Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.482188 | −0.340958 | −0.170479 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170479 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.76749 | −0.883747 | ||||||||
\(5\) | −4.13435 | −1.84894 | −0.924470 | − | 0.381255i | \(-0.875492\pi\) | ||||
−0.924470 | + | 0.381255i | \(0.875492\pi\) | |||||||
\(6\) | 0.482188 | 0.196852 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.81664 | 0.642279 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.99354 | 0.630412 | ||||||||
\(11\) | 0.997504 | 0.300759 | 0.150379 | − | 0.988628i | \(-0.451950\pi\) | ||||
0.150379 | + | 0.988628i | \(0.451950\pi\) | |||||||
\(12\) | 1.76749 | 0.510232 | ||||||||
\(13\) | 0.702717 | 0.194899 | 0.0974494 | − | 0.995240i | \(-0.468932\pi\) | ||||
0.0974494 | + | 0.995240i | \(0.468932\pi\) | |||||||
\(14\) | −0.482188 | −0.128870 | ||||||||
\(15\) | 4.13435 | 1.06749 | ||||||||
\(16\) | 2.65903 | 0.664757 | ||||||||
\(17\) | −2.33904 | −0.567300 | −0.283650 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283650 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(18\) | −0.482188 | −0.113653 | ||||||||
\(19\) | −1.46177 | −0.335353 | −0.167676 | − | 0.985842i | \(-0.553626\pi\) | ||||
−0.167676 | + | 0.985842i | \(0.553626\pi\) | |||||||
\(20\) | 7.30745 | 1.63400 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.480984 | −0.102546 | ||||||||
\(23\) | −6.00006 | −1.25110 | −0.625550 | − | 0.780184i | \(-0.715125\pi\) | ||||
−0.625550 | + | 0.780184i | \(0.715125\pi\) | |||||||
\(24\) | −1.81664 | −0.370820 | ||||||||
\(25\) | 12.0929 | 2.41858 | ||||||||
\(26\) | −0.338842 | −0.0664524 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.76749 | −0.334025 | ||||||||
\(29\) | −3.91669 | −0.727312 | −0.363656 | − | 0.931533i | \(-0.618472\pi\) | ||||
−0.363656 | + | 0.931533i | \(0.618472\pi\) | |||||||
\(30\) | −1.99354 | −0.363968 | ||||||||
\(31\) | 9.76370 | 1.75361 | 0.876806 | − | 0.480844i | \(-0.159670\pi\) | ||||
0.876806 | + | 0.480844i | \(0.159670\pi\) | |||||||
\(32\) | −4.91543 | −0.868934 | ||||||||
\(33\) | −0.997504 | −0.173643 | ||||||||
\(34\) | 1.12786 | 0.193426 | ||||||||
\(35\) | −4.13435 | −0.698834 | ||||||||
\(36\) | −1.76749 | −0.294582 | ||||||||
\(37\) | −7.34101 | −1.20686 | −0.603428 | − | 0.797418i | \(-0.706199\pi\) | ||||
−0.603428 | + | 0.797418i | \(0.706199\pi\) | |||||||
\(38\) | 0.704847 | 0.114341 | ||||||||
\(39\) | −0.702717 | −0.112525 | ||||||||
\(40\) | −7.51064 | −1.18754 | ||||||||
\(41\) | −2.43757 | −0.380684 | −0.190342 | − | 0.981718i | \(-0.560960\pi\) | ||||
−0.190342 | + | 0.981718i | \(0.560960\pi\) | |||||||
\(42\) | 0.482188 | 0.0744032 | ||||||||
\(43\) | −9.17914 | −1.39981 | −0.699903 | − | 0.714238i | \(-0.746774\pi\) | ||||
−0.699903 | + | 0.714238i | \(0.746774\pi\) | |||||||
\(44\) | −1.76308 | −0.265795 | ||||||||
\(45\) | −4.13435 | −0.616313 | ||||||||
\(46\) | 2.89316 | 0.426573 | ||||||||
\(47\) | −11.9268 | −1.73970 | −0.869851 | − | 0.493315i | \(-0.835785\pi\) | ||||
−0.869851 | + | 0.493315i | \(0.835785\pi\) | |||||||
\(48\) | −2.65903 | −0.383798 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.83105 | −0.824635 | ||||||||
\(51\) | 2.33904 | 0.327531 | ||||||||
\(52\) | −1.24205 | −0.172241 | ||||||||
\(53\) | −0.531897 | −0.0730617 | −0.0365309 | − | 0.999333i | \(-0.511631\pi\) | ||||
−0.0365309 | + | 0.999333i | \(0.511631\pi\) | |||||||
\(54\) | 0.482188 | 0.0656175 | ||||||||
\(55\) | −4.12403 | −0.556085 | ||||||||
\(56\) | 1.81664 | 0.242759 | ||||||||
\(57\) | 1.46177 | 0.193616 | ||||||||
\(58\) | 1.88858 | 0.247983 | ||||||||
\(59\) | 9.50800 | 1.23784 | 0.618918 | − | 0.785455i | \(-0.287571\pi\) | ||||
0.618918 | + | 0.785455i | \(0.287571\pi\) | |||||||
\(60\) | −7.30745 | −0.943388 | ||||||||
\(61\) | 0.836502 | 0.107103 | 0.0535516 | − | 0.998565i | \(-0.482946\pi\) | ||||
0.0535516 | + | 0.998565i | \(0.482946\pi\) | |||||||
\(62\) | −4.70794 | −0.597909 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −2.94789 | −0.368486 | ||||||||
\(65\) | −2.90528 | −0.360356 | ||||||||
\(66\) | 0.480984 | 0.0592051 | ||||||||
\(67\) | −6.93613 | −0.847383 | −0.423691 | − | 0.905807i | \(-0.639266\pi\) | ||||
−0.423691 | + | 0.905807i | \(0.639266\pi\) | |||||||
\(68\) | 4.13423 | 0.501349 | ||||||||
\(69\) | 6.00006 | 0.722323 | ||||||||
\(70\) | 1.99354 | 0.238273 | ||||||||
\(71\) | −11.0801 | −1.31497 | −0.657483 | − | 0.753469i | \(-0.728379\pi\) | ||||
−0.657483 | + | 0.753469i | \(0.728379\pi\) | |||||||
\(72\) | 1.81664 | 0.214093 | ||||||||
\(73\) | −8.28151 | −0.969277 | −0.484638 | − | 0.874715i | \(-0.661049\pi\) | ||||
−0.484638 | + | 0.874715i | \(0.661049\pi\) | |||||||
\(74\) | 3.53975 | 0.411487 | ||||||||
\(75\) | −12.0929 | −1.39637 | ||||||||
\(76\) | 2.58367 | 0.296367 | ||||||||
\(77\) | 0.997504 | 0.113676 | ||||||||
\(78\) | 0.338842 | 0.0383663 | ||||||||
\(79\) | 1.46338 | 0.164643 | 0.0823216 | − | 0.996606i | \(-0.473767\pi\) | ||||
0.0823216 | + | 0.996606i | \(0.473767\pi\) | |||||||
\(80\) | −10.9934 | −1.22910 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.17536 | 0.129797 | ||||||||
\(83\) | 11.2131 | 1.23080 | 0.615399 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615399 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(84\) | 1.76749 | 0.192849 | ||||||||
\(85\) | 9.67040 | 1.04890 | ||||||||
\(86\) | 4.42607 | 0.477276 | ||||||||
\(87\) | 3.91669 | 0.419914 | ||||||||
\(88\) | 1.81211 | 0.193171 | ||||||||
\(89\) | 7.66990 | 0.813008 | 0.406504 | − | 0.913649i | \(-0.366748\pi\) | ||||
0.406504 | + | 0.913649i | \(0.366748\pi\) | |||||||
\(90\) | 1.99354 | 0.210137 | ||||||||
\(91\) | 0.702717 | 0.0736648 | ||||||||
\(92\) | 10.6051 | 1.10566 | ||||||||
\(93\) | −9.76370 | −1.01245 | ||||||||
\(94\) | 5.75096 | 0.593166 | ||||||||
\(95\) | 6.04347 | 0.620047 | ||||||||
\(96\) | 4.91543 | 0.501679 | ||||||||
\(97\) | −15.7928 | −1.60351 | −0.801756 | − | 0.597652i | \(-0.796100\pi\) | ||||
−0.801756 | + | 0.597652i | \(0.796100\pi\) | |||||||
\(98\) | −0.482188 | −0.0487083 | ||||||||
\(99\) | 0.997504 | 0.100253 | ||||||||
\(100\) | −21.3741 | −2.13741 | ||||||||
\(101\) | −1.71885 | −0.171032 | −0.0855161 | − | 0.996337i | \(-0.527254\pi\) | ||||
−0.0855161 | + | 0.996337i | \(0.527254\pi\) | |||||||
\(102\) | −1.12786 | −0.111674 | ||||||||
\(103\) | 4.80382 | 0.473334 | 0.236667 | − | 0.971591i | \(-0.423945\pi\) | ||||
0.236667 | + | 0.971591i | \(0.423945\pi\) | |||||||
\(104\) | 1.27658 | 0.125179 | ||||||||
\(105\) | 4.13435 | 0.403472 | ||||||||
\(106\) | 0.256474 | 0.0249110 | ||||||||
\(107\) | −9.04526 | −0.874438 | −0.437219 | − | 0.899355i | \(-0.644037\pi\) | ||||
−0.437219 | + | 0.899355i | \(0.644037\pi\) | |||||||
\(108\) | 1.76749 | 0.170077 | ||||||||
\(109\) | 18.2629 | 1.74927 | 0.874634 | − | 0.484784i | \(-0.161102\pi\) | ||||
0.874634 | + | 0.484784i | \(0.161102\pi\) | |||||||
\(110\) | 1.98856 | 0.189602 | ||||||||
\(111\) | 7.34101 | 0.696778 | ||||||||
\(112\) | 2.65903 | 0.251254 | ||||||||
\(113\) | −18.1350 | −1.70600 | −0.853000 | − | 0.521910i | \(-0.825220\pi\) | ||||
