Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41247 | −1.70587 | −0.852936 | − | 0.522015i | \(-0.825180\pi\) | ||||
−0.852936 | + | 0.522015i | \(0.825180\pi\) | |||||||
\(3\) | 2.73531 | 1.57923 | 0.789616 | − | 0.613601i | \(-0.210280\pi\) | ||||
0.789616 | + | 0.613601i | \(0.210280\pi\) | |||||||
\(4\) | 3.82000 | 1.91000 | ||||||||
\(5\) | −4.06212 | −1.81664 | −0.908318 | − | 0.418281i | \(-0.862633\pi\) | ||||
−0.908318 | + | 0.418281i | \(0.862633\pi\) | |||||||
\(6\) | −6.59885 | −2.69397 | ||||||||
\(7\) | 3.23940 | 1.22438 | 0.612188 | − | 0.790712i | \(-0.290289\pi\) | ||||
0.612188 | + | 0.790712i | \(0.290289\pi\) | |||||||
\(8\) | −4.39069 | −1.55234 | ||||||||
\(9\) | 4.48192 | 1.49397 | ||||||||
\(10\) | 9.79973 | 3.09895 | ||||||||
\(11\) | −4.16401 | −1.25550 | −0.627749 | − | 0.778416i | \(-0.716024\pi\) | ||||
−0.627749 | + | 0.778416i | \(0.716024\pi\) | |||||||
\(12\) | 10.4489 | 3.01633 | ||||||||
\(13\) | 5.20045 | 1.44234 | 0.721172 | − | 0.692756i | \(-0.243604\pi\) | ||||
0.721172 | + | 0.692756i | \(0.243604\pi\) | |||||||
\(14\) | −7.81494 | −2.08863 | ||||||||
\(15\) | −11.1112 | −2.86889 | ||||||||
\(16\) | 2.95241 | 0.738102 | ||||||||
\(17\) | 6.42329 | 1.55788 | 0.778938 | − | 0.627100i | \(-0.215758\pi\) | ||||
0.778938 | + | 0.627100i | \(0.215758\pi\) | |||||||
\(18\) | −10.8125 | −2.54853 | ||||||||
\(19\) | 5.14494 | 1.18033 | 0.590165 | − | 0.807283i | \(-0.299063\pi\) | ||||
0.590165 | + | 0.807283i | \(0.299063\pi\) | |||||||
\(20\) | −15.5173 | −3.46977 | ||||||||
\(21\) | 8.86075 | 1.93358 | ||||||||
\(22\) | 10.0456 | 2.14172 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −12.0099 | −2.45151 | ||||||||
\(25\) | 11.5008 | 2.30016 | ||||||||
\(26\) | −12.5459 | −2.46046 | ||||||||
\(27\) | 4.05351 | 0.780099 | ||||||||
\(28\) | 12.3745 | 2.33856 | ||||||||
\(29\) | 0.970739 | 0.180262 | 0.0901308 | − | 0.995930i | \(-0.471271\pi\) | ||||
0.0901308 | + | 0.995930i | \(0.471271\pi\) | |||||||
\(30\) | 26.8053 | 4.89396 | ||||||||
\(31\) | 5.78906 | 1.03975 | 0.519873 | − | 0.854244i | \(-0.325979\pi\) | ||||
0.519873 | + | 0.854244i | \(0.325979\pi\) | |||||||
\(32\) | 1.65880 | 0.293238 | ||||||||
\(33\) | −11.3899 | −1.98272 | ||||||||
\(34\) | −15.4960 | −2.65754 | ||||||||
\(35\) | −13.1588 | −2.22425 | ||||||||
\(36\) | 17.1209 | 2.85349 | ||||||||
\(37\) | 9.74412 | 1.60192 | 0.800961 | − | 0.598716i | \(-0.204322\pi\) | ||||
0.800961 | + | 0.598716i | \(0.204322\pi\) | |||||||
\(38\) | −12.4120 | −2.01349 | ||||||||
\(39\) | 14.2248 | 2.27780 | ||||||||
\(40\) | 17.8355 | 2.82004 | ||||||||
\(41\) | 9.09773 | 1.42083 | 0.710413 | − | 0.703785i | \(-0.248508\pi\) | ||||
0.710413 | + | 0.703785i | \(0.248508\pi\) | |||||||
\(42\) | −21.3763 | −3.29843 | ||||||||
\(43\) | −5.13587 | −0.783213 | −0.391606 | − | 0.920133i | \(-0.628081\pi\) | ||||
−0.391606 | + | 0.920133i | \(0.628081\pi\) | |||||||
\(44\) | −15.9065 | −2.39800 | ||||||||
\(45\) | −18.2061 | −2.71401 | ||||||||
\(46\) | −2.41247 | −0.355699 | ||||||||
\(47\) | 6.94159 | 1.01254 | 0.506268 | − | 0.862376i | \(-0.331025\pi\) | ||||
0.506268 | + | 0.862376i | \(0.331025\pi\) | |||||||
\(48\) | 8.07575 | 1.16563 | ||||||||
\(49\) | 3.49369 | 0.499099 | ||||||||
\(50\) | −27.7454 | −3.92379 | ||||||||
\(51\) | 17.5697 | 2.46025 | ||||||||
\(52\) | 19.8657 | 2.75488 | ||||||||
\(53\) | 1.05253 | 0.144576 | 0.0722878 | − | 0.997384i | \(-0.476970\pi\) | ||||
0.0722878 | + | 0.997384i | \(0.476970\pi\) | |||||||
\(54\) | −9.77897 | −1.33075 | ||||||||
\(55\) | 16.9147 | 2.28078 | ||||||||
\(56\) | −14.2232 | −1.90066 | ||||||||
\(57\) | 14.0730 | 1.86401 | ||||||||
\(58\) | −2.34188 | −0.307503 | ||||||||
\(59\) | −2.55339 | −0.332423 | −0.166212 | − | 0.986090i | \(-0.553153\pi\) | ||||
−0.166212 | + | 0.986090i | \(0.553153\pi\) | |||||||
\(60\) | −42.4446 | −5.47958 | ||||||||
\(61\) | −12.3008 | −1.57495 | −0.787476 | − | 0.616346i | \(-0.788612\pi\) | ||||
−0.787476 | + | 0.616346i | \(0.788612\pi\) | |||||||
\(62\) | −13.9659 | −1.77367 | ||||||||
\(63\) | 14.5187 | 1.82919 | ||||||||
\(64\) | −9.90662 | −1.23833 | ||||||||
\(65\) | −21.1248 | −2.62021 | ||||||||
\(66\) | 27.4777 | 3.38227 | ||||||||
\(67\) | 0.828885 | 0.101264 | 0.0506322 | − | 0.998717i | \(-0.483876\pi\) | ||||
0.0506322 | + | 0.998717i | \(0.483876\pi\) | |||||||
\(68\) | 24.5370 | 2.97555 | ||||||||
\(69\) | 2.73531 | 0.329293 | ||||||||
\(70\) | 31.7452 | 3.79428 | ||||||||
\(71\) | −11.4798 | −1.36240 | −0.681202 | − | 0.732095i | \(-0.738543\pi\) | ||||
−0.681202 | + | 0.732095i | \(0.738543\pi\) | |||||||
\(72\) | −19.6787 | −2.31916 | ||||||||
\(73\) | −10.0341 | −1.17440 | −0.587200 | − | 0.809442i | \(-0.699770\pi\) | ||||
−0.587200 | + | 0.809442i | \(0.699770\pi\) | |||||||
\(74\) | −23.5074 | −2.73268 | ||||||||
\(75\) | 31.4583 | 3.63249 | ||||||||
\(76\) | 19.6537 | 2.25443 | ||||||||
\(77\) | −13.4889 | −1.53720 | ||||||||
\(78\) | −34.3170 | −3.88563 | ||||||||
\(79\) | −1.85268 | −0.208443 | −0.104222 | − | 0.994554i | \(-0.533235\pi\) | ||||
−0.104222 | + | 0.994554i | \(0.533235\pi\) | |||||||
\(80\) | −11.9930 | −1.34086 | ||||||||
\(81\) | −2.35814 | −0.262016 | ||||||||
\(82\) | −21.9480 | −2.42375 | ||||||||
\(83\) | 7.22276 | 0.792801 | 0.396401 | − | 0.918078i | \(-0.370259\pi\) | ||||
0.396401 | + | 0.918078i | \(0.370259\pi\) | |||||||
\(84\) | 33.8481 | 3.69313 | ||||||||
\(85\) | −26.0922 | −2.83009 | ||||||||
\(86\) | 12.3901 | 1.33606 | ||||||||
\(87\) | 2.65527 | 0.284675 | ||||||||
\(88\) | 18.2829 | 1.94897 | ||||||||
\(89\) | −13.5713 | −1.43855 | −0.719276 | − | 0.694725i | \(-0.755526\pi\) | ||||
−0.719276 | + | 0.694725i | \(0.755526\pi\) | |||||||
\(90\) | 43.9216 | 4.62975 | ||||||||
\(91\) | 16.8463 | 1.76597 | ||||||||
\(92\) | 3.82000 | 0.398263 | ||||||||
\(93\) | 15.8349 | 1.64200 | ||||||||
\(94\) | −16.7464 | −1.72726 | ||||||||
\(95\) | −20.8993 | −2.14423 | ||||||||
\(96\) | 4.53734 | 0.463090 | ||||||||
\(97\) | 17.9077 | 1.81825 | 0.909126 | − | 0.416522i | \(-0.136751\pi\) | ||||
0.909126 | + | 0.416522i | \(0.136751\pi\) | |||||||
\(98\) | −8.42842 | −0.851399 | ||||||||
\(99\) | −18.6628 | −1.87568 | ||||||||
\(100\) | 43.9331 | 4.39331 | ||||||||
\(101\) | 18.7030 | 1.86101 | 0.930507 | − | 0.366274i | \(-0.119367\pi\) | ||||
0.930507 | + | 0.366274i | \(0.119367\pi\) | |||||||
\(102\) | −42.3863 | −4.19687 | ||||||||
\(103\) | −16.1531 | −1.59161 | −0.795804 | − | 0.605554i | \(-0.792952\pi\) | ||||
−0.795804 | + | 0.605554i | \(0.792952\pi\) | |||||||
\(104\) | −22.8336 | −2.23902 | ||||||||
\(105\) | −35.9934 | −3.51260 | ||||||||
\(106\) | −2.53919 | −0.246628 | ||||||||
\(107\) | 9.54927 | 0.923162 | 0.461581 | − | 0.887098i | \(-0.347282\pi\) | ||||
0.461581 | + | 0.887098i | \(0.347282\pi\) | |||||||
\(108\) | 15.4844 | 1.48999 | ||||||||
\(109\) | 2.67242 | 0.255971 | 0.127986 | − | 0.991776i | \(-0.459149\pi\) | ||||
0.127986 | + | 0.991776i | \(0.459149\pi\) | |||||||
\(110\) | −40.8062 | −3.89072 | ||||||||
\(111\) | 26.6532 | 2.52981 | ||||||||
