Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0140467354\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76981 | −1.95855 | −0.979276 | − | 0.202533i | \(-0.935083\pi\) | ||||
−0.979276 | + | 0.202533i | \(0.935083\pi\) | |||||||
\(3\) | 0.446127 | 0.257571 | 0.128786 | − | 0.991672i | \(-0.458892\pi\) | ||||
0.128786 | + | 0.991672i | \(0.458892\pi\) | |||||||
\(4\) | 5.67184 | 2.83592 | ||||||||
\(5\) | −3.40223 | −1.52152 | −0.760762 | − | 0.649031i | \(-0.775175\pi\) | ||||
−0.760762 | + | 0.649031i | \(0.775175\pi\) | |||||||
\(6\) | −1.23569 | −0.504467 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −10.1703 | −3.59575 | ||||||||
\(9\) | −2.80097 | −0.933657 | ||||||||
\(10\) | 9.42353 | 2.97998 | ||||||||
\(11\) | −4.75307 | −1.43310 | −0.716552 | − | 0.697533i | \(-0.754281\pi\) | ||||
−0.716552 | + | 0.697533i | \(0.754281\pi\) | |||||||
\(12\) | 2.53036 | 0.730452 | ||||||||
\(13\) | 1.40588 | 0.389922 | 0.194961 | − | 0.980811i | \(-0.437542\pi\) | ||||
0.194961 | + | 0.980811i | \(0.437542\pi\) | |||||||
\(14\) | 2.76981 | 0.740263 | ||||||||
\(15\) | −1.51783 | −0.391901 | ||||||||
\(16\) | 16.8261 | 4.20653 | ||||||||
\(17\) | 1.31679 | 0.319369 | 0.159684 | − | 0.987168i | \(-0.448952\pi\) | ||||
0.159684 | + | 0.987168i | \(0.448952\pi\) | |||||||
\(18\) | 7.75816 | 1.82861 | ||||||||
\(19\) | −7.71496 | −1.76993 | −0.884966 | − | 0.465655i | \(-0.845819\pi\) | ||||
−0.884966 | + | 0.465655i | \(0.845819\pi\) | |||||||
\(20\) | −19.2969 | −4.31492 | ||||||||
\(21\) | −0.446127 | −0.0973528 | ||||||||
\(22\) | 13.1651 | 2.80681 | ||||||||
\(23\) | 8.19528 | 1.70883 | 0.854417 | − | 0.519588i | \(-0.173914\pi\) | ||||
0.854417 | + | 0.519588i | \(0.173914\pi\) | |||||||
\(24\) | −4.53725 | −0.926162 | ||||||||
\(25\) | 6.57518 | 1.31504 | ||||||||
\(26\) | −3.89403 | −0.763682 | ||||||||
\(27\) | −2.58797 | −0.498055 | ||||||||
\(28\) | −5.67184 | −1.07188 | ||||||||
\(29\) | −1.35232 | −0.251120 | −0.125560 | − | 0.992086i | \(-0.540073\pi\) | ||||
−0.125560 | + | 0.992086i | \(0.540073\pi\) | |||||||
\(30\) | 4.20409 | 0.767558 | ||||||||
\(31\) | 7.01524 | 1.25997 | 0.629987 | − | 0.776606i | \(-0.283060\pi\) | ||||
0.629987 | + | 0.776606i | \(0.283060\pi\) | |||||||
\(32\) | −26.2646 | −4.64296 | ||||||||
\(33\) | −2.12047 | −0.369127 | ||||||||
\(34\) | −3.64726 | −0.625500 | ||||||||
\(35\) | 3.40223 | 0.575082 | ||||||||
\(36\) | −15.8867 | −2.64778 | ||||||||
\(37\) | −0.951364 | −0.156403 | −0.0782017 | − | 0.996938i | \(-0.524918\pi\) | ||||
−0.0782017 | + | 0.996938i | \(0.524918\pi\) | |||||||
\(38\) | 21.3690 | 3.46650 | ||||||||
\(39\) | 0.627202 | 0.100433 | ||||||||
\(40\) | 34.6018 | 5.47102 | ||||||||
\(41\) | −6.52881 | −1.01963 | −0.509814 | − | 0.860284i | \(-0.670286\pi\) | ||||
−0.509814 | + | 0.860284i | \(0.670286\pi\) | |||||||
\(42\) | 1.23569 | 0.190671 | ||||||||
\(43\) | 9.62011 | 1.46705 | 0.733527 | − | 0.679661i | \(-0.237873\pi\) | ||||
0.733527 | + | 0.679661i | \(0.237873\pi\) | |||||||
\(44\) | −26.9587 | −4.06417 | ||||||||
\(45\) | 9.52955 | 1.42058 | ||||||||
\(46\) | −22.6994 | −3.34684 | ||||||||
\(47\) | 4.89227 | 0.713610 | 0.356805 | − | 0.934179i | \(-0.383866\pi\) | ||||
0.356805 | + | 0.934179i | \(0.383866\pi\) | |||||||
\(48\) | 7.50659 | 1.08348 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −18.2120 | −2.57557 | ||||||||
\(51\) | 0.587456 | 0.0822603 | ||||||||
\(52\) | 7.97395 | 1.10579 | ||||||||
\(53\) | −12.1519 | −1.66919 | −0.834596 | − | 0.550862i | \(-0.814299\pi\) | ||||
−0.834596 | + | 0.550862i | \(0.814299\pi\) | |||||||
\(54\) | 7.16818 | 0.975466 | ||||||||
\(55\) | 16.1711 | 2.18050 | ||||||||
\(56\) | 10.1703 | 1.35906 | ||||||||
\(57\) | −3.44185 | −0.455884 | ||||||||
\(58\) | 3.74567 | 0.491831 | ||||||||
\(59\) | 8.88946 | 1.15731 | 0.578654 | − | 0.815573i | \(-0.303578\pi\) | ||||
0.578654 | + | 0.815573i | \(0.303578\pi\) | |||||||
\(60\) | −8.60888 | −1.11140 | ||||||||
\(61\) | −9.41424 | −1.20537 | −0.602685 | − | 0.797979i | \(-0.705902\pi\) | ||||
−0.602685 | + | 0.797979i | \(0.705902\pi\) | |||||||
\(62\) | −19.4309 | −2.46772 | ||||||||
\(63\) | 2.80097 | 0.352889 | ||||||||
\(64\) | 39.0955 | 4.88694 | ||||||||
\(65\) | −4.78314 | −0.593276 | ||||||||
\(66\) | 5.87330 | 0.722954 | ||||||||
\(67\) | 10.2478 | 1.25196 | 0.625982 | − | 0.779838i | \(-0.284698\pi\) | ||||
0.625982 | + | 0.779838i | \(0.284698\pi\) | |||||||
\(68\) | 7.46864 | 0.905705 | ||||||||
\(69\) | 3.65613 | 0.440147 | ||||||||
\(70\) | −9.42353 | −1.12633 | ||||||||
\(71\) | −11.7267 | −1.39171 | −0.695853 | − | 0.718184i | \(-0.744973\pi\) | ||||
−0.695853 | + | 0.718184i | \(0.744973\pi\) | |||||||
\(72\) | 28.4867 | 3.35719 | ||||||||
\(73\) | 4.84575 | 0.567153 | 0.283576 | − | 0.958950i | \(-0.408479\pi\) | ||||
0.283576 | + | 0.958950i | \(0.408479\pi\) | |||||||
\(74\) | 2.63510 | 0.306324 | ||||||||
\(75\) | 2.93337 | 0.338716 | ||||||||
\(76\) | −43.7580 | −5.01939 | ||||||||
\(77\) | 4.75307 | 0.541663 | ||||||||
\(78\) | −1.73723 | −0.196703 | ||||||||
\(79\) | 16.2796 | 1.83160 | 0.915801 | − | 0.401633i | \(-0.131557\pi\) | ||||
0.915801 | + | 0.401633i | \(0.131557\pi\) | |||||||
\(80\) | −57.2464 | −6.40034 | ||||||||
\(81\) | 7.24835 | 0.805372 | ||||||||
\(82\) | 18.0836 | 1.99700 | ||||||||
\(83\) | 11.7536 | 1.29012 | 0.645061 | − | 0.764131i | \(-0.276832\pi\) | ||||
0.645061 | + | 0.764131i | \(0.276832\pi\) | |||||||
\(84\) | −2.53036 | −0.276085 | ||||||||
\(85\) | −4.48003 | −0.485927 | ||||||||
\(86\) | −26.6459 | −2.87330 | ||||||||
\(87\) | −0.603307 | −0.0646813 | ||||||||
\(88\) | 48.3402 | 5.15308 | ||||||||
\(89\) | −0.541072 | −0.0573535 | −0.0286767 | − | 0.999589i | \(-0.509129\pi\) | ||||
−0.0286767 | + | 0.999589i | \(0.509129\pi\) | |||||||
\(90\) | −26.3950 | −2.78228 | ||||||||
\(91\) | −1.40588 | −0.147377 | ||||||||
\(92\) | 46.4824 | 4.84612 | ||||||||
\(93\) | 3.12969 | 0.324533 | ||||||||
\(94\) | −13.5506 | −1.39764 | ||||||||
\(95\) | 26.2481 | 2.69300 | ||||||||
\(96\) | −11.7173 | −1.19589 | ||||||||
\(97\) | −14.8931 | −1.51216 | −0.756082 | − | 0.654477i | \(-0.772889\pi\) | ||||
−0.756082 | + | 0.654477i | \(0.772889\pi\) | |||||||
\(98\) | −2.76981 | −0.279793 | ||||||||
\(99\) | 13.3132 | 1.33803 | ||||||||
\(100\) | 37.2934 | 3.72934 | ||||||||
\(101\) | 12.1772 | 1.21168 | 0.605840 | − | 0.795587i | \(-0.292837\pi\) | ||||
0.605840 | + | 0.795587i | \(0.292837\pi\) | |||||||
\(102\) | −1.62714 | −0.161111 | ||||||||
\(103\) | 11.2623 | 1.10971 | 0.554854 | − | 0.831948i | \(-0.312774\pi\) | ||||
0.554854 | + | 0.831948i | \(0.312774\pi\) | |||||||
\(104\) | −14.2983 | −1.40206 | ||||||||
\(105\) | 1.51783 | 0.148125 | ||||||||
\(106\) | 33.6585 | 3.26920 | ||||||||
\(107\) | 7.68750 | 0.743179 | 0.371589 | − | 0.928397i | \(-0.378813\pi\) | ||||
0.371589 | + | 0.928397i | \(0.378813\pi\) | |||||||
\(108\) | −14.6786 | −1.41244 | ||||||||
\(109\) | 3.81178 | 0.365102 | 0.182551 | − | 0.983196i | \(-0.441564\pi\) | ||||
0.182551 | + | 0.983196i | \(0.441564\pi\) | |||||||
\(110\) | −44.7907 | −4.27063 | ||||||||