−0.853000 | + | 0.521910i | \(0.825220\pi\) | |||||||
\(114\) | −0.704847 | −0.0660150 | ||||||||
\(115\) | 24.8064 | 2.31321 | ||||||||
\(116\) | 6.92274 | 0.642760 | ||||||||
\(117\) | 0.702717 | 0.0649662 | ||||||||
\(118\) | −4.58464 | −0.422051 | ||||||||
\(119\) | −2.33904 | −0.214419 | ||||||||
\(120\) | 7.51064 | 0.685624 | ||||||||
\(121\) | −10.0050 | −0.909544 | ||||||||
\(122\) | −0.403351 | −0.0365177 | ||||||||
\(123\) | 2.43757 | 0.219788 | ||||||||
\(124\) | −17.2573 | −1.54975 | ||||||||
\(125\) | −29.3245 | −2.62287 | ||||||||
\(126\) | −0.482188 | −0.0429567 | ||||||||
\(127\) | −7.55032 | −0.669983 | −0.334991 | − | 0.942221i | \(-0.608733\pi\) | ||||
−0.334991 | + | 0.942221i | \(0.608733\pi\) | |||||||
\(128\) | 11.2523 | 0.994572 | ||||||||
\(129\) | 9.17914 | 0.808179 | ||||||||
\(130\) | 1.40089 | 0.122866 | ||||||||
\(131\) | 16.6976 | 1.45887 | 0.729436 | − | 0.684049i | \(-0.239782\pi\) | ||||
0.729436 | + | 0.684049i | \(0.239782\pi\) | |||||||
\(132\) | 1.76308 | 0.153457 | ||||||||
\(133\) | −1.46177 | −0.126751 | ||||||||
\(134\) | 3.34452 | 0.288922 | ||||||||
\(135\) | 4.13435 | 0.355829 | ||||||||
\(136\) | −4.24919 | −0.364365 | ||||||||
\(137\) | −1.54612 | −0.132094 | −0.0660470 | − | 0.997817i | \(-0.521039\pi\) | ||||
−0.0660470 | + | 0.997817i | \(0.521039\pi\) | |||||||
\(138\) | −2.89316 | −0.246282 | ||||||||
\(139\) | 18.8312 | 1.59724 | 0.798622 | − | 0.601832i | \(-0.205562\pi\) | ||||
0.798622 | + | 0.601832i | \(0.205562\pi\) | |||||||
\(140\) | 7.30745 | 0.617592 | ||||||||
\(141\) | 11.9268 | 1.00442 | ||||||||
\(142\) | 5.34269 | 0.448349 | ||||||||
\(143\) | 0.700963 | 0.0586175 | ||||||||
\(144\) | 2.65903 | 0.221586 | ||||||||
\(145\) | 16.1930 | 1.34476 | ||||||||
\(146\) | 3.99324 | 0.330483 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 12.9752 | 1.06656 | ||||||||
\(149\) | 13.3308 | 1.09210 | 0.546049 | − | 0.837753i | \(-0.316131\pi\) | ||||
0.546049 | + | 0.837753i | \(0.316131\pi\) | |||||||
\(150\) | 5.83105 | 0.476103 | ||||||||
\(151\) | −11.2141 | −0.912592 | −0.456296 | − | 0.889828i | \(-0.650824\pi\) | ||||
−0.456296 | + | 0.889828i | \(0.650824\pi\) | |||||||
\(152\) | −2.65551 | −0.215390 | ||||||||
\(153\) | −2.33904 | −0.189100 | ||||||||
\(154\) | −0.480984 | −0.0387588 | ||||||||
\(155\) | −40.3666 | −3.24232 | ||||||||
\(156\) | 1.24205 | 0.0994435 | ||||||||
\(157\) | 13.1471 | 1.04925 | 0.524626 | − | 0.851333i | \(-0.324205\pi\) | ||||
0.524626 | + | 0.851333i | \(0.324205\pi\) | |||||||
\(158\) | −0.705625 | −0.0561365 | ||||||||
\(159\) | 0.531897 | 0.0421822 | ||||||||
\(160\) | 20.3221 | 1.60661 | ||||||||
\(161\) | −6.00006 | −0.472871 | ||||||||
\(162\) | −0.482188 | −0.0378843 | ||||||||
\(163\) | 1.52517 | 0.119461 | 0.0597304 | − | 0.998215i | \(-0.480976\pi\) | ||||
0.0597304 | + | 0.998215i | \(0.480976\pi\) | |||||||
\(164\) | 4.30838 | 0.336428 | ||||||||
\(165\) | 4.12403 | 0.321056 | ||||||||
\(166\) | −5.40682 | −0.419651 | ||||||||
\(167\) | −22.7114 | −1.75746 | −0.878732 | − | 0.477315i | \(-0.841610\pi\) | ||||
−0.878732 | + | 0.477315i | \(0.841610\pi\) | |||||||
\(168\) | −1.81664 | −0.140157 | ||||||||
\(169\) | −12.5062 | −0.962014 | ||||||||
\(170\) | −4.66295 | −0.357632 | ||||||||
\(171\) | −1.46177 | −0.111784 | ||||||||
\(172\) | 16.2241 | 1.23708 | ||||||||
\(173\) | 23.5569 | 1.79100 | 0.895500 | − | 0.445062i | \(-0.146819\pi\) | ||||
0.895500 | + | 0.445062i | \(0.146819\pi\) | |||||||
\(174\) | −1.88858 | −0.143173 | ||||||||
\(175\) | 12.0929 | 0.914137 | ||||||||
\(176\) | 2.65239 | 0.199931 | ||||||||
\(177\) | −9.50800 | −0.714665 | ||||||||
\(178\) | −3.69833 | −0.277202 | ||||||||
\(179\) | −10.4008 | −0.777389 | −0.388694 | − | 0.921367i | \(-0.627074\pi\) | ||||
−0.388694 | + | 0.921367i | \(0.627074\pi\) | |||||||
\(180\) | 7.30745 | 0.544665 | ||||||||
\(181\) | −11.5176 | −0.856096 | −0.428048 | − | 0.903756i | \(-0.640799\pi\) | ||||
−0.428048 | + | 0.903756i | \(0.640799\pi\) | |||||||
\(182\) | −0.338842 | −0.0251166 | ||||||||
\(183\) | −0.836502 | −0.0618360 | ||||||||
\(184\) | −10.9000 | −0.803556 | ||||||||
\(185\) | 30.3504 | 2.23140 | ||||||||
\(186\) | 4.70794 | 0.345203 | ||||||||
\(187\) | −2.33320 | −0.170620 | ||||||||
\(188\) | 21.0805 | 1.53746 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −2.91409 | −0.211410 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | 2.94789 | 0.212746 | ||||||||
\(193\) | 21.6406 | 1.55773 | 0.778863 | − | 0.627194i | \(-0.215797\pi\) | ||||
0.778863 | + | 0.627194i | \(0.215797\pi\) | |||||||
\(194\) | 7.61508 | 0.546731 | ||||||||
\(195\) | 2.90528 | 0.208052 | ||||||||
\(196\) | −1.76749 | −0.126250 | ||||||||
\(197\) | 14.9802 | 1.06729 | 0.533647 | − | 0.845707i | \(-0.320821\pi\) | ||||
0.533647 | + | 0.845707i | \(0.320821\pi\) | |||||||
\(198\) | −0.480984 | −0.0341821 | ||||||||
\(199\) | 20.5734 | 1.45841 | 0.729204 | − | 0.684297i | \(-0.239891\pi\) | ||||
0.729204 | + | 0.684297i | \(0.239891\pi\) | |||||||
\(200\) | 21.9684 | 1.55340 | ||||||||
\(201\) | 6.93613 | 0.489237 | ||||||||
\(202\) | 0.828810 | 0.0583148 | ||||||||
\(203\) | −3.91669 | −0.274898 | ||||||||
\(204\) | −4.13423 | −0.289454 | ||||||||
\(205\) | 10.0778 | 0.703861 | ||||||||
\(206\) | −2.31634 | −0.161387 | ||||||||
\(207\) | −6.00006 | −0.417033 | ||||||||
\(208\) | 1.86854 | 0.129560 | ||||||||
\(209\) | −1.45812 | −0.100860 | ||||||||
\(210\) | −1.99354 | −0.137567 | ||||||||
\(211\) | 8.51737 | 0.586360 | 0.293180 | − | 0.956057i | \(-0.405287\pi\) | ||||
0.293180 | + | 0.956057i | \(0.405287\pi\) | |||||||
\(212\) | 0.940126 | 0.0645681 | ||||||||
\(213\) | 11.0801 | 0.759196 | ||||||||
\(214\) | 4.36152 | 0.298147 | ||||||||
\(215\) | 37.9498 | 2.58816 | ||||||||
\(216\) | −1.81664 | −0.123607 | ||||||||
\(217\) | 9.76370 | 0.662803 | ||||||||
\(218\) | −8.80615 | −0.596428 | ||||||||
\(219\) | 8.28151 | 0.559612 | ||||||||
\(220\) | 7.28921 | 0.491438 | ||||||||
\(221\) | −1.64368 | −0.110566 | ||||||||
\(222\) | −3.53975 | −0.237572 | ||||||||
\(223\) | 22.2413 | 1.48939 | 0.744694 | − | 0.667406i | \(-0.232596\pi\) | ||||
0.744694 | + | 0.667406i | \(0.232596\pi\) | |||||||
\(224\) | −4.91543 | −0.328426 | ||||||||
\(225\) | 12.0929 | 0.806193 | ||||||||
\(226\) | 8.74450 | 0.581675 | ||||||||
\(227\) | −16.0840 | −1.06753 | −0.533765 | − | 0.845633i | \(-0.679223\pi\) | ||||
−0.533765 | + | 0.845633i | \(0.679223\pi\) | |||||||
\(228\) | −2.58367 | −0.171108 | ||||||||
\(229\) | 24.9029 | 1.64563 | 0.822814 | − | 0.568311i | \(-0.192403\pi\) | ||||
0.822814 | + | 0.568311i | \(0.192403\pi\) | |||||||
\(230\) | −11.9613 | −0.788708 | ||||||||
\(231\) | −0.997504 | −0.0656309 | ||||||||
\(232\) | −7.11522 | −0.467137 | ||||||||
\(233\) | −6.69139 | −0.438367 | −0.219184 | − | 0.975684i | \(-0.570339\pi\) | ||||
−0.219184 | + | 0.975684i | \(0.570339\pi\) | |||||||
\(234\) | −0.338842 | −0.0221508 | ||||||||
\(235\) | 49.3096 | 3.21660 | ||||||||
\(236\) | −16.8053 | −1.09393 | ||||||||
\(237\) | −1.46338 | −0.0950568 | ||||||||
\(238\) | 1.12786 | 0.0731080 | ||||||||
