Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(155\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73747 | −1.93568 | −0.967842 | − | 0.251559i | \(-0.919057\pi\) | ||||
−0.967842 | + | 0.251559i | \(0.919057\pi\) | |||||||
\(3\) | 2.98404 | 1.72284 | 0.861418 | − | 0.507897i | \(-0.169577\pi\) | ||||
0.861418 | + | 0.507897i | \(0.169577\pi\) | |||||||
\(4\) | 5.49374 | 2.74687 | ||||||||
\(5\) | −2.59125 | −1.15884 | −0.579422 | − | 0.815028i | \(-0.696722\pi\) | ||||
−0.579422 | + | 0.815028i | \(0.696722\pi\) | |||||||
\(6\) | −8.16872 | −3.33486 | ||||||||
\(7\) | 4.93159 | 1.86397 | 0.931983 | − | 0.362503i | \(-0.118078\pi\) | ||||
0.931983 | + | 0.362503i | \(0.118078\pi\) | |||||||
\(8\) | −9.56402 | −3.38139 | ||||||||
\(9\) | 5.90448 | 1.96816 | ||||||||
\(10\) | 7.09348 | 2.24315 | ||||||||
\(11\) | −2.39467 | −0.722019 | −0.361010 | − | 0.932562i | \(-0.617568\pi\) | ||||
−0.361010 | + | 0.932562i | \(0.617568\pi\) | |||||||
\(12\) | 16.3935 | 4.73241 | ||||||||
\(13\) | −1.38236 | −0.383399 | −0.191700 | − | 0.981454i | \(-0.561400\pi\) | ||||
−0.191700 | + | 0.981454i | \(0.561400\pi\) | |||||||
\(14\) | −13.5001 | −3.60805 | ||||||||
\(15\) | −7.73240 | −1.99650 | ||||||||
\(16\) | 15.1937 | 3.79843 | ||||||||
\(17\) | −3.63322 | −0.881185 | −0.440592 | − | 0.897707i | \(-0.645232\pi\) | ||||
−0.440592 | + | 0.897707i | \(0.645232\pi\) | |||||||
\(18\) | −16.1633 | −3.80974 | ||||||||
\(19\) | −4.88146 | −1.11988 | −0.559942 | − | 0.828532i | \(-0.689177\pi\) | ||||
−0.559942 | + | 0.828532i | \(0.689177\pi\) | |||||||
\(20\) | −14.2357 | −3.18319 | ||||||||
\(21\) | 14.7160 | 3.21131 | ||||||||
\(22\) | 6.55533 | 1.39760 | ||||||||
\(23\) | 5.06391 | 1.05590 | 0.527949 | − | 0.849276i | \(-0.322961\pi\) | ||||
0.527949 | + | 0.849276i | \(0.322961\pi\) | |||||||
\(24\) | −28.5394 | −5.82558 | ||||||||
\(25\) | 1.71459 | 0.342918 | ||||||||
\(26\) | 3.78418 | 0.742139 | ||||||||
\(27\) | 8.66709 | 1.66798 | ||||||||
\(28\) | 27.0929 | 5.12007 | ||||||||
\(29\) | −2.15653 | −0.400458 | −0.200229 | − | 0.979749i | \(-0.564169\pi\) | ||||
−0.200229 | + | 0.979749i | \(0.564169\pi\) | |||||||
\(30\) | 21.1672 | 3.86458 | ||||||||
\(31\) | −10.6464 | −1.91214 | −0.956071 | − | 0.293134i | \(-0.905302\pi\) | ||||
−0.956071 | + | 0.293134i | \(0.905302\pi\) | |||||||
\(32\) | −22.4643 | −3.97117 | ||||||||
\(33\) | −7.14578 | −1.24392 | ||||||||
\(34\) | 9.94583 | 1.70569 | ||||||||
\(35\) | −12.7790 | −2.16004 | ||||||||
\(36\) | 32.4377 | 5.40629 | ||||||||
\(37\) | 0.572133 | 0.0940580 | 0.0470290 | − | 0.998894i | \(-0.485025\pi\) | ||||
0.0470290 | + | 0.998894i | \(0.485025\pi\) | |||||||
\(38\) | 13.3629 | 2.16774 | ||||||||
\(39\) | −4.12503 | −0.660533 | ||||||||
\(40\) | 24.7828 | 3.91850 | ||||||||
\(41\) | −6.06996 | −0.947968 | −0.473984 | − | 0.880533i | \(-0.657185\pi\) | ||||
−0.473984 | + | 0.880533i | \(0.657185\pi\) | |||||||
\(42\) | −40.2847 | −6.21607 | ||||||||
\(43\) | 4.28416 | 0.653328 | 0.326664 | − | 0.945141i | \(-0.394075\pi\) | ||||
0.326664 | + | 0.945141i | \(0.394075\pi\) | |||||||
\(44\) | −13.1557 | −1.98329 | ||||||||
\(45\) | −15.3000 | −2.28079 | ||||||||
\(46\) | −13.8623 | −2.04389 | ||||||||
\(47\) | −0.417951 | −0.0609644 | −0.0304822 | − | 0.999535i | \(-0.509704\pi\) | ||||
−0.0304822 | + | 0.999535i | \(0.509704\pi\) | |||||||
\(48\) | 45.3386 | 6.54407 | ||||||||
\(49\) | 17.3206 | 2.47437 | ||||||||
\(50\) | −4.69364 | −0.663780 | ||||||||
\(51\) | −10.8417 | −1.51814 | ||||||||
\(52\) | −7.59436 | −1.05315 | ||||||||
\(53\) | 5.93722 | 0.815540 | 0.407770 | − | 0.913085i | \(-0.366306\pi\) | ||||
0.407770 | + | 0.913085i | \(0.366306\pi\) | |||||||
\(54\) | −23.7259 | −3.22869 | ||||||||
\(55\) | 6.20519 | 0.836707 | ||||||||
\(56\) | −47.1658 | −6.30279 | ||||||||
\(57\) | −14.5665 | −1.92937 | ||||||||
\(58\) | 5.90344 | 0.775159 | ||||||||
\(59\) | 1.38009 | 0.179673 | 0.0898365 | − | 0.995957i | \(-0.471366\pi\) | ||||
0.0898365 | + | 0.995957i | \(0.471366\pi\) | |||||||
\(60\) | −42.4798 | −5.48412 | ||||||||
\(61\) | −6.76971 | −0.866772 | −0.433386 | − | 0.901208i | \(-0.642681\pi\) | ||||
−0.433386 | + | 0.901208i | \(0.642681\pi\) | |||||||
\(62\) | 29.1441 | 3.70130 | ||||||||
\(63\) | 29.1185 | 3.66858 | ||||||||
\(64\) | 31.1080 | 3.88850 | ||||||||
\(65\) | 3.58206 | 0.444299 | ||||||||
\(66\) | 19.5614 | 2.40784 | ||||||||
\(67\) | 13.3582 | 1.63197 | 0.815985 | − | 0.578074i | \(-0.196195\pi\) | ||||
0.815985 | + | 0.578074i | \(0.196195\pi\) | |||||||
\(68\) | −19.9600 | −2.42050 | ||||||||
\(69\) | 15.1109 | 1.81914 | ||||||||
\(70\) | 34.9821 | 4.18116 | ||||||||
\(71\) | 1.00000 | 0.118678 | ||||||||
\(72\) | −56.4706 | −6.65512 | ||||||||
\(73\) | 10.5857 | 1.23896 | 0.619480 | − | 0.785012i | \(-0.287343\pi\) | ||||
0.619480 | + | 0.785012i | \(0.287343\pi\) | |||||||
\(74\) | −1.56620 | −0.182067 | ||||||||
\(75\) | 5.11640 | 0.590791 | ||||||||
\(76\) | −26.8175 | −3.07618 | ||||||||
\(77\) | −11.8095 | −1.34582 | ||||||||
\(78\) | 11.2921 | 1.27858 | ||||||||
\(79\) | −16.0351 | −1.80409 | −0.902043 | − | 0.431646i | \(-0.857933\pi\) | ||||
−0.902043 | + | 0.431646i | \(0.857933\pi\) | |||||||
\(80\) | −39.3708 | −4.40179 | ||||||||
\(81\) | 8.14947 | 0.905497 | ||||||||
\(82\) | 16.6163 | 1.83497 | ||||||||
\(83\) | −18.0283 | −1.97886 | −0.989431 | − | 0.145005i | \(-0.953680\pi\) | ||||
−0.989431 | + | 0.145005i | \(0.953680\pi\) | |||||||
\(84\) | 80.8462 | 8.82104 | ||||||||
\(85\) | 9.41458 | 1.02116 | ||||||||
\(86\) | −11.7278 | −1.26464 | ||||||||
\(87\) | −6.43517 | −0.689922 | ||||||||
\(88\) | 22.9026 | 2.44143 | ||||||||
\(89\) | −14.8914 | −1.57848 | −0.789241 | − | 0.614084i | \(-0.789526\pi\) | ||||
−0.789241 | + | 0.614084i | \(0.789526\pi\) | |||||||
\(90\) | 41.8833 | 4.41489 | ||||||||
\(91\) | −6.81725 | −0.714642 | ||||||||
\(92\) | 27.8198 | 2.90042 | ||||||||
\(93\) | −31.7691 | −3.29431 | ||||||||
\(94\) | 1.14413 | 0.118008 | ||||||||
\(95\) | 12.6491 | 1.29777 | ||||||||
\(96\) | −67.0344 | −6.84167 | ||||||||
\(97\) | 8.29927 | 0.842663 | 0.421331 | − | 0.906907i | \(-0.361563\pi\) | ||||
0.421331 | + | 0.906907i | \(0.361563\pi\) | |||||||
\(98\) | −47.4145 | −4.78959 | ||||||||
\(99\) | −14.1393 | −1.42105 | ||||||||
\(100\) | 9.41951 | 0.941951 | ||||||||
\(101\) | 6.46752 | 0.643542 | 0.321771 | − | 0.946818i | \(-0.395722\pi\) | ||||
0.321771 | + | 0.946818i | \(0.395722\pi\) | |||||||
\(102\) | 29.6787 | 2.93863 | ||||||||
\(103\) | 3.63991 | 0.358651 | 0.179325 | − | 0.983790i | \(-0.442609\pi\) | ||||
0.179325 | + | 0.983790i | \(0.442609\pi\) | |||||||
\(104\) | 13.2210 | 1.29642 | ||||||||
\(105\) | −38.1330 | −3.72140 | ||||||||
\(106\) | −16.2530 | −1.57863 | ||||||||
\(107\) | −0.213079 | −0.0205991 | −0.0102996 | − | 0.999947i | \(-0.503279\pi\) | ||||
−0.0102996 | + | 0.999947i | \(0.503279\pi\) | |||||||
\(108\) | 47.6148 | 4.58173 | ||||||||
\(109\) | −15.8856 | −1.52157 | −0.760783 | − | 0.649006i | \(-0.775185\pi\) | ||||
−0.760783 | + | 0.649006i | \(0.775185\pi\) | |||||||
