Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, 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("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60374 | −1.84112 | −0.920562 | − | 0.390598i | \(-0.872268\pi\) | ||||
−0.920562 | + | 0.390598i | \(0.872268\pi\) | |||||||
\(3\) | 2.97894 | 1.71989 | 0.859945 | − | 0.510386i | \(-0.170498\pi\) | ||||
0.859945 | + | 0.510386i | \(0.170498\pi\) | |||||||
\(4\) | 4.77947 | 2.38973 | ||||||||
\(5\) | 0.851432 | 0.380772 | 0.190386 | − | 0.981709i | \(-0.439026\pi\) | ||||
0.190386 | + | 0.981709i | \(0.439026\pi\) | |||||||
\(6\) | −7.75638 | −3.16653 | ||||||||
\(7\) | 3.04314 | 1.15020 | 0.575100 | − | 0.818083i | \(-0.304963\pi\) | ||||
0.575100 | + | 0.818083i | \(0.304963\pi\) | |||||||
\(8\) | −7.23702 | −2.55867 | ||||||||
\(9\) | 5.87407 | 1.95802 | ||||||||
\(10\) | −2.21691 | −0.701048 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 14.2377 | 4.11008 | ||||||||
\(13\) | 1.25630 | 0.348436 | 0.174218 | − | 0.984707i | \(-0.444260\pi\) | ||||
0.174218 | + | 0.984707i | \(0.444260\pi\) | |||||||
\(14\) | −7.92356 | −2.11766 | ||||||||
\(15\) | 2.53636 | 0.654886 | ||||||||
\(16\) | 9.28438 | 2.32110 | ||||||||
\(17\) | −7.73575 | −1.87619 | −0.938097 | − | 0.346373i | \(-0.887413\pi\) | ||||
−0.938097 | + | 0.346373i | \(0.887413\pi\) | |||||||
\(18\) | −15.2946 | −3.60496 | ||||||||
\(19\) | 6.82604 | 1.56600 | 0.783000 | − | 0.622021i | \(-0.213688\pi\) | ||||
0.783000 | + | 0.622021i | \(0.213688\pi\) | |||||||
\(20\) | 4.06939 | 0.909944 | ||||||||
\(21\) | 9.06534 | 1.97822 | ||||||||
\(22\) | 2.60374 | 0.555120 | ||||||||
\(23\) | 8.40462 | 1.75248 | 0.876242 | − | 0.481871i | \(-0.160042\pi\) | ||||
0.876242 | + | 0.481871i | \(0.160042\pi\) | |||||||
\(24\) | −21.5586 | −4.40064 | ||||||||
\(25\) | −4.27506 | −0.855013 | ||||||||
\(26\) | −3.27109 | −0.641514 | ||||||||
\(27\) | 8.56167 | 1.64769 | ||||||||
\(28\) | 14.5446 | 2.74867 | ||||||||
\(29\) | 1.09847 | 0.203980 | 0.101990 | − | 0.994785i | \(-0.467479\pi\) | ||||
0.101990 | + | 0.994785i | \(0.467479\pi\) | |||||||
\(30\) | −6.60403 | −1.20573 | ||||||||
\(31\) | −2.03738 | −0.365924 | −0.182962 | − | 0.983120i | \(-0.558568\pi\) | ||||
−0.182962 | + | 0.983120i | \(0.558568\pi\) | |||||||
\(32\) | −9.70010 | −1.71475 | ||||||||
\(33\) | −2.97894 | −0.518566 | ||||||||
\(34\) | 20.1419 | 3.45430 | ||||||||
\(35\) | 2.59103 | 0.437964 | ||||||||
\(36\) | 28.0749 | 4.67916 | ||||||||
\(37\) | −6.32030 | −1.03905 | −0.519525 | − | 0.854455i | \(-0.673891\pi\) | ||||
−0.519525 | + | 0.854455i | \(0.673891\pi\) | |||||||
\(38\) | −17.7732 | −2.88320 | ||||||||
\(39\) | 3.74245 | 0.599272 | ||||||||
\(40\) | −6.16183 | −0.974271 | ||||||||
\(41\) | −9.82455 | −1.53434 | −0.767168 | − | 0.641446i | \(-0.778335\pi\) | ||||
−0.767168 | + | 0.641446i | \(0.778335\pi\) | |||||||
\(42\) | −23.6038 | −3.64214 | ||||||||
\(43\) | −8.23734 | −1.25618 | −0.628091 | − | 0.778140i | \(-0.716163\pi\) | ||||
−0.628091 | + | 0.778140i | \(0.716163\pi\) | |||||||
\(44\) | −4.77947 | −0.720532 | ||||||||
\(45\) | 5.00137 | 0.745560 | ||||||||
\(46\) | −21.8835 | −3.22654 | ||||||||
\(47\) | 1.11751 | 0.163006 | 0.0815029 | − | 0.996673i | \(-0.474028\pi\) | ||||
0.0815029 | + | 0.996673i | \(0.474028\pi\) | |||||||
\(48\) | 27.6576 | 3.99203 | ||||||||
\(49\) | 2.26073 | 0.322961 | ||||||||
\(50\) | 11.1312 | 1.57418 | ||||||||
\(51\) | −23.0443 | −3.22685 | ||||||||
\(52\) | 6.00447 | 0.832670 | ||||||||
\(53\) | −4.72415 | −0.648912 | −0.324456 | − | 0.945901i | \(-0.605181\pi\) | ||||
−0.324456 | + | 0.945901i | \(0.605181\pi\) | |||||||
\(54\) | −22.2924 | −3.03361 | ||||||||
\(55\) | −0.851432 | −0.114807 | ||||||||
\(56\) | −22.0233 | −2.94299 | ||||||||
\(57\) | 20.3343 | 2.69335 | ||||||||
\(58\) | −2.86013 | −0.375553 | ||||||||
\(59\) | 11.0384 | 1.43708 | 0.718540 | − | 0.695485i | \(-0.244811\pi\) | ||||
0.718540 | + | 0.695485i | \(0.244811\pi\) | |||||||
\(60\) | 12.1225 | 1.56500 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 5.30480 | 0.673711 | ||||||||
\(63\) | 17.8756 | 2.25212 | ||||||||
\(64\) | 6.68778 | 0.835972 | ||||||||
\(65\) | 1.06966 | 0.132675 | ||||||||
\(66\) | 7.75638 | 0.954745 | ||||||||
\(67\) | 6.91010 | 0.844203 | 0.422102 | − | 0.906549i | \(-0.361293\pi\) | ||||
0.422102 | + | 0.906549i | \(0.361293\pi\) | |||||||
\(68\) | −36.9728 | −4.48361 | ||||||||
\(69\) | 25.0368 | 3.01408 | ||||||||
\(70\) | −6.74637 | −0.806346 | ||||||||
\(71\) | −7.00240 | −0.831032 | −0.415516 | − | 0.909586i | \(-0.636399\pi\) | ||||
−0.415516 | + | 0.909586i | \(0.636399\pi\) | |||||||
\(72\) | −42.5107 | −5.00994 | ||||||||
\(73\) | 1.27134 | 0.148799 | 0.0743995 | − | 0.997229i | \(-0.476296\pi\) | ||||
0.0743995 | + | 0.997229i | \(0.476296\pi\) | |||||||
\(74\) | 16.4564 | 1.91302 | ||||||||
\(75\) | −12.7351 | −1.47053 | ||||||||
\(76\) | 32.6248 | 3.74233 | ||||||||
\(77\) | −3.04314 | −0.346798 | ||||||||
\(78\) | −9.74438 | −1.10333 | ||||||||
\(79\) | −3.71107 | −0.417529 | −0.208764 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208764 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(80\) | 7.90502 | 0.883808 | ||||||||
\(81\) | 7.88248 | 0.875832 | ||||||||
\(82\) | 25.5806 | 2.82490 | ||||||||
\(83\) | 11.2940 | 1.23967 | 0.619837 | − | 0.784731i | \(-0.287199\pi\) | ||||
0.619837 | + | 0.784731i | \(0.287199\pi\) | |||||||
\(84\) | 43.3275 | 4.72742 | ||||||||
\(85\) | −6.58646 | −0.714402 | ||||||||
\(86\) | 21.4479 | 2.31279 | ||||||||
\(87\) | 3.27227 | 0.350824 | ||||||||
\(88\) | 7.23702 | 0.771469 | ||||||||
\(89\) | −3.62680 | −0.384440 | −0.192220 | − | 0.981352i | \(-0.561569\pi\) | ||||
−0.192220 | + | 0.981352i | \(0.561569\pi\) | |||||||
\(90\) | −13.0223 | −1.37267 | ||||||||
\(91\) | 3.82312 | 0.400771 | ||||||||
\(92\) | 40.1696 | 4.18797 | ||||||||
\(93\) | −6.06922 | −0.629349 | ||||||||
\(94\) | −2.90971 | −0.300114 | ||||||||
\(95\) | 5.81191 | 0.596289 | ||||||||
\(96\) | −28.8960 | −2.94918 | ||||||||
\(97\) | −0.113236 | −0.0114974 | −0.00574869 | − | 0.999983i | \(-0.501830\pi\) | ||||
−0.00574869 | + | 0.999983i | \(0.501830\pi\) | |||||||
\(98\) | −5.88635 | −0.594611 | ||||||||
\(99\) | −5.87407 | −0.590366 | ||||||||
\(100\) | −20.4325 | −2.04325 | ||||||||
\(101\) | −3.13269 | −0.311714 | −0.155857 | − | 0.987780i | \(-0.549814\pi\) | ||||
−0.155857 | + | 0.987780i | \(0.549814\pi\) | |||||||
\(102\) | 60.0014 | 5.94102 | ||||||||
\(103\) | −0.612788 | −0.0603798 | −0.0301899 | − | 0.999544i | \(-0.509611\pi\) | ||||
−0.0301899 | + | 0.999544i | \(0.509611\pi\) | |||||||
\(104\) | −9.09190 | −0.891534 | ||||||||
\(105\) | 7.71852 | 0.753250 | ||||||||
\(106\) | 12.3005 | 1.19473 | ||||||||
\(107\) | 1.37535 | 0.132960 | 0.0664801 | − | 0.997788i | \(-0.478823\pi\) | ||||
0.0664801 | + | 0.997788i | \(0.478823\pi\) | |||||||
\(108\) | 40.9203 | 3.93755 | ||||||||
\(109\) | 20.5325 | 1.96665 | 0.983327 | − | 0.181845i | \(-0.0582068\pi\) | ||||
0.983327 | + | 0.181845i | \(0.0582068\pi\) | |||||||
\(110\) | 2.21691 | 0.211374 | ||||||||
\(111\) | −18.8278 | −1.78705 | ||||||||
