Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(0\) |
Dimension: | \(98\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76750 | −1.95692 | −0.978460 | − | 0.206438i | \(-0.933813\pi\) | ||||
−0.978460 | + | 0.206438i | \(0.933813\pi\) | |||||||
\(3\) | 0.603367 | 0.348354 | 0.174177 | − | 0.984714i | \(-0.444274\pi\) | ||||
0.174177 | + | 0.984714i | \(0.444274\pi\) | |||||||
\(4\) | 5.65907 | 2.82953 | ||||||||
\(5\) | 3.54828 | 1.58684 | 0.793420 | − | 0.608674i | \(-0.208298\pi\) | ||||
0.793420 | + | 0.608674i | \(0.208298\pi\) | |||||||
\(6\) | −1.66982 | −0.681701 | ||||||||
\(7\) | 1.63115 | 0.616518 | 0.308259 | − | 0.951303i | \(-0.400254\pi\) | ||||
0.308259 | + | 0.951303i | \(0.400254\pi\) | |||||||
\(8\) | −10.1265 | −3.58025 | ||||||||
\(9\) | −2.63595 | −0.878649 | ||||||||
\(10\) | −9.81988 | −3.10532 | ||||||||
\(11\) | 2.00713 | 0.605173 | 0.302587 | − | 0.953122i | \(-0.402150\pi\) | ||||
0.302587 | + | 0.953122i | \(0.402150\pi\) | |||||||
\(12\) | 3.41449 | 0.985679 | ||||||||
\(13\) | −1.95461 | −0.542112 | −0.271056 | − | 0.962564i | \(-0.587373\pi\) | ||||
−0.271056 | + | 0.962564i | \(0.587373\pi\) | |||||||
\(14\) | −4.51422 | −1.20648 | ||||||||
\(15\) | 2.14092 | 0.552782 | ||||||||
\(16\) | 16.7069 | 4.17673 | ||||||||
\(17\) | 7.86913 | 1.90854 | 0.954272 | − | 0.298940i | \(-0.0966332\pi\) | ||||
0.954272 | + | 0.298940i | \(0.0966332\pi\) | |||||||
\(18\) | 7.29499 | 1.71945 | ||||||||
\(19\) | 3.64239 | 0.835622 | 0.417811 | − | 0.908534i | \(-0.362797\pi\) | ||||
0.417811 | + | 0.908534i | \(0.362797\pi\) | |||||||
\(20\) | 20.0800 | 4.49002 | ||||||||
\(21\) | 0.984183 | 0.214766 | ||||||||
\(22\) | −5.55474 | −1.18428 | ||||||||
\(23\) | 9.31928 | 1.94320 | 0.971602 | − | 0.236621i | \(-0.0760399\pi\) | ||||
0.971602 | + | 0.236621i | \(0.0760399\pi\) | |||||||
\(24\) | −6.10998 | −1.24719 | ||||||||
\(25\) | 7.59031 | 1.51806 | ||||||||
\(26\) | 5.40940 | 1.06087 | ||||||||
\(27\) | −3.40054 | −0.654435 | ||||||||
\(28\) | 9.23080 | 1.74446 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −5.92499 | −1.08175 | ||||||||
\(31\) | 5.29310 | 0.950669 | 0.475335 | − | 0.879805i | \(-0.342327\pi\) | ||||
0.475335 | + | 0.879805i | \(0.342327\pi\) | |||||||
\(32\) | −25.9834 | −4.59327 | ||||||||
\(33\) | 1.21104 | 0.210815 | ||||||||
\(34\) | −21.7778 | −3.73487 | ||||||||
\(35\) | 5.78779 | 0.978315 | ||||||||
\(36\) | −14.9170 | −2.48617 | ||||||||
\(37\) | 8.99437 | 1.47866 | 0.739332 | − | 0.673341i | \(-0.235141\pi\) | ||||
0.739332 | + | 0.673341i | \(0.235141\pi\) | |||||||
\(38\) | −10.0803 | −1.63525 | ||||||||
\(39\) | −1.17935 | −0.188847 | ||||||||
\(40\) | −35.9316 | −5.68128 | ||||||||
\(41\) | 2.72014 | 0.424814 | 0.212407 | − | 0.977181i | \(-0.431870\pi\) | ||||
0.212407 | + | 0.977181i | \(0.431870\pi\) | |||||||
\(42\) | −2.72373 | −0.420281 | ||||||||
\(43\) | 3.02984 | 0.462046 | 0.231023 | − | 0.972948i | \(-0.425793\pi\) | ||||
0.231023 | + | 0.972948i | \(0.425793\pi\) | |||||||
\(44\) | 11.3585 | 1.71236 | ||||||||
\(45\) | −9.35309 | −1.39428 | ||||||||
\(46\) | −25.7911 | −3.80269 | ||||||||
\(47\) | −3.91236 | −0.570676 | −0.285338 | − | 0.958427i | \(-0.592106\pi\) | ||||
−0.285338 | + | 0.958427i | \(0.592106\pi\) | |||||||
\(48\) | 10.0804 | 1.45498 | ||||||||
\(49\) | −4.33934 | −0.619906 | ||||||||
\(50\) | −21.0062 | −2.97073 | ||||||||
\(51\) | 4.74797 | 0.664849 | ||||||||
\(52\) | −11.0613 | −1.53392 | ||||||||
\(53\) | −9.09533 | −1.24934 | −0.624670 | − | 0.780889i | \(-0.714766\pi\) | ||||
−0.624670 | + | 0.780889i | \(0.714766\pi\) | |||||||
\(54\) | 9.41101 | 1.28068 | ||||||||
\(55\) | 7.12188 | 0.960313 | ||||||||
\(56\) | −16.5178 | −2.20729 | ||||||||
\(57\) | 2.19770 | 0.291092 | ||||||||
\(58\) | −2.76750 | −0.363391 | ||||||||
\(59\) | −11.9989 | −1.56212 | −0.781060 | − | 0.624456i | \(-0.785321\pi\) | ||||
−0.781060 | + | 0.624456i | \(0.785321\pi\) | |||||||
\(60\) | 12.1156 | 1.56412 | ||||||||
\(61\) | 12.0778 | 1.54641 | 0.773203 | − | 0.634158i | \(-0.218653\pi\) | ||||
0.773203 | + | 0.634158i | \(0.218653\pi\) | |||||||
\(62\) | −14.6487 | −1.86038 | ||||||||
\(63\) | −4.29963 | −0.541703 | ||||||||
\(64\) | 38.4954 | 4.81192 | ||||||||
\(65\) | −6.93552 | −0.860246 | ||||||||
\(66\) | −3.35155 | −0.412547 | ||||||||
\(67\) | −5.75198 | −0.702716 | −0.351358 | − | 0.936241i | \(-0.614280\pi\) | ||||
−0.351358 | + | 0.936241i | \(0.614280\pi\) | |||||||
\(68\) | 44.5319 | 5.40029 | ||||||||
\(69\) | 5.62294 | 0.676923 | ||||||||
\(70\) | −16.0177 | −1.91448 | ||||||||
\(71\) | −4.11448 | −0.488299 | −0.244149 | − | 0.969738i | \(-0.578509\pi\) | ||||
−0.244149 | + | 0.969738i | \(0.578509\pi\) | |||||||
\(72\) | 26.6929 | 3.14578 | ||||||||
\(73\) | −15.7838 | −1.84736 | −0.923678 | − | 0.383170i | \(-0.874832\pi\) | ||||
−0.923678 | + | 0.383170i | \(0.874832\pi\) | |||||||
\(74\) | −24.8919 | −2.89363 | ||||||||
\(75\) | 4.57974 | 0.528823 | ||||||||
\(76\) | 20.6125 | 2.36442 | ||||||||
\(77\) | 3.27394 | 0.373100 | ||||||||
\(78\) | 3.26385 | 0.369558 | ||||||||
\(79\) | −7.70768 | −0.867181 | −0.433591 | − | 0.901110i | \(-0.642754\pi\) | ||||
−0.433591 | + | 0.901110i | \(0.642754\pi\) | |||||||
\(80\) | 59.2808 | 6.62780 | ||||||||
\(81\) | 5.85607 | 0.650674 | ||||||||
\(82\) | −7.52798 | −0.831327 | ||||||||
\(83\) | 0.936447 | 0.102788 | 0.0513942 | − | 0.998678i | \(-0.483634\pi\) | ||||
0.0513942 | + | 0.998678i | \(0.483634\pi\) | |||||||
\(84\) | 5.56956 | 0.607689 | ||||||||
\(85\) | 27.9219 | 3.02855 | ||||||||
\(86\) | −8.38508 | −0.904187 | ||||||||
\(87\) | 0.603367 | 0.0646877 | ||||||||
\(88\) | −20.3252 | −2.16667 | ||||||||
\(89\) | −14.2946 | −1.51522 | −0.757610 | − | 0.652708i | \(-0.773633\pi\) | ||||
−0.757610 | + | 0.652708i | \(0.773633\pi\) | |||||||
\(90\) | 25.8847 | 2.72849 | ||||||||
\(91\) | −3.18827 | −0.334222 | ||||||||
\(92\) | 52.7384 | 5.49836 | ||||||||
\(93\) | 3.19368 | 0.331170 | ||||||||
\(94\) | 10.8275 | 1.11677 | ||||||||
\(95\) | 12.9242 | 1.32600 | ||||||||
\(96\) | −15.6775 | −1.60008 | ||||||||
\(97\) | −3.66196 | −0.371815 | −0.185908 | − | 0.982567i | \(-0.559523\pi\) | ||||
−0.185908 | + | 0.982567i | \(0.559523\pi\) | |||||||
\(98\) | 12.0091 | 1.21311 | ||||||||
\(99\) | −5.29070 | −0.531735 | ||||||||
\(100\) | 42.9541 | 4.29541 | ||||||||
\(101\) | 19.3492 | 1.92532 | 0.962661 | − | 0.270709i | \(-0.0872583\pi\) | ||||
0.962661 | + | 0.270709i | \(0.0872583\pi\) | |||||||
\(102\) | −13.1400 | −1.30106 | ||||||||
\(103\) | −1.94773 | −0.191916 | −0.0959579 | − | 0.995385i | \(-0.530591\pi\) | ||||
−0.0959579 | + | 0.995385i | \(0.530591\pi\) | |||||||
\(104\) | 19.7933 | 1.94090 | ||||||||
\(105\) | 3.49216 | 0.340800 | ||||||||
\(106\) | 25.1713 | 2.44486 | ||||||||
\(107\) | −11.3091 | −1.09329 | −0.546646 | − | 0.837364i | \(-0.684095\pi\) | ||||
−0.546646 | + | 0.837364i | \(0.684095\pi\) | |||||||
\(108\) | −19.2439 | −1.85175 | ||||||||
\(109\) | −0.887913 | −0.0850466 | −0.0425233 | − | 0.999095i | \(-0.513540\pi\) | ||||
−0.0425233 | + | 0.999095i | \(0.513540\pi\) | |||||||