\(239\) | −11.4771 | −0.742390 | −0.371195 | − | 0.928555i | \(-0.621052\pi\) | ||||
−0.371195 | + | 0.928555i | \(0.621052\pi\) | |||||||
\(240\) | 10.9934 | 0.709618 | ||||||||
\(241\) | −27.5046 | −1.77172 | −0.885862 | − | 0.463949i | \(-0.846432\pi\) | ||||
−0.885862 | + | 0.463949i | \(0.846432\pi\) | |||||||
\(242\) | 4.82428 | 0.310117 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.47851 | −0.0946521 | ||||||||
\(245\) | −4.13435 | −0.264134 | ||||||||
\(246\) | −1.17536 | −0.0749385 | ||||||||
\(247\) | −1.02721 | −0.0653598 | ||||||||
\(248\) | 17.7371 | 1.12631 | ||||||||
\(249\) | −11.2131 | −0.710602 | ||||||||
\(250\) | 14.1399 | 0.894288 | ||||||||
\(251\) | 16.5037 | 1.04170 | 0.520852 | − | 0.853647i | \(-0.325614\pi\) | ||||
0.520852 | + | 0.853647i | \(0.325614\pi\) | |||||||
\(252\) | −1.76749 | −0.111342 | ||||||||
\(253\) | −5.98508 | −0.376279 | ||||||||
\(254\) | 3.64067 | 0.228436 | ||||||||
\(255\) | −9.67040 | −0.605584 | ||||||||
\(256\) | 0.470058 | 0.0293787 | ||||||||
\(257\) | −11.5033 | −0.717555 | −0.358777 | − | 0.933423i | \(-0.616806\pi\) | ||||
−0.358777 | + | 0.933423i | \(0.616806\pi\) | |||||||
\(258\) | −4.42607 | −0.275555 | ||||||||
\(259\) | −7.34101 | −0.456148 | ||||||||
\(260\) | 5.13507 | 0.318464 | ||||||||
\(261\) | −3.91669 | −0.242437 | ||||||||
\(262\) | −8.05136 | −0.497415 | ||||||||
\(263\) | 11.6125 | 0.716057 | 0.358028 | − | 0.933711i | \(-0.383449\pi\) | ||||
0.358028 | + | 0.933711i | \(0.383449\pi\) | |||||||
\(264\) | −1.81211 | −0.111527 | ||||||||
\(265\) | 2.19905 | 0.135087 | ||||||||
\(266\) | 0.704847 | 0.0432170 | ||||||||
\(267\) | −7.66990 | −0.469390 | ||||||||
\(268\) | 12.2596 | 0.748872 | ||||||||
\(269\) | −31.2118 | −1.90302 | −0.951510 | − | 0.307619i | \(-0.900468\pi\) | ||||
−0.951510 | + | 0.307619i | \(0.900468\pi\) | |||||||
\(270\) | −1.99354 | −0.121323 | ||||||||
\(271\) | 19.1870 | 1.16553 | 0.582765 | − | 0.812641i | \(-0.301971\pi\) | ||||
0.582765 | + | 0.812641i | \(0.301971\pi\) | |||||||
\(272\) | −6.21956 | −0.377116 | ||||||||
\(273\) | −0.702717 | −0.0425304 | ||||||||
\(274\) | 0.745521 | 0.0450386 | ||||||||
\(275\) | 12.0627 | 0.727408 | ||||||||
\(276\) | −10.6051 | −0.638351 | ||||||||
\(277\) | 8.37683 | 0.503315 | 0.251658 | − | 0.967816i | \(-0.419024\pi\) | ||||
0.251658 | + | 0.967816i | \(0.419024\pi\) | |||||||
\(278\) | −9.08020 | −0.544594 | ||||||||
\(279\) | 9.76370 | 0.584537 | ||||||||
\(280\) | −7.51064 | −0.448846 | ||||||||
\(281\) | −10.8066 | −0.644665 | −0.322333 | − | 0.946626i | \(-0.604467\pi\) | ||||
−0.322333 | + | 0.946626i | \(0.604467\pi\) | |||||||
\(282\) | −5.75096 | −0.342465 | ||||||||
\(283\) | 17.5690 | 1.04437 | 0.522184 | − | 0.852833i | \(-0.325118\pi\) | ||||
0.522184 | + | 0.852833i | \(0.325118\pi\) | |||||||
\(284\) | 19.5840 | 1.16210 | ||||||||
\(285\) | −6.04347 | −0.357984 | ||||||||
\(286\) | −0.337996 | −0.0199861 | ||||||||
\(287\) | −2.43757 | −0.143885 | ||||||||
\(288\) | −4.91543 | −0.289645 | ||||||||
\(289\) | −11.5289 | −0.678171 | ||||||||
\(290\) | −7.80807 | −0.458506 | ||||||||
\(291\) | 15.7928 | 0.925788 | ||||||||
\(292\) | 14.6375 | 0.856596 | ||||||||
\(293\) | 25.0315 | 1.46236 | 0.731178 | − | 0.682187i | \(-0.238971\pi\) | ||||
0.731178 | + | 0.682187i | \(0.238971\pi\) | |||||||
\(294\) | 0.482188 | 0.0281218 | ||||||||
\(295\) | −39.3095 | −2.28868 | ||||||||
\(296\) | −13.3360 | −0.775138 | ||||||||
\(297\) | −0.997504 | −0.0578810 | ||||||||
\(298\) | −6.42793 | −0.372360 | ||||||||
\(299\) | −4.21635 | −0.243838 | ||||||||
\(300\) | 21.3741 | 1.23404 | ||||||||
\(301\) | −9.17914 | −0.529077 | ||||||||
\(302\) | 5.40732 | 0.311156 | ||||||||
\(303\) | 1.71885 | 0.0987454 | ||||||||
\(304\) | −3.88688 | −0.222928 | ||||||||
\(305\) | −3.45840 | −0.198027 | ||||||||
\(306\) | 1.12786 | 0.0644752 | ||||||||
\(307\) | 3.98673 | 0.227535 | 0.113767 | − | 0.993507i | \(-0.463708\pi\) | ||||
0.113767 | + | 0.993507i | \(0.463708\pi\) | |||||||
\(308\) | −1.76308 | −0.100461 | ||||||||
\(309\) | −4.80382 | −0.273280 | ||||||||
\(310\) | 19.4643 | 1.10550 | ||||||||
\(311\) | 15.8134 | 0.896694 | 0.448347 | − | 0.893860i | \(-0.352013\pi\) | ||||
0.448347 | + | 0.893860i | \(0.352013\pi\) | |||||||
\(312\) | −1.27658 | −0.0722724 | ||||||||
\(313\) | −11.6769 | −0.660020 | −0.330010 | − | 0.943977i | \(-0.607052\pi\) | ||||
−0.330010 | + | 0.943977i | \(0.607052\pi\) | |||||||
\(314\) | −6.33937 | −0.357751 | ||||||||
\(315\) | −4.13435 | −0.232945 | ||||||||
\(316\) | −2.58652 | −0.145503 | ||||||||
\(317\) | −5.94931 | −0.334147 | −0.167073 | − | 0.985944i | \(-0.553432\pi\) | ||||
−0.167073 | + | 0.985944i | \(0.553432\pi\) | |||||||
\(318\) | −0.256474 | −0.0143824 | ||||||||
\(319\) | −3.90692 | −0.218745 | ||||||||
\(320\) | 12.1876 | 0.681309 | ||||||||
\(321\) | 9.04526 | 0.504857 | ||||||||
\(322\) | 2.89316 | 0.161229 | ||||||||
\(323\) | 3.41913 | 0.190245 | ||||||||
\(324\) | −1.76749 | −0.0981942 | ||||||||
\(325\) | 8.49788 | 0.471378 | ||||||||
\(326\) | −0.735420 | −0.0407311 | ||||||||
\(327\) | −18.2629 | −1.00994 | ||||||||
\(328\) | −4.42818 | −0.244505 | ||||||||
\(329\) | −11.9268 | −0.657545 | ||||||||
\(330\) | −1.98856 | −0.109467 | ||||||||
\(331\) | −27.8415 | −1.53031 | −0.765154 | − | 0.643848i | \(-0.777337\pi\) | ||||
−0.765154 | + | 0.643848i | \(0.777337\pi\) | |||||||
\(332\) | −19.8191 | −1.08771 | ||||||||
\(333\) | −7.34101 | −0.402285 | ||||||||
\(334\) | 10.9512 | 0.599222 | ||||||||
\(335\) | 28.6764 | 1.56676 | ||||||||
\(336\) | −2.65903 | −0.145062 | ||||||||
\(337\) | 30.8476 | 1.68038 | 0.840189 | − | 0.542294i | \(-0.182444\pi\) | ||||
0.840189 | + | 0.542294i | \(0.182444\pi\) | |||||||
\(338\) | 6.03033 | 0.328007 | ||||||||
\(339\) | 18.1350 | 0.984960 | ||||||||
\(340\) | −17.0924 | −0.926965 | ||||||||
\(341\) | 9.73933 | 0.527414 | ||||||||
\(342\) | 0.704847 | 0.0381138 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −16.6752 | −0.899067 | ||||||||
\(345\) | −24.8064 | −1.33553 | ||||||||
\(346\) | −11.3589 | −0.610656 | ||||||||
\(347\) | −1.62161 | −0.0870525 | −0.0435263 | − | 0.999052i | \(-0.513859\pi\) | ||||
−0.0435263 | + | 0.999052i | \(0.513859\pi\) | |||||||
\(348\) | −6.92274 | −0.371098 | ||||||||
\(349\) | 3.92886 | 0.210307 | 0.105154 | − | 0.994456i | \(-0.466467\pi\) | ||||
0.105154 | + | 0.994456i | \(0.466467\pi\) | |||||||
\(350\) | −5.83105 | −0.311683 | ||||||||
\(351\) | −0.702717 | −0.0375083 | ||||||||
\(352\) | −4.90316 | −0.261339 | ||||||||
\(353\) | 6.90972 | 0.367767 | 0.183884 | − | 0.982948i | \(-0.441133\pi\) | ||||
0.183884 | + | 0.982948i | \(0.441133\pi\) | |||||||
\(354\) | 4.58464 | 0.243671 | ||||||||
\(355\) | 45.8091 | 2.43129 | ||||||||
\(356\) | −13.5565 | −0.718494 | ||||||||
\(357\) | 2.33904 | 0.123795 | ||||||||
\(358\) | 5.01512 | 0.265057 | ||||||||
\(359\) | 24.4506 | 1.29045 | 0.645226 | − | 0.763992i | \(-0.276763\pi\) | ||||
0.645226 | + | 0.763992i | \(0.276763\pi\) | |||||||
\(360\) | −7.51064 | −0.395845 | ||||||||
\(361\) | −16.8632 | −0.887539 | ||||||||
\(362\) | 5.55365 | 0.291893 | ||||||||