\(112\) | 28.2537 | 2.66973 | ||||||||
\(113\) | −0.112340 | −0.0105681 | −0.00528404 | − | 0.999986i | \(-0.501682\pi\) | ||||
−0.00528404 | + | 0.999986i | \(0.501682\pi\) | |||||||
\(114\) | −52.9454 | −4.95879 | ||||||||
\(115\) | 7.15596 | 0.667297 | ||||||||
\(116\) | 5.25010 | 0.487459 | ||||||||
\(117\) | 7.37962 | 0.682246 | ||||||||
\(118\) | −28.7412 | −2.64584 | ||||||||
\(119\) | −23.5410 | −2.15800 | ||||||||
\(120\) | −18.3557 | −1.67564 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.60374 | −0.235732 | ||||||||
\(123\) | −29.2667 | −2.63889 | ||||||||
\(124\) | −9.73758 | −0.874461 | ||||||||
\(125\) | −7.89709 | −0.706337 | ||||||||
\(126\) | −46.5435 | −4.14643 | ||||||||
\(127\) | −12.5972 | −1.11782 | −0.558912 | − | 0.829227i | \(-0.688781\pi\) | ||||
−0.558912 | + | 0.829227i | \(0.688781\pi\) | |||||||
\(128\) | 1.98695 | 0.175624 | ||||||||
\(129\) | −24.5385 | −2.16050 | ||||||||
\(130\) | −2.78511 | −0.244271 | ||||||||
\(131\) | 6.91322 | 0.604011 | 0.302006 | − | 0.953306i | \(-0.402344\pi\) | ||||
0.302006 | + | 0.953306i | \(0.402344\pi\) | |||||||
\(132\) | −14.2377 | −1.23924 | ||||||||
\(133\) | 20.7726 | 1.80121 | ||||||||
\(134\) | −17.9921 | −1.55428 | ||||||||
\(135\) | 7.28968 | 0.627396 | ||||||||
\(136\) | 55.9837 | 4.80056 | ||||||||
\(137\) | −8.75852 | −0.748291 | −0.374146 | − | 0.927370i | \(-0.622064\pi\) | ||||
−0.374146 | + | 0.927370i | \(0.622064\pi\) | |||||||
\(138\) | −65.1895 | −5.54930 | ||||||||
\(139\) | 13.2977 | 1.12790 | 0.563949 | − | 0.825809i | \(-0.309281\pi\) | ||||
0.563949 | + | 0.825809i | \(0.309281\pi\) | |||||||
\(140\) | 12.3837 | 1.04662 | ||||||||
\(141\) | 3.32900 | 0.280352 | ||||||||
\(142\) | 18.2324 | 1.53003 | ||||||||
\(143\) | −1.25630 | −0.105057 | ||||||||
\(144\) | 54.5371 | 4.54476 | ||||||||
\(145\) | 0.935271 | 0.0776700 | ||||||||
\(146\) | −3.31024 | −0.273957 | ||||||||
\(147\) | 6.73457 | 0.555458 | ||||||||
\(148\) | −30.2077 | −2.48305 | ||||||||
\(149\) | 2.50057 | 0.204855 | 0.102428 | − | 0.994740i | \(-0.467339\pi\) | ||||
0.102428 | + | 0.994740i | \(0.467339\pi\) | |||||||
\(150\) | 33.1590 | 2.70742 | ||||||||
\(151\) | 17.4446 | 1.41962 | 0.709811 | − | 0.704392i | \(-0.248780\pi\) | ||||
0.709811 | + | 0.704392i | \(0.248780\pi\) | |||||||
\(152\) | −49.4002 | −4.00688 | ||||||||
\(153\) | −45.4403 | −3.67363 | ||||||||
\(154\) | 7.92356 | 0.638499 | ||||||||
\(155\) | −1.73469 | −0.139334 | ||||||||
\(156\) | 17.8869 | 1.43210 | ||||||||
\(157\) | −21.3392 | −1.70305 | −0.851526 | − | 0.524312i | \(-0.824323\pi\) | ||||
−0.851526 | + | 0.524312i | \(0.824323\pi\) | |||||||
\(158\) | 9.66268 | 0.768721 | ||||||||
\(159\) | −14.0730 | −1.11606 | ||||||||
\(160\) | −8.25897 | −0.652929 | ||||||||
\(161\) | 25.5765 | 2.01571 | ||||||||
\(162\) | −20.5239 | −1.61251 | ||||||||
\(163\) | −13.4618 | −1.05441 | −0.527205 | − | 0.849738i | \(-0.676760\pi\) | ||||
−0.527205 | + | 0.849738i | \(0.676760\pi\) | |||||||
\(164\) | −46.9561 | −3.66666 | ||||||||
\(165\) | −2.53636 | −0.197456 | ||||||||
\(166\) | −29.4065 | −2.28239 | ||||||||
\(167\) | 24.1963 | 1.87237 | 0.936184 | − | 0.351510i | \(-0.114332\pi\) | ||||
0.936184 | + | 0.351510i | \(0.114332\pi\) | |||||||
\(168\) | −65.6060 | −5.06161 | ||||||||
\(169\) | −11.4217 | −0.878592 | ||||||||
\(170\) | 17.1494 | 1.31530 | ||||||||
\(171\) | 40.0966 | 3.06627 | ||||||||
\(172\) | −39.3701 | −3.00194 | ||||||||
\(173\) | −6.87500 | −0.522697 | −0.261348 | − | 0.965245i | \(-0.584167\pi\) | ||||
−0.261348 | + | 0.965245i | \(0.584167\pi\) | |||||||
\(174\) | −8.52014 | −0.645910 | ||||||||
\(175\) | −13.0096 | −0.983436 | ||||||||
\(176\) | −9.28438 | −0.699837 | ||||||||
\(177\) | 32.8828 | 2.47162 | ||||||||
\(178\) | 9.44324 | 0.707801 | ||||||||
\(179\) | −7.18760 | −0.537227 | −0.268613 | − | 0.963248i | \(-0.586565\pi\) | ||||
−0.268613 | + | 0.963248i | \(0.586565\pi\) | |||||||
\(180\) | 23.9039 | 1.78169 | ||||||||
\(181\) | −3.28618 | −0.244260 | −0.122130 | − | 0.992514i | \(-0.538972\pi\) | ||||
−0.122130 | + | 0.992514i | \(0.538972\pi\) | |||||||
\(182\) | −9.95441 | −0.737870 | ||||||||
\(183\) | 2.97894 | 0.220209 | ||||||||
\(184\) | −60.8244 | −4.48403 | ||||||||
\(185\) | −5.38130 | −0.395641 | ||||||||
\(186\) | 15.8027 | 1.15871 | ||||||||
\(187\) | 7.73575 | 0.565694 | ||||||||
\(188\) | 5.34111 | 0.389541 | ||||||||
\(189\) | 26.0544 | 1.89518 | ||||||||
\(190\) | −15.1327 | −1.09784 | ||||||||
\(191\) | −15.9729 | −1.15576 | −0.577878 | − | 0.816123i | \(-0.696119\pi\) | ||||
−0.577878 | + | 0.816123i | \(0.696119\pi\) | |||||||
\(192\) | 19.9225 | 1.43778 | ||||||||
\(193\) | −5.16456 | −0.371753 | −0.185876 | − | 0.982573i | \(-0.559512\pi\) | ||||
−0.185876 | + | 0.982573i | \(0.559512\pi\) | |||||||
\(194\) | 0.294837 | 0.0211681 | ||||||||
\(195\) | 3.18644 | 0.228186 | ||||||||
\(196\) | 10.8051 | 0.771791 | ||||||||
\(197\) | −19.1277 | −1.36280 | −0.681398 | − | 0.731914i | \(-0.738627\pi\) | ||||
−0.681398 | + | 0.731914i | \(0.738627\pi\) | |||||||
\(198\) | 15.2946 | 1.08694 | ||||||||
\(199\) | 0.0471165 | 0.00334000 | 0.00167000 | − | 0.999999i | \(-0.499468\pi\) | ||||
0.00167000 | + | 0.999999i | \(0.499468\pi\) | |||||||
\(200\) | 30.9387 | 2.18770 | ||||||||
\(201\) | 20.5848 | 1.45194 | ||||||||
\(202\) | 8.15672 | 0.573905 | ||||||||
\(203\) | 3.34280 | 0.234618 | ||||||||
\(204\) | −110.140 | −7.71131 | ||||||||
\(205\) | −8.36493 | −0.584232 | ||||||||
\(206\) | 1.59554 | 0.111167 | ||||||||
\(207\) | 49.3693 | 3.43141 | ||||||||
\(208\) | 11.6640 | 0.808754 | ||||||||
\(209\) | −6.82604 | −0.472167 | ||||||||
\(210\) | −20.0970 | −1.38683 | ||||||||
\(211\) | 20.7627 | 1.42936 | 0.714681 | − | 0.699451i | \(-0.246572\pi\) | ||||
0.714681 | + | 0.699451i | \(0.246572\pi\) | |||||||
\(212\) | −22.5789 | −1.55073 | ||||||||
\(213\) | −20.8597 | −1.42928 | ||||||||
\(214\) | −3.58106 | −0.244796 | ||||||||
\(215\) | −7.01353 | −0.478319 | ||||||||
\(216\) | −61.9610 | −4.21591 | ||||||||
\(217\) | −6.20003 | −0.420886 | ||||||||
\(218\) | −53.4613 | −3.62085 | ||||||||
\(219\) | 3.78724 | 0.255918 | ||||||||
\(220\) | −4.06939 | −0.274358 | ||||||||
\(221\) | −9.71845 | −0.653734 | ||||||||
\(222\) | 49.0226 | 3.29018 | ||||||||
\(223\) | 10.9949 | 0.736273 | 0.368137 | − | 0.929772i | \(-0.379996\pi\) | ||||
0.368137 | + | 0.929772i | \(0.379996\pi\) | |||||||
\(224\) | −29.5188 | −1.97231 | ||||||||
\(225\) | −25.1120 | −1.67413 | ||||||||
\(226\) | 0.292505 | 0.0194572 | ||||||||
\(227\) | 9.54696 | 0.633654 | 0.316827 | − | 0.948483i | \(-0.397383\pi\) | ||||
0.316827 | + | 0.948483i | \(0.397383\pi\) | |||||||
\(228\) | 97.1874 | 6.43639 | ||||||||
\(229\) | 9.08724 | 0.600502 | 0.300251 | − | 0.953860i | \(-0.402930\pi\) | ||||
0.300251 | + | 0.953860i | \(0.402930\pi\) | |||||||
\(230\) | −18.6323 | −1.22858 | ||||||||
\(231\) | −9.06534 | −0.596455 | ||||||||
\(232\) | −7.94963 | −0.521919 | ||||||||
\(233\) | −9.22388 | −0.604277 | −0.302138 | − | 0.953264i | \(-0.597700\pi\) | ||||
−0.302138 | + | 0.953264i | \(0.597700\pi\) | |||||||
\(234\) | −19.2146 | −1.25610 | ||||||||