\(110\) | −19.7098 | −1.87926 | ||||||||
\(111\) | 5.42690 | 0.515099 | ||||||||
\(112\) | 27.2515 | 2.57502 | ||||||||
\(113\) | −6.97509 | −0.656162 | −0.328081 | − | 0.944650i | \(-0.606402\pi\) | ||||
−0.328081 | + | 0.944650i | \(0.606402\pi\) | |||||||
\(114\) | −6.08214 | −0.569644 | ||||||||
\(115\) | 33.0674 | 3.08355 | ||||||||
\(116\) | 5.65907 | 0.525431 | ||||||||
\(117\) | 5.15226 | 0.476327 | ||||||||
\(118\) | 33.2069 | 3.05694 | ||||||||
\(119\) | 12.8357 | 1.17665 | ||||||||
\(120\) | −21.6799 | −1.97910 | ||||||||
\(121\) | −6.97142 | −0.633765 | ||||||||
\(122\) | −33.4254 | −3.02619 | ||||||||
\(123\) | 1.64124 | 0.147986 | ||||||||
\(124\) | 29.9540 | 2.68995 | ||||||||
\(125\) | 9.19116 | 0.822083 | ||||||||
\(126\) | 11.8992 | 1.06007 | ||||||||
\(127\) | 11.2577 | 0.998960 | 0.499480 | − | 0.866325i | \(-0.333524\pi\) | ||||
0.499480 | + | 0.866325i | \(0.333524\pi\) | |||||||
\(128\) | −54.5692 | −4.82328 | ||||||||
\(129\) | 1.82810 | 0.160956 | ||||||||
\(130\) | 19.1941 | 1.68343 | ||||||||
\(131\) | −4.16326 | −0.363746 | −0.181873 | − | 0.983322i | \(-0.558216\pi\) | ||||
−0.181873 | + | 0.983322i | \(0.558216\pi\) | |||||||
\(132\) | 6.85334 | 0.596507 | ||||||||
\(133\) | 5.94130 | 0.515176 | ||||||||
\(134\) | 15.9186 | 1.37516 | ||||||||
\(135\) | −12.0661 | −1.03848 | ||||||||
\(136\) | −79.6865 | −6.83306 | ||||||||
\(137\) | −11.2955 | −0.965043 | −0.482522 | − | 0.875884i | \(-0.660279\pi\) | ||||
−0.482522 | + | 0.875884i | \(0.660279\pi\) | |||||||
\(138\) | −15.5615 | −1.32468 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 32.7535 | 2.76818 | ||||||||
\(141\) | −2.36059 | −0.198797 | ||||||||
\(142\) | 11.3868 | 0.955561 | ||||||||
\(143\) | −3.92317 | −0.328072 | ||||||||
\(144\) | −44.0385 | −3.66988 | ||||||||
\(145\) | 3.54828 | 0.294669 | ||||||||
\(146\) | 43.6817 | 3.61513 | ||||||||
\(147\) | −2.61822 | −0.215947 | ||||||||
\(148\) | 50.8997 | 4.18393 | ||||||||
\(149\) | −14.4655 | −1.18506 | −0.592530 | − | 0.805548i | \(-0.701871\pi\) | ||||
−0.592530 | + | 0.805548i | \(0.701871\pi\) | |||||||
\(150\) | −12.6744 | −1.03486 | ||||||||
\(151\) | 24.4204 | 1.98730 | 0.993652 | − | 0.112501i | \(-0.0358862\pi\) | ||||
0.993652 | + | 0.112501i | \(0.0358862\pi\) | |||||||
\(152\) | −36.8846 | −2.99174 | ||||||||
\(153\) | −20.7426 | −1.67694 | ||||||||
\(154\) | −9.06063 | −0.730127 | ||||||||
\(155\) | 18.7814 | 1.50856 | ||||||||
\(156\) | −6.67401 | −0.534349 | ||||||||
\(157\) | −17.0057 | −1.35720 | −0.678599 | − | 0.734509i | \(-0.737413\pi\) | ||||
−0.678599 | + | 0.734509i | \(0.737413\pi\) | |||||||
\(158\) | 21.3310 | 1.69700 | ||||||||
\(159\) | −5.48782 | −0.435213 | ||||||||
\(160\) | −92.1966 | −7.28878 | ||||||||
\(161\) | 15.2012 | 1.19802 | ||||||||
\(162\) | −16.2067 | −1.27332 | ||||||||
\(163\) | 1.59669 | 0.125063 | 0.0625313 | − | 0.998043i | \(-0.480083\pi\) | ||||
0.0625313 | + | 0.998043i | \(0.480083\pi\) | |||||||
\(164\) | 15.3934 | 1.20203 | ||||||||
\(165\) | 4.29710 | 0.334529 | ||||||||
\(166\) | −2.59162 | −0.201149 | ||||||||
\(167\) | −16.3813 | −1.26763 | −0.633813 | − | 0.773486i | \(-0.718511\pi\) | ||||
−0.633813 | + | 0.773486i | \(0.718511\pi\) | |||||||
\(168\) | −9.96631 | −0.768917 | ||||||||
\(169\) | −9.17949 | −0.706114 | ||||||||
\(170\) | −77.2739 | −5.92664 | ||||||||
\(171\) | −9.60116 | −0.734219 | ||||||||
\(172\) | 17.1461 | 1.30737 | ||||||||
\(173\) | 1.03206 | 0.0784662 | 0.0392331 | − | 0.999230i | \(-0.487509\pi\) | ||||
0.0392331 | + | 0.999230i | \(0.487509\pi\) | |||||||
\(174\) | −1.66982 | −0.126589 | ||||||||
\(175\) | 12.3810 | 0.935912 | ||||||||
\(176\) | 33.5330 | 2.52764 | ||||||||
\(177\) | −7.23972 | −0.544171 | ||||||||
\(178\) | 39.5602 | 2.96516 | ||||||||
\(179\) | −22.6790 | −1.69511 | −0.847555 | − | 0.530708i | \(-0.821926\pi\) | ||||
−0.847555 | + | 0.530708i | \(0.821926\pi\) | |||||||
\(180\) | −52.9298 | −3.94515 | ||||||||
\(181\) | 14.2202 | 1.05698 | 0.528491 | − | 0.848939i | \(-0.322758\pi\) | ||||
0.528491 | + | 0.848939i | \(0.322758\pi\) | |||||||
\(182\) | 8.82355 | 0.654045 | ||||||||
\(183\) | 7.28736 | 0.538697 | ||||||||
\(184\) | −94.3714 | −6.95715 | ||||||||
\(185\) | 31.9146 | 2.34640 | ||||||||
\(186\) | −8.83852 | −0.648072 | ||||||||
\(187\) | 15.7944 | 1.15500 | ||||||||
\(188\) | −22.1403 | −1.61475 | ||||||||
\(189\) | −5.54681 | −0.403471 | ||||||||
\(190\) | −35.7679 | −2.59487 | ||||||||
\(191\) | −16.3763 | −1.18494 | −0.592472 | − | 0.805591i | \(-0.701848\pi\) | ||||
−0.592472 | + | 0.805591i | \(0.701848\pi\) | |||||||
\(192\) | 23.2268 | 1.67625 | ||||||||
\(193\) | 18.6561 | 1.34290 | 0.671448 | − | 0.741052i | \(-0.265673\pi\) | ||||
0.671448 | + | 0.741052i | \(0.265673\pi\) | |||||||
\(194\) | 10.1345 | 0.727613 | ||||||||
\(195\) | −4.18466 | −0.299670 | ||||||||
\(196\) | −24.5566 | −1.75404 | ||||||||
\(197\) | 0.0410840 | 0.00292711 | 0.00146356 | − | 0.999999i | \(-0.499534\pi\) | ||||
0.00146356 | + | 0.999999i | \(0.499534\pi\) | |||||||
\(198\) | 14.6420 | 1.04056 | ||||||||
\(199\) | 19.0557 | 1.35082 | 0.675411 | − | 0.737441i | \(-0.263966\pi\) | ||||
0.675411 | + | 0.737441i | \(0.263966\pi\) | |||||||
\(200\) | −76.8631 | −5.43504 | ||||||||
\(201\) | −3.47055 | −0.244794 | ||||||||
\(202\) | −53.5491 | −3.76770 | ||||||||
\(203\) | 1.63115 | 0.114484 | ||||||||
\(204\) | 26.8691 | 1.88121 | ||||||||
\(205\) | 9.65181 | 0.674112 | ||||||||
\(206\) | 5.39035 | 0.375564 | ||||||||
\(207\) | −24.5651 | −1.70740 | ||||||||
\(208\) | −32.6555 | −2.26425 | ||||||||
\(209\) | 7.31077 | 0.505696 | ||||||||
\(210\) | −9.66456 | −0.666918 | ||||||||
\(211\) | 23.8598 | 1.64258 | 0.821288 | − | 0.570513i | \(-0.193256\pi\) | ||||
0.821288 | + | 0.570513i | \(0.193256\pi\) | |||||||
\(212\) | −51.4711 | −3.53505 | ||||||||
\(213\) | −2.48254 | −0.170101 | ||||||||
\(214\) | 31.2979 | 2.13948 | ||||||||
\(215\) | 10.7507 | 0.733193 | ||||||||
\(216\) | 34.4355 | 2.34304 | ||||||||
\(217\) | 8.63386 | 0.586104 | ||||||||
\(218\) | 2.45730 | 0.166429 | ||||||||
\(219\) | −9.52343 | −0.643534 | ||||||||
\(220\) | 40.3032 | 2.71724 | ||||||||
\(221\) | −15.3811 | −1.03464 | ||||||||
\(222\) | −15.0190 | −1.00801 | ||||||||
\(223\) | −0.540056 | −0.0361648 | −0.0180824 | − | 0.999836i | \(-0.505756\pi\) | ||||
−0.0180824 | + | 0.999836i | \(0.505756\pi\) | |||||||
\(224\) | −42.3829 | −2.83183 | ||||||||
\(225\) | −20.0077 | −1.33384 | ||||||||
\(226\) | 19.3036 | 1.28406 | ||||||||
\(227\) | 16.1089 | 1.06919 | 0.534594 | − | 0.845109i | \(-0.320465\pi\) | ||||
0.534594 | + | 0.845109i | \(0.320465\pi\) | |||||||
\(228\) | 12.4369 | 0.823656 | ||||||||
\(229\) | 11.0840 | 0.732448 | 0.366224 | − | 0.930527i | \(-0.380650\pi\) | ||||
0.366224 | + | 0.930527i | \(0.380650\pi\) | |||||||
\(230\) | −91.5142 | −6.03427 | ||||||||
\(231\) | 1.97539 | 0.129971 | ||||||||
\(232\) | −10.1265 | −0.664836 | ||||||||
\(233\) | 4.69091 | 0.307312 | 0.153656 | − | 0.988124i | \(-0.450895\pi\) | ||||
0.153656 | + | 0.988124i | \(0.450895\pi\) | |||||||
\(234\) | −14.2589 | −0.932133 | ||||||||