\(111\) | −0.424429 | −0.0402850 | ||||||||
\(112\) | −16.8261 | −1.58992 | ||||||||
\(113\) | −14.5526 | −1.36899 | −0.684495 | − | 0.729018i | \(-0.739977\pi\) | ||||
−0.684495 | + | 0.729018i | \(0.739977\pi\) | |||||||
\(114\) | 9.53327 | 0.892872 | ||||||||
\(115\) | −27.8822 | −2.60003 | ||||||||
\(116\) | −7.67016 | −0.712156 | ||||||||
\(117\) | −3.93784 | −0.364053 | ||||||||
\(118\) | −24.6221 | −2.26665 | ||||||||
\(119\) | −1.31679 | −0.120710 | ||||||||
\(120\) | 15.4368 | 1.40918 | ||||||||
\(121\) | 11.5917 | 1.05379 | ||||||||
\(122\) | 26.0756 | 2.36078 | ||||||||
\(123\) | −2.91268 | −0.262627 | ||||||||
\(124\) | 39.7894 | 3.57319 | ||||||||
\(125\) | −5.35914 | −0.479336 | ||||||||
\(126\) | −7.75816 | −0.691151 | ||||||||
\(127\) | −14.0170 | −1.24381 | −0.621905 | − | 0.783093i | \(-0.713641\pi\) | ||||
−0.621905 | + | 0.783093i | \(0.713641\pi\) | |||||||
\(128\) | −55.7581 | −4.92837 | ||||||||
\(129\) | 4.29179 | 0.377871 | ||||||||
\(130\) | 13.2484 | 1.16196 | ||||||||
\(131\) | 11.2245 | 0.980686 | 0.490343 | − | 0.871529i | \(-0.336871\pi\) | ||||
0.490343 | + | 0.871529i | \(0.336871\pi\) | |||||||
\(132\) | −12.0270 | −1.04682 | ||||||||
\(133\) | 7.71496 | 0.668972 | ||||||||
\(134\) | −28.3844 | −2.45204 | ||||||||
\(135\) | 8.80487 | 0.757802 | ||||||||
\(136\) | −13.3922 | −1.14837 | ||||||||
\(137\) | 12.8035 | 1.09387 | 0.546936 | − | 0.837174i | \(-0.315794\pi\) | ||||
0.546936 | + | 0.837174i | \(0.315794\pi\) | |||||||
\(138\) | −10.1268 | −0.862050 | ||||||||
\(139\) | 15.6247 | 1.32527 | 0.662635 | − | 0.748943i | \(-0.269438\pi\) | ||||
0.662635 | + | 0.748943i | \(0.269438\pi\) | |||||||
\(140\) | 19.2969 | 1.63089 | ||||||||
\(141\) | 2.18257 | 0.183806 | ||||||||
\(142\) | 32.4808 | 2.72573 | ||||||||
\(143\) | −6.68226 | −0.558799 | ||||||||
\(144\) | −47.1295 | −3.92746 | ||||||||
\(145\) | 4.60091 | 0.382085 | ||||||||
\(146\) | −13.4218 | −1.11080 | ||||||||
\(147\) | 0.446127 | 0.0367959 | ||||||||
\(148\) | −5.39599 | −0.443548 | ||||||||
\(149\) | −0.675917 | −0.0553733 | −0.0276867 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276867 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(150\) | −8.12486 | −0.663392 | ||||||||
\(151\) | 2.17200 | 0.176755 | 0.0883776 | − | 0.996087i | \(-0.471832\pi\) | ||||
0.0883776 | + | 0.996087i | \(0.471832\pi\) | |||||||
\(152\) | 78.4635 | 6.36423 | ||||||||
\(153\) | −3.68829 | −0.298181 | ||||||||
\(154\) | −13.1651 | −1.06087 | ||||||||
\(155\) | −23.8675 | −1.91708 | ||||||||
\(156\) | 3.55739 | 0.284819 | ||||||||
\(157\) | −12.1626 | −0.970685 | −0.485342 | − | 0.874324i | \(-0.661305\pi\) | ||||
−0.485342 | + | 0.874324i | \(0.661305\pi\) | |||||||
\(158\) | −45.0915 | −3.58728 | ||||||||
\(159\) | −5.42129 | −0.429936 | ||||||||
\(160\) | 89.3581 | 7.06438 | ||||||||
\(161\) | −8.19528 | −0.645879 | ||||||||
\(162\) | −20.0766 | −1.57736 | ||||||||
\(163\) | −11.5811 | −0.907102 | −0.453551 | − | 0.891230i | \(-0.649843\pi\) | ||||
−0.453551 | + | 0.891230i | \(0.649843\pi\) | |||||||
\(164\) | −37.0304 | −2.89159 | ||||||||
\(165\) | 7.21434 | 0.561636 | ||||||||
\(166\) | −32.5551 | −2.52677 | ||||||||
\(167\) | −12.5955 | −0.974669 | −0.487335 | − | 0.873215i | \(-0.662031\pi\) | ||||
−0.487335 | + | 0.873215i | \(0.662031\pi\) | |||||||
\(168\) | 4.53725 | 0.350056 | ||||||||
\(169\) | −11.0235 | −0.847961 | ||||||||
\(170\) | 12.4088 | 0.951714 | ||||||||
\(171\) | 21.6094 | 1.65251 | ||||||||
\(172\) | 54.5638 | 4.16045 | ||||||||
\(173\) | 4.94159 | 0.375702 | 0.187851 | − | 0.982197i | \(-0.439848\pi\) | ||||
0.187851 | + | 0.982197i | \(0.439848\pi\) | |||||||
\(174\) | 1.67104 | 0.126682 | ||||||||
\(175\) | −6.57518 | −0.497037 | ||||||||
\(176\) | −79.9758 | −6.02840 | ||||||||
\(177\) | 3.96582 | 0.298090 | ||||||||
\(178\) | 1.49867 | 0.112330 | ||||||||
\(179\) | −6.05157 | −0.452315 | −0.226158 | − | 0.974091i | \(-0.572616\pi\) | ||||
−0.226158 | + | 0.974091i | \(0.572616\pi\) | |||||||
\(180\) | 54.0501 | 4.02866 | ||||||||
\(181\) | −19.9039 | −1.47945 | −0.739724 | − | 0.672910i | \(-0.765044\pi\) | ||||
−0.739724 | + | 0.672910i | \(0.765044\pi\) | |||||||
\(182\) | 3.89403 | 0.288645 | ||||||||
\(183\) | −4.19994 | −0.310469 | ||||||||
\(184\) | −83.3485 | −6.14454 | ||||||||
\(185\) | 3.23676 | 0.237971 | ||||||||
\(186\) | −8.66864 | −0.635615 | ||||||||
\(187\) | −6.25880 | −0.457689 | ||||||||
\(188\) | 27.7482 | 2.02374 | ||||||||
\(189\) | 2.58797 | 0.188247 | ||||||||
\(190\) | −72.7022 | −5.27437 | ||||||||
\(191\) | −3.71936 | −0.269124 | −0.134562 | − | 0.990905i | \(-0.542963\pi\) | ||||
−0.134562 | + | 0.990905i | \(0.542963\pi\) | |||||||
\(192\) | 17.4416 | 1.25874 | ||||||||
\(193\) | −22.0443 | −1.58678 | −0.793391 | − | 0.608712i | \(-0.791687\pi\) | ||||
−0.793391 | + | 0.608712i | \(0.791687\pi\) | |||||||
\(194\) | 41.2510 | 2.96165 | ||||||||
\(195\) | −2.13389 | −0.152811 | ||||||||
\(196\) | 5.67184 | 0.405132 | ||||||||
\(197\) | 5.16453 | 0.367957 | 0.183979 | − | 0.982930i | \(-0.441102\pi\) | ||||
0.183979 | + | 0.982930i | \(0.441102\pi\) | |||||||
\(198\) | −36.8751 | −2.62060 | ||||||||
\(199\) | 4.77902 | 0.338776 | 0.169388 | − | 0.985549i | \(-0.445821\pi\) | ||||
0.169388 | + | 0.985549i | \(0.445821\pi\) | |||||||
\(200\) | −66.8716 | −4.72854 | ||||||||
\(201\) | 4.57180 | 0.322470 | ||||||||
\(202\) | −33.7286 | −2.37314 | ||||||||
\(203\) | 1.35232 | 0.0949144 | ||||||||
\(204\) | 3.33196 | 0.233284 | ||||||||
\(205\) | 22.2125 | 1.55139 | ||||||||
\(206\) | −31.1944 | −2.17342 | ||||||||
\(207\) | −22.9547 | −1.59546 | ||||||||
\(208\) | 23.6556 | 1.64022 | ||||||||
\(209\) | 36.6697 | 2.53650 | ||||||||
\(210\) | −4.20409 | −0.290110 | ||||||||
\(211\) | 8.19709 | 0.564311 | 0.282155 | − | 0.959369i | \(-0.408951\pi\) | ||||
0.282155 | + | 0.959369i | \(0.408951\pi\) | |||||||
\(212\) | −68.9237 | −4.73370 | ||||||||
\(213\) | −5.23160 | −0.358464 | ||||||||
\(214\) | −21.2929 | −1.45555 | ||||||||
\(215\) | −32.7299 | −2.23216 | ||||||||
\(216\) | 26.3204 | 1.79088 | ||||||||
\(217\) | −7.01524 | −0.476226 | ||||||||
\(218\) | −10.5579 | −0.715071 | ||||||||
\(219\) | 2.16182 | 0.146082 | ||||||||
\(220\) | 91.7197 | 6.18374 | ||||||||
\(221\) | 1.85125 | 0.124529 | ||||||||
\(222\) | 1.17559 | 0.0789003 | ||||||||
\(223\) | −0.618391 | −0.0414105 | −0.0207052 | − | 0.999786i | \(-0.506591\pi\) | ||||
−0.0207052 | + | 0.999786i | \(0.506591\pi\) | |||||||
\(224\) | 26.2646 | 1.75487 | ||||||||
\(225\) | −18.4169 | −1.22779 | ||||||||
\(226\) | 40.3078 | 2.68124 | ||||||||
\(227\) | −12.9206 | −0.857572 | −0.428786 | − | 0.903406i | \(-0.641059\pi\) | ||||
−0.428786 | + | 0.903406i | \(0.641059\pi\) | |||||||
\(228\) | −19.5216 | −1.29285 | ||||||||
\(229\) | 6.41836 | 0.424137 | 0.212069 | − | 0.977255i | \(-0.431980\pi\) | ||||
0.212069 | + | 0.977255i | \(0.431980\pi\) | |||||||
\(230\) | 77.2285 | 5.09230 | ||||||||
\(231\) | 2.12047 | 0.139517 | ||||||||
\(232\) | 13.7535 | 0.902963 | ||||||||
\(233\) | 9.49759 | 0.622208 | 0.311104 | − | 0.950376i | \(-0.399301\pi\) | ||||