\(110\) | −16.9865 | −1.61960 | ||||||||
\(111\) | 1.70727 | 0.162046 | ||||||||
\(112\) | 74.9292 | 7.08014 | ||||||||
\(113\) | 1.00000 | 0.0940721 | ||||||||
\(114\) | 39.8753 | 3.73466 | ||||||||
\(115\) | −13.1219 | −1.22362 | ||||||||
\(116\) | −11.8474 | −1.10001 | ||||||||
\(117\) | −8.16215 | −0.754591 | ||||||||
\(118\) | −3.77797 | −0.347790 | ||||||||
\(119\) | −17.9175 | −1.64250 | ||||||||
\(120\) | 73.9528 | 6.75093 | ||||||||
\(121\) | −5.26557 | −0.478688 | ||||||||
\(122\) | 18.5319 | 1.67780 | ||||||||
\(123\) | −18.1130 | −1.63319 | ||||||||
\(124\) | −58.4884 | −5.25241 | ||||||||
\(125\) | 8.51333 | 0.761455 | ||||||||
\(126\) | −79.7110 | −7.10122 | ||||||||
\(127\) | 13.5246 | 1.20011 | 0.600057 | − | 0.799957i | \(-0.295145\pi\) | ||||
0.600057 | + | 0.799957i | \(0.295145\pi\) | |||||||
\(128\) | −40.2285 | −3.55573 | ||||||||
\(129\) | 12.7841 | 1.12558 | ||||||||
\(130\) | −9.80577 | −0.860023 | ||||||||
\(131\) | −11.2403 | −0.982073 | −0.491036 | − | 0.871139i | \(-0.663382\pi\) | ||||
−0.491036 | + | 0.871139i | \(0.663382\pi\) | |||||||
\(132\) | −39.2571 | −3.41689 | ||||||||
\(133\) | −24.0734 | −2.08742 | ||||||||
\(134\) | −36.5678 | −3.15898 | ||||||||
\(135\) | −22.4586 | −1.93293 | ||||||||
\(136\) | 34.7482 | 2.97963 | ||||||||
\(137\) | −6.13584 | −0.524220 | −0.262110 | − | 0.965038i | \(-0.584418\pi\) | ||||
−0.262110 | + | 0.965038i | \(0.584418\pi\) | |||||||
\(138\) | −41.3657 | −3.52128 | ||||||||
\(139\) | −15.2371 | −1.29239 | −0.646196 | − | 0.763172i | \(-0.723641\pi\) | ||||
−0.646196 | + | 0.763172i | \(0.723641\pi\) | |||||||
\(140\) | −70.2045 | −5.93336 | ||||||||
\(141\) | −1.24718 | −0.105032 | ||||||||
\(142\) | −2.73747 | −0.229723 | ||||||||
\(143\) | 3.31030 | 0.276822 | ||||||||
\(144\) | 89.7111 | 7.47592 | ||||||||
\(145\) | 5.58811 | 0.464068 | ||||||||
\(146\) | −28.9780 | −2.39824 | ||||||||
\(147\) | 51.6852 | 4.26293 | ||||||||
\(148\) | 3.14315 | 0.258365 | ||||||||
\(149\) | 19.5160 | 1.59881 | 0.799406 | − | 0.600791i | \(-0.205148\pi\) | ||||
0.799406 | + | 0.600791i | \(0.205148\pi\) | |||||||
\(150\) | −14.0060 | −1.14358 | ||||||||
\(151\) | −16.3064 | −1.32699 | −0.663497 | − | 0.748179i | \(-0.730928\pi\) | ||||
−0.663497 | + | 0.748179i | \(0.730928\pi\) | |||||||
\(152\) | 46.6864 | 3.78676 | ||||||||
\(153\) | −21.4523 | −1.73431 | ||||||||
\(154\) | 32.3282 | 2.60508 | ||||||||
\(155\) | 27.5874 | 2.21587 | ||||||||
\(156\) | −22.6618 | −1.81440 | ||||||||
\(157\) | −18.7400 | −1.49561 | −0.747807 | − | 0.663916i | \(-0.768893\pi\) | ||||
−0.747807 | + | 0.663916i | \(0.768893\pi\) | |||||||
\(158\) | 43.8955 | 3.49214 | ||||||||
\(159\) | 17.7169 | 1.40504 | ||||||||
\(160\) | 58.2108 | 4.60196 | ||||||||
\(161\) | 24.9731 | 1.96816 | ||||||||
\(162\) | −22.3089 | −1.75276 | ||||||||
\(163\) | 10.3827 | 0.813236 | 0.406618 | − | 0.913598i | \(-0.366708\pi\) | ||||
0.406618 | + | 0.913598i | \(0.366708\pi\) | |||||||
\(164\) | −33.3468 | −2.60395 | ||||||||
\(165\) | 18.5165 | 1.44151 | ||||||||
\(166\) | 49.3519 | 3.83045 | ||||||||
\(167\) | −11.6344 | −0.900298 | −0.450149 | − | 0.892953i | \(-0.648629\pi\) | ||||
−0.450149 | + | 0.892953i | \(0.648629\pi\) | |||||||
\(168\) | −140.745 | −10.8587 | ||||||||
\(169\) | −11.0891 | −0.853005 | ||||||||
\(170\) | −25.7721 | −1.97663 | ||||||||
\(171\) | −28.8225 | −2.20411 | ||||||||
\(172\) | 23.5361 | 1.79461 | ||||||||
\(173\) | −0.422922 | −0.0321541 | −0.0160771 | − | 0.999871i | \(-0.505118\pi\) | ||||
−0.0160771 | + | 0.999871i | \(0.505118\pi\) | |||||||
\(174\) | 17.6161 | 1.33547 | ||||||||
\(175\) | 8.45565 | 0.639187 | ||||||||
\(176\) | −36.3839 | −2.74254 | ||||||||
\(177\) | 4.11825 | 0.309547 | ||||||||
\(178\) | 40.7647 | 3.05544 | ||||||||
\(179\) | 4.49068 | 0.335649 | 0.167825 | − | 0.985817i | \(-0.446326\pi\) | ||||
0.167825 | + | 0.985817i | \(0.446326\pi\) | |||||||
\(180\) | −84.0543 | −6.26504 | ||||||||
\(181\) | −10.2264 | −0.760122 | −0.380061 | − | 0.924961i | \(-0.624097\pi\) | ||||
−0.380061 | + | 0.924961i | \(0.624097\pi\) | |||||||
\(182\) | 18.6620 | 1.38332 | ||||||||
\(183\) | −20.2011 | −1.49331 | ||||||||
\(184\) | −48.4313 | −3.57041 | ||||||||
\(185\) | −1.48254 | −0.108999 | ||||||||
\(186\) | 86.9671 | 6.37674 | ||||||||
\(187\) | 8.70035 | 0.636232 | ||||||||
\(188\) | −2.29611 | −0.167461 | ||||||||
\(189\) | 42.7425 | 3.10906 | ||||||||
\(190\) | −34.6265 | −2.51207 | ||||||||
\(191\) | 8.31718 | 0.601810 | 0.300905 | − | 0.953654i | \(-0.402711\pi\) | ||||
0.300905 | + | 0.953654i | \(0.402711\pi\) | |||||||
\(192\) | 92.8274 | 6.69924 | ||||||||
\(193\) | −0.777393 | −0.0559579 | −0.0279790 | − | 0.999609i | \(-0.508907\pi\) | ||||
−0.0279790 | + | 0.999609i | \(0.508907\pi\) | |||||||
\(194\) | −22.7190 | −1.63113 | ||||||||
\(195\) | 10.6890 | 0.765455 | ||||||||
\(196\) | 95.1547 | 6.79677 | ||||||||
\(197\) | −9.79939 | −0.698177 | −0.349089 | − | 0.937090i | \(-0.613509\pi\) | ||||
−0.349089 | + | 0.937090i | \(0.613509\pi\) | |||||||
\(198\) | 38.7058 | 2.75070 | ||||||||
\(199\) | 6.87902 | 0.487641 | 0.243820 | − | 0.969820i | \(-0.421599\pi\) | ||||
0.243820 | + | 0.969820i | \(0.421599\pi\) | |||||||
\(200\) | −16.3984 | −1.15954 | ||||||||
\(201\) | 39.8615 | 2.81161 | ||||||||
\(202\) | −17.7046 | −1.24569 | ||||||||
\(203\) | −10.6351 | −0.746439 | ||||||||
\(204\) | −59.5613 | −4.17012 | ||||||||
\(205\) | 15.7288 | 1.09855 | ||||||||
\(206\) | −9.96414 | −0.694234 | ||||||||
\(207\) | 29.8998 | 2.07818 | ||||||||
\(208\) | −21.0033 | −1.45631 | ||||||||
\(209\) | 11.6895 | 0.808578 | ||||||||
\(210\) | 104.388 | 7.20345 | ||||||||
\(211\) | 17.6853 | 1.21751 | 0.608753 | − | 0.793360i | \(-0.291670\pi\) | ||||
0.608753 | + | 0.793360i | \(0.291670\pi\) | |||||||
\(212\) | 32.6176 | 2.24018 | ||||||||
\(213\) | 2.98404 | 0.204463 | ||||||||
\(214\) | 0.583298 | 0.0398734 | ||||||||
\(215\) | −11.1013 | −0.757105 | ||||||||
\(216\) | −82.8922 | −5.64010 | ||||||||
\(217\) | −52.5035 | −3.56417 | ||||||||
\(218\) | 43.4864 | 2.94527 | ||||||||
\(219\) | 31.5881 | 2.13452 | ||||||||
\(220\) | 34.0897 | 2.29833 | ||||||||
\(221\) | 5.02243 | 0.337845 | ||||||||
\(222\) | −4.67359 | −0.313671 | ||||||||
\(223\) | −14.9901 | −1.00381 | −0.501906 | − | 0.864922i | \(-0.667368\pi\) | ||||
−0.501906 | + | 0.864922i | \(0.667368\pi\) | |||||||
\(224\) | −110.785 | −7.40212 | ||||||||
\(225\) | 10.1238 | 0.674918 | ||||||||
\(226\) | −2.73747 | −0.182094 | ||||||||
\(227\) | 7.60669 | 0.504874 | 0.252437 | − | 0.967613i | \(-0.418768\pi\) | ||||
0.252437 | + | 0.967613i | \(0.418768\pi\) | |||||||
\(228\) | −80.0244 | −5.29974 | ||||||||
\(229\) | −28.7613 | −1.90060 | −0.950300 | − | 0.311335i | \(-0.899224\pi\) | ||||
−0.950300 | + | 0.311335i | \(0.899224\pi\) | |||||||
\(230\) | 35.9207 | 2.36854 | ||||||||
\(231\) | −35.2400 | −2.31862 | ||||||||
\(232\) | 20.6251 | 1.35410 | ||||||||
\(233\) | −15.2594 | −0.999677 | −0.499838 | − | 0.866119i | \(-0.666607\pi\) | ||||
−0.499838 | + | 0.866119i | \(0.666607\pi\) | |||||||
\(234\) | 22.3436 | 1.46065 | ||||||||