\(235\) | −13.8821 | −0.905571 | ||||||||
\(236\) | −67.9024 | −4.42007 | ||||||||
\(237\) | −4.65056 | −0.302086 | ||||||||
\(238\) | −35.5229 | −2.30261 | ||||||||
\(239\) | 12.2738 | 0.793927 | 0.396963 | − | 0.917834i | \(-0.370064\pi\) | ||||
0.396963 | + | 0.917834i | \(0.370064\pi\) | |||||||
\(240\) | 35.7681 | 2.30882 | ||||||||
\(241\) | −23.5813 | −1.51900 | −0.759501 | − | 0.650506i | \(-0.774557\pi\) | ||||
−0.759501 | + | 0.650506i | \(0.774557\pi\) | |||||||
\(242\) | 19.2934 | 1.24023 | ||||||||
\(243\) | 13.7350 | 0.881100 | ||||||||
\(244\) | 68.3492 | 4.37561 | ||||||||
\(245\) | −15.3972 | −0.983692 | ||||||||
\(246\) | −4.54214 | −0.289596 | ||||||||
\(247\) | −7.11947 | −0.453001 | ||||||||
\(248\) | −53.6005 | −3.40363 | ||||||||
\(249\) | 0.565021 | 0.0358068 | ||||||||
\(250\) | −25.4366 | −1.60875 | ||||||||
\(251\) | −1.77874 | −0.112273 | −0.0561366 | − | 0.998423i | \(-0.517878\pi\) | ||||
−0.0561366 | + | 0.998423i | \(0.517878\pi\) | |||||||
\(252\) | −24.3319 | −1.53277 | ||||||||
\(253\) | 18.7050 | 1.17598 | ||||||||
\(254\) | −31.1557 | −1.95488 | ||||||||
\(255\) | 16.8471 | 1.05501 | ||||||||
\(256\) | 74.0296 | 4.62685 | ||||||||
\(257\) | −8.81949 | −0.550145 | −0.275072 | − | 0.961424i | \(-0.588702\pi\) | ||||
−0.275072 | + | 0.961424i | \(0.588702\pi\) | |||||||
\(258\) | −5.05928 | −0.314977 | ||||||||
\(259\) | 14.6712 | 0.911623 | ||||||||
\(260\) | −39.2486 | −2.43409 | ||||||||
\(261\) | −2.63595 | −0.163161 | ||||||||
\(262\) | 11.5218 | 0.711821 | ||||||||
\(263\) | 21.9541 | 1.35375 | 0.676873 | − | 0.736099i | \(-0.263334\pi\) | ||||
0.676873 | + | 0.736099i | \(0.263334\pi\) | |||||||
\(264\) | −12.2635 | −0.754769 | ||||||||
\(265\) | −32.2728 | −1.98250 | ||||||||
\(266\) | −16.4426 | −1.00816 | ||||||||
\(267\) | −8.62486 | −0.527833 | ||||||||
\(268\) | −32.5508 | −1.98836 | ||||||||
\(269\) | 17.9609 | 1.09509 | 0.547547 | − | 0.836775i | \(-0.315562\pi\) | ||||
0.547547 | + | 0.836775i | \(0.315562\pi\) | |||||||
\(270\) | 33.3929 | 2.03223 | ||||||||
\(271\) | 15.7224 | 0.955067 | 0.477533 | − | 0.878614i | \(-0.341531\pi\) | ||||
0.477533 | + | 0.878614i | \(0.341531\pi\) | |||||||
\(272\) | 131.469 | 7.97146 | ||||||||
\(273\) | −1.92370 | −0.116427 | ||||||||
\(274\) | 31.2604 | 1.88851 | ||||||||
\(275\) | 15.2348 | 0.918691 | ||||||||
\(276\) | 31.8206 | 1.91538 | ||||||||
\(277\) | −4.97851 | −0.299130 | −0.149565 | − | 0.988752i | \(-0.547787\pi\) | ||||
−0.149565 | + | 0.988752i | \(0.547787\pi\) | |||||||
\(278\) | 2.76750 | 0.165984 | ||||||||
\(279\) | −13.9523 | −0.835305 | ||||||||
\(280\) | −58.6099 | −3.50261 | ||||||||
\(281\) | 17.2427 | 1.02862 | 0.514308 | − | 0.857606i | \(-0.328049\pi\) | ||||
0.514308 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(282\) | 6.53293 | 0.389030 | ||||||||
\(283\) | −7.85386 | −0.466863 | −0.233432 | − | 0.972373i | \(-0.574996\pi\) | ||||
−0.233432 | + | 0.972373i | \(0.574996\pi\) | |||||||
\(284\) | −23.2841 | −1.38166 | ||||||||
\(285\) | 7.79806 | 0.461917 | ||||||||
\(286\) | 10.8574 | 0.642010 | ||||||||
\(287\) | 4.43696 | 0.261905 | ||||||||
\(288\) | 68.4910 | 4.03587 | ||||||||
\(289\) | 44.9232 | 2.64254 | ||||||||
\(290\) | −9.81988 | −0.576643 | ||||||||
\(291\) | −2.20950 | −0.129523 | ||||||||
\(292\) | −89.3217 | −5.22715 | ||||||||
\(293\) | −8.90737 | −0.520374 | −0.260187 | − | 0.965558i | \(-0.583784\pi\) | ||||
−0.260187 | + | 0.965558i | \(0.583784\pi\) | |||||||
\(294\) | 7.24592 | 0.422590 | ||||||||
\(295\) | −42.5754 | −2.47883 | ||||||||
\(296\) | −91.0812 | −5.29399 | ||||||||
\(297\) | −6.82534 | −0.396047 | ||||||||
\(298\) | 40.0333 | 2.31907 | ||||||||
\(299\) | −18.2156 | −1.05343 | ||||||||
\(300\) | 25.9171 | 1.49632 | ||||||||
\(301\) | 4.94213 | 0.284859 | ||||||||
\(302\) | −67.5835 | −3.88899 | ||||||||
\(303\) | 11.6747 | 0.670694 | ||||||||
\(304\) | 60.8531 | 3.49017 | ||||||||
\(305\) | 42.8555 | 2.45390 | ||||||||
\(306\) | 57.4052 | 3.28164 | ||||||||
\(307\) | −11.2388 | −0.641431 | −0.320716 | − | 0.947176i | \(-0.603923\pi\) | ||||
−0.320716 | + | 0.947176i | \(0.603923\pi\) | |||||||
\(308\) | 18.5274 | 1.05570 | ||||||||
\(309\) | −1.17520 | −0.0668546 | ||||||||
\(310\) | −51.9776 | −2.95213 | ||||||||
\(311\) | 2.46817 | 0.139957 | 0.0699786 | − | 0.997548i | \(-0.477707\pi\) | ||||
0.0699786 | + | 0.997548i | \(0.477707\pi\) | |||||||
\(312\) | 11.9426 | 0.676119 | ||||||||
\(313\) | −1.40490 | −0.0794098 | −0.0397049 | − | 0.999211i | \(-0.512642\pi\) | ||||
−0.0397049 | + | 0.999211i | \(0.512642\pi\) | |||||||
\(314\) | 47.0632 | 2.65593 | ||||||||
\(315\) | −15.2563 | −0.859596 | ||||||||
\(316\) | −43.6183 | −2.45372 | ||||||||
\(317\) | −7.83327 | −0.439960 | −0.219980 | − | 0.975504i | \(-0.570599\pi\) | ||||
−0.219980 | + | 0.975504i | \(0.570599\pi\) | |||||||
\(318\) | 15.1876 | 0.851676 | ||||||||
\(319\) | 2.00713 | 0.112378 | ||||||||
\(320\) | 136.593 | 7.63576 | ||||||||
\(321\) | −6.82353 | −0.380852 | ||||||||
\(322\) | −42.0693 | −2.34443 | ||||||||
\(323\) | 28.6625 | 1.59482 | ||||||||
\(324\) | 33.1399 | 1.84110 | ||||||||
\(325\) | −14.8361 | −0.822960 | ||||||||
\(326\) | −4.41885 | −0.244738 | ||||||||
\(327\) | −0.535737 | −0.0296263 | ||||||||
\(328\) | −27.5454 | −1.52094 | ||||||||
\(329\) | −6.38165 | −0.351832 | ||||||||
\(330\) | −11.8922 | −0.654646 | ||||||||
\(331\) | 0.616015 | 0.0338592 | 0.0169296 | − | 0.999857i | \(-0.494611\pi\) | ||||
0.0169296 | + | 0.999857i | \(0.494611\pi\) | |||||||
\(332\) | 5.29942 | 0.290843 | ||||||||
\(333\) | −23.7087 | −1.29923 | ||||||||
\(334\) | 45.3354 | 2.48064 | ||||||||
\(335\) | −20.4096 | −1.11510 | ||||||||
\(336\) | 16.4427 | 0.897020 | ||||||||
\(337\) | 5.75679 | 0.313592 | 0.156796 | − | 0.987631i | \(-0.449883\pi\) | ||||
0.156796 | + | 0.987631i | \(0.449883\pi\) | |||||||
\(338\) | 25.4042 | 1.38181 | ||||||||
\(339\) | −4.20854 | −0.228577 | ||||||||
\(340\) | 158.012 | 8.56939 | ||||||||
\(341\) | 10.6240 | 0.575320 | ||||||||
\(342\) | 26.5712 | 1.43681 | ||||||||
\(343\) | −18.4962 | −0.998701 | ||||||||
\(344\) | −30.6816 | −1.65424 | ||||||||
\(345\) | 19.9518 | 1.07417 | ||||||||
\(346\) | −2.85623 | −0.153552 | ||||||||
\(347\) | 3.61984 | 0.194323 | 0.0971616 | − | 0.995269i | \(-0.469024\pi\) | ||||
0.0971616 | + | 0.995269i | \(0.469024\pi\) | |||||||
\(348\) | 3.41449 | 0.183036 | ||||||||
\(349\) | 31.6291 | 1.69307 | 0.846533 | − | 0.532337i | \(-0.178686\pi\) | ||||
0.846533 | + | 0.532337i | \(0.178686\pi\) | |||||||
\(350\) | −34.2643 | −1.83150 | ||||||||
\(351\) | 6.64675 | 0.354777 | ||||||||
\(352\) | −52.1522 | −2.77972 | ||||||||
\(353\) | −17.6698 | −0.940467 | −0.470233 | − | 0.882542i | \(-0.655830\pi\) | ||||
−0.470233 | + | 0.882542i | \(0.655830\pi\) | |||||||
\(354\) | 20.0359 | 1.06490 | ||||||||
\(355\) | −14.5993 | −0.774852 | ||||||||
\(356\) | −80.8938 | −4.28736 | ||||||||
\(357\) | 7.74466 | 0.409891 | ||||||||
\(358\) | 62.7642 | 3.31719 | ||||||||
\(359\) | −3.83913 | −0.202622 | −0.101311 | − | 0.994855i | \(-0.532304\pi\) | ||||
−0.101311 | + | 0.994855i | \(0.532304\pi\) | |||||||