\(235\) | 0.951486 | 0.0620681 | ||||||||
\(236\) | 52.7578 | 3.43424 | ||||||||
\(237\) | −11.0551 | −0.718103 | ||||||||
\(238\) | 61.2947 | 3.97314 | ||||||||
\(239\) | −14.5862 | −0.943501 | −0.471751 | − | 0.881732i | \(-0.656378\pi\) | ||||
−0.471751 | + | 0.881732i | \(0.656378\pi\) | |||||||
\(240\) | 23.5486 | 1.52005 | ||||||||
\(241\) | −10.7788 | −0.694325 | −0.347163 | − | 0.937805i | \(-0.612855\pi\) | ||||
−0.347163 | + | 0.937805i | \(0.612855\pi\) | |||||||
\(242\) | −2.60374 | −0.167375 | ||||||||
\(243\) | −2.20359 | −0.141361 | ||||||||
\(244\) | 4.77947 | 0.305974 | ||||||||
\(245\) | 1.92486 | 0.122975 | ||||||||
\(246\) | 76.2029 | 4.85852 | ||||||||
\(247\) | 8.57558 | 0.545651 | ||||||||
\(248\) | 14.7445 | 0.936279 | ||||||||
\(249\) | 33.6440 | 2.13210 | ||||||||
\(250\) | 20.5620 | 1.30045 | ||||||||
\(251\) | 15.2761 | 0.964220 | 0.482110 | − | 0.876111i | \(-0.339871\pi\) | ||||
0.482110 | + | 0.876111i | \(0.339871\pi\) | |||||||
\(252\) | 85.4361 | 5.38197 | ||||||||
\(253\) | −8.40462 | −0.528394 | ||||||||
\(254\) | 32.7999 | 2.05805 | ||||||||
\(255\) | −19.6207 | −1.22869 | ||||||||
\(256\) | −18.5491 | −1.15932 | ||||||||
\(257\) | −4.08000 | −0.254503 | −0.127252 | − | 0.991870i | \(-0.540616\pi\) | ||||
−0.127252 | + | 0.991870i | \(0.540616\pi\) | |||||||
\(258\) | 63.8919 | 3.97774 | ||||||||
\(259\) | −19.2336 | −1.19512 | ||||||||
\(260\) | 5.11240 | 0.317057 | ||||||||
\(261\) | 6.45248 | 0.399398 | ||||||||
\(262\) | −18.0002 | −1.11206 | ||||||||
\(263\) | 1.06475 | 0.0656553 | 0.0328276 | − | 0.999461i | \(-0.489549\pi\) | ||||
0.0328276 | + | 0.999461i | \(0.489549\pi\) | |||||||
\(264\) | 21.5586 | 1.32684 | ||||||||
\(265\) | −4.02230 | −0.247088 | ||||||||
\(266\) | −54.0865 | −3.31626 | ||||||||
\(267\) | −10.8040 | −0.661194 | ||||||||
\(268\) | 33.0266 | 2.01742 | ||||||||
\(269\) | −7.89164 | −0.481162 | −0.240581 | − | 0.970629i | \(-0.577338\pi\) | ||||
−0.240581 | + | 0.970629i | \(0.577338\pi\) | |||||||
\(270\) | −18.9804 | −1.15511 | ||||||||
\(271\) | −21.7155 | −1.31912 | −0.659560 | − | 0.751652i | \(-0.729257\pi\) | ||||
−0.659560 | + | 0.751652i | \(0.729257\pi\) | |||||||
\(272\) | −71.8216 | −4.35483 | ||||||||
\(273\) | 11.3888 | 0.689283 | ||||||||
\(274\) | 22.8049 | 1.37770 | ||||||||
\(275\) | 4.27506 | 0.257796 | ||||||||
\(276\) | 119.663 | 7.20285 | ||||||||
\(277\) | −17.6944 | −1.06316 | −0.531578 | − | 0.847009i | \(-0.678401\pi\) | ||||
−0.531578 | + | 0.847009i | \(0.678401\pi\) | |||||||
\(278\) | −34.6238 | −2.07660 | ||||||||
\(279\) | −11.9677 | −0.716487 | ||||||||
\(280\) | −18.7513 | −1.12061 | ||||||||
\(281\) | 30.9826 | 1.84827 | 0.924133 | − | 0.382072i | \(-0.124789\pi\) | ||||
0.924133 | + | 0.382072i | \(0.124789\pi\) | |||||||
\(282\) | −8.66785 | −0.516163 | ||||||||
\(283\) | −9.38441 | −0.557846 | −0.278923 | − | 0.960314i | \(-0.589977\pi\) | ||||
−0.278923 | + | 0.960314i | \(0.589977\pi\) | |||||||
\(284\) | −33.4677 | −1.98594 | ||||||||
\(285\) | 17.3133 | 1.02555 | ||||||||
\(286\) | 3.27109 | 0.193424 | ||||||||
\(287\) | −29.8975 | −1.76479 | ||||||||
\(288\) | −56.9790 | −3.35752 | ||||||||
\(289\) | 42.8418 | 2.52010 | ||||||||
\(290\) | −2.43520 | −0.143000 | ||||||||
\(291\) | −0.337323 | −0.0197742 | ||||||||
\(292\) | 6.07633 | 0.355590 | ||||||||
\(293\) | −1.25100 | −0.0730845 | −0.0365422 | − | 0.999332i | \(-0.511634\pi\) | ||||
−0.0365422 | + | 0.999332i | \(0.511634\pi\) | |||||||
\(294\) | −17.5351 | −1.02267 | ||||||||
\(295\) | 9.39847 | 0.547200 | ||||||||
\(296\) | 45.7401 | 2.65859 | ||||||||
\(297\) | −8.56167 | −0.496799 | ||||||||
\(298\) | −6.51085 | −0.377163 | ||||||||
\(299\) | 10.5588 | 0.610629 | ||||||||
\(300\) | −60.8672 | −3.51417 | ||||||||
\(301\) | −25.0674 | −1.44486 | ||||||||
\(302\) | −45.4212 | −2.61370 | ||||||||
\(303\) | −9.33209 | −0.536115 | ||||||||
\(304\) | 63.3756 | 3.63484 | ||||||||
\(305\) | 0.851432 | 0.0487529 | ||||||||
\(306\) | 118.315 | 6.76361 | ||||||||
\(307\) | −28.7361 | −1.64005 | −0.820027 | − | 0.572325i | \(-0.806041\pi\) | ||||
−0.820027 | + | 0.572325i | \(0.806041\pi\) | |||||||
\(308\) | −14.5446 | −0.828756 | ||||||||
\(309\) | −1.82546 | −0.103847 | ||||||||
\(310\) | 4.51668 | 0.256530 | ||||||||
\(311\) | 15.3899 | 0.872679 | 0.436339 | − | 0.899782i | \(-0.356275\pi\) | ||||
0.436339 | + | 0.899782i | \(0.356275\pi\) | |||||||
\(312\) | −27.0842 | −1.53334 | ||||||||
\(313\) | 14.0136 | 0.792096 | 0.396048 | − | 0.918230i | \(-0.370381\pi\) | ||||
0.396048 | + | 0.918230i | \(0.370381\pi\) | |||||||
\(314\) | 55.5617 | 3.13553 | ||||||||
\(315\) | 15.2199 | 0.857544 | ||||||||
\(316\) | −17.7370 | −0.997782 | ||||||||
\(317\) | 18.4283 | 1.03504 | 0.517519 | − | 0.855672i | \(-0.326856\pi\) | ||||
0.517519 | + | 0.855672i | \(0.326856\pi\) | |||||||
\(318\) | 36.6423 | 2.05480 | ||||||||
\(319\) | −1.09847 | −0.0615024 | ||||||||
\(320\) | 5.69419 | 0.318315 | ||||||||
\(321\) | 4.09709 | 0.228677 | ||||||||
\(322\) | −66.5945 | −3.71117 | ||||||||
\(323\) | −52.8045 | −2.93812 | ||||||||
\(324\) | 37.6741 | 2.09300 | ||||||||
\(325\) | −5.37078 | −0.297917 | ||||||||
\(326\) | 35.0511 | 1.94130 | ||||||||
\(327\) | 61.1650 | 3.38243 | ||||||||
\(328\) | 71.1004 | 3.92586 | ||||||||
\(329\) | 3.40075 | 0.187489 | ||||||||
\(330\) | 6.60403 | 0.363540 | ||||||||
\(331\) | 32.9871 | 1.81313 | 0.906567 | − | 0.422062i | \(-0.138694\pi\) | ||||
0.906567 | + | 0.422062i | \(0.138694\pi\) | |||||||
\(332\) | 53.9791 | 2.96249 | ||||||||
\(333\) | −37.1259 | −2.03449 | ||||||||
\(334\) | −63.0010 | −3.44726 | ||||||||
\(335\) | 5.88348 | 0.321449 | ||||||||
\(336\) | 84.1661 | 4.59164 | ||||||||
\(337\) | −26.8517 | −1.46271 | −0.731354 | − | 0.681998i | \(-0.761111\pi\) | ||||
−0.731354 | + | 0.681998i | \(0.761111\pi\) | |||||||
\(338\) | 29.7391 | 1.61760 | ||||||||
\(339\) | −0.334655 | −0.0181760 | ||||||||
\(340\) | −31.4798 | −1.70723 | ||||||||
\(341\) | 2.03738 | 0.110330 | ||||||||
\(342\) | −104.401 | −5.64537 | ||||||||
\(343\) | −14.4223 | −0.778731 | ||||||||
\(344\) | 59.6138 | 3.21416 | ||||||||
\(345\) | 21.3172 | 1.14768 | ||||||||
\(346\) | 17.9007 | 0.962349 | ||||||||
\(347\) | −1.44142 | −0.0773795 | −0.0386897 | − | 0.999251i | \(-0.512318\pi\) | ||||
−0.0386897 | + | 0.999251i | \(0.512318\pi\) | |||||||
\(348\) | 15.6397 | 0.838376 | ||||||||
\(349\) | −10.1255 | −0.542004 | −0.271002 | − | 0.962579i | \(-0.587355\pi\) | ||||
−0.271002 | + | 0.962579i | \(0.587355\pi\) | |||||||
\(350\) | 33.8737 | 1.81063 | ||||||||
\(351\) | 10.7561 | 0.574117 | ||||||||
\(352\) | 9.70010 | 0.517017 | ||||||||
\(353\) | 6.94974 | 0.369897 | 0.184949 | − | 0.982748i | \(-0.440788\pi\) | ||||
0.184949 | + | 0.982748i | \(0.440788\pi\) | |||||||
\(354\) | −85.6183 | −4.55056 | ||||||||
\(355\) | −5.96206 | −0.316434 | ||||||||
\(356\) | −17.3342 | −0.918708 | ||||||||
\(357\) | −70.1271 | −3.71152 | ||||||||
\(358\) | 18.7147 | 0.989100 | ||||||||
\(359\) | 16.5539 | 0.873681 | 0.436840 | − | 0.899539i | \(-0.356097\pi\) | ||||
0.436840 | + | 0.899539i | \(0.356097\pi\) | |||||||
\(360\) | −36.1950 | −1.90764 | ||||||||