\(112\) | 9.56402 | 0.903715 | ||||||||
\(113\) | −6.75437 | −0.635398 | −0.317699 | − | 0.948192i | \(-0.602910\pi\) | ||||
−0.317699 | + | 0.948192i | \(0.602910\pi\) | |||||||
\(114\) | −33.9506 | −3.17977 | ||||||||
\(115\) | −4.06212 | −0.378795 | ||||||||
\(116\) | 3.70822 | 0.344300 | ||||||||
\(117\) | 23.3080 | 2.15482 | ||||||||
\(118\) | 6.15998 | 0.567072 | ||||||||
\(119\) | 20.8076 | 1.90743 | ||||||||
\(120\) | 48.7857 | 4.45350 | ||||||||
\(121\) | 6.33902 | 0.576274 | ||||||||
\(122\) | 29.6752 | 2.68667 | ||||||||
\(123\) | 24.8851 | 2.24382 | ||||||||
\(124\) | 22.1142 | 1.98591 | ||||||||
\(125\) | −26.4071 | −2.36192 | ||||||||
\(126\) | −35.0259 | −3.12036 | ||||||||
\(127\) | −16.8356 | −1.49392 | −0.746959 | − | 0.664871i | \(-0.768487\pi\) | ||||
−0.746959 | + | 0.664871i | \(0.768487\pi\) | |||||||
\(128\) | 20.5818 | 1.81919 | ||||||||
\(129\) | −14.0482 | −1.23687 | ||||||||
\(130\) | 50.9630 | 4.46975 | ||||||||
\(131\) | −3.14113 | −0.274442 | −0.137221 | − | 0.990540i | \(-0.543817\pi\) | ||||
−0.137221 | + | 0.990540i | \(0.543817\pi\) | |||||||
\(132\) | −43.5093 | −3.78700 | ||||||||
\(133\) | 16.6665 | 1.44517 | ||||||||
\(134\) | −1.99966 | −0.172744 | ||||||||
\(135\) | −16.4659 | −1.41716 | ||||||||
\(136\) | −28.2027 | −2.41836 | ||||||||
\(137\) | −22.9360 | −1.95955 | −0.979777 | − | 0.200092i | \(-0.935876\pi\) | ||||
−0.979777 | + | 0.200092i | \(0.935876\pi\) | |||||||
\(138\) | −6.59885 | −0.561731 | ||||||||
\(139\) | 9.44831 | 0.801396 | 0.400698 | − | 0.916210i | \(-0.368768\pi\) | ||||
0.400698 | + | 0.916210i | \(0.368768\pi\) | |||||||
\(140\) | −50.2667 | −4.24831 | ||||||||
\(141\) | 18.9874 | 1.59903 | ||||||||
\(142\) | 27.6947 | 2.32409 | ||||||||
\(143\) | −21.6547 | −1.81086 | ||||||||
\(144\) | 13.2325 | 1.10270 | ||||||||
\(145\) | −3.94326 | −0.327470 | ||||||||
\(146\) | 24.2069 | 2.00338 | ||||||||
\(147\) | 9.55633 | 0.788192 | ||||||||
\(148\) | 37.2225 | 3.05967 | ||||||||
\(149\) | 20.6974 | 1.69560 | 0.847799 | − | 0.530318i | \(-0.177927\pi\) | ||||
0.847799 | + | 0.530318i | \(0.177927\pi\) | |||||||
\(150\) | −75.8922 | −6.19657 | ||||||||
\(151\) | 3.43764 | 0.279751 | 0.139875 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139875 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(152\) | −22.5898 | −1.83228 | ||||||||
\(153\) | 28.7887 | 2.32743 | ||||||||
\(154\) | 32.5415 | 2.62227 | ||||||||
\(155\) | −23.5159 | −1.88884 | ||||||||
\(156\) | 54.3389 | 4.35059 | ||||||||
\(157\) | −18.4152 | −1.46969 | −0.734846 | − | 0.678234i | \(-0.762746\pi\) | ||||
−0.734846 | + | 0.678234i | \(0.762746\pi\) | |||||||
\(158\) | 4.46954 | 0.355577 | ||||||||
\(159\) | 2.87899 | 0.228319 | ||||||||
\(160\) | −6.73826 | −0.532706 | ||||||||
\(161\) | 3.23940 | 0.255300 | ||||||||
\(162\) | 5.68895 | 0.446966 | ||||||||
\(163\) | 13.0090 | 1.01894 | 0.509472 | − | 0.860487i | \(-0.329841\pi\) | ||||
0.509472 | + | 0.860487i | \(0.329841\pi\) | |||||||
\(164\) | 34.7533 | 2.71378 | ||||||||
\(165\) | 46.2670 | 3.60188 | ||||||||
\(166\) | −17.4247 | −1.35242 | ||||||||
\(167\) | −2.65845 | −0.205717 | −0.102858 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102858 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(168\) | −38.9049 | −3.00158 | ||||||||
\(169\) | 14.0447 | 1.08036 | ||||||||
\(170\) | 62.9465 | 4.82778 | ||||||||
\(171\) | 23.0592 | 1.76338 | ||||||||
\(172\) | −19.6190 | −1.49594 | ||||||||
\(173\) | −7.77900 | −0.591427 | −0.295713 | − | 0.955277i | \(-0.595557\pi\) | ||||
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(174\) | −6.40576 | −0.485619 | ||||||||
\(175\) | 37.2557 | 2.81627 | ||||||||
\(176\) | −12.2939 | −0.926685 | ||||||||
\(177\) | −6.98432 | −0.524974 | ||||||||
\(178\) | 32.7402 | 2.45399 | ||||||||
\(179\) | −13.8881 | −1.03805 | −0.519023 | − | 0.854760i | \(-0.673704\pi\) | ||||
−0.519023 | + | 0.854760i | \(0.673704\pi\) | |||||||
\(180\) | −69.5473 | −5.18375 | ||||||||
\(181\) | 7.84090 | 0.582810 | 0.291405 | − | 0.956600i | \(-0.405877\pi\) | ||||
0.291405 | + | 0.956600i | \(0.405877\pi\) | |||||||
\(182\) | −40.6412 | −3.01252 | ||||||||
\(183\) | −33.6464 | −2.48721 | ||||||||
\(184\) | −4.39069 | −0.323686 | ||||||||
\(185\) | −39.5818 | −2.91011 | ||||||||
\(186\) | −38.2011 | −2.80104 | ||||||||
\(187\) | −26.7467 | −1.95591 | ||||||||
\(188\) | 26.5169 | 1.93394 | ||||||||
\(189\) | 13.1309 | 0.955136 | ||||||||
\(190\) | 50.4190 | 3.65778 | ||||||||
\(191\) | 2.44333 | 0.176793 | 0.0883965 | − | 0.996085i | \(-0.471826\pi\) | ||||
0.0883965 | + | 0.996085i | \(0.471826\pi\) | |||||||
\(192\) | −27.0977 | −1.95561 | ||||||||
\(193\) | −13.7548 | −0.990094 | −0.495047 | − | 0.868866i | \(-0.664849\pi\) | ||||
−0.495047 | + | 0.868866i | \(0.664849\pi\) | |||||||
\(194\) | −43.2018 | −3.10171 | ||||||||
\(195\) | −57.7830 | −4.13793 | ||||||||
\(196\) | 13.3459 | 0.953279 | ||||||||
\(197\) | 9.87868 | 0.703827 | 0.351914 | − | 0.936033i | \(-0.385531\pi\) | ||||
0.351914 | + | 0.936033i | \(0.385531\pi\) | |||||||
\(198\) | 45.0234 | 3.19967 | ||||||||
\(199\) | −19.9664 | −1.41538 | −0.707690 | − | 0.706523i | \(-0.750263\pi\) | ||||
−0.707690 | + | 0.706523i | \(0.750263\pi\) | |||||||
\(200\) | −50.4966 | −3.57065 | ||||||||
\(201\) | 2.26726 | 0.159920 | ||||||||
\(202\) | −45.1203 | −3.17465 | ||||||||
\(203\) | 3.14461 | 0.220708 | ||||||||
\(204\) | 67.1162 | 4.69908 | ||||||||
\(205\) | −36.9561 | −2.58112 | ||||||||
\(206\) | 38.9687 | 2.71508 | ||||||||
\(207\) | 4.48192 | 0.311515 | ||||||||
\(208\) | 15.3538 | 1.06460 | ||||||||
\(209\) | −21.4236 | −1.48190 | ||||||||
\(210\) | 86.8330 | 5.99205 | ||||||||
\(211\) | 17.5786 | 1.21016 | 0.605082 | − | 0.796163i | \(-0.293140\pi\) | ||||
0.605082 | + | 0.796163i | \(0.293140\pi\) | |||||||
\(212\) | 4.02065 | 0.276140 | ||||||||
\(213\) | −31.4009 | −2.15155 | ||||||||
\(214\) | −23.0373 | −1.57480 | ||||||||
\(215\) | 20.8625 | 1.42281 | ||||||||
\(216\) | −17.7977 | −1.21098 | ||||||||
\(217\) | 18.7531 | 1.27304 | ||||||||
\(218\) | −6.44713 | −0.436655 | ||||||||
\(219\) | −27.4463 | −1.85465 | ||||||||
\(220\) | 64.6143 | 4.35629 | ||||||||
\(221\) | 33.4040 | 2.24700 | ||||||||
\(222\) | −64.2999 | −4.31553 | ||||||||
\(223\) | −12.4494 | −0.833671 | −0.416835 | − | 0.908982i | \(-0.636861\pi\) | ||||
−0.416835 | + | 0.908982i | \(0.636861\pi\) | |||||||
\(224\) | 5.37352 | 0.359033 | ||||||||
\(225\) | 51.5458 | 3.43639 | ||||||||
\(226\) | 16.2947 | 1.08391 | ||||||||
\(227\) | 16.2664 | 1.07964 | 0.539818 | − | 0.841782i | \(-0.318493\pi\) | ||||
0.539818 | + | 0.841782i | \(0.318493\pi\) | |||||||
\(228\) | 53.7589 | 3.56027 | ||||||||
\(229\) | −4.47918 | −0.295992 | −0.147996 | − | 0.988988i | \(-0.547282\pi\) | ||||
−0.147996 | + | 0.988988i | \(0.547282\pi\) | |||||||
\(230\) | 9.79973 | 0.646175 | ||||||||
\(231\) | −36.8963 | −2.42760 | ||||||||
\(232\) | −4.26222 | −0.279828 | ||||||||
\(233\) | 9.37580 | 0.614229 | 0.307115 | − | 0.951673i | \(-0.400637\pi\) | ||||
0.307115 | + | 0.951673i | \(0.400637\pi\) | |||||||