\(235\) | 1.08302 | 0.0706482 | ||||||||
\(236\) | 7.58188 | 0.493538 | ||||||||
\(237\) | −47.8493 | −3.10814 | ||||||||
\(238\) | 49.0487 | 3.17936 | ||||||||
\(239\) | 6.00454 | 0.388401 | 0.194201 | − | 0.980962i | \(-0.437789\pi\) | ||||
0.194201 | + | 0.980962i | \(0.437789\pi\) | |||||||
\(240\) | −117.484 | −7.58355 | ||||||||
\(241\) | 11.4386 | 0.736826 | 0.368413 | − | 0.929662i | \(-0.379901\pi\) | ||||
0.368413 | + | 0.929662i | \(0.379901\pi\) | |||||||
\(242\) | 14.4143 | 0.926589 | ||||||||
\(243\) | −1.68293 | −0.107960 | ||||||||
\(244\) | −37.1910 | −2.38091 | ||||||||
\(245\) | −44.8820 | −2.86740 | ||||||||
\(246\) | 49.5838 | 3.16134 | ||||||||
\(247\) | 6.74796 | 0.429362 | ||||||||
\(248\) | 101.822 | 6.46570 | ||||||||
\(249\) | −53.7971 | −3.40925 | ||||||||
\(250\) | −23.3050 | −1.47394 | ||||||||
\(251\) | −22.3153 | −1.40853 | −0.704264 | − | 0.709939i | \(-0.748723\pi\) | ||||
−0.704264 | + | 0.709939i | \(0.748723\pi\) | |||||||
\(252\) | 159.969 | 10.0771 | ||||||||
\(253\) | −12.1264 | −0.762379 | ||||||||
\(254\) | −37.0232 | −2.32304 | ||||||||
\(255\) | 28.0935 | 1.75928 | ||||||||
\(256\) | 47.9084 | 2.99428 | ||||||||
\(257\) | −3.63304 | −0.226623 | −0.113311 | − | 0.993560i | \(-0.536146\pi\) | ||||
−0.113311 | + | 0.993560i | \(0.536146\pi\) | |||||||
\(258\) | −34.9961 | −2.17876 | ||||||||
\(259\) | 2.82152 | 0.175321 | ||||||||
\(260\) | 19.6789 | 1.22043 | ||||||||
\(261\) | −12.7332 | −0.788165 | ||||||||
\(262\) | 30.7701 | 1.90098 | ||||||||
\(263\) | −14.8817 | −0.917646 | −0.458823 | − | 0.888528i | \(-0.651729\pi\) | ||||
−0.458823 | + | 0.888528i | \(0.651729\pi\) | |||||||
\(264\) | 68.3423 | 4.20618 | ||||||||
\(265\) | −15.3848 | −0.945083 | ||||||||
\(266\) | 65.9001 | 4.04059 | ||||||||
\(267\) | −44.4364 | −2.71946 | ||||||||
\(268\) | 73.3868 | 4.48281 | ||||||||
\(269\) | 6.60815 | 0.402906 | 0.201453 | − | 0.979498i | \(-0.435434\pi\) | ||||
0.201453 | + | 0.979498i | \(0.435434\pi\) | |||||||
\(270\) | 61.4798 | 3.74154 | ||||||||
\(271\) | 1.06822 | 0.0648896 | 0.0324448 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324448 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(272\) | −55.2021 | −3.34712 | ||||||||
\(273\) | −20.3429 | −1.23121 | ||||||||
\(274\) | 16.7967 | 1.01472 | ||||||||
\(275\) | −4.10587 | −0.247593 | ||||||||
\(276\) | 83.0154 | 4.99694 | ||||||||
\(277\) | 26.9706 | 1.62051 | 0.810254 | − | 0.586079i | \(-0.199329\pi\) | ||||
0.810254 | + | 0.586079i | \(0.199329\pi\) | |||||||
\(278\) | 41.7110 | 2.50166 | ||||||||
\(279\) | −62.8613 | −3.76341 | ||||||||
\(280\) | 122.218 | 7.30395 | ||||||||
\(281\) | −6.16900 | −0.368012 | −0.184006 | − | 0.982925i | \(-0.558907\pi\) | ||||
−0.184006 | + | 0.982925i | \(0.558907\pi\) | |||||||
\(282\) | 3.41412 | 0.203308 | ||||||||
\(283\) | 8.61856 | 0.512320 | 0.256160 | − | 0.966634i | \(-0.417543\pi\) | ||||
0.256160 | + | 0.966634i | \(0.417543\pi\) | |||||||
\(284\) | 5.49374 | 0.325994 | ||||||||
\(285\) | 37.7454 | 2.23584 | ||||||||
\(286\) | −9.06186 | −0.535839 | ||||||||
\(287\) | −29.9345 | −1.76698 | ||||||||
\(288\) | −132.640 | −7.81590 | ||||||||
\(289\) | −3.79973 | −0.223513 | ||||||||
\(290\) | −15.2973 | −0.898288 | ||||||||
\(291\) | 24.7653 | 1.45177 | ||||||||
\(292\) | 58.1550 | 3.40327 | ||||||||
\(293\) | −17.6806 | −1.03291 | −0.516457 | − | 0.856313i | \(-0.672749\pi\) | ||||
−0.516457 | + | 0.856313i | \(0.672749\pi\) | |||||||
\(294\) | −141.487 | −8.25168 | ||||||||
\(295\) | −3.57617 | −0.208213 | ||||||||
\(296\) | −5.47189 | −0.318047 | ||||||||
\(297\) | −20.7548 | −1.20432 | ||||||||
\(298\) | −53.4244 | −3.09479 | ||||||||
\(299\) | −7.00017 | −0.404831 | ||||||||
\(300\) | 28.1082 | 1.62283 | ||||||||
\(301\) | 21.1277 | 1.21778 | ||||||||
\(302\) | 44.6382 | 2.56864 | ||||||||
\(303\) | 19.2993 | 1.10872 | ||||||||
\(304\) | −74.1675 | −4.25380 | ||||||||
\(305\) | 17.5420 | 1.00445 | ||||||||
\(306\) | 58.7250 | 3.35708 | ||||||||
\(307\) | −22.2929 | −1.27232 | −0.636161 | − | 0.771557i | \(-0.719478\pi\) | ||||
−0.636161 | + | 0.771557i | \(0.719478\pi\) | |||||||
\(308\) | −64.8784 | −3.69679 | ||||||||
\(309\) | 10.8616 | 0.617896 | ||||||||
\(310\) | −75.5197 | −4.28923 | ||||||||
\(311\) | −22.5361 | −1.27791 | −0.638953 | − | 0.769246i | \(-0.720632\pi\) | ||||
−0.638953 | + | 0.769246i | \(0.720632\pi\) | |||||||
\(312\) | 39.4518 | 2.23352 | ||||||||
\(313\) | −12.9239 | −0.730501 | −0.365251 | − | 0.930909i | \(-0.619017\pi\) | ||||
−0.365251 | + | 0.930909i | \(0.619017\pi\) | |||||||
\(314\) | 51.3001 | 2.89503 | ||||||||
\(315\) | −75.4533 | −4.25131 | ||||||||
\(316\) | −88.0925 | −4.95559 | ||||||||
\(317\) | −2.07544 | −0.116568 | −0.0582841 | − | 0.998300i | \(-0.518563\pi\) | ||||
−0.0582841 | + | 0.998300i | \(0.518563\pi\) | |||||||
\(318\) | −48.4995 | −2.71972 | ||||||||
\(319\) | 5.16417 | 0.289138 | ||||||||
\(320\) | −80.6087 | −4.50616 | ||||||||
\(321\) | −0.635836 | −0.0354889 | ||||||||
\(322\) | −68.3632 | −3.80973 | ||||||||
\(323\) | 17.7354 | 0.986824 | ||||||||
\(324\) | 44.7711 | 2.48728 | ||||||||
\(325\) | −2.37019 | −0.131474 | ||||||||
\(326\) | −28.4223 | −1.57417 | ||||||||
\(327\) | −47.4033 | −2.62141 | ||||||||
\(328\) | 58.0532 | 3.20545 | ||||||||
\(329\) | −2.06116 | −0.113636 | ||||||||
\(330\) | −50.6884 | −2.79031 | ||||||||
\(331\) | 19.0950 | 1.04955 | 0.524777 | − | 0.851240i | \(-0.324149\pi\) | ||||
0.524777 | + | 0.851240i | \(0.324149\pi\) | |||||||
\(332\) | −99.0428 | −5.43568 | ||||||||
\(333\) | 3.37815 | 0.185121 | ||||||||
\(334\) | 31.8489 | 1.74269 | ||||||||
\(335\) | −34.6146 | −1.89120 | ||||||||
\(336\) | 223.592 | 12.1979 | ||||||||
\(337\) | −26.1758 | −1.42588 | −0.712942 | − | 0.701223i | \(-0.752638\pi\) | ||||
−0.712942 | + | 0.701223i | \(0.752638\pi\) | |||||||
\(338\) | 30.3560 | 1.65115 | ||||||||
\(339\) | 2.98404 | 0.162071 | ||||||||
\(340\) | 51.7213 | 2.80498 | ||||||||
\(341\) | 25.4945 | 1.38060 | ||||||||
\(342\) | 78.9007 | 4.26646 | ||||||||
\(343\) | 50.8968 | 2.74817 | ||||||||
\(344\) | −40.9737 | −2.20916 | ||||||||
\(345\) | −39.1562 | −2.10810 | ||||||||
\(346\) | 1.15774 | 0.0622402 | ||||||||
\(347\) | 16.6279 | 0.892631 | 0.446316 | − | 0.894876i | \(-0.352736\pi\) | ||||
0.446316 | + | 0.894876i | \(0.352736\pi\) | |||||||
\(348\) | −35.3532 | −1.89513 | ||||||||
\(349\) | −24.3400 | −1.30289 | −0.651444 | − | 0.758697i | \(-0.725836\pi\) | ||||
−0.651444 | + | 0.758697i | \(0.725836\pi\) | |||||||
\(350\) | −23.1471 | −1.23726 | ||||||||
\(351\) | −11.9811 | −0.639503 | ||||||||
\(352\) | 53.7946 | 2.86726 | ||||||||
\(353\) | −7.44748 | −0.396389 | −0.198195 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198195 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(354\) | −11.2736 | −0.599185 | ||||||||
\(355\) | −2.59125 | −0.137529 | ||||||||
\(356\) | −81.8093 | −4.33588 | ||||||||
\(357\) | −53.4666 | −2.82975 | ||||||||
\(358\) | −12.2931 | −0.649711 | ||||||||
