Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −3.23607 | −0.864876 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 4.23607 | 1.02740 | 0.513699 | − | 0.857971i | \(-0.328275\pi\) | ||||
0.513699 | + | 0.857971i | \(0.328275\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | −6.70820 | −1.53897 | −0.769484 | − | 0.638666i | \(-0.779486\pi\) | ||||
−0.769484 | + | 0.638666i | \(0.779486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 4.85410 | 1.03490 | ||||||||
\(23\) | −5.38197 | −1.12222 | −0.561109 | − | 0.827742i | \(-0.689625\pi\) | ||||
−0.561109 | + | 0.827742i | \(0.689625\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.61803 | −0.317323 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.23607 | 0.233595 | ||||||||
\(29\) | −3.61803 | −0.671852 | −0.335926 | − | 0.941888i | \(-0.609049\pi\) | ||||
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.70820 | 1.56404 | 0.782020 | − | 0.623254i | \(-0.214190\pi\) | ||||
0.782020 | + | 0.623254i | \(0.214190\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | −6.85410 | −1.17547 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 10.8541 | 1.76077 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.38197 | −1.46522 | −0.732608 | − | 0.680650i | \(-0.761697\pi\) | ||||
−0.732608 | + | 0.680650i | \(0.761697\pi\) | |||||||
\(42\) | 3.23607 | 0.499336 | ||||||||
\(43\) | 7.38197 | 1.12574 | 0.562870 | − | 0.826546i | \(-0.309697\pi\) | ||||
0.562870 | + | 0.826546i | \(0.309697\pi\) | |||||||
\(44\) | −1.85410 | −0.279516 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.70820 | 1.28395 | ||||||||
\(47\) | 4.76393 | 0.694891 | 0.347445 | − | 0.937700i | \(-0.387049\pi\) | ||||
0.347445 | + | 0.937700i | \(0.387049\pi\) | |||||||
\(48\) | 4.85410 | 0.700629 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.23607 | −0.593168 | ||||||||
\(52\) | 0.618034 | 0.0857059 | ||||||||
\(53\) | −11.2361 | −1.54339 | −0.771696 | − | 0.635991i | \(-0.780591\pi\) | ||||
−0.771696 | + | 0.635991i | \(0.780591\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.47214 | 0.597614 | ||||||||
\(57\) | 6.70820 | 0.888523 | ||||||||
\(58\) | 5.85410 | 0.768681 | ||||||||
\(59\) | 3.94427 | 0.513500 | 0.256750 | − | 0.966478i | \(-0.417348\pi\) | ||||
0.256750 | + | 0.966478i | \(0.417348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.70820 | 1.11497 | 0.557486 | − | 0.830187i | \(-0.311766\pi\) | ||||
0.557486 | + | 0.830187i | \(0.311766\pi\) | |||||||
\(62\) | −14.0902 | −1.78945 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.85410 | −0.597499 | ||||||||
\(67\) | 13.1803 | 1.61023 | 0.805117 | − | 0.593115i | \(-0.202102\pi\) | ||||
0.805117 | + | 0.593115i | \(0.202102\pi\) | |||||||
\(68\) | 2.61803 | 0.317483 | ||||||||
\(69\) | 5.38197 | 0.647913 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0902 | 1.19748 | 0.598741 | − | 0.800942i | \(-0.295668\pi\) | ||||
0.598741 | + | 0.800942i | \(0.295668\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −15.7082 | −1.83851 | −0.919253 | − | 0.393667i | \(-0.871206\pi\) | ||||
−0.919253 | + | 0.393667i | \(0.871206\pi\) | |||||||
\(74\) | −3.23607 | −0.376185 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.14590 | −0.475567 | ||||||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 1.61803 | 0.183206 | ||||||||
\(79\) | −9.14590 | −1.02899 | −0.514497 | − | 0.857492i | \(-0.672021\pi\) | ||||
−0.514497 | + | 0.857492i | \(0.672021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.1803 | 1.67639 | ||||||||
\(83\) | −9.00000 | −0.987878 | −0.493939 | − | 0.869496i | \(-0.664443\pi\) | ||||
−0.493939 | + | 0.869496i | \(0.664443\pi\) | |||||||
\(84\) | −1.23607 | −0.134866 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.9443 | −1.28798 | ||||||||
\(87\) | 3.61803 | 0.387894 | ||||||||
\(88\) | −6.70820 | −0.715097 | ||||||||
\(89\) | −11.1803 | −1.18511 | −0.592557 | − | 0.805529i | \(-0.701881\pi\) | ||||
−0.592557 | + | 0.805529i | \(0.701881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −3.32624 | −0.346784 | ||||||||
\(93\) | −8.70820 | −0.902999 | ||||||||
\(94\) | −7.70820 | −0.795041 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.38197 | −0.345170 | ||||||||
\(97\) | −3.85410 | −0.391325 | −0.195662 | − | 0.980671i | \(-0.562686\pi\) | ||||
−0.195662 | + | 0.980671i | \(0.562686\pi\) | |||||||
\(98\) | 4.85410 | 0.490338 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.38197 | −0.933541 | −0.466770 | − | 0.884379i | \(-0.654583\pi\) | ||||
−0.466770 | + | 0.884379i | \(0.654583\pi\) | |||||||
\(102\) | 6.85410 | 0.678657 | ||||||||
\(103\) | 14.4164 | 1.42049 | 0.710245 | − | 0.703954i | \(-0.248584\pi\) | ||||
0.710245 | + | 0.703954i | \(0.248584\pi\) | |||||||
\(104\) | 2.23607 | 0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.1803 | 1.76583 | ||||||||
\(107\) | 1.14590 | 0.110778 | 0.0553891 | − | 0.998465i | \(-0.482360\pi\) | ||||
0.0553891 | + | 0.998465i | \(0.482360\pi\) | |||||||
\(108\) | −0.618034 | −0.0594703 | ||||||||
\(109\) | −4.14590 | −0.397105 | −0.198553 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198553 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | −9.70820 | −0.917339 | ||||||||
\(113\) | 3.76393 | 0.354081 | 0.177040 | − | 0.984204i | \(-0.443348\pi\) | ||||
0.177040 | + | 0.984204i | \(0.443348\pi\) | |||||||
\(114\) | −10.8541 | −1.01658 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.23607 | −0.207614 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −6.38197 | −0.587508 | ||||||||
\(119\) | 8.47214 | 0.776639 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −14.0902 | −1.27566 | ||||||||
\(123\) | 9.38197 | 0.845943 | ||||||||
\(124\) | 5.38197 | 0.483315 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.23607 | −0.288292 | ||||||||
\(127\) | −13.6525 | −1.21146 | −0.605731 | − | 0.795670i | \(-0.707119\pi\) | ||||
−0.605731 | + | 0.795670i | \(0.707119\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | −7.38197 | −0.649946 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.1803 | −1.23894 | −0.619471 | − | 0.785020i | \(-0.712653\pi\) | ||||
−0.619471 | + | 0.785020i | \(0.712653\pi\) | |||||||
\(132\) | 1.85410 | 0.161379 | ||||||||
\(133\) | −13.4164 | −1.16335 | ||||||||
\(134\) | −21.3262 | −1.84231 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.47214 | 0.812229 | ||||||||
\(137\) | −0.437694 | −0.0373947 | −0.0186974 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186974 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(138\) | −8.70820 | −0.741292 | ||||||||