\(361\) | 27.5948 | 1.45236 | ||||||||
\(362\) | 8.55637 | 0.449713 | ||||||||
\(363\) | 2.97894 | 0.156354 | ||||||||
\(364\) | 18.2725 | 0.957737 | ||||||||
\(365\) | 1.08246 | 0.0566585 | ||||||||
\(366\) | −7.75638 | −0.405433 | ||||||||
\(367\) | −17.4739 | −0.912132 | −0.456066 | − | 0.889946i | \(-0.650742\pi\) | ||||
−0.456066 | + | 0.889946i | \(0.650742\pi\) | |||||||
\(368\) | 78.0317 | 4.06768 | ||||||||
\(369\) | −57.7101 | −3.00427 | ||||||||
\(370\) | 14.0115 | 0.728424 | ||||||||
\(371\) | −14.3763 | −0.746379 | ||||||||
\(372\) | −29.0076 | −1.50398 | ||||||||
\(373\) | −32.0776 | −1.66092 | −0.830458 | − | 0.557082i | \(-0.811921\pi\) | ||||
−0.830458 | + | 0.557082i | \(0.811921\pi\) | |||||||
\(374\) | −20.1419 | −1.04151 | ||||||||
\(375\) | −23.5249 | −1.21482 | ||||||||
\(376\) | −8.08745 | −0.417079 | ||||||||
\(377\) | 1.38001 | 0.0710742 | ||||||||
\(378\) | −67.8389 | −3.48926 | ||||||||
\(379\) | −5.75540 | −0.295635 | −0.147817 | − | 0.989015i | \(-0.547225\pi\) | ||||
−0.147817 | + | 0.989015i | \(0.547225\pi\) | |||||||
\(380\) | 27.7778 | 1.42497 | ||||||||
\(381\) | −37.5264 | −1.92253 | ||||||||
\(382\) | 41.5892 | 2.12789 | ||||||||
\(383\) | −25.7524 | −1.31589 | −0.657944 | − | 0.753067i | \(-0.728574\pi\) | ||||
−0.657944 | + | 0.753067i | \(0.728574\pi\) | |||||||
\(384\) | 5.91901 | 0.302053 | ||||||||
\(385\) | −2.59103 | −0.132051 | ||||||||
\(386\) | 13.4472 | 0.684443 | ||||||||
\(387\) | −48.3867 | −2.45963 | ||||||||
\(388\) | −0.541208 | −0.0274757 | ||||||||
\(389\) | 19.6307 | 0.995314 | 0.497657 | − | 0.867374i | \(-0.334194\pi\) | ||||
0.497657 | + | 0.867374i | \(0.334194\pi\) | |||||||
\(390\) | −8.29668 | −0.420119 | ||||||||
\(391\) | −65.0160 | −3.28800 | ||||||||
\(392\) | −16.3609 | −0.826351 | ||||||||
\(393\) | 20.5941 | 1.03883 | ||||||||
\(394\) | 49.8037 | 2.50907 | ||||||||
\(395\) | −3.15973 | −0.158983 | ||||||||
\(396\) | −28.0749 | −1.41082 | ||||||||
\(397\) | −16.9311 | −0.849747 | −0.424873 | − | 0.905253i | \(-0.639681\pi\) | ||||
−0.424873 | + | 0.905253i | \(0.639681\pi\) | |||||||
\(398\) | −0.122679 | −0.00614935 | ||||||||
\(399\) | 61.8803 | 3.09789 | ||||||||
\(400\) | −39.6913 | −1.98457 | ||||||||
\(401\) | −8.13681 | −0.406333 | −0.203167 | − | 0.979144i | \(-0.565123\pi\) | ||||
−0.203167 | + | 0.979144i | \(0.565123\pi\) | |||||||
\(402\) | −53.5974 | −2.67320 | ||||||||
\(403\) | −2.55957 | −0.127501 | ||||||||
\(404\) | −14.9726 | −0.744914 | ||||||||
\(405\) | 6.71140 | 0.333492 | ||||||||
\(406\) | −8.70378 | −0.431961 | ||||||||
\(407\) | 6.32030 | 0.313286 | ||||||||
\(408\) | 166.772 | 8.25645 | ||||||||
\(409\) | 16.5019 | 0.815966 | 0.407983 | − | 0.912990i | \(-0.366232\pi\) | ||||
0.407983 | + | 0.912990i | \(0.366232\pi\) | |||||||
\(410\) | 21.7801 | 1.07564 | ||||||||
\(411\) | −26.0911 | −1.28698 | ||||||||
\(412\) | −2.92880 | −0.144292 | ||||||||
\(413\) | 33.5915 | 1.65293 | ||||||||
\(414\) | −128.545 | −6.31764 | ||||||||
\(415\) | 9.61604 | 0.472033 | ||||||||
\(416\) | −12.1863 | −0.597481 | ||||||||
\(417\) | 39.6131 | 1.93986 | ||||||||
\(418\) | 17.7732 | 0.869318 | ||||||||
\(419\) | 4.06852 | 0.198760 | 0.0993802 | − | 0.995050i | \(-0.468314\pi\) | ||||
0.0993802 | + | 0.995050i | \(0.468314\pi\) | |||||||
\(420\) | 36.8904 | 1.80007 | ||||||||
\(421\) | −22.4972 | −1.09645 | −0.548223 | − | 0.836332i | \(-0.684696\pi\) | ||||
−0.548223 | + | 0.836332i | \(0.684696\pi\) | |||||||
\(422\) | −54.0606 | −2.63163 | ||||||||
\(423\) | 6.56434 | 0.319169 | ||||||||
\(424\) | 34.1888 | 1.66035 | ||||||||
\(425\) | 33.0708 | 1.60417 | ||||||||
\(426\) | 54.3133 | 2.63149 | ||||||||
\(427\) | 3.04314 | 0.147268 | ||||||||
\(428\) | 6.57345 | 0.317740 | ||||||||
\(429\) | −3.74245 | −0.180687 | ||||||||
\(430\) | 18.2614 | 0.880644 | ||||||||
\(431\) | 14.8069 | 0.713225 | 0.356613 | − | 0.934252i | \(-0.383932\pi\) | ||||
0.356613 | + | 0.934252i | \(0.383932\pi\) | |||||||
\(432\) | 79.4899 | 3.82446 | ||||||||
\(433\) | 13.8033 | 0.663343 | 0.331671 | − | 0.943395i | \(-0.392387\pi\) | ||||
0.331671 | + | 0.943395i | \(0.392387\pi\) | |||||||
\(434\) | 16.1433 | 0.774902 | ||||||||
\(435\) | 2.78611 | 0.133584 | ||||||||
\(436\) | 98.1343 | 4.69978 | ||||||||
\(437\) | 57.3703 | 2.74439 | ||||||||
\(438\) | −9.86099 | −0.471177 | ||||||||
\(439\) | −19.4862 | −0.930027 | −0.465013 | − | 0.885304i | \(-0.653950\pi\) | ||||
−0.465013 | + | 0.885304i | \(0.653950\pi\) | |||||||
\(440\) | 6.16183 | 0.293754 | ||||||||
\(441\) | 13.2797 | 0.632365 | ||||||||
\(442\) | 25.3043 | 1.20360 | ||||||||
\(443\) | 24.5693 | 1.16732 | 0.583661 | − | 0.811997i | \(-0.301620\pi\) | ||||
0.583661 | + | 0.811997i | \(0.301620\pi\) | |||||||
\(444\) | −89.9867 | −4.27058 | ||||||||
\(445\) | −3.08797 | −0.146384 | ||||||||
\(446\) | −28.6279 | −1.35557 | ||||||||
\(447\) | 7.44906 | 0.352328 | ||||||||
\(448\) | 20.3519 | 0.961535 | ||||||||
\(449\) | 20.1319 | 0.950081 | 0.475041 | − | 0.879964i | \(-0.342433\pi\) | ||||
0.475041 | + | 0.879964i | \(0.342433\pi\) | |||||||
\(450\) | 65.3852 | 3.08229 | ||||||||
\(451\) | 9.82455 | 0.462620 | ||||||||
\(452\) | −0.536927 | −0.0252549 | ||||||||
\(453\) | 51.9664 | 2.44159 | ||||||||
\(454\) | −24.8578 | −1.16664 | ||||||||
\(455\) | 3.25512 | 0.152603 | ||||||||
\(456\) | −147.160 | −6.89140 | ||||||||
\(457\) | −14.6515 | −0.685366 | −0.342683 | − | 0.939451i | \(-0.611336\pi\) | ||||
−0.342683 | + | 0.939451i | \(0.611336\pi\) | |||||||
\(458\) | −23.6608 | −1.10560 | ||||||||
\(459\) | −66.2309 | −3.09140 | ||||||||
\(460\) | 34.2017 | 1.59466 | ||||||||
\(461\) | −8.90582 | −0.414785 | −0.207393 | − | 0.978258i | \(-0.566498\pi\) | ||||
−0.207393 | + | 0.978258i | \(0.566498\pi\) | |||||||
\(462\) | 23.6038 | 1.09815 | ||||||||
\(463\) | −32.9705 | −1.53227 | −0.766133 | − | 0.642681i | \(-0.777822\pi\) | ||||
−0.766133 | + | 0.642681i | \(0.777822\pi\) | |||||||
\(464\) | 10.1986 | 0.473458 | ||||||||
\(465\) | −5.16753 | −0.239638 | ||||||||
\(466\) | 24.0166 | 1.11255 | ||||||||
\(467\) | 21.5869 | 0.998921 | 0.499461 | − | 0.866337i | \(-0.333532\pi\) | ||||
0.499461 | + | 0.866337i | \(0.333532\pi\) | |||||||
\(468\) | 35.2707 | 1.63039 | ||||||||
\(469\) | 21.0284 | 0.971003 | ||||||||
\(470\) | −2.47742 | −0.114275 | ||||||||
\(471\) | −63.5681 | −2.92906 | ||||||||
\(472\) | −79.8853 | −3.67702 | ||||||||
\(473\) | 8.23734 | 0.378753 | ||||||||
\(474\) | 28.7845 | 1.32212 | ||||||||
\(475\) | −29.1818 | −1.33895 | ||||||||
\(476\) | −112.513 | −5.15704 | ||||||||
\(477\) | −27.7500 | −1.27059 | ||||||||
\(478\) | 37.9786 | 1.73710 | ||||||||
\(479\) | −13.8271 | −0.631774 | −0.315887 | − | 0.948797i | \(-0.602302\pi\) | ||||
−0.315887 | + | 0.948797i | \(0.602302\pi\) | |||||||
\(480\) | −24.6030 | −1.12297 | ||||||||
\(481\) | −7.94022 | −0.362043 | ||||||||
\(482\) | 28.0653 | 1.27834 | ||||||||
\(483\) | 76.1907 | 3.46680 | ||||||||
\(484\) | 4.77947 | 0.217249 | ||||||||
\(485\) | −0.0964127 | −0.00437788 | ||||||||
\(486\) | 5.73759 | 0.260262 | ||||||||
\(487\) | 35.7656 | 1.62069 | 0.810347 | − | 0.585950i | \(-0.199279\pi\) | ||||