0.311104 | + | 0.950376i | \(0.399301\pi\) | |||||||
\(234\) | 10.9071 | 0.713017 | ||||||||
\(235\) | −16.6446 | −1.08578 | ||||||||
\(236\) | 50.4196 | 3.28204 | ||||||||
\(237\) | 7.26278 | 0.471768 | ||||||||
\(238\) | 3.64726 | 0.236417 | ||||||||
\(239\) | 12.7222 | 0.822934 | 0.411467 | − | 0.911425i | \(-0.365017\pi\) | ||||
0.411467 | + | 0.911425i | \(0.365017\pi\) | |||||||
\(240\) | −25.5391 | −1.64854 | ||||||||
\(241\) | 27.1248 | 1.74726 | 0.873632 | − | 0.486587i | \(-0.161758\pi\) | ||||
0.873632 | + | 0.486587i | \(0.161758\pi\) | |||||||
\(242\) | −32.1068 | −2.06390 | ||||||||
\(243\) | 10.9976 | 0.705496 | ||||||||
\(244\) | −53.3961 | −3.41833 | ||||||||
\(245\) | −3.40223 | −0.217361 | ||||||||
\(246\) | 8.06756 | 0.514369 | ||||||||
\(247\) | −10.8463 | −0.690135 | ||||||||
\(248\) | −71.3472 | −4.53055 | ||||||||
\(249\) | 5.24358 | 0.332298 | ||||||||
\(250\) | 14.8438 | 0.938804 | ||||||||
\(251\) | −1.24395 | −0.0785174 | −0.0392587 | − | 0.999229i | \(-0.512500\pi\) | ||||
−0.0392587 | + | 0.999229i | \(0.512500\pi\) | |||||||
\(252\) | 15.8867 | 1.00077 | ||||||||
\(253\) | −38.9528 | −2.44894 | ||||||||
\(254\) | 38.8245 | 2.43606 | ||||||||
\(255\) | −1.99866 | −0.125161 | ||||||||
\(256\) | 76.2482 | 4.76552 | ||||||||
\(257\) | −21.6804 | −1.35239 | −0.676194 | − | 0.736723i | \(-0.736372\pi\) | ||||
−0.676194 | + | 0.736723i | \(0.736372\pi\) | |||||||
\(258\) | −11.8874 | −0.740080 | ||||||||
\(259\) | 0.951364 | 0.0591149 | ||||||||
\(260\) | −27.1292 | −1.68248 | ||||||||
\(261\) | 3.78781 | 0.234460 | ||||||||
\(262\) | −31.0896 | −1.92072 | ||||||||
\(263\) | −26.6030 | −1.64041 | −0.820205 | − | 0.572070i | \(-0.806140\pi\) | ||||
−0.820205 | + | 0.572070i | \(0.806140\pi\) | |||||||
\(264\) | 21.5659 | 1.32729 | ||||||||
\(265\) | 41.3436 | 2.53972 | ||||||||
\(266\) | −21.3690 | −1.31022 | ||||||||
\(267\) | −0.241387 | −0.0147726 | ||||||||
\(268\) | 58.1237 | 3.55047 | ||||||||
\(269\) | −24.6355 | −1.50205 | −0.751026 | − | 0.660273i | \(-0.770441\pi\) | ||||
−0.751026 | + | 0.660273i | \(0.770441\pi\) | |||||||
\(270\) | −24.3878 | −1.48419 | ||||||||
\(271\) | 1.36185 | 0.0827266 | 0.0413633 | − | 0.999144i | \(-0.486830\pi\) | ||||
0.0413633 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(272\) | 22.1565 | 1.34344 | ||||||||
\(273\) | −0.627202 | −0.0379600 | ||||||||
\(274\) | −35.4631 | −2.14241 | ||||||||
\(275\) | −31.2523 | −1.88459 | ||||||||
\(276\) | 20.7370 | 1.24822 | ||||||||
\(277\) | 14.7220 | 0.884556 | 0.442278 | − | 0.896878i | \(-0.354170\pi\) | ||||
0.442278 | + | 0.896878i | \(0.354170\pi\) | |||||||
\(278\) | −43.2774 | −2.59561 | ||||||||
\(279\) | −19.6495 | −1.17638 | ||||||||
\(280\) | −34.6018 | −2.06785 | ||||||||
\(281\) | 12.2774 | 0.732411 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(282\) | −6.04531 | −0.359993 | ||||||||
\(283\) | 16.2846 | 0.968019 | 0.484009 | − | 0.875063i | \(-0.339180\pi\) | ||||
0.484009 | + | 0.875063i | \(0.339180\pi\) | |||||||
\(284\) | −66.5121 | −3.94677 | ||||||||
\(285\) | 11.7100 | 0.693639 | ||||||||
\(286\) | 18.5086 | 1.09444 | ||||||||
\(287\) | 6.52881 | 0.385383 | ||||||||
\(288\) | 73.5662 | 4.33493 | ||||||||
\(289\) | −15.2661 | −0.898004 | ||||||||
\(290\) | −12.7436 | −0.748333 | ||||||||
\(291\) | −6.64421 | −0.389490 | ||||||||
\(292\) | 27.4844 | 1.60840 | ||||||||
\(293\) | 2.74008 | 0.160077 | 0.0800385 | − | 0.996792i | \(-0.474496\pi\) | ||||
0.0800385 | + | 0.996792i | \(0.474496\pi\) | |||||||
\(294\) | −1.23569 | −0.0720667 | ||||||||
\(295\) | −30.2440 | −1.76087 | ||||||||
\(296\) | 9.67567 | 0.562387 | ||||||||
\(297\) | 12.3008 | 0.713765 | ||||||||
\(298\) | 1.87216 | 0.108451 | ||||||||
\(299\) | 11.5216 | 0.666312 | ||||||||
\(300\) | 16.6376 | 0.960572 | ||||||||
\(301\) | −9.62011 | −0.554494 | ||||||||
\(302\) | −6.01603 | −0.346184 | ||||||||
\(303\) | 5.43259 | 0.312094 | ||||||||
\(304\) | −129.813 | −7.44528 | ||||||||
\(305\) | 32.0294 | 1.83400 | ||||||||
\(306\) | 10.2159 | 0.584003 | ||||||||
\(307\) | −14.8505 | −0.847564 | −0.423782 | − | 0.905764i | \(-0.639298\pi\) | ||||
−0.423782 | + | 0.905764i | \(0.639298\pi\) | |||||||
\(308\) | 26.9587 | 1.53611 | ||||||||
\(309\) | 5.02442 | 0.285829 | ||||||||
\(310\) | 66.1084 | 3.75470 | ||||||||
\(311\) | 2.72372 | 0.154448 | 0.0772239 | − | 0.997014i | \(-0.475394\pi\) | ||||
0.0772239 | + | 0.997014i | \(0.475394\pi\) | |||||||
\(312\) | −6.37884 | −0.361131 | ||||||||
\(313\) | 22.0385 | 1.24569 | 0.622846 | − | 0.782345i | \(-0.285976\pi\) | ||||
0.622846 | + | 0.782345i | \(0.285976\pi\) | |||||||
\(314\) | 33.6882 | 1.90114 | ||||||||
\(315\) | −9.52955 | −0.536929 | ||||||||
\(316\) | 92.3355 | 5.19428 | ||||||||
\(317\) | −11.7343 | −0.659065 | −0.329532 | − | 0.944144i | \(-0.606891\pi\) | ||||
−0.329532 | + | 0.944144i | \(0.606891\pi\) | |||||||
\(318\) | 15.0159 | 0.842052 | ||||||||
\(319\) | 6.42768 | 0.359881 | ||||||||
\(320\) | −133.012 | −7.43560 | ||||||||
\(321\) | 3.42960 | 0.191422 | ||||||||
\(322\) | 22.6994 | 1.26499 | ||||||||
\(323\) | −10.1590 | −0.565261 | ||||||||
\(324\) | 41.1115 | 2.28397 | ||||||||
\(325\) | 9.24394 | 0.512761 | ||||||||
\(326\) | 32.0774 | 1.77661 | ||||||||
\(327\) | 1.70054 | 0.0940399 | ||||||||
\(328\) | 66.4000 | 3.66633 | ||||||||
\(329\) | −4.89227 | −0.269719 | ||||||||
\(330\) | −19.9823 | −1.09999 | ||||||||
\(331\) | −9.23983 | −0.507867 | −0.253934 | − | 0.967222i | \(-0.581724\pi\) | ||||
−0.253934 | + | 0.967222i | \(0.581724\pi\) | |||||||
\(332\) | 66.6644 | 3.65868 | ||||||||
\(333\) | 2.66474 | 0.146027 | ||||||||
\(334\) | 34.8871 | 1.90894 | ||||||||
\(335\) | −34.8653 | −1.90489 | ||||||||
\(336\) | −7.50659 | −0.409518 | ||||||||
\(337\) | 14.6770 | 0.799506 | 0.399753 | − | 0.916623i | \(-0.369096\pi\) | ||||
0.399753 | + | 0.916623i | \(0.369096\pi\) | |||||||
\(338\) | 30.5330 | 1.66077 | ||||||||
\(339\) | −6.49228 | −0.352613 | ||||||||
\(340\) | −25.4100 | −1.37805 | ||||||||
\(341\) | −33.3439 | −1.80568 | ||||||||
\(342\) | −59.8538 | −3.23653 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −97.8395 | −5.27515 | ||||||||
\(345\) | −12.4390 | −0.669694 | ||||||||
\(346\) | −13.6873 | −0.735833 | ||||||||
\(347\) | 18.6793 | 1.00275 | 0.501377 | − | 0.865229i | \(-0.332827\pi\) | ||||
0.501377 | + | 0.865229i | \(0.332827\pi\) | |||||||
\(348\) | −3.42186 | −0.183431 | ||||||||
\(349\) | 12.3514 | 0.661157 | 0.330578 | − | 0.943779i | \(-0.392756\pi\) | ||||
0.330578 | + | 0.943779i | \(0.392756\pi\) | |||||||
\(350\) | 18.2120 | 0.973473 | ||||||||
\(351\) | −3.63838 | −0.194202 | ||||||||
\(352\) | 124.837 | 6.65385 | ||||||||
\(353\) | −6.02256 | −0.320549 | −0.160274 | − | 0.987073i | \(-0.551238\pi\) | ||||
−0.160274 | + | 0.987073i | \(0.551238\pi\) | |||||||
\(354\) | −10.9846 | −0.583824 | ||||||||
\(355\) | 39.8970 | 2.11751 | ||||||||
\(356\) | −3.06887 | −0.162650 | ||||||||
\(357\) | −0.587456 | −0.0310915 | ||||||||
\(358\) | 16.7617 | 0.885883 | ||||||||
\(359\) | 17.4444 | 0.920678 | 0.460339 | − | 0.887743i | \(-0.347728\pi\) | ||||