\(139\) | 13.4164 | 1.13796 | 0.568982 | − | 0.822350i | \(-0.307337\pi\) | ||||
0.568982 | + | 0.822350i | \(0.307337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.76393 | −0.401195 | ||||||||
\(142\) | −16.3262 | −1.37007 | ||||||||
\(143\) | −3.00000 | −0.250873 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.4164 | 2.10348 | ||||||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | 1.23607 | 0.101604 | ||||||||
\(149\) | −13.0902 | −1.07239 | −0.536194 | − | 0.844095i | \(-0.680139\pi\) | ||||
−0.536194 | + | 0.844095i | \(0.680139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.61803 | −0.538568 | −0.269284 | − | 0.963061i | \(-0.586787\pi\) | ||||
−0.269284 | + | 0.963061i | \(0.586787\pi\) | |||||||
\(152\) | −15.0000 | −1.21666 | ||||||||
\(153\) | 4.23607 | 0.342466 | ||||||||
\(154\) | 9.70820 | 0.782309 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.618034 | −0.0494823 | ||||||||
\(157\) | 2.85410 | 0.227782 | 0.113891 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113891 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(158\) | 14.7984 | 1.17730 | ||||||||
\(159\) | 11.2361 | 0.891078 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7639 | −0.848317 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | −18.2705 | −1.43106 | −0.715528 | − | 0.698584i | \(-0.753814\pi\) | ||||
−0.715528 | + | 0.698584i | \(0.753814\pi\) | |||||||
\(164\) | −5.79837 | −0.452777 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.5623 | 1.13025 | ||||||||
\(167\) | −17.7984 | −1.37728 | −0.688640 | − | 0.725104i | \(-0.741792\pi\) | ||||
−0.688640 | + | 0.725104i | \(0.741792\pi\) | |||||||
\(168\) | −4.47214 | −0.345033 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.70820 | −0.512989 | ||||||||
\(172\) | 4.56231 | 0.347873 | ||||||||
\(173\) | −0.909830 | −0.0691731 | −0.0345865 | − | 0.999402i | \(-0.511011\pi\) | ||||
−0.0345865 | + | 0.999402i | \(0.511011\pi\) | |||||||
\(174\) | −5.85410 | −0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.5623 | 1.09768 | ||||||||
\(177\) | −3.94427 | −0.296470 | ||||||||
\(178\) | 18.0902 | 1.35592 | ||||||||
\(179\) | −15.6525 | −1.16992 | −0.584960 | − | 0.811062i | \(-0.698890\pi\) | ||||
−0.584960 | + | 0.811062i | \(0.698890\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4721 | −0.927047 | −0.463523 | − | 0.886085i | \(-0.653415\pi\) | ||||
−0.463523 | + | 0.886085i | \(0.653415\pi\) | |||||||
\(182\) | −3.23607 | −0.239873 | ||||||||
\(183\) | −8.70820 | −0.643729 | ||||||||
\(184\) | −12.0344 | −0.887191 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.0902 | 1.03314 | ||||||||
\(187\) | −12.7082 | −0.929316 | ||||||||
\(188\) | 2.94427 | 0.214733 | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3262 | 1.25368 | 0.626841 | − | 0.779147i | \(-0.284347\pi\) | ||||
0.626841 | + | 0.779147i | \(0.284347\pi\) | |||||||
\(192\) | −4.23607 | −0.305712 | ||||||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | 6.23607 | 0.447724 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.85410 | −0.132436 | ||||||||
\(197\) | 0.0901699 | 0.00642434 | 0.00321217 | − | 0.999995i | \(-0.498978\pi\) | ||||
0.00321217 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(198\) | 4.85410 | 0.344966 | ||||||||
\(199\) | 11.7082 | 0.829973 | 0.414986 | − | 0.909828i | \(-0.363786\pi\) | ||||
0.414986 | + | 0.909828i | \(0.363786\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.1803 | −0.929669 | ||||||||
\(202\) | 15.1803 | 1.06808 | ||||||||
\(203\) | −7.23607 | −0.507872 | ||||||||
\(204\) | −2.61803 | −0.183299 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.3262 | −1.62522 | ||||||||
\(207\) | −5.38197 | −0.374072 | ||||||||
\(208\) | −4.85410 | −0.336571 | ||||||||
\(209\) | 20.1246 | 1.39205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | −6.94427 | −0.476935 | ||||||||
\(213\) | −10.0902 | −0.691367 | ||||||||
\(214\) | −1.85410 | −0.126744 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 17.4164 | 1.18230 | ||||||||
\(218\) | 6.70820 | 0.454337 | ||||||||
\(219\) | 15.7082 | 1.06146 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.23607 | 0.284949 | ||||||||
\(222\) | 3.23607 | 0.217191 | ||||||||
\(223\) | 10.1459 | 0.679420 | 0.339710 | − | 0.940530i | \(-0.389671\pi\) | ||||
0.339710 | + | 0.940530i | \(0.389671\pi\) | |||||||
\(224\) | 6.76393 | 0.451934 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.09017 | −0.405112 | ||||||||
\(227\) | −5.76393 | −0.382566 | −0.191283 | − | 0.981535i | \(-0.561265\pi\) | ||||
−0.191283 | + | 0.981535i | \(0.561265\pi\) | |||||||
\(228\) | 4.14590 | 0.274569 | ||||||||
\(229\) | −16.1803 | −1.06923 | −0.534613 | − | 0.845097i | \(-0.679543\pi\) | ||||
−0.534613 | + | 0.845097i | \(0.679543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | −8.09017 | −0.531146 | ||||||||
\(233\) | −10.1803 | −0.666936 | −0.333468 | − | 0.942761i | \(-0.608219\pi\) | ||||
−0.333468 | + | 0.942761i | \(0.608219\pi\) | |||||||
\(234\) | −1.61803 | −0.105774 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.43769 | 0.158680 | ||||||||
\(237\) | 9.14590 | 0.594090 | ||||||||
\(238\) | −13.7082 | −0.888571 | ||||||||
\(239\) | 21.3820 | 1.38308 | 0.691542 | − | 0.722336i | \(-0.256932\pi\) | ||||
0.691542 | + | 0.722336i | \(0.256932\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.32624 | 0.471924 | 0.235962 | − | 0.971762i | \(-0.424176\pi\) | ||||
0.235962 | + | 0.971762i | \(0.424176\pi\) | |||||||
\(242\) | 3.23607 | 0.208022 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.38197 | 0.344545 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.1803 | −0.967863 | ||||||||
\(247\) | −6.70820 | −0.426833 | ||||||||
\(248\) | 19.4721 | 1.23648 | ||||||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9787 | −1.19793 | −0.598963 | − | 0.800777i | \(-0.704420\pi\) | ||||
−0.598963 | + | 0.800777i | \(0.704420\pi\) | |||||||
\(252\) | 1.23607 | 0.0778650 | ||||||||
\(253\) | 16.1459 | 1.01508 | ||||||||
\(254\) | 22.0902 | 1.38606 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −31.2148 | −1.94712 | −0.973562 | − | 0.228422i | \(-0.926644\pi\) | ||||
−0.973562 | + | 0.228422i | \(0.926644\pi\) | |||||||
\(258\) | 11.9443 | 0.743618 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.61803 | −0.223951 | ||||||||
\(262\) | 22.9443 | 1.41750 | ||||||||
\(263\) | 12.5066 | 0.771189 | 0.385594 | − | 0.922668i | \(-0.373996\pi\) | ||||