\(234\) | −56.2298 | −3.67586 | ||||||||
\(235\) | −28.1976 | −1.83941 | ||||||||
\(236\) | −9.75396 | −0.634929 | ||||||||
\(237\) | −5.06766 | −0.329180 | ||||||||
\(238\) | −50.1976 | −3.25383 | ||||||||
\(239\) | 22.5974 | 1.46171 | 0.730853 | − | 0.682535i | \(-0.239123\pi\) | ||||
0.730853 | + | 0.682535i | \(0.239123\pi\) | |||||||
\(240\) | −32.8047 | −2.11753 | ||||||||
\(241\) | 5.90408 | 0.380315 | 0.190158 | − | 0.981754i | \(-0.439100\pi\) | ||||
0.190158 | + | 0.981754i | \(0.439100\pi\) | |||||||
\(242\) | −15.2927 | −0.983051 | ||||||||
\(243\) | −18.6108 | −1.19388 | ||||||||
\(244\) | −46.9889 | −3.00816 | ||||||||
\(245\) | −14.1918 | −0.906680 | ||||||||
\(246\) | −60.0345 | −3.82766 | ||||||||
\(247\) | 26.7560 | 1.70244 | ||||||||
\(248\) | −25.4180 | −1.61404 | ||||||||
\(249\) | 19.7565 | 1.25202 | ||||||||
\(250\) | 63.7063 | 4.02914 | ||||||||
\(251\) | −16.2071 | −1.02298 | −0.511492 | − | 0.859288i | \(-0.670907\pi\) | ||||
−0.511492 | + | 0.859288i | \(0.670907\pi\) | |||||||
\(252\) | 55.4615 | 3.49375 | ||||||||
\(253\) | −4.16401 | −0.261789 | ||||||||
\(254\) | 40.6153 | 2.54843 | ||||||||
\(255\) | −71.3702 | −4.46938 | ||||||||
\(256\) | −29.8397 | −1.86498 | ||||||||
\(257\) | 18.5326 | 1.15603 | 0.578015 | − | 0.816026i | \(-0.303827\pi\) | ||||
0.578015 | + | 0.816026i | \(0.303827\pi\) | |||||||
\(258\) | 33.8908 | 2.10995 | ||||||||
\(259\) | 31.5651 | 1.96136 | ||||||||
\(260\) | −80.6969 | −5.00461 | ||||||||
\(261\) | 4.35078 | 0.269306 | ||||||||
\(262\) | 7.57788 | 0.468163 | ||||||||
\(263\) | −4.80820 | −0.296486 | −0.148243 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148243 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(264\) | 50.0094 | 3.07787 | ||||||||
\(265\) | −4.27549 | −0.262641 | ||||||||
\(266\) | −40.2074 | −2.46527 | ||||||||
\(267\) | −37.1216 | −2.27181 | ||||||||
\(268\) | 3.16634 | 0.193415 | ||||||||
\(269\) | −5.86660 | −0.357693 | −0.178846 | − | 0.983877i | \(-0.557237\pi\) | ||||
−0.178846 | + | 0.983877i | \(0.557237\pi\) | |||||||
\(270\) | 39.7234 | 2.41749 | ||||||||
\(271\) | 22.1165 | 1.34348 | 0.671742 | − | 0.740785i | \(-0.265546\pi\) | ||||
0.671742 | + | 0.740785i | \(0.265546\pi\) | |||||||
\(272\) | 18.9642 | 1.14987 | ||||||||
\(273\) | 46.0799 | 2.78888 | ||||||||
\(274\) | 55.3324 | 3.34275 | ||||||||
\(275\) | −47.8896 | −2.88785 | ||||||||
\(276\) | 10.4489 | 0.628949 | ||||||||
\(277\) | −3.87553 | −0.232858 | −0.116429 | − | 0.993199i | \(-0.537145\pi\) | ||||
−0.116429 | + | 0.993199i | \(0.537145\pi\) | |||||||
\(278\) | −22.7938 | −1.36708 | ||||||||
\(279\) | 25.9461 | 1.55335 | ||||||||
\(280\) | 57.7763 | 3.45280 | ||||||||
\(281\) | 20.2207 | 1.20627 | 0.603133 | − | 0.797641i | \(-0.293919\pi\) | ||||
0.603133 | + | 0.797641i | \(0.293919\pi\) | |||||||
\(282\) | −45.8065 | −2.72774 | ||||||||
\(283\) | 9.83391 | 0.584565 | 0.292283 | − | 0.956332i | \(-0.405585\pi\) | ||||
0.292283 | + | 0.956332i | \(0.405585\pi\) | |||||||
\(284\) | −43.8530 | −2.60219 | ||||||||
\(285\) | −57.1662 | −3.38623 | ||||||||
\(286\) | 52.2414 | 3.08910 | ||||||||
\(287\) | 29.4712 | 1.73963 | ||||||||
\(288\) | 7.43462 | 0.438089 | ||||||||
\(289\) | 24.2587 | 1.42698 | ||||||||
\(290\) | 9.51298 | 0.558622 | ||||||||
\(291\) | 48.9831 | 2.87144 | ||||||||
\(292\) | −38.3302 | −2.24310 | ||||||||
\(293\) | 25.1644 | 1.47012 | 0.735059 | − | 0.678003i | \(-0.237154\pi\) | ||||
0.735059 | + | 0.678003i | \(0.237154\pi\) | |||||||
\(294\) | −23.0543 | −1.34456 | ||||||||
\(295\) | 10.3722 | 0.603892 | ||||||||
\(296\) | −42.7834 | −2.48674 | ||||||||
\(297\) | −16.8789 | −0.979413 | ||||||||
\(298\) | −49.9318 | −2.89247 | ||||||||
\(299\) | 5.20045 | 0.300750 | ||||||||
\(300\) | 120.171 | 6.93806 | ||||||||
\(301\) | −16.6371 | −0.958948 | ||||||||
\(302\) | −8.29319 | −0.477219 | ||||||||
\(303\) | 51.1584 | 2.93897 | ||||||||
\(304\) | 15.1899 | 0.871203 | ||||||||
\(305\) | 49.9672 | 2.86111 | ||||||||
\(306\) | −69.4518 | −3.97029 | ||||||||
\(307\) | 1.92498 | 0.109864 | 0.0549321 | − | 0.998490i | \(-0.482506\pi\) | ||||
0.0549321 | + | 0.998490i | \(0.482506\pi\) | |||||||
\(308\) | −51.5276 | −2.93606 | ||||||||
\(309\) | −44.1836 | −2.51352 | ||||||||
\(310\) | 56.7312 | 3.22212 | ||||||||
\(311\) | −4.08616 | −0.231705 | −0.115852 | − | 0.993266i | \(-0.536960\pi\) | ||||
−0.115852 | + | 0.993266i | \(0.536960\pi\) | |||||||
\(312\) | −62.4569 | −3.53593 | ||||||||
\(313\) | 0.436524 | 0.0246738 | 0.0123369 | − | 0.999924i | \(-0.496073\pi\) | ||||
0.0123369 | + | 0.999924i | \(0.496073\pi\) | |||||||
\(314\) | 44.4261 | 2.50711 | ||||||||
\(315\) | −58.9768 | −3.32297 | ||||||||
\(316\) | −7.07725 | −0.398126 | ||||||||
\(317\) | 14.5111 | 0.815025 | 0.407513 | − | 0.913200i | \(-0.366396\pi\) | ||||
0.407513 | + | 0.913200i | \(0.366396\pi\) | |||||||
\(318\) | −6.94546 | −0.389482 | ||||||||
\(319\) | −4.04217 | −0.226318 | ||||||||
\(320\) | 40.2419 | 2.24959 | ||||||||
\(321\) | 26.1202 | 1.45789 | ||||||||
\(322\) | −7.81494 | −0.435510 | ||||||||
\(323\) | 33.0474 | 1.83881 | ||||||||
\(324\) | −9.00811 | −0.500451 | ||||||||
\(325\) | 59.8094 | 3.31763 | ||||||||
\(326\) | −31.3838 | −1.73819 | ||||||||
\(327\) | 7.30990 | 0.404238 | ||||||||
\(328\) | −39.9454 | −2.20561 | ||||||||
\(329\) | 22.4866 | 1.23972 | ||||||||
\(330\) | −111.618 | −6.14435 | ||||||||
\(331\) | 15.4684 | 0.850221 | 0.425110 | − | 0.905141i | \(-0.360235\pi\) | ||||
0.425110 | + | 0.905141i | \(0.360235\pi\) | |||||||
\(332\) | 27.5910 | 1.51425 | ||||||||
\(333\) | 43.6724 | 2.39323 | ||||||||
\(334\) | 6.41341 | 0.350926 | ||||||||
\(335\) | −3.36703 | −0.183961 | ||||||||
\(336\) | 26.1606 | 1.42718 | ||||||||
\(337\) | 18.6319 | 1.01495 | 0.507473 | − | 0.861668i | \(-0.330580\pi\) | ||||
0.507473 | + | 0.861668i | \(0.330580\pi\) | |||||||
\(338\) | −33.8823 | −1.84295 | ||||||||
\(339\) | −18.4753 | −1.00344 | ||||||||
\(340\) | −99.6722 | −5.40548 | ||||||||
\(341\) | −24.1057 | −1.30540 | ||||||||
\(342\) | −55.6296 | −3.00810 | ||||||||
\(343\) | −11.3583 | −0.613292 | ||||||||
\(344\) | 22.5500 | 1.21582 | ||||||||
\(345\) | −11.1112 | −0.598205 | ||||||||
\(346\) | 18.7666 | 1.00890 | ||||||||
\(347\) | −30.0257 | −1.61186 | −0.805932 | − | 0.592008i | \(-0.798335\pi\) | ||||
−0.805932 | + | 0.592008i | \(0.798335\pi\) | |||||||
\(348\) | 10.1431 | 0.543729 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −89.8782 | −4.80419 | ||||||||
\(351\) | 21.0801 | 1.12517 | ||||||||
\(352\) | −6.90728 | −0.368159 | ||||||||
\(353\) | −4.94774 | −0.263342 | −0.131671 | − | 0.991293i | \(-0.542034\pi\) | ||||
−0.131671 | + | 0.991293i | \(0.542034\pi\) | |||||||
\(354\) | 16.8494 | 0.895538 | ||||||||
\(355\) | 46.6324 | 2.47499 | ||||||||
\(356\) | −51.8423 | −2.74763 | ||||||||
\(357\) | 56.9152 | 3.01227 | ||||||||
\(358\) | 33.5046 | 1.77077 | ||||||||
\(359\) | −15.3734 | −0.811378 | −0.405689 | − | 0.914011i | \(-0.632968\pi\) | ||||
−0.405689 | + | 0.914011i | \(0.632968\pi\) | |||||||
\(360\) | 79.9374 | 4.21307 | ||||||||