0.460339 | + | 0.887743i | \(0.347728\pi\) | |||||||
\(360\) | −96.9185 | −5.10805 | ||||||||
\(361\) | 40.5206 | 2.13266 | ||||||||
\(362\) | 55.1301 | 2.89757 | ||||||||
\(363\) | 5.17136 | 0.271426 | ||||||||
\(364\) | −7.97395 | −0.417949 | ||||||||
\(365\) | −16.4864 | −0.862937 | ||||||||
\(366\) | 11.6330 | 0.608069 | ||||||||
\(367\) | −19.7917 | −1.03312 | −0.516560 | − | 0.856251i | \(-0.672788\pi\) | ||||
−0.516560 | + | 0.856251i | \(0.672788\pi\) | |||||||
\(368\) | 137.895 | 7.18827 | ||||||||
\(369\) | 18.2870 | 0.951984 | ||||||||
\(370\) | −8.96521 | −0.466079 | ||||||||
\(371\) | 12.1519 | 0.630895 | ||||||||
\(372\) | 17.7511 | 0.920351 | ||||||||
\(373\) | −29.7338 | −1.53956 | −0.769779 | − | 0.638311i | \(-0.779633\pi\) | ||||
−0.769779 | + | 0.638311i | \(0.779633\pi\) | |||||||
\(374\) | 17.3357 | 0.896407 | ||||||||
\(375\) | −2.39085 | −0.123463 | ||||||||
\(376\) | −49.7559 | −2.56596 | ||||||||
\(377\) | −1.90121 | −0.0979171 | ||||||||
\(378\) | −7.16818 | −0.368691 | ||||||||
\(379\) | −9.00270 | −0.462438 | −0.231219 | − | 0.972902i | \(-0.574271\pi\) | ||||
−0.231219 | + | 0.972902i | \(0.574271\pi\) | |||||||
\(380\) | 148.875 | 7.63713 | ||||||||
\(381\) | −6.25337 | −0.320370 | ||||||||
\(382\) | 10.3019 | 0.527093 | ||||||||
\(383\) | −1.40404 | −0.0717429 | −0.0358715 | − | 0.999356i | \(-0.511421\pi\) | ||||
−0.0358715 | + | 0.999356i | \(0.511421\pi\) | |||||||
\(384\) | −24.8752 | −1.26941 | ||||||||
\(385\) | −16.1711 | −0.824153 | ||||||||
\(386\) | 61.0585 | 3.10780 | ||||||||
\(387\) | −26.9457 | −1.36972 | ||||||||
\(388\) | −84.4713 | −4.28838 | ||||||||
\(389\) | 12.7071 | 0.644278 | 0.322139 | − | 0.946692i | \(-0.395598\pi\) | ||||
0.322139 | + | 0.946692i | \(0.395598\pi\) | |||||||
\(390\) | 5.91046 | 0.299288 | ||||||||
\(391\) | 10.7915 | 0.545748 | ||||||||
\(392\) | −10.1703 | −0.513678 | ||||||||
\(393\) | 5.00754 | 0.252597 | ||||||||
\(394\) | −14.3048 | −0.720663 | ||||||||
\(395\) | −55.3871 | −2.78683 | ||||||||
\(396\) | 75.5105 | 3.79454 | ||||||||
\(397\) | −25.1479 | −1.26214 | −0.631069 | − | 0.775727i | \(-0.717384\pi\) | ||||
−0.631069 | + | 0.775727i | \(0.717384\pi\) | |||||||
\(398\) | −13.2370 | −0.663510 | ||||||||
\(399\) | 3.44185 | 0.172308 | ||||||||
\(400\) | 110.635 | 5.53174 | ||||||||
\(401\) | 0.837339 | 0.0418147 | 0.0209074 | − | 0.999781i | \(-0.493344\pi\) | ||||
0.0209074 | + | 0.999781i | \(0.493344\pi\) | |||||||
\(402\) | −12.6630 | −0.631574 | ||||||||
\(403\) | 9.86261 | 0.491292 | ||||||||
\(404\) | 69.0673 | 3.43623 | ||||||||
\(405\) | −24.6606 | −1.22539 | ||||||||
\(406\) | −3.74567 | −0.185895 | ||||||||
\(407\) | 4.52190 | 0.224142 | ||||||||
\(408\) | −5.97461 | −0.295787 | ||||||||
\(409\) | 19.1821 | 0.948493 | 0.474246 | − | 0.880392i | \(-0.342721\pi\) | ||||
0.474246 | + | 0.880392i | \(0.342721\pi\) | |||||||
\(410\) | −61.5245 | −3.03848 | ||||||||
\(411\) | 5.71196 | 0.281750 | ||||||||
\(412\) | 63.8781 | 3.14705 | ||||||||
\(413\) | −8.88946 | −0.437421 | ||||||||
\(414\) | 63.5803 | 3.12480 | ||||||||
\(415\) | −39.9883 | −1.96295 | ||||||||
\(416\) | −36.9249 | −1.81039 | ||||||||
\(417\) | 6.97060 | 0.341352 | ||||||||
\(418\) | −101.568 | −4.96786 | ||||||||
\(419\) | 2.21259 | 0.108092 | 0.0540460 | − | 0.998538i | \(-0.482788\pi\) | ||||
0.0540460 | + | 0.998538i | \(0.482788\pi\) | |||||||
\(420\) | 8.60888 | 0.420070 | ||||||||
\(421\) | −40.4769 | −1.97272 | −0.986362 | − | 0.164593i | \(-0.947369\pi\) | ||||
−0.986362 | + | 0.164593i | \(0.947369\pi\) | |||||||
\(422\) | −22.7044 | −1.10523 | ||||||||
\(423\) | −13.7031 | −0.666267 | ||||||||
\(424\) | 123.589 | 6.00199 | ||||||||
\(425\) | 8.65814 | 0.419982 | ||||||||
\(426\) | 14.4905 | 0.702069 | ||||||||
\(427\) | 9.41424 | 0.455587 | ||||||||
\(428\) | 43.6023 | 2.10760 | ||||||||
\(429\) | −2.98114 | −0.143931 | ||||||||
\(430\) | 90.6555 | 4.37180 | ||||||||
\(431\) | 15.0417 | 0.724535 | 0.362267 | − | 0.932074i | \(-0.382003\pi\) | ||||
0.362267 | + | 0.932074i | \(0.382003\pi\) | |||||||
\(432\) | −43.5455 | −2.09508 | ||||||||
\(433\) | 4.76772 | 0.229122 | 0.114561 | − | 0.993416i | \(-0.463454\pi\) | ||||
0.114561 | + | 0.993416i | \(0.463454\pi\) | |||||||
\(434\) | 19.4309 | 0.932712 | ||||||||
\(435\) | 2.05259 | 0.0984141 | ||||||||
\(436\) | 21.6198 | 1.03540 | ||||||||
\(437\) | −63.2262 | −3.02452 | ||||||||
\(438\) | −5.98783 | −0.286110 | ||||||||
\(439\) | −14.0390 | −0.670043 | −0.335021 | − | 0.942211i | \(-0.608744\pi\) | ||||
−0.335021 | + | 0.942211i | \(0.608744\pi\) | |||||||
\(440\) | −164.465 | −7.84054 | ||||||||
\(441\) | −2.80097 | −0.133380 | ||||||||
\(442\) | −5.12762 | −0.243896 | ||||||||
\(443\) | 2.68978 | 0.127795 | 0.0638976 | − | 0.997956i | \(-0.479647\pi\) | ||||
0.0638976 | + | 0.997956i | \(0.479647\pi\) | |||||||
\(444\) | −2.40730 | −0.114245 | ||||||||
\(445\) | 1.84085 | 0.0872647 | ||||||||
\(446\) | 1.71282 | 0.0811046 | ||||||||
\(447\) | −0.301545 | −0.0142626 | ||||||||
\(448\) | −39.0955 | −1.84709 | ||||||||
\(449\) | −20.5040 | −0.967644 | −0.483822 | − | 0.875166i | \(-0.660752\pi\) | ||||
−0.483822 | + | 0.875166i | \(0.660752\pi\) | |||||||
\(450\) | 51.0113 | 2.40470 | ||||||||
\(451\) | 31.0319 | 1.46124 | ||||||||
\(452\) | −82.5398 | −3.88235 | ||||||||
\(453\) | 0.968989 | 0.0455271 | ||||||||
\(454\) | 35.7877 | 1.67960 | ||||||||
\(455\) | 4.78314 | 0.224237 | ||||||||
\(456\) | 35.0047 | 1.63924 | ||||||||
\(457\) | 21.3724 | 0.999761 | 0.499880 | − | 0.866094i | \(-0.333377\pi\) | ||||
0.499880 | + | 0.866094i | \(0.333377\pi\) | |||||||
\(458\) | −17.7776 | −0.830694 | ||||||||
\(459\) | −3.40781 | −0.159063 | ||||||||
\(460\) | −158.144 | −7.37349 | ||||||||
\(461\) | 30.8143 | 1.43517 | 0.717583 | − | 0.696473i | \(-0.245248\pi\) | ||||
0.717583 | + | 0.696473i | \(0.245248\pi\) | |||||||
\(462\) | −5.87330 | −0.273251 | ||||||||
\(463\) | 24.0955 | 1.11981 | 0.559906 | − | 0.828556i | \(-0.310837\pi\) | ||||
0.559906 | + | 0.828556i | \(0.310837\pi\) | |||||||
\(464\) | −22.7543 | −1.05634 | ||||||||
\(465\) | −10.6479 | −0.493785 | ||||||||
\(466\) | −26.3065 | −1.21863 | ||||||||
\(467\) | −5.96749 | −0.276143 | −0.138071 | − | 0.990422i | \(-0.544090\pi\) | ||||
−0.138071 | + | 0.990422i | \(0.544090\pi\) | |||||||
\(468\) | −22.3348 | −1.03243 | ||||||||
\(469\) | −10.2478 | −0.473198 | ||||||||
\(470\) | 46.1024 | 2.12655 | ||||||||
\(471\) | −5.42608 | −0.250021 | ||||||||
\(472\) | −90.4085 | −4.16139 | ||||||||
\(473\) | −45.7251 | −2.10244 | ||||||||
\(474\) | −20.1165 | −0.923982 | ||||||||
\(475\) | −50.7273 | −2.32753 | ||||||||
\(476\) | −7.46864 | −0.342324 | ||||||||
\(477\) | 34.0371 | 1.55845 | ||||||||
\(478\) | −35.2382 | −1.61176 | ||||||||
\(479\) | 16.7837 | 0.766868 | 0.383434 | − | 0.923568i | \(-0.374741\pi\) | ||||
0.383434 | + | 0.923568i | \(0.374741\pi\) | |||||||
\(480\) | 39.8650 | 1.81958 | ||||||||
\(481\) | −1.33751 | −0.0609851 | ||||||||
\(482\) | −75.1306 | −3.42211 | ||||||||
\(483\) | −3.65613 | −0.166360 | ||||||||
\(484\) | 65.7462 | 2.98847 | ||||||||
\(485\) | 50.6698 | 2.30080 | ||||||||