0.385594 | + | 0.922668i | \(0.373996\pi\) | |||||||
\(264\) | 6.70820 | 0.412861 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.7082 | 1.33102 | ||||||||
\(267\) | 11.1803 | 0.684226 | ||||||||
\(268\) | 8.14590 | 0.497590 | ||||||||
\(269\) | −20.5279 | −1.25161 | −0.625803 | − | 0.779981i | \(-0.715229\pi\) | ||||
−0.625803 | + | 0.779981i | \(0.715229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.4164 | −0.693497 | −0.346749 | − | 0.937958i | \(-0.612714\pi\) | ||||
−0.346749 | + | 0.937958i | \(0.612714\pi\) | |||||||
\(272\) | −20.5623 | −1.24677 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 0.708204 | 0.0427842 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.32624 | 0.200216 | ||||||||
\(277\) | 13.0557 | 0.784443 | 0.392221 | − | 0.919871i | \(-0.371707\pi\) | ||||
0.392221 | + | 0.919871i | \(0.371707\pi\) | |||||||
\(278\) | −21.7082 | −1.30197 | ||||||||
\(279\) | 8.70820 | 0.521347 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1803 | −0.845928 | −0.422964 | − | 0.906146i | \(-0.639010\pi\) | ||||
−0.422964 | + | 0.906146i | \(0.639010\pi\) | |||||||
\(282\) | 7.70820 | 0.459017 | ||||||||
\(283\) | −2.29180 | −0.136233 | −0.0681166 | − | 0.997677i | \(-0.521699\pi\) | ||||
−0.0681166 | + | 0.997677i | \(0.521699\pi\) | |||||||
\(284\) | 6.23607 | 0.370043 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.85410 | 0.287029 | ||||||||
\(287\) | −18.7639 | −1.10760 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | 0.944272 | 0.0555454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.85410 | 0.225931 | ||||||||
\(292\) | −9.70820 | −0.568130 | ||||||||
\(293\) | 6.32624 | 0.369583 | 0.184791 | − | 0.982778i | \(-0.440839\pi\) | ||||
0.184791 | + | 0.982778i | \(0.440839\pi\) | |||||||
\(294\) | −4.85410 | −0.283097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.47214 | 0.259938 | ||||||||
\(297\) | 3.00000 | 0.174078 | ||||||||
\(298\) | 21.1803 | 1.22694 | ||||||||
\(299\) | −5.38197 | −0.311247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.7639 | 0.850979 | ||||||||
\(302\) | 10.7082 | 0.616188 | ||||||||
\(303\) | 9.38197 | 0.538980 | ||||||||
\(304\) | 32.5623 | 1.86758 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.85410 | −0.391823 | ||||||||
\(307\) | −8.85410 | −0.505330 | −0.252665 | − | 0.967554i | \(-0.581307\pi\) | ||||
−0.252665 | + | 0.967554i | \(0.581307\pi\) | |||||||
\(308\) | −3.70820 | −0.211295 | ||||||||
\(309\) | −14.4164 | −0.820121 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5279 | −0.767095 | −0.383547 | − | 0.923521i | \(-0.625298\pi\) | ||||
−0.383547 | + | 0.923521i | \(0.625298\pi\) | |||||||
\(312\) | −2.23607 | −0.126592 | ||||||||
\(313\) | −2.29180 | −0.129540 | −0.0647700 | − | 0.997900i | \(-0.520631\pi\) | ||||
−0.0647700 | + | 0.997900i | \(0.520631\pi\) | |||||||
\(314\) | −4.61803 | −0.260611 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.65248 | −0.317977 | ||||||||
\(317\) | −20.5623 | −1.15489 | −0.577447 | − | 0.816428i | \(-0.695951\pi\) | ||||
−0.577447 | + | 0.816428i | \(0.695951\pi\) | |||||||
\(318\) | −18.1803 | −1.01950 | ||||||||
\(319\) | 10.8541 | 0.607713 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.14590 | −0.0639578 | ||||||||
\(322\) | 17.4164 | 0.970578 | ||||||||
\(323\) | −28.4164 | −1.58113 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.5623 | 1.63730 | ||||||||
\(327\) | 4.14590 | 0.229269 | ||||||||
\(328\) | −20.9787 | −1.15836 | ||||||||
\(329\) | 9.52786 | 0.525288 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.6869 | −1.68671 | −0.843353 | − | 0.537360i | \(-0.819422\pi\) | ||||
−0.843353 | + | 0.537360i | \(0.819422\pi\) | |||||||
\(332\) | −5.56231 | −0.305271 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 28.7984 | 1.57578 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.70820 | 0.529626 | ||||||||
\(337\) | 33.1803 | 1.80745 | 0.903724 | − | 0.428115i | \(-0.140822\pi\) | ||||
0.903724 | + | 0.428115i | \(0.140822\pi\) | |||||||
\(338\) | 19.4164 | 1.05611 | ||||||||
\(339\) | −3.76393 | −0.204429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.1246 | −1.41473 | ||||||||
\(342\) | 10.8541 | 0.586923 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 16.5066 | 0.889975 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47214 | 0.0791425 | ||||||||
\(347\) | −12.2705 | −0.658715 | −0.329358 | − | 0.944205i | \(-0.606832\pi\) | ||||
−0.329358 | + | 0.944205i | \(0.606832\pi\) | |||||||
\(348\) | 2.23607 | 0.119866 | ||||||||
\(349\) | 7.23607 | 0.387338 | 0.193669 | − | 0.981067i | \(-0.437961\pi\) | ||||
0.193669 | + | 0.981067i | \(0.437961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −10.1459 | −0.540778 | ||||||||
\(353\) | 12.3820 | 0.659026 | 0.329513 | − | 0.944151i | \(-0.393116\pi\) | ||||
0.329513 | + | 0.944151i | \(0.393116\pi\) | |||||||
\(354\) | 6.38197 | 0.339198 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.90983 | −0.366220 | ||||||||
\(357\) | −8.47214 | −0.448393 | ||||||||
\(358\) | 25.3262 | 1.33853 | ||||||||
\(359\) | 23.9443 | 1.26373 | 0.631865 | − | 0.775078i | \(-0.282290\pi\) | ||||
0.631865 | + | 0.775078i | \(0.282290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | 20.1803 | 1.06066 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 1.23607 | 0.0647876 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0902 | 0.736505 | ||||||||
\(367\) | 12.5279 | 0.653949 | 0.326975 | − | 0.945033i | \(-0.393971\pi\) | ||||
0.326975 | + | 0.945033i | \(0.393971\pi\) | |||||||
\(368\) | 26.1246 | 1.36184 | ||||||||
\(369\) | −9.38197 | −0.488406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.4721 | −1.16670 | ||||||||
\(372\) | −5.38197 | −0.279042 | ||||||||
\(373\) | −17.4164 | −0.901787 | −0.450894 | − | 0.892578i | \(-0.648895\pi\) | ||||
−0.450894 | + | 0.892578i | \(0.648895\pi\) | |||||||
\(374\) | 20.5623 | 1.06325 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6525 | 0.549359 | ||||||||
\(377\) | −3.61803 | −0.186338 | ||||||||
\(378\) | 3.23607 | 0.166445 | ||||||||
\(379\) | −13.6180 | −0.699511 | −0.349756 | − | 0.936841i | \(-0.613735\pi\) | ||||
−0.349756 | + | 0.936841i | \(0.613735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6525 | 0.699438 | ||||||||
\(382\) | −28.0344 | −1.43437 | ||||||||
\(383\) | −5.05573 | −0.258336 | −0.129168 | − | 0.991623i | \(-0.541231\pi\) | ||||
−0.129168 | + | 0.991623i | \(0.541231\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.7984 | −0.905913 | ||||||||