\(361\) | 7.47036 | 0.393177 | ||||||||
\(362\) | −18.9159 | −0.994199 | ||||||||
\(363\) | 17.3392 | 0.910071 | ||||||||
\(364\) | 64.3529 | 3.37301 | ||||||||
\(365\) | 40.7596 | 2.13346 | ||||||||
\(366\) | 81.1709 | 4.24287 | ||||||||
\(367\) | 0.276065 | 0.0144105 | 0.00720525 | − | 0.999974i | \(-0.497706\pi\) | ||||
0.00720525 | + | 0.999974i | \(0.497706\pi\) | |||||||
\(368\) | 2.95241 | 0.153905 | ||||||||
\(369\) | 40.7753 | 2.12268 | ||||||||
\(370\) | 95.4898 | 4.96428 | ||||||||
\(371\) | 3.40955 | 0.177015 | ||||||||
\(372\) | 60.4892 | 3.13622 | ||||||||
\(373\) | 17.8704 | 0.925295 | 0.462648 | − | 0.886542i | \(-0.346900\pi\) | ||||
0.462648 | + | 0.886542i | \(0.346900\pi\) | |||||||
\(374\) | 64.5255 | 3.33653 | ||||||||
\(375\) | −72.2317 | −3.73003 | ||||||||
\(376\) | −30.4784 | −1.57180 | ||||||||
\(377\) | 5.04828 | 0.259999 | ||||||||
\(378\) | −31.6780 | −1.62934 | ||||||||
\(379\) | −19.8777 | −1.02105 | −0.510524 | − | 0.859864i | \(-0.670549\pi\) | ||||
−0.510524 | + | 0.859864i | \(0.670549\pi\) | |||||||
\(380\) | −79.8355 | −4.09548 | ||||||||
\(381\) | −46.0506 | −2.35924 | ||||||||
\(382\) | −5.89445 | −0.301586 | ||||||||
\(383\) | −13.0261 | −0.665603 | −0.332801 | − | 0.942997i | \(-0.607994\pi\) | ||||
−0.332801 | + | 0.942997i | \(0.607994\pi\) | |||||||
\(384\) | 56.2976 | 2.87293 | ||||||||
\(385\) | 54.7935 | 2.79254 | ||||||||
\(386\) | 33.1831 | 1.68897 | ||||||||
\(387\) | −23.0186 | −1.17010 | ||||||||
\(388\) | 68.4074 | 3.47286 | ||||||||
\(389\) | −5.98493 | −0.303448 | −0.151724 | − | 0.988423i | \(-0.548482\pi\) | ||||
−0.151724 | + | 0.988423i | \(0.548482\pi\) | |||||||
\(390\) | 139.400 | 7.05877 | ||||||||
\(391\) | 6.42329 | 0.324840 | ||||||||
\(392\) | −15.3397 | −0.774773 | ||||||||
\(393\) | −8.59197 | −0.433407 | ||||||||
\(394\) | −23.8320 | −1.20064 | ||||||||
\(395\) | 7.52582 | 0.378665 | ||||||||
\(396\) | −71.2919 | −3.58255 | ||||||||
\(397\) | −0.0600055 | −0.00301159 | −0.00150580 | − | 0.999999i | \(-0.500479\pi\) | ||||
−0.00150580 | + | 0.999999i | \(0.500479\pi\) | |||||||
\(398\) | 48.1683 | 2.41446 | ||||||||
\(399\) | 45.5880 | 2.28225 | ||||||||
\(400\) | 33.9551 | 1.69776 | ||||||||
\(401\) | 15.1341 | 0.755762 | 0.377881 | − | 0.925854i | \(-0.376653\pi\) | ||||
0.377881 | + | 0.925854i | \(0.376653\pi\) | |||||||
\(402\) | −5.46969 | −0.272803 | ||||||||
\(403\) | 30.1057 | 1.49967 | ||||||||
\(404\) | 71.4453 | 3.55454 | ||||||||
\(405\) | 9.57906 | 0.475988 | ||||||||
\(406\) | −7.58627 | −0.376500 | ||||||||
\(407\) | −40.5746 | −2.01121 | ||||||||
\(408\) | −77.1432 | −3.81916 | ||||||||
\(409\) | 1.63048 | 0.0806221 | 0.0403111 | − | 0.999187i | \(-0.487165\pi\) | ||||
0.0403111 | + | 0.999187i | \(0.487165\pi\) | |||||||
\(410\) | 89.1553 | 4.40307 | ||||||||
\(411\) | −62.7371 | −3.09459 | ||||||||
\(412\) | −61.7047 | −3.03997 | ||||||||
\(413\) | −8.27145 | −0.407011 | ||||||||
\(414\) | −10.8125 | −0.531405 | ||||||||
\(415\) | −29.3397 | −1.44023 | ||||||||
\(416\) | 8.62651 | 0.422950 | ||||||||
\(417\) | 25.8441 | 1.26559 | ||||||||
\(418\) | 51.6837 | 2.52793 | ||||||||
\(419\) | −28.8894 | −1.41134 | −0.705669 | − | 0.708542i | \(-0.749353\pi\) | ||||
−0.705669 | + | 0.708542i | \(0.749353\pi\) | |||||||
\(420\) | −137.495 | −6.70907 | ||||||||
\(421\) | −18.5307 | −0.903133 | −0.451567 | − | 0.892237i | \(-0.649135\pi\) | ||||
−0.451567 | + | 0.892237i | \(0.649135\pi\) | |||||||
\(422\) | −42.4079 | −2.06439 | ||||||||
\(423\) | 31.1117 | 1.51270 | ||||||||
\(424\) | −4.62132 | −0.224431 | ||||||||
\(425\) | 73.8731 | 3.58337 | ||||||||
\(426\) | 75.7536 | 3.67028 | ||||||||
\(427\) | −39.8470 | −1.92833 | ||||||||
\(428\) | 36.4782 | 1.76324 | ||||||||
\(429\) | −59.2324 | −2.85977 | ||||||||
\(430\) | −50.3302 | −2.42714 | ||||||||
\(431\) | −17.5469 | −0.845206 | −0.422603 | − | 0.906315i | \(-0.638883\pi\) | ||||
−0.422603 | + | 0.906315i | \(0.638883\pi\) | |||||||
\(432\) | 11.9676 | 0.575793 | ||||||||
\(433\) | −9.79065 | −0.470508 | −0.235254 | − | 0.971934i | \(-0.575592\pi\) | ||||
−0.235254 | + | 0.971934i | \(0.575592\pi\) | |||||||
\(434\) | −45.2411 | −2.17164 | ||||||||
\(435\) | −10.7860 | −0.517151 | ||||||||
\(436\) | 10.2086 | 0.488906 | ||||||||
\(437\) | 5.14494 | 0.246116 | ||||||||
\(438\) | 66.2133 | 3.16380 | ||||||||
\(439\) | 40.0509 | 1.91152 | 0.955762 | − | 0.294141i | \(-0.0950336\pi\) | ||||
0.955762 | + | 0.294141i | \(0.0950336\pi\) | |||||||
\(440\) | −74.2674 | −3.54056 | ||||||||
\(441\) | 15.6584 | 0.745640 | ||||||||
\(442\) | −80.5860 | −3.83309 | ||||||||
\(443\) | −31.1380 | −1.47941 | −0.739706 | − | 0.672930i | \(-0.765036\pi\) | ||||
−0.739706 | + | 0.672930i | \(0.765036\pi\) | |||||||
\(444\) | 101.815 | 4.83193 | ||||||||
\(445\) | 55.1281 | 2.61332 | ||||||||
\(446\) | 30.0337 | 1.42214 | ||||||||
\(447\) | 56.6138 | 2.67774 | ||||||||
\(448\) | −32.0915 | −1.51618 | ||||||||
\(449\) | 21.4661 | 1.01305 | 0.506523 | − | 0.862226i | \(-0.330930\pi\) | ||||
0.506523 | + | 0.862226i | \(0.330930\pi\) | |||||||
\(450\) | −124.353 | −5.86203 | ||||||||
\(451\) | −37.8831 | −1.78384 | ||||||||
\(452\) | −25.8017 | −1.21361 | ||||||||
\(453\) | 9.40300 | 0.441791 | ||||||||
\(454\) | −39.2421 | −1.84172 | ||||||||
\(455\) | −68.4317 | −3.20813 | ||||||||
\(456\) | −61.7902 | −2.89359 | ||||||||
\(457\) | 15.4413 | 0.722315 | 0.361157 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361157 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(458\) | 10.8059 | 0.504925 | ||||||||
\(459\) | 26.0369 | 1.21530 | ||||||||
\(460\) | −15.5173 | −0.723498 | ||||||||
\(461\) | 33.5834 | 1.56413 | 0.782066 | − | 0.623195i | \(-0.214166\pi\) | ||||
0.782066 | + | 0.623195i | \(0.214166\pi\) | |||||||
\(462\) | 89.0112 | 4.14117 | ||||||||
\(463\) | 0.0989485 | 0.00459853 | 0.00229926 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00229926 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(464\) | 2.86602 | 0.133051 | ||||||||
\(465\) | −64.3231 | −2.98291 | ||||||||
\(466\) | −22.6188 | −1.04780 | ||||||||
\(467\) | 36.6133 | 1.69426 | 0.847131 | − | 0.531384i | \(-0.178328\pi\) | ||||
0.847131 | + | 0.531384i | \(0.178328\pi\) | |||||||
\(468\) | 89.0366 | 4.11572 | ||||||||
\(469\) | 2.68509 | 0.123986 | ||||||||
\(470\) | 68.0258 | 3.13779 | ||||||||
\(471\) | −50.3713 | −2.32099 | ||||||||
\(472\) | 11.2112 | 0.516036 | ||||||||
\(473\) | 21.3858 | 0.983322 | ||||||||
\(474\) | 12.2256 | 0.561539 | ||||||||
\(475\) | 59.1710 | 2.71495 | ||||||||
\(476\) | 79.4850 | 3.64319 | ||||||||
\(477\) | 4.71734 | 0.215992 | ||||||||
\(478\) | −54.5155 | −2.49348 | ||||||||
\(479\) | 14.1938 | 0.648533 | 0.324267 | − | 0.945966i | \(-0.394882\pi\) | ||||
0.324267 | + | 0.945966i | \(0.394882\pi\) | |||||||
\(480\) | −18.4312 | −0.841266 | ||||||||
\(481\) | 50.6738 | 2.31052 | ||||||||
\(482\) | −14.2434 | −0.648769 | ||||||||
\(483\) | 8.86075 | 0.403178 | ||||||||
\(484\) | 24.2151 | 1.10068 | ||||||||
\(485\) | −72.7432 | −3.30310 | ||||||||
\(486\) | 44.8980 | 2.03661 | ||||||||