\(359\) | −8.37028 | −0.441767 | −0.220883 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220883 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(360\) | 146.330 | 7.71224 | ||||||||
\(361\) | 4.82865 | 0.254139 | ||||||||
\(362\) | 27.9945 | 1.47136 | ||||||||
\(363\) | −15.7127 | −0.824701 | ||||||||
\(364\) | −37.4522 | −1.96303 | ||||||||
\(365\) | −27.4302 | −1.43576 | ||||||||
\(366\) | 55.2998 | 2.89057 | ||||||||
\(367\) | 26.8316 | 1.40060 | 0.700300 | − | 0.713849i | \(-0.253050\pi\) | ||||
0.700300 | + | 0.713849i | \(0.253050\pi\) | |||||||
\(368\) | 76.9397 | 4.01076 | ||||||||
\(369\) | −35.8400 | −1.86575 | ||||||||
\(370\) | 4.05841 | 0.210987 | ||||||||
\(371\) | 29.2799 | 1.52014 | ||||||||
\(372\) | −174.532 | −9.04904 | ||||||||
\(373\) | 26.2719 | 1.36031 | 0.680153 | − | 0.733070i | \(-0.261913\pi\) | ||||
0.680153 | + | 0.733070i | \(0.261913\pi\) | |||||||
\(374\) | −23.8169 | −1.23154 | ||||||||
\(375\) | 25.4041 | 1.31186 | ||||||||
\(376\) | 3.99729 | 0.206144 | ||||||||
\(377\) | 2.98111 | 0.153535 | ||||||||
\(378\) | −117.006 | −6.01816 | ||||||||
\(379\) | −11.3835 | −0.584729 | −0.292364 | − | 0.956307i | \(-0.594442\pi\) | ||||
−0.292364 | + | 0.956307i | \(0.594442\pi\) | |||||||
\(380\) | 69.4909 | 3.56481 | ||||||||
\(381\) | 40.3579 | 2.06760 | ||||||||
\(382\) | −22.7680 | −1.16491 | ||||||||
\(383\) | −22.3877 | −1.14396 | −0.571979 | − | 0.820268i | \(-0.693824\pi\) | ||||
−0.571979 | + | 0.820268i | \(0.693824\pi\) | |||||||
\(384\) | −120.043 | −6.12594 | ||||||||
\(385\) | 30.6014 | 1.55959 | ||||||||
\(386\) | 2.12809 | 0.108317 | ||||||||
\(387\) | 25.2957 | 1.28585 | ||||||||
\(388\) | 45.5940 | 2.31469 | ||||||||
\(389\) | −12.8779 | −0.652937 | −0.326469 | − | 0.945208i | \(-0.605859\pi\) | ||||
−0.326469 | + | 0.945208i | \(0.605859\pi\) | |||||||
\(390\) | −29.2608 | −1.48168 | ||||||||
\(391\) | −18.3983 | −0.930442 | ||||||||
\(392\) | −165.654 | −8.36680 | ||||||||
\(393\) | −33.5416 | −1.69195 | ||||||||
\(394\) | 26.8255 | 1.35145 | ||||||||
\(395\) | 41.5509 | 2.09065 | ||||||||
\(396\) | −77.6775 | −3.90344 | ||||||||
\(397\) | −32.6367 | −1.63799 | −0.818995 | − | 0.573801i | \(-0.805468\pi\) | ||||
−0.818995 | + | 0.573801i | \(0.805468\pi\) | |||||||
\(398\) | −18.8311 | −0.943918 | ||||||||
\(399\) | −71.8358 | −3.59629 | ||||||||
\(400\) | 26.0510 | 1.30255 | ||||||||
\(401\) | 11.6239 | 0.580472 | 0.290236 | − | 0.956955i | \(-0.406266\pi\) | ||||
0.290236 | + | 0.956955i | \(0.406266\pi\) | |||||||
\(402\) | −109.120 | −5.44240 | ||||||||
\(403\) | 14.7172 | 0.733114 | ||||||||
\(404\) | 35.5309 | 1.76773 | ||||||||
\(405\) | −21.1173 | −1.04933 | ||||||||
\(406\) | 29.1133 | 1.44487 | ||||||||
\(407\) | −1.37007 | −0.0679117 | ||||||||
\(408\) | 103.690 | 5.13341 | ||||||||
\(409\) | −9.19206 | −0.454518 | −0.227259 | − | 0.973834i | \(-0.572976\pi\) | ||||
−0.227259 | + | 0.973834i | \(0.572976\pi\) | |||||||
\(410\) | −43.0571 | −2.12644 | ||||||||
\(411\) | −18.3096 | −0.903145 | ||||||||
\(412\) | 19.9967 | 0.985167 | ||||||||
\(413\) | 6.80605 | 0.334904 | ||||||||
\(414\) | −81.8498 | −4.02270 | ||||||||
\(415\) | 46.7158 | 2.29319 | ||||||||
\(416\) | 31.0539 | 1.52254 | ||||||||
\(417\) | −45.4680 | −2.22658 | ||||||||
\(418\) | −31.9996 | −1.56515 | ||||||||
\(419\) | 36.7387 | 1.79480 | 0.897402 | − | 0.441214i | \(-0.145452\pi\) | ||||
0.897402 | + | 0.441214i | \(0.145452\pi\) | |||||||
\(420\) | −209.493 | −10.2222 | ||||||||
\(421\) | 28.3554 | 1.38196 | 0.690980 | − | 0.722874i | \(-0.257179\pi\) | ||||
0.690980 | + | 0.722874i | \(0.257179\pi\) | |||||||
\(422\) | −48.4130 | −2.35671 | ||||||||
\(423\) | −2.46778 | −0.119988 | ||||||||
\(424\) | −56.7837 | −2.75766 | ||||||||
\(425\) | −6.22948 | −0.302174 | ||||||||
\(426\) | −8.16872 | −0.395776 | ||||||||
\(427\) | −33.3854 | −1.61563 | ||||||||
\(428\) | −1.17060 | −0.0565832 | ||||||||
\(429\) | 9.87807 | 0.476918 | ||||||||
\(430\) | 30.3896 | 1.46552 | ||||||||
\(431\) | −15.0428 | −0.724587 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(432\) | 131.685 | 6.33571 | ||||||||
\(433\) | 21.8847 | 1.05171 | 0.525856 | − | 0.850574i | \(-0.323745\pi\) | ||||
0.525856 | + | 0.850574i | \(0.323745\pi\) | |||||||
\(434\) | 143.727 | 6.89910 | ||||||||
\(435\) | 16.6751 | 0.799512 | ||||||||
\(436\) | −87.2715 | −4.17955 | ||||||||
\(437\) | −24.7193 | −1.18248 | ||||||||
\(438\) | −86.4714 | −4.13176 | ||||||||
\(439\) | −0.573806 | −0.0273862 | −0.0136931 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136931 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(440\) | −59.3465 | −2.82923 | ||||||||
\(441\) | 102.269 | 4.86995 | ||||||||
\(442\) | −13.7488 | −0.653962 | ||||||||
\(443\) | 26.0554 | 1.23793 | 0.618965 | − | 0.785419i | \(-0.287552\pi\) | ||||
0.618965 | + | 0.785419i | \(0.287552\pi\) | |||||||
\(444\) | 9.37928 | 0.445121 | ||||||||
\(445\) | 38.5873 | 1.82921 | ||||||||
\(446\) | 41.0350 | 1.94306 | ||||||||
\(447\) | 58.2364 | 2.75449 | ||||||||
\(448\) | 153.412 | 7.24803 | ||||||||
\(449\) | 20.9311 | 0.987800 | 0.493900 | − | 0.869519i | \(-0.335571\pi\) | ||||
0.493900 | + | 0.869519i | \(0.335571\pi\) | |||||||
\(450\) | −27.7135 | −1.30643 | ||||||||
\(451\) | 14.5355 | 0.684451 | ||||||||
\(452\) | 5.49374 | 0.258404 | ||||||||
\(453\) | −48.6588 | −2.28619 | ||||||||
\(454\) | −20.8231 | −0.977276 | ||||||||
\(455\) | 17.6652 | 0.828159 | ||||||||
\(456\) | 139.314 | 6.52397 | ||||||||
\(457\) | −9.02122 | −0.421995 | −0.210997 | − | 0.977487i | \(-0.567671\pi\) | ||||
−0.210997 | + | 0.977487i | \(0.567671\pi\) | |||||||
\(458\) | 78.7332 | 3.67896 | ||||||||
\(459\) | −31.4894 | −1.46980 | ||||||||
\(460\) | −72.0882 | −3.36113 | ||||||||
\(461\) | 26.4397 | 1.23142 | 0.615711 | − | 0.787972i | \(-0.288869\pi\) | ||||
0.615711 | + | 0.787972i | \(0.288869\pi\) | |||||||
\(462\) | 96.4686 | 4.48812 | ||||||||
\(463\) | 9.01568 | 0.418994 | 0.209497 | − | 0.977809i | \(-0.432817\pi\) | ||||
0.209497 | + | 0.977809i | \(0.432817\pi\) | |||||||
\(464\) | −32.7657 | −1.52111 | ||||||||
\(465\) | 82.3219 | 3.81759 | ||||||||
\(466\) | 41.7722 | 1.93506 | ||||||||
\(467\) | 14.7630 | 0.683149 | 0.341574 | − | 0.939855i | \(-0.389040\pi\) | ||||
0.341574 | + | 0.939855i | \(0.389040\pi\) | |||||||
\(468\) | −44.8408 | −2.07276 | ||||||||
\(469\) | 65.8774 | 3.04193 | ||||||||
\(470\) | −2.96472 | −0.136753 | ||||||||
\(471\) | −55.9208 | −2.57670 | ||||||||
\(472\) | −13.1992 | −0.607544 | ||||||||
\(473\) | −10.2591 | −0.471715 | ||||||||
\(474\) | 130.986 | 6.01638 | ||||||||
\(475\) | −8.36970 | −0.384028 | ||||||||
\(476\) | −98.4343 | −4.51173 | ||||||||
\(477\) | 35.0562 | 1.60511 | ||||||||
\(478\) | −16.4372 | −0.751822 | ||||||||
\(479\) | −10.7631 | −0.491781 | −0.245890 | − | 0.969298i | \(-0.579080\pi\) | ||||
−0.245890 | + | 0.969298i | \(0.579080\pi\) | |||||||
\(480\) | 173.703 | 7.92843 | ||||||||
\(481\) | −0.790896 | −0.0360618 | ||||||||
\(482\) | −31.3129 | −1.42626 | ||||||||
\(483\) | 74.5208 | 3.39081 | ||||||||
\(484\) | −28.9277 | −1.31489 | ||||||||
\(485\) | −21.5055 | −0.976514 | ||||||||
\(486\) | 4.60696 | 0.208976 | ||||||||