\(486\) | −30.4612 | −1.38175 | ||||||||
\(487\) | −25.2632 | −1.14478 | −0.572391 | − | 0.819981i | \(-0.693984\pi\) | ||||
−0.572391 | + | 0.819981i | \(0.693984\pi\) | |||||||
\(488\) | 95.7457 | 4.33420 | ||||||||
\(489\) | −5.16664 | −0.233644 | ||||||||
\(490\) | 9.42353 | 0.425712 | ||||||||
\(491\) | −32.2986 | −1.45762 | −0.728808 | − | 0.684718i | \(-0.759925\pi\) | ||||
−0.728808 | + | 0.684718i | \(0.759925\pi\) | |||||||
\(492\) | −16.5203 | −0.744790 | ||||||||
\(493\) | −1.78073 | −0.0801998 | ||||||||
\(494\) | 30.0423 | 1.35167 | ||||||||
\(495\) | −45.2946 | −2.03584 | ||||||||
\(496\) | 118.039 | 5.30012 | ||||||||
\(497\) | 11.7267 | 0.526015 | ||||||||
\(498\) | −14.5237 | −0.650823 | ||||||||
\(499\) | 21.4541 | 0.960416 | 0.480208 | − | 0.877155i | \(-0.340561\pi\) | ||||
0.480208 | + | 0.877155i | \(0.340561\pi\) | |||||||
\(500\) | −30.3962 | −1.35936 | ||||||||
\(501\) | −5.61919 | −0.251047 | ||||||||
\(502\) | 3.44550 | 0.153780 | ||||||||
\(503\) | 26.9255 | 1.20055 | 0.600274 | − | 0.799794i | \(-0.295058\pi\) | ||||
0.600274 | + | 0.799794i | \(0.295058\pi\) | |||||||
\(504\) | −28.4867 | −1.26890 | ||||||||
\(505\) | −41.4298 | −1.84360 | ||||||||
\(506\) | 107.892 | 4.79637 | ||||||||
\(507\) | −4.91788 | −0.218411 | ||||||||
\(508\) | −79.5024 | −3.52735 | ||||||||
\(509\) | 15.7335 | 0.697376 | 0.348688 | − | 0.937239i | \(-0.386627\pi\) | ||||
0.348688 | + | 0.937239i | \(0.386627\pi\) | |||||||
\(510\) | 5.53591 | 0.245134 | ||||||||
\(511\) | −4.84575 | −0.214364 | ||||||||
\(512\) | −99.6769 | −4.40514 | ||||||||
\(513\) | 19.9661 | 0.881523 | ||||||||
\(514\) | 60.0507 | 2.64872 | ||||||||
\(515\) | −38.3170 | −1.68845 | ||||||||
\(516\) | 24.3424 | 1.07161 | ||||||||
\(517\) | −23.2533 | −1.02268 | ||||||||
\(518\) | −2.63510 | −0.115780 | ||||||||
\(519\) | 2.20458 | 0.0967702 | ||||||||
\(520\) | 48.6460 | 2.13327 | ||||||||
\(521\) | 9.38850 | 0.411318 | 0.205659 | − | 0.978624i | \(-0.434066\pi\) | ||||
0.205659 | + | 0.978624i | \(0.434066\pi\) | |||||||
\(522\) | −10.4915 | −0.459201 | ||||||||
\(523\) | 12.2663 | 0.536367 | 0.268184 | − | 0.963368i | \(-0.413577\pi\) | ||||
0.268184 | + | 0.963368i | \(0.413577\pi\) | |||||||
\(524\) | 63.6634 | 2.78115 | ||||||||
\(525\) | −2.93337 | −0.128023 | ||||||||
\(526\) | 73.6851 | 3.21283 | ||||||||
\(527\) | 9.23761 | 0.402397 | ||||||||
\(528\) | −35.6793 | −1.55274 | ||||||||
\(529\) | 44.1626 | 1.92011 | ||||||||
\(530\) | −114.514 | −4.97416 | ||||||||
\(531\) | −24.8991 | −1.08053 | ||||||||
\(532\) | 43.7580 | 1.89715 | ||||||||
\(533\) | −9.17874 | −0.397576 | ||||||||
\(534\) | 0.668595 | 0.0289329 | ||||||||
\(535\) | −26.1547 | −1.13076 | ||||||||
\(536\) | −104.223 | −4.50175 | ||||||||
\(537\) | −2.69977 | −0.116503 | ||||||||
\(538\) | 68.2356 | 2.94184 | ||||||||
\(539\) | −4.75307 | −0.204729 | ||||||||
\(540\) | 49.9398 | 2.14907 | ||||||||
\(541\) | 43.4933 | 1.86992 | 0.934962 | − | 0.354747i | \(-0.115433\pi\) | ||||
0.934962 | + | 0.354747i | \(0.115433\pi\) | |||||||
\(542\) | −3.77207 | −0.162024 | ||||||||
\(543\) | −8.87968 | −0.381064 | ||||||||
\(544\) | −34.5849 | −1.48282 | ||||||||
\(545\) | −12.9686 | −0.555512 | ||||||||
\(546\) | 1.73723 | 0.0743466 | ||||||||
\(547\) | −23.8659 | −1.02043 | −0.510217 | − | 0.860046i | \(-0.670435\pi\) | ||||
−0.510217 | + | 0.860046i | \(0.670435\pi\) | |||||||
\(548\) | 72.6192 | 3.10214 | ||||||||
\(549\) | 26.3690 | 1.12540 | ||||||||
\(550\) | 86.5630 | 3.69106 | ||||||||
\(551\) | 10.4331 | 0.444465 | ||||||||
\(552\) | −37.1840 | −1.58266 | ||||||||
\(553\) | −16.2796 | −0.692280 | ||||||||
\(554\) | −40.7770 | −1.73245 | ||||||||
\(555\) | 1.44401 | 0.0612946 | ||||||||
\(556\) | 88.6209 | 3.75836 | ||||||||
\(557\) | 3.84352 | 0.162855 | 0.0814276 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814276 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(558\) | 54.4253 | 2.30401 | ||||||||
\(559\) | 13.5248 | 0.572036 | ||||||||
\(560\) | 57.2464 | 2.41910 | ||||||||
\(561\) | −2.79222 | −0.117888 | ||||||||
\(562\) | −34.0062 | −1.43446 | ||||||||
\(563\) | −35.5165 | −1.49684 | −0.748420 | − | 0.663225i | \(-0.769187\pi\) | ||||
−0.748420 | + | 0.663225i | \(0.769187\pi\) | |||||||
\(564\) | 12.3792 | 0.521258 | ||||||||
\(565\) | 49.5112 | 2.08295 | ||||||||
\(566\) | −45.1052 | −1.89591 | ||||||||
\(567\) | −7.24835 | −0.304402 | ||||||||
\(568\) | 119.264 | 5.00422 | ||||||||
\(569\) | −20.8127 | −0.872514 | −0.436257 | − | 0.899822i | \(-0.643696\pi\) | ||||
−0.436257 | + | 0.899822i | \(0.643696\pi\) | |||||||
\(570\) | −32.4344 | −1.35853 | ||||||||
\(571\) | −37.5999 | −1.57351 | −0.786754 | − | 0.617267i | \(-0.788240\pi\) | ||||
−0.786754 | + | 0.617267i | \(0.788240\pi\) | |||||||
\(572\) | −37.9008 | −1.58471 | ||||||||
\(573\) | −1.65931 | −0.0693186 | ||||||||
\(574\) | −18.0836 | −0.754793 | ||||||||
\(575\) | 53.8855 | 2.24718 | ||||||||
\(576\) | −109.505 | −4.56273 | ||||||||
\(577\) | 8.79207 | 0.366019 | 0.183009 | − | 0.983111i | \(-0.441416\pi\) | ||||
0.183009 | + | 0.983111i | \(0.441416\pi\) | |||||||
\(578\) | 42.2841 | 1.75879 | ||||||||
\(579\) | −9.83455 | −0.408710 | ||||||||
\(580\) | 26.0957 | 1.08356 | ||||||||
\(581\) | −11.7536 | −0.487620 | ||||||||
\(582\) | 18.4032 | 0.762837 | ||||||||
\(583\) | 57.7589 | 2.39213 | ||||||||
\(584\) | −49.2828 | −2.03934 | ||||||||
\(585\) | 13.3974 | 0.553916 | ||||||||
\(586\) | −7.58949 | −0.313519 | ||||||||
\(587\) | −31.5277 | −1.30129 | −0.650644 | − | 0.759383i | \(-0.725501\pi\) | ||||
−0.650644 | + | 0.759383i | \(0.725501\pi\) | |||||||
\(588\) | 2.53036 | 0.104350 | ||||||||
\(589\) | −54.1223 | −2.23007 | ||||||||
\(590\) | 83.7701 | 3.44876 | ||||||||
\(591\) | 2.30403 | 0.0947753 | ||||||||
\(592\) | −16.0078 | −0.657916 | ||||||||
\(593\) | 7.13202 | 0.292877 | 0.146438 | − | 0.989220i | \(-0.453219\pi\) | ||||
0.146438 | + | 0.989220i | \(0.453219\pi\) | |||||||
\(594\) | −34.0709 | −1.39794 | ||||||||
\(595\) | 4.48003 | 0.183663 | ||||||||
\(596\) | −3.83370 | −0.157034 | ||||||||
\(597\) | 2.13205 | 0.0872590 | ||||||||
\(598\) | −31.9127 | −1.30501 | ||||||||
\(599\) | 3.17396 | 0.129685 | 0.0648423 | − | 0.997896i | \(-0.479346\pi\) | ||||
0.0648423 | + | 0.997896i | \(0.479346\pi\) | |||||||
\(600\) | −29.8332 | −1.21794 | ||||||||
\(601\) | −41.9859 | −1.71264 | −0.856319 | − | 0.516447i | \(-0.827254\pi\) | ||||
−0.856319 | + | 0.516447i | \(0.827254\pi\) | |||||||
\(602\) | 26.6459 | 1.08601 | ||||||||
\(603\) | −28.7037 | −1.16890 | ||||||||
\(604\) | 12.3193 | 0.501264 | ||||||||
\(605\) | −39.4376 | −1.60337 | ||||||||
\(606\) | −15.0472 | −0.611252 | ||||||||
\(607\) | −7.35483 | −0.298523 | −0.149262 | − | 0.988798i | \(-0.547690\pi\) | ||||
−0.149262 | + | 0.988798i | \(0.547690\pi\) | |||||||
\(608\) | 202.630 | 8.21773 | ||||||||
\(609\) | 0.603307 | 0.0244472 | ||||||||
\(610\) | −88.7154 | −3.59198 | ||||||||
\(611\) | 6.87795 | 0.278252 | ||||||||
\(612\) | −20.9194 | −0.845618 | ||||||||
\(613\) | −10.3710 | −0.418881 | −0.209441 | − | 0.977821i | \(-0.567164\pi\) | ||||