\(487\) | −33.9233 | −1.53721 | −0.768605 | − | 0.639723i | \(-0.779049\pi\) | ||||
−0.768605 | + | 0.639723i | \(0.779049\pi\) | |||||||
\(488\) | 54.0089 | 2.44487 | ||||||||
\(489\) | 35.5837 | 1.60915 | ||||||||
\(490\) | 34.2372 | 1.54668 | ||||||||
\(491\) | −10.5001 | −0.473862 | −0.236931 | − | 0.971526i | \(-0.576142\pi\) | ||||
−0.236931 | + | 0.971526i | \(0.576142\pi\) | |||||||
\(492\) | 95.0612 | 4.28569 | ||||||||
\(493\) | 6.23534 | 0.280825 | ||||||||
\(494\) | −64.5479 | −2.90415 | ||||||||
\(495\) | 75.8105 | 3.40743 | ||||||||
\(496\) | 17.0917 | 0.767438 | ||||||||
\(497\) | −37.1877 | −1.66810 | ||||||||
\(498\) | −47.6619 | −2.13578 | ||||||||
\(499\) | 4.94415 | 0.221331 | 0.110665 | − | 0.993858i | \(-0.464702\pi\) | ||||
0.110665 | + | 0.993858i | \(0.464702\pi\) | |||||||
\(500\) | −100.875 | −4.51128 | ||||||||
\(501\) | −7.27167 | −0.324874 | ||||||||
\(502\) | 39.0992 | 1.74508 | ||||||||
\(503\) | −3.26214 | −0.145452 | −0.0727259 | − | 0.997352i | \(-0.523170\pi\) | ||||
−0.0727259 | + | 0.997352i | \(0.523170\pi\) | |||||||
\(504\) | −63.7473 | −2.83953 | ||||||||
\(505\) | −75.9737 | −3.38078 | ||||||||
\(506\) | 10.0456 | 0.446579 | ||||||||
\(507\) | 38.4165 | 1.70614 | ||||||||
\(508\) | −64.3120 | −2.85338 | ||||||||
\(509\) | 41.5852 | 1.84323 | 0.921615 | − | 0.388105i | \(-0.126870\pi\) | ||||
0.921615 | + | 0.388105i | \(0.126870\pi\) | |||||||
\(510\) | 172.178 | 7.62418 | ||||||||
\(511\) | −32.5043 | −1.43791 | ||||||||
\(512\) | 30.8237 | 1.36223 | ||||||||
\(513\) | 20.8551 | 0.920774 | ||||||||
\(514\) | −44.7093 | −1.97204 | ||||||||
\(515\) | 65.6157 | 2.89137 | ||||||||
\(516\) | −53.6641 | −2.36243 | ||||||||
\(517\) | −28.9049 | −1.27124 | ||||||||
\(518\) | −76.1497 | −3.34583 | ||||||||
\(519\) | −21.2780 | −0.934000 | ||||||||
\(520\) | 92.7527 | 4.06748 | ||||||||
\(521\) | 16.1396 | 0.707090 | 0.353545 | − | 0.935418i | \(-0.384976\pi\) | ||||
0.353545 | + | 0.935418i | \(0.384976\pi\) | |||||||
\(522\) | −10.4961 | −0.459402 | ||||||||
\(523\) | −17.0067 | −0.743653 | −0.371827 | − | 0.928302i | \(-0.621268\pi\) | ||||
−0.371827 | + | 0.928302i | \(0.621268\pi\) | |||||||
\(524\) | −11.9991 | −0.524184 | ||||||||
\(525\) | 101.906 | 4.44754 | ||||||||
\(526\) | 11.5996 | 0.505768 | ||||||||
\(527\) | 37.1848 | 1.61980 | ||||||||
\(528\) | −33.6275 | −1.46345 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 10.3145 | 0.448032 | ||||||||
\(531\) | −11.4441 | −0.496632 | ||||||||
\(532\) | 63.6660 | 2.76027 | ||||||||
\(533\) | 47.3123 | 2.04932 | ||||||||
\(534\) | 89.5547 | 3.87541 | ||||||||
\(535\) | −38.7903 | −1.67705 | ||||||||
\(536\) | −3.63938 | −0.157197 | ||||||||
\(537\) | −37.9883 | −1.63932 | ||||||||
\(538\) | 14.1530 | 0.610179 | ||||||||
\(539\) | −14.5478 | −0.626617 | ||||||||
\(540\) | −62.8996 | −2.70677 | ||||||||
\(541\) | 39.2315 | 1.68670 | 0.843348 | − | 0.537368i | \(-0.180581\pi\) | ||||
0.843348 | + | 0.537368i | \(0.180581\pi\) | |||||||
\(542\) | −53.3554 | −2.29181 | ||||||||
\(543\) | 21.4473 | 0.920391 | ||||||||
\(544\) | 10.6550 | 0.456828 | ||||||||
\(545\) | −10.8557 | −0.465007 | ||||||||
\(546\) | −111.166 | −4.75748 | ||||||||
\(547\) | 26.3033 | 1.12465 | 0.562325 | − | 0.826916i | \(-0.309907\pi\) | ||||
0.562325 | + | 0.826916i | \(0.309907\pi\) | |||||||
\(548\) | −87.6155 | −3.74275 | ||||||||
\(549\) | −55.1310 | −2.35294 | ||||||||
\(550\) | 115.532 | 4.92630 | ||||||||
\(551\) | 4.99439 | 0.212768 | ||||||||
\(552\) | −12.0099 | −0.511176 | ||||||||
\(553\) | −6.00157 | −0.255213 | ||||||||
\(554\) | 9.34959 | 0.397226 | ||||||||
\(555\) | −108.268 | −4.59574 | ||||||||
\(556\) | 36.0926 | 1.53067 | ||||||||
\(557\) | −38.6045 | −1.63572 | −0.817862 | − | 0.575415i | \(-0.804841\pi\) | ||||
−0.817862 | + | 0.575415i | \(0.804841\pi\) | |||||||
\(558\) | −62.5941 | −2.64982 | ||||||||
\(559\) | −26.7088 | −1.12966 | ||||||||
\(560\) | −38.8502 | −1.64172 | ||||||||
\(561\) | −73.1605 | −3.08884 | ||||||||
\(562\) | −48.7818 | −2.05774 | ||||||||
\(563\) | −14.9804 | −0.631350 | −0.315675 | − | 0.948867i | \(-0.602231\pi\) | ||||
−0.315675 | + | 0.948867i | \(0.602231\pi\) | |||||||
\(564\) | 72.5319 | 3.05414 | ||||||||
\(565\) | 27.4371 | 1.15429 | ||||||||
\(566\) | −23.7240 | −0.997194 | ||||||||
\(567\) | −7.63896 | −0.320806 | ||||||||
\(568\) | 50.4044 | 2.11492 | ||||||||
\(569\) | 4.10009 | 0.171885 | 0.0859424 | − | 0.996300i | \(-0.472610\pi\) | ||||
0.0859424 | + | 0.996300i | \(0.472610\pi\) | |||||||
\(570\) | 137.912 | 5.77648 | ||||||||
\(571\) | −10.1251 | −0.423724 | −0.211862 | − | 0.977300i | \(-0.567953\pi\) | ||||
−0.211862 | + | 0.977300i | \(0.567953\pi\) | |||||||
\(572\) | −82.7211 | −3.45874 | ||||||||
\(573\) | 6.68326 | 0.279197 | ||||||||
\(574\) | −71.0982 | −2.96758 | ||||||||
\(575\) | 11.5008 | 0.479617 | ||||||||
\(576\) | −44.4007 | −1.85003 | ||||||||
\(577\) | −31.0534 | −1.29277 | −0.646384 | − | 0.763012i | \(-0.723720\pi\) | ||||
−0.646384 | + | 0.763012i | \(0.723720\pi\) | |||||||
\(578\) | −58.5233 | −2.43425 | ||||||||
\(579\) | −37.6237 | −1.56359 | ||||||||
\(580\) | −15.0632 | −0.625467 | ||||||||
\(581\) | 23.3974 | 0.970688 | ||||||||
\(582\) | −118.170 | −4.89831 | ||||||||
\(583\) | −4.38274 | −0.181514 | ||||||||
\(584\) | 44.0566 | 1.82307 | ||||||||
\(585\) | −94.6799 | −3.91453 | ||||||||
\(586\) | −60.7083 | −2.50784 | ||||||||
\(587\) | 19.4674 | 0.803505 | 0.401753 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401753 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(588\) | 36.5052 | 1.50545 | ||||||||
\(589\) | 29.7843 | 1.22724 | ||||||||
\(590\) | −25.0226 | −1.03016 | ||||||||
\(591\) | 27.0213 | 1.11151 | ||||||||
\(592\) | 28.7686 | 1.18238 | ||||||||
\(593\) | −21.4563 | −0.881105 | −0.440552 | − | 0.897727i | \(-0.645217\pi\) | ||||
−0.440552 | + | 0.897727i | \(0.645217\pi\) | |||||||
\(594\) | 40.7198 | 1.67075 | ||||||||
\(595\) | −84.5229 | −3.46510 | ||||||||
\(596\) | 79.0641 | 3.23859 | ||||||||
\(597\) | −54.6143 | −2.23521 | ||||||||
\(598\) | −12.5459 | −0.513040 | ||||||||
\(599\) | 8.74498 | 0.357310 | 0.178655 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178655 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(600\) | −138.124 | −5.63888 | ||||||||
\(601\) | −29.4972 | −1.20322 | −0.601608 | − | 0.798792i | \(-0.705473\pi\) | ||||
−0.601608 | + | 0.798792i | \(0.705473\pi\) | |||||||
\(602\) | 40.1365 | 1.63584 | ||||||||
\(603\) | 3.71500 | 0.151286 | ||||||||
\(604\) | 13.1318 | 0.534324 | ||||||||
\(605\) | −25.7499 | −1.04688 | ||||||||
\(606\) | −123.418 | −5.01351 | ||||||||
\(607\) | −32.1118 | −1.30338 | −0.651690 | − | 0.758486i | \(-0.725940\pi\) | ||||
−0.651690 | + | 0.758486i | \(0.725940\pi\) | |||||||
\(608\) | 8.53443 | 0.346117 | ||||||||
\(609\) | 8.60148 | 0.348549 | ||||||||
\(610\) | −120.544 | −4.88069 | ||||||||
\(611\) | 36.0994 | 1.46042 | ||||||||
\(612\) | 109.973 | 4.44539 | ||||||||
\(613\) | −7.54526 | −0.304750 | −0.152375 | − | 0.988323i | \(-0.548692\pi\) | ||||