\(487\) | 0.892579 | 0.0404466 | 0.0202233 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202233 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(488\) | 64.7456 | 2.93089 | ||||||||
\(489\) | 30.9824 | 1.40107 | ||||||||
\(490\) | 122.863 | 5.55039 | ||||||||
\(491\) | −24.5933 | −1.10988 | −0.554941 | − | 0.831890i | \(-0.687259\pi\) | ||||
−0.554941 | + | 0.831890i | \(0.687259\pi\) | |||||||
\(492\) | −99.5081 | −4.48617 | ||||||||
\(493\) | 7.83514 | 0.352877 | ||||||||
\(494\) | −18.4723 | −0.831110 | ||||||||
\(495\) | 36.6384 | 1.64677 | ||||||||
\(496\) | −161.758 | −7.26314 | ||||||||
\(497\) | 4.93159 | 0.221212 | ||||||||
\(498\) | 147.268 | 6.59923 | ||||||||
\(499\) | 4.19706 | 0.187886 | 0.0939430 | − | 0.995578i | \(-0.470053\pi\) | ||||
0.0939430 | + | 0.995578i | \(0.470053\pi\) | |||||||
\(500\) | 46.7700 | 2.09162 | ||||||||
\(501\) | −34.7175 | −1.55107 | ||||||||
\(502\) | 61.0874 | 2.72646 | ||||||||
\(503\) | 15.7243 | 0.701110 | 0.350555 | − | 0.936542i | \(-0.385993\pi\) | ||||
0.350555 | + | 0.936542i | \(0.385993\pi\) | |||||||
\(504\) | −278.490 | −12.4049 | ||||||||
\(505\) | −16.7590 | −0.745764 | ||||||||
\(506\) | 33.1956 | 1.47573 | ||||||||
\(507\) | −33.0902 | −1.46959 | ||||||||
\(508\) | 74.3007 | 3.29656 | ||||||||
\(509\) | −27.9802 | −1.24020 | −0.620099 | − | 0.784523i | \(-0.712908\pi\) | ||||
−0.620099 | + | 0.784523i | \(0.712908\pi\) | |||||||
\(510\) | −76.9051 | −3.40541 | ||||||||
\(511\) | 52.2042 | 2.30938 | ||||||||
\(512\) | −50.6908 | −2.24024 | ||||||||
\(513\) | −42.3080 | −1.86795 | ||||||||
\(514\) | 9.94534 | 0.438670 | ||||||||
\(515\) | −9.43192 | −0.415620 | ||||||||
\(516\) | 70.2325 | 3.09181 | ||||||||
\(517\) | 1.00085 | 0.0440175 | ||||||||
\(518\) | −7.72383 | −0.339366 | ||||||||
\(519\) | −1.26201 | −0.0553963 | ||||||||
\(520\) | −34.2588 | −1.50235 | ||||||||
\(521\) | −23.8689 | −1.04571 | −0.522857 | − | 0.852421i | \(-0.675134\pi\) | ||||
−0.522857 | + | 0.852421i | \(0.675134\pi\) | |||||||
\(522\) | 34.8567 | 1.52564 | ||||||||
\(523\) | −5.58185 | −0.244077 | −0.122039 | − | 0.992525i | \(-0.538943\pi\) | ||||
−0.122039 | + | 0.992525i | \(0.538943\pi\) | |||||||
\(524\) | −61.7515 | −2.69763 | ||||||||
\(525\) | 25.2320 | 1.10121 | ||||||||
\(526\) | 40.7382 | 1.77627 | ||||||||
\(527\) | 38.6805 | 1.68495 | ||||||||
\(528\) | −108.571 | −4.72495 | ||||||||
\(529\) | 2.64321 | 0.114922 | ||||||||
\(530\) | 42.1155 | 1.82938 | ||||||||
\(531\) | 8.14874 | 0.353625 | ||||||||
\(532\) | −132.253 | −5.73389 | ||||||||
\(533\) | 8.39090 | 0.363450 | ||||||||
\(534\) | 121.643 | 5.26402 | ||||||||
\(535\) | 0.552142 | 0.0238712 | ||||||||
\(536\) | −127.758 | −5.51832 | ||||||||
\(537\) | 13.4004 | 0.578269 | ||||||||
\(538\) | −18.0896 | −0.779899 | ||||||||
\(539\) | −41.4770 | −1.78654 | ||||||||
\(540\) | −123.382 | −5.30951 | ||||||||
\(541\) | 9.68449 | 0.416369 | 0.208184 | − | 0.978090i | \(-0.433245\pi\) | ||||
0.208184 | + | 0.978090i | \(0.433245\pi\) | |||||||
\(542\) | −2.92421 | −0.125606 | ||||||||
\(543\) | −30.5160 | −1.30957 | ||||||||
\(544\) | 81.6178 | 3.49933 | ||||||||
\(545\) | 41.1637 | 1.76326 | ||||||||
\(546\) | 55.6882 | 2.38324 | ||||||||
\(547\) | −4.04586 | −0.172988 | −0.0864942 | − | 0.996252i | \(-0.527566\pi\) | ||||
−0.0864942 | + | 0.996252i | \(0.527566\pi\) | |||||||
\(548\) | −33.7087 | −1.43997 | ||||||||
\(549\) | −39.9716 | −1.70595 | ||||||||
\(550\) | 11.2397 | 0.479262 | ||||||||
\(551\) | 10.5270 | 0.448466 | ||||||||
\(552\) | −144.521 | −6.15122 | ||||||||
\(553\) | −79.0784 | −3.36275 | ||||||||
\(554\) | −73.8313 | −3.13679 | ||||||||
\(555\) | −4.42396 | −0.187786 | ||||||||
\(556\) | −83.7085 | −3.55003 | ||||||||
\(557\) | 20.4738 | 0.867503 | 0.433751 | − | 0.901033i | \(-0.357190\pi\) | ||||
0.433751 | + | 0.901033i | \(0.357190\pi\) | |||||||
\(558\) | 172.081 | 7.28476 | ||||||||
\(559\) | −5.92227 | −0.250485 | ||||||||
\(560\) | −194.160 | −8.20478 | ||||||||
\(561\) | 25.9622 | 1.09612 | ||||||||
\(562\) | 16.8875 | 0.712354 | ||||||||
\(563\) | 32.7454 | 1.38005 | 0.690027 | − | 0.723784i | \(-0.257599\pi\) | ||||
0.690027 | + | 0.723784i | \(0.257599\pi\) | |||||||
\(564\) | −6.85169 | −0.288508 | ||||||||
\(565\) | −2.59125 | −0.109015 | ||||||||
\(566\) | −23.5931 | −0.991690 | ||||||||
\(567\) | 40.1899 | 1.68782 | ||||||||
\(568\) | −9.56402 | −0.401297 | ||||||||
\(569\) | 17.3002 | 0.725264 | 0.362632 | − | 0.931932i | \(-0.381878\pi\) | ||||
0.362632 | + | 0.931932i | \(0.381878\pi\) | |||||||
\(570\) | −103.327 | −4.32789 | ||||||||
\(571\) | 21.8202 | 0.913148 | 0.456574 | − | 0.889686i | \(-0.349076\pi\) | ||||
0.456574 | + | 0.889686i | \(0.349076\pi\) | |||||||
\(572\) | 18.1860 | 0.760393 | ||||||||
\(573\) | 24.8188 | 1.03682 | ||||||||
\(574\) | 81.9449 | 3.42031 | ||||||||
\(575\) | 8.68253 | 0.362087 | ||||||||
\(576\) | 183.677 | 7.65319 | ||||||||
\(577\) | −4.93026 | −0.205249 | −0.102625 | − | 0.994720i | \(-0.532724\pi\) | ||||
−0.102625 | + | 0.994720i | \(0.532724\pi\) | |||||||
\(578\) | 10.4016 | 0.432651 | ||||||||
\(579\) | −2.31977 | −0.0964063 | ||||||||
\(580\) | 30.6997 | 1.27473 | ||||||||
\(581\) | −88.9081 | −3.68853 | ||||||||
\(582\) | −67.7944 | −2.81017 | ||||||||
\(583\) | −14.2177 | −0.588836 | ||||||||
\(584\) | −101.242 | −4.18941 | ||||||||
\(585\) | 21.1502 | 0.874453 | ||||||||
\(586\) | 48.4002 | 1.99939 | ||||||||
\(587\) | 35.4082 | 1.46145 | 0.730725 | − | 0.682672i | \(-0.239182\pi\) | ||||
0.730725 | + | 0.682672i | \(0.239182\pi\) | |||||||
\(588\) | 283.945 | 11.7097 | ||||||||
\(589\) | 51.9698 | 2.14138 | ||||||||
\(590\) | 9.78966 | 0.403034 | ||||||||
\(591\) | −29.2417 | −1.20284 | ||||||||
\(592\) | 8.69283 | 0.357273 | ||||||||
\(593\) | 2.30812 | 0.0947830 | 0.0473915 | − | 0.998876i | \(-0.484909\pi\) | ||||
0.0473915 | + | 0.998876i | \(0.484909\pi\) | |||||||
\(594\) | 56.8156 | 2.33117 | ||||||||
\(595\) | 46.4289 | 1.90340 | ||||||||
\(596\) | 107.216 | 4.39173 | ||||||||
\(597\) | 20.5273 | 0.840125 | ||||||||
\(598\) | 19.1628 | 0.783624 | ||||||||
\(599\) | 17.3387 | 0.708441 | 0.354220 | − | 0.935162i | \(-0.384746\pi\) | ||||
0.354220 | + | 0.935162i | \(0.384746\pi\) | |||||||
\(600\) | −48.9333 | −1.99769 | ||||||||
\(601\) | −26.6565 | −1.08734 | −0.543672 | − | 0.839298i | \(-0.682966\pi\) | ||||
−0.543672 | + | 0.839298i | \(0.682966\pi\) | |||||||
\(602\) | −57.8365 | −2.35724 | ||||||||
\(603\) | 78.8735 | 3.21198 | ||||||||
\(604\) | −89.5830 | −3.64508 | ||||||||
\(605\) | 13.6444 | 0.554724 | ||||||||
\(606\) | −52.8313 | −2.14612 | ||||||||
\(607\) | −21.7413 | −0.882453 | −0.441227 | − | 0.897396i | \(-0.645457\pi\) | ||||
−0.441227 | + | 0.897396i | \(0.645457\pi\) | |||||||
\(608\) | 109.659 | 4.44725 | ||||||||
\(609\) | −31.7356 | −1.28599 | ||||||||
\(610\) | −48.0207 | −1.94430 | ||||||||
\(611\) | 0.577760 | 0.0233737 | ||||||||
\(612\) | −117.853 | −4.76394 | ||||||||
\(613\) | 13.4888 | 0.544809 | 0.272404 | − | 0.962183i | \(-0.412181\pi\) | ||||
0.272404 | + | 0.962183i | \(0.412181\pi\) | |||||||