\(363\) | 10.0050 | 0.525126 | ||||||||
\(364\) | −1.24205 | −0.0651011 | ||||||||
\(365\) | 34.2387 | 1.79213 | ||||||||
\(366\) | 0.403351 | 0.0210835 | ||||||||
\(367\) | 9.81317 | 0.512243 | 0.256122 | − | 0.966645i | \(-0.417555\pi\) | ||||
0.256122 | + | 0.966645i | \(0.417555\pi\) | |||||||
\(368\) | −15.9543 | −0.831677 | ||||||||
\(369\) | −2.43757 | −0.126895 | ||||||||
\(370\) | −14.6346 | −0.760815 | ||||||||
\(371\) | −0.531897 | −0.0276147 | ||||||||
\(372\) | 17.2573 | 0.894749 | ||||||||
\(373\) | −26.0314 | −1.34786 | −0.673928 | − | 0.738797i | \(-0.735394\pi\) | ||||
−0.673928 | + | 0.738797i | \(0.735394\pi\) | |||||||
\(374\) | 1.12504 | 0.0581744 | ||||||||
\(375\) | 29.3245 | 1.51431 | ||||||||
\(376\) | −21.6667 | −1.11737 | ||||||||
\(377\) | −2.75233 | −0.141752 | ||||||||
\(378\) | 0.482188 | 0.0248011 | ||||||||
\(379\) | 26.8930 | 1.38140 | 0.690701 | − | 0.723140i | \(-0.257302\pi\) | ||||
0.690701 | + | 0.723140i | \(0.257302\pi\) | |||||||
\(380\) | −10.6818 | −0.547965 | ||||||||
\(381\) | 7.55032 | 0.386815 | ||||||||
\(382\) | 0.482188 | 0.0246709 | ||||||||
\(383\) | −30.0292 | −1.53442 | −0.767210 | − | 0.641396i | \(-0.778356\pi\) | ||||
−0.767210 | + | 0.641396i | \(0.778356\pi\) | |||||||
\(384\) | −11.2523 | −0.574217 | ||||||||
\(385\) | −4.12403 | −0.210180 | ||||||||
\(386\) | −10.4348 | −0.531120 | ||||||||
\(387\) | −9.17914 | −0.466602 | ||||||||
\(388\) | 27.9136 | 1.41710 | ||||||||
\(389\) | 28.5529 | 1.44769 | 0.723844 | − | 0.689963i | \(-0.242373\pi\) | ||||
0.723844 | + | 0.689963i | \(0.242373\pi\) | |||||||
\(390\) | −1.40089 | −0.0709369 | ||||||||
\(391\) | 14.0344 | 0.709748 | ||||||||
\(392\) | 1.81664 | 0.0917542 | ||||||||
\(393\) | −16.6976 | −0.842281 | ||||||||
\(394\) | −7.22327 | −0.363903 | ||||||||
\(395\) | −6.05014 | −0.304415 | ||||||||
\(396\) | −1.76308 | −0.0885982 | ||||||||
\(397\) | −13.3638 | −0.670711 | −0.335355 | − | 0.942092i | \(-0.608856\pi\) | ||||
−0.335355 | + | 0.942092i | \(0.608856\pi\) | |||||||
\(398\) | −9.92023 | −0.497256 | ||||||||
\(399\) | 1.46177 | 0.0731800 | ||||||||
\(400\) | 32.1553 | 1.60777 | ||||||||
\(401\) | −20.6193 | −1.02968 | −0.514839 | − | 0.857287i | \(-0.672148\pi\) | ||||
−0.514839 | + | 0.857287i | \(0.672148\pi\) | |||||||
\(402\) | −3.34452 | −0.166809 | ||||||||
\(403\) | 6.86112 | 0.341777 | ||||||||
\(404\) | 3.03806 | 0.151149 | ||||||||
\(405\) | −4.13435 | −0.205438 | ||||||||
\(406\) | 1.88858 | 0.0937288 | ||||||||
\(407\) | −7.32269 | −0.362972 | ||||||||
\(408\) | 4.24919 | 0.210366 | ||||||||
\(409\) | −13.6973 | −0.677287 | −0.338643 | − | 0.940915i | \(-0.609968\pi\) | ||||
−0.338643 | + | 0.940915i | \(0.609968\pi\) | |||||||
\(410\) | −4.85937 | −0.239987 | ||||||||
\(411\) | 1.54612 | 0.0762645 | ||||||||
\(412\) | −8.49072 | −0.418308 | ||||||||
\(413\) | 9.50800 | 0.467858 | ||||||||
\(414\) | 2.89316 | 0.142191 | ||||||||
\(415\) | −46.3589 | −2.27567 | ||||||||
\(416\) | −3.45416 | −0.169354 | ||||||||
\(417\) | −18.8312 | −0.922170 | ||||||||
\(418\) | 0.703088 | 0.0343892 | ||||||||
\(419\) | −1.44478 | −0.0705821 | −0.0352910 | − | 0.999377i | \(-0.511236\pi\) | ||||
−0.0352910 | + | 0.999377i | \(0.511236\pi\) | |||||||
\(420\) | −7.30745 | −0.356567 | ||||||||
\(421\) | 5.80540 | 0.282938 | 0.141469 | − | 0.989943i | \(-0.454817\pi\) | ||||
0.141469 | + | 0.989943i | \(0.454817\pi\) | |||||||
\(422\) | −4.10697 | −0.199924 | ||||||||
\(423\) | −11.9268 | −0.579901 | ||||||||
\(424\) | −0.966266 | −0.0469260 | ||||||||
\(425\) | −28.2857 | −1.37206 | ||||||||
\(426\) | −5.34269 | −0.258854 | ||||||||
\(427\) | 0.836502 | 0.0404812 | ||||||||
\(428\) | 15.9875 | 0.772783 | ||||||||
\(429\) | −0.700963 | −0.0338428 | ||||||||
\(430\) | −18.2990 | −0.882454 | ||||||||
\(431\) | 28.2360 | 1.36008 | 0.680039 | − | 0.733175i | \(-0.261963\pi\) | ||||
0.680039 | + | 0.733175i | \(0.261963\pi\) | |||||||
\(432\) | −2.65903 | −0.127933 | ||||||||
\(433\) | −13.3156 | −0.639907 | −0.319953 | − | 0.947433i | \(-0.603667\pi\) | ||||
−0.319953 | + | 0.947433i | \(0.603667\pi\) | |||||||
\(434\) | −4.70794 | −0.225988 | ||||||||
\(435\) | −16.1930 | −0.776395 | ||||||||
\(436\) | −32.2796 | −1.54591 | ||||||||
\(437\) | 8.77070 | 0.419560 | ||||||||
\(438\) | −3.99324 | −0.190805 | ||||||||
\(439\) | 6.69269 | 0.319425 | 0.159712 | − | 0.987164i | \(-0.448943\pi\) | ||||
0.159712 | + | 0.987164i | \(0.448943\pi\) | |||||||
\(440\) | −7.49189 | −0.357162 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.792563 | 0.0376984 | ||||||||
\(443\) | 10.0344 | 0.476749 | 0.238374 | − | 0.971173i | \(-0.423385\pi\) | ||||
0.238374 | + | 0.971173i | \(0.423385\pi\) | |||||||
\(444\) | −12.9752 | −0.615776 | ||||||||
\(445\) | −31.7101 | −1.50320 | ||||||||
\(446\) | −10.7245 | −0.507819 | ||||||||
\(447\) | −13.3308 | −0.630523 | ||||||||
\(448\) | −2.94789 | −0.139275 | ||||||||
\(449\) | 9.77498 | 0.461310 | 0.230655 | − | 0.973036i | \(-0.425913\pi\) | ||||
0.230655 | + | 0.973036i | \(0.425913\pi\) | |||||||
\(450\) | −5.83105 | −0.274878 | ||||||||
\(451\) | −2.43148 | −0.114494 | ||||||||
\(452\) | 32.0536 | 1.50767 | ||||||||
\(453\) | 11.2141 | 0.526885 | ||||||||
\(454\) | 7.75549 | 0.363983 | ||||||||
\(455\) | −2.90528 | −0.136202 | ||||||||
\(456\) | 2.65551 | 0.124356 | ||||||||
\(457\) | 16.5366 | 0.773550 | 0.386775 | − | 0.922174i | \(-0.373589\pi\) | ||||
0.386775 | + | 0.922174i | \(0.373589\pi\) | |||||||
\(458\) | −12.0079 | −0.561090 | ||||||||
\(459\) | 2.33904 | 0.109177 | ||||||||
\(460\) | −43.8452 | −2.04429 | ||||||||
\(461\) | −6.79472 | −0.316461 | −0.158231 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158231 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(462\) | 0.480984 | 0.0223774 | ||||||||
\(463\) | 1.60269 | 0.0744835 | 0.0372418 | − | 0.999306i | \(-0.488143\pi\) | ||||
0.0372418 | + | 0.999306i | \(0.488143\pi\) | |||||||
\(464\) | −10.4146 | −0.483485 | ||||||||
\(465\) | 40.3666 | 1.87196 | ||||||||
\(466\) | 3.22651 | 0.149465 | ||||||||
\(467\) | −17.9561 | −0.830911 | −0.415455 | − | 0.909614i | \(-0.636378\pi\) | ||||
−0.415455 | + | 0.909614i | \(0.636378\pi\) | |||||||
\(468\) | −1.24205 | −0.0574137 | ||||||||
\(469\) | −6.93613 | −0.320281 | ||||||||
\(470\) | −23.7765 | −1.09673 | ||||||||
\(471\) | −13.1471 | −0.605786 | ||||||||
\(472\) | 17.2726 | 0.795037 | ||||||||
\(473\) | −9.15623 | −0.421004 | ||||||||
\(474\) | 0.705625 | 0.0324104 | ||||||||
\(475\) | −17.6770 | −0.811077 | ||||||||
\(476\) | 4.13423 | 0.189492 | ||||||||
\(477\) | −0.531897 | −0.0243539 | ||||||||
\(478\) | 5.53411 | 0.253124 | ||||||||
\(479\) | −10.6449 | −0.486380 | −0.243190 | − | 0.969979i | \(-0.578194\pi\) | ||||
−0.243190 | + | 0.969979i | \(0.578194\pi\) | |||||||
\(480\) | −20.3221 | −0.927575 | ||||||||
\(481\) | −5.15866 | −0.235215 | ||||||||
\(482\) | 13.2624 | 0.604084 | ||||||||
\(483\) | 6.00006 | 0.273012 | ||||||||
\(484\) | 17.6838 | 0.803807 | ||||||||
\(485\) | 65.2928 | 2.96480 | ||||||||
\(486\) | 0.482188 | 0.0218725 | ||||||||