−0.152375 | + | 0.988323i | \(0.548692\pi\) | |||||||
\(614\) | −4.64394 | −0.187414 | ||||||||
\(615\) | −101.086 | −4.07619 | ||||||||
\(616\) | 59.2256 | 2.38627 | ||||||||
\(617\) | −19.9929 | −0.804883 | −0.402441 | − | 0.915446i | \(-0.631838\pi\) | ||||
−0.402441 | + | 0.915446i | \(0.631838\pi\) | |||||||
\(618\) | 106.592 | 4.28774 | ||||||||
\(619\) | −34.5889 | −1.39024 | −0.695122 | − | 0.718892i | \(-0.744650\pi\) | ||||
−0.695122 | + | 0.718892i | \(0.744650\pi\) | |||||||
\(620\) | −89.8306 | −3.60768 | ||||||||
\(621\) | 4.05351 | 0.162662 | ||||||||
\(622\) | 9.85773 | 0.395259 | ||||||||
\(623\) | −43.9627 | −1.76133 | ||||||||
\(624\) | 41.9975 | 1.68125 | ||||||||
\(625\) | 49.7648 | 1.99059 | ||||||||
\(626\) | −1.05310 | −0.0420903 | ||||||||
\(627\) | −58.6002 | −2.34026 | ||||||||
\(628\) | −70.3461 | −2.80711 | ||||||||
\(629\) | 62.5893 | 2.49560 | ||||||||
\(630\) | 142.280 | 5.66856 | ||||||||
\(631\) | −23.3604 | −0.929963 | −0.464981 | − | 0.885320i | \(-0.653939\pi\) | ||||
−0.464981 | + | 0.885320i | \(0.653939\pi\) | |||||||
\(632\) | 8.13456 | 0.323576 | ||||||||
\(633\) | 48.0831 | 1.91113 | ||||||||
\(634\) | −35.0076 | −1.39033 | ||||||||
\(635\) | 68.3882 | 2.71390 | ||||||||
\(636\) | 10.9977 | 0.436089 | ||||||||
\(637\) | 18.1688 | 0.719872 | ||||||||
\(638\) | 9.75161 | 0.386070 | ||||||||
\(639\) | −51.4517 | −2.03540 | ||||||||
\(640\) | −83.6057 | −3.30481 | ||||||||
\(641\) | −24.8137 | −0.980082 | −0.490041 | − | 0.871699i | \(-0.663018\pi\) | ||||
−0.490041 | + | 0.871699i | \(0.663018\pi\) | |||||||
\(642\) | −63.0141 | −2.48697 | ||||||||
\(643\) | −15.8611 | −0.625500 | −0.312750 | − | 0.949835i | \(-0.601250\pi\) | ||||
−0.312750 | + | 0.949835i | \(0.601250\pi\) | |||||||
\(644\) | 12.3745 | 0.487624 | ||||||||
\(645\) | 57.0655 | 2.24695 | ||||||||
\(646\) | −79.7258 | −3.13677 | ||||||||
\(647\) | 37.7695 | 1.48487 | 0.742437 | − | 0.669916i | \(-0.233670\pi\) | ||||
0.742437 | + | 0.669916i | \(0.233670\pi\) | |||||||
\(648\) | 10.3539 | 0.406739 | ||||||||
\(649\) | 10.6324 | 0.417357 | ||||||||
\(650\) | −144.288 | −5.65945 | ||||||||
\(651\) | 51.2954 | 2.01043 | ||||||||
\(652\) | 49.6944 | 1.94618 | ||||||||
\(653\) | −26.0114 | −1.01790 | −0.508952 | − | 0.860795i | \(-0.669967\pi\) | ||||
−0.508952 | + | 0.860795i | \(0.669967\pi\) | |||||||
\(654\) | −17.6349 | −0.689579 | ||||||||
\(655\) | 12.7597 | 0.498561 | ||||||||
\(656\) | 26.8602 | 1.04871 | ||||||||
\(657\) | −44.9719 | −1.75452 | ||||||||
\(658\) | −54.2481 | −2.11481 | ||||||||
\(659\) | −25.4702 | −0.992180 | −0.496090 | − | 0.868271i | \(-0.665231\pi\) | ||||
−0.496090 | + | 0.868271i | \(0.665231\pi\) | |||||||
\(660\) | 176.740 | 6.87960 | ||||||||
\(661\) | 8.78925 | 0.341862 | 0.170931 | − | 0.985283i | \(-0.445322\pi\) | ||||
0.170931 | + | 0.985283i | \(0.445322\pi\) | |||||||
\(662\) | −37.3170 | −1.45037 | ||||||||
\(663\) | 91.3703 | 3.54853 | ||||||||
\(664\) | −31.7130 | −1.23070 | ||||||||
\(665\) | −67.7013 | −2.62534 | ||||||||
\(666\) | −105.358 | −4.08255 | ||||||||
\(667\) | 0.970739 | 0.0375872 | ||||||||
\(668\) | −10.1553 | −0.392919 | ||||||||
\(669\) | −34.0529 | −1.31656 | ||||||||
\(670\) | 8.12286 | 0.313813 | ||||||||
\(671\) | 51.2206 | 1.97735 | ||||||||
\(672\) | 14.6982 | 0.566997 | ||||||||
\(673\) | −10.3021 | −0.397118 | −0.198559 | − | 0.980089i | \(-0.563626\pi\) | ||||
−0.198559 | + | 0.980089i | \(0.563626\pi\) | |||||||
\(674\) | −44.9489 | −1.73137 | ||||||||
\(675\) | 46.6187 | 1.79436 | ||||||||
\(676\) | 53.6506 | 2.06348 | ||||||||
\(677\) | −16.9300 | −0.650673 | −0.325336 | − | 0.945598i | \(-0.605478\pi\) | ||||
−0.325336 | + | 0.945598i | \(0.605478\pi\) | |||||||
\(678\) | 44.5711 | 1.71174 | ||||||||
\(679\) | 58.0101 | 2.22623 | ||||||||
\(680\) | 114.563 | 4.39328 | ||||||||
\(681\) | 44.4935 | 1.70500 | ||||||||
\(682\) | 58.1543 | 2.22684 | ||||||||
\(683\) | −5.38235 | −0.205950 | −0.102975 | − | 0.994684i | \(-0.532836\pi\) | ||||
−0.102975 | + | 0.994684i | \(0.532836\pi\) | |||||||
\(684\) | 88.0862 | 3.36806 | ||||||||
\(685\) | 93.1688 | 3.55980 | ||||||||
\(686\) | 27.4016 | 1.04620 | ||||||||
\(687\) | −12.2519 | −0.467441 | ||||||||
\(688\) | −15.1632 | −0.578091 | ||||||||
\(689\) | 5.47361 | 0.208528 | ||||||||
\(690\) | 26.8053 | 1.02046 | ||||||||
\(691\) | 3.22259 | 0.122593 | 0.0612965 | − | 0.998120i | \(-0.480476\pi\) | ||||
0.0612965 | + | 0.998120i | \(0.480476\pi\) | |||||||
\(692\) | −29.7158 | −1.12963 | ||||||||
\(693\) | −60.4562 | −2.29654 | ||||||||
\(694\) | 72.4360 | 2.74963 | ||||||||
\(695\) | −38.3802 | −1.45584 | ||||||||
\(696\) | −11.6585 | −0.441914 | ||||||||
\(697\) | 58.4374 | 2.21347 | ||||||||
\(698\) | 2.41247 | 0.0913133 | ||||||||
\(699\) | 25.6457 | 0.970010 | ||||||||
\(700\) | 142.317 | 5.37907 | ||||||||
\(701\) | 6.50385 | 0.245647 | 0.122824 | − | 0.992429i | \(-0.460805\pi\) | ||||
0.122824 | + | 0.992429i | \(0.460805\pi\) | |||||||
\(702\) | −50.8550 | −1.91940 | ||||||||
\(703\) | 50.1328 | 1.89080 | ||||||||
\(704\) | 41.2513 | 1.55472 | ||||||||
\(705\) | −77.1291 | −2.90485 | ||||||||
\(706\) | 11.9363 | 0.449227 | ||||||||
\(707\) | 60.5863 | 2.27858 | ||||||||
\(708\) | −26.6801 | −1.00270 | ||||||||
\(709\) | 7.58839 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(710\) | −112.499 | −4.22202 | ||||||||
\(711\) | −8.30358 | −0.311409 | ||||||||
\(712\) | 59.5873 | 2.23313 | ||||||||
\(713\) | 5.78906 | 0.216802 | ||||||||
\(714\) | −137.306 | −5.13855 | ||||||||
\(715\) | 87.9642 | 3.28967 | ||||||||
\(716\) | −53.0526 | −1.98267 | ||||||||
\(717\) | 61.8109 | 2.30837 | ||||||||
\(718\) | 37.0879 | 1.38411 | ||||||||
\(719\) | 6.98428 | 0.260470 | 0.130235 | − | 0.991483i | \(-0.458427\pi\) | ||||
0.130235 | + | 0.991483i | \(0.458427\pi\) | |||||||
\(720\) | −53.7518 | −2.00321 | ||||||||
\(721\) | −52.3262 | −1.94873 | ||||||||
\(722\) | −18.0220 | −0.670709 | ||||||||
\(723\) | 16.1495 | 0.600606 | ||||||||
\(724\) | 29.9522 | 1.11317 | ||||||||
\(725\) | 11.1643 | 0.414631 | ||||||||
\(726\) | −41.8302 | −1.55247 | ||||||||
\(727\) | −11.4897 | −0.426130 | −0.213065 | − | 0.977038i | \(-0.568345\pi\) | ||||
−0.213065 | + | 0.977038i | \(0.568345\pi\) | |||||||
\(728\) | −73.9670 | −2.74140 | ||||||||
\(729\) | −43.8319 | −1.62340 | ||||||||
\(730\) | −98.3313 | −3.63940 | ||||||||
\(731\) | −32.9892 | −1.22015 | ||||||||
\(732\) | −128.529 | −4.75058 | ||||||||
\(733\) | 44.6480 | 1.64911 | 0.824556 | − | 0.565780i | \(-0.191425\pi\) | ||||
0.824556 | + | 0.565780i | \(0.191425\pi\) | |||||||
\(734\) | −0.665999 | −0.0245825 | ||||||||
\(735\) | −38.8189 | −1.43186 | ||||||||
\(736\) | 1.65880 | 0.0611443 | ||||||||
\(737\) | −3.45149 | −0.127137 | ||||||||
\(738\) | −98.3691 | −3.62102 | ||||||||
\(739\) | −43.3474 | −1.59456 | −0.797280 | − | 0.603610i | \(-0.793729\pi\) | ||||
−0.797280 | + | 0.603610i | \(0.793729\pi\) | |||||||
\(740\) | −151.202 | −5.55831 | ||||||||
\(741\) | 73.1859 | 2.68855 | ||||||||
\(742\) | −8.22543 | −0.301965 | ||||||||