\(614\) | 61.0261 | 2.46281 | ||||||||
\(615\) | 46.9353 | 1.89261 | ||||||||
\(616\) | 112.946 | 4.55074 | ||||||||
\(617\) | −30.6207 | −1.23274 | −0.616371 | − | 0.787456i | \(-0.711398\pi\) | ||||
−0.616371 | + | 0.787456i | \(0.711398\pi\) | |||||||
\(618\) | −29.7334 | −1.19605 | ||||||||
\(619\) | 28.0471 | 1.12731 | 0.563654 | − | 0.826011i | \(-0.309395\pi\) | ||||
0.563654 | + | 0.826011i | \(0.309395\pi\) | |||||||
\(620\) | 151.558 | 6.08672 | ||||||||
\(621\) | 43.8894 | 1.76122 | ||||||||
\(622\) | 61.6919 | 2.47362 | ||||||||
\(623\) | −73.4381 | −2.94223 | ||||||||
\(624\) | −62.6746 | −2.50899 | ||||||||
\(625\) | −30.6331 | −1.22533 | ||||||||
\(626\) | 35.3788 | 1.41402 | ||||||||
\(627\) | 34.8818 | 1.39305 | ||||||||
\(628\) | −102.953 | −4.10826 | ||||||||
\(629\) | −2.07868 | −0.0828825 | ||||||||
\(630\) | 206.551 | 8.22920 | ||||||||
\(631\) | −23.1214 | −0.920447 | −0.460223 | − | 0.887803i | \(-0.652231\pi\) | ||||
−0.460223 | + | 0.887803i | \(0.652231\pi\) | |||||||
\(632\) | 153.360 | 6.10032 | ||||||||
\(633\) | 52.7736 | 2.09756 | ||||||||
\(634\) | 5.68144 | 0.225639 | ||||||||
\(635\) | −35.0456 | −1.39074 | ||||||||
\(636\) | 97.3321 | 3.85947 | ||||||||
\(637\) | −23.9433 | −0.948670 | ||||||||
\(638\) | −14.1368 | −0.559680 | ||||||||
\(639\) | 5.90448 | 0.233578 | ||||||||
\(640\) | 104.242 | 4.12054 | ||||||||
\(641\) | −25.8997 | −1.02298 | −0.511488 | − | 0.859291i | \(-0.670905\pi\) | ||||
−0.511488 | + | 0.859291i | \(0.670905\pi\) | |||||||
\(642\) | 1.74058 | 0.0686953 | ||||||||
\(643\) | 15.8598 | 0.625451 | 0.312726 | − | 0.949844i | \(-0.398758\pi\) | ||||
0.312726 | + | 0.949844i | \(0.398758\pi\) | |||||||
\(644\) | 137.196 | 5.40628 | ||||||||
\(645\) | −33.1268 | −1.30437 | ||||||||
\(646\) | −48.5501 | −1.91018 | ||||||||
\(647\) | 23.2124 | 0.912574 | 0.456287 | − | 0.889833i | \(-0.349179\pi\) | ||||
0.456287 | + | 0.889833i | \(0.349179\pi\) | |||||||
\(648\) | −77.9417 | −3.06184 | ||||||||
\(649\) | −3.30487 | −0.129727 | ||||||||
\(650\) | 6.48832 | 0.254493 | ||||||||
\(651\) | −156.672 | −6.14047 | ||||||||
\(652\) | 57.0399 | 2.23385 | ||||||||
\(653\) | 20.1594 | 0.788900 | 0.394450 | − | 0.918917i | \(-0.370935\pi\) | ||||
0.394450 | + | 0.918917i | \(0.370935\pi\) | |||||||
\(654\) | 129.765 | 5.07422 | ||||||||
\(655\) | 29.1265 | 1.13807 | ||||||||
\(656\) | −92.2253 | −3.60079 | ||||||||
\(657\) | 62.5030 | 2.43847 | ||||||||
\(658\) | 5.64237 | 0.219962 | ||||||||
\(659\) | 15.8697 | 0.618196 | 0.309098 | − | 0.951030i | \(-0.399973\pi\) | ||||
0.309098 | + | 0.951030i | \(0.399973\pi\) | |||||||
\(660\) | 101.725 | 3.95964 | ||||||||
\(661\) | 35.7403 | 1.39014 | 0.695068 | − | 0.718944i | \(-0.255374\pi\) | ||||
0.695068 | + | 0.718944i | \(0.255374\pi\) | |||||||
\(662\) | −52.2719 | −2.03161 | ||||||||
\(663\) | 14.9871 | 0.582052 | ||||||||
\(664\) | 172.423 | 6.69130 | ||||||||
\(665\) | 62.3801 | 2.41900 | ||||||||
\(666\) | −9.24758 | −0.358336 | ||||||||
\(667\) | −10.9205 | −0.422843 | ||||||||
\(668\) | −63.9165 | −2.47300 | ||||||||
\(669\) | −44.7310 | −1.72940 | ||||||||
\(670\) | 94.7564 | 3.66076 | ||||||||
\(671\) | 16.2112 | 0.625826 | ||||||||
\(672\) | −330.586 | −12.7526 | ||||||||
\(673\) | 40.3804 | 1.55655 | 0.778276 | − | 0.627923i | \(-0.216095\pi\) | ||||
0.778276 | + | 0.627923i | \(0.216095\pi\) | |||||||
\(674\) | 71.6554 | 2.76006 | ||||||||
\(675\) | 14.8605 | 0.571981 | ||||||||
\(676\) | −60.9205 | −2.34310 | ||||||||
\(677\) | 36.8301 | 1.41550 | 0.707748 | − | 0.706465i | \(-0.249711\pi\) | ||||
0.707748 | + | 0.706465i | \(0.249711\pi\) | |||||||
\(678\) | −8.16872 | −0.313718 | ||||||||
\(679\) | 40.9286 | 1.57069 | ||||||||
\(680\) | −90.0412 | −3.45292 | ||||||||
\(681\) | 22.6986 | 0.869814 | ||||||||
\(682\) | −69.7904 | −2.67241 | ||||||||
\(683\) | 3.99781 | 0.152972 | 0.0764860 | − | 0.997071i | \(-0.475630\pi\) | ||||
0.0764860 | + | 0.997071i | \(0.475630\pi\) | |||||||
\(684\) | −158.343 | −6.05441 | ||||||||
\(685\) | 15.8995 | 0.607489 | ||||||||
\(686\) | −139.328 | −5.31959 | ||||||||
\(687\) | −85.8248 | −3.27442 | ||||||||
\(688\) | 65.0923 | 2.48162 | ||||||||
\(689\) | −8.20741 | −0.312677 | ||||||||
\(690\) | 107.189 | 4.08061 | ||||||||
\(691\) | 1.66405 | 0.0633035 | 0.0316517 | − | 0.999499i | \(-0.489923\pi\) | ||||
0.0316517 | + | 0.999499i | \(0.489923\pi\) | |||||||
\(692\) | −2.32342 | −0.0883233 | ||||||||
\(693\) | −69.7291 | −2.64879 | ||||||||
\(694\) | −45.5183 | −1.72785 | ||||||||
\(695\) | 39.4831 | 1.49768 | ||||||||
\(696\) | 61.5460 | 2.33290 | ||||||||
\(697\) | 22.0535 | 0.835335 | ||||||||
\(698\) | 66.6299 | 2.52198 | ||||||||
\(699\) | −45.5347 | −1.72228 | ||||||||
\(700\) | 46.4532 | 1.75576 | ||||||||
\(701\) | −46.8137 | −1.76813 | −0.884065 | − | 0.467364i | \(-0.845204\pi\) | ||||
−0.884065 | + | 0.467364i | \(0.845204\pi\) | |||||||
\(702\) | 32.7978 | 1.23787 | ||||||||
\(703\) | −2.79284 | −0.105334 | ||||||||
\(704\) | −74.4933 | −2.80757 | ||||||||
\(705\) | 3.23176 | 0.121715 | ||||||||
\(706\) | 20.3872 | 0.767284 | ||||||||
\(707\) | 31.8951 | 1.19954 | ||||||||
\(708\) | 22.6246 | 0.850285 | ||||||||
\(709\) | −30.5970 | −1.14909 | −0.574547 | − | 0.818471i | \(-0.694822\pi\) | ||||
−0.574547 | + | 0.818471i | \(0.694822\pi\) | |||||||
\(710\) | 7.09348 | 0.266213 | ||||||||
\(711\) | −94.6788 | −3.55073 | ||||||||
\(712\) | 142.421 | 5.33746 | ||||||||
\(713\) | −53.9122 | −2.01903 | ||||||||
\(714\) | 146.363 | 5.47751 | ||||||||
\(715\) | −8.57783 | −0.320793 | ||||||||
\(716\) | 24.6707 | 0.921986 | ||||||||
\(717\) | 17.9178 | 0.669152 | ||||||||
\(718\) | 22.9134 | 0.855120 | ||||||||
\(719\) | 32.6023 | 1.21586 | 0.607930 | − | 0.793991i | \(-0.292000\pi\) | ||||
0.607930 | + | 0.793991i | \(0.292000\pi\) | |||||||
\(720\) | −232.464 | −8.66342 | ||||||||
\(721\) | 17.9505 | 0.668513 | ||||||||
\(722\) | −13.2183 | −0.491933 | ||||||||
\(723\) | 34.1333 | 1.26943 | ||||||||
\(724\) | −56.1812 | −2.08796 | ||||||||
\(725\) | −3.69756 | −0.137324 | ||||||||
\(726\) | 43.0129 | 1.59636 | ||||||||
\(727\) | 2.54601 | 0.0944265 | 0.0472132 | − | 0.998885i | \(-0.484966\pi\) | ||||
0.0472132 | + | 0.998885i | \(0.484966\pi\) | |||||||
\(728\) | 65.2003 | 2.41649 | ||||||||
\(729\) | −29.4703 | −1.09149 | ||||||||
\(730\) | 75.0893 | 2.77918 | ||||||||
\(731\) | −15.5653 | −0.575703 | ||||||||
\(732\) | −110.979 | −4.10192 | ||||||||
\(733\) | −3.88191 | −0.143382 | −0.0716908 | − | 0.997427i | \(-0.522839\pi\) | ||||
−0.0716908 | + | 0.997427i | \(0.522839\pi\) | |||||||
\(734\) | −73.4508 | −2.71112 | ||||||||
\(735\) | −133.929 | −4.94006 | ||||||||
\(736\) | −113.757 | −4.19315 | ||||||||
\(737\) | −31.9885 | −1.17831 | ||||||||
\(738\) | 98.1108 | 3.61151 | ||||||||
\(739\) | −50.3887 | −1.85358 | −0.926789 | − | 0.375583i | \(-0.877443\pi\) | ||||
−0.926789 | + | 0.375583i | \(0.877443\pi\) | |||||||
\(740\) | −8.14469 | −0.299405 | ||||||||
\(741\) | 20.1362 | 0.739720 | ||||||||
\(742\) | −80.1529 | −2.94251 | ||||||||