\(360\) | 94.7138 | 4.99186 | ||||||||
\(361\) | −5.73297 | −0.301735 | ||||||||
\(362\) | −39.3546 | −2.06843 | ||||||||
\(363\) | −4.20632 | −0.220775 | ||||||||
\(364\) | −18.0426 | −0.945692 | ||||||||
\(365\) | −56.0054 | −2.93146 | ||||||||
\(366\) | −20.1678 | −1.05419 | ||||||||
\(367\) | 5.94711 | 0.310436 | 0.155218 | − | 0.987880i | \(-0.450392\pi\) | ||||
0.155218 | + | 0.987880i | \(0.450392\pi\) | |||||||
\(368\) | 155.696 | 8.11623 | ||||||||
\(369\) | −7.17014 | −0.373263 | ||||||||
\(370\) | −88.3236 | −4.59173 | ||||||||
\(371\) | −14.8359 | −0.770240 | ||||||||
\(372\) | 18.0733 | 0.937055 | ||||||||
\(373\) | −5.17954 | −0.268186 | −0.134093 | − | 0.990969i | \(-0.542812\pi\) | ||||
−0.134093 | + | 0.990969i | \(0.542812\pi\) | |||||||
\(374\) | −43.7110 | −2.26024 | ||||||||
\(375\) | 5.54564 | 0.286376 | ||||||||
\(376\) | 39.6184 | 2.04316 | ||||||||
\(377\) | −1.95461 | −0.100668 | ||||||||
\(378\) | 15.3508 | 0.789560 | ||||||||
\(379\) | 9.41612 | 0.483673 | 0.241837 | − | 0.970317i | \(-0.422250\pi\) | ||||
0.241837 | + | 0.970317i | \(0.422250\pi\) | |||||||
\(380\) | 73.1392 | 3.75196 | ||||||||
\(381\) | 6.79253 | 0.347992 | ||||||||
\(382\) | 45.3213 | 2.31884 | ||||||||
\(383\) | 3.40253 | 0.173861 | 0.0869305 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869305 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(384\) | −32.9253 | −1.68021 | ||||||||
\(385\) | 11.6169 | 0.592050 | ||||||||
\(386\) | −51.6308 | −2.62794 | ||||||||
\(387\) | −7.98650 | −0.405976 | ||||||||
\(388\) | −20.7233 | −1.05206 | ||||||||
\(389\) | −18.0428 | −0.914808 | −0.457404 | − | 0.889259i | \(-0.651221\pi\) | ||||
−0.457404 | + | 0.889259i | \(0.651221\pi\) | |||||||
\(390\) | 11.5811 | 0.586430 | ||||||||
\(391\) | 73.3346 | 3.70869 | ||||||||
\(392\) | 43.9422 | 2.21942 | ||||||||
\(393\) | −2.51197 | −0.126712 | ||||||||
\(394\) | −0.113700 | −0.00572813 | ||||||||
\(395\) | −27.3490 | −1.37608 | ||||||||
\(396\) | −29.9404 | −1.50456 | ||||||||
\(397\) | 9.06306 | 0.454862 | 0.227431 | − | 0.973794i | \(-0.426967\pi\) | ||||
0.227431 | + | 0.973794i | \(0.426967\pi\) | |||||||
\(398\) | −52.7367 | −2.64345 | ||||||||
\(399\) | 3.58478 | 0.179464 | ||||||||
\(400\) | 126.811 | 6.34053 | ||||||||
\(401\) | 8.73285 | 0.436098 | 0.218049 | − | 0.975938i | \(-0.430031\pi\) | ||||
0.218049 | + | 0.975938i | \(0.430031\pi\) | |||||||
\(402\) | 9.60476 | 0.479042 | ||||||||
\(403\) | −10.3460 | −0.515370 | ||||||||
\(404\) | 109.499 | 5.44776 | ||||||||
\(405\) | 20.7790 | 1.03252 | ||||||||
\(406\) | −4.51422 | −0.224037 | ||||||||
\(407\) | 18.0529 | 0.894848 | ||||||||
\(408\) | −48.0802 | −2.38032 | ||||||||
\(409\) | 10.7119 | 0.529668 | 0.264834 | − | 0.964294i | \(-0.414683\pi\) | ||||
0.264834 | + | 0.964294i | \(0.414683\pi\) | |||||||
\(410\) | −26.7114 | −1.31918 | ||||||||
\(411\) | −6.81535 | −0.336177 | ||||||||
\(412\) | −11.0223 | −0.543032 | ||||||||
\(413\) | −19.5720 | −0.963074 | ||||||||
\(414\) | 67.9841 | 3.34123 | ||||||||
\(415\) | 3.32278 | 0.163109 | ||||||||
\(416\) | 50.7876 | 2.49007 | ||||||||
\(417\) | −0.603367 | −0.0295470 | ||||||||
\(418\) | −20.2326 | −0.989607 | ||||||||
\(419\) | −12.8993 | −0.630171 | −0.315085 | − | 0.949063i | \(-0.602033\pi\) | ||||
−0.315085 | + | 0.949063i | \(0.602033\pi\) | |||||||
\(420\) | 19.7624 | 0.964305 | ||||||||
\(421\) | 38.1031 | 1.85703 | 0.928515 | − | 0.371295i | \(-0.121086\pi\) | ||||
0.928515 | + | 0.371295i | \(0.121086\pi\) | |||||||
\(422\) | −66.0321 | −3.21439 | ||||||||
\(423\) | 10.3128 | 0.501424 | ||||||||
\(424\) | 92.1036 | 4.47295 | ||||||||
\(425\) | 59.7291 | 2.89729 | ||||||||
\(426\) | 6.87043 | 0.332874 | ||||||||
\(427\) | 19.7008 | 0.953387 | ||||||||
\(428\) | −63.9989 | −3.09350 | ||||||||
\(429\) | −2.36711 | −0.114285 | ||||||||
\(430\) | −29.7526 | −1.43480 | ||||||||
\(431\) | 13.9410 | 0.671516 | 0.335758 | − | 0.941948i | \(-0.391008\pi\) | ||||
0.335758 | + | 0.941948i | \(0.391008\pi\) | |||||||
\(432\) | −56.8126 | −2.73340 | ||||||||
\(433\) | −12.7801 | −0.614170 | −0.307085 | − | 0.951682i | \(-0.599354\pi\) | ||||
−0.307085 | + | 0.951682i | \(0.599354\pi\) | |||||||
\(434\) | −23.8942 | −1.14696 | ||||||||
\(435\) | 2.14092 | 0.102649 | ||||||||
\(436\) | −5.02476 | −0.240642 | ||||||||
\(437\) | 33.9445 | 1.62379 | ||||||||
\(438\) | 26.3561 | 1.25934 | ||||||||
\(439\) | −6.27910 | −0.299685 | −0.149842 | − | 0.988710i | \(-0.547877\pi\) | ||||
−0.149842 | + | 0.988710i | \(0.547877\pi\) | |||||||
\(440\) | −72.1195 | −3.43816 | ||||||||
\(441\) | 11.4383 | 0.544680 | ||||||||
\(442\) | 42.5672 | 2.02472 | ||||||||
\(443\) | −24.9396 | −1.18491 | −0.592457 | − | 0.805602i | \(-0.701842\pi\) | ||||
−0.592457 | + | 0.805602i | \(0.701842\pi\) | |||||||
\(444\) | 30.7112 | 1.45749 | ||||||||
\(445\) | −50.7211 | −2.40441 | ||||||||
\(446\) | 1.49461 | 0.0707716 | ||||||||
\(447\) | −8.72800 | −0.412820 | ||||||||
\(448\) | 62.7919 | 2.96664 | ||||||||
\(449\) | 14.2677 | 0.673336 | 0.336668 | − | 0.941623i | \(-0.390700\pi\) | ||||
0.336668 | + | 0.941623i | \(0.390700\pi\) | |||||||
\(450\) | 55.3713 | 2.61023 | ||||||||
\(451\) | 5.45968 | 0.257086 | ||||||||
\(452\) | −39.4725 | −1.85663 | ||||||||
\(453\) | 14.7345 | 0.692285 | ||||||||
\(454\) | −44.5815 | −2.09231 | ||||||||
\(455\) | −11.3129 | −0.530357 | ||||||||
\(456\) | −22.2549 | −1.04218 | ||||||||
\(457\) | −4.66582 | −0.218258 | −0.109129 | − | 0.994028i | \(-0.534806\pi\) | ||||
−0.109129 | + | 0.994028i | \(0.534806\pi\) | |||||||
\(458\) | −30.6749 | −1.43334 | ||||||||
\(459\) | −26.7593 | −1.24902 | ||||||||
\(460\) | 187.131 | 8.72502 | ||||||||
\(461\) | −23.1527 | −1.07833 | −0.539164 | − | 0.842201i | \(-0.681260\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(462\) | −5.46689 | −0.254343 | ||||||||
\(463\) | −25.9408 | −1.20557 | −0.602785 | − | 0.797903i | \(-0.705943\pi\) | ||||
−0.602785 | + | 0.797903i | \(0.705943\pi\) | |||||||
\(464\) | 16.7069 | 0.775598 | ||||||||
\(465\) | 11.3321 | 0.525513 | ||||||||
\(466\) | −12.9821 | −0.601384 | ||||||||
\(467\) | 42.3646 | 1.96040 | 0.980201 | − | 0.198006i | \(-0.0634465\pi\) | ||||
0.980201 | + | 0.198006i | \(0.0634465\pi\) | |||||||
\(468\) | 29.1570 | 1.34778 | ||||||||
\(469\) | −9.38235 | −0.433237 | ||||||||
\(470\) | 38.4189 | 1.77213 | ||||||||
\(471\) | −10.2606 | −0.472786 | ||||||||
\(472\) | 121.506 | 5.59278 | ||||||||
\(473\) | 6.08129 | 0.279618 | ||||||||
\(474\) | 12.8704 | 0.591158 | ||||||||
\(475\) | 27.6469 | 1.26853 | ||||||||
\(476\) | 72.6383 | 3.32937 | ||||||||
\(477\) | 23.9748 | 1.09773 | ||||||||
\(478\) | −33.9678 | −1.55365 | ||||||||
\(479\) | 4.27797 | 0.195465 | 0.0977326 | − | 0.995213i | \(-0.468841\pi\) | ||||
0.0977326 | + | 0.995213i | \(0.468841\pi\) | |||||||
\(480\) | −55.6284 | −2.53908 | ||||||||
\(481\) | −17.5805 | −0.801602 | ||||||||
\(482\) | 65.2612 | 2.97256 | ||||||||
\(483\) | 9.17188 | 0.417335 | ||||||||
\(484\) | −39.4517 | −1.79326 | ||||||||
\(485\) | −12.9937 | −0.590012 | ||||||||
\(486\) | −38.0116 | −1.72424 | ||||||||