−0.209441 | + | 0.977821i | \(0.567164\pi\) | |||||||
\(614\) | 41.1331 | 1.66000 | ||||||||
\(615\) | 9.90960 | 0.399594 | ||||||||
\(616\) | −48.3402 | −1.94768 | ||||||||
\(617\) | 48.2081 | 1.94079 | 0.970393 | − | 0.241533i | \(-0.0776503\pi\) | ||||
0.970393 | + | 0.241533i | \(0.0776503\pi\) | |||||||
\(618\) | −13.9167 | −0.559811 | ||||||||
\(619\) | −12.9373 | −0.519993 | −0.259997 | − | 0.965609i | \(-0.583721\pi\) | ||||
−0.259997 | + | 0.965609i | \(0.583721\pi\) | |||||||
\(620\) | −135.373 | −5.43669 | ||||||||
\(621\) | −21.2091 | −0.851093 | ||||||||
\(622\) | −7.54418 | −0.302494 | ||||||||
\(623\) | 0.541072 | 0.0216776 | ||||||||
\(624\) | 10.5534 | 0.422473 | ||||||||
\(625\) | −14.6429 | −0.585715 | ||||||||
\(626\) | −61.0425 | −2.43975 | ||||||||
\(627\) | 16.3594 | 0.653330 | ||||||||
\(628\) | −68.9846 | −2.75279 | ||||||||
\(629\) | −1.25275 | −0.0499503 | ||||||||
\(630\) | 26.3950 | 1.05160 | ||||||||
\(631\) | 27.4004 | 1.09079 | 0.545395 | − | 0.838179i | \(-0.316379\pi\) | ||||
0.545395 | + | 0.838179i | \(0.316379\pi\) | |||||||
\(632\) | −165.569 | −6.58597 | ||||||||
\(633\) | 3.65694 | 0.145350 | ||||||||
\(634\) | 32.5018 | 1.29081 | ||||||||
\(635\) | 47.6892 | 1.89249 | ||||||||
\(636\) | −30.7487 | −1.21927 | ||||||||
\(637\) | 1.40588 | 0.0557031 | ||||||||
\(638\) | −17.8034 | −0.704845 | ||||||||
\(639\) | 32.8462 | 1.29938 | ||||||||
\(640\) | 189.702 | 7.49863 | ||||||||
\(641\) | 9.03773 | 0.356969 | 0.178484 | − | 0.983943i | \(-0.442881\pi\) | ||||
0.178484 | + | 0.983943i | \(0.442881\pi\) | |||||||
\(642\) | −9.49934 | −0.374909 | ||||||||
\(643\) | −23.5916 | −0.930360 | −0.465180 | − | 0.885216i | \(-0.654010\pi\) | ||||
−0.465180 | + | 0.885216i | \(0.654010\pi\) | |||||||
\(644\) | −46.4824 | −1.83166 | ||||||||
\(645\) | −14.6017 | −0.574940 | ||||||||
\(646\) | 28.1385 | 1.10709 | ||||||||
\(647\) | −4.38243 | −0.172291 | −0.0861455 | − | 0.996283i | \(-0.527455\pi\) | ||||
−0.0861455 | + | 0.996283i | \(0.527455\pi\) | |||||||
\(648\) | −73.7180 | −2.89592 | ||||||||
\(649\) | −42.2522 | −1.65854 | ||||||||
\(650\) | −25.6039 | −1.00427 | ||||||||
\(651\) | −3.12969 | −0.122662 | ||||||||
\(652\) | −65.6862 | −2.57247 | ||||||||
\(653\) | 8.41880 | 0.329453 | 0.164727 | − | 0.986339i | \(-0.447326\pi\) | ||||
0.164727 | + | 0.986339i | \(0.447326\pi\) | |||||||
\(654\) | −4.71016 | −0.184182 | ||||||||
\(655\) | −38.1882 | −1.49214 | ||||||||
\(656\) | −109.855 | −4.28910 | ||||||||
\(657\) | −13.5728 | −0.529526 | ||||||||
\(658\) | 13.5506 | 0.528259 | ||||||||
\(659\) | 13.2266 | 0.515235 | 0.257618 | − | 0.966247i | \(-0.417063\pi\) | ||||
0.257618 | + | 0.966247i | \(0.417063\pi\) | |||||||
\(660\) | 40.9186 | 1.59275 | ||||||||
\(661\) | −10.5822 | −0.411600 | −0.205800 | − | 0.978594i | \(-0.565980\pi\) | ||||
−0.205800 | + | 0.978594i | \(0.565980\pi\) | |||||||
\(662\) | 25.5926 | 0.994683 | ||||||||
\(663\) | 0.825894 | 0.0320751 | ||||||||
\(664\) | −119.537 | −4.63895 | ||||||||
\(665\) | −26.2481 | −1.01786 | ||||||||
\(666\) | −7.38083 | −0.286001 | ||||||||
\(667\) | −11.0827 | −0.429122 | ||||||||
\(668\) | −71.4397 | −2.76409 | ||||||||
\(669\) | −0.275881 | −0.0106662 | ||||||||
\(670\) | 96.5702 | 3.73083 | ||||||||
\(671\) | 44.7465 | 1.72742 | ||||||||
\(672\) | 11.7173 | 0.452005 | ||||||||
\(673\) | −43.9020 | −1.69230 | −0.846148 | − | 0.532948i | \(-0.821084\pi\) | ||||
−0.846148 | + | 0.532948i | \(0.821084\pi\) | |||||||
\(674\) | −40.6524 | −1.56587 | ||||||||
\(675\) | −17.0164 | −0.654960 | ||||||||
\(676\) | −62.5235 | −2.40475 | ||||||||
\(677\) | −11.7861 | −0.452975 | −0.226488 | − | 0.974014i | \(-0.572724\pi\) | ||||
−0.226488 | + | 0.974014i | \(0.572724\pi\) | |||||||
\(678\) | 17.9824 | 0.690610 | ||||||||
\(679\) | 14.8931 | 0.571544 | ||||||||
\(680\) | 45.5633 | 1.74727 | ||||||||
\(681\) | −5.76424 | −0.220886 | ||||||||
\(682\) | 92.3564 | 3.53651 | ||||||||
\(683\) | −3.58744 | −0.137269 | −0.0686347 | − | 0.997642i | \(-0.521864\pi\) | ||||
−0.0686347 | + | 0.997642i | \(0.521864\pi\) | |||||||
\(684\) | 122.565 | 4.68639 | ||||||||
\(685\) | −43.5603 | −1.66435 | ||||||||
\(686\) | 2.76981 | 0.105752 | ||||||||
\(687\) | 2.86340 | 0.109246 | ||||||||
\(688\) | 161.869 | 6.17121 | ||||||||
\(689\) | −17.0842 | −0.650854 | ||||||||
\(690\) | 34.4537 | 1.31163 | ||||||||
\(691\) | −50.8252 | −1.93348 | −0.966741 | − | 0.255757i | \(-0.917675\pi\) | ||||
−0.966741 | + | 0.255757i | \(0.917675\pi\) | |||||||
\(692\) | 28.0280 | 1.06546 | ||||||||
\(693\) | −13.3132 | −0.505727 | ||||||||
\(694\) | −51.7380 | −1.96395 | ||||||||
\(695\) | −53.1589 | −2.01643 | ||||||||
\(696\) | 6.13582 | 0.232578 | ||||||||
\(697\) | −8.59708 | −0.325638 | ||||||||
\(698\) | −34.2111 | −1.29491 | ||||||||
\(699\) | 4.23713 | 0.160263 | ||||||||
\(700\) | −37.2934 | −1.40956 | ||||||||
\(701\) | −24.7357 | −0.934254 | −0.467127 | − | 0.884190i | \(-0.654711\pi\) | ||||
−0.467127 | + | 0.884190i | \(0.654711\pi\) | |||||||
\(702\) | 10.0776 | 0.380355 | ||||||||
\(703\) | 7.33973 | 0.276823 | ||||||||
\(704\) | −185.824 | −7.00350 | ||||||||
\(705\) | −7.42561 | −0.279665 | ||||||||
\(706\) | 16.6813 | 0.627811 | ||||||||
\(707\) | −12.1772 | −0.457972 | ||||||||
\(708\) | 22.4935 | 0.845359 | ||||||||
\(709\) | −31.3868 | −1.17876 | −0.589378 | − | 0.807857i | \(-0.700627\pi\) | ||||
−0.589378 | + | 0.807857i | \(0.700627\pi\) | |||||||
\(710\) | −110.507 | −4.14726 | ||||||||
\(711\) | −45.5988 | −1.71009 | ||||||||
\(712\) | 5.50287 | 0.206229 | ||||||||
\(713\) | 57.4919 | 2.15309 | ||||||||
\(714\) | 1.62714 | 0.0608942 | ||||||||
\(715\) | 22.7346 | 0.850226 | ||||||||
\(716\) | −34.3235 | −1.28273 | ||||||||
\(717\) | 5.67574 | 0.211964 | ||||||||
\(718\) | −48.3176 | −1.80320 | ||||||||
\(719\) | −7.82058 | −0.291658 | −0.145829 | − | 0.989310i | \(-0.546585\pi\) | ||||
−0.145829 | + | 0.989310i | \(0.546585\pi\) | |||||||
\(720\) | 160.345 | 5.97572 | ||||||||
\(721\) | −11.2623 | −0.419430 | ||||||||
\(722\) | −112.234 | −4.17693 | ||||||||
\(723\) | 12.1011 | 0.450045 | ||||||||
\(724\) | −112.892 | −4.19560 | ||||||||
\(725\) | −8.89176 | −0.330232 | ||||||||
\(726\) | −14.3237 | −0.531602 | ||||||||
\(727\) | 40.5734 | 1.50479 | 0.752393 | − | 0.658715i | \(-0.228900\pi\) | ||||
0.752393 | + | 0.658715i | \(0.228900\pi\) | |||||||
\(728\) | 14.2983 | 0.529929 | ||||||||
\(729\) | −16.8387 | −0.623657 | ||||||||
\(730\) | 45.6641 | 1.69011 | ||||||||
\(731\) | 12.6677 | 0.468531 | ||||||||
\(732\) | −23.8214 | −0.880465 | ||||||||
\(733\) | −42.9196 | −1.58527 | −0.792636 | − | 0.609695i | \(-0.791292\pi\) | ||||
−0.792636 | + | 0.609695i | \(0.791292\pi\) | |||||||
\(734\) | 54.8193 | 2.02342 | ||||||||
\(735\) | −1.51783 | −0.0559859 | ||||||||
\(736\) | −215.245 | −7.93405 | ||||||||
\(737\) | −48.7084 | −1.79420 | ||||||||
\(738\) | −50.6515 | −1.86451 | ||||||||
\(739\) | 19.8909 | 0.731697 | 0.365849 | − | 0.930674i | \(-0.380779\pi\) | ||||
0.365849 | + | 0.930674i | \(0.380779\pi\) | |||||||
\(740\) | 18.3584 | 0.674869 | ||||||||