\(743\) | 2.79949 | 0.102703 | 0.0513517 | − | 0.998681i | \(-0.483647\pi\) | ||||
0.0513517 | + | 0.998681i | \(0.483647\pi\) | |||||||
\(744\) | 303.841 | 11.1393 | ||||||||
\(745\) | −50.5708 | −1.85277 | ||||||||
\(746\) | −71.9185 | −2.63312 | ||||||||
\(747\) | −106.448 | −3.89472 | ||||||||
\(748\) | 47.7975 | 1.74765 | ||||||||
\(749\) | −1.05082 | −0.0383961 | ||||||||
\(750\) | −69.5430 | −2.53935 | ||||||||
\(751\) | −42.3467 | −1.54525 | −0.772626 | − | 0.634861i | \(-0.781057\pi\) | ||||
−0.772626 | + | 0.634861i | \(0.781057\pi\) | |||||||
\(752\) | −6.35023 | −0.231569 | ||||||||
\(753\) | −66.5896 | −2.42666 | ||||||||
\(754\) | −8.16070 | −0.297195 | ||||||||
\(755\) | 42.2539 | 1.53778 | ||||||||
\(756\) | 234.816 | 8.54019 | ||||||||
\(757\) | 30.1004 | 1.09402 | 0.547008 | − | 0.837127i | \(-0.315767\pi\) | ||||
0.547008 | + | 0.837127i | \(0.315767\pi\) | |||||||
\(758\) | 31.1619 | 1.13185 | ||||||||
\(759\) | −36.1856 | −1.31345 | ||||||||
\(760\) | −120.976 | −4.38827 | ||||||||
\(761\) | 41.5038 | 1.50451 | 0.752255 | − | 0.658872i | \(-0.228966\pi\) | ||||
0.752255 | + | 0.658872i | \(0.228966\pi\) | |||||||
\(762\) | −110.479 | −4.00222 | ||||||||
\(763\) | −78.3413 | −2.83615 | ||||||||
\(764\) | 45.6924 | 1.65309 | ||||||||
\(765\) | 55.5883 | 2.00980 | ||||||||
\(766\) | 61.2857 | 2.21434 | ||||||||
\(767\) | −1.90779 | −0.0688864 | ||||||||
\(768\) | 142.961 | 5.15864 | ||||||||
\(769\) | −38.2825 | −1.38050 | −0.690251 | − | 0.723570i | \(-0.742500\pi\) | ||||
−0.690251 | + | 0.723570i | \(0.742500\pi\) | |||||||
\(770\) | −83.7705 | −3.01888 | ||||||||
\(771\) | −10.8411 | −0.390434 | ||||||||
\(772\) | −4.27079 | −0.153709 | ||||||||
\(773\) | 25.5431 | 0.918720 | 0.459360 | − | 0.888250i | \(-0.348079\pi\) | ||||
0.459360 | + | 0.888250i | \(0.348079\pi\) | |||||||
\(774\) | −69.2463 | −2.48901 | ||||||||
\(775\) | −18.2541 | −0.655708 | ||||||||
\(776\) | −79.3743 | −2.84937 | ||||||||
\(777\) | 8.41953 | 0.302049 | ||||||||
\(778\) | 35.2530 | 1.26388 | ||||||||
\(779\) | 29.6303 | 1.06161 | ||||||||
\(780\) | 58.7226 | 2.10261 | ||||||||
\(781\) | −2.39467 | −0.0856879 | ||||||||
\(782\) | 50.3648 | 1.80104 | ||||||||
\(783\) | −18.6908 | −0.667956 | ||||||||
\(784\) | 263.164 | 9.39871 | ||||||||
\(785\) | 48.5600 | 1.73318 | ||||||||
\(786\) | 91.8191 | 3.27508 | ||||||||
\(787\) | −22.5144 | −0.802550 | −0.401275 | − | 0.915958i | \(-0.631433\pi\) | ||||
−0.401275 | + | 0.915958i | \(0.631433\pi\) | |||||||
\(788\) | −53.8353 | −1.91780 | ||||||||
\(789\) | −44.4076 | −1.58095 | ||||||||
\(790\) | −113.744 | −4.04684 | ||||||||
\(791\) | 4.93159 | 0.175347 | ||||||||
\(792\) | 135.228 | 4.80513 | ||||||||
\(793\) | 9.35820 | 0.332320 | ||||||||
\(794\) | 89.3420 | 3.17063 | ||||||||
\(795\) | −45.9089 | −1.62822 | ||||||||
\(796\) | 37.7916 | 1.33949 | ||||||||
\(797\) | −1.66553 | −0.0589962 | −0.0294981 | − | 0.999565i | \(-0.509391\pi\) | ||||
−0.0294981 | + | 0.999565i | \(0.509391\pi\) | |||||||
\(798\) | 196.648 | 6.96128 | ||||||||
\(799\) | 1.51851 | 0.0537209 | ||||||||
\(800\) | −38.5171 | −1.36179 | ||||||||
\(801\) | −87.9258 | −3.10671 | ||||||||
\(802\) | −31.8202 | −1.12361 | ||||||||
\(803\) | −25.3492 | −0.894553 | ||||||||
\(804\) | 218.989 | 7.72314 | ||||||||
\(805\) | −64.7117 | −2.28079 | ||||||||
\(806\) | −40.2878 | −1.41908 | ||||||||
\(807\) | 19.7190 | 0.694141 | ||||||||
\(808\) | −61.8554 | −2.17607 | ||||||||
\(809\) | −6.44632 | −0.226641 | −0.113320 | − | 0.993559i | \(-0.536149\pi\) | ||||
−0.113320 | + | 0.993559i | \(0.536149\pi\) | |||||||
\(810\) | 57.8081 | 2.03117 | ||||||||
\(811\) | −15.4750 | −0.543402 | −0.271701 | − | 0.962382i | \(-0.587586\pi\) | ||||
−0.271701 | + | 0.962382i | \(0.587586\pi\) | |||||||
\(812\) | −58.4266 | −2.05037 | ||||||||
\(813\) | 3.18760 | 0.111794 | ||||||||
\(814\) | 3.75052 | 0.131456 | ||||||||
\(815\) | −26.9042 | −0.942413 | ||||||||
\(816\) | −164.725 | −5.76654 | ||||||||
\(817\) | −20.9129 | −0.731651 | ||||||||
\(818\) | 25.1630 | 0.879804 | ||||||||
\(819\) | −40.2524 | −1.40653 | ||||||||
\(820\) | 86.4099 | 3.01757 | ||||||||
\(821\) | 50.0046 | 1.74517 | 0.872586 | − | 0.488461i | \(-0.162442\pi\) | ||||
0.872586 | + | 0.488461i | \(0.162442\pi\) | |||||||
\(822\) | 50.1219 | 1.74820 | ||||||||
\(823\) | −28.9017 | −1.00745 | −0.503725 | − | 0.863864i | \(-0.668037\pi\) | ||||
−0.503725 | + | 0.863864i | \(0.668037\pi\) | |||||||
\(824\) | −34.8121 | −1.21274 | ||||||||
\(825\) | −12.2521 | −0.426562 | ||||||||
\(826\) | −18.6314 | −0.648268 | ||||||||
\(827\) | 19.1100 | 0.664519 | 0.332260 | − | 0.943188i | \(-0.392189\pi\) | ||||
0.332260 | + | 0.943188i | \(0.392189\pi\) | |||||||
\(828\) | 164.262 | 5.70849 | ||||||||
\(829\) | −12.6353 | −0.438841 | −0.219420 | − | 0.975630i | \(-0.570417\pi\) | ||||
−0.219420 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(830\) | −127.883 | −4.43889 | ||||||||
\(831\) | 80.4814 | 2.79187 | ||||||||
\(832\) | −43.0026 | −1.49085 | ||||||||
\(833\) | −62.9294 | −2.18037 | ||||||||
\(834\) | 124.467 | 4.30995 | ||||||||
\(835\) | 30.1477 | 1.04330 | ||||||||
\(836\) | 64.2190 | 2.22106 | ||||||||
\(837\) | −92.2730 | −3.18942 | ||||||||
\(838\) | −100.571 | −3.47417 | ||||||||
\(839\) | −6.60303 | −0.227962 | −0.113981 | − | 0.993483i | \(-0.536360\pi\) | ||||
−0.113981 | + | 0.993483i | \(0.536360\pi\) | |||||||
\(840\) | 364.705 | 12.5835 | ||||||||
\(841\) | −24.3494 | −0.839634 | ||||||||
\(842\) | −77.6221 | −2.67504 | ||||||||
\(843\) | −18.4085 | −0.634024 | ||||||||
\(844\) | 97.1585 | 3.34433 | ||||||||
\(845\) | 28.7346 | 0.988499 | ||||||||
\(846\) | 6.75548 | 0.232258 | ||||||||
\(847\) | −25.9676 | −0.892258 | ||||||||
\(848\) | 90.2085 | 3.09777 | ||||||||
\(849\) | 25.7181 | 0.882643 | ||||||||
\(850\) | 17.0530 | 0.584913 | ||||||||
\(851\) | 2.89723 | 0.0993158 | ||||||||
\(852\) | 16.3935 | 0.561633 | ||||||||
\(853\) | 26.0052 | 0.890400 | 0.445200 | − | 0.895431i | \(-0.353133\pi\) | ||||
0.445200 | + | 0.895431i | \(0.353133\pi\) | |||||||
\(854\) | 91.3916 | 3.12735 | ||||||||
\(855\) | 74.6864 | 2.55422 | ||||||||
\(856\) | 2.03789 | 0.0696537 | ||||||||
\(857\) | −4.31988 | −0.147564 | −0.0737822 | − | 0.997274i | \(-0.523507\pi\) | ||||
−0.0737822 | + | 0.997274i | \(0.523507\pi\) | |||||||
\(858\) | −27.0409 | −0.923162 | ||||||||
\(859\) | 48.0163 | 1.63830 | 0.819148 | − | 0.573583i | \(-0.194447\pi\) | ||||
0.819148 | + | 0.573583i | \(0.194447\pi\) | |||||||
\(860\) | −60.9879 | −2.07967 | ||||||||
\(861\) | −89.3258 | −3.04421 | ||||||||
\(862\) | 41.1793 | 1.40257 | ||||||||
\(863\) | 22.9002 | 0.779531 | 0.389765 | − | 0.920914i | \(-0.372556\pi\) | ||||
0.389765 | + | 0.920914i | \(0.372556\pi\) | |||||||
\(864\) | −194.700 | −6.62384 | ||||||||
\(865\) | 1.09590 | 0.0372616 | ||||||||
\(866\) | −59.9087 | −2.03578 | ||||||||
\(867\) | −11.3385 | −0.385077 | ||||||||
\(868\) | −288.441 | −9.79031 | ||||||||
\(869\) | 38.3987 | 1.30259 | ||||||||
\(870\) | −45.6477 | −1.54760 | ||||||||
\(871\) | −18.4660 | −0.625695 | ||||||||
\(872\) | 151.930 | 5.14501 | ||||||||