\(387\) | 7.38197 | 0.375246 | ||||||||
\(388\) | −2.38197 | −0.120926 | ||||||||
\(389\) | 0.652476 | 0.0330818 | 0.0165409 | − | 0.999863i | \(-0.494735\pi\) | ||||
0.0165409 | + | 0.999863i | \(0.494735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7984 | −1.15296 | ||||||||
\(392\) | −6.70820 | −0.338815 | ||||||||
\(393\) | 14.1803 | 0.715304 | ||||||||
\(394\) | −0.145898 | −0.00735024 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.85410 | −0.0931721 | ||||||||
\(397\) | 2.52786 | 0.126870 | 0.0634349 | − | 0.997986i | \(-0.479794\pi\) | ||||
0.0634349 | + | 0.997986i | \(0.479794\pi\) | |||||||
\(398\) | −18.9443 | −0.949591 | ||||||||
\(399\) | 13.4164 | 0.671660 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2705 | 1.81126 | 0.905631 | − | 0.424066i | \(-0.139397\pi\) | ||||
0.905631 | + | 0.424066i | \(0.139397\pi\) | |||||||
\(402\) | 21.3262 | 1.06366 | ||||||||
\(403\) | 8.70820 | 0.433787 | ||||||||
\(404\) | −5.79837 | −0.288480 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.7082 | 0.581068 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | −9.47214 | −0.468941 | ||||||||
\(409\) | −5.12461 | −0.253396 | −0.126698 | − | 0.991941i | \(-0.540438\pi\) | ||||
−0.126698 | + | 0.991941i | \(0.540438\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.437694 | 0.0215899 | ||||||||
\(412\) | 8.90983 | 0.438956 | ||||||||
\(413\) | 7.88854 | 0.388170 | ||||||||
\(414\) | 8.70820 | 0.427985 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.38197 | 0.165815 | ||||||||
\(417\) | −13.4164 | −0.657004 | ||||||||
\(418\) | −32.5623 | −1.59267 | ||||||||
\(419\) | 0.326238 | 0.0159378 | 0.00796888 | − | 0.999968i | \(-0.497463\pi\) | ||||
0.00796888 | + | 0.999968i | \(0.497463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3607 | −1.47969 | −0.739844 | − | 0.672778i | \(-0.765101\pi\) | ||||
−0.739844 | + | 0.672778i | \(0.765101\pi\) | |||||||
\(422\) | 4.85410 | 0.236294 | ||||||||
\(423\) | 4.76393 | 0.231630 | ||||||||
\(424\) | −25.1246 | −1.22016 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.3262 | 0.791009 | ||||||||
\(427\) | 17.4164 | 0.842839 | ||||||||
\(428\) | 0.708204 | 0.0342323 | ||||||||
\(429\) | 3.00000 | 0.144841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.7639 | 1.43368 | 0.716839 | − | 0.697239i | \(-0.245588\pi\) | ||||
0.716839 | + | 0.697239i | \(0.245588\pi\) | |||||||
\(432\) | 4.85410 | 0.233543 | ||||||||
\(433\) | −3.47214 | −0.166860 | −0.0834301 | − | 0.996514i | \(-0.526588\pi\) | ||||
−0.0834301 | + | 0.996514i | \(0.526588\pi\) | |||||||
\(434\) | −28.1803 | −1.35270 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.56231 | −0.122712 | ||||||||
\(437\) | 36.1033 | 1.72706 | ||||||||
\(438\) | −25.4164 | −1.21444 | ||||||||
\(439\) | −32.0344 | −1.52892 | −0.764460 | − | 0.644671i | \(-0.776994\pi\) | ||||
−0.764460 | + | 0.644671i | \(0.776994\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −6.85410 | −0.326016 | ||||||||
\(443\) | 19.4164 | 0.922501 | 0.461251 | − | 0.887270i | \(-0.347401\pi\) | ||||
0.461251 | + | 0.887270i | \(0.347401\pi\) | |||||||
\(444\) | −1.23607 | −0.0586612 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.4164 | −0.777339 | ||||||||
\(447\) | 13.0902 | 0.619144 | ||||||||
\(448\) | 8.47214 | 0.400271 | ||||||||
\(449\) | 16.5066 | 0.778994 | 0.389497 | − | 0.921028i | \(-0.372649\pi\) | ||||
0.389497 | + | 0.921028i | \(0.372649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.1459 | 1.32534 | ||||||||
\(452\) | 2.32624 | 0.109417 | ||||||||
\(453\) | 6.61803 | 0.310942 | ||||||||
\(454\) | 9.32624 | 0.437702 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.0000 | 0.702439 | ||||||||
\(457\) | 9.88854 | 0.462567 | 0.231283 | − | 0.972886i | \(-0.425708\pi\) | ||||
0.231283 | + | 0.972886i | \(0.425708\pi\) | |||||||
\(458\) | 26.1803 | 1.22333 | ||||||||
\(459\) | −4.23607 | −0.197723 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1803 | −0.893317 | −0.446659 | − | 0.894704i | \(-0.647386\pi\) | ||||
−0.446659 | + | 0.894704i | \(0.647386\pi\) | |||||||
\(462\) | −9.70820 | −0.451667 | ||||||||
\(463\) | 33.6869 | 1.56556 | 0.782782 | − | 0.622296i | \(-0.213800\pi\) | ||||
0.782782 | + | 0.622296i | \(0.213800\pi\) | |||||||
\(464\) | 17.5623 | 0.815310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.4721 | 0.763057 | ||||||||
\(467\) | 10.4164 | 0.482014 | 0.241007 | − | 0.970523i | \(-0.422522\pi\) | ||||
0.241007 | + | 0.970523i | \(0.422522\pi\) | |||||||
\(468\) | 0.618034 | 0.0285686 | ||||||||
\(469\) | 26.3607 | 1.21722 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.85410 | −0.131510 | ||||||||
\(472\) | 8.81966 | 0.405958 | ||||||||
\(473\) | −22.1459 | −1.01827 | ||||||||
\(474\) | −14.7984 | −0.679712 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.23607 | 0.239995 | ||||||||
\(477\) | −11.2361 | −0.514464 | ||||||||
\(478\) | −34.5967 | −1.58242 | ||||||||
\(479\) | 4.79837 | 0.219243 | 0.109622 | − | 0.993973i | \(-0.465036\pi\) | ||||
0.109622 | + | 0.993973i | \(0.465036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | −11.8541 | −0.539940 | ||||||||
\(483\) | 10.7639 | 0.489776 | ||||||||
\(484\) | −1.23607 | −0.0561849 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.61803 | 0.0733955 | ||||||||
\(487\) | −16.6180 | −0.753035 | −0.376518 | − | 0.926410i | \(-0.622879\pi\) | ||||
−0.376518 | + | 0.926410i | \(0.622879\pi\) | |||||||
\(488\) | 19.4721 | 0.881462 | ||||||||
\(489\) | 18.2705 | 0.826221 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3262 | 1.00757 | 0.503785 | − | 0.863829i | \(-0.331941\pi\) | ||||
0.503785 | + | 0.863829i | \(0.331941\pi\) | |||||||
\(492\) | 5.79837 | 0.261411 | ||||||||
\(493\) | −15.3262 | −0.690259 | ||||||||
\(494\) | 10.8541 | 0.488349 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −42.2705 | −1.89800 | ||||||||
\(497\) | 20.1803 | 0.905212 | ||||||||
\(498\) | −14.5623 | −0.652553 | ||||||||
\(499\) | −15.0000 | −0.671492 | −0.335746 | − | 0.941953i | \(-0.608988\pi\) | ||||
−0.335746 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7984 | 0.795173 | ||||||||
\(502\) | 30.7082 | 1.37057 | ||||||||
\(503\) | 3.96556 | 0.176815 | 0.0884077 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884077 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(504\) | 4.47214 | 0.199205 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −26.1246 | −1.16138 | ||||||||
\(507\) | 12.0000 | 0.532939 | ||||||||
\(508\) | −8.43769 | −0.374362 | ||||||||