\(487\) | −24.6498 | −1.11699 | −0.558495 | − | 0.829508i | \(-0.688621\pi\) | ||||
−0.558495 | + | 0.829508i | \(0.688621\pi\) | |||||||
\(488\) | 1.51962 | 0.0687901 | ||||||||
\(489\) | −1.52517 | −0.0689707 | ||||||||
\(490\) | 1.99354 | 0.0900588 | ||||||||
\(491\) | 8.62076 | 0.389049 | 0.194525 | − | 0.980898i | \(-0.437684\pi\) | ||||
0.194525 | + | 0.980898i | \(0.437684\pi\) | |||||||
\(492\) | −4.30838 | −0.194237 | ||||||||
\(493\) | 9.16129 | 0.412604 | ||||||||
\(494\) | 0.495308 | 0.0222850 | ||||||||
\(495\) | −4.12403 | −0.185362 | ||||||||
\(496\) | 25.9619 | 1.16573 | ||||||||
\(497\) | −11.0801 | −0.497011 | ||||||||
\(498\) | 5.40682 | 0.242286 | ||||||||
\(499\) | 15.8785 | 0.710820 | 0.355410 | − | 0.934711i | \(-0.384341\pi\) | ||||
0.355410 | + | 0.934711i | \(0.384341\pi\) | |||||||
\(500\) | 51.8309 | 2.31795 | ||||||||
\(501\) | 22.7114 | 1.01467 | ||||||||
\(502\) | −7.95788 | −0.355178 | ||||||||
\(503\) | −7.89783 | −0.352147 | −0.176073 | − | 0.984377i | \(-0.556340\pi\) | ||||
−0.176073 | + | 0.984377i | \(0.556340\pi\) | |||||||
\(504\) | 1.81664 | 0.0809196 | ||||||||
\(505\) | 7.10634 | 0.316228 | ||||||||
\(506\) | 2.88594 | 0.128296 | ||||||||
\(507\) | 12.5062 | 0.555419 | ||||||||
\(508\) | 13.3452 | 0.592095 | ||||||||
\(509\) | 1.84329 | 0.0817025 | 0.0408513 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408513 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(510\) | 4.66295 | 0.206479 | ||||||||
\(511\) | −8.28151 | −0.366352 | ||||||||
\(512\) | −22.7313 | −1.00459 | ||||||||
\(513\) | 1.46177 | 0.0645387 | ||||||||
\(514\) | 5.54674 | 0.244656 | ||||||||
\(515\) | −19.8607 | −0.875167 | ||||||||
\(516\) | −16.2241 | −0.714226 | ||||||||
\(517\) | −11.8970 | −0.523231 | ||||||||
\(518\) | 3.53975 | 0.155528 | ||||||||
\(519\) | −23.5569 | −1.03403 | ||||||||
\(520\) | −5.27786 | −0.231449 | ||||||||
\(521\) | −3.19210 | −0.139849 | −0.0699243 | − | 0.997552i | \(-0.522276\pi\) | ||||
−0.0699243 | + | 0.997552i | \(0.522276\pi\) | |||||||
\(522\) | 1.88858 | 0.0826610 | ||||||||
\(523\) | −33.9792 | −1.48581 | −0.742904 | − | 0.669398i | \(-0.766552\pi\) | ||||
−0.742904 | + | 0.669398i | \(0.766552\pi\) | |||||||
\(524\) | −29.5129 | −1.28927 | ||||||||
\(525\) | −12.0929 | −0.527777 | ||||||||
\(526\) | −5.59940 | −0.244146 | ||||||||
\(527\) | −22.8376 | −0.994824 | ||||||||
\(528\) | −2.65239 | −0.115430 | ||||||||
\(529\) | 13.0007 | 0.565250 | ||||||||
\(530\) | −1.06036 | −0.0460589 | ||||||||
\(531\) | 9.50800 | 0.412612 | ||||||||
\(532\) | 2.58367 | 0.112016 | ||||||||
\(533\) | −1.71292 | −0.0741948 | ||||||||
\(534\) | 3.69833 | 0.160043 | ||||||||
\(535\) | 37.3963 | 1.61678 | ||||||||
\(536\) | −12.6005 | −0.544257 | ||||||||
\(537\) | 10.4008 | 0.448826 | ||||||||
\(538\) | 15.0500 | 0.648850 | ||||||||
\(539\) | 0.997504 | 0.0429655 | ||||||||
\(540\) | −7.30745 | −0.314463 | ||||||||
\(541\) | −15.0752 | −0.648134 | −0.324067 | − | 0.946034i | \(-0.605050\pi\) | ||||
−0.324067 | + | 0.946034i | \(0.605050\pi\) | |||||||
\(542\) | −9.25176 | −0.397397 | ||||||||
\(543\) | 11.5176 | 0.494267 | ||||||||
\(544\) | 11.4974 | 0.492946 | ||||||||
\(545\) | −75.5053 | −3.23429 | ||||||||
\(546\) | 0.338842 | 0.0145011 | ||||||||
\(547\) | 27.9749 | 1.19612 | 0.598061 | − | 0.801450i | \(-0.295938\pi\) | ||||
0.598061 | + | 0.801450i | \(0.295938\pi\) | |||||||
\(548\) | 2.73276 | 0.116738 | ||||||||
\(549\) | 0.836502 | 0.0357010 | ||||||||
\(550\) | −5.81649 | −0.248016 | ||||||||
\(551\) | 5.72530 | 0.243906 | ||||||||
\(552\) | 10.9000 | 0.463933 | ||||||||
\(553\) | 1.46338 | 0.0622293 | ||||||||
\(554\) | −4.03921 | −0.171609 | ||||||||
\(555\) | −30.3504 | −1.28830 | ||||||||
\(556\) | −33.2841 | −1.41156 | ||||||||
\(557\) | 3.94321 | 0.167079 | 0.0835396 | − | 0.996504i | \(-0.473377\pi\) | ||||
0.0835396 | + | 0.996504i | \(0.473377\pi\) | |||||||
\(558\) | −4.70794 | −0.199303 | ||||||||
\(559\) | −6.45034 | −0.272820 | ||||||||
\(560\) | −10.9934 | −0.464554 | ||||||||
\(561\) | 2.33320 | 0.0985077 | ||||||||
\(562\) | 5.21079 | 0.219804 | ||||||||
\(563\) | −20.6132 | −0.868744 | −0.434372 | − | 0.900734i | \(-0.643030\pi\) | ||||
−0.434372 | + | 0.900734i | \(0.643030\pi\) | |||||||
\(564\) | −21.0805 | −0.887651 | ||||||||
\(565\) | 74.9767 | 3.15429 | ||||||||
\(566\) | −8.47155 | −0.356086 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −20.1286 | −0.844576 | ||||||||
\(569\) | −0.658791 | −0.0276180 | −0.0138090 | − | 0.999905i | \(-0.504396\pi\) | ||||
−0.0138090 | + | 0.999905i | \(0.504396\pi\) | |||||||
\(570\) | 2.91409 | 0.122058 | ||||||||
\(571\) | −12.9397 | −0.541510 | −0.270755 | − | 0.962648i | \(-0.587273\pi\) | ||||
−0.270755 | + | 0.962648i | \(0.587273\pi\) | |||||||
\(572\) | −1.23895 | −0.0518031 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | 1.17536 | 0.0490588 | ||||||||
\(575\) | −72.5581 | −3.02588 | ||||||||
\(576\) | −2.94789 | −0.122829 | ||||||||
\(577\) | 28.0362 | 1.16716 | 0.583580 | − | 0.812055i | \(-0.301651\pi\) | ||||
0.583580 | + | 0.812055i | \(0.301651\pi\) | |||||||
\(578\) | 5.55910 | 0.231228 | ||||||||
\(579\) | −21.6406 | −0.899353 | ||||||||
\(580\) | −28.6210 | −1.18842 | ||||||||
\(581\) | 11.2131 | 0.465198 | ||||||||
\(582\) | −7.61508 | −0.315655 | ||||||||
\(583\) | −0.530570 | −0.0219739 | ||||||||
\(584\) | −15.0445 | −0.622547 | ||||||||
\(585\) | −2.90528 | −0.120119 | ||||||||
\(586\) | −12.0699 | −0.498603 | ||||||||
\(587\) | −4.76119 | −0.196515 | −0.0982577 | − | 0.995161i | \(-0.531327\pi\) | ||||
−0.0982577 | + | 0.995161i | \(0.531327\pi\) | |||||||
\(588\) | 1.76749 | 0.0728903 | ||||||||
\(589\) | −14.2723 | −0.588079 | ||||||||
\(590\) | 18.9545 | 0.780346 | ||||||||
\(591\) | −14.9802 | −0.616203 | ||||||||
\(592\) | −19.5200 | −0.802265 | ||||||||
\(593\) | −13.7306 | −0.563848 | −0.281924 | − | 0.959437i | \(-0.590973\pi\) | ||||
−0.281924 | + | 0.959437i | \(0.590973\pi\) | |||||||
\(594\) | 0.480984 | 0.0197350 | ||||||||
\(595\) | 9.67040 | 0.396448 | ||||||||
\(596\) | −23.5620 | −0.965139 | ||||||||
\(597\) | −20.5734 | −0.842012 | ||||||||
\(598\) | 2.03307 | 0.0831385 | ||||||||
\(599\) | 28.7948 | 1.17652 | 0.588261 | − | 0.808671i | \(-0.299813\pi\) | ||||
0.588261 | + | 0.808671i | \(0.299813\pi\) | |||||||
\(600\) | −21.9684 | −0.896858 | ||||||||
\(601\) | 13.5715 | 0.553594 | 0.276797 | − | 0.960928i | \(-0.410727\pi\) | ||||
0.276797 | + | 0.960928i | \(0.410727\pi\) | |||||||
\(602\) | 4.42607 | 0.180393 | ||||||||
\(603\) | −6.93613 | −0.282461 | ||||||||
\(604\) | 19.8209 | 0.806501 | ||||||||
\(605\) | 41.3642 | 1.68169 | ||||||||
\(606\) | −0.828810 | −0.0336681 | ||||||||
\(607\) | 35.3913 | 1.43649 | 0.718245 | − | 0.695790i | \(-0.244946\pi\) | ||||
0.718245 | + | 0.695790i | \(0.244946\pi\) | |||||||
\(608\) | 7.18523 | 0.291399 | ||||||||
\(609\) | 3.91669 | 0.158712 | ||||||||
\(610\) | 1.66760 | 0.0675190 | ||||||||
\(611\) | −8.38117 | −0.339066 | ||||||||
\(612\) | 4.13423 | 0.167116 | ||||||||
\(613\) | 10.7505 | 0.434207 | 0.217103 | − | 0.976149i | \(-0.430339\pi\) | ||||
0.217103 | + | 0.976149i | \(0.430339\pi\) | |||||||
