\) | −3.32700 | −0.107716 | ||||||||
\(955\) | −1.51153 | −0.0489119 | ||||||||
\(956\) | −8.30102 | −0.268474 | ||||||||
\(957\) | −15.4880 | −0.500657 | ||||||||
\(958\) | −49.9944 | −1.61525 | ||||||||
\(959\) | 51.9605 | 1.67789 | ||||||||
\(960\) | −5.42242 | −0.175008 | ||||||||
\(961\) | −19.9528 | −0.643638 | ||||||||
\(962\) | 36.9811 | 1.19232 | ||||||||
\(963\) | −10.6795 | −0.344142 | ||||||||
\(964\) | −1.93144 | −0.0622074 | ||||||||
\(965\) | 33.6649 | 1.08371 | ||||||||
\(966\) | 14.7279 | 0.473863 | ||||||||
\(967\) | 25.6067 | 0.823456 | 0.411728 | − | 0.911307i | \(-0.364925\pi\) | ||||
0.411728 | + | 0.911307i | \(0.364925\pi\) | |||||||
\(968\) | −15.7106 | −0.504957 | ||||||||
\(969\) | −2.21429 | −0.0711334 | ||||||||
\(970\) | −7.48904 | −0.240458 | ||||||||
\(971\) | −37.4406 | −1.20153 | −0.600763 | − | 0.799427i | \(-0.705137\pi\) | ||||
−0.600763 | + | 0.799427i | \(0.705137\pi\) | |||||||
\(972\) | −0.660014 | −0.0211699 | ||||||||
\(973\) | −8.82990 | −0.283073 | ||||||||
\(974\) | 35.3358 | 1.13223 | ||||||||
\(975\) | −6.22147 | −0.199247 | ||||||||
\(976\) | 28.7213 | 0.919346 | ||||||||
\(977\) | −55.0383 | −1.76083 | −0.880415 | − | 0.474203i | \(-0.842736\pi\) | ||||
−0.880415 | + | 0.474203i | \(0.842736\pi\) | |||||||
\(978\) | −27.0696 | −0.865592 | ||||||||
\(979\) | 17.9361 | 0.573239 | ||||||||
\(980\) | −1.24333 | −0.0397166 | ||||||||
\(981\) | −5.11875 | −0.163429 | ||||||||
\(982\) | −16.6900 | −0.532598 | ||||||||
\(983\) | 15.0668 | 0.480555 | 0.240277 | − | 0.970704i | \(-0.422762\pi\) | ||||
0.240277 | + | 0.970704i | \(0.422762\pi\) | |||||||
\(984\) | −8.95554 | −0.285492 | ||||||||
\(985\) | 6.22565 | 0.198366 | ||||||||
\(986\) | 12.9390 | 0.412062 | ||||||||
\(987\) | 0.0984358 | 0.00313325 | ||||||||
\(988\) | −2.95996 | −0.0941688 | ||||||||
\(989\) | 13.7182 | 0.436214 | ||||||||
\(990\) | 4.42133 | 0.140519 | ||||||||
\(991\) | −55.8925 | −1.77548 | −0.887741 | − | 0.460342i | \(-0.847727\pi\) | ||||
−0.887741 | + | 0.460342i | \(0.847727\pi\) | |||||||
\(992\) | −11.9500 | −0.379411 | ||||||||
\(993\) | −23.8782 | −0.757751 | ||||||||
\(994\) | 17.8413 | 0.565890 | ||||||||
\(995\) | −9.40403 | −0.298128 | ||||||||
\(996\) | 8.22206 | 0.260526 | ||||||||
\(997\) | −53.8993 | −1.70701 | −0.853505 | − | 0.521085i | \(-0.825527\pi\) | ||||
−0.853505 | + | 0.521085i | \(0.825527\pi\) | |||||||
\(998\) | −15.7767 | −0.499404 | ||||||||
\(999\) | −11.1954 | −0.354208 |
(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 | 8007.2.a.c.1.10 | ✓ | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.c.1.10 | ✓ | 39 | 1.1 | even | 1 | trivial |