\(509\) | 32.8885 | 1.45776 | 0.728880 | − | 0.684642i | \(-0.240041\pi\) | ||||
0.728880 | + | 0.684642i | \(0.240041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.4164 | −1.38978 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 6.70820 | 0.296174 | ||||||||
\(514\) | 50.5066 | 2.22775 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.56231 | −0.200844 | ||||||||
\(517\) | −14.2918 | −0.628552 | ||||||||
\(518\) | −6.47214 | −0.284369 | ||||||||
\(519\) | 0.909830 | 0.0399371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.0902 | 1.75638 | 0.878191 | − | 0.478310i | \(-0.158750\pi\) | ||||
0.878191 | + | 0.478310i | \(0.158750\pi\) | |||||||
\(522\) | 5.85410 | 0.256227 | ||||||||
\(523\) | −1.56231 | −0.0683149 | −0.0341574 | − | 0.999416i | \(-0.510875\pi\) | ||||
−0.0341574 | + | 0.999416i | \(0.510875\pi\) | |||||||
\(524\) | −8.76393 | −0.382854 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.2361 | −0.882334 | ||||||||
\(527\) | 36.8885 | 1.60689 | ||||||||
\(528\) | −14.5623 | −0.633743 | ||||||||
\(529\) | 5.96556 | 0.259372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.94427 | 0.171167 | ||||||||
\(532\) | −8.29180 | −0.359495 | ||||||||
\(533\) | −9.38197 | −0.406378 | ||||||||
\(534\) | −18.0902 | −0.782838 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 29.4721 | 1.27300 | ||||||||
\(537\) | 15.6525 | 0.675454 | ||||||||
\(538\) | 33.2148 | 1.43199 | ||||||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.2918 | −1.13037 | −0.565186 | − | 0.824963i | \(-0.691196\pi\) | ||||
−0.565186 | + | 0.824963i | \(0.691196\pi\) | |||||||
\(542\) | 18.4721 | 0.793446 | ||||||||
\(543\) | 12.4721 | 0.535231 | ||||||||
\(544\) | 14.3262 | 0.614232 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.23607 | 0.138491 | ||||||||
\(547\) | −24.7082 | −1.05645 | −0.528223 | − | 0.849106i | \(-0.677142\pi\) | ||||
−0.528223 | + | 0.849106i | \(0.677142\pi\) | |||||||
\(548\) | −0.270510 | −0.0115556 | ||||||||
\(549\) | 8.70820 | 0.371657 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.2705 | 1.03396 | ||||||||
\(552\) | 12.0344 | 0.512220 | ||||||||
\(553\) | −18.2918 | −0.777846 | ||||||||
\(554\) | −21.1246 | −0.897499 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.29180 | 0.351650 | ||||||||
\(557\) | 37.6525 | 1.59539 | 0.797693 | − | 0.603063i | \(-0.206053\pi\) | ||||
0.797693 | + | 0.603063i | \(0.206053\pi\) | |||||||
\(558\) | −14.0902 | −0.596484 | ||||||||
\(559\) | 7.38197 | 0.312224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7082 | 0.536541 | ||||||||
\(562\) | 22.9443 | 0.967846 | ||||||||
\(563\) | −9.00000 | −0.379305 | −0.189652 | − | 0.981851i | \(-0.560736\pi\) | ||||
−0.189652 | + | 0.981851i | \(0.560736\pi\) | |||||||
\(564\) | −2.94427 | −0.123976 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.70820 | 0.155867 | ||||||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | 22.5623 | 0.946693 | ||||||||
\(569\) | −10.8541 | −0.455028 | −0.227514 | − | 0.973775i | \(-0.573060\pi\) | ||||
−0.227514 | + | 0.973775i | \(0.573060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.1246 | −1.59547 | −0.797733 | − | 0.603011i | \(-0.793967\pi\) | ||||
−0.797733 | + | 0.603011i | \(0.793967\pi\) | |||||||
\(572\) | −1.85410 | −0.0775239 | ||||||||
\(573\) | −17.3262 | −0.723814 | ||||||||
\(574\) | 30.3607 | 1.26723 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −3.72949 | −0.155261 | −0.0776304 | − | 0.996982i | \(-0.524735\pi\) | ||||
−0.0776304 | + | 0.996982i | \(0.524735\pi\) | |||||||
\(578\) | −1.52786 | −0.0635508 | ||||||||
\(579\) | −11.0000 | −0.457144 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | −6.23607 | −0.258493 | ||||||||
\(583\) | 33.7082 | 1.39605 | ||||||||
\(584\) | −35.1246 | −1.45347 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.2361 | −0.422848 | ||||||||
\(587\) | −39.3050 | −1.62229 | −0.811144 | − | 0.584846i | \(-0.801155\pi\) | ||||
−0.811144 | + | 0.584846i | \(0.801155\pi\) | |||||||
\(588\) | 1.85410 | 0.0764619 | ||||||||
\(589\) | −58.4164 | −2.40701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0901699 | −0.00370910 | ||||||||
\(592\) | −9.70820 | −0.399005 | ||||||||
\(593\) | −17.6180 | −0.723486 | −0.361743 | − | 0.932278i | \(-0.617818\pi\) | ||||
−0.361743 | + | 0.932278i | \(0.617818\pi\) | |||||||
\(594\) | −4.85410 | −0.199166 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.09017 | −0.331386 | ||||||||
\(597\) | −11.7082 | −0.479185 | ||||||||
\(598\) | 8.70820 | 0.356105 | ||||||||
\(599\) | 39.2705 | 1.60455 | 0.802275 | − | 0.596955i | \(-0.203623\pi\) | ||||
0.802275 | + | 0.596955i | \(0.203623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7082 | −1.00787 | −0.503934 | − | 0.863742i | \(-0.668115\pi\) | ||||
−0.503934 | + | 0.863742i | \(0.668115\pi\) | |||||||
\(602\) | −23.8885 | −0.973624 | ||||||||
\(603\) | 13.1803 | 0.536745 | ||||||||
\(604\) | −4.09017 | −0.166427 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.1803 | −0.616659 | ||||||||
\(607\) | 22.8541 | 0.927619 | 0.463810 | − | 0.885935i | \(-0.346482\pi\) | ||||
0.463810 | + | 0.885935i | \(0.346482\pi\) | |||||||
\(608\) | −22.6869 | −0.920076 | ||||||||
\(609\) | 7.23607 | 0.293220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.76393 | 0.192728 | ||||||||
\(612\) | 2.61803 | 0.105828 | ||||||||
\(613\) | 5.87539 | 0.237305 | 0.118652 | − | 0.992936i | \(-0.462143\pi\) | ||||
0.118652 | + | 0.992936i | \(0.462143\pi\) | |||||||
\(614\) | 14.3262 | 0.578160 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.4164 | −0.540562 | ||||||||
\(617\) | −25.2361 | −1.01597 | −0.507983 | − | 0.861367i | \(-0.669609\pi\) | ||||
−0.507983 | + | 0.861367i | \(0.669609\pi\) | |||||||
\(618\) | 23.3262 | 0.938319 | ||||||||
\(619\) | 34.2705 | 1.37745 | 0.688724 | − | 0.725024i | \(-0.258171\pi\) | ||||
0.688724 | + | 0.725024i | \(0.258171\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.38197 | 0.215971 | ||||||||
\(622\) | 21.8885 | 0.877651 | ||||||||
\(623\) | −22.3607 | −0.895862 | ||||||||
\(624\) | 4.85410 | 0.194320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.70820 | 0.148210 | ||||||||
\(627\) | −20.1246 | −0.803700 | ||||||||
\(628\) | 1.76393 | 0.0703886 | ||||||||
\(629\) | 8.47214 | 0.337806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7639 | −0.428505 | −0.214253 | − | 0.976778i | \(-0.568732\pi\) | ||||
−0.214253 | + | 0.976778i | \(0.568732\pi\) | |||||||
\(632\) | −20.4508 | −0.813491 | ||||||||