\(487\) | −12.7240 | −0.576579 | −0.288289 | − | 0.957543i | \(-0.593086\pi\) | ||||
−0.288289 | + | 0.957543i | \(0.593086\pi\) | |||||||
\(488\) | −122.306 | −5.53652 | ||||||||
\(489\) | 0.963392 | 0.0435661 | ||||||||
\(490\) | 42.6118 | 1.92501 | ||||||||
\(491\) | −27.4302 | −1.23791 | −0.618953 | − | 0.785428i | \(-0.712443\pi\) | ||||
−0.618953 | + | 0.785428i | \(0.712443\pi\) | |||||||
\(492\) | 9.28789 | 0.418730 | ||||||||
\(493\) | 7.86913 | 0.354408 | ||||||||
\(494\) | 19.7032 | 0.886487 | ||||||||
\(495\) | −18.7729 | −0.843779 | ||||||||
\(496\) | 88.4314 | 3.97069 | ||||||||
\(497\) | −6.71134 | −0.301045 | ||||||||
\(498\) | −1.56370 | −0.0700710 | ||||||||
\(499\) | −11.3455 | −0.507892 | −0.253946 | − | 0.967218i | \(-0.581729\pi\) | ||||
−0.253946 | + | 0.967218i | \(0.581729\pi\) | |||||||
\(500\) | 52.0134 | 2.32611 | ||||||||
\(501\) | −9.88396 | −0.441583 | ||||||||
\(502\) | 4.92267 | 0.219710 | ||||||||
\(503\) | −29.4217 | −1.31185 | −0.655924 | − | 0.754827i | \(-0.727721\pi\) | ||||
−0.655924 | + | 0.754827i | \(0.727721\pi\) | |||||||
\(504\) | 43.5401 | 1.93943 | ||||||||
\(505\) | 68.6566 | 3.05518 | ||||||||
\(506\) | −51.7662 | −2.30129 | ||||||||
\(507\) | −5.53860 | −0.245978 | ||||||||
\(508\) | 63.7081 | 2.82659 | ||||||||
\(509\) | 25.0866 | 1.11194 | 0.555972 | − | 0.831201i | \(-0.312346\pi\) | ||||
0.555972 | + | 0.831201i | \(0.312346\pi\) | |||||||
\(510\) | −46.6245 | −2.06457 | ||||||||
\(511\) | −25.7458 | −1.13893 | ||||||||
\(512\) | −95.7387 | −4.23109 | ||||||||
\(513\) | −12.3861 | −0.546861 | ||||||||
\(514\) | 24.4080 | 1.07659 | ||||||||
\(515\) | −6.91110 | −0.304540 | ||||||||
\(516\) | 10.3454 | 0.455429 | ||||||||
\(517\) | −7.85262 | −0.345358 | ||||||||
\(518\) | −40.6025 | −1.78397 | ||||||||
\(519\) | 0.622712 | 0.0273340 | ||||||||
\(520\) | 70.2324 | 3.07989 | ||||||||
\(521\) | −17.3165 | −0.758651 | −0.379326 | − | 0.925263i | \(-0.623844\pi\) | ||||
−0.379326 | + | 0.925263i | \(0.623844\pi\) | |||||||
\(522\) | 7.29499 | 0.319293 | ||||||||
\(523\) | 5.82895 | 0.254882 | 0.127441 | − | 0.991846i | \(-0.459324\pi\) | ||||
0.127441 | + | 0.991846i | \(0.459324\pi\) | |||||||
\(524\) | −23.5602 | −1.02923 | ||||||||
\(525\) | 7.47026 | 0.326029 | ||||||||
\(526\) | −60.7580 | −2.64917 | ||||||||
\(527\) | 41.6521 | 1.81439 | ||||||||
\(528\) | 20.2327 | 0.880514 | ||||||||
\(529\) | 63.8490 | 2.77604 | ||||||||
\(530\) | 89.3151 | 3.87960 | ||||||||
\(531\) | 31.6284 | 1.37256 | ||||||||
\(532\) | 33.6222 | 1.45771 | ||||||||
\(533\) | −5.31682 | −0.230297 | ||||||||
\(534\) | 23.8693 | 1.03293 | ||||||||
\(535\) | −40.1279 | −1.73488 | ||||||||
\(536\) | 58.2472 | 2.51590 | ||||||||
\(537\) | −13.6838 | −0.590498 | ||||||||
\(538\) | −49.7068 | −2.14301 | ||||||||
\(539\) | −8.70964 | −0.375151 | ||||||||
\(540\) | −68.2828 | −2.93843 | ||||||||
\(541\) | −4.66792 | −0.200689 | −0.100345 | − | 0.994953i | \(-0.531995\pi\) | ||||
−0.100345 | + | 0.994953i | \(0.531995\pi\) | |||||||
\(542\) | −43.5117 | −1.86899 | ||||||||
\(543\) | 8.58003 | 0.368204 | ||||||||
\(544\) | −204.467 | −8.76645 | ||||||||
\(545\) | −3.15057 | −0.134955 | ||||||||
\(546\) | 5.32384 | 0.227839 | ||||||||
\(547\) | −21.4804 | −0.918434 | −0.459217 | − | 0.888324i | \(-0.651870\pi\) | ||||
−0.459217 | + | 0.888324i | \(0.651870\pi\) | |||||||
\(548\) | −63.9222 | −2.73062 | ||||||||
\(549\) | −31.8365 | −1.35875 | ||||||||
\(550\) | −42.1622 | −1.79780 | ||||||||
\(551\) | 3.64239 | 0.155171 | ||||||||
\(552\) | −56.9406 | −2.42355 | ||||||||
\(553\) | −12.5724 | −0.534633 | ||||||||
\(554\) | 13.7780 | 0.585372 | ||||||||
\(555\) | 19.2562 | 0.817380 | ||||||||
\(556\) | −5.65907 | −0.239998 | ||||||||
\(557\) | −23.0638 | −0.977244 | −0.488622 | − | 0.872495i | \(-0.662500\pi\) | ||||
−0.488622 | + | 0.872495i | \(0.662500\pi\) | |||||||
\(558\) | 38.6131 | 1.63462 | ||||||||
\(559\) | −5.92216 | −0.250481 | ||||||||
\(560\) | 96.6960 | 4.08615 | ||||||||
\(561\) | 9.52981 | 0.402349 | ||||||||
\(562\) | −47.7193 | −2.01292 | ||||||||
\(563\) | −20.6906 | −0.872003 | −0.436002 | − | 0.899946i | \(-0.643606\pi\) | ||||
−0.436002 | + | 0.899946i | \(0.643606\pi\) | |||||||
\(564\) | −13.3587 | −0.562503 | ||||||||
\(565\) | −24.7496 | −1.04122 | ||||||||
\(566\) | 21.7356 | 0.913614 | ||||||||
\(567\) | 9.55214 | 0.401152 | ||||||||
\(568\) | 41.6652 | 1.74823 | ||||||||
\(569\) | 31.4275 | 1.31751 | 0.658755 | − | 0.752358i | \(-0.271083\pi\) | ||||
0.658755 | + | 0.752358i | \(0.271083\pi\) | |||||||
\(570\) | −21.5811 | −0.903935 | ||||||||
\(571\) | 16.6016 | 0.694754 | 0.347377 | − | 0.937726i | \(-0.387072\pi\) | ||||
0.347377 | + | 0.937726i | \(0.387072\pi\) | |||||||
\(572\) | −22.2015 | −0.928290 | ||||||||
\(573\) | −9.88089 | −0.412780 | ||||||||
\(574\) | −12.2793 | −0.512528 | ||||||||
\(575\) | 70.7363 | 2.94991 | ||||||||
\(576\) | −101.472 | −4.22799 | ||||||||
\(577\) | −45.6547 | −1.90063 | −0.950314 | − | 0.311293i | \(-0.899238\pi\) | ||||
−0.950314 | + | 0.311293i | \(0.899238\pi\) | |||||||
\(578\) | −124.325 | −5.17123 | ||||||||
\(579\) | 11.2565 | 0.467803 | ||||||||
\(580\) | 20.0800 | 0.833775 | ||||||||
\(581\) | 1.52749 | 0.0633709 | ||||||||
\(582\) | 6.11481 | 0.253467 | ||||||||
\(583\) | −18.2555 | −0.756067 | ||||||||
\(584\) | 159.834 | 6.61399 | ||||||||
\(585\) | 18.2817 | 0.755854 | ||||||||
\(586\) | 24.6512 | 1.01833 | ||||||||
\(587\) | −31.7886 | −1.31206 | −0.656029 | − | 0.754736i | \(-0.727765\pi\) | ||||
−0.656029 | + | 0.754736i | \(0.727765\pi\) | |||||||
\(588\) | −14.8167 | −0.611029 | ||||||||
\(589\) | 19.2796 | 0.794401 | ||||||||
\(590\) | 117.827 | 4.85088 | ||||||||
\(591\) | 0.0247887 | 0.00101967 | ||||||||
\(592\) | 150.268 | 6.17598 | ||||||||
\(593\) | 26.3983 | 1.08405 | 0.542023 | − | 0.840364i | \(-0.317658\pi\) | ||||
0.542023 | + | 0.840364i | \(0.317658\pi\) | |||||||
\(594\) | 18.8892 | 0.775031 | ||||||||
\(595\) | 45.5449 | 1.86716 | ||||||||
\(596\) | −81.8612 | −3.35317 | ||||||||
\(597\) | 11.4976 | 0.470564 | ||||||||
\(598\) | 50.4117 | 2.06149 | ||||||||
\(599\) | 12.5882 | 0.514341 | 0.257170 | − | 0.966366i | \(-0.417210\pi\) | ||||
0.257170 | + | 0.966366i | \(0.417210\pi\) | |||||||
\(600\) | −46.3766 | −1.89332 | ||||||||
\(601\) | −34.6531 | −1.41353 | −0.706766 | − | 0.707448i | \(-0.749846\pi\) | ||||
−0.706766 | + | 0.707448i | \(0.749846\pi\) | |||||||
\(602\) | −13.6773 | −0.557447 | ||||||||
\(603\) | 15.1619 | 0.617441 | ||||||||
\(604\) | 138.197 | 5.62314 | ||||||||
\(605\) | −24.7366 | −1.00568 | ||||||||
\(606\) | −32.3097 | −1.31249 | ||||||||
\(607\) | −46.8924 | −1.90330 | −0.951651 | − | 0.307181i | \(-0.900614\pi\) | ||||
−0.951651 | + | 0.307181i | \(0.900614\pi\) | |||||||
\(608\) | −94.6419 | −3.83824 | ||||||||
\(609\) | 0.984183 | 0.0398811 | ||||||||
\(610\) | −118.603 | −4.80208 | ||||||||
\(611\) | 7.64714 | 0.309370 | ||||||||
\(612\) | −117.384 | −4.74496 | ||||||||
\(613\) | −22.5128 | −0.909284 | −0.454642 | − | 0.890674i | \(-0.650233\pi\) | ||||
−0.454642 | + | 0.890674i | \(0.650233\pi\) | |||||||