\(743\) | −16.1598 | −0.592847 | −0.296424 | − | 0.955057i | \(-0.595794\pi\) | ||||
−0.296424 | + | 0.955057i | \(0.595794\pi\) | |||||||
\(744\) | −69.5261 | −2.54895 | ||||||||
\(745\) | −84.0754 | −3.08028 | ||||||||
\(746\) | −43.1118 | −1.57844 | ||||||||
\(747\) | 32.3719 | 1.18442 | ||||||||
\(748\) | −102.172 | −3.73579 | ||||||||
\(749\) | 30.9339 | 1.13030 | ||||||||
\(750\) | 174.257 | 6.36295 | ||||||||
\(751\) | −3.80297 | −0.138772 | −0.0693862 | − | 0.997590i | \(-0.522104\pi\) | ||||
−0.0693862 | + | 0.997590i | \(0.522104\pi\) | |||||||
\(752\) | 20.4944 | 0.747354 | ||||||||
\(753\) | −44.3315 | −1.61553 | ||||||||
\(754\) | −12.1788 | −0.443526 | ||||||||
\(755\) | −13.9641 | −0.508205 | ||||||||
\(756\) | 50.1602 | 1.82431 | ||||||||
\(757\) | −43.6685 | −1.58716 | −0.793579 | − | 0.608467i | \(-0.791785\pi\) | ||||
−0.793579 | + | 0.608467i | \(0.791785\pi\) | |||||||
\(758\) | 47.9543 | 1.74178 | ||||||||
\(759\) | −11.3899 | −0.413426 | ||||||||
\(760\) | 91.7626 | 3.32858 | ||||||||
\(761\) | −11.3502 | −0.411445 | −0.205722 | − | 0.978610i | \(-0.565954\pi\) | ||||
−0.205722 | + | 0.978610i | \(0.565954\pi\) | |||||||
\(762\) | 111.095 | 4.02457 | ||||||||
\(763\) | 8.65703 | 0.313405 | ||||||||
\(764\) | 9.33351 | 0.337675 | ||||||||
\(765\) | −116.943 | −4.22809 | ||||||||
\(766\) | 31.4251 | 1.13543 | ||||||||
\(767\) | −13.2788 | −0.479469 | ||||||||
\(768\) | −81.6208 | −2.94524 | ||||||||
\(769\) | −37.3619 | −1.34730 | −0.673652 | − | 0.739049i | \(-0.735275\pi\) | ||||
−0.673652 | + | 0.739049i | \(0.735275\pi\) | |||||||
\(770\) | −132.188 | −4.76371 | ||||||||
\(771\) | 50.6924 | 1.82564 | ||||||||
\(772\) | −52.5434 | −1.89108 | ||||||||
\(773\) | −36.1849 | −1.30148 | −0.650740 | − | 0.759301i | \(-0.725541\pi\) | ||||
−0.650740 | + | 0.759301i | \(0.725541\pi\) | |||||||
\(774\) | 55.5316 | 1.99604 | ||||||||
\(775\) | 66.5789 | 2.39159 | ||||||||
\(776\) | −78.6272 | −2.82255 | ||||||||
\(777\) | 86.3402 | 3.09744 | ||||||||
\(778\) | 14.4384 | 0.517643 | ||||||||
\(779\) | 46.8072 | 1.67704 | ||||||||
\(780\) | −220.731 | −7.90344 | ||||||||
\(781\) | 47.8022 | 1.71050 | ||||||||
\(782\) | −15.4960 | −0.554135 | ||||||||
\(783\) | 3.93490 | 0.140622 | ||||||||
\(784\) | 10.3148 | 0.368386 | ||||||||
\(785\) | 74.8047 | 2.66990 | ||||||||
\(786\) | 20.7278 | 0.739338 | ||||||||
\(787\) | 28.7584 | 1.02513 | 0.512564 | − | 0.858649i | \(-0.328696\pi\) | ||||
0.512564 | + | 0.858649i | \(0.328696\pi\) | |||||||
\(788\) | 37.7366 | 1.34431 | ||||||||
\(789\) | −13.1519 | −0.468220 | ||||||||
\(790\) | −18.1558 | −0.645954 | ||||||||
\(791\) | −21.8801 | −0.777967 | ||||||||
\(792\) | 81.9426 | 2.91170 | ||||||||
\(793\) | −63.9695 | −2.27162 | ||||||||
\(794\) | 0.144761 | 0.00513739 | ||||||||
\(795\) | −11.6948 | −0.414772 | ||||||||
\(796\) | −76.2717 | −2.70338 | ||||||||
\(797\) | 8.20781 | 0.290736 | 0.145368 | − | 0.989378i | \(-0.453563\pi\) | ||||
0.145368 | + | 0.989378i | \(0.453563\pi\) | |||||||
\(798\) | −109.980 | −3.89324 | ||||||||
\(799\) | 44.5879 | 1.57741 | ||||||||
\(800\) | 19.0776 | 0.674495 | ||||||||
\(801\) | −60.8254 | −2.14916 | ||||||||
\(802\) | −36.5106 | −1.28923 | ||||||||
\(803\) | 41.7820 | 1.47446 | ||||||||
\(804\) | 8.66093 | 0.305447 | ||||||||
\(805\) | −13.1588 | −0.463787 | ||||||||
\(806\) | −72.6290 | −2.55825 | ||||||||
\(807\) | −16.0470 | −0.564880 | ||||||||
\(808\) | −82.1190 | −2.88894 | ||||||||
\(809\) | 25.1631 | 0.884686 | 0.442343 | − | 0.896846i | \(-0.354147\pi\) | ||||
0.442343 | + | 0.896846i | \(0.354147\pi\) | |||||||
\(810\) | −23.1092 | −0.811974 | ||||||||
\(811\) | −38.0882 | −1.33746 | −0.668729 | − | 0.743506i | \(-0.733161\pi\) | ||||
−0.668729 | + | 0.743506i | \(0.733161\pi\) | |||||||
\(812\) | 12.0124 | 0.421553 | ||||||||
\(813\) | 60.4956 | 2.12167 | ||||||||
\(814\) | 97.8850 | 3.43087 | ||||||||
\(815\) | −52.8442 | −1.85105 | ||||||||
\(816\) | 51.8729 | 1.81591 | ||||||||
\(817\) | −26.4237 | −0.924449 | ||||||||
\(818\) | −3.93348 | −0.137531 | ||||||||
\(819\) | 75.5038 | 2.63832 | ||||||||
\(820\) | −141.172 | −4.92995 | ||||||||
\(821\) | 39.2693 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259691\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259691\pi\) | |||||||
\(822\) | 151.351 | 5.27898 | ||||||||
\(823\) | 21.9085 | 0.763683 | 0.381842 | − | 0.924228i | \(-0.375290\pi\) | ||||
0.381842 | + | 0.924228i | \(0.375290\pi\) | |||||||
\(824\) | 70.9232 | 2.47073 | ||||||||
\(825\) | −130.993 | −4.56059 | ||||||||
\(826\) | 19.9546 | 0.694309 | ||||||||
\(827\) | −19.2256 | −0.668540 | −0.334270 | − | 0.942477i | \(-0.608490\pi\) | ||||
−0.334270 | + | 0.942477i | \(0.608490\pi\) | |||||||
\(828\) | 17.1209 | 0.594994 | ||||||||
\(829\) | −14.5104 | −0.503966 | −0.251983 | − | 0.967732i | \(-0.581083\pi\) | ||||
−0.251983 | + | 0.967732i | \(0.581083\pi\) | |||||||
\(830\) | 70.7812 | 2.45685 | ||||||||
\(831\) | −10.6008 | −0.367737 | ||||||||
\(832\) | −51.5189 | −1.78610 | ||||||||
\(833\) | 22.4410 | 0.777534 | ||||||||
\(834\) | −62.3480 | −2.15893 | ||||||||
\(835\) | 10.7989 | 0.373712 | ||||||||
\(836\) | −81.8381 | −2.83043 | ||||||||
\(837\) | 23.4660 | 0.811105 | ||||||||
\(838\) | 69.6946 | 2.40756 | ||||||||
\(839\) | 14.7684 | 0.509861 | 0.254931 | − | 0.966959i | \(-0.417947\pi\) | ||||
0.254931 | + | 0.966959i | \(0.417947\pi\) | |||||||
\(840\) | 158.036 | 5.45277 | ||||||||
\(841\) | −28.0577 | −0.967506 | ||||||||
\(842\) | 44.7048 | 1.54063 | ||||||||
\(843\) | 55.3099 | 1.90497 | ||||||||
\(844\) | 67.1505 | 2.31141 | ||||||||
\(845\) | −57.0511 | −1.96262 | ||||||||
\(846\) | −75.0559 | −2.58048 | ||||||||
\(847\) | 20.5346 | 0.705577 | ||||||||
\(848\) | 3.10749 | 0.106712 | ||||||||
\(849\) | 26.8988 | 0.923164 | ||||||||
\(850\) | −178.217 | −6.11278 | ||||||||
\(851\) | 9.74412 | 0.334024 | ||||||||
\(852\) | −119.951 | −4.10947 | ||||||||
\(853\) | 40.0683 | 1.37191 | 0.685956 | − | 0.727643i | \(-0.259384\pi\) | ||||
0.685956 | + | 0.727643i | \(0.259384\pi\) | |||||||
\(854\) | 96.1297 | 3.28949 | ||||||||
\(855\) | −93.6692 | −3.20342 | ||||||||
\(856\) | −41.9279 | −1.43307 | ||||||||
\(857\) | 28.3928 | 0.969878 | 0.484939 | − | 0.874548i | \(-0.338842\pi\) | ||||
0.484939 | + | 0.874548i | \(0.338842\pi\) | |||||||
\(858\) | 142.896 | 4.87840 | ||||||||
\(859\) | 35.5608 | 1.21332 | 0.606660 | − | 0.794962i | \(-0.292509\pi\) | ||||
0.606660 | + | 0.794962i | \(0.292509\pi\) | |||||||
\(860\) | 79.6949 | 2.71757 | ||||||||
\(861\) | 80.6128 | 2.74728 | ||||||||
\(862\) | 42.3314 | 1.44181 | ||||||||
\(863\) | −0.379248 | −0.0129098 | −0.00645488 | − | 0.999979i | \(-0.502055\pi\) | ||||
−0.00645488 | + | 0.999979i | \(0.502055\pi\) | |||||||
\(864\) | 6.72398 | 0.228754 | ||||||||
\(865\) | 31.5992 | 1.07441 | ||||||||
\(866\) | 23.6196 | 0.802627 | ||||||||
\(867\) | 66.3550 | 2.25353 | ||||||||
\(868\) | 71.6367 | 2.43151 | ||||||||
\(869\) | 7.71460 | 0.261700 | ||||||||
\(870\) | 26.0210 | 0.882193 | ||||||||
\(871\) | 4.31057 | 0.146058 | ||||||||
\(872\) | −11.7338 | −0.397356 | ||||||||