0.810347 | + | 0.585950i | \(0.199279\pi\) | |||||||
\(488\) | −7.23702 | −0.327604 | ||||||||
\(489\) | −40.1019 | −1.81347 | ||||||||
\(490\) | −5.01183 | −0.226411 | ||||||||
\(491\) | −30.4054 | −1.37217 | −0.686087 | − | 0.727519i | \(-0.740673\pi\) | ||||
−0.686087 | + | 0.727519i | \(0.740673\pi\) | |||||||
\(492\) | −139.879 | −6.30625 | ||||||||
\(493\) | −8.49747 | −0.382707 | ||||||||
\(494\) | −22.3286 | −1.00461 | ||||||||
\(495\) | −5.00137 | −0.224795 | ||||||||
\(496\) | −18.9158 | −0.849344 | ||||||||
\(497\) | −21.3093 | −0.955853 | ||||||||
\(498\) | −87.6003 | −3.92546 | ||||||||
\(499\) | 4.63293 | 0.207398 | 0.103699 | − | 0.994609i | \(-0.466932\pi\) | ||||
0.103699 | + | 0.994609i | \(0.466932\pi\) | |||||||
\(500\) | −37.7439 | −1.68796 | ||||||||
\(501\) | 72.0794 | 3.22027 | ||||||||
\(502\) | −39.7751 | −1.77525 | ||||||||
\(503\) | 13.7105 | 0.611319 | 0.305660 | − | 0.952141i | \(-0.401123\pi\) | ||||
0.305660 | + | 0.952141i | \(0.401123\pi\) | |||||||
\(504\) | −129.366 | −5.76243 | ||||||||
\(505\) | −2.66727 | −0.118692 | ||||||||
\(506\) | 21.8835 | 0.972838 | ||||||||
\(507\) | −34.0245 | −1.51108 | ||||||||
\(508\) | −60.2081 | −2.67130 | ||||||||
\(509\) | −11.0272 | −0.488771 | −0.244386 | − | 0.969678i | \(-0.578586\pi\) | ||||
−0.244386 | + | 0.969678i | \(0.578586\pi\) | |||||||
\(510\) | 51.0871 | 2.26218 | ||||||||
\(511\) | 3.86887 | 0.171149 | ||||||||
\(512\) | 44.3231 | 1.95882 | ||||||||
\(513\) | 58.4423 | 2.58029 | ||||||||
\(514\) | 10.6233 | 0.468572 | ||||||||
\(515\) | −0.521748 | −0.0229909 | ||||||||
\(516\) | −117.281 | −5.16301 | ||||||||
\(517\) | −1.11751 | −0.0491481 | ||||||||
\(518\) | 50.0793 | 2.20036 | ||||||||
\(519\) | −20.4802 | −0.898981 | ||||||||
\(520\) | −7.74113 | −0.339471 | ||||||||
\(521\) | 5.84854 | 0.256229 | 0.128115 | − | 0.991759i | \(-0.459107\pi\) | ||||
0.128115 | + | 0.991759i | \(0.459107\pi\) | |||||||
\(522\) | −16.8006 | −0.735342 | ||||||||
\(523\) | 26.2499 | 1.14783 | 0.573914 | − | 0.818915i | \(-0.305424\pi\) | ||||
0.573914 | + | 0.818915i | \(0.305424\pi\) | |||||||
\(524\) | 33.0415 | 1.44343 | ||||||||
\(525\) | −38.7549 | −1.69140 | ||||||||
\(526\) | −2.77233 | −0.120879 | ||||||||
\(527\) | 15.7606 | 0.686544 | ||||||||
\(528\) | −27.6576 | −1.20364 | ||||||||
\(529\) | 47.6377 | 2.07120 | ||||||||
\(530\) | 10.4730 | 0.454919 | ||||||||
\(531\) | 64.8405 | 2.81384 | ||||||||
\(532\) | 99.2821 | 4.30442 | ||||||||
\(533\) | −12.3426 | −0.534618 | ||||||||
\(534\) | 28.1308 | 1.21734 | ||||||||
\(535\) | 1.17102 | 0.0506275 | ||||||||
\(536\) | −50.0085 | −2.16004 | ||||||||
\(537\) | −21.4114 | −0.923971 | ||||||||
\(538\) | 20.5478 | 0.885878 | ||||||||
\(539\) | −2.26073 | −0.0973764 | ||||||||
\(540\) | 34.8408 | 1.49931 | ||||||||
\(541\) | 21.5728 | 0.927487 | 0.463743 | − | 0.885970i | \(-0.346506\pi\) | ||||
0.463743 | + | 0.885970i | \(0.346506\pi\) | |||||||
\(542\) | 56.5414 | 2.42866 | ||||||||
\(543\) | −9.78933 | −0.420100 | ||||||||
\(544\) | 75.0375 | 3.21721 | ||||||||
\(545\) | 17.4820 | 0.748847 | ||||||||
\(546\) | −29.6536 | −1.26905 | ||||||||
\(547\) | −13.2689 | −0.567339 | −0.283669 | − | 0.958922i | \(-0.591552\pi\) | ||||
−0.283669 | + | 0.958922i | \(0.591552\pi\) | |||||||
\(548\) | −41.8611 | −1.78822 | ||||||||
\(549\) | 5.87407 | 0.250699 | ||||||||
\(550\) | −11.1312 | −0.474634 | ||||||||
\(551\) | 7.49819 | 0.319434 | ||||||||
\(552\) | −181.192 | −7.71205 | ||||||||
\(553\) | −11.2933 | −0.480241 | ||||||||
\(554\) | 46.0717 | 1.95740 | ||||||||
\(555\) | −16.0306 | −0.680460 | ||||||||
\(556\) | 63.5561 | 2.69538 | ||||||||
\(557\) | −19.7663 | −0.837525 | −0.418762 | − | 0.908096i | \(-0.637536\pi\) | ||||
−0.418762 | + | 0.908096i | \(0.637536\pi\) | |||||||
\(558\) | 31.1608 | 1.31914 | ||||||||
\(559\) | −10.3486 | −0.437699 | ||||||||
\(560\) | 24.0561 | 1.01656 | ||||||||
\(561\) | 23.0443 | 0.972931 | ||||||||
\(562\) | −80.6706 | −3.40288 | ||||||||
\(563\) | −21.9105 | −0.923418 | −0.461709 | − | 0.887032i | \(-0.652763\pi\) | ||||
−0.461709 | + | 0.887032i | \(0.652763\pi\) | |||||||
\(564\) | 15.9108 | 0.669967 | ||||||||
\(565\) | −0.0956501 | −0.00402403 | ||||||||
\(566\) | 24.4346 | 1.02706 | ||||||||
\(567\) | 23.9875 | 1.00738 | ||||||||
\(568\) | 50.6765 | 2.12634 | ||||||||
\(569\) | −33.2783 | −1.39510 | −0.697550 | − | 0.716536i | \(-0.745727\pi\) | ||||
−0.697550 | + | 0.716536i | \(0.745727\pi\) | |||||||
\(570\) | −45.0794 | −1.88817 | ||||||||
\(571\) | 4.34024 | 0.181633 | 0.0908166 | − | 0.995868i | \(-0.471052\pi\) | ||||
0.0908166 | + | 0.995868i | \(0.471052\pi\) | |||||||
\(572\) | −6.00447 | −0.251059 | ||||||||
\(573\) | −47.5822 | −1.98778 | ||||||||
\(574\) | 77.8454 | 3.24920 | ||||||||
\(575\) | −35.9303 | −1.49840 | ||||||||
\(576\) | 39.2845 | 1.63685 | ||||||||
\(577\) | 25.8729 | 1.07710 | 0.538552 | − | 0.842592i | \(-0.318971\pi\) | ||||
0.538552 | + | 0.842592i | \(0.318971\pi\) | |||||||
\(578\) | −111.549 | −4.63982 | ||||||||
\(579\) | −15.3849 | −0.639374 | ||||||||
\(580\) | 4.47010 | 0.185611 | ||||||||
\(581\) | 34.3691 | 1.42587 | ||||||||
\(582\) | 0.878302 | 0.0364068 | ||||||||
\(583\) | 4.72415 | 0.195654 | ||||||||
\(584\) | −9.20070 | −0.380728 | ||||||||
\(585\) | 6.28324 | 0.259780 | ||||||||
\(586\) | 3.25729 | 0.134558 | ||||||||
\(587\) | −13.9531 | −0.575908 | −0.287954 | − | 0.957644i | \(-0.592975\pi\) | ||||
−0.287954 | + | 0.957644i | \(0.592975\pi\) | |||||||
\(588\) | 32.1876 | 1.32740 | ||||||||
\(589\) | −13.9072 | −0.573037 | ||||||||
\(590\) | −24.4712 | −1.00746 | ||||||||
\(591\) | −56.9803 | −2.34386 | ||||||||
\(592\) | −58.6801 | −2.41174 | ||||||||
\(593\) | −41.4876 | −1.70369 | −0.851846 | − | 0.523792i | \(-0.824517\pi\) | ||||
−0.851846 | + | 0.523792i | \(0.824517\pi\) | |||||||
\(594\) | 22.2924 | 0.914668 | ||||||||
\(595\) | −20.0436 | −0.821706 | ||||||||
\(596\) | 11.9514 | 0.489549 | ||||||||
\(597\) | 0.140357 | 0.00574444 | ||||||||
\(598\) | −27.4923 | −1.12424 | ||||||||
\(599\) | 1.63508 | 0.0668077 | 0.0334038 | − | 0.999442i | \(-0.489365\pi\) | ||||
0.0334038 | + | 0.999442i | \(0.489365\pi\) | |||||||
\(600\) | 92.1645 | 3.76260 | ||||||||
\(601\) | 37.8743 | 1.54492 | 0.772462 | − | 0.635062i | \(-0.219025\pi\) | ||||
0.772462 | + | 0.635062i | \(0.219025\pi\) | |||||||
\(602\) | 65.2690 | 2.66017 | ||||||||
\(603\) | 40.5904 | 1.65297 | ||||||||
\(604\) | 83.3759 | 3.39252 | ||||||||
\(605\) | 0.851432 | 0.0346156 | ||||||||
\(606\) | 24.2983 | 0.987053 | ||||||||
\(607\) | 1.25664 | 0.0510055 | 0.0255027 | − | 0.999675i | \(-0.491881\pi\) | ||||
0.0255027 | + | 0.999675i | \(0.491881\pi\) | |||||||
\(608\) | −66.2132 | −2.68530 | ||||||||
\(609\) | 9.95799 | 0.403518 | ||||||||
\(610\) | −2.21691 | −0.0897600 | ||||||||
\(611\) | 1.40394 | 0.0567972 | ||||||||
\(612\) | −217.181 | −8.77900 | ||||||||
\(613\) | 22.7888 | 0.920430 | 0.460215 | − | 0.887807i | \(-0.347772\pi\) | ||||
0.460215 | + | 0.887807i | \(0.347772\pi\) | |||||||
\(614\) | 74.8212 | 3.01954 | ||||||||
\(615\) | −24.9186 | −1.00482 | ||||||||
\(616\) | 22.0233 | 0.887344 | ||||||||