\(614\) | −1.92235 | −0.0775799 | ||||||||
\(615\) | −10.0778 | −0.406374 | ||||||||
\(616\) | 1.81211 | 0.0730118 | ||||||||
\(617\) | −28.4006 | −1.14336 | −0.571682 | − | 0.820475i | \(-0.693709\pi\) | ||||
−0.571682 | + | 0.820475i | \(0.693709\pi\) | |||||||
\(618\) | 2.31634 | 0.0931770 | ||||||||
\(619\) | −14.2460 | −0.572597 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(620\) | 71.3478 | 2.86540 | ||||||||
\(621\) | 6.00006 | 0.240774 | ||||||||
\(622\) | −7.62501 | −0.305735 | ||||||||
\(623\) | 7.66990 | 0.307288 | ||||||||
\(624\) | −1.86854 | −0.0748016 | ||||||||
\(625\) | 60.7735 | 2.43094 | ||||||||
\(626\) | 5.63048 | 0.225039 | ||||||||
\(627\) | 1.45812 | 0.0582317 | ||||||||
\(628\) | −23.2374 | −0.927274 | ||||||||
\(629\) | 17.1709 | 0.684648 | ||||||||
\(630\) | 1.99354 | 0.0794244 | ||||||||
\(631\) | 38.0568 | 1.51502 | 0.757509 | − | 0.652825i | \(-0.226416\pi\) | ||||
0.757509 | + | 0.652825i | \(0.226416\pi\) | |||||||
\(632\) | 2.65844 | 0.105747 | ||||||||
\(633\) | −8.51737 | −0.338535 | ||||||||
\(634\) | 2.86869 | 0.113930 | ||||||||
\(635\) | 31.2157 | 1.23876 | ||||||||
\(636\) | −0.940126 | −0.0372784 | ||||||||
\(637\) | 0.702717 | 0.0278427 | ||||||||
\(638\) | 1.88387 | 0.0745831 | ||||||||
\(639\) | −11.0801 | −0.438322 | ||||||||
\(640\) | −46.5210 | −1.83890 | ||||||||
\(641\) | −44.2616 | −1.74823 | −0.874114 | − | 0.485720i | \(-0.838557\pi\) | ||||
−0.874114 | + | 0.485720i | \(0.838557\pi\) | |||||||
\(642\) | −4.36152 | −0.172135 | ||||||||
\(643\) | 3.12064 | 0.123066 | 0.0615331 | − | 0.998105i | \(-0.480401\pi\) | ||||
0.0615331 | + | 0.998105i | \(0.480401\pi\) | |||||||
\(644\) | 10.6051 | 0.417899 | ||||||||
\(645\) | −37.9498 | −1.49427 | ||||||||
\(646\) | −1.64866 | −0.0648658 | ||||||||
\(647\) | 12.0105 | 0.472180 | 0.236090 | − | 0.971731i | \(-0.424134\pi\) | ||||
0.236090 | + | 0.971731i | \(0.424134\pi\) | |||||||
\(648\) | 1.81664 | 0.0713644 | ||||||||
\(649\) | 9.48427 | 0.372290 | ||||||||
\(650\) | −4.09758 | −0.160720 | ||||||||
\(651\) | −9.76370 | −0.382670 | ||||||||
\(652\) | −2.69573 | −0.105573 | ||||||||
\(653\) | 24.9817 | 0.977610 | 0.488805 | − | 0.872393i | \(-0.337433\pi\) | ||||
0.488805 | + | 0.872393i | \(0.337433\pi\) | |||||||
\(654\) | 8.80615 | 0.344348 | ||||||||
\(655\) | −69.0336 | −2.69737 | ||||||||
\(656\) | −6.48155 | −0.253062 | ||||||||
\(657\) | −8.28151 | −0.323092 | ||||||||
\(658\) | 5.75096 | 0.224196 | ||||||||
\(659\) | 30.9680 | 1.20634 | 0.603170 | − | 0.797612i | \(-0.293904\pi\) | ||||
0.603170 | + | 0.797612i | \(0.293904\pi\) | |||||||
\(660\) | −7.28921 | −0.283732 | ||||||||
\(661\) | 20.9266 | 0.813951 | 0.406976 | − | 0.913439i | \(-0.366583\pi\) | ||||
0.406976 | + | 0.913439i | \(0.366583\pi\) | |||||||
\(662\) | 13.4248 | 0.521771 | ||||||||
\(663\) | 1.64368 | 0.0638353 | ||||||||
\(664\) | 20.3702 | 0.790516 | ||||||||
\(665\) | 6.04347 | 0.234356 | ||||||||
\(666\) | 3.53975 | 0.137162 | ||||||||
\(667\) | 23.5004 | 0.909939 | ||||||||
\(668\) | 40.1424 | 1.55315 | ||||||||
\(669\) | −22.2413 | −0.859898 | ||||||||
\(670\) | −13.8274 | −0.534200 | ||||||||
\(671\) | 0.834414 | 0.0322122 | ||||||||
\(672\) | 4.91543 | 0.189617 | ||||||||
\(673\) | 35.8417 | 1.38160 | 0.690798 | − | 0.723048i | \(-0.257260\pi\) | ||||
0.690798 | + | 0.723048i | \(0.257260\pi\) | |||||||
\(674\) | −14.8744 | −0.572939 | ||||||||
\(675\) | −12.0929 | −0.465456 | ||||||||
\(676\) | 22.1046 | 0.850178 | ||||||||
\(677\) | 25.6544 | 0.985979 | 0.492989 | − | 0.870035i | \(-0.335904\pi\) | ||||
0.492989 | + | 0.870035i | \(0.335904\pi\) | |||||||
\(678\) | −8.74450 | −0.335830 | ||||||||
\(679\) | −15.7928 | −0.606070 | ||||||||
\(680\) | 17.5677 | 0.673689 | ||||||||
\(681\) | 16.0840 | 0.616339 | ||||||||
\(682\) | −4.69619 | −0.179826 | ||||||||
\(683\) | 35.8438 | 1.37153 | 0.685763 | − | 0.727825i | \(-0.259469\pi\) | ||||
0.685763 | + | 0.727825i | \(0.259469\pi\) | |||||||
\(684\) | 2.58367 | 0.0987890 | ||||||||
\(685\) | 6.39221 | 0.244234 | ||||||||
\(686\) | −0.482188 | −0.0184100 | ||||||||
\(687\) | −24.9029 | −0.950103 | ||||||||
\(688\) | −24.4076 | −0.930531 | ||||||||
\(689\) | −0.373773 | −0.0142396 | ||||||||
\(690\) | 11.9613 | 0.455360 | ||||||||
\(691\) | 22.8819 | 0.870468 | 0.435234 | − | 0.900317i | \(-0.356666\pi\) | ||||
0.435234 | + | 0.900317i | \(0.356666\pi\) | |||||||
\(692\) | −41.6367 | −1.58279 | ||||||||
\(693\) | 0.997504 | 0.0378920 | ||||||||
\(694\) | 0.781920 | 0.0296813 | ||||||||
\(695\) | −77.8550 | −2.95321 | ||||||||
\(696\) | 7.11522 | 0.269702 | ||||||||
\(697\) | 5.70155 | 0.215962 | ||||||||
\(698\) | −1.89445 | −0.0717060 | ||||||||
\(699\) | 6.69139 | 0.253092 | ||||||||
\(700\) | −21.3741 | −0.807866 | ||||||||
\(701\) | 6.26507 | 0.236628 | 0.118314 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118314 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(702\) | 0.338842 | 0.0127888 | ||||||||
\(703\) | 10.7309 | 0.404722 | ||||||||
\(704\) | −2.94053 | −0.110826 | ||||||||
\(705\) | −49.3096 | −1.85711 | ||||||||
\(706\) | −3.33179 | −0.125393 | ||||||||
\(707\) | −1.71885 | −0.0646441 | ||||||||
\(708\) | 16.8053 | 0.631583 | ||||||||
\(709\) | −25.2434 | −0.948035 | −0.474017 | − | 0.880515i | \(-0.657197\pi\) | ||||
−0.474017 | + | 0.880515i | \(0.657197\pi\) | |||||||
\(710\) | −22.0886 | −0.828970 | ||||||||
\(711\) | 1.46338 | 0.0548811 | ||||||||
\(712\) | 13.9335 | 0.522178 | ||||||||
\(713\) | −58.5828 | −2.19394 | ||||||||
\(714\) | −1.12786 | −0.0422089 | ||||||||
\(715\) | −2.89803 | −0.108380 | ||||||||
\(716\) | 18.3833 | 0.687015 | ||||||||
\(717\) | 11.4771 | 0.428619 | ||||||||
\(718\) | −11.7898 | −0.439990 | ||||||||
\(719\) | −27.6998 | −1.03303 | −0.516515 | − | 0.856278i | \(-0.672771\pi\) | ||||
−0.516515 | + | 0.856278i | \(0.672771\pi\) | |||||||
\(720\) | −10.9934 | −0.409698 | ||||||||
\(721\) | 4.80382 | 0.178904 | ||||||||
\(722\) | 8.13125 | 0.302614 | ||||||||
\(723\) | 27.5046 | 1.02291 | ||||||||
\(724\) | 20.3573 | 0.756573 | ||||||||
\(725\) | −47.3641 | −1.75906 | ||||||||
\(726\) | −4.82428 | −0.179046 | ||||||||
\(727\) | 19.7569 | 0.732743 | 0.366371 | − | 0.930469i | \(-0.380600\pi\) | ||||
0.366371 | + | 0.930469i | \(0.380600\pi\) | |||||||
\(728\) | 1.27658 | 0.0473134 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −16.5095 | −0.611043 | ||||||||
\(731\) | 21.4703 | 0.794109 | ||||||||
\(732\) | 1.47851 | 0.0546474 | ||||||||
\(733\) | 0.240975 | 0.00890060 | 0.00445030 | − | 0.999990i | \(-0.498583\pi\) | ||||
0.00445030 | + | 0.999990i | \(0.498583\pi\) | |||||||
\(734\) | −4.73179 | −0.174654 | ||||||||
\(735\) | 4.13435 | 0.152498 | ||||||||
\(736\) | 29.4929 | 1.08712 | ||||||||
\(737\) | −6.91881 | −0.254858 | ||||||||
\(738\) | 1.17536 | 0.0432658 | ||||||||
\(739\) | −40.5856 | −1.49297 | −0.746483 | − | 0.665405i | \(-0.768259\pi\) | ||||
−0.746483 | + | 0.665405i | \(0.768259\pi\) | |||||||
\(740\) | −53.6441 | −1.97200 | ||||||||
\(741\) | 1.02721 | 0.0377355 | ||||||||
\(742\) | 0.256474 | 0.00941547 | ||||||||