\(633\) | 3.00000 | 0.119239 | ||||||||
\(634\) | 33.2705 | 1.32134 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.94427 | 0.275358 | ||||||||
\(637\) | −3.00000 | −0.118864 | ||||||||
\(638\) | −17.5623 | −0.695298 | ||||||||
\(639\) | 10.0902 | 0.399161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3262 | −0.921331 | −0.460666 | − | 0.887574i | \(-0.652389\pi\) | ||||
−0.460666 | + | 0.887574i | \(0.652389\pi\) | |||||||
\(642\) | 1.85410 | 0.0731756 | ||||||||
\(643\) | −5.90983 | −0.233061 | −0.116530 | − | 0.993187i | \(-0.537177\pi\) | ||||
−0.116530 | + | 0.993187i | \(0.537177\pi\) | |||||||
\(644\) | −6.65248 | −0.262144 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 45.9787 | 1.80901 | ||||||||
\(647\) | 19.0344 | 0.748321 | 0.374161 | − | 0.927364i | \(-0.377931\pi\) | ||||
0.374161 | + | 0.927364i | \(0.377931\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | −11.8328 | −0.464479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4164 | −0.682603 | ||||||||
\(652\) | −11.2918 | −0.442221 | ||||||||
\(653\) | −29.6525 | −1.16039 | −0.580196 | − | 0.814477i | \(-0.697024\pi\) | ||||
−0.580196 | + | 0.814477i | \(0.697024\pi\) | |||||||
\(654\) | −6.70820 | −0.262312 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 45.5410 | 1.77808 | ||||||||
\(657\) | −15.7082 | −0.612835 | ||||||||
\(658\) | −15.4164 | −0.600994 | ||||||||
\(659\) | −2.23607 | −0.0871048 | −0.0435524 | − | 0.999051i | \(-0.513868\pi\) | ||||
−0.0435524 | + | 0.999051i | \(0.513868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.88854 | 0.190142 | 0.0950712 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950712 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(662\) | 49.6525 | 1.92980 | ||||||||
\(663\) | −4.23607 | −0.164515 | ||||||||
\(664\) | −20.1246 | −0.780986 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.23607 | −0.125395 | ||||||||
\(667\) | 19.4721 | 0.753964 | ||||||||
\(668\) | −11.0000 | −0.425603 | ||||||||
\(669\) | −10.1459 | −0.392263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.1246 | −1.00853 | ||||||||
\(672\) | −6.76393 | −0.260924 | ||||||||
\(673\) | 46.7771 | 1.80312 | 0.901562 | − | 0.432650i | \(-0.142421\pi\) | ||||
0.901562 | + | 0.432650i | \(0.142421\pi\) | |||||||
\(674\) | −53.6869 | −2.06794 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.41641 | −0.285246 | ||||||||
\(677\) | 44.8885 | 1.72521 | 0.862603 | − | 0.505881i | \(-0.168832\pi\) | ||||
0.862603 | + | 0.505881i | \(0.168832\pi\) | |||||||
\(678\) | 6.09017 | 0.233892 | ||||||||
\(679\) | −7.70820 | −0.295814 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.76393 | 0.220874 | ||||||||
\(682\) | 42.2705 | 1.61862 | ||||||||
\(683\) | 0.596748 | 0.0228339 | 0.0114170 | − | 0.999935i | \(-0.496366\pi\) | ||||
0.0114170 | + | 0.999935i | \(0.496366\pi\) | |||||||
\(684\) | −4.14590 | −0.158522 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 32.3607 | 1.23554 | ||||||||
\(687\) | 16.1803 | 0.617318 | ||||||||
\(688\) | −35.8328 | −1.36611 | ||||||||
\(689\) | −11.2361 | −0.428060 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0902 | 0.574057 | 0.287029 | − | 0.957922i | \(-0.407333\pi\) | ||||
0.287029 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(692\) | −0.562306 | −0.0213757 | ||||||||
\(693\) | −6.00000 | −0.227921 | ||||||||
\(694\) | 19.8541 | 0.753651 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.09017 | 0.306657 | ||||||||
\(697\) | −39.7426 | −1.50536 | ||||||||
\(698\) | −11.7082 | −0.443162 | ||||||||
\(699\) | 10.1803 | 0.385056 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.6525 | −1.83758 | −0.918789 | − | 0.394748i | \(-0.870832\pi\) | ||||
−0.918789 | + | 0.394748i | \(0.870832\pi\) | |||||||
\(702\) | 1.61803 | 0.0610688 | ||||||||
\(703\) | −13.4164 | −0.506009 | ||||||||
\(704\) | −12.7082 | −0.478958 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.0344 | −0.754006 | ||||||||
\(707\) | −18.7639 | −0.705690 | ||||||||
\(708\) | −2.43769 | −0.0916142 | ||||||||
\(709\) | −5.20163 | −0.195351 | −0.0976756 | − | 0.995218i | \(-0.531141\pi\) | ||||
−0.0976756 | + | 0.995218i | \(0.531141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.14590 | −0.342998 | ||||||||
\(712\) | −25.0000 | −0.936915 | ||||||||
\(713\) | −46.8673 | −1.75519 | ||||||||
\(714\) | 13.7082 | 0.513017 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.67376 | −0.361525 | ||||||||
\(717\) | −21.3820 | −0.798524 | ||||||||
\(718\) | −38.7426 | −1.44586 | ||||||||
\(719\) | −35.1246 | −1.30993 | −0.654963 | − | 0.755661i | \(-0.727316\pi\) | ||||
−0.654963 | + | 0.755661i | \(0.727316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.8328 | 1.07379 | ||||||||
\(722\) | −42.0689 | −1.56564 | ||||||||
\(723\) | −7.32624 | −0.272466 | ||||||||
\(724\) | −7.70820 | −0.286473 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.23607 | −0.120102 | ||||||||
\(727\) | 14.4377 | 0.535464 | 0.267732 | − | 0.963493i | \(-0.413726\pi\) | ||||
0.267732 | + | 0.963493i | \(0.413726\pi\) | |||||||
\(728\) | 4.47214 | 0.165748 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.2705 | 1.15658 | ||||||||
\(732\) | −5.38197 | −0.198923 | ||||||||
\(733\) | 10.1459 | 0.374747 | 0.187374 | − | 0.982289i | \(-0.440002\pi\) | ||||
0.187374 | + | 0.982289i | \(0.440002\pi\) | |||||||
\(734\) | −20.2705 | −0.748198 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.2016 | −0.670921 | ||||||||
\(737\) | −39.5410 | −1.45651 | ||||||||
\(738\) | 15.1803 | 0.558796 | ||||||||
\(739\) | −1.70820 | −0.0628373 | −0.0314186 | − | 0.999506i | \(-0.510003\pi\) | ||||
−0.0314186 | + | 0.999506i | \(0.510003\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70820 | 0.246432 | ||||||||
\(742\) | 36.3607 | 1.33484 | ||||||||
\(743\) | 16.5279 | 0.606349 | 0.303174 | − | 0.952935i | \(-0.401954\pi\) | ||||
0.303174 | + | 0.952935i | \(0.401954\pi\) | |||||||
\(744\) | −19.4721 | −0.713883 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.1803 | 1.03176 | ||||||||
\(747\) | −9.00000 | −0.329293 | ||||||||
\(748\) | −7.85410 | −0.287174 | ||||||||
\(749\) | 2.29180 | 0.0837404 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2918 | 0.558006 | 0.279003 | − | 0.960290i | \(-0.409996\pi\) | ||||
0.279003 | + | 0.960290i | \(0.409996\pi\) | |||||||
\(752\) | −23.1246 | −0.843268 | ||||||||
\(753\) | 18.9787 | 0.691623 | ||||||||
\(754\) | 5.85410 | 0.213194 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.23607 | −0.0449554 | ||||||||