\(617\) | −9.66482 | −0.389091 | −0.194545 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194545 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(618\) | 4.75302 | 0.191195 | ||||||||
\(619\) | 12.2722 | 0.493263 | 0.246632 | − | 0.969109i | \(-0.420676\pi\) | ||||
0.246632 | + | 0.969109i | \(0.420676\pi\) | |||||||
\(620\) | −8.29089 | −0.332970 | ||||||||
\(621\) | 71.9576 | 2.88756 | ||||||||
\(622\) | −40.0712 | −1.60671 | ||||||||
\(623\) | −11.0369 | −0.442183 | ||||||||
\(624\) | 34.7464 | 1.39097 | ||||||||
\(625\) | 14.6515 | 0.586059 | ||||||||
\(626\) | −36.4878 | −1.45835 | ||||||||
\(627\) | −20.3343 | −0.812076 | ||||||||
\(628\) | −101.990 | −4.06984 | ||||||||
\(629\) | 48.8922 | 1.94946 | ||||||||
\(630\) | −39.6287 | −1.57884 | ||||||||
\(631\) | 32.5982 | 1.29772 | 0.648858 | − | 0.760910i | \(-0.275247\pi\) | ||||
0.648858 | + | 0.760910i | \(0.275247\pi\) | |||||||
\(632\) | 26.8571 | 1.06832 | ||||||||
\(633\) | 61.8507 | 2.45834 | ||||||||
\(634\) | −47.9826 | −1.90563 | ||||||||
\(635\) | −10.7257 | −0.425636 | ||||||||
\(636\) | −67.2613 | −2.66708 | ||||||||
\(637\) | 2.84016 | 0.112531 | ||||||||
\(638\) | 2.86013 | 0.113234 | ||||||||
\(639\) | −41.1326 | −1.62718 | ||||||||
\(640\) | 1.69176 | 0.0668725 | ||||||||
\(641\) | 39.4363 | 1.55764 | 0.778820 | − | 0.627248i | \(-0.215819\pi\) | ||||
0.778820 | + | 0.627248i | \(0.215819\pi\) | |||||||
\(642\) | −10.6678 | −0.421023 | ||||||||
\(643\) | 35.4044 | 1.39621 | 0.698107 | − | 0.715993i | \(-0.254026\pi\) | ||||
0.698107 | + | 0.715993i | \(0.254026\pi\) | |||||||
\(644\) | 122.242 | 4.81701 | ||||||||
\(645\) | −20.8929 | −0.822656 | ||||||||
\(646\) | 137.489 | 5.40944 | ||||||||
\(647\) | −25.6571 | −1.00869 | −0.504343 | − | 0.863504i | \(-0.668265\pi\) | ||||
−0.504343 | + | 0.863504i | \(0.668265\pi\) | |||||||
\(648\) | −57.0457 | −2.24097 | ||||||||
\(649\) | −11.0384 | −0.433296 | ||||||||
\(650\) | 13.9841 | 0.548503 | ||||||||
\(651\) | −18.4695 | −0.723877 | ||||||||
\(652\) | −64.3403 | −2.51976 | ||||||||
\(653\) | −3.64441 | −0.142617 | −0.0713085 | − | 0.997454i | \(-0.522717\pi\) | ||||
−0.0713085 | + | 0.997454i | \(0.522717\pi\) | |||||||
\(654\) | −159.258 | −6.22747 | ||||||||
\(655\) | 5.88614 | 0.229991 | ||||||||
\(656\) | −91.2149 | −3.56134 | ||||||||
\(657\) | 7.46794 | 0.291352 | ||||||||
\(658\) | −8.85467 | −0.345191 | ||||||||
\(659\) | −3.49371 | −0.136095 | −0.0680477 | − | 0.997682i | \(-0.521677\pi\) | ||||
−0.0680477 | + | 0.997682i | \(0.521677\pi\) | |||||||
\(660\) | −12.1225 | −0.471866 | ||||||||
\(661\) | −49.5134 | −1.92585 | −0.962923 | − | 0.269775i | \(-0.913051\pi\) | ||||
−0.962923 | + | 0.269775i | \(0.913051\pi\) | |||||||
\(662\) | −85.8898 | −3.33820 | ||||||||
\(663\) | −28.9507 | −1.12435 | ||||||||
\(664\) | −81.7346 | −3.17192 | ||||||||
\(665\) | 17.6865 | 0.685852 | ||||||||
\(666\) | 96.6662 | 3.74574 | ||||||||
\(667\) | 9.23221 | 0.357473 | ||||||||
\(668\) | 115.646 | 4.47446 | ||||||||
\(669\) | 32.7531 | 1.26631 | ||||||||
\(670\) | −15.3191 | −0.591827 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −87.9346 | −3.39215 | ||||||||
\(673\) | −17.3434 | −0.668538 | −0.334269 | − | 0.942478i | \(-0.608489\pi\) | ||||
−0.334269 | + | 0.942478i | \(0.608489\pi\) | |||||||
\(674\) | 69.9150 | 2.69302 | ||||||||
\(675\) | −36.6017 | −1.40880 | ||||||||
\(676\) | −54.5897 | −2.09960 | ||||||||
\(677\) | 23.0773 | 0.886931 | 0.443466 | − | 0.896291i | \(-0.353749\pi\) | ||||
0.443466 | + | 0.896291i | \(0.353749\pi\) | |||||||
\(678\) | 0.871354 | 0.0334642 | ||||||||
\(679\) | −0.344593 | −0.0132243 | ||||||||
\(680\) | 47.6663 | 1.82792 | ||||||||
\(681\) | 28.4398 | 1.08982 | ||||||||
\(682\) | −5.30480 | −0.203131 | ||||||||
\(683\) | 41.1141 | 1.57319 | 0.786593 | − | 0.617471i | \(-0.211843\pi\) | ||||
0.786593 | + | 0.617471i | \(0.211843\pi\) | |||||||
\(684\) | 191.641 | 7.32756 | ||||||||
\(685\) | −7.45729 | −0.284928 | ||||||||
\(686\) | 37.5519 | 1.43374 | ||||||||
\(687\) | 27.0703 | 1.03280 | ||||||||
\(688\) | −76.4786 | −2.91572 | ||||||||
\(689\) | −5.93498 | −0.226105 | ||||||||
\(690\) | −55.5044 | −2.11302 | ||||||||
\(691\) | 0.00796003 | 0.000302814 0 | 0.000151407 | − | 1.00000i | \(-0.499952\pi\) | ||||
0.000151407 | 1.00000i | \(0.499952\pi\) | ||||||||
\(692\) | −32.8589 | −1.24911 | ||||||||
\(693\) | −17.8756 | −0.679039 | ||||||||
\(694\) | 3.75308 | 0.142465 | ||||||||
\(695\) | 11.3221 | 0.429472 | ||||||||
\(696\) | −23.6815 | −0.897644 | ||||||||
\(697\) | 76.0002 | 2.87871 | ||||||||
\(698\) | 26.3641 | 0.997896 | ||||||||
\(699\) | −27.4774 | −1.03929 | ||||||||
\(700\) | −62.1791 | −2.35015 | ||||||||
\(701\) | 15.6416 | 0.590774 | 0.295387 | − | 0.955378i | \(-0.404551\pi\) | ||||
0.295387 | + | 0.955378i | \(0.404551\pi\) | |||||||
\(702\) | −28.0060 | −1.05702 | ||||||||
\(703\) | −43.1426 | −1.62715 | ||||||||
\(704\) | −6.68778 | −0.252055 | ||||||||
\(705\) | 2.83442 | 0.106750 | ||||||||
\(706\) | −18.0953 | −0.681026 | ||||||||
\(707\) | −9.53323 | −0.358534 | ||||||||
\(708\) | 157.162 | 5.90652 | ||||||||
\(709\) | 16.5953 | 0.623250 | 0.311625 | − | 0.950205i | \(-0.399127\pi\) | ||||
0.311625 | + | 0.950205i | \(0.399127\pi\) | |||||||
\(710\) | 15.5237 | 0.582593 | ||||||||
\(711\) | −21.7991 | −0.817530 | ||||||||
\(712\) | 26.2472 | 0.983655 | ||||||||
\(713\) | −17.1234 | −0.641276 | ||||||||
\(714\) | 182.593 | 6.83337 | ||||||||
\(715\) | −1.06966 | −0.0400029 | ||||||||
\(716\) | −34.3529 | −1.28383 | ||||||||
\(717\) | −43.4513 | −1.62272 | ||||||||
\(718\) | −43.1020 | −1.60855 | ||||||||
\(719\) | −25.8212 | −0.962967 | −0.481484 | − | 0.876455i | \(-0.659902\pi\) | ||||
−0.481484 | + | 0.876455i | \(0.659902\pi\) | |||||||
\(720\) | 46.4346 | 1.73052 | ||||||||
\(721\) | −1.86480 | −0.0694489 | ||||||||
\(722\) | −71.8497 | −2.67397 | ||||||||
\(723\) | −32.1095 | −1.19416 | ||||||||
\(724\) | −15.7062 | −0.583716 | ||||||||
\(725\) | −4.69602 | −0.174406 | ||||||||
\(726\) | −7.75638 | −0.287866 | ||||||||
\(727\) | −20.5085 | −0.760619 | −0.380310 | − | 0.924859i | \(-0.624183\pi\) | ||||
−0.380310 | + | 0.924859i | \(0.624183\pi\) | |||||||
\(728\) | −27.6680 | −1.02544 | ||||||||
\(729\) | −30.2118 | −1.11896 | ||||||||
\(730\) | −2.81844 | −0.104315 | ||||||||
\(731\) | 63.7220 | 2.35684 | ||||||||
\(732\) | 14.2377 | 0.526242 | ||||||||
\(733\) | 46.0269 | 1.70004 | 0.850021 | − | 0.526749i | \(-0.176589\pi\) | ||||
0.850021 | + | 0.526749i | \(0.176589\pi\) | |||||||
\(734\) | 45.4976 | 1.67935 | ||||||||
\(735\) | 5.73402 | 0.211503 | ||||||||
\(736\) | −81.5256 | −3.00508 | ||||||||
\(737\) | −6.91010 | −0.254537 | ||||||||
\(738\) | 150.262 | 5.53122 | ||||||||
\(739\) | 33.7128 | 1.24015 | 0.620073 | − | 0.784544i | \(-0.287103\pi\) | ||||
0.620073 | + | 0.784544i | \(0.287103\pi\) | |||||||
\(740\) | −25.7198 | −0.945478 | ||||||||
\(741\) | 25.5461 | 0.938461 | ||||||||
\(742\) | 37.4321 | 1.37418 | ||||||||
\(743\) | −1.80937 | −0.0663793 | −0.0331896 | − | 0.999449i | \(-0.510567\pi\) | ||||
−0.0331896 | + | 0.999449i | \(0.510567\pi\) | |||||||