\(873\) | 49.0029 | 1.65850 | ||||||||
\(874\) | 67.6683 | 2.28891 | ||||||||
\(875\) | 41.9842 | 1.41933 | ||||||||
\(876\) | 173.537 | 5.86326 | ||||||||
\(877\) | 52.6044 | 1.77632 | 0.888161 | − | 0.459532i | \(-0.151983\pi\) | ||||
0.888161 | + | 0.459532i | \(0.151983\pi\) | |||||||
\(878\) | 1.57078 | 0.0530111 | ||||||||
\(879\) | −52.7597 | −1.77954 | ||||||||
\(880\) | 94.2799 | 3.17817 | ||||||||
\(881\) | 18.4839 | 0.622740 | 0.311370 | − | 0.950289i | \(-0.399212\pi\) | ||||
0.311370 | + | 0.950289i | \(0.399212\pi\) | |||||||
\(882\) | −279.958 | −9.42669 | ||||||||
\(883\) | −12.6002 | −0.424030 | −0.212015 | − | 0.977266i | \(-0.568003\pi\) | ||||
−0.212015 | + | 0.977266i | \(0.568003\pi\) | |||||||
\(884\) | 27.5920 | 0.928018 | ||||||||
\(885\) | −10.6714 | −0.358716 | ||||||||
\(886\) | −71.3259 | −2.39624 | ||||||||
\(887\) | −41.5176 | −1.39402 | −0.697012 | − | 0.717060i | \(-0.745488\pi\) | ||||
−0.697012 | + | 0.717060i | \(0.745488\pi\) | |||||||
\(888\) | −16.3283 | −0.547942 | ||||||||
\(889\) | 66.6978 | 2.23697 | ||||||||
\(890\) | −105.632 | −3.54078 | ||||||||
\(891\) | −19.5153 | −0.653786 | ||||||||
\(892\) | −82.3518 | −2.75734 | ||||||||
\(893\) | 2.04021 | 0.0682730 | ||||||||
\(894\) | −159.421 | −5.33182 | ||||||||
\(895\) | −11.6365 | −0.388965 | ||||||||
\(896\) | −198.391 | −6.62776 | ||||||||
\(897\) | −20.8888 | −0.697456 | ||||||||
\(898\) | −57.2983 | −1.91207 | ||||||||
\(899\) | 22.9592 | 0.765732 | ||||||||
\(900\) | 55.6173 | 1.85391 | ||||||||
\(901\) | −21.5712 | −0.718642 | ||||||||
\(902\) | −39.7906 | −1.32488 | ||||||||
\(903\) | 63.0459 | 2.09804 | ||||||||
\(904\) | −9.56402 | −0.318094 | ||||||||
\(905\) | 26.4992 | 0.880862 | ||||||||
\(906\) | 133.202 | 4.42534 | ||||||||
\(907\) | −54.3138 | −1.80346 | −0.901730 | − | 0.432299i | \(-0.857702\pi\) | ||||
−0.901730 | + | 0.432299i | \(0.857702\pi\) | |||||||
\(908\) | 41.7892 | 1.38682 | ||||||||
\(909\) | 38.1873 | 1.26659 | ||||||||
\(910\) | −48.3580 | −1.60305 | ||||||||
\(911\) | 21.2259 | 0.703246 | 0.351623 | − | 0.936142i | \(-0.385630\pi\) | ||||
0.351623 | + | 0.936142i | \(0.385630\pi\) | |||||||
\(912\) | −221.319 | −7.32860 | ||||||||
\(913\) | 43.1718 | 1.42878 | ||||||||
\(914\) | 24.6953 | 0.816848 | ||||||||
\(915\) | 52.3460 | 1.73051 | ||||||||
\(916\) | −158.007 | −5.22070 | ||||||||
\(917\) | −55.4327 | −1.83055 | ||||||||
\(918\) | 86.2014 | 2.84507 | ||||||||
\(919\) | −21.0346 | −0.693869 | −0.346934 | − | 0.937889i | \(-0.612777\pi\) | ||||
−0.346934 | + | 0.937889i | \(0.612777\pi\) | |||||||
\(920\) | 125.498 | 4.13754 | ||||||||
\(921\) | −66.5228 | −2.19200 | ||||||||
\(922\) | −72.3780 | −2.38364 | ||||||||
\(923\) | −1.38236 | −0.0455011 | ||||||||
\(924\) | −193.600 | −6.36896 | ||||||||
\(925\) | 0.980972 | 0.0322542 | ||||||||
\(926\) | −24.6802 | −0.811040 | ||||||||
\(927\) | 21.4918 | 0.705882 | ||||||||
\(928\) | 48.4450 | 1.59029 | ||||||||
\(929\) | 0.664410 | 0.0217986 | 0.0108993 | − | 0.999941i | \(-0.496531\pi\) | ||||
0.0108993 | + | 0.999941i | \(0.496531\pi\) | |||||||
\(930\) | −225.354 | −7.38964 | ||||||||
\(931\) | −84.5497 | −2.77100 | ||||||||
\(932\) | −83.8313 | −2.74598 | ||||||||
\(933\) | −67.2486 | −2.20162 | ||||||||
\(934\) | −40.4132 | −1.32236 | ||||||||
\(935\) | −22.5448 | −0.737294 | ||||||||
\(936\) | 78.0629 | 2.55157 | ||||||||
\(937\) | 24.5068 | 0.800602 | 0.400301 | − | 0.916384i | \(-0.368906\pi\) | ||||
0.400301 | + | 0.916384i | \(0.368906\pi\) | |||||||
\(938\) | −180.337 | −5.88822 | ||||||||
\(939\) | −38.5654 | −1.25853 | ||||||||
\(940\) | 5.94981 | 0.194061 | ||||||||
\(941\) | 33.4968 | 1.09196 | 0.545982 | − | 0.837797i | \(-0.316157\pi\) | ||||
0.545982 | + | 0.837797i | \(0.316157\pi\) | |||||||
\(942\) | 153.082 | 4.98767 | ||||||||
\(943\) | −30.7377 | −1.00096 | ||||||||
\(944\) | 20.9688 | 0.682475 | ||||||||
\(945\) | −110.757 | −3.60291 | ||||||||
\(946\) | 28.0841 | 0.913092 | ||||||||
\(947\) | −29.2233 | −0.949629 | −0.474814 | − | 0.880086i | \(-0.657485\pi\) | ||||
−0.474814 | + | 0.880086i | \(0.657485\pi\) | |||||||
\(948\) | −262.872 | −8.53767 | ||||||||
\(949\) | −14.6333 | −0.475016 | ||||||||
\(950\) | 22.9118 | 0.743357 | ||||||||
\(951\) | −6.19318 | −0.200828 | ||||||||
\(952\) | 171.364 | 5.55393 | ||||||||
\(953\) | 11.4667 | 0.371442 | 0.185721 | − | 0.982603i | \(-0.440538\pi\) | ||||
0.185721 | + | 0.982603i | \(0.440538\pi\) | |||||||
\(954\) | −95.9654 | −3.10699 | ||||||||
\(955\) | −21.5519 | −0.697403 | ||||||||
\(956\) | 32.9874 | 1.06689 | ||||||||
\(957\) | 15.4101 | 0.498137 | ||||||||
\(958\) | 29.4638 | 0.951932 | ||||||||
\(959\) | −30.2594 | −0.977128 | ||||||||
\(960\) | −240.539 | −7.76337 | ||||||||
\(961\) | 82.3450 | 2.65629 | ||||||||
\(962\) | 2.16505 | 0.0698041 | ||||||||
\(963\) | −1.25812 | −0.0405424 | ||||||||
\(964\) | 62.8408 | 2.02397 | ||||||||
\(965\) | 2.01442 | 0.0648465 | ||||||||
\(966\) | −203.998 | −6.56354 | ||||||||
\(967\) | −35.1574 | −1.13058 | −0.565292 | − | 0.824891i | \(-0.691237\pi\) | ||||
−0.565292 | + | 0.824891i | \(0.691237\pi\) | |||||||
\(968\) | 50.3600 | 1.61863 | ||||||||
\(969\) | 52.9231 | 1.70014 | ||||||||
\(970\) | 58.8707 | 1.89022 | ||||||||
\(971\) | −4.14659 | −0.133070 | −0.0665352 | − | 0.997784i | \(-0.521194\pi\) | ||||
−0.0665352 | + | 0.997784i | \(0.521194\pi\) | |||||||
\(972\) | −9.24557 | −0.296552 | ||||||||
\(973\) | −75.1429 | −2.40897 | ||||||||
\(974\) | −2.44341 | −0.0782919 | ||||||||
\(975\) | −7.07273 | −0.226509 | ||||||||
\(976\) | −102.857 | −3.29237 | ||||||||
\(977\) | 2.91792 | 0.0933526 | 0.0466763 | − | 0.998910i | \(-0.485137\pi\) | ||||
0.0466763 | + | 0.998910i | \(0.485137\pi\) | |||||||
\(978\) | −84.8133 | −2.71203 | ||||||||
\(979\) | 35.6599 | 1.13969 | ||||||||
\(980\) | −246.570 | −7.87639 | ||||||||
\(981\) | −93.7964 | −2.99469 | ||||||||
\(982\) | 67.3235 | 2.14838 | ||||||||
\(983\) | 42.1455 | 1.34423 | 0.672117 | − | 0.740445i | \(-0.265385\pi\) | ||||
0.672117 | + | 0.740445i | \(0.265385\pi\) | |||||||
\(984\) | 173.233 | 5.52246 | ||||||||
\(985\) | 25.3927 | 0.809078 | ||||||||
\(986\) | −21.4485 | −0.683058 | ||||||||
\(987\) | −6.15058 | −0.195775 | ||||||||
\(988\) | 37.0715 | 1.17940 | ||||||||
\(989\) | 21.6946 | 0.689848 | ||||||||
\(990\) | −100.297 | −3.18764 | ||||||||
\(991\) | −24.7112 | −0.784977 | −0.392488 | − | 0.919757i | \(-0.628386\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(992\) | 239.163 | 7.59345 | ||||||||
\(993\) | 56.9801 | 1.80821 | ||||||||
\(994\) | −13.5001 | −0.428196 | ||||||||
\(995\) | −17.8253 | −0.565099 | ||||||||
\(996\) | −295.547 | −9.36478 | ||||||||
\(997\) | −43.0949 | −1.36483 | −0.682414 | − | 0.730965i | \(-0.739070\pi\) | ||||
−0.682414 | + | 0.730965i | \(0.739070\pi\) | |||||||
\(998\) | −11.4893 | −0.363688 | ||||||||
\(999\) | 4.95872 | 0.156887 |
(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 | 8023.2.a.b.1.7 | ✓ | 155 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.b.1.7 | ✓ | 155 | 1.1 | even | 1 | trivial |