\(757\) | −32.2705 | −1.17289 | −0.586446 | − | 0.809988i | \(-0.699473\pi\) | ||||
−0.586446 | + | 0.809988i | \(0.699473\pi\) | |||||||
\(758\) | 22.0344 | 0.800327 | ||||||||
\(759\) | −16.1459 | −0.586059 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.18034 | 0.115287 | 0.0576436 | − | 0.998337i | \(-0.481641\pi\) | ||||
0.0576436 | + | 0.998337i | \(0.481641\pi\) | |||||||
\(762\) | −22.0902 | −0.800242 | ||||||||
\(763\) | −8.29180 | −0.300183 | ||||||||
\(764\) | 10.7082 | 0.387409 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.18034 | 0.295568 | ||||||||
\(767\) | 3.94427 | 0.142419 | ||||||||
\(768\) | −13.5623 | −0.489388 | ||||||||
\(769\) | −36.3050 | −1.30919 | −0.654595 | − | 0.755980i | \(-0.727161\pi\) | ||||
−0.654595 | + | 0.755980i | \(0.727161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2148 | 1.12417 | ||||||||
\(772\) | 6.79837 | 0.244679 | ||||||||
\(773\) | 41.7771 | 1.50262 | 0.751309 | − | 0.659951i | \(-0.229423\pi\) | ||||
0.751309 | + | 0.659951i | \(0.229423\pi\) | |||||||
\(774\) | −11.9443 | −0.429328 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.61803 | −0.309369 | ||||||||
\(777\) | −4.00000 | −0.143499 | ||||||||
\(778\) | −1.05573 | −0.0378497 | ||||||||
\(779\) | 62.9361 | 2.25492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.2705 | −1.08316 | ||||||||
\(782\) | 36.8885 | 1.31913 | ||||||||
\(783\) | 3.61803 | 0.129298 | ||||||||
\(784\) | 14.5623 | 0.520082 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −22.9443 | −0.818395 | ||||||||
\(787\) | −17.1459 | −0.611185 | −0.305593 | − | 0.952162i | \(-0.598855\pi\) | ||||
−0.305593 | + | 0.952162i | \(0.598855\pi\) | |||||||
\(788\) | 0.0557281 | 0.00198523 | ||||||||
\(789\) | −12.5066 | −0.445246 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.52786 | 0.267660 | ||||||||
\(792\) | −6.70820 | −0.238366 | ||||||||
\(793\) | 8.70820 | 0.309237 | ||||||||
\(794\) | −4.09017 | −0.145155 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.23607 | 0.256476 | ||||||||
\(797\) | 30.0132 | 1.06312 | 0.531560 | − | 0.847020i | \(-0.321606\pi\) | ||||
0.531560 | + | 0.847020i | \(0.321606\pi\) | |||||||
\(798\) | −21.7082 | −0.768462 | ||||||||
\(799\) | 20.1803 | 0.713929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1803 | −0.395038 | ||||||||
\(802\) | −58.6869 | −2.07231 | ||||||||
\(803\) | 47.1246 | 1.66299 | ||||||||
\(804\) | −8.14590 | −0.287284 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.0902 | −0.496305 | ||||||||
\(807\) | 20.5279 | 0.722615 | ||||||||
\(808\) | −20.9787 | −0.738029 | ||||||||
\(809\) | −39.9230 | −1.40362 | −0.701809 | − | 0.712365i | \(-0.747624\pi\) | ||||
−0.701809 | + | 0.712365i | \(0.747624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.7771 | −1.18607 | −0.593037 | − | 0.805175i | \(-0.702071\pi\) | ||||
−0.593037 | + | 0.805175i | \(0.702071\pi\) | |||||||
\(812\) | −4.47214 | −0.156941 | ||||||||
\(813\) | 11.4164 | 0.400391 | ||||||||
\(814\) | 9.70820 | 0.340272 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.5623 | 0.719825 | ||||||||
\(817\) | −49.5197 | −1.73248 | ||||||||
\(818\) | 8.29180 | 0.289916 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.94427 | 0.207457 | 0.103728 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103728 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(822\) | −0.708204 | −0.0247014 | ||||||||
\(823\) | 28.5623 | 0.995619 | 0.497810 | − | 0.867286i | \(-0.334138\pi\) | ||||
0.497810 | + | 0.867286i | \(0.334138\pi\) | |||||||
\(824\) | 32.2361 | 1.12300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.7639 | −0.444114 | ||||||||
\(827\) | −48.9787 | −1.70316 | −0.851578 | − | 0.524227i | \(-0.824354\pi\) | ||||
−0.851578 | + | 0.524227i | \(0.824354\pi\) | |||||||
\(828\) | −3.32624 | −0.115595 | ||||||||
\(829\) | −50.1246 | −1.74090 | −0.870450 | − | 0.492257i | \(-0.836172\pi\) | ||||
−0.870450 | + | 0.492257i | \(0.836172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0557 | −0.452898 | ||||||||
\(832\) | 4.23607 | 0.146859 | ||||||||
\(833\) | −12.7082 | −0.440313 | ||||||||
\(834\) | 21.7082 | 0.751694 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.4377 | 0.430167 | ||||||||
\(837\) | −8.70820 | −0.301000 | ||||||||
\(838\) | −0.527864 | −0.0182348 | ||||||||
\(839\) | −3.21478 | −0.110987 | −0.0554933 | − | 0.998459i | \(-0.517673\pi\) | ||||
−0.0554933 | + | 0.998459i | \(0.517673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | 49.1246 | 1.69295 | ||||||||
\(843\) | 14.1803 | 0.488397 | ||||||||
\(844\) | −1.85410 | −0.0638208 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.70820 | −0.265014 | ||||||||
\(847\) | −4.00000 | −0.137442 | ||||||||
\(848\) | 54.5410 | 1.87295 | ||||||||
\(849\) | 2.29180 | 0.0786542 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7639 | −0.368983 | ||||||||
\(852\) | −6.23607 | −0.213644 | ||||||||
\(853\) | 20.3951 | 0.698316 | 0.349158 | − | 0.937064i | \(-0.386468\pi\) | ||||
0.349158 | + | 0.937064i | \(0.386468\pi\) | |||||||
\(854\) | −28.1803 | −0.964311 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.56231 | 0.0875778 | ||||||||
\(857\) | −9.05573 | −0.309338 | −0.154669 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154669 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(858\) | −4.85410 | −0.165716 | ||||||||
\(859\) | 15.1246 | 0.516045 | 0.258023 | − | 0.966139i | \(-0.416929\pi\) | ||||
0.258023 | + | 0.966139i | \(0.416929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.7639 | 0.639473 | ||||||||
\(862\) | −48.1591 | −1.64030 | ||||||||
\(863\) | −13.0689 | −0.444870 | −0.222435 | − | 0.974948i | \(-0.571401\pi\) | ||||
−0.222435 | + | 0.974948i | \(0.571401\pi\) | |||||||
\(864\) | −3.38197 | −0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.61803 | 0.190909 | ||||||||
\(867\) | −0.944272 | −0.0320692 | ||||||||
\(868\) | 10.7639 | 0.365352 | ||||||||
\(869\) | 27.4377 | 0.930760 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1803 | 0.446599 | ||||||||
\(872\) | −9.27051 | −0.313939 | ||||||||
\(873\) | −3.85410 | −0.130442 | ||||||||
\(874\) | −58.4164 | −1.97596 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.70820 | 0.328010 | ||||||||
\(877\) | −43.1246 | −1.45621 | −0.728107 | − | 0.685463i | \(-0.759600\pi\) | ||||
−0.728107 | + | 0.685463i | \(0.759600\pi\) | |||||||
\(878\) | 51.8328 | 1.74927 | ||||||||
\(879\) | −6.32624 | −0.213379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0902 | 0.508401 | 0.254200 | − | 0.967152i | \(-0.418188\pi\) | ||||