\(744\) | 43.9231 | 1.61030 | ||||||||
\(745\) | 2.12907 | 0.0780031 | ||||||||
\(746\) | 83.5218 | 3.05795 | ||||||||
\(747\) | 66.3415 | 2.42731 | ||||||||
\(748\) | 36.9728 | 1.35186 | ||||||||
\(749\) | 4.18539 | 0.152931 | ||||||||
\(750\) | 61.2528 | 2.23664 | ||||||||
\(751\) | −17.2718 | −0.630256 | −0.315128 | − | 0.949049i | \(-0.602047\pi\) | ||||
−0.315128 | + | 0.949049i | \(0.602047\pi\) | |||||||
\(752\) | 10.3754 | 0.378352 | ||||||||
\(753\) | 45.5066 | 1.65835 | ||||||||
\(754\) | −3.59319 | −0.130856 | ||||||||
\(755\) | 14.8529 | 0.540552 | ||||||||
\(756\) | 124.526 | 4.52898 | ||||||||
\(757\) | −0.988737 | −0.0359363 | −0.0179681 | − | 0.999839i | \(-0.505720\pi\) | ||||
−0.0179681 | + | 0.999839i | \(0.505720\pi\) | |||||||
\(758\) | 14.9856 | 0.544300 | ||||||||
\(759\) | −25.0368 | −0.908780 | ||||||||
\(760\) | −42.0609 | −1.52571 | ||||||||
\(761\) | 47.0722 | 1.70636 | 0.853182 | − | 0.521613i | \(-0.174670\pi\) | ||||
0.853182 | + | 0.521613i | \(0.174670\pi\) | |||||||
\(762\) | 97.7090 | 3.53962 | ||||||||
\(763\) | 62.4833 | 2.26205 | ||||||||
\(764\) | −76.3419 | −2.76195 | ||||||||
\(765\) | −38.6893 | −1.39882 | ||||||||
\(766\) | 67.0527 | 2.42271 | ||||||||
\(767\) | 13.8676 | 0.500731 | ||||||||
\(768\) | −55.2565 | −1.99390 | ||||||||
\(769\) | 26.8992 | 0.970009 | 0.485004 | − | 0.874512i | \(-0.338818\pi\) | ||||
0.485004 | + | 0.874512i | \(0.338818\pi\) | |||||||
\(770\) | 6.74637 | 0.243122 | ||||||||
\(771\) | −12.1541 | −0.437718 | ||||||||
\(772\) | −24.6838 | −0.888391 | ||||||||
\(773\) | 12.9507 | 0.465804 | 0.232902 | − | 0.972500i | \(-0.425178\pi\) | ||||
0.232902 | + | 0.972500i | \(0.425178\pi\) | |||||||
\(774\) | 125.986 | 4.52849 | ||||||||
\(775\) | 8.70992 | 0.312869 | ||||||||
\(776\) | 0.819491 | 0.0294180 | ||||||||
\(777\) | −57.2956 | −2.05547 | ||||||||
\(778\) | −51.1132 | −1.83250 | ||||||||
\(779\) | −67.0627 | −2.40277 | ||||||||
\(780\) | 15.2295 | 0.545304 | ||||||||
\(781\) | 7.00240 | 0.250565 | ||||||||
\(782\) | 169.285 | 6.05362 | ||||||||
\(783\) | 9.40473 | 0.336098 | ||||||||
\(784\) | 20.9895 | 0.749623 | ||||||||
\(785\) | −18.1689 | −0.648475 | ||||||||
\(786\) | −53.6216 | −1.91262 | ||||||||
\(787\) | −36.5969 | −1.30454 | −0.652270 | − | 0.757987i | \(-0.726183\pi\) | ||||
−0.652270 | + | 0.757987i | \(0.726183\pi\) | |||||||
\(788\) | −91.4204 | −3.25672 | ||||||||
\(789\) | 3.17182 | 0.112920 | ||||||||
\(790\) | 8.22711 | 0.292708 | ||||||||
\(791\) | −0.341868 | −0.0121554 | ||||||||
\(792\) | 42.5107 | 1.51055 | ||||||||
\(793\) | 1.25630 | 0.0446127 | ||||||||
\(794\) | 44.0842 | 1.56449 | ||||||||
\(795\) | −11.9822 | −0.424964 | ||||||||
\(796\) | 0.225192 | 0.00798172 | ||||||||
\(797\) | 27.8407 | 0.986167 | 0.493083 | − | 0.869982i | \(-0.335870\pi\) | ||||
0.493083 | + | 0.869982i | \(0.335870\pi\) | |||||||
\(798\) | −161.120 | −5.70360 | ||||||||
\(799\) | −8.64479 | −0.305831 | ||||||||
\(800\) | 41.4685 | 1.46613 | ||||||||
\(801\) | −21.3041 | −0.752742 | ||||||||
\(802\) | 21.1862 | 0.748109 | ||||||||
\(803\) | −1.27134 | −0.0448646 | ||||||||
\(804\) | 98.3842 | 3.46974 | ||||||||
\(805\) | 21.7766 | 0.767525 | ||||||||
\(806\) | 6.66445 | 0.234745 | ||||||||
\(807\) | −23.5087 | −0.827545 | ||||||||
\(808\) | 22.6713 | 0.797575 | ||||||||
\(809\) | −1.23289 | −0.0433461 | −0.0216730 | − | 0.999765i | \(-0.506899\pi\) | ||||
−0.0216730 | + | 0.999765i | \(0.506899\pi\) | |||||||
\(810\) | −17.4747 | −0.614000 | ||||||||
\(811\) | −30.2942 | −1.06377 | −0.531886 | − | 0.846816i | \(-0.678516\pi\) | ||||
−0.531886 | + | 0.846816i | \(0.678516\pi\) | |||||||
\(812\) | 15.9768 | 0.560676 | ||||||||
\(813\) | −64.6890 | −2.26874 | ||||||||
\(814\) | −16.4564 | −0.576797 | ||||||||
\(815\) | −11.4618 | −0.401490 | ||||||||
\(816\) | −213.952 | −7.48982 | ||||||||
\(817\) | −56.2284 | −1.96718 | ||||||||
\(818\) | −42.9666 | −1.50229 | ||||||||
\(819\) | 22.4572 | 0.784720 | ||||||||
\(820\) | −39.9799 | −1.39616 | ||||||||
\(821\) | 37.4922 | 1.30849 | 0.654244 | − | 0.756283i | \(-0.272987\pi\) | ||||
0.654244 | + | 0.756283i | \(0.272987\pi\) | |||||||
\(822\) | 67.9345 | 2.36949 | ||||||||
\(823\) | 23.5323 | 0.820285 | 0.410142 | − | 0.912022i | \(-0.365479\pi\) | ||||
0.410142 | + | 0.912022i | \(0.365479\pi\) | |||||||
\(824\) | 4.43476 | 0.154492 | ||||||||
\(825\) | 12.7351 | 0.443381 | ||||||||
\(826\) | −87.4636 | −3.04325 | ||||||||
\(827\) | 26.7937 | 0.931707 | 0.465854 | − | 0.884862i | \(-0.345747\pi\) | ||||
0.465854 | + | 0.884862i | \(0.345747\pi\) | |||||||
\(828\) | 235.959 | 8.20015 | ||||||||
\(829\) | −9.76779 | −0.339249 | −0.169625 | − | 0.985509i | \(-0.554256\pi\) | ||||
−0.169625 | + | 0.985509i | \(0.554256\pi\) | |||||||
\(830\) | −25.0377 | −0.869070 | ||||||||
\(831\) | −52.7106 | −1.82851 | ||||||||
\(832\) | 8.40188 | 0.291283 | ||||||||
\(833\) | −17.4884 | −0.605938 | ||||||||
\(834\) | −103.142 | −3.57152 | ||||||||
\(835\) | 20.6015 | 0.712945 | ||||||||
\(836\) | −32.6248 | −1.12835 | ||||||||
\(837\) | −17.4434 | −0.602931 | ||||||||
\(838\) | −10.5934 | −0.365942 | ||||||||
\(839\) | −2.24302 | −0.0774376 | −0.0387188 | − | 0.999250i | \(-0.512328\pi\) | ||||
−0.0387188 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(840\) | −55.8590 | −1.92732 | ||||||||
\(841\) | −27.7934 | −0.958392 | ||||||||
\(842\) | 58.5769 | 2.01869 | ||||||||
\(843\) | 92.2951 | 3.17881 | ||||||||
\(844\) | 99.2345 | 3.41579 | ||||||||
\(845\) | −9.72480 | −0.334543 | ||||||||
\(846\) | −17.0919 | −0.587630 | ||||||||
\(847\) | 3.04314 | 0.104564 | ||||||||
\(848\) | −43.8609 | −1.50619 | ||||||||
\(849\) | −27.9556 | −0.959433 | ||||||||
\(850\) | −86.1078 | −2.95347 | ||||||||
\(851\) | −53.1197 | −1.82092 | ||||||||
\(852\) | −99.6983 | −3.41561 | ||||||||
\(853\) | −44.3477 | −1.51843 | −0.759217 | − | 0.650837i | \(-0.774418\pi\) | ||||
−0.759217 | + | 0.650837i | \(0.774418\pi\) | |||||||
\(854\) | −7.92356 | −0.271139 | ||||||||
\(855\) | 34.1396 | 1.16755 | ||||||||
\(856\) | −9.95345 | −0.340202 | ||||||||
\(857\) | 19.5439 | 0.667608 | 0.333804 | − | 0.942642i | \(-0.391668\pi\) | ||||
0.333804 | + | 0.942642i | \(0.391668\pi\) | |||||||
\(858\) | 9.74438 | 0.332668 | ||||||||
\(859\) | 21.0704 | 0.718913 | 0.359456 | − | 0.933162i | \(-0.382962\pi\) | ||||
0.359456 | + | 0.933162i | \(0.382962\pi\) | |||||||
\(860\) | −33.5210 | −1.14306 | ||||||||
\(861\) | −89.0628 | −3.03525 | ||||||||
\(862\) | −38.5534 | −1.31314 | ||||||||
\(863\) | −55.0745 | −1.87476 | −0.937380 | − | 0.348309i | \(-0.886756\pi\) | ||||
−0.937380 | + | 0.348309i | \(0.886756\pi\) | |||||||
\(864\) | −83.0491 | −2.82539 | ||||||||
\(865\) | −5.85360 | −0.199028 | ||||||||
\(866\) | −35.9401 | −1.22130 | ||||||||
\(867\) | 127.623 | 4.33430 | ||||||||
\(868\) | −29.6329 | −1.00580 | ||||||||
\(869\) | 3.71107 | 0.125890 | ||||||||
\(870\) | −7.25432 | −0.245945 | ||||||||
\(871\) | 8.68119 | 0.294151 | ||||||||
\(872\) | −148.594 | −5.03202 | ||||||||
\(873\) | −0.665156 | −0.0225121 | ||||||||
\(874\) | −149.377 | −5.05276 | ||||||||
\(875\) | −24.0320 | −0.812429 | ||||||||