\(741\) | −4.83884 | −0.177759 | ||||||||
\(742\) | −33.6585 | −1.23564 | ||||||||
\(743\) | −24.0084 | −0.880782 | −0.440391 | − | 0.897806i | \(-0.645160\pi\) | ||||
−0.440391 | + | 0.897806i | \(0.645160\pi\) | |||||||
\(744\) | −31.8299 | −1.16694 | ||||||||
\(745\) | 2.29963 | 0.0842518 | ||||||||
\(746\) | 82.3569 | 3.01530 | ||||||||
\(747\) | −32.9214 | −1.20453 | ||||||||
\(748\) | −35.4990 | −1.29797 | ||||||||
\(749\) | −7.68750 | −0.280895 | ||||||||
\(750\) | 6.62221 | 0.241809 | ||||||||
\(751\) | −9.96092 | −0.363479 | −0.181739 | − | 0.983347i | \(-0.558173\pi\) | ||||
−0.181739 | + | 0.983347i | \(0.558173\pi\) | |||||||
\(752\) | 82.3179 | 3.00182 | ||||||||
\(753\) | −0.554959 | −0.0202238 | ||||||||
\(754\) | 5.26598 | 0.191776 | ||||||||
\(755\) | −7.38966 | −0.268937 | ||||||||
\(756\) | 14.6786 | 0.533854 | ||||||||
\(757\) | 33.6896 | 1.22447 | 0.612234 | − | 0.790677i | \(-0.290271\pi\) | ||||
0.612234 | + | 0.790677i | \(0.290271\pi\) | |||||||
\(758\) | 24.9358 | 0.905708 | ||||||||
\(759\) | −17.3779 | −0.630777 | ||||||||
\(760\) | −266.951 | −9.68333 | ||||||||
\(761\) | −4.54745 | −0.164845 | −0.0824226 | − | 0.996597i | \(-0.526266\pi\) | ||||
−0.0824226 | + | 0.996597i | \(0.526266\pi\) | |||||||
\(762\) | 17.3206 | 0.627461 | ||||||||
\(763\) | −3.81178 | −0.137996 | ||||||||
\(764\) | −21.0957 | −0.763214 | ||||||||
\(765\) | 12.5484 | 0.453690 | ||||||||
\(766\) | 3.88891 | 0.140512 | ||||||||
\(767\) | 12.4975 | 0.451260 | ||||||||
\(768\) | 34.0164 | 1.22746 | ||||||||
\(769\) | 6.34542 | 0.228822 | 0.114411 | − | 0.993434i | \(-0.463502\pi\) | ||||
0.114411 | + | 0.993434i | \(0.463502\pi\) | |||||||
\(770\) | 44.7907 | 1.61415 | ||||||||
\(771\) | −9.67223 | −0.348337 | ||||||||
\(772\) | −125.032 | −4.49999 | ||||||||
\(773\) | 15.6817 | 0.564033 | 0.282016 | − | 0.959410i | \(-0.408997\pi\) | ||||
0.282016 | + | 0.959410i | \(0.408997\pi\) | |||||||
\(774\) | 74.6343 | 2.68268 | ||||||||
\(775\) | 46.1265 | 1.65691 | ||||||||
\(776\) | 151.467 | 5.43736 | ||||||||
\(777\) | 0.424429 | 0.0152263 | ||||||||
\(778\) | −35.1964 | −1.26185 | ||||||||
\(779\) | 50.3695 | 1.80467 | ||||||||
\(780\) | −12.1031 | −0.433360 | ||||||||
\(781\) | 55.7379 | 1.99446 | ||||||||
\(782\) | −29.8903 | −1.06888 | ||||||||
\(783\) | 3.49977 | 0.125071 | ||||||||
\(784\) | 16.8261 | 0.600933 | ||||||||
\(785\) | 41.3801 | 1.47692 | ||||||||
\(786\) | −13.8699 | −0.494724 | ||||||||
\(787\) | 46.9979 | 1.67529 | 0.837646 | − | 0.546213i | \(-0.183931\pi\) | ||||
0.837646 | + | 0.546213i | \(0.183931\pi\) | |||||||
\(788\) | 29.2924 | 1.04350 | ||||||||
\(789\) | −11.8683 | −0.422523 | ||||||||
\(790\) | 153.412 | 5.45814 | ||||||||
\(791\) | 14.5526 | 0.517429 | ||||||||
\(792\) | −135.400 | −4.81121 | ||||||||
\(793\) | −13.2353 | −0.470000 | ||||||||
\(794\) | 69.6550 | 2.47196 | ||||||||
\(795\) | 18.4445 | 0.654158 | ||||||||
\(796\) | 27.1059 | 0.960742 | ||||||||
\(797\) | 3.08525 | 0.109285 | 0.0546427 | − | 0.998506i | \(-0.482598\pi\) | ||||
0.0546427 | + | 0.998506i | \(0.482598\pi\) | |||||||
\(798\) | −9.53327 | −0.337474 | ||||||||
\(799\) | 6.44209 | 0.227905 | ||||||||
\(800\) | −172.694 | −6.10566 | ||||||||
\(801\) | 1.51553 | 0.0535485 | ||||||||
\(802\) | −2.31927 | −0.0818962 | ||||||||
\(803\) | −23.0322 | −0.812789 | ||||||||
\(804\) | 25.9306 | 0.914500 | ||||||||
\(805\) | 27.8822 | 0.982720 | ||||||||
\(806\) | −27.3175 | −0.962219 | ||||||||
\(807\) | −10.9905 | −0.386885 | ||||||||
\(808\) | −123.846 | −4.35689 | ||||||||
\(809\) | −14.1589 | −0.497801 | −0.248900 | − | 0.968529i | \(-0.580069\pi\) | ||||
−0.248900 | + | 0.968529i | \(0.580069\pi\) | |||||||
\(810\) | 68.3051 | 2.40000 | ||||||||
\(811\) | −5.78504 | −0.203140 | −0.101570 | − | 0.994828i | \(-0.532387\pi\) | ||||
−0.101570 | + | 0.994828i | \(0.532387\pi\) | |||||||
\(812\) | 7.67016 | 0.269170 | ||||||||
\(813\) | 0.607558 | 0.0213080 | ||||||||
\(814\) | −12.5248 | −0.438994 | ||||||||
\(815\) | 39.4016 | 1.38018 | ||||||||
\(816\) | 9.88461 | 0.346031 | ||||||||
\(817\) | −74.2188 | −2.59659 | ||||||||
\(818\) | −53.1307 | −1.85767 | ||||||||
\(819\) | 3.93784 | 0.137599 | ||||||||
\(820\) | 125.986 | 4.39962 | ||||||||
\(821\) | −13.0813 | −0.456540 | −0.228270 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228270 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(822\) | −15.8210 | −0.551822 | ||||||||
\(823\) | −1.68209 | −0.0586338 | −0.0293169 | − | 0.999570i | \(-0.509333\pi\) | ||||
−0.0293169 | + | 0.999570i | \(0.509333\pi\) | |||||||
\(824\) | −114.541 | −3.99023 | ||||||||
\(825\) | −13.9425 | −0.485415 | ||||||||
\(826\) | 24.6221 | 0.856712 | ||||||||
\(827\) | −44.5451 | −1.54899 | −0.774493 | − | 0.632583i | \(-0.781995\pi\) | ||||
−0.774493 | + | 0.632583i | \(0.781995\pi\) | |||||||
\(828\) | −130.196 | −4.52461 | ||||||||
\(829\) | −33.4563 | −1.16198 | −0.580992 | − | 0.813909i | \(-0.697335\pi\) | ||||
−0.580992 | + | 0.813909i | \(0.697335\pi\) | |||||||
\(830\) | 110.760 | 3.84454 | ||||||||
\(831\) | 6.56786 | 0.227836 | ||||||||
\(832\) | 54.9638 | 1.90553 | ||||||||
\(833\) | 1.31679 | 0.0456241 | ||||||||
\(834\) | −19.3072 | −0.668555 | ||||||||
\(835\) | 42.8528 | 1.48298 | ||||||||
\(836\) | 207.985 | 7.19331 | ||||||||
\(837\) | −18.1552 | −0.627536 | ||||||||
\(838\) | −6.12845 | −0.211704 | ||||||||
\(839\) | −50.1379 | −1.73095 | −0.865476 | − | 0.500951i | \(-0.832984\pi\) | ||||
−0.865476 | + | 0.500951i | \(0.832984\pi\) | |||||||
\(840\) | −15.4368 | −0.532619 | ||||||||
\(841\) | −27.1712 | −0.936939 | ||||||||
\(842\) | 112.113 | 3.86368 | ||||||||
\(843\) | 5.47729 | 0.188648 | ||||||||
\(844\) | 46.4926 | 1.60034 | ||||||||
\(845\) | 37.5045 | 1.29019 | ||||||||
\(846\) | 37.9550 | 1.30492 | ||||||||
\(847\) | −11.5917 | −0.398295 | ||||||||
\(848\) | −204.469 | −7.02151 | ||||||||
\(849\) | 7.26499 | 0.249334 | ||||||||
\(850\) | −23.9814 | −0.822556 | ||||||||
\(851\) | −7.79670 | −0.267267 | ||||||||
\(852\) | −29.6728 | −1.01657 | ||||||||
\(853\) | −33.5241 | −1.14784 | −0.573922 | − | 0.818910i | \(-0.694579\pi\) | ||||
−0.573922 | + | 0.818910i | \(0.694579\pi\) | |||||||
\(854\) | −26.0756 | −0.892290 | ||||||||
\(855\) | −73.5201 | −2.51433 | ||||||||
\(856\) | −78.1842 | −2.67228 | ||||||||
\(857\) | 10.3296 | 0.352853 | 0.176427 | − | 0.984314i | \(-0.443546\pi\) | ||||
0.176427 | + | 0.984314i | \(0.443546\pi\) | |||||||
\(858\) | 8.25718 | 0.281895 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | −185.639 | −6.33023 | ||||||||
\(861\) | 2.91268 | 0.0992638 | ||||||||
\(862\) | −41.6627 | −1.41904 | ||||||||
\(863\) | 12.5835 | 0.428347 | 0.214174 | − | 0.976796i | \(-0.431294\pi\) | ||||
0.214174 | + | 0.976796i | \(0.431294\pi\) | |||||||
\(864\) | 67.9718 | 2.31245 | ||||||||
\(865\) | −16.8125 | −0.571641 | ||||||||
\(866\) | −13.2057 | −0.448747 | ||||||||
\(867\) | −6.81060 | −0.231300 | ||||||||
\(868\) | −39.7894 | −1.35054 | ||||||||
\(869\) | −77.3782 | −2.62488 | ||||||||
\(870\) | −5.68528 | −0.192749 | ||||||||
\(871\) | 14.4072 | 0.488168 | ||||||||