\(614\) | 31.1034 | 1.25523 | ||||||||
\(615\) | 5.82358 | 0.234830 | ||||||||
\(616\) | −33.1535 | −1.33579 | ||||||||
\(617\) | 23.4913 | 0.945723 | 0.472861 | − | 0.881137i | \(-0.343221\pi\) | ||||
0.472861 | + | 0.881137i | \(0.343221\pi\) | |||||||
\(618\) | 3.25236 | 0.130829 | ||||||||
\(619\) | −23.9489 | −0.962589 | −0.481295 | − | 0.876559i | \(-0.659833\pi\) | ||||
−0.481295 | + | 0.876559i | \(0.659833\pi\) | |||||||
\(620\) | 106.285 | 4.26852 | ||||||||
\(621\) | −31.6906 | −1.27170 | ||||||||
\(622\) | −6.83067 | −0.273885 | ||||||||
\(623\) | −23.3166 | −0.934160 | ||||||||
\(624\) | −19.7033 | −0.788762 | ||||||||
\(625\) | −5.33871 | −0.213549 | ||||||||
\(626\) | 3.88807 | 0.155398 | ||||||||
\(627\) | 4.41108 | 0.176161 | ||||||||
\(628\) | −96.2361 | −3.84024 | ||||||||
\(629\) | 70.7778 | 2.82210 | ||||||||
\(630\) | 42.2219 | 1.68216 | ||||||||
\(631\) | 26.1384 | 1.04055 | 0.520276 | − | 0.853998i | \(-0.325829\pi\) | ||||
0.520276 | + | 0.853998i | \(0.325829\pi\) | |||||||
\(632\) | 78.0516 | 3.10473 | ||||||||
\(633\) | 14.3962 | 0.572198 | ||||||||
\(634\) | 21.6786 | 0.860967 | ||||||||
\(635\) | 39.9455 | 1.58519 | ||||||||
\(636\) | −31.0559 | −1.23145 | ||||||||
\(637\) | 8.48174 | 0.336059 | ||||||||
\(638\) | −5.55474 | −0.219914 | ||||||||
\(639\) | 10.8456 | 0.429043 | ||||||||
\(640\) | −193.627 | −7.65378 | ||||||||
\(641\) | 45.2762 | 1.78830 | 0.894152 | − | 0.447763i | \(-0.147779\pi\) | ||||
0.894152 | + | 0.447763i | \(0.147779\pi\) | |||||||
\(642\) | 18.8841 | 0.745297 | ||||||||
\(643\) | 14.7293 | 0.580867 | 0.290434 | − | 0.956895i | \(-0.406200\pi\) | ||||
0.290434 | + | 0.956895i | \(0.406200\pi\) | |||||||
\(644\) | 86.0244 | 3.38984 | ||||||||
\(645\) | 6.48663 | 0.255411 | ||||||||
\(646\) | −79.3234 | −3.12094 | ||||||||
\(647\) | −15.5605 | −0.611746 | −0.305873 | − | 0.952072i | \(-0.598948\pi\) | ||||
−0.305873 | + | 0.952072i | \(0.598948\pi\) | |||||||
\(648\) | −59.3013 | −2.32958 | ||||||||
\(649\) | −24.0833 | −0.945353 | ||||||||
\(650\) | 41.0590 | 1.61047 | ||||||||
\(651\) | 5.20938 | 0.204172 | ||||||||
\(652\) | 9.03579 | 0.353869 | ||||||||
\(653\) | 18.3764 | 0.719124 | 0.359562 | − | 0.933121i | \(-0.382926\pi\) | ||||
0.359562 | + | 0.933121i | \(0.382926\pi\) | |||||||
\(654\) | 1.48265 | 0.0579763 | ||||||||
\(655\) | −14.7724 | −0.577207 | ||||||||
\(656\) | 45.4451 | 1.77433 | ||||||||
\(657\) | 41.6053 | 1.62318 | ||||||||
\(658\) | 17.6612 | 0.688506 | ||||||||
\(659\) | 0.770804 | 0.0300263 | 0.0150131 | − | 0.999887i | \(-0.495221\pi\) | ||||
0.0150131 | + | 0.999887i | \(0.495221\pi\) | |||||||
\(660\) | 24.3176 | 0.946561 | ||||||||
\(661\) | 33.5754 | 1.30593 | 0.652965 | − | 0.757388i | \(-0.273525\pi\) | ||||
0.652965 | + | 0.757388i | \(0.273525\pi\) | |||||||
\(662\) | −1.70482 | −0.0662598 | ||||||||
\(663\) | −9.28045 | −0.360423 | ||||||||
\(664\) | −9.48291 | −0.368008 | ||||||||
\(665\) | 21.0814 | 0.817502 | ||||||||
\(666\) | 65.6138 | 2.54248 | ||||||||
\(667\) | 9.31928 | 0.360844 | ||||||||
\(668\) | −92.7031 | −3.58679 | ||||||||
\(669\) | −0.325852 | −0.0125982 | ||||||||
\(670\) | 56.4837 | 2.18216 | ||||||||
\(671\) | 24.2418 | 0.935844 | ||||||||
\(672\) | −25.5725 | −0.986479 | ||||||||
\(673\) | 45.6078 | 1.75805 | 0.879027 | − | 0.476773i | \(-0.158194\pi\) | ||||
0.879027 | + | 0.476773i | \(0.158194\pi\) | |||||||
\(674\) | −15.9319 | −0.613675 | ||||||||
\(675\) | −25.8112 | −0.993473 | ||||||||
\(676\) | −51.9473 | −1.99797 | ||||||||
\(677\) | −15.7225 | −0.604263 | −0.302132 | − | 0.953266i | \(-0.597698\pi\) | ||||
−0.302132 | + | 0.953266i | \(0.597698\pi\) | |||||||
\(678\) | 11.6471 | 0.447306 | ||||||||
\(679\) | −5.97321 | −0.229231 | ||||||||
\(680\) | −282.750 | −10.8430 | ||||||||
\(681\) | 9.71960 | 0.372456 | ||||||||
\(682\) | −29.4018 | −1.12585 | ||||||||
\(683\) | 21.5630 | 0.825086 | 0.412543 | − | 0.910938i | \(-0.364641\pi\) | ||||
0.412543 | + | 0.910938i | \(0.364641\pi\) | |||||||
\(684\) | −54.3336 | −2.07750 | ||||||||
\(685\) | −40.0798 | −1.53137 | ||||||||
\(686\) | 51.1883 | 1.95438 | ||||||||
\(687\) | 6.68769 | 0.255151 | ||||||||
\(688\) | 50.6192 | 1.92984 | ||||||||
\(689\) | 17.7779 | 0.677282 | ||||||||
\(690\) | −55.2166 | −2.10206 | ||||||||
\(691\) | −39.8663 | −1.51659 | −0.758293 | − | 0.651913i | \(-0.773967\pi\) | ||||
−0.758293 | + | 0.651913i | \(0.773967\pi\) | |||||||
\(692\) | 5.84051 | 0.222023 | ||||||||
\(693\) | −8.62993 | −0.327824 | ||||||||
\(694\) | −10.0179 | −0.380275 | ||||||||
\(695\) | −3.54828 | −0.134594 | ||||||||
\(696\) | −6.10998 | −0.231598 | ||||||||
\(697\) | 21.4051 | 0.810776 | ||||||||
\(698\) | −87.5335 | −3.31319 | ||||||||
\(699\) | 2.83034 | 0.107053 | ||||||||
\(700\) | 70.0647 | 2.64820 | ||||||||
\(701\) | −4.33218 | −0.163624 | −0.0818120 | − | 0.996648i | \(-0.526071\pi\) | ||||
−0.0818120 | + | 0.996648i | \(0.526071\pi\) | |||||||
\(702\) | −18.3949 | −0.694271 | ||||||||
\(703\) | 32.7610 | 1.23561 | ||||||||
\(704\) | 77.2654 | 2.91205 | ||||||||
\(705\) | −8.37603 | −0.315459 | ||||||||
\(706\) | 48.9011 | 1.84042 | ||||||||
\(707\) | 31.5616 | 1.18700 | ||||||||
\(708\) | −40.9700 | −1.53975 | ||||||||
\(709\) | −3.28421 | −0.123341 | −0.0616705 | − | 0.998097i | \(-0.519643\pi\) | ||||
−0.0616705 | + | 0.998097i | \(0.519643\pi\) | |||||||
\(710\) | 40.4037 | 1.51632 | ||||||||
\(711\) | 20.3170 | 0.761948 | ||||||||
\(712\) | 144.753 | 5.42486 | ||||||||
\(713\) | 49.3279 | 1.84734 | ||||||||
\(714\) | −21.4334 | −0.802124 | ||||||||
\(715\) | −13.9205 | −0.520598 | ||||||||
\(716\) | −128.342 | −4.79637 | ||||||||
\(717\) | 7.40561 | 0.276568 | ||||||||
\(718\) | 10.6248 | 0.396514 | ||||||||
\(719\) | −37.4447 | −1.39645 | −0.698225 | − | 0.715878i | \(-0.746027\pi\) | ||||
−0.698225 | + | 0.715878i | \(0.746027\pi\) | |||||||
\(720\) | −156.261 | −5.82351 | ||||||||
\(721\) | −3.17705 | −0.118319 | ||||||||
\(722\) | 15.8660 | 0.590471 | ||||||||
\(723\) | −14.2281 | −0.529150 | ||||||||
\(724\) | 80.4733 | 2.99077 | ||||||||
\(725\) | 7.59031 | 0.281897 | ||||||||
\(726\) | 11.6410 | 0.432038 | ||||||||
\(727\) | 38.6672 | 1.43409 | 0.717043 | − | 0.697029i | \(-0.245495\pi\) | ||||
0.717043 | + | 0.697029i | \(0.245495\pi\) | |||||||
\(728\) | 32.2860 | 1.19660 | ||||||||
\(729\) | −9.28097 | −0.343740 | ||||||||
\(730\) | 154.995 | 5.73663 | ||||||||
\(731\) | 23.8422 | 0.881835 | ||||||||
\(732\) | 41.2396 | 1.52426 | ||||||||
\(733\) | −8.60188 | −0.317718 | −0.158859 | − | 0.987301i | \(-0.550781\pi\) | ||||
−0.158859 | + | 0.987301i | \(0.550781\pi\) | |||||||
\(734\) | −16.4586 | −0.607499 | ||||||||
\(735\) | −9.29017 | −0.342673 | ||||||||
\(736\) | −242.147 | −8.92565 | ||||||||
\(737\) | −11.5450 | −0.425265 | ||||||||
\(738\) | 19.8434 | 0.730445 | ||||||||
\(739\) | −0.855576 | −0.0314729 | −0.0157364 | − | 0.999876i | \(-0.505009\pi\) | ||||
−0.0157364 | + | 0.999876i | \(0.505009\pi\) | |||||||
\(740\) | 180.607 | 6.63923 | ||||||||
\(741\) | −4.29565 | −0.157805 | ||||||||
\(742\) | 41.0583 | 1.50730 | ||||||||