\(876\) | 18.1010 | 0.611576 | ||||||||
\(877\) | −14.0361 | −0.473965 | −0.236983 | − | 0.971514i | \(-0.576158\pi\) | ||||
−0.236983 | + | 0.971514i | \(0.576158\pi\) | |||||||
\(878\) | 50.7371 | 1.71229 | ||||||||
\(879\) | −3.72667 | −0.125697 | ||||||||
\(880\) | −7.90502 | −0.266478 | ||||||||
\(881\) | −23.7847 | −0.801326 | −0.400663 | − | 0.916226i | \(-0.631220\pi\) | ||||
−0.400663 | + | 0.916226i | \(0.631220\pi\) | |||||||
\(882\) | −34.5768 | −1.16426 | ||||||||
\(883\) | −13.7523 | −0.462801 | −0.231401 | − | 0.972859i | \(-0.574331\pi\) | ||||
−0.231401 | + | 0.972859i | \(0.574331\pi\) | |||||||
\(884\) | −46.4490 | −1.56225 | ||||||||
\(885\) | 27.9975 | 0.941124 | ||||||||
\(886\) | −63.9721 | −2.14918 | ||||||||
\(887\) | 30.3096 | 1.01770 | 0.508849 | − | 0.860856i | \(-0.330071\pi\) | ||||
0.508849 | + | 0.860856i | \(0.330071\pi\) | |||||||
\(888\) | 136.257 | 4.57248 | ||||||||
\(889\) | −38.3352 | −1.28572 | ||||||||
\(890\) | 8.04027 | 0.269511 | ||||||||
\(891\) | −7.88248 | −0.264073 | ||||||||
\(892\) | 52.5498 | 1.75950 | ||||||||
\(893\) | 7.62818 | 0.255267 | ||||||||
\(894\) | −19.3954 | −0.648680 | ||||||||
\(895\) | −6.11975 | −0.204561 | ||||||||
\(896\) | 6.04659 | 0.202002 | ||||||||
\(897\) | 31.4539 | 1.05022 | ||||||||
\(898\) | −52.4182 | −1.74922 | ||||||||
\(899\) | −2.23799 | −0.0746413 | ||||||||
\(900\) | −120.022 | −4.00074 | ||||||||
\(901\) | 36.5449 | 1.21749 | ||||||||
\(902\) | −25.5806 | −0.851740 | ||||||||
\(903\) | −74.6742 | −2.48500 | ||||||||
\(904\) | 0.813009 | 0.0270403 | ||||||||
\(905\) | −2.79796 | −0.0930073 | ||||||||
\(906\) | −135.307 | −4.49527 | ||||||||
\(907\) | −36.6102 | −1.21562 | −0.607812 | − | 0.794081i | \(-0.707952\pi\) | ||||
−0.607812 | + | 0.794081i | \(0.707952\pi\) | |||||||
\(908\) | 45.6294 | 1.51426 | ||||||||
\(909\) | −18.4016 | −0.610344 | ||||||||
\(910\) | −8.47550 | −0.280960 | ||||||||
\(911\) | 34.9673 | 1.15852 | 0.579258 | − | 0.815144i | \(-0.303342\pi\) | ||||
0.579258 | + | 0.815144i | \(0.303342\pi\) | |||||||
\(912\) | 188.792 | 6.25152 | ||||||||
\(913\) | −11.2940 | −0.373776 | ||||||||
\(914\) | 38.1486 | 1.26184 | ||||||||
\(915\) | 2.53636 | 0.0838496 | ||||||||
\(916\) | 43.4322 | 1.43504 | ||||||||
\(917\) | 21.0379 | 0.694734 | ||||||||
\(918\) | 172.448 | 5.69164 | ||||||||
\(919\) | 6.04826 | 0.199514 | 0.0997568 | − | 0.995012i | \(-0.468194\pi\) | ||||
0.0997568 | + | 0.995012i | \(0.468194\pi\) | |||||||
\(920\) | −51.7878 | −1.70739 | ||||||||
\(921\) | −85.6029 | −2.82071 | ||||||||
\(922\) | 23.1884 | 0.763671 | ||||||||
\(923\) | −8.79714 | −0.289562 | ||||||||
\(924\) | −43.3275 | −1.42537 | ||||||||
\(925\) | 27.0197 | 0.888401 | ||||||||
\(926\) | 85.8465 | 2.82109 | ||||||||
\(927\) | −3.59956 | −0.118225 | ||||||||
\(928\) | −10.6552 | −0.349776 | ||||||||
\(929\) | −50.8532 | −1.66844 | −0.834219 | − | 0.551433i | \(-0.814081\pi\) | ||||
−0.834219 | + | 0.551433i | \(0.814081\pi\) | |||||||
\(930\) | 13.4549 | 0.441204 | ||||||||
\(931\) | 15.4318 | 0.505757 | ||||||||
\(932\) | −44.0853 | −1.44406 | ||||||||
\(933\) | 45.8454 | 1.50091 | ||||||||
\(934\) | −56.2066 | −1.83914 | ||||||||
\(935\) | 6.58646 | 0.215400 | ||||||||
\(936\) | −53.4064 | −1.74564 | ||||||||
\(937\) | 27.2266 | 0.889453 | 0.444726 | − | 0.895666i | \(-0.353301\pi\) | ||||
0.444726 | + | 0.895666i | \(0.353301\pi\) | |||||||
\(938\) | −54.7526 | −1.78774 | ||||||||
\(939\) | 41.7457 | 1.36232 | ||||||||
\(940\) | 4.54760 | 0.148326 | ||||||||
\(941\) | 18.7448 | 0.611064 | 0.305532 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305532 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(942\) | 165.515 | 5.39277 | ||||||||
\(943\) | −82.5716 | −2.68890 | ||||||||
\(944\) | 102.485 | 3.33560 | ||||||||
\(945\) | 22.1836 | 0.721631 | ||||||||
\(946\) | −21.4479 | −0.697331 | ||||||||
\(947\) | 51.2919 | 1.66676 | 0.833381 | − | 0.552698i | \(-0.186402\pi\) | ||||
0.833381 | + | 0.552698i | \(0.186402\pi\) | |||||||
\(948\) | −52.8373 | −1.71608 | ||||||||
\(949\) | 1.59719 | 0.0518470 | ||||||||
\(950\) | 75.9817 | 2.46517 | ||||||||
\(951\) | 54.8969 | 1.78015 | ||||||||
\(952\) | 170.367 | 5.52161 | ||||||||
\(953\) | 12.0797 | 0.391301 | 0.195651 | − | 0.980674i | \(-0.437318\pi\) | ||||
0.195651 | + | 0.980674i | \(0.437318\pi\) | |||||||
\(954\) | 72.2538 | 2.33930 | ||||||||
\(955\) | −13.5998 | −0.440080 | ||||||||
\(956\) | −69.7142 | −2.25472 | ||||||||
\(957\) | −3.27227 | −0.105777 | ||||||||
\(958\) | 36.0021 | 1.16317 | ||||||||
\(959\) | −26.6535 | −0.860685 | ||||||||
\(960\) | 16.9626 | 0.547466 | ||||||||
\(961\) | −26.8491 | −0.866100 | ||||||||
\(962\) | 20.6743 | 0.666565 | ||||||||
\(963\) | 8.07891 | 0.260339 | ||||||||
\(964\) | −51.5171 | −1.65925 | ||||||||
\(965\) | −4.39727 | −0.141553 | ||||||||
\(966\) | −198.381 | −6.38280 | ||||||||
\(967\) | 29.1060 | 0.935985 | 0.467992 | − | 0.883732i | \(-0.344977\pi\) | ||||
0.467992 | + | 0.883732i | \(0.344977\pi\) | |||||||
\(968\) | −7.23702 | −0.232607 | ||||||||
\(969\) | −157.301 | −5.05325 | ||||||||
\(970\) | 0.251034 | 0.00806021 | ||||||||
\(971\) | 6.38454 | 0.204890 | 0.102445 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102445 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(972\) | −10.5320 | −0.337814 | ||||||||
\(973\) | 40.4669 | 1.29731 | ||||||||
\(974\) | −93.1244 | −2.98390 | ||||||||
\(975\) | −15.9992 | −0.512385 | ||||||||
\(976\) | 9.28438 | 0.297186 | ||||||||
\(977\) | −33.0182 | −1.05634 | −0.528172 | − | 0.849137i | \(-0.677122\pi\) | ||||
−0.528172 | + | 0.849137i | \(0.677122\pi\) | |||||||
\(978\) | 104.415 | 3.33882 | ||||||||
\(979\) | 3.62680 | 0.115913 | ||||||||
\(980\) | 9.19979 | 0.293876 | ||||||||
\(981\) | 120.609 | 3.85076 | ||||||||
\(982\) | 79.1677 | 2.52634 | ||||||||
\(983\) | 48.1934 | 1.53713 | 0.768566 | − | 0.639770i | \(-0.220971\pi\) | ||||
0.768566 | + | 0.639770i | \(0.220971\pi\) | |||||||
\(984\) | 211.804 | 6.75206 | ||||||||
\(985\) | −16.2860 | −0.518914 | ||||||||
\(986\) | 22.1252 | 0.704611 | ||||||||
\(987\) | 10.1306 | 0.322461 | ||||||||
\(988\) | 40.9867 | 1.30396 | ||||||||
\(989\) | −69.2317 | −2.20144 | ||||||||
\(990\) | 13.0223 | 0.413875 | ||||||||
\(991\) | 42.8697 | 1.36180 | 0.680900 | − | 0.732376i | \(-0.261589\pi\) | ||||
0.680900 | + | 0.732376i | \(0.261589\pi\) | |||||||
\(992\) | 19.7628 | 0.627468 | ||||||||
\(993\) | 98.2665 | 3.11839 | ||||||||
\(994\) | 55.4839 | 1.75984 | ||||||||
\(995\) | 0.0401165 | 0.00127178 | ||||||||
\(996\) | 160.800 | 5.09516 | ||||||||
\(997\) | 14.1040 | 0.446679 | 0.223340 | − | 0.974741i | \(-0.428304\pi\) | ||||
0.223340 | + | 0.974741i | \(0.428304\pi\) | |||||||
\(998\) | −12.0629 | −0.381846 | ||||||||
\(999\) | −54.1123 | −1.71204 |
(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 | 671.2.a.d.1.2 | ✓ | 21 | |
3.2 | odd | 2 | 6039.2.a.l.1.20 | 21 | |||
11.10 | odd | 2 | 7381.2.a.j.1.20 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.d.1.2 | ✓ | 21 | 1.1 | even | 1 | trivial | |
6039.2.a.l.1.20 | 21 | 3.2 | odd | 2 | |||
7381.2.a.j.1.20 | 21 | 11.10 | odd | 2 |