0.254200 | + | 0.967152i | \(0.418188\pi\) | |||||||
\(882\) | 4.85410 | 0.163446 | ||||||||
\(883\) | −29.2016 | −0.982713 | −0.491356 | − | 0.870959i | \(-0.663499\pi\) | ||||
−0.491356 | + | 0.870959i | \(0.663499\pi\) | |||||||
\(884\) | 2.61803 | 0.0880540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.4164 | −1.05545 | ||||||||
\(887\) | −42.9230 | −1.44121 | −0.720606 | − | 0.693344i | \(-0.756136\pi\) | ||||
−0.720606 | + | 0.693344i | \(0.756136\pi\) | |||||||
\(888\) | −4.47214 | −0.150075 | ||||||||
\(889\) | −27.3050 | −0.915779 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | 6.27051 | 0.209952 | ||||||||
\(893\) | −31.9574 | −1.06941 | ||||||||
\(894\) | −21.1803 | −0.708377 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −27.2361 | −0.909893 | ||||||||
\(897\) | 5.38197 | 0.179699 | ||||||||
\(898\) | −26.7082 | −0.891264 | ||||||||
\(899\) | −31.5066 | −1.05080 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.5967 | −1.58568 | ||||||||
\(902\) | −45.5410 | −1.51635 | ||||||||
\(903\) | −14.7639 | −0.491313 | ||||||||
\(904\) | 8.41641 | 0.279926 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.7082 | −0.355756 | ||||||||
\(907\) | 17.0000 | 0.564476 | 0.282238 | − | 0.959344i | \(-0.408923\pi\) | ||||
0.282238 | + | 0.959344i | \(0.408923\pi\) | |||||||
\(908\) | −3.56231 | −0.118219 | ||||||||
\(909\) | −9.38197 | −0.311180 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8885 | 0.493279 | 0.246640 | − | 0.969107i | \(-0.420674\pi\) | ||||
0.246640 | + | 0.969107i | \(0.420674\pi\) | |||||||
\(912\) | −32.5623 | −1.07825 | ||||||||
\(913\) | 27.0000 | 0.893570 | ||||||||
\(914\) | −16.0000 | −0.529233 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | −28.3607 | −0.936552 | ||||||||
\(918\) | 6.85410 | 0.226219 | ||||||||
\(919\) | −5.00000 | −0.164935 | −0.0824674 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824674 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.85410 | 0.291753 | ||||||||
\(922\) | 31.0344 | 1.02206 | ||||||||
\(923\) | 10.0902 | 0.332122 | ||||||||
\(924\) | 3.70820 | 0.121991 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −54.5066 | −1.79120 | ||||||||
\(927\) | 14.4164 | 0.473497 | ||||||||
\(928\) | −12.2361 | −0.401669 | ||||||||
\(929\) | −29.5967 | −0.971038 | −0.485519 | − | 0.874226i | \(-0.661369\pi\) | ||||
−0.485519 | + | 0.874226i | \(0.661369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.1246 | 0.659558 | ||||||||
\(932\) | −6.29180 | −0.206095 | ||||||||
\(933\) | 13.5279 | 0.442882 | ||||||||
\(934\) | −16.8541 | −0.551483 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.23607 | 0.0730882 | ||||||||
\(937\) | 10.4164 | 0.340289 | 0.170145 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170145 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(938\) | −42.6525 | −1.39265 | ||||||||
\(939\) | 2.29180 | 0.0747899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.9787 | 1.89005 | 0.945026 | − | 0.326995i | \(-0.106036\pi\) | ||||
0.945026 | + | 0.326995i | \(0.106036\pi\) | |||||||
\(942\) | 4.61803 | 0.150464 | ||||||||
\(943\) | 50.4934 | 1.64429 | ||||||||
\(944\) | −19.1459 | −0.623146 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.8328 | 1.16503 | ||||||||
\(947\) | 23.8328 | 0.774462 | 0.387231 | − | 0.921983i | \(-0.373432\pi\) | ||||
0.387231 | + | 0.921983i | \(0.373432\pi\) | |||||||
\(948\) | 5.65248 | 0.183584 | ||||||||
\(949\) | −15.7082 | −0.509910 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.5623 | 0.666778 | ||||||||
\(952\) | 18.9443 | 0.613987 | ||||||||
\(953\) | 42.0557 | 1.36232 | 0.681159 | − | 0.732135i | \(-0.261476\pi\) | ||||
0.681159 | + | 0.732135i | \(0.261476\pi\) | |||||||
\(954\) | 18.1803 | 0.588610 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.2148 | 0.427397 | ||||||||
\(957\) | −10.8541 | −0.350863 | ||||||||
\(958\) | −7.76393 | −0.250841 | ||||||||
\(959\) | −0.875388 | −0.0282678 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.8328 | 1.44622 | ||||||||
\(962\) | −3.23607 | −0.104335 | ||||||||
\(963\) | 1.14590 | 0.0369260 | ||||||||
\(964\) | 4.52786 | 0.145833 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.4164 | −0.560364 | ||||||||
\(967\) | 35.4164 | 1.13891 | 0.569457 | − | 0.822021i | \(-0.307153\pi\) | ||||
0.569457 | + | 0.822021i | \(0.307153\pi\) | |||||||
\(968\) | −4.47214 | −0.143740 | ||||||||
\(969\) | 28.4164 | 0.912867 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.8885 | 0.959169 | 0.479585 | − | 0.877496i | \(-0.340787\pi\) | ||||
0.479585 | + | 0.877496i | \(0.340787\pi\) | |||||||
\(972\) | −0.618034 | −0.0198234 | ||||||||
\(973\) | 26.8328 | 0.860221 | ||||||||
\(974\) | 26.8885 | 0.861565 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.2705 | −1.35305 | ||||||||
\(977\) | 37.6525 | 1.20461 | 0.602305 | − | 0.798266i | \(-0.294249\pi\) | ||||
0.602305 | + | 0.798266i | \(0.294249\pi\) | |||||||
\(978\) | −29.5623 | −0.945298 | ||||||||
\(979\) | 33.5410 | 1.07198 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.14590 | −0.132368 | ||||||||
\(982\) | −36.1246 | −1.15278 | ||||||||
\(983\) | 24.6180 | 0.785193 | 0.392597 | − | 0.919711i | \(-0.371577\pi\) | ||||
0.392597 | + | 0.919711i | \(0.371577\pi\) | |||||||
\(984\) | 20.9787 | 0.668777 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.7984 | 0.789741 | ||||||||
\(987\) | −9.52786 | −0.303275 | ||||||||
\(988\) | −4.14590 | −0.131899 | ||||||||
\(989\) | −39.7295 | −1.26332 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 29.4508 | 0.935065 | ||||||||
\(993\) | 30.6869 | 0.973820 | ||||||||
\(994\) | −32.6525 | −1.03567 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.56231 | 0.176248 | ||||||||
\(997\) | 2.93112 | 0.0928294 | 0.0464147 | − | 0.998922i | \(-0.485220\pi\) | ||||
0.0464147 | + | 0.998922i | \(0.485220\pi\) | |||||||
\(998\) | 24.2705 | 0.768270 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 1875.2.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 5625.2.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 1875.2.b.a.1249.1 | 4 | |||
5.3 | odd | 4 | 1875.2.b.a.1249.4 | 4 | |||
5.4 | even | 2 | 1875.2.a.c.1.2 | yes | 2 | ||
15.14 | odd | 2 | 5625.2.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1875.2.a.c.1.2 | yes | 2 | 5.4 | even | 2 | ||
1875.2.b.a.1249.1 | 4 | 5.2 | odd | 4 | |||
1875.2.b.a.1249.4 | 4 | 5.3 | odd | 4 | |||
5625.2.a.b.1.1 | 2 | 15.14 | odd | 2 | |||
5625.2.a.g.1.2 | 2 | 3.2 | odd | 2 |