\(743\) | 34.0534 | 1.24930 | 0.624650 | − | 0.780905i | \(-0.285242\pi\) | ||||
0.624650 | + | 0.780905i | \(0.285242\pi\) | |||||||
\(744\) | −17.7371 | −0.650275 | ||||||||
\(745\) | −55.1141 | −2.01922 | ||||||||
\(746\) | 12.5520 | 0.459563 | ||||||||
\(747\) | 11.2131 | 0.410266 | ||||||||
\(748\) | 4.12391 | 0.150785 | ||||||||
\(749\) | −9.04526 | −0.330507 | ||||||||
\(750\) | −14.1399 | −0.516317 | ||||||||
\(751\) | 8.93402 | 0.326007 | 0.163004 | − | 0.986625i | \(-0.447882\pi\) | ||||
0.163004 | + | 0.986625i | \(0.447882\pi\) | |||||||
\(752\) | −31.7137 | −1.15648 | ||||||||
\(753\) | −16.5037 | −0.601428 | ||||||||
\(754\) | 1.32714 | 0.0483316 | ||||||||
\(755\) | 46.3632 | 1.68733 | ||||||||
\(756\) | 1.76749 | 0.0642832 | ||||||||
\(757\) | 54.5644 | 1.98318 | 0.991588 | − | 0.129434i | \(-0.0413161\pi\) | ||||
0.991588 | + | 0.129434i | \(0.0413161\pi\) | |||||||
\(758\) | −12.9675 | −0.471001 | ||||||||
\(759\) | 5.98508 | 0.217245 | ||||||||
\(760\) | 10.9788 | 0.398244 | ||||||||
\(761\) | 19.0051 | 0.688936 | 0.344468 | − | 0.938798i | \(-0.388059\pi\) | ||||
0.344468 | + | 0.938798i | \(0.388059\pi\) | |||||||
\(762\) | −3.64067 | −0.131888 | ||||||||
\(763\) | 18.2629 | 0.661161 | ||||||||
\(764\) | 1.76749 | 0.0639457 | ||||||||
\(765\) | 9.67040 | 0.349634 | ||||||||
\(766\) | 14.4797 | 0.523173 | ||||||||
\(767\) | 6.68144 | 0.241253 | ||||||||
\(768\) | −0.470058 | −0.0169618 | ||||||||
\(769\) | 49.3233 | 1.77864 | 0.889322 | − | 0.457282i | \(-0.151177\pi\) | ||||
0.889322 | + | 0.457282i | \(0.151177\pi\) | |||||||
\(770\) | 1.98856 | 0.0716627 | ||||||||
\(771\) | 11.5033 | 0.414280 | ||||||||
\(772\) | −38.2497 | −1.37664 | ||||||||
\(773\) | 41.1780 | 1.48107 | 0.740534 | − | 0.672019i | \(-0.234573\pi\) | ||||
0.740534 | + | 0.672019i | \(0.234573\pi\) | |||||||
\(774\) | 4.42607 | 0.159092 | ||||||||
\(775\) | 118.071 | 4.24125 | ||||||||
\(776\) | −28.6898 | −1.02990 | ||||||||
\(777\) | 7.34101 | 0.263357 | ||||||||
\(778\) | −13.7679 | −0.493602 | ||||||||
\(779\) | 3.56316 | 0.127663 | ||||||||
\(780\) | −5.13507 | −0.183865 | ||||||||
\(781\) | −11.0524 | −0.395488 | ||||||||
\(782\) | −6.76720 | −0.241995 | ||||||||
\(783\) | 3.91669 | 0.139971 | ||||||||
\(784\) | 2.65903 | 0.0949653 | ||||||||
\(785\) | −54.3547 | −1.94000 | ||||||||
\(786\) | 8.05136 | 0.287183 | ||||||||
\(787\) | 44.2586 | 1.57765 | 0.788825 | − | 0.614618i | \(-0.210690\pi\) | ||||
0.788825 | + | 0.614618i | \(0.210690\pi\) | |||||||
\(788\) | −26.4774 | −0.943219 | ||||||||
\(789\) | −11.6125 | −0.413416 | ||||||||
\(790\) | 2.91730 | 0.103793 | ||||||||
\(791\) | −18.1350 | −0.644808 | ||||||||
\(792\) | 1.81211 | 0.0643904 | ||||||||
\(793\) | 0.587824 | 0.0208743 | ||||||||
\(794\) | 6.44387 | 0.228684 | ||||||||
\(795\) | −2.19905 | −0.0779923 | ||||||||
\(796\) | −36.3633 | −1.28886 | ||||||||
\(797\) | 36.5405 | 1.29433 | 0.647166 | − | 0.762349i | \(-0.275954\pi\) | ||||
0.647166 | + | 0.762349i | \(0.275954\pi\) | |||||||
\(798\) | −0.704847 | −0.0249513 | ||||||||
\(799\) | 27.8972 | 0.986932 | ||||||||
\(800\) | −59.4418 | −2.10158 | ||||||||
\(801\) | 7.66990 | 0.271003 | ||||||||
\(802\) | 9.94238 | 0.351078 | ||||||||
\(803\) | −8.26083 | −0.291518 | ||||||||
\(804\) | −12.2596 | −0.432362 | ||||||||
\(805\) | 24.8064 | 0.874310 | ||||||||
\(806\) | −3.30835 | −0.116532 | ||||||||
\(807\) | 31.2118 | 1.09871 | ||||||||
\(808\) | −3.12254 | −0.109850 | ||||||||
\(809\) | 28.9280 | 1.01705 | 0.508527 | − | 0.861046i | \(-0.330190\pi\) | ||||
0.508527 | + | 0.861046i | \(0.330190\pi\) | |||||||
\(810\) | 1.99354 | 0.0700457 | ||||||||
\(811\) | −24.3387 | −0.854646 | −0.427323 | − | 0.904099i | \(-0.640543\pi\) | ||||
−0.427323 | + | 0.904099i | \(0.640543\pi\) | |||||||
\(812\) | 6.92274 | 0.242940 | ||||||||
\(813\) | −19.1870 | −0.672919 | ||||||||
\(814\) | 3.53091 | 0.123758 | ||||||||
\(815\) | −6.30561 | −0.220876 | ||||||||
\(816\) | 6.21956 | 0.217728 | ||||||||
\(817\) | 13.4178 | 0.469429 | ||||||||
\(818\) | 6.60466 | 0.230927 | ||||||||
\(819\) | 0.702717 | 0.0245549 | ||||||||
\(820\) | −17.8124 | −0.622036 | ||||||||
\(821\) | 3.80498 | 0.132795 | 0.0663974 | − | 0.997793i | \(-0.478849\pi\) | ||||
0.0663974 | + | 0.997793i | \(0.478849\pi\) | |||||||
\(822\) | −0.745521 | −0.0260030 | ||||||||
\(823\) | 8.69576 | 0.303115 | 0.151558 | − | 0.988448i | \(-0.451571\pi\) | ||||
0.151558 | + | 0.988448i | \(0.451571\pi\) | |||||||
\(824\) | 8.72681 | 0.304013 | ||||||||
\(825\) | −12.0627 | −0.419969 | ||||||||
\(826\) | −4.58464 | −0.159520 | ||||||||
\(827\) | 43.6574 | 1.51812 | 0.759059 | − | 0.651022i | \(-0.225659\pi\) | ||||
0.759059 | + | 0.651022i | \(0.225659\pi\) | |||||||
\(828\) | 10.6051 | 0.368552 | ||||||||
\(829\) | −2.65304 | −0.0921438 | −0.0460719 | − | 0.998938i | \(-0.514670\pi\) | ||||
−0.0460719 | + | 0.998938i | \(0.514670\pi\) | |||||||
\(830\) | 22.3537 | 0.775909 | ||||||||
\(831\) | −8.37683 | −0.290589 | ||||||||
\(832\) | −2.07153 | −0.0718175 | ||||||||
\(833\) | −2.33904 | −0.0810428 | ||||||||
\(834\) | 9.08020 | 0.314422 | ||||||||
\(835\) | 93.8972 | 3.24945 | ||||||||
\(836\) | 2.57722 | 0.0891350 | ||||||||
\(837\) | −9.76370 | −0.337483 | ||||||||
\(838\) | 0.696655 | 0.0240655 | ||||||||
\(839\) | −40.4459 | −1.39635 | −0.698173 | − | 0.715929i | \(-0.746003\pi\) | ||||
−0.698173 | + | 0.715929i | \(0.746003\pi\) | |||||||
\(840\) | 7.51064 | 0.259142 | ||||||||
\(841\) | −13.6595 | −0.471018 | ||||||||
\(842\) | −2.79929 | −0.0964700 | ||||||||
\(843\) | 10.8066 | 0.372198 | ||||||||
\(844\) | −15.0544 | −0.518194 | ||||||||
\(845\) | 51.7050 | 1.77871 | ||||||||
\(846\) | 5.75096 | 0.197722 | ||||||||
\(847\) | −10.0050 | −0.343775 | ||||||||
\(848\) | −1.41433 | −0.0485683 | ||||||||
\(849\) | −17.5690 | −0.602966 | ||||||||
\(850\) | 13.6390 | 0.467815 | ||||||||
\(851\) | 44.0465 | 1.50990 | ||||||||
\(852\) | −19.5840 | −0.670938 | ||||||||
\(853\) | −45.6157 | −1.56185 | −0.780926 | − | 0.624624i | \(-0.785252\pi\) | ||||
−0.780926 | + | 0.624624i | \(0.785252\pi\) | |||||||
\(854\) | −0.403351 | −0.0138024 | ||||||||
\(855\) | 6.04347 | 0.206682 | ||||||||
\(856\) | −16.4320 | −0.561634 | ||||||||
\(857\) | 32.0881 | 1.09611 | 0.548055 | − | 0.836442i | \(-0.315368\pi\) | ||||
0.548055 | + | 0.836442i | \(0.315368\pi\) | |||||||
\(858\) | 0.337996 | 0.0115390 | ||||||||
\(859\) | 13.4212 | 0.457924 | 0.228962 | − | 0.973435i | \(-0.426467\pi\) | ||||
0.228962 | + | 0.973435i | \(0.426467\pi\) | |||||||
\(860\) | −67.0761 | −2.28728 | ||||||||
\(861\) | 2.43757 | 0.0830720 | ||||||||
\(862\) | −13.6150 | −0.463730 | ||||||||
\(863\) | −12.5105 | −0.425864 | −0.212932 | − | 0.977067i | \(-0.568301\pi\) | ||||
−0.212932 | + | 0.977067i | \(0.568301\pi\) | |||||||
\(864\) | 4.91543 | 0.167226 | ||||||||
\(865\) | −97.3926 | −3.31145 | ||||||||
\(866\) | 6.42062 | 0.218182 | ||||||||
\(867\) | 11.5289 | 0.391542 | ||||||||
\(868\) | −17.2573 | −0.585751 | ||||||||
\(869\) | 1.45973 | 0.0495179 | ||||||||
\(870\) | 7.80807 | 0.264718 | ||||||||
\(871\) | −4.87414 | −0.165154 | ||||||||
\(872\) | 33.1771 | 1.12352 | ||||||||