\(743\) | 2.89880 | 0.106347 | 0.0531733 | − | 0.998585i | \(-0.483066\pi\) | ||||
0.0531733 | + | 0.998585i | \(0.483066\pi\) | |||||||
\(744\) | −32.3407 | −1.18567 | ||||||||
\(745\) | −51.3277 | −1.88050 | ||||||||
\(746\) | 14.3344 | 0.524819 | ||||||||
\(747\) | −2.46843 | −0.0903150 | ||||||||
\(748\) | 89.3815 | 3.26811 | ||||||||
\(749\) | −18.4468 | −0.674033 | ||||||||
\(750\) | −15.3476 | −0.560414 | ||||||||
\(751\) | 12.1810 | 0.444491 | 0.222245 | − | 0.974991i | \(-0.428661\pi\) | ||||
0.222245 | + | 0.974991i | \(0.428661\pi\) | |||||||
\(752\) | −65.3633 | −2.38356 | ||||||||
\(753\) | −1.07323 | −0.0391108 | ||||||||
\(754\) | 5.40940 | 0.196999 | ||||||||
\(755\) | 86.6505 | 3.15353 | ||||||||
\(756\) | −31.3897 | −1.14163 | ||||||||
\(757\) | −11.8034 | −0.429001 | −0.214501 | − | 0.976724i | \(-0.568812\pi\) | ||||
−0.214501 | + | 0.976724i | \(0.568812\pi\) | |||||||
\(758\) | −26.0591 | −0.946510 | ||||||||
\(759\) | 11.2860 | 0.409656 | ||||||||
\(760\) | −130.877 | −4.74741 | ||||||||
\(761\) | −8.98774 | −0.325805 | −0.162903 | − | 0.986642i | \(-0.552086\pi\) | ||||
−0.162903 | + | 0.986642i | \(0.552086\pi\) | |||||||
\(762\) | −18.7983 | −0.680992 | ||||||||
\(763\) | −1.44832 | −0.0524327 | ||||||||
\(764\) | −92.6744 | −3.35284 | ||||||||
\(765\) | −73.6007 | −2.66104 | ||||||||
\(766\) | −9.41650 | −0.340232 | ||||||||
\(767\) | 23.4531 | 0.846844 | ||||||||
\(768\) | 44.6670 | 1.61178 | ||||||||
\(769\) | −22.5382 | −0.812748 | −0.406374 | − | 0.913707i | \(-0.633207\pi\) | ||||
−0.406374 | + | 0.913707i | \(0.633207\pi\) | |||||||
\(770\) | −32.1497 | −1.15859 | ||||||||
\(771\) | −5.32139 | −0.191645 | ||||||||
\(772\) | 105.576 | 3.79977 | ||||||||
\(773\) | −8.91885 | −0.320789 | −0.160394 | − | 0.987053i | \(-0.551277\pi\) | ||||
−0.160394 | + | 0.987053i | \(0.551277\pi\) | |||||||
\(774\) | 22.1026 | 0.794463 | ||||||||
\(775\) | 40.1763 | 1.44318 | ||||||||
\(776\) | 37.0827 | 1.33119 | ||||||||
\(777\) | 8.85210 | 0.317567 | ||||||||
\(778\) | 49.9336 | 1.79021 | ||||||||
\(779\) | 9.90781 | 0.354984 | ||||||||
\(780\) | −23.6813 | −0.847926 | ||||||||
\(781\) | −8.25830 | −0.295505 | ||||||||
\(782\) | −202.954 | −7.25761 | ||||||||
\(783\) | −3.40054 | −0.121526 | ||||||||
\(784\) | −72.4970 | −2.58918 | ||||||||
\(785\) | −60.3409 | −2.15366 | ||||||||
\(786\) | 6.95189 | 0.247966 | ||||||||
\(787\) | −18.0584 | −0.643712 | −0.321856 | − | 0.946789i | \(-0.604307\pi\) | ||||
−0.321856 | + | 0.946789i | \(0.604307\pi\) | |||||||
\(788\) | 0.232497 | 0.00828237 | ||||||||
\(789\) | 13.2464 | 0.471583 | ||||||||
\(790\) | 75.6885 | 2.69287 | ||||||||
\(791\) | −11.3774 | −0.404535 | ||||||||
\(792\) | 53.5761 | 1.90374 | ||||||||
\(793\) | −23.6075 | −0.838326 | ||||||||
\(794\) | −25.0820 | −0.890128 | ||||||||
\(795\) | −19.4723 | −0.690613 | ||||||||
\(796\) | 107.837 | 3.82220 | ||||||||
\(797\) | 5.28890 | 0.187343 | 0.0936713 | − | 0.995603i | \(-0.470140\pi\) | ||||
0.0936713 | + | 0.995603i | \(0.470140\pi\) | |||||||
\(798\) | −9.92089 | −0.351196 | ||||||||
\(799\) | −30.7868 | −1.08916 | ||||||||
\(800\) | −197.222 | −6.97286 | ||||||||
\(801\) | 37.6797 | 1.33135 | ||||||||
\(802\) | −24.1682 | −0.853408 | ||||||||
\(803\) | −31.6802 | −1.11797 | ||||||||
\(804\) | −19.6401 | −0.692652 | ||||||||
\(805\) | 53.9380 | 1.90107 | ||||||||
\(806\) | 28.6325 | 1.00854 | ||||||||
\(807\) | 10.8370 | 0.381480 | ||||||||
\(808\) | −195.940 | −6.89313 | ||||||||
\(809\) | −34.0460 | −1.19699 | −0.598496 | − | 0.801126i | \(-0.704235\pi\) | ||||
−0.598496 | + | 0.801126i | \(0.704235\pi\) | |||||||
\(810\) | −57.5059 | −2.02055 | ||||||||
\(811\) | −49.8297 | −1.74976 | −0.874878 | − | 0.484343i | \(-0.839059\pi\) | ||||
−0.874878 | + | 0.484343i | \(0.839059\pi\) | |||||||
\(812\) | 9.23080 | 0.323938 | ||||||||
\(813\) | 9.48636 | 0.332701 | ||||||||
\(814\) | −49.9614 | −1.75115 | ||||||||
\(815\) | 5.66552 | 0.198454 | ||||||||
\(816\) | 79.3239 | 2.77689 | ||||||||
\(817\) | 11.0359 | 0.386096 | ||||||||
\(818\) | −29.6451 | −1.03652 | ||||||||
\(819\) | 8.40412 | 0.293664 | ||||||||
\(820\) | 54.6203 | 1.90742 | ||||||||
\(821\) | −38.7193 | −1.35131 | −0.675656 | − | 0.737217i | \(-0.736140\pi\) | ||||
−0.675656 | + | 0.737217i | \(0.736140\pi\) | |||||||
\(822\) | 18.8615 | 0.657871 | ||||||||
\(823\) | 12.5201 | 0.436424 | 0.218212 | − | 0.975901i | \(-0.429978\pi\) | ||||
0.218212 | + | 0.975901i | \(0.429978\pi\) | |||||||
\(824\) | 19.7237 | 0.687106 | ||||||||
\(825\) | 9.19215 | 0.320030 | ||||||||
\(826\) | 54.1655 | 1.88466 | ||||||||
\(827\) | −52.8718 | −1.83853 | −0.919266 | − | 0.393637i | \(-0.871217\pi\) | ||||
−0.919266 | + | 0.393637i | \(0.871217\pi\) | |||||||
\(828\) | −139.016 | −4.83113 | ||||||||
\(829\) | −1.46001 | −0.0507083 | −0.0253541 | − | 0.999679i | \(-0.508071\pi\) | ||||
−0.0253541 | + | 0.999679i | \(0.508071\pi\) | |||||||
\(830\) | −9.19580 | −0.319191 | ||||||||
\(831\) | −3.00387 | −0.104203 | ||||||||
\(832\) | −75.2436 | −2.60860 | ||||||||
\(833\) | −34.1468 | −1.18312 | ||||||||
\(834\) | 1.66982 | 0.0578211 | ||||||||
\(835\) | −58.1257 | −2.01152 | ||||||||
\(836\) | 41.3721 | 1.43088 | ||||||||
\(837\) | −17.9994 | −0.622151 | ||||||||
\(838\) | 35.6988 | 1.23319 | ||||||||
\(839\) | 14.5157 | 0.501137 | 0.250568 | − | 0.968099i | \(-0.419382\pi\) | ||||
0.250568 | + | 0.968099i | \(0.419382\pi\) | |||||||
\(840\) | −35.3633 | −1.22015 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −105.450 | −3.63406 | ||||||||
\(843\) | 10.4037 | 0.358322 | ||||||||
\(844\) | 135.024 | 4.64773 | ||||||||
\(845\) | −32.5714 | −1.12049 | ||||||||
\(846\) | −28.5406 | −0.981246 | ||||||||
\(847\) | −11.3714 | −0.390727 | ||||||||
\(848\) | −151.955 | −5.21815 | ||||||||
\(849\) | −4.73876 | −0.162634 | ||||||||
\(850\) | −165.300 | −5.66976 | ||||||||
\(851\) | 83.8210 | 2.87335 | ||||||||
\(852\) | −14.0489 | −0.481306 | ||||||||
\(853\) | 30.3802 | 1.04020 | 0.520100 | − | 0.854106i | \(-0.325895\pi\) | ||||
0.520100 | + | 0.854106i | \(0.325895\pi\) | |||||||
\(854\) | −54.5219 | −1.86570 | ||||||||
\(855\) | −34.0676 | −1.16509 | ||||||||
\(856\) | 114.521 | 3.91425 | ||||||||
\(857\) | −1.79152 | −0.0611973 | −0.0305987 | − | 0.999532i | \(-0.509741\pi\) | ||||
−0.0305987 | + | 0.999532i | \(0.509741\pi\) | |||||||
\(858\) | 6.55098 | 0.223647 | ||||||||
\(859\) | 22.9177 | 0.781943 | 0.390972 | − | 0.920403i | \(-0.372139\pi\) | ||||
0.390972 | + | 0.920403i | \(0.372139\pi\) | |||||||
\(860\) | 60.8391 | 2.07459 | ||||||||
\(861\) | 2.67711 | 0.0912358 | ||||||||
\(862\) | −38.5818 | −1.31410 | ||||||||
\(863\) | −23.5522 | −0.801726 | −0.400863 | − | 0.916138i | \(-0.631290\pi\) | ||||
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(864\) | 88.3578 | 3.00599 | ||||||||
\(865\) | 3.66205 | 0.124513 | ||||||||
\(866\) | 35.3688 | 1.20188 | ||||||||
\(867\) | 27.1051 | 0.920539 | ||||||||
\(868\) | 48.8596 | 1.65840 | ||||||||
\(869\) | −15.4703 | −0.524795 | ||||||||
\(870\) | −5.92499 | −0.200876 | ||||||||
\(871\) | 11.2429 | 0.380951 | ||||||||
\(872\) | 8.99143 | 0.304488 | ||||||||