\(873\) | 80.2609 | 2.71642 | ||||||||
\(874\) | −12.4120 | −0.419842 | ||||||||
\(875\) | −85.5431 | −2.89189 | ||||||||
\(876\) | −104.845 | −3.54238 | ||||||||
\(877\) | −5.02229 | −0.169591 | −0.0847953 | − | 0.996398i | \(-0.527024\pi\) | ||||
−0.0847953 | + | 0.996398i | \(0.527024\pi\) | |||||||
\(878\) | −96.6214 | −3.26082 | ||||||||
\(879\) | 68.8324 | 2.32166 | ||||||||
\(880\) | 49.9392 | 1.68345 | ||||||||
\(881\) | 7.74970 | 0.261094 | 0.130547 | − | 0.991442i | \(-0.458327\pi\) | ||||
0.130547 | + | 0.991442i | \(0.458327\pi\) | |||||||
\(882\) | −37.7755 | −1.27197 | ||||||||
\(883\) | 25.6396 | 0.862840 | 0.431420 | − | 0.902151i | \(-0.358013\pi\) | ||||
0.431420 | + | 0.902151i | \(0.358013\pi\) | |||||||
\(884\) | 127.603 | 4.29176 | ||||||||
\(885\) | 28.3711 | 0.953685 | ||||||||
\(886\) | 75.1195 | 2.52369 | ||||||||
\(887\) | 18.8918 | 0.634323 | 0.317161 | − | 0.948372i | \(-0.397270\pi\) | ||||
0.317161 | + | 0.948372i | \(0.397270\pi\) | |||||||
\(888\) | −117.026 | −3.92713 | ||||||||
\(889\) | −54.5372 | −1.82912 | ||||||||
\(890\) | −132.995 | −4.45800 | ||||||||
\(891\) | 9.81935 | 0.328960 | ||||||||
\(892\) | −47.5566 | −1.59231 | ||||||||
\(893\) | 35.7140 | 1.19512 | ||||||||
\(894\) | −136.579 | −4.56789 | ||||||||
\(895\) | 56.4152 | 1.88575 | ||||||||
\(896\) | 66.6726 | 2.22738 | ||||||||
\(897\) | 14.2248 | 0.474953 | ||||||||
\(898\) | −51.7862 | −1.72813 | ||||||||
\(899\) | 5.61966 | 0.187426 | ||||||||
\(900\) | 196.905 | 6.56350 | ||||||||
\(901\) | 6.76069 | 0.225231 | ||||||||
\(902\) | 91.3917 | 3.04301 | ||||||||
\(903\) | −45.5077 | −1.51440 | ||||||||
\(904\) | 29.6564 | 0.986357 | ||||||||
\(905\) | −31.8507 | −1.05875 | ||||||||
\(906\) | −22.6844 | −0.753640 | ||||||||
\(907\) | −20.9153 | −0.694481 | −0.347240 | − | 0.937776i | \(-0.612881\pi\) | ||||
−0.347240 | + | 0.937776i | \(0.612881\pi\) | |||||||
\(908\) | 62.1375 | 2.06211 | ||||||||
\(909\) | 83.8252 | 2.78031 | ||||||||
\(910\) | 165.089 | 5.47266 | ||||||||
\(911\) | 9.89733 | 0.327913 | 0.163957 | − | 0.986468i | \(-0.447574\pi\) | ||||
0.163957 | + | 0.986468i | \(0.447574\pi\) | |||||||
\(912\) | 41.5492 | 1.37583 | ||||||||
\(913\) | −30.0757 | −0.995360 | ||||||||
\(914\) | −37.2517 | −1.23218 | ||||||||
\(915\) | 136.676 | 4.51836 | ||||||||
\(916\) | −17.1105 | −0.565345 | ||||||||
\(917\) | −10.1754 | −0.336020 | ||||||||
\(918\) | −62.8132 | −2.07314 | ||||||||
\(919\) | 27.4954 | 0.906991 | 0.453495 | − | 0.891259i | \(-0.350177\pi\) | ||||
0.453495 | + | 0.891259i | \(0.350177\pi\) | |||||||
\(920\) | 17.8355 | 0.588020 | ||||||||
\(921\) | 5.26541 | 0.173501 | ||||||||
\(922\) | −81.0188 | −2.66821 | ||||||||
\(923\) | −59.7002 | −1.96506 | ||||||||
\(924\) | −140.944 | −4.63672 | ||||||||
\(925\) | 112.065 | 3.68469 | ||||||||
\(926\) | −0.238710 | −0.00784450 | ||||||||
\(927\) | −72.3968 | −2.37782 | ||||||||
\(928\) | 1.61026 | 0.0528595 | ||||||||
\(929\) | −7.73922 | −0.253916 | −0.126958 | − | 0.991908i | \(-0.540521\pi\) | ||||
−0.126958 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(930\) | 155.178 | 5.08847 | ||||||||
\(931\) | 17.9748 | 0.589101 | ||||||||
\(932\) | 35.8156 | 1.17318 | ||||||||
\(933\) | −11.1769 | −0.365916 | ||||||||
\(934\) | −88.3285 | −2.89020 | ||||||||
\(935\) | 108.648 | 3.55318 | ||||||||
\(936\) | −102.338 | −3.34503 | ||||||||
\(937\) | 36.4677 | 1.19135 | 0.595674 | − | 0.803227i | \(-0.296885\pi\) | ||||
0.595674 | + | 0.803227i | \(0.296885\pi\) | |||||||
\(938\) | −6.47769 | −0.211504 | ||||||||
\(939\) | 1.19403 | 0.0389656 | ||||||||
\(940\) | −107.715 | −3.51327 | ||||||||
\(941\) | −22.1743 | −0.722863 | −0.361431 | − | 0.932399i | \(-0.617712\pi\) | ||||
−0.361431 | + | 0.932399i | \(0.617712\pi\) | |||||||
\(942\) | 121.519 | 3.95931 | ||||||||
\(943\) | 9.09773 | 0.296263 | ||||||||
\(944\) | −7.53865 | −0.245362 | ||||||||
\(945\) | −53.3395 | −1.73513 | ||||||||
\(946\) | −51.5926 | −1.67742 | ||||||||
\(947\) | −24.9134 | −0.809578 | −0.404789 | − | 0.914410i | \(-0.632655\pi\) | ||||
−0.404789 | + | 0.914410i | \(0.632655\pi\) | |||||||
\(948\) | −19.3585 | −0.628734 | ||||||||
\(949\) | −52.1817 | −1.69389 | ||||||||
\(950\) | −142.748 | −4.63136 | ||||||||
\(951\) | 39.6924 | 1.28711 | ||||||||
\(952\) | −91.3598 | −2.96099 | ||||||||
\(953\) | −13.7168 | −0.444332 | −0.222166 | − | 0.975009i | \(-0.571313\pi\) | ||||
−0.222166 | + | 0.975009i | \(0.571313\pi\) | |||||||
\(954\) | −11.3804 | −0.368455 | ||||||||
\(955\) | −9.92509 | −0.321168 | ||||||||
\(956\) | 86.3221 | 2.79186 | ||||||||
\(957\) | −11.0566 | −0.357409 | ||||||||
\(958\) | −34.2422 | −1.10632 | ||||||||
\(959\) | −74.2988 | −2.39923 | ||||||||
\(960\) | 110.074 | 3.55262 | ||||||||
\(961\) | 2.51320 | 0.0810710 | ||||||||
\(962\) | −122.249 | −3.94146 | ||||||||
\(963\) | 42.7991 | 1.37918 | ||||||||
\(964\) | 22.5536 | 0.726402 | ||||||||
\(965\) | 55.8737 | 1.79864 | ||||||||
\(966\) | −21.3763 | −0.687771 | ||||||||
\(967\) | 33.8644 | 1.08900 | 0.544502 | − | 0.838759i | \(-0.316719\pi\) | ||||
0.544502 | + | 0.838759i | \(0.316719\pi\) | |||||||
\(968\) | −27.8327 | −0.894577 | ||||||||
\(969\) | 90.3949 | 2.90390 | ||||||||
\(970\) | 175.491 | 5.63467 | ||||||||
\(971\) | 28.6287 | 0.918738 | 0.459369 | − | 0.888246i | \(-0.348076\pi\) | ||||
0.459369 | + | 0.888246i | \(0.348076\pi\) | |||||||
\(972\) | −71.0933 | −2.28032 | ||||||||
\(973\) | 30.6068 | 0.981210 | ||||||||
\(974\) | 81.8388 | 2.62228 | ||||||||
\(975\) | 163.597 | 5.23931 | ||||||||
\(976\) | −36.3169 | −1.16247 | ||||||||
\(977\) | −47.2993 | −1.51324 | −0.756620 | − | 0.653855i | \(-0.773150\pi\) | ||||
−0.756620 | + | 0.653855i | \(0.773150\pi\) | |||||||
\(978\) | −85.8445 | −2.74500 | ||||||||
\(979\) | 56.5110 | 1.80610 | ||||||||
\(980\) | −54.2127 | −1.73176 | ||||||||
\(981\) | 11.9776 | 0.382415 | ||||||||
\(982\) | 25.3311 | 0.808349 | ||||||||
\(983\) | −6.00170 | −0.191425 | −0.0957123 | − | 0.995409i | \(-0.530513\pi\) | ||||
−0.0957123 | + | 0.995409i | \(0.530513\pi\) | |||||||
\(984\) | −109.263 | −3.48318 | ||||||||
\(985\) | −40.1284 | −1.27860 | ||||||||
\(986\) | −15.0426 | −0.479052 | ||||||||
\(987\) | 61.5077 | 1.95781 | ||||||||
\(988\) | 102.208 | 3.25166 | ||||||||
\(989\) | −5.13587 | −0.163311 | ||||||||
\(990\) | −182.890 | −5.81264 | ||||||||
\(991\) | 19.3602 | 0.614998 | 0.307499 | − | 0.951548i | \(-0.400508\pi\) | ||||
0.307499 | + | 0.951548i | \(0.400508\pi\) | |||||||
\(992\) | 9.60290 | 0.304893 | ||||||||
\(993\) | 42.3109 | 1.34270 | ||||||||
\(994\) | 89.7142 | 2.84556 | ||||||||
\(995\) | 81.1059 | 2.57123 | ||||||||
\(996\) | 75.4699 | 2.39135 | ||||||||
\(997\) | 59.2428 | 1.87624 | 0.938119 | − | 0.346312i | \(-0.112566\pi\) | ||||
0.938119 | + | 0.346312i | \(0.112566\pi\) | |||||||
\(998\) | −11.9276 | −0.377562 | ||||||||
\(999\) | 39.4979 | 1.24966 |
(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 | 8027.2.a.f.1.16 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.16 | ✓ | 176 | 1.1 | even | 1 | trivial |