\(873\) | −15.7928 | −0.534504 | ||||||||
\(874\) | −4.22913 | −0.143052 | ||||||||
\(875\) | −29.3245 | −0.991350 | ||||||||
\(876\) | −14.6375 | −0.494556 | ||||||||
\(877\) | −48.5197 | −1.63839 | −0.819197 | − | 0.573512i | \(-0.805581\pi\) | ||||
−0.819197 | + | 0.573512i | \(0.805581\pi\) | |||||||
\(878\) | −3.22713 | −0.108911 | ||||||||
\(879\) | −25.0315 | −0.844292 | ||||||||
\(880\) | −10.9659 | −0.369661 | ||||||||
\(881\) | −36.3124 | −1.22340 | −0.611698 | − | 0.791091i | \(-0.709513\pi\) | ||||
−0.611698 | + | 0.791091i | \(0.709513\pi\) | |||||||
\(882\) | −0.482188 | −0.0162361 | ||||||||
\(883\) | −2.95751 | −0.0995282 | −0.0497641 | − | 0.998761i | \(-0.515847\pi\) | ||||
−0.0497641 | + | 0.998761i | \(0.515847\pi\) | |||||||
\(884\) | 2.90520 | 0.0977124 | ||||||||
\(885\) | 39.3095 | 1.32137 | ||||||||
\(886\) | −4.83847 | −0.162552 | ||||||||
\(887\) | −14.8873 | −0.499866 | −0.249933 | − | 0.968263i | \(-0.580409\pi\) | ||||
−0.249933 | + | 0.968263i | \(0.580409\pi\) | |||||||
\(888\) | 13.3360 | 0.447526 | ||||||||
\(889\) | −7.55032 | −0.253230 | ||||||||
\(890\) | 15.2902 | 0.512530 | ||||||||
\(891\) | 0.997504 | 0.0334176 | ||||||||
\(892\) | −39.3114 | −1.31624 | ||||||||
\(893\) | 17.4342 | 0.583414 | ||||||||
\(894\) | 6.42793 | 0.214982 | ||||||||
\(895\) | 43.0004 | 1.43735 | ||||||||
\(896\) | 11.2523 | 0.375913 | ||||||||
\(897\) | 4.21635 | 0.140780 | ||||||||
\(898\) | −4.71338 | −0.157288 | ||||||||
\(899\) | −38.2414 | −1.27542 | ||||||||
\(900\) | −21.3741 | −0.712471 | ||||||||
\(901\) | 1.24413 | 0.0414479 | ||||||||
\(902\) | 1.17243 | 0.0390377 | ||||||||
\(903\) | 9.17914 | 0.305463 | ||||||||
\(904\) | −32.9448 | −1.09573 | ||||||||
\(905\) | 47.6178 | 1.58287 | ||||||||
\(906\) | −5.40732 | −0.179646 | ||||||||
\(907\) | −33.2948 | −1.10554 | −0.552768 | − | 0.833335i | \(-0.686428\pi\) | ||||
−0.552768 | + | 0.833335i | \(0.686428\pi\) | |||||||
\(908\) | 28.4283 | 0.943427 | ||||||||
\(909\) | −1.71885 | −0.0570107 | ||||||||
\(910\) | 1.40089 | 0.0464391 | ||||||||
\(911\) | −26.2123 | −0.868453 | −0.434226 | − | 0.900804i | \(-0.642978\pi\) | ||||
−0.434226 | + | 0.900804i | \(0.642978\pi\) | |||||||
\(912\) | 3.88688 | 0.128708 | ||||||||
\(913\) | 11.1851 | 0.370173 | ||||||||
\(914\) | −7.97375 | −0.263748 | ||||||||
\(915\) | 3.45840 | 0.114331 | ||||||||
\(916\) | −44.0157 | −1.45432 | ||||||||
\(917\) | 16.6976 | 0.551402 | ||||||||
\(918\) | −1.12786 | −0.0372248 | ||||||||
\(919\) | 14.1267 | 0.465997 | 0.232998 | − | 0.972477i | \(-0.425146\pi\) | ||||
0.232998 | + | 0.972477i | \(0.425146\pi\) | |||||||
\(920\) | 45.0643 | 1.48573 | ||||||||
\(921\) | −3.98673 | −0.131367 | ||||||||
\(922\) | 3.27633 | 0.107900 | ||||||||
\(923\) | −7.78618 | −0.256285 | ||||||||
\(924\) | 1.76308 | 0.0580012 | ||||||||
\(925\) | −88.7741 | −2.91887 | ||||||||
\(926\) | −0.772800 | −0.0253958 | ||||||||
\(927\) | 4.80382 | 0.157778 | ||||||||
\(928\) | 19.2522 | 0.631986 | ||||||||
\(929\) | 22.9888 | 0.754238 | 0.377119 | − | 0.926165i | \(-0.376915\pi\) | ||||
0.377119 | + | 0.926165i | \(0.376915\pi\) | |||||||
\(930\) | −19.4643 | −0.638259 | ||||||||
\(931\) | −1.46177 | −0.0479075 | ||||||||
\(932\) | 11.8270 | 0.387406 | ||||||||
\(933\) | −15.8134 | −0.517706 | ||||||||
\(934\) | 8.65823 | 0.283306 | ||||||||
\(935\) | 9.64627 | 0.315467 | ||||||||
\(936\) | 1.27658 | 0.0417265 | ||||||||
\(937\) | 2.16799 | 0.0708253 | 0.0354126 | − | 0.999373i | \(-0.488725\pi\) | ||||
0.0354126 | + | 0.999373i | \(0.488725\pi\) | |||||||
\(938\) | 3.34452 | 0.109202 | ||||||||
\(939\) | 11.6769 | 0.381063 | ||||||||
\(940\) | −87.1545 | −2.84267 | ||||||||
\(941\) | 37.9491 | 1.23711 | 0.618553 | − | 0.785743i | \(-0.287719\pi\) | ||||
0.618553 | + | 0.785743i | \(0.287719\pi\) | |||||||
\(942\) | 6.33937 | 0.206548 | ||||||||
\(943\) | 14.6255 | 0.476273 | ||||||||
\(944\) | 25.2820 | 0.822860 | ||||||||
\(945\) | 4.13435 | 0.134491 | ||||||||
\(946\) | 4.41502 | 0.143545 | ||||||||
\(947\) | −14.3486 | −0.466265 | −0.233133 | − | 0.972445i | \(-0.574898\pi\) | ||||
−0.233133 | + | 0.972445i | \(0.574898\pi\) | |||||||
\(948\) | 2.58652 | 0.0840062 | ||||||||
\(949\) | −5.81956 | −0.188911 | ||||||||
\(950\) | 8.52364 | 0.276543 | ||||||||
\(951\) | 5.94931 | 0.192920 | ||||||||
\(952\) | −4.24919 | −0.137717 | ||||||||
\(953\) | 40.2665 | 1.30436 | 0.652179 | − | 0.758065i | \(-0.273855\pi\) | ||||
0.652179 | + | 0.758065i | \(0.273855\pi\) | |||||||
\(954\) | 0.256474 | 0.00830367 | ||||||||
\(955\) | 4.13435 | 0.133785 | ||||||||
\(956\) | 20.2857 | 0.656085 | ||||||||
\(957\) | 3.90692 | 0.126293 | ||||||||
\(958\) | 5.13286 | 0.165835 | ||||||||
\(959\) | −1.54612 | −0.0499268 | ||||||||
\(960\) | −12.1876 | −0.393354 | ||||||||
\(961\) | 64.3299 | 2.07516 | ||||||||
\(962\) | 2.48744 | 0.0801984 | ||||||||
\(963\) | −9.04526 | −0.291479 | ||||||||
\(964\) | 48.6142 | 1.56576 | ||||||||
\(965\) | −89.4700 | −2.88014 | ||||||||
\(966\) | −2.89316 | −0.0930858 | ||||||||
\(967\) | −13.6675 | −0.439517 | −0.219759 | − | 0.975554i | \(-0.570527\pi\) | ||||
−0.219759 | + | 0.975554i | \(0.570527\pi\) | |||||||
\(968\) | −18.1755 | −0.584182 | ||||||||
\(969\) | −3.41913 | −0.109838 | ||||||||
\(970\) | −31.4834 | −1.01087 | ||||||||
\(971\) | −4.15189 | −0.133240 | −0.0666202 | − | 0.997778i | \(-0.521222\pi\) | ||||
−0.0666202 | + | 0.997778i | \(0.521222\pi\) | |||||||
\(972\) | 1.76749 | 0.0566924 | ||||||||
\(973\) | 18.8312 | 0.603702 | ||||||||
\(974\) | 11.8858 | 0.380847 | ||||||||
\(975\) | −8.49788 | −0.272150 | ||||||||
\(976\) | 2.22428 | 0.0711975 | ||||||||
\(977\) | 59.5136 | 1.90401 | 0.952005 | − | 0.306083i | \(-0.0990185\pi\) | ||||
0.952005 | + | 0.306083i | \(0.0990185\pi\) | |||||||
\(978\) | 0.735420 | 0.0235161 | ||||||||
\(979\) | 7.65076 | 0.244519 | ||||||||
\(980\) | 7.30745 | 0.233428 | ||||||||
\(981\) | 18.2629 | 0.583089 | ||||||||
\(982\) | −4.15683 | −0.132650 | ||||||||
\(983\) | 22.9897 | 0.733257 | 0.366628 | − | 0.930367i | \(-0.380512\pi\) | ||||
0.366628 | + | 0.930367i | \(0.380512\pi\) | |||||||
\(984\) | 4.42818 | 0.141165 | ||||||||
\(985\) | −61.9334 | −1.97336 | ||||||||
\(986\) | −4.41746 | −0.140681 | ||||||||
\(987\) | 11.9268 | 0.379634 | ||||||||
\(988\) | 1.81559 | 0.0577616 | ||||||||
\(989\) | 55.0754 | 1.75130 | ||||||||
\(990\) | 1.98856 | 0.0632006 | ||||||||
\(991\) | 31.1292 | 0.988852 | 0.494426 | − | 0.869220i | \(-0.335378\pi\) | ||||
0.494426 | + | 0.869220i | \(0.335378\pi\) | |||||||
\(992\) | −47.9928 | −1.52377 | ||||||||
\(993\) | 27.8415 | 0.883523 | ||||||||
\(994\) | 5.34269 | 0.169460 | ||||||||
\(995\) | −85.0576 | −2.69651 | ||||||||
\(996\) | 19.8191 | 0.627992 | ||||||||
\(997\) | 32.8350 | 1.03990 | 0.519948 | − | 0.854198i | \(-0.325951\pi\) | ||||
0.519948 | + | 0.854198i | \(0.325951\pi\) | |||||||
\(998\) | −7.65643 | −0.242360 | ||||||||
\(999\) | 7.34101 | 0.232259 |
(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 | 4011.2.a.l.1.13 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.l.1.13 | ✓ | 28 | 1.1 | even | 1 | trivial |