\(873\) | 9.65273 | 0.326695 | ||||||||
\(874\) | −93.9414 | −3.17762 | ||||||||
\(875\) | 14.9922 | 0.506828 | ||||||||
\(876\) | −53.8937 | −1.82090 | ||||||||
\(877\) | 12.7394 | 0.430178 | 0.215089 | − | 0.976594i | \(-0.430996\pi\) | ||||
0.215089 | + | 0.976594i | \(0.430996\pi\) | |||||||
\(878\) | 17.3774 | 0.586459 | ||||||||
\(879\) | −5.37441 | −0.181274 | ||||||||
\(880\) | 118.984 | 4.01097 | ||||||||
\(881\) | 4.58539 | 0.154486 | 0.0772429 | − | 0.997012i | \(-0.475388\pi\) | ||||
0.0772429 | + | 0.997012i | \(0.475388\pi\) | |||||||
\(882\) | −31.6555 | −1.06590 | ||||||||
\(883\) | −3.63470 | −0.122317 | −0.0611587 | − | 0.998128i | \(-0.519480\pi\) | ||||
−0.0611587 | + | 0.998128i | \(0.519480\pi\) | |||||||
\(884\) | −87.0427 | −2.92756 | ||||||||
\(885\) | −25.6886 | −0.863512 | ||||||||
\(886\) | 69.0203 | 2.31878 | ||||||||
\(887\) | 7.69792 | 0.258471 | 0.129235 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129235 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(888\) | −54.9554 | −1.84418 | ||||||||
\(889\) | 18.3630 | 0.615877 | ||||||||
\(890\) | 140.371 | 4.70524 | ||||||||
\(891\) | 11.7539 | 0.393771 | ||||||||
\(892\) | −3.05621 | −0.102330 | ||||||||
\(893\) | −14.2503 | −0.476869 | ||||||||
\(894\) | 24.1548 | 0.807856 | ||||||||
\(895\) | −80.4716 | −2.68987 | ||||||||
\(896\) | −89.0107 | −2.97364 | ||||||||
\(897\) | −10.9907 | −0.366968 | ||||||||
\(898\) | −39.4860 | −1.31767 | ||||||||
\(899\) | 5.29310 | 0.176535 | ||||||||
\(900\) | −113.225 | −3.77416 | ||||||||
\(901\) | −71.5723 | −2.38442 | ||||||||
\(902\) | −15.1097 | −0.503097 | ||||||||
\(903\) | 2.98192 | 0.0992319 | ||||||||
\(904\) | 70.6331 | 2.34922 | ||||||||
\(905\) | 50.4575 | 1.67726 | ||||||||
\(906\) | −40.7776 | −1.35475 | ||||||||
\(907\) | 19.4563 | 0.646036 | 0.323018 | − | 0.946393i | \(-0.395303\pi\) | ||||
0.323018 | + | 0.946393i | \(0.395303\pi\) | |||||||
\(908\) | 91.1616 | 3.02530 | ||||||||
\(909\) | −51.0036 | −1.69168 | ||||||||
\(910\) | 31.3085 | 1.03787 | ||||||||
\(911\) | −6.61264 | −0.219086 | −0.109543 | − | 0.993982i | \(-0.534939\pi\) | ||||
−0.109543 | + | 0.993982i | \(0.534939\pi\) | |||||||
\(912\) | 36.7168 | 1.21581 | ||||||||
\(913\) | 1.87957 | 0.0622048 | ||||||||
\(914\) | 12.9127 | 0.427113 | ||||||||
\(915\) | 25.8576 | 0.854826 | ||||||||
\(916\) | 62.7248 | 2.07249 | ||||||||
\(917\) | −6.79091 | −0.224256 | ||||||||
\(918\) | 74.0565 | 2.44423 | ||||||||
\(919\) | 12.7824 | 0.421651 | 0.210826 | − | 0.977524i | \(-0.432385\pi\) | ||||
0.210826 | + | 0.977524i | \(0.432385\pi\) | |||||||
\(920\) | −334.857 | −11.0399 | ||||||||
\(921\) | −6.78111 | −0.223445 | ||||||||
\(922\) | 64.0751 | 2.11020 | ||||||||
\(923\) | 8.04221 | 0.264713 | ||||||||
\(924\) | 11.1788 | 0.367757 | ||||||||
\(925\) | 68.2701 | 2.24471 | ||||||||
\(926\) | 71.7912 | 2.35920 | ||||||||
\(927\) | 5.13412 | 0.168627 | ||||||||
\(928\) | −25.9834 | −0.852948 | ||||||||
\(929\) | −0.917464 | −0.0301010 | −0.0150505 | − | 0.999887i | \(-0.504791\pi\) | ||||
−0.0150505 | + | 0.999887i | \(0.504791\pi\) | |||||||
\(930\) | −31.3616 | −1.02839 | ||||||||
\(931\) | −15.8056 | −0.518007 | ||||||||
\(932\) | 26.5462 | 0.869549 | ||||||||
\(933\) | 1.48921 | 0.0487546 | ||||||||
\(934\) | −117.244 | −3.83635 | ||||||||
\(935\) | 56.0429 | 1.83280 | ||||||||
\(936\) | −52.1742 | −1.70537 | ||||||||
\(937\) | 27.0613 | 0.884053 | 0.442027 | − | 0.897002i | \(-0.354260\pi\) | ||||
0.442027 | + | 0.897002i | \(0.354260\pi\) | |||||||
\(938\) | 25.9657 | 0.847809 | ||||||||
\(939\) | −0.847671 | −0.0276627 | ||||||||
\(940\) | −78.5600 | −2.56234 | ||||||||
\(941\) | 35.5029 | 1.15736 | 0.578681 | − | 0.815554i | \(-0.303568\pi\) | ||||
0.578681 | + | 0.815554i | \(0.303568\pi\) | |||||||
\(942\) | 28.3964 | 0.925203 | ||||||||
\(943\) | 25.3497 | 0.825500 | ||||||||
\(944\) | −200.464 | −6.52454 | ||||||||
\(945\) | −19.6816 | −0.640244 | ||||||||
\(946\) | −16.8300 | −0.547190 | ||||||||
\(947\) | −60.6850 | −1.97200 | −0.985999 | − | 0.166750i | \(-0.946673\pi\) | ||||
−0.985999 | + | 0.166750i | \(0.946673\pi\) | |||||||
\(948\) | −26.3178 | −0.854763 | ||||||||
\(949\) | 30.8513 | 1.00147 | ||||||||
\(950\) | −76.5129 | −2.48241 | ||||||||
\(951\) | −4.72634 | −0.153262 | ||||||||
\(952\) | −129.981 | −4.21270 | ||||||||
\(953\) | 7.88149 | 0.255307 | 0.127653 | − | 0.991819i | \(-0.459256\pi\) | ||||
0.127653 | + | 0.991819i | \(0.459256\pi\) | |||||||
\(954\) | −66.3504 | −2.14817 | ||||||||
\(955\) | −58.1076 | −1.88032 | ||||||||
\(956\) | 69.4583 | 2.24644 | ||||||||
\(957\) | 1.21104 | 0.0391473 | ||||||||
\(958\) | −11.8393 | −0.382510 | ||||||||
\(959\) | −18.4247 | −0.594966 | ||||||||
\(960\) | 82.4154 | 2.65995 | ||||||||
\(961\) | −2.98305 | −0.0962276 | ||||||||
\(962\) | 48.6541 | 1.56867 | ||||||||
\(963\) | 29.8102 | 0.960620 | ||||||||
\(964\) | −133.448 | −4.29807 | ||||||||
\(965\) | 66.1972 | 2.13096 | ||||||||
\(966\) | −25.3832 | −0.816691 | ||||||||
\(967\) | −9.83490 | −0.316269 | −0.158134 | − | 0.987418i | \(-0.550548\pi\) | ||||
−0.158134 | + | 0.987418i | \(0.550548\pi\) | |||||||
\(968\) | 70.5959 | 2.26904 | ||||||||
\(969\) | 17.2940 | 0.555563 | ||||||||
\(970\) | 35.9600 | 1.15461 | ||||||||
\(971\) | −38.5945 | −1.23856 | −0.619279 | − | 0.785171i | \(-0.712575\pi\) | ||||
−0.619279 | + | 0.785171i | \(0.712575\pi\) | |||||||
\(972\) | 77.7272 | 2.49310 | ||||||||
\(973\) | −1.63115 | −0.0522923 | ||||||||
\(974\) | 35.2136 | 1.12832 | ||||||||
\(975\) | −8.95163 | −0.286682 | ||||||||
\(976\) | 201.783 | 6.45891 | ||||||||
\(977\) | 3.68879 | 0.118015 | 0.0590075 | − | 0.998258i | \(-0.481206\pi\) | ||||
0.0590075 | + | 0.998258i | \(0.481206\pi\) | |||||||
\(978\) | −2.66619 | −0.0852553 | ||||||||
\(979\) | −28.6911 | −0.916971 | ||||||||
\(980\) | −87.1339 | −2.78339 | ||||||||
\(981\) | 2.34049 | 0.0747262 | ||||||||
\(982\) | 75.9130 | 2.42248 | ||||||||
\(983\) | −15.5289 | −0.495296 | −0.247648 | − | 0.968850i | \(-0.579658\pi\) | ||||
−0.247648 | + | 0.968850i | \(0.579658\pi\) | |||||||
\(984\) | −16.6200 | −0.529825 | ||||||||
\(985\) | 0.145778 | 0.00464486 | ||||||||
\(986\) | −21.7778 | −0.693547 | ||||||||
\(987\) | −3.85047 | −0.122562 | ||||||||
\(988\) | −40.2896 | −1.28178 | ||||||||
\(989\) | 28.2359 | 0.897850 | ||||||||
\(990\) | 51.9540 | 1.65121 | ||||||||
\(991\) | −46.5909 | −1.48001 | −0.740004 | − | 0.672602i | \(-0.765177\pi\) | ||||
−0.740004 | + | 0.672602i | \(0.765177\pi\) | |||||||
\(992\) | −137.533 | −4.36668 | ||||||||
\(993\) | 0.371683 | 0.0117950 | ||||||||
\(994\) | 18.5736 | 0.589120 | ||||||||
\(995\) | 67.6150 | 2.14354 | ||||||||
\(996\) | 3.19749 | 0.101316 | ||||||||
\(997\) | −16.7210 | −0.529559 | −0.264779 | − | 0.964309i | \(-0.585299\pi\) | ||||
−0.264779 | + | 0.964309i | \(0.585299\pi\) | |||||||
\(998\) | 31.3986 | 0.993904 | ||||||||
\(999\) | −30.5857 | −0.967690 |
(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 | 4031.2.a.d.1.2 | ✓ | 98 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.d.1.2 | ✓ | 98 | 1.1 | even | 1 | trivial |