\(872\) | −38.7670 | −1.31282 | ||||||||
\(873\) | 41.7151 | 1.41184 | ||||||||
\(874\) | 175.125 | 5.92368 | ||||||||
\(875\) | 5.35914 | 0.181172 | ||||||||
\(876\) | 12.2615 | 0.414278 | ||||||||
\(877\) | 5.53870 | 0.187029 | 0.0935143 | − | 0.995618i | \(-0.470190\pi\) | ||||
0.0935143 | + | 0.995618i | \(0.470190\pi\) | |||||||
\(878\) | 38.8852 | 1.31231 | ||||||||
\(879\) | 1.22242 | 0.0412312 | ||||||||
\(880\) | 272.096 | 9.17236 | ||||||||
\(881\) | −16.5508 | −0.557610 | −0.278805 | − | 0.960348i | \(-0.589938\pi\) | ||||
−0.278805 | + | 0.960348i | \(0.589938\pi\) | |||||||
\(882\) | 7.75816 | 0.261231 | ||||||||
\(883\) | 14.7238 | 0.495496 | 0.247748 | − | 0.968825i | \(-0.420310\pi\) | ||||
0.247748 | + | 0.968825i | \(0.420310\pi\) | |||||||
\(884\) | 10.5000 | 0.353154 | ||||||||
\(885\) | −13.4927 | −0.453551 | ||||||||
\(886\) | −7.45017 | −0.250293 | ||||||||
\(887\) | −3.71181 | −0.124630 | −0.0623152 | − | 0.998057i | \(-0.519848\pi\) | ||||
−0.0623152 | + | 0.998057i | \(0.519848\pi\) | |||||||
\(888\) | 4.31657 | 0.144855 | ||||||||
\(889\) | 14.0170 | 0.470116 | ||||||||
\(890\) | −5.09881 | −0.170912 | ||||||||
\(891\) | −34.4519 | −1.15418 | ||||||||
\(892\) | −3.50742 | −0.117437 | ||||||||
\(893\) | −37.7436 | −1.26304 | ||||||||
\(894\) | 0.835222 | 0.0279340 | ||||||||
\(895\) | 20.5888 | 0.688209 | ||||||||
\(896\) | 55.7581 | 1.86275 | ||||||||
\(897\) | 5.14010 | 0.171623 | ||||||||
\(898\) | 56.7922 | 1.89518 | ||||||||
\(899\) | −9.48686 | −0.316404 | ||||||||
\(900\) | −104.458 | −3.48193 | ||||||||
\(901\) | −16.0015 | −0.533088 | ||||||||
\(902\) | −85.9525 | −2.86190 | ||||||||
\(903\) | −4.29179 | −0.142822 | ||||||||
\(904\) | 148.004 | 4.92254 | ||||||||
\(905\) | 67.7178 | 2.25102 | ||||||||
\(906\) | −2.68391 | −0.0891671 | ||||||||
\(907\) | −40.3829 | −1.34089 | −0.670445 | − | 0.741959i | \(-0.733897\pi\) | ||||
−0.670445 | + | 0.741959i | \(0.733897\pi\) | |||||||
\(908\) | −73.2838 | −2.43201 | ||||||||
\(909\) | −34.1081 | −1.13129 | ||||||||
\(910\) | −13.2484 | −0.439180 | ||||||||
\(911\) | 41.3577 | 1.37024 | 0.685120 | − | 0.728430i | \(-0.259750\pi\) | ||||
0.685120 | + | 0.728430i | \(0.259750\pi\) | |||||||
\(912\) | −57.9130 | −1.91769 | ||||||||
\(913\) | −55.8655 | −1.84888 | ||||||||
\(914\) | −59.1976 | −1.95808 | ||||||||
\(915\) | 14.2892 | 0.472386 | ||||||||
\(916\) | 36.4039 | 1.20282 | ||||||||
\(917\) | −11.2245 | −0.370665 | ||||||||
\(918\) | 9.43900 | 0.311533 | ||||||||
\(919\) | 3.74862 | 0.123655 | 0.0618277 | − | 0.998087i | \(-0.480307\pi\) | ||||
0.0618277 | + | 0.998087i | \(0.480307\pi\) | |||||||
\(920\) | 283.571 | 9.34906 | ||||||||
\(921\) | −6.62521 | −0.218308 | ||||||||
\(922\) | −85.3498 | −2.81085 | ||||||||
\(923\) | −16.4864 | −0.542656 | ||||||||
\(924\) | 12.0270 | 0.395659 | ||||||||
\(925\) | −6.25539 | −0.205676 | ||||||||
\(926\) | −66.7398 | −2.19321 | ||||||||
\(927\) | −31.5454 | −1.03609 | ||||||||
\(928\) | 35.5181 | 1.16594 | ||||||||
\(929\) | 31.7149 | 1.04053 | 0.520266 | − | 0.854004i | \(-0.325833\pi\) | ||||
0.520266 | + | 0.854004i | \(0.325833\pi\) | |||||||
\(930\) | 29.4927 | 0.967104 | ||||||||
\(931\) | −7.71496 | −0.252848 | ||||||||
\(932\) | 53.8689 | 1.76453 | ||||||||
\(933\) | 1.21512 | 0.0397814 | ||||||||
\(934\) | 16.5288 | 0.540839 | ||||||||
\(935\) | 21.2939 | 0.696385 | ||||||||
\(936\) | 40.0490 | 1.30904 | ||||||||
\(937\) | 26.9802 | 0.881406 | 0.440703 | − | 0.897653i | \(-0.354729\pi\) | ||||
0.440703 | + | 0.897653i | \(0.354729\pi\) | |||||||
\(938\) | 28.3844 | 0.926782 | ||||||||
\(939\) | 9.83198 | 0.320854 | ||||||||
\(940\) | −94.4057 | −3.07917 | ||||||||
\(941\) | −6.90726 | −0.225170 | −0.112585 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112585 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(942\) | 15.0292 | 0.489678 | ||||||||
\(943\) | −53.5054 | −1.74238 | ||||||||
\(944\) | 149.575 | 4.86826 | ||||||||
\(945\) | −8.80487 | −0.286422 | ||||||||
\(946\) | 126.650 | 4.11774 | ||||||||
\(947\) | −8.52085 | −0.276890 | −0.138445 | − | 0.990370i | \(-0.544210\pi\) | ||||
−0.138445 | + | 0.990370i | \(0.544210\pi\) | |||||||
\(948\) | 41.1933 | 1.33790 | ||||||||
\(949\) | 6.81256 | 0.221145 | ||||||||
\(950\) | 140.505 | 4.55858 | ||||||||
\(951\) | −5.23499 | −0.169756 | ||||||||
\(952\) | 13.3922 | 0.434043 | ||||||||
\(953\) | 36.4130 | 1.17953 | 0.589766 | − | 0.807574i | \(-0.299220\pi\) | ||||
0.589766 | + | 0.807574i | \(0.299220\pi\) | |||||||
\(954\) | −94.2763 | −3.05231 | ||||||||
\(955\) | 12.6541 | 0.409478 | ||||||||
\(956\) | 72.1586 | 2.33378 | ||||||||
\(957\) | 2.86756 | 0.0926951 | ||||||||
\(958\) | −46.4877 | −1.50195 | ||||||||
\(959\) | −12.8035 | −0.413445 | ||||||||
\(960\) | −59.3403 | −1.91520 | ||||||||
\(961\) | 18.2136 | 0.587536 | ||||||||
\(962\) | 3.70464 | 0.119442 | ||||||||
\(963\) | −21.5325 | −0.693874 | ||||||||
\(964\) | 153.848 | 4.95510 | ||||||||
\(965\) | 74.9998 | 2.41433 | ||||||||
\(966\) | 10.1268 | 0.325824 | ||||||||
\(967\) | 34.9291 | 1.12324 | 0.561621 | − | 0.827394i | \(-0.310178\pi\) | ||||
0.561621 | + | 0.827394i | \(0.310178\pi\) | |||||||
\(968\) | −117.891 | −3.78916 | ||||||||
\(969\) | −4.53220 | −0.145595 | ||||||||
\(970\) | −140.346 | −4.50623 | ||||||||
\(971\) | 51.3725 | 1.64862 | 0.824312 | − | 0.566136i | \(-0.191562\pi\) | ||||
0.824312 | + | 0.566136i | \(0.191562\pi\) | |||||||
\(972\) | 62.3766 | 2.00073 | ||||||||
\(973\) | −15.6247 | −0.500905 | ||||||||
\(974\) | 69.9741 | 2.24212 | ||||||||
\(975\) | 4.12397 | 0.132073 | ||||||||
\(976\) | −158.405 | −5.07043 | ||||||||
\(977\) | 33.4625 | 1.07056 | 0.535279 | − | 0.844675i | \(-0.320206\pi\) | ||||
0.535279 | + | 0.844675i | \(0.320206\pi\) | |||||||
\(978\) | 14.3106 | 0.457603 | ||||||||
\(979\) | 2.57175 | 0.0821936 | ||||||||
\(980\) | −19.2969 | −0.616418 | ||||||||
\(981\) | −10.6767 | −0.340880 | ||||||||
\(982\) | 89.4610 | 2.85482 | ||||||||
\(983\) | −3.55823 | −0.113490 | −0.0567449 | − | 0.998389i | \(-0.518072\pi\) | ||||
−0.0567449 | + | 0.998389i | \(0.518072\pi\) | |||||||
\(984\) | 29.6228 | 0.944341 | ||||||||
\(985\) | −17.5709 | −0.559856 | ||||||||
\(986\) | 4.93227 | 0.157075 | ||||||||
\(987\) | −2.18257 | −0.0694720 | ||||||||
\(988\) | −61.5187 | −1.95717 | ||||||||
\(989\) | 78.8395 | 2.50695 | ||||||||
\(990\) | 125.458 | 3.98730 | ||||||||
\(991\) | −17.3632 | −0.551560 | −0.275780 | − | 0.961221i | \(-0.588936\pi\) | ||||
−0.275780 | + | 0.961221i | \(0.588936\pi\) | |||||||
\(992\) | −184.252 | −5.85001 | ||||||||
\(993\) | −4.12214 | −0.130812 | ||||||||
\(994\) | −32.4808 | −1.03023 | ||||||||
\(995\) | −16.2593 | −0.515456 | ||||||||
\(996\) | 29.7408 | 0.942372 | ||||||||
\(997\) | 31.3869 | 0.994032 | 0.497016 | − | 0.867741i | \(-0.334429\pi\) | ||||
0.497016 | + | 0.867741i | \(0.334429\pi\) | |||||||
\(998\) | −59.4237 | −1.88102 | ||||||||
\(999\) | 2.46210 | 0.0778974 |
(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 | 6013.2.a.c.1.4 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.c.1.4 | ✓ | 104 | 1.1 | even | 1 | trivial |